LMFDB - Embedded newform 7.18.c.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,18,Mod(2,7)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 18, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7.2");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	7.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.8255461141$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 231900 x^{18} + 2573595 x^{17} + 36222331443 x^{16} + 522056283042 x^{15} + \cdots + 54\!\cdots\!25 $ x^20 - 5x^19 + 231900x^18 + 2573595x^17 + 36222331443x^16 + 522056283042x^15 + 3095689791534860x^14 + 63517964980290950x^13 + 191169147185579182773x^12 + 4661871029431062841865x^11 + 6728981840934861993437384x^10 + 251477264592720071695768485x^9 + 169785400547236219777139622573x^8 + 7884822396560931315753101896470x^7 + 2084722393634413874384133666310116x^6 + 170299785457406646702831504431152090x^5 + 19136307004107023234373216890155693651x^4 + 919913048844099315146584754515161210807x^3 + 39214983331357496369283116903046958144404x^2 + 515992296986415442815810669806567791765095*x + 5495215718943433371703477919782244002731225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{50}\cdot 3^{18}\cdot 7^{19} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.4
Root			$-35.7008 - 61.8356i$ of defining polynomial
Character	$\chi$	$=$	7.4
Dual form			7.18.c.a.2.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-58.4016 - 101.154i) q^{2} +(-10042.7 + 17394.4i) q^{3} +(58714.5 - 101697. i) q^{4} +(526365. + 911691. i) q^{5} +2.34603e6 q^{6} +(1.15602e7 + 9.94945e6i) q^{7} -2.90257e7 q^{8} +(-1.37140e8 - 2.37533e8i) q^{9} +O(q^{10})$	\(q+(-58.4016 - 101.154i) q^{2} +(-10042.7 + 17394.4i) q^{3} +(58714.5 - 101697. i) q^{4} +(526365. + 911691. i) q^{5} +2.34603e6 q^{6} +(1.15602e7 + 9.94945e6i) q^{7} -2.90257e7 q^{8} +(-1.37140e8 - 2.37533e8i) q^{9} +(6.14811e7 - 1.06488e8i) q^{10} +(-3.23481e8 + 5.60285e8i) q^{11} +(1.17930e9 + 2.04261e9i) q^{12} -2.11036e9 q^{13} +(3.31296e8 - 1.75043e9i) q^{14} -2.11444e10 q^{15} +(-6.00068e9 - 1.03935e10i) q^{16} +(-1.27749e10 + 2.21268e10i) q^{17} +(-1.60183e10 + 2.77446e10i) q^{18} +(-2.09827e10 - 3.63432e10i) q^{19} +1.23621e11 q^{20} +(-2.89160e11 + 1.01164e11i) q^{21} +7.55671e10 q^{22} +(-3.20477e10 - 5.55083e10i) q^{23} +(2.91495e11 - 5.04884e11i) q^{24} +(-1.72651e11 + 2.99041e11i) q^{25} +(1.23248e11 + 2.13472e11i) q^{26} +2.91516e12 q^{27} +(1.69058e12 - 5.91458e11i) q^{28} -3.14286e12 q^{29} +(1.23487e12 + 2.13885e12i) q^{30} +(2.92403e12 - 5.06457e12i) q^{31} +(-2.60313e12 + 4.50875e12i) q^{32} +(-6.49721e12 - 1.12535e13i) q^{33} +2.98430e12 q^{34} +(-2.98593e12 + 1.57764e13i) q^{35} -3.22083e13 q^{36} +(1.83342e13 + 3.17558e13i) q^{37} +(-2.45085e12 + 4.24499e12i) q^{38} +(2.11936e13 - 3.67084e13i) q^{39} +(-1.52781e13 - 2.64625e13i) q^{40} -3.62575e13 q^{41} +(2.71206e13 + 2.33417e13i) q^{42} -1.06805e14 q^{43} +(3.79860e13 + 6.57937e13i) q^{44} +(1.44371e14 - 2.50058e14i) q^{45} +(-3.74328e12 + 6.48354e12i) q^{46} +(1.23301e14 + 2.13564e14i) q^{47} +2.41051e14 q^{48} +(3.46473e13 + 2.30036e14i) q^{49} +4.03324e13 q^{50} +(-2.56588e14 - 4.44424e14i) q^{51} +(-1.23909e14 + 2.14616e14i) q^{52} +(7.99592e13 - 1.38493e14i) q^{53} +(-1.70250e14 - 2.94881e14i) q^{54} -6.81076e14 q^{55} +(-3.35544e14 - 2.88790e14i) q^{56} +8.42889e14 q^{57} +(1.83548e14 + 3.17914e14i) q^{58} +(-2.66791e14 + 4.62096e14i) q^{59} +(-1.24148e15 + 2.15031e15i) q^{60} +(6.97395e14 + 1.20792e15i) q^{61} -6.83072e14 q^{62} +(7.77956e14 - 4.11040e15i) q^{63} -9.64937e14 q^{64} +(-1.11082e15 - 1.92400e15i) q^{65} +(-7.58894e14 + 1.31444e15i) q^{66} +(1.11658e15 - 1.93398e15i) q^{67} +(1.50015e15 + 2.59833e15i) q^{68} +1.28738e15 q^{69} +(1.77024e15 - 6.19327e14i) q^{70} +7.46445e15 q^{71} +(3.98057e15 + 6.89455e15i) q^{72} +(9.28821e14 - 1.60877e15i) q^{73} +(2.14150e15 - 3.70918e15i) q^{74} +(-3.46775e15 - 6.00632e15i) q^{75} -4.92796e15 q^{76} +(-9.31404e15 + 3.25857e15i) q^{77} -4.95096e15 q^{78} +(-4.02333e15 - 6.96861e15i) q^{79} +(6.31710e15 - 1.09415e16i) q^{80} +(-1.15657e16 + 2.00324e16i) q^{81} +(2.11750e15 + 3.66761e15i) q^{82} +1.23318e15 q^{83} +(-6.68984e15 + 3.53464e16i) q^{84} -2.68971e16 q^{85} +(6.23757e15 + 1.08038e16i) q^{86} +(3.15626e16 - 5.46680e16i) q^{87} +(9.38925e15 - 1.62627e16i) q^{88} +(7.01709e15 + 1.21539e16i) q^{89} -3.37260e16 q^{90} +(-2.43963e16 - 2.09969e16i) q^{91} -7.52667e15 q^{92} +(5.87300e16 + 1.01723e17i) q^{93} +(1.44019e16 - 2.49449e16i) q^{94} +(2.20892e16 - 3.82595e16i) q^{95} +(-5.22846e16 - 9.05595e16i) q^{96} +1.70836e16 q^{97} +(2.12457e16 - 1.69392e16i) q^{98} +1.77448e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 270 q^{2} + 6560 q^{3} - 551660 q^{4} + 1089798 q^{5} - 1687556 q^{6} + 14395360 q^{7} - 237823200 q^{8} - 498883228 q^{9}+O(q^{10}) $ 20 * q + 270 * q^2 + 6560 * q^3 - 551660 * q^4 + 1089798 * q^5 - 1687556 * q^6 + 14395360 * q^7 - 237823200 * q^8 - 498883228 * q^9	\( 20 q + 270 q^{2} + 6560 q^{3} - 551660 q^{4} + 1089798 q^{5} - 1687556 q^{6} + 14395360 q^{7} - 237823200 q^{8} - 498883228 q^{9} + 222553738 q^{10} - 148256184 q^{11} + 2808533140 q^{12} + 3578734040 q^{13} + 25683984606 q^{14} - 26900793736 q^{15} - 50209759472 q^{16} + 15259176570 q^{17} + 81764237020 q^{18} - 71656970872 q^{19} - 180641544216 q^{20} - 669146889614 q^{21} + 1499692748380 q^{22} - 316306503180 q^{23} + 694489934496 q^{24} + 591325905568 q^{25} + 4488505674324 q^{26} - 11473086373360 q^{27} + 2858273469380 q^{28} + 284876854680 q^{29} - 9357829097258 q^{30} - 1607821082076 q^{31} + 18893460602400 q^{32} + 9589772011550 q^{33} - 32628298247940 q^{34} - 103506510744 q^{35} + 76724663114416 q^{36} + 5528585266950 q^{37} - 15690283928010 q^{38} + 28451541414128 q^{39} - 91022360866896 q^{40} - 66727631114424 q^{41} - 74393390286880 q^{42} - 93028396916240 q^{43} + 162849953080692 q^{44} + 8592264491540 q^{45} - 563088234018354 q^{46} + 162460135616460 q^{47} + 16\!\cdots\!20 q^{48}+ \cdots + 92\!\cdots\!80 q^{99}+O(q^{100}) \) 20 * q + 270 * q^2 + 6560 * q^3 - 551660 * q^4 + 1089798 * q^5 - 1687556 * q^6 + 14395360 * q^7 - 237823200 * q^8 - 498883228 * q^9 + 222553738 * q^10 - 148256184 * q^11 + 2808533140 * q^12 + 3578734040 * q^13 + 25683984606 * q^14 - 26900793736 * q^15 - 50209759472 * q^16 + 15259176570 * q^17 + 81764237020 * q^18 - 71656970872 * q^19 - 180641544216 * q^20 - 669146889614 * q^21 + 1499692748380 * q^22 - 316306503180 * q^23 + 694489934496 * q^24 + 591325905568 * q^25 + 4488505674324 * q^26 - 11473086373360 * q^27 + 2858273469380 * q^28 + 284876854680 * q^29 - 9357829097258 * q^30 - 1607821082076 * q^31 + 18893460602400 * q^32 + 9589772011550 * q^33 - 32628298247940 * q^34 - 103506510744 * q^35 + 76724663114416 * q^36 + 5528585266950 * q^37 - 15690283928010 * q^38 + 28451541414128 * q^39 - 91022360866896 * q^40 - 66727631114424 * q^41 - 74393390286880 * q^42 - 93028396916240 * q^43 + 162849953080692 * q^44 + 8592264491540 * q^45 - 563088234018354 * q^46 + 162460135616460 * q^47 + 1626223055746720 * q^48 + 37188390461684 * q^49 - 156105592028976 * q^50 - 41571323179104 * q^51 - 664578572037800 * q^52 + 349838159677350 * q^53 - 2197621449925058 * q^54 - 630210277345912 * q^55 - 3391192609585536 * q^56 + 3387478208982380 * q^57 + 1117009291618900 * q^58 + 2898325666051656 * q^59 + 1851302466771436 * q^60 + 4829263771794542 * q^61 - 12440234322280740 * q^62 + 1252577979478000 * q^63 + 2254847316158720 * q^64 + 2323606775562324 * q^65 + 7963993945620406 * q^66 + 1327703510619200 * q^67 + 570001815036780 * q^68 - 19909363410939516 * q^69 - 17777971289904490 * q^70 + 15480661755189216 * q^71 + 16233423509033760 * q^72 - 3163858704730590 * q^73 - 4018632851551110 * q^74 - 8119026314209112 * q^75 - 14641245177256376 * q^76 - 46825571816043510 * q^77 + 48702643123708840 * q^78 + 40826108816616316 * q^79 + 90814104963906864 * q^80 - 69159481630723930 * q^81 + 21247223257167740 * q^82 + 10623055038659280 * q^83 - 178832833754555092 * q^84 + 51769432859611308 * q^85 + 113956439761484328 * q^86 + 171557044814594000 * q^87 - 117726124940340000 * q^88 + 31115179936936434 * q^89 - 503037784464315176 * q^90 - 219799610507722112 * q^91 + 208501803198310920 * q^92 + 257332309943680890 * q^93 + 405400048855155726 * q^94 - 22431094320108540 * q^95 + 232620528206160416 * q^96 - 702800336503765080 * q^97 - 760473415304075970 * q^98 + 928280307128172080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−58.4016	−	101.154i	−0.161313	−	0.279402i	0.774027	−	0.633153i	$-0.218240\pi$
$2$	−58.4016	−	101.154i	−0.161313	−	0.279402i	−0.935340	+	0.353750i	$0.884906\pi$
$3$	−10042.7	+	17394.4i	−0.883726	+	1.53066i	−0.0365593	+	0.999331i	$0.511640\pi$
$3$	−10042.7	+	17394.4i	−0.883726	+	1.53066i	−0.847167	+	0.531327i	$0.821694\pi$
$4$	58714.5	−	101697.i	0.447956	−	0.775883i
$5$	526365.	+	911691.i	0.602618	+	1.04377i	0.992423	+	0.122868i	$0.0392091\pi$
$5$	526365.	+	911691.i	0.602618	+	1.04377i	−0.389805	+	0.920897i	$0.627458\pi$
$6$	2.34603e6			0.570226
$7$	1.15602e7	+	9.94945e6i	0.757937	+	0.652328i
$7$	1.15602e7	+	9.94945e6i	0.757937	+	0.652328i
$8$	−2.90257e7			−0.611671
$9$	−1.37140e8	−	2.37533e8i	−1.06194	−	1.83934i
$10$	6.14811e7	−	1.06488e8i	0.194420	−	0.336746i
$11$	−3.23481e8	+	5.60285e8i	−0.454999	+	0.788082i	−0.998688	−	0.0512050i	$-0.983694\pi$
$11$	−3.23481e8	+	5.60285e8i	−0.454999	+	0.788082i	0.543689	+	0.839287i	$0.317027\pi$
$12$	1.17930e9	+	2.04261e9i	0.791741	+	1.37134i
$13$	−2.11036e9			−0.717527			−0.358764	−	0.933428i	$-0.616802\pi$
$13$	−2.11036e9			−0.717527			−0.358764	+	0.933428i	$0.616802\pi$
$14$	3.31296e8	−	1.75043e9i	0.0599968	−	0.316998i
$15$	−2.11444e10			−2.13020
$16$	−6.00068e9	−	1.03935e10i	−0.349286	−	0.604981i
$17$	−1.27749e10	+	2.21268e10i	−0.444163	+	0.769313i	−0.997993	−	0.0633165i	$-0.979832\pi$
$17$	−1.27749e10	+	2.21268e10i	−0.444163	+	0.769313i	0.553830	+	0.832629i	$0.313166\pi$
$18$	−1.60183e10	+	2.77446e10i	−0.342611	+	0.593419i
$19$	−2.09827e10	−	3.63432e10i	−0.283437	−	0.490927i	0.688792	−	0.724959i	$-0.258141\pi$
$19$	−2.09827e10	−	3.63432e10i	−0.283437	−	0.490927i	−0.972229	+	0.234032i	$0.924808\pi$
$20$	1.23621e11			1.07979
$21$	−2.89160e11	+	1.01164e11i	−1.66830	+	0.583664i
$22$	7.55671e10			0.293589
$23$	−3.20477e10	−	5.55083e10i	−0.0853318	−	0.147799i	0.820201	−	0.572076i	$-0.193862\pi$
$23$	−3.20477e10	−	5.55083e10i	−0.0853318	−	0.147799i	−0.905533	+	0.424277i	$0.860528\pi$
$24$	2.91495e11	−	5.04884e11i	0.540549	−	0.936259i
$25$	−1.72651e11	+	2.99041e11i	−0.226297	+	0.391958i
$26$	1.23248e11	+	2.13472e11i	0.115746	+	0.200479i
$27$	2.91516e12			1.98642
$28$	1.69058e12	−	5.91458e11i	0.845653	−	0.295856i
$29$	−3.14286e12			−1.16665			−0.583326	−	0.812238i	$-0.698249\pi$
$29$	−3.14286e12			−1.16665			−0.583326	+	0.812238i	$0.698249\pi$
$30$	1.23487e12	+	2.13885e12i	0.343629	+	0.595182i
$31$	2.92403e12	−	5.06457e12i	0.615754	−	1.06652i	−0.374497	−	0.927228i	$-0.622185\pi$
$31$	2.92403e12	−	5.06457e12i	0.615754	−	1.06652i	0.990252	−	0.139290i	$-0.0444819\pi$
$32$	−2.60313e12	+	4.50875e12i	−0.418524	+	0.724905i
$33$	−6.49721e12	−	1.12535e13i	−0.804189	−	1.39290i
$34$	2.98430e12			0.286597
$35$	−2.98593e12	+	1.57764e13i	−0.224131	+	1.18421i
$36$	−3.22083e13			−1.90282
$37$	1.83342e13	+	3.17558e13i	0.858120	+	1.48631i	0.873720	+	0.486429i	$0.161701\pi$
$37$	1.83342e13	+	3.17558e13i	0.858120	+	1.48631i	−0.0155996	+	0.999878i	$0.504966\pi$
$38$	−2.45085e12	+	4.24499e12i	−0.0914441	+	0.158386i
$39$	2.11936e13	−	3.67084e13i	0.634098	−	1.09829i
$40$	−1.52781e13	−	2.64625e13i	−0.368604	−	0.638441i
$41$	−3.62575e13			−0.709146			−0.354573	−	0.935028i	$-0.615374\pi$
$41$	−3.62575e13			−0.709146			−0.354573	+	0.935028i	$0.615374\pi$
$42$	2.71206e13	+	2.33417e13i	0.432195	+	0.371974i
$43$	−1.06805e14			−1.39351			−0.696754	−	0.717310i	$-0.745373\pi$
$43$	−1.06805e14			−1.39351			−0.696754	+	0.717310i	$0.745373\pi$
$44$	3.79860e13	+	6.57937e13i	0.407639	+	0.706052i
$45$	1.44371e14	−	2.50058e14i	1.27989	−	2.21684i
$46$	−3.74328e12	+	6.48354e12i	−0.0275303	+	0.0476838i
$47$	1.23301e14	+	2.13564e14i	0.755327	+	1.30826i	0.945212	+	0.326458i	$0.105855\pi$
$47$	1.23301e14	+	2.13564e14i	0.755327	+	1.30826i	−0.189885	+	0.981806i	$0.560812\pi$
$48$	2.41051e14			1.23469
$49$	3.46473e13	+	2.30036e14i	0.148937	+	0.988847i
$50$	4.03324e13			0.146019
$51$	−2.56588e14	−	4.44424e14i	−0.785037	−	1.35972i
$52$	−1.23909e14	+	2.14616e14i	−0.321421	+	0.556717i
$53$	7.99592e13	−	1.38493e14i	0.176410	−	0.305551i	−0.764238	−	0.644934i	$-0.776885\pi$
$53$	7.99592e13	−	1.38493e14i	0.176410	−	0.305551i	0.940648	+	0.339383i	$0.110218\pi$
$54$	−1.70250e14	−	2.94881e14i	−0.320435	−	0.555010i
$55$	−6.81076e14			−1.09676
$56$	−3.35544e14	−	2.88790e14i	−0.463608	−	0.399010i
$57$	8.42889e14			1.00192
$58$	1.83548e14	+	3.17914e14i	0.188196	+	0.325965i
$59$	−2.66791e14	+	4.62096e14i	−0.236554	+	0.409723i	−0.959723	−	0.280948i	$-0.909351\pi$
$59$	−2.66791e14	+	4.62096e14i	−0.236554	+	0.409723i	0.723169	+	0.690671i	$0.242685\pi$
$60$	−1.24148e15	+	2.15031e15i	−0.954235	+	1.65278i
$61$	6.97395e14	+	1.20792e15i	0.465774	+	0.806744i	0.999236	−	0.0390796i	$-0.0124426\pi$
$61$	6.97395e14	+	1.20792e15i	0.465774	+	0.806744i	−0.533462	+	0.845824i	$0.679109\pi$
$62$	−6.83072e14			−0.397317
$63$	7.77956e14	−	4.11040e15i	0.394966	−	2.08684i
$64$	−9.64937e14			−0.428518
$65$	−1.11082e15	−	1.92400e15i	−0.432395	−	0.748930i
$66$	−7.58894e14	+	1.31444e15i	−0.259452	+	0.449385i
$67$	1.11658e15	−	1.93398e15i	0.335935	−	0.581856i	−0.647729	−	0.761871i	$-0.724281\pi$
$67$	1.11658e15	−	1.93398e15i	0.335935	−	0.581856i	0.983664	+	0.180015i	$0.0576145\pi$
$68$	1.50015e15	+	2.59833e15i	0.397931	+	0.689237i
$69$	1.28738e15			0.301640
$70$	1.77024e15	−	6.19327e14i	0.367027	−	0.128406i
$71$	7.46445e15			1.37184			0.685918	−	0.727679i	$-0.259401\pi$
$71$	7.46445e15			1.37184			0.685918	+	0.727679i	$0.259401\pi$
$72$	3.98057e15	+	6.89455e15i	0.649560	+	1.12507i
$73$	9.28821e14	−	1.60877e15i	0.134799	−	0.233479i	−0.790721	−	0.612176i	$-0.790294\pi$
$73$	9.28821e14	−	1.60877e15i	0.134799	−	0.233479i	0.925521	+	0.378697i	$0.123628\pi$
$74$	2.14150e15	−	3.70918e15i	0.276852	−	0.479522i
$75$	−3.46775e15	−	6.00632e15i	−0.399970	−	0.692768i
$76$	−4.92796e15			−0.507869
$77$	−9.31404e15	+	3.25857e15i	−0.858948	+	0.300508i
$78$	−4.95096e15			−0.409153
$79$	−4.02333e15	−	6.96861e15i	−0.298370	−	0.516792i	0.677393	−	0.735621i	$-0.263110\pi$
$79$	−4.02333e15	−	6.96861e15i	−0.298370	−	0.516792i	−0.975763	+	0.218829i	$0.929776\pi$
$80$	6.31710e15	−	1.09415e16i	0.420972	−	0.729145i
$81$	−1.15657e16	+	2.00324e16i	−0.693505	+	1.20119i
$82$	2.11750e15	+	3.66761e15i	0.114394	+	0.198137i
$83$	1.23318e15			0.0600984			0.0300492	−	0.999548i	$-0.490434\pi$
$83$	1.23318e15			0.0600984			0.0300492	+	0.999548i	$0.490434\pi$
$84$	−6.68984e15	+	3.53464e16i	−0.294471	+	1.55586i
$85$	−2.68971e16			−1.07064
$86$	6.23757e15	+	1.08038e16i	0.224791	+	0.389349i
$87$	3.15626e16	−	5.46680e16i	1.03100	−	1.78575i
$88$	9.38925e15	−	1.62627e16i	0.278310	−	0.482047i
$89$	7.01709e15	+	1.21539e16i	0.188948	+	0.327267i	0.944900	−	0.327360i	$-0.106159\pi$
$89$	7.01709e15	+	1.21539e16i	0.188948	+	0.327267i	−0.755952	+	0.654627i	$0.772826\pi$
$90$	−3.37260e16			−0.825854
$91$	−2.43963e16	−	2.09969e16i	−0.543840	−	0.468063i
$92$	−7.52667e15			−0.152900
$93$	5.87300e16	+	1.01723e17i	1.08832	+	1.88502i
$94$	1.44019e16	−	2.49449e16i	0.243688	−	0.422080i
$95$	2.20892e16	−	3.82595e16i	0.341608	−	0.591683i
$96$	−5.22846e16	−	9.05595e16i	−0.739721	−	1.28123i
$97$	1.70836e16			0.221319			0.110660	−	0.993858i	$-0.464704\pi$
$97$	1.70836e16			0.221319			0.110660	+	0.993858i	$0.464704\pi$
$98$	2.12457e16	−	1.69392e16i	0.252261	−	0.201127i
$99$	1.77448e17			1.93273
$100$	2.02743e16	+	3.51160e16i	0.202743	+	0.351160i
$101$	−6.83017e16	+	1.18302e17i	−0.627624	+	1.08708i	0.360403	+	0.932797i	$0.382639\pi$
$101$	−6.83017e16	+	1.18302e17i	−0.627624	+	1.08708i	−0.988027	+	0.154281i	$0.950694\pi$
$102$	−2.99703e16	+	5.19101e16i	−0.253273	+	0.438682i
$103$	4.56563e16	+	7.90790e16i	0.355127	+	0.615098i	0.987140	−	0.159860i	$-0.0511042\pi$
$103$	4.56563e16	+	7.90790e16i	0.355127	+	0.615098i	−0.632012	+	0.774958i	$0.717771\pi$
$104$	6.12547e16			0.438890
$105$	−2.44434e17	−	2.10375e17i	−1.61456	−	1.38959i
$106$	−1.86790e16			−0.113829
$107$	1.84065e16	+	3.18811e16i	0.103564	+	0.179379i	0.913151	−	0.407622i	$-0.133642\pi$
$107$	1.84065e16	+	3.18811e16i	0.103564	+	0.179379i	−0.809586	+	0.587001i	$0.800309\pi$
$108$	1.71162e17	−	2.96462e17i	0.889828	−	1.54123i
$109$	−1.43864e17	+	2.49179e17i	−0.691554	+	1.19781i	0.279774	+	0.960066i	$0.409740\pi$
$109$	−1.43864e17	+	2.49179e17i	−0.691554	+	1.19781i	−0.971328	+	0.237742i	$0.923593\pi$
$110$	3.97759e16	+	6.88939e16i	0.176922	+	0.306438i
$111$	−7.36497e17			−3.03337
$112$	3.40403e16	−	1.79855e17i	0.129909	−	0.686386i
$113$	3.11297e17			1.10156			0.550779	−	0.834651i	$-0.314331\pi$
$113$	3.11297e17			1.10156			0.550779	+	0.834651i	$0.314331\pi$
$114$	−4.92260e16	−	8.52620e16i	−0.161623	−	0.279939i
$115$	3.37376e16	−	5.84353e16i	0.102845	−	0.178133i
$116$	−1.84531e17	+	3.19618e17i	−0.522609	+	0.905186i
$117$	2.89414e17	+	5.01280e17i	0.761973	+	1.31978i
$118$	6.23241e16			0.152637
$119$	−3.67831e17	+	1.28688e17i	−0.838492	+	0.293351i
$120$	6.13731e17			1.30298
$121$	4.34439e16	+	7.52470e16i	0.0859514	+	0.148872i
$122$	8.14579e16	−	1.41089e17i	0.150271	−	0.260277i
$123$	3.64122e17	−	6.30677e17i	0.626691	−	1.08546i
$124$	−3.43366e17	−	5.94727e17i	−0.551662	−	0.955506i
$125$	4.39659e17			0.659753
$126$	−4.61219e17	+	1.61360e17i	−0.646781	+	0.226280i
$127$	−3.87968e17			−0.508703			−0.254351	−	0.967112i	$-0.581862\pi$
$127$	−3.87968e17			−0.508703			−0.254351	+	0.967112i	$0.581862\pi$
$128$	3.97551e17	+	6.88578e17i	0.487650	+	0.844634i
$129$	1.07260e18	−	1.85781e18i	1.23148	−	2.13298i
$130$	−1.29747e17	+	2.24729e17i	−0.139502	+	0.241624i
$131$	5.55922e17	+	9.62885e17i	0.560026	+	0.969993i	0.997493	+	0.0707589i	$0.0225421\pi$
$131$	5.55922e17	+	9.62885e17i	0.560026	+	0.969993i	−0.437468	+	0.899234i	$0.644125\pi$
$132$	−1.52592e18			−1.44097
$133$	1.19029e17	−	6.28902e17i	0.105418	−	0.556986i
$134$	−2.60841e17			−0.216763
$135$	1.53444e18	+	2.65773e18i	1.19705	+	2.07335i
$136$	3.70801e17	−	6.42246e17i	0.271682	−	0.470566i
$137$	2.33367e17	−	4.04204e17i	0.160663	−	0.278276i	−0.774444	−	0.632643i	$-0.781970\pi$
$137$	2.33367e17	−	4.04204e17i	0.160663	−	0.278276i	0.935107	+	0.354367i	$0.115304\pi$
$138$	−7.51848e16	−	1.30224e17i	−0.0486584	−	0.0842789i
$139$	−6.39409e17			−0.389182			−0.194591	−	0.980884i	$-0.562338\pi$
$139$	−6.39409e17			−0.389182			−0.194591	+	0.980884i	$0.562338\pi$
$140$	1.42909e18	+	1.22996e18i	0.818410	+	0.704375i
$141$	−4.95307e18			−2.67001
$142$	−4.35936e17	−	7.55063e17i	−0.221295	−	0.383294i
$143$	6.82661e17	−	1.18240e18i	0.326474	−	0.565470i
$144$	−1.64586e18	+	2.85072e18i	−0.741843	+	1.28491i
$145$	−1.65429e18	−	2.86532e18i	−0.703046	−	1.21771i
$146$	−2.16978e17			−0.0869796
$147$	−4.34928e18	−	1.70750e18i	−1.64521	−	0.645898i
$148$	4.30594e18			1.53760
$149$	8.69464e17	+	1.50596e18i	0.293203	+	0.507842i	0.974565	−	0.224104i	$-0.0719455\pi$
$149$	8.69464e17	+	1.50596e18i	0.293203	+	0.507842i	−0.681362	+	0.731946i	$0.738612\pi$
$150$	−4.05044e17	+	7.01557e17i	−0.129041	+	0.223505i
$151$	5.81779e16	−	1.00767e17i	0.0175168	−	0.0303399i	−0.857134	−	0.515093i	$-0.827757\pi$
$151$	5.81779e16	−	1.00767e17i	0.0175168	−	0.0303399i	0.874651	+	0.484753i	$0.161091\pi$
$152$	6.09038e17	+	1.05489e18i	0.173370	+	0.300286i
$153$	7.00779e18			1.88670
$154$	8.73573e17	+	7.51852e17i	0.222522	+	0.191516i
$155$	6.15643e18			1.48426
$156$	−2.48875e18	−	4.31064e18i	−0.568096	−	0.983971i
$157$	−1.50569e18	+	2.60793e18i	−0.325528	+	0.563830i	−0.981619	−	0.190851i	$-0.938875\pi$
$157$	−1.50569e18	+	2.60793e18i	−0.325528	+	0.563830i	0.656091	+	0.754681i	$0.272209\pi$
$158$	−4.69937e17	+	8.13955e17i	−0.0962620	+	0.166731i
$159$	1.60600e18	+	2.78168e18i	0.311797	+	0.540047i
$160$	−5.48078e18			−1.00884
$161$	1.81798e17	−	9.60546e17i	0.0317373	−	0.167687i
$162$	2.70182e18			0.447485
$163$	−3.72361e18	−	6.44949e18i	−0.585289	−	1.01375i	−0.994839	−	0.101462i	$-0.967648\pi$
$163$	−3.72361e18	−	6.44949e18i	−0.585289	−	1.01375i	0.409551	−	0.912287i	$-0.365685\pi$
$164$	−2.12884e18	+	3.68727e18i	−0.317666	+	0.550214i
$165$	6.83981e18	−	1.18469e19i	0.969238	−	1.67877i
$166$	−7.20196e16	−	1.24742e17i	−0.00969465	−	0.0167916i
$167$	−6.58970e17			−0.0842899			−0.0421450	−	0.999112i	$-0.513419\pi$
$167$	−6.58970e17			−0.0842899			−0.0421450	+	0.999112i	$0.513419\pi$
$168$	8.39307e18	−	2.93636e18i	1.02045	−	0.357010i
$169$	−4.19679e18			−0.485155
$170$	1.57083e18	+	2.72076e18i	0.172709	+	0.299140i
$171$	−5.75512e18	+	9.96817e18i	−0.601988	+	1.04267i
$172$	−6.27100e18	+	1.08617e19i	−0.624230	+	1.08120i
$173$	8.24039e18	+	1.42728e19i	0.780829	+	1.35243i	0.931460	+	0.363845i	$0.118536\pi$
$173$	8.24039e18	+	1.42728e19i	0.780829	+	1.35243i	−0.150631	+	0.988590i	$0.548131\pi$
$174$	−7.37322e18			−0.665256
$175$	−4.97118e18	+	1.73919e18i	−0.427204	+	0.149460i
$176$	7.76442e18			0.635699
$177$	−5.35858e18	−	9.28134e18i	−0.418097	−	0.724166i
$178$	8.19618e17	−	1.41962e18i	0.0609595	−	0.105585i
$179$	5.19452e18	−	8.99718e18i	0.368379	−	0.638051i	−0.620933	−	0.783863i	$-0.713246\pi$
$179$	5.19452e18	−	8.99718e18i	0.368379	−	0.638051i	0.989312	+	0.145812i	$0.0465795\pi$
$180$	−1.69533e19	−	2.93641e19i	−1.14667	−	1.98609i
$181$	4.30101e18			0.277525			0.138763	−	0.990326i	$-0.455687\pi$
$181$	4.30101e18			0.277525			0.138763	+	0.990326i	$0.455687\pi$
$182$	−6.99155e17	+	3.69405e18i	−0.0430494	+	0.227455i
$183$	−2.80148e19			−1.64647
$184$	9.30208e17	+	1.61117e18i	0.0521950	+	0.0904043i
$185$	−1.93010e19	+	3.34303e19i	−1.03424	+	1.79135i
$186$	6.85985e18	−	1.18816e19i	0.351119	−	0.608156i
$187$	−8.26488e18	−	1.43152e19i	−0.404188	−	0.700074i
$188$	2.89582e19			1.35341
$189$	3.36999e19	+	2.90042e19i	1.50558	+	1.29579i
$190$	−5.16017e18			−0.220424
$191$	3.99120e18	+	6.91296e18i	0.163050	+	0.282410i	0.935961	−	0.352104i	$-0.114534\pi$
$191$	3.99120e18	+	6.91296e18i	0.163050	+	0.282410i	−0.772911	+	0.634514i	$0.781200\pi$
$192$	9.69052e18	−	1.67845e19i	0.378692	−	0.655915i
$193$	−6.98724e18	+	1.21023e19i	−0.261257	+	0.452511i	−0.966576	−	0.256379i	$-0.917470\pi$
$193$	−6.98724e18	+	1.21023e19i	−0.261257	+	0.452511i	0.705319	+	0.708890i	$0.250804\pi$
$194$	−9.97708e17	−	1.72808e18i	−0.0357017	−	0.0618371i
$195$	4.46224e19			1.52847
$196$	2.54282e19	+	9.98294e18i	0.833946	+	0.327402i
$197$	−3.18379e19			−0.999958			−0.499979	−	0.866037i	$-0.666659\pi$
$197$	−3.18379e19			−0.999958			−0.499979	+	0.866037i	$0.666659\pi$
$198$	−1.03632e19	−	1.79497e19i	−0.311775	−	0.540010i
$199$	2.45716e19	−	4.25593e19i	0.708244	−	1.22671i	−0.257264	−	0.966341i	$-0.582821\pi$
$199$	2.45716e19	−	4.25593e19i	0.708244	−	1.22671i	0.965508	−	0.260373i	$-0.0838455\pi$
$200$	5.01132e18	−	8.67986e18i	0.138419	−	0.239749i
$201$	2.24269e19	+	3.88445e19i	0.593748	+	1.02840i
$202$	1.59557e19			0.404976
$203$	−3.63321e19	−	3.12697e19i	−0.884249	−	0.761040i
$204$	−6.02618e19			−1.40665
$205$	−1.90847e19	−	3.30557e19i	−0.427344	−	0.740182i
$206$	5.33279e18	−	9.23667e18i	0.114573	−	0.198447i
$207$	−8.79003e18	+	1.52248e19i	−0.181235	+	0.313908i
$208$	1.26636e19	+	2.19340e19i	0.250622	+	0.434090i
$209$	2.71500e19			0.515854
$210$	−7.00506e18	+	3.70119e19i	−0.127805	+	0.675269i
$211$	4.82267e19			0.845058			0.422529	−	0.906349i	$-0.361142\pi$
$211$	4.82267e19			0.845058			0.422529	+	0.906349i	$0.361142\pi$
$212$	−9.38953e18	−	1.62631e19i	−0.158048	−	0.273747i
$213$	−7.49629e19	+	1.29840e20i	−1.21233	+	2.09981i
$214$	2.14994e18	−	3.72381e18i	0.0334125	−	0.0578722i
$215$	−5.62184e19	−	9.73731e19i	−0.839753	−	1.45449i
$216$	−8.46145e19			−1.21503
$217$	8.41921e19	−	2.94551e19i	1.16242	−	0.406680i
$218$	3.36075e19			0.446227
$219$	1.86556e19	+	3.23125e19i	0.238251	+	0.412663i
$220$	−3.99891e19	+	6.92631e19i	−0.491302	+	0.850960i
$221$	2.69597e19	−	4.66956e19i	0.318699	−	0.552003i
$222$	4.30126e19	+	7.45000e19i	0.489323	+	0.847532i
$223$	−1.73263e20			−1.89721			−0.948605	−	0.316461i	$-0.897505\pi$
$223$	−1.73263e20			−1.89721			−0.948605	+	0.316461i	$0.897505\pi$
$224$	−7.49523e19	+	2.62225e19i	−0.790091	+	0.276417i
$225$	9.47092e19			0.961260
$226$	−1.81802e19	−	3.14890e19i	−0.177696	−	0.307778i
$227$	3.23424e19	−	5.60186e19i	0.304475	−	0.527367i	−0.672669	−	0.739943i	$-0.734852\pi$
$227$	3.23424e19	−	5.60186e19i	0.304475	−	0.527367i	0.977144	+	0.212577i	$0.0681856\pi$
$228$	4.94898e19	−	8.57189e19i	0.448817	−	0.777374i
$229$	3.42113e19	+	5.92557e19i	0.298929	+	0.517760i	0.975891	−	0.218258i	$-0.0700373\pi$
$229$	3.42113e19	+	5.92557e19i	0.298929	+	0.517760i	−0.676962	+	0.736018i	$0.736704\pi$
$230$	−7.88132e18			−0.0663609
$231$	3.68569e19	−	1.94737e20i	0.299100	−	1.58032i
$232$	9.12236e19			0.713607
$233$	−5.93818e19	−	1.02852e20i	−0.447846	−	0.775691i	0.550400	−	0.834901i	$-0.314475\pi$
$233$	−5.93818e19	−	1.02852e20i	−0.447846	−	0.775691i	−0.998246	+	0.0592097i	$0.981142\pi$
$234$	3.38045e19	−	5.85511e19i	0.245832	−	0.425794i
$235$	−1.29803e20	+	2.24825e20i	−0.910347	+	1.57677i
$236$	3.13290e19	+	5.42635e19i	0.211931	+	0.367076i
$237$	1.61620e20			1.05471
$238$	3.44992e19	+	2.96922e19i	0.217223	+	0.186955i
$239$	5.46784e19			0.332226			0.166113	−	0.986107i	$-0.446878\pi$
$239$	5.46784e19			0.332226			0.166113	+	0.986107i	$0.446878\pi$
$240$	1.26881e20	+	2.19764e20i	0.744048	+	1.28873i
$241$	1.13599e20	−	1.96759e20i	0.643025	−	1.11375i	−0.341729	−	0.939799i	$-0.611012\pi$
$241$	1.13599e20	−	1.96759e20i	0.643025	−	1.11375i	0.984754	−	0.173954i	$-0.0556543\pi$
$242$	5.07438e18	−	8.78908e18i	0.0277302	−	0.0480301i
$243$	−4.40685e19	−	7.63290e19i	−0.232528	−	0.402750i
$244$	1.63789e20			0.834586
$245$	−1.91485e20	+	1.52671e20i	−0.942372	+	0.751352i
$246$	−8.50611e19			−0.404373
$247$	4.42811e19	+	7.66972e19i	0.203374	+	0.352254i
$248$	−8.48720e19	+	1.47003e20i	−0.376639	+	0.652358i
$249$	−1.23844e19	+	2.14504e19i	−0.0531105	+	0.0919901i
$250$	−2.56768e19	−	4.44735e19i	−0.106427	−	0.184337i
$251$	−2.15159e20			−0.862051			−0.431026	−	0.902340i	$-0.641848\pi$
$251$	−2.15159e20			−0.862051			−0.431026	+	0.902340i	$0.641848\pi$
$252$	−3.72336e20	−	3.20455e20i	−1.44222	−	1.24126i
$253$	4.14673e19			0.155304
$254$	2.26579e19	+	3.92447e19i	0.0820604	+	0.142133i
$255$	2.70118e20	−	4.67858e20i	0.946155	−	1.63879i
$256$	−1.68029e19	+	2.91035e19i	−0.0569305	+	0.0986065i
$257$	−2.37681e20	−	4.11675e20i	−0.779045	−	1.34935i	−0.932493	−	0.361189i	$-0.882371\pi$
$257$	−2.37681e20	−	4.11675e20i	−0.779045	−	1.34935i	0.153447	−	0.988157i	$-0.450963\pi$
$258$	−2.50567e20			−0.794614
$259$	−1.04005e20	+	5.49520e20i	−0.319159	+	1.68630i
$260$	−2.60885e20			−0.774776
$261$	4.31010e20	+	7.46531e20i	1.23892	+	2.14587i
$262$	6.49334e19	−	1.12468e20i	0.180679	−	0.312945i
$263$	−5.97996e19	+	1.03576e20i	−0.161092	+	0.279020i	−0.935261	−	0.353960i	$-0.884835\pi$
$263$	−5.97996e19	+	1.03576e20i	−0.161092	+	0.279020i	0.774168	+	0.632980i	$0.218168\pi$
$264$	1.88586e20	+	3.26641e20i	0.491899	+	0.851994i
$265$	1.68351e20			0.425232
$266$	−7.05677e19	+	2.46885e19i	−0.172628	+	0.0603950i
$267$	−2.81881e20			−0.667912
$268$	−1.31119e20	−	2.27105e20i	−0.300968	−	0.521292i
$269$	1.61376e20	−	2.79512e20i	0.358876	−	0.621592i	−0.628897	−	0.777489i	$-0.716493\pi$
$269$	1.61376e20	−	2.79512e20i	0.358876	−	0.621592i	0.987773	+	0.155896i	$0.0498266\pi$
$270$	1.79227e20	−	3.10431e20i	0.386200	−	0.668918i
$271$	1.96323e19	+	3.40042e19i	0.0409952	+	0.0710057i	0.885795	−	0.464077i	$-0.153614\pi$
$271$	1.96323e19	+	3.40042e19i	0.0409952	+	0.0710057i	−0.844800	+	0.535083i	$0.820281\pi$
$272$	3.06633e20			0.620559
$273$	6.10232e20	−	2.13493e20i	1.19705	−	0.418794i
$274$	−5.45161e19			−0.103668
$275$	−1.11699e20	−	1.93468e20i	−0.205930	−	0.356682i
$276$	7.55877e19	−	1.30922e20i	0.135121	−	0.234037i
$277$	−3.31442e20	+	5.74075e20i	−0.574553	+	0.995155i	0.421537	+	0.906811i	$0.361491\pi$
$277$	−3.31442e20	+	5.74075e20i	−0.574553	+	0.995155i	−0.996090	+	0.0883439i	$0.971843\pi$
$278$	3.73425e19	+	6.46791e19i	0.0627802	+	0.108738i
$279$	−1.60400e21			−2.61559
$280$	8.66686e19	−	4.57921e20i	0.137094	−	0.724348i
$281$	8.64013e20			1.32592			0.662958	−	0.748656i	$-0.269301\pi$
$281$	8.64013e20			1.32592			0.662958	+	0.748656i	$0.269301\pi$
$282$	2.89267e20	+	5.01026e20i	0.430707	+	0.746006i
$283$	2.30691e20	−	3.99568e20i	0.333308	−	0.577307i	−0.649850	−	0.760062i	$-0.725168\pi$
$283$	2.30691e20	−	3.99568e20i	0.333308	−	0.577307i	0.983158	+	0.182756i	$0.0585017\pi$
$284$	4.38272e20	−	7.59109e20i	0.614522	−	1.06438i
$285$	4.43667e20	+	7.68454e20i	0.603777	+	1.04577i
$286$	−1.59474e20			−0.210658
$287$	−4.19145e20	−	3.60743e20i	−0.537488	−	0.462596i
$288$	1.42797e21			1.77780
$289$	8.72228e19	+	1.51074e20i	0.105438	+	0.182625i
$290$	−1.93226e20	+	3.34678e20i	−0.226821	+	0.392865i
$291$	−1.71564e20	+	2.97158e20i	−0.195586	+	0.338764i
$292$	−1.09071e20	−	1.88916e20i	−0.120768	−	0.209177i
$293$	9.42325e20			1.01351			0.506753	−	0.862091i	$-0.330846\pi$
$293$	9.42325e20			1.01351			0.506753	+	0.862091i	$0.330846\pi$
$294$	8.12834e19	+	5.39670e20i	0.0849277	+	0.563866i
$295$	−5.61719e20			−0.570206
$296$	−5.32164e20	−	9.21735e20i	−0.524887	−	0.909131i
$297$	−9.42998e20	+	1.63332e21i	−0.903818	+	1.56546i
$298$	1.01556e20	−	1.75900e20i	0.0945949	−	0.163843i
$299$	6.76323e19	+	1.17143e20i	0.0612279	+	0.106050i
$300$	−8.14429e20			−0.716675
$301$	−1.23469e21	−	1.06265e21i	−1.05619	−	0.909024i
$302$	−1.35907e19			−0.0113027
$303$	−1.37186e21	−	2.37613e21i	−1.10930	−	1.92136i
$304$	−2.51821e20	+	4.36167e20i	−0.198001	+	0.342948i
$305$	−7.34169e20	+	1.27162e21i	−0.561368	+	0.972318i
$306$	−4.09266e20	−	7.08869e20i	−0.304350	−	0.527150i
$307$	2.64995e21			1.91674			0.958368	−	0.285537i	$-0.0921720\pi$
$307$	2.64995e21			1.91674			0.958368	+	0.285537i	$0.0921720\pi$
$308$	−2.15485e20	+	1.13853e21i	−0.151612	+	0.801058i
$309$	−1.83404e21			−1.25534
$310$	−3.59545e20	−	6.22751e20i	−0.239430	−	0.414705i
$311$	−2.19758e20	+	3.80632e20i	−0.142390	+	0.246627i	−0.928396	−	0.371592i	$-0.878812\pi$
$311$	−2.19758e20	+	3.80632e20i	−0.142390	+	0.246627i	0.786006	+	0.618219i	$0.212146\pi$
$312$	−6.15160e20	+	1.06549e21i	−0.387859	+	0.671791i
$313$	1.13907e21	+	1.97293e21i	0.698914	+	1.21055i	0.968843	+	0.247675i	$0.0796664\pi$
$313$	1.13907e21	+	1.97293e21i	0.698914	+	1.21055i	−0.269929	+	0.962880i	$0.587000\pi$
$314$	3.51738e20			0.210047
$315$	4.15690e21	−	1.45431e21i	2.41618	−	0.845315i
$316$	−9.44911e20			−0.534627
$317$	1.13253e21	+	1.96160e21i	0.623800	+	1.08045i	0.988772	+	0.149435i	$0.0477455\pi$
$317$	1.13253e21	+	1.96160e21i	0.623800	+	1.08045i	−0.364971	+	0.931019i	$0.618921\pi$
$318$	1.87586e20	−	3.24909e20i	0.100594	−	0.174233i
$319$	1.01665e21	−	1.76090e21i	0.530826	−	0.919418i
$320$	−5.07909e20	−	8.79724e20i	−0.258233	−	0.447272i
$321$	−7.39402e20			−0.366090
$322$	−1.07781e20	+	3.77077e19i	−0.0519717	+	0.0181826i
$323$	1.07221e21			0.503569
$324$	1.35815e21	+	2.35238e21i	0.621320	+	1.07616i
$325$	3.64356e20	−	6.31084e20i	0.162374	−	0.281241i
$326$	−4.34930e20	+	7.53320e20i	−0.188829	+	0.327062i
$327$	−2.88955e21	−	5.00484e21i	−1.22229	−	2.11707i
$328$	1.05240e21			0.433764
$329$	−6.99453e20	+	3.69562e21i	−0.280927	+	1.48430i
$330$	−1.59782e21			−0.625403
$331$	−1.59846e21	−	2.76861e21i	−0.609766	−	1.05615i	−0.991279	−	0.131782i	$-0.957930\pi$
$331$	−1.59846e21	−	2.76861e21i	−0.609766	−	1.05615i	0.381513	−	0.924364i	$-0.375403\pi$
$332$	7.24056e19	−	1.25410e20i	0.0269214	−	0.0466293i
$333$	5.02870e21	−	8.70996e21i	1.82255	−	3.15675i
$334$	3.84849e19	+	6.66577e19i	0.0135971	+	0.0235508i
$335$	2.35092e21			0.809761
$336$	2.78661e21	+	2.39833e21i	0.935818	+	0.805424i
$337$	−2.52188e21			−0.825792			−0.412896	−	0.910778i	$-0.635483\pi$
$337$	−2.52188e21			−0.825792			−0.412896	+	0.910778i	$0.635483\pi$
$338$	2.45099e20	+	4.24524e20i	0.0782618	+	0.135553i
$339$	−3.12624e21	+	5.41481e21i	−0.973476	+	1.68611i
$340$	−1.57925e21	+	2.73534e21i	−0.479601	+	0.830694i
$341$	1.89174e21	+	3.27658e21i	0.560335	+	0.970529i
$342$	1.34443e21			0.388434
$343$	−1.88820e21	+	3.00399e21i	−0.532167	+	0.846639i
$344$	3.10009e21			0.852368
$345$	6.77631e20	+	1.17369e21i	0.181774	+	0.314841i
$346$	9.62503e20	−	1.66710e21i	0.251916	−	0.436331i
$347$	−1.61546e21	+	2.79806e21i	−0.412568	+	0.714588i	−0.995170	−	0.0981694i	$-0.968701\pi$
$347$	−1.61546e21	+	2.79806e21i	−0.412568	+	0.714588i	0.582602	+	0.812758i	$0.302035\pi$
$348$	−3.70637e21	−	6.41961e21i	−0.923687	−	1.59987i
$349$	−3.99291e21			−0.971122			−0.485561	−	0.874203i	$-0.661385\pi$
$349$	−3.99291e21			−0.971122			−0.485561	+	0.874203i	$0.661385\pi$
$350$	4.66252e20	+	4.01285e20i	0.110673	+	0.0952521i
$351$	−6.15204e21			−1.42531
$352$	−1.68412e21	−	2.91699e21i	−0.380856	−	0.659662i
$353$	1.55923e21	−	2.70067e21i	0.344212	−	0.596192i	−0.640999	−	0.767542i	$-0.721480\pi$
$353$	1.55923e21	−	2.70067e21i	0.344212	−	0.596192i	0.985210	+	0.171350i	$0.0548129\pi$
$354$	−6.25899e20	+	1.08409e21i	−0.134889	+	0.233635i
$355$	3.92903e21	+	6.80528e21i	0.826693	+	1.43187i
$356$	1.64802e21			0.338561
$357$	1.45556e21	−	7.69055e21i	0.291977	−	1.54269i
$358$	−1.21347e21			−0.237697
$359$	−4.55086e21	−	7.88231e21i	−0.870543	−	1.50782i	−0.861436	−	0.507866i	$-0.830434\pi$
$359$	−4.55086e21	−	7.88231e21i	−0.870543	−	1.50782i	−0.00910688	−	0.999959i	$-0.502899\pi$
$360$	−4.19047e21	+	7.25811e21i	−0.782873	+	1.35598i
$361$	1.85964e21	−	3.22100e21i	0.339327	−	0.587732i
$362$	−2.51186e20	−	4.35067e20i	−0.0447685	−	0.0775413i
$363$	−1.74517e21			−0.303830
$364$	−3.56773e21	+	1.24819e21i	−0.606779	+	0.212285i
$365$	1.95560e21			0.324930
$366$	1.63611e21	+	2.83382e21i	0.265597	+	0.460027i
$367$	−3.44651e20	+	5.96953e20i	−0.0546661	+	0.0946844i	−0.892063	−	0.451910i	$-0.850743\pi$
$367$	−3.44651e20	+	5.96953e20i	−0.0546661	+	0.0946844i	0.837397	+	0.546595i	$0.184076\pi$
$368$	−3.84617e20	+	6.66176e20i	−0.0596104	+	0.103248i
$369$	4.97234e21	+	8.61235e21i	0.753073	+	1.30436i
$370$	4.50884e21			0.667344
$371$	2.30228e21	−	8.05465e20i	0.333027	−	0.116511i
$372$	1.37932e22			1.95007
$373$	−1.74407e21	−	3.02082e21i	−0.241012	−	0.417445i	0.719991	−	0.693984i	$-0.244146\pi$
$373$	−1.74407e21	−	3.02082e21i	−0.241012	−	0.417445i	−0.961003	+	0.276539i	$0.910813\pi$
$374$	−9.65364e20	+	1.67206e21i	−0.130401	+	0.225862i
$375$	−4.41535e21	+	7.64760e21i	−0.583041	+	1.00986i
$376$	−3.57890e21	−	6.19883e21i	−0.462011	−	0.800227i
$377$	6.63256e21			0.837105
$378$	9.65782e20	−	5.10279e21i	0.119179	−	0.629691i
$379$	1.26262e22			1.52349			0.761747	−	0.647874i	$-0.224342\pi$
$379$	1.26262e22			1.52349			0.761747	+	0.647874i	$0.224342\pi$
$380$	−2.59391e21	−	4.49278e21i	−0.306051	−	0.530096i
$381$	3.89623e21	−	6.74846e21i	0.449554	−	0.778650i
$382$	4.66184e20	−	8.07455e20i	0.0526041	−	0.0911129i
$383$	−1.23213e21	−	2.13412e21i	−0.135978	−	0.235520i	0.789993	−	0.613116i	$-0.210084\pi$
$383$	−1.23213e21	−	2.13412e21i	−0.135978	−	0.235520i	−0.925971	+	0.377596i	$0.876751\pi$
$384$	−1.59699e22			−1.72379
$385$	−7.87340e21	−	6.77634e21i	−0.831277	−	0.715449i
$386$	1.63226e21			0.168577
$387$	1.46472e22	+	2.53697e22i	1.47983	+	2.56313i
$388$	1.00305e21	−	1.73734e21i	0.0991413	−	0.171718i
$389$	−5.41140e21	+	9.37283e21i	−0.523285	+	0.906356i	0.476348	+	0.879257i	$0.341960\pi$
$389$	−5.41140e21	+	9.37283e21i	−0.523285	+	0.906356i	−0.999633	+	0.0270994i	$0.991373\pi$
$390$	−2.60601e21	−	4.51375e21i	−0.246563	−	0.427059i
$391$	1.63763e21			0.151605
$392$	−1.00566e21	−	6.67695e21i	−0.0911004	−	0.604849i
$393$	−2.23317e22			−1.97964
$394$	1.85938e21	+	3.22055e21i	0.161306	+	0.279391i
$395$	4.23548e21	−	7.33607e21i	0.359606	−	0.622857i
$396$	1.04188e22	−	1.80459e22i	0.865780	−	1.49958i
$397$	5.65256e20	+	9.79052e20i	0.0459754	+	0.0796318i	0.888097	−	0.459655i	$-0.152027\pi$
$397$	5.65256e20	+	9.79052e20i	0.0459754	+	0.0796318i	−0.842122	+	0.539287i	$0.818694\pi$
$398$	−5.74008e21			−0.456996
$399$	9.74399e21	+	8.38628e21i	0.759394	+	0.653582i
$400$	4.14410e21			0.316170
$401$	−4.97617e21	−	8.61898e21i	−0.371679	−	0.643767i	0.618145	−	0.786064i	$-0.287885\pi$
$401$	−4.97617e21	−	8.61898e21i	−0.371679	−	0.643767i	−0.989824	+	0.142297i	$0.954551\pi$
$402$	2.61953e21	−	4.53716e21i	0.191559	−	0.331789i
$403$	−6.17076e21	+	1.06881e22i	−0.441820	+	0.765255i
$404$	8.02060e21	+	1.38921e22i	0.562296	+	0.973926i
$405$	−2.43511e22			−1.67167
$406$	−1.04122e21	+	5.50136e21i	−0.0699954	+	0.369827i
$407$	−2.37231e22			−1.56178
$408$	7.44765e21	+	1.28997e22i	0.480184	+	0.831703i
$409$	2.34535e21	−	4.06227e21i	0.148102	−	0.256520i	−0.782424	−	0.622746i	$-0.786017\pi$
$409$	2.34535e21	−	4.06227e21i	0.148102	−	0.256520i	0.930526	+	0.366226i	$0.119350\pi$
$410$	−2.22915e21	+	3.86101e21i	−0.137872	+	0.238802i
$411$	4.68725e21	+	8.11856e21i	0.283964	+	0.491840i
$412$	1.07227e22			0.636326
$413$	−7.68177e21	+	2.68751e21i	−0.446566	+	0.156234i
$414$	2.05341e21			0.116942
$415$	6.49103e20	+	1.12428e21i	0.0362164	+	0.0627286i
$416$	5.49354e21	−	9.51509e21i	0.300302	−	0.520139i
$417$	6.42136e21	−	1.11221e22i	0.343931	−	0.595705i
$418$	−1.58560e21	−	2.74635e21i	−0.0832140	−	0.144131i
$419$	−5.42554e21			−0.279013			−0.139506	−	0.990221i	$-0.544552\pi$
$419$	−5.42554e21			−0.279013			−0.139506	+	0.990221i	$0.544552\pi$
$420$	−3.57463e22	+	1.25060e22i	−1.80141	+	0.630232i
$421$	7.55814e21			0.373265			0.186632	−	0.982430i	$-0.440243\pi$
$421$	7.55814e21			0.373265			0.186632	+	0.982430i	$0.440243\pi$
$422$	−2.81651e21	−	4.87834e21i	−0.136319	−	0.236111i
$423$	3.38189e22	−	5.85760e22i	1.60423	−	2.77860i
$424$	−2.32087e21	+	4.01987e21i	−0.107905	+	0.186897i
$425$	−4.41121e21	−	7.64044e21i	−0.201026	−	0.348187i
$426$	1.75118e22			0.782256
$427$	−3.95613e21	+	2.09026e22i	−0.173234	+	0.915299i
$428$	4.32292e21			0.185569
$429$	1.37115e22	+	2.37489e22i	0.577028	+	0.999441i
$430$	−6.56648e21	+	1.13735e22i	−0.270926	+	0.469258i
$431$	−4.09128e21	+	7.08630e21i	−0.165502	+	0.286657i	−0.936833	−	0.349776i	$-0.886258\pi$
$431$	−4.09128e21	+	7.08630e21i	−0.165502	+	0.286657i	0.771332	+	0.636433i	$0.219591\pi$
$432$	−1.74930e22	−	3.02987e22i	−0.693827	−	1.20174i
$433$	4.93428e21			0.191901			0.0959503	−	0.995386i	$-0.469411\pi$
$433$	4.93428e21			0.191901			0.0959503	+	0.995386i	$0.469411\pi$
$434$	−7.89646e21	−	6.79619e21i	−0.301141	−	0.259181i
$435$	6.64538e22			2.48520
$436$	1.68938e22	+	2.92609e22i	0.619572	+	1.07313i
$437$	−1.34490e21	+	2.32943e21i	−0.0483724	+	0.0837834i
$438$	2.17904e21	−	3.77420e21i	0.0768661	−	0.133136i
$439$	4.38112e21	+	7.58833e21i	0.151578	+	0.262541i	0.931808	−	0.362952i	$-0.118231\pi$
$439$	4.38112e21	+	7.58833e21i	0.151578	+	0.262541i	−0.780230	+	0.625493i	$0.784898\pi$
$440$	1.97687e22			0.670858
$441$	4.98895e22	−	3.97769e22i	1.66066	−	1.32405i
$442$	−6.29796e21			−0.205641
$443$	−2.24521e22	−	3.88882e22i	−0.719161	−	1.24562i	−0.961333	−	0.275390i	$-0.911193\pi$
$443$	−2.24521e22	−	3.88882e22i	−0.719161	−	1.24562i	0.242172	−	0.970233i	$-0.422140\pi$
$444$	−4.32431e22	+	7.48992e22i	−1.35882	+	2.35354i
$445$	−7.38710e21	+	1.27948e22i	−0.227727	+	0.394434i
$446$	1.01189e22	+	1.75264e22i	0.306045	+	0.530085i
$447$	−3.49269e22			−1.03644
$448$	−1.11549e22	−	9.60059e21i	−0.324790	−	0.279534i
$449$	−4.72087e22			−1.34874			−0.674370	−	0.738393i	$-0.735585\pi$
$449$	−4.72087e22			−1.34874			−0.674370	+	0.738393i	$0.735585\pi$
$450$	−5.53116e21	−	9.58026e21i	−0.155064	−	0.268578i
$451$	1.17286e22	−	2.03146e22i	0.322661	−	0.558865i
$452$	1.82776e22	−	3.16578e22i	0.493450	−	0.854680i
$453$	1.16852e21	+	2.02394e21i	0.0309601	+	0.0536244i
$454$	−7.55538e21			−0.196463
$455$	6.30139e21	−	3.32939e22i	0.160820	−	0.849705i
$456$	−2.44654e22			−0.612847
$457$	−1.87400e22	−	3.24586e22i	−0.460768	−	0.798073i	0.538232	−	0.842797i	$-0.319092\pi$
$457$	−1.87400e22	−	3.24586e22i	−0.460768	−	0.798073i	−0.998999	+	0.0447240i	$0.985759\pi$
$458$	3.99599e21	−	6.92125e21i	0.0964423	−	0.167043i
$459$	−3.72409e22	+	6.45032e22i	−0.882293	+	1.52818i
$460$	−3.96178e21	−	6.86200e21i	−0.0921401	−	0.159591i
$461$	−5.32758e22			−1.21639			−0.608194	−	0.793788i	$-0.708106\pi$
$461$	−5.32758e22			−1.21639			−0.608194	+	0.793788i	$0.708106\pi$
$462$	−2.18510e22	+	7.64468e21i	−0.489795	+	0.171357i
$463$	6.56751e22			1.44531			0.722657	−	0.691207i	$-0.242921\pi$
$463$	6.56751e22			1.44531			0.722657	+	0.691207i	$0.242921\pi$
$464$	1.88593e22	+	3.26652e22i	0.407495	+	0.705802i
$465$	−6.18269e22	+	1.07087e23i	−1.31168	+	2.27189i
$466$	−6.93598e21	+	1.20135e22i	−0.144487	+	0.250258i
$467$	1.94896e22	+	3.37570e22i	0.398667	+	0.690511i	0.993562	−	0.113292i	$-0.0361397\pi$
$467$	1.94896e22	+	3.37570e22i	0.398667	+	0.690511i	−0.594895	+	0.803803i	$0.702806\pi$
$468$	6.79712e22			1.36532
$469$	3.21500e22	−	1.12478e22i	0.634178	−	0.221871i
$470$	3.03227e22			0.587403
$471$	−3.02422e22	−	5.23810e22i	−0.575355	−	0.996543i
$472$	7.74380e21	−	1.34127e22i	0.144693	−	0.250616i
$473$	3.45493e22	−	5.98412e22i	0.634045	−	1.09820i
$474$	−9.43883e21	−	1.63485e22i	−0.170138	−	0.294688i
$475$	1.44908e22			0.256564
$476$	−8.50993e21	+	4.49629e22i	−0.148002	+	0.781980i
$477$	−4.38623e22			−0.749351
$478$	−3.19330e21	−	5.53096e21i	−0.0535924	−	0.0928247i
$479$	−1.71300e22	+	2.96700e22i	−0.282426	+	0.489176i	−0.971982	−	0.235057i	$-0.924472\pi$
$479$	−1.71300e22	+	2.96700e22i	−0.282426	+	0.489176i	0.689556	+	0.724232i	$0.257806\pi$
$480$	5.50416e22	−	9.53348e22i	0.891539	−	1.54419i
$481$	−3.86919e22	−	6.70163e22i	−0.615725	−	1.06647i
$482$	−2.65373e22			−0.414913
$483$	1.48824e22	+	1.28087e22i	0.228624	+	0.196768i
$484$	1.02031e22			0.154010
$485$	8.99220e21	+	1.55750e22i	0.133371	+	0.231005i
$486$	−5.14734e21	+	8.91546e21i	−0.0750196	+	0.129938i
$487$	−2.55794e22	+	4.43048e22i	−0.366348	+	0.634533i	−0.988991	−	0.147972i	$-0.952725\pi$
$487$	−2.55794e22	+	4.43048e22i	−0.366348	+	0.634533i	0.622644	+	0.782506i	$0.286059\pi$
$488$	−2.02424e22	−	3.50608e22i	−0.284900	−	0.493462i
$489$	1.49580e23			2.06894
$490$	2.66263e22	+	1.04533e22i	0.361946	+	0.142098i
$491$	−9.21246e22			−1.23079			−0.615393	−	0.788220i	$-0.711003\pi$
$491$	−9.21246e22			−1.23079			−0.615393	+	0.788220i	$0.711003\pi$
$492$	−4.27585e22	−	7.40598e22i	−0.561460	−	0.972477i
$493$	4.01497e22	−	6.95414e22i	0.518184	−	0.897521i
$494$	5.17218e21	−	8.95847e21i	0.0656136	−	0.113646i
$495$	9.34025e22	+	1.61778e23i	1.16470	+	2.01732i
$496$	−7.01847e22			−0.860297
$497$	8.62908e22	+	7.42672e22i	1.03976	+	0.894886i
$498$	2.89307e21			0.0342697
$499$	−2.52603e21	−	4.37521e21i	−0.0294160	−	0.0509500i	0.850943	−	0.525259i	$-0.176031\pi$
$499$	−2.52603e21	−	4.37521e21i	−0.0294160	−	0.0509500i	−0.880359	+	0.474309i	$0.842698\pi$
$500$	2.58144e22	−	4.47118e22i	0.295540	−	0.511891i
$501$	6.61780e21	−	1.14624e22i	0.0744892	−	0.129019i
$502$	1.25656e22	+	2.17643e22i	0.139060	+	0.240859i
$503$	1.54269e23			1.67861			0.839305	−	0.543660i	$-0.182962\pi$
$503$	1.54269e23			1.67861			0.839305	+	0.543660i	$0.182962\pi$
$504$	−2.25807e22	+	1.19307e23i	−0.241589	+	1.27646i
$505$	−1.43807e23			−1.51287
$506$	−2.42176e21	−	4.19460e21i	−0.0250525	−	0.0433922i
$507$	4.21469e22	−	7.30006e22i	0.428744	−	0.742606i
$508$	−2.27793e22	+	3.94550e22i	−0.227877	+	0.394694i
$509$	1.65035e21	+	2.85850e21i	0.0162359	+	0.0281214i	0.874029	−	0.485873i	$-0.161498\pi$
$509$	1.65035e21	+	2.85850e21i	0.0162359	+	0.0281214i	−0.857793	+	0.513995i	$0.828165\pi$
$510$	−6.31013e22			−0.610509
$511$	2.67437e22	−	9.35643e21i	0.254474	−	0.0890292i
$512$	1.08141e23			1.01203
$513$	−6.11680e22	−	1.05946e23i	−0.563024	−	0.975186i
$514$	−2.77619e22	+	4.80850e22i	−0.251340	+	0.435334i
$515$	−4.80638e22	+	8.32489e22i	−0.428012	+	0.741339i
$516$	−1.25955e23	−	2.18160e23i	−1.10330	−	1.91097i
$517$	−1.59542e23			−1.37469
$518$	6.16605e22	−	2.15723e22i	0.522642	−	0.182849i
$519$	−3.31021e23			−2.76015
$520$	3.22424e22	+	5.58454e22i	0.264483	+	0.458099i
$521$	−8.79850e22	+	1.52394e23i	−0.710048	+	1.22984i	0.254790	+	0.966996i	$0.417993\pi$
$521$	−8.79850e22	+	1.52394e23i	−0.710048	+	1.22984i	−0.964839	+	0.262843i	$0.915340\pi$
$522$	5.03433e22	−	8.71972e22i	0.399708	−	0.692314i
$523$	−3.56968e22	−	6.18287e22i	−0.278846	−	0.482976i	0.692252	−	0.721656i	$-0.256619\pi$
$523$	−3.56968e22	−	6.18287e22i	−0.278846	−	0.482976i	−0.971098	+	0.238680i	$0.923285\pi$
$524$	1.30563e23			1.00347
$525$	1.96716e22	−	1.03937e23i	0.148760	−	0.785986i
$526$	1.39696e22			0.103945
$527$	7.47085e22	+	1.29399e23i	0.546991	+	0.947416i
$528$	−7.79754e22	+	1.35057e23i	−0.561784	+	0.973038i
$529$	6.84709e22	−	1.18595e23i	0.485437	−	0.840801i
$530$	−9.83196e21	−	1.70295e22i	−0.0685954	−	0.118811i
$531$	1.46351e23			1.00483
$532$	−5.69684e22	−	4.90305e22i	−0.384933	−	0.331297i
$533$	7.65165e22			0.508831
$534$	1.64623e22	+	2.85135e22i	0.107743	+	0.186616i
$535$	−1.93771e22	+	3.35622e22i	−0.124819	+	0.216194i
$536$	−3.24096e22	+	5.61350e22i	−0.205481	+	0.355904i
$537$	1.04334e23	+	1.80711e23i	0.651092	+	1.12773i
$538$	−3.76985e22			−0.231566
$539$	−1.40093e23	−	5.49998e22i	−0.847058	−	0.332550i
$540$	3.60375e23			2.14491
$541$	1.60124e23	+	2.77344e23i	0.938168	+	1.62495i	0.768885	+	0.639388i	$0.220812\pi$
$541$	1.60124e23	+	2.77344e23i	0.938168	+	1.62495i	0.169284	+	0.985567i	$0.445855\pi$
$542$	2.29312e21	−	3.97179e21i	0.0132261	−	0.0229083i
$543$	−4.31936e22	+	7.48135e22i	−0.245256	+	0.424797i
$544$	−6.65095e22	−	1.15198e23i	−0.371786	−	0.643952i
$545$	−3.02900e23			−1.66697
$546$	−5.72343e22	−	4.92594e22i	−0.310112	−	0.266902i
$547$	1.42246e23			0.758838			0.379419	−	0.925225i	$-0.376124\pi$
$547$	1.42246e23			0.758838			0.379419	+	0.925225i	$0.376124\pi$
$548$	−2.74041e22	−	4.74653e22i	−0.143940	−	0.249311i
$549$	1.91281e23	−	3.31308e23i	0.989252	−	1.71343i
$550$	−1.30467e22	+	2.25976e22i	−0.0664384	+	0.115075i
$551$	6.59457e22	+	1.14221e23i	0.330672	+	0.572741i
$552$	−3.73670e22			−0.184504
$553$	2.28233e22	−	1.20589e23i	0.110972	−	0.586331i
$554$	7.74270e22			0.370732
$555$	−3.87667e23	−	6.71458e23i	−1.82797	−	3.16613i
$556$	−3.75426e22	+	6.50257e22i	−0.174337	+	0.301960i
$557$	8.93039e22	−	1.54679e23i	0.408414	−	0.707395i	−0.586298	−	0.810096i	$-0.699415\pi$
$557$	8.93039e22	−	1.54679e23i	0.408414	−	0.707395i	0.994712	+	0.102701i	$0.0327485\pi$
$558$	9.36761e22	+	1.62252e23i	0.421928	+	0.730801i
$559$	2.25397e23			0.999880
$560$	1.81890e23	−	6.36350e22i	0.794711	−	0.278034i
$561$	3.32005e23			1.42876
$562$	−5.04597e22	−	8.73987e22i	−0.213888	−	0.370464i
$563$	−7.22556e22	+	1.25150e23i	−0.301683	+	0.522530i	−0.976517	−	0.215439i	$-0.930882\pi$
$563$	−7.22556e22	+	1.25150e23i	−0.301683	+	0.522530i	0.674835	+	0.737969i	$0.264215\pi$
$564$	−2.90817e23	+	5.03710e23i	−1.19605	+	2.07161i
$565$	1.63856e23	+	2.83806e23i	0.663819	+	1.14977i
$566$	−5.38909e22			−0.215068
$567$	−3.33014e23	+	1.16507e23i	−1.30920	+	0.458030i
$568$	−2.16661e23			−0.839112
$569$	2.16069e23	+	3.74242e23i	0.824400	+	1.42790i	0.902377	+	0.430947i	$0.141821\pi$
$569$	2.16069e23	+	3.74242e23i	0.824400	+	1.42790i	−0.0779771	+	0.996955i	$0.524846\pi$
$570$	5.18217e22	−	8.97579e22i	0.194794	−	0.337393i
$571$	1.96272e23	−	3.39953e23i	0.726861	−	1.25896i	−0.231343	−	0.972872i	$-0.574312\pi$
$571$	1.96272e23	−	3.39953e23i	0.726861	−	1.25896i	0.958204	−	0.286087i	$-0.0923548\pi$
$572$	−8.01643e22	−	1.38849e23i	−0.292492	−	0.506612i
$573$	−1.60329e23			−0.576365
$574$	−1.20120e22	+	6.34664e22i	−0.0425465	+	0.224798i
$575$	2.21323e22			0.0772414
$576$	1.32331e23	+	2.29204e23i	0.455062	+	0.788190i
$577$	1.26497e23	−	2.19099e23i	0.428633	−	0.742414i	−0.568119	−	0.822946i	$-0.692329\pi$
$577$	1.26497e23	−	2.19099e23i	0.428633	−	0.742414i	0.996752	+	0.0805324i	$0.0256621\pi$
$578$	1.01879e22	−	1.76460e22i	0.0340172	−	0.0589194i
$579$	−1.40341e23	−	2.43077e23i	−0.461760	−	0.799791i
$580$	−3.88523e23			−1.25974
$581$	1.42558e22	+	1.22695e22i	0.0455508	+	0.0392038i
$582$	4.00785e22			0.126202
$583$	5.17305e22	+	8.95999e22i	0.160533	+	0.278051i
$584$	−2.69597e22	+	4.66955e22i	−0.0824528	+	0.142812i
$585$	−3.04675e23	+	5.27713e23i	−0.918358	+	1.59064i
$586$	−5.50333e22	−	9.53204e22i	−0.163492	−	0.283176i
$587$	−3.01634e23			−0.883195			−0.441598	−	0.897213i	$-0.645588\pi$
$587$	−3.01634e23			−0.883195			−0.441598	+	0.897213i	$0.645588\pi$
$588$	−4.29013e23	+	3.42052e23i	−1.23812	+	0.987153i
$589$	−2.45416e23			−0.698110
$590$	3.28053e22	+	5.68204e22i	0.0919817	+	0.159317i
$591$	3.19737e23	−	5.53801e23i	0.883689	−	1.53059i
$592$	2.20036e23	−	3.81113e23i	0.599458	−	1.03829i
$593$	−2.40319e23	−	4.16245e23i	−0.645392	−	1.11785i	−0.984211	−	0.177000i	$-0.943361\pi$
$593$	−2.40319e23	−	4.16245e23i	−0.645392	−	1.11785i	0.338819	−	0.940852i	$-0.389973\pi$
$594$	2.20290e23			0.583191
$595$	−3.10937e23	−	2.67611e23i	−0.811480	−	0.698410i
$596$	2.04201e23			0.525368
$597$	4.93528e23	+	8.54816e23i	1.25179	+	2.16816i
$598$	7.89967e21	−	1.36826e22i	0.0197537	−	0.0342144i
$599$	2.54623e23	−	4.41019e23i	0.627724	−	1.08725i	−0.360283	−	0.932843i	$-0.617320\pi$
$599$	2.54623e23	−	4.41019e23i	0.627724	−	1.08725i	0.988007	−	0.154407i	$-0.0493468\pi$
$600$	1.00654e23	+	1.74338e23i	0.244650	+	0.423746i
$601$	−1.07848e23			−0.258452			−0.129226	−	0.991615i	$-0.541249\pi$
$601$	−1.07848e23			−0.258452			−0.129226	+	0.991615i	$0.541249\pi$
$602$	−3.53841e22	+	1.86955e23i	−0.0836060	+	0.441740i
$603$	−6.12510e23			−1.42697
$604$	−6.83178e21	−	1.18330e22i	−0.0156935	−	0.0271819i
$605$	−4.57347e22	+	7.92148e22i	−0.103592	+	0.179426i
$606$	−1.60238e23	+	2.77540e23i	−0.357888	+	0.619880i
$607$	4.04975e23	+	7.01437e23i	0.891917	+	1.54485i	0.837574	+	0.546323i	$0.183973\pi$
$607$	4.04975e23	+	7.01437e23i	0.891917	+	1.54485i	0.0543427	+	0.998522i	$0.482694\pi$
$608$	2.18483e23			0.474501
$609$	9.08788e23	−	3.17944e23i	1.94633	−	0.680933i
$610$	1.71507e23			0.362224
$611$	−2.60210e23	−	4.50696e23i	−0.541967	−	0.938715i
$612$	4.11459e23	−	7.12668e23i	0.845161	−	1.46386i
$613$	−2.69746e23	+	4.67213e23i	−0.546437	+	0.946457i	0.452077	+	0.891979i	$0.350683\pi$
$613$	−2.69746e23	+	4.67213e23i	−0.546437	+	0.946457i	−0.998515	+	0.0544788i	$0.982650\pi$
$614$	−1.54761e23	−	2.68055e23i	−0.309194	−	0.535540i
$615$	7.66644e23			1.51062
$616$	2.70347e23	−	9.45822e22i	0.525394	−	0.183812i
$617$	−4.21078e23			−0.807121			−0.403560	−	0.914953i	$-0.632227\pi$
$617$	−4.21078e23			−0.807121			−0.403560	+	0.914953i	$0.632227\pi$
$618$	1.07111e23	+	1.85521e23i	0.202503	+	0.350745i
$619$	5.03779e22	−	8.72571e22i	0.0939442	−	0.162716i	−0.815223	−	0.579147i	$-0.803386\pi$
$619$	5.03779e22	−	8.72571e22i	0.0939442	−	0.162716i	0.909167	+	0.416431i	$0.136719\pi$
$620$	3.61472e23	−	6.26088e23i	0.664883	−	1.15161i
$621$	−9.34243e22	−	1.61816e23i	−0.169504	−	0.293590i
$622$	5.13368e22			0.0918777
$623$	−3.98060e22	+	2.10319e23i	−0.0702749	+	0.371304i
$624$	−5.08705e23			−0.885925
$625$	3.63144e23	+	6.28984e23i	0.623876	+	1.08059i
$626$	1.33047e23	−	2.30444e23i	0.225488	−	0.390557i
$627$	−2.72658e23	+	4.72258e23i	−0.455874	+	0.789597i
$628$	1.76811e23	+	3.06246e23i	0.291644	+	0.505143i
$629$	−9.36874e23			−1.52458
$630$	−3.89880e23	−	3.35555e23i	−0.625945	−	0.538727i
$631$	4.57537e23			0.724731			0.362366	−	0.932036i	$-0.381969\pi$
$631$	4.57537e23			0.724731			0.362366	+	0.932036i	$0.381969\pi$
$632$	1.16780e23	+	2.02269e23i	0.182504	+	0.316107i
$633$	−4.84324e23	+	8.38873e23i	−0.746800	+	1.29350i
$634$	1.32283e23	−	2.29121e23i	0.201254	−	0.348583i
$635$	−2.04213e23	−	3.53707e23i	−0.306554	−	0.530966i
$636$	3.77183e23			0.558685
$637$	−7.31183e22	−	4.85459e23i	−0.106866	−	0.709524i
$638$	−2.37497e23			−0.342517
$639$	−1.02367e24	−	1.77305e24i	−1.45681	−	2.52327i
$640$	−4.18514e23	+	7.24887e23i	−0.587733	+	1.01798i
$641$	−3.93026e23	+	6.80741e23i	−0.544663	+	0.943384i	0.453965	+	0.891019i	$0.350009\pi$
$641$	−3.93026e23	+	6.80741e23i	−0.544663	+	0.943384i	−0.998628	+	0.0523643i	$0.983324\pi$
$642$	4.31822e22	+	7.47938e22i	0.0590550	+	0.102286i
$643$	5.03383e23			0.679369			0.339684	−	0.940539i	$-0.389680\pi$
$643$	5.03383e23			0.679369			0.339684	+	0.940539i	$0.389680\pi$
$644$	−8.70100e22	−	7.48863e22i	−0.115888	−	0.0997407i
$645$	2.25833e24			2.96845
$646$	−6.26188e22	−	1.08459e23i	−0.0812322	−	0.140698i
$647$	−2.13365e23	+	3.69558e23i	−0.273172	+	0.473148i	−0.969672	−	0.244409i	$-0.921406\pi$
$647$	−2.13365e23	+	3.69558e23i	−0.273172	+	0.473148i	0.696500	+	0.717556i	$0.254739\pi$
$648$	3.35703e23	−	5.81454e23i	0.424197	−	0.734730i
$649$	−1.72604e23	−	2.98958e23i	−0.215263	−	0.372847i
$650$	−8.51159e22			−0.104772
$651$	−3.33160e23	+	1.76028e24i	−0.404775	+	2.13866i
$652$	−8.74521e23			−1.04873
$653$	−4.97404e23	−	8.61529e23i	−0.588772	−	1.01978i	−0.994394	−	0.105742i	$-0.966278\pi$
$653$	−4.97404e23	−	8.61529e23i	−0.588772	−	1.01978i	0.405622	−	0.914041i	$-0.367055\pi$
$654$	−3.37508e23	+	5.84581e23i	−0.394342	+	0.683021i
$655$	−5.85236e23	+	1.01366e24i	−0.674963	+	1.16907i
$656$	2.17570e23	+	3.76842e23i	0.247695	+	0.429019i
$657$	−5.09512e23			−0.572597
$658$	4.14678e23	−	1.45077e23i	0.460035	−	0.160946i
$659$	1.02895e24			1.12686			0.563430	−	0.826164i	$-0.309482\pi$
$659$	1.02895e24			1.12686			0.563430	+	0.826164i	$0.309482\pi$
$660$	−8.03192e23	−	1.39117e24i	−0.868353	−	1.50403i
$661$	−1.41626e23	+	2.45303e23i	−0.151158	+	0.261813i	−0.931653	−	0.363349i	$-0.881633\pi$
$661$	−1.41626e23	+	2.45303e23i	−0.151158	+	0.261813i	0.780496	+	0.625161i	$0.214967\pi$
$662$	−1.86705e23	+	3.23382e23i	−0.196726	+	0.340740i
$663$	5.41494e23	+	9.37895e23i	0.563285	+	0.975639i
$664$	−3.57939e22			−0.0367604
$665$	6.36017e23	−	2.22514e23i	0.644889	−	0.225618i
$666$	−1.17474e24			−1.17600
$667$	1.00721e23	+	1.74455e23i	0.0995525	+	0.172430i
$668$	−3.86911e22	+	6.70149e22i	−0.0377582	+	0.0653991i
$669$	1.74002e24	−	3.01381e24i	1.67661	−	2.90398i
$670$	−1.37297e23	−	2.37806e23i	−0.130625	−	0.226249i
$671$	−9.02376e23			−0.847707
$672$	2.96596e23	−	1.56709e24i	0.275123	−	1.45364i
$673$	−3.09199e23			−0.283210			−0.141605	−	0.989923i	$-0.545226\pi$
$673$	−3.09199e23			−0.283210			−0.141605	+	0.989923i	$0.545226\pi$
$674$	1.47282e23	+	2.55100e23i	0.133211	+	0.230728i
$675$	−5.03306e23	+	8.71751e23i	−0.449521	+	0.778593i
$676$	−2.46412e23	+	4.26799e23i	−0.217328	+	0.376423i
$677$	−1.23736e23	−	2.14316e23i	−0.107768	−	0.186660i	0.807098	−	0.590418i	$-0.201037\pi$
$677$	−1.23736e23	−	2.14316e23i	−0.107768	−	0.186660i	−0.914866	+	0.403758i	$0.867704\pi$
$678$	7.30310e23			0.628137
$679$	1.97490e23	+	1.69972e23i	0.167746	+	0.144373i
$680$	7.80707e23			0.654881
$681$	6.49606e23	+	1.12515e24i	0.538146	+	0.932095i
$682$	2.20961e23	−	3.82715e23i	0.180779	−	0.313118i
$683$	6.77959e22	−	1.17426e23i	0.0547807	−	0.0948829i	−0.837335	−	0.546691i	$-0.815887\pi$
$683$	6.77959e22	−	1.17426e23i	0.0547807	−	0.0948829i	0.892115	+	0.451808i	$0.149221\pi$
$684$	6.75819e23	+	1.17055e24i	0.539328	+	0.934144i
$685$	4.91346e23			0.387273
$686$	4.14141e23	+	1.55623e22i	0.322399	+	0.0121149i
$687$	−1.37429e24			−1.05669
$688$	6.40902e23	+	1.11008e24i	0.486732	+	0.843045i
$689$	−1.68743e23	+	2.92271e23i	−0.126579	+	0.219241i
$690$	7.91494e22	−	1.37091e23i	0.0586449	−	0.101576i
$691$	−1.23809e24	−	2.14444e24i	−0.906127	−	1.56946i	−0.819397	−	0.573226i	$-0.805692\pi$
$691$	−1.23809e24	−	2.14444e24i	−0.906127	−	1.56946i	−0.0867295	−	0.996232i	$-0.527642\pi$
$692$	1.93532e24			1.39911
$693$	2.05134e24	+	1.76551e24i	1.46489	+	1.26078i
$694$	3.77381e23			0.266210
$695$	−3.36563e23	−	5.82944e23i	−0.234528	−	0.406215i
$696$	−9.16127e23	+	1.58678e24i	−0.630633	+	1.09229i
$697$	4.63187e23	−	8.02264e23i	0.314976	−	0.545555i
$698$	2.33192e23	+	4.03901e23i	0.156655	+	0.271334i
$699$	2.38540e24			1.58309
$700$	−1.15010e23	+	6.07667e23i	−0.0754056	+	0.398412i
$701$	−2.40386e24			−1.55706			−0.778530	−	0.627608i	$-0.784034\pi$
$701$	−2.40386e24			−1.55706			−0.778530	+	0.627608i	$0.784034\pi$
$702$	3.59289e23	+	6.22306e23i	0.229921	+	0.398234i
$703$	7.69405e23	−	1.33265e24i	0.486446	−	0.842549i
$704$	3.12138e23	−	5.40640e23i	0.194975	−	0.337707i
$705$	−2.60713e24	−	4.51568e24i	−1.60899	−	2.78686i
$706$	−3.64246e23			−0.222103
$707$	−1.96662e24	+	6.88034e23i	−1.18483	+	0.414519i
$708$	−1.25851e24			−0.749157
$709$	−1.30279e24	−	2.25649e24i	−0.766268	−	1.32721i	−0.939574	−	0.342347i	$-0.888778\pi$
$709$	−1.30279e24	−	2.25649e24i	−0.766268	−	1.32721i	0.173306	−	0.984868i	$-0.444555\pi$
$710$	4.58923e23	−	7.94878e23i	0.266713	−	0.461960i
$711$	−1.10352e24	+	1.91134e24i	−0.633704	+	1.09761i
$712$	−2.03676e23	−	3.52777e23i	−0.115574	−	0.200180i
$713$	−3.74834e23			−0.210174
$714$	−8.62940e23	+	3.01904e23i	−0.478130	+	0.167276i
$715$	1.43732e24			0.786957
$716$	−6.09988e23	−	1.05653e24i	−0.330035	−	0.571638i
$717$	−5.49116e23	+	9.51097e23i	−0.293597	+	0.508524i
$718$	−5.31554e23	+	9.20679e23i	−0.280860	+	0.486464i
$719$	1.60596e24	+	2.78160e24i	0.838568	+	1.45244i	0.891092	+	0.453823i	$0.149940\pi$
$719$	1.60596e24	+	2.78160e24i	0.838568	+	1.45244i	−0.0525242	+	0.998620i	$0.516727\pi$
$720$	−3.46530e24			−1.78819
$721$	−2.58996e23	+	1.36843e24i	−0.132082	+	0.697865i
$722$	−4.34424e23			−0.218952
$723$	2.28166e24	+	3.95195e24i	1.13652	+	1.96850i
$724$	2.52532e23	−	4.37398e23i	0.124319	−	0.215327i
$725$	5.42618e23	−	9.39841e23i	0.264010	−	0.457279i
$726$	1.01920e23	+	1.76531e23i	0.0490117	+	0.0848908i
$727$	3.23450e24			1.53732			0.768661	−	0.639657i	$-0.220923\pi$
$727$	3.23450e24			1.53732			0.768661	+	0.639657i	$0.220923\pi$
$728$	7.08118e23	+	6.09451e23i	0.332651	+	0.286300i
$729$	−1.21693e24			−0.565045
$730$	−1.14210e23	−	1.97817e23i	−0.0524155	−	0.0907862i
$731$	1.36442e24	−	2.36325e24i	0.618945	−	1.07204i
$732$	−1.64487e24	+	2.84901e24i	−0.737545	+	1.27747i
$733$	−1.10879e23	−	1.92047e23i	−0.0491433	−	0.0851187i	0.840407	−	0.541955i	$-0.182316\pi$
$733$	−1.10879e23	−	1.92047e23i	−0.0491433	−	0.0851187i	−0.889551	+	0.456837i	$0.848982\pi$
$734$	8.05126e22			0.0352734
$735$	−7.32596e23	−	4.86397e24i	−0.317265	−	2.10644i
$736$	3.33697e23			0.142854
$737$	7.22386e23	+	1.25121e24i	0.305700	+	0.529488i
$738$	5.80785e23	−	1.00595e24i	0.242961	−	0.420821i
$739$	1.84293e23	−	3.19204e23i	0.0762132	−	0.132005i	−0.825400	−	0.564548i	$-0.809050\pi$
$739$	1.84293e23	−	3.19204e23i	0.0762132	−	0.132005i	0.901613	+	0.432543i	$0.142384\pi$
$740$	2.26650e24	+	3.92569e24i	0.926586	+	1.60489i
$741$	−1.77880e24			−0.718906
$742$	−2.15933e23	−	1.85846e23i	−0.0862752	−	0.0742538i
$743$	1.10822e24			0.437744			0.218872	−	0.975754i	$-0.429762\pi$
$743$	1.10822e24			0.437744			0.218872	+	0.975754i	$0.429762\pi$
$744$	−1.70468e24	−	2.95259e24i	−0.665691	−	1.15301i
$745$	−9.15311e23	+	1.58537e24i	−0.353379	+	0.612070i
$746$	−2.03713e23	+	3.52841e23i	−0.0777567	+	0.134679i
$747$	−1.69118e23	−	2.92921e23i	−0.0638211	−	0.110541i
$748$	−1.94107e24			−0.724234
$749$	−1.04415e23	+	5.51687e23i	−0.0385184	+	0.203515i
$750$	1.03145e24			0.376208
$751$	−1.85106e24	−	3.20613e24i	−0.667546	−	1.15622i	−0.978588	−	0.205828i	$-0.934011\pi$
$751$	−1.85106e24	−	3.20613e24i	−0.667546	−	1.15622i	0.311042	−	0.950396i	$-0.399322\pi$
$752$	1.47978e24	−	2.56305e24i	0.527650	−	0.913916i
$753$	2.16077e24	−	3.74256e24i	0.761817	−	1.31951i
$754$	−3.87352e23	−	6.70913e23i	−0.135036	−	0.233889i
$755$	1.22491e23			0.0422237
$756$	4.92831e24	−	1.72419e24i	1.67982	−	0.587693i
$757$	2.31398e24			0.779912			0.389956	−	0.920834i	$-0.372490\pi$
$757$	2.31398e24			0.779912			0.389956	+	0.920834i	$0.372490\pi$
$758$	−7.37392e23	−	1.27720e24i	−0.245760	−	0.425668i
$759$	−4.16442e23	+	7.21298e23i	−0.137246	+	0.237717i
$760$	−6.41153e23	+	1.11051e24i	−0.208952	+	0.361915i
$761$	1.75683e24	+	3.04291e24i	0.566186	+	0.980663i	0.996938	+	0.0781930i	$0.0249150\pi$
$761$	1.75683e24	+	3.04291e24i	0.566186	+	0.980663i	−0.430752	+	0.902470i	$0.641752\pi$
$762$	−9.10183e23			−0.290076
$763$	−4.14230e24	+	1.44921e24i	−1.30552	+	0.456742i
$764$	9.37365e23			0.292156
$765$	3.68866e24	+	6.38894e24i	1.13696	+	1.96928i
$766$	−1.43917e23	+	2.49271e23i	−0.0438699	+	0.0759850i
$767$	5.63026e23	−	9.75190e23i	0.169734	−	0.293987i
$768$	−3.37491e23	−	5.84552e23i	−0.100622	−	0.174282i
$769$	−1.80739e24			−0.532938			−0.266469	−	0.963843i	$-0.585857\pi$
$769$	−1.80739e24			−0.532938			−0.266469	+	0.963843i	$0.585857\pi$
$770$	−2.25638e23	+	1.19218e24i	−0.0658023	+	0.347672i
$771$	9.54778e24			2.75385
$772$	8.20505e23	+	1.42116e24i	0.234064	+	0.405410i
$773$	−2.59989e24	+	4.50315e24i	−0.733550	+	1.27055i	0.221806	+	0.975091i	$0.428805\pi$
$773$	−2.59989e24	+	4.50315e24i	−0.733550	+	1.27055i	−0.955356	+	0.295456i	$0.904529\pi$
$774$	1.71084e24	−	2.96325e24i	0.477431	−	0.826934i
$775$	1.00967e24	+	1.74881e24i	0.278687	+	0.482700i
$776$	−4.95863e23			−0.135374
$777$	−8.51408e24	−	7.32774e24i	−2.29911	−	1.97875i
$778$	1.26414e24			0.337651
$779$	7.60782e23	+	1.31771e24i	0.200998	+	0.348139i
$780$	2.61998e24	−	4.53794e24i	0.684690	−	1.18592i
$781$	−2.41461e24	+	4.18222e24i	−0.624184	+	1.08112i
$782$	−9.56401e22	−	1.65654e23i	−0.0244559	−	0.0423588i
$783$	−9.16193e24			−2.31746
$784$	2.18297e24	−	1.74048e24i	0.546212	−	0.435494i
$785$	−3.17017e24			−0.784676
$786$	1.30421e24	+	2.25895e24i	0.319341	+	0.553115i
$787$	4.13170e22	−	7.15632e22i	0.0100079	−	0.0173342i	−0.860978	−	0.508642i	$-0.830148\pi$
$787$	4.13170e22	−	7.15632e22i	0.0100079	−	0.0173342i	0.870986	+	0.491308i	$0.163481\pi$
$788$	−1.86935e24	+	3.23781e24i	−0.447938	+	0.775851i
$789$	−1.20109e24	−	2.08036e24i	−0.284723	−	0.493154i
$790$	−9.89435e23			−0.232037
$791$	3.59866e24	+	3.09723e24i	0.834912	+	0.718577i
$792$	−5.15055e24			−1.18220
$793$	−1.47176e24	−	2.54916e24i	−0.334206	−	0.578861i
$794$	6.60236e22	−	1.14356e23i	0.0148329	−	0.0256913i
$795$	−1.69069e24	+	2.92836e24i	−0.375788	+	0.650885i
$796$	−2.88542e24	−	4.99770e24i	−0.634524	−	1.09903i
$797$	6.12085e22			0.0133173			0.00665864	−	0.999978i	$-0.497880\pi$
$797$	6.12085e22			0.0133173			0.00665864	+	0.999978i	$0.497880\pi$
$798$	2.79246e23	−	1.47542e24i	0.0601121	−	0.317608i
$799$	−6.30064e24			−1.34195
$800$	−8.98865e23	−	1.55688e24i	−0.189422	−	0.328088i
$801$	1.92464e24	−	3.33357e24i	0.401304	−	0.695078i
$802$	−5.81233e23	+	1.00672e24i	−0.119913	+	0.207696i
$803$	6.00912e23	+	1.04081e24i	0.122667	+	0.212466i
$804$	5.26714e24			1.06389
$805$	9.71414e23	−	3.39854e23i	0.194151	−	0.0679247i
$806$	1.44153e24			0.285086
$807$	3.24129e24	+	5.61408e24i	0.634297	+	1.09863i
$808$	1.98250e24	−	3.43380e24i	0.383899	−	0.664933i
$809$	9.03681e23	−	1.56522e24i	0.173162	−	0.299925i	−0.766362	−	0.642409i	$-0.777935\pi$
$809$	9.03681e23	−	1.56522e24i	0.173162	−	0.299925i	0.939524	+	0.342484i	$0.111268\pi$
$810$	1.42214e24	+	2.46323e24i	0.269663	+	0.467070i
$811$	1.01599e25			1.90639			0.953196	−	0.302352i	$-0.0977717\pi$
$811$	1.01599e25			1.90639			0.953196	+	0.302352i	$0.0977717\pi$
$812$	−5.31324e24	+	1.85887e24i	−0.986583	+	0.345161i
$813$	−7.88642e23			−0.144914
$814$	1.38547e24	+	2.39970e24i	0.251935	+	0.436364i
$815$	3.91996e24	−	6.78957e24i	0.705411	−	1.22181i
$816$	−3.07941e24	+	5.33369e24i	−0.548404	+	0.949864i
$817$	2.24106e24	+	3.88163e24i	0.394971	+	0.684111i
$818$	−5.47889e23			−0.0955630
$819$	−1.64177e24	+	8.67442e24i	−0.283399	+	1.49736i
$820$	−4.48220e24			−0.765726
$821$	−2.14752e24	−	3.71962e24i	−0.363095	−	0.628900i	0.625373	−	0.780326i	$-0.284947\pi$
$821$	−2.14752e24	−	3.71962e24i	−0.363095	−	0.628900i	−0.988469	+	0.151426i	$0.951613\pi$
$822$	5.47486e23	−	9.48273e23i	0.0916141	−	0.158680i
$823$	8.62090e23	−	1.49318e24i	0.142776	−	0.247295i	−0.785765	−	0.618525i	$-0.787731\pi$
$823$	8.62090e23	−	1.49318e24i	0.142776	−	0.247295i	0.928541	+	0.371230i	$0.121064\pi$
$824$	−1.32520e24	−	2.29532e24i	−0.217221	−	0.376238i
$825$	4.48700e24			0.727943
$826$	7.20481e23	+	6.20091e23i	0.115689	+	0.0995692i
$827$	9.12049e24			1.44951			0.724756	−	0.689006i	$-0.241953\pi$
$827$	9.12049e24			1.44951			0.724756	+	0.689006i	$0.241953\pi$
$828$	1.03220e24	+	1.78783e24i	0.162371	+	0.281234i
$829$	−6.25854e23	+	1.08401e24i	−0.0974450	+	0.168780i	−0.910626	−	0.413231i	$-0.864400\pi$
$829$	−6.25854e23	+	1.08401e24i	−0.0974450	+	0.168780i	0.813181	+	0.582010i	$0.197734\pi$
$830$	7.58173e22	−	1.31319e23i	0.0116843	−	0.0202379i
$831$	−6.65712e24	−	1.15305e25i	−1.01550	−	1.75889i
$832$	2.03636e24			0.307473
$833$	−5.53258e24	−	2.17206e24i	−0.826885	−	0.324630i
$834$	−1.50007e24			−0.221922
$835$	−3.46859e23	−	6.00777e23i	−0.0507946	−	0.0879789i
$836$	1.59410e24	−	2.76106e24i	0.231080	−	0.400242i
$837$	8.52401e24	−	1.47640e25i	1.22314	−	2.11855i
$838$	3.16860e23	+	5.48818e23i	0.0450084	+	0.0779568i
$839$	−2.24109e24			−0.315125			−0.157563	−	0.987509i	$-0.550364\pi$
$839$	−2.24109e24			−0.315125			−0.157563	+	0.987509i	$0.550364\pi$
$840$	7.09487e24	+	6.10629e24i	0.987576	+	0.849970i
$841$	2.62040e24			0.361078
$842$	−4.41407e23	−	7.64539e23i	−0.0602125	−	0.104291i
$843$	−8.67698e24	+	1.50290e25i	−1.17175	+	2.02953i
$844$	2.83161e24	−	4.90449e24i	0.378549	−	0.655666i
$845$	−2.20904e24	−	3.82618e24i	−0.292363	−	0.506388i
$846$	−7.90030e24			−1.03513
$847$	−2.46445e23	+	1.30212e24i	−0.0319677	+	0.168904i
$848$	−1.91924e24			−0.246470
$849$	4.63350e24	+	8.02545e24i	0.589106	+	1.02036i
$850$	−5.15243e23	+	8.92427e23i	−0.0648562	+	0.112334i
$851$	1.17514e24	−	2.03541e24i	0.146450	−	0.253659i
$852$	8.80282e24	+	1.52469e25i	1.08614	+	1.88125i
$853$	1.12573e25			1.37520			0.687601	−	0.726088i	$-0.258664\pi$
$853$	1.12573e25			1.37520			0.687601	+	0.726088i	$0.258664\pi$
$854$	2.34543e24	−	8.20562e23i	0.283682	−	0.0992475i
$855$	−1.21172e25			−1.45108
$856$	−5.34262e23	−	9.25370e23i	−0.0633472	−	0.109721i
$857$	4.90400e23	−	8.49398e23i	0.0575723	−	0.0997182i	−0.835803	−	0.549030i	$-0.814997\pi$
$857$	4.90400e23	−	8.49398e23i	0.0575723	−	0.0997182i	0.893375	+	0.449312i	$0.148331\pi$
$858$	1.60154e24	−	2.77395e24i	0.186164	−	0.322446i
$859$	−2.05859e24	−	3.56558e24i	−0.236934	−	0.410383i	0.722899	−	0.690954i	$-0.242809\pi$
$859$	−2.05859e24	−	3.56558e24i	−0.236934	−	0.410383i	−0.959833	+	0.280572i	$0.909476\pi$
$860$	−1.32033e25			−1.50469
$861$	1.04842e25	−	3.66796e24i	1.18307	−	0.413903i
$862$	9.55748e23			0.106790
$863$	−7.54051e24	−	1.30605e25i	−0.834275	−	1.44501i	−0.894620	−	0.446828i	$-0.852553\pi$
$863$	−7.54051e24	−	1.30605e25i	−0.834275	−	1.44501i	0.0603451	−	0.998178i	$-0.480780\pi$
$864$	−7.58853e24	+	1.31437e25i	−0.831363	+	1.43996i
$865$	−8.67491e24	+	1.50254e25i	−0.941083	+	1.63000i
$866$	−2.88170e23	−	4.99124e23i	−0.0309561	−	0.0536175i
$867$	−3.50379e24			−0.372714
$868$	1.94782e24	−	1.02915e25i	0.205178	−	1.08408i
$869$	5.20588e24			0.543033
$870$	−3.88101e24	−	6.72210e24i	−0.400895	−	0.694371i
$871$	−2.35639e24	+	4.08139e24i	−0.241042	+	0.417497i
$872$	4.17575e24	−	7.23261e24i	0.423004	−	0.732664i
$873$	−2.34283e24	−	4.05791e24i	−0.235029	−	0.407081i
$874$	3.14177e23			0.0312124
$875$	5.08256e24	+	4.37437e24i	0.500051	+	0.430375i
$876$	4.38143e24			0.426905
$877$	−3.16045e24	−	5.47406e24i	−0.304966	−	0.528217i	0.672287	−	0.740290i	$-0.265312\pi$
$877$	−3.16045e24	−	5.47406e24i	−0.304966	−	0.528217i	−0.977254	+	0.212073i	$0.931979\pi$
$878$	5.11729e23	−	8.86340e23i	0.0489031	−	0.0847027i
$879$	−9.46344e24	+	1.63912e25i	−0.895661	+	1.55133i
$880$	4.08692e24	+	7.07876e24i	0.383084	+	0.663520i
$881$	−1.92178e25			−1.78406			−0.892028	−	0.451981i	$-0.850717\pi$
$881$	−1.92178e25			−1.78406			−0.892028	+	0.451981i	$0.850717\pi$
$882$	−6.93724e24	−	2.72352e24i	−0.637828	−	0.250407i
$883$	3.43088e24			0.312421			0.156210	−	0.987724i	$-0.450072\pi$
$883$	3.43088e24			0.312421			0.156210	+	0.987724i	$0.450072\pi$
$884$	−3.16585e24	−	5.48342e24i	−0.285526	−	0.494546i
$885$	5.64115e24	−	9.77075e24i	0.503906	−	0.872791i
$886$	−2.62248e24	+	4.54227e24i	−0.232020	+	0.401870i
$887$	1.95663e24	+	3.38898e24i	0.171458	+	0.296974i	0.938930	−	0.344109i	$-0.111819\pi$
$887$	1.95663e24	+	3.38898e24i	0.171458	+	0.296974i	−0.767472	+	0.641083i	$0.778486\pi$
$888$	2.13773e25			1.85543
$889$	−4.48500e24	−	3.86007e24i	−0.385565	−	0.331841i
$890$	1.72567e24			0.146941
$891$	−7.48257e24	−	1.29602e25i	−0.631088	−	1.09308i
$892$	−1.01731e25	+	1.76203e25i	−0.849867	+	1.47201i
$893$	5.17438e24	−	8.96229e24i	0.428175	−	0.741620i
$894$	2.03978e24	+	3.53301e24i	0.167192	+	0.289585i
$895$	1.09369e25			0.887968
$896$	−2.25520e24	+	1.19155e25i	−0.181370	+	0.958287i
$897$	−2.71683e24			−0.216435
$898$	2.75706e24	+	4.77537e24i	0.217569	+	0.376841i
$899$	−9.18981e24	+	1.59172e25i	−0.718371	+	1.24426i
$900$	5.56080e24	−	9.63160e24i	0.430602	−	0.745825i
$901$	2.04295e24	+	3.53849e24i	0.156710	+	0.271429i
$902$	−2.73988e24			−0.208198
$903$	3.08837e25	−	1.08048e25i	2.32479	−	0.813340i
$904$	−9.03560e24			−0.673791
$905$	2.26390e24	+	3.92120e24i	0.167242	+	0.289671i
$906$	1.36487e23	−	2.36402e23i	0.00998853	−	0.0173006i
$907$	1.27183e25	−	2.20287e25i	0.922076	−	1.59708i	0.125878	−	0.992046i	$-0.459825\pi$
$907$	1.27183e25	−	2.20287e25i	0.922076	−	1.59708i	0.796198	−	0.605036i	$-0.206841\pi$
$908$	−3.79793e24	−	6.57821e24i	−0.272783	−	0.472474i
$909$	3.74675e25			2.66601
$910$	−3.73584e24	+	1.30700e24i	−0.263352	+	0.0921351i
$911$	1.45701e25			1.01755			0.508774	−	0.860900i	$-0.330099\pi$
$911$	1.45701e25			1.01755			0.508774	+	0.860900i	$0.330099\pi$
$912$	−5.05791e24	−	8.76055e24i	−0.349957	−	0.606144i
$913$	−3.98910e23	+	6.90932e23i	−0.0273447	+	0.0473624i
$914$	−2.18889e24	+	3.79127e24i	−0.148656	+	0.257479i
$915$	−1.47460e25	−	2.55408e25i	−0.992191	−	1.71852i
$916$	8.03480e24			0.535628
$917$	−3.15360e24	+	1.66623e25i	−0.208289	+	1.10051i
$918$	8.69972e24			0.569301
$919$	3.83890e24	+	6.64917e24i	0.248900	+	0.431107i	0.963221	−	0.268711i	$-0.0865976\pi$
$919$	3.83890e24	+	6.64917e24i	0.248900	+	0.431107i	−0.714321	+	0.699818i	$0.753264\pi$
$920$	−9.79258e23	+	1.69613e24i	−0.0629073	+	0.108959i
$921$	−2.66126e25	+	4.60943e25i	−1.69387	+	2.93387i
$922$	3.11139e24	+	5.38909e24i	0.196219	+	0.339862i
$923$	−1.57527e25			−0.984329
$924$	−1.76400e25	−	1.51821e25i	−1.09216	−	0.939982i
$925$	−1.26617e25			−0.776761
$926$	−3.83553e24	−	6.64333e24i	−0.233148	−	0.403824i
$927$	1.25226e25	−	2.16897e25i	0.754250	−	1.30640i
$928$	8.18125e24	−	1.41703e25i	0.488272	−	0.845712i
$929$	1.25082e25	+	2.16648e25i	0.739707	+	1.28121i	0.952627	+	0.304141i	$0.0983693\pi$
$929$	1.25082e25	+	2.16648e25i	0.739707	+	1.28121i	−0.212920	+	0.977070i	$0.568297\pi$
$930$	1.44431e25			0.846363
$931$	7.63324e24	−	6.08597e24i	0.443237	−	0.353393i
$932$	−1.39463e25			−0.802461
$933$	−4.41390e24	−	7.64510e24i	−0.251668	−	0.435902i
$934$	2.27645e24	−	3.94293e24i	0.128620	−	0.222777i
$935$	8.70070e24	−	1.50700e25i	0.487142	−	0.843754i
$936$	−8.40044e24	−	1.45500e25i	−0.466077	−	0.807269i
$937$	−1.79140e25			−0.984930			−0.492465	−	0.870332i	$-0.663904\pi$
$937$	−1.79140e25			−0.984930			−0.492465	+	0.870332i	$0.663904\pi$
$938$	−3.01538e24	−	2.59522e24i	−0.164292	−	0.141400i
$939$	−4.57572e25			−2.47060
$940$	1.52426e25	+	2.64010e25i	0.815591	+	1.41265i
$941$	1.14751e25	−	1.98755e25i	0.608478	−	1.05392i	−0.383013	−	0.923743i	$-0.625114\pi$
$941$	1.14751e25	−	1.98755e25i	0.608478	−	1.05392i	0.991491	−	0.130172i	$-0.0415530\pi$
$942$	−3.53238e24	+	6.11827e24i	−0.185624	+	0.321511i
$943$	1.16197e24	+	2.01260e24i	0.0605127	+	0.104811i
$944$	6.40372e24			0.330499
$945$	−8.70446e24	+	4.59908e25i	−0.445217	+	2.35234i
$946$	−8.07094e24			−0.409119
$947$	1.55448e25	+	2.69243e25i	0.780924	+	1.35260i	0.931404	+	0.363987i	$0.118585\pi$
$947$	1.55448e25	+	2.69243e25i	0.780924	+	1.35260i	−0.150480	+	0.988613i	$0.548082\pi$
$948$	9.48941e24	−	1.64361e25i	0.472464	−	0.818331i
$949$	−1.96015e24	+	3.39508e24i	−0.0967222	+	0.167528i
$950$	−8.46283e23	−	1.46581e24i	−0.0413871	−	0.0716846i
$951$	−4.54944e25			−2.20507
$952$	1.06765e25	−	3.73525e24i	0.512881	−	0.179434i
$953$	4.40831e24			0.209886			0.104943	−	0.994478i	$-0.466534\pi$
$953$	4.40831e24			0.209886			0.104943	+	0.994478i	$0.466534\pi$
$954$	2.56163e24	+	4.43687e24i	0.120880	+	0.209370i
$955$	−4.20166e24	+	7.27748e24i	−0.196513	+	0.340371i
$956$	3.21041e24	−	5.56060e24i	0.148823	−	0.257768i
$957$	2.04198e25	+	3.53681e25i	0.938210	+	1.62503i
$958$	4.00166e24			0.182236
$959$	6.71939e24	−	2.35081e24i	0.303300	−	0.106111i
$960$	2.04030e25			0.912828
$961$	−5.82484e24	−	1.00889e25i	−0.258307	−	0.447400i
$962$	−4.51933e24	+	7.82771e24i	−0.198649	+	0.344070i
$963$	5.04853e24	−	8.74431e24i	0.219959	−	0.380980i
$964$	−1.33398e25	−	2.31052e25i	−0.576094	−	0.997825i
$965$	−1.47114e25			−0.629754
$966$	4.26503e23	−	2.25347e24i	0.0180974	−	0.0956193i
$967$	−1.56344e25			−0.657590			−0.328795	−	0.944401i	$-0.606642\pi$
$967$	−1.56344e25			−0.657590			−0.328795	+	0.944401i	$0.606642\pi$
$968$	−1.26099e24	−	2.18410e24i	−0.0525740	−	0.0910608i
$969$	−1.07678e25	+	1.86504e25i	−0.445017	+	0.770792i
$970$	1.05032e24	−	1.81920e24i	0.0430290	−	0.0745283i
$971$	−1.75768e25	−	3.04440e25i	−0.713801	−	1.23634i	−0.963420	−	0.267995i	$-0.913639\pi$
$971$	−1.75768e25	−	3.04440e25i	−0.713801	−	1.23634i	0.249620	−	0.968344i	$-0.419694\pi$
$972$	−1.03499e25			−0.416650
$973$	−7.39172e24	−	6.36177e24i	−0.294976	−	0.253874i
$974$	5.97550e24			0.236387
$975$	7.31821e24	+	1.26755e25i	0.286989	+	0.497080i
$976$	8.36970e24	−	1.44967e25i	0.325377	−	0.563569i
$977$	2.47214e25	−	4.28188e25i	0.952730	−	1.65018i	0.213249	−	0.976998i	$-0.431595\pi$
$977$	2.47214e25	−	4.28188e25i	0.952730	−	1.65018i	0.739480	−	0.673178i	$-0.235071\pi$
$978$	−8.73570e24	−	1.51307e25i	−0.333747	−	0.578067i
$979$	−9.07957e24			−0.343884
$980$	4.28313e24	+	2.84373e25i	0.160820	+	1.06774i
$981$	7.89177e25			2.93757
$982$	5.38022e24	+	9.31881e24i	0.198542	+	0.343885i
$983$	4.47724e24	−	7.75481e24i	0.163797	−	0.283705i	−0.772430	−	0.635099i	$-0.780959\pi$
$983$	4.47724e24	−	7.75481e24i	0.163797	−	0.283705i	0.936227	+	0.351395i	$0.114293\pi$
$984$	−1.05689e25	+	1.83059e25i	−0.383328	+	0.663944i
$985$	−1.67584e25	−	2.90264e25i	−0.602593	−	1.04372i
$986$	−9.37923e24			−0.334359
$987$	−5.72587e25	−	4.92804e25i	−2.02370	−	1.74172i
$988$	1.03998e25			0.364410
$989$	3.42286e24	+	5.92856e24i	0.118910	+	0.205959i
$990$	1.09097e25	−	1.88962e25i	0.375763	−	0.650840i
$991$	−2.67004e25	+	4.62464e25i	−0.911783	+	1.57925i	−0.100239	+	0.994963i	$0.531961\pi$
$991$	−2.67004e25	+	4.62464e25i	−0.911783	+	1.57925i	−0.811544	+	0.584291i	$0.801372\pi$
$992$	1.52232e25	+	2.63674e25i	0.515416	+	0.892727i
$993$	6.42110e25			2.15546
$994$	2.47295e24	−	1.30660e25i	0.0823058	−	0.434870i
$995$	5.17346e25			1.70720
$996$	1.45429e24	+	2.51890e24i	0.0475823	+	0.0824150i
$997$	1.10498e24	−	1.91389e24i	0.0358465	−	0.0620880i	−0.847546	−	0.530723i	$-0.821921\pi$
$997$	1.10498e24	−	1.91389e24i	0.0358465	−	0.0620880i	0.883392	+	0.468635i	$0.155254\pi$
$998$	−2.95048e23	+	5.11038e23i	−0.00949037	+	0.0164378i
$999$	5.34472e25	+	9.25733e25i	1.70458	+	2.95243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.18.c.a.4.4	yes	20
7.2	even	3	inner	7.18.c.a.2.4	✓	20
7.3	odd	6		49.18.a.g.1.7		10
7.4	even	3		49.18.a.f.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.18.c.a.2.4	✓	20	7.2	even	3	inner
7.18.c.a.4.4	yes	20	1.1	even	1	trivial
49.18.a.f.1.7		10	7.4	even	3
49.18.a.g.1.7		10	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-58.4016 - 101.154i) q^{2} +(-10042.7 + 17394.4i) q^{3} +(58714.5 - 101697. i) q^{4} +(526365. + 911691. i) q^{5} +2.34603e6 q^{6} +(1.15602e7 + 9.94945e6i) q^{7} -2.90257e7 q^{8} +(-1.37140e8 - 2.37533e8i) q^{9} +O(q^{10})\)	\(q+(-58.4016 - 101.154i) q^{2} +(-10042.7 + 17394.4i) q^{3} +(58714.5 - 101697. i) q^{4} +(526365. + 911691. i) q^{5} +2.34603e6 q^{6} +(1.15602e7 + 9.94945e6i) q^{7} -2.90257e7 q^{8} +(-1.37140e8 - 2.37533e8i) q^{9} +(6.14811e7 - 1.06488e8i) q^{10} +(-3.23481e8 + 5.60285e8i) q^{11} +(1.17930e9 + 2.04261e9i) q^{12} -2.11036e9 q^{13} +(3.31296e8 - 1.75043e9i) q^{14} -2.11444e10 q^{15} +(-6.00068e9 - 1.03935e10i) q^{16} +(-1.27749e10 + 2.21268e10i) q^{17} +(-1.60183e10 + 2.77446e10i) q^{18} +(-2.09827e10 - 3.63432e10i) q^{19} +1.23621e11 q^{20} +(-2.89160e11 + 1.01164e11i) q^{21} +7.55671e10 q^{22} +(-3.20477e10 - 5.55083e10i) q^{23} +(2.91495e11 - 5.04884e11i) q^{24} +(-1.72651e11 + 2.99041e11i) q^{25} +(1.23248e11 + 2.13472e11i) q^{26} +2.91516e12 q^{27} +(1.69058e12 - 5.91458e11i) q^{28} -3.14286e12 q^{29} +(1.23487e12 + 2.13885e12i) q^{30} +(2.92403e12 - 5.06457e12i) q^{31} +(-2.60313e12 + 4.50875e12i) q^{32} +(-6.49721e12 - 1.12535e13i) q^{33} +2.98430e12 q^{34} +(-2.98593e12 + 1.57764e13i) q^{35} -3.22083e13 q^{36} +(1.83342e13 + 3.17558e13i) q^{37} +(-2.45085e12 + 4.24499e12i) q^{38} +(2.11936e13 - 3.67084e13i) q^{39} +(-1.52781e13 - 2.64625e13i) q^{40} -3.62575e13 q^{41} +(2.71206e13 + 2.33417e13i) q^{42} -1.06805e14 q^{43} +(3.79860e13 + 6.57937e13i) q^{44} +(1.44371e14 - 2.50058e14i) q^{45} +(-3.74328e12 + 6.48354e12i) q^{46} +(1.23301e14 + 2.13564e14i) q^{47} +2.41051e14 q^{48} +(3.46473e13 + 2.30036e14i) q^{49} +4.03324e13 q^{50} +(-2.56588e14 - 4.44424e14i) q^{51} +(-1.23909e14 + 2.14616e14i) q^{52} +(7.99592e13 - 1.38493e14i) q^{53} +(-1.70250e14 - 2.94881e14i) q^{54} -6.81076e14 q^{55} +(-3.35544e14 - 2.88790e14i) q^{56} +8.42889e14 q^{57} +(1.83548e14 + 3.17914e14i) q^{58} +(-2.66791e14 + 4.62096e14i) q^{59} +(-1.24148e15 + 2.15031e15i) q^{60} +(6.97395e14 + 1.20792e15i) q^{61} -6.83072e14 q^{62} +(7.77956e14 - 4.11040e15i) q^{63} -9.64937e14 q^{64} +(-1.11082e15 - 1.92400e15i) q^{65} +(-7.58894e14 + 1.31444e15i) q^{66} +(1.11658e15 - 1.93398e15i) q^{67} +(1.50015e15 + 2.59833e15i) q^{68} +1.28738e15 q^{69} +(1.77024e15 - 6.19327e14i) q^{70} +7.46445e15 q^{71} +(3.98057e15 + 6.89455e15i) q^{72} +(9.28821e14 - 1.60877e15i) q^{73} +(2.14150e15 - 3.70918e15i) q^{74} +(-3.46775e15 - 6.00632e15i) q^{75} -4.92796e15 q^{76} +(-9.31404e15 + 3.25857e15i) q^{77} -4.95096e15 q^{78} +(-4.02333e15 - 6.96861e15i) q^{79} +(6.31710e15 - 1.09415e16i) q^{80} +(-1.15657e16 + 2.00324e16i) q^{81} +(2.11750e15 + 3.66761e15i) q^{82} +1.23318e15 q^{83} +(-6.68984e15 + 3.53464e16i) q^{84} -2.68971e16 q^{85} +(6.23757e15 + 1.08038e16i) q^{86} +(3.15626e16 - 5.46680e16i) q^{87} +(9.38925e15 - 1.62627e16i) q^{88} +(7.01709e15 + 1.21539e16i) q^{89} -3.37260e16 q^{90} +(-2.43963e16 - 2.09969e16i) q^{91} -7.52667e15 q^{92} +(5.87300e16 + 1.01723e17i) q^{93} +(1.44019e16 - 2.49449e16i) q^{94} +(2.20892e16 - 3.82595e16i) q^{95} +(-5.22846e16 - 9.05595e16i) q^{96} +1.70836e16 q^{97} +(2.12457e16 - 1.69392e16i) q^{98} +1.77448e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 270 q^{2} + 6560 q^{3} - 551660 q^{4} + 1089798 q^{5} - 1687556 q^{6} + 14395360 q^{7} - 237823200 q^{8} - 498883228 q^{9}+O(q^{10}) \) 20 * q + 270 * q^2 + 6560 * q^3 - 551660 * q^4 + 1089798 * q^5 - 1687556 * q^6 + 14395360 * q^7 - 237823200 * q^8 - 498883228 * q^9	\( 20 q + 270 q^{2} + 6560 q^{3} - 551660 q^{4} + 1089798 q^{5} - 1687556 q^{6} + 14395360 q^{7} - 237823200 q^{8} - 498883228 q^{9} + 222553738 q^{10} - 148256184 q^{11} + 2808533140 q^{12} + 3578734040 q^{13} + 25683984606 q^{14} - 26900793736 q^{15} - 50209759472 q^{16} + 15259176570 q^{17} + 81764237020 q^{18} - 71656970872 q^{19} - 180641544216 q^{20} - 669146889614 q^{21} + 1499692748380 q^{22} - 316306503180 q^{23} + 694489934496 q^{24} + 591325905568 q^{25} + 4488505674324 q^{26} - 11473086373360 q^{27} + 2858273469380 q^{28} + 284876854680 q^{29} - 9357829097258 q^{30} - 1607821082076 q^{31} + 18893460602400 q^{32} + 9589772011550 q^{33} - 32628298247940 q^{34} - 103506510744 q^{35} + 76724663114416 q^{36} + 5528585266950 q^{37} - 15690283928010 q^{38} + 28451541414128 q^{39} - 91022360866896 q^{40} - 66727631114424 q^{41} - 74393390286880 q^{42} - 93028396916240 q^{43} + 162849953080692 q^{44} + 8592264491540 q^{45} - 563088234018354 q^{46} + 162460135616460 q^{47} + 16\!\cdots\!20 q^{48}+ \cdots + 92\!\cdots\!80 q^{99}+O(q^{100}) \) 20 * q + 270 * q^2 + 6560 * q^3 - 551660 * q^4 + 1089798 * q^5 - 1687556 * q^6 + 14395360 * q^7 - 237823200 * q^8 - 498883228 * q^9 + 222553738 * q^10 - 148256184 * q^11 + 2808533140 * q^12 + 3578734040 * q^13 + 25683984606 * q^14 - 26900793736 * q^15 - 50209759472 * q^16 + 15259176570 * q^17 + 81764237020 * q^18 - 71656970872 * q^19 - 180641544216 * q^20 - 669146889614 * q^21 + 1499692748380 * q^22 - 316306503180 * q^23 + 694489934496 * q^24 + 591325905568 * q^25 + 4488505674324 * q^26 - 11473086373360 * q^27 + 2858273469380 * q^28 + 284876854680 * q^29 - 9357829097258 * q^30 - 1607821082076 * q^31 + 18893460602400 * q^32 + 9589772011550 * q^33 - 32628298247940 * q^34 - 103506510744 * q^35 + 76724663114416 * q^36 + 5528585266950 * q^37 - 15690283928010 * q^38 + 28451541414128 * q^39 - 91022360866896 * q^40 - 66727631114424 * q^41 - 74393390286880 * q^42 - 93028396916240 * q^43 + 162849953080692 * q^44 + 8592264491540 * q^45 - 563088234018354 * q^46 + 162460135616460 * q^47 + 1626223055746720 * q^48 + 37188390461684 * q^49 - 156105592028976 * q^50 - 41571323179104 * q^51 - 664578572037800 * q^52 + 349838159677350 * q^53 - 2197621449925058 * q^54 - 630210277345912 * q^55 - 3391192609585536 * q^56 + 3387478208982380 * q^57 + 1117009291618900 * q^58 + 2898325666051656 * q^59 + 1851302466771436 * q^60 + 4829263771794542 * q^61 - 12440234322280740 * q^62 + 1252577979478000 * q^63 + 2254847316158720 * q^64 + 2323606775562324 * q^65 + 7963993945620406 * q^66 + 1327703510619200 * q^67 + 570001815036780 * q^68 - 19909363410939516 * q^69 - 17777971289904490 * q^70 + 15480661755189216 * q^71 + 16233423509033760 * q^72 - 3163858704730590 * q^73 - 4018632851551110 * q^74 - 8119026314209112 * q^75 - 14641245177256376 * q^76 - 46825571816043510 * q^77 + 48702643123708840 * q^78 + 40826108816616316 * q^79 + 90814104963906864 * q^80 - 69159481630723930 * q^81 + 21247223257167740 * q^82 + 10623055038659280 * q^83 - 178832833754555092 * q^84 + 51769432859611308 * q^85 + 113956439761484328 * q^86 + 171557044814594000 * q^87 - 117726124940340000 * q^88 + 31115179936936434 * q^89 - 503037784464315176 * q^90 - 219799610507722112 * q^91 + 208501803198310920 * q^92 + 257332309943680890 * q^93 + 405400048855155726 * q^94 - 22431094320108540 * q^95 + 232620528206160416 * q^96 - 702800336503765080 * q^97 - 760473415304075970 * q^98 + 928280307128172080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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