LMFDB - Embedded newform 8.20.b.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,20,Mod(5,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, 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:	$18.3053357245$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 9 x^{17} + 847482358 x^{16} - 6779858660 x^{15} + \cdots + 11\!\cdots\!76 $ x^18 - 9x^17 + 847482358x^16 - 6779858660x^15 + 288755694526787238x^14 - 2021289743039984830x^13 + 51121850635988052944521232x^12 - 306731077539161966630890980x^11 + 5053028465804290954773516593713297x^10 - 25265139517319958838954290038554593x^9 + 277525242785226225995541366728053703523138x^8 - 1110100819550071174104182779845774739997744x^7 + 7843581170028346695466748185748667347430921666496x^6 - 23530739624732277774733733894667178736900394654048x^5 + 88699644118206331836031766951870758907094189945148981184x^4 - 177399249018514584235839520819873862547126510378177038080x^3 + 27738447216461514660719783835924541644179956872586393406592768x^2 - 27738358516840927193180104500114450400133860395870028292288768*x + 1155804113673024778339834102840085457131269774629483366903990104576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{153}\cdot 3^{16}\cdot 5^{4}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.1
Root			$0.500000 + 222.384i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.20.b.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-696.194 - 199.004i) q^{2} -889.536i q^{3} +(445083. + 277090. i) q^{4} +5.56401e6i q^{5} +(-177021. + 619289. i) q^{6} -4.51327e6 q^{7} +(-2.54722e8 - 2.81482e8i) q^{8} +1.16147e9 q^{9} +O(q^{10})$	\(q+(-696.194 - 199.004i) q^{2} -889.536i q^{3} +(445083. + 277090. i) q^{4} +5.56401e6i q^{5} +(-177021. + 619289. i) q^{6} -4.51327e6 q^{7} +(-2.54722e8 - 2.81482e8i) q^{8} +1.16147e9 q^{9} +(1.10726e9 - 3.87363e9i) q^{10} +1.78940e9i q^{11} +(2.46482e8 - 3.95917e8i) q^{12} -3.40689e10i q^{13} +(3.14211e9 + 8.98157e8i) q^{14} +4.94939e9 q^{15} +(1.21320e11 + 2.46656e11i) q^{16} -4.37021e11 q^{17} +(-8.08608e11 - 2.31137e11i) q^{18} +2.55409e12i q^{19} +(-1.54173e12 + 2.47645e12i) q^{20} +4.01471e9i q^{21} +(3.56097e11 - 1.24577e12i) q^{22} -5.58979e12 q^{23} +(-2.50388e11 + 2.26584e11i) q^{24} -1.18847e13 q^{25} +(-6.77983e12 + 2.37185e13i) q^{26} -2.06704e12i q^{27} +(-2.00878e12 - 1.25058e12i) q^{28} +9.17732e13i q^{29} +(-3.44573e12 - 9.84946e11i) q^{30} -6.96656e13 q^{31} +(-3.53767e13 - 1.95864e14i) q^{32} +1.59173e12 q^{33} +(3.04251e14 + 8.69687e13i) q^{34} -2.51119e13i q^{35} +(5.16951e14 + 3.21832e14i) q^{36} -7.21521e14i q^{37} +(5.08274e14 - 1.77814e15i) q^{38} -3.03055e13 q^{39} +(1.56617e15 - 1.41728e15i) q^{40} -1.74108e15 q^{41} +(7.98943e11 - 2.79502e12i) q^{42} +3.57351e15i q^{43} +(-4.95824e14 + 7.96430e14i) q^{44} +6.46243e15i q^{45} +(3.89158e15 + 1.11239e15i) q^{46} -1.43582e16 q^{47} +(2.19410e14 - 1.07918e14i) q^{48} -1.13785e16 q^{49} +(8.27408e15 + 2.36511e15i) q^{50} +3.88746e14i q^{51} +(9.44015e15 - 1.51635e16i) q^{52} +1.88104e16i q^{53} +(-4.11349e14 + 1.43906e15i) q^{54} -9.95622e15 q^{55} +(1.14963e15 + 1.27040e15i) q^{56} +2.27196e15 q^{57} +(1.82632e16 - 6.38919e16i) q^{58} +4.76955e16i q^{59} +(2.20289e15 + 1.37143e15i) q^{60} -1.16266e17i q^{61} +(4.85007e16 + 1.38637e16i) q^{62} -5.24203e15 q^{63} +(-1.43486e16 + 1.43399e17i) q^{64} +1.89560e17 q^{65} +(-1.10815e15 - 3.16761e14i) q^{66} -1.76329e17i q^{67} +(-1.94510e17 - 1.21094e17i) q^{68} +4.97232e15i q^{69} +(-4.99736e15 + 1.74827e16i) q^{70} +6.82001e16 q^{71} +(-2.95852e17 - 3.26932e17i) q^{72} +5.94941e17 q^{73} +(-1.43585e17 + 5.02318e17i) q^{74} +1.05719e16i q^{75} +(-7.07714e17 + 1.13678e18i) q^{76} -8.07603e15i q^{77} +(2.10985e16 + 6.03090e15i) q^{78} -1.48803e18 q^{79} +(-1.37240e18 + 6.75026e17i) q^{80} +1.34809e18 q^{81} +(1.21213e18 + 3.46481e17i) q^{82} +1.21993e18i q^{83} +(-1.11244e15 + 1.78688e15i) q^{84} -2.43159e18i q^{85} +(7.11143e17 - 2.48786e18i) q^{86} +8.16356e16 q^{87} +(5.03682e17 - 4.55799e17i) q^{88} +3.29788e18 q^{89} +(1.28605e18 - 4.49910e18i) q^{90} +1.53762e17i q^{91} +(-2.48792e18 - 1.54888e18i) q^{92} +6.19700e16i q^{93} +(9.99609e18 + 2.85734e18i) q^{94} -1.42110e19 q^{95} +(-1.74228e17 + 3.14688e16i) q^{96} +4.52106e18 q^{97} +(7.92166e18 + 2.26437e18i) q^{98} +2.07833e18i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9}+O(q^{10}) $ 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9	$ 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9} + 758800104 q^{10} - 9351642296 q^{12} - 122453668784 q^{14} + 156097960432 q^{15} - 696212072432 q^{16} + 14121426692 q^{17} + 1813497117770 q^{18} + 6517087595632 q^{20} - 11074654117412 q^{22} + 2177121583952 q^{23} - 36473014189168 q^{24} - 44414474211734 q^{25} + 26782030269304 q^{26} - 97002327802784 q^{28} + 327847200544208 q^{30} + 428505770260416 q^{31} + 122449430282912 q^{32} - 185380269683736 q^{33} - 478448330325748 q^{34} - 10\!\cdots\!36 q^{36}+ \cdots + 88\!\cdots\!22 q^{98}+O(q^{100}) $ 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9 + 758800104 * q^10 - 9351642296 * q^12 - 122453668784 * q^14 + 156097960432 * q^15 - 696212072432 * q^16 + 14121426692 * q^17 + 1813497117770 * q^18 + 6517087595632 * q^20 - 11074654117412 * q^22 + 2177121583952 * q^23 - 36473014189168 * q^24 - 44414474211734 * q^25 + 26782030269304 * q^26 - 97002327802784 * q^28 + 327847200544208 * q^30 + 428505770260416 * q^31 + 122449430282912 * q^32 - 185380269683736 * q^33 - 478448330325748 * q^34 - 1053851053424436 * q^36 - 486194587539796 * q^38 + 942830575043152 * q^39 - 1697818250610976 * q^40 + 1200260021141524 * q^41 + 4964410757677984 * q^42 + 7031781193616424 * q^44 - 14917443628457488 * q^46 - 1134160959992928 * q^47 - 3197964747991392 * q^48 + 31570092936329058 * q^49 - 34734151321861826 * q^50 - 26877456911772208 * q^52 + 32102189624395064 * q^54 - 51757047863478736 * q^55 + 52858270161183424 * q^56 - 7740744140670520 * q^57 - 20470056808312424 * q^58 - 25825294995349152 * q^60 + 93766686763697984 * q^62 + 430168668665078416 * q^63 - 253721318369185216 * q^64 - 184007586011668640 * q^65 + 479551889901302712 * q^66 + 201388986348307752 * q^68 - 340698473416023872 * q^70 - 1599477989199799056 * q^71 - 115475454880420648 * q^72 - 93004298989809068 * q^73 - 93558253821761240 * q^74 - 1090379619519933176 * q^76 + 2029949680340770544 * q^78 + 1813975801025264480 * q^79 + 3057120301750869696 * q^80 + 1801762045144484330 * q^81 - 2418785089528546244 * q^82 + 141493317659087296 * q^84 + 1332333723895598620 * q^86 - 13124960835754102512 * q^87 - 3097741184498130608 * q^88 + 4470509771045743540 * q^89 - 288100905697646824 * q^90 - 2965990502259463392 * q^92 - 3533635112749329696 * q^94 + 23809730986995679856 * q^95 - 2990158800543707584 * q^96 + 8246429789464117220 * q^97 + 8841667592735478822 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

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 $

$2$	−696.194	−	199.004i	−0.961491	−	0.274838i
$2$	−696.194	−	199.004i	−0.961491	−	0.274838i
$3$		−	889.536i		−	0.0260923i	−0.999915	−	0.0130461i	$-0.995847\pi$
$3$		−	889.536i		−	0.0260923i	0.999915	−	0.0130461i	$-0.00415283\pi$
$4$	445083.	+	277090.i	0.848929	+	0.528508i
$5$			5.56401e6i			1.27401i	0.770860	+	0.637005i	$0.219827\pi$
$5$			5.56401e6i			1.27401i	−0.770860	+	0.637005i	$0.780173\pi$
$6$	−177021.	+	619289.i	−0.00717113	+	0.0250875i
$7$	−4.51327e6			−0.0422727			−0.0211363	−	0.999777i	$-0.506728\pi$
$7$	−4.51327e6			−0.0422727			−0.0211363	+	0.999777i	$0.506728\pi$
$8$	−2.54722e8	−	2.81482e8i	−0.670983	−	0.741473i
$9$	1.16147e9			0.999319
$10$	1.10726e9	−	3.87363e9i	0.350146	−	1.22495i
$11$			1.78940e9i			0.228811i	0.993434	+	0.114405i	$0.0364962\pi$
$11$			1.78940e9i			0.228811i	−0.993434	+	0.114405i	$0.963504\pi$
$12$	2.46482e8	−	3.95917e8i	0.0137900	−	0.0221505i
$13$		−	3.40689e10i		−	0.891037i	−0.895273	−	0.445519i	$-0.853019\pi$
$13$		−	3.40689e10i		−	0.891037i	0.895273	−	0.445519i	$-0.146981\pi$
$14$	3.14211e9	+	8.98157e8i	0.0406448	+	0.0116181i
$15$	4.94939e9			0.0332418
$16$	1.21320e11	+	2.46656e11i	0.441359	+	0.897330i
$17$	−4.37021e11			−0.893794			−0.446897	−	0.894586i	$-0.647471\pi$
$17$	−4.37021e11			−0.893794			−0.446897	+	0.894586i	$0.647471\pi$
$18$	−8.08608e11	−	2.31137e11i	−0.960836	−	0.274651i
$19$			2.55409e12i			1.81584i	0.419144	+	0.907920i	$0.362330\pi$
$19$			2.55409e12i			1.81584i	−0.419144	+	0.907920i	$0.637670\pi$
$20$	−1.54173e12	+	2.47645e12i	−0.673324	+	1.08154i
$21$			4.01471e9i			0.00110299i
$22$	3.56097e11	−	1.24577e12i	0.0628858	−	0.219999i
$23$	−5.58979e12			−0.647114			−0.323557	−	0.946209i	$-0.604879\pi$
$23$	−5.58979e12			−0.647114			−0.323557	+	0.946209i	$0.604879\pi$
$24$	−2.50388e11	+	2.26584e11i	−0.0193467	+	0.0175075i
$25$	−1.18847e13			−0.623102
$26$	−6.77983e12	+	2.37185e13i	−0.244891	+	0.856724i
$27$		−	2.06704e12i		−	0.0521667i
$28$	−2.00878e12	−	1.25058e12i	−0.0358865	−	0.0223414i
$29$			9.17732e13i			1.17472i	0.809325	+	0.587361i	$0.199833\pi$
$29$			9.17732e13i			1.17472i	−0.809325	+	0.587361i	$0.800167\pi$
$30$	−3.44573e12	−	9.84946e11i	−0.0319617	−	0.00913610i
$31$	−6.96656e13			−0.473241			−0.236620	−	0.971602i	$-0.576040\pi$
$31$	−6.96656e13			−0.473241			−0.236620	+	0.971602i	$0.576040\pi$
$32$	−3.53767e13	−	1.95864e14i	−0.177743	−	0.984077i
$33$	1.59173e12			0.00597018
$34$	3.04251e14	+	8.69687e13i	0.859374	+	0.245648i
$35$		−	2.51119e13i		−	0.0538558i
$36$	5.16951e14	+	3.21832e14i	0.848351	+	0.528148i
$37$		−	7.21521e14i		−	0.912710i	−0.889798	−	0.456355i	$-0.849155\pi$
$37$		−	7.21521e14i		−	0.912710i	0.889798	−	0.456355i	$-0.150845\pi$
$38$	5.08274e14	−	1.77814e15i	0.499061	−	1.74591i
$39$	−3.03055e13			−0.0232492
$40$	1.56617e15	−	1.41728e15i	0.944644	−	0.854839i
$41$	−1.74108e15			−0.830561			−0.415281	−	0.909693i	$-0.636317\pi$
$41$	−1.74108e15			−0.830561			−0.415281	+	0.909693i	$0.636317\pi$
$42$	7.98943e11	−	2.79502e12i	0.000303143	−	0.00106051i
$43$			3.57351e15i			1.08429i	0.840285	+	0.542145i	$0.182388\pi$
$43$			3.57351e15i			1.08429i	−0.840285	+	0.542145i	$0.817612\pi$
$44$	−4.95824e14	+	7.96430e14i	−0.120928	+	0.194244i
$45$			6.46243e15i			1.27314i
$46$	3.89158e15	+	1.11239e15i	0.622194	+	0.177851i
$47$	−1.43582e16			−1.87142			−0.935709	−	0.352774i	$-0.885239\pi$
$47$	−1.43582e16			−1.87142			−0.935709	+	0.352774i	$0.885239\pi$
$48$	2.19410e14	−	1.07918e14i	0.0234134	−	0.0115161i
$49$	−1.13785e16			−0.998213
$50$	8.27408e15	+	2.36511e15i	0.599107	+	0.171252i
$51$			3.88746e14i			0.0233211i
$52$	9.44015e15	−	1.51635e16i	0.470920	−	0.756427i
$53$			1.88104e16i			0.783029i	0.920172	+	0.391515i	$0.128049\pi$
$53$			1.88104e16i			0.783029i	−0.920172	+	0.391515i	$0.871951\pi$
$54$	−4.11349e14	+	1.43906e15i	−0.0143374	+	0.0501578i
$55$	−9.95622e15			−0.291507
$56$	1.14963e15	+	1.27040e15i	0.0283643	+	0.0313440i
$57$	2.27196e15			0.0473794
$58$	1.82632e16	−	6.38919e16i	0.322858	−	1.12948i
$59$			4.76955e16i			0.716775i	0.933573	+	0.358388i	$0.116673\pi$
$59$			4.76955e16i			0.716775i	−0.933573	+	0.358388i	$0.883327\pi$
$60$	2.20289e15	+	1.37143e15i	0.0282199	+	0.0175685i
$61$		−	1.16266e17i		−	1.27297i	−0.771290	−	0.636484i	$-0.780388\pi$
$61$		−	1.16266e17i		−	1.27297i	0.771290	−	0.636484i	$-0.219612\pi$
$62$	4.85007e16	+	1.38637e16i	0.455016	+	0.130064i
$63$	−5.24203e15			−0.0422439
$64$	−1.43486e16	+	1.43399e17i	−0.0995633	+	0.995031i
$65$	1.89560e17			1.13519
$66$	−1.10815e15	−	3.16761e14i	−0.00574028	−	0.00164083i
$67$		−	1.76329e17i		−	0.791793i	−0.918295	−	0.395897i	$-0.870434\pi$
$67$		−	1.76329e17i		−	0.791793i	0.918295	−	0.395897i	$-0.129566\pi$
$68$	−1.94510e17	−	1.21094e17i	−0.758767	−	0.472377i
$69$			4.97232e15i			0.0168847i
$70$	−4.99736e15	+	1.74827e16i	−0.0148016	+	0.0517819i
$71$	6.82001e16			0.176535			0.0882675	−	0.996097i	$-0.471867\pi$
$71$	6.82001e16			0.176535			0.0882675	+	0.996097i	$0.471867\pi$
$72$	−2.95852e17	−	3.26932e17i	−0.670526	−	0.740968i
$73$	5.94941e17			1.18279			0.591394	−	0.806383i	$-0.298578\pi$
$73$	5.94941e17			1.18279			0.591394	+	0.806383i	$0.298578\pi$
$74$	−1.43585e17	+	5.02318e17i	−0.250847	+	0.877562i
$75$			1.05719e16i			0.0162581i
$76$	−7.07714e17	+	1.13678e18i	−0.959685	+	1.54152i
$77$		−	8.07603e15i		−	0.00967244i
$78$	2.10985e16	+	6.03090e15i	0.0223539	+	0.00638975i
$79$	−1.48803e18			−1.39687			−0.698433	−	0.715676i	$-0.746119\pi$
$79$	−1.48803e18			−1.39687			−0.698433	+	0.715676i	$0.746119\pi$
$80$	−1.37240e18	+	6.75026e17i	−1.14321	+	0.562297i
$81$	1.34809e18			0.997958
$82$	1.21213e18	+	3.46481e17i	0.798577	+	0.228270i
$83$			1.21993e18i			0.716296i	0.933665	+	0.358148i	$0.116592\pi$
$83$			1.21993e18i			0.716296i	−0.933665	+	0.358148i	$0.883408\pi$
$84$	−1.11244e15	+	1.78688e15i	−0.000582938	+	0.000936359i
$85$		−	2.43159e18i		−	1.13870i
$86$	7.11143e17	−	2.48786e18i	0.298004	−	1.04253i
$87$	8.16356e16			0.0306511
$88$	5.03682e17	−	4.55799e17i	0.169657	−	0.153528i
$89$	3.29788e18			0.997768			0.498884	−	0.866669i	$-0.333743\pi$
$89$	3.29788e18			0.997768			0.498884	+	0.866669i	$0.333743\pi$
$90$	1.28605e18	−	4.49910e18i	0.349908	−	1.22412i
$91$			1.53762e17i			0.0376665i
$92$	−2.48792e18	−	1.54888e18i	−0.549354	−	0.342005i
$93$			6.19700e16i			0.0123479i
$94$	9.99609e18	+	2.85734e18i	1.79935	+	0.514336i
$95$	−1.42110e19			−2.31340
$96$	−1.74228e17	+	3.14688e16i	−0.0256768	+	0.00463771i
$97$	4.52106e18			0.603822			0.301911	−	0.953336i	$-0.402375\pi$
$97$	4.52106e18			0.603822			0.301911	+	0.953336i	$0.402375\pi$
$98$	7.92166e18	+	2.26437e18i	0.959772	+	0.274346i
$99$			2.07833e18i			0.228655i
$100$	−5.28969e18	−	3.29314e18i	−0.528969	−	0.329314i
$101$			1.01147e19i			0.920238i	0.887857	+	0.460119i	$0.152193\pi$
$101$			1.01147e19i			0.920238i	−0.887857	+	0.460119i	$0.847807\pi$
$102$	7.73618e16	−	2.70642e17i	0.00640951	−	0.0224230i
$103$	−1.82500e19			−1.37819			−0.689096	−	0.724670i	$-0.741992\pi$
$103$	−1.82500e19			−1.37819			−0.689096	+	0.724670i	$0.741992\pi$
$104$	−9.58976e18	+	8.67809e18i	−0.660680	+	0.597871i
$105$	−2.23379e16			−0.00140522
$106$	3.74335e18	−	1.30957e19i	0.215206	−	0.752875i
$107$			2.72881e19i			1.43492i	0.696600	+	0.717459i	$0.254695\pi$
$107$			2.72881e19i			1.43492i	−0.696600	+	0.717459i	$0.745305\pi$
$108$	5.72757e17	−	9.20006e17i	0.0275705	−	0.0442858i
$109$		−	1.32939e19i		−	0.586272i	−0.956071	−	0.293136i	$-0.905301\pi$
$109$		−	1.32939e19i		−	0.586272i	0.956071	−	0.293136i	$-0.0946989\pi$
$110$	6.93146e18	+	1.98133e18i	0.280281	+	0.0801171i
$111$	−6.41819e17			−0.0238146
$112$	−5.47550e17	−	1.11323e18i	−0.0186574	−	0.0379326i
$113$	1.83425e19			0.574399			0.287199	−	0.957871i	$-0.407276\pi$
$113$	1.83425e19			0.574399			0.287199	+	0.957871i	$0.407276\pi$
$114$	−1.58172e18	−	4.52128e17i	−0.0455548	−	0.0130216i
$115$		−	3.11016e19i		−	0.824430i
$116$	−2.54295e19	+	4.08467e19i	−0.620849	+	0.997255i
$117$		−	3.95700e19i		−	0.890431i
$118$	9.49158e18	−	3.32053e19i	0.196997	−	0.689173i
$119$	1.97239e18			0.0377831
$120$	−1.26072e18	−	1.39316e18i	−0.0223047	−	0.0246479i
$121$	5.79571e19			0.947646
$122$	−2.31373e19	+	8.09433e19i	−0.349860	+	1.22395i
$123$			1.54875e18i			0.0216712i
$124$	−3.10070e19	−	1.93036e19i	−0.401748	−	0.250111i
$125$			3.99983e19i			0.480171i
$126$	3.64947e18	+	1.04318e18i	0.0406171	+	0.0116102i
$127$	1.55505e20			1.60550			0.802748	−	0.596319i	$-0.203370\pi$
$127$	1.55505e20			1.60550			0.802748	+	0.596319i	$0.203370\pi$
$128$	3.85263e19	−	9.69781e19i	0.369201	−	0.929350i
$129$	3.17877e18			0.0282916
$130$	−1.31970e20	−	3.77231e19i	−1.09148	−	0.311993i
$131$		−	2.39001e20i		−	1.83790i	−0.394376	−	0.918949i	$-0.629039\pi$
$131$		−	2.39001e20i		−	1.83790i	0.394376	−	0.918949i	$-0.370961\pi$
$132$	7.08453e17	+	4.41053e17i	0.00506826	+	0.00315529i
$133$		−	1.15273e19i		−	0.0767604i
$134$	−3.50900e19	+	1.22759e20i	−0.217615	+	0.761302i
$135$	1.15010e19			0.0664610
$136$	1.11319e20	+	1.23013e20i	0.599720	+	0.662723i
$137$	−2.33463e20			−1.17320			−0.586602	−	0.809875i	$-0.699535\pi$
$137$	−2.33463e20			−1.17320			−0.586602	+	0.809875i	$0.699535\pi$
$138$	9.89510e17	−	3.46170e18i	0.00464054	−	0.0162345i
$139$			4.01632e20i			1.75868i	0.476190	+	0.879342i	$0.342017\pi$
$139$			4.01632e20i			1.75868i	−0.476190	+	0.879342i	$0.657983\pi$
$140$	6.95826e18	−	1.11769e19i	0.0284632	−	0.0457198i
$141$			1.27721e19i			0.0488295i
$142$	−4.74805e19	−	1.35721e19i	−0.169737	−	0.0485184i
$143$	6.09627e19			0.203879
$144$	1.40910e20	+	2.86484e20i	0.441059	+	0.896719i
$145$	−5.10627e20			−1.49661
$146$	−4.14194e20	−	1.18395e20i	−1.13724	−	0.325074i
$147$			1.01216e19i			0.0260456i
$148$	1.99926e20	−	3.21137e20i	0.482374	−	0.774825i
$149$			5.08909e20i			1.15178i	0.817526	+	0.575892i	$0.195345\pi$
$149$			5.08909e20i			1.15178i	−0.817526	+	0.575892i	$0.804655\pi$
$150$	2.10385e18	−	7.36009e18i	0.00446835	−	0.0156321i
$151$	3.58863e20			0.715563			0.357782	−	0.933805i	$-0.383533\pi$
$151$	3.58863e20			0.715563			0.357782	+	0.933805i	$0.383533\pi$
$152$	7.18930e20	−	6.50584e20i	1.34640	−	1.21840i
$153$	−5.07586e20			−0.893185
$154$	−1.60716e18	+	5.62248e18i	−0.00265835	+	0.00929996i
$155$		−	3.87620e20i		−	0.602913i
$156$	−1.34885e19	−	8.39735e18i	−0.0197369	−	0.0122874i
$157$		−	1.45807e20i		−	0.200786i	−0.994948	−	0.100393i	$-0.967990\pi$
$157$		−	1.45807e20i		−	0.200786i	0.994948	−	0.100393i	$-0.0320099\pi$
$158$	1.03596e21	+	2.96124e20i	1.34307	+	0.383911i
$159$	1.67326e19			0.0204310
$160$	1.08979e21	−	1.96836e20i	1.25372	−	0.226446i
$161$	2.52282e19			0.0273553
$162$	−9.38534e20	−	2.68276e20i	−0.959527	−	0.274276i
$163$		−	1.25859e21i		−	1.21367i	−0.794828	−	0.606835i	$-0.792439\pi$
$163$		−	1.25859e21i		−	1.21367i	0.794828	−	0.606835i	$-0.207561\pi$
$164$	−7.74925e20	−	4.82436e20i	−0.705087	−	0.438958i
$165$			8.85642e18i			0.00760608i
$166$	2.42770e20	−	8.49306e20i	0.196865	−	0.688712i
$167$	3.81697e20			0.292356			0.146178	−	0.989258i	$-0.453303\pi$
$167$	3.81697e20			0.292356			0.146178	+	0.989258i	$0.453303\pi$
$168$	1.13007e18	−	1.02264e18i	0.000817837	−	0.000740087i
$169$	3.01232e20			0.206053
$170$	−4.83895e20	+	1.69286e21i	−0.312958	+	1.09485i
$171$			2.96650e21i			1.81460i
$172$	−9.90186e20	+	1.59051e21i	−0.573055	+	0.920484i
$173$			7.20483e20i			0.394626i	0.980341	+	0.197313i	$0.0632216\pi$
$173$			7.20483e20i			0.394626i	−0.980341	+	0.197313i	$0.936778\pi$
$174$	−5.68342e19	−	1.62458e19i	−0.0294708	−	0.00842408i
$175$	5.36390e19			0.0263402
$176$	−4.41366e20	+	2.17090e20i	−0.205319	+	0.100988i
$177$	4.24268e19			0.0187023
$178$	−2.29596e21	−	6.56290e20i	−0.959345	−	0.274224i
$179$		−	1.54740e21i		−	0.613055i	−0.951862	−	0.306528i	$-0.900833\pi$
$179$		−	1.54740e21i		−	0.613055i	0.951862	−	0.306528i	$-0.0991672\pi$
$180$	−1.79068e21	+	2.87632e21i	−0.672866	+	1.08081i
$181$		−	3.95197e21i		−	1.40886i	−0.709774	−	0.704429i	$-0.751203\pi$
$181$		−	3.95197e21i		−	1.40886i	0.709774	−	0.704429i	$-0.248797\pi$
$182$	3.05992e19	−	1.07048e20i	0.0103522	−	0.0362160i
$183$	−1.03422e20			−0.0332146
$184$	1.42384e21	+	1.57342e21i	0.434203	+	0.479817i
$185$	4.01455e21			1.16280
$186$	1.23323e19	−	4.31431e19i	0.00339367	−	0.0118724i
$187$		−	7.82003e20i		−	0.204509i
$188$	−6.39060e21	−	3.97852e21i	−1.58870	−	0.989058i
$189$			9.32912e18i			0.00220523i
$190$	9.89361e21	+	2.82804e21i	2.22431	+	0.635809i
$191$	−4.73400e21			−1.01254			−0.506269	−	0.862375i	$-0.668976\pi$
$191$	−4.73400e21			−1.01254			−0.506269	+	0.862375i	$0.668976\pi$
$192$	1.27559e20	+	1.27636e19i	0.0259626	+	0.00259783i
$193$	7.86311e21			1.52335			0.761676	−	0.647959i	$-0.224377\pi$
$193$	7.86311e21			1.52335			0.761676	+	0.647959i	$0.224377\pi$
$194$	−3.14753e21	−	8.99708e20i	−0.580569	−	0.165953i
$195$		−	1.68620e20i		−	0.0296197i
$196$	−5.06439e21	−	3.15288e21i	−0.847412	−	0.527563i
$197$			5.32685e21i			0.849261i	0.905367	+	0.424630i	$0.139596\pi$
$197$			5.32685e21i			0.849261i	−0.905367	+	0.424630i	$0.860404\pi$
$198$	4.13596e20	−	1.44692e21i	0.0628429	−	0.219849i
$199$	−1.72615e21			−0.250019			−0.125010	−	0.992156i	$-0.539896\pi$
$199$	−1.72615e21			−0.250019			−0.125010	+	0.992156i	$0.539896\pi$
$200$	3.02730e21	+	3.34533e21i	0.418091	+	0.462013i
$201$	−1.56851e20			−0.0206597
$202$	2.01286e21	−	7.04179e21i	0.252916	−	0.884800i
$203$		−	4.14197e20i		−	0.0496586i
$204$	−1.07718e20	+	1.73024e20i	−0.0123254	+	0.0197979i
$205$		−	9.68738e21i		−	1.05814i
$206$	1.27055e22	+	3.63182e21i	1.32512	+	0.378779i
$207$	−6.49237e21			−0.646674
$208$	8.40330e21	−	4.13323e21i	0.799555	−	0.393268i
$209$	−4.57029e21			−0.415483
$210$	1.55515e19	+	4.44533e18i	0.00135111	+	0.000386207i
$211$			1.43551e22i			1.19213i	0.802936	+	0.596065i	$0.203270\pi$
$211$			1.43551e22i			1.19213i	−0.802936	+	0.596065i	$0.796730\pi$
$212$	−5.21219e21	+	8.37221e21i	−0.413837	+	0.664736i
$213$		−	6.06664e19i		−	0.00460619i
$214$	5.43043e21	−	1.89978e22i	0.394370	−	1.37966i
$215$	−1.98831e22			−1.38140
$216$	−5.81834e20	+	5.26521e20i	−0.0386802	+	0.0350030i
$217$	3.14419e20			0.0200052
$218$	−2.64553e21	+	9.25510e21i	−0.161130	+	0.563695i
$219$		−	5.29221e20i		−	0.0308616i
$220$	−4.43135e21	−	2.75877e21i	−0.247469	−	0.154064i
$221$			1.48888e22i			0.796403i
$222$	4.46830e20	+	1.27724e20i	0.0228976	+	0.00654516i
$223$	1.36844e22			0.671938			0.335969	−	0.941873i	$-0.390936\pi$
$223$	1.36844e22			0.671938			0.335969	+	0.941873i	$0.390936\pi$
$224$	1.59664e20	+	8.83985e20i	0.00751367	+	0.0415996i
$225$	−1.38038e22			−0.622678
$226$	−1.27699e22	−	3.65023e21i	−0.552279	−	0.157866i
$227$			2.28444e22i			0.947400i	0.880686	+	0.473700i	$0.157082\pi$
$227$			2.28444e22i			0.947400i	−0.880686	+	0.473700i	$0.842918\pi$
$228$	1.01121e21	+	6.29537e20i	0.0402217	+	0.0250403i
$229$			1.15938e22i			0.442371i	0.975232	+	0.221186i	$0.0709927\pi$
$229$			1.15938e22i			0.442371i	−0.975232	+	0.221186i	$0.929007\pi$
$230$	−6.18934e21	+	2.16528e22i	−0.226584	+	0.792682i
$231$	−7.18392e18			−0.000252376
$232$	2.58325e22	−	2.33767e22i	0.871024	−	0.788218i
$233$	−1.44196e22			−0.466736			−0.233368	−	0.972388i	$-0.574975\pi$
$233$	−1.44196e22			−0.466736			−0.233368	+	0.972388i	$0.574975\pi$
$234$	−7.87457e21	+	2.75484e22i	−0.244724	+	0.856141i
$235$		−	7.98892e22i		−	2.38421i
$236$	−1.32160e22	+	2.12285e22i	−0.378821	+	0.608491i
$237$			1.32366e21i			0.0364474i
$238$	−1.37317e21	−	3.92513e20i	−0.0363281	−	0.0103842i
$239$	5.79540e22			1.47334			0.736671	−	0.676252i	$-0.236397\pi$
$239$	5.79540e22			1.47334			0.736671	+	0.676252i	$0.236397\pi$
$240$	6.00460e20	+	1.22080e21i	0.0146716	+	0.0298289i
$241$	2.53834e22			0.596195			0.298097	−	0.954535i	$-0.403648\pi$
$241$	2.53834e22			0.596195			0.298097	+	0.954535i	$0.403648\pi$
$242$	−4.03494e22	−	1.15337e22i	−0.911153	−	0.260449i
$243$		−	3.60162e21i		−	0.0782057i
$244$	3.22160e22	−	5.17478e22i	0.672774	−	1.08066i
$245$		−	6.33102e22i		−	1.27173i
$246$	3.08207e20	−	1.07823e21i	0.00595607	−	0.0208367i
$247$	8.70151e22			1.61798
$248$	1.77454e22	+	1.96096e22i	0.317536	+	0.350895i
$249$	1.08517e21			0.0186898
$250$	7.95981e21	−	2.78466e22i	0.131969	−	0.461680i
$251$			2.45272e22i			0.391514i	0.980652	+	0.195757i	$0.0627164\pi$
$251$			2.45272e22i			0.391514i	−0.980652	+	0.195757i	$0.937284\pi$
$252$	−2.33314e21	−	1.45251e21i	−0.0358621	−	0.0223262i
$253$		−	1.00023e22i		−	0.148067i
$254$	−1.08262e23	−	3.09461e22i	−1.54367	−	0.441251i
$255$	−2.16298e21			−0.0297113
$256$	−4.61208e22	+	5.98487e22i	−0.610404	+	0.792090i
$257$	−7.84682e22			−1.00076			−0.500379	−	0.865807i	$-0.666806\pi$
$257$	−7.84682e22			−1.00076			−0.500379	+	0.865807i	$0.666806\pi$
$258$	−2.21304e21	−	6.32587e20i	−0.0272021	−	0.00777558i
$259$			3.25642e21i			0.0385827i
$260$	8.43698e22	+	5.25251e22i	0.963696	+	0.599957i
$261$			1.06592e23i			1.17392i
$262$	−4.75620e22	+	1.66391e23i	−0.505124	+	1.76712i
$263$	6.14964e22			0.629898			0.314949	−	0.949109i	$-0.398013\pi$
$263$	6.14964e22			0.629898			0.314949	+	0.949109i	$0.398013\pi$
$264$	−4.05449e20	−	4.48043e20i	−0.00400589	−	0.00442673i
$265$	−1.04661e23			−0.997588
$266$	−2.29398e21	+	8.02524e21i	−0.0210967	+	0.0738044i
$267$		−	2.93358e21i		−	0.0260340i
$268$	4.88589e22	−	7.84808e22i	0.418469	−	0.672176i
$269$			3.37452e21i			0.0278975i	0.999903	+	0.0139487i	$0.00444016\pi$
$269$			3.37452e21i			0.0278975i	−0.999903	+	0.0139487i	$0.995560\pi$
$270$	−8.00696e21	−	2.28875e21i	−0.0639016	−	0.0182660i
$271$	−1.70540e23			−1.31407			−0.657035	−	0.753860i	$-0.728189\pi$
$271$	−1.70540e23			−1.31407			−0.657035	+	0.753860i	$0.728189\pi$
$272$	−5.30193e22	−	1.07794e23i	−0.394484	−	0.802028i
$273$	1.36777e20			0.000982805
$274$	1.62536e23	+	4.64601e22i	1.12802	+	0.322441i
$275$		−	2.12665e22i		−	0.142572i
$276$	−1.37778e21	+	2.21309e21i	−0.00892368	+	0.0143339i
$277$			9.88428e22i			0.618568i	0.950970	+	0.309284i	$0.100089\pi$
$277$			9.88428e22i			0.618568i	−0.950970	+	0.309284i	$0.899911\pi$
$278$	7.99263e22	−	2.79614e23i	0.483353	−	1.69096i
$279$	−8.09145e22			−0.472918
$280$	−7.06853e21	+	6.39655e21i	−0.0399326	+	0.0361364i
$281$	1.54967e23			0.846309			0.423154	−	0.906058i	$-0.360923\pi$
$281$	1.54967e23			0.846309			0.423154	+	0.906058i	$0.360923\pi$
$282$	2.54170e21	−	8.89188e21i	0.0134202	−	0.0469491i
$283$			9.10357e22i			0.464773i	0.972624	+	0.232386i	$0.0746534\pi$
$283$			9.10357e22i			0.464773i	−0.972624	+	0.232386i	$0.925347\pi$
$284$	3.03547e22	+	1.88976e22i	0.149866	+	0.0933001i
$285$			1.26412e22i			0.0603618i
$286$	−4.24419e22	−	1.21318e22i	−0.196028	−	0.0560336i
$287$	7.85796e21			0.0351101
$288$	−4.10889e22	−	2.27490e23i	−0.177622	−	0.983407i
$289$	−4.80854e22			−0.201133
$290$	3.55495e23	+	1.01617e23i	1.43897	+	0.411324i
$291$		−	4.02165e21i		−	0.0157551i
$292$	2.64798e23	+	1.64852e23i	1.00410	+	0.625112i
$293$		−	3.76601e23i		−	1.38242i	−0.722655	−	0.691209i	$-0.757078\pi$
$293$		−	3.76601e23i		−	1.38242i	0.722655	−	0.691209i	$-0.242922\pi$
$294$	2.01424e21	−	7.04660e21i	0.00715832	−	0.0250426i
$295$	−2.65378e23			−0.913179
$296$	−2.03095e23	+	1.83787e23i	−0.676749	+	0.612413i
$297$	3.69876e21			0.0119363
$298$	1.01275e23	−	3.54299e23i	0.316553	−	1.10743i
$299$			1.90438e23i			0.576603i
$300$	−2.92937e21	+	4.70537e21i	−0.00859255	+	0.0138020i
$301$		−	1.61282e22i		−	0.0458358i
$302$	−2.49838e23	−	7.14151e22i	−0.688008	−	0.196664i
$303$	8.99739e21			0.0240111
$304$	−6.29983e23	+	3.09862e23i	−1.62941	+	0.801438i
$305$	6.46903e23			1.62178
$306$	3.53378e23	+	1.01012e23i	0.858789	+	0.245481i
$307$			4.06724e22i			0.0958265i	0.998852	+	0.0479132i	$0.0152571\pi$
$307$			4.06724e22i			0.0958265i	−0.998852	+	0.0479132i	$0.984743\pi$
$308$	2.23779e21	−	3.59450e21i	0.00511196	−	0.00821121i
$309$			1.62340e22i			0.0359601i
$310$	−7.71378e22	+	2.69859e23i	−0.165703	+	0.579696i
$311$	−2.11001e23			−0.439604			−0.219802	−	0.975544i	$-0.570541\pi$
$311$	−2.11001e23			−0.439604			−0.219802	+	0.975544i	$0.570541\pi$
$312$	7.71947e21	+	8.53044e21i	0.0155998	+	0.0172386i
$313$	4.32064e23			0.846988			0.423494	−	0.905899i	$-0.360803\pi$
$313$	4.32064e23			0.846988			0.423494	+	0.905899i	$0.360803\pi$
$314$	−2.90162e22	+	1.01510e23i	−0.0551834	+	0.193053i
$315$		−	2.91667e22i		−	0.0538192i
$316$	−6.62297e23	−	4.12319e23i	−1.18584	−	0.738254i
$317$			2.37604e22i			0.0412849i	0.999787	+	0.0206424i	$0.00657116\pi$
$317$			2.37604e22i			0.0412849i	−0.999787	+	0.0206424i	$0.993429\pi$
$318$	−1.16491e22	−	3.32984e21i	−0.0196442	−	0.00561521i
$319$	−1.64219e23			−0.268789
$320$	−7.97874e23	−	7.98357e22i	−1.26768	−	0.126845i
$321$	2.42737e22			0.0374403
$322$	−1.75637e22	−	5.02051e21i	−0.0263018	−	0.00751825i
$323$		−	1.11619e24i		−	1.62299i
$324$	6.00014e23	+	3.73543e23i	0.847195	+	0.527428i
$325$			4.04900e23i			0.555208i
$326$	−2.50463e23	+	8.76220e23i	−0.333562	+	1.16693i
$327$	−1.18254e22			−0.0152972
$328$	4.43491e23	+	4.90082e23i	0.557293	+	0.615839i
$329$	6.48025e22			0.0791098
$330$	1.76246e21	−	6.16578e21i	0.00209044	−	0.00731317i
$331$			1.23591e24i			1.42437i	0.701994	+	0.712183i	$0.252293\pi$
$331$			1.23591e24i			1.42437i	−0.701994	+	0.712183i	$0.747707\pi$
$332$	−3.38030e23	+	5.42970e23i	−0.378568	+	0.608084i
$333$		−	8.38025e23i		−	0.912088i
$334$	−2.65735e23	−	7.59591e22i	−0.281098	−	0.0803504i
$335$	9.81094e23			1.00875
$336$	−9.90255e20	+	4.87065e20i	−0.000989746	+	0.000486815i
$337$	−6.39486e23			−0.621366			−0.310683	−	0.950514i	$-0.600558\pi$
$337$	−6.39486e23			−0.621366			−0.310683	+	0.950514i	$0.600558\pi$
$338$	−2.09716e23	−	5.99463e22i	−0.198118	−	0.0566310i
$339$		−	1.63163e22i		−	0.0149874i
$340$	6.73769e23	−	1.08226e24i	0.601813	−	0.966677i
$341$		−	1.24659e23i		−	0.108282i
$342$	5.90345e23	−	2.06526e24i	0.498721	−	1.74472i
$343$	1.02801e23			0.0844698
$344$	1.00588e24	−	9.10253e23i	0.803971	−	0.727540i
$345$	−2.76660e22			−0.0215112
$346$	1.43379e23	−	5.01596e23i	0.108458	−	0.379429i
$347$		−	6.84162e23i		−	0.503534i	−0.967788	−	0.251767i	$-0.918988\pi$
$347$		−	6.84162e23i		−	0.503534i	0.967788	−	0.251767i	$-0.0810117\pi$
$348$	3.63346e22	+	2.26204e22i	0.0260206	+	0.0161994i
$349$			3.64379e23i			0.253928i	0.991907	+	0.126964i	$0.0405233\pi$
$349$			3.64379e23i			0.253928i	−0.991907	+	0.126964i	$0.959477\pi$
$350$	−3.73431e22	−	1.06744e22i	−0.0253259	−	0.00723928i
$351$	−7.04218e22			−0.0464825
$352$	3.50478e23	−	6.33029e22i	0.225167	−	0.0406694i
$353$	−5.48650e23			−0.343112			−0.171556	−	0.985174i	$-0.554879\pi$
$353$	−5.48650e23			−0.343112			−0.171556	+	0.985174i	$0.554879\pi$
$354$	−2.95373e22	−	8.44310e21i	−0.0179821	−	0.00514009i
$355$			3.79466e23i			0.224907i
$356$	1.46783e24	+	9.13810e23i	0.847034	+	0.527328i
$357$		−	1.75451e21i		−	0.000985845i
$358$	−3.07939e23	+	1.07729e24i	−0.168491	+	0.589447i
$359$	1.28269e24			0.683479			0.341739	−	0.939795i	$-0.388984\pi$
$359$	1.28269e24			0.683479			0.341739	+	0.939795i	$0.388984\pi$
$360$	1.81906e24	−	1.64612e24i	0.944001	−	0.854257i
$361$	−4.54497e24			−2.29727
$362$	−7.86457e23	+	2.75134e24i	−0.387207	+	1.35460i
$363$		−	5.15550e22i		−	0.0247262i
$364$	−4.26059e22	+	6.84369e22i	−0.0199071	+	0.0319762i
$365$			3.31026e24i			1.50688i
$366$	7.20020e22	+	2.05814e22i	0.0319355	+	0.00912863i
$367$	−1.23278e24			−0.532793			−0.266396	−	0.963864i	$-0.585833\pi$
$367$	−1.23278e24			−0.532793			−0.266396	+	0.963864i	$0.585833\pi$
$368$	−6.78153e23	−	1.37876e24i	−0.285610	−	0.580675i
$369$	−2.02221e24			−0.829996
$370$	−2.79491e24	−	7.98911e23i	−1.11802	−	0.319582i
$371$		−	8.48965e22i		−	0.0331008i
$372$	−1.71713e22	+	2.75818e22i	−0.00652597	+	0.0104825i
$373$			1.86125e24i			0.689559i	0.938684	+	0.344780i	$0.112046\pi$
$373$			1.86125e24i			0.689559i	−0.938684	+	0.344780i	$0.887954\pi$
$374$	−1.55622e23	+	5.44426e23i	−0.0562069	+	0.196634i
$375$	3.55799e22			0.0125288
$376$	3.65735e24	+	4.04157e24i	1.25569	+	1.38760i
$377$	3.12661e24			1.04672
$378$	1.85653e21	−	6.49487e21i	0.000606080	−	0.00212031i
$379$		−	1.18195e24i		−	0.376292i	−0.982141	−	0.188146i	$-0.939752\pi$
$379$		−	1.18195e24i		−	0.376292i	0.982141	−	0.188146i	$-0.0602479\pi$
$380$	−6.32508e24	−	3.93773e24i	−1.96391	−	1.22265i
$381$		−	1.38327e23i		−	0.0418910i
$382$	3.29578e24	+	9.42084e23i	0.973546	+	0.278284i
$383$	3.42588e24			0.987150			0.493575	−	0.869703i	$-0.335690\pi$
$383$	3.42588e24			0.987150			0.493575	+	0.869703i	$0.335690\pi$
$384$	−8.62655e22	−	3.42706e22i	−0.0242488	−	0.00963329i
$385$	4.49351e22			0.0123228
$386$	−5.47425e24	−	1.56479e24i	−1.46469	−	0.418674i
$387$			4.15053e24i			1.08355i
$388$	2.01225e24	+	1.25274e24i	0.512602	+	0.319125i
$389$		−	6.91661e24i		−	1.71938i	−0.510815	−	0.859691i	$-0.670656\pi$
$389$		−	6.91661e24i		−	1.71938i	0.510815	−	0.859691i	$-0.329344\pi$
$390$	−3.35560e22	+	1.17392e23i	−0.00814060	+	0.0284790i
$391$	2.44285e24			0.578387
$392$	2.89836e24	+	3.20285e24i	0.669784	+	0.740148i
$393$	−2.12600e23			−0.0479549
$394$	1.06006e24	−	3.70852e24i	0.233409	−	0.816556i
$395$		−	8.27942e24i		−	1.77962i
$396$	−5.75885e23	+	9.25030e23i	−0.120846	+	0.194112i
$397$		−	6.65245e24i		−	1.36293i	−0.731853	−	0.681463i	$-0.761344\pi$
$397$		−	6.65245e24i		−	1.36293i	0.731853	−	0.681463i	$-0.238656\pi$
$398$	1.20173e24	+	3.43510e23i	0.240391	+	0.0687147i
$399$	−1.02540e22			−0.00200285
$400$	−1.44186e24	−	2.93145e24i	−0.275012	−	0.559129i
$401$	6.41010e24			1.19397			0.596984	−	0.802253i	$-0.296365\pi$
$401$	6.41010e24			1.19397			0.596984	+	0.802253i	$0.296365\pi$
$402$	1.09198e23	+	3.12138e22i	0.0198641	+	0.00567806i
$403$			2.37343e24i			0.421675i
$404$	−2.80269e24	+	4.50188e24i	−0.486353	+	0.781216i
$405$			7.50081e24i			1.27141i
$406$	−8.24268e22	+	2.88361e23i	−0.0136481	+	0.0477463i
$407$	1.29109e24			0.208838
$408$	1.09425e23	−	9.90221e22i	0.0172919	−	0.0156481i
$409$	5.52154e24			0.852490			0.426245	−	0.904608i	$-0.359836\pi$
$409$	5.52154e24			0.852490			0.426245	+	0.904608i	$0.359836\pi$
$410$	−1.92782e24	+	6.74429e24i	−0.290818	+	1.01740i
$411$			2.07674e23i			0.0306115i
$412$	−8.12277e24	−	5.05690e24i	−1.16999	−	0.728385i
$413$		−	2.15263e23i		−	0.0303000i
$414$	4.51995e24	+	1.29201e24i	0.621771	+	0.177730i
$415$	−6.78770e24			−0.912569
$416$	−6.67285e24	+	1.20524e24i	−0.876849	+	0.158376i
$417$	3.57266e23			0.0458880
$418$	3.18180e24	+	9.09504e23i	0.399483	+	0.114190i
$419$			3.31446e24i			0.406799i	0.979096	+	0.203400i	$0.0651990\pi$
$419$			3.31446e24i			0.406799i	−0.979096	+	0.203400i	$0.934801\pi$
$420$	−9.94223e21	−	6.18962e21i	−0.00119293	−	0.000742670i
$421$			3.93632e24i			0.461754i	0.972983	+	0.230877i	$0.0741595\pi$
$421$			3.93632e24i			0.461754i	−0.972983	+	0.230877i	$0.925841\pi$
$422$	2.85672e24	−	9.99395e24i	0.327642	−	1.14622i
$423$	−1.66766e25			−1.87014
$424$	5.29479e24	−	4.79143e24i	0.580595	−	0.525399i
$425$	5.19388e24			0.556925
$426$	−1.20728e22	+	4.22356e22i	−0.00126596	+	0.00442881i
$427$			5.24738e23i			0.0538118i
$428$	−7.56126e24	+	1.21455e25i	−0.758365	+	1.21814i
$429$		−	5.42285e22i		−	0.00531966i
$430$	1.38425e25	+	3.95681e24i	1.32820	+	0.379660i
$431$	1.03414e24			0.0970610			0.0485305	−	0.998822i	$-0.484546\pi$
$431$	1.03414e24			0.0970610			0.0485305	+	0.998822i	$0.484546\pi$
$432$	5.09849e23	−	2.50774e23i	0.0468108	−	0.0230243i
$433$	−2.24817e24			−0.201927			−0.100963	−	0.994890i	$-0.532193\pi$
$433$	−2.24817e24			−0.201927			−0.100963	+	0.994890i	$0.532193\pi$
$434$	−2.18897e23	−	6.25706e22i	−0.0192348	−	0.00549817i
$435$			4.54221e23i			0.0390499i
$436$	3.68360e24	−	5.91687e24i	0.309849	−	0.497703i
$437$		−	1.42768e25i		−	1.17506i
$438$	−1.05317e23	+	3.68441e23i	−0.00848193	+	0.0296731i
$439$	−1.13798e25			−0.896856			−0.448428	−	0.893819i	$-0.648016\pi$
$439$	−1.13798e25			−0.896856			−0.448428	+	0.893819i	$0.648016\pi$
$440$	2.53607e24	+	2.80249e24i	0.195596	+	0.216145i
$441$	−1.32158e25			−0.997533
$442$	2.96293e24	−	1.03655e25i	0.218882	−	0.765734i
$443$			2.12719e25i			1.53805i	0.639216	+	0.769027i	$0.279259\pi$
$443$			2.12719e25i			1.53805i	−0.639216	+	0.769027i	$0.720741\pi$
$444$	−2.85663e23	−	1.77842e23i	−0.0202169	−	0.0125862i
$445$			1.83494e25i			1.27117i
$446$	−9.52698e24	−	2.72324e24i	−0.646062	−	0.184674i
$447$	4.52693e23			0.0300526
$448$	6.47590e22	−	6.47199e23i	0.00420881	−	0.0420626i
$449$	5.43638e24			0.345915			0.172958	−	0.984929i	$-0.444668\pi$
$449$	5.43638e24			0.345915			0.172958	+	0.984929i	$0.444668\pi$
$450$	9.61009e24	+	2.74700e24i	0.598699	+	0.171135i
$451$		−	3.11548e24i		−	0.190041i
$452$	8.16394e24	+	5.08253e24i	0.487624	+	0.303574i
$453$		−	3.19222e23i		−	0.0186707i
$454$	4.54611e24	−	1.59041e25i	0.260381	−	0.910916i
$455$	−8.55533e23			−0.0479876
$456$	−5.78718e23	−	6.39514e23i	−0.0317907	−	0.0351305i
$457$	1.03816e25			0.558549			0.279274	−	0.960211i	$-0.409906\pi$
$457$	1.03816e25			0.558549			0.279274	+	0.960211i	$0.409906\pi$
$458$	2.30720e24	−	8.07150e24i	0.121580	−	0.425336i
$459$			9.03340e23i			0.0466263i
$460$	8.61796e24	−	1.38428e25i	0.435718	−	0.699882i
$461$		−	2.01328e25i		−	0.997117i	−0.866856	−	0.498559i	$-0.833863\pi$
$461$		−	2.01328e25i		−	0.997117i	0.866856	−	0.498559i	$-0.166137\pi$
$462$	5.00140e21	+	1.42963e21i	0.000242657	+	6.93623e-5i
$463$	1.68246e25			0.799699			0.399849	−	0.916581i	$-0.369062\pi$
$463$	1.68246e25			0.799699			0.399849	+	0.916581i	$0.369062\pi$
$464$	−2.26364e25	+	1.11339e25i	−1.05411	+	0.518475i
$465$	−3.44802e23			−0.0157314
$466$	1.00388e25	+	2.86955e24i	0.448763	+	0.128277i
$467$		−	2.96900e25i		−	1.30047i	−0.759734	−	0.650234i	$-0.774671\pi$
$467$		−	2.96900e25i		−	1.30047i	0.759734	−	0.650234i	$-0.225329\pi$
$468$	1.09645e25	−	1.76119e25i	0.470599	−	0.755912i
$469$			7.95818e23i			0.0334712i
$470$	−1.58983e25	+	5.56184e25i	−0.655269	+	2.29239i
$471$	−1.29701e23			−0.00523895
$472$	1.34254e25	−	1.21491e25i	0.531469	−	0.480944i
$473$	−6.39444e24			−0.248097
$474$	2.63413e23	−	9.21522e23i	0.0100171	−	0.0350438i
$475$		−	3.03547e25i		−	1.13145i
$476$	8.77878e23	+	5.46530e23i	0.0320751	+	0.0199686i
$477$			2.18478e25i			0.782496i
$478$	−4.03472e25	−	1.15331e25i	−1.41660	−	0.404930i
$479$	3.48219e25			1.19857			0.599287	−	0.800534i	$-0.295451\pi$
$479$	3.48219e25			1.19857			0.599287	+	0.800534i	$0.295451\pi$
$480$	−1.75093e23	−	9.69405e23i	−0.00590849	−	0.0327125i
$481$	−2.45814e25			−0.813258
$482$	−1.76718e25	−	5.05139e24i	−0.573236	−	0.163857i
$483$		−	2.24414e22i		−	0.000713760i
$484$	2.57957e25	+	1.60594e25i	0.804484	+	0.500838i
$485$			2.51552e25i			0.769276i
$486$	−7.16736e23	+	2.50743e24i	−0.0214939	+	0.0751941i
$487$	3.81856e25			1.12299			0.561494	−	0.827481i	$-0.310227\pi$
$487$	3.81856e25			1.12299			0.561494	+	0.827481i	$0.310227\pi$
$488$	−3.27266e25	+	2.96154e25i	−0.943871	+	0.854140i
$489$	−1.11956e24			−0.0316674
$490$	−1.25990e25	+	4.40762e25i	−0.349520	+	1.22276i
$491$			4.66960e25i			1.27059i	0.772270	+	0.635294i	$0.219121\pi$
$491$			4.66960e25i			1.27059i	−0.772270	+	0.635294i	$0.780879\pi$
$492$	−4.29144e23	+	6.89323e23i	−0.0114534	+	0.0183973i
$493$		−	4.01068e25i		−	1.04996i
$494$	−6.05793e25	−	1.73163e25i	−1.55567	−	0.444682i
$495$	−1.15639e25			−0.291309
$496$	−8.45182e24	−	1.71834e25i	−0.208869	−	0.424653i
$497$	−3.07805e23			−0.00746261
$498$	−7.55489e23	−	2.15953e23i	−0.0179700	−	0.00513665i
$499$			1.20220e25i			0.280558i	0.990112	+	0.140279i	$0.0447999\pi$
$499$			1.20220e25i			0.280558i	−0.990112	+	0.140279i	$0.955200\pi$
$500$	−1.10831e25	+	1.78026e25i	−0.253774	+	0.407631i
$501$		−	3.39533e23i		−	0.00762823i
$502$	4.88100e24	−	1.70757e25i	0.107603	−	0.376437i
$503$	3.04737e25			0.659218			0.329609	−	0.944118i	$-0.393083\pi$
$503$	3.04737e25			0.659218			0.329609	+	0.944118i	$0.393083\pi$
$504$	1.33526e24	+	1.47553e24i	0.0283449	+	0.0313227i
$505$	−5.62783e25			−1.17239
$506$	−1.99050e24	+	6.96357e24i	−0.0406943	+	0.142365i
$507$		−	2.67957e23i		−	0.00537637i
$508$	6.92127e25	+	4.30889e25i	1.36295	+	0.848517i
$509$			1.44729e25i			0.279728i	0.990171	+	0.139864i	$0.0446665\pi$
$509$			1.44729e25i			0.279728i	−0.990171	+	0.139864i	$0.955333\pi$
$510$	1.50586e24	+	4.30442e23i	0.0285671	+	0.00816578i
$511$	−2.68513e24			−0.0499996
$512$	4.40191e25	−	3.24880e25i	0.804594	−	0.593826i
$513$	5.27942e24			0.0947264
$514$	5.46290e25	+	1.56155e25i	0.962219	+	0.275046i
$515$		−	1.01543e26i		−	1.75583i
$516$	1.41482e24	+	8.80806e23i	0.0240175	+	0.0149523i
$517$		−	2.56925e25i		−	0.428200i
$518$	6.48039e23	−	2.26710e24i	0.0106040	−	0.0370969i
$519$	6.40896e23			0.0102967
$520$	−4.82850e25	−	5.33575e25i	−0.761694	−	0.841713i
$521$	4.00543e25			0.620426			0.310213	−	0.950667i	$-0.399600\pi$
$521$	4.00543e25			0.620426			0.310213	+	0.950667i	$0.399600\pi$
$522$	2.12122e25	−	7.42086e25i	0.322638	−	1.12871i
$523$			2.12968e25i			0.318088i	0.987271	+	0.159044i	$0.0508412\pi$
$523$			2.12968e25i			0.318088i	−0.987271	+	0.159044i	$0.949159\pi$
$524$	6.62247e25	−	1.06375e26i	0.971343	−	1.56024i
$525$		−	4.77138e22i		−	0.000687276i
$526$	−4.28134e25	−	1.22380e25i	−0.605641	−	0.173120i
$527$	3.04453e25			0.422979
$528$	1.93109e23	+	3.92611e23i	0.00263500	+	0.00535723i
$529$	−4.33697e25			−0.581243
$530$	7.28646e25	+	2.08280e25i	0.959171	+	0.274175i
$531$			5.53969e25i			0.716287i
$532$	3.19410e24	−	5.13061e24i	0.0405685	−	0.0651641i
$533$			5.93166e25i			0.740061i
$534$	−5.83794e23	+	2.04234e24i	−0.00715513	+	0.0250315i
$535$	−1.51831e26			−1.82810
$536$	−4.96332e25	+	4.49148e25i	−0.587093	+	0.531280i
$537$	−1.37647e24			−0.0159960
$538$	6.71541e23	−	2.34932e24i	0.00766727	−	0.0268232i
$539$		−	2.03607e25i		−	0.228402i
$540$	5.11892e24	+	3.18683e24i	0.0564206	+	0.0351251i
$541$			1.51095e26i			1.63635i	0.574971	+	0.818174i	$0.305013\pi$
$541$			1.51095e26i			1.63635i	−0.574971	+	0.818174i	$0.694987\pi$
$542$	1.18729e26	+	3.39381e25i	1.26347	+	0.361156i
$543$	−3.51542e24			−0.0367603
$544$	1.54603e25	+	8.55965e25i	0.158865	+	0.879562i
$545$	7.39672e25			0.746917
$546$	−9.52231e22	−	2.72191e22i	−0.000944958	−	0.000270112i
$547$			1.21086e26i			1.18090i	0.807075	+	0.590449i	$0.201049\pi$
$547$			1.21086e26i			1.18090i	−0.807075	+	0.590449i	$0.798951\pi$
$548$	−1.03911e26	−	6.46904e25i	−0.995967	−	0.620047i
$549$		−	1.35039e26i		−	1.27210i
$550$	−4.23211e24	+	1.48056e25i	−0.0391843	+	0.137082i
$551$	−2.34397e26			−2.13311
$552$	1.39962e24	−	1.26656e24i	0.0125195	−	0.0113293i
$553$	6.71589e24			0.0590493
$554$	1.96701e25	−	6.88137e25i	0.170006	−	0.594747i
$555$		−	3.57109e24i		−	0.0303401i
$556$	−1.11288e26	+	1.78760e26i	−0.929478	+	1.49300i
$557$		−	2.13063e26i		−	1.74938i	−0.484683	−	0.874690i	$-0.661065\pi$
$557$		−	2.13063e26i		−	1.74938i	0.484683	−	0.874690i	$-0.338935\pi$
$558$	5.63321e25	+	1.61023e25i	0.454707	+	0.129976i
$559$	1.21746e26			0.966142
$560$	6.19400e24	−	3.04657e24i	0.0483265	−	0.0237698i
$561$	−6.95620e23			−0.00533611
$562$	−1.07887e26	−	3.08390e25i	−0.813718	−	0.232597i
$563$			2.61624e25i			0.194020i	0.995283	+	0.0970102i	$0.0309279\pi$
$563$			2.61624e25i			0.194020i	−0.995283	+	0.0970102i	$0.969072\pi$
$564$	−3.53904e24	+	5.68466e24i	−0.0258068	+	0.0414528i
$565$			1.02058e26i			0.731790i
$566$	1.81164e25	−	6.33785e25i	0.127737	−	0.446875i
$567$	−6.08431e24			−0.0421864
$568$	−1.73721e25	−	1.91971e25i	−0.118452	−	0.130896i
$569$	1.22661e26			0.822508			0.411254	−	0.911521i	$-0.365091\pi$
$569$	1.22661e26			0.822508			0.411254	+	0.911521i	$0.365091\pi$
$570$	2.51565e24	−	8.80072e24i	0.0165897	−	0.0580373i
$571$			2.63692e25i			0.171023i	0.996337	+	0.0855113i	$0.0272524\pi$
$571$			2.63692e25i			0.171023i	−0.996337	+	0.0855113i	$0.972748\pi$
$572$	2.71335e25	+	1.68922e25i	0.173079	+	0.107751i
$573$			4.21107e24i			0.0264194i
$574$	−5.47066e24	−	1.56376e24i	−0.0337580	−	0.00964957i
$575$	6.64332e25			0.403218
$576$	−1.66654e25	+	1.66554e26i	−0.0994955	+	0.994354i
$577$	1.48000e26			0.869141			0.434571	−	0.900638i	$-0.356900\pi$
$577$	1.48000e26			0.869141			0.434571	+	0.900638i	$0.356900\pi$
$578$	3.34767e25	+	9.56917e24i	0.193388	+	0.0552790i
$579$		−	6.99452e24i		−	0.0397477i
$580$	−2.27272e26	−	1.41490e26i	−1.27051	−	0.790968i
$581$		−	5.50587e24i		−	0.0302798i
$582$	−8.00323e23	+	2.79984e24i	−0.00433009	+	0.0151484i
$583$	−3.36593e25			−0.179165
$584$	−1.51545e26	−	1.67465e26i	−0.793630	−	0.877005i
$585$	2.20168e26			1.13442
$586$	−7.49451e25	+	2.62187e26i	−0.379941	+	1.32918i
$587$		−	3.16221e26i		−	1.57735i	−0.614809	−	0.788676i	$-0.710767\pi$
$587$		−	3.16221e26i		−	1.57735i	0.614809	−	0.788676i	$-0.289233\pi$
$588$	−2.80460e24	+	4.50496e24i	−0.0137653	+	0.0221109i
$589$		−	1.77932e26i		−	0.859329i
$590$	1.84755e26	+	5.28112e25i	0.878013	+	0.250976i
$591$	4.73842e24			0.0221591
$592$	1.77968e26	−	8.75349e25i	0.819002	−	0.402833i
$593$	4.11232e25			0.186238			0.0931188	−	0.995655i	$-0.470316\pi$
$593$	4.11232e25			0.186238			0.0931188	+	0.995655i	$0.470316\pi$
$594$	−2.57505e24	−	7.36067e23i	−0.0114766	−	0.00328054i
$595$			1.09744e25i			0.0481360i
$596$	−1.41014e26	+	2.26507e26i	−0.608726	+	0.977782i
$597$			1.53547e24i			0.00652357i
$598$	3.78978e25	−	1.32582e26i	0.158472	−	0.554398i
$599$	−1.03552e26			−0.426191			−0.213096	−	0.977031i	$-0.568355\pi$
$599$	−1.03552e26			−0.426191			−0.213096	+	0.977031i	$0.568355\pi$
$600$	2.97580e24	−	2.69290e24i	0.0120550	−	0.0109089i
$601$	−1.98522e26			−0.791592			−0.395796	−	0.918338i	$-0.629531\pi$
$601$	−1.98522e26			−0.791592			−0.395796	+	0.918338i	$0.629531\pi$
$602$	−3.20958e24	+	1.12284e25i	−0.0125974	+	0.0440707i
$603$		−	2.04800e26i		−	0.791254i
$604$	1.59724e26	+	9.94375e25i	0.607462	+	0.378181i
$605$			3.22474e26i			1.20731i
$606$	−6.26393e24	−	1.79051e24i	−0.0230864	−	0.00659915i
$607$	4.20554e26			1.52591			0.762956	−	0.646450i	$-0.223747\pi$
$607$	4.20554e26			1.52591			0.762956	+	0.646450i	$0.223747\pi$
$608$	5.00254e26	−	9.03553e25i	1.78693	−	0.322753i
$609$	−3.68443e23			−0.00129571
$610$	−4.50370e26	−	1.28736e26i	−1.55932	−	0.445725i
$611$			4.89168e26i			1.66750i
$612$	−2.25918e26	−	1.40647e26i	−0.758250	−	0.472055i
$613$		−	2.47119e26i		−	0.816641i	−0.912839	−	0.408320i	$-0.866115\pi$
$613$		−	2.47119e26i		−	0.816641i	0.912839	−	0.408320i	$-0.133885\pi$
$614$	8.09396e24	−	2.83159e25i	0.0263367	−	0.0921363i
$615$	−8.61727e24			−0.0276094
$616$	−2.27325e24	+	2.05714e24i	−0.00717185	+	0.00649004i
$617$	−4.47234e26			−1.38939			−0.694697	−	0.719303i	$-0.744462\pi$
$617$	−4.47234e26			−1.38939			−0.694697	+	0.719303i	$0.744462\pi$
$618$	3.23063e24	−	1.13020e25i	0.00988319	−	0.0345753i
$619$		−	9.70369e25i		−	0.292331i	−0.989260	−	0.146166i	$-0.953307\pi$
$619$		−	9.70369e25i		−	0.292331i	0.989260	−	0.146166i	$-0.0466933\pi$
$620$	1.07406e26	−	1.72523e26i	0.318644	−	0.511830i
$621$			1.15543e25i			0.0337578i
$622$	1.46898e26	+	4.19901e25i	0.422675	+	0.120820i
$623$	−1.48842e25			−0.0421783
$624$	−3.67666e24	−	7.47504e24i	−0.0102612	−	0.0208622i
$625$	−4.49234e26			−1.23485
$626$	−3.00800e26	−	8.59824e25i	−0.814371	−	0.232784i
$627$			4.06543e24i			0.0108409i
$628$	4.04018e25	−	6.48963e25i	0.106117	−	0.170453i
$629$			3.15320e26i			0.815774i
$630$	−5.80428e24	+	2.03057e25i	−0.0147915	+	0.0517466i
$631$	−1.42435e26			−0.357551			−0.178776	−	0.983890i	$-0.557214\pi$
$631$	−1.42435e26			−0.357551			−0.178776	+	0.983890i	$0.557214\pi$
$632$	3.79034e26	+	4.18853e26i	0.937273	+	1.03574i
$633$	1.27694e25			0.0311054
$634$	4.72841e24	−	1.65419e25i	0.0113466	−	0.0396950i
$635$			8.65232e26i			2.04542i
$636$	7.44738e24	+	4.63643e24i	0.0173445	+	0.0107979i
$637$			3.87654e26i			0.889445i
$638$	1.14328e26	+	3.26801e25i	0.258438	+	0.0738733i
$639$	7.92124e25			0.176415
$640$	5.39587e26	+	2.14361e26i	1.18400	+	0.470366i
$641$	−7.22851e26			−1.56278			−0.781389	−	0.624044i	$-0.785488\pi$
$641$	−7.22851e26			−1.56278			−0.781389	+	0.624044i	$0.785488\pi$
$642$	−1.68992e25	−	4.83056e24i	−0.0359985	−	0.0102900i
$643$		−	9.33528e26i		−	1.95940i	−0.200470	−	0.979700i	$-0.564247\pi$
$643$		−	9.33528e26i		−	1.95940i	0.200470	−	0.979700i	$-0.435753\pi$
$644$	1.12287e25	+	6.99049e24i	0.0232227	+	0.0144575i
$645$			1.76867e25i			0.0360437i
$646$	−2.22126e26	+	7.77085e26i	−0.446058	+	1.56049i
$647$	−5.11281e26			−1.01174			−0.505870	−	0.862610i	$-0.668828\pi$
$647$	−5.11281e26			−1.01174			−0.505870	+	0.862610i	$0.668828\pi$
$648$	−3.43389e26	−	3.79463e26i	−0.669613	−	0.739959i
$649$	−8.53461e25			−0.164006
$650$	8.05765e25	−	2.81888e26i	0.152592	−	0.533827i
$651$		−	2.79687e23i		−	0.000521980i
$652$	3.48742e26	−	5.60175e26i	0.641434	−	1.03032i
$653$		−	3.98338e26i		−	0.722065i	−0.932553	−	0.361033i	$-0.882424\pi$
$653$		−	3.98338e26i		−	0.722065i	0.932553	−	0.361033i	$-0.117576\pi$
$654$	8.23274e24	+	2.35329e24i	0.0147081	+	0.00420424i
$655$	1.32980e27			2.34150
$656$	−2.11228e26	−	4.29448e26i	−0.366576	−	0.745288i
$657$	6.91006e26			1.18198
$658$	−4.51151e25	−	1.28959e25i	−0.0760634	−	0.0217424i
$659$		−	4.20018e26i		−	0.698001i	−0.937123	−	0.349000i	$-0.886521\pi$
$659$		−	4.20018e26i		−	0.698001i	0.937123	−	0.349000i	$-0.113479\pi$
$660$	−2.45403e24	+	3.94184e24i	−0.00401987	+	0.00645702i
$661$			4.64134e26i			0.749427i	0.927141	+	0.374713i	$0.122259\pi$
$661$			4.64134e26i			0.749427i	−0.927141	+	0.374713i	$0.877741\pi$
$662$	2.45951e26	−	8.60434e26i	0.391469	−	1.36951i
$663$	1.32441e25			0.0207800
$664$	3.43387e26	−	3.10743e26i	0.531114	−	0.480623i
$665$	6.41381e25			0.0977936
$666$	−1.66770e26	+	5.83428e26i	−0.250676	+	0.876964i
$667$		−	5.12993e26i		−	0.760179i
$668$	1.69887e26	+	1.05764e26i	0.248189	+	0.154512i
$669$		−	1.21728e25i		−	0.0175324i
$670$	−6.83031e26	−	1.95241e26i	−0.969907	−	0.277243i
$671$	2.08045e26			0.291269
$672$	7.86337e23	−	1.42027e23i	0.00108543	−	0.000196049i
$673$	2.53795e26			0.345414			0.172707	−	0.984973i	$-0.444749\pi$
$673$	2.53795e26			0.345414			0.172707	+	0.984973i	$0.444749\pi$
$674$	4.45206e26	+	1.27260e26i	0.597437	+	0.170775i
$675$			2.45663e25i			0.0325052i
$676$	1.34073e26	+	8.34685e25i	0.174924	+	0.108900i
$677$		−	6.54796e26i		−	0.842391i	−0.906970	−	0.421195i	$-0.861611\pi$
$677$		−	6.54796e26i		−	0.842391i	0.906970	−	0.421195i	$-0.138389\pi$
$678$	−3.24701e24	+	1.13593e25i	−0.00411909	+	0.0144102i
$679$	−2.04048e25			−0.0255252
$680$	−6.84447e26	+	6.19379e26i	−0.844317	+	0.764050i
$681$	2.03209e25			0.0247198
$682$	−2.48077e25	+	8.67870e25i	−0.0297601	+	0.104113i
$683$			1.26437e27i			1.49582i	0.663802	+	0.747909i	$0.268942\pi$
$683$			1.26437e27i			1.49582i	−0.663802	+	0.747909i	$0.731058\pi$
$684$	−8.21989e26	+	1.32034e27i	−0.959032	+	1.54047i
$685$		−	1.29899e27i		−	1.49467i
$686$	−7.15691e25	−	2.04577e25i	−0.0812170	−	0.0232155i
$687$	1.03131e25			0.0115425
$688$	−8.81430e26	+	4.33539e26i	−0.972966	+	0.478561i
$689$	6.40850e26			0.697708
$690$	1.92609e25	+	5.50564e24i	0.0206829	+	0.00591210i
$691$		−	8.15641e25i		−	0.0863889i	−0.999067	−	0.0431944i	$-0.986247\pi$
$691$		−	8.15641e25i		−	0.0863889i	0.999067	−	0.0431944i	$-0.0137535\pi$
$692$	−1.99639e26	+	3.20675e26i	−0.208563	+	0.335009i
$693$		−	9.38007e24i		−	0.00966585i
$694$	−1.36151e26	+	4.76310e26i	−0.138390	+	0.484144i
$695$	−2.23469e27			−2.24058
$696$	−2.07944e25	−	2.29789e25i	−0.0205664	−	0.0227270i
$697$	7.60887e26			0.742350
$698$	7.25127e25	−	2.53678e26i	0.0697891	−	0.244150i
$699$			1.28267e25i			0.0121782i
$700$	2.38738e25	+	1.48628e25i	0.0223610	+	0.0139210i
$701$			1.50490e27i			1.39055i	0.718744	+	0.695275i	$0.244717\pi$
$701$			1.50490e27i			1.39055i	−0.718744	+	0.695275i	$0.755283\pi$
$702$	4.90272e25	+	1.40142e25i	0.0446925	+	0.0127751i
$703$	1.84283e27			1.65733
$704$	−2.56598e26	−	2.56753e25i	−0.227674	−	0.0227811i
$705$	−7.10643e25			−0.0622093
$706$	3.81966e26	+	1.09183e26i	0.329899	+	0.0943000i
$707$		−	4.56504e25i		−	0.0389009i
$708$	1.88835e25	+	1.17561e25i	0.0158769	+	0.00988430i
$709$			1.48850e25i			0.0123484i	0.999981	+	0.00617420i	$0.00196532\pi$
$709$			1.48850e25i			0.0123484i	−0.999981	+	0.00617420i	$0.998035\pi$
$710$	7.55152e25	−	2.64182e26i	0.0618130	−	0.216246i
$711$	−1.72830e27			−1.39591
$712$	−8.40042e26	−	9.28292e26i	−0.669486	−	0.739818i
$713$	3.89416e26			0.306241
$714$	−3.49155e23	+	1.22148e24i	−0.000270947	+	0.000947881i
$715$			3.39197e26i			0.259744i
$716$	4.28770e26	−	6.88723e26i	0.324004	−	0.520440i
$717$		−	5.15522e25i		−	0.0384428i
$718$	−8.93002e26	−	2.55260e26i	−0.657158	−	0.187846i
$719$	5.98917e25			0.0434953			0.0217476	−	0.999763i	$-0.493077\pi$
$719$	5.98917e25			0.0434953			0.0217476	+	0.999763i	$0.493077\pi$
$720$	−1.59400e27	+	7.84022e26i	−1.14243	+	0.561914i
$721$	8.23672e25			0.0582599
$722$	3.16418e27	+	9.04466e26i	2.20881	+	0.631377i
$723$		−	2.25795e25i		−	0.0155561i
$724$	1.09505e27	−	1.75896e27i	0.744593	−	1.19602i
$725$		−	1.09070e27i		−	0.731972i
$726$	−1.02596e25	+	3.58922e25i	−0.00679569	+	0.0237740i
$727$	−1.58883e27			−1.03872			−0.519362	−	0.854554i	$-0.673831\pi$
$727$	−1.58883e27			−1.03872			−0.519362	+	0.854554i	$0.673831\pi$
$728$	4.32812e25	−	3.91666e25i	0.0279287	−	0.0252736i
$729$	1.56363e27			0.995917
$730$	6.58754e26	−	2.30458e27i	0.414148	−	1.44885i
$731$		−	1.56170e27i		−	0.969131i
$732$	−4.60316e25	−	2.86573e25i	−0.0281968	−	0.0175542i
$733$			7.88881e26i			0.477006i	0.971142	+	0.238503i	$0.0766566\pi$
$733$			7.88881e26i			0.477006i	−0.971142	+	0.238503i	$0.923343\pi$
$734$	8.58254e26	+	2.45328e26i	0.512275	+	0.146432i
$735$	−5.63167e25			−0.0331824
$736$	1.97748e26	+	1.09484e27i	0.115020	+	0.636810i
$737$	3.15522e26			0.181171
$738$	1.40785e27	+	4.02427e26i	0.798033	+	0.228114i
$739$			7.06002e26i			0.395079i	0.980295	+	0.197539i	$0.0632950\pi$
$739$			7.06002e26i			0.395079i	−0.980295	+	0.197539i	$0.936705\pi$
$740$	1.78681e27	+	1.11239e27i	0.987135	+	0.614549i
$741$		−	7.74030e25i		−	0.0422168i
$742$	−1.68947e25	+	5.91044e25i	−0.00909733	+	0.0318261i
$743$	−3.24185e27			−1.72345			−0.861726	−	0.507373i	$-0.830616\pi$
$743$	−3.24185e27			−1.72345			−0.861726	+	0.507373i	$0.830616\pi$
$744$	1.74434e25	−	1.57851e25i	0.00915564	−	0.00828524i
$745$	−2.83158e27			−1.46738
$746$	3.70396e26	−	1.29579e27i	0.189517	−	0.663005i
$747$			1.41691e27i			0.715808i
$748$	2.16685e26	−	3.48056e26i	0.108085	−	0.173614i
$749$		−	1.23158e26i		−	0.0606579i
$750$	−2.47705e25	−	7.08053e24i	−0.0120463	−	0.00344337i
$751$	3.47111e27			1.66682			0.833411	−	0.552654i	$-0.186385\pi$
$751$	3.47111e27			1.66682			0.833411	+	0.552654i	$0.186385\pi$
$752$	−1.74194e27	−	3.54154e27i	−0.825968	−	1.67928i
$753$	2.18178e25			0.0102155
$754$	−2.17673e27	−	6.22207e26i	−1.00641	−	0.287678i
$755$			1.99672e27i			0.911635i
$756$	−2.58501e24	+	4.15223e24i	−0.00116548	+	0.00187208i
$757$			8.85845e26i			0.394409i	0.980362	+	0.197205i	$0.0631863\pi$
$757$			8.85845e26i			0.394409i	−0.980362	+	0.197205i	$0.936814\pi$
$758$	−2.35212e26	+	8.22864e26i	−0.103419	+	0.361802i
$759$	−8.89745e24			−0.00386339
$760$	3.61986e27	+	4.00014e27i	1.55225	+	1.71532i
$761$	3.97430e26			0.168309			0.0841543	−	0.996453i	$-0.473181\pi$
$761$	3.97430e26			0.168309			0.0841543	+	0.996453i	$0.473181\pi$
$762$	−2.75276e25	+	9.63026e25i	−0.0115132	+	0.0402778i
$763$			5.99988e25i			0.0247833i
$764$	−2.10702e27	−	1.31175e27i	−0.859573	−	0.535134i
$765$		−	2.82422e27i		−	1.13793i
$766$	−2.38507e27	−	6.81762e26i	−0.949136	−	0.271306i
$767$	1.62493e27			0.638674
$768$	5.32375e25	+	4.10261e25i	0.0206674	+	0.0159268i
$769$	−2.90265e27			−1.11300			−0.556499	−	0.830848i	$-0.687856\pi$
$769$	−2.90265e27			−1.11300			−0.556499	+	0.830848i	$0.687856\pi$
$770$	−3.12835e25	−	8.94225e24i	−0.0118482	−	0.00338677i
$771$			6.98003e25i			0.0261120i
$772$	3.49974e27	+	2.17879e27i	1.29322	+	0.805103i
$773$			3.03505e27i			1.10780i	0.832584	+	0.553899i	$0.186861\pi$
$773$			3.03505e27i			1.10780i	−0.832584	+	0.553899i	$0.813139\pi$
$774$	8.25971e26	−	2.88957e27i	0.297801	−	1.04182i
$775$	8.27957e26			0.294877
$776$	−1.15161e27	−	1.27260e27i	−0.405154	−	0.447717i
$777$	2.89670e24			0.00100671
$778$	−1.37643e27	+	4.81530e27i	−0.472551	+	1.65317i
$779$		−	4.44688e27i		−	1.50817i
$780$	4.67230e25	−	7.50499e25i	0.0156542	−	0.0251450i
$781$			1.22037e26i			0.0403931i
$782$	−1.70070e27	−	4.86137e26i	−0.556113	−	0.158962i
$783$	1.89699e26			0.0612814
$784$	−1.38044e27	−	2.80659e27i	−0.440571	−	0.895727i
$785$	8.11273e26			0.255803
$786$	1.48010e26	+	4.23081e25i	0.0461082	+	0.0131798i
$787$		−	1.60790e27i		−	0.494879i	−0.968903	−	0.247440i	$-0.920411\pi$
$787$		−	1.60790e27i		−	0.494879i	0.968903	−	0.247440i	$-0.0795892\pi$
$788$	−1.47602e27	+	2.37089e27i	−0.448841	+	0.720962i
$789$		−	5.47033e25i		−	0.0164355i
$790$	−1.64764e27	+	5.76408e27i	−0.489107	+	1.71109i
$791$	−8.27847e25			−0.0242814
$792$	5.85012e26	−	5.29397e26i	0.169541	−	0.153424i
$793$	−3.96104e27			−1.13426
$794$	−1.32386e27	+	4.63140e27i	−0.374583	+	1.31044i
$795$			9.31001e25i			0.0260293i
$796$	−7.68279e26	−	4.78299e26i	−0.212249	−	0.132137i
$797$			2.46654e27i			0.673341i	0.941623	+	0.336670i	$0.109301\pi$
$797$			2.46654e27i			0.673341i	−0.941623	+	0.336670i	$0.890699\pi$
$798$	7.13874e24	+	2.04058e24i	0.00192572	+	0.000550459i
$799$	6.27483e27			1.67266
$800$	4.20442e26	+	2.32779e27i	0.110752	+	0.613181i
$801$	3.83039e27			0.997089
$802$	−4.46267e27	−	1.27563e27i	−1.14799	−	0.328148i
$803$			1.06459e27i			0.270634i
$804$	−6.98115e25	−	4.34617e25i	−0.0175386	−	0.0109188i
$805$			1.40370e26i			0.0348509i
$806$	4.72321e26	−	1.65236e27i	0.115892	−	0.405437i
$807$	3.00175e24			0.000727908
$808$	2.84710e27	−	2.57644e27i	0.682331	−	0.617464i
$809$	3.85670e27			0.913492			0.456746	−	0.889597i	$-0.349015\pi$
$809$	3.85670e27			0.913492			0.456746	+	0.889597i	$0.349015\pi$
$810$	1.49269e27	−	5.22201e27i	0.349431	−	1.22245i
$811$		−	3.23598e27i		−	0.748700i	−0.927288	−	0.374350i	$-0.877866\pi$
$811$		−	3.23598e27i		−	0.748700i	0.927288	−	0.374350i	$-0.122134\pi$
$812$	1.14770e26	−	1.84352e26i	0.0262450	−	0.0421566i
$813$			1.51702e26i			0.0342870i
$814$	−8.98847e26	−	2.56931e26i	−0.200795	−	0.0573964i
$815$	7.00279e27			1.54623
$816$	−9.58865e25	+	4.71626e25i	−0.0209267	+	0.0102930i
$817$	−9.12709e27			−1.96890
$818$	−3.84406e27	−	1.09881e27i	−0.819661	−	0.234296i
$819$			1.78590e26i			0.0376409i
$820$	2.68428e27	−	4.31169e27i	0.559237	−	0.898289i
$821$		−	8.58529e27i		−	1.76805i	−0.467439	−	0.884026i	$-0.654823\pi$
$821$		−	8.58529e27i		−	1.76805i	0.467439	−	0.884026i	$-0.345177\pi$
$822$	4.13279e25	−	1.44581e26i	0.00841320	−	0.0294327i
$823$	3.42172e25			0.00688566			0.00344283	−	0.999994i	$-0.498904\pi$
$823$	3.42172e25			0.00688566			0.00344283	+	0.999994i	$0.498904\pi$
$824$	4.64868e27	+	5.13704e27i	0.924743	+	1.02189i
$825$	−1.89173e25			−0.00372004
$826$	−4.28380e25	+	1.49864e26i	−0.00832759	+	0.0291332i
$827$			7.32223e25i			0.0140715i	0.999975	+	0.00703576i	$0.00223957\pi$
$827$			7.32223e25i			0.0140715i	−0.999975	+	0.00703576i	$0.997760\pi$
$828$	−2.88965e27	−	1.79897e27i	−0.548980	−	0.341772i
$829$		−	3.74412e26i		−	0.0703205i	−0.999382	−	0.0351602i	$-0.988806\pi$
$829$		−	3.74412e26i		−	0.0703205i	0.999382	−	0.0351602i	$-0.0111942\pi$
$830$	4.72555e27	+	1.35078e27i	0.877426	+	0.250808i
$831$	8.79242e25			0.0161398
$832$	4.88545e27	+	4.88840e26i	0.886610	+	0.0887146i
$833$	4.97265e27			0.892196
$834$	−2.48727e26	−	7.10973e25i	−0.0441209	−	0.0126118i
$835$			2.12377e27i			0.372465i
$836$	−2.03416e27	−	1.26638e27i	−0.352716	−	0.219586i
$837$			1.44002e26i			0.0246874i
$838$	6.59590e26	−	2.30751e27i	0.111804	−	0.391134i
$839$	−8.83835e27			−1.48126			−0.740632	−	0.671911i	$-0.765474\pi$
$839$	−8.83835e27			−1.48126			−0.740632	+	0.671911i	$0.765474\pi$
$840$	5.68996e24	+	6.28771e24i	0.000942879	+	0.00104193i
$841$	−2.31906e27			−0.379971
$842$	7.83342e26	−	2.74044e27i	0.126907	−	0.443972i
$843$		−	1.37849e26i		−	0.0220821i
$844$	−3.97766e27	+	6.38922e27i	−0.630050	+	1.01203i
$845$			1.67606e27i			0.262513i
$846$	1.16102e28	+	3.31871e27i	1.79813	+	0.513986i
$847$	−2.61576e26			−0.0400595
$848$	−4.63971e27	+	2.28208e27i	−0.702636	+	0.345597i
$849$	8.09795e25			0.0121270
$850$	−3.61594e27	−	1.03360e27i	−0.535478	−	0.153064i
$851$			4.03315e27i			0.590627i
$852$	1.68101e25	−	2.70016e25i	0.00243441	−	0.00391033i
$853$			1.18640e28i			1.69908i	0.527525	+	0.849540i	$0.323120\pi$
$853$			1.18640e28i			1.69908i	−0.527525	+	0.849540i	$0.676880\pi$
$854$	1.04425e26	−	3.65319e26i	0.0147895	−	0.0517395i
$855$	−1.65057e28			−2.31182
$856$	7.68110e27	−	6.95088e27i	1.06395	−	0.962806i
$857$	−2.48012e27			−0.339746			−0.169873	−	0.985466i	$-0.554336\pi$
$857$	−2.48012e27			−0.339746			−0.169873	+	0.985466i	$0.554336\pi$
$858$	−1.07917e25	+	3.77536e25i	−0.00146204	+	0.00511480i
$859$			8.04241e27i			1.07758i	0.842439	+	0.538792i	$0.181119\pi$
$859$			8.04241e27i			1.07758i	−0.842439	+	0.538792i	$0.818881\pi$
$860$	−8.84962e27	−	5.50941e27i	−1.17271	−	0.730078i
$861$		−	6.98993e24i		−	0.000916101i
$862$	−7.19961e26	−	2.05797e26i	−0.0933233	−	0.0266760i
$863$	4.84578e27			0.621242			0.310621	−	0.950534i	$-0.399463\pi$
$863$	4.84578e27			0.621242			0.310621	+	0.950534i	$0.399463\pi$
$864$	−4.04859e26	+	7.31251e25i	−0.0513361	+	0.00927226i
$865$	−4.00878e27			−0.502758
$866$	1.56516e27	+	4.47394e26i	0.194151	+	0.0554971i
$867$			4.27737e25i			0.00524802i
$868$	1.39943e26	+	8.71225e25i	0.0169829	+	0.0105729i
$869$		−	2.66268e27i		−	0.319618i
$870$	9.03917e25	−	3.16226e26i	0.0107324	−	0.0375461i
$871$	−6.00731e27			−0.705517
$872$	−3.74198e27	+	3.38624e27i	−0.434705	+	0.393379i
$873$	5.25108e27			0.603411
$874$	−2.84114e27	+	9.93945e27i	−0.322950	+	1.12981i
$875$		−	1.80523e26i		−	0.0202981i
$876$	1.46642e26	−	2.35547e26i	0.0163106	−	0.0261993i
$877$			1.11292e28i			1.22452i	0.790655	+	0.612261i	$0.209740\pi$
$877$			1.11292e28i			1.22452i	−0.790655	+	0.612261i	$0.790260\pi$
$878$	7.92256e27	+	2.26463e27i	0.862319	+	0.246490i
$879$	−3.35000e26			−0.0360704
$880$	−1.20789e27	−	2.45577e27i	−0.128659	−	0.261578i
$881$	1.49766e28			1.57813			0.789065	−	0.614310i	$-0.210565\pi$
$881$	1.49766e28			1.57813			0.789065	+	0.614310i	$0.210565\pi$
$882$	9.20077e27	+	2.63000e27i	0.959119	+	0.274160i
$883$		−	1.18632e28i		−	1.22342i	−0.791082	−	0.611711i	$-0.790482\pi$
$883$		−	1.18632e28i		−	1.22342i	0.791082	−	0.611711i	$-0.209518\pi$
$884$	−4.12554e27	+	6.62675e27i	−0.420905	+	0.676090i
$885$			2.36063e26i			0.0238269i
$886$	4.23320e27	−	1.48094e28i	0.422715	−	1.47883i
$887$	−1.21862e28			−1.20391			−0.601953	−	0.798532i	$-0.705611\pi$
$887$	−1.21862e28			−1.20391			−0.601953	+	0.798532i	$0.705611\pi$
$888$	1.63485e26	+	1.80660e26i	0.0159792	+	0.0176579i
$889$	−7.01836e26			−0.0678686
$890$	3.65161e27	−	1.27748e28i	0.349365	−	1.22222i
$891$			2.41227e27i			0.228343i
$892$	6.09069e27	+	3.79181e27i	0.570427	+	0.355124i
$893$		−	3.66722e28i		−	3.39819i
$894$	−3.15162e26	−	9.00876e25i	−0.0288953	−	0.00825959i
$895$	8.60976e27			0.781039
$896$	−1.73880e26	+	4.37688e26i	−0.0156071	+	0.0392861i
$897$	1.69401e26			0.0150449
$898$	−3.78477e27	−	1.08186e27i	−0.332594	−	0.0950705i
$899$		−	6.39343e27i		−	0.555926i
$900$	−6.14382e27	−	3.82489e27i	−0.528609	−	0.329090i
$901$		−	8.22055e27i		−	0.699867i
$902$	−6.19992e26	+	2.16898e27i	−0.0522305	+	0.182723i
$903$	−1.43466e25			−0.00119596
$904$	−4.67224e27	−	5.16308e27i	−0.385412	−	0.425901i
$905$	2.19888e28			1.79490
$906$	−6.35263e25	+	2.22240e26i	−0.00513140	+	0.0179517i
$907$			2.10303e28i			1.68103i	0.541789	+	0.840515i	$0.317747\pi$
$907$			2.10303e28i			1.68103i	−0.541789	+	0.840515i	$0.682253\pi$
$908$	−6.32995e27	+	1.01676e28i	−0.500708	+	0.804275i
$909$			1.17479e28i			0.919612i
$910$	5.95617e26	+	1.70254e26i	0.0461396	+	0.0131888i
$911$	9.47120e27			0.726074			0.363037	−	0.931775i	$-0.381740\pi$
$911$	9.47120e27			0.726074			0.363037	+	0.931775i	$0.381740\pi$
$912$	2.75634e26	+	5.60393e26i	0.0209113	+	0.0425149i
$913$	−2.18294e27			−0.163896
$914$	−7.22761e27	−	2.06598e27i	−0.537039	−	0.153510i
$915$		−	5.75443e26i		−	0.0423158i
$916$	−3.21252e27	+	5.16018e27i	−0.233797	+	0.375542i
$917$			1.07867e27i			0.0776929i
$918$	1.79768e26	−	6.28900e26i	0.0128147	−	0.0448307i
$919$	1.97843e28			1.39580			0.697901	−	0.716194i	$-0.254117\pi$
$919$	1.97843e28			1.39580			0.697901	+	0.716194i	$0.254117\pi$
$920$	−8.75454e27	+	7.92227e27i	−0.611292	+	0.553179i
$921$	3.61796e25			0.00250033
$922$	−4.00651e27	+	1.40164e28i	−0.274045	+	0.958719i
$923$		−	2.32350e27i		−	0.157299i
$924$	−3.19744e24	−	1.99059e24i	−0.000214249	−	0.000133382i
$925$			8.57509e27i			0.568712i
$926$	−1.17132e28	−	3.34817e27i	−0.768903	−	0.219787i
$927$	−2.11969e28			−1.37725
$928$	1.79750e28	−	3.24663e27i	1.15602	−	0.208798i
$929$	2.35154e27			0.149693			0.0748467	−	0.997195i	$-0.476153\pi$
$929$	2.35154e27			0.149693			0.0748467	+	0.997195i	$0.476153\pi$
$930$	2.40049e26	+	6.86168e25i	0.0151256	+	0.00432357i
$931$		−	2.90618e28i		−	1.81259i
$932$	−6.41791e27	−	3.99553e27i	−0.396226	−	0.246674i
$933$			1.87693e26i			0.0114703i
$934$	−5.90842e27	+	2.06700e28i	−0.357418	+	1.25039i
$935$	4.35108e27			0.260547
$936$	−1.11382e28	+	1.00793e28i	−0.660230	+	0.597464i
$937$	−2.37072e28			−1.39109			−0.695544	−	0.718483i	$-0.744837\pi$
$937$	−2.37072e28			−1.39109			−0.695544	+	0.718483i	$0.744837\pi$
$938$	1.58371e26	−	5.54043e26i	0.00919915	−	0.0321823i
$939$		−	3.84337e26i		−	0.0220998i
$940$	2.21365e28	−	3.55573e28i	1.26007	−	2.02402i
$941$			1.63014e28i			0.918592i	0.888283	+	0.459296i	$0.151898\pi$
$941$			1.63014e28i			0.918592i	−0.888283	+	0.459296i	$0.848102\pi$
$942$	9.02969e25	+	2.58109e25i	0.00503720	+	0.00143986i
$943$	9.73226e27			0.537468
$944$	−1.17644e28	+	5.78641e27i	−0.643184	+	0.316356i
$945$	−5.19073e25			−0.00280948
$946$	4.45177e27	+	1.27252e27i	0.238543	+	0.0681864i
$947$			1.67186e28i			0.886899i	0.896299	+	0.443449i	$0.146245\pi$
$947$			1.67186e28i			0.886899i	−0.896299	+	0.443449i	$0.853755\pi$
$948$	−3.66772e26	+	5.89137e26i	−0.0192627	+	0.0309412i
$949$		−	2.02690e28i		−	1.05391i
$950$	−6.04070e27	+	2.11328e28i	−0.310966	+	1.08788i
$951$	2.11357e25			0.00107722
$952$	−5.02412e26	−	5.55192e26i	−0.0253518	−	0.0280151i
$953$	−4.74178e27			−0.236896			−0.118448	−	0.992960i	$-0.537792\pi$
$953$	−4.74178e27			−0.236896			−0.118448	+	0.992960i	$0.537792\pi$
$954$	4.34778e27	−	1.52103e28i	0.215059	−	0.752363i
$955$		−	2.63400e28i		−	1.28998i
$956$	2.57943e28	+	1.60585e28i	1.25076	+	0.778672i
$957$			1.46078e26i			0.00701330i
$958$	−2.42428e28	−	6.92968e27i	−1.15242	−	0.329413i
$959$	1.05368e27			0.0495945
$960$	−7.10167e25	+	7.09738e26i	−0.00330966	+	0.0330766i
$961$	−1.68174e28			−0.776043
$962$	1.71134e28	+	4.89179e27i	0.781940	+	0.223514i
$963$			3.16943e28i			1.43394i
$964$	1.12977e28	+	7.03350e27i	0.506127	+	0.315093i
$965$			4.37504e28i			1.94077i
$966$	−4.46592e24	+	1.56236e25i	−0.000196168	+	0.000686274i
$967$	3.60277e27			0.156706			0.0783529	−	0.996926i	$-0.475034\pi$
$967$	3.60277e27			0.156706			0.0783529	+	0.996926i	$0.475034\pi$
$968$	−1.47630e28	−	1.63139e28i	−0.635854	−	0.702653i
$969$	−9.92892e26			−0.0423474
$970$	5.00599e27	−	1.75129e28i	0.211426	−	0.739651i
$971$			4.48458e27i			0.187559i	0.995593	+	0.0937797i	$0.0298949\pi$
$971$			4.48458e27i			0.187559i	−0.995593	+	0.0937797i	$0.970105\pi$
$972$	9.97974e26	−	1.60302e27i	0.0413323	−	0.0663911i
$973$		−	1.81267e27i		−	0.0743443i
$974$	−2.65846e28	−	7.59908e27i	−1.07974	−	0.308639i
$975$	3.60173e26			0.0144866
$976$	2.86776e28	−	1.41053e28i	1.14227	−	0.561837i
$977$	−3.13619e28			−1.23710			−0.618550	−	0.785746i	$-0.712279\pi$
$977$	−3.13619e28			−1.23710			−0.618550	+	0.785746i	$0.712279\pi$
$978$	7.79429e26	+	2.22796e26i	0.0304479	+	0.00870339i
$979$			5.90121e27i			0.228300i
$980$	1.75426e28	−	2.81783e28i	0.672121	−	1.07961i
$981$		−	1.54404e28i		−	0.585873i
$982$	9.29267e27	−	3.25094e28i	0.349206	−	1.22166i
$983$	5.43983e27			0.202454			0.101227	−	0.994863i	$-0.467723\pi$
$983$	5.43983e27			0.202454			0.101227	+	0.994863i	$0.467723\pi$
$984$	4.35945e26	−	3.94501e26i	0.0160686	−	0.0145410i
$985$	−2.96386e28			−1.08197
$986$	−7.98140e27	+	2.79221e28i	−0.288568	+	1.00953i
$987$		−	5.76441e25i		−	0.00206415i
$988$	3.87289e28	+	2.41110e28i	1.37355	+	0.855115i
$989$		−	1.99752e28i		−	0.701659i
$990$	8.05068e27	+	2.30125e27i	0.280091	+	0.0800626i
$991$	4.64392e28			1.60024			0.800120	−	0.599841i	$-0.204769\pi$
$991$	4.64392e28			1.60024			0.800120	+	0.599841i	$0.204769\pi$
$992$	2.46454e27	+	1.36450e28i	0.0841151	+	0.465705i
$993$	1.09939e27			0.0371649
$994$	2.14292e26	+	6.12544e25i	0.00717523	+	0.00205101i
$995$		−	9.60430e27i		−	0.318527i
$996$	4.82991e26	+	3.00690e26i	0.0158663	+	0.00987769i
$997$			8.60787e27i			0.280086i	0.990145	+	0.140043i	$0.0447241\pi$
$997$			8.60787e27i			0.280086i	−0.990145	+	0.140043i	$0.955276\pi$
$998$	2.39243e27	−	8.36965e27i	0.0771078	−	0.269754i
$999$	−1.49141e27			−0.0476131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.20.b.a.5.1	✓	18
3.2	odd	2		72.20.d.b.37.18		18
4.3	odd	2		32.20.b.a.17.10		18
8.3	odd	2		32.20.b.a.17.9		18
8.5	even	2	inner	8.20.b.a.5.2	yes	18
24.5	odd	2		72.20.d.b.37.17		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.20.b.a.5.1	✓	18	1.1	even	1	trivial
8.20.b.a.5.2	yes	18	8.5	even	2	inner
32.20.b.a.17.9		18	8.3	odd	2
32.20.b.a.17.10		18	4.3	odd	2
72.20.d.b.37.17		18	24.5	odd	2
72.20.d.b.37.18		18	3.2	odd	2

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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-696.194 - 199.004i) q^{2} -889.536i q^{3} +(445083. + 277090. i) q^{4} +5.56401e6i q^{5} +(-177021. + 619289. i) q^{6} -4.51327e6 q^{7} +(-2.54722e8 - 2.81482e8i) q^{8} +1.16147e9 q^{9} +O(q^{10})\)	\(q+(-696.194 - 199.004i) q^{2} -889.536i q^{3} +(445083. + 277090. i) q^{4} +5.56401e6i q^{5} +(-177021. + 619289. i) q^{6} -4.51327e6 q^{7} +(-2.54722e8 - 2.81482e8i) q^{8} +1.16147e9 q^{9} +(1.10726e9 - 3.87363e9i) q^{10} +1.78940e9i q^{11} +(2.46482e8 - 3.95917e8i) q^{12} -3.40689e10i q^{13} +(3.14211e9 + 8.98157e8i) q^{14} +4.94939e9 q^{15} +(1.21320e11 + 2.46656e11i) q^{16} -4.37021e11 q^{17} +(-8.08608e11 - 2.31137e11i) q^{18} +2.55409e12i q^{19} +(-1.54173e12 + 2.47645e12i) q^{20} +4.01471e9i q^{21} +(3.56097e11 - 1.24577e12i) q^{22} -5.58979e12 q^{23} +(-2.50388e11 + 2.26584e11i) q^{24} -1.18847e13 q^{25} +(-6.77983e12 + 2.37185e13i) q^{26} -2.06704e12i q^{27} +(-2.00878e12 - 1.25058e12i) q^{28} +9.17732e13i q^{29} +(-3.44573e12 - 9.84946e11i) q^{30} -6.96656e13 q^{31} +(-3.53767e13 - 1.95864e14i) q^{32} +1.59173e12 q^{33} +(3.04251e14 + 8.69687e13i) q^{34} -2.51119e13i q^{35} +(5.16951e14 + 3.21832e14i) q^{36} -7.21521e14i q^{37} +(5.08274e14 - 1.77814e15i) q^{38} -3.03055e13 q^{39} +(1.56617e15 - 1.41728e15i) q^{40} -1.74108e15 q^{41} +(7.98943e11 - 2.79502e12i) q^{42} +3.57351e15i q^{43} +(-4.95824e14 + 7.96430e14i) q^{44} +6.46243e15i q^{45} +(3.89158e15 + 1.11239e15i) q^{46} -1.43582e16 q^{47} +(2.19410e14 - 1.07918e14i) q^{48} -1.13785e16 q^{49} +(8.27408e15 + 2.36511e15i) q^{50} +3.88746e14i q^{51} +(9.44015e15 - 1.51635e16i) q^{52} +1.88104e16i q^{53} +(-4.11349e14 + 1.43906e15i) q^{54} -9.95622e15 q^{55} +(1.14963e15 + 1.27040e15i) q^{56} +2.27196e15 q^{57} +(1.82632e16 - 6.38919e16i) q^{58} +4.76955e16i q^{59} +(2.20289e15 + 1.37143e15i) q^{60} -1.16266e17i q^{61} +(4.85007e16 + 1.38637e16i) q^{62} -5.24203e15 q^{63} +(-1.43486e16 + 1.43399e17i) q^{64} +1.89560e17 q^{65} +(-1.10815e15 - 3.16761e14i) q^{66} -1.76329e17i q^{67} +(-1.94510e17 - 1.21094e17i) q^{68} +4.97232e15i q^{69} +(-4.99736e15 + 1.74827e16i) q^{70} +6.82001e16 q^{71} +(-2.95852e17 - 3.26932e17i) q^{72} +5.94941e17 q^{73} +(-1.43585e17 + 5.02318e17i) q^{74} +1.05719e16i q^{75} +(-7.07714e17 + 1.13678e18i) q^{76} -8.07603e15i q^{77} +(2.10985e16 + 6.03090e15i) q^{78} -1.48803e18 q^{79} +(-1.37240e18 + 6.75026e17i) q^{80} +1.34809e18 q^{81} +(1.21213e18 + 3.46481e17i) q^{82} +1.21993e18i q^{83} +(-1.11244e15 + 1.78688e15i) q^{84} -2.43159e18i q^{85} +(7.11143e17 - 2.48786e18i) q^{86} +8.16356e16 q^{87} +(5.03682e17 - 4.55799e17i) q^{88} +3.29788e18 q^{89} +(1.28605e18 - 4.49910e18i) q^{90} +1.53762e17i q^{91} +(-2.48792e18 - 1.54888e18i) q^{92} +6.19700e16i q^{93} +(9.99609e18 + 2.85734e18i) q^{94} -1.42110e19 q^{95} +(-1.74228e17 + 3.14688e16i) q^{96} +4.52106e18 q^{97} +(7.92166e18 + 2.26437e18i) q^{98} +2.07833e18i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9}+O(q^{10}) \) 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9	\( 18 q - 458 q^{2} - 412108 q^{4} - 47240948 q^{6} - 80707216 q^{7} - 173313752 q^{8} - 6198727826 q^{9} + 758800104 q^{10} - 9351642296 q^{12} - 122453668784 q^{14} + 156097960432 q^{15} - 696212072432 q^{16} + 14121426692 q^{17} + 1813497117770 q^{18} + 6517087595632 q^{20} - 11074654117412 q^{22} + 2177121583952 q^{23} - 36473014189168 q^{24} - 44414474211734 q^{25} + 26782030269304 q^{26} - 97002327802784 q^{28} + 327847200544208 q^{30} + 428505770260416 q^{31} + 122449430282912 q^{32} - 185380269683736 q^{33} - 478448330325748 q^{34} - 10\!\cdots\!36 q^{36}+ \cdots + 88\!\cdots\!22 q^{98}+O(q^{100}) \) 18 * q - 458 * q^2 - 412108 * q^4 - 47240948 * q^6 - 80707216 * q^7 - 173313752 * q^8 - 6198727826 * q^9 + 758800104 * q^10 - 9351642296 * q^12 - 122453668784 * q^14 + 156097960432 * q^15 - 696212072432 * q^16 + 14121426692 * q^17 + 1813497117770 * q^18 + 6517087595632 * q^20 - 11074654117412 * q^22 + 2177121583952 * q^23 - 36473014189168 * q^24 - 44414474211734 * q^25 + 26782030269304 * q^26 - 97002327802784 * q^28 + 327847200544208 * q^30 + 428505770260416 * q^31 + 122449430282912 * q^32 - 185380269683736 * q^33 - 478448330325748 * q^34 - 1053851053424436 * q^36 - 486194587539796 * q^38 + 942830575043152 * q^39 - 1697818250610976 * q^40 + 1200260021141524 * q^41 + 4964410757677984 * q^42 + 7031781193616424 * q^44 - 14917443628457488 * q^46 - 1134160959992928 * q^47 - 3197964747991392 * q^48 + 31570092936329058 * q^49 - 34734151321861826 * q^50 - 26877456911772208 * q^52 + 32102189624395064 * q^54 - 51757047863478736 * q^55 + 52858270161183424 * q^56 - 7740744140670520 * q^57 - 20470056808312424 * q^58 - 25825294995349152 * q^60 + 93766686763697984 * q^62 + 430168668665078416 * q^63 - 253721318369185216 * q^64 - 184007586011668640 * q^65 + 479551889901302712 * q^66 + 201388986348307752 * q^68 - 340698473416023872 * q^70 - 1599477989199799056 * q^71 - 115475454880420648 * q^72 - 93004298989809068 * q^73 - 93558253821761240 * q^74 - 1090379619519933176 * q^76 + 2029949680340770544 * q^78 + 1813975801025264480 * q^79 + 3057120301750869696 * q^80 + 1801762045144484330 * q^81 - 2418785089528546244 * q^82 + 141493317659087296 * q^84 + 1332333723895598620 * q^86 - 13124960835754102512 * q^87 - 3097741184498130608 * q^88 + 4470509771045743540 * q^89 - 288100905697646824 * q^90 - 2965990502259463392 * q^92 - 3533635112749329696 * q^94 + 23809730986995679856 * q^95 - 2990158800543707584 * q^96 + 8246429789464117220 * q^97 + 8841667592735478822 * q^98

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