LMFDB - Embedded newform 38.10.c.a.7.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.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:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} + 93094 x^{12} + 3763497 x^{11} + 6525212431 x^{10} + 244392759522 x^{9} + \cdots + 37\!\cdots\!25 $ x^14 - 3x^13 + 93094x^12 + 3763497x^11 + 6525212431x^10 + 244392759522x^9 + 198778066371639x^8 + 9216645483921129x^7 + 4530154246073222607x^6 + 142122715974381300066x^5 + 8185019559882294055671x^4 - 135327799885026117969495x^3 + 2044710563339570147369550x^2 - 9649457865335314261798875*x + 37683939484136051622500625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.7
Root			$-104.772 - 181.470i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.10.c.a.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 + 13.8564i) q^{2} +(116.772 + 202.254i) q^{3} +(-128.000 + 221.703i) q^{4} +(-509.754 - 882.920i) q^{5} +(-1868.34 + 3236.07i) q^{6} +2726.62 q^{7} -4096.00 q^{8} +(-17429.7 + 30189.1i) q^{9} +O(q^{10})$	\(q+(8.00000 + 13.8564i) q^{2} +(116.772 + 202.254i) q^{3} +(-128.000 + 221.703i) q^{4} +(-509.754 - 882.920i) q^{5} +(-1868.34 + 3236.07i) q^{6} +2726.62 q^{7} -4096.00 q^{8} +(-17429.7 + 30189.1i) q^{9} +(8156.07 - 14126.7i) q^{10} -83575.7 q^{11} -59787.0 q^{12} +(-84303.0 + 146017. i) q^{13} +(21812.9 + 37781.1i) q^{14} +(119050. - 206200. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(9354.48 + 16202.4i) q^{17} -557750. q^{18} +(445307. - 352689. i) q^{19} +260994. q^{20} +(318391. + 551470. i) q^{21} +(-668606. - 1.15806e6i) q^{22} +(145794. - 252523. i) q^{23} +(-478296. - 828433. i) q^{24} +(456863. - 791311. i) q^{25} -2.69769e6 q^{26} -3.54434e6 q^{27} +(-349007. + 604498. i) q^{28} +(-3.58214e6 + 6.20445e6i) q^{29} +3.80959e6 q^{30} +945649. q^{31} +(524288. - 908093. i) q^{32} +(-9.75926e6 - 1.69035e7i) q^{33} +(-149672. + 259239. i) q^{34} +(-1.38991e6 - 2.40739e6i) q^{35} +(-4.46200e6 - 7.72841e6i) q^{36} +1.52819e7 q^{37} +(8.44946e6 + 3.34884e6i) q^{38} -3.93767e7 q^{39} +(2.08795e6 + 3.61644e6i) q^{40} +(8.09782e6 + 1.40258e7i) q^{41} +(-5.09426e6 + 8.82352e6i) q^{42} +(3.78213e6 + 6.55085e6i) q^{43} +(1.06977e7 - 1.85289e7i) q^{44} +3.55394e7 q^{45} +4.66541e6 q^{46} +(-1.77773e7 + 3.07911e7i) q^{47} +(7.65274e6 - 1.32549e7i) q^{48} -3.29192e7 q^{49} +1.46196e7 q^{50} +(-2.18467e6 + 3.78397e6i) q^{51} +(-2.15816e7 - 3.73804e7i) q^{52} +(5.01344e6 - 8.68353e6i) q^{53} +(-2.83547e7 - 4.91118e7i) q^{54} +(4.26031e7 + 7.37907e7i) q^{55} -1.11682e7 q^{56} +(1.23332e8 + 4.88811e7i) q^{57} -1.14628e8 q^{58} +(8.10962e7 + 1.40463e8i) q^{59} +(3.04767e7 + 5.27872e7i) q^{60} +(3.58069e7 - 6.20193e7i) q^{61} +(7.56519e6 + 1.31033e7i) q^{62} +(-4.75241e7 + 8.23142e7i) q^{63} +1.67772e7 q^{64} +1.71895e8 q^{65} +(1.56148e8 - 2.70457e8i) q^{66} +(-2.98230e7 + 5.16549e7i) q^{67} -4.78949e6 q^{68} +6.80983e7 q^{69} +(2.22385e7 - 3.85182e7i) q^{70} +(-5.33240e7 - 9.23599e7i) q^{71} +(7.13920e7 - 1.23655e8i) q^{72} +(-3.84208e7 - 6.65468e7i) q^{73} +(1.22255e8 + 2.11753e8i) q^{74} +2.13395e8 q^{75} +(2.11928e7 + 1.43870e8i) q^{76} -2.27879e8 q^{77} +(-3.15014e8 - 5.45620e8i) q^{78} +(1.25870e8 + 2.18014e8i) q^{79} +(-3.34073e7 + 5.78631e7i) q^{80} +(-7.08092e7 - 1.22645e8i) q^{81} +(-1.29565e8 + 2.24413e8i) q^{82} -5.74140e8 q^{83} -1.63016e8 q^{84} +(9.53697e6 - 1.65185e7i) q^{85} +(-6.05142e7 + 1.04814e8i) q^{86} -1.67317e9 q^{87} +3.42326e8 q^{88} +(-7.10534e7 + 1.23068e8i) q^{89} +(2.84315e8 + 4.92449e8i) q^{90} +(-2.29862e8 + 3.98133e8i) q^{91} +(3.73233e7 + 6.46458e7i) q^{92} +(1.10425e8 + 1.91261e8i) q^{93} -5.68873e8 q^{94} +(-5.38394e8 - 2.13385e8i) q^{95} +2.44888e8 q^{96} +(5.96831e7 + 1.03374e8i) q^{97} +(-2.63353e8 - 4.56141e8i) q^{98} +(1.45670e9 - 2.52308e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9}+O(q^{10}) $ 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9} - 14544 q^{10} + 15656 q^{11} - 84480 q^{12} + 6423 q^{13} + 29536 q^{14} - 227715 q^{15} - 458752 q^{16} + 313667 q^{17} - 1673152 q^{18} + 1134224 q^{19} - 465408 q^{20} - 1227046 q^{21} + 125248 q^{22} + 3449345 q^{23} - 675840 q^{24} - 2398648 q^{25} + 205536 q^{26} - 1873854 q^{27} - 472576 q^{28} - 7002615 q^{29} - 7286880 q^{30} - 18666588 q^{31} + 7340032 q^{32} - 13827668 q^{33} - 5018672 q^{34} + 2584932 q^{35} - 13385216 q^{36} - 6866080 q^{37} + 22760176 q^{38} + 4568410 q^{39} - 3723264 q^{40} + 3564107 q^{41} + 19632736 q^{42} + 19837521 q^{43} - 2003968 q^{44} - 77788260 q^{45} + 110379040 q^{46} + 60353825 q^{47} + 10813440 q^{48} - 79579650 q^{49} - 76756736 q^{50} - 161350373 q^{51} + 1644288 q^{52} + 54744235 q^{53} - 14990832 q^{54} + 143199990 q^{55} - 15122432 q^{56} + 330686241 q^{57} - 224083680 q^{58} + 164456585 q^{59} - 58295040 q^{60} + 49328881 q^{61} - 149332704 q^{62} + 138012360 q^{63} + 234881024 q^{64} + 788015550 q^{65} + 221242688 q^{66} - 171522309 q^{67} - 160597504 q^{68} + 630323350 q^{69} - 41358912 q^{70} - 74596055 q^{71} + 214163456 q^{72} + 58695287 q^{73} - 54928640 q^{74} - 1115757144 q^{75} + 73801472 q^{76} - 965186644 q^{77} + 36547280 q^{78} + 121854617 q^{79} + 59572224 q^{80} - 368486747 q^{81} - 57025712 q^{82} - 732607256 q^{83} + 628247552 q^{84} + 634697565 q^{85} - 317400336 q^{86} - 2979036210 q^{87} - 64126976 q^{88} - 1652463181 q^{89} - 622306080 q^{90} - 1141270092 q^{91} + 883032320 q^{92} - 1839612746 q^{93} + 1931322400 q^{94} + 2397253503 q^{95} + 346030080 q^{96} + 248805607 q^{97} - 636637200 q^{98} + 520684712 q^{99}+O(q^{100}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9 - 14544 * q^10 + 15656 * q^11 - 84480 * q^12 + 6423 * q^13 + 29536 * q^14 - 227715 * q^15 - 458752 * q^16 + 313667 * q^17 - 1673152 * q^18 + 1134224 * q^19 - 465408 * q^20 - 1227046 * q^21 + 125248 * q^22 + 3449345 * q^23 - 675840 * q^24 - 2398648 * q^25 + 205536 * q^26 - 1873854 * q^27 - 472576 * q^28 - 7002615 * q^29 - 7286880 * q^30 - 18666588 * q^31 + 7340032 * q^32 - 13827668 * q^33 - 5018672 * q^34 + 2584932 * q^35 - 13385216 * q^36 - 6866080 * q^37 + 22760176 * q^38 + 4568410 * q^39 - 3723264 * q^40 + 3564107 * q^41 + 19632736 * q^42 + 19837521 * q^43 - 2003968 * q^44 - 77788260 * q^45 + 110379040 * q^46 + 60353825 * q^47 + 10813440 * q^48 - 79579650 * q^49 - 76756736 * q^50 - 161350373 * q^51 + 1644288 * q^52 + 54744235 * q^53 - 14990832 * q^54 + 143199990 * q^55 - 15122432 * q^56 + 330686241 * q^57 - 224083680 * q^58 + 164456585 * q^59 - 58295040 * q^60 + 49328881 * q^61 - 149332704 * q^62 + 138012360 * q^63 + 234881024 * q^64 + 788015550 * q^65 + 221242688 * q^66 - 171522309 * q^67 - 160597504 * q^68 + 630323350 * q^69 - 41358912 * q^70 - 74596055 * q^71 + 214163456 * q^72 + 58695287 * q^73 - 54928640 * q^74 - 1115757144 * q^75 + 73801472 * q^76 - 965186644 * q^77 + 36547280 * q^78 + 121854617 * q^79 + 59572224 * q^80 - 368486747 * q^81 - 57025712 * q^82 - 732607256 * q^83 + 628247552 * q^84 + 634697565 * q^85 - 317400336 * q^86 - 2979036210 * q^87 - 64126976 * q^88 - 1652463181 * q^89 - 622306080 * q^90 - 1141270092 * q^91 + 883032320 * q^92 - 1839612746 * q^93 + 1931322400 * q^94 + 2397253503 * q^95 + 346030080 * q^96 + 248805607 * q^97 - 636637200 * q^98 + 520684712 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$2$	8.00000	+	13.8564i	0.353553	+	0.612372i
$3$	116.772	+	202.254i	0.832322	+	1.44162i	0.896192	+	0.443666i	$0.146322\pi$
$3$	116.772	+	202.254i	0.832322	+	1.44162i	−0.0638703	+	0.997958i	$0.520344\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	−509.754	−	882.920i	−0.364751	−	0.631766i	0.623986	−	0.781436i	$-0.285512\pi$
$5$	−509.754	−	882.920i	−0.364751	−	0.631766i	−0.988736	+	0.149669i	$0.952179\pi$
$6$	−1868.34	+	3236.07i	−0.588541	+	1.01938i
$7$	2726.62			0.429223			0.214612	−	0.976699i	$-0.431151\pi$
$7$	2726.62			0.429223			0.214612	+	0.976699i	$0.431151\pi$
$8$	−4096.00			−0.353553
$9$	−17429.7	+	30189.1i	−0.885520	+	1.53377i
$10$	8156.07	−	14126.7i	0.257918	−	0.446726i
$11$	−83575.7			−1.72113			−0.860564	−	0.509343i	$-0.829888\pi$
$11$	−83575.7			−1.72113			−0.860564	+	0.509343i	$0.829888\pi$
$12$	−59787.0			−0.832322
$13$	−84303.0	+	146017.i	−0.818649	+	1.41794i	0.0880288	+	0.996118i	$0.471943\pi$
$13$	−84303.0	+	146017.i	−0.818649	+	1.41794i	−0.906678	+	0.421824i	$0.861390\pi$
$14$	21812.9	+	37781.1i	0.151753	+	0.262844i
$15$	119050.	−	206200.i	0.607180	−	1.05167i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	9354.48	+	16202.4i	0.0271644	+	0.0470501i	0.879288	−	0.476290i	$-0.158019\pi$
$17$	9354.48	+	16202.4i	0.0271644	+	0.0470501i	−0.852124	+	0.523341i	$0.824686\pi$
$18$	−557750.			−1.25231
$19$	445307.	−	352689.i	0.783913	−	0.620870i
$19$	445307.	−	352689.i	0.783913	−	0.620870i
$20$	260994.			0.364751
$21$	318391.	+	551470.i	0.357252	+	0.618778i
$22$	−668606.	−	1.15806e6i	−0.608510	−	1.05397i
$23$	145794.	−	252523.i	0.108634	−	0.188159i	−0.806583	−	0.591120i	$-0.798686\pi$
$23$	145794.	−	252523.i	0.108634	−	0.188159i	0.915217	+	0.402961i	$0.132019\pi$
$24$	−478296.	−	828433.i	−0.294270	−	0.509691i
$25$	456863.	−	791311.i	0.233914	−	0.405151i
$26$	−2.69769e6			−1.15774
$27$	−3.54434e6			−1.28351
$28$	−349007.	+	604498.i	−0.107306	+	0.185859i
$29$	−3.58214e6	+	6.20445e6i	−0.940484	+	1.62897i	−0.175935	+	0.984402i	$0.556295\pi$
$29$	−3.58214e6	+	6.20445e6i	−0.940484	+	1.62897i	−0.764550	+	0.644565i	$0.777039\pi$
$30$	3.80959e6			0.858682
$31$	945649.			0.183909			0.0919543	−	0.995763i	$-0.470689\pi$
$31$	945649.			0.183909			0.0919543	+	0.995763i	$0.470689\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$	−9.75926e6	−	1.69035e7i	−1.43253	−	2.48122i
$34$	−149672.	+	259239.i	−0.0192081	+	0.0332694i
$35$	−1.38991e6	−	2.40739e6i	−0.156559	−	0.271169i
$36$	−4.46200e6	−	7.72841e6i	−0.442760	−	0.766883i
$37$	1.52819e7			1.34051			0.670255	−	0.742131i	$-0.266185\pi$
$37$	1.52819e7			1.34051			0.670255	+	0.742131i	$0.266185\pi$
$38$	8.44946e6	+	3.34884e6i	0.657359	+	0.260536i
$39$	−3.93767e7			−2.72552
$40$	2.08795e6	+	3.61644e6i	0.128959	+	0.223363i
$41$	8.09782e6	+	1.40258e7i	0.447549	+	0.775178i	0.998226	−	0.0595408i	$-0.0189636\pi$
$41$	8.09782e6	+	1.40258e7i	0.447549	+	0.775178i	−0.550677	+	0.834719i	$0.685630\pi$
$42$	−5.09426e6	+	8.82352e6i	−0.252615	+	0.437542i
$43$	3.78213e6	+	6.55085e6i	0.168705	+	0.292206i	0.937965	−	0.346730i	$-0.112708\pi$
$43$	3.78213e6	+	6.55085e6i	0.168705	+	0.292206i	−0.769260	+	0.638936i	$0.779375\pi$
$44$	1.06977e7	−	1.85289e7i	0.430282	−	0.745270i
$45$	3.55394e7			1.29198
$46$	4.66541e6			0.153631
$47$	−1.77773e7	+	3.07911e7i	−0.531404	+	0.920418i	0.467924	+	0.883769i	$0.345002\pi$
$47$	−1.77773e7	+	3.07911e7i	−0.531404	+	0.920418i	−0.999328	+	0.0366499i	$0.988331\pi$
$48$	7.65274e6	−	1.32549e7i	0.208080	−	0.360406i
$49$	−3.29192e7			−0.815767
$50$	1.46196e7			0.330804
$51$	−2.18467e6	+	3.78397e6i	−0.0452190	+	0.0783216i
$52$	−2.15816e7	−	3.73804e7i	−0.409325	−	0.708971i
$53$	5.01344e6	−	8.68353e6i	0.0872759	−	0.151166i	−0.819083	−	0.573675i	$-0.805517\pi$
$53$	5.01344e6	−	8.68353e6i	0.0872759	−	0.151166i	0.906359	+	0.422509i	$0.138851\pi$
$54$	−2.83547e7	−	4.91118e7i	−0.453788	−	0.785984i
$55$	4.26031e7	+	7.37907e7i	0.627782	+	1.08735i
$56$	−1.11682e7			−0.151753
$57$	1.23332e8	+	4.88811e7i	1.54753	+	0.613344i
$58$	−1.14628e8			−1.33005
$59$	8.10962e7	+	1.40463e8i	0.871298	+	1.50913i	0.860655	+	0.509189i	$0.170054\pi$
$59$	8.10962e7	+	1.40463e8i	0.871298	+	1.50913i	0.0106429	+	0.999943i	$0.496612\pi$
$60$	3.04767e7	+	5.27872e7i	0.303590	+	0.525833i
$61$	3.58069e7	−	6.20193e7i	0.331118	−	0.573512i	−0.651614	−	0.758551i	$-0.725908\pi$
$61$	3.58069e7	−	6.20193e7i	0.331118	−	0.573512i	0.982731	+	0.185039i	$0.0592410\pi$
$62$	7.56519e6	+	1.31033e7i	0.0650215	+	0.112621i
$63$	−4.75241e7	+	8.23142e7i	−0.380086	+	0.658328i
$64$	1.67772e7			0.125000
$65$	1.71895e8			1.19441
$66$	1.56148e8	−	2.70457e8i	1.01295	−	1.75449i
$67$	−2.98230e7	+	5.16549e7i	−0.180807	+	0.313166i	−0.942155	−	0.335176i	$-0.891204\pi$
$67$	−2.98230e7	+	5.16549e7i	−0.180807	+	0.313166i	0.761349	+	0.648342i	$0.224537\pi$
$68$	−4.78949e6			−0.0271644
$69$	6.80983e7			0.361673
$70$	2.22385e7	−	3.85182e7i	0.110704	−	0.191745i
$71$	−5.33240e7	−	9.23599e7i	−0.249035	−	0.431341i	0.714223	−	0.699918i	$-0.246780\pi$
$71$	−5.33240e7	−	9.23599e7i	−0.249035	−	0.431341i	−0.963258	+	0.268577i	$0.913447\pi$
$72$	7.13920e7	−	1.23655e8i	0.313079	−	0.542268i
$73$	−3.84208e7	−	6.65468e7i	−0.158348	−	0.274267i	0.775925	−	0.630825i	$-0.217284\pi$
$73$	−3.84208e7	−	6.65468e7i	−0.158348	−	0.274267i	−0.934273	+	0.356558i	$0.883950\pi$
$74$	1.22255e8	+	2.11753e8i	0.473942	+	0.820892i
$75$	2.13395e8			0.778767
$76$	2.11928e7	+	1.43870e8i	0.0728665	+	0.494662i
$77$	−2.27879e8			−0.738748
$78$	−3.15014e8	−	5.45620e8i	−0.963616	−	1.66903i
$79$	1.25870e8	+	2.18014e8i	0.363581	+	0.629742i	0.988547	−	0.150910i	$-0.0482205\pi$
$79$	1.25870e8	+	2.18014e8i	0.363581	+	0.629742i	−0.624966	+	0.780652i	$0.714887\pi$
$80$	−3.34073e7	+	5.78631e7i	−0.0911876	+	0.157942i
$81$	−7.08092e7	−	1.22645e8i	−0.182771	−	0.316568i
$82$	−1.29565e8	+	2.24413e8i	−0.316465	+	0.548133i
$83$	−5.74140e8			−1.32790			−0.663952	−	0.747775i	$-0.731122\pi$
$83$	−5.74140e8			−1.32790			−0.663952	+	0.747775i	$0.731122\pi$
$84$	−1.63016e8			−0.357252
$85$	9.53697e6	−	1.65185e7i	0.0198164	−	0.0343231i
$86$	−6.05142e7	+	1.04814e8i	−0.119293	+	0.206621i
$87$	−1.67317e9			−3.13114
$88$	3.42326e8			0.608510
$89$	−7.10534e7	+	1.23068e8i	−0.120041	+	0.207917i	−0.919784	−	0.392426i	$-0.871636\pi$
$89$	−7.10534e7	+	1.23068e8i	−0.120041	+	0.207917i	0.799743	+	0.600343i	$0.204969\pi$
$90$	2.84315e8	+	4.92449e8i	0.456782	+	0.791170i
$91$	−2.29862e8	+	3.98133e8i	−0.351383	+	0.608613i
$92$	3.73233e7	+	6.46458e7i	0.0543168	+	0.0940795i
$93$	1.10425e8	+	1.91261e8i	0.153071	+	0.265127i
$94$	−5.68873e8			−0.751519
$95$	−5.38394e8	−	2.13385e8i	−0.678178	−	0.268787i
$96$	2.44888e8			0.294270
$97$	5.96831e7	+	1.03374e8i	0.0684509	+	0.118560i	0.898220	−	0.439547i	$-0.144861\pi$
$97$	5.96831e7	+	1.03374e8i	0.0684509	+	0.118560i	−0.829769	+	0.558107i	$0.811528\pi$
$98$	−2.63353e8	−	4.56141e8i	−0.288417	−	0.499554i
$99$	1.45670e9	−	2.52308e9i	1.52409	−	2.63981i
$100$	1.16957e8	+	2.02576e8i	0.116957	+	0.202576i
$101$	5.97512e8	−	1.03492e9i	0.571348	−	0.989603i	−0.425080	−	0.905156i	$-0.639754\pi$
$101$	5.97512e8	−	1.03492e9i	0.571348	−	0.989603i	0.996428	−	0.0844475i	$-0.0269125\pi$
$102$	−6.99096e7			−0.0639493
$103$	−1.02699e9			−0.899081			−0.449540	−	0.893260i	$-0.648412\pi$
$103$	−1.02699e9			−0.899081			−0.449540	+	0.893260i	$0.648412\pi$
$104$	3.45305e8	−	5.98086e8i	0.289436	−	0.501318i
$105$	3.24603e8	−	5.62229e8i	0.260616	−	0.451400i
$106$	1.60430e8			0.123427
$107$	2.26605e9			1.67125			0.835625	−	0.549300i	$-0.185105\pi$
$107$	2.26605e9			1.67125			0.835625	+	0.549300i	$0.185105\pi$
$108$	4.53675e8	−	7.85788e8i	0.320877	−	0.555775i
$109$	5.82724e8	+	1.00931e9i	0.395406	+	0.684864i	0.993153	−	0.116821i	$-0.0372705\pi$
$109$	5.82724e8	+	1.00931e9i	0.395406	+	0.684864i	−0.597747	+	0.801685i	$0.703937\pi$
$110$	−6.81649e8	+	1.18065e9i	−0.443909	+	0.768873i
$111$	1.78449e9	+	3.09083e9i	1.11574	+	1.93251i
$112$	−8.93458e7	−	1.54752e8i	−0.0536529	−	0.0929295i
$113$	7.32639e7			0.0422705			0.0211352	−	0.999777i	$-0.493272\pi$
$113$	7.32639e7			0.0422705			0.0211352	+	0.999777i	$0.493272\pi$
$114$	3.09340e8	+	2.09999e9i	0.171540	+	1.16451i
$115$	−2.97276e8			−0.158497
$116$	−9.17028e8	−	1.58834e9i	−0.470242	−	0.814483i
$117$	−2.93875e9	−	5.09006e9i	−1.44986	−	2.51123i
$118$	−1.29754e9	+	2.24740e9i	−0.616101	+	1.06712i
$119$	2.55061e7	+	4.41779e7i	0.0116596	+	0.0201950i
$120$	−4.87627e8	+	8.44595e8i	−0.214670	+	0.371820i
$121$	4.62695e9			1.96228
$122$	1.14582e9			0.468271
$123$	−1.89119e9	+	3.27564e9i	−0.745010	+	1.29039i
$124$	−1.21043e8	+	2.09653e8i	−0.0459772	+	0.0796348i
$125$	−2.92278e9			−1.07078
$126$	−1.52077e9			−0.537522
$127$	1.34833e9	−	2.33537e9i	0.459916	−	0.796598i	−0.539040	−	0.842280i	$-0.681213\pi$
$127$	1.34833e9	−	2.33537e9i	0.459916	−	0.796598i	0.998956	+	0.0456823i	$0.0145462\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$	−8.83291e8	+	1.52991e9i	−0.280834	+	0.486419i
$130$	1.37516e9	+	2.38185e9i	0.422288	+	0.731424i
$131$	1.25177e9	+	2.16814e9i	0.371369	+	0.643229i	0.989776	−	0.142628i	$-0.0455553\pi$
$131$	1.25177e9	+	2.16814e9i	0.371369	+	0.643229i	−0.618408	+	0.785857i	$0.712222\pi$
$132$	4.99674e9			1.43253
$133$	1.21418e9	−	9.61649e8i	0.336474	−	0.266492i
$134$	−9.54335e8			−0.255699
$135$	1.80674e9	+	3.12937e9i	0.468160	+	0.810876i
$136$	−3.83160e7	−	6.63652e7i	−0.00960405	−	0.0166347i
$137$	−3.96836e9	+	6.87341e9i	−0.962429	+	1.66698i	−0.246060	+	0.969255i	$0.579136\pi$
$137$	−3.96836e9	+	6.87341e9i	−0.962429	+	1.66698i	−0.716369	+	0.697722i	$0.754197\pi$
$138$	5.44787e8	+	9.43598e8i	0.127871	+	0.221478i
$139$	8.54549e8	−	1.48012e9i	0.194165	−	0.336303i	−0.752462	−	0.658636i	$-0.771134\pi$
$139$	8.54549e8	−	1.48012e9i	0.194165	−	0.336303i	0.946626	+	0.322333i	$0.104467\pi$
$140$	7.11632e8			0.156559
$141$	−8.30352e9			−1.76920
$142$	8.53185e8	−	1.47776e9i	0.176094	−	0.305004i
$143$	7.04568e9	−	1.22035e10i	1.40900	−	2.44046i
$144$	2.28454e9			0.442760
$145$	7.30405e9			1.37217
$146$	6.14733e8	−	1.06475e9i	0.111969	−	0.193936i
$147$	−3.84402e9	−	6.65804e9i	−0.678981	−	1.17603i
$148$	−1.95609e9	+	3.38804e9i	−0.335128	+	0.580458i
$149$	−5.23733e9	−	9.07133e9i	−0.870506	−	1.50776i	−0.861474	−	0.507802i	$-0.830458\pi$
$149$	−5.23733e9	−	9.07133e9i	−0.870506	−	1.50776i	−0.00903257	−	0.999959i	$-0.502875\pi$
$150$	1.70716e9	+	2.95688e9i	0.275336	+	0.476896i
$151$	5.07406e8			0.0794253			0.0397127	−	0.999211i	$-0.487356\pi$
$151$	5.07406e8			0.0794253			0.0397127	+	0.999211i	$0.487356\pi$
$152$	−1.82398e9	+	1.44462e9i	−0.277155	+	0.219511i
$153$	−6.52183e8			−0.0962183
$154$	−1.82303e9	−	3.15758e9i	−0.261187	−	0.452389i
$155$	−4.82048e8	−	8.34932e8i	−0.0670808	−	0.116187i
$156$	5.04022e9	−	8.72992e9i	0.681380	−	1.18018i
$157$	6.68290e9	+	1.15751e10i	0.877843	+	1.52047i	0.853704	+	0.520759i	$0.174351\pi$
$157$	6.68290e9	+	1.15751e10i	0.877843	+	1.52047i	0.0241391	+	0.999709i	$0.492316\pi$
$158$	−2.01393e9	+	3.48822e9i	−0.257091	+	0.445295i
$159$	2.34171e9			0.290566
$160$	−1.06903e9			−0.128959
$161$	3.97524e8	−	6.88533e8i	0.0466281	−	0.0807622i
$162$	1.13295e9	−	1.96232e9i	0.129238	−	0.223848i
$163$	−6.08257e9			−0.674905			−0.337452	−	0.941343i	$-0.609565\pi$
$163$	−6.08257e9			−0.674905			−0.337452	+	0.941343i	$0.609565\pi$
$164$	−4.14608e9			−0.447549
$165$	−9.94966e9	+	1.72333e10i	−1.04503	+	1.81005i
$166$	−4.59312e9	−	7.95552e9i	−0.469485	−	0.813172i
$167$	−2.46783e9	+	4.27440e9i	−0.245522	+	0.425257i	−0.962278	−	0.272067i	$-0.912293\pi$
$167$	−2.46783e9	+	4.27440e9i	−0.245522	+	0.425257i	0.716756	+	0.697324i	$0.245626\pi$
$168$	−1.30413e9	−	2.25882e9i	−0.126308	−	0.218771i
$169$	−8.91173e9	−	1.54356e10i	−0.840372	−	1.45557i
$170$	3.05183e8			0.0280247
$171$	2.88582e9	+	1.95907e10i	0.258099	+	1.75213i
$172$	−1.93645e9			−0.168705
$173$	−6.36125e9	−	1.10180e10i	−0.539927	−	0.935181i	−0.998907	−	0.0467348i	$-0.985118\pi$
$173$	−6.36125e9	−	1.10180e10i	−0.539927	−	0.935181i	0.458980	−	0.888447i	$-0.348215\pi$
$174$	−1.33853e10	−	2.31841e10i	−1.10703	−	1.91743i
$175$	1.24569e9	−	2.15760e9i	0.100401	−	0.173900i
$176$	2.73861e9	+	4.74341e9i	0.215141	+	0.372635i
$177$	−1.89395e10	+	3.28041e10i	−1.45040	+	2.51217i
$178$	−2.27371e9			−0.169764
$179$	2.70448e10			1.96900			0.984499	−	0.175392i	$-0.0561193\pi$
$179$	2.70448e10			1.96900			0.984499	+	0.175392i	$0.0561193\pi$
$180$	−4.54905e9	+	7.87918e9i	−0.322994	+	0.559442i
$181$	8.78607e9	−	1.52179e10i	0.608473	−	1.05391i	−0.383020	−	0.923740i	$-0.625116\pi$
$181$	8.78607e9	−	1.52179e10i	0.608473	−	1.05391i	0.991492	−	0.130165i	$-0.0415508\pi$
$182$	−7.35558e9			−0.496931
$183$	1.67249e10			1.10239
$184$	−5.97172e8	+	1.03433e9i	−0.0384078	+	0.0665242i
$185$	−7.79003e9	−	1.34927e10i	−0.488952	−	0.846890i
$186$	−1.76680e9	+	3.06018e9i	−0.108238	+	0.187473i
$187$	−7.81807e8	−	1.35413e9i	−0.0467533	−	0.0809791i
$188$	−4.55098e9	−	7.88253e9i	−0.265702	−	0.460209i
$189$	−9.66405e9			−0.550911
$190$	−1.35039e9	−	9.16728e9i	−0.0751742	−	0.510328i
$191$	−4.82883e9			−0.262538			−0.131269	−	0.991347i	$-0.541905\pi$
$191$	−4.82883e9			−0.262538			−0.131269	+	0.991347i	$0.541905\pi$
$192$	1.95910e9	+	3.39326e9i	0.104040	+	0.180203i
$193$	−5.60811e9	−	9.71353e9i	−0.290943	−	0.503929i	0.683090	−	0.730335i	$-0.260636\pi$
$193$	−5.60811e9	−	9.71353e9i	−0.290943	−	0.503929i	−0.974033	+	0.226406i	$0.927302\pi$
$194$	−9.54930e8	+	1.65399e9i	−0.0484021	+	0.0838348i
$195$	2.00725e10	+	3.47665e10i	0.994134	+	1.72189i
$196$	4.21365e9	−	7.29826e9i	0.203942	−	0.353238i
$197$	2.13322e10			1.00911			0.504554	−	0.863380i	$-0.331657\pi$
$197$	2.13322e10			1.00911			0.504554	+	0.863380i	$0.331657\pi$
$198$	4.66143e10			2.15539
$199$	5.90213e9	−	1.02228e10i	0.266790	−	0.462095i	−0.701241	−	0.712925i	$-0.747370\pi$
$199$	5.90213e9	−	1.02228e10i	0.266790	−	0.462095i	0.968031	+	0.250830i	$0.0807035\pi$
$200$	−1.87131e9	+	3.24121e9i	−0.0827011	+	0.143243i
$201$	−1.39299e10			−0.601957
$202$	1.91204e10			0.808008
$203$	−9.76713e9	+	1.69172e10i	−0.403678	+	0.699190i
$204$	−5.59277e8	−	9.68696e8i	−0.0226095	−	0.0391608i
$205$	8.25580e9	−	1.42995e10i	0.326488	−	0.565493i
$206$	−8.21592e9	−	1.42304e10i	−0.317873	−	0.550572i
$207$	5.08229e9	+	8.80278e9i	0.192394	+	0.333237i
$208$	1.10498e10			0.409325
$209$	−3.72168e10	+	2.94763e10i	−1.34921	+	1.06860i
$210$	1.03873e10			0.368566
$211$	1.26085e10	+	2.18386e10i	0.437917	+	0.758495i	0.997529	−	0.0702599i	$-0.0223829\pi$
$211$	1.26085e10	+	2.18386e10i	0.437917	+	0.758495i	−0.559611	+	0.828755i	$0.689050\pi$
$212$	1.28344e9	+	2.22298e9i	0.0436379	+	0.0755831i
$213$	1.24535e10	−	2.15700e10i	0.414555	−	0.718030i
$214$	1.81284e10	+	3.13992e10i	0.590876	+	1.02343i
$215$	3.85592e9	−	6.67865e9i	0.123071	−	0.213165i
$216$	1.45176e10			0.453788
$217$	2.57842e9			0.0789379
$218$	−9.32358e9	+	1.61489e10i	−0.279594	+	0.484272i
$219$	8.97291e9	−	1.55415e10i	0.263594	−	0.456558i
$220$	−2.18128e10			−0.627782
$221$	−3.15444e9			−0.0889523
$222$	−2.85519e10	+	4.94533e10i	−0.788945	+	1.36649i
$223$	−2.35262e10	−	4.07485e10i	−0.637059	−	1.10342i	−0.986075	−	0.166301i	$-0.946818\pi$
$223$	−2.35262e10	−	4.07485e10i	−0.637059	−	1.10342i	0.349016	−	0.937117i	$-0.386516\pi$
$224$	1.42953e9	−	2.47602e9i	0.0379383	−	0.0657111i
$225$	1.59260e10	+	2.75846e10i	0.414271	+	0.717539i
$226$	5.86111e8	+	1.01517e9i	0.0149449	+	0.0258853i
$227$	−1.25066e10			−0.312625			−0.156312	−	0.987708i	$-0.549961\pi$
$227$	−1.25066e10			−0.312625			−0.156312	+	0.987708i	$0.549961\pi$
$228$	−2.66236e10	+	2.10862e10i	−0.652468	+	0.516764i
$229$	5.79038e10			1.39139			0.695693	−	0.718339i	$-0.255097\pi$
$229$	5.79038e10			1.39139			0.695693	+	0.718339i	$0.255097\pi$
$230$	−2.37821e9	−	4.11918e9i	−0.0560370	−	0.0970590i
$231$	−2.66098e10	−	4.60895e10i	−0.614876	−	1.06500i
$232$	1.46724e10	−	2.54134e10i	0.332511	−	0.575927i
$233$	−1.30982e10	−	2.26867e10i	−0.291144	−	0.504277i	0.682936	−	0.730478i	$-0.260703\pi$
$233$	−1.30982e10	−	2.26867e10i	−0.291144	−	0.504277i	−0.974081	+	0.226201i	$0.927369\pi$
$234$	4.70200e10	−	8.14410e10i	1.02521	−	1.77571i
$235$	3.62482e10			0.775319
$236$	−4.15213e10			−0.871298
$237$	−2.93962e10	+	5.09157e10i	−0.605234	+	1.04830i
$238$	−4.08098e8	+	7.06846e8i	−0.00824456	+	0.0142800i
$239$	3.65647e10			0.724890			0.362445	−	0.932005i	$-0.381942\pi$
$239$	3.65647e10			0.724890			0.362445	+	0.932005i	$0.381942\pi$
$240$	−1.56041e10			−0.303590
$241$	4.62178e10	−	8.00516e10i	0.882536	−	1.52860i	0.0340243	−	0.999421i	$-0.489168\pi$
$241$	4.62178e10	−	8.00516e10i	0.882536	−	1.52860i	0.848512	−	0.529176i	$-0.177499\pi$
$242$	3.70156e10	+	6.41129e10i	0.693770	+	1.20165i
$243$	−1.83446e10	+	3.17738e10i	−0.337505	+	0.584576i
$244$	9.16656e9	+	1.58770e10i	0.165559	+	0.286756i
$245$	1.67807e10	+	2.90650e10i	0.297552	+	0.515375i
$246$	−6.05181e10			−1.05360
$247$	1.39580e10	+	9.47551e10i	0.238608	+	1.61982i
$248$	−3.87338e9			−0.0650215
$249$	−6.70432e10	−	1.16122e11i	−1.10524	−	1.91434i
$250$	−2.33822e10	−	4.04992e10i	−0.378579	−	0.655718i
$251$	−3.10018e10	+	5.36968e10i	−0.493010	+	0.853919i	−0.999968	−	0.00805247i	$-0.997437\pi$
$251$	−3.10018e10	+	5.36968e10i	−0.493010	+	0.853919i	0.506957	+	0.861971i	$0.330770\pi$
$252$	−1.21662e10	−	2.10724e10i	−0.190043	−	0.329164i
$253$	−1.21848e10	+	2.11048e10i	−0.186972	+	0.323846i
$254$	4.31465e10			0.650419
$255$	4.45459e9			0.0659746
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	2.21245e10	−	3.83207e10i	0.316354	−	0.547942i	−0.663370	−	0.748291i	$-0.730875\pi$
$257$	2.21245e10	−	3.83207e10i	0.316354	−	0.547942i	0.979724	+	0.200350i	$0.0642078\pi$
$258$	−2.82653e10			−0.397160
$259$	4.16680e10			0.575378
$260$	−2.20026e10	+	3.81096e10i	−0.298603	+	0.517195i
$261$	−1.24871e11	−	2.16283e11i	−1.66564	−	2.88496i
$262$	−2.00284e10	+	3.46902e10i	−0.262597	+	0.454832i
$263$	−1.63036e10	−	2.82387e10i	−0.210128	−	0.363952i	0.741627	−	0.670813i	$-0.234055\pi$
$263$	−1.63036e10	−	2.82387e10i	−0.210128	−	0.363952i	−0.951754	+	0.306861i	$0.900721\pi$
$264$	3.99739e10	+	6.92369e10i	0.506477	+	0.877243i
$265$	−1.02225e10			−0.127336
$266$	2.30384e10	+	9.13100e9i	0.282154	+	0.111828i
$267$	−3.31880e10			−0.399651
$268$	−7.63468e9	−	1.32237e10i	−0.0904033	−	0.156583i
$269$	1.71448e10	+	2.96957e10i	0.199640	+	0.345786i	0.948412	−	0.317042i	$-0.102689\pi$
$269$	1.71448e10	+	2.96957e10i	0.199640	+	0.345786i	−0.748772	+	0.662828i	$0.769356\pi$
$270$	−2.89079e10	+	5.00699e10i	−0.331039	+	0.573376i
$271$	−4.22832e10	−	7.32366e10i	−0.476218	−	0.824834i	0.523411	−	0.852081i	$-0.324659\pi$
$271$	−4.22832e10	−	7.32366e10i	−0.476218	−	0.824834i	−0.999629	+	0.0272466i	$0.991326\pi$
$272$	6.13055e8	−	1.06184e9i	0.00679109	−	0.0117625i
$273$	−1.07365e11			−1.16986
$274$	−1.26988e11			−1.36108
$275$	−3.81827e10	+	6.61344e10i	−0.402596	+	0.697317i
$276$	−8.71659e9	+	1.50976e10i	−0.0904182	+	0.156609i
$277$	6.93819e10			0.708088			0.354044	−	0.935229i	$-0.384806\pi$
$277$	6.93819e10			0.708088			0.354044	+	0.935229i	$0.384806\pi$
$278$	2.73456e10			0.274590
$279$	−1.64824e10	+	2.85483e10i	−0.162855	+	0.282073i
$280$	5.69305e9	+	9.86066e9i	0.0553521	+	0.0958726i
$281$	−9.38178e10	+	1.62497e11i	−0.897650	+	1.55477i	−0.0671586	+	0.997742i	$0.521393\pi$
$281$	−9.38178e10	+	1.62497e11i	−0.897650	+	1.55477i	−0.830491	+	0.557032i	$0.811940\pi$
$282$	−6.64281e10	−	1.15057e11i	−0.625505	−	1.08341i
$283$	4.20733e10	+	7.28731e10i	0.389913	+	0.675349i	0.992437	−	0.122752i	$-0.0391718\pi$
$283$	4.20733e10	+	7.28731e10i	0.389913	+	0.675349i	−0.602525	+	0.798100i	$0.705839\pi$
$284$	2.73019e10			0.249035
$285$	−1.97109e10	−	1.33810e11i	−0.176972	−	1.20139i
$286$	2.25462e11			1.99263
$287$	2.20797e10	+	3.82431e10i	0.192098	+	0.332724i
$288$	1.82764e10	+	3.16556e10i	0.156539	+	0.271134i
$289$	5.91189e10	−	1.02397e11i	0.498524	−	0.863469i
$290$	5.84324e10	+	1.01208e11i	0.485135	+	0.840278i
$291$	−1.39386e10	+	2.41423e10i	−0.113946	+	0.197361i
$292$	1.96714e10			0.158348
$293$	−1.48355e11			−1.17597			−0.587987	−	0.808871i	$-0.700079\pi$
$293$	−1.48355e11			−1.17597			−0.587987	+	0.808871i	$0.700079\pi$
$294$	6.15043e10	−	1.06529e11i	0.480112	−	0.831579i
$295$	8.26783e10	−	1.43203e11i	0.635613	−	1.10091i
$296$	−6.25948e10			−0.473942
$297$	2.96220e11			2.20908
$298$	8.37973e10	−	1.45141e11i	0.615541	−	1.06615i
$299$	2.45817e10	+	4.25768e10i	0.177866	+	0.308072i
$300$	−2.73145e10	+	4.73101e10i	−0.194692	+	0.337216i
$301$	1.03124e10	+	1.78617e10i	0.0724123	+	0.125422i
$302$	4.05925e9	+	7.03082e9i	0.0280811	+	0.0486379i
$303$	2.79090e11			1.90218
$304$	−3.46090e10	−	1.37168e10i	−0.232412	−	0.0921134i
$305$	−7.30109e10			−0.483101
$306$	−5.21746e9	−	9.03691e9i	−0.0340183	−	0.0589215i
$307$	1.18881e11	+	2.05909e11i	0.763821	+	1.32298i	0.940868	+	0.338774i	$0.110012\pi$
$307$	1.18881e11	+	2.05909e11i	0.763821	+	1.32298i	−0.177047	+	0.984202i	$0.556655\pi$
$308$	2.91685e10	−	5.05214e10i	0.184687	−	0.319887i
$309$	−1.19923e11	−	2.07713e11i	−0.748325	−	1.29614i
$310$	7.71278e9	−	1.33589e10i	0.0474333	−	0.0821568i
$311$	−2.29318e11			−1.39001			−0.695003	−	0.719007i	$-0.744597\pi$
$311$	−2.29318e11			−1.39001			−0.695003	+	0.719007i	$0.744597\pi$
$312$	1.61287e11			0.963616
$313$	−1.01705e11	+	1.76159e11i	−0.598955	+	1.03742i	0.394021	+	0.919102i	$0.371084\pi$
$313$	−1.01705e11	+	1.76159e11i	−0.598955	+	1.03742i	−0.992976	+	0.118319i	$0.962250\pi$
$314$	−1.06926e11	+	1.85202e11i	−0.620728	+	1.07513i
$315$	9.69025e10			0.554546
$316$	−6.44457e10			−0.363581
$317$	−4.78318e10	+	8.28472e10i	−0.266042	+	0.460799i	−0.967836	−	0.251581i	$-0.919049\pi$
$317$	−4.78318e10	+	8.28472e10i	−0.266042	+	0.460799i	0.701794	+	0.712380i	$0.252383\pi$
$318$	1.87337e10	+	3.24476e10i	0.102731	+	0.177935i
$319$	2.99380e11	−	5.18541e11i	1.61869	−	2.80366i
$320$	−8.55226e9	−	1.48129e10i	−0.0455938	−	0.0789708i
$321$	2.64610e11	+	4.58317e11i	1.39102	+	2.40932i
$322$	1.27208e10			0.0659420
$323$	9.88004e9	+	3.91583e9i	0.0505065	+	0.0200176i
$324$	3.62543e10			0.182771
$325$	7.70299e10	+	1.33420e11i	0.382987	+	0.663353i
$326$	−4.86605e10	−	8.42825e10i	−0.238615	−	0.413293i
$327$	−1.36091e11	+	2.35717e11i	−0.658211	+	1.14005i
$328$	−3.31687e10	−	5.74498e10i	−0.158232	−	0.274067i
$329$	−4.84718e10	+	8.39557e10i	−0.228091	+	0.395065i
$330$	−3.18389e11			−1.47790
$331$	1.02637e11			0.469978			0.234989	−	0.971998i	$-0.424495\pi$
$331$	1.02637e11			0.469978			0.234989	+	0.971998i	$0.424495\pi$
$332$	7.34900e10	−	1.27288e11i	0.331976	−	0.574999i
$333$	−2.66359e11	+	4.61347e11i	−1.18705	+	2.05603i
$334$	−7.89705e10			−0.347221
$335$	6.08096e10			0.263797
$336$	2.08661e10	−	3.61411e10i	0.0893130	−	0.154695i
$337$	−1.16627e10	−	2.02003e10i	−0.0492565	−	0.0853147i	0.840346	−	0.542050i	$-0.182352\pi$
$337$	−1.16627e10	−	2.02003e10i	−0.0492565	−	0.0853147i	−0.889602	+	0.456736i	$0.849018\pi$
$338$	1.42588e11	−	2.46969e11i	0.594233	−	1.02924i
$339$	8.55514e9	+	1.48179e10i	0.0351826	+	0.0609381i
$340$	2.44147e9	+	4.22874e9i	0.00990822	+	0.0171615i
$341$	−7.90333e10			−0.316530
$342$	−2.48370e11	+	1.96712e11i	−0.981705	+	0.777525i
$343$	−1.99787e11			−0.779369
$344$	−1.54916e10	−	2.68323e10i	−0.0596464	−	0.103311i
$345$	−3.47134e10	−	6.01254e10i	−0.131920	−	0.228493i
$346$	1.01780e11	−	1.76288e11i	0.381786	−	0.661273i
$347$	1.76837e10	+	3.06291e10i	0.0654772	+	0.113410i	0.896906	−	0.442222i	$-0.145810\pi$
$347$	1.76837e10	+	3.06291e10i	0.0654772	+	0.113410i	−0.831428	+	0.555632i	$0.812476\pi$
$348$	2.14166e11	−	3.70946e11i	0.782786	−	1.35582i
$349$	−5.32712e11			−1.92211			−0.961054	−	0.276359i	$-0.910872\pi$
$349$	−5.32712e11			−1.92211			−0.961054	+	0.276359i	$0.910872\pi$
$350$	3.98622e10			0.141989
$351$	2.98798e11	−	5.17533e11i	1.05074	−	1.81994i
$352$	−4.38177e10	+	7.58946e10i	−0.152128	+	0.263493i
$353$	3.14710e11			1.07876			0.539379	−	0.842063i	$-0.318659\pi$
$353$	3.14710e11			1.07876			0.539379	+	0.842063i	$0.318659\pi$
$354$	−6.06063e11			−2.05118
$355$	−5.43643e10	+	9.41618e10i	−0.181671	+	0.314664i
$356$	−1.81897e10	−	3.15054e10i	−0.0600205	−	0.103959i
$357$	−5.95677e9	+	1.03174e10i	−0.0194090	+	0.0336174i
$358$	2.16358e11	+	3.74744e11i	0.696146	+	1.20576i
$359$	−1.13866e10	−	1.97222e10i	−0.0361801	−	0.0626657i	0.847368	−	0.531006i	$-0.178186\pi$
$359$	−1.13866e10	−	1.97222e10i	−0.0361801	−	0.0626657i	−0.883548	+	0.468340i	$0.844852\pi$
$360$	−1.45570e11			−0.456782
$361$	7.39083e10	−	3.14110e11i	0.229040	−	0.973417i
$362$	2.81154e11			0.860510
$363$	5.40296e11	+	9.35821e11i	1.63325	+	2.82887i
$364$	−5.88447e10	−	1.01922e11i	−0.175692	−	0.304307i
$365$	−3.91703e10	+	6.78450e10i	−0.115515	+	0.200078i
$366$	1.33799e11	+	2.31747e11i	0.389752	+	0.675071i
$367$	9.78003e10	−	1.69395e11i	0.281412	−	0.487420i	−0.690321	−	0.723504i	$-0.742531\pi$
$367$	9.78003e10	−	1.69395e11i	0.281412	−	0.487420i	0.971733	+	0.236083i	$0.0758639\pi$
$368$	−1.91095e10			−0.0543168
$369$	−5.64570e11			−1.58525
$370$	1.24640e11	−	2.15884e11i	0.345741	−	0.598841i
$371$	1.36697e10	−	2.36767e10i	0.0374608	−	0.0648841i
$372$	−5.65375e10			−0.153071
$373$	1.99297e11			0.533102			0.266551	−	0.963821i	$-0.414116\pi$
$373$	1.99297e11			0.533102			0.266551	+	0.963821i	$0.414116\pi$
$374$	1.25089e10	−	2.16661e10i	0.0330596	−	0.0572609i
$375$	−3.41298e11	−	5.91145e11i	−0.891236	−	1.54367i
$376$	7.28157e10	−	1.26120e11i	0.187880	−	0.325417i
$377$	−6.03970e11	−	1.04611e12i	−1.53985	−	2.66710i
$378$	−7.73124e10	−	1.33909e11i	−0.194776	−	0.337363i
$379$	−2.06474e11			−0.514031			−0.257016	−	0.966407i	$-0.582739\pi$
$379$	−2.06474e11			−0.514031			−0.257016	+	0.966407i	$0.582739\pi$
$380$	1.16222e11	−	9.20499e10i	0.285933	−	0.226463i
$381$	6.29785e11			1.53119
$382$	−3.86306e10	−	6.69102e10i	−0.0928211	−	0.160771i
$383$	−1.37922e10	−	2.38889e10i	−0.0327522	−	0.0567284i	0.849185	−	0.528096i	$-0.177094\pi$
$383$	−1.37922e10	−	2.38889e10i	−0.0327522	−	0.0567284i	−0.881937	+	0.471368i	$0.843761\pi$
$384$	−3.13456e10	+	5.42922e10i	−0.0735676	+	0.127423i
$385$	1.16162e11	+	2.01199e11i	0.269459	+	0.466716i
$386$	8.97297e10	−	1.55416e11i	0.205728	−	0.356331i
$387$	−2.63686e11			−0.597568
$388$	−3.05578e10			−0.0684509
$389$	2.28925e11	−	3.96510e11i	0.506898	−	0.877973i	−0.493070	−	0.869990i	$-0.664125\pi$
$389$	2.28925e11	−	3.96510e11i	0.506898	−	0.877973i	0.999968	−	0.00798369i	$-0.00254132\pi$
$390$	−3.21160e11	+	5.56265e11i	−0.702959	+	1.21756i
$391$	5.45531e9			0.0118039
$392$	1.34837e11			0.288417
$393$	−2.92343e11	+	5.06353e11i	−0.618196	+	1.07075i
$394$	1.70658e11	+	2.95588e11i	0.356773	+	0.617950i
$395$	1.28326e11	−	2.22267e11i	0.265233	−	0.459397i
$396$	3.72915e11	+	6.45907e11i	0.762046	+	1.31990i
$397$	−1.91209e11	−	3.31184e11i	−0.386324	−	0.669133i	0.605628	−	0.795748i	$-0.292922\pi$
$397$	−1.91209e11	−	3.31184e11i	−0.386324	−	0.669133i	−0.991952	+	0.126615i	$0.959589\pi$
$398$	1.88868e11			0.377299
$399$	3.36279e11	+	1.33280e11i	0.664236	+	0.263261i
$400$	−5.98820e10			−0.116957
$401$	−1.35594e11	−	2.34856e11i	−0.261874	−	0.453579i	0.704866	−	0.709340i	$-0.251007\pi$
$401$	−1.35594e11	−	2.34856e11i	−0.261874	−	0.453579i	−0.966740	+	0.255762i	$0.917674\pi$
$402$	−1.11439e11	−	1.93018e11i	−0.212824	−	0.368622i
$403$	−7.97210e10	+	1.38081e11i	−0.150557	+	0.260772i
$404$	1.52963e11	+	2.64940e11i	0.285674	+	0.494802i
$405$	−7.21905e10	+	1.25038e11i	−0.133331	+	0.230937i
$406$	−3.12548e11			−0.570886
$407$	−1.27720e12			−2.30719
$408$	8.94843e9	−	1.54991e10i	0.0159873	−	0.0276909i
$409$	2.32587e11	−	4.02852e11i	0.410989	−	0.711854i	−0.584009	−	0.811747i	$-0.698517\pi$
$409$	2.32587e11	−	4.02852e11i	0.410989	−	0.711854i	0.994998	+	0.0998932i	$0.0318501\pi$
$410$	2.64185e11			0.461723
$411$	−1.85357e12			−3.20420
$412$	1.31455e11	−	2.27686e11i	0.224770	−	0.389313i
$413$	2.21118e11	+	3.82988e11i	0.373981	+	0.647754i
$414$	−8.13166e10	+	1.40844e11i	−0.136043	+	0.235634i
$415$	2.92671e11	+	5.06920e11i	0.484354	+	0.838925i
$416$	8.83981e10	+	1.53110e11i	0.144718	+	0.250659i
$417$	3.99148e11			0.646430
$418$	−7.06169e11	−	2.79881e11i	−1.13140	−	0.448416i
$419$	−4.73229e11			−0.750081			−0.375041	−	0.927008i	$-0.622371\pi$
$419$	−4.73229e11			−0.750081			−0.375041	+	0.927008i	$0.622371\pi$
$420$	8.30983e10	+	1.43931e11i	0.130308	+	0.225700i
$421$	5.94527e11	+	1.02975e12i	0.922364	+	1.59758i	0.795747	+	0.605629i	$0.207079\pi$
$421$	5.94527e11	+	1.02975e12i	0.922364	+	1.59758i	0.126617	+	0.991952i	$0.459588\pi$
$422$	−2.01736e11	+	3.49417e11i	−0.309654	+	0.536337i
$423$	−6.19704e11	−	1.07336e12i	−0.941137	−	1.63010i
$424$	−2.05350e10	+	3.55677e10i	−0.0308567	+	0.0534453i
$425$	1.70949e10			0.0254165
$426$	3.98511e11			0.586269
$427$	9.76317e10	−	1.69103e11i	0.142123	−	0.246165i
$428$	−2.90054e11	+	5.02388e11i	−0.417813	+	0.723673i
$429$	3.29094e12			4.69096
$430$	1.23389e11			0.174048
$431$	−1.28703e11	+	2.22920e11i	−0.179655	+	0.311172i	−0.941762	−	0.336279i	$-0.890832\pi$
$431$	−1.28703e11	+	2.22920e11i	−0.179655	+	0.311172i	0.762107	+	0.647451i	$0.224165\pi$
$432$	1.16141e11	+	2.01162e11i	0.160438	+	0.277887i
$433$	−4.80763e11	+	8.32707e11i	−0.657258	+	1.13840i	0.324064	+	0.946035i	$0.394951\pi$
$433$	−4.80763e11	+	8.32707e11i	−0.657258	+	1.13840i	−0.981323	+	0.192369i	$0.938383\pi$
$434$	2.06274e10	+	3.57277e10i	0.0279087	+	0.0483394i
$435$	8.52905e11	+	1.47727e12i	1.14209	+	1.97815i
$436$	−2.98355e11			−0.395406
$437$	−2.41390e10	−	1.63870e11i	−0.0316630	−	0.214948i
$438$	2.87133e11			0.372778
$439$	5.24912e11	+	9.09174e11i	0.674522	+	1.16831i	0.976608	+	0.215026i	$0.0689836\pi$
$439$	5.24912e11	+	9.09174e11i	0.674522	+	1.16831i	−0.302086	+	0.953281i	$0.597683\pi$
$440$	−1.74502e11	−	3.02247e11i	−0.221954	−	0.384436i
$441$	5.73771e11	−	9.93800e11i	0.722378	−	1.25120i
$442$	−2.52355e10	−	4.37092e10i	−0.0314494	−	0.0544720i
$443$	5.09367e11	−	8.82249e11i	0.628367	−	1.08836i	−0.359512	−	0.933140i	$-0.617057\pi$
$443$	5.09367e11	−	8.82249e11i	0.628367	−	1.08836i	0.987879	−	0.155224i	$-0.0496099\pi$
$444$	−9.13661e11			−1.11574
$445$	1.44879e11			0.175140
$446$	3.76419e11	−	6.51976e11i	0.450468	−	0.780234i
$447$	1.22314e12	−	2.11855e12i	1.44908	−	2.50989i
$448$	4.57451e10			0.0536529
$449$	1.24944e12			1.45080			0.725400	−	0.688327i	$-0.241655\pi$
$449$	1.24944e12			1.45080			0.725400	+	0.688327i	$0.241655\pi$
$450$	−2.54816e11	+	4.41354e11i	−0.292934	+	0.507376i
$451$	−6.76781e11	−	1.17222e12i	−0.770289	−	1.33418i
$452$	−9.37778e9	+	1.62428e10i	−0.0105676	+	0.0183036i
$453$	5.92505e10	+	1.02625e11i	0.0661075	+	0.114501i
$454$	−1.00053e11	−	1.73297e11i	−0.110530	−	0.191443i
$455$	4.68693e11			0.512669
$456$	−5.05168e11	−	2.00217e11i	−0.547134	−	0.216850i
$457$	5.12552e11			0.549686			0.274843	−	0.961489i	$-0.411374\pi$
$457$	5.12552e11			0.549686			0.274843	+	0.961489i	$0.411374\pi$
$458$	4.63231e11	+	8.02339e11i	0.491929	+	0.852047i
$459$	−3.31554e10	−	5.74269e10i	−0.0348656	−	0.0603891i
$460$	3.80514e10	−	6.59069e10i	0.0396242	−	0.0686311i
$461$	−4.39726e11	−	7.61627e11i	−0.453448	−	0.785395i	0.545149	−	0.838339i	$-0.316473\pi$
$461$	−4.39726e11	−	7.61627e11i	−0.453448	−	0.785395i	−0.998598	+	0.0529436i	$0.983140\pi$
$462$	4.25757e11	−	7.37432e11i	0.434783	−	0.753066i
$463$	−1.29816e12			−1.31285			−0.656425	−	0.754391i	$-0.727932\pi$
$463$	−1.29816e12			−1.31285			−0.656425	+	0.754391i	$0.727932\pi$
$464$	4.69518e11			0.470242
$465$	1.12579e11	−	1.94993e11i	0.111666	−	0.193411i
$466$	2.09570e11	−	3.62987e11i	0.205870	−	0.356578i
$467$	−2.30092e11			−0.223859			−0.111930	−	0.993716i	$-0.535703\pi$
$467$	−2.30092e11			−0.223859			−0.111930	+	0.993716i	$0.535703\pi$
$468$	1.50464e12			1.44986
$469$	−8.13159e10	+	1.40843e11i	−0.0776064	+	0.134418i
$470$	2.89985e11	+	5.02269e11i	0.274117	+	0.474784i
$471$	−1.56075e12	+	2.70329e12i	−1.46130	+	2.53104i
$472$	−3.32170e11	−	5.75336e11i	−0.308050	−	0.533559i
$473$	−3.16095e11	−	5.47492e11i	−0.290363	−	0.502924i
$474$	−9.40677e11			−0.855930
$475$	−7.56425e10	−	5.13507e11i	−0.0681780	−	0.462834i
$476$	−1.30591e10			−0.0116596
$477$	1.74765e11	+	3.02702e11i	0.154569	+	0.267721i
$478$	2.92518e11	+	5.06656e11i	0.256287	+	0.443902i
$479$	−1.00748e12	+	1.74500e12i	−0.874430	+	1.51456i	−0.0170604	+	0.999854i	$0.505431\pi$
$479$	−1.00748e12	+	1.74500e12i	−0.874430	+	1.51456i	−0.857369	+	0.514702i	$0.827903\pi$
$480$	−1.24833e11	−	2.16216e11i	−0.107335	−	0.185910i
$481$	−1.28831e12	+	2.23142e12i	−1.09741	+	1.90077i
$482$	1.47897e12			1.24809
$483$	1.85678e11			0.155238
$484$	−5.92250e11	+	1.02581e12i	−0.490570	+	0.849692i
$485$	6.08475e10	−	1.05391e11i	0.0499350	−	0.0864899i
$486$	−5.87027e11			−0.477304
$487$	6.77251e11			0.545594			0.272797	−	0.962072i	$-0.412051\pi$
$487$	6.77251e11			0.545594			0.272797	+	0.962072i	$0.412051\pi$
$488$	−1.46665e11	+	2.54031e11i	−0.117068	+	0.202767i
$489$	−7.10271e11	−	1.23022e12i	−0.561738	−	0.972959i
$490$	−2.68491e11	+	4.65040e11i	−0.210401	+	0.364425i
$491$	−5.96026e11	−	1.03235e12i	−0.462806	−	0.801603i	0.536294	−	0.844031i	$-0.319824\pi$
$491$	−5.96026e11	−	1.03235e12i	−0.462806	−	0.801603i	−0.999100	+	0.0424285i	$0.986491\pi$
$492$	−4.84144e11	−	8.38563e11i	−0.372505	−	0.645197i
$493$	−1.34036e11			−0.102191
$494$	−1.20130e12	+	9.51448e11i	−0.907571	+	0.718809i
$495$	−2.97023e12			−2.22365
$496$	−3.09870e10	−	5.36711e10i	−0.0229886	−	0.0398174i
$497$	−1.45394e11	−	2.51830e11i	−0.106892	−	0.185142i
$498$	1.07269e12	−	1.85796e12i	0.781525	−	1.35364i
$499$	7.57457e11	+	1.31195e12i	0.546897	+	0.947253i	0.998485	+	0.0550268i	$0.0175244\pi$
$499$	7.57457e11	+	1.31195e12i	0.546897	+	0.947253i	−0.451588	+	0.892227i	$0.649142\pi$
$500$	3.74116e11	−	6.47988e11i	0.267696	−	0.463662i
$501$	−1.15269e12			−0.817414
$502$	−9.92059e11			−0.697222
$503$	8.55922e10	−	1.48250e11i	0.0596182	−	0.103262i	−0.834676	−	0.550741i	$-0.814345\pi$
$503$	8.55922e10	−	1.48250e11i	0.0596182	−	0.103262i	0.894294	+	0.447480i	$0.147678\pi$
$504$	1.94659e11	−	3.37159e11i	0.134381	−	0.232754i
$505$	−1.21834e12			−0.833597
$506$	−3.89915e11			−0.264419
$507$	2.08127e12	−	3.60487e12i	1.39892	−	2.42300i
$508$	3.45172e11	+	5.97855e11i	0.229958	+	0.398299i
$509$	−5.27851e11	+	9.14265e11i	−0.348563	+	0.603729i	−0.985994	−	0.166778i	$-0.946664\pi$
$509$	−5.27851e11	+	9.14265e11i	−0.348563	+	0.603729i	0.637431	+	0.770507i	$0.279997\pi$
$510$	3.56367e10	+	6.17246e10i	0.0233255	+	0.0404010i
$511$	−1.04759e11	−	1.81448e11i	−0.0679668	−	0.117722i
$512$	−6.87195e10			−0.0441942
$513$	−1.57832e12	+	1.25005e12i	−1.00616	+	0.796891i
$514$	7.07983e11			0.447392
$515$	5.23513e11	+	9.06750e11i	0.327940	+	0.568009i
$516$	−2.26123e11	−	3.91656e11i	−0.140417	−	0.243210i
$517$	1.48575e12	−	2.57339e12i	0.914614	−	1.58416i
$518$	3.33344e11	+	5.77368e11i	0.203427	+	0.352346i
$519$	1.48563e12	−	2.57318e12i	0.898787	−	1.55674i
$520$	−7.04083e11			−0.422288
$521$	1.95339e12			1.16150			0.580749	−	0.814083i	$-0.302760\pi$
$521$	1.95339e12			1.16150			0.580749	+	0.814083i	$0.302760\pi$
$522$	1.99794e12	−	3.46053e12i	1.17778	−	2.03998i
$523$	−1.41787e12	+	2.45583e12i	−0.828666	+	1.43529i	0.0704184	+	0.997518i	$0.477567\pi$
$523$	−1.41787e12	+	2.45583e12i	−0.828666	+	1.43529i	−0.899085	+	0.437775i	$0.855767\pi$
$524$	−6.40908e11			−0.371369
$525$	5.81846e11			0.334265
$526$	2.60858e11	−	4.51819e11i	0.148583	−	0.257353i
$527$	8.84605e9	+	1.53218e10i	0.00499576	+	0.00865291i
$528$	−6.39583e11	+	1.10779e12i	−0.358133	+	0.620305i
$529$	8.58065e11	+	1.48621e12i	0.476397	+	0.825145i
$530$	−8.17799e10	−	1.41647e11i	−0.0450200	−	0.0779769i
$531$	−5.65393e12			−3.08621
$532$	5.77848e10	+	3.92278e11i	0.0312760	+	0.212320i
$533$	−2.73068e12			−1.46554
$534$	−2.65504e11	−	4.59867e11i	−0.141298	−	0.244735i
$535$	−1.15513e12	−	2.00074e12i	−0.609590	−	1.05584i
$536$	1.22155e11	−	2.11578e11i	0.0639248	−	0.110721i
$537$	3.15806e12	+	5.46993e12i	1.63884	+	2.83855i
$538$	−2.74317e11	+	4.75131e11i	−0.141167	+	0.244508i
$539$	2.75124e12			1.40404
$540$	−9.25051e11			−0.468160
$541$	2.97769e11	−	5.15751e11i	0.149449	−	0.258853i	−0.781575	−	0.623811i	$-0.785583\pi$
$541$	2.97769e11	−	5.15751e11i	0.149449	−	0.258853i	0.931024	+	0.364958i	$0.118917\pi$
$542$	6.76531e11	−	1.17179e12i	0.336737	−	0.583246i
$543$	4.10385e12			2.02578
$544$	1.96178e10			0.00960405
$545$	5.94092e11	−	1.02900e12i	0.288449	−	0.499609i
$546$	−8.58923e11	−	1.48770e12i	−0.413606	−	0.716387i
$547$	−5.18976e11	+	8.98892e11i	−0.247859	+	0.429304i	−0.962931	−	0.269746i	$-0.913060\pi$
$547$	−5.18976e11	+	8.98892e11i	−0.247859	+	0.429304i	0.715073	+	0.699050i	$0.246394\pi$
$548$	−1.01590e12	−	1.75959e12i	−0.481215	−	0.833488i
$549$	1.24821e12	+	2.16196e12i	0.586422	+	1.01571i
$550$	−1.22185e12			−0.569357
$551$	5.93092e11	+	4.02626e12i	0.274119	+	1.86089i
$552$	−2.78931e11			−0.127871
$553$	3.43201e11	+	5.94441e11i	0.156058	+	0.270300i
$554$	5.55055e11	+	9.61384e11i	0.250347	+	0.433614i
$555$	1.81931e12	−	3.15113e12i	0.813931	−	1.40977i
$556$	2.18765e11	+	3.78911e11i	0.0970824	+	0.168152i
$557$	3.10669e11	−	5.38094e11i	0.136757	−	0.236870i	−0.789510	−	0.613737i	$-0.789665\pi$
$557$	3.10669e11	−	5.38094e11i	0.136757	−	0.236870i	0.926267	+	0.376867i	$0.122999\pi$
$558$	−5.27435e11			−0.230311
$559$	−1.27538e12			−0.552442
$560$	−9.10889e10	+	1.57771e11i	−0.0391398	+	0.0677922i
$561$	1.82586e11	−	3.16248e11i	0.0778276	−	0.134801i
$562$	−3.00217e12			−1.26947
$563$	2.18332e12			0.915862			0.457931	−	0.888988i	$-0.348591\pi$
$563$	2.18332e12			0.915862			0.457931	+	0.888988i	$0.348591\pi$
$564$	1.06285e12	−	1.84091e12i	0.442299	−	0.766085i
$565$	−3.73466e10	−	6.46862e10i	−0.0154182	−	0.0267051i
$566$	−6.73172e11	+	1.16597e12i	−0.275710	+	0.477544i
$567$	−1.93070e11	−	3.34406e11i	−0.0784495	−	0.135878i
$568$	2.18415e11	+	3.78306e11i	0.0880472	+	0.152502i
$569$	−1.75409e12			−0.701529			−0.350764	−	0.936464i	$-0.614078\pi$
$569$	−1.75409e12			−0.701529			−0.350764	+	0.936464i	$0.614078\pi$
$570$	1.69643e12	−	1.34360e12i	0.673132	−	0.533130i
$571$	9.69958e11			0.381848			0.190924	−	0.981605i	$-0.438852\pi$
$571$	9.69958e11			0.381848			0.190924	+	0.981605i	$0.438852\pi$
$572$	1.80369e12	+	3.12409e12i	0.704500	+	1.22023i
$573$	−5.63870e11	−	9.76651e11i	−0.218516	−	0.378481i
$574$	−3.53275e11	+	6.11889e11i	−0.135834	+	0.235272i
$575$	−1.33216e11	−	2.30737e11i	−0.0508219	−	0.0880261i
$576$	−2.92422e11	+	5.06489e11i	−0.110690	+	0.191721i
$577$	9.30386e10			0.0349439			0.0174720	−	0.999847i	$-0.494438\pi$
$577$	9.30386e10			0.0349439			0.0174720	+	0.999847i	$0.494438\pi$
$578$	1.89181e12			0.705020
$579$	1.30974e12	−	2.26853e12i	0.484317	−	0.838862i
$580$	−9.34918e11	+	1.61933e12i	−0.343042	+	0.594166i
$581$	−1.56546e12			−0.569967
$582$	−4.46035e11			−0.161144
$583$	−4.19002e11	+	7.25732e11i	−0.150213	+	0.260176i
$584$	1.57372e11	+	2.72576e11i	0.0559846	+	0.0969682i
$585$	−2.99608e12	+	5.18936e12i	−1.05767	+	1.83195i
$586$	−1.18684e12	−	2.05567e12i	−0.415769	−	0.720134i
$587$	2.34887e11	+	4.06836e11i	0.0816559	+	0.141432i	0.903961	−	0.427614i	$-0.140646\pi$
$587$	2.34887e11	+	4.06836e11i	0.0816559	+	0.141432i	−0.822305	+	0.569046i	$0.807312\pi$
$588$	1.96814e12			0.678981
$589$	4.21104e11	−	3.33520e11i	0.144168	−	0.114183i
$590$	2.64571e12			0.898892
$591$	2.49099e12	+	4.31453e12i	0.839902	+	1.45475i
$592$	−5.00758e11	−	8.67338e11i	−0.167564	−	0.290229i
$593$	1.64008e12	−	2.84070e12i	0.544651	−	0.943364i	−0.453977	−	0.891013i	$-0.649995\pi$
$593$	1.64008e12	−	2.84070e12i	0.544651	−	0.943364i	0.998629	−	0.0523506i	$-0.0166713\pi$
$594$	2.36976e12	+	4.10455e12i	0.781027	+	1.35278i
$595$	2.60037e10	−	4.50397e10i	0.00850567	−	0.0147323i
$596$	2.68151e12			0.870506
$597$	2.75680e12			0.888222
$598$	−3.93308e11	+	6.81229e11i	−0.125770	+	0.217840i
$599$	1.00468e12	−	1.74016e12i	0.318867	−	0.552293i	−0.661385	−	0.750046i	$-0.730031\pi$
$599$	1.00468e12	−	1.74016e12i	0.318867	−	0.552293i	0.980252	+	0.197753i	$0.0633645\pi$
$600$	−8.74064e11			−0.275336
$601$	2.21033e12			0.691071			0.345535	−	0.938406i	$-0.387697\pi$
$601$	2.21033e12			0.691071			0.345535	+	0.938406i	$0.387697\pi$
$602$	−1.64999e11	+	2.85787e11i	−0.0512032	+	0.0886865i
$603$	−1.03961e12	−	1.80066e12i	−0.320216	−	0.554630i
$604$	−6.49479e10	+	1.12493e11i	−0.0198563	+	0.0343922i
$605$	−2.35861e12	−	4.08523e12i	−0.715742	−	1.23970i
$606$	2.23272e12	+	3.86718e12i	0.672522	+	1.16484i
$607$	−1.78837e12			−0.534698			−0.267349	−	0.963600i	$-0.586148\pi$
$607$	−1.78837e12			−0.534698			−0.267349	+	0.963600i	$0.586148\pi$
$608$	−8.68059e10	−	5.89291e11i	−0.0257622	−	0.174889i
$609$	−4.56209e12			−1.34396
$610$	−5.84087e11	−	1.01167e12i	−0.170802	−	0.295838i
$611$	−2.99735e12	−	5.19157e12i	−0.870066	−	1.50700i
$612$	8.34794e10	−	1.44591e11i	0.0240546	−	0.0416638i
$613$	−2.83408e11	−	4.90878e11i	−0.0810663	−	0.140411i	0.822642	−	0.568560i	$-0.192499\pi$
$613$	−2.83408e11	−	4.90878e11i	−0.0810663	−	0.140411i	−0.903708	+	0.428149i	$0.859166\pi$
$614$	−1.90210e12	+	3.29454e12i	−0.540103	+	0.935485i
$615$	3.85617e12			1.08697
$616$	9.33393e11			0.261187
$617$	1.21997e12	−	2.11305e12i	0.338895	−	0.586984i	−0.645330	−	0.763904i	$-0.723280\pi$
$617$	1.21997e12	−	2.11305e12i	0.338895	−	0.586984i	0.984225	+	0.176920i	$0.0566135\pi$
$618$	1.91877e12	−	3.32341e12i	0.529145	−	0.916507i
$619$	3.89516e12			1.06639			0.533197	−	0.845991i	$-0.320991\pi$
$619$	3.89516e12			1.06639			0.533197	+	0.845991i	$0.320991\pi$
$620$	2.46809e11			0.0670808
$621$	−5.16743e11	+	8.95025e11i	−0.139432	+	0.241503i
$622$	−1.83455e12	−	3.17753e12i	−0.491441	−	0.851201i
$623$	−1.93735e11	+	3.35560e11i	−0.0515244	+	0.0892428i
$624$	1.29030e12	+	2.23486e12i	0.340690	+	0.590092i
$625$	5.97589e11	+	1.03505e12i	0.156654	+	0.271333i
$626$	−3.25457e12			−0.847050
$627$	−1.03076e13	−	4.08527e12i	−2.66350	−	1.05564i
$628$	−3.42165e12			−0.877843
$629$	1.42954e11	+	2.47604e11i	0.0364141	+	0.0630711i
$630$	7.75220e11	+	1.34272e12i	0.196062	+	0.339589i
$631$	−1.95489e12	+	3.38597e12i	−0.490897	+	0.850258i	−0.999945	−	0.0104799i	$-0.996664\pi$
$631$	−1.95489e12	+	3.38597e12i	−0.490897	+	0.850258i	0.509048	+	0.860738i	$0.329997\pi$
$632$	−5.15565e11	−	8.92985e11i	−0.128545	−	0.222647i
$633$	−2.94463e12	+	5.10024e12i	−0.728977	+	1.26262i
$634$	−1.53062e12			−0.376240
$635$	−2.74926e12			−0.671018
$636$	−2.99739e11	+	5.19162e11i	−0.0726416	+	0.125819i
$637$	2.77518e12	−	4.80676e12i	0.667827	−	1.15671i
$638$	9.58016e12			2.28918
$639$	3.71768e12			0.882102
$640$	1.36836e11	−	2.37007e11i	0.0322397	−	0.0558408i
$641$	1.03103e12	+	1.78579e12i	0.241218	+	0.417801i	0.961061	−	0.276335i	$-0.0891199\pi$
$641$	1.03103e12	+	1.78579e12i	0.241218	+	0.417801i	−0.719844	+	0.694136i	$0.755787\pi$
$642$	−4.23375e12	+	7.33308e12i	−0.983599	+	1.70364i
$643$	2.13751e12	+	3.70228e12i	0.493127	+	0.854121i	0.999969	−	0.00791790i	$-0.00252037\pi$
$643$	2.13751e12	+	3.70228e12i	0.493127	+	0.854121i	−0.506841	+	0.862039i	$0.669187\pi$
$644$	1.01766e11	+	1.76264e11i	0.0233140	+	0.0403811i
$645$	1.80105e12			0.409738
$646$	2.47810e10	+	1.68228e11i	0.00559851	+	0.0380061i
$647$	1.83219e12			0.411055			0.205528	−	0.978651i	$-0.434109\pi$
$647$	1.83219e12			0.411055			0.205528	+	0.978651i	$0.434109\pi$
$648$	2.90034e11	+	5.02354e11i	0.0646192	+	0.111924i
$649$	−6.77768e12	−	1.17393e13i	−1.49961	−	2.59741i
$650$	−1.23248e12	+	2.13471e12i	−0.270813	+	0.469061i
$651$	3.01086e11	+	5.21497e11i	0.0657017	+	0.113799i
$652$	7.78568e11	−	1.34852e12i	0.168726	−	0.292242i
$653$	−6.12823e12			−1.31894			−0.659472	−	0.751729i	$-0.729220\pi$
$653$	−6.12823e12			−1.31894			−0.659472	+	0.751729i	$0.729220\pi$
$654$	−4.35492e12			−0.930850
$655$	1.27619e12	−	2.21043e12i	0.270914	−	0.469236i
$656$	5.30699e11	−	9.19197e11i	0.111887	−	0.193794i
$657$	2.67865e12			0.560882
$658$	−1.55110e12			−0.322569
$659$	5.33882e11	−	9.24710e11i	0.110271	−	0.190995i	−0.805609	−	0.592448i	$-0.798162\pi$
$659$	5.33882e11	−	9.24710e11i	0.110271	−	0.190995i	0.915879	+	0.401453i	$0.131495\pi$
$660$	−2.54711e12	−	4.41173e12i	−0.522517	−	0.905026i
$661$	−2.19556e12	+	3.80283e12i	−0.447342	+	0.774819i	−0.998212	−	0.0597721i	$-0.980963\pi$
$661$	−2.19556e12	+	3.80283e12i	−0.447342	+	0.774819i	0.550870	+	0.834591i	$0.314296\pi$
$662$	8.21095e11	+	1.42218e12i	0.166162	+	0.287801i
$663$	−3.68349e11	−	6.37999e11i	−0.0740370	−	0.128236i
$664$	2.35168e12			0.469485
$665$	−1.46799e12	−	5.81821e11i	−0.291090	−	0.115370i
$666$	−8.52349e12			−1.67874
$667$	1.04451e12	+	1.80914e12i	0.204336	+	0.353921i
$668$	−6.31764e11	−	1.09425e12i	−0.122761	−	0.212628i
$669$	5.49437e12	−	9.51654e12i	1.06048	−	1.83680i
$670$	4.86476e11	+	8.42602e11i	0.0932664	+	0.161542i
$671$	−2.99259e12	+	5.18331e12i	−0.569895	+	0.987088i
$672$	6.67715e11			0.126308
$673$	−8.10812e12			−1.52353			−0.761767	−	0.647851i	$-0.775668\pi$
$673$	−8.10812e12			−1.52353			−0.761767	+	0.647851i	$0.775668\pi$
$674$	1.86603e11	−	3.23205e11i	0.0348296	−	0.0603266i
$675$	−1.61928e12	+	2.80467e12i	−0.300230	+	0.520014i
$676$	4.56281e12			0.840372
$677$	1.41006e12			0.257981			0.128991	−	0.991646i	$-0.458826\pi$
$677$	1.41006e12			0.257981			0.128991	+	0.991646i	$0.458826\pi$
$678$	−1.36882e11	+	2.37087e11i	−0.0248779	+	0.0430897i
$679$	1.62733e11	+	2.81862e11i	0.0293807	+	0.0508889i
$680$	−3.90634e10	+	6.76599e10i	−0.00700617	+	0.0121350i
$681$	−1.46042e12	−	2.52952e12i	−0.260205	−	0.450687i
$682$	−6.32266e11	−	1.09512e12i	−0.111910	−	0.193834i
$683$	−1.01477e13			−1.78433			−0.892167	−	0.451705i	$-0.850816\pi$
$683$	−1.01477e13			−1.78433			−0.892167	+	0.451705i	$0.850816\pi$
$684$	−4.71269e12	−	1.86781e12i	−0.823220	−	0.326273i
$685$	8.09156e12			1.40419
$686$	−1.59829e12	−	2.76833e12i	−0.275549	−	0.477264i
$687$	6.76152e12	+	1.17113e13i	1.15808	+	2.00586i
$688$	2.47866e11	−	4.29316e11i	0.0421763	−	0.0730516i
$689$	8.45295e11	+	1.46409e12i	0.142897	+	0.247504i
$690$	5.55415e11	−	9.62007e11i	0.0932817	−	0.161569i
$691$	5.73723e12			0.957307			0.478653	−	0.878004i	$-0.341125\pi$
$691$	5.73723e12			0.957307			0.478653	+	0.878004i	$0.341125\pi$
$692$	3.25696e12			0.539927
$693$	3.97186e12	−	6.87946e12i	0.654176	−	1.13307i
$694$	−2.82939e11	+	4.90065e11i	−0.0462994	+	0.0801929i
$695$	−1.74244e12			−0.283287
$696$	6.85330e12			1.10703
$697$	−1.51502e11	+	2.62409e11i	−0.0243148	+	0.0421144i
$698$	−4.26170e12	−	7.38147e12i	−0.679568	−	1.17705i
$699$	3.05898e12	−	5.29831e12i	0.484652	−	0.839441i
$700$	3.18897e11	+	5.52346e11i	0.0502007	+	0.0869501i
$701$	−1.40748e12	−	2.43782e12i	−0.220146	−	0.381304i	0.734706	−	0.678385i	$-0.237320\pi$
$701$	−1.40748e12	−	2.43782e12i	−0.220146	−	0.381304i	−0.954852	+	0.297082i	$0.903987\pi$
$702$	9.56154e12			1.48597
$703$	6.80514e12	−	5.38977e12i	1.05084	−	0.832283i
$704$	−1.40217e12			−0.215141
$705$	4.23275e12	+	7.33134e12i	0.645315	+	1.11772i
$706$	2.51768e12	+	4.36075e12i	0.381399	+	0.660602i
$707$	1.62919e12	−	2.82183e12i	0.245236	−	0.424761i
$708$	−4.84850e12	−	8.39785e12i	−0.725200	−	1.25608i
$709$	4.37352e12	−	7.57515e12i	0.650014	−	1.12586i	−0.333105	−	0.942890i	$-0.608096\pi$
$709$	4.37352e12	−	7.57515e12i	0.650014	−	1.12586i	0.983119	−	0.182967i	$-0.0585702\pi$
$710$	−1.73966e12			−0.256922
$711$	−8.77553e12			−1.28783
$712$	2.91035e11	−	5.04087e11i	0.0424409	−	0.0735098i
$713$	1.37870e11	−	2.38798e11i	0.0199787	−	0.0346041i
$714$	−1.90617e11			−0.0274485
$715$	−1.43663e13			−2.05573
$716$	−3.46173e12	+	5.99590e12i	−0.492249	+	0.852601i
$717$	4.26972e12	+	7.39537e12i	0.603342	+	1.04502i
$718$	1.82186e11	−	3.15555e11i	0.0255832	−	0.0443114i
$719$	5.03417e12	+	8.71944e12i	0.702503	+	1.21677i	0.967585	+	0.252545i	$0.0812676\pi$
$719$	5.03417e12	+	8.71944e12i	0.702503	+	1.21677i	−0.265082	+	0.964226i	$0.585399\pi$
$720$	−1.16456e12	−	2.01707e12i	−0.161497	−	0.279721i
$721$	−2.80021e12			−0.385906
$722$	4.94370e12	−	1.48877e12i	0.677072	−	0.203897i
$723$	2.15877e13			2.93822
$724$	2.24923e12	+	3.89579e12i	0.304236	+	0.526953i
$725$	3.27310e12	+	5.66917e12i	0.439985	+	0.762077i
$726$	−8.64474e12	+	1.49731e13i	−1.15488	+	2.00031i
$727$	4.10050e12	+	7.10227e12i	0.544417	+	0.942958i	0.998643	+	0.0520716i	$0.0165824\pi$
$727$	4.10050e12	+	7.10227e12i	0.544417	+	0.942958i	−0.454226	+	0.890886i	$0.650084\pi$
$728$	9.41515e11	−	1.63075e12i	0.124233	−	0.215177i
$729$	−1.13560e13			−1.48919
$730$	−1.25345e12			−0.163363
$731$	−7.07598e10	+	1.22560e11i	−0.00916555	+	0.0158752i
$732$	−2.14079e12	+	3.70795e12i	−0.275596	+	0.477347i
$733$	−1.11573e12			−0.142755			−0.0713777	−	0.997449i	$-0.522740\pi$
$733$	−1.11573e12			−0.142755			−0.0713777	+	0.997449i	$0.522740\pi$
$734$	3.12961e12			0.397977
$735$	−3.91901e12	+	6.78793e12i	−0.495318	+	0.857915i
$736$	−1.52876e11	−	2.64789e11i	−0.0192039	−	0.0332621i
$737$	2.49248e12	−	4.31709e12i	0.311191	−	0.538999i
$738$	−4.51656e12	−	7.82291e12i	−0.560472	−	0.970766i
$739$	4.66582e12	+	8.08144e12i	0.575477	+	0.996756i	0.995990	+	0.0894691i	$0.0285170\pi$
$739$	4.66582e12	+	8.08144e12i	0.575477	+	0.996756i	−0.420512	+	0.907287i	$0.638150\pi$
$740$	3.98849e12			0.488952
$741$	−1.75347e13	+	1.38878e13i	−2.13657	+	1.69219i
$742$	4.37431e11			0.0529776
$743$	−4.72210e11	−	8.17892e11i	−0.0568441	−	0.0984569i	0.836203	−	0.548420i	$-0.184770\pi$
$743$	−4.72210e11	−	8.17892e11i	−0.0568441	−	0.0984569i	−0.893047	+	0.449963i	$0.851437\pi$
$744$	−4.52300e11	−	7.83407e11i	−0.0541188	−	0.0937366i
$745$	−5.33951e12	+	9.24830e12i	−0.635035	+	1.09991i
$746$	1.59437e12	+	2.76153e12i	0.188480	+	0.326457i
$747$	1.00071e13	−	1.73328e13i	1.17589	−	2.03669i
$748$	4.00285e11			0.0467533
$749$	6.17864e12			0.717340
$750$	5.46076e12	−	9.45832e12i	0.630199	−	1.09154i
$751$	−5.52672e12	+	9.57256e12i	−0.633998	+	1.09812i	0.352729	+	0.935726i	$0.385254\pi$
$751$	−5.52672e12	+	9.57256e12i	−0.633998	+	1.09812i	−0.986727	+	0.162391i	$0.948080\pi$
$752$	2.33010e12			0.265702
$753$	−1.44805e13			−1.64137
$754$	9.66352e12	−	1.67377e13i	1.08884	−	1.88593i
$755$	−2.58652e11	−	4.47999e11i	−0.0289704	−	0.0501783i
$756$	1.23700e12	−	2.14254e12i	0.137728	−	0.238551i
$757$	1.46592e12	+	2.53906e12i	0.162248	+	0.281022i	0.935675	−	0.352864i	$-0.114792\pi$
$757$	1.46592e12	+	2.53906e12i	0.162248	+	0.281022i	−0.773426	+	0.633886i	$0.781459\pi$
$758$	−1.65179e12	−	2.86099e12i	−0.181738	−	0.314779i
$759$	−5.69137e12			−0.622485
$760$	2.20526e12	+	8.74027e11i	0.239772	+	0.0950306i
$761$	−5.58693e12			−0.603868			−0.301934	−	0.953329i	$-0.597632\pi$
$761$	−5.58693e12			−0.603868			−0.301934	+	0.953329i	$0.597632\pi$
$762$	5.03828e12	+	8.72656e12i	0.541358	+	0.937660i
$763$	1.58887e12	+	2.75200e12i	0.169718	+	0.293959i
$764$	6.18090e11	−	1.07056e12i	0.0656344	−	0.113682i
$765$	3.32453e11	+	5.75825e11i	0.0350957	+	0.0607875i
$766$	2.20676e11	−	3.82222e11i	0.0231593	−	0.0401131i
$767$	−2.73466e13			−2.85315
$768$	−1.00306e12			−0.104040
$769$	5.37807e12	−	9.31509e12i	0.554572	−	0.960547i	−0.443365	−	0.896341i	$-0.646215\pi$
$769$	5.37807e12	−	9.31509e12i	0.554572	−	0.960547i	0.997937	−	0.0642054i	$-0.0204513\pi$
$770$	−1.85860e12	+	3.21919e12i	−0.190536	+	0.330018i
$771$	1.03340e13			1.05323
$772$	2.87135e12			0.290943
$773$	5.03781e12	−	8.72574e12i	0.507497	−	0.879011i	−0.492465	−	0.870332i	$-0.663904\pi$
$773$	5.03781e12	−	8.72574e12i	0.507497	−	0.879011i	0.999962	−	0.00867888i	$-0.00276261\pi$
$774$	−2.10949e12	−	3.65374e12i	−0.211272	−	0.365934i
$775$	4.32032e11	−	7.48302e11i	0.0430188	−	0.0745108i
$776$	−2.44462e11	−	4.23421e11i	−0.0242010	−	0.0419174i
$777$	4.86563e12	+	8.42752e12i	0.478900	+	0.829479i
$778$	7.32561e12			0.716862
$779$	8.55277e12	+	3.38978e12i	0.832125	+	0.329802i
$780$	−1.02771e13			−0.994134
$781$	4.45659e12	+	7.71905e12i	0.428621	+	0.742393i
$782$	4.36425e10	+	7.55910e10i	0.00417329	+	0.00722835i
$783$	1.26963e13	−	2.19907e13i	1.20712	−	2.09079i
$784$	1.07870e12	+	1.86835e12i	0.101971	+	0.176619i
$785$	6.81328e12	−	1.18009e13i	0.640387	−	1.10918i
$786$	−9.35498e12			−0.874262
$787$	1.70008e13			1.57973			0.789864	−	0.613282i	$-0.210151\pi$
$787$	1.70008e13			1.57973			0.789864	+	0.613282i	$0.210151\pi$
$788$	−2.73052e12	+	4.72940e12i	−0.252277	+	0.436956i
$789$	3.80760e12	−	6.59496e12i	0.349788	−	0.605850i
$790$	4.10643e12			0.375096
$791$	1.99763e11			0.0181435
$792$	−5.96664e12	+	1.03345e13i	−0.538848	+	0.933312i
$793$	6.03725e12	+	1.04568e13i	0.542138	+	0.939011i
$794$	3.05935e12	−	5.29895e12i	0.273172	−	0.473149i
$795$	−1.19370e12	−	2.06754e12i	−0.105984	−	0.183570i
$796$	1.51095e12	+	2.61704e12i	0.133395	+	0.231047i
$797$	3.94001e11			0.0345887			0.0172944	−	0.999850i	$-0.494495\pi$
$797$	3.94001e11			0.0345887			0.0172944	+	0.999850i	$0.494495\pi$
$798$	8.43452e11	+	5.72586e12i	0.0736288	+	0.499837i
$799$	−6.65188e11			−0.0577410
$800$	−4.79056e11	−	8.29749e11i	−0.0413506	−	0.0716213i
$801$	−2.47688e12	−	4.29007e12i	−0.212597	−	0.368229i
$802$	2.16951e12	−	3.75770e12i	0.185173	−	0.320728i
$803$	3.21105e12	+	5.56169e12i	0.272538	+	0.472049i
$804$	1.78303e12	−	3.08829e12i	0.150489	−	0.260655i
$805$	−8.10559e11			−0.0680305
$806$	−2.55107e12			−0.212919
$807$	−4.00405e12	+	6.93522e12i	−0.332329	+	0.575611i
$808$	−2.44741e12	+	4.23904e12i	−0.202002	+	0.349878i
$809$	−1.92720e13			−1.58182			−0.790911	−	0.611931i	$-0.790393\pi$
$809$	−1.92720e13			−1.58182			−0.790911	+	0.611931i	$0.790393\pi$
$810$	−2.31010e12			−0.188559
$811$	−4.77337e12	+	8.26771e12i	−0.387464	+	0.671107i	−0.992108	−	0.125389i	$-0.959982\pi$
$811$	−4.77337e12	+	8.26771e12i	−0.387464	+	0.671107i	0.604644	+	0.796496i	$0.293315\pi$
$812$	−2.50038e12	−	4.33079e12i	−0.201839	−	0.349595i
$813$	9.87495e12	−	1.71039e13i	0.792734	−	1.37305i
$814$	−1.02176e13	−	1.76974e13i	−0.815715	−	1.41286i
$815$	3.10061e12	+	5.37042e12i	0.246172	+	0.426382i
$816$	2.86350e11			0.0226095
$817$	3.99462e12	+	1.58322e12i	0.313673	+	0.124320i
$818$	7.44278e12			0.581226
$819$	−8.01284e12	−	1.38787e13i	−0.622313	−	1.07788i
$820$	2.11348e12	+	3.66066e12i	0.163244	+	0.282746i
$821$	1.55719e12	−	2.69713e12i	0.119618	−	0.207184i	−0.799998	−	0.600002i	$-0.795166\pi$
$821$	1.55719e12	−	2.69713e12i	0.119618	−	0.207184i	0.919616	+	0.392818i	$0.128500\pi$
$822$	−1.48285e13	−	2.56838e13i	−1.13286	−	1.96217i
$823$	7.43041e12	−	1.28699e13i	0.564565	−	0.977855i	−0.432525	−	0.901622i	$-0.642377\pi$
$823$	7.43041e12	−	1.28699e13i	0.564565	−	0.977855i	0.997090	−	0.0762329i	$-0.0242893\pi$
$824$	4.20655e12			0.317873
$825$	−1.78346e13			−1.34036
$826$	−3.53790e12	+	6.12781e12i	−0.264445	+	0.458032i
$827$	−1.08980e13	+	1.88760e13i	−0.810165	+	1.40325i	0.102583	+	0.994724i	$0.467289\pi$
$827$	−1.08980e13	+	1.88760e13i	−0.810165	+	1.40325i	−0.912748	+	0.408523i	$0.866044\pi$
$828$	−2.60213e12			−0.192394
$829$	−1.97321e12			−0.145104			−0.0725519	−	0.997365i	$-0.523114\pi$
$829$	−1.97321e12			−0.145104			−0.0725519	+	0.997365i	$0.523114\pi$
$830$	−4.68273e12	+	8.11072e12i	−0.342490	+	0.593210i
$831$	8.10183e12	+	1.40328e13i	0.589357	+	1.02080i
$832$	−1.41437e12	+	2.44976e12i	−0.102331	+	0.177243i
$833$	−3.07942e11	−	5.33371e11i	−0.0221598	−	0.0383819i
$834$	3.19318e12	+	5.53076e12i	0.228548	+	0.395856i
$835$	5.03194e12			0.358217
$836$	−1.77121e12	−	1.20240e13i	−0.125413	−	0.851376i
$837$	−3.35170e12			−0.236048
$838$	−3.78583e12	−	6.55726e12i	−0.265194	−	0.459329i
$839$	1.51718e11	+	2.62784e11i	0.0105708	+	0.0183092i	0.871262	−	0.490817i	$-0.163302\pi$
$839$	1.51718e11	+	2.62784e11i	0.0105708	+	0.0183092i	−0.860692	+	0.509127i	$0.829968\pi$
$840$	−1.32957e12	+	2.30289e12i	−0.0921415	+	0.159594i
$841$	−1.84099e13	−	3.18869e13i	−1.26902	−	2.19801i
$842$	−9.51244e12	+	1.64760e13i	−0.652210	+	1.12966i
$843$	−4.38210e13			−2.98853
$844$	−6.45555e12			−0.437917
$845$	−9.08559e12	+	1.57367e13i	−0.613053	+	1.06184i
$846$	9.91527e12	−	1.71738e13i	0.665485	−	1.15265i
$847$	1.26159e13			0.842256
$848$	−6.57121e11			−0.0436379
$849$	−9.82592e12	+	1.70190e13i	−0.649066	+	1.12422i
$850$	1.36759e11	+	2.36874e11i	0.00898609	+	0.0155644i
$851$	2.22801e12	−	3.85903e12i	0.145625	−	0.252229i
$852$	3.18809e12	+	5.52193e12i	0.207277	+	0.359015i
$853$	−5.78285e12	−	1.00162e13i	−0.374000	−	0.647787i	0.616177	−	0.787608i	$-0.288681\pi$
$853$	−5.78285e12	−	1.00162e13i	−0.374000	−	0.647787i	−0.990177	+	0.139821i	$0.955347\pi$
$854$	3.12421e12			0.200993
$855$	1.58259e13	−	1.25344e13i	1.01280	−	0.802149i
$856$	−9.28172e12			−0.590876
$857$	9.76279e12	+	1.69097e13i	0.618245	+	1.07083i	0.989806	+	0.142423i	$0.0454892\pi$
$857$	9.76279e12	+	1.69097e13i	0.618245	+	1.07083i	−0.371561	+	0.928408i	$0.621177\pi$
$858$	2.63275e13	+	4.56006e13i	1.65851	+	2.87262i
$859$	−7.56647e12	+	1.31055e13i	−0.474159	+	0.821268i	−0.999562	−	0.0295855i	$-0.990581\pi$
$859$	−7.56647e12	+	1.31055e13i	−0.474159	+	0.821268i	0.525403	+	0.850854i	$0.323915\pi$
$860$	9.87115e11	+	1.70973e12i	0.0615354	+	0.106582i
$861$	−5.15655e12	+	8.93141e12i	−0.319776	+	0.553867i
$862$	−4.11849e12			−0.254071
$863$	6.60494e12			0.405341			0.202670	−	0.979247i	$-0.435038\pi$
$863$	6.60494e12			0.405341			0.202670	+	0.979247i	$0.435038\pi$
$864$	−1.85825e12	+	3.21859e12i	−0.113447	+	0.196496i
$865$	−6.48535e12	+	1.12330e13i	−0.393877	+	0.682216i
$866$	−1.53844e13			−0.929503
$867$	2.76136e13			1.65973
$868$	−3.30038e11	+	5.71643e11i	−0.0197345	+	0.0341811i
$869$	−1.05197e13	−	1.82207e13i	−0.625770	−	1.08387i
$870$	−1.36465e13	+	2.36364e13i	−0.807577	+	1.39876i
$871$	−5.02833e12	−	8.70932e12i	−0.296034	−	0.512746i
$872$	−2.38684e12	−	4.13412e12i	−0.139797	−	0.242136i
$873$	−4.16103e12			−0.242458
$874$	2.07754e12	−	1.64544e12i	0.120433	−	0.0953850i
$875$	−7.96931e12			−0.459605
$876$	2.29707e12	+	3.97863e12i	0.131797	+	0.228279i
$877$	−1.45598e13	−	2.52183e13i	−0.831106	−	1.43952i	−0.897162	−	0.441702i	$-0.854375\pi$
$877$	−1.45598e13	−	2.52183e13i	−0.831106	−	1.43952i	0.0660559	−	0.997816i	$-0.478958\pi$
$878$	−8.39859e12	+	1.45468e13i	−0.476959	+	0.826117i
$879$	−1.73236e13	−	3.00054e13i	−0.978788	−	1.69531i
$880$	2.79204e12	−	4.83595e12i	0.156946	−	0.271838i
$881$	2.09230e12			0.117013			0.0585063	−	0.998287i	$-0.481366\pi$
$881$	2.09230e12			0.117013			0.0585063	+	0.998287i	$0.481366\pi$
$882$	1.83607e13			1.02160
$883$	1.24685e13	−	2.15961e13i	0.690225	−	1.19550i	−0.281539	−	0.959550i	$-0.590845\pi$
$883$	1.24685e13	−	2.15961e13i	0.690225	−	1.19550i	0.971764	−	0.235955i	$-0.0758218\pi$
$884$	4.03769e11	−	6.99348e11i	0.0222381	−	0.0385175i
$885$	3.86179e13			2.11614
$886$	1.62997e13			0.888646
$887$	1.61945e13	−	2.80496e13i	0.878436	−	1.52150i	0.0253782	−	0.999678i	$-0.491921\pi$
$887$	1.61945e13	−	2.80496e13i	0.878436	−	1.52150i	0.853057	−	0.521817i	$-0.174746\pi$
$888$	−7.30929e12	−	1.26601e13i	−0.394472	−	0.683246i
$889$	3.67637e12	−	6.36767e12i	0.197407	−	0.341918i
$890$	1.15903e12	+	2.00750e12i	0.0619214	+	0.107251i
$891$	5.91792e12	+	1.02501e13i	0.314572	+	0.544854i
$892$	1.20454e13			0.637059
$893$	2.94337e12	+	1.99813e13i	0.154886	+	1.05146i
$894$	3.91406e13			2.04931
$895$	−1.37862e13	−	2.38784e13i	−0.718193	−	1.24395i
$896$	3.65961e11	+	6.33862e11i	0.0189692	+	0.0328556i
$897$	−5.74089e12	+	9.94352e12i	−0.296083	+	0.512831i
$898$	9.99554e12	+	1.73128e13i	0.512936	+	0.888430i
$899$	−3.38745e12	+	5.86723e12i	−0.172963	+	0.299581i
$900$	−8.15410e12			−0.414271
$901$	1.87592e11			0.00948317
$902$	1.08285e13	−	1.87555e13i	0.544677	−	0.943407i
$903$	−2.40840e12	+	4.17147e12i	−0.120541	+	0.208782i
$904$	−3.00089e11			−0.0149449
$905$	−1.79149e13			−0.887763
$906$	−9.48009e11	+	1.64200e12i	−0.0467450	+	0.0809648i
$907$	6.74926e12	+	1.16901e13i	0.331149	+	0.573566i	0.982737	−	0.185006i	$-0.0592305\pi$
$907$	6.74926e12	+	1.16901e13i	0.331149	+	0.573566i	−0.651589	+	0.758572i	$0.725897\pi$
$908$	1.60085e12	−	2.77275e12i	0.0781562	−	0.135371i
$909$	2.08289e13	+	3.60767e13i	1.01188	+	1.75263i
$910$	3.74954e12	+	6.49440e12i	0.181256	+	0.313944i
$911$	1.35873e13			0.653581			0.326790	−	0.945097i	$-0.394033\pi$
$911$	1.35873e13			0.653581			0.326790	+	0.945097i	$0.394033\pi$
$912$	−1.26706e12	−	8.60155e12i	−0.0606484	−	0.411718i
$913$	4.79842e13			2.28549
$914$	4.10041e12	+	7.10212e12i	0.194343	+	0.336613i
$915$	−8.52559e12	−	1.47668e13i	−0.402096	−	0.696450i
$916$	−7.41169e12	+	1.28374e13i	−0.347847	+	0.602488i
$917$	3.41311e12	+	5.91168e12i	0.159400	+	0.276089i
$918$	5.30487e11	−	9.18830e11i	0.0246537	−	0.0427015i
$919$	1.57099e13			0.726530			0.363265	−	0.931686i	$-0.381662\pi$
$919$	1.57099e13			0.726530			0.363265	+	0.931686i	$0.381662\pi$
$920$	1.21764e12			0.0560370
$921$	−2.77639e13	+	4.80885e13i	−1.27149	+	2.20228i
$922$	7.03561e12	−	1.21860e13i	0.320636	−	0.555358i
$923$	1.79815e13			0.815489
$924$	1.36242e13			0.614876
$925$	6.98175e12	−	1.20927e13i	0.313564	−	0.543109i
$926$	−1.03853e13	−	1.79879e13i	−0.464163	−	0.803953i
$927$	1.79001e13	−	3.10039e13i	0.796154	−	1.37898i
$928$	3.75615e12	+	6.50584e12i	0.166256	+	0.287963i
$929$	4.13991e12	+	7.17053e12i	0.182356	+	0.315850i	0.942682	−	0.333691i	$-0.108294\pi$
$929$	4.13991e12	+	7.17053e12i	0.182356	+	0.315850i	−0.760326	+	0.649541i	$0.774961\pi$
$930$	3.60253e12			0.157919
$931$	−1.46591e13	+	1.16102e13i	−0.639491	+	0.506486i
$932$	6.70625e12			0.291144
$933$	−2.67778e13	−	4.63806e13i	−1.15693	−	2.00387i
$934$	−1.84073e12	−	3.18825e12i	−0.0791462	−	0.137085i
$935$	−7.97059e11	+	1.38055e12i	−0.0341066	+	0.0590744i
$936$	1.20371e13	+	2.08489e13i	0.512603	+	0.887854i
$937$	−4.10253e10	+	7.10579e10i	−0.00173870	+	0.00301151i	−0.866893	−	0.498493i	$-0.833887\pi$
$937$	−4.10253e10	+	7.10579e10i	−0.00173870	+	0.00301151i	0.865155	+	0.501505i	$0.167220\pi$
$938$	−2.60211e12			−0.109752
$939$	−4.75051e13			−1.99409
$940$	−4.63976e12	+	8.03631e12i	−0.193830	+	0.335723i
$941$	1.27297e13	−	2.20486e13i	0.529256	−	0.916699i	−0.470161	−	0.882580i	$-0.655804\pi$
$941$	1.27297e13	−	2.20486e13i	0.529256	−	0.916699i	0.999418	−	0.0341186i	$-0.0108624\pi$
$942$	−4.99439e13			−2.06658
$943$	4.72245e12			0.194476
$944$	5.31472e12	−	9.20537e12i	0.217824	−	0.377283i
$945$	4.92629e12	+	8.53259e12i	0.200945	+	0.348047i
$946$	5.05751e12	−	8.75987e12i	0.205318	−	0.355621i
$947$	6.65449e12	+	1.15259e13i	0.268868	+	0.465694i	0.968570	−	0.248742i	$-0.0800170\pi$
$947$	6.65449e12	+	1.15259e13i	0.268868	+	0.465694i	−0.699702	+	0.714435i	$0.746684\pi$
$948$	−7.52542e12	−	1.30344e13i	−0.302617	−	0.524148i
$949$	1.29559e13			0.518527
$950$	6.51022e12	−	5.15619e12i	0.259322	−	0.205387i
$951$	−2.23416e13			−0.885731
$952$	−1.04473e11	−	1.80953e11i	−0.00412228	−	0.00714000i
$953$	2.40498e12	+	4.16555e12i	0.0944483	+	0.163589i	0.909378	−	0.415970i	$-0.136558\pi$
$953$	2.40498e12	+	4.16555e12i	0.0944483	+	0.163589i	−0.814930	+	0.579559i	$0.803225\pi$
$954$	−2.79624e12	+	4.84324e12i	−0.109297	+	0.189308i
$955$	2.46152e12	+	4.26347e12i	0.0957607	+	0.165862i
$956$	−4.68029e12	+	8.10649e12i	−0.181222	+	0.313886i
$957$	1.39836e14			5.38910
$958$	−3.22392e13			−1.23663
$959$	−1.08202e13	+	1.87412e13i	−0.413097	+	0.715505i
$960$	1.99732e12	−	3.45946e12i	0.0758975	−	0.131458i
$961$	−2.55454e13			−0.966178
$962$	−4.12260e13			−1.55197
$963$	−3.94965e13	+	6.84099e13i	−1.47993	+	2.56331i
$964$	1.18318e13	+	2.04932e13i	0.441268	+	0.764299i
$965$	−5.71752e12	+	9.90303e12i	−0.212244	+	0.367617i
$966$	1.48543e12	+	2.57283e12i	0.0548850	+	0.0950636i
$967$	−7.14767e12	−	1.23801e13i	−0.262873	−	0.455309i	0.704131	−	0.710070i	$-0.251337\pi$
$967$	−7.14767e12	−	1.23801e13i	−0.262873	−	0.455309i	−0.967004	+	0.254761i	$0.918003\pi$
$968$	−1.89520e13			−0.693770
$969$	3.61715e11	+	2.45554e12i	0.0131798	+	0.0894725i
$970$	1.94712e12			0.0706187
$971$	1.48848e13	+	2.57812e13i	0.537348	+	0.930714i	0.999046	+	0.0436765i	$0.0139071\pi$
$971$	1.48848e13	+	2.57812e13i	0.537348	+	0.930714i	−0.461698	+	0.887037i	$0.652760\pi$
$972$	−4.69622e12	−	8.13409e12i	−0.168752	−	0.292288i
$973$	2.33003e12	−	4.03573e12i	0.0833400	−	0.144349i
$974$	5.41801e12	+	9.38426e12i	0.192896	+	0.334106i
$975$	−1.79898e13	+	3.11592e13i	−0.637537	+	1.10425i
$976$	−4.69328e12			−0.165559
$977$	1.26774e13			0.445148			0.222574	−	0.974916i	$-0.428554\pi$
$977$	1.26774e13			0.445148			0.222574	+	0.974916i	$0.428554\pi$
$978$	1.13643e13	−	1.96836e13i	0.397209	−	0.687986i
$979$	5.93833e12	−	1.02855e13i	0.206606	−	0.357852i
$980$	−8.59171e12			−0.297552
$981$	−4.06268e13			−1.40056
$982$	9.53642e12	−	1.65176e13i	0.327253	−	0.566819i
$983$	6.51883e11	+	1.12909e12i	0.0222679	+	0.0385691i	0.876945	−	0.480591i	$-0.159578\pi$
$983$	6.51883e11	+	1.12909e12i	0.0222679	+	0.0385691i	−0.854677	+	0.519161i	$0.826245\pi$
$984$	7.74631e12	−	1.34170e13i	0.263401	−	0.456224i
$985$	−1.08742e13	−	1.88346e13i	−0.368073	−	0.637520i
$986$	−1.07229e12	−	1.85726e12i	−0.0361298	−	0.0625787i
$987$	−2.26405e13			−0.759380
$988$	−2.27941e13	−	9.03414e12i	−0.761054	−	0.301634i
$989$	2.20565e12			0.0733083
$990$	−2.37619e13	−	4.11568e13i	−0.786180	−	1.36170i
$991$	−1.35987e13	−	2.35537e13i	−0.447885	−	0.775759i	0.550363	−	0.834925i	$-0.314489\pi$
$991$	−1.35987e13	−	2.35537e13i	−0.447885	−	0.775759i	−0.998248	+	0.0591660i	$0.981156\pi$
$992$	4.95792e11	−	8.58737e11i	0.0162554	−	0.0281551i
$993$	1.19851e13	+	2.07587e13i	0.391173	+	0.677531i
$994$	2.32631e12	−	4.02928e12i	0.0755838	−	0.130915i
$995$	−1.20346e13			−0.389248
$996$	3.43261e13			1.10524
$997$	−4.10329e12	+	7.10711e12i	−0.131524	+	0.227806i	−0.924264	−	0.381754i	$-0.875320\pi$
$997$	−4.10329e12	+	7.10711e12i	−0.131524	+	0.227806i	0.792740	+	0.609559i	$0.208654\pi$
$998$	−1.21193e13	+	2.09913e13i	−0.386715	+	0.669809i
$999$	−5.41643e13			−1.72055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.a.7.7	✓	14
19.11	even	3	inner	38.10.c.a.11.7	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.a.7.7	✓	14	1.1	even	1	trivial
38.10.c.a.11.7	yes	14	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(116.772 + 202.254i) q^{3} +(-128.000 + 221.703i) q^{4} +(-509.754 - 882.920i) q^{5} +(-1868.34 + 3236.07i) q^{6} +2726.62 q^{7} -4096.00 q^{8} +(-17429.7 + 30189.1i) q^{9} +O(q^{10})\)	\(q+(8.00000 + 13.8564i) q^{2} +(116.772 + 202.254i) q^{3} +(-128.000 + 221.703i) q^{4} +(-509.754 - 882.920i) q^{5} +(-1868.34 + 3236.07i) q^{6} +2726.62 q^{7} -4096.00 q^{8} +(-17429.7 + 30189.1i) q^{9} +(8156.07 - 14126.7i) q^{10} -83575.7 q^{11} -59787.0 q^{12} +(-84303.0 + 146017. i) q^{13} +(21812.9 + 37781.1i) q^{14} +(119050. - 206200. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(9354.48 + 16202.4i) q^{17} -557750. q^{18} +(445307. - 352689. i) q^{19} +260994. q^{20} +(318391. + 551470. i) q^{21} +(-668606. - 1.15806e6i) q^{22} +(145794. - 252523. i) q^{23} +(-478296. - 828433. i) q^{24} +(456863. - 791311. i) q^{25} -2.69769e6 q^{26} -3.54434e6 q^{27} +(-349007. + 604498. i) q^{28} +(-3.58214e6 + 6.20445e6i) q^{29} +3.80959e6 q^{30} +945649. q^{31} +(524288. - 908093. i) q^{32} +(-9.75926e6 - 1.69035e7i) q^{33} +(-149672. + 259239. i) q^{34} +(-1.38991e6 - 2.40739e6i) q^{35} +(-4.46200e6 - 7.72841e6i) q^{36} +1.52819e7 q^{37} +(8.44946e6 + 3.34884e6i) q^{38} -3.93767e7 q^{39} +(2.08795e6 + 3.61644e6i) q^{40} +(8.09782e6 + 1.40258e7i) q^{41} +(-5.09426e6 + 8.82352e6i) q^{42} +(3.78213e6 + 6.55085e6i) q^{43} +(1.06977e7 - 1.85289e7i) q^{44} +3.55394e7 q^{45} +4.66541e6 q^{46} +(-1.77773e7 + 3.07911e7i) q^{47} +(7.65274e6 - 1.32549e7i) q^{48} -3.29192e7 q^{49} +1.46196e7 q^{50} +(-2.18467e6 + 3.78397e6i) q^{51} +(-2.15816e7 - 3.73804e7i) q^{52} +(5.01344e6 - 8.68353e6i) q^{53} +(-2.83547e7 - 4.91118e7i) q^{54} +(4.26031e7 + 7.37907e7i) q^{55} -1.11682e7 q^{56} +(1.23332e8 + 4.88811e7i) q^{57} -1.14628e8 q^{58} +(8.10962e7 + 1.40463e8i) q^{59} +(3.04767e7 + 5.27872e7i) q^{60} +(3.58069e7 - 6.20193e7i) q^{61} +(7.56519e6 + 1.31033e7i) q^{62} +(-4.75241e7 + 8.23142e7i) q^{63} +1.67772e7 q^{64} +1.71895e8 q^{65} +(1.56148e8 - 2.70457e8i) q^{66} +(-2.98230e7 + 5.16549e7i) q^{67} -4.78949e6 q^{68} +6.80983e7 q^{69} +(2.22385e7 - 3.85182e7i) q^{70} +(-5.33240e7 - 9.23599e7i) q^{71} +(7.13920e7 - 1.23655e8i) q^{72} +(-3.84208e7 - 6.65468e7i) q^{73} +(1.22255e8 + 2.11753e8i) q^{74} +2.13395e8 q^{75} +(2.11928e7 + 1.43870e8i) q^{76} -2.27879e8 q^{77} +(-3.15014e8 - 5.45620e8i) q^{78} +(1.25870e8 + 2.18014e8i) q^{79} +(-3.34073e7 + 5.78631e7i) q^{80} +(-7.08092e7 - 1.22645e8i) q^{81} +(-1.29565e8 + 2.24413e8i) q^{82} -5.74140e8 q^{83} -1.63016e8 q^{84} +(9.53697e6 - 1.65185e7i) q^{85} +(-6.05142e7 + 1.04814e8i) q^{86} -1.67317e9 q^{87} +3.42326e8 q^{88} +(-7.10534e7 + 1.23068e8i) q^{89} +(2.84315e8 + 4.92449e8i) q^{90} +(-2.29862e8 + 3.98133e8i) q^{91} +(3.73233e7 + 6.46458e7i) q^{92} +(1.10425e8 + 1.91261e8i) q^{93} -5.68873e8 q^{94} +(-5.38394e8 - 2.13385e8i) q^{95} +2.44888e8 q^{96} +(5.96831e7 + 1.03374e8i) q^{97} +(-2.63353e8 - 4.56141e8i) q^{98} +(1.45670e9 - 2.52308e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9}+O(q^{10}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9} - 14544 q^{10} + 15656 q^{11} - 84480 q^{12} + 6423 q^{13} + 29536 q^{14} - 227715 q^{15} - 458752 q^{16} + 313667 q^{17} - 1673152 q^{18} + 1134224 q^{19} - 465408 q^{20} - 1227046 q^{21} + 125248 q^{22} + 3449345 q^{23} - 675840 q^{24} - 2398648 q^{25} + 205536 q^{26} - 1873854 q^{27} - 472576 q^{28} - 7002615 q^{29} - 7286880 q^{30} - 18666588 q^{31} + 7340032 q^{32} - 13827668 q^{33} - 5018672 q^{34} + 2584932 q^{35} - 13385216 q^{36} - 6866080 q^{37} + 22760176 q^{38} + 4568410 q^{39} - 3723264 q^{40} + 3564107 q^{41} + 19632736 q^{42} + 19837521 q^{43} - 2003968 q^{44} - 77788260 q^{45} + 110379040 q^{46} + 60353825 q^{47} + 10813440 q^{48} - 79579650 q^{49} - 76756736 q^{50} - 161350373 q^{51} + 1644288 q^{52} + 54744235 q^{53} - 14990832 q^{54} + 143199990 q^{55} - 15122432 q^{56} + 330686241 q^{57} - 224083680 q^{58} + 164456585 q^{59} - 58295040 q^{60} + 49328881 q^{61} - 149332704 q^{62} + 138012360 q^{63} + 234881024 q^{64} + 788015550 q^{65} + 221242688 q^{66} - 171522309 q^{67} - 160597504 q^{68} + 630323350 q^{69} - 41358912 q^{70} - 74596055 q^{71} + 214163456 q^{72} + 58695287 q^{73} - 54928640 q^{74} - 1115757144 q^{75} + 73801472 q^{76} - 965186644 q^{77} + 36547280 q^{78} + 121854617 q^{79} + 59572224 q^{80} - 368486747 q^{81} - 57025712 q^{82} - 732607256 q^{83} + 628247552 q^{84} + 634697565 q^{85} - 317400336 q^{86} - 2979036210 q^{87} - 64126976 q^{88} - 1652463181 q^{89} - 622306080 q^{90} - 1141270092 q^{91} + 883032320 q^{92} - 1839612746 q^{93} + 1931322400 q^{94} + 2397253503 q^{95} + 346030080 q^{96} + 248805607 q^{97} - 636637200 q^{98} + 520684712 q^{99}+O(q^{100}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9 - 14544 * q^10 + 15656 * q^11 - 84480 * q^12 + 6423 * q^13 + 29536 * q^14 - 227715 * q^15 - 458752 * q^16 + 313667 * q^17 - 1673152 * q^18 + 1134224 * q^19 - 465408 * q^20 - 1227046 * q^21 + 125248 * q^22 + 3449345 * q^23 - 675840 * q^24 - 2398648 * q^25 + 205536 * q^26 - 1873854 * q^27 - 472576 * q^28 - 7002615 * q^29 - 7286880 * q^30 - 18666588 * q^31 + 7340032 * q^32 - 13827668 * q^33 - 5018672 * q^34 + 2584932 * q^35 - 13385216 * q^36 - 6866080 * q^37 + 22760176 * q^38 + 4568410 * q^39 - 3723264 * q^40 + 3564107 * q^41 + 19632736 * q^42 + 19837521 * q^43 - 2003968 * q^44 - 77788260 * q^45 + 110379040 * q^46 + 60353825 * q^47 + 10813440 * q^48 - 79579650 * q^49 - 76756736 * q^50 - 161350373 * q^51 + 1644288 * q^52 + 54744235 * q^53 - 14990832 * q^54 + 143199990 * q^55 - 15122432 * q^56 + 330686241 * q^57 - 224083680 * q^58 + 164456585 * q^59 - 58295040 * q^60 + 49328881 * q^61 - 149332704 * q^62 + 138012360 * q^63 + 234881024 * q^64 + 788015550 * q^65 + 221242688 * q^66 - 171522309 * q^67 - 160597504 * q^68 + 630323350 * q^69 - 41358912 * q^70 - 74596055 * q^71 + 214163456 * q^72 + 58695287 * q^73 - 54928640 * q^74 - 1115757144 * q^75 + 73801472 * q^76 - 965186644 * q^77 + 36547280 * q^78 + 121854617 * q^79 + 59572224 * q^80 - 368486747 * q^81 - 57025712 * q^82 - 732607256 * q^83 + 628247552 * q^84 + 634697565 * q^85 - 317400336 * q^86 - 2979036210 * q^87 - 64126976 * q^88 - 1652463181 * q^89 - 622306080 * q^90 - 1141270092 * q^91 + 883032320 * q^92 - 1839612746 * q^93 + 1931322400 * q^94 + 2397253503 * q^95 + 346030080 * q^96 + 248805607 * q^97 - 636637200 * q^98 + 520684712 * q^99

Introduction

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