LMFDB - Embedded newform 177.4.e.b.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,4,Mod(4,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("177.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.e (of order $29$, degree $28$, 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:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$420$
Relative dimension:	$15$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			7.3
Character	$\chi$	$=$	177.7
Dual form			177.4.e.b.76.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23273 - 3.29303i) q^{2} +(0.162417 - 2.99560i) q^{3} +(-2.89786 + 7.27309i) q^{4} +(3.07784 - 1.42396i) q^{5} +(-10.2272 + 6.15353i) q^{6} +(3.58463 - 12.9107i) q^{7} +(-0.663884 + 0.146132i) q^{8} +(-8.94724 - 0.973071i) q^{9} +O(q^{10})$	\(q+(-2.23273 - 3.29303i) q^{2} +(0.162417 - 2.99560i) q^{3} +(-2.89786 + 7.27309i) q^{4} +(3.07784 - 1.42396i) q^{5} +(-10.2272 + 6.15353i) q^{6} +(3.58463 - 12.9107i) q^{7} +(-0.663884 + 0.146132i) q^{8} +(-8.94724 - 0.973071i) q^{9} +(-11.5611 - 6.95609i) q^{10} +(-4.93694 + 4.67652i) q^{11} +(21.3166 + 9.86211i) q^{12} +(-50.9188 + 5.53775i) q^{13} +(-50.5188 + 17.0218i) q^{14} +(-3.76572 - 9.45124i) q^{15} +(47.4349 + 44.9327i) q^{16} +(-24.1827 - 87.0982i) q^{17} +(16.7724 + 31.6362i) q^{18} +(-122.442 + 93.0779i) q^{19} +(1.43743 + 26.5118i) q^{20} +(-38.0930 - 12.8350i) q^{21} +(26.4228 + 5.81609i) q^{22} +(15.5543 - 29.3385i) q^{23} +(0.329927 + 2.01247i) q^{24} +(-73.4779 + 86.5048i) q^{25} +(131.924 + 155.313i) q^{26} +(-4.36811 + 26.6443i) q^{27} +(83.5128 + 63.4848i) q^{28} +(104.116 - 153.560i) q^{29} +(-22.7154 + 33.5027i) q^{30} +(220.087 + 167.306i) q^{31} +(41.1757 - 251.160i) q^{32} +(13.2071 + 15.5486i) q^{33} +(-232.824 + 274.101i) q^{34} +(-7.35136 - 44.8413i) q^{35} +(33.0051 - 62.2543i) q^{36} +(52.9260 + 11.6499i) q^{37} +(579.888 + 195.387i) q^{38} +(8.31883 + 153.432i) q^{39} +(-1.83524 + 1.39511i) q^{40} +(149.989 + 282.909i) q^{41} +(42.7853 + 154.099i) q^{42} +(-198.932 - 188.438i) q^{43} +(-19.7062 - 49.4587i) q^{44} +(-28.9238 + 9.74555i) q^{45} +(-131.341 + 14.2842i) q^{46} +(-384.405 - 177.845i) q^{47} +(142.305 - 134.798i) q^{48} +(140.066 + 84.2749i) q^{49} +(448.919 + 48.8229i) q^{50} +(-264.839 + 58.2955i) q^{51} +(107.279 - 386.385i) q^{52} +(-398.892 + 240.005i) q^{53} +(97.4934 - 45.1052i) q^{54} +(-8.53592 + 21.4235i) q^{55} +(-0.493118 + 9.09503i) q^{56} +(258.938 + 381.905i) q^{57} -738.140 q^{58} +(423.250 - 161.983i) q^{59} +79.6523 q^{60} +(-227.448 - 335.460i) q^{61} +(59.5482 - 1098.30i) q^{62} +(-44.6356 + 112.027i) q^{63} +(-444.623 + 205.704i) q^{64} +(-148.834 + 89.5505i) q^{65} +(21.7142 - 78.2074i) q^{66} +(-834.378 + 183.661i) q^{67} +(703.551 + 76.5158i) q^{68} +(-85.3601 - 51.3595i) q^{69} +(-131.250 + 124.327i) q^{70} +(-569.238 - 263.357i) q^{71} +(6.08213 - 0.661471i) q^{72} +(-212.801 + 71.7009i) q^{73} +(-79.8060 - 200.298i) q^{74} +(247.200 + 234.160i) q^{75} +(-322.144 - 1160.26i) q^{76} +(42.6799 + 80.5028i) q^{77} +(486.682 - 369.966i) q^{78} +(-45.8392 - 845.455i) q^{79} +(209.979 + 70.7502i) q^{80} +(79.1063 + 17.4126i) q^{81} +(596.744 - 1125.58i) q^{82} +(-112.562 - 686.595i) q^{83} +(203.739 - 239.860i) q^{84} +(-198.455 - 233.639i) q^{85} +(-176.372 + 1075.82i) q^{86} +(-443.093 - 336.831i) q^{87} +(2.59417 - 3.82611i) q^{88} +(-267.085 + 393.922i) q^{89} +(96.6713 + 73.4876i) q^{90} +(-111.029 + 677.247i) q^{91} +(168.307 + 198.147i) q^{92} +(536.927 - 632.120i) q^{93} +(272.625 + 1662.94i) q^{94} +(-244.317 + 460.831i) q^{95} +(-745.689 - 164.139i) q^{96} +(-466.601 - 157.216i) q^{97} +(-35.2097 - 649.404i) q^{98} +(48.7226 - 37.0379i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9}+O(q^{10}) $ 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9} - 754 q^{10} + 64 q^{11} - 168 q^{12} + 90 q^{13} + 1024 q^{14} - 42 q^{15} - 172 q^{16} + 96 q^{17} + 18 q^{18} + 16 q^{19} - 178 q^{20} - 243 q^{21} - 604 q^{22} + 48 q^{23} + 198 q^{24} - 173 q^{25} + 156 q^{26} - 405 q^{27} + 84 q^{28} - 50 q^{29} + 174 q^{30} + 222 q^{31} - 45 q^{32} + 192 q^{33} - 64 q^{34} - 132 q^{35} - 504 q^{36} + 30 q^{37} - 108 q^{38} + 270 q^{39} + 6984 q^{40} + 400 q^{41} + 114 q^{42} + 1220 q^{43} + 1180 q^{44} - 126 q^{45} + 4938 q^{46} + 370 q^{47} - 516 q^{48} + 771 q^{49} + 1048 q^{50} + 288 q^{51} - 1964 q^{52} - 822 q^{53} + 54 q^{54} - 2342 q^{55} - 13824 q^{56} + 48 q^{57} - 13150 q^{58} - 3423 q^{59} - 534 q^{60} - 2182 q^{61} + 845 q^{62} + 54 q^{63} - 8018 q^{64} + 4140 q^{65} - 1812 q^{66} + 506 q^{67} + 4826 q^{68} - 3684 q^{69} + 6882 q^{70} + 5874 q^{71} + 594 q^{72} + 206 q^{73} + 11124 q^{74} - 867 q^{75} + 16940 q^{76} + 9940 q^{77} + 468 q^{78} - 1762 q^{79} - 28954 q^{80} - 1215 q^{81} + 3770 q^{82} - 1216 q^{83} - 8013 q^{84} - 420 q^{85} - 2256 q^{86} + 5940 q^{87} + 13458 q^{88} - 1580 q^{89} + 522 q^{90} - 12204 q^{91} + 4562 q^{92} + 666 q^{93} + 176 q^{94} - 28456 q^{95} + 2040 q^{96} + 2574 q^{97} + 50690 q^{98} + 576 q^{99}+O(q^{100}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9 - 754 * q^10 + 64 * q^11 - 168 * q^12 + 90 * q^13 + 1024 * q^14 - 42 * q^15 - 172 * q^16 + 96 * q^17 + 18 * q^18 + 16 * q^19 - 178 * q^20 - 243 * q^21 - 604 * q^22 + 48 * q^23 + 198 * q^24 - 173 * q^25 + 156 * q^26 - 405 * q^27 + 84 * q^28 - 50 * q^29 + 174 * q^30 + 222 * q^31 - 45 * q^32 + 192 * q^33 - 64 * q^34 - 132 * q^35 - 504 * q^36 + 30 * q^37 - 108 * q^38 + 270 * q^39 + 6984 * q^40 + 400 * q^41 + 114 * q^42 + 1220 * q^43 + 1180 * q^44 - 126 * q^45 + 4938 * q^46 + 370 * q^47 - 516 * q^48 + 771 * q^49 + 1048 * q^50 + 288 * q^51 - 1964 * q^52 - 822 * q^53 + 54 * q^54 - 2342 * q^55 - 13824 * q^56 + 48 * q^57 - 13150 * q^58 - 3423 * q^59 - 534 * q^60 - 2182 * q^61 + 845 * q^62 + 54 * q^63 - 8018 * q^64 + 4140 * q^65 - 1812 * q^66 + 506 * q^67 + 4826 * q^68 - 3684 * q^69 + 6882 * q^70 + 5874 * q^71 + 594 * q^72 + 206 * q^73 + 11124 * q^74 - 867 * q^75 + 16940 * q^76 + 9940 * q^77 + 468 * q^78 - 1762 * q^79 - 28954 * q^80 - 1215 * q^81 + 3770 * q^82 - 1216 * q^83 - 8013 * q^84 - 420 * q^85 - 2256 * q^86 + 5940 * q^87 + 13458 * q^88 - 1580 * q^89 + 522 * q^90 - 12204 * q^91 + 4562 * q^92 + 666 * q^93 + 176 * q^94 - 28456 * q^95 + 2040 * q^96 + 2574 * q^97 + 50690 * q^98 + 576 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{9}{29}\right)$	$1$

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 $

$2$	−2.23273	−	3.29303i	−0.789389	−	1.16426i	−0.983076	−	0.183199i	$-0.941355\pi$
$2$	−2.23273	−	3.29303i	−0.789389	−	1.16426i	0.193686	−	0.981063i	$-0.437956\pi$
$3$	0.162417	−	2.99560i	0.0312571	−	0.576504i
$3$	0.162417	−	2.99560i	0.0312571	−	0.576504i
$4$	−2.89786	+	7.27309i	−0.362233	+	0.909136i
$5$	3.07784	−	1.42396i	0.275290	−	0.127363i	−0.277387	−	0.960758i	$-0.589468\pi$
$5$	3.07784	−	1.42396i	0.275290	−	0.127363i	0.552677	+	0.833396i	$0.313606\pi$
$6$	−10.2272	+	6.15353i	−0.695875	+	0.418694i
$7$	3.58463	−	12.9107i	0.193552	−	0.697111i	−0.801521	−	0.597967i	$-0.795976\pi$
$7$	3.58463	−	12.9107i	0.193552	−	0.697111i	0.995073	−	0.0991447i	$-0.0316107\pi$
$8$	−0.663884	+	0.146132i	−0.0293398	+	0.00645818i
$9$	−8.94724	−	0.973071i	−0.331379	−	0.0360397i
$10$	−11.5611	−	6.95609i	−0.365595	−	0.219971i
$11$	−4.93694	+	4.67652i	−0.135322	+	0.128184i	−0.752367	−	0.658744i	$-0.771088\pi$
$11$	−4.93694	+	4.67652i	−0.135322	+	0.128184i	0.617045	+	0.786928i	$0.288330\pi$
$12$	21.3166	+	9.86211i	0.512798	+	0.237246i
$13$	−50.9188	+	5.53775i	−1.08633	+	0.118146i	−0.633721	−	0.773562i	$-0.718473\pi$
$13$	−50.9188	+	5.53775i	−1.08633	+	0.118146i	−0.452612	+	0.891707i	$0.649508\pi$
$14$	−50.5188	+	17.0218i	−0.964408	+	0.324947i
$15$	−3.76572	−	9.45124i	−0.0648203	−	0.162687i
$16$	47.4349	+	44.9327i	0.741170	+	0.702073i
$17$	−24.1827	−	87.0982i	−0.345010	−	1.24261i	−0.908988	−	0.416823i	$-0.863144\pi$
$17$	−24.1827	−	87.0982i	−0.345010	−	1.24261i	0.563978	−	0.825790i	$-0.309270\pi$
$18$	16.7724	+	31.6362i	0.219628	+	0.414262i
$19$	−122.442	+	93.0779i	−1.47843	+	1.12387i	−0.514570	+	0.857448i	$0.672049\pi$
$19$	−122.442	+	93.0779i	−1.47843	+	1.12387i	−0.963856	+	0.266423i	$0.914158\pi$
$20$	1.43743	+	26.5118i	0.0160709	+	0.296411i
$21$	−38.0930	−	12.8350i	−0.395837	−	0.133373i
$22$	26.4228	+	5.81609i	0.256062	+	0.0563634i
$23$	15.5543	−	29.3385i	0.141013	−	0.265978i	−0.802939	−	0.596061i	$-0.796732\pi$
$23$	15.5543	−	29.3385i	0.141013	−	0.265978i	0.943952	+	0.330082i	$0.107077\pi$
$24$	0.329927	+	2.01247i	0.00280609	+	0.0171164i
$25$	−73.4779	+	86.5048i	−0.587823	+	0.692039i
$26$	131.924	+	155.313i	0.995093	+	1.17151i
$27$	−4.36811	+	26.6443i	−0.0311350	+	0.189915i
$28$	83.5128	+	63.4848i	0.563658	+	0.428482i
$29$	104.116	−	153.560i	0.666685	−	0.983287i	−0.332507	−	0.943101i	$-0.607895\pi$
$29$	104.116	−	153.560i	0.666685	−	0.983287i	0.999192	−	0.0401860i	$-0.0127950\pi$
$30$	−22.7154	+	33.5027i	−0.138241	+	0.203891i
$31$	220.087	+	167.306i	1.27512	+	0.969323i	0.999969	+	0.00792288i	$0.00252196\pi$
$31$	220.087	+	167.306i	1.27512	+	0.969323i	0.275154	+	0.961400i	$0.411271\pi$
$32$	41.1757	−	251.160i	0.227466	−	1.38748i
$33$	13.2071	+	15.5486i	0.0696687	+	0.0820203i
$34$	−232.824	+	274.101i	−1.17438	+	1.38259i
$35$	−7.35136	−	44.8413i	−0.0355031	−	0.216559i
$36$	33.0051	−	62.2543i	0.152801	−	0.288214i
$37$	52.9260	+	11.6499i	0.235162	+	0.0517630i	0.330988	−	0.943635i	$-0.392618\pi$
$37$	52.9260	+	11.6499i	0.235162	+	0.0517630i	−0.0958260	+	0.995398i	$0.530549\pi$
$38$	579.888	+	195.387i	2.47553	+	0.834105i
$39$	8.31883	+	153.432i	0.0341559	+	0.629968i
$40$	−1.83524	+	1.39511i	−0.00725442	+	0.00551467i
$41$	149.989	+	282.909i	0.571325	+	1.07763i	0.985855	+	0.167598i	$0.0536010\pi$
$41$	149.989	+	282.909i	0.571325	+	1.07763i	−0.414530	+	0.910035i	$0.636054\pi$
$42$	42.7853	+	154.099i	0.157188	+	0.566142i
$43$	−198.932	−	188.438i	−0.705507	−	0.668292i	0.248310	−	0.968681i	$-0.420125\pi$
$43$	−198.932	−	188.438i	−0.705507	−	0.668292i	−0.953817	+	0.300389i	$0.902884\pi$
$44$	−19.7062	−	49.4587i	−0.0675185	−	0.169459i
$45$	−28.9238	+	9.74555i	−0.0958155	+	0.0322840i
$46$	−131.341	+	14.2842i	−0.420982	+	0.0457846i
$47$	−384.405	−	177.845i	−1.19301	−	0.551943i	−0.280043	−	0.959987i	$-0.590349\pi$
$47$	−384.405	−	177.845i	−1.19301	−	0.551943i	−0.912962	+	0.408044i	$0.866211\pi$
$48$	142.305	−	134.798i	0.427915	−	0.405342i
$49$	140.066	+	84.2749i	0.408355	+	0.245699i
$50$	448.919	+	48.8229i	1.26974	+	0.138092i
$51$	−264.839	+	58.2955i	−0.727154	+	0.160059i
$52$	107.279	−	386.385i	0.286095	−	1.03042i
$53$	−398.892	+	240.005i	−1.03381	+	0.622024i	−0.928084	−	0.372372i	$-0.878545\pi$
$53$	−398.892	+	240.005i	−1.03381	+	0.622024i	−0.105727	+	0.994395i	$0.533717\pi$
$54$	97.4934	−	45.1052i	0.245688	−	0.113668i
$55$	−8.53592	+	21.4235i	−0.0209270	+	0.0525227i
$56$	−0.493118	+	9.09503i	−0.00117671	+	0.0217031i
$57$	258.938	+	381.905i	0.601704	+	0.887447i
$58$	−738.140			−1.67108
$59$	423.250	−	161.983i	0.933940	−	0.357430i
$59$	423.250	−	161.983i	0.933940	−	0.357430i
$60$	79.6523			0.171384
$61$	−227.448	−	335.460i	−0.477405	−	0.704119i	0.510379	−	0.859950i	$-0.329505\pi$
$61$	−227.448	−	335.460i	−0.477405	−	0.704119i	−0.987784	+	0.155830i	$0.950195\pi$
$62$	59.5482	−	1098.30i	0.121978	−	2.24975i
$63$	−44.6356	+	112.027i	−0.0892628	+	0.224033i
$64$	−444.623	+	205.704i	−0.868403	+	0.401766i
$65$	−148.834	+	89.5505i	−0.284009	+	0.170883i
$66$	21.7142	−	78.2074i	0.0404974	−	0.145859i
$67$	−834.378	+	183.661i	−1.52143	+	0.334891i	−0.895525	−	0.445011i	$-0.853200\pi$
$67$	−834.378	+	183.661i	−1.52143	+	0.334891i	−0.625901	+	0.779902i	$0.715269\pi$
$68$	703.551	+	76.5158i	1.25468	+	0.136454i
$69$	−85.3601	−	51.3595i	−0.148930	−	0.0896081i
$70$	−131.250	+	124.327i	−0.224106	+	0.212284i
$71$	−569.238	−	263.357i	−0.951494	−	0.440208i	−0.118171	−	0.992993i	$-0.537703\pi$
$71$	−569.238	−	263.357i	−0.951494	−	0.440208i	−0.833324	+	0.552785i	$0.813565\pi$
$72$	6.08213	−	0.661471i	0.00995536	−	0.00108271i
$73$	−212.801	+	71.7009i	−0.341184	+	0.114958i	−0.484677	−	0.874693i	$-0.661063\pi$
$73$	−212.801	+	71.7009i	−0.341184	+	0.114958i	0.143493	+	0.989651i	$0.454166\pi$
$74$	−79.8060	−	200.298i	−0.125368	−	0.314651i
$75$	247.200	+	234.160i	0.380589	+	0.360513i
$76$	−322.144	−	1160.26i	−0.486217	−	1.75119i
$77$	42.6799	+	80.5028i	0.0631666	+	0.119145i
$78$	486.682	−	369.966i	0.706486	−	0.537056i
$79$	−45.8392	−	845.455i	−0.0652825	−	1.20406i	−0.829275	−	0.558840i	$-0.811247\pi$
$79$	−45.8392	−	845.455i	−0.0652825	−	1.20406i	0.763993	−	0.645225i	$-0.223236\pi$
$80$	209.979	+	70.7502i	0.293455	+	0.0988763i
$81$	79.1063	+	17.4126i	0.108513	+	0.0238856i
$82$	596.744	−	1125.58i	0.803650	−	1.51584i
$83$	−112.562	−	686.595i	−0.148858	−	0.907996i	−0.950621	−	0.310353i	$-0.899553\pi$
$83$	−112.562	−	686.595i	−0.148858	−	0.907996i	0.801763	−	0.597642i	$-0.203896\pi$
$84$	203.739	−	239.860i	0.264640	−	0.311558i
$85$	−198.455	−	233.639i	−0.253240	−	0.298137i
$86$	−176.372	+	1075.82i	−0.221147	+	1.34894i
$87$	−443.093	−	336.831i	−0.546030	−	0.415081i
$88$	2.59417	−	3.82611i	0.00314249	−	0.00463483i
$89$	−267.085	+	393.922i	−0.318101	+	0.469164i	−0.952801	−	0.303594i	$-0.901813\pi$
$89$	−267.085	+	393.922i	−0.318101	+	0.469164i	0.634700	+	0.772758i	$0.281124\pi$
$90$	96.6713	+	73.4876i	0.113223	+	0.0860697i
$91$	−111.029	+	677.247i	−0.127901	+	0.780163i
$92$	168.307	+	198.147i	0.190731	+	0.224546i
$93$	536.927	−	632.120i	0.598675	−	0.704814i
$94$	272.625	+	1662.94i	0.299139	+	1.82467i
$95$	−244.317	+	460.831i	−0.263857	+	0.497687i
$96$	−745.689	−	164.139i	−0.792777	−	0.174503i
$97$	−466.601	−	157.216i	−0.488413	−	0.164566i	0.0643107	−	0.997930i	$-0.479515\pi$
$97$	−466.601	−	157.216i	−0.488413	−	0.164566i	−0.552724	+	0.833364i	$0.686412\pi$
$98$	−35.2097	−	649.404i	−0.0362930	−	0.669385i
$99$	48.7226	−	37.0379i	0.0494627	−	0.0376005i
$100$	−416.229	−	785.090i	−0.416229	−	0.785090i
$101$	−327.113	−	1178.16i	−0.322267	−	1.16070i	−0.930303	−	0.366792i	$-0.880456\pi$
$101$	−327.113	−	1178.16i	−0.322267	−	1.16070i	0.608036	−	0.793910i	$-0.291958\pi$
$102$	783.283	+	741.965i	0.760358	+	0.720250i
$103$	−129.778	−	325.717i	−0.124149	−	0.311591i	0.853745	−	0.520691i	$-0.174326\pi$
$103$	−129.778	−	325.717i	−0.124149	−	0.311591i	−0.977894	+	0.209100i	$0.932947\pi$
$104$	32.9949	−	11.1173i	0.0311098	−	0.0104821i
$105$	−135.521	+	14.7388i	−0.125957	+	0.0136986i
$106$	1680.96	+	777.696i	1.54028	+	0.712609i
$107$	1041.14	−	986.216i	0.940657	−	0.891038i	−0.0535447	−	0.998565i	$-0.517052\pi$
$107$	1041.14	−	986.216i	0.940657	−	0.891038i	0.994202	+	0.107527i	$0.0342933\pi$
$108$	−181.128	−	108.981i	−0.161380	−	0.0970993i
$109$	556.346	+	60.5063i	0.488884	+	0.0531693i	0.349242	−	0.937033i	$-0.386439\pi$
$109$	556.346	+	60.5063i	0.488884	+	0.0531693i	0.139642	+	0.990202i	$0.455405\pi$
$110$	89.6068	−	19.7240i	0.0776698	−	0.0170964i
$111$	43.4945	−	156.653i	0.0371920	−	0.133954i
$112$	750.148	−	451.349i	0.632878	−	0.380790i
$113$	−1075.19	+	497.434i	−0.895088	+	0.414112i	−0.812831	−	0.582499i	$-0.802075\pi$
$113$	−1075.19	+	497.434i	−0.895088	+	0.414112i	−0.0822571	+	0.996611i	$0.526213\pi$
$114$	679.485	−	1705.38i	0.558242	−	1.40108i
$115$	6.09674	−	112.448i	0.00494369	−	0.0911809i
$116$	815.139	+	1202.24i	0.652446	+	0.962286i
$117$	460.971			0.364246
$118$	−1478.42	−	1032.11i	−1.15338	−	0.805199i
$119$	−1211.18			−0.933016
$120$	3.88113	+	5.72424i	0.00295247	+	0.00435457i
$121$	−69.5553	+	1282.87i	−0.0522580	+	0.963841i
$122$	−596.852	+	1497.98i	−0.442921	+	1.11165i
$123$	871.843	−	403.358i	0.639117	−	0.295687i
$124$	−1854.61	+	1115.88i	−1.34314	+	0.808139i
$125$	−216.381	+	779.335i	−0.154830	+	0.557646i
$126$	468.567	−	103.139i	0.331296	−	0.0729238i
$127$	1515.47	+	164.817i	1.05887	+	0.115159i	0.620946	−	0.783854i	$-0.286749\pi$
$127$	1515.47	+	164.817i	1.05887	+	0.115159i	0.437923	+	0.899012i	$0.355714\pi$
$128$	−74.5394	−	44.8489i	−0.0514720	−	0.0309697i
$129$	−596.795	+	565.315i	−0.407325	+	0.385838i
$130$	627.199	+	290.173i	0.423146	+	0.195768i
$131$	−180.254	+	19.6038i	−0.120220	+	0.0130748i	−0.168031	−	0.985782i	$-0.553741\pi$
$131$	−180.254	+	19.6038i	−0.120220	+	0.0130748i	0.0478110	+	0.998856i	$0.484775\pi$
$132$	−151.359	+	50.9988i	−0.0998039	+	0.0336279i
$133$	762.790	+	1914.46i	0.497311	+	1.24816i
$134$	2467.74	+	2337.57i	1.59090	+	1.50698i
$135$	24.4961	+	88.2268i	0.0156169	+	0.0562471i
$136$	28.7823	+	54.2892i	0.0181475	+	0.0342299i
$137$	−919.607	+	699.067i	−0.573484	+	0.435951i	−0.851297	−	0.524684i	$-0.824183\pi$
$137$	−919.607	+	699.067i	−0.573484	+	0.435951i	0.277813	+	0.960635i	$0.410390\pi$
$138$	21.4578	+	395.765i	0.0132363	+	0.244129i
$139$	−1438.71	−	484.759i	−0.877914	−	0.295804i	−0.155976	−	0.987761i	$-0.549852\pi$
$139$	−1438.71	−	484.759i	−0.877914	−	0.295804i	−0.721939	+	0.691957i	$0.756749\pi$
$140$	347.438	+	76.4769i	0.209742	+	0.0461677i
$141$	−595.185	+	1122.64i	−0.355487	+	0.670520i
$142$	403.710	+	2462.52i	0.238582	+	1.45528i
$143$	225.486	−	265.462i	0.131861	−	0.155238i
$144$	−380.688	−	448.181i	−0.220306	−	0.259364i
$145$	101.789	−	620.888i	0.0582976	−	0.355600i
$146$	711.240	+	540.670i	0.403169	+	0.306481i
$147$	275.203	−	405.894i	0.154411	−	0.227738i
$148$	−238.103	+	351.176i	−0.132243	+	0.195044i
$149$	439.687	+	334.241i	0.241749	+	0.183773i	0.719032	−	0.694977i	$-0.244585\pi$
$149$	439.687	+	334.241i	0.241749	+	0.183773i	−0.477283	+	0.878749i	$0.658378\pi$
$150$	219.166	−	1336.85i	0.119299	−	0.727691i
$151$	−555.505	−	653.991i	−0.299380	−	0.352457i	0.591818	−	0.806071i	$-0.298410\pi$
$151$	−555.505	−	653.991i	−0.299380	−	0.352457i	−0.891198	+	0.453614i	$0.850134\pi$
$152$	67.6856	−	79.6856i	0.0361186	−	0.0425221i
$153$	131.616	+	802.820i	0.0695457	+	0.424210i
$154$	169.806	−	320.287i	0.0888528	−	0.167594i
$155$	915.628	+	201.545i	0.474484	+	0.104442i
$156$	−1140.03	−	384.121i	−0.585099	−	0.197143i
$157$	−180.642	−	3331.75i	−0.0918268	−	1.69365i	−0.575026	−	0.818135i	$-0.695008\pi$
$157$	−180.642	−	3331.75i	−0.0918268	−	1.69365i	0.483199	−	0.875511i	$-0.339475\pi$
$158$	−2681.76	+	2038.62i	−1.35031	+	1.02648i
$159$	654.173	+	1233.90i	0.326285	+	0.615438i
$160$	−230.910	−	831.663i	−0.114094	−	0.410930i
$161$	−323.024	−	305.984i	−0.158123	−	0.149782i
$162$	−119.283	−	299.377i	−0.0578502	−	0.145193i
$163$	2812.39	−	947.604i	1.35143	−	0.455350i	0.451846	−	0.892096i	$-0.350766\pi$
$163$	2812.39	−	947.604i	1.35143	−	0.455350i	0.899585	+	0.436745i	$0.143869\pi$
$164$	−2492.27	+	271.051i	−1.18667	+	0.129058i
$165$	62.7900	+	29.0497i	0.0296254	+	0.0137062i
$166$	−2009.66	+	1903.65i	−0.939638	+	0.890072i
$167$	2231.30	+	1342.53i	1.03391	+	0.622084i	0.928111	−	0.372304i	$-0.121432\pi$
$167$	2231.30	+	1342.53i	1.03391	+	0.622084i	0.105800	+	0.994387i	$0.466260\pi$
$168$	27.1650	+	2.95437i	0.0124751	+	0.00135675i
$169$	416.422	−	91.6615i	0.189541	−	0.0417212i
$170$	−326.284	+	1175.17i	−0.147205	+	0.530185i
$171$	1186.09	−	713.646i	0.530424	−	0.319146i
$172$	1947.00	−	900.780i	0.863126	−	0.399325i
$173$	381.252	−	956.871i	0.167549	−	0.420518i	−0.821095	−	0.570792i	$-0.806636\pi$
$173$	381.252	−	956.871i	0.167549	−	0.420518i	0.988644	+	0.150274i	$0.0480157\pi$
$174$	−119.886	+	2211.17i	−0.0522331	+	0.963382i
$175$	853.445	+	1258.74i	0.368654	+	0.543723i
$176$	−444.311			−0.190291
$177$	−416.493	−	1294.20i	−0.176868	−	0.549592i
$178$	1893.53			0.797336
$179$	−2404.13	−	3545.83i	−1.00387	−	1.48060i	−0.872104	−	0.489321i	$-0.837245\pi$
$179$	−2404.13	−	3545.83i	−1.00387	−	1.48060i	−0.131769	−	0.991280i	$-0.542066\pi$
$180$	12.9369	−	238.606i	0.00535698	−	0.0988037i
$181$	386.512	−	970.071i	0.158725	−	0.398369i	−0.828009	−	0.560715i	$-0.810527\pi$
$181$	386.512	−	970.071i	0.158725	−	0.398369i	0.986734	+	0.162345i	$0.0519058\pi$
$182$	2478.09	−	1146.49i	1.00928	−	0.466942i
$183$	−1041.85	+	626.858i	−0.420850	+	0.253217i
$184$	−6.03895	+	21.7503i	−0.00241955	+	0.00871444i
$185$	179.486	−	39.5079i	0.0713303	−	0.0157010i
$186$	−3280.40	−	356.765i	−1.29318	−	0.140641i
$187$	526.705	+	316.908i	0.205970	+	0.123928i
$188$	2407.43	−	2280.44i	0.933937	−	0.884672i
$189$	328.338	+	151.905i	0.126366	+	0.0584629i
$190$	2063.02	−	224.367i	0.787724	−	0.0856701i
$191$	−2184.37	+	736.001i	−0.827517	+	0.278823i	−0.701018	−	0.713144i	$-0.747271\pi$
$191$	−2184.37	+	736.001i	−0.827517	+	0.278823i	−0.126499	+	0.991967i	$0.540374\pi$
$192$	543.994	+	1365.32i	0.204476	+	0.513196i
$193$	−2856.41	−	2705.74i	−1.06533	−	1.00914i	−0.999936	−	0.0112756i	$-0.996411\pi$
$193$	−2856.41	−	2705.74i	−1.06533	−	1.00914i	−0.0653945	−	0.997859i	$-0.520831\pi$
$194$	524.076	+	1887.55i	0.193951	+	0.698548i
$195$	244.084	+	460.392i	0.0896372	+	0.169074i
$196$	−1018.83	+	774.495i	−0.371294	+	0.282250i
$197$	−88.7162	−	1636.27i	−0.0320851	−	0.591775i	−0.969730	−	0.244180i	$-0.921481\pi$
$197$	−88.7162	−	1636.27i	−0.0320851	−	0.591775i	0.937645	−	0.347595i	$-0.113002\pi$
$198$	−230.751	−	77.7492i	−0.0828222	−	0.0279060i
$199$	−1564.59	−	344.392i	−0.557340	−	0.122680i	−0.0726368	−	0.997358i	$-0.523141\pi$
$199$	−1564.59	−	344.392i	−0.557340	−	0.122680i	−0.484703	+	0.874679i	$0.661072\pi$
$200$	36.1397	−	68.1666i	0.0127773	−	0.0241005i
$201$	414.657	+	2529.29i	0.145511	+	0.887575i
$202$	−3149.35	+	3707.70i	−1.09697	+	1.29145i
$203$	−1609.34	−	1894.66i	−0.556422	−	0.655071i
$204$	343.479	−	2095.13i	0.117884	−	0.719061i
$205$	864.492	+	657.170i	0.294530	+	0.223896i
$206$	−782.839	+	1154.60i	−0.264772	+	0.390509i
$207$	−167.716	+	247.363i	−0.0563145	+	0.0830576i
$208$	−2664.15	−	2025.24i	−0.888104	−	0.675119i
$209$	169.208	−	1032.12i	0.0560017	−	0.341595i
$210$	351.116	+	413.366i	0.115378	+	0.135833i
$211$	−927.852	+	1092.35i	−0.302730	+	0.356401i	−0.892402	−	0.451242i	$-0.850981\pi$
$211$	−927.852	+	1092.35i	−0.302730	+	0.356401i	0.589672	+	0.807643i	$0.299257\pi$
$212$	−589.645	−	3596.68i	−0.191024	−	1.16519i
$213$	−881.367	+	1662.44i	−0.283523	+	0.534780i
$214$	−5572.21	−	1226.54i	−1.77995	−	0.391796i
$215$	−880.607	−	296.711i	−0.279335	−	0.0941188i
$216$	−0.993664	−	18.3271i	−0.000313011	−	0.00577314i
$217$	2948.96	−	2241.74i	0.922529	−	0.701288i
$218$	−1042.92	−	1967.16i	−0.324017	−	0.611160i
$219$	180.225	+	649.111i	0.0556094	+	0.200287i
$220$	−131.079	−	124.165i	−0.0401699	−	0.0380509i
$221$	1713.68	+	4301.02i	0.521605	+	1.30913i
$222$	−612.975	+	206.535i	−0.185316	+	0.0624402i
$223$	2525.05	−	274.616i	0.758251	−	0.0824648i	0.279177	−	0.960240i	$-0.409938\pi$
$223$	2525.05	−	274.616i	0.758251	−	0.0824648i	0.479074	+	0.877775i	$0.340973\pi$
$224$	−3095.05	−	1431.92i	−0.923201	−	0.427118i
$225$	741.600	−	702.480i	0.219733	−	0.208142i
$226$	4038.67	+	2429.99i	1.18871	+	0.715222i
$227$	135.900	+	14.7800i	0.0397358	+	0.00432152i	0.127965	−	0.991779i	$-0.459155\pi$
$227$	135.900	+	14.7800i	0.0397358	+	0.00432152i	−0.0882295	+	0.996100i	$0.528121\pi$
$228$	−3527.99	+	776.570i	−1.02477	+	0.225568i
$229$	−1165.18	+	4196.61i	−0.336234	+	1.21100i	0.581414	+	0.813608i	$0.302500\pi$
$229$	−1165.18	+	4196.61i	−0.336234	+	1.21100i	−0.917647	+	0.397396i	$0.869914\pi$
$230$	−383.906	+	230.989i	−0.110061	+	0.0662215i
$231$	248.086	−	114.777i	0.0706618	−	0.0326916i
$232$	−46.6810	+	117.160i	−0.0132102	+	0.0331550i
$233$	−98.3054	+	1813.14i	−0.0276403	+	0.509796i	0.951631	+	0.307243i	$0.0994065\pi$
$233$	−98.3054	+	1813.14i	−0.0276403	+	0.509796i	−0.979271	+	0.202553i	$0.935076\pi$
$234$	−1029.23	−	1517.99i	−0.287532	−	0.424078i
$235$	−1436.38			−0.398719
$236$	−48.4043	+	3547.74i	−0.0133511	+	0.978552i
$237$	−2540.09			−0.696188
$238$	2704.25	+	3988.46i	0.736513	+	1.08628i
$239$	302.141	−	5572.66i	0.0817736	−	1.50822i	−0.613623	−	0.789599i	$-0.710289\pi$
$239$	302.141	−	5572.66i	0.0817736	−	1.50822i	0.695397	−	0.718626i	$-0.255229\pi$
$240$	246.043	−	617.522i	0.0661751	−	0.166087i
$241$	5723.68	−	2648.06i	1.52985	−	0.707785i	0.538947	−	0.842340i	$-0.318822\pi$
$241$	5723.68	−	2648.06i	1.52985	−	0.707785i	0.990906	+	0.134555i	$0.0429604\pi$
$242$	4379.84	−	2635.26i	1.16342	−	0.700004i
$243$	65.0094	−	234.143i	0.0171620	−	0.0618118i
$244$	3098.94	−	682.129i	0.813072	−	0.178971i
$245$	551.104	+	59.9361i	0.143709	+	0.0156293i
$246$	−3274.86	−	1970.42i	−0.848770	−	0.510688i
$247$	5719.15	−	5417.47i	1.47328	−	1.39557i
$248$	−170.561	−	78.9099i	−0.0436719	−	0.0202048i
$249$	−2075.05	+	225.675i	−0.528115	+	0.0574360i
$250$	3049.49	−	1027.49i	0.771468	−	0.259938i
$251$	212.238	+	532.676i	0.0533718	+	0.133953i	0.953245	−	0.302198i	$-0.0977205\pi$
$251$	212.238	+	532.676i	0.0533718	+	0.133953i	−0.899873	+	0.436151i	$0.856341\pi$
$252$	−685.434	−	649.277i	−0.171342	−	0.162304i
$253$	60.4114	+	217.582i	0.0150120	+	0.0540683i
$254$	−2840.89	−	5358.49i	−0.701785	−	1.32371i
$255$	−732.121	+	556.544i	−0.179793	+	0.136675i
$256$	230.920	+	4259.06i	0.0563768	+	1.03981i
$257$	2063.47	+	695.264i	0.500839	+	0.168752i	0.558371	−	0.829591i	$-0.311427\pi$
$257$	2063.47	+	695.264i	0.500839	+	0.168752i	−0.0575318	+	0.998344i	$0.518323\pi$
$258$	3194.08	+	703.070i	0.770755	+	0.169656i
$259$	340.128	−	641.550i	0.0816005	−	0.153915i
$260$	−220.008	−	1341.99i	−0.0524781	−	0.320103i
$261$	−1080.98	+	1272.62i	−0.256363	+	0.301814i
$262$	467.015	+	549.812i	0.110123	+	0.129647i
$263$	141.824	−	865.087i	0.0332518	−	0.202827i	−0.964976	−	0.262339i	$-0.915506\pi$
$263$	141.824	−	865.087i	0.0332518	−	0.202827i	0.998228	+	0.0595119i	$0.0189544\pi$
$264$	−11.0402	−	8.39251i	−0.00257377	−	0.00195653i
$265$	−885.966	+	1306.70i	−0.205375	+	0.302906i
$266$	4601.27	−	6786.36i	1.06061	−	1.56428i
$267$	1136.65	+	864.061i	0.260532	+	0.198051i
$268$	1082.14	−	6600.73i	0.246649	−	1.50449i
$269$	−2315.82	−	2726.39i	−0.524900	−	0.617960i	0.434273	−	0.900781i	$-0.357005\pi$
$269$	−2315.82	−	2726.39i	−0.524900	−	0.617960i	−0.959173	+	0.282822i	$0.908730\pi$
$270$	235.841	−	277.653i	0.0531585	−	0.0625831i
$271$	784.467	+	4785.04i	0.175841	+	1.07258i	0.916303	+	0.400485i	$0.131158\pi$
$271$	784.467	+	4785.04i	0.175841	+	1.07258i	−0.740462	+	0.672098i	$0.765393\pi$
$272$	2766.45	−	5218.08i	0.616694	−	1.16321i
$273$	2010.73	+	442.595i	0.445769	+	0.0981211i
$274$	4355.28	+	1467.47i	0.960264	+	0.323550i
$275$	−41.7856	−	770.690i	−0.00916278	−	0.168998i
$276$	620.904	−	471.999i	0.135413	−	0.102938i
$277$	408.707	+	770.903i	0.0886528	+	0.167217i	0.923874	−	0.382698i	$-0.125005\pi$
$277$	408.707	+	770.903i	0.0886528	+	0.167217i	−0.835221	+	0.549915i	$0.814660\pi$
$278$	1615.93	+	5820.06i	0.348623	+	1.25563i
$279$	−1806.37	−	1711.09i	−0.387615	−	0.367169i
$280$	11.4332	+	28.6952i	0.00244023	+	0.00612452i
$281$	−2595.65	+	874.577i	−0.551045	+	0.185669i	−0.581031	−	0.813882i	$-0.697350\pi$
$281$	−2595.65	+	874.577i	−0.551045	+	0.185669i	0.0299859	+	0.999550i	$0.490454\pi$
$282$	5025.77	−	546.586i	1.06128	−	0.115421i
$283$	981.899	+	454.275i	0.206247	+	0.0954199i	0.520293	−	0.853988i	$-0.325823\pi$
$283$	981.899	+	454.275i	0.206247	+	0.0954199i	−0.314046	+	0.949408i	$0.601685\pi$
$284$	3565.00	−	3376.94i	0.744872	−	0.705580i
$285$	1340.78	+	806.723i	0.278671	+	0.167671i
$286$	−1377.62	−	149.826i	−0.284827	−	0.0309768i
$287$	4190.20	−	922.334i	0.861811	−	0.189699i
$288$	−612.806	+	2207.13i	−0.125382	+	0.451584i
$289$	−2791.55	+	1679.62i	−0.568197	+	0.341873i
$290$	−2271.87	+	1051.08i	−0.460031	+	0.212833i
$291$	−546.740	+	1372.21i	−0.110139	+	0.276428i
$292$	95.1803	−	1755.50i	0.0190754	−	0.351824i
$293$	3026.26	+	4463.40i	0.603399	+	0.889947i	0.999602	−	0.0282163i	$-0.00898271\pi$
$293$	3026.26	+	4463.40i	0.603399	+	0.889947i	−0.396203	+	0.918163i	$0.629672\pi$
$294$	−1951.07			−0.387037
$295$	1072.04	−	1101.25i	0.211581	−	0.217346i
$296$	−36.8391			−0.00723389
$297$	−103.037	−	151.969i	−0.0201308	−	0.0296907i
$298$	118.965	−	2194.17i	0.0231256	−	0.426527i
$299$	−629.536	+	1580.02i	−0.121763	+	0.305601i
$300$	−2419.42	+	1119.34i	−0.465617	+	0.215418i
$301$	−3145.96	+	1892.86i	−0.602426	+	0.362468i
$302$	−913.320	+	3289.48i	−0.174025	+	0.626783i
$303$	−3582.41	+	788.548i	−0.679222	+	0.149508i
$304$	−9990.26	−	1086.51i	−1.88480	−	0.204985i
$305$	−1177.73	−	708.615i	−0.221103	−	0.133033i
$306$	2349.85	−	2225.89i	0.438993	−	0.415836i
$307$	−5584.67	−	2583.74i	−1.03822	−	0.480333i	−0.174688	−	0.984624i	$-0.555892\pi$
$307$	−5584.67	−	2583.74i	−1.03822	−	0.480333i	−0.863534	+	0.504291i	$0.831754\pi$
$308$	−709.185	+	77.1285i	−0.131200	+	0.0142688i
$309$	−996.797	+	335.860i	−0.183514	+	0.0618331i
$310$	−1380.66	−	3465.19i	−0.252955	−	0.634869i
$311$	−1038.38	−	983.603i	−0.189328	−	0.179341i	0.587164	−	0.809468i	$-0.300244\pi$
$311$	−1038.38	−	983.603i	−0.189328	−	0.179341i	−0.776492	+	0.630127i	$0.783003\pi$
$312$	−27.9440	−	100.645i	−0.00507057	−	0.0182626i
$313$	3589.01	+	6769.58i	0.648123	+	1.22249i	0.962006	+	0.273028i	$0.0880253\pi$
$313$	3589.01	+	6769.58i	0.648123	+	1.22249i	−0.313883	+	0.949462i	$0.601630\pi$
$314$	−10568.2	+	8033.76i	−1.89936	+	1.44386i
$315$	22.1406	+	408.360i	0.00396026	+	0.0730427i
$316$	6281.90	+	2116.62i	1.11831	+	0.376801i
$317$	−6947.30	−	1529.22i	−1.23091	−	0.270944i	−0.448544	−	0.893761i	$-0.648057\pi$
$317$	−6947.30	−	1529.22i	−1.23091	−	0.270944i	−0.782368	+	0.622816i	$0.785988\pi$
$318$	2602.68	−	4909.18i	0.458966	−	0.865702i
$319$	204.110	+	1245.02i	0.0358243	+	0.218519i
$320$	−1075.56	+	1266.25i	−0.187893	+	0.221204i
$321$	−2785.21	−	3279.00i	−0.484284	−	0.570144i
$322$	−286.391	+	1746.91i	−0.0495650	+	0.302333i
$323$	11067.9	+	8413.59i	1.90661	+	1.44937i
$324$	−355.883	+	524.888i	−0.0610224	+	0.0900013i
$325$	3262.36	−	4811.62i	0.556810	−	0.821234i
$326$	−9399.80	−	7145.54i	−1.59695	−	1.21397i
$327$	271.613	−	1656.76i	0.0459334	−	0.280181i
$328$	−140.917	−	165.901i	−0.0237221	−	0.0279278i
$329$	−3674.05	+	4325.42i	−0.615674	+	0.724828i
$330$	−44.5314	−	271.630i	−0.00742841	−	0.0453113i
$331$	1614.69	−	3045.62i	0.268131	−	0.505748i	−0.712485	−	0.701687i	$-0.752431\pi$
$331$	1614.69	−	3045.62i	0.268131	−	0.505748i	0.980616	+	0.195939i	$0.0627754\pi$
$332$	5319.86	+	1170.99i	0.879413	+	0.193573i
$333$	−462.205	−	155.735i	−0.0760622	−	0.0256283i
$334$	−560.903	−	10345.2i	−0.0918899	−	1.69481i
$335$	−2306.55	+	1753.40i	−0.376181	+	0.285965i
$336$	−1230.23	−	2320.45i	−0.199745	−	0.376759i
$337$	2458.40	+	8854.37i	0.397382	+	1.43124i	0.843917	+	0.536474i	$0.180244\pi$
$337$	2458.40	+	8854.37i	0.397382	+	1.43124i	−0.446535	+	0.894766i	$0.647342\pi$
$338$	−1231.60	−	1166.64i	−0.198196	−	0.187742i
$339$	1315.49	+	3301.62i	0.210759	+	0.528966i
$340$	2274.37	−	766.324i	0.362779	−	0.122235i
$341$	−1868.96	+	203.262i	−0.296804	+	0.0322794i
$342$	−4998.28	−	2312.45i	−0.790280	−	0.365623i
$343$	4926.72	−	4666.84i	0.775563	−	0.734652i
$344$	159.604	+	96.0308i	0.0250154	+	0.0150513i
$345$	−335.858	−	36.5268i	−0.0524116	−	0.00570010i
$346$	−4002.24	+	880.959i	−0.621855	+	0.136881i
$347$	−2769.35	+	9974.31i	−0.428434	+	1.54308i	0.362978	+	0.931798i	$0.381760\pi$
$347$	−2769.35	+	9974.31i	−0.428434	+	1.54308i	−0.791412	+	0.611283i	$0.790654\pi$
$348$	3733.82	−	2246.57i	0.575155	−	0.346059i
$349$	−9704.56	+	4489.81i	−1.48846	+	0.688636i	−0.984548	−	0.175118i	$-0.943969\pi$
$349$	−9704.56	+	4489.81i	−1.48846	+	0.688636i	−0.503915	+	0.863753i	$0.668107\pi$
$350$	2239.55	−	5620.84i	0.342025	−	0.858419i
$351$	74.8695	−	1380.89i	0.0113853	−	0.209989i
$352$	971.275	+	1432.52i	0.147071	+	0.216914i
$353$	−5195.99			−0.783440			−0.391720	−	0.920084i	$-0.628120\pi$
$353$	−5195.99			−0.783440			−0.391720	+	0.920084i	$0.628120\pi$
$354$	−3331.91	+	4261.12i	−0.500252	+	0.639762i
$355$	−2127.03			−0.318003
$356$	−2091.05	−	3084.07i	−0.311307	−	0.459144i
$357$	−196.716	+	3628.22i	−0.0291634	+	0.537887i
$358$	−6308.75	+	15833.8i	−0.931362	+	2.33754i
$359$	6351.95	−	2938.73i	0.933825	−	0.432033i	0.106852	−	0.994275i	$-0.465923\pi$
$359$	6351.95	−	2938.73i	0.933825	−	0.432033i	0.826973	+	0.562241i	$0.190061\pi$
$360$	17.7779	−	10.6966i	0.00260271	−	0.00156600i
$361$	4493.55	−	16184.3i	0.655132	−	2.35957i
$362$	−4057.45	+	893.113i	−0.589102	+	0.129671i
$363$	3831.68	+	416.720i	0.554024	+	0.0602538i
$364$	−4603.93	−	2770.09i	−0.662944	−	0.398880i
$365$	−552.866	+	523.703i	−0.0792831	+	0.0751010i
$366$	4390.42	+	2031.23i	0.627025	+	0.290093i
$367$	1189.68	−	129.386i	0.169212	−	0.0184029i	−0.0231207	−	0.999733i	$-0.507360\pi$
$367$	1189.68	−	129.386i	0.169212	−	0.0184029i	0.192333	+	0.981330i	$0.438395\pi$
$368$	2056.07	−	692.772i	0.291251	−	0.0981337i
$369$	−1066.70	−	2677.21i	−0.150488	−	0.377696i
$370$	−530.846	−	502.844i	−0.0745875	−	0.0706530i
$371$	1668.75	+	6010.29i	0.233523	+	0.841075i
$372$	3041.52	+	5736.92i	0.423913	+	0.799584i
$373$	−7237.06	+	5501.47i	−1.00461	+	0.763687i	−0.971808	−	0.235774i	$-0.924237\pi$
$373$	−7237.06	+	5501.47i	−1.00461	+	0.763687i	−0.0328056	+	0.999462i	$0.510444\pi$
$374$	−132.403	−	2442.02i	−0.0183058	−	0.337631i
$375$	2299.43	+	774.769i	0.316646	+	0.106690i
$376$	281.189	+	61.8944i	0.0385671	+	0.00848926i
$377$	−4451.09	+	8395.64i	−0.608071	+	1.14694i
$378$	−232.861	−	1420.39i	−0.0316854	−	0.193273i
$379$	9418.50	−	11088.3i	1.27651	−	1.50282i	0.510682	−	0.859769i	$-0.329393\pi$
$379$	9418.50	−	11088.3i	1.27651	−	1.50282i	0.765824	−	0.643050i	$-0.222331\pi$
$380$	−2643.67	−	3112.36i	−0.356887	−	0.420160i
$381$	739.865	−	4512.98i	0.0994867	−	0.606842i
$382$	7300.79	+	5549.92i	0.977856	+	0.743347i
$383$	4464.41	−	6584.51i	0.595615	−	0.878467i	−0.403722	−	0.914882i	$-0.632284\pi$
$383$	4464.41	−	6584.51i	0.595615	−	0.878467i	0.999337	+	0.0364153i	$0.0115939\pi$
$384$	−146.456	+	216.006i	−0.0194630	+	0.0287058i
$385$	245.994	+	187.000i	0.0325637	+	0.0247543i
$386$	−2532.48	+	15447.4i	−0.333937	+	2.03693i
$387$	1596.53	+	1879.58i	0.209705	+	0.246884i
$388$	2495.59	−	2938.04i	0.326532	−	0.384423i
$389$	429.100	+	2617.39i	0.0559286	+	0.341149i	0.999937	+	0.0112279i	$0.00357401\pi$
$389$	429.100	+	2617.39i	0.0559286	+	0.341149i	−0.944008	+	0.329922i	$0.892978\pi$
$390$	971.111	−	1831.71i	0.126087	−	0.237826i
$391$	−2931.47	−	645.266i	−0.379159	−	0.0834591i
$392$	−105.303	−	35.4806i	−0.0135678	−	0.00457154i
$393$	29.4489	+	543.153i	0.00377990	+	0.0697162i
$394$	−5190.22	+	3945.50i	−0.663654	+	0.504496i
$395$	−1344.98	−	2536.90i	−0.171325	−	0.323152i
$396$	128.189	+	461.695i	0.0162670	+	0.0585884i
$397$	6847.54	+	6486.33i	0.865663	+	0.820000i	0.984946	−	0.172861i	$-0.0553011\pi$
$397$	6847.54	+	6486.33i	0.865663	+	0.820000i	−0.119283	+	0.992860i	$0.538060\pi$
$398$	2359.21	+	5921.17i	0.297127	+	0.745732i
$399$	5858.84	−	1974.07i	0.735110	−	0.247688i
$400$	−7372.31	+	801.787i	−0.921538	+	0.100223i
$401$	7851.33	+	3632.41i	0.977747	+	0.452354i	0.842640	−	0.538477i	$-0.181000\pi$
$401$	7851.33	+	3632.41i	0.977747	+	0.452354i	0.135107	+	0.990831i	$0.456862\pi$
$402$	7403.23	−	7012.71i	0.918506	−	0.870055i
$403$	−12133.1	−	7300.22i	−1.49973	−	0.902358i
$404$	9516.76	+	1035.01i	1.17197	+	0.127460i
$405$	268.271	−	59.0509i	0.0329148	−	0.00724509i
$406$	−2645.96	+	9529.89i	−0.323440	+	1.16493i
$407$	−315.773	+	189.994i	−0.0384577	+	0.0231393i
$408$	167.304	−	77.4029i	0.0203009	−	0.00939219i
$409$	285.941	−	717.657i	0.0345693	−	0.0867625i	−0.910679	−	0.413116i	$-0.864441\pi$
$409$	285.941	−	717.657i	0.0345693	−	0.0867625i	0.945248	+	0.326353i	$0.105820\pi$
$410$	233.903	−	4314.08i	0.0281747	−	0.519652i
$411$	1944.76	+	2868.31i	0.233402	+	0.344242i
$412$	2745.05			0.328250
$413$	−574.114	−	6045.09i	−0.0684027	−	0.720241i
$414$	1189.04			0.141155
$415$	−1324.13	−	1952.94i	−0.156624	−	0.231003i
$416$	−705.751	+	13016.8i	−0.0831786	+	1.53414i
$417$	−1685.82	+	4231.08i	−0.197973	+	0.496875i
$418$	−3776.61	+	1747.24i	−0.441913	+	0.204451i
$419$	−7799.37	+	4692.73i	−0.909366	+	0.547147i	−0.891665	−	0.452696i	$-0.850462\pi$
$419$	−7799.37	+	4692.73i	−0.909366	+	0.547147i	−0.0177008	+	0.999843i	$0.505635\pi$
$420$	285.524	−	1028.36i	0.0331718	−	0.119474i
$421$	10450.2	−	2300.27i	1.20977	−	0.266290i	0.436110	−	0.899893i	$-0.356356\pi$
$421$	10450.2	−	2300.27i	1.20977	−	0.266290i	0.773658	+	0.633603i	$0.218425\pi$
$422$	5668.79	+	616.519i	0.653916	+	0.0711177i
$423$	3266.31	+	1965.27i	0.375445	+	0.225898i
$424$	229.745	−	217.626i	0.0263147	−	0.0249266i
$425$	9311.31	+	4307.87i	1.06274	+	0.491676i
$426$	7442.31	−	809.400i	0.846434	−	0.0920553i
$427$	−5146.34	+	1734.00i	−0.583252	+	0.196521i
$428$	4155.77	+	10430.2i	0.469338	+	1.17795i
$429$	−758.596	−	718.580i	−0.0853738	−	0.0808704i
$430$	989.080	+	3562.34i	0.110925	+	0.399515i
$431$	3004.67	+	5667.41i	0.335800	+	0.633387i	0.992703	−	0.120589i	$-0.0384783\pi$
$431$	3004.67	+	5667.41i	0.335800	+	0.633387i	−0.656902	+	0.753976i	$0.728134\pi$
$432$	−1404.40	+	1067.60i	−0.156410	+	0.118900i
$433$	−245.064	−	4519.94i	−0.0271987	−	0.501650i	−0.980117	−	0.198422i	$-0.936418\pi$
$433$	−245.064	−	4519.94i	−0.0271987	−	0.501650i	0.952918	−	0.303228i	$-0.0980644\pi$
$434$	−13966.4	−	4705.82i	−1.54472	−	0.520476i
$435$	−1843.40	−	405.763i	−0.203182	−	0.0447238i
$436$	−2052.28	+	3871.02i	−0.225428	+	0.425202i
$437$	826.270	+	5040.02i	0.0904482	+	0.551709i
$438$	1735.15	−	2042.78i	0.189289	−	0.222848i
$439$	−1757.99	−	2069.66i	−0.191126	−	0.225011i	0.658250	−	0.752800i	$-0.271297\pi$
$439$	−1757.99	−	2069.66i	−0.191126	−	0.225011i	−0.849376	+	0.527789i	$0.823021\pi$
$440$	2.53620	−	15.4701i	0.000274792	−	0.00167616i
$441$	−1171.20	−	890.322i	−0.126466	−	0.0961367i
$442$	10337.2	−	15246.2i	1.11242	−	1.64070i
$443$	−2271.29	+	3349.91i	−0.243595	+	0.359275i	−0.929757	−	0.368173i	$-0.879983\pi$
$443$	−2271.29	+	3349.91i	−0.243595	+	0.359275i	0.686163	+	0.727448i	$0.259294\pi$
$444$	1013.31	+	770.298i	0.108310	+	0.0823350i
$445$	−261.117	+	1592.74i	−0.0278160	+	0.169670i
$446$	−6542.08	−	7701.93i	−0.694566	−	0.817706i
$447$	1072.67	−	1262.84i	0.113502	−	0.133625i
$448$	1061.97	+	6477.75i	0.111995	+	0.683136i
$449$	−2666.42	+	5029.41i	−0.280259	+	0.528624i	−0.983179	−	0.182644i	$-0.941534\pi$
$449$	−2666.42	+	5029.41i	−0.280259	+	0.528624i	0.702920	+	0.711269i	$0.251879\pi$
$450$	−3969.08	−	873.661i	−0.415787	−	0.0915217i
$451$	−2063.51	−	695.279i	−0.215448	−	0.0725929i
$452$	−502.140	−	9261.42i	−0.0522537	−	0.963762i
$453$	−2049.32	+	1557.85i	−0.212551	+	0.161577i
$454$	−254.758	−	480.524i	−0.0263356	−	0.0496742i
$455$	622.643	+	2242.56i	0.0641537	+	0.231061i
$456$	−227.713	−	215.701i	−0.0233852	−	0.0221516i
$457$	538.902	+	1352.54i	0.0551614	+	0.138445i	0.953975	−	0.299887i	$-0.0969489\pi$
$457$	538.902	+	1352.54i	0.0551614	+	0.138445i	−0.898813	+	0.438332i	$0.855570\pi$
$458$	16421.1	−	5532.92i	1.67535	−	0.564490i
$459$	2426.30	−	263.876i	0.246732	−	0.0268338i
$460$	800.175	+	370.200i	0.0811051	+	0.0375232i
$461$	8836.07	−	8369.97i	0.892704	−	0.845614i	−0.0960173	−	0.995380i	$-0.530610\pi$
$461$	8836.07	−	8369.97i	0.892704	−	0.845614i	0.988722	+	0.149765i	$0.0478518\pi$
$462$	−931.874	−	560.690i	−0.0938413	−	0.0564625i
$463$	5108.98	+	555.635i	0.512818	+	0.0557723i	0.360870	−	0.932616i	$-0.382480\pi$
$463$	5108.98	+	555.635i	0.512818	+	0.0557723i	0.151948	+	0.988388i	$0.451445\pi$
$464$	11838.6	−	2605.87i	1.18447	−	0.260721i
$465$	752.462	−	2710.12i	0.0750421	−	0.270277i
$466$	6190.20	−	3724.52i	0.615355	−	0.370247i
$467$	16128.7	−	7461.95i	1.59818	−	0.739396i	0.600015	−	0.799989i	$-0.295161\pi$
$467$	16128.7	−	7461.95i	1.59818	−	0.739396i	0.998163	+	0.0605932i	$0.0192992\pi$
$468$	−1335.83	+	3352.69i	−0.131942	+	0.331150i
$469$	−619.757	+	11430.7i	−0.0610186	+	1.12542i
$470$	3207.05	+	4730.04i	0.314745	+	0.464214i
$471$	−10009.9			−0.979263
$472$	−257.318	+	169.388i	−0.0250933	+	0.0165185i
$473$	1863.35			0.181135
$474$	5671.34	+	8364.60i	0.549564	+	0.810546i
$475$	945.081	−	17431.0i	0.0912911	−	1.68377i
$476$	3509.84	−	8809.04i	0.337969	−	0.848239i
$477$	3802.52	−	1759.23i	0.365001	−	0.168868i
$478$	−19025.6	+	11447.3i	−1.82052	+	1.09537i
$479$	−1458.27	+	5252.20i	−0.139102	+	0.501000i	−0.999969	−	0.00782937i	$-0.997508\pi$
$479$	−1458.27	+	5252.20i	−0.139102	+	0.501000i	0.860867	+	0.508829i	$0.169922\pi$
$480$	−2528.83	+	556.638i	−0.240469	+	0.0529312i
$481$	−2759.44	−	300.107i	−0.261579	−	0.0284485i
$482$	−21499.6	−	12935.9i	−2.03170	−	1.22243i
$483$	−969.071	+	917.953i	−0.0912924	+	0.0864768i
$484$	−9128.89	−	4223.47i	−0.857333	−	0.396645i
$485$	−1659.99	+	180.535i	−0.155415	+	0.0169024i
$486$	−916.188	+	308.700i	−0.0855126	+	0.0288125i
$487$	−4344.53	−	10903.9i	−0.404249	−	1.01459i	−0.980360	−	0.197217i	$-0.936810\pi$
$487$	−4344.53	−	10903.9i	−0.404249	−	1.01459i	0.576111	−	0.817372i	$-0.304570\pi$
$488$	200.020	+	189.469i	0.0185543	+	0.0175756i
$489$	−2381.86	−	8578.70i	−0.220269	−	0.793338i
$490$	−1033.09	−	1948.62i	−0.0952458	−	0.179653i
$491$	10988.4	−	8353.16i	1.00998	−	0.767766i	0.0371538	−	0.999310i	$-0.488171\pi$
$491$	10988.4	−	8353.16i	1.00998	−	0.767766i	0.972824	+	0.231544i	$0.0743777\pi$
$492$	407.173	+	7509.87i	0.0373105	+	0.688152i
$493$	−15892.6	−	5354.83i	−1.45186	−	0.489188i
$494$	−30609.2	−	6737.60i	−2.78780	−	0.613642i
$495$	97.2196	−	183.376i	0.00882767	−	0.0166507i
$496$	2922.30	+	17825.2i	0.264547	+	1.61366i
$497$	−5440.63	+	6405.21i	−0.491038	+	0.578094i
$498$	5376.18	+	6329.32i	0.483759	+	0.569526i
$499$	2038.24	−	12432.7i	0.182854	−	1.11536i	−0.722710	−	0.691151i	$-0.757104\pi$
$499$	2038.24	−	12432.7i	0.182854	−	1.11536i	0.905564	−	0.424209i	$-0.139448\pi$
$500$	−5041.13	−	3832.17i	−0.450892	−	0.342759i
$501$	4384.08	−	6466.03i	0.390951	−	0.576609i
$502$	1280.25	−	1888.23i	0.113825	−	0.167880i
$503$	5795.73	+	4405.80i	0.513755	+	0.390546i	0.829681	−	0.558237i	$-0.188522\pi$
$503$	5795.73	+	4405.80i	0.513755	+	0.390546i	−0.315926	+	0.948784i	$0.602315\pi$
$504$	13.2622	−	80.8955i	0.00117211	−	0.00714955i
$505$	−2684.45	−	3160.37i	−0.236547	−	0.278485i
$506$	581.623	−	684.739i	0.0510994	−	0.0601588i
$507$	−206.947	−	1262.32i	−0.0181279	−	0.110575i
$508$	−5590.36	+	10544.5i	−0.488252	+	0.920942i
$509$	−3735.29	−	822.199i	−0.325272	−	0.0715979i	0.0493325	−	0.998782i	$-0.484291\pi$
$509$	−3735.29	−	822.199i	−0.325272	−	0.0715979i	−0.374605	+	0.927185i	$0.622222\pi$
$510$	3467.34	+	1168.28i	0.301052	+	0.101436i
$511$	162.895	+	3004.42i	0.0141019	+	0.260094i
$512$	12955.6	−	9848.60i	1.11829	−	0.850099i
$513$	−1945.16	−	3668.96i	−0.167409	−	0.315767i
$514$	−2317.65	−	8347.41i	−0.198885	−	0.716320i
$515$	−863.243	−	817.707i	−0.0738622	−	0.0699660i
$516$	−2382.15	−	5978.75i	−0.203233	−	0.510077i
$517$	2729.48	−	919.668i	0.232190	−	0.0782340i
$518$	−2872.06	+	312.355i	−0.243612	+	0.0264944i
$519$	−2804.48	−	1297.49i	−0.237193	−	0.109737i
$520$	85.7224	−	81.2006i	0.00722919	−	0.00684785i
$521$	−5057.42	−	3042.95i	−0.425277	−	0.255881i	0.286788	−	0.957994i	$-0.407412\pi$
$521$	−5057.42	−	3042.95i	−0.425277	−	0.255881i	−0.712065	+	0.702113i	$0.752240\pi$
$522$	6604.32	+	718.263i	0.553761	+	0.0602251i
$523$	−1548.72	+	340.898i	−0.129485	+	0.0285018i	−0.279240	−	0.960221i	$-0.590083\pi$
$523$	−1548.72	+	340.898i	−0.129485	+	0.0285018i	0.149755	+	0.988723i	$0.452151\pi$
$524$	379.772	−	1367.81i	0.0316611	−	0.114033i
$525$	3909.29	−	2352.14i	0.324982	−	0.195535i
$526$	−3165.41	+	1464.48i	−0.262393	+	0.121396i
$527$	9249.74	−	23215.1i	0.764563	−	1.91891i
$528$	−72.1636	+	1330.98i	−0.00594795	+	0.109704i
$529$	6209.15	+	9157.81i	0.510327	+	0.752676i
$530$	6281.13			0.514783
$531$	−3944.54	+	1037.45i	−0.322370	+	0.0847861i
$532$	−16134.5			−1.31489
$533$	−9203.93	−	13574.8i	−0.747967	−	1.10317i
$534$	307.540	−	5672.25i	0.0249224	−	0.459667i
$535$	1800.11	−	4517.94i	0.145469	−	0.365099i
$536$	527.092	−	243.859i	0.0424756	−	0.0196513i
$537$	−11012.4	+	6625.91i	−0.884950	+	0.532457i
$538$	−3807.50	+	13713.4i	−0.305117	+	1.09893i
$539$	−1085.61	+	238.961i	−0.0867542	+	0.0190960i
$540$	−712.668	−	77.5073i	−0.0567932	−	0.00617664i
$541$	−5473.16	−	3293.09i	−0.434953	−	0.261703i	0.281195	−	0.959651i	$-0.409269\pi$
$541$	−5473.16	−	3293.09i	−0.434953	−	0.261703i	−0.716149	+	0.697948i	$0.754097\pi$
$542$	14005.8	−	13267.0i	1.10996	−	1.05141i
$543$	−2843.17	−	1315.39i	−0.224700	−	0.103957i
$544$	−22871.4	+	2487.41i	−1.80258	+	0.196042i
$545$	1798.50	−	605.986i	0.141357	−	0.0476286i
$546$	−3031.94	−	7609.59i	−0.237646	−	0.596448i
$547$	13328.1	+	12625.1i	1.04181	+	0.986855i	0.999925	−	0.0122677i	$-0.00390504\pi$
$547$	13328.1	+	12625.1i	1.04181	+	0.986855i	0.0418851	+	0.999122i	$0.486664\pi$
$548$	−2419.48	−	8714.18i	−0.188604	−	0.679291i
$549$	1708.60	+	3222.77i	0.132826	+	0.250536i
$550$	−2444.61	+	1858.34i	−0.189525	+	0.144073i
$551$	1544.85	+	28493.0i	0.119442	+	2.20298i
$552$	64.1745	+	21.6229i	0.00494828	+	0.00166727i
$553$	−11079.7	−	2438.83i	−0.852003	−	0.187540i
$554$	1626.08	−	3067.10i	0.124703	−	0.235214i
$555$	−89.1984	−	544.086i	−0.00682209	−	0.0416129i
$556$	7694.89	−	9059.12i	0.586935	−	0.690994i
$557$	3779.93	+	4450.08i	0.287542	+	0.338521i	0.886901	−	0.461960i	$-0.152854\pi$
$557$	3779.93	+	4450.08i	0.287542	+	0.338521i	−0.599359	+	0.800481i	$0.704578\pi$
$558$	−1601.52	+	9768.83i	−0.121501	+	0.741125i
$559$	11172.9	+	8493.41i	0.845372	+	0.642635i
$560$	1666.13	−	2457.36i	0.125727	−	0.185433i
$561$	1034.87	−	1526.33i	0.0778831	−	0.114869i
$562$	8675.40	+	6594.87i	0.651156	+	0.494996i
$563$	3459.65	−	21102.9i	0.258982	−	1.57972i	−0.462074	−	0.886841i	$-0.652895\pi$
$563$	3459.65	−	21102.9i	0.258982	−	1.57972i	0.721056	−	0.692877i	$-0.243657\pi$
$564$	−6440.29	−	7582.09i	−0.480824	−	0.566070i
$565$	−2600.92	+	3062.04i	−0.193666	+	0.228002i
$566$	−696.375	−	4247.70i	−0.0517152	−	0.315449i
$567$	508.376	−	958.898i	0.0376539	−	0.0710228i
$568$	416.393	+	91.6550i	0.0307596	+	0.00677070i
$569$	−8775.01	−	2956.64i	−0.646516	−	0.217836i	−0.0231074	−	0.999733i	$-0.507356\pi$
$569$	−8775.01	−	2956.64i	−0.646516	−	0.217836i	−0.623408	+	0.781896i	$0.714253\pi$
$570$	−337.045	−	6216.44i	−0.0247672	−	0.456803i
$571$	12917.8	−	9819.84i	0.946746	−	0.719698i	−0.0131908	−	0.999913i	$-0.504199\pi$
$571$	12917.8	−	9819.84i	0.946746	−	0.719698i	0.959937	+	0.280215i	$0.0904058\pi$
$572$	1277.30	+	2409.25i	0.0933684	+	0.176112i
$573$	1849.99	+	6663.05i	0.134877	+	0.485782i
$574$	−12392.9	−	11739.1i	−0.901164	−	0.853628i
$575$	1395.03	+	3501.25i	0.101177	+	0.253934i
$576$	4178.31	−	1407.84i	0.302250	−	0.101840i
$577$	5941.30	−	646.156i	0.428665	−	0.0466201i	0.108756	−	0.994068i	$-0.465313\pi$
$577$	5941.30	−	646.156i	0.428665	−	0.0466201i	0.319909	+	0.947448i	$0.396348\pi$
$578$	11763.8	+	5442.52i	0.846558	+	0.391659i
$579$	−8569.23	+	8117.21i	−0.615069	+	0.582624i
$580$	4220.80	+	2539.57i	0.302171	+	0.181810i
$581$	−9267.91	−	1007.95i	−0.661786	−	0.0719735i
$582$	5739.47	−	1263.35i	0.408778	−	0.0899788i
$583$	846.916	−	3050.31i	0.0601641	−	0.216691i
$584$	130.797	−	78.6980i	0.00926785	−	0.00557628i
$585$	1418.79	−	656.404i	0.100273	−	0.0463914i
$586$	7941.28	−	19931.1i	0.559815	−	1.40503i
$587$	1321.44	−	24372.5i	0.0929158	−	1.71373i	−0.466231	−	0.884663i	$-0.654389\pi$
$587$	1321.44	−	24372.5i	0.0929158	−	1.71373i	0.559147	−	0.829069i	$-0.311129\pi$
$588$	2154.60	+	3177.80i	0.151113	+	0.222875i
$589$	−42520.4			−2.97457
$590$	−6020.01	−	1071.46i	−0.420068	−	0.0747651i
$591$	−4916.03			−0.342163
$592$	1987.08	+	2930.72i	0.137953	+	0.203466i
$593$	1349.44	−	24888.9i	0.0934481	−	1.72355i	−0.457671	−	0.889122i	$-0.651316\pi$
$593$	1349.44	−	24888.9i	0.0934481	−	1.72355i	0.551119	−	0.834427i	$-0.314201\pi$
$594$	−270.383	+	678.611i	−0.0186767	+	0.0468750i
$595$	−3727.82	+	1724.67i	−0.256850	+	0.118831i
$596$	−3705.12	+	2229.30i	−0.254644	+	0.153214i
$597$	−1285.78	+	4630.95i	−0.0881462	+	0.317474i
$598$	6608.63	−	1454.67i	0.451918	−	0.0994747i
$599$	−19304.7	−	2099.52i	−1.31681	−	0.143212i	−0.577398	−	0.816463i	$-0.695932\pi$
$599$	−19304.7	−	2099.52i	−1.31681	−	0.143212i	−0.739414	+	0.673251i	$0.764897\pi$
$600$	−198.330	−	119.331i	−0.0134947	−	0.00811947i
$601$	−1906.41	+	1805.85i	−0.129391	+	0.122566i	−0.749659	−	0.661824i	$-0.769782\pi$
$601$	−1906.41	+	1805.85i	−0.129391	+	0.122566i	0.620268	+	0.784390i	$0.287024\pi$
$602$	13257.3	+	6133.50i	0.897556	+	0.415254i
$603$	7644.10	−	831.346i	0.516238	−	0.0561443i
$604$	6366.31	−	2145.06i	0.428877	−	0.144505i
$605$	1612.68	+	4047.51i	0.108371	+	0.271992i
$606$	10595.3	+	10036.4i	0.710237	+	0.672772i
$607$	2388.37	+	8602.15i	0.159705	+	0.575207i	0.999479	+	0.0322703i	$0.0102737\pi$
$607$	2388.37	+	8602.15i	0.159705	+	0.575207i	−0.839774	+	0.542936i	$0.817312\pi$
$608$	18335.9	+	34585.1i	1.22306	+	2.30693i
$609$	−5937.04	+	4513.22i	−0.395043	+	0.300304i
$610$	296.057	+	5460.44i	0.0196508	+	0.362437i
$611$	20558.3	+	6926.90i	1.36121	+	0.458645i
$612$	−6220.39	−	1369.21i	−0.410856	−	0.0904364i
$613$	373.474	−	704.446i	0.0246076	−	0.0464149i	−0.870903	−	0.491454i	$-0.836465\pi$
$613$	373.474	−	704.446i	0.0246076	−	0.0464149i	0.895511	+	0.445039i	$0.146810\pi$
$614$	3960.72	+	24159.3i	0.260328	+	1.58793i
$615$	2109.03	−	2482.94i	0.138283	−	0.162799i
$616$	−40.0985	−	47.2077i	−0.00262275	−	0.00308774i
$617$	−3269.66	+	19944.0i	−0.213341	+	1.30132i	0.635264	+	0.772295i	$0.280891\pi$
$617$	−3269.66	+	19944.0i	−0.213341	+	1.30132i	−0.848605	+	0.529027i	$0.822557\pi$
$618$	3331.58	+	2532.60i	0.216854	+	0.164848i
$619$	−6670.08	+	9837.63i	−0.433107	+	0.638785i	−0.980136	−	0.198329i	$-0.936449\pi$
$619$	−6670.08	+	9837.63i	−0.433107	+	0.638785i	0.547029	+	0.837114i	$0.315759\pi$
$620$	−4119.22	+	6075.40i	−0.266826	+	0.393538i
$621$	713.761	+	542.587i	0.0461228	+	0.0350616i
$622$	−920.620	+	5615.53i	−0.0593464	+	0.361997i
$623$	4128.39	+	4860.32i	0.265490	+	0.312560i
$624$	−6499.50	+	7651.80i	−0.416968	+	0.490893i
$625$	−1851.51	−	11293.7i	−0.118497	−	0.722799i
$626$	14279.2	−	26933.4i	0.911678	−	1.71961i
$627$	−3064.34	−	674.513i	−0.195180	−	0.0429624i
$628$	24755.6	+	8341.13i	1.57302	+	0.530011i
$629$	−265.208	−	4891.48i	−0.0168117	−	0.310073i
$630$	1295.31	−	984.667i	0.0819147	−	0.0622699i
$631$	3703.47	+	6985.49i	0.233650	+	0.440710i	0.972417	−	0.233251i	$-0.0749364\pi$
$631$	3703.47	+	6985.49i	0.233650	+	0.440710i	−0.738767	+	0.673961i	$0.764592\pi$
$632$	153.980	+	554.585i	0.00969144	+	0.0349054i
$633$	3121.55	+	2956.89i	0.196004	+	0.185665i
$634$	10475.7	+	26292.0i	0.656219	+	1.64699i
$635$	4899.07	−	1650.69i	0.306163	−	0.103158i
$636$	−10870.0	+	1182.18i	−0.677708	+	0.0737052i
$637$	−7598.68	−	3515.52i	−0.472639	−	0.218666i
$638$	3644.15	−	3451.92i	0.226134	−	0.214205i
$639$	4836.84	+	2910.23i	0.299441	+	0.180167i
$640$	−293.283	−	31.8964i	−0.0181141	−	0.00197003i
$641$	−1820.18	+	400.652i	−0.112157	+	0.0246877i	−0.270694	−	0.962665i	$-0.587253\pi$
$641$	−1820.18	+	400.652i	−0.112157	+	0.0246877i	0.158537	+	0.987353i	$0.449322\pi$
$642$	−4579.24	+	16492.9i	−0.281508	+	1.01390i
$643$	3817.56	−	2296.95i	0.234137	−	0.140875i	−0.393651	−	0.919260i	$-0.628788\pi$
$643$	3817.56	−	2296.95i	0.234137	−	0.140875i	0.627788	+	0.778385i	$0.283961\pi$
$644$	3161.53	−	1462.68i	0.193450	−	0.0894994i
$645$	−1031.85	+	2589.76i	−0.0629910	+	0.158095i
$646$	2994.60	−	55232.2i	0.182386	−	3.36390i
$647$	−1754.74	−	2588.05i	−0.106624	−	0.157259i	0.770633	−	0.637279i	$-0.219940\pi$
$647$	−1754.74	−	2588.05i	−0.106624	−	0.157259i	−0.877258	+	0.480019i	$0.840630\pi$
$648$	−55.0619			−0.00333802
$649$	−1332.04	+	2779.04i	−0.0805659	+	0.168084i
$650$	−23128.8			−1.39567
$651$	−6236.41	−	9198.01i	−0.375459	−	0.553761i
$652$	−1257.91	+	23200.8i	−0.0755576	+	1.39358i
$653$	−10535.7	+	26442.7i	−0.631385	+	1.58466i	0.169295	+	0.985565i	$0.445851\pi$
$653$	−10535.7	+	26442.7i	−0.631385	+	1.58466i	−0.800680	+	0.599092i	$0.795528\pi$
$654$	−6062.21	+	2804.68i	−0.362464	+	0.167694i
$655$	−526.878	+	317.012i	−0.0314302	+	0.0189109i
$656$	−5597.16	+	20159.2i	−0.333129	+	1.19982i
$657$	1973.75	−	434.455i	0.117204	−	0.0257986i
$658$	22446.9	+	2441.25i	1.32990	+	0.144635i
$659$	−4581.45	−	2756.56i	−0.270816	−	0.162945i	0.373668	−	0.927563i	$-0.378100\pi$
$659$	−4581.45	−	2756.56i	−0.270816	−	0.162945i	−0.644484	+	0.764618i	$0.722928\pi$
$660$	−393.238	+	372.495i	−0.0231921	+	0.0219687i
$661$	20583.7	+	9523.03i	1.21121	+	0.560368i	0.918343	−	0.395784i	$-0.129527\pi$
$661$	20583.7	+	9523.03i	1.21121	+	0.560368i	0.292871	+	0.956152i	$0.405389\pi$
$662$	−13634.5	+	1482.84i	−0.800483	+	0.0870578i
$663$	13162.5	−	4434.95i	0.771022	−	0.259788i
$664$	175.061	+	439.371i	0.0102315	+	0.0256791i
$665$	5073.85	+	4806.21i	0.295873	+	0.280266i
$666$	519.139	+	1869.77i	0.0302046	+	0.108787i
$667$	−2885.76	−	5443.12i	−0.167522	−	0.315980i
$668$	−16230.3	+	12338.0i	−0.940076	+	0.714627i
$669$	−412.529	−	7608.65i	−0.0238405	−	0.439712i
$670$	10923.9	+	3680.69i	0.629892	+	0.212235i
$671$	2691.68	+	592.484i	0.154860	+	0.0340873i
$672$	−4792.16	+	9038.97i	−0.275092	+	0.518878i
$673$	4063.55	+	24786.6i	0.232747	+	1.41969i	0.801899	+	0.597460i	$0.203823\pi$
$673$	4063.55	+	24786.6i	0.232747	+	1.41969i	−0.569152	+	0.822232i	$0.692729\pi$
$674$	23668.8	−	27865.0i	1.35265	−	1.59246i
$675$	−1983.90	−	2335.63i	−0.113127	−	0.133183i
$676$	−540.073	+	3294.30i	−0.0307279	+	0.187432i
$677$	−3481.70	−	2646.72i	−0.197655	−	0.150254i	0.501665	−	0.865062i	$-0.332721\pi$
$677$	−3481.70	−	2646.72i	−0.197655	−	0.150254i	−0.699321	+	0.714808i	$0.746514\pi$
$678$	7935.21	−	11703.6i	0.449484	−	0.662939i
$679$	−3702.36	+	5460.57i	−0.209254	+	0.308627i
$680$	165.893	+	126.108i	0.00935544	+	0.00711182i
$681$	66.3476	−	404.702i	0.00373340	−	0.0227727i
$682$	4842.24	+	5700.73i	0.271876	+	0.320077i
$683$	−15486.5	+	18232.1i	−0.867603	+	1.02142i	0.131942	+	0.991257i	$0.457879\pi$
$683$	−15486.5	+	18232.1i	−0.867603	+	1.02142i	−0.999545	+	0.0301642i	$0.990397\pi$
$684$	1753.29	+	10694.6i	0.0980097	+	0.597833i
$685$	−1834.96	+	3461.09i	−0.102350	+	0.193053i
$686$	−26368.1	−	5804.06i	−1.46755	−	0.323032i
$687$	12382.1	+	4172.02i	0.687638	+	0.231692i
$688$	−969.267	−	17877.1i	−0.0537107	−	0.990635i
$689$	18982.0	−	14429.7i	1.04957	−	0.797865i
$690$	629.597	+	1187.55i	0.0347367	+	0.0655204i
$691$	−1705.82	−	6143.81i	−0.0939110	−	0.338237i	0.901637	−	0.432494i	$-0.142366\pi$
$691$	−1705.82	−	6143.81i	−0.0939110	−	0.338237i	−0.995548	+	0.0942570i	$0.969952\pi$
$692$	5854.59	+	5545.76i	0.321616	+	0.304651i
$693$	−303.532	−	761.809i	−0.0166382	−	0.0417586i
$694$	39028.9	−	13150.4i	2.13475	−	0.719282i
$695$	−5118.40	+	556.659i	−0.279355	+	0.0303817i
$696$	343.384	+	158.866i	0.0187011	+	0.00865204i
$697$	21013.7	−	19905.3i	1.14197	−	1.08173i
$698$	36452.8	+	21932.9i	1.97673	+	1.18936i
$699$	5415.46	+	588.967i	0.293035	+	0.0318695i
$700$	−11628.1	+	2559.53i	−0.627857	+	0.138202i
$701$	−8131.97	+	29288.7i	−0.438146	+	1.57806i	0.333974	+	0.942582i	$0.391610\pi$
$701$	−8131.97	+	29288.7i	−0.438146	+	1.57806i	−0.772120	+	0.635477i	$0.780804\pi$
$702$	−4714.46	+	2836.60i	−0.253470	+	0.152508i
$703$	−7564.71	+	3499.81i	−0.405844	+	0.187763i
$704$	1233.09	−	3094.83i	0.0660142	−	0.165683i
$705$	−233.292	+	4302.82i	−0.0124628	+	0.229863i
$706$	11601.2	+	17110.5i	0.618440	+	0.912130i
$707$	−16383.4			−0.871514
$708$	10619.7	+	721.212i	0.563721	+	0.0382836i
$709$	3460.20			0.183287			0.0916434	−	0.995792i	$-0.470788\pi$
$709$	3460.20			0.183287			0.0916434	+	0.995792i	$0.470788\pi$
$710$	4749.09	+	7004.38i	0.251028	+	0.370239i
$711$	−412.553	+	7609.09i	−0.0217608	+	0.401355i
$712$	119.749	−	300.548i	0.00630308	−	0.0158195i
$713$	8331.80	−	3854.70i	0.437627	−	0.202468i
$714$	12387.1	−	7453.04i	0.649263	−	0.390649i
$715$	316.001	−	1138.13i	0.0165283	−	0.0595296i
$716$	32756.0	−	7210.13i	1.70970	−	0.376334i
$717$	−16644.4	−	1810.19i	−0.866941	−	0.0942855i
$718$	−23859.5	−	14355.8i	−1.24015	−	0.746175i
$719$	−141.922	+	134.435i	−0.00736132	+	0.00697301i	−0.691371	−	0.722500i	$-0.742993\pi$
$719$	−141.922	+	134.435i	−0.00736132	+	0.00697301i	0.684010	+	0.729473i	$0.260234\pi$
$720$	−1809.89	−	837.343i	−0.0936813	−	0.0433416i
$721$	−4670.44	+	507.941i	−0.241243	+	0.0262368i
$722$	−63328.3	+	21337.8i	−3.26431	+	1.09988i
$723$	−7002.89	−	17575.9i	−0.360222	−	0.904089i
$724$	5935.36	+	5622.27i	0.304677	+	0.288605i
$725$	5633.43	+	20289.8i	0.288580	+	1.03937i
$726$	−7182.83	−	13548.3i	−0.367190	−	0.692593i
$727$	−24392.9	+	18543.0i	−1.24440	+	0.945972i	−0.999721	−	0.0236313i	$-0.992477\pi$
$727$	−24392.9	+	18543.0i	−1.24440	+	0.945972i	−0.244684	+	0.969603i	$0.578684\pi$
$728$	−25.2570	−	465.839i	−0.00128584	−	0.0237158i
$729$	−690.839	−	232.771i	−0.0350983	−	0.0118260i
$730$	2958.97	+	651.319i	0.150023	+	0.0330225i
$731$	−11601.9	+	21883.5i	−0.587021	+	1.10724i
$732$	−1540.07	−	9393.99i	−0.0777630	−	0.474333i
$733$	2849.05	−	3354.16i	0.143563	−	0.169016i	−0.685681	−	0.727902i	$-0.740495\pi$
$733$	2849.05	−	3354.16i	0.143563	−	0.169016i	0.829244	+	0.558887i	$0.188771\pi$
$734$	−3082.31	−	3628.78i	−0.155000	−	0.182480i
$735$	269.053	−	1641.15i	0.0135023	−	0.0823603i
$736$	−6728.21	−	5114.65i	−0.336964	−	0.256153i
$737$	3260.38	−	4808.71i	0.162955	−	0.240341i
$738$	−6434.48	+	9490.14i	−0.320944	+	0.473356i
$739$	−19050.6	−	14481.9i	−0.948293	−	0.720873i	0.0119824	−	0.999928i	$-0.496186\pi$
$739$	−19050.6	−	14481.9i	−0.948293	−	0.720873i	−0.960275	+	0.279055i	$0.909979\pi$
$740$	−232.782	+	1419.91i	−0.0115639	+	0.0705364i
$741$	−15299.7	−	18012.2i	−0.758499	−	0.892975i
$742$	16066.2	−	18914.6i	0.794891	−	0.935819i
$743$	−614.555	−	3748.62i	−0.0303443	−	0.185092i	0.967305	−	0.253615i	$-0.0816197\pi$
$743$	−614.555	−	3748.62i	−0.0303443	−	0.185092i	−0.997650	+	0.0685229i	$0.978171\pi$
$744$	−264.085	+	498.116i	−0.0130132	+	0.0245455i
$745$	1829.23	+	402.644i	0.0899568	+	0.0198010i
$746$	34274.9	+	11548.6i	1.68216	+	0.566787i
$747$	339.010	+	6252.66i	0.0166047	+	0.306256i
$748$	−3831.22	+	2912.41i	−0.187277	+	0.142364i
$749$	−9000.63	−	16977.0i	−0.439087	−	0.828205i
$750$	−2582.67	−	9301.95i	−0.125741	−	0.452879i
$751$	−10985.0	−	10405.5i	−0.533751	−	0.505596i	0.372674	−	0.927962i	$-0.378441\pi$
$751$	−10985.0	−	10405.5i	−0.533751	−	0.505596i	−0.906425	+	0.422366i	$0.861200\pi$
$752$	−10243.2	−	25708.4i	−0.496715	−	1.24666i
$753$	1630.16	−	549.264i	0.0788927	−	0.0265820i
$754$	37585.2	−	4087.64i	1.81535	−	0.197431i
$755$	−2641.01	−	1221.86i	−0.127306	−	0.0588981i
$756$	−2056.30	+	1947.83i	−0.0989245	+	0.0937063i
$757$	5079.14	+	3056.02i	0.243863	+	0.146728i	0.632239	−	0.774773i	$-0.282136\pi$
$757$	5079.14	+	3056.02i	0.243863	+	0.146728i	−0.388376	+	0.921501i	$0.626964\pi$
$758$	−57543.2	−	6258.20i	−2.75734	−	0.299878i
$759$	661.601	−	145.629i	0.0316398	−	0.00696445i
$760$	94.8561	−	341.641i	0.00452736	−	0.0163061i
$761$	−5729.62	+	3447.40i	−0.272929	+	0.164216i	−0.645438	−	0.763813i	$-0.723325\pi$
$761$	−5729.62	+	3447.40i	−0.272929	+	0.164216i	0.372509	+	0.928028i	$0.378497\pi$
$762$	−16513.3	+	7639.86i	−0.785057	+	0.363206i
$763$	2775.48	−	6965.92i	0.131689	−	0.330515i
$764$	977.015	−	18020.0i	0.0462659	−	0.853324i
$765$	1548.27	+	2283.53i	0.0731738	+	0.107923i
$766$	−31650.8			−1.49294
$767$	−20654.4	+	10591.8i	−0.972341	+	0.498630i
$768$	12795.9			0.601216
$769$	20463.7	+	30181.6i	0.959608	+	1.41532i	0.909093	+	0.416592i	$0.136776\pi$
$769$	20463.7	+	30181.6i	0.959608	+	1.41532i	0.0505144	+	0.998723i	$0.483914\pi$
$770$	66.5579	−	1227.59i	0.00311504	−	0.0574535i
$771$	2417.87	−	6068.41i	0.112941	−	0.283461i
$772$	27956.5	−	12934.1i	1.30334	−	0.602989i
$773$	−4148.85	+	2496.28i	−0.193045	+	0.116151i	−0.608795	−	0.793328i	$-0.708347\pi$
$773$	−4148.85	+	2496.28i	−0.193045	+	0.116151i	0.415750	+	0.909479i	$0.363519\pi$
$774$	2624.89	−	9454.00i	0.121899	−	0.439040i
$775$	−30644.3	+	6745.32i	−1.42036	+	0.312644i
$776$	332.743	+	36.1880i	0.0153928	+	0.00167406i
$777$	−1866.58	−	1123.09i	−0.0861819	−	0.0518539i
$778$	7661.09	−	7256.97i	0.353038	−	0.334415i
$779$	−44697.5	−	20679.3i	−2.05578	−	0.951106i
$780$	−4055.80	+	441.095i	−0.186181	+	0.0202484i
$781$	4041.89	−	1361.87i	0.185186	−	0.0623964i
$782$	4420.31	+	11094.1i	0.202136	+	0.507322i
$783$	3636.70	+	3444.87i	0.165984	+	0.157228i
$784$	2857.31	+	10291.1i	0.130162	+	0.468800i
$785$	−5300.26	−	9997.35i	−0.240986	−	0.454549i
$786$	1722.87	−	1309.69i	0.0781841	−	0.0594340i
$787$	−623.086	−	11492.1i	−0.0282219	−	0.520522i	−0.978130	−	0.207993i	$-0.933307\pi$
$787$	−623.086	−	11492.1i	−0.0282219	−	0.520522i	0.949908	−	0.312529i	$-0.101176\pi$
$788$	12157.9	+	4096.46i	0.549626	+	0.185191i
$789$	−2568.42	−	565.352i	−0.115891	−	0.0255096i
$790$	−5351.11	+	10093.3i	−0.240992	+	0.454560i
$791$	2568.07	+	15664.5i	0.115436	+	0.704128i
$792$	−26.9337	+	31.7088i	−0.00120839	+	0.00142263i
$793$	13439.1	+	15821.7i	0.601810	+	0.708505i
$794$	6070.99	−	37031.4i	0.271349	−	1.65516i
$795$	3770.46	+	2866.23i	0.168207	+	0.127868i
$796$	7038.76	−	10381.4i	0.313420	−	0.462259i
$797$	−6858.51	+	10115.5i	−0.304819	+	0.449574i	−0.948990	−	0.315308i	$-0.897892\pi$
$797$	−6858.51	+	10115.5i	−0.304819	+	0.449574i	0.644171	+	0.764882i	$0.277203\pi$
$798$	−19581.9	−	14885.8i	−0.868662	−	0.660339i
$799$	−6194.00	+	37781.7i	−0.274253	+	1.67287i
$800$	18701.1	+	22016.6i	0.826480	+	0.973007i
$801$	2772.99	−	3264.62i	0.122321	−	0.144007i
$802$	−5568.26	−	33964.9i	−0.245165	−	1.49544i
$803$	715.273	−	1349.15i	0.0314339	−	0.0592907i
$804$	−19597.4	−	4313.71i	−0.859636	−	0.189220i
$805$	−1429.92	−	481.797i	−0.0626064	−	0.0210945i
$806$	3050.00	+	56254.0i	0.133290	+	2.45839i
$807$	−8543.31	+	6494.46i	−0.372663	+	0.283291i
$808$	389.331	+	734.357i	0.0169513	+	0.0319735i
$809$	−11120.9	−	40053.7i	−0.483299	−	1.74069i	−0.655089	−	0.755552i	$-0.727369\pi$
$809$	−11120.9	−	40053.7i	−0.483299	−	1.74069i	0.171790	−	0.985134i	$-0.445045\pi$
$810$	−793.433	−	751.580i	−0.0344178	−	0.0326022i
$811$	−1041.44	−	2613.82i	−0.0450924	−	0.113173i	0.904705	−	0.426038i	$-0.140091\pi$
$811$	−1041.44	−	2613.82i	−0.0450924	−	0.113173i	−0.949798	+	0.312864i	$0.898712\pi$
$812$	18443.7	−	6214.41i	0.797103	−	0.268575i
$813$	14461.5	−	1572.78i	0.623845	−	0.0678472i
$814$	1330.69	+	615.645i	0.0572983	+	0.0265090i
$815$	7306.72	−	6921.30i	0.314041	−	0.297475i
$816$	−15182.0	−	9134.69i	−0.651318	−	0.391885i
$817$	41897.0	+	4556.58i	1.79411	+	0.195122i
$818$	−3001.69	+	660.723i	−0.128303	+	0.0282416i
$819$	1652.41	−	5951.46i	0.0705006	−	0.253920i
$820$	−7284.83	+	4383.14i	−0.310241	+	0.186666i
$821$	3302.16	−	1527.74i	0.140373	−	0.0649434i	−0.348445	−	0.937329i	$-0.613290\pi$
$821$	3302.16	−	1527.74i	0.140373	−	0.0649434i	0.488818	+	0.872386i	$0.337428\pi$
$822$	5103.31	−	12808.3i	0.216543	−	0.543482i
$823$	2170.65	−	40035.3i	0.0919369	−	1.69568i	−0.481516	−	0.876437i	$-0.659914\pi$
$823$	2170.65	−	40035.3i	0.0919369	−	1.69568i	0.573453	−	0.819239i	$-0.305604\pi$
$824$	133.755	+	197.274i	0.00565483	+	0.00834025i
$825$	−2315.46			−0.0977141
$826$	−18624.8	+	15387.6i	−0.784554	+	0.648190i
$827$	−39281.9			−1.65171			−0.825855	−	0.563883i	$-0.809307\pi$
$827$	−39281.9			−1.65171			−0.825855	+	0.563883i	$0.809307\pi$
$828$	−1313.08	−	1936.64i	−0.0551117	−	0.0812837i
$829$	−1010.82	+	18643.6i	−0.0423491	+	0.781083i	0.897818	+	0.440368i	$0.145152\pi$
$829$	−1010.82	+	18643.6i	−0.0423491	+	0.781083i	−0.940167	+	0.340715i	$0.889331\pi$
$830$	−3474.68	+	8720.80i	−0.145311	+	0.364703i
$831$	2375.70	−	1099.11i	0.0991721	−	0.0458819i
$832$	21500.5	−	12936.4i	0.895909	−	0.539050i
$833$	3953.02	−	14237.5i	0.164422	−	0.592196i
$834$	17697.0	−	3895.41i	0.734770	−	0.161735i
$835$	8779.28	+	954.804i	0.363856	+	0.0395717i
$836$	7016.37	+	4221.61i	0.290271	+	0.174650i
$837$	−5419.11	+	5133.26i	−0.223790	+	0.211985i
$838$	32867.2	+	15206.0i	1.35487	+	0.626828i
$839$	28896.8	−	3142.72i	1.18907	−	0.129319i	0.507881	−	0.861427i	$-0.330429\pi$
$839$	28896.8	−	3142.72i	1.18907	−	0.129319i	0.681189	+	0.732108i	$0.261463\pi$
$840$	87.8162	−	29.5887i	0.00360708	−	0.00121537i
$841$	−3713.12	−	9319.23i	−0.152246	−	0.382108i
$842$	−30907.4	−	29277.0i	−1.26501	−	1.19828i
$843$	2198.30	+	7917.58i	0.0898145	+	0.323483i
$844$	−5255.99	−	9913.84i	−0.214358	−	0.404323i
$845$	1151.16	−	875.087i	0.0468651	−	0.0356259i
$846$	−821.083	−	15144.0i	−0.0333681	−	0.615438i
$847$	16313.4	+	5496.63i	0.661790	+	0.222983i
$848$	−29705.5	−	6538.66i	−1.20294	−	0.264786i
$849$	1520.30	−	2867.60i	0.0614566	−	0.115919i
$850$	−6603.69	−	40280.7i	−0.266476	−	1.62543i
$851$	1165.02	−	1371.56i	0.0469286	−	0.0552486i
$852$	−9536.96	−	11227.8i	−0.383487	−	0.451476i
$853$	−4259.99	+	25984.8i	−0.170995	+	1.04303i	0.752268	+	0.658858i	$0.228960\pi$
$853$	−4259.99	+	25984.8i	−0.170995	+	1.04303i	−0.923263	+	0.384168i	$0.874488\pi$
$854$	17200.5	+	13075.5i	0.689215	+	0.523927i
$855$	2634.38	−	3885.43i	0.105373	−	0.155414i
$856$	−547.076	+	806.876i	−0.0218442	+	0.0322178i
$857$	−36584.6	−	27810.9i	−1.45823	−	1.10852i	−0.972081	−	0.234646i	$-0.924607\pi$
$857$	−36584.6	−	27810.9i	−1.45823	−	1.10852i	−0.486153	−	0.873874i	$-0.661600\pi$
$858$	−672.567	+	4102.48i	−0.0267611	+	0.163236i
$859$	−21444.8	−	25246.8i	−0.851789	−	1.00280i	−0.999904	−	0.0138334i	$-0.995597\pi$
$859$	−21444.8	−	25246.8i	−0.851789	−	1.00280i	0.148115	−	0.988970i	$-0.452679\pi$
$860$	4709.89	−	5544.91i	0.186751	−	0.219860i
$861$	−2082.38	−	12702.0i	−0.0824244	−	0.502767i
$862$	11954.3	−	22548.3i	0.472351	−	0.890949i
$863$	−3564.33	−	784.568i	−0.140592	−	0.0309467i	0.144117	−	0.989561i	$-0.453966\pi$
$863$	−3564.33	−	784.568i	−0.140592	−	0.0309467i	−0.284709	+	0.958614i	$0.591897\pi$
$864$	6512.14	+	2194.20i	0.256421	+	0.0863982i
$865$	−189.113	−	3487.98i	−0.00743355	−	0.137104i
$866$	−14337.1	+	10898.8i	−0.562582	+	0.427664i
$867$	4578.08	+	8635.17i	0.179331	+	0.338253i
$868$	7758.71	+	27944.3i	0.303396	+	1.09273i
$869$	4180.09	+	3959.59i	0.163176	+	0.154568i
$870$	2779.63	+	6976.34i	0.108320	+	0.271862i
$871$	41468.5	−	13972.4i	1.61321	−	0.543554i
$872$	−378.191	+	41.1308i	−0.0146871	+	0.00159732i
$873$	4021.81	+	1860.69i	0.155919	+	0.0721359i
$874$	14752.1	−	13973.9i	0.570936	−	0.540819i
$875$	9286.09	+	5587.26i	0.358774	+	0.215867i
$876$	−5243.31	−	570.244i	−0.202232	−	0.0219940i
$877$	−2481.90	+	546.308i	−0.0955619	+	0.0210348i	−0.262494	−	0.964934i	$-0.584545\pi$
$877$	−2481.90	+	546.308i	−0.0955619	+	0.0210348i	0.166932	+	0.985968i	$0.446614\pi$
$878$	−2890.35	+	10410.1i	−0.111099	+	0.400141i
$879$	13862.1	−	8340.53i	0.531918	−	0.320044i
$880$	−1367.52	+	632.681i	−0.0523852	+	0.0242360i
$881$	−26.1836	+	65.7159i	−0.00100130	+	0.00251308i	−0.929477	−	0.368881i	$-0.879741\pi$
$881$	−26.1836	+	65.7159i	−0.00100130	+	0.00251308i	0.928475	+	0.371394i	$0.121120\pi$
$882$	−316.887	+	5844.64i	−0.0120977	+	0.223128i
$883$	3860.75	+	5694.18i	0.147140	+	0.217015i	0.894116	−	0.447836i	$-0.147805\pi$
$883$	3860.75	+	5694.18i	0.147140	+	0.217015i	−0.746976	+	0.664851i	$0.768495\pi$
$884$	−36247.7			−1.37912
$885$	−3124.78	−	3390.25i	−0.118687	−	0.128771i
$886$	16102.5			0.610582
$887$	14827.1	+	21868.4i	0.561270	+	0.827811i	0.997399	−	0.0720729i	$-0.0229614\pi$
$887$	14827.1	+	21868.4i	0.561270	+	0.827811i	−0.436130	+	0.899884i	$0.643651\pi$
$888$	−5.98329	+	110.355i	−0.000226111	+	0.00417036i
$889$	7560.31	−	18975.0i	0.285225	−	0.715860i
$890$	5827.96	−	2696.30i	0.219499	−	0.101551i
$891$	−471.973	+	283.977i	−0.0177460	+	0.0106774i
$892$	−5319.95	+	19160.7i	−0.199692	+	0.719225i
$893$	63620.7	−	14004.0i	2.38408	−	0.524776i
$894$	−6553.54	−	712.741i	−0.245172	−	0.0266640i
$895$	−12448.6	−	7490.09i	−0.464929	−	0.279739i
$896$	−846.226	+	801.587i	−0.0315518	+	0.0298875i
$897$	4630.85	+	2142.46i	0.172374	+	0.0797488i
$898$	22515.4	−	2448.70i	0.836691	−	0.0909956i
$899$	48606.0	−	16377.3i	1.80323	−	0.607578i
$900$	2960.15	+	7429.41i	0.109635	+	0.275163i
$901$	30550.3	+	28938.8i	1.12961	+	1.07002i
$902$	2317.70	+	8347.59i	0.0855553	+	0.308142i
$903$	5159.30	+	9731.48i	0.190134	+	0.358630i
$904$	641.108	−	487.358i	0.0235873	−	0.0179306i
$905$	−191.722	−	3536.10i	−0.00704204	−	0.129883i
$906$	9705.63	+	3270.21i	0.355903	+	0.119918i
$907$	−28205.4	−	6208.47i	−1.03257	−	0.227287i	−0.333811	−	0.942640i	$-0.608335\pi$
$907$	−28205.4	−	6208.47i	−1.03257	−	0.227287i	−0.698763	+	0.715354i	$0.746266\pi$
$908$	−501.317	+	945.584i	−0.0183225	+	0.0345598i
$909$	1780.33	+	10859.5i	0.0649614	+	0.396247i
$910$	5994.61	−	7057.41i	0.218373	−	0.257089i
$911$	17987.8	+	21176.9i	0.654185	+	0.770166i	0.984817	−	0.173593i	$-0.0555379\pi$
$911$	17987.8	+	21176.9i	0.654185	+	0.770166i	−0.330632	+	0.943760i	$0.607262\pi$
$912$	−4877.32	+	29750.4i	−0.177088	+	1.08019i
$913$	3766.58	+	2863.28i	0.136534	+	0.103791i
$914$	3250.74	−	4794.48i	0.117642	−	0.173509i
$915$	−2314.01	+	3412.91i	−0.0836053	+	0.123309i
$916$	−27145.8	−	20635.7i	−0.979173	−	0.744348i
$917$	−393.046	+	2397.48i	−0.0141543	+	0.0863377i
$918$	−6286.24	−	7400.73i	−0.226010	−	0.266079i
$919$	5308.97	−	6250.20i	0.190562	−	0.224347i	−0.658581	−	0.752510i	$-0.728843\pi$
$919$	5308.97	−	6250.20i	0.190562	−	0.224347i	0.849143	+	0.528163i	$0.177119\pi$
$920$	12.3847	+	75.5432i	0.000443816	+	0.00270716i
$921$	−8646.91	+	16309.8i	−0.309365	+	0.583525i
$922$	−47291.1	−	10409.6i	−1.68921	−	0.371823i
$923$	30443.3	+	10257.5i	1.08565	+	0.365798i
$924$	115.863	+	2136.96i	0.00412511	+	0.0760832i
$925$	−4896.66	+	3722.34i	−0.174055	+	0.132313i
$926$	−9577.26	−	18064.6i	−0.339879	−	0.641080i
$927$	844.206	+	3040.56i	0.0299109	+	0.107729i
$928$	−34281.1	−	32472.8i	−1.21264	−	1.14868i
$929$	−15574.0	−	39087.8i	−0.550018	−	1.38044i	−0.896775	−	0.442486i	$-0.854097\pi$
$929$	−15574.0	−	39087.8i	−0.550018	−	1.38044i	0.346757	−	0.937955i	$-0.387283\pi$
$930$	−10604.6	+	3573.09i	−0.373911	+	0.125985i
$931$	−24994.1	+	2718.27i	−0.879858	+	0.0956903i
$932$	−12902.2	−	5969.20i	−0.453462	−	0.209794i
$933$	−3115.13	+	2950.81i	−0.109309	+	0.103543i
$934$	−60583.5	−	36451.9i	−2.12244	−	1.27703i
$935$	2072.37	+	225.384i	0.0724854	+	0.00788326i
$936$	−306.032	+	67.3626i	−0.0106869	+	0.00235237i
$937$	−13781.7	+	49637.3i	−0.480501	+	1.73061i	0.183635	+	0.982995i	$0.441214\pi$
$937$	−13781.7	+	49637.3i	−0.480501	+	1.73061i	−0.664135	+	0.747612i	$0.731200\pi$
$938$	39025.6	−	23480.9i	1.35845	−	0.817355i
$939$	20861.9	−	9651.73i	0.725028	−	0.335434i
$940$	4162.43	−	10446.9i	0.144429	−	0.362490i
$941$	2890.18	−	53306.2i	0.100124	−	1.84669i	−0.330077	−	0.943954i	$-0.607075\pi$
$941$	2890.18	−	53306.2i	0.100124	−	1.84669i	0.430201	−	0.902733i	$-0.358443\pi$
$942$	22349.5	+	32963.0i	0.773020	+	1.14012i
$943$	10633.1			0.367191
$944$	27355.1	+	11334.1i	0.943150	+	0.390778i
$945$	1226.88			0.0422332
$946$	−4160.35	−	6136.06i	−0.142986	−	0.210889i
$947$	−761.561	+	14046.2i	−0.0261324	+	0.481984i	0.955950	+	0.293531i	$0.0948303\pi$
$947$	−761.561	+	14046.2i	−0.0261324	+	0.481984i	−0.982082	+	0.188454i	$0.939653\pi$
$948$	7360.83	−	18474.3i	0.252182	−	0.632930i
$949$	10438.5	−	4829.36i	0.357058	−	0.165192i
$950$	−59510.9	+	35806.5i	−2.03241	+	1.22286i
$951$	−5709.28	+	20563.0i	−0.194675	+	0.701156i
$952$	804.085	−	176.992i	0.0273745	−	0.00602559i
$953$	21339.7	+	2320.83i	0.725352	+	0.0788868i	0.463343	−	0.886179i	$-0.346650\pi$
$953$	21339.7	+	2320.83i	0.725352	+	0.0788868i	0.262008	+	0.965066i	$0.415615\pi$
$954$	−14283.2	−	8593.93i	−0.484734	−	0.291655i
$955$	−5675.11	+	5375.75i	−0.192295	+	0.182152i
$956$	39654.9	+	18346.3i	1.34156	+	0.620672i
$957$	3762.72	−	409.220i	0.127097	−	0.0138226i
$958$	20551.6	−	6924.63i	0.693101	−	0.233533i
$959$	5728.98	+	14378.6i	0.192907	+	0.484161i
$960$	3618.48	+	3427.61i	0.121652	+	0.115235i
$961$	12477.1	+	44938.6i	0.418822	+	1.50846i
$962$	5172.83	+	9756.99i	0.173367	+	0.327004i
$963$	−10274.9	+	7810.81i	−0.343827	+	0.261371i
$964$	2673.11	+	49302.5i	0.0893101	+	1.64723i
$965$	−12644.4	−	4260.40i	−0.421801	−	0.142121i
$966$	5186.52	+	1141.64i	0.172747	+	0.0380245i
$967$	−19844.7	+	37431.1i	−0.659941	+	1.24478i	0.297105	+	0.954845i	$0.403979\pi$
$967$	−19844.7	+	37431.1i	−0.659941	+	1.24478i	−0.957046	+	0.289936i	$0.906366\pi$
$968$	−141.292	−	861.843i	−0.00469142	−	0.0286164i
$969$	27001.4	−	31788.5i	0.895159	−	1.05386i
$970$	4300.81	+	5063.31i	0.142362	+	0.167601i
$971$	6431.33	−	39229.3i	0.212555	−	1.29653i	−0.637752	−	0.770242i	$-0.720135\pi$
$971$	6431.33	−	39229.3i	0.212555	−	1.29653i	0.850307	−	0.526287i	$-0.176416\pi$
$972$	1514.55	+	1151.33i	0.0499787	+	0.0379928i
$973$	−11415.8	+	16837.1i	−0.376130	+	0.554750i
$974$	−26206.9	+	38652.2i	−0.862138	+	1.27156i
$975$	−13883.8	−	10554.2i	−0.456040	−	0.346672i
$976$	4284.18	−	26132.3i	0.140505	−	0.857045i
$977$	10626.2	+	12510.1i	0.347965	+	0.409656i	0.908106	−	0.418741i	$-0.137529\pi$
$977$	10626.2	+	12510.1i	0.347965	+	0.409656i	−0.560140	+	0.828398i	$0.689253\pi$
$978$	−22931.9	+	26997.5i	−0.749775	+	0.882704i
$979$	−523.596	−	3193.80i	−0.0170932	−	0.104264i
$980$	−2032.94	+	3834.54i	−0.0662653	+	0.124990i
$981$	−4918.89	−	1082.73i	−0.160090	−	0.0352384i
$982$	−52041.3	−	17534.8i	−1.69115	−	0.569814i
$983$	−1366.87	−	25210.4i	−0.0443504	−	0.817994i	−0.933103	−	0.359608i	$-0.882910\pi$
$983$	−1366.87	−	25210.4i	−0.0443504	−	0.817994i	0.888753	−	0.458386i	$-0.151572\pi$
$984$	−519.859	+	395.187i	−0.0168420	+	0.0128029i
$985$	−2603.04	−	4909.85i	−0.0842028	−	0.158823i
$986$	17850.2	+	64290.6i	0.576538	+	2.07650i
$987$	12360.5	+	11708.5i	0.398622	+	0.377594i
$988$	22828.4	+	57295.0i	0.735090	+	1.84494i
$989$	−8622.73	+	2905.34i	−0.277237	+	0.0934119i
$990$	−820.927	+	89.2812i	−0.0263543	+	0.00286620i
$991$	−26699.7	−	12352.6i	−0.855847	−	0.395957i	−0.0576379	−	0.998338i	$-0.518357\pi$
$991$	−26699.7	−	12352.6i	−0.855847	−	0.395957i	−0.798209	+	0.602381i	$0.794219\pi$
$992$	51082.8	−	48388.2i	1.63496	−	1.54872i
$993$	−8861.22	−	5331.62i	−0.283185	−	0.170386i
$994$	33240.0	+	3615.07i	1.06067	+	0.115355i
$995$	−5305.94	+	1167.93i	−0.169055	+	0.0372118i
$996$	4371.85	−	15746.0i	0.139084	−	0.500934i
$997$	49703.9	−	29905.9i	1.57888	−	0.949978i	0.588986	−	0.808143i	$-0.299527\pi$
$997$	49703.9	−	29905.9i	1.57888	−	0.949978i	0.989890	−	0.141835i	$-0.0453003\pi$
$998$	−45492.1	+	21046.9i	−1.44291	+	0.667563i
$999$	−541.590	+	1359.29i	−0.0171523	+	0.0430490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.e.b.7.3	✓	420
59.17	even	29	inner	177.4.e.b.76.3	yes	420

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.e.b.7.3	✓	420	1.1	even	1	trivial
177.4.e.b.76.3	yes	420	59.17	even	29	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.23273 - 3.29303i) q^{2} +(0.162417 - 2.99560i) q^{3} +(-2.89786 + 7.27309i) q^{4} +(3.07784 - 1.42396i) q^{5} +(-10.2272 + 6.15353i) q^{6} +(3.58463 - 12.9107i) q^{7} +(-0.663884 + 0.146132i) q^{8} +(-8.94724 - 0.973071i) q^{9} +O(q^{10})\)	\(q+(-2.23273 - 3.29303i) q^{2} +(0.162417 - 2.99560i) q^{3} +(-2.89786 + 7.27309i) q^{4} +(3.07784 - 1.42396i) q^{5} +(-10.2272 + 6.15353i) q^{6} +(3.58463 - 12.9107i) q^{7} +(-0.663884 + 0.146132i) q^{8} +(-8.94724 - 0.973071i) q^{9} +(-11.5611 - 6.95609i) q^{10} +(-4.93694 + 4.67652i) q^{11} +(21.3166 + 9.86211i) q^{12} +(-50.9188 + 5.53775i) q^{13} +(-50.5188 + 17.0218i) q^{14} +(-3.76572 - 9.45124i) q^{15} +(47.4349 + 44.9327i) q^{16} +(-24.1827 - 87.0982i) q^{17} +(16.7724 + 31.6362i) q^{18} +(-122.442 + 93.0779i) q^{19} +(1.43743 + 26.5118i) q^{20} +(-38.0930 - 12.8350i) q^{21} +(26.4228 + 5.81609i) q^{22} +(15.5543 - 29.3385i) q^{23} +(0.329927 + 2.01247i) q^{24} +(-73.4779 + 86.5048i) q^{25} +(131.924 + 155.313i) q^{26} +(-4.36811 + 26.6443i) q^{27} +(83.5128 + 63.4848i) q^{28} +(104.116 - 153.560i) q^{29} +(-22.7154 + 33.5027i) q^{30} +(220.087 + 167.306i) q^{31} +(41.1757 - 251.160i) q^{32} +(13.2071 + 15.5486i) q^{33} +(-232.824 + 274.101i) q^{34} +(-7.35136 - 44.8413i) q^{35} +(33.0051 - 62.2543i) q^{36} +(52.9260 + 11.6499i) q^{37} +(579.888 + 195.387i) q^{38} +(8.31883 + 153.432i) q^{39} +(-1.83524 + 1.39511i) q^{40} +(149.989 + 282.909i) q^{41} +(42.7853 + 154.099i) q^{42} +(-198.932 - 188.438i) q^{43} +(-19.7062 - 49.4587i) q^{44} +(-28.9238 + 9.74555i) q^{45} +(-131.341 + 14.2842i) q^{46} +(-384.405 - 177.845i) q^{47} +(142.305 - 134.798i) q^{48} +(140.066 + 84.2749i) q^{49} +(448.919 + 48.8229i) q^{50} +(-264.839 + 58.2955i) q^{51} +(107.279 - 386.385i) q^{52} +(-398.892 + 240.005i) q^{53} +(97.4934 - 45.1052i) q^{54} +(-8.53592 + 21.4235i) q^{55} +(-0.493118 + 9.09503i) q^{56} +(258.938 + 381.905i) q^{57} -738.140 q^{58} +(423.250 - 161.983i) q^{59} +79.6523 q^{60} +(-227.448 - 335.460i) q^{61} +(59.5482 - 1098.30i) q^{62} +(-44.6356 + 112.027i) q^{63} +(-444.623 + 205.704i) q^{64} +(-148.834 + 89.5505i) q^{65} +(21.7142 - 78.2074i) q^{66} +(-834.378 + 183.661i) q^{67} +(703.551 + 76.5158i) q^{68} +(-85.3601 - 51.3595i) q^{69} +(-131.250 + 124.327i) q^{70} +(-569.238 - 263.357i) q^{71} +(6.08213 - 0.661471i) q^{72} +(-212.801 + 71.7009i) q^{73} +(-79.8060 - 200.298i) q^{74} +(247.200 + 234.160i) q^{75} +(-322.144 - 1160.26i) q^{76} +(42.6799 + 80.5028i) q^{77} +(486.682 - 369.966i) q^{78} +(-45.8392 - 845.455i) q^{79} +(209.979 + 70.7502i) q^{80} +(79.1063 + 17.4126i) q^{81} +(596.744 - 1125.58i) q^{82} +(-112.562 - 686.595i) q^{83} +(203.739 - 239.860i) q^{84} +(-198.455 - 233.639i) q^{85} +(-176.372 + 1075.82i) q^{86} +(-443.093 - 336.831i) q^{87} +(2.59417 - 3.82611i) q^{88} +(-267.085 + 393.922i) q^{89} +(96.6713 + 73.4876i) q^{90} +(-111.029 + 677.247i) q^{91} +(168.307 + 198.147i) q^{92} +(536.927 - 632.120i) q^{93} +(272.625 + 1662.94i) q^{94} +(-244.317 + 460.831i) q^{95} +(-745.689 - 164.139i) q^{96} +(-466.601 - 157.216i) q^{97} +(-35.2097 - 649.404i) q^{98} +(48.7226 - 37.0379i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9}+O(q^{10}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9	\( 420 q + 2 q^{2} - 45 q^{3} - 56 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} + 66 q^{8} - 135 q^{9} - 754 q^{10} + 64 q^{11} - 168 q^{12} + 90 q^{13} + 1024 q^{14} - 42 q^{15} - 172 q^{16} + 96 q^{17} + 18 q^{18} + 16 q^{19} - 178 q^{20} - 243 q^{21} - 604 q^{22} + 48 q^{23} + 198 q^{24} - 173 q^{25} + 156 q^{26} - 405 q^{27} + 84 q^{28} - 50 q^{29} + 174 q^{30} + 222 q^{31} - 45 q^{32} + 192 q^{33} - 64 q^{34} - 132 q^{35} - 504 q^{36} + 30 q^{37} - 108 q^{38} + 270 q^{39} + 6984 q^{40} + 400 q^{41} + 114 q^{42} + 1220 q^{43} + 1180 q^{44} - 126 q^{45} + 4938 q^{46} + 370 q^{47} - 516 q^{48} + 771 q^{49} + 1048 q^{50} + 288 q^{51} - 1964 q^{52} - 822 q^{53} + 54 q^{54} - 2342 q^{55} - 13824 q^{56} + 48 q^{57} - 13150 q^{58} - 3423 q^{59} - 534 q^{60} - 2182 q^{61} + 845 q^{62} + 54 q^{63} - 8018 q^{64} + 4140 q^{65} - 1812 q^{66} + 506 q^{67} + 4826 q^{68} - 3684 q^{69} + 6882 q^{70} + 5874 q^{71} + 594 q^{72} + 206 q^{73} + 11124 q^{74} - 867 q^{75} + 16940 q^{76} + 9940 q^{77} + 468 q^{78} - 1762 q^{79} - 28954 q^{80} - 1215 q^{81} + 3770 q^{82} - 1216 q^{83} - 8013 q^{84} - 420 q^{85} - 2256 q^{86} + 5940 q^{87} + 13458 q^{88} - 1580 q^{89} + 522 q^{90} - 12204 q^{91} + 4562 q^{92} + 666 q^{93} + 176 q^{94} - 28456 q^{95} + 2040 q^{96} + 2574 q^{97} + 50690 q^{98} + 576 q^{99}+O(q^{100}) \) 420 * q + 2 * q^2 - 45 * q^3 - 56 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 + 66 * q^8 - 135 * q^9 - 754 * q^10 + 64 * q^11 - 168 * q^12 + 90 * q^13 + 1024 * q^14 - 42 * q^15 - 172 * q^16 + 96 * q^17 + 18 * q^18 + 16 * q^19 - 178 * q^20 - 243 * q^21 - 604 * q^22 + 48 * q^23 + 198 * q^24 - 173 * q^25 + 156 * q^26 - 405 * q^27 + 84 * q^28 - 50 * q^29 + 174 * q^30 + 222 * q^31 - 45 * q^32 + 192 * q^33 - 64 * q^34 - 132 * q^35 - 504 * q^36 + 30 * q^37 - 108 * q^38 + 270 * q^39 + 6984 * q^40 + 400 * q^41 + 114 * q^42 + 1220 * q^43 + 1180 * q^44 - 126 * q^45 + 4938 * q^46 + 370 * q^47 - 516 * q^48 + 771 * q^49 + 1048 * q^50 + 288 * q^51 - 1964 * q^52 - 822 * q^53 + 54 * q^54 - 2342 * q^55 - 13824 * q^56 + 48 * q^57 - 13150 * q^58 - 3423 * q^59 - 534 * q^60 - 2182 * q^61 + 845 * q^62 + 54 * q^63 - 8018 * q^64 + 4140 * q^65 - 1812 * q^66 + 506 * q^67 + 4826 * q^68 - 3684 * q^69 + 6882 * q^70 + 5874 * q^71 + 594 * q^72 + 206 * q^73 + 11124 * q^74 - 867 * q^75 + 16940 * q^76 + 9940 * q^77 + 468 * q^78 - 1762 * q^79 - 28954 * q^80 - 1215 * q^81 + 3770 * q^82 - 1216 * q^83 - 8013 * q^84 - 420 * q^85 - 2256 * q^86 + 5940 * q^87 + 13458 * q^88 - 1580 * q^89 + 522 * q^90 - 12204 * q^91 + 4562 * q^92 + 666 * q^93 + 176 * q^94 - 28456 * q^95 + 2040 * q^96 + 2574 * q^97 + 50690 * q^98 + 576 * q^99

Introduction

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