LMFDB - Embedded newform 175.2.x.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	175.17
Dual form			175.2.x.a.103.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08800 + 0.109427i) q^{2} +(-0.522748 + 0.645540i) q^{3} +(2.35872 - 0.247911i) q^{4} +(1.15075 + 1.91723i) q^{5} +(1.02086 - 1.40509i) q^{6} +(-1.53148 - 2.15744i) q^{7} +(-0.767632 + 0.121581i) q^{8} +(0.480279 + 2.25953i) q^{9} +O(q^{10})$	\(q+(-2.08800 + 0.109427i) q^{2} +(-0.522748 + 0.645540i) q^{3} +(2.35872 - 0.247911i) q^{4} +(1.15075 + 1.91723i) q^{5} +(1.02086 - 1.40509i) q^{6} +(-1.53148 - 2.15744i) q^{7} +(-0.767632 + 0.121581i) q^{8} +(0.480279 + 2.25953i) q^{9} +(-2.61256 - 3.87725i) q^{10} +(1.02734 + 0.218367i) q^{11} +(-1.07298 + 1.65224i) q^{12} +(-4.08239 + 2.08008i) q^{13} +(3.43382 + 4.33715i) q^{14} +(-1.83920 - 0.259375i) q^{15} +(-3.05026 + 0.648353i) q^{16} +(-0.808289 + 2.10566i) q^{17} +(-1.25008 - 4.66535i) q^{18} +(-0.520869 + 4.95574i) q^{19} +(3.18960 + 4.23693i) q^{20} +(2.19329 + 0.139164i) q^{21} +(-2.16897 - 0.343531i) q^{22} +(0.325733 + 6.21536i) q^{23} +(0.322792 - 0.559093i) q^{24} +(-2.35156 + 4.41250i) q^{25} +(8.29642 - 4.78994i) q^{26} +(-3.93004 - 2.00245i) q^{27} +(-4.14720 - 4.70913i) q^{28} +(-0.743348 - 1.02313i) q^{29} +(3.86863 + 0.340316i) q^{30} +(-4.14336 - 9.30613i) q^{31} +(7.79943 - 2.08985i) q^{32} +(-0.678002 + 0.549035i) q^{33} +(1.45729 - 4.48507i) q^{34} +(2.37396 - 5.41888i) q^{35} +(1.69301 + 5.21054i) q^{36} +(5.27200 + 3.42368i) q^{37} +(0.545281 - 10.4046i) q^{38} +(0.791286 - 3.72271i) q^{39} +(-1.11645 - 1.33182i) q^{40} +(5.32280 + 1.72948i) q^{41} +(-4.59482 - 0.0505673i) q^{42} +(4.80861 - 4.80861i) q^{43} +(2.47733 + 0.260378i) q^{44} +(-3.77937 + 3.52096i) q^{45} +(-1.36026 - 12.9420i) q^{46} +(0.292218 - 0.112172i) q^{47} +(1.17598 - 2.30799i) q^{48} +(-2.30911 + 6.60818i) q^{49} +(4.42720 - 9.47062i) q^{50} +(-0.936759 - 1.62251i) q^{51} +(-9.11355 + 5.91841i) q^{52} +(-0.217690 - 0.176281i) q^{53} +(8.42504 + 3.75107i) q^{54} +(0.763545 + 2.22093i) q^{55} +(1.43792 + 1.46992i) q^{56} +(-2.92684 - 2.92684i) q^{57} +(1.66407 + 2.05495i) q^{58} +(4.60084 + 5.10975i) q^{59} +(-4.40246 - 0.155834i) q^{60} +(-3.94111 - 3.54859i) q^{61} +(9.66967 + 18.9778i) q^{62} +(4.13927 - 4.49661i) q^{63} +(-10.1249 + 3.28979i) q^{64} +(-8.68581 - 5.43324i) q^{65} +(1.35559 - 1.22058i) q^{66} +(11.4671 + 4.40181i) q^{67} +(-1.38451 + 5.16706i) q^{68} +(-4.18254 - 3.03879i) q^{69} +(-4.36386 + 11.5744i) q^{70} +(-1.66579 + 1.21027i) q^{71} +(-0.643393 - 1.67610i) q^{72} +(-0.705919 - 1.08702i) q^{73} +(-11.3826 - 6.57173i) q^{74} +(-1.61917 - 3.82465i) q^{75} +11.8183i q^{76} +(-1.10223 - 2.55084i) q^{77} +(-1.24484 + 7.85959i) q^{78} +(4.40735 - 9.89907i) q^{79} +(-4.75312 - 5.10197i) q^{80} +(-2.98382 + 1.32848i) q^{81} +(-11.3033 - 3.02870i) q^{82} +(0.579789 + 3.66064i) q^{83} +(5.20787 - 0.215495i) q^{84} +(-4.96718 + 0.873412i) q^{85} +(-9.51417 + 10.5666i) q^{86} +(1.04906 + 0.0549787i) q^{87} +(-0.815165 - 0.0427210i) q^{88} +(-7.09604 + 7.88095i) q^{89} +(7.50603 - 7.76533i) q^{90} +(10.7398 + 5.62191i) q^{91} +(2.30917 + 14.5795i) q^{92} +(8.17341 + 2.19006i) q^{93} +(-0.597877 + 0.266192i) q^{94} +(-10.1007 + 4.70418i) q^{95} +(-2.72805 + 6.12730i) q^{96} +(0.775456 - 4.89604i) q^{97} +(4.09830 - 14.0505i) q^{98} +2.42618i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−2.08800	+	0.109427i	−1.47644	+	0.0773768i	−0.773465	−	0.633839i	$-0.781478\pi$
$2$	−2.08800	+	0.109427i	−1.47644	+	0.0773768i	−0.702973	+	0.711216i	$0.748145\pi$
$3$	−0.522748	+	0.645540i	−0.301809	+	0.372703i	−0.905377	−	0.424609i	$-0.860412\pi$
$3$	−0.522748	+	0.645540i	−0.301809	+	0.372703i	0.603568	+	0.797311i	$0.293745\pi$
$4$	2.35872	−	0.247911i	1.17936	−	0.123956i
$5$	1.15075	+	1.91723i	0.514630	+	0.857412i
$5$	1.15075	+	1.91723i	0.514630	+	0.857412i
$6$	1.02086	−	1.40509i	0.416763	−	0.573625i
$7$	−1.53148	−	2.15744i	−0.578847	−	0.815436i
$7$	−1.53148	−	2.15744i	−0.578847	−	0.815436i
$8$	−0.767632	+	0.121581i	−0.271399	+	0.0429853i
$9$	0.480279	+	2.25953i	0.160093	+	0.753178i
$10$	−2.61256	−	3.87725i	−0.826163	−	1.22610i
$11$	1.02734	+	0.218367i	0.309753	+	0.0658401i	0.360166	−	0.932888i	$-0.382720\pi$
$11$	1.02734	+	0.218367i	0.309753	+	0.0658401i	−0.0504122	+	0.998728i	$0.516054\pi$
$12$	−1.07298	+	1.65224i	−0.309742	+	0.476961i
$13$	−4.08239	+	2.08008i	−1.13225	+	0.576911i	−0.916698	−	0.399580i	$-0.869156\pi$
$13$	−4.08239	+	2.08008i	−1.13225	+	0.576911i	−0.215554	+	0.976492i	$0.569156\pi$
$14$	3.43382	+	4.33715i	0.917727	+	1.15915i
$15$	−1.83920	−	0.259375i	−0.474879	−	0.0669703i
$16$	−3.05026	+	0.648353i	−0.762565	+	0.162088i
$17$	−0.808289	+	2.10566i	−0.196039	+	0.510699i	−0.996000	−	0.0893531i	$-0.971520\pi$
$17$	−0.808289	+	2.10566i	−0.196039	+	0.510699i	0.799961	+	0.600052i	$0.204853\pi$
$18$	−1.25008	−	4.66535i	−0.294646	−	1.09963i
$19$	−0.520869	+	4.95574i	−0.119496	+	1.13692i	0.756294	+	0.654232i	$0.227008\pi$
$19$	−0.520869	+	4.95574i	−0.119496	+	1.13692i	−0.875790	+	0.482693i	$0.839659\pi$
$20$	3.18960	+	4.23693i	0.713215	+	0.947406i
$21$	2.19329	+	0.139164i	0.478616	+	0.0303680i
$22$	−2.16897	−	0.343531i	−0.462426	−	0.0732411i
$23$	0.325733	+	6.21536i	0.0679201	+	1.29599i	0.793804	+	0.608174i	$0.208098\pi$
$23$	0.325733	+	6.21536i	0.0679201	+	1.29599i	−0.725884	+	0.687818i	$0.758569\pi$
$24$	0.322792	−	0.559093i	0.0658897	−	0.114124i
$25$	−2.35156	+	4.41250i	−0.470311	+	0.882501i
$26$	8.29642	−	4.78994i	1.62706	−	0.939384i
$27$	−3.93004	−	2.00245i	−0.756336	−	0.385373i
$28$	−4.14720	−	4.70913i	−0.783747	−	0.889942i
$29$	−0.743348	−	1.02313i	−0.138036	−	0.189991i	0.734402	−	0.678714i	$-0.237463\pi$
$29$	−0.743348	−	1.02313i	−0.138036	−	0.189991i	−0.872439	+	0.488724i	$0.837463\pi$
$30$	3.86863	+	0.340316i	0.706312	+	0.0621329i
$31$	−4.14336	−	9.30613i	−0.744169	−	1.67143i	−0.741063	−	0.671435i	$-0.765678\pi$
$31$	−4.14336	−	9.30613i	−0.744169	−	1.67143i	−0.00310567	−	0.999995i	$-0.500989\pi$
$32$	7.79943	−	2.08985i	1.37876	−	0.369437i
$33$	−0.678002	+	0.549035i	−0.118025	+	0.0955748i
$34$	1.45729	−	4.48507i	0.249923	−	0.769184i
$35$	2.37396	−	5.41888i	0.401273	−	0.915958i
$36$	1.69301	+	5.21054i	0.282168	+	0.868424i
$37$	5.27200	+	3.42368i	0.866712	+	0.562849i	0.899652	−	0.436608i	$-0.143820\pi$
$37$	5.27200	+	3.42368i	0.866712	+	0.562849i	−0.0329402	+	0.999457i	$0.510487\pi$
$38$	0.545281	−	10.4046i	0.0884562	−	1.68785i
$39$	0.791286	−	3.72271i	0.126707	−	0.596110i
$40$	−1.11645	−	1.33182i	−0.176526	−	0.210579i
$41$	5.32280	+	1.72948i	0.831282	+	0.270100i	0.693585	−	0.720374i	$-0.256030\pi$
$41$	5.32280	+	1.72948i	0.831282	+	0.270100i	0.137697	+	0.990474i	$0.456030\pi$
$42$	−4.59482	−	0.0505673i	−0.708997	−	0.00780270i
$43$	4.80861	−	4.80861i	0.733306	−	0.733306i	−0.237968	−	0.971273i	$-0.576481\pi$
$43$	4.80861	−	4.80861i	0.733306	−	0.733306i	0.971273	+	0.237968i	$0.0764812\pi$
$44$	2.47733	+	0.260378i	0.373472	+	0.0392535i
$45$	−3.77937	+	3.52096i	−0.563395	+	0.524874i
$46$	−1.36026	−	12.9420i	−0.200559	−	1.90820i
$47$	0.292218	−	0.112172i	0.0426244	−	0.0163620i	−0.336962	−	0.941518i	$-0.609400\pi$
$47$	0.292218	−	0.112172i	0.0426244	−	0.0163620i	0.379587	+	0.925156i	$0.376066\pi$
$48$	1.17598	−	2.30799i	0.169738	−	0.333130i
$49$	−2.30911	+	6.60818i	−0.329873	+	0.944025i
$50$	4.42720	−	9.47062i	0.626101	−	1.33935i
$51$	−0.936759	−	1.62251i	−0.131172	−	0.227197i
$52$	−9.11355	+	5.91841i	−1.26382	+	0.820736i
$53$	−0.217690	−	0.176281i	−0.0299020	−	0.0242141i	0.614253	−	0.789109i	$-0.289457\pi$
$53$	−0.217690	−	0.176281i	−0.0299020	−	0.0242141i	−0.644155	+	0.764895i	$0.722791\pi$
$54$	8.42504	+	3.75107i	1.14650	+	0.510456i
$55$	0.763545	+	2.22093i	0.102956	+	0.299470i
$56$	1.43792	+	1.46992i	0.192150	+	0.196426i
$57$	−2.92684	−	2.92684i	−0.387670	−	0.387670i
$58$	1.66407	+	2.05495i	0.218503	+	0.269829i
$59$	4.60084	+	5.10975i	0.598978	+	0.665232i	0.964042	−	0.265750i	$-0.0856196\pi$
$59$	4.60084	+	5.10975i	0.598978	+	0.665232i	−0.365064	+	0.930982i	$0.618953\pi$
$60$	−4.40246	−	0.155834i	−0.568355	−	0.0201181i
$61$	−3.94111	−	3.54859i	−0.504607	−	0.454350i	0.377083	−	0.926180i	$-0.376927\pi$
$61$	−3.94111	−	3.54859i	−0.504607	−	0.454350i	−0.881690	+	0.471829i	$0.843594\pi$
$62$	9.66967	+	18.9778i	1.22805	+	2.41018i
$63$	4.13927	−	4.49661i	0.521499	−	0.566520i
$64$	−10.1249	+	3.28979i	−1.26562	+	0.411224i
$65$	−8.68581	−	5.43324i	−1.07734	−	0.673911i
$66$	1.35559	−	1.22058i	0.166861	−	0.150243i
$67$	11.4671	+	4.40181i	1.40093	+	0.537767i	0.937382	−	0.348304i	$-0.113242\pi$
$67$	11.4671	+	4.40181i	1.40093	+	0.537767i	0.463550	+	0.886071i	$0.346575\pi$
$68$	−1.38451	+	5.16706i	−0.167896	+	0.626598i
$69$	−4.18254	−	3.03879i	−0.503518	−	0.365827i
$70$	−4.36386	+	11.5744i	−0.521581	+	1.38341i
$71$	−1.66579	+	1.21027i	−0.197693	+	0.143632i	−0.682228	−	0.731140i	$-0.738989\pi$
$71$	−1.66579	+	1.21027i	−0.197693	+	0.143632i	0.484535	+	0.874772i	$0.338989\pi$
$72$	−0.643393	−	1.67610i	−0.0758246	−	0.197530i
$73$	−0.705919	−	1.08702i	−0.0826215	−	0.127226i	0.794944	−	0.606683i	$-0.207500\pi$
$73$	−0.705919	−	1.08702i	−0.0826215	−	0.127226i	−0.877565	+	0.479457i	$0.840834\pi$
$74$	−11.3826	−	6.57173i	−1.32320	−	0.763948i
$75$	−1.61917	−	3.82465i	−0.186966	−	0.441632i
$76$			11.8183i			1.35566i
$77$	−1.10223	−	2.55084i	−0.125611	−	0.290696i
$78$	−1.24484	+	7.85959i	−0.140950	+	0.889924i
$79$	4.40735	−	9.89907i	0.495865	−	1.11373i	−0.476267	−	0.879301i	$-0.658011\pi$
$79$	4.40735	−	9.89907i	0.495865	−	1.11373i	0.972133	−	0.234431i	$-0.0753228\pi$
$80$	−4.75312	−	5.10197i	−0.531415	−	0.570417i
$81$	−2.98382	+	1.32848i	−0.331536	+	0.147609i
$82$	−11.3033	−	3.02870i	−1.24824	−	0.334464i
$83$	0.579789	+	3.66064i	0.0636401	+	0.401808i	0.998860	+	0.0477399i	$0.0152019\pi$
$83$	0.579789	+	3.66064i	0.0636401	+	0.401808i	−0.935220	+	0.354068i	$0.884798\pi$
$84$	5.20787	−	0.215495i	0.568225	−	0.0235124i
$85$	−4.96718	+	0.873412i	−0.538767	+	0.0947349i
$86$	−9.51417	+	10.5666i	−1.02594	+	1.13942i
$87$	1.04906	+	0.0549787i	0.112471	+	0.00589433i
$88$	−0.815165	−	0.0427210i	−0.0868968	−	0.00455407i
$89$	−7.09604	+	7.88095i	−0.752179	+	0.835379i	−0.990743	−	0.135747i	$-0.956656\pi$
$89$	−7.09604	+	7.88095i	−0.752179	+	0.835379i	0.238565	+	0.971127i	$0.423323\pi$
$90$	7.50603	−	7.76533i	0.791205	−	0.818537i
$91$	10.7398	+	5.62191i	1.12584	+	0.589337i
$92$	2.30917	+	14.5795i	0.240748	+	1.52002i
$93$	8.17341	+	2.19006i	0.847543	+	0.227098i
$94$	−0.597877	+	0.266192i	−0.0616663	+	0.0274556i
$95$	−10.1007	+	4.70418i	−1.03631	+	0.482639i
$96$	−2.72805	+	6.12730i	−0.278431	+	0.625365i
$97$	0.775456	−	4.89604i	0.0787356	−	0.497117i	−0.916533	−	0.399958i	$-0.869025\pi$
$97$	0.775456	−	4.89604i	0.0787356	−	0.497117i	0.995269	−	0.0971587i	$-0.0309754\pi$
$98$	4.09830	−	14.0505i	0.413991	−	1.41932i
$99$			2.42618i			0.243840i
$100$	−4.45275	+	10.9908i	−0.445275	+	1.09908i
$101$	13.1637	+	7.60006i	1.30984	+	0.756234i	0.982069	−	0.188524i	$-0.0603704\pi$
$101$	13.1637	+	7.60006i	1.30984	+	0.756234i	0.327767	+	0.944758i	$0.393704\pi$
$102$	2.13350	+	3.28530i	0.211248	+	0.325293i
$103$	2.43305	+	6.33830i	0.239735	+	0.624532i	0.999676	−	0.0254609i	$-0.00810533\pi$
$103$	2.43305	+	6.33830i	0.239735	+	0.624532i	−0.759941	+	0.649993i	$0.774772\pi$
$104$	2.88088	−	2.09308i	0.282493	−	0.205243i
$105$	2.25712	+	4.36520i	0.220272	+	0.426000i
$106$	0.473825	+	0.344254i	0.0460220	+	0.0334369i
$107$	5.09063	−	18.9985i	0.492130	−	1.83665i	−0.0534166	−	0.998572i	$-0.517011\pi$
$107$	5.09063	−	18.9985i	0.492130	−	1.83665i	0.545546	−	0.838081i	$-0.316322\pi$
$108$	−9.76629	−	3.74893i	−0.939762	−	0.360741i
$109$	14.2080	−	12.7930i	1.36088	−	1.22535i	0.411428	−	0.911442i	$-0.365030\pi$
$109$	14.2080	−	12.7930i	1.36088	−	1.22535i	0.949455	−	0.313903i	$-0.101637\pi$
$110$	−1.83731	−	4.55374i	−0.175181	−	0.434182i
$111$	−4.96605	+	1.61357i	−0.471356	+	0.153153i
$112$	6.07021	+	5.58782i	0.573581	+	0.527999i
$113$	3.96233	+	7.77652i	0.372745	+	0.731553i	0.998838	−	0.0481952i	$-0.0153470\pi$
$113$	3.96233	+	7.77652i	0.372745	+	0.731553i	−0.626093	+	0.779748i	$0.715347\pi$
$114$	6.43152	+	5.79097i	0.602367	+	0.542374i
$115$	−11.5414	+	7.77682i	−1.07625	+	0.725192i
$116$	−2.00700	−	2.22900i	−0.186345	−	0.206957i
$117$	−6.66071	−	8.22529i	−0.615783	−	0.760428i
$118$	−10.1657	−	10.1657i	−0.935827	−	0.935827i
$119$	5.78073	−	1.48096i	0.529919	−	0.135759i
$120$	1.44336	−	0.0245072i	0.131760	−	0.00223719i
$121$	−9.04127	−	4.02543i	−0.821933	−	0.365948i
$122$	8.61734	+	6.97819i	0.780177	+	0.631775i
$123$	−3.89893	+	2.53200i	−0.351555	+	0.228303i
$124$	−12.0801	−	20.9234i	−1.08483	−	1.87897i
$125$	−11.1658	+	0.569199i	−0.998703	+	0.0509107i
$126$	−8.15074	+	9.84188i	−0.726126	+	0.876784i
$127$	5.89827	−	11.5760i	0.523386	−	1.02720i	−0.466390	−	0.884579i	$-0.654446\pi$
$127$	5.89827	−	11.5760i	0.523386	−	1.02720i	0.989777	−	0.142625i	$-0.0455542\pi$
$128$	5.70438	−	2.18971i	0.504201	−	0.193544i
$129$	0.590458	+	5.61783i	0.0519869	+	0.494623i
$130$	18.7305	+	10.3941i	1.64277	+	0.911627i
$131$	3.52330	+	0.370314i	0.307832	+	0.0323545i	0.257185	−	0.966362i	$-0.417205\pi$
$131$	3.52330	+	0.370314i	0.307832	+	0.0323545i	0.0506472	+	0.998717i	$0.483872\pi$
$132$	−1.46310	+	1.46310i	−0.127347	+	0.127347i
$133$	11.4894	−	6.46590i	0.996260	−	0.560664i
$134$	−24.4250	−	7.93617i	−2.11000	−	0.685580i
$135$	−0.683315	−	9.83912i	−0.0588104	−	0.846816i
$136$	0.364459	−	1.71465i	0.0312521	−	0.147030i
$137$	0.396425	−	7.56424i	0.0338689	−	0.646257i	−0.927972	−	0.372649i	$-0.878450\pi$
$137$	0.396425	−	7.56424i	0.0338689	−	0.646257i	0.961841	−	0.273608i	$-0.0882171\pi$
$138$	9.06566	+	5.88731i	0.771720	+	0.501161i
$139$	−2.73221	−	8.40888i	−0.231743	−	0.713232i	−0.997537	−	0.0701455i	$-0.977654\pi$
$139$	−2.73221	−	8.40888i	−0.231743	−	0.713232i	0.765794	−	0.643086i	$-0.222346\pi$
$140$	4.25611	−	13.3702i	0.359707	−	1.12998i
$141$	−0.0803449	+	0.247276i	−0.00676626	+	0.0208244i
$142$	3.34573	−	2.70932i	0.280767	−	0.227361i
$143$	−4.64821	+	1.24548i	−0.388703	+	0.104153i
$144$	−2.92995	−	6.58078i	−0.244163	−	0.548398i
$145$	1.10617	−	2.60254i	0.0918627	−	0.216129i
$146$	1.59291	+	2.19245i	0.131830	+	0.181448i
$147$	−3.05876	−	4.94503i	−0.252282	−	0.407859i
$148$	13.2839	+	6.76851i	1.09193	+	0.556368i
$149$	−1.52475	+	0.880317i	−0.124913	+	0.0721183i	−0.561154	−	0.827711i	$-0.689643\pi$
$149$	−1.52475	+	0.880317i	−0.124913	+	0.0721183i	0.436242	+	0.899830i	$0.356309\pi$
$150$	3.79936	+	7.80868i	0.310216	+	0.637576i
$151$	−3.13479	+	5.42962i	−0.255106	+	0.441856i	−0.964924	−	0.262529i	$-0.915444\pi$
$151$	−3.13479	+	5.42962i	−0.255106	+	0.441856i	0.709819	+	0.704385i	$0.248777\pi$
$152$	−0.202688	−	3.86751i	−0.0164401	−	0.313697i
$153$	−5.14602	−	0.815050i	−0.416031	−	0.0658929i
$154$	2.58060	+	5.20554i	0.207950	+	0.419474i
$155$	13.0741	−	18.6528i	1.05013	−	1.49823i
$156$	0.943520	−	8.97699i	0.0755420	−	0.718735i
$157$	2.79709	+	10.4389i	0.223232	+	0.833115i	0.983105	+	0.183043i	$0.0585947\pi$
$157$	2.79709	+	10.4389i	0.223232	+	0.833115i	−0.759872	+	0.650072i	$0.774739\pi$
$158$	−8.11931	+	21.1515i	−0.645937	+	1.68272i
$159$	0.227593	−	0.0483765i	0.0180493	−	0.00383650i
$160$	12.9819	+	12.5484i	1.02631	+	0.992040i
$161$	12.9104	−	10.2215i	1.01748	−	0.805565i
$162$	6.08485	−	3.10038i	0.478071	−	0.243589i
$163$	−3.03858	+	4.67900i	−0.238000	+	0.366488i	−0.937407	−	0.348236i	$-0.886781\pi$
$163$	−3.03858	+	4.67900i	−0.238000	+	0.366488i	0.699407	+	0.714724i	$0.253448\pi$
$164$	12.9838	+	2.75978i	1.01386	+	0.215503i
$165$	−1.83284	−	0.668086i	−0.142686	−	0.0520104i
$166$	−1.61117	−	7.57998i	−0.125051	−	0.588320i
$167$	−10.3561	+	1.64024i	−0.801379	+	0.126926i	−0.543673	−	0.839297i	$-0.682967\pi$
$167$	−10.3561	+	1.64024i	−0.801379	+	0.126926i	−0.257706	+	0.966223i	$0.582967\pi$
$168$	−1.70056	+	0.159836i	−0.131201	+	0.0123316i
$169$	4.69799	−	6.46623i	0.361384	−	0.497402i
$170$	10.2759	−	2.36723i	0.788125	−	0.181558i
$171$	−11.4478	+	1.20322i	−0.875437	+	0.0920122i
$172$	10.1500	−	12.5343i	0.773934	−	0.955729i
$173$	−13.7091	+	0.718462i	−1.04228	+	0.0546236i	−0.565785	−	0.824553i	$-0.691427\pi$
$173$	−13.7091	+	0.718462i	−1.04228	+	0.0546236i	−0.476496	+	0.879177i	$0.658093\pi$
$174$	−2.19644			−0.166512
$175$	13.1211	−	1.68433i	0.991861	−	0.127324i
$176$	−3.27522			−0.246879
$177$	−5.70362	+	0.298914i	−0.428710	+	0.0224678i
$178$	13.9541	−	17.2319i	1.04591	−	1.29159i
$179$	1.60078	−	0.168248i	0.119648	−	0.0125755i	−0.0445154	−	0.999009i	$-0.514174\pi$
$179$	1.60078	−	0.168248i	0.119648	−	0.0125755i	0.164163	+	0.986433i	$0.447508\pi$
$180$	−8.04159	+	9.24191i	−0.599385	+	0.688851i
$181$	−2.04450	+	2.81402i	−0.151967	+	0.209164i	−0.878212	−	0.478271i	$-0.841264\pi$
$181$	−2.04450	+	2.81402i	−0.151967	+	0.209164i	0.726245	+	0.687436i	$0.241264\pi$
$182$	−23.0398	−	10.5633i	−1.70783	−	0.783005i
$183$	4.35096	−	0.689125i	0.321632	−	0.0509416i
$184$	−1.00571	−	4.73150i	−0.0741421	−	0.348811i
$185$	−0.497238	+	14.0474i	−0.0365577	+	1.03279i
$186$	−17.3057	−	3.67844i	−1.26892	−	0.269717i
$187$	−1.29019	+	1.98672i	−0.0943481	+	0.145283i
$188$	0.661452	−	0.337027i	0.0482414	−	0.0245802i
$189$	1.69861	+	11.5456i	0.123556	+	0.839816i
$190$	20.5755	−	10.9276i	1.49270	−	0.792773i
$191$	2.89987	−	0.616386i	0.209827	−	0.0446001i	−0.101799	−	0.994805i	$-0.532460\pi$
$191$	2.89987	−	0.616386i	0.209827	−	0.0446001i	0.311626	+	0.950205i	$0.399126\pi$
$192$	3.16910	−	8.25579i	0.228710	−	0.595810i
$193$	4.41207	+	16.4661i	0.317588	+	1.18525i	0.921556	+	0.388246i	$0.126919\pi$
$193$	4.41207	+	16.4661i	0.317588	+	1.18525i	−0.603968	+	0.797009i	$0.706414\pi$
$194$	−1.08339	+	10.3078i	−0.0777829	+	0.740055i
$195$	8.04786	−	2.76682i	0.576319	−	0.198136i
$196$	−3.80830	+	16.1593i	−0.272022	+	1.15424i
$197$	19.1171	+	3.02785i	1.36204	+	0.215725i	0.794320	−	0.607499i	$-0.207827\pi$
$197$	19.1171	+	3.02785i	1.36204	+	0.215725i	0.567716	+	0.823225i	$0.307827\pi$
$198$	−0.265490	−	5.06585i	−0.0188676	−	0.360015i
$199$	−0.0959424	+	0.166177i	−0.00680118	+	0.0117800i	−0.869406	−	0.494098i	$-0.835498\pi$
$199$	−0.0959424	+	0.166177i	−0.00680118	+	0.0117800i	0.862605	+	0.505878i	$0.168832\pi$
$200$	1.26865	−	3.67308i	0.0897073	−	0.259726i
$201$	−8.83596	+	5.10144i	−0.623240	+	0.359828i
$202$	−28.3174	−	14.4284i	−1.99241	−	1.01518i
$203$	−1.06892	+	3.17064i	−0.0750234	+	0.222535i
$204$	−2.61179	−	3.59482i	−0.182862	−	0.251688i
$205$	2.80939	+	12.1953i	0.196216	+	0.851753i
$206$	−5.77378	−	12.9681i	−0.402278	−	0.903532i
$207$	−13.8874	+	3.72111i	−0.965239	+	0.258635i
$208$	11.1037	−	8.99163i	0.769906	−	0.623457i
$209$	−1.61728	+	4.97747i	−0.111869	+	0.344299i
$210$	−5.19054	−	8.86753i	−0.358181	−	0.611918i
$211$	1.96658	+	6.05250i	0.135385	+	0.416671i	0.995650	−	0.0931759i	$-0.0297019\pi$
$211$	1.96658	+	6.05250i	0.135385	+	0.416671i	−0.860265	+	0.509847i	$0.829702\pi$
$212$	−0.557171	−	0.361831i	−0.0382666	−	0.0248507i
$213$	0.0895123	−	1.70800i	0.00613328	−	0.117030i
$214$	−8.55027	+	40.2259i	−0.584485	+	2.74978i
$215$	14.7527	+	3.68572i	1.00613	+	0.251364i
$216$	3.26028	+	1.05933i	0.221834	+	0.0720783i
$217$	−13.7319	+	23.1912i	−0.932185	+	1.57432i
$218$	−28.2665	+	28.2665i	−1.91445	+	1.91445i
$219$	1.07073	+	0.112538i	0.0723533	+	0.00760464i
$220$	2.35158	+	5.04925i	0.158544	+	0.340420i
$221$	−1.08020	−	10.2775i	−0.0726624	−	0.691337i
$222$	10.1925	−	3.91254i	0.684078	−	0.262593i
$223$	−6.05349	+	11.8807i	−0.405372	+	0.795587i	−0.999964	−	0.00843996i	$-0.997313\pi$
$223$	−6.05349	+	11.8807i	−0.405372	+	0.795587i	0.594592	+	0.804027i	$0.297313\pi$
$224$	−16.4534	−	13.6262i	−1.09934	−	0.910441i
$225$	−11.0996	−	3.19419i	−0.739974	−	0.212946i
$226$	−9.12431	−	15.8038i	−0.606940	−	1.05125i
$227$	−4.06947	+	2.64274i	−0.270100	+	0.175405i	−0.672581	−	0.740023i	$-0.734815\pi$
$227$	−4.06947	+	2.64274i	−0.270100	+	0.175405i	0.402481	+	0.915428i	$0.368148\pi$
$228$	−7.62920	−	6.17801i	−0.505256	−	0.409149i
$229$	−6.10856	−	2.71971i	−0.403665	−	0.179723i	0.194853	−	0.980832i	$-0.437577\pi$
$229$	−6.10856	−	2.71971i	−0.403665	−	0.179723i	−0.598518	+	0.801109i	$0.704244\pi$
$230$	23.2475	−	17.5009i	1.53290	−	1.15398i
$231$	2.22286	+	0.621911i	0.146254	+	0.0409187i
$232$	0.695011	+	0.695011i	0.0456297	+	0.0456297i
$233$	−5.43374	−	6.71012i	−0.355976	−	0.439594i	0.567428	−	0.823423i	$-0.307939\pi$
$233$	−5.43374	−	6.71012i	−0.355976	−	0.439594i	−0.923404	+	0.383829i	$0.874605\pi$
$234$	14.8076	+	16.4455i	0.968004	+	1.07508i
$235$	0.551330	+	0.431168i	0.0359648	+	0.0281263i
$236$	12.1189	+	10.9119i	0.788870	+	0.710302i
$237$	4.08631	+	8.01983i	0.265434	+	0.520944i
$238$	−11.9081	+	3.72480i	−0.771887	+	0.241443i
$239$	−18.2461	+	5.92852i	−1.18024	+	0.383484i	−0.832457	−	0.554090i	$-0.813066\pi$
$239$	−18.2461	+	5.92852i	−1.18024	+	0.383484i	−0.347785	+	0.937574i	$0.613066\pi$
$240$	5.77821	−	0.401289i	0.372982	−	0.0259031i
$241$	19.2863	−	17.3654i	1.24234	−	1.11861i	0.253861	−	0.967241i	$-0.418300\pi$
$241$	19.2863	−	17.3654i	1.24234	−	1.11861i	0.988478	−	0.151366i	$-0.0483671\pi$
$242$	19.3186	+	7.41573i	1.24185	+	0.476701i
$243$	4.12698	−	15.4021i	0.264746	−	0.988046i
$244$	−10.1757	−	7.39308i	−0.651433	−	0.473294i
$245$	−15.3266	+	3.17725i	−0.979181	+	0.202987i
$246$	7.86390	−	5.71346i	0.501384	−	0.364277i
$247$	−8.18196	−	21.3147i	−0.520606	−	1.35622i
$248$	4.31202	+	6.63993i	0.273814	+	0.421636i
$249$	−2.66617	−	1.53932i	−0.168962	−	0.0975502i
$250$	23.2520	−	2.41034i	1.47058	−	0.152443i
$251$		−	15.4133i		−	0.972880i	−0.873714	−	0.486440i	$-0.838295\pi$
$251$		−	15.4133i		−	0.972880i	0.873714	−	0.486440i	$-0.161705\pi$
$252$	8.64862	−	11.6324i	0.544812	−	0.732774i
$253$	−1.02259	+	6.45639i	−0.0642898	+	0.405910i
$254$	−11.0488	+	24.8161i	−0.693266	+	1.55710i
$255$	2.03276	−	3.66309i	0.127296	−	0.229392i
$256$	7.78009	−	3.46392i	0.486256	−	0.216495i
$257$	29.5275	+	7.91188i	1.84188	+	0.493529i	0.999006	−	0.0445856i	$-0.0141967\pi$
$257$	29.5275	+	7.91188i	1.84188	+	0.493529i	0.842871	+	0.538115i	$0.180863\pi$
$258$	−1.84762	−	11.6654i	−0.115028	−	0.726257i
$259$	−0.687603	−	16.6173i	−0.0427256	−	1.03255i
$260$	−21.8344	−	10.6622i	−1.35411	−	0.661241i
$261$	1.95479	−	2.17101i	0.120998	−	0.134382i
$262$	−7.39718	−	0.387670i	−0.456999	−	0.0239503i
$263$	−0.407151	−	0.0213379i	−0.0251060	−	0.00131575i	0.0397788	−	0.999209i	$-0.487335\pi$
$263$	−0.407151	−	0.0213379i	−0.0251060	−	0.00131575i	−0.0648848	+	0.997893i	$0.520668\pi$
$264$	0.453704	−	0.503889i	0.0279235	−	0.0310122i
$265$	0.0874667	−	0.620217i	0.00537304	−	0.0380996i
$266$	−23.2824	+	14.7580i	−1.42753	+	0.904873i
$267$	−1.37803	−	8.70053i	−0.0843340	−	0.532464i
$268$	28.1390	+	7.53982i	1.71886	+	0.460568i
$269$	17.4978	−	7.79051i	1.06686	−	0.474996i	0.203233	−	0.979130i	$-0.434855\pi$
$269$	17.4978	−	7.79051i	1.06686	−	0.474996i	0.863625	+	0.504134i	$0.168188\pi$
$270$	2.50343	+	20.4693i	0.152354	+	1.24572i
$271$	−7.85265	+	17.6373i	−0.477015	+	1.07139i	0.501489	+	0.865164i	$0.332786\pi$
$271$	−7.85265	+	17.6373i	−0.477015	+	1.07139i	−0.978504	+	0.206228i	$0.933881\pi$
$272$	1.10028	−	6.94688i	0.0667141	−	0.421216i
$273$	−9.24337	+	3.99411i	−0.559434	+	0.241735i
$274$			15.8375i			0.956779i
$275$	−3.37938	+	4.01962i	−0.203784	+	0.242392i
$276$	−10.6188	−	6.13076i	−0.639176	−	0.369028i
$277$	−4.16515	−	6.41377i	−0.250260	−	0.385366i	0.691106	−	0.722753i	$-0.257124\pi$
$277$	−4.16515	−	6.41377i	−0.250260	−	0.385366i	−0.941366	+	0.337387i	$0.890457\pi$
$278$	6.62501	+	17.2587i	0.397342	+	1.03511i
$279$	19.0376	−	13.8316i	1.13975	−	0.828076i
$280$	−1.16350	+	4.44834i	−0.0695322	+	0.265839i
$281$	15.1432	+	11.0022i	0.903367	+	0.656334i	0.939329	−	0.343019i	$-0.111449\pi$
$281$	15.1432	+	11.0022i	0.903367	+	0.656334i	−0.0359618	+	0.999353i	$0.511449\pi$
$282$	0.140701	−	0.525104i	0.00837864	−	0.0312695i
$283$	2.66042	+	1.02124i	0.158145	+	0.0607063i	0.436153	−	0.899873i	$-0.356341\pi$
$283$	2.66042	+	1.02124i	0.158145	+	0.0607063i	−0.278008	+	0.960579i	$0.589674\pi$
$284$	−3.62909	+	3.26765i	−0.215347	+	0.193899i
$285$	2.24338	−	8.97950i	0.132886	−	0.531900i
$286$	9.56917	−	3.10921i	0.565837	−	0.183852i
$287$	−4.42053	−	14.1323i	−0.260936	−	0.834204i
$288$	8.46799	+	16.6194i	0.498981	+	0.979305i
$289$	8.85297	+	7.97125i	0.520763	+	0.468897i
$290$	−2.02490	+	5.55514i	−0.118906	+	0.326209i
$291$	2.75522	+	3.05998i	0.161514	+	0.179379i
$292$	−1.93455	−	2.38897i	−0.113211	−	0.139804i
$293$	0.584948	+	0.584948i	0.0341730	+	0.0341730i	0.723987	−	0.689814i	$-0.242308\pi$
$293$	0.584948	+	0.584948i	0.0341730	+	0.0341730i	−0.689814	+	0.723987i	$0.742308\pi$
$294$	6.92781	+	9.99051i	0.404038	+	0.582658i
$295$	−4.50217	+	14.7009i	−0.262126	+	0.855920i
$296$	−4.46321	−	1.98715i	−0.259419	−	0.115501i
$297$	−3.60020	−	2.91538i	−0.208905	−	0.169168i
$298$	3.08735	−	2.00495i	0.178845	−	0.116144i
$299$	−14.2582	−	24.6960i	−0.824575	−	1.42821i
$300$	−4.76735	−	8.61986i	−0.275243	−	0.497668i
$301$	−17.7386	−	3.00998i	−1.02244	−	0.173492i
$302$	5.95129	−	11.6801i	0.342458	−	0.672112i
$303$	−11.7874	+	4.52477i	−0.677170	+	0.259941i
$304$	−1.62428	−	15.4540i	−0.0931589	−	0.886348i
$305$	2.26825	−	11.6396i	0.129879	−	0.666479i
$306$	10.8341	+	1.13871i	0.619343	+	0.0650956i
$307$	−10.4006	+	10.4006i	−0.593593	+	0.593593i	−0.938600	−	0.345007i	$-0.887877\pi$
$307$	−10.4006	+	10.4006i	−0.593593	+	0.593593i	0.345007	+	0.938600i	$0.387877\pi$
$308$	−3.23225	−	5.74347i	−0.184174	−	0.327264i
$309$	−5.36350	−	1.74271i	−0.305119	−	0.0991391i
$310$	−25.2575	+	40.3777i	−1.43453	+	2.29330i
$311$	−2.47049	+	11.6228i	−0.140089	+	0.659066i	0.850923	+	0.525291i	$0.176043\pi$
$311$	−2.47049	+	11.6228i	−0.140089	+	0.659066i	−0.991012	+	0.133776i	$0.957290\pi$
$312$	−0.154806	+	2.95387i	−0.00876416	+	0.167230i
$313$	−8.44819	−	5.48632i	−0.477520	−	0.310105i	0.283342	−	0.959019i	$-0.408557\pi$
$313$	−8.44819	−	5.48632i	−0.477520	−	0.310105i	−0.760862	+	0.648914i	$0.775223\pi$
$314$	−6.98263	−	21.4903i	−0.394053	−	1.21277i
$315$	13.3843	+	2.76148i	0.754121	+	0.155592i
$316$	7.94161	−	24.4418i	0.446750	−	1.37496i
$317$	14.6927	−	11.8979i	0.825223	−	0.668252i	−0.120684	−	0.992691i	$-0.538509\pi$
$317$	14.6927	−	11.8979i	0.825223	−	0.668252i	0.945907	+	0.324439i	$0.105175\pi$
$318$	−0.469921	+	0.125915i	−0.0263519	+	0.00706096i
$319$	−0.540250	−	1.21342i	−0.0302482	−	0.0679386i
$320$	−17.9586	−	15.6261i	−1.00391	−	0.873528i
$321$	9.60316	+	13.2176i	0.535996	+	0.737736i
$322$	−25.8384	+	22.7552i	−1.43992	+	1.26810i
$323$	−10.0141	−	5.10245i	−0.557200	−	0.283908i
$324$	−6.70866	+	3.87325i	−0.372703	+	0.215180i
$325$	0.421608	−	22.9050i	0.0233866	−	1.27054i
$326$	5.83254	−	10.1023i	0.323035	−	0.559512i
$327$	0.831154	+	15.8594i	0.0459629	+	0.877024i
$328$	−4.29622	−	0.680455i	−0.237219	−	0.0375719i
$329$	−0.689532	−	0.458654i	−0.0380152	−	0.0252864i
$330$	3.90007	+	1.19440i	0.214692	+	0.0657495i
$331$	−3.25235	+	30.9441i	−0.178766	+	1.70084i	0.426232	+	0.904614i	$0.359841\pi$
$331$	−3.25235	+	30.9441i	−0.178766	+	1.70084i	−0.604998	+	0.796227i	$0.706826\pi$
$332$	2.27508	+	8.49070i	0.124861	+	0.465988i
$333$	−5.20388	+	13.5566i	−0.285171	+	0.742896i
$334$	21.4440	−	4.55807i	1.17336	−	0.249406i
$335$	4.75647	+	27.0505i	0.259874	+	1.47793i
$336$	−6.78035	+	0.997543i	−0.369898	+	0.0544204i
$337$	−31.0198	+	15.8054i	−1.68976	+	0.860974i	−0.700696	+	0.713460i	$0.747127\pi$
$337$	−31.0198	+	15.8054i	−1.68976	+	0.860974i	−0.989060	+	0.147514i	$0.952873\pi$
$338$	−9.10181	+	14.0156i	−0.495073	+	0.762346i
$339$	−7.09135	−	1.50731i	−0.385149	−	0.0818660i
$340$	−11.4997	+	3.29156i	−0.623657	+	0.178510i
$341$	−2.22447	−	10.4653i	−0.120462	−	0.566727i
$342$	23.7714	−	3.76502i	1.28541	−	0.203589i
$343$	17.7931	−	5.13855i	0.960738	−	0.277456i
$344$	−3.10660	+	4.27587i	−0.167497	+	0.230540i
$345$	1.01302	−	11.5158i	0.0545392	−	0.619989i
$346$	28.5459	−	3.00029i	1.53464	−	0.161297i
$347$	−16.9534	+	20.9357i	−0.910107	+	1.12389i	0.0817651	+	0.996652i	$0.473944\pi$
$347$	−16.9534	+	20.9357i	−0.910107	+	1.12389i	−0.991872	+	0.127237i	$0.959389\pi$
$348$	2.48806	−	0.130394i	0.133374	−	0.00698983i
$349$	28.9278			1.54847			0.774236	−	0.632897i	$-0.218134\pi$
$349$	28.9278			1.54847			0.774236	+	0.632897i	$0.218134\pi$
$350$	−27.2125	+	4.95269i	−1.45457	+	0.264732i
$351$	20.2092			1.07869
$352$	8.46898	−	0.443841i	0.451398	−	0.0236568i
$353$	−7.34270	+	9.06748i	−0.390813	+	0.482613i	−0.934140	−	0.356908i	$-0.883831\pi$
$353$	−7.34270	+	9.06748i	−0.390813	+	0.482613i	0.543327	+	0.839521i	$0.317164\pi$
$354$	11.8764	−	1.24826i	0.631226	−	0.0663445i
$355$	−4.23727	−	1.80099i	−0.224891	−	0.0955867i
$356$	−14.7838	+	20.3482i	−0.783540	+	1.07845i
$357$	−2.06585	+	4.50586i	−0.109336	+	0.238475i
$358$	−3.32401	+	0.526471i	−0.175679	+	0.0278248i
$359$	0.925593	+	4.35457i	0.0488509	+	0.229826i	0.995800	−	0.0915592i	$-0.0291851\pi$
$359$	0.925593	+	4.35457i	0.0488509	+	0.229826i	−0.946949	+	0.321385i	$0.895852\pi$
$360$	2.47308	−	3.16230i	0.130343	−	0.166668i
$361$	−5.70326	−	1.21227i	−0.300172	−	0.0638034i
$362$	3.96099	−	6.09939i	0.208185	−	0.320577i
$363$	7.32488	−	3.73221i	0.384456	−	0.195890i
$364$	26.7259	+	10.5980i	1.40082	+	0.555486i
$365$	1.27173	−	2.60430i	0.0665656	−	0.136315i
$366$	−9.00939	+	1.91501i	−0.470928	+	0.100099i
$367$	9.20390	−	23.9770i	0.480440	−	1.25159i	−0.452567	−	0.891730i	$-0.649492\pi$
$367$	9.20390	−	23.9770i	0.480440	−	1.25159i	0.933007	−	0.359858i	$-0.117175\pi$
$368$	−5.02332	−	18.7473i	−0.261858	−	0.977269i
$369$	−1.35140	+	12.8577i	−0.0703510	+	0.669345i
$370$	−0.498942	−	29.3854i	−0.0259387	−	1.52768i
$371$	−0.0469289	+	0.739625i	−0.00243643	+	0.0383994i
$372$	19.8217	+	3.13945i	1.02771	+	0.162773i
$373$	−1.87432	−	35.7641i	−0.0970485	−	1.85180i	−0.422655	−	0.906291i	$-0.638902\pi$
$373$	−1.87432	−	35.7641i	−0.0970485	−	1.85180i	0.325606	−	0.945506i	$-0.394432\pi$
$374$	2.47652	−	4.28945i	0.128058	−	0.221802i
$375$	5.46948	−	7.50554i	0.282443	−	0.387584i
$376$	−0.210678	+	0.121635i	−0.0108649	+	0.00627285i
$377$	5.16284	+	2.63060i	0.265900	+	0.135483i
$378$	−4.81010	−	23.9212i	−0.247405	−	1.23038i
$379$	−13.3436	−	18.3659i	−0.685416	−	0.943394i	0.314567	−	0.949235i	$-0.398141\pi$
$379$	−13.3436	−	18.3659i	−0.685416	−	0.943394i	−0.999983	+	0.00584095i	$0.998141\pi$
$380$	−22.6585	+	13.5999i	−1.16236	+	0.697662i
$381$	4.38946	+	9.85889i	0.224879	+	0.505086i
$382$	−5.98747	+	1.60434i	−0.306346	+	0.0820850i
$383$	16.9050	−	13.6894i	0.863806	−	0.699496i	−0.0912802	−	0.995825i	$-0.529096\pi$
$383$	16.9050	−	13.6894i	0.863806	−	0.699496i	0.955086	+	0.296329i	$0.0957626\pi$
$384$	−1.56841	+	4.82707i	−0.0800375	+	0.246330i
$385$	3.62216	−	5.04862i	0.184602	−	0.257301i
$386$	−11.0142	−	33.8984i	−0.560610	−	1.72538i
$387$	13.1747	+	8.55574i	0.669707	+	0.434913i
$388$	0.615300	−	11.7406i	0.0312371	−	0.596040i
$389$	2.70252	−	12.7143i	0.137023	−	0.644643i	−0.855004	−	0.518621i	$-0.826446\pi$
$389$	2.70252	−	12.7143i	0.137023	−	0.644643i	0.992027	−	0.126022i	$-0.0402210\pi$
$390$	−16.5012	+	6.65777i	−0.835569	+	0.337129i
$391$	−13.3507	−	4.33792i	−0.675176	−	0.219378i
$392$	0.969118	−	5.35339i	0.0489478	−	0.270387i
$393$	−2.08085	+	2.08085i	−0.104965	+	0.104965i
$394$	−40.2478	−	4.23021i	−2.02765	−	0.213115i
$395$	24.0506	−	2.94142i	1.21011	−	0.147999i
$396$	0.601477	+	5.72267i	0.0302254	+	0.287575i
$397$	−4.46102	+	1.71242i	−0.223892	+	0.0859441i	−0.467728	−	0.883872i	$-0.654927\pi$
$397$	−4.46102	+	1.71242i	−0.223892	+	0.0859441i	0.243836	+	0.969816i	$0.421594\pi$
$398$	0.182143	−	0.357476i	0.00913002	−	0.0179187i
$399$	−1.83208	+	10.7969i	−0.0917187	+	0.540522i
$400$	4.31200	−	14.9839i	0.215600	−	0.749196i
$401$	7.58351	+	13.1350i	0.378702	+	0.655932i	0.990874	−	0.134793i	$-0.0430370\pi$
$401$	7.58351	+	13.1350i	0.378702	+	0.655932i	−0.612171	+	0.790725i	$0.709704\pi$
$402$	17.8912	−	11.6187i	0.892333	−	0.579488i
$403$	36.2724	+	29.3728i	1.80685	+	1.46316i
$404$	32.9336	+	14.6630i	1.63851	+	0.729511i
$405$	−5.98064	−	4.19193i	−0.297180	−	0.208299i
$406$	1.88495	−	6.73726i	0.0935484	−	0.334365i
$407$	4.66850	+	4.66850i	0.231409	+	0.231409i
$408$	0.916352	+	1.13160i	0.0453662	+	0.0560226i
$409$	6.87712	+	7.63781i	0.340052	+	0.377666i	0.888779	−	0.458336i	$-0.151554\pi$
$409$	6.87712	+	7.63781i	0.340052	+	0.377666i	−0.548728	+	0.836001i	$0.684888\pi$
$410$	−7.20049	−	25.1562i	−0.355607	−	1.24238i
$411$	4.67579	+	4.21010i	0.230640	+	0.207669i
$412$	7.31021	+	14.3471i	0.360148	+	0.706831i
$413$	3.97787	−	17.7515i	0.195738	−	0.873496i
$414$	28.5896	−	9.28933i	1.40510	−	0.456546i
$415$	−6.35111	+	5.32407i	−0.311764	+	0.261348i
$416$	−27.4933	+	24.7551i	−1.34797	+	1.21372i
$417$	6.85652	+	2.63197i	0.335765	+	0.128888i
$418$	2.83220	−	10.5699i	0.138528	−	0.516992i
$419$	−14.4852	−	10.5241i	−0.707648	−	0.514137i	0.174766	−	0.984610i	$-0.444083\pi$
$419$	−14.4852	−	10.5241i	−0.707648	−	0.514137i	−0.882414	+	0.470473i	$0.844083\pi$
$420$	6.40610	+	9.73671i	0.312586	+	0.475103i
$421$	13.5865	−	9.87120i	0.662168	−	0.481093i	−0.205227	−	0.978714i	$-0.565793\pi$
$421$	13.5865	−	9.87120i	0.662168	−	0.481093i	0.867394	+	0.497621i	$0.165793\pi$
$422$	−4.76852	−	12.4224i	−0.232128	−	0.604714i
$423$	0.393803	+	0.606403i	0.0191473	+	0.0294843i
$424$	0.188538	+	0.108852i	0.00915621	+	0.00528634i
$425$	−7.39051	−	8.51817i	−0.358492	−	0.413192i
$426$			3.57609i			0.173262i
$427$	−1.62013	+	13.9373i	−0.0784036	+	0.674474i
$428$	7.29743	−	46.0741i	0.352734	−	2.22708i
$429$	1.62583	−	3.65168i	0.0784959	−	0.176305i
$430$	−31.2070	−	6.08142i	−1.50493	−	0.293272i
$431$	−8.17166	+	3.63826i	−0.393615	+	0.175249i	−0.593993	−	0.804470i	$-0.702449\pi$
$431$	−8.17166	+	3.63826i	−0.393615	+	0.175249i	0.200378	+	0.979719i	$0.435783\pi$
$432$	13.2859	+	3.55996i	0.639220	+	0.171278i
$433$	−2.75652	−	17.4040i	−0.132470	−	0.836382i	−0.961022	−	0.276471i	$-0.910835\pi$
$433$	−2.75652	−	17.4040i	−0.132470	−	0.836382i	0.828552	−	0.559912i	$-0.189165\pi$
$434$	26.1345	−	49.9259i	1.25450	−	2.39652i
$435$	1.10179	+	2.07455i	0.0528269	+	0.0994670i
$436$	30.3413	−	33.6974i	1.45308	−	1.61381i
$437$	−30.9714	−	1.62314i	−1.48156	−	0.0776454i
$438$	−2.24800	−	0.117813i	−0.107414	−	0.00562931i
$439$	−18.3365	+	20.3647i	−0.875151	+	0.971954i	−0.999795	−	0.0202474i	$-0.993555\pi$
$439$	−18.3365	+	20.3647i	−0.875151	+	0.971954i	0.124644	+	0.992202i	$0.460221\pi$
$440$	−0.856143	−	1.61202i	−0.0408150	−	0.0768501i
$441$	−16.0404	−	2.04375i	−0.763829	−	0.0973212i
$442$	3.38010	+	21.3411i	0.160775	+	1.01509i
$443$	−10.7062	−	2.86872i	−0.508667	−	0.136297i	−0.00464732	−	0.999989i	$-0.501479\pi$
$443$	−10.7062	−	2.86872i	−0.508667	−	0.136297i	−0.504019	+	0.863692i	$0.668146\pi$
$444$	−11.3135	+	5.03709i	−0.536914	+	0.239050i
$445$	−23.2754	−	4.53577i	−1.10336	−	0.215016i
$446$	11.3396	−	25.4692i	0.536947	−	1.20600i
$447$	0.228782	−	1.44447i	0.0108210	−	0.0683212i
$448$	22.6037	+	16.8057i	1.06793	+	0.793995i
$449$			40.1154i			1.89316i	0.322465	+	0.946581i	$0.395489\pi$
$449$			40.1154i			1.89316i	−0.322465	+	0.946581i	$0.604511\pi$
$450$	23.5255	+	5.45487i	1.10900	+	0.257145i
$451$	5.09064	+	2.93909i	0.239709	+	0.138396i
$452$	11.2739	+	17.3603i	0.530281	+	0.816561i
$453$	−1.86633	−	4.86195i	−0.0876878	−	0.228434i
$454$	8.20786	−	5.96336i	0.385214	−	0.279874i
$455$	1.58028	+	27.0601i	0.0740846	+	1.26860i
$456$	2.60259	+	1.89089i	0.121877	+	0.0885490i
$457$	−8.79489	+	32.8230i	−0.411408	+	1.53539i	0.380516	+	0.924774i	$0.375746\pi$
$457$	−8.79489	+	32.8230i	−0.411408	+	1.53539i	−0.791924	+	0.610620i	$0.790920\pi$
$458$	13.0523	+	5.01030i	0.609893	+	0.234116i
$459$	7.39310	−	6.65678i	0.345081	−	0.310712i
$460$	−25.2951	+	21.2046i	−1.17939	+	0.988669i
$461$	30.0506	−	9.76402i	1.39959	−	0.454756i	0.490535	−	0.871422i	$-0.336802\pi$
$461$	30.0506	−	9.76402i	1.39959	−	0.454756i	0.909060	+	0.416666i	$0.136802\pi$
$462$	−4.70938	−	1.05531i	−0.219100	−	0.0490973i
$463$	−8.64582	−	16.9684i	−0.401805	−	0.788587i	0.598113	−	0.801412i	$-0.295918\pi$
$463$	−8.64582	−	16.9684i	−0.401805	−	0.788587i	−0.999918	+	0.0128250i	$0.995918\pi$
$464$	2.93076	+	2.63886i	0.136057	+	0.122506i
$465$	5.20668	+	18.1905i	0.241454	+	0.843565i
$466$	12.0799	+	13.4161i	0.559592	+	0.621489i
$467$	3.74989	+	4.63073i	0.173524	+	0.214285i	0.856487	−	0.516169i	$-0.172642\pi$
$467$	3.74989	+	4.63073i	0.173524	+	0.214285i	−0.682963	+	0.730453i	$0.739309\pi$
$468$	−17.7499	−	17.7499i	−0.820489	−	0.820489i
$469$	−8.06506	−	31.4810i	−0.372410	−	1.45366i
$470$	−1.19836	−	0.839948i	−0.0552761	−	0.0387439i
$471$	−8.20090	−	3.65128i	−0.377877	−	0.168242i
$472$	−4.15300	−	3.36303i	−0.191157	−	0.154796i
$473$	5.99009	−	3.89001i	0.275425	−	0.178863i
$474$	−9.40980	−	16.2982i	−0.432206	−	0.748603i
$475$	−20.6424	−	13.9520i	−0.947137	−	0.640164i
$476$	13.2680	−	4.92627i	0.608137	−	0.225795i
$477$	0.293762	−	0.576541i	0.0134505	−	0.0263980i
$478$	37.4491	−	14.3754i	1.71288	−	0.657513i
$479$	2.17952	+	20.7367i	0.0995846	+	0.947484i	0.924231	+	0.381835i	$0.124708\pi$
$479$	2.17952	+	20.7367i	0.0995846	+	0.947484i	−0.824646	+	0.565649i	$0.808626\pi$
$480$	−14.8868	+	1.82068i	−0.679485	+	0.0831021i
$481$	−28.6439	−	3.01060i	−1.30605	−	0.137271i
$482$	−38.3695	+	38.3695i	−1.74768	+	1.74768i
$483$	−0.150524	+	13.6774i	−0.00684907	+	0.622345i
$484$	−22.3238	−	7.25343i	−1.01472	−	0.329701i
$485$	10.2792	−	4.14738i	0.466754	−	0.188323i
$486$	−6.93172	+	32.6112i	−0.314429	+	1.47927i
$487$	1.53608	−	29.3101i	0.0696064	−	1.32817i	−0.711021	−	0.703171i	$-0.751767\pi$
$487$	1.53608	−	29.3101i	0.0696064	−	1.32817i	0.780627	−	0.624997i	$-0.214900\pi$
$488$	3.45676	+	2.24485i	0.156480	+	0.101619i
$489$	−1.43207	−	4.40746i	−0.0647605	−	0.199312i
$490$	31.6543	−	8.31124i	1.42999	−	0.375464i
$491$	−5.56395	+	17.1241i	−0.251097	+	0.772798i	0.743476	+	0.668762i	$0.233176\pi$
$491$	−5.56395	+	17.1241i	−0.251097	+	0.772798i	−0.994574	+	0.104036i	$0.966824\pi$
$492$	−8.56878	+	6.93886i	−0.386311	+	0.312828i
$493$	2.75521	−	0.738256i	0.124088	−	0.0332494i
$494$	19.4163	+	43.6098i	0.873583	+	1.96210i
$495$	−4.65154	+	2.79192i	−0.209071	+	0.125487i
$496$	18.6720	+	25.6998i	0.838396	+	1.15395i
$497$	5.16221	+	1.74034i	0.231557	+	0.0780648i
$498$	5.73541	+	2.92234i	0.257010	+	0.130953i
$499$	4.60639	−	2.65950i	0.206210	−	0.119056i	−0.393339	−	0.919394i	$-0.628680\pi$
$499$	4.60639	−	2.65950i	0.206210	−	0.119056i	0.599549	+	0.800338i	$0.295347\pi$
$500$	−26.1960	+	4.11072i	−1.17152	+	0.183837i
$501$	4.35478	−	7.54270i	0.194557	−	0.336983i
$502$	1.68664	+	32.1830i	0.0752784	+	1.43640i
$503$	−26.0759	−	4.13001i	−1.16267	−	0.184148i	−0.454865	−	0.890560i	$-0.650313\pi$
$503$	−26.0759	−	4.13001i	−1.16267	−	0.184148i	−0.707801	+	0.706412i	$0.750313\pi$
$504$	−2.63073	+	3.95500i	−0.117182	+	0.176170i
$505$	0.577015	+	33.9836i	0.0256768	+	1.51225i
$506$	1.42866	−	13.5928i	0.0635119	−	0.604275i
$507$	1.71834	+	6.41294i	0.0763143	+	0.284809i
$508$	11.0425	−	28.7668i	0.489933	−	1.27632i
$509$	4.37813	−	0.930600i	0.194057	−	0.0412481i	−0.109858	−	0.993947i	$-0.535040\pi$
$509$	4.37813	−	0.930600i	0.194057	−	0.0412481i	0.303915	+	0.952699i	$0.401706\pi$
$510$	−3.84356	+	7.87096i	−0.170196	+	0.348532i
$511$	−1.26408	+	3.18773i	−0.0559195	+	0.141017i
$512$	−26.7543	+	13.6320i	−1.18238	+	0.602454i
$513$	11.9707	−	18.4332i	0.528519	−	0.813847i
$514$	−62.5192	−	13.2889i	−2.75760	−	0.586147i
$515$	−9.35217	+	11.9585i	−0.412106	+	0.526955i
$516$	2.78545	+	13.1045i	0.122623	+	0.576894i
$517$	0.324701	−	0.0514276i	0.0142803	−	0.00226178i
$518$	3.25411	+	34.6217i	0.142977	+	1.52119i
$519$	6.70259	−	9.22532i	0.294211	−	0.404947i
$520$	7.32808	+	3.11470i	0.321358	+	0.136589i
$521$	−25.5618	+	2.68665i	−1.11988	+	0.117704i	−0.646327	−	0.763060i	$-0.723696\pi$
$521$	−25.5618	+	2.68665i	−1.11988	+	0.117704i	−0.473554	+	0.880765i	$0.657029\pi$
$522$	−3.84402	+	4.74697i	−0.168248	+	0.207769i
$523$	−21.9690	+	1.15135i	−0.960639	+	0.0503450i	−0.526204	−	0.850358i	$-0.676385\pi$
$523$	−21.9690	+	1.15135i	−0.960639	+	0.0503450i	−0.434435	+	0.900703i	$0.643052\pi$
$524$	8.40229			0.367056
$525$	−5.77172	+	9.35067i	−0.251898	+	0.408097i
$526$	0.852467			0.0371693
$527$	22.9446	−	1.20248i	0.999483	−	0.0523807i
$528$	1.71211	−	2.11428i	0.0745102	−	0.0920124i
$529$	−15.6506	+	1.64494i	−0.680460	+	0.0715192i
$530$	−0.114762	+	1.30458i	−0.00498493	+	0.0566675i
$531$	−9.33596	+	12.8499i	−0.405146	+	0.557636i
$532$	25.4974	−	18.0996i	1.10545	−	0.784717i
$533$	−25.3273	+	4.01144i	−1.09705	+	0.173755i
$534$	3.82940	+	18.0159i	0.165714	+	0.779624i
$535$	42.2825	−	12.1026i	1.82803	−	0.523239i
$536$	−9.33770	−	1.98479i	−0.403327	−	0.0857299i
$537$	−0.728191	+	1.12132i	−0.0314238	+	0.0483883i
$538$	−35.6828	+	18.1813i	−1.53840	+	0.783852i
$539$	−3.81524	+	6.28458i	−0.164334	+	0.270696i
$540$	−4.05098	−	23.0383i	−0.174326	−	0.991412i
$541$	−7.92633	+	1.68479i	−0.340780	+	0.0724349i	−0.375123	−	0.926975i	$-0.622399\pi$
$541$	−7.92633	+	1.68479i	−0.340780	+	0.0724349i	0.0343432	+	0.999410i	$0.489066\pi$
$542$	14.4663	−	37.6860i	0.621381	−	1.61875i
$543$	−0.747801	−	2.79083i	−0.0320912	−	0.119766i
$544$	−1.90367	+	18.1122i	−0.0816190	+	0.776553i
$545$	40.8770	+	12.5186i	1.75098	+	0.536239i
$546$	18.8631	−	9.35118i	0.807265	−	0.400194i
$547$	19.0836	+	3.02255i	0.815958	+	0.129235i	0.550444	−	0.834872i	$-0.314458\pi$
$547$	19.0836	+	3.02255i	0.815958	+	0.129235i	0.265514	+	0.964107i	$0.414458\pi$
$548$	−0.940206	−	17.9402i	−0.0401636	−	0.766368i
$549$	6.12533	−	10.6094i	0.261423	−	0.452797i
$550$	6.61629	−	8.76276i	0.282120	−	0.373645i
$551$	5.45756	−	3.15092i	0.232500	−	0.134234i
$552$	3.58011	+	1.82416i	0.152379	+	0.0776412i
$553$	−28.1064	+	5.65167i	−1.19521	+	0.240333i
$554$	9.39867	+	12.9362i	0.399311	+	0.549605i
$555$	−8.80825	−	7.66425i	−0.373889	−	0.325329i
$556$	−8.52918	−	19.1568i	−0.361718	−	0.812431i
$557$	−17.9964	+	4.82211i	−0.762531	+	0.204320i	−0.619069	−	0.785336i	$-0.712490\pi$
$557$	−17.9964	+	4.82211i	−0.762531	+	0.204320i	−0.143462	+	0.989656i	$0.545823\pi$
$558$	−38.2368	+	30.9636i	−1.61869	+	1.31079i
$559$	−9.62832	+	29.6329i	−0.407235	+	1.25334i
$560$	−3.72786	+	18.0682i	−0.157531	+	0.763520i
$561$	−0.608062	−	1.87142i	−0.0256724	−	0.0790116i
$562$	−32.8229	−	21.3154i	−1.38455	−	0.899137i
$563$	−1.13153	+	21.5909i	−0.0476883	+	0.909947i	0.865122	+	0.501562i	$0.167241\pi$
$563$	−1.13153	+	21.5909i	−0.0476883	+	0.909947i	−0.912810	+	0.408385i	$0.866092\pi$
$564$	−0.128209	+	0.603174i	−0.00539855	+	0.0253982i
$565$	−10.3497	+	16.5455i	−0.435417	+	0.696076i
$566$	−5.66670	−	1.84122i	−0.238189	−	0.0773923i
$567$	7.43581	+	4.40287i	0.312275	+	0.184903i
$568$	1.13157	−	1.13157i	0.0474795	−	0.0474795i
$569$	39.9222	+	4.19599i	1.67362	+	0.175905i	0.893297	−	0.449466i	$-0.148386\pi$
$569$	39.9222	+	4.19599i	1.67362	+	0.175905i	0.780327	+	0.625371i	$0.215053\pi$
$570$	−3.70157	+	18.9947i	−0.155042	+	0.795599i
$571$	−3.48054	−	33.1151i	−0.145656	−	1.38582i	−0.786233	−	0.617930i	$-0.787971\pi$
$571$	−3.48054	−	33.1151i	−0.145656	−	1.38582i	0.640577	−	0.767894i	$-0.278695\pi$
$572$	−10.6551	+	4.09009i	−0.445510	+	0.171015i
$573$	−1.11800	+	2.19419i	−0.0467050	+	0.0916638i
$574$	10.7765	+	29.0245i	0.449803	+	1.21146i
$575$	−28.1913	−	13.1785i	−1.17566	−	0.549580i
$576$	−12.2962	−	21.2976i	−0.512342	−	0.887402i
$577$	4.80800	−	3.12235i	0.200160	−	0.129985i	−0.440667	−	0.897670i	$-0.645258\pi$
$577$	4.80800	−	3.12235i	0.200160	−	0.129985i	0.640827	+	0.767685i	$0.278592\pi$
$578$	−19.3573	−	15.6752i	−0.805156	−	0.652002i
$579$	−12.9359	−	5.75944i	−0.537598	−	0.239354i
$580$	1.96395	−	6.41289i	0.0815487	−	0.266281i
$581$	7.00969	−	6.85708i	0.290811	−	0.284480i
$582$	−6.08774	−	6.08774i	−0.252345	−	0.252345i
$583$	−0.185146	−	0.228636i	−0.00766797	−	0.00946915i
$584$	0.674046	+	0.748604i	0.0278922	+	0.0309775i
$585$	8.10499	−	22.2354i	0.335100	−	0.919319i
$586$	−1.28538	−	1.15736i	−0.0530985	−	0.0478101i
$587$	5.48135	+	10.7577i	0.226239	+	0.444020i	0.976024	−	0.217662i	$-0.0698430\pi$
$587$	5.48135	+	10.7577i	0.226239	+	0.444020i	−0.749785	+	0.661682i	$0.769843\pi$
$588$	−8.44069	−	10.9056i	−0.348088	−	0.449741i
$589$	48.2769	−	15.6861i	1.98922	−	0.646335i
$590$	7.79184	−	31.1881i	0.320785	−	1.28400i
$591$	−11.9480	+	10.7580i	−0.491475	+	0.442526i
$592$	−18.3007	−	7.02499i	−0.752155	−	0.288725i
$593$	11.2370	−	41.9372i	0.461449	−	1.72215i	−0.206951	−	0.978351i	$-0.566354\pi$
$593$	11.2370	−	41.9372i	0.461449	−	1.72215i	0.668401	−	0.743802i	$-0.266979\pi$
$594$	7.83623	+	5.69336i	0.321525	+	0.233601i
$595$	9.49150	+	9.37879i	0.389114	+	0.384493i
$596$	−3.37823	+	2.45442i	−0.138377	+	0.100537i
$597$	−0.0571202	−	0.148803i	−0.00233778	−	0.00609011i
$598$	32.4736	+	50.0050i	1.32794	+	2.04485i
$599$	−0.677665	−	0.391250i	−0.0276887	−	0.0159860i	0.486092	−	0.873908i	$-0.338422\pi$
$599$	−0.677665	−	0.391250i	−0.0276887	−	0.0159860i	−0.513780	+	0.857922i	$0.671755\pi$
$600$	1.70793	+	2.73906i	0.0697261	+	0.111822i
$601$		−	7.23002i		−	0.294919i	−0.989068	−	0.147459i	$-0.952890\pi$
$601$		−	7.23002i		−	0.294919i	0.989068	−	0.147459i	$-0.0471095\pi$
$602$	37.3675	+	4.34375i	1.52299	+	0.177038i
$603$	−4.43864	+	28.0244i	−0.180755	+	1.14124i
$604$	−6.04803	+	13.5841i	−0.246091	+	0.552729i
$605$	−2.68654	−	21.9665i	−0.109223	−	0.893064i
$606$	24.1170	−	10.7376i	0.979686	−	0.436184i
$607$	−1.71540	−	0.459640i	−0.0696260	−	0.0186562i	0.223838	−	0.974626i	$-0.428141\pi$
$607$	−1.71540	−	0.459640i	−0.0696260	−	0.0186562i	−0.293464	+	0.955970i	$0.594808\pi$
$608$	6.29427	+	39.7405i	0.255267	+	1.61169i
$609$	−1.48800	−	2.34747i	−0.0602968	−	0.0951245i
$610$	−3.46241	+	24.5516i	−0.140189	+	0.994064i
$611$	−0.959623	+	1.06577i	−0.0388222	+	0.0431164i
$612$	−12.3401	−	0.646717i	−0.498819	−	0.0261420i
$613$	−1.09418	−	0.0573433i	−0.0441934	−	0.00231608i	0.0302265	−	0.999543i	$-0.490377\pi$
$613$	−1.09418	−	0.0573433i	−0.0441934	−	0.00231608i	−0.0744198	+	0.997227i	$0.523710\pi$
$614$	20.5783	−	22.8545i	0.830473	−	0.922334i
$615$	−9.34112	−	4.56147i	−0.376670	−	0.183936i
$616$	1.15624	+	1.82410i	0.0465864	+	0.0734950i
$617$	5.03752	+	31.8056i	0.202803	+	1.28045i	0.853494	+	0.521103i	$0.174479\pi$
$617$	5.03752	+	31.8056i	0.202803	+	1.28045i	−0.650691	+	0.759343i	$0.725521\pi$
$618$	11.3897	+	3.05185i	0.458160	+	0.122764i
$619$	−16.9052	+	7.52667i	−0.679476	+	0.302522i	−0.717302	−	0.696762i	$-0.754623\pi$
$619$	−16.9052	+	7.52667i	−0.679476	+	0.302522i	0.0378261	+	0.999284i	$0.487957\pi$
$620$	26.2138	−	47.2379i	1.05277	−	1.89712i
$621$	11.1658	−	25.0789i	0.448069	−	1.00638i
$622$	3.88654	−	24.5386i	0.155836	−	0.983910i
$623$	27.8702	+	3.23974i	1.11660	+	0.129797i
$624$			11.8683i			0.475111i
$625$	−13.9404	−	20.7525i	−0.557614	−	0.830100i
$626$	18.2402	+	10.5310i	0.729023	+	0.420902i
$627$	−2.36773	−	3.64598i	−0.0945578	−	0.145606i
$628$	9.18549	+	23.9290i	0.366541	+	0.954871i
$629$	−11.4704	+	8.33374i	−0.457355	+	0.332288i
$630$	−28.2486	−	4.30135i	−1.12545	−	0.171370i
$631$	20.5730	+	14.9472i	0.818998	+	0.595037i	0.916425	−	0.400206i	$-0.131061\pi$
$631$	20.5730	+	14.9472i	0.818998	+	0.595037i	−0.0974273	+	0.995243i	$0.531061\pi$
$632$	−2.17968	+	8.13469i	−0.0867031	+	0.323580i
$633$	−4.93515	−	1.89443i	−0.196155	−	0.0752968i
$634$	−29.3763	+	26.4506i	−1.16668	+	1.05049i
$635$	28.9813	−	2.01272i	1.15009	−	0.0798722i
$636$	0.524836	−	0.170530i	0.0208111	−	0.00676194i
$637$	−4.31887	−	31.7803i	−0.171120	−	1.25918i
$638$	1.26082	+	2.47450i	0.0499165	+	0.0979666i
$639$	−3.53468	−	3.18264i	−0.139830	−	0.125903i
$640$	10.7625	+	8.41682i	0.425424	+	0.332704i
$641$	25.0351	+	27.8043i	0.988828	+	1.09820i	0.995164	+	0.0982243i	$0.0313163\pi$
$641$	25.0351	+	27.8043i	0.988828	+	1.09820i	−0.00633676	+	0.999980i	$0.502017\pi$
$642$	−21.4978	−	26.5475i	−0.848449	−	1.04775i
$643$	14.7951	+	14.7951i	0.583460	+	0.583460i	0.935852	−	0.352392i	$-0.114632\pi$
$643$	14.7951	+	14.7951i	0.583460	+	0.583460i	−0.352392	+	0.935852i	$0.614632\pi$
$644$	27.9180	−	27.3102i	1.10012	−	1.07617i
$645$	−10.0912	+	7.59676i	−0.397341	+	0.299122i
$646$	21.4678	+	9.55808i	0.844639	+	0.376058i
$647$	−20.0874	−	16.2665i	−0.789719	−	0.639502i	0.147177	−	0.989110i	$-0.452981\pi$
$647$	−20.0874	−	16.2665i	−0.789719	−	0.639502i	−0.936896	+	0.349608i	$0.886315\pi$
$648$	2.12896	−	1.38256i	0.0836334	−	0.0543122i
$649$	3.61080	+	6.25410i	0.141736	+	0.245495i
$650$	1.62612	+	47.8718i	0.0637816	+	1.87769i
$651$	−7.79252	−	20.9877i	−0.305413	−	0.822572i
$652$	−6.00718	+	11.7898i	−0.235259	+	0.461723i
$653$	−24.5514	+	9.42440i	−0.960770	+	0.368805i	−0.787669	−	0.616099i	$-0.788712\pi$
$653$	−24.5514	+	9.42440i	−0.960770	+	0.368805i	−0.173101	+	0.984904i	$0.555379\pi$
$654$	−3.47089	−	33.0234i	−0.135723	−	1.29132i
$655$	3.34446	+	7.18113i	0.130679	+	0.280590i
$656$	−17.3573	−	1.82432i	−0.677687	−	0.0712278i
$657$	2.11712	−	2.11712i	0.0825967	−	0.0825967i
$658$	1.48993	+	0.882215i	0.0580836	+	0.0343923i
$659$	−5.69893	−	1.85169i	−0.221999	−	0.0721317i	0.195906	−	0.980623i	$-0.437235\pi$
$659$	−5.69893	−	1.85169i	−0.221999	−	0.0721317i	−0.417904	+	0.908491i	$0.637235\pi$
$660$	−4.48878	−	1.12145i	−0.174725	−	0.0436522i
$661$	9.56586	−	45.0038i	0.372069	−	1.75045i	−0.250723	−	0.968059i	$-0.580668\pi$
$661$	9.56586	−	45.0038i	0.372069	−	1.75045i	0.622792	−	0.782387i	$-0.285998\pi$
$662$	3.40478	−	64.9671i	0.132331	−	2.52502i
$663$	7.19918	+	4.67520i	0.279593	+	0.181570i
$664$	−0.890129	−	2.73954i	−0.0345437	−	0.106315i
$665$	25.6181	+	14.5873i	0.993426	+	0.565670i
$666$	9.38224	−	28.8756i	0.363555	−	1.11891i
$667$	6.11699	−	4.95344i	0.236851	−	0.191798i
$668$	−24.0205	+	6.43627i	−0.929381	+	0.249027i
$669$	−4.50498	−	10.1184i	−0.174173	−	0.391198i
$670$	−12.8916	−	55.9609i	−0.498045	−	2.16196i
$671$	−3.27395	−	4.50620i	−0.126389	−	0.173960i
$672$	17.3973	−	3.49826i	0.671114	−	0.134948i
$673$	−15.5853	−	7.94108i	−0.600767	−	0.306106i	0.127030	−	0.991899i	$-0.459456\pi$
$673$	−15.5853	−	7.94108i	−0.600767	−	0.306106i	−0.727797	+	0.685793i	$0.759456\pi$
$674$	63.0398	−	36.3960i	2.42820	−	1.40192i
$675$	18.0775	−	12.6324i	0.695805	−	0.486222i
$676$	9.47819	−	16.4167i	0.364546	−	0.631412i
$677$	−1.82763	−	34.8733i	−0.0702417	−	1.34029i	−0.775503	−	0.631344i	$-0.782504\pi$
$677$	−1.82763	−	34.8733i	−0.0702417	−	1.34029i	0.705262	−	0.708947i	$-0.250830\pi$
$678$	14.9717	+	2.37128i	0.574984	+	0.0910685i
$679$	−11.7505	+	5.82520i	−0.450943	+	0.223551i
$680$	3.70678	−	1.27437i	0.142148	−	0.0488700i
$681$	0.421309	−	4.00849i	0.0161446	−	0.153606i
$682$	5.78987	+	21.6081i	0.221706	+	0.827417i
$683$	14.5817	−	37.9867i	0.557954	−	1.45352i	−0.307020	−	0.951703i	$-0.599332\pi$
$683$	14.5817	−	37.9867i	0.557954	−	1.45352i	0.864974	−	0.501817i	$-0.167335\pi$
$684$	−26.7039	+	5.67610i	−1.02105	+	0.217031i
$685$	14.9586	−	7.94450i	0.571538	−	0.303544i
$686$	−36.5897	+	12.6763i	−1.39700	+	0.483985i
$687$	4.94891	−	2.52160i	0.188813	−	0.0962049i
$688$	−11.5498	+	17.7852i	−0.440333	+	0.678053i
$689$	1.25537	+	0.266838i	0.0478260	+	0.0101657i
$690$	−0.855044	+	24.1558i	−0.0325510	+	0.919595i
$691$	−3.69969	−	17.4057i	−0.140743	−	0.662144i	−0.990787	−	0.135432i	$-0.956758\pi$
$691$	−3.69969	−	17.4057i	−0.140743	−	0.662144i	0.850044	−	0.526712i	$-0.176575\pi$
$692$	−32.1577	+	5.09328i	−1.22245	+	0.193618i
$693$	5.23434	−	3.71565i	0.198836	−	0.141146i
$694$	33.1078	−	45.5689i	1.25675	−	1.72977i
$695$	12.9777	−	14.9148i	0.492272	−	0.565750i
$696$	−0.811972	+	0.0853417i	−0.0307777	+	0.00323487i
$697$	−7.94408	+	9.81012i	−0.300903	+	0.371585i
$698$	−60.4013	+	3.16550i	−2.28622	+	0.119816i
$699$	7.17212			0.271275
$700$	30.5314	−	7.22574i	1.15398	−	0.273107i
$701$	−20.8675			−0.788156			−0.394078	−	0.919077i	$-0.628936\pi$
$701$	−20.8675			−0.788156			−0.394078	+	0.919077i	$0.628936\pi$
$702$	−42.1969	+	2.21144i	−1.59262	+	0.0834656i
$703$	−19.7129	+	24.3434i	−0.743485	+	0.918128i
$704$	−11.1201	+	1.16877i	−0.419105	+	0.0440497i
$705$	−0.566543	+	0.130513i	−0.0213372	+	0.00491540i
$706$	14.3393	−	19.7364i	0.539667	−	0.742788i
$707$	−3.76330	−	40.0393i	−0.141533	−	1.50583i
$708$	−13.3791	+	2.11905i	−0.502819	+	0.0796387i
$709$	0.161305	+	0.758882i	0.00605795	+	0.0285004i	0.981073	−	0.193639i	$-0.0620292\pi$
$709$	0.161305	+	0.758882i	0.00605795	+	0.0285004i	−0.975015	+	0.222140i	$0.928696\pi$
$710$	9.04448	+	3.29680i	0.339433	+	0.123727i
$711$	24.4840	+	5.20424i	0.918223	+	0.195174i
$712$	4.48897	−	6.91241i	0.168231	−	0.259054i
$713$	56.4913	−	28.7838i	2.11562	−	1.07796i
$714$	3.82042	−	9.63428i	0.142976	−	0.360554i
$715$	−7.73680	−	7.47846i	−0.289340	−	0.279679i
$716$	3.73407	−	0.793701i	0.139549	−	0.0296620i
$717$	5.71101	−	14.8777i	0.213282	−	0.555618i
$718$	−2.40915	−	8.99106i	−0.0899086	−	0.335543i
$719$	−3.85474	+	36.6754i	−0.143757	+	1.36776i	0.650189	+	0.759773i	$0.274690\pi$
$719$	−3.85474	+	36.6754i	−0.143757	+	1.36776i	−0.793946	+	0.607988i	$0.791977\pi$
$720$	9.24524	−	13.1902i	0.344550	−	0.491570i
$721$	9.94835	−	14.9562i	0.370496	−	0.556997i
$722$	12.0411	+	1.90712i	0.448122	+	0.0709755i
$723$	1.12822	+	21.5278i	0.0419591	+	0.800628i
$724$	−4.12478	+	7.14434i	−0.153296	+	0.265517i
$725$	6.26259	−	0.874075i	0.232587	−	0.0324623i
$726$	−14.8859	+	8.59439i	−0.552468	+	0.318968i
$727$	17.7421	+	9.04006i	0.658019	+	0.335277i	0.750915	−	0.660398i	$-0.229613\pi$
$727$	17.7421	+	9.04006i	0.658019	+	0.335277i	−0.0928967	+	0.995676i	$0.529613\pi$
$728$	−8.92772	−	3.00980i	−0.330883	−	0.111551i
$729$	2.02583	+	2.78831i	0.0750307	+	0.103271i
$730$	−2.37040	+	5.57693i	−0.0877323	+	0.206411i
$731$	6.23857	+	14.0121i	0.230742	+	0.518254i
$732$	10.0919	−	2.70410i	0.373006	−	0.0999466i
$733$	−0.0311408	+	0.0252173i	−0.00115021	+	0.000931422i	−0.629895	−	0.776680i	$-0.716902\pi$
$733$	−0.0311408	+	0.0252173i	−0.00115021	+	0.000931422i	0.628745	+	0.777611i	$0.283569\pi$
$734$	−16.5940	+	51.0711i	−0.612496	+	1.88507i
$735$	5.96091	−	11.5548i	0.219872	−	0.426207i
$736$	15.5297	+	47.7955i	0.572432	+	1.76177i
$737$	10.8194	+	7.02618i	0.398537	+	0.258813i
$738$	1.41473	−	26.9947i	0.0520771	−	0.993689i
$739$	−4.01685	+	18.8978i	−0.147762	+	0.695167i	0.840427	+	0.541925i	$0.182304\pi$
$739$	−4.01685	+	18.8978i	−0.147762	+	0.695167i	−0.988189	+	0.153241i	$0.951029\pi$
$740$	2.30968	+	33.2572i	0.0849054	+	1.22256i
$741$	18.0366	+	5.86045i	0.662592	+	0.215289i
$742$	0.0170523	−	1.54947i	0.000626011	−	0.0568829i
$743$	16.7789	−	16.7789i	0.615557	−	0.615557i	−0.328831	−	0.944389i	$-0.606655\pi$
$743$	16.7789	−	16.7789i	0.615557	−	0.615557i	0.944389	+	0.328831i	$0.106655\pi$
$744$	−6.54044	−	0.687427i	−0.239784	−	0.0252023i
$745$	−3.44238	−	1.91028i	−0.126119	−	0.0699873i
$746$	7.82715	+	74.4703i	0.286572	+	2.72655i
$747$	−7.99289	+	3.06818i	−0.292445	+	0.112259i
$748$	−2.55067	+	5.00597i	−0.0932617	+	0.183036i
$749$	−48.7843	+	18.1132i	−1.78254	+	0.661840i
$750$	−10.5989	+	16.2701i	−0.387019	+	0.594099i
$751$	−6.63402	−	11.4905i	−0.242079	−	0.419293i	0.719227	−	0.694775i	$-0.244496\pi$
$751$	−6.63402	−	11.4905i	−0.242079	−	0.419293i	−0.961306	+	0.275482i	$0.911163\pi$
$752$	−0.818615	+	0.531615i	−0.0298518	+	0.0193860i
$753$	9.94991	+	8.05728i	0.362595	+	0.293623i
$754$	−11.0679	−	4.92773i	−0.403068	−	0.179457i
$755$	−14.0172	+	0.238001i	−0.510138	+	0.00866174i
$756$	6.86883	+	26.8116i	0.249817	+	0.975130i
$757$	1.13591	+	1.13591i	0.0412853	+	0.0412853i	0.727448	−	0.686163i	$-0.240706\pi$
$757$	1.13591	+	1.13591i	0.0412853	+	0.0412853i	−0.686163	+	0.727448i	$0.740706\pi$
$758$	29.8712	+	36.8879i	1.08497	+	1.33983i
$759$	−3.63330	−	4.03519i	−0.131880	−	0.146468i
$760$	7.18167	−	4.83913i	0.260507	−	0.175534i
$761$	−23.6079	−	21.2567i	−0.855787	−	0.770554i	0.119187	−	0.992872i	$-0.461971\pi$
$761$	−23.6079	−	21.2567i	−0.855787	−	0.770554i	−0.974974	+	0.222318i	$0.928638\pi$
$762$	−10.2440	−	20.1050i	−0.371102	−	0.728328i
$763$	−49.3595	−	11.0608i	−1.78693	−	0.400427i
$764$	6.68717	−	2.17279i	0.241933	−	0.0786089i
$765$	−4.35914	−	10.8040i	−0.157605	−	0.390621i
$766$	−33.7996	+	30.4333i	−1.22123	+	1.09960i

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08800 + 0.109427i) q^{2} +(-0.522748 + 0.645540i) q^{3} +(2.35872 - 0.247911i) q^{4} +(1.15075 + 1.91723i) q^{5} +(1.02086 - 1.40509i) q^{6} +(-1.53148 - 2.15744i) q^{7} +(-0.767632 + 0.121581i) q^{8} +(0.480279 + 2.25953i) q^{9} +O(q^{10})\)	\(q+(-2.08800 + 0.109427i) q^{2} +(-0.522748 + 0.645540i) q^{3} +(2.35872 - 0.247911i) q^{4} +(1.15075 + 1.91723i) q^{5} +(1.02086 - 1.40509i) q^{6} +(-1.53148 - 2.15744i) q^{7} +(-0.767632 + 0.121581i) q^{8} +(0.480279 + 2.25953i) q^{9} +(-2.61256 - 3.87725i) q^{10} +(1.02734 + 0.218367i) q^{11} +(-1.07298 + 1.65224i) q^{12} +(-4.08239 + 2.08008i) q^{13} +(3.43382 + 4.33715i) q^{14} +(-1.83920 - 0.259375i) q^{15} +(-3.05026 + 0.648353i) q^{16} +(-0.808289 + 2.10566i) q^{17} +(-1.25008 - 4.66535i) q^{18} +(-0.520869 + 4.95574i) q^{19} +(3.18960 + 4.23693i) q^{20} +(2.19329 + 0.139164i) q^{21} +(-2.16897 - 0.343531i) q^{22} +(0.325733 + 6.21536i) q^{23} +(0.322792 - 0.559093i) q^{24} +(-2.35156 + 4.41250i) q^{25} +(8.29642 - 4.78994i) q^{26} +(-3.93004 - 2.00245i) q^{27} +(-4.14720 - 4.70913i) q^{28} +(-0.743348 - 1.02313i) q^{29} +(3.86863 + 0.340316i) q^{30} +(-4.14336 - 9.30613i) q^{31} +(7.79943 - 2.08985i) q^{32} +(-0.678002 + 0.549035i) q^{33} +(1.45729 - 4.48507i) q^{34} +(2.37396 - 5.41888i) q^{35} +(1.69301 + 5.21054i) q^{36} +(5.27200 + 3.42368i) q^{37} +(0.545281 - 10.4046i) q^{38} +(0.791286 - 3.72271i) q^{39} +(-1.11645 - 1.33182i) q^{40} +(5.32280 + 1.72948i) q^{41} +(-4.59482 - 0.0505673i) q^{42} +(4.80861 - 4.80861i) q^{43} +(2.47733 + 0.260378i) q^{44} +(-3.77937 + 3.52096i) q^{45} +(-1.36026 - 12.9420i) q^{46} +(0.292218 - 0.112172i) q^{47} +(1.17598 - 2.30799i) q^{48} +(-2.30911 + 6.60818i) q^{49} +(4.42720 - 9.47062i) q^{50} +(-0.936759 - 1.62251i) q^{51} +(-9.11355 + 5.91841i) q^{52} +(-0.217690 - 0.176281i) q^{53} +(8.42504 + 3.75107i) q^{54} +(0.763545 + 2.22093i) q^{55} +(1.43792 + 1.46992i) q^{56} +(-2.92684 - 2.92684i) q^{57} +(1.66407 + 2.05495i) q^{58} +(4.60084 + 5.10975i) q^{59} +(-4.40246 - 0.155834i) q^{60} +(-3.94111 - 3.54859i) q^{61} +(9.66967 + 18.9778i) q^{62} +(4.13927 - 4.49661i) q^{63} +(-10.1249 + 3.28979i) q^{64} +(-8.68581 - 5.43324i) q^{65} +(1.35559 - 1.22058i) q^{66} +(11.4671 + 4.40181i) q^{67} +(-1.38451 + 5.16706i) q^{68} +(-4.18254 - 3.03879i) q^{69} +(-4.36386 + 11.5744i) q^{70} +(-1.66579 + 1.21027i) q^{71} +(-0.643393 - 1.67610i) q^{72} +(-0.705919 - 1.08702i) q^{73} +(-11.3826 - 6.57173i) q^{74} +(-1.61917 - 3.82465i) q^{75} +11.8183i q^{76} +(-1.10223 - 2.55084i) q^{77} +(-1.24484 + 7.85959i) q^{78} +(4.40735 - 9.89907i) q^{79} +(-4.75312 - 5.10197i) q^{80} +(-2.98382 + 1.32848i) q^{81} +(-11.3033 - 3.02870i) q^{82} +(0.579789 + 3.66064i) q^{83} +(5.20787 - 0.215495i) q^{84} +(-4.96718 + 0.873412i) q^{85} +(-9.51417 + 10.5666i) q^{86} +(1.04906 + 0.0549787i) q^{87} +(-0.815165 - 0.0427210i) q^{88} +(-7.09604 + 7.88095i) q^{89} +(7.50603 - 7.76533i) q^{90} +(10.7398 + 5.62191i) q^{91} +(2.30917 + 14.5795i) q^{92} +(8.17341 + 2.19006i) q^{93} +(-0.597877 + 0.266192i) q^{94} +(-10.1007 + 4.70418i) q^{95} +(-2.72805 + 6.12730i) q^{96} +(0.775456 - 4.89604i) q^{97} +(4.09830 - 14.0505i) q^{98} +2.42618i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more