LMFDB - Embedded newform 175.2.x.a.3.14

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			3.14
Character	$\chi$	$=$	175.3
Dual form			175.2.x.a.117.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.882496 - 1.35892i) q^{2} +(-0.978941 + 2.55023i) q^{3} +(-0.254403 - 0.571398i) q^{4} +(-1.48415 + 1.67252i) q^{5} +(2.60166 + 3.58087i) q^{6} +(-2.64114 + 0.156130i) q^{7} +(2.19977 + 0.348409i) q^{8} +(-3.31591 - 2.98566i) q^{9} +O(q^{10})$	\(q+(0.882496 - 1.35892i) q^{2} +(-0.978941 + 2.55023i) q^{3} +(-0.254403 - 0.571398i) q^{4} +(-1.48415 + 1.67252i) q^{5} +(2.60166 + 3.58087i) q^{6} +(-2.64114 + 0.156130i) q^{7} +(2.19977 + 0.348409i) q^{8} +(-3.31591 - 2.98566i) q^{9} +(0.963067 + 3.49283i) q^{10} +(2.62811 + 2.91881i) q^{11} +(1.70624 - 0.0894203i) q^{12} +(0.0865535 + 0.0441012i) q^{13} +(-2.11863 + 3.72689i) q^{14} +(-2.81240 - 5.42221i) q^{15} +(3.25179 - 3.61148i) q^{16} +(2.10918 - 2.60462i) q^{17} +(-6.98356 + 1.87124i) q^{18} +(5.56832 + 2.47917i) q^{19} +(1.33324 + 0.422546i) q^{20} +(2.18736 - 6.88836i) q^{21} +(6.28573 - 0.995562i) q^{22} +(-4.39848 - 2.85640i) q^{23} +(-3.04197 + 5.26884i) q^{24} +(-0.594613 - 4.96452i) q^{25} +(0.136313 - 0.0787005i) q^{26} +(3.55840 - 1.81310i) q^{27} +(0.761125 + 1.46942i) q^{28} +(2.51245 - 3.45809i) q^{29} +(-9.85031 - 0.963234i) q^{30} +(-0.701840 + 0.0737664i) q^{31} +(-0.885159 - 3.30346i) q^{32} +(-10.0164 + 3.84493i) q^{33} +(-1.67814 - 5.16477i) q^{34} +(3.65871 - 4.64907i) q^{35} +(-0.862422 + 2.65426i) q^{36} +(0.403914 + 7.70713i) q^{37} +(8.28302 - 5.37906i) q^{38} +(-0.197199 + 0.177559i) q^{39} +(-3.84750 + 3.16206i) q^{40} +(-0.124652 + 0.0405019i) q^{41} +(-7.43042 - 9.05139i) q^{42} +(8.25770 + 8.25770i) q^{43} +(0.999203 - 2.24425i) q^{44} +(9.91486 - 1.11475i) q^{45} +(-7.76327 + 3.45643i) q^{46} +(2.10528 - 1.70482i) q^{47} +(6.02679 + 11.8282i) q^{48} +(6.95125 - 0.824720i) q^{49} +(-7.27115 - 3.57313i) q^{50} +(4.57761 + 7.92865i) q^{51} +(0.00317989 - 0.0606759i) q^{52} +(-10.9795 - 4.21462i) q^{53} +(0.676413 - 6.43564i) q^{54} +(-8.78225 + 0.0636062i) q^{55} +(-5.86430 - 0.576749i) q^{56} +(-11.7735 + 11.7735i) q^{57} +(-2.48206 - 6.46598i) q^{58} +(-5.04772 - 1.07293i) q^{59} +(-2.38276 + 2.98643i) q^{60} +(-1.48307 - 6.97731i) q^{61} +(-0.519128 + 1.01885i) q^{62} +(9.22393 + 7.36783i) q^{63} +(3.97346 + 1.29105i) q^{64} +(-0.202218 + 0.0793093i) q^{65} +(-3.61445 + 17.0046i) q^{66} +(0.433773 + 0.351262i) q^{67} +(-2.02485 - 0.542557i) q^{68} +(11.5903 - 8.42087i) q^{69} +(-3.08893 - 9.07469i) q^{70} +(0.818370 + 0.594581i) q^{71} +(-6.25400 - 7.72305i) q^{72} +(-2.13084 - 0.111673i) q^{73} +(10.8299 + 6.25262i) q^{74} +(13.2428 + 3.34357i) q^{75} -3.81243i q^{76} +(-7.39691 - 7.29866i) q^{77} +(0.0672616 + 0.424673i) q^{78} +(15.3675 + 1.61519i) q^{79} +(1.21412 + 10.7986i) q^{80} +(-0.258873 - 2.46301i) q^{81} +(-0.0549659 + 0.205136i) q^{82} +(1.69214 - 10.6837i) q^{83} +(-4.49246 + 0.502566i) q^{84} +(1.22593 + 7.39326i) q^{85} +(18.5090 - 3.93420i) q^{86} +(6.35939 + 9.79260i) q^{87} +(4.76429 + 7.33636i) q^{88} +(-0.981714 + 0.208670i) q^{89} +(7.23495 - 14.4573i) q^{90} +(-0.235485 - 0.102964i) q^{91} +(-0.513159 + 3.23996i) q^{92} +(0.498939 - 1.86207i) q^{93} +(-0.458824 - 4.36542i) q^{94} +(-12.4107 + 5.63363i) q^{95} +(9.29110 + 0.976534i) q^{96} +(-1.77133 - 11.1837i) q^{97} +(5.01371 - 10.1740i) q^{98} -17.5251i 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	0.882496	−	1.35892i	0.624019	−	0.960904i	−0.375402	−	0.926862i	$-0.622495\pi$
$2$	0.882496	−	1.35892i	0.624019	−	0.960904i	0.999420	−	0.0340422i	$-0.0108381\pi$
$3$	−0.978941	+	2.55023i	−0.565192	+	1.47238i	0.291512	+	0.956567i	$0.405842\pi$
$3$	−0.978941	+	2.55023i	−0.565192	+	1.47238i	−0.856704	+	0.515808i	$0.827492\pi$
$4$	−0.254403	−	0.571398i	−0.127201	−	0.285699i
$5$	−1.48415	+	1.67252i	−0.663731	+	0.747971i
$5$	−1.48415	+	1.67252i	−0.663731	+	0.747971i
$6$	2.60166	+	3.58087i	1.06212	+	1.46189i
$7$	−2.64114	+	0.156130i	−0.998257	+	0.0590114i
$7$	−2.64114	+	0.156130i	−0.998257	+	0.0590114i
$8$	2.19977	+	0.348409i	0.777736	+	0.123181i
$9$	−3.31591	−	2.98566i	−1.10530	−	0.995219i
$10$	0.963067	+	3.49283i	0.304549	+	1.10453i
$11$	2.62811	+	2.91881i	0.792404	+	0.880054i	0.995068	−	0.0991947i	$-0.0316267\pi$
$11$	2.62811	+	2.91881i	0.792404	+	0.880054i	−0.202664	+	0.979248i	$0.564960\pi$
$12$	1.70624	−	0.0894203i	0.492549	−	0.0258134i
$13$	0.0865535	+	0.0441012i	0.0240056	+	0.0122315i	0.465952	−	0.884810i	$-0.345712\pi$
$13$	0.0865535	+	0.0441012i	0.0240056	+	0.0122315i	−0.441946	+	0.897041i	$0.645712\pi$
$14$	−2.11863	+	3.72689i	−0.566227	+	0.996054i
$15$	−2.81240	−	5.42221i	−0.726160	−	1.40001i
$16$	3.25179	−	3.61148i	0.812948	−	0.902871i
$17$	2.10918	−	2.60462i	0.511550	−	0.631712i	−0.454289	−	0.890854i	$-0.650107\pi$
$17$	2.10918	−	2.60462i	0.511550	−	0.631712i	0.965839	+	0.259142i	$0.0834399\pi$
$18$	−6.98356	+	1.87124i	−1.64604	+	0.441055i
$19$	5.56832	+	2.47917i	1.27746	+	0.568762i	0.929526	−	0.368757i	$-0.120217\pi$
$19$	5.56832	+	2.47917i	1.27746	+	0.568762i	0.347934	+	0.937519i	$0.386883\pi$
$20$	1.33324	+	0.422546i	0.298122	+	0.0944842i
$21$	2.18736	−	6.88836i	0.477320	−	1.50316i
$22$	6.28573	−	0.995562i	1.34012	−	0.212254i
$23$	−4.39848	−	2.85640i	−0.917146	−	0.595601i	−0.00256149	−	0.999997i	$-0.500815\pi$
$23$	−4.39848	−	2.85640i	−0.917146	−	0.595601i	−0.914584	+	0.404395i	$0.867482\pi$
$24$	−3.04197	+	5.26884i	−0.620939	+	1.07550i
$25$	−0.594613	−	4.96452i	−0.118923	−	0.992904i
$26$	0.136313	−	0.0787005i	0.0267332	−	0.0154344i
$27$	3.55840	−	1.81310i	0.684814	−	0.348930i
$28$	0.761125	+	1.46942i	0.143839	+	0.277695i
$29$	2.51245	−	3.45809i	0.466550	−	0.642152i	−0.509301	−	0.860589i	$-0.670096\pi$
$29$	2.51245	−	3.45809i	0.466550	−	0.642152i	0.975851	+	0.218437i	$0.0700959\pi$
$30$	−9.85031	−	0.963234i	−1.79841	−	0.175862i
$31$	−0.701840	+	0.0737664i	−0.126054	+	0.0132488i	−0.167345	−	0.985898i	$-0.553520\pi$
$31$	−0.701840	+	0.0737664i	−0.126054	+	0.0132488i	0.0412913	+	0.999147i	$0.486853\pi$
$32$	−0.885159	−	3.30346i	−0.156475	−	0.583975i
$33$	−10.0164	+	3.84493i	−1.74363	+	0.669317i
$34$	−1.67814	−	5.16477i	−0.287798	−	0.885751i
$35$	3.65871	−	4.64907i	0.618435	−	0.785836i
$36$	−0.862422	+	2.65426i	−0.143737	+	0.442377i
$37$	0.403914	+	7.70713i	0.0664030	+	1.26704i	0.805154	+	0.593066i	$0.202083\pi$
$37$	0.403914	+	7.70713i	0.0664030	+	1.26704i	−0.738751	+	0.673978i	$0.764584\pi$
$38$	8.28302	−	5.37906i	1.34368	−	0.872599i
$39$	−0.197199	+	0.177559i	−0.0315771	+	0.0284322i
$40$	−3.84750	+	3.16206i	−0.608343	+	0.499965i
$41$	−0.124652	+	0.0405019i	−0.0194674	+	0.00632534i	−0.318735	−	0.947844i	$-0.603258\pi$
$41$	−0.124652	+	0.0405019i	−0.0194674	+	0.00632534i	0.299267	+	0.954169i	$0.403258\pi$
$42$	−7.43042	−	9.05139i	−1.14654	−	1.39666i
$43$	8.25770	+	8.25770i	1.25929	+	1.25929i	0.951434	+	0.307854i	$0.0996108\pi$
$43$	8.25770	+	8.25770i	1.25929	+	1.25929i	0.307854	+	0.951434i	$0.400389\pi$
$44$	0.999203	−	2.24425i	0.150636	−	0.338333i
$45$	9.91486	−	1.11475i	1.47802	−	0.166177i
$46$	−7.76327	+	3.45643i	−1.14463	+	0.509623i
$47$	2.10528	−	1.70482i	0.307087	−	0.248674i	−0.463372	−	0.886164i	$-0.653361\pi$
$47$	2.10528	−	1.70482i	0.307087	−	0.248674i	0.770459	+	0.637490i	$0.220027\pi$
$48$	6.02679	+	11.8282i	0.869893	+	1.70726i
$49$	6.95125	−	0.824720i	0.993035	−	0.117817i
$50$	−7.27115	−	3.57313i	−1.02830	−	0.505317i
$51$	4.57761	+	7.92865i	0.640993	+	1.11023i
$52$	0.00317989	−	0.0606759i	0.000440972	−	0.00841424i
$53$	−10.9795	−	4.21462i	−1.50814	−	0.578922i	−0.542791	−	0.839868i	$-0.682632\pi$
$53$	−10.9795	−	4.21462i	−1.50814	−	0.578922i	−0.965354	+	0.260945i	$0.915966\pi$
$54$	0.676413	−	6.43564i	0.0920482	−	0.875780i
$55$	−8.78225	+	0.0636062i	−1.18420	+	0.00857666i
$56$	−5.86430	−	0.576749i	−0.783649	−	0.0770713i
$57$	−11.7735	+	11.7735i	−1.55944	+	1.55944i
$58$	−2.48206	−	6.46598i	−0.325910	−	0.849025i
$59$	−5.04772	−	1.07293i	−0.657157	−	0.139683i	−0.132748	−	0.991150i	$-0.542380\pi$
$59$	−5.04772	−	1.07293i	−0.657157	−	0.139683i	−0.524409	+	0.851467i	$0.675714\pi$
$60$	−2.38276	+	2.98643i	−0.307612	+	0.385546i
$61$	−1.48307	−	6.97731i	−0.189888	−	0.893354i	−0.965147	−	0.261709i	$-0.915714\pi$
$61$	−1.48307	−	6.97731i	−0.189888	−	0.893354i	0.775259	−	0.631644i	$-0.217620\pi$
$62$	−0.519128	+	1.01885i	−0.0659293	+	0.129394i
$63$	9.22393	+	7.36783i	1.16211	+	0.928260i
$64$	3.97346	+	1.29105i	0.496682	+	0.161382i
$65$	−0.202218	+	0.0793093i	−0.0250821	+	0.00983711i
$66$	−3.61445	+	17.0046i	−0.444908	+	2.09313i
$67$	0.433773	+	0.351262i	0.0529938	+	0.0429135i	0.655451	−	0.755237i	$-0.272478\pi$
$67$	0.433773	+	0.351262i	0.0529938	+	0.0429135i	−0.602458	+	0.798151i	$0.705812\pi$
$68$	−2.02485	−	0.542557i	−0.245549	−	0.0657947i
$69$	11.5903	−	8.42087i	1.39531	−	1.01375i
$70$	−3.08893	−	9.07469i	−0.369198	−	1.08463i
$71$	0.818370	+	0.594581i	0.0971227	+	0.0705637i	0.635287	−	0.772276i	$-0.280882\pi$
$71$	0.818370	+	0.594581i	0.0971227	+	0.0705637i	−0.538164	+	0.842840i	$0.680882\pi$
$72$	−6.25400	−	7.72305i	−0.737041	−	0.910170i
$73$	−2.13084	−	0.111673i	−0.249396	−	0.0130703i	−0.0727716	−	0.997349i	$-0.523184\pi$
$73$	−2.13084	−	0.111673i	−0.249396	−	0.0130703i	−0.176624	+	0.984278i	$0.556518\pi$
$74$	10.8299	+	6.25262i	1.25894	+	0.726852i
$75$	13.2428	+	3.34357i	1.52914	+	0.386082i
$76$		−	3.81243i		−	0.437316i
$77$	−7.39691	−	7.29866i	−0.842956	−	0.831759i
$78$	0.0672616	+	0.424673i	0.00761588	+	0.0480848i
$79$	15.3675	+	1.61519i	1.72898	+	0.181723i	0.916167	−	0.400797i	$-0.131267\pi$
$79$	15.3675	+	1.61519i	1.72898	+	0.181723i	0.812816	+	0.582521i	$0.197933\pi$
$80$	1.21412	+	10.7986i	0.135743	+	1.20733i
$81$	−0.258873	−	2.46301i	−0.0287636	−	0.273668i
$82$	−0.0549659	+	0.205136i	−0.00606997	+	0.0226534i
$83$	1.69214	−	10.6837i	0.185736	−	1.17269i	−0.701944	−	0.712232i	$-0.747684\pi$
$83$	1.69214	−	10.6837i	0.185736	−	1.17269i	0.887680	−	0.460461i	$-0.152316\pi$
$84$	−4.49246	+	0.502566i	−0.490168	+	0.0548345i
$85$	1.22593	+	7.39326i	0.132971	+	0.801912i
$86$	18.5090	−	3.93420i	1.99587	−	0.424236i
$87$	6.35939	+	9.79260i	0.681798	+	1.04988i
$88$	4.76429	+	7.33636i	0.507875	+	0.782058i
$89$	−0.981714	+	0.208670i	−0.104061	+	0.0221190i	−0.259648	−	0.965703i	$-0.583607\pi$
$89$	−0.981714	+	0.208670i	−0.104061	+	0.0221190i	0.155587	+	0.987822i	$0.450273\pi$
$90$	7.23495	−	14.4573i	0.762631	−	1.52393i
$91$	−0.235485	−	0.102964i	−0.0246856	−	0.0107936i
$92$	−0.513159	+	3.23996i	−0.0535005	+	0.337789i
$93$	0.498939	−	1.86207i	0.0517376	−	0.193087i
$94$	−0.458824	−	4.36542i	−0.0473241	−	0.450259i
$95$	−12.4107	+	5.63363i	−1.27331	+	0.577999i
$96$	9.29110	+	0.976534i	0.948269	+	0.0996670i
$97$	−1.77133	−	11.1837i	−0.179851	−	1.13554i	−0.898113	−	0.439764i	$-0.855062\pi$
$97$	−1.77133	−	11.1837i	−0.179851	−	1.13554i	0.718262	−	0.695773i	$-0.244938\pi$
$98$	5.01371	−	10.1740i	0.506461	−	1.02773i
$99$		−	17.5251i		−	1.76134i
$100$	−2.68544	+	1.60275i	−0.268544	+	0.160275i
$101$	−10.1623	−	5.86718i	−1.01118	−	0.583807i	−0.0996449	−	0.995023i	$-0.531771\pi$
$101$	−10.1623	−	5.86718i	−1.01118	−	0.583807i	−0.911538	+	0.411216i	$0.865104\pi$
$102$	14.8141	+	0.776377i	1.46682	+	0.0768727i
$103$	6.33822	+	7.82705i	0.624523	+	0.771222i	0.986991	−	0.160774i	$-0.0513991\pi$
$103$	6.33822	+	7.82705i	0.624523	+	0.771222i	−0.362468	+	0.931996i	$0.618066\pi$
$104$	0.175032	+	0.127168i	0.0171633	+	0.0124699i
$105$	8.27452	+	13.8817i	0.807511	+	1.35472i
$106$	−15.4167	+	11.2009i	−1.49740	+	1.08792i
$107$	1.09349	+	0.292999i	0.105711	+	0.0283253i	0.311287	−	0.950316i	$-0.399240\pi$
$107$	1.09349	+	0.292999i	0.105711	+	0.0283253i	−0.205576	+	0.978641i	$0.565907\pi$
$108$	−1.94126	−	1.57201i	−0.186798	−	0.151266i
$109$	−0.608654	+	2.86349i	−0.0582985	+	0.274273i	−0.997636	−	0.0687217i	$-0.978108\pi$
$109$	−0.608654	+	2.86349i	−0.0582985	+	0.274273i	0.939337	+	0.342995i	$0.111441\pi$
$110$	−7.66386	+	11.9905i	−0.730720	+	1.14325i
$111$	−20.0504	−	6.51476i	−1.90310	−	0.618353i
$112$	−8.02458	+	10.0461i	−0.758252	+	0.949271i
$113$	−2.12100	+	4.16270i	−0.199527	+	0.391594i	−0.968991	−	0.247097i	$-0.920523\pi$
$113$	−2.12100	+	4.16270i	−0.199527	+	0.391594i	0.769464	+	0.638690i	$0.220523\pi$
$114$	5.60924	+	26.3894i	0.525353	+	2.47159i
$115$	11.3054	−	3.11719i	1.05423	−	0.290680i
$116$	−2.61512	−	0.555861i	−0.242808	−	0.0516104i
$117$	−0.155332	−	0.404655i	−0.0143605	−	0.0374103i
$118$	−5.91261	+	5.91261i	−0.544300	+	0.544300i
$119$	−5.16397	+	7.20846i	−0.473381	+	0.660798i
$120$	−4.29749	−	12.9075i	−0.392305	−	1.17829i
$121$	−0.462683	+	4.40213i	−0.0420621	+	0.400194i
$122$	−10.7904	−	4.14206i	−0.976921	−	0.375005i
$123$	0.0187379	−	0.357541i	0.00168954	−	0.0322383i
$124$	0.220700	+	0.382263i	0.0198194	+	0.0343283i
$125$	9.18572	+	6.37358i	0.821596	+	0.570070i
$126$	18.1524	−	6.03254i	1.61714	−	0.537422i
$127$	−7.51832	−	14.7555i	−0.667143	−	1.30934i	−0.937971	−	0.346713i	$-0.887298\pi$
$127$	−7.51832	−	14.7555i	−0.667143	−	1.30934i	0.270829	−	0.962628i	$-0.412702\pi$
$128$	10.5767	−	8.56482i	0.934854	−	0.757030i
$129$	−29.1428	+	12.9752i	−2.56588	+	1.14240i
$130$	−0.0706812	+	0.344789i	−0.00619915	+	0.0302400i
$131$	−0.163724	+	0.367729i	−0.0143046	+	0.0321287i	−0.920557	−	0.390609i	$-0.872264\pi$
$131$	−0.163724	+	0.367729i	−0.0143046	+	0.0321287i	0.906252	+	0.422738i	$0.138931\pi$
$132$	4.74518	+	4.74518i	0.413015	+	0.413015i
$133$	−15.0938	−	5.67847i	−1.30880	−	0.492386i
$134$	0.860142	−	0.279477i	0.0743049	−	0.0241431i
$135$	−2.24876	+	8.64238i	−0.193543	+	0.743817i
$136$	5.54717	−	4.99470i	0.475666	−	0.428292i
$137$	10.6234	−	6.89895i	0.907623	−	0.589417i	−0.00420463	−	0.999991i	$-0.501338\pi$
$137$	10.6234	−	6.89895i	0.907623	−	0.589417i	0.911827	+	0.410574i	$0.134672\pi$
$138$	−1.21491	−	23.1818i	−0.103420	−	1.97336i
$139$	−4.44619	+	13.6840i	−0.377121	+	1.16066i	0.564915	+	0.825149i	$0.308909\pi$
$139$	−4.44619	+	13.6840i	−0.377121	+	1.16066i	−0.942036	+	0.335511i	$0.891091\pi$
$140$	−3.58725	−	0.907845i	−0.303178	−	0.0767269i
$141$	2.28674	+	7.03788i	0.192579	+	0.592696i
$142$	1.53020	−	0.587388i	0.128411	−	0.0492925i
$143$	0.0987488	+	0.368536i	0.00825779	+	0.0308185i
$144$	−21.5653	+	2.26661i	−1.79711	+	0.188884i
$145$	2.05486	+	9.33443i	0.170647	+	0.775182i
$146$	−2.03221	+	2.79710i	−0.168187	+	0.231489i
$147$	−4.70164	+	18.5346i	−0.387785	+	1.52871i
$148$	4.30108	−	2.19151i	0.353547	−	0.180141i
$149$	−9.24670	+	5.33859i	−0.757519	+	0.437354i	−0.828404	−	0.560131i	$-0.810751\pi$
$149$	−9.24670	+	5.33859i	−0.757519	+	0.437354i	0.0708851	+	0.997484i	$0.477418\pi$
$150$	16.2303	−	15.0452i	1.32520	−	1.22844i
$151$	−10.4396	+	18.0820i	−0.849565	+	1.47149i	0.0320315	+	0.999487i	$0.489802\pi$
$151$	−10.4396	+	18.0820i	−0.849565	+	1.47149i	−0.881597	+	0.472003i	$0.843531\pi$
$152$	11.3852	+	7.39366i	0.923465	+	0.599705i
$153$	−14.7703	+	2.33939i	−1.19411	+	0.189128i
$154$	−16.4461	+	3.61081i	−1.32526	+	0.290967i
$155$	0.918259	−	1.28332i	0.0737563	−	0.103079i
$156$	0.151625	+	0.0675076i	0.0121397	+	0.00540494i
$157$	11.5468	−	3.09395i	0.921533	−	0.246924i	0.233293	−	0.972407i	$-0.425050\pi$
$157$	11.5468	−	3.09395i	0.921533	−	0.246924i	0.688241	+	0.725483i	$0.258383\pi$
$158$	15.7567	−	19.4579i	1.25354	−	1.54799i
$159$	21.4965	−	23.8743i	1.70478	−	1.89335i
$160$	6.83879	+	3.42238i	0.540654	+	0.270563i
$161$	12.0630	+	6.85743i	0.950695	+	0.540441i
$162$	−3.57550	−	1.82181i	−0.280918	−	0.143135i
$163$	−14.4820	+	0.758967i	−1.13431	+	0.0594469i	−0.610234	−	0.792222i	$-0.708924\pi$
$163$	−14.4820	+	0.758967i	−1.13431	+	0.0594469i	−0.524081	+	0.851668i	$0.675591\pi$
$164$	0.0548546	+	0.0609222i	0.00428342	+	0.00475722i
$165$	8.43509	−	22.4590i	0.656671	−	1.74843i
$166$	−13.0251	−	11.7278i	−1.01094	−	0.910257i
$167$	−1.65219	−	0.261681i	−0.127850	−	0.0202495i	0.0921813	−	0.995742i	$-0.470616\pi$
$167$	−1.65219	−	0.261681i	−0.127850	−	0.0202495i	−0.220032	+	0.975493i	$0.570616\pi$
$168$	7.21164	−	14.3907i	0.556390	−	1.11027i
$169$	−7.63566	−	10.5096i	−0.587359	−	0.808430i
$170$	11.1288	+	4.85857i	0.853537	+	0.372636i
$171$	−11.0621	−	24.8458i	−0.845937	−	1.90001i
$172$	2.61765	−	6.81921i	0.199594	−	0.519960i
$173$	−0.153180	+	0.235876i	−0.0116460	+	0.0179333i	−0.844446	−	0.535641i	$-0.820070\pi$
$173$	−0.153180	+	0.235876i	−0.0116460	+	0.0179333i	0.832800	+	0.553575i	$0.186737\pi$
$174$	18.9195			1.43429
$175$	2.34556	+	13.0192i	0.177308	+	0.984155i
$176$	19.0873			1.43876
$177$	7.67763	−	11.8225i	0.577086	−	0.888634i
$178$	−0.582792	+	1.51822i	−0.0436821	+	0.113796i
$179$	−5.33375	−	11.9798i	−0.398663	−	0.895412i	−0.995651	−	0.0931620i	$-0.970303\pi$
$179$	−5.33375	−	11.9798i	−0.398663	−	0.895412i	0.596988	−	0.802250i	$-0.296364\pi$
$180$	−3.15933	−	5.38173i	−0.235483	−	0.401131i
$181$	−13.5383	−	18.6338i	−1.00629	−	1.38504i	−0.921384	−	0.388653i	$-0.872940\pi$
$181$	−13.5383	−	18.6338i	−1.00629	−	1.38504i	−0.0849076	−	0.996389i	$-0.527060\pi$
$182$	−0.347735	+	0.229142i	−0.0257758	+	0.0169851i
$183$	19.2456	+	3.04820i	1.42268	+	0.225330i
$184$	−8.68043	−	7.81590i	−0.639930	−	0.576196i
$185$	−13.4898	−	10.7630i	−0.991787	−	0.791309i
$186$	−2.09009	−	2.32129i	−0.153253	−	0.170205i
$187$	13.1455	−	0.688927i	0.961295	−	0.0503793i
$188$	−1.50972	−	0.769242i	−0.110108	−	0.0561027i
$189$	−9.11516	+	5.34421i	−0.663030	+	0.388734i
$190$	−3.29667	+	21.8368i	−0.239166	+	1.58421i
$191$	2.70749	−	3.00698i	0.195907	−	0.217577i	−0.637185	−	0.770711i	$-0.719901\pi$
$191$	2.70749	−	3.00698i	0.195907	−	0.217577i	0.833093	+	0.553133i	$0.186568\pi$
$192$	−7.18227	+	8.86936i	−0.518335	+	0.640091i
$193$	−2.96976	+	0.795745i	−0.213768	+	0.0572790i	−0.364114	−	0.931355i	$-0.618628\pi$
$193$	−2.96976	+	0.795745i	−0.213768	+	0.0572790i	0.150346	+	0.988634i	$0.451961\pi$
$194$	−16.7611	−	7.46250i	−1.20337	−	0.535776i
$195$	−0.00429733	−	0.593342i	−0.000307738	−	0.0424901i
$196$	−2.23966	−	3.76212i	−0.159976	−	0.268723i
$197$	12.4561	−	1.97286i	0.887464	−	0.140560i	0.303973	−	0.952681i	$-0.401687\pi$
$197$	12.4561	−	1.97286i	0.887464	−	0.140560i	0.583490	+	0.812120i	$0.301687\pi$
$198$	−23.8153	−	15.4658i	−1.69248	−	1.09911i
$199$	2.17496	−	3.76715i	0.154179	−	0.267046i	−0.778581	−	0.627545i	$-0.784060\pi$
$199$	2.17496	−	3.76715i	0.154179	−	0.267046i	0.932760	+	0.360498i	$0.117393\pi$
$200$	0.421673	−	11.1280i	0.0298168	−	0.786866i
$201$	−1.32044	+	0.762355i	−0.0931365	+	0.0537724i
$202$	−16.9412	+	8.63198i	−1.19198	+	0.607344i
$203$	−6.09583	+	9.52558i	−0.427843	+	0.668564i
$204$	3.36586	−	4.63270i	0.235657	−	0.324354i
$205$	0.117262	−	0.268593i	0.00818994	−	0.0187594i
$206$	16.2298	−	1.70582i	1.13078	−	0.118850i
$207$	6.05670	+	22.6039i	0.420970	+	1.57108i
$208$	0.440725	−	0.169178i	0.0305588	−	0.0117304i
$209$	7.39789	+	22.7684i	0.511723	+	1.57492i
$210$	26.1664	+	1.00611i	1.80566	+	0.0694283i
$211$	2.05986	−	6.33961i	0.141807	−	0.436437i	−0.854780	−	0.518991i	$-0.826308\pi$
$211$	2.05986	−	6.33961i	0.141807	−	0.436437i	0.996587	+	0.0825543i	$0.0263078\pi$
$212$	0.384980	+	7.34585i	0.0264405	+	0.504515i
$213$	−2.31745	+	1.50497i	−0.158789	+	0.103119i
$214$	1.36316	−	1.22740i	0.0931838	−	0.0839031i
$215$	−26.0668	+	1.55548i	−1.77774	+	0.106083i
$216$	8.45936	−	2.74861i	0.575586	−	0.187019i
$217$	1.84214	−	0.304405i	0.125053	−	0.0206644i
$218$	3.35413	+	3.35413i	0.227171	+	0.227171i
$219$	2.37076	−	5.32481i	0.160201	−	0.359817i
$220$	2.27057	+	5.00197i	0.153082	+	0.337233i
$221$	0.297423	−	0.132421i	0.0200069	−	0.00890762i
$222$	−26.5474	+	21.4977i	−1.78175	+	1.44283i
$223$	6.99626	+	13.7309i	0.468504	+	0.919491i	0.997486	+	0.0708583i	$0.0225738\pi$
$223$	6.99626	+	13.7309i	0.468504	+	0.919491i	−0.528982	+	0.848633i	$0.677426\pi$
$224$	2.85360	+	8.58670i	0.190664	+	0.573723i
$225$	−12.8507	+	18.2372i	−0.856711	+	1.21581i
$226$	3.78502	+	6.55584i	0.251776	+	0.436088i
$227$	0.693452	−	13.2319i	0.0460260	−	0.878229i	−0.873892	−	0.486119i	$-0.838412\pi$
$227$	0.693452	−	13.2319i	0.0460260	−	0.878229i	0.919918	−	0.392110i	$-0.128255\pi$
$228$	9.72258	+	3.73215i	0.643893	+	0.247168i
$229$	−0.433550	+	4.12495i	−0.0286498	+	0.272584i	0.970814	+	0.239834i	$0.0770932\pi$
$229$	−0.433550	+	4.12495i	−0.0286498	+	0.272584i	−0.999464	+	0.0327499i	$0.989574\pi$
$230$	5.74091	−	18.1140i	0.378544	−	1.19440i
$231$	25.8544	−	11.7189i	1.70109	−	0.771044i
$232$	6.73164	−	6.73164i	0.441954	−	0.441954i
$233$	9.23458	+	24.0569i	0.604977	+	1.57602i	0.803101	+	0.595843i	$0.203182\pi$
$233$	9.23458	+	24.0569i	0.604977	+	1.57602i	−0.198124	+	0.980177i	$0.563485\pi$
$234$	−0.686975	−	0.146021i	−0.0449090	−	0.00954570i
$235$	−0.273206	+	6.05133i	−0.0178220	+	0.394745i
$236$	0.671086	+	3.15721i	0.0436840	+	0.205517i
$237$	−19.1630	+	37.6096i	−1.24477	+	2.44300i
$238$	5.23857	+	13.3789i	0.339566	+	0.867224i
$239$	−0.618920	−	0.201099i	−0.0400346	−	0.0130080i	0.288931	−	0.957350i	$-0.406700\pi$
$239$	−0.618920	−	0.201099i	−0.0400346	−	0.0130080i	−0.328966	+	0.944342i	$0.606700\pi$
$240$	−28.7276	−	7.47496i	−1.85436	−	0.482507i
$241$	0.238703	−	1.12301i	0.0153762	−	0.0723393i	−0.969791	−	0.243939i	$-0.921560\pi$
$241$	0.238703	−	1.12301i	0.0153762	−	0.0723393i	0.985167	+	0.171600i	$0.0548936\pi$
$242$	5.57385	+	4.51361i	0.358300	+	0.290146i
$243$	18.1075	+	4.85188i	1.16159	+	0.311248i
$244$	−3.60952	+	2.62247i	−0.231076	+	0.167887i
$245$	−8.93732	+	12.8501i	−0.570984	+	0.820961i
$246$	−0.469334	−	0.340991i	−0.0299237	−	0.0217408i
$247$	0.372623	+	0.460151i	0.0237094	+	0.0292787i
$248$	−1.56959	−	0.0822585i	−0.0996688	−	0.00522342i
$249$	25.5895	+	14.7741i	1.62167	+	0.936270i
$250$	16.7676	−	6.85805i	1.06047	−	0.433741i
$251$		−	13.8492i		−	0.874153i	−0.899424	−	0.437076i	$-0.856014\pi$
$251$		−	13.8492i		−	0.874153i	0.899424	−	0.437076i	$-0.143986\pi$
$252$	1.86337	−	7.14493i	0.117381	−	0.450088i
$253$	−3.22237	−	20.3452i	−0.202589	−	1.27909i
$254$	−26.6865	−	2.80487i	−1.67446	−	0.175993i
$255$	−20.0546	−	4.11117i	−1.25587	−	0.257451i
$256$	−1.43165	−	13.6212i	−0.0894778	−	0.851325i
$257$	−0.0943752	+	0.352213i	−0.00588696	+	0.0219704i	−0.968807	−	0.247817i	$-0.920287\pi$
$257$	−0.0943752	+	0.352213i	−0.00588696	+	0.0219704i	0.962920	+	0.269788i	$0.0869535\pi$
$258$	−8.08608	+	51.0535i	−0.503417	+	3.17845i
$259$	−2.27010	−	20.2925i	−0.141057	−	1.26092i
$260$	0.0967620	+	0.0953705i	0.00600092	+	0.00591462i
$261$	−18.6557	+	3.96540i	−1.15476	+	0.245452i
$262$	0.355231	+	0.547007i	0.0219462	+	0.0337942i
$263$	−16.2018	−	24.9486i	−0.999045	−	1.53839i	−0.833744	−	0.552151i	$-0.813807\pi$
$263$	−16.2018	−	24.9486i	−0.999045	−	1.53839i	−0.165301	−	0.986243i	$-0.552859\pi$
$264$	−23.3734	+	4.96816i	−1.43853	+	0.305769i
$265$	23.3441	−	12.1082i	1.43402	−	0.743800i
$266$	−21.0368	+	15.5001i	−1.28985	+	0.950371i
$267$	0.428885	−	2.70787i	0.0262473	−	0.165719i
$268$	0.0903576	−	0.337219i	0.00551947	−	0.0205989i
$269$	2.16638	+	20.6117i	0.132087	+	1.25672i	0.836911	+	0.547338i	$0.184359\pi$
$269$	2.16638	+	20.6117i	0.132087	+	1.25672i	−0.704825	+	0.709381i	$0.748974\pi$
$270$	9.75981	+	10.6828i	0.593963	+	0.650132i
$271$	−5.57572	−	0.586032i	−0.338701	−	0.0355989i	−0.0663487	−	0.997796i	$-0.521135\pi$
$271$	−5.57572	−	0.586032i	−0.338701	−	0.0355989i	−0.272352	+	0.962198i	$0.587802\pi$
$272$	−2.54792	−	16.0869i	−0.154490	−	0.975413i
$273$	0.493108	−	0.499746i	0.0298443	−	0.0302460i
$274$		−	20.5248i		−	1.23995i
$275$	12.9278	−	14.7828i	0.779574	−	0.891439i
$276$	−7.76028	−	4.48040i	−0.467114	−	0.269688i
$277$	5.90329	+	0.309378i	0.354694	+	0.0185887i	0.228851	−	0.973461i	$-0.426503\pi$
$277$	5.90329	+	0.309378i	0.354694	+	0.0185887i	0.125843	+	0.992050i	$0.459836\pi$
$278$	14.6717	+	18.1181i	0.879953	+	1.08665i
$279$	2.54748	+	1.85085i	0.152514	+	0.110808i
$280$	9.66810	−	8.95214i	0.577779	−	0.534993i
$281$	−6.92124	+	5.02858i	−0.412887	+	0.299980i	−0.774769	−	0.632244i	$-0.782134\pi$
$281$	−6.92124	+	5.02858i	−0.412887	+	0.299980i	0.361883	+	0.932224i	$0.382134\pi$
$282$	11.5820	+	3.10338i	0.689697	+	0.184804i
$283$	11.7275	+	9.49677i	0.697130	+	0.564525i	0.911035	−	0.412330i	$-0.135285\pi$
$283$	11.7275	+	9.49677i	0.697130	+	0.564525i	−0.213905	+	0.976855i	$0.568618\pi$
$284$	0.131547	−	0.618878i	0.00780585	−	0.0367236i
$285$	−2.21775	−	37.1650i	−0.131368	−	2.20147i
$286$	0.587957	+	0.191039i	0.0347666	+	0.0112964i
$287$	0.322900	−	0.126433i	0.0190602	−	0.00746312i
$288$	−6.92789	+	13.5968i	−0.408230	+	0.801196i
$289$	1.19910	+	5.64132i	0.0705353	+	0.331843i
$290$	14.4982	+	5.44519i	0.851363	+	0.319753i
$291$	30.2551	+	6.43093i	1.77359	+	0.376988i
$292$	0.478282	+	1.24597i	0.0279893	+	0.0729147i
$293$	7.80680	−	7.80680i	0.456078	−	0.456078i	−0.441288	−	0.897366i	$-0.645478\pi$
$293$	7.80680	−	7.80680i	0.456078	−	0.456078i	0.897366	+	0.441288i	$0.145478\pi$
$294$	21.0380	+	22.7459i	1.22696	+	1.32657i
$295$	9.28604	−	6.85000i	0.540654	−	0.398823i
$296$	−1.79672	+	17.0946i	−0.104432	+	0.993605i
$297$	14.6439	+	5.62128i	0.849727	+	0.326180i
$298$	−0.905441	+	17.2768i	−0.0524508	+	1.00082i
$299$	−0.254733	−	0.441210i	−0.0147316	−	0.0255158i
$300$	−1.45848	−	8.41749i	−0.0842055	−	0.485984i
$301$	−23.0990	−	20.5205i	−1.33141	−	1.18278i
$302$	15.3591	+	30.1439i	0.883817	+	1.73459i
$303$	24.9109	−	20.1725i	1.43109	−	1.15888i
$304$	27.0605	−	12.0481i	1.55203	−	0.691007i
$305$	13.8708	+	7.87490i	0.794238	+	0.450915i
$306$	−9.85570	+	22.1363i	−0.563413	+	1.26545i
$307$	8.14095	+	8.14095i	0.464628	+	0.464628i	0.900169	−	0.435541i	$-0.143443\pi$
$307$	8.14095	+	8.14095i	0.464628	+	0.464628i	−0.435541	+	0.900169i	$0.643443\pi$
$308$	−2.28864	+	6.08338i	−0.130407	+	0.346632i
$309$	−26.1655	+	8.50169i	−1.48850	+	0.483644i
$310$	−0.933573	−	2.38037i	−0.0530234	−	0.135196i
$311$	−21.3562	+	19.2292i	−1.21100	+	1.09039i	−0.217556	+	0.976048i	$0.569808\pi$
$311$	−21.3562	+	19.2292i	−1.21100	+	1.09039i	−0.993442	+	0.114339i	$0.963525\pi$
$312$	−0.495655	+	0.321882i	−0.0280610	+	0.0182230i
$313$	0.498133	+	9.50493i	0.0281561	+	0.537251i	0.975900	+	0.218218i	$0.0700245\pi$
$313$	0.498133	+	9.50493i	0.0281561	+	0.537251i	−0.947744	+	0.319032i	$0.896642\pi$
$314$	5.98554	−	18.4216i	0.337783	−	1.03959i
$315$	−26.0125	+	4.49222i	−1.46564	+	0.253108i
$316$	−2.98662	−	9.19189i	−0.168011	−	0.517084i
$317$	7.28729	−	2.79733i	0.409295	−	0.157114i	−0.145004	−	0.989431i	$-0.546320\pi$
$317$	7.28729	−	2.79733i	0.409295	−	0.157114i	0.554299	+	0.832317i	$0.312986\pi$
$318$	−13.4728	−	50.2810i	−0.755515	−	2.81962i
$319$	16.6965	−	1.75487i	0.934824	−	0.0982540i
$320$	−8.05650	+	4.72955i	−0.450372	+	0.264390i
$321$	−1.81768	+	2.50182i	−0.101453	+	0.139638i
$322$	19.9642	−	10.3410i	1.11256	−	0.576281i
$323$	18.2019	−	9.27431i	1.01278	−	0.516036i
$324$	−1.34150	+	0.774516i	−0.0745278	+	0.0430287i
$325$	0.167475	−	0.455920i	0.00928986	−	0.0252899i
$326$	−11.7489	+	20.3497i	−0.650711	+	1.12706i
$327$	−6.70673	−	4.35540i	−0.370883	−	0.240854i
$328$	−0.288317	+	0.0456650i	−0.0159197	+	0.00252143i
$329$	−5.29417	+	4.83138i	−0.291877	+	0.266362i
$330$	−23.0762	−	31.2826i	−1.27030	−	1.72205i
$331$	0.945325	+	0.420886i	0.0519597	+	0.0231340i	0.432552	−	0.901609i	$-0.357613\pi$
$331$	0.945325	+	0.420886i	0.0519597	+	0.0231340i	−0.380592	+	0.924743i	$0.624280\pi$
$332$	−6.53515	+	1.75109i	−0.358663	+	0.0961035i
$333$	21.6715	−	26.7621i	1.18759	−	1.46655i
$334$	−1.81366	+	2.01427i	−0.0992388	+	0.110216i
$335$	−1.23127	+	0.204167i	−0.0672717	+	0.0111548i
$336$	−17.7644	−	30.2991i	−0.969125	−	1.65295i
$337$	−1.66773	−	0.849753i	−0.0908472	−	0.0462890i	0.407977	−	0.912992i	$-0.366235\pi$
$337$	−1.66773	−	0.849753i	−0.0908472	−	0.0462890i	−0.498824	+	0.866703i	$0.666235\pi$
$338$	−21.0202	+	1.10162i	−1.14335	+	0.0599202i
$339$	−8.53950	−	9.48407i	−0.463802	−	0.515104i
$340$	3.91261	−	2.58136i	0.212191	−	0.139994i
$341$	−2.05982	−	1.85467i	−0.111545	−	0.100436i
$342$	−43.5258	−	6.89381i	−2.35361	−	0.372774i
$343$	−18.2305	+	3.26350i	−0.984352	+	0.176212i
$344$	15.2880	+	21.0421i	0.824272	+	1.13451i
$345$	−3.11773	+	31.8828i	−0.167853	+	1.71651i
$346$	0.185357	+	0.416319i	0.00996486	+	0.0223814i
$347$	0.712508	−	1.85615i	0.0382494	−	0.0996431i	−0.913125	−	0.407679i	$-0.866338\pi$
$347$	0.712508	−	1.85615i	0.0382494	−	0.0996431i	0.951375	+	0.308036i	$0.0996716\pi$
$348$	3.97762	−	6.12500i	0.213223	−	0.328335i
$349$	4.37015			0.233929			0.116964	−	0.993136i	$-0.462684\pi$
$349$	4.37015			0.233929			0.116964	+	0.993136i	$0.462684\pi$
$350$	19.7620	+	8.30190i	1.05632	+	0.443755i
$351$	0.387952			0.0207073
$352$	7.31587	−	11.2654i	0.389937	−	0.600450i
$353$	6.69256	−	17.4347i	0.356209	−	0.927957i	−0.632017	−	0.774955i	$-0.717773\pi$
$353$	6.69256	−	17.4347i	0.356209	−	0.927957i	0.988226	−	0.153002i	$-0.0488940\pi$
$354$	−9.29042	−	20.8666i	−0.493780	−	1.10905i
$355$	−2.20903	+	0.486291i	−0.117243	+	0.0258096i
$356$	0.368984	+	0.507863i	0.0195561	+	0.0269167i
$357$	−13.3280	−	20.2260i	−0.705393	−	1.07047i
$358$	−20.9867	−	3.32396i	−1.10918	−	0.175677i
$359$	−12.4207	−	11.1836i	−0.655539	−	0.590250i	0.272761	−	0.962082i	$-0.412063\pi$
$359$	−12.4207	−	11.1836i	−0.655539	−	0.590250i	−0.928300	+	0.371832i	$0.878730\pi$
$360$	22.1988	+	1.00223i	1.16998	+	0.0528223i
$361$	12.1464	+	13.4899i	0.639282	+	0.709995i
$362$	−37.2694	+	1.95321i	−1.95884	+	0.102658i
$363$	−10.7735	−	5.48937i	−0.565462	−	0.288117i
$364$	0.00107477	+	0.160750i	5.63332e−5	+	0.00842560i
$365$	3.34925	−	3.39812i	0.175308	−	0.177866i
$366$	21.1264	−	23.4633i	1.10430	−	1.22644i
$367$	−6.07938	+	7.50742i	−0.317341	+	0.391884i	−0.910710	−	0.413047i	$-0.864464\pi$
$367$	−6.07938	+	7.50742i	−0.317341	+	0.391884i	0.593368	+	0.804931i	$0.297798\pi$
$368$	−24.6188	+	6.59659i	−1.28334	+	0.343871i
$369$	0.534260	+	0.237868i	0.0278125	+	0.0123829i
$370$	−26.5307	+	8.83328i	−1.37927	+	0.459221i
$371$	29.6563	+	9.41718i	1.53968	+	0.488916i
$372$	−1.19091	+	0.188622i	−0.0617459	+	0.00977959i
$373$	−4.12458	−	2.67853i	−0.213563	−	0.138689i	0.433425	−	0.901190i	$-0.357305\pi$
$373$	−4.12458	−	2.67853i	−0.213563	−	0.138689i	−0.646988	+	0.762500i	$0.723972\pi$
$374$	10.6647	−	18.4717i	0.551456	−	0.955150i
$375$	−25.2464	+	17.1863i	−1.30372	+	0.887499i
$376$	5.22511	−	3.01672i	0.269465	−	0.155575i
$377$	0.369967	−	0.188508i	0.0190543	−	0.00970865i
$378$	−0.781708	+	17.1030i	−0.0402067	+	0.879686i
$379$	7.39900	−	10.1839i	0.380061	−	0.523109i	−0.575540	−	0.817774i	$-0.695208\pi$
$379$	7.39900	−	10.1839i	0.380061	−	0.523109i	0.955601	+	0.294665i	$0.0952079\pi$
$380$	6.37635	+	5.65821i	0.327100	+	0.290260i
$381$	44.9900	−	4.72864i	2.30491	−	0.242255i
$382$	−1.69690	−	6.33292i	−0.0868210	−	0.324020i
$383$	−16.7403	+	6.42601i	−0.855391	+	0.328354i	−0.746245	−	0.665672i	$-0.768145\pi$
$383$	−16.7403	+	6.42601i	−0.855391	+	0.328354i	−0.109146	+	0.994026i	$0.534812\pi$
$384$	11.4883	+	35.3574i	0.586260	+	1.80432i
$385$	23.1852	−	1.53916i	1.18163	−	0.0784429i
$386$	−1.53944	+	4.73792i	−0.0783556	+	0.241154i
$387$	−2.72712	−	52.0365i	−0.138627	−	2.64516i
$388$	−5.93974	+	3.85731i	−0.301544	+	0.195825i
$389$	−8.86329	+	7.98055i	−0.449387	+	0.404630i	−0.862506	−	0.506047i	$-0.831106\pi$
$389$	−8.86329	+	7.98055i	−0.449387	+	0.404630i	0.413119	+	0.910677i	$0.364439\pi$
$390$	−0.810099	−	0.517782i	−0.0410209	−	0.0262189i
$391$	−16.7170	+	5.43168i	−0.845415	+	0.274692i
$392$	15.5785	+	0.607684i	0.786832	+	0.0306927i
$393$	−0.777518	−	0.777518i	−0.0392206	−	0.0392206i
$394$	8.31153	−	18.6680i	0.418729	−	0.940480i
$395$	−25.5091	+	23.3052i	−1.28350	+	1.17261i
$396$	−10.0138	+	4.45844i	−0.503213	+	0.224045i
$397$	29.1590	−	23.6125i	1.46345	−	1.18508i	0.519732	−	0.854329i	$-0.326032\pi$
$397$	29.1590	−	23.6125i	1.46345	−	1.18508i	0.943719	−	0.330750i	$-0.107302\pi$
$398$	−3.19987	−	6.28010i	−0.160395	−	0.314793i
$399$	29.2573	−	32.9337i	1.46470	−	1.64875i
$400$	−19.8628	−	13.9962i	−0.993141	−	0.699808i
$401$	0.106730	+	0.184861i	0.00532982	+	0.00923152i	0.868678	−	0.495377i	$-0.164970\pi$
$401$	0.106730	+	0.184861i	0.00532982	+	0.00923152i	−0.863348	+	0.504609i	$0.831637\pi$
$402$	−0.129298	+	2.46715i	−0.00644879	+	0.123050i
$403$	−0.0639999	−	0.0245673i	−0.00318806	−	0.00122378i
$404$	−0.767189	+	7.29932i	−0.0381691	+	0.363155i
$405$	4.50363	+	3.22250i	0.223787	+	0.160127i
$406$	7.56499	+	16.6900i	0.375444	+	0.828313i
$407$	−21.4341	+	21.4341i	−1.06245	+	1.06245i
$408$	7.30726	+	19.0361i	0.361763	+	0.942426i
$409$	31.2443	+	6.64117i	1.54493	+	0.328385i	0.900011	−	0.435867i	$-0.143558\pi$
$409$	31.2443	+	6.64117i	1.54493	+	0.328385i	0.644918	+	0.764252i	$0.276891\pi$
$410$	−0.261515	−	0.396383i	−0.0129153	−	0.0195759i
$411$	7.19417	+	33.8459i	0.354862	+	1.66950i
$412$	2.85990	−	5.61287i	0.140897	−	0.276526i
$413$	13.4992	+	2.04565i	0.664255	+	0.100660i
$414$	36.0620	+	11.7173i	1.77235	+	0.575872i
$415$	15.3573	+	18.6864i	0.753862	+	0.917278i
$416$	0.0690729	−	0.324962i	0.00338658	−	0.0159326i
$417$	−30.5447	−	24.7346i	−1.49578	−	1.21126i
$418$	37.4691	+	10.0398i	1.83267	+	0.491063i
$419$	−8.57555	+	6.23050i	−0.418943	+	0.304380i	−0.777212	−	0.629238i	$-0.783367\pi$
$419$	−8.57555	+	6.23050i	−0.418943	+	0.304380i	0.358269	+	0.933618i	$0.383367\pi$
$420$	5.82692	−	8.25959i	0.284325	−	0.403027i
$421$	7.12732	+	5.17830i	0.347364	+	0.252375i	0.747762	−	0.663966i	$-0.231128\pi$
$421$	7.12732	+	5.17830i	0.347364	+	0.252375i	−0.400398	+	0.916341i	$0.631128\pi$
$422$	−6.79723	−	8.39388i	−0.330884	−	0.408608i
$423$	−12.0710	−	0.632612i	−0.586910	−	0.0307586i
$424$	−22.6839	−	13.0965i	−1.10163	−	0.636024i
$425$	−14.1848	−	8.92230i	−0.688064	−	0.432795i
$426$			4.47737i			0.216929i
$427$	5.00637	+	18.1965i	0.242275	+	0.880591i
$428$	−0.110767	−	0.699356i	−0.00535413	−	0.0338047i
$429$	−1.03652	−	0.108943i	−0.0500436	−	0.00525980i
$430$	−20.8900	+	36.7955i	−1.00741	+	1.77444i
$431$	−0.640581	−	6.09472i	−0.0308557	−	0.293572i	−0.999058	−	0.0434025i	$-0.986180\pi$
$431$	−0.640581	−	6.09472i	−0.0308557	−	0.293572i	0.968202	−	0.250170i	$-0.0804864\pi$
$432$	5.02322	−	18.7469i	0.241680	−	0.901961i
$433$	5.58866	−	35.2854i	0.268574	−	1.69571i	−0.372339	−	0.928097i	$-0.621444\pi$
$433$	5.58866	−	35.2854i	0.268574	−	1.69571i	0.640913	−	0.767613i	$-0.278556\pi$
$434$	1.21202	−	2.77197i	0.0581787	−	0.133059i
$435$	−25.8165	−	3.89749i	−1.23781	−	0.186870i
$436$	1.79104	−	0.380697i	0.0857751	−	0.0182321i
$437$	−17.4106	−	26.8100i	−0.832861	−	1.28249i
$438$	−5.14383	−	7.92080i	−0.245782	−	0.378470i
$439$	−25.5065	+	5.42157i	−1.21736	+	0.258757i	−0.771431	−	0.636312i	$-0.780459\pi$
$439$	−25.5065	+	5.42157i	−1.21736	+	0.258757i	−0.445926	+	0.895070i	$0.647126\pi$
$440$	−19.3411	−	2.91990i	−0.922049	−	0.139201i
$441$	−25.5120	−	18.0194i	−1.21486	−	0.858064i
$442$	0.0825241	−	0.521037i	0.00392527	−	0.0247832i
$443$	−8.76626	+	32.7161i	−0.416498	+	1.55439i	0.365319	+	0.930882i	$0.380960\pi$
$443$	−8.76626	+	32.7161i	−0.416498	+	1.55439i	−0.781817	+	0.623508i	$0.785707\pi$
$444$	1.37835	+	13.1141i	0.0654135	+	0.622368i
$445$	1.10801	−	1.95163i	0.0525245	−	0.0925160i
$446$	24.8335	+	2.61010i	1.17590	+	0.123592i
$447$	−4.56264	−	28.8074i	−0.215805	−	1.36254i
$448$	−10.6960	−	2.78948i	−0.505340	−	0.131791i
$449$		−	17.8247i		−	0.841199i	−0.907246	−	0.420600i	$-0.861820\pi$
$449$		−	17.8247i		−	0.841199i	0.907246	−	0.420600i	$-0.138180\pi$
$450$	13.4423	+	33.5573i	0.633677	+	1.58191i
$451$	−0.445816	−	0.257392i	−0.0209927	−	0.0121201i
$452$	2.91814	+	0.152933i	0.137258	+	0.00719338i
$453$	−35.8934	−	44.3247i	−1.68642	−	2.08255i
$454$	−17.3691	−	12.6194i	−0.815173	−	0.592258i
$455$	0.521704	−	0.241039i	0.0244579	−	0.0113001i
$456$	−30.0010	+	21.7970i	−1.40493	+	1.02074i
$457$	8.24133	+	2.20826i	0.385513	+	0.103298i	0.446370	−	0.894849i	$-0.352717\pi$
$457$	8.24133	+	2.20826i	0.385513	+	0.103298i	−0.0608568	+	0.998147i	$0.519383\pi$
$458$	5.22289	+	4.22941i	0.244050	+	0.197627i
$459$	2.78288	−	13.0924i	0.129893	−	0.611101i
$460$	−4.65727	−	5.66684i	−0.217146	−	0.264218i
$461$	25.2246	+	8.19596i	1.17483	+	0.381724i	0.830442	−	0.557105i	$-0.188088\pi$
$461$	25.2246	+	8.19596i	1.17483	+	0.381724i	0.344384	+	0.938829i	$0.388088\pi$
$462$	6.89134	−	45.4760i	0.320614	−	2.11573i
$463$	−10.3899	+	20.3912i	−0.482857	+	0.947661i	0.513142	+	0.858304i	$0.328481\pi$
$463$	−10.3899	+	20.3912i	−0.482857	+	0.947661i	−0.996000	+	0.0893575i	$0.971519\pi$
$464$	−4.31887	−	20.3187i	−0.200498	−	0.943271i
$465$	2.37383	+	3.59806i	0.110084	+	0.166856i
$466$	40.8410	+	8.68102i	1.89192	+	0.402140i
$467$	3.19548	+	8.32450i	0.147869	+	0.385212i	0.987431	−	0.158052i	$-0.0505215\pi$
$467$	3.19548	+	8.32450i	0.147869	+	0.385212i	−0.839562	+	0.543264i	$0.817188\pi$
$468$	−0.191702	+	0.191702i	−0.00886142	+	0.00886142i
$469$	−1.20050	−	0.860009i	−0.0554338	−	0.0397115i
$470$	7.98219	+	5.71154i	0.368191	+	0.263453i
$471$	−3.41334	+	32.4757i	−0.157278	+	1.49640i
$472$	−10.7300	−	4.11886i	−0.493888	−	0.189586i
$473$	−2.40053	+	45.8047i	−0.110376	+	2.10610i
$474$	34.1972	+	59.2314i	1.57073	+	2.72059i
$475$	8.99691	−	29.1182i	0.412807	−	1.33603i
$476$	5.43263	+	1.11683i	0.249004	+	0.0511899i
$477$	23.8235	+	46.7562i	1.09080	+	2.14082i
$478$	−0.819472	+	0.663596i	−0.0374818	+	0.0303522i
$479$	−2.18656	+	0.973518i	−0.0999064	+	0.0444812i	−0.456081	−	0.889938i	$-0.650747\pi$
$479$	−2.18656	+	0.973518i	−0.0999064	+	0.0444812i	0.356175	+	0.934419i	$0.384081\pi$
$480$	−15.4226	+	14.0902i	−0.703943	+	0.643126i
$481$	−0.304934	+	0.684892i	−0.0139038	+	0.0312284i
$482$	−1.31543	−	1.31543i	−0.0599161	−	0.0599161i
$483$	−29.2970	+	24.0503i	−1.33306	+	1.09433i
$484$	2.63308	−	0.855538i	0.119685	−	0.0388881i
$485$	21.3339	+	13.6357i	0.968722	+	0.619167i
$486$	22.5731	−	20.3249i	1.02394	−	0.921957i
$487$	−4.06415	+	2.63929i	−0.184164	+	0.119598i	−0.633428	−	0.773801i	$-0.718353\pi$
$487$	−4.06415	+	2.63929i	−0.184164	+	0.119598i	0.449264	+	0.893399i	$0.351686\pi$
$488$	−0.831460	−	15.8652i	−0.0376384	−	0.718184i
$489$	12.2414	−	37.6753i	0.553577	−	1.70374i
$490$	9.57513	+	23.4853i	0.432560	+	1.06096i
$491$	−9.20020	−	28.3153i	−0.415199	−	1.27785i	−0.912073	−	0.410029i	$-0.865519\pi$
$491$	−9.20020	−	28.3153i	−0.415199	−	1.27785i	0.496874	−	0.867823i	$-0.334481\pi$
$492$	−0.209065	+	0.0802525i	−0.00942537	+	0.00361806i
$493$	−3.70780	−	13.8377i	−0.166991	−	0.623218i
$494$	0.954148	−	0.100285i	0.0429291	−	0.00451203i
$495$	29.3110	+	26.0099i	1.31743	+	1.16906i
$496$	−2.01583	+	2.77456i	−0.0905136	+	0.124581i
$497$	−2.25426	−	1.44260i	−0.101117	−	0.0647094i
$498$	42.6595	−	21.7361i	1.91162	−	0.974018i
$499$	−33.6862	+	19.4488i	−1.50800	+	0.870646i	−0.508046	+	0.861330i	$0.669632\pi$
$499$	−33.6862	+	19.4488i	−1.50800	+	0.870646i	−0.999957	+	0.00931623i	$0.997035\pi$
$500$	1.30498	−	6.87016i	0.0583603	−	0.307243i
$501$	2.28474	−	3.95729i	0.102075	−	0.176799i
$502$	−18.8200	−	12.2218i	−0.839977	−	0.545488i
$503$	37.4880	−	5.93752i	1.67151	−	0.264741i	0.752389	−	0.658719i	$-0.228902\pi$
$503$	37.4880	−	5.93752i	1.67151	−	0.264741i	0.919120	+	0.393979i	$0.128902\pi$
$504$	17.7235	+	19.4212i	0.789467	+	0.865090i
$505$	24.8952	−	8.28877i	1.10782	−	0.368845i
$506$	−30.4914	−	13.5756i	−1.35551	−	0.603510i
$507$	34.2767	−	9.18442i	1.52228	−	0.407894i
$508$	−6.51859	+	8.04979i	−0.289216	+	0.357152i
$509$	−6.94597	+	7.71429i	−0.307875	+	0.341930i	−0.877149	−	0.480218i	$-0.840558\pi$
$509$	−6.94597	+	7.71429i	−0.307875	+	0.341930i	0.569274	+	0.822148i	$0.307224\pi$
$510$	−23.2849	+	23.6246i	−1.03107	+	1.04612i
$511$	5.64528	−	0.0377441i	0.249733	−	0.00166970i
$512$	4.47894	+	2.28214i	0.197943	+	0.100857i
$513$	24.3093	−	1.27400i	1.07328	−	0.0562483i
$514$	0.395345	+	0.439075i	0.0174379	+	0.0193668i
$515$	−22.4977	−	1.01573i	−0.991368	−	0.0447583i
$516$	14.8280	+	13.3512i	0.652768	+	0.587755i
$517$	10.5090	+	1.66446i	0.462184	+	0.0732027i
$518$	−29.5794	−	14.8232i	−1.29964	−	0.651293i
$519$	−0.451584	−	0.621552i	−0.0198223	−	0.0272831i
$520$	−0.472465	+	0.104008i	−0.0207190	+	0.00456103i
$521$	−4.89041	−	10.9840i	−0.214253	−	0.481219i	0.774164	−	0.632985i	$-0.218171\pi$
$521$	−4.89041	−	10.9840i	−0.214253	−	0.481219i	−0.988416	+	0.151766i	$0.951504\pi$
$522$	−11.0749	+	28.8512i	−0.484737	+	1.26278i
$523$	−13.0588	+	20.1088i	−0.571023	+	0.879298i	−0.999708	−	0.0241556i	$-0.992310\pi$
$523$	−13.0588	+	20.1088i	−0.571023	+	0.879298i	0.428685	+	0.903454i	$0.358977\pi$
$524$	0.251771			0.0109987
$525$	−35.4980	−	6.76326i	−1.54926	−	0.295173i
$526$	−48.2012			−2.10167
$527$	−1.28817	+	1.98361i	−0.0561136	+	0.0864074i
$528$	−18.6853	+	48.6769i	−0.813175	+	2.11839i
$529$	1.83261	+	4.11611i	0.0796787	+	0.178961i
$530$	4.14699	−	42.4083i	0.180134	−	1.84210i
$531$	13.5344	+	18.6285i	0.587342	+	0.808407i
$532$	0.595233	+	10.0692i	0.0258066	+	0.436554i
$533$	−0.0125753	−	0.00199173i	−0.000544695	−	8.62712e-5i
$534$	−3.30130	−	2.97251i	−0.142861	−	0.128633i
$535$	−2.11294	+	1.39402i	−0.0913505	+	0.0602688i
$536$	0.831817	+	0.923827i	0.0359290	+	0.0399032i
$537$	35.7727	−	1.87477i	1.54370	−	0.0809021i
$538$	29.9216	+	15.2458i	1.29001	+	0.657294i
$539$	20.6758	+	18.1219i	0.890570	+	0.780565i
$540$	5.51033	−	0.913707i	0.237127	−	0.0393197i
$541$	−12.8091	+	14.2259i	−0.550705	+	0.611620i	−0.952659	−	0.304040i	$-0.901664\pi$
$541$	−12.8091	+	14.2259i	−0.550705	+	0.611620i	0.401954	+	0.915660i	$0.368331\pi$
$542$	−5.71693	+	7.05982i	−0.245563	+	0.303245i
$543$	60.7737	−	16.2843i	2.60805	−	0.698825i
$544$	−10.4712	−	4.66208i	−0.448949	−	0.199885i
$545$	−3.88590	−	5.26783i	−0.166454	−	0.225649i
$546$	−0.243952	−	1.11112i	−0.0104402	−	0.0475516i
$547$	−12.3236	+	1.95187i	−0.526919	+	0.0834558i	−0.414226	−	0.910174i	$-0.635948\pi$
$547$	−12.3236	+	1.95187i	−0.526919	+	0.0834558i	−0.112693	+	0.993630i	$0.535948\pi$
$548$	−6.64468	−	4.31510i	−0.283847	−	0.184332i
$549$	−15.9141	+	27.5641i	−0.679199	+	1.17641i
$550$	−8.68006	−	30.6136i	−0.370119	−	1.30537i
$551$	22.5633	−	13.0269i	0.961230	−	0.554967i
$552$	28.4300	−	14.4858i	1.21006	−	0.616556i
$553$	−40.8400	−	1.86663i	−1.73669	−	0.0793770i
$554$	5.63005	−	7.74910i	0.239198	−	0.329228i
$555$	40.6537	−	23.8657i	1.72565	−	1.01304i
$556$	8.95012	−	0.940695i	0.379570	−	0.0398944i
$557$	−5.89390	−	21.9963i	−0.249732	−	0.932014i	−0.970946	−	0.239301i	$-0.923082\pi$
$557$	−5.89390	−	21.9963i	−0.249732	−	0.932014i	0.721213	−	0.692713i	$-0.243585\pi$
$558$	4.76331	−	1.82846i	0.201647	−	0.0774050i
$559$	0.350558	+	1.07891i	0.0148270	+	0.0456329i
$560$	−4.89264	−	28.3312i	−0.206752	−	1.19721i
$561$	−11.1118	+	34.1985i	−0.469139	+	1.44386i
$562$	0.725488	+	13.8431i	0.0306029	+	0.583937i
$563$	−24.4754	+	15.8945i	−1.03152	+	0.669874i	−0.945233	−	0.326397i	$-0.894165\pi$
$563$	−24.4754	+	15.8945i	−1.03152	+	0.669874i	−0.0862825	+	0.996271i	$0.527499\pi$
$564$	3.43967	−	3.09710i	0.144836	−	0.130411i
$565$	−3.81430	−	9.72546i	−0.160469	−	0.409153i
$566$	23.2549	−	7.55597i	0.977476	−	0.317601i
$567$	1.06827	+	6.46474i	0.0448631	+	0.271494i
$568$	1.59307	+	1.59307i	0.0668436	+	0.0668436i
$569$	0.645950	−	1.45083i	0.0270796	−	0.0608218i	−0.899499	−	0.436922i	$-0.856069\pi$
$569$	0.645950	−	1.45083i	0.0270796	−	0.0608218i	0.926579	+	0.376100i	$0.122735\pi$
$570$	−52.4616	−	29.7842i	−2.19737	−	1.24752i
$571$	3.28341	−	1.46187i	0.137406	−	0.0611773i	−0.336882	−	0.941547i	$-0.609372\pi$
$571$	3.28341	−	1.46187i	0.137406	−	0.0611773i	0.474288	+	0.880370i	$0.342706\pi$
$572$	0.185458	−	0.150181i	0.00775441	−	0.00627940i
$573$	5.01800	+	9.84838i	0.209630	+	0.411422i
$574$	0.113145	−	0.550374i	0.00472258	−	0.0229722i
$575$	−11.5653	+	23.5348i	−0.482305	+	0.981468i
$576$	−9.32098	−	16.1444i	−0.388374	−	0.672683i
$577$	−1.16904	+	22.3066i	−0.0486677	+	0.928634i	0.859788	+	0.510652i	$0.170596\pi$
$577$	−1.16904	+	22.3066i	−0.0486677	+	0.928634i	−0.908455	+	0.417982i	$0.862737\pi$
$578$	8.72433	+	3.34896i	0.362884	+	0.139298i
$579$	0.877889	−	8.35256i	0.0364838	−	0.347121i
$580$	4.81091	−	3.54885i	0.199762	−	0.147358i
$581$	−2.80113	+	28.4815i	−0.116210	+	1.18161i
$582$	35.4392	−	35.4392i	1.46900	−	1.46900i
$583$	−16.5535	−	43.1234i	−0.685577	−	1.78599i
$584$	−4.64845	−	0.988058i	−0.192354	−	0.0408861i
$585$	0.907327	+	0.340772i	0.0375134	+	0.0140892i
$586$	−3.71938	−	17.4983i	−0.153646	−	0.722848i
$587$	−19.7026	+	38.6684i	−0.813211	+	1.59602i	−0.0102788	+	0.999947i	$0.503272\pi$
$587$	−19.7026	+	38.6684i	−0.813211	+	1.59602i	−0.802933	+	0.596070i	$0.796728\pi$
$588$	11.7868	−	2.02875i	0.486078	−	0.0836644i
$589$	−4.09095	−	1.32923i	−0.168565	−	0.0547699i
$590$	−1.11374	−	18.6641i	−0.0458521	−	0.768390i
$591$	−7.16259	+	33.6973i	−0.294630	+	1.38612i
$592$	29.1476	+	23.6033i	1.19796	+	0.970088i
$593$	−12.4912	−	3.34701i	−0.512953	−	0.137445i	−0.00694789	−	0.999976i	$-0.502212\pi$
$593$	−12.4912	−	3.34701i	−0.512953	−	0.137445i	−0.506005	+	0.862531i	$0.668878\pi$
$594$	20.5621	−	14.9392i	0.843673	−	0.612964i
$595$	−4.39216	−	19.3352i	−0.180061	−	0.792668i
$596$	5.40284	+	3.92539i	0.221309	+	0.160790i
$597$	7.47793	+	9.23448i	0.306051	+	0.377942i
$598$	−0.824371	−	0.0432035i	−0.0337110	−	0.00176672i
$599$	19.9444	+	11.5149i	0.814905	+	0.470485i	0.848656	−	0.528945i	$-0.177412\pi$
$599$	19.9444	+	11.5149i	0.814905	+	0.470485i	−0.0337516	+	0.999430i	$0.510745\pi$
$600$	27.9661	+	11.9690i	1.14171	+	0.488632i
$601$			14.0409i			0.572740i	0.958119	+	0.286370i	$0.0924486\pi$
$601$			14.0409i			0.572740i	−0.958119	+	0.286370i	$0.907551\pi$
$602$	−48.2705	+	13.2806i	−1.96736	+	0.541276i
$603$	−0.389602	−	2.45985i	−0.0158658	−	0.100173i
$604$	12.9879	+	1.36508i	0.528469	+	0.0555443i
$605$	−6.67594	−	7.30725i	−0.271416	−	0.297082i
$606$	−5.42907	−	51.6542i	−0.220541	−	2.09831i
$607$	10.2468	−	38.2415i	0.415904	−	1.55218i	−0.367113	−	0.930176i	$-0.619654\pi$
$607$	10.2468	−	38.2415i	0.415904	−	1.55218i	0.783017	−	0.622000i	$-0.213680\pi$
$608$	3.26100	−	20.5892i	0.132251	−	0.835001i
$609$	−18.3249	−	24.8707i	−0.742564	−	1.00781i
$610$	22.9423	−	11.8997i	0.928906	−	0.481807i
$611$	0.257404	−	0.0547130i	0.0104135	−	0.00221345i
$612$	5.09433	+	7.84459i	0.205926	+	0.317099i
$613$	2.11361	+	3.25467i	0.0853679	+	0.131455i	0.878775	−	0.477236i	$-0.158361\pi$
$613$	2.11361	+	3.25467i	0.0853679	+	0.131455i	−0.793407	+	0.608691i	$0.791695\pi$
$614$	18.2473	−	3.87858i	0.736400	−	0.156527i
$615$	0.570182	+	0.561982i	0.0229920	+	0.0226613i
$616$	−13.7286	−	18.6325i	−0.553140	−	0.750725i
$617$	−4.36290	+	27.5463i	−0.175644	+	1.10897i	0.729536	+	0.683943i	$0.239736\pi$
$617$	−4.36290	+	27.5463i	−0.175644	+	1.10897i	−0.905180	+	0.425029i	$0.860264\pi$
$618$	−11.5378	+	43.0597i	−0.464118	+	1.73211i
$619$	−2.82187	−	26.8483i	−0.113421	−	1.07913i	−0.892142	−	0.451755i	$-0.850798\pi$
$619$	−2.82187	−	26.8483i	−0.113421	−	1.07913i	0.778721	−	0.627370i	$-0.215869\pi$
$620$	−0.966893	−	0.198211i	−0.0388313	−	0.00796036i
$621$	−20.8305	−	2.18937i	−0.835898	−	0.0878564i
$622$	7.28427	+	45.9911i	0.292073	+	1.84408i
$623$	2.56027	−	0.704401i	0.102575	−	0.0282212i
$624$			1.28957i			0.0516239i
$625$	−24.2929	+	5.90393i	−0.971715	+	0.236157i
$626$	13.3561	+	7.71114i	0.533816	+	0.308199i
$627$	−65.3067	−	3.42258i	−2.60810	−	0.136685i
$628$	−4.70541	−	5.81069i	−0.187766	−	0.231872i
$629$	20.9260	+	15.2037i	0.834376	+	0.606209i
$630$	−16.8513	+	39.3134i	−0.671373	+	1.56628i
$631$	8.70119	−	6.32178i	0.346389	−	0.251666i	−0.400964	−	0.916094i	$-0.631325\pi$
$631$	8.70119	−	6.32178i	0.346389	−	0.251666i	0.747353	+	0.664428i	$0.231325\pi$
$632$	33.2423	+	8.90724i	1.32231	+	0.354311i
$633$	14.1510	+	11.4592i	0.562451	+	0.455464i
$634$	2.62964	−	12.3715i	0.104436	−	0.491335i
$635$	35.8371	+	9.32488i	1.42215	+	0.370047i
$636$	−19.1105	−	6.20937i	−0.757780	−	0.246217i
$637$	0.638026	+	0.235176i	0.0252795	+	0.00931801i
$638$	12.3498	−	24.2379i	0.488935	−	0.959589i
$639$	−0.938426	−	4.41495i	−0.0371236	−	0.174653i
$640$	−1.37255	+	30.4011i	−0.0542548	+	1.20171i
$641$	−29.4673	−	6.26346i	−1.16389	−	0.247392i	−0.414831	−	0.909898i	$-0.636159\pi$
$641$	−29.4673	−	6.26346i	−1.16389	−	0.247392i	−0.749056	+	0.662506i	$0.769493\pi$
$642$	1.79569	+	4.67792i	0.0708701	+	0.184623i
$643$	−20.4056	+	20.4056i	−0.804720	+	0.804720i	−0.983829	−	0.179110i	$-0.942678\pi$
$643$	−20.4056	+	20.4056i	−0.804720	+	0.804720i	0.179110	+	0.983829i	$0.442678\pi$
$644$	0.849471	−	8.63730i	0.0334739	−	0.340357i
$645$	21.5510	−	67.9990i	0.848570	−	2.67746i
$646$	3.45998	−	32.9195i	0.136131	−	1.29520i
$647$	−17.8718	−	6.86034i	−0.702613	−	0.269708i	−0.0192794	−	0.999814i	$-0.506137\pi$
$647$	−17.8718	−	6.86034i	−0.702613	−	0.269708i	−0.683334	+	0.730106i	$0.739471\pi$
$648$	0.288675	−	5.50825i	0.0113402	−	0.216384i
$649$	−10.1343	−	17.5531i	−0.397805	−	0.689019i
$650$	−0.471764	−	0.629933i	−0.0185041	−	0.0247080i
$651$	−1.02704	+	4.99588i	−0.0402531	+	0.195804i
$652$	4.11792	+	8.08188i	0.161270	+	0.316511i
$653$	9.38043	−	7.59612i	0.367084	−	0.297259i	−0.427975	−	0.903791i	$-0.640773\pi$
$653$	9.38043	−	7.59612i	0.367084	−	0.297259i	0.795060	+	0.606531i	$0.207440\pi$
$654$	−11.8373	+	5.27031i	−0.462876	+	0.206086i
$655$	−0.372043	−	0.819595i	−0.0145369	−	0.0320242i
$656$	−0.259071	+	0.581883i	−0.0101150	+	0.0227187i
$657$	6.73225	+	6.73225i	0.262650	+	0.262650i
$658$	1.89339	+	11.4580i	0.0738120	+	0.446681i
$659$	15.5052	−	5.03793i	0.603995	−	0.196250i	0.00897383	−	0.999960i	$-0.497144\pi$
$659$	15.5052	−	5.03793i	0.603995	−	0.196250i	0.595022	+	0.803710i	$0.297144\pi$
$660$	−14.9789	+	0.893839i	−0.583054	+	0.0347926i
$661$	10.4225	−	9.38450i	0.405390	−	0.365015i	−0.441065	−	0.897475i	$-0.645399\pi$
$661$	10.4225	−	9.38450i	0.405390	−	0.365015i	0.846455	+	0.532460i	$0.178732\pi$
$662$	1.40620	−	0.913195i	0.0546534	−	0.0354923i
$663$	0.0465449	+	0.888130i	0.00180766	+	0.0344921i
$664$	7.44463	−	22.9122i	0.288908	−	0.889166i
$665$	31.8987	−	16.8169i	1.23698	−	0.652131i
$666$	−17.2426	−	53.0674i	−0.668138	−	2.05632i
$667$	−20.9287	+	8.03376i	−0.810361	+	0.311069i
$668$	0.270798	+	1.01063i	0.0104775	+	0.0391025i
$669$	−41.8660	+	4.40029i	−1.61863	+	0.170125i
$670$	−0.809148	+	1.85338i	−0.0312601	+	0.0716025i
$671$	16.4678	−	22.6659i	0.635731	−	0.875008i
$672$	−24.6916	−	1.12855i	−0.952498	−	0.0435347i
$673$	−0.252552	+	0.128682i	−0.00973515	+	0.00496031i	−0.458851	−	0.888513i	$-0.651739\pi$
$673$	−0.252552	+	0.128682i	−0.00973515	+	0.00496031i	0.449116	+	0.893473i	$0.351739\pi$
$674$	−2.62652	+	1.51642i	−0.101170	+	0.0584103i
$675$	−11.1170	−	16.5876i	−0.427894	−	0.638459i
$676$	−4.06262	+	7.03667i	−0.156255	+	0.270641i
$677$	−28.0912	−	18.2427i	−1.07963	−	0.701123i	−0.122998	−	0.992407i	$-0.539251\pi$
$677$	−28.0912	−	18.2427i	−1.07963	−	0.701123i	−0.956637	+	0.291284i	$0.905917\pi$
$678$	−20.4242	+	3.23488i	−0.784387	+	0.124235i
$679$	6.42445	+	29.2613i	0.246548	+	1.12295i
$680$	0.120883	+	16.6906i	0.00463566	+	0.640055i
$681$	33.0654	+	14.7217i	1.26707	+	0.564136i
$682$	−4.33814	+	1.16240i	−0.166116	+	0.0445106i
$683$	−14.2385	+	17.5831i	−0.544821	+	0.672798i	−0.972976	−	0.230907i	$-0.925831\pi$
$683$	−14.2385	+	17.5831i	−0.544821	+	0.672798i	0.428155	+	0.903706i	$0.359164\pi$
$684$	−11.3826	+	12.6417i	−0.435225	+	0.483367i
$685$	−4.22817	+	28.0069i	−0.161550	+	1.07009i
$686$	−11.6535	+	27.6538i	−0.444931	+	1.05583i
$687$	−10.0951	−	5.14374i	−0.385154	−	0.196246i
$688$	56.6749	−	2.97020i	2.16071	−	0.113238i
$689$	−0.764441	−	0.848997i	−0.0291229	−	0.0323442i
$690$	40.5750	+	32.3732i	1.54466	+	1.23243i
$691$	21.1493	+	19.0429i	0.804557	+	0.724427i	0.964895	−	0.262636i	$-0.0845917\pi$
$691$	21.1493	+	19.0429i	0.804557	+	0.724427i	−0.160338	+	0.987062i	$0.551258\pi$
$692$	0.173748	+	0.0275190i	0.00660492	+	0.00104612i
$693$	2.73619	+	46.2863i	0.103939	+	1.75827i
$694$	−1.89358	−	2.60628i	−0.0718792	−	0.0989332i
$695$	−16.2879	−	27.7454i	−0.617833	−	1.05244i
$696$	10.5773	+	23.7571i	0.400933	+	0.900511i
$697$	−0.157421	+	0.410097i	−0.00596276	+	0.0155335i
$698$	3.85664	−	5.93870i	0.145976	−	0.224783i
$699$	−70.3907			−2.66242
$700$	6.84240	−	4.65236i	0.258618	−	0.175843i
$701$	29.7376			1.12317			0.561587	−	0.827418i	$-0.310191\pi$
$701$	29.7376			1.12317			0.561587	+	0.827418i	$0.310191\pi$
$702$	0.342366	−	0.527197i	0.0129218	−	0.0198978i
$703$	−16.8582	+	43.9171i	−0.635819	+	1.65637i
$704$	6.67433	+	14.9908i	0.251548	+	0.564986i
$705$	−15.1648	−	6.62063i	−0.571140	−	0.249347i
$706$	−17.7863	−	24.4807i	−0.669396	−	0.921345i
$707$	27.7560	+	13.9094i	1.04387	+	0.523118i
$708$	−8.70856	−	1.37930i	−0.327288	−	0.0518373i
$709$	−6.43362	−	5.79286i	−0.241620	−	0.217555i	0.539420	−	0.842037i	$-0.318644\pi$
$709$	−6.43362	−	5.79286i	−0.241620	−	0.217555i	−0.781039	+	0.624482i	$0.785310\pi$
$710$	−1.28862	+	3.43105i	−0.0483612	+	0.128765i
$711$	−46.1349	−	51.2380i	−1.73020	−	1.92158i
$712$	−2.23225	+	0.116987i	−0.0836570	+	0.00438428i
$713$	3.29773	+	1.68028i	0.123501	+	0.0629269i
$714$	−39.2475	+	0.262407i	−1.46880	+	0.00982033i
$715$	−0.762939	−	0.381802i	−0.0285323	−	0.0142786i
$716$	−5.48831	+	6.09539i	−0.205108	+	0.227795i
$717$	1.11873	−	1.38152i	0.0417799	−	0.0515939i
$718$	−26.1589	+	7.00926i	−0.976242	+	0.261583i
$719$	−24.7026	−	10.9983i	−0.921251	−	0.410167i	−0.109377	−	0.994000i	$-0.534886\pi$
$719$	−24.7026	−	10.9983i	−0.921251	−	0.410167i	−0.811874	+	0.583833i	$0.801552\pi$
$720$	28.2152	−	39.4323i	1.05152	−	1.46955i
$721$	−17.9622	−	19.6828i	−0.668946	−	0.733024i
$722$	29.0509	−	4.60121i	1.08116	−	0.171239i
$723$	2.63025	+	1.70811i	0.0978201	+	0.0635251i
$724$	−7.20316	+	12.4762i	−0.267703	+	0.463676i
$725$	−18.6617	−	10.4169i	−0.693078	−	0.386873i
$726$	−16.9672	+	9.79602i	−0.629712	+	0.363565i
$727$	15.5218	−	7.90873i	0.575670	−	0.293318i	−0.141814	−	0.989893i	$-0.545294\pi$
$727$	15.5218	−	7.90873i	0.575670	−	0.293318i	0.717484	+	0.696575i	$0.245294\pi$
$728$	−0.482140	−	0.308542i	−0.0178693	−	0.0114353i
$729$	−25.7325	+	35.4177i	−0.953055	+	1.31177i
$730$	−1.66209	−	7.55021i	−0.0615166	−	0.279446i
$731$	38.9251	−	4.09119i	1.43970	−	0.151318i
$732$	−3.15439	−	11.7724i	−0.116590	−	0.435119i
$733$	42.8618	−	16.4531i	1.58314	−	0.607709i	0.601567	−	0.798822i	$-0.294543\pi$
$733$	42.8618	−	16.4531i	1.58314	−	0.607709i	0.981568	+	0.191113i	$0.0612098\pi$
$734$	4.83698	+	14.8867i	0.178536	+	0.549477i
$735$	−24.0215	−	35.3717i	−0.886047	−	1.30470i
$736$	−5.54266	+	17.0586i	−0.204305	+	0.628787i
$737$	0.114734	+	2.18925i	0.00422628	+	0.0806422i
$738$	0.794727	−	0.516102i	0.0292543	−	0.0189980i
$739$	−18.2915	+	16.4697i	−0.672864	+	0.605849i	−0.933066	−	0.359705i	$-0.882877\pi$
$739$	−18.2915	+	16.4697i	−0.672864	+	0.605849i	0.260202	+	0.965554i	$0.416211\pi$
$740$	−2.71810	+	10.4461i	−0.0999195	+	0.384008i
$741$	−1.53827	+	0.499813i	−0.0565096	+	0.0183611i
$742$	38.9688	−	31.9901i	1.43059	−	1.17439i
$743$	−10.2323	−	10.2323i	−0.375388	−	0.375388i	0.494047	−	0.869435i	$-0.335517\pi$
$743$	−10.2323	−	10.2323i	−0.375388	−	0.375388i	−0.869435	+	0.494047i	$0.835517\pi$
$744$	1.74631	−	3.92228i	0.0640229	−	0.143798i
$745$	4.79460	−	23.3885i	0.175661	−	0.856888i
$746$	−7.27985	+	3.24120i	−0.266534	+	0.118669i
$747$	−37.5090	+	30.3742i	−1.37238	+	1.11133i
$748$	−3.73790	−	7.33605i	−0.136671	−	0.268233i
$749$	−2.93380	−	0.603126i	−0.107199	−	0.0220377i
$750$	1.07513	+	49.4748i	0.0392581	+	1.80656i
$751$	5.60583	+	9.70959i	0.204560	+	0.354308i	0.949992	−	0.312273i	$-0.101090\pi$
$751$	5.60583	+	9.70959i	0.204560	+	0.354308i	−0.745433	+	0.666581i	$0.767757\pi$
$752$	0.689001	−	13.1469i	0.0251253	−	0.479419i
$753$	35.3186	+	13.5575i	1.28708	+	0.494064i
$754$	0.0703268	−	0.669115i	0.00256115	−	0.0243677i
$755$	−14.7484	−	44.2968i	−0.536750	−	1.61212i
$756$	5.37259	+	3.84880i	0.195399	+	0.139979i
$757$	−34.2009	+	34.2009i	−1.24305	+	1.24305i	−0.284326	+	0.958728i	$0.591770\pi$
$757$	−34.2009	+	34.2009i	−1.24305	+	1.24305i	−0.958728	+	0.284326i	$0.908230\pi$
$758$	−7.30949	−	19.0419i	−0.265493	−	0.691632i
$759$	55.0395	+	11.6990i	1.99781	+	0.424647i
$760$	−29.2634	+	8.06870i	−1.06149	+	0.292683i
$761$	−3.57175	−	16.8038i	−0.129476	−	0.609135i	−0.994260	−	0.106992i	$-0.965878\pi$
$761$	−3.57175	−	16.8038i	−0.129476	−	0.609135i	0.864784	−	0.502144i	$-0.167455\pi$
$762$	33.2776	−	65.3109i	1.20552	−	2.36597i
$763$	1.16047	−	7.65792i	0.0420117	−	0.277235i
$764$	−2.40697	−	0.782073i	−0.0870812	−	0.0282944i
$765$	18.0087	−	28.1756i	0.651105	−	1.01869i
$766$	−6.04081	+	28.4198i	−0.218263	+	1.02685i

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)

\(f(q)\)	\(=\)	\(q+(0.882496 - 1.35892i) q^{2} +(-0.978941 + 2.55023i) q^{3} +(-0.254403 - 0.571398i) q^{4} +(-1.48415 + 1.67252i) q^{5} +(2.60166 + 3.58087i) q^{6} +(-2.64114 + 0.156130i) q^{7} +(2.19977 + 0.348409i) q^{8} +(-3.31591 - 2.98566i) q^{9} +O(q^{10})\)	\(q+(0.882496 - 1.35892i) q^{2} +(-0.978941 + 2.55023i) q^{3} +(-0.254403 - 0.571398i) q^{4} +(-1.48415 + 1.67252i) q^{5} +(2.60166 + 3.58087i) q^{6} +(-2.64114 + 0.156130i) q^{7} +(2.19977 + 0.348409i) q^{8} +(-3.31591 - 2.98566i) q^{9} +(0.963067 + 3.49283i) q^{10} +(2.62811 + 2.91881i) q^{11} +(1.70624 - 0.0894203i) q^{12} +(0.0865535 + 0.0441012i) q^{13} +(-2.11863 + 3.72689i) q^{14} +(-2.81240 - 5.42221i) q^{15} +(3.25179 - 3.61148i) q^{16} +(2.10918 - 2.60462i) q^{17} +(-6.98356 + 1.87124i) q^{18} +(5.56832 + 2.47917i) q^{19} +(1.33324 + 0.422546i) q^{20} +(2.18736 - 6.88836i) q^{21} +(6.28573 - 0.995562i) q^{22} +(-4.39848 - 2.85640i) q^{23} +(-3.04197 + 5.26884i) q^{24} +(-0.594613 - 4.96452i) q^{25} +(0.136313 - 0.0787005i) q^{26} +(3.55840 - 1.81310i) q^{27} +(0.761125 + 1.46942i) q^{28} +(2.51245 - 3.45809i) q^{29} +(-9.85031 - 0.963234i) q^{30} +(-0.701840 + 0.0737664i) q^{31} +(-0.885159 - 3.30346i) q^{32} +(-10.0164 + 3.84493i) q^{33} +(-1.67814 - 5.16477i) q^{34} +(3.65871 - 4.64907i) q^{35} +(-0.862422 + 2.65426i) q^{36} +(0.403914 + 7.70713i) q^{37} +(8.28302 - 5.37906i) q^{38} +(-0.197199 + 0.177559i) q^{39} +(-3.84750 + 3.16206i) q^{40} +(-0.124652 + 0.0405019i) q^{41} +(-7.43042 - 9.05139i) q^{42} +(8.25770 + 8.25770i) q^{43} +(0.999203 - 2.24425i) q^{44} +(9.91486 - 1.11475i) q^{45} +(-7.76327 + 3.45643i) q^{46} +(2.10528 - 1.70482i) q^{47} +(6.02679 + 11.8282i) q^{48} +(6.95125 - 0.824720i) q^{49} +(-7.27115 - 3.57313i) q^{50} +(4.57761 + 7.92865i) q^{51} +(0.00317989 - 0.0606759i) q^{52} +(-10.9795 - 4.21462i) q^{53} +(0.676413 - 6.43564i) q^{54} +(-8.78225 + 0.0636062i) q^{55} +(-5.86430 - 0.576749i) q^{56} +(-11.7735 + 11.7735i) q^{57} +(-2.48206 - 6.46598i) q^{58} +(-5.04772 - 1.07293i) q^{59} +(-2.38276 + 2.98643i) q^{60} +(-1.48307 - 6.97731i) q^{61} +(-0.519128 + 1.01885i) q^{62} +(9.22393 + 7.36783i) q^{63} +(3.97346 + 1.29105i) q^{64} +(-0.202218 + 0.0793093i) q^{65} +(-3.61445 + 17.0046i) q^{66} +(0.433773 + 0.351262i) q^{67} +(-2.02485 - 0.542557i) q^{68} +(11.5903 - 8.42087i) q^{69} +(-3.08893 - 9.07469i) q^{70} +(0.818370 + 0.594581i) q^{71} +(-6.25400 - 7.72305i) q^{72} +(-2.13084 - 0.111673i) q^{73} +(10.8299 + 6.25262i) q^{74} +(13.2428 + 3.34357i) q^{75} -3.81243i q^{76} +(-7.39691 - 7.29866i) q^{77} +(0.0672616 + 0.424673i) q^{78} +(15.3675 + 1.61519i) q^{79} +(1.21412 + 10.7986i) q^{80} +(-0.258873 - 2.46301i) q^{81} +(-0.0549659 + 0.205136i) q^{82} +(1.69214 - 10.6837i) q^{83} +(-4.49246 + 0.502566i) q^{84} +(1.22593 + 7.39326i) q^{85} +(18.5090 - 3.93420i) q^{86} +(6.35939 + 9.79260i) q^{87} +(4.76429 + 7.33636i) q^{88} +(-0.981714 + 0.208670i) q^{89} +(7.23495 - 14.4573i) q^{90} +(-0.235485 - 0.102964i) q^{91} +(-0.513159 + 3.23996i) q^{92} +(0.498939 - 1.86207i) q^{93} +(-0.458824 - 4.36542i) q^{94} +(-12.4107 + 5.63363i) q^{95} +(9.29110 + 0.976534i) q^{96} +(-1.77133 - 11.1837i) q^{97} +(5.01371 - 10.1740i) q^{98} -17.5251i 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