LMFDB - Embedded newform 531.2.i.c.28.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,2,Mod(19,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 38]))

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

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

chi := DirichletCharacter("531.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.i (of order $29$, degree $28$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 177)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			28.5
Character	$\chi$	$=$	531.28
Dual form			531.2.i.c.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07727 + 2.03195i) q^{2} +(-1.84595 + 2.72257i) q^{4} +(3.23491 + 0.712057i) q^{5} +(1.31099 + 0.996592i) q^{7} +(-2.94796 - 0.320610i) q^{8} +O(q^{10})$	\(q+(1.07727 + 2.03195i) q^{2} +(-1.84595 + 2.72257i) q^{4} +(3.23491 + 0.712057i) q^{5} +(1.31099 + 0.996592i) q^{7} +(-2.94796 - 0.320610i) q^{8} +(2.03802 + 7.34027i) q^{10} +(0.922770 - 2.31598i) q^{11} +(0.119964 - 2.21261i) q^{13} +(-0.612729 + 3.73748i) q^{14} +(-0.0892630 - 0.224033i) q^{16} +(2.34147 - 1.77994i) q^{17} +(-6.93750 - 2.33752i) q^{19} +(-7.91009 + 7.49283i) q^{20} +(5.70004 - 0.619916i) q^{22} +(-2.37337 - 1.42801i) q^{23} +(5.41973 + 2.50743i) q^{25} +(4.62515 - 2.13982i) q^{26} +(-5.13331 + 1.72961i) q^{28} +(-1.14256 + 2.15509i) q^{29} +(-7.57979 + 2.55393i) q^{31} +(-3.48038 + 4.09742i) q^{32} +(6.13915 + 2.84027i) q^{34} +(3.53132 + 4.15739i) q^{35} +(-9.97984 + 1.08537i) q^{37} +(-2.72386 - 16.6148i) q^{38} +(-9.30809 - 3.13626i) q^{40} +(9.34133 - 5.62049i) q^{41} +(-2.62534 - 6.58910i) q^{43} +(4.60202 + 6.78747i) q^{44} +(0.344881 - 6.36095i) q^{46} +(-6.67879 + 1.47011i) q^{47} +(-1.14719 - 4.13180i) q^{49} +(0.743543 + 13.7138i) q^{50} +(5.80252 + 4.41096i) q^{52} +(-0.271871 + 0.979189i) q^{53} +(4.63418 - 6.83491i) q^{55} +(-3.54524 - 3.35823i) q^{56} -5.60990 q^{58} +(-0.287330 + 7.67577i) q^{59} +(1.09816 + 2.07134i) q^{61} +(-13.3550 - 12.6505i) q^{62} +(-12.5461 - 2.76162i) q^{64} +(1.96357 - 7.07216i) q^{65} +(16.2238 + 1.76445i) q^{67} +(0.523775 + 9.66046i) q^{68} +(-4.64343 + 11.6541i) q^{70} +(6.36506 - 1.40106i) q^{71} +(-1.45289 + 8.86226i) q^{73} +(-12.9564 - 19.1093i) q^{74} +(19.1703 - 14.5729i) q^{76} +(3.51783 - 2.11661i) q^{77} +(9.22548 - 8.73884i) q^{79} +(-0.129233 - 0.788288i) q^{80} +(21.4838 + 12.9263i) q^{82} +(-0.0827415 - 0.0974108i) q^{83} +(8.84184 - 4.09067i) q^{85} +(10.5605 - 12.4328i) q^{86} +(-3.46281 + 6.53156i) q^{88} +(-3.29319 + 6.21161i) q^{89} +(2.36234 - 2.78116i) q^{91} +(8.26897 - 3.82564i) q^{92} +(-10.1821 - 11.9873i) q^{94} +(-20.7777 - 12.5016i) q^{95} +(-2.41950 - 14.7583i) q^{97} +(7.15979 - 6.78211i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	$ 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) $ 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{10}{29}\right)$

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 $

$2$	1.07727	+	2.03195i	0.761748	+	1.43681i	0.895159	+	0.445748i	$0.147062\pi$
$2$	1.07727	+	2.03195i	0.761748	+	1.43681i	−0.133411	+	0.991061i	$0.542593\pi$
$3$		0			0
$3$		0			0
$4$	−1.84595	+	2.72257i	−0.922973	+	1.36128i
$5$	3.23491	+	0.712057i	1.44670	+	0.318442i	0.867781	−	0.496947i	$-0.165546\pi$
$5$	3.23491	+	0.712057i	1.44670	+	0.318442i	0.578914	+	0.815388i	$0.303477\pi$
$6$		0			0
$7$	1.31099	+	0.996592i	0.495509	+	0.376676i	0.822876	−	0.568221i	$-0.192368\pi$
$7$	1.31099	+	0.996592i	0.495509	+	0.376676i	−0.327367	+	0.944897i	$0.606161\pi$
$8$	−2.94796	−	0.320610i	−1.04226	−	0.113353i
$9$		0			0
$10$	2.03802	+	7.34027i	0.644477	+	2.32120i
$11$	0.922770	−	2.31598i	0.278226	−	0.698293i	−0.721756	−	0.692148i	$-0.756665\pi$
$11$	0.922770	−	2.31598i	0.278226	−	0.698293i	0.999981	−	0.00614541i	$-0.00195616\pi$
$12$		0			0
$13$	0.119964	−	2.21261i	0.0332720	−	0.613666i	−0.933586	−	0.358353i	$-0.883339\pi$
$13$	0.119964	−	2.21261i	0.0332720	−	0.613666i	0.966858	−	0.255314i	$-0.0821787\pi$
$14$	−0.612729	+	3.73748i	−0.163759	+	0.998884i
$15$		0			0
$16$	−0.0892630	−	0.224033i	−0.0223158	−	0.0560083i
$17$	2.34147	−	1.77994i	0.567889	−	0.431698i	−0.281427	−	0.959583i	$-0.590808\pi$
$17$	2.34147	−	1.77994i	0.567889	−	0.431698i	0.849316	+	0.527885i	$0.177015\pi$
$18$		0			0
$19$	−6.93750	−	2.33752i	−1.59157	−	0.536263i	−0.622411	−	0.782691i	$-0.713847\pi$
$19$	−6.93750	−	2.33752i	−1.59157	−	0.536263i	−0.969161	+	0.246428i	$0.920743\pi$
$20$	−7.91009	+	7.49283i	−1.76875	+	1.67545i
$21$		0			0
$22$	5.70004	−	0.619916i	1.21525	−	0.132167i
$23$	−2.37337	−	1.42801i	−0.494883	−	0.297761i	0.246148	−	0.969232i	$-0.420835\pi$
$23$	−2.37337	−	1.42801i	−0.494883	−	0.297761i	−0.741031	+	0.671471i	$0.765663\pi$
$24$		0			0
$25$	5.41973	+	2.50743i	1.08395	+	0.501487i
$26$	4.62515	−	2.13982i	0.907066	−	0.419653i
$27$		0			0
$28$	−5.13331	+	1.72961i	−0.970104	+	0.326866i
$29$	−1.14256	+	2.15509i	−0.212168	+	0.400191i	−0.966639	−	0.256142i	$-0.917549\pi$
$29$	−1.14256	+	2.15509i	−0.212168	+	0.400191i	0.754471	+	0.656333i	$0.227893\pi$
$30$		0			0
$31$	−7.57979	+	2.55393i	−1.36137	+	0.458699i	−0.902839	−	0.429979i	$-0.858521\pi$
$31$	−7.57979	+	2.55393i	−1.36137	+	0.458699i	−0.458532	+	0.888678i	$0.651624\pi$
$32$	−3.48038	+	4.09742i	−0.615250	+	0.724329i
$33$		0			0
$34$	6.13915	+	2.84027i	1.05286	+	0.487103i
$35$	3.53132	+	4.15739i	0.596901	+	0.702727i
$36$		0			0
$37$	−9.97984	+	1.08537i	−1.64068	+	0.178434i	−0.881412	−	0.472349i	$-0.843406\pi$
$37$	−9.97984	+	1.08537i	−1.64068	+	0.178434i	−0.759264	+	0.650783i	$0.774441\pi$
$38$	−2.72386	−	16.6148i	−0.441869	−	2.69528i
$39$		0			0
$40$	−9.30809	−	3.13626i	−1.47174	−	0.495886i
$41$	9.34133	−	5.62049i	1.45887	−	0.877773i	0.458928	−	0.888474i	$-0.348234\pi$
$41$	9.34133	−	5.62049i	1.45887	−	0.877773i	0.999943	+	0.0107003i	$0.00340608\pi$
$42$		0			0
$43$	−2.62534	−	6.58910i	−0.400360	−	1.00483i	−0.981575	−	0.191078i	$-0.938802\pi$
$43$	−2.62534	−	6.58910i	−0.400360	−	1.00483i	0.581215	−	0.813750i	$-0.302578\pi$
$44$	4.60202	+	6.78747i	0.693780	+	1.02325i
$45$		0			0
$46$	0.344881	−	6.36095i	0.0508499	−	0.937871i
$47$	−6.67879	+	1.47011i	−0.974201	+	0.214438i	−0.673424	−	0.739256i	$-0.735177\pi$
$47$	−6.67879	+	1.47011i	−0.974201	+	0.214438i	−0.300777	+	0.953694i	$0.597246\pi$
$48$		0			0
$49$	−1.14719	−	4.13180i	−0.163884	−	0.590257i
$50$	0.743543	+	13.7138i	0.105153	+	1.93943i
$51$		0			0
$52$	5.80252	+	4.41096i	0.804664	+	0.611690i
$53$	−0.271871	+	0.979189i	−0.0373443	+	0.134502i	−0.979872	−	0.199625i	$-0.936028\pi$
$53$	−0.271871	+	0.979189i	−0.0373443	+	0.134502i	0.942528	+	0.334127i	$0.108441\pi$
$54$		0			0
$55$	4.63418	−	6.83491i	0.624873	−	0.921619i
$56$	−3.54524	−	3.35823i	−0.473753	−	0.448763i
$57$		0			0
$58$	−5.60990			−0.736616
$59$	−0.287330	+	7.67577i	−0.0374072	+	0.999300i
$59$	−0.287330	+	7.67577i	−0.0374072	+	0.999300i
$60$		0			0
$61$	1.09816	+	2.07134i	0.140605	+	0.265208i	0.943807	−	0.330499i	$-0.107217\pi$
$61$	1.09816	+	2.07134i	0.140605	+	0.265208i	−0.803202	+	0.595707i	$0.796872\pi$
$62$	−13.3550	−	12.6505i	−1.69608	−	1.60662i
$63$		0			0
$64$	−12.5461	−	2.76162i	−1.56827	−	0.345202i
$65$	1.96357	−	7.07216i	0.243551	−	0.877193i
$66$		0			0
$67$	16.2238	+	1.76445i	1.98206	+	0.215562i	0.999573	+	0.0292179i	$0.00930167\pi$
$67$	16.2238	+	1.76445i	1.98206	+	0.215562i	0.982485	+	0.186344i	$0.0596638\pi$
$68$	0.523775	+	9.66046i	0.0635170	+	1.17150i
$69$		0			0
$70$	−4.64343	+	11.6541i	−0.554995	+	1.39293i
$71$	6.36506	−	1.40106i	0.755394	−	0.166275i	0.179454	−	0.983766i	$-0.442567\pi$
$71$	6.36506	−	1.40106i	0.755394	−	0.166275i	0.575940	+	0.817492i	$0.304636\pi$
$72$		0			0
$73$	−1.45289	+	8.86226i	−0.170048	+	1.03725i	0.754532	+	0.656263i	$0.227864\pi$
$73$	−1.45289	+	8.86226i	−0.170048	+	1.03725i	−0.924581	+	0.380987i	$0.875584\pi$
$74$	−12.9564	−	19.1093i	−1.50616	−	2.22141i
$75$		0			0
$76$	19.1703	−	14.5729i	2.19898	−	1.67162i
$77$	3.51783	−	2.11661i	0.400894	−	0.241210i
$78$		0			0
$79$	9.22548	−	8.73884i	1.03795	−	0.983196i	0.0380764	−	0.999275i	$-0.487877\pi$
$79$	9.22548	−	8.73884i	1.03795	−	0.983196i	0.999871	+	0.0160790i	$0.00511834\pi$
$80$	−0.129233	−	0.788288i	−0.0144487	−	0.0881332i
$81$		0			0
$82$	21.4838	+	12.9263i	2.37248	+	1.42748i
$83$	−0.0827415	−	0.0974108i	−0.00908206	−	0.0106922i	0.757602	−	0.652716i	$-0.226371\pi$
$83$	−0.0827415	−	0.0974108i	−0.00908206	−	0.0106922i	−0.766684	+	0.642024i	$0.778095\pi$
$84$		0			0
$85$	8.84184	−	4.09067i	0.959033	−	0.443696i
$86$	10.5605	−	12.4328i	1.13877	−	1.34067i
$87$		0			0
$88$	−3.46281	+	6.53156i	−0.369137	+	0.696267i
$89$	−3.29319	+	6.21161i	−0.349077	+	0.658430i	−0.994423	−	0.105461i	$-0.966368\pi$
$89$	−3.29319	+	6.21161i	−0.349077	+	0.658430i	0.645346	+	0.763890i	$0.276713\pi$
$90$		0			0
$91$	2.36234	−	2.78116i	0.247640	−	0.291545i
$92$	8.26897	−	3.82564i	0.862100	−	0.398850i
$93$		0			0
$94$	−10.1821	−	11.9873i	−1.05020	−	1.23639i
$95$	−20.7777	−	12.5016i	−2.13175	−	1.28263i
$96$		0			0
$97$	−2.41950	−	14.7583i	−0.245663	−	1.49848i	−0.765069	−	0.643948i	$-0.777295\pi$
$97$	−2.41950	−	14.7583i	−0.245663	−	1.49848i	0.519407	−	0.854527i	$-0.326153\pi$
$98$	7.15979	−	6.78211i	0.723248	−	0.685097i
$99$		0			0
$100$	−16.8312	+	10.1270i	−1.68312	+	1.01270i
$101$	8.04581	−	6.11627i	0.800588	−	0.608591i	−0.122812	−	0.992430i	$-0.539191\pi$
$101$	8.04581	−	6.11627i	0.800588	−	0.608591i	0.923400	+	0.383839i	$0.125398\pi$
$102$		0			0
$103$	1.38787	+	2.04695i	0.136751	+	0.201692i	0.889898	−	0.456160i	$-0.150776\pi$
$103$	1.38787	+	2.04695i	0.136751	+	0.201692i	−0.753147	+	0.657852i	$0.771465\pi$
$104$	−1.06303	+	6.48421i	−0.104239	+	0.635829i
$105$		0			0
$106$	−2.28255	+	0.502427i	−0.221701	+	0.0488000i
$107$	−4.54178	+	11.3990i	−0.439070	+	1.10198i	0.528399	+	0.848996i	$0.322792\pi$
$107$	−4.54178	+	11.3990i	−0.439070	+	1.10198i	−0.967470	+	0.252987i	$0.918587\pi$
$108$		0			0
$109$	0.851925	+	15.7128i	0.0815997	+	1.50502i	0.697153	+	0.716922i	$0.254450\pi$
$109$	0.851925	+	15.7128i	0.0815997	+	1.50502i	−0.615554	+	0.788095i	$0.711068\pi$
$110$	18.8805	+	2.05338i	1.80019	+	0.195782i
$111$		0			0
$112$	0.106246	−	0.382665i	0.0100393	−	0.0361585i
$113$	5.10089	+	1.12279i	0.479851	+	0.105623i	0.448308	−	0.893879i	$-0.352027\pi$
$113$	5.10089	+	1.12279i	0.479851	+	0.105623i	0.0315432	+	0.999502i	$0.489958\pi$
$114$		0			0
$115$	−6.66082	−	6.30947i	−0.621125	−	0.588361i
$116$	−3.75829	−	7.08888i	−0.348948	−	0.658186i
$117$		0			0
$118$	−15.9063	+	7.68507i	−1.46430	+	0.707468i
$119$	4.84352			0.444005
$120$		0			0
$121$	3.47370	+	3.29047i	0.315791	+	0.299133i
$122$	−3.02586	+	4.46281i	−0.273948	+	0.404044i
$123$		0			0
$124$	7.03864	−	25.3509i	0.632089	−	2.27658i
$125$	2.56221	+	1.94774i	0.229171	+	0.174211i
$126$		0			0
$127$	−0.197707	−	3.64649i	−0.0175436	−	0.323573i	−0.994111	−	0.108363i	$-0.965439\pi$
$127$	−0.197707	−	3.64649i	−0.0175436	−	0.323573i	0.976568	−	0.215210i	$-0.0690437\pi$
$128$	−5.02767	−	18.1080i	−0.444387	−	1.60054i
$129$		0			0
$130$	16.4856	−	3.62876i	1.44588	−	0.318263i
$131$	−0.561485	+	10.3560i	−0.0490572	+	0.904807i	0.865640	+	0.500667i	$0.166912\pi$
$131$	−0.561485	+	10.3560i	−0.0490572	+	0.904807i	−0.914697	+	0.404140i	$0.867571\pi$
$132$		0			0
$133$	−6.76547	−	9.97833i	−0.586641	−	0.865231i
$134$	13.8922	+	34.8669i	1.20011	+	3.01204i
$135$		0			0
$136$	−7.47322	+	4.49648i	−0.640823	+	0.385570i
$137$	10.6203	+	3.57838i	0.907351	+	0.305722i	0.734009	−	0.679140i	$-0.237647\pi$
$137$	10.6203	+	3.57838i	0.907351	+	0.305722i	0.173342	+	0.984862i	$0.444544\pi$
$138$		0			0
$139$	−0.283066	−	1.72663i	−0.0240094	−	0.146451i	0.972101	−	0.234561i	$-0.0753654\pi$
$139$	−0.283066	−	1.72663i	−0.0240094	−	0.146451i	−0.996111	+	0.0881107i	$0.971917\pi$
$140$	−17.8374	+	1.93993i	−1.50753	+	0.163954i
$141$		0			0
$142$	9.70380	+	11.4242i	0.814325	+	0.958697i
$143$	−5.01364	−	2.31956i	−0.419262	−	0.193971i
$144$		0			0
$145$	−5.23062	+	6.15797i	−0.434380	+	0.511391i
$146$	−19.5729	+	6.59487i	−1.61986	+	0.545796i
$147$		0			0
$148$	15.4672	−	29.1743i	1.27140	−	2.39811i
$149$	8.50392	−	2.86531i	0.696668	−	0.234735i	0.0513859	−	0.998679i	$-0.483636\pi$
$149$	8.50392	−	2.86531i	0.696668	−	0.234735i	0.645283	+	0.763944i	$0.276740\pi$
$150$		0			0
$151$	−14.7204	+	6.81037i	−1.19793	+	0.554220i	−0.914427	−	0.404751i	$-0.867358\pi$
$151$	−14.7204	+	6.81037i	−1.19793	+	0.554220i	−0.283501	+	0.958972i	$0.591496\pi$
$152$	19.7021	+	9.11514i	1.59805	+	0.739336i
$153$		0			0
$154$	8.09052	+	4.86790i	0.651953	+	0.392267i
$155$	−26.3385	+	2.86448i	−2.11556	+	0.230081i
$156$		0			0
$157$	−13.7517	+	13.0263i	−1.09750	+	1.03961i	−0.0984939	+	0.995138i	$0.531403\pi$
$157$	−13.7517	+	13.0263i	−1.09750	+	1.03961i	−0.999011	+	0.0444738i	$0.985839\pi$
$158$	27.6953	+	9.33163i	2.20332	+	0.742384i
$159$		0			0
$160$	−14.1763	+	10.7766i	−1.12074	+	0.851961i
$161$	−1.68833	−	4.23740i	−0.133059	−	0.333954i
$162$		0			0
$163$	−0.748385	+	4.56495i	−0.0586181	+	0.357554i	0.941188	+	0.337882i	$0.109711\pi$
$163$	−0.748385	+	4.56495i	−0.0586181	+	0.357554i	−0.999806	+	0.0196722i	$0.993738\pi$
$164$	−1.94143	+	35.8075i	−0.151600	+	2.79610i
$165$		0			0
$166$	0.108799	−	0.273065i	0.00844445	−	0.0211940i
$167$	−2.34446	−	8.44398i	−0.181420	−	0.653414i	−0.997182	−	0.0750266i	$-0.976096\pi$
$167$	−2.34446	−	8.44398i	−0.181420	−	0.653414i	0.815762	−	0.578388i	$-0.196318\pi$
$168$		0			0
$169$	8.04256	+	0.874681i	0.618659	+	0.0672832i
$170$	17.8371	+	13.5594i	1.36805	+	1.03996i
$171$		0			0
$172$	22.7855	+	5.01546i	1.73738	+	0.382426i
$173$	3.08678	−	4.55266i	0.234684	−	0.346133i	−0.692051	−	0.721848i	$-0.743293\pi$
$173$	3.08678	−	4.55266i	0.234684	−	0.346133i	0.926735	+	0.375716i	$0.122603\pi$
$174$		0			0
$175$	4.60635	+	8.68849i	0.348207	+	0.656788i
$176$	−0.601225			−0.0453190
$177$		0			0
$178$	−16.1694			−1.21195
$179$	3.47244	+	6.54971i	0.259542	+	0.489549i	0.978699	−	0.205299i	$-0.0658166\pi$
$179$	3.47244	+	6.54971i	0.259542	+	0.489549i	−0.719157	+	0.694848i	$0.755472\pi$
$180$		0			0
$181$	7.59459	−	11.2012i	0.564501	−	0.832577i	−0.433132	−	0.901330i	$-0.642592\pi$
$181$	7.59459	−	11.2012i	0.564501	−	0.832577i	0.997634	+	0.0687531i	$0.0219021\pi$
$182$	8.19607	+	1.80409i	0.607533	+	0.133728i
$183$		0			0
$184$	6.53878	+	4.97065i	0.482045	+	0.366441i
$185$	−33.0567	−	3.59513i	−2.43038	−	0.264320i
$186$		0			0
$187$	−1.96166	−	7.06525i	−0.143451	−	0.516662i
$188$	8.32620	−	20.8972i	0.607250	−	1.52408i
$189$		0			0
$190$	3.01926	−	55.6870i	0.219040	−	4.03996i
$191$	1.01560	−	6.19490i	0.0734864	−	0.448247i	−0.924295	−	0.381678i	$-0.875346\pi$
$191$	1.01560	−	6.19490i	0.0734864	−	0.448247i	0.997782	−	0.0665692i	$-0.0212053\pi$
$192$		0			0
$193$	2.77074	+	6.95404i	0.199442	+	0.500562i	0.994348	−	0.106171i	$-0.0338590\pi$
$193$	2.77074	+	6.95404i	0.199442	+	0.500562i	−0.794906	+	0.606733i	$0.792480\pi$
$194$	27.3817	−	20.8150i	1.96589	−	1.49443i
$195$		0			0
$196$	13.3667	+	4.50378i	0.954767	+	0.321698i
$197$	13.9693	−	13.2324i	0.995272	−	0.942772i	−0.00308911	−	0.999995i	$-0.500983\pi$
$197$	13.9693	−	13.2324i	0.995272	−	0.942772i	0.998361	+	0.0572232i	$0.0182247\pi$
$198$		0			0
$199$	−12.5469	+	1.36456i	−0.889427	+	0.0967311i	−0.541412	−	0.840758i	$-0.682110\pi$
$199$	−12.5469	+	1.36456i	−0.889427	+	0.0967311i	−0.348016	+	0.937489i	$0.613144\pi$
$200$	−15.1732	−	9.12944i	−1.07291	−	0.645549i
$201$		0			0
$202$	21.0955	+	9.75983i	1.48428	+	0.686699i
$203$	−3.64564	+	1.68665i	−0.255874	+	0.118380i
$204$		0			0
$205$	34.2205	−	11.5302i	2.39006	−	0.805305i
$206$	−2.66420	+	5.02521i	−0.185623	+	0.350123i
$207$		0			0
$208$	−0.506406	+	0.170628i	−0.0351129	+	0.0118309i
$209$	−11.8154	+	13.9101i	−0.817285	+	0.962182i
$210$		0			0
$211$	−10.7657	−	4.98073i	−0.741140	−	0.342888i	0.0127236	−	0.999919i	$-0.495950\pi$
$211$	−10.7657	−	4.98073i	−0.741140	−	0.342888i	−0.753863	+	0.657031i	$0.771812\pi$
$212$	−2.16405	−	2.54772i	−0.148628	−	0.174978i
$213$		0			0
$214$	−28.0550	+	3.05116i	−1.91780	+	0.208573i
$215$	−3.80091	−	23.1845i	−0.259220	−	1.58117i
$216$		0			0
$217$	−12.4823	−	4.20577i	−0.847353	−	0.285506i
$218$	−31.0100	+	18.6581i	−2.10026	+	1.26369i
$219$		0			0
$220$	10.0540	+	25.2337i	0.677843	+	1.70126i
$221$	−3.65740	−	5.39427i	−0.246024	−	0.362858i
$222$		0			0
$223$	0.358488	−	6.61193i	0.0240062	−	0.442767i	−0.961680	−	0.274175i	$-0.911595\pi$
$223$	0.358488	−	6.61193i	0.0240062	−	0.442767i	0.985686	−	0.168592i	$-0.0539221\pi$
$224$	−8.64622	+	1.90318i	−0.577700	+	0.127161i
$225$		0			0
$226$	3.21360	+	11.5743i	0.213765	+	0.769913i
$227$	0.267345	+	4.93089i	0.0177443	+	0.327275i	0.993906	+	0.110230i	$0.0351589\pi$
$227$	0.267345	+	4.93089i	0.0177443	+	0.327275i	−0.976162	+	0.217044i	$0.930358\pi$
$228$		0			0
$229$	0.733073	+	0.557268i	0.0484429	+	0.0368253i	0.629115	−	0.777312i	$-0.283417\pi$
$229$	0.733073	+	0.557268i	0.0484429	+	0.0368253i	−0.580673	+	0.814137i	$0.697210\pi$
$230$	5.64502	−	20.3315i	0.372221	−	1.34062i
$231$		0			0
$232$	4.05916	−	5.98682i	0.266497	−	0.393054i
$233$	−2.35861	−	2.23419i	−0.154517	−	0.146367i	0.606536	−	0.795056i	$-0.292559\pi$
$233$	−2.35861	−	2.23419i	−0.154517	−	0.146367i	−0.761053	+	0.648690i	$0.775317\pi$
$234$		0			0
$235$	−22.6521			−1.47766
$236$	−20.3674	−	14.9513i	−1.32580	−	0.973248i
$237$		0			0
$238$	5.21780	+	9.84181i	0.338219	+	0.637950i
$239$	−11.9293	−	11.3000i	−0.771641	−	0.730937i	0.196729	−	0.980458i	$-0.436968\pi$
$239$	−11.9293	−	11.3000i	−0.771641	−	0.730937i	−0.968369	+	0.249521i	$0.919727\pi$
$240$		0			0
$241$	3.76281	+	0.828256i	0.242384	+	0.0533527i	0.334501	−	0.942396i	$-0.391432\pi$
$241$	3.76281	+	0.828256i	0.242384	+	0.0533527i	−0.0921170	+	0.995748i	$0.529363\pi$
$242$	−2.94395	+	10.6031i	−0.189244	+	0.681596i
$243$		0			0
$244$	−7.66650	−	0.833782i	−0.490798	−	0.0533774i
$245$	−0.768972	−	14.1829i	−0.0491278	−	0.906109i
$246$		0			0
$247$	−6.00425	+	15.0695i	−0.382041	+	0.958852i
$248$	23.1637	−	5.09873i	1.47090	−	0.323769i
$249$		0			0
$250$	−1.19752	+	7.30454i	−0.0757377	+	0.461980i
$251$	−8.48180	−	12.5097i	−0.535366	−	0.789606i	0.459778	−	0.888034i	$-0.347929\pi$
$251$	−8.48180	−	12.5097i	−0.535366	−	0.789606i	−0.995144	+	0.0984277i	$0.968619\pi$
$252$		0			0
$253$	−5.49732	+	4.17895i	−0.345614	+	0.262729i
$254$	7.19651	−	4.32999i	0.451549	−	0.271688i
$255$		0			0
$256$	12.7255	−	12.0543i	0.795345	−	0.753391i
$257$	3.23780	+	19.7497i	0.201968	+	1.23195i	0.871958	+	0.489581i	$0.162850\pi$
$257$	3.23780	+	19.7497i	0.201968	+	1.23195i	−0.669990	+	0.742370i	$0.733701\pi$
$258$		0			0
$259$	−14.1652	−	8.52291i	−0.880182	−	0.529588i
$260$	15.6298	+	18.4008i	0.969316	+	1.14117i
$261$		0			0
$262$	−21.6478	+	10.0153i	−1.33740	+	0.618749i
$263$	−14.6913	+	17.2960i	−0.905905	+	1.06651i	0.0915909	+	0.995797i	$0.470805\pi$
$263$	−14.6913	+	17.2960i	−0.905905	+	1.06651i	−0.997496	+	0.0707176i	$0.977471\pi$
$264$		0			0
$265$	−1.57672	+	2.97400i	−0.0968569	+	0.182691i
$266$	12.9872	−	24.4965i	0.796299	−	1.50198i
$267$		0			0
$268$	−34.7522	+	40.9134i	−2.12283	+	2.49918i
$269$	13.6637	−	6.32150i	0.833090	−	0.385429i	0.0434927	−	0.999054i	$-0.486151\pi$
$269$	13.6637	−	6.32150i	0.833090	−	0.385429i	0.789597	+	0.613625i	$0.210289\pi$
$270$		0			0
$271$	−2.21100	−	2.60300i	−0.134309	−	0.158121i	0.690896	−	0.722954i	$-0.257216\pi$
$271$	−2.21100	−	2.60300i	−0.134309	−	0.158121i	−0.825205	+	0.564833i	$0.808940\pi$
$272$	−0.607771	−	0.365684i	−0.0368515	−	0.0221728i
$273$		0			0
$274$	4.16982	+	25.4348i	0.251908	+	1.53657i
$275$	10.8083	−	10.2382i	0.651767	−	0.617386i
$276$		0			0
$277$	4.32147	−	2.60014i	0.259652	−	0.156227i	−0.379776	−	0.925078i	$-0.623999\pi$
$277$	4.32147	−	2.60014i	0.259652	−	0.156227i	0.639428	+	0.768851i	$0.279171\pi$
$278$	3.20349	−	2.43523i	0.192132	−	0.146055i
$279$		0			0
$280$	−9.07728	−	13.3880i	−0.542471	−	0.800085i
$281$	−0.602315	+	3.67396i	−0.0359311	+	0.219170i	−0.998689	−	0.0511964i	$-0.983697\pi$
$281$	−0.602315	+	3.67396i	−0.0359311	+	0.219170i	0.962758	+	0.270366i	$0.0871448\pi$
$282$		0			0
$283$	−4.99083	+	1.09856i	−0.296674	+	0.0653029i	−0.360813	−	0.932638i	$-0.617501\pi$
$283$	−4.99083	+	1.09856i	−0.296674	+	0.0653029i	0.0641394	+	0.997941i	$0.479570\pi$
$284$	−7.93509	+	19.9156i	−0.470861	+	1.18177i
$285$		0			0
$286$	−0.687831	−	12.6863i	−0.0406723	−	0.750157i
$287$	17.8478	+	1.94106i	1.05352	+	0.114577i
$288$		0			0
$289$	−2.23369	+	8.04503i	−0.131394	+	0.473237i
$290$	−18.1475	−	3.99457i	−1.06566	−	0.234569i
$291$		0			0
$292$	−21.4461	−	20.3149i	−1.25504	−	1.18884i
$293$	11.4836	+	21.6603i	0.670878	+	1.26541i	0.952106	+	0.305769i	$0.0989134\pi$
$293$	11.4836	+	21.6603i	0.670878	+	1.26541i	−0.281228	+	0.959641i	$0.590742\pi$
$294$		0			0
$295$	−6.39507	+	24.6258i	−0.372336	+	1.43377i
$296$	29.7682			1.73024
$297$		0			0
$298$	14.9832	+	14.1929i	0.867955	+	0.822171i
$299$	−3.44435	+	5.08003i	−0.199192	+	0.293786i
$300$		0			0
$301$	3.12484	−	11.2547i	0.180113	−	0.648708i
$302$	−29.6963	−	22.5745i	−1.70883	−	1.29902i
$303$		0			0
$304$	0.0955808	+	1.76288i	0.00548194	+	0.101108i
$305$	2.07752	+	7.48255i	0.118958	+	0.428450i
$306$		0			0
$307$	6.09492	−	1.34159i	0.347856	−	0.0765688i	−0.0376061	−	0.999293i	$-0.511973\pi$
$307$	6.09492	−	1.34159i	0.347856	−	0.0765688i	0.385462	+	0.922724i	$0.374042\pi$
$308$	−0.731117	+	13.4847i	−0.0416593	+	0.768360i
$309$		0			0
$310$	−34.1943	−	50.4327i	−1.94210	−	2.86439i
$311$	−11.8739	−	29.8013i	−0.673308	−	1.68988i	−0.722760	−	0.691099i	$-0.757127\pi$
$311$	−11.8739	−	29.8013i	−0.673308	−	1.68988i	0.0494517	−	0.998777i	$-0.484253\pi$
$312$		0			0
$313$	18.3380	−	11.0336i	1.03652	−	0.623656i	0.107703	−	0.994183i	$-0.465650\pi$
$313$	18.3380	−	11.0336i	1.03652	−	0.623656i	0.928822	+	0.370527i	$0.120823\pi$
$314$	−41.2832	−	13.9099i	−2.32974	−	0.784982i
$315$		0			0
$316$	6.76233	+	41.2484i	0.380411	+	2.32040i
$317$	−27.9293	+	3.03749i	−1.56866	+	0.170602i	−0.850766	−	0.525545i	$-0.823861\pi$
$317$	−27.9293	+	3.03749i	−1.56866	+	0.170602i	−0.717898	+	0.696148i	$0.754896\pi$
$318$		0			0
$319$	3.93683	+	4.63480i	0.220420	+	0.259499i
$320$	−38.6192	−	17.8671i	−2.15888	−	0.998804i
$321$		0			0
$322$	6.79141	−	7.99546i	0.378470	−	0.445570i
$323$	−20.4046	+	6.87509i	−1.13534	+	0.382540i
$324$		0			0
$325$	6.19814	−	11.6909i	0.343811	−	0.648496i
$326$	−10.0820	+	3.39702i	−0.558389	+	0.188143i
$327$		0			0
$328$	−29.3399	+	13.5741i	−1.62002	+	0.749502i
$329$	−10.2210	−	4.72872i	−0.563499	−	0.260703i
$330$		0			0
$331$	16.6324	+	10.0074i	0.914200	+	0.550056i	0.893168	−	0.449723i	$-0.148477\pi$
$331$	16.6324	+	10.0074i	0.914200	+	0.550056i	0.0210321	+	0.999779i	$0.493305\pi$
$332$	0.417944	−	0.0454541i	0.0229376	−	0.00249462i
$333$		0			0
$334$	14.6321	−	13.8603i	0.800636	−	0.758402i
$335$	51.2263	+	17.2601i	2.79879	+	0.943022i
$336$		0			0
$337$	−5.17764	+	3.93594i	−0.282044	+	0.214404i	−0.736626	−	0.676301i	$-0.763582\pi$
$337$	−5.17764	+	3.93594i	−0.282044	+	0.214404i	0.454581	+	0.890705i	$0.349789\pi$
$338$	6.88673	+	17.2844i	0.374589	+	0.940147i
$339$		0			0
$340$	−5.18444	+	31.6237i	−0.281166	+	1.71503i
$341$	−1.07956	+	19.9113i	−0.0584614	+	1.07826i
$342$		0			0
$343$	6.88053	−	17.2688i	0.371513	−	0.932428i
$344$	5.62686	+	20.2661i	0.303380	+	1.09268i
$345$		0			0
$346$	12.5761	+	1.36773i	0.676096	+	0.0735299i
$347$	28.9733	+	22.0249i	1.55537	+	1.18236i	0.907078	+	0.420963i	$0.138308\pi$
$347$	28.9733	+	22.0249i	1.55537	+	1.18236i	0.648288	+	0.761395i	$0.275485\pi$
$348$		0			0
$349$	−19.8007	−	4.35847i	−1.05991	−	0.233303i	−0.349386	−	0.936979i	$-0.613610\pi$
$349$	−19.8007	−	4.35847i	−1.05991	−	0.233303i	−0.710522	+	0.703675i	$0.751541\pi$
$350$	−12.6923	+	18.7198i	−0.678433	+	1.00061i
$351$		0			0
$352$	6.27795	+	11.8415i	0.334616	+	0.631152i
$353$	−10.5120			−0.559498			−0.279749	−	0.960073i	$-0.590251\pi$
$353$	−10.5120			−0.559498			−0.279749	+	0.960073i	$0.590251\pi$
$354$		0			0
$355$	21.5880			1.14577
$356$	−10.8325	−	20.4322i	−0.574120	−	1.08291i
$357$		0			0
$358$	−9.56795	+	14.1117i	−0.505682	+	0.745825i
$359$	3.75805	+	0.827208i	0.198342	+	0.0436584i	0.313030	−	0.949743i	$-0.398656\pi$
$359$	3.75805	+	0.827208i	0.198342	+	0.0436584i	−0.114688	+	0.993402i	$0.536587\pi$
$360$		0			0
$361$	27.5392	+	20.9347i	1.44943	+	1.10183i
$362$	30.9417	+	3.36512i	1.62626	+	0.176867i
$363$		0			0
$364$	3.21114	+	11.5655i	0.168309	+	0.606196i
$365$	−11.0104	+	27.6341i	−0.576312	+	1.44643i
$366$		0			0
$367$	0.990788	−	18.2740i	0.0517187	−	0.953896i	−0.851403	−	0.524512i	$-0.824248\pi$
$367$	0.990788	−	18.2740i	0.0517187	−	0.953896i	0.903122	−	0.429384i	$-0.141269\pi$
$368$	−0.108068	+	0.659183i	−0.00563341	+	0.0343623i
$369$		0			0
$370$	−28.3060	−	71.0427i	−1.47156	−	3.69333i
$371$	−1.33227	+	1.01277i	−0.0691682	+	0.0525803i
$372$		0			0
$373$	−6.52367	−	2.19808i	−0.337783	−	0.113812i	0.145298	−	0.989388i	$-0.453586\pi$
$373$	−6.52367	−	2.19808i	−0.337783	−	0.113812i	−0.483081	+	0.875576i	$0.660482\pi$
$374$	12.2430	−	11.5972i	0.633072	−	0.599678i
$375$		0			0
$376$	20.1601	−	2.19255i	1.03968	−	0.113072i
$377$	4.63131	+	2.78657i	0.238525	+	0.143515i
$378$		0			0
$379$	3.31802	+	1.53508i	0.170435	+	0.0788517i	0.503252	−	0.864140i	$-0.332137\pi$
$379$	3.31802	+	1.53508i	0.170435	+	0.0788517i	−0.332816	+	0.942992i	$0.607999\pi$
$380$	72.3909	−	33.4916i	3.71357	−	1.71808i
$381$		0			0
$382$	13.6818	−	4.60995i	0.700023	−	0.235865i
$383$	−6.85564	+	12.9311i	−0.350307	+	0.660749i	−0.994572	−	0.104053i	$-0.966819\pi$
$383$	−6.85564	+	12.9311i	−0.350307	+	0.660749i	0.644265	+	0.764803i	$0.277164\pi$
$384$		0			0
$385$	12.8870	−	4.34214i	0.656783	−	0.221296i
$386$	−11.1454	+	13.1214i	−0.567288	+	0.667863i
$387$		0			0
$388$	44.6466	+	20.6557i	2.26659	+	1.04864i
$389$	−14.5352	−	17.1121i	−0.736963	−	0.867620i	0.258176	−	0.966098i	$-0.416878\pi$
$389$	−14.5352	−	17.1121i	−0.736963	−	0.867620i	−0.995139	+	0.0984780i	$0.968603\pi$
$390$		0			0
$391$	−8.09894	+	0.880813i	−0.409581	+	0.0445446i
$392$	2.05717	+	12.5482i	0.103903	+	0.633779i
$393$		0			0
$394$	41.9365	+	14.1300i	2.11273	+	0.711861i
$395$	36.0661	−	21.7003i	1.81468	−	1.09186i
$396$		0			0
$397$	9.48004	+	23.7931i	0.475790	+	1.19414i	0.949586	+	0.313507i	$0.101504\pi$
$397$	9.48004	+	23.7931i	0.475790	+	1.19414i	−0.473796	+	0.880634i	$0.657117\pi$
$398$	−16.2892	−	24.0248i	−0.816503	−	1.20425i
$399$		0			0
$400$	0.0779673	−	1.43802i	0.00389836	−	0.0719011i
$401$	21.5722	−	4.74841i	1.07727	−	0.237124i	0.359314	−	0.933217i	$-0.383011\pi$
$401$	21.5722	−	4.74841i	1.07727	−	0.237124i	0.717952	+	0.696092i	$0.245080\pi$
$402$		0			0
$403$	4.74153	+	17.0775i	0.236193	+	0.850689i
$404$	1.79981	+	33.1955i	0.0895439	+	1.65154i
$405$		0			0
$406$	−7.35455	−	5.59078i	−0.365000	−	0.277466i
$407$	−6.69539	+	24.1146i	−0.331878	+	1.19532i
$408$		0			0
$409$	−0.0878626	+	0.129588i	−0.00434453	+	0.00640770i	−0.829855	−	0.557979i	$-0.811577\pi$
$409$	−0.0878626	+	0.129588i	−0.00434453	+	0.00640770i	0.825511	+	0.564387i	$0.190887\pi$
$410$	60.2937	+	57.1132i	2.97769	+	2.82062i
$411$		0			0
$412$	−8.13488			−0.400777
$413$	−8.02630	+	9.77654i	−0.394948	+	0.481072i
$414$		0			0
$415$	−0.198299	−	0.374032i	−0.00973412	−	0.0183605i
$416$	8.64846	+	8.19225i	0.424026	+	0.401658i
$417$		0			0
$418$	−40.9931	−	9.02326i	−2.00504	−	0.441342i
$419$	−1.96214	+	7.06701i	−0.0958570	+	0.345246i	−0.995889	−	0.0905771i	$-0.971129\pi$
$419$	−1.96214	+	7.06701i	−0.0958570	+	0.345246i	0.900032	+	0.435823i	$0.143543\pi$
$420$		0			0
$421$	−24.2330	−	2.63550i	−1.18104	−	0.128446i	−0.503544	−	0.863969i	$-0.667971\pi$
$421$	−24.2330	−	2.63550i	−1.18104	−	0.128446i	−0.677499	+	0.735523i	$0.736936\pi$
$422$	−1.47696	−	27.2410i	−0.0718974	−	1.32607i
$423$		0			0
$424$	1.11540	−	2.79945i	0.0541687	−	0.135953i
$425$	17.1532	−	3.77570i	0.832052	−	0.183148i
$426$		0			0
$427$	−0.624607	+	3.80993i	−0.0302268	+	0.184376i
$428$	−22.6507	−	33.4072i	−1.09486	−	1.61480i
$429$		0			0
$430$	43.0153	−	32.6994i	2.07438	−	1.57690i
$431$	−18.3953	+	11.0681i	−0.886071	+	0.533131i	−0.884327	−	0.466867i	$-0.845383\pi$
$431$	−18.3953	+	11.0681i	−0.886071	+	0.533131i	−0.00174341	+	0.999998i	$0.500555\pi$
$432$		0			0
$433$	−5.27017	+	4.99217i	−0.253268	+	0.239909i	−0.803791	−	0.594912i	$-0.797187\pi$
$433$	−5.27017	+	4.99217i	−0.253268	+	0.239909i	0.550523	+	0.834820i	$0.314428\pi$
$434$	−4.90091	−	29.8942i	−0.235251	−	1.43497i
$435$		0			0
$436$	−44.3518	−	26.6856i	−2.12407	−	1.27801i
$437$	13.1273	+	15.4546i	0.627963	+	0.739295i
$438$		0			0
$439$	8.14734	−	3.76936i	0.388851	−	0.179902i	−0.215715	−	0.976456i	$-0.569208\pi$
$439$	8.14734	−	3.76936i	0.388851	−	0.179902i	0.604567	+	0.796555i	$0.293346\pi$
$440$	−15.8527	+	18.6633i	−0.755750	+	0.889737i
$441$		0			0
$442$	7.02088	−	13.2428i	0.333949	−	0.629895i
$443$	−1.00406	+	1.89386i	−0.0477044	+	0.0899800i	−0.906218	−	0.422811i	$-0.861044\pi$
$443$	−1.00406	+	1.89386i	−0.0477044	+	0.0899800i	0.858514	+	0.512791i	$0.171388\pi$
$444$		0			0
$445$	−15.0762	+	17.7491i	−0.714680	+	0.841386i
$446$	13.8213	−	6.39443i	0.654459	−	0.302785i
$447$		0			0
$448$	−13.6957	−	16.1238i	−0.647062	−	0.761780i
$449$	13.3209	+	8.01492i	0.628652	+	0.378247i	0.793938	−	0.607998i	$-0.208027\pi$
$449$	13.3209	+	8.01492i	0.628652	+	0.378247i	−0.165286	+	0.986246i	$0.552855\pi$
$450$		0			0
$451$	−4.39703	−	26.8207i	−0.207048	−	1.26294i
$452$	−12.4728	+	11.8149i	−0.586673	+	0.555726i
$453$		0			0
$454$	−9.73134	+	5.85515i	−0.456714	+	0.274796i
$455$	9.62229	−	7.31467i	0.451100	−	0.342917i
$456$		0			0
$457$	−4.81325	−	7.09901i	−0.225154	−	0.332078i	0.698287	−	0.715818i	$-0.253946\pi$
$457$	−4.81325	−	7.09901i	−0.225154	−	0.332078i	−0.923441	+	0.383741i	$0.874636\pi$
$458$	−0.342622	+	2.08990i	−0.0160097	+	0.0976547i
$459$		0			0
$460$	29.4734	−	6.48760i	1.37421	−	0.302486i
$461$	11.2734	−	28.2942i	0.525056	−	1.31779i	−0.392341	−	0.919820i	$-0.628335\pi$
$461$	11.2734	−	28.2942i	0.525056	−	1.31779i	0.917398	−	0.397972i	$-0.130286\pi$
$462$		0			0
$463$	1.87299	+	34.5452i	0.0870450	+	1.60545i	0.637409	+	0.770526i	$0.280006\pi$
$463$	1.87299	+	34.5452i	0.0870450	+	1.60545i	−0.550364	+	0.834925i	$0.685511\pi$
$464$	0.584801	+	0.0636010i	0.0271487	+	0.00295260i
$465$		0			0
$466$	1.99891	−	7.19942i	0.0925976	−	0.333507i
$467$	20.1323	+	4.43145i	0.931610	+	0.205063i	0.654748	−	0.755847i	$-0.272775\pi$
$467$	20.1323	+	4.43145i	0.931610	+	0.205063i	0.276862	+	0.960910i	$0.410706\pi$
$468$		0			0
$469$	19.5109	+	18.4817i	0.900931	+	0.853407i
$470$	−24.4025	−	46.0280i	−1.12560	−	2.12311i
$471$		0			0
$472$	3.30797	−	22.5358i	0.152262	−	1.03729i
$473$	−17.6828			−0.813055
$474$		0			0
$475$	−31.7382	−	30.0640i	−1.45625	−	1.37943i
$476$	−8.94087	+	13.1868i	−0.409804	+	0.604416i
$477$		0			0
$478$	10.1100	−	36.4129i	0.462421	−	1.66549i
$479$	19.3772	+	14.7302i	0.885368	+	0.673040i	0.945666	−	0.325141i	$-0.105412\pi$
$479$	19.3772	+	14.7302i	0.885368	+	0.673040i	−0.0602971	+	0.998180i	$0.519205\pi$
$480$		0			0
$481$	1.20428	+	22.2117i	0.0549105	+	1.01276i
$482$	2.37059	+	8.53811i	0.107978	+	0.388900i
$483$		0			0
$484$	−15.3708	+	3.38336i	−0.698672	+	0.153789i
$485$	2.68189	−	49.4645i	0.121778	−	2.24607i
$486$		0			0
$487$	−16.5241	−	24.3712i	−0.748778	−	1.10436i	−0.990963	−	0.134135i	$-0.957175\pi$
$487$	−16.5241	−	24.3712i	−0.748778	−	1.10436i	0.242185	−	0.970230i	$-0.422136\pi$
$488$	−2.57323	−	6.45832i	−0.116485	−	0.292354i
$489$		0			0
$490$	27.9905	−	16.8413i	1.26448	−	0.760814i
$491$	−7.97632	−	2.68754i	−0.359966	−	0.121287i	0.133507	−	0.991048i	$-0.457376\pi$
$491$	−7.97632	−	2.68754i	−0.359966	−	0.121287i	−0.493473	+	0.869761i	$0.664273\pi$
$492$		0			0
$493$	1.16067	+	7.07976i	0.0522739	+	0.318856i
$494$	−37.0888	+	4.03365i	−1.66871	+	0.181483i
$495$		0			0
$496$	1.24876	+	1.47015i	0.0560710	+	0.0660119i
$497$	9.74084	+	4.50659i	0.436936	+	0.202148i
$498$		0			0
$499$	−18.1083	+	21.3187i	−0.810639	+	0.954358i	−0.999618	−	0.0276234i	$-0.991206\pi$
$499$	−18.1083	+	21.3187i	−0.810639	+	0.954358i	0.188980	+	0.981981i	$0.439482\pi$
$500$	−10.0325	+	3.38036i	−0.448669	+	0.151174i
$501$		0			0
$502$	16.2820	−	30.7110i	0.726699	−	1.37070i
$503$	25.8744	−	8.71810i	1.15368	−	0.388721i	0.323509	−	0.946225i	$-0.395138\pi$
$503$	25.8744	−	8.71810i	1.15368	−	0.388721i	0.830174	+	0.557504i	$0.188241\pi$
$504$		0			0
$505$	30.3826	−	14.0565i	1.35201	−	0.625505i
$506$	−14.4136	−	6.66843i	−0.640761	−	0.296448i
$507$		0			0
$508$	10.2928	+	6.19294i	0.456667	+	0.274767i
$509$	2.73734	−	0.297703i	0.121330	−	0.0131955i	−0.0472524	−	0.998883i	$-0.515046\pi$
$509$	2.73734	−	0.297703i	0.121330	−	0.0131955i	0.168583	+	0.985688i	$0.446081\pi$
$510$		0			0
$511$	−10.7368	+	10.1704i	−0.474968	+	0.449914i
$512$	2.58401	+	0.870655i	0.114198	+	0.0384779i
$513$		0			0
$514$	−36.6425	+	27.8549i	−1.61623	+	1.22863i
$515$	3.03207	+	7.60993i	0.133609	+	0.335334i
$516$		0			0
$517$	−2.75824	+	16.8245i	−0.121307	+	0.739940i
$518$	2.05838	−	37.9645i	0.0904399	−	1.66807i
$519$		0			0
$520$	−8.05595	+	20.2189i	−0.353277	+	0.886657i
$521$	−7.30611	−	26.3142i	−0.320086	−	1.15285i	−0.932160	−	0.362046i	$-0.882078\pi$
$521$	−7.30611	−	26.3142i	−0.320086	−	1.15285i	0.612074	−	0.790801i	$-0.290336\pi$
$522$		0			0
$523$	30.4037	+	3.30660i	1.32946	+	0.144588i	0.745125	−	0.666925i	$-0.232390\pi$
$523$	30.4037	+	3.30660i	1.32946	+	0.144588i	0.584335	+	0.811512i	$0.301355\pi$
$524$	−27.1584	−	20.6453i	−1.18642	−	0.901893i
$525$		0			0
$526$	−50.9712	−	11.2196i	−2.22245	−	0.489198i
$527$	−13.2020	+	19.4715i	−0.575088	+	0.848191i
$528$		0			0
$529$	−7.17971	−	13.5424i	−0.312161	−	0.588798i
$530$	−7.74159			−0.336273
$531$		0			0
$532$	39.6554			1.71928
$533$	−11.3153	−	21.3429i	−0.490120	−	0.924465i
$534$		0			0
$535$	−22.8090	+	33.6407i	−0.986118	+	1.45442i
$536$	−47.2616	−	10.4031i	−2.04139	−	0.449344i
$537$		0			0
$538$	27.5645	+	20.9540i	1.18839	+	0.903392i
$539$	−10.6277	−	1.15584i	−0.457769	−	0.0497854i
$540$		0			0
$541$	−1.85601	−	6.68474i	−0.0797960	−	0.287399i	0.912876	−	0.408236i	$-0.133856\pi$
$541$	−1.85601	−	6.68474i	−0.0797960	−	0.287399i	−0.992672	+	0.120837i	$0.961442\pi$
$542$	2.90731	−	7.29680i	0.124880	−	0.313424i
$543$		0			0
$544$	−0.856045	+	15.7888i	−0.0367026	+	0.676940i
$545$	−8.43254	+	51.4362i	−0.361210	+	2.20329i
$546$		0			0
$547$	4.54991	+	11.4194i	0.194540	+	0.488259i	0.993595	−	0.112999i	$-0.0360458\pi$
$547$	4.54991	+	11.4194i	0.194540	+	0.488259i	−0.799055	+	0.601258i	$0.794666\pi$
$548$	−29.3468	+	22.3089i	−1.25363	+	0.952988i
$549$		0			0
$550$	32.4471	+	10.9327i	1.38355	+	0.466171i
$551$	12.9641	−	12.2802i	0.552288	−	0.523155i
$552$		0			0
$553$	20.8036	−	2.26253i	0.884659	−	0.0962125i
$554$	9.93877	+	5.97996i	0.422258	+	0.254064i
$555$		0			0
$556$	5.22338	+	2.41659i	0.221521	+	0.102486i
$557$	13.6858	−	6.33174i	0.579887	−	0.268284i	−0.107942	−	0.994157i	$-0.534426\pi$
$557$	13.6858	−	6.33174i	0.579887	−	0.268284i	0.687829	+	0.725873i	$0.258564\pi$
$558$		0			0
$559$	−14.8940	+	5.01838i	−0.629950	+	0.212255i
$560$	0.616177	−	1.16223i	0.0260382	−	0.0491133i
$561$		0			0
$562$	−8.11417	+	2.73398i	−0.342276	+	0.115326i
$563$	12.0959	−	14.2404i	0.509782	−	0.600162i	−0.445710	−	0.895177i	$-0.647049\pi$
$563$	12.0959	−	14.2404i	0.509782	−	0.600162i	0.955493	+	0.295015i	$0.0953247\pi$
$564$		0			0
$565$	15.7014	+	7.26425i	0.660563	+	0.305609i
$566$	−7.60872	−	8.95768i	−0.319818	−	0.376519i
$567$		0			0
$568$	−19.2131	+	2.08956i	−0.806166	+	0.0876758i
$569$	−3.99832	−	24.3887i	−0.167618	−	1.02243i	−0.927899	−	0.372832i	$-0.878387\pi$
$569$	−3.99832	−	24.3887i	−0.167618	−	1.02243i	0.760280	−	0.649595i	$-0.225062\pi$
$570$		0			0
$571$	−15.6373	−	5.26883i	−0.654402	−	0.220494i	−0.0275360	−	0.999621i	$-0.508766\pi$
$571$	−15.6373	−	5.26883i	−0.654402	−	0.220494i	−0.626866	+	0.779127i	$0.715663\pi$
$572$	15.5701	−	9.36820i	0.651017	−	0.391704i
$573$		0			0
$574$	15.2828	+	38.3569i	0.637891	+	1.60099i
$575$	−9.28240	−	13.6905i	−0.387103	−	0.570934i
$576$		0			0
$577$	2.39235	−	44.1243i	0.0995949	−	1.83692i	−0.341993	−	0.939703i	$-0.611102\pi$
$577$	2.39235	−	44.1243i	0.0995949	−	1.83692i	0.441588	−	0.897218i	$-0.354415\pi$
$578$	−18.7534	+	4.12794i	−0.780040	+	0.171700i
$579$		0			0
$580$	−7.11002	−	25.6080i	−0.295228	−	1.06331i
$581$	−0.0113948	−	0.210164i	−0.000472735	−	0.00871909i
$582$		0			0
$583$	2.01691	+	1.53321i	0.0835317	+	0.0634992i
$584$	7.12441	−	25.6598i	0.294810	−	1.06181i
$585$		0			0
$586$	−31.6418	+	46.6682i	−1.30711	+	1.92785i
$587$	−19.8997	−	18.8500i	−0.821347	−	0.778021i	0.156426	−	0.987690i	$-0.450003\pi$
$587$	−19.8997	−	18.8500i	−0.821347	−	0.778021i	−0.977772	+	0.209669i	$0.932761\pi$
$588$		0			0
$589$	58.5547			2.41270
$590$	−56.9278	+	13.5343i	−2.34368	+	0.557196i
$591$		0			0
$592$	1.13399	+	2.13893i	0.0466067	+	0.0879096i
$593$	30.4879	+	28.8797i	1.25199	+	1.18595i	0.974295	+	0.225277i	$0.0723287\pi$
$593$	30.4879	+	28.8797i	1.25199	+	1.18595i	0.277694	+	0.960670i	$0.410430\pi$
$594$		0			0
$595$	15.6683	+	3.44886i	0.642339	+	0.141390i
$596$	−7.89679	+	28.4417i	−0.323465	+	1.16502i
$597$		0			0
$598$	−14.0329	−	1.52617i	−0.573848	−	0.0624097i
$599$	−1.00798	−	18.5910i	−0.0411848	−	0.759610i	−0.944073	−	0.329735i	$-0.893041\pi$
$599$	−1.00798	−	18.5910i	−0.0411848	−	0.759610i	0.902889	−	0.429875i	$-0.141442\pi$
$600$		0			0
$601$	−2.81985	+	7.07730i	−0.115024	+	0.288689i	−0.975206	−	0.221298i	$-0.928971\pi$
$601$	−2.81985	+	7.07730i	−0.115024	+	0.288689i	0.860182	+	0.509987i	$0.170350\pi$
$602$	26.2353	−	5.77482i	1.06927	−	0.235364i
$603$		0			0
$604$	8.63133	−	52.6488i	0.351204	−	2.14225i
$605$	8.89411	+	13.1178i	0.361597	+	0.533316i
$606$		0			0
$607$	−11.0411	+	8.39322i	−0.448144	+	0.340670i	−0.804780	−	0.593573i	$-0.797717\pi$
$607$	−11.0411	+	8.39322i	−0.448144	+	0.340670i	0.356636	+	0.934243i	$0.383924\pi$
$608$	33.7229	−	20.2904i	1.36765	−	0.822885i
$609$		0			0
$610$	−12.9661	+	12.2822i	−0.524984	+	0.497291i
$611$	2.45156	+	14.9539i	0.0991797	+	0.604969i
$612$		0			0
$613$	−14.6348	−	8.80548i	−0.591095	−	0.355650i	0.188368	−	0.982099i	$-0.439680\pi$
$613$	−14.6348	−	8.80548i	−0.591095	−	0.355650i	−0.779463	+	0.626449i	$0.784508\pi$
$614$	9.29196	+	10.9393i	0.374993	+	0.441476i
$615$		0			0
$616$	−11.0490	+	5.11183i	−0.445178	+	0.205961i
$617$	2.57683	−	3.03368i	0.103739	−	0.122131i	−0.707842	−	0.706371i	$-0.750331\pi$
$617$	2.57683	−	3.03368i	0.103739	−	0.122131i	0.811581	+	0.584239i	$0.198607\pi$
$618$		0			0
$619$	6.10790	−	11.5207i	0.245497	−	0.463057i	−0.729887	−	0.683567i	$-0.760428\pi$
$619$	6.10790	−	11.5207i	0.245497	−	0.463057i	0.975385	+	0.220511i	$0.0707723\pi$
$620$	40.8206	−	76.9959i	1.63940	−	3.09223i
$621$		0			0
$622$	47.7634	−	56.2314i	1.91514	−	2.25467i
$623$	−10.5078	+	4.86142i	−0.420986	+	0.194769i
$624$		0			0
$625$	−12.4282	−	14.6317i	−0.497130	−	0.585267i
$626$	42.1748	+	25.3758i	1.68565	+	1.01422i
$627$		0			0
$628$	−10.0801	−	61.4857i	−0.402239	−	2.45355i
$629$	−21.4356	+	20.3048i	−0.854692	+	0.809607i
$630$		0			0
$631$	16.4816	−	9.91663i	0.656121	−	0.394775i	−0.148210	−	0.988956i	$-0.547351\pi$
$631$	16.4816	−	9.91663i	0.656121	−	0.394775i	0.804331	+	0.594181i	$0.202524\pi$
$632$	−29.9981	+	22.8040i	−1.19326	+	0.907093i
$633$		0			0
$634$	−36.2595	−	53.4788i	−1.44005	−	2.12391i
$635$	1.95694	−	11.9368i	0.0776589	−	0.473698i
$636$		0			0
$637$	−9.27966	+	2.04261i	−0.367673	+	0.0809311i
$638$	−5.17665	+	12.9924i	−0.204945	+	0.514374i
$639$		0			0
$640$	−3.37010	−	62.1578i	−0.133215	−	2.45700i
$641$	24.8197	+	2.69931i	0.980320	+	0.106616i	0.584224	−	0.811593i	$-0.301399\pi$
$641$	24.8197	+	2.69931i	0.980320	+	0.106616i	0.396096	+	0.918209i	$0.370365\pi$
$642$		0			0
$643$	3.56498	−	12.8399i	0.140589	−	0.506356i	−0.859399	−	0.511306i	$-0.829162\pi$
$643$	3.56498	−	12.8399i	0.140589	−	0.506356i	0.999988	+	0.00495015i	$0.00157569\pi$
$644$	14.6532	+	3.22541i	0.577416	+	0.127099i
$645$		0			0
$646$	−35.9512	−	34.0548i	−1.41448	−	1.33987i
$647$	−18.9087	−	35.6656i	−0.743377	−	1.40216i	−0.909352	−	0.416028i	$-0.863422\pi$
$647$	−18.9087	−	35.6656i	−0.743377	−	1.40216i	0.165975	−	0.986130i	$-0.446923\pi$
$648$		0			0
$649$	17.5118	+	7.74842i	0.687397	+	0.304152i
$650$	30.4325			1.19366
$651$		0			0
$652$	−11.0469	−	10.4642i	−0.432630	−	0.409809i
$653$	−12.6247	+	18.6200i	−0.494041	+	0.728656i	−0.990212	−	0.139568i	$-0.955429\pi$
$653$	−12.6247	+	18.6200i	−0.494041	+	0.728656i	0.496171	+	0.868225i	$0.334739\pi$
$654$		0			0
$655$	−9.19041	+	33.1009i	−0.359099	+	1.29336i
$656$	−2.09301	−	1.59107i	−0.0817184	−	0.0621207i
$657$		0			0
$658$	−1.40223	−	25.8626i	−0.0546647	−	1.00823i
$659$	−5.10327	−	18.3803i	−0.198795	−	0.715996i	−0.993974	−	0.109620i	$-0.965037\pi$
$659$	−5.10327	−	18.3803i	−0.198795	−	0.715996i	0.795178	−	0.606376i	$-0.207377\pi$
$660$		0			0
$661$	−30.4956	+	6.71259i	−1.18614	+	0.261089i	−0.763864	−	0.645377i	$-0.776700\pi$
$661$	−30.4956	+	6.71259i	−1.18614	+	0.261089i	−0.422277	+	0.906467i	$0.638769\pi$
$662$	−2.41690	+	44.5770i	−0.0939353	+	1.73254i
$663$		0			0
$664$	0.212688	+	0.313691i	0.00825389	+	0.0121736i
$665$	−14.7806	−	37.0964i	−0.573165	−	1.43854i
$666$		0			0
$667$	5.78922	−	3.48326i	0.224160	−	0.134872i
$668$	27.3170	+	9.20418i	1.05693	+	0.356120i
$669$		0			0
$670$	20.1129	+	122.683i	0.777029	+	4.73967i
$671$	5.81053	−	0.631933i	0.224313	−	0.0243955i
$672$		0			0
$673$	6.29442	+	7.41036i	0.242632	+	0.285649i	0.869976	−	0.493094i	$-0.164134\pi$
$673$	6.29442	+	7.41036i	0.242632	+	0.285649i	−0.627344	+	0.778742i	$0.715858\pi$
$674$	−13.5754	−	6.28065i	−0.522905	−	0.241922i
$675$		0			0
$676$	−17.2275	+	20.2818i	−0.662596	+	0.780069i
$677$	−5.30152	+	1.78629i	−0.203754	+	0.0686527i	−0.419328	−	0.907835i	$-0.637734\pi$
$677$	−5.30152	+	1.78629i	−0.203754	+	0.0686527i	0.215574	+	0.976488i	$0.430838\pi$
$678$		0			0
$679$	11.5360	−	21.7593i	0.442712	−	0.835044i
$680$	−27.3769	+	9.22436i	−1.04986	+	0.353738i
$681$		0			0
$682$	−41.6219	+	19.2563i	−1.59378	+	0.737363i
$683$	15.0737	+	6.97382i	0.576778	+	0.266846i	0.686516	−	0.727115i	$-0.259139\pi$
$683$	15.0737	+	6.97382i	0.576778	+	0.266846i	−0.109738	+	0.993961i	$0.535001\pi$
$684$		0			0
$685$	31.8076	+	19.1380i	1.21531	+	0.731225i
$686$	42.5017	−	4.62233i	1.62272	−	0.176482i
$687$		0			0
$688$	−1.24183	+	1.17633i	−0.0473444	+	0.0448470i
$689$	2.13395	+	0.719010i	0.0812968	+	0.0273921i
$690$		0			0
$691$	29.0878	−	22.1120i	1.10655	−	0.841180i	0.118145	−	0.992996i	$-0.462305\pi$
$691$	29.0878	−	22.1120i	1.10655	−	0.841180i	0.988409	+	0.151816i	$0.0485121\pi$
$692$	6.69689	+	16.8079i	0.254578	+	0.638942i
$693$		0			0
$694$	−13.5414	+	82.5992i	−0.514026	+	3.13542i
$695$	0.313764	−	5.78704i	0.0119018	−	0.219515i
$696$		0			0
$697$	11.8683	−	29.7872i	0.449543	−	1.12827i
$698$	−12.4746	−	44.9294i	−0.472170	−	1.70060i
$699$		0			0
$700$	−32.1581	−	3.49740i	−1.21546	−	0.132189i
$701$	11.1921	+	8.50803i	0.422720	+	0.321344i	0.794816	−	0.606851i	$-0.207567\pi$
$701$	11.1921	+	8.50803i	0.422720	+	0.321344i	−0.372095	+	0.928195i	$0.621361\pi$
$702$		0			0
$703$	71.7722	+	15.7983i	2.70694	+	0.595843i
$704$	−17.9730	+	26.5083i	−0.677385	+	0.999067i
$705$		0			0
$706$	−11.3243	−	21.3599i	−0.426197	−	0.803892i
$707$	16.6434			0.625941
$708$		0			0
$709$	8.71519			0.327306			0.163653	−	0.986518i	$-0.447672\pi$
$709$	8.71519			0.327306			0.163653	+	0.986518i	$0.447672\pi$
$710$	23.2562	+	43.8659i	0.872790	+	1.64626i
$711$		0			0
$712$	11.6997	−	17.2558i	0.438465	−	0.646687i
$713$	21.6367	+	4.76260i	0.810301	+	0.178361i
$714$		0			0
$715$	−14.5670	−	11.0736i	−0.544776	−	0.414128i
$716$	−24.2420	−	2.63647i	−0.905965	−	0.0985296i
$717$		0			0
$718$	2.36760	+	8.52731i	0.0883579	+	0.318236i
$719$	1.41106	−	3.54149i	0.0526236	−	0.132075i	−0.900315	−	0.435239i	$-0.856664\pi$
$719$	1.41106	−	3.54149i	0.0526236	−	0.132075i	0.952938	+	0.303164i	$0.0980430\pi$
$720$		0			0
$721$	−0.220489	+	4.06667i	−0.00821143	+	0.151451i
$722$	−12.8712	+	78.5108i	−0.479016	+	2.92187i
$723$		0			0
$724$	16.4768	+	41.3535i	0.612354	+	1.53689i
$725$	−11.5961	+	8.81514i	−0.430669	+	0.327386i
$726$		0			0
$727$	−11.4538	−	3.85923i	−0.424797	−	0.143131i	0.0987796	−	0.995109i	$-0.468506\pi$
$727$	−11.4538	−	3.85923i	−0.424797	−	0.143131i	−0.523577	+	0.851978i	$0.675403\pi$
$728$	−7.85574	+	7.44136i	−0.291153	+	0.275795i
$729$		0			0
$730$	−68.0124	+	7.39680i	−2.51725	+	0.273768i
$731$	−17.8753	−	10.7552i	−0.661142	−	0.397796i
$732$		0			0
$733$	38.8273	+	17.9634i	1.43412	+	0.663495i	0.974452	−	0.224596i	$-0.0721063\pi$
$733$	38.8273	+	17.9634i	1.43412	+	0.663495i	0.459668	+	0.888091i	$0.347968\pi$
$734$	38.1993	−	17.6729i	1.40996	−	0.652318i
$735$		0			0
$736$	14.1114	−	4.75469i	0.520154	−	0.175260i
$737$	19.0573	−	35.9459i	0.701984	−	1.32408i
$738$		0			0
$739$	−39.8067	+	13.4125i	−1.46431	+	0.493385i	−0.934879	−	0.354965i	$-0.884493\pi$
$739$	−39.8067	+	13.4125i	−1.46431	+	0.493385i	−0.529435	+	0.848350i	$0.677596\pi$
$740$	70.8089	−	83.3627i	2.60299	−	3.06447i
$741$		0			0
$742$	−3.49312	−	1.61609i	−0.128236	−	0.0593285i
$743$	9.99369	+	11.7655i	0.366633	+	0.431634i	0.914284	−	0.405073i	$-0.132754\pi$
$743$	9.99369	+	11.7655i	0.366633	+	0.431634i	−0.547651	+	0.836707i	$0.684478\pi$
$744$		0			0
$745$	29.5497	−	3.21372i	1.08262	−	0.117742i
$746$	−2.56138	−	15.6237i	−0.0937788	−	0.572025i
$747$		0			0
$748$	22.8567	+	7.70133i	0.835725	+	0.281588i
$749$	−17.3144	+	10.4177i	−0.632654	+	0.380655i
$750$		0			0
$751$	7.17407	+	18.0056i	0.261785	+	0.657032i	0.999843	−	0.0177055i	$-0.00563614\pi$
$751$	7.17407	+	18.0056i	0.261785	+	0.657032i	−0.738058	+	0.674738i	$0.764257\pi$
$752$	0.925523	+	1.36504i	0.0337503	+	0.0497780i
$753$		0			0
$754$	−0.672986	+	12.4125i	−0.0245087	+	0.452037i
$755$	−52.4685	+	11.5492i	−1.90952	+	0.420318i
$756$		0			0
$757$	5.06755	+	18.2517i	0.184183	+	0.663368i	0.996754	+	0.0805054i	$0.0256534\pi$
$757$	5.06755	+	18.2517i	0.184183	+	0.663368i	−0.812571	+	0.582862i	$0.801933\pi$
$758$	0.455205	+	8.39576i	0.0165338	+	0.304948i
$759$		0			0
$760$	57.2438	+	43.5156i	2.07645	+	1.57848i
$761$	−10.1850	+	36.6829i	−0.369205	+	1.32976i	0.512797	+	0.858510i	$0.328609\pi$
$761$	−10.1850	+	36.6829i	−0.369205	+	1.32976i	−0.882002	+	0.471245i	$0.843805\pi$
$762$		0			0
$763$	−14.5424	+	21.4485i	−0.526471	+	0.776487i
$764$	14.9913	+	14.2005i	0.542365	+	0.513756i
$765$		0			0
$766$	−33.6608			−1.21622
$767$	16.9490	+	1.55656i	0.611992	+	0.0562043i
$768$		0			0
$769$	−25.3965	−	47.9029i	−0.915822	−	1.72742i	−0.643909	−	0.765102i	$-0.722689\pi$
$769$	−25.3965	−	47.9029i	−0.915822	−	1.72742i	−0.271913	−	0.962322i	$-0.587656\pi$
$770$	22.7059	+	21.5081i	0.818262	+	0.775099i
$771$		0			0
$772$	−24.0475	−	5.29324i	−0.865487	−	0.190508i
$773$	−8.57083	+	30.8693i	−0.308271	+	1.11029i	0.633418	+	0.773810i	$0.281651\pi$
$773$	−8.57083	+	30.8693i	−0.308271	+	1.11029i	−0.941689	+	0.336483i	$0.890762\pi$
$774$		0			0
$775$	−47.4842	−	5.16422i	−1.70568	−	0.185504i
$776$	2.40093	+	44.2825i	0.0861883	+	1.58965i
$777$		0			0
$778$	19.1127	−	47.9693i	0.685224	−	1.71978i
$779$	−77.9435	+	17.1567i	−2.79261	+	0.614701i
$780$		0			0
$781$	2.62867	−	16.0342i	0.0940613	−	0.573748i
$782$	−10.5146	−	15.5078i	−0.376000	−	0.554558i
$783$		0			0
$784$	−0.823259	+	0.625825i	−0.0294021	+	0.0223509i
$785$	−53.7609	+	32.3469i	−1.91881	+	1.15451i
$786$		0			0
$787$	−6.37008	+	6.03406i	−0.227069	+	0.215091i	−0.792773	−	0.609517i	$-0.791363\pi$
$787$	−6.37008	+	6.03406i	−0.227069	+	0.215091i	0.565704	+	0.824609i	$0.308605\pi$
$788$	10.2396	+	62.4587i	0.364770	+	2.22500i
$789$		0			0
$790$	82.9471	+	49.9076i	2.95112	+	1.77563i
$791$	5.56827	+	6.55547i	0.197985	+	0.233086i
$792$		0			0
$793$	4.71480	−	2.18130i	0.167428	−	0.0774602i
$794$	−38.1339	+	44.8947i	−1.35332	+	1.59325i
$795$		0			0
$796$	19.4458	−	36.6787i	0.689239	−	1.30004i
$797$	−11.4172	+	21.5350i	−0.404417	+	0.762811i	−0.999155	−	0.0411089i	$-0.986911\pi$
$797$	−11.4172	+	21.5350i	−0.404417	+	0.762811i	0.594738	+	0.803920i	$0.297256\pi$
$798$		0			0
$799$	−13.0214	+	15.3300i	−0.460666	+	0.542338i
$800$	−29.1368	+	13.4801i	−1.03014	+	0.476593i
$801$		0			0
$802$	32.8878	+	38.7185i	1.16131	+	1.36720i
$803$	19.1841	+	11.5427i	0.676993	+	0.407333i
$804$		0			0
$805$	−2.44434	−	14.9098i	−0.0861515	−	0.525501i
$806$	−29.5927	+	28.0317i	−1.04236	+	0.987374i
$807$		0			0
$808$	−25.6797	+	15.4510i	−0.903408	+	0.543563i
$809$	−26.4405	+	20.0995i	−0.929597	+	0.706661i	−0.956116	−	0.292987i	$-0.905351\pi$
$809$	−26.4405	+	20.0995i	−0.929597	+	0.706661i	0.0265194	+	0.999648i	$0.491558\pi$
$810$		0			0
$811$	−3.35793	−	4.95258i	−0.117913	−	0.173909i	0.764152	−	0.645036i	$-0.223158\pi$
$811$	−3.35793	−	4.95258i	−0.117913	−	0.173909i	−0.882065	+	0.471127i	$0.843847\pi$
$812$	2.13763	−	13.0390i	0.0750160	−	0.457578i
$813$		0			0
$814$	−56.2126	+	12.3733i	−1.97025	+	0.433685i
$815$	−5.67146	+	14.2343i	−0.198663	+	0.498606i
$816$		0			0
$817$	2.81115	+	51.8487i	0.0983498	+	1.81395i
$818$	−0.357968	−	0.0389314i	−0.0125161	−	0.00136121i
$819$		0			0
$820$	−31.7773	+	114.452i	−1.10971	+	3.99682i
$821$	−10.4010	−	2.28944i	−0.362998	−	0.0799018i	0.0297266	−	0.999558i	$-0.490536\pi$
$821$	−10.4010	−	2.28944i	−0.362998	−	0.0799018i	−0.392724	+	0.919656i	$0.628467\pi$
$822$		0			0
$823$	6.26048	+	5.93024i	0.218227	+	0.206715i	0.789001	−	0.614391i	$-0.210598\pi$
$823$	6.26048	+	5.93024i	0.218227	+	0.206715i	−0.570775	+	0.821107i	$0.693357\pi$
$824$	−3.43510	−	6.47929i	−0.119667	−	0.225717i
$825$		0			0
$826$	−28.5120	−	5.77706i	−0.992059	−	0.201010i
$827$	34.9004			1.21361			0.606803	−	0.794852i	$-0.292452\pi$
$827$	34.9004			1.21361			0.606803	+	0.794852i	$0.292452\pi$
$828$		0			0
$829$	−36.9188	−	34.9713i	−1.28224	−	1.21461i	−0.963789	−	0.266667i	$-0.914078\pi$
$829$	−36.9188	−	34.9713i	−1.28224	−	1.21461i	−0.318454	−	0.947938i	$-0.603164\pi$
$830$	0.546393	−	0.805869i	0.0189656	−	0.0279721i
$831$		0			0
$832$	−7.61545	+	27.4284i	−0.264018	+	0.950908i
$833$	−10.0404	−	7.63254i	−0.347881	−	0.264452i
$834$		0			0
$835$	−1.57151	−	28.9849i	−0.0543845	−	1.00306i
$836$	−16.0607	−	57.8454i	−0.555470	−	2.00062i
$837$		0			0
$838$	−16.4736	+	3.62611i	−0.569071	+	0.125262i
$839$	1.78615	−	32.9436i	0.0616648	−	1.13734i	−0.789950	−	0.613171i	$-0.789894\pi$
$839$	1.78615	−	32.9436i	0.0616648	−	1.13734i	0.851615	−	0.524168i	$-0.175624\pi$
$840$		0			0
$841$	12.9354	+	19.0783i	0.446049	+	0.657874i
$842$	−20.7504	−	52.0795i	−0.715105	−	1.79478i
$843$		0			0
$844$	33.4332	−	20.1161i	1.15082	−	0.692425i
$845$	25.3941	+	8.55628i	0.873585	+	0.294345i
$846$		0			0
$847$	1.27475	+	7.77565i	0.0438010	+	0.267174i
$848$	0.243639	−	0.0264973i	0.00836660	−	0.000909922i
$849$		0			0
$850$	26.1507	+	30.7870i	0.896963	+	1.05599i
$851$	25.2358	+	11.6753i	0.865073	+	0.400225i
$852$		0			0
$853$	−27.5141	+	32.3922i	−0.942067	+	1.10909i	0.0518174	+	0.998657i	$0.483499\pi$
$853$	−27.5141	+	32.3922i	−0.942067	+	1.10909i	−0.993884	+	0.110430i	$0.964777\pi$
$854$	−8.41448	+	2.83517i	−0.287938	+	0.0970175i
$855$		0			0
$856$	17.0436	−	32.1477i	0.582539	−	1.09878i
$857$	12.1521	−	4.09453i	0.415109	−	0.139867i	−0.103995	−	0.994578i	$-0.533162\pi$
$857$	12.1521	−	4.09453i	0.415109	−	0.139867i	0.519104	+	0.854711i	$0.326266\pi$
$858$		0			0
$859$	−52.6781	+	24.3715i	−1.79735	+	0.831545i	−0.840024	+	0.542550i	$0.817459\pi$
$859$	−52.6781	+	24.3715i	−1.79735	+	0.831545i	−0.957331	+	0.288995i	$0.906679\pi$
$860$	70.1377	+	32.4491i	2.39167	+	1.10651i
$861$		0			0
$862$	−42.3066	−	25.4551i	−1.44097	−	0.867003i
$863$	15.3001	−	1.66398i	0.520820	−	0.0566426i	0.156066	−	0.987747i	$-0.450119\pi$
$863$	15.3001	−	1.66398i	0.520820	−	0.0566426i	0.364754	+	0.931104i	$0.381153\pi$
$864$		0			0
$865$	13.2272	−	12.5295i	0.449739	−	0.426015i
$866$	−15.8213	−	5.33081i	−0.537629	−	0.181148i
$867$		0			0
$868$	34.4921	−	26.2202i	1.17074	−	0.889972i
$869$	−11.7260	−	29.4299i	−0.397776	−	0.998342i
$870$		0			0
$871$	5.85031	−	35.6853i	0.198230	−	1.20915i
$872$	2.52625	−	46.5940i	0.0855497	−	1.57787i
$873$		0			0
$874$	−17.2614	+	43.3229i	−0.583877	+	1.46542i
$875$	1.41794	+	5.10695i	0.0479350	+	0.172646i
$876$		0			0
$877$	3.59352	+	0.390819i	0.121345	+	0.0131970i	0.168590	−	0.985686i	$-0.446079\pi$
$877$	3.59352	+	0.390819i	0.121345	+	0.0131970i	−0.0472451	+	0.998883i	$0.515044\pi$
$878$	16.4361	+	12.4944i	0.554691	+	0.421665i
$879$		0			0
$880$	−1.94491	−	0.428107i	−0.0655628	−	0.0144315i
$881$	27.2385	−	40.1737i	0.917687	−	1.35349i	−0.0176927	−	0.999843i	$-0.505632\pi$
$881$	27.2385	−	40.1737i	0.917687	−	1.35349i	0.935380	−	0.353644i	$-0.115058\pi$
$882$		0			0
$883$	−24.7023	−	46.5936i	−0.831300	−	1.56800i	−0.823006	−	0.568032i	$-0.807705\pi$
$883$	−24.7023	−	46.5936i	−0.831300	−	1.56800i	−0.00829384	−	0.999966i	$-0.502640\pi$
$884$	21.4376			0.721025
$885$		0			0
$886$	−4.92989			−0.165623
$887$	−13.8667	−	26.1553i	−0.465597	−	0.878209i	−0.999467	−	0.0326425i	$-0.989608\pi$
$887$	−13.8667	−	26.1553i	−0.465597	−	0.878209i	0.533870	−	0.845566i	$-0.320737\pi$
$888$		0			0
$889$	3.37487	−	4.97755i	0.113189	−	0.166942i
$890$	−52.3065	−	11.5135i	−1.75332	−	0.385934i
$891$		0			0
$892$	17.3397	+	13.1813i	0.580575	+	0.441341i
$893$	49.7705	+	5.41287i	1.66551	+	0.181135i
$894$		0			0
$895$	6.56925	+	23.6603i	0.219586	+	0.790877i
$896$	11.4551	−	28.7501i	0.382687	−	0.960472i
$897$		0			0
$898$	−1.93569	+	35.7017i	−0.0645949	+	1.19138i
$899$	3.15640	−	19.2532i	0.105272	−	0.642130i
$900$		0			0
$901$	1.10632	+	2.77665i	0.0368568	+	0.0925036i
$902$	49.7617	−	37.8278i	1.65688	−	1.25953i
$903$		0			0
$904$	−14.6772	−	4.94534i	−0.488158	−	0.164479i
$905$	32.5437	−	30.8270i	1.08179	−	1.02472i
$906$		0			0
$907$	1.42208	−	0.154660i	0.0472192	−	0.00513540i	−0.0844789	−	0.996425i	$-0.526923\pi$
$907$	1.42208	−	0.154660i	0.0472192	−	0.00513540i	0.131698	+	0.991290i	$0.457957\pi$
$908$	−13.9182	−	8.37429i	−0.461891	−	0.277911i
$909$		0			0
$910$	25.2289	+	11.6721i	0.836331	+	0.386928i
$911$	−39.2332	+	18.1512i	−1.29985	+	0.601376i	−0.943003	−	0.332785i	$-0.892012\pi$
$911$	−39.2332	+	18.1512i	−1.29985	+	0.601376i	−0.356851	+	0.934161i	$0.616150\pi$
$912$		0			0
$913$	−0.301953	+	0.101740i	−0.00999317	+	0.00336709i
$914$	9.23967	−	17.4279i	0.305621	−	0.576463i
$915$		0			0
$916$	−2.87041	+	0.967154i	−0.0948411	+	0.0319557i
$917$	−11.0568	+	13.0171i	−0.365128	+	0.429861i
$918$		0			0
$919$	−30.3345	−	14.0342i	−1.00064	−	0.462947i	−0.149998	−	0.988686i	$-0.547927\pi$
$919$	−30.3345	−	14.0342i	−1.00064	−	0.462947i	−0.850646	+	0.525739i	$0.823789\pi$
$920$	17.6130	+	20.7356i	0.580682	+	0.683632i
$921$		0			0
$922$	69.6371	−	7.57349i	2.29338	−	0.249420i
$923$	−2.33641	−	14.2514i	−0.0769037	−	0.469092i
$924$		0			0
$925$	−56.8095	−	19.1414i	−1.86789	−	0.629364i
$926$	−68.1765	+	41.0204i	−2.24042	+	1.34802i
$927$		0			0
$928$	−4.85379	−	12.1821i	−0.159334	−	0.399897i
$929$	−8.94476	−	13.1925i	−0.293468	−	0.432833i	0.652161	−	0.758081i	$-0.273863\pi$
$929$	−8.94476	−	13.1925i	−0.293468	−	0.432833i	−0.945629	+	0.325248i	$0.894552\pi$
$930$		0			0
$931$	−1.69953	+	31.3459i	−0.0556997	+	1.02732i
$932$	10.4366	−	2.29727i	0.341862	−	0.0752495i
$933$		0			0
$934$	12.6835	+	45.6817i	0.415016	+	1.49475i
$935$	−1.31492	−	24.2523i	−0.0430025	−	0.793134i
$936$		0			0
$937$	−21.5854	−	16.4088i	−0.705164	−	0.536052i	0.190003	−	0.981784i	$-0.439150\pi$
$937$	−21.5854	−	16.4088i	−0.705164	−	0.536052i	−0.895167	+	0.445732i	$0.852943\pi$
$938$	−16.5354	+	59.5552i	−0.539901	+	1.94455i
$939$		0			0
$940$	41.8145	−	61.6718i	1.36384	−	2.01151i
$941$	−7.85497	−	7.44062i	−0.256065	−	0.242557i	0.548889	−	0.835895i	$-0.315051\pi$
$941$	−7.85497	−	7.44062i	−0.256065	−	0.242557i	−0.804953	+	0.593338i	$0.797810\pi$
$942$		0			0
$943$	−30.1966			−0.983336
$944$	1.74528	−	0.620791i	0.0568039	−	0.0202050i
$945$		0			0
$946$	−19.0492	−	35.9306i	−0.619343	−	1.16821i
$947$	−5.21649	−	4.94132i	−0.169513	−	0.160571i	0.598240	−	0.801317i	$-0.295867\pi$
$947$	−5.21649	−	4.94132i	−0.169513	−	0.160571i	−0.767753	+	0.640745i	$0.778625\pi$
$948$		0			0
$949$	19.4344	+	4.27783i	0.630867	+	0.138864i
$950$	26.8980	−	96.8779i	0.872686	−	3.14313i
$951$		0			0
$952$	−14.2785	−	1.55288i	−0.462769	−	0.0503292i
$953$	3.04200	+	56.1063i	0.0985400	+	1.81746i	0.463125	+	0.886293i	$0.346728\pi$
$953$	3.04200	+	56.1063i	0.0985400	+	1.81746i	−0.364585	+	0.931170i	$0.618789\pi$
$954$		0			0
$955$	7.69650	−	19.3168i	0.249053	−	0.625076i
$956$	52.7858	−	11.6190i	1.70721	−	0.375786i
$957$		0			0
$958$	−9.05648	+	55.2421i	−0.292602	+	1.78479i
$959$	10.3569	+	15.2753i	0.334442	+	0.493266i
$960$		0			0
$961$	26.2518	−	19.9561i	0.846832	−	0.643745i
$962$	−43.8357	+	26.3751i	−1.41332	+	0.850367i
$963$		0			0
$964$	−9.20092	+	8.71557i	−0.296342	+	0.280710i
$965$	4.01142	+	24.4686i	0.129132	+	0.787672i
$966$		0			0
$967$	−9.97401	−	6.00116i	−0.320742	−	0.192984i	0.346072	−	0.938208i	$-0.387515\pi$
$967$	−9.97401	−	6.00116i	−0.320742	−	0.192984i	−0.666815	+	0.745224i	$0.732343\pi$
$968$	−9.18539	−	10.8139i	−0.295229	−	0.347571i
$969$		0			0
$970$	103.399	−	47.8373i	3.31993	−	1.53596i
$971$	−11.3655	+	13.3805i	−0.364737	+	0.429402i	−0.913665	−	0.406468i	$-0.866760\pi$
$971$	−11.3655	+	13.3805i	−0.364737	+	0.429402i	0.548928	+	0.835870i	$0.315036\pi$
$972$		0			0
$973$	1.34964	−	2.54570i	0.0432676	−	0.0816114i
$974$	31.7202	−	59.8307i	1.01638	−	1.91710i
$975$		0			0
$976$	0.366025	−	0.430918i	0.0117162	−	0.0137933i
$977$	−29.7631	+	13.7699i	−0.952205	+	0.440537i	−0.833578	−	0.552402i	$-0.813711\pi$
$977$	−29.7631	+	13.7699i	−0.952205	+	0.440537i	−0.118627	+	0.992939i	$0.537849\pi$
$978$		0			0
$979$	11.3471	+	13.3588i	0.362655	+	0.426950i
$980$	40.0332	+	24.0872i	1.27881	+	0.769437i
$981$		0			0
$982$	−3.13173	−	19.1027i	−0.0999377	−	0.609593i
$983$	30.6059	−	28.9915i	0.976178	−	0.924685i	−0.0209983	−	0.999780i	$-0.506684\pi$
$983$	30.6059	−	28.9915i	0.976178	−	0.924685i	0.997176	+	0.0750944i	$0.0239258\pi$
$984$		0			0
$985$	54.6117	−	32.8588i	1.74007	−	1.04697i
$986$	−13.1354	+	9.98527i	−0.418316	+	0.317996i
$987$		0			0
$988$	−29.9443	−	44.1645i	−0.952655	−	1.40506i
$989$	−3.17840	+	19.3874i	−0.101067	+	0.616484i
$990$		0			0
$991$	23.1509	−	5.09590i	0.735413	−	0.161877i	0.168555	−	0.985692i	$-0.446090\pi$
$991$	23.1509	−	5.09590i	0.735413	−	0.161877i	0.566858	+	0.823816i	$0.308159\pi$
$992$	15.9160	−	39.9462i	0.505335	−	1.26829i
$993$		0			0
$994$	1.33636	+	24.6478i	0.0423869	+	0.781780i
$995$	−41.5598	−	4.51990i	−1.31753	−	0.143290i
$996$		0			0
$997$	9.03220	−	32.5311i	0.286053	−	1.03027i	−0.671262	−	0.741220i	$-0.734247\pi$
$997$	9.03220	−	32.5311i	0.286053	−	1.03027i	0.957314	−	0.289049i	$-0.0933389\pi$
$998$	−62.8263	−	13.8291i	−1.98873	−	0.437753i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.c.28.5		140
3.2	odd	2		177.2.e.a.28.1	yes	140
59.19	even	29	inner	531.2.i.c.19.5		140
177.137	odd	58		177.2.e.a.19.1	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.a.19.1	✓	140	177.137	odd	58
177.2.e.a.28.1	yes	140	3.2	odd	2
531.2.i.c.19.5		140	59.19	even	29	inner
531.2.i.c.28.5		140	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07727 + 2.03195i) q^{2} +(-1.84595 + 2.72257i) q^{4} +(3.23491 + 0.712057i) q^{5} +(1.31099 + 0.996592i) q^{7} +(-2.94796 - 0.320610i) q^{8} +O(q^{10})\)	\(q+(1.07727 + 2.03195i) q^{2} +(-1.84595 + 2.72257i) q^{4} +(3.23491 + 0.712057i) q^{5} +(1.31099 + 0.996592i) q^{7} +(-2.94796 - 0.320610i) q^{8} +(2.03802 + 7.34027i) q^{10} +(0.922770 - 2.31598i) q^{11} +(0.119964 - 2.21261i) q^{13} +(-0.612729 + 3.73748i) q^{14} +(-0.0892630 - 0.224033i) q^{16} +(2.34147 - 1.77994i) q^{17} +(-6.93750 - 2.33752i) q^{19} +(-7.91009 + 7.49283i) q^{20} +(5.70004 - 0.619916i) q^{22} +(-2.37337 - 1.42801i) q^{23} +(5.41973 + 2.50743i) q^{25} +(4.62515 - 2.13982i) q^{26} +(-5.13331 + 1.72961i) q^{28} +(-1.14256 + 2.15509i) q^{29} +(-7.57979 + 2.55393i) q^{31} +(-3.48038 + 4.09742i) q^{32} +(6.13915 + 2.84027i) q^{34} +(3.53132 + 4.15739i) q^{35} +(-9.97984 + 1.08537i) q^{37} +(-2.72386 - 16.6148i) q^{38} +(-9.30809 - 3.13626i) q^{40} +(9.34133 - 5.62049i) q^{41} +(-2.62534 - 6.58910i) q^{43} +(4.60202 + 6.78747i) q^{44} +(0.344881 - 6.36095i) q^{46} +(-6.67879 + 1.47011i) q^{47} +(-1.14719 - 4.13180i) q^{49} +(0.743543 + 13.7138i) q^{50} +(5.80252 + 4.41096i) q^{52} +(-0.271871 + 0.979189i) q^{53} +(4.63418 - 6.83491i) q^{55} +(-3.54524 - 3.35823i) q^{56} -5.60990 q^{58} +(-0.287330 + 7.67577i) q^{59} +(1.09816 + 2.07134i) q^{61} +(-13.3550 - 12.6505i) q^{62} +(-12.5461 - 2.76162i) q^{64} +(1.96357 - 7.07216i) q^{65} +(16.2238 + 1.76445i) q^{67} +(0.523775 + 9.66046i) q^{68} +(-4.64343 + 11.6541i) q^{70} +(6.36506 - 1.40106i) q^{71} +(-1.45289 + 8.86226i) q^{73} +(-12.9564 - 19.1093i) q^{74} +(19.1703 - 14.5729i) q^{76} +(3.51783 - 2.11661i) q^{77} +(9.22548 - 8.73884i) q^{79} +(-0.129233 - 0.788288i) q^{80} +(21.4838 + 12.9263i) q^{82} +(-0.0827415 - 0.0974108i) q^{83} +(8.84184 - 4.09067i) q^{85} +(10.5605 - 12.4328i) q^{86} +(-3.46281 + 6.53156i) q^{88} +(-3.29319 + 6.21161i) q^{89} +(2.36234 - 2.78116i) q^{91} +(8.26897 - 3.82564i) q^{92} +(-10.1821 - 11.9873i) q^{94} +(-20.7777 - 12.5016i) q^{95} +(-2.41950 - 14.7583i) q^{97} +(7.15979 - 6.78211i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8}+O(q^{10}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8	\( 140 q + q^{2} - 9 q^{4} + 2 q^{5} - 2 q^{7} + 9 q^{8} + 88 q^{10} + 14 q^{11} - 12 q^{13} + q^{14} - 41 q^{16} + 16 q^{17} - 10 q^{19} + 32 q^{20} - 26 q^{22} + 22 q^{23} + 27 q^{25} + 56 q^{26} - 50 q^{28} + 24 q^{29} - 24 q^{31} - 106 q^{32} - 54 q^{34} + 70 q^{35} - 28 q^{37} + 80 q^{38} - 50 q^{40} + 40 q^{41} + 4 q^{43} + 104 q^{44} - 28 q^{46} - 31 q^{47} - q^{49} - 39 q^{50} + 62 q^{52} - 4 q^{53} + 5 q^{55} - 96 q^{56} + 128 q^{58} + q^{59} - 16 q^{61} - 223 q^{62} + 97 q^{64} - 121 q^{65} - 12 q^{67} - 10 q^{68} - 2 q^{70} + 22 q^{71} + 179 q^{73} + 38 q^{74} + 112 q^{76} + 62 q^{77} - 84 q^{79} - 204 q^{80} - 152 q^{82} + 88 q^{83} - 118 q^{85} + 118 q^{86} + 18 q^{88} + 86 q^{89} + 78 q^{91} + 174 q^{92} - 164 q^{94} - 218 q^{95} - 84 q^{97} - 129 q^{98}+O(q^{100}) \) 140 * q + q^2 - 9 * q^4 + 2 * q^5 - 2 * q^7 + 9 * q^8 + 88 * q^10 + 14 * q^11 - 12 * q^13 + q^14 - 41 * q^16 + 16 * q^17 - 10 * q^19 + 32 * q^20 - 26 * q^22 + 22 * q^23 + 27 * q^25 + 56 * q^26 - 50 * q^28 + 24 * q^29 - 24 * q^31 - 106 * q^32 - 54 * q^34 + 70 * q^35 - 28 * q^37 + 80 * q^38 - 50 * q^40 + 40 * q^41 + 4 * q^43 + 104 * q^44 - 28 * q^46 - 31 * q^47 - q^49 - 39 * q^50 + 62 * q^52 - 4 * q^53 + 5 * q^55 - 96 * q^56 + 128 * q^58 + q^59 - 16 * q^61 - 223 * q^62 + 97 * q^64 - 121 * q^65 - 12 * q^67 - 10 * q^68 - 2 * q^70 + 22 * q^71 + 179 * q^73 + 38 * q^74 + 112 * q^76 + 62 * q^77 - 84 * q^79 - 204 * q^80 - 152 * q^82 + 88 * q^83 - 118 * q^85 + 118 * q^86 + 18 * q^88 + 86 * q^89 + 78 * q^91 + 174 * q^92 - 164 * q^94 - 218 * q^95 - 84 * q^97 - 129 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more