LMFDB - Embedded newform 891.2.k.a.404.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(161,891)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("891.161"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.k (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			404.20
Character	$\chi$	$=$	891.404
Dual form			891.2.k.a.161.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.17940 - 1.58343i) q^{2} +(1.62452 - 4.99975i) q^{4} +(0.850459 - 1.17056i) q^{5} +(1.37298 + 0.446107i) q^{7} +(-2.71136 - 8.34470i) q^{8} -3.89775i q^{10} +(-0.371076 + 3.29580i) q^{11} +(-1.74976 - 2.40833i) q^{13} +(3.69865 - 1.20176i) q^{14} +(-10.6163 - 7.71319i) q^{16} +(3.35854 + 2.44012i) q^{17} +(-1.19136 + 0.387096i) q^{19} +(-4.47090 - 6.15367i) q^{20} +(4.40994 + 7.77045i) q^{22} -5.80743i q^{23} +(0.898164 + 2.76426i) q^{25} +(-7.62685 - 2.47811i) q^{26} +(4.46085 - 6.13983i) q^{28} +(0.0300853 - 0.0925930i) q^{29} +(-3.30738 + 2.40295i) q^{31} -17.8022 q^{32} +11.1834 q^{34} +(1.68985 - 1.22775i) q^{35} +(-3.08635 + 9.49880i) q^{37} +(-1.98351 + 2.73007i) q^{38} +(-12.0738 - 3.92303i) q^{40} +(1.41240 + 4.34693i) q^{41} +2.12626i q^{43} +(15.8754 + 7.20937i) q^{44} +(-9.19566 - 12.6567i) q^{46} +(6.90361 - 2.24312i) q^{47} +(-3.97707 - 2.88951i) q^{49} +(6.33448 + 4.60227i) q^{50} +(-14.8836 + 4.83597i) q^{52} +(0.197492 + 0.271824i) q^{53} +(3.54233 + 3.23731i) q^{55} -12.6666i q^{56} +(-0.0810465 - 0.249436i) q^{58} +(2.87859 + 0.935310i) q^{59} +(0.187098 - 0.257518i) q^{61} +(-3.40321 + 10.4740i) q^{62} +(-17.5657 + 12.7622i) q^{64} -4.30718 q^{65} +3.43656 q^{67} +(17.6560 - 12.8278i) q^{68} +(1.73882 - 5.35153i) q^{70} +(5.38901 - 7.41734i) q^{71} +(-6.75113 - 2.19358i) q^{73} +(8.31428 + 25.5887i) q^{74} +6.58534i q^{76} +(-1.97976 + 4.35952i) q^{77} +(-5.88983 - 8.10666i) q^{79} +(-18.0574 + 5.86722i) q^{80} +(9.96124 + 7.23727i) q^{82} +(4.82527 + 3.50577i) q^{83} +(5.71260 - 1.85614i) q^{85} +(3.36679 + 4.63399i) q^{86} +(28.5086 - 5.83958i) q^{88} +5.11584i q^{89} +(-1.32800 - 4.08716i) q^{91} +(-29.0357 - 9.43428i) q^{92} +(11.4939 - 15.8200i) q^{94} +(-0.560084 + 1.72376i) q^{95} +(-4.88722 + 3.55077i) q^{97} -13.2430 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) $ 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.17940	−	1.58343i	1.54107	−	1.11965i	0.591412	−	0.806370i	$-0.298571\pi$
$2$	2.17940	−	1.58343i	1.54107	−	1.11965i	0.949660	−	0.313284i	$-0.101429\pi$
$3$		0			0
$3$		0			0
$4$	1.62452	−	4.99975i	0.812259	−	2.49988i
$5$	0.850459	−	1.17056i	0.380337	−	0.523488i	−0.575337	−	0.817916i	$-0.695129\pi$
$5$	0.850459	−	1.17056i	0.380337	−	0.523488i	0.955674	+	0.294428i	$0.0951291\pi$
$6$		0			0
$7$	1.37298	+	0.446107i	0.518936	+	0.168613i	0.556763	−	0.830672i	$-0.312043\pi$
$7$	1.37298	+	0.446107i	0.518936	+	0.168613i	−0.0378262	+	0.999284i	$0.512043\pi$
$8$	−2.71136	−	8.34470i	−0.958610	−	2.95030i
$9$		0			0
$10$		−	3.89775i		−	1.23258i
$11$	−0.371076	+	3.29580i	−0.111883	+	0.993721i
$11$	−0.371076	+	3.29580i	−0.111883	+	0.993721i
$12$		0			0
$13$	−1.74976	−	2.40833i	−0.485295	−	0.667951i	0.494217	−	0.869339i	$-0.335455\pi$
$13$	−1.74976	−	2.40833i	−0.485295	−	0.667951i	−0.979512	+	0.201388i	$0.935455\pi$
$14$	3.69865	−	1.20176i	0.988506	−	0.321185i
$15$		0			0
$16$	−10.6163	−	7.71319i	−2.65408	−	1.92830i
$17$	3.35854	+	2.44012i	0.814566	+	0.591817i	0.915151	−	0.403112i	$-0.132071\pi$
$17$	3.35854	+	2.44012i	0.814566	+	0.591817i	−0.100585	+	0.994928i	$0.532071\pi$
$18$		0			0
$19$	−1.19136	+	0.387096i	−0.273317	+	0.0888059i	−0.442468	−	0.896784i	$-0.645897\pi$
$19$	−1.19136	+	0.387096i	−0.273317	+	0.0888059i	0.169152	+	0.985590i	$0.445897\pi$
$20$	−4.47090	−	6.15367i	−0.999724	−	1.37600i
$21$		0			0
$22$	4.40994	+	7.77045i	0.940203	+	1.65667i
$23$		−	5.80743i		−	1.21093i	−0.795871	−	0.605467i	$-0.792986\pi$
$23$		−	5.80743i		−	1.21093i	0.795871	−	0.605467i	$-0.207014\pi$
$24$		0			0
$25$	0.898164	+	2.76426i	0.179633	+	0.552853i
$26$	−7.62685	−	2.47811i	−1.49575	−	0.485998i
$27$		0			0
$28$	4.46085	−	6.13983i	0.843021	−	1.16032i
$29$	0.0300853	−	0.0925930i	0.00558670	−	0.0171941i	−0.948224	−	0.317601i	$-0.897123\pi$
$29$	0.0300853	−	0.0925930i	0.00558670	−	0.0171941i	0.953811	+	0.300407i	$0.0971226\pi$
$30$		0			0
$31$	−3.30738	+	2.40295i	−0.594023	+	0.431583i	−0.843752	−	0.536733i	$-0.819658\pi$
$31$	−3.30738	+	2.40295i	−0.594023	+	0.431583i	0.249730	+	0.968316i	$0.419658\pi$
$32$	−17.8022			−3.14702
$33$		0			0
$34$	11.1834			1.91793
$35$	1.68985	−	1.22775i	0.285637	−	0.207528i
$36$		0			0
$37$	−3.08635	+	9.49880i	−0.507392	+	1.56159i	0.289319	+	0.957233i	$0.406571\pi$
$37$	−3.08635	+	9.49880i	−0.507392	+	1.56159i	−0.796711	+	0.604360i	$0.793429\pi$
$38$	−1.98351	+	2.73007i	−0.321768	+	0.442876i
$39$		0			0
$40$	−12.0738	−	3.92303i	−1.90904	−	0.620285i
$41$	1.41240	+	4.34693i	0.220580	+	0.678876i	0.998710	+	0.0507726i	$0.0161684\pi$
$41$	1.41240	+	4.34693i	0.220580	+	0.678876i	−0.778130	+	0.628103i	$0.783832\pi$
$42$		0			0
$43$			2.12626i			0.324252i	0.986770	+	0.162126i	$0.0518351\pi$
$43$			2.12626i			0.324252i	−0.986770	+	0.162126i	$0.948165\pi$
$44$	15.8754	+	7.20937i	2.39330	+	1.08685i
$45$		0			0
$46$	−9.19566	−	12.6567i	−1.35583	−	1.86614i
$47$	6.90361	−	2.24312i	1.00700	−	0.327193i	0.241338	−	0.970441i	$-0.422414\pi$
$47$	6.90361	−	2.24312i	1.00700	−	0.327193i	0.765657	+	0.643249i	$0.222414\pi$
$48$		0			0
$49$	−3.97707	−	2.88951i	−0.568152	−	0.412787i
$50$	6.33448	+	4.60227i	0.895831	+	0.650859i
$51$		0			0
$52$	−14.8836	+	4.83597i	−2.06398	+	0.670628i
$53$	0.197492	+	0.271824i	0.0271276	+	0.0373379i	0.822365	−	0.568960i	$-0.192654\pi$
$53$	0.197492	+	0.271824i	0.0271276	+	0.0373379i	−0.795238	+	0.606298i	$0.792654\pi$
$54$		0			0
$55$	3.54233	+	3.23731i	0.477648	+	0.436518i
$56$		−	12.6666i		−	1.69265i
$57$		0			0
$58$	−0.0810465	−	0.249436i	−0.0106419	−	0.0327525i
$59$	2.87859	+	0.935310i	0.374760	+	0.121767i	0.490340	−	0.871531i	$-0.336873\pi$
$59$	2.87859	+	0.935310i	0.374760	+	0.121767i	−0.115580	+	0.993298i	$0.536873\pi$
$60$		0			0
$61$	0.187098	−	0.257518i	0.0239554	−	0.0329718i	−0.796871	−	0.604149i	$-0.793513\pi$
$61$	0.187098	−	0.257518i	0.0239554	−	0.0329718i	0.820827	+	0.571177i	$0.193513\pi$
$62$	−3.40321	+	10.4740i	−0.432208	+	1.33020i
$63$		0			0
$64$	−17.5657	+	12.7622i	−2.19571	+	1.59527i
$65$	−4.30718			−0.534240
$66$		0			0
$67$	3.43656			0.419843			0.209922	−	0.977718i	$-0.432679\pi$
$67$	3.43656			0.419843			0.209922	+	0.977718i	$0.432679\pi$
$68$	17.6560	−	12.8278i	2.14111	−	1.55561i
$69$		0			0
$70$	1.73882	−	5.35153i	0.207828	−	0.639630i
$71$	5.38901	−	7.41734i	0.639558	−	0.880276i	−0.359034	−	0.933325i	$-0.616894\pi$
$71$	5.38901	−	7.41734i	0.639558	−	0.880276i	0.998592	+	0.0530483i	$0.0168937\pi$
$72$		0			0
$73$	−6.75113	−	2.19358i	−0.790160	−	0.256739i	−0.113988	−	0.993482i	$-0.536363\pi$
$73$	−6.75113	−	2.19358i	−0.790160	−	0.256739i	−0.676172	+	0.736743i	$0.736363\pi$
$74$	8.31428	+	25.5887i	0.966516	+	2.97463i
$75$		0			0
$76$			6.58534i			0.755391i
$77$	−1.97976	+	4.35952i	−0.225614	+	0.496813i
$78$		0			0
$79$	−5.88983	−	8.10666i	−0.662658	−	0.912071i	0.336908	−	0.941538i	$-0.390619\pi$
$79$	−5.88983	−	8.10666i	−0.662658	−	0.912071i	−0.999566	+	0.0294671i	$0.990619\pi$
$80$	−18.0574	+	5.86722i	−2.01888	+	0.655975i
$81$		0			0
$82$	9.96124	+	7.23727i	1.10004	+	0.799222i
$83$	4.82527	+	3.50577i	0.529643	+	0.384808i	0.820224	−	0.572042i	$-0.193849\pi$
$83$	4.82527	+	3.50577i	0.529643	+	0.384808i	−0.290581	+	0.956850i	$0.593849\pi$
$84$		0			0
$85$	5.71260	−	1.85614i	0.619619	−	0.201326i
$86$	3.36679	+	4.63399i	0.363050	+	0.499696i
$87$		0			0
$88$	28.5086	−	5.83958i	3.03903	−	0.622501i
$89$			5.11584i			0.542278i	0.962540	+	0.271139i	$0.0874004\pi$
$89$			5.11584i			0.542278i	−0.962540	+	0.271139i	$0.912600\pi$
$90$		0			0
$91$	−1.32800	−	4.08716i	−0.139212	−	0.428451i
$92$	−29.0357	−	9.43428i	−3.02718	−	0.983592i
$93$		0			0
$94$	11.4939	−	15.8200i	1.18551	−	1.63171i
$95$	−0.560084	+	1.72376i	−0.0574634	+	0.176854i
$96$		0			0
$97$	−4.88722	+	3.55077i	−0.496222	+	0.360526i	−0.807572	−	0.589769i	$-0.799219\pi$
$97$	−4.88722	+	3.55077i	−0.496222	+	0.360526i	0.311350	+	0.950295i	$0.399219\pi$
$98$	−13.2430			−1.33774
$99$		0			0
$100$	15.2797			1.52797
$101$	9.41885	−	6.84320i	0.937211	−	0.680923i	−0.0105370	−	0.999944i	$-0.503354\pi$
$101$	9.41885	−	6.84320i	0.937211	−	0.680923i	0.947748	+	0.319021i	$0.103354\pi$
$102$		0			0
$103$	−1.03517	+	3.18593i	−0.101999	+	0.313919i	−0.989014	−	0.147820i	$-0.952774\pi$
$103$	−1.03517	+	3.18593i	−0.101999	+	0.313919i	0.887016	+	0.461739i	$0.152774\pi$
$104$	−15.3526	+	21.1310i	−1.50545	+	2.07207i
$105$		0			0
$106$	0.860829	+	0.279700i	0.0836111	+	0.0271669i
$107$	2.92166	+	8.99195i	0.282448	+	0.869285i	0.987152	+	0.159784i	$0.0510797\pi$
$107$	2.92166	+	8.99195i	0.282448	+	0.869285i	−0.704704	+	0.709501i	$0.748920\pi$
$108$		0			0
$109$		−	4.11325i		−	0.393978i	−0.980406	−	0.196989i	$-0.936884\pi$
$109$		−	4.11325i		−	0.393978i	0.980406	−	0.196989i	$-0.0631163\pi$
$110$	12.8462	+	1.44636i	1.22484	+	0.137905i
$111$		0			0
$112$	−11.1350	−	15.3260i	−1.05216	−	1.44818i
$113$	−19.2327	+	6.24909i	−1.80926	+	0.587864i	−0.809261	+	0.587449i	$0.800132\pi$
$113$	−19.2327	+	6.24909i	−1.80926	+	0.587864i	−1.00000		0.000415145i	$0.999868\pi$
$114$		0			0
$115$	−6.79793	−	4.93898i	−0.633910	−	0.460562i
$116$	−0.414068	−	0.300838i	−0.0384452	−	0.0279321i
$117$		0			0
$118$	7.75460	−	2.51962i	0.713869	−	0.231950i
$119$	3.52264	+	4.84850i	0.322920	+	0.444461i
$120$		0			0
$121$	−10.7246	−	2.44598i	−0.974964	−	0.222362i
$122$		−	0.857491i		−	0.0776336i
$123$		0			0
$124$	6.64126	+	20.4397i	0.596403	+	1.83554i
$125$	10.8799	+	3.53510i	0.973131	+	0.316189i
$126$		0			0
$127$	−0.0604870	+	0.0832533i	−0.00536736	+	0.00738753i	−0.811692	−	0.584085i	$-0.801453\pi$
$127$	−0.0604870	+	0.0832533i	−0.00536736	+	0.00738753i	0.806325	+	0.591473i	$0.201453\pi$
$128$	−7.07223	+	21.7661i	−0.625103	+	1.92387i
$129$		0			0
$130$	−9.38709	+	6.82012i	−0.823302	+	0.598164i
$131$	15.3653			1.34248			0.671238	−	0.741242i	$-0.265763\pi$
$131$	15.3653			1.34248			0.671238	+	0.741242i	$0.265763\pi$
$132$		0			0
$133$	−1.80839			−0.156808
$134$	7.48966	−	5.44156i	0.647008	−	0.470079i
$135$		0			0
$136$	11.2559	−	34.6421i	0.965185	−	2.97053i
$137$	2.18861	−	3.01236i	0.186986	−	0.257364i	−0.705225	−	0.708984i	$-0.749154\pi$
$137$	2.18861	−	3.01236i	0.186986	−	0.257364i	0.892210	+	0.451620i	$0.149154\pi$
$138$		0			0
$139$	16.1833	+	5.25827i	1.37265	+	0.446001i	0.900246	−	0.435381i	$-0.143386\pi$
$139$	16.1833	+	5.25827i	1.37265	+	0.446001i	0.472404	+	0.881382i	$0.343386\pi$
$140$	−3.39325	−	10.4433i	−0.286782	−	0.882624i
$141$		0			0
$142$		−	24.6985i		−	2.07265i
$143$	8.58668	−	4.87317i	0.718054	−	0.407515i
$144$		0			0
$145$	−0.0827990	−	0.113963i	−0.00687608	−	0.00946412i
$146$	−18.1868	+	5.90925i	−1.50515	+	0.489053i
$147$		0			0
$148$	42.4778	+	30.8619i	3.49166	+	2.53684i
$149$	9.26481	+	6.73128i	0.759003	+	0.551448i	0.898604	−	0.438760i	$-0.144582\pi$
$149$	9.26481	+	6.73128i	0.759003	+	0.551448i	−0.139601	+	0.990208i	$0.544582\pi$
$150$		0			0
$151$	1.01097	−	0.328485i	0.0822718	−	0.0267317i	−0.267592	−	0.963532i	$-0.586228\pi$
$151$	1.01097	−	0.328485i	0.0822718	−	0.0267317i	0.349864	+	0.936801i	$0.386228\pi$
$152$	6.46040	+	8.89198i	0.524008	+	0.721235i
$153$		0			0
$154$	2.58830	+	12.6360i	0.208571	+	1.01823i
$155$			5.91508i			0.475111i
$156$		0			0
$157$	−0.0263869	−	0.0812104i	−0.00210590	−	0.00648129i	0.949998	−	0.312256i	$-0.101085\pi$
$157$	−0.0263869	−	0.0812104i	−0.00210590	−	0.00648129i	−0.952104	+	0.305775i	$0.901085\pi$
$158$	−25.6727	−	8.34155i	−2.04241	−	0.663618i
$159$		0			0
$160$	−15.1401	+	20.8385i	−1.19693	+	1.64743i
$161$	2.59074	−	7.97347i	0.204179	−	0.628398i
$162$		0			0
$163$	−2.37021	+	1.72206i	−0.185650	+	0.134882i	−0.676728	−	0.736233i	$-0.736603\pi$
$163$	−2.37021	+	1.72206i	−0.185650	+	0.134882i	0.491079	+	0.871115i	$0.336603\pi$
$164$	24.0280			1.87627
$165$		0			0
$166$	16.0674			1.24707
$167$	3.60309	−	2.61780i	0.278816	−	0.202571i	−0.439585	−	0.898201i	$-0.644875\pi$
$167$	3.60309	−	2.61780i	0.278816	−	0.202571i	0.718401	+	0.695630i	$0.244875\pi$
$168$		0			0
$169$	1.27880	−	3.93575i	0.0983694	−	0.302750i
$170$	9.51100	−	13.0908i	0.729461	−	1.00402i
$171$		0			0
$172$	10.6308	+	3.45415i	0.810590	+	0.263377i
$173$	−3.22935	−	9.93891i	−0.245523	−	0.755641i	−0.995550	−	0.0942343i	$-0.969960\pi$
$173$	−3.22935	−	9.93891i	−0.245523	−	0.755641i	0.750027	−	0.661407i	$-0.230040\pi$
$174$		0			0
$175$			4.19595i			0.317184i
$176$	29.3606	−	32.1270i	2.21314	−	2.42167i
$177$		0			0
$178$	8.10058	+	11.1495i	0.607164	+	0.835690i
$179$	−9.58188	+	3.11334i	−0.716183	+	0.232702i	−0.644368	−	0.764716i	$-0.722879\pi$
$179$	−9.58188	+	3.11334i	−0.716183	+	0.232702i	−0.0718157	+	0.997418i	$0.522879\pi$
$180$		0			0
$181$	12.5433	+	9.11327i	0.932339	+	0.677384i	0.946564	−	0.322515i	$-0.104528\pi$
$181$	12.5433	+	9.11327i	0.932339	+	0.677384i	−0.0142256	+	0.999899i	$0.504528\pi$
$182$	−9.36598	−	6.80478i	−0.694253	−	0.504404i
$183$		0			0
$184$	−48.4613	+	15.7460i	−3.57261	+	1.16081i
$185$	8.49407	+	11.6911i	0.624496	+	0.859545i
$186$		0			0
$187$	−9.28843	+	10.1636i	−0.679237	+	0.743237i
$188$		−	38.1603i		−	2.78313i
$189$		0			0
$190$	1.50881	+	4.64363i	0.109460	+	0.336884i
$191$	3.53297	+	1.14793i	0.255637	+	0.0830615i	0.434032	−	0.900897i	$-0.357090\pi$
$191$	3.53297	+	1.14793i	0.255637	+	0.0830615i	−0.178395	+	0.983959i	$0.557090\pi$
$192$		0			0
$193$	−14.6578	+	20.1747i	−1.05509	+	1.45221i	−0.170779	+	0.985309i	$0.554628\pi$
$193$	−14.6578	+	20.1747i	−1.05509	+	1.45221i	−0.884311	+	0.466898i	$0.845372\pi$
$194$	−5.02883	+	15.4771i	−0.361049	+	1.11119i
$195$		0			0
$196$	−20.9076	+	15.1903i	−1.49340	+	1.08502i
$197$	−19.2214			−1.36947			−0.684733	−	0.728794i	$-0.740081\pi$
$197$	−19.2214			−1.36947			−0.684733	+	0.728794i	$0.740081\pi$
$198$		0			0
$199$	−26.0126			−1.84399			−0.921993	−	0.387206i	$-0.873440\pi$
$199$	−26.0126			−1.84399			−0.921993	+	0.387206i	$0.873440\pi$
$200$	20.6317	−	14.9898i	1.45888	−	1.05994i
$201$		0			0
$202$	9.69176	−	29.8282i	0.681910	−	2.09870i
$203$	0.0826128	−	0.113707i	0.00579828	−	0.00798065i
$204$		0			0
$205$	6.28951	+	2.04358i	0.439278	+	0.142730i
$206$	2.78864	+	8.58255i	0.194294	+	0.597975i
$207$		0			0
$208$			39.0638i			2.70859i
$209$	−0.833707	−	4.07012i	−0.0576687	−	0.281536i
$210$		0			0
$211$	−13.3646	−	18.3948i	−0.920057	−	1.26635i	−0.963614	−	0.267299i	$-0.913869\pi$
$211$	−13.3646	−	18.3948i	−0.920057	−	1.26635i	0.0435567	−	0.999051i	$-0.486131\pi$
$212$	1.67988	−	0.545827i	0.115375	−	0.0374875i
$213$		0			0
$214$	20.6056	+	14.9708i	1.40857	+	1.02339i
$215$	2.48891	+	1.80830i	0.169742	+	0.123325i
$216$		0			0
$217$	−5.61293	+	1.82375i	−0.381030	+	0.123804i
$218$	−6.51304	−	8.96443i	−0.441119	−	0.607148i
$219$		0			0
$220$	21.9403	−	12.4517i	1.47922	−	0.839495i
$221$		−	12.3581i		−	0.831296i
$222$		0			0
$223$	−7.02963	−	21.6350i	−0.470739	−	1.44878i	−0.851619	−	0.524161i	$-0.824379\pi$
$223$	−7.02963	−	21.6350i	−0.470739	−	1.44878i	0.380881	−	0.924624i	$-0.375621\pi$
$224$	−24.4421	−	7.94170i	−1.63310	−	0.530627i
$225$		0			0
$226$	−32.0208	+	44.0729i	−2.13000	+	2.93169i
$227$	−2.51159	+	7.72987i	−0.166700	+	0.513050i	−0.999158	−	0.0410390i	$-0.986933\pi$
$227$	−2.51159	+	7.72987i	−0.166700	+	0.513050i	0.832458	+	0.554089i	$0.186933\pi$
$228$		0			0
$229$	−10.9974	+	7.99008i	−0.726728	+	0.527999i	−0.888527	−	0.458825i	$-0.848271\pi$
$229$	−10.9974	+	7.99008i	−0.726728	+	0.527999i	0.161798	+	0.986824i	$0.448271\pi$
$230$	−22.6360			−1.49257
$231$		0			0
$232$	−0.854233			−0.0560831
$233$	−4.09157	+	2.97270i	−0.268048	+	0.194748i	−0.713687	−	0.700464i	$-0.752976\pi$
$233$	−4.09157	+	2.97270i	−0.268048	+	0.194748i	0.445640	+	0.895212i	$0.352976\pi$
$234$		0			0
$235$	3.24554	−	9.98874i	0.211716	−	0.651594i
$236$	9.35264	−	12.8728i	0.608805	−	0.837948i
$237$		0			0
$238$	15.3545	+	4.98899i	0.995286	+	0.323388i
$239$	−6.23162	−	19.1790i	−0.403090	−	1.24058i	−0.922480	−	0.386046i	$-0.873841\pi$
$239$	−6.23162	−	19.1790i	−0.403090	−	1.24058i	0.519390	−	0.854538i	$-0.326159\pi$
$240$		0			0
$241$			28.3011i			1.82303i	0.411264	+	0.911516i	$0.365087\pi$
$241$			28.3011i			1.82303i	−0.411264	+	0.911516i	$0.634913\pi$
$242$	−27.2463	+	11.6509i	−1.75146	+	0.748947i
$243$		0			0
$244$	−0.983581	−	1.35378i	−0.0629674	−	0.0866671i
$245$	−6.76466	+	2.19797i	−0.432178	+	0.140423i
$246$		0			0
$247$	3.01684	+	2.19187i	0.191957	+	0.139465i
$248$	29.0194	+	21.0838i	1.84273	+	1.33882i
$249$		0			0
$250$	29.3093	−	9.52318i	1.85369	−	0.602299i
$251$	−13.7475	−	18.9219i	−0.867737	−	1.19434i	−0.979669	−	0.200622i	$-0.935704\pi$
$251$	−13.7475	−	18.9219i	−0.867737	−	1.19434i	0.111931	−	0.993716i	$-0.464296\pi$
$252$		0			0
$253$	19.1401	+	2.15500i	1.20333	+	0.135483i
$254$			0.277219i			0.0173943i
$255$		0			0
$256$	5.63285	+	17.3361i	0.352053	+	1.08351i
$257$	0.396081	+	0.128695i	0.0247069	+	0.00802775i	0.321344	−	0.946962i	$-0.395865\pi$
$257$	0.396081	+	0.128695i	0.0247069	+	0.00802775i	−0.296637	+	0.954990i	$0.595865\pi$
$258$		0			0
$259$	−8.47497	+	11.6648i	−0.526609	+	0.724815i
$260$	−6.99709	+	21.5348i	−0.433941	+	1.33553i
$261$		0			0
$262$	33.4873	−	24.3299i	2.06885	−	1.50311i
$263$	−28.1176			−1.73380			−0.866902	−	0.498478i	$-0.833892\pi$
$263$	−28.1176			−1.73380			−0.866902	+	0.498478i	$0.833892\pi$
$264$		0			0
$265$	0.486144			0.0298636
$266$	−3.94122	+	2.86347i	−0.241652	+	0.175570i
$267$		0			0
$268$	5.58276	−	17.1820i	0.341021	−	1.04956i
$269$	−7.97137	+	10.9716i	−0.486023	+	0.668953i	−0.979648	−	0.200721i	$-0.935671\pi$
$269$	−7.97137	+	10.9716i	−0.486023	+	0.668953i	0.493625	+	0.869675i	$0.335671\pi$
$270$		0			0
$271$	−10.5963	−	3.44294i	−0.643678	−	0.209144i	−0.0310533	−	0.999518i	$-0.509886\pi$
$271$	−10.5963	−	3.44294i	−0.643678	−	0.209144i	−0.612624	+	0.790374i	$0.709886\pi$
$272$	−16.8341	−	51.8102i	−1.02072	−	3.14145i
$273$		0			0
$274$		−	10.0307i		−	0.605975i
$275$	−9.44375	+	1.93442i	−0.569480	+	0.116650i
$276$		0			0
$277$	−5.75105	−	7.91564i	−0.345547	−	0.475605i	0.600504	−	0.799622i	$-0.294967\pi$
$277$	−5.75105	−	7.91564i	−0.345547	−	0.475605i	−0.946051	+	0.324017i	$0.894967\pi$
$278$	43.5961	−	14.1652i	2.61472	−	0.849573i
$279$		0			0
$280$	−14.8270	−	10.7724i	−0.886083	−	0.643777i
$281$	9.85777	+	7.16209i	0.588065	+	0.427254i	0.841623	−	0.540066i	$-0.181601\pi$
$281$	9.85777	+	7.16209i	0.588065	+	0.427254i	−0.253558	+	0.967320i	$0.581601\pi$
$282$		0			0
$283$	14.6399	−	4.75680i	0.870253	−	0.282762i	0.160348	−	0.987060i	$-0.448738\pi$
$283$	14.6399	−	4.75680i	0.870253	−	0.282762i	0.709904	+	0.704298i	$0.248738\pi$
$284$	−28.3303	−	38.9933i	−1.68109	−	2.31383i
$285$		0			0
$286$	10.9975	−	24.2170i	0.650296	−	1.43198i
$287$			6.59831i			0.389486i
$288$		0			0
$289$	0.0723102	+	0.222548i	0.00425354	+	0.0130911i
$290$	−0.360905	−	0.117265i	−0.0211931	−	0.00688604i
$291$		0			0
$292$	−21.9347	+	30.1905i	−1.28363	+	1.76676i
$293$	8.41119	−	25.8870i	0.491387	−	1.51233i	−0.331125	−	0.943587i	$-0.607428\pi$
$293$	8.41119	−	25.8870i	0.491387	−	1.51233i	0.822512	−	0.568747i	$-0.192572\pi$
$294$		0			0
$295$	3.54295	−	2.57411i	0.206279	−	0.149870i
$296$	87.6328			5.09356
$297$		0			0
$298$	30.8503			1.78711
$299$	−13.9862	+	10.1616i	−0.808845	+	0.587660i
$300$		0			0
$301$	−0.948542	+	2.91931i	−0.0546730	+	0.168266i
$302$	1.68319	−	2.31671i	0.0968564	−	0.133311i
$303$		0			0
$304$	15.6336	+	5.07966i	0.896647	+	0.291338i
$305$	−0.142320	−	0.438016i	−0.00814923	−	0.0250807i
$306$		0			0
$307$		−	31.0795i		−	1.77380i	−0.461960	−	0.886901i	$-0.652854\pi$
$307$		−	31.0795i		−	1.77380i	0.461960	−	0.886901i	$-0.347146\pi$
$308$	18.5804	+	16.9804i	1.05871	+	0.967549i
$309$		0			0
$310$	9.36611	+	12.8914i	0.531960	+	0.732179i
$311$	5.43478	−	1.76587i	0.308178	−	0.100133i	−0.150845	−	0.988557i	$-0.548200\pi$
$311$	5.43478	−	1.76587i	0.308178	−	0.100133i	0.459023	+	0.888424i	$0.348200\pi$
$312$		0			0
$313$	21.3843	+	15.5366i	1.20871	+	0.878180i	0.995113	−	0.0987412i	$-0.0314816\pi$
$313$	21.3843	+	15.5366i	1.20871	+	0.878180i	0.213598	+	0.976922i	$0.431482\pi$
$314$	−0.186099	−	0.135209i	−0.0105021	−	0.00763026i
$315$		0			0
$316$	−50.0994	+	16.2783i	−2.81831	+	0.915725i
$317$	−1.16373	−	1.60174i	−0.0653617	−	0.0899627i	0.775085	−	0.631857i	$-0.217707\pi$
$317$	−1.16373	−	1.60174i	−0.0653617	−	0.0899627i	−0.840446	+	0.541895i	$0.817707\pi$
$318$		0			0
$319$	0.294004	+	0.133514i	0.0164611	+	0.00747536i
$320$			31.4153i			1.75617i
$321$		0			0
$322$	−6.97917	−	21.4797i	−0.388934	−	1.19701i
$323$	−4.94579	−	1.60698i	−0.275191	−	0.0894150i
$324$		0			0
$325$	5.08570	−	6.99986i	0.282104	−	0.388283i
$326$	−2.43889	+	7.50614i	−0.135078	+	0.415726i
$327$		0			0
$328$	32.4443	−	23.5721i	1.79143	−	1.30155i
$329$	10.4792			0.577735
$330$		0			0
$331$	−4.07717			−0.224101			−0.112051	−	0.993702i	$-0.535742\pi$
$331$	−4.07717			−0.224101			−0.112051	+	0.993702i	$0.535742\pi$
$332$	25.3667	−	18.4300i	1.39218	−	1.01148i
$333$		0			0
$334$	3.70749	−	11.4105i	0.202865	−	0.624354i
$335$	2.92266	−	4.02269i	0.159682	−	0.219783i
$336$		0			0
$337$	−27.1314	−	8.81552i	−1.47794	−	0.480212i	−0.544444	−	0.838797i	$-0.683259\pi$
$337$	−27.1314	−	8.81552i	−1.47794	−	0.480212i	−0.933497	+	0.358585i	$0.883259\pi$
$338$	−3.44495	−	10.6025i	−0.187381	−	0.576699i
$339$		0			0
$340$		−	31.5769i		−	1.71250i
$341$	−6.69236	−	11.7921i	−0.362412	−	0.638580i
$342$		0			0
$343$	−10.1112	−	13.9169i	−0.545954	−	0.751441i
$344$	17.7430	−	5.76506i	0.956640	−	0.310831i
$345$		0			0
$346$	−22.7756	−	16.5474i	−1.22442	−	0.889596i
$347$	−8.36428	−	6.07700i	−0.449018	−	0.326231i	0.340190	−	0.940357i	$-0.389509\pi$
$347$	−8.36428	−	6.07700i	−0.449018	−	0.326231i	−0.789208	+	0.614126i	$0.789509\pi$
$348$		0			0
$349$	17.5504	−	5.70248i	0.939453	−	0.305247i	0.201030	−	0.979585i	$-0.435571\pi$
$349$	17.5504	−	5.70248i	0.939453	−	0.305247i	0.738423	+	0.674338i	$0.235571\pi$
$350$	6.64399	+	9.14466i	0.355136	+	0.488803i
$351$		0			0
$352$	6.60597	−	58.6726i	0.352100	−	3.12726i
$353$		−	13.3918i		−	0.712772i	−0.934339	−	0.356386i	$-0.884009\pi$
$353$		−	13.3918i		−	0.712772i	0.934339	−	0.356386i	$-0.115991\pi$
$354$		0			0
$355$	−4.09928	−	12.6163i	−0.217567	−	0.669603i
$356$	25.5780	+	8.31078i	1.35563	+	0.440470i
$357$		0			0
$358$	−15.9530	+	21.9575i	−0.843144	+	1.16049i
$359$	−1.92854	+	5.93545i	−0.101785	+	0.313261i	−0.988962	−	0.148167i	$-0.952663\pi$
$359$	−1.92854	+	5.93545i	−0.101785	+	0.313261i	0.887178	+	0.461428i	$0.152663\pi$
$360$		0			0
$361$	−14.1018	+	10.2456i	−0.742202	+	0.539241i
$362$	41.7672			2.19524
$363$		0			0
$364$	−22.5922			−1.18415
$365$	−8.30926	+	6.03703i	−0.434927	+	0.315993i
$366$		0			0
$367$	−2.37952	+	7.32341i	−0.124210	+	0.382279i	−0.993756	−	0.111572i	$-0.964411\pi$
$367$	−2.37952	+	7.32341i	−0.124210	+	0.382279i	0.869546	+	0.493851i	$0.164411\pi$
$368$	−44.7939	+	61.6535i	−2.33504	+	3.21391i
$369$		0			0
$370$	37.0240	+	12.0298i	1.92479	+	0.625401i
$371$	0.149889	+	0.461311i	0.00778185	+	0.0239501i
$372$		0			0
$373$			21.0593i			1.09041i	0.838304	+	0.545204i	$0.183548\pi$
$373$			21.0593i			1.09041i	−0.838304	+	0.545204i	$0.816452\pi$
$374$	−4.14988	+	36.8582i	−0.214585	+	1.90589i
$375$		0			0
$376$	−37.4363	−	51.5267i	−1.93063	−	2.65729i
$377$	−0.275637	+	0.0895598i	−0.0141960	+	0.00461256i
$378$		0			0
$379$	24.0003	+	17.4372i	1.23281	+	0.895691i	0.997098	−	0.0761314i	$-0.0242568\pi$
$379$	24.0003	+	17.4372i	1.23281	+	0.895691i	0.235715	+	0.971822i	$0.424257\pi$
$380$	7.70851	+	5.60056i	0.395438	+	0.287303i
$381$		0			0
$382$	9.51744	−	3.09241i	0.486955	−	0.158221i
$383$	−1.56826	−	2.15852i	−0.0801343	−	0.110295i	0.767068	−	0.641566i	$-0.221715\pi$
$383$	−1.56826	−	2.15852i	−0.0801343	−	0.110295i	−0.847202	+	0.531270i	$0.821715\pi$
$384$		0			0
$385$	3.41936	+	6.02501i	0.174267	+	0.307063i
$386$			67.1784i			3.41929i
$387$		0			0
$388$	9.81361	+	30.2032i	0.498210	+	1.53333i
$389$	−0.606242	−	0.196980i	−0.0307377	−	0.00998729i	0.293608	−	0.955926i	$-0.405144\pi$
$389$	−0.606242	−	0.196980i	−0.0307377	−	0.00998729i	−0.324346	+	0.945939i	$0.605144\pi$
$390$		0			0
$391$	14.1709	−	19.5045i	0.716651	−	0.986385i
$392$	−13.3288	+	41.0219i	−0.673207	+	2.07192i
$393$		0			0
$394$	−41.8911	+	30.4357i	−2.11044	+	1.53333i
$395$	−14.4984			−0.729492
$396$		0			0
$397$	−25.2145			−1.26548			−0.632741	−	0.774364i	$-0.718070\pi$
$397$	−25.2145			−1.26548			−0.632741	+	0.774364i	$0.718070\pi$
$398$	−56.6920	+	41.1892i	−2.84171	+	2.06463i
$399$		0			0
$400$	11.7861	−	36.2740i	0.589306	−	1.81370i
$401$	−17.1458	+	23.5992i	−0.856221	+	1.17849i	0.126236	+	0.992000i	$0.459710\pi$
$401$	−17.1458	+	23.5992i	−0.856221	+	1.17849i	−0.982457	+	0.186487i	$0.940290\pi$
$402$		0			0
$403$	11.5742	+	3.76069i	0.576552	+	0.187333i
$404$	−18.9132	−	58.2088i	−0.940966	−	2.89600i
$405$		0			0
$406$		−	0.378625i		−	0.0187908i
$407$	−30.1609	−	13.6968i	−1.49502	−	0.678923i
$408$		0			0
$409$	9.76208	+	13.4363i	0.482704	+	0.664384i	0.979022	−	0.203756i	$-0.0653150\pi$
$409$	9.76208	+	13.4363i	0.482704	+	0.664384i	−0.496318	+	0.868141i	$0.665315\pi$
$410$	16.9432	−	5.50520i	0.836767	−	0.271882i
$411$		0			0
$412$	14.2472	+	10.3512i	0.701910	+	0.509967i
$413$	3.53499	+	2.56832i	0.173945	+	0.126379i
$414$		0			0
$415$	8.20739	−	2.66674i	0.402885	−	0.130905i
$416$	31.1496	+	42.8737i	1.52723	+	2.10206i
$417$		0			0
$418$	−8.26174	−	7.55033i	−0.404095	−	0.369299i
$419$			9.37377i			0.457939i	0.973434	+	0.228969i	$0.0735356\pi$
$419$			9.37377i			0.457939i	−0.973434	+	0.228969i	$0.926464\pi$
$420$		0			0
$421$	−1.02317	−	3.14901i	−0.0498664	−	0.153473i	0.923022	−	0.384746i	$-0.125711\pi$
$421$	−1.02317	−	3.14901i	−0.0498664	−	0.153473i	−0.972889	+	0.231273i	$0.925711\pi$
$422$	−58.2537	−	18.9278i	−2.83575	−	0.921390i
$423$		0			0
$424$	1.73282	−	2.38502i	0.0841532	−	0.115827i
$425$	−3.72862	+	11.4755i	−0.180865	+	0.556645i
$426$		0			0
$427$	0.371761	−	0.270100i	0.0179908	−	0.0130711i
$428$	49.7038			2.40252
$429$		0			0
$430$	8.28766			0.399666
$431$	1.72195	−	1.25107i	0.0829434	−	0.0602619i	−0.545541	−	0.838084i	$-0.683676\pi$
$431$	1.72195	−	1.25107i	0.0829434	−	0.0602619i	0.628484	+	0.777822i	$0.283676\pi$
$432$		0			0
$433$	−4.76068	+	14.6519i	−0.228784	+	0.704124i	0.769102	+	0.639126i	$0.220704\pi$
$433$	−4.76068	+	14.6519i	−0.228784	+	0.704124i	−0.997885	+	0.0649975i	$0.979296\pi$
$434$	−9.34505	+	12.8624i	−0.448577	+	0.617413i
$435$		0			0
$436$	−20.5652	−	6.68205i	−0.984896	−	0.320012i
$437$	2.24803	+	6.91874i	0.107538	+	0.330968i
$438$		0			0
$439$		−	35.8053i		−	1.70889i	−0.519539	−	0.854447i	$-0.673896\pi$
$439$		−	35.8053i		−	1.70889i	0.519539	−	0.854447i	$-0.326104\pi$
$440$	17.4098	−	38.3372i	0.829981	−	1.82765i
$441$		0			0
$442$	−19.5682	−	26.9333i	−0.930764	−	1.28109i
$443$	11.4104	−	3.70747i	0.542125	−	0.176147i	−0.0251376	−	0.999684i	$-0.508002\pi$
$443$	11.4104	−	3.70747i	0.542125	−	0.176147i	0.567263	+	0.823537i	$0.308002\pi$
$444$		0			0
$445$	5.98838	+	4.35081i	0.283877	+	0.206248i
$446$	−49.5779	−	36.0204i	−2.34758	−	1.70562i
$447$		0			0
$448$	−29.8105	+	9.68603i	−1.40842	+	0.457622i
$449$	−15.0088	−	20.6578i	−0.708307	−	0.974901i	−0.999832	−	0.0183378i	$-0.994163\pi$
$449$	−15.0088	−	20.6578i	−0.708307	−	0.974901i	0.291525	−	0.956563i	$-0.405837\pi$
$450$		0			0
$451$	−14.8507	+	3.04196i	−0.699292	+	0.143240i
$452$			106.310i			5.00043i
$453$		0			0
$454$	6.76595	+	20.8234i	0.317542	+	0.977292i
$455$	−5.91366	−	1.92146i	−0.277237	−	0.0900797i
$456$		0			0
$457$	0.599502	−	0.825144i	0.0280435	−	0.0385986i	−0.794765	−	0.606917i	$-0.792406\pi$
$457$	0.599502	−	0.825144i	0.0280435	−	0.0385986i	0.822809	+	0.568319i	$0.192406\pi$
$458$	−11.3160	+	34.8272i	−0.528764	+	1.62737i
$459$		0			0
$460$	−35.7370	+	25.9645i	−1.66625	+	1.21060i
$461$	4.52405			0.210706			0.105353	−	0.994435i	$-0.466403\pi$
$461$	4.52405			0.210706			0.105353	+	0.994435i	$0.466403\pi$
$462$		0			0
$463$	−8.45187			−0.392792			−0.196396	−	0.980525i	$-0.562924\pi$
$463$	−8.45187			−0.392792			−0.196396	+	0.980525i	$0.562924\pi$
$464$	−1.03358	+	0.750942i	−0.0479829	+	0.0348616i
$465$		0			0
$466$	−4.21012	+	12.9574i	−0.195030	+	0.600241i
$467$	−3.64591	+	5.01817i	−0.168713	+	0.232213i	−0.884998	−	0.465594i	$-0.845841\pi$
$467$	−3.64591	+	5.01817i	−0.168713	+	0.232213i	0.716286	+	0.697807i	$0.245841\pi$
$468$		0			0
$469$	4.71832	+	1.53308i	0.217872	+	0.0707909i
$470$	−8.74313	−	26.9086i	−0.403290	−	1.24120i
$471$		0			0
$472$		−	26.5569i		−	1.22238i
$473$	−7.00774	−	0.789005i	−0.322216	−	0.0362785i
$474$		0			0
$475$	−2.14007	−	2.94556i	−0.0981932	−	0.135151i
$476$	29.9639	−	9.73586i	1.37339	−	0.446242i
$477$		0			0
$478$	−43.9497	−	31.9314i	−2.01021	−	1.46051i
$479$	−18.0462	−	13.1113i	−0.824550	−	0.599071i	0.0934623	−	0.995623i	$-0.470207\pi$
$479$	−18.0462	−	13.1113i	−0.824550	−	0.599071i	−0.918012	+	0.396552i	$0.870207\pi$
$480$		0			0
$481$	28.2766	−	9.18763i	1.28930	−	0.418920i
$482$	44.8128	+	61.6795i	2.04117	+	2.80942i
$483$		0			0
$484$	−29.6516	+	49.6468i	−1.34780	+	2.25667i
$485$			8.74055i			0.396888i
$486$		0			0
$487$	10.5290	+	32.4051i	0.477117	+	1.46841i	0.843082	+	0.537786i	$0.180739\pi$
$487$	10.5290	+	32.4051i	0.477117	+	1.46841i	−0.365965	+	0.930629i	$0.619261\pi$
$488$	−2.65620	−	0.863051i	−0.120240	−	0.0390685i
$489$		0			0
$490$	−11.2626	+	15.5016i	−0.508792	+	0.700292i
$491$	5.81717	−	17.9034i	0.262525	−	0.807970i	−0.729728	−	0.683738i	$-0.760353\pi$
$491$	5.81717	−	17.9034i	0.262525	−	0.807970i	0.992253	−	0.124232i	$-0.0396467\pi$
$492$		0			0
$493$	0.326981	−	0.237566i	0.0147265	−	0.0106994i
$494$	10.0456			0.451972
$495$		0			0
$496$	53.6466			2.40880
$497$	10.7079	−	7.77976i	0.480316	−	0.348970i
$498$		0			0
$499$	2.34788	−	7.22603i	0.105106	−	0.323482i	−0.884650	−	0.466256i	$-0.845602\pi$
$499$	2.34788	−	7.22603i	0.105106	−	0.323482i	0.989755	+	0.142775i	$0.0456024\pi$
$500$	35.3493	−	48.6541i	1.58087	−	2.17588i
$501$		0			0
$502$	−59.9229	−	19.4701i	−2.67449	−	0.868995i
$503$	8.18033	+	25.1765i	0.364743	+	1.12256i	0.950142	+	0.311818i	$0.100938\pi$
$503$	8.18033	+	25.1765i	0.364743	+	1.12256i	−0.585399	+	0.810745i	$0.699062\pi$
$504$		0			0
$505$		−	16.8451i		−	0.749599i
$506$	45.1264	−	25.6105i	2.00611	−	1.13852i
$507$		0			0
$508$	0.317983	+	0.437666i	0.0141082	+	0.0194183i
$509$	−12.1254	+	3.93980i	−0.537451	+	0.174628i	−0.565150	−	0.824988i	$-0.691182\pi$
$509$	−12.1254	+	3.93980i	−0.537451	+	0.174628i	0.0276995	+	0.999616i	$0.491182\pi$
$510$		0			0
$511$	−8.29058	−	6.02346i	−0.366754	−	0.266462i
$512$	2.69612	+	1.95884i	0.119153	+	0.0865695i
$513$		0			0
$514$	1.06700	−	0.346689i	0.0470633	−	0.0152918i
$515$	2.84894	+	3.92123i	0.125539	+	0.172790i
$516$		0			0
$517$	4.83111	+	23.5853i	0.212472	+	1.03728i
$518$			38.8418i			1.70661i
$519$		0			0
$520$	11.6783	+	35.9421i	0.512128	+	1.57617i
$521$	6.80629	+	2.21150i	0.298189	+	0.0968875i	0.454291	−	0.890854i	$-0.349893\pi$
$521$	6.80629	+	2.21150i	0.298189	+	0.0968875i	−0.156102	+	0.987741i	$0.549893\pi$
$522$		0			0
$523$	18.1933	−	25.0410i	0.795539	−	1.09497i	−0.197857	−	0.980231i	$-0.563398\pi$
$523$	18.1933	−	25.0410i	0.795539	−	1.09497i	0.993396	−	0.114734i	$-0.0366017\pi$
$524$	24.9613	−	76.8229i	1.09044	−	3.35602i
$525$		0			0
$526$	−61.2796	+	44.5222i	−2.67192	+	1.94126i
$527$	−16.9715			−0.739289
$528$		0			0
$529$	−10.7263			−0.466360
$530$	1.05950	−	0.769775i	0.0460219	−	0.0334369i
$531$		0			0
$532$	−2.93777	+	9.04152i	−0.127368	+	0.392000i
$533$	7.99748	−	11.0076i	0.346409	−	0.476792i
$534$		0			0
$535$	13.0103	+	4.22731i	0.562486	+	0.182763i
$536$	−9.31775	−	28.6771i	−0.402466	−	1.23866i
$537$		0			0
$538$			36.5338i			1.57508i
$539$	10.9990	−	12.0354i	0.473762	−	0.518401i
$540$		0			0
$541$	25.5272	+	35.1352i	1.09750	+	1.51058i	0.838656	+	0.544661i	$0.183342\pi$
$541$	25.5272	+	35.1352i	1.09750	+	1.51058i	0.258845	+	0.965919i	$0.416658\pi$
$542$	−28.5452	+	9.27490i	−1.22612	+	0.398391i
$543$		0			0
$544$	−59.7895	−	43.4396i	−2.56346	−	1.86246i
$545$	−4.81479	−	3.49815i	−0.206243	−	0.149844i
$546$		0			0
$547$	7.10797	−	2.30952i	0.303915	−	0.0987480i	−0.153090	−	0.988212i	$-0.548922\pi$
$547$	7.10797	−	2.30952i	0.303915	−	0.0987480i	0.457005	+	0.889464i	$0.348922\pi$
$548$	−11.5056	−	15.8361i	−0.491496	−	0.676487i
$549$		0			0
$550$	−17.5187	+	19.1694i	−0.747001	+	0.817386i
$551$			0.121957i			0.00519556i
$552$		0			0
$553$	−4.47017	−	13.7578i	−0.190091	−	0.585039i
$554$	−25.0677	−	8.14499i	−1.06503	−	0.346048i
$555$		0			0
$556$	52.5801	−	72.3703i	2.22989	−	3.06919i
$557$	8.26967	−	25.4514i	0.350397	−	1.07841i	−0.608233	−	0.793758i	$-0.708121\pi$
$557$	8.26967	−	25.4514i	0.350397	−	1.07841i	0.958631	−	0.284653i	$-0.0918785\pi$
$558$		0			0
$559$	5.12075	−	3.72044i	0.216585	−	0.157358i
$560$	−27.4099			−1.15828
$561$		0			0
$562$	32.8247			1.38463
$563$	−18.8904	+	13.7247i	−0.796136	+	0.578427i	−0.909778	−	0.415095i	$-0.863748\pi$
$563$	−18.8904	+	13.7247i	−0.796136	+	0.578427i	0.113642	+	0.993522i	$0.463748\pi$
$564$		0			0
$565$	−9.04172	+	27.8275i	−0.380388	+	1.17071i
$566$	24.3742	−	33.5483i	1.02453	−	1.41014i
$567$		0			0
$568$	−76.5070	−	24.8586i	−3.21016	−	1.04305i
$569$	1.67819	+	5.16494i	0.0703534	+	0.216526i	0.980051	−	0.198746i	$-0.0636867\pi$
$569$	1.67819	+	5.16494i	0.0703534	+	0.216526i	−0.909698	+	0.415271i	$0.863687\pi$
$570$		0			0
$571$			10.1542i			0.424940i	0.977168	+	0.212470i	$0.0681508\pi$
$571$			10.1542i			0.424940i	−0.977168	+	0.212470i	$0.931849\pi$
$572$	−10.4154	−	50.8478i	−0.435492	−	2.12605i
$573$		0			0
$574$	10.4480	+	14.3804i	0.436089	+	0.600225i
$575$	16.0533	−	5.21603i	0.669468	−	0.217523i
$576$		0			0
$577$	17.0075	+	12.3566i	0.708029	+	0.514414i	0.882537	−	0.470242i	$-0.155833\pi$
$577$	17.0075	+	12.3566i	0.708029	+	0.514414i	−0.174508	+	0.984656i	$0.555833\pi$
$578$	0.509982	+	0.370524i	0.0212125	+	0.0154118i
$579$		0			0
$580$	−0.704295	+	0.228839i	−0.0292443	+	0.00950204i
$581$	5.06104	+	6.96593i	0.209967	+	0.288995i
$582$		0			0
$583$	−0.969163	+	0.550026i	−0.0401386	+	0.0227798i
$584$			62.2837i			2.57732i
$585$		0			0
$586$	−22.6588	−	69.7367i	−0.936028	−	2.88080i
$587$	41.4845	+	13.4791i	1.71225	+	0.556343i	0.990705	−	0.136027i	$-0.0434334\pi$
$587$	41.4845	+	13.4791i	1.71225	+	0.556343i	0.721543	+	0.692370i	$0.243433\pi$
$588$		0			0
$589$	3.01010	−	4.14305i	0.124029	−	0.170711i
$590$	3.64561	−	11.2200i	0.150087	−	0.461921i
$591$		0			0
$592$	106.032	−	77.0365i	4.35788	−	3.16618i
$593$	37.0300			1.52064			0.760319	−	0.649549i	$-0.225042\pi$
$593$	37.0300			1.52064			0.760319	+	0.649549i	$0.225042\pi$
$594$		0			0
$595$	8.67130			0.355489
$596$	48.7056	−	35.3867i	1.99506	−	1.44949i
$597$		0			0
$598$	−14.3915	+	44.2924i	−0.588511	+	1.81125i
$599$	−14.1622	+	19.4926i	−0.578652	+	0.796446i	−0.993547	−	0.113423i	$-0.963818\pi$
$599$	−14.1622	+	19.4926i	−0.578652	+	0.796446i	0.414895	+	0.909869i	$0.363818\pi$
$600$		0			0
$601$	−17.7661	−	5.77256i	−0.724694	−	0.235467i	−0.0766371	−	0.997059i	$-0.524418\pi$
$601$	−17.7661	−	5.77256i	−0.724694	−	0.235467i	−0.648057	+	0.761592i	$0.724418\pi$
$602$	2.55527	+	7.86431i	0.104145	+	0.320525i
$603$		0			0
$604$		−	5.58824i		−	0.227382i
$605$	−11.9840	+	10.4735i	−0.487219	+	0.425810i
$606$		0			0
$607$	−14.4621	−	19.9054i	−0.587000	−	0.807936i	0.407441	−	0.913231i	$-0.366421\pi$
$607$	−14.4621	−	19.9054i	−0.587000	−	0.807936i	−0.994441	+	0.105296i	$0.966421\pi$
$608$	21.2089	−	6.89117i	0.860133	−	0.279474i
$609$		0			0
$610$	−1.00374	−	0.729261i	−0.0406403	−	0.0295269i
$611$	−17.4818	−	12.7013i	−0.707238	−	0.513839i
$612$		0			0
$613$	21.4976	−	6.98501i	0.868282	−	0.282122i	0.159199	−	0.987247i	$-0.449109\pi$
$613$	21.4976	−	6.98501i	0.868282	−	0.282122i	0.709083	+	0.705125i	$0.249109\pi$
$614$	−49.2122	−	67.7348i	−1.98604	−	2.73355i
$615$		0			0
$616$	41.7467	+	4.70028i	1.68202	+	0.189380i
$617$		−	9.43688i		−	0.379915i	−0.981792	−	0.189957i	$-0.939165\pi$
$617$		−	9.43688i		−	0.379915i	0.981792	−	0.189957i	$-0.0608349\pi$
$618$		0			0
$619$	−4.13730	−	12.7333i	−0.166292	−	0.511794i	0.832837	−	0.553518i	$-0.186715\pi$
$619$	−4.13730	−	12.7333i	−0.166292	−	0.511794i	−0.999129	+	0.0417238i	$0.986715\pi$
$620$	29.5739	+	9.60915i	1.18772	+	0.385913i
$621$		0			0
$622$	9.04845	−	12.4541i	0.362810	−	0.499365i
$623$	−2.28222	+	7.02394i	−0.0914350	+	0.281408i
$624$		0			0
$625$	1.63385	−	1.18706i	0.0653540	−	0.0474824i
$626$	71.2061			2.84597
$627$		0			0
$628$	−0.448898			−0.0179130
$629$	−33.5439	+	24.3710i	−1.33748	+	0.971737i
$630$		0			0
$631$	−3.99811	+	12.3049i	−0.159162	+	0.489851i	−0.998559	−	0.0536685i	$-0.982909\pi$
$631$	−3.99811	+	12.3049i	−0.159162	+	0.489851i	0.839397	+	0.543519i	$0.182909\pi$
$632$	−51.6782	+	71.1290i	−2.05565	+	2.82936i
$633$		0			0
$634$	−5.07249	−	1.64815i	−0.201454	−	0.0654564i
$635$	0.0460109	+	0.141607i	0.00182589	+	0.00561950i
$636$		0			0
$637$			14.6340i			0.579821i
$638$	0.852164	−	0.174554i	0.0337375	−	0.00691065i
$639$		0			0
$640$	19.4638	+	26.7896i	0.769373	+	1.05895i
$641$	−9.50152	+	3.08723i	−0.375288	+	0.121938i	−0.490586	−	0.871393i	$-0.663217\pi$
$641$	−9.50152	+	3.08723i	−0.375288	+	0.121938i	0.115299	+	0.993331i	$0.463217\pi$
$642$		0			0
$643$	10.2607	+	7.45486i	0.404644	+	0.293991i	0.771430	−	0.636314i	$-0.219542\pi$
$643$	10.2607	+	7.45486i	0.404644	+	0.293991i	−0.366786	+	0.930305i	$0.619542\pi$
$644$	−35.6567	−	25.9061i	−1.40507	−	1.02084i
$645$		0			0
$646$	−13.3234	+	4.32904i	−0.524203	+	0.170324i
$647$	19.3401	+	26.6193i	0.760337	+	1.04651i	0.997186	+	0.0749678i	$0.0238854\pi$
$647$	19.3401	+	26.6193i	0.760337	+	1.04651i	−0.236849	+	0.971547i	$0.576115\pi$
$648$		0			0
$649$	−4.15077	+	9.14018i	−0.162932	+	0.358784i
$650$		−	23.3084i		−	0.914230i
$651$		0			0
$652$	4.75943	+	14.6480i	0.186393	+	0.573660i
$653$	−20.3171	−	6.60143i	−0.795070	−	0.258334i	−0.116809	−	0.993154i	$-0.537266\pi$
$653$	−20.3171	−	6.60143i	−0.795070	−	0.258334i	−0.678262	+	0.734820i	$0.737266\pi$
$654$		0			0
$655$	13.0676	−	17.9860i	0.510593	−	0.702771i
$656$	18.5342	−	57.0424i	0.723639	−	2.22713i
$657$		0			0
$658$	22.8383	−	16.5930i	0.890331	−	0.646863i
$659$	10.6922			0.416508			0.208254	−	0.978075i	$-0.433222\pi$
$659$	10.6922			0.416508			0.208254	+	0.978075i	$0.433222\pi$
$660$		0			0
$661$	29.2602			1.13809			0.569045	−	0.822306i	$-0.307313\pi$
$661$	29.2602			1.13809			0.569045	+	0.822306i	$0.307313\pi$
$662$	−8.88580	+	6.45591i	−0.345356	+	0.250916i
$663$		0			0
$664$	16.1715	−	49.7709i	0.627577	−	1.93148i
$665$	−1.53796	+	2.11683i	−0.0596397	+	0.0820870i
$666$		0			0
$667$	−0.537728	−	0.174718i	−0.0208209	−	0.00676512i
$668$	−7.23506	−	22.2672i	−0.279933	−	0.861544i
$669$		0			0
$670$		−	13.3949i		−	0.517490i
$671$	0.779300	+	0.712195i	0.0300845	+	0.0274940i
$672$		0			0
$673$	−24.5320	−	33.7655i	−0.945641	−	1.30156i	−0.953437	−	0.301593i	$-0.902481\pi$
$673$	−24.5320	−	33.7655i	−0.945641	−	1.30156i	0.00779576	−	0.999970i	$-0.497519\pi$
$674$	−73.0890	+	23.7481i	−2.81528	+	0.914741i
$675$		0			0
$676$	−17.6003	−	12.7874i	−0.676935	−	0.491822i
$677$	−24.0662	−	17.4851i	−0.924940	−	0.672008i	0.0198090	−	0.999804i	$-0.493694\pi$
$677$	−24.0662	−	17.4851i	−0.924940	−	0.672008i	−0.944749	+	0.327796i	$0.893694\pi$
$678$		0			0
$679$	−8.29406	+	2.69491i	−0.318297	+	0.103421i
$680$	−30.9778	−	42.6373i	−1.18794	−	1.63507i
$681$		0			0
$682$	−33.2574	−	15.1029i	−1.27349	−	0.578322i
$683$		−	27.9122i		−	1.06803i	−0.845475	−	0.534015i	$-0.820683\pi$
$683$		−	27.9122i		−	1.06803i	0.845475	−	0.534015i	$-0.179317\pi$
$684$		0			0
$685$	−1.66482	−	5.12378i	−0.0636094	−	0.195770i
$686$	−44.0728	−	14.3201i	−1.68271	−	0.546745i
$687$		0			0
$688$	16.4003	−	22.5731i	0.625255	−	0.860590i
$689$	0.309081	−	0.951252i	0.0117750	−	0.0362398i
$690$		0			0
$691$	−1.03840	+	0.754441i	−0.0395026	+	0.0287003i	−0.607361	−	0.794426i	$-0.707772\pi$
$691$	−1.03840	+	0.754441i	−0.0395026	+	0.0287003i	0.567859	+	0.823126i	$0.307772\pi$
$692$	−54.9382			−2.08844
$693$		0			0
$694$	−27.8516			−1.05723
$695$	19.9183	−	14.4715i	0.755545	−	0.548936i
$696$		0			0
$697$	−5.86342	+	18.0458i	−0.222093	+	0.683532i
$698$	29.2200	−	40.2179i	1.10599	−	1.52227i
$699$		0			0
$700$	20.9787	+	6.81639i	0.792920	+	0.257635i
$701$	−9.82030	−	30.2238i	−0.370908	−	1.14154i	−0.946198	−	0.323588i	$-0.895111\pi$
$701$	−9.82030	−	30.2238i	−0.370908	−	1.14154i	0.575290	−	0.817949i	$-0.304889\pi$
$702$		0			0
$703$		−	12.5112i		−	0.471869i
$704$	−35.5435	−	62.6286i	−1.33959	−	2.36041i
$705$		0			0
$706$	−21.2049	−	29.1861i	−0.798058	−	1.09843i
$707$	15.9847	−	5.19373i	0.601165	−	0.195330i
$708$		0			0
$709$	−0.387633	−	0.281632i	−0.0145579	−	0.0105769i	0.580483	−	0.814273i	$-0.302864\pi$
$709$	−0.387633	−	0.281632i	−0.0145579	−	0.0105769i	−0.595040	+	0.803696i	$0.702864\pi$
$710$	−28.9110	−	21.0050i	−1.08501	−	0.788305i
$711$		0			0
$712$	42.6902	−	13.8709i	1.59988	−	0.519833i
$713$	13.9550	+	19.2074i	0.522618	+	0.719322i
$714$		0			0
$715$	1.59829	−	14.1956i	0.0597727	−	0.530886i
$716$			52.9647i			1.97938i
$717$		0			0
$718$	5.19529	+	15.9895i	0.193886	+	0.596721i
$719$	22.0526	+	7.16534i	0.822425	+	0.267222i	0.689851	−	0.723951i	$-0.257676\pi$
$719$	22.0526	+	7.16534i	0.822425	+	0.267222i	0.132574	+	0.991173i	$0.457676\pi$
$720$		0			0
$721$	−2.84253	+	3.91241i	−0.105862	+	0.145706i
$722$	−14.5104	+	44.6585i	−0.540022	+	1.66202i
$723$		0			0
$724$	65.9409	−	47.9089i	2.45068	−	1.78052i
$725$	0.282973			0.0105094
$726$		0			0
$727$	39.4438			1.46289			0.731444	−	0.681902i	$-0.238847\pi$
$727$	39.4438			1.46289			0.731444	+	0.681902i	$0.238847\pi$
$728$	−30.5055	+	22.1635i	−1.13061	+	0.821435i
$729$		0			0
$730$	−8.55002	+	26.3143i	−0.316450	+	0.973934i
$731$	−5.18835	+	7.14114i	−0.191898	+	0.264125i
$732$		0			0
$733$	9.29818	+	3.02116i	0.343436	+	0.111589i	0.475656	−	0.879631i	$-0.342211\pi$
$733$	9.29818	+	3.02116i	0.343436	+	0.111589i	−0.132220	+	0.991220i	$0.542211\pi$
$734$	6.41017	+	19.7285i	0.236604	+	0.728191i
$735$		0			0
$736$			103.385i			3.81083i
$737$	−1.27523	+	11.3262i	−0.0469735	+	0.417207i
$738$		0			0
$739$	−14.0478	−	19.3351i	−0.516757	−	0.711255i	0.468284	−	0.883578i	$-0.344873\pi$
$739$	−14.0478	−	19.3351i	−0.516757	−	0.711255i	−0.985040	+	0.172324i	$0.944873\pi$
$740$	72.2512	−	23.4759i	2.65601	−	0.862990i
$741$		0			0
$742$	1.05712	+	0.768044i	0.0388082	+	0.0281958i
$743$	29.7914	+	21.6447i	1.09294	+	0.794067i	0.979893	−	0.199523i	$-0.0639392\pi$
$743$	29.7914	+	21.6447i	1.09294	+	0.794067i	0.113046	+	0.993590i	$0.463939\pi$
$744$		0			0
$745$	15.7587	−	5.12031i	0.577353	−	0.187593i
$746$	33.3459	+	45.8967i	1.22088	+	1.68040i
$747$		0			0
$748$	35.7263	+	62.9508i	1.30628	+	2.30171i
$749$			13.6491i			0.498728i
$750$		0			0
$751$	−9.48714	−	29.1984i	−0.346191	−	1.06547i	−0.960943	−	0.276746i	$-0.910744\pi$
$751$	−9.48714	−	29.1984i	−0.346191	−	1.06547i	0.614752	−	0.788720i	$-0.289256\pi$
$752$	−90.5924	−	29.4353i	−3.30357	−	1.07339i
$753$		0			0
$754$	−0.458912	+	0.631638i	−0.0167126	+	0.0230029i
$755$	0.475281	−	1.46276i	0.0172972	−	0.0532354i
$756$		0			0
$757$	−34.5971	+	25.1362i	−1.25745	+	0.913592i	−0.998630	−	0.0523331i	$-0.983334\pi$
$757$	−34.5971	+	25.1362i	−1.25745	+	0.913592i	−0.258822	+	0.965925i	$0.583334\pi$
$758$	79.9170			2.90272
$759$		0			0
$760$	15.9029			0.576857
$761$	21.8523	−	15.8766i	0.792145	−	0.575527i	−0.116454	−	0.993196i	$-0.537153\pi$
$761$	21.8523	−	15.8766i	0.792145	−	0.575527i	0.908599	+	0.417669i	$0.137153\pi$
$762$		0			0
$763$	1.83495	−	5.64740i	0.0664297	−	0.204450i
$764$	11.4788	−	15.7991i	0.415287	−	0.571593i
$765$		0			0
$766$	−6.83574	−	2.22107i	−0.246985	−	0.0802504i
$767$	−2.78429	−	8.56916i	−0.100535	−	0.309415i
$768$		0			0
$769$		−	48.3934i		−	1.74511i	−0.488517	−	0.872555i	$-0.662462\pi$
$769$		−	48.3934i		−	1.74511i	0.488517	−	0.872555i	$-0.337538\pi$
$770$	16.9923	+	7.71661i	0.612361	+	0.278087i
$771$		0			0
$772$	77.0567	+	106.059i	2.77333	+	3.81716i
$773$	33.6456	−	10.9321i	1.21015	−	0.393201i	0.366664	−	0.930354i	$-0.380500\pi$
$773$	33.6456	−	10.9321i	1.21015	−	0.393201i	0.843485	+	0.537152i	$0.180500\pi$
$774$		0			0
$775$	−9.61296	−	6.98422i	−0.345308	−	0.250881i
$776$	42.8811	+	31.1550i	1.53934	+	1.11840i
$777$		0			0
$778$	−1.63315	+	0.530643i	−0.0585513	+	0.0190245i
$779$	−3.36536	−	4.63201i	−0.120576	−	0.165959i
$780$		0			0
$781$	22.4463	+	20.5135i	0.803193	+	0.734031i
$782$		−	64.9467i		−	2.32249i
$783$		0			0
$784$	19.9344	+	61.3518i	0.711943	+	2.19113i
$785$	−0.117502	−	0.0381788i	−0.00419383	−	0.00136266i
$786$		0			0
$787$	15.1588	−	20.8643i	0.540353	−	0.743732i	−0.448311	−	0.893878i	$-0.647974\pi$
$787$	15.1588	−	20.8643i	0.540353	−	0.743732i	0.988664	+	0.150146i	$0.0479743\pi$
$788$	−31.2255	+	96.1021i	−1.11236	+	3.42349i
$789$		0			0
$790$	−31.5978	+	22.9571i	−1.12420	+	0.816778i
$791$	−29.1938			−1.03801
$792$		0			0
$793$	−0.947564			−0.0336490
$794$	−54.9527	+	39.9254i	−1.95020	+	1.41690i
$795$		0			0
$796$	−42.2580	+	130.057i	−1.49779	+	4.60974i
$797$	10.0269	−	13.8009i	0.355171	−	0.488851i	−0.593624	−	0.804742i	$-0.702303\pi$
$797$	10.0269	−	13.8009i	0.355171	−	0.488851i	0.948795	+	0.315891i	$0.102303\pi$
$798$		0			0
$799$	28.6596	+	9.31205i	1.01390	+	0.329437i
$800$	−15.9893	−	49.2101i	−0.565308	−	1.73984i
$801$		0			0
$802$			78.5813i			2.77480i
$803$	9.73477	−	21.4364i	0.343533	−	0.756474i
$804$		0			0
$805$	−7.13008	−	9.81371i	−0.251302	−	0.345888i
$806$	31.1797	−	10.1309i	1.09826	−	0.356845i
$807$		0			0
$808$	−82.6423	−	60.0431i	−2.90735	−	2.11231i
$809$	38.7684	+	28.1669i	1.36302	+	0.990295i	0.998246	+	0.0592001i	$0.0188550\pi$
$809$	38.7684	+	28.1669i	1.36302	+	0.990295i	0.364778	+	0.931095i	$0.381145\pi$
$810$		0			0
$811$	45.0299	−	14.6311i	1.58121	−	0.513768i	0.618845	−	0.785513i	$-0.287601\pi$
$811$	45.0299	−	14.6311i	1.58121	−	0.513768i	0.962369	+	0.271745i	$0.0876009\pi$
$812$	−0.434300	−	0.597762i	−0.0152409	−	0.0209773i
$813$		0			0
$814$	−87.4206	+	17.9069i	−3.06409	+	0.627636i
$815$			4.23901i			0.148486i
$816$		0			0
$817$	−0.823068	−	2.53314i	−0.0287955	−	0.0886235i
$818$	42.5510	+	13.8257i	1.48776	+	0.483403i
$819$		0			0
$820$	20.4348	−	28.1261i	0.713615	−	0.982207i
$821$	5.43200	−	16.7180i	0.189578	−	0.583461i	−0.810419	−	0.585851i	$-0.800761\pi$
$821$	5.43200	−	16.7180i	0.189578	−	0.583461i	0.999997	+	0.00238936i	$0.000760556\pi$
$822$		0			0
$823$	−23.1389	+	16.8114i	−0.806571	+	0.586008i	−0.912835	−	0.408330i	$-0.866111\pi$
$823$	−23.1389	+	16.8114i	−0.806571	+	0.586008i	0.106263	+	0.994338i	$0.466111\pi$
$824$	29.3924			1.02393
$825$		0			0
$826$	11.7709			0.409562
$827$	13.0031	−	9.44733i	0.452163	−	0.328516i	−0.338286	−	0.941043i	$-0.609847\pi$
$827$	13.0031	−	9.44733i	0.452163	−	0.328516i	0.790449	+	0.612527i	$0.209847\pi$
$828$		0			0
$829$	0.324003	−	0.997179i	0.0112531	−	0.0346335i	−0.945272	−	0.326282i	$-0.894204\pi$
$829$	0.324003	−	0.997179i	0.0112531	−	0.0346335i	0.956525	+	0.291649i	$0.0942039\pi$
$830$	13.6646	−	18.8077i	0.474306	−	0.652826i
$831$		0			0
$832$	61.4712	+	19.9732i	2.13113	+	0.692446i
$833$	−6.30639	−	19.4091i	−0.218503	−	0.672484i
$834$		0			0
$835$		−	6.44395i		−	0.223002i
$836$	−21.7040	−	2.44366i	−0.750648	−	0.0845158i
$837$		0			0
$838$	14.8427	+	20.4292i	0.512733	+	0.705716i
$839$	19.9651	−	6.48707i	0.689273	−	0.223958i	0.0566224	−	0.998396i	$-0.481967\pi$
$839$	19.9651	−	6.48707i	0.689273	−	0.223958i	0.632651	+	0.774437i	$0.281967\pi$
$840$		0			0
$841$	23.4538	+	17.0402i	0.808753	+	0.587593i
$842$	−7.21614	−	5.24283i	−0.248685	−	0.180680i
$843$		0			0
$844$	−113.680	+	36.9370i	−3.91304	+	1.27142i
$845$	−3.51944	−	4.84410i	−0.121073	−	0.166642i
$846$		0			0
$847$	−13.6335	−	8.14260i	−0.468451	−	0.279783i
$848$		−	4.40906i		−	0.151408i
$849$		0			0
$850$	10.0445	+	30.9138i	0.344524	+	1.06034i
$851$	55.1637	+	17.9238i	1.89099	+	0.614419i
$852$		0			0
$853$	−3.11090	+	4.28178i	−0.106515	+	0.146605i	−0.858947	−	0.512065i	$-0.828881\pi$
$853$	−3.11090	+	4.28178i	−0.106515	+	0.146605i	0.752432	+	0.658670i	$0.228881\pi$
$854$	0.382533	−	1.17732i	0.0130900	−	0.0402869i
$855$		0			0
$856$	67.1135	−	48.7608i	2.29389	−	1.66661i
$857$	−7.76042			−0.265091			−0.132545	−	0.991177i	$-0.542315\pi$
$857$	−7.76042			−0.265091			−0.132545	+	0.991177i	$0.542315\pi$
$858$		0			0
$859$	−48.6716			−1.66065			−0.830326	−	0.557278i	$-0.811846\pi$
$859$	−48.6716			−1.66065			−0.830326	+	0.557278i	$0.811846\pi$
$860$	13.0843	−	9.50632i	0.446172	−	0.324163i
$861$		0			0
$862$	1.77184	−	5.45317i	0.0603492	−	0.185736i
$863$	−8.87079	+	12.2096i	−0.301965	+	0.415619i	−0.932854	−	0.360253i	$-0.882690\pi$
$863$	−8.87079	+	12.2096i	−0.301965	+	0.415619i	0.630889	+	0.775873i	$0.282690\pi$
$864$		0			0
$865$	−14.3805	−	4.67250i	−0.488951	−	0.158870i
$866$	12.8248	+	39.4705i	0.435803	+	1.34126i
$867$		0			0
$868$			31.0260i			1.05309i
$869$	28.9035	−	16.4035i	0.980485	−	0.556452i
$870$		0			0
$871$	−6.01315	−	8.27639i	−0.203748	−	0.280435i
$872$	−34.3238	+	11.1525i	−1.16235	+	0.377671i
$873$		0			0
$874$	15.8547	+	11.5191i	0.536294	+	0.389640i
$875$	13.3609	+	9.70723i	0.451679	+	0.328164i
$876$		0			0
$877$	21.0670	−	6.84508i	0.711382	−	0.231142i	0.0690993	−	0.997610i	$-0.477987\pi$
$877$	21.0670	−	6.84508i	0.711382	−	0.231142i	0.642283	+	0.766468i	$0.277987\pi$
$878$	−56.6952	−	78.0342i	−1.91337	−	2.63353i
$879$		0			0
$880$	−12.6365	−	61.6909i	−0.425977	−	2.07960i
$881$			18.8235i			0.634180i	0.948395	+	0.317090i	$0.102706\pi$
$881$			18.8235i			0.634180i	−0.948395	+	0.317090i	$0.897294\pi$
$882$		0			0
$883$	−11.7223	−	36.0776i	−0.394488	−	1.21411i	−0.929360	−	0.369175i	$-0.879640\pi$
$883$	−11.7223	−	36.0776i	−0.394488	−	1.21411i	0.534872	−	0.844933i	$-0.320360\pi$
$884$	−61.7874	−	20.0760i	−2.07814	−	0.675228i
$885$		0			0
$886$	18.9974	−	26.1477i	0.638230	−	0.878448i
$887$	−8.99644	+	27.6882i	−0.302071	+	0.929679i	0.678683	+	0.734431i	$0.262551\pi$
$887$	−8.99644	+	27.6882i	−0.302071	+	0.929679i	−0.980754	+	0.195247i	$0.937449\pi$
$888$		0			0
$889$	−0.120187	+	0.0873211i	−0.00403095	+	0.00292866i
$890$	19.9403			0.668401
$891$		0			0
$892$	−119.589			−4.00414
$893$	−7.35638	+	5.34472i	−0.246172	+	0.178854i
$894$		0			0
$895$	−4.50465	+	13.8639i	−0.150574	+	0.463419i
$896$	−19.4200	+	26.7293i	−0.648777	+	0.892965i
$897$		0			0
$898$	−65.4203	−	21.2563i	−2.18310	−	0.709333i
$899$	0.122993	+	0.378534i	0.00410205	+	0.0126248i
$900$		0			0
$901$			1.39484i			0.0464688i
$902$	−27.5490	+	30.1447i	−0.917280	+	1.00371i
$903$		0			0
$904$	104.293	+	143.548i	3.46875	+	4.77432i
$905$	21.3352	−	6.93222i	0.709205	−	0.230435i
$906$		0			0
$907$	15.0107	+	10.9059i	0.498423	+	0.362126i	0.808414	−	0.588614i	$-0.200326\pi$
$907$	15.0107	+	10.9059i	0.498423	+	0.362126i	−0.309991	+	0.950739i	$0.600326\pi$
$908$	34.5673	+	25.1146i	1.14716	+	0.833458i
$909$		0			0
$910$	−15.9308	+	5.17622i	−0.528100	+	0.171590i
$911$	19.5259	+	26.8751i	0.646922	+	0.890411i	0.998961	−	0.0455740i	$-0.0145117\pi$
$911$	19.5259	+	26.8751i	0.646922	+	0.890411i	−0.352039	+	0.935985i	$0.614512\pi$
$912$		0			0
$913$	−13.3449	+	14.6022i	−0.441650	+	0.483264i
$914$		−	2.74759i		−	0.0908823i
$915$		0			0
$916$	22.0829	+	67.9643i	0.729640	+	2.24560i
$917$	21.0963	+	6.85459i	0.696660	+	0.226359i
$918$		0			0
$919$	−10.8277	+	14.9031i	−0.357173	+	0.491606i	−0.949358	−	0.314195i	$-0.898265\pi$
$919$	−10.8277	+	14.9031i	−0.357173	+	0.491606i	0.592185	+	0.805802i	$0.298265\pi$
$920$	−22.7827	+	70.1180i	−0.751124	+	2.31172i
$921$		0			0
$922$	9.85973	−	7.16351i	0.324713	−	0.235918i
$923$	−27.2929			−0.898356
$924$		0			0
$925$	−29.0292			−0.954476
$926$	−18.4200	+	13.3829i	−0.605320	+	0.439791i
$927$		0			0
$928$	−0.535586	+	1.64836i	−0.0175815	+	0.0541102i
$929$	−17.2134	+	23.6922i	−0.564752	+	0.777315i	−0.991921	−	0.126857i	$-0.959511\pi$
$929$	−17.2134	+	23.6922i	−0.564752	+	0.777315i	0.427169	+	0.904172i	$0.359511\pi$
$930$		0			0
$931$	5.85663	+	1.90293i	0.191943	+	0.0623662i
$932$	8.21593	+	25.2860i	0.269122	+	0.828272i
$933$		0			0
$934$			16.7097i			0.546757i
$935$	3.99765	+	19.5164i	0.130737	+	0.638253i
$936$		0			0
$937$	−9.28756	−	12.7832i	−0.303411	−	0.417610i	0.629901	−	0.776675i	$-0.283095\pi$
$937$	−9.28756	−	12.7832i	−0.303411	−	0.417610i	−0.933312	+	0.359066i	$0.883095\pi$
$938$	12.7106	−	4.12994i	0.415017	−	0.134847i
$939$		0			0
$940$	−44.6688	−	32.4538i	−1.45694	−	1.05853i
$941$	6.70118	+	4.86869i	0.218452	+	0.158715i	0.691630	−	0.722252i	$-0.256893\pi$
$941$	6.70118	+	4.86869i	0.218452	+	0.158715i	−0.473177	+	0.880967i	$0.656893\pi$
$942$		0			0
$943$	25.2445	−	8.20243i	0.822073	−	0.267108i
$944$	−23.3457	−	32.1326i	−0.759839	−	1.04583i
$945$		0			0
$946$	−16.5220	+	9.37671i	−0.537178	+	0.304863i
$947$		−	4.91237i		−	0.159631i	−0.996810	−	0.0798154i	$-0.974567\pi$
$947$		−	4.91237i		−	0.159631i	0.996810	−	0.0798154i	$-0.0254331\pi$
$948$		0			0
$949$	6.52997	+	20.0972i	0.211972	+	0.652382i
$950$	−9.32816	−	3.03090i	−0.302645	−	0.0983355i
$951$		0			0
$952$	30.9081	−	42.5414i	1.00174	−	1.37878i
$953$	−1.81366	+	5.58186i	−0.0587501	+	0.180814i	−0.976125	−	0.217211i	$-0.930304\pi$
$953$	−1.81366	+	5.58186i	−0.0587501	+	0.180814i	0.917375	+	0.398025i	$0.130304\pi$
$954$		0			0
$955$	4.34837	−	3.15927i	0.140710	−	0.102232i
$956$	−106.013			−3.42872
$957$		0			0
$958$	−60.0907			−1.94144
$959$	4.34875	−	3.15955i	0.140428	−	0.102027i
$960$		0			0
$961$	−4.41495	+	13.5878i	−0.142418	+	0.438317i
$962$	47.0782	−	64.7976i	1.51786	−	2.08916i
$963$		0			0
$964$	141.498	+	45.9756i	4.55735	+	1.48077i
$965$	11.1498	+	34.3155i	0.358924	+	1.10466i
$966$		0			0
$967$		−	17.5410i		−	0.564080i	−0.959403	−	0.282040i	$-0.908989\pi$
$967$		−	17.5410i		−	0.564080i	0.959403	−	0.282040i	$-0.0910110\pi$
$968$	8.66725	+	96.1256i	0.278576	+	3.08959i
$969$		0			0
$970$	13.8400	+	19.0492i	0.444377	+	0.611633i
$971$	−46.6836	+	15.1684i	−1.49815	+	0.486778i	−0.939478	−	0.342610i	$-0.888689\pi$
$971$	−46.6836	+	15.1684i	−1.49815	+	0.486778i	−0.558672	+	0.829389i	$0.688689\pi$
$972$		0			0
$973$	19.8735	+	14.4390i	0.637117	+	0.462892i
$974$	74.2582	+	53.9518i	2.37939	+	1.72873i
$975$		0			0
$976$	−3.97257	+	1.29077i	−0.127159	+	0.0413164i
$977$	−7.37573	−	10.1518i	−0.235970	−	0.324785i	0.674566	−	0.738215i	$-0.264331\pi$
$977$	−7.37573	−	10.1518i	−0.235970	−	0.324785i	−0.910536	+	0.413429i	$0.864331\pi$
$978$		0			0
$979$	−16.8608	−	1.89836i	−0.538874	−	0.0606720i
$980$			37.3923i			1.19445i
$981$		0			0
$982$	−15.6708	−	48.2298i	−0.500076	−	1.53908i
$983$	−20.0460	−	6.51333i	−0.639367	−	0.207743i	−0.0286471	−	0.999590i	$-0.509120\pi$
$983$	−20.0460	−	6.51333i	−0.639367	−	0.207743i	−0.610720	+	0.791847i	$0.709120\pi$
$984$		0			0
$985$	−16.3470	+	22.4997i	−0.520858	+	0.716900i
$986$	0.336455	−	1.03550i	0.0107149	−	0.0329771i
$987$		0			0
$988$	15.8597	−	11.5227i	0.504564	−	0.366587i
$989$	12.3481			0.392648
$990$		0			0
$991$	60.3045			1.91564			0.957818	−	0.287375i	$-0.0927826\pi$
$991$	60.3045			1.91564			0.957818	+	0.287375i	$0.0927826\pi$
$992$	58.8787	−	42.7779i	1.86940	−	1.35820i
$993$		0			0
$994$	11.0182	−	33.9105i	0.349475	−	1.07557i
$995$	−22.1227	+	30.4492i	−0.701336	+	0.965306i
$996$		0			0
$997$	53.4551	+	17.3686i	1.69294	+	0.550069i	0.987351	−	0.158553i	$-0.0506828\pi$
$997$	53.4551	+	17.3686i	1.69294	+	0.550069i	0.705588	+	0.708622i	$0.250683\pi$
$998$	−6.32493	−	19.4661i	−0.200212	−	0.616190i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.k.a.404.20		80
3.2	odd	2	inner	891.2.k.a.404.1		80
9.2	odd	6		297.2.t.a.206.10		80
9.4	even	3		297.2.t.a.8.10		80
9.5	odd	6		99.2.p.a.74.1	yes	80
9.7	even	3		99.2.p.a.41.1	yes	80
11.7	odd	10	inner	891.2.k.a.161.1		80
33.29	even	10	inner	891.2.k.a.161.20		80
99.7	odd	30		99.2.p.a.95.1	yes	80
99.29	even	30		297.2.t.a.260.10		80
99.40	odd	30		297.2.t.a.62.10		80
99.95	even	30		99.2.p.a.29.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.1	✓	80	99.95	even	30
99.2.p.a.41.1	yes	80	9.7	even	3
99.2.p.a.74.1	yes	80	9.5	odd	6
99.2.p.a.95.1	yes	80	99.7	odd	30
297.2.t.a.8.10		80	9.4	even	3
297.2.t.a.62.10		80	99.40	odd	30
297.2.t.a.206.10		80	9.2	odd	6
297.2.t.a.260.10		80	99.29	even	30
891.2.k.a.161.1		80	11.7	odd	10	inner
891.2.k.a.161.20		80	33.29	even	10	inner
891.2.k.a.404.1		80	3.2	odd	2	inner
891.2.k.a.404.20		80	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.17940 - 1.58343i) q^{2} +(1.62452 - 4.99975i) q^{4} +(0.850459 - 1.17056i) q^{5} +(1.37298 + 0.446107i) q^{7} +(-2.71136 - 8.34470i) q^{8} -3.89775i q^{10} +(-0.371076 + 3.29580i) q^{11} +(-1.74976 - 2.40833i) q^{13} +(3.69865 - 1.20176i) q^{14} +(-10.6163 - 7.71319i) q^{16} +(3.35854 + 2.44012i) q^{17} +(-1.19136 + 0.387096i) q^{19} +(-4.47090 - 6.15367i) q^{20} +(4.40994 + 7.77045i) q^{22} -5.80743i q^{23} +(0.898164 + 2.76426i) q^{25} +(-7.62685 - 2.47811i) q^{26} +(4.46085 - 6.13983i) q^{28} +(0.0300853 - 0.0925930i) q^{29} +(-3.30738 + 2.40295i) q^{31} -17.8022 q^{32} +11.1834 q^{34} +(1.68985 - 1.22775i) q^{35} +(-3.08635 + 9.49880i) q^{37} +(-1.98351 + 2.73007i) q^{38} +(-12.0738 - 3.92303i) q^{40} +(1.41240 + 4.34693i) q^{41} +2.12626i q^{43} +(15.8754 + 7.20937i) q^{44} +(-9.19566 - 12.6567i) q^{46} +(6.90361 - 2.24312i) q^{47} +(-3.97707 - 2.88951i) q^{49} +(6.33448 + 4.60227i) q^{50} +(-14.8836 + 4.83597i) q^{52} +(0.197492 + 0.271824i) q^{53} +(3.54233 + 3.23731i) q^{55} -12.6666i q^{56} +(-0.0810465 - 0.249436i) q^{58} +(2.87859 + 0.935310i) q^{59} +(0.187098 - 0.257518i) q^{61} +(-3.40321 + 10.4740i) q^{62} +(-17.5657 + 12.7622i) q^{64} -4.30718 q^{65} +3.43656 q^{67} +(17.6560 - 12.8278i) q^{68} +(1.73882 - 5.35153i) q^{70} +(5.38901 - 7.41734i) q^{71} +(-6.75113 - 2.19358i) q^{73} +(8.31428 + 25.5887i) q^{74} +6.58534i q^{76} +(-1.97976 + 4.35952i) q^{77} +(-5.88983 - 8.10666i) q^{79} +(-18.0574 + 5.86722i) q^{80} +(9.96124 + 7.23727i) q^{82} +(4.82527 + 3.50577i) q^{83} +(5.71260 - 1.85614i) q^{85} +(3.36679 + 4.63399i) q^{86} +(28.5086 - 5.83958i) q^{88} +5.11584i q^{89} +(-1.32800 - 4.08716i) q^{91} +(-29.0357 - 9.43428i) q^{92} +(11.4939 - 15.8200i) q^{94} +(-0.560084 + 1.72376i) q^{95} +(-4.88722 + 3.55077i) q^{97} -13.2430 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{4} + 10 q^{7} + 10 q^{13} - 10 q^{16} - 50 q^{19} + 22 q^{22} + 4 q^{25} - 20 q^{28} + 12 q^{31} + 20 q^{34} - 6 q^{37} - 30 q^{40} - 40 q^{46} + 2 q^{49} + 10 q^{52} - 18 q^{55} + 58 q^{58}+ \cdots - 54 q^{97}+O(q^{100}) \) 80 * q - 10 * q^4 + 10 * q^7 + 10 * q^13 - 10 * q^16 - 50 * q^19 + 22 * q^22 + 4 * q^25 - 20 * q^28 + 12 * q^31 + 20 * q^34 - 6 * q^37 - 30 * q^40 - 40 * q^46 + 2 * q^49 + 10 * q^52 - 18 * q^55 + 58 * q^58 + 10 * q^61 - 8 * q^64 - 20 * q^67 - 60 * q^70 - 20 * q^73 + 10 * q^79 - 2 * q^82 + 10 * q^85 + 118 * q^88 + 52 * q^91 + 10 * q^94 - 54 * q^97

Introduction

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