LMFDB - Embedded newform 975.2.n.o.824.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(749,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1]))

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

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

chi := DirichletCharacter("975.749");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.n (of order $4$, degree $2$, not 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:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			824.2
Root			$-1.49094 - 1.49094i$ of defining polynomial
Character	$\chi$	$=$	975.824
Dual form			975.2.n.o.749.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.664640 - 0.664640i) q^{2} +(1.29021 - 1.15558i) q^{3} +1.11651i q^{4} +(0.0894818 - 1.62557i) q^{6} +(2.20073 - 2.20073i) q^{7} +(2.07136 + 2.07136i) q^{8} +(0.329281 - 2.98187i) q^{9} +(0.820218 - 0.820218i) q^{11} +(1.29021 + 1.44053i) q^{12} +(0.173703 + 3.60136i) q^{13} -2.92539i q^{14} +0.520402 q^{16} -0.688845i q^{17} +(-1.76302 - 2.20073i) q^{18} +(1.82630 - 1.82630i) q^{19} +(0.296288 - 5.38251i) q^{21} -1.09030i q^{22} +4.86537i q^{23} +(5.06610 + 0.278871i) q^{24} +(2.50906 + 2.27816i) q^{26} +(-3.02095 - 4.22775i) q^{27} +(2.45713 + 2.45713i) q^{28} -1.93998i q^{29} +(-0.910518 + 0.910518i) q^{31} +(-3.79683 + 3.79683i) q^{32} +(0.110427 - 2.00608i) q^{33} +(-0.457834 - 0.457834i) q^{34} +(3.32928 + 0.367644i) q^{36} +(1.82630 - 1.82630i) q^{37} -2.42766i q^{38} +(4.38577 + 4.44579i) q^{39} +(-5.96093 - 5.96093i) q^{41} +(-3.38051 - 3.77436i) q^{42} +2.50580 q^{43} +(0.915778 + 0.915778i) q^{44} +(3.23372 + 3.23372i) q^{46} +(-8.62839 - 8.62839i) q^{47} +(0.671427 - 0.601365i) q^{48} -2.68640i q^{49} +(-0.796014 - 0.888754i) q^{51} +(-4.02095 + 0.193941i) q^{52} +8.99159 q^{53} +(-4.81778 - 0.802092i) q^{54} +9.11698 q^{56} +(0.245878 - 4.46673i) q^{57} +(-1.28939 - 1.28939i) q^{58} +(-3.46755 + 3.46755i) q^{59} +13.9094 q^{61} +1.21033i q^{62} +(-5.83764 - 7.28695i) q^{63} +6.08786i q^{64} +(-1.25993 - 1.40672i) q^{66} +(5.39820 + 5.39820i) q^{67} +0.769099 q^{68} +(5.62231 + 6.27734i) q^{69} +(-5.58324 - 5.58324i) q^{71} +(6.85858 - 5.49447i) q^{72} +(-9.43292 + 9.43292i) q^{73} -2.42766i q^{74} +(2.03907 + 2.03907i) q^{76} -3.61015i q^{77} +(5.86981 + 0.0398898i) q^{78} +6.07461 q^{79} +(-8.78315 - 1.96375i) q^{81} -7.92375 q^{82} +(-3.93390 + 3.93390i) q^{83} +(6.00961 + 0.330807i) q^{84} +(1.66546 - 1.66546i) q^{86} +(-2.24180 - 2.50298i) q^{87} +3.39793 q^{88} +(1.07814 - 1.07814i) q^{89} +(8.30790 + 7.54335i) q^{91} -5.43221 q^{92} +(-0.122585 + 2.22693i) q^{93} -11.4696 q^{94} +(-0.511175 + 9.28624i) q^{96} +(7.02377 + 7.02377i) q^{97} +(-1.78549 - 1.78549i) q^{98} +(-2.17570 - 2.71587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} + 2 q^{3} - 4 q^{6} + 14 q^{7} - 12 q^{8} + 4 q^{9} - 4 q^{11} + 2 q^{12} + 14 q^{13} - 8 q^{16} + 30 q^{18} + 2 q^{19} - 8 q^{21} + 34 q^{24} + 32 q^{26} - 10 q^{27} - 24 q^{28} - 12 q^{31}+ \cdots + 28 q^{99}+O(q^{100}) $ 8 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 + 14 * q^7 - 12 * q^8 + 4 * q^9 - 4 * q^11 + 2 * q^12 + 14 * q^13 - 8 * q^16 + 30 * q^18 + 2 * q^19 - 8 * q^21 + 34 * q^24 + 32 * q^26 - 10 * q^27 - 24 * q^28 - 12 * q^31 - 18 * q^32 - 18 * q^33 - 10 * q^34 + 28 * q^36 + 2 * q^37 + 20 * q^39 - 38 * q^41 - 34 * q^42 - 4 * q^43 - 10 * q^44 + 34 * q^46 - 22 * q^47 + 54 * q^48 + 26 * q^51 - 18 * q^52 + 28 * q^53 - 12 * q^54 - 76 * q^56 + 6 * q^57 + 18 * q^58 - 14 * q^59 - 8 * q^61 - 10 * q^63 + 18 * q^66 - 40 * q^68 + 10 * q^71 + 4 * q^72 - 10 * q^73 + 26 * q^76 + 2 * q^78 + 56 * q^79 + 8 * q^81 - 16 * q^82 - 38 * q^83 + 58 * q^84 + 34 * q^86 + 34 * q^87 + 8 * q^88 + 28 * q^89 + 8 * q^91 + 72 * q^92 + 22 * q^93 - 20 * q^94 + 72 * q^96 + 4 * q^97 - 26 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

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 $

$2$	0.664640	−	0.664640i	0.469972	−	0.469972i	−0.431934	−	0.901905i	$-0.642169\pi$
$2$	0.664640	−	0.664640i	0.469972	−	0.469972i	0.901905	+	0.431934i	$0.142169\pi$
$3$	1.29021	−	1.15558i	0.744903	−	0.667173i
$3$	1.29021	−	1.15558i	0.744903	−	0.667173i
$4$			1.11651i			0.558253i
$5$		0			0
$5$		0			0
$6$	0.0894818	−	1.62557i	0.0365308	−	0.663636i
$7$	2.20073	−	2.20073i	0.831797	−	0.831797i	−0.155966	−	0.987762i	$-0.549849\pi$
$7$	2.20073	−	2.20073i	0.831797	−	0.831797i	0.987762	+	0.155966i	$0.0498489\pi$
$8$	2.07136	+	2.07136i	0.732335	+	0.732335i
$9$	0.329281	−	2.98187i	0.109760	−	0.993958i
$10$		0			0
$11$	0.820218	−	0.820218i	0.247305	−	0.247305i	−0.572559	−	0.819864i	$-0.694049\pi$
$11$	0.820218	−	0.820218i	0.247305	−	0.247305i	0.819864	+	0.572559i	$0.194049\pi$
$12$	1.29021	+	1.44053i	0.372451	+	0.415844i
$13$	0.173703	+	3.60136i	0.0481766	+	0.998839i
$13$	0.173703	+	3.60136i	0.0481766	+	0.998839i
$14$		−	2.92539i		−	0.781842i
$15$		0			0
$16$	0.520402			0.130100
$17$		−	0.688845i		−	0.167069i	−0.996505	−	0.0835347i	$-0.973379\pi$
$17$		−	0.688845i		−	0.167069i	0.996505	−	0.0835347i	$-0.0266209\pi$
$18$	−1.76302	−	2.20073i	−0.415548	−	0.518716i
$19$	1.82630	−	1.82630i	0.418981	−	0.418981i	−0.465871	−	0.884852i	$-0.654259\pi$
$19$	1.82630	−	1.82630i	0.418981	−	0.418981i	0.884852	+	0.465871i	$0.154259\pi$
$20$		0			0
$21$	0.296288	−	5.38251i	0.0646554	−	1.17456i
$22$		−	1.09030i		−	0.232453i
$23$			4.86537i			1.01450i	0.861799	+	0.507250i	$0.169338\pi$
$23$			4.86537i			1.01450i	−0.861799	+	0.507250i	$0.830662\pi$
$24$	5.06610	+	0.278871i	1.03411	+	0.0569242i
$25$		0			0
$26$	2.50906	+	2.27816i	0.492068	+	0.446784i
$27$	−3.02095	−	4.22775i	−0.581381	−	0.813631i
$28$	2.45713	+	2.45713i	0.464353	+	0.464353i
$29$		−	1.93998i		−	0.360246i	−0.983644	−	0.180123i	$-0.942350\pi$
$29$		−	1.93998i		−	0.360246i	0.983644	−	0.180123i	$-0.0576495\pi$
$30$		0			0
$31$	−0.910518	+	0.910518i	−0.163534	+	0.163534i	−0.784130	−	0.620596i	$-0.786891\pi$
$31$	−0.910518	+	0.910518i	−0.163534	+	0.163534i	0.620596	+	0.784130i	$0.286891\pi$
$32$	−3.79683	+	3.79683i	−0.671191	+	0.671191i
$33$	0.110427	−	2.00608i	0.0192230	−	0.349213i
$34$	−0.457834	−	0.457834i	−0.0785179	−	0.0785179i
$35$		0			0
$36$	3.32928	+	0.367644i	0.554880	+	0.0612740i
$37$	1.82630	−	1.82630i	0.300241	−	0.300241i	−0.540867	−	0.841108i	$-0.681904\pi$
$37$	1.82630	−	1.82630i	0.300241	−	0.300241i	0.841108	+	0.540867i	$0.181904\pi$
$38$		−	2.42766i		−	0.393819i
$39$	4.38577	+	4.44579i	0.702285	+	0.711896i
$40$		0			0
$41$	−5.96093	−	5.96093i	−0.930941	−	0.930941i	0.0668241	−	0.997765i	$-0.478713\pi$
$41$	−5.96093	−	5.96093i	−0.930941	−	0.930941i	−0.997765	+	0.0668241i	$0.978713\pi$
$42$	−3.38051	−	3.77436i	−0.521624	−	0.582396i
$43$	2.50580			0.382132			0.191066	−	0.981577i	$-0.438806\pi$
$43$	2.50580			0.382132			0.191066	+	0.981577i	$0.438806\pi$
$44$	0.915778	+	0.915778i	0.138059	+	0.138059i
$45$		0			0
$46$	3.23372	+	3.23372i	0.476786	+	0.476786i
$47$	−8.62839	−	8.62839i	−1.25858	−	1.25858i	−0.951771	−	0.306809i	$-0.900739\pi$
$47$	−8.62839	−	8.62839i	−1.25858	−	1.25858i	−0.306809	−	0.951771i	$-0.599261\pi$
$48$	0.671427	−	0.601365i	0.0969122	−	0.0867995i
$49$		−	2.68640i		−	0.383772i
$50$		0			0
$51$	−0.796014	−	0.888754i	−0.111464	−	0.124450i
$52$	−4.02095	+	0.193941i	−0.557605	+	0.0268948i
$53$	8.99159			1.23509			0.617545	−	0.786536i	$-0.288127\pi$
$53$	8.99159			1.23509			0.617545	+	0.786536i	$0.288127\pi$
$54$	−4.81778	−	0.802092i	−0.655617	−	0.109151i
$55$		0			0
$56$	9.11698			1.21831
$57$	0.245878	−	4.46673i	0.0325673	−	0.591633i
$58$	−1.28939	−	1.28939i	−0.169305	−	0.169305i
$59$	−3.46755	+	3.46755i	−0.451437	+	0.451437i	−0.895831	−	0.444394i	$-0.853419\pi$
$59$	−3.46755	+	3.46755i	−0.451437	+	0.451437i	0.444394	+	0.895831i	$0.353419\pi$
$60$		0			0
$61$	13.9094			1.78091			0.890456	−	0.455069i	$-0.150385\pi$
$61$	13.9094			1.78091			0.890456	+	0.455069i	$0.150385\pi$
$62$			1.21033i			0.153713i
$63$	−5.83764	−	7.28695i	−0.735473	−	0.918070i
$64$			6.08786i			0.760982i
$65$		0			0
$66$	−1.25993	−	1.40672i	−0.155086	−	0.173155i
$67$	5.39820	+	5.39820i	0.659495	+	0.659495i	0.955260	−	0.295766i	$-0.0955748\pi$
$67$	5.39820	+	5.39820i	0.659495	+	0.659495i	−0.295766	+	0.955260i	$0.595575\pi$
$68$	0.769099			0.0932670
$69$	5.62231	+	6.27734i	0.676847	+	0.755703i
$70$		0			0
$71$	−5.58324	−	5.58324i	−0.662609	−	0.662609i	0.293386	−	0.955994i	$-0.405218\pi$
$71$	−5.58324	−	5.58324i	−0.662609	−	0.662609i	−0.955994	+	0.293386i	$0.905218\pi$
$72$	6.85858	−	5.49447i	0.808292	−	0.647529i
$73$	−9.43292	+	9.43292i	−1.10404	+	1.10404i	−0.110122	+	0.993918i	$0.535124\pi$
$73$	−9.43292	+	9.43292i	−1.10404	+	1.10404i	−0.993918	+	0.110122i	$0.964876\pi$
$74$		−	2.42766i		−	0.282210i
$75$		0			0
$76$	2.03907	+	2.03907i	0.233898	+	0.233898i
$77$		−	3.61015i		−	0.411415i
$78$	5.86981	+	0.0398898i	0.664625	+	0.00451663i
$79$	6.07461			0.683448			0.341724	−	0.939800i	$-0.388989\pi$
$79$	6.07461			0.683448			0.341724	+	0.939800i	$0.388989\pi$
$80$		0			0
$81$	−8.78315	−	1.96375i	−0.975905	−	0.218194i
$82$	−7.92375			−0.875032
$83$	−3.93390	+	3.93390i	−0.431802	+	0.431802i	−0.889241	−	0.457439i	$-0.848767\pi$
$83$	−3.93390	+	3.93390i	−0.431802	+	0.431802i	0.457439	+	0.889241i	$0.348767\pi$
$84$	6.00961	+	0.330807i	0.655702	+	0.0360941i
$85$		0			0
$86$	1.66546	−	1.66546i	0.179591	−	0.179591i
$87$	−2.24180	−	2.50298i	−0.240346	−	0.268348i
$88$	3.39793			0.362220
$89$	1.07814	−	1.07814i	0.114283	−	0.114283i	−0.647653	−	0.761936i	$-0.724249\pi$
$89$	1.07814	−	1.07814i	0.114283	−	0.114283i	0.761936	+	0.647653i	$0.224249\pi$
$90$		0			0
$91$	8.30790	+	7.54335i	0.870904	+	0.790758i
$92$	−5.43221			−0.566347
$93$	−0.122585	+	2.22693i	−0.0127114	+	0.230922i
$94$	−11.4696			−1.18299
$95$		0			0
$96$	−0.511175	+	9.28624i	−0.0521715	+	0.947773i
$97$	7.02377	+	7.02377i	0.713155	+	0.713155i	0.967194	−	0.254039i	$-0.0817591\pi$
$97$	7.02377	+	7.02377i	0.713155	+	0.713155i	−0.254039	+	0.967194i	$0.581759\pi$
$98$	−1.78549	−	1.78549i	−0.180362	−	0.180362i
$99$	−2.17570	−	2.71587i	−0.218667	−	0.272955i
$100$		0			0
$101$	−19.0737			−1.89791			−0.948954	−	0.315415i	$-0.897856\pi$
$101$	−19.0737			−1.89791			−0.948954	+	0.315415i	$0.897856\pi$
$102$	−1.11976	−	0.0616391i	−0.110873	−	0.00610318i
$103$	−14.1165			−1.39094			−0.695470	−	0.718555i	$-0.744804\pi$
$103$	−14.1165			−1.39094			−0.695470	+	0.718555i	$0.744804\pi$
$104$	−7.09991	+	7.81951i	−0.696203	+	0.766766i
$105$		0			0
$106$	5.97618	−	5.97618i	0.580457	−	0.580457i
$107$	−18.1484			−1.75447			−0.877234	−	0.480064i	$-0.840614\pi$
$107$	−18.1484			−1.75447			−0.877234	+	0.480064i	$0.840614\pi$
$108$	4.72031	−	3.37290i	0.454212	−	0.324558i
$109$	9.49294	−	9.49294i	0.909259	−	0.909259i	−0.0869537	−	0.996212i	$-0.527713\pi$
$109$	9.49294	−	9.49294i	0.909259	−	0.909259i	0.996212	+	0.0869537i	$0.0277132\pi$
$110$		0			0
$111$	0.245878	−	4.46673i	0.0233377	−	0.423964i
$112$	1.14526	−	1.14526i	0.108217	−	0.108217i
$113$	−7.29303			−0.686070			−0.343035	−	0.939323i	$-0.611455\pi$
$113$	−7.29303			−0.686070			−0.343035	+	0.939323i	$0.611455\pi$
$114$	−2.80535	−	3.13219i	−0.262745	−	0.293357i
$115$		0			0
$116$	2.16600			0.201108
$117$	10.7960	+	0.667899i	0.998092	+	0.0617473i
$118$			4.60935i			0.424325i
$119$	−1.51596	−	1.51596i	−0.138968	−	0.138968i
$120$		0			0
$121$			9.65448i			0.877680i
$122$	9.24473	−	9.24473i	0.836979	−	0.836979i
$123$	−14.5792	−	0.802531i	−1.31456	−	0.0723618i
$124$	−1.01660	−	1.01660i	−0.0912933	−	0.0912933i
$125$		0			0
$126$	−8.72313	−	0.963274i	−0.777118	−	0.0858152i
$127$	−12.1706			−1.07996			−0.539981	−	0.841677i	$-0.681569\pi$
$127$	−12.1706			−1.07996			−0.539981	+	0.841677i	$0.681569\pi$
$128$	−3.54743	−	3.54743i	−0.313551	−	0.313551i
$129$	3.23301	−	2.89565i	0.284651	−	0.254948i
$130$		0			0
$131$			9.06213i			0.791762i	0.918302	+	0.395881i	$0.129561\pi$
$131$			9.06213i			0.791762i	−0.918302	+	0.395881i	$0.870439\pi$
$132$	2.23980	+	0.123293i	0.194949	+	0.0107313i
$133$		−	8.03836i		−	0.697014i
$134$	7.17572			0.619888
$135$		0			0
$136$	1.42684	−	1.42684i	0.122351	−	0.122351i
$137$	13.0162	+	13.0162i	1.11205	+	1.11205i	0.992874	+	0.119172i	$0.0380240\pi$
$137$	13.0162	+	13.0162i	1.11205	+	1.11205i	0.119172	+	0.992874i	$0.461976\pi$
$138$	7.90899	+	0.435362i	0.673258	+	0.0370605i
$139$	−5.96375			−0.505839			−0.252919	−	0.967487i	$-0.581391\pi$
$139$	−5.96375			−0.505839			−0.252919	+	0.967487i	$0.581391\pi$
$140$		0			0
$141$	−21.1032	−	1.16166i	−1.77721	−	0.0978291i
$142$	−7.42169			−0.622815
$143$	3.09638	+	2.81143i	0.258932	+	0.235104i
$144$	0.171358	−	1.55177i	0.0142799	−	0.129314i
$145$		0			0
$146$			12.5390i			1.03774i
$147$	−3.10435	−	3.46602i	−0.256042	−	0.285873i
$148$	2.03907	+	2.03907i	0.167611	+	0.167611i
$149$	−3.10679	−	3.10679i	−0.254518	−	0.254518i	0.568302	−	0.822820i	$-0.307601\pi$
$149$	−3.10679	−	3.10679i	−0.254518	−	0.254518i	−0.822820	+	0.568302i	$0.807601\pi$
$150$		0			0
$151$	0.0298443	+	0.0298443i	0.00242869	+	0.00242869i	0.708320	−	0.705891i	$-0.249453\pi$
$151$	0.0298443	+	0.0298443i	0.00242869	+	0.00242869i	−0.705891	+	0.708320i	$0.749453\pi$
$152$	7.56582			0.613669
$153$	−2.05405	−	0.226823i	−0.166060	−	0.0183376i
$154$	−2.39945	−	2.39945i	−0.193353	−	0.193353i
$155$		0			0
$156$	−4.96375	+	4.89674i	−0.397418	+	0.392053i
$157$			18.6772i			1.49060i	0.666729	+	0.745300i	$0.267694\pi$
$157$			18.6772i			1.49060i	−0.666729	+	0.745300i	$0.732306\pi$
$158$	4.03743	−	4.03743i	0.321201	−	0.321201i
$159$	11.6010	−	10.3905i	0.920022	−	0.824019i
$160$		0			0
$161$	10.7074	+	10.7074i	0.843857	+	0.843857i
$162$	−7.14282	+	4.53245i	−0.561193	+	0.356103i
$163$	−2.74196	+	2.74196i	−0.214767	+	0.214767i	−0.806289	−	0.591522i	$-0.798527\pi$
$163$	−2.74196	+	2.74196i	−0.214767	+	0.214767i	0.591522	+	0.806289i	$0.298527\pi$
$164$	6.65541	−	6.65541i	0.519700	−	0.519700i
$165$		0			0
$166$			5.22926i			0.405870i
$167$	12.0831	+	12.0831i	0.935016	+	0.935016i	0.998014	−	0.0629973i	$-0.0200660\pi$
$167$	12.0831	+	12.0831i	0.935016	+	0.935016i	−0.0629973	+	0.998014i	$0.520066\pi$
$168$	11.7628	−	10.5354i	0.907521	−	0.812822i
$169$	−12.9397	+	1.25114i	−0.995358	+	0.0962414i
$170$		0			0
$171$	−4.84442	−	6.04715i	−0.370462	−	0.462437i
$172$			2.79775i			0.213326i
$173$			24.0678i			1.82984i	0.403637	+	0.914919i	$0.367746\pi$
$173$			24.0678i			1.82984i	−0.403637	+	0.914919i	$0.632254\pi$
$174$	−3.15358	−	0.173593i	−0.239072	−	0.0131601i
$175$		0			0
$176$	0.426843	−	0.426843i	0.0321745	−	0.0321745i
$177$	−0.466843	+	8.48089i	−0.0350901	+	0.637463i
$178$		−	1.43315i		−	0.107419i
$179$	−9.42733			−0.704632			−0.352316	−	0.935881i	$-0.614606\pi$
$179$	−9.42733			−0.704632			−0.352316	+	0.935881i	$0.614606\pi$
$180$		0			0
$181$		−	17.8034i		−	1.32332i	−0.749806	−	0.661658i	$-0.769853\pi$
$181$		−	17.8034i		−	1.32332i	0.749806	−	0.661658i	$-0.230147\pi$
$182$	10.5354	−	0.508149i	0.780934	−	0.0376665i
$183$	17.9460	−	16.0734i	1.32661	−	1.18818i
$184$	−10.0779	+	10.0779i	−0.742953	+	0.742953i
$185$		0			0
$186$	1.39864	+	1.56158i	0.102553	+	0.114501i
$187$	−0.565003	−	0.565003i	−0.0413171	−	0.0413171i
$188$	9.63365	−	9.63365i	0.702606	−	0.702606i
$189$	−15.9524	−	2.65585i	−1.16037	−	0.193185i
$190$		0			0
$191$		−	7.08269i		−	0.512486i	−0.966612	−	0.256243i	$-0.917515\pi$
$191$		−	7.08269i		−	0.512486i	0.966612	−	0.256243i	$-0.0824847\pi$
$192$	7.03499	+	7.85461i	0.507707	+	0.566858i
$193$	4.47645	−	4.47645i	0.322222	−	0.322222i	−0.527397	−	0.849619i	$-0.676832\pi$
$193$	4.47645	−	4.47645i	0.322222	−	0.322222i	0.849619	+	0.527397i	$0.176832\pi$
$194$	9.33656			0.670326
$195$		0			0
$196$	2.99939			0.214242
$197$	17.0750	−	17.0750i	1.21654	−	1.21654i	0.247708	−	0.968835i	$-0.420323\pi$
$197$	17.0750	−	17.0750i	1.21654	−	1.21654i	0.968835	−	0.247708i	$-0.0796775\pi$
$198$	−3.25114	−	0.359015i	−0.231048	−	0.0255141i
$199$		−	2.76666i		−	0.196123i	−0.995180	−	0.0980616i	$-0.968736\pi$
$199$		−	2.76666i		−	0.196123i	0.995180	−	0.0980616i	$-0.0312642\pi$
$200$		0			0
$201$	13.2028	+	0.726769i	0.931256	+	0.0512624i
$202$	−12.6772	+	12.6772i	−0.891963	+	0.891963i
$203$	−4.26937	−	4.26937i	−0.299651	−	0.299651i
$204$	0.992299	−	0.888754i	0.0694749	−	0.0622252i
$205$		0			0
$206$	−9.38240	+	9.38240i	−0.653703	+	0.653703i
$207$	14.5079	+	1.60207i	1.00837	+	0.111352i
$208$	0.0903955	+	1.87416i	0.00626780	+	0.129949i
$209$		−	2.99592i		−	0.207232i
$210$		0			0
$211$	−8.53412			−0.587513			−0.293757	−	0.955880i	$-0.594906\pi$
$211$	−8.53412			−0.587513			−0.293757	+	0.955880i	$0.594906\pi$
$212$			10.0392i			0.689493i
$213$	−13.6554	−	0.751682i	−0.935654	−	0.0515044i
$214$	−12.0621	+	12.0621i	−0.824550	+	0.824550i
$215$		0			0
$216$	2.49973	−	15.0146i	0.170085	−	1.02162i
$217$			4.00761i			0.272054i
$218$		−	12.6188i		−	0.854652i
$219$	−1.26997	+	23.0709i	−0.0858168	+	1.55899i
$220$		0			0
$221$	2.48078	−	0.119655i	0.166875	−	0.00804884i
$222$	−2.80535	−	3.13219i	−0.188283	−	0.210219i
$223$	17.3123	+	17.3123i	1.15932	+	1.15932i	0.984622	+	0.174698i	$0.0558949\pi$
$223$	17.3123	+	17.3123i	1.15932	+	1.15932i	0.174698	+	0.984622i	$0.444105\pi$
$224$			16.7116i			1.11659i
$225$		0			0
$226$	−4.84724	+	4.84724i	−0.322434	+	0.322434i
$227$	7.27653	−	7.27653i	0.482960	−	0.482960i	−0.423116	−	0.906076i	$-0.639064\pi$
$227$	7.27653	−	7.27653i	0.482960	−	0.482960i	0.906076	+	0.423116i	$0.139064\pi$
$228$	4.98713	+	0.274524i	0.330281	+	0.0181808i
$229$	−15.2314	−	15.2314i	−1.00652	−	1.00652i	−0.999979	−	0.00653900i	$-0.997919\pi$
$229$	−15.2314	−	15.2314i	−1.00652	−	1.00652i	−0.00653900	−	0.999979i	$-0.502081\pi$
$230$		0			0
$231$	−4.17181	−	4.65785i	−0.274485	−	0.306464i
$232$	4.01840	−	4.01840i	0.263821	−	0.263821i
$233$		−	10.5507i		−	0.691198i	−0.938382	−	0.345599i	$-0.887676\pi$
$233$		−	10.5507i		−	0.691198i	0.938382	−	0.345599i	$-0.112324\pi$
$234$	7.61938	−	6.73155i	0.498094	−	0.440055i
$235$		0			0
$236$	−3.87154	−	3.87154i	−0.252016	−	0.252016i
$237$	7.83753	−	7.01969i	0.509102	−	0.455978i
$238$	−2.01514			−0.130622
$239$	10.7892	+	10.7892i	0.697897	+	0.697897i	0.963957	−	0.266060i	$-0.0857218\pi$
$239$	10.7892	+	10.7892i	0.697897	+	0.697897i	−0.266060	+	0.963957i	$0.585722\pi$
$240$		0			0
$241$	4.73192	+	4.73192i	0.304810	+	0.304810i	0.842892	−	0.538082i	$-0.180851\pi$
$241$	4.73192	+	4.73192i	0.304810	+	0.304810i	−0.538082	+	0.842892i	$0.680851\pi$
$242$	6.41676	+	6.41676i	0.412485	+	0.412485i
$243$	−13.6014	+	7.61596i	−0.872528	+	0.488564i
$244$			15.5299i			0.994200i
$245$		0			0
$246$	−10.2233	+	9.15651i	−0.651814	+	0.583798i
$247$	6.89439	+	6.25993i	0.438680	+	0.398310i
$248$	−3.77201			−0.239523
$249$	−0.529629	+	9.62149i	−0.0335639	+	0.609737i
$250$		0			0
$251$	23.8077			1.50273			0.751365	−	0.659887i	$-0.229396\pi$
$251$	23.8077			1.50273			0.751365	+	0.659887i	$0.229396\pi$
$252$	8.13593	−	6.51776i	0.512515	−	0.410580i
$253$	3.99066	+	3.99066i	0.250891	+	0.250891i
$254$	−8.08904	+	8.08904i	−0.507552	+	0.507552i
$255$		0			0
$256$	−16.8912			−1.05570
$257$			27.4019i			1.70929i	0.519217	+	0.854643i	$0.326224\pi$
$257$			27.4019i			1.70929i	−0.519217	+	0.854643i	$0.673776\pi$
$258$	0.224224	−	4.07336i	0.0139596	−	0.253596i
$259$		−	8.03836i		−	0.499480i
$260$		0			0
$261$	−5.78478	−	0.638799i	−0.358069	−	0.0395407i
$262$	6.02306	+	6.02306i	0.372106	+	0.372106i
$263$	−21.4135			−1.32042			−0.660208	−	0.751083i	$-0.729532\pi$
$263$	−21.4135			−1.32042			−0.660208	+	0.751083i	$0.729532\pi$
$264$	4.38404	−	3.92657i	0.269819	−	0.241664i
$265$		0			0
$266$	−5.34262	−	5.34262i	−0.327577	−	0.327577i
$267$	0.145152	−	2.63691i	0.00888318	−	0.161376i
$268$	−6.02712	+	6.02712i	−0.368165	+	0.368165i
$269$			2.04786i			0.124860i	0.998049	+	0.0624301i	$0.0198851\pi$
$269$			2.04786i			0.124860i	−0.998049	+	0.0624301i	$0.980115\pi$
$270$		0			0
$271$	−12.9996	−	12.9996i	−0.789667	−	0.789667i	0.191772	−	0.981439i	$-0.438576\pi$
$271$	−12.9996	−	12.9996i	−0.789667	−	0.789667i	−0.981439	+	0.191772i	$0.938576\pi$
$272$		−	0.358476i		−	0.0217358i
$273$	19.4359	+	0.132081i	1.17631	+	0.00799393i
$274$	17.3021			1.04526
$275$		0			0
$276$	−7.00869	+	6.27734i	−0.421874	+	0.377852i
$277$	−3.90482			−0.234618			−0.117309	−	0.993095i	$-0.537427\pi$
$277$	−3.90482			−0.234618			−0.117309	+	0.993095i	$0.537427\pi$
$278$	−3.96375	+	3.96375i	−0.237730	+	0.237730i
$279$	2.41523	+	3.01487i	0.144596	+	0.180495i
$280$		0			0
$281$	11.0540	−	11.0540i	0.659429	−	0.659429i	−0.295816	−	0.955245i	$-0.595591\pi$
$281$	11.0540	−	11.0540i	0.659429	−	0.659429i	0.955245	+	0.295816i	$0.0955914\pi$
$282$	−14.7981	+	13.2540i	−0.881216	+	0.789262i
$283$	4.52473			0.268967			0.134484	−	0.990916i	$-0.457062\pi$
$283$	4.52473			0.268967			0.134484	+	0.990916i	$0.457062\pi$
$284$	6.23372	−	6.23372i	0.369903	−	0.369903i
$285$		0			0
$286$	3.92657	−	0.189389i	0.232183	−	0.0111988i
$287$	−26.2368			−1.54871
$288$	10.0715	+	12.5719i	0.593466	+	0.740806i
$289$	16.5255			0.972088
$290$		0			0
$291$	17.1786	+	0.945623i	1.00703	+	0.0554334i
$292$	−10.5319	−	10.5319i	−0.616334	−	0.616334i
$293$	−7.37736	−	7.37736i	−0.430990	−	0.430990i	0.457975	−	0.888965i	$-0.348575\pi$
$293$	−7.37736	−	7.37736i	−0.430990	−	0.430990i	−0.888965	+	0.457975i	$0.848575\pi$
$294$	−4.36694	−	0.240384i	−0.254685	−	0.0140195i
$295$		0			0
$296$	7.56582			0.439754
$297$	−5.94551	−	0.989844i	−0.344994	−	0.0574366i
$298$	−4.12980			−0.239233
$299$	−17.5220	+	0.845131i	−1.01332	+	0.0488752i
$300$		0			0
$301$	5.51459	−	5.51459i	0.317856	−	0.317856i
$302$	0.0396715			0.00228284
$303$	−24.6091	+	22.0412i	−1.41376	+	1.26623i
$304$	0.950408	−	0.950408i	0.0545096	−	0.0545096i
$305$		0			0
$306$	−1.51596	+	1.21445i	−0.0866617	+	0.0694254i
$307$	1.80981	−	1.80981i	0.103291	−	0.103291i	−0.653573	−	0.756864i	$-0.726731\pi$
$307$	1.80981	−	1.80981i	0.103291	−	0.103291i	0.756864	+	0.653573i	$0.226731\pi$
$308$	4.03076			0.229674
$309$	−18.2132	+	16.3127i	−1.03612	+	0.927998i
$310$		0			0
$311$	−12.9697			−0.735445			−0.367723	−	0.929936i	$-0.619862\pi$
$311$	−12.9697			−0.735445			−0.367723	+	0.929936i	$0.619862\pi$
$312$	−0.124317	+	18.2933i	−0.00703806	+	1.03565i
$313$		−	25.7774i		−	1.45703i	−0.685032	−	0.728513i	$-0.740212\pi$
$313$		−	25.7774i		−	1.45703i	0.685032	−	0.728513i	$-0.259788\pi$
$314$	12.4136	+	12.4136i	0.700540	+	0.700540i
$315$		0			0
$316$			6.78234i			0.381537i
$317$	−1.18422	+	1.18422i	−0.0665126	+	0.0665126i	−0.739581	−	0.673068i	$-0.764976\pi$
$317$	−1.18422	+	1.18422i	−0.0665126	+	0.0665126i	0.673068	+	0.739581i	$0.264976\pi$
$318$	0.804584	−	14.6165i	0.0451188	−	0.819650i
$319$	−1.59121	−	1.59121i	−0.0890906	−	0.0890906i
$320$		0			0
$321$	−23.4152	+	20.9718i	−1.30691	+	1.17053i
$322$	14.2331			0.793178
$323$	−1.25804	−	1.25804i	−0.0699989	−	0.0699989i
$324$	2.19254	−	9.80644i	0.121808	−	0.544802i
$325$		0			0
$326$			3.64484i			0.201869i
$327$	1.27805	−	23.2177i	0.0706764	−	1.28394i
$328$		−	24.6944i		−	1.36352i
$329$	−37.9775			−2.09377
$330$		0			0
$331$	1.79656	−	1.79656i	0.0987480	−	0.0987480i	−0.656007	−	0.754755i	$-0.727756\pi$
$331$	1.79656	−	1.79656i	0.0987480	−	0.0987480i	0.754755	+	0.656007i	$0.227756\pi$
$332$	−4.39223	−	4.39223i	−0.241055	−	0.241055i
$333$	−4.84442	−	6.04715i	−0.265473	−	0.331382i
$334$	16.0618			0.878863
$335$		0			0
$336$	0.154189	−	2.80107i	0.00841169	−	0.152811i
$337$	10.2757			0.559753			0.279877	−	0.960036i	$-0.409706\pi$
$337$	10.2757			0.559753			0.279877	+	0.960036i	$0.409706\pi$
$338$	−7.76866	+	9.43177i	−0.422559	+	0.513021i
$339$	−9.40954	+	8.42766i	−0.511056	+	0.457728i
$340$		0			0
$341$			1.49365i			0.0808855i
$342$	−7.23898	−	0.799383i	−0.391439	−	0.0432257i
$343$	9.49305	+	9.49305i	0.512576	+	0.512576i
$344$	5.19041	+	5.19041i	0.279848	+	0.279848i
$345$		0			0
$346$	15.9964	+	15.9964i	0.859972	+	0.859972i
$347$	−16.8673			−0.905482			−0.452741	−	0.891642i	$-0.649554\pi$
$347$	−16.8673			−0.905482			−0.452741	+	0.891642i	$0.649554\pi$
$348$	2.79460	−	2.50298i	0.149806	−	0.134174i
$349$	−14.9509	−	14.9509i	−0.800302	−	0.800302i	0.182840	−	0.983143i	$-0.441471\pi$
$349$	−14.9509	−	14.9509i	−0.800302	−	0.800302i	−0.983143	+	0.182840i	$0.941471\pi$
$350$		0			0
$351$	14.7009	−	11.6139i	0.784677	−	0.619904i
$352$			6.22846i			0.331978i
$353$	6.54324	−	6.54324i	0.348261	−	0.348261i	−0.511200	−	0.859462i	$-0.670799\pi$
$353$	6.54324	−	6.54324i	0.348261	−	0.348261i	0.859462	+	0.511200i	$0.170799\pi$
$354$	5.32646	+	5.94703i	0.283098	+	0.316081i
$355$		0			0
$356$	1.20375	+	1.20375i	0.0637988	+	0.0637988i
$357$	−3.70772	−	0.204097i	−0.196233	−	0.0108019i
$358$	−6.26579	+	6.26579i	−0.331157	+	0.331157i
$359$	13.2705	−	13.2705i	0.700388	−	0.700388i	−0.264106	−	0.964494i	$-0.585077\pi$
$359$	13.2705	−	13.2705i	0.700388	−	0.700388i	0.964494	+	0.264106i	$0.0850767\pi$
$360$		0			0
$361$			12.3293i			0.648910i
$362$	−11.8329	−	11.8329i	−0.621921	−	0.621921i
$363$	11.1565	+	12.4563i	0.585565	+	0.653787i
$364$	−8.42220	+	9.27582i	−0.441443	+	0.486185i
$365$		0			0
$366$	1.24464	−	22.6106i	0.0650581	−	1.18188i
$367$		−	15.3590i		−	0.801734i	−0.916136	−	0.400867i	$-0.868709\pi$
$367$		−	15.3590i		−	0.801734i	0.916136	−	0.400867i	$-0.131291\pi$
$368$			2.53195i			0.131987i
$369$	−19.7376	+	15.8119i	−1.02750	+	0.823136i
$370$		0			0
$371$	19.7880	−	19.7880i	1.02734	−	1.02734i
$372$	−2.48639	−	0.136867i	−0.128913	−	0.00709621i
$373$		−	8.55388i		−	0.442903i	−0.975171	−	0.221452i	$-0.928920\pi$
$373$		−	8.55388i		−	0.442903i	0.975171	−	0.221452i	$-0.0710795\pi$
$374$	−0.751048			−0.0388357
$375$		0			0
$376$		−	35.7449i		−	1.84340i
$377$	6.98659	−	0.336981i	0.359827	−	0.0173554i
$378$	−12.3678	+	8.83743i	−0.636131	+	0.454548i
$379$	12.1073	−	12.1073i	0.621909	−	0.621909i	−0.324110	−	0.946019i	$-0.605065\pi$
$379$	12.1073	−	12.1073i	0.621909	−	0.621909i	0.946019	+	0.324110i	$0.105065\pi$
$380$		0			0
$381$	−15.7026	+	14.0640i	−0.804467	+	0.720522i
$382$	−4.70745	−	4.70745i	−0.240854	−	0.240854i
$383$	17.3280	−	17.3280i	0.885421	−	0.885421i	−0.108658	−	0.994079i	$-0.534655\pi$
$383$	17.3280	−	17.3280i	0.885421	−	0.885421i	0.994079	+	0.108658i	$0.0346555\pi$
$384$	−8.67625	−	0.477597i	−0.442758	−	0.0243723i
$385$		0			0
$386$		−	5.95046i		−	0.302870i
$387$	0.825113	−	7.47199i	0.0419429	−	0.379823i
$388$	−7.84208	+	7.84208i	−0.398121	+	0.398121i
$389$	18.7474			0.950533			0.475267	−	0.879842i	$-0.342352\pi$
$389$	18.7474			0.950533			0.475267	+	0.879842i	$0.342352\pi$
$390$		0			0
$391$	3.35148			0.169492
$392$	5.56450	−	5.56450i	0.281050	−	0.281050i
$393$	10.4720	+	11.6920i	0.528242	+	0.589786i
$394$		−	22.6975i		−	1.14348i
$395$		0			0
$396$	3.03228	−	2.42919i	0.152378	−	0.122071i
$397$	−18.5498	+	18.5498i	−0.930988	+	0.930988i	−0.997768	−	0.0667796i	$-0.978728\pi$
$397$	−18.5498	+	18.5498i	−0.930988	+	0.930988i	0.0667796	+	0.997768i	$0.478728\pi$
$398$	−1.83883	−	1.83883i	−0.0921724	−	0.0921724i
$399$	−9.28895	−	10.3712i	−0.465029	−	0.519208i
$400$		0			0
$401$	−20.2282	+	20.2282i	−1.01015	+	1.01015i	−0.0102015	+	0.999948i	$0.503247\pi$
$401$	−20.2282	+	20.2282i	−1.01015	+	1.01015i	−0.999948	+	0.0102015i	$0.996753\pi$
$402$	9.25818	−	8.29210i	0.461756	−	0.413572i
$403$	−3.43727	−	3.12095i	−0.171223	−	0.155465i
$404$		−	21.2959i		−	1.05951i
$405$		0			0
$406$	−5.67520			−0.281655
$407$		−	2.99592i		−	0.148502i
$408$	0.192099	−	3.48975i	0.00951030	−	0.172769i
$409$	1.85494	−	1.85494i	0.0917210	−	0.0917210i	−0.659758	−	0.751479i	$-0.729341\pi$
$409$	1.85494	−	1.85494i	0.0917210	−	0.0917210i	0.751479	+	0.659758i	$0.229341\pi$
$410$		0			0
$411$	31.8348	+	1.75239i	1.57029	+	0.0864390i
$412$		−	15.7612i		−	0.776497i
$413$			15.2623i			0.751007i
$414$	10.7074	−	8.57775i	0.526238	−	0.421573i
$415$		0			0
$416$	−14.3333	−	13.0143i	−0.702748	−	0.638076i
$417$	−7.69448	+	6.89157i	−0.376801	+	0.337482i
$418$	−1.99121	−	1.99121i	−0.0973933	−	0.0973933i
$419$		−	22.6906i		−	1.10851i	−0.832347	−	0.554255i	$-0.813003\pi$
$419$		−	22.6906i		−	1.10851i	0.832347	−	0.554255i	$-0.186997\pi$
$420$		0			0
$421$	0.559853	−	0.559853i	0.0272856	−	0.0272856i	−0.693332	−	0.720618i	$-0.743858\pi$
$421$	0.559853	−	0.559853i	0.0272856	−	0.0272856i	0.720618	+	0.693332i	$0.243858\pi$
$422$	−5.67212	+	5.67212i	−0.276115	+	0.276115i
$423$	−28.5699	+	22.8876i	−1.38912	+	1.11283i
$424$	18.6248	+	18.6248i	0.904500	+	0.904500i
$425$		0			0
$426$	−9.57554	+	8.57634i	−0.463936	+	0.415525i
$427$	30.6107	−	30.6107i	1.48136	−	1.48136i
$428$		−	20.2627i		−	0.979437i
$429$	7.24380	+	0.0492271i	0.349734	+	0.00237671i
$430$		0			0
$431$	−25.5824	−	25.5824i	−1.23226	−	1.23226i	−0.963094	−	0.269165i	$-0.913252\pi$
$431$	−25.5824	−	25.5824i	−1.23226	−	1.23226i	−0.269165	−	0.963094i	$-0.586748\pi$
$432$	−1.57211	−	2.20013i	−0.0756380	−	0.105854i
$433$	−18.8544			−0.906087			−0.453043	−	0.891488i	$-0.649662\pi$
$433$	−18.8544			−0.906087			−0.453043	+	0.891488i	$0.649662\pi$
$434$	2.66362	+	2.66362i	0.127858	+	0.127858i
$435$		0			0
$436$	10.5989	+	10.5989i	0.507596	+	0.507596i
$437$	8.88561	+	8.88561i	0.425056	+	0.425056i
$438$	14.4898	+	16.1779i	0.692349	+	0.773012i
$439$			18.3463i			0.875620i	0.899068	+	0.437810i	$0.144246\pi$
$439$			18.3463i			0.875620i	−0.899068	+	0.437810i	$0.855754\pi$
$440$		0			0
$441$	−8.01052	−	0.884582i	−0.381453	−	0.0421229i
$442$	1.56930	−	1.72836i	0.0746440	−	0.0822095i
$443$	7.32597			0.348067			0.174034	−	0.984740i	$-0.444320\pi$
$443$	7.32597			0.348067			0.174034	+	0.984740i	$0.444320\pi$
$444$	4.98713	+	0.274524i	0.236679	+	0.0130283i
$445$		0			0
$446$	23.0130			1.08970
$447$	−7.59854	−	0.418273i	−0.359399	−	0.0197836i
$448$	13.3977	+	13.3977i	0.632983	+	0.632983i
$449$	20.5433	−	20.5433i	0.969498	−	0.969498i	−0.0300506	−	0.999548i	$-0.509567\pi$
$449$	20.5433	−	20.5433i	0.969498	−	0.969498i	0.999548	+	0.0300506i	$0.00956684\pi$
$450$		0			0
$451$	−9.77852			−0.460453
$452$		−	8.14271i		−	0.383001i
$453$	0.0729928	+	0.00401799i	0.00342950	+	0.000188782i
$454$		−	9.67255i		−	0.453955i
$455$		0			0
$456$	9.76149	−	8.74289i	0.457124	−	0.409424i
$457$	12.2258	+	12.2258i	0.571898	+	0.571898i	0.932659	−	0.360760i	$-0.117483\pi$
$457$	12.2258	+	12.2258i	0.571898	+	0.571898i	−0.360760	+	0.932659i	$0.617483\pi$
$458$	−20.2468			−0.946070
$459$	−2.91227	+	2.08096i	−0.135933	+	0.0971310i
$460$		0			0
$461$	20.3228	+	20.3228i	0.946525	+	0.946525i	0.998641	−	0.0521156i	$-0.0165964\pi$
$461$	20.3228	+	20.3228i	0.946525	+	0.946525i	−0.0521156	+	0.998641i	$0.516596\pi$
$462$	−5.86855	−	0.323043i	−0.273030	−	0.0150293i
$463$	−6.93836	+	6.93836i	−0.322453	+	0.322453i	−0.849707	−	0.527254i	$-0.823221\pi$
$463$	−6.93836	+	6.93836i	−0.322453	+	0.322453i	0.527254	+	0.849707i	$0.323221\pi$
$464$		−	1.00957i		−	0.0468681i
$465$		0			0
$466$	−7.01241	−	7.01241i	−0.324844	−	0.324844i
$467$		−	14.5021i		−	0.671075i	−0.942027	−	0.335538i	$-0.891082\pi$
$467$		−	14.5021i		−	0.671075i	0.942027	−	0.335538i	$-0.108918\pi$
$468$	−0.745713	+	12.0538i	−0.0344706	+	0.557188i
$469$	23.7599			1.09713
$470$		0			0
$471$	21.5829	+	24.0975i	0.994488	+	1.11035i
$472$	−14.3651			−0.661206
$473$	2.05531	−	2.05531i	0.0945031	−	0.0945031i
$474$	0.543567	−	9.87471i	0.0249669	−	0.453560i
$475$		0			0
$476$	1.69258	−	1.69258i	0.0775792	−	0.0775792i
$477$	2.96076	−	26.8118i	0.135564	−	1.22763i
$478$	14.3419			0.655984
$479$	12.9148	−	12.9148i	0.590095	−	0.590095i	−0.347562	−	0.937657i	$-0.612990\pi$
$479$	12.9148	−	12.9148i	0.590095	−	0.590095i	0.937657	+	0.347562i	$0.112990\pi$
$480$		0			0
$481$	6.89439	+	6.25993i	0.314357	+	0.285428i
$482$	6.29005			0.286504
$483$	26.1879	+	1.44155i	1.19159	+	0.0655928i
$484$	−10.7793			−0.489968
$485$		0			0
$486$	−3.97814	+	14.1019i	−0.180452	+	0.639675i
$487$	2.48442	+	2.48442i	0.112580	+	0.112580i	0.761153	−	0.648573i	$-0.224634\pi$
$487$	2.48442	+	2.48442i	0.112580	+	0.112580i	−0.648573	+	0.761153i	$0.724634\pi$
$488$	28.8113	+	28.8113i	1.30422	+	1.30422i
$489$	−0.369156	+	6.70626i	−0.0166938	+	0.303268i
$490$		0			0
$491$	−16.8134			−0.758780			−0.379390	−	0.925237i	$-0.623866\pi$
$491$	−16.8134			−0.758780			−0.379390	+	0.925237i	$0.623866\pi$
$492$	0.896031	−	16.2777i	0.0403962	−	0.733856i
$493$	−1.33635			−0.0601860
$494$	8.74289	−	0.421693i	0.393361	−	0.0189729i
$495$		0			0
$496$	−0.473835	+	0.473835i	−0.0212758	+	0.0212758i
$497$	−24.5744			−1.10231
$498$	6.04282	+	6.74685i	0.270785	+	0.302333i
$499$	11.5502	−	11.5502i	0.517060	−	0.517060i	−0.399621	−	0.916681i	$-0.630858\pi$
$499$	11.5502	−	11.5502i	0.517060	−	0.517060i	0.916681	+	0.399621i	$0.130858\pi$
$500$		0			0
$501$	29.5526	+	1.62677i	1.32031	+	0.0726786i
$502$	15.8236	−	15.8236i	0.706241	−	0.706241i
$503$	11.9608			0.533304			0.266652	−	0.963793i	$-0.414083\pi$
$503$	11.9608			0.533304			0.266652	+	0.963793i	$0.414083\pi$
$504$	3.00205	−	27.1857i	0.133722	−	1.21095i
$505$		0			0
$506$	5.30471			0.235823
$507$	−15.2491	+	16.5670i	−0.677235	+	0.735767i
$508$		−	13.5885i		−	0.602892i
$509$	−1.50135	−	1.50135i	−0.0665461	−	0.0665461i	0.673050	−	0.739597i	$-0.264984\pi$
$509$	−1.50135	−	1.50135i	−0.0665461	−	0.0665461i	−0.739597	+	0.673050i	$0.764984\pi$
$510$		0			0
$511$			41.5186i			1.83667i
$512$	−4.13175	+	4.13175i	−0.182599	+	0.182599i
$513$	−13.2383	−	2.20399i	−0.584484	−	0.0973084i
$514$	18.2124	+	18.2124i	0.803316	+	0.803316i
$515$		0			0
$516$	3.23301	+	3.60968i	0.142325	+	0.158907i
$517$	−14.1543			−0.622506
$518$	−5.34262	−	5.34262i	−0.234741	−	0.234741i
$519$	27.8122	+	31.0525i	1.22082	+	1.36305i
$520$		0			0
$521$			8.71097i			0.381635i	0.981626	+	0.190817i	$0.0611138\pi$
$521$			8.71097i			0.381635i	−0.981626	+	0.190817i	$0.938886\pi$
$522$	−4.26937	+	3.42023i	−0.186865	+	0.149699i
$523$		−	5.25678i		−	0.229863i	−0.993373	−	0.114931i	$-0.963335\pi$
$523$		−	5.25678i		−	0.229863i	0.993373	−	0.114931i	$-0.0366648\pi$
$524$	−10.1179			−0.442003
$525$		0			0
$526$	−14.2323	+	14.2323i	−0.620558	+	0.620558i
$527$	0.627206	+	0.627206i	0.0273215	+	0.0273215i
$528$	0.0574667	−	1.04397i	0.00250092	−	0.0454328i
$529$	−0.671807			−0.0292090
$530$		0			0
$531$	9.19800	+	11.4816i	0.399159	+	0.498259i
$532$	8.97488			0.389110
$533$	20.4320	−	22.5029i	0.885010	−	0.974709i
$534$	−1.65612	−	1.84907i	−0.0716674	−	0.0800171i
$535$		0			0
$536$			22.3632i			0.965942i
$537$	−12.1632	+	10.8940i	−0.524882	+	0.470111i
$538$	1.36109	+	1.36109i	0.0586808	+	0.0586808i
$539$	−2.20344	−	2.20344i	−0.0949088	−	0.0949088i
$540$		0			0
$541$	−7.12828	−	7.12828i	−0.306469	−	0.306469i	0.537069	−	0.843538i	$-0.319531\pi$
$541$	−7.12828	−	7.12828i	−0.306469	−	0.306469i	−0.843538	+	0.537069i	$0.819531\pi$
$542$	−17.2801			−0.742243
$543$	−20.5732	−	22.9701i	−0.882880	−	0.985741i
$544$	2.61543	+	2.61543i	0.112136	+	0.112136i
$545$		0			0
$546$	13.0056	−	12.8301i	0.556590	−	0.549076i
$547$		−	34.7849i		−	1.48730i	−0.668571	−	0.743648i	$-0.733094\pi$
$547$		−	34.7849i		−	1.48730i	0.668571	−	0.743648i	$-0.266906\pi$
$548$	−14.5326	+	14.5326i	−0.620803	+	0.620803i
$549$	4.58009	−	41.4760i	0.195473	−	1.77015i
$550$		0			0
$551$	−3.54298	−	3.54298i	−0.150936	−	0.150936i
$552$	−1.35681	+	24.6484i	−0.0577496	+	1.04911i
$553$	13.3686	−	13.3686i	0.568490	−	0.568490i
$554$	−2.59530	+	2.59530i	−0.110264	+	0.110264i
$555$		0			0
$556$		−	6.65856i		−	0.282386i
$557$	−7.60755	−	7.60755i	−0.322342	−	0.322342i	0.527323	−	0.849665i	$-0.323196\pi$
$557$	−7.60755	−	7.60755i	−0.322342	−	0.322342i	−0.849665	+	0.527323i	$0.823196\pi$
$558$	3.60907	+	0.398540i	0.152784	+	0.0168715i
$559$	0.435267	+	9.02431i	0.0184098	+	0.381688i
$560$		0			0
$561$	−1.38188	−	0.0760674i	−0.0583429	−	0.00321157i
$562$		−	14.6939i		−	0.619826i
$563$			21.5401i			0.907807i	0.891051	+	0.453903i	$0.149969\pi$
$563$			21.5401i			0.907807i	−0.891051	+	0.453903i	$0.850031\pi$
$564$	1.29700	−	23.5619i	0.0546134	−	0.992133i
$565$		0			0
$566$	3.00732	−	3.00732i	0.126407	−	0.126407i
$567$	−23.6510	+	15.0076i	−0.993248	+	0.630262i
$568$		−	23.1298i		−	0.970503i
$569$	30.7745			1.29013			0.645067	−	0.764126i	$-0.276829\pi$
$569$	30.7745			1.29013			0.645067	+	0.764126i	$0.276829\pi$
$570$		0			0
$571$		−	25.0540i		−	1.04848i	−0.851572	−	0.524238i	$-0.824350\pi$
$571$		−	25.0540i		−	1.04848i	0.851572	−	0.524238i	$-0.175650\pi$
$572$	−3.13898	+	3.45713i	−0.131247	+	0.144550i
$573$	−8.18460	−	9.13816i	−0.341917	−	0.381752i
$574$	−17.4380	+	17.4380i	−0.727849	+	0.727849i
$575$		0			0
$576$	18.1532	+	2.00462i	0.756385	+	0.0835257i
$577$	−13.6669	−	13.6669i	−0.568959	−	0.568959i	0.362878	−	0.931837i	$-0.381794\pi$
$577$	−13.6669	−	13.6669i	−0.568959	−	0.568959i	−0.931837	+	0.362878i	$0.881794\pi$
$578$	10.9835	−	10.9835i	0.456854	−	0.456854i
$579$	0.602673	−	10.9484i	0.0250462	−	0.455002i
$580$		0			0
$581$			17.3149i			0.718343i
$582$	12.0461	−	10.7891i	0.499328	−	0.447223i
$583$	7.37507	−	7.37507i	0.305444	−	0.305444i
$584$	−39.0779			−1.61705
$585$		0			0
$586$	−9.80659			−0.405106
$587$	−5.19514	+	5.19514i	−0.214426	+	0.214426i	−0.806145	−	0.591718i	$-0.798450\pi$
$587$	−5.19514	+	5.19514i	−0.214426	+	0.214426i	0.591718	+	0.806145i	$0.298450\pi$
$588$	3.86984	−	3.46602i	0.159589	−	0.142936i
$589$			3.32575i			0.137035i
$590$		0			0
$591$	2.29884	−	41.7618i	0.0945616	−	1.71785i
$592$	0.950408	−	0.950408i	0.0390615	−	0.0390615i
$593$	−4.27083	−	4.27083i	−0.175382	−	0.175382i	0.613957	−	0.789339i	$-0.289577\pi$
$593$	−4.27083	−	4.27083i	−0.175382	−	0.175382i	−0.789339	+	0.613957i	$0.789577\pi$
$594$	−4.60952	+	3.29374i	−0.189131	+	0.135144i
$595$		0			0
$596$	3.46875	−	3.46875i	0.142086	−	0.142086i
$597$	−3.19709	−	3.56957i	−0.130848	−	0.146093i
$598$	−11.0841	+	12.2075i	−0.453262	+	0.499202i
$599$			17.0139i			0.695171i	0.937648	+	0.347585i	$0.112998\pi$
$599$			17.0139i			0.695171i	−0.937648	+	0.347585i	$0.887002\pi$
$600$		0			0
$601$	−36.2957			−1.48053			−0.740266	−	0.672314i	$-0.765300\pi$
$601$	−36.2957			−1.48053			−0.740266	+	0.672314i	$0.765300\pi$
$602$		−	7.33044i		−	0.298767i
$603$	17.8743	−	14.3192i	0.727896	−	0.583124i
$604$	−0.0333213	+	0.0333213i	−0.00135583	+	0.00135583i
$605$		0			0
$606$	−1.70675	+	31.0057i	−0.0693321	+	1.25952i
$607$		−	37.6421i		−	1.52785i	−0.645306	−	0.763924i	$-0.723270\pi$
$607$		−	37.6421i		−	1.52785i	0.645306	−	0.763924i	$-0.276730\pi$
$608$			13.8683i			0.562433i
$609$	−10.4420	−	0.574794i	−0.423130	−	0.0232918i
$610$		0			0
$611$	29.5752	−	32.5728i	1.19648	−	1.31775i
$612$	0.253250	−	2.29336i	0.0102370	−	0.0927035i
$613$	10.7888	+	10.7888i	0.435755	+	0.435755i	0.890581	−	0.454826i	$-0.150298\pi$
$613$	10.7888	+	10.7888i	0.435755	+	0.435755i	−0.454826	+	0.890581i	$0.650298\pi$
$614$		−	2.40574i		−	0.0970879i
$615$		0			0
$616$	7.47791	−	7.47791i	0.301294	−	0.301294i
$617$	27.1551	−	27.1551i	1.09322	−	1.09322i	0.0980399	−	0.995182i	$-0.468743\pi$
$617$	27.1551	−	27.1551i	1.09322	−	1.09322i	0.995182	−	0.0980399i	$-0.0312573\pi$
$618$	−1.26317	+	22.9474i	−0.0508122	+	0.923078i
$619$	−12.5227	−	12.5227i	−0.503329	−	0.503329i	0.409142	−	0.912471i	$-0.365828\pi$
$619$	−12.5227	−	12.5227i	−0.503329	−	0.503329i	−0.912471	+	0.409142i	$0.865828\pi$
$620$		0			0
$621$	20.5696	−	14.6980i	0.825428	−	0.589811i
$622$	−8.62020	+	8.62020i	−0.345638	+	0.345638i
$623$		−	4.74540i		−	0.190120i
$624$	2.28236	+	2.31360i	0.0913676	+	0.0926179i
$625$		0			0
$626$	−17.1327	−	17.1327i	−0.684761	−	0.684761i
$627$	−3.46202	−	3.86537i	−0.138260	−	0.154368i
$628$	−20.8532			−0.832132
$629$	−1.25804	−	1.25804i	−0.0501611	−	0.0501611i
$630$		0			0
$631$	−0.0650570	−	0.0650570i	−0.00258988	−	0.00258988i	0.705811	−	0.708401i	$-0.250583\pi$
$631$	−0.0650570	−	0.0650570i	−0.00258988	−	0.00258988i	−0.708401	+	0.705811i	$0.750583\pi$
$632$	12.5827	+	12.5827i	0.500513	+	0.500513i
$633$	−11.0108	+	9.86184i	−0.437640	+	0.391973i
$634$			1.57417i			0.0625181i
$635$		0			0
$636$	11.6010	+	12.9526i	0.460011	+	0.513605i
$637$	9.67472	−	0.466637i	0.383326	−	0.0184888i
$638$	−2.11516			−0.0837401
$639$	−18.4870	+	14.8101i	−0.731333	+	0.585877i
$640$		0			0
$641$	−5.72335			−0.226059			−0.113029	−	0.993592i	$-0.536055\pi$
$641$	−5.72335			−0.226059			−0.113029	+	0.993592i	$0.536055\pi$
$642$	−1.62395	+	29.5014i	−0.0640921	+	1.16433i
$643$	24.0577	+	24.0577i	0.948742	+	0.948742i	0.998749	−	0.0500069i	$-0.0159243\pi$
$643$	24.0577	+	24.0577i	0.948742	+	0.948742i	−0.0500069	+	0.998749i	$0.515924\pi$
$644$	−11.9548	+	11.9548i	−0.471086	+	0.471086i
$645$		0			0
$646$	−1.67228			−0.0657951
$647$		−	33.6947i		−	1.32468i	−0.749205	−	0.662338i	$-0.769564\pi$
$647$		−	33.6947i		−	1.32468i	0.749205	−	0.662338i	$-0.230436\pi$
$648$	−14.1254	−	22.2606i	−0.554898	−	0.874481i
$649$			5.68830i			0.223285i
$650$		0			0
$651$	4.63110	+	5.17065i	0.181507	+	0.202654i
$652$	−3.06142	−	3.06142i	−0.119894	−	0.119894i
$653$	−6.47341			−0.253324			−0.126662	−	0.991946i	$-0.540426\pi$
$653$	−6.47341			−0.253324			−0.126662	+	0.991946i	$0.540426\pi$
$654$	−14.5820	−	16.2809i	−0.570201	−	0.636632i
$655$		0			0
$656$	−3.10208	−	3.10208i	−0.121116	−	0.121116i
$657$	25.0217	+	31.2339i	0.976190	+	1.21855i
$658$	−25.2414	+	25.2414i	−0.984011	+	0.984011i
$659$			0.908137i			0.0353760i	0.999844	+	0.0176880i	$0.00563056\pi$
$659$			0.908137i			0.0353760i	−0.999844	+	0.0176880i	$0.994369\pi$
$660$		0			0
$661$	−22.4502	−	22.4502i	−0.873210	−	0.873210i	0.119610	−	0.992821i	$-0.461835\pi$
$661$	−22.4502	−	22.4502i	−0.873210	−	0.873210i	−0.992821	+	0.119610i	$0.961835\pi$
$662$		−	2.38814i		−	0.0928176i
$663$	3.06246	−	3.02111i	0.118936	−	0.117330i
$664$	−16.2970			−0.632448
$665$		0			0
$666$	−7.23898	−	0.799383i	−0.280505	−	0.0309754i
$667$	9.43873			0.365469
$668$	−13.4908	+	13.4908i	−0.521976	+	0.521976i
$669$	42.3423	+	2.33079i	1.63705	+	0.0901137i
$670$		0			0
$671$	11.4087	−	11.4087i	0.440429	−	0.440429i
$672$	19.3115	+	21.5614i	0.744959	+	0.831751i
$673$	40.5282			1.56225			0.781123	−	0.624377i	$-0.214647\pi$
$673$	40.5282			1.56225			0.781123	+	0.624377i	$0.214647\pi$
$674$	6.82965	−	6.82965i	0.263068	−	0.263068i
$675$		0			0
$676$	−1.39690	−	14.4472i	−0.0537270	−	0.555662i
$677$	16.4579			0.632527			0.316264	−	0.948671i	$-0.397572\pi$
$677$	16.4579			0.632527			0.316264	+	0.948671i	$0.397572\pi$
$678$	−0.652593	+	11.8553i	−0.0250627	+	0.455301i
$679$	30.9148			1.18640
$680$		0			0
$681$	0.979652	−	17.7968i	0.0375404	−	0.681976i
$682$	0.992738	+	0.992738i	0.0380139	+	0.0380139i
$683$	8.30681	+	8.30681i	0.317851	+	0.317851i	0.847941	−	0.530090i	$-0.177842\pi$
$683$	8.30681	+	8.30681i	0.317851	+	0.317851i	−0.530090	+	0.847941i	$0.677842\pi$
$684$	6.75168	−	5.40883i	0.258157	−	0.206812i
$685$		0			0
$686$	12.6189			0.481793
$687$	−37.2527	−	2.05063i	−1.42128	−	0.0782364i
$688$	1.30402			0.0497155
$689$	1.56187	+	32.3820i	0.0595025	+	1.23366i
$690$		0			0
$691$	24.4080	−	24.4080i	0.928524	−	0.928524i	−0.0690863	−	0.997611i	$-0.522008\pi$
$691$	24.4080	−	24.4080i	0.928524	−	0.928524i	0.997611	+	0.0690863i	$0.0220084\pi$
$692$	−26.8718			−1.02151
$693$	−10.7650	−	1.18875i	−0.408929	−	0.0451570i
$694$	−11.2107	+	11.2107i	−0.425551	+	0.425551i
$695$		0			0
$696$	0.541004	−	9.82814i	0.0205067	−	0.372535i
$697$	−4.10615	+	4.10615i	−0.155532	+	0.155532i
$698$	−19.8739			−0.752239
$699$	−12.1921	−	13.6126i	−0.461149	−	0.514876i
$700$		0			0
$701$	−25.2071			−0.952058			−0.476029	−	0.879430i	$-0.657924\pi$
$701$	−25.2071			−0.952058			−0.476029	+	0.879430i	$0.657924\pi$
$702$	2.05176	−	17.4899i	0.0774388	−	0.660114i
$703$		−	6.67072i		−	0.251591i
$704$	4.99337	+	4.99337i	0.188195	+	0.188195i
$705$		0			0
$706$		−	8.69780i		−	0.327346i
$707$	−41.9761	+	41.9761i	−1.57867	+	1.57867i
$708$	−9.46897	−	0.521233i	−0.355866	−	0.0195891i
$709$	−3.27176	−	3.27176i	−0.122873	−	0.122873i	0.642996	−	0.765869i	$-0.277691\pi$
$709$	−3.27176	−	3.27176i	−0.122873	−	0.122873i	−0.765869	+	0.642996i	$0.777691\pi$
$710$		0			0
$711$	2.00025	−	18.1137i	0.0750154	−	0.679318i
$712$	4.46644			0.167387
$713$	−4.43001	−	4.43001i	−0.165905	−	0.165905i
$714$	−2.59995	+	2.32865i	−0.0973006	+	0.0871474i
$715$		0			0
$716$		−	10.5257i		−	0.393363i
$717$	26.3882	+	1.45257i	0.985484	+	0.0542474i
$718$		−	17.6402i		−	0.658325i
$719$	−12.3985			−0.462385			−0.231192	−	0.972908i	$-0.574263\pi$
$719$	−12.3985			−0.462385			−0.231192	+	0.972908i	$0.574263\pi$
$720$		0			0
$721$	−31.0666	+	31.0666i	−1.15698	+	1.15698i
$722$	8.19454	+	8.19454i	0.304969	+	0.304969i
$723$	11.5733	+	0.637067i	0.430414	+	0.0236928i
$724$	19.8776			0.738745
$725$		0			0
$726$	15.6940	+	0.863901i	0.582460	+	0.0320624i
$727$	14.6064			0.541722			0.270861	−	0.962619i	$-0.412692\pi$
$727$	14.6064			0.541722			0.270861	+	0.962619i	$0.412692\pi$
$728$	1.58365	+	32.8336i	0.0586940	+	1.21689i
$729$	−8.74777	+	25.5436i	−0.323992	+	0.946060i
$730$		0			0
$731$		−	1.72611i		−	0.0638425i
$732$	17.9460	+	20.0368i	0.663303	+	0.740582i
$733$	−24.5952	−	24.5952i	−0.908445	−	0.908445i	0.0877014	−	0.996147i	$-0.472048\pi$
$733$	−24.5952	−	24.5952i	−0.908445	−	0.908445i	−0.996147	+	0.0877014i	$0.972048\pi$
$734$	−10.2082	−	10.2082i	−0.376792	−	0.376792i
$735$		0			0
$736$	−18.4730	−	18.4730i	−0.680923	−	0.680923i
$737$	8.85540			0.326193
$738$	−2.60914	+	23.6276i	−0.0960437	+	0.869745i
$739$	32.1016	+	32.1016i	1.18088	+	1.18088i	0.979518	+	0.201357i	$0.0645352\pi$
$739$	32.1016	+	32.1016i	1.18088	+	1.18088i	0.201357	+	0.979518i	$0.435465\pi$
$740$		0			0
$741$	16.1290	+	0.109609i	0.592515	+	0.00402659i
$742$		−	26.3039i		−	0.965645i
$743$	31.6922	−	31.6922i	1.16268	−	1.16268i	0.178788	−	0.983888i	$-0.442782\pi$
$743$	31.6922	−	31.6922i	1.16268	−	1.16268i	0.983888	−	0.178788i	$-0.0572177\pi$
$744$	−4.86669	+	4.35886i	−0.178421	+	0.159803i
$745$		0			0
$746$	−5.68526	−	5.68526i	−0.208152	−	0.208152i
$747$	10.4350	+	13.0258i	0.381798	+	0.476588i
$748$	0.630829	−	0.630829i	0.0230654	−	0.0230654i
$749$	−39.9396	+	39.9396i	−1.45936	+	1.45936i
$750$		0			0
$751$		−	8.44360i		−	0.308111i	−0.988062	−	0.154056i	$-0.950766\pi$
$751$		−	8.44360i		−	0.308111i	0.988062	−	0.154056i	$-0.0492335\pi$
$752$	−4.49023	−	4.49023i	−0.163742	−	0.163742i
$753$	30.7169	−	27.5117i	1.11939	−	1.00258i
$754$	4.41960	−	4.86754i	0.160952	−	0.177265i
$755$		0			0
$756$	2.96528	−	17.8110i	0.107846	−	0.647778i
$757$			33.4040i			1.21409i	0.794667	+	0.607045i	$0.207645\pi$
$757$			33.4040i			1.21409i	−0.794667	+	0.607045i	$0.792355\pi$
$758$		−	16.0940i		−	0.584559i
$759$	9.76031	+	0.537270i	0.354277	+	0.0195017i
$760$		0			0
$761$	−2.45709	+	2.45709i	−0.0890694	+	0.0890694i	−0.750238	−	0.661168i	$-0.770061\pi$
$761$	−2.45709	+	2.45709i	−0.0890694	+	0.0890694i	0.661168	+	0.750238i	$0.270061\pi$
$762$	−1.08904	+	19.7841i	−0.0394519	+	0.716701i
$763$		−	41.7827i		−	1.51264i
$764$	7.90787			0.286097
$765$		0			0
$766$		−	23.0338i		−	0.832245i
$767$	−13.0902	−	11.8856i	−0.472661	−	0.429164i
$768$	−21.7932	+	19.5191i	−0.786396	+	0.704336i
$769$	−10.9256	+	10.9256i	−0.393987	+	0.393987i	−0.876106	−	0.482119i	$-0.839867\pi$
$769$	−10.9256	+	10.9256i	−0.393987	+	0.393987i	0.482119	+	0.876106i	$0.339867\pi$
$770$		0			0
$771$	31.6651	+	35.3542i	1.14039	+	1.27325i
$772$	4.99798	+	4.99798i	0.179881	+	0.179881i
$773$	−28.7466	+	28.7466i	−1.03394	+	1.03394i	−0.0345388	+	0.999403i	$0.510996\pi$
$773$	−28.7466	+	28.7466i	−1.03394	+	1.03394i	−0.999403	+	0.0345388i	$0.989004\pi$
$774$	−4.41779	−	5.51459i	−0.158794	−	0.198218i
$775$		0			0
$776$			29.0974i			1.04454i
$777$	−9.28895	−	10.3712i	−0.333239	−	0.372064i
$778$	12.4603	−	12.4603i	0.446724	−	0.446724i
$779$	−21.7728			−0.780093
$780$		0			0
$781$	−9.15895			−0.327733
$782$	2.22753	−	2.22753i	0.0796564	−	0.0796564i
$783$	−8.20177	+	5.86058i	−0.293107	+	0.209440i
$784$		−	1.39801i		−	0.0499289i
$785$		0			0
$786$	14.7311	+	0.810896i	0.525442	+	0.0289237i
$787$	17.0605	−	17.0605i	0.608141	−	0.608141i	−0.334319	−	0.942460i	$-0.608506\pi$
$787$	17.0605	−	17.0605i	0.608141	−	0.608141i	0.942460	+	0.334319i	$0.108506\pi$
$788$	19.0643	+	19.0643i	0.679139	+	0.679139i
$789$	−27.6280	+	24.7450i	−0.983581	+	0.880946i
$790$		0			0
$791$	−16.0500	+	16.0500i	−0.570671	+	0.570671i
$792$	1.11887	−	10.1322i	0.0397574	−	0.360032i
$793$	2.41610	+	50.0927i	0.0857984	+	1.77884i
$794$			24.6579i			0.875076i
$795$		0			0
$796$	3.08899			0.109486
$797$			43.7007i			1.54796i	0.633212	+	0.773979i	$0.281736\pi$
$797$			43.7007i			1.54796i	−0.633212	+	0.773979i	$0.718264\pi$
$798$	−13.0669	−	0.719287i	−0.462564	−	0.0254625i
$799$	−5.94362	+	5.94362i	−0.210270	+	0.210270i
$800$		0			0
$801$	−2.85987	−	3.56990i	−0.101049	−	0.126136i
$802$			26.8890i			0.949483i
$803$			15.4741i			0.546069i
$804$	−0.811442	+	14.7411i	−0.0286174	+	0.519877i
$805$		0			0
$806$	−4.35886	+	0.210239i	−0.153534	+	0.00740536i
$807$	2.36646	+	2.64217i	0.0833034	+	0.0930087i
$808$	−39.5085	−	39.5085i	−1.38990	−	1.38990i
$809$			37.8152i			1.32951i	0.747060	+	0.664757i	$0.231465\pi$
$809$			37.8152i			1.32951i	−0.747060	+	0.664757i	$0.768535\pi$
$810$		0			0
$811$	−33.4507	+	33.4507i	−1.17461	+	1.17461i	−0.193514	+	0.981098i	$0.561988\pi$
$811$	−33.4507	+	33.4507i	−1.17461	+	1.17461i	−0.981098	+	0.193514i	$0.938012\pi$
$812$	4.76678	−	4.76678i	0.167281	−	0.167281i
$813$	−31.7942	−	1.75016i	−1.11507	−	0.0613806i
$814$	−1.99121	−	1.99121i	−0.0697919	−	0.0697919i
$815$		0			0
$816$	−0.414247	−	0.462509i	−0.0145015	−	0.0161911i
$817$	4.57634	−	4.57634i	0.160106	−	0.160106i
$818$		−	2.46574i		−	0.0862126i
$819$	25.2290	−	22.2892i	0.881571	−	0.778848i
$820$		0			0
$821$	−9.07369	−	9.07369i	−0.316674	−	0.316674i	0.530814	−	0.847488i	$-0.321886\pi$
$821$	−9.07369	−	9.07369i	−0.316674	−	0.316674i	−0.847488	+	0.530814i	$0.821886\pi$
$822$	22.3234	−	19.9940i	0.778617	−	0.697369i
$823$	45.6468			1.59115			0.795574	−	0.605856i	$-0.207169\pi$
$823$	45.6468			1.59115			0.795574	+	0.605856i	$0.207169\pi$
$824$	−29.2403	−	29.2403i	−1.01863	−	1.01863i
$825$		0			0
$826$	10.1439	+	10.1439i	0.352952	+	0.352952i
$827$	4.08085	+	4.08085i	0.141905	+	0.141905i	0.774491	−	0.632585i	$-0.218006\pi$
$827$	4.08085	+	4.08085i	0.141905	+	0.141905i	−0.632585	+	0.774491i	$0.718006\pi$
$828$	−1.78872	+	16.1982i	−0.0621625	+	0.562926i
$829$		−	33.3484i		−	1.15824i	−0.815243	−	0.579119i	$-0.803397\pi$
$829$		−	33.3484i		−	1.15824i	0.815243	−	0.579119i	$-0.196603\pi$
$830$		0			0
$831$	−5.03803	+	4.51232i	−0.174767	+	0.156531i
$832$	−21.9246	+	1.05748i	−0.760099	+	0.0366616i
$833$	−1.85052			−0.0641166
$834$	−0.533647	+	9.69448i	−0.0184787	+	0.335693i
$835$		0			0
$836$	3.34497			0.115688
$837$	6.60007	+	1.09882i	0.228132	+	0.0379807i
$838$	−15.0811	−	15.0811i	−0.520968	−	0.520968i
$839$	24.9303	−	24.9303i	0.860690	−	0.860690i	−0.130728	−	0.991418i	$-0.541732\pi$
$839$	24.9303	−	24.9303i	0.860690	−	0.860690i	0.991418	+	0.130728i	$0.0417315\pi$
$840$		0			0
$841$	25.2365			0.870223
$842$		−	0.744202i		−	0.0256469i
$843$	1.48823	−	27.0358i	0.0512573	−	0.931164i
$844$		−	9.52840i		−	0.327981i
$845$		0			0
$846$	−3.77670	+	34.2008i	−0.129846	+	1.17585i
$847$	21.2469	+	21.2469i	0.730052	+	0.730052i
$848$	4.67924			0.160686
$849$	5.83785	−	5.22868i	0.200355	−	0.179448i
$850$		0			0
$851$	8.88561	+	8.88561i	0.304595	+	0.304595i
$852$	0.839258	−	15.2464i	0.0287525	−	0.522331i
$853$	15.5260	−	15.5260i	0.531602	−	0.531602i	−0.389447	−	0.921049i	$-0.627334\pi$
$853$	15.5260	−	15.5260i	0.531602	−	0.531602i	0.921049	+	0.389447i	$0.127334\pi$
$854$		−	40.6903i		−	1.39239i
$855$		0			0
$856$	−37.5917	−	37.5917i	−1.28486	−	1.28486i
$857$		−	7.92513i		−	0.270717i	−0.990797	−	0.135359i	$-0.956781\pi$
$857$		−	7.92513i		−	0.270717i	0.990797	−	0.135359i	$-0.0432187\pi$
$858$	4.84724	−	4.78181i	0.165482	−	0.163248i
$859$	−28.7269			−0.980148			−0.490074	−	0.871681i	$-0.663030\pi$
$859$	−28.7269			−0.980148			−0.490074	+	0.871681i	$0.663030\pi$
$860$		0			0
$861$	−33.8509	+	30.3186i	−1.15364	+	1.03326i
$862$	−34.0061			−1.15825
$863$	−3.03332	+	3.03332i	−0.103255	+	0.103255i	−0.756847	−	0.653592i	$-0.773261\pi$
$863$	−3.03332	+	3.03332i	−0.103255	+	0.103255i	0.653592	+	0.756847i	$0.273261\pi$
$864$	27.5221	+	4.58204i	0.936320	+	0.155884i
$865$		0			0
$866$	−12.5314	+	12.5314i	−0.425835	+	0.425835i
$867$	21.3213	−	19.0965i	0.724111	−	0.648551i
$868$	−4.47452			−0.151875
$869$	4.98251	−	4.98251i	0.169020	−	0.169020i
$870$		0			0
$871$	−18.5032	+	20.3786i	−0.626957	+	0.690501i
$872$	39.3265			1.33176
$873$	23.2568	−	18.6312i	0.787123	−	0.630570i
$874$	11.8115			0.399529
$875$		0			0
$876$	−25.7588	−	1.41793i	−0.870310	−	0.0479075i
$877$	−0.402259	−	0.402259i	−0.0135833	−	0.0135833i	0.700283	−	0.713866i	$-0.253057\pi$
$877$	−0.402259	−	0.402259i	−0.0135833	−	0.0135833i	−0.713866	+	0.700283i	$0.753057\pi$
$878$	12.1937	+	12.1937i	0.411517	+	0.411517i
$879$	−18.0435	−	0.993228i	−0.608591	−	0.0335007i
$880$		0			0
$881$	38.6903			1.30351			0.651755	−	0.758430i	$-0.274033\pi$
$881$	38.6903			1.30351			0.651755	+	0.758430i	$0.274033\pi$
$882$	−5.91204	+	4.73619i	−0.199069	+	0.159476i
$883$	−23.4454			−0.789000			−0.394500	−	0.918896i	$-0.629082\pi$
$883$	−23.4454			−0.789000			−0.394500	+	0.918896i	$0.629082\pi$
$884$	0.133595	+	2.76981i	0.00449329	+	0.0931587i
$885$		0			0
$886$	4.86914	−	4.86914i	0.163582	−	0.163582i
$887$	37.0936			1.24548			0.622740	−	0.782429i	$-0.286019\pi$
$887$	37.0936			1.24548			0.622740	+	0.782429i	$0.286019\pi$
$888$	9.76149	−	8.74289i	0.327574	−	0.293392i
$889$	−26.7841	+	26.7841i	−0.898309	+	0.898309i
$890$		0			0
$891$	−8.81480	+	5.59339i	−0.295307	+	0.187386i
$892$	−19.3293	+	19.3293i	−0.647194	+	0.647194i
$893$	−31.5160			−1.05464
$894$	−5.32830	+	4.77230i	−0.178205	+	0.159610i
$895$		0			0
$896$	−15.6138			−0.521622
$897$	−21.6304	+	21.3384i	−0.722218	+	0.712468i
$898$		−	27.3078i		−	0.911273i
$899$	1.76639	+	1.76639i	0.0589124	+	0.0589124i
$900$		0			0
$901$		−	6.19381i		−	0.206346i
$902$	−6.49920	+	6.49920i	−0.216400	+	0.216400i
$903$	0.742440	−	13.4875i	0.0247069	−	0.448837i
$904$	−15.1065	−	15.1065i	−0.502433	−	0.502433i
$905$		0			0
$906$	0.0511845	−	0.0458435i	0.00170049	−	0.00152305i
$907$	−23.1351			−0.768189			−0.384094	−	0.923294i	$-0.625486\pi$
$907$	−23.1351			−0.768189			−0.384094	+	0.923294i	$0.625486\pi$
$908$	8.12429	+	8.12429i	0.269614	+	0.269614i
$909$	−6.28062	+	56.8755i	−0.208315	+	1.88644i
$910$		0			0
$911$			51.2489i			1.69795i	0.528432	+	0.848976i	$0.322780\pi$
$911$			51.2489i			1.69795i	−0.528432	+	0.848976i	$0.677220\pi$
$912$	0.127955	−	2.32450i	0.00423702	−	0.0769717i
$913$			6.45332i			0.213574i
$914$	16.2515			0.537552
$915$		0			0
$916$	17.0059	−	17.0059i	0.561892	−	0.561892i
$917$	19.9433	+	19.9433i	0.658585	+	0.658585i
$918$	−0.552517	+	3.31870i	−0.0182358	+	0.109533i
$919$	52.3805			1.72787			0.863936	−	0.503602i	$-0.167992\pi$
$919$	52.3805			1.72787			0.863936	+	0.503602i	$0.167992\pi$
$920$		0			0
$921$	0.243658	−	4.42640i	0.00802880	−	0.145855i
$922$	27.0147			0.889680
$923$	19.1375	−	21.0771i	0.629917	−	0.693761i
$924$	5.20052	−	4.65785i	0.171085	−	0.153232i
$925$		0			0
$926$			9.22303i			0.303088i
$927$	−4.64830	+	42.0936i	−0.152670	+	1.38254i
$928$	7.36579	+	7.36579i	0.241794	+	0.241794i
$929$	−35.5168	−	35.5168i	−1.16527	−	1.16527i	−0.983305	−	0.181963i	$-0.941755\pi$
$929$	−35.5168	−	35.5168i	−1.16527	−	1.16527i	−0.181963	−	0.983305i	$-0.558245\pi$
$930$		0			0
$931$	−4.90617	−	4.90617i	−0.160793	−	0.160793i
$932$	11.7799			0.385864
$933$	−16.7337	+	14.9875i	−0.547835	+	0.490669i
$934$	−9.63865	−	9.63865i	−0.315386	−	0.315386i
$935$		0			0
$936$	20.9789	+	23.7458i	0.685718	+	0.776157i
$937$			28.4360i			0.928962i	0.885583	+	0.464481i	$0.153759\pi$
$937$			28.4360i			0.928962i	−0.885583	+	0.464481i	$0.846241\pi$
$938$	15.7918	−	15.7918i	0.515621	−	0.515621i
$939$	−29.7878	−	33.2583i	−0.972089	−	1.08534i
$940$		0			0
$941$	−7.42076	−	7.42076i	−0.241910	−	0.241910i	0.575730	−	0.817640i	$-0.304718\pi$
$941$	−7.42076	−	7.42076i	−0.241910	−	0.241910i	−0.817640	+	0.575730i	$0.804718\pi$
$942$	30.3610	+	1.67127i	0.989215	+	0.0544528i
$943$	29.0021	−	29.0021i	0.944439	−	0.944439i
$944$	−1.80452	+	1.80452i	−0.0587321	+	0.0587321i
$945$		0			0
$946$		−	2.73208i		−	0.0888275i
$947$	−0.253519	−	0.253519i	−0.00823827	−	0.00823827i	0.702976	−	0.711214i	$-0.251854\pi$
$947$	−0.253519	−	0.253519i	−0.00823827	−	0.00823827i	−0.711214	+	0.702976i	$0.751854\pi$
$948$	7.83753	+	8.75065i	0.254551	+	0.284208i
$949$	−35.6099	−	32.3329i	−1.15595	−	1.04957i
$950$		0			0
$951$	−0.159434	+	2.89636i	−0.00517001	+	0.0939209i
$952$		−	6.28019i		−	0.203542i
$953$		−	52.1909i		−	1.69063i	−0.534268	−	0.845315i	$-0.679413\pi$
$953$		−	52.1909i		−	1.69063i	0.534268	−	0.845315i	$-0.320587\pi$
$954$	−15.8524	−	19.7880i	−0.513239	−	0.640662i
$955$		0			0
$956$	−12.0462	+	12.0462i	−0.389603	+	0.389603i
$957$	−3.89176	−	0.214227i	−0.125803	−	0.00692499i
$958$		−	17.1675i		−	0.554656i
$959$	57.2900			1.84999
$960$		0			0
$961$			29.3419i			0.946513i
$962$	8.74289	−	0.421693i	0.281882	−	0.0135959i
$963$	−5.97591	+	54.1161i	−0.192571	+	1.74387i
$964$	−5.28322	+	5.28322i	−0.170161	+	0.170161i
$965$		0			0
$966$	18.3636	−	16.4474i	0.590841	−	0.529187i
$967$	−18.9172	−	18.9172i	−0.608336	−	0.608336i	0.334175	−	0.942511i	$-0.391542\pi$
$967$	−18.9172	−	18.9172i	−0.608336	−	0.608336i	−0.942511	+	0.334175i	$0.891542\pi$
$968$	−19.9979	+	19.9979i	−0.642756	+	0.642756i
$969$	−3.07689	−	0.169372i	−0.0988438	−	0.00544100i
$970$		0			0
$971$			30.9230i			0.992367i	0.868218	+	0.496183i	$0.165266\pi$
$971$			30.9230i			0.992367i	−0.868218	+	0.496183i	$0.834734\pi$
$972$	−8.50327	−	15.1860i	−0.272742	−	0.487091i
$973$	−13.1246	+	13.1246i	−0.420755	+	0.420755i
$974$	3.30249			0.105819
$975$		0			0
$976$	7.23846			0.231698
$977$	14.2630	−	14.2630i	0.456313	−	0.456313i	−0.441130	−	0.897443i	$-0.645422\pi$
$977$	14.2630	−	14.2630i	0.456313	−	0.456313i	0.897443	+	0.441130i	$0.145422\pi$
$978$	4.21190	+	4.70261i	0.134682	+	0.150373i
$979$		−	1.76862i		−	0.0565255i
$980$		0			0
$981$	−25.1809	−	31.4326i	−0.803964	−	1.00357i
$982$	−11.1749	+	11.1749i	−0.356605	+	0.356605i
$983$	23.7893	+	23.7893i	0.758760	+	0.758760i	0.976097	−	0.217337i	$-0.0697369\pi$
$983$	23.7893	+	23.7893i	0.758760	+	0.758760i	−0.217337	+	0.976097i	$0.569737\pi$
$984$	−28.5363	−	31.8610i	−0.909704	−	1.01569i
$985$		0			0
$986$	−0.888190	+	0.888190i	−0.0282857	+	0.0282857i
$987$	−48.9989	+	43.8859i	−1.55965	+	1.39690i
$988$	−6.98925	+	7.69763i	−0.222358	+	0.244894i
$989$			12.1917i			0.387672i
$990$		0			0
$991$	−47.6939			−1.51505			−0.757523	−	0.652809i	$-0.773591\pi$
$991$	−47.6939			−1.51505			−0.757523	+	0.652809i	$0.773591\pi$
$992$		−	6.91417i		−	0.219525i
$993$	0.241875	−	4.39401i	0.00767566	−	0.139440i
$994$	−16.3331	+	16.3331i	−0.518055	+	0.518055i
$995$		0			0
$996$	−10.7425	−	0.591334i	−0.340388	−	0.0187371i
$997$			51.2235i			1.62226i	0.584863	+	0.811132i	$0.301148\pi$
$997$			51.2235i			1.62226i	−0.584863	+	0.811132i	$0.698852\pi$
$998$		−	15.3535i		−	0.486007i
$999$	−13.2383	−	2.20399i	−0.418840	−	0.0697310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.n.o.824.2		8
3.2	odd	2		975.2.n.n.824.3		8
5.2	odd	4		975.2.o.o.551.2	yes	8
5.3	odd	4		975.2.o.l.551.3	yes	8
5.4	even	2		975.2.n.m.824.3		8
13.8	odd	4		975.2.n.p.749.2		8
15.2	even	4		975.2.o.m.551.3	yes	8
15.8	even	4		975.2.o.n.551.2	yes	8
15.14	odd	2		975.2.n.p.824.2		8
39.8	even	4		975.2.n.m.749.3		8
65.8	even	4		975.2.o.n.476.2	yes	8
65.34	odd	4		975.2.n.n.749.3		8
65.47	even	4		975.2.o.m.476.3	yes	8
195.8	odd	4		975.2.o.l.476.3	✓	8
195.47	odd	4		975.2.o.o.476.2	yes	8
195.164	even	4	inner	975.2.n.o.749.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.n.m.749.3		8	39.8	even	4
975.2.n.m.824.3		8	5.4	even	2
975.2.n.n.749.3		8	65.34	odd	4
975.2.n.n.824.3		8	3.2	odd	2
975.2.n.o.749.2		8	195.164	even	4	inner
975.2.n.o.824.2		8	1.1	even	1	trivial
975.2.n.p.749.2		8	13.8	odd	4
975.2.n.p.824.2		8	15.14	odd	2
975.2.o.l.476.3	✓	8	195.8	odd	4
975.2.o.l.551.3	yes	8	5.3	odd	4
975.2.o.m.476.3	yes	8	65.47	even	4
975.2.o.m.551.3	yes	8	15.2	even	4
975.2.o.n.476.2	yes	8	65.8	even	4
975.2.o.n.551.2	yes	8	15.8	even	4
975.2.o.o.476.2	yes	8	195.47	odd	4
975.2.o.o.551.2	yes	8	5.2	odd	4

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.n (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.664640 - 0.664640i) q^{2} +(1.29021 - 1.15558i) q^{3} +1.11651i q^{4} +(0.0894818 - 1.62557i) q^{6} +(2.20073 - 2.20073i) q^{7} +(2.07136 + 2.07136i) q^{8} +(0.329281 - 2.98187i) q^{9} +(0.820218 - 0.820218i) q^{11} +(1.29021 + 1.44053i) q^{12} +(0.173703 + 3.60136i) q^{13} -2.92539i q^{14} +0.520402 q^{16} -0.688845i q^{17} +(-1.76302 - 2.20073i) q^{18} +(1.82630 - 1.82630i) q^{19} +(0.296288 - 5.38251i) q^{21} -1.09030i q^{22} +4.86537i q^{23} +(5.06610 + 0.278871i) q^{24} +(2.50906 + 2.27816i) q^{26} +(-3.02095 - 4.22775i) q^{27} +(2.45713 + 2.45713i) q^{28} -1.93998i q^{29} +(-0.910518 + 0.910518i) q^{31} +(-3.79683 + 3.79683i) q^{32} +(0.110427 - 2.00608i) q^{33} +(-0.457834 - 0.457834i) q^{34} +(3.32928 + 0.367644i) q^{36} +(1.82630 - 1.82630i) q^{37} -2.42766i q^{38} +(4.38577 + 4.44579i) q^{39} +(-5.96093 - 5.96093i) q^{41} +(-3.38051 - 3.77436i) q^{42} +2.50580 q^{43} +(0.915778 + 0.915778i) q^{44} +(3.23372 + 3.23372i) q^{46} +(-8.62839 - 8.62839i) q^{47} +(0.671427 - 0.601365i) q^{48} -2.68640i q^{49} +(-0.796014 - 0.888754i) q^{51} +(-4.02095 + 0.193941i) q^{52} +8.99159 q^{53} +(-4.81778 - 0.802092i) q^{54} +9.11698 q^{56} +(0.245878 - 4.46673i) q^{57} +(-1.28939 - 1.28939i) q^{58} +(-3.46755 + 3.46755i) q^{59} +13.9094 q^{61} +1.21033i q^{62} +(-5.83764 - 7.28695i) q^{63} +6.08786i q^{64} +(-1.25993 - 1.40672i) q^{66} +(5.39820 + 5.39820i) q^{67} +0.769099 q^{68} +(5.62231 + 6.27734i) q^{69} +(-5.58324 - 5.58324i) q^{71} +(6.85858 - 5.49447i) q^{72} +(-9.43292 + 9.43292i) q^{73} -2.42766i q^{74} +(2.03907 + 2.03907i) q^{76} -3.61015i q^{77} +(5.86981 + 0.0398898i) q^{78} +6.07461 q^{79} +(-8.78315 - 1.96375i) q^{81} -7.92375 q^{82} +(-3.93390 + 3.93390i) q^{83} +(6.00961 + 0.330807i) q^{84} +(1.66546 - 1.66546i) q^{86} +(-2.24180 - 2.50298i) q^{87} +3.39793 q^{88} +(1.07814 - 1.07814i) q^{89} +(8.30790 + 7.54335i) q^{91} -5.43221 q^{92} +(-0.122585 + 2.22693i) q^{93} -11.4696 q^{94} +(-0.511175 + 9.28624i) q^{96} +(7.02377 + 7.02377i) q^{97} +(-1.78549 - 1.78549i) q^{98} +(-2.17570 - 2.71587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} + 2 q^{3} - 4 q^{6} + 14 q^{7} - 12 q^{8} + 4 q^{9} - 4 q^{11} + 2 q^{12} + 14 q^{13} - 8 q^{16} + 30 q^{18} + 2 q^{19} - 8 q^{21} + 34 q^{24} + 32 q^{26} - 10 q^{27} - 24 q^{28} - 12 q^{31}+ \cdots + 28 q^{99}+O(q^{100}) \) 8 * q + 6 * q^2 + 2 * q^3 - 4 * q^6 + 14 * q^7 - 12 * q^8 + 4 * q^9 - 4 * q^11 + 2 * q^12 + 14 * q^13 - 8 * q^16 + 30 * q^18 + 2 * q^19 - 8 * q^21 + 34 * q^24 + 32 * q^26 - 10 * q^27 - 24 * q^28 - 12 * q^31 - 18 * q^32 - 18 * q^33 - 10 * q^34 + 28 * q^36 + 2 * q^37 + 20 * q^39 - 38 * q^41 - 34 * q^42 - 4 * q^43 - 10 * q^44 + 34 * q^46 - 22 * q^47 + 54 * q^48 + 26 * q^51 - 18 * q^52 + 28 * q^53 - 12 * q^54 - 76 * q^56 + 6 * q^57 + 18 * q^58 - 14 * q^59 - 8 * q^61 - 10 * q^63 + 18 * q^66 - 40 * q^68 + 10 * q^71 + 4 * q^72 - 10 * q^73 + 26 * q^76 + 2 * q^78 + 56 * q^79 + 8 * q^81 - 16 * q^82 - 38 * q^83 + 58 * q^84 + 34 * q^86 + 34 * q^87 + 8 * q^88 + 28 * q^89 + 8 * q^91 + 72 * q^92 + 22 * q^93 - 20 * q^94 + 72 * q^96 + 4 * q^97 - 26 * q^98 + 28 * q^99

Introduction

L-functions

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