LMFDB - Embedded newform 680.2.h.c.509.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(509,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.509"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] 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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			509.16
Character	$\chi$	$=$	680.509
Dual form			680.2.h.c.509.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.909039 + 1.08335i) q^{2} +2.68098i q^{3} +(-0.347296 - 1.96962i) q^{4} +(2.10758 + 0.747066i) q^{5} +(-2.90444 - 2.43712i) q^{6} +0.590069 q^{7} +(2.44949 + 1.41421i) q^{8} -4.18766 q^{9} +(-2.72521 + 1.60414i) q^{10} +5.24673 q^{11} +(5.28050 - 0.931095i) q^{12} +2.44949 q^{13} +(-0.536396 + 0.639252i) q^{14} +(-2.00287 + 5.65038i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(4.03667 - 0.839805i) q^{17} +(3.80675 - 4.53671i) q^{18} +2.57115i q^{19} +(0.739479 - 4.41057i) q^{20} +1.58196i q^{21} +(-4.76948 + 5.68404i) q^{22} -7.58646 q^{23} +(-3.79148 + 6.56704i) q^{24} +(3.88378 + 3.14900i) q^{25} +(-2.22668 + 2.65366i) q^{26} -3.18410i q^{27} +(-0.204929 - 1.16221i) q^{28} +3.32207 q^{29} +(-4.30066 - 7.30623i) q^{30} +4.11271i q^{31} +(1.93476 - 5.31570i) q^{32} +14.0664i q^{33} +(-2.75969 + 5.13655i) q^{34} +(1.24362 + 0.440821i) q^{35} +(1.45436 + 8.24809i) q^{36} -8.73391i q^{37} +(-2.78546 - 2.33728i) q^{38} +6.56704i q^{39} +(4.10598 + 4.81050i) q^{40} -10.8958i q^{41} +(-1.71382 - 1.43807i) q^{42} +6.08842 q^{43} +(-1.82217 - 10.3340i) q^{44} +(-8.82583 - 3.12846i) q^{45} +(6.89639 - 8.21880i) q^{46} -5.98771i q^{47} +(-3.66780 - 10.0772i) q^{48} -6.65182 q^{49} +(-6.94199 + 1.34493i) q^{50} +(2.25150 + 10.8222i) q^{51} +(-0.850699 - 4.82455i) q^{52} -10.8139 q^{53} +(3.44950 + 2.89448i) q^{54} +(11.0579 + 3.91965i) q^{55} +(1.44537 + 0.834484i) q^{56} -6.89321 q^{57} +(-3.01989 + 3.59897i) q^{58} +7.40726i q^{59} +(11.8247 + 1.98253i) q^{60} -6.60514 q^{61} +(-4.45551 - 3.73862i) q^{62} -2.47101 q^{63} +(4.00000 + 6.92820i) q^{64} +(5.16249 + 1.82993i) q^{65} +(-15.2388 - 12.7869i) q^{66} -7.40124 q^{67} +(-3.05601 - 7.65903i) q^{68} -20.3392i q^{69} +(-1.60806 + 0.946550i) q^{70} +0.239853i q^{71} +(-10.2576 - 5.92225i) q^{72} -5.97435 q^{73} +(9.46189 + 7.93947i) q^{74} +(-8.44242 + 10.4124i) q^{75} +(5.06418 - 0.892951i) q^{76} +3.09593 q^{77} +(-7.11440 - 5.96969i) q^{78} -10.4890i q^{79} +(-8.94396 + 0.0752882i) q^{80} -4.02646 q^{81} +(11.8039 + 9.90468i) q^{82} -6.83277 q^{83} +(3.11586 - 0.549410i) q^{84} +(9.13500 + 1.24571i) q^{85} +(-5.53461 + 6.59590i) q^{86} +8.90641i q^{87} +(12.8518 + 7.41999i) q^{88} -13.4029 q^{89} +(11.4122 - 6.71758i) q^{90} +1.44537 q^{91} +(2.63475 + 14.9424i) q^{92} -11.0261 q^{93} +(6.48679 + 5.44306i) q^{94} +(-1.92082 + 5.41890i) q^{95} +(14.2513 + 5.18705i) q^{96} +17.0326 q^{97} +(6.04676 - 7.20625i) q^{98} -21.9715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 96 q^{9} - 48 q^{15} + 24 q^{34} - 96 q^{36} + 96 q^{49} + 48 q^{60} + 192 q^{64} - 144 q^{66} - 96 q^{70} + 96 q^{76} - 192 q^{84} - 192 q^{86} - 48 q^{89} - 144 q^{94}+O(q^{100}) $ 48 * q - 96 * q^9 - 48 * q^15 + 24 * q^34 - 96 * q^36 + 96 * q^49 + 48 * q^60 + 192 * q^64 - 144 * q^66 - 96 * q^70 + 96 * q^76 - 192 * q^84 - 192 * q^86 - 48 * q^89 - 144 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−0.909039	+	1.08335i	−0.642788	+	0.766044i
$2$	−0.909039	+	1.08335i	−0.642788	+	0.766044i
$3$			2.68098i			1.54787i	0.633268	+	0.773933i	$0.281713\pi$
$3$			2.68098i			1.54787i	−0.633268	+	0.773933i	$0.718287\pi$
$4$	−0.347296	−	1.96962i	−0.173648	−	0.984808i
$5$	2.10758	+	0.747066i	0.942538	+	0.334098i
$5$	2.10758	+	0.747066i	0.942538	+	0.334098i
$6$	−2.90444	−	2.43712i	−1.18573	−	0.994949i
$7$	0.590069			0.223025			0.111513	−	0.993763i	$-0.464430\pi$
$7$	0.590069			0.223025			0.111513	+	0.993763i	$0.464430\pi$
$8$	2.44949	+	1.41421i	0.866025	+	0.500000i
$9$	−4.18766			−1.39589
$10$	−2.72521	+	1.60414i	−0.861786	+	0.507272i
$11$	5.24673			1.58195			0.790974	−	0.611850i	$-0.209574\pi$
$11$	5.24673			1.58195			0.790974	+	0.611850i	$0.209574\pi$
$12$	5.28050	−	0.931095i	1.52435	−	0.268784i
$13$	2.44949			0.679366			0.339683	−	0.940540i	$-0.389680\pi$
$13$	2.44949			0.679366			0.339683	+	0.940540i	$0.389680\pi$
$14$	−0.536396	+	0.639252i	−0.143358	+	0.170847i
$15$	−2.00287	+	5.65038i	−0.517139	+	1.45892i
$16$	−3.75877	+	1.36808i	−0.939693	+	0.342020i
$17$	4.03667	−	0.839805i	0.979037	−	0.203683i
$17$	4.03667	−	0.839805i	0.979037	−	0.203683i
$18$	3.80675	−	4.53671i	0.897259	−	1.06931i
$19$			2.57115i			0.589862i	0.955518	+	0.294931i	$0.0952967\pi$
$19$			2.57115i			0.589862i	−0.955518	+	0.294931i	$0.904703\pi$
$20$	0.739479	−	4.41057i	0.165352	−	0.986235i
$21$			1.58196i			0.345213i
$22$	−4.76948	+	5.68404i	−1.01686	+	1.21184i
$23$	−7.58646			−1.58189			−0.790943	−	0.611889i	$-0.790410\pi$
$23$	−7.58646			−1.58189			−0.790943	+	0.611889i	$0.790410\pi$
$24$	−3.79148	+	6.56704i	−0.773933	+	1.34049i
$25$	3.88378	+	3.14900i	0.776757	+	0.629801i
$26$	−2.22668	+	2.65366i	−0.436688	+	0.520425i
$27$		−	3.18410i		−	0.612781i
$28$	−0.204929	−	1.16221i	−0.0387279	−	0.219637i
$29$	3.32207			0.616893			0.308446	−	0.951242i	$-0.400191\pi$
$29$	3.32207			0.616893			0.308446	+	0.951242i	$0.400191\pi$
$30$	−4.30066	−	7.30623i	−0.785189	−	1.33393i
$31$			4.11271i			0.738665i	0.929297	+	0.369333i	$0.120414\pi$
$31$			4.11271i			0.738665i	−0.929297	+	0.369333i	$0.879586\pi$
$32$	1.93476	−	5.31570i	0.342020	−	0.939693i
$33$			14.0664i			2.44864i
$34$	−2.75969	+	5.13655i	−0.473283	+	0.880911i
$35$	1.24362	+	0.440821i	0.210210	+	0.0745123i
$36$	1.45436	+	8.24809i	0.242393	+	1.37468i
$37$		−	8.73391i		−	1.43585i	−0.696122	−	0.717923i	$-0.745093\pi$
$37$		−	8.73391i		−	1.43585i	0.696122	−	0.717923i	$-0.254907\pi$
$38$	−2.78546	−	2.33728i	−0.451861	−	0.379156i
$39$			6.56704i			1.05157i
$40$	4.10598	+	4.81050i	0.649213	+	0.760607i
$41$		−	10.8958i		−	1.70163i	−0.525463	−	0.850817i	$-0.676108\pi$
$41$		−	10.8958i		−	1.70163i	0.525463	−	0.850817i	$-0.323892\pi$
$42$	−1.71382	−	1.43807i	−0.264448	−	0.221899i
$43$	6.08842			0.928476			0.464238	−	0.885711i	$-0.346328\pi$
$43$	6.08842			0.928476			0.464238	+	0.885711i	$0.346328\pi$
$44$	−1.82217	−	10.3340i	−0.274702	−	1.55791i
$45$	−8.82583	−	3.12846i	−1.31568	−	0.466364i
$46$	6.89639	−	8.21880i	1.01682	−	1.21180i
$47$		−	5.98771i		−	0.873397i	−0.899608	−	0.436699i	$-0.856148\pi$
$47$		−	5.98771i		−	0.873397i	0.899608	−	0.436699i	$-0.143852\pi$
$48$	−3.66780	−	10.0772i	−0.529401	−	1.45452i
$49$	−6.65182			−0.950260
$50$	−6.94199	+	1.34493i	−0.981745	+	0.190202i
$51$	2.25150	+	10.8222i	0.315273	+	1.51542i
$52$	−0.850699	−	4.82455i	−0.117971	−	0.669045i
$53$	−10.8139			−1.48540			−0.742699	−	0.669626i	$-0.766455\pi$
$53$	−10.8139			−1.48540			−0.742699	+	0.669626i	$0.766455\pi$
$54$	3.44950	+	2.89448i	0.469418	+	0.393888i
$55$	11.0579	+	3.91965i	1.49105	+	0.528526i
$56$	1.44537	+	0.834484i	0.193145	+	0.111513i
$57$	−6.89321			−0.913028
$58$	−3.01989	+	3.59897i	−0.396531	+	0.472567i
$59$			7.40726i			0.964343i	0.876077	+	0.482172i	$0.160152\pi$
$59$			7.40726i			0.964343i	−0.876077	+	0.482172i	$0.839848\pi$
$60$	11.8247	+	1.98253i	1.52656	+	0.255943i
$61$	−6.60514			−0.845702			−0.422851	−	0.906199i	$-0.638971\pi$
$61$	−6.60514			−0.845702			−0.422851	+	0.906199i	$0.638971\pi$
$62$	−4.45551	−	3.73862i	−0.565850	−	0.474805i
$63$	−2.47101			−0.311318
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	5.16249	+	1.82993i	0.640329	+	0.226975i
$66$	−15.2388	−	12.7869i	−1.87577	−	1.57396i
$67$	−7.40124			−0.904206			−0.452103	−	0.891966i	$-0.649326\pi$
$67$	−7.40124			−0.904206			−0.452103	+	0.891966i	$0.649326\pi$
$68$	−3.05601	−	7.65903i	−0.370596	−	0.928794i
$69$		−	20.3392i		−	2.44855i
$70$	−1.60806	+	0.946550i	−0.192200	+	0.113134i
$71$			0.239853i			0.0284654i	0.999899	+	0.0142327i	$0.00453056\pi$
$71$			0.239853i			0.0284654i	−0.999899	+	0.0142327i	$0.995469\pi$
$72$	−10.2576	−	5.92225i	−1.20887	−	0.697944i
$73$	−5.97435			−0.699244			−0.349622	−	0.936891i	$-0.613690\pi$
$73$	−5.97435			−0.699244			−0.349622	+	0.936891i	$0.613690\pi$
$74$	9.46189	+	7.93947i	1.09992	+	0.922944i
$75$	−8.44242	+	10.4124i	−0.974847	+	1.20232i
$76$	5.06418	−	0.892951i	0.580901	−	0.102429i
$77$	3.09593			0.352814
$78$	−7.11440	−	5.96969i	−0.805548	−	0.675935i
$79$		−	10.4890i		−	1.18011i	−0.807364	−	0.590054i	$-0.799107\pi$
$79$		−	10.4890i		−	1.18011i	0.807364	−	0.590054i	$-0.200893\pi$
$80$	−8.94396	+	0.0752882i	−0.999965	+	0.00841747i
$81$	−4.02646			−0.447385
$82$	11.8039	+	9.90468i	1.30353	+	1.09379i
$83$	−6.83277			−0.749994			−0.374997	−	0.927026i	$-0.622356\pi$
$83$	−6.83277			−0.749994			−0.374997	+	0.927026i	$0.622356\pi$
$84$	3.11586	−	0.549410i	0.339968	−	0.0599456i
$85$	9.13500	+	1.24571i	0.990830	+	0.135116i
$86$	−5.53461	+	6.59590i	−0.596813	+	0.711254i
$87$			8.90641i			0.954867i
$88$	12.8518	+	7.41999i	1.37001	+	0.790974i
$89$	−13.4029			−1.42070			−0.710350	−	0.703849i	$-0.751463\pi$
$89$	−13.4029			−1.42070			−0.710350	+	0.703849i	$0.751463\pi$
$90$	11.4122	−	6.71758i	1.20296	−	0.708095i
$91$	1.44537			0.151516
$92$	2.63475	+	14.9424i	0.274692	+	1.55785i
$93$	−11.0261			−1.14335
$94$	6.48679	+	5.44306i	0.669061	+	0.561409i
$95$	−1.92082	+	5.41890i	−0.197072	+	0.555968i
$96$	14.2513	+	5.18705i	1.45452	+	0.529401i
$97$	17.0326			1.72940			0.864702	−	0.502286i	$-0.167507\pi$
$97$	17.0326			1.72940			0.864702	+	0.502286i	$0.167507\pi$
$98$	6.04676	−	7.20625i	0.610815	−	0.727941i
$99$	−21.9715			−2.20822
$100$	4.85350	−	8.74320i	0.485350	−	0.874320i
$101$		−	13.9640i		−	1.38947i	−0.719268	−	0.694733i	$-0.755523\pi$
$101$		−	13.9640i		−	1.38947i	0.719268	−	0.694733i	$-0.244477\pi$
$102$	−13.7710	−	7.39868i	−1.36353	−	0.732578i
$103$		−	7.16730i		−	0.706215i	−0.935583	−	0.353107i	$-0.885125\pi$
$103$		−	7.16730i		−	0.706215i	0.935583	−	0.353107i	$-0.114875\pi$
$104$	6.00000	+	3.46410i	0.588348	+	0.339683i
$105$	−1.18183	+	3.33412i	−0.115335	+	0.325376i
$106$	9.83022	−	11.7152i	0.954795	−	1.13788i
$107$			8.65923i			0.837120i	0.908189	+	0.418560i	$0.137465\pi$
$107$			8.65923i			0.837120i	−0.908189	+	0.418560i	$0.862535\pi$
$108$	−6.27146	+	1.10583i	−0.603472	+	0.106408i
$109$	4.10165			0.392867			0.196433	−	0.980517i	$-0.437064\pi$
$109$	4.10165			0.392867			0.196433	+	0.980517i	$0.437064\pi$
$110$	−14.2984	+	8.41646i	−1.36330	+	0.802478i
$111$	23.4155			2.22250
$112$	−2.21793	+	0.807262i	−0.209575	+	0.0762791i
$113$	1.89669			0.178426			0.0892128	−	0.996013i	$-0.471565\pi$
$113$	1.89669			0.178426			0.0892128	+	0.996013i	$0.471565\pi$
$114$	6.26619	−	7.46776i	0.586883	−	0.699420i
$115$	−15.9891	−	5.66759i	−1.49099	−	0.528506i
$116$	−1.15374	−	6.54320i	−0.107122	−	0.607521i
$117$	−10.2576			−0.948319
$118$	−8.02466	−	6.73349i	−0.738730	−	0.619868i
$119$	2.38192	−	0.495543i	0.218350	−	0.0454263i
$120$	−12.8969	+	11.0081i	−1.17732	+	1.00489i
$121$	16.5282			1.50256
$122$	6.00433	−	7.15568i	0.543607	−	0.647845i
$123$	29.2114			2.63390
$124$	8.10047	−	1.42833i	0.727443	−	0.128268i
$125$	5.83287	+	9.53822i	0.521708	+	0.853124i
$126$	2.24624	−	2.67697i	0.200111	−	0.238483i
$127$			10.0968i			0.895943i	0.894048	+	0.447972i	$0.147853\pi$
$127$			10.0968i			0.895943i	−0.894048	+	0.447972i	$0.852147\pi$
$128$	−11.1418	−	1.96460i	−0.984808	−	0.173648i
$129$			16.3230i			1.43716i
$130$	−6.67537	+	3.92931i	−0.585468	+	0.344623i
$131$	3.48732			0.304688			0.152344	−	0.988327i	$-0.451318\pi$
$131$	3.48732			0.304688			0.152344	+	0.988327i	$0.451318\pi$
$132$	27.7054	−	4.88520i	2.41144	−	0.425202i
$133$			1.51716i			0.131554i
$134$	6.72802	−	8.01814i	0.581212	−	0.692662i
$135$	2.37874	−	6.71075i	0.204729	−	0.577570i
$136$	11.0755	+	3.65162i	0.949712	+	0.313124i
$137$			6.73804i			0.575669i	0.957680	+	0.287835i	$0.0929354\pi$
$137$			6.73804i			0.575669i	−0.957680	+	0.287835i	$0.907065\pi$
$138$	22.0344	+	18.4891i	1.87570	+	1.57390i
$139$	1.58506			0.134443			0.0672217	−	0.997738i	$-0.478587\pi$
$139$	1.58506			0.134443			0.0672217	+	0.997738i	$0.478587\pi$
$140$	0.436343	−	2.60254i	0.0368777	−	0.219955i
$141$	16.0529			1.35190
$142$	−0.259845	−	0.218036i	−0.0218057	−	0.0182972i
$143$	12.8518			1.07472
$144$	15.7405	−	5.72906i	1.31171	−	0.477422i
$145$	7.00153	+	2.48181i	0.581445	+	0.206103i
$146$	5.43091	−	6.47231i	0.449466	−	0.535652i
$147$		−	17.8334i		−	1.47087i
$148$	−17.2024	+	3.03326i	−1.41403	+	0.249332i
$149$			14.8180i			1.21394i	0.794726	+	0.606968i	$0.207614\pi$
$149$			14.8180i			1.21394i	−0.794726	+	0.606968i	$0.792386\pi$
$150$	−3.60574	−	18.6113i	−0.294407	−	1.51961i
$151$	2.36759			0.192672			0.0963359	−	0.995349i	$-0.469288\pi$
$151$	2.36759			0.192672			0.0963359	+	0.995349i	$0.469288\pi$
$152$	−3.63616	+	6.29801i	−0.294931	+	0.510836i
$153$	−16.9042	+	3.51682i	−1.36663	+	0.284318i
$154$	−2.81432	+	3.35398i	−0.226785	+	0.270271i
$155$	−3.07247	+	8.66787i	−0.246787	+	0.696220i
$156$	12.9345	−	2.28071i	1.03559	−	0.182603i
$157$	3.98012			0.317648			0.158824	−	0.987307i	$-0.449230\pi$
$157$	3.98012			0.317648			0.158824	+	0.987307i	$0.449230\pi$
$158$	11.3633	+	9.53493i	0.904015	+	0.758559i
$159$		−	28.9918i		−	2.29920i
$160$	8.04884	−	9.75788i	0.636317	−	0.771428i
$161$	−4.47654			−0.352801
$162$	3.66021	−	4.36207i	0.287573	−	0.342717i
$163$			10.1715i			0.796695i	0.917235	+	0.398348i	$0.130416\pi$
$163$			10.1715i			0.796695i	−0.917235	+	0.398348i	$0.869584\pi$
$164$	−21.4605	+	3.78406i	−1.67578	+	0.295486i
$165$	−10.5085	+	29.6460i	−0.818087	+	2.30794i
$166$	6.21126	−	7.40229i	0.482087	−	0.574529i
$167$	−13.1952			−1.02107			−0.510536	−	0.859856i	$-0.670553\pi$
$167$	−13.1952			−1.02107			−0.510536	+	0.859856i	$0.670553\pi$
$168$	−2.23724	+	3.87501i	−0.172606	+	0.298963i
$169$	−7.00000			−0.538462
$170$	−9.65361	+	8.76401i	−0.740398	+	0.672169i
$171$		−	10.7671i		−	0.823382i
$172$	−2.11449	−	11.9919i	−0.161228	−	0.914370i
$173$		−	9.02967i		−	0.686513i	−0.939242	−	0.343256i	$-0.888470\pi$
$173$		−	9.02967i		−	0.686513i	0.939242	−	0.343256i	$-0.111530\pi$
$174$	−9.64876	−	8.09627i	−0.731471	−	0.613777i
$175$	2.29170	+	1.85813i	0.173236	+	0.140461i
$176$	−19.7212	+	7.17795i	−1.48654	+	0.541058i
$177$	−19.8587			−1.49267
$178$	12.1837	−	14.5200i	0.913208	−	1.08832i
$179$		−	0.650086i		−	0.0485897i	−0.999705	−	0.0242948i	$-0.992266\pi$
$179$		−	0.650086i		−	0.0485897i	0.999705	−	0.0242948i	$-0.00773405\pi$
$180$	−3.09669	+	18.4700i	−0.230813	+	1.37667i
$181$	13.6022			1.01104			0.505522	−	0.862814i	$-0.331300\pi$
$181$	13.6022			1.01104			0.505522	+	0.862814i	$0.331300\pi$
$182$	−1.31390	+	1.56584i	−0.0973924	+	0.116068i
$183$		−	17.7083i		−	1.30903i
$184$	−18.5830	−	10.7289i	−1.36995	−	0.790943i
$185$	6.52481	−	18.4074i	0.479714	−	1.35334i
$186$	10.0232	−	11.9451i	0.734934	−	0.875860i
$187$	21.1793	−	4.40623i	1.54879	−	0.322215i
$188$	−11.7935	+	2.07951i	−0.860129	+	0.151664i
$189$		−	1.87884i		−	0.136666i
$190$	−4.12447	−	7.00692i	−0.299221	−	0.508335i
$191$	−2.68686			−0.194414			−0.0972070	−	0.995264i	$-0.530991\pi$
$191$	−2.68686			−0.194414			−0.0972070	+	0.995264i	$0.530991\pi$
$192$	−18.5744	+	10.7239i	−1.34049	+	0.773933i
$193$	1.50477			0.108316			0.0541578	−	0.998532i	$-0.482753\pi$
$193$	1.50477			0.108316			0.0541578	+	0.998532i	$0.482753\pi$
$194$	−15.4833	+	18.4523i	−1.11164	+	1.32480i
$195$	−4.90601	+	13.8406i	−0.351327	+	0.991143i
$196$	2.31015	+	13.1015i	0.165011	+	0.935823i
$197$		−	10.7106i		−	0.763098i	−0.924349	−	0.381549i	$-0.875391\pi$
$197$		−	10.7106i		−	0.763098i	0.924349	−	0.381549i	$-0.124609\pi$
$198$	19.9730	−	23.8029i	1.41942	−	1.69160i
$199$			19.4313i			1.37744i	0.725025	+	0.688722i	$0.241828\pi$
$199$			19.4313i			1.37744i	−0.725025	+	0.688722i	$0.758172\pi$
$200$	5.05993	+	13.2060i	0.357791	+	0.933802i
$201$		−	19.8426i		−	1.39959i
$202$	15.1279	+	12.6938i	1.06439	+	0.893131i
$203$	1.96025			0.137583
$204$	20.5337	−	8.19312i	1.43765	−	0.573633i
$205$	8.13986	−	22.9637i	0.568513	−	1.60385i
$206$	7.76470	+	6.51535i	0.540992	+	0.453946i
$207$	31.7696			2.20814
$208$	−9.20707	+	3.35110i	−0.638395	+	0.232357i
$209$			13.4901i			0.933132i
$210$	−2.53768	−	4.31118i	−0.175117	−	0.297500i
$211$	12.9096			0.888732			0.444366	−	0.895845i	$-0.353429\pi$
$211$	12.9096			0.888732			0.444366	+	0.895845i	$0.353429\pi$
$212$	3.75561	+	21.2991i	0.257937	+	1.46283i
$213$	−0.643043			−0.0440606
$214$	−9.38098	−	7.87158i	−0.641271	−	0.538090i
$215$	12.8318	+	4.54846i	0.875124	+	0.310202i
$216$	4.50300	−	7.79943i	0.306391	−	0.530684i
$217$			2.42679i			0.164741i
$218$	−3.72856	+	4.44352i	−0.252530	+	0.300953i
$219$		−	16.0171i		−	1.08234i
$220$	3.87984	−	23.1411i	0.261579	−	1.56017i
$221$	9.88779	−	2.05709i	0.665125	−	0.138375i
$222$	−21.2856	+	25.3671i	−1.42859	+	1.70253i
$223$		−	9.88986i		−	0.662274i	−0.943583	−	0.331137i	$-0.892568\pi$
$223$		−	9.88986i		−	0.662274i	0.943583	−	0.331137i	$-0.107432\pi$
$224$	1.14164	−	3.13663i	0.0762791	−	0.209575i
$225$	−16.2640	−	13.1870i	−1.08427	−	0.879131i
$226$	−1.72417	+	2.05478i	−0.114690	+	0.136682i
$227$		−	15.1612i		−	1.00629i	−0.864203	−	0.503143i	$-0.832177\pi$
$227$		−	15.1612i		−	1.00629i	0.864203	−	0.503143i	$-0.167823\pi$
$228$	2.39399	+	13.5770i	0.158546	+	0.899157i
$229$		−	5.19117i		−	0.343042i	−0.985180	−	0.171521i	$-0.945132\pi$
$229$		−	5.19117i		−	0.343042i	0.985180	−	0.171521i	$-0.0548682\pi$
$230$	20.6747	−	12.1697i	1.36325	−	0.802447i
$231$			8.30014i			0.546109i
$232$	8.13738	+	4.69812i	0.534245	+	0.308446i
$233$	6.57405			0.430680			0.215340	−	0.976539i	$-0.430914\pi$
$233$	6.57405			0.430680			0.215340	+	0.976539i	$0.430914\pi$
$234$	9.32459	−	11.1126i	0.609568	−	0.726455i
$235$	4.47322	−	12.6196i	0.291801	−	0.823211i
$236$	14.5895	−	2.57251i	0.949693	−	0.167456i
$237$	28.1209			1.82665
$238$	−1.62841	+	3.03092i	−0.105554	+	0.196465i
$239$	−8.86248			−0.573266			−0.286633	−	0.958040i	$-0.592536\pi$
$239$	−8.86248			−0.573266			−0.286633	+	0.958040i	$0.592536\pi$
$240$	−0.201846	−	23.9786i	−0.0130291	−	1.54781i
$241$			19.3789i			1.24830i	0.781303	+	0.624152i	$0.214555\pi$
$241$			19.3789i			1.24830i	−0.781303	+	0.624152i	$0.785445\pi$
$242$	−15.0247	+	17.9058i	−0.965827	+	1.15103i
$243$		−	20.3472i		−	1.30527i
$244$	2.29394	+	13.0096i	0.146855	+	0.832853i
$245$	−14.0192	−	4.96935i	−0.895656	−	0.317480i
$246$	−26.5543	+	31.6461i	−1.69304	+	2.01768i
$247$			6.29801i			0.400733i
$248$	−5.81626	+	10.0741i	−0.369333	+	0.639703i
$249$		−	18.3185i		−	1.16089i
$250$	−15.6355	−	2.35157i	−0.988878	−	0.148726i
$251$			16.7259i			1.05573i	0.849329	+	0.527864i	$0.177007\pi$
$251$			16.7259i			1.05573i	−0.849329	+	0.527864i	$0.822993\pi$
$252$	0.858173	+	4.86694i	0.0540598	+	0.306588i
$253$	−39.8041			−2.50246
$254$	−10.9383	−	9.17836i	−0.686332	−	0.575901i
$255$	−3.33972	+	24.4908i	−0.209141	+	1.53367i
$256$	12.2567	−	10.2846i	0.766044	−	0.642788i
$257$		−	17.7274i		−	1.10580i	−0.833247	−	0.552901i	$-0.813521\pi$
$257$		−	17.7274i		−	1.10580i	0.833247	−	0.552901i	$-0.186479\pi$
$258$	−17.6835	−	14.8382i	−1.10093	−	0.923786i
$259$		−	5.15361i		−	0.320230i
$260$	1.81135	−	10.8037i	0.112335	−	0.670014i
$261$	−13.9117			−0.861113
$262$	−3.17011	+	3.77799i	−0.195850	+	0.233405i
$263$		−	12.7203i		−	0.784367i	−0.919887	−	0.392183i	$-0.871720\pi$
$263$		−	12.7203i		−	0.784367i	0.919887	−	0.392183i	$-0.128280\pi$
$264$	−19.8929	+	34.4555i	−1.22432	+	2.12059i
$265$	−22.7911	−	8.07867i	−1.40004	−	0.496269i
$266$	−1.64361	−	1.37915i	−0.100776	−	0.0845614i
$267$		−	35.9328i		−	2.19905i
$268$	2.57043	+	14.5776i	0.157014	+	0.890469i
$269$	3.92774			0.239478			0.119739	−	0.992805i	$-0.461794\pi$
$269$	3.92774			0.239478			0.119739	+	0.992805i	$0.461794\pi$
$270$	5.10773	+	8.67734i	0.310847	+	0.528086i
$271$	−13.0760			−0.794312			−0.397156	−	0.917751i	$-0.630003\pi$
$271$	−13.0760			−0.794312			−0.397156	+	0.917751i	$0.630003\pi$
$272$	−14.0240	+	8.67913i	−0.850330	+	0.526249i
$273$			3.87501i			0.234526i
$274$	−7.29966	−	6.12514i	−0.440988	−	0.370033i
$275$	20.3772	+	16.5220i	1.22879	+	0.996312i
$276$	−40.0603	+	7.06372i	−2.41135	+	0.425186i
$277$			8.80827i			0.529238i	0.964353	+	0.264619i	$0.0852461\pi$
$277$			8.80827i			0.529238i	−0.964353	+	0.264619i	$0.914754\pi$
$278$	−1.44088	+	1.71718i	−0.0864185	+	0.102990i
$279$		−	17.2227i		−	1.03109i
$280$	2.42281	+	2.83853i	0.144791	+	0.169634i
$281$	−27.7050			−1.65274			−0.826371	−	0.563126i	$-0.809599\pi$
$281$	−27.7050			−1.65274			−0.826371	+	0.563126i	$0.809599\pi$
$282$	−14.5928	+	17.3910i	−0.868986	+	1.03562i
$283$			4.87332i			0.289689i	0.989454	+	0.144844i	$0.0462682\pi$
$283$			4.87332i			0.289689i	−0.989454	+	0.144844i	$0.953732\pi$
$284$	0.472419	−	0.0833002i	0.0280329	−	0.00494296i
$285$	−14.5280	−	5.14968i	−0.860564	−	0.305041i
$286$	−11.6828	+	13.9230i	−0.690818	+	0.823285i
$287$		−	6.42926i		−	0.379507i
$288$	−8.10212	+	22.2604i	−0.477422	+	1.31171i
$289$	15.5895	−	6.78004i	0.917027	−	0.398826i
$290$	−9.05333	+	5.32905i	−0.531630	+	0.312933i
$291$			45.6642i			2.67688i
$292$	2.07487	+	11.7672i	0.121423	+	0.688621i
$293$	16.8991			0.987254			0.493627	−	0.869674i	$-0.335671\pi$
$293$	16.8991			0.987254			0.493627	+	0.869674i	$0.335671\pi$
$294$	19.3198	+	16.2113i	1.12676	+	0.945460i
$295$	−5.53371	+	15.6114i	−0.322185	+	0.908930i
$296$	12.3516	−	21.3936i	0.717923	−	1.24348i
$297$		−	16.7061i		−	0.969388i
$298$	−16.0531	−	13.4701i	−0.929929	−	0.780303i
$299$	−18.5830			−1.07468
$300$	23.4404	+	13.0121i	1.35333	+	0.751257i
$301$	3.59259			0.207073
$302$	−2.15223	+	2.56493i	−0.123847	+	0.147595i
$303$	37.4371			2.15071
$304$	−3.51754	−	9.66436i	−0.201745	−	0.554289i
$305$	−13.9209	−	4.93448i	−0.797106	−	0.282547i
$306$	11.5567	−	21.5101i	0.660650	−	1.22965i
$307$	1.27785			0.0729310			0.0364655	−	0.999335i	$-0.488390\pi$
$307$	1.27785			0.0729310			0.0364655	+	0.999335i	$0.488390\pi$
$308$	−1.07521	−	6.09779i	−0.0612655	−	0.347454i
$309$	19.2154			1.09313
$310$	−6.59735	−	11.2080i	−0.374704	−	0.636571i
$311$		−	28.2277i		−	1.60064i	−0.599571	−	0.800322i	$-0.704662\pi$
$311$		−	28.2277i		−	1.60064i	0.599571	−	0.800322i	$-0.295338\pi$
$312$	−9.28719	+	16.0859i	−0.525784	+	0.910684i
$313$	2.22638			0.125843			0.0629213	−	0.998018i	$-0.479958\pi$
$313$	2.22638			0.125843			0.0629213	+	0.998018i	$0.479958\pi$
$314$	−3.61808	+	4.31187i	−0.204180	+	0.243333i
$315$	−5.20785	−	1.84601i	−0.293429	−	0.104011i
$316$	−20.6593	+	3.64280i	−1.16218	+	0.204924i
$317$		−	27.5279i		−	1.54612i	−0.634333	−	0.773060i	$-0.718725\pi$
$317$		−	27.5279i		−	1.54612i	0.634333	−	0.773060i	$-0.281275\pi$
$318$	31.4082	+	26.3546i	1.76129	+	1.47789i
$319$	17.4300			0.975893
$320$	3.25449	+	17.5900i	0.181932	+	0.983311i
$321$	−23.2152			−1.29575
$322$	4.06935	−	4.84966i	0.226776	−	0.270261i
$323$	2.15926	+	10.3789i	0.120145	+	0.577497i
$324$	1.39838	+	7.93059i	0.0776876	+	0.440588i
$325$	9.51329	+	7.71345i	0.527702	+	0.427865i
$326$	−11.0193	−	9.24631i	−0.610304	−	0.512106i
$327$			10.9964i			0.608105i
$328$	15.4089	−	26.6891i	0.850817	−	1.47366i
$329$		−	3.53316i		−	0.194790i
$330$	−22.5644	−	38.3338i	−1.24213	−	2.11021i
$331$		−	25.4287i		−	1.39769i	−0.715275	−	0.698843i	$-0.753699\pi$
$331$		−	25.4287i		−	1.39769i	0.715275	−	0.698843i	$-0.246301\pi$
$332$	2.37300	+	13.4579i	0.130235	+	0.738600i
$333$			36.5747i			2.00428i
$334$	11.9949	−	14.2950i	0.656333	−	0.782187i
$335$	−15.5987	−	5.52922i	−0.852249	−	0.302094i
$336$	−2.16425	−	5.94624i	−0.118070	−	0.324394i
$337$	13.0469			0.710708			0.355354	−	0.934732i	$-0.384360\pi$
$337$	13.0469			0.710708			0.355354	+	0.934732i	$0.384360\pi$
$338$	6.36327	−	7.58345i	0.346116	−	0.412485i
$339$			5.08499i			0.276179i
$340$	−0.718990	−	18.4251i	−0.0389927	−	0.999239i
$341$			21.5783i			1.16853i
$342$	11.6646	+	9.78773i	0.630747	+	0.529260i
$343$	−8.05552			−0.434957
$344$	14.9135	+	8.61033i	0.804084	+	0.464238i
$345$	15.1947	−	42.8664i	0.818056	−	2.30785i
$346$	9.78229	+	8.20832i	0.525899	+	0.441282i
$347$			26.0425i			1.39804i	0.715104	+	0.699018i	$0.246379\pi$
$347$			26.0425i			1.39804i	−0.715104	+	0.699018i	$0.753621\pi$
$348$	17.5422	−	3.09316i	0.940361	−	0.165811i
$349$			18.6985i			1.00091i	0.865763	+	0.500455i	$0.166834\pi$
$349$			18.6985i			1.00091i	−0.865763	+	0.500455i	$0.833166\pi$
$350$	−4.09625	+	0.793603i	−0.218954	+	0.0424199i
$351$		−	7.79943i		−	0.416303i
$352$	10.1511	−	27.8901i	0.541058	−	1.48654i
$353$			15.1999i			0.809010i	0.914536	+	0.404505i	$0.132556\pi$
$353$			15.1999i			0.809010i	−0.914536	+	0.404505i	$0.867444\pi$
$354$	18.0524	−	21.5140i	0.959472	−	1.14345i
$355$	−0.179186	+	0.505510i	−0.00951023	+	0.0268297i
$356$	4.65476	+	26.3985i	0.246702	+	1.39912i
$357$	1.32854	+	6.38587i	0.0703139	+	0.337976i
$358$	0.704271	+	0.590953i	0.0372219	+	0.0312329i
$359$	−18.9154			−0.998317			−0.499158	−	0.866511i	$-0.666357\pi$
$359$	−18.9154			−0.998317			−0.499158	+	0.866511i	$0.666357\pi$
$360$	−17.1945	−	20.1448i	−0.906229	−	1.06172i
$361$	12.3892			0.652062
$362$	−12.3649	+	14.7359i	−0.649886	+	0.774504i
$363$			44.3117i			2.32576i
$364$	−0.501971	−	2.84682i	−0.0263104	−	0.149214i
$365$	−12.5914	−	4.46323i	−0.659065	−	0.233616i
$366$	19.1843	+	16.0975i	1.00278	+	0.841430i
$367$	−12.9709			−0.677073			−0.338537	−	0.940953i	$-0.609932\pi$
$367$	−12.9709			−0.677073			−0.338537	+	0.940953i	$0.609932\pi$
$368$	28.5158	−	10.3789i	1.48649	−	0.541037i
$369$			45.6278i			2.37529i
$370$	14.0104	+	23.8017i	0.728365	+	1.23739i
$371$	−6.38092			−0.331281
$372$	3.82933	+	21.7172i	0.198541	+	1.12598i
$373$	−3.90153			−0.202014			−0.101007	−	0.994886i	$-0.532206\pi$
$373$	−3.90153			−0.202014			−0.101007	+	0.994886i	$0.532206\pi$
$374$	−14.4793	+	26.9501i	−0.748709	+	1.39355i
$375$	−25.5718	+	15.6378i	−1.32052	+	0.807533i
$376$	8.46790	−	14.6668i	0.436699	−	0.756384i
$377$	8.13738			0.419096
$378$	2.03544	+	1.70794i	0.104692	+	0.0878470i
$379$	19.9672			1.02565			0.512824	−	0.858494i	$-0.328599\pi$
$379$	19.9672			1.02565			0.512824	+	0.858494i	$0.328599\pi$
$380$	11.3403	+	1.90131i	0.581743	+	0.0975352i
$381$	−27.0693			−1.38680
$382$	2.44246	−	2.91081i	0.124967	−	0.148930i
$383$		−	28.0933i		−	1.43550i	−0.696301	−	0.717750i	$-0.745172\pi$
$383$		−	28.0933i		−	1.43550i	0.696301	−	0.717750i	$-0.254828\pi$
$384$	5.26707	−	29.8710i	0.268784	−	1.52435i
$385$	6.52492	+	2.31287i	0.332541	+	0.117875i
$386$	−1.36789	+	1.63019i	−0.0696240	+	0.0829746i
$387$	−25.4963			−1.29605
$388$	−5.91538	−	33.5478i	−0.300308	−	1.70313i
$389$		−	6.13012i		−	0.310810i	−0.987851	−	0.155405i	$-0.950332\pi$
$389$		−	6.13012i		−	0.310810i	0.987851	−	0.155405i	$-0.0496682\pi$
$390$	−10.5344	−	17.8965i	−0.533431	−	0.906226i
$391$	−30.6241	+	6.37115i	−1.54873	+	0.322203i
$392$	−16.2936	−	9.40709i	−0.822949	−	0.475130i
$393$			9.34944i			0.471617i
$394$	11.6033	+	9.73634i	0.584567	+	0.490510i
$395$	7.83600	−	22.1065i	0.394272	−	1.11230i
$396$	7.63063	+	43.2755i	0.383454	+	2.17467i
$397$		−	5.63325i		−	0.282725i	−0.989958	−	0.141362i	$-0.954852\pi$
$397$		−	5.63325i		−	0.282725i	0.989958	−	0.141362i	$-0.0451483\pi$
$398$	−21.0509	−	17.6638i	−1.05518	−	0.885405i
$399$	−4.06747			−0.203628
$400$	−18.9063	−	6.52305i	−0.945317	−	0.326153i
$401$			1.02106i			0.0509893i	0.999675	+	0.0254946i	$0.00811608\pi$
$401$			1.02106i			0.0509893i	−0.999675	+	0.0254946i	$0.991884\pi$
$402$	21.4965	+	18.0377i	1.07215	+	0.899639i
$403$			10.0741i			0.501824i
$404$	−27.5036	+	4.84963i	−1.36836	+	0.241278i
$405$	−8.48609	−	3.00804i	−0.421677	−	0.149470i
$406$	−1.78194	+	2.12364i	−0.0884364	+	0.105394i
$407$		−	45.8245i		−	2.27143i
$408$	−9.78994	+	29.6931i	−0.484674	+	1.47003i
$409$	30.6157			1.51385			0.756925	−	0.653502i	$-0.226701\pi$
$409$	30.6157			1.51385			0.756925	+	0.653502i	$0.226701\pi$
$410$	17.4783	+	29.6932i	0.863191	+	1.46644i
$411$	−18.0646			−0.891059
$412$	−14.1168	+	2.48918i	−0.695486	+	0.122633i
$413$			4.37079i			0.215073i
$414$	−28.8798	+	34.4176i	−1.41936	+	1.69153i
$415$	−14.4006	−	5.10453i	−0.706898	−	0.250572i
$416$	4.73917	−	13.0208i	0.232357	−	0.638395i
$417$			4.24953i			0.208100i
$418$	−14.6145	−	12.2631i	−0.714820	−	0.599805i
$419$	−16.4593			−0.804088			−0.402044	−	0.915620i	$-0.631700\pi$
$419$	−16.4593			−0.804088			−0.402044	+	0.915620i	$0.631700\pi$
$420$	6.97737	+	1.16983i	0.340461	+	0.0570818i
$421$			35.3101i			1.72091i	0.509527	+	0.860455i	$0.329820\pi$
$421$			35.3101i			1.72091i	−0.509527	+	0.860455i	$0.670180\pi$
$422$	−11.7353	+	13.9856i	−0.571266	+	0.680808i
$423$			25.0745i			1.21916i
$424$	−26.4884	−	15.2931i	−1.28639	−	0.742699i
$425$	18.3221	+	9.44987i	0.888753	+	0.458386i
$426$	0.584551	−	0.696641i	0.0283216	−	0.0337524i
$427$	−3.89749			−0.188613
$428$	17.0554	−	3.00732i	0.824402	−	0.145364i
$429$			34.4555i			1.66353i
$430$	−16.5922	+	9.76665i	−0.800147	+	0.470990i
$431$			8.63834i			0.416094i	0.978119	+	0.208047i	$0.0667108\pi$
$431$			8.63834i			0.416094i	−0.978119	+	0.208047i	$0.933289\pi$
$432$	4.35611	+	11.9683i	0.209584	+	0.575826i
$433$		−	31.8980i		−	1.53292i	−0.642292	−	0.766460i	$-0.722016\pi$
$433$		−	31.8980i		−	1.53292i	0.642292	−	0.766460i	$-0.277984\pi$
$434$	−2.62906	−	2.20604i	−0.126199	−	0.105893i
$435$	−6.65368	+	18.7710i	−0.319019	+	0.899999i
$436$	−1.42449	−	8.07867i	−0.0682206	−	0.386898i
$437$		−	19.5059i		−	0.933096i
$438$	17.3522	+	14.5602i	0.829118	+	0.695712i
$439$		−	24.7914i		−	1.18323i	−0.806222	−	0.591614i	$-0.798491\pi$
$439$		−	24.7914i		−	1.18323i	0.806222	−	0.591614i	$-0.201509\pi$
$440$	21.5430	+	25.2394i	1.02702	+	1.20324i
$441$	27.8556			1.32646
$442$	−6.75983	+	12.5819i	−0.321532	+	0.598461i
$443$	13.4991			0.641364			0.320682	−	0.947187i	$-0.396088\pi$
$443$	13.4991			0.641364			0.320682	+	0.947187i	$0.396088\pi$
$444$	−8.13210	−	46.1195i	−0.385933	−	2.18873i
$445$	−28.2476	−	10.0128i	−1.33906	−	0.474653i
$446$	10.7142	+	8.99027i	0.507331	+	0.425702i
$447$	−39.7267			−1.87901
$448$	2.36028	+	4.08812i	0.111513	+	0.193145i
$449$			28.4034i			1.34044i	0.742163	+	0.670220i	$0.233800\pi$
$449$			28.4034i			1.34044i	−0.742163	+	0.670220i	$0.766200\pi$
$450$	29.0707	−	5.63212i	1.37041	−	0.265501i
$451$		−	57.1671i		−	2.69190i
$452$	−0.658714	−	3.73575i	−0.0309833	−	0.175715i
$453$			6.34747i			0.298230i
$454$	16.4249	+	13.7822i	0.770861	+	0.646829i
$455$	3.04623	+	1.07979i	0.142809	+	0.0506211i
$456$	−16.8848	−	9.74847i	−0.790705	−	0.456514i
$457$			8.91339i			0.416951i	0.978028	+	0.208475i	$0.0668501\pi$
$457$			8.91339i			0.416951i	−0.978028	+	0.208475i	$0.933150\pi$
$458$	5.62386	+	4.71898i	0.262786	+	0.220503i
$459$	−2.67403	−	12.8532i	−0.124813	−	0.599935i
$460$	−5.61003	+	33.4607i	−0.261569	+	1.56011i
$461$		−	36.8616i		−	1.71682i	−0.512968	−	0.858408i	$-0.671454\pi$
$461$		−	36.8616i		−	1.71682i	0.512968	−	0.858408i	$-0.328546\pi$
$462$	−8.99196	−	7.54515i	−0.418344	−	0.351032i
$463$			15.6345i			0.726597i	0.931673	+	0.363298i	$0.118349\pi$
$463$			15.6345i			0.726597i	−0.931673	+	0.363298i	$0.881651\pi$
$464$	−12.4869	+	4.54486i	−0.579690	+	0.210990i
$465$	−23.2384	−	8.23724i	−1.07766	−	0.381993i
$466$	−5.97606	+	7.12200i	−0.276836	+	0.329920i
$467$	2.86172			0.132425			0.0662124	−	0.997806i	$-0.478909\pi$
$467$	2.86172			0.132425			0.0662124	+	0.997806i	$0.478909\pi$
$468$	3.56244	+	20.2036i	0.164674	+	0.933912i
$469$	−4.36725			−0.201661
$470$	9.60510	+	16.3178i	0.443050	+	0.752682i
$471$			10.6706i			0.491677i
$472$	−10.4754	+	18.1440i	−0.482172	+	0.835146i
$473$	31.9443			1.46880
$474$	−25.5630	+	30.4648i	−1.17415	+	1.39929i
$475$	−8.09656	+	9.98579i	−0.371496	+	0.458180i
$476$	−1.80326	−	4.51936i	−0.0826523	−	0.207144i
$477$	45.2848			2.07345
$478$	8.05634	−	9.60117i	0.368488	−	0.439147i
$479$			13.1532i			0.600985i	0.953784	+	0.300492i	$0.0971510\pi$
$479$			13.1532i			0.600985i	−0.953784	+	0.300492i	$0.902849\pi$
$480$	26.1607	+	21.5788i	1.19407	+	0.984933i
$481$		−	21.3936i		−	0.975465i
$482$	−20.9941	−	17.6162i	−0.956257	−	0.802395i
$483$		−	12.0015i		−	0.546088i
$484$	−5.74017	−	32.5541i	−0.260917	−	1.47973i
$485$	35.8977	+	12.7245i	1.63003	+	0.577791i
$486$	22.0431	+	18.4964i	0.999897	+	0.839013i
$487$	17.0600			0.773062			0.386531	−	0.922276i	$-0.373673\pi$
$487$	17.0600			0.773062			0.386531	+	0.922276i	$0.373673\pi$
$488$	−16.1792	−	9.34108i	−0.732399	−	0.422851i
$489$	−27.2697			−1.23318
$490$	18.1276	−	10.6704i	0.818921	−	0.482040i
$491$			14.7216i			0.664376i	0.943213	+	0.332188i	$0.107787\pi$
$491$			14.7216i			0.664376i	−0.943213	+	0.332188i	$0.892213\pi$
$492$	−10.1450	−	57.5351i	−0.457372	−	2.59388i
$493$	13.4101	−	2.78989i	0.603961	−	0.125650i
$494$	−6.82295	−	5.72513i	−0.306979	−	0.257586i
$495$	−46.3068	−	16.4142i	−2.08133	−	0.737763i
$496$	−5.62652	−	15.4587i	−0.252638	−	0.694118i
$497$			0.141530i			0.00634849i
$498$	19.8454	+	16.6523i	0.889294	+	0.746206i
$499$	1.06323			0.0475968			0.0237984	−	0.999717i	$-0.492424\pi$
$499$	1.06323			0.0475968			0.0237984	+	0.999717i	$0.492424\pi$
$500$	16.7609	−	14.8011i	0.749570	−	0.661925i
$501$		−	35.3760i		−	1.58048i
$502$	−18.1200	−	15.2045i	−0.808734	−	0.678609i
$503$	−27.4571			−1.22425			−0.612125	−	0.790761i	$-0.709685\pi$
$503$	−27.4571			−1.22425			−0.612125	+	0.790761i	$0.709685\pi$
$504$	−6.05272	−	3.49454i	−0.269609	−	0.155659i
$505$	10.4320	−	29.4301i	0.464218	−	1.30962i
$506$	36.1835	−	43.1218i	1.60855	−	1.91700i
$507$		−	18.7669i		−	0.833466i
$508$	19.8868	−	3.50657i	0.882332	−	0.155579i
$509$			16.8197i			0.745520i	0.927928	+	0.372760i	$0.121588\pi$
$509$			16.8197i			0.745520i	−0.927928	+	0.372760i	$0.878412\pi$
$510$	−23.4962	−	25.8811i	−1.04043	−	1.14604i
$511$	−3.52528			−0.155949
$512$			22.6274i			1.00000i
$513$	8.18681			0.361457
$514$	19.2049	+	16.1149i	0.847094	+	0.710796i
$515$	5.35445	−	15.1057i	0.235945	−	0.665635i
$516$	32.1499	−	5.66890i	1.41532	−	0.249559i
$517$		−	31.4159i		−	1.38167i
$518$	5.58317	+	4.68483i	0.245310	+	0.205840i
$519$	24.2084			1.06263
$520$	10.0576	+	11.7833i	0.441053	+	0.516730i
$521$		−	29.1842i		−	1.27858i	−0.768964	−	0.639292i	$-0.779228\pi$
$521$		−	29.1842i		−	1.27858i	0.768964	−	0.639292i	$-0.220772\pi$
$522$	12.6463	−	15.0713i	0.553513	−	0.659651i
$523$	−42.9036			−1.87604			−0.938021	−	0.346578i	$-0.887344\pi$
$523$	−42.9036			−1.87604			−0.938021	+	0.346578i	$0.887344\pi$
$524$	−1.21113	−	6.86868i	−0.0529086	−	0.300059i
$525$	−4.98161	+	6.14401i	−0.217415	+	0.268146i
$526$	13.7805	+	11.5632i	0.600860	+	0.504181i
$527$	3.45388	+	16.6017i	0.150453	+	0.723181i
$528$	−19.2439	−	52.8723i	−0.837485	−	2.30097i
$529$	34.5544			1.50237
$530$	29.4700	−	17.3469i	1.28009	−	0.753501i
$531$		−	31.0191i		−	1.34611i
$532$	2.98821	−	0.526903i	0.129556	−	0.0228441i
$533$		−	26.6891i		−	1.15603i
$534$	38.9278	+	32.6643i	1.68457	+	1.41352i
$535$	−6.46902	+	18.2500i	−0.279680	+	0.789017i
$536$	−18.1293	−	10.4669i	−0.783065	−	0.452103i
$537$	1.74287			0.0752103
$538$	−3.57047	+	4.25512i	−0.153934	+	0.183451i
$539$	−34.9003			−1.50326
$540$	−14.0437	−	2.35458i	−0.604346	−	0.101325i
$541$	−26.2365			−1.12799			−0.563997	−	0.825777i	$-0.690737\pi$
$541$	−26.2365			−1.12799			−0.563997	+	0.825777i	$0.690737\pi$
$542$	11.8866	−	14.1659i	0.510574	−	0.608479i
$543$			36.4672i			1.56496i
$544$	3.34583	−	23.0826i	0.143451	−	0.989657i
$545$	8.64455	+	3.06420i	0.370292	+	0.131256i
$546$	−4.19799	−	3.52253i	−0.179657	−	0.150750i
$547$			3.46142i			0.148000i	0.997258	+	0.0739999i	$0.0235765\pi$
$547$			3.46142i			0.148000i	−0.997258	+	0.0739999i	$0.976424\pi$
$548$	13.2713	−	2.34010i	0.566924	−	0.0999640i
$549$	27.6601			1.18050
$550$	−36.4227	+	7.05649i	−1.55307	+	0.300890i
$551$			8.54154i			0.363882i
$552$	28.7639	−	49.8206i	1.22427	−	2.12051i
$553$		−	6.18925i		−	0.263194i
$554$	−9.54244	−	8.00706i	−0.405419	−	0.340187i
$555$	49.3499	+	17.4929i	2.09479	+	0.742532i
$556$	−0.550487	−	3.12197i	−0.0233458	−	0.132401i
$557$	−4.47936			−0.189797			−0.0948983	−	0.995487i	$-0.530253\pi$
$557$	−4.47936			−0.189797			−0.0948983	+	0.995487i	$0.530253\pi$
$558$	18.6582	+	15.6561i	0.789864	+	0.662774i
$559$	14.9135			0.630775
$560$	−5.27755	+	0.0444252i	−0.223017	+	0.00187731i
$561$	11.8130	+	56.7814i	0.498746	+	2.39731i
$562$	25.1849	−	30.0142i	1.06236	−	1.26607i
$563$	−0.670970			−0.0282780			−0.0141390	−	0.999900i	$-0.504501\pi$
$563$	−0.670970			−0.0282780			−0.0141390	+	0.999900i	$0.504501\pi$
$564$	−5.57513	−	31.6181i	−0.234755	−	1.33136i
$565$	3.99743	+	1.41695i	0.168173	+	0.0596117i
$566$	−5.27951	−	4.43004i	−0.221915	−	0.186208i
$567$	−2.37589			−0.0997781
$568$	−0.339204	+	0.587519i	−0.0142327	+	0.0246517i
$569$	22.3013			0.934919			0.467459	−	0.884015i	$-0.345169\pi$
$569$	22.3013			0.934919			0.467459	+	0.884015i	$0.345169\pi$
$570$	18.7854	−	11.0576i	0.786834	−	0.463153i
$571$	41.6316			1.74223			0.871114	−	0.491081i	$-0.163398\pi$
$571$	41.6316			1.74223			0.871114	+	0.491081i	$0.163398\pi$
$572$	−4.46339	−	25.3131i	−0.186624	−	1.05839i
$573$		−	7.20341i		−	0.300927i
$574$	6.96514	+	5.84444i	0.290719	+	0.243942i
$575$	−29.4642	−	23.8898i	−1.22874	−	0.996273i
$576$	−16.7507	−	29.0130i	−0.697944	−	1.20887i
$577$			35.7159i			1.48687i	0.668807	+	0.743436i	$0.266805\pi$
$577$			35.7159i			1.48687i	−0.668807	+	0.743436i	$0.733195\pi$
$578$	−6.82627	+	23.0522i	−0.283935	+	0.958843i
$579$			4.03426i			0.167658i
$580$	2.45660	−	14.6522i	0.102005	−	0.608401i
$581$	−4.03181			−0.167268
$582$	−49.4704	−	41.5106i	−2.05061	−	1.72067i
$583$	−56.7374			−2.34982
$584$	−14.6341	−	8.44900i	−0.605563	−	0.349622i
$585$	−21.6188	−	7.66314i	−0.893827	−	0.316832i
$586$	−15.3619	+	18.3076i	−0.634594	+	0.756280i
$587$	27.8951			1.15135			0.575677	−	0.817677i	$-0.304739\pi$
$587$	27.8951			1.15135			0.575677	+	0.817677i	$0.304739\pi$
$588$	−35.1250	+	6.19348i	−1.44853	+	0.255415i
$589$	−10.5744			−0.435711
$590$	−11.8822	−	20.1863i	−0.489184	−	0.831057i
$591$	28.7149			1.18117
$592$	11.9487	+	32.8288i	0.491088	+	1.34925i
$593$		−	10.8444i		−	0.445325i	−0.974896	−	0.222662i	$-0.928525\pi$
$593$		−	10.8444i		−	0.445325i	0.974896	−	0.222662i	$-0.0714748\pi$
$594$	18.0986	+	15.1865i	0.742594	+	0.623111i
$595$	5.39028	+	0.735053i	0.220980	+	0.0301342i
$596$	29.1857	−	5.14623i	1.19549	−	0.210798i
$597$	−52.0948			−2.13210
$598$	16.8926	−	20.1319i	0.690791	−	0.823253i
$599$	45.5313			1.86036			0.930178	−	0.367108i	$-0.119652\pi$
$599$	45.5313			1.86036			0.930178	+	0.367108i	$0.119652\pi$
$600$	−35.4049	+	13.5656i	−1.44540	+	0.553812i
$601$			6.37954i			0.260227i	0.991499	+	0.130113i	$0.0415341\pi$
$601$			6.37954i			0.260227i	−0.991499	+	0.130113i	$0.958466\pi$
$602$	−3.26580	+	3.89203i	−0.133104	+	0.158627i
$603$	30.9939			1.26217
$604$	−0.822256	−	4.66324i	−0.0334571	−	0.189745i
$605$	34.8344	+	12.3476i	1.41622	+	0.502002i
$606$	−34.0318	+	40.5575i	−1.38245	+	1.64754i
$607$	16.5424			0.671434			0.335717	−	0.941963i	$-0.391021\pi$
$607$	16.5424			0.671434			0.335717	+	0.941963i	$0.391021\pi$
$608$	13.6675	+	4.97455i	0.554289	+	0.201745i
$609$			5.25540i			0.212959i
$610$	18.0004	−	10.5955i	0.728814	−	0.429001i
$611$		−	14.6668i		−	0.593357i
$612$	12.7976	+	32.0735i	0.517311	+	1.29649i
$613$	18.9747			0.766379			0.383189	−	0.923670i	$-0.374826\pi$
$613$	18.9747			0.766379			0.383189	+	0.923670i	$0.374826\pi$
$614$	−1.16162	+	1.38436i	−0.0468791	+	0.0558684i
$615$	61.5653	+	21.8228i	2.48255	+	0.879981i
$616$	7.58345	+	4.37831i	0.305546	+	0.176407i
$617$	−0.795132			−0.0320108			−0.0160054	−	0.999872i	$-0.505095\pi$
$617$	−0.795132			−0.0320108			−0.0160054	+	0.999872i	$0.505095\pi$
$618$	−17.4675	+	20.8170i	−0.702648	+	0.837383i
$619$	−1.58506			−0.0637091			−0.0318545	−	0.999493i	$-0.510141\pi$
$619$	−1.58506			−0.0637091			−0.0318545	+	0.999493i	$0.510141\pi$
$620$	18.1394	+	3.04126i	0.728497	+	0.122140i
$621$			24.1561i			0.969351i
$622$	30.5804	+	25.6600i	1.22616	+	1.02887i
$623$	−7.90861			−0.316852
$624$	−8.98424	−	24.6840i	−0.359657	−	0.988150i
$625$	5.16756	+	24.4601i	0.206702	+	0.978404i
$626$	−2.02387	+	2.41195i	−0.0808901	+	0.0964010i
$627$	−36.1668			−1.44436
$628$	−1.38228	−	7.83931i	−0.0551590	−	0.312822i
$629$	−7.33478	−	35.2559i	−0.292457	−	1.40575i
$630$	6.73401	−	3.96383i	0.268290	−	0.157923i
$631$	−24.9094			−0.991627			−0.495814	−	0.868429i	$-0.665130\pi$
$631$	−24.9094			−0.991627			−0.495814	+	0.868429i	$0.665130\pi$
$632$	14.8337	−	25.6928i	0.590054	−	1.02200i
$633$			34.6103i			1.37564i
$634$	29.8223	+	25.0239i	1.18440	+	0.993826i
$635$	−7.54296	+	21.2797i	−0.299333	+	0.844461i
$636$	−57.1026	+	10.0687i	−2.26427	+	0.399251i
$637$	−16.2936			−0.645574
$638$	−15.8445	+	18.8828i	−0.627292	+	0.747577i
$639$		−	1.00443i		−	0.0397345i
$640$	−22.0146	−	12.4642i	−0.870203	−	0.492693i
$641$		−	26.7986i		−	1.05848i	−0.848472	−	0.529240i	$-0.822477\pi$
$641$		−	26.7986i		−	1.05848i	0.848472	−	0.529240i	$-0.177523\pi$
$642$	21.1036	−	25.1502i	0.832891	−	0.992601i
$643$			8.22151i			0.324225i	0.986772	+	0.162112i	$0.0518307\pi$
$643$			8.22151i			0.324225i	−0.986772	+	0.162112i	$0.948169\pi$
$644$	1.55468	+	8.81706i	0.0612632	+	0.347441i
$645$	−12.1943	+	34.4019i	−0.480151	+	1.35457i
$646$	−13.2068	−	7.09558i	−0.519616	−	0.279172i
$647$		−	2.52907i		−	0.0994281i	−0.998763	−	0.0497141i	$-0.984169\pi$
$647$		−	2.52907i		−	0.0994281i	0.998763	−	0.0497141i	$-0.0158310\pi$
$648$	−9.86278	−	5.69428i	−0.387447	−	0.223692i
$649$			38.8639i			1.52554i
$650$	−17.0043	+	3.29440i	−0.666964	+	0.129217i
$651$	−6.50617			−0.254997
$652$	20.0340	−	3.53253i	0.784592	−	0.138345i
$653$			11.8623i			0.464207i	0.972691	+	0.232104i	$0.0745608\pi$
$653$			11.8623i			0.464207i	−0.972691	+	0.232104i	$0.925439\pi$
$654$	−11.9130	−	9.99619i	−0.465835	−	0.390882i
$655$	7.34980	+	2.60526i	0.287180	+	0.101796i
$656$	14.9063	+	40.9547i	0.581993	+	1.59901i
$657$	25.0186			0.976067
$658$	3.82765	+	3.21178i	0.149217	+	0.125208i
$659$		−	22.2352i		−	0.866160i	−0.901356	−	0.433080i	$-0.857427\pi$
$659$		−	22.2352i		−	0.866160i	0.901356	−	0.433080i	$-0.142573\pi$
$660$	62.0408	+	10.4018i	2.41494	+	0.404889i
$661$			31.2369i			1.21498i	0.794329	+	0.607488i	$0.207823\pi$
$661$			31.2369i			1.21498i	−0.794329	+	0.607488i	$0.792177\pi$
$662$	27.5482	+	23.1157i	1.07069	+	0.898415i
$663$	5.51503	+	26.5090i	0.214186	+	1.02952i
$664$	−16.7368	−	9.66300i	−0.649514	−	0.374997i
$665$	−1.13342	+	3.19753i	−0.0439520	+	0.123995i
$666$	−39.6232	−	33.2478i	−1.53537	−	1.28833i
$667$	−25.2028			−0.975855
$668$	4.58263	+	25.9894i	0.177307	+	1.00556i
$669$	26.5145			1.02511
$670$	20.1699	−	11.8726i	0.779232	−	0.458678i
$671$	−34.6554			−1.33786
$672$	8.40925	+	3.06072i	0.324394	+	0.118070i
$673$	38.4573			1.48242			0.741210	−	0.671273i	$-0.234252\pi$
$673$	38.4573			1.48242			0.741210	+	0.671273i	$0.234252\pi$
$674$	−11.8601	+	14.1343i	−0.456834	+	0.544434i
$675$	10.0268	−	12.3664i	0.385930	−	0.475982i
$676$	2.43107	+	13.7873i	0.0935029	+	0.530281i
$677$			44.7009i			1.71799i	0.511980	+	0.858997i	$0.328912\pi$
$677$			44.7009i			1.71799i	−0.511980	+	0.858997i	$0.671088\pi$
$678$	−5.50883	−	4.62246i	−0.211565	−	0.177524i
$679$	10.0504			0.385700
$680$	20.6144	+	15.9702i	0.790526	+	0.612429i
$681$	40.6470			1.55760
$682$	−23.3769	−	19.6155i	−0.895146	−	0.751117i
$683$		−	43.2946i		−	1.65662i	−0.560268	−	0.828311i	$-0.689302\pi$
$683$		−	43.2946i		−	1.65662i	0.560268	−	0.828311i	$-0.310698\pi$
$684$	−21.2071	+	3.73938i	−0.810873	+	0.142979i
$685$	−5.03376	+	14.2010i	−0.192330	+	0.542591i
$686$	7.32278	−	8.72695i	0.279585	−	0.333196i
$687$	13.9174			0.530984
$688$	−22.8850	+	8.32945i	−0.872482	+	0.317557i
$689$	−26.4884			−1.00913
$690$	32.6268	+	55.4284i	1.24208	+	2.11012i
$691$	−39.0764			−1.48653			−0.743267	−	0.668994i	$-0.766725\pi$
$691$	−39.0764			−1.48653			−0.743267	+	0.668994i	$0.766725\pi$
$692$	−17.7850	+	3.13597i	−0.676083	+	0.119212i
$693$	−12.9647			−0.492489
$694$	−28.2132	−	23.6737i	−1.07096	−	0.898641i
$695$	3.34065	+	1.18415i	0.126718	+	0.0449173i
$696$	−12.5956	+	21.8162i	−0.477434	+	0.826939i
$697$	−9.15032	−	43.9827i	−0.346593	−	1.66596i
$698$	−20.2571	−	16.9977i	−0.766741	−	0.643372i
$699$			17.6249i			0.666635i
$700$	2.86390	−	5.15909i	0.108245	−	0.194995i
$701$			2.70302i			0.102092i	0.998696	+	0.0510458i	$0.0162554\pi$
$701$			2.70302i			0.102092i	−0.998696	+	0.0510458i	$0.983745\pi$
$702$	8.44952	+	7.08999i	0.318906	+	0.267594i
$703$	22.4562			0.846952
$704$	20.9869	+	36.3504i	0.790974	+	1.37001i
$705$	33.8329	+	11.9926i	1.27422	+	0.451668i
$706$	−16.4668	−	13.8173i	−0.619738	−	0.520022i
$707$		−	8.23970i		−	0.309886i
$708$	6.89686	+	39.1141i	0.259200	+	1.47000i
$709$	46.1190			1.73203			0.866017	−	0.500014i	$-0.166672\pi$
$709$	46.1190			1.73203			0.866017	+	0.500014i	$0.166672\pi$
$710$	−0.384757	−	0.653650i	−0.0144397	−	0.0245311i
$711$			43.9245i			1.64730i
$712$	−32.8302	−	18.9545i	−1.23036	−	0.710350i
$713$		−	31.2010i		−	1.16848i
$714$	−8.12583	−	4.36573i	−0.304102	−	0.163383i
$715$	27.0862	+	9.60115i	1.01297	+	0.359063i
$716$	−1.28042	+	0.225772i	−0.0478515	+	0.00843751i
$717$		−	23.7601i		−	0.887339i
$718$	17.1948	−	20.4920i	0.641706	−	0.764755i
$719$		−	7.11654i		−	0.265402i	−0.991156	−	0.132701i	$-0.957635\pi$
$719$		−	7.11654i		−	0.265402i	0.991156	−	0.132701i	$-0.0423651\pi$
$720$	37.4543	−	0.315281i	1.39584	−	0.0117498i
$721$		−	4.22920i		−	0.157504i
$722$	−11.2623	+	13.4218i	−0.419138	+	0.499509i
$723$	−51.9545			−1.93221
$724$	−4.72399	−	26.7911i	−0.175566	−	0.995683i
$725$	12.9022	+	10.4612i	0.479176	+	0.388520i
$726$	−48.0051	−	40.2810i	−1.78164	−	1.49497i
$727$			19.9877i			0.741301i	0.928772	+	0.370651i	$0.120865\pi$
$727$			19.9877i			0.741301i	−0.928772	+	0.370651i	$0.879135\pi$
$728$	3.54041	+	2.04406i	0.131216	+	0.0757579i
$729$	42.4711			1.57300
$730$	16.2813	−	9.58366i	0.602599	−	0.354707i
$731$	24.5770	−	5.11309i	0.909012	−	0.189114i
$732$	−34.8785	+	6.15001i	−1.28915	+	0.227311i
$733$	42.5930			1.57321			0.786604	−	0.617458i	$-0.211837\pi$
$733$	42.5930			1.57321			0.786604	+	0.617458i	$0.211837\pi$
$734$	11.7910	−	14.0520i	0.435214	−	0.518668i
$735$	13.3227	−	37.5853i	0.491416	−	1.38636i
$736$	−14.6780	+	40.3274i	−0.541037	+	1.48649i
$737$	−38.8323			−1.43041
$738$	−49.4309	−	41.4775i	−1.81958	−	1.52681i
$739$			22.9061i			0.842614i	0.906918	+	0.421307i	$0.138428\pi$
$739$			22.9061i			0.842614i	−0.906918	+	0.421307i	$0.861572\pi$
$740$	−38.5216	−	6.45854i	−1.41608	−	0.237421i
$741$	−16.8848			−0.620280
$742$	5.80051	−	6.91278i	0.212943	−	0.253776i
$743$	28.2281			1.03559			0.517795	−	0.855505i	$-0.326753\pi$
$743$	28.2281			1.03559			0.517795	+	0.855505i	$0.326753\pi$
$744$	−27.0083	−	15.5933i	−0.990174	−	0.571677i
$745$	−11.0700	+	31.2301i	−0.405574	+	1.14418i
$746$	3.54665	−	4.22673i	0.129852	−	0.154751i
$747$	28.6134			1.04691
$748$	−16.0341	−	40.1849i	−0.586264	−	1.46930i
$749$			5.10954i			0.186699i
$750$	6.30452	−	41.9186i	0.230208	−	1.53065i
$751$			39.6316i			1.44618i	0.690754	+	0.723089i	$0.257279\pi$
$751$			39.6316i			1.44618i	−0.690754	+	0.723089i	$0.742721\pi$
$752$	8.19167	+	22.5064i	0.298720	+	0.820725i
$753$	−44.8418			−1.63412
$754$	−7.39719	+	8.81563i	−0.269390	+	0.321046i
$755$	4.98989	+	1.76875i	0.181601	+	0.0643713i
$756$	−3.70060	+	0.652515i	−0.134589	+	0.0237317i
$757$	−23.6246			−0.858649			−0.429324	−	0.903150i	$-0.641248\pi$
$757$	−23.6246			−0.858649			−0.429324	+	0.903150i	$0.641248\pi$
$758$	−18.1510	+	21.6315i	−0.659274	+	0.785692i
$759$		−	106.714i		−	3.87348i
$760$	−12.3685	+	10.5571i	−0.448653	+	0.382946i
$761$	−38.5749			−1.39834			−0.699170	−	0.714955i	$-0.746447\pi$
$761$	−38.5749			−1.39834			−0.699170	+	0.714955i	$0.746447\pi$
$762$	24.6070	−	29.3255i	0.891418	−	1.06235i
$763$	2.42026			0.0876191
$764$	0.933135	+	5.29207i	0.0337597	+	0.191461i
$765$	−38.2543	−	5.21660i	−1.38309	−	0.188607i
$766$	30.4349	+	25.5379i	1.09966	+	0.922722i
$767$			18.1440i			0.655142i
$768$	27.5728	+	32.8600i	0.994949	+	1.18573i
$769$	−13.5299			−0.487901			−0.243950	−	0.969788i	$-0.578443\pi$
$769$	−13.5299			−0.487901			−0.243950	+	0.969788i	$0.578443\pi$
$770$	−8.43705	+	4.96629i	−0.304050	+	0.178973i
$771$	47.5267			1.71163
$772$	−0.522601	−	2.96382i	−0.0188088	−	0.106670i
$773$	−5.05914			−0.181965			−0.0909823	−	0.995853i	$-0.529001\pi$
$773$	−5.05914			−0.181965			−0.0909823	+	0.995853i	$0.529001\pi$
$774$	23.1771	−	27.6214i	0.833084	−	0.992830i
$775$	−12.9510	+	15.9729i	−0.465212	+	0.573763i
$776$	41.7213	+	24.0878i	1.49771	+	0.864702i
$777$	13.8167			0.495673
$778$	6.64107	+	5.57252i	0.238094	+	0.199785i
$779$	28.0147			1.00373
$780$	28.9644	+	4.85618i	1.03709	+	0.173879i
$781$			1.25845i			0.0450307i
$782$	20.9363	−	38.9682i	0.748680	−	1.39350i
$783$		−	10.5778i		−	0.378020i
$784$	25.0027	−	9.10022i	0.892952	−	0.325008i
$785$	8.38842	+	2.97341i	0.299396	+	0.106126i
$786$	−10.1287	−	8.49900i	−0.361279	−	0.303149i
$787$		−	24.0659i		−	0.857855i	−0.903339	−	0.428928i	$-0.858892\pi$
$787$		−	24.0659i		−	0.857855i	0.903339	−	0.428928i	$-0.141108\pi$
$788$	−21.0957	+	3.71975i	−0.751504	+	0.132511i
$789$	34.1029			1.21409
$790$	16.8258	+	28.5848i	0.598636	+	1.01700i
$791$	1.11918			0.0397934
$792$	−53.8190	−	31.0724i	−1.91238	−	1.10411i
$793$	−16.1792			−0.574541
$794$	6.10279	+	5.12084i	0.216580	+	0.181732i
$795$	21.6588	−	61.1024i	0.768157	−	2.16708i
$796$	38.2721	−	6.74840i	1.35652	−	0.239191i
$797$	11.6549			0.412838			0.206419	−	0.978464i	$-0.433819\pi$
$797$	11.6549			0.412838			0.206419	+	0.978464i	$0.433819\pi$
$798$	3.69749	−	4.40649i	0.130890	−	0.155988i
$799$	−5.02851	−	24.1704i	−0.177896	−	0.855088i
$800$	24.2534	−	14.5525i	0.857486	−	0.514508i
$801$	56.1266			1.98314
$802$	−1.10617	−	0.928183i	−0.0390601	−	0.0327753i
$803$	−31.3458			−1.10617
$804$	−39.0823	+	6.89126i	−1.37833	+	0.243036i
$805$	−9.43466	−	3.34427i	−0.332528	−	0.117870i
$806$	−10.9137	−	9.15771i	−0.384420	−	0.322566i
$807$			10.5302i			0.370680i
$808$	19.7480	−	34.2046i	0.694733	−	1.20331i
$809$		−	0.998466i		−	0.0351042i	−0.999846	−	0.0175521i	$-0.994413\pi$
$809$		−	0.998466i		−	0.0351042i	0.999846	−	0.0175521i	$-0.00558729\pi$
$810$	10.9729	−	6.45899i	0.385550	−	0.226946i
$811$	−38.7092			−1.35926			−0.679632	−	0.733553i	$-0.737861\pi$
$811$	−38.7092			−1.35926			−0.679632	+	0.733553i	$0.737861\pi$
$812$	−0.680788	−	3.86094i	−0.0238910	−	0.135492i
$813$		−	35.0566i		−	1.22949i
$814$	49.6439	+	41.6562i	1.74002	+	1.46005i
$815$	−7.59880	+	21.4373i	−0.266174	+	0.750916i
$816$	−23.2686	−	37.5981i	−0.814563	−	1.31620i
$817$			15.6543i			0.547673i
$818$	−27.8309	+	33.1676i	−0.973084	+	1.15968i
$819$	−6.05272			−0.211499
$820$	−48.0566	−	8.05719i	−1.67821	−	0.281369i
$821$	−36.8698			−1.28676			−0.643382	−	0.765545i	$-0.722469\pi$
$821$	−36.8698			−1.28676			−0.643382	+	0.765545i	$0.722469\pi$
$822$	16.4214	−	19.5702i	0.572762	−	0.682591i
$823$	10.6486			0.371186			0.185593	−	0.982627i	$-0.440579\pi$
$823$	10.6486			0.371186			0.185593	+	0.982627i	$0.440579\pi$
$824$	10.1361	−	17.5562i	0.353107	−	0.611600i
$825$	−44.2951	+	54.6308i	−1.54216	+	1.90200i
$826$	−4.73510	−	3.97322i	−0.164755	−	0.138246i
$827$			0.372763i			0.0129622i	0.999979	+	0.00648112i	$0.00206302\pi$
$827$			0.372763i			0.0129622i	−0.999979	+	0.00648112i	$0.997937\pi$
$828$	−11.0335	−	62.5738i	−0.383439	−	2.17459i
$829$			41.9147i			1.45576i	0.685705	+	0.727879i	$0.259494\pi$
$829$			41.9147i			1.45576i	−0.685705	+	0.727879i	$0.740506\pi$
$830$	18.6207	−	10.9607i	0.646335	−	0.380451i
$831$	−23.6148			−0.819189
$832$	9.79796	+	16.9706i	0.339683	+	0.588348i
$833$	−26.8512	+	5.58623i	−0.930339	+	0.193551i
$834$	−4.60373	−	3.86299i	−0.159414	−	0.133764i
$835$	−27.8099	−	9.85767i	−0.962400	−	0.341139i
$836$	26.5704	−	4.68507i	0.918955	−	0.162037i
$837$	13.0953			0.452640
$838$	14.9621	−	17.8312i	0.516858	−	0.615967i
$839$		−	20.2832i		−	0.700256i	−0.936702	−	0.350128i	$-0.886138\pi$
$839$		−	20.2832i		−	0.700256i	0.936702	−	0.350128i	$-0.113862\pi$
$840$	−7.61004	+	6.49552i	−0.262571	+	0.224117i
$841$	−17.9638			−0.619443
$842$	−38.2532	−	32.0983i	−1.31829	−	1.10618i
$843$		−	74.2766i		−	2.55822i
$844$	−4.48345	−	25.4269i	−0.154327	−	0.875230i
$845$	−14.7531	−	5.22946i	−0.507521	−	0.179899i
$846$	−27.1645	−	22.7937i	−0.933935	−	0.783664i
$847$	9.75275			0.335108
$848$	40.6468	−	14.7942i	1.39582	−	0.508036i
$849$	−13.0653			−0.448399
$850$	−26.8930	+	11.2590i	−0.922424	+	0.386179i
$851$			66.2595i			2.27135i
$852$	0.223326	+	1.26655i	0.00765104	+	0.0433912i
$853$			43.1040i			1.47585i	0.674881	+	0.737926i	$0.264195\pi$
$853$			43.1040i			1.47585i	−0.674881	+	0.737926i	$0.735805\pi$
$854$	3.54297	−	4.22235i	0.121238	−	0.144486i
$855$	8.04375	−	22.6925i	0.275090	−	0.776069i
$856$	−12.2460	+	21.2107i	−0.418560	+	0.724967i
$857$	−14.2658			−0.487310			−0.243655	−	0.969862i	$-0.578346\pi$
$857$	−14.2658			−0.487310			−0.243655	+	0.969862i	$0.578346\pi$
$858$	−37.3273	−	31.3214i	−1.27433	−	1.06929i
$859$		−	54.5523i		−	1.86130i	−0.365912	−	0.930650i	$-0.619243\pi$
$859$		−	54.5523i		−	1.86130i	0.365912	−	0.930650i	$-0.380757\pi$
$860$	4.50226	−	26.8534i	0.153526	−	0.915695i
$861$	17.2367			0.587426
$862$	−9.35835	−	7.85259i	−0.318747	−	0.267460i
$863$			4.40558i			0.149968i	0.997185	+	0.0749838i	$0.0238905\pi$
$863$			4.40558i			0.149968i	−0.997185	+	0.0749838i	$0.976109\pi$
$864$	−16.9258	−	6.16047i	−0.575826	−	0.209584i
$865$	6.74576	−	19.0307i	0.229363	−	0.647065i
$866$	34.5567	+	28.9965i	1.17429	+	0.985342i
$867$	18.1772	+	41.7950i	0.617328	+	1.41943i
$868$	4.77983	−	0.842814i	0.162238	−	0.0286070i
$869$		−	55.0331i		−	1.86687i
$870$	−14.2871	−	24.2718i	−0.484378	−	0.822891i
$871$	−18.1293			−0.614287
$872$	10.0469	+	5.80061i	0.340232	+	0.196433i
$873$	−71.3270			−2.41405
$874$	21.1318	+	17.7317i	0.714793	+	0.599782i
$875$	3.44180	+	5.62821i	0.116354	+	0.190268i
$876$	−31.5476	+	5.56269i	−1.06589	+	0.187946i
$877$			50.7096i			1.71234i	0.516694	+	0.856170i	$0.327163\pi$
$877$			50.7096i			1.71234i	−0.516694	+	0.856170i	$0.672837\pi$
$878$	26.8577	+	22.5363i	0.906405	+	0.760564i
$879$			45.3061i			1.52814i
$880$	−46.9265	+	0.395016i	−1.58189	+	0.0133160i
$881$		−	19.6951i		−	0.663545i	−0.943359	−	0.331773i	$-0.892353\pi$
$881$		−	19.6951i		−	0.663545i	0.943359	−	0.331773i	$-0.107647\pi$
$882$	−25.3218	+	30.1774i	−0.852630	+	1.01612i
$883$	−20.3159			−0.683683			−0.341842	−	0.939758i	$-0.611051\pi$
$883$	−20.3159			−0.683683			−0.341842	+	0.939758i	$0.611051\pi$
$884$	−7.48568	−	18.7607i	−0.251771	−	0.630991i
$885$	−41.8539	−	14.8358i	−1.40690	−	0.498700i
$886$	−12.2712	+	14.6243i	−0.412261	+	0.491313i
$887$	5.06252			0.169983			0.0849914	−	0.996382i	$-0.472914\pi$
$887$	5.06252			0.169983			0.0849914	+	0.996382i	$0.472914\pi$
$888$	57.3559	+	33.1145i	1.92474	+	1.11125i
$889$			5.95779i			0.199818i
$890$	36.5255	−	21.5000i	1.22434	−	0.720681i
$891$	−21.1258			−0.707740
$892$	−19.4792	+	3.43471i	−0.652213	+	0.115003i
$893$	15.3953			0.515184
$894$	36.1131	−	43.0380i	1.20780	−	1.43940i
$895$	0.485657	−	1.37011i	0.0162337	−	0.0457976i
$896$	−6.57445	−	1.15925i	−0.219637	−	0.0387279i
$897$		−	49.8206i		−	1.66346i
$898$	−30.7708	−	25.8198i	−1.02684	−	0.861618i
$899$			13.6627i			0.455677i
$900$	−20.3248	+	36.6136i	−0.677494	+	1.22045i
$901$	−43.6520	+	9.08153i	−1.45426	+	0.302550i
$902$	61.9320	+	51.9672i	2.06211	+	1.73032i
$903$			9.63167i			0.320522i
$904$	4.64592	+	2.68233i	0.154521	+	0.0892128i
$905$	28.6677	+	10.1617i	0.952947	+	0.337788i
$906$	−6.87653	−	5.77010i	−0.228457	−	0.191699i
$907$			40.3689i			1.34043i	0.742168	+	0.670214i	$0.233798\pi$
$907$			40.3689i			1.34043i	−0.742168	+	0.670214i	$0.766202\pi$
$908$	−29.8618	+	5.26544i	−0.990999	+	0.174740i
$909$			58.4763i			1.93954i
$910$	−3.93893	+	2.31857i	−0.130574	+	0.0768597i
$911$			29.5250i			0.978208i	0.872225	+	0.489104i	$0.162676\pi$
$911$			29.5250i			0.978208i	−0.872225	+	0.489104i	$0.837324\pi$
$912$	25.9100	−	9.43046i	0.857965	−	0.312274i
$913$	−35.8497			−1.18645
$914$	−9.65633	−	8.10262i	−0.319403	−	0.268011i
$915$	13.2292	−	37.3216i	0.437345	−	1.23381i
$916$	−10.2246	+	1.80288i	−0.337831	+	0.0595687i
$917$	2.05776			0.0679532
$918$	16.3553	+	8.78714i	0.539805	+	0.290019i
$919$	−34.2077			−1.12841			−0.564204	−	0.825636i	$-0.690817\pi$
$919$	−34.2077			−1.12841			−0.564204	+	0.825636i	$0.690817\pi$
$920$	−31.1499	−	36.4947i	−1.02698	−	1.20319i
$921$			3.42590i			0.112887i
$922$	39.9340	+	33.5086i	1.31516	+	1.10355i
$923$			0.587519i			0.0193384i
$924$	16.3481	−	2.88261i	0.537812	−	0.0948308i
$925$	27.5031	−	33.9206i	0.904297	−	1.11530i
$926$	−16.9376	−	14.2124i	−0.556605	−	0.467047i
$927$			30.0142i			0.985797i
$928$	6.42740	−	17.6591i	0.210990	−	0.579690i
$929$		−	32.8396i		−	1.07743i	−0.842487	−	0.538716i	$-0.818910\pi$
$929$		−	32.8396i		−	1.07743i	0.842487	−	0.538716i	$-0.181090\pi$
$930$	30.0484	−	17.6874i	0.985327	−	0.579992i
$931$		−	17.1028i		−	0.560522i
$932$	−2.28314	−	12.9483i	−0.0747868	−	0.424137i
$933$	75.6778			2.47758
$934$	−2.60142	+	3.10025i	−0.0851210	+	0.101443i
$935$	47.9289	+	6.53588i	1.56744	+	0.213746i
$936$	−25.1260	−	14.5065i	−0.821268	−	0.474160i
$937$			47.3997i			1.54848i	0.632892	+	0.774240i	$0.281868\pi$
$937$			47.3997i			1.54848i	−0.632892	+	0.774240i	$0.718132\pi$
$938$	3.97000	−	4.73126i	0.129625	−	0.154481i
$939$			5.96889i			0.194787i
$940$	−26.4093	−	4.42778i	−0.861375	−	0.144418i
$941$	−22.1334			−0.721527			−0.360764	−	0.932657i	$-0.617484\pi$
$941$	−22.1334			−0.721527			−0.360764	+	0.932657i	$0.617484\pi$
$942$	−11.5600	−	9.70002i	−0.376646	−	0.316044i
$943$			82.6604i			2.69179i
$944$	−10.1337	−	27.8422i	−0.329825	−	0.906186i
$945$	1.40362	−	3.95981i	0.0456597	−	0.128813i
$946$	−29.0386	+	34.6069i	−0.944127	+	1.12517i
$947$			1.44639i			0.0470013i	0.999724	+	0.0235006i	$0.00748117\pi$
$947$			1.44639i			0.0470013i	−0.999724	+	0.0235006i	$0.992519\pi$
$948$	−9.76628	−	55.3873i	−0.317194	−	1.79890i
$949$	−14.6341			−0.475043
$950$	−3.45802	−	17.8489i	−0.112193	−	0.579094i
$951$	73.8017			2.39318
$952$	6.53528	+	2.15471i	0.211810	+	0.0698346i
$953$		−	31.5446i		−	1.02183i	−0.859631	−	0.510915i	$-0.829307\pi$
$953$		−	31.5446i		−	1.02183i	0.859631	−	0.510915i	$-0.170693\pi$
$954$	−41.1656	+	49.0593i	−1.33279	+	1.58835i
$955$	−5.66276	−	2.00726i	−0.183243	−	0.0649534i
$956$	3.07791	+	17.4557i	0.0995466	+	0.564557i
$957$			46.7295i			1.51055i
$958$	−14.2495	−	11.9568i	−0.460381	−	0.386306i
$959$			3.97591i			0.128389i
$960$	−47.1585	+	8.72523i	−1.52203	+	0.281606i
$961$	14.0856			0.454374
$962$	23.1768	+	19.4476i	0.747250	+	0.627017i
$963$		−	36.2620i		−	1.16853i
$964$	38.1690	−	6.73022i	1.22934	−	0.216766i
$965$	3.17142	+	1.12416i	0.102092	+	0.0361881i
$966$	13.0018	+	10.9098i	0.418328	+	0.351018i
$967$		−	30.2037i		−	0.971286i	−0.874157	−	0.485643i	$-0.838586\pi$
$967$		−	30.2037i		−	0.971286i	0.874157	−	0.485643i	$-0.161414\pi$
$968$	40.4855	+	23.3743i	1.30125	+	0.751280i
$969$	−27.8256	+	5.78895i	−0.893888	+	0.185968i
$970$	−46.4175	+	27.3227i	−1.49038	+	0.877278i
$971$		−	38.3436i		−	1.23050i	−0.788331	−	0.615252i	$-0.789054\pi$
$971$		−	38.3436i		−	1.23050i	0.788331	−	0.615252i	$-0.210946\pi$
$972$	−40.0761	+	7.06651i	−1.28544	+	0.226658i
$973$	0.935297			0.0299842
$974$	−15.5082	+	18.4819i	−0.496915	+	0.592200i
$975$	−20.6796	+	25.5050i	−0.662278	+	0.816812i
$976$	24.8272	−	9.03636i	0.794700	−	0.289247i
$977$			12.1582i			0.388975i	0.980905	+	0.194487i	$0.0623043\pi$
$977$			12.1582i			0.388975i	−0.980905	+	0.194487i	$0.937696\pi$
$978$	24.7892	−	29.5426i	0.792671	−	0.944669i
$979$	−70.3211			−2.24747
$980$	−4.91888	+	29.3383i	−0.157128	+	0.937179i
$981$	−17.1763			−0.548398
$982$	−15.9486	−	13.3825i	−0.508941	−	0.427052i
$983$	42.5044			1.35568			0.677839	−	0.735210i	$-0.262917\pi$
$983$	42.5044			1.35568			0.677839	+	0.735210i	$0.262917\pi$
$984$	71.5529	+	41.3111i	2.28102	+	1.31695i
$985$	8.00152	−	22.5734i	0.254950	−	0.719249i
$986$	−9.16788	+	17.0640i	−0.291965	+	0.543427i
$987$	9.47235			0.301508
$988$	12.4047	−	2.18727i	0.394645	−	0.0695865i
$989$	−46.1896			−1.46874
$990$	59.8770	−	35.2453i	1.90301	−	1.12017i
$991$		−	40.8846i		−	1.29874i	−0.760472	−	0.649371i	$-0.775032\pi$
$991$		−	40.8846i		−	1.29874i	0.760472	−	0.649371i	$-0.224968\pi$
$992$	21.8620	+	7.95711i	0.694118	+	0.252638i
$993$	68.1738			2.16343
$994$	−0.153327	−	0.128656i	−0.00486323	−	0.00408073i
$995$	−14.5164	+	40.9529i	−0.460202	+	1.29829i
$996$	−36.0805	+	6.36196i	−1.14325	+	0.201586i
$997$			6.50535i			0.206026i	0.994680	+	0.103013i	$0.0328484\pi$
$997$			6.50535i			0.206026i	−0.994680	+	0.103013i	$0.967152\pi$
$998$	−0.966519	+	1.15185i	−0.0305946	+	0.0364613i
$999$	−27.8097			−0.879860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.h.c.509.16	yes	48
5.4	even	2	inner	680.2.h.c.509.33	yes	48
8.5	even	2	inner	680.2.h.c.509.37	yes	48
17.16	even	2	inner	680.2.h.c.509.13	yes	48
40.29	even	2	inner	680.2.h.c.509.12	yes	48
85.84	even	2	inner	680.2.h.c.509.36	yes	48
136.101	even	2	inner	680.2.h.c.509.40	yes	48
680.509	even	2	inner	680.2.h.c.509.9	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.h.c.509.9	✓	48	680.509	even	2	inner
680.2.h.c.509.12	yes	48	40.29	even	2	inner
680.2.h.c.509.13	yes	48	17.16	even	2	inner
680.2.h.c.509.16	yes	48	1.1	even	1	trivial
680.2.h.c.509.33	yes	48	5.4	even	2	inner
680.2.h.c.509.36	yes	48	85.84	even	2	inner
680.2.h.c.509.37	yes	48	8.5	even	2	inner
680.2.h.c.509.40	yes	48	136.101	even	2	inner

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909039 + 1.08335i) q^{2} +2.68098i q^{3} +(-0.347296 - 1.96962i) q^{4} +(2.10758 + 0.747066i) q^{5} +(-2.90444 - 2.43712i) q^{6} +0.590069 q^{7} +(2.44949 + 1.41421i) q^{8} -4.18766 q^{9} +(-2.72521 + 1.60414i) q^{10} +5.24673 q^{11} +(5.28050 - 0.931095i) q^{12} +2.44949 q^{13} +(-0.536396 + 0.639252i) q^{14} +(-2.00287 + 5.65038i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(4.03667 - 0.839805i) q^{17} +(3.80675 - 4.53671i) q^{18} +2.57115i q^{19} +(0.739479 - 4.41057i) q^{20} +1.58196i q^{21} +(-4.76948 + 5.68404i) q^{22} -7.58646 q^{23} +(-3.79148 + 6.56704i) q^{24} +(3.88378 + 3.14900i) q^{25} +(-2.22668 + 2.65366i) q^{26} -3.18410i q^{27} +(-0.204929 - 1.16221i) q^{28} +3.32207 q^{29} +(-4.30066 - 7.30623i) q^{30} +4.11271i q^{31} +(1.93476 - 5.31570i) q^{32} +14.0664i q^{33} +(-2.75969 + 5.13655i) q^{34} +(1.24362 + 0.440821i) q^{35} +(1.45436 + 8.24809i) q^{36} -8.73391i q^{37} +(-2.78546 - 2.33728i) q^{38} +6.56704i q^{39} +(4.10598 + 4.81050i) q^{40} -10.8958i q^{41} +(-1.71382 - 1.43807i) q^{42} +6.08842 q^{43} +(-1.82217 - 10.3340i) q^{44} +(-8.82583 - 3.12846i) q^{45} +(6.89639 - 8.21880i) q^{46} -5.98771i q^{47} +(-3.66780 - 10.0772i) q^{48} -6.65182 q^{49} +(-6.94199 + 1.34493i) q^{50} +(2.25150 + 10.8222i) q^{51} +(-0.850699 - 4.82455i) q^{52} -10.8139 q^{53} +(3.44950 + 2.89448i) q^{54} +(11.0579 + 3.91965i) q^{55} +(1.44537 + 0.834484i) q^{56} -6.89321 q^{57} +(-3.01989 + 3.59897i) q^{58} +7.40726i q^{59} +(11.8247 + 1.98253i) q^{60} -6.60514 q^{61} +(-4.45551 - 3.73862i) q^{62} -2.47101 q^{63} +(4.00000 + 6.92820i) q^{64} +(5.16249 + 1.82993i) q^{65} +(-15.2388 - 12.7869i) q^{66} -7.40124 q^{67} +(-3.05601 - 7.65903i) q^{68} -20.3392i q^{69} +(-1.60806 + 0.946550i) q^{70} +0.239853i q^{71} +(-10.2576 - 5.92225i) q^{72} -5.97435 q^{73} +(9.46189 + 7.93947i) q^{74} +(-8.44242 + 10.4124i) q^{75} +(5.06418 - 0.892951i) q^{76} +3.09593 q^{77} +(-7.11440 - 5.96969i) q^{78} -10.4890i q^{79} +(-8.94396 + 0.0752882i) q^{80} -4.02646 q^{81} +(11.8039 + 9.90468i) q^{82} -6.83277 q^{83} +(3.11586 - 0.549410i) q^{84} +(9.13500 + 1.24571i) q^{85} +(-5.53461 + 6.59590i) q^{86} +8.90641i q^{87} +(12.8518 + 7.41999i) q^{88} -13.4029 q^{89} +(11.4122 - 6.71758i) q^{90} +1.44537 q^{91} +(2.63475 + 14.9424i) q^{92} -11.0261 q^{93} +(6.48679 + 5.44306i) q^{94} +(-1.92082 + 5.41890i) q^{95} +(14.2513 + 5.18705i) q^{96} +17.0326 q^{97} +(6.04676 - 7.20625i) q^{98} -21.9715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{9} - 48 q^{15} + 24 q^{34} - 96 q^{36} + 96 q^{49} + 48 q^{60} + 192 q^{64} - 144 q^{66} - 96 q^{70} + 96 q^{76} - 192 q^{84} - 192 q^{86} - 48 q^{89} - 144 q^{94}+O(q^{100}) \) 48 * q - 96 * q^9 - 48 * q^15 + 24 * q^34 - 96 * q^36 + 96 * q^49 + 48 * q^60 + 192 * q^64 - 144 * q^66 - 96 * q^70 + 96 * q^76 - 192 * q^84 - 192 * q^86 - 48 * q^89 - 144 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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