LMFDB - Embedded newform 403.2.i.a.216.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(216,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("403.216");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.i (of order $4$, degree $2$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			216.8
Character	$\chi$	$=$	403.216
Dual form			403.2.i.a.278.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30566 - 1.30566i) q^{2} +2.35582i q^{3} +1.40948i q^{4} +(-3.07515 - 3.07515i) q^{5} +(3.07590 - 3.07590i) q^{6} +(1.59752 - 1.59752i) q^{7} +(-0.771014 + 0.771014i) q^{8} -2.54991 q^{9} +O(q^{10})$	\(q+(-1.30566 - 1.30566i) q^{2} +2.35582i q^{3} +1.40948i q^{4} +(-3.07515 - 3.07515i) q^{5} +(3.07590 - 3.07590i) q^{6} +(1.59752 - 1.59752i) q^{7} +(-0.771014 + 0.771014i) q^{8} -2.54991 q^{9} +8.03019i q^{10} +(1.55908 + 1.55908i) q^{11} -3.32049 q^{12} +(-1.38259 + 3.32993i) q^{13} -4.17164 q^{14} +(7.24451 - 7.24451i) q^{15} +4.83232 q^{16} -2.58632 q^{17} +(3.32930 + 3.32930i) q^{18} +(-0.709142 - 0.709142i) q^{19} +(4.33437 - 4.33437i) q^{20} +(3.76348 + 3.76348i) q^{21} -4.07124i q^{22} -6.84836 q^{23} +(-1.81637 - 1.81637i) q^{24} +13.9131i q^{25} +(6.15294 - 2.54256i) q^{26} +1.06034i q^{27} +(2.25168 + 2.25168i) q^{28} +6.98975i q^{29} -18.9177 q^{30} +(-3.77737 + 4.09042i) q^{31} +(-4.76733 - 4.76733i) q^{32} +(-3.67291 + 3.67291i) q^{33} +(3.37685 + 3.37685i) q^{34} -9.82526 q^{35} -3.59405i q^{36} +(-4.46075 - 4.46075i) q^{37} +1.85179i q^{38} +(-7.84473 - 3.25715i) q^{39} +4.74197 q^{40} +(4.15291 + 4.15291i) q^{41} -9.82764i q^{42} +0.679033 q^{43} +(-2.19749 + 2.19749i) q^{44} +(7.84134 + 7.84134i) q^{45} +(8.94161 + 8.94161i) q^{46} +(-2.20639 + 2.20639i) q^{47} +11.3841i q^{48} +1.89583i q^{49} +(18.1658 - 18.1658i) q^{50} -6.09291i q^{51} +(-4.69348 - 1.94874i) q^{52} -9.83116i q^{53} +(1.38445 - 1.38445i) q^{54} -9.58880i q^{55} +2.46343i q^{56} +(1.67061 - 1.67061i) q^{57} +(9.12622 - 9.12622i) q^{58} +(0.254021 - 0.254021i) q^{59} +(10.2110 + 10.2110i) q^{60} +6.77285i q^{61} +(10.2726 - 0.408737i) q^{62} +(-4.07353 + 4.07353i) q^{63} +2.78435i q^{64} +(14.4917 - 5.98836i) q^{65} +9.59113 q^{66} +(8.89709 + 8.89709i) q^{67} -3.64537i q^{68} -16.1335i q^{69} +(12.8284 + 12.8284i) q^{70} +(-6.95145 - 6.95145i) q^{71} +(1.96601 - 1.96601i) q^{72} +(2.79224 + 2.79224i) q^{73} +11.6484i q^{74} -32.7768 q^{75} +(0.999523 - 0.999523i) q^{76} +4.98133 q^{77} +(5.98981 + 14.4952i) q^{78} -11.2270i q^{79} +(-14.8601 - 14.8601i) q^{80} -10.1477 q^{81} -10.8446i q^{82} +(-2.60512 + 2.60512i) q^{83} +(-5.30456 + 5.30456i) q^{84} +(7.95332 + 7.95332i) q^{85} +(-0.886584 - 0.886584i) q^{86} -16.4666 q^{87} -2.40414 q^{88} +(6.56656 + 6.56656i) q^{89} -20.4762i q^{90} +(3.11092 + 7.52837i) q^{91} -9.65264i q^{92} +(-9.63630 - 8.89881i) q^{93} +5.76159 q^{94} +4.36144i q^{95} +(11.2310 - 11.2310i) q^{96} +(-9.16349 - 9.16349i) q^{97} +(2.47531 - 2.47531i) q^{98} +(-3.97550 - 3.97550i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	$ 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) $ 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.30566	−	1.30566i	−0.923239	−	0.923239i	0.0740178	−	0.997257i	$-0.476418\pi$
$2$	−1.30566	−	1.30566i	−0.923239	−	0.923239i	−0.997257	+	0.0740178i	$0.976418\pi$
$3$			2.35582i			1.36014i	0.733149	+	0.680068i	$0.238050\pi$
$3$			2.35582i			1.36014i	−0.733149	+	0.680068i	$0.761950\pi$
$4$			1.40948i			0.704741i
$5$	−3.07515	−	3.07515i	−1.37525	−	1.37525i	−0.852465	−	0.522784i	$-0.824893\pi$
$5$	−3.07515	−	3.07515i	−1.37525	−	1.37525i	−0.522784	−	0.852465i	$-0.675107\pi$
$6$	3.07590	−	3.07590i	1.25573	−	1.25573i
$7$	1.59752	−	1.59752i	0.603807	−	0.603807i	−0.337513	−	0.941321i	$-0.609586\pi$
$7$	1.59752	−	1.59752i	0.603807	−	0.603807i	0.941321	+	0.337513i	$0.109586\pi$
$8$	−0.771014	+	0.771014i	−0.272595	+	0.272595i
$9$	−2.54991			−0.849968
$10$			8.03019i			2.53937i
$11$	1.55908	+	1.55908i	0.470079	+	0.470079i	0.901940	−	0.431861i	$-0.142143\pi$
$11$	1.55908	+	1.55908i	0.470079	+	0.470079i	−0.431861	+	0.901940i	$0.642143\pi$
$12$	−3.32049			−0.958543
$13$	−1.38259	+	3.32993i	−0.383462	+	0.923557i
$13$	−1.38259	+	3.32993i	−0.383462	+	0.923557i
$14$	−4.17164			−1.11492
$15$	7.24451	−	7.24451i	1.87053	−	1.87053i
$16$	4.83232			1.20808
$17$	−2.58632			−0.627274			−0.313637	−	0.949543i	$-0.601548\pi$
$17$	−2.58632			−0.627274			−0.313637	+	0.949543i	$0.601548\pi$
$18$	3.32930	+	3.32930i	0.784724	+	0.784724i
$19$	−0.709142	−	0.709142i	−0.162688	−	0.162688i	0.621068	−	0.783757i	$-0.286699\pi$
$19$	−0.709142	−	0.709142i	−0.162688	−	0.162688i	−0.783757	+	0.621068i	$0.786699\pi$
$20$	4.33437	−	4.33437i	0.969195	−	0.969195i
$21$	3.76348	+	3.76348i	0.821260	+	0.821260i
$22$		−	4.07124i		−	0.867992i
$23$	−6.84836			−1.42798			−0.713991	−	0.700155i	$-0.753114\pi$
$23$	−6.84836			−1.42798			−0.713991	+	0.700155i	$0.753114\pi$
$24$	−1.81637	−	1.81637i	−0.370766	−	0.370766i
$25$			13.9131i			2.78262i
$26$	6.15294	−	2.54256i	1.20669	−	0.498636i
$27$			1.06034i			0.204063i
$28$	2.25168	+	2.25168i	0.425528	+	0.425528i
$29$			6.98975i			1.29796i	0.760804	+	0.648982i	$0.224805\pi$
$29$			6.98975i			1.29796i	−0.760804	+	0.648982i	$0.775195\pi$
$30$	−18.9177			−3.45388
$31$	−3.77737	+	4.09042i	−0.678435	+	0.734661i
$31$	−3.77737	+	4.09042i	−0.678435	+	0.734661i
$32$	−4.76733	−	4.76733i	−0.842753	−	0.842753i
$33$	−3.67291	+	3.67291i	−0.639372	+	0.639372i
$34$	3.37685	+	3.37685i	0.579124	+	0.579124i
$35$	−9.82526			−1.66077
$36$		−	3.59405i		−	0.599008i
$37$	−4.46075	−	4.46075i	−0.733343	−	0.733343i	0.237938	−	0.971280i	$-0.423529\pi$
$37$	−4.46075	−	4.46075i	−0.733343	−	0.733343i	−0.971280	+	0.237938i	$0.923529\pi$
$38$			1.85179i			0.300400i
$39$	−7.84473	−	3.25715i	−1.25616	−	0.521561i
$40$	4.74197			0.749771
$41$	4.15291	+	4.15291i	0.648576	+	0.648576i	0.952649	−	0.304073i	$-0.0983466\pi$
$41$	4.15291	+	4.15291i	0.648576	+	0.648576i	−0.304073	+	0.952649i	$0.598347\pi$
$42$		−	9.82764i		−	1.51644i
$43$	0.679033			0.103551			0.0517757	−	0.998659i	$-0.483512\pi$
$43$	0.679033			0.103551			0.0517757	+	0.998659i	$0.483512\pi$
$44$	−2.19749	+	2.19749i	−0.331284	+	0.331284i
$45$	7.84134	+	7.84134i	1.16892	+	1.16892i
$46$	8.94161	+	8.94161i	1.31837	+	1.31837i
$47$	−2.20639	+	2.20639i	−0.321836	+	0.321836i	−0.849471	−	0.527635i	$-0.823079\pi$
$47$	−2.20639	+	2.20639i	−0.321836	+	0.321836i	0.527635	+	0.849471i	$0.323079\pi$
$48$			11.3841i			1.64315i
$49$			1.89583i			0.270833i
$50$	18.1658	−	18.1658i	2.56903	−	2.56903i
$51$		−	6.09291i		−	0.853178i
$52$	−4.69348	−	1.94874i	−0.650868	−	0.270242i
$53$		−	9.83116i		−	1.35041i	−0.737628	−	0.675207i	$-0.764054\pi$
$53$		−	9.83116i		−	1.35041i	0.737628	−	0.675207i	$-0.235946\pi$
$54$	1.38445	−	1.38445i	0.188399	−	0.188399i
$55$		−	9.58880i		−	1.29295i
$56$			2.46343i			0.329189i
$57$	1.67061	−	1.67061i	0.221278	−	0.221278i
$58$	9.12622	−	9.12622i	1.19833	−	1.19833i
$59$	0.254021	−	0.254021i	0.0330707	−	0.0330707i	−0.690378	−	0.723449i	$-0.742556\pi$
$59$	0.254021	−	0.254021i	0.0330707	−	0.0330707i	0.723449	+	0.690378i	$0.242556\pi$
$60$	10.2110	+	10.2110i	1.31824	+	1.31824i
$61$			6.77285i			0.867175i	0.901111	+	0.433588i	$0.142752\pi$
$61$			6.77285i			0.867175i	−0.901111	+	0.433588i	$0.857248\pi$
$62$	10.2726	−	0.408737i	1.30463	−	0.0519097i
$63$	−4.07353	+	4.07353i	−0.513217	+	0.513217i
$64$			2.78435i			0.348044i
$65$	14.4917	−	5.98836i	1.79748	−	0.742764i
$66$	9.59113			1.18059
$67$	8.89709	+	8.89709i	1.08695	+	1.08695i	0.995841	+	0.0911117i	$0.0290420\pi$
$67$	8.89709	+	8.89709i	1.08695	+	1.08695i	0.0911117	+	0.995841i	$0.470958\pi$
$68$		−	3.64537i		−	0.442066i
$69$		−	16.1335i		−	1.94225i
$70$	12.8284	+	12.8284i	1.53329	+	1.53329i
$71$	−6.95145	−	6.95145i	−0.824986	−	0.824986i	0.161833	−	0.986818i	$-0.448260\pi$
$71$	−6.95145	−	6.95145i	−0.824986	−	0.824986i	−0.986818	+	0.161833i	$0.948260\pi$
$72$	1.96601	−	1.96601i	0.231697	−	0.231697i
$73$	2.79224	+	2.79224i	0.326807	+	0.326807i	0.851371	−	0.524564i	$-0.175772\pi$
$73$	2.79224	+	2.79224i	0.326807	+	0.326807i	−0.524564	+	0.851371i	$0.675772\pi$
$74$			11.6484i			1.35410i
$75$	−32.7768			−3.78474
$76$	0.999523	−	0.999523i	0.114653	−	0.114653i
$77$	4.98133			0.567675
$78$	5.98981	+	14.4952i	0.678213	+	1.64126i
$79$		−	11.2270i		−	1.26313i	−0.775322	−	0.631566i	$-0.782412\pi$
$79$		−	11.2270i		−	1.26313i	0.775322	−	0.631566i	$-0.217588\pi$
$80$	−14.8601	−	14.8601i	−1.66141	−	1.66141i
$81$	−10.1477			−1.12752
$82$		−	10.8446i		−	1.19758i
$83$	−2.60512	+	2.60512i	−0.285949	+	0.285949i	−0.835476	−	0.549527i	$-0.814808\pi$
$83$	−2.60512	+	2.60512i	−0.285949	+	0.285949i	0.549527	+	0.835476i	$0.314808\pi$
$84$	−5.30456	+	5.30456i	−0.578775	+	0.578775i
$85$	7.95332	+	7.95332i	0.862659	+	0.862659i
$86$	−0.886584	−	0.886584i	−0.0956028	−	0.0956028i
$87$	−16.4666			−1.76541
$88$	−2.40414			−0.256282
$89$	6.56656	+	6.56656i	0.696054	+	0.696054i	0.963557	−	0.267503i	$-0.0861984\pi$
$89$	6.56656	+	6.56656i	0.696054	+	0.696054i	−0.267503	+	0.963557i	$0.586198\pi$
$90$		−	20.4762i		−	2.15838i
$91$	3.11092	+	7.52837i	0.326113	+	0.789188i
$92$		−	9.65264i		−	1.00636i
$93$	−9.63630	−	8.89881i	−0.999238	−	0.922763i
$94$	5.76159			0.594262
$95$			4.36144i			0.447474i
$96$	11.2310	−	11.2310i	1.14626	−	1.14626i
$97$	−9.16349	−	9.16349i	−0.930411	−	0.930411i	0.0673201	−	0.997731i	$-0.478555\pi$
$97$	−9.16349	−	9.16349i	−0.930411	−	0.930411i	−0.997731	+	0.0673201i	$0.978555\pi$
$98$	2.47531	−	2.47531i	0.250044	−	0.250044i
$99$	−3.97550	−	3.97550i	−0.399553	−	0.399553i
$100$	−19.6103			−1.96103
$101$			10.2422i			1.01913i	0.860431	+	0.509566i	$0.170194\pi$
$101$			10.2422i			1.01913i	−0.860431	+	0.509566i	$0.829806\pi$
$102$	−7.95525	+	7.95525i	−0.787687	+	0.787687i
$103$		−	4.24969i		−	0.418734i	−0.977837	−	0.209367i	$-0.932860\pi$
$103$		−	4.24969i		−	0.418734i	0.977837	−	0.209367i	$-0.0671404\pi$
$104$	−1.50142	−	3.63342i	−0.147227	−	0.356286i
$105$		−	23.1466i		−	2.25887i
$106$	−12.8361	+	12.8361i	−1.24676	+	1.24676i
$107$	−1.27425			−0.123186			−0.0615932	−	0.998101i	$-0.519618\pi$
$107$	−1.27425			−0.123186			−0.0615932	+	0.998101i	$0.519618\pi$
$108$	−1.49454			−0.143812
$109$	−4.41108	−	4.41108i	−0.422505	−	0.422505i	0.463560	−	0.886065i	$-0.346572\pi$
$109$	−4.41108	−	4.41108i	−0.422505	−	0.422505i	−0.886065	+	0.463560i	$0.846572\pi$
$110$	−12.5197	+	12.5197i	−1.19370	+	1.19370i
$111$	10.5087	−	10.5087i	0.997445	−	0.997445i
$112$	7.71975	−	7.71975i	0.729448	−	0.729448i
$113$	2.83127			0.266344			0.133172	−	0.991093i	$-0.457484\pi$
$113$	2.83127			0.266344			0.133172	+	0.991093i	$0.457484\pi$
$114$	−4.36250			−0.408585
$115$	21.0597	+	21.0597i	1.96383	+	1.96383i
$116$	−9.85192			−0.914728
$117$	3.52548	−	8.49101i	0.325931	−	0.784994i
$118$	−0.663328			−0.0610643
$119$	−4.13171	+	4.13171i	−0.378753	+	0.378753i
$120$			11.1712i			1.01979i
$121$		−	6.13856i		−	0.558051i
$122$	8.84303	−	8.84303i	0.800610	−	0.800610i
$123$	−9.78353	+	9.78353i	−0.882151	+	0.882151i
$124$	−5.76537	−	5.32413i	−0.517745	−	0.478121i
$125$	27.4092	−	27.4092i	2.45155	−	2.45155i
$126$	10.6373			0.947644
$127$	−6.80514			−0.603859			−0.301929	−	0.953330i	$-0.597631\pi$
$127$	−6.80514			−0.603859			−0.301929	+	0.953330i	$0.597631\pi$
$128$	−5.89925	+	5.89925i	−0.521425	+	0.521425i
$129$			1.59968i			0.140844i
$130$	−26.7400	−	11.1025i	−2.34525	−	0.973752i
$131$	4.66798			0.407843			0.203922	−	0.978987i	$-0.434631\pi$
$131$	4.66798			0.407843			0.203922	+	0.978987i	$0.434631\pi$
$132$	−5.17690	−	5.17690i	−0.450592	−	0.450592i
$133$	−2.26574			−0.196465
$134$		−	23.2331i		−	2.00703i
$135$	3.26072	−	3.26072i	0.280638	−	0.280638i
$136$	1.99409	−	1.99409i	0.170992	−	0.170992i
$137$	−8.46710	−	8.46710i	−0.723393	−	0.723393i	0.245902	−	0.969295i	$-0.420916\pi$
$137$	−8.46710	−	8.46710i	−0.723393	−	0.723393i	−0.969295	+	0.245902i	$0.920916\pi$
$138$	−21.0649	+	21.0649i	−1.79316	+	1.79316i
$139$			5.35097i			0.453863i	0.973911	+	0.226932i	$0.0728694\pi$
$139$			5.35097i			0.453863i	−0.973911	+	0.226932i	$0.927131\pi$
$140$		−	13.8485i		−	1.17041i
$141$	−5.19787	−	5.19787i	−0.437740	−	0.437740i
$142$			18.1524i			1.52332i
$143$	−7.34719	+	3.03605i	−0.614403	+	0.253887i
$144$	−12.3220			−1.02683
$145$	21.4945	−	21.4945i	1.78502	−	1.78502i
$146$		−	7.29141i		−	0.603442i
$147$	−4.46625			−0.368370
$148$	6.28735	−	6.28735i	0.516817	−	0.516817i
$149$	4.13505	+	4.13505i	0.338756	+	0.338756i	0.855899	−	0.517143i	$-0.173004\pi$
$149$	4.13505	+	4.13505i	0.338756	+	0.338756i	−0.517143	+	0.855899i	$0.673004\pi$
$150$	42.7953	+	42.7953i	3.49422	+	3.49422i
$151$	−9.02741	−	9.02741i	−0.734640	−	0.734640i	0.236895	−	0.971535i	$-0.423870\pi$
$151$	−9.02741	−	9.02741i	−0.734640	−	0.734640i	−0.971535	+	0.236895i	$0.923870\pi$
$152$	1.09352			0.0886959
$153$	6.59487			0.533163
$154$	−6.50391	−	6.50391i	−0.524100	−	0.524100i
$155$	24.1946	−	0.962679i	1.94336	−	0.0773242i
$156$	4.59089	−	11.0570i	0.367565	−	0.885269i
$157$	−3.71307			−0.296335			−0.148168	−	0.988962i	$-0.547337\pi$
$157$	−3.71307			−0.296335			−0.148168	+	0.988962i	$0.547337\pi$
$158$	−14.6586	+	14.6586i	−1.16617	+	1.16617i
$159$	23.1605			1.83675
$160$			29.3205i			2.31799i
$161$	−10.9404	+	10.9404i	−0.862226	+	0.862226i
$162$	13.2494	+	13.2494i	1.04097	+	1.04097i
$163$	−17.9446	+	17.9446i	−1.40553	+	1.40553i	−0.624538	+	0.780995i	$0.714713\pi$
$163$	−17.9446	+	17.9446i	−1.40553	+	1.40553i	−0.780995	+	0.624538i	$0.785287\pi$
$164$	−5.85346	+	5.85346i	−0.457078	+	0.457078i
$165$	22.5895			1.75859
$166$	6.80278			0.527998
$167$	−17.8871	−	17.8871i	−1.38415	−	1.38415i	−0.837105	−	0.547043i	$-0.815753\pi$
$167$	−17.8871	−	17.8871i	−1.38415	−	1.38415i	−0.547043	−	0.837105i	$-0.684247\pi$
$168$	−5.80340			−0.447742
$169$	−9.17687	−	9.20788i	−0.705913	−	0.708298i
$170$		−	20.7686i		−	1.59288i
$171$	1.80824	+	1.80824i	0.138280	+	0.138280i
$172$			0.957084i			0.0729770i
$173$			17.7118i			1.34660i	0.739370	+	0.673300i	$0.235124\pi$
$173$			17.7118i			1.34660i	−0.739370	+	0.673300i	$0.764876\pi$
$174$	21.4998	+	21.4998i	1.62989	+	1.62989i
$175$	22.2265	+	22.2265i	1.68017	+	1.68017i
$176$	7.53397	+	7.53397i	0.567894	+	0.567894i
$177$	0.598428	+	0.598428i	0.0449806	+	0.0449806i
$178$		−	17.1474i		−	1.28525i
$179$	13.3159			0.995279			0.497639	−	0.867384i	$-0.334200\pi$
$179$	13.3159			0.995279			0.497639	+	0.867384i	$0.334200\pi$
$180$	−11.0522	+	11.0522i	−0.823785	+	0.823785i
$181$	1.46024			0.108539			0.0542694	−	0.998526i	$-0.482717\pi$
$181$	1.46024			0.108539			0.0542694	+	0.998526i	$0.482717\pi$
$182$	5.76768	−	13.8913i	0.427529	−	1.02969i
$183$	−15.9556			−1.17948
$184$	5.28018	−	5.28018i	0.389260	−	0.389260i
$185$			27.4350i			2.01706i
$186$	0.962913	+	24.2005i	0.0706042	+	1.77447i
$187$	−4.03227	−	4.03227i	−0.294869	−	0.294869i
$188$	−3.10987	−	3.10987i	−0.226811	−	0.226811i
$189$	1.69392	+	1.69392i	0.123215	+	0.123215i
$190$	5.69454	−	5.69454i	0.413126	−	0.413126i
$191$	13.0616			0.945103			0.472552	−	0.881303i	$-0.343333\pi$
$191$	13.0616			0.945103			0.472552	+	0.881303i	$0.343333\pi$
$192$	−6.55945			−0.473387
$193$	−2.52932	+	2.52932i	−0.182065	+	0.182065i	−0.792255	−	0.610190i	$-0.791093\pi$
$193$	−2.52932	+	2.52932i	−0.182065	+	0.182065i	0.610190	+	0.792255i	$0.291093\pi$
$194$			23.9288i			1.71798i
$195$	14.1075	+	34.1399i	1.01026	+	2.44481i
$196$	−2.67214			−0.190867
$197$	−16.6415	+	16.6415i	−1.18565	+	1.18565i	−0.207398	+	0.978257i	$0.566499\pi$
$197$	−16.6415	+	16.6415i	−1.18565	+	1.18565i	−0.978257	+	0.207398i	$0.933501\pi$
$198$			10.3813i			0.737765i
$199$	−12.3919			−0.878437			−0.439218	−	0.898380i	$-0.644745\pi$
$199$	−12.3919			−0.878437			−0.439218	+	0.898380i	$0.644745\pi$
$200$	−10.7272	−	10.7272i	−0.758528	−	0.758528i
$201$	−20.9600	+	20.9600i	−1.47840	+	1.47840i
$202$	13.3727	−	13.3727i	0.940903	−	0.940903i
$203$	11.1663	+	11.1663i	0.783720	+	0.783720i
$204$	8.58785			0.601270
$205$		−	25.5417i		−	1.78391i
$206$	−5.54864	+	5.54864i	−0.386592	+	0.386592i
$207$	17.4627			1.21374
$208$	−6.68114	+	16.0913i	−0.463254	+	1.11573i
$209$		−	2.21121i		−	0.152953i
$210$	−30.2215	+	30.2215i	−2.08548	+	2.08548i
$211$	10.8538			0.747208			0.373604	−	0.927588i	$-0.378122\pi$
$211$	10.8538			0.747208			0.373604	+	0.927588i	$0.378122\pi$
$212$	13.8568			0.951692
$213$	16.3764	−	16.3764i	1.12209	−	1.12209i
$214$	1.66374	+	1.66374i	0.113731	+	0.113731i
$215$	−2.08813	−	2.08813i	−0.142409	−	0.142409i
$216$	−0.817540	−	0.817540i	−0.0556265	−	0.0556265i
$217$	0.500106	+	12.5690i	0.0339494	+	0.853237i
$218$			11.5187i			0.780147i
$219$	−6.57802	+	6.57802i	−0.444502	+	0.444502i
$220$	13.5152			0.911197
$221$	3.57583	−	8.61226i	0.240536	−	0.579323i
$222$	−27.4416			−1.84176
$223$	6.77948	−	6.77948i	0.453988	−	0.453988i	−0.442688	−	0.896676i	$-0.645975\pi$
$223$	6.77948	−	6.77948i	0.453988	−	0.453988i	0.896676	+	0.442688i	$0.145975\pi$
$224$	−15.2319			−1.01772
$225$		−	35.4771i		−	2.36514i
$226$	−3.69667	−	3.69667i	−0.245899	−	0.245899i
$227$	−1.88547	−	1.88547i	−0.125143	−	0.125143i	0.641761	−	0.766904i	$-0.278204\pi$
$227$	−1.88547	−	1.88547i	−0.125143	−	0.125143i	−0.766904	+	0.641761i	$0.778204\pi$
$228$	2.35470	+	2.35470i	0.155944	+	0.155944i
$229$	11.5009	+	11.5009i	0.760002	+	0.760002i	0.976322	−	0.216320i	$-0.0694056\pi$
$229$	11.5009	+	11.5009i	0.760002	+	0.760002i	−0.216320	+	0.976322i	$0.569406\pi$
$230$		−	54.9936i		−	3.62617i
$231$			11.7351i			0.772115i
$232$	−5.38919	−	5.38919i	−0.353818	−	0.353818i
$233$		−	10.7713i		−	0.705653i	−0.935689	−	0.352827i	$-0.885221\pi$
$233$		−	10.7713i		−	0.705653i	0.935689	−	0.352827i	$-0.114779\pi$
$234$	−15.6894	+	6.48328i	−1.02565	+	0.423825i
$235$	13.5700			0.885208
$236$	0.358038	+	0.358038i	0.0233063	+	0.0233063i
$237$	26.4487			1.71803
$238$	10.7892			0.699359
$239$	16.7658	−	16.7658i	1.08449	−	1.08449i	0.0884044	−	0.996085i	$-0.471823\pi$
$239$	16.7658	−	16.7658i	1.08449	−	1.08449i	0.996085	−	0.0884044i	$-0.0281768\pi$
$240$	35.0078	−	35.0078i	2.25975	−	2.25975i
$241$	−19.6660	−	19.6660i	−1.26680	−	1.26680i	−0.947733	−	0.319063i	$-0.896632\pi$
$241$	−19.6660	−	19.6660i	−1.26680	−	1.26680i	−0.319063	−	0.947733i	$-0.603368\pi$
$242$	−8.01485	+	8.01485i	−0.515214	+	0.515214i
$243$		−	20.7252i		−	1.32952i
$244$	−9.54622			−0.611134
$245$	5.82998	−	5.82998i	0.372463	−	0.372463i
$246$	25.5479			1.62887
$247$	3.34185	−	1.38094i	0.212637	−	0.0878670i
$248$	−0.241367	−	6.06617i	−0.0153268	−	0.385202i
$249$	−6.13719	−	6.13719i	−0.388929	−	0.388929i
$250$	−71.5739			−4.52673
$251$	−15.9413			−1.00621			−0.503103	−	0.864226i	$-0.667808\pi$
$251$	−15.9413			−1.00621			−0.503103	+	0.864226i	$0.667808\pi$
$252$	−5.74157	−	5.74157i	−0.361685	−	0.361685i
$253$	−10.6771	−	10.6771i	−0.671265	−	0.671265i
$254$	8.88519	+	8.88519i	0.557506	+	0.557506i
$255$	−18.7366	+	18.7366i	−1.17333	+	1.17333i
$256$	20.9735			1.31084
$257$			5.43249i			0.338870i	0.985541	+	0.169435i	$0.0541942\pi$
$257$			5.43249i			0.338870i	−0.985541	+	0.169435i	$0.945806\pi$
$258$	2.08864	−	2.08864i	0.130033	−	0.130033i
$259$	−14.2523			−0.885595
$260$	8.44048	+	20.4258i	0.523456	+	1.26676i
$261$		−	17.8232i		−	1.10323i
$262$	−6.09478	−	6.09478i	−0.376537	−	0.376537i
$263$			9.93335i			0.612517i	0.951948	+	0.306258i	$0.0990771\pi$
$263$			9.93335i			0.612517i	−0.951948	+	0.306258i	$0.900923\pi$
$264$		−	5.66373i		−	0.348579i
$265$	−30.2323	+	30.2323i	−1.85716	+	1.85716i
$266$	2.95828	+	2.95828i	0.181384	+	0.181384i
$267$	−15.4697	+	15.4697i	−0.946728	+	0.946728i
$268$	−12.5403	+	12.5403i	−0.766020	+	0.766020i
$269$			15.6130i			0.951943i	0.879461	+	0.475971i	$0.157903\pi$
$269$			15.6130i			0.951943i	−0.879461	+	0.475971i	$0.842097\pi$
$270$	−8.51476			−0.518192
$271$	4.07179	+	4.07179i	0.247343	+	0.247343i	0.819879	−	0.572536i	$-0.194040\pi$
$271$	4.07179	+	4.07179i	0.247343	+	0.247343i	−0.572536	+	0.819879i	$0.694040\pi$
$272$	−12.4979			−0.757798
$273$	−17.7355	+	7.32878i	−1.07340	+	0.443558i
$274$			22.1103i			1.33573i
$275$	−21.6916	+	21.6916i	−1.30805	+	1.30805i
$276$	22.7399			1.36878
$277$	12.7645			0.766943			0.383471	−	0.923553i	$-0.374729\pi$
$277$	12.7645			0.766943			0.383471	+	0.923553i	$0.374729\pi$
$278$	6.98653	−	6.98653i	0.419024	−	0.419024i
$279$	9.63192	−	10.4302i	0.576648	−	0.624438i
$280$	7.57541	−	7.57541i	0.452717	−	0.452717i
$281$	19.3999	−	19.3999i	1.15730	−	1.15730i	0.172250	−	0.985053i	$-0.444896\pi$
$281$	19.3999	−	19.3999i	1.15730	−	1.15730i	0.985053	−	0.172250i	$-0.0551036\pi$
$282$			13.5733i			0.808277i
$283$		−	1.40282i		−	0.0833887i	−0.999130	−	0.0416944i	$-0.986724\pi$
$283$		−	1.40282i		−	0.0833887i	0.999130	−	0.0416944i	$-0.0132756\pi$
$284$	9.79795	−	9.79795i	0.581401	−	0.581401i
$285$	−10.2748			−0.608625
$286$	13.5570	+	5.62887i	0.801639	+	0.332842i
$287$	13.2688			0.783230
$288$	12.1562	+	12.1562i	0.716314	+	0.716314i
$289$	−10.3110			−0.606527
$290$	−56.1290			−3.29601
$291$	21.5876	−	21.5876i	1.26549	−	1.26549i
$292$	−3.93561	+	3.93561i	−0.230314	+	0.230314i
$293$	8.93146	−	8.93146i	0.521782	−	0.521782i	−0.396327	−	0.918109i	$-0.629716\pi$
$293$	8.93146	−	8.93146i	0.521782	−	0.521782i	0.918109	+	0.396327i	$0.129716\pi$
$294$	5.83139	+	5.83139i	0.340094	+	0.340094i
$295$	−1.56230			−0.0909608
$296$	6.87860			0.399810
$297$	−1.65316	+	1.65316i	−0.0959260	+	0.0959260i
$298$		−	10.7979i		−	0.625506i
$299$	9.46849	−	22.8046i	0.547577	−	1.31882i
$300$		−	46.1984i		−	2.66726i
$301$	1.08477	−	1.08477i	0.0625252	−	0.0625252i
$302$			23.5734i			1.35650i
$303$	−24.1287			−1.38616
$304$	−3.42680	−	3.42680i	−0.196541	−	0.196541i
$305$	20.8275	−	20.8275i	1.19258	−	1.19258i
$306$	−8.61064	−	8.61064i	−0.492237	−	0.492237i
$307$	−7.81126	+	7.81126i	−0.445812	+	0.445812i	−0.893960	−	0.448147i	$-0.852084\pi$
$307$	−7.81126	+	7.81126i	−0.445812	+	0.445812i	0.448147	+	0.893960i	$0.352084\pi$
$308$			7.02109i			0.400064i
$309$	10.0115			0.569535
$310$	−32.8468	−	30.3330i	−1.86557	−	1.72280i
$311$			20.7530i			1.17679i	0.808572	+	0.588397i	$0.200241\pi$
$311$			20.7530i			1.17679i	−0.808572	+	0.588397i	$0.799759\pi$
$312$	8.55970	−	3.53709i	0.484598	−	0.200248i
$313$			27.3998i			1.54873i	0.632740	+	0.774364i	$0.281930\pi$
$313$			27.3998i			1.54873i	−0.632740	+	0.774364i	$0.718070\pi$
$314$	4.84799	+	4.84799i	0.273588	+	0.273588i
$315$	25.0535			1.41160
$316$	15.8242			0.890181
$317$	17.3199	+	17.3199i	0.972785	+	0.972785i	0.999639	−	0.0268548i	$-0.00854917\pi$
$317$	17.3199	+	17.3199i	0.972785	+	0.972785i	−0.0268548	+	0.999639i	$0.508549\pi$
$318$	−30.2397	−	30.2397i	−1.69576	−	1.69576i
$319$	−10.8976	+	10.8976i	−0.610146	+	0.610146i
$320$	8.56231	−	8.56231i	0.478648	−	0.478648i
$321$		−	3.00191i		−	0.167550i
$322$	28.5689			1.59208
$323$	1.83407	+	1.83407i	0.102050	+	0.102050i
$324$		−	14.3030i		−	0.794611i
$325$	−46.3297	−	19.2362i	−2.56991	−	1.06703i
$326$	46.8591			2.59529
$327$	10.3917	−	10.3917i	0.574664	−	0.574664i
$328$	−6.40391			−0.353597
$329$			7.04953i			0.388653i
$330$	−29.4942	−	29.4942i	−1.62360	−	1.62360i
$331$	−6.53743	+	6.53743i	−0.359330	+	0.359330i	−0.863566	−	0.504236i	$-0.831774\pi$
$331$	−6.53743	+	6.53743i	−0.359330	+	0.359330i	0.504236	+	0.863566i	$0.331774\pi$
$332$	−3.67187	−	3.67187i	−0.201520	−	0.201520i
$333$	11.3745	+	11.3745i	0.623318	+	0.623318i
$334$			46.7089i			2.55580i
$335$		−	54.7198i		−	2.98966i
$336$	18.1864	+	18.1864i	0.992148	+	0.992148i
$337$	6.63526			0.361445			0.180723	−	0.983534i	$-0.442156\pi$
$337$	6.63526			0.361445			0.180723	+	0.983534i	$0.442156\pi$
$338$	−0.0404797	+	24.0042i	−0.00220181	+	1.30566i
$339$			6.66998i			0.362264i
$340$	−11.2101	+	11.2101i	−0.607951	+	0.607951i
$341$	−12.2665	+	0.488071i	−0.664267	+	0.0264305i
$342$		−	4.72190i		−	0.255331i
$343$	14.2113	+	14.2113i	0.767339	+	0.767339i
$344$	−0.523544	+	0.523544i	−0.0282276	+	0.0282276i
$345$	−49.6130	+	49.6130i	−2.67108	+	2.67108i
$346$	23.1255	−	23.1255i	1.24323	−	1.24323i
$347$		−	7.99785i		−	0.429347i	−0.976686	−	0.214673i	$-0.931131\pi$
$347$		−	7.99785i		−	0.429347i	0.976686	−	0.214673i	$-0.0688687\pi$
$348$		−	23.2094i		−	1.24415i
$349$	−1.71837	+	1.71837i	−0.0919822	+	0.0919822i	−0.751601	−	0.659618i	$-0.770718\pi$
$349$	−1.71837	+	1.71837i	−0.0919822	+	0.0919822i	0.659618	+	0.751601i	$0.270718\pi$
$350$		−	58.0405i		−	3.10239i
$351$	−3.53087	−	1.46602i	−0.188464	−	0.0782506i
$352$		−	14.8653i		−	0.792322i
$353$	0.443383	−	0.443383i	0.0235989	−	0.0235989i	−0.695209	−	0.718808i	$-0.744688\pi$
$353$	0.443383	−	0.443383i	0.0235989	−	0.0235989i	0.718808	+	0.695209i	$0.244688\pi$
$354$		−	1.56268i		−	0.0830557i
$355$			42.7535i			2.26912i
$356$	−9.25546	+	9.25546i	−0.490538	+	0.490538i
$357$	−9.73357	−	9.73357i	−0.515155	−	0.515155i
$358$	−17.3860	−	17.3860i	−0.918880	−	0.918880i
$359$	−21.7747	+	21.7747i	−1.14923	+	1.14923i	−0.162521	+	0.986705i	$0.551962\pi$
$359$	−21.7747	+	21.7747i	−1.14923	+	1.14923i	−0.986705	+	0.162521i	$0.948038\pi$
$360$	−12.0916			−0.637282
$361$		−	17.9942i		−	0.947065i
$362$	−1.90657	−	1.90657i	−0.100207	−	0.100207i
$363$	14.4614			0.759024
$364$	−10.6111	+	4.38478i	−0.556173	+	0.229825i
$365$		−	17.1731i		−	0.898882i
$366$	20.8326	+	20.8326i	1.08894	+	1.08894i
$367$			14.2583i			0.744277i	0.928177	+	0.372139i	$0.121375\pi$
$367$			14.2583i			0.744277i	−0.928177	+	0.372139i	$0.878625\pi$
$368$	−33.0935			−1.72512
$369$	−10.5895	−	10.5895i	−0.551269	−	0.551269i
$370$	35.8206	−	35.8206i	1.86223	−	1.86223i
$371$	−15.7055	−	15.7055i	−0.815390	−	0.815390i
$372$	12.5427	−	13.5822i	0.650309	−	0.704204i
$373$	−8.91759			−0.461736			−0.230868	−	0.972985i	$-0.574156\pi$
$373$	−8.91759			−0.461736			−0.230868	+	0.972985i	$0.574156\pi$
$374$			10.5295i			0.544469i
$375$	64.5711	+	64.5711i	3.33444	+	3.33444i
$376$		−	3.40232i		−	0.175461i
$377$	−23.2754	−	9.66398i	−1.19874	−	0.497720i
$378$		−	4.42337i		−	0.227514i
$379$	−9.49656	−	9.49656i	−0.487806	−	0.487806i	0.419807	−	0.907613i	$-0.362098\pi$
$379$	−9.49656	−	9.49656i	−0.487806	−	0.487806i	−0.907613	+	0.419807i	$0.862098\pi$
$380$	−6.14737			−0.315353
$381$		−	16.0317i		−	0.821330i
$382$	−17.0540	−	17.0540i	−0.872557	−	0.872557i
$383$	−9.74032	+	9.74032i	−0.497707	+	0.497707i	−0.910724	−	0.413016i	$-0.864475\pi$
$383$	−9.74032	+	9.74032i	−0.497707	+	0.497707i	0.413016	+	0.910724i	$0.364475\pi$
$384$	−13.8976	−	13.8976i	−0.709209	−	0.709209i
$385$	−15.3183	−	15.3183i	−0.780695	−	0.780695i
$386$	6.60486			0.336178
$387$	−1.73147			−0.0880155
$388$	12.9158	−	12.9158i	0.655699	−	0.655699i
$389$	25.5972			1.29783			0.648914	−	0.760861i	$-0.275223\pi$
$389$	25.5972			1.29783			0.648914	+	0.760861i	$0.275223\pi$
$390$	26.1555	−	62.9946i	1.32443	−	3.18986i
$391$	17.7120			0.895736
$392$	−1.46171	−	1.46171i	−0.0738277	−	0.0738277i
$393$			10.9969i			0.554722i
$394$	43.4561			2.18929
$395$	−34.5246	+	34.5246i	−1.73712	+	1.73712i
$396$	5.60340	−	5.60340i	0.281581	−	0.281581i
$397$	14.2698	−	14.2698i	0.716183	−	0.716183i	−0.251638	−	0.967821i	$-0.580969\pi$
$397$	14.2698	−	14.2698i	0.716183	−	0.716183i	0.967821	+	0.251638i	$0.0809693\pi$
$398$	16.1795	+	16.1795i	0.811007	+	0.811007i
$399$		−	5.33769i		−	0.267219i
$400$			67.2327i			3.36163i
$401$	1.95421	+	1.95421i	0.0975884	+	0.0975884i	0.754215	−	0.656627i	$-0.228017\pi$
$401$	1.95421	+	1.95421i	0.0975884	+	0.0975884i	−0.656627	+	0.754215i	$0.728017\pi$
$402$	54.7331			2.72984
$403$	−8.39824	−	18.2337i	−0.418346	−	0.908288i
$404$	−14.4361			−0.718225
$405$	31.2057	+	31.2057i	1.55062	+	1.55062i
$406$		−	29.1587i		−	1.44712i
$407$		−	13.9093i		−	0.689459i
$408$	4.69772	+	4.69772i	0.232572	+	0.232572i
$409$	−9.02458	+	9.02458i	−0.446237	+	0.446237i	−0.894101	−	0.447864i	$-0.852185\pi$
$409$	−9.02458	+	9.02458i	−0.446237	+	0.446237i	0.447864	+	0.894101i	$0.352185\pi$
$410$	−33.3487	+	33.3487i	−1.64697	+	1.64697i
$411$	19.9470	−	19.9470i	0.983913	−	0.983913i
$412$	5.98986			0.295099
$413$		−	0.811608i		−	0.0399366i
$414$	−22.8003	−	22.8003i	−1.12057	−	1.12057i
$415$	16.0223			0.786501
$416$	22.4662	−	9.28360i	1.10149	−	0.455166i
$417$	−12.6059			−0.617316
$418$	−2.88709	+	2.88709i	−0.141212	+	0.141212i
$419$	−8.16245			−0.398762			−0.199381	−	0.979922i	$-0.563893\pi$
$419$	−8.16245			−0.398762			−0.199381	+	0.979922i	$0.563893\pi$
$420$	32.6247			1.59192
$421$	−19.3002	−	19.3002i	−0.940635	−	0.940635i	0.0576989	−	0.998334i	$-0.481624\pi$
$421$	−19.3002	−	19.3002i	−0.940635	−	0.940635i	−0.998334	+	0.0576989i	$0.981624\pi$
$422$	−14.1714	−	14.1714i	−0.689852	−	0.689852i
$423$	5.62610	−	5.62610i	0.273550	−	0.273550i
$424$	7.57996	+	7.57996i	0.368116	+	0.368116i
$425$		−	35.9837i		−	1.74547i
$426$	−42.7639			−2.07192
$427$	10.8198	+	10.8198i	0.523607	+	0.523607i
$428$		−	1.79603i		−	0.0868146i
$429$	−7.15240	−	17.3087i	−0.345321	−	0.835671i
$430$			5.45276i			0.262955i
$431$	21.1469	+	21.1469i	1.01861	+	1.01861i	0.999823	+	0.0187885i	$0.00598093\pi$
$431$	21.1469	+	21.1469i	1.01861	+	1.01861i	0.0187885	+	0.999823i	$0.494019\pi$
$432$			5.12393i			0.246525i
$433$	25.6839			1.23429			0.617144	−	0.786851i	$-0.288290\pi$
$433$	25.6839			1.23429			0.617144	+	0.786851i	$0.288290\pi$
$434$	15.7578	−	17.0637i	0.756399	−	0.819086i
$435$	50.6373	+	50.6373i	2.42787	+	2.42787i
$436$	6.21734	−	6.21734i	0.297757	−	0.297757i
$437$	4.85646	+	4.85646i	0.232316	+	0.232316i
$438$	17.1773			0.820762
$439$		−	11.4151i		−	0.544814i	−0.962182	−	0.272407i	$-0.912180\pi$
$439$		−	11.4151i		−	0.544814i	0.962182	−	0.272407i	$-0.0878198\pi$
$440$	7.39310	+	7.39310i	0.352452	+	0.352452i
$441$		−	4.83420i		−	0.230200i
$442$	−15.9135	+	6.57586i	−0.756926	+	0.312782i
$443$	17.6592			0.839012			0.419506	−	0.907753i	$-0.362203\pi$
$443$	17.6592			0.839012			0.419506	+	0.907753i	$0.362203\pi$
$444$	14.8119	+	14.8119i	0.702941	+	0.702941i
$445$		−	40.3864i		−	1.91450i
$446$	−17.7034			−0.838279
$447$	−9.74144	+	9.74144i	−0.460754	+	0.460754i
$448$	4.44807	+	4.44807i	0.210152	+	0.210152i
$449$	21.2231	+	21.2231i	1.00158	+	1.00158i	0.999999	+	0.00158328i	$0.000503975\pi$
$449$	21.2231	+	21.2231i	1.00158	+	1.00158i	0.00158328	+	0.999999i	$0.499496\pi$
$450$	−46.3209	+	46.3209i	−2.18359	+	2.18359i
$451$			12.9494i			0.609765i
$452$			3.99063i			0.187703i
$453$	21.2670	−	21.2670i	0.999210	−	0.999210i
$454$			4.92355i			0.231074i
$455$	13.5843	−	32.7174i	0.636843	−	1.53382i
$456$			2.57613i			0.120638i
$457$	8.98495	−	8.98495i	0.420298	−	0.420298i	−0.465008	−	0.885306i	$-0.653949\pi$
$457$	8.98495	−	8.98495i	0.420298	−	0.420298i	0.885306	+	0.465008i	$0.153949\pi$
$458$		−	30.0325i		−	1.40333i
$459$		−	2.74239i		−	0.128004i
$460$	−29.6833	+	29.6833i	−1.38399	+	1.38399i
$461$	−3.17727	+	3.17727i	−0.147980	+	0.147980i	−0.777215	−	0.629235i	$-0.783368\pi$
$461$	−3.17727	+	3.17727i	−0.147980	+	0.147980i	0.629235	+	0.777215i	$0.283368\pi$
$462$	15.3221	−	15.3221i	0.712847	−	0.712847i
$463$	−7.50702	−	7.50702i	−0.348881	−	0.348881i	0.510812	−	0.859693i	$-0.329345\pi$
$463$	−7.50702	−	7.50702i	−0.348881	−	0.348881i	−0.859693	+	0.510812i	$0.829345\pi$
$464$			33.7767i			1.56805i
$465$	2.26790	+	56.9983i	0.105171	+	2.64323i
$466$	−14.0637	+	14.0637i	−0.651487	+	0.651487i
$467$			9.85292i			0.455939i	0.973668	+	0.227969i	$0.0732086\pi$
$467$			9.85292i			0.455939i	−0.973668	+	0.227969i	$0.926791\pi$
$468$	11.9679	+	4.96910i	0.553217	+	0.229697i
$469$	28.4266			1.31262
$470$	−17.7178	−	17.7178i	−0.817259	−	0.817259i
$471$		−	8.74733i		−	0.403056i
$472$			0.391707i			0.0180298i
$473$	1.05866	+	1.05866i	0.0486774	+	0.0486774i
$474$	−34.5330	−	34.5330i	−1.58615	−	1.58615i
$475$	9.86637	−	9.86637i	0.452700	−	0.452700i
$476$	−5.82357	−	5.82357i	−0.266923	−	0.266923i
$477$			25.0685i			1.14781i
$478$	−43.7808			−2.00249
$479$	−17.0900	+	17.0900i	−0.780861	+	0.780861i	−0.979976	−	0.199115i	$-0.936193\pi$
$479$	−17.0900	+	17.0900i	−0.780861	+	0.780861i	0.199115	+	0.979976i	$0.436193\pi$
$480$	−69.0740			−3.15278
$481$	21.0214	−	8.68658i	0.958493	−	0.396074i
$482$			51.3540i			2.33911i
$483$	−25.7737	−	25.7737i	−1.17274	−	1.17274i
$484$	8.65219			0.393281
$485$			56.3582i			2.55910i
$486$	−27.0600	+	27.0600i	−1.22746	+	1.22746i
$487$	−10.4725	+	10.4725i	−0.474555	+	0.474555i	−0.903385	−	0.428830i	$-0.858926\pi$
$487$	−10.4725	+	10.4725i	−0.474555	+	0.474555i	0.428830	+	0.903385i	$0.358926\pi$
$488$	−5.22196	−	5.22196i	−0.236387	−	0.236387i
$489$	−42.2744	−	42.2744i	−1.91171	−	1.91171i
$490$	−15.2239			−0.687746
$491$	−4.28820			−0.193524			−0.0967618	−	0.995308i	$-0.530848\pi$
$491$	−4.28820			−0.193524			−0.0967618	+	0.995308i	$0.530848\pi$
$492$	−13.7897	−	13.7897i	−0.621688	−	0.621688i
$493$		−	18.0777i		−	0.814179i
$494$	−6.16634	−	2.56028i	−0.277437	−	0.115192i
$495$			24.4505i			1.09897i
$496$	−18.2535	+	19.7662i	−0.819604	+	0.887529i
$497$	−22.2102			−0.996265
$498$			16.0261i			0.718149i
$499$	19.6921	−	19.6921i	0.881540	−	0.881540i	−0.112151	−	0.993691i	$-0.535774\pi$
$499$	19.6921	−	19.6921i	0.881540	−	0.881540i	0.993691	+	0.112151i	$0.0357739\pi$
$500$	38.6327	+	38.6327i	1.72771	+	1.72771i
$501$	42.1389	−	42.1389i	1.88263	−	1.88263i
$502$	20.8139	+	20.8139i	0.928969	+	0.928969i
$503$	0.821432			0.0366258			0.0183129	−	0.999832i	$-0.494170\pi$
$503$	0.821432			0.0366258			0.0183129	+	0.999832i	$0.494170\pi$
$504$		−	6.28150i		−	0.279800i
$505$	31.4962	−	31.4962i	1.40156	−	1.40156i
$506$			27.8813i			1.23948i
$507$	21.6921	−	21.6191i	0.963382	−	0.960138i
$508$		−	9.59173i		−	0.425564i
$509$	16.9258	−	16.9258i	0.750222	−	0.750222i	−0.224299	−	0.974520i	$-0.572009\pi$
$509$	16.9258	−	16.9258i	0.750222	−	0.750222i	0.974520	+	0.224299i	$0.0720091\pi$
$510$	48.9272			2.16653
$511$	8.92134			0.394657
$512$	−15.5857	−	15.5857i	−0.688798	−	0.688798i
$513$	0.751934	−	0.751934i	0.0331987	−	0.0331987i
$514$	7.09297	−	7.09297i	0.312858	−	0.312858i
$515$	−13.0684	+	13.0684i	−0.575864	+	0.575864i
$516$	−2.25472			−0.0992586
$517$	−6.87988			−0.302577
$518$	18.6086	+	18.6086i	0.817616	+	0.817616i
$519$	−41.7258			−1.83156
$520$	−6.55621	+	15.7904i	−0.287509	+	0.692456i
$521$	−34.2254			−1.49944			−0.749721	−	0.661754i	$-0.769812\pi$
$521$	−34.2254			−1.49944			−0.749721	+	0.661754i	$0.769812\pi$
$522$	−23.2710	+	23.2710i	−1.01854	+	1.01854i
$523$		−	24.4876i		−	1.07077i	−0.844608	−	0.535385i	$-0.820167\pi$
$523$		−	24.4876i		−	1.07077i	0.844608	−	0.535385i	$-0.179833\pi$
$524$			6.57943i			0.287424i
$525$	−52.3618	+	52.3618i	−2.28526	+	2.28526i
$526$	12.9696	−	12.9696i	0.565499	−	0.565499i
$527$	9.76947	−	10.5791i	0.425565	−	0.460834i
$528$	−17.7487	+	17.7487i	−0.772413	+	0.772413i
$529$	23.9000			1.03913
$530$	78.9461			3.42920
$531$	−0.647729	+	0.647729i	−0.0281090	+	0.0281090i
$532$		−	3.19352i		−	0.138457i
$533$	−19.5707	+	8.08712i	−0.847701	+	0.350292i
$534$	40.3962			1.74811
$535$	3.91851	+	3.91851i	0.169412	+	0.169412i
$536$	−13.7196			−0.592595
$537$			31.3700i			1.35371i
$538$	20.3853	−	20.3853i	0.878871	−	0.878871i
$539$	−2.95575	+	2.95575i	−0.127313	+	0.127313i
$540$	4.59592	+	4.59592i	0.197777	+	0.197777i
$541$	24.4393	−	24.4393i	1.05073	−	1.05073i	0.0520848	−	0.998643i	$-0.483413\pi$
$541$	24.4393	−	24.4393i	1.05073	−	1.05073i	0.998643	−	0.0520848i	$-0.0165866\pi$
$542$		−	10.6327i		−	0.456714i
$543$			3.44007i			0.147627i
$544$	12.3298	+	12.3298i	0.528637	+	0.528637i
$545$			27.1295i			1.16210i
$546$	32.7254	+	13.5876i	1.40052	+	0.581497i
$547$	−0.705450			−0.0301629			−0.0150814	−	0.999886i	$-0.504801\pi$
$547$	−0.705450			−0.0301629			−0.0150814	+	0.999886i	$0.504801\pi$
$548$	11.9342	−	11.9342i	0.509805	−	0.509805i
$549$		−	17.2701i		−	0.737071i
$550$	56.6436			2.41529
$551$	4.95672	−	4.95672i	0.211164	−	0.211164i
$552$	12.4392	+	12.4392i	0.529446	+	0.529446i
$553$	−17.9353	−	17.9353i	−0.762689	−	0.762689i
$554$	−16.6660	−	16.6660i	−0.708071	−	0.708071i
$555$	−64.6319			−2.74347
$556$	−7.54210			−0.319856
$557$	−13.3150	−	13.3150i	−0.564177	−	0.564177i	0.366314	−	0.930491i	$-0.380619\pi$
$557$	−13.3150	−	13.3150i	−0.564177	−	0.564177i	−0.930491	+	0.366314i	$0.880619\pi$
$558$	−26.1942	+	1.04224i	−1.10889	+	0.0441216i
$559$	−0.938826	+	2.26113i	−0.0397081	+	0.0956357i
$560$	−47.4788			−2.00635
$561$	9.49932	−	9.49932i	0.401061	−	0.401061i
$562$	−50.6593			−2.13693
$563$		−	6.41472i		−	0.270348i	−0.990822	−	0.135174i	$-0.956841\pi$
$563$		−	6.41472i		−	0.270348i	0.990822	−	0.135174i	$-0.0431593\pi$
$564$	7.32631	−	7.32631i	0.308493	−	0.308493i
$565$	−8.70659	−	8.70659i	−0.366289	−	0.366289i
$566$	−1.83160	+	1.83160i	−0.0769877	+	0.0769877i
$567$	−16.2112	+	16.2112i	−0.680806	+	0.680806i
$568$	10.7193			0.449773
$569$	1.84427			0.0773157			0.0386579	−	0.999253i	$-0.487692\pi$
$569$	1.84427			0.0773157			0.0386579	+	0.999253i	$0.487692\pi$
$570$	13.4153	+	13.4153i	0.561907	+	0.561907i
$571$	18.1260			0.758548			0.379274	−	0.925284i	$-0.376174\pi$
$571$	18.1260			0.758548			0.379274	+	0.925284i	$0.376174\pi$
$572$	−4.27926	−	10.3557i	−0.178925	−	0.432995i
$573$			30.7708i			1.28547i
$574$	−17.3245	−	17.3245i	−0.723109	−	0.723109i
$575$		−	95.2820i		−	3.97353i
$576$		−	7.09984i		−	0.295827i
$577$	16.1240	+	16.1240i	0.671251	+	0.671251i	0.958004	−	0.286753i	$-0.0925761\pi$
$577$	16.1240	+	16.1240i	0.671251	+	0.671251i	−0.286753	+	0.958004i	$0.592576\pi$
$578$	13.4626	+	13.4626i	0.559969	+	0.559969i
$579$	−5.95864	−	5.95864i	−0.247633	−	0.247633i
$580$	30.2962	+	30.2962i	1.25798	+	1.25798i
$581$			8.32347i			0.345316i
$582$	−56.3719			−2.33669
$583$	15.3275	−	15.3275i	0.634802	−	0.634802i
$584$	−4.30571			−0.178172
$585$	−36.9525	+	15.2697i	−1.52780	+	0.631326i
$586$	−23.3229			−0.963459
$587$	−30.2571	+	30.2571i	−1.24884	+	1.24884i	−0.292611	+	0.956232i	$0.594524\pi$
$587$	−30.2571	+	30.2571i	−1.24884	+	1.24884i	−0.956232	+	0.292611i	$0.905476\pi$
$588$		−	6.29510i		−	0.259606i
$589$	5.57937	−	0.221998i	0.229894	−	0.00914725i
$590$	2.03983	+	2.03983i	0.0839786	+	0.0839786i
$591$	−39.2043	−	39.2043i	−1.61265	−	1.61265i
$592$	−21.5558	−	21.5558i	−0.885937	−	0.885937i
$593$	−3.67194	+	3.67194i	−0.150788	+	0.150788i	−0.778470	−	0.627682i	$-0.784004\pi$
$593$	−3.67194	+	3.67194i	−0.150788	+	0.150788i	0.627682	+	0.778470i	$0.284004\pi$
$594$	4.31692			0.177125
$595$	25.4112			1.04176
$596$	−5.82827	+	5.82827i	−0.238735	+	0.238735i
$597$		−	29.1931i		−	1.19479i
$598$	−42.1375	+	17.4123i	−1.72313	+	0.712043i
$599$	3.90216			0.159438			0.0797189	−	0.996817i	$-0.474598\pi$
$599$	3.90216			0.159438			0.0797189	+	0.996817i	$0.474598\pi$
$600$	25.2714	−	25.2714i	1.03170	−	1.03170i
$601$		−	2.15503i		−	0.0879054i	−0.999034	−	0.0439527i	$-0.986005\pi$
$601$		−	2.15503i		−	0.0879054i	0.999034	−	0.0439527i	$-0.0139951\pi$
$602$	−2.83268			−0.115451
$603$	−22.6867	−	22.6867i	−0.923875	−	0.923875i
$604$	12.7240	−	12.7240i	0.517731	−	0.517731i
$605$	−18.8770	+	18.8770i	−0.767459	+	0.767459i
$606$	31.5038	+	31.5038i	1.27976	+	1.27976i
$607$	34.4423			1.39797			0.698984	−	0.715137i	$-0.253636\pi$
$607$	34.4423			1.39797			0.698984	+	0.715137i	$0.253636\pi$
$608$			6.76143i			0.274212i
$609$	−26.3058	+	26.3058i	−1.06597	+	1.06597i
$610$	−54.3873			−2.20208
$611$	−4.29659	−	10.3977i	−0.173822	−	0.420645i
$612$			9.29535i			0.375742i
$613$	18.4791	−	18.4791i	0.746365	−	0.746365i	−0.227430	−	0.973794i	$-0.573032\pi$
$613$	18.4791	−	18.4791i	0.746365	−	0.746365i	0.973794	+	0.227430i	$0.0730322\pi$
$614$	20.3977			0.823183
$615$	60.1717			2.42636
$616$	−3.84067	+	3.84067i	−0.154745	+	0.154745i
$617$	−6.93866	−	6.93866i	−0.279340	−	0.279340i	0.553505	−	0.832846i	$-0.313290\pi$
$617$	−6.93866	−	6.93866i	−0.279340	−	0.279340i	−0.832846	+	0.553505i	$0.813290\pi$
$618$	−13.0716	−	13.0716i	−0.525817	−	0.525817i
$619$	5.84317	+	5.84317i	0.234857	+	0.234857i	0.814716	−	0.579860i	$-0.196893\pi$
$619$	5.84317	+	5.84317i	0.234857	+	0.234857i	−0.579860	+	0.814716i	$0.696893\pi$
$620$	1.35688	+	34.1019i	0.0544936	+	1.36956i
$621$		−	7.26162i		−	0.291399i
$622$	27.0963	−	27.0963i	1.08646	−	1.08646i
$623$	20.9805			0.840566
$624$	−37.9083	−	15.7396i	−1.51755	−	0.630088i
$625$	−99.0090			−3.96036
$626$	35.7747	−	35.7747i	1.42985	−	1.42985i
$627$	5.20923			0.208037
$628$		−	5.23350i		−	0.208840i
$629$	11.5369	+	11.5369i	0.460007	+	0.460007i
$630$	−32.7112	−	32.7112i	−1.30325	−	1.30325i
$631$	−14.9641	−	14.9641i	−0.595712	−	0.595712i	0.343456	−	0.939169i	$-0.388402\pi$
$631$	−14.9641	−	14.9641i	−0.595712	−	0.595712i	−0.939169	+	0.343456i	$0.888402\pi$
$632$	8.65615	+	8.65615i	0.344323	+	0.344323i
$633$			25.5697i			1.01630i
$634$		−	45.2278i		−	1.79623i
$635$	20.9268	+	20.9268i	0.830457	+	0.830457i
$636$			32.6443i			1.29443i
$637$	−6.31299	−	2.62117i	−0.250130	−	0.103854i
$638$	28.4569			1.12662
$639$	17.7255	+	17.7255i	0.701212	+	0.701212i
$640$	36.2822			1.43418
$641$	7.86464			0.310635			0.155317	−	0.987865i	$-0.450360\pi$
$641$	7.86464			0.310635			0.155317	+	0.987865i	$0.450360\pi$
$642$	−3.91947	+	3.91947i	−0.154689	+	0.154689i
$643$	−3.03103	+	3.03103i	−0.119532	+	0.119532i	−0.764343	−	0.644810i	$-0.776936\pi$
$643$	−3.03103	+	3.03103i	−0.119532	+	0.119532i	0.644810	+	0.764343i	$0.276936\pi$
$644$	−15.4203	−	15.4203i	−0.607646	−	0.607646i
$645$	4.91926	−	4.91926i	0.193696	−	0.193696i
$646$		−	4.78933i		−	0.188433i
$647$	−2.05765			−0.0808946			−0.0404473	−	0.999182i	$-0.512878\pi$
$647$	−2.05765			−0.0808946			−0.0404473	+	0.999182i	$0.512878\pi$
$648$	7.82402	−	7.82402i	0.307356	−	0.307356i
$649$	0.792076			0.0310917
$650$	35.3748	+	85.6065i	1.38752	+	3.35776i
$651$	−29.6103	+	1.17816i	−1.16052	+	0.0461758i
$652$	−25.2926	−	25.2926i	−0.990536	−	0.990536i
$653$	31.9575			1.25059			0.625297	−	0.780387i	$-0.284978\pi$
$653$	31.9575			1.25059			0.625297	+	0.780387i	$0.284978\pi$
$654$	−27.1361			−1.06111
$655$	−14.3547	−	14.3547i	−0.560886	−	0.560886i
$656$	20.0682	+	20.0682i	0.783533	+	0.783533i
$657$	−7.11994	−	7.11994i	−0.277775	−	0.277775i
$658$	9.20428	−	9.20428i	0.358820	−	0.358820i
$659$	−41.2230			−1.60582			−0.802910	−	0.596101i	$-0.796716\pi$
$659$	−41.2230			−1.60582			−0.802910	+	0.596101i	$0.796716\pi$
$660$			31.8395i			1.23935i
$661$	−26.2341	+	26.2341i	−1.02039	+	1.02039i	−0.0206015	+	0.999788i	$0.506558\pi$
$661$	−26.2341	+	26.2341i	−1.02039	+	1.02039i	−0.999788	+	0.0206015i	$0.993442\pi$
$662$	17.0713			0.663495
$663$	20.2890	+	8.42401i	0.787958	+	0.327162i
$664$		−	4.01716i		−	0.155896i
$665$	6.96750	+	6.96750i	0.270188	+	0.270188i
$666$		−	29.7024i		−	1.15094i
$667$		−	47.8683i		−	1.85347i
$668$	25.2116	−	25.2116i	0.975466	−	0.975466i
$669$	15.9713	+	15.9713i	0.617485	+	0.617485i
$670$	−71.4453	+	71.4453i	−2.76017	+	2.76017i
$671$	−10.5594	+	10.5594i	−0.407641	+	0.407641i
$672$		−	35.8836i		−	1.38424i
$673$	34.5314			1.33109			0.665544	−	0.746358i	$-0.268199\pi$
$673$	34.5314			1.33109			0.665544	+	0.746358i	$0.268199\pi$
$674$	−8.66337	−	8.66337i	−0.333701	−	0.333701i
$675$	−14.7527			−0.567831
$676$	12.9783	−	12.9346i	0.499167	−	0.497486i
$677$		−	6.09914i		−	0.234409i	−0.993108	−	0.117204i	$-0.962607\pi$
$677$		−	6.09914i		−	0.234409i	0.993108	−	0.117204i	$-0.0373933\pi$
$678$	8.70871	−	8.70871i	0.334456	−	0.334456i
$679$	−29.2778			−1.12358
$680$	−12.2642			−0.470312
$681$	4.44183	−	4.44183i	0.170211	−	0.170211i
$682$	16.6531	+	15.3786i	0.637679	+	0.588876i
$683$	−9.09352	+	9.09352i	−0.347954	+	0.347954i	−0.859347	−	0.511393i	$-0.829130\pi$
$683$	−9.09352	+	9.09352i	−0.347954	+	0.347954i	0.511393	+	0.859347i	$0.329130\pi$
$684$	−2.54869	+	2.54869i	−0.0974516	+	0.0974516i
$685$			52.0752i			1.98969i
$686$		−	37.1102i		−	1.41687i
$687$	−27.0941	+	27.0941i	−1.03371	+	1.03371i
$688$	3.28131			0.125099
$689$	32.7371	+	13.5925i	1.24718	+	0.517833i
$690$	129.555			4.93208
$691$	24.0003	+	24.0003i	0.913013	+	0.913013i	0.996508	−	0.0834950i	$-0.0266082\pi$
$691$	24.0003	+	24.0003i	0.913013	+	0.913013i	−0.0834950	+	0.996508i	$0.526608\pi$
$692$	−24.9644			−0.949004
$693$	−12.7019			−0.482506
$694$	−10.4424	+	10.4424i	−0.396390	+	0.396390i
$695$	16.4550	−	16.4550i	0.624175	−	0.624175i
$696$	12.6960	−	12.6960i	0.481240	−	0.481240i
$697$	−10.7408	−	10.7408i	−0.406835	−	0.406835i
$698$	4.48720			0.169843
$699$	25.3754			0.959784
$700$	−31.3279	+	31.3279i	−1.18408	+	1.18408i
$701$			18.8945i			0.713634i	0.934174	+	0.356817i	$0.116138\pi$
$701$			18.8945i			0.713634i	−0.934174	+	0.356817i	$0.883862\pi$
$702$	2.69598	+	6.52423i	0.101753	+	0.246241i
$703$			6.32661i			0.238613i
$704$	−4.34102	+	4.34102i	−0.163609	+	0.163609i
$705$			31.9685i			1.20400i
$706$	−1.15781			−0.0435749
$707$	16.3621	+	16.3621i	0.615360	+	0.615360i
$708$	−0.843473	+	0.843473i	−0.0316997	+	0.0316997i
$709$	7.52128	+	7.52128i	0.282468	+	0.282468i	0.834092	−	0.551625i	$-0.185992\pi$
$709$	7.52128	+	7.52128i	0.282468	+	0.282468i	−0.551625	+	0.834092i	$0.685992\pi$
$710$	55.8215	−	55.8215i	2.09494	−	2.09494i
$711$			28.6277i			1.07362i
$712$	−10.1258			−0.379481
$713$	25.8688	−	28.0126i	0.968793	−	1.04908i
$714$			25.4174i			0.951223i
$715$	31.9300	+	13.2574i	1.19412	+	0.495799i
$716$			18.7686i			0.701414i
$717$	39.4973	+	39.4973i	1.47505	+	1.47505i
$718$	56.8606			2.12202
$719$	−22.2494			−0.829761			−0.414880	−	0.909876i	$-0.636177\pi$
$719$	−22.2494			−0.829761			−0.414880	+	0.909876i	$0.636177\pi$
$720$	37.8919	+	37.8919i	1.41215	+	1.41215i
$721$	−6.78898	−	6.78898i	−0.252835	−	0.252835i
$722$	−23.4943	+	23.4943i	−0.874368	+	0.874368i
$723$	46.3296	−	46.3296i	1.72302	−	1.72302i
$724$			2.05818i			0.0764917i
$725$	−97.2491			−3.61174
$726$	−18.8816	−	18.8816i	−0.700761	−	0.700761i
$727$			31.9876i			1.18635i	0.805072	+	0.593177i	$0.202126\pi$
$727$			31.9876i			1.18635i	−0.805072	+	0.593177i	$0.797874\pi$
$728$	−8.20304	−	3.40592i	−0.304025	−	0.126232i
$729$	18.3817			0.680804
$730$	−22.4222	+	22.4222i	−0.829883	+	0.829883i
$731$	−1.75619			−0.0649552
$732$		−	22.4892i		−	0.831225i
$733$	10.0781	+	10.0781i	0.372245	+	0.372245i	0.868294	−	0.496049i	$-0.165217\pi$
$733$	10.0781	+	10.0781i	0.372245	+	0.372245i	−0.496049	+	0.868294i	$0.665217\pi$
$734$	18.6165	−	18.6165i	0.687146	−	0.687146i
$735$	13.7344	+	13.7344i	0.506601	+	0.506601i
$736$	32.6484	+	32.6484i	1.20344	+	1.20344i
$737$			27.7425i			1.02191i
$738$			27.6526i			1.01791i
$739$	−6.27002	−	6.27002i	−0.230646	−	0.230646i	0.582316	−	0.812962i	$-0.302147\pi$
$739$	−6.27002	−	6.27002i	−0.230646	−	0.230646i	−0.812962	+	0.582316i	$0.802147\pi$
$740$	−38.6691			−1.42150
$741$	3.25325	+	7.87280i	0.119511	+	0.289215i
$742$			41.0121i			1.50560i
$743$	−9.69562	+	9.69562i	−0.355698	+	0.355698i	−0.862224	−	0.506526i	$-0.830929\pi$
$743$	−9.69562	+	9.69562i	−0.355698	+	0.355698i	0.506526	+	0.862224i	$0.330929\pi$
$744$	14.2908	−	0.568617i	0.523927	−	0.0208465i
$745$		−	25.4318i		−	0.931748i
$746$	11.6433	+	11.6433i	0.426292	+	0.426292i
$747$	6.64280	−	6.64280i	0.243047	−	0.243047i
$748$	5.68341	−	5.68341i	0.207806	−	0.207806i
$749$	−2.03565	+	2.03565i	−0.0743809	+	0.0743809i
$750$		−	168.616i		−	6.15697i
$751$		−	28.2989i		−	1.03264i	−0.856396	−	0.516320i	$-0.827301\pi$
$751$		−	28.2989i		−	1.03264i	0.856396	−	0.516320i	$-0.172699\pi$
$752$	−10.6620	+	10.6620i	−0.388804	+	0.388804i
$753$		−	37.5549i		−	1.36858i
$754$	17.7718	+	43.0075i	0.647212	+	1.56624i
$755$			55.5213i			2.02063i
$756$	−2.38756	+	2.38756i	−0.0868346	+	0.0868346i
$757$			33.4573i			1.21602i	0.793928	+	0.608012i	$0.208033\pi$
$757$			33.4573i			1.21602i	−0.793928	+	0.608012i	$0.791967\pi$
$758$			24.7985i			0.900723i
$759$	25.1534	−	25.1534i	0.913011	−	0.913011i
$760$	−3.36273	−	3.36273i	−0.121979	−	0.121979i
$761$	32.2695	+	32.2695i	1.16977	+	1.16977i	0.982264	+	0.187504i	$0.0600398\pi$
$761$	32.2695	+	32.2695i	1.16977	+	1.16977i	0.187504	+	0.982264i	$0.439960\pi$
$762$	−20.9319	+	20.9319i	−0.758284	+	0.758284i
$763$	−14.0936			−0.510223
$764$			18.4101i			0.666053i
$765$	−20.2802	−	20.2802i	−0.733233	−	0.733233i
$766$	25.4350			0.919005
$767$	0.494664	+	1.19708i	0.0178613	+	0.0432240i
$768$			49.4099i			1.78293i
$769$	−17.7618	−	17.7618i	−0.640507	−	0.640507i	0.310173	−	0.950680i	$-0.399613\pi$
$769$	−17.7618	−	17.7618i	−0.640507	−	0.640507i	−0.950680	+	0.310173i	$0.899613\pi$
$770$			40.0010i			1.44154i
$771$	−12.7980			−0.460909
$772$	−3.56504	−	3.56504i	−0.128308	−	0.128308i
$773$	32.4655	−	32.4655i	1.16770	−	1.16770i	0.184957	−	0.982747i	$-0.440786\pi$
$773$	32.4655	−	32.4655i	1.16770	−	1.16770i	0.982747	−	0.184957i	$-0.0592144\pi$
$774$	2.26070	+	2.26070i	0.0812594	+	0.0812594i
$775$	−56.9104	−	52.5549i	−2.04428	−	1.88783i
$776$	14.1304			0.507250
$777$		−	33.5759i		−	1.20453i
$778$	−33.4212	−	33.4212i	−1.19821	−	1.19821i
$779$		−	5.89001i		−	0.211032i
$780$	−48.1196	+	19.8843i	−1.72296	+	0.711972i
$781$		−	21.6757i		−	0.775618i
$782$	−23.1258	−	23.1258i	−0.826979	−	0.826979i
$783$	−7.41154			−0.264867
$784$			9.16128i			0.327189i
$785$	11.4182	+	11.4182i	0.407535	+	0.407535i
$786$	14.3582	−	14.3582i	0.512141	−	0.512141i
$787$	−17.4254	−	17.4254i	−0.621147	−	0.621147i	0.324677	−	0.945825i	$-0.394744\pi$
$787$	−17.4254	−	17.4254i	−0.621147	−	0.621147i	−0.945825	+	0.324677i	$0.894744\pi$
$788$	−23.4558	−	23.4558i	−0.835579	−	0.835579i
$789$	−23.4012			−0.833106
$790$	90.1546			3.20756
$791$	4.52303	−	4.52303i	0.160820	−	0.160820i
$792$	6.13033			0.217832
$793$	−22.5531	−	9.36410i	−0.800885	−	0.332529i
$794$	−37.2631			−1.32242
$795$	−71.2220	−	71.2220i	−2.52598	−	2.52598i
$796$		−	17.4661i		−	0.619070i
$797$	3.56213			0.126177			0.0630886	−	0.998008i	$-0.479905\pi$
$797$	3.56213			0.126177			0.0630886	+	0.998008i	$0.479905\pi$
$798$	−6.96919	+	6.96919i	−0.246707	+	0.246707i
$799$	5.70644	−	5.70644i	0.201879	−	0.201879i
$800$	66.3284	−	66.3284i	2.34506	−	2.34506i
$801$	−16.7441	−	16.7441i	−0.591624	−	0.591624i
$802$		−	5.10305i		−	0.180195i
$803$			8.70663i			0.307250i
$804$	−29.5427	−	29.5427i	−1.04189	−	1.04189i
$805$	67.2869			2.37155
$806$	−12.8418	+	34.7723i	−0.452333	+	1.22480i
$807$	−36.7815			−1.29477
$808$	−7.89684	−	7.89684i	−0.277810	−	0.277810i
$809$		−	42.6208i		−	1.49847i	−0.662306	−	0.749233i	$-0.730422\pi$
$809$		−	42.6208i		−	1.49847i	0.662306	−	0.749233i	$-0.269578\pi$
$810$		−	81.4879i		−	2.86319i
$811$	11.2213	+	11.2213i	0.394034	+	0.394034i	0.876122	−	0.482089i	$-0.160122\pi$
$811$	11.2213	+	11.2213i	0.394034	+	0.394034i	−0.482089	+	0.876122i	$0.660122\pi$
$812$	−15.7387	+	15.7387i	−0.552320	+	0.552320i
$813$	−9.59241	+	9.59241i	−0.336420	+	0.336420i
$814$	−18.1608	+	18.1608i	−0.636535	+	0.636535i
$815$	110.365			3.86591
$816$		−	29.4429i		−	1.03071i
$817$	−0.481530	−	0.481530i	−0.0168466	−	0.0168466i
$818$	23.5660			0.823967
$819$	−7.93255	−	19.1966i	−0.277186	−	0.670784i
$820$	36.0005			1.25719
$821$	−18.6793	+	18.6793i	−0.651911	+	0.651911i	−0.953453	−	0.301542i	$-0.902499\pi$
$821$	−18.6793	+	18.6793i	−0.651911	+	0.651911i	0.301542	+	0.953453i	$0.402499\pi$
$822$	−52.0879			−1.81677
$823$	−21.9879			−0.766449			−0.383224	−	0.923655i	$-0.625186\pi$
$823$	−21.9879			−0.766449			−0.383224	+	0.923655i	$0.625186\pi$
$824$	3.27657	+	3.27657i	0.114145	+	0.114145i
$825$	−51.1016	−	51.1016i	−1.77913	−	1.77913i
$826$	−1.05968	+	1.05968i	−0.0368711	+	0.0368711i
$827$	−7.01784	−	7.01784i	−0.244034	−	0.244034i	0.574482	−	0.818517i	$-0.305203\pi$
$827$	−7.01784	−	7.01784i	−0.244034	−	0.244034i	−0.818517	+	0.574482i	$0.805203\pi$
$828$			24.6133i			0.855372i
$829$	14.8876			0.517069			0.258535	−	0.966002i	$-0.416760\pi$
$829$	14.8876			0.517069			0.258535	+	0.966002i	$0.416760\pi$
$830$	−20.9196	−	20.9196i	−0.726129	−	0.726129i
$831$			30.0708i			1.04315i
$832$	−9.27171	−	3.84963i	−0.321439	−	0.133462i
$833$		−	4.90323i		−	0.169887i
$834$	16.4590	+	16.4590i	0.569930	+	0.569930i
$835$			110.011i			3.80710i
$836$	3.11667			0.107792
$837$	−4.33725	−	4.00531i	−0.149917	−	0.138444i
$838$	10.6574	+	10.6574i	0.368153	+	0.368153i
$839$	4.26374	−	4.26374i	0.147201	−	0.147201i	−0.629666	−	0.776866i	$-0.716808\pi$
$839$	4.26374	−	4.26374i	0.147201	−	0.147201i	0.776866	+	0.629666i	$0.216808\pi$
$840$	17.8463	+	17.8463i	0.615757	+	0.615757i
$841$	−19.8566			−0.684709
$842$			50.3989i			1.73686i
$843$	45.7028	+	45.7028i	1.57409	+	1.57409i
$844$			15.2983i			0.526588i
$845$	−0.0953399	+	56.5359i	−0.00327979	+	1.94489i
$846$	−14.6915			−0.505104
$847$	−9.80649	−	9.80649i	−0.336955	−	0.336955i
$848$		−	47.5074i		−	1.63141i
$849$	3.30479			0.113420
$850$	−46.9824	+	46.9824i	−1.61148	+	1.61148i
$851$	30.5488	+	30.5488i	1.04720	+	1.04720i
$852$	23.0822	+	23.0822i	0.790784	+	0.790784i
$853$	−33.9390	+	33.9390i	−1.16205	+	1.16205i	−0.178021	+	0.984027i	$0.556970\pi$
$853$	−33.9390	+	33.9390i	−1.16205	+	1.16205i	−0.984027	+	0.178021i	$0.943030\pi$
$854$		−	28.2539i		−	0.966828i
$855$		−	11.1213i		−	0.380339i
$856$	0.982465	−	0.982465i	0.0335800	−	0.0335800i
$857$		−	10.3810i		−	0.354607i	−0.984156	−	0.177304i	$-0.943263\pi$
$857$		−	10.3810i		−	0.354607i	0.984156	−	0.177304i	$-0.0567375\pi$
$858$	−13.2606	+	31.9378i	−0.452710	+	1.09034i
$859$			6.58595i			0.224710i	0.993668	+	0.112355i	$0.0358393\pi$
$859$			6.58595i			0.224710i	−0.993668	+	0.112355i	$0.964161\pi$
$860$	2.94318	−	2.94318i	0.100362	−	0.100362i
$861$			31.2589i			1.06530i
$862$		−	55.2213i		−	1.88084i
$863$	11.2503	−	11.2503i	0.382963	−	0.382963i	−0.489205	−	0.872169i	$-0.662713\pi$
$863$	11.2503	−	11.2503i	0.382963	−	0.382963i	0.872169	+	0.489205i	$0.162713\pi$
$864$	5.05501	−	5.05501i	0.171975	−	0.171975i
$865$	54.4663	−	54.4663i	1.85191	−	1.85191i
$866$	−33.5343	−	33.5343i	−1.13954	−	1.13954i
$867$		−	24.2908i		−	0.824959i
$868$	−17.7157	+	0.704891i	−0.601311	+	0.0239256i
$869$	17.5037	−	17.5037i	0.593773	−	0.593773i
$870$		−	132.230i		−	4.48302i
$871$	−41.9277	+	17.3256i	−1.42067	+	0.587057i
$872$	6.80201			0.230345
$873$	23.3660	+	23.3660i	0.790820	+	0.790820i
$874$		−	12.6817i		−	0.428966i
$875$		−	87.5736i		−	2.96053i
$876$	−9.27160	−	9.27160i	−0.313259	−	0.313259i
$877$	27.0647	+	27.0647i	0.913912	+	0.913912i	0.996577	−	0.0826657i	$-0.0263434\pi$
$877$	27.0647	+	27.0647i	0.913912	+	0.913912i	−0.0826657	+	0.996577i	$0.526343\pi$
$878$	−14.9042	+	14.9042i	−0.502994	+	0.502994i
$879$	21.0410	+	21.0410i	0.709694	+	0.709694i
$880$		−	46.3362i		−	1.56199i
$881$	35.0496			1.18085			0.590425	−	0.807093i	$-0.298960\pi$
$881$	35.0496			1.18085			0.590425	+	0.807093i	$0.298960\pi$
$882$	−6.31180	+	6.31180i	−0.212530	+	0.212530i
$883$	−19.9120			−0.670091			−0.335046	−	0.942202i	$-0.608752\pi$
$883$	−19.9120			−0.670091			−0.335046	+	0.942202i	$0.608752\pi$
$884$	12.1388	+	5.04006i	0.408273	+	0.169516i
$885$		−	3.68051i		−	0.123719i
$886$	−23.0568	−	23.0568i	−0.774608	−	0.774608i
$887$	−24.2027			−0.812646			−0.406323	−	0.913729i	$-0.633189\pi$
$887$	−24.2027			−0.812646			−0.406323	+	0.913729i	$0.633189\pi$
$888$			16.2048i			0.543796i
$889$	−10.8714	+	10.8714i	−0.364614	+	0.364614i
$890$	−52.7307	+	52.7307i	−1.76754	+	1.76754i
$891$	−15.8210	−	15.8210i	−0.530025	−	0.530025i
$892$	9.55556	+	9.55556i	0.319944	+	0.319944i
$893$	3.12929			0.104718
$894$	25.4380			0.850773
$895$	−40.9485	−	40.9485i	−1.36876	−	1.36876i
$896$			18.8484i			0.629680i
$897$	53.7235	+	22.3061i	1.79378	+	0.744779i
$898$		−	55.4203i		−	1.84940i
$899$	−28.5910	−	26.4028i	−0.953563	−	0.880584i
$900$	50.0044			1.66681
$901$			25.4265i			0.847080i
$902$	16.9075	−	16.9075i	0.562959	−	0.562959i
$903$	2.55553	+	2.55553i	0.0850427	+	0.0850427i
$904$	−2.18295	+	2.18295i	−0.0726039	+	0.0726039i
$905$	−4.49046	−	4.49046i	−0.149268	−	0.149268i
$906$	−55.5348			−1.84502
$907$		−	1.64928i		−	0.0547634i	−0.999625	−	0.0273817i	$-0.991283\pi$
$907$		−	1.64928i		−	0.0547634i	0.999625	−	0.0273817i	$-0.00871695\pi$
$908$	2.65753	−	2.65753i	0.0881933	−	0.0881933i
$909$		−	26.1165i		−	0.866230i
$910$	−60.4542	+	24.9813i	−2.00404	+	0.828121i
$911$			55.1425i			1.82695i	0.406893	+	0.913476i	$0.366612\pi$
$911$			55.1425i			1.82695i	−0.406893	+	0.913476i	$0.633388\pi$
$912$	8.07295	−	8.07295i	0.267322	−	0.267322i
$913$	−8.12316			−0.268837
$914$	−23.4625			−0.776072
$915$	49.0660	+	49.0660i	1.62207	+	1.62207i
$916$	−16.2103	+	16.2103i	−0.535605	+	0.535605i
$917$	7.45721	−	7.45721i	0.246259	−	0.246259i
$918$	−3.58062	+	3.58062i	−0.118178	+	0.118178i
$919$	−5.65026			−0.186385			−0.0931924	−	0.995648i	$-0.529707\pi$
$919$	−5.65026			−0.186385			−0.0931924	+	0.995648i	$0.529707\pi$
$920$	−32.4747			−1.07066
$921$	−18.4020	−	18.4020i	−0.606365	−	0.606365i
$922$	8.29686			0.273242
$923$	32.7589	−	13.5368i	1.07827	−	0.445570i
$924$	−16.5405			−0.544141
$925$	62.0629	−	62.0629i	2.04061	−	2.04061i
$926$			19.6032i			0.644201i
$927$			10.8363i			0.355911i
$928$	33.3224	−	33.3224i	1.09386	−	1.09386i
$929$	−25.8066	+	25.8066i	−0.846686	+	0.846686i	−0.989718	−	0.143032i	$-0.954315\pi$
$929$	−25.8066	+	25.8066i	−0.846686	+	0.846686i	0.143032	+	0.989718i	$0.454315\pi$
$930$	71.4591	−	77.3813i	2.34324	−	2.53743i
$931$	1.34442	−	1.34442i	0.0440614	−	0.0440614i
$932$	15.1820			0.497303
$933$	−48.8904			−1.60060
$934$	12.8645	−	12.8645i	0.420941	−	0.420941i
$935$			24.7997i			0.811036i
$936$	3.82849	+	9.26488i	0.125138	+	0.302832i
$937$	41.8045			1.36569			0.682847	−	0.730562i	$-0.260742\pi$
$937$	41.8045			1.36569			0.682847	+	0.730562i	$0.260742\pi$
$938$	−37.1154	−	37.1154i	−1.21186	−	1.21186i
$939$	−64.5491			−2.10648
$940$			19.1267i			0.623843i
$941$	21.0009	−	21.0009i	0.684609	−	0.684609i	−0.276426	−	0.961035i	$-0.589150\pi$
$941$	21.0009	−	21.0009i	0.684609	−	0.684609i	0.961035	+	0.276426i	$0.0891500\pi$
$942$	−11.4210	+	11.4210i	−0.372117	+	0.372117i
$943$	−28.4406	−	28.4406i	−0.926155	−	0.926155i
$944$	1.22751	−	1.22751i	0.0399521	−	0.0399521i
$945$		−	10.4181i		−	0.338902i
$946$		−	2.76451i		−	0.0898818i
$947$	39.0124	+	39.0124i	1.26773	+	1.26773i	0.947256	+	0.320477i	$0.103843\pi$
$947$	39.0124	+	39.0124i	1.26773	+	1.26773i	0.320477	+	0.947256i	$0.396157\pi$
$948$			37.2790i			1.21077i
$949$	−13.1585	+	5.43743i	−0.427143	+	0.176506i
$950$	−25.7642			−0.835901
$951$	−40.8027	+	40.8027i	−1.32312	+	1.32312i
$952$		−	6.37121i		−	0.206492i
$953$	34.3301			1.11206			0.556030	−	0.831162i	$-0.312324\pi$
$953$	34.3301			1.11206			0.556030	+	0.831162i	$0.312324\pi$
$954$	32.7309	−	32.7309i	1.05970	−	1.05970i
$955$	−40.1664	−	40.1664i	−1.29975	−	1.29975i
$956$	23.6311	+	23.6311i	0.764284	+	0.764284i
$957$	−25.6727	−	25.6727i	−0.829881	−	0.829881i
$958$	44.6273			1.44184
$959$	−27.0528			−0.873580
$960$	20.1713	+	20.1713i	0.651026	+	0.651026i
$961$	−2.46302	−	30.9020i	−0.0794521	−	0.996839i
$962$	−38.7884	−	16.1050i	−1.25059	−	0.519247i
$963$	3.24922			0.104705
$964$	27.7188	−	27.7188i	0.892764	−	0.892764i
$965$	15.5561			0.500769
$966$			67.3032i			2.16545i
$967$	−33.0827	+	33.0827i	−1.06387	+	1.06387i	−0.0660500	+	0.997816i	$0.521040\pi$
$967$	−33.0827	+	33.0827i	−1.06387	+	1.06387i	−0.997816	+	0.0660500i	$0.978960\pi$
$968$	4.73291	+	4.73291i	0.152122	+	0.152122i
$969$	−4.32074	+	4.32074i	−0.138802	+	0.138802i
$970$	73.5845	−	73.5845i	2.36266	−	2.36266i
$971$	−55.8955			−1.79377			−0.896886	−	0.442261i	$-0.854176\pi$
$971$	−55.8955			−1.79377			−0.896886	+	0.442261i	$0.854176\pi$
$972$	29.2117			0.936967
$973$	8.54830	+	8.54830i	0.274046	+	0.274046i
$974$	27.3471			0.876256
$975$	45.3170	−	109.145i	1.45131	−	3.49542i
$976$			32.7286i			1.04762i
$977$	15.9176	+	15.9176i	0.509249	+	0.509249i	0.914296	−	0.405047i	$-0.132745\pi$
$977$	15.9176	+	15.9176i	0.509249	+	0.509249i	−0.405047	+	0.914296i	$0.632745\pi$
$978$			110.392i			3.52994i
$979$			20.4756i			0.654402i
$980$	8.21725	+	8.21725i	0.262490	+	0.262490i
$981$	11.2478	+	11.2478i	0.359116	+	0.359116i
$982$	5.59891	+	5.59891i	0.178669	+	0.178669i
$983$	−43.1735	−	43.1735i	−1.37702	−	1.37702i	−0.849612	−	0.527408i	$-0.823164\pi$
$983$	−43.1735	−	43.1735i	−1.37702	−	1.37702i	−0.527408	−	0.849612i	$-0.676836\pi$
$984$		−	15.0865i		−	0.480939i
$985$	102.350			3.26114
$986$	−23.6033	+	23.6033i	−0.751682	+	0.751682i
$987$	−16.6075			−0.528621
$988$	1.94641	+	4.71028i	0.0619235	+	0.149854i
$989$	−4.65026			−0.147870
$990$	31.9240	−	31.9240i	1.01461	−	1.01461i
$991$			24.0778i			0.764858i	0.923985	+	0.382429i	$0.124912\pi$
$991$			24.0778i			0.764858i	−0.923985	+	0.382429i	$0.875088\pi$
$992$	37.5083	−	1.49242i	1.19089	−	0.0473843i
$993$	−15.4010	−	15.4010i	−0.488737	−	0.488737i
$994$	28.9989	+	28.9989i	0.919791	+	0.919791i
$995$	38.1069	+	38.1069i	1.20807	+	1.20807i
$996$	8.65027	−	8.65027i	0.274094	−	0.274094i
$997$	−7.99553			−0.253221			−0.126611	−	0.991953i	$-0.540410\pi$
$997$	−7.99553			−0.253221			−0.126611	+	0.991953i	$0.540410\pi$
$998$	−51.4223			−1.62775
$999$	4.72993	−	4.72993i	0.149648	−	0.149648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.i.a.216.8	yes	68
13.5	odd	4	inner	403.2.i.a.278.8	yes	68
31.30	odd	2	inner	403.2.i.a.216.7	✓	68
403.278	even	4	inner	403.2.i.a.278.7	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.i.a.216.7	✓	68	31.30	odd	2	inner
403.2.i.a.216.8	yes	68	1.1	even	1	trivial
403.2.i.a.278.7	yes	68	403.278	even	4	inner
403.2.i.a.278.8	yes	68	13.5	odd	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30566 - 1.30566i) q^{2} +2.35582i q^{3} +1.40948i q^{4} +(-3.07515 - 3.07515i) q^{5} +(3.07590 - 3.07590i) q^{6} +(1.59752 - 1.59752i) q^{7} +(-0.771014 + 0.771014i) q^{8} -2.54991 q^{9} +O(q^{10})\)	\(q+(-1.30566 - 1.30566i) q^{2} +2.35582i q^{3} +1.40948i q^{4} +(-3.07515 - 3.07515i) q^{5} +(3.07590 - 3.07590i) q^{6} +(1.59752 - 1.59752i) q^{7} +(-0.771014 + 0.771014i) q^{8} -2.54991 q^{9} +8.03019i q^{10} +(1.55908 + 1.55908i) q^{11} -3.32049 q^{12} +(-1.38259 + 3.32993i) q^{13} -4.17164 q^{14} +(7.24451 - 7.24451i) q^{15} +4.83232 q^{16} -2.58632 q^{17} +(3.32930 + 3.32930i) q^{18} +(-0.709142 - 0.709142i) q^{19} +(4.33437 - 4.33437i) q^{20} +(3.76348 + 3.76348i) q^{21} -4.07124i q^{22} -6.84836 q^{23} +(-1.81637 - 1.81637i) q^{24} +13.9131i q^{25} +(6.15294 - 2.54256i) q^{26} +1.06034i q^{27} +(2.25168 + 2.25168i) q^{28} +6.98975i q^{29} -18.9177 q^{30} +(-3.77737 + 4.09042i) q^{31} +(-4.76733 - 4.76733i) q^{32} +(-3.67291 + 3.67291i) q^{33} +(3.37685 + 3.37685i) q^{34} -9.82526 q^{35} -3.59405i q^{36} +(-4.46075 - 4.46075i) q^{37} +1.85179i q^{38} +(-7.84473 - 3.25715i) q^{39} +4.74197 q^{40} +(4.15291 + 4.15291i) q^{41} -9.82764i q^{42} +0.679033 q^{43} +(-2.19749 + 2.19749i) q^{44} +(7.84134 + 7.84134i) q^{45} +(8.94161 + 8.94161i) q^{46} +(-2.20639 + 2.20639i) q^{47} +11.3841i q^{48} +1.89583i q^{49} +(18.1658 - 18.1658i) q^{50} -6.09291i q^{51} +(-4.69348 - 1.94874i) q^{52} -9.83116i q^{53} +(1.38445 - 1.38445i) q^{54} -9.58880i q^{55} +2.46343i q^{56} +(1.67061 - 1.67061i) q^{57} +(9.12622 - 9.12622i) q^{58} +(0.254021 - 0.254021i) q^{59} +(10.2110 + 10.2110i) q^{60} +6.77285i q^{61} +(10.2726 - 0.408737i) q^{62} +(-4.07353 + 4.07353i) q^{63} +2.78435i q^{64} +(14.4917 - 5.98836i) q^{65} +9.59113 q^{66} +(8.89709 + 8.89709i) q^{67} -3.64537i q^{68} -16.1335i q^{69} +(12.8284 + 12.8284i) q^{70} +(-6.95145 - 6.95145i) q^{71} +(1.96601 - 1.96601i) q^{72} +(2.79224 + 2.79224i) q^{73} +11.6484i q^{74} -32.7768 q^{75} +(0.999523 - 0.999523i) q^{76} +4.98133 q^{77} +(5.98981 + 14.4952i) q^{78} -11.2270i q^{79} +(-14.8601 - 14.8601i) q^{80} -10.1477 q^{81} -10.8446i q^{82} +(-2.60512 + 2.60512i) q^{83} +(-5.30456 + 5.30456i) q^{84} +(7.95332 + 7.95332i) q^{85} +(-0.886584 - 0.886584i) q^{86} -16.4666 q^{87} -2.40414 q^{88} +(6.56656 + 6.56656i) q^{89} -20.4762i q^{90} +(3.11092 + 7.52837i) q^{91} -9.65264i q^{92} +(-9.63630 - 8.89881i) q^{93} +5.76159 q^{94} +4.36144i q^{95} +(11.2310 - 11.2310i) q^{96} +(-9.16349 - 9.16349i) q^{97} +(2.47531 - 2.47531i) q^{98} +(-3.97550 - 3.97550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9}+O(q^{10}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9	\( 68 q - 4 q^{2} - 4 q^{5} + 8 q^{7} + 16 q^{8} - 60 q^{9} - 48 q^{14} - 40 q^{16} + 4 q^{18} - 24 q^{19} - 16 q^{20} + 44 q^{28} + 24 q^{31} + 28 q^{32} - 40 q^{35} - 24 q^{39} + 24 q^{40} + 20 q^{41} - 24 q^{45} - 36 q^{47} + 80 q^{50} + 28 q^{59} - 76 q^{63} + 152 q^{66} - 32 q^{67} - 48 q^{70} + 20 q^{71} - 32 q^{72} + 72 q^{76} + 84 q^{78} - 20 q^{80} + 52 q^{81} - 112 q^{87} - 8 q^{93} - 16 q^{94} - 4 q^{97} - 92 q^{98}+O(q^{100}) \) 68 * q - 4 * q^2 - 4 * q^5 + 8 * q^7 + 16 * q^8 - 60 * q^9 - 48 * q^14 - 40 * q^16 + 4 * q^18 - 24 * q^19 - 16 * q^20 + 44 * q^28 + 24 * q^31 + 28 * q^32 - 40 * q^35 - 24 * q^39 + 24 * q^40 + 20 * q^41 - 24 * q^45 - 36 * q^47 + 80 * q^50 + 28 * q^59 - 76 * q^63 + 152 * q^66 - 32 * q^67 - 48 * q^70 + 20 * q^71 - 32 * q^72 + 72 * q^76 + 84 * q^78 - 20 * q^80 + 52 * q^81 - 112 * q^87 - 8 * q^93 - 16 * q^94 - 4 * q^97 - 92 * q^98

Introduction

L-functions

Modular forms

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Representations

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Database

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