LMFDB - Embedded newform 403.2.i.a.216.13

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			216.13
Character	$\chi$	$=$	403.216
Dual form			403.2.i.a.278.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.471532 - 0.471532i) q^{2} -3.39270i q^{3} -1.55532i q^{4} +(1.41859 + 1.41859i) q^{5} +(-1.59977 + 1.59977i) q^{6} +(-1.23146 + 1.23146i) q^{7} +(-1.67644 + 1.67644i) q^{8} -8.51044 q^{9} +O(q^{10})$	\(q+(-0.471532 - 0.471532i) q^{2} -3.39270i q^{3} -1.55532i q^{4} +(1.41859 + 1.41859i) q^{5} +(-1.59977 + 1.59977i) q^{6} +(-1.23146 + 1.23146i) q^{7} +(-1.67644 + 1.67644i) q^{8} -8.51044 q^{9} -1.33782i q^{10} +(0.153867 + 0.153867i) q^{11} -5.27673 q^{12} +(-1.68055 - 3.18995i) q^{13} +1.16134 q^{14} +(4.81284 - 4.81284i) q^{15} -1.52964 q^{16} -2.00099 q^{17} +(4.01294 + 4.01294i) q^{18} +(-1.59557 - 1.59557i) q^{19} +(2.20635 - 2.20635i) q^{20} +(4.17797 + 4.17797i) q^{21} -0.145107i q^{22} +2.20261 q^{23} +(5.68768 + 5.68768i) q^{24} -0.975228i q^{25} +(-0.711729 + 2.29659i) q^{26} +18.6953i q^{27} +(1.91531 + 1.91531i) q^{28} -6.69098i q^{29} -4.53881 q^{30} +(3.51027 - 4.32180i) q^{31} +(4.07416 + 4.07416i) q^{32} +(0.522026 - 0.522026i) q^{33} +(0.943528 + 0.943528i) q^{34} -3.49386 q^{35} +13.2364i q^{36} +(-2.11822 - 2.11822i) q^{37} +1.50472i q^{38} +(-10.8225 + 5.70160i) q^{39} -4.75636 q^{40} +(1.62248 + 1.62248i) q^{41} -3.94009i q^{42} +4.87116 q^{43} +(0.239312 - 0.239312i) q^{44} +(-12.0728 - 12.0728i) q^{45} +(-1.03860 - 1.03860i) q^{46} +(6.23697 - 6.23697i) q^{47} +5.18962i q^{48} +3.96703i q^{49} +(-0.459851 + 0.459851i) q^{50} +6.78875i q^{51} +(-4.96137 + 2.61378i) q^{52} -6.37574i q^{53} +(8.81542 - 8.81542i) q^{54} +0.436548i q^{55} -4.12894i q^{56} +(-5.41329 + 5.41329i) q^{57} +(-3.15501 + 3.15501i) q^{58} +(7.34023 - 7.34023i) q^{59} +(-7.48549 - 7.48549i) q^{60} -5.35337i q^{61} +(-3.69307 + 0.382661i) q^{62} +(10.4802 - 10.4802i) q^{63} -0.782910i q^{64} +(2.14121 - 6.90922i) q^{65} -0.492304 q^{66} +(-5.10003 - 5.10003i) q^{67} +3.11217i q^{68} -7.47280i q^{69} +(1.64746 + 1.64746i) q^{70} +(7.36475 + 7.36475i) q^{71} +(14.2673 - 14.2673i) q^{72} +(-7.23487 - 7.23487i) q^{73} +1.99762i q^{74} -3.30866 q^{75} +(-2.48161 + 2.48161i) q^{76} -0.378962 q^{77} +(7.79166 + 2.41469i) q^{78} +8.32650i q^{79} +(-2.16993 - 2.16993i) q^{80} +37.8963 q^{81} -1.53010i q^{82} +(-9.26976 + 9.26976i) q^{83} +(6.49806 - 6.49806i) q^{84} +(-2.83857 - 2.83857i) q^{85} +(-2.29691 - 2.29691i) q^{86} -22.7005 q^{87} -0.515900 q^{88} +(-2.28976 - 2.28976i) q^{89} +11.3854i q^{90} +(5.99781 + 1.85876i) q^{91} -3.42575i q^{92} +(-14.6626 - 11.9093i) q^{93} -5.88186 q^{94} -4.52690i q^{95} +(13.8224 - 13.8224i) q^{96} +(10.7692 + 10.7692i) q^{97} +(1.87058 - 1.87058i) q^{98} +(-1.30948 - 1.30948i) 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 $

$2$	−0.471532	−	0.471532i	−0.333423	−	0.333423i	0.520462	−	0.853885i	$-0.325760\pi$
$2$	−0.471532	−	0.471532i	−0.333423	−	0.333423i	−0.853885	+	0.520462i	$0.825760\pi$
$3$		−	3.39270i		−	1.95878i	−0.201981	−	0.979389i	$-0.564738\pi$
$3$		−	3.39270i		−	1.95878i	0.201981	−	0.979389i	$-0.435262\pi$
$4$		−	1.55532i		−	0.777658i
$5$	1.41859	+	1.41859i	0.634411	+	0.634411i	0.949171	−	0.314760i	$-0.101924\pi$
$5$	1.41859	+	1.41859i	0.634411	+	0.634411i	−0.314760	+	0.949171i	$0.601924\pi$
$6$	−1.59977	+	1.59977i	−0.653102	+	0.653102i
$7$	−1.23146	+	1.23146i	−0.465447	+	0.465447i	−0.900436	−	0.434989i	$-0.856752\pi$
$7$	−1.23146	+	1.23146i	−0.465447	+	0.465447i	0.434989	+	0.900436i	$0.356752\pi$
$8$	−1.67644	+	1.67644i	−0.592712	+	0.592712i
$9$	−8.51044			−2.83681
$10$		−	1.33782i		−	0.423055i
$11$	0.153867	+	0.153867i	0.0463928	+	0.0463928i	0.729923	−	0.683530i	$-0.239556\pi$
$11$	0.153867	+	0.153867i	0.0463928	+	0.0463928i	−0.683530	+	0.729923i	$0.739556\pi$
$12$	−5.27673			−1.52326
$13$	−1.68055	−	3.18995i	−0.466100	−	0.884732i
$13$	−1.68055	−	3.18995i	−0.466100	−	0.884732i
$14$	1.16134			0.310382
$15$	4.81284	−	4.81284i	1.24267	−	1.24267i
$16$	−1.52964			−0.382410
$17$	−2.00099			−0.485310			−0.242655	−	0.970113i	$-0.578018\pi$
$17$	−2.00099			−0.485310			−0.242655	+	0.970113i	$0.578018\pi$
$18$	4.01294	+	4.01294i	0.945859	+	0.945859i
$19$	−1.59557	−	1.59557i	−0.366048	−	0.366048i	0.499985	−	0.866034i	$-0.333339\pi$
$19$	−1.59557	−	1.59557i	−0.366048	−	0.366048i	−0.866034	+	0.499985i	$0.833339\pi$
$20$	2.20635	−	2.20635i	0.493355	−	0.493355i
$21$	4.17797	+	4.17797i	0.911708	+	0.911708i
$22$		−	0.145107i		−	0.0309368i
$23$	2.20261			0.459276			0.229638	−	0.973276i	$-0.426246\pi$
$23$	2.20261			0.459276			0.229638	+	0.973276i	$0.426246\pi$
$24$	5.68768	+	5.68768i	1.16099	+	1.16099i
$25$		−	0.975228i		−	0.195046i
$26$	−0.711729	+	2.29659i	−0.139581	+	0.450399i
$27$			18.6953i			3.59791i
$28$	1.91531	+	1.91531i	0.361959	+	0.361959i
$29$		−	6.69098i		−	1.24248i	−0.783619	−	0.621242i	$-0.786628\pi$
$29$		−	6.69098i		−	1.24248i	0.783619	−	0.621242i	$-0.213372\pi$
$30$	−4.53881			−0.828670
$31$	3.51027	−	4.32180i	0.630464	−	0.776219i
$31$	3.51027	−	4.32180i	0.630464	−	0.776219i
$32$	4.07416	+	4.07416i	0.720217	+	0.720217i
$33$	0.522026	−	0.522026i	0.0908731	−	0.0908731i
$34$	0.943528	+	0.943528i	0.161814	+	0.161814i
$35$	−3.49386			−0.590569
$36$			13.2364i			2.20607i
$37$	−2.11822	−	2.11822i	−0.348234	−	0.348234i	0.511218	−	0.859451i	$-0.329195\pi$
$37$	−2.11822	−	2.11822i	−0.348234	−	0.348234i	−0.859451	+	0.511218i	$0.829195\pi$
$38$			1.50472i			0.244098i
$39$	−10.8225	+	5.70160i	−1.73299	+	0.912987i
$40$	−4.75636			−0.752046
$41$	1.62248	+	1.62248i	0.253389	+	0.253389i	0.822359	−	0.568970i	$-0.192658\pi$
$41$	1.62248	+	1.62248i	0.253389	+	0.253389i	−0.568970	+	0.822359i	$0.692658\pi$
$42$		−	3.94009i		−	0.607969i
$43$	4.87116			0.742845			0.371422	−	0.928464i	$-0.378870\pi$
$43$	4.87116			0.742845			0.371422	+	0.928464i	$0.378870\pi$
$44$	0.239312	−	0.239312i	0.0360777	−	0.0360777i
$45$	−12.0728	−	12.0728i	−1.79971	−	1.79971i
$46$	−1.03860	−	1.03860i	−0.153133	−	0.153133i
$47$	6.23697	−	6.23697i	0.909756	−	0.909756i	−0.0864963	−	0.996252i	$-0.527567\pi$
$47$	6.23697	−	6.23697i	0.909756	−	0.909756i	0.996252	+	0.0864963i	$0.0275671\pi$
$48$			5.18962i			0.749057i
$49$			3.96703i			0.566718i
$50$	−0.459851	+	0.459851i	−0.0650327	+	0.0650327i
$51$			6.78875i			0.950616i
$52$	−4.96137	+	2.61378i	−0.688019	+	0.362467i
$53$		−	6.37574i		−	0.875775i	−0.899030	−	0.437888i	$-0.855727\pi$
$53$		−	6.37574i		−	0.875775i	0.899030	−	0.437888i	$-0.144273\pi$
$54$	8.81542	−	8.81542i	1.19963	−	1.19963i
$55$			0.436548i			0.0588641i
$56$		−	4.12894i		−	0.551752i
$57$	−5.41329	+	5.41329i	−0.717008	+	0.717008i
$58$	−3.15501	+	3.15501i	−0.414273	+	0.414273i
$59$	7.34023	−	7.34023i	0.955616	−	0.955616i	−0.0434398	−	0.999056i	$-0.513832\pi$
$59$	7.34023	−	7.34023i	0.955616	−	0.955616i	0.999056	+	0.0434398i	$0.0138317\pi$
$60$	−7.48549	−	7.48549i	−0.966373	−	0.966373i
$61$		−	5.35337i		−	0.685429i	−0.939440	−	0.342715i	$-0.888654\pi$
$61$		−	5.35337i		−	0.685429i	0.939440	−	0.342715i	$-0.111346\pi$
$62$	−3.69307	+	0.382661i	−0.469020	+	0.0485980i
$63$	10.4802	−	10.4802i	1.32039	−	1.32039i
$64$		−	0.782910i		−	0.0978637i
$65$	2.14121	−	6.90922i	0.265585	−	0.856983i
$66$	−0.492304			−0.0605984
$67$	−5.10003	−	5.10003i	−0.623068	−	0.623068i	0.323246	−	0.946315i	$-0.395226\pi$
$67$	−5.10003	−	5.10003i	−0.623068	−	0.623068i	−0.946315	+	0.323246i	$0.895226\pi$
$68$			3.11217i			0.377406i
$69$		−	7.47280i		−	0.899620i
$70$	1.64746	+	1.64746i	0.196910	+	0.196910i
$71$	7.36475	+	7.36475i	0.874035	+	0.874035i	0.992909	−	0.118874i	$-0.0379286\pi$
$71$	7.36475	+	7.36475i	0.874035	+	0.874035i	−0.118874	+	0.992909i	$0.537929\pi$
$72$	14.2673	−	14.2673i	1.68141	−	1.68141i
$73$	−7.23487	−	7.23487i	−0.846778	−	0.846778i	0.142952	−	0.989730i	$-0.454341\pi$
$73$	−7.23487	−	7.23487i	−0.846778	−	0.846778i	−0.989730	+	0.142952i	$0.954341\pi$
$74$			1.99762i			0.232218i
$75$	−3.30866			−0.382051
$76$	−2.48161	+	2.48161i	−0.284660	+	0.284660i
$77$	−0.378962			−0.0431867
$78$	7.79166	+	2.41469i	0.882231	+	0.273409i
$79$			8.32650i			0.936805i	0.883515	+	0.468402i	$0.155170\pi$
$79$			8.32650i			0.936805i	−0.883515	+	0.468402i	$0.844830\pi$
$80$	−2.16993	−	2.16993i	−0.242605	−	0.242605i
$81$	37.8963			4.21070
$82$		−	1.53010i		−	0.168972i
$83$	−9.26976	+	9.26976i	−1.01749	+	1.01749i	−0.0176438	+	0.999844i	$0.505616\pi$
$83$	−9.26976	+	9.26976i	−1.01749	+	1.01749i	−0.999844	+	0.0176438i	$0.994384\pi$
$84$	6.49806	−	6.49806i	0.708997	−	0.708997i
$85$	−2.83857	−	2.83857i	−0.307886	−	0.307886i
$86$	−2.29691	−	2.29691i	−0.247682	−	0.247682i
$87$	−22.7005			−2.43375
$88$	−0.515900			−0.0549951
$89$	−2.28976	−	2.28976i	−0.242714	−	0.242714i	0.575258	−	0.817972i	$-0.304902\pi$
$89$	−2.28976	−	2.28976i	−0.242714	−	0.242714i	−0.817972	+	0.575258i	$0.804902\pi$
$90$			11.3854i			1.20013i
$91$	5.99781	+	1.85876i	0.628741	+	0.194851i
$92$		−	3.42575i		−	0.357159i
$93$	−14.6626	−	11.9093i	−1.52044	−	1.23494i
$94$	−5.88186			−0.606667
$95$		−	4.52690i		−	0.464450i
$96$	13.8224	−	13.8224i	1.41075	−	1.41075i
$97$	10.7692	+	10.7692i	1.09345	+	1.09345i	0.995158	+	0.0982898i	$0.0313372\pi$
$97$	10.7692	+	10.7692i	1.09345	+	1.09345i	0.0982898	+	0.995158i	$0.468663\pi$
$98$	1.87058	−	1.87058i	0.188957	−	0.188957i
$99$	−1.30948	−	1.30948i	−0.131608	−	0.131608i
$100$	−1.51679			−0.151679
$101$		−	11.6115i		−	1.15539i	−0.816254	−	0.577693i	$-0.803953\pi$
$101$		−	11.6115i		−	1.15539i	0.816254	−	0.577693i	$-0.196047\pi$
$102$	3.20111	−	3.20111i	0.316957	−	0.316957i
$103$			19.6198i			1.93320i	0.256296	+	0.966598i	$0.417498\pi$
$103$			19.6198i			1.93320i	−0.256296	+	0.966598i	$0.582502\pi$
$104$	8.16511	+	2.53042i	0.800655	+	0.248128i
$105$			11.8536i			1.15679i
$106$	−3.00636	+	3.00636i	−0.292004	+	0.292004i
$107$	−10.7471			−1.03896			−0.519481	−	0.854482i	$-0.673875\pi$
$107$	−10.7471			−1.03896			−0.519481	+	0.854482i	$0.673875\pi$
$108$	29.0771			2.79795
$109$	7.92824	+	7.92824i	0.759388	+	0.759388i	0.976211	−	0.216823i	$-0.0695695\pi$
$109$	7.92824	+	7.92824i	0.759388	+	0.759388i	−0.216823	+	0.976211i	$0.569570\pi$
$110$	0.205846	−	0.205846i	0.0196267	−	0.0196267i
$111$	−7.18651	+	7.18651i	−0.682113	+	0.682113i
$112$	1.88369	−	1.88369i	0.177992	−	0.177992i
$113$	8.75380			0.823488			0.411744	−	0.911300i	$-0.364920\pi$
$113$	8.75380			0.823488			0.411744	+	0.911300i	$0.364920\pi$
$114$	5.10507			0.478134
$115$	3.12459	+	3.12459i	0.291370	+	0.291370i
$116$	−10.4066			−0.966228
$117$	14.3022	+	27.1479i	1.32224	+	2.50982i
$118$	−6.92230			−0.637249
$119$	2.46413	−	2.46413i	0.225886	−	0.225886i
$120$			16.1369i			1.47309i
$121$		−	10.9526i		−	0.995695i
$122$	−2.52428	+	2.52428i	−0.228538	+	0.228538i
$123$	5.50460	−	5.50460i	0.496333	−	0.496333i
$124$	−6.72177	−	5.45959i	−0.603633	−	0.490285i
$125$	8.47637	−	8.47637i	0.758150	−	0.758150i
$126$	−9.88353			−0.880495
$127$	−18.1490			−1.61047			−0.805233	−	0.592959i	$-0.797960\pi$
$127$	−18.1490			−1.61047			−0.805233	+	0.592959i	$0.797960\pi$
$128$	7.77915	−	7.77915i	0.687587	−	0.687587i
$129$		−	16.5264i		−	1.45507i
$130$	−4.26756	+	2.24826i	−0.374290	+	0.197186i
$131$	2.57443			0.224929			0.112465	−	0.993656i	$-0.464126\pi$
$131$	2.57443			0.224929			0.112465	+	0.993656i	$0.464126\pi$
$132$	−0.811916	−	0.811916i	−0.0706682	−	0.0706682i
$133$	3.92975			0.340752
$134$			4.80965i			0.415491i
$135$	−26.5209	+	26.5209i	−2.28255	+	2.28255i
$136$	3.35454	−	3.35454i	0.287649	−	0.287649i
$137$	4.98134	+	4.98134i	0.425585	+	0.425585i	0.887121	−	0.461536i	$-0.152702\pi$
$137$	4.98134	+	4.98134i	0.425585	+	0.425585i	−0.461536	+	0.887121i	$0.652702\pi$
$138$	−3.52366	+	3.52366i	−0.299954	+	0.299954i
$139$		−	10.3179i		−	0.875154i	−0.899181	−	0.437577i	$-0.855837\pi$
$139$		−	10.3179i		−	0.875154i	0.899181	−	0.437577i	$-0.144163\pi$
$140$			5.43405i			0.459261i
$141$	−21.1602	−	21.1602i	−1.78201	−	1.78201i
$142$		−	6.94542i		−	0.582847i
$143$	0.232247	−	0.749410i	0.0194215	−	0.0626688i
$144$	13.0179			1.08483
$145$	9.49173	−	9.49173i	0.788246	−	0.788246i
$146$			6.82294i			0.564671i
$147$	13.4589			1.11008
$148$	−3.29451	+	3.29451i	−0.270807	+	0.270807i
$149$	−0.148367	−	0.148367i	−0.0121547	−	0.0121547i	0.701003	−	0.713158i	$-0.252736\pi$
$149$	−0.148367	−	0.148367i	−0.0121547	−	0.0121547i	−0.713158	+	0.701003i	$0.752736\pi$
$150$	1.56014	+	1.56014i	0.127385	+	0.127385i
$151$	5.64533	+	5.64533i	0.459411	+	0.459411i	0.898462	−	0.439051i	$-0.144685\pi$
$151$	5.64533	+	5.64533i	0.459411	+	0.459411i	−0.439051	+	0.898462i	$0.644685\pi$
$152$	5.34976			0.433923
$153$	17.0293			1.37674
$154$	0.178693	+	0.178693i	0.0143995	+	0.0143995i
$155$	11.1105	−	1.15122i	0.892415	−	0.0924684i
$156$	8.86780	+	16.8325i	0.709992	+	1.34768i
$157$	−19.0873			−1.52333			−0.761665	−	0.647971i	$-0.775618\pi$
$157$	−19.0873			−1.52333			−0.761665	+	0.647971i	$0.775618\pi$
$158$	3.92621	−	3.92621i	0.312352	−	0.312352i
$159$	−21.6310			−1.71545
$160$			11.5591i			0.913827i
$161$	−2.71242	+	2.71242i	−0.213769	+	0.213769i
$162$	−17.8693	−	17.8693i	−1.40394	−	1.40394i
$163$	−4.41433	+	4.41433i	−0.345757	+	0.345757i	−0.858526	−	0.512769i	$-0.828620\pi$
$163$	−4.41433	+	4.41433i	−0.345757	+	0.345757i	0.512769	+	0.858526i	$0.328620\pi$
$164$	2.52347	−	2.52347i	0.197050	−	0.197050i
$165$	1.48108			0.115302
$166$	8.74197			0.678508
$167$	−8.18454	−	8.18454i	−0.633339	−	0.633339i	0.315565	−	0.948904i	$-0.397806\pi$
$167$	−8.18454	−	8.18454i	−0.633339	−	0.633339i	−0.948904	+	0.315565i	$0.897806\pi$
$168$	−14.0083			−1.08076
$169$	−7.35152	+	10.7217i	−0.565501	+	0.824748i
$170$			2.67695i			0.205313i
$171$	13.5790	+	13.5790i	1.03841	+	1.03841i
$172$		−	7.57619i		−	0.577679i
$173$		−	14.0688i		−	1.06963i	−0.844968	−	0.534817i	$-0.820381\pi$
$173$		−	14.0688i		−	1.06963i	0.844968	−	0.534817i	$-0.179619\pi$
$174$	10.7040	+	10.7040i	0.811469	+	0.811469i
$175$	1.20095	+	1.20095i	0.0907834	+	0.0907834i
$176$	−0.235362	−	0.235362i	−0.0177411	−	0.0177411i
$177$	−24.9032	−	24.9032i	−1.87184	−	1.87184i
$178$			2.15939i			0.161853i
$179$	23.3847			1.74785			0.873927	−	0.486058i	$-0.161566\pi$
$179$	23.3847			1.74785			0.873927	+	0.486058i	$0.161566\pi$
$180$	−18.7770	+	18.7770i	−1.39956	+	1.39956i
$181$	4.92465			0.366047			0.183023	−	0.983109i	$-0.441412\pi$
$181$	4.92465			0.366047			0.183023	+	0.983109i	$0.441412\pi$
$182$	−1.95169	−	3.70462i	−0.144669	−	0.274605i
$183$	−18.1624			−1.34260
$184$	−3.69255	+	3.69255i	−0.272218	+	0.272218i
$185$		−	6.00977i		−	0.441847i
$186$	1.29826	+	12.5295i	0.0951927	+	0.918707i
$187$	−0.307886	−	0.307886i	−0.0225149	−	0.0225149i
$188$	−9.70046	−	9.70046i	−0.707479	−	0.707479i
$189$	−23.0225	−	23.0225i	−1.67464	−	1.67464i
$190$	−2.13458	+	2.13458i	−0.154858	+	0.154858i
$191$	16.1309			1.16719			0.583597	−	0.812043i	$-0.301645\pi$
$191$	16.1309			1.16719			0.583597	+	0.812043i	$0.301645\pi$
$192$	−2.65618			−0.191693
$193$	−1.40966	+	1.40966i	−0.101470	+	0.101470i	−0.756019	−	0.654549i	$-0.772858\pi$
$193$	−1.40966	+	1.40966i	−0.101470	+	0.101470i	0.654549	+	0.756019i	$0.272858\pi$
$194$		−	10.1560i		−	0.729161i
$195$	−23.4409	−	7.26450i	−1.67864	−	0.520221i
$196$	6.16998			0.440713
$197$	−8.99193	+	8.99193i	−0.640648	+	0.640648i	−0.950715	−	0.310067i	$-0.899649\pi$
$197$	−8.99193	+	8.99193i	−0.640648	+	0.640648i	0.310067	+	0.950715i	$0.399649\pi$
$198$			1.23492i			0.0877621i
$199$	10.1495			0.719479			0.359739	−	0.933053i	$-0.382866\pi$
$199$	10.1495			0.719479			0.359739	+	0.933053i	$0.382866\pi$
$200$	1.63491	+	1.63491i	0.115606	+	0.115606i
$201$	−17.3029	+	17.3029i	−1.22045	+	1.22045i
$202$	−5.47518	+	5.47518i	−0.385232	+	0.385232i
$203$	8.23966	+	8.23966i	0.578311	+	0.578311i
$204$	10.5587			0.739254
$205$			4.60326i			0.321506i
$206$	9.25136	−	9.25136i	0.644573	−	0.644573i
$207$	−18.7452			−1.30288
$208$	2.57063	+	4.87947i	0.178241	+	0.338330i
$209$		−	0.491012i		−	0.0339640i
$210$	5.58936	−	5.58936i	0.385702	−	0.385702i
$211$	−15.2368			−1.04895			−0.524473	−	0.851427i	$-0.675737\pi$
$211$	−15.2368			−1.04895			−0.524473	+	0.851427i	$0.675737\pi$
$212$	−9.91629			−0.681054
$213$	24.9864	−	24.9864i	1.71204	−	1.71204i
$214$	5.06760	+	5.06760i	0.346414	+	0.346414i
$215$	6.91016	+	6.91016i	0.471269	+	0.471269i
$216$	−31.3416	−	31.3416i	−2.13253	−	2.13253i
$217$	0.999362	+	9.64487i	0.0678411	+	0.654736i
$218$		−	7.47683i		−	0.506395i
$219$	−24.5458	+	24.5458i	−1.65865	+	1.65865i
$220$	0.678970			0.0457762
$221$	3.36275	+	6.38304i	0.226203	+	0.429370i
$222$	6.77733			0.454865
$223$	−3.00466	+	3.00466i	−0.201207	+	0.201207i	−0.800517	−	0.599310i	$-0.795442\pi$
$223$	−3.00466	+	3.00466i	−0.201207	+	0.201207i	0.599310	+	0.800517i	$0.295442\pi$
$224$	−10.0343			−0.670446
$225$			8.29962i			0.553308i
$226$	−4.12769	−	4.12769i	−0.274570	−	0.274570i
$227$	16.1187	+	16.1187i	1.06983	+	1.06983i	0.997371	+	0.0724630i	$0.0230859\pi$
$227$	16.1187	+	16.1187i	1.06983	+	1.06983i	0.0724630	+	0.997371i	$0.476914\pi$
$228$	8.41938	+	8.41938i	0.557587	+	0.557587i
$229$	12.4993	+	12.4993i	0.825976	+	0.825976i	0.986957	−	0.160981i	$-0.0514659\pi$
$229$	12.4993	+	12.4993i	0.825976	+	0.825976i	−0.160981	+	0.986957i	$0.551466\pi$
$230$		−	2.94669i		−	0.194299i
$231$			1.28571i			0.0845933i
$232$	11.2171	+	11.2171i	0.736436	+	0.736436i
$233$		−	7.45673i		−	0.488506i	−0.969711	−	0.244253i	$-0.921457\pi$
$233$		−	7.45673i		−	0.488506i	0.969711	−	0.244253i	$-0.0785428\pi$
$234$	6.05713	−	19.5450i	0.395967	−	1.27770i
$235$	17.6954			1.15432
$236$	−11.4164	−	11.4164i	−0.743143	−	0.743143i
$237$	28.2494			1.83499
$238$	−2.32383			−0.150631
$239$	−3.44082	+	3.44082i	−0.222568	+	0.222568i	−0.809579	−	0.587011i	$-0.800305\pi$
$239$	−3.44082	+	3.44082i	−0.222568	+	0.222568i	0.587011	+	0.809579i	$0.300305\pi$
$240$	−7.36192	+	7.36192i	−0.475210	+	0.475210i
$241$	−12.0077	−	12.0077i	−0.773481	−	0.773481i	0.205233	−	0.978713i	$-0.434205\pi$
$241$	−12.0077	−	12.0077i	−0.773481	−	0.773481i	−0.978713	+	0.205233i	$0.934205\pi$
$242$	−5.16452	+	5.16452i	−0.331988	+	0.331988i
$243$		−	72.4850i		−	4.64992i
$244$	−8.32619			−0.533029
$245$	−5.62757	+	5.62757i	−0.359532	+	0.359532i
$246$	−5.19118			−0.330978
$247$	−2.40835	+	7.77120i	−0.153239	+	0.494470i
$248$	1.36048	+	13.1300i	0.0863906	+	0.833758i
$249$	31.4495	+	31.4495i	1.99303	+	1.99303i
$250$	−7.99376			−0.505569
$251$	19.4214			1.22587			0.612934	−	0.790134i	$-0.289989\pi$
$251$	19.4214			1.22587			0.612934	+	0.790134i	$0.289989\pi$
$252$	−16.3001	−	16.3001i	−1.02681	−	1.02681i
$253$	0.338910	+	0.338910i	0.0213071	+	0.0213071i
$254$	8.55783	+	8.55783i	0.536966	+	0.536966i
$255$	−9.63043	+	9.63043i	−0.603081	+	0.603081i
$256$	−8.90205			−0.556378
$257$			1.52619i			0.0952013i	0.998866	+	0.0476007i	$0.0151575\pi$
$257$			1.52619i			0.0952013i	−0.998866	+	0.0476007i	$0.984843\pi$
$258$	−7.79272	+	7.79272i	−0.485154	+	0.485154i
$259$	5.21700			0.324169
$260$	−10.7460	−	3.33026i	−0.666439	−	0.206534i
$261$			56.9432i			3.52470i
$262$	−1.21393	−	1.21393i	−0.0749966	−	0.0749966i
$263$			20.6854i			1.27552i	0.770236	+	0.637759i	$0.220138\pi$
$263$			20.6854i			1.27552i	−0.770236	+	0.637759i	$0.779862\pi$
$264$			1.75030i			0.107723i
$265$	9.04453	−	9.04453i	0.555601	−	0.555601i
$266$	−1.85300	−	1.85300i	−0.113615	−	0.113615i
$267$	−7.76848	+	7.76848i	−0.475423	+	0.475423i
$268$	−7.93217	+	7.93217i	−0.484534	+	0.484534i
$269$		−	11.1390i		−	0.679160i	−0.940577	−	0.339580i	$-0.889715\pi$
$269$		−	11.1390i		−	0.679160i	0.940577	−	0.339580i	$-0.110285\pi$
$270$	25.0109			1.52211
$271$	20.0135	+	20.0135i	1.21573	+	1.21573i	0.969112	+	0.246621i	$0.0793204\pi$
$271$	20.0135	+	20.0135i	1.21573	+	1.21573i	0.246621	+	0.969112i	$0.420680\pi$
$272$	3.06079			0.185588
$273$	6.30622	−	20.3488i	0.381670	−	1.23156i
$274$		−	4.69772i		−	0.283800i
$275$	0.150056	−	0.150056i	0.00904870	−	0.00904870i
$276$	−11.6226			−0.699596
$277$	−9.74683			−0.585630			−0.292815	−	0.956169i	$-0.594592\pi$
$277$	−9.74683			−0.585630			−0.292815	+	0.956169i	$0.594592\pi$
$278$	−4.86522	+	4.86522i	−0.291797	+	0.291797i
$279$	−29.8740	+	36.7804i	−1.78851	+	2.20199i
$280$	5.85725	−	5.85725i	0.350038	−	0.350038i
$281$	4.41232	−	4.41232i	0.263217	−	0.263217i	−0.563143	−	0.826360i	$-0.690408\pi$
$281$	4.41232	−	4.41232i	0.263217	−	0.263217i	0.826360	+	0.563143i	$0.190408\pi$
$282$			19.9554i			1.18833i
$283$		−	22.9593i		−	1.36479i	−0.730985	−	0.682393i	$-0.760939\pi$
$283$		−	22.9593i		−	1.36479i	0.730985	−	0.682393i	$-0.239061\pi$
$284$	11.4545	−	11.4545i	0.679700	−	0.679700i
$285$	−15.3584			−0.909755
$286$	−0.462882	+	0.243859i	−0.0273708	+	0.0144197i
$287$	−3.99603			−0.235878
$288$	−34.6729	−	34.6729i	−2.04312	−	2.04312i
$289$	−12.9961			−0.764474
$290$	−8.95130			−0.525639
$291$	36.5367	−	36.5367i	2.14182	−	2.14182i
$292$	−11.2525	+	11.2525i	−0.658504	+	0.658504i
$293$	−18.9518	+	18.9518i	−1.10717	+	1.10717i	−0.113654	+	0.993520i	$0.536256\pi$
$293$	−18.9518	+	18.9518i	−1.10717	+	1.10717i	−0.993520	+	0.113654i	$0.963744\pi$
$294$	−6.34632	−	6.34632i	−0.370125	−	0.370125i
$295$	20.8255			1.21251
$296$	7.10217			0.412805
$297$	−2.87660	+	2.87660i	−0.166917	+	0.166917i
$298$			0.139919i			0.00810531i
$299$	−3.70159	−	7.02620i	−0.214069	−	0.406336i
$300$			5.14601i			0.297105i
$301$	−5.99862	+	5.99862i	−0.345755	+	0.345755i
$302$		−	5.32390i		−	0.306356i
$303$	−39.3943			−2.26314
$304$	2.44064	+	2.44064i	0.139981	+	0.139981i
$305$	7.59422	−	7.59422i	0.434844	−	0.434844i
$306$	−8.02984	−	8.02984i	−0.459035	−	0.459035i
$307$	17.4439	−	17.4439i	0.995577	−	0.995577i	−0.00441361	−	0.999990i	$-0.501405\pi$
$307$	17.4439	−	17.4439i	0.995577	−	0.995577i	0.999990	+	0.00441361i	$0.00140490\pi$
$308$			0.589406i			0.0335845i
$309$	66.5642			3.78670
$310$	−5.78178	−	4.69610i	−0.328383	−	0.266721i
$311$			18.2771i			1.03640i	0.855260	+	0.518199i	$0.173397\pi$
$311$			18.2771i			1.03640i	−0.855260	+	0.518199i	$0.826603\pi$
$312$	8.58497	−	27.7018i	0.486028	−	1.56831i
$313$			20.9353i			1.18333i	0.806182	+	0.591667i	$0.201530\pi$
$313$			20.9353i			1.18333i	−0.806182	+	0.591667i	$0.798470\pi$
$314$	9.00025	+	9.00025i	0.507913	+	0.507913i
$315$	29.7343			1.67534
$316$	12.9503			0.728514
$317$	−5.49631	−	5.49631i	−0.308704	−	0.308704i	0.535703	−	0.844407i	$-0.320047\pi$
$317$	−5.49631	−	5.49631i	−0.308704	−	0.308704i	−0.844407	+	0.535703i	$0.820047\pi$
$318$	10.1997	+	10.1997i	0.571971	+	0.571971i
$319$	1.02952	−	1.02952i	0.0576423	−	0.0576423i
$320$	1.11063	−	1.11063i	0.0620858	−	0.0620858i
$321$			36.4618i			2.03510i
$322$	2.55798			0.142551
$323$	3.19271	+	3.19271i	0.177647	+	0.177647i
$324$		−	58.9407i		−	3.27448i
$325$	−3.11092	+	1.63892i	−0.172563	+	0.0909108i
$326$	4.16299			0.230567
$327$	26.8982	−	26.8982i	1.48747	−	1.48747i
$328$	−5.44000			−0.300374
$329$			15.3611i			0.846886i
$330$	−0.698375	−	0.698375i	−0.0384443	−	0.0384443i
$331$	3.55420	−	3.55420i	0.195357	−	0.195357i	−0.602649	−	0.798006i	$-0.705888\pi$
$331$	3.55420	−	3.55420i	0.195357	−	0.195357i	0.798006	+	0.602649i	$0.205888\pi$
$332$	14.4174	+	14.4174i	0.791258	+	0.791258i
$333$	18.0270	+	18.0270i	0.987875	+	0.987875i
$334$			7.71854i			0.422340i
$335$		−	14.4697i		−	0.790563i
$336$	−6.39079	−	6.39079i	−0.348646	−	0.348646i
$337$	22.2860			1.21400			0.606998	−	0.794704i	$-0.292374\pi$
$337$	22.2860			1.21400			0.606998	+	0.794704i	$0.292374\pi$
$338$	8.52210	−	1.58916i	0.463541	−	0.0864387i
$339$		−	29.6990i		−	1.61303i
$340$	−4.41488	+	4.41488i	−0.239430	+	0.239430i
$341$	1.20510	−	0.124868i	0.0652599	−	0.00676196i
$342$		−	12.8058i		−	0.692461i
$343$	−13.5054	−	13.5054i	−0.729224	−	0.729224i
$344$	−8.16622	+	8.16622i	−0.440293	+	0.440293i
$345$	10.6008	−	10.6008i	0.570728	−	0.570728i
$346$	−6.63390	+	6.63390i	−0.356641	+	0.356641i
$347$		−	18.6240i		−	0.999786i	−0.866087	−	0.499893i	$-0.833373\pi$
$347$		−	18.6240i		−	0.999786i	0.866087	−	0.499893i	$-0.166627\pi$
$348$			35.3065i			1.89263i
$349$	14.2269	−	14.2269i	0.761551	−	0.761551i	−0.215052	−	0.976603i	$-0.568992\pi$
$349$	14.2269	−	14.2269i	0.761551	−	0.761551i	0.976603	+	0.215052i	$0.0689921\pi$
$350$		−	1.13257i		−	0.0605385i
$351$	59.6370	−	31.4184i	3.18319	−	1.67699i
$352$			1.25376i			0.0668257i
$353$	8.24278	−	8.24278i	0.438719	−	0.438719i	−0.452862	−	0.891581i	$-0.649597\pi$
$353$	8.24278	−	8.24278i	0.438719	−	0.438719i	0.891581	+	0.452862i	$0.149597\pi$
$354$			23.4853i			1.24823i
$355$			20.8951i			1.10899i
$356$	−3.56130	+	3.56130i	−0.188749	+	0.188749i
$357$	−8.36006	−	8.36006i	−0.442461	−	0.442461i
$358$	−11.0266	−	11.0266i	−0.582775	−	0.582775i
$359$	−0.624529	+	0.624529i	−0.0329614	+	0.0329614i	−0.723395	−	0.690434i	$-0.757420\pi$
$359$	−0.624529	+	0.624529i	−0.0329614	+	0.0329614i	0.690434	+	0.723395i	$0.257420\pi$
$360$	40.4787			2.13342
$361$		−	13.9083i		−	0.732017i
$362$	−2.32213	−	2.32213i	−0.122048	−	0.122048i
$363$	−37.1591			−1.95035
$364$	2.89096	−	9.32848i	0.151527	−	0.488945i
$365$		−	20.5266i		−	1.07441i
$366$	8.56415	+	8.56415i	0.447655	+	0.447655i
$367$		−	22.2312i		−	1.16046i	−0.814454	−	0.580229i	$-0.802963\pi$
$367$		−	22.2312i		−	1.16046i	0.814454	−	0.580229i	$-0.197037\pi$
$368$	−3.36920			−0.175632
$369$	−13.8080	−	13.8080i	−0.718818	−	0.718818i
$370$	−2.83379	+	2.83379i	−0.147322	+	0.147322i
$371$	7.85145	+	7.85145i	0.407627	+	0.407627i
$372$	−18.5228	+	22.8050i	−0.960360	+	1.18238i
$373$	5.53621			0.286654			0.143327	−	0.989675i	$-0.454220\pi$
$373$	5.53621			0.286654			0.143327	+	0.989675i	$0.454220\pi$
$374$			0.290356i			0.0150140i
$375$	−28.7578	−	28.7578i	−1.48505	−	1.48505i
$376$			20.9119i			1.07845i
$377$	−21.3439	+	11.2445i	−1.09927	+	0.579122i
$378$			21.7116i			1.11673i
$379$	−5.42896	−	5.42896i	−0.278867	−	0.278867i	0.553790	−	0.832657i	$-0.313181\pi$
$379$	−5.42896	−	5.42896i	−0.278867	−	0.278867i	−0.832657	+	0.553790i	$0.813181\pi$
$380$	−7.04076			−0.361183
$381$			61.5743i			3.15454i
$382$	−7.60625	−	7.60625i	−0.389170	−	0.389170i
$383$	−5.07544	+	5.07544i	−0.259343	+	0.259343i	−0.824787	−	0.565444i	$-0.808705\pi$
$383$	−5.07544	+	5.07544i	−0.259343	+	0.259343i	0.565444	+	0.824787i	$0.308705\pi$
$384$	−26.3924	−	26.3924i	−1.34683	−	1.34683i
$385$	−0.537590	−	0.537590i	−0.0273981	−	0.0273981i
$386$	1.32940			0.0676648
$387$	−41.4557			−2.10731
$388$	16.7495	−	16.7495i	0.850328	−	0.850328i
$389$	−16.9100			−0.857369			−0.428685	−	0.903454i	$-0.641023\pi$
$389$	−16.9100			−0.857369			−0.428685	+	0.903454i	$0.641023\pi$
$390$	7.62770	+	14.4786i	0.386243	+	0.733151i
$391$	−4.40739			−0.222891
$392$	−6.65050	−	6.65050i	−0.335901	−	0.335901i
$393$		−	8.73429i		−	0.440586i
$394$	8.47995			0.427214
$395$	−11.8119	+	11.8119i	−0.594319	+	0.594319i
$396$	−2.03665	+	2.03665i	−0.102346	+	0.102346i
$397$	14.6353	−	14.6353i	0.734524	−	0.734524i	−0.236989	−	0.971512i	$-0.576160\pi$
$397$	14.6353	−	14.6353i	0.734524	−	0.734524i	0.971512	+	0.236989i	$0.0761604\pi$
$398$	−4.78581	−	4.78581i	−0.239891	−	0.239891i
$399$		−	13.3325i		−	0.667458i
$400$			1.49175i			0.0745874i
$401$	17.3672	+	17.3672i	0.867278	+	0.867278i	0.992170	−	0.124893i	$-0.0398586\pi$
$401$	17.3672	+	17.3672i	0.867278	+	0.867278i	−0.124893	+	0.992170i	$0.539859\pi$
$402$	16.3177			0.813855
$403$	−19.6855	−	3.93459i	−0.980605	−	0.195996i
$404$	−18.0595			−0.898495
$405$	53.7592	+	53.7592i	2.67131	+	2.67131i
$406$		−	7.77052i		−	0.385644i
$407$		−	0.651851i		−	0.0323111i
$408$	−11.3810	−	11.3810i	−0.563442	−	0.563442i
$409$	1.80417	−	1.80417i	0.0892105	−	0.0892105i	−0.661093	−	0.750304i	$-0.729907\pi$
$409$	1.80417	−	1.80417i	0.0892105	−	0.0892105i	0.750304	+	0.661093i	$0.229907\pi$
$410$	2.17058	−	2.17058i	0.107197	−	0.107197i
$411$	16.9002	−	16.9002i	0.833627	−	0.833627i
$412$	30.5150			1.50337
$413$			18.0784i			0.889578i
$414$	8.83894	+	8.83894i	0.434410	+	0.434410i
$415$	−26.2999			−1.29101
$416$	6.14953	−	19.8432i	0.301506	−	0.972892i
$417$	−35.0056			−1.71423
$418$	−0.231527	+	0.231527i	−0.0113244	+	0.0113244i
$419$	6.62543			0.323674			0.161837	−	0.986818i	$-0.448258\pi$
$419$	6.62543			0.323674			0.161837	+	0.986818i	$0.448258\pi$
$420$	18.4361			0.899591
$421$	−9.87369	−	9.87369i	−0.481214	−	0.481214i	0.424305	−	0.905519i	$-0.360518\pi$
$421$	−9.87369	−	9.87369i	−0.481214	−	0.481214i	−0.905519	+	0.424305i	$0.860518\pi$
$422$	7.18464	+	7.18464i	0.349743	+	0.349743i
$423$	−53.0794	+	53.0794i	−2.58081	+	2.58081i
$424$	10.6886	+	10.6886i	0.519083	+	0.519083i
$425$			1.95142i			0.0946576i
$426$	−23.5638			−1.14167
$427$	6.59245	+	6.59245i	0.319031	+	0.319031i
$428$			16.7152i			0.807957i
$429$	−2.54253	−	0.787946i	−0.122754	−	0.0380424i
$430$		−	6.51671i		−	0.314264i
$431$	19.0927	+	19.0927i	0.919662	+	0.919662i	0.997005	−	0.0773423i	$-0.0246434\pi$
$431$	19.0927	+	19.0927i	0.919662	+	0.919662i	−0.0773423	+	0.997005i	$0.524643\pi$
$432$		−	28.5971i		−	1.37588i
$433$	−18.9092			−0.908717			−0.454358	−	0.890819i	$-0.650131\pi$
$433$	−18.9092			−0.908717			−0.454358	+	0.890819i	$0.650131\pi$
$434$	4.07663	−	5.01909i	0.195684	−	0.240924i
$435$	−32.2026	−	32.2026i	−1.54400	−	1.54400i
$436$	12.3309	−	12.3309i	0.590544	−	0.590544i
$437$	−3.51441	−	3.51441i	−0.168117	−	0.168117i
$438$	23.1482			1.10606
$439$		−	11.4178i		−	0.544944i	−0.962164	−	0.272472i	$-0.912159\pi$
$439$		−	11.4178i		−	0.544944i	0.962164	−	0.272472i	$-0.0878412\pi$
$440$	−0.731848	−	0.731848i	−0.0348895	−	0.0348895i
$441$		−	33.7611i		−	1.60767i
$442$	1.42416	−	4.59545i	0.0677404	−	0.218583i
$443$	35.9497			1.70802			0.854012	−	0.520254i	$-0.174163\pi$
$443$	35.9497			1.70802			0.854012	+	0.520254i	$0.174163\pi$
$444$	11.1773	+	11.1773i	0.530451	+	0.530451i
$445$		−	6.49644i		−	0.307961i
$446$	2.83358			0.134174
$447$	−0.503365	+	0.503365i	−0.0238083	+	0.0238083i
$448$	0.964120	+	0.964120i	0.0455504	+	0.0455504i
$449$	−6.31211	−	6.31211i	−0.297887	−	0.297887i	0.542299	−	0.840186i	$-0.317554\pi$
$449$	−6.31211	−	6.31211i	−0.297887	−	0.297887i	−0.840186	+	0.542299i	$0.817554\pi$
$450$	3.91353	−	3.91353i	0.184486	−	0.184486i
$451$			0.499294i			0.0235108i
$452$		−	13.6149i		−	0.640392i
$453$	19.1529	−	19.1529i	0.899884	−	0.899884i
$454$		−	15.2009i		−	0.713415i
$455$	5.87159	+	11.1452i	0.275265	+	0.522496i
$456$		−	18.1502i		−	0.849959i
$457$	16.0328	−	16.0328i	0.749982	−	0.749982i	−0.224493	−	0.974476i	$-0.572073\pi$
$457$	16.0328	−	16.0328i	0.749982	−	0.749982i	0.974476	+	0.224493i	$0.0720727\pi$
$458$		−	11.7876i		−	0.550799i
$459$		−	37.4090i		−	1.74610i
$460$	4.85973	−	4.85973i	0.226586	−	0.226586i
$461$	−6.99615	+	6.99615i	−0.325843	+	0.325843i	−0.851003	−	0.525160i	$-0.824005\pi$
$461$	−6.99615	+	6.99615i	−0.325843	+	0.325843i	0.525160	+	0.851003i	$0.324005\pi$
$462$	0.606251	−	0.606251i	0.0282054	−	0.0282054i
$463$	−12.7641	−	12.7641i	−0.593200	−	0.593200i	0.345295	−	0.938494i	$-0.387779\pi$
$463$	−12.7641	−	12.7641i	−0.593200	−	0.593200i	−0.938494	+	0.345295i	$0.887779\pi$
$464$			10.2348i			0.475138i
$465$	−3.90576	−	37.6946i	−0.181125	−	1.74804i
$466$	−3.51608	+	3.51608i	−0.162879	+	0.162879i
$467$			12.0123i			0.555861i	0.960601	+	0.277931i	$0.0896485\pi$
$467$			12.0123i			0.555861i	−0.960601	+	0.277931i	$0.910351\pi$
$468$	42.2235	−	22.2445i	1.95178	−	1.02825i
$469$	12.5609			0.580011
$470$	−8.34392	−	8.34392i	−0.384876	−	0.384876i
$471$			64.7575i			2.98387i
$472$			24.6110i			1.13281i
$473$	0.749512	+	0.749512i	0.0344626	+	0.0344626i
$474$	−13.3205	−	13.3205i	−0.611829	−	0.611829i
$475$	−1.55604	+	1.55604i	−0.0713961	+	0.0713961i
$476$	−3.83250	−	3.83250i	−0.175662	−	0.175662i
$477$			54.2604i			2.48441i
$478$	3.24491			0.148419
$479$	11.9809	−	11.9809i	0.547421	−	0.547421i	−0.378273	−	0.925694i	$-0.623482\pi$
$479$	11.9809	−	11.9809i	0.547421	−	0.547421i	0.925694	+	0.378273i	$0.123482\pi$
$480$	39.2166			1.78998
$481$	−3.19724	+	10.3168i	−0.145782	+	0.470405i
$482$			11.3240i			0.515793i
$483$	9.20243	+	9.20243i	0.418725	+	0.418725i
$484$	−17.0348			−0.774311
$485$			30.5541i			1.38739i
$486$	−34.1790	+	34.1790i	−1.55039	+	1.55039i
$487$	22.6533	−	22.6533i	1.02652	−	1.02652i	0.0268792	−	0.999639i	$-0.491443\pi$
$487$	22.6533	−	22.6533i	1.02652	−	1.02652i	0.999639	−	0.0268792i	$-0.00855693\pi$
$488$	8.97463	+	8.97463i	0.406262	+	0.406262i
$489$	14.9765	+	14.9765i	0.677261	+	0.677261i
$490$	5.30715			0.239753
$491$	−11.8012			−0.532582			−0.266291	−	0.963893i	$-0.585798\pi$
$491$	−11.8012			−0.532582			−0.266291	+	0.963893i	$0.585798\pi$
$492$	−8.56139	−	8.56139i	−0.385977	−	0.385977i
$493$			13.3886i			0.602991i
$494$	4.79998	−	2.52876i	0.215961	−	0.113774i
$495$		−	3.71522i		−	0.166987i
$496$	−5.36946	+	6.61080i	−0.241096	+	0.296834i
$497$	−18.1387			−0.813634
$498$		−	29.6589i		−	1.32905i
$499$	4.98799	−	4.98799i	0.223293	−	0.223293i	−0.586591	−	0.809884i	$-0.699530\pi$
$499$	4.98799	−	4.98799i	0.223293	−	0.223293i	0.809884	+	0.586591i	$0.199530\pi$
$500$	−13.1834	−	13.1834i	−0.589581	−	0.589581i
$501$	−27.7677	+	27.7677i	−1.24057	+	1.24057i
$502$	−9.15780	−	9.15780i	−0.408733	−	0.408733i
$503$	3.21405			0.143307			0.0716536	−	0.997430i	$-0.477172\pi$
$503$	3.21405			0.143307			0.0716536	+	0.997430i	$0.477172\pi$
$504$			35.1391i			1.56522i
$505$	16.4719	−	16.4719i	0.732989	−	0.732989i
$506$		−	0.319613i		−	0.0142085i
$507$	36.3756	+	24.9415i	1.61550	+	1.10769i
$508$			28.2275i			1.25239i
$509$	−20.7161	+	20.7161i	−0.918225	+	0.918225i	−0.996900	−	0.0786756i	$-0.974931\pi$
$509$	−20.7161	+	20.7161i	−0.918225	+	0.918225i	0.0786756	+	0.996900i	$0.474931\pi$
$510$	9.08210			0.402162
$511$	17.8189			0.788261
$512$	−11.3607	−	11.3607i	−0.502077	−	0.502077i
$513$	29.8296	−	29.8296i	1.31701	−	1.31701i
$514$	0.719648	−	0.719648i	0.0317423	−	0.0317423i
$515$	−27.8324	+	27.8324i	−1.22644	+	1.22644i
$516$	−25.7038			−1.13155
$517$	1.91933			0.0844122
$518$	−2.45998	−	2.45998i	−0.108085	−	0.108085i
$519$	−47.7314			−2.09518
$520$	7.99329	+	15.1725i	0.350529	+	0.665359i
$521$	24.4942			1.07311			0.536555	−	0.843866i	$-0.319726\pi$
$521$	24.4942			1.07311			0.536555	+	0.843866i	$0.319726\pi$
$522$	26.8505	−	26.8505i	1.17522	−	1.17522i
$523$			20.7846i			0.908847i	0.890786	+	0.454424i	$0.150155\pi$
$523$			20.7846i			0.908847i	−0.890786	+	0.454424i	$0.849845\pi$
$524$		−	4.00406i		−	0.174918i
$525$	4.07447	−	4.07447i	0.177825	−	0.177825i
$526$	9.75382	−	9.75382i	0.425287	−	0.425287i
$527$	−7.02401	+	8.64787i	−0.305971	+	0.376707i
$528$	−0.798513	+	0.798513i	−0.0347508	+	0.0347508i
$529$	−18.1485			−0.789066
$530$	−8.52957			−0.370501
$531$	−62.4686	+	62.4686i	−2.71091	+	2.71091i
$532$		−	6.11200i		−	0.264989i
$533$	2.44897	−	7.90229i	0.106077	−	0.342286i
$534$	7.32617			0.317034
$535$	−15.2457	−	15.2457i	−0.659129	−	0.659129i
$536$	17.0998			0.738601
$537$		−	79.3373i		−	3.42366i
$538$	−5.25241	+	5.25241i	−0.226448	+	0.226448i
$539$	−0.610396	+	0.610396i	−0.0262916	+	0.0262916i
$540$	41.2484	+	41.2484i	1.77505	+	1.77505i
$541$	10.8200	−	10.8200i	0.465187	−	0.465187i	−0.435164	−	0.900351i	$-0.643310\pi$
$541$	10.8200	−	10.8200i	0.465187	−	0.465187i	0.900351	+	0.435164i	$0.143310\pi$
$542$		−	18.8740i		−	0.810707i
$543$		−	16.7079i		−	0.717004i
$544$	−8.15234	−	8.15234i	−0.349529	−	0.349529i
$545$			22.4938i			0.963528i
$546$	−12.5687	+	6.62151i	−0.537890	+	0.283374i
$547$	9.67781			0.413793			0.206897	−	0.978363i	$-0.433664\pi$
$547$	9.67781			0.413793			0.206897	+	0.978363i	$0.433664\pi$
$548$	7.74757	−	7.74757i	0.330960	−	0.330960i
$549$			45.5596i			1.94443i
$550$	−0.141512			−0.00603409
$551$	−10.6759	+	10.6759i	−0.454809	+	0.454809i
$552$	12.5277	+	12.5277i	0.533216	+	0.533216i
$553$	−10.2537	−	10.2537i	−0.436033	−	0.436033i
$554$	4.59594	+	4.59594i	0.195263	+	0.195263i
$555$	−20.3894			−0.865480
$556$	−16.0476			−0.680570
$557$	−19.2333	−	19.2333i	−0.814942	−	0.814942i	0.170428	−	0.985370i	$-0.445485\pi$
$557$	−19.2333	−	19.2333i	−0.814942	−	0.814942i	−0.985370	+	0.170428i	$0.945485\pi$
$558$	31.4297	−	3.25661i	1.33052	−	0.137863i
$559$	−8.18622	−	15.5387i	−0.346240	−	0.657219i
$560$	5.34434			0.225840
$561$	−1.04457	+	1.04457i	−0.0441017	+	0.0441017i
$562$	−4.16109			−0.175525
$563$			34.4267i			1.45091i	0.688267	+	0.725457i	$0.258372\pi$
$563$			34.4267i			1.45091i	−0.688267	+	0.725457i	$0.741628\pi$
$564$	−32.9108	+	32.9108i	−1.38579	+	1.38579i
$565$	12.4180	+	12.4180i	0.522430	+	0.522430i
$566$	−10.8260	+	10.8260i	−0.455051	+	0.455051i
$567$	−46.6677	+	46.6677i	−1.95986	+	1.95986i
$568$	−24.6932			−1.03610
$569$	5.70178			0.239031			0.119515	−	0.992832i	$-0.461866\pi$
$569$	5.70178			0.239031			0.119515	+	0.992832i	$0.461866\pi$
$570$	7.24199	+	7.24199i	0.303333	+	0.303333i
$571$	−4.48395			−0.187647			−0.0938237	−	0.995589i	$-0.529909\pi$
$571$	−4.48395			−0.187647			−0.0938237	+	0.995589i	$0.529909\pi$
$572$	−1.16557	−	0.361218i	−0.0487349	−	0.0151033i
$573$		−	54.7275i		−	2.28628i
$574$	1.88426	+	1.88426i	0.0786473	+	0.0786473i
$575$		−	2.14805i		−	0.0895797i
$576$			6.66291i			0.277621i
$577$	−10.3382	−	10.3382i	−0.430386	−	0.430386i	0.458374	−	0.888760i	$-0.348432\pi$
$577$	−10.3382	−	10.3382i	−0.430386	−	0.430386i	−0.888760	+	0.458374i	$0.848432\pi$
$578$	6.12805	+	6.12805i	0.254893	+	0.254893i
$579$	4.78257	+	4.78257i	0.198757	+	0.198757i
$580$	−14.7626	−	14.7626i	−0.612986	−	0.612986i
$581$		−	22.8306i		−	0.947174i
$582$	−34.4565			−1.42827
$583$	0.981018	−	0.981018i	0.0406296	−	0.0406296i
$584$	24.2577			1.00379
$585$	−18.2227	+	58.8005i	−0.753414	+	2.43110i
$586$	17.8727			0.738315
$587$	28.2063	−	28.2063i	1.16420	−	1.16420i	0.180653	−	0.983547i	$-0.442179\pi$
$587$	28.2063	−	28.2063i	1.16420	−	1.16420i	0.983547	−	0.180653i	$-0.0578211\pi$
$588$		−	20.9329i		−	0.863259i
$589$	−12.4966	+	1.29485i	−0.514914	+	0.0533533i
$590$	−9.81987	−	9.81987i	−0.404278	−	0.404278i
$591$	30.5070	+	30.5070i	1.25489	+	1.25489i
$592$	3.24012	+	3.24012i	0.133168	+	0.133168i
$593$	12.8593	−	12.8593i	0.528067	−	0.528067i	−0.391928	−	0.919996i	$-0.628192\pi$
$593$	12.8593	−	12.8593i	0.528067	−	0.528067i	0.919996	+	0.391928i	$0.128192\pi$
$594$	2.71281			0.111308
$595$	6.99116			0.286610
$596$	−0.230757	+	0.230757i	−0.00945219	+	0.00945219i
$597$		−	34.4342i		−	1.40930i
$598$	−1.56766	+	5.05849i	−0.0641064	+	0.206857i
$599$	−19.4629			−0.795234			−0.397617	−	0.917551i	$-0.630163\pi$
$599$	−19.4629			−0.795234			−0.397617	+	0.917551i	$0.630163\pi$
$600$	5.54678	−	5.54678i	0.226446	−	0.226446i
$601$			9.52833i			0.388669i	0.980935	+	0.194334i	$0.0622547\pi$
$601$			9.52833i			0.388669i	−0.980935	+	0.194334i	$0.937745\pi$
$602$	5.65708			0.230565
$603$	43.4035	+	43.4035i	1.76753	+	1.76753i
$604$	8.78028	−	8.78028i	0.357264	−	0.357264i
$605$	15.5373	−	15.5373i	0.631680	−	0.631680i
$606$	18.5757	+	18.5757i	0.754585	+	0.754585i
$607$	−8.34524			−0.338723			−0.169361	−	0.985554i	$-0.554171\pi$
$607$	−8.34524			−0.338723			−0.169361	+	0.985554i	$0.554171\pi$
$608$		−	13.0012i		−	0.527268i
$609$	27.9547	−	27.9547i	1.13278	−	1.13278i
$610$	−7.16183			−0.289974
$611$	−30.3771	−	9.41407i	−1.22893	−	0.380853i
$612$		−	26.4859i		−	1.07063i
$613$	−27.5204	+	27.5204i	−1.11154	+	1.11154i	−0.118598	+	0.992942i	$0.537840\pi$
$613$	−27.5204	+	27.5204i	−1.11154	+	1.11154i	−0.992942	+	0.118598i	$0.962160\pi$
$614$	−16.4507			−0.663897
$615$	15.6175			0.629758
$616$	0.635309	−	0.635309i	0.0255973	−	0.0255973i
$617$	2.44147	+	2.44147i	0.0982899	+	0.0982899i	0.754542	−	0.656252i	$-0.227859\pi$
$617$	2.44147	+	2.44147i	0.0982899	+	0.0982899i	−0.656252	+	0.754542i	$0.727859\pi$
$618$	−31.3871	−	31.3871i	−1.26258	−	1.26258i
$619$	−9.60323	−	9.60323i	−0.385987	−	0.385987i	0.487267	−	0.873253i	$-0.337994\pi$
$619$	−9.60323	−	9.60323i	−0.385987	−	0.385987i	−0.873253	+	0.487267i	$0.837994\pi$
$620$	−1.79051	−	17.2803i	−0.0719088	−	0.693993i
$621$			41.1784i			1.65243i
$622$	8.61822	−	8.61822i	0.345559	−	0.345559i
$623$	5.63948			0.225941
$624$	16.5546	−	8.72140i	0.662714	−	0.349135i
$625$	19.1728			0.766912
$626$	9.87167	−	9.87167i	0.394551	−	0.394551i
$627$	−1.66586			−0.0665279
$628$			29.6867i			1.18463i
$629$	4.23854	+	4.23854i	0.169002	+	0.169002i
$630$	−14.0206	−	14.0206i	−0.558596	−	0.558596i
$631$	−28.3201	−	28.3201i	−1.12740	−	1.12740i	−0.990598	−	0.136806i	$-0.956316\pi$
$631$	−28.3201	−	28.3201i	−1.12740	−	1.12740i	−0.136806	−	0.990598i	$-0.543684\pi$
$632$	−13.9589	−	13.9589i	−0.555256	−	0.555256i
$633$			51.6940i			2.05465i
$634$			5.18337i			0.205858i
$635$	−25.7459	−	25.7459i	−1.02170	−	1.02170i
$636$			33.6430i			1.33403i
$637$	12.6546	−	6.66678i	0.501394	−	0.264147i
$638$	−0.970906			−0.0384385
$639$	−62.6773	−	62.6773i	−2.47947	−	2.47947i
$640$	22.0708			0.872425
$641$	−41.7500			−1.64903			−0.824513	−	0.565842i	$-0.808551\pi$
$641$	−41.7500			−1.64903			−0.824513	+	0.565842i	$0.808551\pi$
$642$	17.1929	−	17.1929i	0.678549	−	0.678549i
$643$	−1.57363	+	1.57363i	−0.0620579	+	0.0620579i	−0.737455	−	0.675397i	$-0.763972\pi$
$643$	−1.57363	+	1.57363i	−0.0620579	+	0.0620579i	0.675397	+	0.737455i	$0.263972\pi$
$644$	4.21867	+	4.21867i	0.166239	+	0.166239i
$645$	23.4441	−	23.4441i	0.923111	−	0.923111i
$646$		−	3.01093i		−	0.118463i
$647$	−11.9760			−0.470823			−0.235412	−	0.971896i	$-0.575644\pi$
$647$	−11.9760			−0.470823			−0.235412	+	0.971896i	$0.575644\pi$
$648$	−63.5310	+	63.5310i	−2.49573	+	2.49573i
$649$	2.25884			0.0886673
$650$	2.23970	+	0.694097i	0.0878482	+	0.0272247i
$651$	32.7222	−	3.39054i	1.28248	−	0.132886i
$652$	6.86568	+	6.86568i	0.268881	+	0.268881i
$653$	−46.6935			−1.82726			−0.913629	−	0.406550i	$-0.866732\pi$
$653$	−46.6935			−1.82726			−0.913629	+	0.406550i	$0.866732\pi$
$654$	−25.3667			−0.991915
$655$	3.65205	+	3.65205i	0.142698	+	0.142698i
$656$	−2.48181	−	2.48181i	−0.0968985	−	0.0968985i
$657$	61.5720	+	61.5720i	2.40215	+	2.40215i
$658$	7.24326	−	7.24326i	0.282372	−	0.282372i
$659$	−3.37897			−0.131626			−0.0658131	−	0.997832i	$-0.520964\pi$
$659$	−3.37897			−0.131626			−0.0658131	+	0.997832i	$0.520964\pi$
$660$		−	2.30355i		−	0.0896654i
$661$	−22.3469	+	22.3469i	−0.869196	+	0.869196i	−0.992383	−	0.123188i	$-0.960688\pi$
$661$	−22.3469	+	22.3469i	−0.869196	+	0.869196i	0.123188	+	0.992383i	$0.460688\pi$
$662$	−3.35184			−0.130273
$663$	21.6558	−	11.4088i	0.841040	−	0.443082i
$664$		−	31.0805i		−	1.20616i
$665$	5.57468	+	5.57468i	0.216177	+	0.216177i
$666$		−	17.0006i		−	0.658761i
$667$		−	14.7376i		−	0.570643i
$668$	−12.7295	+	12.7295i	−0.492521	+	0.492521i
$669$	10.1939	+	10.1939i	0.394120	+	0.394120i
$670$	−6.82291	+	6.82291i	−0.263592	+	0.263592i
$671$	0.823709	−	0.823709i	0.0317989	−	0.0317989i
$672$			34.0434i			1.31325i
$673$	−9.88983			−0.381225			−0.190613	−	0.981665i	$-0.561047\pi$
$673$	−9.88983			−0.381225			−0.190613	+	0.981665i	$0.561047\pi$
$674$	−10.5085	−	10.5085i	−0.404774	−	0.404774i
$675$	18.2322			0.701757
$676$	16.6757	+	11.4339i	0.641372	+	0.439767i
$677$			12.9528i			0.497815i	0.968527	+	0.248908i	$0.0800715\pi$
$677$			12.9528i			0.497815i	−0.968527	+	0.248908i	$0.919928\pi$
$678$	−14.0040	+	14.0040i	−0.537822	+	0.537822i
$679$	−26.5236			−1.01788
$680$	9.51741			0.364976
$681$	54.6859	−	54.6859i	2.09557	−	2.09557i
$682$	−0.627122	−	0.509364i	−0.0240137	−	0.0195046i
$683$	20.2919	−	20.2919i	0.776449	−	0.776449i	−0.202776	−	0.979225i	$-0.564996\pi$
$683$	20.2919	−	20.2919i	0.776449	−	0.776449i	0.979225	+	0.202776i	$0.0649963\pi$
$684$	21.1196	−	21.1196i	0.807529	−	0.807529i
$685$			14.1329i			0.539992i
$686$			12.7365i			0.486281i
$687$	42.4064	−	42.4064i	1.61790	−	1.61790i
$688$	−7.45112			−0.284071
$689$	−20.3383	+	10.7147i	−0.774826	+	0.408199i
$690$	−9.99723			−0.380588
$691$	−12.1507	−	12.1507i	−0.462235	−	0.462235i	0.437152	−	0.899387i	$-0.355987\pi$
$691$	−12.1507	−	12.1507i	−0.462235	−	0.462235i	−0.899387	+	0.437152i	$0.855987\pi$
$692$	−21.8815			−0.831809
$693$	3.22514			0.122513
$694$	−8.78178	+	8.78178i	−0.333352	+	0.333352i
$695$	14.6368	−	14.6368i	0.555207	−	0.555207i
$696$	38.0561	−	38.0561i	1.44251	−	1.44251i
$697$	−3.24656	−	3.24656i	−0.122972	−	0.122972i
$698$	−13.4169			−0.507837
$699$	−25.2985			−0.956876
$700$	1.86786	−	1.86786i	0.0705984	−	0.0705984i
$701$		−	10.7311i		−	0.405308i	−0.979250	−	0.202654i	$-0.935043\pi$
$701$		−	10.7311i		−	0.405308i	0.979250	−	0.202654i	$-0.0649567\pi$
$702$	−42.9355	−	13.3060i	−1.62049	−	0.502202i
$703$			6.75954i			0.254941i
$704$	0.120464	−	0.120464i	0.00454017	−	0.00454017i
$705$		−	60.0351i		−	2.26105i
$706$	−7.77347			−0.292558
$707$	14.2990	+	14.2990i	0.537771	+	0.537771i
$708$	−38.7324	+	38.7324i	−1.45565	+	1.45565i
$709$	−22.4253	−	22.4253i	−0.842199	−	0.842199i	0.146946	−	0.989145i	$-0.453056\pi$
$709$	−22.4253	−	22.4253i	−0.842199	−	0.842199i	−0.989145	+	0.146946i	$0.953056\pi$
$710$	9.85268	−	9.85268i	0.369764	−	0.369764i
$711$		−	70.8622i		−	2.65754i
$712$	7.67731			0.287719
$713$	7.73176	−	9.51924i	0.289557	−	0.356498i
$714$			7.88406i			0.295054i
$715$	1.39257	−	0.733640i	0.0520790	−	0.0274366i
$716$		−	36.3706i		−	1.35923i
$717$	11.6737	+	11.6737i	0.435962	+	0.435962i
$718$	0.588970			0.0219802
$719$	10.0526			0.374899			0.187450	−	0.982274i	$-0.439978\pi$
$719$	10.0526			0.374899			0.187450	+	0.982274i	$0.439978\pi$
$720$	18.4670	+	18.4670i	0.688226	+	0.688226i
$721$	−24.1610	−	24.1610i	−0.899801	−	0.899801i
$722$	−6.55821	+	6.55821i	−0.244071	+	0.244071i
$723$	−40.7384	+	40.7384i	−1.51508	+	1.51508i
$724$		−	7.65939i		−	0.284659i
$725$	−6.52523			−0.242341
$726$	17.5217	+	17.5217i	0.650291	+	0.650291i
$727$			1.70021i			0.0630573i	0.999503	+	0.0315286i	$0.0100375\pi$
$727$			1.70021i			0.0630573i	−0.999503	+	0.0315286i	$0.989962\pi$
$728$	−13.1711	+	6.93888i	−0.488153	+	0.257172i
$729$	−132.231			−4.89746
$730$	−9.67893	+	9.67893i	−0.358233	+	0.358233i
$731$	−9.74712			−0.360510
$732$			28.2483i			1.04409i
$733$	18.8815	+	18.8815i	0.697404	+	0.697404i	0.963850	−	0.266446i	$-0.0858495\pi$
$733$	18.8815	+	18.8815i	0.697404	+	0.697404i	−0.266446	+	0.963850i	$0.585849\pi$
$734$	−10.4827	+	10.4827i	−0.386923	+	0.386923i
$735$	19.0927	+	19.0927i	0.704244	+	0.704244i
$736$	8.97378	+	8.97378i	0.330778	+	0.330778i
$737$		−	1.56946i		−	0.0578117i
$738$			13.0218i			0.479341i
$739$	6.21786	+	6.21786i	0.228728	+	0.228728i	0.812161	−	0.583433i	$-0.198291\pi$
$739$	6.21786	+	6.21786i	0.228728	+	0.228728i	−0.583433	+	0.812161i	$0.698291\pi$
$740$	−9.34708			−0.343606
$741$	26.3654	+	8.17081i	0.968557	+	0.300162i
$742$		−	7.40441i		−	0.271825i
$743$	−23.5703	+	23.5703i	−0.864709	+	0.864709i	−0.991881	−	0.127172i	$-0.959410\pi$
$743$	−23.5703	+	23.5703i	−0.864709	+	0.864709i	0.127172	+	0.991881i	$0.459410\pi$
$744$	44.5463	−	4.61571i	1.63315	−	0.169220i
$745$		−	0.420942i		−	0.0154221i
$746$	−2.61050	−	2.61050i	−0.0955771	−	0.0955771i
$747$	78.8897	−	78.8897i	2.88642	−	2.88642i
$748$	−0.478861	+	0.478861i	−0.0175089	+	0.0175089i
$749$	13.2346	−	13.2346i	0.483582	−	0.483582i
$750$			27.1204i			0.990299i
$751$		−	0.125372i		−	0.00457489i	−0.999997	−	0.00228745i	$-0.999272\pi$
$751$		−	0.125372i		−	0.00457489i	0.999997	−	0.00228745i	$-0.000728117\pi$
$752$	−9.54032	+	9.54032i	−0.347900	+	0.347900i
$753$		−	65.8910i		−	2.40120i
$754$	15.3665	+	4.76216i	0.559613	+	0.173428i
$755$			16.0168i			0.582910i
$756$	−35.8072	+	35.8072i	−1.30230	+	1.30230i
$757$		−	22.3019i		−	0.810576i	−0.914189	−	0.405288i	$-0.867171\pi$
$757$		−	22.3019i		−	0.810576i	0.914189	−	0.405288i	$-0.132829\pi$
$758$			5.11985i			0.185961i
$759$	1.14982	−	1.14982i	0.0417358	−	0.0417358i
$760$	7.58909	+	7.58909i	0.275285	+	0.275285i
$761$	36.5552	+	36.5552i	1.32512	+	1.32512i	0.909567	+	0.415558i	$0.136414\pi$
$761$	36.5552	+	36.5552i	1.32512	+	1.32512i	0.415558	+	0.909567i	$0.363586\pi$
$762$	29.0342	−	29.0342i	1.05180	−	1.05180i
$763$	−19.5266			−0.706910
$764$		−	25.0887i		−	0.907678i
$765$	24.1575	+	24.1575i	0.873416	+	0.873416i
$766$	4.78646			0.172942
$767$	−35.7505	−	11.0793i	−1.29088	−	0.400051i
$768$			30.2020i			1.08982i
$769$	25.4412	+	25.4412i	0.917434	+	0.917434i	0.996842	−	0.0794081i	$-0.0253030\pi$
$769$	25.4412	+	25.4412i	0.917434	+	0.917434i	−0.0794081	+	0.996842i	$0.525303\pi$
$770$			0.506982i			0.0182704i
$771$	5.17792			0.186478
$772$	2.19247	+	2.19247i	0.0789088	+	0.0789088i
$773$	−38.8692	+	38.8692i	−1.39803	+	1.39803i	−0.592338	+	0.805689i	$0.701795\pi$
$773$	−38.8692	+	38.8692i	−1.39803	+	1.39803i	−0.805689	+	0.592338i	$0.798205\pi$
$774$	19.5477	+	19.5477i	0.702627	+	0.702627i
$775$	−4.21474	−	3.42332i	−0.151398	−	0.122969i
$776$	−36.1079			−1.29620
$777$		−	17.6998i		−	0.634975i
$778$	7.97358	+	7.97358i	0.285867	+	0.285867i
$779$		−	5.17756i		−	0.185505i
$780$	−11.2986	+	36.4580i	−0.404554	+	1.30541i
$781$			2.26639i			0.0810978i
$782$	2.07822	+	2.07822i	0.0743171	+	0.0743171i
$783$	125.090			4.47035
$784$		−	6.06812i		−	0.216719i
$785$	−27.0769	−	27.0769i	−0.966417	−	0.966417i
$786$	−4.11849	+	4.11849i	−0.146902	+	0.146902i
$787$	32.4230	+	32.4230i	1.15576	+	1.15576i	0.985379	+	0.170377i	$0.0544984\pi$
$787$	32.4230	+	32.4230i	1.15576	+	1.15576i	0.170377	+	0.985379i	$0.445502\pi$
$788$	13.9853	+	13.9853i	0.498205	+	0.498205i
$789$	70.1795			2.49846
$790$	11.1393			0.396319
$791$	−10.7799	+	10.7799i	−0.383290	+	0.383290i
$792$	4.39054			0.156011
$793$	−17.0770	+	8.99660i	−0.606421	+	0.319479i
$794$	−13.8020			−0.489814
$795$	−30.6854	−	30.6854i	−1.08830	−	1.08830i
$796$		−	15.7857i		−	0.559508i
$797$	32.1372			1.13836			0.569179	−	0.822213i	$-0.307261\pi$
$797$	32.1372			1.13836			0.569179	+	0.822213i	$0.307261\pi$
$798$	−6.28668	+	6.28668i	−0.222546	+	0.222546i
$799$	−12.4801	+	12.4801i	−0.441514	+	0.441514i
$800$	3.97323	−	3.97323i	0.140475	−	0.140475i
$801$	19.4869	+	19.4869i	0.688535	+	0.688535i
$802$		−	16.3784i		−	0.578341i
$803$		−	2.22642i		−	0.0785687i
$804$	26.9115	+	26.9115i	0.949095	+	0.949095i
$805$	−7.69560			−0.271234
$806$	7.42705	+	11.1376i	0.261607	+	0.392306i
$807$	−37.7915			−1.33032
$808$	19.4660	+	19.4660i	0.684811	+	0.684811i
$809$		−	24.5469i		−	0.863023i	−0.902108	−	0.431511i	$-0.857980\pi$
$809$		−	24.5469i		−	0.863023i	0.902108	−	0.431511i	$-0.142020\pi$
$810$		−	50.6983i		−	1.78136i
$811$	16.8217	+	16.8217i	0.590690	+	0.590690i	0.937818	−	0.347128i	$-0.112843\pi$
$811$	16.8217	+	16.8217i	0.590690	+	0.590690i	−0.347128	+	0.937818i	$0.612843\pi$
$812$	12.8153	−	12.8153i	0.449728	−	0.449728i
$813$	67.8999	−	67.8999i	2.38135	−	2.38135i
$814$	−0.307368	+	0.307368i	−0.0107733	+	0.0107733i
$815$	−12.5242			−0.438704
$816$		−	10.3844i		−	0.363525i
$817$	−7.77227	−	7.77227i	−0.271917	−	0.271917i
$818$	−1.70145			−0.0594897
$819$	−51.0440	−	15.8189i	−1.78362	−	0.552756i
$820$	7.15952			0.250021
$821$	27.9344	−	27.9344i	0.974917	−	0.974917i	−0.0247756	−	0.999693i	$-0.507887\pi$
$821$	27.9344	−	27.9344i	0.974917	−	0.974917i	0.999693	+	0.0247756i	$0.00788712\pi$
$822$	−15.9380			−0.555901
$823$	−28.9960			−1.01074			−0.505368	−	0.862904i	$-0.668643\pi$
$823$	−28.9960			−1.01074			−0.505368	+	0.862904i	$0.668643\pi$
$824$	−32.8915	−	32.8915i	−1.14583	−	1.14583i
$825$	−0.509095	−	0.509095i	−0.0177244	−	0.0177244i
$826$	8.52451	−	8.52451i	0.296606	−	0.296606i
$827$	30.8342	+	30.8342i	1.07221	+	1.07221i	0.997181	+	0.0750291i	$0.0239050\pi$
$827$	30.8342	+	30.8342i	1.07221	+	1.07221i	0.0750291	+	0.997181i	$0.476095\pi$
$828$			29.1547i			1.01319i
$829$	21.7574			0.755664			0.377832	−	0.925874i	$-0.376670\pi$
$829$	21.7574			0.755664			0.377832	+	0.925874i	$0.376670\pi$
$830$	12.4012	+	12.4012i	0.430453	+	0.430453i
$831$			33.0681i			1.14712i
$832$	−2.49744	+	1.31572i	−0.0865832	+	0.0456143i
$833$		−	7.93796i		−	0.275034i
$834$	16.5063	+	16.5063i	0.571565	+	0.571565i
$835$		−	23.2210i		−	0.803594i
$836$	−0.763678			−0.0264124
$837$	80.7974	+	65.6256i	2.79277	+	2.26835i
$838$	−3.12410	−	3.12410i	−0.107920	−	0.107920i
$839$	2.96916	−	2.96916i	0.102507	−	0.102507i	−0.653993	−	0.756500i	$-0.726908\pi$
$839$	2.96916	−	2.96916i	0.102507	−	0.102507i	0.756500	+	0.653993i	$0.226908\pi$
$840$	−19.8719	−	19.8719i	−0.685647	−	0.685647i
$841$	−15.7692			−0.543767
$842$			9.31151i			0.320896i
$843$	−14.9697	−	14.9697i	−0.515583	−	0.515583i
$844$			23.6981i			0.815721i
$845$	−25.6384	+	4.78092i	−0.881989	+	0.164469i
$846$	50.0572			1.72100
$847$	13.4877	+	13.4877i	0.463444	+	0.463444i
$848$			9.75259i			0.334905i
$849$	−77.8940			−2.67332
$850$	0.920155	−	0.920155i	0.0315610	−	0.0315610i
$851$	−4.66562	−	4.66562i	−0.159935	−	0.159935i
$852$	−38.8618	−	38.8618i	−1.33138	−	1.33138i
$853$	9.67080	−	9.67080i	0.331122	−	0.331122i	−0.521891	−	0.853012i	$-0.674773\pi$
$853$	9.67080	−	9.67080i	0.331122	−	0.331122i	0.853012	+	0.521891i	$0.174773\pi$
$854$		−	6.21709i		−	0.212745i
$855$			38.5259i			1.31756i
$856$	18.0169	−	18.0169i	0.615806	−	0.615806i
$857$			38.1828i			1.30430i	0.758090	+	0.652150i	$0.226133\pi$
$857$			38.1828i			1.30430i	−0.758090	+	0.652150i	$0.773867\pi$
$858$	0.827340	+	1.57042i	0.0282449	+	0.0536134i
$859$			25.2702i			0.862208i	0.902302	+	0.431104i	$0.141876\pi$
$859$			25.2702i			0.862208i	−0.902302	+	0.431104i	$0.858124\pi$
$860$	10.7475	−	10.7475i	0.366486	−	0.366486i
$861$			13.5574i			0.462034i
$862$		−	18.0056i		−	0.613273i
$863$	−2.68597	+	2.68597i	−0.0914315	+	0.0914315i	−0.751343	−	0.659912i	$-0.770594\pi$
$863$	−2.68597	+	2.68597i	−0.0914315	+	0.0914315i	0.659912	+	0.751343i	$0.270594\pi$
$864$	−76.1677	+	76.1677i	−2.59128	+	2.59128i
$865$	19.9579	−	19.9579i	0.678587	−	0.678587i
$866$	8.91627	+	8.91627i	0.302987	+	0.302987i
$867$			44.0918i			1.49743i
$868$	15.0008	−	1.55432i	0.509161	−	0.0527572i
$869$	−1.28118	+	1.28118i	−0.0434609	+	0.0434609i
$870$			30.3691i			1.02961i
$871$	−7.69798	+	24.8397i	−0.260836	+	0.841661i
$872$	−26.5825			−0.900197
$873$	−91.6507	−	91.6507i	−3.10191	−	3.10191i
$874$			3.31431i			0.112108i
$875$			20.8766i			0.705757i
$876$	38.1765	+	38.1765i	1.28986	+	1.28986i
$877$	25.3023	+	25.3023i	0.854397	+	0.854397i	0.990671	−	0.136274i	$-0.0435129\pi$
$877$	25.3023	+	25.3023i	0.854397	+	0.854397i	−0.136274	+	0.990671i	$0.543513\pi$
$878$	−5.38387	+	5.38387i	−0.181697	+	0.181697i
$879$	64.2978	+	64.2978i	2.16871	+	2.16871i
$880$		−	0.667762i		−	0.0225102i
$881$	32.7389			1.10300			0.551501	−	0.834174i	$-0.314055\pi$
$881$	32.7389			1.10300			0.551501	+	0.834174i	$0.314055\pi$
$882$	−15.9194	+	15.9194i	−0.536036	+	0.536036i
$883$	29.1238			0.980094			0.490047	−	0.871696i	$-0.336980\pi$
$883$	29.1238			0.980094			0.490047	+	0.871696i	$0.336980\pi$
$884$	9.92764	−	5.23015i	0.333903	−	0.175909i
$885$		−	70.6547i		−	2.37503i
$886$	−16.9514	−	16.9514i	−0.569495	−	0.569495i
$887$	16.3285			0.548256			0.274128	−	0.961693i	$-0.411611\pi$
$887$	16.3285			0.548256			0.274128	+	0.961693i	$0.411611\pi$
$888$		−	24.0955i		−	0.808594i
$889$	22.3497	−	22.3497i	0.749586	−	0.749586i
$890$	−3.06328	+	3.06328i	−0.102681	+	0.102681i
$891$	5.83100	+	5.83100i	0.195346	+	0.195346i
$892$	4.67319	+	4.67319i	0.156470	+	0.156470i
$893$	−19.9030			−0.666029
$894$	0.474705			0.0158765
$895$	33.1732	+	33.1732i	1.10886	+	1.10886i
$896$			19.1594i			0.640070i
$897$	−23.8378	+	12.5584i	−0.795922	+	0.419313i
$898$			5.95271i			0.198645i
$899$	−28.9171	−	23.4872i	−0.964439	−	0.783341i
$900$	12.9085			0.430284
$901$			12.7578i			0.425023i
$902$	0.235433	−	0.235433i	0.00783906	−	0.00783906i
$903$	20.3516	+	20.3516i	0.677257	+	0.677257i
$904$	−14.6752	+	14.6752i	−0.488091	+	0.488091i
$905$	6.98604	+	6.98604i	0.232224	+	0.232224i
$906$	−18.0624			−0.600084
$907$		−	10.2762i		−	0.341215i	−0.985339	−	0.170607i	$-0.945427\pi$
$907$		−	10.2762i		−	0.341215i	0.985339	−	0.170607i	$-0.0545730\pi$
$908$	25.0696	−	25.0696i	0.831965	−	0.831965i
$909$			98.8188i			3.27761i
$910$	2.48668	−	8.02396i	0.0824326	−	0.265992i
$911$		−	14.5756i		−	0.482911i	−0.970412	−	0.241455i	$-0.922375\pi$
$911$		−	14.5756i		−	0.482911i	0.970412	−	0.241455i	$-0.0776248\pi$
$912$	8.28039	−	8.28039i	0.274191	−	0.274191i
$913$	−2.85263			−0.0944082
$914$	−15.1199			−0.500123
$915$	−25.7649	−	25.7649i	−0.851763	−	0.851763i
$916$	19.4403	−	19.4403i	0.642327	−	0.642327i
$917$	−3.17030	+	3.17030i	−0.104693	+	0.104693i
$918$	−17.6395	+	17.6395i	−0.582192	+	0.582192i
$919$	5.95951			0.196586			0.0982931	−	0.995158i	$-0.468662\pi$
$919$	5.95951			0.196586			0.0982931	+	0.995158i	$0.468662\pi$
$920$	−10.4764			−0.345397
$921$	−59.1820	−	59.1820i	−1.95011	−	1.95011i
$922$	6.59781			0.217287
$923$	11.1163	−	35.8700i	0.365899	−	1.18067i
$924$	1.99968			0.0657846
$925$	−2.06575	+	2.06575i	−0.0679215	+	0.0679215i
$926$			12.0374i			0.395573i
$927$		−	166.973i		−	5.48412i
$928$	27.2601	−	27.2601i	0.894858	−	0.894858i
$929$	14.3822	−	14.3822i	0.471864	−	0.471864i	−0.430653	−	0.902517i	$-0.641717\pi$
$929$	14.3822	−	14.3822i	0.471864	−	0.471864i	0.902517	+	0.430653i	$0.141717\pi$
$930$	−15.9325	+	19.6159i	−0.522447	+	0.643229i
$931$	6.32966	−	6.32966i	0.207446	−	0.207446i
$932$	−11.5976			−0.379891
$933$	62.0087			2.03007
$934$	5.66416	−	5.66416i	0.185337	−	0.185337i
$935$		−	0.873527i		−	0.0285674i
$936$	−69.4887	−	21.5350i	−2.27131	−	0.703893i
$937$	25.1105			0.820324			0.410162	−	0.912013i	$-0.365472\pi$
$937$	25.1105			0.820324			0.410162	+	0.912013i	$0.365472\pi$
$938$	−5.92288	−	5.92288i	−0.193389	−	0.193389i
$939$	71.0274			2.31789
$940$		−	27.5219i		−	0.897665i
$941$	8.42758	−	8.42758i	0.274731	−	0.274731i	−0.556270	−	0.831001i	$-0.687768\pi$
$941$	8.42758	−	8.42758i	0.274731	−	0.274731i	0.831001	+	0.556270i	$0.187768\pi$
$942$	30.5352	−	30.5352i	0.994890	−	0.994890i
$943$	3.57369	+	3.57369i	0.116375	+	0.116375i
$944$	−11.2279	+	11.2279i	−0.365437	+	0.365437i
$945$		−	65.3187i		−	2.12482i
$946$		−	0.706837i		−	0.0229813i
$947$	29.2178	+	29.2178i	0.949452	+	0.949452i	0.998783	−	0.0493304i	$-0.0157087\pi$
$947$	29.2178	+	29.2178i	0.949452	+	0.949452i	−0.0493304	+	0.998783i	$0.515709\pi$
$948$		−	43.9367i		−	1.42700i
$949$	−10.9203	+	35.2374i	−0.354488	+	1.14385i
$950$	1.46745			0.0476102
$951$	−18.6474	+	18.6474i	−0.604682	+	0.604682i
$952$			8.26195i			0.267771i
$953$	1.73942			0.0563455			0.0281727	−	0.999603i	$-0.491031\pi$
$953$	1.73942			0.0563455			0.0281727	+	0.999603i	$0.491031\pi$
$954$	25.5855	−	25.5855i	0.828360	−	0.828360i
$955$	22.8831	+	22.8831i	0.740481	+	0.740481i
$956$	5.35156	+	5.35156i	0.173082	+	0.173082i
$957$	−3.49287	−	3.49287i	−0.112908	−	0.112908i
$958$	−11.2987			−0.365046
$959$	−12.2686			−0.396175
$960$	−3.76802	−	3.76802i	−0.121612	−	0.121612i
$961$	−6.35595	−	30.3414i	−0.205031	−	0.978756i
$962$	6.37230	−	3.35709i	0.205451	−	0.108237i
$963$	91.4627			2.94734
$964$	−18.6757	+	18.6757i	−0.601504	+	0.601504i
$965$	−3.99946			−0.128747
$966$		−	8.67848i		−	0.279225i
$967$	12.7849	−	12.7849i	0.411133	−	0.411133i	−0.471000	−	0.882133i	$-0.656107\pi$
$967$	12.7849	−	12.7849i	0.411133	−	0.411133i	0.882133	+	0.471000i	$0.156107\pi$
$968$	18.3615	+	18.3615i	0.590161	+	0.590161i
$969$	10.8319	−	10.8319i	0.347971	−	0.347971i
$970$	14.4072	−	14.4072i	0.462588	−	0.462588i
$971$	−11.7052			−0.375639			−0.187820	−	0.982204i	$-0.560142\pi$
$971$	−11.7052			−0.375639			−0.187820	+	0.982204i	$0.560142\pi$
$972$	−112.737			−3.61605
$973$	12.7061	+	12.7061i	0.407338	+	0.407338i
$974$	−21.3635			−0.684530
$975$	5.56036	+	10.5544i	0.178074	+	0.338013i
$976$			8.18873i			0.262115i
$977$	14.6348	+	14.6348i	0.468210	+	0.468210i	0.901334	−	0.433124i	$-0.142589\pi$
$977$	14.6348	+	14.6348i	0.468210	+	0.468210i	−0.433124	+	0.901334i	$0.642589\pi$
$978$		−	14.1238i		−	0.451629i
$979$		−	0.704639i		−	0.0225204i
$980$	8.75265	+	8.75265i	0.279593	+	0.279593i
$981$	−67.4728	−	67.4728i	−2.15424	−	2.15424i
$982$	5.56466	+	5.56466i	0.177575	+	0.177575i
$983$	4.33028	+	4.33028i	0.138114	+	0.138114i	0.772784	−	0.634669i	$-0.218864\pi$
$983$	4.33028	+	4.33028i	0.138114	+	0.138114i	−0.634669	+	0.772784i	$0.718864\pi$
$984$			18.4563i			0.588365i
$985$	−25.5116			−0.812869
$986$	6.31313	−	6.31313i	0.201051	−	0.201051i
$987$	52.1158			1.65886
$988$	12.0867	+	3.74574i	0.384529	+	0.119168i
$989$	10.7293			0.341171
$990$	−1.75184	+	1.75184i	−0.0556772	+	0.0556772i
$991$			22.2542i			0.706927i	0.935448	+	0.353464i	$0.114996\pi$
$991$			22.2542i			0.706927i	−0.935448	+	0.353464i	$0.885004\pi$
$992$	31.9091	−	3.30629i	1.01312	−	0.104975i
$993$	−12.0584	−	12.0584i	−0.382660	−	0.382660i
$994$	8.55299	+	8.55299i	0.271284	+	0.271284i
$995$	14.3979	+	14.3979i	0.456445	+	0.456445i
$996$	48.9140	−	48.9140i	1.54990	−	1.54990i
$997$	−16.1861			−0.512620			−0.256310	−	0.966595i	$-0.582507\pi$
$997$	−16.1861			−0.512620			−0.256310	+	0.966595i	$0.582507\pi$
$998$	−4.70399			−0.148902
$999$	39.6008	−	39.6008i	1.25291	−	1.25291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.i.a.216.13	✓	68
13.5	odd	4	inner	403.2.i.a.278.13	yes	68
31.30	odd	2	inner	403.2.i.a.216.14	yes	68
403.278	even	4	inner	403.2.i.a.278.14	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.i.a.216.13	✓	68	1.1	even	1	trivial
403.2.i.a.216.14	yes	68	31.30	odd	2	inner
403.2.i.a.278.13	yes	68	13.5	odd	4	inner
403.2.i.a.278.14	yes	68	403.278	even	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)

\(f(q)\)	\(=\)	\(q+(-0.471532 - 0.471532i) q^{2} -3.39270i q^{3} -1.55532i q^{4} +(1.41859 + 1.41859i) q^{5} +(-1.59977 + 1.59977i) q^{6} +(-1.23146 + 1.23146i) q^{7} +(-1.67644 + 1.67644i) q^{8} -8.51044 q^{9} +O(q^{10})\)	\(q+(-0.471532 - 0.471532i) q^{2} -3.39270i q^{3} -1.55532i q^{4} +(1.41859 + 1.41859i) q^{5} +(-1.59977 + 1.59977i) q^{6} +(-1.23146 + 1.23146i) q^{7} +(-1.67644 + 1.67644i) q^{8} -8.51044 q^{9} -1.33782i q^{10} +(0.153867 + 0.153867i) q^{11} -5.27673 q^{12} +(-1.68055 - 3.18995i) q^{13} +1.16134 q^{14} +(4.81284 - 4.81284i) q^{15} -1.52964 q^{16} -2.00099 q^{17} +(4.01294 + 4.01294i) q^{18} +(-1.59557 - 1.59557i) q^{19} +(2.20635 - 2.20635i) q^{20} +(4.17797 + 4.17797i) q^{21} -0.145107i q^{22} +2.20261 q^{23} +(5.68768 + 5.68768i) q^{24} -0.975228i q^{25} +(-0.711729 + 2.29659i) q^{26} +18.6953i q^{27} +(1.91531 + 1.91531i) q^{28} -6.69098i q^{29} -4.53881 q^{30} +(3.51027 - 4.32180i) q^{31} +(4.07416 + 4.07416i) q^{32} +(0.522026 - 0.522026i) q^{33} +(0.943528 + 0.943528i) q^{34} -3.49386 q^{35} +13.2364i q^{36} +(-2.11822 - 2.11822i) q^{37} +1.50472i q^{38} +(-10.8225 + 5.70160i) q^{39} -4.75636 q^{40} +(1.62248 + 1.62248i) q^{41} -3.94009i q^{42} +4.87116 q^{43} +(0.239312 - 0.239312i) q^{44} +(-12.0728 - 12.0728i) q^{45} +(-1.03860 - 1.03860i) q^{46} +(6.23697 - 6.23697i) q^{47} +5.18962i q^{48} +3.96703i q^{49} +(-0.459851 + 0.459851i) q^{50} +6.78875i q^{51} +(-4.96137 + 2.61378i) q^{52} -6.37574i q^{53} +(8.81542 - 8.81542i) q^{54} +0.436548i q^{55} -4.12894i q^{56} +(-5.41329 + 5.41329i) q^{57} +(-3.15501 + 3.15501i) q^{58} +(7.34023 - 7.34023i) q^{59} +(-7.48549 - 7.48549i) q^{60} -5.35337i q^{61} +(-3.69307 + 0.382661i) q^{62} +(10.4802 - 10.4802i) q^{63} -0.782910i q^{64} +(2.14121 - 6.90922i) q^{65} -0.492304 q^{66} +(-5.10003 - 5.10003i) q^{67} +3.11217i q^{68} -7.47280i q^{69} +(1.64746 + 1.64746i) q^{70} +(7.36475 + 7.36475i) q^{71} +(14.2673 - 14.2673i) q^{72} +(-7.23487 - 7.23487i) q^{73} +1.99762i q^{74} -3.30866 q^{75} +(-2.48161 + 2.48161i) q^{76} -0.378962 q^{77} +(7.79166 + 2.41469i) q^{78} +8.32650i q^{79} +(-2.16993 - 2.16993i) q^{80} +37.8963 q^{81} -1.53010i q^{82} +(-9.26976 + 9.26976i) q^{83} +(6.49806 - 6.49806i) q^{84} +(-2.83857 - 2.83857i) q^{85} +(-2.29691 - 2.29691i) q^{86} -22.7005 q^{87} -0.515900 q^{88} +(-2.28976 - 2.28976i) q^{89} +11.3854i q^{90} +(5.99781 + 1.85876i) q^{91} -3.42575i q^{92} +(-14.6626 - 11.9093i) q^{93} -5.88186 q^{94} -4.52690i q^{95} +(13.8224 - 13.8224i) q^{96} +(10.7692 + 10.7692i) q^{97} +(1.87058 - 1.87058i) q^{98} +(-1.30948 - 1.30948i) 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

Varieties

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Representations

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Database

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