LMFDB - Embedded newform 416.2.bd.a.411.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

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

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, degree $4$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			411.13
Character	$\chi$	$=$	416.411
Dual form			416.2.bd.a.83.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.01464 + 0.985142i) q^{2} +(2.77489 - 1.14940i) q^{3} +(0.0589886 - 1.99913i) q^{4} +(0.336989 + 0.813563i) q^{5} +(-1.68319 + 3.89989i) q^{6} +2.04545i q^{7} +(1.90958 + 2.08651i) q^{8} +(4.25758 - 4.25758i) q^{9} +(-1.14340 - 0.493492i) q^{10} +(2.41961 - 1.00223i) q^{11} +(-2.13411 - 5.61517i) q^{12} +(-0.624670 + 3.55103i) q^{13} +(-2.01506 - 2.07540i) q^{14} +(1.87021 + 1.87021i) q^{15} +(-3.99304 - 0.235852i) q^{16} -1.32433 q^{17} +(-0.125588 + 8.51423i) q^{18} +(-0.0902070 + 0.217779i) q^{19} +(1.64630 - 0.625694i) q^{20} +(2.35104 + 5.67591i) q^{21} +(-1.46769 + 3.40056i) q^{22} +(-0.792801 + 0.792801i) q^{23} +(7.69709 + 3.59497i) q^{24} +(2.98721 - 2.98721i) q^{25} +(-2.86445 - 4.21840i) q^{26} +(3.47247 - 8.38329i) q^{27} +(4.08913 + 0.120659i) q^{28} +(-3.41680 - 8.24889i) q^{29} +(-3.74002 - 0.0551667i) q^{30} +(1.40454 - 1.40454i) q^{31} +(4.28385 - 3.69441i) q^{32} +(5.56218 - 5.56218i) q^{33} +(1.34372 - 1.30466i) q^{34} +(-1.66411 + 0.689295i) q^{35} +(-8.26030 - 8.76260i) q^{36} +(4.08486 - 1.69200i) q^{37} +(-0.123016 - 0.309834i) q^{38} +(2.34815 + 10.5717i) q^{39} +(-1.05400 + 2.25669i) q^{40} -5.02357 q^{41} +(-7.97703 - 3.44290i) q^{42} +(-2.93034 + 7.07448i) q^{43} +(-1.86087 - 4.89623i) q^{44} +(4.89856 + 2.02905i) q^{45} +(0.0233857 - 1.58543i) q^{46} +(-1.26673 + 1.26673i) q^{47} +(-11.3513 + 3.93513i) q^{48} +2.81612 q^{49} +(-0.0881153 + 5.97377i) q^{50} +(-3.67488 + 1.52219i) q^{51} +(7.06211 + 1.45827i) q^{52} +(-2.71826 + 6.56247i) q^{53} +(4.73542 + 11.9269i) q^{54} +(1.63076 + 1.63076i) q^{55} +(-4.26786 + 3.90595i) q^{56} +0.707996i q^{57} +(11.5932 + 5.00362i) q^{58} +(-4.13988 - 9.99456i) q^{59} +(3.84912 - 3.62848i) q^{60} +(-1.03362 - 2.49538i) q^{61} +(-0.0414304 + 2.80877i) q^{62} +(8.70868 + 8.70868i) q^{63} +(-0.707043 + 7.96869i) q^{64} +(-3.09949 + 0.688448i) q^{65} +(-0.164070 + 11.1231i) q^{66} +(-10.2043 - 4.22678i) q^{67} +(-0.0781207 + 2.64752i) q^{68} +(-1.28869 + 3.11118i) q^{69} +(1.00941 - 2.33877i) q^{70} -14.3248 q^{71} +(17.0136 + 0.753310i) q^{72} +11.6519i q^{73} +(-2.47780 + 5.74094i) q^{74} +(4.85569 - 11.7227i) q^{75} +(0.430047 + 0.193182i) q^{76} +(2.05002 + 4.94919i) q^{77} +(-12.7972 - 8.41321i) q^{78} +11.7123 q^{79} +(-1.15373 - 3.32807i) q^{80} -9.19057i q^{81} +(5.09711 - 4.94893i) q^{82} +(-3.08227 + 7.44125i) q^{83} +(11.4856 - 4.36522i) q^{84} +(-0.446286 - 1.07743i) q^{85} +(-3.99612 - 10.0649i) q^{86} +(-18.9625 - 18.9625i) q^{87} +(6.71159 + 3.13469i) q^{88} -0.488704 q^{89} +(-6.96919 + 2.76703i) q^{90} +(-7.26346 - 1.27773i) q^{91} +(1.53815 + 1.63168i) q^{92} +(2.28307 - 5.51181i) q^{93} +(0.0373653 - 2.53318i) q^{94} -0.207576 q^{95} +(7.64086 - 15.1754i) q^{96} +(6.29808 + 6.29808i) q^{97} +(-2.85735 + 2.77428i) q^{98} +(6.03457 - 14.5688i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24}+ \cdots - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.01464	+	0.985142i	−0.717459	+	0.696601i
$2$	−1.01464	+	0.985142i	−0.717459	+	0.696601i
$3$	2.77489	−	1.14940i	1.60208	−	0.663605i	0.610375	−	0.792113i	$-0.291019\pi$
$3$	2.77489	−	1.14940i	1.60208	−	0.663605i	0.991708	+	0.128508i	$0.0410189\pi$
$4$	0.0589886	−	1.99913i	0.0294943	−	0.999565i
$5$	0.336989	+	0.813563i	0.150706	+	0.363836i	0.981145	−	0.193273i	$-0.0619103\pi$
$5$	0.336989	+	0.813563i	0.150706	+	0.363836i	−0.830439	+	0.557110i	$0.811910\pi$
$6$	−1.68319	+	3.89989i	−0.687161	+	1.59212i
$7$			2.04545i			0.773109i	0.922267	+	0.386554i	$0.126335\pi$
$7$			2.04545i			0.773109i	−0.922267	+	0.386554i	$0.873665\pi$
$8$	1.90958	+	2.08651i	0.675137	+	0.737692i
$9$	4.25758	−	4.25758i	1.41919	−	1.41919i
$10$	−1.14340	−	0.493492i	−0.361574	−	0.156056i
$11$	2.41961	−	1.00223i	0.729539	−	0.302185i	0.0131763	−	0.999913i	$-0.495806\pi$
$11$	2.41961	−	1.00223i	0.729539	−	0.302185i	0.716362	+	0.697728i	$0.245806\pi$
$12$	−2.13411	−	5.61517i	−0.616064	−	1.62096i
$13$	−0.624670	+	3.55103i	−0.173252	+	0.984877i
$13$	−0.624670	+	3.55103i	−0.173252	+	0.984877i
$14$	−2.01506	−	2.07540i	−0.538548	−	0.554674i
$15$	1.87021	+	1.87021i	0.482887	+	0.482887i
$16$	−3.99304	−	0.235852i	−0.998260	−	0.0589630i
$17$	−1.32433			−0.321198			−0.160599	−	0.987020i	$-0.551343\pi$
$17$	−1.32433			−0.321198			−0.160599	+	0.987020i	$0.551343\pi$
$18$	−0.125588	+	8.51423i	−0.0296014	+	2.00682i
$19$	−0.0902070	+	0.217779i	−0.0206949	+	0.0499619i	−0.933889	−	0.357563i	$-0.883608\pi$
$19$	−0.0902070	+	0.217779i	−0.0206949	+	0.0499619i	0.913194	+	0.407524i	$0.133608\pi$
$20$	1.64630	−	0.625694i	0.368123	−	0.139909i
$21$	2.35104	+	5.67591i	0.513039	+	1.23858i
$22$	−1.46769	+	3.40056i	−0.312912	+	0.725002i
$23$	−0.792801	+	0.792801i	−0.165310	+	0.165310i	−0.784914	−	0.619604i	$-0.787293\pi$
$23$	−0.792801	+	0.792801i	−0.165310	+	0.165310i	0.619604	+	0.784914i	$0.287293\pi$
$24$	7.69709	+	3.59497i	1.57116	+	0.733821i
$25$	2.98721	−	2.98721i	0.597442	−	0.597442i
$26$	−2.86445	−	4.21840i	−0.561765	−	0.827297i
$27$	3.47247	−	8.38329i	0.668277	−	1.61336i
$28$	4.08913	+	0.120659i	0.772772	+	0.0228023i
$29$	−3.41680	−	8.24889i	−0.634484	−	1.53178i	−0.833929	−	0.551872i	$-0.813914\pi$
$29$	−3.41680	−	8.24889i	−0.634484	−	1.53178i	0.199445	−	0.979909i	$-0.436086\pi$
$30$	−3.74002	−	0.0551667i	−0.682831	−	0.0100720i
$31$	1.40454	−	1.40454i	0.252263	−	0.252263i	−0.569635	−	0.821898i	$-0.692915\pi$
$31$	1.40454	−	1.40454i	0.252263	−	0.252263i	0.821898	+	0.569635i	$0.192915\pi$
$32$	4.28385	−	3.69441i	0.757284	−	0.653085i
$33$	5.56218	−	5.56218i	0.968250	−	0.968250i
$34$	1.34372	−	1.30466i	0.230446	−	0.223747i
$35$	−1.66411	+	0.689295i	−0.281285	+	0.116512i
$36$	−8.26030	−	8.76260i	−1.37672	−	1.46043i
$37$	4.08486	−	1.69200i	0.671546	−	0.278164i	−0.0207417	−	0.999785i	$-0.506603\pi$
$37$	4.08486	−	1.69200i	0.671546	−	0.278164i	0.692288	+	0.721621i	$0.256603\pi$
$38$	−0.123016	−	0.309834i	−0.0199558	−	0.0502617i
$39$	2.34815	+	10.5717i	0.376005	+	1.69283i
$40$	−1.05400	+	2.25669i	−0.166652	+	0.356814i
$41$	−5.02357			−0.784549			−0.392275	−	0.919848i	$-0.628312\pi$
$41$	−5.02357			−0.784549			−0.392275	+	0.919848i	$0.628312\pi$
$42$	−7.97703	−	3.44290i	−1.23088	−	0.531250i
$43$	−2.93034	+	7.07448i	−0.446873	+	1.07885i	0.526614	+	0.850105i	$0.323461\pi$
$43$	−2.93034	+	7.07448i	−0.446873	+	1.07885i	−0.973487	+	0.228743i	$0.926539\pi$
$44$	−1.86087	−	4.89623i	−0.280536	−	0.738134i
$45$	4.89856	+	2.02905i	0.730235	+	0.302473i
$46$	0.0233857	−	1.58543i	0.00344803	−	0.233759i
$47$	−1.26673	+	1.26673i	−0.184771	+	0.184771i	−0.793431	−	0.608660i	$-0.791707\pi$
$47$	−1.26673	+	1.26673i	−0.184771	+	0.184771i	0.608660	+	0.793431i	$0.291707\pi$
$48$	−11.3513	+	3.93513i	−1.63842	+	0.567986i
$49$	2.81612			0.402303
$50$	−0.0881153	+	5.97377i	−0.0124614	+	0.844819i
$51$	−3.67488	+	1.52219i	−0.514586	+	0.213149i
$52$	7.06211	+	1.45827i	0.979339	+	0.202225i
$53$	−2.71826	+	6.56247i	−0.373382	+	0.901424i	0.619790	+	0.784768i	$0.287218\pi$
$53$	−2.71826	+	6.56247i	−0.373382	+	0.901424i	−0.993172	+	0.116657i	$0.962782\pi$
$54$	4.73542	+	11.9269i	0.644410	+	1.62305i
$55$	1.63076	+	1.63076i	0.219892	+	0.219892i
$56$	−4.26786	+	3.90595i	−0.570316	+	0.521954i
$57$			0.707996i			0.0937764i
$58$	11.5932	+	5.00362i	1.52226	+	0.657007i
$59$	−4.13988	−	9.99456i	−0.538967	−	1.30118i	−0.925445	−	0.378882i	$-0.876309\pi$
$59$	−4.13988	−	9.99456i	−0.538967	−	1.30118i	0.386478	−	0.922299i	$-0.373691\pi$
$60$	3.84912	−	3.62848i	0.496919	−	0.468435i
$61$	−1.03362	−	2.49538i	−0.132342	−	0.319501i	0.843792	−	0.536670i	$-0.180318\pi$
$61$	−1.03362	−	2.49538i	−0.132342	−	0.319501i	−0.976134	+	0.217168i	$0.930318\pi$
$62$	−0.0414304	+	2.80877i	−0.00526167	+	0.356714i
$63$	8.70868	+	8.70868i	1.09719	+	1.09719i
$64$	−0.707043	+	7.96869i	−0.0883803	+	0.996087i
$65$	−3.09949	+	0.688448i	−0.384445	+	0.0853914i
$66$	−0.164070	+	11.1231i	−0.0201957	+	1.36916i
$67$	−10.2043	−	4.22678i	−1.24666	−	0.516383i	−0.340869	−	0.940111i	$-0.610721\pi$
$67$	−10.2043	−	4.22678i	−1.24666	−	0.516383i	−0.905789	+	0.423728i	$0.860721\pi$
$68$	−0.0781207	+	2.64752i	−0.00947352	+	0.321058i
$69$	−1.28869	+	3.11118i	−0.155140	+	0.374542i
$70$	1.00941	−	2.33877i	0.120648	−	0.279536i
$71$	−14.3248			−1.70004			−0.850018	−	0.526754i	$-0.823409\pi$
$71$	−14.3248			−1.70004			−0.850018	+	0.526754i	$0.823409\pi$
$72$	17.0136	+	0.753310i	2.00508	+	0.0887784i
$73$			11.6519i			1.36375i	0.731467	+	0.681876i	$0.238836\pi$
$73$			11.6519i			1.36375i	−0.731467	+	0.681876i	$0.761164\pi$
$74$	−2.47780	+	5.74094i	−0.288038	+	0.667371i
$75$	4.85569	−	11.7227i	0.560687	−	1.35362i
$76$	0.430047	+	0.193182i	0.0493298	+	0.0221595i
$77$	2.05002	+	4.94919i	0.233622	+	0.564013i
$78$	−12.7972	−	8.41321i	−1.44899	−	0.952608i
$79$	11.7123			1.31773			0.658866	−	0.752260i	$-0.271036\pi$
$79$	11.7123			1.31773			0.658866	+	0.752260i	$0.271036\pi$
$80$	−1.15373	−	3.32807i	−0.128991	−	0.372090i
$81$		−	9.19057i		−	1.02117i
$82$	5.09711	−	4.94893i	0.562882	−	0.546518i
$83$	−3.08227	+	7.44125i	−0.338323	+	0.816783i	0.659554	+	0.751657i	$0.270745\pi$
$83$	−3.08227	+	7.44125i	−0.338323	+	0.816783i	−0.997877	+	0.0651264i	$0.979255\pi$
$84$	11.4856	−	4.36522i	1.25318	−	0.476284i
$85$	−0.446286	−	1.07743i	−0.0484065	−	0.116864i
$86$	−3.99612	−	10.0649i	−0.430913	−	1.08532i
$87$	−18.9625	−	18.9625i	−2.03299	−	2.03299i
$88$	6.71159	+	3.13469i	0.715458	+	0.334159i
$89$	−0.488704			−0.0518025			−0.0259013	−	0.999665i	$-0.508246\pi$
$89$	−0.488704			−0.0518025			−0.0259013	+	0.999665i	$0.508246\pi$
$90$	−6.96919	+	2.76703i	−0.734617	+	0.291670i
$91$	−7.26346	−	1.27773i	−0.761417	−	0.133943i
$92$	1.53815	+	1.63168i	0.160363	+	0.170114i
$93$	2.28307	−	5.51181i	0.236743	−	0.571548i
$94$	0.0373653	−	2.53318i	0.00385394	−	0.261277i
$95$	−0.207576			−0.0212968
$96$	7.64086	−	15.1754i	0.779842	−	1.54883i
$97$	6.29808	+	6.29808i	0.639473	+	0.639473i	0.950425	−	0.310953i	$-0.100648\pi$
$97$	6.29808	+	6.29808i	0.639473	+	0.639473i	−0.310953	+	0.950425i	$0.600648\pi$
$98$	−2.85735	+	2.77428i	−0.288636	+	0.280245i
$99$	6.03457	−	14.5688i	0.606497	−	1.46421i
$100$	−5.79561	−	6.14803i	−0.579561	−	0.614803i
$101$	0.303914	−	0.733713i	0.0302406	−	0.0730072i	−0.908038	−	0.418888i	$-0.862420\pi$
$101$	0.303914	−	0.733713i	0.0302406	−	0.0730072i	0.938278	+	0.345881i	$0.112420\pi$
$102$	2.22911	−	5.16475i	0.220715	−	0.511387i
$103$	−10.0131	−	10.0131i	−0.986623	−	0.986623i	0.0132886	−	0.999912i	$-0.495770\pi$
$103$	−10.0131	−	10.0131i	−0.986623	−	0.986623i	−0.999912	+	0.0132886i	$0.995770\pi$
$104$	−8.60210	+	5.47757i	−0.843506	+	0.537120i
$105$	−3.82544	+	3.82544i	−0.373324	+	0.373324i
$106$	−3.70691	−	9.33642i	−0.360047	−	0.906833i
$107$	−17.3930	−	7.20442i	−1.68145	−	0.696477i	−0.682052	−	0.731304i	$-0.738912\pi$
$107$	−17.3930	−	7.20442i	−1.68145	−	0.696477i	−0.999393	+	0.0348263i	$0.988912\pi$
$108$	−16.5544	−	7.43644i	−1.59295	−	0.715572i
$109$	5.49260	+	2.27511i	0.526095	+	0.217916i	0.629892	−	0.776683i	$-0.283099\pi$
$109$	5.49260	+	2.27511i	0.526095	+	0.217916i	−0.103797	+	0.994599i	$0.533099\pi$
$110$	−3.26117	−	0.0481034i	−0.310940	−	0.00458648i
$111$	9.39024	−	9.39024i	0.891283	−	0.891283i
$112$	0.482424	−	8.16758i	0.0455848	−	0.771764i
$113$		−	21.2146i		−	1.99571i	−0.0654917	−	0.997853i	$-0.520862\pi$
$113$		−	21.2146i		−	1.99571i	0.0654917	−	0.997853i	$-0.479138\pi$
$114$	−0.697477	−	0.718361i	−0.0653247	−	0.0672807i
$115$	−0.912158	−	0.377828i	−0.0850592	−	0.0352327i
$116$	−16.6922	+	6.34404i	−1.54983	+	0.589029i
$117$	12.4592	+	17.7784i	1.15185	+	1.64361i
$118$	14.0466	+	6.06251i	1.29309	+	0.558099i
$119$		−	2.70886i		−	0.248321i
$120$	−0.330904	+	7.47353i	−0.0302073	+	0.682237i
$121$	−2.92815	+	2.92815i	−0.266196	+	0.266196i
$122$	3.50706	+	1.51365i	0.317515	+	0.137040i
$123$	−13.9398	+	5.77407i	−1.25691	+	0.520631i
$124$	−2.72500	−	2.89071i	−0.244712	−	0.259593i
$125$	7.50476	+	3.10857i	0.671246	+	0.278039i
$126$	−17.4155	−	0.256884i	−1.55149	−	0.0228851i
$127$	−13.3282			−1.18268			−0.591342	−	0.806421i	$-0.701402\pi$
$127$	−13.3282			−1.18268			−0.591342	+	0.806421i	$0.701402\pi$
$128$	−7.13291	−	8.78189i	−0.630466	−	0.776217i
$129$			22.9990i			2.02495i
$130$	2.46665	−	3.75197i	0.216339	−	0.329069i
$131$	14.0457	−	5.81791i	1.22718	−	0.508313i	0.327492	−	0.944854i	$-0.393797\pi$
$131$	14.0457	−	5.81791i	1.22718	−	0.508313i	0.899684	+	0.436541i	$0.143797\pi$
$132$	−10.7914	−	11.4476i	−0.939271	−	0.996387i
$133$	−0.445457	−	0.184514i	−0.0386260	−	0.0159994i
$134$	14.5177	−	5.76407i	1.25414	−	0.497940i
$135$	7.99052			0.687714
$136$	−2.52892	−	2.76324i	−0.216853	−	0.236945i
$137$			11.5513i			0.986892i	0.869777	+	0.493446i	$0.164263\pi$
$137$			11.5513i			0.986892i	−0.869777	+	0.493446i	$0.835737\pi$
$138$	−1.75739	−	4.42627i	−0.149599	−	0.376789i
$139$	9.95127	+	4.12195i	0.844055	+	0.349619i	0.762451	−	0.647046i	$-0.223996\pi$
$139$	9.95127	+	4.12195i	0.844055	+	0.349619i	0.0816041	+	0.996665i	$0.473996\pi$
$140$	1.27983	+	3.36742i	0.108165	+	0.284599i
$141$	−2.05905	+	4.97100i	−0.173404	+	0.418633i
$142$	14.5345	−	14.1119i	1.21971	−	1.18425i
$143$	2.04750	+	9.21815i	0.171221	+	0.770860i
$144$	−18.0048	+	15.9965i	−1.50040	+	1.33304i
$145$	5.55957	−	5.55957i	0.461697	−	0.461697i
$146$	−11.4788	−	11.8225i	−0.949991	−	0.978436i
$147$	7.81442	−	3.23684i	0.644523	−	0.266970i
$148$	−3.14157	−	8.26597i	−0.258236	−	0.679458i
$149$	7.97171	−	3.30199i	0.653068	−	0.270510i	−0.0314502	−	0.999505i	$-0.510013\pi$
$149$	7.97171	−	3.30199i	0.653068	−	0.270510i	0.684518	+	0.728996i	$0.260013\pi$
$150$	6.62172	+	16.6778i	0.540661	+	1.36174i
$151$	−23.1017			−1.87999			−0.939996	−	0.341185i	$-0.889172\pi$
$151$	−23.1017			−1.87999			−0.939996	+	0.341185i	$0.889172\pi$
$152$	−0.626655	+	0.227648i	−0.0508284	+	0.0184647i
$153$	−5.63846	+	5.63846i	−0.455842	+	0.455842i
$154$	−6.95569	−	3.00208i	−0.560506	−	0.241915i
$155$	1.61599	+	0.669367i	0.129800	+	0.0537648i
$156$	21.2727	−	4.07064i	1.70318	−	0.325912i
$157$	4.91154	+	11.8575i	0.391984	+	0.946332i	0.989508	+	0.144481i	$0.0461512\pi$
$157$	4.91154	+	11.8575i	0.391984	+	0.946332i	−0.597524	+	0.801851i	$0.703849\pi$
$158$	−11.8837	+	11.5382i	−0.945419	+	0.917934i
$159$			21.3345i			1.69193i
$160$	4.44924	+	2.24020i	0.351744	+	0.177104i
$161$	−1.62164	−	1.62164i	−0.127803	−	0.127803i
$162$	9.05402	+	9.32512i	0.711351	+	0.732651i
$163$	5.28803	−	12.7664i	0.414191	−	0.999945i	−0.569809	−	0.821777i	$-0.692983\pi$
$163$	5.28803	−	12.7664i	0.414191	−	0.999945i	0.984000	−	0.178168i	$-0.0570171\pi$
$164$	−0.296333	+	10.0428i	−0.0231397	+	0.784208i
$165$	6.39957	+	2.65079i	0.498206	+	0.206364i
$166$	−4.20330	−	10.5867i	−0.326239	−	0.821684i
$167$			23.9648i			1.85446i	0.374498	+	0.927228i	$0.377815\pi$
$167$			23.9648i			1.85446i	−0.374498	+	0.927228i	$0.622185\pi$
$168$	−7.35335	+	15.7440i	−0.567323	+	1.21468i
$169$	−12.2196	−	4.43644i	−0.939967	−	0.341265i
$170$	1.51424	+	0.653548i	0.116137	+	0.0501248i
$171$	0.543148	+	1.31127i	0.0415355	+	0.100276i
$172$	13.9699	+	6.27545i	1.06520	+	0.478499i
$173$	−9.29479	−	22.4396i	−0.706670	−	1.70605i	−0.708159	−	0.706053i	$-0.750474\pi$
$173$	−9.29479	−	22.4396i	−0.706670	−	1.70605i	0.00148854	−	0.999999i	$-0.499526\pi$
$174$	37.9209	+	0.559347i	2.87477	+	0.0424040i
$175$	6.11020	+	6.11020i	0.461888	+	0.461888i
$176$	−9.89796	+	3.43129i	−0.746087	+	0.258643i
$177$	−22.9754	−	22.9754i	−1.72694	−	1.72694i
$178$	0.495859	−	0.481443i	0.0371662	−	0.0360857i
$179$	5.89870	−	2.44332i	0.440890	−	0.182623i	−0.151185	−	0.988505i	$-0.548309\pi$
$179$	5.89870	−	2.44332i	0.440890	−	0.182623i	0.592075	+	0.805883i	$0.298309\pi$
$180$	4.34530	−	9.67318i	0.323879	−	0.720996i
$181$	15.2960	+	6.33581i	1.13694	+	0.470937i	0.870135	−	0.492813i	$-0.164031\pi$
$181$	15.2960	+	6.33581i	1.13694	+	0.470937i	0.266807	+	0.963750i	$0.414031\pi$
$182$	8.62855	−	5.85910i	0.639590	−	0.434306i
$183$	−5.73637	−	5.73637i	−0.424045	−	0.424045i
$184$	−3.16810	−	0.140273i	−0.233555	−	0.0103411i
$185$	2.75310	+	2.75310i	0.202412	+	0.202412i
$186$	3.11343	+	7.84165i	0.228288	+	0.574978i
$187$	−3.20437	+	1.32729i	−0.234327	+	0.0970612i
$188$	2.45763	+	2.60707i	0.179241	+	0.190140i
$189$	17.1476	+	7.10278i	1.24731	+	0.516651i
$190$	0.210615	−	0.204492i	0.0152796	−	0.0148354i
$191$			0.887537i			0.0642199i	0.999484	+	0.0321100i	$0.0102227\pi$
$191$			0.887537i			0.0642199i	−0.999484	+	0.0321100i	$0.989777\pi$
$192$	7.19723	+	22.9249i	0.519415	+	1.65446i
$193$	13.1942	−	13.1942i	0.949738	−	0.949738i	−0.0490580	−	0.998796i	$-0.515622\pi$
$193$	13.1942	−	13.1942i	0.949738	−	0.949738i	0.998796	+	0.0490580i	$0.0156219\pi$
$194$	−12.5948	−	0.185778i	−0.904253	−	0.0133381i
$195$	−7.80944	+	5.47291i	−0.559246	+	0.391923i
$196$	0.166119	−	5.62979i	0.0118657	−	0.402128i
$197$	−0.770054	−	1.85907i	−0.0548641	−	0.132454i	0.894071	−	0.447926i	$-0.147837\pi$
$197$	−0.770054	−	1.85907i	−0.0548641	−	0.132454i	−0.948935	+	0.315472i	$0.897837\pi$
$198$	8.22937	+	20.7270i	0.584836	+	1.47300i
$199$	−8.84593	−	8.84593i	−0.627071	−	0.627071i	0.320259	−	0.947330i	$-0.396230\pi$
$199$	−8.84593	−	8.84593i	−0.627071	−	0.627071i	−0.947330	+	0.320259i	$0.896230\pi$
$200$	11.9371	+	0.528539i	0.844084	+	0.0373733i
$201$	−33.1742			−2.33992
$202$	0.414449	+	1.04385i	0.0291605	+	0.0734452i
$203$	16.8727	−	6.98891i	1.18423	−	0.490525i
$204$	2.82627	+	7.43636i	0.197878	+	0.520649i
$205$	−1.69289	−	4.08699i	−0.118236	−	0.285448i
$206$	20.0241	+	0.295363i	1.39514	+	0.0205789i
$207$			6.75082i			0.469215i
$208$	3.33185	−	14.0321i	0.231022	−	0.972948i
$209$			0.617348i			0.0427028i
$210$	0.112841	−	7.65004i	0.00778676	−	0.527903i
$211$	6.54966	+	15.8123i	0.450897	+	1.08856i	0.971982	+	0.235057i	$0.0755278\pi$
$211$	6.54966	+	15.8123i	0.450897	+	1.08856i	−0.521084	+	0.853505i	$0.674472\pi$
$212$	12.9589	+	5.82127i	0.890019	+	0.399807i
$213$	−39.7496	+	16.4648i	−2.72360	+	1.12815i
$214$	24.7450	−	9.82470i	1.69153	−	0.671602i
$215$	−6.74303			−0.459871
$216$	24.1228	−	8.76318i	1.64135	−	0.596259i
$217$	2.87292	+	2.87292i	0.195026	+	0.195026i
$218$	−7.81432	+	3.10258i	−0.529252	+	0.210133i
$219$	13.3927	+	32.3328i	0.904993	+	2.18485i
$220$	3.35630	−	3.16391i	0.226282	−	0.213310i
$221$	0.827272	−	4.70275i	0.0556483	−	0.316341i
$222$	−0.276989	+	18.7784i	−0.0185903	+	1.26033i
$223$	−8.81150	+	8.81150i	−0.590062	+	0.590062i	−0.937648	−	0.347586i	$-0.887001\pi$
$223$	−8.81150	+	8.81150i	−0.590062	+	0.590062i	0.347586	+	0.937648i	$0.387001\pi$
$224$	7.55674	+	8.76241i	0.504906	+	0.585463i
$225$		−	25.4366i		−	1.69577i
$226$	20.8995	+	21.5252i	1.39021	+	1.43184i
$227$	−2.43048	−	1.00674i	−0.161316	−	0.0668195i	0.300564	−	0.953762i	$-0.402825\pi$
$227$	−2.43048	−	1.00674i	−0.161316	−	0.0668195i	−0.461880	+	0.886942i	$0.652825\pi$
$228$	1.41538	+	0.0417637i	0.0937356	+	0.00276587i
$229$	15.5606	−	6.44541i	1.02827	−	0.425925i	0.196184	−	0.980567i	$-0.437145\pi$
$229$	15.5606	−	6.44541i	1.02827	−	0.425925i	0.832089	+	0.554642i	$0.187145\pi$
$230$	1.29773	−	0.515246i	0.0855696	−	0.0339743i
$231$	11.3772	+	11.3772i	0.748563	+	0.748563i
$232$	10.6867	−	22.8811i	0.701619	−	1.50222i
$233$	18.2011	+	18.2011i	1.19240	+	1.19240i	0.976393	+	0.216004i	$0.0693024\pi$
$233$	18.2011	+	18.2011i	1.19240	+	1.19240i	0.216004	+	0.976393i	$0.430698\pi$
$234$	−30.1558	−	5.76455i	−1.97135	−	0.376841i
$235$	−1.45743	−	0.603689i	−0.0950725	−	0.0393803i
$236$	−20.2246	+	7.68660i	−1.31651	+	0.500355i
$237$	32.5002	−	13.4620i	2.11112	−	0.874453i
$238$	2.66862	+	2.74852i	0.172981	+	0.178160i
$239$	−6.16768	−	6.16768i	−0.398954	−	0.398954i	0.478910	−	0.877864i	$-0.341032\pi$
$239$	−6.16768	−	6.16768i	−0.398954	−	0.398954i	−0.877864	+	0.478910i	$0.841032\pi$
$240$	−7.02675	−	7.90893i	−0.453574	−	0.510519i
$241$	−2.38145	−	2.38145i	−0.153403	−	0.153403i	0.626233	−	0.779636i	$-0.284596\pi$
$241$	−2.38145	−	2.38145i	−0.153403	−	0.153403i	−0.779636	+	0.626233i	$0.784596\pi$
$242$	0.0863733	−	5.85567i	0.00555229	−	0.376417i
$243$	−0.146198	−	0.352954i	−0.00937864	−	0.0226420i
$244$	−5.04957	+	1.91915i	−0.323266	+	0.122861i
$245$	0.949001	+	2.29109i	0.0606295	+	0.146372i
$246$	8.45564	−	19.5913i	0.539112	−	1.24910i
$247$	−0.716989	−	0.456367i	−0.0456209	−	0.0290380i
$248$	5.61265	+	0.248510i	0.356404	+	0.0157804i
$249$			24.1914i			1.53307i
$250$	−10.6770	+	4.23917i	−0.675274	+	0.268109i
$251$	3.24010	+	1.34209i	0.204513	+	0.0847121i	0.482589	−	0.875847i	$-0.339697\pi$
$251$	3.24010	+	1.34209i	0.204513	+	0.0847121i	−0.278076	+	0.960559i	$0.589697\pi$
$252$	17.9235	−	16.8961i	1.12907	−	1.06435i
$253$	−1.12369	+	2.71284i	−0.0706460	+	0.170555i
$254$	13.5233	−	13.1301i	0.848527	−	0.823859i
$255$	−2.47679	−	2.47679i	−0.155102	−	0.155102i
$256$	15.8887	+	1.88353i	0.993047	+	0.117721i
$257$			16.3122i			1.01753i	0.860907	+	0.508763i	$0.169897\pi$
$257$			16.3122i			1.01753i	−0.860907	+	0.508763i	$0.830103\pi$
$258$	−22.6573	−	23.3357i	−1.41058	−	1.45282i
$259$	3.46091	+	8.35538i	0.215051	+	0.519178i
$260$	1.19346	+	6.23690i	0.0740153	+	0.386796i
$261$	−49.6676	−	20.5730i	−3.07435	−	1.27344i
$262$	−8.51983	+	19.7401i	−0.526357	+	1.21955i
$263$	6.92075	−	6.92075i	0.426751	−	0.426751i	−0.460769	−	0.887520i	$-0.652426\pi$
$263$	6.92075	−	6.92075i	0.426751	−	0.426751i	0.887520	+	0.460769i	$0.152426\pi$
$264$	22.2269	+	0.984137i	1.36797	+	0.0605695i
$265$	−6.25501			−0.384242
$266$	0.633751	−	0.251623i	0.0388578	−	0.0154280i
$267$	−1.35610	+	0.561715i	−0.0829919	+	0.0343764i
$268$	−9.05181	+	20.1505i	−0.552928	+	1.23089i
$269$	9.99891	−	4.14168i	0.609644	−	0.252523i	−0.0564322	−	0.998406i	$-0.517972\pi$
$269$	9.99891	−	4.14168i	0.609644	−	0.252523i	0.666076	+	0.745884i	$0.267972\pi$
$270$	−8.10750	+	7.87180i	−0.493407	+	0.479062i
$271$	−2.52241	+	2.52241i	−0.153226	+	0.153226i	−0.779557	−	0.626331i	$-0.784556\pi$
$271$	−2.52241	+	2.52241i	−0.153226	+	0.153226i	0.626331	+	0.779557i	$0.284556\pi$
$272$	5.28812	+	0.312347i	0.320639	+	0.0189388i
$273$	−21.6239	+	4.80303i	−1.30874	+	0.290692i
$274$	−11.3796	−	11.7204i	−0.687470	−	0.708054i
$275$	4.23399	−	10.2218i	0.255319	−	0.616395i
$276$	6.14363	+	2.75979i	0.369803	+	0.166120i
$277$	−0.0292439	−	0.0121132i	−0.00175709	−	0.000727812i	0.381805	−	0.924243i	$-0.375303\pi$
$277$	−0.0292439	−	0.0121132i	−0.00175709	−	0.000727812i	−0.383562	+	0.923515i	$0.625303\pi$
$278$	−14.1577	+	5.62112i	−0.849120	+	0.337132i
$279$		−	11.9599i		−	0.716018i
$280$	−4.61596	−	2.15591i	−0.275856	−	0.128840i
$281$	−24.4931			−1.46113			−0.730567	−	0.682841i	$-0.760744\pi$
$281$	−24.4931			−1.46113			−0.730567	+	0.682841i	$0.760744\pi$
$282$	−2.80794	−	7.07223i	−0.167210	−	0.421145i
$283$	7.30232	+	3.02472i	0.434078	+	0.179801i	0.589013	−	0.808124i	$-0.299517\pi$
$283$	7.30232	+	3.02472i	0.434078	+	0.179801i	−0.154935	+	0.987925i	$0.549517\pi$
$284$	−0.844998	+	28.6370i	−0.0501414	+	1.69930i
$285$	−0.576000	+	0.238587i	−0.0341193	+	0.0141327i
$286$	−11.1587	−	7.33602i	−0.659826	−	0.433788i
$287$		−	10.2755i		−	0.606542i
$288$	2.50958	−	33.9680i	0.147878	−	2.00159i
$289$	−15.2461			−0.896832
$290$	−0.163994	+	11.1179i	−0.00963003	+	0.652867i
$291$	24.7155	+	10.2375i	1.44885	+	0.600132i
$292$	23.2937	+	0.687330i	1.36316	+	0.0402230i
$293$	18.4115	−	7.62631i	1.07561	−	0.445534i	0.226645	−	0.973977i	$-0.427224\pi$
$293$	18.4115	−	7.62631i	1.07561	−	0.445534i	0.848968	+	0.528444i	$0.177224\pi$
$294$	−4.74008	+	10.9825i	−0.276447	+	0.640515i
$295$	6.73611	−	6.73611i	0.392192	−	0.392192i
$296$	11.3307	+	5.29208i	0.658585	+	0.307596i
$297$		−	23.7645i		−	1.37896i
$298$	−4.83549	+	11.2036i	−0.280112	+	0.649007i
$299$	−2.32002	−	3.31049i	−0.134170	−	0.191451i
$300$	−23.1487	−	10.3987i	−1.33649	−	0.600367i
$301$	−14.4705	−	5.99388i	−0.834066	−	0.345482i
$302$	23.4399	−	22.7585i	1.34882	−	1.30960i
$303$		−	2.38529i		−	0.137031i
$304$	0.411564	−	0.848325i	0.0236048	−	0.0486548i
$305$	1.68183	−	1.68183i	0.0963015	−	0.0963015i
$306$	0.166321	−	11.2757i	0.00950791	−	0.644588i
$307$	9.86958	+	4.08811i	0.563287	+	0.233321i	0.646111	−	0.763243i	$-0.276394\pi$
$307$	9.86958	+	4.08811i	0.563287	+	0.233321i	−0.0828246	+	0.996564i	$0.526394\pi$
$308$	10.0150	−	3.80631i	0.570658	−	0.216885i
$309$	−39.2944	−	16.2763i	−2.23538	−	0.925925i
$310$	−2.29907	+	0.912818i	−0.130579	+	0.0518446i
$311$	0.531265	−	0.531265i	0.0301252	−	0.0301252i	−0.691884	−	0.722009i	$-0.743219\pi$
$311$	0.531265	−	0.531265i	0.0301252	−	0.0301252i	0.722009	+	0.691884i	$0.243219\pi$
$312$	−17.5740	+	25.0869i	−0.994931	+	1.42027i
$313$	10.3681	+	10.3681i	0.586040	+	0.586040i	0.936557	−	0.350517i	$-0.113994\pi$
$313$	10.3681	+	10.3681i	0.586040	+	0.586040i	−0.350517	+	0.936557i	$0.613994\pi$
$314$	−16.6648	−	7.19253i	−0.940448	−	0.405898i
$315$	−4.15033	+	10.0198i	−0.233845	+	0.564551i
$316$	0.690890	−	23.4143i	0.0388656	−	1.31716i
$317$	−1.65591	+	3.99772i	−0.0930052	+	0.224534i	−0.963536	−	0.267580i	$-0.913776\pi$
$317$	−1.65591	+	3.99772i	−0.0930052	+	0.224534i	0.870530	+	0.492115i	$0.163776\pi$
$318$	−21.0175	−	21.6468i	−1.17860	−	1.21389i
$319$	−16.5346	−	16.5346i	−0.925762	−	0.925762i
$320$	−6.72130	+	2.11014i	−0.375732	+	0.117960i
$321$	−56.5444			−3.15600
$322$	3.24292	+	0.0478343i	0.180721	+	0.00266570i
$323$	0.119464	−	0.288412i	0.00664717	−	0.0160477i
$324$	−18.3731	−	0.542139i	−1.02073	−	0.0301188i
$325$	8.74164	+	12.4737i	0.484899	+	0.691916i
$326$	7.21131	+	18.1628i	0.399398	+	1.00595i
$327$	17.8564			0.987459
$328$	−9.59288	−	10.4817i	−0.529678	−	0.578756i
$329$	−2.59103	−	2.59103i	−0.142848	−	0.142848i
$330$	−9.10467	+	3.61489i	−0.501195	+	0.198993i
$331$	4.55281	+	10.9914i	0.250245	+	0.604145i	0.998224	−	0.0595781i	$-0.0189755\pi$
$331$	4.55281	+	10.9914i	0.250245	+	0.604145i	−0.747979	+	0.663723i	$0.768976\pi$
$332$	14.6942	+	6.60080i	0.806449	+	0.362266i
$333$	10.1878	−	24.5954i	0.558286	−	1.34782i
$334$	−23.6088	−	24.3157i	−1.29182	−	1.33050i
$335$		−	9.72625i		−	0.531402i
$336$	−8.04912	−	23.2186i	−0.439115	−	1.26668i
$337$	28.9168			1.57520			0.787598	−	0.616189i	$-0.211324\pi$
$337$	28.9168			1.57520			0.787598	+	0.616189i	$0.211324\pi$
$338$	16.7690	−	7.53663i	0.912113	−	0.409939i
$339$	−24.3841	−	58.8683i	−1.32436	−	3.19729i
$340$	−2.18025	+	0.828627i	−0.118240	+	0.0449386i
$341$	1.99075	−	4.80610i	0.107805	−	0.260265i
$342$	−1.84289	−	0.795394i	−0.0996521	−	0.0430100i
$343$			20.0784i			1.08413i
$344$	−20.3567	+	7.39506i	−1.09756	+	0.398715i
$345$	−2.96541			−0.159652
$346$	31.5371	+	13.6114i	1.69544	+	0.731755i
$347$	−4.81115	+	11.6151i	−0.258276	+	0.623534i	−0.998825	−	0.0484691i	$-0.984566\pi$
$347$	−4.81115	+	11.6151i	−0.258276	+	0.623534i	0.740549	+	0.672003i	$0.234566\pi$
$348$	−39.0271	+	36.7899i	−2.09207	+	1.97215i
$349$	5.05694	+	2.09465i	0.270692	+	0.112124i	0.513901	−	0.857850i	$-0.328200\pi$
$349$	5.05694	+	2.09465i	0.270692	+	0.112124i	−0.243209	+	0.969974i	$0.578200\pi$
$350$	−12.2191	−	0.180236i	−0.653137	−	0.00963401i
$351$	27.6001	+	17.5676i	1.47319	+	0.937691i
$352$	6.66256	−	13.2324i	0.355116	−	0.705291i
$353$	−8.33924	−	8.33924i	−0.443853	−	0.443853i	0.449452	−	0.893305i	$-0.351619\pi$
$353$	−8.33924	−	8.33924i	−0.443853	−	0.443853i	−0.893305	+	0.449452i	$0.851619\pi$
$354$	45.9459	+	0.677718i	2.44200	+	0.0360203i
$355$	−4.82728	−	11.6541i	−0.256206	−	0.618535i
$356$	−0.0288280	+	0.976983i	−0.00152788	+	0.0517800i
$357$	−3.11356	−	7.51680i	−0.164787	−	0.397831i
$358$	−3.57804	+	8.29016i	−0.189105	+	0.438148i
$359$			15.8350i			0.835741i	0.908507	+	0.417871i	$0.137223\pi$
$359$			15.8350i			0.835741i	−0.908507	+	0.417871i	$0.862777\pi$
$360$	5.12054	+	14.0955i	0.269876	+	0.742900i
$361$	13.3957	+	13.3957i	0.705039	+	0.705039i
$362$	−21.7616	+	8.64017i	−1.14376	+	0.454117i
$363$	−4.75969	+	11.4909i	−0.249819	+	0.603117i
$364$	−2.98282	+	14.4452i	−0.156342	+	0.757136i
$365$	−9.47956	+	3.92656i	−0.496183	+	0.205526i
$366$	11.4715	+	0.169209i	0.599625	+	0.00884469i
$367$	−10.8970			−0.568820			−0.284410	−	0.958703i	$-0.591798\pi$
$367$	−10.8970			−0.568820			−0.284410	+	0.958703i	$0.591798\pi$
$368$	3.35267	−	2.97870i	0.174770	−	0.155276i
$369$	−21.3882	+	21.3882i	−1.11343	+	1.11343i
$370$	−5.50561	−	0.0812097i	−0.286223	−	0.00422189i
$371$	−13.4232	−	5.56008i	−0.696899	−	0.288665i
$372$	−10.8841	−	4.88928i	−0.564317	−	0.253497i
$373$	10.0195	−	24.1893i	0.518792	−	1.25247i	−0.419854	−	0.907592i	$-0.637919\pi$
$373$	10.0195	−	24.1893i	0.518792	−	1.25247i	0.938646	−	0.344882i	$-0.112081\pi$
$374$	1.94371	−	4.50348i	0.100507	−	0.232869i
$375$	24.3979			1.25990
$376$	−5.06194	−	0.224127i	−0.261050	−	0.0115585i
$377$	31.4264	−	6.98032i	1.61854	−	0.359505i
$378$	−24.3959	+	9.68609i	−1.25479	+	0.498199i
$379$	17.1837	−	7.11774i	0.882670	−	0.365614i	0.105138	−	0.994458i	$-0.466472\pi$
$379$	17.1837	−	7.11774i	0.882670	−	0.365614i	0.777532	+	0.628844i	$0.216472\pi$
$380$	−0.0122446	+	0.414971i	−0.000628135	+	0.0212875i
$381$	−36.9842	+	15.3194i	−1.89476	+	0.784834i
$382$	−0.874351	−	0.900531i	−0.0447357	−	0.0460752i
$383$	22.3775	−	22.3775i	1.14344	−	1.14344i	0.155622	−	0.987817i	$-0.450262\pi$
$383$	22.3775	−	22.3775i	1.14344	−	1.14344i	0.987817	−	0.155622i	$-0.0497383\pi$
$384$	−29.8869	−	16.1702i	−1.52516	−	0.825184i
$385$	−3.33564	+	3.33564i	−0.170000	+	0.170000i
$386$	−0.389196	+	26.3855i	−0.0198095	+	1.34299i
$387$	17.6440	+	42.5963i	0.896893	+	2.16529i
$388$	12.9622	−	12.2192i	0.658055	−	0.620334i
$389$	2.82052	−	6.80935i	0.143006	−	0.345248i	−0.836106	−	0.548568i	$-0.815173\pi$
$389$	2.82052	−	6.80935i	0.143006	−	0.345248i	0.979112	+	0.203320i	$0.0651732\pi$
$390$	2.53218	−	13.2464i	0.128222	−	0.670760i
$391$	1.04993	−	1.04993i	0.0530974	−	0.0530974i
$392$	5.37759	+	5.87586i	0.271610	+	0.296776i
$393$	32.2881	−	32.2881i	1.62872	−	1.62872i
$394$	2.61278	+	1.12768i	0.131630	+	0.0568116i
$395$	3.94690	+	9.52866i	0.198590	+	0.479439i
$396$	−28.7689	−	12.9233i	−1.44569	−	0.649420i
$397$	1.08766	−	2.62584i	0.0545880	−	0.131787i	−0.894233	−	0.447602i	$-0.852278\pi$
$397$	1.08766	−	2.62584i	0.0545880	−	0.131787i	0.948821	+	0.315815i	$0.102278\pi$
$398$	17.6899	+	0.260933i	0.886716	+	0.0130794i
$399$	−1.44817			−0.0724993
$400$	−12.6326	+	11.2235i	−0.631630	+	0.561176i
$401$	0.501908	+	0.501908i	0.0250641	+	0.0250641i	0.719528	−	0.694464i	$-0.244358\pi$
$401$	0.501908	+	0.501908i	0.0250641	+	0.0250641i	−0.694464	+	0.719528i	$0.744358\pi$
$402$	33.6598	−	32.6813i	1.67880	−	1.62999i
$403$	4.11018	+	5.86493i	0.204743	+	0.292153i
$404$	−1.44886	−	0.650844i	−0.0720835	−	0.0323807i
$405$	7.47711	−	3.09712i	0.371541	−	0.153897i
$406$	−10.2347	+	23.7133i	−0.507938	+	1.17687i
$407$	8.18796	−	8.18796i	0.405862	−	0.405862i
$408$	−10.1935	−	4.76095i	−0.504654	−	0.235702i
$409$		−	30.1355i		−	1.49010i	−0.667007	−	0.745052i	$-0.732425\pi$
$409$		−	30.1355i		−	1.49010i	0.667007	−	0.745052i	$-0.267575\pi$
$410$	5.74394	+	2.47909i	0.283673	+	0.122433i
$411$	13.2770	+	32.0535i	0.654906	+	1.58108i
$412$	−20.6082	+	19.4269i	−1.01529	+	0.957094i
$413$	20.4434	−	8.46794i	1.00595	−	0.416680i
$414$	−6.65052	−	6.84965i	−0.326855	−	0.336642i
$415$	−7.09262			−0.348163
$416$	10.4430	+	17.5198i	0.512008	+	0.858981i
$417$	32.3514			1.58426
$418$	−0.608176	−	0.626386i	−0.0297468	−	0.0306375i
$419$	18.6369	−	7.71966i	0.910472	−	0.377130i	0.122235	−	0.992501i	$-0.460994\pi$
$419$	18.6369	−	7.71966i	0.910472	−	0.377130i	0.788237	+	0.615371i	$0.210994\pi$
$420$	7.42188	+	7.87320i	0.362151	+	0.384173i
$421$	−1.37908	−	3.32940i	−0.0672123	−	0.162265i	0.886704	−	0.462337i	$-0.152989\pi$
$421$	−1.37908	−	3.32940i	−0.0672123	−	0.162265i	−0.953916	+	0.300073i	$0.902989\pi$
$422$	−22.2229	−	9.59143i	−1.08179	−	0.466903i
$423$			10.7864i			0.524451i
$424$	−18.8834	+	6.85985i	−0.917058	+	0.333144i
$425$	−3.95606	+	3.95606i	−0.191897	+	0.191897i
$426$	24.1113	−	55.8649i	1.16820	−	2.70666i
$427$	5.10419	−	2.11423i	0.247009	−	0.102315i
$428$	−15.4286	+	34.3459i	−0.745768	+	1.66017i
$429$	16.2769	+	23.2260i	0.785856	+	1.12136i
$430$	6.84174	−	6.64284i	0.329938	−	0.320346i
$431$	20.6967	+	20.6967i	0.996926	+	0.996926i	0.999995	−	0.00306931i	$-0.000976992\pi$
$431$	20.6967	+	20.6967i	0.996926	+	0.996926i	−0.00306931	+	0.999995i	$0.500977\pi$
$432$	−15.8429	+	32.6558i	−0.762244	+	1.57115i
$433$	3.98645			0.191576			0.0957882	−	0.995402i	$-0.469463\pi$
$433$	3.98645			0.191576			0.0957882	+	0.995402i	$0.469463\pi$
$434$	−5.74521	−	0.0847440i	−0.275779	−	0.00406784i
$435$	9.03704	−	21.8173i	0.433293	−	1.04606i
$436$	4.87224	−	10.8462i	0.233338	−	0.519439i
$437$	−0.101139	−	0.244171i	−0.00483814	−	0.0116803i
$438$	−45.4411	−	19.6124i	−2.17126	−	0.937118i
$439$	−5.98016	+	5.98016i	−0.285418	+	0.285418i	−0.835265	−	0.549847i	$-0.814686\pi$
$439$	−5.98016	+	5.98016i	−0.285418	+	0.285418i	0.549847	+	0.835265i	$0.314686\pi$
$440$	−0.288537	+	6.51666i	−0.0137554	+	0.310669i
$441$	11.9899	−	11.9899i	0.570945	−	0.570945i
$442$	3.79349	+	5.58657i	0.180438	+	0.265726i
$443$	0.512828	−	1.23808i	0.0243652	−	0.0588228i	−0.911229	−	0.411901i	$-0.864865\pi$
$443$	0.512828	−	1.23808i	0.0243652	−	0.0588228i	0.935594	+	0.353078i	$0.114865\pi$
$444$	−18.2184	−	19.3262i	−0.864607	−	0.917183i
$445$	−0.164688	−	0.397592i	−0.00780695	−	0.0188476i
$446$	0.259918	−	17.6211i	0.0123075	−	0.834383i
$447$	18.3253	−	18.3253i	0.866758	−	0.866758i
$448$	−16.2996	−	1.44622i	−0.770083	−	0.0683276i
$449$	−6.61290	+	6.61290i	−0.312082	+	0.312082i	−0.845716	−	0.533634i	$-0.820826\pi$
$449$	−6.61290	+	6.61290i	−0.312082	+	0.312082i	0.533634	+	0.845716i	$0.320826\pi$
$450$	25.0586	+	25.8090i	1.18128	+	1.21665i
$451$	−12.1551	+	5.03479i	−0.572359	+	0.237079i
$452$	−42.4108	−	1.25142i	−1.99484	−	0.0588620i
$453$	−64.1047	+	26.5531i	−3.01190	+	1.24757i
$454$	3.45784	−	1.37289i	0.162284	−	0.0644330i
$455$	−1.40819	−	6.33986i	−0.0660168	−	0.297217i
$456$	−1.47724	+	1.35197i	−0.0691781	+	0.0633119i
$457$	18.8000			0.879428			0.439714	−	0.898138i	$-0.355080\pi$
$457$	18.8000			0.879428			0.439714	+	0.898138i	$0.355080\pi$
$458$	−9.43875	+	21.8692i	−0.441044	+	1.02188i
$459$	−4.59871	+	11.1023i	−0.214650	+	0.518210i
$460$	−0.809135	+	1.80124i	−0.0377261	+	0.0839830i
$461$	−4.06653	−	1.68441i	−0.189397	−	0.0784509i	0.285969	−	0.958239i	$-0.407684\pi$
$461$	−4.06653	−	1.68441i	−0.189397	−	0.0784509i	−0.475366	+	0.879788i	$0.657684\pi$
$462$	−22.7519	−	0.335598i	−1.05851	−	0.0156135i
$463$	−6.48479	+	6.48479i	−0.301374	+	0.301374i	−0.841551	−	0.540177i	$-0.818357\pi$
$463$	−6.48479	+	6.48479i	−0.301374	+	0.301374i	0.540177	+	0.841551i	$0.318357\pi$
$464$	11.6979	+	33.7440i	0.543062	+	1.56653i
$465$	5.25357			0.243629
$466$	−36.3983	−	0.536889i	−1.68612	−	0.0248709i
$467$	−0.813407	+	0.336924i	−0.0376400	+	0.0155910i	−0.401424	−	0.915892i	$-0.631485\pi$
$467$	−0.813407	+	0.336924i	−0.0376400	+	0.0155910i	0.363784	+	0.931483i	$0.381485\pi$
$468$	36.2762	−	23.8588i	1.67687	−	1.10287i
$469$	8.64567	−	20.8725i	0.399220	−	0.963803i
$470$	2.07349	−	0.823253i	0.0956430	−	0.0379738i
$471$	27.2580	+	27.2580i	1.25598	+	1.25598i
$472$	12.9483	−	27.7233i	0.595995	−	1.27607i
$473$			20.0543i			0.922099i
$474$	−19.7140	+	45.6765i	−0.905495	+	2.09799i
$475$	0.381084	+	0.920019i	0.0174853	+	0.0422134i
$476$	−5.41537	−	0.159792i	−0.248213	−	0.00732406i
$477$	16.3670	+	39.5134i	0.749394	+	1.80920i
$478$	12.3340	+	0.181931i	0.564145	+	0.00832134i
$479$	1.28653	+	1.28653i	0.0587830	+	0.0587830i	0.735887	−	0.677104i	$-0.236765\pi$
$479$	1.28653	+	1.28653i	0.0587830	+	0.0587830i	−0.677104	+	0.735887i	$0.736765\pi$
$480$	14.9210	+	1.10237i	0.681049	+	0.0503163i
$481$	3.45666	+	15.5624i	0.157610	+	0.709583i
$482$	4.76238	+	0.0702468i	0.216920	+	0.00319966i
$483$	−6.36377	−	2.63596i	−0.289561	−	0.119940i
$484$	5.68103	+	6.02649i	0.258229	+	0.273931i
$485$	−3.00150	+	7.24626i	−0.136291	+	0.329036i
$486$	0.496049	+	0.214095i	0.0225012	+	0.00971156i
$487$	16.1723			0.732836			0.366418	−	0.930450i	$-0.380584\pi$
$487$	16.1723			0.732836			0.366418	+	0.930450i	$0.380584\pi$
$488$	3.23286	−	6.92179i	0.146345	−	0.313335i
$489$		−	41.5035i		−	1.87685i
$490$	−3.21995	−	1.38973i	−0.145462	−	0.0627817i
$491$	10.5046	−	25.3603i	0.474065	−	1.14449i	−0.488286	−	0.872684i	$-0.662378\pi$
$491$	10.5046	−	25.3603i	0.474065	−	1.14449i	0.962351	−	0.271811i	$-0.0876224\pi$
$492$	10.7208	+	28.2082i	0.483332	+	1.27172i
$493$	4.52499	+	10.9243i	0.203795	+	0.492005i
$494$	1.17707	−	0.243288i	0.0529590	−	0.0109460i
$495$	13.8862			0.624137
$496$	−5.93964	+	5.27711i	−0.266698	+	0.236949i
$497$		−	29.3006i		−	1.31431i
$498$	−23.8320	−	24.5456i	−1.06794	−	1.09991i
$499$	−9.43132	+	22.7692i	−0.422204	+	1.01929i	0.559492	+	0.828836i	$0.310996\pi$
$499$	−9.43132	+	22.7692i	−0.422204	+	1.01929i	−0.981696	+	0.190454i	$0.939004\pi$
$500$	6.65713	−	14.8196i	0.297716	−	0.662753i
$501$	27.5451	+	66.4998i	1.23063	+	2.97099i
$502$	−4.60969	+	1.83022i	−0.205740	+	0.0816866i
$503$	−22.6293	−	22.6293i	−1.00899	−	1.00899i	−0.999959	−	0.00903146i	$-0.997125\pi$
$503$	−22.6293	−	22.6293i	−1.00899	−	1.00899i	−0.00903146	−	0.999959i	$-0.502875\pi$
$504$	−1.54086	+	34.8006i	−0.0686354	+	1.55014i
$505$	0.699337			0.0311201
$506$	−1.53239	−	3.85955i	−0.0681229	−	0.171578i
$507$	−39.0072	+	1.73451i	−1.73237	+	0.0770321i
$508$	−0.786211	+	26.6447i	−0.0348825	+	1.18217i
$509$	6.31826	−	15.2536i	0.280052	−	0.676106i	−0.719784	−	0.694198i	$-0.755759\pi$
$509$	6.31826	−	15.2536i	0.280052	−	0.676106i	0.999836	+	0.0180922i	$0.00575924\pi$
$510$	4.95304	+	0.0730591i	0.219324	+	0.00323511i
$511$	−23.8334			−1.05433
$512$	−17.9769	+	13.7416i	−0.794475	+	0.607297i
$513$	1.51246	+	1.51246i	0.0667768	+	0.0667768i
$514$	−16.0698	−	16.5510i	−0.708810	−	0.730033i
$515$	4.77200	−	11.5206i	0.210279	−	0.507659i
$516$	45.9780	+	1.35668i	2.02407	+	0.0597245i
$517$	−1.79542	+	4.33453i	−0.0789626	+	0.190633i
$518$	−11.7428	−	5.06821i	−0.515950	−	0.222685i
$519$	−51.5840	−	51.5840i	−2.26429	−	2.26429i
$520$	−7.35516	−	5.15247i	−0.322545	−	0.225951i
$521$	2.13044	−	2.13044i	0.0933361	−	0.0933361i	−0.658897	−	0.752233i	$-0.728977\pi$
$521$	2.13044	−	2.13044i	0.0933361	−	0.0933361i	0.752233	+	0.658897i	$0.228977\pi$
$522$	70.6621	−	28.0555i	3.09279	−	1.22796i
$523$	−10.8856	−	4.50897i	−0.475995	−	0.197163i	0.131771	−	0.991280i	$-0.457934\pi$
$523$	−10.8856	−	4.50897i	−0.475995	−	0.197163i	−0.607765	+	0.794117i	$0.707934\pi$
$524$	−10.8022	−	28.4223i	−0.471897	−	1.24163i
$525$	23.9782	+	9.93209i	1.04649	+	0.433472i
$526$	−0.204145	+	13.8400i	−0.00890114	+	0.603452i
$527$	−1.86008	+	1.86008i	−0.0810263	+	0.0810263i
$528$	−23.5218	+	20.8981i	−1.02366	+	0.909475i
$529$			21.7429i			0.945345i
$530$	6.34658	−	6.16207i	0.275678	−	0.267663i
$531$	−60.1785	−	24.9267i	−2.61152	−	1.08173i
$532$	−0.395145	+	0.879642i	−0.0171317	+	0.0381373i
$533$	3.13807	−	17.8388i	0.135925	−	0.772685i
$534$	0.822584	−	1.90589i	0.0355967	−	0.0824759i
$535$		−	16.5781i		−	0.716734i
$536$	−10.6667	−	29.3628i	−0.460733	−	1.26828i
$537$	13.5599	−	13.5599i	0.585153	−	0.585153i
$538$	−6.06514	+	14.0527i	−0.261487	+	0.605853i
$539$	6.81390	−	2.82241i	0.293496	−	0.121570i
$540$	0.471350	−	15.9741i	0.0202837	−	0.687415i
$541$	−34.7478	−	14.3930i	−1.49392	−	0.618804i	−0.521758	−	0.853094i	$-0.674723\pi$
$541$	−34.7478	−	14.3930i	−1.49392	−	0.618804i	−0.972167	+	0.234290i	$0.924723\pi$
$542$	0.0744049	−	5.04428i	0.00319597	−	0.216670i
$543$	49.7270			2.13399
$544$	−5.67324	+	4.89263i	−0.243238	+	0.209770i
$545$			5.23526i			0.224254i
$546$	17.2088	−	26.1760i	0.736470	−	1.12023i
$547$	−5.84700	+	2.42191i	−0.250000	+	0.103553i	−0.504164	−	0.863608i	$-0.668199\pi$
$547$	−5.84700	+	2.42191i	−0.250000	+	0.103553i	0.254165	+	0.967161i	$0.418199\pi$
$548$	23.0925	+	0.681394i	0.986462	+	0.0291077i
$549$	−15.0250	−	6.22357i	−0.641252	−	0.265615i
$550$	5.77391	+	14.5425i	0.246200	+	0.620094i
$551$	2.10465			0.0896613
$552$	−8.95235	+	3.25216i	−0.381037	+	0.138421i
$553$			23.9569i			1.01875i
$554$	0.0416052	−	0.0165188i	0.00176764	−	0.000701818i
$555$	10.8040	+	4.47515i	0.458603	+	0.189959i
$556$	8.82732	−	19.6507i	0.374362	−	0.833376i
$557$	−2.95448	+	7.13275i	−0.125185	+	0.302224i	−0.974030	−	0.226418i	$-0.927299\pi$
$557$	−2.95448	+	7.13275i	−0.125185	+	0.302224i	0.848845	+	0.528642i	$0.177299\pi$
$558$	11.7822	+	12.1350i	0.498779	+	0.513714i
$559$	−23.2912	−	14.8249i	−0.985111	−	0.627028i
$560$	6.80741	−	2.35990i	0.287666	−	0.0997240i
$561$	−7.36618	+	7.36618i	−0.311000	+	0.311000i
$562$	24.8517	−	24.1292i	1.04830	−	1.01783i
$563$	29.3773	−	12.1685i	1.23811	−	0.512840i	0.334984	−	0.942224i	$-0.391269\pi$
$563$	29.3773	−	12.1685i	1.23811	−	0.512840i	0.903122	+	0.429384i	$0.141269\pi$
$564$	9.81620	+	4.40955i	0.413337	+	0.185675i
$565$	17.2595	−	7.14910i	0.726111	−	0.300765i
$566$	−10.3890	+	4.12482i	−0.436683	+	0.173379i
$567$	18.7989			0.789479
$568$	−27.3542	−	29.8887i	−1.14776	−	1.25410i
$569$	−0.400472	+	0.400472i	−0.0167886	+	0.0167886i	−0.715451	−	0.698663i	$-0.753779\pi$
$569$	−0.400472	+	0.400472i	−0.0167886	+	0.0167886i	0.698663	+	0.715451i	$0.253779\pi$
$570$	0.349390	−	0.809521i	0.0146343	−	0.0339071i
$571$	−14.4764	−	5.99632i	−0.605819	−	0.250938i	0.0586208	−	0.998280i	$-0.481330\pi$
$571$	−14.4764	−	5.99632i	−0.605819	−	0.250938i	−0.664440	+	0.747342i	$0.731330\pi$
$572$	18.5491	−	3.54946i	0.775575	−	0.148410i
$573$	1.02013	+	2.46282i	0.0426166	+	0.102886i
$574$	10.1228	+	10.4259i	0.422518	+	0.435169i
$575$			4.73652i			0.197527i
$576$	30.9171	+	36.9376i	1.28821	+	1.53907i
$577$	−15.7622	−	15.7622i	−0.656189	−	0.656189i	0.298287	−	0.954476i	$-0.403585\pi$
$577$	−15.7622	−	15.7622i	−0.656189	−	0.656189i	−0.954476	+	0.298287i	$0.903585\pi$
$578$	15.4693	−	15.0196i	0.643440	−	0.624734i
$579$	21.4470	−	51.7777i	0.891309	−	2.15181i
$580$	−10.7863	−	11.4423i	−0.447879	−	0.475114i
$581$	−15.2207	−	6.30463i	−0.631462	−	0.261560i
$582$	−35.1627	+	13.9609i	−1.45754	+	0.578698i
$583$			18.6029i			0.770454i
$584$	−24.3118	+	22.2502i	−1.00603	+	0.920720i
$585$	−10.2652	+	16.1274i	−0.424414	+	0.666788i
$586$	−11.1681	+	25.8759i	−0.461349	+	1.06893i
$587$	−16.9991	−	41.0394i	−0.701627	−	1.69388i	−0.719932	−	0.694045i	$-0.755827\pi$
$587$	−16.9991	−	41.0394i	−0.701627	−	1.69388i	0.0183051	−	0.999832i	$-0.494173\pi$
$588$	−6.00990	−	15.8130i	−0.247844	−	0.652116i
$589$	0.179180	+	0.432578i	0.00738297	+	0.0178241i
$590$	−0.198699	+	13.4708i	−0.00818029	+	0.554582i
$591$	−4.27363	−	4.27363i	−0.175794	−	0.175794i
$592$	−16.7101	+	5.79282i	−0.686779	+	0.238083i
$593$	16.2632	+	16.2632i	0.667849	+	0.667849i	0.957218	−	0.289369i	$-0.0934453\pi$
$593$	16.2632	+	16.2632i	0.667849	+	0.667849i	−0.289369	+	0.957218i	$0.593445\pi$
$594$	23.4114	+	24.1124i	0.960581	+	0.989343i
$595$	2.20383	−	0.912857i	0.0903483	−	0.0374235i
$596$	−6.13087	−	16.1313i	−0.251130	−	0.660763i
$597$	−34.7140	−	14.3790i	−1.42075	−	0.588493i
$598$	5.61529	+	1.07341i	0.229626	+	0.0438951i
$599$	8.42004	+	8.42004i	0.344033	+	0.344033i	0.857881	−	0.513848i	$-0.171780\pi$
$599$	8.42004	+	8.42004i	0.344033	+	0.344033i	−0.513848	+	0.857881i	$0.671780\pi$
$600$	33.7318	−	12.2539i	1.37709	−	0.500263i
$601$	15.0789	+	15.0789i	0.615079	+	0.615079i	0.944265	−	0.329186i	$-0.106774\pi$
$601$	15.0789	+	15.0789i	0.615079	+	0.615079i	−0.329186	+	0.944265i	$0.606774\pi$
$602$	20.5872	−	8.17388i	0.839071	−	0.333143i
$603$	−61.4416	+	25.4499i	−2.50210	+	1.03640i
$604$	−1.36274	+	46.1834i	−0.0554491	+	1.87917i
$605$	−3.36899	−	1.39548i	−0.136969	−	0.0567344i
$606$	2.34985	+	2.42021i	0.0954561	+	0.0983143i
$607$			16.4206i			0.666490i	0.942840	+	0.333245i	$0.108144\pi$
$607$			16.4206i			0.666490i	−0.942840	+	0.333245i	$0.891856\pi$
$608$	0.418132	+	1.26619i	0.0169575	+	0.0513509i
$609$	38.7869	−	38.7869i	1.57173	−	1.57173i
$610$	−0.0496099	+	3.36330i	−0.00200865	+	0.136176i
$611$	−3.70689	−	5.28946i	−0.149965	−	0.213989i
$612$	10.9394	+	11.6046i	0.442199	+	0.469089i
$613$	−11.7082	−	28.2660i	−0.472889	−	1.14165i	−0.962881	−	0.269927i	$-0.913000\pi$
$613$	−11.7082	−	28.2660i	−0.472889	−	1.14165i	0.489992	−	0.871727i	$-0.337000\pi$
$614$	−14.0414	+	5.57498i	−0.566667	+	0.224988i
$615$	−9.39514	−	9.39514i	−0.378849	−	0.378849i
$616$	−6.41186	+	13.7282i	−0.258341	+	0.553127i
$617$	−2.11544			−0.0851643			−0.0425822	−	0.999093i	$-0.513558\pi$
$617$	−2.11544			−0.0851643			−0.0425822	+	0.999093i	$0.513558\pi$
$618$	55.9041	−	22.1960i	2.24879	−	0.892855i
$619$	−42.1776	+	17.4705i	−1.69526	+	0.702199i	−0.999865	−	0.0164291i	$-0.994770\pi$
$619$	−42.1776	+	17.4705i	−1.69526	+	0.702199i	−0.695394	+	0.718628i	$0.744770\pi$
$620$	1.43348	−	3.19110i	0.0575698	−	0.128158i
$621$	3.89330	+	9.39925i	0.156233	+	0.377179i
$622$	−0.0156710	+	1.06241i	−0.000628349	+	0.0425989i
$623$		−	0.999621i		−	0.0400490i
$624$	−6.88289	−	42.7670i	−0.275536	−	1.71205i
$625$		−	13.9696i		−	0.558785i
$626$	−20.7340	−	0.305833i	−0.828695	−	0.0122236i
$627$	0.709578	+	1.71307i	0.0283378	+	0.0684135i
$628$	23.9944	−	9.11935i	0.957482	−	0.363902i
$629$	−5.40972	+	2.24078i	−0.215699	+	0.0893457i
$630$	−5.65982	−	14.2551i	−0.225493	−	0.567939i
$631$	6.75019			0.268721			0.134360	−	0.990933i	$-0.457102\pi$
$631$	6.75019			0.268721			0.134360	+	0.990933i	$0.457102\pi$
$632$	22.3654	+	24.4377i	0.889650	+	0.972081i
$633$	36.3492	+	36.3492i	1.44475	+	1.44475i
$634$	−2.25817	−	5.68756i	−0.0896835	−	0.225882i
$635$	−4.49145	−	10.8433i	−0.178238	−	0.430304i
$636$	42.6504	+	1.25849i	1.69120	+	0.0499025i
$637$	−1.75915	+	10.0001i	−0.0696999	+	0.396219i
$638$	33.0657	+	0.487731i	1.30908	+	0.0193094i
$639$	−60.9888	+	60.9888i	−2.41268	+	2.41268i
$640$	4.74091	−	8.76247i	0.187401	−	0.346367i
$641$			21.8862i			0.864452i	0.901765	+	0.432226i	$0.142272\pi$
$641$			21.8862i			0.864452i	−0.901765	+	0.432226i	$0.857728\pi$
$642$	57.3722	−	55.7043i	2.26430	−	2.19847i
$643$	31.0385	+	12.8566i	1.22404	+	0.507013i	0.898691	−	0.438582i	$-0.144519\pi$
$643$	31.0385	+	12.8566i	1.22404	+	0.507013i	0.325346	+	0.945595i	$0.394519\pi$
$644$	−3.33752	+	3.14620i	−0.131517	+	0.123978i
$645$	−18.7112	+	7.75041i	−0.736751	+	0.305172i
$646$	0.162914	+	0.410324i	0.00640976	+	0.0161440i
$647$	16.4555	+	16.4555i	0.646934	+	0.646934i	0.952251	−	0.305317i	$-0.0987623\pi$
$647$	16.4555	+	16.4555i	0.646934	+	0.646934i	−0.305317	+	0.952251i	$0.598762\pi$
$648$	19.1762	−	17.5501i	0.753313	−	0.689433i
$649$	−20.0338	−	20.0338i	−0.786394	−	0.786394i
$650$	−21.1580	−	4.04454i	−0.829884	−	0.158640i
$651$	11.2742	+	4.66991i	0.441869	+	0.183028i
$652$	−25.2098	−	11.3245i	−0.987294	−	0.443503i
$653$	19.4973	−	8.07603i	0.762987	−	0.316040i	0.0329589	−	0.999457i	$-0.489507\pi$
$653$	19.4973	−	8.07603i	0.762987	−	0.316040i	0.730028	+	0.683417i	$0.239507\pi$
$654$	−18.1178	+	17.5911i	−0.708461	+	0.687865i
$655$	9.46647	+	9.46647i	0.369886	+	0.369886i
$656$	20.0593	+	1.18482i	0.783184	+	0.0462594i
$657$	49.6089	+	49.6089i	1.93543	+	1.93543i
$658$	5.18149	+	0.0764290i	0.201996	+	0.00297951i
$659$	6.48122	+	15.6470i	0.252472	+	0.609522i	0.998402	−	0.0565021i	$-0.0179947\pi$
$659$	6.48122	+	15.6470i	0.252472	+	0.609522i	−0.745930	+	0.666024i	$0.767995\pi$
$660$	5.67677	−	12.6372i	0.220968	−	0.491903i
$661$	−7.59696	−	18.3407i	−0.295488	−	0.713370i	−0.999993	−	0.00367191i	$-0.998831\pi$
$661$	−7.59696	−	18.3407i	−0.295488	−	0.713370i	0.704506	−	0.709698i	$-0.251169\pi$
$662$	−15.4476	−	6.66720i	−0.600388	−	0.259128i
$663$	−3.10973	−	14.0005i	−0.120772	−	0.543733i
$664$	−21.4121	+	7.77845i	−0.830949	+	0.301862i
$665$		−	0.424586i		−	0.0164648i
$666$	13.8931	+	34.9919i	0.538347	+	1.35591i
$667$	9.24857	+	3.83088i	0.358106	+	0.148332i
$668$	47.9088	+	1.41365i	1.85365	+	0.0546959i
$669$	−14.3230	+	34.5789i	−0.553760	+	1.33690i
$670$	9.58174	+	9.86864i	0.370175	+	0.381259i
$671$	−5.00192	−	5.00192i	−0.193097	−	0.193097i
$672$	31.0406	+	15.6290i	1.19742	+	0.602903i
$673$		−	25.0840i		−	0.966918i	−0.875367	−	0.483459i	$-0.839380\pi$
$673$		−	25.0840i		−	0.966918i	0.875367	−	0.483459i	$-0.160620\pi$
$674$	−29.3401	+	28.4871i	−1.13014	+	1.09728i
$675$	−14.6696	−	35.4156i	−0.564635	−	1.36315i
$676$	−9.58984	+	24.1668i	−0.368840	+	0.929493i
$677$	11.3920	+	4.71874i	0.437832	+	0.181356i	0.590701	−	0.806891i	$-0.298851\pi$
$677$	11.3920	+	4.71874i	0.437832	+	0.181356i	−0.152869	+	0.988246i	$0.548851\pi$
$678$	82.7347	+	35.7084i	3.17741	+	1.37137i
$679$	−12.8824	+	12.8824i	−0.494382	+	0.494382i
$680$	1.39585	−	2.98861i	0.0535284	−	0.114608i
$681$	−7.90145			−0.302784
$682$	2.71480	+	6.83764i	0.103955	+	0.261827i
$683$	−19.9239	+	8.25274i	−0.762366	+	0.315782i	−0.729776	−	0.683686i	$-0.760376\pi$
$683$	−19.9239	+	8.25274i	−0.762366	+	0.315782i	−0.0325902	+	0.999469i	$0.510376\pi$
$684$	2.65345	−	1.00847i	0.101457	−	0.0385599i
$685$	−9.39769	+	3.89265i	−0.359067	+	0.148730i
$686$	−19.7801	−	20.3724i	−0.755208	−	0.777821i
$687$	35.7706	−	35.7706i	1.36473	−	1.36473i
$688$	13.3695	−	27.5575i	0.509708	−	1.05062i
$689$	−21.6055	−	13.7520i	−0.823103	−	0.523910i
$690$	3.00883	−	2.92135i	0.114544	−	0.111214i
$691$	−15.3375	+	37.0279i	−0.583465	+	1.40861i	0.306189	+	0.951971i	$0.400946\pi$
$691$	−15.3375	+	37.0279i	−0.583465	+	1.40861i	−0.889653	+	0.456637i	$0.849054\pi$
$692$	−45.4080	+	17.2578i	−1.72615	+	0.656044i
$693$	29.7997	+	12.3434i	1.13200	+	0.468889i
$694$	−6.56099	−	16.5249i	−0.249052	−	0.627275i
$695$			9.48503i			0.359788i
$696$	3.35511	−	75.7758i	0.127175	−	2.87227i
$697$	6.65288			0.251996
$698$	−7.19450	+	2.85649i	−0.272316	+	0.108120i
$699$	71.4265	+	29.5858i	2.70160	+	1.11904i
$700$	12.5755	−	11.8547i	0.475310	−	0.448064i
$701$	8.28403	−	3.43136i	0.312884	−	0.129601i	−0.220715	−	0.975338i	$-0.570839\pi$
$701$	8.28403	−	3.43136i	0.312884	−	0.129601i	0.533599	+	0.845738i	$0.320839\pi$
$702$	−45.3108	+	9.36524i	−1.71015	+	0.353468i
$703$			1.04223i			0.0393083i
$704$	6.27573	+	19.9897i	0.236525	+	0.753391i
$705$	−4.73810			−0.178447
$706$	16.6767	+	0.245987i	0.627635	+	0.00925784i
$707$	1.50078	+	0.621642i	0.0564425	+	0.0233792i
$708$	−47.2862	+	44.5756i	−1.77712	+	1.67525i
$709$	−21.3407	+	8.83963i	−0.801468	+	0.331979i	−0.745544	−	0.666456i	$-0.767810\pi$
$709$	−21.3407	+	8.83963i	−0.801468	+	0.331979i	−0.0559240	+	0.998435i	$0.517810\pi$
$710$	16.3789	+	7.06915i	0.614689	+	0.265300i
$711$	49.8659	−	49.8659i	1.87012	−	1.87012i
$712$	−0.933217	−	1.01969i	−0.0349738	−	0.0382143i
$713$			2.22704i			0.0834032i
$714$	10.5643	+	4.55954i	0.395357	+	0.170637i
$715$	−6.80956	+	4.77219i	−0.254663	+	0.178470i
$716$	−4.53656	−	11.9364i	−0.169539	−	0.446084i
$717$	−24.2037	−	10.0255i	−0.903905	−	0.374410i
$718$	−15.5998	−	16.0669i	−0.582178	−	0.599610i
$719$		−	8.78906i		−	0.327777i	−0.986479	−	0.163888i	$-0.947596\pi$
$719$		−	8.78906i		−	0.327777i	0.986479	−	0.163888i	$-0.0524037\pi$
$720$	−19.0816	−	9.25742i	−0.711130	−	0.345004i
$721$	20.4814	−	20.4814i	0.762767	−	0.762767i
$722$	−26.7886	−	0.395141i	−0.996967	−	0.0147056i
$723$	−9.34548	−	3.87103i	−0.347562	−	0.143965i
$724$	13.5684	−	30.2049i	0.504265	−	1.12256i
$725$	−34.8479	−	14.4345i	−1.29422	−	0.536083i
$726$	−6.49081	−	16.3481i	−0.240897	−	0.606735i
$727$	−17.8903	+	17.8903i	−0.663514	+	0.663514i	−0.956207	−	0.292693i	$-0.905449\pi$
$727$	−17.8903	+	17.8903i	−0.663514	+	0.663514i	0.292693	+	0.956207i	$0.405449\pi$
$728$	−11.2041	−	17.5952i	−0.415252	−	0.652122i
$729$	18.6848	+	18.6848i	0.692029	+	0.692029i
$730$	5.75012	−	13.3228i	0.212821	−	0.493098i
$731$	3.88075	−	9.36897i	0.143535	−	0.346524i
$732$	−11.8061	+	11.1294i	−0.436367	+	0.411354i
$733$	9.72782	−	23.4850i	0.359305	−	0.867440i	−0.636093	−	0.771613i	$-0.719450\pi$
$733$	9.72782	−	23.4850i	0.359305	−	0.867440i	0.995398	−	0.0958272i	$-0.0305496\pi$
$734$	11.0566	−	10.7351i	0.408105	−	0.396240i
$735$	5.26675	+	5.26675i	0.194267	+	0.194267i
$736$	−0.467306	+	6.32517i	−0.0172251	+	0.233149i
$737$	−28.9267			−1.06553
$738$	0.630900	−	42.7718i	0.0232237	−	1.57445i
$739$	3.36238	−	8.11750i	0.123687	−	0.298607i	−0.849892	−	0.526957i	$-0.823333\pi$
$739$	3.36238	−	8.11750i	0.123687	−	0.298607i	0.973579	+	0.228350i	$0.0733330\pi$
$740$	5.66621	−	5.34141i	0.208294	−	0.196354i
$741$	−2.51411	−	0.442264i	−0.0923582	−	0.0162470i
$742$	19.0972	−	7.58231i	0.701081	−	0.278355i
$743$	−23.3239			−0.855672			−0.427836	−	0.903856i	$-0.640724\pi$
$743$	−23.3239			−0.855672			−0.427836	+	0.903856i	$0.640724\pi$
$744$	15.8601	−	5.76158i	0.581461	−	0.211230i
$745$	5.37276	+	5.37276i	0.196843	+	0.196843i
$746$	13.6637	+	34.4141i	0.500263	+	1.25999i
$747$	18.5587	+	44.8047i	0.679028	+	1.63932i
$748$	2.46441	+	6.48424i	0.0901077	+	0.237087i
$749$	14.7363	−	35.5766i	0.538453	−	1.29994i
$750$	−24.7550	+	24.0354i	−0.903926	+	0.877647i
$751$		−	1.58052i		−	0.0576741i	−0.999584	−	0.0288371i	$-0.990820\pi$
$751$		−	1.58052i		−	0.0576741i	0.999584	−	0.0288371i	$-0.00918040\pi$
$752$	5.35685	−	4.75933i	0.195344	−	0.173555i
$753$	10.5335			0.383863
$754$	−25.0099	+	38.0420i	−0.910806	+	1.38541i
$755$	−7.78503	−	18.7947i	−0.283326	−	0.684010i
$756$	15.2109	−	33.8613i	0.553215	−	1.23153i
$757$	−10.6823	+	25.7894i	−0.388255	+	0.937331i	0.602055	+	0.798455i	$0.294349\pi$
$757$	−10.6823	+	25.7894i	−0.388255	+	0.937331i	−0.990310	+	0.138876i	$0.955651\pi$
$758$	−10.4233	+	24.1504i	−0.378592	+	0.877181i
$759$			8.81939i			0.320124i
$760$	−0.396381	−	0.433109i	−0.0143783	−	0.0157105i
$761$	−37.3789			−1.35498			−0.677492	−	0.735530i	$-0.736933\pi$
$761$	−37.3789			−1.35498			−0.677492	+	0.735530i	$0.736933\pi$
$762$	22.4339	−	51.9783i	0.812694	−	1.88298i
$763$	−4.65363	+	11.2349i	−0.168473	+	0.406729i
$764$	1.77430	+	0.0523546i	0.0641920	+	0.00189412i
$765$	−6.48734	−	2.68714i	−0.234550	−	0.0971539i
$766$	−0.660082	+	44.7502i	−0.0238497	+	1.61689i
$767$	38.0770	−	8.45753i	1.37488	−	0.305384i
$768$	46.2544	−	13.0359i	1.66906	−	0.470392i
$769$	19.3582	+	19.3582i	0.698076	+	0.698076i	0.963995	−	0.265919i	$-0.0856754\pi$
$769$	19.3582	+	19.3582i	0.698076	+	0.698076i	−0.265919	+	0.963995i	$0.585675\pi$
$770$	0.0983933	−	6.67056i	0.00354585	−	0.240390i

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01464 + 0.985142i) q^{2} +(2.77489 - 1.14940i) q^{3} +(0.0589886 - 1.99913i) q^{4} +(0.336989 + 0.813563i) q^{5} +(-1.68319 + 3.89989i) q^{6} +2.04545i q^{7} +(1.90958 + 2.08651i) q^{8} +(4.25758 - 4.25758i) q^{9} +(-1.14340 - 0.493492i) q^{10} +(2.41961 - 1.00223i) q^{11} +(-2.13411 - 5.61517i) q^{12} +(-0.624670 + 3.55103i) q^{13} +(-2.01506 - 2.07540i) q^{14} +(1.87021 + 1.87021i) q^{15} +(-3.99304 - 0.235852i) q^{16} -1.32433 q^{17} +(-0.125588 + 8.51423i) q^{18} +(-0.0902070 + 0.217779i) q^{19} +(1.64630 - 0.625694i) q^{20} +(2.35104 + 5.67591i) q^{21} +(-1.46769 + 3.40056i) q^{22} +(-0.792801 + 0.792801i) q^{23} +(7.69709 + 3.59497i) q^{24} +(2.98721 - 2.98721i) q^{25} +(-2.86445 - 4.21840i) q^{26} +(3.47247 - 8.38329i) q^{27} +(4.08913 + 0.120659i) q^{28} +(-3.41680 - 8.24889i) q^{29} +(-3.74002 - 0.0551667i) q^{30} +(1.40454 - 1.40454i) q^{31} +(4.28385 - 3.69441i) q^{32} +(5.56218 - 5.56218i) q^{33} +(1.34372 - 1.30466i) q^{34} +(-1.66411 + 0.689295i) q^{35} +(-8.26030 - 8.76260i) q^{36} +(4.08486 - 1.69200i) q^{37} +(-0.123016 - 0.309834i) q^{38} +(2.34815 + 10.5717i) q^{39} +(-1.05400 + 2.25669i) q^{40} -5.02357 q^{41} +(-7.97703 - 3.44290i) q^{42} +(-2.93034 + 7.07448i) q^{43} +(-1.86087 - 4.89623i) q^{44} +(4.89856 + 2.02905i) q^{45} +(0.0233857 - 1.58543i) q^{46} +(-1.26673 + 1.26673i) q^{47} +(-11.3513 + 3.93513i) q^{48} +2.81612 q^{49} +(-0.0881153 + 5.97377i) q^{50} +(-3.67488 + 1.52219i) q^{51} +(7.06211 + 1.45827i) q^{52} +(-2.71826 + 6.56247i) q^{53} +(4.73542 + 11.9269i) q^{54} +(1.63076 + 1.63076i) q^{55} +(-4.26786 + 3.90595i) q^{56} +0.707996i q^{57} +(11.5932 + 5.00362i) q^{58} +(-4.13988 - 9.99456i) q^{59} +(3.84912 - 3.62848i) q^{60} +(-1.03362 - 2.49538i) q^{61} +(-0.0414304 + 2.80877i) q^{62} +(8.70868 + 8.70868i) q^{63} +(-0.707043 + 7.96869i) q^{64} +(-3.09949 + 0.688448i) q^{65} +(-0.164070 + 11.1231i) q^{66} +(-10.2043 - 4.22678i) q^{67} +(-0.0781207 + 2.64752i) q^{68} +(-1.28869 + 3.11118i) q^{69} +(1.00941 - 2.33877i) q^{70} -14.3248 q^{71} +(17.0136 + 0.753310i) q^{72} +11.6519i q^{73} +(-2.47780 + 5.74094i) q^{74} +(4.85569 - 11.7227i) q^{75} +(0.430047 + 0.193182i) q^{76} +(2.05002 + 4.94919i) q^{77} +(-12.7972 - 8.41321i) q^{78} +11.7123 q^{79} +(-1.15373 - 3.32807i) q^{80} -9.19057i q^{81} +(5.09711 - 4.94893i) q^{82} +(-3.08227 + 7.44125i) q^{83} +(11.4856 - 4.36522i) q^{84} +(-0.446286 - 1.07743i) q^{85} +(-3.99612 - 10.0649i) q^{86} +(-18.9625 - 18.9625i) q^{87} +(6.71159 + 3.13469i) q^{88} -0.488704 q^{89} +(-6.96919 + 2.76703i) q^{90} +(-7.26346 - 1.27773i) q^{91} +(1.53815 + 1.63168i) q^{92} +(2.28307 - 5.51181i) q^{93} +(0.0373653 - 2.53318i) q^{94} -0.207576 q^{95} +(7.64086 - 15.1754i) q^{96} +(6.29808 + 6.29808i) q^{97} +(-2.85735 + 2.77428i) q^{98} +(6.03457 - 14.5688i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24}+ \cdots - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

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