LMFDB - Embedded newform 930.2.bg.h.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	930.121
Dual form			930.2.bg.h.661.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-4.34565 + 0.923697i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-4.34565 + 0.923697i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(0.280861 + 0.311928i) q^{11} +(-0.913545 - 0.406737i) q^{12} +(-4.57137 + 2.03530i) q^{13} +(-2.97277 + 3.30160i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.519612 + 0.577087i) q^{17} +(-0.913545 + 0.406737i) q^{18} +(4.80198 + 2.13798i) q^{19} +(0.669131 + 0.743145i) q^{20} +(0.464393 + 4.41840i) q^{21} +(0.410568 + 0.0872689i) q^{22} +(1.73329 + 5.33453i) q^{23} +(-0.978148 + 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.50199 + 4.33358i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.464393 + 4.41840i) q^{28} +(-3.73700 + 2.71509i) q^{29} +1.00000 q^{30} +(-4.06704 + 3.80253i) q^{31} -1.00000 q^{32} +(0.339577 - 0.246717i) q^{33} +(-0.0811713 + 0.772294i) q^{34} +(1.37288 - 4.22529i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.38159 - 5.85709i) q^{37} +(5.14155 - 1.09287i) q^{38} +(1.54632 + 4.75907i) q^{39} +(0.978148 + 0.207912i) q^{40} +(-0.00274207 - 0.0260891i) q^{41} +(2.97277 + 3.30160i) q^{42} +(-6.04175 - 2.68996i) q^{43} +(0.383452 - 0.170724i) q^{44} +(0.669131 - 0.743145i) q^{45} +(4.53782 + 3.29692i) q^{46} +(-6.32909 - 4.59835i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(11.6367 - 5.18098i) q^{49} +(-0.913545 - 0.406737i) q^{50} +(0.519612 + 0.577087i) q^{51} +(0.523059 + 4.97657i) q^{52} +(-2.05340 - 0.436464i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-0.410568 + 0.0872689i) q^{55} +(2.22137 + 3.84752i) q^{56} +(2.62821 - 4.55219i) q^{57} +(-1.42741 + 4.39311i) q^{58} +(0.124576 - 1.18526i) q^{59} +(0.809017 - 0.587785i) q^{60} +4.03692 q^{61} +(-1.05523 + 5.46685i) q^{62} +4.44274 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.523059 - 4.97657i) q^{65} +(0.129707 - 0.399197i) q^{66} +(-3.48366 + 6.03388i) q^{67} +(0.388274 + 0.672510i) q^{68} +(5.48649 - 1.16619i) q^{69} +(-1.37288 - 4.22529i) q^{70} +(-14.2882 - 3.03706i) q^{71} +(0.104528 + 0.994522i) q^{72} +(7.94938 + 8.82868i) q^{73} +(-6.17847 - 2.75083i) q^{74} +(-0.913545 + 0.406737i) q^{75} +(3.51723 - 3.90628i) q^{76} +(-1.50865 - 1.09610i) q^{77} +(4.04831 + 2.94127i) q^{78} +(-4.29806 + 4.77348i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-0.0175532 - 0.0194948i) q^{82} +(-0.629081 - 5.98531i) q^{83} +(4.34565 + 0.923697i) q^{84} +(-0.239966 - 0.738541i) q^{85} +(-6.46900 + 1.37503i) q^{86} +(2.30959 + 4.00033i) q^{87} +(0.209870 - 0.363506i) q^{88} +(3.59017 - 11.0494i) q^{89} +(0.104528 - 0.994522i) q^{90} +(17.9856 - 13.0673i) q^{91} +5.60906 q^{92} +(3.35658 + 4.44223i) q^{93} -7.82319 q^{94} +(-4.25253 + 3.08964i) q^{95} +(-0.104528 + 0.994522i) q^{96} +(3.76259 - 11.5801i) q^{97} +(6.36896 - 11.0314i) q^{98} +(-0.209870 - 0.363506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{15}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$3$	0.104528	−	0.994522i	0.0603495	−	0.574187i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−4.34565	+	0.923697i	−1.64250	+	0.349125i	−0.934190	−	0.356775i	$-0.883876\pi$
$7$	−4.34565	+	0.923697i	−1.64250	+	0.349125i	−0.708312	+	0.705899i	$0.750543\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	0.104528	+	0.994522i	0.0330548	+	0.314495i
$11$	0.280861	+	0.311928i	0.0846828	+	0.0940498i	0.783997	−	0.620765i	$-0.213178\pi$
$11$	0.280861	+	0.311928i	0.0846828	+	0.0940498i	−0.699314	+	0.714815i	$0.746511\pi$
$12$	−0.913545	−	0.406737i	−0.263718	−	0.117415i
$13$	−4.57137	+	2.03530i	−1.26787	+	0.564492i	−0.926803	−	0.375547i	$-0.877455\pi$
$13$	−4.57137	+	2.03530i	−1.26787	+	0.564492i	−0.341066	+	0.940039i	$0.610788\pi$
$14$	−2.97277	+	3.30160i	−0.794507	+	0.882389i
$15$	0.809017	+	0.587785i	0.208887	+	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.519612	+	0.577087i	−0.126024	+	0.139964i	−0.802855	−	0.596175i	$-0.796686\pi$
$17$	−0.519612	+	0.577087i	−0.126024	+	0.139964i	0.676830	+	0.736139i	$0.263353\pi$
$18$	−0.913545	+	0.406737i	−0.215325	+	0.0958687i
$19$	4.80198	+	2.13798i	1.10165	+	0.490486i	0.875310	−	0.483563i	$-0.160658\pi$
$19$	4.80198	+	2.13798i	1.10165	+	0.490486i	0.226339	+	0.974049i	$0.427324\pi$
$20$	0.669131	+	0.743145i	0.149622	+	0.166172i
$21$	0.464393	+	4.41840i	0.101339	+	0.964174i
$22$	0.410568	+	0.0872689i	0.0875334	+	0.0186058i
$23$	1.73329	+	5.33453i	0.361417	+	1.11233i	0.952195	+	0.305492i	$0.0988211\pi$
$23$	1.73329	+	5.33453i	0.361417	+	1.11233i	−0.590778	+	0.806834i	$0.701179\pi$
$24$	−0.978148	+	0.207912i	−0.199664	+	0.0424398i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.50199	+	4.33358i	−0.490681	+	0.849885i
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−0.464393	+	4.41840i	−0.0877619	+	0.834999i
$29$	−3.73700	+	2.71509i	−0.693944	+	0.504180i	−0.877954	−	0.478745i	$-0.841092\pi$
$29$	−3.73700	+	2.71509i	−0.693944	+	0.504180i	0.184011	+	0.982924i	$0.441092\pi$
$30$	1.00000			0.182574
$31$	−4.06704	+	3.80253i	−0.730461	+	0.682954i
$31$	−4.06704	+	3.80253i	−0.730461	+	0.682954i
$32$	−1.00000			−0.176777
$33$	0.339577	−	0.246717i	0.0591128	−	0.0429480i
$34$	−0.0811713	+	0.772294i	−0.0139208	+	0.132447i
$35$	1.37288	−	4.22529i	0.232059	−	0.714205i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.38159	−	5.85709i	−0.555930	−	0.962899i	−0.997831	−	0.0658350i	$-0.979029\pi$
$37$	−3.38159	−	5.85709i	−0.555930	−	0.962899i	0.441900	−	0.897064i	$-0.354304\pi$
$38$	5.14155	−	1.09287i	0.834070	−	0.177287i
$39$	1.54632	+	4.75907i	0.247609	+	0.762062i
$40$	0.978148	+	0.207912i	0.154659	+	0.0328737i
$41$	−0.00274207	−	0.0260891i	−0.000428240	−	0.00407443i	0.994306	−	0.106565i	$-0.0339854\pi$
$41$	−0.00274207	−	0.0260891i	−0.000428240	−	0.00407443i	−0.994734	+	0.102491i	$0.967319\pi$
$42$	2.97277	+	3.30160i	0.458709	+	0.509448i
$43$	−6.04175	−	2.68996i	−0.921358	−	0.410215i	−0.109445	−	0.993993i	$-0.534907\pi$
$43$	−6.04175	−	2.68996i	−0.921358	−	0.410215i	−0.811914	+	0.583778i	$0.801574\pi$
$44$	0.383452	−	0.170724i	0.0578076	−	0.0257376i
$45$	0.669131	−	0.743145i	0.0997481	−	0.110781i
$46$	4.53782	+	3.29692i	0.669066	+	0.486105i
$47$	−6.32909	−	4.59835i	−0.923193	−	0.670739i	0.0211238	−	0.999777i	$-0.493276\pi$
$47$	−6.32909	−	4.59835i	−0.923193	−	0.670739i	−0.944317	+	0.329038i	$0.893276\pi$
$48$	−0.669131	+	0.743145i	−0.0965807	+	0.107264i
$49$	11.6367	−	5.18098i	1.66238	−	0.740140i
$50$	−0.913545	−	0.406737i	−0.129195	−	0.0575212i
$51$	0.519612	+	0.577087i	0.0727602	+	0.0808084i
$52$	0.523059	+	4.97657i	0.0725352	+	0.690127i
$53$	−2.05340	−	0.436464i	−0.282057	−	0.0599530i	0.0647111	−	0.997904i	$-0.479387\pi$
$53$	−2.05340	−	0.436464i	−0.282057	−	0.0599530i	−0.346768	+	0.937951i	$0.612721\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	−0.410568	+	0.0872689i	−0.0553610	+	0.0117673i
$56$	2.22137	+	3.84752i	0.296843	+	0.514147i
$57$	2.62821	−	4.55219i	0.348115	−	0.602952i
$58$	−1.42741	+	4.39311i	−0.187428	+	0.576843i
$59$	0.124576	−	1.18526i	0.0162184	−	0.154308i	−0.983415	−	0.181367i	$-0.941948\pi$
$59$	0.124576	−	1.18526i	0.0162184	−	0.154308i	0.999634	+	0.0270595i	$0.00861436\pi$
$60$	0.809017	−	0.587785i	0.104444	−	0.0758827i
$61$	4.03692			0.516874			0.258437	−	0.966028i	$-0.416793\pi$
$61$	4.03692			0.516874			0.258437	+	0.966028i	$0.416793\pi$
$62$	−1.05523	+	5.46685i	−0.134015	+	0.694291i
$63$	4.44274			0.559732
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.523059	−	4.97657i	0.0648775	−	0.617268i
$66$	0.129707	−	0.399197i	0.0159658	−	0.0491377i
$67$	−3.48366	+	6.03388i	−0.425597	+	0.737155i	−0.996476	−	0.0838788i	$-0.973269\pi$
$67$	−3.48366	+	6.03388i	−0.425597	+	0.737155i	0.570879	+	0.821034i	$0.306602\pi$
$68$	0.388274	+	0.672510i	0.0470851	+	0.0815538i
$69$	5.48649	−	1.16619i	0.660495	−	0.140393i
$70$	−1.37288	−	4.22529i	−0.164091	−	0.505019i
$71$	−14.2882	−	3.03706i	−1.69570	−	0.360433i	−0.744172	−	0.667988i	$-0.767156\pi$
$71$	−14.2882	−	3.03706i	−1.69570	−	0.360433i	−0.951530	+	0.307555i	$0.900489\pi$
$72$	0.104528	+	0.994522i	0.0123188	+	0.117206i
$73$	7.94938	+	8.82868i	0.930404	+	1.03332i	0.999363	+	0.0356990i	$0.0113658\pi$
$73$	7.94938	+	8.82868i	0.930404	+	1.03332i	−0.0689584	+	0.997620i	$0.521968\pi$
$74$	−6.17847	−	2.75083i	−0.718233	−	0.319778i
$75$	−0.913545	+	0.406737i	−0.105487	+	0.0469659i
$76$	3.51723	−	3.90628i	0.403454	−	0.448081i
$77$	−1.50865	−	1.09610i	−0.171927	−	0.124912i
$78$	4.04831	+	2.94127i	0.458381	+	0.333033i
$79$	−4.29806	+	4.77348i	−0.483569	+	0.537058i	−0.934718	−	0.355391i	$-0.884348\pi$
$79$	−4.29806	+	4.77348i	−0.483569	+	0.537058i	0.451148	+	0.892449i	$0.351015\pi$
$80$	0.913545	−	0.406737i	0.102137	−	0.0454745i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	−0.0175532	−	0.0194948i	−0.00193842	−	0.00215284i
$83$	−0.629081	−	5.98531i	−0.0690506	−	0.656973i	−0.973232	−	0.229824i	$-0.926185\pi$
$83$	−0.629081	−	5.98531i	−0.0690506	−	0.656973i	0.904181	−	0.427149i	$-0.140482\pi$
$84$	4.34565	+	0.923697i	0.474150	+	0.100784i
$85$	−0.239966	−	0.738541i	−0.0260280	−	0.0801060i
$86$	−6.46900	+	1.37503i	−0.697570	+	0.148273i
$87$	2.30959	+	4.00033i	0.247614	+	0.428881i
$88$	0.209870	−	0.363506i	0.0223722	−	0.0387499i
$89$	3.59017	−	11.0494i	0.380557	−	1.17123i	−0.559095	−	0.829103i	$-0.688851\pi$
$89$	3.59017	−	11.0494i	0.380557	−	1.17123i	0.939652	−	0.342131i	$-0.111149\pi$
$90$	0.104528	−	0.994522i	0.0110183	−	0.104832i
$91$	17.9856	−	13.0673i	1.88540	−	1.36982i
$92$	5.60906			0.584785
$93$	3.35658	+	4.44223i	0.348061	+	0.460638i
$94$	−7.82319			−0.806900
$95$	−4.25253	+	3.08964i	−0.436300	+	0.316991i
$96$	−0.104528	+	0.994522i	−0.0106684	+	0.101503i
$97$	3.76259	−	11.5801i	0.382033	−	1.17578i	−0.556577	−	0.830796i	$-0.687886\pi$
$97$	3.76259	−	11.5801i	0.382033	−	1.17578i	0.938610	−	0.344980i	$-0.112114\pi$
$98$	6.36896	−	11.0314i	0.643362	−	1.11434i
$99$	−0.209870	−	0.363506i	−0.0210927	−	0.0365337i
$100$	−0.978148	+	0.207912i	−0.0978148	+	0.0207912i
$101$	−2.66956	−	8.21605i	−0.265631	−	0.817527i	−0.991547	−	0.129745i	$-0.958584\pi$
$101$	−2.66956	−	8.21605i	−0.265631	−	0.817527i	0.725917	−	0.687783i	$-0.241416\pi$
$102$	0.759578	+	0.161453i	0.0752095	+	0.0159863i
$103$	−1.06769	−	10.1584i	−0.105203	−	1.00094i	−0.912023	−	0.410139i	$-0.865480\pi$
$103$	−1.06769	−	10.1584i	−0.105203	−	1.00094i	0.806821	−	0.590797i	$-0.201186\pi$
$104$	3.34832	+	3.71869i	0.328330	+	0.364647i
$105$	−4.05864	−	1.80702i	−0.396083	−	0.176348i
$106$	−1.91779	+	0.853853i	−0.186272	+	0.0829335i
$107$	−10.4661	+	11.6238i	−1.01179	+	1.12371i	−0.0194989	+	0.999810i	$0.506207\pi$
$107$	−10.4661	+	11.6238i	−1.01179	+	1.12371i	−0.992295	+	0.123901i	$0.960460\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	12.6851	+	9.21630i	1.21502	+	0.882761i	0.995677	−	0.0928869i	$-0.0296095\pi$
$109$	12.6851	+	9.21630i	1.21502	+	0.882761i	0.219340	+	0.975648i	$0.429610\pi$
$110$	−0.280861	+	0.311928i	−0.0267791	+	0.0297412i
$111$	−6.17847	+	2.75083i	−0.586435	+	0.261098i
$112$	4.05864	+	1.80702i	0.383506	+	0.170748i
$113$	10.3741	+	11.5216i	0.975914	+	1.08386i	0.996460	+	0.0840732i	$0.0267930\pi$
$113$	10.3741	+	11.5216i	0.975914	+	1.08386i	−0.0205457	+	0.999789i	$0.506540\pi$
$114$	−0.549445	−	5.22762i	−0.0514603	−	0.489612i
$115$	−5.48649	−	1.16619i	−0.511618	−	0.108748i
$116$	1.42741	+	4.39311i	0.132531	+	0.407890i
$117$	4.89464	−	1.04039i	0.452509	−	0.0961838i
$118$	−0.595895	−	1.03212i	−0.0548566	−	0.0950144i
$119$	1.72500	−	2.98779i	0.158130	−	0.273890i
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	1.13140	−	10.7645i	0.102854	−	0.978593i
$122$	3.26593	−	2.37284i	0.295684	−	0.214827i
$123$	−0.0262328			−0.00236533
$124$	2.35964	+	5.04303i	0.211902	+	0.452877i
$125$	1.00000			0.0894427
$126$	3.59425	−	2.61138i	0.320201	−	0.232640i
$127$	−0.558866	+	5.31725i	−0.0495913	+	0.471830i	0.941340	+	0.337460i	$0.109568\pi$
$127$	−0.558866	+	5.31725i	−0.0495913	+	0.471830i	−0.990931	+	0.134370i	$0.957099\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−3.30676	+	5.72748i	−0.291144	+	0.504276i
$130$	−2.50199	−	4.33358i	−0.219439	−	0.380080i
$131$	−14.4952	+	3.08106i	−1.26645	+	0.269193i	−0.791692	−	0.610921i	$-0.790799\pi$
$131$	−14.4952	+	3.08106i	−1.26645	+	0.269193i	−0.474763	+	0.880114i	$0.657466\pi$
$132$	−0.129707	−	0.399197i	−0.0112895	−	0.0347456i
$133$	−22.8426	−	4.85534i	−1.98070	−	0.421011i
$134$	0.728283	+	6.92915i	0.0629141	+	0.598588i
$135$	−0.669131	−	0.743145i	−0.0575896	−	0.0639597i
$136$	0.709412	+	0.315850i	0.0608315	+	0.0270839i
$137$	−13.7488	+	6.12136i	−1.17464	+	0.522983i	−0.898859	−	0.438237i	$-0.855603\pi$
$137$	−13.7488	+	6.12136i	−1.17464	+	0.522983i	−0.275780	+	0.961221i	$0.588936\pi$
$138$	3.75319	−	4.16834i	0.319493	−	0.354833i
$139$	17.2269	+	12.5161i	1.46117	+	1.06160i	0.983057	+	0.183299i	$0.0586776\pi$
$139$	17.2269	+	12.5161i	1.46117	+	1.06160i	0.478109	+	0.878301i	$0.341322\pi$
$140$	−3.59425	−	2.61138i	−0.303770	−	0.220702i
$141$	−5.23473	+	5.81376i	−0.440844	+	0.489607i
$142$	−13.3446	+	5.94139i	−1.11985	+	0.498590i
$143$	−1.91879	−	0.854299i	−0.160457	−	0.0714401i
$144$	0.669131	+	0.743145i	0.0557609	+	0.0619287i
$145$	−0.482837	−	4.59388i	−0.0400974	−	0.381501i
$146$	11.6205	+	2.47002i	0.961723	+	0.204421i
$147$	−3.93623	−	12.1145i	−0.324655	−	0.999186i
$148$	−6.61539	+	1.40614i	−0.543782	+	0.115584i
$149$	7.74810	+	13.4201i	0.634749	+	1.09942i	0.986568	+	0.163350i	$0.0522300\pi$
$149$	7.74810	+	13.4201i	0.634749	+	1.09942i	−0.351819	+	0.936068i	$0.614437\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	3.82142	−	11.7611i	0.310982	−	0.957105i	−0.666394	−	0.745600i	$-0.732163\pi$
$151$	3.82142	−	11.7611i	0.310982	−	0.957105i	0.977377	−	0.211506i	$-0.0678368\pi$
$152$	0.549445	−	5.22762i	0.0445659	−	0.424016i
$153$	0.628240	−	0.456443i	0.0507902	−	0.0369013i
$154$	−1.86480			−0.150270
$155$	−1.25957	−	5.42342i	−0.101171	−	0.435620i
$156$	5.00399			0.400640
$157$	10.1847	−	7.39960i	0.812825	−	0.590552i	−0.101823	−	0.994803i	$-0.532468\pi$
$157$	10.1847	−	7.39960i	0.812825	−	0.590552i	0.914648	+	0.404250i	$0.132468\pi$
$158$	−0.671423	+	6.38816i	−0.0534155	+	0.508215i
$159$	−0.648712	+	1.99653i	−0.0514462	+	0.158335i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−12.4598	−	21.5810i	−0.981969	−	1.70082i
$162$	0.978148	−	0.207912i	0.0768505	−	0.0163351i
$163$	4.62950	+	14.2481i	0.362610	+	1.11600i	0.951464	+	0.307760i	$0.0995795\pi$
$163$	4.62950	+	14.2481i	0.362610	+	1.11600i	−0.588853	+	0.808240i	$0.700420\pi$
$164$	−0.0256595	−	0.00545410i	−0.00200367	−	0.000425894i
$165$	0.0438748	+	0.417441i	0.00341565	+	0.0324977i
$166$	−4.02701	−	4.47245i	−0.312557	−	0.347130i
$167$	−9.66325	−	4.30236i	−0.747765	−	0.332926i	−0.00276945	−	0.999996i	$-0.500882\pi$
$167$	−9.66325	−	4.30236i	−0.747765	−	0.332926i	−0.744995	+	0.667070i	$0.767548\pi$
$168$	4.05864	−	1.80702i	0.313131	−	0.139415i
$169$	8.05625	−	8.94737i	0.619711	−	0.688259i
$170$	−0.628240	−	0.456443i	−0.0481838	−	0.0350076i
$171$	−4.25253	−	3.08964i	−0.325199	−	0.236271i
$172$	−4.42531	+	4.91480i	−0.337427	+	0.374750i
$173$	−15.5143	+	6.90742i	−1.17953	+	0.525162i	−0.900388	−	0.435087i	$-0.856717\pi$
$173$	−15.5143	+	6.90742i	−1.17953	+	0.525162i	−0.279144	+	0.960249i	$0.590051\pi$
$174$	4.21984	+	1.87879i	0.319905	+	0.142431i
$175$	2.97277	+	3.30160i	0.224720	+	0.249577i
$176$	−0.0438748	−	0.417441i	−0.00330719	−	0.0314658i
$177$	−1.16575	−	0.247787i	−0.0876229	−	0.0186248i
$178$	−3.59017	−	11.0494i	−0.269095	−	0.828188i
$179$	−1.09445	+	0.232631i	−0.0818027	+	0.0173877i	−0.248631	−	0.968598i	$-0.579981\pi$
$179$	−1.09445	+	0.232631i	−0.0818027	+	0.0173877i	0.166829	+	0.985986i	$0.446647\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	6.30004	−	10.9120i	0.468278	−	0.811081i	−0.531065	−	0.847331i	$-0.678208\pi$
$181$	6.30004	−	10.9120i	0.468278	−	0.811081i	0.999343	+	0.0362500i	$0.0115413\pi$
$182$	6.86988	−	21.1433i	0.509229	−	1.56725i
$183$	0.421973	−	4.01480i	0.0311931	−	0.296783i
$184$	4.53782	−	3.29692i	0.334533	−	0.243052i
$185$	6.76318			0.497239
$186$	5.32660	+	1.62089i	0.390566	+	0.118850i
$187$	−0.325948			−0.0238357
$188$	−6.32909	+	4.59835i	−0.461596	+	0.335369i
$189$	0.464393	−	4.41840i	0.0337796	−	0.321391i
$190$	−1.62432	+	4.99915i	−0.117841	+	0.362676i
$191$	−1.44059	+	2.49518i	−0.104238	+	0.180545i	−0.913426	−	0.407004i	$-0.866574\pi$
$191$	−1.44059	+	2.49518i	−0.104238	+	0.180545i	0.809189	+	0.587549i	$0.199907\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	10.0477	−	2.13571i	0.723251	−	0.153732i	0.168445	−	0.985711i	$-0.446126\pi$
$193$	10.0477	−	2.13571i	0.723251	−	0.153732i	0.554807	+	0.831979i	$0.312792\pi$
$194$	−3.76259	−	11.5801i	−0.270138	−	0.831399i
$195$	−4.89464	−	1.04039i	−0.350512	−	0.0745037i
$196$	−1.33148	−	12.6681i	−0.0951054	−	0.904867i
$197$	−0.487161	−	0.541048i	−0.0347088	−	0.0385480i	0.725540	−	0.688180i	$-0.241590\pi$
$197$	−0.487161	−	0.541048i	−0.0347088	−	0.0385480i	−0.760249	+	0.649631i	$0.774923\pi$
$198$	−0.383452	−	0.170724i	−0.0272507	−	0.0121328i
$199$	−15.2770	+	6.80178i	−1.08296	+	0.482165i	−0.869069	−	0.494692i	$-0.835281\pi$
$199$	−15.2770	+	6.80178i	−1.08296	+	0.482165i	−0.213893	+	0.976857i	$0.568614\pi$
$200$	−0.669131	+	0.743145i	−0.0473147	+	0.0525483i
$201$	5.63668	+	4.09529i	0.397581	+	0.288859i
$202$	−6.98899	−	5.07780i	−0.491744	−	0.357273i
$203$	13.7318	−	15.2507i	0.963783	−	1.07039i
$204$	0.709412	−	0.315850i	0.0496687	−	0.0221140i
$205$	0.0239648	+	0.0106698i	0.00167378	+	0.000745214i
$206$	−6.83473	−	7.59073i	−0.476198	−	0.528871i
$207$	−0.586306	−	5.57833i	−0.0407511	−	0.387721i
$208$	4.89464	+	1.04039i	0.339382	+	0.0721379i
$209$	0.681794	+	2.09834i	0.0471606	+	0.145146i
$210$	−4.34565	+	0.923697i	−0.299879	+	0.0637412i
$211$	−10.7522	−	18.6234i	−0.740215	−	1.28209i	−0.952397	−	0.304860i	$-0.901390\pi$
$211$	−10.7522	−	18.6234i	−0.740215	−	1.28209i	0.212182	−	0.977230i	$-0.431943\pi$
$212$	−1.04964	+	1.81803i	−0.0720895	+	0.124863i
$213$	−4.51395	+	13.8925i	−0.309291	+	0.951899i
$214$	−1.63496	+	15.5556i	−0.111764	+	1.06336i
$215$	5.35045	−	3.88733i	0.364898	−	0.265114i
$216$	1.00000			0.0680414
$217$	14.1615	−	20.2812i	0.961348	−	1.37678i
$218$	15.6797			1.06196
$219$	9.61125	−	6.98298i	0.649468	−	0.471866i
$220$	−0.0438748	+	0.417441i	−0.00295804	+	0.0281439i
$221$	1.20079	−	3.69565i	0.0807738	−	0.248596i
$222$	−3.38159	+	5.85709i	−0.226957	+	0.393102i
$223$	9.83440	+	17.0337i	0.658560	+	1.14066i	0.980988	+	0.194066i	$0.0621676\pi$
$223$	9.83440	+	17.0337i	0.658560	+	1.14066i	−0.322428	+	0.946594i	$0.604499\pi$
$224$	4.34565	−	0.923697i	0.290356	−	0.0617171i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	15.1651	+	3.22343i	1.00876	+	0.214420i
$227$	−0.272572	−	2.59335i	−0.0180912	−	0.172126i	0.981745	−	0.190200i	$-0.0609135\pi$
$227$	−0.272572	−	2.59335i	−0.0180912	−	0.172126i	−0.999837	+	0.0180731i	$0.994247\pi$
$228$	−3.51723	−	3.90628i	−0.232934	−	0.258700i
$229$	−20.0344	−	8.91988i	−1.32391	−	0.589442i	−0.381644	−	0.924309i	$-0.624642\pi$
$229$	−20.0344	−	8.91988i	−1.32391	−	0.589442i	−0.942265	+	0.334867i	$0.891309\pi$
$230$	−5.12413	+	2.28141i	−0.337875	+	0.150432i
$231$	−1.24779	+	1.38581i	−0.0820987	+	0.0911799i
$232$	3.73700	+	2.71509i	0.245346	+	0.178254i
$233$	0.275141	+	0.199901i	0.0180251	+	0.0130960i	0.596761	−	0.802419i	$-0.296454\pi$
$233$	0.275141	+	0.199901i	0.0180251	+	0.0130960i	−0.578736	+	0.815515i	$0.696454\pi$
$234$	3.34832	−	3.71869i	0.218887	−	0.243098i
$235$	7.14684	−	3.18198i	0.466208	−	0.207569i
$236$	−1.08875	−	0.484745i	−0.0708719	−	0.0315542i
$237$	4.29806	+	4.77348i	0.279189	+	0.310071i
$238$	−0.360623	−	3.43110i	−0.0233757	−	0.222405i
$239$	26.3999	+	5.61148i	1.70767	+	0.362976i	0.955271	−	0.295732i	$-0.0955635\pi$
$239$	26.3999	+	5.61148i	1.70767	+	0.362976i	0.752398	+	0.658708i	$0.228897\pi$
$240$	−0.309017	−	0.951057i	−0.0199470	−	0.0613904i
$241$	6.77393	−	1.43984i	0.436347	−	0.0927485i	0.0154998	−	0.999880i	$-0.495066\pi$
$241$	6.77393	−	1.43984i	0.436347	−	0.0927485i	0.420848	+	0.907131i	$0.361733\pi$
$242$	−5.41191	−	9.37370i	−0.347891	−	0.602564i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.24748	−	3.83934i	0.0798615	−	0.245788i
$245$	−1.33148	+	12.6681i	−0.0850648	+	0.809338i
$246$	−0.0212228	+	0.0154192i	−0.00135311	+	0.000983095i
$247$	−26.3030			−1.67362
$248$	4.87320	+	2.69294i	0.309449	+	0.171002i
$249$	−6.01828			−0.381393
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−0.885342	+	8.42347i	−0.0558823	+	0.531685i	0.930392	+	0.366567i	$0.119467\pi$
$251$	−0.885342	+	8.42347i	−0.0558823	+	0.531685i	−0.986274	+	0.165117i	$0.947200\pi$
$252$	1.37288	−	4.22529i	0.0864834	−	0.266169i
$253$	−1.17717	+	2.03893i	−0.0740083	+	0.128186i
$254$	2.67327	+	4.63024i	0.167736	+	0.290527i
$255$	−0.759578	+	0.161453i	−0.0475666	+	0.0101106i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−21.4481	−	4.55894i	−1.33790	−	0.284379i	−0.517260	−	0.855828i	$-0.673048\pi$
$257$	−21.4481	−	4.55894i	−1.33790	−	0.284379i	−0.820637	+	0.571450i	$0.806381\pi$
$258$	0.691301	+	6.57729i	0.0430385	+	0.409484i
$259$	20.1054	+	22.3293i	1.24929	+	1.38748i
$260$	−4.57137	−	2.03530i	−0.283504	−	0.126224i
$261$	4.21984	−	1.87879i	0.261201	−	0.116294i
$262$	−9.91589	+	11.0127i	−0.612606	+	0.680368i
$263$	−7.78242	−	5.65426i	−0.479885	−	0.348657i	0.321396	−	0.946945i	$-0.395848\pi$
$263$	−7.78242	−	5.65426i	−0.479885	−	0.348657i	−0.801281	+	0.598288i	$0.795848\pi$
$264$	−0.339577	−	0.246717i	−0.0208995	−	0.0151844i
$265$	1.40469	−	1.56007i	0.0862895	−	0.0958342i
$266$	−21.3339	+	9.49847i	−1.30807	+	0.582389i
$267$	−10.6136	−	4.72548i	−0.649542	−	0.289195i
$268$	4.66205	+	5.17773i	0.284780	+	0.316280i
$269$	−0.400341	−	3.80899i	−0.0244092	−	0.232238i	−0.999924	−	0.0123055i	$-0.996083\pi$
$269$	−0.400341	−	3.80899i	−0.0244092	−	0.232238i	0.975515	−	0.219933i	$-0.0705837\pi$
$270$	−0.978148	−	0.207912i	−0.0595282	−	0.0126531i
$271$	6.52582	+	20.0844i	0.396415	+	1.22004i	0.927854	+	0.372944i	$0.121652\pi$
$271$	6.52582	+	20.0844i	0.396415	+	1.22004i	−0.531439	+	0.847097i	$0.678348\pi$
$272$	0.759578	−	0.161453i	0.0460562	−	0.00978955i
$273$	−11.1157	−	19.2530i	−0.672753	−	1.16524i
$274$	−7.52497	+	13.0336i	−0.454600	+	0.787391i
$275$	0.129707	−	0.399197i	0.00782162	−	0.0240725i
$276$	0.586306	−	5.57833i	0.0352915	−	0.335776i
$277$	8.55129	−	6.21287i	0.513797	−	0.373295i	−0.300465	−	0.953793i	$-0.597142\pi$
$277$	8.55129	−	6.21287i	0.513797	−	0.373295i	0.814262	+	0.580497i	$0.197142\pi$
$278$	21.2936			1.27711
$279$	4.76875	−	2.87385i	0.285498	−	0.172053i
$280$	−4.44274			−0.265504
$281$	−12.2601	+	8.90749i	−0.731377	+	0.531376i	−0.889999	−	0.455963i	$-0.849295\pi$
$281$	−12.2601	+	8.90749i	−0.731377	+	0.531376i	0.158622	+	0.987339i	$0.449295\pi$
$282$	−0.817746	+	7.78033i	−0.0486961	+	0.463312i
$283$	3.58230	−	11.0252i	0.212945	−	0.655378i	−0.786348	−	0.617784i	$-0.788031\pi$
$283$	3.58230	−	11.0252i	0.212945	−	0.655378i	0.999293	−	0.0375943i	$-0.0119694\pi$
$284$	−7.30373	+	12.6504i	−0.433396	+	0.750665i
$285$	2.62821	+	4.55219i	0.155682	+	0.269648i
$286$	−2.05448	+	0.436692i	−0.121484	+	0.0258222i
$287$	0.0360145	+	0.110841i	0.00212587	+	0.00654275i
$288$	0.978148	+	0.207912i	0.0576379	+	0.0122513i
$289$	1.71395	+	16.3071i	0.100821	+	0.959244i
$290$	−3.09084	−	3.43272i	−0.181500	−	0.201577i
$291$	−11.1233	−	4.95242i	−0.652060	−	0.290316i
$292$	10.8531	−	4.83210i	0.635128	−	0.282777i
$293$	3.91291	−	4.34573i	0.228595	−	0.253880i	−0.617926	−	0.786237i	$-0.712027\pi$
$293$	3.91291	−	4.34573i	0.228595	−	0.253880i	0.846520	+	0.532356i	$0.178693\pi$
$294$	−10.3052	−	7.48716i	−0.601011	−	0.436660i
$295$	0.964178	+	0.700517i	0.0561366	+	0.0407857i
$296$	−4.52545	+	5.02602i	−0.263037	+	0.292132i
$297$	−0.383452	+	0.170724i	−0.0222501	+	0.00990640i
$298$	14.1565	+	6.30287i	0.820063	+	0.365116i
$299$	−18.7809	−	20.8583i	−1.08613	−	1.20627i
$300$	0.104528	+	0.994522i	0.00603495	+	0.0574187i
$301$	28.7401	+	6.10889i	1.65655	+	0.352110i
$302$	−3.82142	−	11.7611i	−0.219898	−	0.676776i
$303$	−8.45009	+	1.79612i	−0.485445	+	0.103184i
$304$	−2.62821	−	4.55219i	−0.150738	−	0.261086i
$305$	−2.01846	+	3.49607i	−0.115577	+	0.200185i
$306$	0.239966	−	0.738541i	0.0137180	−	0.0422196i
$307$	−2.10091	+	19.9888i	−0.119905	+	1.14082i	0.754728	+	0.656037i	$0.227769\pi$
$307$	−2.10091	+	19.9888i	−0.119905	+	1.14082i	−0.874634	+	0.484785i	$0.838898\pi$
$308$	−1.50865	+	1.09610i	−0.0859634	+	0.0624561i
$309$	−10.2143			−0.581073
$310$	−4.20682	−	3.64728i	−0.238931	−	0.207152i
$311$	32.0194			1.81566			0.907828	−	0.419343i	$-0.137740\pi$
$311$	32.0194			1.81566			0.907828	+	0.419343i	$0.137740\pi$
$312$	4.04831	−	2.94127i	0.229190	−	0.166517i
$313$	−0.161358	+	1.53522i	−0.00912048	+	0.0867756i	−0.998135	−	0.0610411i	$-0.980558\pi$
$313$	−0.161358	+	1.53522i	−0.00912048	+	0.0867756i	0.989015	+	0.147817i	$0.0472246\pi$
$314$	3.89020	−	11.9728i	0.219537	−	0.675664i
$315$	−2.22137	+	3.84752i	−0.125160	+	0.216783i
$316$	3.21167	+	5.56278i	0.180671	+	0.312931i
$317$	19.3525	−	4.11349i	1.08694	−	0.231037i	0.370605	−	0.928791i	$-0.379150\pi$
$317$	19.3525	−	4.11349i	1.08694	−	0.231037i	0.716337	+	0.697754i	$0.245817\pi$
$318$	0.648712	+	1.99653i	0.0363780	+	0.111960i
$319$	−1.89649	−	0.403111i	−0.106183	−	0.0225699i
$320$	−0.104528	−	0.994522i	−0.00584332	−	0.0555955i
$321$	10.4661	+	11.6238i	0.584159	+	0.648775i
$322$	−22.7652	−	10.1357i	−1.26865	−	0.564841i
$323$	−3.72896	+	1.66024i	−0.207485	+	0.0923783i
$324$	0.669131	−	0.743145i	0.0371739	−	0.0412858i
$325$	4.04831	+	2.94127i	0.224560	+	0.163152i
$326$	12.1202	+	8.80583i	0.671275	+	0.487710i
$327$	10.4918	−	11.6523i	0.580196	−	0.644373i
$328$	−0.0239648	+	0.0106698i	−0.00132324	+	0.000589143i
$329$	31.7515	+	14.1367i	1.75052	+	0.779381i
$330$	0.280861	+	0.311928i	0.0154609	+	0.0171711i
$331$	3.52254	+	33.5147i	0.193616	+	1.84214i	0.471919	+	0.881642i	$0.343562\pi$
$331$	3.52254	+	33.5147i	0.193616	+	1.84214i	−0.278302	+	0.960494i	$0.589772\pi$
$332$	−5.88676	−	1.25127i	−0.323078	−	0.0686724i
$333$	2.08994	+	6.43217i	0.114528	+	0.352481i
$334$	−10.3466	+	2.19924i	−0.566140	+	0.120337i
$335$	−3.48366	−	6.03388i	−0.190333	−	0.329666i
$336$	2.22137	−	3.84752i	0.121186	−	0.209900i
$337$	0.253162	−	0.779153i	0.0137906	−	0.0424432i	−0.943924	−	0.330162i	$-0.892897\pi$
$337$	0.253162	−	0.779153i	0.0137906	−	0.0424432i	0.957715	+	0.287718i	$0.0928967\pi$
$338$	1.25851	−	11.9739i	0.0684539	−	0.651295i
$339$	12.5429	−	9.11294i	0.681236	−	0.494947i
$340$	−0.776548			−0.0421142
$341$	−2.32839	−	0.200640i	−0.126089	−	0.0108653i
$342$	−5.25642			−0.284234
$343$	−20.6235	+	14.9839i	−1.11357	+	0.809052i
$344$	−0.691301	+	6.57729i	−0.0372725	+	0.354624i
$345$	−1.73329	+	5.33453i	−0.0933174	+	0.287202i
$346$	−8.49127	+	14.7073i	−0.456494	+	0.790670i
$347$	−9.03048	−	15.6412i	−0.484782	−	0.839666i	0.515066	−	0.857151i	$-0.327768\pi$
$347$	−9.03048	−	15.6412i	−0.484782	−	0.839666i	−0.999847	+	0.0174845i	$0.994434\pi$
$348$	4.51825	−	0.960383i	0.242203	−	0.0514819i
$349$	−5.87386	−	18.0779i	−0.314421	−	0.967688i	−0.975992	−	0.217805i	$-0.930110\pi$
$349$	−5.87386	−	18.0779i	−0.314421	−	0.967688i	0.661571	−	0.749882i	$-0.269890\pi$
$350$	4.34565	+	0.923697i	0.232285	+	0.0493737i
$351$	−0.523059	−	4.97657i	−0.0279188	−	0.265630i
$352$	−0.280861	−	0.311928i	−0.0149699	−	0.0166258i
$353$	6.75218	+	3.00627i	0.359382	+	0.160007i	0.578482	−	0.815695i	$-0.303645\pi$
$353$	6.75218	+	3.00627i	0.359382	+	0.160007i	−0.219100	+	0.975703i	$0.570312\pi$
$354$	−1.08875	+	0.484745i	−0.0578666	+	0.0257639i
$355$	9.77429	−	10.8555i	0.518766	−	0.576148i
$356$	−9.39918	−	6.82891i	−0.498156	−	0.361931i
$357$	−2.79111	−	2.02786i	−0.147721	−	0.107326i
$358$	−0.748687	+	0.831502i	−0.0395694	+	0.0439462i
$359$	−4.31108	+	1.91942i	−0.227530	+	0.101303i	−0.517336	−	0.855783i	$-0.673076\pi$
$359$	−4.31108	+	1.91942i	−0.227530	+	0.101303i	0.289805	+	0.957086i	$0.406409\pi$
$360$	−0.913545	−	0.406737i	−0.0481481	−	0.0214369i
$361$	5.77454	+	6.41328i	0.303923	+	0.337541i
$362$	−1.31707	−	12.5310i	−0.0692235	−	0.658617i
$363$	−10.5873	−	2.25040i	−0.555689	−	0.118115i
$364$	−6.86988	−	21.1433i	−0.360080	−	1.10821i
$365$	−11.6205	+	2.47002i	−0.608247	+	0.129287i
$366$	−2.01846	−	3.49607i	−0.105507	−	0.182743i
$367$	−5.32711	+	9.22683i	−0.278073	+	0.481637i	−0.970906	−	0.239462i	$-0.923029\pi$
$367$	−5.32711	+	9.22683i	−0.278073	+	0.481637i	0.692833	+	0.721098i	$0.256362\pi$
$368$	1.73329	−	5.33453i	0.0903542	−	0.278082i
$369$	−0.00274207	+	0.0260891i	−0.000142747	+	0.00135814i
$370$	5.47153	−	3.97530i	0.284451	−	0.206666i
$371$	9.32654			0.484210
$372$	5.26205	−	1.81957i	0.272825	−	0.0943403i
$373$	−8.12194			−0.420538			−0.210269	−	0.977644i	$-0.567434\pi$
$373$	−8.12194			−0.420538			−0.210269	+	0.977644i	$0.567434\pi$
$374$	−0.263698	+	0.191588i	−0.0136355	+	0.00990676i
$375$	0.104528	−	0.994522i	0.00539783	−	0.0513569i
$376$	−2.41750	+	7.44029i	−0.124673	+	0.383704i
$377$	11.5572	−	20.0176i	0.595225	−	1.03096i
$378$	−2.22137	−	3.84752i	−0.114255	−	0.197895i
$379$	11.0939	−	2.35808i	0.569856	−	0.121127i	0.0860325	−	0.996292i	$-0.472581\pi$
$379$	11.0939	−	2.35808i	0.569856	−	0.121127i	0.483823	+	0.875166i	$0.339248\pi$
$380$	1.62432	+	4.99915i	0.0833260	+	0.256451i
$381$	5.22971	+	1.11161i	0.267926	+	0.0569495i
$382$	0.301166	+	2.86540i	0.0154090	+	0.146607i
$383$	3.80379	+	4.22454i	0.194365	+	0.215864i	0.832448	−	0.554104i	$-0.186939\pi$
$383$	3.80379	+	4.22454i	0.194365	+	0.215864i	−0.638083	+	0.769968i	$0.720272\pi$
$384$	0.913545	+	0.406737i	0.0466192	+	0.0207562i
$385$	1.70358	−	0.758481i	0.0868223	−	0.0386558i
$386$	6.87344	−	7.63373i	0.349849	−	0.388547i
$387$	5.35045	+	3.88733i	0.271979	+	0.197604i
$388$	−9.85058	−	7.15686i	−0.500087	−	0.363335i
$389$	−10.2485	+	11.3821i	−0.519619	+	0.577095i	−0.944648	−	0.328084i	$-0.893597\pi$
$389$	−10.2485	+	11.3821i	−0.519619	+	0.577095i	0.425030	+	0.905179i	$0.360264\pi$
$390$	−4.57137	+	2.03530i	−0.231480	+	0.103062i
$391$	−3.97913	−	1.77162i	−0.201233	−	0.0895949i
$392$	−8.52333	−	9.46612i	−0.430493	−	0.478111i
$393$	1.54901	+	14.7379i	0.0781374	+	0.743428i
$394$	−0.712142	−	0.151370i	−0.0358772	−	0.00762593i
$395$	−1.98492	−	6.10897i	−0.0998724	−	0.307376i
$396$	−0.410568	+	0.0872689i	−0.0206318	+	0.00438543i
$397$	3.56432	+	6.17359i	0.178888	+	0.309844i	0.941500	−	0.337013i	$-0.109417\pi$
$397$	3.56432	+	6.17359i	0.178888	+	0.309844i	−0.762612	+	0.646856i	$0.776083\pi$
$398$	−8.36141	+	14.4824i	−0.419119	+	0.725936i
$399$	−7.21644	+	22.2099i	−0.361274	+	1.11189i
$400$	−0.104528	+	0.994522i	−0.00522642	+	0.0497261i
$401$	−15.5266	+	11.2807i	−0.775362	+	0.563333i	−0.903583	−	0.428412i	$-0.859073\pi$
$401$	−15.5266	+	11.2807i	−0.775362	+	0.563333i	0.128222	+	0.991746i	$0.459073\pi$
$402$	6.96732			0.347498
$403$	10.8526	−	25.6604i	0.540607	−	1.27824i
$404$	−8.63886			−0.429800
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$	2.14512	−	20.4094i	0.106460	−	1.01290i
$407$	0.877231	−	2.69984i	0.0434827	−	0.133826i
$408$	0.388274	−	0.672510i	0.0192224	−	0.0332942i
$409$	10.0464	+	17.4009i	0.496763	+	0.860420i	0.999993	−	0.00373319i	$-0.00118832\pi$
$409$	10.0464	+	17.4009i	0.496763	+	0.860420i	−0.503230	+	0.864153i	$0.667855\pi$
$410$	0.0256595	−	0.00545410i	0.00126723	−	0.000269359i
$411$	4.65069	+	14.3133i	0.229402	+	0.706025i
$412$	−9.99113	−	2.12368i	−0.492228	−	0.104626i
$413$	0.553458	+	5.26581i	0.0272339	+	0.259113i
$414$	−3.75319	−	4.16834i	−0.184459	−	0.204863i
$415$	5.49797	+	2.44785i	0.269885	+	0.120160i
$416$	4.57137	−	2.03530i	0.224130	−	0.0997890i
$417$	14.2482	−	15.8242i	0.697738	−	0.774916i
$418$	1.78496	+	1.29685i	0.0873052	+	0.0634309i
$419$	−23.7330	−	17.2431i	−1.15944	−	0.842379i	−0.169729	−	0.985491i	$-0.554289\pi$
$419$	−23.7330	−	17.2431i	−1.15944	−	0.842379i	−0.989707	+	0.143112i	$0.954289\pi$
$420$	−2.97277	+	3.30160i	−0.145056	+	0.161101i
$421$	−6.35744	+	2.83052i	−0.309843	+	0.137951i	−0.555767	−	0.831338i	$-0.687575\pi$
$421$	−6.35744	+	2.83052i	−0.309843	+	0.137951i	0.245924	+	0.969289i	$0.420909\pi$
$422$	−19.6453	−	8.74667i	−0.956320	−	0.425781i
$423$	5.23473	+	5.81376i	0.254522	+	0.282675i
$424$	0.219434	+	2.08778i	0.0106567	+	0.101391i
$425$	0.759578	+	0.161453i	0.0368450	+	0.00783164i
$426$	4.51395	+	13.8925i	0.218702	+	0.673094i
$427$	−17.5430	+	3.72889i	−0.848967	+	0.180454i
$428$	7.82065	+	13.5458i	0.378025	+	0.654759i
$429$	−1.05019	+	1.81898i	−0.0507035	+	0.0878211i
$430$	2.04369	−	6.28983i	0.0985555	−	0.303323i
$431$	−1.76004	+	16.7457i	−0.0847781	+	0.806610i	0.866687	+	0.498853i	$0.166245\pi$
$431$	−1.76004	+	16.7457i	−0.0847781	+	0.806610i	−0.951465	+	0.307757i	$0.900422\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	10.1365			0.487129			0.243564	−	0.969885i	$-0.421683\pi$
$433$	10.1365			0.487129			0.243564	+	0.969885i	$0.421683\pi$
$434$	−0.464046	−	24.7318i	−0.0222749	−	1.18716i
$435$	−4.61919			−0.221473
$436$	12.6851	−	9.21630i	0.607508	−	0.441381i
$437$	−3.08187	+	29.3220i	−0.147426	+	1.40266i
$438$	3.67117	−	11.2987i	0.175415	−	0.539873i
$439$	−6.21113	+	10.7580i	−0.296441	+	0.513451i	−0.975319	−	0.220800i	$-0.929133\pi$
$439$	−6.21113	+	10.7580i	−0.296441	+	0.513451i	0.678878	+	0.734251i	$0.262467\pi$
$440$	0.209870	+	0.363506i	0.0100052	+	0.0173295i
$441$	−12.4596	+	2.64836i	−0.593313	+	0.126112i
$442$	−1.20079	−	3.69565i	−0.0571157	−	0.175784i
$443$	−25.7602	−	5.47550i	−1.22390	−	0.260149i	−0.449754	−	0.893152i	$-0.648489\pi$
$443$	−25.7602	−	5.47550i	−1.22390	−	0.260149i	−0.774149	+	0.633004i	$0.781822\pi$
$444$	0.706945	+	6.72613i	0.0335501	+	0.319208i
$445$	7.77398	+	8.63388i	0.368522	+	0.409285i
$446$	17.9683	+	8.00002i	0.850826	+	0.378812i
$447$	14.1565	−	6.30287i	0.669579	−	0.298116i
$448$	2.97277	−	3.30160i	0.140450	−	0.155986i
$449$	24.2739	+	17.6360i	1.14556	+	0.832295i	0.987884	−	0.155197i	$-0.0496011\pi$
$449$	24.2739	+	17.6360i	1.14556	+	0.832295i	0.157672	+	0.987492i	$0.449601\pi$
$450$	0.809017	+	0.587785i	0.0381374	+	0.0277085i
$451$	0.00736777	−	0.00818274i	0.000346935	−	0.000385310i
$452$	14.1635	−	6.30599i	0.666194	−	0.296609i
$453$	−11.2972	−	5.02985i	−0.530790	−	0.236323i
$454$	−1.74485	−	1.93785i	−0.0818897	−	0.0909477i
$455$	2.32381	+	22.1096i	0.108942	+	1.03651i
$456$	−5.14155	−	1.09287i	−0.240775	−	0.0511784i
$457$	5.86924	+	18.0637i	0.274551	+	0.844982i	0.989338	+	0.145639i	$0.0465239\pi$
$457$	5.86924	+	18.0637i	0.274551	+	0.844982i	−0.714786	+	0.699343i	$0.753476\pi$
$458$	−21.4511	+	4.55958i	−1.00235	+	0.213055i
$459$	−0.388274	−	0.672510i	−0.0181231	−	0.0313901i
$460$	−2.80453	+	4.85759i	−0.130762	+	0.226486i
$461$	−2.41175	+	7.42261i	−0.112327	+	0.345706i	−0.991380	−	0.131018i	$-0.958176\pi$
$461$	−2.41175	+	7.42261i	−0.112327	+	0.345706i	0.879053	+	0.476723i	$0.158176\pi$
$462$	−0.194924	+	1.85458i	−0.00906870	+	0.0862829i
$463$	−9.49082	+	6.89548i	−0.441076	+	0.320460i	−0.786062	−	0.618147i	$-0.787883\pi$
$463$	−9.49082	+	6.89548i	−0.441076	+	0.320460i	0.344987	+	0.938608i	$0.387883\pi$
$464$	4.61919			0.214440
$465$	−5.52537	+	0.685766i	−0.256233	+	0.0318016i
$466$	0.340092			0.0157545
$467$	−0.249221	+	0.181070i	−0.0115326	+	0.00837891i	−0.593537	−	0.804807i	$-0.702269\pi$
$467$	−0.249221	+	0.181070i	−0.0115326	+	0.00837891i	0.582004	+	0.813186i	$0.302269\pi$
$468$	0.523059	−	4.97657i	0.0241784	−	0.230042i
$469$	9.56530	−	29.4390i	0.441685	−	1.35937i
$470$	3.91159	−	6.77508i	0.180428	−	0.312511i
$471$	−6.29447	−	10.9023i	−0.290034	−	0.502354i
$472$	−1.16575	+	0.247787i	−0.0536578	+	0.0114053i
$473$	−0.857819	−	2.64010i	−0.0394426	−	0.121392i
$474$	6.28298	+	1.33549i	0.288587	+	0.0613411i
$475$	−0.549445	−	5.22762i	−0.0252103	−	0.239860i
$476$	−2.30850	−	2.56385i	−0.105810	−	0.117514i
$477$	1.91779	+	0.853853i	0.0878094	+	0.0390952i
$478$	24.6563	−	10.9777i	1.12775	−	0.502109i
$479$	−23.6810	+	26.3005i	−1.08201	+	1.20170i	−0.103692	+	0.994609i	$0.533066\pi$
$479$	−23.6810	+	26.3005i	−1.08201	+	1.20170i	−0.978322	+	0.207089i	$0.933601\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	27.3794	+	19.8923i	1.24840	+	0.907012i
$482$	4.63391	−	5.14648i	0.211069	−	0.234416i
$483$	−22.7652	+	10.1357i	−1.03585	+	0.461191i
$484$	−9.88805	−	4.40244i	−0.449457	−	0.200111i
$485$	8.14732	+	9.04852i	0.369951	+	0.410872i
$486$	−0.104528	−	0.994522i	−0.00474151	−	0.0451124i
$487$	−38.9834	−	8.28618i	−1.76651	−	0.375483i	−0.793921	−	0.608021i	$-0.791964\pi$
$487$	−38.9834	−	8.28618i	−1.76651	−	0.375483i	−0.972587	+	0.232538i	$0.925297\pi$
$488$	−1.24748	−	3.83934i	−0.0564706	−	0.173799i
$489$	14.6540	−	3.11480i	0.662677	−	0.140856i
$490$	6.36896	+	11.0314i	0.287720	+	0.498346i
$491$	−10.6225	+	18.3986i	−0.479385	+	0.830319i	−0.999720	−	0.0236428i	$-0.992474\pi$
$491$	−10.6225	+	18.3986i	−0.479385	+	0.830319i	0.520336	+	0.853962i	$0.325807\pi$
$492$	−0.00810638	+	0.0249489i	−0.000365464	+	0.00112478i
$493$	0.374946	−	3.56737i	0.0168867	−	0.160666i
$494$	−21.2796	+	15.4605i	−0.957415	+	0.695602i
$495$	0.419740			0.0188659
$496$	5.52537	−	0.685766i	0.248096	−	0.0307918i
$497$	64.8971			2.91103
$498$	−4.86889	+	3.53745i	−0.218180	+	0.158517i
$499$	−1.53333	+	14.5886i	−0.0686412	+	0.653078i	0.905065	+	0.425272i	$0.139822\pi$
$499$	−1.53333	+	14.5886i	−0.0686412	+	0.653078i	−0.973707	+	0.227805i	$0.926845\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	−5.28887	+	9.16059i	−0.236289	+	0.409265i
$502$	4.23493	+	7.33512i	0.189014	+	0.327382i
$503$	37.4611	−	7.96260i	1.67031	−	0.355035i	0.726918	−	0.686724i	$-0.240952\pi$
$503$	37.4611	−	7.96260i	1.67031	−	0.355035i	0.943389	+	0.331690i	$0.107619\pi$
$504$	−1.37288	−	4.22529i	−0.0611530	−	0.188210i
$505$	8.45009	+	1.79612i	0.376024	+	0.0799263i
$506$	0.246096	+	2.34145i	0.0109403	+	0.104090i
$507$	−8.05625	−	8.94737i	−0.357791	−	0.397367i
$508$	4.88431	+	2.17464i	0.216706	+	0.0964838i
$509$	20.2252	−	9.00484i	0.896466	−	0.399133i	0.0938211	−	0.995589i	$-0.470092\pi$
$509$	20.2252	−	9.00484i	0.896466	−	0.399133i	0.802645	+	0.596456i	$0.203425\pi$
$510$	−0.519612	+	0.577087i	−0.0230088	+	0.0255539i
$511$	−42.7003	−	31.0236i	−1.88895	−	1.37240i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−3.51723	+	3.90628i	−0.155289	+	0.172466i
$514$	−20.0316	+	8.91863i	−0.883555	+	0.393384i
$515$	9.33126	+	4.15455i	0.411185	+	0.183071i
$516$	4.42531	+	4.91480i	0.194813	+	0.216362i
$517$	−0.343241	−	3.26572i	−0.0150957	−	0.143626i
$518$	29.3904	+	6.24713i	1.29134	+	0.274483i
$519$	5.24790	+	16.1514i	0.230357	+	0.708966i
$520$	−4.89464	+	1.04039i	−0.214644	+	0.0456240i
$521$	−9.60135	−	16.6300i	−0.420643	−	0.728575i	0.575360	−	0.817900i	$-0.304862\pi$
$521$	−9.60135	−	16.6300i	−0.420643	−	0.728575i	−0.996002	+	0.0893259i	$0.971529\pi$
$522$	2.30959	−	4.00033i	0.101088	−	0.175090i
$523$	−6.27218	+	19.3038i	−0.274263	+	0.844095i	0.715150	+	0.698971i	$0.246358\pi$
$523$	−6.27218	+	19.3038i	−0.274263	+	0.844095i	−0.989413	+	0.145124i	$0.953642\pi$
$524$	−1.54901	+	14.7379i	−0.0676690	+	0.643828i
$525$	3.59425	−	2.61138i	0.156866	−	0.113970i
$526$	−9.61961			−0.419435
$527$	−0.0811107	−	4.32287i	−0.00353324	−	0.188307i
$528$	−0.419740			−0.0182669
$529$	−6.84553	+	4.97357i	−0.297632	+	0.216242i
$530$	0.219434	−	2.08778i	0.00953161	−	0.0906872i
$531$	−0.368283	+	1.13346i	−0.0159821	+	0.0491880i
$532$	−11.6764	+	20.2242i	−0.506238	+	0.876830i
$533$	0.0656343	+	0.113682i	0.00284294	+	0.00492411i
$534$	−11.3641	+	2.41552i	−0.491775	+	0.104530i
$535$	−4.83343	−	14.8758i	−0.208967	−	0.643135i
$536$	6.81507	+	1.44859i	0.294366	+	0.0625694i
$537$	0.116956	+	1.11277i	0.00504704	+	0.0480194i
$538$	−2.56275	−	2.84622i	−0.110488	−	0.122709i
$539$	4.88438	+	2.17467i	0.210385	+	0.0936695i
$540$	−0.913545	+	0.406737i	−0.0393127	+	0.0175032i
$541$	−2.67419	+	2.96999i	−0.114972	+	0.127690i	−0.797883	−	0.602812i	$-0.794047\pi$
$541$	−2.67419	+	2.96999i	−0.114972	+	0.127690i	0.682911	+	0.730502i	$0.260714\pi$
$542$	17.0848	+	12.4128i	0.733856	+	0.533177i
$543$	−10.1937	−	7.40614i	−0.437452	−	0.317828i
$544$	0.519612	−	0.577087i	0.0222782	−	0.0247424i
$545$	−14.3241	+	6.37751i	−0.613578	+	0.273183i
$546$	−20.3094	−	9.04232i	−0.869162	−	0.386976i
$547$	−2.75082	−	3.05509i	−0.117616	−	0.130626i	0.681461	−	0.731854i	$-0.261345\pi$
$547$	−2.75082	−	3.05509i	−0.117616	−	0.130626i	−0.799077	+	0.601228i	$0.794678\pi$
$548$	1.57315	+	14.9675i	0.0672015	+	0.639380i
$549$	−3.94870	−	0.839322i	−0.168526	−	0.0358214i
$550$	−0.129707	−	0.399197i	−0.00553072	−	0.0170218i
$551$	−23.7498	+	5.04817i	−1.01177	+	0.215059i
$552$	−2.80453	−	4.85759i	−0.119369	−	0.206753i
$553$	14.2686	−	24.7140i	0.606764	−	1.05095i
$554$	3.26630	−	10.0526i	0.138772	−	0.427096i
$555$	0.706945	−	6.72613i	0.0300081	−	0.285508i
$556$	17.2269	−	12.5161i	0.730583	−	0.530800i
$557$	−7.82428			−0.331526			−0.165763	−	0.986166i	$-0.553009\pi$
$557$	−7.82428			−0.331526			−0.165763	+	0.986166i	$0.553009\pi$
$558$	2.16880	−	5.12799i	0.0918124	−	0.217085i
$559$	33.0940			1.39973
$560$	−3.59425	+	2.61138i	−0.151885	+	0.110351i
$561$	−0.0340709	+	0.324163i	−0.00143847	+	0.0136862i
$562$	−4.68294	+	14.4126i	−0.197538	+	0.607960i
$563$	9.08710	−	15.7393i	0.382976	−	0.663333i	−0.608510	−	0.793546i	$-0.708233\pi$
$563$	9.08710	−	15.7393i	0.382976	−	0.663333i	0.991486	+	0.130212i	$0.0415660\pi$
$564$	3.91159	+	6.77508i	0.164708	+	0.285282i
$565$	−15.1651	+	3.22343i	−0.637999	+	0.135611i
$566$	−3.58230	−	11.0252i	−0.150575	−	0.463422i
$567$	−4.34565	−	0.923697i	−0.182500	−	0.0387916i
$568$	1.52689	+	14.5274i	0.0640671	+	0.609557i
$569$	26.9899	+	29.9753i	1.13147	+	1.25663i	0.962581	+	0.270995i	$0.0873526\pi$
$569$	26.9899	+	29.9753i	1.13147	+	1.25663i	0.168893	+	0.985634i	$0.445981\pi$
$570$	4.80198	+	2.13798i	0.201133	+	0.0895500i
$571$	7.50211	−	3.34016i	0.313954	−	0.139781i	−0.243710	−	0.969848i	$-0.578365\pi$
$571$	7.50211	−	3.34016i	0.313954	−	0.139781i	0.557664	+	0.830067i	$0.311698\pi$
$572$	−1.40543	+	1.56088i	−0.0587638	+	0.0652638i
$573$	2.33093	+	1.69352i	0.0973759	+	0.0707477i
$574$	0.0942872	+	0.0685037i	0.00393547	+	0.00285929i
$575$	3.75319	−	4.16834i	0.156519	−	0.173832i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	−23.7045	−	10.5539i	−0.986830	−	0.439365i	−0.151108	−	0.988517i	$-0.548284\pi$
$577$	−23.7045	−	10.5539i	−0.986830	−	0.439365i	−0.835722	+	0.549152i	$0.814951\pi$
$578$	10.9717	+	12.1853i	0.456363	+	0.506843i
$579$	−1.07374	−	10.2159i	−0.0446230	−	0.424560i
$580$	−4.51825	−	0.960383i	−0.187610	−	0.0398777i
$581$	8.26238	+	25.4290i	0.342781	+	1.05497i
$582$	−11.9099	+	2.53153i	−0.493682	+	0.104935i
$583$	−0.440576	−	0.763099i	−0.0182468	−	0.0316044i
$584$	5.94008	−	10.2885i	0.245802	−	0.425742i
$585$	−1.54632	+	4.75907i	−0.0639323	+	0.196763i
$586$	0.611257	−	5.81572i	0.0252508	−	0.240245i
$587$	−4.04357	+	2.93782i	−0.166896	+	0.121257i	−0.668098	−	0.744073i	$-0.732891\pi$
$587$	−4.04357	+	2.93782i	−0.166896	+	0.121257i	0.501202	+	0.865330i	$0.332891\pi$
$588$	−12.7379			−0.525303
$589$	−27.6595	+	9.56441i	−1.13969	+	0.394095i
$590$	1.19179			0.0490652
$591$	−0.589006	+	0.427938i	−0.0242285	+	0.0176030i
$592$	−0.706945	+	6.72613i	−0.0290553	+	0.276442i
$593$	7.21890	−	22.2175i	0.296445	−	0.912363i	−0.686288	−	0.727330i	$-0.740761\pi$
$593$	7.21890	−	22.2175i	0.296445	−	0.912363i	0.982732	−	0.185033i	$-0.0592390\pi$
$594$	−0.209870	+	0.363506i	−0.00861108	+	0.0149148i
$595$	1.72500	+	2.98779i	0.0707181	+	0.122487i
$596$	15.1576	−	3.22184i	0.620879	−	0.131972i
$597$	5.16763	+	15.9043i	0.211497	+	0.650921i
$598$	−27.4543	−	5.83559i	−1.12269	−	0.238635i
$599$	−2.87735	−	27.3762i	−0.117565	−	1.11856i	−0.881145	−	0.472847i	$-0.843226\pi$
$599$	−2.87735	−	27.3762i	−0.117565	−	1.11856i	0.763579	−	0.645714i	$-0.223440\pi$
$600$	0.669131	+	0.743145i	0.0273171	+	0.0303388i
$601$	−20.5408	−	9.14536i	−0.837878	−	0.373047i	−0.0574922	−	0.998346i	$-0.518310\pi$
$601$	−20.5408	−	9.14536i	−0.837878	−	0.373047i	−0.780385	+	0.625299i	$0.784977\pi$
$602$	26.8419	−	11.9508i	1.09399	−	0.487078i
$603$	4.66205	−	5.17773i	0.189853	−	0.210853i
$604$	−10.0046	−	7.26876i	−0.407081	−	0.295762i
$605$	8.75665	+	6.36208i	0.356009	+	0.258655i
$606$	−5.78053	+	6.41993i	−0.234818	+	0.260792i
$607$	14.0873	−	6.27209i	0.571787	−	0.254576i	−0.100412	−	0.994946i	$-0.532016\pi$
$607$	14.0873	−	6.27209i	0.571787	−	0.254576i	0.672200	+	0.740370i	$0.265350\pi$
$608$	−4.80198	−	2.13798i	−0.194746	−	0.0867064i
$609$	−13.7318	−	15.2507i	−0.556440	−	0.617989i
$610$	0.421973	+	4.01480i	0.0170852	+	0.162555i
$611$	38.2917	+	8.13914i	1.54911	+	0.329275i
$612$	−0.239966	−	0.738541i	−0.00970007	−	0.0298537i
$613$	−4.17452	+	0.887321i	−0.168607	+	0.0358386i	−0.291442	−	0.956589i	$-0.594135\pi$
$613$	−4.17452	+	0.887321i	−0.168607	+	0.0358386i	0.122834	+	0.992427i	$0.460802\pi$
$614$	10.0495	+	17.4062i	0.405563	+	0.702456i
$615$	0.0131164	−	0.0227183i	0.000528904	−	0.000916089i
$616$	−0.576254	+	1.77353i	−0.0232179	+	0.0714574i
$617$	−4.88197	+	46.4488i	−0.196541	+	1.86996i	0.240680	+	0.970604i	$0.422630\pi$
$617$	−4.88197	+	46.4488i	−0.196541	+	1.86996i	−0.437221	+	0.899354i	$0.644037\pi$
$618$	−8.26357	+	6.00384i	−0.332410	+	0.241510i
$619$	−21.7904			−0.875832			−0.437916	−	0.899016i	$-0.644283\pi$
$619$	−21.7904			−0.875832			−0.437916	+	0.899016i	$0.644283\pi$
$620$	−5.54721	−	0.478009i	−0.222781	−	0.0191973i
$621$	−5.60906			−0.225084
$622$	25.9043	−	18.8206i	1.03867	−	0.754635i
$623$	−5.39533	+	51.3331i	−0.216159	+	2.05662i
$624$	1.54632	−	4.75907i	0.0619022	−	0.190515i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.771837	+	1.33686i	0.0308488	+	0.0534317i
$627$	2.15812	−	0.458722i	0.0861869	−	0.0183196i
$628$	−3.89020	−	11.9728i	−0.155236	−	0.477767i
$629$	5.13717	+	1.09194i	0.204832	+	0.0435384i
$630$	0.464393	+	4.41840i	0.0185018	+	0.176033i
$631$	−10.4788	−	11.6379i	−0.417155	−	0.463297i	0.497541	−	0.867441i	$-0.334236\pi$
$631$	−10.4788	−	11.6379i	−0.417155	−	0.463297i	−0.914696	+	0.404143i	$0.867570\pi$
$632$	5.86802	+	2.61261i	0.233417	+	0.103924i
$633$	−19.6453	+	8.74667i	−0.780832	+	0.347649i
$634$	13.2386	−	14.7030i	0.525773	−	0.583930i
$635$	−4.32544	−	3.14262i	−0.171650	−	0.124711i
$636$	1.69835	+	1.23392i	0.0673440	+	0.0489283i
$637$	−42.6506	+	47.3683i	−1.68988	+	1.87680i
$638$	−1.77124	+	0.788605i	−0.0701239	+	0.0312212i
$639$	13.3446	+	5.94139i	0.527903	+	0.235038i
$640$	−0.669131	−	0.743145i	−0.0264497	−	0.0293754i
$641$	2.87396	+	27.3439i	0.113515	+	1.08002i	0.891900	+	0.452233i	$0.149372\pi$
$641$	2.87396	+	27.3439i	0.113515	+	1.08002i	−0.778385	+	0.627787i	$0.783961\pi$
$642$	15.2995	+	3.25201i	0.603823	+	0.128347i
$643$	2.64319	+	8.13489i	0.104237	+	0.320809i	0.989551	−	0.144186i	$-0.0460563\pi$
$643$	2.64319	+	8.13489i	0.104237	+	0.320809i	−0.885314	+	0.464995i	$0.846056\pi$
$644$	−24.3750	+	5.18107i	−0.960511	+	0.204163i
$645$	−3.30676	−	5.72748i	−0.130204	−	0.225519i
$646$	−2.04093	+	3.53499i	−0.0802993	+	0.139082i
$647$	−6.60146	+	20.3172i	−0.259530	+	0.798752i	0.733373	+	0.679827i	$0.237945\pi$
$647$	−6.60146	+	20.3172i	−0.259530	+	0.798752i	−0.992903	+	0.118926i	$0.962055\pi$
$648$	0.104528	−	0.994522i	0.00410627	−	0.0390685i
$649$	0.404705	−	0.294035i	0.0158860	−	0.0115419i
$650$	5.00399			0.196272
$651$	−18.6898	−	16.2039i	−0.732511	−	0.635082i
$652$	14.9814			0.586716
$653$	33.2443	−	24.1534i	1.30095	−	0.945197i	0.300987	−	0.953628i	$-0.402684\pi$
$653$	33.2443	−	24.1534i	1.30095	−	0.945197i	0.999964	+	0.00843175i	$0.00268394\pi$
$654$	1.63898	−	15.5938i	0.0640890	−	0.609766i
$655$	4.57934	−	14.0938i	0.178930	−	0.550689i
$656$	−0.0131164	+	0.0227183i	−0.000512109	+	0.000886999i
$657$	−5.94008	−	10.2885i	−0.231745	−	0.401393i
$658$	33.9969	−	7.22626i	1.32534	−	0.281709i
$659$	−6.81132	−	20.9631i	−0.265331	−	0.816606i	−0.991617	−	0.129213i	$-0.958755\pi$
$659$	−6.81132	−	20.9631i	−0.265331	−	0.816606i	0.726285	−	0.687393i	$-0.241245\pi$
$660$	0.410568	+	0.0872689i	0.0159813	+	0.00339694i
$661$	−3.23702	−	30.7982i	−0.125905	−	1.19791i	−0.856884	−	0.515509i	$-0.827603\pi$
$661$	−3.23702	−	30.7982i	−0.125905	−	1.19791i	0.730979	−	0.682400i	$-0.239064\pi$
$662$	22.5493	+	25.0435i	0.876402	+	0.973343i
$663$	−3.54989	−	1.58051i	−0.137866	−	0.0613820i
$664$	−5.49797	+	2.44785i	−0.213363	+	0.0949951i
$665$	15.6261	−	17.3546i	0.605955	−	0.672981i
$666$	5.47153	+	3.97530i	0.212017	+	0.154040i
$667$	−20.9611	−	15.2291i	−0.811615	−	0.589673i
$668$	−7.07789	+	7.86079i	−0.273852	+	0.304143i
$669$	17.9683	−	8.00002i	0.694696	−	0.309299i
$670$	−6.36496	−	2.83386i	−0.245900	−	0.109482i
$671$	1.13381	+	1.25923i	0.0437704	+	0.0486119i
$672$	−0.464393	−	4.41840i	−0.0179143	−	0.170443i
$673$	14.3994	+	3.06069i	0.555056	+	0.117981i	0.476896	−	0.878960i	$-0.341762\pi$
$673$	14.3994	+	3.06069i	0.555056	+	0.117981i	0.0781606	+	0.996941i	$0.475095\pi$
$674$	−0.253162	−	0.779153i	−0.00975144	−	0.0300118i
$675$	0.978148	−	0.207912i	0.0376489	−	0.00800252i
$676$	−6.01994	−	10.4268i	−0.231536	−	0.401032i
$677$	13.0409	−	22.5875i	0.501203	−	0.868109i	−0.498796	−	0.866719i	$-0.666224\pi$
$677$	13.0409	−	22.5875i	0.501203	−	0.868109i	0.999999	−	0.00138946i	$-0.000442278\pi$
$678$	4.79096	−	14.7450i	0.183996	−	0.566280i
$679$	−5.65444	+	53.7984i	−0.216997	+	2.06459i
$680$	−0.628240	+	0.456443i	−0.0240919	+	0.0175038i
$681$	−2.60763			−0.0999247
$682$	−2.00164	+	1.20627i	−0.0766467	+	0.0461905i
$683$	5.30105			0.202839			0.101419	−	0.994844i	$-0.467662\pi$
$683$	5.30105			0.202839			0.101419	+	0.994844i	$0.467662\pi$
$684$	−4.25253	+	3.08964i	−0.162600	+	0.118136i
$685$	1.57315	−	14.9675i	0.0601069	−	0.571879i
$686$	−7.87748	+	24.2444i	−0.300764	+	0.925655i
$687$	−10.9652	+	18.9923i	−0.418348	+	0.724600i
$688$	3.30676	+	5.72748i	0.126069	+	0.218358i
$689$	10.2752	−	2.18406i	0.391454	−	0.0832061i
$690$	1.73329	+	5.33453i	0.0659854	+	0.203082i
$691$	−3.97569	−	0.845058i	−0.151242	−	0.0321475i	0.131668	−	0.991294i	$-0.457967\pi$
$691$	−3.97569	−	0.845058i	−0.151242	−	0.0321475i	−0.282911	+	0.959146i	$0.591300\pi$
$692$	1.77516	+	16.8895i	0.0674814	+	0.642043i
$693$	1.24779	+	1.38581i	0.0473997	+	0.0526427i
$694$	−16.4995	−	7.34605i	−0.626313	−	0.278852i
$695$	−19.4527	+	8.66089i	−0.737882	+	0.328526i
$696$	3.09084	−	3.43272i	0.117158	−	0.130117i
$697$	0.0164805	+	0.0119738i	0.000624243	+	0.000453539i
$698$	−15.3780	−	11.1728i	−0.582065	−	0.422895i
$699$	0.227566	−	0.252738i	0.00860735	−	0.00955943i
$700$	4.05864	−	1.80702i	0.153402	−	0.0682991i
$701$	11.7304	+	5.22272i	0.443051	+	0.197259i	0.616123	−	0.787650i	$-0.288702\pi$
$701$	11.7304	+	5.22272i	0.443051	+	0.197259i	−0.173071	+	0.984909i	$0.555369\pi$
$702$	−3.34832	−	3.71869i	−0.126374	−	0.140353i
$703$	−3.71600	−	35.3554i	−0.140151	−	1.33345i
$704$	−0.410568	−	0.0872689i	−0.0154739	−	0.00328907i
$705$	−2.41750	−	7.44029i	−0.0910482	−	0.280218i
$706$	7.22967	−	1.53671i	0.272092	−	0.0578350i
$707$	19.1901	+	33.2382i	0.721718	+	1.25005i
$708$	−0.595895	+	1.03212i	−0.0223951	+	0.0387895i
$709$	11.2803	−	34.7173i	0.423642	−	1.30383i	−0.480647	−	0.876914i	$-0.659598\pi$
$709$	11.2803	−	34.7173i	0.423642	−	1.30383i	0.904289	−	0.426921i	$-0.140402\pi$
$710$	1.52689	−	14.5274i	0.0573033	−	0.545205i
$711$	5.19660	−	3.77555i	0.194888	−	0.141594i
$712$	−11.6180			−0.435404
$713$	−27.3341	−	15.1048i	−1.02367	−	0.565680i
$714$	−3.45000			−0.129113
$715$	1.69924	−	1.23457i	0.0635479	−	0.0461703i
$716$	−0.116956	+	1.11277i	−0.00437087	+	0.0415860i
$717$	8.34028	−	25.6687i	0.311474	−	0.958617i
$718$	−2.35953	+	4.08683i	−0.0880569	+	0.152519i
$719$	−1.36967	−	2.37234i	−0.0510800	−	0.0884732i	0.839355	−	0.543584i	$-0.182933\pi$
$719$	−1.36967	−	2.37234i	−0.0510800	−	0.0884732i	−0.890435	+	0.455111i	$0.849600\pi$
$720$	−0.978148	+	0.207912i	−0.0364534	+	0.00774841i
$721$	14.0231	+	43.1586i	0.522247	+	1.60731i
$722$	8.44133	+	1.79426i	0.314154	+	0.0667755i
$723$	−0.723887	−	6.88733i	−0.0269217	−	0.256142i
$724$	−8.43109	−	9.36368i	−0.313339	−	0.347998i
$725$	4.21984	+	1.87879i	0.156721	+	0.0697766i
$726$	−9.88805	+	4.40244i	−0.366980	+	0.163390i
$727$	−4.41410	+	4.90236i	−0.163710	+	0.181818i	−0.819418	−	0.573196i	$-0.805703\pi$
$727$	−4.41410	+	4.90236i	−0.163710	+	0.181818i	0.655708	+	0.755014i	$0.272370\pi$
$728$	−17.9856	−	13.0673i	−0.666590	−	0.484306i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−7.94938	+	8.82868i	−0.294220	+	0.326764i
$731$	4.69171	−	2.08888i	0.173529	−	0.0772601i
$732$	−3.68791	−	1.64196i	−0.136309	−	0.0606887i
$733$	−3.55458	−	3.94776i	−0.131291	−	0.145814i	0.673914	−	0.738810i	$-0.264612\pi$
$733$	−3.55458	−	3.94776i	−0.131291	−	0.145814i	−0.805206	+	0.592996i	$0.797945\pi$
$734$	1.11367	+	10.5959i	0.0411063	+	0.391100i
$735$	12.4596	+	2.64836i	0.459578	+	0.0976863i
$736$	−1.73329	−	5.33453i	−0.0638901	−	0.196633i
$737$	−2.86056	+	0.608031i	−0.105370	+	0.0223971i
$738$	0.0131164	+	0.0227183i	0.000482821	+	0.000836271i
$739$	13.7638	−	23.8395i	0.506308	−	0.876952i	−0.493665	−	0.869652i	$-0.664343\pi$
$739$	13.7638	−	23.8395i	0.506308	−	0.876952i	0.999973	−	0.00729974i	$-0.00232360\pi$
$740$	2.08994	−	6.43217i	0.0768276	−	0.236451i
$741$	−2.74942	+	26.1589i	−0.101002	+	0.960973i
$742$	7.54533	−	5.48200i	0.276998	−	0.201251i
$743$	7.70811			0.282783			0.141392	−	0.989954i	$-0.454842\pi$
$743$	7.70811			0.282783			0.141392	+	0.989954i	$0.454842\pi$
$744$	3.18757	−	4.56502i	0.116862	−	0.167362i
$745$	−15.4962			−0.567737
$746$	−6.57079	+	4.77396i	−0.240574	+	0.174787i
$747$	−0.629081	+	5.98531i	−0.0230169	+	0.218991i
$748$	−0.100724	+	0.309995i	−0.00368282	+	0.0113346i
$749$	34.7451	−	60.1803i	1.26956	−	2.19894i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	29.0669	−	6.17835i	1.06066	−	0.225451i	0.355632	−	0.934626i	$-0.384266\pi$
$751$	29.0669	−	6.17835i	1.06066	−	0.225451i	0.705033	+	0.709175i	$0.250932\pi$
$752$	2.41750	+	7.44029i	0.0881571	+	0.271320i
$753$	8.28478	+	1.76098i	0.301914	+	0.0641738i
$754$	−2.41611	−	22.9877i	−0.0879894	−	0.837163i
$755$	8.27471	+	9.19000i	0.301148	+	0.334458i
$756$	−4.05864	−	1.80702i	−0.147611	−	0.0657208i
$757$	−8.59581	+	3.82710i	−0.312420	+	0.139098i	−0.556956	−	0.830542i	$-0.688031\pi$
$757$	−8.59581	+	3.82710i	−0.312420	+	0.139098i	0.244536	+	0.969640i	$0.421364\pi$
$758$	7.58911	−	8.42856i	0.275649	−	0.306139i
$759$	1.90471	+	1.38385i	0.0691365	+	0.0502306i
$760$	4.25253	+	3.08964i	0.154255	+	0.112073i
$761$	−30.6215	+	34.0086i	−1.11003	+	1.23281i	−0.139913	+	0.990164i	$0.544682\pi$
$761$	−30.6215	+	34.0086i	−1.11003	+	1.23281i	−0.970115	+	0.242647i	$0.921984\pi$
$762$	4.88431	−	2.17464i	0.176940	−	0.0787787i
$763$	−63.6383	−	28.3336i	−2.30386	−	1.02575i
$764$	1.92789	+	2.14114i	0.0697486	+	0.0774636i
$765$	0.0811713	+	0.772294i	0.00293476	+	0.0279223i
$766$	5.56046	+	1.18191i	0.200908	+	0.0427042i
$767$	1.84288	+	5.67182i	0.0665427	+	0.204797i
$768$	0.978148	−	0.207912i	0.0352959	−	0.00750237i
$769$	−7.05349	−	12.2170i	−0.254355	−	0.440556i	0.710365	−	0.703833i	$-0.248530\pi$
$769$	−7.05349	−	12.2170i	−0.254355	−	0.440556i	−0.964720	+	0.263277i	$0.915197\pi$
$770$	0.932398	−	1.61496i	0.0336013	−	0.0581992i
$771$	−6.77590	+	20.8541i	−0.244028	+	0.751042i
$772$	1.07374	−	10.2159i	0.0386447	−	0.367679i
$773$	−7.14207	+	5.18902i	−0.256882	+	0.186636i	−0.708772	−	0.705438i	$-0.750750\pi$
$773$	−7.14207	+	5.18902i	−0.256882	+	0.186636i	0.451889	+	0.892074i	$0.350750\pi$
$774$	6.61352			0.237718
$775$	5.32660	+	1.62089i	0.191337	+	0.0582242i
$776$	−12.1760			−0.437092
$777$	24.3086	−	17.6612i	0.872065	−	0.633592i
$778$	−1.60097	+	15.2322i	−0.0573976	+	0.546101i
$779$	0.0426105	−	0.131142i	0.00152668	−	0.00469864i
$780$	−2.50199	+	4.33358i	−0.0895857	+	0.155167i
$781$	−3.06567	−	5.30989i	−0.109698	−	0.190003i
$782$	−4.26052	+	0.905601i	−0.152356	+	0.0323842i
$783$	−1.42741	−	4.39311i	−0.0510114	−	0.156997i
$784$	−12.4596	−	2.64836i	−0.444984	−	0.0945844i
$785$	1.31590	+	12.5200i	0.0469666	+	0.446857i
$786$	9.91589	+	11.0127i	0.353688	+	0.392810i
$787$	38.4085	+	17.1006i	1.36912	+	0.609570i	0.953892	−	0.300149i	$-0.0970364\pi$
$787$	38.4085	+	17.1006i	1.36912	+	0.609570i	0.415224	+	0.909719i	$0.363703\pi$
$788$	−0.665108	+	0.296125i	−0.0236935	+	0.0105490i
$789$	−6.43677	+	7.14876i	−0.229155	+	0.254503i
$790$	−5.19660	−	3.77555i	−0.184887	−	0.134328i
$791$	−55.7248	−	40.4864i	−1.98134	−	1.43953i
$792$	−0.280861	+	0.311928i	−0.00997997	+	0.0110839i
$793$	−18.4542	+	8.21635i	−0.655329	+	0.291771i
$794$	6.51234	+	2.89948i	0.231114	+	0.102899i
$795$	−1.40469	−	1.56007i	−0.0498192	−	0.0553299i
$796$	1.74801	+	16.6312i	0.0619566	+	0.589477i
$797$	−12.7248	−	2.70474i	−0.450735	−	0.0958067i	−0.0230496	−	0.999734i	$-0.507338\pi$
$797$	−12.7248	−	2.70474i	−0.450735	−	0.0958067i	−0.427685	+	0.903928i	$0.640671\pi$
$798$	7.21644	+	22.2099i	0.255459	+	0.786222i
$799$	5.94232	−	1.26308i	0.210224	−	0.0446846i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−5.80901	+	10.0615i	−0.205251	+	0.355506i
$802$	−5.93063	+	18.2526i	−0.209418	+	0.644522i
$803$	−0.521240	+	4.95926i	−0.0183942	+	0.175009i
$804$	5.63668	−	4.09529i	0.198790	−	0.144430i
$805$	24.9196			0.878300
$806$	−6.30286	−	27.1387i	−0.222009	−	0.955921i
$807$	−3.82997			−0.134821
$808$	−6.98899	+	5.07780i	−0.245872	+	0.178636i
$809$	4.77035	−	45.3868i	0.167716	−	1.59572i	−0.509857	−	0.860259i	$-0.670302\pi$
$809$	4.77035	−	45.3868i	0.167716	−	1.59572i	0.677573	−	0.735456i	$-0.263032\pi$
$810$	−0.309017	+	0.951057i	−0.0108578	+	0.0334167i
$811$	26.5836	−	46.0441i	0.933476	−	1.61683i	0.156147	−	0.987734i	$-0.450093\pi$
$811$	26.5836	−	46.0441i	0.933476	−	1.61683i	0.777329	−	0.629094i	$-0.216574\pi$
$812$	−10.2609	−	17.7724i	−0.360088	−	0.623690i
$813$	20.6565	−	4.39068i	0.724455	−	0.153988i
$814$	−0.877231	−	2.69984i	−0.0307469	−	0.0946294i
$815$	−14.6540	−	3.11480i	−0.513307	−	0.109107i
$816$	−0.0811713	−	0.772294i	−0.00284157	−	0.0270357i
$817$	−23.2613	−	25.8343i	−0.813809	−	0.903826i
$818$	18.3557	+	8.17249i	0.641793	+	0.285745i
$819$	−20.3094	+	9.04232i	−0.709668	+	0.315964i
$820$	0.0175532	−	0.0194948i	0.000612983	−	0.000680787i
$821$	−44.2303	−	32.1352i	−1.54365	−	1.12153i	−0.947994	−	0.318287i	$-0.896892\pi$
$821$	−44.2303	−	32.1352i	−1.54365	−	1.12153i	−0.595656	−	0.803240i	$-0.703108\pi$
$822$	12.1757	+	8.84613i	0.424675	+	0.308544i
$823$	−16.5865	+	18.4212i	−0.578168	+	0.642121i	−0.959296	−	0.282401i	$-0.908869\pi$
$823$	−16.5865	+	18.4212i	−0.578168	+	0.642121i	0.381128	+	0.924522i	$0.375536\pi$
$824$	−9.33126	+	4.15455i	−0.325070	+	0.144730i
$825$	−0.383452	−	0.170724i	−0.0133501	−	0.00594384i
$826$	3.54292	+	3.93481i	0.123274	+	0.136910i
$827$	−0.532330	−	5.06478i	−0.0185109	−	0.176120i	0.981360	−	0.192178i	$-0.0615550\pi$
$827$	−0.532330	−	5.06478i	−0.0185109	−	0.176120i	−0.999871	+	0.0160580i	$0.994888\pi$
$828$	−5.48649	−	1.16619i	−0.190669	−	0.0405279i
$829$	9.65993	+	29.7302i	0.335503	+	1.03257i	0.966474	+	0.256766i	$0.0826568\pi$
$829$	9.65993	+	29.7302i	0.335503	+	1.03257i	−0.630971	+	0.775807i	$0.717343\pi$
$830$	5.88676	−	1.25127i	0.204333	−	0.0434322i
$831$	−5.28499	−	9.15386i	−0.183334	−	0.317544i
$832$	2.50199	−	4.33358i	0.0867410	−	0.150240i
$833$	−3.05667	+	9.40747i	−0.105907	+	0.325950i
$834$	2.22579	−	21.1770i	0.0770728	−	0.733298i
$835$	8.55757	−	6.21744i	0.296147	−	0.215163i
$836$	2.20633			0.0763075
$837$	−2.35964	−	5.04303i	−0.0815609	−	0.174313i
$838$	−29.3357			−1.01338
$839$	8.34812	−	6.06527i	0.288209	−	0.209396i	−0.434281	−	0.900778i	$-0.642997\pi$
$839$	8.34812	−	6.06527i	0.288209	−	0.209396i	0.722490	+	0.691381i	$0.242997\pi$
$840$	−0.464393	+	4.41840i	−0.0160231	+	0.152449i
$841$	−2.36803	+	7.28805i	−0.0816563	+	0.251312i
$842$	−3.47954	+	6.02675i	−0.119913	+	0.207695i
$843$	7.57716	+	13.1240i	0.260971	+	0.452016i
$844$	−21.0346	+	4.47104i	−0.724040	+	0.153899i
$845$	3.72053	+	11.4506i	0.127990	+	0.393913i
$846$	7.65223	+	1.62653i	0.263089	+	0.0559213i
$847$	5.02650	+	47.8240i	0.172713	+	1.64325i
$848$	1.40469	+	1.56007i	0.0482373	+	0.0535729i
$849$	−10.5903	−	4.71512i	−0.363459	−	0.161822i
$850$	0.709412	−	0.315850i	0.0243326	−	0.0108336i
$851$	25.3835	−	28.1913i	0.870136	−	0.966384i
$852$	11.8177	+	8.58604i	0.404867	+	0.294153i
$853$	13.1457	+	9.55093i	0.450101	+	0.327018i	0.789636	−	0.613576i	$-0.210270\pi$
$853$	13.1457	+	9.55093i	0.450101	+	0.327018i	−0.339535	+	0.940594i	$0.610270\pi$
$854$	−12.0008	+	13.3283i	−0.410660	+	0.456084i
$855$	4.80198	−	2.13798i	0.164224	−	0.0731173i
$856$	14.2890	+	6.36189i	0.488389	+	0.217445i
$857$	−26.5416	−	29.4774i	−0.906644	−	1.00693i	−0.999936	−	0.0112914i	$-0.996406\pi$
$857$	−26.5416	−	29.4774i	−0.906644	−	1.00693i	0.0932923	−	0.995639i	$-0.470261\pi$
$858$	0.219549	+	2.08887i	0.00749528	+	0.0713128i
$859$	−40.7839	−	8.66888i	−1.39153	−	0.295779i	−0.549627	−	0.835410i	$-0.685230\pi$
$859$	−40.7839	−	8.66888i	−1.39153	−	0.295779i	−0.841901	+	0.539631i	$0.818564\pi$
$860$	−2.04369	−	6.28983i	−0.0696892	−	0.214481i
$861$	0.113999	−	0.0242312i	0.00388506	−	0.000825796i
$862$	8.41895	+	14.5820i	0.286750	+	0.496666i
$863$	−23.7783	+	41.1852i	−0.809423	+	1.40196i	0.103841	+	0.994594i	$0.466887\pi$
$863$	−23.7783	+	41.1852i	−0.809423	+	1.40196i	−0.913264	+	0.407368i	$0.866447\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	1.77516	−	16.8895i	0.0603572	−	0.574261i
$866$	8.20059	−	5.95808i	0.278667	−	0.202464i
$867$	16.3970			0.556870
$868$	−14.9124	−	19.7357i	−0.506159	−	0.669872i
$869$	−2.69614			−0.0914602
$870$	−3.73700	+	2.71509i	−0.126696	+	0.0920502i
$871$	3.64432	−	34.6734i	0.123483	−	1.17486i
$872$	4.84530	−	14.9123i	0.164082	−	0.504994i
$873$	−6.08799	+	10.5447i	−0.206047	+	0.356884i
$874$	14.7418	+	25.5335i	0.498648	+	0.863684i
$875$	−4.34565	+	0.923697i	−0.146910	+	0.0312267i
$876$	−3.67117	−	11.2987i	−0.124037	−	0.381748i
$877$	9.31957	+	1.98094i	0.314699	+	0.0668914i	0.362554	−	0.931963i	$-0.381905\pi$
$877$	9.31957	+	1.98094i	0.314699	+	0.0668914i	−0.0478542	+	0.998854i	$0.515238\pi$
$878$	1.29848	+	12.3542i	0.0438216	+	0.416935i
$879$	−3.91291	−	4.34573i	−0.131979	−	0.146578i
$880$	0.383452	+	0.170724i	0.0129262	+	0.00575510i
$881$	−39.9431	+	17.7838i	−1.34572	+	0.599152i	−0.947975	−	0.318346i	$-0.896873\pi$
$881$	−39.9431	+	17.7838i	−1.34572	+	0.599152i	−0.397742	+	0.917497i	$0.630206\pi$
$882$	−8.52333	+	9.46612i	−0.286995	+	0.318741i
$883$	46.5303	+	33.8062i	1.56587	+	1.13767i	0.930982	+	0.365065i	$0.118953\pi$
$883$	46.5303	+	33.8062i	1.56587	+	1.13767i	0.634887	+	0.772605i	$0.281047\pi$
$884$	−3.14371	−	2.28404i	−0.105734	−	0.0768204i
$885$	0.797463	−	0.885673i	0.0268064	−	0.0297716i
$886$	−24.0588	+	10.7117i	−0.808273	+	0.359866i
$887$	23.8244	+	10.6073i	0.799945	+	0.356158i	0.765653	−	0.643253i	$-0.222416\pi$
$887$	23.8244	+	10.6073i	0.799945	+	0.356158i	0.0342916	+	0.999412i	$0.489083\pi$
$888$	4.52545	+	5.02602i	0.151864	+	0.168662i
$889$	−2.48290	−	23.6232i	−0.0832736	−	0.792296i
$890$	11.3641	+	2.41552i	0.380927	+	0.0809686i
$891$	0.129707	+	0.399197i	0.00434534	+	0.0133736i
$892$	19.2390	−	4.08937i	0.644169	−	0.136922i
$893$	−20.5610	−	35.6126i	−0.688047	−	1.19173i
$894$	7.74810	−	13.4201i	0.259135	−	0.448836i
$895$	0.345758	−	1.06413i	0.0115574	−	0.0355700i
$896$	0.464393	−	4.41840i	0.0155143	−	0.147608i
$897$	−22.7072	+	16.4978i	−0.758172	+	0.550844i
$898$	30.0042			1.00125
$899$	4.87431	−	25.2524i	0.162567	−	0.842215i
$900$	1.00000			0.0333333
$901$	1.31885	−	0.958201i	0.0439373	−	0.0319223i
$902$	0.00115096	−	0.0109506i	3.83227e−5	−	0.000364617i
$903$	9.07958	−	27.9441i	0.302149	−	0.929920i
$904$	7.75193	−	13.4267i	0.257825	−	0.446567i
$905$	6.30004	+	10.9120i	0.209420	+	0.362727i
$906$	−12.0961	+	2.57111i	−0.401867	+	0.0854194i
$907$	−13.4131	−	41.2811i	−0.445373	−	1.37072i	−0.882074	−	0.471111i	$-0.843853\pi$
$907$	−13.4131	−	41.2811i	−0.445373	−	1.37072i	0.436701	−	0.899607i	$-0.356147\pi$
$908$	−2.55065	−	0.542157i	−0.0846463	−	0.0179921i
$909$	0.903007	+	8.59154i	0.0299509	+	0.284963i
$910$	14.8757	+	16.5211i	0.493125	+	0.547671i
$911$	45.7510	+	20.3697i	1.51580	+	0.674877i	0.984989	−	0.172615i	$-0.0552215\pi$
$911$	45.7510	+	20.3697i	1.51580	+	0.674877i	0.530809	+	0.847491i	$0.321888\pi$
$912$	−4.80198	+	2.13798i	−0.159009	+	0.0707955i
$913$	1.69030	−	1.87727i	0.0559408	−	0.0621285i
$914$	15.3659	+	11.1640i	0.508258	+	0.369271i
$915$	3.26593	+	2.37284i	0.107968	+	0.0784437i
$916$	−14.6743	+	16.2974i	−0.484852	+	0.538482i
$917$	60.1453	−	26.7784i	1.98617	−	0.884301i
$918$	−0.709412	−	0.315850i	−0.0234141	−	0.0104246i
$919$	−27.6626	−	30.7224i	−0.912503	−	1.01344i	−0.999851	−	0.0172598i	$-0.994506\pi$
$919$	−27.6626	−	30.7224i	−0.912503	−	1.01344i	0.0873476	−	0.996178i	$-0.472161\pi$
$920$	0.586306	+	5.57833i	0.0193299	+	0.183912i
$921$	19.6597	+	4.17880i	0.647810	+	0.137696i
$922$	2.41175	+	7.42261i	0.0794269	+	0.244451i
$923$	71.4982	−	15.1974i	2.35339	−	0.500229i
$924$	0.932398	+	1.61496i	0.0306736	+	0.0531283i
$925$	−3.38159	+	5.85709i	−0.111186	+	0.192580i
$926$	−3.62517	+	11.1571i	−0.119130	+	0.366646i
$927$	−1.06769	+	10.1584i	−0.0350675	+	0.333645i
$928$	3.73700	−	2.71509i	0.122673	−	0.0891272i
$929$	−22.1255			−0.725915			−0.362957	−	0.931806i	$-0.618233\pi$
$929$	−22.1255			−0.725915			−0.362957	+	0.931806i	$0.618233\pi$
$930$	−4.06704	+	3.80253i	−0.133363	+	0.124690i
$931$	66.9558			2.19439
$932$	0.275141	−	0.199901i	0.00901253	−	0.00654798i
$933$	3.34694	−	31.8440i	0.109574	−	1.04253i
$934$	−0.0951940	+	0.292977i	−0.00311484	+	0.00958650i
$935$	0.162974	−	0.282280i	0.00532983	−	0.00923153i
$936$	−2.50199	−	4.33358i	−0.0817802	−	0.141647i
$937$	49.2379	−	10.4658i	1.60853	−	0.341904i	0.685934	−	0.727664i	$-0.259394\pi$
$937$	49.2379	−	10.4658i	1.60853	−	0.341904i	0.922599	+	0.385759i	$0.126061\pi$
$938$	−9.56530	−	29.4390i	−0.312318	−	0.961217i
$939$	1.50994	+	0.320948i	0.0492750	+	0.0104737i
$940$	−0.817746	−	7.78033i	−0.0266719	−	0.253766i
$941$	24.3774	+	27.0739i	0.794682	+	0.882584i	0.995276	−	0.0970909i	$-0.0309538\pi$
$941$	24.3774	+	27.0739i	0.794682	+	0.882584i	−0.200594	+	0.979675i	$0.564287\pi$
$942$	−11.5006	−	5.12039i	−0.374709	−	0.166831i
$943$	0.134420	−	0.0598477i	0.00437733	−	0.00194891i
$944$	−0.797463	+	0.885673i	−0.0259552	+	0.0288262i
$945$	3.59425	+	2.61138i	0.116921	+	0.0849481i
$946$	−2.24580	−	1.63167i	−0.0730172	−	0.0530501i
$947$	8.97209	−	9.96452i	0.291554	−	0.323803i	−0.579518	−	0.814960i	$-0.696759\pi$
$947$	8.97209	−	9.96452i	0.291554	−	0.323803i	0.871071	+	0.491156i	$0.163426\pi$
$948$	5.86802	−	2.61261i	0.190584	−	0.0848537i
$949$	−54.3086	−	24.1797i	−1.76293	−	0.784907i
$950$	−3.51723	−	3.90628i	−0.114114	−	0.126736i
$951$	−2.06807	−	19.6764i	−0.0670619	−	0.638052i
$952$	−3.37461	−	0.717295i	−0.109372	−	0.0232477i
$953$	−6.36722	−	19.5963i	−0.206254	−	0.634786i	−0.999660	−	0.0260918i	$-0.991694\pi$
$953$	−6.36722	−	19.5963i	−0.206254	−	0.634786i	0.793405	−	0.608694i	$-0.208306\pi$
$954$	2.05340	−	0.436464i	0.0664814	−	0.0141311i
$955$	−1.44059	−	2.49518i	−0.0466165	−	0.0807421i
$956$	13.4949	−	23.3738i	0.436455	−	0.755962i
$957$	−0.599140	+	1.84396i	−0.0193675	+	0.0596069i
$958$	−3.69934	+	35.1969i	−0.119520	+	1.13716i
$959$	54.0933	−	39.3011i	1.74676	−	1.26910i
$960$	−1.00000			−0.0322749
$961$	2.08157	−	30.9300i	0.0671473	−	0.997743i
$962$	33.8429			1.09114
$963$	12.6541	−	9.19373i	0.407772	−	0.296264i
$964$	0.723887	−	6.88733i	0.0233148	−	0.221826i
$965$	−3.17428	+	9.76944i	−0.102184	+	0.314490i
$966$	−12.4598	+	21.5810i	−0.400887	+	0.694357i
$967$	27.4424	+	47.5316i	0.882488	+	1.52851i	0.848566	+	0.529090i	$0.177467\pi$
$967$	27.4424	+	47.5316i	0.882488	+	1.52851i	0.0339228	+	0.999424i	$0.489200\pi$
$968$	−10.5873	+	2.25040i	−0.340288	+	0.0723305i
$969$	1.26136	+	3.88208i	0.0405208	+	0.124710i
$970$	11.9099	+	2.53153i	0.382404	+	0.0812825i
$971$	−2.61964	−	24.9242i	−0.0840683	−	0.799856i	−0.952601	−	0.304224i	$-0.901603\pi$
$971$	−2.61964	−	24.9242i	−0.0840683	−	0.799856i	0.868532	−	0.495632i	$-0.165064\pi$
$972$	−0.669131	−	0.743145i	−0.0214624	−	0.0238364i
$973$	−86.4232	−	38.4781i	−2.77060	−	1.23355i
$974$	−36.4088	+	16.2102i	−1.16661	+	0.519409i
$975$	3.34832	−	3.71869i	0.107232	−	0.119093i
$976$	−3.26593	−	2.37284i	−0.104540	−	0.0759528i
$977$	−45.8315	−	33.2986i	−1.46628	−	1.06532i	−0.981671	−	0.190585i	$-0.938962\pi$
$977$	−45.8315	−	33.2986i	−1.46628	−	1.06532i	−0.484610	−	0.874730i	$-0.661038\pi$
$978$	10.0245	−	11.1333i	0.320548	−	0.356005i
$979$	4.45496	−	1.98347i	0.142381	−	0.0633921i
$980$	11.6367	+	5.18098i	0.371720	+	0.165500i
$981$	−10.4918	−	11.6523i	−0.334976	−	0.372029i
$982$	2.22070	+	21.1285i	0.0708654	+	0.674239i
$983$	−47.7760	−	10.1551i	−1.52382	−	0.323898i	−0.631525	−	0.775355i	$-0.717571\pi$
$983$	−47.7760	−	10.1551i	−1.52382	−	0.323898i	−0.892293	+	0.451458i	$0.850904\pi$
$984$	0.00810638	+	0.0249489i	0.000258422	+	0.000795341i
$985$	0.712142	−	0.151370i	0.0226907	−	0.00482306i
$986$	−1.79351	−	3.10645i	−0.0571170	−	0.0989295i
$987$	17.3782	−	30.0999i	0.553154	−	0.958090i
$988$	−8.12808	+	25.0157i	−0.258589	+	0.795855i
$989$	3.87755	−	36.8924i	0.123299	−	1.17311i
$990$	0.339577	−	0.246717i	0.0107925	−	0.00784119i
$991$	24.6021			0.781511			0.390755	−	0.920495i	$-0.372214\pi$
$991$	24.6021			0.781511			0.390755	+	0.920495i	$0.372214\pi$
$992$	4.06704	−	3.80253i	0.129129	−	0.120730i
$993$	33.6993			1.06942
$994$	52.5028	−	38.1455i	1.66529	−	1.20990i
$995$	1.74801	−	16.6312i	0.0554156	−	0.527245i
$996$	−1.85975	+	5.72372i	−0.0589284	+	0.181363i
$997$	22.9232	−	39.7042i	0.725986	−	1.25744i	−0.232581	−	0.972577i	$-0.574717\pi$
$997$	22.9232	−	39.7042i	0.725986	−	1.25744i	0.958567	−	0.284867i	$-0.0919496\pi$
$998$	7.33450	+	12.7037i	0.232170	+	0.402130i
$999$	6.61539	−	1.40614i	0.209302	−	0.0444884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.h.121.1	✓	24
31.10	even	15	inner	930.2.bg.h.661.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.h.121.1	✓	24	1.1	even	1	trivial
930.2.bg.h.661.1	yes	24	31.10	even	15	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-4.34565 + 0.923697i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.104528 - 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-4.34565 + 0.923697i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(0.104528 + 0.994522i) q^{10} +(0.280861 + 0.311928i) q^{11} +(-0.913545 - 0.406737i) q^{12} +(-4.57137 + 2.03530i) q^{13} +(-2.97277 + 3.30160i) q^{14} +(0.809017 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.519612 + 0.577087i) q^{17} +(-0.913545 + 0.406737i) q^{18} +(4.80198 + 2.13798i) q^{19} +(0.669131 + 0.743145i) q^{20} +(0.464393 + 4.41840i) q^{21} +(0.410568 + 0.0872689i) q^{22} +(1.73329 + 5.33453i) q^{23} +(-0.978148 + 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.50199 + 4.33358i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-0.464393 + 4.41840i) q^{28} +(-3.73700 + 2.71509i) q^{29} +1.00000 q^{30} +(-4.06704 + 3.80253i) q^{31} -1.00000 q^{32} +(0.339577 - 0.246717i) q^{33} +(-0.0811713 + 0.772294i) q^{34} +(1.37288 - 4.22529i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.38159 - 5.85709i) q^{37} +(5.14155 - 1.09287i) q^{38} +(1.54632 + 4.75907i) q^{39} +(0.978148 + 0.207912i) q^{40} +(-0.00274207 - 0.0260891i) q^{41} +(2.97277 + 3.30160i) q^{42} +(-6.04175 - 2.68996i) q^{43} +(0.383452 - 0.170724i) q^{44} +(0.669131 - 0.743145i) q^{45} +(4.53782 + 3.29692i) q^{46} +(-6.32909 - 4.59835i) q^{47} +(-0.669131 + 0.743145i) q^{48} +(11.6367 - 5.18098i) q^{49} +(-0.913545 - 0.406737i) q^{50} +(0.519612 + 0.577087i) q^{51} +(0.523059 + 4.97657i) q^{52} +(-2.05340 - 0.436464i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-0.410568 + 0.0872689i) q^{55} +(2.22137 + 3.84752i) q^{56} +(2.62821 - 4.55219i) q^{57} +(-1.42741 + 4.39311i) q^{58} +(0.124576 - 1.18526i) q^{59} +(0.809017 - 0.587785i) q^{60} +4.03692 q^{61} +(-1.05523 + 5.46685i) q^{62} +4.44274 q^{63} +(-0.809017 + 0.587785i) q^{64} +(0.523059 - 4.97657i) q^{65} +(0.129707 - 0.399197i) q^{66} +(-3.48366 + 6.03388i) q^{67} +(0.388274 + 0.672510i) q^{68} +(5.48649 - 1.16619i) q^{69} +(-1.37288 - 4.22529i) q^{70} +(-14.2882 - 3.03706i) q^{71} +(0.104528 + 0.994522i) q^{72} +(7.94938 + 8.82868i) q^{73} +(-6.17847 - 2.75083i) q^{74} +(-0.913545 + 0.406737i) q^{75} +(3.51723 - 3.90628i) q^{76} +(-1.50865 - 1.09610i) q^{77} +(4.04831 + 2.94127i) q^{78} +(-4.29806 + 4.77348i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-0.0175532 - 0.0194948i) q^{82} +(-0.629081 - 5.98531i) q^{83} +(4.34565 + 0.923697i) q^{84} +(-0.239966 - 0.738541i) q^{85} +(-6.46900 + 1.37503i) q^{86} +(2.30959 + 4.00033i) q^{87} +(0.209870 - 0.363506i) q^{88} +(3.59017 - 11.0494i) q^{89} +(0.104528 - 0.994522i) q^{90} +(17.9856 - 13.0673i) q^{91} +5.60906 q^{92} +(3.35658 + 4.44223i) q^{93} -7.82319 q^{94} +(-4.25253 + 3.08964i) q^{95} +(-0.104528 + 0.994522i) q^{96} +(3.76259 - 11.5801i) q^{97} +(6.36896 - 11.0314i) q^{98} +(-0.209870 - 0.363506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 24 * q + 6 * q^2 - 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 - 11 * q^7 + 6 * q^8 + 3 * q^9 - 3 * q^10 - 5 * q^11 - 3 * q^12 - 13 * q^13 - 4 * q^14 + 6 * q^15 - 6 * q^16 + 31 * q^17 - 3 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 + 5 * q^22 - 9 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 + 6 * q^27 + 4 * q^28 + 11 * q^29 + 24 * q^30 + 17 * q^31 - 24 * q^32 + 10 * q^33 + 9 * q^34 + 7 * q^35 - 12 * q^36 + 8 * q^37 - 2 * q^38 - q^39 - 3 * q^40 + 12 * q^41 + 4 * q^42 - 7 * q^43 - 10 * q^44 + 3 * q^45 - 6 * q^46 - 46 * q^47 - 3 * q^48 + 20 * q^49 - 3 * q^50 - 31 * q^51 + 17 * q^52 + 48 * q^53 - 6 * q^54 - 5 * q^55 + q^56 - 2 * q^57 + 14 * q^58 + 12 * q^59 + 6 * q^60 - 4 * q^61 + 13 * q^62 + 2 * q^63 - 6 * q^64 + 17 * q^65 + 10 * q^66 - 33 * q^67 + q^68 - 12 * q^69 - 7 * q^70 - 35 * q^71 - 3 * q^72 + 19 * q^73 + 7 * q^74 - 3 * q^75 + 2 * q^76 + 26 * q^77 - 4 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 - 12 * q^82 + 11 * q^84 - 2 * q^85 - 48 * q^86 + 3 * q^87 + 21 * q^89 - 3 * q^90 + 72 * q^91 + 6 * q^92 + 19 * q^93 - 14 * q^94 + 6 * q^95 + 3 * q^96 - 35 * q^97 - 5 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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