LMFDB - Embedded newform 91.2.q.a.36.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(36,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("91.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.2
Root			$0.759479 - 1.19298i$ of defining polynomial
Character	$\chi$	$=$	91.36
Dual form			91.2.q.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20027 + 0.692976i) q^{2} +(1.41289 + 2.44719i) q^{3} +(-0.0395678 + 0.0685334i) q^{4} -0.518957i q^{5} +(-3.39169 - 1.95819i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.88158i q^{8} +(-2.49250 + 4.31714i) q^{9} +O(q^{10})$	\(q+(-1.20027 + 0.692976i) q^{2} +(1.41289 + 2.44719i) q^{3} +(-0.0395678 + 0.0685334i) q^{4} -0.518957i q^{5} +(-3.39169 - 1.95819i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.88158i q^{8} +(-2.49250 + 4.31714i) q^{9} +(0.359625 + 0.622889i) q^{10} +(1.40656 - 0.812080i) q^{11} -0.223619 q^{12} +(1.42641 + 3.31140i) q^{13} +1.38595 q^{14} +(1.26999 - 0.733228i) q^{15} +(1.91773 + 3.32161i) q^{16} +(0.974127 - 1.68724i) q^{17} -6.90897i q^{18} +(2.15740 + 1.24558i) q^{19} +(0.0355659 + 0.0205340i) q^{20} -2.82577i q^{21} +(-1.12550 + 1.94943i) q^{22} +(-4.57029 - 7.91598i) q^{23} +(7.05179 - 4.07135i) q^{24} +4.73068 q^{25} +(-4.00680 - 2.98610i) q^{26} -5.60916 q^{27} +(0.0685334 - 0.0395678i) q^{28} +(2.61498 + 4.52928i) q^{29} +(-1.01622 + 1.76014i) q^{30} -5.79391i q^{31} +(0.387453 + 0.223696i) q^{32} +(3.97463 + 2.29475i) q^{33} +2.70019i q^{34} +(-0.259479 + 0.449430i) q^{35} +(-0.197245 - 0.341639i) q^{36} +(-8.85879 + 5.11463i) q^{37} -3.45262 q^{38} +(-6.08826 + 8.16934i) q^{39} -1.49542 q^{40} +(3.64513 - 2.10452i) q^{41} +(1.95819 + 3.39169i) q^{42} +(-0.498655 + 0.863697i) q^{43} +0.128529i q^{44} +(2.24041 + 1.29350i) q^{45} +(10.9712 + 6.33421i) q^{46} -4.51725i q^{47} +(-5.41908 + 9.38612i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-5.67810 + 3.27825i) q^{50} +5.50532 q^{51} +(-0.283381 - 0.0332676i) q^{52} -8.89651 q^{53} +(6.73251 - 3.88701i) q^{54} +(-0.421434 - 0.729946i) q^{55} +(-1.44079 + 2.49552i) q^{56} +7.03944i q^{57} +(-6.27736 - 3.62424i) q^{58} +(-5.37392 - 3.10263i) q^{59} +0.116049i q^{60} +(6.73536 - 11.6660i) q^{61} +(4.01504 + 6.95426i) q^{62} +(4.31714 - 2.49250i) q^{63} -8.29100 q^{64} +(1.71847 - 0.740247i) q^{65} -6.36084 q^{66} +(-7.25094 + 4.18633i) q^{67} +(0.0770880 + 0.133520i) q^{68} +(12.9146 - 22.3688i) q^{69} -0.719250i q^{70} +(-4.50168 - 2.59905i) q^{71} +(12.4402 + 7.18234i) q^{72} -11.8395i q^{73} +(7.08863 - 12.2779i) q^{74} +(6.68392 + 11.5769i) q^{75} +(-0.170727 + 0.0985694i) q^{76} -1.62416 q^{77} +(1.64640 - 14.0244i) q^{78} +0.982310 q^{79} +(1.72377 - 0.995221i) q^{80} +(-0.447609 - 0.775281i) q^{81} +(-2.91676 + 5.05197i) q^{82} +8.91851i q^{83} +(0.193660 + 0.111810i) q^{84} +(-0.875603 - 0.505530i) q^{85} -1.38223i q^{86} +(-7.38934 + 12.7987i) q^{87} +(-2.34008 - 4.05313i) q^{88} +(-10.4087 + 6.00949i) q^{89} -3.58546 q^{90} +(0.420388 - 3.58096i) q^{91} +0.723345 q^{92} +(14.1788 - 8.18614i) q^{93} +(3.13035 + 5.42193i) q^{94} +(0.646401 - 1.11960i) q^{95} +1.26423i q^{96} +(3.82981 + 2.21114i) q^{97} +(-1.20027 - 0.692976i) q^{98} +8.09643i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9	$ 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} - 30 q^{33} + 6 q^{35} - 10 q^{36} - 42 q^{37} + 4 q^{38} - 4 q^{39} + 92 q^{40} + 30 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{46} - 2 q^{48} + 6 q^{49} - 18 q^{50} + 52 q^{51} + 2 q^{52} - 44 q^{53} + 12 q^{54} - 6 q^{55} - 12 q^{56} - 12 q^{58} + 18 q^{59} + 14 q^{61} - 4 q^{62} + 12 q^{63} - 52 q^{64} + 60 q^{65} - 52 q^{66} - 24 q^{67} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} + 46 q^{75} - 18 q^{76} + 8 q^{77} - 10 q^{78} - 56 q^{79} - 72 q^{80} + 2 q^{81} + 14 q^{82} + 18 q^{84} - 48 q^{85} - 2 q^{87} - 14 q^{88} - 12 q^{89} + 24 q^{90} + 14 q^{91} + 24 q^{92} - 18 q^{93} + 4 q^{94} - 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9 + 12 * q^10 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 8 * q^14 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 12 * q^24 - 20 * q^25 - 42 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 - 30 * q^33 + 6 * q^35 - 10 * q^36 - 42 * q^37 + 4 * q^38 - 4 * q^39 + 92 * q^40 + 30 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^46 - 2 * q^48 + 6 * q^49 - 18 * q^50 + 52 * q^51 + 2 * q^52 - 44 * q^53 + 12 * q^54 - 6 * q^55 - 12 * q^56 - 12 * q^58 + 18 * q^59 + 14 * q^61 - 4 * q^62 + 12 * q^63 - 52 * q^64 + 60 * q^65 - 52 * q^66 - 24 * q^67 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 + 46 * q^75 - 18 * q^76 + 8 * q^77 - 10 * q^78 - 56 * q^79 - 72 * q^80 + 2 * q^81 + 14 * q^82 + 18 * q^84 - 48 * q^85 - 2 * q^87 - 14 * q^88 - 12 * q^89 + 24 * q^90 + 14 * q^91 + 24 * q^92 - 18 * q^93 + 4 * q^94 - 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.20027	+	0.692976i	−0.848719	+	0.490008i	−0.860218	−	0.509926i	$-0.829673\pi$
$2$	−1.20027	+	0.692976i	−0.848719	+	0.490008i	0.0114993	+	0.999934i	$0.496340\pi$
$3$	1.41289	+	2.44719i	0.815731	+	1.41289i	0.908802	+	0.417228i	$0.136998\pi$
$3$	1.41289	+	2.44719i	0.815731	+	1.41289i	−0.0930713	+	0.995659i	$0.529668\pi$
$4$	−0.0395678	+	0.0685334i	−0.0197839	+	0.0342667i
$5$		−	0.518957i		−	0.232085i	−0.993244	−	0.116042i	$-0.962979\pi$
$5$		−	0.518957i		−	0.232085i	0.993244	−	0.116042i	$-0.0370208\pi$
$6$	−3.39169	−	1.95819i	−1.38465	−	0.799429i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		−	2.88158i		−	1.01879i
$9$	−2.49250	+	4.31714i	−0.830833	+	1.43905i
$10$	0.359625	+	0.622889i	0.113723	+	0.196975i
$11$	1.40656	−	0.812080i	0.424095	−	0.244851i	−0.272733	−	0.962090i	$-0.587928\pi$
$11$	1.40656	−	0.812080i	0.424095	−	0.244851i	0.696828	+	0.717239i	$0.254594\pi$
$12$	−0.223619			−0.0645533
$13$	1.42641	+	3.31140i	0.395616	+	0.918416i
$13$	1.42641	+	3.31140i	0.395616	+	0.918416i
$14$	1.38595			0.370411
$15$	1.26999	−	0.733228i	0.327909	−	0.189319i
$16$	1.91773	+	3.32161i	0.479433	+	0.830403i
$17$	0.974127	−	1.68724i	0.236260	−	0.409215i	−0.723378	−	0.690452i	$-0.757411\pi$
$17$	0.974127	−	1.68724i	0.236260	−	0.409215i	0.959638	+	0.281237i	$0.0907448\pi$
$18$		−	6.90897i		−	1.62846i
$19$	2.15740	+	1.24558i	0.494942	+	0.285755i	0.726622	−	0.687037i	$-0.241089\pi$
$19$	2.15740	+	1.24558i	0.494942	+	0.285755i	−0.231680	+	0.972792i	$0.574422\pi$
$20$	0.0355659	+	0.0205340i	0.00795277	+	0.00459154i
$21$		−	2.82577i		−	0.616634i
$22$	−1.12550	+	1.94943i	−0.239958	+	0.415620i
$23$	−4.57029	−	7.91598i	−0.952971	−	1.65059i	−0.738943	−	0.673767i	$-0.764675\pi$
$23$	−4.57029	−	7.91598i	−0.952971	−	1.65059i	−0.214028	−	0.976828i	$-0.568658\pi$
$24$	7.05179	−	4.07135i	1.43944	−	0.831061i
$25$	4.73068			0.946137
$26$	−4.00680	−	2.98610i	−0.785798	−	0.585622i
$27$	−5.60916			−1.07948
$28$	0.0685334	−	0.0395678i	0.0129516	−	0.00747761i
$29$	2.61498	+	4.52928i	0.485589	+	0.841065i	0.999863	−	0.0165608i	$-0.00527172\pi$
$29$	2.61498	+	4.52928i	0.485589	+	0.841065i	−0.514274	+	0.857626i	$0.671938\pi$
$30$	−1.01622	+	1.76014i	−0.185535	+	0.321357i
$31$		−	5.79391i		−	1.04062i	−0.853978	−	0.520308i	$-0.825817\pi$
$31$		−	5.79391i		−	1.04062i	0.853978	−	0.520308i	$-0.174183\pi$
$32$	0.387453	+	0.223696i	0.0684926	+	0.0395442i
$33$	3.97463	+	2.29475i	0.691894	+	0.399465i
$34$			2.70019i			0.463078i
$35$	−0.259479	+	0.449430i	−0.0438599	+	0.0759675i
$36$	−0.197245	−	0.341639i	−0.0328742	−	0.0569398i
$37$	−8.85879	+	5.11463i	−1.45638	+	0.840840i	−0.998831	−	0.0483462i	$-0.984605\pi$
$37$	−8.85879	+	5.11463i	−1.45638	+	0.840840i	−0.457546	+	0.889186i	$0.651272\pi$
$38$	−3.45262			−0.560089
$39$	−6.08826	+	8.16934i	−0.974902	+	1.30814i
$40$	−1.49542			−0.236446
$41$	3.64513	−	2.10452i	0.569273	−	0.328670i	−0.187586	−	0.982248i	$-0.560066\pi$
$41$	3.64513	−	2.10452i	0.569273	−	0.328670i	0.756859	+	0.653578i	$0.226733\pi$
$42$	1.95819	+	3.39169i	0.302156	+	0.523349i
$43$	−0.498655	+	0.863697i	−0.0760442	+	0.131712i	−0.901540	−	0.432696i	$-0.857562\pi$
$43$	−0.498655	+	0.863697i	−0.0760442	+	0.131712i	0.825496	+	0.564408i	$0.190896\pi$
$44$			0.128529i			0.0193764i
$45$	2.24041	+	1.29350i	0.333980	+	0.192824i
$46$	10.9712	+	6.33421i	1.61761	+	0.933928i
$47$		−	4.51725i		−	0.658909i	−0.944171	−	0.329455i	$-0.893135\pi$
$47$		−	4.51725i		−	0.658909i	0.944171	−	0.329455i	$-0.106865\pi$
$48$	−5.41908	+	9.38612i	−0.782177	+	1.35477i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−5.67810	+	3.27825i	−0.803004	+	0.463615i
$51$	5.50532			0.770899
$52$	−0.283381	−	0.0332676i	−0.0392979	−	0.00461339i
$53$	−8.89651			−1.22203			−0.611015	−	0.791619i	$-0.709238\pi$
$53$	−8.89651			−1.22203			−0.611015	+	0.791619i	$0.709238\pi$
$54$	6.73251	−	3.88701i	0.916178	−	0.528956i
$55$	−0.421434	−	0.729946i	−0.0568262	−	0.0984259i
$56$	−1.44079	+	2.49552i	−0.192534	+	0.333478i
$57$			7.03944i			0.932397i
$58$	−6.27736	−	3.62424i	−0.824258	−	0.475886i
$59$	−5.37392	−	3.10263i	−0.699624	−	0.403928i	0.107583	−	0.994196i	$-0.465689\pi$
$59$	−5.37392	−	3.10263i	−0.699624	−	0.403928i	−0.807207	+	0.590268i	$0.799022\pi$
$60$			0.116049i			0.0149818i
$61$	6.73536	−	11.6660i	0.862375	−	1.49368i	−0.00725571	−	0.999974i	$-0.502310\pi$
$61$	6.73536	−	11.6660i	0.862375	−	1.49368i	0.869630	−	0.493703i	$-0.164357\pi$
$62$	4.01504	+	6.95426i	0.509911	+	0.883191i
$63$	4.31714	−	2.49250i	0.543908	−	0.314025i
$64$	−8.29100			−1.03637
$65$	1.71847	−	0.740247i	0.213150	−	0.0918164i
$66$	−6.36084			−0.782965
$67$	−7.25094	+	4.18633i	−0.885843	+	0.511442i	−0.872580	−	0.488470i	$-0.837555\pi$
$67$	−7.25094	+	4.18633i	−0.885843	+	0.511442i	−0.0132624	+	0.999912i	$0.504222\pi$
$68$	0.0770880	+	0.133520i	0.00934830	+	0.0161917i
$69$	12.9146	−	22.3688i	1.55474	−	2.69288i
$70$		−	0.719250i		−	0.0859668i
$71$	−4.50168	−	2.59905i	−0.534251	−	0.308450i	0.208495	−	0.978023i	$-0.433144\pi$
$71$	−4.50168	−	2.59905i	−0.534251	−	0.308450i	−0.742746	+	0.669573i	$0.766477\pi$
$72$	12.4402	+	7.18234i	1.46609	+	0.846447i
$73$		−	11.8395i		−	1.38571i	−0.721076	−	0.692856i	$-0.756352\pi$
$73$		−	11.8395i		−	1.38571i	0.721076	−	0.692856i	$-0.243648\pi$
$74$	7.08863	−	12.2779i	0.824037	−	1.42727i
$75$	6.68392	+	11.5769i	0.771793	+	1.33678i
$76$	−0.170727	+	0.0985694i	−0.0195838	+	0.0113067i
$77$	−1.62416			−0.185090
$78$	1.64640	−	14.0244i	0.186418	−	1.58795i
$79$	0.982310			0.110518			0.0552592	−	0.998472i	$-0.482401\pi$
$79$	0.982310			0.110518			0.0552592	+	0.998472i	$0.482401\pi$
$80$	1.72377	−	0.995221i	0.192724	−	0.111269i
$81$	−0.447609	−	0.775281i	−0.0497343	−	0.0861423i
$82$	−2.91676	+	5.05197i	−0.322102	+	0.557897i
$83$			8.91851i			0.978934i	0.872022	+	0.489467i	$0.162809\pi$
$83$			8.91851i			0.978934i	−0.872022	+	0.489467i	$0.837191\pi$
$84$	0.193660	+	0.111810i	0.0211300	+	0.0121994i
$85$	−0.875603	−	0.505530i	−0.0949725	−	0.0548324i
$86$		−	1.38223i		−	0.149049i
$87$	−7.38934	+	12.7987i	−0.792220	+	1.37217i
$88$	−2.34008	−	4.05313i	−0.249453	−	0.432065i
$89$	−10.4087	+	6.00949i	−1.10332	+	0.637005i	−0.937092	−	0.349082i	$-0.886494\pi$
$89$	−10.4087	+	6.00949i	−1.10332	+	0.637005i	−0.166233	+	0.986087i	$0.553160\pi$
$90$	−3.58546			−0.377941
$91$	0.420388	−	3.58096i	0.0440686	−	0.375387i
$92$	0.723345			0.0754139
$93$	14.1788	−	8.18614i	1.47027	−	0.848863i
$94$	3.13035	+	5.42193i	0.322871	+	0.559229i
$95$	0.646401	−	1.11960i	0.0663194	−	0.114869i
$96$			1.26423i			0.129030i
$97$	3.82981	+	2.21114i	0.388858	+	0.224507i	0.681665	−	0.731664i	$-0.261256\pi$
$97$	3.82981	+	2.21114i	0.388858	+	0.224507i	−0.292807	+	0.956172i	$0.594589\pi$
$98$	−1.20027	−	0.692976i	−0.121246	−	0.0700012i
$99$			8.09643i			0.813722i
$100$	−0.187183	+	0.324210i	−0.0187183	+	0.0324210i
$101$	9.15132	+	15.8506i	0.910591	+	1.57719i	0.813231	+	0.581940i	$0.197706\pi$
$101$	9.15132	+	15.8506i	0.910591	+	1.57719i	0.0973594	+	0.995249i	$0.468960\pi$
$102$	−6.60787	+	3.81506i	−0.654277	+	0.377747i
$103$	−5.02046			−0.494680			−0.247340	−	0.968929i	$-0.579556\pi$
$103$	−5.02046			−0.494680			−0.247340	+	0.968929i	$0.579556\pi$
$104$	9.54206	−	4.11033i	0.935676	−	0.403051i
$105$	−1.46646			−0.143111
$106$	10.6782	−	6.16507i	1.03716	−	0.598804i
$107$	−3.07228	−	5.32134i	−0.297008	−	0.514434i	0.678442	−	0.734654i	$-0.262656\pi$
$107$	−3.07228	−	5.32134i	−0.297008	−	0.514434i	−0.975450	+	0.220221i	$0.929322\pi$
$108$	0.221942	−	0.384415i	0.0213564	−	0.0369903i
$109$		−	11.8962i		−	1.13945i	−0.821834	−	0.569727i	$-0.807049\pi$
$109$		−	11.8962i		−	1.13945i	0.821834	−	0.569727i	$-0.192951\pi$
$110$	1.01167	+	0.584088i	0.0964590	+	0.0556906i
$111$	−25.0330	−	14.4528i	−2.37602	−	1.37180i
$112$		−	3.83547i		−	0.362418i
$113$	−1.77806	+	3.07969i	−0.167266	+	0.289713i	−0.937458	−	0.348099i	$-0.886827\pi$
$113$	−1.77806	+	3.07969i	−0.167266	+	0.289713i	0.770192	+	0.637812i	$0.220161\pi$
$114$	−4.87817	−	8.44923i	−0.456882	−	0.791343i
$115$	−4.10805	+	2.37178i	−0.383078	+	0.221170i
$116$	−0.413875			−0.0384274
$117$	−17.8511	−	2.09563i	−1.65033	−	0.193741i
$118$	8.60020			0.791713
$119$	−1.68724	+	0.974127i	−0.154669	+	0.0892980i
$120$	−2.11286	−	3.65957i	−0.192877	−	0.334072i
$121$	−4.18105	+	7.24180i	−0.380096	+	0.658345i
$122$			18.6698i			1.69028i
$123$	10.3003	+	5.94689i	0.928748	+	0.536213i
$124$	0.397076	+	0.229252i	0.0356585	+	0.0205874i
$125$		−	5.04981i		−	0.451668i
$126$	−3.45449	+	5.98335i	−0.307750	+	0.533039i
$127$	−0.711749	−	1.23279i	−0.0631575	−	0.109392i	0.832718	−	0.553698i	$-0.186784\pi$
$127$	−0.711749	−	1.23279i	−0.0631575	−	0.109392i	−0.895875	+	0.444306i	$0.853450\pi$
$128$	9.17653	−	5.29807i	0.811098	−	0.468288i
$129$	−2.81818			−0.248127
$130$	−1.54966	+	2.07936i	−0.135914	+	0.182372i
$131$	8.67374			0.757828			0.378914	−	0.925432i	$-0.376298\pi$
$131$	8.67374			0.757828			0.378914	+	0.925432i	$0.376298\pi$
$132$	−0.314535	+	0.181597i	−0.0273767	+	0.0158060i
$133$	−1.24558	−	2.15740i	−0.108005	−	0.187071i
$134$	5.80205	−	10.0495i	0.501221	−	0.868141i
$135$			2.91091i			0.250531i
$136$	−4.86191	−	2.80703i	−0.416906	−	0.240701i
$137$	7.37667	+	4.25892i	0.630231	+	0.363864i	0.780842	−	0.624729i	$-0.214791\pi$
$137$	7.37667	+	4.25892i	0.630231	+	0.363864i	−0.150611	+	0.988593i	$0.548124\pi$
$138$			35.7981i			3.04733i
$139$	2.51922	−	4.36342i	0.213677	−	0.370100i	−0.739185	−	0.673502i	$-0.764789\pi$
$139$	2.51922	−	4.36342i	0.213677	−	0.370100i	0.952863	+	0.303402i	$0.0981225\pi$
$140$	−0.0205340	−	0.0355659i	−0.00173544	−	0.00300587i
$141$	11.0546	−	6.38237i	0.930964	−	0.537493i
$142$	7.20431			0.604572
$143$	4.69546	+	3.49933i	0.392654	+	0.292628i
$144$	−19.1198			−1.59332
$145$	2.35050	−	1.35706i	0.195198	−	0.112698i
$146$	8.20451	+	14.2106i	0.679010	+	1.17608i
$147$	−1.41289	+	2.44719i	−0.116533	+	0.201841i
$148$		−	0.809498i		−	0.0665403i
$149$	2.91409	+	1.68245i	0.238732	+	0.137832i	0.614594	−	0.788844i	$-0.289320\pi$
$149$	2.91409	+	1.68245i	0.238732	+	0.137832i	−0.375862	+	0.926676i	$0.622653\pi$
$150$	−16.0450	−	9.26360i	−1.31007	−	0.756370i
$151$			12.6566i			1.02998i	0.857196	+	0.514991i	$0.172205\pi$
$151$			12.6566i			1.02998i	−0.857196	+	0.514991i	$0.827795\pi$
$152$	3.58924	−	6.21674i	0.291125	−	0.504244i
$153$	4.85602	+	8.41087i	0.392586	+	0.679979i
$154$	1.94943	−	1.12550i	0.157090	−	0.0906957i
$155$	−3.00679			−0.241511
$156$	−0.318973	−	0.740492i	−0.0255383	−	0.0592868i
$157$	10.3691			0.827547			0.413773	−	0.910380i	$-0.364211\pi$
$157$	10.3691			0.827547			0.413773	+	0.910380i	$0.364211\pi$
$158$	−1.17904	+	0.680717i	−0.0937992	+	0.0541550i
$159$	−12.5698	−	21.7715i	−0.996847	−	1.72659i
$160$	0.116089	−	0.201071i	0.00917761	−	0.0158961i
$161$			9.14058i			0.720379i
$162$	1.07450	+	0.620364i	0.0844209	+	0.0487404i
$163$	13.6428	+	7.87669i	1.06859	+	0.616950i	0.927796	−	0.373089i	$-0.121701\pi$
$163$	13.6428	+	7.87669i	1.06859	+	0.616950i	0.140794	+	0.990039i	$0.455035\pi$
$164$			0.333084i			0.0260095i
$165$	1.19088	−	2.06266i	0.0927098	−	0.160578i
$166$	−6.18032	−	10.7046i	−0.479686	−	0.830840i
$167$	−14.2016	+	8.19930i	−1.09895	+	0.634481i	−0.935946	−	0.352144i	$-0.885453\pi$
$167$	−14.2016	+	8.19930i	−1.09895	+	0.634481i	−0.163007	+	0.986625i	$0.552119\pi$
$168$	−8.14270			−0.628223
$169$	−8.93069	+	9.44684i	−0.686976	+	0.726680i
$170$	1.40128			0.107473
$171$	−10.7547	+	6.20920i	−0.822429	+	0.474830i
$172$	−0.0394614	−	0.0683491i	−0.00300890	−	0.00521157i
$173$	−0.150677	+	0.260981i	−0.0114558	+	0.0198420i	−0.871696	−	0.490046i	$-0.836980\pi$
$173$	−0.150677	+	0.260981i	−0.0114558	+	0.0198420i	0.860241	+	0.509888i	$0.170313\pi$
$174$		−	20.4825i		−	1.55278i
$175$	−4.09689	−	2.36534i	−0.309696	−	0.178803i
$176$	5.39483	+	3.11470i	0.406650	+	0.234780i
$177$		−	17.5347i		−	1.31799i
$178$	8.32887	−	14.4260i	0.624275	−	1.08128i
$179$	−4.90791	−	8.50075i	−0.366834	−	0.635376i	0.622234	−	0.782831i	$-0.286225\pi$
$179$	−4.90791	−	8.50075i	−0.366834	−	0.635376i	−0.989069	+	0.147455i	$0.952892\pi$
$180$	−0.177296	+	0.102362i	−0.0132149	+	0.00762960i
$181$	12.4320			0.924062			0.462031	−	0.886864i	$-0.347121\pi$
$181$	12.4320			0.924062			0.462031	+	0.886864i	$0.347121\pi$
$182$	1.97694	+	4.58944i	0.146541	+	0.340192i
$183$	38.0652			2.81386
$184$	−22.8105	+	13.1697i	−1.68162	+	0.970881i
$185$	2.65427	+	4.59733i	0.195146	+	0.338003i
$186$	−11.3456	+	19.6512i	−0.831900	+	1.44089i
$187$		−	3.16427i		−	0.231395i
$188$	0.309583	+	0.178738i	0.0225786	+	0.0130358i
$189$	4.85767	+	2.80458i	0.353344	+	0.204003i
$190$			1.79176i			0.129988i
$191$	6.12346	−	10.6061i	0.443078	−	0.767434i	−0.554838	−	0.831958i	$-0.687220\pi$
$191$	6.12346	−	10.6061i	0.443078	−	0.767434i	0.997916	+	0.0645248i	$0.0205531\pi$
$192$	−11.7142	−	20.2897i	−0.845403	−	1.46428i
$193$	−10.0752	+	5.81692i	−0.725229	+	0.418711i	−0.816674	−	0.577099i	$-0.804185\pi$
$193$	−10.0752	+	5.81692i	−0.725229	+	0.418711i	0.0914452	+	0.995810i	$0.470851\pi$
$194$	−6.12908			−0.440042
$195$	4.23953	+	3.15955i	0.303599	+	0.226260i
$196$	−0.0791355			−0.00565254
$197$	−1.55984	+	0.900572i	−0.111134	+	0.0641631i	−0.554537	−	0.832159i	$-0.687104\pi$
$197$	−1.55984	+	0.900572i	−0.111134	+	0.0641631i	0.443403	+	0.896322i	$0.353771\pi$
$198$	−5.61064	−	9.71791i	−0.398731	−	0.690622i
$199$	3.29657	−	5.70982i	0.233687	−	0.404759i	−0.725203	−	0.688535i	$-0.758254\pi$
$199$	3.29657	−	5.70982i	0.233687	−	0.404759i	0.958890	+	0.283777i	$0.0915874\pi$
$200$		−	13.6319i		−	0.963918i
$201$	−20.4895	−	11.8296i	−1.44522	−	0.834397i
$202$	−21.9681	−	12.6833i	−1.54567	−	0.892394i
$203$		−	5.22996i		−	0.367071i
$204$	−0.217833	+	0.377298i	−0.0152514	+	0.0264162i
$205$	−1.09215	−	1.89166i	−0.0762793	−	0.132120i
$206$	6.02590	−	3.47906i	0.419845	−	0.242397i
$207$	45.5658			3.16704
$208$	−8.26369	+	11.0884i	−0.572984	+	0.768840i
$209$	4.04603			0.279870
$210$	1.76014	−	1.01622i	0.121461	−	0.0701258i
$211$	−5.35996	−	9.28373i	−0.368995	−	0.639118i	0.620414	−	0.784275i	$-0.286965\pi$
$211$	−5.35996	−	9.28373i	−0.368995	−	0.639118i	−0.989409	+	0.145157i	$0.953631\pi$
$212$	0.352015	−	0.609708i	0.0241765	−	0.0418749i
$213$		−	14.6886i		−	1.00645i
$214$	7.37513	+	4.25803i	0.504154	+	0.291073i
$215$	0.448221	+	0.258781i	0.0305684	+	0.0176487i
$216$			16.1633i			1.09977i
$217$	−2.89695	+	5.01767i	−0.196658	+	0.340622i
$218$	8.24382	+	14.2787i	0.558342	+	0.967076i
$219$	28.9736	−	16.7279i	1.95785	−	1.13037i
$220$	0.0667009			0.00449697
$221$	6.97662	+	0.819021i	0.469298	+	0.0550933i
$222$	40.0617			2.68877
$223$	−11.1612	+	6.44392i	−0.747409	+	0.431517i	−0.824757	−	0.565487i	$-0.808688\pi$
$223$	−11.1612	+	6.44392i	−0.747409	+	0.431517i	0.0773480	+	0.997004i	$0.475355\pi$
$224$	−0.223696	−	0.387453i	−0.0149463	−	0.0258878i
$225$	−11.7912	+	20.4230i	−0.786082	+	1.36153i
$226$		−	4.92862i		−	0.327847i
$227$	−0.605486	−	0.349577i	−0.0401875	−	0.0232023i	0.479772	−	0.877393i	$-0.340720\pi$
$227$	−0.605486	−	0.349577i	−0.0401875	−	0.0232023i	−0.519959	+	0.854191i	$0.674053\pi$
$228$	−0.482437	−	0.278535i	−0.0319502	−	0.0184464i
$229$			18.2868i			1.20843i	0.796822	+	0.604214i	$0.206513\pi$
$229$			18.2868i			1.20843i	−0.796822	+	0.604214i	$0.793487\pi$
$230$	3.28718	−	5.69356i	0.216750	−	0.375422i
$231$	−2.29475	−	3.97463i	−0.150984	−	0.261511i
$232$	13.0515	−	7.53528i	0.856872	−	0.494715i
$233$	−26.7796			−1.75439			−0.877194	−	0.480137i	$-0.840587\pi$
$233$	−26.7796			−1.75439			−0.877194	+	0.480137i	$0.840587\pi$
$234$	22.8783	−	9.85505i	1.49560	−	0.644245i
$235$	−2.34426			−0.152923
$236$	0.425268	−	0.245528i	0.0276826	−	0.0159825i
$237$	1.38789	+	2.40390i	0.0901533	+	0.156150i
$238$	1.35009	−	2.33843i	0.0875135	−	0.151578i
$239$			16.6177i			1.07491i	0.843293	+	0.537454i	$0.180614\pi$
$239$			16.6177i			1.07491i	−0.843293	+	0.537454i	$0.819386\pi$
$240$	4.87099	+	2.81227i	0.314421	+	0.181531i
$241$	15.0800	+	8.70643i	0.971387	+	0.560830i	0.899659	−	0.436594i	$-0.143815\pi$
$241$	15.0800	+	8.70643i	0.971387	+	0.560830i	0.0717279	+	0.997424i	$0.477149\pi$
$242$		−	11.5895i		−	0.745000i
$243$	−7.14890	+	12.3823i	−0.458602	+	0.794322i
$244$	0.533007	+	0.923194i	0.0341222	+	0.0591015i
$245$	0.449430	−	0.259479i	0.0287130	−	0.0165775i
$246$	−16.4842			−1.05099
$247$	−1.04725	+	8.92073i	−0.0666350	+	0.567612i
$248$	−16.6956			−1.06017
$249$	−21.8253	+	12.6008i	−1.38312	+	0.798546i
$250$	3.49940	+	6.06113i	0.221321	+	0.383340i
$251$	−3.22491	+	5.58571i	−0.203554	+	0.352567i	−0.949671	−	0.313249i	$-0.898583\pi$
$251$	−3.22491	+	5.58571i	−0.203554	+	0.352567i	0.746117	+	0.665815i	$0.231916\pi$
$252$			0.394491i			0.0248506i
$253$	−12.8568	−	7.42288i	−0.808300	−	0.466672i
$254$	1.70858	+	0.986451i	0.107206	+	0.0618954i
$255$		−	2.85703i		−	0.178914i
$256$	0.948120	−	1.64219i	0.0592575	−	0.102637i
$257$	−1.83578	−	3.17966i	−0.114513	−	0.198342i	0.803072	−	0.595882i	$-0.203197\pi$
$257$	−1.83578	−	3.17966i	−0.114513	−	0.198342i	−0.917585	+	0.397540i	$0.869864\pi$
$258$	3.38257	−	1.95293i	0.210590	−	0.121584i
$259$	10.2293			0.635615
$260$	−0.0172645	+	0.147063i	−0.00107070	+	0.00912044i
$261$	−26.0713			−1.61377
$262$	−10.4108	+	6.01070i	−0.643183	+	0.371342i
$263$	−9.15964	−	15.8650i	−0.564807	−	0.978275i	−0.997068	−	0.0765263i	$-0.975617\pi$
$263$	−9.15964	−	15.8650i	−0.564807	−	0.978275i	0.432260	−	0.901749i	$-0.357716\pi$
$264$	6.61252	−	11.4532i	0.406973	−	0.704897i
$265$			4.61690i			0.283614i
$266$	2.99006	+	1.72631i	0.183332	+	0.105847i
$267$	−29.4128	−	16.9815i	−1.80003	−	1.03925i
$268$		−	0.662575i		−	0.0404732i
$269$	−13.7715	+	23.8529i	−0.839661	+	1.45434i	0.0505171	+	0.998723i	$0.483913\pi$
$269$	−13.7715	+	23.8529i	−0.839661	+	1.45434i	−0.890178	+	0.455613i	$0.849420\pi$
$270$	−2.01719	−	3.49388i	−0.122762	−	0.212631i
$271$	5.64582	−	3.25961i	0.342959	−	0.198007i	−0.318621	−	0.947882i	$-0.603220\pi$
$271$	5.64582	−	3.25961i	0.342959	−	0.198007i	0.661580	+	0.749875i	$0.269886\pi$
$272$	7.47246			0.453084
$273$	9.35726	−	4.03072i	0.566327	−	0.243950i
$274$	−11.8053			−0.713186
$275$	6.65401	−	3.84169i	0.401252	−	0.231663i
$276$	1.02200	+	1.77016i	0.0615174	+	0.106551i
$277$	2.72093	−	4.71279i	0.163485	−	0.283164i	−0.772631	−	0.634855i	$-0.781060\pi$
$277$	2.72093	−	4.71279i	0.163485	−	0.283164i	0.936116	+	0.351691i	$0.114393\pi$
$278$			6.98304i			0.418815i
$279$	25.0131	+	14.4413i	1.49749	+	0.864579i
$280$	1.29507	+	0.747709i	0.0773952	+	0.0446842i
$281$			3.54237i			0.211320i	0.994402	+	0.105660i	$0.0336955\pi$
$281$			3.54237i			0.211320i	−0.994402	+	0.105660i	$0.966304\pi$
$282$	−8.84566	+	15.3211i	−0.526752	+	0.912360i
$283$	−7.06956	−	12.2448i	−0.420242	−	0.727880i	0.575721	−	0.817646i	$-0.304721\pi$
$283$	−7.06956	−	12.2448i	−0.420242	−	0.727880i	−0.995963	+	0.0897658i	$0.971388\pi$
$284$	0.356243	−	0.205677i	0.0211391	−	0.0122047i
$285$	3.65317			0.216395
$286$	−8.06077	−	0.946296i	−0.476643	−	0.0559556i
$287$	−4.20903			−0.248451
$288$	−1.93145	+	1.11512i	−0.113812	+	0.0657093i
$289$	6.60215	+	11.4353i	0.388362	+	0.672663i
$290$	−1.88082	+	3.25768i	−0.110446	+	0.191298i
$291$			12.4964i			0.732551i
$292$	0.811403	+	0.468464i	0.0474838	+	0.0274148i
$293$	−7.23071	−	4.17465i	−0.422423	−	0.243886i	0.273691	−	0.961818i	$-0.411756\pi$
$293$	−7.23071	−	4.17465i	−0.422423	−	0.243886i	−0.696113	+	0.717932i	$0.745089\pi$
$294$		−	3.91639i		−	0.228408i
$295$	−1.61013	+	2.78883i	−0.0937455	+	0.162372i
$296$	14.7382	+	25.5274i	0.856642	+	1.48375i
$297$	−7.88964	+	4.55508i	−0.457803	+	0.264313i
$298$	−4.66359			−0.270155
$299$	19.6938	−	26.4255i	1.13892	−	1.52823i
$300$	−1.05787			−0.0610762
$301$	0.863697	−	0.498655i	0.0497826	−	0.0287420i
$302$	−8.77074	−	15.1914i	−0.504699	−	0.874165i
$303$	−25.8596	+	44.7901i	−1.48559	+	2.57312i
$304$			9.55474i			0.548002i
$305$	−6.05415	−	3.49536i	−0.346659	−	0.200144i
$306$	−11.6571	−	6.73021i	−0.666390	−	0.384741i
$307$		−	8.33362i		−	0.475625i	−0.971311	−	0.237813i	$-0.923570\pi$
$307$		−	8.33362i		−	0.475625i	0.971311	−	0.237813i	$-0.0764304\pi$
$308$	0.0642644	−	0.111309i	0.00366180	−	0.00634243i
$309$	−7.09334	−	12.2860i	−0.403526	−	0.698927i
$310$	3.60896	−	2.08363i	0.204975	−	0.118342i
$311$	14.6227			0.829176			0.414588	−	0.910009i	$-0.363926\pi$
$311$	14.6227			0.829176			0.414588	+	0.910009i	$0.363926\pi$
$312$	23.5406	+	17.5438i	1.33273	+	0.993224i
$313$	17.1328			0.968404			0.484202	−	0.874956i	$-0.339110\pi$
$313$	17.1328			0.968404			0.484202	+	0.874956i	$0.339110\pi$
$314$	−12.4458	+	7.18556i	−0.702355	+	0.405505i
$315$	−1.29350	−	2.24041i	−0.0728805	−	0.126233i
$316$	−0.0388678	+	0.0673210i	−0.00218649	+	0.00378710i
$317$			14.0000i			0.786320i	0.919470	+	0.393160i	$0.128618\pi$
$317$			14.0000i			0.786320i	−0.919470	+	0.393160i	$0.871382\pi$
$318$	30.1742	+	17.4211i	1.69209	+	0.976926i
$319$	7.35627	+	4.24714i	0.411872	+	0.237794i
$320$			4.30267i			0.240527i
$321$	8.68157	−	15.0369i	0.484558	−	0.839279i
$322$	−6.33421	−	10.9712i	−0.352991	−	0.611399i
$323$	4.20317	−	2.42670i	0.233871	−	0.135025i
$324$	0.0708435			0.00393575
$325$	6.74791	+	15.6652i	0.374307	+	0.868947i
$326$	−21.8334			−1.20924
$327$	29.1124	−	16.8081i	1.60992	−	0.929487i
$328$	−6.06434	−	10.5037i	−0.334847	−	0.579972i
$329$	−2.25863	+	3.91206i	−0.124522	+	0.215679i
$330$			3.30100i			0.181714i
$331$	5.99286	+	3.45998i	0.329397	+	0.190178i	0.655574	−	0.755131i	$-0.272427\pi$
$331$	5.99286	+	3.45998i	0.329397	+	0.190178i	−0.326176	+	0.945309i	$0.605760\pi$
$332$	−0.611216	−	0.352886i	−0.0335448	−	0.0193671i
$333$		−	50.9928i		−	2.79439i
$334$	11.3638	−	19.6827i	0.621801	−	1.07699i
$335$	2.17253	+	3.76292i	0.118698	+	0.205591i
$336$	9.38612	−	5.41908i	0.512055	−	0.295635i
$337$	11.1559			0.607703			0.303852	−	0.952719i	$-0.401727\pi$
$337$	11.1559			0.607703			0.303852	+	0.952719i	$0.401727\pi$
$338$	4.17280	−	17.5275i	0.226970	−	0.953371i
$339$	−10.0488			−0.545776
$340$	0.0692913	−	0.0400054i	0.00375785	−	0.00216960i
$341$	−4.70512	−	8.14950i	−0.254796	−	0.441320i
$342$	8.60566	−	14.9054i	0.465341	−	0.805994i
$343$		−	1.00000i		−	0.0539949i
$344$	2.48881	+	1.43692i	0.134188	+	0.0774734i
$345$	−11.6084	−	6.70213i	−0.624977	−	0.360830i
$346$		−	0.417663i		−	0.0224537i
$347$	2.46255	−	4.26527i	0.132197	−	0.228971i	−0.792326	−	0.610097i	$-0.791130\pi$
$347$	2.46255	−	4.26527i	0.132197	−	0.228971i	0.924523	+	0.381126i	$0.124464\pi$
$348$	−0.584759	−	1.01283i	−0.0313464	−	0.0542935i
$349$	1.31926	−	0.761675i	0.0706183	−	0.0407715i	−0.464275	−	0.885691i	$-0.653685\pi$
$349$	1.31926	−	0.761675i	0.0706183	−	0.0407715i	0.534893	+	0.844920i	$0.320352\pi$
$350$	6.55650			0.350460
$351$	−8.00098	−	18.5741i	−0.427061	−	0.991415i
$352$	0.726636			0.0387298
$353$	15.5261	−	8.96401i	0.826372	−	0.477106i	−0.0262367	−	0.999656i	$-0.508352\pi$
$353$	15.5261	−	8.96401i	0.826372	−	0.477106i	0.852609	+	0.522550i	$0.175019\pi$
$354$	12.1511	+	21.0463i	0.645824	+	1.11860i
$355$	−1.34879	+	2.33618i	−0.0715865	+	0.123991i
$356$		−	0.951129i		−	0.0504097i
$357$	−4.76775	−	2.75266i	−0.252336	−	0.145686i
$358$	11.7816	+	6.80213i	0.622679	+	0.359504i
$359$		−	20.0014i		−	1.05563i	−0.849359	−	0.527816i	$-0.823011\pi$
$359$		−	20.0014i		−	1.05563i	0.849359	−	0.527816i	$-0.176989\pi$
$360$	3.72733	−	6.45592i	0.196447	−	0.340257i
$361$	−6.39707	−	11.0801i	−0.336688	−	0.583161i
$362$	−14.9217	+	8.61507i	−0.784269	+	0.452798i
$363$	−23.6294			−1.24022
$364$	0.228782	+	0.170501i	0.0119914	+	0.00893669i
$365$	−6.14421			−0.321602
$366$	−45.6885	+	26.3783i	−2.38818	+	1.37882i
$367$	−13.7078	−	23.7427i	−0.715544	−	1.23936i	−0.962749	−	0.270395i	$-0.912846\pi$
$367$	−13.7078	−	23.7427i	−0.715544	−	1.23936i	0.247206	−	0.968963i	$-0.420488\pi$
$368$	17.5292	−	30.3615i	0.913772	−	1.58270i
$369$			20.9820i			1.09228i
$370$	−6.37169	−	3.67870i	−0.331248	−	0.191246i
$371$	7.70460	+	4.44825i	0.400003	+	0.230942i
$372$			1.29563i			0.0671752i
$373$	7.94643	−	13.7636i	0.411451	−	0.712653i	−0.583598	−	0.812043i	$-0.698356\pi$
$373$	7.94643	−	13.7636i	0.411451	−	0.712653i	0.995049	+	0.0993893i	$0.0316889\pi$
$374$	2.19277	+	3.79798i	0.113385	+	0.196389i
$375$	12.3578	−	7.13481i	0.638156	−	0.368440i
$376$	−13.0168			−0.671292
$377$	−11.2682	+	15.1199i	−0.580341	+	0.778712i
$378$	−7.77403			−0.399853
$379$	7.60284	−	4.38950i	0.390532	−	0.225474i	−0.291859	−	0.956461i	$-0.594274\pi$
$379$	7.60284	−	4.38950i	0.390532	−	0.225474i	0.682390	+	0.730988i	$0.260940\pi$
$380$	0.0511533	+	0.0886001i	0.00262411	+	0.00454509i
$381$	2.01124	−	3.48357i	0.103039	−	0.178469i
$382$			16.9736i			0.868447i
$383$	6.89562	+	3.98119i	0.352349	+	0.203429i	0.665720	−	0.746202i	$-0.268125\pi$
$383$	6.89562	+	3.98119i	0.352349	+	0.203429i	−0.313370	+	0.949631i	$0.601458\pi$
$384$	25.9308	+	14.9712i	1.32328	+	0.763994i
$385$			0.842869i			0.0429566i
$386$	8.06198	−	13.9638i	0.410344	−	0.710736i
$387$	−2.48580	−	4.30553i	−0.126360	−	0.218862i
$388$	−0.303074	+	0.174980i	−0.0153863	+	0.00888326i
$389$	−32.0434			−1.62467			−0.812333	−	0.583194i	$-0.801803\pi$
$389$	−32.0434			−1.62467			−0.812333	+	0.583194i	$0.801803\pi$
$390$	−7.27808	−	0.854411i	−0.368540	−	0.0432648i
$391$	−17.8082			−0.900598
$392$	2.49552	−	1.44079i	0.126043	−	0.0727710i
$393$	12.2550	+	21.2263i	0.618184	+	1.07073i
$394$	1.24815	−	2.16186i	0.0628809	−	0.108913i
$395$		−	0.509777i		−	0.0256496i
$396$	−0.554876	−	0.320358i	−0.0278836	−	0.0160986i
$397$	5.57251	+	3.21729i	0.279676	+	0.161471i	0.633277	−	0.773925i	$-0.281710\pi$
$397$	5.57251	+	3.21729i	0.279676	+	0.161471i	−0.353601	+	0.935396i	$0.615043\pi$
$398$			9.13777i			0.458035i
$399$	3.51972	−	6.09633i	0.176206	−	0.305198i
$400$	9.07219	+	15.7135i	0.453609	+	0.785675i
$401$	−0.462092	+	0.266789i	−0.0230758	+	0.0133228i	−0.511494	−	0.859287i	$-0.670908\pi$
$401$	−0.462092	+	0.266789i	−0.0230758	+	0.0133228i	0.488418	+	0.872610i	$0.337574\pi$
$402$	32.7906			1.63545
$403$	19.1859	−	8.26451i	0.955719	−	0.411685i
$404$	−1.44839			−0.0720601
$405$	−0.402337	+	0.232290i	−0.0199923	+	0.0115426i
$406$	3.62424	+	6.27736i	0.179868	+	0.311540i
$407$	−8.30697	+	14.3881i	−0.411761	+	0.713191i
$408$		−	15.8640i		−	0.785387i
$409$	−34.4269	−	19.8764i	−1.70230	−	0.982824i	−0.943424	−	0.331590i	$-0.892415\pi$
$409$	−34.4269	−	19.8764i	−1.70230	−	0.982824i	−0.758877	−	0.651234i	$-0.774252\pi$
$410$	2.62176	+	1.51367i	0.129479	+	0.0747550i
$411$			24.0695i			1.18726i
$412$	0.198648	−	0.344069i	0.00978670	−	0.0169511i
$413$	3.10263	+	5.37392i	0.152671	+	0.264433i
$414$	−54.6913	+	31.5760i	−2.68793	+	1.55188i
$415$	4.62832			0.227195
$416$	−0.188078	+	1.60209i	−0.00922128	+	0.0785490i
$417$	14.2375			0.697213
$418$	−4.85633	+	2.80380i	−0.237531	+	0.137139i
$419$	−11.9088	−	20.6266i	−0.581783	−	1.00768i	−0.995268	−	0.0971665i	$-0.969022\pi$
$419$	−11.9088	−	20.6266i	−0.581783	−	1.00768i	0.413485	−	0.910511i	$-0.364311\pi$
$420$	0.0580244	−	0.100501i	0.00283130	−	0.00490395i
$421$		−	23.2419i		−	1.13274i	−0.824151	−	0.566370i	$-0.808347\pi$
$421$		−	23.2419i		−	1.13274i	0.824151	−	0.566370i	$-0.191653\pi$
$422$	12.8668	+	7.42865i	0.626346	+	0.361621i
$423$	19.5016	+	11.2593i	0.948200	+	0.547444i
$424$			25.6360i			1.24500i
$425$	4.60828	−	7.98178i	0.223535	−	0.387173i
$426$	10.1789	+	17.6303i	0.493168	+	0.854192i
$427$	−11.6660	+	6.73536i	−0.564557	+	0.325947i
$428$	0.486253			0.0235039
$429$	−1.92937	+	16.4348i	−0.0931510	+	0.793482i
$430$	−0.717316			−0.0345920
$431$	−2.34424	+	1.35345i	−0.112918	+	0.0651932i	−0.555395	−	0.831586i	$-0.687433\pi$
$431$	−2.34424	+	1.35345i	−0.112918	+	0.0651932i	0.442477	+	0.896780i	$0.354100\pi$
$432$	−10.7569	−	18.6314i	−0.517540	−	0.896406i
$433$	−2.90945	+	5.03932i	−0.139819	+	0.242174i	−0.927428	−	0.374002i	$-0.877985\pi$
$433$	−2.90945	+	5.03932i	−0.139819	+	0.242174i	0.787609	+	0.616176i	$0.211319\pi$
$434$		−	8.03008i		−	0.385456i
$435$	6.64198	+	3.83475i	0.318459	+	0.183862i
$436$	0.815290	+	0.470708i	0.0390453	+	0.0225428i
$437$		−	22.7706i		−	1.08927i
$438$	−23.1841	+	40.1560i	−1.10778	+	1.91873i
$439$	19.0851	+	33.0563i	0.910882	+	1.57769i	0.812822	+	0.582513i	$0.197930\pi$
$439$	19.0851	+	33.0563i	0.910882	+	1.57769i	0.0980599	+	0.995181i	$0.468736\pi$
$440$	−2.10340	+	1.21440i	−0.100276	+	0.0578942i
$441$	−4.98500			−0.237381
$442$	−8.94139	+	3.85158i	−0.425298	+	0.183201i
$443$	−31.6740			−1.50488			−0.752440	−	0.658661i	$-0.771123\pi$
$443$	−31.6740			−1.50488			−0.752440	+	0.658661i	$0.771123\pi$
$444$	1.98100	−	1.14373i	0.0940139	−	0.0542790i
$445$	3.11867	+	5.40169i	0.147839	+	0.256065i
$446$	8.93097	−	15.4689i	0.422894	−	0.732473i
$447$			9.50845i			0.449734i
$448$	7.18021	+	4.14550i	0.339233	+	0.195856i
$449$	27.1975	+	15.7025i	1.28353	+	0.741045i	0.977491	−	0.210975i	$-0.0676638\pi$
$449$	27.1975	+	15.7025i	1.28353	+	0.741045i	0.306036	+	0.952020i	$0.400997\pi$
$450$		−	32.6842i		−	1.54075i
$451$	3.41807	−	5.92027i	0.160951	−	0.278775i
$452$	−0.140708	−	0.243713i	−0.00661834	−	0.0114633i
$453$	−30.9732	+	17.8824i	−1.45525	+	0.840187i
$454$	0.968995			0.0454772
$455$	−1.85836	−	0.218163i	−0.0871215	−	0.0102276i
$456$	20.2847			0.949920
$457$	27.5640	−	15.9141i	1.28939	−	0.744429i	0.310844	−	0.950461i	$-0.399388\pi$
$457$	27.5640	−	15.9141i	1.28939	−	0.744429i	0.978545	+	0.206032i	$0.0660551\pi$
$458$	−12.6723	−	21.9491i	−0.592140	−	1.02562i
$459$	−5.46403	+	9.46398i	−0.255039	+	0.441741i
$460$		−	0.375385i		−	0.0175024i
$461$	1.01005	+	0.583153i	0.0470427	+	0.0271601i	0.523337	−	0.852126i	$-0.324687\pi$
$461$	1.01005	+	0.583153i	0.0470427	+	0.0271601i	−0.476294	+	0.879286i	$0.658020\pi$
$462$	5.50865	+	3.18042i	0.256286	+	0.147967i
$463$			20.3441i			0.945469i	0.881205	+	0.472734i	$0.156733\pi$
$463$			20.3441i			0.945469i	−0.881205	+	0.472734i	$0.843267\pi$
$464$	−10.0297	+	17.3719i	−0.465615	+	0.806470i
$465$	−4.24825	−	7.35819i	−0.197008	−	0.341228i
$466$	32.1427	−	18.5576i	1.48898	−	0.859664i
$467$	1.56939			0.0726229			0.0363114	−	0.999341i	$-0.488439\pi$
$467$	1.56939			0.0726229			0.0363114	+	0.999341i	$0.488439\pi$
$468$	0.849948	−	1.14048i	0.0392889	−	0.0527185i
$469$	8.37266			0.386614
$470$	2.81375	−	1.62452i	0.129788	−	0.0749334i
$471$	14.6504	+	25.3753i	0.675055	+	1.16923i
$472$	−8.94049	+	15.4854i	−0.411519	+	0.712773i
$473$			1.61979i			0.0744781i
$474$	−3.33169	−	1.92355i	−0.153030	−	0.0883517i
$475$	10.2060	+	5.89243i	0.468283	+	0.270363i
$476$		−	0.154176i		−	0.00706665i
$477$	22.1745	−	38.4074i	1.01530	−	1.75856i
$478$	−11.5157	−	19.9457i	−0.526714	−	0.912295i
$479$	6.68501	−	3.85959i	0.305446	−	0.176349i	−0.339441	−	0.940627i	$-0.610238\pi$
$479$	6.68501	−	3.85959i	0.305446	−	0.176349i	0.644887	+	0.764278i	$0.276905\pi$
$480$	0.656080			0.0299458
$481$	−29.5729	−	22.0394i	−1.34841	−	1.00491i
$482$	−24.1334			−1.09925
$483$	−22.3688	+	12.9146i	−1.01781	+	0.587635i
$484$	−0.330870	−	0.573083i	−0.0150395	−	0.0260492i
$485$	1.14749	−	1.98751i	0.0521047	−	0.0902481i
$486$		−	19.8161i		−	0.898875i
$487$	−0.0659739	−	0.0380900i	−0.00298956	−	0.00172602i	0.498504	−	0.866887i	$-0.333883\pi$
$487$	−0.0659739	−	0.0380900i	−0.00298956	−	0.00172602i	−0.501494	+	0.865161i	$0.667216\pi$
$488$	−33.6165	−	19.4085i	−1.52175	−	0.878582i
$489$			44.5155i			2.01306i
$490$	−0.359625	+	0.622889i	−0.0162462	+	0.0281392i
$491$	0.893574	+	1.54772i	0.0403264	+	0.0698474i	0.885484	−	0.464670i	$-0.153827\pi$
$491$	0.893574	+	1.54772i	0.0403264	+	0.0698474i	−0.845158	+	0.534517i	$0.820494\pi$
$492$	−0.815121	+	0.470610i	−0.0367485	+	0.0212167i
$493$	10.1893			0.458902
$494$	−4.92487	−	11.4330i	−0.221580	−	0.514395i
$495$	4.20170			0.188852
$496$	19.2451	−	11.1112i	0.864131	−	0.498906i
$497$	2.59905	+	4.50168i	0.116583	+	0.201928i
$498$	17.4642	−	30.2488i	0.782589	−	1.35548i
$499$		−	8.33493i		−	0.373123i	−0.982443	−	0.186561i	$-0.940266\pi$
$499$		−	8.33493i		−	0.373123i	0.982443	−	0.186561i	$-0.0597343\pi$
$500$	0.346080	+	0.199810i	0.0154772	+	0.00893576i
$501$	−40.1305	−	23.1694i	−1.79290	−	1.03513i
$502$		−	8.93914i		−	0.398973i
$503$	−0.720238	+	1.24749i	−0.0321138	+	0.0556228i	−0.881636	−	0.471931i	$-0.843557\pi$
$503$	−0.720238	+	1.24749i	−0.0321138	+	0.0556228i	0.849522	+	0.527554i	$0.176891\pi$
$504$	−7.18234	−	12.4402i	−0.319927	−	0.554130i
$505$	8.22576	−	4.74914i	0.366041	−	0.211334i
$506$	20.5755			0.914693
$507$	−35.7363	−	8.50779i	−1.58710	−	0.377844i
$508$	0.112649			0.00499801
$509$	12.8394	−	7.41282i	0.569096	−	0.328568i	−0.187692	−	0.982228i	$-0.560101\pi$
$509$	12.8394	−	7.41282i	0.569096	−	0.328568i	0.756788	+	0.653660i	$0.226767\pi$
$510$	1.97985	+	3.42920i	0.0876693	+	0.151848i
$511$	−5.91976	+	10.2533i	−0.261875	+	0.453581i
$512$			23.8204i			1.05272i
$513$	−12.1012	−	6.98664i	−0.534282	−	0.308468i
$514$	4.40686	+	2.54430i	0.194378	+	0.112224i
$515$			2.60540i			0.114808i
$516$	0.111509	−	0.193139i	0.00490891	−	0.00850248i
$517$	−3.66837	−	6.35380i	−0.161335	−	0.279440i
$518$	−12.2779	+	7.08863i	−0.539459	+	0.311457i
$519$	−0.851561			−0.0373794
$520$	−2.13308	−	4.95192i	−0.0935419	−	0.217156i
$521$	−0.334388			−0.0146498			−0.00732489	−	0.999973i	$-0.502332\pi$
$521$	−0.334388			−0.0146498			−0.00732489	+	0.999973i	$0.502332\pi$
$522$	31.2926	−	18.0668i	1.36964	−	0.790763i
$523$	16.2533	+	28.1515i	0.710705	+	1.23098i	0.964593	+	0.263744i	$0.0849574\pi$
$523$	16.2533	+	28.1515i	0.710705	+	1.23098i	−0.253887	+	0.967234i	$0.581709\pi$
$524$	−0.343201	+	0.594441i	−0.0149928	+	0.0259683i
$525$		−	13.3678i		−	0.583420i
$526$	21.9881	+	12.6948i	0.958726	+	0.553521i
$527$	−9.77570	−	5.64400i	−0.425836	−	0.245857i
$528$			17.6029i			0.766068i
$529$	−30.2751	+	52.4380i	−1.31631	+	2.27991i
$530$	−3.19941	−	5.54153i	−0.138973	−	0.240709i
$531$	26.7890	−	15.4666i	1.16254	−	0.671194i
$532$	0.197139			0.00854706
$533$	12.1683	+	9.06855i	0.527070	+	0.392803i
$534$	47.0710			2.03696
$535$	−2.76155	+	1.59438i	−0.119392	+	0.0689311i
$536$	12.0633	+	20.8942i	0.521053	+	0.902491i
$537$	13.8686	−	24.0212i	0.598476	−	1.03659i
$538$		−	38.1732i		−	1.64576i
$539$	1.40656	+	0.812080i	0.0605850	+	0.0349787i
$540$	−0.199495	−	0.115178i	−0.00858488	−	0.00495649i
$541$			10.6015i			0.455796i	0.973685	+	0.227898i	$0.0731852\pi$
$541$			10.6015i			0.455796i	−0.973685	+	0.227898i	$0.926815\pi$
$542$	−4.51767	+	7.82483i	−0.194051	+	0.336105i
$543$	17.5650	+	30.4235i	0.753786	+	1.30560i
$544$	0.754856	−	0.435816i	0.0323642	−	0.0186855i
$545$	−6.17364			−0.264450
$546$	−8.43804	+	11.3223i	−0.361115	+	0.484550i
$547$	10.2327			0.437519			0.218760	−	0.975779i	$-0.429799\pi$
$547$	10.2327			0.437519			0.218760	+	0.975779i	$0.429799\pi$
$548$	−0.583756	+	0.337032i	−0.0249368	+	0.0143973i
$549$	33.5758	+	58.1549i	1.43298	+	2.48199i
$550$	−5.32440	+	9.22214i	−0.227033	+	0.393233i
$551$			13.0286i			0.555038i
$552$	−64.4574	−	37.2145i	−2.74349	−	1.58396i
$553$	−0.850705	−	0.491155i	−0.0361757	−	0.0208860i
$554$			7.54216i			0.320436i
$555$	−7.50037	+	12.9910i	−0.318373	+	0.551438i
$556$	0.199360	+	0.345301i	0.00845474	+	0.0146440i
$557$	27.7067	−	15.9965i	1.17397	−	0.677793i	0.219359	−	0.975644i	$-0.429603\pi$
$557$	27.7067	−	15.9965i	1.17397	−	0.677793i	0.954612	+	0.297851i	$0.0962700\pi$
$558$	−40.0300			−1.69460
$559$	−3.57133	−	0.419257i	−0.151051	−	0.0177327i
$560$	−1.99044			−0.0841115
$561$	7.74359	−	4.47076i	0.326934	−	0.188756i
$562$	−2.45478	−	4.25180i	−0.103549	−	0.179351i
$563$	5.39566	−	9.34556i	0.227400	−	0.393868i	−0.729637	−	0.683835i	$-0.760311\pi$
$563$	5.39566	−	9.34556i	0.227400	−	0.393868i	0.957037	+	0.289967i	$0.0936442\pi$
$564$			1.01014i			0.0425348i
$565$	1.59823	+	0.922737i	0.0672380	+	0.0388199i
$566$	16.9708	+	9.79808i	0.713335	+	0.411844i
$567$			0.895217i			0.0375956i
$568$	−7.48937	+	12.9720i	−0.314247	+	0.544292i
$569$	−12.3007	−	21.3054i	−0.515672	−	0.893170i	−0.999835	−	0.0181917i	$-0.994209\pi$
$569$	−12.3007	−	21.3054i	−0.515672	−	0.893170i	0.484163	−	0.874978i	$-0.339124\pi$
$570$	−4.38479	+	2.53156i	−0.183659	+	0.106035i
$571$	−16.5724			−0.693534			−0.346767	−	0.937951i	$-0.612721\pi$
$571$	−16.5724			−0.693534			−0.346767	+	0.937951i	$0.612721\pi$
$572$	−0.425610	+	0.183335i	−0.0177956	+	0.00766563i
$573$	34.6070			1.44573
$574$	5.05197	−	2.91676i	0.210865	−	0.121743i
$575$	−21.6206	−	37.4480i	−0.901641	−	1.56169i
$576$	20.6653	−	35.7934i	0.861054	−	1.49139i
$577$		−	14.6611i		−	0.610348i	−0.952297	−	0.305174i	$-0.901285\pi$
$577$		−	14.6611i		−	0.610348i	0.952297	−	0.305174i	$-0.0987147\pi$
$578$	−15.8487	−	9.15027i	−0.659221	−	0.380601i
$579$	−28.4702	−	16.4373i	−1.18318	−	0.683111i
$580$			0.214784i			0.00891840i
$581$	4.45926	−	7.72366i	0.185001	−	0.320431i
$582$	−8.65969	−	14.9990i	−0.358956	−	0.621730i
$583$	−12.5135	+	7.22467i	−0.518256	+	0.299215i
$584$	−34.1166			−1.41175
$585$	−1.08754	+	9.26394i	−0.0449644	+	0.383017i
$586$	11.5717			0.478024
$587$	30.5998	−	17.6668i	1.26299	−	0.729186i	0.289336	−	0.957227i	$-0.406565\pi$
$587$	30.5998	−	17.6668i	1.26299	−	0.729186i	0.973652	+	0.228041i	$0.0732320\pi$
$588$	−0.111810	−	0.193660i	−0.00461095	−	0.00798640i
$589$	7.21676	−	12.4998i	0.297362	−	0.515045i
$590$		−	4.46313i		−	0.183744i
$591$	−4.40775	−	2.54481i	−0.181310	−	0.104680i
$592$	−33.9776	−	19.6170i	−1.39647	−	0.806253i
$593$			16.4294i			0.674675i	0.941384	+	0.337338i	$0.109526\pi$
$593$			16.4294i			0.674675i	−0.941384	+	0.337338i	$0.890474\pi$
$594$	6.31313	−	10.9347i	0.259031	−	0.448655i
$595$	0.505530	+	0.875603i	0.0207247	+	0.0358962i
$596$	−0.230608	+	0.133142i	−0.00944608	+	0.00545370i
$597$	18.6307			0.762504
$598$	−5.32564	+	45.3651i	−0.217782	+	1.85512i
$599$	12.0819			0.493653			0.246826	−	0.969060i	$-0.420612\pi$
$599$	12.0819			0.493653			0.246826	+	0.969060i	$0.420612\pi$
$600$	33.3598	−	19.2603i	1.36191	−	0.786297i
$601$	−3.90743	−	6.76787i	−0.159387	−	0.276067i	0.775261	−	0.631642i	$-0.217619\pi$
$601$	−3.90743	−	6.76787i	−0.159387	−	0.276067i	−0.934648	+	0.355574i	$0.884285\pi$
$602$	−0.691113	+	1.19704i	−0.0281677	+	0.0487878i
$603$		−	41.7377i		−	1.69969i
$604$	−0.867401	−	0.500794i	−0.0352941	−	0.0203770i
$605$	3.75818	+	2.16979i	0.152792	+	0.0882144i
$606$		−	71.6803i		−	2.91181i
$607$	−17.7825	+	30.8001i	−0.721768	+	1.25014i	0.238523	+	0.971137i	$0.423337\pi$
$607$	−17.7825	+	30.8001i	−0.721768	+	1.25014i	−0.960291	+	0.279002i	$0.909996\pi$
$608$	0.557261	+	0.965205i	0.0225999	+	0.0391442i
$609$	12.7987	−	7.38934i	0.518630	−	0.299431i
$610$	9.68882			0.392289
$611$	14.9584	−	6.44347i	0.605153	−	0.260675i
$612$	−0.768568			−0.0310675
$613$	−10.3376	+	5.96839i	−0.417530	+	0.241061i	−0.694020	−	0.719956i	$-0.744162\pi$
$613$	−10.3376	+	5.96839i	−0.417530	+	0.241061i	0.276490	+	0.961017i	$0.410829\pi$
$614$	5.77500	+	10.0026i	0.233060	+	0.403672i
$615$	3.08618	−	5.34542i	0.124447	−	0.215548i
$616$			4.68015i			0.188569i
$617$	−20.4124	−	11.7851i	−0.821772	−	0.474450i	0.0292550	−	0.999572i	$-0.490687\pi$
$617$	−20.4124	−	11.7851i	−0.821772	−	0.474450i	−0.851027	+	0.525122i	$0.824020\pi$
$618$	17.0278	+	9.83103i	0.684960	+	0.395462i
$619$			28.5571i			1.14781i	0.818923	+	0.573904i	$0.194572\pi$
$619$			28.5571i			1.14781i	−0.818923	+	0.573904i	$0.805428\pi$
$620$	0.118972	−	0.206066i	0.00477803	−	0.00827579i
$621$	25.6355	+	44.4020i	1.02872	+	1.78179i
$622$	−17.5512	+	10.1332i	−0.703738	+	0.406303i
$623$	12.0190			0.481530
$624$	−38.8110	−	4.55623i	−1.55368	−	0.182395i
$625$	21.0328			0.841311
$626$	−20.5640	+	11.8726i	−0.821903	+	0.474526i
$627$	5.71659	+	9.90142i	0.228298	+	0.395425i
$628$	−0.410283	+	0.710632i	−0.0163721	+	0.0283573i
$629$			19.9292i			0.794628i
$630$	3.10510	+	1.79273i	0.123710	+	0.0714241i
$631$	−38.9646	−	22.4962i	−1.55116	−	0.895561i	−0.998048	−	0.0624526i	$-0.980108\pi$
$631$	−38.9646	−	22.4962i	−1.55116	−	0.895561i	−0.553109	−	0.833109i	$-0.686559\pi$
$632$		−	2.83061i		−	0.112596i
$633$	15.1460	−	26.2337i	0.602001	−	1.04270i
$634$	−9.70169	−	16.8038i	−0.385303	−	0.667365i
$635$	−0.639763	+	0.369367i	−0.0253882	+	0.0146579i
$636$	1.98943			0.0788860
$637$	−2.15455	+	2.89101i	−0.0853662	+	0.114546i
$638$	−11.7727			−0.466085
$639$	22.4409	−	12.9562i	0.887747	−	0.512541i
$640$	−2.74947	−	4.76222i	−0.108682	−	0.188243i
$641$	−1.26650	+	2.19364i	−0.0500238	+	0.0866437i	−0.889953	−	0.456052i	$-0.849263\pi$
$641$	−1.26650	+	2.19364i	−0.0500238	+	0.0866437i	0.839929	+	0.542696i	$0.182596\pi$
$642$			24.0645i			0.949749i
$643$	15.9150	+	9.18853i	0.627627	+	0.362360i	0.779832	−	0.625988i	$-0.215304\pi$
$643$	15.9150	+	9.18853i	0.627627	+	0.362360i	−0.152206	+	0.988349i	$0.548638\pi$
$644$	−0.626435	−	0.361672i	−0.0246850	−	0.0142519i
$645$			1.46251i			0.0575863i
$646$	−3.36329	+	5.82539i	−0.132327	+	0.229197i
$647$	10.4643	+	18.1248i	0.411396	+	0.712558i	0.995043	−	0.0994494i	$-0.0317081\pi$
$647$	10.4643	+	18.1248i	0.411396	+	0.712558i	−0.583647	+	0.812008i	$0.698375\pi$
$648$	−2.23404	+	1.28982i	−0.0877612	+	0.0506690i
$649$	−10.0783			−0.395609
$650$	−18.9549	−	14.1263i	−0.743473	−	0.554079i
$651$	−16.3723			−0.641680
$652$	−1.07963	+	0.623326i	−0.0422817	+	0.0244113i
$653$	24.0580	+	41.6696i	0.941461	+	1.63066i	0.762686	+	0.646769i	$0.223880\pi$
$653$	24.0580	+	41.6696i	0.941461	+	1.63066i	0.178775	+	0.983890i	$0.442786\pi$
$654$	−23.2952	+	40.3484i	−0.910913	+	1.57775i
$655$		−	4.50130i		−	0.175880i
$656$	13.9808	+	8.07180i	0.545857	+	0.315151i
$657$	51.1129	+	29.5100i	1.99410	+	1.15130i
$658$		−	6.26070i		−	0.244068i
$659$	1.10819	−	1.91944i	0.0431690	−	0.0747708i	−0.843634	−	0.536919i	$-0.819588\pi$
$659$	1.10819	−	1.91944i	0.0431690	−	0.0747708i	0.886803	+	0.462148i	$0.152921\pi$
$660$	0.0942408	+	0.163230i	0.00366832	+	0.00635371i
$661$	−0.552034	+	0.318717i	−0.0214716	+	0.0123966i	−0.510697	−	0.859761i	$-0.670613\pi$
$661$	−0.552034	+	0.318717i	−0.0214716	+	0.0123966i	0.489226	+	0.872157i	$0.337279\pi$
$662$	−9.59073			−0.372754
$663$	7.85287	+	18.2303i	0.304980	+	0.708006i
$664$	25.6994			0.997331
$665$	−1.11960	+	0.646401i	−0.0434162	+	0.0250664i
$666$	35.3368	+	61.2052i	1.36927	+	2.37165i
$667$	23.9024	−	41.4002i	0.925506	−	1.60302i
$668$		−	1.29771i		−	0.0502100i
$669$	−31.5390	−	18.2091i	−1.21937	−	0.704003i
$670$	−5.21523	−	3.01102i	−0.201482	−	0.116326i
$671$		−	21.8786i		−	0.844614i
$672$	0.632114	−	1.09485i	0.0243843	−	0.0422349i
$673$	7.70343	+	13.3427i	0.296945	+	0.514324i	0.975436	−	0.220285i	$-0.0706988\pi$
$673$	7.70343	+	13.3427i	0.296945	+	0.514324i	−0.678490	+	0.734609i	$0.737365\pi$
$674$	−13.3901	+	7.73081i	−0.515769	+	0.297780i
$675$	−26.5352			−1.02134
$676$	−0.294057	−	0.985841i	−0.0113099	−	0.0379170i
$677$	−11.6812			−0.448945			−0.224473	−	0.974480i	$-0.572066\pi$
$677$	−11.6812			−0.448945			−0.224473	+	0.974480i	$0.572066\pi$
$678$	12.0613	−	6.96358i	0.463210	−	0.267435i
$679$	−2.21114	−	3.82981i	−0.0848559	−	0.146975i
$680$	−1.45673	+	2.52312i	−0.0558629	+	0.0967574i
$681$		−	1.97565i		−	0.0757072i
$682$	11.2948	+	6.52107i	0.432501	+	0.249705i
$683$	19.8419	+	11.4557i	0.759227	+	0.438340i	0.829018	−	0.559221i	$-0.188900\pi$
$683$	19.8419	+	11.4557i	0.759227	+	0.438340i	−0.0697909	+	0.997562i	$0.522233\pi$
$684$		−	0.982737i		−	0.0375759i
$685$	2.21020	−	3.82817i	0.0844473	−	0.146267i
$686$	0.692976	+	1.20027i	0.0264580	+	0.0458265i
$687$	−44.7514	+	25.8372i	−1.70737	+	0.985752i
$688$	−3.82515			−0.145833
$689$	−12.6901	−	29.4599i	−0.483454	−	1.12233i
$690$	18.5777			0.707239
$691$	−40.9046	+	23.6163i	−1.55608	+	0.898405i	−0.558458	+	0.829533i	$0.688607\pi$
$691$	−40.9046	+	23.6163i	−1.55608	+	0.898405i	−0.997625	+	0.0688729i	$0.978060\pi$
$692$	−0.0119239	−	0.0206529i	−0.000453280	−	0.000785104i
$693$	4.04822	−	7.01172i	0.153779	−	0.266353i
$694$			6.82596i			0.259110i
$695$	−2.26443	−	1.30737i	−0.0858946	−	0.0495913i
$696$	36.8805	+	21.2930i	1.39795	+	0.807109i
$697$		−	8.20026i		−	0.310607i
$698$	−1.05565	+	1.82843i	−0.0399568	+	0.0692071i
$699$	−37.8365	−	65.5347i	−1.43111	−	2.47875i
$700$	0.324210	−	0.187183i	0.0122540	−	0.00707484i
$701$	12.2098			0.461158			0.230579	−	0.973054i	$-0.425938\pi$
$701$	12.2098			0.461158			0.230579	+	0.973054i	$0.425938\pi$
$702$	22.4748	+	16.7495i	0.848256	+	0.632169i
$703$	−25.4827			−0.961097
$704$	−11.6618	+	6.73295i	−0.439521	+	0.253758i
$705$	−3.31218	−	5.73686i	−0.124744	−	0.216063i
$706$	−12.4237	+	21.5185i	−0.467572	+	0.809858i
$707$		−	18.3026i		−	0.688342i
$708$	1.20171	+	0.693808i	0.0451630	+	0.0260749i
$709$	−15.4910	−	8.94374i	−0.581777	−	0.335889i	0.180062	−	0.983655i	$-0.442370\pi$
$709$	−15.4910	−	8.94374i	−0.581777	−	0.335889i	−0.761839	+	0.647766i	$0.775703\pi$
$710$		−	3.73873i		−	0.140312i
$711$	−2.44841	+	4.24076i	−0.0918224	+	0.159041i
$712$	17.3169	+	29.9937i	0.648977	+	1.12406i
$713$	−45.8644	+	26.4798i	−1.71764	+	0.991678i
$714$	7.63012			0.285550
$715$	1.81600	−	2.43674i	0.0679146	−	0.0911290i
$716$	0.776780			0.0290296
$717$	−40.6667	+	23.4789i	−1.51872	+	0.876836i
$718$	13.8605	+	24.0070i	0.517268	+	0.895935i
$719$	4.56317	−	7.90364i	0.170178	−	0.294756i	−0.768304	−	0.640085i	$-0.778899\pi$
$719$	4.56317	−	7.90364i	0.170178	−	0.294756i	0.938482	+	0.345329i	$0.112233\pi$
$720$			9.92235i			0.369784i
$721$	4.34784	+	2.51023i	0.161922	+	0.0934858i
$722$	15.3564	+	8.86604i	0.571507	+	0.329960i
$723$			49.2048i			1.82995i
$724$	−0.491906	+	0.852006i	−0.0182815	+	0.0316646i
$725$	12.3706	+	21.4266i	0.459434	+	0.795763i
$726$	28.3617	−	16.3746i	1.05260	−	0.607719i
$727$	33.6859			1.24934			0.624670	−	0.780889i	$-0.285233\pi$
$727$	33.6859			1.24934			0.624670	+	0.780889i	$0.285233\pi$
$728$	−10.3188	−	1.21138i	−0.382441	−	0.0448968i
$729$	−43.0880			−1.59585
$730$	7.37471	−	4.25779i	0.272950	−	0.157588i
$731$	0.971507	+	1.68270i	0.0359325	+	0.0622369i
$732$	−1.50616	+	2.60874i	−0.0556691	+	0.0964218i
$733$		−	46.4344i		−	1.71509i	−0.514406	−	0.857547i	$-0.671987\pi$
$733$		−	46.4344i		−	1.71509i	0.514406	−	0.857547i	$-0.328013\pi$
$734$	32.9062	+	18.9984i	1.21459	+	0.701245i
$735$	1.26999	+	0.733228i	0.0468442	+	0.0270455i
$736$		−	4.08942i		−	0.150738i
$737$	−6.79927	+	11.7767i	−0.250454	+	0.433799i
$738$	−14.5400	−	25.1841i	−0.535226	−	0.927039i
$739$	−1.60237	+	0.925127i	−0.0589440	+	0.0340314i	−0.529182	−	0.848508i	$-0.677501\pi$
$739$	−1.60237	+	0.925127i	−0.0589440	+	0.0340314i	0.470238	+	0.882539i	$0.344168\pi$
$740$	−0.420095			−0.0154430
$741$	−23.3104	+	10.0412i	−0.856328	+	0.368871i
$742$	−12.3301			−0.452654
$743$	28.7095	−	16.5755i	1.05325	−	0.608094i	0.129693	−	0.991554i	$-0.458601\pi$
$743$	28.7095	−	16.5755i	1.05325	−	0.608094i	0.923558	+	0.383460i	$0.125268\pi$
$744$	−23.5890	−	40.8574i	−0.864816	−	1.49791i
$745$	0.873120	−	1.51229i	0.0319886	−	0.0554059i
$746$			22.0268i			0.806457i
$747$	−38.5024	−	22.2294i	−1.40873	−	0.813331i
$748$	0.216858	+	0.125203i	0.00792913	+	0.00457788i
$749$			6.14456i			0.224517i
$750$	−9.88850	+	17.1274i	−0.361077	+	0.625404i
$751$	−10.3871	−	17.9910i	−0.379032	−	0.656503i	0.611890	−	0.790943i	$-0.290410\pi$
$751$	−10.3871	−	17.9910i	−0.379032	−	0.656503i	−0.990922	+	0.134441i	$0.957076\pi$
$752$	15.0046	−	8.66289i	0.547160	−	0.315903i
$753$	−18.2257			−0.664182
$754$	3.04717	−	25.9565i	0.110971	−	0.945280i
$755$	6.56824			0.239043
$756$	−0.384415	+	0.221942i	−0.0139810	+	0.00807195i
$757$	−21.8075	−	37.7717i	−0.792607	−	1.37283i	−0.924348	−	0.381551i	$-0.875390\pi$
$757$	−21.8075	−	37.7717i	−0.792607	−	1.37283i	0.131741	−	0.991284i	$-0.457943\pi$
$758$	−6.08364	+	10.5372i	−0.220968	+	0.382727i
$759$		−	41.9508i		−	1.52272i
$760$	−3.22622	−	1.86266i	−0.117027	−	0.0675657i
$761$	10.7302	+	6.19511i	0.388971	+	0.224573i	0.681714	−	0.731619i	$-0.261235\pi$
$761$	10.7302	+	6.19511i	0.388971	+	0.224573i	−0.292743	+	0.956191i	$0.594568\pi$
$762$			5.57497i			0.201960i
$763$	−5.94812	+	10.3025i	−0.215337	+	0.372974i
$764$	0.484583	+	0.839323i	0.0175316	+	0.0303656i
$765$	4.36488	−	2.52007i	0.157813	−	0.0911132i
$766$	−11.0355			−0.398728
$767$	2.60862	−	22.2208i	0.0941917	−	0.802347i
$768$	5.35835			0.193353
$769$	−4.80955	+	2.77680i	−0.173437	+	0.100134i	−0.584205	−	0.811606i	$-0.698594\pi$
$769$	−4.80955	+	2.77680i	−0.173437	+	0.100134i	0.410769	+	0.911740i	$0.365260\pi$
$770$	−0.584088	−	1.01167i	−0.0210491	−	0.0364581i

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20027 + 0.692976i) q^{2} +(1.41289 + 2.44719i) q^{3} +(-0.0395678 + 0.0685334i) q^{4} -0.518957i q^{5} +(-3.39169 - 1.95819i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.88158i q^{8} +(-2.49250 + 4.31714i) q^{9} +O(q^{10})\)	\(q+(-1.20027 + 0.692976i) q^{2} +(1.41289 + 2.44719i) q^{3} +(-0.0395678 + 0.0685334i) q^{4} -0.518957i q^{5} +(-3.39169 - 1.95819i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.88158i q^{8} +(-2.49250 + 4.31714i) q^{9} +(0.359625 + 0.622889i) q^{10} +(1.40656 - 0.812080i) q^{11} -0.223619 q^{12} +(1.42641 + 3.31140i) q^{13} +1.38595 q^{14} +(1.26999 - 0.733228i) q^{15} +(1.91773 + 3.32161i) q^{16} +(0.974127 - 1.68724i) q^{17} -6.90897i q^{18} +(2.15740 + 1.24558i) q^{19} +(0.0355659 + 0.0205340i) q^{20} -2.82577i q^{21} +(-1.12550 + 1.94943i) q^{22} +(-4.57029 - 7.91598i) q^{23} +(7.05179 - 4.07135i) q^{24} +4.73068 q^{25} +(-4.00680 - 2.98610i) q^{26} -5.60916 q^{27} +(0.0685334 - 0.0395678i) q^{28} +(2.61498 + 4.52928i) q^{29} +(-1.01622 + 1.76014i) q^{30} -5.79391i q^{31} +(0.387453 + 0.223696i) q^{32} +(3.97463 + 2.29475i) q^{33} +2.70019i q^{34} +(-0.259479 + 0.449430i) q^{35} +(-0.197245 - 0.341639i) q^{36} +(-8.85879 + 5.11463i) q^{37} -3.45262 q^{38} +(-6.08826 + 8.16934i) q^{39} -1.49542 q^{40} +(3.64513 - 2.10452i) q^{41} +(1.95819 + 3.39169i) q^{42} +(-0.498655 + 0.863697i) q^{43} +0.128529i q^{44} +(2.24041 + 1.29350i) q^{45} +(10.9712 + 6.33421i) q^{46} -4.51725i q^{47} +(-5.41908 + 9.38612i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-5.67810 + 3.27825i) q^{50} +5.50532 q^{51} +(-0.283381 - 0.0332676i) q^{52} -8.89651 q^{53} +(6.73251 - 3.88701i) q^{54} +(-0.421434 - 0.729946i) q^{55} +(-1.44079 + 2.49552i) q^{56} +7.03944i q^{57} +(-6.27736 - 3.62424i) q^{58} +(-5.37392 - 3.10263i) q^{59} +0.116049i q^{60} +(6.73536 - 11.6660i) q^{61} +(4.01504 + 6.95426i) q^{62} +(4.31714 - 2.49250i) q^{63} -8.29100 q^{64} +(1.71847 - 0.740247i) q^{65} -6.36084 q^{66} +(-7.25094 + 4.18633i) q^{67} +(0.0770880 + 0.133520i) q^{68} +(12.9146 - 22.3688i) q^{69} -0.719250i q^{70} +(-4.50168 - 2.59905i) q^{71} +(12.4402 + 7.18234i) q^{72} -11.8395i q^{73} +(7.08863 - 12.2779i) q^{74} +(6.68392 + 11.5769i) q^{75} +(-0.170727 + 0.0985694i) q^{76} -1.62416 q^{77} +(1.64640 - 14.0244i) q^{78} +0.982310 q^{79} +(1.72377 - 0.995221i) q^{80} +(-0.447609 - 0.775281i) q^{81} +(-2.91676 + 5.05197i) q^{82} +8.91851i q^{83} +(0.193660 + 0.111810i) q^{84} +(-0.875603 - 0.505530i) q^{85} -1.38223i q^{86} +(-7.38934 + 12.7987i) q^{87} +(-2.34008 - 4.05313i) q^{88} +(-10.4087 + 6.00949i) q^{89} -3.58546 q^{90} +(0.420388 - 3.58096i) q^{91} +0.723345 q^{92} +(14.1788 - 8.18614i) q^{93} +(3.13035 + 5.42193i) q^{94} +(0.646401 - 1.11960i) q^{95} +1.26423i q^{96} +(3.82981 + 2.21114i) q^{97} +(-1.20027 - 0.692976i) q^{98} +8.09643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9	\( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} - 30 q^{33} + 6 q^{35} - 10 q^{36} - 42 q^{37} + 4 q^{38} - 4 q^{39} + 92 q^{40} + 30 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{46} - 2 q^{48} + 6 q^{49} - 18 q^{50} + 52 q^{51} + 2 q^{52} - 44 q^{53} + 12 q^{54} - 6 q^{55} - 12 q^{56} - 12 q^{58} + 18 q^{59} + 14 q^{61} - 4 q^{62} + 12 q^{63} - 52 q^{64} + 60 q^{65} - 52 q^{66} - 24 q^{67} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} + 46 q^{75} - 18 q^{76} + 8 q^{77} - 10 q^{78} - 56 q^{79} - 72 q^{80} + 2 q^{81} + 14 q^{82} + 18 q^{84} - 48 q^{85} - 2 q^{87} - 14 q^{88} - 12 q^{89} + 24 q^{90} + 14 q^{91} + 24 q^{92} - 18 q^{93} + 4 q^{94} - 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9 + 12 * q^10 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 8 * q^14 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 12 * q^24 - 20 * q^25 - 42 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 - 30 * q^33 + 6 * q^35 - 10 * q^36 - 42 * q^37 + 4 * q^38 - 4 * q^39 + 92 * q^40 + 30 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^46 - 2 * q^48 + 6 * q^49 - 18 * q^50 + 52 * q^51 + 2 * q^52 - 44 * q^53 + 12 * q^54 - 6 * q^55 - 12 * q^56 - 12 * q^58 + 18 * q^59 + 14 * q^61 - 4 * q^62 + 12 * q^63 - 52 * q^64 + 60 * q^65 - 52 * q^66 - 24 * q^67 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 + 46 * q^75 - 18 * q^76 + 8 * q^77 - 10 * q^78 - 56 * q^79 - 72 * q^80 + 2 * q^81 + 14 * q^82 + 18 * q^84 - 48 * q^85 - 2 * q^87 - 14 * q^88 - 12 * q^89 + 24 * q^90 + 14 * q^91 + 24 * q^92 - 18 * q^93 + 4 * q^94 - 22 * q^95 + 6 * q^97

Introduction

L-functions

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