LMFDB - Embedded newform 315.2.cg.d.283.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(157,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3, 2]))

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

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

chi := DirichletCharacter("315.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			283.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.283
Dual form			315.2.cg.d.187.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.133975 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-0.232051 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +(1.36603 + 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.133975 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-0.232051 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +(1.36603 + 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +(0.866025 - 0.767949i) q^{10} -2.00000 q^{11} +3.00000 q^{12} +(-0.0980762 - 0.366025i) q^{13} +(1.36603 - 0.0980762i) q^{14} +(0.232051 - 3.86603i) q^{15} +(1.23205 - 2.13397i) q^{16} +(-2.00000 + 0.535898i) q^{17} +(-1.09808 + 1.09808i) q^{18} +(0.366025 + 0.633975i) q^{19} +(-3.23205 - 2.13397i) q^{20} +(3.00000 - 3.46410i) q^{21} +(-0.267949 - 1.00000i) q^{22} +(4.46410 + 4.46410i) q^{23} +(0.866025 + 3.23205i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(0.169873 - 0.0980762i) q^{26} +5.19615i q^{27} +(-1.50000 - 4.33013i) q^{28} +(-8.59808 + 4.96410i) q^{29} +(1.96410 - 0.401924i) q^{30} +(-4.73205 + 2.73205i) q^{31} +(4.96410 + 1.33013i) q^{32} +(-3.00000 - 1.73205i) q^{33} +(-0.535898 - 0.928203i) q^{34} +(-5.69615 + 1.59808i) q^{35} +(4.50000 + 2.59808i) q^{36} +(8.83013 + 2.36603i) q^{37} +(-0.267949 + 0.267949i) q^{38} +(0.169873 - 0.633975i) q^{39} +(1.36603 - 4.09808i) q^{40} +(-2.59808 - 1.50000i) q^{41} +(2.13397 + 1.03590i) q^{42} +(-0.232051 + 0.866025i) q^{43} +(-3.00000 + 1.73205i) q^{44} +(3.69615 - 5.59808i) q^{45} +(-1.63397 + 2.83013i) q^{46} +(4.96410 - 1.33013i) q^{47} +(3.69615 - 2.13397i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-2.40192 - 0.964102i) q^{50} +(-3.46410 - 0.928203i) q^{51} +(-0.464102 - 0.464102i) q^{52} +(-1.00000 + 0.267949i) q^{53} +(-2.59808 + 0.696152i) q^{54} +(2.00000 + 4.00000i) q^{55} +(4.23205 - 2.86603i) q^{56} +1.26795i q^{57} +(-3.63397 - 3.63397i) q^{58} +(-4.56218 - 7.90192i) q^{59} +(-3.00000 - 6.00000i) q^{60} +(9.46410 + 5.46410i) q^{61} +(-2.00000 - 2.00000i) q^{62} +(7.50000 - 2.59808i) q^{63} -2.26795i q^{64} +(-0.633975 + 0.562178i) q^{65} +(0.464102 - 1.73205i) q^{66} +(-3.36603 - 0.901924i) q^{67} +(-2.53590 + 2.53590i) q^{68} +(2.83013 + 10.5622i) q^{69} +(-1.56218 - 2.63397i) q^{70} +1.26795 q^{71} +(-1.50000 + 5.59808i) q^{72} +(-3.46410 - 12.9282i) q^{73} +4.73205i q^{74} +(-7.96410 + 3.40192i) q^{75} +(1.09808 + 0.633975i) q^{76} +(-1.00000 + 5.19615i) q^{77} +0.339746 q^{78} +(-9.92820 - 5.73205i) q^{79} +(-5.50000 - 0.330127i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(0.401924 - 1.50000i) q^{82} +(-9.96410 - 2.66987i) q^{83} +(1.50000 - 7.79423i) q^{84} +(3.07180 + 3.46410i) q^{85} -0.464102 q^{86} -17.1962 q^{87} +(-2.73205 - 2.73205i) q^{88} +(-0.535898 - 0.928203i) q^{89} +(3.29423 + 1.09808i) q^{90} +(-1.00000 + 0.0717968i) q^{91} +(10.5622 + 2.83013i) q^{92} -9.46410 q^{93} +(1.33013 + 2.30385i) q^{94} +(0.901924 - 1.36603i) q^{95} +(6.29423 + 6.29423i) q^{96} +(2.43782 - 9.09808i) q^{97} +(0.428203 - 3.59808i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} + 2 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 + 2 * q^8 + 6 * q^9	\( 4 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} + 2 q^{8} + 6 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{13} + 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} + 6 q^{18} - 2 q^{19} - 6 q^{20} + 12 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{25} + 18 q^{26} - 6 q^{28} - 24 q^{29} - 6 q^{30} - 12 q^{31} + 6 q^{32} - 12 q^{33} - 16 q^{34} - 2 q^{35} + 18 q^{36} + 18 q^{37} - 8 q^{38} + 18 q^{39} + 2 q^{40} + 12 q^{42} + 6 q^{43} - 12 q^{44} - 6 q^{45} - 10 q^{46} + 6 q^{47} - 6 q^{48} - 26 q^{49} - 20 q^{50} + 12 q^{52} - 4 q^{53} + 8 q^{55} + 10 q^{56} - 18 q^{58} + 6 q^{59} - 12 q^{60} + 24 q^{61} - 8 q^{62} + 30 q^{63} - 6 q^{65} - 12 q^{66} - 10 q^{67} - 24 q^{68} - 6 q^{69} + 18 q^{70} + 12 q^{71} - 6 q^{72} - 18 q^{75} - 6 q^{76} - 4 q^{77} + 36 q^{78} - 12 q^{79} - 22 q^{80} - 18 q^{81} + 12 q^{82} - 26 q^{83} + 6 q^{84} + 40 q^{85} + 12 q^{86} - 48 q^{87} - 4 q^{88} - 16 q^{89} - 18 q^{90} - 4 q^{91} + 18 q^{92} - 24 q^{93} - 12 q^{94} + 14 q^{95} - 6 q^{96} + 34 q^{97} - 26 q^{98} - 12 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 + 2 * q^8 + 6 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^13 + 2 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 + 6 * q^18 - 2 * q^19 - 6 * q^20 + 12 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^25 + 18 * q^26 - 6 * q^28 - 24 * q^29 - 6 * q^30 - 12 * q^31 + 6 * q^32 - 12 * q^33 - 16 * q^34 - 2 * q^35 + 18 * q^36 + 18 * q^37 - 8 * q^38 + 18 * q^39 + 2 * q^40 + 12 * q^42 + 6 * q^43 - 12 * q^44 - 6 * q^45 - 10 * q^46 + 6 * q^47 - 6 * q^48 - 26 * q^49 - 20 * q^50 + 12 * q^52 - 4 * q^53 + 8 * q^55 + 10 * q^56 - 18 * q^58 + 6 * q^59 - 12 * q^60 + 24 * q^61 - 8 * q^62 + 30 * q^63 - 6 * q^65 - 12 * q^66 - 10 * q^67 - 24 * q^68 - 6 * q^69 + 18 * q^70 + 12 * q^71 - 6 * q^72 - 18 * q^75 - 6 * q^76 - 4 * q^77 + 36 * q^78 - 12 * q^79 - 22 * q^80 - 18 * q^81 + 12 * q^82 - 26 * q^83 + 6 * q^84 + 40 * q^85 + 12 * q^86 - 48 * q^87 - 4 * q^88 - 16 * q^89 - 18 * q^90 - 4 * q^91 + 18 * q^92 - 24 * q^93 - 12 * q^94 + 14 * q^95 - 6 * q^96 + 34 * q^97 - 26 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.133975	+	0.500000i	0.0947343	+	0.353553i	0.996979	−	0.0776710i	$-0.0247484\pi$
$2$	0.133975	+	0.500000i	0.0947343	+	0.353553i	−0.902245	+	0.431224i	$0.858082\pi$
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	1.50000	−	0.866025i	0.750000	−	0.433013i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$	−0.232051	+	0.866025i	−0.0947343	+	0.353553i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$	1.36603	+	1.36603i	0.482963	+	0.482963i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	0.866025	−	0.767949i	0.273861	−	0.242847i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$	3.00000			0.866025
$13$	−0.0980762	−	0.366025i	−0.0272014	−	0.101517i	0.950991	−	0.309220i	$-0.100068\pi$
$13$	−0.0980762	−	0.366025i	−0.0272014	−	0.101517i	−0.978192	+	0.207703i	$0.933401\pi$
$14$	1.36603	−	0.0980762i	0.365086	−	0.0262120i
$15$	0.232051	−	3.86603i	0.0599153	−	0.998203i
$16$	1.23205	−	2.13397i	0.308013	−	0.533494i
$17$	−2.00000	+	0.535898i	−0.485071	+	0.129974i	−0.493063	−	0.869994i	$-0.664123\pi$
$17$	−2.00000	+	0.535898i	−0.485071	+	0.129974i	0.00799174	+	0.999968i	$0.497456\pi$
$18$	−1.09808	+	1.09808i	−0.258819	+	0.258819i
$19$	0.366025	+	0.633975i	0.0839720	+	0.145444i	0.904953	−	0.425512i	$-0.139906\pi$
$19$	0.366025	+	0.633975i	0.0839720	+	0.145444i	−0.820981	+	0.570956i	$0.806573\pi$
$20$	−3.23205	−	2.13397i	−0.722709	−	0.477171i
$21$	3.00000	−	3.46410i	0.654654	−	0.755929i
$22$	−0.267949	−	1.00000i	−0.0571270	−	0.213201i
$23$	4.46410	+	4.46410i	0.930830	+	0.930830i	0.997758	−	0.0669283i	$-0.0213199\pi$
$23$	4.46410	+	4.46410i	0.930830	+	0.930830i	−0.0669283	+	0.997758i	$0.521320\pi$
$24$	0.866025	+	3.23205i	0.176777	+	0.659740i
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	0.169873	−	0.0980762i	0.0333148	−	0.0192343i
$27$			5.19615i			1.00000i
$28$	−1.50000	−	4.33013i	−0.283473	−	0.818317i
$29$	−8.59808	+	4.96410i	−1.59662	+	0.921811i	−0.604491	+	0.796612i	$0.706623\pi$
$29$	−8.59808	+	4.96410i	−1.59662	+	0.921811i	−0.992132	+	0.125199i	$0.960043\pi$
$30$	1.96410	−	0.401924i	0.358594	−	0.0733809i
$31$	−4.73205	+	2.73205i	−0.849901	+	0.490691i	−0.860618	−	0.509252i	$-0.829922\pi$
$31$	−4.73205	+	2.73205i	−0.849901	+	0.490691i	0.0107162	+	0.999943i	$0.496589\pi$
$32$	4.96410	+	1.33013i	0.877537	+	0.235135i
$33$	−3.00000	−	1.73205i	−0.522233	−	0.301511i
$34$	−0.535898	−	0.928203i	−0.0919058	−	0.159186i
$35$	−5.69615	+	1.59808i	−0.962825	+	0.270124i
$36$	4.50000	+	2.59808i	0.750000	+	0.433013i
$37$	8.83013	+	2.36603i	1.45166	+	0.388972i	0.896602	−	0.442837i	$-0.146028\pi$
$37$	8.83013	+	2.36603i	1.45166	+	0.388972i	0.555062	+	0.831809i	$0.312695\pi$
$38$	−0.267949	+	0.267949i	−0.0434671	+	0.0434671i
$39$	0.169873	−	0.633975i	0.0272014	−	0.101517i
$40$	1.36603	−	4.09808i	0.215988	−	0.647963i
$41$	−2.59808	−	1.50000i	−0.405751	−	0.234261i	0.283211	−	0.959058i	$-0.408600\pi$
$41$	−2.59808	−	1.50000i	−0.405751	−	0.234261i	−0.688963	+	0.724797i	$0.741934\pi$
$42$	2.13397	+	1.03590i	0.329279	+	0.159843i
$43$	−0.232051	+	0.866025i	−0.0353874	+	0.132068i	−0.981360	−	0.192180i	$-0.938444\pi$
$43$	−0.232051	+	0.866025i	−0.0353874	+	0.132068i	0.945972	+	0.324247i	$0.105111\pi$
$44$	−3.00000	+	1.73205i	−0.452267	+	0.261116i
$45$	3.69615	−	5.59808i	0.550990	−	0.834512i
$46$	−1.63397	+	2.83013i	−0.240916	+	0.417279i
$47$	4.96410	−	1.33013i	0.724089	−	0.194019i	0.122093	−	0.992519i	$-0.461039\pi$
$47$	4.96410	−	1.33013i	0.724089	−	0.194019i	0.601995	+	0.798500i	$0.294373\pi$
$48$	3.69615	−	2.13397i	0.533494	−	0.308013i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	−2.40192	−	0.964102i	−0.339683	−	0.136345i
$51$	−3.46410	−	0.928203i	−0.485071	−	0.129974i
$52$	−0.464102	−	0.464102i	−0.0643593	−	0.0643593i
$53$	−1.00000	+	0.267949i	−0.137361	+	0.0368057i	−0.326844	−	0.945078i	$-0.605985\pi$
$53$	−1.00000	+	0.267949i	−0.137361	+	0.0368057i	0.189484	+	0.981884i	$0.439319\pi$
$54$	−2.59808	+	0.696152i	−0.353553	+	0.0947343i
$55$	2.00000	+	4.00000i	0.269680	+	0.539360i
$56$	4.23205	−	2.86603i	0.565532	−	0.382989i
$57$			1.26795i			0.167944i
$58$	−3.63397	−	3.63397i	−0.477164	−	0.477164i
$59$	−4.56218	−	7.90192i	−0.593945	−	1.02874i	−0.993695	−	0.112119i	$-0.964236\pi$
$59$	−4.56218	−	7.90192i	−0.593945	−	1.02874i	0.399750	−	0.916624i	$-0.369097\pi$
$60$	−3.00000	−	6.00000i	−0.387298	−	0.774597i
$61$	9.46410	+	5.46410i	1.21175	+	0.699607i	0.963141	−	0.268996i	$-0.0866920\pi$
$61$	9.46410	+	5.46410i	1.21175	+	0.699607i	0.248613	+	0.968603i	$0.420025\pi$
$62$	−2.00000	−	2.00000i	−0.254000	−	0.254000i
$63$	7.50000	−	2.59808i	0.944911	−	0.327327i
$64$		−	2.26795i		−	0.283494i
$65$	−0.633975	+	0.562178i	−0.0786349	+	0.0697296i
$66$	0.464102	−	1.73205i	0.0571270	−	0.213201i
$67$	−3.36603	−	0.901924i	−0.411225	−	0.110188i	0.0472746	−	0.998882i	$-0.484946\pi$
$67$	−3.36603	−	0.901924i	−0.411225	−	0.110188i	−0.458500	+	0.888694i	$0.651613\pi$
$68$	−2.53590	+	2.53590i	−0.307523	+	0.307523i
$69$	2.83013	+	10.5622i	0.340707	+	1.27154i
$70$	−1.56218	−	2.63397i	−0.186716	−	0.314820i
$71$	1.26795			0.150478			0.0752389	−	0.997166i	$-0.476028\pi$
$71$	1.26795			0.150478			0.0752389	+	0.997166i	$0.476028\pi$
$72$	−1.50000	+	5.59808i	−0.176777	+	0.659740i
$73$	−3.46410	−	12.9282i	−0.405442	−	1.51313i	−0.803238	−	0.595658i	$-0.796891\pi$
$73$	−3.46410	−	12.9282i	−0.405442	−	1.51313i	0.397796	−	0.917474i	$-0.369775\pi$
$74$			4.73205i			0.550090i
$75$	−7.96410	+	3.40192i	−0.919615	+	0.392820i
$76$	1.09808	+	0.633975i	0.125958	+	0.0727219i
$77$	−1.00000	+	5.19615i	−0.113961	+	0.592157i
$78$	0.339746			0.0384687
$79$	−9.92820	−	5.73205i	−1.11701	−	0.644906i	−0.176374	−	0.984323i	$-0.556437\pi$
$79$	−9.92820	−	5.73205i	−1.11701	−	0.644906i	−0.940636	+	0.339417i	$0.889770\pi$
$80$	−5.50000	−	0.330127i	−0.614919	−	0.0369093i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	0.401924	−	1.50000i	0.0443851	−	0.165647i
$83$	−9.96410	−	2.66987i	−1.09370	−	0.293057i	−0.333505	−	0.942748i	$-0.608231\pi$
$83$	−9.96410	−	2.66987i	−1.09370	−	0.293057i	−0.760198	+	0.649692i	$0.774898\pi$
$84$	1.50000	−	7.79423i	0.163663	−	0.850420i
$85$	3.07180	+	3.46410i	0.333183	+	0.375735i
$86$	−0.464102			−0.0500454
$87$	−17.1962			−1.84362
$88$	−2.73205	−	2.73205i	−0.291238	−	0.291238i
$89$	−0.535898	−	0.928203i	−0.0568051	−	0.0983893i	0.836224	−	0.548387i	$-0.184758\pi$
$89$	−0.535898	−	0.928203i	−0.0568051	−	0.0983893i	−0.893030	+	0.449998i	$0.851425\pi$
$90$	3.29423	+	1.09808i	0.347242	+	0.115747i
$91$	−1.00000	+	0.0717968i	−0.104828	+	0.00752635i
$92$	10.5622	+	2.83013i	1.10118	+	0.295061i
$93$	−9.46410			−0.981382
$94$	1.33013	+	2.30385i	0.137192	+	0.237624i
$95$	0.901924	−	1.36603i	0.0925354	−	0.140151i
$96$	6.29423	+	6.29423i	0.642402	+	0.642402i
$97$	2.43782	−	9.09808i	0.247523	−	0.923770i	−0.724575	−	0.689196i	$-0.757964\pi$
$97$	2.43782	−	9.09808i	0.247523	−	0.923770i	0.972098	−	0.234574i	$-0.0753694\pi$
$98$	0.428203	−	3.59808i	0.0432551	−	0.363461i
$99$	−3.00000	−	5.19615i	−0.301511	−	0.522233i
$100$	−1.03590	+	8.59808i	−0.103590	+	0.859808i
$101$		−	0.267949i		−	0.0266619i	−0.999911	−	0.0133310i	$-0.995756\pi$
$101$		−	0.267949i		−	0.0266619i	0.999911	−	0.0133310i	$-0.00424351\pi$
$102$		−	1.85641i		−	0.183812i
$103$	−4.63397	+	4.63397i	−0.456599	+	0.456599i	−0.897537	−	0.440938i	$-0.854646\pi$
$103$	−4.63397	+	4.63397i	−0.456599	+	0.456599i	0.440938	+	0.897537i	$0.354646\pi$
$104$	0.366025	−	0.633975i	0.0358917	−	0.0621663i
$105$	−9.92820	−	2.53590i	−0.968893	−	0.247478i
$106$	−0.267949	−	0.464102i	−0.0260255	−	0.0450775i
$107$	9.06218	+	2.42820i	0.876074	+	0.234743i	0.668712	−	0.743521i	$-0.266846\pi$
$107$	9.06218	+	2.42820i	0.876074	+	0.234743i	0.207361	+	0.978264i	$0.433512\pi$
$108$	4.50000	+	7.79423i	0.433013	+	0.750000i
$109$	8.42820	+	4.86603i	0.807275	+	0.466081i	0.846009	−	0.533169i	$-0.178999\pi$
$109$	8.42820	+	4.86603i	0.807275	+	0.466081i	−0.0387334	+	0.999250i	$0.512332\pi$
$110$	−1.73205	+	1.53590i	−0.165145	+	0.146442i
$111$	11.1962	+	11.1962i	1.06269	+	1.06269i
$112$	−4.92820	−	4.26795i	−0.465671	−	0.403283i
$113$	9.46410	−	2.53590i	0.890308	−	0.238557i	0.215459	−	0.976513i	$-0.430875\pi$
$113$	9.46410	−	2.53590i	0.890308	−	0.238557i	0.674849	+	0.737956i	$0.264209\pi$
$114$	−0.633975	+	0.169873i	−0.0593772	+	0.0159101i
$115$	4.46410	−	13.3923i	0.416280	−	1.24884i
$116$	−8.59808	+	14.8923i	−0.798311	+	1.38272i
$117$	0.803848	−	0.803848i	0.0743157	−	0.0743157i
$118$	3.33975	−	3.33975i	0.307449	−	0.307449i
$119$	0.392305	+	5.46410i	0.0359625	+	0.500893i
$120$	5.59808	−	4.96410i	0.511032	−	0.453158i
$121$	−7.00000			−0.636364
$122$	−1.46410	+	5.46410i	−0.132554	+	0.494697i
$123$	−2.59808	−	4.50000i	−0.234261	−	0.405751i
$124$	−4.73205	+	8.19615i	−0.424951	+	0.736036i
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$	2.30385	+	3.40192i	0.205243	+	0.303067i
$127$	11.3660	−	11.3660i	1.00857	−	1.00857i	0.00860872	−	0.999963i	$-0.497260\pi$
$127$	11.3660	−	11.3660i	1.00857	−	1.00857i	0.999963	−	0.00860872i	$-0.00274027\pi$
$128$	11.0622	−	2.96410i	0.977768	−	0.261992i
$129$	−1.09808	+	1.09808i	−0.0966802	+	0.0966802i
$130$	−0.366025	−	0.241670i	−0.0321026	−	0.0211958i
$131$		−	18.9282i		−	1.65376i	−0.562375	−	0.826882i	$-0.690112\pi$
$131$		−	18.9282i		−	1.65376i	0.562375	−	0.826882i	$-0.309888\pi$
$132$	−6.00000			−0.522233
$133$	1.83013	−	0.633975i	0.158692	−	0.0549726i
$134$		−	1.80385i		−	0.155829i
$135$	10.3923	−	5.19615i	0.894427	−	0.447214i
$136$	−3.46410	−	2.00000i	−0.297044	−	0.171499i
$137$	1.00000	−	1.00000i	0.0854358	−	0.0854358i	−0.663097	−	0.748533i	$-0.730758\pi$
$137$	1.00000	−	1.00000i	0.0854358	−	0.0854358i	0.748533	+	0.663097i	$0.230758\pi$
$138$	−4.90192	+	2.83013i	−0.417279	+	0.240916i
$139$	−9.29423	+	16.0981i	−0.788326	+	1.36542i	0.138666	+	0.990339i	$0.455719\pi$
$139$	−9.29423	+	16.0981i	−0.788326	+	1.36542i	−0.926992	+	0.375082i	$0.877615\pi$
$140$	−7.16025	+	7.33013i	−0.605152	+	0.619509i
$141$	8.59808	+	2.30385i	0.724089	+	0.194019i
$142$	0.169873	+	0.633975i	0.0142554	+	0.0532020i
$143$	0.196152	+	0.732051i	0.0164031	+	0.0612172i
$144$	7.39230			0.616025
$145$	18.5263	+	12.2321i	1.53852	+	1.01582i
$146$	6.00000	−	3.46410i	0.496564	−	0.286691i
$147$	−7.50000	−	9.52628i	−0.618590	−	0.785714i
$148$	15.2942	−	4.09808i	1.25718	−	0.336860i
$149$			8.53590i			0.699288i	0.936883	+	0.349644i	$0.113697\pi$
$149$			8.53590i			0.699288i	−0.936883	+	0.349644i	$0.886303\pi$
$150$	−2.76795	−	3.52628i	−0.226002	−	0.287920i
$151$	−0.339746			−0.0276481			−0.0138241	−	0.999904i	$-0.504400\pi$
$151$	−0.339746			−0.0276481			−0.0138241	+	0.999904i	$0.504400\pi$
$152$	−0.366025	+	1.36603i	−0.0296886	+	0.110799i
$153$	−4.39230	−	4.39230i	−0.355097	−	0.355097i
$154$	−2.73205	+	0.196152i	−0.220155	+	0.0158064i
$155$	10.1962	+	6.73205i	0.818975	+	0.540731i
$156$	−0.294229	−	1.09808i	−0.0235571	−	0.0879165i
$157$	−1.16987	+	4.36603i	−0.0933660	+	0.348447i	−0.996767	−	0.0803508i	$-0.974396\pi$
$157$	−1.16987	+	4.36603i	−0.0933660	+	0.348447i	0.903401	+	0.428798i	$0.141063\pi$
$158$	1.53590	−	5.73205i	0.122190	−	0.456017i
$159$	−1.73205	−	0.464102i	−0.137361	−	0.0368057i
$160$	−2.30385	−	11.2583i	−0.182135	−	0.890049i
$161$	13.8301	−	9.36603i	1.08997	−	0.738146i
$162$	−4.50000	−	1.20577i	−0.353553	−	0.0947343i
$163$	−6.29423	+	23.4904i	−0.493002	+	1.83991i	0.0479421	+	0.998850i	$0.484734\pi$
$163$	−6.29423	+	23.4904i	−0.493002	+	1.83991i	−0.540944	+	0.841059i	$0.681933\pi$
$164$	−5.19615			−0.405751
$165$	−0.464102	+	7.73205i	−0.0361303	+	0.601939i
$166$		−	5.33975i		−	0.414445i
$167$	−6.09808	+	1.63397i	−0.471883	+	0.126441i	−0.486921	−	0.873446i	$-0.661880\pi$
$167$	−6.09808	+	1.63397i	−0.471883	+	0.126441i	0.0150374	+	0.999887i	$0.495213\pi$
$168$	8.83013	−	0.633975i	0.681259	−	0.0489122i
$169$	11.1340	−	6.42820i	0.856460	−	0.494477i
$170$	−1.32051	+	2.00000i	−0.101278	+	0.153393i
$171$	−1.09808	+	1.90192i	−0.0839720	+	0.145444i
$172$	0.401924	+	1.50000i	0.0306464	+	0.114374i
$173$	−5.85641	−	21.8564i	−0.445254	−	1.66171i	−0.715264	−	0.698854i	$-0.753694\pi$
$173$	−5.85641	−	21.8564i	−0.445254	−	1.66171i	0.270010	−	0.962858i	$-0.412973\pi$
$174$	−2.30385	−	8.59808i	−0.174654	−	0.651818i
$175$	8.89230	+	9.79423i	0.672195	+	0.740374i
$176$	−2.46410	+	4.26795i	−0.185739	+	0.321709i
$177$		−	15.8038i		−	1.18789i
$178$	0.392305	−	0.392305i	0.0294045	−	0.0294045i
$179$	−4.09808	−	2.36603i	−0.306305	−	0.176845i	0.338967	−	0.940798i	$-0.389922\pi$
$179$	−4.09808	−	2.36603i	−0.306305	−	0.176845i	−0.645272	+	0.763953i	$0.723256\pi$
$180$	0.696152	−	11.5981i	0.0518881	−	0.864470i
$181$		−	4.12436i		−	0.306561i	−0.988183	−	0.153280i	$-0.951016\pi$
$181$		−	4.12436i		−	0.306561i	0.988183	−	0.153280i	$-0.0489838\pi$
$182$	−0.169873	−	0.490381i	−0.0125918	−	0.0363495i
$183$	9.46410	+	16.3923i	0.699607	+	1.21175i
$184$			12.1962i			0.899112i
$185$	−4.09808	−	20.0263i	−0.301297	−	1.47236i
$186$	−1.26795	−	4.73205i	−0.0929705	−	0.346971i
$187$	4.00000	−	1.07180i	0.292509	−	0.0783775i
$188$	6.29423	−	6.29423i	0.459054	−	0.459054i
$189$	13.5000	+	2.59808i	0.981981	+	0.188982i
$190$	0.803848	+	0.267949i	0.0583172	+	0.0194391i
$191$	10.0981	−	17.4904i	0.730671	−	1.26556i	−0.225926	−	0.974145i	$-0.572541\pi$
$191$	10.0981	−	17.4904i	0.730671	−	1.26556i	0.956597	−	0.291415i	$-0.0941260\pi$
$192$	1.96410	−	3.40192i	0.141747	−	0.245513i
$193$	−3.73205	+	13.9282i	−0.268639	+	1.00257i	0.691346	+	0.722523i	$0.257018\pi$
$193$	−3.73205	+	13.9282i	−0.268639	+	1.00257i	−0.959985	+	0.280051i	$0.909649\pi$
$194$	4.87564			0.350051
$195$	−1.43782	+	0.294229i	−0.102965	+	0.0210702i
$196$	−12.0000	+	1.73205i	−0.857143	+	0.123718i
$197$	4.00000	−	4.00000i	0.284988	−	0.284988i	−0.550106	−	0.835095i	$-0.685413\pi$
$197$	4.00000	−	4.00000i	0.284988	−	0.284988i	0.835095	+	0.550106i	$0.185413\pi$
$198$	2.19615	−	2.19615i	0.156074	−	0.156074i
$199$	−8.19615	+	14.1962i	−0.581010	+	1.00634i	0.414350	+	0.910118i	$0.364009\pi$
$199$	−8.19615	+	14.1962i	−0.581010	+	1.00634i	−0.995360	+	0.0962210i	$0.969324\pi$
$200$	−9.56218	+	1.36603i	−0.676148	+	0.0965926i
$201$	−4.26795	−	4.26795i	−0.301038	−	0.301038i
$202$	0.133975	−	0.0358984i	0.00942642	−	0.00252580i
$203$	8.59808	+	24.8205i	0.603467	+	1.74206i
$204$	−6.00000	+	1.60770i	−0.420084	+	0.112561i
$205$	−0.401924	+	6.69615i	−0.0280716	+	0.467680i
$206$	−2.93782	−	1.69615i	−0.204688	−	0.118177i
$207$	−4.90192	+	18.2942i	−0.340707	+	1.27154i
$208$	−0.901924	−	0.241670i	−0.0625372	−	0.0167568i
$209$	−0.732051	−	1.26795i	−0.0506370	−	0.0877059i
$210$	−0.0621778	−	5.30385i	−0.00429068	−	0.366000i
$211$	−13.4641	+	23.3205i	−0.926907	+	1.60545i	−0.138442	+	0.990371i	$0.544209\pi$
$211$	−13.4641	+	23.3205i	−0.926907	+	1.60545i	−0.788465	+	0.615079i	$0.789124\pi$
$212$	−1.26795	+	1.26795i	−0.0870831	+	0.0870831i
$213$	1.90192	+	1.09808i	0.130318	+	0.0752389i
$214$			4.85641i			0.331977i
$215$	1.96410	−	0.401924i	0.133951	−	0.0274110i
$216$	−7.09808	+	7.09808i	−0.482963	+	0.482963i
$217$	4.73205	+	13.6603i	0.321233	+	0.927318i
$218$	−1.30385	+	4.86603i	−0.0883077	+	0.329569i
$219$	6.00000	−	22.3923i	0.405442	−	1.51313i
$220$	6.46410	+	4.26795i	0.435810	+	0.287745i
$221$	0.392305	+	0.679492i	0.0263893	+	0.0457076i
$222$	−4.09808	+	7.09808i	−0.275045	+	0.476392i
$223$	−4.96410	−	1.33013i	−0.332421	−	0.0890719i	0.0887481	−	0.996054i	$-0.471713\pi$
$223$	−4.96410	−	1.33013i	−0.332421	−	0.0890719i	−0.421169	+	0.906982i	$0.638380\pi$
$224$	5.93782	−	12.2321i	0.396737	−	0.817288i
$225$	−14.8923	−	1.79423i	−0.992820	−	0.119615i
$226$	2.53590	+	4.39230i	0.168685	+	0.292172i
$227$	17.5885	+	17.5885i	1.16739	+	1.16739i	0.982820	+	0.184567i	$0.0590883\pi$
$227$	17.5885	+	17.5885i	1.16739	+	1.16739i	0.184567	+	0.982820i	$0.440912\pi$
$228$	1.09808	+	1.90192i	0.0727219	+	0.125958i
$229$	22.6603			1.49743			0.748716	−	0.662891i	$-0.230671\pi$
$229$	22.6603			1.49743			0.748716	+	0.662891i	$0.230671\pi$
$230$	7.29423	+	0.437822i	0.480967	+	0.0288691i
$231$	−6.00000	+	6.92820i	−0.394771	+	0.455842i
$232$	−18.5263	−	4.96410i	−1.21631	−	0.325909i
$233$	5.53590	−	20.6603i	0.362669	−	1.35350i	−0.507885	−	0.861425i	$-0.669573\pi$
$233$	5.53590	−	20.6603i	0.362669	−	1.35350i	0.870554	−	0.492073i	$-0.163761\pi$
$234$	0.509619	+	0.294229i	0.0333148	+	0.0192343i
$235$	−7.62436	−	8.59808i	−0.497358	−	0.560877i
$236$	−13.6865	−	7.90192i	−0.890917	−	0.514371i
$237$	−9.92820	−	17.1962i	−0.644906	−	1.11701i
$238$	−2.67949	+	0.928203i	−0.173686	+	0.0601665i
$239$	1.73205	+	1.00000i	0.112037	+	0.0646846i	0.554971	−	0.831869i	$-0.312729\pi$
$239$	1.73205	+	1.00000i	0.112037	+	0.0646846i	−0.442934	+	0.896554i	$0.646063\pi$
$240$	−7.96410	−	5.25833i	−0.514081	−	0.339424i
$241$		−	15.5359i		−	1.00076i	−0.865807	−	0.500378i	$-0.833195\pi$
$241$		−	15.5359i		−	1.00076i	0.865807	−	0.500378i	$-0.166805\pi$
$242$	−0.937822	−	3.50000i	−0.0602855	−	0.224989i
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	18.9282			1.21175
$245$	1.30385	+	15.5981i	0.0832998	+	0.996525i
$246$	1.90192	−	1.90192i	0.121262	−	0.121262i
$247$	0.196152	−	0.196152i	0.0124809	−	0.0124809i
$248$	−10.1962	−	2.73205i	−0.647456	−	0.173485i
$249$	−12.6340	−	12.6340i	−0.800646	−	0.800646i
$250$	0.473721	+	5.76795i	0.0299607	+	0.364797i
$251$			13.6603i			0.862228i	0.902298	+	0.431114i	$0.141879\pi$
$251$			13.6603i			0.862228i	−0.902298	+	0.431114i	$0.858121\pi$
$252$	9.00000	−	10.3923i	0.566947	−	0.654654i
$253$	−8.92820	−	8.92820i	−0.561311	−	0.561311i
$254$	7.20577	+	4.16025i	0.452130	+	0.261038i
$255$	1.60770	+	7.85641i	0.100678	+	0.491987i
$256$	0.696152	+	1.20577i	0.0435095	+	0.0753607i
$257$	10.1962	+	10.1962i	0.636019	+	0.636019i	0.949571	−	0.313552i	$-0.101519\pi$
$257$	10.1962	+	10.1962i	0.636019	+	0.636019i	−0.313552	+	0.949571i	$0.601519\pi$
$258$	−0.696152	−	0.401924i	−0.0433406	−	0.0250227i
$259$	10.5622	−	21.7583i	0.656302	−	1.35200i
$260$	−0.464102	+	1.39230i	−0.0287824	+	0.0863471i
$261$	−25.7942	−	14.8923i	−1.59662	−	0.921811i
$262$	9.46410	−	2.53590i	0.584694	−	0.156668i
$263$	9.09808	+	9.09808i	0.561011	+	0.561011i	0.929595	−	0.368583i	$-0.120157\pi$
$263$	9.09808	+	9.09808i	0.561011	+	0.561011i	−0.368583	+	0.929595i	$0.620157\pi$
$264$	−1.73205	−	6.46410i	−0.106600	−	0.397838i
$265$	1.53590	+	1.73205i	0.0943495	+	0.106399i
$266$	0.562178	+	0.830127i	0.0344693	+	0.0508984i
$267$		−	1.85641i		−	0.113610i
$268$	−5.83013	+	1.56218i	−0.356132	+	0.0954252i
$269$	3.80385	−	6.58846i	0.231925	−	0.401705i	−0.726450	−	0.687220i	$-0.758831\pi$
$269$	3.80385	−	6.58846i	0.231925	−	0.401705i	0.958374	+	0.285514i	$0.0921644\pi$
$270$	3.99038	+	4.50000i	0.242847	+	0.273861i
$271$	1.22243	−	0.705771i	0.0742574	−	0.0428726i	−0.462412	−	0.886665i	$-0.653016\pi$
$271$	1.22243	−	0.705771i	0.0742574	−	0.0428726i	0.536669	+	0.843793i	$0.319682\pi$
$272$	−1.32051	+	4.92820i	−0.0800676	+	0.298816i
$273$	−1.56218	−	0.758330i	−0.0945473	−	0.0458962i
$274$	0.633975	+	0.366025i	0.0382998	+	0.0221124i
$275$	6.00000	−	8.00000i	0.361814	−	0.482418i
$276$	13.3923	+	13.3923i	0.806122	+	0.806122i
$277$	2.19615	−	2.19615i	0.131954	−	0.131954i	−0.638045	−	0.769999i	$-0.720257\pi$
$277$	2.19615	−	2.19615i	0.131954	−	0.131954i	0.769999	+	0.638045i	$0.220257\pi$
$278$	−9.29423	−	2.49038i	−0.557431	−	0.149363i
$279$	−14.1962	−	8.19615i	−0.849901	−	0.490691i
$280$	−9.96410	−	5.59808i	−0.595469	−	0.334549i
$281$	−12.8660	−	22.2846i	−0.767523	−	1.32939i	−0.938902	−	0.344183i	$-0.888156\pi$
$281$	−12.8660	−	22.2846i	−0.767523	−	1.32939i	0.171380	−	0.985205i	$-0.445178\pi$
$282$			4.60770i			0.274384i
$283$	−15.5263	−	4.16025i	−0.922942	−	0.247301i	−0.234099	−	0.972213i	$-0.575214\pi$
$283$	−15.5263	−	4.16025i	−0.922942	−	0.247301i	−0.688842	+	0.724911i	$0.741881\pi$
$284$	1.90192	−	1.09808i	0.112858	−	0.0651588i
$285$	2.53590	−	1.26795i	0.150214	−	0.0751068i
$286$	−0.339746	+	0.196152i	−0.0200896	+	0.0115987i
$287$	−5.19615	+	6.00000i	−0.306719	+	0.354169i
$288$	3.99038	+	14.8923i	0.235135	+	0.877537i
$289$	−11.0096	+	6.35641i	−0.647625	+	0.373906i
$290$	−3.63397	+	10.9019i	−0.213394	+	0.640183i
$291$	11.5359	−	11.5359i	0.676246	−	0.676246i
$292$	−16.3923	−	16.3923i	−0.959287	−	0.959287i
$293$	−3.26795	−	12.1962i	−0.190916	−	0.712507i	−0.993286	−	0.115681i	$-0.963095\pi$
$293$	−3.26795	−	12.1962i	−0.190916	−	0.712507i	0.802371	−	0.596826i	$-0.203572\pi$
$294$	3.75833	−	5.02628i	0.219190	−	0.293139i
$295$	−11.2417	+	17.0263i	−0.654515	+	0.991308i
$296$	8.83013	+	15.2942i	0.513241	+	0.888959i
$297$		−	10.3923i		−	0.603023i
$298$	−4.26795	+	1.14359i	−0.247236	+	0.0662466i
$299$	1.19615	−	2.07180i	0.0691753	−	0.119815i
$300$	−9.00000	+	12.0000i	−0.519615	+	0.692820i
$301$	2.13397	+	1.03590i	0.123000	+	0.0597082i
$302$	−0.0455173	−	0.169873i	−0.00261923	−	0.00977509i
$303$	0.232051	−	0.401924i	0.0133310	−	0.0230899i
$304$	1.80385			0.103458
$305$	1.46410	−	24.3923i	0.0838342	−	1.39670i
$306$	1.60770	−	2.78461i	0.0919058	−	0.159186i
$307$	−3.63397	−	3.63397i	−0.207402	−	0.207402i	0.595760	−	0.803162i	$-0.296851\pi$
$307$	−3.63397	−	3.63397i	−0.207402	−	0.207402i	−0.803162	+	0.595760i	$0.796851\pi$
$308$	3.00000	+	8.66025i	0.170941	+	0.493464i
$309$	−10.9641	+	2.93782i	−0.623726	+	0.167127i
$310$	−2.00000	+	6.00000i	−0.113592	+	0.340777i
$311$	−14.8301	+	8.56218i	−0.840939	+	0.485517i	−0.857583	−	0.514345i	$-0.828035\pi$
$311$	−14.8301	+	8.56218i	−0.840939	+	0.485517i	0.0166441	+	0.999861i	$0.494702\pi$
$312$	1.09808	−	0.633975i	0.0621663	−	0.0358917i
$313$	8.19615	+	30.5885i	0.463274	+	1.72896i	0.662549	+	0.749018i	$0.269475\pi$
$313$	8.19615	+	30.5885i	0.463274	+	1.72896i	−0.199275	+	0.979944i	$0.563859\pi$
$314$	−2.33975			−0.132040
$315$	−12.6962	−	12.4019i	−0.715347	−	0.698769i
$316$	−19.8564			−1.11701
$317$	0.562178	+	2.09808i	0.0315751	+	0.117840i	0.979915	−	0.199417i	$-0.0639049\pi$
$317$	0.562178	+	2.09808i	0.0315751	+	0.117840i	−0.948340	+	0.317257i	$0.897238\pi$
$318$		−	0.928203i		−	0.0520511i
$319$	17.1962	−	9.92820i	0.962800	−	0.555873i
$320$	−4.53590	+	2.26795i	−0.253564	+	0.126782i
$321$	11.4904	+	11.4904i	0.641331	+	0.641331i
$322$	6.53590	+	5.66025i	0.364231	+	0.315434i
$323$	−1.07180	−	1.07180i	−0.0596364	−	0.0596364i
$324$			15.5885i			0.866025i
$325$	1.75833	+	0.705771i	0.0975346	+	0.0391492i
$326$	−12.5885			−0.697210
$327$	8.42820	+	14.5981i	0.466081	+	0.807275i
$328$	−1.50000	−	5.59808i	−0.0828236	−	0.309102i
$329$	−0.973721	−	13.5622i	−0.0536830	−	0.747707i
$330$	−3.92820	+	0.803848i	−0.216240	+	0.0442504i
$331$	3.00000	−	5.19615i	0.164895	−	0.285606i	−0.771723	−	0.635959i	$-0.780605\pi$
$331$	3.00000	−	5.19615i	0.164895	−	0.285606i	0.936618	+	0.350352i	$0.113938\pi$
$332$	−17.2583	+	4.62436i	−0.947174	+	0.253794i
$333$	7.09808	+	26.4904i	0.388972	+	1.45166i
$334$	−1.63397	−	2.83013i	−0.0894071	−	0.154858i
$335$	1.56218	+	7.63397i	0.0853509	+	0.417089i
$336$	−3.69615	−	10.6699i	−0.201642	−	0.582089i
$337$	−5.63397	−	21.0263i	−0.306902	−	1.14537i	−0.931296	−	0.364264i	$-0.881320\pi$
$337$	−5.63397	−	21.0263i	−0.306902	−	1.14537i	0.624393	−	0.781110i	$-0.285346\pi$
$338$	4.70577	+	4.70577i	0.255960	+	0.255960i
$339$	16.3923	+	4.39230i	0.890308	+	0.238557i
$340$	7.60770	+	2.53590i	0.412585	+	0.137528i
$341$	9.46410	−	5.46410i	0.512510	−	0.295898i
$342$	−1.09808	−	0.294229i	−0.0593772	−	0.0159101i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−1.50000	+	0.866025i	−0.0808746	+	0.0466930i
$345$	18.2942	−	16.2224i	0.984928	−	0.873386i
$346$	10.1436	−	5.85641i	0.545323	−	0.314842i
$347$	−11.4282	−	3.06218i	−0.613498	−	0.164386i	−0.0613278	−	0.998118i	$-0.519534\pi$
$347$	−11.4282	−	3.06218i	−0.613498	−	0.164386i	−0.552170	+	0.833731i	$0.686200\pi$
$348$	−25.7942	+	14.8923i	−1.38272	+	0.798311i
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$	−3.70577	+	5.75833i	−0.198082	+	0.307796i
$351$	1.90192	−	0.509619i	0.101517	−	0.0272014i
$352$	−9.92820	−	2.66025i	−0.529175	−	0.141792i
$353$	−5.53590	+	5.53590i	−0.294646	+	0.294646i	−0.838912	−	0.544266i	$-0.816808\pi$
$353$	−5.53590	+	5.53590i	−0.294646	+	0.294646i	0.544266	+	0.838912i	$0.316808\pi$
$354$	7.90192	−	2.11731i	0.419983	−	0.112534i
$355$	−1.26795	−	2.53590i	−0.0672958	−	0.134592i
$356$	−1.60770	−	0.928203i	−0.0852077	−	0.0491947i
$357$	−4.14359	+	8.53590i	−0.219302	+	0.451768i
$358$	0.633975	−	2.36603i	0.0335066	−	0.125048i
$359$	2.53590	−	1.46410i	0.133840	−	0.0772723i	−0.431585	−	0.902072i	$-0.642046\pi$
$359$	2.53590	−	1.46410i	0.133840	−	0.0772723i	0.565425	+	0.824800i	$0.308712\pi$
$360$	12.6962	−	2.59808i	0.669146	−	0.136931i
$361$	9.23205	−	15.9904i	0.485897	−	0.841599i
$362$	2.06218	−	0.552559i	0.108386	−	0.0290419i
$363$	−10.5000	−	6.06218i	−0.551107	−	0.318182i
$364$	−1.43782	+	0.973721i	−0.0753624	+	0.0510368i
$365$	−22.3923	+	19.8564i	−1.17207	+	1.03933i
$366$	−6.92820	+	6.92820i	−0.362143	+	0.362143i
$367$	9.09808	+	9.09808i	0.474916	+	0.474916i	0.903501	−	0.428586i	$-0.140988\pi$
$367$	9.09808	+	9.09808i	0.474916	+	0.474916i	−0.428586	+	0.903501i	$0.640988\pi$
$368$	15.0263	−	4.02628i	0.783299	−	0.209884i
$369$		−	9.00000i		−	0.468521i
$370$	9.46410	−	4.73205i	0.492015	−	0.246008i
$371$	0.196152	+	2.73205i	0.0101837	+	0.141841i
$372$	−14.1962	+	8.19615i	−0.736036	+	0.424951i
$373$	−12.4641	−	12.4641i	−0.645367	−	0.645367i	0.306503	−	0.951870i	$-0.400841\pi$
$373$	−12.4641	−	12.4641i	−0.645367	−	0.645367i	−0.951870	+	0.306503i	$0.900841\pi$
$374$	1.07180	+	1.85641i	0.0554213	+	0.0959925i
$375$	14.7679	+	12.5263i	0.762614	+	0.646854i
$376$	8.59808	+	4.96410i	0.443412	+	0.256004i
$377$	2.66025	+	2.66025i	0.137010	+	0.137010i
$378$	0.509619	+	7.09808i	0.0262120	+	0.365086i
$379$		−	27.5167i		−	1.41344i	−0.707495	−	0.706718i	$-0.750175\pi$
$379$		−	27.5167i		−	1.41344i	0.707495	−	0.706718i	$-0.249825\pi$
$380$	0.169873	−	2.83013i	0.00871430	−	0.145182i
$381$	26.8923	−	7.20577i	1.37773	−	0.369163i
$382$	10.0981	+	2.70577i	0.516663	+	0.138439i
$383$	14.7583	−	14.7583i	0.754115	−	0.754115i	−0.221129	−	0.975245i	$-0.570974\pi$
$383$	14.7583	−	14.7583i	0.754115	−	0.754115i	0.975245	+	0.221129i	$0.0709742\pi$
$384$	19.1603	+	5.13397i	0.977768	+	0.261992i
$385$	11.3923	−	3.19615i	0.580606	−	0.162891i
$386$	−7.46410			−0.379913
$387$	−2.59808	+	0.696152i	−0.132068	+	0.0353874i
$388$	−4.22243	−	15.7583i	−0.214362	−	0.800008i
$389$		−	29.0526i		−	1.47302i	−0.676425	−	0.736512i	$-0.736472\pi$
$389$		−	29.0526i		−	1.47302i	0.676425	−	0.736512i	$-0.263528\pi$
$390$	−0.339746	−	0.679492i	−0.0172037	−	0.0344074i
$391$	−11.3205	−	6.53590i	−0.572503	−	0.330535i
$392$	−5.33013	−	12.4282i	−0.269212	−	0.627719i
$393$	16.3923	−	28.3923i	0.826882	−	1.43220i
$394$	2.53590	+	1.46410i	0.127757	+	0.0737604i
$395$	−1.53590	+	25.5885i	−0.0772794	+	1.28750i
$396$	−9.00000	−	5.19615i	−0.452267	−	0.261116i
$397$	−5.32051	+	19.8564i	−0.267029	+	0.996564i	0.693968	+	0.720006i	$0.255861\pi$
$397$	−5.32051	+	19.8564i	−0.267029	+	0.996564i	−0.960997	+	0.276559i	$0.910806\pi$
$398$	−8.19615	−	2.19615i	−0.410836	−	0.110083i
$399$	3.29423	+	0.633975i	0.164918	+	0.0317384i
$400$	4.83975	+	11.3301i	0.241987	+	0.566506i
$401$	11.3923			0.568905			0.284452	−	0.958690i	$-0.408188\pi$
$401$	11.3923			0.568905			0.284452	+	0.958690i	$0.408188\pi$
$402$	1.56218	−	2.70577i	0.0779143	−	0.134952i
$403$	1.46410	+	1.46410i	0.0729321	+	0.0729321i
$404$	−0.232051	−	0.401924i	−0.0115450	−	0.0199965i
$405$	20.0885	+	1.20577i	0.998203	+	0.0599153i
$406$	−11.2583	+	7.62436i	−0.558742	+	0.378390i
$407$	−17.6603	−	4.73205i	−0.875386	−	0.234559i
$408$	−3.46410	−	6.00000i	−0.171499	−	0.297044i
$409$	−6.16025	−	10.6699i	−0.304605	−	0.527591i	0.672568	−	0.740035i	$-0.265191\pi$
$409$	−6.16025	−	10.6699i	−0.304605	−	0.527591i	−0.977173	+	0.212444i	$0.931858\pi$
$410$	−3.40192	+	0.696152i	−0.168009	+	0.0343805i
$411$	2.36603	−	0.633975i	0.116707	−	0.0312717i
$412$	−2.93782	+	10.9641i	−0.144736	+	0.540163i
$413$	−22.8109	+	7.90192i	−1.12245	+	0.388828i
$414$	−9.80385			−0.481833
$415$	4.62436	+	22.5981i	0.227001	+	1.10930i
$416$		−	1.94744i		−	0.0954812i
$417$	−27.8827	+	16.0981i	−1.36542	+	0.788326i
$418$	0.535898	−	0.535898i	0.0262116	−	0.0262116i
$419$	−9.83013	+	17.0263i	−0.480233	+	0.831788i	−0.999743	−	0.0226764i	$-0.992781\pi$
$419$	−9.83013	+	17.0263i	−0.480233	+	0.831788i	0.519510	+	0.854465i	$0.326115\pi$
$420$	−17.0885	+	4.79423i	−0.833831	+	0.233934i
$421$	−7.59808	−	13.1603i	−0.370308	−	0.641392i	0.619305	−	0.785150i	$-0.287414\pi$
$421$	−7.59808	−	13.1603i	−0.370308	−	0.641392i	−0.989613	+	0.143759i	$0.954081\pi$
$422$	−13.4641	−	3.60770i	−0.655422	−	0.175620i
$423$	10.9019	+	10.9019i	0.530070	+	0.530070i
$424$	−1.73205	−	1.00000i	−0.0841158	−	0.0485643i
$425$	3.85641	−	9.60770i	0.187063	−	0.466042i
$426$	−0.294229	+	1.09808i	−0.0142554	+	0.0532020i
$427$	18.9282	−	21.8564i	0.916000	−	1.05771i
$428$	15.6962	−	4.20577i	0.758702	−	0.203294i
$429$	−0.339746	+	1.26795i	−0.0164031	+	0.0612172i
$430$	0.464102	+	0.928203i	0.0223810	+	0.0447619i
$431$	5.29423	−	9.16987i	0.255014	−	0.441697i	−0.709885	−	0.704317i	$-0.751253\pi$
$431$	5.29423	−	9.16987i	0.255014	−	0.441697i	0.964899	+	0.262620i	$0.0845866\pi$
$432$	11.0885	+	6.40192i	0.533494	+	0.308013i
$433$	24.1244	−	24.1244i	1.15934	−	1.15934i	0.174725	−	0.984617i	$-0.444096\pi$
$433$	24.1244	−	24.1244i	1.15934	−	1.15934i	0.984617	−	0.174725i	$-0.0559037\pi$
$434$	−6.19615	+	4.19615i	−0.297425	+	0.201422i
$435$	17.1962	+	34.3923i	0.824492	+	1.64898i
$436$	16.8564			0.807275
$437$	−1.19615	+	4.46410i	−0.0572197	+	0.213547i
$438$	12.0000			0.573382
$439$	4.07180	−	7.05256i	0.194336	−	0.336600i	−0.752346	−	0.658768i	$-0.771078\pi$
$439$	4.07180	−	7.05256i	0.194336	−	0.336600i	0.946683	+	0.322167i	$0.104411\pi$
$440$	−2.73205	+	8.19615i	−0.130245	+	0.390736i
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$	−0.287187	+	0.287187i	−0.0136601	+	0.0136601i
$443$	−14.1603	+	3.79423i	−0.672774	+	0.180269i	−0.579004	−	0.815325i	$-0.696558\pi$
$443$	−14.1603	+	3.79423i	−0.672774	+	0.180269i	−0.0937699	+	0.995594i	$0.529892\pi$
$444$	26.4904	+	7.09808i	1.25718	+	0.336860i
$445$	−1.32051	+	2.00000i	−0.0625981	+	0.0948091i
$446$		−	2.66025i		−	0.125967i
$447$	−7.39230	+	12.8038i	−0.349644	+	0.605601i
$448$	−5.89230	−	1.13397i	−0.278385	−	0.0535753i
$449$			24.6603i			1.16379i	0.813264	+	0.581895i	$0.197688\pi$
$449$			24.6603i			1.16379i	−0.813264	+	0.581895i	$0.802312\pi$
$450$	−1.09808	−	7.68653i	−0.0517638	−	0.362347i
$451$	5.19615	+	3.00000i	0.244677	+	0.141264i
$452$	12.0000	−	12.0000i	0.564433	−	0.564433i
$453$	−0.509619	−	0.294229i	−0.0239440	−	0.0138241i
$454$	−6.43782	+	11.1506i	−0.302142	+	0.523325i
$455$	1.14359	+	1.92820i	0.0536125	+	0.0903956i
$456$	−1.73205	+	1.73205i	−0.0811107	+	0.0811107i
$457$	5.50962	+	20.5622i	0.257729	+	0.961858i	0.966552	+	0.256471i	$0.0825600\pi$
$457$	5.50962	+	20.5622i	0.257729	+	0.961858i	−0.708823	+	0.705387i	$0.750773\pi$
$458$	3.03590	+	11.3301i	0.141858	+	0.529422i
$459$	−2.78461	−	10.3923i	−0.129974	−	0.485071i
$460$	−4.90192	−	23.9545i	−0.228553	−	1.11688i
$461$	24.2321	−	13.9904i	1.12860	−	0.651597i	0.185017	−	0.982735i	$-0.440766\pi$
$461$	24.2321	−	13.9904i	1.12860	−	0.651597i	0.943582	+	0.331138i	$0.107433\pi$
$462$	−4.26795	−	2.07180i	−0.198563	−	0.0963887i
$463$	21.1603	−	5.66987i	0.983400	−	0.263501i	0.268924	−	0.963161i	$-0.413332\pi$
$463$	21.1603	−	5.66987i	0.983400	−	0.263501i	0.714476	+	0.699660i	$0.246665\pi$
$464$			24.4641i			1.13572i
$465$	9.46410	+	18.9282i	0.438887	+	0.877774i
$466$	11.0718			0.512891
$467$	−2.50000	+	9.33013i	−0.115686	+	0.431747i	−0.999337	−	0.0363992i	$-0.988411\pi$
$467$	−2.50000	+	9.33013i	−0.115686	+	0.431747i	0.883651	+	0.468146i	$0.155078\pi$
$468$	0.509619	−	1.90192i	0.0235571	−	0.0879165i
$469$	−4.02628	+	8.29423i	−0.185916	+	0.382992i
$470$	3.27757	−	4.96410i	0.151183	−	0.228977i
$471$	−5.53590	+	5.53590i	−0.255081	+	0.255081i
$472$	4.56218	−	17.0263i	0.209991	−	0.783698i
$473$	0.464102	−	1.73205i	0.0213394	−	0.0796398i
$474$	7.26795	−	7.26795i	0.333828	−	0.333828i
$475$	−3.63397	−	0.437822i	−0.166738	−	0.0200887i
$476$	5.32051	+	7.85641i	0.243865	+	0.360098i
$477$	−2.19615	−	2.19615i	−0.100555	−	0.100555i
$478$	−0.267949	+	1.00000i	−0.0122557	+	0.0457389i
$479$	−20.7321			−0.947272			−0.473636	−	0.880721i	$-0.657059\pi$
$479$	−20.7321			−0.947272			−0.473636	+	0.880721i	$0.657059\pi$
$480$	6.29423	−	18.8827i	0.287291	−	0.861873i
$481$		−	3.46410i		−	0.157949i
$482$	7.76795	−	2.08142i	0.353820	−	0.0948059i
$483$	28.8564	−	2.07180i	1.31301	−	0.0942700i
$484$	−10.5000	+	6.06218i	−0.477273	+	0.275554i
$485$	−20.6340	+	4.22243i	−0.936941	+	0.191731i
$486$	−5.70577	−	5.70577i	−0.258819	−	0.258819i
$487$	−7.24167	−	27.0263i	−0.328151	−	1.22468i	−0.911106	−	0.412173i	$-0.864770\pi$
$487$	−7.24167	−	27.0263i	−0.328151	−	1.22468i	0.582954	−	0.812505i	$-0.301897\pi$
$488$	5.46410	+	20.3923i	0.247348	+	0.923116i
$489$	−29.7846	+	29.7846i	−1.34691	+	1.34691i
$490$	−7.62436	+	2.74167i	−0.344433	+	0.123856i
$491$	−7.29423	+	12.6340i	−0.329184	+	0.570163i	−0.982350	−	0.187051i	$-0.940107\pi$
$491$	−7.29423	+	12.6340i	−0.329184	+	0.570163i	0.653166	+	0.757215i	$0.273440\pi$
$492$	−7.79423	−	4.50000i	−0.351391	−	0.202876i
$493$	14.5359	−	14.5359i	0.654664	−	0.654664i
$494$	0.124356	+	0.0717968i	0.00559503	+	0.00323029i
$495$	−7.39230	+	11.1962i	−0.332259	+	0.503230i
$496$			13.4641i			0.604556i
$497$	0.633975	−	3.29423i	0.0284376	−	0.147766i
$498$	4.62436	−	8.00962i	0.207222	−	0.358920i
$499$		−	38.3923i		−	1.71868i	−0.511408	−	0.859338i	$-0.670876\pi$
$499$		−	38.3923i		−	1.71868i	0.511408	−	0.859338i	$-0.329124\pi$
$500$	18.2321	−	6.52628i	0.815362	−	0.291864i
$501$	−10.5622	−	2.83013i	−0.471883	−	0.126441i
$502$	−6.83013	+	1.83013i	−0.304843	+	0.0816826i
$503$	2.63397	−	2.63397i	0.117443	−	0.117443i	−0.645943	−	0.763386i	$-0.723536\pi$
$503$	2.63397	−	2.63397i	0.117443	−	0.117443i	0.763386	+	0.645943i	$0.223536\pi$
$504$	13.7942	+	6.69615i	0.614444	+	0.298270i
$505$	−0.535898	+	0.267949i	−0.0238472	+	0.0119236i
$506$	3.26795	−	5.66025i	0.145278	−	0.251629i
$507$	22.2679			0.988954
$508$	7.20577	−	26.8923i	0.319704	−	1.19315i
$509$	32.9090			1.45866			0.729332	−	0.684160i	$-0.239831\pi$
$509$	32.9090			1.45866			0.729332	+	0.684160i	$0.239831\pi$
$510$	−3.71281	+	1.85641i	−0.164406	+	0.0822031i
$511$	−35.3205	+	2.53590i	−1.56249	+	0.112182i
$512$	15.6865	−	15.6865i	0.693253	−	0.693253i
$513$	−3.29423	+	1.90192i	−0.145444	+	0.0839720i
$514$	−3.73205	+	6.46410i	−0.164614	+	0.285119i
$515$	13.9019	+	4.63397i	0.612592	+	0.204197i
$516$	−0.696152	+	2.59808i	−0.0306464	+	0.114374i
$517$	−9.92820	+	2.66025i	−0.436642	+	0.116998i
$518$	12.2942	+	2.36603i	0.540177	+	0.103957i
$519$	10.1436	−	37.8564i	0.445254	−	1.66171i
$520$	−1.63397	−	0.0980762i	−0.0716545	−	0.00430093i
$521$	21.3564	+	12.3301i	0.935641	+	0.540193i	0.888591	−	0.458700i	$-0.151685\pi$
$521$	21.3564	+	12.3301i	0.935641	+	0.540193i	0.0470499	+	0.998893i	$0.485018\pi$
$522$	3.99038	−	14.8923i	0.174654	−	0.651818i
$523$	2.76795	+	0.741670i	0.121034	+	0.0324310i	0.318828	−	0.947813i	$-0.396711\pi$
$523$	2.76795	+	0.741670i	0.121034	+	0.0324310i	−0.197794	+	0.980244i	$0.563378\pi$
$524$	−16.3923	−	28.3923i	−0.716101	−	1.24032i
$525$	4.85641	+	22.3923i	0.211951	+	0.977280i
$526$	−3.33013	+	5.76795i	−0.145200	+	0.251495i
$527$	8.00000	−	8.00000i	0.348485	−	0.348485i
$528$	−7.39230	+	4.26795i	−0.321709	+	0.185739i
$529$			16.8564i			0.732887i
$530$	−0.660254	+	1.00000i	−0.0286796	+	0.0434372i
$531$	13.6865	−	23.7058i	0.593945	−	1.02874i
$532$	2.19615	−	2.53590i	0.0952153	−	0.109945i
$533$	−0.294229	+	1.09808i	−0.0127445	+	0.0475630i
$534$	0.928203	−	0.248711i	0.0401673	−	0.0107628i
$535$	−4.20577	−	20.5526i	−0.181831	−	0.888565i
$536$	−3.36603	−	5.83013i	−0.145390	−	0.251823i
$537$	−4.09808	−	7.09808i	−0.176845	−	0.306305i
$538$	3.80385	+	1.01924i	0.163996	+	0.0439425i
$539$	13.0000	+	5.19615i	0.559950	+	0.223814i
$540$	11.0885	−	16.7942i	0.477171	−	0.722709i
$541$	−3.46410	−	6.00000i	−0.148933	−	0.257960i	0.781900	−	0.623404i	$-0.214251\pi$
$541$	−3.46410	−	6.00000i	−0.148933	−	0.257960i	−0.930834	+	0.365444i	$0.880917\pi$
$542$	0.516660	+	0.516660i	0.0221925	+	0.0221925i
$543$	3.57180	−	6.18653i	0.153280	−	0.265490i
$544$	−10.6410			−0.456230
$545$	1.30385	−	21.7224i	0.0558507	−	0.930487i
$546$	0.169873	−	0.882686i	0.00726989	−	0.0377755i
$547$	−15.5981	−	4.17949i	−0.666926	−	0.178702i	−0.0905561	−	0.995891i	$-0.528864\pi$
$547$	−15.5981	−	4.17949i	−0.666926	−	0.178702i	−0.576370	+	0.817189i	$0.695531\pi$
$548$	0.633975	−	2.36603i	0.0270821	−	0.101072i
$549$			32.7846i			1.39921i
$550$	4.80385	+	1.92820i	0.204837	+	0.0822189i
$551$	−6.29423	−	3.63397i	−0.268143	−	0.154813i
$552$	−10.5622	+	18.2942i	−0.449556	+	0.778654i
$553$	−19.8564	+	22.9282i	−0.844380	+	0.975006i
$554$	1.39230	+	0.803848i	0.0591534	+	0.0341522i
$555$	11.1962	−	33.5885i	0.475250	−	1.42575i
$556$			32.1962i			1.36542i
$557$	6.67949	+	24.9282i	0.283019	+	1.05624i	0.950275	+	0.311413i	$0.100802\pi$
$557$	6.67949	+	24.9282i	0.283019	+	1.05624i	−0.667256	+	0.744829i	$0.732531\pi$
$558$	2.19615	−	8.19615i	0.0929705	−	0.346971i
$559$	0.339746			0.0143697
$560$	−3.60770	+	14.1244i	−0.152453	+	0.596863i
$561$	6.92820	+	1.85641i	0.292509	+	0.0783775i
$562$	9.41858	−	9.41858i	0.397299	−	0.397299i
$563$	4.09808	+	1.09808i	0.172713	+	0.0462784i	0.344139	−	0.938919i	$-0.388171\pi$
$563$	4.09808	+	1.09808i	0.172713	+	0.0462784i	−0.171426	+	0.985197i	$0.554837\pi$
$564$	14.8923	−	3.99038i	0.627079	−	0.168025i
$565$	−14.5359	−	16.3923i	−0.611530	−	0.689629i
$566$		−	8.32051i		−	0.349737i
$567$	18.0000	+	15.5885i	0.755929	+	0.654654i
$568$	1.73205	+	1.73205i	0.0726752	+	0.0726752i
$569$	2.53590	+	1.46410i	0.106310	+	0.0613783i	0.552212	−	0.833703i	$-0.313784\pi$
$569$	2.53590	+	1.46410i	0.106310	+	0.0613783i	−0.445902	+	0.895082i	$0.647117\pi$
$570$	0.973721	+	1.09808i	0.0407847	+	0.0459934i
$571$	2.09808	+	3.63397i	0.0878018	+	0.152077i	0.906582	−	0.422030i	$-0.138682\pi$
$571$	2.09808	+	3.63397i	0.0878018	+	0.152077i	−0.818780	+	0.574108i	$0.805349\pi$
$572$	0.928203	+	0.928203i	0.0388101	+	0.0388101i
$573$	30.2942	−	17.4904i	1.26556	−	0.730671i
$574$	−3.69615	−	1.79423i	−0.154274	−	0.0748897i
$575$	−31.2487	+	4.46410i	−1.30316	+	0.186166i
$576$	5.89230	−	3.40192i	0.245513	−	0.141747i
$577$	19.1962	−	5.14359i	0.799146	−	0.214131i	0.163937	−	0.986471i	$-0.447581\pi$
$577$	19.1962	−	5.14359i	0.799146	−	0.214131i	0.635209	+	0.772340i	$0.280914\pi$
$578$	−4.65321	−	4.65321i	−0.193548	−	0.193548i
$579$	−17.6603	+	17.6603i	−0.733935	+	0.733935i
$580$	38.3827	+	2.30385i	1.59375	+	0.0956621i
$581$	−11.9186	+	24.5526i	−0.494466	+	1.01861i
$582$	7.31347	+	4.22243i	0.303153	+	0.175025i
$583$	2.00000	−	0.535898i	0.0828315	−	0.0221946i
$584$	12.9282	−	22.3923i	0.534973	−	0.926600i
$585$	−2.41154	−	0.803848i	−0.0997050	−	0.0332350i
$586$	5.66025	−	3.26795i	0.233823	−	0.134998i
$587$	−8.83975	+	32.9904i	−0.364855	+	1.36166i	0.502761	+	0.864425i	$0.332317\pi$
$587$	−8.83975	+	32.9904i	−0.364855	+	1.36166i	−0.867617	+	0.497234i	$0.834349\pi$
$588$	−19.5000	−	7.79423i	−0.804166	−	0.321429i
$589$	−3.46410	−	2.00000i	−0.142736	−	0.0824086i
$590$	−10.0192	−	3.33975i	−0.412485	−	0.137495i
$591$	9.46410	−	2.53590i	0.389301	−	0.104313i
$592$	15.9282	−	15.9282i	0.654645	−	0.654645i
$593$	−14.7583	−	3.95448i	−0.606052	−	0.162391i	−0.0572729	−	0.998359i	$-0.518241\pi$
$593$	−14.7583	−	3.95448i	−0.606052	−	0.162391i	−0.548779	+	0.835967i	$0.684907\pi$
$594$	5.19615	−	1.39230i	0.213201	−	0.0571270i
$595$	10.5359	−	6.24871i	0.431930	−	0.256172i
$596$	7.39230	+	12.8038i	0.302801	+	0.524466i
$597$	−24.5885	+	14.1962i	−1.00634	+	0.581010i
$598$	1.19615	+	0.320508i	0.0489143	+	0.0131065i
$599$	−39.7128	+	22.9282i	−1.62262	+	0.936821i	−0.636406	+	0.771354i	$0.719580\pi$
$599$	−39.7128	+	22.9282i	−1.62262	+	0.936821i	−0.986215	+	0.165467i	$0.947087\pi$
$600$	−15.5263	−	6.23205i	−0.633858	−	0.254422i
$601$	−5.32051	+	3.07180i	−0.217028	+	0.125301i	−0.604573	−	0.796549i	$-0.706656\pi$
$601$	−5.32051	+	3.07180i	−0.217028	+	0.125301i	0.387545	+	0.921851i	$0.373323\pi$
$602$	−0.232051	+	1.20577i	−0.00945768	+	0.0491436i
$603$	−2.70577	−	10.0981i	−0.110188	−	0.411225i
$604$	−0.509619	+	0.294229i	−0.0207361	+	0.0119720i
$605$	7.00000	+	14.0000i	0.284590	+	0.569181i
$606$	0.232051	+	0.0621778i	0.00942642	+	0.00252580i
$607$	18.2942	+	18.2942i	0.742540	+	0.742540i	0.973066	−	0.230526i	$-0.0740448\pi$
$607$	18.2942	+	18.2942i	0.742540	+	0.742540i	−0.230526	+	0.973066i	$0.574045\pi$
$608$	0.973721	+	3.63397i	0.0394896	+	0.147377i
$609$	−8.59808	+	44.6769i	−0.348412	+	1.81040i
$610$	12.3923	−	2.53590i	0.501750	−	0.102676i
$611$	−0.973721	−	1.68653i	−0.0393925	−	0.0682298i
$612$	−10.3923	−	2.78461i	−0.420084	−	0.112561i
$613$	0.901924	−	0.241670i	0.0364284	−	0.00976095i	−0.240559	−	0.970635i	$-0.577331\pi$
$613$	0.901924	−	0.241670i	0.0364284	−	0.00976095i	0.276987	+	0.960874i	$0.410664\pi$
$614$	1.33013	−	2.30385i	0.0536796	−	0.0929757i
$615$	−6.40192	+	9.69615i	−0.258150	+	0.390987i
$616$	−8.46410	+	5.73205i	−0.341028	+	0.230951i
$617$	−8.39230	−	31.3205i	−0.337861	−	1.26092i	−0.900734	−	0.434372i	$-0.856970\pi$
$617$	−8.39230	−	31.3205i	−0.337861	−	1.26092i	0.562872	−	0.826544i	$-0.309696\pi$
$618$	−2.93782	−	5.08846i	−0.118177	−	0.204688i
$619$	0.784610			0.0315361			0.0157681	−	0.999876i	$-0.494981\pi$
$619$	0.784610			0.0315361			0.0157681	+	0.999876i	$0.494981\pi$
$620$	21.1244	+	1.26795i	0.848375	+	0.0509221i
$621$	−23.1962	+	23.1962i	−0.930830	+	0.930830i
$622$	−6.26795	−	6.26795i	−0.251322	−	0.251322i
$623$	−2.67949	+	0.928203i	−0.107352	+	0.0371877i
$624$	−1.14359	−	1.14359i	−0.0457804	−	0.0457804i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−14.1962	+	8.19615i	−0.567392	+	0.327584i
$627$		−	2.53590i		−	0.101274i
$628$	2.02628	+	7.56218i	0.0808574	+	0.301764i
$629$	−18.9282			−0.754717
$630$	4.50000	−	8.00962i	0.179284	−	0.319111i
$631$	−11.8564			−0.471996			−0.235998	−	0.971754i	$-0.575836\pi$
$631$	−11.8564			−0.471996			−0.235998	+	0.971754i	$0.575836\pi$
$632$	−5.73205	−	21.3923i	−0.228009	−	0.850940i
$633$	−40.3923	+	23.3205i	−1.60545	+	0.926907i
$634$	−0.973721	+	0.562178i	−0.0386714	+	0.0223269i
$635$	−34.0981	−	11.3660i	−1.35314	−	0.451047i
$636$	−3.00000	+	0.803848i	−0.118958	+	0.0318746i
$637$	−0.313467	+	2.63397i	−0.0124200	+	0.104362i
$638$	7.26795	+	7.26795i	0.287741	+	0.287741i
$639$	1.90192	+	3.29423i	0.0752389	+	0.130318i
$640$	−16.9904	−	19.1603i	−0.671604	−	0.757376i
$641$	17.6077			0.695462			0.347731	−	0.937594i	$-0.386952\pi$
$641$	17.6077			0.695462			0.347731	+	0.937594i	$0.386952\pi$
$642$	−4.20577	+	7.28461i	−0.165989	+	0.287501i
$643$	6.65064	+	24.8205i	0.262275	+	0.978825i	0.963897	+	0.266275i	$0.0857931\pi$
$643$	6.65064	+	24.8205i	0.262275	+	0.978825i	−0.701622	+	0.712550i	$0.747540\pi$
$644$	12.6340	−	26.0263i	0.497848	−	1.02558i
$645$	3.29423	+	1.09808i	0.129710	+	0.0432367i
$646$	0.392305	−	0.679492i	0.0154350	−	0.0267343i
$647$	−12.5981	+	3.37564i	−0.495281	+	0.132710i	−0.497809	−	0.867287i	$-0.665862\pi$
$647$	−12.5981	+	3.37564i	−0.495281	+	0.132710i	0.00252779	+	0.999997i	$0.499195\pi$
$648$	−16.7942	+	4.50000i	−0.659740	+	0.176777i
$649$	9.12436	+	15.8038i	0.358162	+	0.620355i
$650$	−0.117314	+	0.973721i	−0.00460144	+	0.0381925i
$651$	−4.73205	+	24.5885i	−0.185464	+	0.963698i
$652$	10.9019	+	40.6865i	0.426952	+	1.59341i
$653$	14.7321	+	14.7321i	0.576510	+	0.576510i	0.933940	−	0.357430i	$-0.116347\pi$
$653$	14.7321	+	14.7321i	0.576510	+	0.576510i	−0.357430	+	0.933940i	$0.616347\pi$
$654$	−6.16987	+	6.16987i	−0.241261	+	0.241261i
$655$	−37.8564	+	18.9282i	−1.47917	+	0.739586i
$656$	−6.40192	+	3.69615i	−0.249953	+	0.144311i
$657$	28.3923	−	28.3923i	1.10769	−	1.10769i
$658$	6.65064	−	2.30385i	0.259269	−	0.0898133i
$659$	−19.3468	+	11.1699i	−0.753644	+	0.435116i	−0.827009	−	0.562189i	$-0.809959\pi$
$659$	−19.3468	+	11.1699i	−0.753644	+	0.435116i	0.0733652	+	0.997305i	$0.476626\pi$
$660$	6.00000	+	12.0000i	0.233550	+	0.467099i
$661$	−2.25833	+	1.30385i	−0.0878389	+	0.0507138i	−0.543276	−	0.839554i	$-0.682816\pi$
$661$	−2.25833	+	1.30385i	−0.0878389	+	0.0507138i	0.455437	+	0.890268i	$0.349483\pi$
$662$	3.00000	+	0.803848i	0.116598	+	0.0312424i
$663$			1.35898i			0.0527786i
$664$	−9.96410	−	17.2583i	−0.386682	−	0.669753i
$665$	−3.09808	−	3.02628i	−0.120138	−	0.117354i
$666$	−12.2942	+	7.09808i	−0.476392	+	0.275045i
$667$	−60.5429	−	16.2224i	−2.34423	−	0.628135i
$668$	−7.73205	+	7.73205i	−0.299162	+	0.299162i
$669$	−6.29423	−	6.29423i	−0.243349	−	0.243349i
$670$	−3.60770	+	1.80385i	−0.139377	+	0.0696887i
$671$	−18.9282	−	10.9282i	−0.730715	−	0.421879i
$672$	19.5000	−	13.2058i	0.752229	−	0.509424i
$673$	−1.43782	+	5.36603i	−0.0554240	+	0.206845i	−0.988085	−	0.153909i	$-0.950814\pi$
$673$	−1.43782	+	5.36603i	−0.0554240	+	0.206845i	0.932661	+	0.360754i	$0.117481\pi$
$674$	9.75833	−	5.63397i	0.375877	−	0.217013i
$675$	−20.7846	−	15.5885i	−0.800000	−	0.600000i
$676$	11.1340	−	19.2846i	0.428230	−	0.741716i
$677$	−14.3660	+	3.84936i	−0.552131	+	0.147943i	−0.524089	−	0.851664i	$-0.675594\pi$
$677$	−14.3660	+	3.84936i	−0.552131	+	0.147943i	−0.0280424	+	0.999607i	$0.508927\pi$
$678$			8.78461i			0.337371i
$679$	−22.4186	−	10.8827i	−0.860346	−	0.417639i
$680$	−0.535898	+	8.92820i	−0.0205508	+	0.342381i
$681$	11.1506	+	41.6147i	0.427293	+	1.59468i
$682$	4.00000	+	4.00000i	0.153168	+	0.153168i
$683$	−42.9186	+	11.5000i	−1.64223	+	0.440035i	−0.957424	−	0.288686i	$-0.906782\pi$
$683$	−42.9186	+	11.5000i	−1.64223	+	0.440035i	−0.684810	+	0.728721i	$0.740115\pi$
$684$			3.80385i			0.145444i
$685$	−3.00000	−	1.00000i	−0.114624	−	0.0382080i
$686$	−9.13397	−	2.91154i	−0.348737	−	0.111163i
$687$	33.9904	+	19.6244i	1.29681	+	0.748716i
$688$	1.56218	+	1.56218i	0.0595575	+	0.0595575i
$689$	0.196152	+	0.339746i	0.00747281	+	0.0129433i
$690$	10.5622	+	6.97372i	0.402095	+	0.265485i
$691$	−16.8564	−	9.73205i	−0.641248	−	0.370225i	0.143847	−	0.989600i	$-0.454053\pi$
$691$	−16.8564	−	9.73205i	−0.641248	−	0.370225i	−0.785095	+	0.619375i	$0.787386\pi$
$692$	−27.7128	−	27.7128i	−1.05348	−	1.05348i
$693$	−15.0000	+	5.19615i	−0.569803	+	0.197386i
$694$		−	6.12436i		−	0.232477i
$695$	41.4904	+	2.49038i	1.57382	+	0.0944655i
$696$	−23.4904	−	23.4904i	−0.890401	−	0.890401i
$697$	6.00000	+	1.60770i	0.227266	+	0.0608958i
$698$	−3.66025	+	3.66025i	−0.138543	+	0.138543i
$699$	26.1962	−	26.1962i	0.990829	−	0.990829i
$700$	21.8205	+	6.99038i	0.824738	+	0.264212i
$701$	11.0526			0.417449			0.208725	−	0.977974i	$-0.433069\pi$
$701$	11.0526			0.417449			0.208725	+	0.977974i	$0.433069\pi$
$702$	0.509619	+	0.882686i	0.0192343	+	0.0333148i
$703$	1.73205	+	6.46410i	0.0653255	+	0.243798i
$704$			4.53590i			0.170953i
$705$	−3.99038	−	19.5000i	−0.150286	−	0.734412i
$706$	−3.50962	−	2.02628i	−0.132086	−	0.0762600i
$707$	−0.696152	−	0.133975i	−0.0261815	−	0.00503863i
$708$	−13.6865	−	23.7058i	−0.514371	−	0.890917i
$709$	35.1962	+	20.3205i	1.32182	+	0.763153i	0.984019	−	0.178065i	$-0.0569837\pi$
$709$	35.1962	+	20.3205i	1.32182	+	0.763153i	0.337801	+	0.941218i	$0.390317\pi$
$710$	1.09808	−	0.973721i	0.0412101	−	0.0365431i
$711$		−	34.3923i		−	1.28981i
$712$	0.535898	−	2.00000i	0.0200836	−	0.0749532i
$713$	−33.3205	−	8.92820i	−1.24786	−	0.334364i
$714$	−4.82309	−	0.928203i	−0.180499	−	0.0347371i
$715$	1.26795	−	1.12436i	0.0474186	−	0.0420485i
$716$	−8.19615			−0.306305
$717$	1.73205	+	3.00000i	0.0646846	+	0.112037i
$718$	1.07180	+	1.07180i	0.0399991	+	0.0399991i
$719$	11.4641	+	19.8564i	0.427539	+	0.740519i	0.996654	−	0.0817390i	$-0.0260474\pi$
$719$	11.4641	+	19.8564i	0.427539	+	0.740519i	−0.569115	+	0.822258i	$0.692714\pi$
$720$	−7.39230	−	14.7846i	−0.275495	−	0.550990i
$721$	9.72243	+	14.3564i	0.362082	+	0.534661i
$722$	9.23205	+	2.47372i	0.343581	+	0.0920623i
$723$	13.4545	−	23.3038i	0.500378	−	0.866679i
$724$	−3.57180	−	6.18653i	−0.132745	−	0.229921i
$725$	5.93782	−	49.2846i	0.220525	−	1.83038i
$726$	1.62436	−	6.06218i	0.0602855	−	0.224989i
$727$	6.75833	−	25.2224i	0.250653	−	0.935448i	−0.719805	−	0.694176i	$-0.755769\pi$
$727$	6.75833	−	25.2224i	0.250653	−	0.935448i	0.970458	−	0.241272i	$-0.0775646\pi$
$728$	−1.46410	−	1.26795i	−0.0542632	−	0.0469933i
$729$	−27.0000			−1.00000
$730$	−12.9282	−	8.53590i	−0.478494	−	0.315928i
$731$		−	1.85641i		−	0.0686617i
$732$	28.3923	+	16.3923i	1.04941	+	0.605877i
$733$	−4.32051	+	4.32051i	−0.159582	+	0.159582i	−0.782381	−	0.622800i	$-0.785995\pi$
$733$	−4.32051	+	4.32051i	−0.159582	+	0.159582i	0.622800	+	0.782381i	$0.285995\pi$
$734$	−3.33013	+	5.76795i	−0.122917	+	0.212899i
$735$	−11.5526	+	24.5263i	−0.426123	+	0.904665i
$736$	16.2224	+	28.0981i	0.597967	+	1.03571i
$737$	6.73205	+	1.80385i	0.247978	+	0.0664456i
$738$	4.50000	−	1.20577i	0.165647	−	0.0443851i
$739$	−0.679492	−	0.392305i	−0.0249955	−	0.0144312i	0.487450	−	0.873151i	$-0.337927\pi$
$739$	−0.679492	−	0.392305i	−0.0249955	−	0.0144312i	−0.512446	+	0.858720i	$0.671260\pi$
$740$	−23.4904	−	26.4904i	−0.863524	−	0.973806i
$741$	0.464102	−	0.124356i	0.0170492	−	0.00456832i
$742$	−1.33975	+	0.464102i	−0.0491836	+	0.0170377i
$743$	−34.9186	+	9.35641i	−1.28104	+	0.343253i	−0.834250	−	0.551386i	$-0.814099\pi$
$743$	−34.9186	+	9.35641i	−1.28104	+	0.343253i	−0.446789	+	0.894640i	$0.647432\pi$
$744$	−12.9282	−	12.9282i	−0.473971	−	0.473971i
$745$	17.0718	−	8.53590i	0.625462	−	0.312731i
$746$	4.56218	−	7.90192i	0.167033	−	0.289310i
$747$	−8.00962	−	29.8923i	−0.293057	−	1.09370i
$748$	5.07180	−	5.07180i	0.185443	−	0.185443i
$749$	10.8397	−	22.3301i	0.396076	−	0.815925i
$750$	−4.28461	+	9.06218i	−0.156452	+	0.330904i
$751$	24.8756			0.907725			0.453863	−	0.891072i	$-0.350046\pi$
$751$	24.8756			0.907725			0.453863	+	0.891072i	$0.350046\pi$
$752$	3.27757	−	12.2321i	0.119521	−	0.446057i
$753$	−11.8301	+	20.4904i	−0.431114	+	0.746711i
$754$	−0.973721	+	1.68653i	−0.0354608	+	0.0614199i
$755$	0.339746	+	0.679492i	0.0123646	+	0.0247292i
$756$	22.5000	−	7.79423i	0.818317	−	0.283473i
$757$	−14.3923	+	14.3923i	−0.523097	+	0.523097i	−0.918505	−	0.395408i	$-0.870603\pi$
$757$	−14.3923	+	14.3923i	−0.523097	+	0.523097i	0.395408	+	0.918505i	$0.370603\pi$
$758$	13.7583	−	3.68653i	0.499725	−	0.133901i
$759$	−5.66025	−	21.1244i	−0.205454	−	0.766766i
$760$	3.09808	−	0.633975i	0.112379	−	0.0229967i
$761$			9.19615i			0.333360i	0.986011	+	0.166680i	$0.0533047\pi$
$761$			9.19615i			0.333360i	−0.986011	+	0.166680i	$0.946695\pi$
$762$	7.20577	+	12.4808i	0.261038	+	0.452130i
$763$	16.8564	−	19.4641i	0.610243	−	0.704648i
$764$		−	34.9808i		−	1.26556i
$765$	−4.39230	+	13.1769i	−0.158804	+	0.476412i
$766$	9.35641	+	5.40192i	0.338061	+	0.195179i
$767$	−2.44486	+	2.44486i	−0.0882789	+	0.0882789i
$768$			2.41154i			0.0870191i
$769$	−12.5981	+	21.8205i	−0.454298	+	0.786868i	−0.998648	−	0.0519910i	$-0.983443\pi$
$769$	−12.5981	+	21.8205i	−0.454298	+	0.786868i	0.544349	+	0.838859i	$0.316777\pi$
$770$	3.12436	+	5.26795i	0.112594	+	0.189844i
$771$	6.46410	+	24.1244i	0.232799	+	0.868817i
$772$	6.46410	+	24.1244i	0.232648	+	0.868255i
$773$	−4.58142	−	17.0981i	−0.164782	−	0.614975i	−0.998068	−	0.0621327i	$-0.980210\pi$
$773$	−4.58142	−	17.0981i	−0.164782	−	0.614975i	0.833286	−	0.552842i	$-0.186457\pi$
$774$	−0.696152	−	1.20577i	−0.0250227	−	0.0433406i
$775$	3.26795	−	27.1244i	0.117388	−	0.974336i
$776$	15.7583	−	9.09808i	0.565691	−	0.326602i
$777$	34.6865	−	23.4904i	1.24437	−	0.842713i
$778$	14.5263	−	3.89230i	0.520792	−	0.139546i
$779$		−	2.19615i		−	0.0786853i
$780$	−1.90192	+	1.68653i	−0.0680998	+	0.0603876i
$781$	−2.53590			−0.0907416
$782$	1.75129	−	6.53590i	0.0626260	−	0.233723i
$783$	−25.7942	−	44.6769i	−0.921811	−	1.59662i
$784$	−13.5526	+	10.6699i	−0.484020	+	0.381067i
$785$	9.90192	−	2.02628i	0.353415	−	0.0723210i
$786$	16.3923	+	4.39230i	0.584694	+	0.156668i
$787$	−10.6769	+	39.8468i	−0.380591	+	1.42038i	0.464410	+	0.885620i	$0.346266\pi$
$787$	−10.6769	+	39.8468i	−0.380591	+	1.42038i	−0.845001	+	0.534764i	$0.820400\pi$
$788$	2.53590	−	9.46410i	0.0903376	−	0.337145i
$789$	5.76795	+	21.5263i	0.205344	+	0.766356i
$790$	−13.0000	+	2.66025i	−0.462519	+	0.0946476i
$791$	−1.85641	−	25.8564i	−0.0660062	−	0.919348i
$792$	3.00000	−	11.1962i	0.106600	−	0.397838i
$793$	1.07180	−	4.00000i	0.0380606	−	0.142044i
$794$	−10.6410			−0.377636
$795$	0.803848	+	3.92820i	0.0285095	+	0.139319i
$796$			28.3923i			1.00634i
$797$	34.8827	−	9.34679i	1.23561	−	0.331080i	0.418847	−	0.908057i	$-0.362434\pi$
$797$	34.8827	−	9.34679i	1.23561	−	0.331080i	0.816761	+	0.576976i	$0.195768\pi$
$798$	0.124356	+	1.73205i	0.00440214	+	0.0613139i
$799$	−9.21539	+	5.32051i	−0.326017	+	0.188226i
$800$	−20.2128	+	15.8660i	−0.714631	+	0.560949i
$801$	1.60770	−	2.78461i	0.0568051	−	0.0983893i
$802$	1.52628	+	5.69615i	0.0538948	+	0.201138i
$803$	6.92820	+	25.8564i	0.244491	+	0.912453i
$804$	−10.0981	−	2.70577i	−0.356132	−	0.0954252i
$805$	−32.5622	−	18.2942i	−1.14767	−	0.644787i
$806$	−0.535898	+	0.928203i	−0.0188762	+	0.0326946i
$807$	11.4115	−	6.58846i	0.401705	−	0.231925i
$808$	0.366025	−	0.366025i	0.0128767	−	0.0128767i
$809$	38.3827	+	22.1603i	1.34946	+	0.779113i	0.988173	−	0.153340i	$-0.0490031\pi$
$809$	38.3827	+	22.1603i	1.34946	+	0.779113i	0.361290	+	0.932454i	$0.382336\pi$
$810$	2.08846	+	10.2058i	0.0733809	+	0.358594i
$811$		−	6.58846i		−	0.231352i	−0.993287	−	0.115676i	$-0.963097\pi$
$811$		−	6.58846i		−	0.231352i	0.993287	−	0.115676i	$-0.0369034\pi$
$812$	34.3923	+	29.7846i	1.20693	+	1.04523i
$813$	2.44486			0.0857451
$814$		−	9.46410i		−	0.331717i
$815$	53.2750	−	10.9019i	1.86614	−	0.381878i
$816$	−6.24871	+	6.24871i	−0.218749	+	0.218749i
$817$	−0.633975	+	0.169873i	−0.0221800	+	0.00594310i
$818$	4.50962	−	4.50962i	0.157675	−	0.157675i
$819$	−1.68653	−	2.49038i	−0.0589322	−	0.0870210i
$820$	5.19615	+	10.3923i	0.181458	+	0.362915i
$821$	−20.7942	+	36.0167i	−0.725724	+	1.25699i	0.232952	+	0.972488i	$0.425162\pi$
$821$	−20.7942	+	36.0167i	−0.725724	+	1.25699i	−0.958675	+	0.284502i	$0.908172\pi$
$822$	0.633975	+	1.09808i	0.0221124	+	0.0382998i
$823$	2.72243	−	10.1603i	0.0948980	−	0.354164i	−0.902106	−	0.431515i	$-0.857979\pi$
$823$	2.72243	−	10.1603i	0.0948980	−	0.354164i	0.997004	+	0.0773504i	$0.0246460\pi$
$824$	−12.6603			−0.441041
$825$	15.9282	−	6.80385i	0.554549	−	0.236880i
$826$	−7.00704	−	10.3468i	−0.243806	−	0.360011i
$827$	14.1699	−	14.1699i	0.492735	−	0.492735i	−0.416432	−	0.909167i	$-0.636720\pi$
$827$	14.1699	−	14.1699i	0.492735	−	0.492735i	0.909167	+	0.416432i	$0.136720\pi$
$828$	8.49038	+	31.6865i	0.295061	+	1.10118i
$829$	−22.1603	+	38.3827i	−0.769657	+	1.33309i	0.168091	+	0.985771i	$0.446240\pi$
$829$	−22.1603	+	38.3827i	−0.769657	+	1.33309i	−0.937749	+	0.347314i	$0.887094\pi$
$830$	−10.6795	+	5.33975i	−0.370691	+	0.185345i
$831$	5.19615	−	1.39230i	0.180253	−	0.0482985i
$832$	−0.830127	+	0.222432i	−0.0287795	+	0.00771144i
$833$	14.3923	+	1.71281i	0.498664	+	0.0593455i
$834$	−11.7846	−	11.7846i	−0.408068	−	0.408068i
$835$	9.36603	+	10.5622i	0.324125	+	0.365519i
$836$	−2.19615	−	1.26795i	−0.0759555	−	0.0438529i
$837$	−14.1962	−	24.5885i	−0.490691	−	0.849901i
$838$	−9.83013	−	2.63397i	−0.339576	−	0.0909891i
$839$	22.6147	+	39.1699i	0.780747	+	1.35229i	0.931507	+	0.363724i	$0.118495\pi$
$839$	22.6147	+	39.1699i	0.780747	+	1.35229i	−0.150759	+	0.988570i	$0.548172\pi$
$840$	−10.0981	−	17.0263i	−0.348417	−	0.587462i
$841$	34.7846	−	60.2487i	1.19947	−	2.07754i
$842$	5.56218	−	5.56218i	0.191685	−	0.191685i
$843$		−	44.5692i		−	1.53505i
$844$			46.6410i			1.60545i
$845$	−23.9904	−	15.8397i	−0.825294	−	0.544904i
$846$	−3.99038	+	6.91154i	−0.137192	+	0.237624i
$847$	−3.50000	+	18.1865i	−0.120261	+	0.624897i
$848$	−0.660254	+	2.46410i	−0.0226732	+	0.0846176i
$849$	−19.6865	−	19.6865i	−0.675640	−	0.675640i
$850$	5.32051	+	0.641016i	0.182492	+	0.0219867i
$851$	28.8564	+	49.9808i	0.989185	+	1.71332i
$852$	3.80385			0.130318
$853$	−24.1244	−	6.46410i	−0.826002	−	0.221327i	−0.179033	−	0.983843i	$-0.557297\pi$
$853$	−24.1244	−	6.46410i	−0.826002	−	0.221327i	−0.646969	+	0.762516i	$0.723964\pi$
$854$	13.4641	+	6.53590i	0.460732	+	0.223654i
$855$	4.90192	+	0.294229i	0.167642	+	0.0100624i
$856$	9.06218	+	15.6962i	0.309739	+	0.536483i
$857$	−8.92820	−	8.92820i	−0.304982	−	0.304982i	0.537978	−	0.842959i	$-0.319189\pi$
$857$	−8.92820	−	8.92820i	−0.304982	−	0.304982i	−0.842959	+	0.537978i	$0.819189\pi$
$858$	−0.679492			−0.0231975
$859$	27.6603			0.943756			0.471878	−	0.881664i	$-0.343576\pi$
$859$	27.6603			0.943756			0.471878	+	0.881664i	$0.343576\pi$
$860$	2.59808	−	2.30385i	0.0885937	−	0.0785606i
$861$	−12.9904	+	4.50000i	−0.442711	+	0.153360i
$862$	5.29423	+	1.41858i	0.180322	+	0.0483172i
$863$	12.6147	−	47.0788i	0.429411	−	1.60258i	−0.324688	−	0.945821i	$-0.605259\pi$
$863$	12.6147	−	47.0788i	0.429411	−	1.60258i	0.754099	−	0.656761i	$-0.228074\pi$
$864$	−6.91154	+	25.7942i	−0.235135	+	0.877537i
$865$	−37.8564	+	33.5692i	−1.28716	+	1.14139i
$866$	15.2942	+	8.83013i	0.519719	+	0.300060i
$867$	−22.0192			−0.747813
$868$	18.9282	+	16.3923i	0.642465	+	0.556391i
$869$	19.8564	+	11.4641i	0.673582	+	0.388893i
$870$	−14.8923	+	13.2058i	−0.504896	+	0.447718i
$871$			1.32051i			0.0447437i
$872$	4.86603	+	18.1603i	0.164784	+	0.614984i
$873$	27.2942	−	7.31347i	0.923770	−	0.247523i
$874$	−2.39230			−0.0809209
$875$	10.6962	−	27.5788i	0.361596	−	0.932335i
$876$	−10.3923	−	38.7846i	−0.351123	−	1.31041i
$877$	1.19615	−	1.19615i	0.0403912	−	0.0403912i	−0.686623	−	0.727014i	$-0.740908\pi$
$877$	1.19615	−	1.19615i	0.0403912	−	0.0403912i	0.727014	+	0.686623i	$0.240908\pi$
$878$	4.07180	+	1.09103i	0.137416	+	0.0368206i
$879$	5.66025	−	21.1244i	0.190916	−	0.712507i
$880$	11.0000	+	0.660254i	0.370810	+	0.0222572i
$881$			39.0333i			1.31507i	0.753426	+	0.657533i	$0.228400\pi$
$881$			39.0333i			1.31507i	−0.753426	+	0.657533i	$0.771600\pi$
$882$	9.99038	−	4.28461i	0.336394	−	0.144270i
$883$	31.5622	+	31.5622i	1.06215	+	1.06215i	0.997936	+	0.0642158i	$0.0204546\pi$
$883$	31.5622	+	31.5622i	1.06215	+	1.06215i	0.0642158	+	0.997936i	$0.479545\pi$
$884$	1.17691	+	0.679492i	0.0395839	+	0.0228538i
$885$	−31.6077	+	15.8038i	−1.06248	+	0.531241i
$886$	−3.79423	−	6.57180i	−0.127470	−	0.220784i
$887$	19.4904	+	19.4904i	0.654423	+	0.654423i	0.954055	−	0.299632i	$-0.0968639\pi$
$887$	19.4904	+	19.4904i	0.654423	+	0.654423i	−0.299632	+	0.954055i	$0.596864\pi$
$888$			30.5885i			1.02648i
$889$	−23.8468	−	35.2128i	−0.799796	−	1.18100i
$890$	−1.17691	−	0.392305i	−0.0394503	−	0.0131501i
$891$	9.00000	−	15.5885i	0.301511	−	0.522233i
$892$	−8.59808	+	2.30385i	−0.287885	+	0.0771385i
$893$	2.66025	+	2.66025i	0.0890220	+	0.0890220i
$894$	−7.39230	−	1.98076i	−0.247236	−	0.0662466i
$895$	−0.633975	+	10.5622i	−0.0211914	+	0.353055i
$896$	−2.16987	−	30.2224i	−0.0724904	−	1.00966i
$897$	3.58846	−	2.07180i	0.119815	−	0.0691753i
$898$	−12.3301	+	3.30385i	−0.411462	+	0.110251i
$899$	27.1244	−	46.9808i	0.904648	−	1.56690i
$900$	−23.8923	+	10.2058i	−0.796410	+	0.340192i
$901$	1.85641	−	1.07180i	0.0618459	−	0.0357067i
$902$	−0.803848	+	3.00000i	−0.0267652	+	0.0998891i
$903$	2.30385	+	3.40192i	0.0766672	+	0.113209i
$904$	16.3923	+	9.46410i	0.545200	+	0.314771i
$905$	−8.24871	+	4.12436i	−0.274196	+	0.137098i
$906$	0.0788383	−	0.294229i	0.00261923	−	0.00977509i
$907$	7.63397	−	7.63397i	0.253482	−	0.253482i	−0.568915	−	0.822397i	$-0.692637\pi$
$907$	7.63397	−	7.63397i	0.253482	−	0.253482i	0.822397	+	0.568915i	$0.192637\pi$
$908$	41.6147	+	11.1506i	1.38103	+	0.370047i
$909$	0.696152	−	0.401924i	0.0230899	−	0.0133310i
$910$	−0.810889	+	0.830127i	−0.0268807	+	0.0275184i
$911$	−2.36603	−	4.09808i	−0.0783899	−	0.135775i	0.824165	−	0.566349i	$-0.191645\pi$
$911$	−2.36603	−	4.09808i	−0.0783899	−	0.135775i	−0.902555	+	0.430574i	$0.858311\pi$
$912$	2.70577	+	1.56218i	0.0895970	+	0.0517289i
$913$	19.9282	+	5.33975i	0.659527	+	0.176720i
$914$	−9.54294	+	5.50962i	−0.315652	+	0.182242i
$915$	23.3205	−	35.3205i	0.770952	−	1.16766i
$916$	33.9904	−	19.6244i	1.12307	−	0.648407i
$917$	−49.1769	−	9.46410i	−1.62396	−	0.312532i
$918$	4.82309	−	2.78461i	0.159186	−	0.0919058i
$919$	10.9019	−	6.29423i	0.359621	−	0.207627i	−0.309293	−	0.950967i	$-0.600092\pi$
$919$	10.9019	−	6.29423i	0.359621	−	0.207627i	0.668915	+	0.743339i	$0.266759\pi$
$920$	24.3923	−	12.1962i	0.804190	−	0.402095i
$921$	−2.30385	−	8.59808i	−0.0759144	−	0.283316i
$922$	10.2417	+	10.2417i	0.337291	+	0.337291i
$923$	−0.124356	−	0.464102i	−0.00409322	−	0.0152761i
$924$	−3.00000	+	15.5885i	−0.0986928	+	0.512823i
$925$	−35.9545	+	28.2224i	−1.18218	+	0.927948i
$926$	5.66987	+	9.82051i	0.186324	+	0.322722i
$927$	−18.9904	−	5.08846i	−0.623726	−	0.167127i
$928$	−49.2846	+	13.2058i	−1.61785	+	0.433501i
$929$	4.89230	−	8.47372i	0.160511	−	0.278014i	−0.774541	−	0.632524i	$-0.782019\pi$
$929$	4.89230	−	8.47372i	0.160511	−	0.278014i	0.935052	+	0.354510i	$0.115352\pi$
$930$	−8.19615	+	7.26795i	−0.268762	+	0.238325i
$931$	−0.732051	−	5.07180i	−0.0239920	−	0.166221i
$932$	−9.58846	−	35.7846i	−0.314080	−	1.17216i
$933$	−29.6603			−0.971033
$934$	−5.00000			−0.163605
$935$	−6.14359	−	6.92820i	−0.200917	−	0.226576i
$936$	2.19615			0.0717835
$937$	12.4641	+	12.4641i	0.407184	+	0.407184i	0.880756	−	0.473571i	$-0.157035\pi$
$937$	12.4641	+	12.4641i	0.407184	+	0.407184i	−0.473571	+	0.880756i	$0.657035\pi$
$938$	−4.68653	−	0.901924i	−0.153021	−	0.0294489i
$939$	−14.1962	+	52.9808i	−0.463274	+	1.72896i
$940$	−18.8827	−	6.29423i	−0.615885	−	0.205295i
$941$	−26.8923	+	15.5263i	−0.876664	+	0.506142i	−0.869557	−	0.493833i	$-0.835596\pi$
$941$	−26.8923	+	15.5263i	−0.876664	+	0.506142i	−0.00710703	+	0.999975i	$0.502262\pi$
$942$	−3.50962	−	2.02628i	−0.114350	−	0.0660198i
$943$	−4.90192	−	18.2942i	−0.159629	−	0.595742i
$944$	−22.4833			−0.731770
$945$	−8.30385	−	29.5981i	−0.270124	−	0.962825i
$946$	0.928203			0.0301785
$947$	1.83013	+	6.83013i	0.0594711	+	0.221949i	0.989265	−	0.146131i	$-0.0466820\pi$
$947$	1.83013	+	6.83013i	0.0594711	+	0.221949i	−0.929794	+	0.368080i	$0.880015\pi$
$948$	−29.7846	−	17.1962i	−0.967359	−	0.558505i
$949$	−4.39230	+	2.53590i	−0.142580	+	0.0823187i
$950$	−0.267949	−	1.87564i	−0.00869342	−	0.0608539i
$951$	−0.973721	+	3.63397i	−0.0315751	+	0.117840i
$952$	−6.92820	+	8.00000i	−0.224544	+	0.259281i
$953$	−16.0526	−	16.0526i	−0.519993	−	0.519993i	0.397576	−	0.917569i	$-0.369852\pi$
$953$	−16.0526	−	16.0526i	−0.519993	−	0.519993i	−0.917569	+	0.397576i	$0.869852\pi$
$954$	0.803848	−	1.39230i	0.0260255	−	0.0450775i
$955$	−45.0788	−	2.70577i	−1.45872	−	0.0875567i
$956$	3.46410			0.112037
$957$	34.3923			1.11175
$958$	−2.77757	−	10.3660i	−0.0897392	−	0.334911i
$959$	−2.09808	−	3.09808i	−0.0677504	−	0.100042i
$960$	−8.76795	−	0.526279i	−0.282984	−	0.0169856i
$961$	−0.571797	+	0.990381i	−0.0184451	+	0.0319478i
$962$	1.73205	−	0.464102i	0.0558436	−	0.0149632i
$963$	7.28461	+	27.1865i	0.234743	+	0.876074i
$964$	−13.4545	−	23.3038i	−0.433340	−	0.750566i
$965$	31.5885	−	6.46410i	1.01687	−	0.208087i
$966$	4.90192	+	14.1506i	0.157717	+	0.455289i
$967$	6.07884	+	22.6865i	0.195482	+	0.729550i	0.992141	+	0.125121i	$0.0399319\pi$
$967$	6.07884	+	22.6865i	0.195482	+	0.729550i	−0.796659	+	0.604429i	$0.793401\pi$
$968$	−9.56218	−	9.56218i	−0.307340	−	0.307340i
$969$	−0.679492	−	2.53590i	−0.0218284	−	0.0814648i
$970$	−4.87564	−	9.75129i	−0.156548	−	0.313095i
$971$	16.2224	−	9.36603i	0.520603	−	0.300570i	−0.216579	−	0.976265i	$-0.569490\pi$
$971$	16.2224	−	9.36603i	0.520603	−	0.300570i	0.737181	+	0.675695i	$0.236156\pi$
$972$	−13.5000	+	23.3827i	−0.433013	+	0.750000i
$973$	37.1769	+	32.1962i	1.19184	+	1.03216i
$974$	12.5429	−	7.24167i	0.401902	−	0.232038i
$975$	2.02628	+	2.58142i	0.0648929	+	0.0826715i
$976$	23.3205	−	13.4641i	0.746471	−	0.430975i
$977$	24.3205	+	6.51666i	0.778082	+	0.208486i	0.625939	−	0.779872i	$-0.284716\pi$
$977$	24.3205	+	6.51666i	0.778082	+	0.208486i	0.152143	+	0.988358i	$0.451383\pi$
$978$	−18.8827	−	10.9019i	−0.603802	−	0.348605i
$979$	1.07180	+	1.85641i	0.0342548	+	0.0593310i
$980$	15.4641	+	22.2679i	0.493983	+	0.711324i
$981$			29.1962i			0.932161i
$982$	−7.29423	−	1.95448i	−0.232768	−	0.0623700i
$983$	40.0263	−	40.0263i	1.27664	−	1.27664i	0.334104	−	0.942536i	$-0.391566\pi$
$983$	40.0263	−	40.0263i	1.27664	−	1.27664i	0.942536	−	0.334104i	$-0.108434\pi$
$984$	2.59808	−	9.69615i	0.0828236	−	0.309102i
$985$	−12.0000	−	4.00000i	−0.382352	−	0.127451i
$986$	9.21539	+	5.32051i	0.293478	+	0.169439i
$987$	10.2846	−	21.1865i	0.327363	−	0.674375i
$988$	0.124356	−	0.464102i	0.00395628	−	0.0147650i
$989$	−4.90192	+	2.83013i	−0.155872	+	0.0899928i
$990$	−6.58846	−	2.19615i	−0.209395	−	0.0697983i
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	−0.795474	−	0.605988i	$-0.792778\pi$
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	0.922538	+	0.385906i	$0.126111\pi$
$992$	−27.1244	+	7.26795i	−0.861199	+	0.230758i
$993$	9.00000	−	5.19615i	0.285606	−	0.164895i
$994$	1.73205	−	0.124356i	0.0549373	−	0.00394432i
$995$	36.5885	+	2.19615i	1.15993	+	0.0696227i
$996$	−29.8923	−	8.00962i	−0.947174	−	0.253794i
$997$	24.8038	+	24.8038i	0.785546	+	0.785546i	0.980761	−	0.195215i	$-0.0625404\pi$
$997$	24.8038	+	24.8038i	0.785546	+	0.785546i	−0.195215	+	0.980761i	$0.562540\pi$
$998$	19.1962	−	5.14359i	0.607644	−	0.162818i
$999$	−12.2942	+	45.8827i	−0.388972	+	1.45166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.cg.d.283.1	yes	4
3.2	odd	2		945.2.cj.b.388.1		4
5.2	odd	4		315.2.cg.b.157.1	yes	4
7.5	odd	6		315.2.bs.d.103.1	yes	4
9.2	odd	6		945.2.bv.b.73.1		4
9.7	even	3		315.2.bs.a.178.1	✓	4
15.2	even	4		945.2.cj.c.577.1		4
21.5	even	6		945.2.bv.c.523.1		4
35.12	even	12		315.2.bs.a.292.1	yes	4
45.2	even	12		945.2.bv.c.262.1		4
45.7	odd	12		315.2.bs.d.52.1	yes	4
63.47	even	6		945.2.cj.c.208.1		4
63.61	odd	6		315.2.cg.b.313.1	yes	4
105.47	odd	12		945.2.bv.b.712.1		4
315.47	odd	12		945.2.cj.b.397.1		4
315.187	even	12	inner	315.2.cg.d.187.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.a.178.1	✓	4	9.7	even	3
315.2.bs.a.292.1	yes	4	35.12	even	12
315.2.bs.d.52.1	yes	4	45.7	odd	12
315.2.bs.d.103.1	yes	4	7.5	odd	6
315.2.cg.b.157.1	yes	4	5.2	odd	4
315.2.cg.b.313.1	yes	4	63.61	odd	6
315.2.cg.d.187.1	yes	4	315.187	even	12	inner
315.2.cg.d.283.1	yes	4	1.1	even	1	trivial
945.2.bv.b.73.1		4	9.2	odd	6
945.2.bv.b.712.1		4	105.47	odd	12
945.2.bv.c.262.1		4	45.2	even	12
945.2.bv.c.523.1		4	21.5	even	6
945.2.cj.b.388.1		4	3.2	odd	2
945.2.cj.b.397.1		4	315.47	odd	12
945.2.cj.c.208.1		4	63.47	even	6
945.2.cj.c.577.1		4	15.2	even	4

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.133975 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-0.232051 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +(1.36603 + 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.133975 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.50000 - 0.866025i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-0.232051 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +(1.36603 + 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +(0.866025 - 0.767949i) q^{10} -2.00000 q^{11} +3.00000 q^{12} +(-0.0980762 - 0.366025i) q^{13} +(1.36603 - 0.0980762i) q^{14} +(0.232051 - 3.86603i) q^{15} +(1.23205 - 2.13397i) q^{16} +(-2.00000 + 0.535898i) q^{17} +(-1.09808 + 1.09808i) q^{18} +(0.366025 + 0.633975i) q^{19} +(-3.23205 - 2.13397i) q^{20} +(3.00000 - 3.46410i) q^{21} +(-0.267949 - 1.00000i) q^{22} +(4.46410 + 4.46410i) q^{23} +(0.866025 + 3.23205i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(0.169873 - 0.0980762i) q^{26} +5.19615i q^{27} +(-1.50000 - 4.33013i) q^{28} +(-8.59808 + 4.96410i) q^{29} +(1.96410 - 0.401924i) q^{30} +(-4.73205 + 2.73205i) q^{31} +(4.96410 + 1.33013i) q^{32} +(-3.00000 - 1.73205i) q^{33} +(-0.535898 - 0.928203i) q^{34} +(-5.69615 + 1.59808i) q^{35} +(4.50000 + 2.59808i) q^{36} +(8.83013 + 2.36603i) q^{37} +(-0.267949 + 0.267949i) q^{38} +(0.169873 - 0.633975i) q^{39} +(1.36603 - 4.09808i) q^{40} +(-2.59808 - 1.50000i) q^{41} +(2.13397 + 1.03590i) q^{42} +(-0.232051 + 0.866025i) q^{43} +(-3.00000 + 1.73205i) q^{44} +(3.69615 - 5.59808i) q^{45} +(-1.63397 + 2.83013i) q^{46} +(4.96410 - 1.33013i) q^{47} +(3.69615 - 2.13397i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-2.40192 - 0.964102i) q^{50} +(-3.46410 - 0.928203i) q^{51} +(-0.464102 - 0.464102i) q^{52} +(-1.00000 + 0.267949i) q^{53} +(-2.59808 + 0.696152i) q^{54} +(2.00000 + 4.00000i) q^{55} +(4.23205 - 2.86603i) q^{56} +1.26795i q^{57} +(-3.63397 - 3.63397i) q^{58} +(-4.56218 - 7.90192i) q^{59} +(-3.00000 - 6.00000i) q^{60} +(9.46410 + 5.46410i) q^{61} +(-2.00000 - 2.00000i) q^{62} +(7.50000 - 2.59808i) q^{63} -2.26795i q^{64} +(-0.633975 + 0.562178i) q^{65} +(0.464102 - 1.73205i) q^{66} +(-3.36603 - 0.901924i) q^{67} +(-2.53590 + 2.53590i) q^{68} +(2.83013 + 10.5622i) q^{69} +(-1.56218 - 2.63397i) q^{70} +1.26795 q^{71} +(-1.50000 + 5.59808i) q^{72} +(-3.46410 - 12.9282i) q^{73} +4.73205i q^{74} +(-7.96410 + 3.40192i) q^{75} +(1.09808 + 0.633975i) q^{76} +(-1.00000 + 5.19615i) q^{77} +0.339746 q^{78} +(-9.92820 - 5.73205i) q^{79} +(-5.50000 - 0.330127i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(0.401924 - 1.50000i) q^{82} +(-9.96410 - 2.66987i) q^{83} +(1.50000 - 7.79423i) q^{84} +(3.07180 + 3.46410i) q^{85} -0.464102 q^{86} -17.1962 q^{87} +(-2.73205 - 2.73205i) q^{88} +(-0.535898 - 0.928203i) q^{89} +(3.29423 + 1.09808i) q^{90} +(-1.00000 + 0.0717968i) q^{91} +(10.5622 + 2.83013i) q^{92} -9.46410 q^{93} +(1.33013 + 2.30385i) q^{94} +(0.901924 - 1.36603i) q^{95} +(6.29423 + 6.29423i) q^{96} +(2.43782 - 9.09808i) q^{97} +(0.428203 - 3.59808i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} + 2 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 + 2 * q^8 + 6 * q^9	\( 4 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} + 2 q^{8} + 6 q^{9} - 8 q^{11} + 12 q^{12} + 10 q^{13} + 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} + 6 q^{18} - 2 q^{19} - 6 q^{20} + 12 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{25} + 18 q^{26} - 6 q^{28} - 24 q^{29} - 6 q^{30} - 12 q^{31} + 6 q^{32} - 12 q^{33} - 16 q^{34} - 2 q^{35} + 18 q^{36} + 18 q^{37} - 8 q^{38} + 18 q^{39} + 2 q^{40} + 12 q^{42} + 6 q^{43} - 12 q^{44} - 6 q^{45} - 10 q^{46} + 6 q^{47} - 6 q^{48} - 26 q^{49} - 20 q^{50} + 12 q^{52} - 4 q^{53} + 8 q^{55} + 10 q^{56} - 18 q^{58} + 6 q^{59} - 12 q^{60} + 24 q^{61} - 8 q^{62} + 30 q^{63} - 6 q^{65} - 12 q^{66} - 10 q^{67} - 24 q^{68} - 6 q^{69} + 18 q^{70} + 12 q^{71} - 6 q^{72} - 18 q^{75} - 6 q^{76} - 4 q^{77} + 36 q^{78} - 12 q^{79} - 22 q^{80} - 18 q^{81} + 12 q^{82} - 26 q^{83} + 6 q^{84} + 40 q^{85} + 12 q^{86} - 48 q^{87} - 4 q^{88} - 16 q^{89} - 18 q^{90} - 4 q^{91} + 18 q^{92} - 24 q^{93} - 12 q^{94} + 14 q^{95} - 6 q^{96} + 34 q^{97} - 26 q^{98} - 12 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 + 2 * q^8 + 6 * q^9 - 8 * q^11 + 12 * q^12 + 10 * q^13 + 2 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 + 6 * q^18 - 2 * q^19 - 6 * q^20 + 12 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^25 + 18 * q^26 - 6 * q^28 - 24 * q^29 - 6 * q^30 - 12 * q^31 + 6 * q^32 - 12 * q^33 - 16 * q^34 - 2 * q^35 + 18 * q^36 + 18 * q^37 - 8 * q^38 + 18 * q^39 + 2 * q^40 + 12 * q^42 + 6 * q^43 - 12 * q^44 - 6 * q^45 - 10 * q^46 + 6 * q^47 - 6 * q^48 - 26 * q^49 - 20 * q^50 + 12 * q^52 - 4 * q^53 + 8 * q^55 + 10 * q^56 - 18 * q^58 + 6 * q^59 - 12 * q^60 + 24 * q^61 - 8 * q^62 + 30 * q^63 - 6 * q^65 - 12 * q^66 - 10 * q^67 - 24 * q^68 - 6 * q^69 + 18 * q^70 + 12 * q^71 - 6 * q^72 - 18 * q^75 - 6 * q^76 - 4 * q^77 + 36 * q^78 - 12 * q^79 - 22 * q^80 - 18 * q^81 + 12 * q^82 - 26 * q^83 + 6 * q^84 + 40 * q^85 + 12 * q^86 - 48 * q^87 - 4 * q^88 - 16 * q^89 - 18 * q^90 - 4 * q^91 + 18 * q^92 - 24 * q^93 - 12 * q^94 + 14 * q^95 - 6 * q^96 + 34 * q^97 - 26 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more