LMFDB - Embedded newform 315.2.bz.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(73,315)]

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([0, 9, 2]))

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

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

chi := DirichletCharacter("315.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bz (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:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.73
Dual form			315.2.bz.b.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.86603 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(0.866025 + 2.50000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +O(q^{10})$	\(q+(1.86603 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(0.866025 + 2.50000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(-0.866025 + 4.23205i) q^{10} +(0.366025 - 0.633975i) q^{11} +(2.00000 - 2.00000i) q^{13} +(0.366025 + 5.09808i) q^{14} +(-2.23205 - 3.86603i) q^{16} +(-1.00000 + 0.267949i) q^{17} +(1.36603 + 2.36603i) q^{19} +(-1.73205 + 3.46410i) q^{20} +(1.00000 - 1.00000i) q^{22} +(1.86603 - 6.96410i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(4.73205 - 2.73205i) q^{26} +(-0.866025 + 4.50000i) q^{28} -3.00000i q^{29} +(0.464102 + 0.267949i) q^{31} +(-1.96410 - 7.33013i) q^{32} -2.00000 q^{34} +(-5.46410 + 2.26795i) q^{35} +(4.73205 + 1.26795i) q^{37} +(1.36603 + 5.09808i) q^{38} +(0.767949 - 0.866025i) q^{40} -0.464102i q^{41} +(-5.83013 - 5.83013i) q^{43} +(1.09808 - 0.633975i) q^{44} +(6.96410 - 12.0622i) q^{46} +(-0.169873 + 0.633975i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(-9.56218 - 1.36603i) q^{50} +(4.73205 - 1.26795i) q^{52} +(-6.83013 + 1.83013i) q^{53} +(1.46410 + 0.732051i) q^{55} +(0.598076 - 1.23205i) q^{56} +(1.50000 - 5.59808i) q^{58} +(1.09808 - 1.90192i) q^{59} +(-7.33013 + 4.23205i) q^{61} +(0.732051 + 0.732051i) q^{62} -5.73205i q^{64} +(4.73205 + 4.19615i) q^{65} +(-0.303848 - 1.13397i) q^{67} +(-1.73205 - 0.464102i) q^{68} +(-11.3301 + 1.50000i) q^{70} -4.73205 q^{71} +(0.928203 + 3.46410i) q^{73} +(8.19615 + 4.73205i) q^{74} +4.73205i q^{76} +(1.90192 + 0.366025i) q^{77} +(5.83013 - 3.36603i) q^{79} +(8.33013 - 5.50000i) q^{80} +(0.232051 - 0.866025i) q^{82} +(3.09808 - 3.09808i) q^{83} +(-0.732051 - 2.19615i) q^{85} +(-7.96410 - 13.7942i) q^{86} +(-0.366025 + 0.0980762i) q^{88} +(8.33013 + 14.4282i) q^{89} +(6.73205 + 3.26795i) q^{91} +(8.83013 - 8.83013i) q^{92} +(-0.633975 + 1.09808i) q^{94} +(-5.09808 + 3.36603i) q^{95} +(-7.92820 - 7.92820i) q^{97} +(-12.4282 + 5.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{4} + 4 q^{5} + 2 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 6 * q^4 + 4 * q^5 + 2 * q^8	$ 4 q + 4 q^{2} + 6 q^{4} + 4 q^{5} + 2 q^{8} - 2 q^{11} + 8 q^{13} - 2 q^{14} - 2 q^{16} - 4 q^{17} + 2 q^{19} + 4 q^{22} + 4 q^{23} - 6 q^{25} + 12 q^{26} - 12 q^{31} + 6 q^{32} - 8 q^{34} - 8 q^{35} + 12 q^{37} + 2 q^{38} + 10 q^{40} - 6 q^{43} - 6 q^{44} + 14 q^{46} - 18 q^{47} - 22 q^{49} - 14 q^{50} + 12 q^{52} - 10 q^{53} - 8 q^{55} - 8 q^{56} + 6 q^{58} - 6 q^{59} - 12 q^{61} - 4 q^{62} + 12 q^{65} - 22 q^{67} - 28 q^{70} - 12 q^{71} - 24 q^{73} + 12 q^{74} + 18 q^{77} + 6 q^{79} + 16 q^{80} - 6 q^{82} + 2 q^{83} + 4 q^{85} - 18 q^{86} + 2 q^{88} + 16 q^{89} + 20 q^{91} + 18 q^{92} - 6 q^{94} - 10 q^{95} - 4 q^{97} - 22 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 6 * q^4 + 4 * q^5 + 2 * q^8 - 2 * q^11 + 8 * q^13 - 2 * q^14 - 2 * q^16 - 4 * q^17 + 2 * q^19 + 4 * q^22 + 4 * q^23 - 6 * q^25 + 12 * q^26 - 12 * q^31 + 6 * q^32 - 8 * q^34 - 8 * q^35 + 12 * q^37 + 2 * q^38 + 10 * q^40 - 6 * q^43 - 6 * q^44 + 14 * q^46 - 18 * q^47 - 22 * q^49 - 14 * q^50 + 12 * q^52 - 10 * q^53 - 8 * q^55 - 8 * q^56 + 6 * q^58 - 6 * q^59 - 12 * q^61 - 4 * q^62 + 12 * q^65 - 22 * q^67 - 28 * q^70 - 12 * q^71 - 24 * q^73 + 12 * q^74 + 18 * q^77 + 6 * q^79 + 16 * q^80 - 6 * q^82 + 2 * q^83 + 4 * q^85 - 18 * q^86 + 2 * q^88 + 16 * q^89 + 20 * q^91 + 18 * q^92 - 6 * q^94 - 10 * q^95 - 4 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.86603	+	0.500000i	1.31948	+	0.353553i	0.848783	−	0.528742i	$-0.177336\pi$
$2$	1.86603	+	0.500000i	1.31948	+	0.353553i	0.470696	+	0.882295i	$0.344003\pi$
$3$		0			0
$3$		0			0
$4$	1.50000	+	0.866025i	0.750000	+	0.433013i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$		0			0
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$8$	−0.366025	−	0.366025i	−0.129410	−	0.129410i
$9$		0			0
$10$	−0.866025	+	4.23205i	−0.273861	+	1.33829i
$11$	0.366025	−	0.633975i	0.110361	−	0.191151i	−0.805555	−	0.592521i	$-0.798133\pi$
$11$	0.366025	−	0.633975i	0.110361	−	0.191151i	0.915916	+	0.401371i	$0.131466\pi$
$12$		0			0
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	−0.373094	−	0.927794i	$-0.621703\pi$
$13$	2.00000	−	2.00000i	0.554700	−	0.554700i	0.927794	+	0.373094i	$0.121703\pi$
$14$	0.366025	+	5.09808i	0.0978244	+	1.36252i
$15$		0			0
$16$	−2.23205	−	3.86603i	−0.558013	−	0.966506i
$17$	−1.00000	+	0.267949i	−0.242536	+	0.0649872i	−0.378039	−	0.925790i	$-0.623401\pi$
$17$	−1.00000	+	0.267949i	−0.242536	+	0.0649872i	0.135503	+	0.990777i	$0.456735\pi$
$18$		0			0
$19$	1.36603	+	2.36603i	0.313388	+	0.542803i	0.979093	−	0.203411i	$-0.0652027\pi$
$19$	1.36603	+	2.36603i	0.313388	+	0.542803i	−0.665706	+	0.746214i	$0.731869\pi$
$20$	−1.73205	+	3.46410i	−0.387298	+	0.774597i
$21$		0			0
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	1.86603	−	6.96410i	0.389093	−	1.45212i	−0.442519	−	0.896759i	$-0.645915\pi$
$23$	1.86603	−	6.96410i	0.389093	−	1.45212i	0.831612	−	0.555357i	$-0.187418\pi$
$24$		0			0
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	4.73205	−	2.73205i	0.928032	−	0.535799i
$27$		0			0
$28$	−0.866025	+	4.50000i	−0.163663	+	0.850420i
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$		0			0
$31$	0.464102	+	0.267949i	0.0833551	+	0.0481251i	0.541098	−	0.840959i	$-0.318009\pi$
$31$	0.464102	+	0.267949i	0.0833551	+	0.0481251i	−0.457743	+	0.889085i	$0.651342\pi$
$32$	−1.96410	−	7.33013i	−0.347207	−	1.29580i
$33$		0			0
$34$	−2.00000			−0.342997
$35$	−5.46410	+	2.26795i	−0.923602	+	0.383353i
$36$		0			0
$37$	4.73205	+	1.26795i	0.777944	+	0.208450i	0.625878	−	0.779921i	$-0.284741\pi$
$37$	4.73205	+	1.26795i	0.777944	+	0.208450i	0.152066	+	0.988370i	$0.451407\pi$
$38$	1.36603	+	5.09808i	0.221599	+	0.827017i
$39$		0			0
$40$	0.767949	−	0.866025i	0.121423	−	0.136931i
$41$		−	0.464102i		−	0.0724805i	−0.999343	−	0.0362402i	$-0.988462\pi$
$41$		−	0.464102i		−	0.0724805i	0.999343	−	0.0362402i	$-0.0115382\pi$
$42$		0			0
$43$	−5.83013	−	5.83013i	−0.889086	−	0.889086i	0.105349	−	0.994435i	$-0.466404\pi$
$43$	−5.83013	−	5.83013i	−0.889086	−	0.889086i	−0.994435	+	0.105349i	$0.966404\pi$
$44$	1.09808	−	0.633975i	0.165541	−	0.0955753i
$45$		0			0
$46$	6.96410	−	12.0622i	1.02680	−	1.77847i
$47$	−0.169873	+	0.633975i	−0.0247785	+	0.0924747i	−0.977208	−	0.212285i	$-0.931909\pi$
$47$	−0.169873	+	0.633975i	−0.0247785	+	0.0924747i	0.952429	+	0.304760i	$0.0985762\pi$
$48$		0			0
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$	−9.56218	−	1.36603i	−1.35230	−	0.193185i
$51$		0			0
$52$	4.73205	−	1.26795i	0.656217	−	0.175833i
$53$	−6.83013	+	1.83013i	−0.938190	+	0.251387i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	−6.83013	+	1.83013i	−0.938190	+	0.251387i	−0.242846	+	0.970065i	$0.578081\pi$
$54$		0			0
$55$	1.46410	+	0.732051i	0.197419	+	0.0987097i
$56$	0.598076	−	1.23205i	0.0799213	−	0.164640i
$57$		0			0
$58$	1.50000	−	5.59808i	0.196960	−	0.735063i
$59$	1.09808	−	1.90192i	0.142957	−	0.247609i	−0.785652	−	0.618669i	$-0.787672\pi$
$59$	1.09808	−	1.90192i	0.142957	−	0.247609i	0.928609	+	0.371060i	$0.121005\pi$
$60$		0			0
$61$	−7.33013	+	4.23205i	−0.938527	+	0.541859i	−0.889498	−	0.456939i	$-0.848946\pi$
$61$	−7.33013	+	4.23205i	−0.938527	+	0.541859i	−0.0490285	+	0.998797i	$0.515613\pi$
$62$	0.732051	+	0.732051i	0.0929705	+	0.0929705i
$63$		0			0
$64$		−	5.73205i		−	0.716506i
$65$	4.73205	+	4.19615i	0.586939	+	0.520469i
$66$		0			0
$67$	−0.303848	−	1.13397i	−0.0371209	−	0.138537i	0.944878	−	0.327421i	$-0.106180\pi$
$67$	−0.303848	−	1.13397i	−0.0371209	−	0.138537i	−0.981999	+	0.188884i	$0.939513\pi$
$68$	−1.73205	−	0.464102i	−0.210042	−	0.0562806i
$69$		0			0
$70$	−11.3301	+	1.50000i	−1.35421	+	0.179284i
$71$	−4.73205			−0.561591			−0.280796	−	0.959768i	$-0.590598\pi$
$71$	−4.73205			−0.561591			−0.280796	+	0.959768i	$0.590598\pi$
$72$		0			0
$73$	0.928203	+	3.46410i	0.108638	+	0.405442i	0.998732	−	0.0503336i	$-0.0160285\pi$
$73$	0.928203	+	3.46410i	0.108638	+	0.405442i	−0.890094	+	0.455776i	$0.849362\pi$
$74$	8.19615	+	4.73205i	0.952783	+	0.550090i
$75$		0			0
$76$			4.73205i			0.542803i
$77$	1.90192	+	0.366025i	0.216744	+	0.0417125i
$78$		0			0
$79$	5.83013	−	3.36603i	0.655941	−	0.378707i	−0.134788	−	0.990874i	$-0.543035\pi$
$79$	5.83013	−	3.36603i	0.655941	−	0.378707i	0.790728	+	0.612167i	$0.209702\pi$
$80$	8.33013	−	5.50000i	0.931337	−	0.614919i
$81$		0			0
$82$	0.232051	−	0.866025i	0.0256257	−	0.0956365i
$83$	3.09808	−	3.09808i	0.340058	−	0.340058i	−0.516331	−	0.856389i	$-0.672703\pi$
$83$	3.09808	−	3.09808i	0.340058	−	0.340058i	0.856389	+	0.516331i	$0.172703\pi$
$84$		0			0
$85$	−0.732051	−	2.19615i	−0.0794021	−	0.238206i
$86$	−7.96410	−	13.7942i	−0.858791	−	1.48747i
$87$		0			0
$88$	−0.366025	+	0.0980762i	−0.0390184	+	0.0104550i
$89$	8.33013	+	14.4282i	0.882992	+	1.52939i	0.847998	+	0.529999i	$0.177808\pi$
$89$	8.33013	+	14.4282i	0.882992	+	1.52939i	0.0349934	+	0.999388i	$0.488859\pi$
$90$		0			0
$91$	6.73205	+	3.26795i	0.705711	+	0.342574i
$92$	8.83013	−	8.83013i	0.920604	−	0.920604i
$93$		0			0
$94$	−0.633975	+	1.09808i	−0.0653895	+	0.113258i
$95$	−5.09808	+	3.36603i	−0.523052	+	0.345347i
$96$		0			0
$97$	−7.92820	−	7.92820i	−0.804987	−	0.804987i	0.178883	−	0.983870i	$-0.442752\pi$
$97$	−7.92820	−	7.92820i	−0.804987	−	0.804987i	−0.983870	+	0.178883i	$0.942752\pi$
$98$	−12.4282	+	5.33013i	−1.25544	+	0.538424i
$99$		0			0
$100$	−7.96410	−	3.40192i	−0.796410	−	0.340192i
$101$	10.1603	+	5.86603i	1.01098	+	0.583691i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	10.1603	+	5.86603i	1.01098	+	0.583691i	0.0995037	+	0.995037i	$0.468274\pi$
$102$		0			0
$103$	−2.23205	−	0.598076i	−0.219931	−	0.0589302i	0.147171	−	0.989111i	$-0.452983\pi$
$103$	−2.23205	−	0.598076i	−0.219931	−	0.0589302i	−0.367102	+	0.930181i	$0.619650\pi$
$104$	−1.46410			−0.143567
$105$		0			0
$106$	−13.6603			−1.32680
$107$	8.59808	+	2.30385i	0.831207	+	0.222721i	0.649240	−	0.760583i	$-0.275087\pi$
$107$	8.59808	+	2.30385i	0.831207	+	0.222721i	0.181967	+	0.983305i	$0.441754\pi$
$108$		0			0
$109$	12.2321	+	7.06218i	1.17162	+	0.676434i	0.954061	−	0.299614i	$-0.0968578\pi$
$109$	12.2321	+	7.06218i	1.17162	+	0.676434i	0.217557	+	0.976048i	$0.430191\pi$
$110$	2.36603	+	2.09808i	0.225592	+	0.200044i
$111$		0			0
$112$	7.73205	−	8.92820i	0.730610	−	0.843636i
$113$	4.26795	+	4.26795i	0.401495	+	0.401495i	0.878760	−	0.477265i	$-0.158372\pi$
$113$	4.26795	+	4.26795i	0.401495	+	0.401495i	−0.477265	+	0.878760i	$0.658372\pi$
$114$		0			0
$115$	15.7942	+	3.23205i	1.47282	+	0.301390i
$116$	2.59808	−	4.50000i	0.241225	−	0.417815i
$117$		0			0
$118$	3.00000	−	3.00000i	0.276172	−	0.276172i
$119$	−1.53590	−	2.26795i	−0.140796	−	0.207903i
$120$		0			0
$121$	5.23205	+	9.06218i	0.475641	+	0.823834i
$122$	−15.7942	+	4.23205i	−1.42994	+	0.383152i
$123$		0			0
$124$	0.464102	+	0.803848i	0.0416776	+	0.0721876i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	−6.46410	+	6.46410i	−0.573596	+	0.573596i	−0.933132	−	0.359535i	$-0.882935\pi$
$127$	−6.46410	+	6.46410i	−0.573596	+	0.573596i	0.359535	+	0.933132i	$0.382935\pi$
$128$	−1.06218	+	3.96410i	−0.0938841	+	0.350380i
$129$		0			0
$130$	6.73205	+	10.1962i	0.590440	+	0.894262i
$131$	−7.39230	+	4.26795i	−0.645869	+	0.372892i	−0.786872	−	0.617117i	$-0.788301\pi$
$131$	−7.39230	+	4.26795i	−0.645869	+	0.372892i	0.141003	+	0.990009i	$0.454967\pi$
$132$		0			0
$133$	−4.73205	+	5.46410i	−0.410321	+	0.473798i
$134$		−	2.26795i		−	0.195921i
$135$		0			0
$136$	0.464102	+	0.267949i	0.0397964	+	0.0229765i
$137$	−2.80385	−	10.4641i	−0.239549	−	0.894009i	−0.976045	−	0.217567i	$-0.930188\pi$
$137$	−2.80385	−	10.4641i	−0.239549	−	0.894009i	0.736496	−	0.676441i	$-0.236479\pi$
$138$		0			0
$139$	−11.6603			−0.989010			−0.494505	−	0.869175i	$-0.664651\pi$
$139$	−11.6603			−0.989010			−0.494505	+	0.869175i	$0.664651\pi$
$140$	−10.1603	−	1.33013i	−0.858698	−	0.112416i
$141$		0			0
$142$	−8.83013	−	2.36603i	−0.741008	−	0.198552i
$143$	−0.535898	−	2.00000i	−0.0448141	−	0.167248i
$144$		0			0
$145$	6.69615	−	0.401924i	0.556085	−	0.0333780i
$146$			6.92820i			0.573382i
$147$		0			0
$148$	6.00000	+	6.00000i	0.493197	+	0.493197i
$149$	−9.69615	+	5.59808i	−0.794340	+	0.458612i	−0.841488	−	0.540276i	$-0.818320\pi$
$149$	−9.69615	+	5.59808i	−0.794340	+	0.458612i	0.0471484	+	0.998888i	$0.484987\pi$
$150$		0			0
$151$	6.92820	−	12.0000i	0.563809	−	0.976546i	−0.433350	−	0.901226i	$-0.642669\pi$
$151$	6.92820	−	12.0000i	0.563809	−	0.976546i	0.997159	−	0.0753205i	$-0.0239980\pi$
$152$	0.366025	−	1.36603i	0.0296886	−	0.110799i
$153$		0			0
$154$	3.36603	+	1.63397i	0.271242	+	0.131669i
$155$	−0.535898	+	1.07180i	−0.0430444	+	0.0860888i
$156$		0			0
$157$	−23.7583	+	6.36603i	−1.89612	+	0.508064i	−0.898513	+	0.438948i	$0.855351\pi$
$157$	−23.7583	+	6.36603i	−1.89612	+	0.508064i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	12.5622	−	3.36603i	0.999393	−	0.267787i
$159$		0			0
$160$	16.0981	−	5.36603i	1.27266	−	0.424222i
$161$	19.0263	−	1.36603i	1.49948	−	0.107658i
$162$		0			0
$163$	1.43782	−	5.36603i	0.112619	−	0.420300i	−0.886479	−	0.462769i	$-0.846856\pi$
$163$	1.43782	−	5.36603i	0.112619	−	0.420300i	0.999098	+	0.0424696i	$0.0135226\pi$
$164$	0.401924	−	0.696152i	0.0313850	−	0.0543604i
$165$		0			0
$166$	7.33013	−	4.23205i	0.568928	−	0.328471i
$167$	−10.7583	−	10.7583i	−0.832505	−	0.832505i	0.155354	−	0.987859i	$-0.450348\pi$
$167$	−10.7583	−	10.7583i	−0.832505	−	0.832505i	−0.987859	+	0.155354i	$0.950348\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$	−0.267949	−	4.46410i	−0.0205508	−	0.342381i
$171$		0			0
$172$	−3.69615	−	13.7942i	−0.281829	−	1.05180i
$173$	−22.6603	−	6.07180i	−1.72283	−	0.461630i	−0.744317	−	0.667827i	$-0.767225\pi$
$173$	−22.6603	−	6.07180i	−1.72283	−	0.461630i	−0.978511	+	0.206197i	$0.933891\pi$
$174$		0			0
$175$	−5.79423	−	11.8923i	−0.438003	−	0.898974i
$176$	−3.26795			−0.246331
$177$		0			0
$178$	8.33013	+	31.0885i	0.624369	+	2.33018i
$179$	17.1962	+	9.92820i	1.28530	+	0.742069i	0.977812	−	0.209483i	$-0.0671781\pi$
$179$	17.1962	+	9.92820i	1.28530	+	0.742069i	0.307488	+	0.951552i	$0.400511\pi$
$180$		0			0
$181$			9.19615i			0.683545i	0.939783	+	0.341772i	$0.111027\pi$
$181$			9.19615i			0.683545i	−0.939783	+	0.341772i	$0.888973\pi$
$182$	10.9282	+	9.46410i	0.810052	+	0.701526i
$183$		0			0
$184$	−3.23205	+	1.86603i	−0.238270	+	0.137565i
$185$	−2.19615	+	10.7321i	−0.161464	+	0.789036i
$186$		0			0
$187$	−0.196152	+	0.732051i	−0.0143441	+	0.0535329i
$188$	−0.803848	+	0.803848i	−0.0586266	+	0.0586266i
$189$		0			0
$190$	−11.1962	+	3.73205i	−0.812254	+	0.270751i
$191$	8.36603	+	14.4904i	0.605344	+	1.04849i	0.991997	+	0.126262i	$0.0402979\pi$
$191$	8.36603	+	14.4904i	0.605344	+	1.04849i	−0.386653	+	0.922225i	$0.626369\pi$
$192$		0			0
$193$	−3.09808	+	0.830127i	−0.223004	+	0.0597539i	−0.368591	−	0.929592i	$-0.620160\pi$
$193$	−3.09808	+	0.830127i	−0.223004	+	0.0597539i	0.145587	+	0.989346i	$0.453493\pi$
$194$	−10.8301	−	18.7583i	−0.777558	−	1.34677i
$195$		0			0
$196$	−12.0000	+	1.73205i	−0.857143	+	0.123718i
$197$	−14.1244	+	14.1244i	−1.00632	+	1.00632i	−0.00633876	+	0.999980i	$0.502018\pi$
$197$	−14.1244	+	14.1244i	−1.00632	+	1.00632i	−0.999980	+	0.00633876i	$0.997982\pi$
$198$		0			0
$199$	12.4641	−	21.5885i	0.883557	−	1.53037i	0.0361978	−	0.999345i	$-0.488475\pi$
$199$	12.4641	−	21.5885i	0.883557	−	1.53037i	0.847359	−	0.531021i	$-0.178191\pi$
$200$	2.03590	+	1.59808i	0.143960	+	0.113001i
$201$		0			0
$202$	16.0263	+	16.0263i	1.12761	+	1.12761i
$203$	7.50000	−	2.59808i	0.526397	−	0.182349i
$204$		0			0
$205$	1.03590	−	0.0621778i	0.0723503	−	0.00434269i
$206$	−3.86603	−	2.23205i	−0.269359	−	0.155514i
$207$		0			0
$208$	−12.1962	−	3.26795i	−0.845651	−	0.226592i
$209$	2.00000			0.138343
$210$		0			0
$211$	10.1962			0.701932			0.350966	−	0.936388i	$-0.385853\pi$
$211$	10.1962			0.701932			0.350966	+	0.936388i	$0.385853\pi$
$212$	−11.8301	−	3.16987i	−0.812496	−	0.217708i
$213$		0			0
$214$	14.8923	+	8.59808i	1.01802	+	0.587752i
$215$	12.2321	−	13.7942i	0.834219	−	0.940759i
$216$		0			0
$217$	−0.267949	+	1.39230i	−0.0181896	+	0.0945158i
$218$	19.2942	+	19.2942i	1.30677	+	1.30677i
$219$		0			0
$220$	1.56218	+	2.36603i	0.105322	+	0.159517i
$221$	−1.46410	+	2.53590i	−0.0984861	+	0.170583i
$222$		0			0
$223$	6.12436	−	6.12436i	0.410117	−	0.410117i	−0.471662	−	0.881779i	$-0.656346\pi$
$223$	6.12436	−	6.12436i	0.410117	−	0.410117i	0.881779	+	0.471662i	$0.156346\pi$
$224$	16.6244	−	11.2583i	1.11076	−	0.752229i
$225$		0			0
$226$	5.83013	+	10.0981i	0.387814	+	0.671714i
$227$	−0.0980762	+	0.0262794i	−0.00650955	+	0.00174423i	−0.262072	−	0.965048i	$-0.584406\pi$
$227$	−0.0980762	+	0.0262794i	−0.00650955	+	0.00174423i	0.255563	+	0.966792i	$0.417739\pi$
$228$		0			0
$229$	−1.19615	−	2.07180i	−0.0790440	−	0.136908i	0.823794	−	0.566890i	$-0.191853\pi$
$229$	−1.19615	−	2.07180i	−0.0790440	−	0.136908i	−0.902838	+	0.429981i	$0.858520\pi$
$230$	27.8564	+	13.9282i	1.83680	+	0.918399i
$231$		0			0
$232$	−1.09808	+	1.09808i	−0.0720922	+	0.0720922i
$233$	0.464102	−	1.73205i	0.0304043	−	0.113470i	−0.949056	−	0.315107i	$-0.897959\pi$
$233$	0.464102	−	1.73205i	0.0304043	−	0.113470i	0.979460	+	0.201637i	$0.0646261\pi$
$234$		0			0
$235$	−1.43782	−	0.294229i	−0.0937932	−	0.0191934i
$236$	3.29423	−	1.90192i	0.214436	−	0.123805i
$237$		0			0
$238$	−1.73205	−	5.00000i	−0.112272	−	0.324102i
$239$		−	18.3923i		−	1.18970i	−0.803837	−	0.594850i	$-0.797212\pi$
$239$		−	18.3923i		−	1.18970i	0.803837	−	0.594850i	$-0.202788\pi$
$240$		0			0
$241$	14.5359	+	8.39230i	0.936340	+	0.540596i	0.888811	−	0.458274i	$-0.151532\pi$
$241$	14.5359	+	8.39230i	0.936340	+	0.540596i	0.0475286	+	0.998870i	$0.484865\pi$
$242$	5.23205	+	19.5263i	0.336329	+	1.25520i
$243$		0			0
$244$	−14.6603			−0.938527
$245$	−10.4019	−	11.6962i	−0.664555	−	0.747240i
$246$		0			0
$247$	7.46410	+	2.00000i	0.474929	+	0.127257i
$248$	−0.0717968	−	0.267949i	−0.00455910	−	0.0170148i
$249$		0			0
$250$	1.76795	−	21.5263i	0.111815	−	1.36144i
$251$			5.85641i			0.369653i	0.982771	+	0.184827i	$0.0591723\pi$
$251$			5.85641i			0.369653i	−0.982771	+	0.184827i	$0.940828\pi$
$252$		0			0
$253$	−3.73205	−	3.73205i	−0.234632	−	0.234632i
$254$	−15.2942	+	8.83013i	−0.959645	+	0.554051i
$255$		0			0
$256$	−9.69615	+	16.7942i	−0.606010	+	1.04964i
$257$	−0.732051	+	2.73205i	−0.0456641	+	0.170421i	−0.984992	−	0.172600i	$-0.944783\pi$
$257$	−0.732051	+	2.73205i	−0.0456641	+	0.170421i	0.939328	+	0.343020i	$0.111450\pi$
$258$		0			0
$259$	0.928203	+	12.9282i	0.0576757	+	0.803319i
$260$	3.46410	+	10.3923i	0.214834	+	0.644503i
$261$		0			0
$262$	−15.9282	+	4.26795i	−0.984048	+	0.263675i
$263$	8.06218	−	2.16025i	0.497135	−	0.133207i	−0.00153494	−	0.999999i	$-0.500489\pi$
$263$	8.06218	−	2.16025i	0.497135	−	0.133207i	0.498670	+	0.866792i	$0.333822\pi$
$264$		0			0
$265$	−5.00000	−	15.0000i	−0.307148	−	0.921443i
$266$	−11.5622	+	7.83013i	−0.708923	+	0.480096i
$267$		0			0
$268$	0.526279	−	1.96410i	0.0321476	−	0.119977i
$269$	−2.42820	+	4.20577i	−0.148050	+	0.256430i	−0.930507	−	0.366275i	$-0.880633\pi$
$269$	−2.42820	+	4.20577i	−0.148050	+	0.256430i	0.782457	+	0.622705i	$0.213966\pi$
$270$		0			0
$271$	−21.4186	+	12.3660i	−1.30109	+	0.751183i	−0.980590	−	0.196067i	$-0.937183\pi$
$271$	−21.4186	+	12.3660i	−1.30109	+	0.751183i	−0.320496	+	0.947250i	$0.603850\pi$
$272$	3.26795	+	3.26795i	0.198149	+	0.198149i
$273$		0			0
$274$		−	20.9282i		−	1.26432i
$275$	−1.43782	+	3.36603i	−0.0867039	+	0.202979i
$276$		0			0
$277$	−5.19615	−	19.3923i	−0.312207	−	1.16517i	−0.926562	−	0.376141i	$-0.877251\pi$
$277$	−5.19615	−	19.3923i	−0.312207	−	1.16517i	0.614356	−	0.789029i	$-0.289416\pi$
$278$	−21.7583	−	5.83013i	−1.30498	−	0.349668i
$279$		0			0
$280$	2.83013	+	1.16987i	0.169132	+	0.0699133i
$281$	−12.9282			−0.771232			−0.385616	−	0.922659i	$-0.626011\pi$
$281$	−12.9282			−0.771232			−0.385616	+	0.922659i	$0.626011\pi$
$282$		0			0
$283$	−7.09808	−	26.4904i	−0.421937	−	1.57469i	−0.770523	−	0.637413i	$-0.780005\pi$
$283$	−7.09808	−	26.4904i	−0.421937	−	1.57469i	0.348586	−	0.937277i	$-0.386662\pi$
$284$	−7.09808	−	4.09808i	−0.421193	−	0.243176i
$285$		0			0
$286$		−	4.00000i		−	0.236525i
$287$	1.16025	−	0.401924i	0.0684876	−	0.0237248i
$288$		0			0
$289$	−13.7942	+	7.96410i	−0.811425	+	0.468477i
$290$	12.6962	+	2.59808i	0.745544	+	0.152564i
$291$		0			0
$292$	−1.60770	+	6.00000i	−0.0940832	+	0.351123i
$293$	18.3923	−	18.3923i	1.07449	−	1.07449i	0.0774974	−	0.996993i	$-0.475307\pi$
$293$	18.3923	−	18.3923i	1.07449	−	1.07449i	0.996993	−	0.0774974i	$-0.0246929\pi$
$294$		0			0
$295$	4.39230	+	2.19615i	0.255730	+	0.127865i
$296$	−1.26795	−	2.19615i	−0.0736980	−	0.127649i
$297$		0			0
$298$	−20.8923	+	5.59808i	−1.21026	+	0.324288i
$299$	−10.1962	−	17.6603i	−0.589659	−	1.02132i
$300$		0			0
$301$	9.52628	−	19.6244i	0.549086	−	1.13113i
$302$	18.9282	−	18.9282i	1.08920	−	1.08920i
$303$		0			0
$304$	6.09808	−	10.5622i	0.349749	−	0.605782i
$305$	−10.4282	−	15.7942i	−0.597117	−	0.904375i
$306$		0			0
$307$	9.29423	+	9.29423i	0.530450	+	0.530450i	0.920706	−	0.390257i	$-0.127614\pi$
$307$	9.29423	+	9.29423i	0.530450	+	0.530450i	−0.390257	+	0.920706i	$0.627614\pi$
$308$	2.53590	+	2.19615i	0.144496	+	0.125137i
$309$		0			0
$310$	−1.53590	+	1.73205i	−0.0872332	+	0.0983739i
$311$	−16.2224	−	9.36603i	−0.919890	−	0.531099i	−0.0362898	−	0.999341i	$-0.511554\pi$
$311$	−16.2224	−	9.36603i	−0.919890	−	0.531099i	−0.883600	+	0.468243i	$0.844887\pi$
$312$		0			0
$313$	19.3923	+	5.19615i	1.09612	+	0.293704i	0.761183	−	0.648537i	$-0.224619\pi$
$313$	19.3923	+	5.19615i	1.09612	+	0.293704i	0.334935	+	0.942241i	$0.391286\pi$
$314$	−47.5167			−2.68152
$315$		0			0
$316$	11.6603			0.655941
$317$	−4.46410	−	1.19615i	−0.250729	−	0.0671826i	0.131265	−	0.991347i	$-0.458096\pi$
$317$	−4.46410	−	1.19615i	−0.250729	−	0.0671826i	−0.381994	+	0.924165i	$0.624763\pi$
$318$		0			0
$319$	−1.90192	−	1.09808i	−0.106487	−	0.0614805i
$320$	12.7942	−	0.767949i	0.715219	−	0.0429297i
$321$		0			0
$322$	36.1865	+	6.96410i	2.01660	+	0.388094i
$323$	−2.00000	−	2.00000i	−0.111283	−	0.111283i
$324$		0			0
$325$	−8.73205	+	11.1244i	−0.484367	+	0.617068i
$326$	5.36603	−	9.29423i	0.297197	−	0.514760i
$327$		0			0
$328$	−0.169873	+	0.169873i	−0.00937967	+	0.00937967i
$329$	−1.73205	+	0.124356i	−0.0954911	+	0.00685595i
$330$		0			0
$331$	−12.9282	−	22.3923i	−0.710598	−	1.23079i	−0.964633	−	0.263597i	$-0.915091\pi$
$331$	−12.9282	−	22.3923i	−0.710598	−	1.23079i	0.254035	−	0.967195i	$-0.418242\pi$
$332$	7.33013	−	1.96410i	0.402293	−	0.107794i
$333$		0			0
$334$	−14.6962	−	25.4545i	−0.804138	−	1.39281i
$335$	2.49038	−	0.830127i	0.136064	−	0.0453547i
$336$		0			0
$337$	16.4641	−	16.4641i	0.896857	−	0.896857i	−0.0983001	−	0.995157i	$-0.531340\pi$
$337$	16.4641	−	16.4641i	0.896857	−	0.896857i	0.995157	+	0.0983001i	$0.0313405\pi$
$338$	−2.50000	+	9.33013i	−0.135982	+	0.507492i
$339$		0			0
$340$	0.803848	−	3.92820i	0.0435948	−	0.213037i
$341$	0.339746	−	0.196152i	0.0183983	−	0.0106222i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$			4.26795i			0.230112i
$345$		0			0
$346$	−39.2487	−	22.6603i	−2.11002	−	1.21822i
$347$	2.08846	+	7.79423i	0.112114	+	0.418416i	0.999055	−	0.0434674i	$-0.0138405\pi$
$347$	2.08846	+	7.79423i	0.112114	+	0.418416i	−0.886941	+	0.461884i	$0.847174\pi$
$348$		0			0
$349$	−9.73205			−0.520945			−0.260472	−	0.965481i	$-0.583878\pi$
$349$	−9.73205			−0.520945			−0.260472	+	0.965481i	$0.583878\pi$
$350$	−4.86603	−	25.0885i	−0.260100	−	1.34103i
$351$		0			0
$352$	−5.36603	−	1.43782i	−0.286010	−	0.0766362i
$353$	−1.43782	−	5.36603i	−0.0765276	−	0.285605i	0.917048	−	0.398777i	$-0.130565\pi$
$353$	−1.43782	−	5.36603i	−0.0765276	−	0.285605i	−0.993575	+	0.113173i	$0.963899\pi$
$354$		0			0
$355$	−0.633975	−	10.5622i	−0.0336479	−	0.560582i
$356$			28.8564i			1.52939i
$357$		0			0
$358$	27.1244	+	27.1244i	1.43357	+	1.43357i
$359$	12.3397	−	7.12436i	0.651267	−	0.376009i	−0.137675	−	0.990478i	$-0.543963\pi$
$359$	12.3397	−	7.12436i	0.651267	−	0.376009i	0.788941	+	0.614468i	$0.210629\pi$
$360$		0			0
$361$	5.76795	−	9.99038i	0.303576	−	0.525810i
$362$	−4.59808	+	17.1603i	−0.241670	+	0.901923i
$363$		0			0
$364$	7.26795	+	10.7321i	0.380944	+	0.562512i
$365$	−7.60770	+	2.53590i	−0.398205	+	0.132735i
$366$		0			0
$367$	1.86603	−	0.500000i	0.0974057	−	0.0260998i	−0.209787	−	0.977747i	$-0.567277\pi$
$367$	1.86603	−	0.500000i	0.0974057	−	0.0260998i	0.307193	+	0.951647i	$0.400610\pi$
$368$	−31.0885	+	8.33013i	−1.62060	+	0.434238i
$369$		0			0
$370$	−9.46410	+	18.9282i	−0.492015	+	0.984030i
$371$	−10.4904	−	15.4904i	−0.544633	−	0.804221i
$372$		0			0
$373$	−4.26795	+	15.9282i	−0.220986	+	0.824731i	0.762987	+	0.646414i	$0.223732\pi$
$373$	−4.26795	+	15.9282i	−0.220986	+	0.824731i	−0.983973	+	0.178317i	$0.942935\pi$
$374$	−0.732051	+	1.26795i	−0.0378534	+	0.0655641i
$375$		0			0
$376$	0.294229	−	0.169873i	0.0151737	−	0.00876053i
$377$	−6.00000	−	6.00000i	−0.309016	−	0.309016i
$378$		0			0
$379$		−	19.6603i		−	1.00988i	−0.863155	−	0.504940i	$-0.831515\pi$
$379$		−	19.6603i		−	1.00988i	0.863155	−	0.504940i	$-0.168485\pi$
$380$	−10.5622	+	0.633975i	−0.541828	+	0.0325222i
$381$		0			0
$382$	8.36603	+	31.2224i	0.428043	+	1.59748i
$383$	28.1865	+	7.55256i	1.44026	+	0.385918i	0.892626	−	0.450797i	$-0.148860\pi$
$383$	28.1865	+	7.55256i	1.44026	+	0.385918i	0.547638	+	0.836715i	$0.315527\pi$
$384$		0			0
$385$	−0.562178	+	4.29423i	−0.0286512	+	0.218854i
$386$	−6.19615			−0.315376
$387$		0			0
$388$	−5.02628	−	18.7583i	−0.255171	−	0.952310i
$389$	−7.73205	−	4.46410i	−0.392031	−	0.226339i	0.291009	−	0.956720i	$-0.406009\pi$
$389$	−7.73205	−	4.46410i	−0.392031	−	0.226339i	−0.683040	+	0.730381i	$0.739342\pi$
$390$		0			0
$391$			7.46410i			0.377476i
$392$	3.59808	+	0.428203i	0.181730	+	0.0216275i
$393$		0			0
$394$	−33.4186	+	19.2942i	−1.68360	+	0.972029i
$395$	8.29423	+	12.5622i	0.417328	+	0.632072i
$396$		0			0
$397$	−5.36603	+	20.0263i	−0.269313	+	1.00509i	0.690244	+	0.723577i	$0.257503\pi$
$397$	−5.36603	+	20.0263i	−0.269313	+	1.00509i	−0.959557	+	0.281514i	$0.909164\pi$
$398$	34.0526	−	34.0526i	1.70690	−	1.70690i
$399$		0			0
$400$	13.3923	+	17.8564i	0.669615	+	0.892820i
$401$	5.50000	+	9.52628i	0.274657	+	0.475720i	0.970049	−	0.242911i	$-0.0781024\pi$
$401$	5.50000	+	9.52628i	0.274657	+	0.475720i	−0.695392	+	0.718631i	$0.744769\pi$
$402$		0			0
$403$	1.46410	−	0.392305i	0.0729321	−	0.0195421i
$404$	10.1603	+	17.5981i	0.505492	+	0.875537i
$405$		0			0
$406$	15.2942	−	1.09808i	0.759040	−	0.0544966i
$407$	2.53590	−	2.53590i	0.125700	−	0.125700i
$408$		0			0
$409$	−3.42820	+	5.93782i	−0.169514	+	0.293606i	−0.938249	−	0.345961i	$-0.887553\pi$
$409$	−3.42820	+	5.93782i	−0.169514	+	0.293606i	0.768735	+	0.639567i	$0.220886\pi$
$410$	1.96410	+	0.401924i	0.0970001	+	0.0198496i
$411$		0			0
$412$	−2.83013	−	2.83013i	−0.139430	−	0.139430i
$413$	5.70577	+	1.09808i	0.280763	+	0.0540328i
$414$		0			0
$415$	7.33013	+	6.50000i	0.359822	+	0.319072i
$416$	−18.5885	−	10.7321i	−0.911374	−	0.526182i
$417$		0			0
$418$	3.73205	+	1.00000i	0.182541	+	0.0489116i
$419$	−3.85641			−0.188398			−0.0941989	−	0.995553i	$-0.530029\pi$
$419$	−3.85641			−0.188398			−0.0941989	+	0.995553i	$0.530029\pi$
$420$		0			0
$421$	−34.6603			−1.68924			−0.844619	−	0.535368i	$-0.820173\pi$
$421$	−34.6603			−1.68924			−0.844619	+	0.535368i	$0.820173\pi$
$422$	19.0263	+	5.09808i	0.926185	+	0.248170i
$423$		0			0
$424$	3.16987	+	1.83013i	0.153943	+	0.0888788i
$425$	4.80385	−	1.92820i	0.233021	−	0.0935316i
$426$		0			0
$427$	−16.9282	−	14.6603i	−0.819213	−	0.709459i
$428$	10.9019	+	10.9019i	0.526964	+	0.526964i
$429$		0			0
$430$	29.7224	−	19.6244i	1.43334	−	0.946370i
$431$	−2.09808	+	3.63397i	−0.101061	+	0.175042i	−0.912122	−	0.409919i	$-0.865557\pi$
$431$	−2.09808	+	3.63397i	−0.101061	+	0.175042i	0.811061	+	0.584961i	$0.198890\pi$
$432$		0			0
$433$	24.4641	−	24.4641i	1.17567	−	1.17567i	0.194833	−	0.980836i	$-0.437583\pi$
$433$	24.4641	−	24.4641i	1.17567	−	1.17567i	0.980836	−	0.194833i	$-0.0624166\pi$
$434$	−1.19615	+	2.46410i	−0.0574172	+	0.118281i
$435$		0			0
$436$	12.2321	+	21.1865i	0.585809	+	1.01465i
$437$	19.0263	−	5.09808i	0.910150	−	0.243874i
$438$		0			0
$439$	15.6603	+	27.1244i	0.747423	+	1.29457i	0.949054	+	0.315113i	$0.102043\pi$
$439$	15.6603	+	27.1244i	0.747423	+	1.29457i	−0.201631	+	0.979462i	$0.564624\pi$
$440$	−0.267949	−	0.803848i	−0.0127740	−	0.0383219i
$441$		0			0
$442$	−4.00000	+	4.00000i	−0.190261	+	0.190261i
$443$	−0.937822	+	3.50000i	−0.0445573	+	0.166290i	−0.984619	−	0.174713i	$-0.944100\pi$
$443$	−0.937822	+	3.50000i	−0.0445573	+	0.166290i	0.940062	+	0.341003i	$0.110767\pi$
$444$		0			0
$445$	−31.0885	+	20.5263i	−1.47373	+	0.973039i
$446$	14.4904	−	8.36603i	0.686139	−	0.396143i
$447$		0			0
$448$	14.3301	−	4.96410i	0.677035	−	0.234532i
$449$			5.05256i			0.238445i	0.992868	+	0.119222i	$0.0380402\pi$
$449$			5.05256i			0.238445i	−0.992868	+	0.119222i	$0.961960\pi$
$450$		0			0
$451$	−0.294229	−	0.169873i	−0.0138547	−	0.00799901i
$452$	2.70577	+	10.0981i	0.127269	+	0.474974i
$453$		0			0
$454$	−0.196152			−0.00920589
$455$	−6.39230	+	15.4641i	−0.299676	+	0.724968i
$456$		0			0
$457$	30.8564	+	8.26795i	1.44340	+	0.386758i	0.893724	−	0.448618i	$-0.148084\pi$
$457$	30.8564	+	8.26795i	1.44340	+	0.386758i	0.549678	+	0.835376i	$0.314750\pi$
$458$	−1.19615	−	4.46410i	−0.0558925	−	0.208594i
$459$		0			0
$460$	20.8923	+	18.5263i	0.974109	+	0.863792i
$461$			26.3923i			1.22921i	0.788834	+	0.614606i	$0.210685\pi$
$461$			26.3923i			1.22921i	−0.788834	+	0.614606i	$0.789315\pi$
$462$		0			0
$463$	17.7583	+	17.7583i	0.825300	+	0.825300i	0.986862	−	0.161563i	$-0.0516534\pi$
$463$	17.7583	+	17.7583i	0.825300	+	0.825300i	−0.161563	+	0.986862i	$0.551653\pi$
$464$	−11.5981	+	6.69615i	−0.538427	+	0.310861i
$465$		0			0
$466$	1.73205	−	3.00000i	0.0802357	−	0.138972i
$467$	−8.40192	+	31.3564i	−0.388795	+	1.45100i	0.443303	+	0.896372i	$0.353807\pi$
$467$	−8.40192	+	31.3564i	−0.388795	+	1.45100i	−0.832097	+	0.554629i	$0.812860\pi$
$468$		0			0
$469$	2.57180	−	1.74167i	0.118755	−	0.0804228i
$470$	−2.53590	−	1.26795i	−0.116972	−	0.0584861i
$471$		0			0
$472$	−1.09808	+	0.294229i	−0.0505431	+	0.0135430i
$473$	−5.83013	+	1.56218i	−0.268070	+	0.0718290i
$474$		0			0
$475$	−8.19615	−	10.9282i	−0.376065	−	0.501420i
$476$	−0.339746	−	4.73205i	−0.0155722	−	0.216893i
$477$		0			0
$478$	9.19615	−	34.3205i	0.420622	−	1.56978i
$479$	13.4641	−	23.3205i	0.615191	−	1.06554i	−0.375161	−	0.926960i	$-0.622412\pi$
$479$	13.4641	−	23.3205i	0.615191	−	1.06554i	0.990351	−	0.138581i	$-0.0442542\pi$
$480$		0			0
$481$	12.0000	−	6.92820i	0.547153	−	0.315899i
$482$	22.9282	+	22.9282i	1.04435	+	1.04435i
$483$		0			0
$484$			18.1244i			0.823834i
$485$	16.6340	−	18.7583i	0.755310	−	0.851772i
$486$		0			0
$487$	2.22243	+	8.29423i	0.100708	+	0.375847i	0.997823	−	0.0659498i	$-0.0210077\pi$
$487$	2.22243	+	8.29423i	0.100708	+	0.375847i	−0.897115	+	0.441797i	$0.854341\pi$
$488$	4.23205	+	1.13397i	0.191576	+	0.0513326i
$489$		0			0
$490$	−13.5622	−	27.0263i	−0.612677	−	1.22092i
$491$	17.7128			0.799368			0.399684	−	0.916653i	$-0.369120\pi$
$491$	17.7128			0.799368			0.399684	+	0.916653i	$0.369120\pi$
$492$		0			0
$493$	0.803848	+	3.00000i	0.0362035	+	0.135113i
$494$	12.9282	+	7.46410i	0.581667	+	0.335826i
$495$		0			0
$496$		−	2.39230i		−	0.107418i
$497$	−4.09808	−	11.8301i	−0.183824	−	0.530654i
$498$		0			0
$499$	29.0263	−	16.7583i	1.29939	−	0.750206i	0.319095	−	0.947723i	$-0.396621\pi$
$499$	29.0263	−	16.7583i	1.29939	−	0.750206i	0.980300	+	0.197517i	$0.0632877\pi$
$500$	6.52628	−	18.2321i	0.291864	−	0.815362i
$501$		0			0
$502$	−2.92820	+	10.9282i	−0.130692	+	0.487750i
$503$	−19.3660	+	19.3660i	−0.863488	+	0.863488i	−0.991741	−	0.128253i	$-0.959063\pi$
$503$	−19.3660	+	19.3660i	−0.863488	+	0.863488i	0.128253	+	0.991741i	$0.459063\pi$
$504$		0			0
$505$	−11.7321	+	23.4641i	−0.522069	+	1.04414i
$506$	−5.09808	−	8.83013i	−0.226637	−	0.392547i
$507$		0			0
$508$	−15.2942	+	4.09808i	−0.678572	+	0.181823i
$509$	13.4545	+	23.3038i	0.596359	+	1.03292i	0.993353	+	0.115104i	$0.0367200\pi$
$509$	13.4545	+	23.3038i	0.596359	+	1.03292i	−0.396994	+	0.917821i	$0.629947\pi$
$510$		0			0
$511$	−7.85641	+	5.32051i	−0.347547	+	0.235365i
$512$	−20.6865	+	20.6865i	−0.914224	+	0.914224i
$513$		0			0
$514$	−2.73205	+	4.73205i	−0.120506	+	0.208722i
$515$	1.03590	−	5.06218i	0.0456471	−	0.223066i
$516$		0			0
$517$	0.339746	+	0.339746i	0.0149420	+	0.0149420i
$518$	−4.73205	+	24.5885i	−0.207914	+	1.08035i
$519$		0			0
$520$	−0.196152	−	3.26795i	−0.00860185	−	0.143309i
$521$	3.33975	+	1.92820i	0.146317	+	0.0844761i	0.571371	−	0.820692i	$-0.306412\pi$
$521$	3.33975	+	1.92820i	0.146317	+	0.0844761i	−0.425054	+	0.905168i	$0.639745\pi$
$522$		0			0
$523$	14.4904	+	3.88269i	0.633620	+	0.169778i	0.561312	−	0.827604i	$-0.310297\pi$
$523$	14.4904	+	3.88269i	0.633620	+	0.169778i	0.0723082	+	0.997382i	$0.476963\pi$
$524$	−14.7846			−0.645869
$525$		0			0
$526$	16.1244			0.703055
$527$	−0.535898	−	0.143594i	−0.0233441	−	0.00625503i
$528$		0			0
$529$	−25.0981	−	14.4904i	−1.09122	−	0.630017i
$530$	−1.83013	−	30.4904i	−0.0794956	−	1.32442i
$531$		0			0
$532$	−11.8301	+	4.09808i	−0.512901	+	0.177674i
$533$	−0.928203	−	0.928203i	−0.0402049	−	0.0402049i
$534$		0			0
$535$	−3.99038	+	19.5000i	−0.172519	+	0.843059i
$536$	−0.303848	+	0.526279i	−0.0131242	+	0.0227318i
$537$		0			0
$538$	−6.63397	+	6.63397i	−0.286011	+	0.286011i
$539$	0.732051	+	5.07180i	0.0315317	+	0.218458i
$540$		0			0
$541$	9.35641	+	16.2058i	0.402263	+	0.696741i	0.993999	−	0.109392i	$-0.0348903\pi$
$541$	9.35641	+	16.2058i	0.402263	+	0.696741i	−0.591735	+	0.806132i	$0.701557\pi$
$542$	−46.1506	+	12.3660i	−1.98234	+	0.531166i
$543$		0			0
$544$	3.92820	+	6.80385i	0.168420	+	0.291713i
$545$	−14.1244	+	28.2487i	−0.605021	+	1.21004i
$546$		0			0
$547$	5.75833	−	5.75833i	0.246208	−	0.246208i	−0.573204	−	0.819413i	$-0.694300\pi$
$547$	5.75833	−	5.75833i	0.246208	−	0.246208i	0.819413	+	0.573204i	$0.194300\pi$
$548$	4.85641	−	18.1244i	0.207455	−	0.774234i
$549$		0			0
$550$	−4.36603	+	5.56218i	−0.186168	+	0.237172i
$551$	7.09808	−	4.09808i	0.302388	−	0.174584i
$552$		0			0
$553$	13.4641	+	11.6603i	0.572552	+	0.495844i
$554$		−	38.7846i		−	1.64780i
$555$		0			0
$556$	−17.4904	−	10.0981i	−0.741757	−	0.428254i
$557$	1.77757	+	6.63397i	0.0753180	+	0.281091i	0.993305	−	0.115519i	$-0.0368532\pi$
$557$	1.77757	+	6.63397i	0.0753180	+	0.281091i	−0.917987	+	0.396610i	$0.870187\pi$
$558$		0			0
$559$	−23.3205			−0.986352
$560$	20.9641	+	16.0622i	0.885895	+	0.678751i
$561$		0			0
$562$	−24.1244	−	6.46410i	−1.01762	−	0.272672i
$563$	−5.72243	−	21.3564i	−0.241172	−	0.900065i	−0.975269	−	0.221021i	$-0.929061\pi$
$563$	−5.72243	−	21.3564i	−0.241172	−	0.900065i	0.734097	−	0.679044i	$-0.237606\pi$
$564$		0			0
$565$	−8.95448	+	10.0981i	−0.376718	+	0.424829i
$566$		−	52.9808i		−	2.22695i
$567$		0			0
$568$	1.73205	+	1.73205i	0.0726752	+	0.0726752i
$569$	13.0526	−	7.53590i	0.547192	−	0.315921i	−0.200797	−	0.979633i	$-0.564353\pi$
$569$	13.0526	−	7.53590i	0.547192	−	0.315921i	0.747989	+	0.663712i	$0.231020\pi$
$570$		0			0
$571$	−10.0263	+	17.3660i	−0.419587	+	0.726746i	−0.995898	−	0.0904849i	$-0.971158\pi$
$571$	−10.0263	+	17.3660i	−0.419587	+	0.726746i	0.576311	+	0.817230i	$0.304492\pi$
$572$	0.928203	−	3.46410i	0.0388101	−	0.144841i
$573$		0			0
$574$	2.36603	−	0.169873i	0.0987560	−	0.00709036i
$575$	−5.09808	+	35.6865i	−0.212604	+	1.48823i
$576$		0			0
$577$	27.4904	−	7.36603i	1.14444	−	0.306652i	0.363705	−	0.931514i	$-0.381512\pi$
$577$	27.4904	−	7.36603i	1.14444	−	0.306652i	0.780735	+	0.624863i	$0.214845\pi$
$578$	−29.7224	+	7.96410i	−1.23629	+	0.331263i
$579$		0			0
$580$	10.3923	+	5.19615i	0.431517	+	0.215758i
$581$	10.4282	+	5.06218i	0.432635	+	0.210015i
$582$		0			0
$583$	−1.33975	+	5.00000i	−0.0554866	+	0.207079i
$584$	0.928203	−	1.60770i	0.0384093	−	0.0665269i
$585$		0			0
$586$	43.5167	−	25.1244i	1.79766	−	1.03788i
$587$	−25.7846	−	25.7846i	−1.06424	−	1.06424i	−0.997789	−	0.0664553i	$-0.978831\pi$
$587$	−25.7846	−	25.7846i	−1.06424	−	1.06424i	−0.0664553	−	0.997789i	$-0.521169\pi$
$588$		0			0
$589$			1.46410i			0.0603273i
$590$	7.09808	+	6.29423i	0.292223	+	0.259129i
$591$		0			0
$592$	−5.66025	−	21.1244i	−0.232635	−	0.868206i
$593$	6.56218	+	1.75833i	0.269476	+	0.0722060i	0.391027	−	0.920379i	$-0.372120\pi$
$593$	6.56218	+	1.75833i	0.269476	+	0.0722060i	−0.121550	+	0.992585i	$0.538787\pi$
$594$		0			0
$595$	4.85641	−	3.73205i	0.199093	−	0.152999i
$596$	−19.3923			−0.794340
$597$		0			0
$598$	−10.1962	−	38.0526i	−0.416952	−	1.55608i
$599$	−32.6603	−	18.8564i	−1.33446	−	0.770452i	−0.348482	−	0.937316i	$-0.613303\pi$
$599$	−32.6603	−	18.8564i	−1.33446	−	0.770452i	−0.985980	+	0.166864i	$0.946636\pi$
$600$		0			0
$601$			21.1769i			0.863824i	0.901916	+	0.431912i	$0.142161\pi$
$601$			21.1769i			0.863824i	−0.901916	+	0.431912i	$0.857839\pi$
$602$	27.5885	−	31.8564i	1.12442	−	1.29837i
$603$		0			0
$604$	20.7846	−	12.0000i	0.845714	−	0.488273i
$605$	−19.5263	+	12.8923i	−0.793856	+	0.524147i
$606$		0			0
$607$	2.30385	−	8.59808i	0.0935103	−	0.348985i	−0.903279	−	0.429053i	$-0.858847\pi$
$607$	2.30385	−	8.59808i	0.0935103	−	0.348985i	0.996789	+	0.0800683i	$0.0255139\pi$
$608$	14.6603	−	14.6603i	0.594552	−	0.594552i
$609$		0			0
$610$	−11.5622	−	34.6865i	−0.468139	−	1.40442i
$611$	0.928203	+	1.60770i	0.0375511	+	0.0650404i
$612$		0			0
$613$	−13.4641	+	3.60770i	−0.543810	+	0.145713i	−0.520258	−	0.854009i	$-0.674164\pi$
$613$	−13.4641	+	3.60770i	−0.543810	+	0.145713i	−0.0235520	+	0.999723i	$0.507498\pi$
$614$	12.6962	+	21.9904i	0.512375	+	0.887460i
$615$		0			0
$616$	−0.562178	−	0.830127i	−0.0226508	−	0.0334468i
$617$	31.9090	−	31.9090i	1.28461	−	1.28461i	0.346590	−	0.938017i	$-0.387340\pi$
$617$	31.9090	−	31.9090i	1.28461	−	1.28461i	0.938017	−	0.346590i	$-0.112660\pi$
$618$		0			0
$619$	0.0980762	−	0.169873i	0.00394202	−	0.00682777i	−0.864048	−	0.503410i	$-0.832079\pi$
$619$	0.0980762	−	0.169873i	0.00394202	−	0.00682777i	0.867990	+	0.496582i	$0.165412\pi$
$620$	−1.73205	+	1.14359i	−0.0695608	+	0.0459278i
$621$		0			0
$622$	−25.5885	−	25.5885i	−1.02600	−	1.02600i
$623$	−28.8564	+	33.3205i	−1.15611	+	1.33496i
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	33.5885	+	19.3923i	1.34246	+	0.775072i
$627$		0			0
$628$	−41.1506	−	11.0263i	−1.64209	−	0.439996i
$629$	−5.07180			−0.202226
$630$		0			0
$631$	26.5885			1.05847			0.529235	−	0.848475i	$-0.322479\pi$
$631$	26.5885			1.05847			0.529235	+	0.848475i	$0.322479\pi$
$632$	−3.36603	−	0.901924i	−0.133893	−	0.0358766i
$633$		0			0
$634$	−7.73205	−	4.46410i	−0.307079	−	0.177292i
$635$	−15.2942	−	13.5622i	−0.606933	−	0.538199i
$636$		0			0
$637$	−2.33975	+	19.6603i	−0.0927041	+	0.778968i
$638$	−3.00000	−	3.00000i	−0.118771	−	0.118771i
$639$		0			0
$640$	−8.99038	−	1.83975i	−0.355376	−	0.0727223i
$641$	−3.33013	+	5.76795i	−0.131532	+	0.227820i	−0.924267	−	0.381746i	$-0.875323\pi$
$641$	−3.33013	+	5.76795i	−0.131532	+	0.227820i	0.792735	+	0.609566i	$0.208656\pi$
$642$		0			0
$643$	−24.4641	+	24.4641i	−0.964770	+	0.964770i	−0.999400	−	0.0346302i	$-0.988975\pi$
$643$	−24.4641	+	24.4641i	−0.964770	+	0.964770i	0.0346302	+	0.999400i	$0.488975\pi$
$644$	29.7224	+	14.4282i	1.17123	+	0.568551i
$645$		0			0
$646$	−2.73205	−	4.73205i	−0.107491	−	0.186180i
$647$	−5.40192	+	1.44744i	−0.212372	+	0.0569048i	−0.363436	−	0.931619i	$-0.618397\pi$
$647$	−5.40192	+	1.44744i	−0.212372	+	0.0569048i	0.151065	+	0.988524i	$0.451730\pi$
$648$		0			0
$649$	−0.803848	−	1.39230i	−0.0315538	−	0.0546527i
$650$	−21.8564	+	16.3923i	−0.857279	+	0.642959i
$651$		0			0
$652$	6.80385	−	6.80385i	0.266459	−	0.266459i
$653$	−2.33975	+	8.73205i	−0.0915613	+	0.341712i	−0.996476	−	0.0838822i	$-0.973268\pi$
$653$	−2.33975	+	8.73205i	−0.0915613	+	0.341712i	0.904914	+	0.425594i	$0.139935\pi$
$654$		0			0
$655$	−10.5167	−	15.9282i	−0.410920	−	0.622366i
$656$	−1.79423	+	1.03590i	−0.0700529	+	0.0404450i
$657$		0			0
$658$	−3.29423	−	0.633975i	−0.128422	−	0.0247149i
$659$		−	10.3397i		−	0.402779i	−0.979511	−	0.201390i	$-0.935454\pi$
$659$		−	10.3397i		−	0.402779i	0.979511	−	0.201390i	$-0.0645457\pi$
$660$		0			0
$661$	−12.2776	−	7.08846i	−0.477542	−	0.275709i	0.241850	−	0.970314i	$-0.422246\pi$
$661$	−12.2776	−	7.08846i	−0.477542	−	0.275709i	−0.719392	+	0.694605i	$0.755579\pi$
$662$	−12.9282	−	48.2487i	−0.502469	−	1.87524i
$663$		0			0
$664$	−2.26795			−0.0880135
$665$	−12.8301	−	9.83013i	−0.497531	−	0.381196i
$666$		0			0
$667$	−20.8923	−	5.59808i	−0.808953	−	0.216758i
$668$	−6.82051	−	25.4545i	−0.263893	−	0.984864i
$669$		0			0
$670$	5.06218	−	0.303848i	0.195569	−	0.0117387i
$671$			6.19615i			0.239200i
$672$		0			0
$673$	−16.3923	−	16.3923i	−0.631877	−	0.631877i	0.316662	−	0.948539i	$-0.397438\pi$
$673$	−16.3923	−	16.3923i	−0.631877	−	0.631877i	−0.948539	+	0.316662i	$0.897438\pi$
$674$	38.9545	−	22.4904i	1.50047	−	0.866297i
$675$		0			0
$676$	−4.33013	+	7.50000i	−0.166543	+	0.288462i
$677$	−1.85641	+	6.92820i	−0.0713475	+	0.266272i	−0.992380	−	0.123213i	$-0.960680\pi$
$677$	−1.85641	+	6.92820i	−0.0713475	+	0.266272i	0.921033	+	0.389485i	$0.127347\pi$
$678$		0			0
$679$	12.9545	−	26.6865i	0.497147	−	1.02414i
$680$	−0.535898	+	1.07180i	−0.0205508	+	0.0411015i
$681$		0			0
$682$	0.732051	−	0.196152i	0.0280317	−	0.00751106i
$683$	18.4282	−	4.93782i	0.705136	−	0.188941i	0.111606	−	0.993753i	$-0.464401\pi$
$683$	18.4282	−	4.93782i	0.705136	−	0.188941i	0.593530	+	0.804812i	$0.297734\pi$
$684$		0			0
$685$	22.9808	−	7.66025i	0.878050	−	0.292683i
$686$	−24.0885	−	26.4545i	−0.919702	−	1.01004i
$687$		0			0
$688$	−9.52628	+	35.5526i	−0.363186	+	1.35543i
$689$	−10.0000	+	17.3205i	−0.380970	+	0.659859i
$690$		0			0
$691$	−24.9737	+	14.4186i	−0.950045	+	0.548509i	−0.893095	−	0.449868i	$-0.851471\pi$
$691$	−24.9737	+	14.4186i	−0.950045	+	0.548509i	−0.0569502	+	0.998377i	$0.518138\pi$
$692$	−28.7321	−	28.7321i	−1.09223	−	1.09223i
$693$		0			0
$694$			15.5885i			0.591730i
$695$	−1.56218	−	26.0263i	−0.0592568	−	0.987233i
$696$		0			0
$697$	0.124356	+	0.464102i	0.00471031	+	0.0175791i
$698$	−18.1603	−	4.86603i	−0.687376	−	0.184182i
$699$		0			0
$700$	1.60770	−	22.8564i	0.0607652	−	0.863891i
$701$	23.7321			0.896347			0.448174	−	0.893947i	$-0.352075\pi$
$701$	23.7321			0.896347			0.448174	+	0.893947i	$0.352075\pi$
$702$		0			0
$703$	3.46410	+	12.9282i	0.130651	+	0.487596i
$704$	−3.63397	−	2.09808i	−0.136961	−	0.0790742i
$705$		0			0
$706$		−	10.7321i		−	0.403906i
$707$	−5.86603	+	30.4808i	−0.220615	+	1.14635i
$708$		0			0
$709$	6.99038	−	4.03590i	0.262529	−	0.151571i	−0.362959	−	0.931805i	$-0.618233\pi$
$709$	6.99038	−	4.03590i	0.262529	−	0.151571i	0.625488	+	0.780234i	$0.284900\pi$
$710$	4.09808	−	20.0263i	0.153798	−	0.751573i
$711$		0			0
$712$	2.23205	−	8.33013i	0.0836496	−	0.312185i
$713$	2.73205	−	2.73205i	0.102316	−	0.102316i
$714$		0			0
$715$	4.39230	−	1.46410i	0.164263	−	0.0547543i
$716$	17.1962	+	29.7846i	0.642650	+	1.11310i
$717$		0			0
$718$	26.5885	−	7.12436i	0.992272	−	0.265879i
$719$	3.70577	+	6.41858i	0.138202	+	0.239373i	0.926816	−	0.375516i	$-0.122534\pi$
$719$	3.70577	+	6.41858i	0.138202	+	0.239373i	−0.788614	+	0.614888i	$0.789201\pi$
$720$		0			0
$721$	−0.437822	−	6.09808i	−0.0163053	−	0.227104i
$722$	15.7583	−	15.7583i	0.586464	−	0.586464i
$723$		0			0
$724$	−7.96410	+	13.7942i	−0.295984	+	0.512658i
$725$	1.79423	+	14.8923i	0.0666360	+	0.553086i
$726$		0			0
$727$	4.90192	+	4.90192i	0.181802	+	0.181802i	0.792141	−	0.610338i	$-0.208967\pi$
$727$	4.90192	+	4.90192i	0.181802	+	0.181802i	−0.610338	+	0.792141i	$0.708967\pi$
$728$	−1.26795	−	3.66025i	−0.0469933	−	0.135658i
$729$		0			0
$730$	−15.4641	+	0.928203i	−0.572352	+	0.0343543i
$731$	7.39230	+	4.26795i	0.273414	+	0.157856i
$732$		0			0
$733$	−9.83013	−	2.63397i	−0.363084	−	0.0972881i	0.0726647	−	0.997356i	$-0.476850\pi$
$733$	−9.83013	−	2.63397i	−0.363084	−	0.0972881i	−0.435749	+	0.900068i	$0.643516\pi$
$734$	3.73205			0.137753
$735$		0			0
$736$	−54.7128			−2.01674
$737$	−0.830127	−	0.222432i	−0.0305781	−	0.00819338i
$738$		0			0
$739$	7.43782	+	4.29423i	0.273605	+	0.157966i	0.630525	−	0.776169i	$-0.282840\pi$
$739$	7.43782	+	4.29423i	0.273605	+	0.157966i	−0.356920	+	0.934135i	$0.616173\pi$
$740$	−12.5885	+	14.1962i	−0.462761	+	0.521861i
$741$		0			0
$742$	−11.8301	−	34.1506i	−0.434298	−	1.25371i
$743$	14.8301	+	14.8301i	0.544065	+	0.544065i	0.924718	−	0.380653i	$-0.124301\pi$
$743$	14.8301	+	14.8301i	0.544065	+	0.544065i	−0.380653	+	0.924718i	$0.624301\pi$
$744$		0			0
$745$	−13.7942	−	20.8923i	−0.505381	−	0.765435i
$746$	−15.9282	+	27.5885i	−0.583173	+	1.01009i
$747$		0			0
$748$	−0.928203	+	0.928203i	−0.0339385	+	0.0339385i
$749$	1.68653	+	23.4904i	0.0616246	+	0.858320i
$750$		0			0
$751$	−7.19615	−	12.4641i	−0.262591	−	0.454822i	0.704338	−	0.709864i	$-0.251244\pi$
$751$	−7.19615	−	12.4641i	−0.262591	−	0.454822i	−0.966930	+	0.255043i	$0.917910\pi$
$752$	2.83013	−	0.758330i	0.103204	−	0.0276535i
$753$		0			0
$754$	−8.19615	−	14.1962i	−0.298486	−	0.516993i
$755$	27.7128	+	13.8564i	1.00857	+	0.504286i
$756$		0			0
$757$	9.26795	−	9.26795i	0.336849	−	0.336849i	−0.518331	−	0.855180i	$-0.673446\pi$
$757$	9.26795	−	9.26795i	0.336849	−	0.336849i	0.855180	+	0.518331i	$0.173446\pi$
$758$	9.83013	−	36.6865i	0.357046	−	1.33251i
$759$		0			0
$760$	3.09808	+	0.633975i	0.112379	+	0.0229967i
$761$	−11.0718	+	6.39230i	−0.401352	+	0.231721i	−0.687067	−	0.726594i	$-0.741102\pi$
$761$	−11.0718	+	6.39230i	−0.401352	+	0.231721i	0.285715	+	0.958315i	$0.407769\pi$
$762$		0			0
$763$	−7.06218	+	36.6962i	−0.255668	+	1.32849i
$764$			28.9808i			1.04849i
$765$		0			0
$766$	48.8205	+	28.1865i	1.76396	+	1.01842i
$767$	−1.60770	−	6.00000i	−0.0580505	−	0.216647i
$768$		0			0
$769$	47.1769			1.70124			0.850622	−	0.525778i	$-0.176226\pi$
$769$	47.1769			1.70124			0.850622	+	0.525778i	$0.176226\pi$
$770$	−3.19615	+	7.73205i	−0.115181	+	0.278644i
$771$		0			0
$772$	−5.36603	−	1.43782i	−0.193127	−	0.0517484i
$773$	−4.80385	−	17.9282i	−0.172782	−	0.644833i	−0.996919	−	0.0784412i	$-0.975006\pi$
$773$	−4.80385	−	17.9282i	−0.172782	−	0.644833i	0.824136	−	0.566391i	$-0.191661\pi$
$774$		0			0
$775$	−2.46410	−	1.05256i	−0.0885131	−	0.0378090i
$776$			5.80385i			0.208346i
$777$		0			0
$778$	−12.1962	−	12.1962i	−0.437253	−	0.437253i
$779$	1.09808	−	0.633975i	0.0393427	−	0.0227145i
$780$		0			0
$781$	−1.73205	+	3.00000i	−0.0619777	+	0.107348i
$782$	−3.73205	+	13.9282i	−0.133458	+	0.498072i
$783$		0			0
$784$	29.0167	+	11.5981i	1.03631	+	0.414217i
$785$	−17.3923	−	52.1769i	−0.620758	−	1.86227i
$786$		0			0
$787$	−19.3564	+	5.18653i	−0.689981	+	0.184880i	−0.586739	−	0.809776i	$-0.699588\pi$
$787$	−19.3564	+	5.18653i	−0.689981	+	0.184880i	−0.103243	+	0.994656i	$0.532922\pi$
$788$	−33.4186	+	8.95448i	−1.19049	+	0.318990i
$789$		0			0
$790$	9.19615	+	27.5885i	0.327184	+	0.981553i
$791$	−6.97372	+	14.3660i	−0.247957	+	0.510797i
$792$		0			0
$793$	−6.19615	+	23.1244i	−0.220032	+	0.821170i
$794$	−20.0263	+	34.6865i	−0.710706	+	1.23098i
$795$		0			0
$796$	37.3923	−	21.5885i	1.32534	−	0.765183i
$797$	29.4641	+	29.4641i	1.04367	+	1.04367i	0.999002	+	0.0446702i	$0.0142237\pi$
$797$	29.4641	+	29.4641i	1.04367	+	1.04367i	0.0446702	+	0.999002i	$0.485776\pi$
$798$		0			0
$799$		−	0.679492i		−	0.0240387i
$800$	14.1340	+	35.2128i	0.499711	+	1.24496i
$801$		0			0
$802$	5.50000	+	20.5263i	0.194212	+	0.724808i
$803$	2.53590	+	0.679492i	0.0894899	+	0.0239787i
$804$		0			0
$805$	5.59808	+	42.2846i	0.197306	+	1.49034i
$806$	2.92820			0.103142
$807$		0			0
$808$	−1.57180	−	5.86603i	−0.0552956	−	0.206366i
$809$	21.9904	+	12.6962i	0.773141	+	0.446373i	0.833994	−	0.551774i	$-0.186049\pi$
$809$	21.9904	+	12.6962i	0.773141	+	0.446373i	−0.0608532	+	0.998147i	$0.519382\pi$
$810$		0			0
$811$			29.0718i			1.02085i	0.859923	+	0.510424i	$0.170512\pi$
$811$			29.0718i			1.02085i	−0.859923	+	0.510424i	$0.829488\pi$
$812$	13.5000	+	2.59808i	0.473757	+	0.0911746i
$813$		0			0
$814$	6.00000	−	3.46410i	0.210300	−	0.121417i
$815$	12.1699	+	2.49038i	0.426292	+	0.0872342i
$816$		0			0
$817$	5.83013	−	21.7583i	0.203970	−	0.761228i
$818$	−9.36603	+	9.36603i	−0.327475	+	0.327475i
$819$		0			0
$820$	1.60770	+	0.803848i	0.0561432	+	0.0280716i
$821$	−7.33975	−	12.7128i	−0.256159	−	0.443680i	0.709051	−	0.705157i	$-0.249124\pi$
$821$	−7.33975	−	12.7128i	−0.256159	−	0.443680i	−0.965210	+	0.261477i	$0.915790\pi$
$822$		0			0
$823$	24.6962	−	6.61731i	0.860854	−	0.230665i	0.198725	−	0.980055i	$-0.436320\pi$
$823$	24.6962	−	6.61731i	0.860854	−	0.230665i	0.662129	+	0.749390i	$0.269653\pi$
$824$	0.598076	+	1.03590i	0.0208350	+	0.0360872i
$825$		0			0
$826$	10.0981	+	4.90192i	0.351357	+	0.170560i
$827$	3.77757	−	3.77757i	0.131359	−	0.131359i	−0.638370	−	0.769729i	$-0.720391\pi$
$827$	3.77757	−	3.77757i	0.131359	−	0.131359i	0.769729	+	0.638370i	$0.220391\pi$
$828$		0			0
$829$	10.7321	−	18.5885i	0.372740	−	0.645604i	−0.617246	−	0.786770i	$-0.711752\pi$
$829$	10.7321	−	18.5885i	0.372740	−	0.645604i	0.989986	+	0.141166i	$0.0450852\pi$
$830$	10.4282	+	15.7942i	0.361968	+	0.548226i
$831$		0			0
$832$	−11.4641	−	11.4641i	−0.397446	−	0.397446i
$833$	4.33975	−	5.80385i	0.150363	−	0.201091i
$834$		0			0
$835$	22.5718	−	25.4545i	0.781129	−	0.880889i
$836$	3.00000	+	1.73205i	0.103757	+	0.0599042i
$837$		0			0
$838$	−7.19615	−	1.92820i	−0.248587	−	0.0666087i
$839$	31.1244			1.07453			0.537266	−	0.843413i	$-0.319457\pi$
$839$	31.1244			1.07453			0.537266	+	0.843413i	$0.319457\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	−64.6769	−	17.3301i	−2.22891	−	0.597236i
$843$		0			0
$844$	15.2942	+	8.83013i	0.526449	+	0.303946i
$845$	−11.1603	+	0.669873i	−0.383924	+	0.0230443i
$846$		0			0
$847$	−18.1244	+	20.9282i	−0.622760	+	0.719102i
$848$	22.3205	+	22.3205i	0.766489	+	0.766489i
$849$		0			0
$850$	9.92820	−	1.19615i	0.340535	−	0.0410277i
$851$	17.6603	−	30.5885i	0.605386	−	1.04856i
$852$		0			0
$853$	−6.12436	+	6.12436i	−0.209694	+	0.209694i	−0.804137	−	0.594443i	$-0.797372\pi$
$853$	−6.12436	+	6.12436i	−0.209694	+	0.209694i	0.594443	+	0.804137i	$0.297372\pi$
$854$	−24.2583	−	35.8205i	−0.830103	−	1.22575i
$855$		0			0
$856$	−2.30385	−	3.99038i	−0.0787439	−	0.136388i
$857$	22.0263	−	5.90192i	0.752403	−	0.201606i	0.137820	−	0.990457i	$-0.455991\pi$
$857$	22.0263	−	5.90192i	0.752403	−	0.201606i	0.614584	+	0.788851i	$0.289324\pi$
$858$		0			0
$859$	10.5359	+	18.2487i	0.359480	+	0.622638i	0.987874	−	0.155257i	$-0.0496207\pi$
$859$	10.5359	+	18.2487i	0.359480	+	0.622638i	−0.628394	+	0.777895i	$0.716287\pi$
$860$	30.2942	−	10.0981i	1.03302	−	0.344342i
$861$		0			0
$862$	−5.73205	+	5.73205i	−0.195234	+	0.195234i
$863$	−8.94486	+	33.3827i	−0.304487	+	1.13636i	0.628900	+	0.777487i	$0.283506\pi$
$863$	−8.94486	+	33.3827i	−0.304487	+	1.13636i	−0.933386	+	0.358873i	$0.883161\pi$
$864$		0			0
$865$	10.5167	−	51.3923i	0.357577	−	1.74739i
$866$	57.8827	−	33.4186i	1.96693	−	1.13561i
$867$		0			0
$868$	−1.60770	+	1.85641i	−0.0545687	+	0.0630105i
$869$		−	4.92820i		−	0.167178i
$870$		0			0
$871$	−2.87564	−	1.66025i	−0.0974375	−	0.0562556i
$872$	−1.89230	−	7.06218i	−0.0640815	−	0.239156i
$873$		0			0
$874$	38.0526			1.28715
$875$	25.7679	−	14.5263i	0.871116	−	0.491078i
$876$		0			0
$877$	−15.4904	−	4.15064i	−0.523073	−	0.140157i	−0.0123853	−	0.999923i	$-0.503942\pi$
$877$	−15.4904	−	4.15064i	−0.523073	−	0.140157i	−0.510688	+	0.859766i	$0.670609\pi$
$878$	15.6603	+	58.4449i	0.528508	+	1.97242i
$879$		0			0
$880$	−0.437822	−	7.29423i	−0.0147590	−	0.245888i
$881$		−	52.8564i		−	1.78078i	−0.455201	−	0.890389i	$-0.650433\pi$
$881$		−	52.8564i		−	1.78078i	0.455201	−	0.890389i	$-0.349567\pi$
$882$		0			0
$883$	21.9282	+	21.9282i	0.737943	+	0.737943i	0.972180	−	0.234237i	$-0.0752591\pi$
$883$	21.9282	+	21.9282i	0.737943	+	0.737943i	−0.234237	+	0.972180i	$0.575259\pi$
$884$	−4.39230	+	2.53590i	−0.147729	+	0.0852915i
$885$		0			0
$886$	−3.50000	+	6.06218i	−0.117585	+	0.203663i
$887$	9.89230	−	36.9186i	0.332151	−	1.23960i	−0.574774	−	0.818312i	$-0.694910\pi$
$887$	9.89230	−	36.9186i	0.332151	−	1.23960i	0.906925	−	0.421292i	$-0.138423\pi$
$888$		0			0
$889$	−21.7583	−	10.5622i	−0.729751	−	0.354244i
$890$	−68.2750	+	22.7583i	−2.28858	+	0.762861i
$891$		0			0
$892$	14.4904	−	3.88269i	0.485174	−	0.130002i
$893$	−1.73205	+	0.464102i	−0.0579609	+	0.0155306i
$894$		0			0
$895$	−19.8564	+	39.7128i	−0.663726	+	1.32745i
$896$	−10.8301	+	0.777568i	−0.361809	+	0.0259767i
$897$		0			0
$898$	−2.52628	+	9.42820i	−0.0843030	+	0.314623i
$899$	0.803848	−	1.39230i	0.0268098	−	0.0464360i
$900$		0			0
$901$	6.33975	−	3.66025i	0.211208	−	0.121941i
$902$	−0.464102	−	0.464102i	−0.0154529	−	0.0154529i
$903$		0			0
$904$		−	3.12436i		−	0.103915i
$905$	−20.5263	+	1.23205i	−0.682317	+	0.0409548i
$906$		0			0
$907$	−0.454483	−	1.69615i	−0.0150908	−	0.0563198i	0.957970	−	0.286869i	$-0.0926144\pi$
$907$	−0.454483	−	1.69615i	−0.0150908	−	0.0563198i	−0.973061	+	0.230549i	$0.925948\pi$
$908$	−0.169873	−	0.0455173i	−0.00563743	−	0.00151055i
$909$		0			0
$910$	−19.6603	+	25.6603i	−0.651731	+	0.850629i
$911$	−37.5167			−1.24298			−0.621491	−	0.783421i	$-0.713473\pi$
$911$	−37.5167			−1.24298			−0.621491	+	0.783421i	$0.713473\pi$
$912$		0			0
$913$	−0.830127	−	3.09808i	−0.0274732	−	0.102531i
$914$	53.4449	+	30.8564i	1.76780	+	1.02064i
$915$		0			0
$916$		−	4.14359i		−	0.136908i
$917$	−17.0718	−	14.7846i	−0.563760	−	0.488231i
$918$		0			0
$919$	−39.6673	+	22.9019i	−1.30850	+	0.755465i	−0.981846	−	0.189678i	$-0.939256\pi$
$919$	−39.6673	+	22.9019i	−1.30850	+	0.755465i	−0.326657	+	0.945143i	$0.605922\pi$
$920$	−4.59808	−	6.96410i	−0.151594	−	0.229600i
$921$		0			0
$922$	−13.1962	+	49.2487i	−0.434592	+	1.62192i
$923$	−9.46410	+	9.46410i	−0.311515	+	0.311515i
$924$		0			0
$925$	−24.2487	−	3.46410i	−0.797293	−	0.113899i
$926$	24.2583	+	42.0167i	0.797178	+	1.38075i
$927$		0			0
$928$	−21.9904	+	5.89230i	−0.721870	+	0.193424i
$929$	−0.839746	−	1.45448i	−0.0275512	−	0.0477200i	0.851921	−	0.523670i	$-0.175438\pi$
$929$	−0.839746	−	1.45448i	−0.0275512	−	0.0477200i	−0.879472	+	0.475950i	$0.842104\pi$
$930$		0			0
$931$	−17.7583	−	7.09808i	−0.582006	−	0.232630i
$932$	2.19615	−	2.19615i	0.0719374	−	0.0719374i
$933$		0			0
$934$	−31.3564	+	54.3109i	−1.02601	+	1.77711i
$935$	−1.66025	−	0.339746i	−0.0542961	−	0.0111109i
$936$		0			0
$937$	−30.9282	−	30.9282i	−1.01038	−	1.01038i	−0.999946	−	0.0104348i	$-0.996678\pi$
$937$	−30.9282	−	30.9282i	−1.01038	−	1.01038i	−0.0104348	−	0.999946i	$-0.503322\pi$
$938$	5.66987	−	1.96410i	0.185128	−	0.0641302i
$939$		0			0
$940$	−1.90192	−	1.68653i	−0.0620339	−	0.0550087i
$941$	−24.8038	−	14.3205i	−0.808582	−	0.466835i	0.0378810	−	0.999282i	$-0.487939\pi$
$941$	−24.8038	−	14.3205i	−0.808582	−	0.466835i	−0.846463	+	0.532447i	$0.821273\pi$
$942$		0			0
$943$	−3.23205	−	0.866025i	−0.105250	−	0.0282017i
$944$	−9.80385			−0.319088
$945$		0			0
$946$	−11.6603			−0.379108
$947$	−43.6506	−	11.6962i	−1.41846	−	0.380074i	−0.533520	−	0.845788i	$-0.679131\pi$
$947$	−43.6506	−	11.6962i	−1.41846	−	0.380074i	−0.884935	+	0.465714i	$0.845798\pi$
$948$		0			0
$949$	8.78461	+	5.07180i	0.285160	+	0.164637i
$950$	−9.83013	−	24.4904i	−0.318931	−	0.794573i
$951$		0			0
$952$	−0.267949	+	1.39230i	−0.00868428	+	0.0451249i
$953$	10.1436	+	10.1436i	0.328583	+	0.328583i	0.852048	−	0.523464i	$-0.175361\pi$
$953$	10.1436	+	10.1436i	0.328583	+	0.328583i	−0.523464	+	0.852048i	$0.675361\pi$
$954$		0			0
$955$	−31.2224	+	20.6147i	−1.01033	+	0.667077i
$956$	15.9282	−	27.5885i	0.515155	−	0.892274i
$957$		0			0
$958$	36.7846	−	36.7846i	1.18846	−	1.18846i
$959$	23.7321	−	16.0718i	0.766348	−	0.518985i
$960$		0			0
$961$	−15.3564	−	26.5981i	−0.495368	−	0.858002i
$962$	25.8564	−	6.92820i	0.833644	−	0.223374i
$963$		0			0
$964$	14.5359	+	25.1769i	0.468170	+	0.810894i
$965$	−2.26795	−	6.80385i	−0.0730079	−	0.219024i
$966$		0			0
$967$	−1.43782	+	1.43782i	−0.0462372	+	0.0462372i	−0.729847	−	0.683610i	$-0.760409\pi$
$967$	−1.43782	+	1.43782i	−0.0462372	+	0.0462372i	0.683610	+	0.729847i	$0.260409\pi$
$968$	1.40192	−	5.23205i	0.0450595	−	0.168164i
$969$		0			0
$970$	40.4186	−	26.6865i	1.29776	−	0.856853i
$971$	−42.9282	+	24.7846i	−1.37763	+	0.795376i	−0.991874	−	0.127224i	$-0.959393\pi$
$971$	−42.9282	+	24.7846i	−1.37763	+	0.795376i	−0.385758	+	0.922600i	$0.626060\pi$
$972$		0			0
$973$	−10.0981	−	29.1506i	−0.323729	−	0.934526i
$974$			16.5885i			0.531528i
$975$		0			0
$976$	32.7224	+	18.8923i	1.04742	+	0.604728i
$977$	11.5622	+	43.1506i	0.369907	+	1.38051i	0.860646	+	0.509204i	$0.170060\pi$
$977$	11.5622	+	43.1506i	0.369907	+	1.38051i	−0.490739	+	0.871307i	$0.663273\pi$
$978$		0			0
$979$	12.1962			0.389791
$980$	−5.47372	−	26.5526i	−0.174852	−	0.848190i
$981$		0			0
$982$	33.0526	+	8.85641i	1.05475	+	0.282619i
$983$	−3.88526	−	14.5000i	−0.123921	−	0.462478i	0.875878	−	0.482532i	$-0.160283\pi$
$983$	−3.88526	−	14.5000i	−0.123921	−	0.462478i	−0.999799	+	0.0200540i	$0.993616\pi$
$984$		0			0
$985$	−33.4186	−	29.6340i	−1.06480	−	0.944217i
$986$			6.00000i			0.191079i
$987$		0			0
$988$	9.46410	+	9.46410i	0.301093	+	0.301093i
$989$	−51.4808	+	29.7224i	−1.63699	+	0.945118i
$990$		0			0
$991$	11.8564	−	20.5359i	0.376631	−	0.652344i	−0.613939	−	0.789354i	$-0.710416\pi$
$991$	11.8564	−	20.5359i	0.376631	−	0.652344i	0.990570	+	0.137009i	$0.0437491\pi$
$992$	1.05256	−	3.92820i	0.0334188	−	0.124721i
$993$		0			0
$994$	−1.73205	−	24.1244i	−0.0549373	−	0.765178i
$995$	49.8564	+	24.9282i	1.58055	+	0.790277i
$996$		0			0
$997$	25.6865	−	6.88269i	0.813501	−	0.217977i	0.171998	−	0.985097i	$-0.444978\pi$
$997$	25.6865	−	6.88269i	0.813501	−	0.217977i	0.641503	+	0.767121i	$0.278311\pi$
$998$	62.5429	−	16.7583i	1.97976	−	0.530476i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bz.b.73.1		4
3.2	odd	2		35.2.k.a.3.1	✓	4
5.2	odd	4		315.2.bz.a.262.1		4
7.5	odd	6		315.2.bz.a.208.1		4
12.11	even	2		560.2.ci.a.353.1		4
15.2	even	4		35.2.k.b.17.1	yes	4
15.8	even	4		175.2.o.a.157.1		4
15.14	odd	2		175.2.o.b.143.1		4
21.2	odd	6		245.2.l.b.68.1		4
21.5	even	6		35.2.k.b.33.1	yes	4
21.11	odd	6		245.2.f.a.48.2		4
21.17	even	6		245.2.f.b.48.2		4
21.20	even	2		245.2.l.a.178.1		4
35.12	even	12	inner	315.2.bz.b.82.1		4
60.47	odd	4		560.2.ci.b.17.1		4
84.47	odd	6		560.2.ci.b.33.1		4
105.2	even	12		245.2.l.a.117.1		4
105.17	odd	12		245.2.f.a.97.2		4
105.32	even	12		245.2.f.b.97.2		4
105.47	odd	12		35.2.k.a.12.1	yes	4
105.62	odd	4		245.2.l.b.227.1		4
105.68	odd	12		175.2.o.b.82.1		4
105.89	even	6		175.2.o.a.68.1		4
420.47	even	12		560.2.ci.a.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.3.1	✓	4	3.2	odd	2
35.2.k.a.12.1	yes	4	105.47	odd	12
35.2.k.b.17.1	yes	4	15.2	even	4
35.2.k.b.33.1	yes	4	21.5	even	6
175.2.o.a.68.1		4	105.89	even	6
175.2.o.a.157.1		4	15.8	even	4
175.2.o.b.82.1		4	105.68	odd	12
175.2.o.b.143.1		4	15.14	odd	2
245.2.f.a.48.2		4	21.11	odd	6
245.2.f.a.97.2		4	105.17	odd	12
245.2.f.b.48.2		4	21.17	even	6
245.2.f.b.97.2		4	105.32	even	12
245.2.l.a.117.1		4	105.2	even	12
245.2.l.a.178.1		4	21.20	even	2
245.2.l.b.68.1		4	21.2	odd	6
245.2.l.b.227.1		4	105.62	odd	4
315.2.bz.a.208.1		4	7.5	odd	6
315.2.bz.a.262.1		4	5.2	odd	4
315.2.bz.b.73.1		4	1.1	even	1	trivial
315.2.bz.b.82.1		4	35.12	even	12	inner
560.2.ci.a.257.1		4	420.47	even	12
560.2.ci.a.353.1		4	12.11	even	2
560.2.ci.b.17.1		4	60.47	odd	4
560.2.ci.b.33.1		4	84.47	odd	6

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.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86603 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(0.866025 + 2.50000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +O(q^{10})\)	\(q+(1.86603 + 0.500000i) q^{2} +(1.50000 + 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} +(0.866025 + 2.50000i) q^{7} +(-0.366025 - 0.366025i) q^{8} +(-0.866025 + 4.23205i) q^{10} +(0.366025 - 0.633975i) q^{11} +(2.00000 - 2.00000i) q^{13} +(0.366025 + 5.09808i) q^{14} +(-2.23205 - 3.86603i) q^{16} +(-1.00000 + 0.267949i) q^{17} +(1.36603 + 2.36603i) q^{19} +(-1.73205 + 3.46410i) q^{20} +(1.00000 - 1.00000i) q^{22} +(1.86603 - 6.96410i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(4.73205 - 2.73205i) q^{26} +(-0.866025 + 4.50000i) q^{28} -3.00000i q^{29} +(0.464102 + 0.267949i) q^{31} +(-1.96410 - 7.33013i) q^{32} -2.00000 q^{34} +(-5.46410 + 2.26795i) q^{35} +(4.73205 + 1.26795i) q^{37} +(1.36603 + 5.09808i) q^{38} +(0.767949 - 0.866025i) q^{40} -0.464102i q^{41} +(-5.83013 - 5.83013i) q^{43} +(1.09808 - 0.633975i) q^{44} +(6.96410 - 12.0622i) q^{46} +(-0.169873 + 0.633975i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(-9.56218 - 1.36603i) q^{50} +(4.73205 - 1.26795i) q^{52} +(-6.83013 + 1.83013i) q^{53} +(1.46410 + 0.732051i) q^{55} +(0.598076 - 1.23205i) q^{56} +(1.50000 - 5.59808i) q^{58} +(1.09808 - 1.90192i) q^{59} +(-7.33013 + 4.23205i) q^{61} +(0.732051 + 0.732051i) q^{62} -5.73205i q^{64} +(4.73205 + 4.19615i) q^{65} +(-0.303848 - 1.13397i) q^{67} +(-1.73205 - 0.464102i) q^{68} +(-11.3301 + 1.50000i) q^{70} -4.73205 q^{71} +(0.928203 + 3.46410i) q^{73} +(8.19615 + 4.73205i) q^{74} +4.73205i q^{76} +(1.90192 + 0.366025i) q^{77} +(5.83013 - 3.36603i) q^{79} +(8.33013 - 5.50000i) q^{80} +(0.232051 - 0.866025i) q^{82} +(3.09808 - 3.09808i) q^{83} +(-0.732051 - 2.19615i) q^{85} +(-7.96410 - 13.7942i) q^{86} +(-0.366025 + 0.0980762i) q^{88} +(8.33013 + 14.4282i) q^{89} +(6.73205 + 3.26795i) q^{91} +(8.83013 - 8.83013i) q^{92} +(-0.633975 + 1.09808i) q^{94} +(-5.09808 + 3.36603i) q^{95} +(-7.92820 - 7.92820i) q^{97} +(-12.4282 + 5.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{4} + 4 q^{5} + 2 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 6 * q^4 + 4 * q^5 + 2 * q^8	\( 4 q + 4 q^{2} + 6 q^{4} + 4 q^{5} + 2 q^{8} - 2 q^{11} + 8 q^{13} - 2 q^{14} - 2 q^{16} - 4 q^{17} + 2 q^{19} + 4 q^{22} + 4 q^{23} - 6 q^{25} + 12 q^{26} - 12 q^{31} + 6 q^{32} - 8 q^{34} - 8 q^{35} + 12 q^{37} + 2 q^{38} + 10 q^{40} - 6 q^{43} - 6 q^{44} + 14 q^{46} - 18 q^{47} - 22 q^{49} - 14 q^{50} + 12 q^{52} - 10 q^{53} - 8 q^{55} - 8 q^{56} + 6 q^{58} - 6 q^{59} - 12 q^{61} - 4 q^{62} + 12 q^{65} - 22 q^{67} - 28 q^{70} - 12 q^{71} - 24 q^{73} + 12 q^{74} + 18 q^{77} + 6 q^{79} + 16 q^{80} - 6 q^{82} + 2 q^{83} + 4 q^{85} - 18 q^{86} + 2 q^{88} + 16 q^{89} + 20 q^{91} + 18 q^{92} - 6 q^{94} - 10 q^{95} - 4 q^{97} - 22 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^4 + 4 * q^5 + 2 * q^8 - 2 * q^11 + 8 * q^13 - 2 * q^14 - 2 * q^16 - 4 * q^17 + 2 * q^19 + 4 * q^22 + 4 * q^23 - 6 * q^25 + 12 * q^26 - 12 * q^31 + 6 * q^32 - 8 * q^34 - 8 * q^35 + 12 * q^37 + 2 * q^38 + 10 * q^40 - 6 * q^43 - 6 * q^44 + 14 * q^46 - 18 * q^47 - 22 * q^49 - 14 * q^50 + 12 * q^52 - 10 * q^53 - 8 * q^55 - 8 * q^56 + 6 * q^58 - 6 * q^59 - 12 * q^61 - 4 * q^62 + 12 * q^65 - 22 * q^67 - 28 * q^70 - 12 * q^71 - 24 * q^73 + 12 * q^74 + 18 * q^77 + 6 * q^79 + 16 * q^80 - 6 * q^82 + 2 * q^83 + 4 * q^85 - 18 * q^86 + 2 * q^88 + 16 * q^89 + 20 * q^91 + 18 * q^92 - 6 * q^94 - 10 * q^95 - 4 * q^97 - 22 * q^98

Introduction

L-functions

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