LMFDB - Embedded newform 315.2.bz.a.262.1

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:	$1$
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			262.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.262
Dual form			315.2.bz.a.208.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 1.86603i) q^{2} +(-1.50000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.366025 + 0.366025i) q^{8} +O(q^{10})$	\(q+(-0.500000 + 1.86603i) q^{2} +(-1.50000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(3.23205 - 2.86603i) q^{10} +(0.366025 - 0.633975i) q^{11} +(-2.00000 - 2.00000i) q^{13} +(-0.366025 - 5.09808i) q^{14} +(-2.23205 - 3.86603i) q^{16} +(-0.267949 - 1.00000i) q^{17} +(-1.36603 - 2.36603i) q^{19} +(1.73205 + 3.46410i) q^{20} +(1.00000 + 1.00000i) q^{22} +(-6.96410 - 1.86603i) q^{23} +(1.96410 + 4.59808i) q^{25} +(4.73205 - 2.73205i) q^{26} +(4.50000 + 0.866025i) q^{28} +3.00000i q^{29} +(0.464102 + 0.267949i) q^{31} +(7.33013 - 1.96410i) q^{32} +2.00000 q^{34} +(5.73205 + 1.46410i) q^{35} +(-1.26795 + 4.73205i) q^{37} +(5.09808 - 1.36603i) q^{38} +(1.13397 - 0.232051i) q^{40} -0.464102i q^{41} +(-5.83013 + 5.83013i) q^{43} +(-1.09808 + 0.633975i) q^{44} +(6.96410 - 12.0622i) q^{46} +(-0.633975 - 0.169873i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-9.56218 + 1.36603i) q^{50} +(1.26795 + 4.73205i) q^{52} +(1.83013 + 6.83013i) q^{53} +(-1.46410 + 0.732051i) q^{55} +(0.598076 - 1.23205i) q^{56} +(-5.59808 - 1.50000i) q^{58} +(-1.09808 + 1.90192i) q^{59} +(-7.33013 + 4.23205i) q^{61} +(-0.732051 + 0.732051i) q^{62} +5.73205i q^{64} +(1.26795 + 6.19615i) q^{65} +(1.13397 - 0.303848i) q^{67} +(-0.464102 + 1.73205i) q^{68} +(-5.59808 + 9.96410i) q^{70} -4.73205 q^{71} +(3.46410 - 0.928203i) q^{73} +(-8.19615 - 4.73205i) q^{74} +4.73205i q^{76} +(-0.366025 + 1.90192i) q^{77} +(-5.83013 + 3.36603i) q^{79} +(-0.598076 + 9.96410i) q^{80} +(0.866025 + 0.232051i) q^{82} +(-3.09808 - 3.09808i) q^{83} +(-0.732051 + 2.19615i) q^{85} +(-7.96410 - 13.7942i) q^{86} +(0.0980762 + 0.366025i) q^{88} +(-8.33013 - 14.4282i) q^{89} +(6.73205 + 3.26795i) q^{91} +(8.83013 + 8.83013i) q^{92} +(0.633975 - 1.09808i) q^{94} +(-0.366025 + 6.09808i) q^{95} +(7.92820 - 7.92820i) q^{97} +(5.33013 + 12.4282i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{4} - 4 q^{5} - 10 q^{7} + 2 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 - 10 * q^7 + 2 * q^8	$ 4 q - 2 q^{2} - 6 q^{4} - 4 q^{5} - 10 q^{7} + 2 q^{8} + 6 q^{10} - 2 q^{11} - 8 q^{13} + 2 q^{14} - 2 q^{16} - 8 q^{17} - 2 q^{19} + 4 q^{22} - 14 q^{23} - 6 q^{25} + 12 q^{26} + 18 q^{28} - 12 q^{31} + 12 q^{32} + 8 q^{34} + 16 q^{35} - 12 q^{37} + 10 q^{38} + 8 q^{40} - 6 q^{43} + 6 q^{44} + 14 q^{46} - 6 q^{47} + 22 q^{49} - 14 q^{50} + 12 q^{52} - 10 q^{53} + 8 q^{55} - 8 q^{56} - 12 q^{58} + 6 q^{59} - 12 q^{61} + 4 q^{62} + 12 q^{65} + 8 q^{67} + 12 q^{68} - 12 q^{70} - 12 q^{71} - 12 q^{74} + 2 q^{77} - 6 q^{79} + 8 q^{80} - 2 q^{83} + 4 q^{85} - 18 q^{86} - 10 q^{88} - 16 q^{89} + 20 q^{91} + 18 q^{92} + 6 q^{94} + 2 q^{95} + 4 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 - 10 * q^7 + 2 * q^8 + 6 * q^10 - 2 * q^11 - 8 * q^13 + 2 * q^14 - 2 * q^16 - 8 * q^17 - 2 * q^19 + 4 * q^22 - 14 * q^23 - 6 * q^25 + 12 * q^26 + 18 * q^28 - 12 * q^31 + 12 * q^32 + 8 * q^34 + 16 * q^35 - 12 * q^37 + 10 * q^38 + 8 * q^40 - 6 * q^43 + 6 * q^44 + 14 * q^46 - 6 * q^47 + 22 * q^49 - 14 * q^50 + 12 * q^52 - 10 * q^53 + 8 * q^55 - 8 * q^56 - 12 * q^58 + 6 * q^59 - 12 * q^61 + 4 * q^62 + 12 * q^65 + 8 * q^67 + 12 * q^68 - 12 * q^70 - 12 * q^71 - 12 * q^74 + 2 * q^77 - 6 * q^79 + 8 * q^80 - 2 * q^83 + 4 * q^85 - 18 * q^86 - 10 * q^88 - 16 * q^89 + 20 * q^91 + 18 * q^92 + 6 * q^94 + 2 * q^95 + 4 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	+	1.86603i	−0.353553	+	1.31948i	0.528742	+	0.848783i	$0.322664\pi$
$2$	−0.500000	+	1.86603i	−0.353553	+	1.31948i	−0.882295	+	0.470696i	$0.844003\pi$
$3$		0			0
$3$		0			0
$4$	−1.50000	−	0.866025i	−0.750000	−	0.433013i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	−0.366025	+	0.366025i	−0.129410	+	0.129410i
$9$		0			0
$10$	3.23205	−	2.86603i	1.02206	−	0.906317i
$11$	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	$-0.378297\pi$
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	−0.927794	+	0.373094i	$0.878297\pi$
$14$	−0.366025	−	5.09808i	−0.0978244	−	1.36252i
$15$		0			0
$16$	−2.23205	−	3.86603i	−0.558013	−	0.966506i
$17$	−0.267949	−	1.00000i	−0.0649872	−	0.242536i	0.925790	−	0.378039i	$-0.123401\pi$
$17$	−0.267949	−	1.00000i	−0.0649872	−	0.242536i	−0.990777	+	0.135503i	$0.956735\pi$
$18$		0			0
$19$	−1.36603	−	2.36603i	−0.313388	−	0.542803i	0.665706	−	0.746214i	$-0.268131\pi$
$19$	−1.36603	−	2.36603i	−0.313388	−	0.542803i	−0.979093	+	0.203411i	$0.934797\pi$
$20$	1.73205	+	3.46410i	0.387298	+	0.774597i
$21$		0			0
$22$	1.00000	+	1.00000i	0.213201	+	0.213201i
$23$	−6.96410	−	1.86603i	−1.45212	−	0.389093i	−0.555357	−	0.831612i	$-0.687418\pi$
$23$	−6.96410	−	1.86603i	−1.45212	−	0.389093i	−0.896759	+	0.442519i	$0.854085\pi$
$24$		0			0
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	4.73205	−	2.73205i	0.928032	−	0.535799i
$27$		0			0
$28$	4.50000	+	0.866025i	0.850420	+	0.163663i
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$		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	$0.651342\pi$
$32$	7.33013	−	1.96410i	1.29580	−	0.347207i
$33$		0			0
$34$	2.00000			0.342997
$35$	5.73205	+	1.46410i	0.968893	+	0.247478i
$36$		0			0
$37$	−1.26795	+	4.73205i	−0.208450	+	0.777944i	0.779921	+	0.625878i	$0.215259\pi$
$37$	−1.26795	+	4.73205i	−0.208450	+	0.777944i	−0.988370	+	0.152066i	$0.951407\pi$
$38$	5.09808	−	1.36603i	0.827017	−	0.221599i
$39$		0			0
$40$	1.13397	−	0.232051i	0.179297	−	0.0366905i
$41$		−	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	−0.994435	−	0.105349i	$-0.966404\pi$
$43$	−5.83013	+	5.83013i	−0.889086	+	0.889086i	0.105349	+	0.994435i	$0.466404\pi$
$44$	−1.09808	+	0.633975i	−0.165541	+	0.0955753i
$45$		0			0
$46$	6.96410	−	12.0622i	1.02680	−	1.77847i
$47$	−0.633975	−	0.169873i	−0.0924747	−	0.0247785i	0.212285	−	0.977208i	$-0.431909\pi$
$47$	−0.633975	−	0.169873i	−0.0924747	−	0.0247785i	−0.304760	+	0.952429i	$0.598576\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−9.56218	+	1.36603i	−1.35230	+	0.193185i
$51$		0			0
$52$	1.26795	+	4.73205i	0.175833	+	0.656217i
$53$	1.83013	+	6.83013i	0.251387	+	0.938190i	0.970065	+	0.242846i	$0.0780811\pi$
$53$	1.83013	+	6.83013i	0.251387	+	0.938190i	−0.718677	+	0.695344i	$0.755252\pi$
$54$		0			0
$55$	−1.46410	+	0.732051i	−0.197419	+	0.0987097i
$56$	0.598076	−	1.23205i	0.0799213	−	0.164640i
$57$		0			0
$58$	−5.59808	−	1.50000i	−0.735063	−	0.196960i
$59$	−1.09808	+	1.90192i	−0.142957	+	0.247609i	−0.928609	−	0.371060i	$-0.878995\pi$
$59$	−1.09808	+	1.90192i	−0.142957	+	0.247609i	0.785652	+	0.618669i	$0.212328\pi$
$60$		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
$65$	1.26795	+	6.19615i	0.157270	+	0.768538i
$66$		0			0
$67$	1.13397	−	0.303848i	0.138537	−	0.0371209i	−0.188884	−	0.981999i	$-0.560487\pi$
$67$	1.13397	−	0.303848i	0.138537	−	0.0371209i	0.327421	+	0.944878i	$0.393820\pi$
$68$	−0.464102	+	1.73205i	−0.0562806	+	0.210042i
$69$		0			0
$70$	−5.59808	+	9.96410i	−0.669098	+	1.19094i
$71$	−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
$73$	3.46410	−	0.928203i	0.405442	−	0.108638i	−0.0503336	−	0.998732i	$-0.516028\pi$
$73$	3.46410	−	0.928203i	0.405442	−	0.108638i	0.455776	+	0.890094i	$0.349362\pi$
$74$	−8.19615	−	4.73205i	−0.952783	−	0.550090i
$75$		0			0
$76$			4.73205i			0.542803i
$77$	−0.366025	+	1.90192i	−0.0417125	+	0.216744i
$78$		0			0
$79$	−5.83013	+	3.36603i	−0.655941	+	0.378707i	−0.790728	−	0.612167i	$-0.790298\pi$
$79$	−5.83013	+	3.36603i	−0.655941	+	0.378707i	0.134788	+	0.990874i	$0.456965\pi$
$80$	−0.598076	+	9.96410i	−0.0668670	+	1.11402i
$81$		0			0
$82$	0.866025	+	0.232051i	0.0956365	+	0.0256257i
$83$	−3.09808	−	3.09808i	−0.340058	−	0.340058i	0.516331	−	0.856389i	$-0.327297\pi$
$83$	−3.09808	−	3.09808i	−0.340058	−	0.340058i	−0.856389	+	0.516331i	$0.827297\pi$
$84$		0			0
$85$	−0.732051	+	2.19615i	−0.0794021	+	0.238206i
$86$	−7.96410	−	13.7942i	−0.858791	−	1.48747i
$87$		0			0
$88$	0.0980762	+	0.366025i	0.0104550	+	0.0390184i
$89$	−8.33013	−	14.4282i	−0.882992	−	1.52939i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$	−8.33013	−	14.4282i	−0.882992	−	1.52939i	−0.0349934	−	0.999388i	$-0.511141\pi$
$90$		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
$95$	−0.366025	+	6.09808i	−0.0375534	+	0.625649i
$96$		0			0
$97$	7.92820	−	7.92820i	0.804987	−	0.804987i	−0.178883	−	0.983870i	$-0.557248\pi$
$97$	7.92820	−	7.92820i	0.804987	−	0.804987i	0.983870	+	0.178883i	$0.0572484\pi$
$98$	5.33013	+	12.4282i	0.538424	+	1.25544i
$99$		0			0
$100$	1.03590	−	8.59808i	0.103590	−	0.859808i
$101$	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
$103$	−0.598076	+	2.23205i	−0.0589302	+	0.219931i	−0.989111	−	0.147171i	$-0.952983\pi$
$103$	−0.598076	+	2.23205i	−0.0589302	+	0.219931i	0.930181	+	0.367102i	$0.119650\pi$
$104$	1.46410			0.143567
$105$		0			0
$106$	−13.6603			−1.32680
$107$	−2.30385	+	8.59808i	−0.222721	+	0.831207i	0.760583	+	0.649240i	$0.224913\pi$
$107$	−2.30385	+	8.59808i	−0.222721	+	0.831207i	−0.983305	+	0.181967i	$0.941754\pi$
$108$		0			0
$109$	−12.2321	−	7.06218i	−1.17162	−	0.676434i	−0.217557	−	0.976048i	$-0.569809\pi$
$109$	−12.2321	−	7.06218i	−1.17162	−	0.676434i	−0.954061	+	0.299614i	$0.903142\pi$
$110$	−0.633975	−	3.09808i	−0.0604471	−	0.295390i
$111$		0			0
$112$	8.92820	+	7.73205i	0.843636	+	0.730610i
$113$	4.26795	−	4.26795i	0.401495	−	0.401495i	−0.477265	−	0.878760i	$-0.658372\pi$
$113$	4.26795	−	4.26795i	0.401495	−	0.401495i	0.878760	+	0.477265i	$0.158372\pi$
$114$		0			0
$115$	10.6962	+	12.0622i	0.997421	+	1.12480i
$116$	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
$122$	−4.23205	−	15.7942i	−0.383152	−	1.42994i
$123$		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	0.359535	−	0.933132i	$-0.382935\pi$
$127$	−6.46410	−	6.46410i	−0.573596	−	0.573596i	−0.933132	+	0.359535i	$0.882935\pi$
$128$	3.96410	+	1.06218i	0.350380	+	0.0938841i
$129$		0			0
$130$	−12.1962	−	0.732051i	−1.06967	−	0.0642051i
$131$	−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
$133$	5.46410	+	4.73205i	0.473798	+	0.410321i
$134$			2.26795i			0.195921i
$135$		0			0
$136$	0.464102	+	0.267949i	0.0397964	+	0.0229765i
$137$	10.4641	−	2.80385i	0.894009	−	0.239549i	0.217567	−	0.976045i	$-0.430188\pi$
$137$	10.4641	−	2.80385i	0.894009	−	0.239549i	0.676441	+	0.736496i	$0.263521\pi$
$138$		0			0
$139$	11.6603			0.989010			0.494505	−	0.869175i	$-0.335349\pi$
$139$	11.6603			0.989010			0.494505	+	0.869175i	$0.335349\pi$
$140$	−7.33013	−	7.16025i	−0.619509	−	0.605152i
$141$		0			0
$142$	2.36603	−	8.83013i	0.198552	−	0.741008i
$143$	−2.00000	+	0.535898i	−0.167248	+	0.0448141i
$144$		0			0
$145$	3.69615	−	5.59808i	0.306949	−	0.464895i
$146$			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	−0.0471484	−	0.998888i	$-0.515013\pi$
$149$	9.69615	−	5.59808i	0.794340	−	0.458612i	0.841488	+	0.540276i	$0.181680\pi$
$150$		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	$-0.0239980\pi$
$152$	1.36603	+	0.366025i	0.110799	+	0.0296886i
$153$		0			0
$154$	−3.36603	−	1.63397i	−0.271242	−	0.131669i
$155$	−0.535898	−	1.07180i	−0.0430444	−	0.0860888i
$156$		0			0
$157$	−6.36603	−	23.7583i	−0.508064	−	1.89612i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	−6.36603	−	23.7583i	−0.508064	−	1.89612i	−0.0691164	−	0.997609i	$-0.522018\pi$
$158$	−3.36603	−	12.5622i	−0.267787	−	0.999393i
$159$		0			0
$160$	−16.0981	−	5.36603i	−1.27266	−	0.424222i
$161$	19.0263	−	1.36603i	1.49948	−	0.107658i
$162$		0			0
$163$	−5.36603	−	1.43782i	−0.420300	−	0.112619i	0.0424696	−	0.999098i	$-0.486477\pi$
$163$	−5.36603	−	1.43782i	−0.420300	−	0.112619i	−0.462769	+	0.886479i	$0.653144\pi$
$164$	−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	$-0.549652\pi$
$167$	10.7583	−	10.7583i	0.832505	−	0.832505i	0.987859	+	0.155354i	$0.0496519\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$	−3.73205	−	2.46410i	−0.286235	−	0.188988i
$171$		0			0
$172$	13.7942	−	3.69615i	1.05180	−	0.281829i
$173$	−6.07180	+	22.6603i	−0.461630	+	1.72283i	0.206197	+	0.978511i	$0.433891\pi$
$173$	−6.07180	+	22.6603i	−0.461630	+	1.72283i	−0.667827	+	0.744317i	$0.732775\pi$
$174$		0			0
$175$	−8.89230	−	9.79423i	−0.672195	−	0.740374i
$176$	−3.26795			−0.246331
$177$		0			0
$178$	31.0885	−	8.33013i	2.33018	−	0.624369i
$179$	−17.1962	−	9.92820i	−1.28530	−	0.742069i	−0.307488	−	0.951552i	$-0.599489\pi$
$179$	−17.1962	−	9.92820i	−1.28530	−	0.742069i	−0.977812	+	0.209483i	$0.932822\pi$
$180$		0			0
$181$			9.19615i			0.683545i	0.939783	+	0.341772i	$0.111027\pi$
$181$			9.19615i			0.683545i	−0.939783	+	0.341772i	$0.888973\pi$
$182$	−9.46410	+	10.9282i	−0.701526	+	0.810052i
$183$		0			0
$184$	3.23205	−	1.86603i	0.238270	−	0.137565i
$185$	8.19615	−	7.26795i	0.602593	−	0.534350i
$186$		0			0
$187$	−0.732051	−	0.196152i	−0.0535329	−	0.0143441i
$188$	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
$193$	0.830127	+	3.09808i	0.0597539	+	0.223004i	0.989346	−	0.145587i	$-0.0465070\pi$
$193$	0.830127	+	3.09808i	0.0597539	+	0.223004i	−0.929592	+	0.368591i	$0.879840\pi$
$194$	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	−0.999980	−	0.00633876i	$-0.997982\pi$
$197$	−14.1244	−	14.1244i	−1.00632	−	1.00632i	−0.00633876	−	0.999980i	$-0.502018\pi$
$198$		0			0
$199$	−12.4641	+	21.5885i	−0.883557	+	1.53037i	−0.0361978	+	0.999345i	$0.511525\pi$
$199$	−12.4641	+	21.5885i	−0.883557	+	1.53037i	−0.847359	+	0.531021i	$0.821809\pi$
$200$	−2.40192	−	0.964102i	−0.169842	−	0.0681723i
$201$		0			0
$202$	−16.0263	+	16.0263i	−1.12761	+	1.12761i
$203$	−2.59808	−	7.50000i	−0.182349	−	0.526397i
$204$		0			0
$205$	−0.571797	+	0.866025i	−0.0399360	+	0.0604858i
$206$	−3.86603	−	2.23205i	−0.269359	−	0.155514i
$207$		0			0
$208$	−3.26795	+	12.1962i	−0.226592	+	0.845651i
$209$	−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	$0.385853\pi$
$212$	3.16987	−	11.8301i	0.217708	−	0.812496i
$213$		0			0
$214$	−14.8923	−	8.59808i	−1.01802	−	0.587752i
$215$	18.0622	−	3.69615i	1.23183	−	0.252076i
$216$		0			0
$217$	−1.39230	−	0.267949i	−0.0945158	−	0.0181896i
$218$	19.2942	−	19.2942i	1.30677	−	1.30677i
$219$		0			0
$220$	2.83013	+	0.169873i	0.190807	+	0.0114528i
$221$	−1.46410	+	2.53590i	−0.0984861	+	0.170583i
$222$		0			0
$223$	−6.12436	−	6.12436i	−0.410117	−	0.410117i	0.471662	−	0.881779i	$-0.343654\pi$
$223$	−6.12436	−	6.12436i	−0.410117	−	0.410117i	−0.881779	+	0.471662i	$0.843654\pi$
$224$	−16.6244	+	11.2583i	−1.11076	+	0.752229i
$225$		0			0
$226$	5.83013	+	10.0981i	0.387814	+	0.671714i
$227$	−0.0262794	−	0.0980762i	−0.00174423	−	0.00650955i	0.965048	−	0.262072i	$-0.0844059\pi$
$227$	−0.0262794	−	0.0980762i	−0.00174423	−	0.00650955i	−0.966792	+	0.255563i	$0.917739\pi$
$228$		0			0
$229$	1.19615	+	2.07180i	0.0790440	+	0.136908i	0.902838	−	0.429981i	$-0.141480\pi$
$229$	1.19615	+	2.07180i	0.0790440	+	0.136908i	−0.823794	+	0.566890i	$0.808147\pi$
$230$	−27.8564	+	13.9282i	−1.83680	+	0.918399i
$231$		0			0
$232$	−1.09808	−	1.09808i	−0.0720922	−	0.0720922i
$233$	−1.73205	−	0.464102i	−0.113470	−	0.0304043i	0.201637	−	0.979460i	$-0.435374\pi$
$233$	−1.73205	−	0.464102i	−0.113470	−	0.0304043i	−0.315107	+	0.949056i	$0.602041\pi$
$234$		0			0
$235$	0.973721	+	1.09808i	0.0635185	+	0.0716306i
$236$	3.29423	−	1.90192i	0.214436	−	0.123805i
$237$		0			0
$238$	−5.00000	+	1.73205i	−0.324102	+	0.112272i
$239$			18.3923i			1.18970i	0.803837	+	0.594850i	$0.202788\pi$
$239$			18.3923i			1.18970i	−0.803837	+	0.594850i	$0.797212\pi$
$240$		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	$0.484865\pi$
$242$	−19.5263	+	5.23205i	−1.25520	+	0.336329i
$243$		0			0
$244$	14.6603			0.938527
$245$	−15.5981	+	1.30385i	−0.996525	+	0.0832998i
$246$		0			0
$247$	−2.00000	+	7.46410i	−0.127257	+	0.474929i
$248$	−0.267949	+	0.0717968i	−0.0170148	+	0.00455910i
$249$		0			0
$250$	19.5263	+	9.23205i	1.23495	+	0.583886i
$251$			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
$257$	−2.73205	−	0.732051i	−0.170421	−	0.0456641i	0.172600	−	0.984992i	$-0.444783\pi$
$257$	−2.73205	−	0.732051i	−0.170421	−	0.0456641i	−0.343020	+	0.939328i	$0.611450\pi$
$258$		0			0
$259$	−0.928203	−	12.9282i	−0.0576757	−	0.803319i
$260$	3.46410	−	10.3923i	0.214834	−	0.644503i
$261$		0			0
$262$	−4.26795	−	15.9282i	−0.263675	−	0.984048i
$263$	−2.16025	−	8.06218i	−0.133207	−	0.497135i	0.866792	−	0.498670i	$-0.166178\pi$
$263$	−2.16025	−	8.06218i	−0.133207	−	0.497135i	−0.999999	+	0.00153494i	$0.999511\pi$
$264$		0			0
$265$	5.00000	−	15.0000i	0.307148	−	0.921443i
$266$	−11.5622	+	7.83013i	−0.708923	+	0.480096i
$267$		0			0
$268$	−1.96410	−	0.526279i	−0.119977	−	0.0321476i
$269$	2.42820	−	4.20577i	0.148050	−	0.256430i	−0.782457	−	0.622705i	$-0.786034\pi$
$269$	2.42820	−	4.20577i	0.148050	−	0.256430i	0.930507	+	0.366275i	$0.119367\pi$
$270$		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
$275$	3.63397	+	0.437822i	0.219137	+	0.0264017i
$276$		0			0
$277$	19.3923	−	5.19615i	1.16517	−	0.312207i	0.376141	−	0.926562i	$-0.377251\pi$
$277$	19.3923	−	5.19615i	1.16517	−	0.312207i	0.789029	+	0.614356i	$0.210584\pi$
$278$	−5.83013	+	21.7583i	−0.349668	+	1.30498i
$279$		0			0
$280$	−2.63397	+	1.56218i	−0.157410	+	0.0933580i
$281$	−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
$283$	−26.4904	+	7.09808i	−1.57469	+	0.421937i	−0.937277	−	0.348586i	$-0.886662\pi$
$283$	−26.4904	+	7.09808i	−1.57469	+	0.421937i	−0.637413	+	0.770523i	$0.719995\pi$
$284$	7.09808	+	4.09808i	0.421193	+	0.243176i
$285$		0			0
$286$		−	4.00000i		−	0.236525i
$287$	0.401924	+	1.16025i	0.0237248	+	0.0684876i
$288$		0			0
$289$	13.7942	−	7.96410i	0.811425	−	0.468477i
$290$	8.59808	+	9.69615i	0.504896	+	0.569378i
$291$		0			0
$292$	−6.00000	−	1.60770i	−0.351123	−	0.0940832i
$293$	−18.3923	−	18.3923i	−1.07449	−	1.07449i	−0.996993	−	0.0774974i	$-0.975307\pi$
$293$	−18.3923	−	18.3923i	−1.07449	−	1.07449i	−0.0774974	−	0.996993i	$-0.524693\pi$
$294$		0			0
$295$	4.39230	−	2.19615i	0.255730	−	0.127865i
$296$	−1.26795	−	2.19615i	−0.0736980	−	0.127649i
$297$		0			0
$298$	5.59808	+	20.8923i	0.324288	+	1.21026i
$299$	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
$305$	18.8923	+	1.13397i	1.08177	+	0.0649312i
$306$		0			0
$307$	−9.29423	+	9.29423i	−0.530450	+	0.530450i	−0.920706	−	0.390257i	$-0.872386\pi$
$307$	−9.29423	+	9.29423i	−0.530450	+	0.530450i	0.390257	+	0.920706i	$0.372386\pi$
$308$	2.19615	−	2.53590i	0.125137	−	0.144496i
$309$		0			0
$310$	2.26795	−	0.464102i	0.128811	−	0.0263592i
$311$	−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
$313$	5.19615	−	19.3923i	0.293704	−	1.09612i	−0.648537	−	0.761183i	$-0.724619\pi$
$313$	5.19615	−	19.3923i	0.293704	−	1.09612i	0.942241	−	0.334935i	$-0.108714\pi$
$314$	47.5167			2.68152
$315$		0			0
$316$	11.6603			0.655941
$317$	1.19615	−	4.46410i	0.0671826	−	0.250729i	−0.924165	−	0.381994i	$-0.875237\pi$
$317$	1.19615	−	4.46410i	0.0671826	−	0.250729i	0.991347	+	0.131265i	$0.0419040\pi$
$318$		0			0
$319$	1.90192	+	1.09808i	0.106487	+	0.0614805i
$320$	7.06218	−	10.6962i	0.394788	−	0.597933i
$321$		0			0
$322$	−6.96410	+	36.1865i	−0.388094	+	2.01660i
$323$	−2.00000	+	2.00000i	−0.111283	+	0.111283i
$324$		0			0
$325$	5.26795	−	13.1244i	0.292213	−	0.728008i
$326$	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	$-0.418242\pi$
$332$	1.96410	+	7.33013i	0.107794	+	0.402293i
$333$		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	0.995157	−	0.0983001i	$-0.0313405\pi$
$337$	16.4641	+	16.4641i	0.896857	+	0.896857i	−0.0983001	+	0.995157i	$0.531340\pi$
$338$	9.33013	+	2.50000i	0.507492	+	0.135982i
$339$		0			0
$340$	3.00000	−	2.66025i	0.162698	−	0.144273i
$341$	0.339746	−	0.196152i	0.0183983	−	0.0106222i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		−	4.26795i		−	0.230112i
$345$		0			0
$346$	−39.2487	−	22.6603i	−2.11002	−	1.21822i
$347$	−7.79423	+	2.08846i	−0.418416	+	0.112114i	−0.461884	−	0.886941i	$-0.652826\pi$
$347$	−7.79423	+	2.08846i	−0.418416	+	0.112114i	0.0434674	+	0.999055i	$0.486160\pi$
$348$		0			0
$349$	9.73205			0.520945			0.260472	−	0.965481i	$-0.416122\pi$
$349$	9.73205			0.520945			0.260472	+	0.965481i	$0.416122\pi$
$350$	22.7224	−	11.6962i	1.21457	−	0.625186i
$351$		0			0
$352$	1.43782	−	5.36603i	0.0766362	−	0.286010i
$353$	−5.36603	+	1.43782i	−0.285605	+	0.0765276i	−0.398777	−	0.917048i	$-0.630565\pi$
$353$	−5.36603	+	1.43782i	−0.285605	+	0.0765276i	0.113173	+	0.993575i	$0.463899\pi$
$354$		0			0
$355$	8.83013	+	5.83013i	0.468654	+	0.309431i
$356$			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	−0.788941	−	0.614468i	$-0.789371\pi$
$359$	−12.3397	+	7.12436i	−0.651267	+	0.376009i	0.137675	+	0.990478i	$0.456037\pi$
$360$		0			0
$361$	5.76795	−	9.99038i	0.303576	−	0.525810i
$362$	−17.1603	−	4.59808i	−0.901923	−	0.241670i
$363$		0			0
$364$	−7.26795	−	10.7321i	−0.380944	−	0.562512i
$365$	−7.60770	−	2.53590i	−0.398205	−	0.132735i
$366$		0			0
$367$	0.500000	+	1.86603i	0.0260998	+	0.0974057i	0.977747	−	0.209787i	$-0.0672770\pi$
$367$	0.500000	+	1.86603i	0.0260998	+	0.0974057i	−0.951647	+	0.307193i	$0.900610\pi$
$368$	8.33013	+	31.0885i	0.434238	+	1.62060i
$369$		0			0
$370$	9.46410	+	18.9282i	0.492015	+	0.984030i
$371$	−10.4904	−	15.4904i	−0.544633	−	0.804221i
$372$		0			0
$373$	15.9282	+	4.26795i	0.824731	+	0.220986i	0.646414	−	0.762987i	$-0.276268\pi$
$373$	15.9282	+	4.26795i	0.824731	+	0.220986i	0.178317	+	0.983973i	$0.442935\pi$
$374$	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	$0.168485\pi$
$379$			19.6603i			1.00988i	−0.863155	+	0.504940i	$0.831515\pi$
$380$	5.83013	−	8.83013i	0.299079	−	0.452976i
$381$		0			0
$382$	−31.2224	+	8.36603i	−1.59748	+	0.428043i
$383$	7.55256	−	28.1865i	0.385918	−	1.44026i	−0.450797	−	0.892626i	$-0.648860\pi$
$383$	7.55256	−	28.1865i	0.385918	−	1.44026i	0.836715	−	0.547638i	$-0.184473\pi$
$384$		0			0
$385$	3.02628	−	3.09808i	0.154233	−	0.157893i
$386$	−6.19615			−0.315376
$387$		0			0
$388$	−18.7583	+	5.02628i	−0.952310	+	0.255171i
$389$	7.73205	+	4.46410i	0.392031	+	0.226339i	0.683040	−	0.730381i	$-0.260658\pi$
$389$	7.73205	+	4.46410i	0.392031	+	0.226339i	−0.291009	+	0.956720i	$0.593991\pi$
$390$		0			0
$391$			7.46410i			0.377476i
$392$	−0.428203	+	3.59808i	−0.0216275	+	0.181730i
$393$		0			0
$394$	33.4186	−	19.2942i	1.68360	−	0.972029i
$395$	15.0263	+	0.901924i	0.756054	+	0.0453807i
$396$		0			0
$397$	−20.0263	−	5.36603i	−1.00509	−	0.269313i	−0.281514	−	0.959557i	$-0.590836\pi$
$397$	−20.0263	−	5.36603i	−1.00509	−	0.269313i	−0.723577	+	0.690244i	$0.757503\pi$
$398$	−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
$403$	−0.392305	−	1.46410i	−0.0195421	−	0.0729321i
$404$	−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	−0.768735	−	0.639567i	$-0.779114\pi$
$409$	3.42820	−	5.93782i	0.169514	−	0.293606i	0.938249	+	0.345961i	$0.112447\pi$
$410$	−1.33013	−	1.50000i	−0.0656903	−	0.0740797i
$411$		0			0
$412$	2.83013	−	2.83013i	0.139430	−	0.139430i
$413$	1.09808	−	5.70577i	0.0540328	−	0.280763i
$414$		0			0
$415$	1.96410	+	9.59808i	0.0964140	+	0.471151i
$416$	−18.5885	−	10.7321i	−0.911374	−	0.526182i
$417$		0			0
$418$	1.00000	−	3.73205i	0.0489116	−	0.182541i
$419$	3.85641			0.188398			0.0941989	−	0.995553i	$-0.469971\pi$
$419$	3.85641			0.188398			0.0941989	+	0.995553i	$0.469971\pi$
$420$		0			0
$421$	−34.6603			−1.68924			−0.844619	−	0.535368i	$-0.820173\pi$
$421$	−34.6603			−1.68924			−0.844619	+	0.535368i	$0.820173\pi$
$422$	−5.09808	+	19.0263i	−0.248170	+	0.926185i
$423$		0			0
$424$	−3.16987	−	1.83013i	−0.153943	−	0.0888788i
$425$	4.07180	−	3.19615i	0.197511	−	0.155036i
$426$		0			0
$427$	14.6603	−	16.9282i	0.709459	−	0.819213i
$428$	10.9019	−	10.9019i	0.526964	−	0.526964i
$429$		0			0
$430$	−2.13397	+	35.5526i	−0.102909	+	1.71450i
$431$	−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	−0.980836	−	0.194833i	$-0.937583\pi$
$433$	−24.4641	−	24.4641i	−1.17567	−	1.17567i	−0.194833	−	0.980836i	$-0.562417\pi$
$434$	1.19615	−	2.46410i	0.0574172	−	0.118281i
$435$		0			0
$436$	12.2321	+	21.1865i	0.585809	+	1.01465i
$437$	5.09808	+	19.0263i	0.243874	+	0.910150i
$438$		0			0
$439$	−15.6603	−	27.1244i	−0.747423	−	1.29457i	−0.949054	−	0.315113i	$-0.897957\pi$
$439$	−15.6603	−	27.1244i	−0.747423	−	1.29457i	0.201631	−	0.979462i	$-0.435376\pi$
$440$	0.267949	−	0.803848i	0.0127740	−	0.0383219i
$441$		0			0
$442$	−4.00000	−	4.00000i	−0.190261	−	0.190261i
$443$	3.50000	+	0.937822i	0.166290	+	0.0445573i	0.341003	−	0.940062i	$-0.389233\pi$
$443$	3.50000	+	0.937822i	0.166290	+	0.0445573i	−0.174713	+	0.984619i	$0.555900\pi$
$444$		0			0
$445$	−2.23205	+	37.1865i	−0.105809	+	1.76281i
$446$	14.4904	−	8.36603i	0.686139	−	0.396143i
$447$		0			0
$448$	−4.96410	−	14.3301i	−0.234532	−	0.677035i
$449$		−	5.05256i		−	0.238445i	−0.992868	−	0.119222i	$-0.961960\pi$
$449$		−	5.05256i		−	0.238445i	0.992868	−	0.119222i	$-0.0380402\pi$
$450$		0			0
$451$	−0.294229	−	0.169873i	−0.0138547	−	0.00799901i
$452$	−10.0981	+	2.70577i	−0.474974	+	0.127269i
$453$		0			0
$454$	0.196152			0.00920589
$455$	−8.53590	−	14.3923i	−0.400169	−	0.674722i
$456$		0			0
$457$	−8.26795	+	30.8564i	−0.386758	+	1.44340i	0.448618	+	0.893724i	$0.351916\pi$
$457$	−8.26795	+	30.8564i	−0.386758	+	1.44340i	−0.835376	+	0.549678i	$0.814750\pi$
$458$	−4.46410	+	1.19615i	−0.208594	+	0.0558925i
$459$		0			0
$460$	−5.59808	−	27.3564i	−0.261012	−	1.27550i
$461$			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	−0.161563	−	0.986862i	$-0.551653\pi$
$463$	17.7583	−	17.7583i	0.825300	−	0.825300i	0.986862	+	0.161563i	$0.0516534\pi$
$464$	11.5981	−	6.69615i	0.538427	−	0.310861i
$465$		0			0
$466$	1.73205	−	3.00000i	0.0802357	−	0.138972i
$467$	−31.3564	−	8.40192i	−1.45100	−	0.388795i	−0.554629	−	0.832097i	$-0.687140\pi$
$467$	−31.3564	−	8.40192i	−1.45100	−	0.388795i	−0.896372	+	0.443303i	$0.853807\pi$
$468$		0			0
$469$	−2.57180	+	1.74167i	−0.118755	+	0.0804228i
$470$	−2.53590	+	1.26795i	−0.116972	+	0.0584861i
$471$		0			0
$472$	−0.294229	−	1.09808i	−0.0135430	−	0.0505431i
$473$	1.56218	+	5.83013i	0.0718290	+	0.268070i
$474$		0			0
$475$	8.19615	−	10.9282i	0.376065	−	0.501420i
$476$	−0.339746	−	4.73205i	−0.0155722	−	0.216893i
$477$		0			0
$478$	−34.3205	−	9.19615i	−1.56978	−	0.420622i
$479$	−13.4641	+	23.3205i	−0.615191	+	1.06554i	0.375161	+	0.926960i	$0.377588\pi$
$479$	−13.4641	+	23.3205i	−0.615191	+	1.06554i	−0.990351	+	0.138581i	$0.955746\pi$
$480$		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
$485$	−24.5622	+	5.02628i	−1.11531	+	0.228232i
$486$		0			0
$487$	−8.29423	+	2.22243i	−0.375847	+	0.100708i	−0.441797	−	0.897115i	$-0.645659\pi$
$487$	−8.29423	+	2.22243i	−0.375847	+	0.100708i	0.0659498	+	0.997823i	$0.478992\pi$
$488$	1.13397	−	4.23205i	0.0513326	−	0.191576i
$489$		0			0
$490$	5.36603	−	29.7583i	0.242412	−	1.34434i
$491$	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
$493$	3.00000	−	0.803848i	0.135113	−	0.0362035i
$494$	−12.9282	−	7.46410i	−0.581667	−	0.335826i
$495$		0			0
$496$		−	2.39230i		−	0.107418i
$497$	11.8301	−	4.09808i	0.530654	−	0.183824i
$498$		0			0
$499$	−29.0263	+	16.7583i	−1.29939	+	0.750206i	−0.980300	−	0.197517i	$-0.936712\pi$
$499$	−29.0263	+	16.7583i	−1.29939	+	0.750206i	−0.319095	+	0.947723i	$0.603379\pi$
$500$	−12.5263	+	14.7679i	−0.560192	+	0.660443i
$501$		0			0
$502$	−10.9282	−	2.92820i	−0.487750	−	0.130692i
$503$	19.3660	+	19.3660i	0.863488	+	0.863488i	0.991741	−	0.128253i	$-0.0409370\pi$
$503$	19.3660	+	19.3660i	0.863488	+	0.863488i	−0.128253	+	0.991741i	$0.540937\pi$
$504$		0			0
$505$	−11.7321	−	23.4641i	−0.522069	−	1.04414i
$506$	−5.09808	−	8.83013i	−0.226637	−	0.392547i
$507$		0			0
$508$	4.09808	+	15.2942i	0.181823	+	0.678572i
$509$	−13.4545	−	23.3038i	−0.596359	−	1.03292i	−0.993353	−	0.115104i	$-0.963280\pi$
$509$	−13.4545	−	23.3038i	−0.596359	−	1.03292i	0.396994	−	0.917821i	$-0.370053\pi$
$510$		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
$515$	3.86603	−	3.42820i	0.170357	−	0.151065i
$516$		0			0
$517$	−0.339746	+	0.339746i	−0.0149420	+	0.0149420i
$518$	24.5885	+	4.73205i	1.08035	+	0.207914i
$519$		0			0
$520$	−2.73205	−	1.80385i	−0.119808	−	0.0791039i
$521$	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
$523$	3.88269	−	14.4904i	0.169778	−	0.633620i	−0.827604	−	0.561312i	$-0.810297\pi$
$523$	3.88269	−	14.4904i	0.169778	−	0.633620i	0.997382	−	0.0723082i	$-0.0230365\pi$
$524$	14.7846			0.645869
$525$		0			0
$526$	16.1244			0.703055
$527$	0.143594	−	0.535898i	0.00625503	−	0.0233441i
$528$		0			0
$529$	25.0981	+	14.4904i	1.09122	+	0.630017i
$530$	25.4904	+	16.8301i	1.10723	+	0.731054i
$531$		0			0
$532$	−4.09808	−	11.8301i	−0.177674	−	0.512901i
$533$	−0.928203	+	0.928203i	−0.0402049	+	0.0402049i
$534$		0			0
$535$	14.8923	−	13.2058i	0.643850	−	0.570935i
$536$	−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	$0.701557\pi$
$542$	−12.3660	−	46.1506i	−0.531166	−	1.98234i
$543$		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	0.819413	−	0.573204i	$-0.194300\pi$
$547$	5.75833	+	5.75833i	0.246208	+	0.246208i	−0.573204	+	0.819413i	$0.694300\pi$
$548$	−18.1244	−	4.85641i	−0.774234	−	0.207455i
$549$		0			0
$550$	−2.63397	+	6.56218i	−0.112313	+	0.279812i
$551$	7.09808	−	4.09808i	0.302388	−	0.174584i
$552$		0			0
$553$	11.6603	−	13.4641i	0.495844	−	0.572552i
$554$			38.7846i			1.64780i
$555$		0			0
$556$	−17.4904	−	10.0981i	−0.741757	−	0.428254i
$557$	−6.63397	+	1.77757i	−0.281091	+	0.0753180i	−0.396610	−	0.917987i	$-0.629813\pi$
$557$	−6.63397	+	1.77757i	−0.281091	+	0.0753180i	0.115519	+	0.993305i	$0.463147\pi$
$558$		0			0
$559$	23.3205			0.986352
$560$	−7.13397	−	25.4282i	−0.301465	−	1.07454i
$561$		0			0
$562$	6.46410	−	24.1244i	0.272672	−	1.01762i
$563$	−21.3564	+	5.72243i	−0.900065	+	0.241172i	−0.679044	−	0.734097i	$-0.737606\pi$
$563$	−21.3564	+	5.72243i	−0.900065	+	0.241172i	−0.221021	+	0.975269i	$0.570939\pi$
$564$		0			0
$565$	−13.2224	+	2.70577i	−0.556272	+	0.113833i
$566$		−	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	−0.747989	−	0.663712i	$-0.768980\pi$
$569$	−13.0526	+	7.53590i	−0.547192	+	0.315921i	0.200797	+	0.979633i	$0.435647\pi$
$570$		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	$0.304492\pi$
$572$	3.46410	+	0.928203i	0.144841	+	0.0388101i
$573$		0			0
$574$	−2.36603	+	0.169873i	−0.0987560	+	0.00709036i
$575$	−5.09808	−	35.6865i	−0.212604	−	1.48823i
$576$		0			0
$577$	7.36603	+	27.4904i	0.306652	+	1.14444i	0.931514	+	0.363705i	$0.118488\pi$
$577$	7.36603	+	27.4904i	0.306652	+	1.14444i	−0.624863	+	0.780735i	$0.714845\pi$
$578$	7.96410	+	29.7224i	0.331263	+	1.23629i
$579$		0			0
$580$	−10.3923	+	5.19615i	−0.431517	+	0.215758i
$581$	10.4282	+	5.06218i	0.432635	+	0.210015i
$582$		0			0
$583$	5.00000	+	1.33975i	0.207079	+	0.0554866i
$584$	−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	0.0664553	−	0.997789i	$-0.478831\pi$
$587$	25.7846	−	25.7846i	1.06424	−	1.06424i	0.997789	−	0.0664553i	$-0.0211690\pi$
$588$		0			0
$589$		−	1.46410i		−	0.0603273i
$590$	1.90192	+	9.29423i	0.0783010	+	0.382637i
$591$		0			0
$592$	21.1244	−	5.66025i	0.868206	−	0.232635i
$593$	1.75833	−	6.56218i	0.0722060	−	0.269476i	−0.920379	−	0.391027i	$-0.872120\pi$
$593$	1.75833	−	6.56218i	0.0722060	−	0.269476i	0.992585	+	0.121550i	$0.0387866\pi$
$594$		0			0
$595$	−0.0717968	−	6.12436i	−0.00294338	−	0.251074i
$596$	−19.3923			−0.794340
$597$		0			0
$598$	−38.0526	+	10.1962i	−1.55608	+	0.416952i
$599$	32.6603	+	18.8564i	1.33446	+	0.770452i	0.985980	−	0.166864i	$-0.0533640\pi$
$599$	32.6603	+	18.8564i	1.33446	+	0.770452i	0.348482	+	0.937316i	$0.386697\pi$
$600$		0			0
$601$			21.1769i			0.863824i	0.901916	+	0.431912i	$0.142161\pi$
$601$			21.1769i			0.863824i	−0.901916	+	0.431912i	$0.857839\pi$
$602$	31.8564	+	27.5885i	1.29837	+	1.12442i
$603$		0			0
$604$	−20.7846	+	12.0000i	−0.845714	+	0.488273i
$605$	1.40192	−	23.3564i	0.0569963	−	0.949573i
$606$		0			0
$607$	8.59808	+	2.30385i	0.348985	+	0.0935103i	0.429053	−	0.903279i	$-0.358847\pi$
$607$	8.59808	+	2.30385i	0.348985	+	0.0935103i	−0.0800683	+	0.996789i	$0.525514\pi$
$608$	−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
$613$	3.60770	+	13.4641i	0.145713	+	0.543810i	0.999723	+	0.0235520i	$0.00749753\pi$
$613$	3.60770	+	13.4641i	0.145713	+	0.543810i	−0.854009	+	0.520258i	$0.825836\pi$
$614$	−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	0.938017	+	0.346590i	$0.112660\pi$
$617$	31.9090	+	31.9090i	1.28461	+	1.28461i	0.346590	+	0.938017i	$0.387340\pi$
$618$		0			0
$619$	−0.0980762	+	0.169873i	−0.00394202	+	0.00682777i	−0.867990	−	0.496582i	$-0.834588\pi$
$619$	−0.0980762	+	0.169873i	−0.00394202	+	0.00682777i	0.864048	+	0.503410i	$0.167921\pi$
$620$	−0.124356	+	2.07180i	−0.00499424	+	0.0832054i
$621$		0			0
$622$	25.5885	−	25.5885i	1.02600	−	1.02600i
$623$	33.3205	+	28.8564i	1.33496	+	1.15611i
$624$		0			0
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	33.5885	+	19.3923i	1.34246	+	0.775072i
$627$		0			0
$628$	−11.0263	+	41.1506i	−0.439996	+	1.64209i
$629$	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	$0.322479\pi$
$632$	0.901924	−	3.36603i	0.0358766	−	0.133893i
$633$		0			0
$634$	7.73205	+	4.46410i	0.307079	+	0.177292i
$635$	4.09808	+	20.0263i	0.162627	+	0.794719i
$636$		0			0
$637$	−19.6603	−	2.33975i	−0.778968	−	0.0927041i
$638$	−3.00000	+	3.00000i	−0.118771	+	0.118771i
$639$		0			0
$640$	−6.08846	−	6.86603i	−0.240667	−	0.271403i
$641$	−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	$-0.0110253\pi$
$643$	24.4641	+	24.4641i	0.964770	+	0.964770i	−0.0346302	+	0.999400i	$0.511025\pi$
$644$	−29.7224	−	14.4282i	−1.17123	−	0.568551i
$645$		0			0
$646$	−2.73205	−	4.73205i	−0.107491	−	0.186180i
$647$	−1.44744	−	5.40192i	−0.0569048	−	0.212372i	0.931619	−	0.363436i	$-0.118397\pi$
$647$	−1.44744	−	5.40192i	−0.0569048	−	0.212372i	−0.988524	+	0.151065i	$0.951730\pi$
$648$		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
$653$	8.73205	+	2.33975i	0.341712	+	0.0915613i	0.425594	−	0.904914i	$-0.360065\pi$
$653$	8.73205	+	2.33975i	0.341712	+	0.0915613i	−0.0838822	+	0.996476i	$0.526732\pi$
$654$		0			0
$655$	19.0526	+	1.14359i	0.744445	+	0.0446839i
$656$	−1.79423	+	1.03590i	−0.0700529	+	0.0404450i
$657$		0			0
$658$	−0.633975	+	3.29423i	−0.0247149	+	0.128422i
$659$			10.3397i			0.402779i	0.979511	+	0.201390i	$0.0645457\pi$
$659$			10.3397i			0.402779i	−0.979511	+	0.201390i	$0.935454\pi$
$660$		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	$0.755579\pi$
$662$	48.2487	−	12.9282i	1.87524	−	0.502469i
$663$		0			0
$664$	2.26795			0.0880135
$665$	−4.36603	−	15.5622i	−0.169307	−	0.603475i
$666$		0			0
$667$	5.59808	−	20.8923i	0.216758	−	0.808953i
$668$	−25.4545	+	6.82051i	−0.984864	+	0.263893i
$669$		0			0
$670$	2.79423	−	4.23205i	0.107950	−	0.163498i
$671$			6.19615i			0.239200i
$672$		0			0
$673$	−16.3923	+	16.3923i	−0.631877	+	0.631877i	−0.948539	−	0.316662i	$-0.897438\pi$
$673$	−16.3923	+	16.3923i	−0.631877	+	0.631877i	0.316662	+	0.948539i	$0.397438\pi$
$674$	−38.9545	+	22.4904i	−1.50047	+	0.866297i
$675$		0			0
$676$	−4.33013	+	7.50000i	−0.166543	+	0.288462i
$677$	−6.92820	−	1.85641i	−0.266272	−	0.0713475i	0.123213	−	0.992380i	$-0.460680\pi$
$677$	−6.92820	−	1.85641i	−0.266272	−	0.0713475i	−0.389485	+	0.921033i	$0.627347\pi$
$678$		0			0
$679$	−12.9545	+	26.6865i	−0.497147	+	1.02414i
$680$	−0.535898	−	1.07180i	−0.0205508	−	0.0411015i
$681$		0			0
$682$	0.196152	+	0.732051i	0.00751106	+	0.0280317i
$683$	−4.93782	−	18.4282i	−0.188941	−	0.705136i	−0.993753	−	0.111606i	$-0.964401\pi$
$683$	−4.93782	−	18.4282i	−0.188941	−	0.705136i	0.804812	−	0.593530i	$-0.202266\pi$
$684$		0			0
$685$	−22.9808	−	7.66025i	−0.878050	−	0.292683i
$686$	−24.0885	−	26.4545i	−0.919702	−	1.01004i
$687$		0			0
$688$	35.5526	+	9.52628i	1.35543	+	0.363186i
$689$	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
$695$	−21.7583	−	14.3660i	−0.825341	−	0.544934i
$696$		0			0
$697$	−0.464102	+	0.124356i	−0.0175791	+	0.00471031i
$698$	−4.86603	+	18.1603i	−0.184182	+	0.687376i
$699$		0			0
$700$	4.85641	+	22.3923i	0.183555	+	0.846350i
$701$	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
$703$	12.9282	−	3.46410i	0.487596	−	0.130651i
$704$	3.63397	+	2.09808i	0.136961	+	0.0790742i
$705$		0			0
$706$		−	10.7321i		−	0.403906i
$707$	−30.4808	−	5.86603i	−1.14635	−	0.220615i
$708$		0			0
$709$	−6.99038	+	4.03590i	−0.262529	+	0.151571i	−0.625488	−	0.780234i	$-0.715100\pi$
$709$	−6.99038	+	4.03590i	−0.262529	+	0.151571i	0.362959	+	0.931805i	$0.381767\pi$
$710$	−15.2942	+	13.5622i	−0.573982	+	0.508979i
$711$		0			0
$712$	8.33013	+	2.23205i	0.312185	+	0.0836496i
$713$	−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
$718$	−7.12436	−	26.5885i	−0.265879	−	0.992272i
$719$	−3.70577	−	6.41858i	−0.138202	−	0.239373i	0.788614	−	0.614888i	$-0.210799\pi$
$719$	−3.70577	−	6.41858i	−0.138202	−	0.239373i	−0.926816	+	0.375516i	$0.877466\pi$
$720$		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
$725$	−13.7942	+	5.89230i	−0.512305	+	0.218835i
$726$		0			0
$727$	−4.90192	+	4.90192i	−0.181802	+	0.181802i	−0.792141	−	0.610338i	$-0.791033\pi$
$727$	−4.90192	+	4.90192i	−0.181802	+	0.181802i	0.610338	+	0.792141i	$0.291033\pi$
$728$	−3.66025	+	1.26795i	−0.135658	+	0.0469933i
$729$		0			0
$730$	8.53590	−	12.9282i	0.315928	−	0.478494i
$731$	7.39230	+	4.26795i	0.273414	+	0.157856i
$732$		0			0
$733$	−2.63397	+	9.83013i	−0.0972881	+	0.363084i	−0.997356	−	0.0726647i	$-0.976850\pi$
$733$	−2.63397	+	9.83013i	−0.0972881	+	0.363084i	0.900068	+	0.435749i	$0.143516\pi$
$734$	−3.73205			−0.137753
$735$		0			0
$736$	−54.7128			−2.01674
$737$	0.222432	−	0.830127i	0.00819338	−	0.0305781i
$738$		0			0
$739$	−7.43782	−	4.29423i	−0.273605	−	0.157966i	0.356920	−	0.934135i	$-0.383827\pi$
$739$	−7.43782	−	4.29423i	−0.273605	−	0.157966i	−0.630525	+	0.776169i	$0.717160\pi$
$740$	−18.5885	+	3.80385i	−0.683325	+	0.139832i
$741$		0			0
$742$	34.1506	−	11.8301i	1.25371	−	0.434298i
$743$	14.8301	−	14.8301i	0.544065	−	0.544065i	−0.380653	−	0.924718i	$-0.624301\pi$
$743$	14.8301	−	14.8301i	0.544065	−	0.544065i	0.924718	+	0.380653i	$0.124301\pi$
$744$		0			0
$745$	−24.9904	−	1.50000i	−0.915577	−	0.0549557i
$746$	−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	$0.917910\pi$
$752$	0.758330	+	2.83013i	0.0276535	+	0.103204i
$753$		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	0.855180	−	0.518331i	$-0.173446\pi$
$757$	9.26795	+	9.26795i	0.336849	+	0.336849i	−0.518331	+	0.855180i	$0.673446\pi$
$758$	−36.6865	−	9.83013i	−1.33251	−	0.357046i
$759$		0			0
$760$	−2.09808	−	2.36603i	−0.0761052	−	0.0858248i
$761$	−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
$763$	36.6962	+	7.06218i	1.32849	+	0.255668i
$764$		−	28.9808i		−	1.04849i
$765$		0			0
$766$	48.8205	+	28.1865i	1.76396	+	1.01842i
$767$	6.00000	−	1.60770i	0.216647	−	0.0580505i
$768$		0			0
$769$	−47.1769			−1.70124			−0.850622	−	0.525778i	$-0.823774\pi$
$769$	−47.1769			−1.70124			−0.850622	+	0.525778i	$0.823774\pi$
$770$	4.26795	+	7.19615i	0.153806	+	0.259331i
$771$		0			0
$772$	1.43782	−	5.36603i	0.0517484	−	0.193127i
$773$	−17.9282	+	4.80385i	−0.644833	+	0.172782i	−0.566391	−	0.824136i	$-0.691661\pi$
$773$	−17.9282	+	4.80385i	−0.644833	+	0.172782i	−0.0784412	+	0.996919i	$0.524994\pi$
$774$		0			0
$775$	−0.320508	+	2.66025i	−0.0115130	+	0.0955591i
$776$			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
$782$	−13.9282	−	3.73205i	−0.498072	−	0.133458i
$783$		0			0
$784$	−29.0167	−	11.5981i	−1.03631	−	0.414217i
$785$	−17.3923	+	52.1769i	−0.620758	+	1.86227i
$786$		0			0
$787$	−5.18653	−	19.3564i	−0.184880	−	0.689981i	−0.994656	−	0.103243i	$-0.967078\pi$
$787$	−5.18653	−	19.3564i	−0.184880	−	0.689981i	0.809776	−	0.586739i	$-0.199588\pi$
$788$	8.95448	+	33.4186i	0.318990	+	1.19049i
$789$		0			0
$790$	−9.19615	+	27.5885i	−0.327184	+	0.981553i
$791$	−6.97372	+	14.3660i	−0.247957	+	0.510797i
$792$		0			0
$793$	23.1244	+	6.19615i	0.821170	+	0.220032i
$794$	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	−0.0446702	+	0.999002i	$0.514224\pi$
$797$	−29.4641	+	29.4641i	−1.04367	+	1.04367i	−0.999002	+	0.0446702i	$0.985776\pi$
$798$		0			0
$799$			0.679492i			0.0240387i
$800$	23.4282	+	29.8468i	0.828312	+	1.05524i
$801$		0			0
$802$	−20.5263	+	5.50000i	−0.724808	+	0.194212i
$803$	0.679492	−	2.53590i	0.0239787	−	0.0894899i
$804$		0			0
$805$	−37.1865	−	20.8923i	−1.31065	−	0.736357i
$806$	2.92820			0.103142
$807$		0			0
$808$	−5.86603	+	1.57180i	−0.206366	+	0.0552956i
$809$	−21.9904	−	12.6962i	−0.773141	−	0.446373i	0.0608532	−	0.998147i	$-0.480618\pi$
$809$	−21.9904	−	12.6962i	−0.773141	−	0.446373i	−0.833994	+	0.551774i	$0.813951\pi$
$810$		0			0
$811$			29.0718i			1.02085i	0.859923	+	0.510424i	$0.170512\pi$
$811$			29.0718i			1.02085i	−0.859923	+	0.510424i	$0.829488\pi$
$812$	−2.59808	+	13.5000i	−0.0911746	+	0.473757i
$813$		0			0
$814$	−6.00000	+	3.46410i	−0.210300	+	0.121417i
$815$	8.24167	+	9.29423i	0.288693	+	0.325563i
$816$		0			0
$817$	21.7583	+	5.83013i	0.761228	+	0.203970i
$818$	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
$823$	−6.61731	−	24.6962i	−0.230665	−	0.860854i	−0.980055	−	0.198725i	$-0.936320\pi$
$823$	−6.61731	−	24.6962i	−0.230665	−	0.860854i	0.749390	−	0.662129i	$-0.230347\pi$
$824$	−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	0.769729	−	0.638370i	$-0.220391\pi$
$827$	3.77757	+	3.77757i	0.131359	+	0.131359i	−0.638370	+	0.769729i	$0.720391\pi$
$828$		0			0
$829$	−10.7321	+	18.5885i	−0.372740	+	0.645604i	−0.989986	−	0.141166i	$-0.954915\pi$
$829$	−10.7321	+	18.5885i	−0.372740	+	0.645604i	0.617246	+	0.786770i	$0.288248\pi$
$830$	−18.8923	−	1.13397i	−0.655761	−	0.0393608i
$831$		0			0
$832$	11.4641	−	11.4641i	0.397446	−	0.397446i
$833$	−5.80385	−	4.33975i	−0.201091	−	0.150363i
$834$		0			0
$835$	−33.3301	+	6.82051i	−1.15344	+	0.236033i
$836$	3.00000	+	1.73205i	0.103757	+	0.0599042i
$837$		0			0
$838$	−1.92820	+	7.19615i	−0.0666087	+	0.248587i
$839$	−31.1244			−1.07453			−0.537266	−	0.843413i	$-0.680543\pi$
$839$	−31.1244			−1.07453			−0.537266	+	0.843413i	$0.680543\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$	17.3301	−	64.6769i	0.597236	−	2.22891i
$843$		0			0
$844$	−15.2942	−	8.83013i	−0.526449	−	0.303946i
$845$	−6.16025	+	9.33013i	−0.211919	+	0.320966i
$846$		0			0
$847$	−20.9282	−	18.1244i	−0.719102	−	0.622760i
$848$	22.3205	−	22.3205i	0.766489	−	0.766489i
$849$		0			0
$850$	3.92820	+	9.19615i	0.134736	+	0.315425i
$851$	17.6603	−	30.5885i	0.605386	−	1.04856i
$852$		0			0
$853$	6.12436	+	6.12436i	0.209694	+	0.209694i	0.804137	−	0.594443i	$-0.202628\pi$
$853$	6.12436	+	6.12436i	0.209694	+	0.209694i	−0.594443	+	0.804137i	$0.702628\pi$
$854$	24.2583	+	35.8205i	0.830103	+	1.22575i
$855$		0			0
$856$	−2.30385	−	3.99038i	−0.0787439	−	0.136388i
$857$	5.90192	+	22.0263i	0.201606	+	0.752403i	0.990457	+	0.137820i	$0.0440094\pi$
$857$	5.90192	+	22.0263i	0.201606	+	0.752403i	−0.788851	+	0.614584i	$0.789324\pi$
$858$		0			0
$859$	−10.5359	−	18.2487i	−0.359480	−	0.622638i	0.628394	−	0.777895i	$-0.283713\pi$
$859$	−10.5359	−	18.2487i	−0.359480	−	0.622638i	−0.987874	+	0.155257i	$0.950379\pi$
$860$	−30.2942	−	10.0981i	−1.03302	−	0.344342i
$861$		0			0
$862$	−5.73205	−	5.73205i	−0.195234	−	0.195234i
$863$	33.3827	+	8.94486i	1.13636	+	0.304487i	0.777487	−	0.628900i	$-0.216494\pi$
$863$	33.3827	+	8.94486i	1.13636	+	0.304487i	0.358873	+	0.933386i	$0.383161\pi$
$864$		0			0
$865$	39.2487	−	34.8038i	1.33450	−	1.18337i
$866$	57.8827	−	33.4186i	1.96693	−	1.13561i
$867$		0			0
$868$	1.85641	+	1.60770i	0.0630105	+	0.0545687i
$869$			4.92820i			0.167178i
$870$		0			0
$871$	−2.87564	−	1.66025i	−0.0974375	−	0.0562556i
$872$	7.06218	−	1.89230i	0.239156	−	0.0640815i
$873$		0			0
$874$	−38.0526			−1.28715
$875$	4.52628	+	29.2321i	0.153016	+	0.988224i
$876$		0			0
$877$	4.15064	−	15.4904i	0.140157	−	0.523073i	−0.859766	−	0.510688i	$-0.829391\pi$
$877$	4.15064	−	15.4904i	0.140157	−	0.523073i	0.999923	−	0.0123853i	$-0.00394248\pi$
$878$	58.4449	−	15.6603i	1.97242	−	0.528508i
$879$		0			0
$880$	6.09808	+	4.02628i	0.205566	+	0.135726i
$881$		−	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	−0.234237	−	0.972180i	$-0.575259\pi$
$883$	21.9282	−	21.9282i	0.737943	−	0.737943i	0.972180	+	0.234237i	$0.0752591\pi$
$884$	4.39230	−	2.53590i	0.147729	−	0.0852915i
$885$		0			0
$886$	−3.50000	+	6.06218i	−0.117585	+	0.203663i
$887$	36.9186	+	9.89230i	1.23960	+	0.332151i	0.818312	−	0.574774i	$-0.194910\pi$
$887$	36.9186	+	9.89230i	1.23960	+	0.332151i	0.421292	+	0.906925i	$0.361577\pi$
$888$		0			0
$889$	21.7583	+	10.5622i	0.729751	+	0.354244i
$890$	−68.2750	−	22.7583i	−2.28858	−	0.762861i
$891$		0			0
$892$	3.88269	+	14.4904i	0.130002	+	0.485174i
$893$	0.464102	+	1.73205i	0.0155306	+	0.0579609i
$894$		0			0
$895$	19.8564	+	39.7128i	0.663726	+	1.32745i
$896$	−10.8301	+	0.777568i	−0.361809	+	0.0259767i
$897$		0			0
$898$	9.42820	+	2.52628i	0.314623	+	0.0843030i
$899$	−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
$905$	11.3301	−	17.1603i	0.376626	−	0.570426i
$906$		0			0
$907$	1.69615	−	0.454483i	0.0563198	−	0.0150908i	−0.230549	−	0.973061i	$-0.574052\pi$
$907$	1.69615	−	0.454483i	0.0563198	−	0.0150908i	0.286869	+	0.957970i	$0.407386\pi$
$908$	−0.0455173	+	0.169873i	−0.00151055	+	0.00563743i
$909$		0			0
$910$	31.1244	−	8.73205i	1.03176	−	0.289465i
$911$	−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
$913$	−3.09808	+	0.830127i	−0.102531	+	0.0274732i
$914$	−53.4449	−	30.8564i	−1.76780	−	1.02064i
$915$		0			0
$916$		−	4.14359i		−	0.136908i
$917$	14.7846	−	17.0718i	0.488231	−	0.563760i
$918$		0			0
$919$	39.6673	−	22.9019i	1.30850	−	0.755465i	0.326657	−	0.945143i	$-0.394078\pi$
$919$	39.6673	−	22.9019i	1.30850	−	0.755465i	0.981846	+	0.189678i	$0.0607445\pi$
$920$	−8.33013	−	0.500000i	−0.274636	−	0.0164845i
$921$		0			0
$922$	−49.2487	−	13.1962i	−1.62192	−	0.434592i
$923$	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
$928$	5.89230	+	21.9904i	0.193424	+	0.721870i
$929$	0.839746	+	1.45448i	0.0275512	+	0.0477200i	0.879472	−	0.475950i	$-0.157896\pi$
$929$	0.839746	+	1.45448i	0.0275512	+	0.0477200i	−0.851921	+	0.523670i	$0.824562\pi$
$930$		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
$935$	1.12436	+	1.26795i	0.0367704	+	0.0414664i
$936$		0			0
$937$	30.9282	−	30.9282i	1.01038	−	1.01038i	0.0104348	−	0.999946i	$-0.496678\pi$
$937$	30.9282	−	30.9282i	1.01038	−	1.01038i	0.999946	−	0.0104348i	$-0.00332156\pi$
$938$	−1.96410	−	5.66987i	−0.0641302	−	0.185128i
$939$		0			0
$940$	−0.509619	−	2.49038i	−0.0166219	−	0.0812273i
$941$	−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
$943$	−0.866025	+	3.23205i	−0.0282017	+	0.105250i
$944$	9.80385			0.319088
$945$		0			0
$946$	−11.6603			−0.379108
$947$	11.6962	−	43.6506i	0.380074	−	1.41846i	−0.465714	−	0.884935i	$-0.654202\pi$
$947$	11.6962	−	43.6506i	0.380074	−	1.41846i	0.845788	−	0.533520i	$-0.179131\pi$
$948$		0			0
$949$	−8.78461	−	5.07180i	−0.285160	−	0.164637i
$950$	16.2942	+	20.7583i	0.528655	+	0.673489i
$951$		0			0
$952$	−1.39230	−	0.267949i	−0.0451249	−	0.00868428i
$953$	10.1436	−	10.1436i	0.328583	−	0.328583i	−0.523464	−	0.852048i	$-0.675361\pi$
$953$	10.1436	−	10.1436i	0.328583	−	0.328583i	0.852048	+	0.523464i	$0.175361\pi$
$954$		0			0
$955$	2.24167	−	37.3468i	0.0725387	−	1.20851i
$956$	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
$962$	6.92820	+	25.8564i	0.223374	+	0.833644i
$963$		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	0.683610	−	0.729847i	$-0.260409\pi$
$967$	−1.43782	−	1.43782i	−0.0462372	−	0.0462372i	−0.729847	+	0.683610i	$0.760409\pi$
$968$	−5.23205	−	1.40192i	−0.168164	−	0.0450595i
$969$		0			0
$970$	2.90192	−	48.3468i	0.0931752	−	1.55232i
$971$	−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
$973$	−29.1506	+	10.0981i	−0.934526	+	0.323729i
$974$		−	16.5885i		−	0.531528i
$975$		0			0
$976$	32.7224	+	18.8923i	1.04742	+	0.604728i
$977$	−43.1506	+	11.5622i	−1.38051	+	0.369907i	−0.871307	−	0.490739i	$-0.836727\pi$
$977$	−43.1506	+	11.5622i	−1.38051	+	0.369907i	−0.509204	+	0.860646i	$0.670060\pi$
$978$		0			0
$979$	−12.1962			−0.389791
$980$	24.5263	+	11.5526i	0.783463	+	0.369033i
$981$		0			0
$982$	−8.85641	+	33.0526i	−0.282619	+	1.05475i
$983$	−14.5000	+	3.88526i	−0.462478	+	0.123921i	−0.482532	−	0.875878i	$-0.660283\pi$
$983$	−14.5000	+	3.88526i	−0.462478	+	0.123921i	0.0200540	+	0.999799i	$0.493616\pi$
$984$		0			0
$985$	8.95448	+	43.7583i	0.285314	+	1.39426i
$986$			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	$0.0437491\pi$
$992$	3.92820	+	1.05256i	0.124721	+	0.0334188i
$993$		0			0
$994$	1.73205	+	24.1244i	0.0549373	+	0.765178i
$995$	49.8564	−	24.9282i	1.58055	−	0.790277i
$996$		0			0
$997$	6.88269	+	25.6865i	0.217977	+	0.813501i	0.985097	+	0.171998i	$0.0550222\pi$
$997$	6.88269	+	25.6865i	0.217977	+	0.813501i	−0.767121	+	0.641503i	$0.778311\pi$
$998$	−16.7583	−	62.5429i	−0.530476	−	1.97976i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.3.1	✓	4	15.8	even	4
35.2.k.a.12.1	yes	4	21.5	even	6
35.2.k.b.17.1	yes	4	3.2	odd	2
35.2.k.b.33.1	yes	4	105.68	odd	12
175.2.o.a.68.1		4	105.47	odd	12
175.2.o.a.157.1		4	15.14	odd	2
175.2.o.b.82.1		4	105.89	even	6
175.2.o.b.143.1		4	15.2	even	4
245.2.f.a.48.2		4	105.53	even	12
245.2.f.a.97.2		4	21.17	even	6
245.2.f.b.48.2		4	105.38	odd	12
245.2.f.b.97.2		4	21.11	odd	6
245.2.l.a.117.1		4	21.2	odd	6
245.2.l.a.178.1		4	105.83	odd	4
245.2.l.b.68.1		4	105.23	even	12
245.2.l.b.227.1		4	21.20	even	2
315.2.bz.a.208.1		4	35.33	even	12	inner
315.2.bz.a.262.1		4	1.1	even	1	trivial
315.2.bz.b.73.1		4	5.3	odd	4
315.2.bz.b.82.1		4	7.5	odd	6
560.2.ci.a.257.1		4	84.47	odd	6
560.2.ci.a.353.1		4	60.23	odd	4
560.2.ci.b.17.1		4	12.11	even	2
560.2.ci.b.33.1		4	420.383	even	12

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 1.86603i) q^{2} +(-1.50000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.366025 + 0.366025i) q^{8} +O(q^{10})\)	\(q+(-0.500000 + 1.86603i) q^{2} +(-1.50000 - 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(3.23205 - 2.86603i) q^{10} +(0.366025 - 0.633975i) q^{11} +(-2.00000 - 2.00000i) q^{13} +(-0.366025 - 5.09808i) q^{14} +(-2.23205 - 3.86603i) q^{16} +(-0.267949 - 1.00000i) q^{17} +(-1.36603 - 2.36603i) q^{19} +(1.73205 + 3.46410i) q^{20} +(1.00000 + 1.00000i) q^{22} +(-6.96410 - 1.86603i) q^{23} +(1.96410 + 4.59808i) q^{25} +(4.73205 - 2.73205i) q^{26} +(4.50000 + 0.866025i) q^{28} +3.00000i q^{29} +(0.464102 + 0.267949i) q^{31} +(7.33013 - 1.96410i) q^{32} +2.00000 q^{34} +(5.73205 + 1.46410i) q^{35} +(-1.26795 + 4.73205i) q^{37} +(5.09808 - 1.36603i) q^{38} +(1.13397 - 0.232051i) q^{40} -0.464102i q^{41} +(-5.83013 + 5.83013i) q^{43} +(-1.09808 + 0.633975i) q^{44} +(6.96410 - 12.0622i) q^{46} +(-0.633975 - 0.169873i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-9.56218 + 1.36603i) q^{50} +(1.26795 + 4.73205i) q^{52} +(1.83013 + 6.83013i) q^{53} +(-1.46410 + 0.732051i) q^{55} +(0.598076 - 1.23205i) q^{56} +(-5.59808 - 1.50000i) q^{58} +(-1.09808 + 1.90192i) q^{59} +(-7.33013 + 4.23205i) q^{61} +(-0.732051 + 0.732051i) q^{62} +5.73205i q^{64} +(1.26795 + 6.19615i) q^{65} +(1.13397 - 0.303848i) q^{67} +(-0.464102 + 1.73205i) q^{68} +(-5.59808 + 9.96410i) q^{70} -4.73205 q^{71} +(3.46410 - 0.928203i) q^{73} +(-8.19615 - 4.73205i) q^{74} +4.73205i q^{76} +(-0.366025 + 1.90192i) q^{77} +(-5.83013 + 3.36603i) q^{79} +(-0.598076 + 9.96410i) q^{80} +(0.866025 + 0.232051i) q^{82} +(-3.09808 - 3.09808i) q^{83} +(-0.732051 + 2.19615i) q^{85} +(-7.96410 - 13.7942i) q^{86} +(0.0980762 + 0.366025i) q^{88} +(-8.33013 - 14.4282i) q^{89} +(6.73205 + 3.26795i) q^{91} +(8.83013 + 8.83013i) q^{92} +(0.633975 - 1.09808i) q^{94} +(-0.366025 + 6.09808i) q^{95} +(7.92820 - 7.92820i) q^{97} +(5.33013 + 12.4282i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{4} - 4 q^{5} - 10 q^{7} + 2 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 - 10 * q^7 + 2 * q^8	\( 4 q - 2 q^{2} - 6 q^{4} - 4 q^{5} - 10 q^{7} + 2 q^{8} + 6 q^{10} - 2 q^{11} - 8 q^{13} + 2 q^{14} - 2 q^{16} - 8 q^{17} - 2 q^{19} + 4 q^{22} - 14 q^{23} - 6 q^{25} + 12 q^{26} + 18 q^{28} - 12 q^{31} + 12 q^{32} + 8 q^{34} + 16 q^{35} - 12 q^{37} + 10 q^{38} + 8 q^{40} - 6 q^{43} + 6 q^{44} + 14 q^{46} - 6 q^{47} + 22 q^{49} - 14 q^{50} + 12 q^{52} - 10 q^{53} + 8 q^{55} - 8 q^{56} - 12 q^{58} + 6 q^{59} - 12 q^{61} + 4 q^{62} + 12 q^{65} + 8 q^{67} + 12 q^{68} - 12 q^{70} - 12 q^{71} - 12 q^{74} + 2 q^{77} - 6 q^{79} + 8 q^{80} - 2 q^{83} + 4 q^{85} - 18 q^{86} - 10 q^{88} - 16 q^{89} + 20 q^{91} + 18 q^{92} + 6 q^{94} + 2 q^{95} + 4 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 - 10 * q^7 + 2 * q^8 + 6 * q^10 - 2 * q^11 - 8 * q^13 + 2 * q^14 - 2 * q^16 - 8 * q^17 - 2 * q^19 + 4 * q^22 - 14 * q^23 - 6 * q^25 + 12 * q^26 + 18 * q^28 - 12 * q^31 + 12 * q^32 + 8 * q^34 + 16 * q^35 - 12 * q^37 + 10 * q^38 + 8 * q^40 - 6 * q^43 + 6 * q^44 + 14 * q^46 - 6 * q^47 + 22 * q^49 - 14 * q^50 + 12 * q^52 - 10 * q^53 + 8 * q^55 - 8 * q^56 - 12 * q^58 + 6 * q^59 - 12 * q^61 + 4 * q^62 + 12 * q^65 + 8 * q^67 + 12 * q^68 - 12 * q^70 - 12 * q^71 - 12 * q^74 + 2 * q^77 - 6 * q^79 + 8 * q^80 - 2 * q^83 + 4 * q^85 - 18 * q^86 - 10 * q^88 - 16 * q^89 + 20 * q^91 + 18 * q^92 + 6 * q^94 + 2 * q^95 + 4 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more