LMFDB - Embedded newform 1170.2.m.d.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(73,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1170.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1170.73
Dual form			1170.2.m.d.577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-1.23205 - 1.86603i) q^{5} -1.00000i q^{7} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.23205 - 1.86603i) q^{5} -1.00000i q^{7} -1.00000 q^{8} +(1.23205 + 1.86603i) q^{10} +(3.73205 - 3.73205i) q^{11} +(3.46410 - 1.00000i) q^{13} +1.00000i q^{14} +1.00000 q^{16} +(5.09808 + 5.09808i) q^{17} +(-3.46410 + 3.46410i) q^{19} +(-1.23205 - 1.86603i) q^{20} +(-3.73205 + 3.73205i) q^{22} +(0.267949 - 0.267949i) q^{23} +(-1.96410 + 4.59808i) q^{25} +(-3.46410 + 1.00000i) q^{26} -1.00000i q^{28} -3.26795i q^{29} +(-5.00000 - 5.00000i) q^{31} -1.00000 q^{32} +(-5.09808 - 5.09808i) q^{34} +(-1.86603 + 1.23205i) q^{35} -2.46410i q^{37} +(3.46410 - 3.46410i) q^{38} +(1.23205 + 1.86603i) q^{40} +(-6.19615 - 6.19615i) q^{41} +(8.29423 - 8.29423i) q^{43} +(3.73205 - 3.73205i) q^{44} +(-0.267949 + 0.267949i) q^{46} -0.267949i q^{47} +6.00000 q^{49} +(1.96410 - 4.59808i) q^{50} +(3.46410 - 1.00000i) q^{52} +(-1.53590 - 1.53590i) q^{53} +(-11.5622 - 2.36603i) q^{55} +1.00000i q^{56} +3.26795i q^{58} +(1.26795 + 1.26795i) q^{59} -4.92820 q^{61} +(5.00000 + 5.00000i) q^{62} +1.00000 q^{64} +(-6.13397 - 5.23205i) q^{65} +10.7321 q^{67} +(5.09808 + 5.09808i) q^{68} +(1.86603 - 1.23205i) q^{70} +(-8.56218 - 8.56218i) q^{71} +2.46410i q^{74} +(-3.46410 + 3.46410i) q^{76} +(-3.73205 - 3.73205i) q^{77} +0.196152i q^{79} +(-1.23205 - 1.86603i) q^{80} +(6.19615 + 6.19615i) q^{82} +2.19615i q^{83} +(3.23205 - 15.7942i) q^{85} +(-8.29423 + 8.29423i) q^{86} +(-3.73205 + 3.73205i) q^{88} +(0.196152 + 0.196152i) q^{89} +(-1.00000 - 3.46410i) q^{91} +(0.267949 - 0.267949i) q^{92} +0.267949i q^{94} +(10.7321 + 2.19615i) q^{95} +0.196152 q^{97} -6.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 4 * q^8	$ 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 4 q^{8} - 2 q^{10} + 8 q^{11} + 4 q^{16} + 10 q^{17} + 2 q^{20} - 8 q^{22} + 8 q^{23} + 6 q^{25} - 20 q^{31} - 4 q^{32} - 10 q^{34} - 4 q^{35} - 2 q^{40} - 4 q^{41} + 2 q^{43} + 8 q^{44} - 8 q^{46} + 24 q^{49} - 6 q^{50} - 20 q^{53} - 22 q^{55} + 12 q^{59} + 8 q^{61} + 20 q^{62} + 4 q^{64} - 28 q^{65} + 36 q^{67} + 10 q^{68} + 4 q^{70} - 10 q^{71} - 8 q^{77} + 2 q^{80} + 4 q^{82} + 6 q^{85} - 2 q^{86} - 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} + 36 q^{95} - 20 q^{97} - 24 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 4 * q^8 - 2 * q^10 + 8 * q^11 + 4 * q^16 + 10 * q^17 + 2 * q^20 - 8 * q^22 + 8 * q^23 + 6 * q^25 - 20 * q^31 - 4 * q^32 - 10 * q^34 - 4 * q^35 - 2 * q^40 - 4 * q^41 + 2 * q^43 + 8 * q^44 - 8 * q^46 + 24 * q^49 - 6 * q^50 - 20 * q^53 - 22 * q^55 + 12 * q^59 + 8 * q^61 + 20 * q^62 + 4 * q^64 - 28 * q^65 + 36 * q^67 + 10 * q^68 + 4 * q^70 - 10 * q^71 - 8 * q^77 + 2 * q^80 + 4 * q^82 + 6 * q^85 - 2 * q^86 - 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 + 36 * q^95 - 20 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$6$		0			0
$7$		−	1.00000i		−	0.377964i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$		−	1.00000i		−	0.377964i	0.981981	−	0.188982i	$-0.0605189\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.23205	+	1.86603i	0.389609	+	0.590089i
$11$	3.73205	−	3.73205i	1.12526	−	1.12526i	0.134317	−	0.990938i	$-0.457116\pi$
$11$	3.73205	−	3.73205i	1.12526	−	1.12526i	0.990938	−	0.134317i	$-0.0428841\pi$
$12$		0			0
$13$	3.46410	−	1.00000i	0.960769	−	0.277350i
$13$	3.46410	−	1.00000i	0.960769	−	0.277350i
$14$			1.00000i			0.267261i
$15$		0			0
$16$	1.00000			0.250000
$17$	5.09808	+	5.09808i	1.23647	+	1.23647i	0.961436	+	0.275029i	$0.0886875\pi$
$17$	5.09808	+	5.09808i	1.23647	+	1.23647i	0.275029	+	0.961436i	$0.411312\pi$
$18$		0			0
$19$	−3.46410	+	3.46410i	−0.794719	+	0.794719i	−0.982257	−	0.187538i	$-0.939949\pi$
$19$	−3.46410	+	3.46410i	−0.794719	+	0.794719i	0.187538	+	0.982257i	$0.439949\pi$
$20$	−1.23205	−	1.86603i	−0.275495	−	0.417256i
$21$		0			0
$22$	−3.73205	+	3.73205i	−0.795676	+	0.795676i
$23$	0.267949	−	0.267949i	0.0558713	−	0.0558713i	−0.678619	−	0.734490i	$-0.737421\pi$
$23$	0.267949	−	0.267949i	0.0558713	−	0.0558713i	0.734490	+	0.678619i	$0.237421\pi$
$24$		0			0
$25$	−1.96410	+	4.59808i	−0.392820	+	0.919615i
$26$	−3.46410	+	1.00000i	−0.679366	+	0.196116i
$27$		0			0
$28$		−	1.00000i		−	0.188982i
$29$		−	3.26795i		−	0.606843i	−0.952856	−	0.303421i	$-0.901871\pi$
$29$		−	3.26795i		−	0.606843i	0.952856	−	0.303421i	$-0.0981290\pi$
$30$		0			0
$31$	−5.00000	−	5.00000i	−0.898027	−	0.898027i	0.0972349	−	0.995261i	$-0.469000\pi$
$31$	−5.00000	−	5.00000i	−0.898027	−	0.898027i	−0.995261	+	0.0972349i	$0.969000\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−5.09808	−	5.09808i	−0.874313	−	0.874313i
$35$	−1.86603	+	1.23205i	−0.315416	+	0.208255i
$36$		0			0
$37$		−	2.46410i		−	0.405096i	−0.979272	−	0.202548i	$-0.935078\pi$
$37$		−	2.46410i		−	0.405096i	0.979272	−	0.202548i	$-0.0649222\pi$
$38$	3.46410	−	3.46410i	0.561951	−	0.561951i
$39$		0			0
$40$	1.23205	+	1.86603i	0.194804	+	0.295045i
$41$	−6.19615	−	6.19615i	−0.967676	−	0.967676i	0.0318173	−	0.999494i	$-0.489871\pi$
$41$	−6.19615	−	6.19615i	−0.967676	−	0.967676i	−0.999494	+	0.0318173i	$0.989871\pi$
$42$		0			0
$43$	8.29423	−	8.29423i	1.26486	−	1.26486i	0.316148	−	0.948710i	$-0.397610\pi$
$43$	8.29423	−	8.29423i	1.26486	−	1.26486i	0.948710	−	0.316148i	$-0.102390\pi$
$44$	3.73205	−	3.73205i	0.562628	−	0.562628i
$45$		0			0
$46$	−0.267949	+	0.267949i	−0.0395070	+	0.0395070i
$47$		−	0.267949i		−	0.0390844i	−0.999809	−	0.0195422i	$-0.993779\pi$
$47$		−	0.267949i		−	0.0390844i	0.999809	−	0.0195422i	$-0.00622087\pi$
$48$		0			0
$49$	6.00000			0.857143
$50$	1.96410	−	4.59808i	0.277766	−	0.650266i
$51$		0			0
$52$	3.46410	−	1.00000i	0.480384	−	0.138675i
$53$	−1.53590	−	1.53590i	−0.210972	−	0.210972i	0.593708	−	0.804680i	$-0.297663\pi$
$53$	−1.53590	−	1.53590i	−0.210972	−	0.210972i	−0.804680	+	0.593708i	$0.797663\pi$
$54$		0			0
$55$	−11.5622	−	2.36603i	−1.55904	−	0.319035i
$56$			1.00000i			0.133631i
$57$		0			0
$58$			3.26795i			0.429103i
$59$	1.26795	+	1.26795i	0.165073	+	0.165073i	0.784810	−	0.619737i	$-0.212761\pi$
$59$	1.26795	+	1.26795i	0.165073	+	0.165073i	−0.619737	+	0.784810i	$0.712761\pi$
$60$		0			0
$61$	−4.92820			−0.630992			−0.315496	−	0.948927i	$-0.602171\pi$
$61$	−4.92820			−0.630992			−0.315496	+	0.948927i	$0.602171\pi$
$62$	5.00000	+	5.00000i	0.635001	+	0.635001i
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.13397	−	5.23205i	−0.760826	−	0.648956i
$66$		0			0
$67$	10.7321			1.31113			0.655564	−	0.755139i	$-0.272431\pi$
$67$	10.7321			1.31113			0.655564	+	0.755139i	$0.272431\pi$
$68$	5.09808	+	5.09808i	0.618233	+	0.618233i
$69$		0			0
$70$	1.86603	−	1.23205i	0.223033	−	0.147258i
$71$	−8.56218	−	8.56218i	−1.01614	−	1.01614i	−0.999868	−	0.0162760i	$-0.994819\pi$
$71$	−8.56218	−	8.56218i	−1.01614	−	1.01614i	−0.0162760	−	0.999868i	$-0.505181\pi$
$72$		0			0
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$			2.46410i			0.286446i
$75$		0			0
$76$	−3.46410	+	3.46410i	−0.397360	+	0.397360i
$77$	−3.73205	−	3.73205i	−0.425307	−	0.425307i
$78$		0			0
$79$			0.196152i			0.0220689i	0.999939	+	0.0110344i	$0.00351244\pi$
$79$			0.196152i			0.0220689i	−0.999939	+	0.0110344i	$0.996488\pi$
$80$	−1.23205	−	1.86603i	−0.137747	−	0.208628i
$81$		0			0
$82$	6.19615	+	6.19615i	0.684251	+	0.684251i
$83$			2.19615i			0.241059i	0.992710	+	0.120530i	$0.0384592\pi$
$83$			2.19615i			0.241059i	−0.992710	+	0.120530i	$0.961541\pi$
$84$		0			0
$85$	3.23205	−	15.7942i	0.350565	−	1.71312i
$86$	−8.29423	+	8.29423i	−0.894390	+	0.894390i
$87$		0			0
$88$	−3.73205	+	3.73205i	−0.397838	+	0.397838i
$89$	0.196152	+	0.196152i	0.0207921	+	0.0207921i	0.717426	−	0.696634i	$-0.245320\pi$
$89$	0.196152	+	0.196152i	0.0207921	+	0.0207921i	−0.696634	+	0.717426i	$0.745320\pi$
$90$		0			0
$91$	−1.00000	−	3.46410i	−0.104828	−	0.363137i
$92$	0.267949	−	0.267949i	0.0279356	−	0.0279356i
$93$		0			0
$94$			0.267949i			0.0276368i
$95$	10.7321	+	2.19615i	1.10109	+	0.225320i
$96$		0			0
$97$	0.196152			0.0199163			0.00995813	−	0.999950i	$-0.496830\pi$
$97$	0.196152			0.0199163			0.00995813	+	0.999950i	$0.496830\pi$
$98$	−6.00000			−0.606092
$99$		0			0
$100$	−1.96410	+	4.59808i	−0.196410	+	0.459808i
$101$		−	0.928203i		−	0.0923597i	−0.998933	−	0.0461798i	$-0.985295\pi$
$101$		−	0.928203i		−	0.0923597i	0.998933	−	0.0461798i	$-0.0147047\pi$
$102$		0			0
$103$	−4.66025	+	4.66025i	−0.459188	+	0.459188i	−0.898389	−	0.439201i	$-0.855262\pi$
$103$	−4.66025	+	4.66025i	−0.459188	+	0.459188i	0.439201	+	0.898389i	$0.355262\pi$
$104$	−3.46410	+	1.00000i	−0.339683	+	0.0980581i
$105$		0			0
$106$	1.53590	+	1.53590i	0.149180	+	0.149180i
$107$	5.00000	−	5.00000i	0.483368	−	0.483368i	−0.422837	−	0.906206i	$-0.638966\pi$
$107$	5.00000	−	5.00000i	0.483368	−	0.483368i	0.906206	+	0.422837i	$0.138966\pi$
$108$		0			0
$109$	−1.63397	+	1.63397i	−0.156506	+	0.156506i	−0.781017	−	0.624510i	$-0.785299\pi$
$109$	−1.63397	+	1.63397i	−0.156506	+	0.156506i	0.624510	+	0.781017i	$0.285299\pi$
$110$	11.5622	+	2.36603i	1.10241	+	0.225592i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	0.803848	+	0.803848i	0.0756196	+	0.0756196i	0.743905	−	0.668285i	$-0.232971\pi$
$113$	0.803848	+	0.803848i	0.0756196	+	0.0756196i	−0.668285	+	0.743905i	$0.732971\pi$
$114$		0			0
$115$	−0.830127	−	0.169873i	−0.0774097	−	0.0158407i
$116$		−	3.26795i		−	0.303421i
$117$		0			0
$118$	−1.26795	−	1.26795i	−0.116724	−	0.116724i
$119$	5.09808	−	5.09808i	0.467340	−	0.467340i
$120$		0			0
$121$		−	16.8564i		−	1.53240i
$122$	4.92820			0.446179
$123$		0			0
$124$	−5.00000	−	5.00000i	−0.449013	−	0.449013i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$	−5.53590	−	5.53590i	−0.491232	−	0.491232i	0.417463	−	0.908694i	$-0.362919\pi$
$127$	−5.53590	−	5.53590i	−0.491232	−	0.491232i	−0.908694	+	0.417463i	$0.862919\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	6.13397	+	5.23205i	0.537985	+	0.458881i
$131$	12.4641			1.08899			0.544497	−	0.838763i	$-0.316721\pi$
$131$	12.4641			1.08899			0.544497	+	0.838763i	$0.316721\pi$
$132$		0			0
$133$	3.46410	+	3.46410i	0.300376	+	0.300376i
$134$	−10.7321			−0.927108
$135$		0			0
$136$	−5.09808	−	5.09808i	−0.437156	−	0.437156i
$137$		−	11.6603i		−	0.996203i	−0.867119	−	0.498101i	$-0.834031\pi$
$137$		−	11.6603i		−	0.996203i	0.867119	−	0.498101i	$-0.165969\pi$
$138$		0			0
$139$		−	6.26795i		−	0.531641i	−0.964023	−	0.265820i	$-0.914357\pi$
$139$		−	6.26795i		−	0.531641i	0.964023	−	0.265820i	$-0.0856428\pi$
$140$	−1.86603	+	1.23205i	−0.157708	+	0.104127i
$141$		0			0
$142$	8.56218	+	8.56218i	0.718522	+	0.718522i
$143$	9.19615	−	16.6603i	0.769021	−	1.39320i
$144$		0			0
$145$	−6.09808	+	4.02628i	−0.506418	+	0.334364i
$146$		0			0
$147$		0			0
$148$		−	2.46410i		−	0.202548i
$149$	−10.6603	+	10.6603i	−0.873322	+	0.873322i	−0.992833	−	0.119511i	$-0.961867\pi$
$149$	−10.6603	+	10.6603i	−0.873322	+	0.873322i	0.119511	+	0.992833i	$0.461867\pi$
$150$		0			0
$151$	7.90192	−	7.90192i	0.643049	−	0.643049i	−0.308254	−	0.951304i	$-0.599745\pi$
$151$	7.90192	−	7.90192i	0.643049	−	0.643049i	0.951304	+	0.308254i	$0.0997448\pi$
$152$	3.46410	−	3.46410i	0.280976	−	0.280976i
$153$		0			0
$154$	3.73205	+	3.73205i	0.300737	+	0.300737i
$155$	−3.16987	+	15.4904i	−0.254610	+	1.24422i
$156$		0			0
$157$	−15.4641	+	15.4641i	−1.23417	+	1.23417i	−0.271822	+	0.962347i	$0.587626\pi$
$157$	−15.4641	+	15.4641i	−1.23417	+	1.23417i	−0.962347	+	0.271822i	$0.912374\pi$
$158$		−	0.196152i		−	0.0156050i
$159$		0			0
$160$	1.23205	+	1.86603i	0.0974022	+	0.147522i
$161$	−0.267949	−	0.267949i	−0.0211174	−	0.0211174i
$162$		0			0
$163$	−0.732051			−0.0573386			−0.0286693	−	0.999589i	$-0.509127\pi$
$163$	−0.732051			−0.0573386			−0.0286693	+	0.999589i	$0.509127\pi$
$164$	−6.19615	−	6.19615i	−0.483838	−	0.483838i
$165$		0			0
$166$		−	2.19615i		−	0.170454i
$167$			6.53590i			0.505763i	0.967497	+	0.252882i	$0.0813783\pi$
$167$			6.53590i			0.505763i	−0.967497	+	0.252882i	$0.918622\pi$
$168$		0			0
$169$	11.0000	−	6.92820i	0.846154	−	0.532939i
$170$	−3.23205	+	15.7942i	−0.247887	+	1.21136i
$171$		0			0
$172$	8.29423	−	8.29423i	0.632429	−	0.632429i
$173$	1.73205	−	1.73205i	0.131685	−	0.131685i	−0.638192	−	0.769877i	$-0.720317\pi$
$173$	1.73205	−	1.73205i	0.131685	−	0.131685i	0.769877	+	0.638192i	$0.220317\pi$
$174$		0			0
$175$	4.59808	+	1.96410i	0.347582	+	0.148472i
$176$	3.73205	−	3.73205i	0.281314	−	0.281314i
$177$		0			0
$178$	−0.196152	−	0.196152i	−0.0147022	−	0.0147022i
$179$	−21.3923			−1.59894			−0.799468	−	0.600709i	$-0.794885\pi$
$179$	−21.3923			−1.59894			−0.799468	+	0.600709i	$0.794885\pi$
$180$		0			0
$181$		−	6.19615i		−	0.460556i	−0.973125	−	0.230278i	$-0.926036\pi$
$181$		−	6.19615i		−	0.460556i	0.973125	−	0.230278i	$-0.0739636\pi$
$182$	1.00000	+	3.46410i	0.0741249	+	0.256776i
$183$		0			0
$184$	−0.267949	+	0.267949i	−0.0197535	+	0.0197535i
$185$	−4.59808	+	3.03590i	−0.338057	+	0.223204i
$186$		0			0
$187$	38.0526			2.78268
$188$		−	0.267949i		−	0.0195422i
$189$		0			0
$190$	−10.7321	−	2.19615i	−0.778585	−	0.159326i
$191$	−13.1244			−0.949645			−0.474823	−	0.880082i	$-0.657488\pi$
$191$	−13.1244			−0.949645			−0.474823	+	0.880082i	$0.657488\pi$
$192$		0			0
$193$	−11.2679			−0.811085			−0.405542	−	0.914076i	$-0.632917\pi$
$193$	−11.2679			−0.811085			−0.405542	+	0.914076i	$0.632917\pi$
$194$	−0.196152			−0.0140829
$195$		0			0
$196$	6.00000			0.428571
$197$	−3.33975			−0.237947			−0.118974	−	0.992897i	$-0.537960\pi$
$197$	−3.33975			−0.237947			−0.118974	+	0.992897i	$0.537960\pi$
$198$		0			0
$199$	−24.5885			−1.74303			−0.871515	−	0.490369i	$-0.836862\pi$
$199$	−24.5885			−1.74303			−0.871515	+	0.490369i	$0.836862\pi$
$200$	1.96410	−	4.59808i	0.138883	−	0.325133i
$201$		0			0
$202$			0.928203i			0.0653082i
$203$	−3.26795			−0.229365
$204$		0			0
$205$	−3.92820	+	19.1962i	−0.274358	+	1.34072i
$206$	4.66025	−	4.66025i	0.324695	−	0.324695i
$207$		0			0
$208$	3.46410	−	1.00000i	0.240192	−	0.0693375i
$209$			25.8564i			1.78853i
$210$		0			0
$211$	10.2679			0.706875			0.353437	−	0.935458i	$-0.385013\pi$
$211$	10.2679			0.706875			0.353437	+	0.935458i	$0.385013\pi$
$212$	−1.53590	−	1.53590i	−0.105486	−	0.105486i
$213$		0			0
$214$	−5.00000	+	5.00000i	−0.341793	+	0.341793i
$215$	−25.6962	−	5.25833i	−1.75246	−	0.358615i
$216$		0			0
$217$	−5.00000	+	5.00000i	−0.339422	+	0.339422i
$218$	1.63397	−	1.63397i	0.110667	−	0.110667i
$219$		0			0
$220$	−11.5622	−	2.36603i	−0.779522	−	0.159517i
$221$	22.7583	+	12.5622i	1.53089	+	0.845024i
$222$		0			0
$223$		−	6.12436i		−	0.410117i	−0.978750	−	0.205059i	$-0.934262\pi$
$223$		−	6.12436i		−	0.410117i	0.978750	−	0.205059i	$-0.0657385\pi$
$224$			1.00000i			0.0668153i
$225$		0			0
$226$	−0.803848	−	0.803848i	−0.0534711	−	0.0534711i
$227$	−6.00000			−0.398234			−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000			−0.398234			−0.199117	+	0.979976i	$0.563807\pi$
$228$		0			0
$229$	10.0981	+	10.0981i	0.667300	+	0.667300i	0.957090	−	0.289790i	$-0.0935856\pi$
$229$	10.0981	+	10.0981i	0.667300	+	0.667300i	−0.289790	+	0.957090i	$0.593586\pi$
$230$	0.830127	+	0.169873i	0.0547370	+	0.0112011i
$231$		0			0
$232$			3.26795i			0.214551i
$233$	−14.2942	+	14.2942i	−0.936446	+	0.936446i	−0.998098	−	0.0616517i	$-0.980363\pi$
$233$	−14.2942	+	14.2942i	−0.936446	+	0.936446i	0.0616517	+	0.998098i	$0.480363\pi$
$234$		0			0
$235$	−0.500000	+	0.330127i	−0.0326164	+	0.0215351i
$236$	1.26795	+	1.26795i	0.0825365	+	0.0825365i
$237$		0			0
$238$	−5.09808	+	5.09808i	−0.330459	+	0.330459i
$239$	16.4904	−	16.4904i	1.06667	−	1.06667i	0.0690617	−	0.997612i	$-0.477999\pi$
$239$	16.4904	−	16.4904i	1.06667	−	1.06667i	0.997612	−	0.0690617i	$-0.0220005\pi$
$240$		0			0
$241$	−10.5359	+	10.5359i	−0.678677	+	0.678677i	−0.959701	−	0.281024i	$-0.909326\pi$
$241$	−10.5359	+	10.5359i	−0.678677	+	0.678677i	0.281024	+	0.959701i	$0.409326\pi$
$242$			16.8564i			1.08357i
$243$		0			0
$244$	−4.92820			−0.315496
$245$	−7.39230	−	11.1962i	−0.472277	−	0.715296i
$246$		0			0
$247$	−8.53590	+	15.4641i	−0.543126	+	0.983957i
$248$	5.00000	+	5.00000i	0.317500	+	0.317500i
$249$		0			0
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$		−	12.9282i		−	0.816021i	−0.912977	−	0.408010i	$-0.866223\pi$
$251$		−	12.9282i		−	0.816021i	0.912977	−	0.408010i	$-0.133777\pi$
$252$		0			0
$253$		−	2.00000i		−	0.125739i
$254$	5.53590	+	5.53590i	0.347353	+	0.347353i
$255$		0			0
$256$	1.00000			0.0625000
$257$	16.0981	+	16.0981i	1.00417	+	1.00417i	0.999991	+	0.00417914i	$0.00133026\pi$
$257$	16.0981	+	16.0981i	1.00417	+	1.00417i	0.00417914	+	0.999991i	$0.498670\pi$
$258$		0			0
$259$	−2.46410			−0.153112
$260$	−6.13397	−	5.23205i	−0.380413	−	0.324478i
$261$		0			0
$262$	−12.4641			−0.770035
$263$	20.1962	+	20.1962i	1.24535	+	1.24535i	0.957752	+	0.287596i	$0.0928562\pi$
$263$	20.1962	+	20.1962i	1.24535	+	1.24535i	0.287596	+	0.957752i	$0.407144\pi$
$264$		0			0
$265$	−0.973721	+	4.75833i	−0.0598152	+	0.292302i
$266$	−3.46410	−	3.46410i	−0.212398	−	0.212398i
$267$		0			0
$268$	10.7321			0.655564
$269$			20.0000i			1.21942i	0.792624	+	0.609711i	$0.208714\pi$
$269$			20.0000i			1.21942i	−0.792624	+	0.609711i	$0.791286\pi$
$270$		0			0
$271$	19.6865	−	19.6865i	1.19587	−	1.19587i	0.220480	−	0.975391i	$-0.429238\pi$
$271$	19.6865	−	19.6865i	1.19587	−	1.19587i	0.975391	−	0.220480i	$-0.0707625\pi$
$272$	5.09808	+	5.09808i	0.309116	+	0.309116i
$273$		0			0
$274$			11.6603i			0.704422i
$275$	9.83013	+	24.4904i	0.592779	+	1.47683i
$276$		0			0
$277$	1.46410	+	1.46410i	0.0879693	+	0.0879693i	0.749722	−	0.661753i	$-0.230187\pi$
$277$	1.46410	+	1.46410i	0.0879693	+	0.0879693i	−0.661753	+	0.749722i	$0.730187\pi$
$278$			6.26795i			0.375927i
$279$		0			0
$280$	1.86603	−	1.23205i	0.111516	−	0.0736291i
$281$	5.66025	−	5.66025i	0.337662	−	0.337662i	−0.517824	−	0.855487i	$-0.673258\pi$
$281$	5.66025	−	5.66025i	0.337662	−	0.337662i	0.855487	+	0.517824i	$0.173258\pi$
$282$		0			0
$283$	8.66025	−	8.66025i	0.514799	−	0.514799i	−0.401194	−	0.915993i	$-0.631405\pi$
$283$	8.66025	−	8.66025i	0.514799	−	0.514799i	0.915993	+	0.401194i	$0.131405\pi$
$284$	−8.56218	−	8.56218i	−0.508072	−	0.508072i
$285$		0			0
$286$	−9.19615	+	16.6603i	−0.543780	+	0.985141i
$287$	−6.19615	+	6.19615i	−0.365747	+	0.365747i
$288$		0			0
$289$			34.9808i			2.05769i
$290$	6.09808	−	4.02628i	0.358091	−	0.236431i
$291$		0			0
$292$		0			0
$293$	24.8564			1.45213			0.726063	−	0.687628i	$-0.241348\pi$
$293$	24.8564			1.45213			0.726063	+	0.687628i	$0.241348\pi$
$294$		0			0
$295$	0.803848	−	3.92820i	0.0468018	−	0.228709i
$296$			2.46410i			0.143223i
$297$		0			0
$298$	10.6603	−	10.6603i	0.617532	−	0.617532i
$299$	0.660254	−	1.19615i	0.0381835	−	0.0691753i
$300$		0			0
$301$	−8.29423	−	8.29423i	−0.478071	−	0.478071i
$302$	−7.90192	+	7.90192i	−0.454705	+	0.454705i
$303$		0			0
$304$	−3.46410	+	3.46410i	−0.198680	+	0.198680i
$305$	6.07180	+	9.19615i	0.347670	+	0.526570i
$306$		0			0
$307$			12.3923i			0.707266i	0.935384	+	0.353633i	$0.115054\pi$
$307$			12.3923i			0.707266i	−0.935384	+	0.353633i	$0.884946\pi$
$308$	−3.73205	−	3.73205i	−0.212653	−	0.212653i
$309$		0			0
$310$	3.16987	−	15.4904i	0.180037	−	0.879795i
$311$		−	10.0000i		−	0.567048i	−0.958965	−	0.283524i	$-0.908496\pi$
$311$		−	10.0000i		−	0.567048i	0.958965	−	0.283524i	$-0.0915036\pi$
$312$		0			0
$313$	15.1699	+	15.1699i	0.857452	+	0.857452i	0.991037	−	0.133585i	$-0.0426490\pi$
$313$	15.1699	+	15.1699i	0.857452	+	0.857452i	−0.133585	+	0.991037i	$0.542649\pi$
$314$	15.4641	−	15.4641i	0.872690	−	0.872690i
$315$		0			0
$316$			0.196152i			0.0110344i
$317$	23.7128			1.33184			0.665922	−	0.746021i	$-0.268038\pi$
$317$	23.7128			1.33184			0.665922	+	0.746021i	$0.268038\pi$
$318$		0			0
$319$	−12.1962	−	12.1962i	−0.682853	−	0.682853i
$320$	−1.23205	−	1.86603i	−0.0688737	−	0.104314i
$321$		0			0
$322$	0.267949	+	0.267949i	0.0149322	+	0.0149322i
$323$	−35.3205			−1.96529
$324$		0			0
$325$	−2.20577	+	17.8923i	−0.122354	+	0.992487i
$326$	0.732051			0.0405445
$327$		0			0
$328$	6.19615	+	6.19615i	0.342125	+	0.342125i
$329$	−0.267949			−0.0147725
$330$		0			0
$331$	9.00000	+	9.00000i	0.494685	+	0.494685i	0.909779	−	0.415094i	$-0.136251\pi$
$331$	9.00000	+	9.00000i	0.494685	+	0.494685i	−0.415094	+	0.909779i	$0.636251\pi$
$332$			2.19615i			0.120530i
$333$		0			0
$334$		−	6.53590i		−	0.357628i
$335$	−13.2224	−	20.0263i	−0.722419	−	1.09415i
$336$		0			0
$337$	1.36603	+	1.36603i	0.0744121	+	0.0744121i	0.743333	−	0.668921i	$-0.233244\pi$
$337$	1.36603	+	1.36603i	0.0744121	+	0.0744121i	−0.668921	+	0.743333i	$0.733244\pi$
$338$	−11.0000	+	6.92820i	−0.598321	+	0.376845i
$339$		0			0
$340$	3.23205	−	15.7942i	0.175283	−	0.856562i
$341$	−37.3205			−2.02102
$342$		0			0
$343$		−	13.0000i		−	0.701934i
$344$	−8.29423	+	8.29423i	−0.447195	+	0.447195i
$345$		0			0
$346$	−1.73205	+	1.73205i	−0.0931156	+	0.0931156i
$347$	4.63397	−	4.63397i	0.248765	−	0.248765i	−0.571699	−	0.820464i	$-0.693715\pi$
$347$	4.63397	−	4.63397i	0.248765	−	0.248765i	0.820464	+	0.571699i	$0.193715\pi$
$348$		0			0
$349$	−20.0263	−	20.0263i	−1.07198	−	1.07198i	−0.997200	−	0.0747823i	$-0.976174\pi$
$349$	−20.0263	−	20.0263i	−1.07198	−	1.07198i	−0.0747823	−	0.997200i	$-0.523826\pi$
$350$	−4.59808	−	1.96410i	−0.245778	−	0.104986i
$351$		0			0
$352$	−3.73205	+	3.73205i	−0.198919	+	0.198919i
$353$			29.5167i			1.57101i	0.618853	+	0.785507i	$0.287598\pi$
$353$			29.5167i			1.57101i	−0.618853	+	0.785507i	$0.712402\pi$
$354$		0			0
$355$	−5.42820	+	26.5263i	−0.288099	+	1.40787i
$356$	0.196152	+	0.196152i	0.0103961	+	0.0103961i
$357$		0			0
$358$	21.3923			1.13062
$359$	19.7846	+	19.7846i	1.04419	+	1.04419i	0.998977	+	0.0452145i	$0.0143971\pi$
$359$	19.7846	+	19.7846i	1.04419	+	1.04419i	0.0452145	+	0.998977i	$0.485603\pi$
$360$		0			0
$361$		−	5.00000i		−	0.263158i
$362$			6.19615i			0.325663i
$363$		0			0
$364$	−1.00000	−	3.46410i	−0.0524142	−	0.181568i
$365$		0			0
$366$		0			0
$367$	20.6603	−	20.6603i	1.07846	−	1.07846i	0.0818084	−	0.996648i	$-0.473930\pi$
$367$	20.6603	−	20.6603i	1.07846	−	1.07846i	0.996648	−	0.0818084i	$-0.0260696\pi$
$368$	0.267949	−	0.267949i	0.0139678	−	0.0139678i
$369$		0			0
$370$	4.59808	−	3.03590i	0.239043	−	0.157829i
$371$	−1.53590	+	1.53590i	−0.0797399	+	0.0797399i
$372$		0			0
$373$	8.00000	+	8.00000i	0.414224	+	0.414224i	0.883207	−	0.468983i	$-0.155379\pi$
$373$	8.00000	+	8.00000i	0.414224	+	0.414224i	−0.468983	+	0.883207i	$0.655379\pi$
$374$	−38.0526			−1.96765
$375$		0			0
$376$			0.267949i			0.0138184i
$377$	−3.26795	−	11.3205i	−0.168308	−	0.583036i
$378$		0			0
$379$	−19.0000	+	19.0000i	−0.975964	+	0.975964i	−0.999718	−	0.0237534i	$-0.992438\pi$
$379$	−19.0000	+	19.0000i	−0.975964	+	0.975964i	0.0237534	+	0.999718i	$0.492438\pi$
$380$	10.7321	+	2.19615i	0.550543	+	0.112660i
$381$		0			0
$382$	13.1244			0.671500
$383$			5.53590i			0.282871i	0.989947	+	0.141436i	$0.0451718\pi$
$383$			5.53590i			0.282871i	−0.989947	+	0.141436i	$0.954828\pi$
$384$		0			0
$385$	−2.36603	+	11.5622i	−0.120584	+	0.589263i
$386$	11.2679			0.573524
$387$		0			0
$388$	0.196152			0.00995813
$389$	13.4641			0.682657			0.341329	−	0.939944i	$-0.389123\pi$
$389$	13.4641			0.682657			0.341329	+	0.939944i	$0.389123\pi$
$390$		0			0
$391$	2.73205			0.138166
$392$	−6.00000			−0.303046
$393$		0			0
$394$	3.33975			0.168254
$395$	0.366025	−	0.241670i	0.0184167	−	0.0121597i
$396$		0			0
$397$			15.0718i			0.756432i	0.925717	+	0.378216i	$0.123462\pi$
$397$			15.0718i			0.756432i	−0.925717	+	0.378216i	$0.876538\pi$
$398$	24.5885			1.23251
$399$		0			0
$400$	−1.96410	+	4.59808i	−0.0982051	+	0.229904i
$401$	13.1962	−	13.1962i	0.658984	−	0.658984i	−0.296155	−	0.955140i	$-0.595705\pi$
$401$	13.1962	−	13.1962i	0.658984	−	0.658984i	0.955140	+	0.296155i	$0.0957046\pi$
$402$		0			0
$403$	−22.3205	−	12.3205i	−1.11186	−	0.613728i
$404$		−	0.928203i		−	0.0461798i
$405$		0			0
$406$	3.26795			0.162186
$407$	−9.19615	−	9.19615i	−0.455836	−	0.455836i
$408$		0			0
$409$	−6.80385	+	6.80385i	−0.336429	+	0.336429i	−0.855021	−	0.518593i	$-0.826456\pi$
$409$	−6.80385	+	6.80385i	−0.336429	+	0.336429i	0.518593	+	0.855021i	$0.326456\pi$
$410$	3.92820	−	19.1962i	0.194000	−	0.948030i
$411$		0			0
$412$	−4.66025	+	4.66025i	−0.229594	+	0.229594i
$413$	1.26795	−	1.26795i	0.0623917	−	0.0623917i
$414$		0			0
$415$	4.09808	−	2.70577i	0.201167	−	0.132821i
$416$	−3.46410	+	1.00000i	−0.169842	+	0.0490290i
$417$		0			0
$418$		−	25.8564i		−	1.26468i
$419$		−	12.2679i		−	0.599329i	−0.954045	−	0.299664i	$-0.903125\pi$
$419$		−	12.2679i		−	0.599329i	0.954045	−	0.299664i	$-0.0968747\pi$
$420$		0			0
$421$	16.0981	+	16.0981i	0.784572	+	0.784572i	0.980599	−	0.196026i	$-0.0628038\pi$
$421$	16.0981	+	16.0981i	0.784572	+	0.784572i	−0.196026	+	0.980599i	$0.562804\pi$
$422$	−10.2679			−0.499836
$423$		0			0
$424$	1.53590	+	1.53590i	0.0745898	+	0.0745898i
$425$	−33.4545	+	13.4282i	−1.62278	+	0.651364i
$426$		0			0
$427$			4.92820i			0.238492i
$428$	5.00000	−	5.00000i	0.241684	−	0.241684i
$429$		0			0
$430$	25.6962	+	5.25833i	1.23918	+	0.253579i
$431$	12.2942	+	12.2942i	0.592192	+	0.592192i	0.938223	−	0.346031i	$-0.112471\pi$
$431$	12.2942	+	12.2942i	0.592192	+	0.592192i	−0.346031	+	0.938223i	$0.612471\pi$
$432$		0			0
$433$	2.36603	−	2.36603i	0.113704	−	0.113704i	−0.647966	−	0.761670i	$-0.724380\pi$
$433$	2.36603	−	2.36603i	0.113704	−	0.113704i	0.761670	+	0.647966i	$0.224380\pi$
$434$	5.00000	−	5.00000i	0.240008	−	0.240008i
$435$		0			0
$436$	−1.63397	+	1.63397i	−0.0782532	+	0.0782532i
$437$			1.85641i			0.0888040i
$438$		0			0
$439$	15.3205			0.731208			0.365604	−	0.930771i	$-0.380862\pi$
$439$	15.3205			0.731208			0.365604	+	0.930771i	$0.380862\pi$
$440$	11.5622	+	2.36603i	0.551205	+	0.112796i
$441$		0			0
$442$	−22.7583	−	12.5622i	−1.08250	−	0.597522i
$443$	−18.1506	−	18.1506i	−0.862363	−	0.862363i	0.129249	−	0.991612i	$-0.458743\pi$
$443$	−18.1506	−	18.1506i	−0.862363	−	0.862363i	−0.991612	+	0.129249i	$0.958743\pi$
$444$		0			0
$445$	0.124356	−	0.607695i	0.00589502	−	0.0288075i
$446$			6.12436i			0.289997i
$447$		0			0
$448$		−	1.00000i		−	0.0472456i
$449$	11.3923	+	11.3923i	0.537636	+	0.537636i	0.922834	−	0.385198i	$-0.125867\pi$
$449$	11.3923	+	11.3923i	0.537636	+	0.537636i	−0.385198	+	0.922834i	$0.625867\pi$
$450$		0			0
$451$	−46.2487			−2.17777
$452$	0.803848	+	0.803848i	0.0378098	+	0.0378098i
$453$		0			0
$454$	6.00000			0.281594
$455$	−5.23205	+	6.13397i	−0.245282	+	0.287565i
$456$		0			0
$457$	14.0000			0.654892			0.327446	−	0.944870i	$-0.393812\pi$
$457$	14.0000			0.654892			0.327446	+	0.944870i	$0.393812\pi$
$458$	−10.0981	−	10.0981i	−0.471852	−	0.471852i
$459$		0			0
$460$	−0.830127	−	0.169873i	−0.0387049	−	0.00792037i
$461$	5.09808	+	5.09808i	0.237441	+	0.237441i	0.815790	−	0.578349i	$-0.196303\pi$
$461$	5.09808	+	5.09808i	0.237441	+	0.237441i	−0.578349	+	0.815790i	$0.696303\pi$
$462$		0			0
$463$	−13.4641			−0.625730			−0.312865	−	0.949798i	$-0.601289\pi$
$463$	−13.4641			−0.625730			−0.312865	+	0.949798i	$0.601289\pi$
$464$		−	3.26795i		−	0.151711i
$465$		0			0
$466$	14.2942	−	14.2942i	0.662167	−	0.662167i
$467$	18.8564	+	18.8564i	0.872570	+	0.872570i	0.992752	−	0.120182i	$-0.0383477\pi$
$467$	18.8564	+	18.8564i	0.872570	+	0.872570i	−0.120182	+	0.992752i	$0.538348\pi$
$468$		0			0
$469$		−	10.7321i		−	0.495560i
$470$	0.500000	−	0.330127i	0.0230633	−	0.0152276i
$471$		0			0
$472$	−1.26795	−	1.26795i	−0.0583621	−	0.0583621i
$473$		−	61.9090i		−	2.84658i
$474$		0			0
$475$	−9.12436	−	22.7321i	−0.418654	−	1.04302i
$476$	5.09808	−	5.09808i	0.233670	−	0.233670i
$477$		0			0
$478$	−16.4904	+	16.4904i	−0.754252	+	0.754252i
$479$	−16.4186	−	16.4186i	−0.750184	−	0.750184i	0.224329	−	0.974513i	$-0.427981\pi$
$479$	−16.4186	−	16.4186i	−0.750184	−	0.750184i	−0.974513	+	0.224329i	$0.927981\pi$
$480$		0			0
$481$	−2.46410	−	8.53590i	−0.112353	−	0.389203i
$482$	10.5359	−	10.5359i	0.479897	−	0.479897i
$483$		0			0
$484$		−	16.8564i		−	0.766200i
$485$	−0.241670	−	0.366025i	−0.0109737	−	0.0166204i
$486$		0			0
$487$	−15.8564			−0.718522			−0.359261	−	0.933237i	$-0.616971\pi$
$487$	−15.8564			−0.718522			−0.359261	+	0.933237i	$0.616971\pi$
$488$	4.92820			0.223089
$489$		0			0
$490$	7.39230	+	11.1962i	0.333950	+	0.505791i
$491$			13.8756i			0.626199i	0.949720	+	0.313100i	$0.101367\pi$
$491$			13.8756i			0.626199i	−0.949720	+	0.313100i	$0.898633\pi$
$492$		0			0
$493$	16.6603	−	16.6603i	0.750340	−	0.750340i
$494$	8.53590	−	15.4641i	0.384048	−	0.695763i
$495$		0			0
$496$	−5.00000	−	5.00000i	−0.224507	−	0.224507i
$497$	−8.56218	+	8.56218i	−0.384066	+	0.384066i
$498$		0			0
$499$	16.5885	−	16.5885i	0.742601	−	0.742601i	−0.230477	−	0.973078i	$-0.574028\pi$
$499$	16.5885	−	16.5885i	0.742601	−	0.742601i	0.973078	+	0.230477i	$0.0740285\pi$
$500$	11.0000	−	2.00000i	0.491935	−	0.0894427i
$501$		0			0
$502$			12.9282i			0.577014i
$503$	1.26795	+	1.26795i	0.0565351	+	0.0565351i	0.734809	−	0.678274i	$-0.237272\pi$
$503$	1.26795	+	1.26795i	0.0565351	+	0.0565351i	−0.678274	+	0.734809i	$0.737272\pi$
$504$		0			0
$505$	−1.73205	+	1.14359i	−0.0770752	+	0.0508892i
$506$			2.00000i			0.0889108i
$507$		0			0
$508$	−5.53590	−	5.53590i	−0.245616	−	0.245616i
$509$	1.33975	−	1.33975i	0.0593832	−	0.0593832i	−0.676792	−	0.736175i	$-0.736630\pi$
$509$	1.33975	−	1.33975i	0.0593832	−	0.0593832i	0.736175	+	0.676792i	$0.236630\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−16.0981	−	16.0981i	−0.710056	−	0.710056i
$515$	14.4378	+	2.95448i	0.636206	+	0.130190i
$516$		0			0
$517$	−1.00000	−	1.00000i	−0.0439799	−	0.0439799i
$518$	2.46410			0.108266
$519$		0			0
$520$	6.13397	+	5.23205i	0.268993	+	0.229441i
$521$	6.60770			0.289488			0.144744	−	0.989469i	$-0.453764\pi$
$521$	6.60770			0.289488			0.144744	+	0.989469i	$0.453764\pi$
$522$		0			0
$523$	−18.4641	−	18.4641i	−0.807379	−	0.807379i	0.176858	−	0.984236i	$-0.443407\pi$
$523$	−18.4641	−	18.4641i	−0.807379	−	0.807379i	−0.984236	+	0.176858i	$0.943407\pi$
$524$	12.4641			0.544497
$525$		0			0
$526$	−20.1962	−	20.1962i	−0.880594	−	0.880594i
$527$		−	50.9808i		−	2.22076i
$528$		0			0
$529$			22.8564i			0.993757i
$530$	0.973721	−	4.75833i	0.0422957	−	0.206689i
$531$		0			0
$532$	3.46410	+	3.46410i	0.150188	+	0.150188i
$533$	−27.6603	−	15.2679i	−1.19810	−	0.661328i
$534$		0			0
$535$	−15.4904	−	3.16987i	−0.669708	−	0.137046i
$536$	−10.7321			−0.463554
$537$		0			0
$538$		−	20.0000i		−	0.862261i
$539$	22.3923	−	22.3923i	0.964505	−	0.964505i
$540$		0			0
$541$	10.6865	−	10.6865i	0.459450	−	0.459450i	−0.439025	−	0.898475i	$-0.644676\pi$
$541$	10.6865	−	10.6865i	0.459450	−	0.459450i	0.898475	+	0.439025i	$0.144676\pi$
$542$	−19.6865	+	19.6865i	−0.845609	+	0.845609i
$543$		0			0
$544$	−5.09808	−	5.09808i	−0.218578	−	0.218578i
$545$	5.06218	+	1.03590i	0.216840	+	0.0443730i
$546$		0			0
$547$	13.3660	−	13.3660i	0.571490	−	0.571490i	−0.361055	−	0.932545i	$-0.617583\pi$
$547$	13.3660	−	13.3660i	0.571490	−	0.571490i	0.932545	+	0.361055i	$0.117583\pi$
$548$		−	11.6603i		−	0.498101i
$549$		0			0
$550$	−9.83013	−	24.4904i	−0.419158	−	1.04427i
$551$	11.3205	+	11.3205i	0.482270	+	0.482270i
$552$		0			0
$553$	0.196152			0.00834125
$554$	−1.46410	−	1.46410i	−0.0622037	−	0.0622037i
$555$		0			0
$556$		−	6.26795i		−	0.265820i
$557$		−	5.05256i		−	0.214084i	−0.994255	−	0.107042i	$-0.965862\pi$
$557$		−	5.05256i		−	0.214084i	0.994255	−	0.107042i	$-0.0341379\pi$
$558$		0			0
$559$	20.4378	−	37.0263i	0.864428	−	1.56604i
$560$	−1.86603	+	1.23205i	−0.0788540	+	0.0520636i
$561$		0			0
$562$	−5.66025	+	5.66025i	−0.238763	+	0.238763i
$563$	12.4904	−	12.4904i	0.526407	−	0.526407i	−0.393092	−	0.919499i	$-0.628595\pi$
$563$	12.4904	−	12.4904i	0.526407	−	0.526407i	0.919499	+	0.393092i	$0.128595\pi$
$564$		0			0
$565$	0.509619	−	2.49038i	0.0214398	−	0.104771i
$566$	−8.66025	+	8.66025i	−0.364018	+	0.364018i
$567$		0			0
$568$	8.56218	+	8.56218i	0.359261	+	0.359261i
$569$	−22.0718			−0.925298			−0.462649	−	0.886542i	$-0.653101\pi$
$569$	−22.0718			−0.925298			−0.462649	+	0.886542i	$0.653101\pi$
$570$		0			0
$571$			38.8564i			1.62609i	0.582201	+	0.813045i	$0.302192\pi$
$571$			38.8564i			1.62609i	−0.582201	+	0.813045i	$0.697808\pi$
$572$	9.19615	−	16.6603i	0.384510	−	0.696600i
$573$		0			0
$574$	6.19615	−	6.19615i	0.258622	−	0.258622i
$575$	0.705771	+	1.75833i	0.0294327	+	0.0733274i
$576$		0			0
$577$	12.3923			0.515898			0.257949	−	0.966158i	$-0.416953\pi$
$577$	12.3923			0.515898			0.257949	+	0.966158i	$0.416953\pi$
$578$		−	34.9808i		−	1.45501i
$579$		0			0
$580$	−6.09808	+	4.02628i	−0.253209	+	0.167182i
$581$	2.19615			0.0911118
$582$		0			0
$583$	−11.4641			−0.474795
$584$		0			0
$585$		0			0
$586$	−24.8564			−1.02681
$587$	−5.66025			−0.233624			−0.116812	−	0.993154i	$-0.537267\pi$
$587$	−5.66025			−0.233624			−0.116812	+	0.993154i	$0.537267\pi$
$588$		0			0
$589$	34.6410			1.42736
$590$	−0.803848	+	3.92820i	−0.0330939	+	0.161722i
$591$		0			0
$592$		−	2.46410i		−	0.101274i
$593$	14.7321			0.604973			0.302486	−	0.953154i	$-0.402183\pi$
$593$	14.7321			0.604973			0.302486	+	0.953154i	$0.402183\pi$
$594$		0			0
$595$	−15.7942	−	3.23205i	−0.647500	−	0.132501i
$596$	−10.6603	+	10.6603i	−0.436661	+	0.436661i
$597$		0			0
$598$	−0.660254	+	1.19615i	−0.0269998	+	0.0489143i
$599$			16.7846i			0.685801i	0.939372	+	0.342900i	$0.111409\pi$
$599$			16.7846i			0.685801i	−0.939372	+	0.342900i	$0.888591\pi$
$600$		0			0
$601$	30.2679			1.23466			0.617328	−	0.786706i	$-0.288215\pi$
$601$	30.2679			1.23466			0.617328	+	0.786706i	$0.288215\pi$
$602$	8.29423	+	8.29423i	0.338048	+	0.338048i
$603$		0			0
$604$	7.90192	−	7.90192i	0.321525	−	0.321525i
$605$	−31.4545	+	20.7679i	−1.27881	+	0.844337i
$606$		0			0
$607$	−3.12436	+	3.12436i	−0.126814	+	0.126814i	−0.767665	−	0.640851i	$-0.778581\pi$
$607$	−3.12436	+	3.12436i	−0.126814	+	0.126814i	0.640851	+	0.767665i	$0.278581\pi$
$608$	3.46410	−	3.46410i	0.140488	−	0.140488i
$609$		0			0
$610$	−6.07180	−	9.19615i	−0.245840	−	0.372341i
$611$	−0.267949	−	0.928203i	−0.0108401	−	0.0375511i
$612$		0			0
$613$			24.7846i			1.00104i	0.865725	+	0.500520i	$0.166858\pi$
$613$			24.7846i			1.00104i	−0.865725	+	0.500520i	$0.833142\pi$
$614$		−	12.3923i		−	0.500113i
$615$		0			0
$616$	3.73205	+	3.73205i	0.150369	+	0.150369i
$617$	−4.78461			−0.192621			−0.0963106	−	0.995351i	$-0.530704\pi$
$617$	−4.78461			−0.192621			−0.0963106	+	0.995351i	$0.530704\pi$
$618$		0			0
$619$	30.2487	+	30.2487i	1.21580	+	1.21580i	0.969090	+	0.246709i	$0.0793491\pi$
$619$	30.2487	+	30.2487i	1.21580	+	1.21580i	0.246709	+	0.969090i	$0.420651\pi$
$620$	−3.16987	+	15.4904i	−0.127305	+	0.622109i
$621$		0			0
$622$			10.0000i			0.400963i
$623$	0.196152	−	0.196152i	0.00785868	−	0.00785868i
$624$		0			0
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	−15.1699	−	15.1699i	−0.606310	−	0.606310i
$627$		0			0
$628$	−15.4641	+	15.4641i	−0.617085	+	0.617085i
$629$	12.5622	−	12.5622i	0.500887	−	0.500887i
$630$		0			0
$631$	−8.09808	+	8.09808i	−0.322379	+	0.322379i	−0.849679	−	0.527300i	$-0.823204\pi$
$631$	−8.09808	+	8.09808i	−0.322379	+	0.322379i	0.527300	+	0.849679i	$0.323204\pi$
$632$		−	0.196152i		−	0.00780252i
$633$		0			0
$634$	−23.7128			−0.941756
$635$	−3.50962	+	17.1506i	−0.139275	+	0.680602i
$636$		0			0
$637$	20.7846	−	6.00000i	0.823516	−	0.237729i
$638$	12.1962	+	12.1962i	0.482850	+	0.482850i
$639$		0			0
$640$	1.23205	+	1.86603i	0.0487011	+	0.0737611i
$641$		−	32.5359i		−	1.28509i	−0.766248	−	0.642545i	$-0.777878\pi$
$641$		−	32.5359i		−	1.28509i	0.766248	−	0.642545i	$-0.222122\pi$
$642$		0			0
$643$			13.6603i			0.538708i	0.963041	+	0.269354i	$0.0868101\pi$
$643$			13.6603i			0.538708i	−0.963041	+	0.269354i	$0.913190\pi$
$644$	−0.267949	−	0.267949i	−0.0105587	−	0.0105587i
$645$		0			0
$646$	35.3205			1.38967
$647$	−27.8564	−	27.8564i	−1.09515	−	1.09515i	−0.994969	−	0.100179i	$-0.968058\pi$
$647$	−27.8564	−	27.8564i	−1.09515	−	1.09515i	−0.100179	−	0.994969i	$-0.531942\pi$
$648$		0			0
$649$	9.46410			0.371498
$650$	2.20577	−	17.8923i	0.0865175	−	0.701794i
$651$		0			0
$652$	−0.732051			−0.0286693
$653$	−2.19615	−	2.19615i	−0.0859421	−	0.0859421i	0.662829	−	0.748771i	$-0.269356\pi$
$653$	−2.19615	−	2.19615i	−0.0859421	−	0.0859421i	−0.748771	+	0.662829i	$0.769356\pi$
$654$		0			0
$655$	−15.3564	−	23.2583i	−0.600024	−	0.908778i
$656$	−6.19615	−	6.19615i	−0.241919	−	0.241919i
$657$		0			0
$658$	0.267949			0.0104457
$659$			0.392305i			0.0152820i	0.999971	+	0.00764101i	$0.00243223\pi$
$659$			0.392305i			0.0152820i	−0.999971	+	0.00764101i	$0.997568\pi$
$660$		0			0
$661$	−6.85641	+	6.85641i	−0.266683	+	0.266683i	−0.827762	−	0.561079i	$-0.810386\pi$
$661$	−6.85641	+	6.85641i	−0.266683	+	0.266683i	0.561079	+	0.827762i	$0.310386\pi$
$662$	−9.00000	−	9.00000i	−0.349795	−	0.349795i
$663$		0			0
$664$		−	2.19615i		−	0.0852272i
$665$	2.19615	−	10.7321i	0.0851631	−	0.416171i
$666$		0			0
$667$	−0.875644	−	0.875644i	−0.0339051	−	0.0339051i
$668$			6.53590i			0.252882i
$669$		0			0
$670$	13.2224	+	20.0263i	0.510827	+	0.773683i
$671$	−18.3923	+	18.3923i	−0.710027	+	0.710027i
$672$		0			0
$673$	−2.09808	+	2.09808i	−0.0808749	+	0.0808749i	−0.746387	−	0.665512i	$-0.768213\pi$
$673$	−2.09808	+	2.09808i	−0.0808749	+	0.0808749i	0.665512	+	0.746387i	$0.268213\pi$
$674$	−1.36603	−	1.36603i	−0.0526173	−	0.0526173i
$675$		0			0
$676$	11.0000	−	6.92820i	0.423077	−	0.266469i
$677$	−34.9090	+	34.9090i	−1.34166	+	1.34166i	−0.447253	+	0.894407i	$0.647598\pi$
$677$	−34.9090	+	34.9090i	−1.34166	+	1.34166i	−0.894407	+	0.447253i	$0.852402\pi$
$678$		0			0
$679$		−	0.196152i		−	0.00752764i
$680$	−3.23205	+	15.7942i	−0.123943	+	0.605681i
$681$		0			0
$682$	37.3205			1.42908
$683$	−13.5167			−0.517201			−0.258600	−	0.965984i	$-0.583261\pi$
$683$	−13.5167			−0.517201			−0.258600	+	0.965984i	$0.583261\pi$
$684$		0			0
$685$	−21.7583	+	14.3660i	−0.831343	+	0.548898i
$686$			13.0000i			0.496342i
$687$		0			0
$688$	8.29423	−	8.29423i	0.316215	−	0.316215i
$689$	−6.85641	−	3.78461i	−0.261208	−	0.144182i
$690$		0			0
$691$	26.7846	+	26.7846i	1.01893	+	1.01893i	0.999817	+	0.0191173i	$0.00608560\pi$
$691$	26.7846	+	26.7846i	1.01893	+	1.01893i	0.0191173	+	0.999817i	$0.493914\pi$
$692$	1.73205	−	1.73205i	0.0658427	−	0.0658427i
$693$		0			0
$694$	−4.63397	+	4.63397i	−0.175903	+	0.175903i
$695$	−11.6962	+	7.72243i	−0.443660	+	0.292929i
$696$		0			0
$697$		−	63.1769i		−	2.39300i
$698$	20.0263	+	20.0263i	0.758006	+	0.758006i
$699$		0			0
$700$	4.59808	+	1.96410i	0.173791	+	0.0742361i
$701$		−	10.9808i		−	0.414738i	−0.978263	−	0.207369i	$-0.933510\pi$
$701$		−	10.9808i		−	0.414738i	0.978263	−	0.207369i	$-0.0664900\pi$
$702$		0			0
$703$	8.53590	+	8.53590i	0.321938	+	0.321938i
$704$	3.73205	−	3.73205i	0.140657	−	0.140657i
$705$		0			0
$706$		−	29.5167i		−	1.11087i
$707$	−0.928203			−0.0349087
$708$		0			0
$709$	−6.12436	−	6.12436i	−0.230005	−	0.230005i	0.582690	−	0.812695i	$-0.302000\pi$
$709$	−6.12436	−	6.12436i	−0.230005	−	0.230005i	−0.812695	+	0.582690i	$0.802000\pi$
$710$	5.42820	−	26.5263i	0.203717	−	0.995514i
$711$		0			0
$712$	−0.196152	−	0.196152i	−0.00735112	−	0.00735112i
$713$	−2.67949			−0.100348
$714$		0			0
$715$	−42.4186	+	3.36603i	−1.58637	+	0.125882i
$716$	−21.3923			−0.799468
$717$		0			0
$718$	−19.7846	−	19.7846i	−0.738355	−	0.738355i
$719$	41.9090			1.56294			0.781470	−	0.623942i	$-0.214470\pi$
$719$	41.9090			1.56294			0.781470	+	0.623942i	$0.214470\pi$
$720$		0			0
$721$	4.66025	+	4.66025i	0.173557	+	0.173557i
$722$			5.00000i			0.186081i
$723$		0			0
$724$		−	6.19615i		−	0.230278i
$725$	15.0263	+	6.41858i	0.558062	+	0.238380i
$726$		0			0
$727$	5.73205	+	5.73205i	0.212590	+	0.212590i	0.805367	−	0.592777i	$-0.201968\pi$
$727$	5.73205	+	5.73205i	0.212590	+	0.212590i	−0.592777	+	0.805367i	$0.701968\pi$
$728$	1.00000	+	3.46410i	0.0370625	+	0.128388i
$729$		0			0
$730$		0			0
$731$	84.5692			3.12791
$732$		0			0
$733$			15.3923i			0.568528i	0.958746	+	0.284264i	$0.0917492\pi$
$733$			15.3923i			0.568528i	−0.958746	+	0.284264i	$0.908251\pi$
$734$	−20.6603	+	20.6603i	−0.762584	+	0.762584i
$735$		0			0
$736$	−0.267949	+	0.267949i	−0.00987674	+	0.00987674i
$737$	40.0526	−	40.0526i	1.47535	−	1.47535i
$738$		0			0
$739$	13.3205	+	13.3205i	0.490003	+	0.490003i	0.908307	−	0.418304i	$-0.137375\pi$
$739$	13.3205	+	13.3205i	0.490003	+	0.490003i	−0.418304	+	0.908307i	$0.637375\pi$
$740$	−4.59808	+	3.03590i	−0.169029	+	0.111602i
$741$		0			0
$742$	1.53590	−	1.53590i	0.0563846	−	0.0563846i
$743$		−	47.1051i		−	1.72812i	−0.503390	−	0.864060i	$-0.667914\pi$
$743$		−	47.1051i		−	1.72812i	0.503390	−	0.864060i	$-0.332086\pi$
$744$		0			0
$745$	33.0263	+	6.75833i	1.20999	+	0.247606i
$746$	−8.00000	−	8.00000i	−0.292901	−	0.292901i
$747$		0			0
$748$	38.0526			1.39134
$749$	−5.00000	−	5.00000i	−0.182696	−	0.182696i
$750$		0			0
$751$		−	26.2487i		−	0.957829i	−0.877862	−	0.478915i	$-0.841030\pi$
$751$		−	26.2487i		−	0.957829i	0.877862	−	0.478915i	$-0.158970\pi$
$752$		−	0.267949i		−	0.00977110i
$753$		0			0
$754$	3.26795	+	11.3205i	0.119012	+	0.412269i
$755$	−24.4808	−	5.00962i	−0.890946	−	0.182319i
$756$		0			0
$757$	−24.8564	+	24.8564i	−0.903421	+	0.903421i	−0.995730	−	0.0923090i	$-0.970575\pi$
$757$	−24.8564	+	24.8564i	−0.903421	+	0.903421i	0.0923090	+	0.995730i	$0.470575\pi$
$758$	19.0000	−	19.0000i	0.690111	−	0.690111i
$759$		0			0
$760$	−10.7321	−	2.19615i	−0.389292	−	0.0796628i
$761$	−11.8038	+	11.8038i	−0.427889	+	0.427889i	−0.887909	−	0.460020i	$-0.847842\pi$
$761$	−11.8038	+	11.8038i	−0.427889	+	0.427889i	0.460020	+	0.887909i	$0.347842\pi$
$762$		0			0
$763$	1.63397	+	1.63397i	0.0591539	+	0.0591539i
$764$	−13.1244			−0.474823
$765$		0			0
$766$		−	5.53590i		−	0.200020i
$767$	5.66025	+	3.12436i	0.204380	+	0.112814i
$768$		0			0
$769$	−27.5167	+	27.5167i	−0.992276	+	0.992276i	−0.999970	−	0.00769424i	$-0.997551\pi$
$769$	−27.5167	+	27.5167i	−0.992276	+	0.992276i	0.00769424	+	0.999970i	$0.497551\pi$
$770$	2.36603	−	11.5622i	0.0852656	−	0.416672i
$771$		0			0
$772$	−11.2679			−0.405542
$773$			48.3731i			1.73986i	0.493177	+	0.869929i	$0.335836\pi$
$773$			48.3731i			1.73986i	−0.493177	+	0.869929i	$0.664164\pi$
$774$		0			0
$775$	32.8109	−	13.1699i	1.17860	−	0.473076i
$776$	−0.196152			−0.00704146
$777$		0			0
$778$	−13.4641			−0.482711
$779$	42.9282			1.53806
$780$		0			0
$781$	−63.9090			−2.28684
$782$	−2.73205			−0.0976979
$783$		0			0
$784$	6.00000			0.214286
$785$	47.9090	+	9.80385i	1.70994	+	0.349914i
$786$		0			0
$787$		−	25.1769i		−	0.897460i	−0.893667	−	0.448730i	$-0.851876\pi$
$787$		−	25.1769i		−	0.897460i	0.893667	−	0.448730i	$-0.148124\pi$
$788$	−3.33975			−0.118974
$789$		0			0
$790$	−0.366025	+	0.241670i	−0.0130226	+	0.00859822i
$791$	0.803848	−	0.803848i	0.0285815	−	0.0285815i
$792$		0			0
$793$	−17.0718	+	4.92820i	−0.606237	+	0.175006i
$794$		−	15.0718i		−	0.534878i
$795$		0			0
$796$	−24.5885			−0.871515
$797$	28.5359	+	28.5359i	1.01079	+	1.01079i	0.999941	+	0.0108523i	$0.00345445\pi$
$797$	28.5359	+	28.5359i	1.01079	+	1.01079i	0.0108523	+	0.999941i	$0.496546\pi$
$798$		0			0
$799$	1.36603	−	1.36603i	0.0483265	−	0.0483265i
$800$	1.96410	−	4.59808i	0.0694415	−	0.162567i
$801$		0			0
$802$	−13.1962	+	13.1962i	−0.465972	+	0.465972i
$803$		0			0
$804$		0			0
$805$	−0.169873	+	0.830127i	−0.00598724	+	0.0292581i
$806$	22.3205	+	12.3205i	0.786206	+	0.433971i
$807$		0			0
$808$			0.928203i			0.0326541i
$809$			25.3923i			0.892746i	0.894847	+	0.446373i	$0.147285\pi$
$809$			25.3923i			0.892746i	−0.894847	+	0.446373i	$0.852715\pi$
$810$		0			0
$811$	−6.87564	−	6.87564i	−0.241437	−	0.241437i	0.576008	−	0.817444i	$-0.304610\pi$
$811$	−6.87564	−	6.87564i	−0.241437	−	0.241437i	−0.817444	+	0.576008i	$0.804610\pi$
$812$	−3.26795			−0.114683
$813$		0			0
$814$	9.19615	+	9.19615i	0.322325	+	0.322325i
$815$	0.901924	+	1.36603i	0.0315930	+	0.0478498i
$816$		0			0
$817$			57.4641i			2.01041i
$818$	6.80385	−	6.80385i	0.237891	−	0.237891i
$819$		0			0
$820$	−3.92820	+	19.1962i	−0.137179	+	0.670359i
$821$	−19.7583	−	19.7583i	−0.689570	−	0.689570i	0.272566	−	0.962137i	$-0.412128\pi$
$821$	−19.7583	−	19.7583i	−0.689570	−	0.689570i	−0.962137	+	0.272566i	$0.912128\pi$
$822$		0			0
$823$	18.0000	−	18.0000i	0.627441	−	0.627441i	−0.319983	−	0.947423i	$-0.603677\pi$
$823$	18.0000	−	18.0000i	0.627441	−	0.627441i	0.947423	+	0.319983i	$0.103677\pi$
$824$	4.66025	−	4.66025i	0.162348	−	0.162348i
$825$		0			0
$826$	−1.26795	+	1.26795i	−0.0441176	+	0.0441176i
$827$			54.7846i			1.90505i	0.304464	+	0.952524i	$0.401523\pi$
$827$			54.7846i			1.90505i	−0.304464	+	0.952524i	$0.598477\pi$
$828$		0			0
$829$	−27.1244			−0.942068			−0.471034	−	0.882115i	$-0.656119\pi$
$829$	−27.1244			−0.942068			−0.471034	+	0.882115i	$0.656119\pi$
$830$	−4.09808	+	2.70577i	−0.142246	+	0.0939187i
$831$		0			0
$832$	3.46410	−	1.00000i	0.120096	−	0.0346688i
$833$	30.5885	+	30.5885i	1.05983	+	1.05983i
$834$		0			0
$835$	12.1962	−	8.05256i	0.422065	−	0.278670i
$836$			25.8564i			0.894263i
$837$		0			0
$838$			12.2679i			0.423789i
$839$	−30.3205	−	30.3205i	−1.04678	−	1.04678i	−0.998851	−	0.0479295i	$-0.984738\pi$
$839$	−30.3205	−	30.3205i	−1.04678	−	1.04678i	−0.0479295	−	0.998851i	$-0.515262\pi$
$840$		0			0
$841$	18.3205			0.631742
$842$	−16.0981	−	16.0981i	−0.554776	−	0.554776i
$843$		0			0
$844$	10.2679			0.353437
$845$	−26.4808	−	11.9904i	−0.910966	−	0.412482i
$846$		0			0
$847$	−16.8564			−0.579193
$848$	−1.53590	−	1.53590i	−0.0527430	−	0.0527430i
$849$		0			0
$850$	33.4545	−	13.4282i	1.14748	−	0.460584i
$851$	−0.660254	−	0.660254i	−0.0226332	−	0.0226332i
$852$		0			0
$853$	12.6603			0.433479			0.216739	−	0.976229i	$-0.430458\pi$
$853$	12.6603			0.433479			0.216739	+	0.976229i	$0.430458\pi$
$854$		−	4.92820i		−	0.168640i
$855$		0			0
$856$	−5.00000	+	5.00000i	−0.170896	+	0.170896i
$857$	−13.1962	−	13.1962i	−0.450772	−	0.450772i	0.444839	−	0.895611i	$-0.353261\pi$
$857$	−13.1962	−	13.1962i	−0.450772	−	0.450772i	−0.895611	+	0.444839i	$0.853261\pi$
$858$		0			0
$859$		−	30.1051i		−	1.02717i	−0.858038	−	0.513587i	$-0.828316\pi$
$859$		−	30.1051i		−	1.02717i	0.858038	−	0.513587i	$-0.171684\pi$
$860$	−25.6962	−	5.25833i	−0.876232	−	0.179308i
$861$		0			0
$862$	−12.2942	−	12.2942i	−0.418743	−	0.418743i
$863$		−	0.0192379i		−	0.000654865i	−1.00000		0.000327433i	$-0.999896\pi$
$863$		−	0.0192379i		−	0.000654865i	1.00000		0.000327433i	$-0.000104225\pi$
$864$		0			0
$865$	−5.36603	−	1.09808i	−0.182450	−	0.0373357i
$866$	−2.36603	+	2.36603i	−0.0804008	+	0.0804008i
$867$		0			0
$868$	−5.00000	+	5.00000i	−0.169711	+	0.169711i
$869$	0.732051	+	0.732051i	0.0248331	+	0.0248331i
$870$		0			0
$871$	37.1769	−	10.7321i	1.25969	−	0.363642i
$872$	1.63397	−	1.63397i	0.0553334	−	0.0553334i
$873$		0			0
$874$		−	1.85641i		−	0.0627939i
$875$	−2.00000	−	11.0000i	−0.0676123	−	0.371868i
$876$		0			0
$877$	−35.4449			−1.19689			−0.598444	−	0.801165i	$-0.704214\pi$
$877$	−35.4449			−1.19689			−0.598444	+	0.801165i	$0.704214\pi$
$878$	−15.3205			−0.517042
$879$		0			0
$880$	−11.5622	−	2.36603i	−0.389761	−	0.0797587i
$881$		−	17.9808i		−	0.605787i	−0.953024	−	0.302894i	$-0.902047\pi$
$881$		−	17.9808i		−	0.605787i	0.953024	−	0.302894i	$-0.0979527\pi$
$882$		0			0
$883$	0.562178	−	0.562178i	0.0189188	−	0.0189188i	−0.697584	−	0.716503i	$-0.745742\pi$
$883$	0.562178	−	0.562178i	0.0189188	−	0.0189188i	0.716503	+	0.697584i	$0.245742\pi$
$884$	22.7583	+	12.5622i	0.765445	+	0.422512i
$885$		0			0
$886$	18.1506	+	18.1506i	0.609783	+	0.609783i
$887$	−25.3205	+	25.3205i	−0.850179	+	0.850179i	−0.990155	−	0.139976i	$-0.955298\pi$
$887$	−25.3205	+	25.3205i	−0.850179	+	0.850179i	0.139976	+	0.990155i	$0.455298\pi$
$888$		0			0
$889$	−5.53590	+	5.53590i	−0.185668	+	0.185668i
$890$	−0.124356	+	0.607695i	−0.00416841	+	0.0203700i
$891$		0			0
$892$		−	6.12436i		−	0.205059i
$893$	0.928203	+	0.928203i	0.0310611	+	0.0310611i
$894$		0			0
$895$	26.3564	+	39.9186i	0.880998	+	1.33433i
$896$			1.00000i			0.0334077i
$897$		0			0
$898$	−11.3923	−	11.3923i	−0.380166	−	0.380166i
$899$	−16.3397	+	16.3397i	−0.544961	+	0.544961i
$900$		0			0
$901$		−	15.6603i		−	0.521719i
$902$	46.2487			1.53991
$903$		0			0
$904$	−0.803848	−	0.803848i	−0.0267356	−	0.0267356i
$905$	−11.5622	+	7.63397i	−0.384340	+	0.253762i
$906$		0			0
$907$	−30.6147	−	30.6147i	−1.01655	−	1.01655i	−0.999861	−	0.0166848i	$-0.994689\pi$
$907$	−30.6147	−	30.6147i	−1.01655	−	1.01655i	−0.0166848	−	0.999861i	$-0.505311\pi$
$908$	−6.00000			−0.199117
$909$		0			0
$910$	5.23205	−	6.13397i	0.173441	−	0.203339i
$911$	4.98076			0.165020			0.0825100	−	0.996590i	$-0.473706\pi$
$911$	4.98076			0.165020			0.0825100	+	0.996590i	$0.473706\pi$
$912$		0			0
$913$	8.19615	+	8.19615i	0.271253	+	0.271253i
$914$	−14.0000			−0.463079
$915$		0			0
$916$	10.0981	+	10.0981i	0.333650	+	0.333650i
$917$		−	12.4641i		−	0.411601i
$918$		0			0
$919$		−	40.1051i		−	1.32295i	−0.749969	−	0.661473i	$-0.769932\pi$
$919$		−	40.1051i		−	1.32295i	0.749969	−	0.661473i	$-0.230068\pi$
$920$	0.830127	+	0.169873i	0.0273685	+	0.00560055i
$921$		0			0
$922$	−5.09808	−	5.09808i	−0.167896	−	0.167896i
$923$	−38.2224	−	21.0981i	−1.25811	−	0.694452i
$924$		0			0
$925$	11.3301	+	4.83975i	0.372532	+	0.159130i
$926$	13.4641			0.442458
$927$		0			0
$928$			3.26795i			0.107276i
$929$	−2.33975	+	2.33975i	−0.0767646	+	0.0767646i	−0.744447	−	0.667682i	$-0.767287\pi$
$929$	−2.33975	+	2.33975i	−0.0767646	+	0.0767646i	0.667682	+	0.744447i	$0.267287\pi$
$930$		0			0
$931$	−20.7846	+	20.7846i	−0.681188	+	0.681188i
$932$	−14.2942	+	14.2942i	−0.468223	+	0.468223i
$933$		0			0
$934$	−18.8564	−	18.8564i	−0.617000	−	0.617000i
$935$	−46.8827	−	71.0070i	−1.53323	−	2.32218i
$936$		0			0
$937$	5.19615	−	5.19615i	0.169751	−	0.169751i	−0.617119	−	0.786870i	$-0.711700\pi$
$937$	5.19615	−	5.19615i	0.169751	−	0.169751i	0.786870	+	0.617119i	$0.211700\pi$
$938$			10.7321i			0.350414i
$939$		0			0
$940$	−0.500000	+	0.330127i	−0.0163082	+	0.0107676i
$941$	−0.241670	−	0.241670i	−0.00787821	−	0.00787821i	0.703157	−	0.711035i	$-0.251773\pi$
$941$	−0.241670	−	0.241670i	−0.00787821	−	0.00787821i	−0.711035	+	0.703157i	$0.751773\pi$
$942$		0			0
$943$	−3.32051			−0.108131
$944$	1.26795	+	1.26795i	0.0412682	+	0.0412682i
$945$		0			0
$946$			61.9090i			2.01283i
$947$		−	26.3013i		−	0.854676i	−0.904092	−	0.427338i	$-0.859451\pi$
$947$		−	26.3013i		−	0.854676i	0.904092	−	0.427338i	$-0.140549\pi$
$948$		0			0
$949$		0			0
$950$	9.12436	+	22.7321i	0.296033	+	0.737525i
$951$		0			0
$952$	−5.09808	+	5.09808i	−0.165230	+	0.165230i
$953$	−43.0788	+	43.0788i	−1.39546	+	1.39546i	−0.582959	+	0.812502i	$0.698105\pi$
$953$	−43.0788	+	43.0788i	−1.39546	+	1.39546i	−0.812502	+	0.582959i	$0.801895\pi$
$954$		0			0
$955$	16.1699	+	24.4904i	0.523245	+	0.792490i
$956$	16.4904	−	16.4904i	0.533337	−	0.533337i
$957$		0			0
$958$	16.4186	+	16.4186i	0.530460	+	0.530460i
$959$	−11.6603			−0.376529
$960$		0			0
$961$			19.0000i			0.612903i
$962$	2.46410	+	8.53590i	0.0794458	+	0.275208i
$963$		0			0
$964$	−10.5359	+	10.5359i	−0.339338	+	0.339338i
$965$	13.8827	+	21.0263i	0.446899	+	0.676860i
$966$		0			0
$967$	−45.8372			−1.47402			−0.737012	−	0.675880i	$-0.763764\pi$
$967$	−45.8372			−1.47402			−0.737012	+	0.675880i	$0.763764\pi$
$968$			16.8564i			0.541785i
$969$		0			0
$970$	0.241670	+	0.366025i	0.00775955	+	0.0117524i
$971$	22.5167			0.722594			0.361297	−	0.932451i	$-0.382334\pi$
$971$	22.5167			0.722594			0.361297	+	0.932451i	$0.382334\pi$
$972$		0			0
$973$	−6.26795			−0.200941
$974$	15.8564			0.508072
$975$		0			0
$976$	−4.92820			−0.157748
$977$	−25.6603			−0.820944			−0.410472	−	0.911873i	$-0.634636\pi$
$977$	−25.6603			−0.820944			−0.410472	+	0.911873i	$0.634636\pi$
$978$		0			0
$979$	1.46410			0.0467929
$980$	−7.39230	−	11.1962i	−0.236139	−	0.357648i
$981$		0			0
$982$		−	13.8756i		−	0.442790i
$983$	−1.73205			−0.0552438			−0.0276219	−	0.999618i	$-0.508793\pi$
$983$	−1.73205			−0.0552438			−0.0276219	+	0.999618i	$0.508793\pi$
$984$		0			0
$985$	4.11474	+	6.23205i	0.131106	+	0.198570i
$986$	−16.6603	+	16.6603i	−0.530571	+	0.530571i
$987$		0			0
$988$	−8.53590	+	15.4641i	−0.271563	+	0.491979i
$989$		−	4.44486i		−	0.141338i
$990$		0			0
$991$	22.9282			0.728338			0.364169	−	0.931333i	$-0.381353\pi$
$991$	22.9282			0.728338			0.364169	+	0.931333i	$0.381353\pi$
$992$	5.00000	+	5.00000i	0.158750	+	0.158750i
$993$		0			0
$994$	8.56218	−	8.56218i	0.271576	−	0.271576i
$995$	30.2942	+	45.8827i	0.960392	+	1.45458i
$996$		0			0
$997$	19.9282	−	19.9282i	0.631133	−	0.631133i	−0.317220	−	0.948352i	$-0.602749\pi$
$997$	19.9282	−	19.9282i	0.631133	−	0.631133i	0.948352	+	0.317220i	$0.102749\pi$
$998$	−16.5885	+	16.5885i	−0.525098	+	0.525098i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.m.d.73.1		4
3.2	odd	2		130.2.g.e.73.1	yes	4
5.2	odd	4		1170.2.w.d.307.1		4
12.11	even	2		1040.2.bg.i.593.2		4
13.5	odd	4		1170.2.w.d.343.1		4
15.2	even	4		130.2.j.e.47.1	yes	4
15.8	even	4		650.2.j.g.307.2		4
15.14	odd	2		650.2.g.f.593.2		4
39.5	even	4		130.2.j.e.83.1	yes	4
60.47	odd	4		1040.2.cd.k.177.2		4
65.57	even	4	inner	1170.2.m.d.577.1		4
156.83	odd	4		1040.2.cd.k.993.2		4
195.44	even	4		650.2.j.g.343.2		4
195.83	odd	4		650.2.g.f.57.2		4
195.122	odd	4		130.2.g.e.57.1	✓	4
780.707	even	4		1040.2.bg.i.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.e.57.1	✓	4	195.122	odd	4
130.2.g.e.73.1	yes	4	3.2	odd	2
130.2.j.e.47.1	yes	4	15.2	even	4
130.2.j.e.83.1	yes	4	39.5	even	4
650.2.g.f.57.2		4	195.83	odd	4
650.2.g.f.593.2		4	15.14	odd	2
650.2.j.g.307.2		4	15.8	even	4
650.2.j.g.343.2		4	195.44	even	4
1040.2.bg.i.577.2		4	780.707	even	4
1040.2.bg.i.593.2		4	12.11	even	2
1040.2.cd.k.177.2		4	60.47	odd	4
1040.2.cd.k.993.2		4	156.83	odd	4
1170.2.m.d.73.1		4	1.1	even	1	trivial
1170.2.m.d.577.1		4	65.57	even	4	inner
1170.2.w.d.307.1		4	5.2	odd	4
1170.2.w.d.343.1		4	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.23205 - 1.86603i) q^{5} -1.00000i q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.23205 - 1.86603i) q^{5} -1.00000i q^{7} -1.00000 q^{8} +(1.23205 + 1.86603i) q^{10} +(3.73205 - 3.73205i) q^{11} +(3.46410 - 1.00000i) q^{13} +1.00000i q^{14} +1.00000 q^{16} +(5.09808 + 5.09808i) q^{17} +(-3.46410 + 3.46410i) q^{19} +(-1.23205 - 1.86603i) q^{20} +(-3.73205 + 3.73205i) q^{22} +(0.267949 - 0.267949i) q^{23} +(-1.96410 + 4.59808i) q^{25} +(-3.46410 + 1.00000i) q^{26} -1.00000i q^{28} -3.26795i q^{29} +(-5.00000 - 5.00000i) q^{31} -1.00000 q^{32} +(-5.09808 - 5.09808i) q^{34} +(-1.86603 + 1.23205i) q^{35} -2.46410i q^{37} +(3.46410 - 3.46410i) q^{38} +(1.23205 + 1.86603i) q^{40} +(-6.19615 - 6.19615i) q^{41} +(8.29423 - 8.29423i) q^{43} +(3.73205 - 3.73205i) q^{44} +(-0.267949 + 0.267949i) q^{46} -0.267949i q^{47} +6.00000 q^{49} +(1.96410 - 4.59808i) q^{50} +(3.46410 - 1.00000i) q^{52} +(-1.53590 - 1.53590i) q^{53} +(-11.5622 - 2.36603i) q^{55} +1.00000i q^{56} +3.26795i q^{58} +(1.26795 + 1.26795i) q^{59} -4.92820 q^{61} +(5.00000 + 5.00000i) q^{62} +1.00000 q^{64} +(-6.13397 - 5.23205i) q^{65} +10.7321 q^{67} +(5.09808 + 5.09808i) q^{68} +(1.86603 - 1.23205i) q^{70} +(-8.56218 - 8.56218i) q^{71} +2.46410i q^{74} +(-3.46410 + 3.46410i) q^{76} +(-3.73205 - 3.73205i) q^{77} +0.196152i q^{79} +(-1.23205 - 1.86603i) q^{80} +(6.19615 + 6.19615i) q^{82} +2.19615i q^{83} +(3.23205 - 15.7942i) q^{85} +(-8.29423 + 8.29423i) q^{86} +(-3.73205 + 3.73205i) q^{88} +(0.196152 + 0.196152i) q^{89} +(-1.00000 - 3.46410i) q^{91} +(0.267949 - 0.267949i) q^{92} +0.267949i q^{94} +(10.7321 + 2.19615i) q^{95} +0.196152 q^{97} -6.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 4 * q^8	\( 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 4 q^{8} - 2 q^{10} + 8 q^{11} + 4 q^{16} + 10 q^{17} + 2 q^{20} - 8 q^{22} + 8 q^{23} + 6 q^{25} - 20 q^{31} - 4 q^{32} - 10 q^{34} - 4 q^{35} - 2 q^{40} - 4 q^{41} + 2 q^{43} + 8 q^{44} - 8 q^{46} + 24 q^{49} - 6 q^{50} - 20 q^{53} - 22 q^{55} + 12 q^{59} + 8 q^{61} + 20 q^{62} + 4 q^{64} - 28 q^{65} + 36 q^{67} + 10 q^{68} + 4 q^{70} - 10 q^{71} - 8 q^{77} + 2 q^{80} + 4 q^{82} + 6 q^{85} - 2 q^{86} - 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} + 36 q^{95} - 20 q^{97} - 24 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 4 * q^8 - 2 * q^10 + 8 * q^11 + 4 * q^16 + 10 * q^17 + 2 * q^20 - 8 * q^22 + 8 * q^23 + 6 * q^25 - 20 * q^31 - 4 * q^32 - 10 * q^34 - 4 * q^35 - 2 * q^40 - 4 * q^41 + 2 * q^43 + 8 * q^44 - 8 * q^46 + 24 * q^49 - 6 * q^50 - 20 * q^53 - 22 * q^55 + 12 * q^59 + 8 * q^61 + 20 * q^62 + 4 * q^64 - 28 * q^65 + 36 * q^67 + 10 * q^68 + 4 * q^70 - 10 * q^71 - 8 * q^77 + 2 * q^80 + 4 * q^82 + 6 * q^85 - 2 * q^86 - 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 + 36 * q^95 - 20 * q^97 - 24 * q^98

Introduction

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