LMFDB - Embedded newform 1170.2.cu.a.431.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(71,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("1170.71");

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.cu (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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			431.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1170.431
Dual form			1170.2.cu.a.1151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.36603 + 0.633975i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.36603 + 0.633975i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{10} +(-0.965926 - 0.258819i) q^{11} +(1.00000 - 3.46410i) q^{13} -2.44949i q^{14} +(0.500000 + 0.866025i) q^{16} +(2.63896 - 4.57081i) q^{17} +(-1.00000 - 3.73205i) q^{19} +(-0.258819 - 0.965926i) q^{20} +(0.500000 - 0.866025i) q^{22} +(0.258819 + 0.448288i) q^{23} +1.00000i q^{25} +(3.08725 + 1.86250i) q^{26} +(2.36603 + 0.633975i) q^{28} +(8.03699 - 4.64016i) q^{29} +(-7.09808 + 7.09808i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(3.73205 + 3.73205i) q^{34} +(-2.12132 - 1.22474i) q^{35} +(-0.133975 + 0.500000i) q^{37} +3.86370 q^{38} +1.00000 q^{40} +(2.82843 - 10.5558i) q^{41} +(10.7942 + 6.23205i) q^{43} +(0.707107 + 0.707107i) q^{44} +(-0.500000 + 0.133975i) q^{46} +(3.53553 - 3.53553i) q^{47} +(-0.866025 + 0.500000i) q^{49} +(-0.965926 - 0.258819i) q^{50} +(-2.59808 + 2.50000i) q^{52} +10.1769i q^{53} +(-0.500000 - 0.866025i) q^{55} +(-1.22474 + 2.12132i) q^{56} +(2.40192 + 8.96410i) q^{58} +(-3.55412 - 13.2641i) q^{59} +(5.83013 - 10.0981i) q^{61} +(-5.01910 - 8.69333i) q^{62} -1.00000i q^{64} +(3.15660 - 1.74238i) q^{65} +(-4.09808 - 1.09808i) q^{67} +(-4.57081 + 2.63896i) q^{68} +(1.73205 - 1.73205i) q^{70} +(14.0914 - 3.77577i) q^{71} +(-7.92820 - 7.92820i) q^{73} +(-0.448288 - 0.258819i) q^{74} +(-1.00000 + 3.73205i) q^{76} +2.44949 q^{77} +5.92820 q^{79} +(-0.258819 + 0.965926i) q^{80} +(9.46410 + 5.46410i) q^{82} +(7.72741 + 7.72741i) q^{83} +(5.09808 - 1.36603i) q^{85} +(-8.81345 + 8.81345i) q^{86} +(-0.866025 + 0.500000i) q^{88} +(-9.84873 - 2.63896i) q^{89} +(-0.169873 + 8.83013i) q^{91} -0.517638i q^{92} +(2.50000 + 4.33013i) q^{94} +(1.93185 - 3.34607i) q^{95} +(0.464102 + 1.73205i) q^{97} +(-0.258819 - 0.965926i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{7}+O(q^{10}) $ 8 * q - 12 * q^7	$ 8 q - 12 q^{7} + 8 q^{13} + 4 q^{16} - 8 q^{19} + 4 q^{22} + 12 q^{28} - 36 q^{31} + 16 q^{34} - 8 q^{37} + 8 q^{40} + 24 q^{43} - 4 q^{46} - 4 q^{55} + 40 q^{58} + 12 q^{61} - 12 q^{67} - 8 q^{73} - 8 q^{76} - 8 q^{79} + 48 q^{82} + 20 q^{85} - 36 q^{91} + 20 q^{94} - 24 q^{97}+O(q^{100}) $ 8 * q - 12 * q^7 + 8 * q^13 + 4 * q^16 - 8 * q^19 + 4 * q^22 + 12 * q^28 - 36 * q^31 + 16 * q^34 - 8 * q^37 + 8 * q^40 + 24 * q^43 - 4 * q^46 - 4 * q^55 + 40 * q^58 + 12 * q^61 - 12 * q^67 - 8 * q^73 - 8 * q^76 - 8 * q^79 + 48 * q^82 + 20 * q^85 - 36 * q^91 + 20 * q^94 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{12}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$	−2.36603	+	0.633975i	−0.894274	+	0.239620i	−0.676555	−	0.736392i	$-0.736528\pi$
$7$	−2.36603	+	0.633975i	−0.894274	+	0.239620i	−0.217718	+	0.976012i	$0.569861\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$	−0.965926	−	0.258819i	−0.291238	−	0.0780369i	0.110242	−	0.993905i	$-0.464837\pi$
$11$	−0.965926	−	0.258819i	−0.291238	−	0.0780369i	−0.401480	+	0.915868i	$0.631504\pi$
$12$		0			0
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$13$	1.00000	−	3.46410i	0.277350	−	0.960769i
$14$		−	2.44949i		−	0.654654i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.63896	−	4.57081i	0.640041	−	1.10858i	−0.345382	−	0.938462i	$-0.612251\pi$
$17$	2.63896	−	4.57081i	0.640041	−	1.10858i	0.985423	−	0.170122i	$-0.0544162\pi$
$18$		0			0
$19$	−1.00000	−	3.73205i	−0.229416	−	0.856191i	−0.980587	−	0.196084i	$-0.937177\pi$
$19$	−1.00000	−	3.73205i	−0.229416	−	0.856191i	0.751171	−	0.660107i	$-0.229489\pi$
$20$	−0.258819	−	0.965926i	−0.0578737	−	0.215988i
$21$		0			0
$22$	0.500000	−	0.866025i	0.106600	−	0.184637i
$23$	0.258819	+	0.448288i	0.0539675	+	0.0934745i	0.891747	−	0.452534i	$-0.149480\pi$
$23$	0.258819	+	0.448288i	0.0539675	+	0.0934745i	−0.837780	+	0.546009i	$0.816147\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$	3.08725	+	1.86250i	0.605459	+	0.365267i
$27$		0			0
$28$	2.36603	+	0.633975i	0.447137	+	0.119810i
$29$	8.03699	−	4.64016i	1.49243	−	0.861656i	0.492470	−	0.870329i	$-0.336094\pi$
$29$	8.03699	−	4.64016i	1.49243	−	0.861656i	0.999962	+	0.00867333i	$0.00276084\pi$
$30$		0			0
$31$	−7.09808	+	7.09808i	−1.27485	+	1.27485i	−0.331341	+	0.943511i	$0.607501\pi$
$31$	−7.09808	+	7.09808i	−1.27485	+	1.27485i	−0.943511	+	0.331341i	$0.892499\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$	3.73205	+	3.73205i	0.640041	+	0.640041i
$35$	−2.12132	−	1.22474i	−0.358569	−	0.207020i
$36$		0			0
$37$	−0.133975	+	0.500000i	−0.0220253	+	0.0821995i	−0.976064	−	0.217485i	$-0.930215\pi$
$37$	−0.133975	+	0.500000i	−0.0220253	+	0.0821995i	0.954038	+	0.299684i	$0.0968814\pi$
$38$	3.86370			0.626775
$39$		0			0
$40$	1.00000			0.158114
$41$	2.82843	−	10.5558i	0.441726	−	1.64854i	−0.282712	−	0.959205i	$-0.591234\pi$
$41$	2.82843	−	10.5558i	0.441726	−	1.64854i	0.724438	−	0.689340i	$-0.242099\pi$
$42$		0			0
$43$	10.7942	+	6.23205i	1.64610	+	0.950379i	0.978600	+	0.205773i	$0.0659709\pi$
$43$	10.7942	+	6.23205i	1.64610	+	0.950379i	0.667505	+	0.744606i	$0.267362\pi$
$44$	0.707107	+	0.707107i	0.106600	+	0.106600i
$45$		0			0
$46$	−0.500000	+	0.133975i	−0.0737210	+	0.0197535i
$47$	3.53553	−	3.53553i	0.515711	−	0.515711i	−0.400560	−	0.916271i	$-0.631184\pi$
$47$	3.53553	−	3.53553i	0.515711	−	0.515711i	0.916271	+	0.400560i	$0.131184\pi$
$48$		0			0
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	−0.965926	−	0.258819i	−0.136603	−	0.0366025i
$51$		0			0
$52$	−2.59808	+	2.50000i	−0.360288	+	0.346688i
$53$			10.1769i			1.39790i	0.715168	+	0.698952i	$0.246350\pi$
$53$			10.1769i			1.39790i	−0.715168	+	0.698952i	$0.753650\pi$
$54$		0			0
$55$	−0.500000	−	0.866025i	−0.0674200	−	0.116775i
$56$	−1.22474	+	2.12132i	−0.163663	+	0.283473i
$57$		0			0
$58$	2.40192	+	8.96410i	0.315388	+	1.17704i
$59$	−3.55412	−	13.2641i	−0.462707	−	1.72684i	−0.664383	−	0.747392i	$-0.731306\pi$
$59$	−3.55412	−	13.2641i	−0.462707	−	1.72684i	0.201677	−	0.979452i	$-0.435361\pi$
$60$		0			0
$61$	5.83013	−	10.0981i	0.746471	−	1.29293i	−0.203033	−	0.979172i	$-0.565080\pi$
$61$	5.83013	−	10.0981i	0.746471	−	1.29293i	0.949504	−	0.313754i	$-0.101587\pi$
$62$	−5.01910	−	8.69333i	−0.637426	−	1.10405i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	3.15660	−	1.74238i	0.391528	−	0.216116i
$66$		0			0
$67$	−4.09808	−	1.09808i	−0.500660	−	0.134151i	−0.000353546	−	1.00000i	$-0.500113\pi$
$67$	−4.09808	−	1.09808i	−0.500660	−	0.134151i	−0.500306	+	0.865849i	$0.666779\pi$
$68$	−4.57081	+	2.63896i	−0.554292	+	0.320021i
$69$		0			0
$70$	1.73205	−	1.73205i	0.207020	−	0.207020i
$71$	14.0914	−	3.77577i	1.67234	−	0.448102i	0.706598	−	0.707615i	$-0.250229\pi$
$71$	14.0914	−	3.77577i	1.67234	−	0.448102i	0.965739	+	0.259513i	$0.0835622\pi$
$72$		0			0
$73$	−7.92820	−	7.92820i	−0.927926	−	0.927926i	0.0696458	−	0.997572i	$-0.477813\pi$
$73$	−7.92820	−	7.92820i	−0.927926	−	0.927926i	−0.997572	+	0.0696458i	$0.977813\pi$
$74$	−0.448288	−	0.258819i	−0.0521124	−	0.0300871i
$75$		0			0
$76$	−1.00000	+	3.73205i	−0.114708	+	0.428096i
$77$	2.44949			0.279145
$78$		0			0
$79$	5.92820			0.666975			0.333487	−	0.942755i	$-0.391775\pi$
$79$	5.92820			0.666975			0.333487	+	0.942755i	$0.391775\pi$
$80$	−0.258819	+	0.965926i	−0.0289368	+	0.107994i
$81$		0			0
$82$	9.46410	+	5.46410i	1.04514	+	0.603409i
$83$	7.72741	+	7.72741i	0.848193	+	0.848193i	0.989908	−	0.141715i	$-0.0452615\pi$
$83$	7.72741	+	7.72741i	0.848193	+	0.848193i	−0.141715	+	0.989908i	$0.545261\pi$
$84$		0			0
$85$	5.09808	−	1.36603i	0.552964	−	0.148166i
$86$	−8.81345	+	8.81345i	−0.950379	+	0.950379i
$87$		0			0
$88$	−0.866025	+	0.500000i	−0.0923186	+	0.0533002i
$89$	−9.84873	−	2.63896i	−1.04396	−	0.279729i	−0.304208	−	0.952606i	$-0.598392\pi$
$89$	−9.84873	−	2.63896i	−1.04396	−	0.279729i	−0.739755	+	0.672877i	$0.765059\pi$
$90$		0			0
$91$	−0.169873	+	8.83013i	−0.0178075	+	0.925649i
$92$		−	0.517638i		−	0.0539675i
$93$		0			0
$94$	2.50000	+	4.33013i	0.257855	+	0.446619i
$95$	1.93185	−	3.34607i	0.198204	−	0.343299i
$96$		0			0
$97$	0.464102	+	1.73205i	0.0471224	+	0.175863i	0.985476	−	0.169813i	$-0.0543163\pi$
$97$	0.464102	+	1.73205i	0.0471224	+	0.175863i	−0.938354	+	0.345676i	$0.887650\pi$
$98$	−0.258819	−	0.965926i	−0.0261447	−	0.0975732i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−0.328169	−	0.568406i	−0.0326541	−	0.0565585i	0.849237	−	0.528013i	$-0.177063\pi$
$101$	−0.328169	−	0.568406i	−0.0326541	−	0.0565585i	−0.881891	+	0.471454i	$0.843729\pi$
$102$		0			0
$103$		−	2.00000i		−	0.197066i	−0.995134	−	0.0985329i	$-0.968585\pi$
$103$		−	2.00000i		−	0.197066i	0.995134	−	0.0985329i	$-0.0314150\pi$
$104$	−1.74238	−	3.15660i	−0.170855	−	0.309530i
$105$		0			0
$106$	−9.83013	−	2.63397i	−0.954786	−	0.255834i
$107$	−3.67423	+	2.12132i	−0.355202	+	0.205076i	−0.666974	−	0.745081i	$-0.732411\pi$
$107$	−3.67423	+	2.12132i	−0.355202	+	0.205076i	0.311772	+	0.950157i	$0.399077\pi$
$108$		0			0
$109$	9.92820	−	9.92820i	0.950949	−	0.950949i	−0.0479026	−	0.998852i	$-0.515254\pi$
$109$	9.92820	−	9.92820i	0.950949	−	0.950949i	0.998852	+	0.0479026i	$0.0152537\pi$
$110$	0.965926	−	0.258819i	0.0920974	−	0.0246774i
$111$		0			0
$112$	−1.73205	−	1.73205i	−0.163663	−	0.163663i
$113$	9.91808	+	5.72620i	0.933014	+	0.538676i	0.887764	−	0.460300i	$-0.152258\pi$
$113$	9.91808	+	5.72620i	0.933014	+	0.538676i	0.0452506	+	0.998976i	$0.485591\pi$
$114$		0			0
$115$	−0.133975	+	0.500000i	−0.0124932	+	0.0466252i
$116$	−9.28032			−0.861656
$117$		0			0
$118$	13.7321			1.26414
$119$	−3.34607	+	12.4877i	−0.306733	+	1.14474i
$120$		0			0
$121$	−8.66025	−	5.00000i	−0.787296	−	0.454545i
$122$	8.24504	+	8.24504i	0.746471	+	0.746471i
$123$		0			0
$124$	9.69615	−	2.59808i	0.870740	−	0.233314i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−2.53590	+	1.46410i	−0.225025	+	0.129918i	−0.608275	−	0.793727i	$-0.708138\pi$
$127$	−2.53590	+	1.46410i	−0.225025	+	0.129918i	0.383250	+	0.923645i	$0.374805\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$	0.866025	+	3.50000i	0.0759555	+	0.306970i
$131$		−	6.55343i		−	0.572576i	−0.958144	−	0.286288i	$-0.907579\pi$
$131$		−	6.55343i		−	0.572576i	0.958144	−	0.286288i	$-0.0924214\pi$
$132$		0			0
$133$	4.73205	+	8.19615i	0.410321	+	0.710697i
$134$	2.12132	−	3.67423i	0.183254	−	0.317406i
$135$		0			0
$136$	−1.36603	−	5.09808i	−0.117136	−	0.437156i
$137$	0.360355	+	1.34486i	0.0307872	+	0.114899i	0.979609	−	0.200911i	$-0.0643903\pi$
$137$	0.360355	+	1.34486i	0.0307872	+	0.114899i	−0.948822	+	0.315811i	$0.897724\pi$
$138$		0			0
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	−0.996335	−	0.0855324i	$-0.972741\pi$
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	0.572241	+	0.820086i	$0.306074\pi$
$140$	1.22474	+	2.12132i	0.103510	+	0.179284i
$141$		0			0
$142$			14.5885i			1.22424i
$143$	−1.86250	+	3.08725i	−0.155750	+	0.258168i
$144$		0			0
$145$	8.96410	+	2.40192i	0.744428	+	0.199469i
$146$	9.71003	−	5.60609i	0.803607	−	0.463963i
$147$		0			0
$148$	0.366025	−	0.366025i	0.0300871	−	0.0300871i
$149$	14.1607	−	3.79435i	1.16009	−	0.310846i	0.373089	−	0.927796i	$-0.378299\pi$
$149$	14.1607	−	3.79435i	1.16009	−	0.310846i	0.787002	+	0.616950i	$0.211632\pi$
$150$		0			0
$151$	−9.00000	−	9.00000i	−0.732410	−	0.732410i	0.238687	−	0.971097i	$-0.423283\pi$
$151$	−9.00000	−	9.00000i	−0.732410	−	0.732410i	−0.971097	+	0.238687i	$0.923283\pi$
$152$	−3.34607	−	1.93185i	−0.271402	−	0.156694i
$153$		0			0
$154$	−0.633975	+	2.36603i	−0.0510871	+	0.190660i
$155$	−10.0382			−0.806287
$156$		0			0
$157$	−21.3923			−1.70729			−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−21.3923			−1.70729			−0.853646	+	0.520854i	$0.825614\pi$
$158$	−1.53433	+	5.72620i	−0.122065	+	0.455552i
$159$		0			0
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−0.896575	−	0.896575i	−0.0706600	−	0.0706600i
$162$		0			0
$163$	6.69615	−	1.79423i	0.524483	−	0.140535i	0.0131436	−	0.999914i	$-0.495816\pi$
$163$	6.69615	−	1.79423i	0.524483	−	0.140535i	0.511340	+	0.859379i	$0.329149\pi$
$164$	−7.72741	+	7.72741i	−0.603409	+	0.603409i
$165$		0			0
$166$	−9.46410	+	5.46410i	−0.734557	+	0.424097i
$167$	−8.36516	−	2.24144i	−0.647316	−	0.173448i	−0.0798008	−	0.996811i	$-0.525428\pi$
$167$	−8.36516	−	2.24144i	−0.647316	−	0.173448i	−0.567515	+	0.823363i	$0.692095\pi$
$168$		0			0
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$			5.27792i			0.404798i
$171$		0			0
$172$	−6.23205	−	10.7942i	−0.475189	−	0.823052i
$173$	−2.82843	+	4.89898i	−0.215041	+	0.372463i	−0.953285	−	0.302071i	$-0.902322\pi$
$173$	−2.82843	+	4.89898i	−0.215041	+	0.372463i	0.738244	+	0.674534i	$0.235655\pi$
$174$		0			0
$175$	−0.633975	−	2.36603i	−0.0479240	−	0.178855i
$176$	−0.258819	−	0.965926i	−0.0195092	−	0.0728094i
$177$		0			0
$178$	5.09808	−	8.83013i	0.382117	−	0.661846i
$179$	6.19307	+	10.7267i	0.462892	+	0.801753i	0.999104	−	0.0423310i	$-0.0134784\pi$
$179$	6.19307	+	10.7267i	0.462892	+	0.801753i	−0.536212	+	0.844084i	$0.680145\pi$
$180$		0			0
$181$			2.39230i			0.177819i	0.996040	+	0.0889093i	$0.0283381\pi$
$181$			2.39230i			0.177819i	−0.996040	+	0.0889093i	$0.971662\pi$
$182$	−8.48528	−	2.44949i	−0.628971	−	0.181568i
$183$		0			0
$184$	0.500000	+	0.133975i	0.0368605	+	0.00987674i
$185$	−0.448288	+	0.258819i	−0.0329588	+	0.0190288i
$186$		0			0
$187$	−3.73205	+	3.73205i	−0.272915	+	0.272915i
$188$	−4.82963	+	1.29410i	−0.352237	+	0.0943816i
$189$		0			0
$190$	2.73205	+	2.73205i	0.198204	+	0.198204i
$191$	−10.3664	−	5.98502i	−0.750084	−	0.433061i	0.0756404	−	0.997135i	$-0.475900\pi$
$191$	−10.3664	−	5.98502i	−0.750084	−	0.433061i	−0.825724	+	0.564074i	$0.809233\pi$
$192$		0			0
$193$	0.509619	−	1.90192i	0.0366832	−	0.136903i	−0.945156	−	0.326620i	$-0.894090\pi$
$193$	0.509619	−	1.90192i	0.0366832	−	0.136903i	0.981839	+	0.189717i	$0.0607569\pi$
$194$	−1.79315			−0.128741
$195$		0			0
$196$	1.00000			0.0714286
$197$	−1.98262	+	7.39924i	−0.141256	+	0.527174i	0.858638	+	0.512583i	$0.171311\pi$
$197$	−1.98262	+	7.39924i	−0.141256	+	0.527174i	−0.999894	+	0.0145909i	$0.995355\pi$
$198$		0			0
$199$	22.0526	+	12.7321i	1.56326	+	0.902551i	0.996924	+	0.0783801i	$0.0249748\pi$
$199$	22.0526	+	12.7321i	1.56326	+	0.902551i	0.566341	+	0.824171i	$0.308359\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$		0			0
$202$	0.633975	−	0.169873i	0.0446063	−	0.0119522i
$203$	−16.0740	+	16.0740i	−1.12817	+	1.12817i
$204$		0			0
$205$	9.46410	−	5.46410i	0.661002	−	0.381629i
$206$	1.93185	+	0.517638i	0.134598	+	0.0360656i
$207$		0			0
$208$	3.50000	−	0.866025i	0.242681	−	0.0600481i
$209$			3.86370i			0.267258i
$210$		0			0
$211$	0.901924	+	1.56218i	0.0620910	+	0.107545i	0.895400	−	0.445263i	$-0.146890\pi$
$211$	0.901924	+	1.56218i	0.0620910	+	0.107545i	−0.833309	+	0.552808i	$0.813556\pi$
$212$	5.08845	−	8.81345i	0.349476	−	0.605310i
$213$		0			0
$214$	−1.09808	−	4.09808i	−0.0750629	−	0.280139i
$215$	3.22595	+	12.0394i	0.220008	+	0.821080i
$216$		0			0
$217$	12.2942	−	21.2942i	0.834587	−	1.44555i
$218$	7.02030	+	12.1595i	0.475475	+	0.823546i
$219$		0			0
$220$			1.00000i			0.0674200i
$221$	−13.1948	−	13.7124i	−0.887578	−	0.922398i
$222$		0			0
$223$	−9.92820	−	2.66025i	−0.664842	−	0.178144i	−0.0894116	−	0.995995i	$-0.528499\pi$
$223$	−9.92820	−	2.66025i	−0.664842	−	0.178144i	−0.575430	+	0.817851i	$0.695165\pi$
$224$	2.12132	−	1.22474i	0.141737	−	0.0818317i
$225$		0			0
$226$	−8.09808	+	8.09808i	−0.538676	+	0.538676i
$227$	−6.12372	+	1.64085i	−0.406446	+	0.108907i	−0.456249	−	0.889852i	$-0.650807\pi$
$227$	−6.12372	+	1.64085i	−0.406446	+	0.108907i	0.0498030	+	0.998759i	$0.484141\pi$
$228$		0			0
$229$	−13.1962	−	13.1962i	−0.872026	−	0.872026i	0.120667	−	0.992693i	$-0.461497\pi$
$229$	−13.1962	−	13.1962i	−0.872026	−	0.872026i	−0.992693	+	0.120667i	$0.961497\pi$
$230$	−0.448288	−	0.258819i	−0.0295592	−	0.0170660i
$231$		0			0
$232$	2.40192	−	8.96410i	0.157694	−	0.588522i
$233$	−0.998111			−0.0653885			−0.0326942	−	0.999465i	$-0.510409\pi$
$233$	−0.998111			−0.0653885			−0.0326942	+	0.999465i	$0.510409\pi$
$234$		0			0
$235$	5.00000			0.326164
$236$	−3.55412	+	13.2641i	−0.231353	+	0.863422i
$237$		0			0
$238$	−11.1962	−	6.46410i	−0.725739	−	0.419005i
$239$	−10.7961	−	10.7961i	−0.698340	−	0.698340i	0.265713	−	0.964052i	$-0.414393\pi$
$239$	−10.7961	−	10.7961i	−0.698340	−	0.698340i	−0.964052	+	0.265713i	$0.914393\pi$
$240$		0			0
$241$	−17.8923	+	4.79423i	−1.15254	+	0.308823i	−0.783984	−	0.620780i	$-0.786816\pi$
$241$	−17.8923	+	4.79423i	−1.15254	+	0.308823i	−0.368560	+	0.929604i	$0.620149\pi$
$242$	7.07107	−	7.07107i	0.454545	−	0.454545i
$243$		0			0
$244$	−10.0981	+	5.83013i	−0.646463	+	0.373236i
$245$	−0.965926	−	0.258819i	−0.0617107	−	0.0165353i
$246$		0			0
$247$	−13.9282	−	0.267949i	−0.886230	−	0.0170492i
$248$			10.0382i			0.637426i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	1.81173	−	3.13801i	0.114356	−	0.198070i	−0.803166	−	0.595755i	$-0.796853\pi$
$251$	1.81173	−	3.13801i	0.114356	−	0.198070i	0.917522	+	0.397685i	$0.130186\pi$
$252$		0			0
$253$	−0.133975	−	0.500000i	−0.00842291	−	0.0314347i
$254$	−0.757875	−	2.82843i	−0.0475533	−	0.177471i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.12252	+	7.14042i	0.257156	+	0.445407i	0.965479	−	0.260481i	$-0.0838813\pi$
$257$	4.12252	+	7.14042i	0.257156	+	0.445407i	−0.708323	+	0.705888i	$0.750548\pi$
$258$		0			0
$259$		−	1.26795i		−	0.0787865i
$260$	−3.60488	−	0.0693504i	−0.223565	−	0.00430093i
$261$		0			0
$262$	6.33013	+	1.69615i	0.391077	+	0.104789i
$263$	11.4710	−	6.62278i	0.707332	−	0.408378i	−0.102741	−	0.994708i	$-0.532761\pi$
$263$	11.4710	−	6.62278i	0.707332	−	0.408378i	0.810072	+	0.586330i	$0.199428\pi$
$264$		0			0
$265$	−7.19615	+	7.19615i	−0.442056	+	0.442056i
$266$	−9.14162	+	2.44949i	−0.560509	+	0.150188i
$267$		0			0
$268$	3.00000	+	3.00000i	0.183254	+	0.183254i
$269$	−20.4046	−	11.7806i	−1.24409	−	0.718275i	−0.274164	−	0.961683i	$-0.588401\pi$
$269$	−20.4046	−	11.7806i	−1.24409	−	0.718275i	−0.969924	+	0.243408i	$0.921734\pi$
$270$		0			0
$271$	−0.624356	+	2.33013i	−0.0379269	+	0.141545i	−0.982293	−	0.187351i	$-0.940010\pi$
$271$	−0.624356	+	2.33013i	−0.0379269	+	0.141545i	0.944366	+	0.328896i	$0.106677\pi$
$272$	5.27792			0.320021
$273$		0			0
$274$	−1.39230			−0.0841122
$275$	0.258819	−	0.965926i	0.0156074	−	0.0582475i
$276$		0			0
$277$	−9.23205	−	5.33013i	−0.554700	−	0.320256i	0.196315	−	0.980541i	$-0.437102\pi$
$277$	−9.23205	−	5.33013i	−0.554700	−	0.320256i	−0.751016	+	0.660285i	$0.770436\pi$
$278$	−7.07107	−	7.07107i	−0.424094	−	0.424094i
$279$		0			0
$280$	−2.36603	+	0.633975i	−0.141397	+	0.0378872i
$281$	4.52004	−	4.52004i	0.269643	−	0.269643i	−0.559313	−	0.828956i	$-0.688935\pi$
$281$	4.52004	−	4.52004i	0.269643	−	0.269643i	0.828956	+	0.559313i	$0.188935\pi$
$282$		0			0
$283$	8.76795	−	5.06218i	0.521200	−	0.300915i	−0.216225	−	0.976344i	$-0.569375\pi$
$283$	8.76795	−	5.06218i	0.521200	−	0.300915i	0.737426	+	0.675428i	$0.236041\pi$
$284$	−14.0914	−	3.77577i	−0.836169	−	0.224051i
$285$		0			0
$286$	−2.50000	−	2.59808i	−0.147828	−	0.153627i
$287$			26.7685i			1.58010i
$288$		0			0
$289$	−5.42820	−	9.40192i	−0.319306	−	0.553054i
$290$	−4.64016	+	8.03699i	−0.272480	+	0.471949i
$291$		0			0
$292$	2.90192	+	10.8301i	0.169822	+	0.633785i
$293$	2.82843	+	10.5558i	0.165238	+	0.616678i	0.998010	+	0.0630611i	$0.0200863\pi$
$293$	2.82843	+	10.5558i	0.165238	+	0.616678i	−0.832771	+	0.553617i	$0.813247\pi$
$294$		0			0
$295$	6.86603	−	11.8923i	0.399755	−	0.692397i
$296$	0.258819	+	0.448288i	0.0150436	+	0.0260562i
$297$		0			0
$298$			14.6603i			0.849246i
$299$	1.81173	−	0.448288i	0.104775	−	0.0259251i
$300$		0			0
$301$	−29.4904	−	7.90192i	−1.69980	−	0.455459i
$302$	11.0227	−	6.36396i	0.634285	−	0.366205i
$303$		0			0
$304$	2.73205	−	2.73205i	0.156694	−	0.156694i
$305$	11.2629	−	3.01790i	0.644914	−	0.172804i
$306$		0			0
$307$	−24.1244	−	24.1244i	−1.37685	−	1.37685i	−0.849891	−	0.526959i	$-0.823332\pi$
$307$	−24.1244	−	24.1244i	−1.37685	−	1.37685i	−0.526959	−	0.849891i	$-0.676668\pi$
$308$	−2.12132	−	1.22474i	−0.120873	−	0.0697863i
$309$		0			0
$310$	2.59808	−	9.69615i	0.147561	−	0.550704i
$311$	6.59059			0.373718			0.186859	−	0.982387i	$-0.440169\pi$
$311$	6.59059			0.373718			0.186859	+	0.982387i	$0.440169\pi$
$312$		0			0
$313$	18.5359			1.04771			0.523855	−	0.851807i	$-0.324493\pi$
$313$	18.5359			1.04771			0.523855	+	0.851807i	$0.324493\pi$
$314$	5.53674	−	20.6634i	0.312456	−	1.16610i
$315$		0			0
$316$	−5.13397	−	2.96410i	−0.288809	−	0.166744i
$317$	21.7308	+	21.7308i	1.22053	+	1.22053i	0.967445	+	0.253080i	$0.0814437\pi$
$317$	21.7308	+	21.7308i	1.22053	+	1.22053i	0.253080	+	0.967445i	$0.418556\pi$
$318$		0			0
$319$	−8.96410	+	2.40192i	−0.501893	+	0.134482i
$320$	0.707107	−	0.707107i	0.0395285	−	0.0395285i
$321$		0			0
$322$	1.09808	−	0.633975i	0.0611934	−	0.0353300i
$323$	−19.6975	−	5.27792i	−1.09600	−	0.293671i
$324$		0			0
$325$	3.46410	+	1.00000i	0.192154	+	0.0554700i
$326$			6.93237i			0.383948i
$327$		0			0
$328$	−5.46410	−	9.46410i	−0.301705	−	0.522568i
$329$	−6.12372	+	10.6066i	−0.337612	+	0.584761i
$330$		0			0
$331$	2.66025	+	9.92820i	0.146221	+	0.545703i	0.999698	+	0.0245733i	$0.00782271\pi$
$331$	2.66025	+	9.92820i	0.146221	+	0.545703i	−0.853477	+	0.521130i	$0.825511\pi$
$332$	−2.82843	−	10.5558i	−0.155230	−	0.579327i
$333$		0			0
$334$	4.33013	−	7.50000i	0.236934	−	0.410382i
$335$	−2.12132	−	3.67423i	−0.115900	−	0.200745i
$336$		0			0
$337$			17.5167i			0.954193i	0.878851	+	0.477097i	$0.158311\pi$
$337$			17.5167i			0.954193i	−0.878851	+	0.477097i	$0.841689\pi$
$338$	9.53914	−	8.83203i	0.518861	−	0.480399i
$339$		0			0
$340$	−5.09808	−	1.36603i	−0.276482	−	0.0740831i
$341$	8.69333	−	5.01910i	0.470770	−	0.271799i
$342$		0			0
$343$	13.8564	−	13.8564i	0.748176	−	0.748176i
$344$	12.0394	−	3.22595i	0.649121	−	0.173931i
$345$		0			0
$346$	−4.00000	−	4.00000i	−0.215041	−	0.215041i
$347$	−27.4249	−	15.8338i	−1.47224	−	0.850000i	−0.472731	−	0.881207i	$-0.656732\pi$
$347$	−27.4249	−	15.8338i	−1.47224	−	0.850000i	−0.999513	+	0.0312067i	$0.990065\pi$
$348$		0			0
$349$	−4.49038	+	16.7583i	−0.240365	+	0.897053i	0.735292	+	0.677750i	$0.237045\pi$
$349$	−4.49038	+	16.7583i	−0.240365	+	0.897053i	−0.975657	+	0.219303i	$0.929622\pi$
$350$	2.44949			0.130931
$351$		0			0
$352$	1.00000			0.0533002
$353$	−5.55532	+	20.7327i	−0.295680	+	1.10349i	0.644996	+	0.764186i	$0.276859\pi$
$353$	−5.55532	+	20.7327i	−0.295680	+	1.10349i	−0.940676	+	0.339306i	$0.889808\pi$
$354$		0			0
$355$	12.6340	+	7.29423i	0.670542	+	0.387137i
$356$	7.20977	+	7.20977i	0.382117	+	0.382117i
$357$		0			0
$358$	−11.9641	+	3.20577i	−0.632322	+	0.169430i
$359$	−7.45001	+	7.45001i	−0.393196	+	0.393196i	−0.875825	−	0.482629i	$-0.839682\pi$
$359$	−7.45001	+	7.45001i	−0.393196	+	0.393196i	0.482629	+	0.875825i	$0.339682\pi$
$360$		0			0
$361$	3.52628	−	2.03590i	0.185594	−	0.107153i
$362$	−2.31079	−	0.619174i	−0.121452	−	0.0325431i
$363$		0			0
$364$	4.56218	−	7.56218i	0.239123	−	0.396366i
$365$		−	11.2122i		−	0.586872i
$366$		0			0
$367$	−1.16987	−	2.02628i	−0.0610669	−	0.105771i	0.833876	−	0.551952i	$-0.186117\pi$
$367$	−1.16987	−	2.02628i	−0.0610669	−	0.105771i	−0.894943	+	0.446181i	$0.852784\pi$
$368$	−0.258819	+	0.448288i	−0.0134919	+	0.0233686i
$369$		0			0
$370$	−0.133975	−	0.500000i	−0.00696501	−	0.0259938i
$371$	−6.45189	−	24.0788i	−0.334966	−	1.25011i
$372$		0			0
$373$	5.40192	−	9.35641i	0.279701	−	0.484456i	−0.691609	−	0.722272i	$-0.743098\pi$
$373$	5.40192	−	9.35641i	0.279701	−	0.484456i	0.971310	+	0.237815i	$0.0764313\pi$
$374$	−2.63896	−	4.57081i	−0.136457	−	0.236351i
$375$		0			0
$376$		−	5.00000i		−	0.257855i
$377$	−8.03699	−	32.4811i	−0.413926	−	1.67286i
$378$		0			0
$379$	−34.6865	−	9.29423i	−1.78173	−	0.477412i	−0.790831	−	0.612035i	$-0.790351\pi$
$379$	−34.6865	−	9.29423i	−1.78173	−	0.477412i	−0.990897	+	0.134623i	$0.957018\pi$
$380$	−3.34607	+	1.93185i	−0.171650	+	0.0991019i
$381$		0			0
$382$	8.46410	−	8.46410i	0.433061	−	0.433061i
$383$	16.6102	−	4.45069i	0.848742	−	0.227420i	0.191869	−	0.981421i	$-0.438545\pi$
$383$	16.6102	−	4.45069i	0.848742	−	0.227420i	0.656873	+	0.754001i	$0.271879\pi$
$384$		0			0
$385$	1.73205	+	1.73205i	0.0882735	+	0.0882735i
$386$	1.70522	+	0.984508i	0.0867933	+	0.0501101i
$387$		0			0
$388$	0.464102	−	1.73205i	0.0235612	−	0.0879316i
$389$	19.9377			1.01088			0.505441	−	0.862861i	$-0.331330\pi$
$389$	19.9377			1.01088			0.505441	+	0.862861i	$0.331330\pi$
$390$		0			0
$391$	2.73205			0.138166
$392$	−0.258819	+	0.965926i	−0.0130723	+	0.0487866i
$393$		0			0
$394$	−6.63397	−	3.83013i	−0.334215	−	0.192959i
$395$	4.19187	+	4.19187i	0.210916	+	0.210916i
$396$		0			0
$397$	23.7942	−	6.37564i	1.19420	−	0.319984i	0.393654	−	0.919259i	$-0.371211\pi$
$397$	23.7942	−	6.37564i	1.19420	−	0.319984i	0.800544	+	0.599274i	$0.204544\pi$
$398$	−18.0058	+	18.0058i	−0.902551	+	0.902551i
$399$		0			0
$400$	−0.866025	+	0.500000i	−0.0433013	+	0.0250000i
$401$	−7.58871	−	2.03339i	−0.378962	−	0.101543i	0.0643095	−	0.997930i	$-0.479516\pi$
$401$	−7.58871	−	2.03339i	−0.378962	−	0.101543i	−0.443271	+	0.896387i	$0.646182\pi$
$402$		0			0
$403$	17.4904	+	31.6865i	0.871258	+	1.57842i
$404$			0.656339i			0.0326541i
$405$		0			0
$406$	−11.3660	−	19.6865i	−0.564086	−	0.977026i
$407$	0.258819	−	0.448288i	0.0128292	−	0.0222208i
$408$		0			0
$409$	1.50962	+	5.63397i	0.0746459	+	0.278582i	0.993153	−	0.116823i	$-0.0372710\pi$
$409$	1.50962	+	5.63397i	0.0746459	+	0.278582i	−0.918507	+	0.395405i	$0.870604\pi$
$410$	2.82843	+	10.5558i	0.139686	+	0.521315i
$411$		0			0
$412$	−1.00000	+	1.73205i	−0.0492665	+	0.0853320i
$413$	16.8183	+	29.1301i	0.827572	+	1.43340i
$414$		0			0
$415$			10.9282i			0.536444i
$416$	−0.0693504	+	3.60488i	−0.00340018	+	0.176744i
$417$		0			0
$418$	−3.73205	−	1.00000i	−0.182541	−	0.0489116i
$419$	−9.88589	+	5.70762i	−0.482957	+	0.278836i	−0.721648	−	0.692260i	$-0.756615\pi$
$419$	−9.88589	+	5.70762i	−0.482957	+	0.278836i	0.238691	+	0.971096i	$0.423282\pi$
$420$		0			0
$421$	13.9282	−	13.9282i	0.678819	−	0.678819i	−0.280914	−	0.959733i	$-0.590638\pi$
$421$	13.9282	−	13.9282i	0.678819	−	0.678819i	0.959733	+	0.280914i	$0.0906375\pi$
$422$	−1.74238	+	0.466870i	−0.0848179	+	0.0227269i
$423$		0			0
$424$	7.19615	+	7.19615i	0.349476	+	0.349476i
$425$	4.57081	+	2.63896i	0.221717	+	0.128008i
$426$		0			0
$427$	−7.39230	+	27.5885i	−0.357739	+	1.33510i
$428$	4.24264			0.205076
$429$		0			0
$430$	−12.4641			−0.601072
$431$	−1.88108	+	7.02030i	−0.0906086	+	0.338156i	−0.996317	−	0.0857451i	$-0.972673\pi$
$431$	−1.88108	+	7.02030i	−0.0906086	+	0.338156i	0.905708	+	0.423901i	$0.139340\pi$
$432$		0			0
$433$	24.8827	+	14.3660i	1.19579	+	0.690387i	0.959613	−	0.281324i	$-0.0907736\pi$
$433$	24.8827	+	14.3660i	1.19579	+	0.690387i	0.236173	+	0.971711i	$0.424107\pi$
$434$	17.3867	+	17.3867i	0.834587	+	0.834587i
$435$		0			0
$436$	−13.5622	+	3.63397i	−0.649511	+	0.174036i
$437$	1.41421	−	1.41421i	0.0676510	−	0.0676510i
$438$		0			0
$439$	−25.5167	+	14.7321i	−1.21784	+	0.703122i	−0.964456	−	0.264242i	$-0.914878\pi$
$439$	−25.5167	+	14.7321i	−1.21784	+	0.703122i	−0.253387	+	0.967365i	$0.581545\pi$
$440$	−0.965926	−	0.258819i	−0.0460487	−	0.0123387i
$441$		0			0
$442$	16.6603	−	9.19615i	0.792447	−	0.437416i
$443$			17.9043i			0.850659i	0.905039	+	0.425330i	$0.139842\pi$
$443$			17.9043i			0.850659i	−0.905039	+	0.425330i	$0.860158\pi$
$444$		0			0
$445$	−5.09808	−	8.83013i	−0.241672	−	0.418588i
$446$	5.13922	−	8.90138i	0.243349	−	0.421493i
$447$		0			0
$448$	0.633975	+	2.36603i	0.0299525	+	0.111784i
$449$	0.998111	+	3.72500i	0.0471038	+	0.175794i	0.985470	−	0.169848i	$-0.0543278\pi$
$449$	0.998111	+	3.72500i	0.0471038	+	0.175794i	−0.938366	+	0.345642i	$0.887661\pi$
$450$		0			0
$451$	−5.46410	+	9.46410i	−0.257294	+	0.445647i
$452$	−5.72620	−	9.91808i	−0.269338	−	0.466507i
$453$		0			0
$454$		−	6.33975i		−	0.297539i
$455$	−6.36396	+	6.12372i	−0.298347	+	0.287085i
$456$		0			0
$457$	−3.92820	−	1.05256i	−0.183754	−	0.0492366i	0.165769	−	0.986165i	$-0.446989\pi$
$457$	−3.92820	−	1.05256i	−0.183754	−	0.0492366i	−0.349522	+	0.936928i	$0.613656\pi$
$458$	16.1619	−	9.33109i	0.755197	−	0.436013i
$459$		0			0
$460$	0.366025	−	0.366025i	0.0170660	−	0.0170660i
$461$	28.2521	−	7.57012i	1.31583	−	0.352576i	0.468416	−	0.883508i	$-0.344825\pi$
$461$	28.2521	−	7.57012i	1.31583	−	0.352576i	0.847414	+	0.530932i	$0.178158\pi$
$462$		0			0
$463$	21.0000	+	21.0000i	0.975953	+	0.975953i	0.999718	−	0.0237648i	$-0.00756529\pi$
$463$	21.0000	+	21.0000i	0.975953	+	0.975953i	−0.0237648	+	0.999718i	$0.507565\pi$
$464$	8.03699	+	4.64016i	0.373108	+	0.215414i
$465$		0			0
$466$	0.258330	−	0.964102i	0.0119669	−	0.0446611i
$467$	−8.10634			−0.375117			−0.187558	−	0.982253i	$-0.560057\pi$
$467$	−8.10634			−0.375117			−0.187558	+	0.982253i	$0.560057\pi$
$468$		0			0
$469$	10.3923			0.479872
$470$	−1.29410	+	4.82963i	−0.0596922	+	0.222774i
$471$		0			0
$472$	−11.8923	−	6.86603i	−0.547388	−	0.316034i
$473$	−8.81345	−	8.81345i	−0.405243	−	0.405243i
$474$		0			0
$475$	3.73205	−	1.00000i	0.171238	−	0.0458831i
$476$	9.14162	−	9.14162i	0.419005	−	0.419005i
$477$		0			0
$478$	13.2224	−	7.63397i	0.604780	−	0.349170i
$479$	5.22715	+	1.40061i	0.238835	+	0.0639955i	0.376251	−	0.926518i	$-0.377213\pi$
$479$	5.22715	+	1.40061i	0.238835	+	0.0639955i	−0.137416	+	0.990513i	$0.543880\pi$
$480$		0			0
$481$	1.59808	+	0.964102i	0.0728660	+	0.0439592i
$482$		−	18.5235i		−	0.843721i
$483$		0			0
$484$	5.00000	+	8.66025i	0.227273	+	0.393648i
$485$	−0.896575	+	1.55291i	−0.0407114	+	0.0705142i
$486$		0			0
$487$	5.78461	+	21.5885i	0.262126	+	0.978266i	0.963986	+	0.265952i	$0.0856863\pi$
$487$	5.78461	+	21.5885i	0.262126	+	0.978266i	−0.701861	+	0.712314i	$0.747647\pi$
$488$	−3.01790	−	11.2629i	−0.136614	−	0.509849i
$489$		0			0
$490$	0.500000	−	0.866025i	0.0225877	−	0.0391230i
$491$	−3.53553	−	6.12372i	−0.159556	−	0.276360i	0.775152	−	0.631774i	$-0.217673\pi$
$491$	−3.53553	−	6.12372i	−0.159556	−	0.276360i	−0.934709	+	0.355415i	$0.884340\pi$
$492$		0			0
$493$		−	48.9808i		−	2.20598i
$494$	3.86370	−	13.3843i	0.173836	−	0.602186i
$495$		0			0
$496$	−9.69615	−	2.59808i	−0.435370	−	0.116657i
$497$	−30.9468	+	17.8671i	−1.38815	+	0.801451i
$498$		0			0
$499$	−30.3205	+	30.3205i	−1.35733	+	1.35733i	−0.480141	+	0.877191i	$0.659415\pi$
$499$	−30.3205	+	30.3205i	−1.35733	+	1.35733i	−0.877191	+	0.480141i	$0.840585\pi$
$500$	0.965926	−	0.258819i	0.0431975	−	0.0115747i
$501$		0			0
$502$	2.56218	+	2.56218i	0.114356	+	0.114356i
$503$	−28.4094	−	16.4022i	−1.26671	−	0.731336i	−0.292347	−	0.956312i	$-0.594436\pi$
$503$	−28.4094	−	16.4022i	−1.26671	−	0.731336i	−0.974364	+	0.224976i	$0.927770\pi$
$504$		0			0
$505$	0.169873	−	0.633975i	0.00755925	−	0.0282115i
$506$	0.517638			0.0230118
$507$		0			0
$508$	2.92820			0.129918
$509$	−4.77886	+	17.8350i	−0.211819	+	0.790520i	0.775443	+	0.631418i	$0.217527\pi$
$509$	−4.77886	+	17.8350i	−0.211819	+	0.790520i	−0.987262	+	0.159103i	$0.949140\pi$
$510$		0			0
$511$	23.7846	+	13.7321i	1.05217	+	0.607470i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−7.96410	+	2.13397i	−0.351281	+	0.0941256i
$515$	1.41421	−	1.41421i	0.0623177	−	0.0623177i
$516$		0			0
$517$	−4.33013	+	2.50000i	−0.190439	+	0.109950i
$518$	1.22474	+	0.328169i	0.0538122	+	0.0144189i
$519$		0			0
$520$	1.00000	−	3.46410i	0.0438529	−	0.151911i
$521$			9.24316i			0.404950i	0.979287	+	0.202475i	$0.0648985\pi$
$521$			9.24316i			0.404950i	−0.979287	+	0.202475i	$0.935102\pi$
$522$		0			0
$523$	18.8205	+	32.5981i	0.822963	+	1.42541i	0.903466	+	0.428660i	$0.141014\pi$
$523$	18.8205	+	32.5981i	0.822963	+	1.42541i	−0.0805026	+	0.996754i	$0.525653\pi$
$524$	−3.27671	+	5.67544i	−0.143144	+	0.247933i
$525$		0			0
$526$	3.42820	+	12.7942i	0.149477	+	0.557855i
$527$	13.7124	+	51.1755i	0.597323	+	2.22924i
$528$		0			0
$529$	11.3660	−	19.6865i	0.494175	−	0.855936i
$530$	−5.08845	−	8.81345i	−0.221028	−	0.382832i
$531$		0			0
$532$		−	9.46410i		−	0.410321i
$533$	−33.7381	−	20.3538i	−1.46136	−	0.881621i
$534$		0			0
$535$	−4.09808	−	1.09808i	−0.177175	−	0.0474740i
$536$	−3.67423	+	2.12132i	−0.158703	+	0.0916271i
$537$		0			0
$538$	16.6603	−	16.6603i	0.718275	−	0.718275i
$539$	0.965926	−	0.258819i	0.0416054	−	0.0111481i
$540$		0			0
$541$	18.0000	+	18.0000i	0.773880	+	0.773880i	0.978782	−	0.204902i	$-0.0656876\pi$
$541$	18.0000	+	18.0000i	0.773880	+	0.773880i	−0.204902	+	0.978782i	$0.565688\pi$
$542$	−2.08913	−	1.20616i	−0.0897360	−	0.0518091i
$543$		0			0
$544$	−1.36603	+	5.09808i	−0.0585679	+	0.218578i
$545$	14.0406			0.601433
$546$		0			0
$547$	38.7846			1.65831			0.829155	−	0.559019i	$-0.188822\pi$
$547$	38.7846			1.65831			0.829155	+	0.559019i	$0.188822\pi$
$548$	0.360355	−	1.34486i	0.0153936	−	0.0574497i
$549$		0			0
$550$	0.866025	+	0.500000i	0.0369274	+	0.0213201i
$551$	−25.3543	−	25.3543i	−1.08013	−	1.08013i
$552$		0			0
$553$	−14.0263	+	3.75833i	−0.596458	+	0.159820i
$554$	7.53794	−	7.53794i	0.320256	−	0.320256i
$555$		0			0
$556$	8.66025	−	5.00000i	0.367277	−	0.212047i
$557$	24.9754	+	6.69213i	1.05824	+	0.283555i	0.745653	−	0.666334i	$-0.232138\pi$
$557$	24.9754	+	6.69213i	1.05824	+	0.283555i	0.312587	+	0.949889i	$0.398804\pi$
$558$		0			0
$559$	32.3827	−	31.1603i	1.36964	−	1.31794i
$560$		−	2.44949i		−	0.103510i
$561$		0			0
$562$	3.19615	+	5.53590i	0.134822	+	0.233518i
$563$	19.2306	−	33.3083i	0.810472	−	1.40378i	−0.102061	−	0.994778i	$-0.532544\pi$
$563$	19.2306	−	33.3083i	0.810472	−	1.40378i	0.912534	−	0.409001i	$-0.134123\pi$
$564$		0			0
$565$	2.96410	+	11.0622i	0.124701	+	0.465389i
$566$	2.62038	+	9.77938i	0.110143	+	0.411058i
$567$		0			0
$568$	7.29423	−	12.6340i	0.306059	−	0.530110i
$569$	4.38134	+	7.58871i	0.183675	+	0.318135i	0.943129	−	0.332426i	$-0.107867\pi$
$569$	4.38134	+	7.58871i	0.183675	+	0.318135i	−0.759454	+	0.650561i	$0.774534\pi$
$570$		0			0
$571$			9.12436i			0.381842i	0.981605	+	0.190921i	$0.0611475\pi$
$571$			9.12436i			0.381842i	−0.981605	+	0.190921i	$0.938853\pi$
$572$	3.15660	−	1.74238i	0.131984	−	0.0728527i
$573$		0			0
$574$	−25.8564	−	6.92820i	−1.07923	−	0.289178i
$575$	−0.448288	+	0.258819i	−0.0186949	+	0.0107935i
$576$		0			0
$577$	−23.9282	+	23.9282i	−0.996144	+	0.996144i	−0.999993	−	0.00384846i	$-0.998775\pi$
$577$	−23.9282	+	23.9282i	−0.996144	+	0.996144i	0.00384846	+	0.999993i	$0.498775\pi$
$578$	10.4865	−	2.80984i	0.436180	−	0.116874i
$579$		0			0
$580$	−6.56218	−	6.56218i	−0.272480	−	0.272480i
$581$	−23.1822	−	13.3843i	−0.961761	−	0.555273i
$582$		0			0
$583$	2.63397	−	9.83013i	0.109088	−	0.407122i
$584$	−11.2122			−0.463963
$585$		0			0
$586$	−10.9282			−0.451440
$587$	6.32680	−	23.6119i	0.261135	−	0.974568i	−0.703439	−	0.710756i	$-0.748353\pi$
$587$	6.32680	−	23.6119i	0.261135	−	0.974568i	0.964574	−	0.263813i	$-0.0849801\pi$
$588$		0			0
$589$	33.5885	+	19.3923i	1.38399	+	0.799046i
$590$	9.71003	+	9.71003i	0.399755	+	0.399755i
$591$		0			0
$592$	−0.500000	+	0.133975i	−0.0205499	+	0.00550632i
$593$	19.9241	−	19.9241i	0.818184	−	0.818184i	−0.167661	−	0.985845i	$-0.553621\pi$
$593$	19.9241	−	19.9241i	0.818184	−	0.818184i	0.985845	+	0.167661i	$0.0536213\pi$
$594$		0			0
$595$	−11.1962	+	6.46410i	−0.458997	+	0.265002i
$596$	−14.1607	−	3.79435i	−0.580046	−	0.155423i
$597$		0			0
$598$	−0.0358984	+	1.86603i	−0.00146799	+	0.0763075i
$599$			9.04008i			0.369368i	0.982798	+	0.184684i	$0.0591261\pi$
$599$			9.04008i			0.369368i	−0.982798	+	0.184684i	$0.940874\pi$
$600$		0			0
$601$	13.2321	+	22.9186i	0.539747	+	0.934869i	0.998917	+	0.0465205i	$0.0148133\pi$
$601$	13.2321	+	22.9186i	0.539747	+	0.934869i	−0.459171	+	0.888348i	$0.651853\pi$
$602$	15.2653	−	26.4404i	0.622169	−	1.07763i
$603$		0			0
$604$	3.29423	+	12.2942i	0.134040	+	0.500245i
$605$	−2.58819	−	9.65926i	−0.105225	−	0.392705i
$606$		0			0
$607$	1.70577	−	2.95448i	0.0692351	−	0.119919i	−0.829330	−	0.558760i	$-0.811277\pi$
$607$	1.70577	−	2.95448i	0.0692351	−	0.119919i	0.898565	+	0.438841i	$0.144611\pi$
$608$	1.93185	+	3.34607i	0.0783469	+	0.135701i
$609$		0			0
$610$			11.6603i			0.472110i
$611$	−8.71191	−	15.7830i	−0.352446	−	0.638511i
$612$		0			0
$613$	−9.96410	−	2.66987i	−0.402446	−	0.107835i	0.0519175	−	0.998651i	$-0.483467\pi$
$613$	−9.96410	−	2.66987i	−0.402446	−	0.107835i	−0.454364	+	0.890816i	$0.650133\pi$
$614$	29.5462	−	17.0585i	1.19239	−	0.688425i
$615$		0			0
$616$	1.73205	−	1.73205i	0.0697863	−	0.0697863i
$617$	29.4768	−	7.89829i	1.18669	−	0.317973i	0.389115	−	0.921189i	$-0.372781\pi$
$617$	29.4768	−	7.89829i	1.18669	−	0.317973i	0.797578	+	0.603216i	$0.206114\pi$
$618$		0			0
$619$	6.05256	+	6.05256i	0.243273	+	0.243273i	0.818203	−	0.574930i	$-0.194971\pi$
$619$	6.05256	+	6.05256i	0.243273	+	0.243273i	−0.574930	+	0.818203i	$0.694971\pi$
$620$	8.69333	+	5.01910i	0.349133	+	0.201572i
$621$		0			0
$622$	−1.70577	+	6.36603i	−0.0683952	+	0.255254i
$623$	24.9754			1.00062
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	−4.79744	+	17.9043i	−0.191744	+	0.715600i
$627$		0			0
$628$	18.5263	+	10.6962i	0.739279	+	0.426823i
$629$	1.93185	+	1.93185i	0.0770280	+	0.0770280i
$630$		0			0
$631$	34.1506	−	9.15064i	1.35952	−	0.364281i	0.495877	−	0.868393i	$-0.334847\pi$
$631$	34.1506	−	9.15064i	1.35952	−	0.364281i	0.863638	+	0.504112i	$0.168180\pi$
$632$	4.19187	−	4.19187i	0.166744	−	0.166744i
$633$		0			0
$634$	−26.6147	+	15.3660i	−1.05701	+	0.610263i
$635$	−2.82843	−	0.757875i	−0.112243	−	0.0300753i
$636$		0			0
$637$	0.866025	+	3.50000i	0.0343132	+	0.138675i
$638$		−	9.28032i		−	0.367411i
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−1.36345	+	2.36156i	−0.0538529	+	0.0932759i	−0.891695	−	0.452636i	$-0.850484\pi$
$641$	−1.36345	+	2.36156i	−0.0538529	+	0.0932759i	0.837842	+	0.545912i	$0.183817\pi$
$642$		0			0
$643$	7.29423	+	27.2224i	0.287656	+	1.07355i	0.946876	+	0.321598i	$0.104220\pi$
$643$	7.29423	+	27.2224i	0.287656	+	1.07355i	−0.659220	+	0.751950i	$0.729113\pi$
$644$	0.328169	+	1.22474i	0.0129317	+	0.0482617i
$645$		0			0
$646$	10.1962	−	17.6603i	0.401162	−	0.694833i
$647$	11.5403	+	19.9885i	0.453698	+	0.785827i	0.998612	−	0.0526641i	$-0.0167713\pi$
$647$	11.5403	+	19.9885i	0.453698	+	0.785827i	−0.544915	+	0.838492i	$0.683438\pi$
$648$		0			0
$649$			13.7321i			0.539030i
$650$	−1.86250	+	3.08725i	−0.0730533	+	0.121092i
$651$		0			0
$652$	−6.69615	−	1.79423i	−0.262242	−	0.0702674i
$653$	2.27362	−	1.31268i	0.0889738	−	0.0513690i	−0.454853	−	0.890567i	$-0.650308\pi$
$653$	2.27362	−	1.31268i	0.0889738	−	0.0513690i	0.543827	+	0.839198i	$0.316975\pi$
$654$		0			0
$655$	4.63397	−	4.63397i	0.181064	−	0.181064i
$656$	10.5558	−	2.82843i	0.412136	−	0.110432i
$657$		0			0
$658$	−8.66025	−	8.66025i	−0.337612	−	0.337612i
$659$	−0.120118	−	0.0693504i	−0.00467915	−	0.00270151i	0.497659	−	0.867373i	$-0.334193\pi$
$659$	−0.120118	−	0.0693504i	−0.00467915	−	0.00270151i	−0.502338	+	0.864671i	$0.667527\pi$
$660$		0			0
$661$	2.11731	−	7.90192i	0.0823540	−	0.307349i	−0.912446	−	0.409197i	$-0.865809\pi$
$661$	2.11731	−	7.90192i	0.0823540	−	0.307349i	0.994800	+	0.101848i	$0.0324755\pi$
$662$	−10.2784			−0.399483
$663$		0			0
$664$	10.9282			0.424097
$665$	−2.44949	+	9.14162i	−0.0949871	+	0.354497i
$666$		0			0
$667$	4.16025	+	2.40192i	0.161086	+	0.0930029i
$668$	6.12372	+	6.12372i	0.236934	+	0.236934i
$669$		0			0
$670$	4.09808	−	1.09808i	0.158322	−	0.0424224i
$671$	−8.24504	+	8.24504i	−0.318296	+	0.318296i
$672$		0			0
$673$	6.12436	−	3.53590i	0.236077	−	0.136299i	−0.377296	−	0.926093i	$-0.623146\pi$
$673$	6.12436	−	3.53590i	0.236077	−	0.136299i	0.613372	+	0.789794i	$0.289813\pi$
$674$	−16.9198	−	4.53365i	−0.651726	−	0.174629i
$675$		0			0
$676$	6.06218	+	11.5000i	0.233161	+	0.442308i
$677$		−	42.8797i		−	1.64800i	−0.566590	−	0.824000i	$-0.691738\pi$
$677$		−	42.8797i		−	1.64800i	0.566590	−	0.824000i	$-0.308262\pi$
$678$		0			0
$679$	−2.19615	−	3.80385i	−0.0842806	−	0.145978i
$680$	2.63896	−	4.57081i	0.101199	−	0.175283i
$681$		0			0
$682$	2.59808	+	9.69615i	0.0994855	+	0.371285i
$683$	−0.175865	−	0.656339i	−0.00672930	−	0.0251141i	0.962480	−	0.271354i	$-0.0874715\pi$
$683$	−0.175865	−	0.656339i	−0.00672930	−	0.0251141i	−0.969209	+	0.246240i	$0.920805\pi$
$684$		0			0
$685$	−0.696152	+	1.20577i	−0.0265986	+	0.0460702i
$686$	9.79796	+	16.9706i	0.374088	+	0.647939i
$687$		0			0
$688$			12.4641i			0.475189i
$689$	35.2538	+	10.1769i	1.34306	+	0.387709i
$690$		0			0
$691$	11.6603	+	3.12436i	0.443577	+	0.118856i	0.473692	−	0.880690i	$-0.342921\pi$
$691$	11.6603	+	3.12436i	0.443577	+	0.118856i	−0.0301155	+	0.999546i	$0.509588\pi$
$692$	4.89898	−	2.82843i	0.186231	−	0.107521i
$693$		0			0
$694$	22.3923	−	22.3923i	0.850000	−	0.850000i
$695$	−9.65926	+	2.58819i	−0.366397	+	0.0981757i
$696$		0			0
$697$	−40.7846	−	40.7846i	−1.54483	−	1.54483i
$698$	−15.0251	−	8.67475i	−0.568709	−	0.328344i
$699$		0			0
$700$	−0.633975	+	2.36603i	−0.0239620	+	0.0894274i
$701$	45.3663			1.71346			0.856731	−	0.515763i	$-0.172492\pi$
$701$	45.3663			1.71346			0.856731	+	0.515763i	$0.172492\pi$
$702$		0			0
$703$	2.00000			0.0754314
$704$	−0.258819	+	0.965926i	−0.00975461	+	0.0364047i
$705$		0			0
$706$	−18.5885	−	10.7321i	−0.699586	−	0.403906i
$707$	1.13681	+	1.13681i	0.0427542	+	0.0427542i
$708$		0			0
$709$	18.1244	−	4.85641i	0.680674	−	0.182386i	0.0981160	−	0.995175i	$-0.468718\pi$
$709$	18.1244	−	4.85641i	0.680674	−	0.182386i	0.582558	+	0.812789i	$0.302052\pi$
$710$	−10.3156	+	10.3156i	−0.387137	+	0.387137i
$711$		0			0
$712$	−8.83013	+	5.09808i	−0.330923	+	0.191058i
$713$	−5.01910	−	1.34486i	−0.187967	−	0.0503655i
$714$		0			0
$715$	−3.50000	+	0.866025i	−0.130893	+	0.0323875i
$716$		−	12.3861i		−	0.462892i
$717$		0			0
$718$	−5.26795	−	9.12436i	−0.196598	−	0.340518i
$719$	−6.55343	+	11.3509i	−0.244402	+	0.423316i	−0.961963	−	0.273179i	$-0.911925\pi$
$719$	−6.55343	+	11.3509i	−0.244402	+	0.423316i	0.717562	+	0.696495i	$0.245258\pi$
$720$		0			0
$721$	1.26795	+	4.73205i	0.0472209	+	0.176231i
$722$	1.05386	+	3.93305i	0.0392206	+	0.146373i
$723$		0			0
$724$	1.19615	−	2.07180i	0.0444547	−	0.0769977i
$725$	4.64016	+	8.03699i	0.172331	+	0.298486i
$726$		0			0
$727$			14.3923i			0.533781i	0.963727	+	0.266891i	$0.0859962\pi$
$727$			14.3923i			0.533781i	−0.963727	+	0.266891i	$0.914004\pi$
$728$	6.12372	+	6.36396i	0.226960	+	0.235864i
$729$		0			0
$730$	10.8301	+	2.90192i	0.400841	+	0.107405i
$731$	56.9710	−	32.8922i	2.10715	−	1.21656i
$732$		0			0
$733$	−8.66025	+	8.66025i	−0.319874	+	0.319874i	−0.848719	−	0.528845i	$-0.822625\pi$
$733$	−8.66025	+	8.66025i	−0.319874	+	0.319874i	0.528845	+	0.848719i	$0.322625\pi$
$734$	2.26002	−	0.605571i	0.0834189	−	0.0223520i
$735$		0			0
$736$	−0.366025	−	0.366025i	−0.0134919	−	0.0134919i
$737$	3.67423	+	2.12132i	0.135342	+	0.0781398i
$738$		0			0
$739$	−2.29423	+	8.56218i	−0.0843946	+	0.314965i	−0.995199	−	0.0978736i	$-0.968796\pi$
$739$	−2.29423	+	8.56218i	−0.0843946	+	0.314965i	0.910804	+	0.412838i	$0.135463\pi$
$740$	0.517638			0.0190288
$741$		0			0
$742$	24.9282			0.915143
$743$	4.08536	−	15.2468i	0.149877	−	0.559349i	−0.849612	−	0.527407i	$-0.823164\pi$
$743$	4.08536	−	15.2468i	0.149877	−	0.559349i	0.999490	−	0.0319420i	$-0.0101692\pi$
$744$		0			0
$745$	12.6962	+	7.33013i	0.465151	+	0.268555i
$746$	7.63947	+	7.63947i	0.279701	+	0.279701i
$747$		0			0
$748$	5.09808	−	1.36603i	0.186404	−	0.0499468i
$749$	7.34847	−	7.34847i	0.268507	−	0.268507i
$750$		0			0
$751$	36.3564	−	20.9904i	1.32666	−	0.765950i	0.341882	−	0.939743i	$-0.388936\pi$
$751$	36.3564	−	20.9904i	1.32666	−	0.765950i	0.984782	+	0.173793i	$0.0556024\pi$
$752$	4.82963	+	1.29410i	0.176118	+	0.0471908i
$753$		0			0
$754$	33.4545	+	0.643594i	1.21834	+	0.0234383i
$755$		−	12.7279i		−	0.463217i
$756$		0			0
$757$	−7.80385	−	13.5167i	−0.283636	−	0.491271i	0.688642	−	0.725102i	$-0.258207\pi$
$757$	−7.80385	−	13.5167i	−0.283636	−	0.491271i	−0.972277	+	0.233830i	$0.924874\pi$
$758$	17.9551	−	31.0991i	0.652158	−	1.12957i
$759$		0			0
$760$	−1.00000	−	3.73205i	−0.0362738	−	0.135376i
$761$	−8.24504	−	30.7709i	−0.298883	−	1.11545i	−0.938085	−	0.346406i	$-0.887402\pi$
$761$	−8.24504	−	30.7709i	−0.298883	−	1.11545i	0.639202	−	0.769039i	$-0.279265\pi$
$762$		0			0
$763$	−17.1962	+	29.7846i	−0.622543	+	1.07828i
$764$	5.98502	+	10.3664i	0.216531	+	0.375042i
$765$		0			0
$766$			17.1962i			0.621322i
$767$	−49.5025	−	0.952323i	−1.78743	−	0.0343864i
$768$		0			0
$769$	6.50000	+	1.74167i	0.234396	+	0.0628062i	0.374105	−	0.927386i	$-0.377950\pi$
$769$	6.50000	+	1.74167i	0.234396	+	0.0628062i	−0.139709	+	0.990193i	$0.544617\pi$
$770$	−2.12132	+	1.22474i	−0.0764471	+	0.0441367i
$771$		0			0
$772$	−1.39230	+	1.39230i	−0.0501101	+	0.0501101i
$773$	−35.9101	+	9.62209i	−1.29160	+	0.346083i	−0.838267	−	0.545260i	$-0.816431\pi$
$773$	−35.9101	+	9.62209i	−1.29160	+	0.346083i	−0.453331	+	0.891342i	$0.649764\pi$
$774$		0			0
$775$	−7.09808	−	7.09808i	−0.254970	−	0.254970i
$776$	1.55291	+	0.896575i	0.0557464	+	0.0321852i
$777$		0			0
$778$	−5.16025	+	19.2583i	−0.185004	+	0.690445i
$779$	−42.2233			−1.51281
$780$		0			0
$781$	−14.5885			−0.522016
$782$	−0.707107	+	2.63896i	−0.0252861	+	0.0943690i
$783$		0			0
$784$	−0.866025	−	0.500000i	−0.0309295	−	0.0178571i
$785$	−15.1266	−	15.1266i	−0.539893	−	0.539893i
$786$		0			0
$787$	−7.33013	+	1.96410i	−0.261291	+	0.0700127i	−0.387086	−	0.922044i	$-0.626518\pi$
$787$	−7.33013	+	1.96410i	−0.261291	+	0.0700127i	0.125795	+	0.992056i	$0.459852\pi$
$788$	5.41662	−	5.41662i	0.192959	−	0.192959i
$789$		0			0
$790$	−5.13397	+	2.96410i	−0.182659	+	0.105458i
$791$	−27.0967	−	7.26054i	−0.963447	−	0.258155i
$792$		0			0
$793$	−29.1506	−	30.2942i	−1.03517	−	1.07578i
$794$			24.6336i			0.874214i
$795$		0			0
$796$	−12.7321	−	22.0526i	−0.451276	−	0.781632i
$797$	−3.06866	+	5.31508i	−0.108698	+	0.188270i	−0.915243	−	0.402903i	$-0.868001\pi$
$797$	−3.06866	+	5.31508i	−0.108698	+	0.188270i	0.806545	+	0.591172i	$0.201335\pi$
$798$		0			0
$799$	−6.83013	−	25.4904i	−0.241633	−	0.901785i
$800$	−0.258819	−	0.965926i	−0.00915064	−	0.0341506i
$801$		0			0
$802$	3.92820	−	6.80385i	0.138710	−	0.240252i
$803$	5.60609	+	9.71003i	0.197834	+	0.342659i
$804$		0			0
$805$		−	1.26795i		−	0.0446893i
$806$	−35.1337	+	8.69333i	−1.23753	+	0.306210i
$807$		0			0
$808$	−0.633975	−	0.169873i	−0.0223031	−	0.00597611i
$809$	41.2017	−	23.7878i	1.44857	−	0.836334i	0.450177	−	0.892940i	$-0.351361\pi$
$809$	41.2017	−	23.7878i	1.44857	−	0.836334i	0.998397	+	0.0566053i	$0.0180277\pi$
$810$		0			0
$811$	−36.0526	+	36.0526i	−1.26598	+	1.26598i	−0.317828	+	0.948148i	$0.602954\pi$
$811$	−36.0526	+	36.0526i	−1.26598	+	1.26598i	−0.948148	+	0.317828i	$0.897046\pi$
$812$	21.9575	−	5.88349i	0.770556	−	0.206470i
$813$		0			0
$814$	0.366025	+	0.366025i	0.0128292	+	0.0128292i
$815$	6.00361	+	3.46618i	0.210297	+	0.121415i
$816$		0			0
$817$	12.4641	−	46.5167i	0.436064	−	1.62741i
$818$	−5.83272			−0.203936
$819$		0			0
$820$	−10.9282			−0.381629
$821$	−6.24384	+	23.3023i	−0.217912	+	0.813257i	0.767210	+	0.641396i	$0.221645\pi$
$821$	−6.24384	+	23.3023i	−0.217912	+	0.813257i	−0.985121	+	0.171861i	$0.945022\pi$
$822$		0			0
$823$	−47.0263	−	27.1506i	−1.63923	−	0.946412i	−0.981098	−	0.193512i	$-0.938012\pi$
$823$	−47.0263	−	27.1506i	−1.63923	−	0.946412i	−0.658135	−	0.752900i	$-0.728654\pi$
$824$	−1.41421	−	1.41421i	−0.0492665	−	0.0492665i
$825$		0			0
$826$	−32.4904	+	8.70577i	−1.13048	+	0.302913i
$827$	−18.0430	+	18.0430i	−0.627417	+	0.627417i	−0.947417	−	0.320001i	$-0.896317\pi$
$827$	−18.0430	+	18.0430i	−0.627417	+	0.627417i	0.320001	+	0.947417i	$0.396317\pi$
$828$		0			0
$829$	−29.0263	+	16.7583i	−1.00812	+	0.582041i	−0.910642	−	0.413196i	$-0.864412\pi$
$829$	−29.0263	+	16.7583i	−1.00812	+	0.582041i	−0.0974824	+	0.995237i	$0.531079\pi$
$830$	−10.5558	−	2.82843i	−0.366398	−	0.0981761i
$831$		0			0
$832$	−3.46410	−	1.00000i	−0.120096	−	0.0346688i
$833$			5.27792i			0.182869i
$834$		0			0
$835$	−4.33013	−	7.50000i	−0.149850	−	0.259548i
$836$	1.93185	−	3.34607i	0.0668145	−	0.115726i
$837$		0			0
$838$	−2.95448	−	11.0263i	−0.102061	−	0.380897i
$839$	10.5930	+	39.5336i	0.365711	+	1.36485i	0.866454	+	0.499256i	$0.166393\pi$
$839$	10.5930	+	39.5336i	0.365711	+	1.36485i	−0.500744	+	0.865596i	$0.666940\pi$
$840$		0			0
$841$	28.5622	−	49.4711i	0.984903	−	1.70590i
$842$	9.84873	+	17.0585i	0.339410	+	0.587875i
$843$		0			0
$844$		−	1.80385i		−	0.0620910i
$845$	−2.87920	−	12.6772i	−0.0990473	−	0.436107i
$846$		0			0
$847$	23.6603	+	6.33975i	0.812976	+	0.217836i
$848$	−8.81345	+	5.08845i	−0.302655	+	0.174738i
$849$		0			0
$850$	−3.73205	+	3.73205i	−0.128008	+	0.128008i
$851$	−0.258819	+	0.0693504i	−0.00887220	+	0.00237730i
$852$		0			0
$853$	−23.1699	−	23.1699i	−0.793321	−	0.793321i	0.188711	−	0.982033i	$-0.439569\pi$
$853$	−23.1699	−	23.1699i	−0.793321	−	0.793321i	−0.982033	+	0.188711i	$0.939569\pi$
$854$	−24.7351	−	14.2808i	−0.846419	−	0.488680i
$855$		0			0
$856$	−1.09808	+	4.09808i	−0.0375315	+	0.140069i
$857$	−26.7314			−0.913126			−0.456563	−	0.889691i	$-0.650920\pi$
$857$	−26.7314			−0.913126			−0.456563	+	0.889691i	$0.650920\pi$
$858$		0			0
$859$	−26.5885			−0.907186			−0.453593	−	0.891209i	$-0.649858\pi$
$859$	−26.5885			−0.907186			−0.453593	+	0.891209i	$0.649858\pi$
$860$	3.22595	−	12.0394i	0.110004	−	0.410540i
$861$		0			0
$862$	−6.29423	−	3.63397i	−0.214382	−	0.123774i
$863$	16.6796	+	16.6796i	0.567779	+	0.567779i	0.931506	−	0.363727i	$-0.118496\pi$
$863$	16.6796	+	16.6796i	0.567779	+	0.567779i	−0.363727	+	0.931506i	$0.618496\pi$
$864$		0			0
$865$	−5.46410	+	1.46410i	−0.185785	+	0.0497809i
$866$	−20.3166	+	20.3166i	−0.690387	+	0.690387i
$867$		0			0
$868$	−21.2942	+	12.2942i	−0.722773	+	0.417293i
$869$	−5.72620	−	1.53433i	−0.194248	−	0.0520486i
$870$		0			0
$871$	−7.90192	+	13.0981i	−0.267746	+	0.443811i
$872$		−	14.0406i		−	0.475475i
$873$		0			0
$874$	1.00000	+	1.73205i	0.0338255	+	0.0585875i
$875$	1.22474	−	2.12132i	0.0414039	−	0.0717137i
$876$		0			0
$877$	6.37564	+	23.7942i	0.215290	+	0.803474i	0.986064	+	0.166365i	$0.0532031\pi$
$877$	6.37564	+	23.7942i	0.215290	+	0.803474i	−0.770774	+	0.637109i	$0.780130\pi$
$878$	−7.62587	−	28.4601i	−0.257361	−	0.960483i
$879$		0			0
$880$	0.500000	−	0.866025i	0.0168550	−	0.0291937i
$881$	5.46739	+	9.46979i	0.184201	+	0.319045i	0.943307	−	0.331922i	$-0.107697\pi$
$881$	5.46739	+	9.46979i	0.184201	+	0.319045i	−0.759106	+	0.650967i	$0.774364\pi$
$882$		0			0
$883$		−	20.6077i		−	0.693504i	−0.937957	−	0.346752i	$-0.887285\pi$
$883$		−	20.6077i		−	0.693504i	0.937957	−	0.346752i	$-0.112715\pi$
$884$	4.57081	+	18.4727i	0.153733	+	0.621304i
$885$		0			0
$886$	−17.2942	−	4.63397i	−0.581011	−	0.155681i
$887$	31.3951	−	18.1260i	1.05414	−	0.608610i	0.130337	−	0.991470i	$-0.458394\pi$
$887$	31.3951	−	18.1260i	1.05414	−	0.608610i	0.923807	+	0.382860i	$0.125061\pi$
$888$		0			0
$889$	5.07180	−	5.07180i	0.170103	−	0.170103i
$890$	9.84873	−	2.63896i	0.330130	−	0.0884581i
$891$		0			0
$892$	7.26795	+	7.26795i	0.243349	+	0.243349i
$893$	−16.7303	−	9.65926i	−0.559859	−	0.323235i
$894$		0			0
$895$	−3.20577	+	11.9641i	−0.107157	+	0.399916i
$896$	−2.44949			−0.0818317
$897$		0			0
$898$	−3.85641			−0.128690
$899$	−24.1110	+	89.9834i	−0.804146	+	3.00111i
$900$		0			0
$901$	46.5167	+	26.8564i	1.54969	+	0.894717i
$902$	−7.72741	−	7.72741i	−0.257294	−	0.257294i
$903$		0			0
$904$	11.0622	−	2.96410i	0.367923	−	0.0985846i
$905$	−1.69161	+	1.69161i	−0.0562312	+	0.0562312i
$906$		0			0
$907$	−4.16025	+	2.40192i	−0.138139	+	0.0797546i	−0.567477	−	0.823389i	$-0.692080\pi$
$907$	−4.16025	+	2.40192i	−0.138139	+	0.0797546i	0.429338	+	0.903144i	$0.358747\pi$
$908$	6.12372	+	1.64085i	0.203223	+	0.0544534i
$909$		0			0
$910$	−4.26795	−	7.73205i	−0.141481	−	0.256315i
$911$		−	10.2784i		−	0.340540i	−0.985397	−	0.170270i	$-0.945536\pi$
$911$		−	10.2784i		−	0.340540i	0.985397	−	0.170270i	$-0.0544639\pi$
$912$		0			0
$913$	−5.46410	−	9.46410i	−0.180835	−	0.313216i
$914$	2.03339	−	3.52193i	0.0672585	−	0.116495i
$915$		0			0
$916$	4.83013	+	18.0263i	0.159592	+	0.595605i
$917$	4.15471	+	15.5056i	0.137201	+	0.512039i
$918$		0			0
$919$	−0.392305	+	0.679492i	−0.0129409	+	0.0224144i	−0.872423	−	0.488751i	$-0.837453\pi$
$919$	−0.392305	+	0.679492i	−0.0129409	+	0.0224144i	0.859482	+	0.511165i	$0.170786\pi$
$920$	0.258819	+	0.448288i	0.00853301	+	0.0147796i
$921$		0			0
$922$			29.2487i			0.963255i
$923$	1.01171	−	52.5897i	0.0333010	−	1.73101i
$924$		0			0
$925$	−0.500000	−	0.133975i	−0.0164399	−	0.00440506i
$926$	−25.7196	+	14.8492i	−0.845200	+	0.487976i
$927$		0			0
$928$	−6.56218	+	6.56218i	−0.215414	+	0.215414i
$929$	35.3925	−	9.48339i	1.16119	−	0.311140i	0.373749	−	0.927530i	$-0.378072\pi$
$929$	35.3925	−	9.48339i	1.16119	−	0.311140i	0.787441	+	0.616390i	$0.211405\pi$
$930$		0			0
$931$	2.73205	+	2.73205i	0.0895393	+	0.0895393i
$932$	0.864390	+	0.499056i	0.0283140	+	0.0163471i
$933$		0			0
$934$	2.09808	−	7.83013i	0.0686512	−	0.256210i
$935$	−5.27792			−0.172606
$936$		0			0
$937$	−5.07180			−0.165688			−0.0828442	−	0.996563i	$-0.526400\pi$
$937$	−5.07180			−0.165688			−0.0828442	+	0.996563i	$0.526400\pi$
$938$	−2.68973	+	10.0382i	−0.0878227	+	0.327759i
$939$		0			0
$940$	−4.33013	−	2.50000i	−0.141233	−	0.0815410i
$941$	31.1870	+	31.1870i	1.01667	+	1.01667i	0.999859	+	0.0168093i	$0.00535083\pi$
$941$	31.1870	+	31.1870i	1.01667	+	1.01667i	0.0168093	+	0.999859i	$0.494649\pi$
$942$		0			0
$943$	5.46410	−	1.46410i	0.177936	−	0.0476777i
$944$	9.71003	−	9.71003i	0.316034	−	0.316034i
$945$		0			0
$946$	10.7942	−	6.23205i	0.350951	−	0.202621i
$947$	−34.0662	−	9.12802i	−1.10700	−	0.296621i	−0.341390	−	0.939922i	$-0.610898\pi$
$947$	−34.0662	−	9.12802i	−1.10700	−	0.296621i	−0.765613	+	0.643301i	$0.777564\pi$
$948$		0			0
$949$	−35.3923	+	19.5359i	−1.14888	+	0.634162i
$950$			3.86370i			0.125355i
$951$		0			0
$952$	6.46410	+	11.1962i	0.209503	+	0.362869i
$953$	−2.34297	+	4.05815i	−0.0758964	+	0.131456i	−0.901476	−	0.432830i	$-0.857515\pi$
$953$	−2.34297	+	4.05815i	−0.0758964	+	0.131456i	0.825579	+	0.564286i	$0.190848\pi$
$954$		0			0
$955$	−3.09808	−	11.5622i	−0.100251	−	0.374143i
$956$	3.95164	+	14.7477i	0.127805	+	0.476975i
$957$		0			0
$958$	−2.70577	+	4.68653i	−0.0874195	+	0.151415i
$959$	−1.70522	−	2.95352i	−0.0550644	−	0.0953743i
$960$		0			0
$961$		−	69.7654i		−	2.25050i
$962$	−1.34486	+	1.29410i	−0.0433601	+	0.0417233i
$963$		0			0
$964$	17.8923	+	4.79423i	0.576272	+	0.154412i
$965$	1.70522	−	0.984508i	0.0548929	−	0.0316924i
$966$		0			0
$967$	−17.7321	+	17.7321i	−0.570224	+	0.570224i	−0.932191	−	0.361967i	$-0.882105\pi$
$967$	−17.7321	+	17.7321i	−0.570224	+	0.570224i	0.361967	+	0.932191i	$0.382105\pi$
$968$	−9.65926	+	2.58819i	−0.310460	+	0.0831876i
$969$		0			0
$970$	−1.26795	−	1.26795i	−0.0407114	−	0.0407114i
$971$	20.3402	+	11.7434i	0.652748	+	0.376864i	0.789508	−	0.613740i	$-0.210336\pi$
$971$	20.3402	+	11.7434i	0.652748	+	0.376864i	−0.136760	+	0.990604i	$0.543669\pi$
$972$		0			0
$973$	6.33975	−	23.6603i	0.203243	−	0.758513i
$974$	−22.3500			−0.716141
$975$		0			0
$976$	11.6603			0.373236
$977$	−12.8852	+	48.0882i	−0.412234	+	1.53848i	0.378077	+	0.925774i	$0.376585\pi$
$977$	−12.8852	+	48.0882i	−0.412234	+	1.53848i	−0.790312	+	0.612705i	$0.790081\pi$
$978$		0			0
$979$	8.83013	+	5.09808i	0.282212	+	0.162935i
$980$	0.707107	+	0.707107i	0.0225877	+	0.0225877i
$981$		0			0
$982$	6.83013	−	1.83013i	0.217958	−	0.0584017i
$983$	28.7883	−	28.7883i	0.918204	−	0.918204i	−0.0786944	−	0.996899i	$-0.525075\pi$
$983$	28.7883	−	28.7883i	0.918204	−	0.918204i	0.996899	+	0.0786944i	$0.0250751\pi$
$984$		0			0
$985$	−6.63397	+	3.83013i	−0.211376	+	0.122038i
$986$	47.3118	+	12.6772i	1.50671	+	0.403723i
$987$		0			0
$988$	11.9282	+	7.19615i	0.379487	+	0.228940i
$989$			6.45189i			0.205158i
$990$		0			0
$991$	4.25833	+	7.37564i	0.135270	+	0.234295i	0.925701	−	0.378257i	$-0.123476\pi$
$991$	4.25833	+	7.37564i	0.135270	+	0.234295i	−0.790430	+	0.612552i	$0.790143\pi$
$992$	5.01910	−	8.69333i	0.159357	−	0.276014i
$993$		0			0
$994$	−9.24871	−	34.5167i	−0.293351	−	1.09480i
$995$	6.59059	+	24.5964i	0.208936	+	0.779759i
$996$		0			0
$997$	−24.0526	+	41.6603i	−0.761752	+	1.31939i	0.180195	+	0.983631i	$0.442327\pi$
$997$	−24.0526	+	41.6603i	−0.761752	+	1.31939i	−0.941947	+	0.335762i	$0.891006\pi$
$998$	−21.4398	−	37.1349i	−0.678666	−	1.17548i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.cu.a.431.1	✓	8
3.2	odd	2	inner	1170.2.cu.a.431.2	yes	8
13.7	odd	12	inner	1170.2.cu.a.1151.2	yes	8
39.20	even	12	inner	1170.2.cu.a.1151.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.cu.a.431.1	✓	8	1.1	even	1	trivial
1170.2.cu.a.431.2	yes	8	3.2	odd	2	inner
1170.2.cu.a.1151.1	yes	8	39.20	even	12	inner
1170.2.cu.a.1151.2	yes	8	13.7	odd	12	inner

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.36603 + 0.633975i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-2.36603 + 0.633975i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{10} +(-0.965926 - 0.258819i) q^{11} +(1.00000 - 3.46410i) q^{13} -2.44949i q^{14} +(0.500000 + 0.866025i) q^{16} +(2.63896 - 4.57081i) q^{17} +(-1.00000 - 3.73205i) q^{19} +(-0.258819 - 0.965926i) q^{20} +(0.500000 - 0.866025i) q^{22} +(0.258819 + 0.448288i) q^{23} +1.00000i q^{25} +(3.08725 + 1.86250i) q^{26} +(2.36603 + 0.633975i) q^{28} +(8.03699 - 4.64016i) q^{29} +(-7.09808 + 7.09808i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(3.73205 + 3.73205i) q^{34} +(-2.12132 - 1.22474i) q^{35} +(-0.133975 + 0.500000i) q^{37} +3.86370 q^{38} +1.00000 q^{40} +(2.82843 - 10.5558i) q^{41} +(10.7942 + 6.23205i) q^{43} +(0.707107 + 0.707107i) q^{44} +(-0.500000 + 0.133975i) q^{46} +(3.53553 - 3.53553i) q^{47} +(-0.866025 + 0.500000i) q^{49} +(-0.965926 - 0.258819i) q^{50} +(-2.59808 + 2.50000i) q^{52} +10.1769i q^{53} +(-0.500000 - 0.866025i) q^{55} +(-1.22474 + 2.12132i) q^{56} +(2.40192 + 8.96410i) q^{58} +(-3.55412 - 13.2641i) q^{59} +(5.83013 - 10.0981i) q^{61} +(-5.01910 - 8.69333i) q^{62} -1.00000i q^{64} +(3.15660 - 1.74238i) q^{65} +(-4.09808 - 1.09808i) q^{67} +(-4.57081 + 2.63896i) q^{68} +(1.73205 - 1.73205i) q^{70} +(14.0914 - 3.77577i) q^{71} +(-7.92820 - 7.92820i) q^{73} +(-0.448288 - 0.258819i) q^{74} +(-1.00000 + 3.73205i) q^{76} +2.44949 q^{77} +5.92820 q^{79} +(-0.258819 + 0.965926i) q^{80} +(9.46410 + 5.46410i) q^{82} +(7.72741 + 7.72741i) q^{83} +(5.09808 - 1.36603i) q^{85} +(-8.81345 + 8.81345i) q^{86} +(-0.866025 + 0.500000i) q^{88} +(-9.84873 - 2.63896i) q^{89} +(-0.169873 + 8.83013i) q^{91} -0.517638i q^{92} +(2.50000 + 4.33013i) q^{94} +(1.93185 - 3.34607i) q^{95} +(0.464102 + 1.73205i) q^{97} +(-0.258819 - 0.965926i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{7}+O(q^{10}) \) 8 * q - 12 * q^7	\( 8 q - 12 q^{7} + 8 q^{13} + 4 q^{16} - 8 q^{19} + 4 q^{22} + 12 q^{28} - 36 q^{31} + 16 q^{34} - 8 q^{37} + 8 q^{40} + 24 q^{43} - 4 q^{46} - 4 q^{55} + 40 q^{58} + 12 q^{61} - 12 q^{67} - 8 q^{73} - 8 q^{76} - 8 q^{79} + 48 q^{82} + 20 q^{85} - 36 q^{91} + 20 q^{94} - 24 q^{97}+O(q^{100}) \) 8 * q - 12 * q^7 + 8 * q^13 + 4 * q^16 - 8 * q^19 + 4 * q^22 + 12 * q^28 - 36 * q^31 + 16 * q^34 - 8 * q^37 + 8 * q^40 + 24 * q^43 - 4 * q^46 - 4 * q^55 + 40 * q^58 + 12 * q^61 - 12 * q^67 - 8 * q^73 - 8 * q^76 - 8 * q^79 + 48 * q^82 + 20 * q^85 - 36 * q^91 + 20 * q^94 - 24 * q^97

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