LMFDB - Embedded newform 156.2.h.b.155.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(155,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("156.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.h (of order $2$, degree $1$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 43x^{12} + 517x^{8} + 1804x^{4} + 16 $ x^16 + 43x^12 + 517x^8 + 1804*x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			155.4
Root			$-1.29309 + 1.29309i$ of defining polynomial
Character	$\chi$	$=$	156.155
Dual form			156.2.h.b.155.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17915 + 0.780776i) q^{2} +(1.26870 + 1.17915i) q^{3} +(0.780776 - 1.84130i) q^{4} -0.662153 q^{5} +(-2.41664 - 0.399813i) q^{6} +3.83206 q^{7} +(0.516994 + 2.78078i) q^{8} +(0.219224 + 2.99198i) q^{9} +O(q^{10})$	\(q+(-1.17915 + 0.780776i) q^{2} +(1.26870 + 1.17915i) q^{3} +(0.780776 - 1.84130i) q^{4} -0.662153 q^{5} +(-2.41664 - 0.399813i) q^{6} +3.83206 q^{7} +(0.516994 + 2.78078i) q^{8} +(0.219224 + 2.99198i) q^{9} +(0.780776 - 0.516994i) q^{10} -2.00000i q^{11} +(3.16174 - 1.41542i) q^{12} +(-2.56155 + 2.53741i) q^{13} +(-4.51856 + 2.99198i) q^{14} +(-0.840077 - 0.780776i) q^{15} +(-2.78078 - 2.87529i) q^{16} +1.68015i q^{17} +(-2.59456 - 3.35682i) q^{18} -2.15190 q^{19} +(-0.516994 + 1.21922i) q^{20} +(4.86175 + 4.51856i) q^{21} +(1.56155 + 2.35829i) q^{22} +6.49971 q^{23} +(-2.62303 + 4.13760i) q^{24} -4.56155 q^{25} +(1.03930 - 4.99198i) q^{26} +(-3.24985 + 4.05444i) q^{27} +(2.99198 - 7.05597i) q^{28} -7.66411i q^{29} +(1.60019 + 0.264738i) q^{30} +2.15190 q^{31} +(5.52390 + 1.21922i) q^{32} +(2.35829 - 2.53741i) q^{33} +(-1.31182 - 1.98115i) q^{34} -2.53741 q^{35} +(5.68030 + 1.93241i) q^{36} -9.03712i q^{37} +(2.53741 - 1.68015i) q^{38} +(-6.24183 + 0.198776i) q^{39} +(-0.342329 - 1.84130i) q^{40} -6.41273 q^{41} +(-9.26070 - 1.53211i) q^{42} -3.68260i q^{43} +(-3.68260 - 1.56155i) q^{44} +(-0.145160 - 1.98115i) q^{45} +(-7.66411 + 5.07482i) q^{46} -6.68466i q^{47} +(-0.137596 - 6.92684i) q^{48} +7.68466 q^{49} +(5.37874 - 3.56155i) q^{50} +(-1.98115 + 2.13162i) q^{51} +(2.67213 + 6.69774i) q^{52} +(0.666449 - 7.31819i) q^{54} +1.32431i q^{55} +(1.98115 + 10.6561i) q^{56} +(-2.73013 - 2.53741i) q^{57} +(5.98396 + 9.03712i) q^{58} -2.87689i q^{59} +(-2.09356 + 0.937223i) q^{60} +3.12311 q^{61} +(-2.53741 + 1.68015i) q^{62} +(0.840077 + 11.4654i) q^{63} +(-7.46543 + 2.87529i) q^{64} +(1.69614 - 1.68015i) q^{65} +(-0.799627 + 4.83328i) q^{66} -5.51221 q^{67} +(3.09367 + 1.31182i) q^{68} +(8.24621 + 7.66411i) q^{69} +(2.99198 - 1.98115i) q^{70} +14.6847i q^{71} +(-8.20669 + 2.15645i) q^{72} +12.9994i q^{73} +(7.05597 + 10.6561i) q^{74} +(-5.78726 - 5.37874i) q^{75} +(-1.68015 + 3.96230i) q^{76} -7.66411i q^{77} +(7.20484 - 5.10786i) q^{78} -8.10887i q^{79} +(1.84130 + 1.90388i) q^{80} +(-8.90388 + 1.31182i) q^{81} +(7.56155 - 5.00691i) q^{82} -6.00000i q^{83} +(12.1160 - 5.42396i) q^{84} -1.11252i q^{85} +(2.87529 + 4.34233i) q^{86} +(9.03712 - 9.72350i) q^{87} +(5.56155 - 1.03399i) q^{88} -11.7100 q^{89} +(1.71800 + 2.22273i) q^{90} +(-9.81602 + 9.72350i) q^{91} +(5.07482 - 11.9679i) q^{92} +(2.73013 + 2.53741i) q^{93} +(5.21922 + 7.88220i) q^{94} +1.42489 q^{95} +(5.57056 + 8.06033i) q^{96} -7.92460i q^{97} +(-9.06134 + 6.00000i) q^{98} +(5.98396 - 0.438447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 20 q^{9}+O(q^{10}) $ 16 * q - 4 * q^4 + 20 * q^9	$ 16 q - 4 q^{4} + 20 q^{9} - 4 q^{10} + 10 q^{12} - 8 q^{13} - 28 q^{16} - 8 q^{22} - 40 q^{25} + 18 q^{30} - 22 q^{36} + 44 q^{40} - 34 q^{42} + 46 q^{48} + 24 q^{49} - 32 q^{52} - 16 q^{61} - 4 q^{64} - 28 q^{66} + 34 q^{78} - 60 q^{81} + 88 q^{82} + 56 q^{88} - 22 q^{90} + 100 q^{94}+O(q^{100}) $ 16 * q - 4 * q^4 + 20 * q^9 - 4 * q^10 + 10 * q^12 - 8 * q^13 - 28 * q^16 - 8 * q^22 - 40 * q^25 + 18 * q^30 - 22 * q^36 + 44 * q^40 - 34 * q^42 + 46 * q^48 + 24 * q^49 - 32 * q^52 - 16 * q^61 - 4 * q^64 - 28 * q^66 + 34 * q^78 - 60 * q^81 + 88 * q^82 + 56 * q^88 - 22 * q^90 + 100 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.17915	+	0.780776i	−0.833783	+	0.552092i
$2$	−1.17915	+	0.780776i	−0.833783	+	0.552092i
$3$	1.26870	+	1.17915i	0.732487	+	0.680781i
$3$	1.26870	+	1.17915i	0.732487	+	0.680781i
$4$	0.780776	−	1.84130i	0.390388	−	0.920650i
$5$	−0.662153			−0.296124			−0.148062	−	0.988978i	$-0.547304\pi$
$5$	−0.662153			−0.296124			−0.148062	+	0.988978i	$0.547304\pi$
$6$	−2.41664	−	0.399813i	−0.986589	−	0.163223i
$7$	3.83206			1.44838			0.724191	−	0.689600i	$-0.242214\pi$
$7$	3.83206			1.44838			0.724191	+	0.689600i	$0.242214\pi$
$8$	0.516994	+	2.78078i	0.182785	+	0.983153i
$9$	0.219224	+	2.99198i	0.0730745	+	0.997326i
$10$	0.780776	−	0.516994i	0.246903	−	0.163488i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$	3.16174	−	1.41542i	0.912716	−	0.408596i
$13$	−2.56155	+	2.53741i	−0.710447	+	0.703751i
$13$	−2.56155	+	2.53741i	−0.710447	+	0.703751i
$14$	−4.51856	+	2.99198i	−1.20764	+	0.799640i
$15$	−0.840077	−	0.780776i	−0.216907	−	0.201596i
$16$	−2.78078	−	2.87529i	−0.695194	−	0.718822i
$17$			1.68015i			0.407497i	0.979023	+	0.203749i	$0.0653125\pi$
$17$			1.68015i			0.407497i	−0.979023	+	0.203749i	$0.934687\pi$
$18$	−2.59456	−	3.35682i	−0.611545	−	0.791210i
$19$	−2.15190			−0.493680			−0.246840	−	0.969056i	$-0.579392\pi$
$19$	−2.15190			−0.493680			−0.246840	+	0.969056i	$0.579392\pi$
$20$	−0.516994	+	1.21922i	−0.115603	+	0.272627i
$21$	4.86175	+	4.51856i	1.06092	+	0.986030i
$22$	1.56155	+	2.35829i	0.332924	+	0.502790i
$23$	6.49971			1.35528			0.677641	−	0.735392i	$-0.263002\pi$
$23$	6.49971			1.35528			0.677641	+	0.735392i	$0.263002\pi$
$24$	−2.62303	+	4.13760i	−0.535424	+	0.844583i
$25$	−4.56155			−0.912311
$26$	1.03930	−	4.99198i	0.203823	−	0.979008i
$27$	−3.24985	+	4.05444i	−0.625435	+	0.780276i
$28$	2.99198	−	7.05597i	0.565431	−	1.33345i
$29$		−	7.66411i		−	1.42319i	−0.702590	−	0.711595i	$-0.747973\pi$
$29$		−	7.66411i		−	1.42319i	0.702590	−	0.711595i	$-0.252027\pi$
$30$	1.60019	+	0.264738i	0.292153	+	0.0483343i
$31$	2.15190			0.386493			0.193247	−	0.981150i	$-0.438098\pi$
$31$	2.15190			0.386493			0.193247	+	0.981150i	$0.438098\pi$
$32$	5.52390	+	1.21922i	0.976497	+	0.215530i
$33$	2.35829	−	2.53741i	0.410526	−	0.441706i
$34$	−1.31182	−	1.98115i	−0.224976	−	0.339764i
$35$	−2.53741			−0.428900
$36$	5.68030	+	1.93241i	0.946716	+	0.322068i
$37$		−	9.03712i		−	1.48569i	−0.669462	−	0.742847i	$-0.733475\pi$
$37$		−	9.03712i		−	1.48569i	0.669462	−	0.742847i	$-0.266525\pi$
$38$	2.53741	−	1.68015i	0.411622	−	0.272557i
$39$	−6.24183	+	0.198776i	−0.999493	+	0.0318296i
$40$	−0.342329	−	1.84130i	−0.0541270	−	0.291135i
$41$	−6.41273			−1.00150			−0.500750	−	0.865592i	$-0.666942\pi$
$41$	−6.41273			−1.00150			−0.500750	+	0.865592i	$0.666942\pi$
$42$	−9.26070	−	1.53211i	−1.42896	−	0.236409i
$43$		−	3.68260i		−	0.561591i	−0.959768	−	0.280796i	$-0.909402\pi$
$43$		−	3.68260i		−	0.561591i	0.959768	−	0.280796i	$-0.0905983\pi$
$44$	−3.68260	−	1.56155i	−0.555173	−	0.235413i
$45$	−0.145160	−	1.98115i	−0.0216391	−	0.295332i
$46$	−7.66411	+	5.07482i	−1.13001	+	0.748241i
$47$		−	6.68466i		−	0.975058i	−0.873107	−	0.487529i	$-0.837898\pi$
$47$		−	6.68466i		−	0.975058i	0.873107	−	0.487529i	$-0.162102\pi$
$48$	−0.137596	−	6.92684i	−0.0198603	−	0.999803i
$49$	7.68466			1.09781
$50$	5.37874	−	3.56155i	0.760669	−	0.503680i
$51$	−1.98115	+	2.13162i	−0.277416	+	0.298487i
$52$	2.67213	+	6.69774i	0.370558	+	0.928809i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	0.666449	−	7.31819i	0.0906922	−	0.995879i
$55$			1.32431i			0.178570i
$56$	1.98115	+	10.6561i	0.264742	+	1.42398i
$57$	−2.73013	−	2.53741i	−0.361614	−	0.336088i
$58$	5.98396	+	9.03712i	0.785732	+	1.18663i
$59$		−	2.87689i		−	0.374540i	−0.982309	−	0.187270i	$-0.940036\pi$
$59$		−	2.87689i		−	0.374540i	0.982309	−	0.187270i	$-0.0599639\pi$
$60$	−2.09356	+	0.937223i	−0.270277	+	0.120995i
$61$	3.12311			0.399873			0.199936	−	0.979809i	$-0.435926\pi$
$61$	3.12311			0.399873			0.199936	+	0.979809i	$0.435926\pi$
$62$	−2.53741	+	1.68015i	−0.322251	+	0.213380i
$63$	0.840077	+	11.4654i	0.105840	+	1.44451i
$64$	−7.46543	+	2.87529i	−0.933179	+	0.359411i
$65$	1.69614	−	1.68015i	0.210380	−	0.208398i
$66$	−0.799627	+	4.83328i	−0.0984273	+	0.594936i
$67$	−5.51221			−0.673424			−0.336712	−	0.941608i	$-0.609315\pi$
$67$	−5.51221			−0.673424			−0.336712	+	0.941608i	$0.609315\pi$
$68$	3.09367	+	1.31182i	0.375163	+	0.159082i
$69$	8.24621	+	7.66411i	0.992727	+	0.922651i
$70$	2.99198	−	1.98115i	0.357610	−	0.236793i
$71$			14.6847i			1.74275i	0.490619	+	0.871374i	$0.336771\pi$
$71$			14.6847i			1.74275i	−0.490619	+	0.871374i	$0.663229\pi$
$72$	−8.20669	+	2.15645i	−0.967168	+	0.254140i
$73$			12.9994i			1.52147i	0.649065	+	0.760733i	$0.275161\pi$
$73$			12.9994i			1.52147i	−0.649065	+	0.760733i	$0.724839\pi$
$74$	7.05597	+	10.6561i	0.820240	+	1.23875i
$75$	−5.78726	−	5.37874i	−0.668256	−	0.621084i
$76$	−1.68015	+	3.96230i	−0.192727	+	0.454507i
$77$		−	7.66411i		−	0.873407i
$78$	7.20484	−	5.10786i	0.815788	−	0.578352i
$79$		−	8.10887i		−	0.912319i	−0.889898	−	0.456160i	$-0.849225\pi$
$79$		−	8.10887i		−	0.912319i	0.889898	−	0.456160i	$-0.150775\pi$
$80$	1.84130	+	1.90388i	0.205864	+	0.212860i
$81$	−8.90388	+	1.31182i	−0.989320	+	0.145758i
$82$	7.56155	−	5.00691i	0.835034	−	0.552921i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	12.1160	−	5.42396i	1.32196	−	0.591802i
$85$		−	1.11252i		−	0.120670i
$86$	2.87529	+	4.34233i	0.310050	+	0.468245i
$87$	9.03712	−	9.72350i	0.968881	−	1.04247i
$88$	5.56155	−	1.03399i	0.592864	−	0.110223i
$89$	−11.7100			−1.24125			−0.620627	−	0.784106i	$-0.713122\pi$
$89$	−11.7100			−1.24125			−0.620627	+	0.784106i	$0.713122\pi$
$90$	1.71800	+	2.22273i	0.181093	+	0.234296i
$91$	−9.81602	+	9.72350i	−1.02900	+	1.01930i
$92$	5.07482	−	11.9679i	0.529086	−	1.24774i
$93$	2.73013	+	2.53741i	0.283101	+	0.263117i
$94$	5.21922	+	7.88220i	0.538322	+	0.812986i
$95$	1.42489			0.146191
$96$	5.57056	+	8.06033i	0.568543	+	0.822654i
$97$		−	7.92460i		−	0.804621i	−0.915503	−	0.402311i	$-0.868207\pi$
$97$		−	7.92460i		−	0.804621i	0.915503	−	0.402311i	$-0.131793\pi$
$98$	−9.06134	+	6.00000i	−0.915334	+	0.606092i
$99$	5.98396	−	0.438447i	0.601410	−	0.0440656i
$100$	−3.56155	+	8.39919i	−0.356155	+	0.839919i
$101$			15.3282i			1.52522i	0.646861	+	0.762608i	$0.276081\pi$
$101$			15.3282i			1.52522i	−0.646861	+	0.762608i	$0.723919\pi$
$102$	0.671748	−	4.06033i	0.0665130	−	0.402032i
$103$		−	0.580639i		−	0.0572120i	−0.999591	−	0.0286060i	$-0.990893\pi$
$103$		−	0.580639i		−	0.0572120i	0.999591	−	0.0286060i	$-0.00910682\pi$
$104$	−8.38028	−	5.81128i	−0.821754	−	0.569843i
$105$	−3.21922	−	2.99198i	−0.314164	−	0.291987i
$106$		0			0
$107$	−12.9994			−1.25670			−0.628351	−	0.777930i	$-0.716270\pi$
$107$	−12.9994			−1.25670			−0.628351	+	0.777930i	$0.716270\pi$
$108$	4.92803	+	9.14957i	0.474199	+	0.880417i
$109$			3.96230i			0.379519i	0.981831	+	0.189760i	$0.0607709\pi$
$109$			3.96230i			0.379519i	−0.981831	+	0.189760i	$0.939229\pi$
$110$	−1.03399	−	1.56155i	−0.0985868	−	0.148888i
$111$	10.6561	−	11.4654i	1.01143	−	1.08825i
$112$	−10.6561	−	11.0183i	−1.00691	−	1.04113i
$113$		−	4.30380i		−	0.404868i	−0.979296	−	0.202434i	$-0.935115\pi$
$113$		−	4.30380i		−	0.404868i	0.979296	−	0.202434i	$-0.0648851\pi$
$114$	5.20037	+	0.860359i	0.487060	+	0.0805800i
$115$	−4.30380			−0.401332
$116$	−14.1119	−	5.98396i	−1.31026	−	0.555597i
$117$	−8.15343	−	7.10785i	−0.753785	−	0.657121i
$118$	2.24621	+	3.39228i	0.206781	+	0.312285i
$119$			6.43845i			0.590211i
$120$	1.73685	−	2.73972i	0.158552	−	0.250101i
$121$	7.00000			0.636364
$122$	−3.68260	+	2.43845i	−0.333407	+	0.220767i
$123$	−8.13586	−	7.56155i	−0.733586	−	0.681802i
$124$	1.68015	−	3.96230i	0.150882	−	0.355825i
$125$	6.33122			0.566281
$126$	−9.94252	−	12.8635i	−0.885750	−	1.14597i
$127$			3.39228i			0.301016i	0.988609	+	0.150508i	$0.0480910\pi$
$127$			3.39228i			0.301016i	−0.988609	+	0.150508i	$0.951909\pi$
$128$	6.55789	−	9.21922i	0.579641	−	0.814872i
$129$	4.34233	−	4.67213i	0.382321	−	0.411358i
$130$	−0.688175	+	3.30546i	−0.0603569	+	0.289908i
$131$	9.03712			0.789577			0.394788	−	0.918772i	$-0.370818\pi$
$131$	9.03712			0.789577			0.394788	+	0.918772i	$0.370818\pi$
$132$	−2.83083	−	6.32348i	−0.246392	−	0.550388i
$133$	−8.24621			−0.715037
$134$	6.49971	−	4.30380i	0.561489	−	0.371792i
$135$	2.15190	−	2.68466i	0.185206	−	0.231059i
$136$	−4.67213	+	0.868629i	−0.400632	+	0.0744844i
$137$	16.4265			1.40341			0.701707	−	0.712465i	$-0.252421\pi$
$137$	16.4265			1.40341			0.701707	+	0.712465i	$0.252421\pi$
$138$	−15.7075	−	2.59867i	−1.33711	−	0.221214i
$139$			15.7644i			1.33712i	0.743659	+	0.668559i	$0.233089\pi$
$139$			15.7644i			1.33712i	−0.743659	+	0.668559i	$0.766911\pi$
$140$	−1.98115	+	4.67213i	−0.167438	+	0.394867i
$141$	7.88220	−	8.48086i	0.663801	−	0.714217i
$142$	−11.4654	−	17.3154i	−0.962158	−	1.45307i
$143$	5.07482	+	5.12311i	0.424378	+	0.428416i
$144$	7.99319	−	8.95036i	0.666099	−	0.745863i
$145$			5.07482i			0.421441i
$146$	−10.1496	−	15.3282i	−0.839990	−	1.26857i
$147$	9.74956	+	9.06134i	0.804130	+	0.747367i
$148$	−16.6401	−	7.05597i	−1.36780	−	0.579997i
$149$	−13.7779			−1.12873			−0.564366	−	0.825525i	$-0.690879\pi$
$149$	−13.7779			−1.12873			−0.564366	+	0.825525i	$0.690879\pi$
$150$	11.0236	+	1.82377i	0.900076	+	0.148910i
$151$	20.1038			1.63602			0.818011	−	0.575202i	$-0.195077\pi$
$151$	20.1038			1.63602			0.818011	+	0.575202i	$0.195077\pi$
$152$	−1.11252	−	5.98396i	−0.0902373	−	0.485363i
$153$	−5.02699	+	0.368330i	−0.406408	+	0.0297777i
$154$	5.98396	+	9.03712i	0.482201	+	0.728232i
$155$	−1.42489			−0.114450
$156$	−4.50747	+	11.6483i	−0.360886	+	0.932610i
$157$	−10.2462			−0.817737			−0.408868	−	0.912593i	$-0.634076\pi$
$157$	−10.2462			−0.817737			−0.408868	+	0.912593i	$0.634076\pi$
$158$	6.33122	+	9.56155i	0.503684	+	0.760676i
$159$		0			0
$160$	−3.65767	−	0.807313i	−0.289164	−	0.0638237i
$161$	24.9073			1.96297
$162$	9.47475	−	8.49878i	0.744406	−	0.667727i
$163$	14.1198			1.10595			0.552975	−	0.833198i	$-0.313493\pi$
$163$	14.1198			1.10595			0.552975	+	0.833198i	$0.313493\pi$
$164$	−5.00691	+	11.8078i	−0.390974	+	0.922031i
$165$	−1.56155	+	1.68015i	−0.121567	+	0.130800i
$166$	4.68466	+	7.07488i	0.363600	+	0.549117i
$167$		−	7.36932i		−	0.570255i	−0.958490	−	0.285127i	$-0.907964\pi$
$167$		−	7.36932i		−	0.570255i	0.958490	−	0.285127i	$-0.0920359\pi$
$168$	−10.0516	+	15.8555i	−0.775498	+	1.22328i
$169$	0.123106	−	12.9994i	0.00946966	−	0.999955i
$170$	0.868629	+	1.31182i	0.0666208	+	0.100612i
$171$	−0.471748	−	6.43845i	−0.0360755	−	0.492360i
$172$	−6.78078	−	2.87529i	−0.517029	−	0.219239i
$173$			11.9679i			0.909904i	0.890516	+	0.454952i	$0.150344\pi$
$173$			11.9679i			0.909904i	−0.890516	+	0.454952i	$0.849656\pi$
$174$	−3.06422	+	18.5214i	−0.232298	+	1.40410i
$175$	−17.4801			−1.32137
$176$	−5.75058	+	5.56155i	−0.433466	+	0.419218i
$177$	3.39228	−	3.64993i	0.254980	−	0.274346i
$178$	13.8078	−	9.14286i	1.03494	−	0.685286i
$179$	−9.03712			−0.675466			−0.337733	−	0.941242i	$-0.609660\pi$
$179$	−9.03712			−0.675466			−0.337733	+	0.941242i	$0.609660\pi$
$180$	−3.76123	−	1.27955i	−0.280345	−	0.0953722i
$181$	−5.36932			−0.399098			−0.199549	−	0.979888i	$-0.563948\pi$
$181$	−5.36932			−0.399098			−0.199549	+	0.979888i	$0.563948\pi$
$182$	3.98265	−	19.1295i	0.295214	−	1.41798i
$183$	3.96230	+	3.68260i	0.292902	+	0.272226i
$184$	3.36031	+	18.0742i	0.247725	+	1.33245i
$185$			5.98396i			0.439949i
$186$	−5.20037	−	0.860359i	−0.381310	−	0.0630846i
$187$	3.36031			0.245730
$188$	−12.3085	−	5.21922i	−0.897687	−	0.380651i
$189$	−12.4536	+	15.5368i	−0.905868	+	1.13014i
$190$	−1.68015	+	1.11252i	−0.121891	+	0.0807107i
$191$	−1.42489			−0.103101			−0.0515507	−	0.998670i	$-0.516416\pi$
$191$	−1.42489			−0.103101			−0.0515507	+	0.998670i	$0.516416\pi$
$192$	−12.8618	−	5.15495i	−0.928222	−	0.372027i
$193$			15.2245i			1.09588i	0.836518	+	0.547940i	$0.184588\pi$
$193$			15.2245i			1.09588i	−0.836518	+	0.547940i	$0.815412\pi$
$194$	6.18734	+	9.34427i	0.444225	+	0.670879i
$195$	4.13305	−	0.131620i	0.295974	−	0.00942550i
$196$	6.00000	−	14.1498i	0.428571	−	1.01070i
$197$	8.02736			0.571925			0.285963	−	0.958241i	$-0.407687\pi$
$197$	8.02736			0.571925			0.285963	+	0.958241i	$0.407687\pi$
$198$	−6.71364	+	5.18913i	−0.477118	+	0.368775i
$199$		−	18.1227i		−	1.28468i	−0.766418	−	0.642342i	$-0.777963\pi$
$199$		−	18.1227i		−	1.28468i	0.766418	−	0.642342i	$-0.222037\pi$
$200$	−2.35829	−	12.6847i	−0.166757	−	0.896941i
$201$	−6.99337	−	6.49971i	−0.493274	−	0.458454i
$202$	−11.9679	−	18.0742i	−0.842060	−	1.27170i
$203$		−	29.3693i		−	2.06132i
$204$	2.37812	+	5.31221i	0.166502	+	0.371929i
$205$	4.24621			0.296568
$206$	0.453349	+	0.684658i	0.0315863	+	0.0477024i
$207$	1.42489	+	19.4470i	0.0990367	+	1.35166i
$208$	14.4189	+	0.309234i	0.999770	+	0.0214415i
$209$			4.30380i			0.297700i
$210$	6.13201	+	1.01449i	0.423149	+	0.0700065i
$211$			2.35829i			0.162352i	0.996700	+	0.0811758i	$0.0258675\pi$
$211$			2.35829i			0.162352i	−0.996700	+	0.0811758i	$0.974132\pi$
$212$		0			0
$213$	−17.3154	+	18.6305i	−1.18643	+	1.27654i
$214$	15.3282	−	10.1496i	1.04782	−	0.693815i
$215$			2.43845i			0.166301i
$216$	−12.9546	−	6.94100i	−0.881451	−	0.472275i
$217$	8.24621			0.559789
$218$	−3.09367	−	4.67213i	−0.209530	−	0.316437i
$219$	−15.3282	+	16.4924i	−1.03579	+	1.11445i
$220$	2.43845	+	1.03399i	0.164400	+	0.0697114i
$221$	−4.26324	−	4.30380i	−0.286777	−	0.289505i
$222$	−3.61316	+	21.8395i	−0.242500	+	1.46577i
$223$	10.5527			0.706659			0.353330	−	0.935499i	$-0.385049\pi$
$223$	10.5527			0.706659			0.353330	+	0.935499i	$0.385049\pi$
$224$	21.1679	+	4.67213i	1.41434	+	0.312170i
$225$	−1.00000	−	13.6481i	−0.0666667	−	0.909871i
$226$	3.36031	+	5.07482i	0.223524	+	0.337572i
$227$			24.2462i			1.60928i	0.593765	+	0.804639i	$0.297641\pi$
$227$			24.2462i			1.60928i	−0.593765	+	0.804639i	$0.702359\pi$
$228$	−6.80375	+	3.04584i	−0.450590	+	0.201716i
$229$		−	11.2622i		−	0.744224i	−0.928188	−	0.372112i	$-0.878634\pi$
$229$		−	11.2622i		−	0.744224i	0.928188	−	0.372112i	$-0.121366\pi$
$230$	5.07482	−	3.36031i	0.334624	−	0.221572i
$231$	9.03712	−	9.72350i	0.594599	−	0.639759i
$232$	21.3122	−	3.96230i	1.39921	−	0.260138i
$233$			17.9519i			1.17607i	0.808837	+	0.588033i	$0.200098\pi$
$233$			17.9519i			1.17607i	−0.808837	+	0.588033i	$0.799902\pi$
$234$	15.1637	+	2.01520i	0.991285	+	0.131738i
$235$			4.42627i			0.288738i
$236$	−5.29723	−	2.24621i	−0.344820	−	0.146216i
$237$	9.56155	−	10.2878i	0.621090	−	0.668262i
$238$	−5.02699	−	7.59188i	−0.325851	−	0.492108i
$239$			8.93087i			0.577690i	0.957376	+	0.288845i	$0.0932712\pi$
$239$			8.93087i			0.577690i	−0.957376	+	0.288845i	$0.906729\pi$
$240$	0.0911097	+	4.58663i	0.00588111	+	0.296066i
$241$			18.0742i			1.16426i	0.813094	+	0.582132i	$0.197781\pi$
$241$			18.0742i			1.16426i	−0.813094	+	0.582132i	$0.802219\pi$
$242$	−8.25403	+	5.46543i	−0.530589	+	0.351331i
$243$	−12.8432	−	8.83467i	−0.823894	−	0.566744i
$244$	2.43845	−	5.75058i	0.156106	−	0.368143i
$245$	−5.08842			−0.325087
$246$	15.4973	+	2.56390i	0.988069	+	0.163468i
$247$	5.51221	−	5.46026i	0.350734	−	0.347428i
$248$	1.11252	+	5.98396i	0.0706451	+	0.379982i
$249$	7.07488	−	7.61223i	0.448353	−	0.482405i
$250$	−7.46543	+	4.94326i	−0.472156	+	0.312639i
$251$	3.64993			0.230382			0.115191	−	0.993343i	$-0.463252\pi$
$251$	3.64993			0.230382			0.115191	+	0.993343i	$0.463252\pi$
$252$	21.7672	+	7.40511i	1.37121	+	0.466478i
$253$		−	12.9994i		−	0.817266i
$254$	−2.64861	−	4.00000i	−0.166189	−	0.250982i
$255$	1.31182	−	1.41146i	0.0821497	−	0.0883890i
$256$	−0.534565	+	15.9911i	−0.0334103	+	0.999442i
$257$		−	21.3122i		−	1.32942i	−0.747103	−	0.664709i	$-0.768556\pi$
$257$		−	21.3122i		−	1.32942i	0.747103	−	0.664709i	$-0.231444\pi$
$258$	−1.47235	+	8.89952i	−0.0916647	+	0.554060i
$259$		−	34.6307i		−	2.15185i
$260$	−1.76936	−	4.43493i	−0.109731	−	0.275043i
$261$	22.9309	−	1.68015i	1.41939	−	0.103999i
$262$	−10.6561	+	7.05597i	−0.658336	+	0.435919i
$263$	18.0742			1.11451			0.557253	−	0.830343i	$-0.311856\pi$
$263$	18.0742			1.11451			0.557253	+	0.830343i	$0.311856\pi$
$264$	8.27519	+	5.24606i	0.509303	+	0.322873i
$265$		0			0
$266$	9.72350	−	6.43845i	0.596186	−	0.394767i
$267$	−14.8565	−	13.8078i	−0.909202	−	0.845021i
$268$	−4.30380	+	10.1496i	−0.262897	+	0.619988i
$269$			16.2717i			0.992104i	0.868293	+	0.496052i	$0.165218\pi$
$269$			16.2717i			0.992104i	−0.868293	+	0.496052i	$0.834782\pi$
$270$	−0.441292	+	4.84576i	−0.0268561	+	0.294904i
$271$	−19.1603			−1.16390			−0.581952	−	0.813223i	$-0.697711\pi$
$271$	−19.1603			−1.16390			−0.581952	+	0.813223i	$0.697711\pi$
$272$	4.83093	−	4.67213i	0.292918	−	0.283290i
$273$	−23.9191	+	0.761720i	−1.44765	+	0.0461014i
$274$	−19.3693	+	12.8255i	−1.17014	+	0.774814i
$275$			9.12311i			0.550144i
$276$	20.5504	−	9.19980i	1.23699	−	0.553763i
$277$	−20.2462			−1.21648			−0.608238	−	0.793754i	$-0.708124\pi$
$277$	−20.2462			−1.21648			−0.608238	+	0.793754i	$0.708124\pi$
$278$	−12.3085	−	18.5885i	−0.738213	−	1.11487i
$279$	0.471748	+	6.43845i	0.0282428	+	0.385460i
$280$	−1.31182	−	7.05597i	−0.0783965	−	0.421675i
$281$	−19.2382			−1.14765			−0.573827	−	0.818976i	$-0.694542\pi$
$281$	−19.2382			−1.14765			−0.573827	+	0.818976i	$0.694542\pi$
$282$	−2.67262	+	16.1544i	−0.159152	+	0.961981i
$283$			16.0547i			0.954354i	0.878807	+	0.477177i	$0.158340\pi$
$283$			16.0547i			0.954354i	−0.878807	+	0.477177i	$0.841660\pi$
$284$	27.0389	+	11.4654i	1.60446	+	0.680348i
$285$	1.80776	+	1.68015i	0.107083	+	0.0995238i
$286$	−9.98396	−	2.07860i	−0.590364	−	0.122910i
$287$	−24.5739			−1.45055
$288$	−2.43692	+	16.7947i	−0.143597	+	0.989636i
$289$	14.1771			0.833946
$290$	−3.96230	−	5.98396i	−0.232674	−	0.351390i
$291$	9.34427	−	10.0540i	0.547771	−	0.589374i
$292$	23.9358	+	10.1496i	1.40074	+	0.593963i
$293$	10.0953			0.589776			0.294888	−	0.955532i	$-0.404718\pi$
$293$	10.0953			0.589776			0.294888	+	0.955532i	$0.404718\pi$
$294$	−18.5711	−	3.07243i	−1.08309	−	0.179188i
$295$			1.90495i			0.110910i
$296$	25.1302	−	4.67213i	1.46066	−	0.271562i
$297$	8.10887	+	6.49971i	0.470524	+	0.377151i
$298$	16.2462	−	10.7575i	0.941118	−	0.623164i
$299$	−16.6493	+	16.4924i	−0.962857	+	0.953781i
$300$	−14.4224	+	6.45650i	−0.832680	+	0.372766i
$301$		−	14.1119i		−	0.813399i
$302$	−23.7053	+	15.6966i	−1.36409	+	0.903235i
$303$	−18.0742	+	19.4470i	−1.03834	+	1.11720i
$304$	5.98396	+	6.18734i	0.343204	+	0.354868i
$305$	−2.06798			−0.118412
$306$	5.63998	−	4.35927i	0.322416	−	0.249203i
$307$	9.81602			0.560230			0.280115	−	0.959967i	$-0.409627\pi$
$307$	9.81602			0.560230			0.280115	+	0.959967i	$0.409627\pi$
$308$	−14.1119	−	5.98396i	−0.804102	−	0.340968i
$309$	0.684658	−	0.736659i	0.0389489	−	0.0419071i
$310$	1.68015	−	1.11252i	0.0954264	−	0.0631869i
$311$	−8.72475			−0.494735			−0.247368	−	0.968922i	$-0.579566\pi$
$311$	−8.72475			−0.494735			−0.247368	+	0.968922i	$0.579566\pi$
$312$	−3.77974	−	17.2544i	−0.213986	−	0.976837i
$313$	11.5616			0.653498			0.326749	−	0.945111i	$-0.394047\pi$
$313$	11.5616			0.653498			0.326749	+	0.945111i	$0.394047\pi$
$314$	12.0818	−	8.00000i	0.681815	−	0.451466i
$315$	−0.556260	−	7.59188i	−0.0313417	−	0.427754i
$316$	−14.9309	−	6.33122i	−0.839927	−	0.356159i
$317$	13.7779			0.773846			0.386923	−	0.922112i	$-0.373538\pi$
$317$	13.7779			0.773846			0.386923	+	0.922112i	$0.373538\pi$
$318$		0			0
$319$	−15.3282			−0.858216
$320$	4.94326	−	1.90388i	0.276337	−	0.106430i
$321$	−16.4924	−	15.3282i	−0.920517	−	0.855538i
$322$	−29.3693	+	19.4470i	−1.63669	+	1.08374i
$323$		−	3.61553i		−	0.201173i
$324$	−4.53648	+	17.4190i	−0.252026	+	0.967720i
$325$	11.6847	−	11.5745i	0.648148	−	0.642039i
$326$	−16.6493	+	11.0244i	−0.922122	+	0.610586i
$327$	−4.67213	+	5.02699i	−0.258370	+	0.277993i
$328$	−3.31534	−	17.8324i	−0.183059	−	0.984628i
$329$		−	25.6160i		−	1.41226i
$330$	0.529476	−	3.20037i	0.0291467	−	0.176175i
$331$	−2.15190			−0.118279			−0.0591396	−	0.998250i	$-0.518836\pi$
$331$	−2.15190			−0.118279			−0.0591396	+	0.998250i	$0.518836\pi$
$332$	−11.0478	−	4.68466i	−0.606327	−	0.257104i
$333$	27.0389	−	1.98115i	1.48172	−	0.108566i
$334$	5.75379	+	8.68951i	0.314833	+	0.475469i
$335$	3.64993			0.199417
$336$	−0.527276	−	26.5440i	−0.0287653	−	1.44810i
$337$	2.68466			0.146243			0.0731213	−	0.997323i	$-0.476704\pi$
$337$	2.68466			0.146243			0.0731213	+	0.997323i	$0.476704\pi$
$338$	10.0045	+	15.4243i	0.544172	+	0.838974i
$339$	5.07482	−	5.46026i	0.275626	−	0.296560i
$340$	−2.04848	−	0.868629i	−0.111095	−	0.0471080i
$341$		−	4.30380i		−	0.233064i
$342$	5.58325	+	7.22355i	0.301907	+	0.390605i
$343$	2.62365			0.141664
$344$	10.2405	−	1.90388i	0.552130	−	0.102650i
$345$	−5.46026	−	5.07482i	−0.293970	−	0.273219i
$346$	−9.34427	−	14.1119i	−0.502351	−	0.758662i
$347$	5.38719			0.289199			0.144600	−	0.989490i	$-0.453811\pi$
$347$	5.38719			0.289199			0.144600	+	0.989490i	$0.453811\pi$
$348$	−10.8479	−	24.2319i	−0.581509	−	1.29897i
$349$		−	9.03712i		−	0.483746i	−0.970308	−	0.241873i	$-0.922238\pi$
$349$		−	9.03712i		−	0.483746i	0.970308	−	0.241873i	$-0.0777617\pi$
$350$	20.6116	−	13.6481i	1.10174	−	0.729520i
$351$	−1.96309	−	18.6319i	−0.104782	−	0.994495i
$352$	2.43845	−	11.0478i	0.129970	−	0.588850i
$353$	−10.9663			−0.583677			−0.291838	−	0.956468i	$-0.594267\pi$
$353$	−10.9663			−0.583677			−0.291838	+	0.956468i	$0.594267\pi$
$354$	−1.15022	+	6.95242i	−0.0611336	+	0.369517i
$355$		−	9.72350i		−	0.516070i
$356$	−9.14286	+	21.5616i	−0.484571	+	1.14276i
$357$	−7.59188	+	8.16849i	−0.401805	+	0.432322i
$358$	10.6561	−	7.05597i	0.563192	−	0.372920i
$359$			2.87689i			0.151837i	0.997114	+	0.0759183i	$0.0241888\pi$
$359$			2.87689i			0.151837i	−0.997114	+	0.0759183i	$0.975811\pi$
$360$	5.43409	−	1.42790i	0.286402	−	0.0752569i
$361$	−14.3693			−0.756280
$362$	6.33122	−	4.19224i	0.332761	−	0.220339i
$363$	8.88093	+	8.25403i	0.466128	+	0.433224i
$364$	10.2398	+	25.6661i	0.536710	+	1.34527i
$365$		−	8.60761i		−	0.450543i
$366$	−7.54742	−	1.24866i	−0.394510	−	0.0652685i
$367$			4.13595i			0.215895i	0.994157	+	0.107947i	$0.0344278\pi$
$367$			4.13595i			0.215895i	−0.994157	+	0.107947i	$0.965572\pi$
$368$	−18.0742	−	18.6885i	−0.942185	−	0.974207i
$369$	−1.40582	−	19.1868i	−0.0731842	−	0.998823i
$370$	−4.67213	−	7.05597i	−0.242893	−	0.366822i
$371$		0			0
$372$	6.80375	−	3.04584i	0.352758	−	0.157919i
$373$	−9.12311			−0.472377			−0.236188	−	0.971707i	$-0.575898\pi$
$373$	−9.12311			−0.472377			−0.236188	+	0.971707i	$0.575898\pi$
$374$	−3.96230	+	2.62365i	−0.204886	+	0.135666i
$375$	8.03244	+	7.46543i	0.414794	+	0.385513i
$376$	18.5885	−	3.45593i	0.958631	−	0.178226i
$377$	19.4470	+	19.6320i	1.00157	+	1.01110i
$378$	2.55387	−	28.0437i	0.131357	−	1.44241i
$379$	−5.51221			−0.283143			−0.141572	−	0.989928i	$-0.545216\pi$
$379$	−5.51221			−0.283143			−0.141572	+	0.989928i	$0.545216\pi$
$380$	1.11252	−	2.62365i	0.0570711	−	0.134590i
$381$	−4.00000	+	4.30380i	−0.204926	+	0.220491i
$382$	1.68015	−	1.11252i	0.0859642	−	0.0569215i
$383$		−	23.5616i		−	1.20394i	−0.798519	−	0.601970i	$-0.794383\pi$
$383$		−	23.5616i		−	1.20394i	0.798519	−	0.601970i	$-0.205617\pi$
$384$	19.1908	−	3.96376i	0.979329	−	0.202275i
$385$			5.07482i			0.258637i
$386$	−11.8869	−	17.9519i	−0.605027	−	0.913726i
$387$	11.0183	−	0.807313i	0.560090	−	0.0410380i
$388$	−14.5916	−	6.18734i	−0.740775	−	0.314115i
$389$		−	12.9114i		−	0.654635i	−0.944914	−	0.327317i	$-0.893855\pi$
$389$		−	12.9114i		−	0.654635i	0.944914	−	0.327317i	$-0.106145\pi$
$390$	−4.77071	+	3.38219i	−0.241574	+	0.171264i
$391$			10.9205i			0.552274i
$392$	3.97292	+	21.3693i	0.200663	+	1.07931i
$393$	11.4654	+	10.6561i	0.578355	+	0.537529i
$394$	−9.46543	+	6.26757i	−0.476862	+	0.315756i
$395$			5.36932i			0.270160i
$396$	3.86482	−	11.3606i	0.194215	−	0.570891i
$397$			18.0742i			0.907120i	0.891226	+	0.453560i	$0.149846\pi$
$397$			18.0742i			0.907120i	−0.891226	+	0.453560i	$0.850154\pi$
$398$	14.1498	+	21.3693i	0.709264	+	1.07115i
$399$	−10.4620	−	9.72350i	−0.523755	−	0.486784i
$400$	12.6847	+	13.1158i	0.634233	+	0.655789i
$401$	−36.0366			−1.79958			−0.899790	−	0.436323i	$-0.856281\pi$
$401$	−36.0366			−1.79958			−0.899790	+	0.436323i	$0.856281\pi$
$402$	13.3210	+	2.20386i	0.664393	+	0.109918i
$403$	−5.51221	+	5.46026i	−0.274583	+	0.271995i
$404$	28.2239	+	11.9679i	1.40419	+	0.595426i
$405$	5.89574	−	0.868629i	0.292961	−	0.0431625i
$406$	22.9309	+	34.6307i	1.13804	+	1.71870i
$407$	−18.0742			−0.895907
$408$	−6.95180	−	4.40710i	−0.344165	−	0.218184i
$409$			23.1491i			1.14465i	0.820028	+	0.572324i	$0.193958\pi$
$409$			23.1491i			1.14465i	−0.820028	+	0.572324i	$0.806042\pi$
$410$	−5.00691	+	3.31534i	−0.247274	+	0.163733i
$411$	20.8404	+	19.3693i	1.02798	+	0.955418i
$412$	−1.06913	−	0.453349i	−0.0526723	−	0.0223349i
$413$		−	11.0244i		−	0.542476i
$414$	−16.8639	−	21.8183i	−0.828816	−	1.07231i
$415$			3.97292i			0.195023i
$416$	−17.2434	+	10.8933i	−0.845429	+	0.534088i
$417$	−18.5885	+	20.0004i	−0.910285	+	0.979422i
$418$	−3.36031	−	5.07482i	−0.164358	−	0.248218i
$419$	24.8863			1.21578			0.607888	−	0.794023i	$-0.292017\pi$
$419$	24.8863			1.21578			0.607888	+	0.794023i	$0.292017\pi$
$420$	−8.02263	+	3.59149i	−0.391464	+	0.175247i
$421$			3.96230i			0.193111i	0.995328	+	0.0965553i	$0.0307825\pi$
$421$			3.96230i			0.193111i	−0.995328	+	0.0965553i	$0.969218\pi$
$422$	−1.84130	−	2.78078i	−0.0896331	−	0.135366i
$423$	20.0004	−	1.46543i	0.972451	−	0.0712519i
$424$		0			0
$425$		−	7.66411i		−	0.371764i
$426$	5.87112	−	35.4875i	0.284457	−	1.71938i
$427$	11.9679			0.579168
$428$	−10.1496	+	23.9358i	−0.490601	+	1.15698i
$429$	0.397551	+	12.4837i	0.0191940	+	0.602717i
$430$	−1.90388	−	2.87529i	−0.0918133	−	0.138659i
$431$		−	29.8078i		−	1.43579i	−0.696152	−	0.717895i	$-0.745106\pi$
$431$		−	29.8078i		−	1.43579i	0.696152	−	0.717895i	$-0.254894\pi$
$432$	20.6948	−	1.93021i	0.995678	−	0.0928673i
$433$	−9.17708			−0.441022			−0.220511	−	0.975384i	$-0.570773\pi$
$433$	−9.17708			−0.441022			−0.220511	+	0.975384i	$0.570773\pi$
$434$	−9.72350	+	6.43845i	−0.466743	+	0.309055i
$435$	−5.98396	+	6.43845i	−0.286909	+	0.308700i
$436$	7.29578	+	3.09367i	0.349405	+	0.148160i
$437$	−13.9867			−0.669076
$438$	5.19734	−	31.4149i	0.248339	−	1.50106i
$439$			7.94584i			0.379234i	0.981858	+	0.189617i	$0.0607247\pi$
$439$			7.94584i			0.379234i	−0.981858	+	0.189617i	$0.939275\pi$
$440$	−3.68260	+	0.684658i	−0.175561	+	0.0326398i
$441$	1.68466	+	22.9923i	0.0802218	+	1.09487i
$442$	8.38730	+	1.74618i	0.398943	+	0.0830574i
$443$	9.03712			0.429366			0.214683	−	0.976684i	$-0.431128\pi$
$443$	9.03712			0.429366			0.214683	+	0.976684i	$0.431128\pi$
$444$	−12.7913	−	28.5730i	−0.607048	−	1.35602i
$445$	7.75379			0.367565
$446$	−12.4432	+	8.23928i	−0.589201	+	0.390141i
$447$	−17.4801	−	16.2462i	−0.826782	−	0.768419i
$448$	−28.6080	+	11.0183i	−1.35160	+	0.520564i
$449$	3.76412			0.177640			0.0888198	−	0.996048i	$-0.471690\pi$
$449$	3.76412			0.177640			0.0888198	+	0.996048i	$0.471690\pi$
$450$	11.8352	+	15.3123i	0.557919	+	0.721829i
$451$			12.8255i			0.603927i
$452$	−7.92460	−	3.36031i	−0.372742	−	0.158056i
$453$	25.5058	+	23.7053i	1.19837	+	1.11377i
$454$	−18.9309	−	28.5899i	−0.888470	−	1.34179i
$455$	6.49971	−	6.43845i	0.304711	−	0.301839i
$456$	5.64451	−	8.90370i	0.264328	−	0.416954i
$457$		−	5.07482i		−	0.237390i	−0.992931	−	0.118695i	$-0.962129\pi$
$457$		−	5.07482i		−	0.237390i	0.992931	−	0.118695i	$-0.0378711\pi$
$458$	8.79323	+	13.2797i	0.410881	+	0.620522i
$459$	−6.81208	−	5.46026i	−0.317961	−	0.254863i
$460$	−3.36031	+	7.92460i	−0.156675	+	0.369486i
$461$	24.9888			1.16384			0.581921	−	0.813245i	$-0.302301\pi$
$461$	24.9888			1.16384			0.581921	+	0.813245i	$0.302301\pi$
$462$	−3.06422	+	18.5214i	−0.142560	+	0.861694i
$463$	−10.7595			−0.500037			−0.250018	−	0.968241i	$-0.580437\pi$
$463$	−10.7595			−0.500037			−0.250018	+	0.968241i	$0.580437\pi$
$464$	−22.0365	+	21.3122i	−1.02302	+	0.989393i
$465$	−1.80776	−	1.68015i	−0.0838331	−	0.0779153i
$466$	−14.0164	−	21.1679i	−0.649297	−	0.980584i
$467$	39.7984			1.84165			0.920825	−	0.389976i	$-0.127517\pi$
$467$	39.7984			1.84165			0.920825	+	0.389976i	$0.127517\pi$
$468$	−19.4537	+	9.46327i	−0.899248	+	0.437440i
$469$	−21.1231			−0.975374
$470$	−3.45593	−	5.21922i	−0.159410	−	0.240745i
$471$	−12.9994	−	12.0818i	−0.598982	−	0.556700i
$472$	8.00000	−	1.48734i	0.368230	−	0.0684602i
$473$	−7.36520			−0.338652
$474$	−3.24204	+	19.5962i	−0.148912	+	0.900084i
$475$	9.81602			0.450390
$476$	11.8551	+	5.02699i	0.543378	+	0.230412i
$477$		0			0
$478$	−6.97301	−	10.5308i	−0.318938	−	0.481668i
$479$		−	11.5616i		−	0.528261i	−0.964487	−	0.264130i	$-0.914915\pi$
$479$		−	11.5616i		−	0.528261i	0.964487	−	0.264130i	$-0.0850849\pi$
$480$	−3.68856	−	5.33717i	−0.168359	−	0.243608i
$481$	22.9309	+	23.1491i	1.04556	+	1.05551i
$482$	−14.1119	−	21.3122i	−0.642781	−	0.970743i
$483$	31.5999	+	29.3693i	1.43785	+	1.33635i
$484$	5.46543	−	12.8891i	0.248429	−	0.585868i
$485$			5.24730i			0.238268i
$486$	22.0420	+	0.389683i	0.999844	+	0.0176764i
$487$	−2.15190			−0.0975120			−0.0487560	−	0.998811i	$-0.515526\pi$
$487$	−2.15190			−0.0975120			−0.0487560	+	0.998811i	$0.515526\pi$
$488$	1.61463	+	8.68466i	0.0730907	+	0.393136i
$489$	17.9139	+	16.6493i	0.810094	+	0.752909i
$490$	6.00000	−	3.97292i	0.271052	−	0.179478i
$491$	−17.7619			−0.801582			−0.400791	−	0.916170i	$-0.631265\pi$
$491$	−17.7619			−0.801582			−0.400791	+	0.916170i	$0.631265\pi$
$492$	−20.2754	+	9.07668i	−0.914085	+	0.409209i
$493$	12.8769			0.579946
$494$	−2.23647	+	10.7423i	−0.100623	+	0.483317i
$495$	−3.96230	+	0.290319i	−0.178092	+	0.0130489i
$496$	−5.98396	−	6.18734i	−0.268688	−	0.277820i
$497$			56.2724i			2.52416i
$498$	−2.39888	+	14.4998i	−0.107496	+	0.649753i
$499$	2.15190			0.0963324			0.0481662	−	0.998839i	$-0.484662\pi$
$499$	2.15190			0.0963324			0.0481662	+	0.998839i	$0.484662\pi$
$500$	4.94326	−	11.6577i	0.221069	−	0.521347i
$501$	8.68951	−	9.34949i	0.388219	−	0.417704i
$502$	−4.30380	+	2.84978i	−0.192088	+	0.127192i
$503$	38.3735			1.71099			0.855495	−	0.517811i	$-0.173253\pi$
$503$	38.3735			1.71099			0.855495	+	0.517811i	$0.173253\pi$
$504$	−31.4485	+	8.26363i	−1.40083	+	0.368091i
$505$		−	10.1496i		−	0.451653i
$506$	10.1496	+	15.3282i	0.451206	+	0.681423i
$507$	15.4844	−	16.3473i	0.687687	−	0.726007i
$508$	6.24621	+	2.64861i	0.277131	+	0.117513i
$509$	−30.7393			−1.36250			−0.681249	−	0.732052i	$-0.738563\pi$
$509$	−30.7393			−1.36250			−0.681249	+	0.732052i	$0.738563\pi$
$510$	−0.444800	+	2.68856i	−0.0196961	+	0.119051i
$511$			49.8145i			2.20366i
$512$	−11.8551	−	19.2732i	−0.523927	−	0.851763i
$513$	6.99337	−	8.72475i	0.308765	−	0.385207i
$514$	16.6401	+	25.1302i	0.733961	+	1.10845i
$515$			0.384472i			0.0169419i
$516$	−5.21242	−	11.6434i	−0.229464	−	0.512573i
$517$	−13.3693			−0.587982
$518$	27.0389	+	40.8348i	1.18802	+	1.79418i
$519$	−14.1119	+	15.1838i	−0.619445	+	0.666493i
$520$	5.54903	+	3.84796i	0.243341	+	0.168744i
$521$		−	10.2878i		−	0.450715i	−0.974276	−	0.225358i	$-0.927645\pi$
$521$		−	10.2878i		−	0.450715i	0.974276	−	0.225358i	$-0.0723550\pi$
$522$	−25.7270	+	19.8850i	−1.12604	+	0.870344i
$523$			0.580639i			0.0253896i	0.999919	+	0.0126948i	$0.00404098\pi$
$523$			0.580639i			0.0253896i	−0.999919	+	0.0126948i	$0.995959\pi$
$524$	7.05597	−	16.6401i	0.308241	−	0.726924i
$525$	−22.1771	−	20.6116i	−0.967889	−	0.899566i
$526$	−21.3122	+	14.1119i	−0.929255	+	0.615310i
$527$			3.61553i			0.157495i
$528$	−13.8537	+	0.275192i	−0.602904	+	0.0119762i
$529$	19.2462			0.836792
$530$		0			0
$531$	8.60761	−	0.630683i	0.373538	−	0.0273693i
$532$	−6.43845	+	15.1838i	−0.279142	+	0.658299i
$533$	16.4265	−	16.2717i	0.711513	−	0.704807i
$534$	28.2988	+	4.68180i	1.22461	+	0.202601i
$535$	8.60761			0.372139
$536$	−2.84978	−	15.3282i	−0.123092	−	0.662079i
$537$	−11.4654	−	10.6561i	−0.494770	−	0.459844i
$538$	−12.7046	−	19.1868i	−0.547733	−	0.827200i
$539$		−	15.3693i		−	0.662003i
$540$	−3.26311	−	6.05842i	−0.140422	−	0.260713i
$541$			6.18734i			0.266014i	0.991115	+	0.133007i	$0.0424634\pi$
$541$			6.18734i			0.266014i	−0.991115	+	0.133007i	$0.957537\pi$
$542$	22.5928	−	14.9599i	0.970444	−	0.642583i
$543$	−6.81208	−	6.33122i	−0.292334	−	0.271698i
$544$	−2.04848	+	9.28101i	−0.0878280	+	0.397920i
$545$		−	2.62365i		−	0.112385i
$546$	27.6094	−	19.5736i	1.18157	−	0.837674i
$547$		−	38.7667i		−	1.65754i	−0.559586	−	0.828772i	$-0.689040\pi$
$547$		−	38.7667i		−	1.65754i	0.559586	−	0.828772i	$-0.310960\pi$
$548$	12.8255	−	30.2462i	0.547876	−	1.29205i
$549$	0.684658	+	9.34427i	0.0292205	+	0.398804i
$550$	−7.12311	−	10.7575i	−0.303730	−	0.458701i
$551$			16.4924i			0.702601i
$552$	−17.0489	+	26.8932i	−0.725651	+	1.14465i
$553$		−	31.0737i		−	1.32139i
$554$	23.8733	−	15.8078i	1.01428	−	0.671608i
$555$	−7.05597	+	7.59188i	−0.299509	+	0.322257i
$556$	29.0270	+	12.3085i	1.23102	+	0.521995i
$557$	−21.5965			−0.915072			−0.457536	−	0.889191i	$-0.651268\pi$
$557$	−21.5965			−0.915072			−0.457536	+	0.889191i	$0.651268\pi$
$558$	−5.58325	−	7.22355i	−0.236358	−	0.305797i
$559$	9.34427	+	9.43318i	0.395220	+	0.398981i
$560$	7.05597	+	7.29578i	0.298169	+	0.308303i
$561$	4.26324	+	3.96230i	0.179994	+	0.167288i
$562$	22.6847	−	15.0207i	0.956895	−	0.633611i
$563$	19.1868			0.808625			0.404313	−	0.914621i	$-0.367511\pi$
$563$	19.1868			0.808625			0.404313	+	0.914621i	$0.367511\pi$
$564$	−9.46158	−	21.1351i	−0.398404	−	0.889950i
$565$			2.84978i			0.119891i
$566$	−12.5351	−	18.9309i	−0.526891	−	0.795724i
$567$	−34.1202	+	5.02699i	−1.43291	+	0.211114i
$568$	−40.8348	+	7.59188i	−1.71339	+	0.318548i
$569$		−	21.3122i		−	0.893453i	−0.894670	−	0.446727i	$-0.852590\pi$
$569$		−	21.3122i		−	0.893453i	0.894670	−	0.446727i	$-0.147410\pi$
$570$	−3.44344	−	0.569690i	−0.144230	−	0.0238617i
$571$		−	15.0207i		−	0.628598i	−0.949324	−	0.314299i	$-0.898231\pi$
$571$		−	15.0207i		−	0.628598i	0.949324	−	0.314299i	$-0.101769\pi$
$572$	13.3955	−	5.34427i	0.560093	−	0.223455i
$573$	−1.80776	−	1.68015i	−0.0755204	−	0.0701895i
$574$	28.9763	−	19.1868i	1.20945	−	0.800840i
$575$	−29.6488			−1.23644
$576$	−10.2394	−	21.7061i	−0.426642	−	0.904421i
$577$		−	2.84978i		−	0.118638i	−0.998239	−	0.0593189i	$-0.981107\pi$
$577$		−	2.84978i		−	0.118638i	0.998239	−	0.0593189i	$-0.0188929\pi$
$578$	−16.7169	+	11.0691i	−0.695330	+	0.460415i
$579$	−17.9519	+	19.3153i	−0.746055	+	0.802718i
$580$	9.34427	+	3.96230i	0.388000	+	0.164526i
$581$		−	22.9923i		−	0.953883i
$582$	−3.16836	+	19.1509i	−0.131333	+	0.793830i
$583$		0			0
$584$	−36.1485	+	6.72062i	−1.49583	+	0.278101i
$585$	5.39882	+	4.70649i	0.223214	+	0.194589i
$586$	−11.9039	+	7.88220i	−0.491745	+	0.325611i
$587$		−	25.6155i		−	1.05727i	−0.848850	−	0.528633i	$-0.822705\pi$
$587$		−	25.6155i		−	1.05727i	0.848850	−	0.528633i	$-0.177295\pi$
$588$	24.2969	−	10.8770i	1.00199	−	0.448560i
$589$	−4.63068			−0.190804
$590$	−1.48734	−	2.24621i	−0.0612327	−	0.0924751i
$591$	10.1843	+	9.46543i	0.418928	+	0.389356i
$592$	−25.9843	+	25.1302i	−1.06795	+	1.03285i
$593$	1.53311			0.0629573			0.0314787	−	0.999504i	$-0.489978\pi$
$593$	1.53311			0.0629573			0.0314787	+	0.999504i	$0.489978\pi$
$594$	−14.6364	−	1.33290i	−0.600538	−	0.0546895i
$595$		−	4.26324i		−	0.174776i
$596$	−10.7575	+	25.3693i	−0.440644	+	1.03917i
$597$	21.3693	−	22.9923i	0.874588	−	0.941014i
$598$	6.75514	−	32.4464i	0.276238	−	1.32683i
$599$	15.8492			0.647581			0.323790	−	0.946129i	$-0.395043\pi$
$599$	15.8492			0.647581			0.323790	+	0.946129i	$0.395043\pi$
$600$	11.9651	−	18.8739i	0.488473	−	0.770522i
$601$	−17.8078			−0.726394			−0.363197	−	0.931712i	$-0.618315\pi$
$601$	−17.8078			−0.726394			−0.363197	+	0.931712i	$0.618315\pi$
$602$	11.0183	+	16.6401i	0.449071	+	0.678198i
$603$	−1.20841	−	16.4924i	−0.0492101	−	0.671623i
$604$	15.6966	−	37.0171i	0.638684	−	1.50620i
$605$	−4.63507			−0.188443
$606$	6.12843	−	37.0428i	0.248951	−	1.50476i
$607$		−	6.78456i		−	0.275377i	−0.990476	−	0.137688i	$-0.956033\pi$
$607$		−	6.78456i		−	0.275377i	0.990476	−	0.137688i	$-0.0439673\pi$
$608$	−11.8869	−	2.62365i	−0.482077	−	0.106403i
$609$	34.6307	−	37.2610i	1.40331	−	1.50989i
$610$	2.43845	−	1.61463i	0.0987298	−	0.0653743i
$611$	16.9617	+	17.1231i	0.686198	+	0.692727i
$612$	−3.24675	+	9.54378i	−0.131242	+	0.385784i
$613$		−	5.07482i		−	0.204970i	−0.994735	−	0.102485i	$-0.967321\pi$
$613$		−	5.07482i		−	0.204970i	0.994735	−	0.102485i	$-0.0326794\pi$
$614$	−11.5745	+	7.66411i	−0.467110	+	0.309298i
$615$	5.38719	+	5.00691i	0.217232	+	0.201898i
$616$	21.3122	−	3.96230i	0.858692	−	0.159646i
$617$	2.43981			0.0982230			0.0491115	−	0.998793i	$-0.484361\pi$
$617$	2.43981			0.0982230			0.0491115	+	0.998793i	$0.484361\pi$
$618$	−0.232147	+	1.40319i	−0.00933833	+	0.0564448i
$619$	−37.1122			−1.49166			−0.745832	−	0.666134i	$-0.767948\pi$
$619$	−37.1122			−1.49166			−0.745832	+	0.666134i	$0.767948\pi$
$620$	−1.11252	+	2.62365i	−0.0446799	+	0.105368i
$621$	−21.1231	+	26.3526i	−0.847641	+	1.05750i
$622$	10.2878	−	6.81208i	0.412502	−	0.273139i
$623$	−44.8732			−1.79781
$624$	17.9287	+	17.3943i	0.717722	+	0.696330i
$625$	18.6155			0.744621
$626$	−13.6328	+	9.02699i	−0.544875	+	0.360791i
$627$	−5.07482	+	5.46026i	−0.202669	+	0.218062i
$628$	−8.00000	+	18.8664i	−0.319235	+	0.752850i
$629$	15.1838			0.605416
$630$	6.58347	+	8.51763i	0.262292	+	0.339350i
$631$	−16.7435			−0.666547			−0.333274	−	0.942830i	$-0.608153\pi$
$631$	−16.7435			−0.666547			−0.333274	+	0.942830i	$0.608153\pi$
$632$	22.5490	−	4.19224i	0.896949	−	0.166758i
$633$	−2.78078	+	2.99198i	−0.110526	+	0.118921i
$634$	−16.2462	+	10.7575i	−0.645219	+	0.427234i
$635$		−	2.24621i		−	0.0891382i
$636$		0			0
$637$	−19.6847	+	19.4991i	−0.779935	+	0.772583i
$638$	18.0742	−	11.9679i	0.715566	−	0.473814i
$639$	−43.9362	+	3.21922i	−1.73809	+	0.127351i
$640$	−4.34233	+	6.10454i	−0.171646	+	0.241303i
$641$		−	34.9603i		−	1.38085i	−0.723405	−	0.690424i	$-0.757424\pi$
$641$		−	34.9603i		−	1.38085i	0.723405	−	0.690424i	$-0.242576\pi$
$642$	31.4149	+	5.19734i	1.23985	+	0.205123i
$643$	44.7763			1.76580			0.882902	−	0.469557i	$-0.155587\pi$
$643$	44.7763			1.76580			0.882902	+	0.469557i	$0.155587\pi$
$644$	19.4470	−	45.8617i	0.766319	−	1.80721i
$645$	−2.87529	+	3.09367i	−0.113214	+	0.121813i
$646$	2.82292	+	4.26324i	0.111066	+	0.167735i
$647$	−15.8492			−0.623096			−0.311548	−	0.950230i	$-0.600848\pi$
$647$	−15.8492			−0.623096			−0.311548	+	0.950230i	$0.600848\pi$
$648$	−8.25114	−	24.0815i	−0.324136	−	0.946011i
$649$	−5.75379			−0.225856
$650$	−4.74081	+	22.7712i	−0.185950	+	0.893159i
$651$	10.4620	+	9.72350i	0.410038	+	0.381094i
$652$	11.0244	−	25.9988i	0.431750	−	1.01819i
$653$		−	28.2396i		−	1.10510i	−0.833479	−	0.552551i	$-0.813654\pi$
$653$		−	28.2396i		−	1.10510i	0.833479	−	0.552551i	$-0.186346\pi$
$654$	1.58418	−	9.57545i	0.0619464	−	0.374430i
$655$	−5.98396			−0.233813
$656$	17.8324	+	18.4384i	0.696237	+	0.719900i
$657$	−38.8940	+	2.84978i	−1.51740	+	0.111180i
$658$	20.0004	+	30.2050i	0.779695	+	1.17751i
$659$	−49.9480			−1.94570			−0.972850	−	0.231438i	$-0.925657\pi$
$659$	−49.9480			−1.94570			−0.972850	+	0.231438i	$0.925657\pi$
$660$	1.87445	+	4.18711i	0.0729627	+	0.162983i
$661$		−	2.22504i		−	0.0865440i	−0.999063	−	0.0432720i	$-0.986222\pi$
$661$		−	2.22504i		−	0.0865440i	0.999063	−	0.0432720i	$-0.0137782\pi$
$662$	2.53741	−	1.68015i	0.0986192	−	0.0653011i
$663$	−0.333974	−	10.4872i	−0.0129705	−	0.407291i
$664$	16.6847	−	3.10196i	0.647490	−	0.120380i
$665$	5.46026			0.211740
$666$	−30.3360	+	23.4474i	−1.17550	+	0.908568i
$667$		−	49.8145i		−	1.92883i
$668$	−13.5691	−	5.75379i	−0.525005	−	0.222621i
$669$	13.3882	+	12.4432i	0.517619	+	0.481080i
$670$	−4.30380	+	2.84978i	−0.166270	+	0.110097i
$671$		−	6.24621i		−	0.241132i
$672$	21.3467	+	30.8876i	0.823466	+	1.19152i
$673$	0.684658			0.0263916			0.0131958	−	0.999913i	$-0.495800\pi$
$673$	0.684658			0.0263916			0.0131958	+	0.999913i	$0.495800\pi$
$674$	−3.16561	+	2.09612i	−0.121935	+	0.0807394i
$675$	14.8244	−	18.4945i	0.570591	−	0.711854i
$676$	−23.8397	−	10.3763i	−0.916912	−	0.399089i
$677$			20.5755i			0.790782i	0.918513	+	0.395391i	$0.129391\pi$
$677$			20.5755i			0.790782i	−0.918513	+	0.395391i	$0.870609\pi$
$678$	−1.72072	+	10.4007i	−0.0660838	+	0.399438i
$679$		−	30.3675i		−	1.16540i
$680$	3.09367	−	0.575166i	0.118637	−	0.0220566i
$681$	−28.5899	+	30.7613i	−1.09557	+	1.17877i
$682$	3.36031	+	5.07482i	0.128673	+	0.194325i
$683$			26.9848i			1.03255i	0.856424	+	0.516273i	$0.172681\pi$
$683$			26.9848i			1.03255i	−0.856424	+	0.516273i	$0.827319\pi$
$684$	−12.2234	−	4.15836i	−0.467375	−	0.158999i
$685$	−10.8769			−0.415585
$686$	−3.09367	+	2.04848i	−0.118117	+	0.0782115i
$687$	13.2797	−	14.2884i	0.506654	−	0.545135i
$688$	−10.5885	+	10.2405i	−0.403684	+	0.390415i
$689$		0			0
$690$	10.4007	+	1.72072i	0.395950	+	0.0655066i
$691$	−31.8649			−1.21220			−0.606098	−	0.795390i	$-0.707266\pi$
$691$	−31.8649			−1.21220			−0.606098	+	0.795390i	$0.707266\pi$
$692$	22.0365	+	9.34427i	0.837703	+	0.355216i
$693$	22.9309	−	1.68015i	0.871072	−	0.0638238i
$694$	−6.35229	+	4.20619i	−0.241130	+	0.159665i
$695$		−	10.4384i		−	0.395953i
$696$	31.7110	+	20.1032i	1.20200	+	0.762010i
$697$		−	10.7744i		−	0.408109i
$698$	7.05597	+	10.6561i	0.267072	+	0.403339i
$699$	−21.1679	+	22.7756i	−0.800644	+	0.861454i
$700$	−13.6481	+	32.1862i	−0.515849	+	1.21652i
$701$			28.2396i			1.06660i	0.845927	+	0.533298i	$0.179048\pi$
$701$			28.2396i			1.06660i	−0.845927	+	0.533298i	$0.820952\pi$
$702$	16.8621	+	20.4370i	0.636419	+	0.771344i
$703$			19.4470i			0.733457i
$704$	5.75058	+	14.9309i	0.216733	+	0.562728i
$705$	−5.21922	+	5.61563i	−0.196567	+	0.211497i
$706$	12.9309	−	8.56222i	0.486660	−	0.322243i
$707$			58.7386i			2.20909i
$708$	−4.07200	−	9.09599i	−0.153035	−	0.341848i
$709$		−	44.0731i		−	1.65520i	−0.561319	−	0.827599i	$-0.689706\pi$
$709$		−	44.0731i		−	1.65520i	0.561319	−	0.827599i	$-0.310294\pi$
$710$	7.59188	+	11.4654i	0.284918	+	0.430290i
$711$	24.2616	−	1.77766i	0.909880	−	0.0666673i
$712$	−6.05398	−	32.5628i	−0.226882	−	1.22034i
$713$	13.9867			0.523807
$714$	2.57418	−	15.5594i	0.0963362	−	0.582296i
$715$	−3.36031	−	3.39228i	−0.125668	−	0.126864i
$716$	−7.05597	+	16.6401i	−0.263694	+	0.621868i
$717$	−10.5308	+	11.3306i	−0.393280	+	0.423150i
$718$	−2.24621	−	3.39228i	−0.0838279	−	0.126599i
$719$	−13.7996			−0.514637			−0.257319	−	0.966327i	$-0.582839\pi$
$719$	−13.7996			−0.514637			−0.257319	+	0.966327i	$0.582839\pi$
$720$	−5.29272	+	5.92651i	−0.197248	+	0.220868i
$721$		−	2.22504i		−	0.0828648i
$722$	16.9435	−	11.2192i	0.630573	−	0.417536i
$723$	−21.3122	+	22.9309i	−0.792609	+	0.852808i
$724$	−4.19224	+	9.88653i	−0.155803	+	0.367430i
$725$			34.9603i			1.29839i
$726$	−16.9165	−	2.79869i	−0.627829	−	0.103869i
$727$			20.1907i			0.748830i	0.927261	+	0.374415i	$0.122156\pi$
$727$			20.1907i			0.748830i	−0.927261	+	0.374415i	$0.877844\pi$
$728$	−32.1137	−	22.2692i	−1.19021	−	0.825350i
$729$	−5.87689	−	26.3526i	−0.217663	−	0.976024i
$730$	6.72062	+	10.1496i	0.248741	+	0.375655i
$731$	6.18734			0.228847
$732$	9.87445	−	4.42050i	0.364970	−	0.163386i
$733$		−	27.1114i		−	1.00138i	−0.865626	−	0.500690i	$-0.833080\pi$
$733$		−	27.1114i		−	1.00138i	0.865626	−	0.500690i	$-0.166920\pi$
$734$	−3.22925	−	4.87689i	−0.119194	−	0.180009i
$735$	−6.45571	−	6.00000i	−0.238122	−	0.221313i
$736$	35.9038	+	7.92460i	1.32343	+	0.292105i
$737$			11.0244i			0.406090i
$738$	16.6382	+	21.5264i	0.612462	+	0.792397i
$739$	43.8328			1.61241			0.806207	−	0.591633i	$-0.201517\pi$
$739$	43.8328			1.61241			0.806207	+	0.591633i	$0.201517\pi$
$740$	11.0183	+	4.67213i	0.405040	+	0.171751i
$741$	13.4318	−	0.427746i	0.493430	−	0.0157136i
$742$		0			0
$743$			8.43845i			0.309577i	0.987948	+	0.154788i	$0.0494695\pi$
$743$			8.43845i			0.309577i	−0.987948	+	0.154788i	$0.950530\pi$
$744$	−5.64451	+	8.90370i	−0.206938	+	0.326426i
$745$	9.12311			0.334245
$746$	10.7575	−	7.12311i	0.393860	−	0.260795i
$747$	17.9519	−	1.31534i	0.656825	−	0.0481258i
$748$	2.62365	−	6.18734i	0.0959301	−	0.226232i
$749$	−49.8145			−1.82018
$750$	−15.3003	−	2.53130i	−0.558687	−	0.0924302i
$751$		−	37.1521i		−	1.35570i	−0.735201	−	0.677849i	$-0.762912\pi$
$751$		−	37.1521i		−	1.35570i	0.735201	−	0.677849i	$-0.237088\pi$
$752$	−19.2203	+	18.5885i	−0.700893	+	0.677854i
$753$	4.63068	+	4.30380i	0.168751	+	0.156839i
$754$	−38.2591	−	7.96530i	−1.39331	−	0.290079i
$755$	−13.3118			−0.484466
$756$	18.8845	+	35.0617i	0.686822	+	1.27518i
$757$	28.4924			1.03557			0.517787	−	0.855509i	$-0.326756\pi$
$757$	28.4924			1.03557			0.517787	+	0.855509i	$0.326756\pi$
$758$	6.49971	−	4.30380i	0.236080	−	0.156321i
$759$	15.3282	−	16.4924i	0.556379	−	0.598637i
$760$	0.736659	+	3.96230i	0.0267214	+	0.143728i
$761$	11.8730			0.430395			0.215198	−	0.976570i	$-0.430960\pi$
$761$	11.8730			0.430395			0.215198	+	0.976570i	$0.430960\pi$
$762$	1.35628	−	8.19792i	0.0491328	−	0.296979i
$763$			15.1838i			0.549689i
$764$	−1.11252	+	2.62365i	−0.0402496	+	0.0949203i
$765$	3.32864	−	0.243891i	0.120347	−	0.00881789i
$766$	18.3963	+	27.7825i	0.664686	+	1.00382i
$767$	7.29986	+	7.36932i	0.263583	+	0.266091i
$768$	−19.5340	+	19.6576i	−0.704874	+	0.709333i
$769$			43.4483i			1.56679i	0.621526	+	0.783393i	$0.286513\pi$
$769$			43.4483i			1.56679i	−0.621526	+	0.783393i	$0.713487\pi$
$770$	−3.96230	−	5.98396i	−0.142791	−	0.215647i
$771$	25.1302	−	27.0389i	0.905042	−	0.973781i
$772$	28.0328	+	11.8869i	1.00892	+	0.427819i
$773$	0.662153			0.0238160			0.0119080	−	0.999929i	$-0.496209\pi$
$773$	0.662153			0.0238160			0.0119080	+	0.999929i	$0.496209\pi$
$774$	−12.3618	+	9.55474i	−0.444337	+	0.343438i
$775$	−9.81602			−0.352602
$776$	22.0365	−	4.09697i	0.791066	−	0.147073i
$777$	40.8348	−	43.9362i	1.46494	−	1.57620i
$778$	10.0809	+	15.2245i	0.361419	+	0.545823i
$779$	13.7996			0.494421
$780$	2.98464	−	7.71296i	0.106867	−	0.276168i
$781$	29.3693			1.05092
$782$	−8.52648	−	12.8769i	−0.304906	−	0.460477i
$783$	31.0737	+	24.9073i	1.11048	+	0.890113i
$784$	−21.3693	−	22.0956i	−0.763190	−	0.789129i
$785$	6.78456			0.242151
$786$	−21.8395	−	3.61316i	−0.778988	−	0.128877i
$787$	19.8969			0.709249			0.354625	−	0.935009i	$-0.384609\pi$
$787$	19.8969			0.709249			0.354625	+	0.935009i	$0.384609\pi$
$788$	6.26757	−	14.7808i	0.223273	−	0.526543i
$789$	22.9309	+	21.3122i	0.816361	+	0.758734i
$790$	−4.19224	−	6.33122i	−0.149153	−	0.225255i
$791$		−	16.4924i		−	0.586403i
$792$	4.31289	+	16.4134i	0.153252	+	0.583224i
$793$	−8.00000	+	7.92460i	−0.284088	+	0.281411i
$794$	−14.1119	−	21.3122i	−0.500814	−	0.756341i
$795$		0			0
$796$	−33.3693	−	14.1498i	−1.18274	−	0.501525i
$797$			38.3206i			1.35738i	0.734423	+	0.678692i	$0.237453\pi$
$797$			38.3206i			1.35738i	−0.734423	+	0.678692i	$0.762547\pi$
$798$	19.9281	+	3.29695i	0.705448	+	0.116711i
$799$	11.2313			0.397333
$800$	−25.1976	−	5.56155i	−0.890869	−	0.196631i
$801$	−2.56710	−	35.0360i	−0.0907040	−	1.23793i
$802$	42.4924	−	28.1365i	1.50046	−	0.993534i
$803$	25.9988			0.917479
$804$	−17.4282	+	7.80208i	−0.614644	+	0.275158i
$805$	−16.4924			−0.581282
$806$	2.23647	−	10.7423i	0.0787762	−	0.378380i
$807$	−19.1868	+	20.6440i	−0.675406	+	0.726704i
$808$	−42.6244	+	7.92460i	−1.49952	+	0.278786i
$809$		−	44.3045i		−	1.55766i	−0.627232	−	0.778832i	$-0.715812\pi$
$809$		−	44.3045i		−	1.55766i	0.627232	−	0.778832i	$-0.284188\pi$
$810$	−6.27374	+	5.62749i	−0.220437	+	0.197730i
$811$	−18.4236			−0.646941			−0.323470	−	0.946238i	$-0.604850\pi$
$811$	−18.4236			−0.646941			−0.323470	+	0.946238i	$0.604850\pi$
$812$	−54.0777	−	22.9309i	−1.89776	−	0.804716i
$813$	−24.3087	−	22.5928i	−0.852545	−	0.792364i
$814$	21.3122	−	14.1119i	0.746992	−	0.494623i
$815$	−9.34949			−0.327498
$816$	11.6382	−	0.231183i	0.407417	−	0.00809301i
$817$			7.92460i			0.277247i
$818$	−18.0742	−	27.2961i	−0.631951	−	0.954387i
$819$	−31.2444	−	27.2377i	−1.09177	−	0.951762i
$820$	3.31534	−	7.81855i	0.115777	−	0.273036i
$821$	24.2451			0.846160			0.423080	−	0.906092i	$-0.360949\pi$
$821$	24.2451			0.846160			0.423080	+	0.906092i	$0.360949\pi$
$822$	−39.6971	−	6.56755i	−1.38459	−	0.229070i
$823$			18.8664i			0.657640i	0.944393	+	0.328820i	$0.106651\pi$
$823$			18.8664i			0.657640i	−0.944393	+	0.328820i	$0.893349\pi$
$824$	1.61463	−	0.300187i	0.0562482	−	0.0104575i
$825$	−10.7575	+	11.5745i	−0.374528	+	0.402973i
$826$	8.60761	+	12.9994i	0.299497	+	0.452308i
$827$			46.4924i			1.61670i	0.588702	+	0.808350i	$0.299639\pi$
$827$			46.4924i			1.61670i	−0.588702	+	0.808350i	$0.700361\pi$
$828$	36.9203	+	12.5601i	1.28307	+	0.436494i
$829$	24.0000			0.833554			0.416777	−	0.909009i	$-0.363160\pi$
$829$	24.0000			0.833554			0.416777	+	0.909009i	$0.363160\pi$
$830$	−3.10196	−	4.68466i	−0.107671	−	0.162607i
$831$	−25.6865	−	23.8733i	−0.891054	−	0.828154i
$832$	11.8273	−	26.3081i	0.410039	−	0.912068i
$833$			12.9114i			0.447354i
$834$	6.30282	−	38.0969i	0.218249	−	1.31919i
$835$			4.87962i			0.168866i
$836$	7.92460	+	3.36031i	0.274078	+	0.116219i
$837$	−6.99337	+	8.72475i	−0.241726	+	0.301571i
$838$	−29.3446	+	19.4306i	−1.01369	+	0.671221i
$839$			10.8769i			0.375512i	0.982216	+	0.187756i	$0.0601214\pi$
$839$			10.8769i			0.375512i	−0.982216	+	0.187756i	$0.939879\pi$
$840$	6.65571	−	10.4988i	0.229644	−	0.362242i
$841$	−29.7386			−1.02547
$842$	−3.09367	−	4.67213i	−0.106615	−	0.161012i
$843$	−24.4076	−	22.6847i	−0.840642	−	0.781301i
$844$	4.34233	+	1.84130i	0.149469	+	0.0633802i
$845$	−0.0815148	+	8.60761i	−0.00280419	+	0.296111i
$846$	−22.4392	+	17.3438i	−0.771475	+	0.596291i
$847$	26.8244			0.921697
$848$		0			0
$849$	−18.9309	+	20.3687i	−0.649706	+	0.699052i
$850$	5.98396	+	9.03712i	0.205248	+	0.309971i
$851$		−	58.7386i		−	2.01353i
$852$	20.7849	+	46.4291i	0.712079	+	1.59063i
$853$			6.18734i			0.211850i	0.994374	+	0.105925i	$0.0337804\pi$
$853$			6.18734i			0.211850i	−0.994374	+	0.105925i	$0.966220\pi$
$854$	−14.1119	+	9.34427i	−0.482901	+	0.319754i
$855$	0.312369	+	4.26324i	0.0106828	+	0.145800i
$856$	−6.72062	−	36.1485i	−0.229706	−	1.23553i
$857$			1.88699i			0.0644584i	0.999481	+	0.0322292i	$0.0102606\pi$
$857$			1.88699i			0.0644584i	−0.999481	+	0.0322292i	$0.989739\pi$
$858$	−10.2157	−	14.4097i	−0.348759	−	0.491938i
$859$			8.10887i			0.276671i	0.990385	+	0.138336i	$0.0441752\pi$
$859$			8.10887i			0.276671i	−0.990385	+	0.138336i	$0.955825\pi$
$860$	4.48991	+	1.90388i	0.153105	+	0.0649218i
$861$	−31.1771	−	28.9763i	−1.06251	−	0.987510i
$862$	23.2732	+	35.1477i	0.792688	+	1.19714i
$863$			3.56155i			0.121237i	0.998161	+	0.0606183i	$0.0193073\pi$
$863$			3.56155i			0.121237i	−0.998161	+	0.0606183i	$0.980693\pi$
$864$	−22.8951	+	18.4340i	−0.778908	+	0.627138i
$865$		−	7.92460i		−	0.269444i
$866$	10.8211	−	7.16525i	0.367717	−	0.243485i
$867$	17.9865	+	16.7169i	0.610855	+	0.567735i
$868$	6.43845	−	15.1838i	0.218535	−	0.515370i
$869$	−16.2177			−0.550149
$870$	2.02898	−	12.2640i	0.0687889	−	0.415789i
$871$	14.1198	−	13.9867i	0.478432	−	0.473923i
$872$	−11.0183	+	2.04848i	−0.373126	+	0.0693704i
$873$	23.7102	−	1.73726i	0.802470	−	0.0587973i
$874$	16.4924	−	10.9205i	0.557865	−	0.369392i
$875$	24.2616			0.820191
$876$	18.3996	+	41.1008i	0.621665	+	1.38867i
$877$		−	1.11252i		−	0.0375671i	−0.999824	−	0.0187836i	$-0.994021\pi$
$877$		−	1.11252i		−	0.0375671i	0.999824	−	0.0187836i	$-0.00597935\pi$
$878$	−6.20393	−	9.36932i	−0.209372	−	0.316199i
$879$	12.8080	+	11.9039i	0.432003	+	0.401508i
$880$	3.80776	−	3.68260i	0.128360	−	0.124140i
$881$			31.3931i			1.05766i	0.848728	+	0.528830i	$0.177369\pi$
$881$			31.3931i			1.05766i	−0.848728	+	0.528830i	$0.822631\pi$
$882$	−19.9383	−	25.7960i	−0.671359	−	0.868597i
$883$			22.9666i			0.772886i	0.922313	+	0.386443i	$0.126296\pi$
$883$			22.9666i			0.772886i	−0.922313	+	0.386443i	$0.873704\pi$
$884$	−11.2532	+	4.48960i	−0.378487	+	0.151002i
$885$	−2.24621	+	2.41681i	−0.0755056	+	0.0812403i
$886$	−10.6561	+	7.05597i	−0.357998	+	0.237050i
$887$	−4.27467			−0.143529			−0.0717647	−	0.997422i	$-0.522863\pi$
$887$	−4.27467			−0.143529			−0.0717647	+	0.997422i	$0.522863\pi$
$888$	37.3919	+	23.7047i	1.25479	+	0.795476i
$889$			12.9994i			0.435986i
$890$	−9.14286	+	6.05398i	−0.306469	+	0.202930i
$891$	2.62365	+	17.8078i	0.0878956	+	0.596583i
$892$	8.23928	−	19.4306i	0.275871	−	0.650586i
$893$			14.3847i			0.481367i
$894$	33.2963	+	5.50860i	1.11359	+	0.184235i
$895$	5.98396			0.200022
$896$	25.1302	−	35.3286i	0.839541	−	1.18025i
$897$	−40.5701	+	1.29198i	−1.35460	+	0.0431381i
$898$	−4.43845	+	2.93893i	−0.148113	+	0.0980735i
$899$		−	16.4924i		−	0.550053i
$900$	−25.9110	−	8.81479i	−0.863699	−	0.293826i
$901$		0			0
$902$	−10.0138	−	15.1231i	−0.333424	−	0.503544i
$903$	16.6401	−	17.9039i	0.553746	−	0.595804i
$904$	11.9679	−	2.22504i	0.398047	−	0.0740037i
$905$	3.55531			0.118183
$906$	−48.5836	−	8.03776i	−1.61408	−	0.267037i
$907$			42.1590i			1.39987i	0.714209	+	0.699933i	$0.246787\pi$
$907$			42.1590i			1.39987i	−0.714209	+	0.699933i	$0.753213\pi$
$908$	44.6446	+	18.9309i	1.48158	+	0.628243i
$909$	−45.8617	+	3.36031i	−1.52114	+	0.111454i
$910$	−2.63713	+	12.6667i	−0.0874199	+	0.419897i
$911$	24.5739			0.814171			0.407086	−	0.913390i	$-0.366545\pi$
$911$	24.5739			0.814171			0.407086	+	0.913390i	$0.366545\pi$
$912$	0.296093	+	14.9059i	0.00980463	+	0.493583i
$913$	−12.0000			−0.397142
$914$	3.96230	+	5.98396i	0.131061	+	0.197932i
$915$	−2.62365	−	2.43845i	−0.0867352	−	0.0806126i
$916$	−20.7370	−	8.79323i	−0.685170	−	0.290536i
$917$	34.6307			1.14361
$918$	12.2957	+	1.11974i	0.405818	+	0.0369568i
$919$		−	52.8807i		−	1.74437i	−0.489172	−	0.872187i	$-0.662701\pi$
$919$		−	52.8807i		−	1.74437i	0.489172	−	0.872187i	$-0.337299\pi$
$920$	−2.22504	−	11.9679i	−0.0733574	−	0.394571i
$921$	12.4536	+	11.5745i	0.410361	+	0.381394i
$922$	−29.4654	+	19.5106i	−0.970392	+	0.642549i
$923$	−37.2610	−	37.6155i	−1.22646	−	1.23813i
$924$	−10.8479	−	24.2319i	−0.356870	−	0.797172i
$925$			41.2233i			1.35541i
$926$	12.6870	−	8.40077i	0.416922	−	0.276067i
$927$	1.73726	−	0.127290i	0.0570591	−	0.00418074i
$928$	9.34427	−	42.3358i	0.306741	−	1.38974i
$929$	43.9824			1.44302			0.721508	−	0.692406i	$-0.243449\pi$
$929$	43.9824			1.44302			0.721508	+	0.692406i	$0.243449\pi$
$930$	3.44344	+	0.569690i	0.112915	+	0.0186809i
$931$	−16.5366			−0.541966
$932$	33.0548	+	14.0164i	1.08275	+	0.459123i
$933$	−11.0691	−	10.2878i	−0.362387	−	0.336806i
$934$	−46.9282	+	31.0737i	−1.53554	+	1.01676i
$935$	−2.22504			−0.0727666
$936$	15.5501	−	26.3476i	0.508270	−	0.861198i
$937$	−1.86174			−0.0608204			−0.0304102	−	0.999538i	$-0.509681\pi$
$937$	−1.86174			−0.0608204			−0.0304102	+	0.999538i	$0.509681\pi$
$938$	24.9073	−	16.4924i	0.813251	−	0.538497i
$939$	14.6682	+	13.6328i	0.478679	+	0.444889i
$940$	8.15009	+	3.45593i	0.265827	+	0.112720i
$941$	53.5429			1.74545			0.872724	−	0.488214i	$-0.162351\pi$
$941$	53.5429			1.74545			0.872724	+	0.488214i	$0.162351\pi$
$942$	24.7614	+	4.09657i	0.806770	+	0.133474i
$943$	−41.6809			−1.35732
$944$	−8.27190	+	8.00000i	−0.269227	+	0.260378i
$945$	8.24621	−	10.2878i	0.268249	−	0.334661i
$946$	8.68466	−	5.75058i	0.282363	−	0.186967i
$947$		−	2.00000i		−	0.0649913i	−0.999472	−	0.0324956i	$-0.989654\pi$
$947$		−	2.00000i		−	0.0649913i	0.999472	−	0.0324956i	$-0.0103455\pi$
$948$	−11.4774	−	25.6381i	−0.372770	−	0.832688i
$949$	−32.9848	−	33.2987i	−1.07073	−	1.08092i
$950$	−11.5745	+	7.66411i	−0.375527	+	0.248657i
$951$	17.4801	+	16.2462i	0.566832	+	0.526819i
$952$	−17.9039	+	3.32864i	−0.580268	+	0.107882i
$953$			28.0328i			0.908072i	0.890983	+	0.454036i	$0.150016\pi$
$953$			28.0328i			0.908072i	−0.890983	+	0.454036i	$0.849984\pi$
$954$		0			0
$955$	0.943495			0.0305308
$956$	16.4444	+	6.97301i	0.531850	+	0.225523i
$957$	−19.4470	−	18.0742i	−0.628632	−	0.584257i
$958$	9.02699	+	13.6328i	0.291649	+	0.440455i
$959$	62.9475			2.03268
$960$	8.51650	+	3.41337i	0.274869	+	0.110166i
$961$	−26.3693			−0.850623
$962$	−45.1131	−	9.39226i	−1.45450	−	0.302819i
$963$	−2.84978	−	38.8940i	−0.0918328	−	1.25334i
$964$	33.2801	+	14.1119i	1.07188	+	0.454515i
$965$		−	10.0809i		−	0.324517i
$966$	−60.1919	−	9.95825i	−1.93664	−	0.320402i
$967$	−28.7114			−0.923296			−0.461648	−	0.887063i	$-0.652742\pi$
$967$	−28.7114			−0.923296			−0.461648	+	0.887063i	$0.652742\pi$
$968$	3.61896	+	19.4654i	0.116318	+	0.625643i
$969$	4.26324	−	4.58704i	0.136955	−	0.147357i
$970$	−4.09697	−	6.18734i	−0.131546	−	0.198663i
$971$	−25.6865			−0.824318			−0.412159	−	0.911112i	$-0.635225\pi$
$971$	−25.6865			−0.824318			−0.412159	+	0.911112i	$0.635225\pi$
$972$	−26.2950	+	16.7504i	−0.843412	+	0.537268i
$973$			60.4100i			1.93666i
$974$	2.53741	−	1.68015i	0.0813038	−	0.0538356i
$975$	28.4725	−	0.906726i	0.911848	−	0.0290385i
$976$	−8.68466	−	8.97983i	−0.277989	−	0.287437i
$977$	6.24970			0.199946			0.0999728	−	0.994990i	$-0.468124\pi$
$977$	6.24970			0.199946			0.0999728	+	0.994990i	$0.468124\pi$
$978$	−34.1225	−	5.64529i	−1.09112	−	0.180517i
$979$			23.4199i			0.748504i
$980$	−3.97292	+	9.36932i	−0.126910	+	0.299292i
$981$	−11.8551	+	0.868629i	−0.378505	+	0.0277332i
$982$	20.9439	−	13.8680i	0.668345	−	0.442547i
$983$			7.06913i			0.225470i	0.993625	+	0.112735i	$0.0359612\pi$
$983$			7.06913i			0.225470i	−0.993625	+	0.112735i	$0.964039\pi$
$984$	16.8208	−	26.5333i	0.536227	−	0.845850i
$985$	−5.31534			−0.169361
$986$	−15.1838	+	10.0540i	−0.483549	+	0.320184i
$987$	30.2050	−	32.4991i	0.961437	−	1.03446i
$988$	−5.75017	−	14.4129i	−0.182937	−	0.458535i
$989$		−	23.9358i		−	0.761115i
$990$	4.44546	−	3.43600i	0.141286	−	0.109203i
$991$			42.1232i			1.33809i	0.743222	+	0.669044i	$0.233296\pi$
$991$			42.1232i			1.33809i	−0.743222	+	0.669044i	$0.766704\pi$
$992$	11.8869	+	2.62365i	0.377409	+	0.0833010i
$993$	−2.73013	−	2.53741i	−0.0866380	−	0.0805223i
$994$	−43.9362	−	66.3535i	−1.39357	−	2.10461i
$995$			12.0000i			0.380426i
$996$	−8.49250	−	18.9704i	−0.269095	−	0.601101i
$997$	10.0000			0.316703			0.158352	−	0.987383i	$-0.449382\pi$
$997$	10.0000			0.316703			0.158352	+	0.987383i	$0.449382\pi$
$998$	−2.53741	+	1.68015i	−0.0803203	+	0.0531844i
$999$	36.6404	+	29.3693i	1.15925	+	0.929204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.h.b.155.4	yes	16
3.2	odd	2	inner	156.2.h.b.155.13	yes	16
4.3	odd	2	inner	156.2.h.b.155.1	✓	16
12.11	even	2	inner	156.2.h.b.155.16	yes	16
13.12	even	2	inner	156.2.h.b.155.14	yes	16
39.38	odd	2	inner	156.2.h.b.155.3	yes	16
52.51	odd	2	inner	156.2.h.b.155.15	yes	16
156.155	even	2	inner	156.2.h.b.155.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.h.b.155.1	✓	16	4.3	odd	2	inner
156.2.h.b.155.2	yes	16	156.155	even	2	inner
156.2.h.b.155.3	yes	16	39.38	odd	2	inner
156.2.h.b.155.4	yes	16	1.1	even	1	trivial
156.2.h.b.155.13	yes	16	3.2	odd	2	inner
156.2.h.b.155.14	yes	16	13.12	even	2	inner
156.2.h.b.155.15	yes	16	52.51	odd	2	inner
156.2.h.b.155.16	yes	16	12.11	even	2	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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17915 + 0.780776i) q^{2} +(1.26870 + 1.17915i) q^{3} +(0.780776 - 1.84130i) q^{4} -0.662153 q^{5} +(-2.41664 - 0.399813i) q^{6} +3.83206 q^{7} +(0.516994 + 2.78078i) q^{8} +(0.219224 + 2.99198i) q^{9} +O(q^{10})\)	\(q+(-1.17915 + 0.780776i) q^{2} +(1.26870 + 1.17915i) q^{3} +(0.780776 - 1.84130i) q^{4} -0.662153 q^{5} +(-2.41664 - 0.399813i) q^{6} +3.83206 q^{7} +(0.516994 + 2.78078i) q^{8} +(0.219224 + 2.99198i) q^{9} +(0.780776 - 0.516994i) q^{10} -2.00000i q^{11} +(3.16174 - 1.41542i) q^{12} +(-2.56155 + 2.53741i) q^{13} +(-4.51856 + 2.99198i) q^{14} +(-0.840077 - 0.780776i) q^{15} +(-2.78078 - 2.87529i) q^{16} +1.68015i q^{17} +(-2.59456 - 3.35682i) q^{18} -2.15190 q^{19} +(-0.516994 + 1.21922i) q^{20} +(4.86175 + 4.51856i) q^{21} +(1.56155 + 2.35829i) q^{22} +6.49971 q^{23} +(-2.62303 + 4.13760i) q^{24} -4.56155 q^{25} +(1.03930 - 4.99198i) q^{26} +(-3.24985 + 4.05444i) q^{27} +(2.99198 - 7.05597i) q^{28} -7.66411i q^{29} +(1.60019 + 0.264738i) q^{30} +2.15190 q^{31} +(5.52390 + 1.21922i) q^{32} +(2.35829 - 2.53741i) q^{33} +(-1.31182 - 1.98115i) q^{34} -2.53741 q^{35} +(5.68030 + 1.93241i) q^{36} -9.03712i q^{37} +(2.53741 - 1.68015i) q^{38} +(-6.24183 + 0.198776i) q^{39} +(-0.342329 - 1.84130i) q^{40} -6.41273 q^{41} +(-9.26070 - 1.53211i) q^{42} -3.68260i q^{43} +(-3.68260 - 1.56155i) q^{44} +(-0.145160 - 1.98115i) q^{45} +(-7.66411 + 5.07482i) q^{46} -6.68466i q^{47} +(-0.137596 - 6.92684i) q^{48} +7.68466 q^{49} +(5.37874 - 3.56155i) q^{50} +(-1.98115 + 2.13162i) q^{51} +(2.67213 + 6.69774i) q^{52} +(0.666449 - 7.31819i) q^{54} +1.32431i q^{55} +(1.98115 + 10.6561i) q^{56} +(-2.73013 - 2.53741i) q^{57} +(5.98396 + 9.03712i) q^{58} -2.87689i q^{59} +(-2.09356 + 0.937223i) q^{60} +3.12311 q^{61} +(-2.53741 + 1.68015i) q^{62} +(0.840077 + 11.4654i) q^{63} +(-7.46543 + 2.87529i) q^{64} +(1.69614 - 1.68015i) q^{65} +(-0.799627 + 4.83328i) q^{66} -5.51221 q^{67} +(3.09367 + 1.31182i) q^{68} +(8.24621 + 7.66411i) q^{69} +(2.99198 - 1.98115i) q^{70} +14.6847i q^{71} +(-8.20669 + 2.15645i) q^{72} +12.9994i q^{73} +(7.05597 + 10.6561i) q^{74} +(-5.78726 - 5.37874i) q^{75} +(-1.68015 + 3.96230i) q^{76} -7.66411i q^{77} +(7.20484 - 5.10786i) q^{78} -8.10887i q^{79} +(1.84130 + 1.90388i) q^{80} +(-8.90388 + 1.31182i) q^{81} +(7.56155 - 5.00691i) q^{82} -6.00000i q^{83} +(12.1160 - 5.42396i) q^{84} -1.11252i q^{85} +(2.87529 + 4.34233i) q^{86} +(9.03712 - 9.72350i) q^{87} +(5.56155 - 1.03399i) q^{88} -11.7100 q^{89} +(1.71800 + 2.22273i) q^{90} +(-9.81602 + 9.72350i) q^{91} +(5.07482 - 11.9679i) q^{92} +(2.73013 + 2.53741i) q^{93} +(5.21922 + 7.88220i) q^{94} +1.42489 q^{95} +(5.57056 + 8.06033i) q^{96} -7.92460i q^{97} +(-9.06134 + 6.00000i) q^{98} +(5.98396 - 0.438447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 20 q^{9}+O(q^{10}) \) 16 * q - 4 * q^4 + 20 * q^9	\( 16 q - 4 q^{4} + 20 q^{9} - 4 q^{10} + 10 q^{12} - 8 q^{13} - 28 q^{16} - 8 q^{22} - 40 q^{25} + 18 q^{30} - 22 q^{36} + 44 q^{40} - 34 q^{42} + 46 q^{48} + 24 q^{49} - 32 q^{52} - 16 q^{61} - 4 q^{64} - 28 q^{66} + 34 q^{78} - 60 q^{81} + 88 q^{82} + 56 q^{88} - 22 q^{90} + 100 q^{94}+O(q^{100}) \) 16 * q - 4 * q^4 + 20 * q^9 - 4 * q^10 + 10 * q^12 - 8 * q^13 - 28 * q^16 - 8 * q^22 - 40 * q^25 + 18 * q^30 - 22 * q^36 + 44 * q^40 - 34 * q^42 + 46 * q^48 + 24 * q^49 - 32 * q^52 - 16 * q^61 - 4 * q^64 - 28 * q^66 + 34 * q^78 - 60 * q^81 + 88 * q^82 + 56 * q^88 - 22 * q^90 + 100 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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