LMFDB - Embedded newform 950.2.f.d.493.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(493,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("950.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.16
Character	$\chi$	$=$	950.493
Dual form			950.2.f.d.607.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(2.10096 - 2.10096i) q^{3} +1.00000i q^{4} +2.97120 q^{6} +(0.978377 - 0.978377i) q^{7} +(-0.707107 + 0.707107i) q^{8} -5.82806i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(2.10096 - 2.10096i) q^{3} +1.00000i q^{4} +2.97120 q^{6} +(0.978377 - 0.978377i) q^{7} +(-0.707107 + 0.707107i) q^{8} -5.82806i q^{9} +2.43153 q^{11} +(2.10096 + 2.10096i) q^{12} +(1.31299 - 1.31299i) q^{13} +1.38363 q^{14} -1.00000 q^{16} +(-5.11008 + 5.11008i) q^{17} +(4.12106 - 4.12106i) q^{18} +(3.48940 - 2.61229i) q^{19} -4.11106i q^{21} +(1.71935 + 1.71935i) q^{22} +(-1.29579 - 1.29579i) q^{23} +2.97120i q^{24} +1.85685 q^{26} +(-5.94163 - 5.94163i) q^{27} +(0.978377 + 0.978377i) q^{28} -0.448895 q^{29} -3.46410i q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.10855 - 5.10855i) q^{33} -7.22675 q^{34} +5.82806 q^{36} +(4.60388 + 4.60388i) q^{37} +(4.31455 + 0.620212i) q^{38} -5.51709i q^{39} +6.28197i q^{41} +(2.90696 - 2.90696i) q^{42} +(-7.27794 - 7.27794i) q^{43} +2.43153i q^{44} -1.83253i q^{46} +(6.15951 - 6.15951i) q^{47} +(-2.10096 + 2.10096i) q^{48} +5.08556i q^{49} +21.4721i q^{51} +(1.31299 + 1.31299i) q^{52} +(-9.37595 + 9.37595i) q^{53} -8.40274i q^{54} +1.38363i q^{56} +(1.84278 - 12.8194i) q^{57} +(-0.317417 - 0.317417i) q^{58} +5.89371 q^{59} -2.00000 q^{61} +(2.44949 - 2.44949i) q^{62} +(-5.70204 - 5.70204i) q^{63} -1.00000i q^{64} +7.22458 q^{66} +(-4.17716 - 4.17716i) q^{67} +(-5.11008 - 5.11008i) q^{68} -5.44482 q^{69} +14.6544i q^{71} +(4.12106 + 4.12106i) q^{72} +(8.04521 + 8.04521i) q^{73} +6.51088i q^{74} +(2.61229 + 3.48940i) q^{76} +(2.37896 - 2.37896i) q^{77} +(3.90117 - 3.90117i) q^{78} +6.23137 q^{79} -7.48208 q^{81} +(-4.44203 + 4.44203i) q^{82} +(-11.7200 - 11.7200i) q^{83} +4.11106 q^{84} -10.2926i q^{86} +(-0.943110 + 0.943110i) q^{87} +(-1.71935 + 1.71935i) q^{88} -3.31375 q^{89} -2.56920i q^{91} +(1.29579 - 1.29579i) q^{92} +(-7.27794 - 7.27794i) q^{93} +8.71086 q^{94} -2.97120 q^{96} +(-6.78718 - 6.78718i) q^{97} +(-3.59603 + 3.59603i) q^{98} -14.1711i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{6}+O(q^{10}) $ 32 * q - 8 * q^6	$ 32 q - 8 q^{6} - 24 q^{11} - 32 q^{16} + 32 q^{26} + 56 q^{36} - 64 q^{61} + 72 q^{66} + 4 q^{76} - 32 q^{81} + 8 q^{96}+O(q^{100}) $ 32 * q - 8 * q^6 - 24 * q^11 - 32 * q^16 + 32 * q^26 + 56 * q^36 - 64 * q^61 + 72 * q^66 + 4 * q^76 - 32 * q^81 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	2.10096	−	2.10096i	1.21299	−	1.21299i	0.242951	−	0.970039i	$-0.421885\pi$
$3$	2.10096	−	2.10096i	1.21299	−	1.21299i	0.970039	−	0.242951i	$-0.0781153\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	2.97120			1.21299
$7$	0.978377	−	0.978377i	0.369792	−	0.369792i	−0.497609	−	0.867401i	$-0.665789\pi$
$7$	0.978377	−	0.978377i	0.369792	−	0.369792i	0.867401	+	0.497609i	$0.165789\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	5.82806i		−	1.94269i
$10$		0			0
$11$	2.43153			0.733135			0.366567	−	0.930392i	$-0.380533\pi$
$11$	2.43153			0.733135			0.366567	+	0.930392i	$0.380533\pi$
$12$	2.10096	+	2.10096i	0.606495	+	0.606495i
$13$	1.31299	−	1.31299i	0.364159	−	0.364159i	−0.501183	−	0.865341i	$-0.667102\pi$
$13$	1.31299	−	1.31299i	0.364159	−	0.364159i	0.865341	+	0.501183i	$0.167102\pi$
$14$	1.38363			0.369792
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−5.11008	+	5.11008i	−1.23938	+	1.23938i	−0.279120	+	0.960256i	$0.590043\pi$
$17$	−5.11008	+	5.11008i	−1.23938	+	1.23938i	−0.960256	+	0.279120i	$0.909957\pi$
$18$	4.12106	−	4.12106i	0.971343	−	0.971343i
$19$	3.48940	−	2.61229i	0.800524	−	0.599301i
$19$	3.48940	−	2.61229i	0.800524	−	0.599301i
$20$		0			0
$21$		−	4.11106i		−	0.897107i
$22$	1.71935	+	1.71935i	0.366567	+	0.366567i
$23$	−1.29579	−	1.29579i	−0.270192	−	0.270192i	0.558986	−	0.829177i	$-0.311191\pi$
$23$	−1.29579	−	1.29579i	−0.270192	−	0.270192i	−0.829177	+	0.558986i	$0.811191\pi$
$24$			2.97120i			0.606495i
$25$		0			0
$26$	1.85685			0.364159
$27$	−5.94163	−	5.94163i	−1.14347	−	1.14347i
$28$	0.978377	+	0.978377i	0.184896	+	0.184896i
$29$	−0.448895			−0.0833577			−0.0416789	−	0.999131i	$-0.513271\pi$
$29$	−0.448895			−0.0833577			−0.0416789	+	0.999131i	$0.513271\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	5.10855	−	5.10855i	0.889285	−	0.889285i
$34$	−7.22675			−1.23938
$35$		0			0
$36$	5.82806			0.971343
$37$	4.60388	+	4.60388i	0.756874	+	0.756874i	0.975752	−	0.218878i	$-0.0702397\pi$
$37$	4.60388	+	4.60388i	0.756874	+	0.756874i	−0.218878	+	0.975752i	$0.570240\pi$
$38$	4.31455	+	0.620212i	0.699912	+	0.100612i
$39$		−	5.51709i		−	0.883441i
$40$		0			0
$41$			6.28197i			0.981079i	0.871419	+	0.490540i	$0.163200\pi$
$41$			6.28197i			0.981079i	−0.871419	+	0.490540i	$0.836800\pi$
$42$	2.90696	−	2.90696i	0.448553	−	0.448553i
$43$	−7.27794	−	7.27794i	−1.10987	−	1.10987i	−0.993166	−	0.116709i	$-0.962766\pi$
$43$	−7.27794	−	7.27794i	−1.10987	−	1.10987i	−0.116709	−	0.993166i	$-0.537234\pi$
$44$			2.43153i			0.366567i
$45$		0			0
$46$		−	1.83253i		−	0.270192i
$47$	6.15951	−	6.15951i	0.898456	−	0.898456i	−0.0968433	−	0.995300i	$-0.530875\pi$
$47$	6.15951	−	6.15951i	0.898456	−	0.898456i	0.995300	+	0.0968433i	$0.0308746\pi$
$48$	−2.10096	+	2.10096i	−0.303247	+	0.303247i
$49$			5.08556i			0.726508i
$50$		0			0
$51$			21.4721i			3.00670i
$52$	1.31299	+	1.31299i	0.182079	+	0.182079i
$53$	−9.37595	+	9.37595i	−1.28789	+	1.28789i	−0.351816	+	0.936069i	$0.614436\pi$
$53$	−9.37595	+	9.37595i	−1.28789	+	1.28789i	−0.936069	+	0.351816i	$0.885564\pi$
$54$		−	8.40274i		−	1.14347i
$55$		0			0
$56$			1.38363i			0.184896i
$57$	1.84278	−	12.8194i	0.244082	−	1.69797i
$58$	−0.317417	−	0.317417i	−0.0416789	−	0.0416789i
$59$	5.89371			0.767296			0.383648	−	0.923479i	$-0.374668\pi$
$59$	5.89371			0.767296			0.383648	+	0.923479i	$0.374668\pi$
$60$		0			0
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$	2.44949	−	2.44949i	0.311086	−	0.311086i
$63$	−5.70204	−	5.70204i	−0.718389	−	0.718389i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	7.22458			0.889285
$67$	−4.17716	−	4.17716i	−0.510322	−	0.510322i	0.404303	−	0.914625i	$-0.367514\pi$
$67$	−4.17716	−	4.17716i	−0.510322	−	0.510322i	−0.914625	+	0.404303i	$0.867514\pi$
$68$	−5.11008	−	5.11008i	−0.619688	−	0.619688i
$69$	−5.44482			−0.655479
$70$		0			0
$71$			14.6544i			1.73916i	0.493790	+	0.869581i	$0.335611\pi$
$71$			14.6544i			1.73916i	−0.493790	+	0.869581i	$0.664389\pi$
$72$	4.12106	+	4.12106i	0.485671	+	0.485671i
$73$	8.04521	+	8.04521i	0.941621	+	0.941621i	0.998387	−	0.0567667i	$-0.0180791\pi$
$73$	8.04521	+	8.04521i	0.941621	+	0.941621i	−0.0567667	+	0.998387i	$0.518079\pi$
$74$			6.51088i			0.756874i
$75$		0			0
$76$	2.61229	+	3.48940i	0.299650	+	0.400262i
$77$	2.37896	−	2.37896i	0.271107	−	0.271107i
$78$	3.90117	−	3.90117i	0.441721	−	0.441721i
$79$	6.23137			0.701084			0.350542	−	0.936547i	$-0.385997\pi$
$79$	6.23137			0.701084			0.350542	+	0.936547i	$0.385997\pi$
$80$		0			0
$81$	−7.48208			−0.831342
$82$	−4.44203	+	4.44203i	−0.490540	+	0.490540i
$83$	−11.7200	−	11.7200i	−1.28643	−	1.28643i	−0.936938	−	0.349494i	$-0.886353\pi$
$83$	−11.7200	−	11.7200i	−1.28643	−	1.28643i	−0.349494	−	0.936938i	$-0.613647\pi$
$84$	4.11106			0.448553
$85$		0			0
$86$		−	10.2926i		−	1.10987i
$87$	−0.943110	+	0.943110i	−0.101112	+	0.101112i
$88$	−1.71935	+	1.71935i	−0.183284	+	0.183284i
$89$	−3.31375			−0.351257			−0.175628	−	0.984457i	$-0.556196\pi$
$89$	−3.31375			−0.351257			−0.175628	+	0.984457i	$0.556196\pi$
$90$		0			0
$91$		−	2.56920i		−	0.269326i
$92$	1.29579	−	1.29579i	0.135096	−	0.135096i
$93$	−7.27794	−	7.27794i	−0.754687	−	0.754687i
$94$	8.71086			0.898456
$95$		0			0
$96$	−2.97120			−0.303247
$97$	−6.78718	−	6.78718i	−0.689134	−	0.689134i	0.272907	−	0.962041i	$-0.412015\pi$
$97$	−6.78718	−	6.78718i	−0.689134	−	0.689134i	−0.962041	+	0.272907i	$0.912015\pi$
$98$	−3.59603	+	3.59603i	−0.363254	+	0.363254i
$99$		−	14.1711i		−	1.42425i
$100$		0			0
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	−15.1831	+	15.1831i	−1.50335	+	1.50335i
$103$	−11.0298	+	11.0298i	−1.08680	+	1.08680i	−0.0909447	+	0.995856i	$0.528989\pi$
$103$	−11.0298	+	11.0298i	−1.08680	+	1.08680i	−0.995856	+	0.0909447i	$0.971011\pi$
$104$			1.85685i			0.182079i
$105$		0			0
$106$	−13.2596			−1.28789
$107$	3.75484	+	3.75484i	0.362994	+	0.362994i	0.864914	−	0.501920i	$-0.167373\pi$
$107$	3.75484	+	3.75484i	0.362994	+	0.362994i	−0.501920	+	0.864914i	$0.667373\pi$
$108$	5.94163	−	5.94163i	0.571734	−	0.571734i
$109$	10.9794			1.05163			0.525816	−	0.850598i	$-0.323760\pi$
$109$	10.9794			1.05163			0.525816	+	0.850598i	$0.323760\pi$
$110$		0			0
$111$	19.3451			1.83616
$112$	−0.978377	+	0.978377i	−0.0924479	+	0.0924479i
$113$	2.52329	−	2.52329i	0.237371	−	0.237371i	−0.578390	−	0.815761i	$-0.696319\pi$
$113$	2.52329	−	2.52329i	0.237371	−	0.237371i	0.815761	+	0.578390i	$0.196319\pi$
$114$	10.3677	−	7.76165i	0.971027	−	0.726945i
$115$		0			0
$116$		−	0.448895i		−	0.0416789i
$117$	−7.65220	−	7.65220i	−0.707446	−	0.707446i
$118$	4.16749	+	4.16749i	0.383648	+	0.383648i
$119$			9.99917i			0.916622i
$120$		0			0
$121$	−5.08765			−0.462513
$122$	−1.41421	−	1.41421i	−0.128037	−	0.128037i
$123$	13.1982	+	13.1982i	1.19004	+	1.19004i
$124$	3.46410			0.311086
$125$		0			0
$126$		−	8.06390i		−	0.718389i
$127$	9.25728	+	9.25728i	0.821451	+	0.821451i	0.986316	−	0.164865i	$-0.0527190\pi$
$127$	9.25728	+	9.25728i	0.821451	+	0.821451i	−0.164865	+	0.986316i	$0.552719\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−30.5813			−2.69253
$130$		0			0
$131$	−3.65611			−0.319436			−0.159718	−	0.987163i	$-0.551059\pi$
$131$	−3.65611			−0.319436			−0.159718	+	0.987163i	$0.551059\pi$
$132$	5.10855	+	5.10855i	0.444642	+	0.444642i
$133$	0.858147	−	5.96976i	0.0744107	−	0.517644i
$134$		−	5.90740i		−	0.510322i
$135$		0			0
$136$		−	7.22675i		−	0.619688i
$137$	9.68455	−	9.68455i	0.827407	−	0.827407i	−0.159751	−	0.987157i	$-0.551069\pi$
$137$	9.68455	−	9.68455i	0.827407	−	0.827407i	0.987157	+	0.159751i	$0.0510690\pi$
$138$	−3.85007	−	3.85007i	−0.327740	−	0.327740i
$139$			4.36152i			0.369939i	0.982744	+	0.184969i	$0.0592186\pi$
$139$			4.36152i			0.369939i	−0.982744	+	0.184969i	$0.940781\pi$
$140$		0			0
$141$		−	25.8817i		−	2.17964i
$142$	−10.3623	+	10.3623i	−0.869581	+	0.869581i
$143$	3.19259	−	3.19259i	0.266977	−	0.266977i
$144$			5.82806i			0.485671i
$145$		0			0
$146$			11.3776i			0.941621i
$147$	10.6845	+	10.6845i	0.881247	+	0.881247i
$148$	−4.60388	+	4.60388i	−0.378437	+	0.378437i
$149$			10.8631i			0.889937i	0.895546	+	0.444969i	$0.146785\pi$
$149$			10.8631i			0.889937i	−0.895546	+	0.444969i	$0.853215\pi$
$150$		0			0
$151$			4.85777i			0.395320i	0.980271	+	0.197660i	$0.0633341\pi$
$151$			4.85777i			0.395320i	−0.980271	+	0.197660i	$0.936666\pi$
$152$	−0.620212	+	4.31455i	−0.0503058	+	0.349956i
$153$	29.7818	+	29.7818i	2.40772	+	2.40772i
$154$	3.36435			0.271107
$155$		0			0
$156$	5.51709			0.441721
$157$	−17.0054	+	17.0054i	−1.35718	+	1.35718i	−0.479795	+	0.877381i	$0.659289\pi$
$157$	−17.0054	+	17.0054i	−1.35718	+	1.35718i	−0.877381	+	0.479795i	$0.840711\pi$
$158$	4.40624	+	4.40624i	0.350542	+	0.350542i
$159$			39.3970i			3.12438i
$160$		0			0
$161$	−2.53555			−0.199829
$162$	−5.29063	−	5.29063i	−0.415671	−	0.415671i
$163$	−12.0706	−	12.0706i	−0.945442	−	0.945442i	0.0531445	−	0.998587i	$-0.483076\pi$
$163$	−12.0706	−	12.0706i	−0.945442	−	0.945442i	−0.998587	+	0.0531445i	$0.983076\pi$
$164$	−6.28197			−0.490540
$165$		0			0
$166$		−	16.5745i		−	1.28643i
$167$	14.2631	+	14.2631i	1.10371	+	1.10371i	0.993959	+	0.109756i	$0.0350068\pi$
$167$	14.2631	+	14.2631i	1.10371	+	1.10371i	0.109756	+	0.993959i	$0.464993\pi$
$168$	2.90696	+	2.90696i	0.224277	+	0.224277i
$169$			9.55210i			0.734777i
$170$		0			0
$171$	−15.2246	−	20.3364i	−1.16425	−	1.55517i
$172$	7.27794	−	7.27794i	0.554937	−	0.554937i
$173$	−17.2504	+	17.2504i	−1.31152	+	1.31152i	−0.391226	+	0.920295i	$0.627949\pi$
$173$	−17.2504	+	17.2504i	−1.31152	+	1.31152i	−0.920295	+	0.391226i	$0.872051\pi$
$174$	−1.33376			−0.101112
$175$		0			0
$176$	−2.43153			−0.183284
$177$	12.3825	−	12.3825i	0.930722	−	0.930722i
$178$	−2.34317	−	2.34317i	−0.175628	−	0.175628i
$179$	−4.39957			−0.328839			−0.164420	−	0.986390i	$-0.552575\pi$
$179$	−4.39957			−0.328839			−0.164420	+	0.986390i	$0.552575\pi$
$180$		0			0
$181$			5.74263i			0.426847i	0.976960	+	0.213423i	$0.0684613\pi$
$181$			5.74263i			0.426847i	−0.976960	+	0.213423i	$0.931539\pi$
$182$	1.81670	−	1.81670i	0.134663	−	0.134663i
$183$	−4.20192	+	4.20192i	−0.310615	+	0.310615i
$184$	1.83253			0.135096
$185$		0			0
$186$		−	10.2926i		−	0.754687i
$187$	−12.4253	+	12.4253i	−0.908630	+	0.908630i
$188$	6.15951	+	6.15951i	0.449228	+	0.449228i
$189$	−11.6263			−0.845690
$190$		0			0
$191$	23.3451			1.68920			0.844598	−	0.535401i	$-0.179840\pi$
$191$	23.3451			1.68920			0.844598	+	0.535401i	$0.179840\pi$
$192$	−2.10096	−	2.10096i	−0.151624	−	0.151624i
$193$	2.53207	−	2.53207i	0.182263	−	0.182263i	−0.610078	−	0.792341i	$-0.708862\pi$
$193$	2.53207	−	2.53207i	0.182263	−	0.182263i	0.792341	+	0.610078i	$0.208862\pi$
$194$		−	9.59852i		−	0.689134i
$195$		0			0
$196$	−5.08556			−0.363254
$197$	2.09885	−	2.09885i	0.149537	−	0.149537i	−0.628374	−	0.777911i	$-0.716279\pi$
$197$	2.09885	−	2.09885i	0.149537	−	0.149537i	0.777911	+	0.628374i	$0.216279\pi$
$198$	10.0205	−	10.0205i	0.712125	−	0.712125i
$199$		−	24.2238i		−	1.71718i	−0.512666	−	0.858588i	$-0.671342\pi$
$199$		−	24.2238i		−	1.71718i	0.512666	−	0.858588i	$-0.328658\pi$
$200$		0			0
$201$	−17.5521			−1.23803
$202$	−4.24264	−	4.24264i	−0.298511	−	0.298511i
$203$	−0.439189	+	0.439189i	−0.0308250	+	0.0308250i
$204$	−21.4721			−1.50335
$205$		0			0
$206$	−15.5985			−1.08680
$207$	−7.55196	+	7.55196i	−0.524898	+	0.524898i
$208$	−1.31299	+	1.31299i	−0.0910397	+	0.0910397i
$209$	8.48460	−	6.35187i	0.586892	−	0.439368i
$210$		0			0
$211$		−	4.34969i		−	0.299445i	−0.988728	−	0.149723i	$-0.952162\pi$
$211$		−	4.34969i		−	0.299445i	0.988728	−	0.149723i	$-0.0478381\pi$
$212$	−9.37595	−	9.37595i	−0.643943	−	0.643943i
$213$	30.7884	+	30.7884i	2.10959	+	2.10959i
$214$			5.31014i			0.362994i
$215$		0			0
$216$	8.40274			0.571734
$217$	−3.38920	−	3.38920i	−0.230074	−	0.230074i
$218$	7.76358	+	7.76358i	0.525816	+	0.525816i
$219$	33.8053			2.28435
$220$		0			0
$221$			13.4190i			0.902660i
$222$	13.6791	+	13.6791i	0.918080	+	0.918080i
$223$	8.40384	−	8.40384i	0.562762	−	0.562762i	−0.367329	−	0.930091i	$-0.619728\pi$
$223$	8.40384	−	8.40384i	0.562762	−	0.562762i	0.930091	+	0.367329i	$0.119728\pi$
$224$	−1.38363			−0.0924479
$225$		0			0
$226$	3.56847			0.237371
$227$	−8.32589	−	8.32589i	−0.552609	−	0.552609i	0.374584	−	0.927193i	$-0.377785\pi$
$227$	−8.32589	−	8.32589i	−0.552609	−	0.552609i	−0.927193	+	0.374584i	$0.877785\pi$
$228$	12.8194	+	1.84278i	0.848986	+	0.122041i
$229$		−	19.4833i		−	1.28750i	−0.765238	−	0.643748i	$-0.777379\pi$
$229$		−	19.4833i		−	1.28750i	0.765238	−	0.643748i	$-0.222621\pi$
$230$		0			0
$231$		−	9.99618i		−	0.657700i
$232$	0.317417	−	0.317417i	0.0208394	−	0.0208394i
$233$	−13.2953	−	13.2953i	−0.871007	−	0.871007i	0.121575	−	0.992582i	$-0.461205\pi$
$233$	−13.2953	−	13.2953i	−0.871007	−	0.871007i	−0.992582	+	0.121575i	$0.961205\pi$
$234$		−	10.8218i		−	0.707446i
$235$		0			0
$236$			5.89371i			0.383648i
$237$	13.0919	−	13.0919i	0.850407	−	0.850407i
$238$	−7.07048	+	7.07048i	−0.458311	+	0.458311i
$239$			13.7943i			0.892280i	0.894963	+	0.446140i	$0.147202\pi$
$239$			13.7943i			0.892280i	−0.894963	+	0.446140i	$0.852798\pi$
$240$		0			0
$241$		−	16.5745i		−	1.06766i	−0.845592	−	0.533830i	$-0.820752\pi$
$241$		−	16.5745i		−	1.06766i	0.845592	−	0.533830i	$-0.179248\pi$
$242$	−3.59751	−	3.59751i	−0.231257	−	0.231257i
$243$	2.10535	−	2.10535i	0.135058	−	0.135058i
$244$		−	2.00000i		−	0.128037i
$245$		0			0
$246$			18.6650i			1.19004i
$247$	1.15164	−	8.01148i	0.0732773	−	0.509758i
$248$	2.44949	+	2.44949i	0.155543	+	0.155543i
$249$	−49.2463			−3.12086
$250$		0			0
$251$	−3.63848			−0.229659			−0.114830	−	0.993385i	$-0.536632\pi$
$251$	−3.63848			−0.229659			−0.114830	+	0.993385i	$0.536632\pi$
$252$	5.70204	−	5.70204i	0.359195	−	0.359195i
$253$	−3.15077	−	3.15077i	−0.198087	−	0.198087i
$254$			13.0918i			0.821451i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−11.1201	−	11.1201i	−0.693650	−	0.693650i	0.269383	−	0.963033i	$-0.413180\pi$
$257$	−11.1201	−	11.1201i	−0.693650	−	0.693650i	−0.963033	+	0.269383i	$0.913180\pi$
$258$	−21.6242	−	21.6242i	−1.34627	−	1.34627i
$259$	9.00867			0.559772
$260$		0			0
$261$			2.61619i			0.161938i
$262$	−2.58526	−	2.58526i	−0.159718	−	0.159718i
$263$	−6.36300	−	6.36300i	−0.392359	−	0.392359i	0.483168	−	0.875528i	$-0.339486\pi$
$263$	−6.36300	−	6.36300i	−0.392359	−	0.392359i	−0.875528	+	0.483168i	$0.839486\pi$
$264$			7.22458i			0.444642i
$265$		0			0
$266$	4.82806	−	3.61445i	0.296027	−	0.221616i
$267$	−6.96205	+	6.96205i	−0.426071	+	0.426071i
$268$	4.17716	−	4.17716i	0.255161	−	0.255161i
$269$	10.6004			0.646318			0.323159	−	0.946345i	$-0.395255\pi$
$269$	10.6004			0.646318			0.323159	+	0.946345i	$0.395255\pi$
$270$		0			0
$271$	−2.38098			−0.144635			−0.0723173	−	0.997382i	$-0.523039\pi$
$271$	−2.38098			−0.144635			−0.0723173	+	0.997382i	$0.523039\pi$
$272$	5.11008	−	5.11008i	0.309844	−	0.309844i
$273$	−5.39779	−	5.39779i	−0.326689	−	0.326689i
$274$	13.6960			0.827407
$275$		0			0
$276$		−	5.44482i		−	0.327740i
$277$	−9.30625	+	9.30625i	−0.559159	+	0.559159i	−0.929068	−	0.369909i	$-0.879389\pi$
$277$	−9.30625	+	9.30625i	−0.559159	+	0.559159i	0.369909	+	0.929068i	$0.379389\pi$
$278$	−3.08406	+	3.08406i	−0.184969	+	0.184969i
$279$	−20.1890			−1.20868
$280$		0			0
$281$			12.4627i			0.743465i	0.928340	+	0.371732i	$0.121236\pi$
$281$			12.4627i			0.743465i	−0.928340	+	0.371732i	$0.878764\pi$
$282$	18.3012	−	18.3012i	1.08982	−	1.08982i
$283$	9.26944	+	9.26944i	0.551011	+	0.551011i	0.926733	−	0.375722i	$-0.122605\pi$
$283$	9.26944	+	9.26944i	0.551011	+	0.551011i	−0.375722	+	0.926733i	$0.622605\pi$
$284$	−14.6544			−0.869581
$285$		0			0
$286$	4.51500			0.266977
$287$	6.14614	+	6.14614i	0.362795	+	0.362795i
$288$	−4.12106	+	4.12106i	−0.242836	+	0.242836i
$289$		−	35.2258i		−	2.07211i
$290$		0			0
$291$	−28.5192			−1.67182
$292$	−8.04521	+	8.04521i	−0.470810	+	0.470810i
$293$	15.8630	−	15.8630i	0.926724	−	0.926724i	−0.0707683	−	0.997493i	$-0.522545\pi$
$293$	15.8630	−	15.8630i	0.926724	−	0.926724i	0.997493	+	0.0707683i	$0.0225451\pi$
$294$			15.1102i			0.881247i
$295$		0			0
$296$	−6.51088			−0.378437
$297$	−14.4473	−	14.4473i	−0.838316	−	0.838316i
$298$	−7.68135	+	7.68135i	−0.444969	+	0.444969i
$299$	−3.40274			−0.196785
$300$		0			0
$301$	−14.2411			−0.820845
$302$	−3.43496	+	3.43496i	−0.197660	+	0.197660i
$303$	−12.6058	+	12.6058i	−0.724182	+	0.724182i
$304$	−3.48940	+	2.61229i	−0.200131	+	0.149825i
$305$		0			0
$306$			42.1179i			2.40772i
$307$	−15.6620	−	15.6620i	−0.893875	−	0.893875i	0.101010	−	0.994885i	$-0.467793\pi$
$307$	−15.6620	−	15.6620i	−0.893875	−	0.893875i	−0.994885	+	0.101010i	$0.967793\pi$
$308$	2.37896	+	2.37896i	0.135554	+	0.135554i
$309$			46.3464i			2.63656i
$310$		0			0
$311$	−10.5676			−0.599236			−0.299618	−	0.954059i	$-0.596859\pi$
$311$	−10.5676			−0.599236			−0.299618	+	0.954059i	$0.596859\pi$
$312$	3.90117	+	3.90117i	0.220860	+	0.220860i
$313$	−3.89448	−	3.89448i	−0.220129	−	0.220129i	0.588424	−	0.808553i	$-0.299749\pi$
$313$	−3.89448	−	3.89448i	−0.220129	−	0.220129i	−0.808553	+	0.588424i	$0.799749\pi$
$314$	−24.0492			−1.35718
$315$		0			0
$316$			6.23137i			0.350542i
$317$	−3.77959	−	3.77959i	−0.212283	−	0.212283i	0.592954	−	0.805237i	$-0.297962\pi$
$317$	−3.77959	−	3.77959i	−0.212283	−	0.212283i	−0.805237	+	0.592954i	$0.797962\pi$
$318$	−27.8579	+	27.8579i	−1.56219	+	1.56219i
$319$	−1.09150			−0.0611124
$320$		0			0
$321$	15.7775			0.880615
$322$	−1.79290	−	1.79290i	−0.0999147	−	0.0999147i
$323$	−4.48211	+	31.1801i	−0.249392	+	1.73491i
$324$		−	7.48208i		−	0.415671i
$325$		0			0
$326$		−	17.0704i		−	0.945442i
$327$	23.0672	−	23.0672i	1.27562	−	1.27562i
$328$	−4.44203	−	4.44203i	−0.245270	−	0.245270i
$329$		−	12.0526i		−	0.664484i
$330$		0			0
$331$			6.73087i			0.369962i	0.982742	+	0.184981i	$0.0592224\pi$
$331$			6.73087i			0.369962i	−0.982742	+	0.184981i	$0.940778\pi$
$332$	11.7200	−	11.7200i	0.643216	−	0.643216i
$333$	26.8317	−	26.8317i	1.47037	−	1.47037i
$334$			20.1711i			1.10371i
$335$		0			0
$336$			4.11106i			0.224277i
$337$	−2.68796	−	2.68796i	−0.146423	−	0.146423i	0.630095	−	0.776518i	$-0.283016\pi$
$337$	−2.68796	−	2.68796i	−0.146423	−	0.146423i	−0.776518	+	0.630095i	$0.783016\pi$
$338$	−6.75435	+	6.75435i	−0.367388	+	0.367388i
$339$		−	10.6026i		−	0.575857i
$340$		0			0
$341$		−	8.42308i		−	0.456135i
$342$	3.61463	−	25.1454i	0.195457	−	1.35971i
$343$	11.8242	+	11.8242i	0.638448	+	0.638448i
$344$	10.2926			0.554937
$345$		0			0
$346$	−24.3957			−1.31152
$347$	−10.7345	+	10.7345i	−0.576258	+	0.576258i	−0.933870	−	0.357612i	$-0.883591\pi$
$347$	−10.7345	+	10.7345i	−0.576258	+	0.576258i	0.357612	+	0.933870i	$0.383591\pi$
$348$	−0.943110	−	0.943110i	−0.0505560	−	0.0505560i
$349$		−	19.2111i		−	1.02835i	−0.857686	−	0.514174i	$-0.828098\pi$
$349$		−	19.2111i		−	1.02835i	0.857686	−	0.514174i	$-0.171902\pi$
$350$		0			0
$351$	−15.6026			−0.832808
$352$	−1.71935	−	1.71935i	−0.0916418	−	0.0916418i
$353$	−5.31409	−	5.31409i	−0.282840	−	0.282840i	0.551400	−	0.834241i	$-0.314094\pi$
$353$	−5.31409	−	5.31409i	−0.282840	−	0.282840i	−0.834241	+	0.551400i	$0.814094\pi$
$354$	17.5114			0.930722
$355$		0			0
$356$		−	3.31375i		−	0.175628i
$357$	21.0078	+	21.0078i	1.11185	+	1.11185i
$358$	−3.11097	−	3.11097i	−0.164420	−	0.164420i
$359$			8.87861i			0.468595i	0.972165	+	0.234297i	$0.0752790\pi$
$359$			8.87861i			0.468595i	−0.972165	+	0.234297i	$0.924721\pi$
$360$		0			0
$361$	5.35187	−	18.2307i	0.281677	−	0.959509i
$362$	−4.06065	+	4.06065i	−0.213423	+	0.213423i
$363$	−10.6889	+	10.6889i	−0.561024	+	0.561024i
$364$	2.56920			0.134663
$365$		0			0
$366$	−5.94241			−0.310615
$367$	3.22233	−	3.22233i	0.168204	−	0.168204i	−0.617985	−	0.786190i	$-0.712051\pi$
$367$	3.22233	−	3.22233i	0.168204	−	0.168204i	0.786190	+	0.617985i	$0.212051\pi$
$368$	1.29579	+	1.29579i	0.0675479	+	0.0675479i
$369$	36.6117			1.90593
$370$		0			0
$371$			18.3464i			0.952499i
$372$	7.27794	−	7.27794i	0.377343	−	0.377343i
$373$	14.8413	−	14.8413i	0.768456	−	0.768456i	−0.209379	−	0.977835i	$-0.567144\pi$
$373$	14.8413	−	14.8413i	0.768456	−	0.768456i	0.977835	+	0.209379i	$0.0671442\pi$
$374$	−17.5721			−0.908630
$375$		0			0
$376$			8.71086i			0.449228i
$377$	−0.589396	+	0.589396i	−0.0303554	+	0.0303554i
$378$	−8.22105	−	8.22105i	−0.422845	−	0.422845i
$379$	17.7572			0.912126			0.456063	−	0.889947i	$-0.349259\pi$
$379$	17.7572			0.912126			0.456063	+	0.889947i	$0.349259\pi$
$380$		0			0
$381$	38.8983			1.99282
$382$	16.5075	+	16.5075i	0.844598	+	0.844598i
$383$	−7.73086	+	7.73086i	−0.395028	+	0.395028i	−0.876475	−	0.481447i	$-0.840111\pi$
$383$	−7.73086	+	7.73086i	−0.395028	+	0.395028i	0.481447	+	0.876475i	$0.340111\pi$
$384$		−	2.97120i		−	0.151624i
$385$		0			0
$386$	3.58089			0.182263
$387$	−42.4162	+	42.4162i	−2.15614	+	2.15614i
$388$	6.78718	−	6.78718i	0.344567	−	0.344567i
$389$		−	9.37806i		−	0.475487i	−0.971328	−	0.237743i	$-0.923592\pi$
$389$		−	9.37806i		−	0.475487i	0.971328	−	0.237743i	$-0.0764077\pi$
$390$		0			0
$391$	13.2432			0.669738
$392$	−3.59603	−	3.59603i	−0.181627	−	0.181627i
$393$	−7.68135	+	7.68135i	−0.387473	+	0.387473i
$394$	2.96822			0.149537
$395$		0			0
$396$	14.1711			0.712125
$397$	−22.6813	+	22.6813i	−1.13834	+	1.13834i	−0.149593	+	0.988748i	$0.547796\pi$
$397$	−22.6813	+	22.6813i	−1.13834	+	1.13834i	−0.988748	+	0.149593i	$0.952204\pi$
$398$	17.1288	−	17.1288i	0.858588	−	0.858588i
$399$	−10.7393	−	14.3451i	−0.537637	−	0.718156i
$400$		0			0
$401$		−	5.38418i		−	0.268873i	−0.990922	−	0.134437i	$-0.957078\pi$
$401$		−	5.38418i		−	0.268873i	0.990922	−	0.134437i	$-0.0429225\pi$
$402$	−12.4112	−	12.4112i	−0.619015	−	0.619015i
$403$	−4.54834	−	4.54834i	−0.226569	−	0.226569i
$404$		−	6.00000i		−	0.298511i
$405$		0			0
$406$	−0.621107			−0.0308250
$407$	11.1945	+	11.1945i	0.554891	+	0.554891i
$408$	−15.1831	−	15.1831i	−0.751675	−	0.751675i
$409$	32.0256			1.58356			0.791781	−	0.610805i	$-0.209154\pi$
$409$	32.0256			1.58356			0.791781	+	0.610805i	$0.209154\pi$
$410$		0			0
$411$		−	40.6937i		−	2.00727i
$412$	−11.0298	−	11.0298i	−0.543400	−	0.543400i
$413$	5.76627	−	5.76627i	0.283740	−	0.283740i
$414$	−10.6801			−0.524898
$415$		0			0
$416$	−1.85685			−0.0910397
$417$	9.16337	+	9.16337i	0.448732	+	0.448732i
$418$	10.4910	+	1.50807i	0.513130	+	0.0737619i
$419$		−	11.8096i		−	0.576937i	−0.957489	−	0.288468i	$-0.906854\pi$
$419$		−	11.8096i		−	0.576937i	0.957489	−	0.288468i	$-0.0931460\pi$
$420$		0			0
$421$		−	19.1530i		−	0.933462i	−0.884399	−	0.466731i	$-0.845432\pi$
$421$		−	19.1530i		−	0.933462i	0.884399	−	0.466731i	$-0.154568\pi$
$422$	3.07570	−	3.07570i	0.149723	−	0.149723i
$423$	−35.8980	−	35.8980i	−1.74542	−	1.74542i
$424$		−	13.2596i		−	0.643943i
$425$		0			0
$426$			43.5414i			2.10959i
$427$	−1.95675	+	1.95675i	−0.0946940	+	0.0946940i
$428$	−3.75484	+	3.75484i	−0.181497	+	0.181497i
$429$		−	13.4150i		−	0.647682i
$430$		0			0
$431$		−	26.3206i		−	1.26782i	−0.773407	−	0.633909i	$-0.781449\pi$
$431$		−	26.3206i		−	1.26782i	0.773407	−	0.633909i	$-0.218551\pi$
$432$	5.94163	+	5.94163i	0.285867	+	0.285867i
$433$	27.9402	−	27.9402i	1.34272	−	1.34272i	0.449379	−	0.893341i	$-0.351645\pi$
$433$	27.9402	−	27.9402i	1.34272	−	1.34272i	0.893341	−	0.449379i	$-0.148355\pi$
$434$		−	4.79305i		−	0.230074i
$435$		0			0
$436$			10.9794i			0.525816i
$437$	−7.90654	−	1.13656i	−0.378221	−	0.0543689i
$438$	23.9040	+	23.9040i	1.14218	+	1.14218i
$439$	−19.8071			−0.945343			−0.472671	−	0.881239i	$-0.656710\pi$
$439$	−19.8071			−0.945343			−0.472671	+	0.881239i	$0.656710\pi$
$440$		0			0
$441$	29.6389			1.41138
$442$	−9.48867	+	9.48867i	−0.451330	+	0.451330i
$443$	−21.6600	−	21.6600i	−1.02910	−	1.02910i	−0.999564	−	0.0295348i	$-0.990597\pi$
$443$	−21.6600	−	21.6600i	−1.02910	−	1.02910i	−0.0295348	−	0.999564i	$-0.509403\pi$
$444$			19.3451i			0.918080i
$445$		0			0
$446$	11.8848			0.562762
$447$	22.8229	+	22.8229i	1.07948	+	1.07948i
$448$	−0.978377	−	0.978377i	−0.0462240	−	0.0462240i
$449$	38.7528			1.82886			0.914429	−	0.404746i	$-0.132640\pi$
$449$	38.7528			1.82886			0.914429	+	0.404746i	$0.132640\pi$
$450$		0			0
$451$			15.2748i			0.719263i
$452$	2.52329	+	2.52329i	0.118685	+	0.118685i
$453$	10.2060	+	10.2060i	0.479518	+	0.479518i
$454$		−	11.7746i		−	0.552609i
$455$		0			0
$456$	7.76165	+	10.3677i	0.363473	+	0.485514i
$457$	−1.12501	+	1.12501i	−0.0526257	+	0.0526257i	−0.732930	−	0.680304i	$-0.761848\pi$
$457$	−1.12501	+	1.12501i	−0.0526257	+	0.0526257i	0.680304	+	0.732930i	$0.261848\pi$
$458$	13.7768	−	13.7768i	0.643748	−	0.643748i
$459$	60.7244			2.83437
$460$		0			0
$461$	8.58920			0.400039			0.200019	−	0.979792i	$-0.435899\pi$
$461$	8.58920			0.400039			0.200019	+	0.979792i	$0.435899\pi$
$462$	7.06837	−	7.06837i	0.328850	−	0.328850i
$463$	−4.18856	−	4.18856i	−0.194659	−	0.194659i	0.603047	−	0.797706i	$-0.293953\pi$
$463$	−4.18856	−	4.18856i	−0.194659	−	0.194659i	−0.797706	+	0.603047i	$0.793953\pi$
$464$	0.448895			0.0208394
$465$		0			0
$466$		−	18.8025i		−	0.871007i
$467$	12.3180	−	12.3180i	0.570008	−	0.570008i	−0.362122	−	0.932131i	$-0.617948\pi$
$467$	12.3180	−	12.3180i	0.570008	−	0.570008i	0.932131	+	0.362122i	$0.117948\pi$
$468$	7.65220	−	7.65220i	0.353723	−	0.353723i
$469$	−8.17368			−0.377426
$470$		0			0
$471$			71.4551i			3.29248i
$472$	−4.16749	+	4.16749i	−0.191824	+	0.191824i
$473$	−17.6965	−	17.6965i	−0.813688	−	0.813688i
$474$	18.5147			0.850407
$475$		0			0
$476$	−9.99917			−0.458311
$477$	54.6436	+	54.6436i	2.50196	+	2.50196i
$478$	−9.75405	+	9.75405i	−0.446140	+	0.446140i
$479$			29.5368i			1.34957i	0.738014	+	0.674786i	$0.235764\pi$
$479$			29.5368i			1.34957i	−0.738014	+	0.674786i	$0.764236\pi$
$480$		0			0
$481$	12.0897			0.551245
$482$	11.7200	−	11.7200i	0.533830	−	0.533830i
$483$	−5.32709	+	5.32709i	−0.242391	+	0.242391i
$484$		−	5.08765i		−	0.231257i
$485$		0			0
$486$	2.97742			0.135058
$487$	−20.2288	−	20.2288i	−0.916655	−	0.916655i	0.0801298	−	0.996784i	$-0.474467\pi$
$487$	−20.2288	−	20.2288i	−0.916655	−	0.916655i	−0.996784	+	0.0801298i	$0.974467\pi$
$488$	1.41421	−	1.41421i	0.0640184	−	0.0640184i
$489$	−50.7197			−2.29362
$490$		0			0
$491$	26.5192			1.19679			0.598397	−	0.801200i	$-0.295805\pi$
$491$	26.5192			1.19679			0.598397	+	0.801200i	$0.295805\pi$
$492$	−13.1982	+	13.1982i	−0.595019	+	0.595019i
$493$	2.29389	−	2.29389i	0.103312	−	0.103312i
$494$	6.47931	−	4.85064i	0.291518	−	0.218241i
$495$		0			0
$496$			3.46410i			0.155543i
$497$	14.3376	+	14.3376i	0.643128	+	0.643128i
$498$	−34.8224	−	34.8224i	−1.56043	−	1.56043i
$499$			8.51500i			0.381184i	0.981669	+	0.190592i	$0.0610407\pi$
$499$			8.51500i			0.381184i	−0.981669	+	0.190592i	$0.938959\pi$
$500$		0			0
$501$	59.9325			2.67759
$502$	−2.57280	−	2.57280i	−0.114830	−	0.114830i
$503$	25.6567	+	25.6567i	1.14398	+	1.14398i	0.987716	+	0.156261i	$0.0499440\pi$
$503$	25.6567	+	25.6567i	1.14398	+	1.14398i	0.156261	+	0.987716i	$0.450056\pi$
$504$	8.06390			0.359195
$505$		0			0
$506$		−	4.45585i		−	0.198087i
$507$	20.0686	+	20.0686i	0.891276	+	0.891276i
$508$	−9.25728	+	9.25728i	−0.410725	+	0.410725i
$509$	21.5712			0.956126			0.478063	−	0.878326i	$-0.341339\pi$
$509$	21.5712			0.956126			0.478063	+	0.878326i	$0.341339\pi$
$510$		0			0
$511$	15.7425			0.696407
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−36.2540	−	5.21148i	−1.60065	−	0.230092i
$514$		−	15.7261i		−	0.693650i
$515$		0			0
$516$		−	30.5813i		−	1.34627i
$517$	14.9770	−	14.9770i	0.658690	−	0.658690i
$518$	6.37009	+	6.37009i	0.279886	+	0.279886i
$519$			72.4846i			3.18172i
$520$		0			0
$521$			7.17976i			0.314551i	0.987555	+	0.157276i	$0.0502711\pi$
$521$			7.17976i			0.314551i	−0.987555	+	0.157276i	$0.949729\pi$
$522$	−1.84992	+	1.84992i	−0.0809689	+	0.0809689i
$523$	28.0501	−	28.0501i	1.22654	−	1.22654i	0.261281	−	0.965263i	$-0.415855\pi$
$523$	28.0501	−	28.0501i	1.22654	−	1.22654i	0.965263	−	0.261281i	$-0.0841451\pi$
$524$		−	3.65611i		−	0.159718i
$525$		0			0
$526$		−	8.99864i		−	0.392359i
$527$	17.7018	+	17.7018i	0.771104	+	0.771104i
$528$	−5.10855	+	5.10855i	−0.222321	+	0.222321i
$529$		−	19.6418i		−	0.853993i
$530$		0			0
$531$		−	34.3489i		−	1.49062i
$532$	5.96976	+	0.858147i	0.258822	+	0.0372054i
$533$	8.24819	+	8.24819i	0.357269	+	0.357269i
$534$	−9.84582			−0.426071
$535$		0			0
$536$	5.90740			0.255161
$537$	−9.24331	+	9.24331i	−0.398878	+	0.398878i
$538$	7.49562	+	7.49562i	0.323159	+	0.323159i
$539$			12.3657i			0.532628i
$540$		0			0
$541$	19.8272			0.852439			0.426220	−	0.904620i	$-0.359845\pi$
$541$	19.8272			0.852439			0.426220	+	0.904620i	$0.359845\pi$
$542$	−1.68361	−	1.68361i	−0.0723173	−	0.0723173i
$543$	12.0650	+	12.0650i	0.517760	+	0.517760i
$544$	7.22675			0.309844
$545$		0			0
$546$		−	7.63363i		−	0.326689i
$547$	−0.784465	−	0.784465i	−0.0335413	−	0.0335413i	0.690137	−	0.723679i	$-0.257550\pi$
$547$	−0.784465	−	0.784465i	−0.0335413	−	0.0335413i	−0.723679	+	0.690137i	$0.757550\pi$
$548$	9.68455	+	9.68455i	0.413703	+	0.413703i
$549$			11.6561i			0.497471i
$550$		0			0
$551$	−1.56638	+	1.17264i	−0.0667299	+	0.0499563i
$552$	3.85007	−	3.85007i	0.163870	−	0.163870i
$553$	6.09663	−	6.09663i	0.259255	−	0.259255i
$554$	−13.1610			−0.559159
$555$		0			0
$556$	−4.36152			−0.184969
$557$	17.5686	−	17.5686i	0.744407	−	0.744407i	−0.229016	−	0.973423i	$-0.573551\pi$
$557$	17.5686	−	17.5686i	0.744407	−	0.744407i	0.973423	+	0.229016i	$0.0735508\pi$
$558$	−14.2758	−	14.2758i	−0.604341	−	0.604341i
$559$	−19.1118			−0.808341
$560$		0			0
$561$			52.2102i			2.20432i
$562$	−8.81249	+	8.81249i	−0.371732	+	0.371732i
$563$	9.66803	−	9.66803i	0.407459	−	0.407459i	−0.473393	−	0.880852i	$-0.656971\pi$
$563$	9.66803	−	9.66803i	0.407459	−	0.407459i	0.880852	+	0.473393i	$0.156971\pi$
$564$	25.8817			1.08982
$565$		0			0
$566$			13.1090i			0.551011i
$567$	−7.32030	+	7.32030i	−0.307424	+	0.307424i
$568$	−10.3623	−	10.3623i	−0.434791	−	0.434791i
$569$	−34.9880			−1.46677			−0.733387	−	0.679812i	$-0.762061\pi$
$569$	−34.9880			−1.46677			−0.733387	+	0.679812i	$0.762061\pi$
$570$		0			0
$571$	−28.1053			−1.17617			−0.588085	−	0.808799i	$-0.700118\pi$
$571$	−28.1053			−1.17617			−0.588085	+	0.808799i	$0.700118\pi$
$572$	3.19259	+	3.19259i	0.133489	+	0.133489i
$573$	49.0472	−	49.0472i	2.04898	−	2.04898i
$574$			8.69195i			0.362795i
$575$		0			0
$576$	−5.82806			−0.242836
$577$	11.4812	−	11.4812i	0.477969	−	0.477969i	−0.426513	−	0.904482i	$-0.640258\pi$
$577$	11.4812	−	11.4812i	0.477969	−	0.477969i	0.904482	+	0.426513i	$0.140258\pi$
$578$	24.9084	−	24.9084i	1.03605	−	1.03605i
$579$		−	10.6396i		−	0.442165i
$580$		0			0
$581$	−22.9331			−0.951425
$582$	−20.1661	−	20.1661i	−0.835912	−	0.835912i
$583$	−22.7979	+	22.7979i	−0.944193	+	0.944193i
$584$	−11.3776			−0.470810
$585$		0			0
$586$	22.4336			0.926724
$587$	11.5256	−	11.5256i	0.475713	−	0.475713i	−0.428045	−	0.903758i	$-0.640797\pi$
$587$	11.5256	−	11.5256i	0.475713	−	0.475713i	0.903758	+	0.428045i	$0.140797\pi$
$588$	−10.6845	+	10.6845i	−0.440623	+	0.440623i
$589$	−9.04924	−	12.0876i	−0.372867	−	0.498063i
$590$		0			0
$591$		−	8.81920i		−	0.362774i
$592$	−4.60388	−	4.60388i	−0.189219	−	0.189219i
$593$	9.63025	+	9.63025i	0.395467	+	0.395467i	0.876631	−	0.481164i	$-0.159786\pi$
$593$	9.63025	+	9.63025i	0.395467	+	0.395467i	−0.481164	+	0.876631i	$0.659786\pi$
$594$		−	20.4315i		−	0.838316i
$595$		0			0
$596$	−10.8631			−0.444969
$597$	−50.8931	−	50.8931i	−2.08292	−	2.08292i
$598$	−2.40610	−	2.40610i	−0.0983927	−	0.0983927i
$599$	−26.3407			−1.07625			−0.538125	−	0.842865i	$-0.680867\pi$
$599$	−26.3407			−1.07625			−0.538125	+	0.842865i	$0.680867\pi$
$600$		0			0
$601$		−	4.31129i		−	0.175861i	−0.996127	−	0.0879306i	$-0.971975\pi$
$601$		−	4.31129i		−	0.175861i	0.996127	−	0.0879306i	$-0.0280254\pi$
$602$	−10.0700	−	10.0700i	−0.410423	−	0.410423i
$603$	−24.3447	+	24.3447i	−0.991395	+	0.991395i
$604$	−4.85777			−0.197660
$605$		0			0
$606$	−17.8272			−0.724182
$607$	1.98494	+	1.98494i	0.0805664	+	0.0805664i	0.746242	−	0.665675i	$-0.231856\pi$
$607$	1.98494	+	1.98494i	0.0805664	+	0.0805664i	−0.665675	+	0.746242i	$0.731856\pi$
$608$	−4.31455	−	0.620212i	−0.174978	−	0.0251529i
$609$			1.84543i			0.0747808i
$610$		0			0
$611$		−	16.1748i		−	0.654362i
$612$	−29.7818	+	29.7818i	−1.20386	+	1.20386i
$613$	−4.06979	−	4.06979i	−0.164377	−	0.164377i	0.620125	−	0.784503i	$-0.287082\pi$
$613$	−4.06979	−	4.06979i	−0.164377	−	0.164377i	−0.784503	+	0.620125i	$0.787082\pi$
$614$		−	22.1494i		−	0.893875i
$615$		0			0
$616$			3.36435i			0.135554i
$617$	−24.2219	+	24.2219i	−0.975137	+	0.975137i	−0.999698	−	0.0245613i	$-0.992181\pi$
$617$	−24.2219	+	24.2219i	−0.975137	+	0.975137i	0.0245613	+	0.999698i	$0.492181\pi$
$618$	−32.7719	+	32.7719i	−1.31828	+	1.31828i
$619$		−	39.0342i		−	1.56892i	−0.620182	−	0.784458i	$-0.712941\pi$
$619$		−	39.0342i		−	1.56892i	0.620182	−	0.784458i	$-0.287059\pi$
$620$		0			0
$621$			15.3983i			0.617911i
$622$	−7.47245	−	7.47245i	−0.299618	−	0.299618i
$623$	−3.24210	+	3.24210i	−0.129892	+	0.129892i
$624$			5.51709i			0.220860i
$625$		0			0
$626$		−	5.50762i		−	0.220129i
$627$	4.48077	−	31.1708i	0.178945	−	1.24484i
$628$	−17.0054	−	17.0054i	−0.678588	−	0.678588i
$629$	−47.0524			−1.87610
$630$		0			0
$631$	−15.9507			−0.634988			−0.317494	−	0.948260i	$-0.602841\pi$
$631$	−15.9507			−0.634988			−0.317494	+	0.948260i	$0.602841\pi$
$632$	−4.40624	+	4.40624i	−0.175271	+	0.175271i
$633$	−9.13853	−	9.13853i	−0.363224	−	0.363224i
$634$		−	5.34515i		−	0.212283i
$635$		0			0
$636$	−39.3970			−1.56219
$637$	6.67730	+	6.67730i	0.264564	+	0.264564i
$638$	−0.771809	−	0.771809i	−0.0305562	−	0.0305562i
$639$	85.4070			3.37865
$640$		0			0
$641$			42.1678i			1.66553i	0.553629	+	0.832763i	$0.313242\pi$
$641$			42.1678i			1.66553i	−0.553629	+	0.832763i	$0.686758\pi$
$642$	11.1564	+	11.1564i	0.440307	+	0.440307i
$643$	−3.77141	−	3.77141i	−0.148730	−	0.148730i	0.628821	−	0.777550i	$-0.283538\pi$
$643$	−3.77141	−	3.77141i	−0.148730	−	0.148730i	−0.777550	+	0.628821i	$0.783538\pi$
$644$		−	2.53555i		−	0.0999147i
$645$		0			0
$646$	−25.2170	+	18.8784i	−0.992151	+	0.742759i
$647$	4.69344	−	4.69344i	0.184518	−	0.184518i	−0.608803	−	0.793321i	$-0.708350\pi$
$647$	4.69344	−	4.69344i	0.184518	−	0.184518i	0.793321	+	0.608803i	$0.208350\pi$
$648$	5.29063	−	5.29063i	0.207836	−	0.207836i
$649$	14.3308			0.562532
$650$		0			0
$651$	−14.2411			−0.558154
$652$	12.0706	−	12.0706i	0.472721	−	0.472721i
$653$	18.6820	+	18.6820i	0.731084	+	0.731084i	0.970834	−	0.239751i	$-0.0770658\pi$
$653$	18.6820	+	18.6820i	0.731084	+	0.731084i	−0.239751	+	0.970834i	$0.577066\pi$
$654$	32.6219			1.27562
$655$		0			0
$656$		−	6.28197i		−	0.245270i
$657$	46.8880	−	46.8880i	1.82927	−	1.82927i
$658$	8.52250	−	8.52250i	0.332242	−	0.332242i
$659$	−6.58693			−0.256590			−0.128295	−	0.991736i	$-0.540950\pi$
$659$	−6.58693			−0.256590			−0.128295	+	0.991736i	$0.540950\pi$
$660$		0			0
$661$		−	6.27981i		−	0.244256i	−0.992514	−	0.122128i	$-0.961028\pi$
$661$		−	6.27981i		−	0.244256i	0.992514	−	0.122128i	$-0.0389719\pi$
$662$	−4.75944	+	4.75944i	−0.184981	+	0.184981i
$663$	28.1928	+	28.1928i	1.09492	+	1.09492i
$664$	16.5745			0.643216
$665$		0			0
$666$	37.9458			1.47037
$667$	0.581675	+	0.581675i	0.0225226	+	0.0225226i
$668$	−14.2631	+	14.2631i	−0.551857	+	0.551857i
$669$		−	35.3122i		−	1.36525i
$670$		0			0
$671$	−4.86307			−0.187737
$672$	−2.90696	+	2.90696i	−0.112138	+	0.112138i
$673$	−21.3284	+	21.3284i	−0.822148	+	0.822148i	−0.986416	−	0.164268i	$-0.947474\pi$
$673$	−21.3284	+	21.3284i	−0.822148	+	0.822148i	0.164268	+	0.986416i	$0.447474\pi$
$674$		−	3.80135i		−	0.146423i
$675$		0			0
$676$	−9.55210			−0.367388
$677$	−0.766712	−	0.766712i	−0.0294671	−	0.0294671i	0.692220	−	0.721687i	$-0.256633\pi$
$677$	−0.766712	−	0.766712i	−0.0294671	−	0.0294671i	−0.721687	+	0.692220i	$0.756633\pi$
$678$	7.49720	−	7.49720i	0.287928	−	0.287928i
$679$	−13.2808			−0.509672
$680$		0			0
$681$	−34.9847			−1.34062
$682$	5.95601	−	5.95601i	0.228068	−	0.228068i
$683$	−3.22088	+	3.22088i	−0.123244	+	0.123244i	−0.766038	−	0.642795i	$-0.777775\pi$
$683$	−3.22088	+	3.22088i	−0.123244	+	0.123244i	0.642795	+	0.766038i	$0.277775\pi$
$684$	20.3364	−	15.2246i	0.777583	−	0.582126i
$685$		0			0
$686$			16.7220i			0.638448i
$687$	−40.9337	−	40.9337i	−1.56172	−	1.56172i
$688$	7.27794	+	7.27794i	0.277469	+	0.277469i
$689$			24.6211i			0.937989i
$690$		0			0
$691$	−28.2588			−1.07501			−0.537507	−	0.843259i	$-0.680634\pi$
$691$	−28.2588			−1.07501			−0.537507	+	0.843259i	$0.680634\pi$
$692$	−17.2504	−	17.2504i	−0.655760	−	0.655760i
$693$	−13.8647	−	13.8647i	−0.526676	−	0.526676i
$694$	−15.1809			−0.576258
$695$		0			0
$696$		−	1.33376i		−	0.0505560i
$697$	−32.1014	−	32.1014i	−1.21593	−	1.21593i
$698$	13.5843	−	13.5843i	0.514174	−	0.514174i
$699$	−55.8659			−2.11304
$700$		0			0
$701$	29.5844			1.11739			0.558694	−	0.829374i	$-0.311302\pi$
$701$	29.5844			1.11739			0.558694	+	0.829374i	$0.311302\pi$
$702$	−11.0327	−	11.0327i	−0.416404	−	0.416404i
$703$	28.0915	+	4.03812i	1.05949	+	0.152301i
$704$		−	2.43153i		−	0.0916418i
$705$		0			0
$706$		−	7.51525i		−	0.282840i
$707$	−5.87026	+	5.87026i	−0.220774	+	0.220774i
$708$	12.3825	+	12.3825i	0.465361	+	0.465361i
$709$		−	36.4475i		−	1.36881i	−0.729100	−	0.684407i	$-0.760061\pi$
$709$		−	36.4475i		−	1.36881i	0.729100	−	0.684407i	$-0.239939\pi$
$710$		0			0
$711$		−	36.3168i		−	1.36199i
$712$	2.34317	−	2.34317i	0.0878142	−	0.0878142i
$713$	−4.48876	+	4.48876i	−0.168105	+	0.168105i
$714$			29.7096i			1.11185i
$715$		0			0
$716$		−	4.39957i		−	0.164420i
$717$	28.9813	+	28.9813i	1.08233	+	1.08233i
$718$	−6.27812	+	6.27812i	−0.234297	+	0.234297i
$719$			23.3451i			0.870627i	0.900279	+	0.435314i	$0.143362\pi$
$719$			23.3451i			0.870627i	−0.900279	+	0.435314i	$0.856638\pi$
$720$		0			0
$721$			21.5827i			0.803780i
$722$	16.6754	−	9.10669i	0.620593	−	0.338916i
$723$	−34.8224	−	34.8224i	−1.29506	−	1.29506i
$724$	−5.74263			−0.213423
$725$		0			0
$726$	−15.1164			−0.561024
$727$	34.8179	−	34.8179i	1.29132	−	1.29132i	0.357355	−	0.933969i	$-0.383679\pi$
$727$	34.8179	−	34.8179i	1.29132	−	1.29132i	0.933969	−	0.357355i	$-0.116321\pi$
$728$	1.81670	+	1.81670i	0.0673315	+	0.0673315i
$729$		−	31.2928i		−	1.15899i
$730$		0			0
$731$	74.3817			2.75111
$732$	−4.20192	−	4.20192i	−0.155307	−	0.155307i
$733$	−8.05487	−	8.05487i	−0.297513	−	0.297513i	0.542526	−	0.840039i	$-0.317468\pi$
$733$	−8.05487	−	8.05487i	−0.297513	−	0.297513i	−0.840039	+	0.542526i	$0.817468\pi$
$734$	4.55706			0.168204
$735$		0			0
$736$			1.83253i			0.0675479i
$737$	−10.1569	−	10.1569i	−0.374135	−	0.374135i
$738$	25.8884	+	25.8884i	0.952965	+	0.952965i
$739$		−	14.0042i		−	0.515152i	−0.966258	−	0.257576i	$-0.917076\pi$
$739$		−	14.0042i		−	0.515152i	0.966258	−	0.257576i	$-0.0829238\pi$
$740$		0			0
$741$	−14.4122	−	19.2514i	−0.529447	−	0.707216i
$742$	−12.9729	+	12.9729i	−0.476249	+	0.476249i
$743$	−19.1875	+	19.1875i	−0.703922	+	0.703922i	−0.965250	−	0.261328i	$-0.915840\pi$
$743$	−19.1875	+	19.1875i	−0.703922	+	0.703922i	0.261328	+	0.965250i	$0.415840\pi$
$744$	10.2926			0.377343
$745$		0			0
$746$	20.9888			0.768456
$747$	−68.3046	+	68.3046i	−2.49913	+	2.49913i
$748$	−12.4253	−	12.4253i	−0.454315	−	0.454315i
$749$	7.34729			0.268464
$750$		0			0
$751$		−	0.675311i		−	0.0246424i	−0.999924	−	0.0123212i	$-0.996078\pi$
$751$		−	0.675311i		−	0.0246424i	0.999924	−	0.0123212i	$-0.00392207\pi$
$752$	−6.15951	+	6.15951i	−0.224614	+	0.224614i
$753$	−7.64431	+	7.64431i	−0.278574	+	0.278574i
$754$	−0.833532			−0.0303554
$755$		0			0
$756$		−	11.6263i		−	0.422845i
$757$	11.3477	−	11.3477i	0.412440	−	0.412440i	−0.470148	−	0.882588i	$-0.655799\pi$
$757$	11.3477	−	11.3477i	0.412440	−	0.412440i	0.882588	+	0.470148i	$0.155799\pi$
$758$	12.5562	+	12.5562i	0.456063	+	0.456063i
$759$	−13.2393			−0.480555
$760$		0			0
$761$	−27.0715			−0.981342			−0.490671	−	0.871345i	$-0.663248\pi$
$761$	−27.0715			−0.981342			−0.490671	+	0.871345i	$0.663248\pi$
$762$	27.5053	+	27.5053i	0.996411	+	0.996411i
$763$	10.7419	−	10.7419i	0.388885	−	0.388885i
$764$			23.3451i			0.844598i
$765$		0			0
$766$	−10.9331			−0.395028
$767$	7.73841	−	7.73841i	0.279418	−	0.279418i
$768$	2.10096	−	2.10096i	0.0758118	−	0.0758118i
$769$			33.4854i			1.20752i	0.797168	+	0.603758i	$0.206331\pi$
$769$			33.4854i			1.20752i	−0.797168	+	0.603758i	$0.793669\pi$
$770$		0			0
$771$	−46.7256			−1.68278
$772$	2.53207	+	2.53207i	0.0911313	+	0.0911313i
$773$	12.2649	−	12.2649i	0.441137	−	0.441137i	−0.451257	−	0.892394i	$-0.649024\pi$
$773$	12.2649	−	12.2649i	0.441137	−	0.441137i	0.892394	+	0.451257i	$0.149024\pi$
$774$	−59.9856			−2.15614
$775$		0			0
$776$	9.59852			0.344567
$777$	18.9268	−	18.9268i	0.678997	−	0.678997i
$778$	6.63129	−	6.63129i	0.237743	−	0.237743i
$779$	16.4103	+	21.9203i	0.587962	+	0.785378i
$780$		0			0
$781$			35.6328i			1.27504i
$782$	9.36437	+	9.36437i	0.334869	+	0.334869i
$783$	2.66717	+	2.66717i	0.0953169	+	0.0953169i
$784$		−	5.08556i		−	0.181627i
$785$		0			0
$786$	−10.8631			−0.387473
$787$	20.4103	+	20.4103i	0.727549	+	0.727549i	0.970131	−	0.242582i	$-0.0779944\pi$
$787$	20.4103	+	20.4103i	0.727549	+	0.727549i	−0.242582	+	0.970131i	$0.577994\pi$
$788$	2.09885	+	2.09885i	0.0747685	+	0.0747685i
$789$	−26.7368			−0.951855
$790$		0			0
$791$		−	4.93745i		−	0.175556i
$792$	10.0205	+	10.0205i	0.356063	+	0.356063i
$793$	−2.62599	+	2.62599i	−0.0932515	+	0.0932515i
$794$	−32.0762			−1.13834
$795$		0			0
$796$	24.2238			0.858588
$797$	−15.8630	−	15.8630i	−0.561895	−	0.561895i	0.367950	−	0.929845i	$-0.380060\pi$
$797$	−15.8630	−	15.8630i	−0.561895	−	0.561895i	−0.929845	+	0.367950i	$0.880060\pi$
$798$	2.54973	−	17.7374i	0.0902594	−	0.627896i
$799$			62.9511i			2.22705i
$800$		0			0
$801$			19.3127i			0.682381i
$802$	3.80719	−	3.80719i	0.134437	−	0.134437i
$803$	19.5622	+	19.5622i	0.690335	+	0.690335i
$804$		−	17.5521i		−	0.619015i
$805$		0			0
$806$		−	6.43233i		−	0.226569i
$807$	22.2710	−	22.2710i	0.783977	−	0.783977i
$808$	4.24264	−	4.24264i	0.149256	−	0.149256i
$809$		−	0.0173772i		−	0.000610952i	−1.00000		0.000305476i	$-0.999903\pi$
$809$		−	0.0173772i		−	0.000610952i	1.00000		0.000305476i	$-9.72360e-5\pi$
$810$		0			0
$811$		−	18.4034i		−	0.646232i	−0.946359	−	0.323116i	$-0.895270\pi$
$811$		−	18.4034i		−	0.646232i	0.946359	−	0.323116i	$-0.104730\pi$
$812$	−0.439189	−	0.439189i	−0.0154125	−	0.0154125i
$813$	−5.00235	+	5.00235i	−0.175440	+	0.175440i
$814$			15.8314i			0.554891i
$815$		0			0
$816$		−	21.4721i		−	0.751675i
$817$	−44.4077	−	6.38357i	−1.55363	−	0.223333i
$818$	22.6455	+	22.6455i	0.791781	+	0.791781i
$819$	−14.9735			−0.523215
$820$		0			0
$821$	−29.2364			−1.02036			−0.510178	−	0.860069i	$-0.670421\pi$
$821$	−29.2364			−1.02036			−0.510178	+	0.860069i	$0.670421\pi$
$822$	28.7748	−	28.7748i	1.00364	−	1.00364i
$823$	−14.4582	−	14.4582i	−0.503980	−	0.503980i	0.408692	−	0.912672i	$-0.365985\pi$
$823$	−14.4582	−	14.4582i	−0.503980	−	0.503980i	−0.912672	+	0.408692i	$0.865985\pi$
$824$		−	15.5985i		−	0.543400i
$825$		0			0
$826$	8.15474			0.283740
$827$	18.5102	+	18.5102i	0.643663	+	0.643663i	0.951454	−	0.307791i	$-0.0995898\pi$
$827$	18.5102	+	18.5102i	0.643663	+	0.643663i	−0.307791	+	0.951454i	$0.599590\pi$
$828$	−7.55196	−	7.55196i	−0.262449	−	0.262449i
$829$	−38.5469			−1.33879			−0.669394	−	0.742907i	$-0.733446\pi$
$829$	−38.5469			−1.33879			−0.669394	+	0.742907i	$0.733446\pi$
$830$		0			0
$831$			39.1041i			1.35651i
$832$	−1.31299	−	1.31299i	−0.0455198	−	0.0455198i
$833$	−25.9876	−	25.9876i	−0.900417	−	0.900417i
$834$			12.9590i			0.448732i
$835$		0			0
$836$	6.35187	+	8.48460i	0.219684	+	0.293446i
$837$	−20.5824	+	20.5824i	−0.711432	+	0.711432i
$838$	8.35065	−	8.35065i	0.288468	−	0.288468i
$839$	24.0478			0.830221			0.415110	−	0.909771i	$-0.363743\pi$
$839$	24.0478			0.830221			0.415110	+	0.909771i	$0.363743\pi$
$840$		0			0
$841$	−28.7985			−0.993051
$842$	13.5432	−	13.5432i	0.466731	−	0.466731i
$843$	26.1837	+	26.1837i	0.901815	+	0.901815i
$844$	4.34969			0.149723
$845$		0			0
$846$		−	50.7674i		−	1.74542i
$847$	−4.97764	+	4.97764i	−0.171034	+	0.171034i
$848$	9.37595	−	9.37595i	0.321971	−	0.321971i
$849$	38.9494			1.33674
$850$		0			0
$851$		−	11.9314i		−	0.409002i
$852$	−30.7884	+	30.7884i	−1.05479	+	1.05479i
$853$	34.3807	+	34.3807i	1.17717	+	1.17717i	0.980462	+	0.196710i	$0.0630257\pi$
$853$	34.3807	+	34.3807i	1.17717	+	1.17717i	0.196710	+	0.980462i	$0.436974\pi$
$854$	−2.76727			−0.0946940
$855$		0			0
$856$	−5.31014			−0.181497
$857$	15.0795	+	15.0795i	0.515107	+	0.515107i	0.916087	−	0.400980i	$-0.131330\pi$
$857$	15.0795	+	15.0795i	0.515107	+	0.515107i	−0.400980	+	0.916087i	$0.631330\pi$
$858$	9.48583	−	9.48583i	0.323841	−	0.323841i
$859$		−	15.4674i		−	0.527740i	−0.964558	−	0.263870i	$-0.915001\pi$
$859$		−	15.4674i		−	0.527740i	0.964558	−	0.263870i	$-0.0849990\pi$
$860$		0			0
$861$	25.8256			0.880133
$862$	18.6115	−	18.6115i	0.633909	−	0.633909i
$863$	−15.3381	+	15.3381i	−0.522116	+	0.522116i	−0.918210	−	0.396094i	$-0.870365\pi$
$863$	−15.3381	+	15.3381i	−0.522116	+	0.522116i	0.396094	+	0.918210i	$0.370365\pi$
$864$			8.40274i			0.285867i
$865$		0			0
$866$	39.5134			1.34272
$867$	−74.0081	−	74.0081i	−2.51345	−	2.51345i
$868$	3.38920	−	3.38920i	0.115037	−	0.115037i
$869$	15.1518			0.513989
$870$		0			0
$871$	−10.9692			−0.371676
$872$	−7.76358	+	7.76358i	−0.262908	+	0.262908i
$873$	−39.5561	+	39.5561i	−1.33877	+	1.33877i
$874$	−4.78710	−	6.39443i	−0.161926	−	0.216295i
$875$		0			0
$876$			33.8053i			1.14218i
$877$	−9.56444	−	9.56444i	−0.322968	−	0.322968i	0.526936	−	0.849905i	$-0.323341\pi$
$877$	−9.56444	−	9.56444i	−0.322968	−	0.322968i	−0.849905	+	0.526936i	$0.823341\pi$
$878$	−14.0058	−	14.0058i	−0.472671	−	0.472671i
$879$		−	66.6549i		−	2.24821i
$880$		0			0
$881$	−5.53681			−0.186540			−0.0932700	−	0.995641i	$-0.529732\pi$
$881$	−5.53681			−0.186540			−0.0932700	+	0.995641i	$0.529732\pi$
$882$	20.9579	+	20.9579i	0.705688	+	0.705688i
$883$	23.6873	+	23.6873i	0.797141	+	0.797141i	0.982644	−	0.185502i	$-0.0593913\pi$
$883$	23.6873	+	23.6873i	0.797141	+	0.797141i	−0.185502	+	0.982644i	$0.559391\pi$
$884$	−13.4190			−0.451330
$885$		0			0
$886$		−	30.6319i		−	1.02910i
$887$	21.1405	+	21.1405i	0.709830	+	0.709830i	0.966499	−	0.256669i	$-0.0826251\pi$
$887$	21.1405	+	21.1405i	0.709830	+	0.709830i	−0.256669	+	0.966499i	$0.582625\pi$
$888$	−13.6791	+	13.6791i	−0.459040	+	0.459040i
$889$	18.1142			0.607531
$890$		0			0
$891$	−18.1929			−0.609486
$892$	8.40384	+	8.40384i	0.281381	+	0.281381i
$893$	5.40258	−	37.5834i	0.180790	−	1.25768i
$894$			32.2764i			1.07948i
$895$		0			0
$896$		−	1.38363i		−	0.0462240i
$897$	−7.14901	+	7.14901i	−0.238699	+	0.238699i
$898$	27.4024	+	27.4024i	0.914429	+	0.914429i
$899$			1.55502i			0.0518628i
$900$		0			0
$901$		−	95.8237i		−	3.19235i
$902$	−10.8009	+	10.8009i	−0.359632	+	0.359632i
$903$	−29.9200	+	29.9200i	−0.995676	+	0.995676i
$904$			3.56847i			0.118685i
$905$		0			0
$906$			14.4334i			0.479518i
$907$	13.3405	+	13.3405i	0.442965	+	0.442965i	0.893007	−	0.450042i	$-0.148591\pi$
$907$	13.3405	+	13.3405i	0.442965	+	0.442965i	−0.450042	+	0.893007i	$0.648591\pi$
$908$	8.32589	−	8.32589i	0.276304	−	0.276304i
$909$			34.9683i			1.15983i
$910$		0			0
$911$		−	18.8154i		−	0.623381i	−0.950184	−	0.311691i	$-0.899105\pi$
$911$		−	18.8154i		−	0.623381i	0.950184	−	0.311691i	$-0.100895\pi$
$912$	−1.84278	+	12.8194i	−0.0610204	+	0.424493i
$913$	−28.4975	−	28.4975i	−0.943129	−	0.943129i
$914$	−1.59100			−0.0526257
$915$		0			0
$916$	19.4833			0.643748
$917$	−3.57706	+	3.57706i	−0.118125	+	0.118125i
$918$	42.9387	+	42.9387i	1.41719	+	1.41719i
$919$			12.6764i			0.418156i	0.977899	+	0.209078i	$0.0670463\pi$
$919$			12.6764i			0.418156i	−0.977899	+	0.209078i	$0.932954\pi$
$920$		0			0
$921$	−65.8103			−2.16852
$922$	6.07348	+	6.07348i	0.200019	+	0.200019i
$923$	19.2412	+	19.2412i	0.633331	+	0.633331i
$924$	9.99618			0.328850
$925$		0			0
$926$		−	5.92352i		−	0.194659i
$927$	64.2824	+	64.2824i	2.11131	+	2.11131i
$928$	0.317417	+	0.317417i	0.0104197	+	0.0104197i
$929$		−	9.79013i		−	0.321204i	−0.987019	−	0.160602i	$-0.948656\pi$
$929$		−	9.79013i		−	0.321204i	0.987019	−	0.160602i	$-0.0513435\pi$
$930$		0			0
$931$	13.2850	+	17.7456i	0.435397	+	0.581587i
$932$	13.2953	−	13.2953i	0.435503	−	0.435503i
$933$	−22.2022	+	22.2022i	−0.726867	+	0.726867i
$934$	17.4203			0.570008
$935$		0			0
$936$	10.8218			0.353723
$937$	2.50430	−	2.50430i	0.0818121	−	0.0818121i	−0.665017	−	0.746829i	$-0.731576\pi$
$937$	2.50430	−	2.50430i	0.0818121	−	0.0818121i	0.746829	+	0.665017i	$0.231576\pi$
$938$	−5.77967	−	5.77967i	−0.188713	−	0.188713i
$939$	−16.3643			−0.534028
$940$		0			0
$941$		−	42.9543i		−	1.40027i	−0.714010	−	0.700135i	$-0.753123\pi$
$941$		−	42.9543i		−	1.40027i	0.714010	−	0.700135i	$-0.246877\pi$
$942$	−50.5264	+	50.5264i	−1.64624	+	1.64624i
$943$	8.14014	−	8.14014i	0.265079	−	0.265079i
$944$	−5.89371			−0.191824
$945$		0			0
$946$		−	25.0267i		−	0.813688i
$947$	−18.0614	+	18.0614i	−0.586916	+	0.586916i	−0.936795	−	0.349879i	$-0.886223\pi$
$947$	−18.0614	+	18.0614i	−0.586916	+	0.586916i	0.349879	+	0.936795i	$0.386223\pi$
$948$	13.0919	+	13.0919i	0.425204	+	0.425204i
$949$	21.1266			0.685799
$950$		0			0
$951$	−15.8815			−0.514994
$952$	−7.07048	−	7.07048i	−0.229156	−	0.229156i
$953$	−26.3730	+	26.3730i	−0.854307	+	0.854307i	−0.990660	−	0.136353i	$-0.956462\pi$
$953$	−26.3730	+	26.3730i	−0.854307	+	0.854307i	0.136353	+	0.990660i	$0.456462\pi$
$954$			77.2777i			2.50196i
$955$		0			0
$956$	−13.7943			−0.446140
$957$	−2.29320	+	2.29320i	−0.0741287	+	0.0741287i
$958$	−20.8857	+	20.8857i	−0.674786	+	0.674786i
$959$		−	18.9503i		−	0.611936i
$960$		0			0
$961$	19.0000			0.612903
$962$	8.54874	+	8.54874i	0.275622	+	0.275622i
$963$	21.8834	−	21.8834i	0.705183	−	0.705183i
$964$	16.5745			0.533830
$965$		0			0
$966$	−7.53364			−0.242391
$967$	−33.7448	+	33.7448i	−1.08516	+	1.08516i	−0.0891408	+	0.996019i	$0.528412\pi$
$967$	−33.7448	+	33.7448i	−1.08516	+	1.08516i	−0.996019	+	0.0891408i	$0.971588\pi$
$968$	3.59751	−	3.59751i	0.115628	−	0.115628i
$969$	56.0915	+	74.9250i	1.80192	+	2.40694i
$970$		0			0
$971$		−	31.7048i		−	1.01746i	−0.860928	−	0.508728i	$-0.830116\pi$
$971$		−	31.7048i		−	1.01746i	0.860928	−	0.508728i	$-0.169884\pi$
$972$	2.10535	+	2.10535i	0.0675292	+	0.0675292i
$973$	4.26721	+	4.26721i	0.136800	+	0.136800i
$974$		−	28.6079i		−	0.916655i
$975$		0			0
$976$	2.00000			0.0640184
$977$	−21.1530	−	21.1530i	−0.676745	−	0.676745i	0.282517	−	0.959262i	$-0.408831\pi$
$977$	−21.1530	−	21.1530i	−0.676745	−	0.676745i	−0.959262	+	0.282517i	$0.908831\pi$
$978$	−35.8642	−	35.8642i	−1.14681	−	1.14681i
$979$	−8.05749			−0.257518
$980$		0			0
$981$		−	63.9883i		−	2.04299i
$982$	18.7519	+	18.7519i	0.598397	+	0.598397i
$983$	43.3066	−	43.3066i	1.38127	−	1.38127i	0.538887	−	0.842378i	$-0.318845\pi$
$983$	43.3066	−	43.3066i	1.38127	−	1.38127i	0.842378	−	0.538887i	$-0.181155\pi$
$984$	−18.6650			−0.595019
$985$		0			0
$986$	3.24405			0.103312
$987$	−25.3221	−	25.3221i	−0.806011	−	0.806011i
$988$	8.01148	+	1.15164i	0.254879	+	0.0366386i
$989$			18.8614i			0.599758i
$990$		0			0
$991$			27.3181i			0.867789i	0.900964	+	0.433895i	$0.142861\pi$
$991$			27.3181i			0.867789i	−0.900964	+	0.433895i	$0.857139\pi$
$992$	−2.44949	+	2.44949i	−0.0777714	+	0.0777714i
$993$	14.1413	+	14.1413i	0.448760	+	0.448760i
$994$			20.2764i			0.643128i
$995$		0			0
$996$		−	49.2463i		−	1.56043i
$997$	−16.4984	+	16.4984i	−0.522511	+	0.522511i	−0.918329	−	0.395818i	$-0.870461\pi$
$997$	−16.4984	+	16.4984i	−0.522511	+	0.522511i	0.395818	+	0.918329i	$0.370461\pi$
$998$	−6.02101	+	6.02101i	−0.190592	+	0.190592i
$999$		−	54.7092i		−	1.73092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.f.d.493.16	yes	32
5.2	odd	4	inner	950.2.f.d.607.2	yes	32
5.3	odd	4	inner	950.2.f.d.607.15	yes	32
5.4	even	2	inner	950.2.f.d.493.1	✓	32
19.18	odd	2	inner	950.2.f.d.493.2	yes	32
95.18	even	4	inner	950.2.f.d.607.1	yes	32
95.37	even	4	inner	950.2.f.d.607.16	yes	32
95.94	odd	2	inner	950.2.f.d.493.15	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.f.d.493.1	✓	32	5.4	even	2	inner
950.2.f.d.493.2	yes	32	19.18	odd	2	inner
950.2.f.d.493.15	yes	32	95.94	odd	2	inner
950.2.f.d.493.16	yes	32	1.1	even	1	trivial
950.2.f.d.607.1	yes	32	95.18	even	4	inner
950.2.f.d.607.2	yes	32	5.2	odd	4	inner
950.2.f.d.607.15	yes	32	5.3	odd	4	inner
950.2.f.d.607.16	yes	32	95.37	even	4	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(2.10096 - 2.10096i) q^{3} +1.00000i q^{4} +2.97120 q^{6} +(0.978377 - 0.978377i) q^{7} +(-0.707107 + 0.707107i) q^{8} -5.82806i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(2.10096 - 2.10096i) q^{3} +1.00000i q^{4} +2.97120 q^{6} +(0.978377 - 0.978377i) q^{7} +(-0.707107 + 0.707107i) q^{8} -5.82806i q^{9} +2.43153 q^{11} +(2.10096 + 2.10096i) q^{12} +(1.31299 - 1.31299i) q^{13} +1.38363 q^{14} -1.00000 q^{16} +(-5.11008 + 5.11008i) q^{17} +(4.12106 - 4.12106i) q^{18} +(3.48940 - 2.61229i) q^{19} -4.11106i q^{21} +(1.71935 + 1.71935i) q^{22} +(-1.29579 - 1.29579i) q^{23} +2.97120i q^{24} +1.85685 q^{26} +(-5.94163 - 5.94163i) q^{27} +(0.978377 + 0.978377i) q^{28} -0.448895 q^{29} -3.46410i q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.10855 - 5.10855i) q^{33} -7.22675 q^{34} +5.82806 q^{36} +(4.60388 + 4.60388i) q^{37} +(4.31455 + 0.620212i) q^{38} -5.51709i q^{39} +6.28197i q^{41} +(2.90696 - 2.90696i) q^{42} +(-7.27794 - 7.27794i) q^{43} +2.43153i q^{44} -1.83253i q^{46} +(6.15951 - 6.15951i) q^{47} +(-2.10096 + 2.10096i) q^{48} +5.08556i q^{49} +21.4721i q^{51} +(1.31299 + 1.31299i) q^{52} +(-9.37595 + 9.37595i) q^{53} -8.40274i q^{54} +1.38363i q^{56} +(1.84278 - 12.8194i) q^{57} +(-0.317417 - 0.317417i) q^{58} +5.89371 q^{59} -2.00000 q^{61} +(2.44949 - 2.44949i) q^{62} +(-5.70204 - 5.70204i) q^{63} -1.00000i q^{64} +7.22458 q^{66} +(-4.17716 - 4.17716i) q^{67} +(-5.11008 - 5.11008i) q^{68} -5.44482 q^{69} +14.6544i q^{71} +(4.12106 + 4.12106i) q^{72} +(8.04521 + 8.04521i) q^{73} +6.51088i q^{74} +(2.61229 + 3.48940i) q^{76} +(2.37896 - 2.37896i) q^{77} +(3.90117 - 3.90117i) q^{78} +6.23137 q^{79} -7.48208 q^{81} +(-4.44203 + 4.44203i) q^{82} +(-11.7200 - 11.7200i) q^{83} +4.11106 q^{84} -10.2926i q^{86} +(-0.943110 + 0.943110i) q^{87} +(-1.71935 + 1.71935i) q^{88} -3.31375 q^{89} -2.56920i q^{91} +(1.29579 - 1.29579i) q^{92} +(-7.27794 - 7.27794i) q^{93} +8.71086 q^{94} -2.97120 q^{96} +(-6.78718 - 6.78718i) q^{97} +(-3.59603 + 3.59603i) q^{98} -14.1711i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{6}+O(q^{10}) \) 32 * q - 8 * q^6	\( 32 q - 8 q^{6} - 24 q^{11} - 32 q^{16} + 32 q^{26} + 56 q^{36} - 64 q^{61} + 72 q^{66} + 4 q^{76} - 32 q^{81} + 8 q^{96}+O(q^{100}) \) 32 * q - 8 * q^6 - 24 * q^11 - 32 * q^16 + 32 * q^26 + 56 * q^36 - 64 * q^61 + 72 * q^66 + 4 * q^76 - 32 * q^81 + 8 * q^96

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