LMFDB - Embedded newform 676.2.f.j.99.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [676,2,Mod(99,676)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(676, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("676.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	676.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:	$5.39788717664$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			99.18
Character	$\chi$	$=$	676.99
Dual form			676.2.f.j.239.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0293598 + 1.41391i) q^{2} +1.05568i q^{3} +(-1.99828 - 0.0830241i) q^{4} +(1.55574 + 1.55574i) q^{5} +(-1.49263 - 0.0309945i) q^{6} +(-0.0324435 - 0.0324435i) q^{7} +(0.176057 - 2.82294i) q^{8} +1.88554 q^{9} +O(q^{10})$	\(q+(-0.0293598 + 1.41391i) q^{2} +1.05568i q^{3} +(-1.99828 - 0.0830241i) q^{4} +(1.55574 + 1.55574i) q^{5} +(-1.49263 - 0.0309945i) q^{6} +(-0.0324435 - 0.0324435i) q^{7} +(0.176057 - 2.82294i) q^{8} +1.88554 q^{9} +(-2.24535 + 2.15400i) q^{10} +(3.95413 + 3.95413i) q^{11} +(0.0876468 - 2.10954i) q^{12} +(0.0468246 - 0.0449196i) q^{14} +(-1.64236 + 1.64236i) q^{15} +(3.98621 + 0.331810i) q^{16} +4.37761i q^{17} +(-0.0553591 + 2.66598i) q^{18} +(2.17637 - 2.17637i) q^{19} +(-2.97964 - 3.23796i) q^{20} +(0.0342499 - 0.0342499i) q^{21} +(-5.70687 + 5.47469i) q^{22} -8.07122 q^{23} +(2.98012 + 0.185860i) q^{24} -0.159342i q^{25} +5.15757i q^{27} +(0.0621374 + 0.0675246i) q^{28} -6.53129 q^{29} +(-2.27393 - 2.37037i) q^{30} +(5.23380 - 5.23380i) q^{31} +(-0.586184 + 5.62640i) q^{32} +(-4.17429 + 4.17429i) q^{33} +(-6.18954 - 0.128526i) q^{34} -0.100947i q^{35} +(-3.76783 - 0.156545i) q^{36} +(1.62865 - 1.62865i) q^{37} +(3.01329 + 3.14109i) q^{38} +(4.66567 - 4.11787i) q^{40} +(-0.936980 - 0.936980i) q^{41} +(0.0474207 + 0.0494318i) q^{42} +1.55207 q^{43} +(-7.57315 - 8.22973i) q^{44} +(2.93341 + 2.93341i) q^{45} +(0.236969 - 11.4120i) q^{46} +(-3.73081 - 3.73081i) q^{47} +(-0.350285 + 4.20816i) q^{48} -6.99789i q^{49} +(0.225295 + 0.00467824i) q^{50} -4.62136 q^{51} -9.84644 q^{53} +(-7.29233 - 0.151425i) q^{54} +12.3032i q^{55} +(-0.0972980 + 0.0858741i) q^{56} +(2.29755 + 2.29755i) q^{57} +(0.191757 - 9.23465i) q^{58} +(7.45449 + 7.45449i) q^{59} +(3.41825 - 3.14554i) q^{60} +7.94117 q^{61} +(7.24646 + 7.55378i) q^{62} +(-0.0611735 - 0.0611735i) q^{63} +(-7.93801 - 0.994000i) q^{64} +(-5.77951 - 6.02463i) q^{66} +(1.70258 - 1.70258i) q^{67} +(0.363447 - 8.74768i) q^{68} -8.52062i q^{69} +(0.142730 + 0.00296379i) q^{70} +(-0.0628261 + 0.0628261i) q^{71} +(0.331963 - 5.32277i) q^{72} +(-5.75309 + 5.75309i) q^{73} +(2.25495 + 2.35058i) q^{74} +0.168214 q^{75} +(-4.52968 + 4.16830i) q^{76} -0.256571i q^{77} -0.739145i q^{79} +(5.68530 + 6.71773i) q^{80} +0.211886 q^{81} +(1.35231 - 1.29730i) q^{82} +(5.41775 - 5.41775i) q^{83} +(-0.0712843 + 0.0655972i) q^{84} +(-6.81043 + 6.81043i) q^{85} +(-0.0455686 + 2.19449i) q^{86} -6.89495i q^{87} +(11.8584 - 10.4661i) q^{88} +(-10.6202 + 10.6202i) q^{89} +(-4.23370 + 4.06145i) q^{90} +(16.1285 + 0.670106i) q^{92} +(5.52522 + 5.52522i) q^{93} +(5.38457 - 5.16549i) q^{94} +6.77174 q^{95} +(-5.93968 - 0.618822i) q^{96} +(-1.89084 - 1.89084i) q^{97} +(9.89438 + 0.205457i) q^{98} +(7.45567 + 7.45567i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 64 q^{9}+O(q^{10}) $ 72 * q - 64 * q^9	$ 72 q - 64 q^{9} + 4 q^{14} + 76 q^{16} - 72 q^{22} - 16 q^{29} + 84 q^{40} - 224 q^{42} + 224 q^{48} + 32 q^{53} - 16 q^{61} - 140 q^{66} + 152 q^{68} - 168 q^{74} + 88 q^{81} - 56 q^{92} - 300 q^{94}+O(q^{100}) $ 72 * q - 64 * q^9 + 4 * q^14 + 76 * q^16 - 72 * q^22 - 16 * q^29 + 84 * q^40 - 224 * q^42 + 224 * q^48 + 32 * q^53 - 16 * q^61 - 140 * q^66 + 152 * q^68 - 168 * q^74 + 88 * q^81 - 56 * q^92 - 300 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/676\mathbb{Z}\right)^\times$.

$n$	$339$	$509$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.0293598	+	1.41391i	−0.0207605	+	0.999784i
$2$	−0.0293598	+	1.41391i	−0.0207605	+	0.999784i
$3$			1.05568i			0.609497i	0.952433	+	0.304748i	$0.0985724\pi$
$3$			1.05568i			0.609497i	−0.952433	+	0.304748i	$0.901428\pi$
$4$	−1.99828	−	0.0830241i	−0.999138	−	0.0415120i
$5$	1.55574	+	1.55574i	0.695748	+	0.695748i	0.963491	−	0.267742i	$-0.0862775\pi$
$5$	1.55574	+	1.55574i	0.695748	+	0.695748i	−0.267742	+	0.963491i	$0.586278\pi$
$6$	−1.49263	−	0.0309945i	−0.609365	−	0.0126535i
$7$	−0.0324435	−	0.0324435i	−0.0122625	−	0.0122625i	0.700949	−	0.713211i	$-0.252760\pi$
$7$	−0.0324435	−	0.0324435i	−0.0122625	−	0.0122625i	−0.713211	+	0.700949i	$0.752760\pi$
$8$	0.176057	−	2.82294i	0.0622457	−	0.998061i
$9$	1.88554			0.628514
$10$	−2.24535	+	2.15400i	−0.710043	+	0.681154i
$11$	3.95413	+	3.95413i	1.19221	+	1.19221i	0.976444	+	0.215771i	$0.0692264\pi$
$11$	3.95413	+	3.95413i	1.19221	+	1.19221i	0.215771	+	0.976444i	$0.430774\pi$
$12$	0.0876468	−	2.10954i	0.0253015	−	0.608971i
$13$		0			0
$13$		0			0
$14$	0.0468246	−	0.0449196i	0.0125144	−	0.0120053i
$15$	−1.64236	+	1.64236i	−0.424056	+	0.424056i
$16$	3.98621	+	0.331810i	0.996554	+	0.0829525i
$17$			4.37761i			1.06173i	0.847457	+	0.530863i	$0.178132\pi$
$17$			4.37761i			1.06173i	−0.847457	+	0.530863i	$0.821868\pi$
$18$	−0.0553591	+	2.66598i	−0.0130483	+	0.628378i
$19$	2.17637	−	2.17637i	0.499294	−	0.499294i	−0.411924	−	0.911218i	$-0.635143\pi$
$19$	2.17637	−	2.17637i	0.499294	−	0.499294i	0.911218	+	0.411924i	$0.135143\pi$
$20$	−2.97964	−	3.23796i	−0.666267	−	0.724031i
$21$	0.0342499	−	0.0342499i	0.00747394	−	0.00747394i
$22$	−5.70687	+	5.47469i	−1.21671	+	1.16721i
$23$	−8.07122			−1.68297			−0.841483	−	0.540284i	$-0.818317\pi$
$23$	−8.07122			−1.68297			−0.841483	+	0.540284i	$0.818317\pi$
$24$	2.98012	+	0.185860i	0.608315	+	0.0379386i
$25$		−	0.159342i		−	0.0318683i
$26$		0			0
$27$			5.15757i			0.992574i
$28$	0.0621374	+	0.0675246i	0.0117429	+	0.0127609i
$29$	−6.53129			−1.21283			−0.606415	−	0.795148i	$-0.707393\pi$
$29$	−6.53129			−1.21283			−0.606415	+	0.795148i	$0.707393\pi$
$30$	−2.27393	−	2.37037i	−0.415161	−	0.432769i
$31$	5.23380	−	5.23380i	0.940019	−	0.940019i	−0.0582813	−	0.998300i	$-0.518562\pi$
$31$	5.23380	−	5.23380i	0.940019	−	0.940019i	0.998300	+	0.0582813i	$0.0185620\pi$
$32$	−0.586184	+	5.62640i	−0.103624	+	0.994617i
$33$	−4.17429	+	4.17429i	−0.726651	+	0.726651i
$34$	−6.18954	−	0.128526i	−1.06150	−	0.0220420i
$35$		−	0.100947i		−	0.0170632i
$36$	−3.76783	−	0.156545i	−0.627972	−	0.0260909i
$37$	1.62865	−	1.62865i	0.267748	−	0.267748i	−0.560444	−	0.828192i	$-0.689369\pi$
$37$	1.62865	−	1.62865i	0.267748	−	0.267748i	0.828192	+	0.560444i	$0.189369\pi$
$38$	3.01329	+	3.14109i	0.488821	+	0.509552i
$39$		0			0
$40$	4.66567	−	4.11787i	0.737707	−	0.651092i
$41$	−0.936980	−	0.936980i	−0.146332	−	0.146332i	0.630145	−	0.776477i	$-0.282995\pi$
$41$	−0.936980	−	0.936980i	−0.146332	−	0.146332i	−0.776477	+	0.630145i	$0.782995\pi$
$42$	0.0474207	+	0.0494318i	0.00731717	+	0.00762749i
$43$	1.55207			0.236689			0.118345	−	0.992973i	$-0.462241\pi$
$43$	1.55207			0.236689			0.118345	+	0.992973i	$0.462241\pi$
$44$	−7.57315	−	8.22973i	−1.14170	−	1.24068i
$45$	2.93341	+	2.93341i	0.437287	+	0.437287i
$46$	0.236969	−	11.4120i	0.0349392	−	1.68260i
$47$	−3.73081	−	3.73081i	−0.544195	−	0.544195i	0.380561	−	0.924756i	$-0.375731\pi$
$47$	−3.73081	−	3.73081i	−0.544195	−	0.544195i	−0.924756	+	0.380561i	$0.875731\pi$
$48$	−0.350285	+	4.20816i	−0.0505593	+	0.607396i
$49$		−	6.99789i		−	0.999699i
$50$	0.225295	+	0.00467824i	0.0318615	+	0.000661603i
$51$	−4.62136			−0.647119
$52$		0			0
$53$	−9.84644			−1.35251			−0.676256	−	0.736667i	$-0.736399\pi$
$53$	−9.84644			−1.35251			−0.676256	+	0.736667i	$0.736399\pi$
$54$	−7.29233	−	0.151425i	−0.992360	−	0.0206063i
$55$			12.3032i			1.65896i
$56$	−0.0972980	+	0.0858741i	−0.0130020	+	0.0114754i
$57$	2.29755	+	2.29755i	0.304318	+	0.304318i
$58$	0.191757	−	9.23465i	0.0251790	−	1.21257i
$59$	7.45449	+	7.45449i	0.970492	+	0.970492i	0.999577	−	0.0290853i	$-0.00925946\pi$
$59$	7.45449	+	7.45449i	0.970492	+	0.970492i	−0.0290853	+	0.999577i	$0.509259\pi$
$60$	3.41825	−	3.14554i	0.441294	−	0.406087i
$61$	7.94117			1.01676			0.508381	−	0.861132i	$-0.330244\pi$
$61$	7.94117			1.01676			0.508381	+	0.861132i	$0.330244\pi$
$62$	7.24646	+	7.55378i	0.920301	+	0.959332i
$63$	−0.0611735	−	0.0611735i	−0.00770713	−	0.00770713i
$64$	−7.93801	−	0.994000i	−0.992251	−	0.124250i
$65$		0			0
$66$	−5.77951	−	6.02463i	−0.711409	−	0.741580i
$67$	1.70258	−	1.70258i	0.208003	−	0.208003i	−0.595415	−	0.803418i	$-0.703012\pi$
$67$	1.70258	−	1.70258i	0.208003	−	0.208003i	0.803418	+	0.595415i	$0.203012\pi$
$68$	0.363447	−	8.74768i	0.0440745	−	1.06081i
$69$		−	8.52062i		−	1.02576i
$70$	0.142730	+	0.00296379i	0.0170595	+	0.000354241i
$71$	−0.0628261	+	0.0628261i	−0.00745609	+	0.00745609i	−0.710825	−	0.703369i	$-0.751678\pi$
$71$	−0.0628261	+	0.0628261i	−0.00745609	+	0.00745609i	0.703369	+	0.710825i	$0.251678\pi$
$72$	0.331963	−	5.32277i	0.0391223	−	0.627295i
$73$	−5.75309	+	5.75309i	−0.673348	+	0.673348i	−0.958486	−	0.285138i	$-0.907960\pi$
$73$	−5.75309	+	5.75309i	−0.673348	+	0.673348i	0.285138	+	0.958486i	$0.407960\pi$
$74$	2.25495	+	2.35058i	0.262132	+	0.273249i
$75$	0.168214			0.0194237
$76$	−4.52968	+	4.16830i	−0.519590	+	0.478137i
$77$		−	0.256571i		−	0.0292390i
$78$		0			0
$79$		−	0.739145i		−	0.0831603i	−0.999135	−	0.0415801i	$-0.986761\pi$
$79$		−	0.739145i		−	0.0831603i	0.999135	−	0.0415801i	$-0.0132392\pi$
$80$	5.68530	+	6.71773i	0.635636	+	0.751065i
$81$	0.211886			0.0235429
$82$	1.35231	−	1.29730i	0.149338	−	0.143262i
$83$	5.41775	−	5.41775i	0.594675	−	0.594675i	−0.344216	−	0.938891i	$-0.611855\pi$
$83$	5.41775	−	5.41775i	0.594675	−	0.594675i	0.938891	+	0.344216i	$0.111855\pi$
$84$	−0.0712843	+	0.0655972i	−0.00777776	+	0.00715724i
$85$	−6.81043	+	6.81043i	−0.738695	+	0.738695i
$86$	−0.0455686	+	2.19449i	−0.00491378	+	0.236638i
$87$		−	6.89495i		−	0.739216i
$88$	11.8584	−	10.4661i	1.26411	−	1.11569i
$89$	−10.6202	+	10.6202i	−1.12574	+	1.12574i	−0.134877	+	0.990862i	$0.543064\pi$
$89$	−10.6202	+	10.6202i	−1.12574	+	1.12574i	−0.990862	+	0.134877i	$0.956936\pi$
$90$	−4.23370	+	4.06145i	−0.446271	+	0.428115i
$91$		0			0
$92$	16.1285	+	0.670106i	1.68152	+	0.0698634i
$93$	5.52522	+	5.52522i	0.572939	+	0.572939i
$94$	5.38457	−	5.16549i	0.555376	−	0.532780i
$95$	6.77174			0.694766
$96$	−5.93968	−	0.618822i	−0.606216	−	0.0631583i
$97$	−1.89084	−	1.89084i	−0.191986	−	0.191986i	0.604568	−	0.796554i	$-0.293346\pi$
$97$	−1.89084	−	1.89084i	−0.191986	−	0.191986i	−0.796554	+	0.604568i	$0.793346\pi$
$98$	9.89438	+	0.205457i	0.999484	+	0.0207543i
$99$	7.45567	+	7.45567i	0.749323	+	0.749323i
$100$	−0.0132292	+	0.318409i	−0.00132292	+	0.0318409i
$101$			0.506842i			0.0504326i	0.999682	+	0.0252163i	$0.00802746\pi$
$101$			0.506842i			0.0504326i	−0.999682	+	0.0252163i	$0.991973\pi$
$102$	0.135682	−	6.53418i	0.0134345	−	0.646980i
$103$	3.11965			0.307388			0.153694	−	0.988119i	$-0.450883\pi$
$103$	3.11965			0.307388			0.153694	+	0.988119i	$0.450883\pi$
$104$		0			0
$105$	0.106568			0.0104000
$106$	0.289089	−	13.9220i	0.0280788	−	1.35222i
$107$		−	4.30629i		−	0.416305i	−0.978096	−	0.208152i	$-0.933255\pi$
$107$		−	4.30629i		−	0.416305i	0.978096	−	0.208152i	$-0.0667450\pi$
$108$	0.428202	−	10.3062i	0.0412038	−	0.991718i
$109$	1.69159	+	1.69159i	0.162025	+	0.162025i	0.783463	−	0.621438i	$-0.213451\pi$
$109$	1.69159	+	1.69159i	0.162025	+	0.162025i	−0.621438	+	0.783463i	$0.713451\pi$
$110$	−17.3956	−	0.361219i	−1.65861	−	0.0344409i
$111$	1.71933	+	1.71933i	0.163192	+	0.163192i
$112$	−0.118562	−	0.140092i	−0.0112030	−	0.0132374i
$113$	1.54737			0.145564			0.0727821	−	0.997348i	$-0.476812\pi$
$113$	1.54737			0.145564			0.0727821	+	0.997348i	$0.476812\pi$
$114$	−3.31598	+	3.18107i	−0.310570	+	0.297935i
$115$	−12.5567	−	12.5567i	−1.17092	−	1.17092i
$116$	13.0513	+	0.542254i	1.21178	+	0.0503471i
$117$		0			0
$118$	−10.7588	+	10.3211i	−0.990430	+	0.950135i
$119$	0.142025	−	0.142025i	0.0130194	−	0.0130194i
$120$	4.34715	+	4.92545i	0.396838	+	0.449630i
$121$			20.2703i			1.84275i
$122$	−0.233151	+	11.2281i	−0.0211085	+	1.01654i
$123$	0.989151	−	0.989151i	0.0891887	−	0.0891887i
$124$	−10.8931	+	10.0241i	−0.978231	+	0.900186i
$125$	8.02660	−	8.02660i	0.717921	−	0.717921i
$126$	0.0882898	−	0.0846977i	0.00786548	−	0.00754547i
$127$	5.31252			0.471410			0.235705	−	0.971825i	$-0.424260\pi$
$127$	5.31252			0.471410			0.235705	+	0.971825i	$0.424260\pi$
$128$	1.63848	−	11.1944i	0.144823	−	0.989458i
$129$			1.63849i			0.144261i
$130$		0			0
$131$		−	4.53888i		−	0.396564i	−0.980145	−	0.198282i	$-0.936464\pi$
$131$		−	4.53888i		−	0.396564i	0.980145	−	0.198282i	$-0.0635362\pi$
$132$	8.68796	−	7.99482i	0.756190	−	0.695860i
$133$	−0.141218			−0.0122452
$134$	2.35730	+	2.45727i	0.203640	+	0.212276i
$135$	−8.02383	+	8.02383i	−0.690582	+	0.690582i
$136$	12.3577	+	0.770711i	1.05967	+	0.0660879i
$137$	6.24523	−	6.24523i	0.533566	−	0.533566i	−0.388066	−	0.921632i	$-0.626857\pi$
$137$	6.24523	−	6.24523i	0.533566	−	0.533566i	0.921632	+	0.388066i	$0.126857\pi$
$138$	12.0474	+	0.250164i	1.02554	+	0.0212953i
$139$		−	20.9034i		−	1.77300i	−0.462725	−	0.886502i	$-0.653128\pi$
$139$		−	20.9034i		−	1.77300i	0.462725	−	0.886502i	$-0.346872\pi$
$140$	−0.00838105	+	0.201720i	−0.000708328	+	0.0170485i
$141$	3.93854	−	3.93854i	0.331685	−	0.331685i
$142$	−0.0869859	−	0.0906750i	−0.00729969	−	0.00760927i
$143$		0			0
$144$	7.51617	+	0.625641i	0.626347	+	0.0521368i
$145$	−10.1610	−	10.1610i	−0.843824	−	0.843824i
$146$	−7.96543	−	8.30325i	−0.659224	−	0.687182i
$147$	7.38753			0.609314
$148$	−3.38971	+	3.11927i	−0.278632	+	0.256403i
$149$	6.69536	+	6.69536i	0.548505	+	0.548505i	0.926008	−	0.377503i	$-0.123217\pi$
$149$	6.69536	+	6.69536i	0.548505	+	0.548505i	−0.377503	+	0.926008i	$0.623217\pi$
$150$	−0.00493872	+	0.237839i	−0.000403245	+	0.0194195i
$151$	6.69198	+	6.69198i	0.544586	+	0.544586i	0.924870	−	0.380284i	$-0.124174\pi$
$151$	6.69198	+	6.69198i	0.544586	+	0.544586i	−0.380284	+	0.924870i	$0.624174\pi$
$152$	−5.76061	−	6.52694i	−0.467247	−	0.529405i
$153$			8.25417i			0.667310i
$154$	0.362769	+	0.00753288i	0.0292327	+	0.000607017i
$155$	16.2849			1.30803
$156$		0			0
$157$	4.47044			0.356780			0.178390	−	0.983960i	$-0.442911\pi$
$157$	4.47044			0.356780			0.178390	+	0.983960i	$0.442911\pi$
$158$	1.04508	+	0.0217011i	0.0831423	+	0.00172645i
$159$		−	10.3947i		−	0.824352i
$160$	−9.66517	+	7.84127i	−0.764099	+	0.619907i
$161$	0.261858	+	0.261858i	0.0206373	+	0.0206373i
$162$	−0.00622094	+	0.299588i	−0.000488763	+	0.0235379i
$163$	−3.15031	−	3.15031i	−0.246751	−	0.246751i	0.572885	−	0.819636i	$-0.305824\pi$
$163$	−3.15031	−	3.15031i	−0.246751	−	0.246751i	−0.819636	+	0.572885i	$0.805824\pi$
$164$	1.79455	+	1.95014i	0.140131	+	0.152280i
$165$	−12.9882			−1.01113
$166$	7.50114	+	7.81926i	0.582201	+	0.606892i
$167$	10.8729	+	10.8729i	0.841367	+	0.841367i	0.989037	−	0.147670i	$-0.0471773\pi$
$167$	10.8729	+	10.8729i	0.841367	+	0.841367i	−0.147670	+	0.989037i	$0.547177\pi$
$168$	−0.0906556	−	0.102715i	−0.00699423	−	0.00792467i
$169$		0			0
$170$	−9.42937	−	9.82928i	−0.723200	−	0.753871i
$171$	4.10364	−	4.10364i	0.313813	−	0.313813i
$172$	−3.10147	−	0.128860i	−0.236485	−	0.00982545i
$173$		−	11.9180i		−	0.906110i	−0.891483	−	0.453055i	$-0.850334\pi$
$173$		−	11.9180i		−	0.906110i	0.891483	−	0.453055i	$-0.149666\pi$
$174$	9.74883	+	0.202434i	0.739057	+	0.0153465i
$175$	−0.00516960	+	0.00516960i	−0.000390785	+	0.000390785i
$176$	14.4500	+	17.0740i	1.08921	+	1.28700i
$177$	−7.86955	+	7.86955i	−0.591512	+	0.591512i
$178$	−14.7042	−	15.3278i	−1.10213	−	1.14887i
$179$	19.1261			1.42955			0.714774	−	0.699355i	$-0.246529\pi$
$179$	19.1261			1.42955			0.714774	+	0.699355i	$0.246529\pi$
$180$	−5.61822	−	6.10531i	−0.418758	−	0.455063i
$181$		−	3.04856i		−	0.226597i	−0.993561	−	0.113299i	$-0.963858\pi$
$181$		−	3.04856i		−	0.226597i	0.993561	−	0.113299i	$-0.0361417\pi$
$182$		0			0
$183$			8.38333i			0.619713i
$184$	−1.42100	+	22.7846i	−0.104757	+	1.67970i
$185$	5.06751			0.372571
$186$	−7.97438	+	7.64994i	−0.584710	+	0.560921i
$187$	−17.3096	+	17.3096i	−1.26581	+	1.26581i
$188$	7.14545	+	7.76494i	0.521135	+	0.566317i
$189$	0.167329	−	0.167329i	0.0121714	−	0.0121714i
$190$	−0.198817	+	9.57462i	−0.0144237	+	0.694616i
$191$			16.2417i			1.17521i	0.809149	+	0.587603i	$0.199928\pi$
$191$			16.2417i			1.17521i	−0.809149	+	0.587603i	$0.800072\pi$
$192$	1.04935	−	8.37999i	0.0757300	−	0.604774i
$193$	9.83020	−	9.83020i	0.707593	−	0.707593i	−0.258435	−	0.966029i	$-0.583207\pi$
$193$	9.83020	−	9.83020i	0.707593	−	0.707593i	0.966029	+	0.258435i	$0.0832069\pi$
$194$	2.72899	−	2.61797i	0.195930	−	0.187959i
$195$		0			0
$196$	−0.580994	+	13.9837i	−0.0414996	+	0.998838i
$197$	5.01548	+	5.01548i	0.357338	+	0.357338i	0.862831	−	0.505493i	$-0.168689\pi$
$197$	5.01548	+	5.01548i	0.357338	+	0.357338i	−0.505493	+	0.862831i	$0.668689\pi$
$198$	−10.7605	+	10.3227i	−0.764718	+	0.733605i
$199$	−19.0115			−1.34769			−0.673844	−	0.738874i	$-0.735358\pi$
$199$	−19.0115			−1.34769			−0.673844	+	0.738874i	$0.735358\pi$
$200$	−0.449812	−	0.0280533i	−0.0318065	−	0.00198367i
$201$	1.79737	+	1.79737i	0.126777	+	0.126777i
$202$	−0.716628	−	0.0148808i	−0.0504218	−	0.00104701i
$203$	0.211898	+	0.211898i	0.0148723	+	0.0148723i
$204$	9.23474	+	0.383684i	0.646561	+	0.0268632i
$205$		−	2.91540i		−	0.203620i
$206$	−0.0915921	+	4.41089i	−0.00638152	+	0.307322i
$207$	−15.2186			−1.05777
$208$		0			0
$209$	17.2113			1.19053
$210$	−0.00312881	+	0.150677i	−0.000215908	+	0.0103977i
$211$			2.98532i			0.205518i	0.994706	+	0.102759i	$0.0327670\pi$
$211$			2.98532i			0.205518i	−0.994706	+	0.102759i	$0.967233\pi$
$212$	19.6759	+	0.817491i	1.35135	+	0.0561455i
$213$	−0.0663243	−	0.0663243i	−0.00454446	−	0.00454446i
$214$	6.08870	+	0.126432i	0.416215	+	0.00864269i
$215$	2.41462	+	2.41462i	0.164676	+	0.164676i
$216$	14.5595	+	0.908028i	0.990649	+	0.0617835i
$217$	−0.339606			−0.0230539
$218$	−2.44142	+	2.34209i	−0.165354	+	0.158626i
$219$	−6.07342	−	6.07342i	−0.410403	−	0.410403i
$220$	1.02146	−	24.5852i	0.0688670	−	1.65753i
$221$		0			0
$222$	−2.48146	+	2.38050i	−0.166545	+	0.159769i
$223$	−0.130684	+	0.130684i	−0.00875127	+	0.00875127i	−0.711469	−	0.702718i	$-0.751970\pi$
$223$	−0.130684	+	0.130684i	−0.00875127	+	0.00875127i	0.702718	+	0.711469i	$0.251970\pi$
$224$	0.201558	−	0.163522i	0.0134671	−	0.0109258i
$225$		−	0.300445i		−	0.0200297i
$226$	−0.0454304	+	2.18784i	−0.00302198	+	0.145533i
$227$	−11.0089	+	11.0089i	−0.730689	+	0.730689i	−0.970756	−	0.240067i	$-0.922831\pi$
$227$	−11.0089	+	11.0089i	−0.730689	+	0.730689i	0.240067	+	0.970756i	$0.422831\pi$
$228$	−4.40039	−	4.78189i	−0.291423	−	0.316689i
$229$	10.7997	−	10.7997i	0.713666	−	0.713666i	−0.253634	−	0.967300i	$-0.581626\pi$
$229$	10.7997	−	10.7997i	0.713666	−	0.713666i	0.967300	+	0.253634i	$0.0816260\pi$
$230$	18.1227	−	17.3854i	1.19498	−	1.14636i
$231$	0.270857			0.0178211
$232$	−1.14988	+	18.4375i	−0.0754934	+	1.21048i
$233$		−	8.21274i		−	0.538035i	−0.963135	−	0.269017i	$-0.913301\pi$
$233$		−	8.21274i		−	0.538035i	0.963135	−	0.269017i	$-0.0866989\pi$
$234$		0			0
$235$		−	11.6084i		−	0.757246i
$236$	−14.2772	−	15.5150i	−0.929368	−	1.00994i
$237$	0.780300			0.0506859
$238$	0.196640	+	0.204980i	0.0127463	+	0.0132869i
$239$	8.24382	−	8.24382i	0.533248	−	0.533248i	−0.388289	−	0.921538i	$-0.626934\pi$
$239$	8.24382	−	8.24382i	0.533248	−	0.533248i	0.921538	+	0.388289i	$0.126934\pi$
$240$	−7.09177	+	6.00186i	−0.457771	+	0.387418i
$241$	20.4381	−	20.4381i	1.31653	−	1.31653i	0.400027	−	0.916503i	$-0.369001\pi$
$241$	20.4381	−	20.4381i	1.31653	−	1.31653i	0.916503	−	0.400027i	$-0.130999\pi$
$242$	−28.6603	−	0.595131i	−1.84236	−	0.0382565i
$243$			15.6964i			1.00692i
$244$	−15.8686	−	0.659308i	−1.01589	−	0.0422079i
$245$	10.8869	−	10.8869i	0.695539	−	0.695539i
$246$	1.36953	+	1.42761i	0.0873179	+	0.0910211i
$247$		0			0
$248$	−13.8533	−	15.6962i	−0.879684	−	0.996708i
$249$	5.71940	+	5.71940i	0.362452	+	0.362452i
$250$	11.1132	+	11.5845i	0.702862	+	0.732670i
$251$	−10.1662			−0.641687			−0.320843	−	0.947132i	$-0.603966\pi$
$251$	−10.1662			−0.641687			−0.320843	+	0.947132i	$0.603966\pi$
$252$	0.117163	+	0.127320i	0.00738055	+	0.00802043i
$253$	−31.9147	−	31.9147i	−2.00646	−	2.00646i
$254$	−0.155974	+	7.51142i	−0.00978670	+	0.471308i
$255$	−7.18963	−	7.18963i	−0.450232	−	0.450232i
$256$	15.7798	+	2.64533i	0.986238	+	0.165333i
$257$			3.47141i			0.216541i	0.994121	+	0.108270i	$0.0345312\pi$
$257$			3.47141i			0.216541i	−0.994121	+	0.108270i	$0.965469\pi$
$258$	−2.31668	−	0.0481058i	−0.144230	−	0.00299494i
$259$	−0.105678			−0.00656652
$260$		0			0
$261$	−12.3150			−0.762280
$262$	6.41757	+	0.133261i	0.396479	+	0.00823287i
$263$		−	31.3121i		−	1.93079i	−0.260793	−	0.965395i	$-0.583984\pi$
$263$		−	31.3121i		−	1.93079i	0.260793	−	0.965395i	$-0.416016\pi$
$264$	11.0489	+	12.5187i	0.680011	+	0.770473i
$265$	−15.3185	−	15.3185i	−0.941008	−	0.941008i
$266$	0.00414613	−	0.199670i	0.000254216	−	0.0122425i
$267$	−11.2115	−	11.2115i	−0.686135	−	0.686135i
$268$	−3.54357	+	3.26086i	−0.216458	+	0.199189i
$269$	−10.7274			−0.654064			−0.327032	−	0.945013i	$-0.606048\pi$
$269$	−10.7274			−0.654064			−0.327032	+	0.945013i	$0.606048\pi$
$270$	−11.1094	−	11.5805i	−0.676096	−	0.704770i
$271$	−5.71755	−	5.71755i	−0.347317	−	0.347317i	0.511792	−	0.859109i	$-0.328982\pi$
$271$	−5.71755	−	5.71755i	−0.347317	−	0.347317i	−0.859109	+	0.511792i	$0.828982\pi$
$272$	−1.45254	+	17.4501i	−0.0880729	+	1.05807i
$273$		0			0
$274$	8.64682	+	9.01354i	0.522374	+	0.544528i
$275$	0.630058	−	0.630058i	0.0379939	−	0.0379939i
$276$	−0.707417	+	17.0266i	−0.0425815	+	1.02488i
$277$		−	26.4517i		−	1.58933i	−0.607048	−	0.794665i	$-0.707646\pi$
$277$		−	26.4517i		−	1.58933i	0.607048	−	0.794665i	$-0.292354\pi$
$278$	29.5555	+	0.613719i	1.77262	+	0.0368084i
$279$	9.86855	−	9.86855i	0.590815	−	0.590815i
$280$	−0.284968	−	0.0177725i	−0.0170301	−	0.00106211i
$281$	−0.572296	+	0.572296i	−0.0341403	+	0.0341403i	−0.723971	−	0.689831i	$-0.757685\pi$
$281$	−0.572296	+	0.572296i	−0.0341403	+	0.0341403i	0.689831	+	0.723971i	$0.257685\pi$
$282$	5.45311	+	5.68438i	0.324728	+	0.338500i
$283$	−15.7749			−0.937720			−0.468860	−	0.883272i	$-0.655335\pi$
$283$	−15.7749			−0.937720			−0.468860	+	0.883272i	$0.655335\pi$
$284$	0.130760	−	0.120328i	0.00775918	−	0.00714015i
$285$			7.14879i			0.423458i
$286$		0			0
$287$			0.0607978i			0.00358878i
$288$	−1.10527	+	10.6088i	−0.0651288	+	0.625130i
$289$	−2.16349			−0.127264
$290$	14.6650	−	14.0684i	0.861161	−	0.826124i
$291$	1.99612	−	1.99612i	0.117015	−	0.117015i
$292$	11.9739	−	11.0186i	0.700720	−	0.644815i
$293$	−9.64056	+	9.64056i	−0.563207	+	0.563207i	−0.930217	−	0.367010i	$-0.880382\pi$
$293$	−9.64056	+	9.64056i	−0.563207	+	0.563207i	0.367010	+	0.930217i	$0.380382\pi$
$294$	−0.216896	+	10.4453i	−0.0126497	+	0.609182i
$295$			23.1945i			1.35044i
$296$	−4.31085	−	4.88432i	−0.250563	−	0.283895i
$297$	−20.3937	+	20.3937i	−1.18336	+	1.18336i
$298$	−9.66320	+	9.27005i	−0.559774	+	0.537000i
$299$		0			0
$300$	−0.336138	−	0.0139658i	−0.0194069	−	0.000806316i
$301$	−0.0503547	−	0.0503547i	−0.00290240	−	0.00290240i
$302$	−9.65832	+	9.26537i	−0.555774	+	0.533162i
$303$	−0.535062			−0.0307385
$304$	9.39763	−	7.95334i	0.538991	−	0.456155i
$305$	12.3544	+	12.3544i	0.707411	+	0.707411i
$306$	−11.6706	−	0.242340i	−0.667166	−	0.0138537i
$307$	−13.9837	−	13.9837i	−0.798091	−	0.798091i	0.184704	−	0.982794i	$-0.440867\pi$
$307$	−13.9837	−	13.9837i	−0.798091	−	0.798091i	−0.982794	+	0.184704i	$0.940867\pi$
$308$	−0.0213016	+	0.512700i	−0.00121377	+	0.0292138i
$309$			3.29335i			0.187352i
$310$	−0.478121	+	23.0253i	−0.0271554	+	1.30775i
$311$	−0.682780			−0.0387169			−0.0193585	−	0.999813i	$-0.506162\pi$
$311$	−0.682780			−0.0387169			−0.0193585	+	0.999813i	$0.506162\pi$
$312$		0			0
$313$	18.0941			1.02274			0.511371	−	0.859360i	$-0.329138\pi$
$313$	18.0941			1.02274			0.511371	+	0.859360i	$0.329138\pi$
$314$	−0.131251	+	6.32080i	−0.00740694	+	0.356703i
$315$		−	0.190340i		−	0.0107245i
$316$	−0.0613668	+	1.47702i	−0.00345215	+	0.0830886i
$317$	−10.3563	−	10.3563i	−0.581670	−	0.581670i	0.353692	−	0.935362i	$-0.384926\pi$
$317$	−10.3563	−	10.3563i	−0.581670	−	0.581670i	−0.935362	+	0.353692i	$0.884926\pi$
$318$	14.6971	+	0.305185i	0.824174	+	0.0171140i
$319$	−25.8256	−	25.8256i	−1.44595	−	1.44595i
$320$	−10.8031	−	13.8959i	−0.603910	−	0.776804i
$321$	4.54606			0.253736
$322$	−0.377932	+	0.362556i	−0.0210613	+	0.0202044i
$323$	9.52731	+	9.52731i	0.530114	+	0.530114i
$324$	−0.423408	−	0.0175917i	−0.0235226	−	0.000977315i
$325$		0			0
$326$	4.54674	−	4.36176i	0.251821	−	0.241575i
$327$	−1.78578	+	1.78578i	−0.0987536	+	0.0987536i
$328$	−2.81000	+	2.48008i	−0.155157	+	0.136939i
$329$			0.242081i			0.0133464i
$330$	0.381332	−	18.3642i	0.0209916	−	1.01091i
$331$	−6.47783	+	6.47783i	−0.356054	+	0.356054i	−0.862356	−	0.506302i	$-0.831012\pi$
$331$	−6.47783	+	6.47783i	−0.356054	+	0.356054i	0.506302	+	0.862356i	$0.331012\pi$
$332$	−11.2760	+	10.3763i	−0.618848	+	0.569476i
$333$	3.07089	−	3.07089i	0.168283	−	0.168283i
$334$	−15.6925	+	15.0540i	−0.858653	+	0.823718i
$335$	5.29753			0.289435
$336$	0.147892	−	0.125163i	0.00806817	−	0.00682820i
$337$			28.8118i			1.56948i	0.619827	+	0.784738i	$0.287203\pi$
$337$			28.8118i			1.56948i	−0.619827	+	0.784738i	$0.712797\pi$
$338$		0			0
$339$			1.63353i			0.0887209i
$340$	14.1745	−	13.0437i	0.768723	−	0.707393i
$341$	41.3903			2.24141
$342$	5.68169	+	5.92265i	0.307230	+	0.320260i
$343$	−0.454140	+	0.454140i	−0.0245213	+	0.0245213i
$344$	0.273254	−	4.38142i	0.0147329	−	0.236230i
$345$	13.2559	−	13.2559i	0.713673	−	0.713673i
$346$	16.8510	+	0.349910i	0.905915	+	0.0188113i
$347$			19.2401i			1.03286i	0.856329	+	0.516430i	$0.172739\pi$
$347$			19.2401i			1.03286i	−0.856329	+	0.516430i	$0.827261\pi$
$348$	−0.572447	+	13.7780i	−0.0306864	+	0.738579i
$349$	14.1654	−	14.1654i	0.758258	−	0.758258i	−0.217747	−	0.976005i	$-0.569871\pi$
$349$	14.1654	−	14.1654i	0.758258	−	0.758258i	0.976005	+	0.217747i	$0.0698708\pi$
$350$	−0.00715756	−	0.00746112i	−0.000382588	−	0.000398814i
$351$		0			0
$352$	−24.5654	+	19.9297i	−1.30934	+	1.06226i
$353$	−16.6275	−	16.6275i	−0.884994	−	0.884994i	0.109043	−	0.994037i	$-0.465221\pi$
$353$	−16.6275	−	16.6275i	−0.884994	−	0.884994i	−0.994037	+	0.109043i	$0.965221\pi$
$354$	−10.8958	−	11.3579i	−0.579104	−	0.603664i
$355$	−0.195482			−0.0103751
$356$	22.1038	−	20.3404i	1.17150	−	1.07804i
$357$	0.149933	+	0.149933i	0.00793529	+	0.00793529i
$358$	−0.561537	+	27.0425i	−0.0296781	+	1.42924i
$359$	−19.2533	−	19.2533i	−1.01615	−	1.01615i	−0.999867	−	0.0162812i	$-0.994817\pi$
$359$	−19.2533	−	19.2533i	−1.01615	−	1.01615i	−0.0162812	−	0.999867i	$-0.505183\pi$
$360$	8.79730	−	7.76441i	0.463659	−	0.409220i
$361$			9.52681i			0.501411i
$362$	4.31038	+	0.0895049i	0.226549	+	0.00470427i
$363$	−21.3989			−1.12315
$364$		0			0
$365$	−17.9006			−0.936962
$366$	−11.8533	−	0.246133i	−0.619580	−	0.0128656i
$367$			36.8799i			1.92511i	0.271081	+	0.962557i	$0.412619\pi$
$367$			36.8799i			1.92511i	−0.271081	+	0.962557i	$0.587381\pi$
$368$	−32.1736	−	2.67811i	−1.67717	−	0.139606i
$369$	−1.76671	−	1.76671i	−0.0919715	−	0.0919715i
$370$	−0.148781	+	7.16500i	−0.00773476	+	0.372491i
$371$	0.319453	+	0.319453i	0.0165851	+	0.0165851i
$372$	−10.5822	−	11.4996i	−0.548661	−	0.596229i
$373$	−15.9140			−0.823996			−0.411998	−	0.911185i	$-0.635169\pi$
$373$	−15.9140			−0.823996			−0.411998	+	0.911185i	$0.635169\pi$
$374$	−23.9661	−	24.9825i	−1.23926	−	1.29181i
$375$	8.47351	+	8.47351i	0.437570	+	0.437570i
$376$	−11.1887	+	9.87503i	−0.577014	+	0.509266i
$377$		0			0
$378$	0.231676	+	0.241501i	0.0119161	+	0.0124215i
$379$	−16.3032	+	16.3032i	−0.837441	+	0.837441i	−0.988521	−	0.151080i	$-0.951725\pi$
$379$	−16.3032	+	16.3032i	−0.837441	+	0.837441i	0.151080	+	0.988521i	$0.451725\pi$
$380$	−13.5318	−	0.562218i	−0.694167	−	0.0288412i
$381$			5.60832i			0.287323i
$382$	−22.9642	−	0.476852i	−1.17495	−	0.0243979i
$383$	−8.38336	+	8.38336i	−0.428370	+	0.428370i	−0.888073	−	0.459703i	$-0.847956\pi$
$383$	−8.38336	+	8.38336i	−0.428370	+	0.428370i	0.459703	+	0.888073i	$0.347956\pi$
$384$	11.8177	+	1.72971i	0.603071	+	0.0882691i
$385$	0.399159	−	0.399159i	0.0203430	−	0.0203430i
$386$	13.6104	+	14.1876i	0.692751	+	0.722131i
$387$	2.92650			0.148762
$388$	3.62144	+	3.93541i	0.183851	+	0.199790i
$389$		−	9.59221i		−	0.486345i	−0.969983	−	0.243172i	$-0.921812\pi$
$389$		−	9.59221i		−	0.486345i	0.969983	−	0.243172i	$-0.0781880\pi$
$390$		0			0
$391$		−	35.3327i		−	1.78685i
$392$	−19.7547	−	1.23203i	−0.997761	−	0.0622270i
$393$	4.79160			0.241704
$394$	−7.23869	+	6.94418i	−0.364680	+	0.349843i
$395$	1.14992	−	1.14992i	0.0578586	−	0.0578586i
$396$	−14.2795	−	15.5175i	−0.717571	−	0.779783i
$397$	−5.36344	+	5.36344i	−0.269183	+	0.269183i	−0.828771	−	0.559588i	$-0.810959\pi$
$397$	−5.36344	+	5.36344i	−0.269183	+	0.269183i	0.559588	+	0.828771i	$0.310959\pi$
$398$	0.558173	−	26.8805i	0.0279787	−	1.34740i
$399$		−	0.149081i		−	0.00746339i
$400$	0.0528712	−	0.635170i	0.00264356	−	0.0317585i
$401$	−9.84615	+	9.84615i	−0.491693	+	0.491693i	−0.908839	−	0.417146i	$-0.863030\pi$
$401$	−9.84615	+	9.84615i	−0.491693	+	0.491693i	0.417146	+	0.908839i	$0.363030\pi$
$402$	−2.59409	+	2.48855i	−0.129382	+	0.124118i
$403$		0			0
$404$	0.0420801	−	1.01281i	0.00209356	−	0.0503892i
$405$	0.329640	+	0.329640i	0.0163800	+	0.0163800i
$406$	−0.305825	+	0.293383i	−0.0151779	+	0.0145603i
$407$	12.8798			0.638427
$408$	−0.813624	+	13.0458i	−0.0402804	+	0.645864i
$409$	16.1658	+	16.1658i	0.799349	+	0.799349i	0.982993	−	0.183644i	$-0.0587894\pi$
$409$	16.1658	+	16.1658i	0.799349	+	0.799349i	−0.183644	+	0.982993i	$0.558789\pi$
$410$	4.12211	+	0.0855954i	0.203576	+	0.00422726i
$411$	6.59296	+	6.59296i	0.325207	+	0.325207i
$412$	−6.23391	−	0.259006i	−0.307123	−	0.0127603i
$413$		−	0.483699i		−	0.0238013i
$414$	0.446815	−	21.5177i	0.0219598	−	1.05754i
$415$	16.8572			0.827488
$416$		0			0
$417$	22.0673			1.08064
$418$	−0.505320	+	24.3352i	−0.0247160	+	1.19027i
$419$		−	18.2462i		−	0.891385i	−0.895186	−	0.445693i	$-0.852957\pi$
$419$		−	18.2462i		−	0.891385i	0.895186	−	0.445693i	$-0.147043\pi$
$420$	−0.212952	−	0.00884771i	−0.0103910	−	0.000431724i
$421$	4.57385	+	4.57385i	0.222916	+	0.222916i	0.809725	−	0.586809i	$-0.199616\pi$
$421$	4.57385	+	4.57385i	0.222916	+	0.222916i	−0.586809	+	0.809725i	$0.699616\pi$
$422$	−4.22097	−	0.0876483i	−0.205474	−	0.00426665i
$423$	−7.03460	−	7.03460i	−0.342034	−	0.342034i
$424$	−1.73354	+	27.7959i	−0.0841881	+	1.34989i
$425$	0.697536			0.0338355
$426$	0.0957237	−	0.0918292i	0.00463783	−	0.00444914i
$427$	−0.257639	−	0.257639i	−0.0124680	−	0.0124680i
$428$	−0.357526	+	8.60515i	−0.0172817	+	0.415946i
$429$		0			0
$430$	−3.48495	+	3.34317i	−0.168059	+	0.161222i
$431$	−3.59839	+	3.59839i	−0.173328	+	0.173328i	−0.788440	−	0.615112i	$-0.789111\pi$
$431$	−3.59839	+	3.59839i	−0.173328	+	0.173328i	0.615112	+	0.788440i	$0.289111\pi$
$432$	−1.71133	+	20.5592i	−0.0823365	+	0.989153i
$433$			14.0128i			0.673410i	0.941610	+	0.336705i	$0.109313\pi$
$433$			14.0128i			0.673410i	−0.941610	+	0.336705i	$0.890687\pi$
$434$	0.00997074	−	0.480171i	0.000478611	−	0.0230490i
$435$	10.7268	−	10.7268i	0.514308	−	0.514308i
$436$	−3.23982	−	3.52070i	−0.155159	−	0.168611i
$437$	−17.5660	+	17.5660i	−0.840295	+	0.840295i
$438$	8.76557	−	8.40894i	0.418835	−	0.401795i
$439$	−27.7647			−1.32514			−0.662568	−	0.749002i	$-0.730533\pi$
$439$	−27.7647			−1.32514			−0.662568	+	0.749002i	$0.730533\pi$
$440$	34.7312	+	2.16607i	1.65575	+	0.103263i
$441$		−	13.1948i		−	0.628325i
$442$		0			0
$443$		−	5.46945i		−	0.259861i	−0.991523	−	0.129931i	$-0.958525\pi$
$443$		−	5.46945i		−	0.259861i	0.991523	−	0.129931i	$-0.0414755\pi$
$444$	−3.29295	−	3.57845i	−0.156277	−	0.169826i
$445$	−33.0446			−1.56646
$446$	−0.180939	−	0.188613i	−0.00856770	−	0.00893106i
$447$	−7.06815	+	7.06815i	−0.334312	+	0.334312i
$448$	0.225288	+	0.289785i	0.0106438	+	0.0136911i
$449$	13.7409	−	13.7409i	0.648472	−	0.648472i	−0.304151	−	0.952624i	$-0.598373\pi$
$449$	13.7409	−	13.7409i	0.648472	−	0.648472i	0.952624	+	0.304151i	$0.0983729\pi$
$450$	0.424802	+	0.00882101i	0.0200254	+	0.000415826i
$451$		−	7.40988i		−	0.348918i
$452$	−3.09207	−	0.128469i	−0.145439	−	0.00604267i
$453$	−7.06459	+	7.06459i	−0.331923	+	0.331923i
$454$	−15.2424	−	15.8889i	−0.715362	−	0.745701i
$455$		0			0
$456$	6.89035	−	6.08135i	0.322670	−	0.284785i
$457$	11.0480	+	11.0480i	0.516804	+	0.516804i	0.916603	−	0.399799i	$-0.130920\pi$
$457$	11.0480	+	11.0480i	0.516804	+	0.516804i	−0.399799	+	0.916603i	$0.630920\pi$
$458$	14.9527	+	15.5869i	0.698696	+	0.728328i
$459$	−22.5778			−1.05384
$460$	24.0493	+	26.1343i	1.12130	+	1.21852i
$461$	−16.3738	−	16.3738i	−0.762602	−	0.762602i	0.214190	−	0.976792i	$-0.431289\pi$
$461$	−16.3738	−	16.3738i	−0.762602	−	0.762602i	−0.976792	+	0.214190i	$0.931289\pi$
$462$	−0.00795231	+	0.382967i	−0.000369975	+	0.0178173i
$463$	17.5627	+	17.5627i	0.816207	+	0.816207i	0.985556	−	0.169349i	$-0.0541665\pi$
$463$	17.5627	+	17.5627i	0.816207	+	0.816207i	−0.169349	+	0.985556i	$0.554166\pi$
$464$	−26.0351	−	2.16715i	−1.20865	−	0.100607i
$465$			17.1916i			0.797242i
$466$	11.6121	+	0.241124i	0.537919	+	0.0111699i
$467$	14.2468			0.659265			0.329633	−	0.944109i	$-0.393075\pi$
$467$	14.2468			0.659265			0.329633	+	0.944109i	$0.393075\pi$
$468$		0			0
$469$	−0.110475			−0.00510126
$470$	16.4132	+	0.340819i	0.757083	+	0.0157208i
$471$			4.71936i			0.217456i
$472$	22.3560	−	19.7312i	1.02902	−	0.908201i
$473$	6.13710	+	6.13710i	0.282184	+	0.282184i
$474$	−0.0229094	+	1.10327i	−0.00105226	+	0.0506750i
$475$	−0.346787	−	0.346787i	−0.0159117	−	0.0159117i
$476$	−0.295597	+	0.272014i	−0.0135486	+	0.0124677i
$477$	−18.5659			−0.850072
$478$	11.4140	+	11.8980i	0.522063	+	0.544204i
$479$	−5.81389	−	5.81389i	−0.265643	−	0.265643i	0.561699	−	0.827342i	$-0.310148\pi$
$479$	−5.81389	−	5.81389i	−0.265643	−	0.265643i	−0.827342	+	0.561699i	$0.810148\pi$
$480$	−8.27787	−	10.2033i	−0.377831	−	0.465716i
$481$		0			0
$482$	28.2975	+	29.4976i	1.28892	+	1.34358i
$483$	−0.276439	+	0.276439i	−0.0125784	+	0.0125784i
$484$	1.68292	−	40.5056i	0.0764964	−	1.84116i
$485$		−	5.88332i		−	0.267148i
$486$	−22.1932	−	0.460842i	−1.00671	−	0.0209042i
$487$	−20.2588	+	20.2588i	−0.918012	+	0.918012i	−0.996885	−	0.0788729i	$-0.974868\pi$
$487$	−20.2588	+	20.2588i	−0.918012	+	0.918012i	0.0788729	+	0.996885i	$0.474868\pi$
$488$	1.39810	−	22.4175i	0.0632891	−	1.01479i
$489$	3.32572	−	3.32572i	0.150394	−	0.150394i
$490$	15.0735	+	15.7127i	0.680950	+	0.709829i
$491$	4.09337			0.184731			0.0923655	−	0.995725i	$-0.470557\pi$
$491$	4.09337			0.184731			0.0923655	+	0.995725i	$0.470557\pi$
$492$	−2.05872	+	1.89447i	−0.0928143	+	0.0854095i
$493$		−	28.5915i		−	1.28769i
$494$		0			0
$495$			23.1982i			1.04268i
$496$	22.5997	−	19.1264i	1.01476	−	0.858802i
$497$	0.00407660			0.000182860
$498$	−8.25464	+	7.91879i	−0.369899	+	0.354850i
$499$	10.2828	−	10.2828i	0.460323	−	0.460323i	−0.438438	−	0.898761i	$-0.644468\pi$
$499$	10.2828	−	10.2828i	0.460323	−	0.460323i	0.898761	+	0.438438i	$0.144468\pi$
$500$	−16.7058	+	15.3730i	−0.747104	+	0.687500i
$501$	−11.4783	+	11.4783i	−0.512810	+	0.512810i
$502$	0.298478	−	14.3741i	0.0133217	−	0.641548i
$503$		−	35.4638i		−	1.58125i	−0.612299	−	0.790627i	$-0.709755\pi$
$503$		−	35.4638i		−	1.58125i	0.612299	−	0.790627i	$-0.290245\pi$
$504$	−0.183459	+	0.161919i	−0.00817193	+	0.00721245i
$505$	−0.788514	+	0.788514i	−0.0350884	+	0.0350884i
$506$	46.0614	−	44.1874i	2.04768	−	1.96437i
$507$		0			0
$508$	−10.6159	−	0.441067i	−0.471004	−	0.0195692i
$509$	27.2535	+	27.2535i	1.20799	+	1.20799i	0.971677	+	0.236312i	$0.0759387\pi$
$509$	27.2535	+	27.2535i	1.20799	+	1.20799i	0.236312	+	0.971677i	$0.424061\pi$
$510$	10.3766	−	9.95440i	0.459482	−	0.440788i
$511$	0.373300			0.0165138
$512$	−4.20355	+	22.2335i	−0.185772	+	0.982593i
$513$	11.2248	+	11.2248i	0.495586	+	0.495586i
$514$	−4.90826	−	0.101920i	−0.216494	−	0.00449549i
$515$	4.85336	+	4.85336i	0.213865	+	0.213865i
$516$	0.136034	−	3.27416i	0.00598858	−	0.144137i
$517$		−	29.5042i		−	1.29760i
$518$	0.00310269	−	0.149419i	0.000136324	−	0.00656510i
$519$	12.5816			0.552271
$520$		0			0
$521$	−21.1353			−0.925956			−0.462978	−	0.886370i	$-0.653219\pi$
$521$	−21.1353			−0.925956			−0.462978	+	0.886370i	$0.653219\pi$
$522$	0.361566	−	17.4123i	0.0158253	−	0.762116i
$523$		−	3.57551i		−	0.156346i	−0.996940	−	0.0781730i	$-0.975091\pi$
$523$		−	3.57551i		−	0.156346i	0.996940	−	0.0781730i	$-0.0249087\pi$
$524$	−0.376837	+	9.06994i	−0.0164622	+	0.396222i
$525$	−0.00545744	−	0.00545744i	−0.000238182	−	0.000238182i
$526$	44.2725	+	0.919318i	1.93037	+	0.0400842i
$527$	22.9116	+	22.9116i	0.998043	+	0.998043i
$528$	−18.0247	+	15.2546i	−0.784424	+	0.663869i
$529$	42.1446			1.83237
$530$	22.1087	−	21.2092i	0.960341	−	0.921269i
$531$	14.0557	+	14.0557i	0.609967	+	0.609967i
$532$	0.282193	+	0.0117245i	0.0122346	+	0.000508322i
$533$		0			0
$534$	16.1813	−	15.5229i	0.700231	−	0.671742i
$535$	6.69947	−	6.69947i	0.289643	−	0.289643i
$536$	−4.50652	−	5.10602i	−0.194652	−	0.220547i
$537$			20.1910i			0.871305i
$538$	0.314955	−	15.1676i	0.0135787	−	0.653923i
$539$	27.6706	−	27.6706i	1.19186	−	1.19186i
$540$	16.7000	−	15.3677i	0.718654	−	0.661319i
$541$	21.6649	−	21.6649i	0.931447	−	0.931447i	−0.0663494	−	0.997796i	$-0.521135\pi$
$541$	21.6649	−	21.6649i	0.931447	−	0.931447i	0.997796	+	0.0663494i	$0.0211352\pi$
$542$	8.25197	−	7.91623i	0.354452	−	0.340031i
$543$	3.21830			0.138110
$544$	−24.6302	−	2.56608i	−1.05601	−	0.110020i
$545$			5.26335i			0.225457i
$546$		0			0
$547$			32.6786i			1.39724i	0.715494	+	0.698618i	$0.246201\pi$
$547$			32.6786i			1.39724i	−0.715494	+	0.698618i	$0.753799\pi$
$548$	−12.9982	+	11.9612i	−0.555255	+	0.510956i
$549$	14.9734			0.639049
$550$	0.872346	+	0.909342i	0.0371969	+	0.0387745i
$551$	−14.2145	+	14.2145i	−0.605559	+	0.605559i
$552$	−24.0532	−	1.50012i	−1.02377	−	0.0638493i
$553$	−0.0239804	+	0.0239804i	−0.00101975	+	0.00101975i
$554$	37.4003	+	0.776617i	1.58899	+	0.0329953i
$555$			5.34967i			0.227081i
$556$	−1.73549	+	41.7708i	−0.0736010	+	1.77148i
$557$	20.8787	−	20.8787i	0.884661	−	0.884661i	−0.109343	−	0.994004i	$-0.534875\pi$
$557$	20.8787	−	20.8787i	0.884661	−	0.884661i	0.994004	+	0.109343i	$0.0348748\pi$
$558$	13.6635	+	14.2430i	0.578422	+	0.602953i
$559$		0			0
$560$	0.0334953	−	0.402397i	0.00141544	−	0.0170044i
$561$	−18.2734	−	18.2734i	−0.771505	−	0.771505i
$562$	−0.792372	−	0.825977i	−0.0334242	−	0.0348417i
$563$	8.95998			0.377618			0.188809	−	0.982014i	$-0.439537\pi$
$563$	8.95998			0.377618			0.188809	+	0.982014i	$0.439537\pi$
$564$	−8.19729	+	7.54330i	−0.345168	+	0.317630i
$565$	2.40730	+	2.40730i	0.101276	+	0.101276i
$566$	0.463148	−	22.3043i	0.0194675	−	0.937518i
$567$	−0.00687433	−	0.00687433i	−0.000288695	−	0.000288695i
$568$	0.166294	+	0.188416i	0.00697752	+	0.00790574i
$569$			30.5627i			1.28125i	0.767852	+	0.640627i	$0.221325\pi$
$569$			30.5627i			1.28125i	−0.767852	+	0.640627i	$0.778675\pi$
$570$	−10.1077	−	0.209887i	−0.423366	−	0.00879119i
$571$	−15.4319			−0.645805			−0.322903	−	0.946432i	$-0.604659\pi$
$571$	−15.4319			−0.645805			−0.322903	+	0.946432i	$0.604659\pi$
$572$		0			0
$573$	−17.1460			−0.716284
$574$	−0.0859625	−	0.00178501i	−0.00358801	−	7.45049e-5i
$575$			1.28608i			0.0536333i
$576$	−14.9674	−	1.87423i	−0.623643	−	0.0780928i
$577$	28.5522	+	28.5522i	1.18864	+	1.18864i	0.977442	+	0.211202i	$0.0677379\pi$
$577$	28.5522	+	28.5522i	1.18864	+	1.18864i	0.211202	+	0.977442i	$0.432262\pi$
$578$	0.0635196	−	3.05898i	0.00264207	−	0.127237i
$579$	10.3775	+	10.3775i	0.431276	+	0.431276i
$580$	19.4609	+	21.1481i	0.808068	+	0.878126i
$581$	−0.351541			−0.0145844
$582$	2.76373	+	2.88094i	0.114560	+	0.119419i
$583$	−38.9341	−	38.9341i	−1.61248	−	1.61248i
$584$	15.2278	+	17.2535i	0.630129	+	0.713955i
$585$		0			0
$586$	−13.3478	−	13.9139i	−0.551393	−	0.574778i
$587$	31.5306	−	31.5306i	1.30141	−	1.30141i	0.373967	−	0.927442i	$-0.377997\pi$
$587$	31.5306	−	31.5306i	1.30141	−	1.30141i	0.927442	−	0.373967i	$-0.122003\pi$
$588$	−14.7623	−	0.613343i	−0.608788	−	0.0252939i
$589$		−	22.7814i		−	0.938691i
$590$	−32.7949	−	0.680985i	−1.35014	−	0.0280357i
$591$	−5.29474	+	5.29474i	−0.217797	+	0.217797i
$592$	7.03255	−	5.95174i	0.289036	−	0.244615i
$593$	−13.0126	+	13.0126i	−0.534363	+	0.534363i	−0.921868	−	0.387504i	$-0.873337\pi$
$593$	−13.0126	+	13.0126i	−0.534363	+	0.534363i	0.387504	+	0.921868i	$0.373337\pi$
$594$	−28.2361	−	29.4336i	−1.15854	−	1.20767i
$595$	0.441908			0.0181165
$596$	−12.8233	−	13.9350i	−0.525263	−	0.570802i
$597$		−	20.0700i		−	0.821411i
$598$		0			0
$599$			8.91538i			0.364273i	0.983273	+	0.182136i	$0.0583012\pi$
$599$			8.91538i			0.364273i	−0.983273	+	0.182136i	$0.941699\pi$
$600$	0.0296153	−	0.474858i	0.00120904	−	0.0193860i
$601$	−30.3363			−1.23744			−0.618721	−	0.785611i	$-0.712349\pi$
$601$	−30.3363			−1.23744			−0.618721	+	0.785611i	$0.712349\pi$
$602$	0.0726753	−	0.0697185i	0.00296202	−	0.00284151i
$603$	3.21028	−	3.21028i	0.130733	−	0.130733i
$604$	−12.8168	−	13.9280i	−0.521509	−	0.566723i
$605$	−31.5353	+	31.5353i	−1.28209	+	1.28209i
$606$	0.0157093	−	0.756530i	0.000638147	−	0.0307319i
$607$		−	31.2197i		−	1.26717i	−0.773673	−	0.633585i	$-0.781583\pi$
$607$		−	31.2197i		−	1.26717i	0.773673	−	0.633585i	$-0.218417\pi$
$608$	10.9694	+	13.5209i	0.444867	+	0.548345i
$609$	−0.223696	+	0.223696i	−0.00906462	+	0.00906462i
$610$	−17.8307	+	17.1053i	−0.721944	+	0.692572i
$611$		0			0
$612$	0.685295	−	16.4941i	0.0277014	−	0.666735i
$613$	−19.3296	−	19.3296i	−0.780716	−	0.780716i	0.199236	−	0.979952i	$-0.436154\pi$
$613$	−19.3296	−	19.3296i	−0.780716	−	0.780716i	−0.979952	+	0.199236i	$0.936154\pi$
$614$	20.1822	−	19.3611i	0.814487	−	0.781350i
$615$	3.07773			0.124106
$616$	−0.724286	−	0.0451713i	−0.0291823	−	0.00182000i
$617$	−1.16300	−	1.16300i	−0.0468207	−	0.0468207i	0.683309	−	0.730130i	$-0.260540\pi$
$617$	−1.16300	−	1.16300i	−0.0468207	−	0.0468207i	−0.730130	+	0.683309i	$0.760540\pi$
$618$	−4.65649	−	0.0966919i	−0.187312	−	0.00388952i
$619$	−7.43277	−	7.43277i	−0.298748	−	0.298748i	0.541775	−	0.840523i	$-0.317752\pi$
$619$	−7.43277	−	7.43277i	−0.298748	−	0.298748i	−0.840523	+	0.541775i	$0.817752\pi$
$620$	−32.5417	−	1.35204i	−1.30691	−	0.0542991i
$621$		−	41.6278i		−	1.67047i
$622$	0.0200463	−	0.965389i	0.000803783	−	0.0387086i
$623$	0.689113			0.0276087
$624$		0			0
$625$	24.1779			0.967116
$626$	−0.531240	+	25.5835i	−0.0212326	+	1.02252i
$627$			18.1696i			0.725625i
$628$	−8.93318	−	0.371155i	−0.356473	−	0.0148107i
$629$	7.12960	+	7.12960i	0.284276	+	0.284276i
$630$	0.269124	+	0.00558834i	0.0107221	+	0.000222645i
$631$	31.7061	+	31.7061i	1.26220	+	1.26220i	0.950024	+	0.312177i	$0.101058\pi$
$631$	31.7061	+	31.7061i	1.26220	+	1.26220i	0.312177	+	0.950024i	$0.398942\pi$
$632$	−2.08656	−	0.130132i	−0.0829990	−	0.00517637i
$633$	−3.15154			−0.125263
$634$	14.9470	−	14.3389i	0.593620	−	0.569469i
$635$	8.26490	+	8.26490i	0.327983	+	0.327983i
$636$	−0.863009	+	20.7714i	−0.0342205	+	0.823641i
$637$		0			0
$638$	37.2732	−	35.7568i	1.47566	−	1.41562i
$639$	−0.118461	+	0.118461i	−0.00468625	+	0.00468625i
$640$	19.9647	−	14.8666i	0.789174	−	0.587653i
$641$			14.2822i			0.564113i	0.959398	+	0.282057i	$0.0910166\pi$
$641$			14.2822i			0.564113i	−0.959398	+	0.282057i	$0.908983\pi$
$642$	−0.133471	+	6.42771i	−0.00526769	+	0.253682i
$643$	−18.8510	+	18.8510i	−0.743411	+	0.743411i	−0.973233	−	0.229822i	$-0.926186\pi$
$643$	−18.8510	+	18.8510i	−0.743411	+	0.743411i	0.229822	+	0.973233i	$0.426186\pi$
$644$	−0.501525	−	0.545006i	−0.0197628	−	0.0214762i
$645$	−2.54907	+	2.54907i	−0.100370	+	0.100370i
$646$	−13.7505	+	13.1910i	−0.541005	+	0.518994i
$647$	42.5975			1.67468			0.837341	−	0.546681i	$-0.184109\pi$
$647$	42.5975			1.67468			0.837341	+	0.546681i	$0.184109\pi$
$648$	0.0373042	−	0.598143i	0.00146545	−	0.0234973i
$649$			58.9520i			2.31407i
$650$		0			0
$651$		−	0.358515i		−	0.0140513i
$652$	6.03364	+	6.55674i	0.236295	+	0.256782i
$653$	−25.6749			−1.00474			−0.502368	−	0.864654i	$-0.667538\pi$
$653$	−25.6749			−1.00474			−0.502368	+	0.864654i	$0.667538\pi$
$654$	−2.47249	−	2.57735i	−0.0966822	−	0.100783i
$655$	7.06132	−	7.06132i	0.275909	−	0.275909i
$656$	−3.42410	−	4.04590i	−0.133689	−	0.157966i
$657$	−10.8477	+	10.8477i	−0.423208	+	0.423208i
$658$	−0.342281	−	0.00710745i	−0.0133435	−	0.000277077i
$659$		−	22.0088i		−	0.857342i	−0.903461	−	0.428671i	$-0.858982\pi$
$659$		−	22.0088i		−	0.857342i	0.903461	−	0.428671i	$-0.141018\pi$
$660$	25.9541	+	1.07834i	1.01026	+	0.0419742i
$661$	15.1957	−	15.1957i	0.591046	−	0.591046i	−0.346868	−	0.937914i	$-0.612755\pi$
$661$	15.1957	−	15.1957i	0.591046	−	0.591046i	0.937914	+	0.346868i	$0.112755\pi$
$662$	−8.96888	−	9.34925i	−0.348585	−	0.363369i
$663$		0			0
$664$	−14.3402	−	16.2478i	−0.556506	−	0.630538i
$665$	−0.219699	−	0.219699i	−0.00851955	−	0.00851955i
$666$	4.25179	+	4.43211i	0.164754	+	0.171741i
$667$	52.7155			2.04115
$668$	−20.8243	−	22.6297i	−0.805715	−	0.875569i
$669$	−0.137961	−	0.137961i	−0.00533387	−	0.00533387i
$670$	−0.155534	+	7.49023i	−0.00600882	+	0.289373i
$671$	31.4004	+	31.4004i	1.21220	+	1.21220i
$672$	0.172627	+	0.212780i	0.00665923	+	0.00820818i
$673$		−	31.5996i		−	1.21807i	−0.793142	−	0.609037i	$-0.791556\pi$
$673$		−	31.5996i		−	1.21807i	0.793142	−	0.609037i	$-0.208444\pi$
$674$	−40.7372	−	0.845907i	−1.56914	−	0.0325831i
$675$	0.821815			0.0316317
$676$		0			0
$677$	−21.3186			−0.819341			−0.409671	−	0.912234i	$-0.634356\pi$
$677$	−21.3186			−0.819341			−0.409671	+	0.912234i	$0.634356\pi$
$678$	−2.30966	−	0.0479599i	−0.0887018	−	0.00184189i
$679$			0.122691i			0.00470845i
$680$	18.0264	+	20.4245i	0.691282	+	0.783243i
$681$	−11.6219	−	11.6219i	−0.445353	−	0.445353i
$682$	−1.21521	+	58.5221i	−0.0465328	+	2.24093i
$683$	19.9129	+	19.9129i	0.761944	+	0.761944i	0.976674	−	0.214729i	$-0.0688869\pi$
$683$	19.9129	+	19.9129i	0.761944	+	0.761944i	−0.214729	+	0.976674i	$0.568887\pi$
$684$	−8.54090	+	7.85950i	−0.326570	+	0.300515i
$685$	19.4319			0.742455
$686$	−0.628779	−	0.655446i	−0.0240069	−	0.0250251i
$687$	11.4010	+	11.4010i	0.434977	+	0.434977i
$688$	6.18690	+	0.514994i	0.235873	+	0.0196340i
$689$		0			0
$690$	18.3534	+	19.1318i	0.698703	+	0.728335i
$691$	−16.4063	+	16.4063i	−0.624124	+	0.624124i	−0.946583	−	0.322460i	$-0.895490\pi$
$691$	−16.4063	+	16.4063i	−0.624124	+	0.624124i	0.322460	+	0.946583i	$0.395490\pi$
$692$	−0.989483	+	23.8155i	−0.0376145	+	0.905329i
$693$		−	0.483776i		−	0.0183771i
$694$	−27.2037	−	0.564884i	−1.03264	−	0.0214427i
$695$	32.5203	−	32.5203i	1.23356	−	1.23356i
$696$	−19.4640	−	1.21391i	−0.737783	−	0.0460130i
$697$	4.10174	−	4.10174i	0.155364	−	0.155364i
$698$	19.6127	+	20.4445i	0.742353	+	0.773836i
$699$	8.67002			0.327930
$700$	0.0107595	−	0.00990108i	0.000406670	−	0.000374226i
$701$			18.0110i			0.680268i	0.940377	+	0.340134i	$0.110472\pi$
$701$			18.0110i			0.680268i	−0.940377	+	0.340134i	$0.889528\pi$
$702$		0			0
$703$		−	7.08909i		−	0.267370i
$704$	−27.4575	−	35.3183i	−1.03484	−	1.33111i
$705$	12.2547			0.461539
$706$	23.9980	−	23.0216i	0.903176	−	0.866430i
$707$	0.0164437	−	0.0164437i	0.000618429	−	0.000618429i
$708$	16.3789	−	15.0722i	0.615557	−	0.566447i
$709$	−6.21757	+	6.21757i	−0.233506	+	0.233506i	−0.814154	−	0.580648i	$-0.802799\pi$
$709$	−6.21757	+	6.21757i	−0.233506	+	0.233506i	0.580648	+	0.814154i	$0.302799\pi$
$710$	0.00573932	−	0.276394i	0.000215393	−	0.0103729i
$711$		−	1.39369i		−	0.0522674i
$712$	28.1105	+	31.8500i	1.05348	+	1.19363i
$713$	−42.2432	+	42.2432i	−1.58202	+	1.58202i
$714$	−0.216393	+	0.207589i	−0.00809832	+	0.00776884i
$715$		0			0
$716$	−38.2191	−	1.58792i	−1.42832	−	0.0593435i
$717$	8.70283	+	8.70283i	0.325013	+	0.325013i
$718$	27.7876	−	26.6571i	1.03703	−	0.994834i
$719$	−18.4651			−0.688630			−0.344315	−	0.938854i	$-0.611889\pi$
$719$	−18.4651			−0.688630			−0.344315	+	0.938854i	$0.611889\pi$
$720$	10.7199	+	12.6665i	0.399506	+	0.472054i
$721$	−0.101212	−	0.101212i	−0.00376934	−	0.00376934i
$722$	−13.4700	−	0.279705i	−0.501303	−	0.0104095i
$723$	21.5760	+	21.5760i	0.802421	+	0.802421i
$724$	−0.253104	+	6.09186i	−0.00940652	+	0.226402i
$725$			1.04071i			0.0386509i
$726$	0.628268	−	30.2561i	0.0233172	−	1.12291i
$727$	−27.5508			−1.02180			−0.510901	−	0.859640i	$-0.670688\pi$
$727$	−27.5508			−1.02180			−0.510901	+	0.859640i	$0.670688\pi$
$728$		0			0
$729$	−15.9347			−0.590174
$730$	0.525558	−	25.3099i	0.0194518	−	0.936760i
$731$			6.79438i			0.251299i
$732$	0.696018	−	16.7522i	0.0257256	−	0.619179i
$733$	−14.8382	−	14.8382i	−0.548060	−	0.548060i	0.377819	−	0.925879i	$-0.376674\pi$
$733$	−14.8382	−	14.8382i	−0.548060	−	0.548060i	−0.925879	+	0.377819i	$0.876674\pi$
$734$	−52.1448	−	1.08278i	−1.92470	−	0.0399663i
$735$	11.4931	+	11.4931i	0.423929	+	0.423929i
$736$	4.73122	−	45.4119i	0.174395	−	1.67391i
$737$	13.4644			0.495968
$738$	2.54984	−	2.44610i	0.0938611	−	0.0900423i
$739$	−8.46178	−	8.46178i	−0.311272	−	0.311272i	0.534130	−	0.845402i	$-0.320639\pi$
$739$	−8.46178	−	8.46178i	−0.311272	−	0.311272i	−0.845402	+	0.534130i	$0.820639\pi$
$740$	−10.1263	−	0.420726i	−0.372250	−	0.0154662i
$741$		0			0
$742$	−0.461056	+	0.442298i	−0.0169259	+	0.0162373i
$743$	4.43245	−	4.43245i	0.162611	−	0.162611i	−0.621111	−	0.783722i	$-0.713319\pi$
$743$	4.43245	−	4.43245i	0.162611	−	0.162611i	0.783722	+	0.621111i	$0.213319\pi$
$744$	16.5701	−	14.6246i	0.607490	−	0.536165i
$745$			20.8325i			0.763243i
$746$	0.467231	−	22.5009i	0.0171066	−	0.823818i
$747$	10.2154	−	10.2154i	0.373761	−	0.373761i
$748$	36.0266	−	33.1523i	1.31726	−	1.21217i
$749$	−0.139711	+	0.139711i	−0.00510493	+	0.00510493i
$750$	−12.2296	+	11.7320i	−0.446560	+	0.428392i
$751$	−2.19830			−0.0802170			−0.0401085	−	0.999195i	$-0.512770\pi$
$751$	−2.19830			−0.0802170			−0.0401085	+	0.999195i	$0.512770\pi$
$752$	−13.6339	−	16.1097i	−0.497177	−	0.587462i
$753$		−	10.7323i		−	0.391106i
$754$		0			0
$755$			20.8220i			0.757789i
$756$	−0.348263	+	0.320478i	−0.0126662	+	0.0116557i
$757$	−17.4999			−0.636043			−0.318021	−	0.948084i	$-0.603018\pi$
$757$	−17.4999			−0.636043			−0.318021	+	0.948084i	$0.603018\pi$
$758$	−22.5726	−	23.5300i	−0.819875	−	0.854646i
$759$	33.6916	−	33.6916i	1.22293	−	1.22293i
$760$	1.19222	−	19.1162i	0.0432462	−	0.693419i
$761$	−4.01237	+	4.01237i	−0.145448	+	0.145448i	−0.776081	−	0.630633i	$-0.782795\pi$
$761$	−4.01237	+	4.01237i	−0.145448	+	0.145448i	0.630633	+	0.776081i	$0.282795\pi$
$762$	−7.92965	−	0.164659i	−0.287261	−	0.00596497i
$763$		−	0.109762i		−	0.00397365i
$764$	1.34845	−	32.4553i	0.0487852	−	1.17419i
$765$	−12.8413	+	12.8413i	−0.464280	+	0.464280i
$766$	−11.6072	−	12.0994i	−0.419384	−	0.437170i
$767$		0			0
$768$	−2.79262	+	16.6584i	−0.100770	+	0.601109i
$769$	−6.35568	−	6.35568i	−0.229192	−	0.229192i	0.583163	−	0.812355i	$-0.301815\pi$
$769$	−6.35568	−	6.35568i	−0.229192	−	0.229192i	−0.812355	+	0.583163i	$0.801815\pi$
$770$	0.552655	+	0.576093i	0.0199163	+	0.0207609i
$771$	−3.66470			−0.131981
$772$	−20.4596	+	18.8273i	−0.736357	+	0.677610i
$773$	−0.0118844	−	0.0118844i	−0.000427451	−	0.000427451i	0.706893	−	0.707320i	$-0.250096\pi$
$773$	−0.0118844	−	0.0118844i	−0.000427451	−	0.000427451i	−0.707320	+	0.706893i	$0.750096\pi$
$774$	−0.0859214	+	4.13780i	−0.00308838	+	0.148730i
$775$	−0.833963	−	0.833963i	−0.0299568	−	0.0299568i
$776$	−5.67064	+	5.00485i	−0.203564	+	0.179663i
$777$		−	0.111562i		−	0.00400227i
$778$	13.5625	+	0.281625i	0.486240	+	0.0100968i
$779$	−4.07844			−0.146125
$780$		0			0
$781$	−0.496845			−0.0177785
$782$	49.9572	+	1.03736i	1.78647	+	0.0370959i
$783$		−	33.6856i		−	1.20382i
$784$	2.32197	−	27.8951i	0.0829276	−	0.996254i
$785$	6.95485	+	6.95485i	0.248229	+	0.248229i
$786$	−0.140680	+	6.77489i	−0.00501791	+	0.241652i
$787$	−12.8932	−	12.8932i	−0.459593	−	0.459593i	0.438929	−	0.898522i	$-0.355358\pi$
$787$	−12.8932	−	12.8932i	−0.459593	−	0.459593i	−0.898522	+	0.438929i	$0.855358\pi$
$788$	−9.60591	−	10.4387i	−0.342196	−	0.371864i
$789$	33.0556			1.17681
$790$	1.59212	+	1.65964i	0.0566450	+	0.0590473i
$791$	−0.0502020	−	0.0502020i	−0.00178498	−	0.00178498i
$792$	22.3596	−	19.7343i	0.794512	−	0.701228i
$793$		0			0
$794$	−7.42594	−	7.74088i	−0.263537	−	0.274714i
$795$	16.1714	−	16.1714i	0.573541	−	0.573541i
$796$	37.9902	+	1.57841i	1.34653	+	0.0559453i
$797$			19.4307i			0.688269i	0.938920	+	0.344135i	$0.111828\pi$
$797$			19.4307i			0.688269i	−0.938920	+	0.344135i	$0.888172\pi$
$798$	0.210787	+	0.00437699i	0.00746178	+	0.000154944i
$799$	16.3321	−	16.3321i	0.577787	−	0.577787i
$800$	0.896520	+	0.0934035i	0.0316968	+	0.00330231i
$801$	−20.0248	+	20.0248i	−0.707542	+	0.707542i
$802$	−13.6325	−	14.2106i	−0.481379	−	0.501795i
$803$	−45.4969			−1.60555
$804$	−3.44242	−	3.74088i	−0.121405	−	0.131931i
$805$			0.814768i			0.0287168i
$806$		0			0
$807$		−	11.3247i		−	0.398650i
$808$	1.43079	+	0.0892333i	0.0503348	+	0.00313922i
$809$	−35.6151			−1.25216			−0.626080	−	0.779759i	$-0.715342\pi$
$809$	−35.6151			−1.25216			−0.626080	+	0.779759i	$0.715342\pi$
$810$	−0.475760	+	0.456403i	−0.0167165	+	0.0160364i
$811$	15.4505	−	15.4505i	0.542539	−	0.542539i	−0.381734	−	0.924272i	$-0.624673\pi$
$811$	15.4505	−	15.4505i	0.542539	−	0.542539i	0.924272	+	0.381734i	$0.124673\pi$
$812$	−0.405837	−	0.441023i	−0.0142421	−	0.0154769i
$813$	6.03591	−	6.03591i	0.211688	−	0.211688i
$814$	−0.378148	+	18.2108i	−0.0132541	+	0.638290i
$815$		−	9.80213i		−	0.343354i
$816$	−18.4217	−	1.53341i	−0.644889	−	0.0536802i
$817$	3.37789	−	3.37789i	0.118177	−	0.118177i
$818$	−23.3316	+	22.3824i	−0.815771	+	0.782582i
$819$		0			0
$820$	−0.242048	+	5.82577i	−0.00845269	+	0.203445i
$821$	11.8729	+	11.8729i	0.414367	+	0.414367i	0.883257	−	0.468889i	$-0.155346\pi$
$821$	11.8729	+	11.8729i	0.414367	+	0.414367i	−0.468889	+	0.883257i	$0.655346\pi$
$822$	−9.51541	+	9.12827i	−0.331888	+	0.318385i
$823$	50.1778			1.74909			0.874544	−	0.484946i	$-0.161161\pi$
$823$	50.1778			1.74909			0.874544	+	0.484946i	$0.161161\pi$
$824$	0.549237	−	8.80658i	0.0191336	−	0.306792i
$825$	0.665139	+	0.665139i	0.0231572	+	0.0231572i
$826$	0.683906	+	0.0142013i	0.0237961	+	0.000494126i
$827$	−21.3532	−	21.3532i	−0.742523	−	0.742523i	0.230540	−	0.973063i	$-0.425951\pi$
$827$	−21.3532	−	21.3532i	−0.742523	−	0.742523i	−0.973063	+	0.230540i	$0.925951\pi$
$828$	30.4110	+	1.26351i	1.05686	+	0.0439101i
$829$			36.4070i			1.26447i	0.774778	+	0.632233i	$0.217862\pi$
$829$			36.4070i			1.26447i	−0.774778	+	0.632233i	$0.782138\pi$
$830$	−0.494924	+	23.8346i	−0.0171791	+	0.827310i
$831$	27.9246			0.968692
$832$		0			0
$833$	30.6341			1.06141
$834$	−0.647891	+	31.2011i	−0.0224346	+	1.08041i
$835$			33.8307i			1.17076i
$836$	−34.3929	−	1.42895i	−1.18951	−	0.0494214i
$837$	26.9937	+	26.9937i	0.933038	+	0.933038i
$838$	25.7985	+	0.535704i	0.891193	+	0.0185056i
$839$	−23.2878	−	23.2878i	−0.803983	−	0.803983i	0.179732	−	0.983716i	$-0.442477\pi$
$839$	−23.2878	−	23.2878i	−0.803983	−	0.803983i	−0.983716	+	0.179732i	$0.942477\pi$
$840$	0.0187621	−	0.300835i	0.000647353	−	0.0103798i
$841$	13.6577			0.470956
$842$	−6.60130	+	6.33272i	−0.227496	+	0.218240i
$843$	−0.604161	−	0.604161i	−0.0208084	−	0.0208084i
$844$	0.247853	−	5.96549i	0.00853147	−	0.205341i
$845$		0			0
$846$	10.1528	−	9.73975i	0.349061	−	0.334860i
$847$	0.657638	−	0.657638i	0.0225967	−	0.0225967i
$848$	−39.2500	−	3.26715i	−1.34785	−	0.112194i
$849$		−	16.6532i		−	0.571538i
$850$	−0.0204795	+	0.986253i	−0.000702441	+	0.0338282i
$851$	−13.1452	+	13.1452i	−0.450611	+	0.450611i
$852$	0.127028	+	0.138041i	0.00435190	+	0.00472920i
$853$	−17.6542	+	17.6542i	−0.604470	+	0.604470i	−0.941495	−	0.337026i	$-0.890579\pi$
$853$	−17.6542	+	17.6542i	−0.604470	+	0.604470i	0.337026	+	0.941495i	$0.390579\pi$
$854$	0.371842	−	0.356714i	0.0127242	−	0.0122065i
$855$	12.7684			0.436670
$856$	−12.1564	−	0.758154i	−0.415497	−	0.0259132i
$857$		−	37.1459i		−	1.26888i	−0.772973	−	0.634439i	$-0.781231\pi$
$857$		−	37.1459i		−	1.26888i	0.772973	−	0.634439i	$-0.218769\pi$
$858$		0			0
$859$		−	36.3219i		−	1.23929i	−0.784883	−	0.619644i	$-0.787277\pi$
$859$		−	36.3219i		−	1.23929i	0.784883	−	0.619644i	$-0.212723\pi$
$860$	−4.62462	−	5.02556i	−0.157698	−	0.171370i
$861$	−0.0641830			−0.00218735
$862$	−4.98214	−	5.19344i	−0.169693	−	0.176889i
$863$	−5.14048	+	5.14048i	−0.174984	+	0.174984i	−0.789165	−	0.614181i	$-0.789486\pi$
$863$	−5.14048	+	5.14048i	−0.174984	+	0.174984i	0.614181	+	0.789165i	$0.289486\pi$
$864$	−29.0185	−	3.02328i	−0.987230	−	0.102854i
$865$	18.5413	−	18.5413i	0.630425	−	0.630425i
$866$	−19.8128	−	0.411412i	−0.673265	−	0.0139803i
$867$		−	2.28395i		−	0.0775671i
$868$	0.678626	+	0.0281954i	0.0230341	+	0.000957016i
$869$	2.92267	−	2.92267i	0.0991449	−	0.0991449i
$870$	14.8517	+	15.4816i	0.503520	+	0.524875i
$871$		0			0
$872$	5.07307	−	4.47744i	0.171796	−	0.151625i
$873$	−3.56526	−	3.56526i	−0.120666	−	0.120666i
$874$	−24.3210	−	25.3524i	−0.822669	−	0.857558i
$875$	−0.520821			−0.0176070
$876$	11.6321	+	12.6406i	0.393013	+	0.427086i
$877$	5.74330	+	5.74330i	0.193937	+	0.193937i	0.797395	−	0.603458i	$-0.206211\pi$
$877$	5.74330	+	5.74330i	0.193937	+	0.193937i	−0.603458	+	0.797395i	$0.706211\pi$
$878$	0.815165	−	39.2567i	0.0275105	−	1.32485i
$879$	−10.1773	−	10.1773i	−0.343273	−	0.343273i
$880$	−4.08233	+	49.0432i	−0.137615	+	1.65325i
$881$		−	40.9399i		−	1.37930i	−0.724143	−	0.689650i	$-0.757765\pi$
$881$		−	40.9399i		−	1.37930i	0.724143	−	0.689650i	$-0.242235\pi$
$882$	18.6563	+	0.387397i	0.628189	+	0.0130443i
$883$	32.3850			1.08984			0.544922	−	0.838487i	$-0.316559\pi$
$883$	32.3850			1.08984			0.544922	+	0.838487i	$0.316559\pi$
$884$		0			0
$885$	−24.4860			−0.823086
$886$	7.73330	+	0.160582i	0.259805	+	0.00539485i
$887$			38.2292i			1.28361i	0.766867	+	0.641806i	$0.221815\pi$
$887$			38.2292i			1.28361i	−0.766867	+	0.641806i	$0.778185\pi$
$888$	5.15628	−	4.55087i	0.173033	−	0.152717i
$889$	−0.172357	−	0.172357i	−0.00578065	−	0.00578065i
$890$	0.970181	−	46.7220i	0.0325205	−	1.56613i
$891$	0.837826	+	0.837826i	0.0280682	+	0.0280682i
$892$	0.271993	−	0.250293i	0.00910701	−	0.00838044i
$893$	−16.2393			−0.543427
$894$	−9.78620	−	10.2012i	−0.327300	−	0.341181i
$895$	29.7552	+	29.7552i	0.994606	+	0.994606i
$896$	−0.416344	+	0.310028i	−0.0139091	+	0.0103573i
$897$		0			0
$898$	19.0249	+	19.8318i	0.634870	+	0.661795i
$899$	−34.1835	+	34.1835i	−1.14008	+	1.14008i
$900$	−0.0249442	+	0.600373i	−0.000831473	+	0.0200124i
$901$		−	43.1039i		−	1.43600i
$902$	10.4769	+	0.217553i	0.348843	+	0.00724371i
$903$	0.0531584	−	0.0531584i	0.00176900	−	0.00176900i
$904$	0.272426	−	4.36813i	0.00906074	−	0.145282i
$905$	4.74276	−	4.74276i	0.157655	−	0.157655i
$906$	−9.78127	−	10.1961i	−0.324961	−	0.338743i
$907$	−33.8595			−1.12428			−0.562142	−	0.827040i	$-0.690023\pi$
$907$	−33.8595			−1.12428			−0.562142	+	0.827040i	$0.690023\pi$
$908$	22.9129	−	21.0849i	0.760392	−	0.699727i
$909$			0.955671i			0.0316976i
$910$		0			0
$911$			49.3176i			1.63397i	0.576662	+	0.816983i	$0.304355\pi$
$911$			49.3176i			1.63397i	−0.576662	+	0.816983i	$0.695645\pi$
$912$	8.39618	+	9.92088i	0.278025	+	0.328513i
$913$	42.8449			1.41796
$914$	−15.9452	+	15.2965i	−0.527422	+	0.505964i
$915$	−13.0423	+	13.0423i	−0.431164	+	0.431164i
$916$	−22.4775	+	20.6842i	−0.742676	+	0.683425i
$917$	−0.147257	+	0.147257i	−0.00486286	+	0.00486286i
$918$	0.662880	−	31.9230i	0.0218783	−	1.05362i
$919$		−	2.47203i		−	0.0815449i	−0.999168	−	0.0407724i	$-0.987018\pi$
$919$		−	2.47203i		−	0.0815449i	0.999168	−	0.0407724i	$-0.0129819\pi$
$920$	−37.6576	+	33.2362i	−1.24154	+	1.09577i
$921$	14.7623	−	14.7623i	0.486434	−	0.486434i
$922$	23.6317	−	22.6703i	0.778270	−	0.746606i
$923$		0			0
$924$	−0.541247	−	0.0224877i	−0.0178057	−	0.000739790i
$925$	−0.259512	−	0.259512i	−0.00853270	−	0.00853270i
$926$	−25.3477	+	24.3164i	−0.832976	+	0.799086i
$927$	5.88222			0.193197
$928$	3.82853	−	36.7477i	0.125678	−	1.20630i
$929$	25.0924	+	25.0924i	0.823253	+	0.823253i	0.986573	−	0.163320i	$-0.0522202\pi$
$929$	25.0924	+	25.0924i	0.823253	+	0.823253i	−0.163320	+	0.986573i	$0.552220\pi$
$930$	−24.3074	−	0.504742i	−0.797070	−	0.0165511i
$931$	−15.2300	−	15.2300i	−0.499144	−	0.499144i
$932$	−0.681855	+	16.4113i	−0.0223349	+	0.537571i
$933$		−	0.720797i		−	0.0235978i
$934$	−0.418284	+	20.1437i	−0.0136867	+	0.659123i
$935$	−53.8586			−1.76137
$936$		0			0
$937$	−0.721776			−0.0235794			−0.0117897	−	0.999930i	$-0.503753\pi$
$937$	−0.721776			−0.0235794			−0.0117897	+	0.999930i	$0.503753\pi$
$938$	0.00324352	−	0.156201i	0.000105905	−	0.00510016i
$939$			19.1016i			0.623358i
$940$	−0.963773	+	23.1967i	−0.0314348	+	0.756593i
$941$	−9.25153	−	9.25153i	−0.301591	−	0.301591i	0.540045	−	0.841636i	$-0.318407\pi$
$941$	−9.25153	−	9.25153i	−0.301591	−	0.301591i	−0.841636	+	0.540045i	$0.818407\pi$
$942$	−6.67274	−	0.138559i	−0.217410	−	0.00451450i
$943$	7.56258	+	7.56258i	0.246271	+	0.246271i
$944$	27.2417	+	32.1887i	0.886642	+	1.04765i
$945$	0.520642			0.0169365
$946$	−8.85749	+	8.49712i	−0.287982	+	0.276265i
$947$	4.64082	+	4.64082i	0.150806	+	0.150806i	0.778478	−	0.627672i	$-0.215992\pi$
$947$	4.64082	+	4.64082i	0.150806	+	0.150806i	−0.627672	+	0.778478i	$0.715992\pi$
$948$	−1.55925	−	0.0647837i	−0.0506422	−	0.00210408i
$949$		0			0
$950$	0.500506	−	0.480143i	0.0162386	−	0.0155779i
$951$	10.9330	−	10.9330i	0.354526	−	0.354526i
$952$	−0.375924	−	0.425933i	−0.0121838	−	0.0138046i
$953$			53.4787i			1.73235i	0.499745	+	0.866173i	$0.333427\pi$
$953$			53.4787i			1.73235i	−0.499745	+	0.866173i	$0.666573\pi$
$954$	0.545089	−	26.2504i	0.0176479	−	0.849889i
$955$	−25.2678	+	25.2678i	−0.817648	+	0.817648i
$956$	−17.1579	+	15.7890i	−0.554925	+	0.510652i
$957$	27.2635	−	27.2635i	0.881304	−	0.881304i
$958$	8.39100	−	8.04961i	0.271101	−	0.260071i
$959$	−0.405234			−0.0130857
$960$	14.6696	−	11.4046i	0.473459	−	0.368081i
$961$		−	23.7854i		−	0.767271i
$962$		0			0
$963$		−	8.11968i		−	0.261653i
$964$	−42.5377	+	39.1440i	−1.37005	+	1.26074i
$965$	30.5865			0.984614
$966$	−0.382743	−	0.398975i	−0.0123145	−	0.0128368i
$967$	−30.0293	+	30.0293i	−0.965678	+	0.965678i	−0.999430	−	0.0337524i	$-0.989254\pi$
$967$	−30.0293	+	30.0293i	−0.965678	+	0.965678i	0.0337524	+	0.999430i	$0.489254\pi$
$968$	57.2218	+	3.56873i	1.83918	+	0.114703i
$969$	−10.0578	+	10.0578i	−0.323103	+	0.323103i
$970$	8.31848	+	0.172733i	0.267090	+	0.00554613i
$971$			18.9395i			0.607799i	0.952704	+	0.303899i	$0.0982887\pi$
$971$			18.9395i			0.607799i	−0.952704	+	0.303899i	$0.901711\pi$
$972$	1.30318	−	31.3657i	0.0417994	−	1.00606i
$973$	−0.678179	+	0.678179i	−0.0217414	+	0.0217414i
$974$	−28.0492	−	29.2388i	−0.898756	−	0.936872i
$975$		0			0
$976$	31.6552	+	2.63496i	1.01326	+	0.0843430i
$977$	−9.50047	−	9.50047i	−0.303947	−	0.303947i	0.538609	−	0.842556i	$-0.318950\pi$
$977$	−9.50047	−	9.50047i	−0.303947	−	0.303947i	−0.842556	+	0.538609i	$0.818950\pi$
$978$	4.60462	+	4.79990i	0.147239	+	0.153484i
$979$	−83.9873			−2.68425
$980$	−22.6589	+	20.8512i	−0.723813	+	0.666066i
$981$	3.18956	+	3.18956i	0.101835	+	0.101835i
$982$	−0.120180	+	5.78765i	−0.00383511	+	0.184691i
$983$	8.02059	+	8.02059i	0.255817	+	0.255817i	0.823350	−	0.567533i	$-0.192102\pi$
$983$	8.02059	+	8.02059i	0.255817	+	0.255817i	−0.567533	+	0.823350i	$0.692102\pi$
$984$	−2.61817	−	2.96646i	−0.0834642	−	0.0945674i
$985$			15.6056i			0.497235i
$986$	40.4257	+	0.839439i	1.28742	+	0.0267332i
$987$	−0.255560			−0.00813457
$988$		0			0
$989$	−12.5271			−0.398340
$990$	−32.8001	−	0.681094i	−1.04246	−	0.0216466i
$991$		−	22.5491i		−	0.716297i	−0.933665	−	0.358148i	$-0.883408\pi$
$991$		−	22.5491i		−	0.716297i	0.933665	−	0.358148i	$-0.116592\pi$
$992$	26.3795	+	32.5154i	0.837550	+	1.03237i
$993$	−6.83851	−	6.83851i	−0.217014	−	0.217014i
$994$	−0.000119688		0.00576393i	−3.79627e−6		0.000182821i
$995$	−29.5769	−	29.5769i	−0.937651	−	0.937651i
$996$	−10.9541	−	11.9038i	−0.347094	−	0.377186i
$997$	−28.3660			−0.898359			−0.449179	−	0.893442i	$-0.648284\pi$
$997$	−28.3660			−0.898359			−0.449179	+	0.893442i	$0.648284\pi$
$998$	14.2371	+	14.8409i	0.450668	+	0.469781i
$999$	8.39987	+	8.39987i	0.265760	+	0.265760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.2.f.j.99.18	yes	72
4.3	odd	2	inner	676.2.f.j.99.36	yes	72
13.2	odd	12		676.2.l.n.19.13		144
13.3	even	3		676.2.l.n.319.6		144
13.4	even	6		676.2.l.n.427.6		144
13.5	odd	4	inner	676.2.f.j.239.36	yes	72
13.6	odd	12		676.2.l.n.587.13		144
13.7	odd	12		676.2.l.n.587.24		144
13.8	odd	4	inner	676.2.f.j.239.1	yes	72
13.9	even	3		676.2.l.n.427.31		144
13.10	even	6		676.2.l.n.319.31		144
13.11	odd	12		676.2.l.n.19.24		144
13.12	even	2	inner	676.2.f.j.99.19	yes	72
52.3	odd	6		676.2.l.n.319.13		144
52.7	even	12		676.2.l.n.587.31		144
52.11	even	12		676.2.l.n.19.6		144
52.15	even	12		676.2.l.n.19.31		144
52.19	even	12		676.2.l.n.587.6		144
52.23	odd	6		676.2.l.n.319.24		144
52.31	even	4	inner	676.2.f.j.239.18	yes	72
52.35	odd	6		676.2.l.n.427.13		144
52.43	odd	6		676.2.l.n.427.24		144
52.47	even	4	inner	676.2.f.j.239.19	yes	72
52.51	odd	2	inner	676.2.f.j.99.1	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
676.2.f.j.99.1	✓	72	52.51	odd	2	inner
676.2.f.j.99.18	yes	72	1.1	even	1	trivial
676.2.f.j.99.19	yes	72	13.12	even	2	inner
676.2.f.j.99.36	yes	72	4.3	odd	2	inner
676.2.f.j.239.1	yes	72	13.8	odd	4	inner
676.2.f.j.239.18	yes	72	52.31	even	4	inner
676.2.f.j.239.19	yes	72	52.47	even	4	inner
676.2.f.j.239.36	yes	72	13.5	odd	4	inner
676.2.l.n.19.6		144	52.11	even	12
676.2.l.n.19.13		144	13.2	odd	12
676.2.l.n.19.24		144	13.11	odd	12
676.2.l.n.19.31		144	52.15	even	12
676.2.l.n.319.6		144	13.3	even	3
676.2.l.n.319.13		144	52.3	odd	6
676.2.l.n.319.24		144	52.23	odd	6
676.2.l.n.319.31		144	13.10	even	6
676.2.l.n.427.6		144	13.4	even	6
676.2.l.n.427.13		144	52.35	odd	6
676.2.l.n.427.24		144	52.43	odd	6
676.2.l.n.427.31		144	13.9	even	3
676.2.l.n.587.6		144	52.19	even	12
676.2.l.n.587.13		144	13.6	odd	12
676.2.l.n.587.24		144	13.7	odd	12
676.2.l.n.587.31		144	52.7	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	676.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0293598 + 1.41391i) q^{2} +1.05568i q^{3} +(-1.99828 - 0.0830241i) q^{4} +(1.55574 + 1.55574i) q^{5} +(-1.49263 - 0.0309945i) q^{6} +(-0.0324435 - 0.0324435i) q^{7} +(0.176057 - 2.82294i) q^{8} +1.88554 q^{9} +O(q^{10})\)	\(q+(-0.0293598 + 1.41391i) q^{2} +1.05568i q^{3} +(-1.99828 - 0.0830241i) q^{4} +(1.55574 + 1.55574i) q^{5} +(-1.49263 - 0.0309945i) q^{6} +(-0.0324435 - 0.0324435i) q^{7} +(0.176057 - 2.82294i) q^{8} +1.88554 q^{9} +(-2.24535 + 2.15400i) q^{10} +(3.95413 + 3.95413i) q^{11} +(0.0876468 - 2.10954i) q^{12} +(0.0468246 - 0.0449196i) q^{14} +(-1.64236 + 1.64236i) q^{15} +(3.98621 + 0.331810i) q^{16} +4.37761i q^{17} +(-0.0553591 + 2.66598i) q^{18} +(2.17637 - 2.17637i) q^{19} +(-2.97964 - 3.23796i) q^{20} +(0.0342499 - 0.0342499i) q^{21} +(-5.70687 + 5.47469i) q^{22} -8.07122 q^{23} +(2.98012 + 0.185860i) q^{24} -0.159342i q^{25} +5.15757i q^{27} +(0.0621374 + 0.0675246i) q^{28} -6.53129 q^{29} +(-2.27393 - 2.37037i) q^{30} +(5.23380 - 5.23380i) q^{31} +(-0.586184 + 5.62640i) q^{32} +(-4.17429 + 4.17429i) q^{33} +(-6.18954 - 0.128526i) q^{34} -0.100947i q^{35} +(-3.76783 - 0.156545i) q^{36} +(1.62865 - 1.62865i) q^{37} +(3.01329 + 3.14109i) q^{38} +(4.66567 - 4.11787i) q^{40} +(-0.936980 - 0.936980i) q^{41} +(0.0474207 + 0.0494318i) q^{42} +1.55207 q^{43} +(-7.57315 - 8.22973i) q^{44} +(2.93341 + 2.93341i) q^{45} +(0.236969 - 11.4120i) q^{46} +(-3.73081 - 3.73081i) q^{47} +(-0.350285 + 4.20816i) q^{48} -6.99789i q^{49} +(0.225295 + 0.00467824i) q^{50} -4.62136 q^{51} -9.84644 q^{53} +(-7.29233 - 0.151425i) q^{54} +12.3032i q^{55} +(-0.0972980 + 0.0858741i) q^{56} +(2.29755 + 2.29755i) q^{57} +(0.191757 - 9.23465i) q^{58} +(7.45449 + 7.45449i) q^{59} +(3.41825 - 3.14554i) q^{60} +7.94117 q^{61} +(7.24646 + 7.55378i) q^{62} +(-0.0611735 - 0.0611735i) q^{63} +(-7.93801 - 0.994000i) q^{64} +(-5.77951 - 6.02463i) q^{66} +(1.70258 - 1.70258i) q^{67} +(0.363447 - 8.74768i) q^{68} -8.52062i q^{69} +(0.142730 + 0.00296379i) q^{70} +(-0.0628261 + 0.0628261i) q^{71} +(0.331963 - 5.32277i) q^{72} +(-5.75309 + 5.75309i) q^{73} +(2.25495 + 2.35058i) q^{74} +0.168214 q^{75} +(-4.52968 + 4.16830i) q^{76} -0.256571i q^{77} -0.739145i q^{79} +(5.68530 + 6.71773i) q^{80} +0.211886 q^{81} +(1.35231 - 1.29730i) q^{82} +(5.41775 - 5.41775i) q^{83} +(-0.0712843 + 0.0655972i) q^{84} +(-6.81043 + 6.81043i) q^{85} +(-0.0455686 + 2.19449i) q^{86} -6.89495i q^{87} +(11.8584 - 10.4661i) q^{88} +(-10.6202 + 10.6202i) q^{89} +(-4.23370 + 4.06145i) q^{90} +(16.1285 + 0.670106i) q^{92} +(5.52522 + 5.52522i) q^{93} +(5.38457 - 5.16549i) q^{94} +6.77174 q^{95} +(-5.93968 - 0.618822i) q^{96} +(-1.89084 - 1.89084i) q^{97} +(9.89438 + 0.205457i) q^{98} +(7.45567 + 7.45567i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 64 q^{9}+O(q^{10}) \) 72 * q - 64 * q^9	\( 72 q - 64 q^{9} + 4 q^{14} + 76 q^{16} - 72 q^{22} - 16 q^{29} + 84 q^{40} - 224 q^{42} + 224 q^{48} + 32 q^{53} - 16 q^{61} - 140 q^{66} + 152 q^{68} - 168 q^{74} + 88 q^{81} - 56 q^{92} - 300 q^{94}+O(q^{100}) \) 72 * q - 64 * q^9 + 4 * q^14 + 76 * q^16 - 72 * q^22 - 16 * q^29 + 84 * q^40 - 224 * q^42 + 224 * q^48 + 32 * q^53 - 16 * q^61 - 140 * q^66 + 152 * q^68 - 168 * q^74 + 88 * q^81 - 56 * q^92 - 300 * q^94

Introduction

L-functions

Modular forms

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