LMFDB - Embedded newform 525.2.bc.e.418.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			418.7
Character	$\chi$	$=$	525.418
Dual form			525.2.bc.e.157.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.461174 + 1.72112i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-1.01754 + 0.587476i) q^{4} -1.78184i q^{6} +(-2.04329 + 1.68076i) q^{7} +(1.03952 + 1.03952i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.461174 + 1.72112i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-1.01754 + 0.587476i) q^{4} -1.78184i q^{6} +(-2.04329 + 1.68076i) q^{7} +(1.03952 + 1.03952i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.46711 + 2.54110i) q^{11} +(1.13492 - 0.304100i) q^{12} +(-0.187911 + 0.187911i) q^{13} +(-3.83511 - 2.74164i) q^{14} +(-2.48470 + 4.30362i) q^{16} +(0.868882 - 3.24271i) q^{17} +(-0.461174 + 1.72112i) q^{18} +(-1.81824 + 3.14928i) q^{19} +(2.40868 - 1.09464i) q^{21} +(-3.69696 + 3.69696i) q^{22} +(-9.07540 + 2.43175i) q^{23} +(-0.735051 - 1.27315i) q^{24} +(-0.410078 - 0.236759i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.09173 - 2.91062i) q^{28} +0.815162i q^{29} +(-3.76330 + 2.17274i) q^{31} +(-5.71292 - 1.53077i) q^{32} +(-0.759430 - 2.83423i) q^{33} +5.98182 q^{34} -1.17495 q^{36} +(1.69304 + 6.31853i) q^{37} +(-6.25883 - 1.67705i) q^{38} +(0.230143 - 0.132873i) q^{39} +2.45734i q^{41} +(2.99484 + 3.64082i) q^{42} +(3.59998 + 3.59998i) q^{43} +(-2.98567 - 1.72378i) q^{44} +(-8.37068 - 14.4984i) q^{46} +(9.24785 - 2.47795i) q^{47} +(3.51389 - 3.51389i) q^{48} +(1.35010 - 6.86857i) q^{49} +(-1.67855 + 2.90734i) q^{51} +(0.0808136 - 0.301600i) q^{52} +(1.30744 - 4.87944i) q^{53} +(0.890920 - 1.54312i) q^{54} +(-3.87122 - 0.376863i) q^{56} +(2.57138 - 2.57138i) q^{57} +(-1.40300 + 0.375932i) q^{58} +(-5.41228 - 9.37435i) q^{59} +(8.07692 + 4.66321i) q^{61} +(-5.47509 - 5.47509i) q^{62} +(-2.60992 + 0.433932i) q^{63} -0.599827i q^{64} +(4.52784 - 2.61415i) q^{66} +(15.3155 + 4.10379i) q^{67} +(1.02090 + 3.81003i) q^{68} +9.39554 q^{69} +2.68111 q^{71} +(0.380490 + 1.42001i) q^{72} +(-1.89619 - 0.508083i) q^{73} +(-10.0942 + 5.82788i) q^{74} -4.27269i q^{76} +(-7.26871 - 2.72637i) q^{77} +(0.334828 + 0.334828i) q^{78} +(4.44293 + 2.56513i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-4.22938 + 1.13326i) q^{82} +(6.09879 - 6.09879i) q^{83} +(-1.80785 + 2.52889i) q^{84} +(-4.53580 + 7.85623i) q^{86} +(0.210980 - 0.787386i) q^{87} +(-1.11644 + 4.16661i) q^{88} +(4.87057 - 8.43608i) q^{89} +(0.0681246 - 0.699791i) q^{91} +(7.80598 - 7.80598i) q^{92} +(4.19741 - 1.12469i) q^{93} +(8.52974 + 14.7739i) q^{94} +(5.12207 + 2.95723i) q^{96} +(-5.93610 - 5.93610i) q^{97} +(12.4443 - 0.843909i) q^{98} +2.93421i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 32 * q - 8 * q^7 + 24 * q^8	$ 32 q - 8 q^{7} + 24 q^{8} - 8 q^{11} - 8 q^{21} + 8 q^{22} + 8 q^{23} + 24 q^{26} + 24 q^{28} + 24 q^{31} - 24 q^{32} + 36 q^{33} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} - 8 q^{51} + 108 q^{52} + 24 q^{53} - 48 q^{56} - 16 q^{57} - 4 q^{58} - 24 q^{61} - 4 q^{63} + 72 q^{66} - 8 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 16 q^{81} - 12 q^{82} - 16 q^{86} + 24 q^{87} + 32 q^{88} - 24 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98}+O(q^{100}) $ 32 * q - 8 * q^7 + 24 * q^8 - 8 * q^11 - 8 * q^21 + 8 * q^22 + 8 * q^23 + 24 * q^26 + 24 * q^28 + 24 * q^31 - 24 * q^32 + 36 * q^33 - 32 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^42 - 40 * q^43 - 40 * q^46 + 60 * q^47 - 8 * q^51 + 108 * q^52 + 24 * q^53 - 48 * q^56 - 16 * q^57 - 4 * q^58 - 24 * q^61 - 4 * q^63 + 72 * q^66 - 8 * q^67 - 132 * q^68 - 16 * q^71 - 12 * q^72 - 36 * q^73 - 60 * q^77 - 80 * q^78 + 16 * q^81 - 12 * q^82 - 16 * q^86 + 24 * q^87 + 32 * q^88 - 24 * q^91 + 56 * q^92 + 24 * q^93 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.461174	+	1.72112i	0.326099	+	1.21702i	0.913202	+	0.407507i	$0.133602\pi$
$2$	0.461174	+	1.72112i	0.326099	+	1.21702i	−0.587103	+	0.809512i	$0.699732\pi$
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	−1.01754	+	0.587476i	−0.508769	+	0.293738i
$5$		0			0
$5$		0			0
$6$		−	1.78184i		−	0.727433i
$7$	−2.04329	+	1.68076i	−0.772293	+	0.635267i
$7$	−2.04329	+	1.68076i	−0.772293	+	0.635267i
$8$	1.03952	+	1.03952i	0.367526	+	0.367526i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	1.46711	+	2.54110i	0.442349	+	0.766171i	0.997863	−	0.0653360i	$-0.0208119\pi$
$11$	1.46711	+	2.54110i	0.442349	+	0.766171i	−0.555514	+	0.831507i	$0.687479\pi$
$12$	1.13492	−	0.304100i	0.327622	−	0.0877861i
$13$	−0.187911	+	0.187911i	−0.0521172	+	0.0521172i	−0.732685	−	0.680568i	$-0.761733\pi$
$13$	−0.187911	+	0.187911i	−0.0521172	+	0.0521172i	0.680568	+	0.732685i	$0.261733\pi$
$14$	−3.83511	−	2.74164i	−1.02498	−	0.732735i
$15$		0			0
$16$	−2.48470	+	4.30362i	−0.621174	+	1.07590i
$17$	0.868882	−	3.24271i	0.210735	−	0.786473i	−0.776890	−	0.629637i	$-0.783204\pi$
$17$	0.868882	−	3.24271i	0.210735	−	0.786473i	0.987625	−	0.156837i	$-0.0501296\pi$
$18$	−0.461174	+	1.72112i	−0.108700	+	0.405673i
$19$	−1.81824	+	3.14928i	−0.417132	+	0.722494i	−0.995650	−	0.0931757i	$-0.970298\pi$
$19$	−1.81824	+	3.14928i	−0.417132	+	0.722494i	0.578517	+	0.815670i	$0.303631\pi$
$20$		0			0
$21$	2.40868	−	1.09464i	0.525618	−	0.238871i
$22$	−3.69696	+	3.69696i	−0.788195	+	0.788195i
$23$	−9.07540	+	2.43175i	−1.89235	+	0.507054i	−0.894105	+	0.447858i	$0.852187\pi$
$23$	−9.07540	+	2.43175i	−1.89235	+	0.507054i	−0.998246	+	0.0591961i	$0.981146\pi$
$24$	−0.735051	−	1.27315i	−0.150042	−	0.259880i
$25$		0			0
$26$	−0.410078	−	0.236759i	−0.0804230	−	0.0464322i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.09173	−	2.91062i	0.206317	−	0.550056i
$29$			0.815162i			0.151372i	0.997132	+	0.0756859i	$0.0241146\pi$
$29$			0.815162i			0.151372i	−0.997132	+	0.0756859i	$0.975885\pi$
$30$		0			0
$31$	−3.76330	+	2.17274i	−0.675908	+	0.390236i	−0.798312	−	0.602245i	$-0.794273\pi$
$31$	−3.76330	+	2.17274i	−0.675908	+	0.390236i	0.122403	+	0.992480i	$0.460940\pi$
$32$	−5.71292	−	1.53077i	−1.00991	−	0.270605i
$33$	−0.759430	−	2.83423i	−0.132200	−	0.493376i
$34$	5.98182			1.02587
$35$		0			0
$36$	−1.17495			−0.195825
$37$	1.69304	+	6.31853i	0.278335	+	1.03876i	0.953574	+	0.301160i	$0.0973738\pi$
$37$	1.69304	+	6.31853i	0.278335	+	1.03876i	−0.675239	+	0.737599i	$0.735959\pi$
$38$	−6.25883	−	1.67705i	−1.01532	−	0.272053i
$39$	0.230143	−	0.132873i	0.0368524	−	0.0212768i
$40$		0			0
$41$			2.45734i			0.383772i	0.981417	+	0.191886i	$0.0614603\pi$
$41$			2.45734i			0.383772i	−0.981417	+	0.191886i	$0.938540\pi$
$42$	2.99484	+	3.64082i	0.462114	+	0.561791i
$43$	3.59998	+	3.59998i	0.548992	+	0.548992i	0.926149	−	0.377157i	$-0.123098\pi$
$43$	3.59998	+	3.59998i	0.548992	+	0.548992i	−0.377157	+	0.926149i	$0.623098\pi$
$44$	−2.98567	−	1.72378i	−0.450107	−	0.259870i
$45$		0			0
$46$	−8.37068	−	14.4984i	−1.23419	−	2.13768i
$47$	9.24785	−	2.47795i	1.34894	−	0.361447i	0.489195	−	0.872174i	$-0.337291\pi$
$47$	9.24785	−	2.47795i	1.34894	−	0.361447i	0.859743	+	0.510728i	$0.170624\pi$
$48$	3.51389	−	3.51389i	0.507186	−	0.507186i
$49$	1.35010	−	6.86857i	0.192872	−	0.981224i
$50$		0			0
$51$	−1.67855	+	2.90734i	−0.235044	+	0.407109i
$52$	0.0808136	−	0.301600i	0.0112068	−	0.0418244i
$53$	1.30744	−	4.87944i	0.179591	−	0.670243i	−0.816133	−	0.577864i	$-0.803886\pi$
$53$	1.30744	−	4.87944i	0.179591	−	0.670243i	0.995724	−	0.0923788i	$-0.0294471\pi$
$54$	0.890920	−	1.54312i	0.121239	−	0.209992i
$55$		0			0
$56$	−3.87122	−	0.376863i	−0.517314	−	0.0503605i
$57$	2.57138	−	2.57138i	0.340587	−	0.340587i
$58$	−1.40300	+	0.375932i	−0.184222	+	0.0493623i
$59$	−5.41228	−	9.37435i	−0.704619	−	1.22044i	−0.966829	−	0.255425i	$-0.917784\pi$
$59$	−5.41228	−	9.37435i	−0.704619	−	1.22044i	0.262209	−	0.965011i	$-0.415549\pi$
$60$		0			0
$61$	8.07692	+	4.66321i	1.03414	+	0.597063i	0.918169	−	0.396189i	$-0.129667\pi$
$61$	8.07692	+	4.66321i	1.03414	+	0.597063i	0.115975	+	0.993252i	$0.463001\pi$
$62$	−5.47509	−	5.47509i	−0.695338	−	0.695338i
$63$	−2.60992	+	0.433932i	−0.328820	+	0.0546703i
$64$		−	0.599827i		−	0.0749784i
$65$		0			0
$66$	4.52784	−	2.61415i	0.557338	−	0.321779i
$67$	15.3155	+	4.10379i	1.87109	+	0.501357i	0.999947	+	0.0103305i	$0.00328837\pi$
$67$	15.3155	+	4.10379i	1.87109	+	0.501357i	0.871144	+	0.491027i	$0.163378\pi$
$68$	1.02090	+	3.81003i	0.123802	+	0.462035i
$69$	9.39554			1.13109
$70$		0			0
$71$	2.68111			0.318189			0.159094	−	0.987263i	$-0.449143\pi$
$71$	2.68111			0.318189			0.159094	+	0.987263i	$0.449143\pi$
$72$	0.380490	+	1.42001i	0.0448412	+	0.167350i
$73$	−1.89619	−	0.508083i	−0.221932	−	0.0594666i	0.146139	−	0.989264i	$-0.453315\pi$
$73$	−1.89619	−	0.508083i	−0.221932	−	0.0594666i	−0.368072	+	0.929797i	$0.619982\pi$
$74$	−10.0942	+	5.82788i	−1.17343	+	0.677477i
$75$		0			0
$76$		−	4.27269i		−	0.490111i
$77$	−7.26871	−	2.72637i	−0.828346	−	0.310699i
$78$	0.334828	+	0.334828i	0.0379118	+	0.0379118i
$79$	4.44293	+	2.56513i	0.499868	+	0.288599i	0.728659	−	0.684876i	$-0.240144\pi$
$79$	4.44293	+	2.56513i	0.499868	+	0.288599i	−0.228791	+	0.973476i	$0.573477\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−4.22938	+	1.13326i	−0.467057	+	0.125148i
$83$	6.09879	−	6.09879i	0.669430	−	0.669430i	−0.288154	−	0.957584i	$-0.593042\pi$
$83$	6.09879	−	6.09879i	0.669430	−	0.669430i	0.957584	+	0.288154i	$0.0930416\pi$
$84$	−1.80785	+	2.52889i	−0.197253	+	0.275924i
$85$		0			0
$86$	−4.53580	+	7.85623i	−0.489108	+	0.847159i
$87$	0.210980	−	0.787386i	0.0226194	−	0.0844167i
$88$	−1.11644	+	4.16661i	−0.119013	+	0.444162i
$89$	4.87057	−	8.43608i	0.516280	−	0.894223i	−0.483541	−	0.875321i	$-0.660650\pi$
$89$	4.87057	−	8.43608i	0.516280	−	0.894223i	0.999821	−	0.0189016i	$-0.00601692\pi$
$90$		0			0
$91$	0.0681246	−	0.699791i	0.00714140	−	0.0733580i
$92$	7.80598	−	7.80598i	0.813829	−	0.813829i
$93$	4.19741	−	1.12469i	0.435251	−	0.116625i
$94$	8.52974	+	14.7739i	0.879775	+	1.52382i
$95$		0			0
$96$	5.12207	+	2.95723i	0.522769	+	0.301821i
$97$	−5.93610	−	5.93610i	−0.602720	−	0.602720i	0.338314	−	0.941033i	$-0.390143\pi$
$97$	−5.93610	−	5.93610i	−0.602720	−	0.602720i	−0.941033	+	0.338314i	$0.890143\pi$
$98$	12.4443	−	0.843909i	1.25706	−	0.0852477i
$99$			2.93421i			0.294899i
$100$		0			0
$101$	−1.51710	+	0.875897i	−0.150957	+	0.0871550i	−0.573576	−	0.819152i	$-0.694444\pi$
$101$	−1.51710	+	0.875897i	−0.150957	+	0.0871550i	0.422619	+	0.906307i	$0.361111\pi$
$102$	−5.77800	−	1.54821i	−0.572107	−	0.153296i
$103$	3.76901	+	14.0661i	0.371371	+	1.38598i	0.858575	+	0.512688i	$0.171350\pi$
$103$	3.76901	+	14.0661i	0.371371	+	1.38598i	−0.487204	+	0.873288i	$0.661983\pi$
$104$	−0.390675			−0.0383088
$105$		0			0
$106$	9.00109			0.874263
$107$	−1.47208	−	5.49389i	−0.142312	−	0.531115i	−0.999860	−	0.0167117i	$-0.994680\pi$
$107$	−1.47208	−	5.49389i	−0.142312	−	0.531115i	0.857549	−	0.514403i	$-0.171986\pi$
$108$	1.13492	+	0.304100i	0.109207	+	0.0292620i
$109$	0.642034	−	0.370678i	0.0614957	−	0.0355045i	−0.468937	−	0.883232i	$-0.655363\pi$
$109$	0.642034	−	0.370678i	0.0614957	−	0.0355045i	0.530433	+	0.847727i	$0.322030\pi$
$110$		0			0
$111$		−	6.54142i		−	0.620884i
$112$	−2.15638	−	12.9697i	−0.203759	−	1.22552i
$113$	7.30619	+	7.30619i	0.687309	+	0.687309i	0.961636	−	0.274327i	$-0.0884552\pi$
$113$	7.30619	+	7.30619i	0.687309	+	0.687309i	−0.274327	+	0.961636i	$0.588455\pi$
$114$	5.61151	+	3.23981i	0.525566	+	0.303436i
$115$		0			0
$116$	−0.478889	−	0.829459i	−0.0444637	−	0.0770134i
$117$	−0.256691	+	0.0687803i	−0.0237311	+	0.00635874i
$118$	13.6384	−	13.6384i	1.25552	−	1.25552i
$119$	3.67483	+	8.08620i	0.336872	+	0.741261i
$120$		0			0
$121$	1.19520	−	2.07015i	0.108655	−	0.188196i
$122$	−4.30111	+	16.0519i	−0.389404	+	1.45327i
$123$	0.636006	−	2.37361i	0.0573467	−	0.214021i
$124$	2.55287	−	4.42170i	0.229254	−	0.397080i
$125$		0			0
$126$	−1.95048	−	4.29189i	−0.173763	−	0.382352i
$127$	1.87455	−	1.87455i	0.166339	−	0.166339i	−0.619029	−	0.785368i	$-0.712474\pi$
$127$	1.87455	−	1.87455i	0.166339	−	0.166339i	0.785368	+	0.619029i	$0.212474\pi$
$128$	−10.3935	+	2.78492i	−0.918662	+	0.246155i
$129$	−2.54557	−	4.40906i	−0.224125	−	0.388196i
$130$		0			0
$131$	8.34312	+	4.81690i	0.728941	+	0.420855i	0.818035	−	0.575169i	$-0.195064\pi$
$131$	8.34312	+	4.81690i	0.728941	+	0.420855i	−0.0890934	+	0.996023i	$0.528397\pi$
$132$	2.43779	+	2.43779i	0.212183	+	0.212183i
$133$	−1.57798	−	9.49092i	−0.136829	−	0.822967i
$134$			28.2525i			2.44065i
$135$		0			0
$136$	4.27408	−	2.46764i	0.366500	−	0.211599i
$137$	−12.7354	−	3.41243i	−1.08806	−	0.291544i	−0.330164	−	0.943923i	$-0.607104\pi$
$137$	−12.7354	−	3.41243i	−1.08806	−	0.291544i	−0.757892	+	0.652380i	$0.773771\pi$
$138$	4.33298	+	16.1709i	0.368848	+	1.37656i
$139$	−15.4480			−1.31028			−0.655140	−	0.755508i	$-0.727390\pi$
$139$	−15.4480			−1.31028			−0.655140	+	0.755508i	$0.727390\pi$
$140$		0			0
$141$	−9.57408			−0.806283
$142$	1.23646	+	4.61452i	0.103761	+	0.387242i
$143$	−0.753187	−	0.201816i	−0.0629847	−	0.0168767i
$144$	−4.30362	+	2.48470i	−0.358635	+	0.207058i
$145$		0			0
$146$		−	3.49790i		−	0.289488i
$147$	−3.08182	+	6.28509i	−0.254184	+	0.518386i
$148$	−5.43472	−	5.43472i	−0.446731	−	0.446731i
$149$	1.48069	+	0.854874i	0.121302	+	0.0700340i	0.559424	−	0.828882i	$-0.311023\pi$
$149$	1.48069	+	0.854874i	0.121302	+	0.0700340i	−0.438121	+	0.898916i	$0.644356\pi$
$150$		0			0
$151$	1.29058	+	2.23536i	0.105026	+	0.181911i	0.913749	−	0.406279i	$-0.133174\pi$
$151$	1.29058	+	2.23536i	0.105026	+	0.181911i	−0.808723	+	0.588190i	$0.799841\pi$
$152$	−5.16383	+	1.38364i	−0.418842	+	0.112228i
$153$	2.37383	−	2.37383i	0.191913	−	0.191913i
$154$	1.34028	−	13.7677i	0.108003	−	1.10943i
$155$		0			0
$156$	−0.156120	+	0.270407i	−0.0124996	+	0.0216499i
$157$	2.31897	−	8.65453i	0.185074	−	0.690707i	−0.809540	−	0.587064i	$-0.800284\pi$
$157$	2.31897	−	8.65453i	0.185074	−	0.690707i	0.994615	−	0.103642i	$-0.0330498\pi$
$158$	−2.36594	+	8.82980i	−0.188224	+	0.702461i
$159$	−2.52579	+	4.37479i	−0.200308	+	0.346943i
$160$		0			0
$161$	14.4565	−	20.2223i	1.13933	−	1.59374i
$162$	−1.25995	+	1.25995i	−0.0989911	+	0.0989911i
$163$	−12.5967	+	3.37528i	−0.986652	+	0.264373i	−0.715844	−	0.698261i	$-0.753958\pi$
$163$	−12.5967	+	3.37528i	−0.986652	+	0.264373i	−0.270809	+	0.962633i	$0.587291\pi$
$164$	−1.44363	−	2.50044i	−0.112728	−	0.195251i
$165$		0			0
$166$	13.3094	+	7.68418i	1.03301	+	0.596408i
$167$	13.8731	+	13.8731i	1.07353	+	1.07353i	0.997073	+	0.0764613i	$0.0243622\pi$
$167$	13.8731	+	13.8731i	1.07353	+	1.07353i	0.0764613	+	0.997073i	$0.475638\pi$
$168$	3.64178	+	1.36597i	0.280969	+	0.105387i
$169$			12.9294i			0.994568i
$170$		0			0
$171$	−3.14928	+	1.81824i	−0.240831	+	0.139044i
$172$	−5.77802	−	1.54822i	−0.440570	−	0.118050i
$173$	−0.649834	−	2.42521i	−0.0494059	−	0.184385i	0.936813	−	0.349830i	$-0.113761\pi$
$173$	−0.649834	−	2.42521i	−0.0494059	−	0.184385i	−0.986219	+	0.165445i	$0.947094\pi$
$174$	1.45249			0.110113
$175$		0			0
$176$	−14.5812			−1.09910
$177$	2.80160	+	10.4557i	0.210581	+	0.785901i
$178$	16.7657	+	4.49237i	1.25665	+	0.336717i
$179$	1.77730	−	1.02612i	0.132841	−	0.0766961i	−0.432107	−	0.901823i	$-0.642230\pi$
$179$	1.77730	−	1.02612i	0.132841	−	0.0766961i	0.564948	+	0.825127i	$0.308896\pi$
$180$		0			0
$181$		−	0.400573i		−	0.0297743i	−0.999889	−	0.0148872i	$-0.995261\pi$
$181$		−	0.400573i		−	0.0297743i	0.999889	−	0.0148872i	$-0.00473891\pi$
$182$	1.23585	−	0.205475i	0.0916069	−	0.0152308i
$183$	−6.59478	−	6.59478i	−0.487500	−	0.487500i
$184$	−11.9619	−	6.90620i	−0.881843	−	0.509132i
$185$		0			0
$186$	3.87148	+	6.70559i	0.283870	+	0.491678i
$187$	9.51481	−	2.54948i	0.695791	−	0.186437i
$188$	−7.95431	+	7.95431i	−0.580128	+	0.580128i
$189$	2.63330	+	0.256352i	0.191545	+	0.0186468i
$190$		0			0
$191$	−2.67712	+	4.63691i	−0.193710	+	0.335515i	−0.946477	−	0.322772i	$-0.895385\pi$
$191$	−2.67712	+	4.63691i	−0.193710	+	0.335515i	0.752767	+	0.658287i	$0.228719\pi$
$192$	−0.155247	+	0.579388i	−0.0112040	+	0.0418138i
$193$	6.66206	−	24.8631i	0.479545	−	1.78969i	−0.123913	−	0.992293i	$-0.539544\pi$
$193$	6.66206	−	24.8631i	0.479545	−	1.78969i	0.603458	−	0.797394i	$-0.293789\pi$
$194$	7.47919	−	12.9543i	0.536975	−	0.930068i
$195$		0			0
$196$	2.66134	+	7.78219i	0.190096	+	0.555871i
$197$	4.64089	−	4.64089i	0.330650	−	0.330650i	−0.522183	−	0.852833i	$-0.674882\pi$
$197$	4.64089	−	4.64089i	0.330650	−	0.330650i	0.852833	+	0.522183i	$0.174882\pi$
$198$	−5.05014	+	1.35318i	−0.358898	+	0.0961665i
$199$	7.26057	+	12.5757i	0.514688	+	0.891466i	0.999855	+	0.0170441i	$0.00542556\pi$
$199$	7.26057	+	12.5757i	0.514688	+	0.891466i	−0.485167	+	0.874422i	$0.661241\pi$
$200$		0			0
$201$	−13.7315	−	7.92791i	−0.968548	−	0.559191i
$202$	−2.20718	−	2.20718i	−0.155296	−	0.155296i
$203$	−1.37009	−	1.66562i	−0.0961615	−	0.116903i
$204$		−	3.94444i		−	0.276166i
$205$		0			0
$206$	−22.4714	+	12.9739i	−1.56566	+	0.903932i
$207$	−9.07540	−	2.43175i	−0.630784	−	0.169018i
$208$	−0.341796	−	1.27560i	−0.0236993	−	0.0884470i
$209$	−10.6702			−0.738072
$210$		0			0
$211$	−9.70780			−0.668312			−0.334156	−	0.942518i	$-0.608451\pi$
$211$	−9.70780			−0.668312			−0.334156	+	0.942518i	$0.608451\pi$
$212$	1.53618	+	5.73312i	0.105506	+	0.393752i
$213$	−2.58975	−	0.693922i	−0.177447	−	0.0475467i
$214$	8.77679	−	5.06728i	0.599969	−	0.346392i
$215$		0			0
$216$		−	1.47010i		−	0.100028i
$217$	4.03767	−	10.7647i	0.274095	−	0.730758i
$218$	0.934073	+	0.934073i	0.0632634	+	0.0632634i
$219$	1.70008	+	0.981540i	0.114881	+	0.0663264i
$220$		0			0
$221$	0.446069	+	0.772615i	0.0300059	+	0.0519717i
$222$	11.2586	−	3.01673i	0.755628	−	0.202470i
$223$	−14.5593	+	14.5593i	−0.974963	+	0.974963i	−0.999694	−	0.0247308i	$-0.992127\pi$
$223$	−14.5593	+	14.5593i	−0.974963	+	0.974963i	0.0247308	+	0.999694i	$0.492127\pi$
$224$	14.2460	−	6.47422i	0.951854	−	0.432577i
$225$		0			0
$226$	−9.20545	+	15.9443i	−0.612337	+	1.06060i
$227$	1.17563	−	4.38751i	0.0780294	−	0.291210i	−0.915874	−	0.401466i	$-0.868501\pi$
$227$	1.17563	−	4.38751i	0.0780294	−	0.291210i	0.993903	+	0.110257i	$0.0351673\pi$
$228$	−1.10585	+	4.12710i	−0.0732369	+	0.273324i
$229$	6.20185	−	10.7419i	0.409830	−	0.709846i	−0.585040	−	0.811004i	$-0.698921\pi$
$229$	6.20185	−	10.7419i	0.409830	−	0.709846i	0.994870	+	0.101158i	$0.0322547\pi$
$230$		0			0
$231$	6.31539	+	4.51475i	0.415522	+	0.297049i
$232$	−0.847377	+	0.847377i	−0.0556330	+	0.0556330i
$233$	23.9511	−	6.41768i	1.56909	−	0.420436i	0.633562	−	0.773692i	$-0.281592\pi$
$233$	23.9511	−	6.41768i	1.56909	−	0.420436i	0.935527	+	0.353256i	$0.114926\pi$
$234$	−0.236759	−	0.410078i	−0.0154774	−	0.0268077i
$235$		0			0
$236$	11.0144	+	6.35918i	0.716977	+	0.413947i
$237$	−3.62763	−	3.62763i	−0.235640	−	0.235640i
$238$	−12.2226	+	10.0540i	−0.792275	+	0.651704i
$239$		−	22.9830i		−	1.48665i	−0.668931	−	0.743325i	$-0.733248\pi$
$239$		−	22.9830i		−	1.48665i	0.668931	−	0.743325i	$-0.266752\pi$
$240$		0			0
$241$	13.5317	−	7.81253i	0.871654	−	0.503249i	0.00375619	−	0.999993i	$-0.498804\pi$
$241$	13.5317	−	7.81253i	0.871654	−	0.503249i	0.867897	+	0.496744i	$0.165471\pi$
$242$	4.11418	+	1.10239i	0.264470	+	0.0708645i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	−10.9581			−0.701521
$245$		0			0
$246$	4.37858			0.279168
$247$	−0.250118	−	0.933452i	−0.0159146	−	0.0593941i
$248$	−6.17063	−	1.65341i	−0.391835	−	0.104992i
$249$	−7.46947	+	4.31250i	−0.473358	+	0.273293i
$250$		0			0
$251$		−	9.59480i		−	0.605618i	−0.953051	−	0.302809i	$-0.902075\pi$
$251$		−	9.59480i		−	0.605618i	0.953051	−	0.302809i	$-0.0979245\pi$
$252$	2.40077	−	1.97481i	0.151235	−	0.124401i
$253$	−19.4939	−	19.4939i	−1.22557	−	1.22557i
$254$	4.09082	+	2.36184i	0.256681	+	0.148195i
$255$		0			0
$256$	−10.1862	−	17.6431i	−0.636639	−	1.10269i
$257$	−9.44423	+	2.53057i	−0.589115	+	0.157853i	−0.541049	−	0.840991i	$-0.681972\pi$
$257$	−9.44423	+	2.53057i	−0.589115	+	0.157853i	−0.0480661	+	0.998844i	$0.515306\pi$
$258$	6.41459	−	6.41459i	0.399355	−	0.399355i
$259$	−14.0793	−	10.0650i	−0.874845	−	0.625409i
$260$		0			0
$261$	−0.407581	+	0.705951i	−0.0252286	+	0.0436973i
$262$	−4.44286	+	16.5810i	−0.274481	+	1.02438i
$263$	0.0787141	−	0.293765i	0.00485372	−	0.0181143i	−0.963457	−	0.267865i	$-0.913682\pi$
$263$	0.0787141	−	0.293765i	0.00485372	−	0.0181143i	0.968310	+	0.249751i	$0.0803486\pi$
$264$	2.15680	−	3.73568i	0.132742	−	0.229915i
$265$		0			0
$266$	15.6073	−	7.09287i	0.956947	−	0.434892i
$267$	−6.88803	+	6.88803i	−0.421541	+	0.421541i
$268$	−17.9950	+	4.82176i	−1.09922	+	0.294536i
$269$	−0.191447	−	0.331597i	−0.0116728	−	0.0202178i	0.860130	−	0.510075i	$-0.170382\pi$
$269$	−0.191447	−	0.331597i	−0.0116728	−	0.0202178i	−0.871803	+	0.489857i	$0.837049\pi$
$270$		0			0
$271$	−10.1392	−	5.85388i	−0.615913	−	0.355598i	0.159363	−	0.987220i	$-0.449056\pi$
$271$	−10.1392	−	5.85388i	−0.615913	−	0.355598i	−0.775276	+	0.631622i	$0.782389\pi$
$272$	11.7965	+	11.7965i	0.715268	+	0.715268i
$273$	−0.246923	+	0.658314i	−0.0149444	+	0.0398430i
$274$		−	23.4929i		−	1.41926i
$275$		0			0
$276$	−9.56033	+	5.51966i	−0.575464	+	0.332244i
$277$	11.9216	+	3.19438i	0.716299	+	0.191932i	0.598520	−	0.801108i	$-0.295756\pi$
$277$	11.9216	+	3.19438i	0.716299	+	0.191932i	0.117779	+	0.993040i	$0.462423\pi$
$278$	−7.12420	−	26.5879i	−0.427281	−	1.59463i
$279$	−4.34548			−0.260157
$280$		0			0
$281$	−7.83022			−0.467111			−0.233556	−	0.972343i	$-0.575036\pi$
$281$	−7.83022			−0.467111			−0.233556	+	0.972343i	$0.575036\pi$
$282$	−4.41532	−	16.4782i	−0.262928	−	0.981262i
$283$	−3.13735	−	0.840650i	−0.186496	−	0.0499714i	0.164362	−	0.986400i	$-0.447443\pi$
$283$	−3.13735	−	0.840650i	−0.186496	−	0.0499714i	−0.350858	+	0.936429i	$0.614110\pi$
$284$	−2.72813	+	1.57509i	−0.161885	+	0.0934642i
$285$		0			0
$286$		−	1.38940i		−	0.0821570i
$287$	−4.13019	−	5.02106i	−0.243797	−	0.296384i
$288$	−4.18215	−	4.18215i	−0.246436	−	0.246436i
$289$	4.96220	+	2.86493i	0.291894	+	0.168525i
$290$		0			0
$291$	4.19746	+	7.27021i	0.246059	+	0.426187i
$292$	2.22793	−	0.596973i	0.130380	−	0.0349352i
$293$	−10.9441	+	10.9441i	−0.639361	+	0.639361i	−0.950398	−	0.311037i	$-0.899324\pi$
$293$	−10.9441	+	10.9441i	−0.639361	+	0.639361i	0.311037	+	0.950398i	$0.399324\pi$
$294$	−12.2387	−	2.40567i	−0.713775	−	0.140301i
$295$		0			0
$296$	−4.80828	+	8.32818i	−0.279475	+	0.484066i
$297$	0.759430	−	2.83423i	0.0440666	−	0.164459i
$298$	−0.788492	+	2.94269i	−0.0456761	+	0.170465i
$299$	1.24842	−	2.16232i	0.0721978	−	0.125050i
$300$		0			0
$301$	−13.4065	−	1.30512i	−0.772739	−	0.0752260i
$302$	−3.25214	+	3.25214i	−0.187140	+	0.187140i
$303$	1.69210	−	0.453398i	0.0972088	−	0.0260470i
$304$	−9.03553	−	15.6500i	−0.518223	−	0.897589i
$305$		0			0
$306$	5.18041	+	2.99091i	0.296144	+	0.170979i
$307$	−17.7315	−	17.7315i	−1.01199	−	1.01199i	−0.999927	−	0.0120630i	$-0.996160\pi$
$307$	−17.7315	−	17.7315i	−1.01199	−	1.01199i	−0.0120630	−	0.999927i	$-0.503840\pi$
$308$	8.99787	−	1.49601i	0.512701	−	0.0852429i
$309$		−	14.5623i		−	0.828422i
$310$		0			0
$311$	13.8127	−	7.97477i	0.783247	−	0.452208i	−0.0543330	−	0.998523i	$-0.517303\pi$
$311$	13.8127	−	7.97477i	0.783247	−	0.452208i	0.837580	+	0.546315i	$0.183970\pi$
$312$	0.377363	+	0.101114i	0.0213640	+	0.00572445i
$313$	7.82807	+	29.2148i	0.442469	+	1.65132i	0.722535	+	0.691335i	$0.242977\pi$
$313$	7.82807	+	29.2148i	0.442469	+	1.65132i	−0.280066	+	0.959981i	$0.590356\pi$
$314$	15.9650			0.900956
$315$		0			0
$316$	−6.02780			−0.339090
$317$	4.46597	+	16.6672i	0.250834	+	0.936125i	0.970361	+	0.241660i	$0.0776920\pi$
$317$	4.46597	+	16.6672i	0.250834	+	0.936125i	−0.719527	+	0.694464i	$0.755641\pi$
$318$	−8.69439	−	2.32965i	−0.487557	−	0.130641i
$319$	−2.07141	+	1.19593i	−0.115977	+	0.0669592i
$320$		0			0
$321$			5.68770i			0.317456i
$322$	41.4721	+	15.5555i	2.31115	+	0.866873i
$323$	8.63238	+	8.63238i	0.480318	+	0.480318i
$324$	−1.01754	−	0.587476i	−0.0565299	−	0.0326376i
$325$		0			0
$326$	−11.6186	−	20.1240i	−0.643493	−	1.11456i
$327$	−0.716095	+	0.191877i	−0.0396002	+	0.0106108i
$328$	−2.55445	+	2.55445i	−0.141046	+	0.141046i
$329$	−14.7312	+	20.6066i	−0.812159	+	1.13608i
$330$		0			0
$331$	−0.449328	+	0.778259i	−0.0246973	+	0.0427770i	−0.878110	−	0.478459i	$-0.841196\pi$
$331$	−0.449328	+	0.778259i	−0.0246973	+	0.0427770i	0.853413	+	0.521236i	$0.174529\pi$
$332$	−2.62286	+	9.78866i	−0.143948	+	0.537222i
$333$	−1.69304	+	6.31853i	−0.0927782	+	0.346253i
$334$	−17.4794	+	30.2753i	−0.956433	+	1.65659i
$335$		0			0
$336$	−1.27391	+	13.0859i	−0.0694976	+	0.713895i
$337$	−21.9343	+	21.9343i	−1.19484	+	1.19484i	−0.219145	+	0.975692i	$0.570327\pi$
$337$	−21.9343	+	21.9343i	−1.19484	+	1.19484i	−0.975692	+	0.219145i	$0.929673\pi$
$338$	−22.2531	+	5.96269i	−1.21041	+	0.324328i
$339$	−5.16626	−	8.94822i	−0.280593	−	0.486001i
$340$		0			0
$341$	−11.0423	−	6.37528i	−0.597975	−	0.345241i
$342$	−4.58178	−	4.58178i	−0.247754	−	0.247754i
$343$	8.78574	+	16.3037i	0.474386	+	0.880317i
$344$			7.48450i			0.403537i
$345$		0			0
$346$	3.87441	−	2.23689i	0.208289	−	0.120256i
$347$	15.4180	+	4.13123i	0.827680	+	0.221776i	0.647701	−	0.761894i	$-0.275730\pi$
$347$	15.4180	+	4.13123i	0.827680	+	0.221776i	0.179979	+	0.983670i	$0.442397\pi$
$348$	0.247891	+	0.925142i	0.0132884	+	0.0495928i
$349$	−5.03837			−0.269698			−0.134849	−	0.990866i	$-0.543055\pi$
$349$	−5.03837			−0.269698			−0.134849	+	0.990866i	$0.543055\pi$
$350$		0			0
$351$	0.265747			0.0141845
$352$	−4.49161	−	16.7629i	−0.239404	−	0.893467i
$353$	−6.06624	−	1.62544i	−0.322874	−	0.0865137i	0.0937419	−	0.995597i	$-0.470117\pi$
$353$	−6.06624	−	1.62544i	−0.322874	−	0.0865137i	−0.416615	+	0.909083i	$0.636784\pi$
$354$	−16.7036	+	9.64382i	−0.887786	+	0.512563i
$355$		0			0
$356$			11.4454i			0.606604i
$357$	−1.45676	−	8.76179i	−0.0770997	−	0.463723i
$358$	2.58573	+	2.58573i	0.136660	+	0.136660i
$359$	26.9712	+	15.5718i	1.42348	+	0.821849i	0.996595	−	0.0824548i	$-0.0262760\pi$
$359$	26.9712	+	15.5718i	1.42348	+	0.821849i	0.426889	+	0.904304i	$0.359609\pi$
$360$		0			0
$361$	2.88803	+	5.00221i	0.152001	+	0.263274i
$362$	0.689436	−	0.184734i	0.0362359	−	0.00970939i
$363$	−1.69027	+	1.69027i	−0.0887162	+	0.0887162i
$364$	0.341791	+	0.752086i	0.0179147	+	0.0394200i
$365$		0			0
$366$	8.30910	−	14.3918i	0.434323	−	0.752270i
$367$	−8.13558	+	30.3624i	−0.424674	+	1.58490i	0.339960	+	0.940440i	$0.389586\pi$
$367$	−8.13558	+	30.3624i	−0.424674	+	1.58490i	−0.764634	+	0.644465i	$0.777080\pi$
$368$	12.0843	−	45.0992i	0.629937	−	2.35096i
$369$	−1.22867	+	2.12812i	−0.0639619	+	0.110785i
$370$		0			0
$371$	5.52968	+	12.1676i	0.287086	+	0.631712i
$372$	−3.61030	+	3.61030i	−0.187185	+	0.187185i
$373$	21.1509	−	5.66737i	1.09515	−	0.293445i	0.334363	−	0.942444i	$-0.391479\pi$
$373$	21.1509	−	5.66737i	1.09515	−	0.293445i	0.760789	+	0.648999i	$0.224812\pi$
$374$	8.77596	+	15.2004i	0.453794	+	0.785995i
$375$		0			0
$376$	12.1892	+	7.03744i	0.628610	+	0.362928i
$377$	−0.153178	−	0.153178i	−0.00788908	−	0.00788908i
$378$	0.773198	+	4.65047i	0.0397690	+	0.239194i
$379$			0.993329i			0.0510239i	0.999675	+	0.0255119i	$0.00812158\pi$
$379$			0.993329i			0.0510239i	−0.999675	+	0.0255119i	$0.991878\pi$
$380$		0			0
$381$	−2.29584	+	1.32550i	−0.117619	+	0.0679076i
$382$	−9.21532	−	2.46924i	−0.471497	−	0.126337i
$383$	−3.37533	−	12.5969i	−0.172471	−	0.643672i	−0.996969	−	0.0778058i	$-0.975209\pi$
$383$	−3.37533	−	12.5969i	−0.172471	−	0.643672i	0.824497	−	0.565866i	$-0.191458\pi$
$384$	10.7601			0.549100
$385$		0			0
$386$	45.8649			2.33446
$387$	1.31768	+	4.91766i	0.0669816	+	0.249979i
$388$	9.52753	+	2.55289i	0.483687	+	0.129604i
$389$	12.3488	−	7.12960i	0.626111	−	0.361485i	−0.153134	−	0.988205i	$-0.548936\pi$
$389$	12.3488	−	7.12960i	0.626111	−	0.361485i	0.779244	+	0.626720i	$0.215603\pi$
$390$		0			0
$391$			31.5418i			1.59514i
$392$	8.54347	−	5.73655i	0.431510	−	0.289740i
$393$	−6.81213	−	6.81213i	−0.343626	−	0.343626i
$394$	10.1278	+	5.84729i	0.510232	+	0.294582i
$395$		0			0
$396$	−1.72378	−	2.98567i	−0.0866232	−	0.150036i
$397$	−19.8747	+	5.32540i	−0.997481	+	0.267274i	−0.720390	−	0.693569i	$-0.756037\pi$
$397$	−19.8747	+	5.32540i	−0.997481	+	0.267274i	−0.277091	+	0.960844i	$0.589370\pi$
$398$	−18.2959	+	18.2959i	−0.917091	+	0.917091i
$399$	−0.932216	+	9.57594i	−0.0466692	+	0.479397i
$400$		0			0
$401$	4.95698	−	8.58574i	0.247540	−	0.428751i	−0.715303	−	0.698815i	$-0.753711\pi$
$401$	4.95698	−	8.58574i	0.247540	−	0.428751i	0.962843	+	0.270063i	$0.0870446\pi$
$402$	7.31229	−	27.2898i	0.364704	−	1.36109i
$403$	0.298883	−	1.11545i	0.0148884	−	0.0555644i
$404$	1.02914	−	1.78252i	0.0512015	−	0.0886836i
$405$		0			0
$406$	2.23488	−	3.12624i	0.110915	−	0.155153i
$407$	−13.5721	+	13.5721i	−0.672746	+	0.672746i
$408$	−4.76712	+	1.27735i	−0.236008	+	0.0632380i
$409$	18.7178	+	32.4202i	0.925535	+	1.60307i	0.790698	+	0.612207i	$0.209718\pi$
$409$	18.7178	+	32.4202i	0.925535	+	1.60307i	0.134838	+	0.990868i	$0.456949\pi$
$410$		0			0
$411$	11.4182	+	6.59232i	0.563220	+	0.325175i
$412$	−12.0986	−	12.0986i	−0.596057	−	0.596057i
$413$	26.8149	+	10.0578i	1.31948	+	0.494913i
$414$		−	16.7414i		−	0.822792i
$415$		0			0
$416$	1.36117	−	0.785873i	0.0667369	−	0.0385306i
$417$	14.9216	+	3.99823i	0.730713	+	0.195794i
$418$	−4.92081	−	18.3647i	−0.240685	−	0.898248i
$419$	−22.2223			−1.08563			−0.542816	−	0.839851i	$-0.682642\pi$
$419$	−22.2223			−1.08563			−0.542816	+	0.839851i	$0.682642\pi$
$420$		0			0
$421$	−33.9692			−1.65556			−0.827780	−	0.561053i	$-0.810396\pi$
$421$	−33.9692			−1.65556			−0.827780	+	0.561053i	$0.810396\pi$
$422$	−4.47698	−	16.7083i	−0.217936	−	0.813349i
$423$	9.24785	+	2.47795i	0.449646	+	0.120482i
$424$	6.43139	−	3.71316i	0.312336	−	0.180327i
$425$		0			0
$426$		−	4.77730i		−	0.231461i
$427$	−24.3413	+	4.04704i	−1.17796	+	0.195850i
$428$	4.72543	+	4.72543i	0.228413	+	0.228413i
$429$	0.675289	+	0.389878i	0.0326033	+	0.0188235i
$430$		0			0
$431$	−7.90386	−	13.6899i	−0.380716	−	0.659419i	0.610449	−	0.792055i	$-0.290989\pi$
$431$	−7.90386	−	13.6899i	−0.380716	−	0.659419i	−0.991165	+	0.132637i	$0.957656\pi$
$432$	4.80006	−	1.28617i	0.230943	−	0.0618810i
$433$	4.33729	−	4.33729i	0.208437	−	0.208437i	−0.595166	−	0.803603i	$-0.702914\pi$
$433$	4.33729	−	4.33729i	0.208437	−	0.208437i	0.803603	+	0.595166i	$0.202914\pi$
$434$	20.3895	+	1.98492i	0.978729	+	0.0952791i
$435$		0			0
$436$	−0.435529	+	0.754359i	−0.0208581	+	0.0361272i
$437$	8.84298	−	33.0025i	0.423017	−	1.57872i
$438$	−0.905322	+	3.37871i	−0.0432580	+	0.161441i
$439$	−5.34596	+	9.25948i	−0.255149	+	0.441931i	−0.964936	−	0.262485i	$-0.915458\pi$
$439$	−5.34596	+	9.25948i	−0.255149	+	0.441931i	0.709787	+	0.704416i	$0.248791\pi$
$440$		0			0
$441$	4.60351	−	5.27330i	0.219215	−	0.251110i
$442$	−1.12405	+	1.12405i	−0.0534657	+	0.0534657i
$443$	21.2098	−	5.68315i	1.00771	−	0.270015i	0.283037	−	0.959109i	$-0.408658\pi$
$443$	21.2098	−	5.68315i	1.00771	−	0.270015i	0.724672	+	0.689094i	$0.241991\pi$
$444$	3.84293	+	6.65615i	0.182377	+	0.315887i
$445$		0			0
$446$	−31.7728	−	18.3440i	−1.50448	−	0.868614i
$447$	−1.20897	−	1.20897i	−0.0571825	−	0.0571825i
$448$	1.00816	+	1.22562i	0.0476313	+	0.0579053i
$449$		−	2.98493i		−	0.140868i	−0.997516	−	0.0704338i	$-0.977562\pi$
$449$		−	2.98493i		−	0.140868i	0.997516	−	0.0704338i	$-0.0224384\pi$
$450$		0			0
$451$	−6.24434	+	3.60517i	−0.294035	+	0.169761i
$452$	−11.7266	−	3.14212i	−0.551571	−	0.147793i
$453$	−0.668055	−	2.49322i	−0.0313880	−	0.117142i
$454$	8.09363			0.379853
$455$		0			0
$456$	5.34599			0.250349
$457$	−5.49087	−	20.4922i	−0.256852	−	0.958585i	−0.967051	−	0.254583i	$-0.918062\pi$
$457$	−5.49087	−	20.4922i	−0.256852	−	0.958585i	0.710199	−	0.704001i	$-0.248605\pi$
$458$	21.3483	+	5.72027i	0.997542	+	0.267291i
$459$	−2.90734	+	1.67855i	−0.135703	+	0.0783481i
$460$		0			0
$461$			12.3910i			0.577105i	0.957464	+	0.288552i	$0.0931739\pi$
$461$			12.3910i			0.577105i	−0.957464	+	0.288552i	$0.906826\pi$
$462$	−4.85795	+	12.9517i	−0.226012	+	0.602566i
$463$	3.29804	+	3.29804i	0.153273	+	0.153273i	0.779578	−	0.626305i	$-0.215434\pi$
$463$	3.29804	+	3.29804i	0.153273	+	0.153273i	−0.626305	+	0.779578i	$0.715434\pi$
$464$	−3.50815	−	2.02543i	−0.162862	−	0.0940283i
$465$		0			0
$466$	22.0912	+	38.2632i	1.02336	+	1.77251i
$467$	0.420251	−	0.112606i	0.0194469	−	0.00521079i	−0.249082	−	0.968482i	$-0.580129\pi$
$467$	0.420251	−	0.112606i	0.0194469	−	0.00521079i	0.268529	+	0.963271i	$0.413462\pi$
$468$	0.220787	−	0.220787i	0.0102059	−	0.0102059i
$469$	−38.1916	+	17.3565i	−1.76353	+	0.801448i
$470$		0			0
$471$	−4.47992	+	7.75944i	−0.206424	+	0.357536i
$472$	4.11864	−	15.3710i	0.189576	−	0.707507i
$473$	−3.86636	+	14.4295i	−0.177776	+	0.663467i
$474$	4.57064	−	7.91658i	0.209937	−	0.363621i
$475$		0			0
$476$	−8.48974	−	6.06914i	−0.389126	−	0.278179i
$477$	3.57200	−	3.57200i	0.163551	−	0.163551i
$478$	39.5567	−	10.5992i	1.80928	−	0.484795i
$479$	−10.8544	−	18.8003i	−0.495948	−	0.859008i	0.504041	−	0.863680i	$-0.331846\pi$
$479$	−10.8544	−	18.8003i	−0.495948	−	0.859008i	−0.999989	+	0.00467229i	$0.998513\pi$
$480$		0			0
$481$	−1.50546	−	0.869180i	−0.0686432	−	0.0396312i
$482$	19.6868	+	19.6868i	0.896710	+	0.896710i
$483$	−19.1979	+	15.7916i	−0.873533	+	0.718544i
$484$			2.80861i			0.127664i
$485$		0			0
$486$	1.54312	−	0.890920i	0.0699973	−	0.0404129i
$487$	1.85366	+	0.496688i	0.0839976	+	0.0225071i	0.300573	−	0.953759i	$-0.402822\pi$
$487$	1.85366	+	0.496688i	0.0839976	+	0.0225071i	−0.216575	+	0.976266i	$0.569489\pi$
$488$	3.54862	+	13.2436i	0.160638	+	0.599510i
$489$	13.0411			0.589739
$490$		0			0
$491$	7.49344			0.338174			0.169087	−	0.985601i	$-0.445918\pi$
$491$	7.49344			0.338174			0.169087	+	0.985601i	$0.445918\pi$
$492$	0.747276	+	2.78887i	0.0336898	+	0.125732i
$493$	2.64334	+	0.708280i	0.119050	+	0.0318993i
$494$	1.49124	−	0.860968i	0.0670941	−	0.0387368i
$495$		0			0
$496$		−	21.5944i		−	0.969617i
$497$	−5.47829	+	4.50629i	−0.245735	+	0.202135i
$498$	−10.8671	−	10.8671i	−0.486965	−	0.486965i
$499$	2.01654	+	1.16425i	0.0902726	+	0.0521189i	0.544457	−	0.838789i	$-0.316736\pi$
$499$	2.01654	+	1.16425i	0.0902726	+	0.0521189i	−0.454184	+	0.890908i	$0.650069\pi$
$500$		0			0
$501$	−9.80977	−	16.9910i	−0.438268	−	0.759103i
$502$	16.5139	−	4.42487i	0.737049	−	0.197492i
$503$	−23.1484	+	23.1484i	−1.03213	+	1.03213i	−0.0326680	+	0.999466i	$0.510400\pi$
$503$	−23.1484	+	23.1484i	−1.03213	+	1.03213i	−0.999466	+	0.0326680i	$0.989600\pi$
$504$	−3.16415	−	2.26199i	−0.140942	−	0.100757i
$505$		0			0
$506$	24.5613	−	42.5415i	1.09188	−	1.89120i
$507$	3.34637	−	12.4888i	0.148617	−	0.554648i
$508$	−0.806172	+	3.00867i	−0.0357681	+	0.133488i
$509$	−1.08951	+	1.88709i	−0.0482917	+	0.0836437i	−0.889161	−	0.457595i	$-0.848711\pi$
$509$	−1.08951	+	1.88709i	−0.0482917	+	0.0836437i	0.840869	+	0.541238i	$0.182044\pi$
$510$		0			0
$511$	4.72844	−	2.14888i	0.209174	−	0.0950606i
$512$	10.4512	−	10.4512i	0.461882	−	0.461882i
$513$	3.51257	−	0.941189i	0.155084	−	0.0415545i
$514$	−8.71086	−	15.0877i	−0.384220	−	0.665488i
$515$		0			0
$516$	5.18043	+	2.99092i	0.228056	+	0.131668i
$517$	19.8643	+	19.8643i	0.873631	+	0.873631i
$518$	10.8301	−	28.8740i	0.475849	−	1.26865i
$519$			2.51076i			0.110210i
$520$		0			0
$521$	13.2441	−	7.64651i	0.580236	−	0.335000i	−0.180991	−	0.983485i	$-0.557930\pi$
$521$	13.2441	−	7.64651i	0.580236	−	0.335000i	0.761227	+	0.648485i	$0.224597\pi$
$522$	−1.40300	−	0.375932i	−0.0614075	−	0.0164541i
$523$	−0.731228	−	2.72898i	−0.0319743	−	0.119330i	0.948094	−	0.317990i	$-0.103008\pi$
$523$	−0.731228	−	2.72898i	−0.0319743	−	0.119330i	−0.980068	+	0.198660i	$0.936341\pi$
$524$	−11.3193			−0.494484
$525$		0			0
$526$	0.541907			0.0236283
$527$	3.77571	+	14.0911i	0.164473	+	0.613820i
$528$	14.0844	+	3.77390i	0.612945	+	0.164238i
$529$	56.5309	−	32.6381i	2.45786	−	1.41905i
$530$		0			0
$531$		−	10.8246i		−	0.469746i
$532$	7.18135	+	8.73035i	0.311351	+	0.378509i
$533$	−0.461761	−	0.461761i	−0.0200011	−	0.0200011i
$534$	−15.0317	−	8.67858i	−0.650487	−	0.375559i
$535$		0			0
$536$	11.6548	+	20.1868i	0.503412	+	0.871935i
$537$	−1.98232	+	0.531161i	−0.0855434	+	0.0229213i
$538$	0.482429	−	0.482429i	0.0207990	−	0.0207990i
$539$	19.4345	−	6.64616i	0.837102	−	0.286271i
$540$		0			0
$541$	13.7644	−	23.8407i	0.591779	−	1.02499i	−0.402214	−	0.915546i	$-0.631759\pi$
$541$	13.7644	−	23.8407i	0.591779	−	1.02499i	0.993993	−	0.109445i	$-0.0349074\pi$
$542$	5.39931	−	20.1505i	0.231920	−	0.865538i
$543$	−0.103676	+	0.386923i	−0.00444916	+	0.0166045i
$544$	−9.92772	+	17.1953i	−0.425647	+	0.737243i
$545$		0			0
$546$	−1.24692	−	0.121387i	−0.0533631	−	0.00519489i
$547$	13.0361	−	13.0361i	0.557385	−	0.557385i	−0.371177	−	0.928562i	$-0.621046\pi$
$547$	13.0361	−	13.0361i	0.557385	−	0.557385i	0.928562	+	0.371177i	$0.121046\pi$
$548$	14.9635	−	4.00945i	0.639208	−	0.171275i
$549$	4.66321	+	8.07692i	0.199021	+	0.344715i
$550$		0			0
$551$	−2.56717	−	1.48216i	−0.109365	−	0.0631421i
$552$	9.76685	+	9.76685i	0.415705	+	0.415705i
$553$	−13.3896	+	2.22618i	−0.569382	+	0.0946668i
$554$			21.9917i			0.934338i
$555$		0			0
$556$	15.7189	−	9.07531i	0.666630	−	0.384879i
$557$	−11.0124	−	2.95077i	−0.466612	−	0.125028i	0.0178499	−	0.999841i	$-0.494318\pi$
$557$	−11.0124	−	2.95077i	−0.466612	−	0.125028i	−0.484462	+	0.874812i	$0.660985\pi$
$558$	−2.00402	−	7.47912i	−0.0848371	−	0.316616i
$559$	−1.35295			−0.0572238
$560$		0			0
$561$	−9.85045			−0.415886
$562$	−3.61109	−	13.4768i	−0.152325	−	0.568484i
$563$	−25.9678	−	6.95804i	−1.09441	−	0.293247i	−0.333924	−	0.942600i	$-0.608373\pi$
$563$	−25.9678	−	6.95804i	−1.09441	−	0.293247i	−0.760487	+	0.649353i	$0.775040\pi$
$564$	9.74200	−	5.62454i	0.410212	−	0.236836i
$565$		0			0
$566$		−	5.78745i		−	0.243265i
$567$	−2.47723	−	0.929166i	−0.104034	−	0.0390213i
$568$	2.78706	+	2.78706i	0.116943	+	0.116943i
$569$	−2.25223	−	1.30033i	−0.0944184	−	0.0545125i	0.452047	−	0.891994i	$-0.350694\pi$
$569$	−2.25223	−	1.30033i	−0.0944184	−	0.0545125i	−0.546466	+	0.837481i	$0.684027\pi$
$570$		0			0
$571$	−6.25437	−	10.8329i	−0.261737	−	0.453342i	0.704967	−	0.709241i	$-0.250962\pi$
$571$	−6.25437	−	10.8329i	−0.261737	−	0.453342i	−0.966704	+	0.255899i	$0.917629\pi$
$572$	0.884959	−	0.237124i	0.0370020	−	0.00991465i
$573$	3.78602	−	3.78602i	0.158163	−	0.158163i
$574$	6.73714	−	9.42416i	0.281203	−	0.393357i
$575$		0			0
$576$	0.299914	−	0.519465i	0.0124964	−	0.0216444i
$577$	−2.92422	+	10.9134i	−0.121737	+	0.454329i	−0.999702	−	0.0243953i	$-0.992234\pi$
$577$	−2.92422	+	10.9134i	−0.121737	+	0.454329i	0.877965	+	0.478724i	$0.158901\pi$
$578$	−2.64246	+	9.86180i	−0.109912	+	0.410197i
$579$	−12.8701	+	22.2917i	−0.534863	+	0.926410i
$580$		0			0
$581$	−2.21103	+	22.7122i	−0.0917291	+	0.942262i
$582$	−10.5772	+	10.5772i	−0.438438	+	0.438438i
$583$	14.3173	−	3.83631i	0.592963	−	0.158884i
$584$	−1.44296	−	2.49929i	−0.0597103	−	0.103421i
$585$		0			0
$586$	−23.8833	−	13.7890i	−0.986609	−	0.569619i
$587$	−0.811118	−	0.811118i	−0.0334784	−	0.0334784i	0.690169	−	0.723648i	$-0.257536\pi$
$587$	−0.811118	−	0.811118i	−0.0334784	−	0.0334784i	−0.723648	+	0.690169i	$0.757536\pi$
$588$	−0.556477	−	8.20582i	−0.0229487	−	0.338402i
$589$		−	15.8022i		−	0.651120i
$590$		0			0
$591$	−5.68391	+	3.28161i	−0.233805	+	0.134987i
$592$	−31.3992	−	8.41340i	−1.29050	−	0.345788i
$593$	−3.09100	−	11.5358i	−0.126932	−	0.473717i	0.872969	−	0.487776i	$-0.162192\pi$
$593$	−3.09100	−	11.5358i	−0.126932	−	0.473717i	−0.999901	+	0.0140585i	$0.995525\pi$
$594$	5.22829			0.214520
$595$		0			0
$596$	−2.00887			−0.0822867
$597$	−3.75835	−	14.0263i	−0.153819	−	0.574060i
$598$	4.29736	+	1.15147i	0.175732	+	0.0470873i
$599$	1.51812	−	0.876486i	0.0620286	−	0.0358122i	−0.468665	−	0.883376i	$-0.655265\pi$
$599$	1.51812	−	0.876486i	0.0620286	−	0.0358122i	0.530694	+	0.847564i	$0.321932\pi$
$600$		0			0
$601$			18.7443i			0.764595i	0.924039	+	0.382297i	$0.124867\pi$
$601$			18.7443i			0.764595i	−0.924039	+	0.382297i	$0.875133\pi$
$602$	−3.93646	−	23.6762i	−0.160438	−	0.964969i
$603$	11.2118	+	11.2118i	0.456578	+	0.456578i
$604$	−2.62644	−	1.51637i	−0.106868	−	0.0617004i
$605$		0			0
$606$	1.56071	+	2.70323i	0.0633995	+	0.109811i
$607$	17.4212	−	4.66799i	0.707104	−	0.189468i	0.112694	−	0.993630i	$-0.464052\pi$
$607$	17.4212	−	4.66799i	0.707104	−	0.189468i	0.594411	+	0.804162i	$0.297385\pi$
$608$	15.2083	−	15.2083i	0.616778	−	0.616778i
$609$	0.892313	+	1.96347i	0.0361583	+	0.0795637i
$610$		0			0
$611$	−1.27214	+	2.20341i	−0.0514652	+	0.0891404i
$612$	−1.02090	+	3.81003i	−0.0412673	+	0.154012i
$613$	1.12662	−	4.20460i	0.0455037	−	0.169822i	−0.939435	−	0.342728i	$-0.888649\pi$
$613$	1.12662	−	4.20460i	0.0455037	−	0.169822i	0.984938	+	0.172906i	$0.0553157\pi$
$614$	22.3408	−	38.6954i	0.901602	−	1.56162i
$615$		0			0
$616$	−4.72185	−	10.3901i	−0.190249	−	0.418628i
$617$	21.5544	−	21.5544i	0.867748	−	0.867748i	−0.124475	−	0.992223i	$-0.539725\pi$
$617$	21.5544	−	21.5544i	0.867748	−	0.867748i	0.992223	+	0.124475i	$0.0397246\pi$
$618$	25.0636	−	6.71577i	1.00821	−	0.270148i
$619$	−10.6477	−	18.4424i	−0.427967	−	0.741261i	0.568725	−	0.822528i	$-0.307437\pi$
$619$	−10.6477	−	18.4424i	−0.427967	−	0.741261i	−0.996692	+	0.0812668i	$0.974103\pi$
$620$		0			0
$621$	8.13678	+	4.69777i	0.326518	+	0.188515i
$622$	20.0956	+	20.0956i	0.805762	+	0.805762i
$623$	4.22700	+	25.4237i	0.169351	+	1.01858i
$624$			1.32060i			0.0528663i
$625$		0			0
$626$	−46.6721	+	26.9462i	−1.86539	+	1.07699i
$627$	10.3066	+	2.76165i	0.411606	+	0.110290i
$628$	2.72469	+	10.1687i	0.108727	+	0.405774i
$629$	21.9602			0.875611
$630$		0			0
$631$	−14.7032			−0.585327			−0.292664	−	0.956215i	$-0.594542\pi$
$631$	−14.7032			−0.585327			−0.292664	+	0.956215i	$0.594542\pi$
$632$	1.95201	+	7.28500i	0.0776468	+	0.289782i
$633$	9.37701	+	2.51256i	0.372703	+	0.0998654i
$634$	−26.6268	+	15.3730i	−1.05748	+	0.610539i
$635$		0			0
$636$		−	5.93536i		−	0.235352i
$637$	1.03698	+	1.54438i	0.0410867	+	0.0611906i
$638$	−3.01362	−	3.01362i	−0.119311	−	0.119311i
$639$	2.32191	+	1.34055i	0.0918532	+	0.0530315i
$640$		0			0
$641$	11.0943	+	19.2159i	0.438198	+	0.758981i	0.997551	−	0.0699487i	$-0.0222836\pi$
$641$	11.0943	+	19.2159i	0.438198	+	0.758981i	−0.559353	+	0.828930i	$0.688950\pi$
$642$	−9.78924	+	2.62302i	−0.386350	+	0.103522i
$643$	9.54667	−	9.54667i	0.376484	−	0.376484i	−0.493348	−	0.869832i	$-0.664227\pi$
$643$	9.54667	−	9.54667i	0.376484	−	0.376484i	0.869832	+	0.493348i	$0.164227\pi$
$644$	−2.82995	+	29.0699i	−0.111516	+	1.14551i
$645$		0			0
$646$	−10.8764	+	18.8384i	−0.427925	+	0.741188i
$647$	−0.952279	+	3.55395i	−0.0374380	+	0.139720i	−0.982115	−	0.188281i	$-0.939708\pi$
$647$	−0.952279	+	3.55395i	−0.0374380	+	0.139720i	0.944677	+	0.328001i	$0.106375\pi$
$648$	−0.380490	+	1.42001i	−0.0149471	+	0.0557832i
$649$	15.8808	−	27.5063i	0.623375	−	1.07972i
$650$		0			0
$651$	−6.68621	+	9.35292i	−0.262053	+	0.366570i
$652$	10.8348	−	10.8348i	0.424322	−	0.424322i
$653$	−25.9802	+	6.96138i	−1.01669	+	0.272420i	−0.728420	−	0.685131i	$-0.759745\pi$
$653$	−25.9802	+	6.96138i	−1.01669	+	0.272420i	−0.288265	+	0.957551i	$0.593078\pi$
$654$	−0.660489	−	1.14400i	−0.0258272	−	0.0447340i
$655$		0			0
$656$	−10.5754	−	6.10574i	−0.412902	−	0.238389i
$657$	−1.38811	−	1.38811i	−0.0541552	−	0.0541552i
$658$	−42.2602	−	15.8511i	−1.64747	−	0.617939i
$659$			5.85098i			0.227922i	0.993485	+	0.113961i	$0.0363539\pi$
$659$			5.85098i			0.227922i	−0.993485	+	0.113961i	$0.963646\pi$
$660$		0			0
$661$	7.57292	−	4.37223i	0.294552	−	0.170060i	−0.345441	−	0.938441i	$-0.612271\pi$
$661$	7.57292	−	4.37223i	0.294552	−	0.170060i	0.639993	+	0.768381i	$0.278937\pi$
$662$	−1.54670	−	0.414437i	−0.0601142	−	0.0161076i
$663$	−0.230903	−	0.861740i	−0.00896751	−	0.0334672i
$664$	12.6796			0.492065
$665$		0			0
$666$	−11.6558			−0.451651
$667$	−1.98227	−	7.39792i	−0.0767537	−	0.286449i
$668$	−22.2666	−	5.96631i	−0.861519	−	0.230843i
$669$	17.8314	−	10.2950i	0.689403	−	0.398027i
$670$		0			0
$671$			27.3657i			1.05644i
$672$	−15.4363	+	2.56647i	−0.595467	+	0.0990038i
$673$	−20.2896	−	20.2896i	−0.782107	−	0.782107i	0.198079	−	0.980186i	$-0.436530\pi$
$673$	−20.2896	−	20.2896i	−0.782107	−	0.782107i	−0.980186	+	0.198079i	$0.936530\pi$
$674$	−47.8672	−	27.6361i	−1.84378	−	1.06450i
$675$		0			0
$676$	−7.59570	−	13.1561i	−0.292142	−	0.506006i
$677$	−44.8571	+	12.0194i	−1.72400	+	0.461944i	−0.978786	−	0.204884i	$-0.934318\pi$
$677$	−44.8571	+	12.0194i	−1.72400	+	0.461944i	−0.745212	+	0.666828i	$0.767652\pi$
$678$	13.0185	−	13.0185i	0.499971	−	0.499971i
$679$	22.1063	+	2.15205i	0.848364	+	0.0825881i
$680$		0			0
$681$	−2.27114	+	3.93374i	−0.0870305	+	0.150741i
$682$	5.88023	−	21.9453i	0.225166	−	0.840329i
$683$	−2.82209	+	10.5322i	−0.107984	+	0.403003i	−0.998667	−	0.0516231i	$-0.983561\pi$
$683$	−2.82209	+	10.5322i	−0.107984	+	0.403003i	0.890682	+	0.454626i	$0.150227\pi$
$684$	2.13634	−	3.70025i	0.0816851	−	0.141483i
$685$		0			0
$686$	−24.0090	+	22.6402i	−0.916666	+	0.864407i
$687$	−8.77075	+	8.77075i	−0.334625	+	0.334625i
$688$	−24.4378	+	6.54809i	−0.931682	+	0.249643i
$689$	0.671219	+	1.16259i	0.0255714	+	0.0442910i
$690$		0			0
$691$	26.6156	+	15.3665i	1.01251	+	0.584571i	0.911924	−	0.410358i	$-0.134596\pi$
$691$	26.6156	+	15.3665i	1.01251	+	0.584571i	0.100582	+	0.994929i	$0.467930\pi$
$692$	2.08599	+	2.08599i	0.0792973	+	0.0792973i
$693$	−4.93170	−	5.99546i	−0.187340	−	0.227749i
$694$			28.4415i			1.07962i
$695$		0			0
$696$	1.03782	−	0.599186i	0.0393385	−	0.0227121i
$697$	7.96844	+	2.13514i	0.301826	+	0.0808741i
$698$	−2.32357	−	8.67167i	−0.0879483	−	0.328228i
$699$	−24.7960			−0.937871
$700$		0			0
$701$	17.3574			0.655579			0.327790	−	0.944751i	$-0.393696\pi$
$701$	17.3574			0.655579			0.327790	+	0.944751i	$0.393696\pi$
$702$	0.122555	+	0.457383i	0.00462556	+	0.0172628i
$703$	−22.9772	−	6.15671i	−0.866600	−	0.232205i
$704$	1.52422	−	0.880010i	0.0574463	−	0.0331666i
$705$		0			0
$706$		−	11.1904i		−	0.421155i
$707$	1.62771	−	4.33959i	0.0612162	−	0.163207i
$708$	−8.99323	−	8.99323i	−0.337986	−	0.337986i
$709$	8.56028	+	4.94228i	0.321488	+	0.185611i	0.652056	−	0.758171i	$-0.273907\pi$
$709$	8.56028	+	4.94228i	0.321488	+	0.185611i	−0.330568	+	0.943782i	$0.607240\pi$
$710$		0			0
$711$	2.56513	+	4.44293i	0.0961997	+	0.166623i
$712$	13.8325	−	3.70641i	0.518396	−	0.138904i
$713$	28.8699	−	28.8699i	1.08118	−	1.08118i
$714$	14.4083	−	6.54797i	0.539217	−	0.245051i
$715$		0			0
$716$	−1.20565	+	2.08824i	−0.0450571	+	0.0780412i
$717$	−5.94845	+	22.1999i	−0.222149	+	0.829071i
$718$	−14.3626	+	53.6021i	−0.536009	+	2.00041i
$719$	−13.8682	+	24.0204i	−0.517197	+	0.895811i	0.482604	+	0.875839i	$0.339691\pi$
$719$	−13.8682	+	24.0204i	−0.517197	+	0.895811i	−0.999801	+	0.0199723i	$0.993642\pi$
$720$		0			0
$721$	−31.3429	−	22.4064i	−1.16727	−	0.834460i
$722$	−7.27754	+	7.27754i	−0.270842	+	0.270842i
$723$	−15.0927	+	4.04406i	−0.561302	+	0.150400i
$724$	0.235327	+	0.407598i	0.00874586	+	0.0151483i
$725$		0			0
$726$	−3.68868	−	2.12966i	−0.136900	−	0.0790390i
$727$	−4.65452	−	4.65452i	−0.172626	−	0.172626i	0.615506	−	0.788132i	$-0.288952\pi$
$727$	−4.65452	−	4.65452i	−0.172626	−	0.172626i	−0.788132	+	0.615506i	$0.788952\pi$
$728$	0.798263	−	0.656630i	0.0295856	−	0.0243363i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	14.8017	−	8.54574i	0.547459	−	0.316076i
$732$	10.5847	+	2.83617i	0.391222	+	0.104828i
$733$	−2.71600	−	10.1362i	−0.100318	−	0.374390i	0.897454	−	0.441107i	$-0.145414\pi$
$733$	−2.71600	−	10.1362i	−0.100318	−	0.374390i	−0.997772	+	0.0667169i	$0.978748\pi$
$734$	−56.0094			−2.06735
$735$		0			0
$736$	55.5695			2.04832
$737$	12.0414	+	44.9390i	0.443550	+	1.65535i
$738$	−4.22938	−	1.13326i	−0.155686	−	0.0417159i
$739$	−44.5007	+	25.6925i	−1.63699	+	0.945114i	−0.655122	+	0.755523i	$0.727383\pi$
$739$	−44.5007	+	25.6925i	−1.63699	+	0.945114i	−0.981863	+	0.189591i	$0.939284\pi$
$740$		0			0
$741$			0.966381i			0.0355009i
$742$	−18.3919	+	15.1287i	−0.675187	+	0.555391i
$743$	16.6359	+	16.6359i	0.610313	+	0.610313i	0.943028	−	0.332715i	$-0.107965\pi$
$743$	16.6359	+	16.6359i	0.610313	+	0.610313i	−0.332715	+	0.943028i	$0.607965\pi$
$744$	5.53243	+	3.19415i	0.202829	+	0.117103i
$745$		0			0
$746$	19.5085	+	33.7897i	0.714257	+	1.23713i
$747$	8.33111	−	2.23231i	0.304819	−	0.0816761i
$748$	−8.18392	+	8.18392i	−0.299234	+	0.299234i
$749$	12.2418	+	8.75142i	0.447306	+	0.319770i
$750$		0			0
$751$	23.5482	−	40.7867i	0.859286	−	1.48833i	−0.0133254	−	0.999911i	$-0.504242\pi$
$751$	23.5482	−	40.7867i	0.859286	−	1.48833i	0.872611	−	0.488415i	$-0.162425\pi$
$752$	−12.3139	+	45.9562i	−0.449043	+	1.67585i
$753$	−2.48332	+	9.26787i	−0.0904971	+	0.337740i
$754$	0.192997	−	0.334281i	0.00702853	−	0.0121738i
$755$		0			0
$756$	−2.83009	+	1.28616i	−0.102929	+	0.0467770i
$757$	7.76199	−	7.76199i	0.282114	−	0.282114i	−0.551837	−	0.833952i	$-0.686073\pi$
$757$	7.76199	−	7.76199i	0.282114	−	0.282114i	0.833952	+	0.551837i	$0.186073\pi$
$758$	−1.70964	+	0.458097i	−0.0620970	+	0.0166388i
$759$	13.7843	+	23.8750i	0.500337	+	0.866609i
$760$		0			0
$761$	−16.3521	−	9.44089i	−0.592763	−	0.342232i	0.173426	−	0.984847i	$-0.444516\pi$
$761$	−16.3521	−	9.44089i	−0.592763	−	0.342232i	−0.766189	+	0.642615i	$0.777850\pi$
$762$	−3.34014	−	3.34014i	−0.121001	−	0.121001i
$763$	−0.688843	+	1.83651i	−0.0249378	+	0.0664861i
$764$		−	6.29098i		−	0.227600i
$765$		0			0
$766$	20.1242	−	11.6187i	0.727118	−	0.419802i
$767$	2.77857	+	0.744517i	0.100328	+	0.0268829i
$768$	5.27278	+	19.6783i	0.190265	+	0.710079i
$769$	6.17963			0.222843			0.111422	−	0.993773i	$-0.464460\pi$
$769$	6.17963			0.222843			0.111422	+	0.993773i	$0.464460\pi$
$770$		0			0
$771$	9.77738			0.352124
$772$	7.82760	+	29.2130i	0.281722	+	1.05140i
$773$	6.94812	+	1.86174i	0.249907	+	0.0669623i	0.381598	−	0.924329i	$-0.375374\pi$
$773$	6.94812	+	1.86174i	0.249907	+	0.0669623i	−0.131691	+	0.991291i	$0.542041\pi$
$774$	−7.85623	+	4.53580i	−0.282386	+	0.163036i
$775$		0			0
$776$		−	12.3414i		−	0.443030i
$777$	10.9945	+	13.3660i	0.394427	+	0.479504i
$778$	17.9659	+	17.9659i	0.644109	+	0.644109i
$779$	−7.73884	−	4.46802i	−0.277273	−	0.160084i
$780$		0			0
$781$	3.93347	+	6.81297i	0.140751	+	0.243787i
$782$	−54.2874	+	14.5463i	−1.94131	+	0.520173i
$783$	0.576407	−	0.576407i	0.0205991	−	0.0205991i
$784$	26.2051	+	22.8766i	0.935897	+	0.817023i
$785$		0			0
$786$	8.58294	−	14.8661i	0.306143	−	0.530256i
$787$	−5.75494	+	21.4777i	−0.205141	+	0.765598i	0.784265	+	0.620426i	$0.213040\pi$
$787$	−5.75494	+	21.4777i	−0.205141	+	0.765598i	−0.989406	+	0.145172i	$0.953626\pi$
$788$	−1.99587	+	7.44870i	−0.0711000	+	0.265349i
$789$	−0.152064	+	0.263383i	−0.00541362	+	0.00937667i
$790$		0			0
$791$	−27.2087	−	2.64876i	−0.967428	−	0.0941790i
$792$	−3.05017	+	3.05017i	−0.108383	+	0.108383i
$793$	−2.39401	+	0.641474i	−0.0850139	+	0.0227794i
$794$	−18.3314	−	31.7508i	−0.650556	−	1.12680i
$795$		0			0
$796$	−14.7758	−	8.53082i	−0.523715	−	0.302367i
$797$	−19.6877	−	19.6877i	−0.697374	−	0.697374i	0.266469	−	0.963843i	$-0.414143\pi$
$797$	−19.6877	−	19.6877i	−0.697374	−	0.697374i	−0.963843	+	0.266469i	$0.914143\pi$
$798$	−16.9113	+	2.81171i	−0.598654	+	0.0995336i
$799$		−	32.1412i		−	1.13707i
$800$		0			0
$801$	8.43608	−	4.87057i	0.298074	−	0.172093i
$802$	17.0632	+	4.57206i	0.602521	+	0.161445i
$803$	−1.49082	−	5.56382i	−0.0526100	−	0.196343i
$804$	18.6298			0.657023
$805$		0			0
$806$	2.05766			0.0724781
$807$	0.0991004	+	0.369848i	0.00348850	+	0.0130193i
$808$	−2.48757	−	0.666541i	−0.0875122	−	0.0234488i
$809$	−32.7914	+	18.9321i	−1.15288	+	0.665617i	−0.949588	−	0.313500i	$-0.898498\pi$
$809$	−32.7914	+	18.9321i	−1.15288	+	0.665617i	−0.203295	+	0.979118i	$0.565165\pi$
$810$		0			0
$811$		−	6.84166i		−	0.240243i	−0.992759	−	0.120122i	$-0.961672\pi$
$811$		−	6.84166i		−	0.240243i	0.992759	−	0.120122i	$-0.0383284\pi$
$812$	2.37263	+	0.889934i	0.0832630	+	0.0312306i
$813$	8.27863	+	8.27863i	0.290344	+	0.290344i
$814$	−29.6185	−	17.1002i	−1.03813	−	0.599363i
$815$		0			0
$816$	−8.34138	−	14.4477i	−0.292007	−	0.505771i
$817$	−17.8830	+	4.79172i	−0.625646	+	0.167641i
$818$	−47.1670	+	47.1670i	−1.64916	+	1.64916i
$819$	0.408893	−	0.571975i	0.0142879	−	0.0199864i
$820$		0			0
$821$	−20.7921	+	36.0129i	−0.725648	+	1.25686i	0.233058	+	0.972463i	$0.425127\pi$
$821$	−20.7921	+	36.0129i	−0.725648	+	1.25686i	−0.958707	+	0.284397i	$0.908207\pi$
$822$	−6.08041	+	22.6924i	−0.212079	+	0.791488i
$823$	4.11673	−	15.3638i	0.143500	−	0.535550i	−0.856317	−	0.516450i	$-0.827253\pi$
$823$	4.11673	−	15.3638i	0.143500	−	0.535550i	0.999818	−	0.0191000i	$-0.00608010\pi$
$824$	−10.7041	+	18.5400i	−0.372893	+	0.645870i
$825$		0			0
$826$	−4.94442	+	50.7902i	−0.172038	+	1.76722i
$827$	30.8225	−	30.8225i	1.07180	−	1.07180i	0.0745879	−	0.997214i	$-0.476236\pi$
$827$	30.8225	−	30.8225i	1.07180	−	1.07180i	0.997214	−	0.0745879i	$-0.0237641\pi$
$828$	10.6632	−	2.85719i	0.370570	−	0.0992941i
$829$	−16.1369	−	27.9499i	−0.560458	−	0.970741i	−0.997456	−	0.0712790i	$-0.977292\pi$
$829$	−16.1369	−	27.9499i	−0.560458	−	0.970741i	0.436999	−	0.899462i	$-0.356041\pi$
$830$		0			0
$831$	−10.6886	−	6.17107i	−0.370784	−	0.214072i
$832$	0.112714	+	0.112714i	0.00390766	+	0.00390766i
$833$	−21.0997	−	10.3460i	−0.731062	−	0.358467i
$834$			27.5258i			0.953140i
$835$		0			0
$836$	10.8573	−	6.26848i	0.375509	−	0.216800i
$837$	4.19741	+	1.12469i	0.145084	+	0.0388751i
$838$	−10.2484	−	38.2474i	−0.354024	−	1.32124i
$839$	−40.5766			−1.40086			−0.700429	−	0.713722i	$-0.747008\pi$
$839$	−40.5766			−1.40086			−0.700429	+	0.713722i	$0.747008\pi$
$840$		0			0
$841$	28.3355			0.977087
$842$	−15.6657	−	58.4653i	−0.539877	−	2.01485i
$843$	7.56341	+	2.02661i	0.260498	+	0.0698001i
$844$	9.87806	−	5.70310i	0.340017	−	0.196309i
$845$		0			0
$846$			17.0595i			0.586517i
$847$	1.03727	+	6.23877i	0.0356411	+	0.214367i
$848$	17.7507	+	17.7507i	0.609561	+	0.609561i
$849$	2.81287	+	1.62401i	0.0965374	+	0.0557359i
$850$		0			0
$851$	−30.7301	−	53.2261i	−1.05341	−	1.82457i
$852$	3.04284	−	0.815325i	0.104246	−	0.0279326i
$853$	8.16242	−	8.16242i	0.279476	−	0.279476i	−0.553424	−	0.832900i	$-0.686679\pi$
$853$	8.16242	−	8.16242i	0.279476	−	0.279476i	0.832900	+	0.553424i	$0.186679\pi$
$854$	−18.1910	−	40.0280i	−0.622484	−	1.36973i
$855$		0			0
$856$	4.18075	−	7.24127i	0.142895	−	0.247501i
$857$	−2.75283	+	10.2737i	−0.0940347	+	0.350942i	−0.996871	−	0.0790414i	$-0.974814\pi$
$857$	−2.75283	+	10.2737i	−0.0940347	+	0.350942i	0.902837	+	0.429984i	$0.141481\pi$
$858$	−0.359603	+	1.34206i	−0.0122767	+	0.0458171i
$859$	1.67553	−	2.90210i	0.0571683	−	0.0990183i	−0.836025	−	0.548691i	$-0.815126\pi$
$859$	1.67553	−	2.90210i	0.0571683	−	0.0990183i	0.893193	+	0.449673i	$0.148460\pi$
$860$		0			0
$861$	2.68991	+	5.91895i	0.0916719	+	0.201717i
$862$	19.9169	−	19.9169i	0.678374	−	0.678374i
$863$	3.18428	−	0.853225i	0.108394	−	0.0290441i	−0.204214	−	0.978926i	$-0.565464\pi$
$863$	3.18428	−	0.853225i	0.108394	−	0.0290441i	0.312608	+	0.949882i	$0.398797\pi$
$864$	2.95723	+	5.12207i	0.100607	+	0.174256i
$865$		0			0
$866$	9.46526	+	5.46477i	0.321643	+	0.185700i
$867$	−4.05162	−	4.05162i	−0.137600	−	0.137600i
$868$	2.21554	+	13.3256i	0.0752004	+	0.452300i
$869$			15.0532i			0.510646i
$870$		0			0
$871$	−3.64911	+	2.10681i	−0.123645	+	0.0713867i
$872$	1.05273	+	0.282079i	0.0356501	+	0.00955240i
$873$	−2.17276	−	8.10886i	−0.0735369	−	0.274443i
$874$	60.8795			2.05928
$875$		0			0
$876$	−2.30653			−0.0779303
$877$	0.964837	+	3.60082i	0.0325802	+	0.121591i	0.980301	−	0.197510i	$-0.0632856\pi$
$877$	0.964837	+	3.60082i	0.0325802	+	0.121591i	−0.947721	+	0.319101i	$0.896619\pi$
$878$	−18.4021	−	4.93084i	−0.621042	−	0.166408i
$879$	13.4037	−	7.73864i	0.452096	−	0.261018i
$880$		0			0
$881$			37.0966i			1.24982i	0.780698	+	0.624909i	$0.214864\pi$
$881$			37.0966i			1.24982i	−0.780698	+	0.624909i	$0.785136\pi$
$882$	11.1990	+	5.49130i	0.377091	+	0.184902i
$883$	−3.70321	−	3.70321i	−0.124623	−	0.124623i	0.642044	−	0.766667i	$-0.278086\pi$
$883$	−3.70321	−	3.70321i	−0.124623	−	0.124623i	−0.766667	+	0.642044i	$0.778086\pi$
$884$	−0.907786	−	0.524110i	−0.0305321	−	0.0176277i
$885$		0			0
$886$	19.5628	+	33.8838i	0.657226	+	1.13835i
$887$	33.6955	−	9.02867i	1.13138	−	0.303153i	0.355901	−	0.934523i	$-0.384174\pi$
$887$	33.6955	−	9.02867i	1.13138	−	0.303153i	0.775481	+	0.631370i	$0.217507\pi$
$888$	6.79993	−	6.79993i	0.228191	−	0.228191i
$889$	−0.679590	+	6.98091i	−0.0227927	+	0.234132i
$890$		0			0
$891$	−1.46711	+	2.54110i	−0.0491499	+	0.0851301i
$892$	6.26141	−	23.3679i	0.209648	−	0.782415i
$893$	−9.01102	+	33.6296i	−0.301542	+	1.12537i
$894$	1.52325	−	2.63834i	0.0509451	−	0.0882394i
$895$		0			0
$896$	16.5561	−	23.1593i	0.553102	−	0.773699i
$897$	−1.76553	+	1.76553i	−0.0589493	+	0.0589493i
$898$	5.13744	−	1.37657i	0.171439	−	0.0459368i
$899$	−1.77114	−	3.06770i	−0.0590707	−	0.102313i
$900$		0			0
$901$	−14.6866	−	8.47933i	−0.489282	−	0.282487i
$902$	−9.08468	−	9.08468i	−0.302487	−	0.302487i
$903$	12.6119	+	4.73051i	0.419698	+	0.157422i
$904$			15.1899i			0.505207i
$905$		0			0
$906$	3.98305	−	2.29961i	0.132328	−	0.0763995i
$907$	4.49276	+	1.20383i	0.149180	+	0.0399726i	0.332636	−	0.943055i	$-0.392062\pi$
$907$	4.49276	+	1.20383i	0.149180	+	0.0399726i	−0.183456	+	0.983028i	$0.558729\pi$
$908$	1.38131	+	5.15512i	0.0458404	+	0.171079i
$909$	−1.75179			−0.0581034
$910$		0			0
$911$	−36.9996			−1.22585			−0.612925	−	0.790141i	$-0.710007\pi$
$911$	−36.9996			−1.22585			−0.612925	+	0.790141i	$0.710007\pi$
$912$	4.67714	+	17.4553i	0.154875	+	0.578003i
$913$	24.4452	+	6.55008i	0.809019	+	0.216776i
$914$	32.7374	−	18.9009i	1.08286	−	0.625187i
$915$		0			0
$916$			14.5738i			0.481531i
$917$	−25.1435	+	4.18042i	−0.830311	+	0.138050i
$918$	−4.22979	−	4.22979i	−0.139604	−	0.139604i
$919$	−21.2647	−	12.2772i	−0.701457	−	0.404987i	0.106433	−	0.994320i	$-0.466057\pi$
$919$	−21.2647	−	12.2772i	−0.701457	−	0.404987i	−0.807890	+	0.589333i	$0.799390\pi$
$920$		0			0
$921$	12.5381	+	21.7166i	0.413143	+	0.715585i
$922$	−21.3264	+	5.71439i	−0.702347	+	0.188193i
$923$	−0.503810	+	0.503810i	−0.0165831	+	0.0165831i
$924$	−9.07847	−	0.883788i	−0.298660	−	0.0290745i
$925$		0			0
$926$	−4.15537	+	7.19732i	−0.136554	+	0.236519i
$927$	−3.76901	+	14.0661i	−0.123790	+	0.461992i
$928$	1.24783	−	4.65696i	0.0409620	−	0.152872i
$929$	−11.8073	+	20.4509i	−0.387386	+	0.670972i	−0.992097	−	0.125473i	$-0.959955\pi$
$929$	−11.8073	+	20.4509i	−0.387386	+	0.670972i	0.604711	+	0.796445i	$0.293289\pi$
$930$		0			0
$931$	19.1762	+	16.7405i	0.628476	+	0.548649i
$932$	−20.6009	+	20.6009i	−0.674806	+	0.674806i
$933$	−15.4061	+	4.12804i	−0.504372	+	0.135146i
$934$	0.387618	+	0.671374i	0.0126833	+	0.0219680i
$935$		0			0
$936$	−0.338334	−	0.195337i	−0.0110588	−	0.00638480i
$937$	−17.6902	−	17.6902i	−0.577913	−	0.577913i	0.356415	−	0.934328i	$-0.383999\pi$
$937$	−17.6902	−	17.6902i	−0.577913	−	0.577913i	−0.934328	+	0.356415i	$0.883999\pi$
$938$	−47.4857	−	57.7282i	−1.55046	−	1.88489i
$939$		−	30.2453i		−	0.987019i
$940$		0			0
$941$	45.4456	−	26.2380i	1.48148	−	0.855335i	0.481705	−	0.876334i	$-0.340018\pi$
$941$	45.4456	−	26.2380i	1.48148	−	0.855335i	0.999780	+	0.0209982i	$0.00668442\pi$
$942$	−15.4210	−	4.13204i	−0.502443	−	0.134629i
$943$	−5.97562	−	22.3013i	−0.194593	−	0.726231i
$944$	53.7915			1.75076
$945$		0			0
$946$	−26.6180			−0.865425
$947$	−10.7125	−	39.9796i	−0.348109	−	1.29916i	−0.888937	−	0.458029i	$-0.848556\pi$
$947$	−10.7125	−	39.9796i	−0.348109	−	1.29916i	0.540828	−	0.841133i	$-0.318111\pi$
$948$	5.82241	+	1.56011i	0.189103	+	0.0506700i
$949$	0.451790	−	0.260841i	0.0146657	−	0.00846726i
$950$		0			0
$951$		−	17.2552i		−	0.559538i
$952$	−4.58570	+	12.2258i	−0.148623	+	0.396241i
$953$	−15.4152	−	15.4152i	−0.499347	−	0.499347i	0.411888	−	0.911235i	$-0.364870\pi$
$953$	−15.4152	−	15.4152i	−0.499347	−	0.499347i	−0.911235	+	0.411888i	$0.864870\pi$
$954$	7.79517	+	4.50055i	0.252378	+	0.145711i
$955$		0			0
$956$	13.5020	+	23.3861i	0.436686	+	0.756362i
$957$	2.31036	−	0.619059i	0.0746833	−	0.0200113i
$958$	27.3519	−	27.3519i	0.883700	−	0.883700i
$959$	31.7576	−	14.4325i	1.02551	−	0.466049i
$960$		0			0
$961$	−6.05840	+	10.4935i	−0.195432	+	0.338498i
$962$	0.801686	−	2.99193i	0.0258474	−	0.0964638i
$963$	1.47208	−	5.49389i	0.0474372	−	0.177038i
$964$	−9.17936	+	15.8991i	−0.295647	+	0.512076i
$965$		0			0
$966$	−36.0329	−	25.7592i	−1.15934	−	0.828789i
$967$	−2.82501	+	2.82501i	−0.0908461	+	0.0908461i	−0.751069	−	0.660223i	$-0.770462\pi$
$967$	−2.82501	+	2.82501i	−0.0908461	+	0.0908461i	0.660223	+	0.751069i	$0.270462\pi$
$968$	3.39440	−	0.909526i	0.109100	−	0.0292333i
$969$	−6.10401	−	10.5725i	−0.196089	−	0.339636i
$970$		0			0
$971$	−24.7793	−	14.3063i	−0.795204	−	0.459111i	0.0465872	−	0.998914i	$-0.485165\pi$
$971$	−24.7793	−	14.3063i	−0.795204	−	0.459111i	−0.841791	+	0.539803i	$0.818499\pi$
$972$	0.830817	+	0.830817i	0.0266485	+	0.0266485i
$973$	31.5647	−	25.9643i	1.01192	−	0.832377i
$974$			3.41945i			0.109566i
$975$		0			0
$976$	−40.1374	+	23.1733i	−1.28477	+	0.741760i
$977$	6.81922	+	1.82720i	0.218166	+	0.0584574i	0.366246	−	0.930518i	$-0.380643\pi$
$977$	6.81922	+	1.82720i	0.218166	+	0.0584574i	−0.148080	+	0.988975i	$0.547309\pi$
$978$	6.01422	+	22.4454i	0.192313	+	0.717723i
$979$	28.5826			0.913504
$980$		0			0
$981$	0.741356			0.0236697
$982$	3.45578	+	12.8971i	0.110278	+	0.411564i
$983$	23.0548	+	6.17752i	0.735334	+	0.197032i	0.607003	−	0.794699i	$-0.292371\pi$
$983$	23.0548	+	6.17752i	0.735334	+	0.197032i	0.128331	+	0.991731i	$0.459038\pi$
$984$	3.12855	−	1.80627i	0.0997345	−	0.0575817i
$985$		0			0
$986$			4.87616i			0.155288i
$987$	19.5627	−	16.0917i	0.622686	−	0.512205i
$988$	0.802885	+	0.802885i	0.0255432	+	0.0255432i
$989$	−41.4255	−	23.9170i	−1.31725	−	0.760517i
$990$		0			0
$991$	23.3416	+	40.4288i	0.741470	+	1.28426i	0.951826	+	0.306638i	$0.0992042\pi$
$991$	23.3416	+	40.4288i	0.741470	+	1.28426i	−0.210356	+	0.977625i	$0.567462\pi$
$992$	24.8254	−	6.65195i	0.788207	−	0.211200i
$993$	0.635446	−	0.635446i	0.0201653	−	0.0201653i
$994$	−10.2823	−	7.35064i	−0.326136	−	0.233148i
$995$		0			0
$996$	5.06698	−	8.77627i	0.160553	−	0.278087i
$997$	14.0974	−	52.6121i	0.446468	−	1.66624i	−0.265562	−	0.964094i	$-0.585557\pi$
$997$	14.0974	−	52.6121i	0.446468	−	1.66624i	0.712030	−	0.702149i	$-0.247776\pi$
$998$	−1.07384	+	4.00764i	−0.0339919	+	0.126859i
$999$	3.27071	−	5.66503i	0.103481	−	0.179234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.e.418.7		32
5.2	odd	4	inner	525.2.bc.e.82.2		32
5.3	odd	4		105.2.u.a.82.7	yes	32
5.4	even	2		105.2.u.a.103.2	yes	32
7.3	odd	6	inner	525.2.bc.e.493.2		32
15.8	even	4		315.2.bz.d.82.2		32
15.14	odd	2		315.2.bz.d.208.7		32
35.3	even	12		105.2.u.a.52.2	✓	32
35.4	even	6		735.2.v.b.178.7		32
35.9	even	6		735.2.m.c.538.3		32
35.13	even	4		735.2.v.b.607.7		32
35.17	even	12	inner	525.2.bc.e.157.7		32
35.18	odd	12		735.2.v.b.472.2		32
35.19	odd	6		735.2.m.c.538.4		32
35.23	odd	12		735.2.m.c.97.4		32
35.24	odd	6		105.2.u.a.73.7	yes	32
35.33	even	12		735.2.m.c.97.3		32
35.34	odd	2		735.2.v.b.313.2		32
105.38	odd	12		315.2.bz.d.262.7		32
105.59	even	6		315.2.bz.d.73.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.u.a.52.2	✓	32	35.3	even	12
105.2.u.a.73.7	yes	32	35.24	odd	6
105.2.u.a.82.7	yes	32	5.3	odd	4
105.2.u.a.103.2	yes	32	5.4	even	2
315.2.bz.d.73.2		32	105.59	even	6
315.2.bz.d.82.2		32	15.8	even	4
315.2.bz.d.208.7		32	15.14	odd	2
315.2.bz.d.262.7		32	105.38	odd	12
525.2.bc.e.82.2		32	5.2	odd	4	inner
525.2.bc.e.157.7		32	35.17	even	12	inner
525.2.bc.e.418.7		32	1.1	even	1	trivial
525.2.bc.e.493.2		32	7.3	odd	6	inner
735.2.m.c.97.3		32	35.33	even	12
735.2.m.c.97.4		32	35.23	odd	12
735.2.m.c.538.3		32	35.9	even	6
735.2.m.c.538.4		32	35.19	odd	6
735.2.v.b.178.7		32	35.4	even	6
735.2.v.b.313.2		32	35.34	odd	2
735.2.v.b.472.2		32	35.18	odd	12
735.2.v.b.607.7		32	35.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.461174 + 1.72112i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-1.01754 + 0.587476i) q^{4} -1.78184i q^{6} +(-2.04329 + 1.68076i) q^{7} +(1.03952 + 1.03952i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.461174 + 1.72112i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(-1.01754 + 0.587476i) q^{4} -1.78184i q^{6} +(-2.04329 + 1.68076i) q^{7} +(1.03952 + 1.03952i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.46711 + 2.54110i) q^{11} +(1.13492 - 0.304100i) q^{12} +(-0.187911 + 0.187911i) q^{13} +(-3.83511 - 2.74164i) q^{14} +(-2.48470 + 4.30362i) q^{16} +(0.868882 - 3.24271i) q^{17} +(-0.461174 + 1.72112i) q^{18} +(-1.81824 + 3.14928i) q^{19} +(2.40868 - 1.09464i) q^{21} +(-3.69696 + 3.69696i) q^{22} +(-9.07540 + 2.43175i) q^{23} +(-0.735051 - 1.27315i) q^{24} +(-0.410078 - 0.236759i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.09173 - 2.91062i) q^{28} +0.815162i q^{29} +(-3.76330 + 2.17274i) q^{31} +(-5.71292 - 1.53077i) q^{32} +(-0.759430 - 2.83423i) q^{33} +5.98182 q^{34} -1.17495 q^{36} +(1.69304 + 6.31853i) q^{37} +(-6.25883 - 1.67705i) q^{38} +(0.230143 - 0.132873i) q^{39} +2.45734i q^{41} +(2.99484 + 3.64082i) q^{42} +(3.59998 + 3.59998i) q^{43} +(-2.98567 - 1.72378i) q^{44} +(-8.37068 - 14.4984i) q^{46} +(9.24785 - 2.47795i) q^{47} +(3.51389 - 3.51389i) q^{48} +(1.35010 - 6.86857i) q^{49} +(-1.67855 + 2.90734i) q^{51} +(0.0808136 - 0.301600i) q^{52} +(1.30744 - 4.87944i) q^{53} +(0.890920 - 1.54312i) q^{54} +(-3.87122 - 0.376863i) q^{56} +(2.57138 - 2.57138i) q^{57} +(-1.40300 + 0.375932i) q^{58} +(-5.41228 - 9.37435i) q^{59} +(8.07692 + 4.66321i) q^{61} +(-5.47509 - 5.47509i) q^{62} +(-2.60992 + 0.433932i) q^{63} -0.599827i q^{64} +(4.52784 - 2.61415i) q^{66} +(15.3155 + 4.10379i) q^{67} +(1.02090 + 3.81003i) q^{68} +9.39554 q^{69} +2.68111 q^{71} +(0.380490 + 1.42001i) q^{72} +(-1.89619 - 0.508083i) q^{73} +(-10.0942 + 5.82788i) q^{74} -4.27269i q^{76} +(-7.26871 - 2.72637i) q^{77} +(0.334828 + 0.334828i) q^{78} +(4.44293 + 2.56513i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-4.22938 + 1.13326i) q^{82} +(6.09879 - 6.09879i) q^{83} +(-1.80785 + 2.52889i) q^{84} +(-4.53580 + 7.85623i) q^{86} +(0.210980 - 0.787386i) q^{87} +(-1.11644 + 4.16661i) q^{88} +(4.87057 - 8.43608i) q^{89} +(0.0681246 - 0.699791i) q^{91} +(7.80598 - 7.80598i) q^{92} +(4.19741 - 1.12469i) q^{93} +(8.52974 + 14.7739i) q^{94} +(5.12207 + 2.95723i) q^{96} +(-5.93610 - 5.93610i) q^{97} +(12.4443 - 0.843909i) q^{98} +2.93421i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 32 * q - 8 * q^7 + 24 * q^8	\( 32 q - 8 q^{7} + 24 q^{8} - 8 q^{11} - 8 q^{21} + 8 q^{22} + 8 q^{23} + 24 q^{26} + 24 q^{28} + 24 q^{31} - 24 q^{32} + 36 q^{33} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} - 8 q^{51} + 108 q^{52} + 24 q^{53} - 48 q^{56} - 16 q^{57} - 4 q^{58} - 24 q^{61} - 4 q^{63} + 72 q^{66} - 8 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 16 q^{81} - 12 q^{82} - 16 q^{86} + 24 q^{87} + 32 q^{88} - 24 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98}+O(q^{100}) \) 32 * q - 8 * q^7 + 24 * q^8 - 8 * q^11 - 8 * q^21 + 8 * q^22 + 8 * q^23 + 24 * q^26 + 24 * q^28 + 24 * q^31 - 24 * q^32 + 36 * q^33 - 32 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^42 - 40 * q^43 - 40 * q^46 + 60 * q^47 - 8 * q^51 + 108 * q^52 + 24 * q^53 - 48 * q^56 - 16 * q^57 - 4 * q^58 - 24 * q^61 - 4 * q^63 + 72 * q^66 - 8 * q^67 - 132 * q^68 - 16 * q^71 - 12 * q^72 - 36 * q^73 - 60 * q^77 - 80 * q^78 + 16 * q^81 - 12 * q^82 - 16 * q^86 + 24 * q^87 + 32 * q^88 - 24 * q^91 + 56 * q^92 + 24 * q^93 + 72 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more