LMFDB - Embedded newform 950.2.f.d.493.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("950.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			493.9
Character	$\chi$	$=$	950.493
Dual form			950.2.f.d.607.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-1.91489 + 1.91489i) q^{3} +1.00000i q^{4} -2.70806 q^{6} +(-2.95447 + 2.95447i) q^{7} +(-0.707107 + 0.707107i) q^{8} -4.33358i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.91489 + 1.91489i) q^{3} +1.00000i q^{4} -2.70806 q^{6} +(-2.95447 + 2.95447i) q^{7} +(-0.707107 + 0.707107i) q^{8} -4.33358i q^{9} -3.90336 q^{11} +(-1.91489 - 1.91489i) q^{12} +(4.27208 - 4.27208i) q^{13} -4.17825 q^{14} -1.00000 q^{16} +(-3.82166 + 3.82166i) q^{17} +(3.06430 - 3.06430i) q^{18} +(-0.797842 - 4.28526i) q^{19} -11.3149i q^{21} +(-2.76009 - 2.76009i) q^{22} +(4.44500 + 4.44500i) q^{23} -2.70806i q^{24} +6.04164 q^{26} +(2.55366 + 2.55366i) q^{27} +(-2.95447 - 2.95447i) q^{28} +2.10793 q^{29} +3.46410i q^{31} +(-0.707107 - 0.707107i) q^{32} +(7.47449 - 7.47449i) q^{33} -5.40464 q^{34} +4.33358 q^{36} +(1.05164 + 1.05164i) q^{37} +(2.46598 - 3.59430i) q^{38} +16.3611i q^{39} -6.48808i q^{41} +(8.00087 - 8.00087i) q^{42} +(-6.63336 - 6.63336i) q^{43} -3.90336i q^{44} +6.28618i q^{46} +(-2.35306 + 2.35306i) q^{47} +(1.91489 - 1.91489i) q^{48} -10.4578i q^{49} -14.6361i q^{51} +(4.27208 + 4.27208i) q^{52} +(-3.83975 + 3.83975i) q^{53} +3.61142i q^{54} -4.17825i q^{56} +(9.73356 + 6.67801i) q^{57} +(1.49053 + 1.49053i) q^{58} +14.9154 q^{59} -2.00000 q^{61} +(-2.44949 + 2.44949i) q^{62} +(12.8034 + 12.8034i) q^{63} -1.00000i q^{64} +10.5705 q^{66} +(-4.04760 - 4.04760i) q^{67} +(-3.82166 - 3.82166i) q^{68} -17.0233 q^{69} +1.70103i q^{71} +(3.06430 + 3.06430i) q^{72} +(-5.04174 - 5.04174i) q^{73} +1.48724i q^{74} +(4.28526 - 0.797842i) q^{76} +(11.5323 - 11.5323i) q^{77} +(-11.5691 + 11.5691i) q^{78} -11.8206 q^{79} +3.22082 q^{81} +(4.58776 - 4.58776i) q^{82} +(-2.04560 - 2.04560i) q^{83} +11.3149 q^{84} -9.38099i q^{86} +(-4.03645 + 4.03645i) q^{87} +(2.76009 - 2.76009i) q^{88} -10.9767 q^{89} +25.2435i q^{91} +(-4.44500 + 4.44500i) q^{92} +(-6.63336 - 6.63336i) q^{93} -3.32773 q^{94} +2.70806 q^{96} +(3.35802 + 3.35802i) q^{97} +(7.39475 - 7.39475i) q^{98} +16.9155i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{6}+O(q^{10}) $ 32 * q - 8 * q^6	$ 32 q - 8 q^{6} - 24 q^{11} - 32 q^{16} + 32 q^{26} + 56 q^{36} - 64 q^{61} + 72 q^{66} + 4 q^{76} - 32 q^{81} + 8 q^{96}+O(q^{100}) $ 32 * q - 8 * q^6 - 24 * q^11 - 32 * q^16 + 32 * q^26 + 56 * q^36 - 64 * q^61 + 72 * q^66 + 4 * q^76 - 32 * q^81 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.91489	+	1.91489i	−1.10556	+	1.10556i	−0.111833	+	0.993727i	$0.535672\pi$
$3$	−1.91489	+	1.91489i	−1.10556	+	1.10556i	−0.993727	+	0.111833i	$0.964328\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	−2.70806			−1.10556
$7$	−2.95447	+	2.95447i	−1.11668	+	1.11668i	−0.124459	+	0.992225i	$0.539720\pi$
$7$	−2.95447	+	2.95447i	−1.11668	+	1.11668i	−0.992225	+	0.124459i	$0.960280\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		−	4.33358i		−	1.44453i
$10$		0			0
$11$	−3.90336			−1.17691			−0.588453	−	0.808531i	$-0.700263\pi$
$11$	−3.90336			−1.17691			−0.588453	+	0.808531i	$0.700263\pi$
$12$	−1.91489	−	1.91489i	−0.552780	−	0.552780i
$13$	4.27208	−	4.27208i	1.18486	−	1.18486i	0.206394	−	0.978469i	$-0.433827\pi$
$13$	4.27208	−	4.27208i	1.18486	−	1.18486i	0.978469	−	0.206394i	$-0.0661729\pi$
$14$	−4.17825			−1.11668
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.82166	+	3.82166i	−0.926888	+	0.926888i	−0.997504	−	0.0706153i	$-0.977504\pi$
$17$	−3.82166	+	3.82166i	−0.926888	+	0.926888i	0.0706153	+	0.997504i	$0.477504\pi$
$18$	3.06430	−	3.06430i	0.722263	−	0.722263i
$19$	−0.797842	−	4.28526i	−0.183037	−	0.983106i
$19$	−0.797842	−	4.28526i	−0.183037	−	0.983106i
$20$		0			0
$21$		−	11.3149i		−	2.46912i
$22$	−2.76009	−	2.76009i	−0.588453	−	0.588453i
$23$	4.44500	+	4.44500i	0.926846	+	0.926846i	0.997501	−	0.0706544i	$-0.0225087\pi$
$23$	4.44500	+	4.44500i	0.926846	+	0.926846i	−0.0706544	+	0.997501i	$0.522509\pi$
$24$		−	2.70806i		−	0.552780i
$25$		0			0
$26$	6.04164			1.18486
$27$	2.55366	+	2.55366i	0.491451	+	0.491451i
$28$	−2.95447	−	2.95447i	−0.558342	−	0.558342i
$29$	2.10793			0.391433			0.195716	−	0.980661i	$-0.437297\pi$
$29$	2.10793			0.391433			0.195716	+	0.980661i	$0.437297\pi$
$30$		0			0
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	7.47449	−	7.47449i	1.30114	−	1.30114i
$34$	−5.40464			−0.926888
$35$		0			0
$36$	4.33358			0.722263
$37$	1.05164	+	1.05164i	0.172888	+	0.172888i	0.788247	−	0.615359i	$-0.210989\pi$
$37$	1.05164	+	1.05164i	0.172888	+	0.172888i	−0.615359	+	0.788247i	$0.710989\pi$
$38$	2.46598	−	3.59430i	0.400034	−	0.583072i
$39$			16.3611i			2.61987i
$40$		0			0
$41$		−	6.48808i		−	1.01327i	−0.862161	−	0.506634i	$-0.830890\pi$
$41$		−	6.48808i		−	1.01327i	0.862161	−	0.506634i	$-0.169110\pi$
$42$	8.00087	−	8.00087i	1.23456	−	1.23456i
$43$	−6.63336	−	6.63336i	−1.01158	−	1.01158i	−0.999932	−	0.0116460i	$-0.996293\pi$
$43$	−6.63336	−	6.63336i	−1.01158	−	1.01158i	−0.0116460	−	0.999932i	$-0.503707\pi$
$44$		−	3.90336i		−	0.588453i
$45$		0			0
$46$			6.28618i			0.926846i
$47$	−2.35306	+	2.35306i	−0.343230	+	0.343230i	−0.857580	−	0.514350i	$-0.828033\pi$
$47$	−2.35306	+	2.35306i	−0.343230	+	0.343230i	0.514350	+	0.857580i	$0.328033\pi$
$48$	1.91489	−	1.91489i	0.276390	−	0.276390i
$49$		−	10.4578i		−	1.49397i
$50$		0			0
$51$		−	14.6361i		−	2.04946i
$52$	4.27208	+	4.27208i	0.592431	+	0.592431i
$53$	−3.83975	+	3.83975i	−0.527430	+	0.527430i	−0.919805	−	0.392375i	$-0.871653\pi$
$53$	−3.83975	+	3.83975i	−0.527430	+	0.527430i	0.392375	+	0.919805i	$0.371653\pi$
$54$			3.61142i			0.491451i
$55$		0			0
$56$		−	4.17825i		−	0.558342i
$57$	9.73356	+	6.67801i	1.28924	+	0.884524i
$58$	1.49053	+	1.49053i	0.195716	+	0.195716i
$59$	14.9154			1.94182			0.970910	−	0.239443i	$-0.0769648\pi$
$59$	14.9154			1.94182			0.970910	+	0.239443i	$0.0769648\pi$
$60$		0			0
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$	−2.44949	+	2.44949i	−0.311086	+	0.311086i
$63$	12.8034	+	12.8034i	1.61308	+	1.61308i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	10.5705			1.30114
$67$	−4.04760	−	4.04760i	−0.494494	−	0.494494i	0.415225	−	0.909719i	$-0.363703\pi$
$67$	−4.04760	−	4.04760i	−0.494494	−	0.494494i	−0.909719	+	0.415225i	$0.863703\pi$
$68$	−3.82166	−	3.82166i	−0.463444	−	0.463444i
$69$	−17.0233			−2.04937
$70$		0			0
$71$			1.70103i			0.201875i	0.994893	+	0.100937i	$0.0321842\pi$
$71$			1.70103i			0.201875i	−0.994893	+	0.100937i	$0.967816\pi$
$72$	3.06430	+	3.06430i	0.361132	+	0.361132i
$73$	−5.04174	−	5.04174i	−0.590091	−	0.590091i	0.347565	−	0.937656i	$-0.387009\pi$
$73$	−5.04174	−	5.04174i	−0.590091	−	0.590091i	−0.937656	+	0.347565i	$0.887009\pi$
$74$			1.48724i			0.172888i
$75$		0			0
$76$	4.28526	−	0.797842i	0.491553	−	0.0915187i
$77$	11.5323	−	11.5323i	1.31423	−	1.31423i
$78$	−11.5691	+	11.5691i	−1.30994	+	1.30994i
$79$	−11.8206			−1.32992			−0.664961	−	0.746878i	$-0.731552\pi$
$79$	−11.8206			−1.32992			−0.664961	+	0.746878i	$0.731552\pi$
$80$		0			0
$81$	3.22082			0.357869
$82$	4.58776	−	4.58776i	0.506634	−	0.506634i
$83$	−2.04560	−	2.04560i	−0.224534	−	0.224534i	0.585871	−	0.810404i	$-0.300753\pi$
$83$	−2.04560	−	2.04560i	−0.224534	−	0.224534i	−0.810404	+	0.585871i	$0.800753\pi$
$84$	11.3149			1.23456
$85$		0			0
$86$		−	9.38099i		−	1.01158i
$87$	−4.03645	+	4.03645i	−0.432753	+	0.432753i
$88$	2.76009	−	2.76009i	0.294227	−	0.294227i
$89$	−10.9767			−1.16353			−0.581763	−	0.813359i	$-0.697637\pi$
$89$	−10.9767			−1.16353			−0.581763	+	0.813359i	$0.697637\pi$
$90$		0			0
$91$			25.2435i			2.64623i
$92$	−4.44500	+	4.44500i	−0.463423	+	0.463423i
$93$	−6.63336	−	6.63336i	−0.687848	−	0.687848i
$94$	−3.32773			−0.343230
$95$		0			0
$96$	2.70806			0.276390
$97$	3.35802	+	3.35802i	0.340955	+	0.340955i	0.856726	−	0.515771i	$-0.172495\pi$
$97$	3.35802	+	3.35802i	0.340955	+	0.340955i	−0.515771	+	0.856726i	$0.672495\pi$
$98$	7.39475	−	7.39475i	0.746983	−	0.746983i
$99$			16.9155i			1.70007i
$100$		0			0
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	10.3493	−	10.3493i	1.02473	−	1.02473i
$103$	−0.884622	+	0.884622i	−0.0871644	+	0.0871644i	−0.749345	−	0.662180i	$-0.769631\pi$
$103$	−0.884622	+	0.884622i	−0.0871644	+	0.0871644i	0.662180	+	0.749345i	$0.269631\pi$
$104$			6.04164i			0.592431i
$105$		0			0
$106$	−5.43022			−0.527430
$107$	−4.87001	−	4.87001i	−0.470802	−	0.470802i	0.431372	−	0.902174i	$-0.358030\pi$
$107$	−4.87001	−	4.87001i	−0.470802	−	0.470802i	−0.902174	+	0.431372i	$0.858030\pi$
$108$	−2.55366	+	2.55366i	−0.245726	+	0.245726i
$109$	0.310347			0.0297259			0.0148629	−	0.999890i	$-0.495269\pi$
$109$	0.310347			0.0297259			0.0148629	+	0.999890i	$0.495269\pi$
$110$		0			0
$111$	−4.02753			−0.382276
$112$	2.95447	−	2.95447i	0.279171	−	0.279171i
$113$	7.00273	−	7.00273i	0.658762	−	0.658762i	−0.296326	−	0.955087i	$-0.595761\pi$
$113$	7.00273	−	7.00273i	0.658762	−	0.658762i	0.955087	+	0.296326i	$0.0957613\pi$
$114$	2.16060	+	11.6047i	0.202359	+	1.08688i
$115$		0			0
$116$			2.10793i			0.195716i
$117$	−18.5134	−	18.5134i	−1.71157	−	1.71157i
$118$	10.5468	+	10.5468i	0.970910	+	0.970910i
$119$		−	22.5819i		−	2.07008i
$120$		0			0
$121$	4.23619			0.385109
$122$	−1.41421	−	1.41421i	−0.128037	−	0.128037i
$123$	12.4239	+	12.4239i	1.12023	+	1.12023i
$124$	−3.46410			−0.311086
$125$		0			0
$126$			18.1068i			1.61308i
$127$	−13.6515	−	13.6515i	−1.21137	−	1.21137i	−0.970575	−	0.240798i	$-0.922591\pi$
$127$	−13.6515	−	13.6515i	−1.21137	−	1.21137i	−0.240798	−	0.970575i	$-0.577409\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	25.4043			2.23672
$130$		0			0
$131$	−0.667162			−0.0582902			−0.0291451	−	0.999575i	$-0.509278\pi$
$131$	−0.667162			−0.0582902			−0.0291451	+	0.999575i	$0.509278\pi$
$132$	7.47449	+	7.47449i	0.650570	+	0.650570i
$133$	15.0179	+	10.3035i	1.30221	+	0.893423i
$134$		−	5.72418i		−	0.494494i
$135$		0			0
$136$		−	5.40464i		−	0.463444i
$137$	−9.46015	+	9.46015i	−0.808235	+	0.808235i	−0.984367	−	0.176132i	$-0.943642\pi$
$137$	−9.46015	+	9.46015i	−0.808235	+	0.808235i	0.176132	+	0.984367i	$0.443642\pi$
$138$	−12.0373	−	12.0373i	−1.02468	−	1.02468i
$139$			20.3772i			1.72837i	0.503171	+	0.864187i	$0.332167\pi$
$139$			20.3772i			1.72837i	−0.503171	+	0.864187i	$0.667833\pi$
$140$		0			0
$141$		−	9.01170i		−	0.758922i
$142$	−1.20281	+	1.20281i	−0.100937	+	0.100937i
$143$	−16.6755	+	16.6755i	−1.39447	+	1.39447i
$144$			4.33358i			0.361132i
$145$		0			0
$146$		−	7.13010i		−	0.590091i
$147$	20.0254	+	20.0254i	1.65167	+	1.65167i
$148$	−1.05164	+	1.05164i	−0.0864441	+	0.0864441i
$149$		−	1.80671i		−	0.148012i	−0.997258	−	0.0740059i	$-0.976422\pi$
$149$		−	1.80671i		−	0.148012i	0.997258	−	0.0740059i	$-0.0235784\pi$
$150$		0			0
$151$			6.32069i			0.514370i	0.966362	+	0.257185i	$0.0827950\pi$
$151$			6.32069i			0.514370i	−0.966362	+	0.257185i	$0.917205\pi$
$152$	3.59430	+	2.46598i	0.291536	+	0.200017i
$153$	16.5615	+	16.5615i	1.33892	+	1.33892i
$154$	16.3092			1.31423
$155$		0			0
$156$	−16.3611			−1.30994
$157$	−10.8172	+	10.8172i	−0.863309	+	0.863309i	−0.991721	−	0.128412i	$-0.959012\pi$
$157$	−10.8172	+	10.8172i	−0.863309	+	0.863309i	0.128412	+	0.991721i	$0.459012\pi$
$158$	−8.35842	−	8.35842i	−0.664961	−	0.664961i
$159$		−	14.7054i		−	1.16621i
$160$		0			0
$161$	−26.2652			−2.06999
$162$	2.27746	+	2.27746i	0.178934	+	0.178934i
$163$	−11.9456	−	11.9456i	−0.935648	−	0.935648i	0.0624032	−	0.998051i	$-0.480124\pi$
$163$	−11.9456	−	11.9456i	−0.935648	−	0.935648i	−0.998051	+	0.0624032i	$0.980124\pi$
$164$	6.48808			0.506634
$165$		0			0
$166$		−	2.89291i		−	0.224534i
$167$	−7.71843	−	7.71843i	−0.597270	−	0.597270i	0.342315	−	0.939585i	$-0.388789\pi$
$167$	−7.71843	−	7.71843i	−0.597270	−	0.597270i	−0.939585	+	0.342315i	$0.888789\pi$
$168$	8.00087	+	8.00087i	0.617281	+	0.617281i
$169$		−	23.5014i		−	1.80780i
$170$		0			0
$171$	−18.5705	+	3.45751i	−1.42012	+	0.264403i
$172$	6.63336	−	6.63336i	0.505789	−	0.505789i
$173$	2.36527	−	2.36527i	0.179828	−	0.179828i	−0.611453	−	0.791281i	$-0.709415\pi$
$173$	2.36527	−	2.36527i	0.179828	−	0.179828i	0.791281	+	0.611453i	$0.209415\pi$
$174$	−5.70840			−0.432753
$175$		0			0
$176$	3.90336			0.294227
$177$	−28.5613	+	28.5613i	−2.14680	+	2.14680i
$178$	−7.76168	−	7.76168i	−0.581763	−	0.581763i
$179$	−9.68475			−0.723872			−0.361936	−	0.932203i	$-0.617884\pi$
$179$	−9.68475			−0.723872			−0.361936	+	0.932203i	$0.617884\pi$
$180$		0			0
$181$			14.1370i			1.05080i	0.850857	+	0.525398i	$0.176084\pi$
$181$			14.1370i			1.05080i	−0.850857	+	0.525398i	$0.823916\pi$
$182$	−17.8498	+	17.8498i	−1.32312	+	1.32312i
$183$	3.82977	−	3.82977i	0.283105	−	0.283105i
$184$	−6.28618			−0.463423
$185$		0			0
$186$		−	9.38099i		−	0.687848i
$187$	14.9173	−	14.9173i	1.09086	−	1.09086i
$188$	−2.35306	−	2.35306i	−0.171615	−	0.171615i
$189$	−15.0894			−1.09759
$190$		0			0
$191$	−0.0275325			−0.00199218			−0.000996089	−	1.00000i	$-0.500317\pi$
$191$	−0.0275325			−0.00199218			−0.000996089		1.00000i	$0.500317\pi$
$192$	1.91489	+	1.91489i	0.138195	+	0.138195i
$193$	−16.8244	+	16.8244i	−1.21105	+	1.21105i	−0.240368	+	0.970682i	$0.577268\pi$
$193$	−16.8244	+	16.8244i	−1.21105	+	1.21105i	−0.970682	+	0.240368i	$0.922732\pi$
$194$			4.74896i			0.340955i
$195$		0			0
$196$	10.4578			0.746983
$197$	−12.3494	+	12.3494i	−0.879861	+	0.879861i	−0.993520	−	0.113658i	$-0.963743\pi$
$197$	−12.3494	+	12.3494i	−0.879861	+	0.879861i	0.113658	+	0.993520i	$0.463743\pi$
$198$	−11.9611	+	11.9611i	−0.850037	+	0.850037i
$199$			5.01141i			0.355250i	0.984098	+	0.177625i	$0.0568414\pi$
$199$			5.01141i			0.355250i	−0.984098	+	0.177625i	$0.943159\pi$
$200$		0			0
$201$	15.5014			1.09339
$202$	−4.24264	−	4.24264i	−0.298511	−	0.298511i
$203$	−6.22781	+	6.22781i	−0.437107	+	0.437107i
$204$	14.6361			1.02473
$205$		0			0
$206$	−1.25104			−0.0871644
$207$	19.2628	−	19.2628i	1.33885	−	1.33885i
$208$	−4.27208	+	4.27208i	−0.296216	+	0.296216i
$209$	3.11426	+	16.7269i	0.215418	+	1.15702i
$210$		0			0
$211$		−	19.5714i		−	1.34735i	−0.739028	−	0.673675i	$-0.764715\pi$
$211$		−	19.5714i		−	1.34735i	0.739028	−	0.673675i	$-0.235285\pi$
$212$	−3.83975	−	3.83975i	−0.263715	−	0.263715i
$213$	−3.25727	−	3.25727i	−0.223185	−	0.223185i
$214$		−	6.88724i		−	0.470802i
$215$		0			0
$216$	−3.61142			−0.245726
$217$	−10.2346	−	10.2346i	−0.694768	−	0.694768i
$218$	0.219449	+	0.219449i	0.0148629	+	0.0148629i
$219$	19.3087			1.30476
$220$		0			0
$221$			32.6529i			2.19647i
$222$	−2.84790	−	2.84790i	−0.191138	−	0.191138i
$223$	−7.65955	+	7.65955i	−0.512921	+	0.512921i	−0.915420	−	0.402499i	$-0.868142\pi$
$223$	−7.65955	+	7.65955i	−0.512921	+	0.512921i	0.402499	+	0.915420i	$0.368142\pi$
$224$	4.17825			0.279171
$225$		0			0
$226$	9.90336			0.658762
$227$	17.0784	+	17.0784i	1.13353	+	1.13353i	0.989586	+	0.143945i	$0.0459788\pi$
$227$	17.0784	+	17.0784i	1.13353	+	1.13353i	0.143945	+	0.989586i	$0.454021\pi$
$228$	−6.67801	+	9.73356i	−0.442262	+	0.644621i
$229$			17.5812i			1.16180i	0.813976	+	0.580899i	$0.197299\pi$
$229$			17.5812i			1.16180i	−0.813976	+	0.580899i	$0.802701\pi$
$230$		0			0
$231$			44.1662i			2.90593i
$232$	−1.49053	+	1.49053i	−0.0978582	+	0.0978582i
$233$	−10.7208	−	10.7208i	−0.702343	−	0.702343i	0.262570	−	0.964913i	$-0.415430\pi$
$233$	−10.7208	−	10.7208i	−0.702343	−	0.702343i	−0.964913	+	0.262570i	$0.915430\pi$
$234$		−	26.1819i		−	1.71157i
$235$		0			0
$236$			14.9154i			0.970910i
$237$	22.6351	−	22.6351i	1.47031	−	1.47031i
$238$	15.9678	−	15.9678i	1.03504	−	1.03504i
$239$		−	2.88649i		−	0.186712i	−0.995633	−	0.0933559i	$-0.970241\pi$
$239$		−	2.88649i		−	0.186712i	0.995633	−	0.0933559i	$-0.0297594\pi$
$240$		0			0
$241$		−	2.89291i		−	0.186349i	−0.995650	−	0.0931744i	$-0.970299\pi$
$241$		−	2.89291i		−	0.186349i	0.995650	−	0.0931744i	$-0.0297014\pi$
$242$	2.99544	+	2.99544i	0.192554	+	0.192554i
$243$	−13.8285	+	13.8285i	−0.887097	+	0.887097i
$244$		−	2.00000i		−	0.128037i
$245$		0			0
$246$			17.5701i			1.12023i
$247$	−21.7154	−	14.8985i	−1.38172	−	0.947972i
$248$	−2.44949	−	2.44949i	−0.155543	−	0.155543i
$249$	7.83417			0.496471
$250$		0			0
$251$	12.3772			0.781244			0.390622	−	0.920551i	$-0.372260\pi$
$251$	12.3772			0.781244			0.390622	+	0.920551i	$0.372260\pi$
$252$	−12.8034	+	12.8034i	−0.806540	+	0.806540i
$253$	−17.3504	−	17.3504i	−1.09081	−	1.09081i
$254$		−	19.3061i		−	1.21137i
$255$		0			0
$256$	1.00000			0.0625000
$257$	6.79772	+	6.79772i	0.424030	+	0.424030i	0.886589	−	0.462559i	$-0.153069\pi$
$257$	6.79772	+	6.79772i	0.424030	+	0.424030i	−0.462559	+	0.886589i	$0.653069\pi$
$258$	17.9635	+	17.9635i	1.11836	+	1.11836i
$259$	−6.21406			−0.386123
$260$		0			0
$261$		−	9.13489i		−	0.565435i
$262$	−0.471755	−	0.471755i	−0.0291451	−	0.0291451i
$263$	14.2674	+	14.2674i	0.879763	+	0.879763i	0.993510	−	0.113747i	$-0.0362852\pi$
$263$	14.2674	+	14.2674i	0.879763	+	0.879763i	−0.113747	+	0.993510i	$0.536285\pi$
$264$			10.5705i			0.650570i
$265$		0			0
$266$	3.33358	+	17.9049i	0.204395	+	1.09782i
$267$	21.0191	−	21.0191i	1.28635	−	1.28635i
$268$	4.04760	−	4.04760i	0.247247	−	0.247247i
$269$	20.4577			1.24733			0.623664	−	0.781692i	$-0.285643\pi$
$269$	20.4577			1.24733			0.623664	+	0.781692i	$0.285643\pi$
$270$		0			0
$271$	−0.414105			−0.0251551			−0.0125775	−	0.999921i	$-0.504004\pi$
$271$	−0.414105			−0.0251551			−0.0125775	+	0.999921i	$0.504004\pi$
$272$	3.82166	−	3.82166i	0.231722	−	0.231722i
$273$	−48.3384	−	48.3384i	−2.92557	−	2.92557i
$274$	−13.3787			−0.808235
$275$		0			0
$276$		−	17.0233i		−	1.02468i
$277$	−8.26575	+	8.26575i	−0.496641	+	0.496641i	−0.910391	−	0.413750i	$-0.864219\pi$
$277$	−8.26575	+	8.26575i	−0.496641	+	0.496641i	0.413750	+	0.910391i	$0.364219\pi$
$278$	−14.4089	+	14.4089i	−0.864187	+	0.864187i
$279$	15.0120			0.898743
$280$		0			0
$281$		−	23.6412i		−	1.41032i	−0.709050	−	0.705158i	$-0.750876\pi$
$281$		−	23.6412i		−	1.41032i	0.709050	−	0.705158i	$-0.249124\pi$
$282$	6.37223	−	6.37223i	0.379461	−	0.379461i
$283$	−17.0281	−	17.0281i	−1.01221	−	1.01221i	−0.999924	−	0.0122889i	$-0.996088\pi$
$283$	−17.0281	−	17.0281i	−1.01221	−	1.01221i	−0.0122889	−	0.999924i	$-0.503912\pi$
$284$	−1.70103			−0.100937
$285$		0			0
$286$	−23.5827			−1.39447
$287$	19.1688	+	19.1688i	1.13150	+	1.13150i
$288$	−3.06430	+	3.06430i	−0.180566	+	0.180566i
$289$		−	12.2101i		−	0.718244i
$290$		0			0
$291$	−12.8604			−0.753893
$292$	5.04174	−	5.04174i	0.295046	−	0.295046i
$293$	15.7814	−	15.7814i	0.921957	−	0.921957i	−0.0752111	−	0.997168i	$-0.523963\pi$
$293$	15.7814	−	15.7814i	0.921957	−	0.921957i	0.997168	+	0.0752111i	$0.0239631\pi$
$294$			28.3202i			1.65167i
$295$		0			0
$296$	−1.48724			−0.0864441
$297$	−9.96783	−	9.96783i	−0.578392	−	0.578392i
$298$	1.27754	−	1.27754i	0.0740059	−	0.0740059i
$299$	37.9788			2.19637
$300$		0			0
$301$	39.1961			2.25923
$302$	−4.46940	+	4.46940i	−0.257185	+	0.257185i
$303$	11.4893	−	11.4893i	0.660044	−	0.660044i
$304$	0.797842	+	4.28526i	0.0457594	+	0.245776i
$305$		0			0
$306$			23.4215i			1.33892i
$307$	−0.784894	−	0.784894i	−0.0447962	−	0.0447962i	0.684354	−	0.729150i	$-0.260084\pi$
$307$	−0.784894	−	0.784894i	−0.0447962	−	0.0447962i	−0.729150	+	0.684354i	$0.760084\pi$
$308$	11.5323	+	11.5323i	0.657116	+	0.657116i
$309$		−	3.38790i		−	0.192731i
$310$		0			0
$311$	15.6786			0.889050			0.444525	−	0.895766i	$-0.353372\pi$
$311$	15.6786			0.889050			0.444525	+	0.895766i	$0.353372\pi$
$312$	−11.5691	−	11.5691i	−0.654969	−	0.654969i
$313$	3.46164	+	3.46164i	0.195663	+	0.195663i	0.798138	−	0.602475i	$-0.205819\pi$
$313$	3.46164	+	3.46164i	0.195663	+	0.195663i	−0.602475	+	0.798138i	$0.705819\pi$
$314$	−15.2979			−0.863309
$315$		0			0
$316$		−	11.8206i		−	0.664961i
$317$	12.7474	+	12.7474i	0.715965	+	0.715965i	0.967776	−	0.251812i	$-0.0810263\pi$
$317$	12.7474	+	12.7474i	0.715965	+	0.715965i	−0.251812	+	0.967776i	$0.581026\pi$
$318$	10.3983	−	10.3983i	0.583106	−	0.583106i
$319$	−8.22801			−0.460680
$320$		0			0
$321$	18.6510			1.04100
$322$	−18.5723	−	18.5723i	−1.03499	−	1.03499i
$323$	19.4259	+	13.3277i	1.08088	+	0.741574i
$324$			3.22082i			0.178934i
$325$		0			0
$326$		−	16.8936i		−	0.935648i
$327$	−0.594280	+	0.594280i	−0.0328638	+	0.0328638i
$328$	4.58776	+	4.58776i	0.253317	+	0.253317i
$329$		−	13.9041i		−	0.766558i
$330$		0			0
$331$		−	8.59601i		−	0.472479i	−0.971695	−	0.236240i	$-0.924085\pi$
$331$		−	8.59601i		−	0.472479i	0.971695	−	0.236240i	$-0.0759151\pi$
$332$	2.04560	−	2.04560i	0.112267	−	0.112267i
$333$	4.55736	−	4.55736i	0.249742	−	0.249742i
$334$		−	10.9155i		−	0.597270i
$335$		0			0
$336$			11.3149i			0.617281i
$337$	−2.01319	−	2.01319i	−0.109666	−	0.109666i	0.650145	−	0.759810i	$-0.274708\pi$
$337$	−2.01319	−	2.01319i	−0.109666	−	0.109666i	−0.759810	+	0.650145i	$0.774708\pi$
$338$	16.6180	−	16.6180i	0.903900	−	0.903900i
$339$			26.8189i			1.45660i
$340$		0			0
$341$		−	13.5216i		−	0.732237i
$342$	−15.5762	−	10.6865i	−0.842263	−	0.577860i
$343$	10.2158	+	10.2158i	0.551603	+	0.551603i
$344$	9.38099			0.505789
$345$		0			0
$346$	3.34499			0.179828
$347$	4.87329	−	4.87329i	0.261612	−	0.261612i	−0.564097	−	0.825709i	$-0.690775\pi$
$347$	4.87329	−	4.87329i	0.261612	−	0.261612i	0.825709	+	0.564097i	$0.190775\pi$
$348$	−4.03645	−	4.03645i	−0.216376	−	0.216376i
$349$		−	21.9692i		−	1.17599i	−0.808866	−	0.587993i	$-0.799918\pi$
$349$		−	21.9692i		−	1.17599i	0.808866	−	0.587993i	$-0.200082\pi$
$350$		0			0
$351$	21.8189			1.16461
$352$	2.76009	+	2.76009i	0.147113	+	0.147113i
$353$	−2.66894	−	2.66894i	−0.142053	−	0.142053i	0.632504	−	0.774557i	$-0.282027\pi$
$353$	−2.66894	−	2.66894i	−0.142053	−	0.142053i	−0.774557	+	0.632504i	$0.782027\pi$
$354$	−40.3918			−2.14680
$355$		0			0
$356$		−	10.9767i		−	0.581763i
$357$	43.2418	+	43.2418i	2.28860	+	2.28860i
$358$	−6.84815	−	6.84815i	−0.361936	−	0.361936i
$359$			3.01612i			0.159185i	0.996827	+	0.0795923i	$0.0253619\pi$
$359$			3.01612i			0.159185i	−0.996827	+	0.0795923i	$0.974638\pi$
$360$		0			0
$361$	−17.7269	+	6.83792i	−0.932995	+	0.359890i
$362$	−9.99638	+	9.99638i	−0.525398	+	0.525398i
$363$	−8.11183	+	8.11183i	−0.425761	+	0.425761i
$364$	−25.2435			−1.32312
$365$		0			0
$366$	5.41612			0.283105
$367$	24.8917	−	24.8917i	1.29934	−	1.29934i	0.370510	−	0.928829i	$-0.379183\pi$
$367$	24.8917	−	24.8917i	1.29934	−	1.29934i	0.928829	−	0.370510i	$-0.120817\pi$
$368$	−4.44500	−	4.44500i	−0.231712	−	0.231712i
$369$	−28.1166			−1.46369
$370$		0			0
$371$		−	22.6888i		−	1.17795i
$372$	6.63336	−	6.63336i	0.343924	−	0.343924i
$373$	20.0368	−	20.0368i	1.03747	−	1.03747i	0.0381967	−	0.999270i	$-0.487839\pi$
$373$	20.0368	−	20.0368i	1.03747	−	1.03747i	0.999270	−	0.0381967i	$-0.0121614\pi$
$374$	21.0962			1.09086
$375$		0			0
$376$		−	3.32773i		−	0.171615i
$377$	9.00526	−	9.00526i	0.463794	−	0.463794i
$378$	−10.6698	−	10.6698i	−0.548796	−	0.548796i
$379$	7.82292			0.401836			0.200918	−	0.979608i	$-0.435607\pi$
$379$	7.82292			0.401836			0.200918	+	0.979608i	$0.435607\pi$
$380$		0			0
$381$	52.2821			2.67849
$382$	−0.0194684	−	0.0194684i	−0.000996089	−	0.000996089i
$383$	17.0323	−	17.0323i	0.870310	−	0.870310i	−0.122196	−	0.992506i	$-0.538994\pi$
$383$	17.0323	−	17.0323i	0.870310	−	0.870310i	0.992506	+	0.122196i	$0.0389937\pi$
$384$			2.70806i			0.138195i
$385$		0			0
$386$	−23.7933			−1.21105
$387$	−28.7462	+	28.7462i	−1.46125	+	1.46125i
$388$	−3.35802	+	3.35802i	−0.170478	+	0.170478i
$389$			31.3894i			1.59151i	0.605622	+	0.795753i	$0.292924\pi$
$389$			31.3894i			1.59151i	−0.605622	+	0.795753i	$0.707076\pi$
$390$		0			0
$391$	−33.9745			−1.71817
$392$	7.39475	+	7.39475i	0.373491	+	0.373491i
$393$	1.27754	−	1.27754i	0.0644433	−	0.0644433i
$394$	−17.4648			−0.879861
$395$		0			0
$396$	−16.9155			−0.850037
$397$	3.50332	−	3.50332i	0.175827	−	0.175827i	−0.613707	−	0.789534i	$-0.710322\pi$
$397$	3.50332	−	3.50332i	0.175827	−	0.175827i	0.789534	+	0.613707i	$0.210322\pi$
$398$	−3.54360	+	3.54360i	−0.177625	+	0.177625i
$399$	−48.4875	+	9.02753i	−2.42741	+	0.451942i
$400$		0			0
$401$			2.27222i			0.113469i	0.998389	+	0.0567345i	$0.0180689\pi$
$401$			2.27222i			0.113469i	−0.998389	+	0.0567345i	$0.981931\pi$
$402$	10.9612	+	10.9612i	0.546693	+	0.546693i
$403$	14.7989	+	14.7989i	0.737187	+	0.737187i
$404$		−	6.00000i		−	0.298511i
$405$		0			0
$406$	−8.80746			−0.437107
$407$	−4.10492	−	4.10492i	−0.203473	−	0.203473i
$408$	10.3493	+	10.3493i	0.512365	+	0.512365i
$409$	−10.2870			−0.508657			−0.254329	−	0.967118i	$-0.581855\pi$
$409$	−10.2870			−0.508657			−0.254329	+	0.967118i	$0.581855\pi$
$410$		0			0
$411$		−	36.2302i		−	1.78710i
$412$	−0.884622	−	0.884622i	−0.0435822	−	0.0435822i
$413$	−44.0671	+	44.0671i	−2.16840	+	2.16840i
$414$	27.2417			1.33885
$415$		0			0
$416$	−6.04164			−0.296216
$417$	−39.0201	−	39.0201i	−1.91082	−	1.91082i
$418$	−9.62559	+	14.0298i	−0.470803	+	0.686221i
$419$			35.2927i			1.72416i	0.506769	+	0.862082i	$0.330840\pi$
$419$			35.2927i			1.72416i	−0.506769	+	0.862082i	$0.669160\pi$
$420$		0			0
$421$			23.6067i			1.15052i	0.817971	+	0.575260i	$0.195099\pi$
$421$			23.6067i			1.15052i	−0.817971	+	0.575260i	$0.804901\pi$
$422$	13.8391	−	13.8391i	0.673675	−	0.673675i
$423$	10.1972	+	10.1972i	0.495804	+	0.495804i
$424$		−	5.43022i		−	0.263715i
$425$		0			0
$426$		−	4.60648i		−	0.223185i
$427$	5.90894	−	5.90894i	0.285953	−	0.285953i
$428$	4.87001	−	4.87001i	0.235401	−	0.235401i
$429$		−	63.8633i		−	3.08335i
$430$		0			0
$431$			7.05927i			0.340033i	0.985441	+	0.170016i	$0.0543821\pi$
$431$			7.05927i			0.340033i	−0.985441	+	0.170016i	$0.945618\pi$
$432$	−2.55366	−	2.55366i	−0.122863	−	0.122863i
$433$	−12.8930	+	12.8930i	−0.619600	+	0.619600i	−0.945429	−	0.325829i	$-0.894357\pi$
$433$	−12.8930	+	12.8930i	−0.619600	+	0.619600i	0.325829	+	0.945429i	$0.394357\pi$
$434$		−	14.4739i		−	0.694768i
$435$		0			0
$436$			0.310347i			0.0148629i
$437$	15.5016	−	22.5944i	0.741541	−	1.08084i
$438$	13.6533	+	13.6533i	0.652382	+	0.652382i
$439$	−31.1306			−1.48578			−0.742892	−	0.669412i	$-0.766546\pi$
$439$	−31.1306			−1.48578			−0.742892	+	0.669412i	$0.766546\pi$
$440$		0			0
$441$	−45.3195			−2.15807
$442$	−23.0891	+	23.0891i	−1.09824	+	1.09824i
$443$	14.1929	+	14.1929i	0.674324	+	0.674324i	0.958710	−	0.284386i	$-0.0917898\pi$
$443$	14.1929	+	14.1929i	0.674324	+	0.674324i	−0.284386	+	0.958710i	$0.591790\pi$
$444$		−	4.02753i		−	0.191138i
$445$		0			0
$446$	−10.8322			−0.512921
$447$	3.45965	+	3.45965i	0.163636	+	0.163636i
$448$	2.95447	+	2.95447i	0.139585	+	0.139585i
$449$	−8.10691			−0.382589			−0.191294	−	0.981533i	$-0.561269\pi$
$449$	−8.10691			−0.382589			−0.191294	+	0.981533i	$0.561269\pi$
$450$		0			0
$451$			25.3253i			1.19252i
$452$	7.00273	+	7.00273i	0.329381	+	0.329381i
$453$	−12.1034	−	12.1034i	−0.568667	−	0.568667i
$454$			24.1525i			1.13353i
$455$		0			0
$456$	−11.6047	+	2.16060i	−0.543441	+	0.101179i
$457$	−8.09821	+	8.09821i	−0.378818	+	0.378818i	−0.870676	−	0.491858i	$-0.836318\pi$
$457$	−8.09821	+	8.09821i	−0.378818	+	0.378818i	0.491858	+	0.870676i	$0.336318\pi$
$458$	−12.4318	+	12.4318i	−0.580899	+	0.580899i
$459$	−19.5184			−0.911041
$460$		0			0
$461$	−29.4201			−1.37023			−0.685116	−	0.728434i	$-0.740249\pi$
$461$	−29.4201			−1.37023			−0.685116	+	0.728434i	$0.740249\pi$
$462$	−31.2303	+	31.2303i	−1.45296	+	1.45296i
$463$	16.1908	+	16.1908i	0.752452	+	0.752452i	0.974936	−	0.222484i	$-0.0714165\pi$
$463$	16.1908	+	16.1908i	0.752452	+	0.752452i	−0.222484	+	0.974936i	$0.571417\pi$
$464$	−2.10793			−0.0978582
$465$		0			0
$466$		−	15.1615i		−	0.702343i
$467$	−26.2293	+	26.2293i	−1.21375	+	1.21375i	−0.243961	+	0.969785i	$0.578447\pi$
$467$	−26.2293	+	26.2293i	−1.21375	+	1.21375i	−0.969785	+	0.243961i	$0.921553\pi$
$468$	18.5134	−	18.5134i	0.855783	−	0.855783i
$469$	23.9170			1.10439
$470$		0			0
$471$		−	41.4275i		−	1.90888i
$472$	−10.5468	+	10.5468i	−0.485455	+	0.485455i
$473$	25.8924	+	25.8924i	1.19053	+	1.19053i
$474$	32.0109			1.47031
$475$		0			0
$476$	22.5819			1.03504
$477$	16.6399	+	16.6399i	0.761887	+	0.761887i
$478$	2.04106	−	2.04106i	0.0933559	−	0.0933559i
$479$			26.9048i			1.22931i	0.788795	+	0.614657i	$0.210705\pi$
$479$			26.9048i			1.22931i	−0.788795	+	0.614657i	$0.789295\pi$
$480$		0			0
$481$	8.98537			0.409697
$482$	2.04560	−	2.04560i	0.0931744	−	0.0931744i
$483$	50.2949	−	50.2949i	2.28850	−	2.28850i
$484$			4.23619i			0.192554i
$485$		0			0
$486$	−19.5564			−0.887097
$487$	−26.8151	−	26.8151i	−1.21511	−	1.21511i	−0.969325	−	0.245781i	$-0.920955\pi$
$487$	−26.8151	−	26.8151i	−1.21511	−	1.21511i	−0.245781	−	0.969325i	$-0.579045\pi$
$488$	1.41421	−	1.41421i	0.0640184	−	0.0640184i
$489$	45.7488			2.06883
$490$		0			0
$491$	10.8604			0.490125			0.245063	−	0.969507i	$-0.421191\pi$
$491$	10.8604			0.490125			0.245063	+	0.969507i	$0.421191\pi$
$492$	−12.4239	+	12.4239i	−0.560114	+	0.560114i
$493$	−8.05579	+	8.05579i	−0.362815	+	0.362815i
$494$	−4.82027	−	25.8900i	−0.216874	−	1.16485i
$495$		0			0
$496$		−	3.46410i		−	0.155543i
$497$	−5.02563	−	5.02563i	−0.225430	−	0.225430i
$498$	5.53960	+	5.53960i	0.248235	+	0.248235i
$499$		−	19.5827i		−	0.876641i	−0.898819	−	0.438320i	$-0.855574\pi$
$499$		−	19.5827i		−	0.876641i	0.898819	−	0.438320i	$-0.144426\pi$
$500$		0			0
$501$	29.5598			1.32064
$502$	8.75203	+	8.75203i	0.390622	+	0.390622i
$503$	8.89712	+	8.89712i	0.396703	+	0.396703i	0.877068	−	0.480365i	$-0.159496\pi$
$503$	8.89712	+	8.89712i	0.396703	+	0.396703i	−0.480365	+	0.877068i	$0.659496\pi$
$504$	−18.1068			−0.806540
$505$		0			0
$506$		−	24.5372i		−	1.09081i
$507$	45.0025	+	45.0025i	1.99863	+	1.99863i
$508$	13.6515	−	13.6515i	0.605687	−	0.605687i
$509$	37.2433			1.65078			0.825391	−	0.564561i	$-0.190955\pi$
$509$	37.2433			1.65078			0.825391	+	0.564561i	$0.190955\pi$
$510$		0			0
$511$	29.7913			1.31789
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	8.90567	−	12.9805i	0.393195	−	0.573103i
$514$			9.61343i			0.424030i
$515$		0			0
$516$			25.4043i			1.11836i
$517$	9.18485	−	9.18485i	0.403949	−	0.403949i
$518$	−4.39400	−	4.39400i	−0.193061	−	0.193061i
$519$			9.05844i			0.397621i
$520$		0			0
$521$		−	10.7039i		−	0.468948i	−0.972122	−	0.234474i	$-0.924663\pi$
$521$		−	10.7039i		−	0.468948i	0.972122	−	0.234474i	$-0.0753368\pi$
$522$	6.45934	−	6.45934i	0.282718	−	0.282718i
$523$	28.4254	−	28.4254i	1.24295	−	1.24295i	0.284185	−	0.958769i	$-0.408277\pi$
$523$	28.4254	−	28.4254i	1.24295	−	1.24295i	0.958769	−	0.284185i	$-0.0917230\pi$
$524$		−	0.667162i		−	0.0291451i
$525$		0			0
$526$			20.1771i			0.879763i
$527$	−13.2386	−	13.2386i	−0.576683	−	0.576683i
$528$	−7.47449	+	7.47449i	−0.325285	+	0.325285i
$529$			16.5160i			0.718089i
$530$		0			0
$531$		−	64.6371i		−	2.80501i
$532$	−10.3035	+	15.0179i	−0.446712	+	0.651107i
$533$	−27.7176	−	27.7176i	−1.20058	−	1.20058i
$534$	29.7255			1.28635
$535$		0			0
$536$	5.72418			0.247247
$537$	18.5452	−	18.5452i	0.800284	−	0.800284i
$538$	14.4658	+	14.4658i	0.623664	+	0.623664i
$539$			40.8204i			1.75826i
$540$		0			0
$541$	−14.2484			−0.612584			−0.306292	−	0.951938i	$-0.599088\pi$
$541$	−14.2484			−0.612584			−0.306292	+	0.951938i	$0.599088\pi$
$542$	−0.292816	−	0.292816i	−0.0125775	−	0.0125775i
$543$	−27.0708	−	27.0708i	−1.16172	−	1.16172i
$544$	5.40464			0.231722
$545$		0			0
$546$		−	68.3608i		−	2.92557i
$547$	12.9130	+	12.9130i	0.552119	+	0.552119i	0.927052	−	0.374933i	$-0.122334\pi$
$547$	12.9130	+	12.9130i	0.552119	+	0.552119i	−0.374933	+	0.927052i	$0.622334\pi$
$548$	−9.46015	−	9.46015i	−0.404117	−	0.404117i
$549$			8.66716i			0.369905i
$550$		0			0
$551$	−1.68180	−	9.03303i	−0.0716469	−	0.384820i
$552$	12.0373	−	12.0373i	0.512342	−	0.512342i
$553$	34.9236	−	34.9236i	1.48510	−	1.48510i
$554$	−11.6895			−0.496641
$555$		0			0
$556$	−20.3772			−0.864187
$557$	0.294848	−	0.294848i	0.0124931	−	0.0124931i	−0.700833	−	0.713326i	$-0.747188\pi$
$557$	0.294848	−	0.294848i	0.0124931	−	0.0124931i	0.713326	+	0.700833i	$0.247188\pi$
$558$	10.6151	+	10.6151i	0.449371	+	0.449371i
$559$	−56.6766			−2.39716
$560$		0			0
$561$			57.1299i			2.41202i
$562$	16.7168	−	16.7168i	0.705158	−	0.705158i
$563$	−32.5972	+	32.5972i	−1.37381	+	1.37381i	−0.519091	+	0.854719i	$0.673729\pi$
$563$	−32.5972	+	32.5972i	−1.37381	+	1.37381i	−0.854719	+	0.519091i	$0.826271\pi$
$564$	9.01170			0.379461
$565$		0			0
$566$		−	24.0813i		−	1.01221i
$567$	−9.51580	+	9.51580i	−0.399626	+	0.399626i
$568$	−1.20281	−	1.20281i	−0.0504687	−	0.0504687i
$569$	−24.2387			−1.01614			−0.508070	−	0.861315i	$-0.669641\pi$
$569$	−24.2387			−1.01614			−0.508070	+	0.861315i	$0.669641\pi$
$570$		0			0
$571$	−31.8082			−1.33113			−0.665566	−	0.746339i	$-0.731810\pi$
$571$	−31.8082			−1.33113			−0.665566	+	0.746339i	$0.731810\pi$
$572$	−16.6755	−	16.6755i	−0.697236	−	0.697236i
$573$	0.0527215	−	0.0527215i	0.00220247	−	0.00220247i
$574$			27.1088i			1.13150i
$575$		0			0
$576$	−4.33358			−0.180566
$577$	20.9508	−	20.9508i	0.872194	−	0.872194i	−0.120518	−	0.992711i	$-0.538455\pi$
$577$	20.9508	−	20.9508i	0.872194	−	0.872194i	0.992711	+	0.120518i	$0.0384554\pi$
$578$	8.63388	−	8.63388i	0.359122	−	0.359122i
$579$		−	64.4338i		−	2.67778i
$580$		0			0
$581$	12.0873			0.501466
$582$	−9.09371	−	9.09371i	−0.376946	−	0.376946i
$583$	14.9879	−	14.9879i	0.620736	−	0.620736i
$584$	7.13010			0.295046
$585$		0			0
$586$	22.3182			0.921957
$587$	5.45185	−	5.45185i	0.225022	−	0.225022i	−0.585587	−	0.810609i	$-0.699136\pi$
$587$	5.45185	−	5.45185i	0.225022	−	0.225022i	0.810609	+	0.585587i	$0.199136\pi$
$588$	−20.0254	+	20.0254i	−0.825834	+	0.825834i
$589$	14.8446	−	2.76381i	0.611660	−	0.113881i
$590$		0			0
$591$		−	47.2956i		−	1.94548i
$592$	−1.05164	−	1.05164i	−0.0432220	−	0.0432220i
$593$	5.88700	+	5.88700i	0.241750	+	0.241750i	0.817574	−	0.575824i	$-0.195319\pi$
$593$	5.88700	+	5.88700i	0.241750	+	0.241750i	−0.575824	+	0.817574i	$0.695319\pi$
$594$		−	14.0966i		−	0.578392i
$595$		0			0
$596$	1.80671			0.0740059
$597$	−9.59629	−	9.59629i	−0.392750	−	0.392750i
$598$	26.8551	+	26.8551i	1.09819	+	1.09819i
$599$	−20.8668			−0.852595			−0.426297	−	0.904583i	$-0.640182\pi$
$599$	−20.8668			−0.852595			−0.426297	+	0.904583i	$0.640182\pi$
$600$		0			0
$601$			13.0125i			0.530790i	0.964140	+	0.265395i	$0.0855024\pi$
$601$			13.0125i			0.530790i	−0.964140	+	0.265395i	$0.914498\pi$
$602$	27.7158	+	27.7158i	1.12961	+	1.12961i
$603$	−17.5406	+	17.5406i	−0.714309	+	0.714309i
$604$	−6.32069			−0.257185
$605$		0			0
$606$	16.2484			0.660044
$607$	31.0710	+	31.0710i	1.26113	+	1.26113i	0.950544	+	0.310589i	$0.100526\pi$
$607$	31.0710	+	31.0710i	1.26113	+	1.26113i	0.310589	+	0.950544i	$0.399474\pi$
$608$	−2.46598	+	3.59430i	−0.100009	+	0.145768i
$609$		−	23.8511i		−	0.966496i
$610$		0			0
$611$			20.1050i			0.813360i
$612$	−16.5615	+	16.5615i	−0.669458	+	0.669458i
$613$	−1.48834	−	1.48834i	−0.0601134	−	0.0601134i	0.676411	−	0.736524i	$-0.263534\pi$
$613$	−1.48834	−	1.48834i	−0.0601134	−	0.0601134i	−0.736524	+	0.676411i	$0.763534\pi$
$614$		−	1.11001i		−	0.0447962i
$615$		0			0
$616$			16.3092i			0.657116i
$617$	−22.9244	+	22.9244i	−0.922901	+	0.922901i	−0.997234	−	0.0743326i	$-0.976317\pi$
$617$	−22.9244	+	22.9244i	−0.922901	+	0.922901i	0.0743326	+	0.997234i	$0.476317\pi$
$618$	2.39561	−	2.39561i	0.0963655	−	0.0963655i
$619$			4.72223i			0.189802i	0.995487	+	0.0949012i	$0.0302535\pi$
$619$			4.72223i			0.189802i	−0.995487	+	0.0949012i	$0.969746\pi$
$620$		0			0
$621$			22.7020i			0.911000i
$622$	11.0864	+	11.0864i	0.444525	+	0.444525i
$623$	32.4302	−	32.4302i	1.29929	−	1.29929i
$624$		−	16.3611i		−	0.654969i
$625$		0			0
$626$			4.89550i			0.195663i
$627$	−37.9936	−	26.0667i	−1.51732	−	1.04100i
$628$	−10.8172	−	10.8172i	−0.431655	−	0.431655i
$629$	−8.03800			−0.320496
$630$		0			0
$631$	6.04291			0.240564			0.120282	−	0.992740i	$-0.461620\pi$
$631$	6.04291			0.240564			0.120282	+	0.992740i	$0.461620\pi$
$632$	8.35842	−	8.35842i	0.332480	−	0.332480i
$633$	37.4770	+	37.4770i	1.48958	+	1.48958i
$634$			18.0275i			0.715965i
$635$		0			0
$636$	14.7054			0.583106
$637$	−44.6764	−	44.6764i	−1.77014	−	1.77014i
$638$	−5.81808	−	5.81808i	−0.230340	−	0.230340i
$639$	7.37154			0.291614
$640$		0			0
$641$			13.5348i			0.534593i	0.963614	+	0.267296i	$0.0861302\pi$
$641$			13.5348i			0.534593i	−0.963614	+	0.267296i	$0.913870\pi$
$642$	13.1883	+	13.1883i	0.520500	+	0.520500i
$643$	5.37736	+	5.37736i	0.212062	+	0.212062i	0.805143	−	0.593081i	$-0.202088\pi$
$643$	5.37736	+	5.37736i	0.212062	+	0.212062i	−0.593081	+	0.805143i	$0.702088\pi$
$644$		−	26.2652i		−	1.03499i
$645$		0			0
$646$	4.31205	+	23.1603i	0.169655	+	0.911229i
$647$	25.3967	−	25.3967i	0.998448	−	0.998448i	−0.00155076	−	0.999999i	$-0.500494\pi$
$647$	25.3967	−	25.3967i	0.998448	−	0.998448i	0.999999	+	0.00155076i	$0.000493622\pi$
$648$	−2.27746	+	2.27746i	−0.0894672	+	0.0894672i
$649$	−58.2202			−2.28534
$650$		0			0
$651$	39.1961			1.53622
$652$	11.9456	−	11.9456i	0.467824	−	0.467824i
$653$	−18.9735	−	18.9735i	−0.742490	−	0.742490i	0.230567	−	0.973057i	$-0.425942\pi$
$653$	−18.9735	−	18.9735i	−0.742490	−	0.742490i	−0.973057	+	0.230567i	$0.925942\pi$
$654$	−0.840439			−0.0328638
$655$		0			0
$656$			6.48808i			0.253317i
$657$	−21.8488	+	21.8488i	−0.852403	+	0.852403i
$658$	9.83168	−	9.83168i	0.383279	−	0.383279i
$659$	−30.5839			−1.19138			−0.595689	−	0.803215i	$-0.703121\pi$
$659$	−30.5839			−1.19138			−0.595689	+	0.803215i	$0.703121\pi$
$660$		0			0
$661$		−	34.7263i		−	1.35070i	−0.737499	−	0.675349i	$-0.763993\pi$
$661$		−	34.7263i		−	1.35070i	0.737499	−	0.675349i	$-0.236007\pi$
$662$	6.07830	−	6.07830i	0.236240	−	0.236240i
$663$	−62.5266	−	62.5266i	−2.42833	−	2.42833i
$664$	2.89291			0.112267
$665$		0			0
$666$	6.44507			0.249742
$667$	9.36975	+	9.36975i	0.362798	+	0.362798i
$668$	7.71843	−	7.71843i	0.298635	−	0.298635i
$669$		−	29.3343i		−	1.13413i
$670$		0			0
$671$	7.80671			0.301375
$672$	−8.00087	+	8.00087i	−0.308640	+	0.308640i
$673$	−31.9784	+	31.9784i	−1.23268	+	1.23268i	−0.269746	+	0.962931i	$0.586940\pi$
$673$	−31.9784	+	31.9784i	−1.23268	+	1.23268i	−0.962931	+	0.269746i	$0.913060\pi$
$674$		−	2.84708i		−	0.109666i
$675$		0			0
$676$	23.5014			0.903900
$677$	−8.41642	−	8.41642i	−0.323469	−	0.323469i	0.526627	−	0.850096i	$-0.323456\pi$
$677$	−8.41642	−	8.41642i	−0.323469	−	0.323469i	−0.850096	+	0.526627i	$0.823456\pi$
$678$	−18.9638	+	18.9638i	−0.728301	+	0.728301i
$679$	−19.8423			−0.761478
$680$		0			0
$681$	−65.4063			−2.50637
$682$	9.56123	−	9.56123i	0.366119	−	0.366119i
$683$	−7.28467	+	7.28467i	−0.278740	+	0.278740i	−0.832606	−	0.553866i	$-0.813152\pi$
$683$	−7.28467	+	7.28467i	−0.278740	+	0.278740i	0.553866	+	0.832606i	$0.313152\pi$
$684$	−3.45751	−	18.5705i	−0.132201	−	0.710062i
$685$		0			0
$686$			14.4474i			0.551603i
$687$	−33.6660	−	33.6660i	−1.28444	−	1.28444i
$688$	6.63336	+	6.63336i	0.252895	+	0.252895i
$689$			32.8075i			1.24986i
$690$		0			0
$691$	12.1517			0.462273			0.231136	−	0.972921i	$-0.425756\pi$
$691$	12.1517			0.462273			0.231136	+	0.972921i	$0.425756\pi$
$692$	2.36527	+	2.36527i	0.0899140	+	0.0899140i
$693$	−49.9763	−	49.9763i	−1.89844	−	1.89844i
$694$	6.89188			0.261612
$695$		0			0
$696$		−	5.70840i		−	0.216376i
$697$	24.7952	+	24.7952i	0.939186	+	0.939186i
$698$	15.5346	−	15.5346i	0.587993	−	0.587993i
$699$	41.0583			1.55297
$700$		0			0
$701$	−16.2161			−0.612474			−0.306237	−	0.951955i	$-0.599070\pi$
$701$	−16.2161			−0.612474			−0.306237	+	0.951955i	$0.599070\pi$
$702$	15.4283	+	15.4283i	0.582303	+	0.582303i
$703$	3.66750	−	5.34558i	0.138322	−	0.201612i
$704$			3.90336i			0.147113i
$705$		0			0
$706$		−	3.77445i		−	0.142053i
$707$	17.7268	−	17.7268i	0.666685	−	0.666685i
$708$	−28.5613	−	28.5613i	−1.07340	−	1.07340i
$709$			22.0228i			0.827085i	0.910485	+	0.413542i	$0.135709\pi$
$709$			22.0228i			0.827085i	−0.910485	+	0.413542i	$0.864291\pi$
$710$		0			0
$711$			51.2255i			1.92111i
$712$	7.76168	−	7.76168i	0.290881	−	0.290881i
$713$	−15.3979	+	15.3979i	−0.576657	+	0.576657i
$714$			61.1532i			2.28860i
$715$		0			0
$716$		−	9.68475i		−	0.361936i
$717$	5.52731	+	5.52731i	0.206421	+	0.206421i
$718$	−2.13272	+	2.13272i	−0.0795923	+	0.0795923i
$719$		−	0.0275325i		−	0.00102679i	−1.00000		0.000513394i	$-0.999837\pi$
$719$		−	0.0275325i		−	0.00102679i	1.00000		0.000513394i	$-0.000163418\pi$
$720$		0			0
$721$		−	5.22718i		−	0.194670i
$722$	−17.3699	−	7.69967i	−0.646443	−	0.286552i
$723$	5.53960	+	5.53960i	0.206020	+	0.206020i
$724$	−14.1370			−0.525398
$725$		0			0
$726$	−11.4719			−0.425761
$727$	−23.0328	+	23.0328i	−0.854239	+	0.854239i	−0.990652	−	0.136413i	$-0.956442\pi$
$727$	−23.0328	+	23.0328i	−0.854239	+	0.854239i	0.136413	+	0.990652i	$0.456442\pi$
$728$	−17.8498	−	17.8498i	−0.661559	−	0.661559i
$729$		−	43.2975i		−	1.60361i
$730$		0			0
$731$	50.7009			1.87524
$732$	3.82977	+	3.82977i	0.141552	+	0.141552i
$733$	2.78821	+	2.78821i	0.102985	+	0.102985i	0.756722	−	0.653737i	$-0.226800\pi$
$733$	2.78821	+	2.78821i	0.102985	+	0.102985i	−0.653737	+	0.756722i	$0.726800\pi$
$734$	35.2022			1.29934
$735$		0			0
$736$		−	6.28618i		−	0.231712i
$737$	15.7992	+	15.7992i	0.581973	+	0.581973i
$738$	−19.8814	−	19.8814i	−0.731846	−	0.731846i
$739$		−	26.4431i		−	0.972726i	−0.873757	−	0.486363i	$-0.838323\pi$
$739$		−	26.4431i		−	0.972726i	0.873757	−	0.486363i	$-0.161677\pi$
$740$		0			0
$741$	70.1116	−	13.0536i	2.57561	−	0.479535i
$742$	16.0434	−	16.0434i	0.588973	−	0.588973i
$743$	17.9302	−	17.9302i	0.657796	−	0.657796i	−0.297062	−	0.954858i	$-0.596007\pi$
$743$	17.9302	−	17.9302i	0.657796	−	0.657796i	0.954858	+	0.297062i	$0.0960069\pi$
$744$	9.38099			0.343924
$745$		0			0
$746$	28.3363			1.03747
$747$	−8.86476	+	8.86476i	−0.324345	+	0.324345i
$748$	14.9173	+	14.9173i	0.545430	+	0.545430i
$749$	28.7766			1.05147
$750$		0			0
$751$			53.4720i			1.95122i	0.219508	+	0.975611i	$0.429555\pi$
$751$			53.4720i			1.95122i	−0.219508	+	0.975611i	$0.570445\pi$
$752$	2.35306	−	2.35306i	0.0858074	−	0.0858074i
$753$	−23.7010	+	23.7010i	−0.863712	+	0.863712i
$754$	12.7354			0.463794
$755$		0			0
$756$		−	15.0894i		−	0.548796i
$757$	8.12170	−	8.12170i	0.295188	−	0.295188i	−0.543938	−	0.839126i	$-0.683067\pi$
$757$	8.12170	−	8.12170i	0.295188	−	0.295188i	0.839126	+	0.543938i	$0.183067\pi$
$758$	5.53164	+	5.53164i	0.200918	+	0.200918i
$759$	66.4482			2.41192
$760$		0			0
$761$	−15.5881			−0.565069			−0.282535	−	0.959257i	$-0.591175\pi$
$761$	−15.5881			−0.565069			−0.282535	+	0.959257i	$0.591175\pi$
$762$	36.9690	+	36.9690i	1.33925	+	1.33925i
$763$	−0.916911	+	0.916911i	−0.0331944	+	0.0331944i
$764$		−	0.0275325i		−	0.000996089i
$765$		0			0
$766$	24.0873			0.870310
$767$	63.7199	−	63.7199i	2.30079	−	2.30079i
$768$	−1.91489	+	1.91489i	−0.0690975	+	0.0690975i
$769$			2.64037i			0.0952143i	0.998866	+	0.0476071i	$0.0151596\pi$
$769$			2.64037i			0.0952143i	−0.998866	+	0.0476071i	$0.984840\pi$
$770$		0			0
$771$	−26.0337			−0.937582
$772$	−16.8244	−	16.8244i	−0.605525	−	0.605525i
$773$	−4.26211	+	4.26211i	−0.153297	+	0.153297i	−0.779589	−	0.626292i	$-0.784572\pi$
$773$	−4.26211	+	4.26211i	−0.153297	+	0.153297i	0.626292	+	0.779589i	$0.284572\pi$
$774$	−40.6533			−1.46125
$775$		0			0
$776$	−4.74896			−0.170478
$777$	11.8992	−	11.8992i	0.426882	−	0.426882i
$778$	−22.1956	+	22.1956i	−0.795753	+	0.795753i
$779$	−27.8031	+	5.17646i	−0.996149	+	0.185466i
$780$		0			0
$781$		−	6.63972i		−	0.237588i
$782$	−24.0236	−	24.0236i	−0.859083	−	0.859083i
$783$	5.38293	+	5.38293i	0.192370	+	0.192370i
$784$			10.4578i			0.373491i
$785$		0			0
$786$	1.80671			0.0644433
$787$	−5.97579	−	5.97579i	−0.213014	−	0.213014i	0.592533	−	0.805546i	$-0.298128\pi$
$787$	−5.97579	−	5.97579i	−0.213014	−	0.213014i	−0.805546	+	0.592533i	$0.798128\pi$
$788$	−12.3494	−	12.3494i	−0.439931	−	0.439931i
$789$	−54.6408			−1.94526
$790$		0			0
$791$			41.3787i			1.47126i
$792$	−11.9611	−	11.9611i	−0.425018	−	0.425018i
$793$	−8.54417	+	8.54417i	−0.303412	+	0.303412i
$794$	4.95444			0.175827
$795$		0			0
$796$	−5.01141			−0.177625
$797$	−15.7814	−	15.7814i	−0.559004	−	0.559004i	0.370020	−	0.929024i	$-0.379351\pi$
$797$	−15.7814	−	15.7814i	−0.559004	−	0.559004i	−0.929024	+	0.370020i	$0.879351\pi$
$798$	−40.6692	−	27.9024i	−1.43968	−	0.987733i
$799$		−	17.9852i		−	0.636271i
$800$		0			0
$801$			47.5683i			1.68074i
$802$	−1.60670	+	1.60670i	−0.0567345	+	0.0567345i
$803$	19.6797	+	19.6797i	0.694482	+	0.694482i
$804$			15.5014i			0.546693i
$805$		0			0
$806$			20.9289i			0.737187i
$807$	−39.1742	+	39.1742i	−1.37900	+	1.37900i
$808$	4.24264	−	4.24264i	0.149256	−	0.149256i
$809$			24.1847i			0.850288i	0.905126	+	0.425144i	$0.139777\pi$
$809$			24.1847i			0.850288i	−0.905126	+	0.425144i	$0.860223\pi$
$810$		0			0
$811$		−	7.38279i		−	0.259245i	−0.991563	−	0.129622i	$-0.958623\pi$
$811$		−	7.38279i		−	0.259245i	0.991563	−	0.129622i	$-0.0413765\pi$
$812$	−6.22781	−	6.22781i	−0.218553	−	0.218553i
$813$	0.792964	−	0.792964i	0.0278105	−	0.0278105i
$814$		−	5.80523i		−	0.203473i
$815$		0			0
$816$			14.6361i			0.512365i
$817$	−23.1333	+	33.7180i	−0.809332	+	1.17965i
$818$	−7.27398	−	7.27398i	−0.254329	−	0.254329i
$819$	109.395			3.82256
$820$		0			0
$821$	31.9921			1.11653			0.558266	−	0.829662i	$-0.311467\pi$
$821$	31.9921			1.11653			0.558266	+	0.829662i	$0.311467\pi$
$822$	25.6186	−	25.6186i	0.893552	−	0.893552i
$823$	−4.20827	−	4.20827i	−0.146691	−	0.146691i	0.629947	−	0.776638i	$-0.283077\pi$
$823$	−4.20827	−	4.20827i	−0.146691	−	0.146691i	−0.776638	+	0.629947i	$0.783077\pi$
$824$		−	1.25104i		−	0.0435822i
$825$		0			0
$826$	−62.3203			−2.16840
$827$	9.72213	+	9.72213i	0.338072	+	0.338072i	0.855641	−	0.517569i	$-0.173163\pi$
$827$	9.72213	+	9.72213i	0.338072	+	0.338072i	−0.517569	+	0.855641i	$0.673163\pi$
$828$	19.2628	+	19.2628i	0.669427	+	0.669427i
$829$	−6.70058			−0.232721			−0.116360	−	0.993207i	$-0.537123\pi$
$829$	−6.70058			−0.232721			−0.116360	+	0.993207i	$0.537123\pi$
$830$		0			0
$831$		−	31.6559i		−	1.09813i
$832$	−4.27208	−	4.27208i	−0.148108	−	0.148108i
$833$	39.9660	+	39.9660i	1.38474	+	1.38474i
$834$		−	55.1827i		−	1.91082i
$835$		0			0
$836$	−16.7269	+	3.11426i	−0.578512	+	0.107709i
$837$	−8.84612	+	8.84612i	−0.305767	+	0.305767i
$838$	−24.9557	+	24.9557i	−0.862082	+	0.862082i
$839$	−15.1405			−0.522707			−0.261353	−	0.965243i	$-0.584169\pi$
$839$	−15.1405			−0.522707			−0.261353	+	0.965243i	$0.584169\pi$
$840$		0			0
$841$	−24.5566			−0.846780
$842$	−16.6924	+	16.6924i	−0.575260	+	0.575260i
$843$	45.2702	+	45.2702i	1.55919	+	1.55919i
$844$	19.5714			0.673675
$845$		0			0
$846$			14.4210i			0.495804i
$847$	−12.5157	+	12.5157i	−0.430045	+	0.430045i
$848$	3.83975	−	3.83975i	0.131857	−	0.131857i
$849$	65.2136			2.23813
$850$		0			0
$851$			9.34906i			0.320481i
$852$	3.25727	−	3.25727i	0.111592	−	0.111592i
$853$	36.0415	+	36.0415i	1.23404	+	1.23404i	0.962400	+	0.271637i	$0.0875651\pi$
$853$	36.0415	+	36.0415i	1.23404	+	1.23404i	0.271637	+	0.962400i	$0.412435\pi$
$854$	8.35650			0.285953
$855$		0			0
$856$	6.88724			0.235401
$857$	11.2682	+	11.2682i	0.384913	+	0.384913i	0.872869	−	0.487955i	$-0.162257\pi$
$857$	11.2682	+	11.2682i	0.384913	+	0.384913i	−0.487955	+	0.872869i	$0.662257\pi$
$858$	45.1581	−	45.1581i	1.54167	−	1.54167i
$859$		−	30.5383i		−	1.04195i	−0.853571	−	0.520976i	$-0.825568\pi$
$859$		−	30.5383i		−	1.04195i	0.853571	−	0.520976i	$-0.174432\pi$
$860$		0			0
$861$	−73.4122			−2.50188
$862$	−4.99166	+	4.99166i	−0.170016	+	0.170016i
$863$	−31.6472	+	31.6472i	−1.07728	+	1.07728i	−0.0805325	+	0.996752i	$0.525662\pi$
$863$	−31.6472	+	31.6472i	−1.07728	+	1.07728i	−0.996752	+	0.0805325i	$0.974338\pi$
$864$		−	3.61142i		−	0.122863i
$865$		0			0
$866$	−18.2335			−0.619600
$867$	23.3810	+	23.3810i	0.794062	+	0.794062i
$868$	10.2346	−	10.2346i	0.347384	−	0.347384i
$869$	46.1400			1.56519
$870$		0			0
$871$	−34.5834			−1.17181
$872$	−0.219449	+	0.219449i	−0.00743147	+	0.00743147i
$873$	14.5522	−	14.5522i	0.492519	−	0.492519i
$874$	26.9379	−	5.01538i	0.911188	−	0.169648i
$875$		0			0
$876$			19.3087i			0.652382i
$877$	15.4991	+	15.4991i	0.523367	+	0.523367i	0.918587	−	0.395220i	$-0.129332\pi$
$877$	15.4991	+	15.4991i	0.523367	+	0.523367i	−0.395220	+	0.918587i	$0.629332\pi$
$878$	−22.0127	−	22.0127i	−0.742892	−	0.742892i
$879$			60.4390i			2.03856i
$880$		0			0
$881$	−2.90484			−0.0978666			−0.0489333	−	0.998802i	$-0.515582\pi$
$881$	−2.90484			−0.0978666			−0.0489333	+	0.998802i	$0.515582\pi$
$882$	−32.0458	−	32.0458i	−1.07904	−	1.07904i
$883$	−34.0836	−	34.0836i	−1.14701	−	1.14701i	−0.987139	−	0.159867i	$-0.948893\pi$
$883$	−34.0836	−	34.0836i	−1.14701	−	1.14701i	−0.159867	−	0.987139i	$-0.551107\pi$
$884$	−32.6529			−1.09824
$885$		0			0
$886$			20.0718i			0.674324i
$887$	−18.7588	−	18.7588i	−0.629859	−	0.629859i	0.318174	−	0.948032i	$-0.396930\pi$
$887$	−18.7588	−	18.7588i	−0.629859	−	0.629859i	−0.948032	+	0.318174i	$0.896930\pi$
$888$	2.84790	−	2.84790i	0.0955691	−	0.0955691i
$889$	80.6657			2.70544
$890$		0			0
$891$	−12.5720			−0.421178
$892$	−7.65955	−	7.65955i	−0.256461	−	0.256461i
$893$	11.9609	+	8.20612i	0.400255	+	0.274607i
$894$			4.89269i			0.163636i
$895$		0			0
$896$			4.17825i			0.139585i
$897$	−72.7251	+	72.7251i	−2.42822	+	2.42822i
$898$	−5.73245	−	5.73245i	−0.191294	−	0.191294i
$899$			7.30209i			0.243538i
$900$		0			0
$901$		−	29.3484i		−	0.977737i
$902$	−17.9077	+	17.9077i	−0.596261	+	0.596261i
$903$	−75.0561	+	75.0561i	−2.49771	+	2.49771i
$904$			9.90336i			0.329381i
$905$		0			0
$906$		−	17.1168i		−	0.568667i
$907$	−34.9725	−	34.9725i	−1.16124	−	1.16124i	−0.984204	−	0.177038i	$-0.943348\pi$
$907$	−34.9725	−	34.9725i	−1.16124	−	1.16124i	−0.177038	−	0.984204i	$-0.556652\pi$
$908$	−17.0784	+	17.0784i	−0.566765	+	0.566765i
$909$			26.0015i			0.862415i
$910$		0			0
$911$		−	3.12932i		−	0.103679i	−0.998655	−	0.0518395i	$-0.983492\pi$
$911$		−	3.12932i		−	0.103679i	0.998655	−	0.0518395i	$-0.0165084\pi$
$912$	−9.73356	−	6.67801i	−0.322310	−	0.221131i
$913$	7.98470	+	7.98470i	0.264255	+	0.264255i
$914$	−11.4526			−0.378818
$915$		0			0
$916$	−17.5812			−0.580899
$917$	1.97111	−	1.97111i	0.0650917	−	0.0650917i
$918$	−13.8016	−	13.8016i	−0.455521	−	0.455521i
$919$			24.2860i			0.801120i	0.916271	+	0.400560i	$0.131184\pi$
$919$			24.2860i			0.801120i	−0.916271	+	0.400560i	$0.868816\pi$
$920$		0			0
$921$	3.00596			0.0990499
$922$	−20.8032	−	20.8032i	−0.685116	−	0.685116i
$923$	7.26693	+	7.26693i	0.239194	+	0.239194i
$924$	−44.1662			−1.45296
$925$		0			0
$926$			22.8973i			0.752452i
$927$	3.83358	+	3.83358i	0.125911	+	0.125911i
$928$	−1.49053	−	1.49053i	−0.0489291	−	0.0489291i
$929$			19.3296i			0.634184i	0.948395	+	0.317092i	$0.102706\pi$
$929$			19.3296i			0.634184i	−0.948395	+	0.317092i	$0.897294\pi$
$930$		0			0
$931$	−44.8142	+	8.34364i	−1.46873	+	0.273452i
$932$	10.7208	−	10.7208i	0.351172	−	0.351172i
$933$	−30.0227	+	30.0227i	−0.982899	+	0.982899i
$934$	−37.0938			−1.21375
$935$		0			0
$936$	26.1819			0.855783
$937$	−7.03506	+	7.03506i	−0.229825	+	0.229825i	−0.812620	−	0.582794i	$-0.801959\pi$
$937$	−7.03506	+	7.03506i	−0.229825	+	0.229825i	0.582794	+	0.812620i	$0.301959\pi$
$938$	16.9119	+	16.9119i	0.552193	+	0.552193i
$939$	−13.2573			−0.432636
$940$		0			0
$941$			15.3091i			0.499063i	0.968367	+	0.249532i	$0.0802767\pi$
$941$			15.3091i			0.499063i	−0.968367	+	0.249532i	$0.919723\pi$
$942$	29.2937	−	29.2937i	0.954440	−	0.954440i
$943$	28.8395	−	28.8395i	0.939143	−	0.939143i
$944$	−14.9154			−0.485455
$945$		0			0
$946$			36.6174i			1.19053i
$947$	−3.75429	+	3.75429i	−0.121998	+	0.121998i	−0.765470	−	0.643472i	$-0.777493\pi$
$947$	−3.75429	+	3.75429i	−0.121998	+	0.121998i	0.643472	+	0.765470i	$0.277493\pi$
$948$	22.6351	+	22.6351i	0.735154	+	0.735154i
$949$	−43.0775			−1.39836
$950$		0			0
$951$	−48.8196			−1.58308
$952$	15.9678	+	15.9678i	0.517521	+	0.517521i
$953$	24.3463	−	24.3463i	0.788653	−	0.788653i	−0.192621	−	0.981273i	$-0.561699\pi$
$953$	24.3463	−	24.3463i	0.788653	−	0.788653i	0.981273	+	0.192621i	$0.0616987\pi$
$954$			23.5323i			0.761887i
$955$		0			0
$956$	2.88649			0.0933559
$957$	15.7557	−	15.7557i	0.509309	−	0.509309i
$958$	−19.0246	+	19.0246i	−0.614657	+	0.614657i
$959$		−	55.8994i		−	1.80509i
$960$		0			0
$961$	19.0000			0.612903
$962$	6.35361	+	6.35361i	0.204849	+	0.204849i
$963$	−21.1046	+	21.1046i	−0.680086	+	0.680086i
$964$	2.89291			0.0931744
$965$		0			0
$966$	71.1277			2.28850
$967$	−17.4994	+	17.4994i	−0.562743	+	0.562743i	−0.930086	−	0.367343i	$-0.880268\pi$
$967$	−17.4994	+	17.4994i	−0.562743	+	0.562743i	0.367343	+	0.930086i	$0.380268\pi$
$968$	−2.99544	+	2.99544i	−0.0962772	+	0.0962772i
$969$	−62.7194	+	11.6773i	−2.01484	+	0.375128i
$970$		0			0
$971$			9.33148i			0.299462i	0.988727	+	0.149731i	$0.0478407\pi$
$971$			9.33148i			0.299462i	−0.988727	+	0.149731i	$0.952159\pi$
$972$	−13.8285	−	13.8285i	−0.443548	−	0.443548i
$973$	−60.2039	−	60.2039i	−1.93005	−	1.93005i
$974$		−	37.9222i		−	1.21511i
$975$		0			0
$976$	2.00000			0.0640184
$977$	9.53501	+	9.53501i	0.305052	+	0.305052i	0.842987	−	0.537935i	$-0.180795\pi$
$977$	9.53501	+	9.53501i	0.305052	+	0.305052i	−0.537935	+	0.842987i	$0.680795\pi$
$978$	32.3493	+	32.3493i	1.03442	+	1.03442i
$979$	42.8459			1.36936
$980$		0			0
$981$		−	1.34492i		−	0.0429399i
$982$	7.67950	+	7.67950i	0.245063	+	0.245063i
$983$	17.6028	−	17.6028i	0.561443	−	0.561443i	−0.368274	−	0.929717i	$-0.620051\pi$
$983$	17.6028	−	17.6028i	0.561443	−	0.561443i	0.929717	+	0.368274i	$0.120051\pi$
$984$	−17.5701			−0.560114
$985$		0			0
$986$	−11.3926			−0.362815
$987$	26.6248	+	26.6248i	0.847476	+	0.847476i
$988$	14.8985	−	21.7154i	0.473986	−	0.690860i
$989$		−	58.9706i		−	1.87516i
$990$		0			0
$991$		−	31.0484i		−	0.986286i	−0.869948	−	0.493143i	$-0.835848\pi$
$991$		−	31.0484i		−	0.986286i	0.869948	−	0.493143i	$-0.164152\pi$
$992$	2.44949	−	2.44949i	0.0777714	−	0.0777714i
$993$	16.4604	+	16.4604i	0.522354	+	0.522354i
$994$		−	7.10731i		−	0.225430i
$995$		0			0
$996$			7.83417i			0.248235i
$997$	12.3889	−	12.3889i	0.392361	−	0.392361i	−0.483167	−	0.875528i	$-0.660514\pi$
$997$	12.3889	−	12.3889i	0.392361	−	0.392361i	0.875528	+	0.483167i	$0.160514\pi$
$998$	13.8470	−	13.8470i	0.438320	−	0.438320i
$999$			5.37104i			0.169932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.f.d.493.9	yes	32
5.2	odd	4	inner	950.2.f.d.607.7	yes	32
5.3	odd	4	inner	950.2.f.d.607.10	yes	32
5.4	even	2	inner	950.2.f.d.493.8	yes	32
19.18	odd	2	inner	950.2.f.d.493.7	✓	32
95.18	even	4	inner	950.2.f.d.607.8	yes	32
95.37	even	4	inner	950.2.f.d.607.9	yes	32
95.94	odd	2	inner	950.2.f.d.493.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.f.d.493.7	✓	32	19.18	odd	2	inner
950.2.f.d.493.8	yes	32	5.4	even	2	inner
950.2.f.d.493.9	yes	32	1.1	even	1	trivial
950.2.f.d.493.10	yes	32	95.94	odd	2	inner
950.2.f.d.607.7	yes	32	5.2	odd	4	inner
950.2.f.d.607.8	yes	32	95.18	even	4	inner
950.2.f.d.607.9	yes	32	95.37	even	4	inner
950.2.f.d.607.10	yes	32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.91489 + 1.91489i) q^{3} +1.00000i q^{4} -2.70806 q^{6} +(-2.95447 + 2.95447i) q^{7} +(-0.707107 + 0.707107i) q^{8} -4.33358i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.91489 + 1.91489i) q^{3} +1.00000i q^{4} -2.70806 q^{6} +(-2.95447 + 2.95447i) q^{7} +(-0.707107 + 0.707107i) q^{8} -4.33358i q^{9} -3.90336 q^{11} +(-1.91489 - 1.91489i) q^{12} +(4.27208 - 4.27208i) q^{13} -4.17825 q^{14} -1.00000 q^{16} +(-3.82166 + 3.82166i) q^{17} +(3.06430 - 3.06430i) q^{18} +(-0.797842 - 4.28526i) q^{19} -11.3149i q^{21} +(-2.76009 - 2.76009i) q^{22} +(4.44500 + 4.44500i) q^{23} -2.70806i q^{24} +6.04164 q^{26} +(2.55366 + 2.55366i) q^{27} +(-2.95447 - 2.95447i) q^{28} +2.10793 q^{29} +3.46410i q^{31} +(-0.707107 - 0.707107i) q^{32} +(7.47449 - 7.47449i) q^{33} -5.40464 q^{34} +4.33358 q^{36} +(1.05164 + 1.05164i) q^{37} +(2.46598 - 3.59430i) q^{38} +16.3611i q^{39} -6.48808i q^{41} +(8.00087 - 8.00087i) q^{42} +(-6.63336 - 6.63336i) q^{43} -3.90336i q^{44} +6.28618i q^{46} +(-2.35306 + 2.35306i) q^{47} +(1.91489 - 1.91489i) q^{48} -10.4578i q^{49} -14.6361i q^{51} +(4.27208 + 4.27208i) q^{52} +(-3.83975 + 3.83975i) q^{53} +3.61142i q^{54} -4.17825i q^{56} +(9.73356 + 6.67801i) q^{57} +(1.49053 + 1.49053i) q^{58} +14.9154 q^{59} -2.00000 q^{61} +(-2.44949 + 2.44949i) q^{62} +(12.8034 + 12.8034i) q^{63} -1.00000i q^{64} +10.5705 q^{66} +(-4.04760 - 4.04760i) q^{67} +(-3.82166 - 3.82166i) q^{68} -17.0233 q^{69} +1.70103i q^{71} +(3.06430 + 3.06430i) q^{72} +(-5.04174 - 5.04174i) q^{73} +1.48724i q^{74} +(4.28526 - 0.797842i) q^{76} +(11.5323 - 11.5323i) q^{77} +(-11.5691 + 11.5691i) q^{78} -11.8206 q^{79} +3.22082 q^{81} +(4.58776 - 4.58776i) q^{82} +(-2.04560 - 2.04560i) q^{83} +11.3149 q^{84} -9.38099i q^{86} +(-4.03645 + 4.03645i) q^{87} +(2.76009 - 2.76009i) q^{88} -10.9767 q^{89} +25.2435i q^{91} +(-4.44500 + 4.44500i) q^{92} +(-6.63336 - 6.63336i) q^{93} -3.32773 q^{94} +2.70806 q^{96} +(3.35802 + 3.35802i) q^{97} +(7.39475 - 7.39475i) q^{98} +16.9155i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{6}+O(q^{10}) \) 32 * q - 8 * q^6	\( 32 q - 8 q^{6} - 24 q^{11} - 32 q^{16} + 32 q^{26} + 56 q^{36} - 64 q^{61} + 72 q^{66} + 4 q^{76} - 32 q^{81} + 8 q^{96}+O(q^{100}) \) 32 * q - 8 * q^6 - 24 * q^11 - 32 * q^16 + 32 * q^26 + 56 * q^36 - 64 * q^61 + 72 * q^66 + 4 * q^76 - 32 * q^81 + 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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