LMFDB - Embedded newform 676.4.e.h.653.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [676,4,Mod(529,676)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("676.529"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(676, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 676 = 2^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	676.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$39.8852911639$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 102 x^{14} + 7641 x^{12} - 240214 x^{10} + 5505396 x^{8} - 56148534 x^{6} + 414761593 x^{4} + \cdots + 43046721 $ x^16 - 102x^14 + 7641x^12 - 240214x^10 + 5505396x^8 - 56148534x^6 + 414761593x^4 - 136508166*x^2 + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 52)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			653.2
Root			$-3.01134 + 1.73860i$ of defining polynomial
Character	$\chi$	$=$	676.653
Dual form			676.4.e.h.529.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.48104 - 7.76138i) q^{3} +11.8097 q^{5} +(16.0936 - 27.8750i) q^{7} +(-26.6594 + 46.1754i) q^{9} +(-6.04263 - 10.4661i) q^{11} +(-52.9195 - 91.6593i) q^{15} +(-44.8791 + 77.7328i) q^{17} +(-9.58572 + 16.6029i) q^{19} -288.465 q^{21} +(-7.88869 - 13.6636i) q^{23} +14.4680 q^{25} +235.870 q^{27} +(-131.197 - 227.240i) q^{29} +84.0297 q^{31} +(-54.1544 + 93.7982i) q^{33} +(190.060 - 329.194i) q^{35} +(-135.599 - 234.864i) q^{37} +(-82.6122 - 143.088i) q^{41} +(-135.153 + 234.092i) q^{43} +(-314.838 + 545.315i) q^{45} -238.811 q^{47} +(-346.511 - 600.174i) q^{49} +804.419 q^{51} -94.2765 q^{53} +(-71.3613 - 123.601i) q^{55} +171.816 q^{57} +(123.655 - 214.177i) q^{59} +(-101.847 + 176.404i) q^{61} +(858.092 + 1486.26i) q^{63} +(115.725 + 200.442i) q^{67} +(-70.6990 + 122.454i) q^{69} +(374.863 - 649.282i) q^{71} +153.347 q^{73} +(-64.8316 - 112.292i) q^{75} -388.991 q^{77} -881.413 q^{79} +(-337.140 - 583.944i) q^{81} -197.016 q^{83} +(-530.006 + 917.998i) q^{85} +(-1175.80 + 2036.54i) q^{87} +(695.321 + 1204.33i) q^{89} +(-376.540 - 652.186i) q^{93} +(-113.204 + 196.075i) q^{95} +(-561.433 + 972.430i) q^{97} +644.370 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 140 q^{9} - 176 q^{17} + 40 q^{23} + 168 q^{25} - 864 q^{27} - 968 q^{29} + 80 q^{35} - 1008 q^{43} - 1844 q^{49} + 3616 q^{51} - 2328 q^{53} - 2256 q^{55} - 2448 q^{61} - 3476 q^{69} - 2896 q^{75}+ \cdots - 4800 q^{95}+O(q^{100}) $ 16 * q - 140 * q^9 - 176 * q^17 + 40 * q^23 + 168 * q^25 - 864 * q^27 - 968 * q^29 + 80 * q^35 - 1008 * q^43 - 1844 * q^49 + 3616 * q^51 - 2328 * q^53 - 2256 * q^55 - 2448 * q^61 - 3476 * q^69 - 2896 * q^75 + 7944 * q^77 - 7936 * q^79 - 8264 * q^81 - 3320 * q^87 - 4800 * q^95

Character values

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

$n$	$339$	$509$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−4.48104	−	7.76138i	−0.862376	−	1.49368i	−0.869630	−	0.493705i	$-0.835642\pi$
$3$	−4.48104	−	7.76138i	−0.862376	−	1.49368i	0.00725381	−	0.999974i	$-0.497691\pi$
$4$		0			0
$5$	11.8097			1.05629			0.528144	−	0.849155i	$-0.322888\pi$
$5$	11.8097			1.05629			0.528144	+	0.849155i	$0.322888\pi$
$6$		0			0
$7$	16.0936	−	27.8750i	0.868975	−	1.50511i	0.00592959	−	0.999982i	$-0.498113\pi$
$7$	16.0936	−	27.8750i	0.868975	−	1.50511i	0.863045	−	0.505126i	$-0.168554\pi$
$8$		0			0
$9$	−26.6594	+	46.1754i	−0.987384	+	1.71020i
$10$		0			0
$11$	−6.04263	−	10.4661i	−0.165629	−	0.286878i	0.771249	−	0.636533i	$-0.219632\pi$
$11$	−6.04263	−	10.4661i	−0.165629	−	0.286878i	−0.936879	+	0.349655i	$0.886299\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−52.9195	−	91.6593i	−0.910917	−	1.57775i
$16$		0			0
$17$	−44.8791	+	77.7328i	−0.640281	+	1.10900i	0.345089	+	0.938570i	$0.387849\pi$
$17$	−44.8791	+	77.7328i	−0.640281	+	1.10900i	−0.985370	+	0.170429i	$0.945485\pi$
$18$		0			0
$19$	−9.58572	+	16.6029i	−0.115743	+	0.200473i	−0.918076	−	0.396403i	$-0.870258\pi$
$19$	−9.58572	+	16.6029i	−0.115743	+	0.200473i	0.802334	+	0.596876i	$0.203592\pi$
$20$		0			0
$21$	−288.465			−2.99753
$22$		0			0
$23$	−7.88869	−	13.6636i	−0.0715176	−	0.123872i	0.828049	−	0.560656i	$-0.189451\pi$
$23$	−7.88869	−	13.6636i	−0.0715176	−	0.123872i	−0.899567	+	0.436784i	$0.856118\pi$
$24$		0			0
$25$	14.4680			0.115744
$26$		0			0
$27$	235.870			1.68123
$28$		0			0
$29$	−131.197	−	227.240i	−0.840093	−	1.45508i	−0.889815	−	0.456321i	$-0.849167\pi$
$29$	−131.197	−	227.240i	−0.840093	−	1.45508i	0.0497219	−	0.998763i	$-0.484166\pi$
$30$		0			0
$31$	84.0297			0.486844			0.243422	−	0.969920i	$-0.421730\pi$
$31$	84.0297			0.486844			0.243422	+	0.969920i	$0.421730\pi$
$32$		0			0
$33$	−54.1544	+	93.7982i	−0.285669	+	0.494793i
$34$		0			0
$35$	190.060	−	329.194i	0.917888	−	1.58983i
$36$		0			0
$37$	−135.599	−	234.864i	−0.602495	−	1.04355i	−0.992442	−	0.122714i	$-0.960840\pi$
$37$	−135.599	−	234.864i	−0.602495	−	1.04355i	0.389947	−	0.920837i	$-0.372493\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−82.6122	−	143.088i	−0.314679	−	0.545041i	0.664690	−	0.747119i	$-0.268564\pi$
$41$	−82.6122	−	143.088i	−0.314679	−	0.545041i	−0.979369	+	0.202079i	$0.935230\pi$
$42$		0			0
$43$	−135.153	+	234.092i	−0.479318	+	0.830204i	−0.999719	−	0.0237186i	$-0.992449\pi$
$43$	−135.153	+	234.092i	−0.479318	+	0.830204i	0.520400	+	0.853922i	$0.325783\pi$
$44$		0			0
$45$	−314.838	+	545.315i	−1.04296	+	1.80646i
$46$		0			0
$47$	−238.811			−0.741153			−0.370577	−	0.928802i	$-0.620840\pi$
$47$	−238.811			−0.741153			−0.370577	+	0.928802i	$0.620840\pi$
$48$		0			0
$49$	−346.511	−	600.174i	−1.01024	−	1.74978i
$50$		0			0
$51$	804.419			2.20865
$52$		0			0
$53$	−94.2765			−0.244337			−0.122169	−	0.992509i	$-0.538985\pi$
$53$	−94.2765			−0.244337			−0.122169	+	0.992509i	$0.538985\pi$
$54$		0			0
$55$	−71.3613	−	123.601i	−0.174952	−	0.303026i
$56$		0			0
$57$	171.816			0.399255
$58$		0			0
$59$	123.655	−	214.177i	0.272856	−	0.472601i	−0.696736	−	0.717328i	$-0.745365\pi$
$59$	123.655	−	214.177i	0.272856	−	0.472601i	0.969592	+	0.244727i	$0.0786983\pi$
$60$		0			0
$61$	−101.847	+	176.404i	−0.213774	+	0.370267i	−0.952893	−	0.303308i	$-0.901909\pi$
$61$	−101.847	+	176.404i	−0.213774	+	0.370267i	0.739119	+	0.673575i	$0.235242\pi$
$62$		0			0
$63$	858.092	+	1486.26i	1.71602	+	2.97224i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	115.725	+	200.442i	0.211016	+	0.365491i	0.952033	−	0.305996i	$-0.0989893\pi$
$67$	115.725	+	200.442i	0.211016	+	0.365491i	−0.741016	+	0.671487i	$0.765656\pi$
$68$		0			0
$69$	−70.6990	+	122.454i	−0.123350	+	0.213649i
$70$		0			0
$71$	374.863	−	649.282i	0.626593	−	1.08529i	−0.361638	−	0.932319i	$-0.617782\pi$
$71$	374.863	−	649.282i	0.626593	−	1.08529i	0.988231	−	0.152972i	$-0.0488844\pi$
$72$		0			0
$73$	153.347			0.245862			0.122931	−	0.992415i	$-0.460771\pi$
$73$	153.347			0.245862			0.122931	+	0.992415i	$0.460771\pi$
$74$		0			0
$75$	−64.8316	−	112.292i	−0.0998148	−	0.172884i
$76$		0			0
$77$	−388.991			−0.575710
$78$		0			0
$79$	−881.413			−1.25527			−0.627637	−	0.778506i	$-0.715978\pi$
$79$	−881.413			−1.25527			−0.627637	+	0.778506i	$0.715978\pi$
$80$		0			0
$81$	−337.140	−	583.944i	−0.462470	−	0.801021i
$82$		0			0
$83$	−197.016			−0.260546			−0.130273	−	0.991478i	$-0.541585\pi$
$83$	−197.016			−0.260546			−0.130273	+	0.991478i	$0.541585\pi$
$84$		0			0
$85$	−530.006	+	917.998i	−0.676321	+	1.17142i
$86$		0			0
$87$	−1175.80	+	2036.54i	−1.44895	+	2.50966i
$88$		0			0
$89$	695.321	+	1204.33i	0.828133	+	1.43437i	0.899501	+	0.436918i	$0.143930\pi$
$89$	695.321	+	1204.33i	0.828133	+	1.43437i	−0.0713683	+	0.997450i	$0.522737\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−376.540	−	652.186i	−0.419843	−	0.727189i
$94$		0			0
$95$	−113.204	+	196.075i	−0.122258	+	0.211757i
$96$		0			0
$97$	−561.433	+	972.430i	−0.587679	+	1.01789i	0.406857	+	0.913492i	$0.366625\pi$
$97$	−561.433	+	972.430i	−0.587679	+	1.01789i	−0.994536	+	0.104398i	$0.966709\pi$
$98$		0			0
$99$	644.370			0.654158
$100$		0			0
$101$	596.702	+	1033.52i	0.587862	+	1.01821i	0.994512	+	0.104623i	$0.0333636\pi$
$101$	596.702	+	1033.52i	0.587862	+	1.01821i	−0.406650	+	0.913584i	$0.633303\pi$
$102$		0			0
$103$	−1367.61			−1.30830			−0.654149	−	0.756366i	$-0.726973\pi$
$103$	−1367.61			−1.30830			−0.654149	+	0.756366i	$0.726973\pi$
$104$		0			0
$105$	−3406.67			−3.16626
$106$		0			0
$107$	−868.434	−	1504.17i	−0.784623	−	1.35901i	−0.929224	−	0.369517i	$-0.879523\pi$
$107$	−868.434	−	1504.17i	−0.784623	−	1.35901i	0.144601	−	0.989490i	$-0.453810\pi$
$108$		0			0
$109$	−946.465			−0.831697			−0.415848	−	0.909434i	$-0.636515\pi$
$109$	−946.465			−0.831697			−0.415848	+	0.909434i	$0.636515\pi$
$110$		0			0
$111$	−1215.25	+	2104.87i	−1.03915	+	1.79987i
$112$		0			0
$113$	485.712	−	841.279i	0.404354	−	0.700361i	−0.589892	−	0.807482i	$-0.700830\pi$
$113$	485.712	−	841.279i	0.404354	−	0.700361i	0.994246	+	0.107121i	$0.0341631\pi$
$114$		0			0
$115$	−93.1627	−	161.362i	−0.0755432	−	0.130845i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1444.54	+	2502.01i	1.11278	+	1.92738i
$120$		0			0
$121$	592.473	−	1026.19i	0.445134	−	0.770995i
$122$		0			0
$123$	−740.376	+	1282.37i	−0.542744	+	0.940060i
$124$		0			0
$125$	−1305.35			−0.934029
$126$		0			0
$127$	801.930	+	1388.98i	0.560313	+	0.970491i	0.997469	+	0.0711048i	$0.0226525\pi$
$127$	801.930	+	1388.98i	0.560313	+	0.970491i	−0.437156	+	0.899386i	$0.644014\pi$
$128$		0			0
$129$	2422.51			1.65341
$130$		0			0
$131$	1677.20			1.11861			0.559305	−	0.828962i	$-0.311068\pi$
$131$	1677.20			1.11861			0.559305	+	0.828962i	$0.311068\pi$
$132$		0			0
$133$	308.538	+	534.404i	0.201155	+	0.348411i
$134$		0			0
$135$	2785.55			1.77586
$136$		0			0
$137$	−292.032	+	505.815i	−0.182117	+	0.315436i	−0.942601	−	0.333921i	$-0.891628\pi$
$137$	−292.032	+	505.815i	−0.182117	+	0.315436i	0.760484	+	0.649356i	$0.224962\pi$
$138$		0			0
$139$	−78.3050	+	135.628i	−0.0477823	+	0.0827614i	−0.888927	−	0.458048i	$-0.848549\pi$
$139$	−78.3050	+	135.628i	−0.0477823	+	0.0827614i	0.841145	+	0.540810i	$0.181882\pi$
$140$		0			0
$141$	1070.12	+	1853.51i	0.639153	+	1.10704i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−1549.39	−	2683.63i	−0.887380	−	1.53699i
$146$		0			0
$147$	−3105.45	+	5378.80i	−1.74240	+	3.01793i
$148$		0			0
$149$	−593.508	+	1027.99i	−0.326322	+	0.565207i	−0.981779	−	0.190026i	$-0.939143\pi$
$149$	−593.508	+	1027.99i	−0.326322	+	0.565207i	0.655457	+	0.755233i	$0.272476\pi$
$150$		0			0
$151$	2022.29			1.08988			0.544939	−	0.838476i	$-0.316553\pi$
$151$	2022.29			1.08988			0.544939	+	0.838476i	$0.316553\pi$
$152$		0			0
$153$	−2392.89	−	4144.62i	−1.26441	−	2.19001i
$154$		0			0
$155$	992.361			0.514248
$156$		0			0
$157$	1429.86			0.726848			0.363424	−	0.931624i	$-0.381608\pi$
$157$	1429.86			0.726848			0.363424	+	0.931624i	$0.381608\pi$
$158$		0			0
$159$	422.457	+	731.716i	0.210711	+	0.364961i
$160$		0			0
$161$	−507.831			−0.248588
$162$		0			0
$163$	555.347	−	961.889i	0.266860	−	0.462215i	−0.701189	−	0.712975i	$-0.747347\pi$
$163$	555.347	−	961.889i	0.266860	−	0.462215i	0.968049	+	0.250760i	$0.0806806\pi$
$164$		0			0
$165$	−639.545	+	1107.73i	−0.301749	+	0.522644i
$166$		0			0
$167$	−142.185	−	246.272i	−0.0658841	−	0.114115i	0.831202	−	0.555971i	$-0.187653\pi$
$167$	−142.185	−	246.272i	−0.0658841	−	0.114115i	−0.897086	+	0.441856i	$0.854320\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$	−511.098	−	885.248i	−0.228565	−	0.395887i
$172$		0			0
$173$	2170.41	−	3759.26i	0.953834	−	1.65209i	0.216820	−	0.976212i	$-0.430431\pi$
$173$	2170.41	−	3759.26i	0.953834	−	1.65209i	0.737014	−	0.675878i	$-0.236235\pi$
$174$		0			0
$175$	232.843	−	403.295i	0.100579	−	0.174207i
$176$		0			0
$177$	−2216.41			−0.941219
$178$		0			0
$179$	−325.394	−	563.599i	−0.135872	−	0.235337i	0.790058	−	0.613032i	$-0.210050\pi$
$179$	−325.394	−	563.599i	−0.135872	−	0.235337i	−0.925930	+	0.377694i	$0.876717\pi$
$180$		0			0
$181$	−454.138			−0.186496			−0.0932482	−	0.995643i	$-0.529725\pi$
$181$	−454.138			−0.186496			−0.0932482	+	0.995643i	$0.529725\pi$
$182$		0			0
$183$	1825.52			0.737413
$184$		0			0
$185$	−1601.38	−	2773.66i	−0.636408	−	1.10229i
$186$		0			0
$187$	1084.75			0.424197
$188$		0			0
$189$	3796.01	−	6574.88i	1.46095	−	2.53044i
$190$		0			0
$191$	1407.63	−	2438.09i	0.533259	−	0.923633i	−0.465986	−	0.884792i	$-0.654300\pi$
$191$	1407.63	−	2438.09i	0.533259	−	0.923633i	0.999245	−	0.0388404i	$-0.0123664\pi$
$192$		0			0
$193$	−576.786	−	999.023i	−0.215119	−	0.372597i	0.738190	−	0.674593i	$-0.235681\pi$
$193$	−576.786	−	999.023i	−0.215119	−	0.372597i	−0.953309	+	0.301995i	$0.902347\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	203.329	+	352.175i	0.0735359	+	0.127368i	0.900449	−	0.434962i	$-0.143238\pi$
$197$	203.329	+	352.175i	0.0735359	+	0.127368i	−0.826913	+	0.562330i	$0.809905\pi$
$198$		0			0
$199$	404.699	−	700.960i	0.144163	−	0.249697i	−0.784898	−	0.619626i	$-0.787284\pi$
$199$	404.699	−	700.960i	0.144163	−	0.249697i	0.929060	+	0.369929i	$0.120618\pi$
$200$		0			0
$201$	1037.14	−	1796.38i	0.363951	−	0.630381i
$202$		0			0
$203$	−8445.76			−2.92008
$204$		0			0
$205$	−975.621	−	1689.83i	−0.332392	−	0.575720i
$206$		0			0
$207$	841.229			0.282461
$208$		0			0
$209$	231.692			0.0766815
$210$		0			0
$211$	−1800.27	−	3118.16i	−0.587373	−	1.01736i	−0.994575	−	0.104021i	$-0.966829\pi$
$211$	−1800.27	−	3118.16i	−0.587373	−	1.01736i	0.407202	−	0.913338i	$-0.366504\pi$
$212$		0			0
$213$	−6719.10			−2.16143
$214$		0			0
$215$	−1596.11	+	2764.55i	−0.506298	+	0.876934i
$216$		0			0
$217$	1352.34	−	2342.33i	0.423055	−	0.732754i
$218$		0			0
$219$	−687.155	−	1190.19i	−0.212026	−	0.367239i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−1305.40	−	2261.02i	−0.392000	−	0.678964i	0.600713	−	0.799465i	$-0.294883\pi$
$223$	−1305.40	−	2261.02i	−0.392000	−	0.678964i	−0.992713	+	0.120501i	$0.961550\pi$
$224$		0			0
$225$	−385.708	+	668.065i	−0.114284	+	0.197945i
$226$		0			0
$227$	2330.43	−	4036.43i	0.681394	−	1.18021i	−0.293162	−	0.956063i	$-0.594708\pi$
$227$	2330.43	−	4036.43i	0.681394	−	1.18021i	0.974556	−	0.224145i	$-0.0719591\pi$
$228$		0			0
$229$	−123.893			−0.0357515			−0.0178757	−	0.999840i	$-0.505690\pi$
$229$	−123.893			−0.0357515			−0.0178757	+	0.999840i	$0.505690\pi$
$230$		0			0
$231$	1743.08	+	3019.11i	0.496478	+	0.859926i
$232$		0			0
$233$	1186.44			0.333590			0.166795	−	0.985992i	$-0.446658\pi$
$233$	1186.44			0.333590			0.166795	+	0.985992i	$0.446658\pi$
$234$		0			0
$235$	−2820.28			−0.782871
$236$		0			0
$237$	3949.64	+	6840.98i	1.08252	+	1.87498i
$238$		0			0
$239$	4543.56			1.22970			0.614850	−	0.788644i	$-0.289217\pi$
$239$	4543.56			1.22970			0.614850	+	0.788644i	$0.289217\pi$
$240$		0			0
$241$	−3142.08	+	5442.24i	−0.839831	+	1.45463i	0.0502054	+	0.998739i	$0.484012\pi$
$241$	−3142.08	+	5442.24i	−0.839831	+	1.45463i	−0.890036	+	0.455890i	$0.849321\pi$
$242$		0			0
$243$	162.773	−	281.931i	0.0429707	−	0.0744275i
$244$		0			0
$245$	−4092.17	−	7087.85i	−1.06710	−	1.84827i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	882.836	+	1529.12i	0.224689	+	0.389172i
$250$		0			0
$251$	−462.404	+	800.908i	−0.116282	+	0.201406i	−0.918291	−	0.395905i	$-0.870431\pi$
$251$	−462.404	+	800.908i	−0.116282	+	0.201406i	0.802010	+	0.597311i	$0.203764\pi$
$252$		0			0
$253$	−95.3368	+	165.128i	−0.0236908	+	0.0410337i
$254$		0			0
$255$	9499.91			2.33297
$256$		0			0
$257$	271.205	+	469.741i	0.0658261	+	0.114014i	0.897060	−	0.441908i	$-0.145698\pi$
$257$	271.205	+	469.741i	0.0658261	+	0.114014i	−0.831234	+	0.555923i	$0.812365\pi$
$258$		0			0
$259$	−8729.11			−2.09421
$260$		0			0
$261$	13990.5			3.31798
$262$		0			0
$263$	2624.40	+	4545.59i	0.615312	+	1.06575i	0.990330	+	0.138734i	$0.0443034\pi$
$263$	2624.40	+	4545.59i	0.615312	+	1.06575i	−0.375017	+	0.927018i	$0.622363\pi$
$264$		0			0
$265$	−1113.37			−0.258091
$266$		0			0
$267$	6231.51	−	10793.3i	1.42832	−	2.47393i
$268$		0			0
$269$	165.080	−	285.927i	0.0374168	−	0.0648078i	−0.846711	−	0.532054i	$-0.821420\pi$
$269$	165.080	−	285.927i	0.0374168	−	0.0648078i	0.884127	+	0.467246i	$0.154754\pi$
$270$		0			0
$271$	−716.940	−	1241.78i	−0.160705	−	0.278349i	0.774417	−	0.632676i	$-0.218043\pi$
$271$	−716.940	−	1241.78i	−0.160705	−	0.278349i	−0.935122	+	0.354327i	$0.884710\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−87.4247	−	151.424i	−0.0191706	−	0.0332044i
$276$		0			0
$277$	1070.54	−	1854.22i	0.232211	−	0.402200i	−0.726248	−	0.687433i	$-0.758738\pi$
$277$	1070.54	−	1854.22i	0.232211	−	0.402200i	0.958458	+	0.285233i	$0.0920708\pi$
$278$		0			0
$279$	−2240.18	+	3880.10i	−0.480702	+	0.832600i
$280$		0			0
$281$	5857.04			1.24342			0.621711	−	0.783246i	$-0.286438\pi$
$281$	5857.04			1.24342			0.621711	+	0.783246i	$0.286438\pi$
$282$		0			0
$283$	853.748	+	1478.73i	0.179329	+	0.310606i	0.941651	−	0.336591i	$-0.109274\pi$
$283$	853.748	+	1478.73i	0.179329	+	0.310606i	−0.762322	+	0.647198i	$0.775941\pi$
$284$		0			0
$285$	2029.09			0.421729
$286$		0			0
$287$	−5318.12			−1.09379
$288$		0			0
$289$	−1571.76	−	2722.37i	−0.319919	−	0.554116i
$290$		0			0
$291$	10063.2			2.02720
$292$		0			0
$293$	−891.643	+	1544.37i	−0.177783	+	0.307929i	−0.941121	−	0.338071i	$-0.890226\pi$
$293$	−891.643	+	1544.37i	−0.177783	+	0.307929i	0.763338	+	0.645999i	$0.223559\pi$
$294$		0			0
$295$	1460.32	−	2529.36i	0.288215	−	0.499203i
$296$		0			0
$297$	−1425.28	−	2468.65i	−0.278461	−	0.482308i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	4350.22	+	7534.80i	0.833032	+	1.44285i
$302$		0			0
$303$	5347.69	−	9262.47i	1.01392	−	1.75615i
$304$		0			0
$305$	−1202.78	+	2083.28i	−0.225807	+	0.391108i
$306$		0			0
$307$	4027.85			0.748801			0.374400	−	0.927267i	$-0.377849\pi$
$307$	4027.85			0.748801			0.374400	+	0.927267i	$0.377849\pi$
$308$		0			0
$309$	6128.31	+	10614.5i	1.12824	+	1.95418i
$310$		0			0
$311$	80.6308			0.0147014			0.00735072	−	0.999973i	$-0.497660\pi$
$311$	80.6308			0.0147014			0.00735072	+	0.999973i	$0.497660\pi$
$312$		0			0
$313$	−4628.22			−0.835790			−0.417895	−	0.908495i	$-0.637232\pi$
$313$	−4628.22			−0.835790			−0.417895	+	0.908495i	$0.637232\pi$
$314$		0			0
$315$	10133.8	+	17552.2i	1.81261	+	3.13954i
$316$		0			0
$317$	−10723.3			−1.89993			−0.949966	−	0.312354i	$-0.898882\pi$
$317$	−10723.3			−1.89993			−0.949966	+	0.312354i	$0.898882\pi$
$318$		0			0
$319$	−1585.55	+	2746.25i	−0.278288	+	0.482009i
$320$		0			0
$321$	−7782.97	+	13480.5i	−1.35328	+	2.34395i
$322$		0			0
$323$	−860.396	−	1490.25i	−0.148216	−	0.256717i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	4241.15	+	7345.88i	0.717235	+	1.24229i
$328$		0			0
$329$	−3843.34	+	6656.87i	−0.644044	+	1.11552i
$330$		0			0
$331$	2596.26	−	4496.86i	0.431128	−	0.746736i	−0.565843	−	0.824513i	$-0.691449\pi$
$331$	2596.26	−	4496.86i	0.431128	−	0.746736i	0.996971	+	0.0777775i	$0.0247824\pi$
$332$		0			0
$333$	14459.9			2.37957
$334$		0			0
$335$	1366.68	+	2367.15i	0.222894	+	0.386064i
$336$		0			0
$337$	−2676.49			−0.432635			−0.216317	−	0.976323i	$-0.569405\pi$
$337$	−2676.49			−0.432635			−0.216317	+	0.976323i	$0.569405\pi$
$338$		0			0
$339$	−8705.98			−1.39482
$340$		0			0
$341$	−507.760	−	879.466i	−0.0806356	−	0.139665i
$342$		0			0
$343$	−11266.2			−1.77353
$344$		0			0
$345$	−834.931	+	1446.14i	−0.130293	+	0.225674i
$346$		0			0
$347$	4924.23	−	8529.02i	0.761806	−	1.31949i	−0.180113	−	0.983646i	$-0.557646\pi$
$347$	4924.23	−	8529.02i	0.761806	−	1.31949i	0.941919	−	0.335840i	$-0.109020\pi$
$348$		0			0
$349$	−3255.67	−	5638.99i	−0.499347	−	0.864894i	0.500653	−	0.865648i	$-0.333093\pi$
$349$	−3255.67	−	5638.99i	−0.499347	−	0.864894i	−1.00000		0.000754175i	$0.999760\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5548.23	−	9609.82i	−0.836552	−	1.44895i	−0.892761	−	0.450531i	$-0.851235\pi$
$353$	−5548.23	−	9609.82i	−0.836552	−	1.44895i	0.0562092	−	0.998419i	$-0.482099\pi$
$354$		0			0
$355$	4427.01	−	7667.80i	0.661862	−	1.14638i
$356$		0			0
$357$	12946.0	−	22423.2i	1.91926	−	3.32426i
$358$		0			0
$359$	−7844.27			−1.15322			−0.576608	−	0.817021i	$-0.695624\pi$
$359$	−7844.27			−1.15322			−0.576608	+	0.817021i	$0.695624\pi$
$360$		0			0
$361$	3245.73	+	5621.77i	0.473207	+	0.819619i
$362$		0			0
$363$	−10619.6			−1.53549
$364$		0			0
$365$	1810.98			0.259701
$366$		0			0
$367$	−1637.80	−	2836.75i	−0.232949	−	0.403479i	0.725726	−	0.687984i	$-0.241504\pi$
$367$	−1637.80	−	2836.75i	−0.232949	−	0.403479i	−0.958675	+	0.284505i	$0.908171\pi$
$368$		0			0
$369$	8809.55			1.24284
$370$		0			0
$371$	−1517.25	+	2627.96i	−0.212323	+	0.367754i
$372$		0			0
$373$	812.650	−	1407.55i	0.112808	−	0.195389i	−0.804093	−	0.594503i	$-0.797349\pi$
$373$	812.650	−	1407.55i	0.112808	−	0.195389i	0.916901	+	0.399114i	$0.130682\pi$
$374$		0			0
$375$	5849.30	+	10131.3i	0.805484	+	1.39514i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	6459.52	+	11188.2i	0.875470	+	1.51636i	0.856262	+	0.516542i	$0.172781\pi$
$379$	6459.52	+	11188.2i	0.875470	+	1.51636i	0.0192081	+	0.999816i	$0.493885\pi$
$380$		0			0
$381$	7186.95	−	12448.2i	0.966401	−	1.67386i
$382$		0			0
$383$	−2482.96	+	4300.61i	−0.331261	+	0.573762i	−0.982759	−	0.184889i	$-0.940808\pi$
$383$	−2482.96	+	4300.61i	−0.331261	+	0.573762i	0.651498	+	0.758650i	$0.274141\pi$
$384$		0			0
$385$	−4593.86			−0.608116
$386$		0			0
$387$	−7206.20	−	12481.5i	−0.946543	−	1.63946i
$388$		0			0
$389$	−8704.29			−1.13451			−0.567256	−	0.823542i	$-0.691995\pi$
$389$	−8704.29			−1.13451			−0.567256	+	0.823542i	$0.691995\pi$
$390$		0			0
$391$	1416.15			0.183165
$392$		0			0
$393$	−7515.61	−	13017.4i	−0.964662	−	1.67084i
$394$		0			0
$395$	−10409.2			−1.32593
$396$		0			0
$397$	2197.12	−	3805.52i	0.277759	−	0.481092i	−0.693069	−	0.720871i	$-0.743742\pi$
$397$	2197.12	−	3805.52i	0.277759	−	0.481092i	0.970827	+	0.239779i	$0.0770751\pi$
$398$		0			0
$399$	2765.14	−	4789.36i	0.346943	−	0.600923i
$400$		0			0
$401$	−1624.85	−	2814.32i	−0.202347	−	0.350475i	0.746937	−	0.664894i	$-0.231524\pi$
$401$	−1624.85	−	2814.32i	−0.202347	−	0.350475i	−0.949284	+	0.314419i	$0.898190\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−3981.51	−	6896.18i	−0.488501	−	0.846109i
$406$		0			0
$407$	−1638.75	+	2838.39i	−0.199581	+	0.345685i
$408$		0			0
$409$	3282.71	−	5685.82i	0.396870	−	0.687398i	−0.596468	−	0.802637i	$-0.703430\pi$
$409$	3282.71	−	5685.82i	0.396870	−	0.687398i	0.993338	+	0.115238i	$0.0367632\pi$
$410$		0			0
$411$	5234.43			0.628213
$412$		0			0
$413$	−3980.12	−	6893.77i	−0.474211	−	0.821357i
$414$		0			0
$415$	−2326.69			−0.275212
$416$		0			0
$417$	1403.55			0.164825
$418$		0			0
$419$	5682.35	+	9842.12i	0.662532	+	1.14754i	0.979948	+	0.199253i	$0.0638516\pi$
$419$	5682.35	+	9842.12i	0.662532	+	1.14754i	−0.317416	+	0.948286i	$0.602815\pi$
$420$		0			0
$421$	3657.27			0.423383			0.211692	−	0.977337i	$-0.432103\pi$
$421$	3657.27			0.423383			0.211692	+	0.977337i	$0.432103\pi$
$422$		0			0
$423$	6366.56	−	11027.2i	0.731803	−	1.26752i
$424$		0			0
$425$	−649.310	+	1124.64i	−0.0741086	+	0.128360i
$426$		0			0
$427$	3278.18	+	5677.98i	0.371528	+	0.643505i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−6683.84	−	11576.7i	−0.746982	−	1.29381i	−0.949263	−	0.314483i	$-0.898169\pi$
$431$	−6683.84	−	11576.7i	−0.746982	−	1.29381i	0.202281	−	0.979328i	$-0.435165\pi$
$432$		0			0
$433$	−3031.38	+	5250.50i	−0.336440	+	0.582731i	−0.983760	−	0.179487i	$-0.942556\pi$
$433$	−3031.38	+	5250.50i	−0.336440	+	0.582731i	0.647320	+	0.762218i	$0.275890\pi$
$434$		0			0
$435$	−13885.8	+	24050.9i	−1.53051	+	2.65092i
$436$		0			0
$437$	302.475			0.0331106
$438$		0			0
$439$	855.711	+	1482.13i	0.0930315	+	0.161135i	0.908785	−	0.417264i	$-0.137011\pi$
$439$	855.711	+	1482.13i	0.0930315	+	0.161135i	−0.815754	+	0.578399i	$0.803678\pi$
$440$		0			0
$441$	36951.0			3.98996
$442$		0			0
$443$	14253.1			1.52864			0.764320	−	0.644837i	$-0.223075\pi$
$443$	14253.1			1.52864			0.764320	+	0.644837i	$0.223075\pi$
$444$		0			0
$445$	8211.50	+	14222.7i	0.874747	+	1.51511i
$446$		0			0
$447$	10638.1			1.12565
$448$		0			0
$449$	1766.25	−	3059.23i	0.185644	−	0.321546i	−0.758149	−	0.652081i	$-0.773896\pi$
$449$	1766.25	−	3059.23i	0.185644	−	0.321546i	0.943793	+	0.330536i	$0.107229\pi$
$450$		0			0
$451$	−998.389	+	1729.26i	−0.104240	+	0.180549i
$452$		0			0
$453$	−9061.95	−	15695.8i	−0.939884	−	1.62793i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2793.74	+	4838.91i	0.285965	+	0.495305i	0.972843	−	0.231468i	$-0.0743527\pi$
$457$	2793.74	+	4838.91i	0.285965	+	0.495305i	−0.686878	+	0.726773i	$0.741019\pi$
$458$		0			0
$459$	−10585.6	+	18334.9i	−1.07646	+	1.86448i
$460$		0			0
$461$	1344.09	−	2328.04i	0.135793	−	0.235201i	−0.790107	−	0.612969i	$-0.789975\pi$
$461$	1344.09	−	2328.04i	0.135793	−	0.235201i	0.925900	+	0.377768i	$0.123308\pi$
$462$		0			0
$463$	−19314.2			−1.93868			−0.969340	−	0.245723i	$-0.920975\pi$
$463$	−19314.2			−1.93868			−0.969340	+	0.245723i	$0.920975\pi$
$464$		0			0
$465$	−4446.81	−	7702.10i	−0.443475	−	0.768121i
$466$		0			0
$467$	5482.16			0.543221			0.271611	−	0.962407i	$-0.412444\pi$
$467$	5482.16			0.543221			0.271611	+	0.962407i	$0.412444\pi$
$468$		0			0
$469$	7449.77			0.733472
$470$		0			0
$471$	−6407.25	−	11097.7i	−0.626816	−	1.08568i
$472$		0			0
$473$	3266.72			0.317556
$474$		0			0
$475$	−138.686	+	240.211i	−0.0133965	+	0.0232035i
$476$		0			0
$477$	2513.35	−	4353.25i	0.241255	−	0.417865i
$478$		0			0
$479$	−2534.27	−	4389.48i	−0.241740	−	0.418707i	0.719470	−	0.694524i	$-0.244385\pi$
$479$	−2534.27	−	4389.48i	−0.241740	−	0.418707i	−0.961210	+	0.275817i	$0.911052\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	2275.61	+	3941.47i	0.214376	+	0.371311i
$484$		0			0
$485$	−6630.33	+	11484.1i	−0.620758	+	1.07518i
$486$		0			0
$487$	−6816.65	+	11806.8i	−0.634275	+	1.09860i	0.352393	+	0.935852i	$0.385368\pi$
$487$	−6816.65	+	11806.8i	−0.634275	+	1.09860i	−0.986668	+	0.162744i	$0.947965\pi$
$488$		0			0
$489$	−9954.12			−0.920533
$490$		0			0
$491$	−332.094	−	575.204i	−0.0305238	−	0.0528688i	0.850360	−	0.526201i	$-0.176384\pi$
$491$	−332.094	−	575.204i	−0.0305238	−	0.0528688i	−0.880884	+	0.473333i	$0.843051\pi$
$492$		0			0
$493$	23552.0			2.15158
$494$		0			0
$495$	7609.79			0.690979
$496$		0			0
$497$	−12065.8	−	20898.6i	−1.08899	−	1.88618i
$498$		0			0
$499$	14754.0			1.32361			0.661805	−	0.749676i	$-0.269791\pi$
$499$	14754.0			1.32361			0.661805	+	0.749676i	$0.269791\pi$
$500$		0			0
$501$	−1274.28	+	2207.11i	−0.113634	+	0.196819i
$502$		0			0
$503$	2641.84	−	4575.80i	0.234182	−	0.405616i	−0.724852	−	0.688904i	$-0.758092\pi$
$503$	2641.84	−	4575.80i	0.234182	−	0.405616i	0.959035	+	0.283288i	$0.0914253\pi$
$504$		0			0
$505$	7046.85	+	12205.5i	0.620952	+	1.07552i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3800.32	−	6582.35i	−0.330936	−	0.573197i	0.651760	−	0.758425i	$-0.274031\pi$
$509$	−3800.32	−	6582.35i	−0.330936	−	0.573197i	−0.982696	+	0.185228i	$0.940698\pi$
$510$		0			0
$511$	2467.92	−	4274.56i	0.213648	−	0.370050i
$512$		0			0
$513$	−2260.99	+	3916.14i	−0.194591	+	0.337041i
$514$		0			0
$515$	−16151.0			−1.38194
$516$		0			0
$517$	1443.05	+	2499.43i	0.122757	+	0.212621i
$518$		0			0
$519$	−38902.8			−3.29025
$520$		0			0
$521$	10834.5			0.911074			0.455537	−	0.890217i	$-0.349447\pi$
$521$	10834.5			0.911074			0.455537	+	0.890217i	$0.349447\pi$
$522$		0			0
$523$	−4518.24	−	7825.83i	−0.377761	−	0.654301i	0.612975	−	0.790102i	$-0.289973\pi$
$523$	−4518.24	−	7825.83i	−0.377761	−	0.654301i	−0.990736	+	0.135801i	$0.956639\pi$
$524$		0			0
$525$	−4173.51			−0.346946
$526$		0			0
$527$	−3771.17	+	6531.86i	−0.311717	+	0.539910i
$528$		0			0
$529$	5959.04	−	10321.4i	0.489770	−	0.848307i
$530$		0			0
$531$	6593.13	+	11419.6i	0.538828	+	0.933277i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−10255.9	−	17763.7i	−0.828788	−	1.43550i
$536$		0			0
$537$	−2916.21	+	5051.02i	−0.234346	+	0.405899i
$538$		0			0
$539$	−4187.67	+	7253.25i	−0.334649	+	0.579628i
$540$		0			0
$541$	8389.76			0.666735			0.333368	−	0.942797i	$-0.391815\pi$
$541$	8389.76			0.666735			0.333368	+	0.942797i	$0.391815\pi$
$542$		0			0
$543$	2035.01	+	3524.74i	0.160830	+	0.278566i
$544$		0			0
$545$	−11177.4			−0.878511
$546$		0			0
$547$	−23840.9			−1.86355			−0.931777	−	0.363032i	$-0.881742\pi$
$547$	−23840.9			−1.86355			−0.931777	+	0.363032i	$0.881742\pi$
$548$		0			0
$549$	−5430.36	−	9405.66i	−0.422153	−	0.731191i
$550$		0			0
$551$	5030.48			0.388939
$552$		0			0
$553$	−14185.1	+	24569.4i	−1.09080	+	1.88933i
$554$		0			0
$555$	−14351.6	+	24857.8i	−1.09765	+	1.90118i
$556$		0			0
$557$	−9409.46	−	16297.7i	−0.715784	−	1.23977i	−0.962657	−	0.270726i	$-0.912736\pi$
$557$	−9409.46	−	16297.7i	−0.715784	−	1.23977i	0.246873	−	0.969048i	$-0.420597\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−4860.80	−	8419.16i	−0.365817	−	0.633613i
$562$		0			0
$563$	4276.04	−	7406.32i	0.320095	−	0.554421i	−0.660412	−	0.750903i	$-0.729618\pi$
$563$	4276.04	−	7406.32i	0.320095	−	0.554421i	0.980507	+	0.196482i	$0.0629517\pi$
$564$		0			0
$565$	5736.10	−	9935.21i	0.427114	−	0.739783i
$566$		0			0
$567$	−21703.3			−1.60750
$568$		0			0
$569$	−13111.9	−	22710.4i	−0.966041	−	1.67323i	−0.706792	−	0.707422i	$-0.749858\pi$
$569$	−13111.9	−	22710.4i	−0.966041	−	1.67323i	−0.259250	−	0.965810i	$-0.583475\pi$
$570$		0			0
$571$	3528.25			0.258586			0.129293	−	0.991606i	$-0.458729\pi$
$571$	3528.25			0.258586			0.129293	+	0.991606i	$0.458729\pi$
$572$		0			0
$573$	−25230.6			−1.83948
$574$		0			0
$575$	−114.133	−	197.685i	−0.00827773	−	0.0143375i
$576$		0			0
$577$	−26672.4			−1.92441			−0.962206	−	0.272322i	$-0.912208\pi$
$577$	−26672.4			−1.92441			−0.962206	+	0.272322i	$0.912208\pi$
$578$		0			0
$579$	−5169.20	+	8953.32i	−0.371027	+	0.642638i
$580$		0			0
$581$	−3170.71	+	5491.83i	−0.226408	+	0.392150i
$582$		0			0
$583$	569.678	+	986.711i	0.0404694	+	0.0700950i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2319.24	−	4017.05i	−0.163076	−	0.282455i	0.772895	−	0.634534i	$-0.218808\pi$
$587$	−2319.24	−	4017.05i	−0.163076	−	0.282455i	−0.935970	+	0.352079i	$0.885475\pi$
$588$		0			0
$589$	−805.484	+	1395.14i	−0.0563487	+	0.0975989i
$590$		0			0
$591$	1822.25	−	3156.22i	0.126831	−	0.219678i
$592$		0			0
$593$	−5932.05			−0.410793			−0.205396	−	0.978679i	$-0.565848\pi$
$593$	−5932.05			−0.410793			−0.205396	+	0.978679i	$0.565848\pi$
$594$		0			0
$595$	17059.5	+	29547.9i	1.17541	+	2.03587i
$596$		0			0
$597$	−7253.89			−0.497289
$598$		0			0
$599$	−8927.94			−0.608991			−0.304496	−	0.952514i	$-0.598488\pi$
$599$	−8927.94			−0.608991			−0.304496	+	0.952514i	$0.598488\pi$
$600$		0			0
$601$	−5217.26	−	9036.57i	−0.354104	−	0.613327i	0.632860	−	0.774266i	$-0.281881\pi$
$601$	−5217.26	−	9036.57i	−0.354104	−	0.613327i	−0.986964	+	0.160940i	$0.948548\pi$
$602$		0			0
$603$	−12340.7			−0.833417
$604$		0			0
$605$	6996.91	−	12119.0i	0.470190	−	0.814392i
$606$		0			0
$607$	−4468.87	+	7740.30i	−0.298823	+	0.517577i	−0.975867	−	0.218366i	$-0.929927\pi$
$607$	−4468.87	+	7740.30i	−0.298823	+	0.517577i	0.677044	+	0.735943i	$0.263261\pi$
$608$		0			0
$609$	37845.8	+	65550.8i	2.51821	+	4.36166i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	11984.2	+	20757.2i	0.789620	+	1.36766i	0.926200	+	0.377032i	$0.123055\pi$
$613$	11984.2	+	20757.2i	0.789620	+	1.36766i	−0.136580	+	0.990629i	$0.543611\pi$
$614$		0			0
$615$	−8743.59	+	15144.3i	−0.573293	+	0.992973i
$616$		0			0
$617$	−6551.98	+	11348.4i	−0.427509	+	0.740467i	−0.996651	−	0.0817724i	$-0.973942\pi$
$617$	−6551.98	+	11348.4i	−0.427509	+	0.740467i	0.569142	+	0.822239i	$0.307275\pi$
$618$		0			0
$619$	25051.3			1.62665			0.813324	−	0.581810i	$-0.197655\pi$
$619$	25051.3			1.62665			0.813324	+	0.581810i	$0.197655\pi$
$620$		0			0
$621$	−1860.71	−	3222.84i	−0.120238	−	0.208258i
$622$		0			0
$623$	44761.0			2.87851
$624$		0			0
$625$	−17224.2			−1.10235
$626$		0			0
$627$	−1038.22	−	1798.25i	−0.0661283	−	0.114538i
$628$		0			0
$629$	24342.2			1.54306
$630$		0			0
$631$	−27.8467	+	48.2319i	−0.00175683	+	0.00304292i	−0.866902	−	0.498478i	$-0.833893\pi$
$631$	−27.8467	+	48.2319i	−0.00175683	+	0.00304292i	0.865146	+	0.501521i	$0.167226\pi$
$632$		0			0
$633$	−16134.1	+	27945.2i	−1.01307	+	1.75469i
$634$		0			0
$635$	9470.51	+	16403.4i	0.591852	+	1.02512i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	19987.2	+	34618.9i	1.23738	+	2.14320i
$640$		0			0
$641$	8949.61	−	15501.2i	0.551464	−	0.955164i	−0.446705	−	0.894681i	$-0.647403\pi$
$641$	8949.61	−	15501.2i	0.551464	−	0.955164i	0.998169	−	0.0604827i	$-0.0192640\pi$
$642$		0			0
$643$	12940.2	−	22413.1i	0.793643	−	1.37463i	−0.130054	−	0.991507i	$-0.541515\pi$
$643$	12940.2	−	22413.1i	0.793643	−	1.37463i	0.923697	−	0.383123i	$-0.125152\pi$
$644$		0			0
$645$	28609.0			1.74648
$646$		0			0
$647$	68.8528	+	119.257i	0.00418375	+	0.00724646i	0.868110	−	0.496372i	$-0.165335\pi$
$647$	68.8528	+	119.257i	0.00418375	+	0.00724646i	−0.863926	+	0.503619i	$0.832002\pi$
$648$		0			0
$649$	−2988.81			−0.180772
$650$		0			0
$651$	−24239.6			−1.45933
$652$		0			0
$653$	−8047.59	−	13938.8i	−0.482277	−	0.835328i	0.517516	−	0.855673i	$-0.326857\pi$
$653$	−8047.59	−	13938.8i	−0.482277	−	0.835328i	−0.999793	+	0.0203456i	$0.993523\pi$
$654$		0			0
$655$	19807.2			1.18157
$656$		0			0
$657$	−4088.14	+	7080.87i	−0.242760	+	0.420473i
$658$		0			0
$659$	3527.57	−	6109.93i	0.208520	−	0.361167i	−0.742729	−	0.669593i	$-0.766469\pi$
$659$	3527.57	−	6109.93i	0.208520	−	0.361167i	0.951248	+	0.308426i	$0.0998021\pi$
$660$		0			0
$661$	2021.31	+	3501.02i	0.118941	+	0.206012i	0.919348	−	0.393445i	$-0.128717\pi$
$661$	2021.31	+	3501.02i	0.118941	+	0.206012i	−0.800407	+	0.599457i	$0.795383\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3643.73	+	6311.13i	0.212478	+	0.368022i
$666$		0			0
$667$	−2069.95	+	3585.25i	−0.120163	+	0.208128i
$668$		0			0
$669$	−11699.1	+	20263.4i	−0.676103	+	1.17104i
$670$		0			0
$671$	2461.70			0.141629
$672$		0			0
$673$	−11358.9	−	19674.2i	−0.650598	−	1.12687i	−0.982978	−	0.183724i	$-0.941185\pi$
$673$	−11358.9	−	19674.2i	−0.650598	−	1.12687i	0.332380	−	0.943146i	$-0.392148\pi$
$674$		0			0
$675$	3412.57			0.194592
$676$		0			0
$677$	19237.7			1.09212			0.546058	−	0.837747i	$-0.316128\pi$
$677$	19237.7			1.09212			0.546058	+	0.837747i	$0.316128\pi$
$678$		0			0
$679$	18071.0	+	31299.9i	1.02136	+	1.76904i
$680$		0			0
$681$	−41771.0			−2.35047
$682$		0			0
$683$	12541.5	−	21722.4i	0.702614	−	1.21696i	−0.264932	−	0.964267i	$-0.585349\pi$
$683$	12541.5	−	21722.4i	0.702614	−	1.21696i	0.967546	−	0.252696i	$-0.0813172\pi$
$684$		0			0
$685$	−3448.80	+	5973.50i	−0.192368	+	0.333191i
$686$		0			0
$687$	555.169	+	961.581i	0.0308312	+	0.0534012i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−5630.80	−	9752.83i	−0.309994	−	0.536925i	0.668367	−	0.743832i	$-0.266994\pi$
$691$	−5630.80	−	9752.83i	−0.309994	−	0.536925i	−0.978361	+	0.206907i	$0.933660\pi$
$692$		0			0
$693$	10370.3	−	17961.8i	0.568447	−	0.984579i
$694$		0			0
$695$	−924.755	+	1601.72i	−0.0504719	+	0.0874198i
$696$		0			0
$697$	14830.2			0.805933
$698$		0			0
$699$	−5316.50	−	9208.44i	−0.287680	−	0.498276i
$700$		0			0
$701$	−15678.7			−0.844761			−0.422381	−	0.906419i	$-0.638805\pi$
$701$	−15678.7			−0.844761			−0.422381	+	0.906419i	$0.638805\pi$
$702$		0			0
$703$	5199.25			0.278938
$704$		0			0
$705$	12637.8	+	21889.3i	0.675129	+	1.16936i
$706$		0			0
$707$	38412.4			2.04335
$708$		0			0
$709$	−8797.84	+	15238.3i	−0.466022	+	0.807174i	−0.999247	−	0.0387995i	$-0.987647\pi$
$709$	−8797.84	+	15238.3i	−0.466022	+	0.807174i	0.533225	+	0.845974i	$0.320980\pi$
$710$		0			0
$711$	23497.9	−	40699.6i	1.23944	−	2.14677i
$712$		0			0
$713$	−662.884	−	1148.15i	−0.0348179	−	0.0603064i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−20359.8	−	35264.3i	−1.06046	−	1.83678i
$718$		0			0
$719$	−8305.36	+	14385.3i	−0.430790	+	0.746150i	−0.996942	−	0.0781513i	$-0.975098\pi$
$719$	−8305.36	+	14385.3i	−0.430790	+	0.746150i	0.566152	+	0.824301i	$0.308432\pi$
$720$		0			0
$721$	−22009.8	+	38122.1i	−1.13688	+	1.96913i
$722$		0			0
$723$	56319.1			2.89700
$724$		0			0
$725$	−1898.16	−	3287.71i	−0.0972357	−	0.168417i
$726$		0			0
$727$	−8614.24			−0.439456			−0.219728	−	0.975561i	$-0.570517\pi$
$727$	−8614.24			−0.439456			−0.219728	+	0.975561i	$0.570517\pi$
$728$		0			0
$729$	−21123.1			−1.07317
$730$		0			0
$731$	−12131.1	−	21011.7i	−0.613797	−	1.06313i
$732$		0			0
$733$	−22282.4			−1.12281			−0.561405	−	0.827541i	$-0.689739\pi$
$733$	−22282.4			−1.12281			−0.561405	+	0.827541i	$0.689739\pi$
$734$		0			0
$735$	−36674.3	+	63521.8i	−1.84048	+	3.18781i
$736$		0			0
$737$	1398.57	−	2422.39i	0.0699009	−	0.121072i
$738$		0			0
$739$	13495.0	+	23374.0i	0.671748	+	1.16350i	0.977408	+	0.211361i	$0.0677896\pi$
$739$	13495.0	+	23374.0i	0.671748	+	1.16350i	−0.305660	+	0.952141i	$0.598877\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4605.04	+	7976.16i	0.227379	+	0.393832i	0.957030	−	0.289987i	$-0.0936511\pi$
$743$	4605.04	+	7976.16i	0.227379	+	0.393832i	−0.729652	+	0.683819i	$0.760318\pi$
$744$		0			0
$745$	−7009.12	+	12140.2i	−0.344690	+	0.597021i
$746$		0			0
$747$	5252.32	−	9097.29i	0.257259	−	0.445586i
$748$		0			0
$749$	−55905.1			−2.72727
$750$		0			0
$751$	−11115.8	−	19253.2i	−0.540109	−	0.935496i	−0.998897	−	0.0469505i	$-0.985050\pi$
$751$	−11115.8	−	19253.2i	−0.540109	−	0.935496i	0.458788	−	0.888546i	$-0.348284\pi$
$752$		0			0
$753$	8288.20			0.401114
$754$		0			0
$755$	23882.5			1.15123
$756$		0			0
$757$	10967.4	+	18996.2i	0.526576	+	0.912057i	0.999520	+	0.0309645i	$0.00985788\pi$
$757$	10967.4	+	18996.2i	0.526576	+	0.912057i	−0.472944	+	0.881092i	$0.656809\pi$
$758$		0			0
$759$	1708.83			0.0817215
$760$		0			0
$761$	12119.6	−	20991.7i	0.577311	−	0.999932i	−0.418475	−	0.908228i	$-0.637435\pi$
$761$	12119.6	−	20991.7i	0.577311	−	0.999932i	0.995786	−	0.0917041i	$-0.0292314\pi$
$762$		0			0
$763$	−15232.1	+	26382.7i	−0.722724	+	1.25179i
$764$		0			0
$765$	−28259.3	−	48946.5i	−1.33558	−	2.31329i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	15487.4	+	26825.0i	0.726256	+	1.25791i	0.958455	+	0.285243i	$0.0920745\pi$
$769$	15487.4	+	26825.0i	0.726256	+	1.25791i	−0.232199	+	0.972668i	$0.574592\pi$
$770$		0			0
$771$	2430.56	−	4209.85i	0.113534	−	0.196646i
$772$		0			0
$773$	16088.3	−	27865.7i	0.748583	−	1.29658i	−0.199918	−	0.979813i	$-0.564068\pi$
$773$	16088.3	−	27865.7i	0.748583	−	1.29658i	0.948502	−	0.316772i	$-0.102599\pi$
$774$		0			0
$775$	1215.74			0.0563493
$776$		0			0
$777$	39115.5	+	67750.0i	1.80600	+	3.12808i
$778$		0			0
$779$	3167.59			0.145688
$780$		0			0
$781$	−9060.63			−0.415128
$782$		0			0
$783$	−30945.5	−	53599.2i	−1.41239	−	2.44633i
$784$		0			0
$785$	16886.1			0.767760
$786$		0			0
$787$	13008.6	−	22531.5i	0.589206	−	1.02053i	−0.405131	−	0.914259i	$-0.632774\pi$
$787$	13008.6	−	22531.5i	0.589206	−	1.02053i	0.994337	−	0.106276i	$-0.0338926\pi$
$788$		0			0
$789$	23520.0	−	40737.9i	1.06126	−	1.83816i
$790$		0			0
$791$	−15633.8	−	27078.5i	−0.702747	−	1.21719i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	4989.07	+	8641.32i	0.222571	+	0.385504i
$796$		0			0
$797$	9450.96	−	16369.5i	0.420038	−	0.727527i	−0.575905	−	0.817517i	$-0.695350\pi$
$797$	9450.96	−	16369.5i	0.420038	−	0.727527i	0.995943	+	0.0899897i	$0.0286834\pi$
$798$		0			0
$799$	10717.6	−	18563.5i	0.474546	−	0.821938i
$800$		0			0
$801$	−74147.2			−3.27074
$802$		0			0
$803$	−926.621	−	1604.95i	−0.0407220	−	0.0705325i
$804$		0			0
$805$	−5997.31			−0.262580
$806$		0			0
$807$	−2958.92			−0.129069
$808$		0			0
$809$	−363.787	−	630.098i	−0.0158097	−	0.0273833i	0.858012	−	0.513629i	$-0.171699\pi$
$809$	−363.787	−	630.098i	−0.0158097	−	0.0273833i	−0.873822	+	0.486246i	$0.838366\pi$
$810$		0			0
$811$	−23940.1			−1.03656			−0.518281	−	0.855210i	$-0.673428\pi$
$811$	−23940.1			−1.03656			−0.518281	+	0.855210i	$0.673428\pi$
$812$		0			0
$813$	−6425.26	+	11128.9i	−0.277176	+	0.480082i
$814$		0			0
$815$	6558.46	−	11359.6i	0.281881	−	0.488232i
$816$		0			0
$817$	−2591.08	−	4487.89i	−0.110955	−	0.192180i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3780.69	−	6548.34i	−0.160715	−	0.278366i	0.774410	−	0.632684i	$-0.218047\pi$
$821$	−3780.69	−	6548.34i	−0.160715	−	0.278366i	−0.935125	+	0.354317i	$0.884713\pi$
$822$		0			0
$823$	−10413.0	+	18035.9i	−0.441038	+	0.763901i	−0.997767	−	0.0667938i	$-0.978723\pi$
$823$	−10413.0	+	18035.9i	−0.441038	+	0.763901i	0.556729	+	0.830695i	$0.312056\pi$
$824$		0			0
$825$	−783.506	+	1357.07i	−0.0330645	+	0.0572693i
$826$		0			0
$827$	−34592.6			−1.45454			−0.727268	−	0.686353i	$-0.759210\pi$
$827$	−34592.6			−1.45454			−0.727268	+	0.686353i	$0.759210\pi$
$828$		0			0
$829$	10442.0	+	18086.1i	0.437474	+	0.757727i	0.997494	−	0.0707518i	$-0.0225398\pi$
$829$	10442.0	+	18086.1i	0.437474	+	0.757727i	−0.560020	+	0.828479i	$0.689206\pi$
$830$		0			0
$831$	−19188.5			−0.801011
$832$		0			0
$833$	62204.3			2.58734
$834$		0			0
$835$	−1679.16	−	2908.39i	−0.0695925	−	0.120538i
$836$		0			0
$837$	19820.1			0.818498
$838$		0			0
$839$	21991.7	−	38090.7i	0.904932	−	1.56739i	0.0839231	−	0.996472i	$-0.473255\pi$
$839$	21991.7	−	38090.7i	0.904932	−	1.56739i	0.821009	−	0.570916i	$-0.193412\pi$
$840$		0			0
$841$	−22230.9	+	38505.0i	−0.911513	+	1.57879i
$842$		0			0
$843$	−26245.6	−	45458.7i	−1.07230	−	1.85727i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−19070.1	−	33030.4i	−0.773621	−	1.33995i
$848$		0			0
$849$	7651.35	−	13252.5i	0.309297	−	0.535719i
$850$		0			0
$851$	−2139.39	+	3705.54i	−0.0861779	+	0.149265i
$852$		0			0
$853$	16552.4			0.664412			0.332206	−	0.943207i	$-0.392207\pi$
$853$	16552.4			0.664412			0.332206	+	0.943207i	$0.392207\pi$
$854$		0			0
$855$	−6035.89	−	10454.5i	−0.241431	−	0.418170i
$856$		0			0
$857$	12869.9			0.512983			0.256492	−	0.966546i	$-0.417433\pi$
$857$	12869.9			0.512983			0.256492	+	0.966546i	$0.417433\pi$
$858$		0			0
$859$	21172.2			0.840961			0.420481	−	0.907302i	$-0.361861\pi$
$859$	21172.2			0.840961			0.420481	+	0.907302i	$0.361861\pi$
$860$		0			0
$861$	23830.7	+	41276.0i	0.943261	+	1.63378i
$862$		0			0
$863$	−47889.1			−1.88895			−0.944475	−	0.328584i	$-0.893429\pi$
$863$	−47889.1			−1.88895			−0.944475	+	0.328584i	$0.893429\pi$
$864$		0			0
$865$	25631.8	−	44395.6i	1.00752	−	1.74508i
$866$		0			0
$867$	−14086.2	+	24398.1i	−0.551781	+	0.955712i
$868$		0			0
$869$	5326.05	+	9224.99i	0.207910	+	0.360111i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−29934.9	−	51848.7i	−1.16053	−	2.01010i
$874$		0			0
$875$	−21007.8	+	36386.5i	−0.811648	+	1.40582i
$876$		0			0
$877$	−21792.4	+	37745.6i	−0.839085	+	1.45334i	0.0515750	+	0.998669i	$0.483576\pi$
$877$	−21792.4	+	37745.6i	−0.839085	+	1.45334i	−0.890660	+	0.454669i	$0.849757\pi$
$878$		0			0
$879$	15981.9			0.613262
$880$		0			0
$881$	−21279.2	−	36856.7i	−0.813751	−	1.40946i	−0.910221	−	0.414122i	$-0.864089\pi$
$881$	−21279.2	−	36856.7i	−0.813751	−	1.40946i	0.0964705	−	0.995336i	$-0.469245\pi$
$882$		0			0
$883$	22522.3			0.858364			0.429182	−	0.903218i	$-0.358802\pi$
$883$	22522.3			0.858364			0.429182	+	0.903218i	$0.358802\pi$
$884$		0			0
$885$	−26175.1			−0.994198
$886$		0			0
$887$	3089.40	+	5351.00i	0.116947	+	0.202558i	0.918556	−	0.395290i	$-0.129356\pi$
$887$	3089.40	+	5351.00i	0.116947	+	0.202558i	−0.801609	+	0.597848i	$0.796023\pi$
$888$		0			0
$889$	51623.9			1.94759
$890$		0			0
$891$	−4074.43	+	7057.11i	−0.153197	+	0.265345i
$892$		0			0
$893$	2289.18	−	3964.97i	0.0857832	−	0.148581i
$894$		0			0
$895$	−3842.79	−	6655.92i	−0.143520	−	0.248584i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−11024.5	−	19094.9i	−0.408995	−	0.708399i
$900$		0			0
$901$	4231.04	−	7328.38i	0.156445	−	0.270970i
$902$		0			0
$903$	38987.0	−	67527.4i	1.43677	−	2.48856i
$904$		0			0
$905$	−5363.22			−0.196994
$906$		0			0
$907$	−13077.7	−	22651.3i	−0.478764	−	0.829244i	0.520939	−	0.853594i	$-0.325582\pi$
$907$	−13077.7	−	22651.3i	−0.478764	−	0.829244i	−0.999703	+	0.0243499i	$0.992248\pi$
$908$		0			0
$909$	−63630.8			−2.32178
$910$		0			0
$911$	29386.6			1.06874			0.534369	−	0.845251i	$-0.320549\pi$
$911$	29386.6			1.06874			0.534369	+	0.845251i	$0.320549\pi$
$912$		0			0
$913$	1190.49	+	2062.00i	0.0431540	+	0.0747450i
$914$		0			0
$915$	21558.8			0.778920
$916$		0			0
$917$	26992.3	−	46752.0i	0.972044	−	1.68363i
$918$		0			0
$919$	−11348.9	+	19656.9i	−0.407363	+	0.705573i	−0.994593	−	0.103847i	$-0.966885\pi$
$919$	−11348.9	+	19656.9i	−0.407363	+	0.705573i	0.587231	+	0.809420i	$0.300218\pi$
$920$		0			0
$921$	−18049.0	−	31261.7i	−0.645747	−	1.11847i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1961.84	−	3398.01i	−0.0697351	−	0.120785i
$926$		0			0
$927$	36459.6	−	63149.9i	1.29179	−	2.23745i
$928$		0			0
$929$	−20396.3	+	35327.4i	−0.720324	+	1.24764i	0.240546	+	0.970638i	$0.422673\pi$
$929$	−20396.3	+	35327.4i	−0.720324	+	1.24764i	−0.960870	+	0.277000i	$0.910660\pi$
$930$		0			0
$931$	13286.2			0.467710
$932$		0			0
$933$	−361.309	−	625.806i	−0.0126782	−	0.0219592i
$934$		0			0
$935$	12810.5			0.448074
$936$		0			0
$937$	22015.2			0.767560			0.383780	−	0.923424i	$-0.374622\pi$
$937$	22015.2			0.767560			0.383780	+	0.923424i	$0.374622\pi$
$938$		0			0
$939$	20739.2	+	35921.3i	0.720765	+	1.24840i
$940$		0			0
$941$	−7774.05			−0.269316			−0.134658	−	0.990892i	$-0.542994\pi$
$941$	−7774.05			−0.269316			−0.134658	+	0.990892i	$0.542994\pi$
$942$		0			0
$943$	−1303.40	+	2257.56i	−0.0450102	+	0.0779600i
$944$		0			0
$945$	44829.6	−	77647.1i	1.54318	−	2.67287i
$946$		0			0
$947$	7936.44	+	13746.3i	0.272333	+	0.471695i	0.969459	−	0.245254i	$-0.0788714\pi$
$947$	7936.44	+	13746.3i	0.272333	+	0.471695i	−0.697126	+	0.716949i	$0.745538\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	48051.3	+	83227.3i	1.63845	+	2.83789i
$952$		0			0
$953$	−21907.7	+	37945.3i	−0.744659	+	1.28979i	0.205695	+	0.978616i	$0.434055\pi$
$953$	−21907.7	+	37945.3i	−0.744659	+	1.28979i	−0.950354	+	0.311171i	$0.899279\pi$
$954$		0			0
$955$	16623.6	−	28793.0i	0.563275	−	0.975622i
$956$		0			0
$957$	28419.6			0.959955
$958$		0			0
$959$	9399.73	+	16280.8i	0.316510	+	0.548212i
$960$		0			0
$961$	−22730.0			−0.762983
$962$		0			0
$963$	92607.6			3.09890
$964$		0			0
$965$	−6811.65	−	11798.1i	−0.227228	−	0.393570i
$966$		0			0
$967$	−6323.57			−0.210292			−0.105146	−	0.994457i	$-0.533531\pi$
$967$	−6323.57			−0.210292			−0.105146	+	0.994457i	$0.533531\pi$
$968$		0			0
$969$	−7710.93	+	13355.7i	−0.255635	+	0.442774i
$970$		0			0
$971$	24755.4	−	42877.5i	0.818164	−	1.41710i	−0.0888698	−	0.996043i	$-0.528326\pi$
$971$	24755.4	−	42877.5i	0.818164	−	1.41710i	0.907034	−	0.421058i	$-0.138341\pi$
$972$		0			0
$973$	2520.42	+	4365.50i	0.0830433	+	0.143835i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2827.58	−	4897.51i	−0.0925918	−	0.160374i	0.816009	−	0.578039i	$-0.196182\pi$
$977$	−2827.58	−	4897.51i	−0.0925918	−	0.160374i	−0.908601	+	0.417665i	$0.862848\pi$
$978$		0			0
$979$	8403.12	−	14554.6i	0.274326	−	0.475146i
$980$		0			0
$981$	25232.2	−	43703.4i	0.821204	−	1.42237i
$982$		0			0
$983$	4051.62			0.131461			0.0657307	−	0.997837i	$-0.479062\pi$
$983$	4051.62			0.131461			0.0657307	+	0.997837i	$0.479062\pi$
$984$		0			0
$985$	2401.24	+	4159.07i	0.0776750	+	0.134537i
$986$		0			0
$987$	68888.6			2.22163
$988$		0			0
$989$	4264.73			0.137119
$990$		0			0
$991$	10104.2	+	17500.9i	0.323884	+	0.560984i	0.981286	−	0.192556i	$-0.0616778\pi$
$991$	10104.2	+	17500.9i	0.323884	+	0.560984i	−0.657402	+	0.753540i	$0.728345\pi$
$992$		0			0
$993$	−46535.7			−1.48718
$994$		0			0
$995$	4779.36	−	8278.09i	0.152277	−	0.263752i
$996$		0			0
$997$	23139.1	−	40078.2i	0.735029	−	1.27311i	−0.219681	−	0.975572i	$-0.570502\pi$
$997$	23139.1	−	40078.2i	0.735029	−	1.27311i	0.954711	−	0.297536i	$-0.0961649\pi$
$998$		0			0
$999$	−31983.7	−	55397.4i	−1.01293	−	1.75445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	676.4.e.h.653.2		16
13.2	odd	12		676.4.d.d.337.7		8
13.3	even	3		676.4.a.g.1.8		8
13.4	even	6	inner	676.4.e.h.529.1		16
13.5	odd	4		676.4.h.e.361.1		8
13.6	odd	12		52.4.h.a.17.1	✓	8
13.7	odd	12		676.4.h.e.485.1		8
13.8	odd	4		52.4.h.a.49.1	yes	8
13.9	even	3	inner	676.4.e.h.529.2		16
13.10	even	6		676.4.a.g.1.7		8
13.11	odd	12		676.4.d.d.337.8		8
13.12	even	2	inner	676.4.e.h.653.1		16
39.8	even	4		468.4.t.g.361.2		8
39.32	even	12		468.4.t.g.433.3		8
52.19	even	12		208.4.w.c.17.4		8
52.47	even	4		208.4.w.c.49.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.4.h.a.17.1	✓	8	13.6	odd	12
52.4.h.a.49.1	yes	8	13.8	odd	4
208.4.w.c.17.4		8	52.19	even	12
208.4.w.c.49.4		8	52.47	even	4
468.4.t.g.361.2		8	39.8	even	4
468.4.t.g.433.3		8	39.32	even	12
676.4.a.g.1.7		8	13.10	even	6
676.4.a.g.1.8		8	13.3	even	3
676.4.d.d.337.7		8	13.2	odd	12
676.4.d.d.337.8		8	13.11	odd	12
676.4.e.h.529.1		16	13.4	even	6	inner
676.4.e.h.529.2		16	13.9	even	3	inner
676.4.e.h.653.1		16	13.12	even	2	inner
676.4.e.h.653.2		16	1.1	even	1	trivial
676.4.h.e.361.1		8	13.5	odd	4
676.4.h.e.485.1		8	13.7	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	676.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.48104 - 7.76138i) q^{3} +11.8097 q^{5} +(16.0936 - 27.8750i) q^{7} +(-26.6594 + 46.1754i) q^{9} +(-6.04263 - 10.4661i) q^{11} +(-52.9195 - 91.6593i) q^{15} +(-44.8791 + 77.7328i) q^{17} +(-9.58572 + 16.6029i) q^{19} -288.465 q^{21} +(-7.88869 - 13.6636i) q^{23} +14.4680 q^{25} +235.870 q^{27} +(-131.197 - 227.240i) q^{29} +84.0297 q^{31} +(-54.1544 + 93.7982i) q^{33} +(190.060 - 329.194i) q^{35} +(-135.599 - 234.864i) q^{37} +(-82.6122 - 143.088i) q^{41} +(-135.153 + 234.092i) q^{43} +(-314.838 + 545.315i) q^{45} -238.811 q^{47} +(-346.511 - 600.174i) q^{49} +804.419 q^{51} -94.2765 q^{53} +(-71.3613 - 123.601i) q^{55} +171.816 q^{57} +(123.655 - 214.177i) q^{59} +(-101.847 + 176.404i) q^{61} +(858.092 + 1486.26i) q^{63} +(115.725 + 200.442i) q^{67} +(-70.6990 + 122.454i) q^{69} +(374.863 - 649.282i) q^{71} +153.347 q^{73} +(-64.8316 - 112.292i) q^{75} -388.991 q^{77} -881.413 q^{79} +(-337.140 - 583.944i) q^{81} -197.016 q^{83} +(-530.006 + 917.998i) q^{85} +(-1175.80 + 2036.54i) q^{87} +(695.321 + 1204.33i) q^{89} +(-376.540 - 652.186i) q^{93} +(-113.204 + 196.075i) q^{95} +(-561.433 + 972.430i) q^{97} +644.370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 140 q^{9} - 176 q^{17} + 40 q^{23} + 168 q^{25} - 864 q^{27} - 968 q^{29} + 80 q^{35} - 1008 q^{43} - 1844 q^{49} + 3616 q^{51} - 2328 q^{53} - 2256 q^{55} - 2448 q^{61} - 3476 q^{69} - 2896 q^{75}+ \cdots - 4800 q^{95}+O(q^{100}) \) 16 * q - 140 * q^9 - 176 * q^17 + 40 * q^23 + 168 * q^25 - 864 * q^27 - 968 * q^29 + 80 * q^35 - 1008 * q^43 - 1844 * q^49 + 3616 * q^51 - 2328 * q^53 - 2256 * q^55 - 2448 * q^61 - 3476 * q^69 - 2896 * q^75 + 7944 * q^77 - 7936 * q^79 - 8264 * q^81 - 3320 * q^87 - 4800 * q^95

Introduction

L-functions

Modular forms

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Representations

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Database

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