LMFDB - Embedded newform 736.2.r.a.527.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [736,2,Mod(15,736)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(736, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 17]))

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

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

chi := DirichletCharacter("736.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 736 = 2^{5} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	736.r (of order $22$, degree $10$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.87698958877$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	no (minimal twist has level 184)
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			527.11
Character	$\chi$	$=$	736.527
Dual form			736.2.r.a.655.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.00352593 - 0.0245234i) q^{3} +(-3.56863 - 1.04785i) q^{5} +(-1.35535 + 1.56416i) q^{7} +(2.87789 - 0.845025i) q^{9} +O(q^{10})$	\(q+(-0.00352593 - 0.0245234i) q^{3} +(-3.56863 - 1.04785i) q^{5} +(-1.35535 + 1.56416i) q^{7} +(2.87789 - 0.845025i) q^{9} +(1.98812 + 3.09358i) q^{11} +(2.32067 - 2.01087i) q^{13} +(-0.0131140 + 0.0912096i) q^{15} +(-3.89631 - 1.77939i) q^{17} +(1.30211 - 0.594653i) q^{19} +(0.0431373 + 0.0277227i) q^{21} +(2.42579 + 4.13709i) q^{23} +(7.43090 + 4.77555i) q^{25} +(-0.0617465 - 0.135206i) q^{27} +(2.72932 + 1.24644i) q^{29} +(6.07375 + 0.873274i) q^{31} +(0.0688551 - 0.0596633i) q^{33} +(6.47575 - 4.16171i) q^{35} +(7.98668 - 2.34510i) q^{37} +(-0.0574960 - 0.0498206i) q^{39} +(7.37673 + 2.16600i) q^{41} +(7.98064 - 1.14744i) q^{43} -11.1556 q^{45} -3.26843i q^{47} +(0.386588 + 2.68878i) q^{49} +(-0.0298984 + 0.101825i) q^{51} +(-0.700256 + 0.808138i) q^{53} +(-3.85329 - 13.1231i) q^{55} +(-0.0191741 - 0.0298354i) q^{57} +(0.117997 + 0.136175i) q^{59} +(-0.643931 + 4.47864i) q^{61} +(-2.57880 + 5.64678i) q^{63} +(-10.3887 + 4.74437i) q^{65} +(-7.25750 + 11.2929i) q^{67} +(0.0929024 - 0.0740756i) q^{69} +(-4.86718 + 7.57348i) q^{71} +(-4.65097 - 10.1842i) q^{73} +(0.0909118 - 0.199069i) q^{75} +(-7.53346 - 1.08315i) q^{77} +(-8.76095 - 10.1107i) q^{79} +(7.56663 - 4.86278i) q^{81} +(-3.37850 - 11.5061i) q^{83} +(12.0400 + 10.4327i) q^{85} +(0.0209435 - 0.0713271i) q^{87} +(4.45134 - 0.640006i) q^{89} +6.35534i q^{91} -0.152028i q^{93} +(-5.26985 + 0.757691i) q^{95} +(2.42428 - 8.25634i) q^{97} +(8.33575 + 7.22297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 18 q^{3} - 36 q^{9}+O(q^{10}) $ 220 * q + 18 * q^3 - 36 * q^9	$ 220 q + 18 q^{3} - 36 q^{9} + 22 q^{11} - 22 q^{17} + 22 q^{19} - 32 q^{25} + 18 q^{27} - 22 q^{33} - 2 q^{35} - 18 q^{41} + 22 q^{43} - 28 q^{49} + 22 q^{51} - 22 q^{57} + 6 q^{59} - 22 q^{65} + 22 q^{67} - 18 q^{73} - 14 q^{75} + 4 q^{81} + 22 q^{83} - 22 q^{89} - 22 q^{97} + 22 q^{99}+O(q^{100}) $ 220 * q + 18 * q^3 - 36 * q^9 + 22 * q^11 - 22 * q^17 + 22 * q^19 - 32 * q^25 + 18 * q^27 - 22 * q^33 - 2 * q^35 - 18 * q^41 + 22 * q^43 - 28 * q^49 + 22 * q^51 - 22 * q^57 + 6 * q^59 - 22 * q^65 + 22 * q^67 - 18 * q^73 - 14 * q^75 + 4 * q^81 + 22 * q^83 - 22 * q^89 - 22 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/736\mathbb{Z}\right)^\times$.

$n$	$97$	$415$	$645$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$-1$	$-1$

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			0
$2$		0			0
$3$	−0.00352593	−	0.0245234i	−0.00203570	−	0.0141586i	0.988778	−	0.149390i	$-0.0477311\pi$
$3$	−0.00352593	−	0.0245234i	−0.00203570	−	0.0141586i	−0.990814	+	0.135232i	$0.956822\pi$
$4$		0			0
$5$	−3.56863	−	1.04785i	−1.59594	−	0.468611i	−0.641528	−	0.767099i	$-0.721699\pi$
$5$	−3.56863	−	1.04785i	−1.59594	−	0.468611i	−0.954413	+	0.298489i	$0.903518\pi$
$6$		0			0
$7$	−1.35535	+	1.56416i	−0.512275	+	0.591196i	−0.951680	−	0.307093i	$-0.900644\pi$
$7$	−1.35535	+	1.56416i	−0.512275	+	0.591196i	0.439405	+	0.898289i	$0.355189\pi$
$8$		0			0
$9$	2.87789	−	0.845025i	0.959297	−	0.281675i
$10$		0			0
$11$	1.98812	+	3.09358i	0.599442	+	0.932750i	0.999865	+	0.0164194i	$0.00522669\pi$
$11$	1.98812	+	3.09358i	0.599442	+	0.932750i	−0.400423	+	0.916330i	$0.631137\pi$
$12$		0			0
$13$	2.32067	−	2.01087i	0.643639	−	0.557716i	−0.270701	−	0.962663i	$-0.587256\pi$
$13$	2.32067	−	2.01087i	0.643639	−	0.557716i	0.914340	+	0.404947i	$0.132710\pi$
$14$		0			0
$15$	−0.0131140	+	0.0912096i	−0.00338601	+	0.0235502i
$16$		0			0
$17$	−3.89631	−	1.77939i	−0.944994	−	0.431564i	−0.117522	−	0.993070i	$-0.537495\pi$
$17$	−3.89631	−	1.77939i	−0.944994	−	0.431564i	−0.827473	+	0.561506i	$0.810222\pi$
$18$		0			0
$19$	1.30211	−	0.594653i	0.298724	−	0.136423i	−0.260414	−	0.965497i	$-0.583859\pi$
$19$	1.30211	−	0.594653i	0.298724	−	0.136423i	0.559139	+	0.829074i	$0.311132\pi$
$20$		0			0
$21$	0.0431373	+	0.0277227i	0.00941334	+	0.00604959i
$22$		0			0
$23$	2.42579	+	4.13709i	0.505812	+	0.862644i
$23$	2.42579	+	4.13709i	0.505812	+	0.862644i
$24$		0			0
$25$	7.43090	+	4.77555i	1.48618	+	0.955110i
$26$		0			0
$27$	−0.0617465	−	0.135206i	−0.0118831	−	0.0260204i
$28$		0			0
$29$	2.72932	+	1.24644i	0.506822	+	0.231458i	0.652380	−	0.757892i	$-0.273770\pi$
$29$	2.72932	+	1.24644i	0.506822	+	0.231458i	−0.145558	+	0.989350i	$0.546498\pi$
$30$		0			0
$31$	6.07375	+	0.873274i	1.09088	+	0.156845i	0.664197	−	0.747558i	$-0.268774\pi$
$31$	6.07375	+	0.873274i	1.09088	+	0.156845i	0.426681	+	0.904402i	$0.359683\pi$
$32$		0			0
$33$	0.0688551	−	0.0596633i	0.0119861	−	0.0103860i
$34$		0			0
$35$	6.47575	−	4.16171i	1.09460	−	0.703458i
$36$		0			0
$37$	7.98668	−	2.34510i	1.31300	−	0.385532i	0.451039	−	0.892504i	$-0.351053\pi$
$37$	7.98668	−	2.34510i	1.31300	−	0.385532i	0.861962	+	0.506972i	$0.169235\pi$
$38$		0			0
$39$	−0.0574960	−	0.0498206i	−0.00920673	−	0.00797767i
$40$		0			0
$41$	7.37673	+	2.16600i	1.15205	+	0.338273i	0.801339	−	0.598210i	$-0.204121\pi$
$41$	7.37673	+	2.16600i	1.15205	+	0.338273i	0.350713	+	0.936483i	$0.385939\pi$
$42$		0			0
$43$	7.98064	−	1.14744i	1.21704	−	0.174983i	0.496274	−	0.868166i	$-0.334701\pi$
$43$	7.98064	−	1.14744i	1.21704	−	0.174983i	0.720762	+	0.693182i	$0.243792\pi$
$44$		0			0
$45$	−11.1556			−1.66298
$46$		0			0
$47$		−	3.26843i		−	0.476749i	−0.971173	−	0.238375i	$-0.923385\pi$
$47$		−	3.26843i		−	0.476749i	0.971173	−	0.238375i	$-0.0766146\pi$
$48$		0			0
$49$	0.386588	+	2.68878i	0.0552269	+	0.384112i
$50$		0			0
$51$	−0.0298984	+	0.101825i	−0.00418662	+	0.0142583i
$52$		0			0
$53$	−0.700256	+	0.808138i	−0.0961876	+	0.111006i	−0.801802	−	0.597589i	$-0.796125\pi$
$53$	−0.700256	+	0.808138i	−0.0961876	+	0.111006i	0.705615	+	0.708595i	$0.250671\pi$
$54$		0			0
$55$	−3.85329	−	13.1231i	−0.519578	−	1.76952i
$56$		0			0
$57$	−0.0191741	−	0.0298354i	−0.00253967	−	0.00395180i
$58$		0			0
$59$	0.117997	+	0.136175i	0.0153619	+	0.0177285i	0.763379	−	0.645951i	$-0.223539\pi$
$59$	0.117997	+	0.136175i	0.0153619	+	0.0177285i	−0.748017	+	0.663680i	$0.768994\pi$
$60$		0			0
$61$	−0.643931	+	4.47864i	−0.0824469	+	0.573431i	0.906163	+	0.422929i	$0.138998\pi$
$61$	−0.643931	+	4.47864i	−0.0824469	+	0.573431i	−0.988610	+	0.150502i	$0.951911\pi$
$62$		0			0
$63$	−2.57880	+	5.64678i	−0.324898	+	0.711428i
$64$		0			0
$65$	−10.3887	+	4.74437i	−1.28856	+	0.588467i
$66$		0			0
$67$	−7.25750	+	11.2929i	−0.886645	+	1.37965i	0.0381865	+	0.999271i	$0.487842\pi$
$67$	−7.25750	+	11.2929i	−0.886645	+	1.37965i	−0.924832	+	0.380376i	$0.875794\pi$
$68$		0			0
$69$	0.0929024	−	0.0740756i	0.0111841	−	0.00891766i
$70$		0			0
$71$	−4.86718	+	7.57348i	−0.577628	+	0.898806i	−0.999971	−	0.00762975i	$-0.997571\pi$
$71$	−4.86718	+	7.57348i	−0.577628	+	0.898806i	0.422343	+	0.906436i	$0.361208\pi$
$72$		0			0
$73$	−4.65097	−	10.1842i	−0.544355	−	1.19197i	−0.959369	−	0.282155i	$-0.908951\pi$
$73$	−4.65097	−	10.1842i	−0.544355	−	1.19197i	0.415014	−	0.909815i	$-0.363777\pi$
$74$		0			0
$75$	0.0909118	−	0.199069i	0.0104976	−	0.0229865i
$76$		0			0
$77$	−7.53346	−	1.08315i	−0.858517	−	0.123436i
$78$		0			0
$79$	−8.76095	−	10.1107i	−0.985684	−	1.13754i	−0.990495	−	0.137551i	$-0.956077\pi$
$79$	−8.76095	−	10.1107i	−0.985684	−	1.13754i	0.00481112	−	0.999988i	$-0.498469\pi$
$80$		0			0
$81$	7.56663	−	4.86278i	0.840737	−	0.540309i
$82$		0			0
$83$	−3.37850	−	11.5061i	−0.370838	−	1.26296i	−0.907818	−	0.419364i	$-0.862253\pi$
$83$	−3.37850	−	11.5061i	−0.370838	−	1.26296i	0.536980	−	0.843595i	$-0.319565\pi$
$84$		0			0
$85$	12.0400	+	10.4327i	1.30592	+	1.13159i
$86$		0			0
$87$	0.0209435	−	0.0713271i	0.00224538	−	0.00764707i
$88$		0			0
$89$	4.45134	−	0.640006i	0.471841	−	0.0678405i	0.0977072	−	0.995215i	$-0.468849\pi$
$89$	4.45134	−	0.640006i	0.471841	−	0.0678405i	0.374134	+	0.927375i	$0.377940\pi$
$90$		0			0
$91$			6.35534i			0.666221i
$92$		0			0
$93$		−	0.152028i		−	0.0157646i
$94$		0			0
$95$	−5.26985	+	0.757691i	−0.540676	+	0.0777374i
$96$		0			0
$97$	2.42428	−	8.25634i	0.246148	−	0.838304i	−0.740024	−	0.672580i	$-0.765186\pi$
$97$	2.42428	−	8.25634i	0.246148	−	0.838304i	0.986172	−	0.165724i	$-0.0529959\pi$
$98$		0			0
$99$	8.33575	+	7.22297i	0.837775	+	0.725936i
$100$		0			0
$101$	3.68978	+	12.5663i	0.367147	+	1.25039i	0.911419	+	0.411480i	$0.134988\pi$
$101$	3.68978	+	12.5663i	0.367147	+	1.25039i	−0.544272	+	0.838909i	$0.683194\pi$
$102$		0			0
$103$	6.11533	−	3.93009i	0.602562	−	0.387243i	−0.203499	−	0.979075i	$-0.565232\pi$
$103$	6.11533	−	3.93009i	0.602562	−	0.387243i	0.806061	+	0.591832i	$0.201595\pi$
$104$		0			0
$105$	−0.124892	−	0.144133i	−0.0121882	−	0.0140660i
$106$		0			0
$107$	−14.1244	−	2.03079i	−1.36546	−	0.196324i	−0.579688	−	0.814839i	$-0.696825\pi$
$107$	−14.1244	−	2.03079i	−1.36546	−	0.196324i	−0.785773	+	0.618515i	$0.787735\pi$
$108$		0			0
$109$	0.241840	−	0.529556i	0.0231641	−	0.0507222i	−0.897696	−	0.440615i	$-0.854761\pi$
$109$	0.241840	−	0.529556i	0.0231641	−	0.0507222i	0.920860	+	0.389892i	$0.127488\pi$
$110$		0			0
$111$	−0.0856703	−	0.187592i	−0.00813146	−	0.0178054i
$112$		0			0
$113$	−9.73384	+	15.1462i	−0.915683	+	1.42483i	−0.0104355	+	0.999946i	$0.503322\pi$
$113$	−9.73384	+	15.1462i	−0.915683	+	1.42483i	−0.905247	+	0.424885i	$0.860315\pi$
$114$		0			0
$115$	−4.32171	−	17.3056i	−0.403002	−	1.61376i
$116$		0			0
$117$	4.97940	−	7.74810i	0.460346	−	0.716312i
$118$		0			0
$119$	8.06411	−	3.68276i	0.739236	−	0.337598i
$120$		0			0
$121$	−1.04804	+	2.29489i	−0.0952764	+	0.208626i
$122$		0			0
$123$	0.0271079	−	0.188540i	0.00244424	−	0.0170001i
$124$		0			0
$125$	−9.33603	−	10.7744i	−0.835040	−	0.963688i
$126$		0			0
$127$	4.90050	+	7.62533i	0.434849	+	0.676638i	0.987650	−	0.156675i	$-0.0500775\pi$
$127$	4.90050	+	7.62533i	0.434849	+	0.676638i	−0.552801	+	0.833313i	$0.686441\pi$
$128$		0			0
$129$	−0.0562784	−	0.191667i	−0.00495504	−	0.0168753i
$130$		0			0
$131$	−12.9101	+	14.8991i	−1.12796	+	1.30174i	−0.179889	+	0.983687i	$0.557574\pi$
$131$	−12.9101	+	14.8991i	−1.12796	+	1.30174i	−0.948074	+	0.318051i	$0.896972\pi$
$132$		0			0
$133$	−0.834683	+	2.84267i	−0.0723762	+	0.246491i
$134$		0			0
$135$	0.0786757	+	0.547202i	0.00677133	+	0.0470956i
$136$		0			0
$137$		−	0.641072i		−	0.0547705i	−0.999625	−	0.0273852i	$-0.991282\pi$
$137$		−	0.641072i		−	0.0547705i	0.999625	−	0.0273852i	$-0.00871808\pi$
$138$		0			0
$139$	6.83879			0.580059			0.290029	−	0.957018i	$-0.406335\pi$
$139$	6.83879			0.580059			0.290029	+	0.957018i	$0.406335\pi$
$140$		0			0
$141$	−0.0801529	+	0.0115243i	−0.00675009	+	0.000970517i
$142$		0			0
$143$	10.8346	+	3.18132i	0.906034	+	0.266036i
$144$		0			0
$145$	−8.43388	−	7.30800i	−0.700395	−	0.606896i
$146$		0			0
$147$	0.0645749	−	0.0189609i	0.00532605	−	0.00156387i
$148$		0			0
$149$	12.3750	−	7.95290i	1.01380	−	0.651527i	0.0754232	−	0.997152i	$-0.475969\pi$
$149$	12.3750	−	7.95290i	1.01380	−	0.651527i	0.938373	+	0.345624i	$0.112333\pi$
$150$		0			0
$151$	5.39215	−	4.67232i	0.438807	−	0.380228i	−0.407254	−	0.913315i	$-0.633514\pi$
$151$	5.39215	−	4.67232i	0.438807	−	0.380228i	0.846060	+	0.533087i	$0.178968\pi$
$152$		0			0
$153$	−12.7168	−	1.82840i	−1.02809	−	0.147817i
$154$		0			0
$155$	−20.7599	−	9.48075i	−1.66748	−	0.761512i
$156$		0			0
$157$	−2.49078	−	5.45405i	−0.198786	−	0.435281i	0.783819	−	0.620990i	$-0.213269\pi$
$157$	−2.49078	−	5.45405i	−0.198786	−	0.435281i	−0.982605	+	0.185709i	$0.940542\pi$
$158$		0			0
$159$	0.0222873	+	0.0143232i	0.00176750	+	0.00113590i
$160$		0			0
$161$	−9.75887	−	1.81290i	−0.769106	−	0.142877i
$162$		0			0
$163$	15.6529	+	10.0595i	1.22603	+	0.787923i	0.983268	−	0.182162i	$-0.0583096\pi$
$163$	15.6529	+	10.0595i	1.22603	+	0.787923i	0.242764	+	0.970085i	$0.421946\pi$
$164$		0			0
$165$	−0.308236	+	0.140767i	−0.0239962	+	0.0109587i
$166$		0			0
$167$	4.75934	+	2.17352i	0.368289	+	0.168192i	0.590958	−	0.806702i	$-0.298750\pi$
$167$	4.75934	+	2.17352i	0.368289	+	0.168192i	−0.222670	+	0.974894i	$0.571477\pi$
$168$		0			0
$169$	−0.508186	+	3.53451i	−0.0390912	+	0.271886i
$170$		0			0
$171$	3.24483	−	2.81166i	0.248138	−	0.215013i
$172$		0			0
$173$	−5.75876	−	8.96080i	−0.437830	−	0.681277i	0.550288	−	0.834975i	$-0.314518\pi$
$173$	−5.75876	−	8.96080i	−0.437830	−	0.681277i	−0.988118	+	0.153698i	$0.950882\pi$
$174$		0			0
$175$	−17.5412	+	5.15056i	−1.32599	+	0.389346i
$176$		0			0
$177$	0.00292343	−	0.00337382i	0.000219739	−	0.000253592i
$178$		0			0
$179$	−8.77433	−	2.57638i	−0.655824	−	0.192567i	−0.0631431	−	0.998004i	$-0.520112\pi$
$179$	−8.77433	−	2.57638i	−0.655824	−	0.192567i	−0.592681	+	0.805437i	$0.701931\pi$
$180$		0			0
$181$	1.59976	+	11.1266i	0.118910	+	0.827034i	0.958760	+	0.284216i	$0.0917334\pi$
$181$	1.59976	+	11.1266i	0.118910	+	0.827034i	−0.839851	+	0.542818i	$0.817358\pi$
$182$		0			0
$183$	0.112102			0.00828681
$184$		0			0
$185$	−30.9588			−2.27614
$186$		0			0
$187$	−2.24168	−	15.5912i	−0.163928	−	1.14014i
$188$		0			0
$189$	0.295172	+	0.0866703i	0.0214706	+	0.00630434i
$190$		0			0
$191$	6.34859	−	7.32666i	0.459368	−	0.530138i	−0.478056	−	0.878329i	$-0.658658\pi$
$191$	6.34859	−	7.32666i	0.459368	−	0.530138i	0.937424	+	0.348191i	$0.113204\pi$
$192$		0			0
$193$	17.2501	−	5.06508i	1.24169	−	0.364593i	0.406039	−	0.913856i	$-0.366910\pi$
$193$	17.2501	−	5.06508i	1.24169	−	0.364593i	0.835649	+	0.549263i	$0.185092\pi$
$194$		0			0
$195$	0.152978	+	0.238038i	0.0109550	+	0.0170463i
$196$		0			0
$197$	3.86285	−	3.34718i	0.275216	−	0.238476i	−0.506305	−	0.862354i	$-0.668989\pi$
$197$	3.86285	−	3.34718i	0.275216	−	0.238476i	0.781522	+	0.623878i	$0.214444\pi$
$198$		0			0
$199$	−3.64001	+	25.3168i	−0.258033	+	1.79466i	0.288767	+	0.957399i	$0.406755\pi$
$199$	−3.64001	+	25.3168i	−0.258033	+	1.79466i	−0.546801	+	0.837263i	$0.684154\pi$
$200$		0			0
$201$	0.302530	+	0.138161i	0.0213388	+	0.00974510i
$202$		0			0
$203$	−5.64882	+	2.57973i	−0.396469	+	0.181062i
$204$		0			0
$205$	−24.0552	−	15.4594i	−1.68009	−	1.07973i
$206$		0			0
$207$	10.4771	+	9.85625i	0.728209	+	0.685057i
$208$		0			0
$209$	4.42836	+	2.84593i	0.306316	+	0.196857i
$210$		0			0
$211$	−7.55252	−	16.5377i	−0.519937	−	1.13850i	−0.969464	−	0.245236i	$-0.921135\pi$
$211$	−7.55252	−	16.5377i	−0.519937	−	1.13850i	0.449527	−	0.893267i	$-0.351593\pi$
$212$		0			0
$213$	0.202889	+	0.0926561i	0.0139017	+	0.00634869i
$214$		0			0
$215$	−29.6823	−	4.26768i	−2.02432	−	0.291053i
$216$		0			0
$217$	−9.59800	+	8.31672i	−0.651555	+	0.564576i
$218$		0			0
$219$	−0.233352	+	0.149966i	−0.0157685	+	0.0101338i
$220$		0			0
$221$	−12.6202	+	3.70562i	−0.848926	+	0.249267i
$222$		0			0
$223$	−4.71647	−	4.08684i	−0.315838	−	0.273675i	0.482486	−	0.875904i	$-0.339734\pi$
$223$	−4.71647	−	4.08684i	−0.315838	−	0.273675i	−0.798324	+	0.602229i	$0.794280\pi$
$224$		0			0
$225$	25.4208	+	7.46421i	1.69472	+	0.497614i
$226$		0			0
$227$	5.20890	−	0.748927i	0.345727	−	0.0497080i	0.0327356	−	0.999464i	$-0.489578\pi$
$227$	5.20890	−	0.748927i	0.345727	−	0.0497080i	0.312991	+	0.949756i	$0.398669\pi$
$228$		0			0
$229$	9.33871			0.617119			0.308560	−	0.951205i	$-0.400153\pi$
$229$	9.33871			0.617119			0.308560	+	0.951205i	$0.400153\pi$
$230$		0			0
$231$			0.188565i			0.0124067i
$232$		0			0
$233$	−0.196034	−	1.36345i	−0.0128426	−	0.0893225i	0.982392	−	0.186831i	$-0.0598217\pi$
$233$	−0.196034	−	1.36345i	−0.0128426	−	0.0893225i	−0.995235	+	0.0975087i	$0.968913\pi$
$234$		0			0
$235$	−3.42481	+	11.6638i	−0.223410	+	0.760864i
$236$		0			0
$237$	−0.217057	+	0.250498i	−0.0140994	+	0.0162716i
$238$		0			0
$239$	1.95869	+	6.67067i	0.126697	+	0.431490i	0.998271	−	0.0587731i	$-0.0187188\pi$
$239$	1.95869	+	6.67067i	0.126697	+	0.431490i	−0.871574	+	0.490263i	$0.836901\pi$
$240$		0			0
$241$	3.22788	+	5.02269i	0.207926	+	0.323540i	0.929516	−	0.368781i	$-0.120225\pi$
$241$	3.22788	+	5.02269i	0.207926	+	0.323540i	−0.721590	+	0.692321i	$0.756588\pi$
$242$		0			0
$243$	−0.437943	−	0.505413i	−0.0280941	−	0.0324223i
$244$		0			0
$245$	1.43783	−	10.0004i	0.0918599	−	0.638900i
$246$		0			0
$247$	1.82600	−	3.99837i	0.116185	−	0.254410i
$248$		0			0
$249$	−0.270256	+	0.123422i	−0.0171268	+	0.00782155i
$250$		0			0
$251$	3.41213	−	5.30938i	0.215372	−	0.335125i	−0.716711	−	0.697370i	$-0.754353\pi$
$251$	3.41213	−	5.30938i	0.215372	−	0.335125i	0.932083	+	0.362245i	$0.117990\pi$
$252$		0			0
$253$	−7.97567	+	15.7294i	−0.501426	+	0.988900i
$254$		0			0
$255$	0.213393	−	0.332046i	0.0133632	−	0.0207935i
$256$		0			0
$257$	−7.57027	−	16.5766i	−0.472220	−	1.03402i	−0.984530	−	0.175217i	$-0.943937\pi$
$257$	−7.57027	−	16.5766i	−0.472220	−	1.03402i	0.512309	−	0.858801i	$-0.328790\pi$
$258$		0			0
$259$	−7.15664	+	15.6709i	−0.444692	+	0.973740i
$260$		0			0
$261$	8.90796	+	1.28077i	0.551389	+	0.0792778i
$262$		0			0
$263$	7.99883	+	9.23114i	0.493229	+	0.569217i	0.946726	−	0.322041i	$-0.104369\pi$
$263$	7.99883	+	9.23114i	0.493229	+	0.569217i	−0.453497	+	0.891258i	$0.649824\pi$
$264$		0			0
$265$	3.34576	−	2.15019i	0.205528	−	0.132085i
$266$		0			0
$267$	−0.0313902	−	0.106905i	−0.00192105	−	0.00654250i
$268$		0			0
$269$	2.83160	+	2.45359i	0.172646	+	0.149598i	0.736898	−	0.676004i	$-0.236290\pi$
$269$	2.83160	+	2.45359i	0.172646	+	0.149598i	−0.564252	+	0.825603i	$0.690835\pi$
$270$		0			0
$271$	8.24323	−	28.0739i	0.500741	−	1.70537i	−0.189583	−	0.981865i	$-0.560714\pi$
$271$	8.24323	−	28.0739i	0.500741	−	1.70537i	0.690323	−	0.723501i	$-0.257468\pi$
$272$		0			0
$273$	0.155855	−	0.0224085i	0.00943275	−	0.00135622i
$274$		0			0
$275$			32.4825i			1.95877i
$276$		0			0
$277$			15.0045i			0.901535i	0.892641	+	0.450767i	$0.148850\pi$
$277$			15.0045i			0.901535i	−0.892641	+	0.450767i	$0.851150\pi$
$278$		0			0
$279$	18.2175	−	2.61928i	1.09065	−	0.156812i
$280$		0			0
$281$	5.48845	−	18.6920i	0.327414	−	1.11507i	−0.617179	−	0.786823i	$-0.711724\pi$
$281$	5.48845	−	18.6920i	0.327414	−	1.11507i	0.944592	−	0.328245i	$-0.106457\pi$
$282$		0			0
$283$	14.8941	+	12.9058i	0.885360	+	0.767169i	0.973439	−	0.228945i	$-0.0735274\pi$
$283$	14.8941	+	12.9058i	0.885360	+	0.767169i	−0.0880793	+	0.996113i	$0.528073\pi$
$284$		0			0
$285$	0.0371623	+	0.126563i	0.00220130	+	0.00749695i
$286$		0			0
$287$	−13.3860	+	8.60269i	−0.790153	+	0.507800i
$288$		0			0
$289$	0.882399	+	1.01834i	0.0519058	+	0.0599025i
$290$		0			0
$291$	−0.211021	−	0.0303403i	−0.0123703	−	0.00177858i
$292$		0			0
$293$	1.62805	−	3.56494i	0.0951118	−	0.208266i	−0.856096	−	0.516817i	$-0.827117\pi$
$293$	1.62805	−	3.56494i	0.0951118	−	0.208266i	0.951208	+	0.308551i	$0.0998441\pi$
$294$		0			0
$295$	−0.278396	−	0.609602i	−0.0162088	−	0.0354924i
$296$		0			0
$297$	0.295511	−	0.459824i	0.0171473	−	0.0266817i
$298$		0			0
$299$	13.9486	+	4.72289i	0.806671	+	0.273132i
$300$		0			0
$301$	−9.02179	+	14.0382i	−0.520007	+	0.809147i
$302$		0			0
$303$	0.295157	−	0.134794i	0.0169563	−	0.00774370i
$304$		0			0
$305$	6.99087	−	15.3079i	0.400296	−	0.876527i
$306$		0			0
$307$	2.76475	−	19.2293i	0.157793	−	1.09747i	−0.744897	−	0.667179i	$-0.767501\pi$
$307$	2.76475	−	19.2293i	0.157793	−	1.09747i	0.902690	−	0.430292i	$-0.141590\pi$
$308$		0			0
$309$	−0.117941	−	0.136112i	−0.00670945	−	0.00774311i
$310$		0			0
$311$	−6.50617	−	10.1238i	−0.368931	−	0.574068i	0.606305	−	0.795232i	$-0.292651\pi$
$311$	−6.50617	−	10.1238i	−0.368931	−	0.574068i	−0.975237	+	0.221164i	$0.929015\pi$
$312$		0			0
$313$	4.08787	+	13.9220i	0.231060	+	0.786919i	0.990640	+	0.136504i	$0.0435866\pi$
$313$	4.08787	+	13.9220i	0.231060	+	0.786919i	−0.759579	+	0.650415i	$0.774595\pi$
$314$		0			0
$315$	15.1197	−	17.4491i	0.851901	−	0.983146i
$316$		0			0
$317$	9.43485	−	32.1321i	0.529914	−	1.80472i	−0.0611907	−	0.998126i	$-0.519490\pi$
$317$	9.43485	−	32.1321i	0.529914	−	1.80472i	0.591105	−	0.806595i	$-0.298692\pi$
$318$		0			0
$319$	1.57027	+	10.9215i	0.0879181	+	0.611484i
$320$		0			0
$321$			0.353539i			0.0197326i
$322$		0			0
$323$	−6.13154			−0.341168
$324$		0			0
$325$	26.8477	−	3.86012i	1.48924	−	0.214121i
$326$		0			0
$327$	−0.0138392	−	0.00406356i	−0.000765310	−	0.000224715i
$328$		0			0
$329$	5.11234	+	4.42987i	0.281852	+	0.244227i
$330$		0			0
$331$	−8.24268	+	2.42027i	−0.453059	+	0.133030i	−0.500298	−	0.865854i	$-0.666776\pi$
$331$	−8.24268	+	2.42027i	−0.453059	+	0.133030i	0.0472387	+	0.998884i	$0.484958\pi$
$332$		0			0
$333$	21.0031	−	13.4979i	1.15096	−	0.739679i
$334$		0			0
$335$	37.7326	−	32.6955i	2.06155	−	1.78634i
$336$		0			0
$337$	10.7870	+	1.55094i	0.587607	+	0.0844851i	0.429705	−	0.902970i	$-0.358618\pi$
$337$	10.7870	+	1.55094i	0.587607	+	0.0844851i	0.157903	+	0.987455i	$0.449527\pi$
$338$		0			0
$339$	0.405756	+	0.185302i	0.0220376	+	0.0100643i
$340$		0			0
$341$	9.37382	+	20.5258i	0.507621	+	1.11154i
$342$		0			0
$343$	−16.9175	−	10.8722i	−0.913460	−	0.587045i
$344$		0			0
$345$	−0.409155	+	0.167001i	−0.0220281	+	0.00899106i
$346$		0			0
$347$	−15.2769	−	9.81786i	−0.820107	−	0.527051i	0.0620134	−	0.998075i	$-0.480248\pi$
$347$	−15.2769	−	9.81786i	−0.820107	−	0.527051i	−0.882120	+	0.471025i	$0.843884\pi$
$348$		0			0
$349$	−19.1617	+	8.75087i	−1.02570	+	0.468423i	−0.855948	−	0.517063i	$-0.827025\pi$
$349$	−19.1617	+	8.75087i	−1.02570	+	0.468423i	−0.169757	+	0.985486i	$0.554298\pi$
$350$		0			0
$351$	−0.415176	−	0.189605i	−0.0221605	−	0.0101203i
$352$		0			0
$353$	−3.10654	+	21.6064i	−0.165344	+	1.14999i	0.723011	+	0.690837i	$0.242758\pi$
$353$	−3.10654	+	21.6064i	−0.165344	+	1.14999i	−0.888355	+	0.459157i	$0.848151\pi$
$354$		0			0
$355$	25.3050	−	21.9269i	1.34305	−	1.16376i
$356$		0			0
$357$	−0.118747	−	0.184774i	−0.00628477	−	0.00977929i
$358$		0			0
$359$	−14.5073	+	4.25973i	−0.765667	+	0.224820i	−0.641169	−	0.767400i	$-0.721550\pi$
$359$	−14.5073	+	4.25973i	−0.765667	+	0.224820i	−0.124498	+	0.992220i	$0.539732\pi$
$360$		0			0
$361$	−11.1005	+	12.8106i	−0.584236	+	0.674244i
$362$		0			0
$363$	0.0599737	+	0.0176099i	0.00314781	+	0.000924279i
$364$		0			0
$365$	5.92613	+	41.2172i	0.310188	+	2.15741i
$366$		0			0
$367$	−31.1705			−1.62708			−0.813542	−	0.581506i	$-0.802464\pi$
$367$	−31.1705			−1.62708			−0.813542	+	0.581506i	$0.802464\pi$
$368$		0			0
$369$	23.0598			1.20044
$370$		0			0
$371$	−0.314964	−	2.19062i	−0.0163521	−	0.113731i
$372$		0			0
$373$	9.10707	+	2.67408i	0.471546	+	0.138458i	0.508868	−	0.860845i	$-0.330064\pi$
$373$	9.10707	+	2.67408i	0.471546	+	0.138458i	−0.0373213	+	0.999303i	$0.511882\pi$
$374$		0			0
$375$	−0.231306	+	0.266941i	−0.0119446	+	0.0137848i
$376$		0			0
$377$	8.84030	−	2.59575i	0.455299	−	0.133688i
$378$		0			0
$379$	6.91860	+	10.7656i	0.355385	+	0.552989i	0.972210	−	0.234111i	$-0.0752179\pi$
$379$	6.91860	+	10.7656i	0.355385	+	0.552989i	−0.616825	+	0.787100i	$0.711582\pi$
$380$		0			0
$381$	0.169720	−	0.147063i	0.00869502	−	0.00753428i
$382$		0			0
$383$	1.49113	−	10.3710i	0.0761929	−	0.529933i	−0.915601	−	0.402088i	$-0.868285\pi$
$383$	1.49113	−	10.3710i	0.0761929	−	0.529933i	0.991794	−	0.127846i	$-0.0408062\pi$
$384$		0			0
$385$	25.7492	+	11.7593i	1.31230	+	0.599307i
$386$		0			0
$387$	21.9978	−	10.0461i	1.11821	−	0.510670i
$388$		0			0
$389$	−6.16578	−	3.96250i	−0.312617	−	0.200907i	0.374918	−	0.927058i	$-0.377671\pi$
$389$	−6.16578	−	3.96250i	−0.312617	−	0.200907i	−0.687535	+	0.726151i	$0.741307\pi$
$390$		0			0
$391$	−2.09014	−	20.4358i	−0.105703	−	1.03348i
$392$		0			0
$393$	0.410896	+	0.264067i	0.0207270	+	0.0133204i
$394$		0			0
$395$	20.6702	+	45.2614i	1.04003	+	2.27735i
$396$		0			0
$397$	−5.19709	−	2.37343i	−0.260835	−	0.119119i	0.280706	−	0.959794i	$-0.409431\pi$
$397$	−5.19709	−	2.37343i	−0.260835	−	0.119119i	−0.541540	+	0.840675i	$0.682159\pi$
$398$		0			0
$399$	0.0726549	+	0.0104462i	0.00363729	+	0.000522964i
$400$		0			0
$401$	−5.12279	+	4.43893i	−0.255820	+	0.221669i	−0.773323	−	0.634012i	$-0.781407\pi$
$401$	−5.12279	+	4.43893i	−0.255820	+	0.221669i	0.517503	+	0.855681i	$0.326862\pi$
$402$		0			0
$403$	15.8512	−	10.1870i	0.789606	−	0.507449i
$404$		0			0
$405$	−32.0980	+	9.42482i	−1.59496	+	0.468323i
$406$		0			0
$407$	23.1333	+	20.0451i	1.14667	+	0.993598i
$408$		0			0
$409$	17.2830	+	5.07475i	0.854590	+	0.250930i	0.679549	−	0.733631i	$-0.262176\pi$
$409$	17.2830	+	5.07475i	0.854590	+	0.250930i	0.175042	+	0.984561i	$0.443994\pi$
$410$		0			0
$411$	−0.0157213	+	0.00226037i	−0.000775472	+	0.000111496i
$412$		0			0
$413$	−0.372927			−0.0183505
$414$		0			0
$415$			44.6012i			2.18939i
$416$		0			0
$417$	−0.0241131	−	0.167710i	−0.00118082	−	0.00821281i
$418$		0			0
$419$	1.13673	−	3.87135i	0.0555330	−	0.189128i	−0.927055	−	0.374925i	$-0.877668\pi$
$419$	1.13673	−	3.87135i	0.0555330	−	0.189128i	0.982588	+	0.185797i	$0.0594867\pi$
$420$		0			0
$421$	5.56610	−	6.42362i	0.271275	−	0.313068i	−0.603723	−	0.797194i	$-0.706317\pi$
$421$	5.56610	−	6.42362i	0.271275	−	0.313068i	0.874998	+	0.484126i	$0.160862\pi$
$422$		0			0
$423$	−2.76190	−	9.40618i	−0.134288	−	0.457344i
$424$		0			0
$425$	−20.4556	−	31.8295i	−0.992240	−	1.54396i
$426$		0			0
$427$	−6.13255	−	7.07734i	−0.296775	−	0.342496i
$428$		0			0
$429$	0.0398148	−	0.276918i	0.00192228	−	0.0133697i
$430$		0			0
$431$	−4.59971	+	10.0720i	−0.221560	+	0.485149i	−0.987472	−	0.157797i	$-0.949561\pi$
$431$	−4.59971	+	10.0720i	−0.221560	+	0.485149i	0.765911	+	0.642946i	$0.222288\pi$
$432$		0			0
$433$	−2.06643	+	0.943707i	−0.0993063	+	0.0453517i	−0.464449	−	0.885600i	$-0.653748\pi$
$433$	−2.06643	+	0.943707i	−0.0993063	+	0.0453517i	0.365143	+	0.930952i	$0.381020\pi$
$434$		0			0
$435$	−0.149480	+	0.232595i	−0.00716700	+	0.0111521i
$436$		0			0
$437$	5.61878	+	3.94444i	0.268782	+	0.188688i
$438$		0			0
$439$	−8.02681	+	12.4900i	−0.383099	+	0.596113i	−0.978232	−	0.207514i	$-0.933463\pi$
$439$	−8.02681	+	12.4900i	−0.383099	+	0.596113i	0.595133	+	0.803627i	$0.297099\pi$
$440$		0			0
$441$	3.38465	+	7.41134i	0.161174	+	0.352921i
$442$		0			0
$443$	1.21028	−	2.65014i	0.0575020	−	0.125912i	−0.878700	−	0.477375i	$-0.841588\pi$
$443$	1.21028	−	2.65014i	0.0575020	−	0.125912i	0.936202	+	0.351463i	$0.114316\pi$
$444$		0			0
$445$	−16.5558	−	2.38037i	−0.784822	−	0.112840i
$446$		0			0
$447$	−0.238665	−	0.275435i	−0.0112885	−	0.0130276i
$448$		0			0
$449$	−30.6429	+	19.6930i	−1.44613	+	0.929371i	−0.446732	+	0.894668i	$0.647412\pi$
$449$	−30.6429	+	19.6930i	−1.44613	+	0.929371i	−0.999398	+	0.0347030i	$0.988951\pi$
$450$		0			0
$451$	7.96515	+	27.1268i	0.375064	+	1.27735i
$452$		0			0
$453$	−0.133593	−	0.115759i	−0.00627677	−	0.00543885i
$454$		0			0
$455$	6.65942	−	22.6799i	0.312198	−	1.06325i
$456$		0			0
$457$	−5.06624	+	0.728415i	−0.236989	+	0.0340738i	−0.259786	−	0.965666i	$-0.583652\pi$
$457$	−5.06624	+	0.728415i	−0.236989	+	0.0340738i	0.0227971	+	0.999740i	$0.492743\pi$
$458$		0			0
$459$			0.636676i			0.0297175i
$460$		0			0
$461$		−	17.1103i		−	0.796904i	−0.917189	−	0.398452i	$-0.869548\pi$
$461$		−	17.1103i		−	0.796904i	0.917189	−	0.398452i	$-0.130452\pi$
$462$		0			0
$463$	−15.8582	+	2.28006i	−0.736992	+	0.105963i	−0.500581	−	0.865690i	$-0.666880\pi$
$463$	−15.8582	+	2.28006i	−0.736992	+	0.105963i	−0.236411	+	0.971653i	$0.575971\pi$
$464$		0			0
$465$	−0.159302	+	0.542532i	−0.00738745	+	0.0251593i
$466$		0			0
$467$	−15.0517	−	13.0424i	−0.696512	−	0.603531i	0.232933	−	0.972493i	$-0.425168\pi$
$467$	−15.0517	−	13.0424i	−0.696512	−	0.603531i	−0.929444	+	0.368962i	$0.879713\pi$
$468$		0			0
$469$	−7.82742	−	26.6577i	−0.361436	−	1.23094i
$470$		0			0
$471$	−0.124970	+	0.0803130i	−0.00575829	+	0.00370063i
$472$		0			0
$473$	19.4162	+	22.4075i	0.892759	+	1.03030i
$474$		0			0
$475$	12.5156	+	1.79948i	0.574257	+	0.0825656i
$476$		0			0
$477$	−1.33236	+	2.91747i	−0.0610047	+	0.133582i
$478$		0			0
$479$	3.67994	+	8.05795i	0.168141	+	0.368177i	0.974880	−	0.222731i	$-0.0714971\pi$
$479$	3.67994	+	8.05795i	0.168141	+	0.368177i	−0.806739	+	0.590908i	$0.798770\pi$
$480$		0			0
$481$	13.8188	−	21.5024i	0.630082	−	0.980426i
$482$		0			0
$483$	−0.0100494	+	0.245713i	−0.000457261	+	0.0111803i
$484$		0			0
$485$	−17.3027	+	26.9236i	−0.785676	+	1.22254i
$486$		0			0
$487$	1.63901	−	0.748509i	0.0742704	−	0.0339182i	−0.377933	−	0.925833i	$-0.623365\pi$
$487$	1.63901	−	0.748509i	0.0742704	−	0.0339182i	0.452204	+	0.891915i	$0.350638\pi$
$488$		0			0
$489$	0.191503	−	0.419332i	0.00866005	−	0.0189629i
$490$		0			0
$491$	3.80470	−	26.4623i	0.171704	−	1.19423i	−0.703580	−	0.710616i	$-0.748416\pi$
$491$	3.80470	−	26.4623i	0.171704	−	1.19423i	0.875284	−	0.483610i	$-0.160675\pi$
$492$		0			0
$493$	−8.41639	−	9.71304i	−0.379055	−	0.437453i
$494$		0			0
$495$	−22.1787	−	34.5107i	−0.996858	−	1.55114i
$496$		0			0
$497$	−5.24938	−	17.8778i	−0.235467	−	0.801927i
$498$		0			0
$499$	−3.01960	+	3.48481i	−0.135176	+	0.156002i	−0.819302	−	0.573363i	$-0.805639\pi$
$499$	−3.01960	+	3.48481i	−0.135176	+	0.156002i	0.684126	+	0.729364i	$0.260184\pi$
$500$		0			0
$501$	0.0365209	−	0.124379i	0.00163163	−	0.00555683i
$502$		0			0
$503$	3.03110	+	21.0818i	0.135150	+	0.939989i	0.938696	+	0.344746i	$0.112035\pi$
$503$	3.03110	+	21.0818i	0.135150	+	0.939989i	−0.803546	+	0.595243i	$0.797056\pi$
$504$		0			0
$505$		−	48.7107i		−	2.16760i
$506$		0			0
$507$	0.0884700			0.00392909
$508$		0			0
$509$	−8.75338	+	1.25855i	−0.387987	+	0.0557841i	−0.333548	−	0.942733i	$-0.608246\pi$
$509$	−8.75338	+	1.25855i	−0.387987	+	0.0557841i	−0.0544385	+	0.998517i	$0.517337\pi$
$510$		0			0
$511$	22.2334	+	6.52831i	0.983548	+	0.288796i
$512$		0			0
$513$	−0.160801	−	0.139335i	−0.00709955	−	0.00615180i
$514$		0			0
$515$	−25.9415	+	7.61712i	−1.14312	+	0.335650i
$516$		0			0
$517$	10.1111	−	6.49804i	0.444688	−	0.285783i
$518$		0			0
$519$	−0.199444	+	0.172819i	−0.00875463	+	0.00758593i
$520$		0			0
$521$	27.2656	+	3.92020i	1.19453	+	0.171747i	0.710751	−	0.703444i	$-0.248355\pi$
$521$	27.2656	+	3.92020i	1.19453	+	0.171747i	0.483777	+	0.875191i	$0.339264\pi$
$522$		0			0
$523$	0.407535	+	0.186115i	0.0178203	+	0.00813825i	0.424305	−	0.905519i	$-0.360518\pi$
$523$	0.407535	+	0.186115i	0.0178203	+	0.00813825i	−0.406485	+	0.913657i	$0.633246\pi$
$524$		0			0
$525$	0.188158	+	0.412009i	0.00821190	+	0.0179815i
$526$		0			0
$527$	−22.1113	−	14.2101i	−0.963185	−	0.619001i
$528$		0			0
$529$	−11.2311	+	20.0714i	−0.488309	+	0.872671i
$530$		0			0
$531$	0.454653	+	0.292188i	0.0197303	+	0.0126799i
$532$		0			0
$533$	21.4746	−	9.80710i	0.930166	−	0.424793i
$534$		0			0
$535$	48.2770	+	22.0474i	2.08720	+	0.953191i
$536$		0			0
$537$	−0.0322438	+	0.224260i	−0.00139142	+	0.00967755i
$538$		0			0
$539$	−7.54938	+	6.54157i	−0.325175	+	0.281765i
$540$		0			0
$541$	−21.1654	−	32.9341i	−0.909973	−	1.41595i	−0.909389	−	0.415946i	$-0.863451\pi$
$541$	−21.1654	−	32.9341i	−0.909973	−	1.41595i	−0.000583485	−	1.00000i	$-0.500186\pi$
$542$		0			0
$543$	0.267221	−	0.0784633i	0.0114676	−	0.00336718i
$544$		0			0
$545$	−1.41793	+	1.63638i	−0.0607375	+	0.0700948i
$546$		0			0
$547$	−24.4002	−	7.16455i	−1.04328	−	0.306334i	−0.285179	−	0.958474i	$-0.592053\pi$
$547$	−24.4002	−	7.16455i	−1.04328	−	0.306334i	−0.758098	+	0.652140i	$0.773871\pi$
$548$		0			0
$549$	1.93140	+	13.4332i	0.0824300	+	0.573313i
$550$		0			0
$551$	4.29507			0.182976
$552$		0			0
$553$	27.6889			1.17745
$554$		0			0
$555$	0.109159	+	0.759215i	0.00463353	+	0.0322269i
$556$		0			0
$557$	4.61131	+	1.35400i	0.195388	+	0.0573710i	0.377962	−	0.925821i	$-0.376625\pi$
$557$	4.61131	+	1.35400i	0.195388	+	0.0573710i	−0.182575	+	0.983192i	$0.558443\pi$
$558$		0			0
$559$	16.2131	−	18.7109i	0.685741	−	0.791388i
$560$		0			0
$561$	−0.374445	+	0.109947i	−0.0158091	+	0.00464196i
$562$		0			0
$563$	7.85142	+	12.2170i	0.330898	+	0.514887i	0.966342	−	0.257259i	$-0.0828195\pi$
$563$	7.85142	+	12.2170i	0.330898	+	0.514887i	−0.635445	+	0.772147i	$0.719183\pi$
$564$		0			0
$565$	50.6073	−	43.8515i	2.12907	−	1.84485i
$566$		0			0
$567$	−2.64929	+	18.4262i	−0.111260	+	0.773827i
$568$		0			0
$569$	22.9400	+	10.4763i	0.961695	+	0.439191i	0.833477	−	0.552555i	$-0.186347\pi$
$569$	22.9400	+	10.4763i	0.961695	+	0.439191i	0.128218	+	0.991746i	$0.459074\pi$
$570$		0			0
$571$	15.3570	−	7.01330i	0.642670	−	0.293498i	−0.0672965	−	0.997733i	$-0.521437\pi$
$571$	15.3570	−	7.01330i	0.642670	−	0.293498i	0.709966	+	0.704235i	$0.248710\pi$
$572$		0			0
$573$	−0.202059	−	0.129856i	−0.00844114	−	0.00542479i
$574$		0			0
$575$	−1.73112	+	42.3268i	−0.0721925	+	1.76515i
$576$		0			0
$577$	−38.7065	−	24.8752i	−1.61137	−	1.03557i	−0.961228	−	0.275756i	$-0.911072\pi$
$577$	−38.7065	−	24.8752i	−1.61137	−	1.03557i	−0.650145	−	0.759810i	$-0.725292\pi$
$578$		0			0
$579$	−0.185036	−	0.405171i	−0.00768982	−	0.0168383i
$580$		0			0
$581$	22.5764	+	10.3103i	0.936628	+	0.427744i
$582$		0			0
$583$	−3.89224	−	0.559619i	−0.161200	−	0.0231771i
$584$		0			0
$585$	−25.8885	+	22.4325i	−1.07036	+	0.927470i
$586$		0			0
$587$	−32.1758	+	20.6781i	−1.32804	+	0.853477i	−0.995962	−	0.0897759i	$-0.971385\pi$
$587$	−32.1758	+	20.6781i	−1.32804	+	0.853477i	−0.332075	+	0.943253i	$0.607749\pi$
$588$		0			0
$589$	8.42798	−	2.47468i	0.347269	−	0.101967i
$590$		0			0
$591$	−0.0957042	−	0.0829282i	−0.00393674	−	0.00341121i
$592$		0			0
$593$	−33.3678	−	9.79766i	−1.37025	−	0.402342i	−0.487885	−	0.872908i	$-0.662231\pi$
$593$	−33.3678	−	9.79766i	−1.37025	−	0.402342i	−0.882365	+	0.470566i	$0.844050\pi$
$594$		0			0
$595$	−32.6368	+	4.69247i	−1.33798	+	0.192372i
$596$		0			0
$597$	0.633689			0.0259352
$598$		0			0
$599$		−	30.9121i		−	1.26303i	−0.775362	−	0.631517i	$-0.782432\pi$
$599$		−	30.9121i		−	1.26303i	0.775362	−	0.631517i	$-0.217568\pi$
$600$		0			0
$601$	1.95405	+	13.5907i	0.0797075	+	0.554378i	0.990071	+	0.140568i	$0.0448930\pi$
$601$	1.95405	+	13.5907i	0.0797075	+	0.554378i	−0.910363	+	0.413810i	$0.864198\pi$
$602$		0			0
$603$	−11.3435	+	38.6325i	−0.461944	+	1.57324i
$604$		0			0
$605$	6.14476	−	7.09143i	0.249820	−	0.288308i
$606$		0			0
$607$	10.4010	+	35.4227i	0.422165	+	1.43776i	0.846564	+	0.532287i	$0.178667\pi$
$607$	10.4010	+	35.4227i	0.422165	+	1.43776i	−0.424399	+	0.905475i	$0.639515\pi$
$608$		0			0
$609$	0.0831811	+	0.129432i	0.00337067	+	0.00524486i
$610$		0			0
$611$	−6.57240	−	7.58495i	−0.265891	−	0.306854i
$612$		0			0
$613$	−3.87135	+	26.9259i	−0.156363	+	1.08753i	0.748903	+	0.662679i	$0.230581\pi$
$613$	−3.87135	+	26.9259i	−0.156363	+	1.08753i	−0.905266	+	0.424846i	$0.860328\pi$
$614$		0			0
$615$	−0.294299	+	0.644424i	−0.0118673	+	0.0259857i
$616$		0			0
$617$	9.33589	−	4.26356i	0.375849	−	0.171644i	−0.218529	−	0.975830i	$-0.570126\pi$
$617$	9.33589	−	4.26356i	0.375849	−	0.171644i	0.594378	+	0.804186i	$0.297399\pi$
$618$		0			0
$619$	13.6857	−	21.2954i	0.550075	−	0.855933i	−0.449223	−	0.893420i	$-0.648299\pi$
$619$	13.6857	−	21.2954i	0.550075	−	0.855933i	0.999297	+	0.0374872i	$0.0119353\pi$
$620$		0			0
$621$	0.409576	−	0.583432i	0.0164357	−	0.0234123i
$622$		0			0
$623$	−5.03206	+	7.83003i	−0.201605	+	0.313704i
$624$		0			0
$625$	3.67996	+	8.05798i	0.147198	+	0.322319i
$626$		0			0
$627$	0.0541779	−	0.118633i	0.00216366	−	0.00473774i
$628$		0			0
$629$	−35.2914	−	5.07414i	−1.40716	−	0.202319i
$630$		0			0
$631$	−21.2063	−	24.4734i	−0.844209	−	0.974269i	0.155700	−	0.987804i	$-0.450237\pi$
$631$	−21.2063	−	24.4734i	−0.844209	−	0.974269i	−0.999908	+	0.0135355i	$0.995691\pi$
$632$		0			0
$633$	−0.378931	+	0.243524i	−0.0150611	+	0.00967921i
$634$		0			0
$635$	−9.49792	−	32.3470i	−0.376914	−	1.28365i
$636$		0			0
$637$	6.30395	+	5.46240i	0.249772	+	0.216428i
$638$		0			0
$639$	−7.60743	+	25.9085i	−0.300945	+	1.02493i
$640$		0			0
$641$	−34.3261	+	4.93534i	−1.35580	+	0.194934i	−0.781599	−	0.623782i	$-0.785595\pi$
$641$	−34.3261	+	4.93534i	−1.35580	+	0.194934i	−0.574199	+	0.818716i	$0.694686\pi$
$642$		0			0
$643$		−	9.44763i		−	0.372578i	−0.982495	−	0.186289i	$-0.940354\pi$
$643$		−	9.44763i		−	0.372578i	0.982495	−	0.186289i	$-0.0596461\pi$
$644$		0			0
$645$			0.742959i			0.0292540i
$646$		0			0
$647$	19.0910	−	2.74488i	0.750546	−	0.107912i	0.243583	−	0.969880i	$-0.421677\pi$
$647$	19.0910	−	2.74488i	0.750546	−	0.107912i	0.506963	+	0.861968i	$0.330768\pi$
$648$		0			0
$649$	−0.186678	+	0.635766i	−0.00732774	+	0.0249560i
$650$		0			0
$651$	0.237796	+	0.206051i	0.00931996	+	0.00807579i
$652$		0			0
$653$	4.39869	+	14.9806i	0.172134	+	0.586235i	0.999691	+	0.0248533i	$0.00791186\pi$
$653$	4.39869	+	14.9806i	0.172134	+	0.586235i	−0.827557	+	0.561382i	$0.810270\pi$
$654$		0			0
$655$	61.6834	−	39.6415i	2.41017	−	1.54892i
$656$		0			0
$657$	−21.9909	−	25.3788i	−0.857946	−	0.990122i
$658$		0			0
$659$	32.7585	+	4.70996i	1.27609	+	0.183474i	0.746846	−	0.664996i	$-0.231567\pi$
$659$	32.7585	+	4.70996i	1.27609	+	0.183474i	0.529243	+	0.848470i	$0.322476\pi$
$660$		0			0
$661$	−13.9543	+	30.5557i	−0.542761	+	1.18848i	0.417320	+	0.908759i	$0.362969\pi$
$661$	−13.9543	+	30.5557i	−0.542761	+	1.18848i	−0.960081	+	0.279721i	$0.909758\pi$
$662$		0			0
$663$	0.135372	+	0.296424i	0.00525742	+	0.0115122i
$664$		0			0
$665$	5.95735	−	9.26982i	0.231016	−	0.359468i
$666$		0			0
$667$	1.46412	+	14.3151i	0.0566908	+	0.554282i
$668$		0			0
$669$	−0.0835933	+	0.130074i	−0.00323190	+	0.00502894i
$670$		0			0
$671$	−15.1352	+	6.91203i	−0.584289	+	0.266836i
$672$		0			0
$673$	1.51470	−	3.31673i	0.0583874	−	0.127851i	−0.878189	−	0.478313i	$-0.841248\pi$
$673$	1.51470	−	3.31673i	0.0583874	−	0.127851i	0.936577	+	0.350463i	$0.113976\pi$
$674$		0			0
$675$	0.186851	−	1.29958i	0.00719189	−	0.0500207i
$676$		0			0
$677$	−25.6741	−	29.6295i	−0.986736	−	1.13875i	−0.990326	−	0.138761i	$-0.955688\pi$
$677$	−25.6741	−	29.6295i	−0.986736	−	1.13875i	0.00358966	−	0.999994i	$-0.498857\pi$
$678$		0			0
$679$	9.62847	+	14.9822i	0.369507	+	0.574964i
$680$		0			0
$681$	−0.0367324	−	0.125099i	−0.00140759	−	0.00479381i
$682$		0			0
$683$	6.51891	−	7.52323i	0.249439	−	0.287868i	−0.617197	−	0.786809i	$-0.711732\pi$
$683$	6.51891	−	7.52323i	0.249439	−	0.287868i	0.866636	+	0.498940i	$0.166277\pi$
$684$		0			0
$685$	−0.671744	+	2.28775i	−0.0256660	+	0.0874104i
$686$		0			0
$687$	−0.0329276	−	0.229017i	−0.00125627	−	0.00873753i
$688$		0			0
$689$			3.28355i			0.125093i
$690$		0			0
$691$	26.4116			1.00474			0.502371	−	0.864652i	$-0.332461\pi$
$691$	26.4116			1.00474			0.502371	+	0.864652i	$0.332461\pi$
$692$		0			0
$693$	−22.5957	+	3.24878i	−0.858341	+	0.123411i
$694$		0			0
$695$	−24.4051	−	7.16599i	−0.925740	−	0.271822i
$696$		0			0
$697$	−24.8879	−	21.5655i	−0.942696	−	0.816851i
$698$		0			0
$699$	−0.0327452	+	0.00961485i	−0.00123854	+	0.000363667i
$700$		0			0
$701$	−12.5889	+	8.09036i	−0.475474	+	0.305569i	−0.756340	−	0.654178i	$-0.773015\pi$
$701$	−12.5889	+	8.09036i	−0.475474	+	0.305569i	0.280866	+	0.959747i	$0.409378\pi$
$702$		0			0
$703$	9.00500	−	7.80288i	0.339630	−	0.294291i
$704$		0			0
$705$	0.298112	+	0.0428620i	0.0112275	+	0.00161428i
$706$		0			0
$707$	−24.6566	−	11.2603i	−0.927306	−	0.423486i
$708$		0			0
$709$	−4.30878	−	9.43491i	−0.161820	−	0.354336i	0.811302	−	0.584627i	$-0.198759\pi$
$709$	−4.30878	−	9.43491i	−0.161820	−	0.354336i	−0.973122	+	0.230292i	$0.926032\pi$
$710$		0			0
$711$	−33.7568	−	21.6942i	−1.26598	−	0.813595i
$712$		0			0
$713$	11.1208	+	27.2461i	0.416478	+	1.02037i
$714$		0			0
$715$	−35.3311	−	22.7059i	−1.32131	−	0.849154i
$716$		0			0
$717$	0.156681	−	0.0715540i	0.00585137	−	0.00267223i
$718$		0			0
$719$	−27.9338	−	12.7570i	−1.04176	−	0.475754i	−0.180314	−	0.983609i	$-0.557711\pi$
$719$	−27.9338	−	12.7570i	−1.04176	−	0.475754i	−0.861443	+	0.507855i	$0.830439\pi$
$720$		0			0
$721$	−2.14115	+	14.8920i	−0.0797405	+	0.554607i
$722$		0			0
$723$	0.111792	−	0.0968683i	0.00415759	−	0.00360257i
$724$		0			0
$725$	14.3289	+	22.2962i	0.532162	+	0.828060i
$726$		0			0
$727$	−32.0565	+	9.41265i	−1.18891	+	0.349096i	−0.815603	−	0.578612i	$-0.803595\pi$
$727$	−32.0565	+	9.41265i	−1.18891	+	0.349096i	−0.373308	+	0.927708i	$0.621776\pi$
$728$		0			0
$729$	17.6595	−	20.3802i	0.654057	−	0.754822i
$730$		0			0
$731$	−33.1368	−	9.72985i	−1.22561	−	0.359871i
$732$		0			0
$733$	−3.33190	−	23.1739i	−0.123067	−	0.855947i	−0.954050	−	0.299649i	$-0.903130\pi$
$733$	−3.33190	−	23.1739i	−0.123067	−	0.855947i	0.830983	−	0.556298i	$-0.187779\pi$
$734$		0			0
$735$	−0.250312			−0.00923291
$736$		0			0
$737$	−49.3643			−1.81836
$738$		0			0
$739$	0.698412	+	4.85756i	0.0256915	+	0.178688i	0.998627	−	0.0523898i	$-0.0166838\pi$
$739$	0.698412	+	4.85756i	0.0256915	+	0.178688i	−0.972935	+	0.231078i	$0.925775\pi$
$740$		0			0
$741$	−0.104492	−	0.0306816i	−0.00383861	−	0.00112712i
$742$		0			0
$743$	−29.6022	+	34.1627i	−1.08600	+	1.25331i	−0.120551	+	0.992707i	$0.538466\pi$
$743$	−29.6022	+	34.1627i	−1.08600	+	1.25331i	−0.965447	+	0.260601i	$0.916079\pi$
$744$		0			0
$745$	−52.4951	+	15.4140i	−1.92327	+	0.564724i
$746$		0			0
$747$	−19.4459	−	30.2584i	−0.711488	−	1.10710i
$748$		0			0
$749$	22.3200	−	19.3404i	0.815557	−	0.706684i
$750$		0			0
$751$	5.66092	−	39.3726i	0.206570	−	1.43673i	−0.577671	−	0.816270i	$-0.696038\pi$
$751$	5.66092	−	39.3726i	0.206570	−	1.43673i	0.784241	−	0.620456i	$-0.213053\pi$
$752$		0			0
$753$	−0.142235	−	0.0649565i	−0.00518333	−	0.00236715i
$754$		0			0
$755$	−24.1385	+	11.0237i	−0.878489	+	0.401192i
$756$		0			0
$757$	−19.3523	−	12.4370i	−0.703371	−	0.452029i	0.139446	−	0.990230i	$-0.455468\pi$
$757$	−19.3523	−	12.4370i	−0.703371	−	0.452029i	−0.842817	+	0.538200i	$0.819104\pi$
$758$		0			0
$759$	0.413860	+	0.140130i	0.0150222	+	0.00508638i
$760$		0			0
$761$	−8.95963	−	5.75801i	−0.324786	−	0.208728i	0.368079	−	0.929795i	$-0.380016\pi$
$761$	−8.95963	−	5.75801i	−0.324786	−	0.208728i	−0.692865	+	0.721067i	$0.743652\pi$
$762$		0			0
$763$	0.500531	+	1.09601i	0.0181204	+	0.0396782i
$764$		0			0
$765$	43.4657	+	19.8501i	1.57150	+	0.717682i
$766$		0			0
$767$	0.547663	+	0.0787421i	0.0197750	+	0.00284321i
$768$		0			0
$769$	9.09525	−	7.88108i	0.327983	−	0.284199i	−0.475266	−	0.879842i	$-0.657648\pi$
$769$	9.09525	−	7.88108i	0.327983	−	0.284199i	0.803249	+	0.595643i	$0.203103\pi$
$770$		0			0
$771$	−0.379822	+	0.244097i	−0.0136789	+	0.00879092i
$772$		0			0
$773$	−23.5083	+	6.90267i	−0.845537	+	0.248272i	−0.675678	−	0.737197i	$-0.736149\pi$
$773$	−23.5083	+	6.90267i	−0.845537	+	0.248272i	−0.169858	+	0.985469i	$0.554331\pi$
$774$		0			0
$775$	40.9631	+	35.4947i	1.47144	+	1.27501i
$776$		0			0
$777$	0.409537	+	0.120251i	0.0146920	+	0.00431397i
$778$		0			0
$779$	10.8933	−	1.56622i	0.390294	−	0.0561158i
$780$		0			0
$781$	−33.1057			−1.18462
$782$		0			0
$783$		−	0.445984i		−	0.0159382i
$784$		0			0
$785$	3.17369	+	22.0735i	0.113274	+	0.787836i
$786$		0			0
$787$	−4.27073	+	14.5448i	−0.152235	+	0.518465i	−0.999928	−	0.0120225i	$-0.996173\pi$
$787$	−4.27073	+	14.5448i	−0.152235	+	0.518465i	0.847693	+	0.530488i	$0.177991\pi$
$788$		0			0
$789$	0.198176	−	0.228707i	0.00705524	−	0.00814218i
$790$		0			0
$791$	−10.4982	−	35.7536i	−0.373274	−	1.27125i
$792$		0			0
$793$	7.51163	+	11.6883i	0.266746	+	0.415064i
$794$		0			0
$795$	−0.0645269	−	0.0744680i	−0.00228853	−	0.00264111i
$796$		0			0
$797$	−7.85734	+	54.6490i	−0.278321	+	1.93577i	0.0680795	+	0.997680i	$0.478313\pi$
$797$	−7.85734	+	54.6490i	−0.278321	+	1.93577i	−0.346401	+	0.938087i	$0.612596\pi$
$798$		0			0
$799$	−5.81579	+	12.7348i	−0.205748	+	0.450525i
$800$		0			0
$801$	12.2696	−	5.60336i	0.433527	−	0.197985i
$802$		0			0
$803$	22.2589	−	34.6356i	0.785501	−	1.22226i
$804$		0			0
$805$	32.9262	+	16.6954i	1.16050	+	0.588434i
$806$		0			0
$807$	0.0501864	−	0.0780916i	0.00176665	−	0.00274896i
$808$		0			0
$809$	18.9590	+	41.5145i	0.666564	+	1.45957i	0.876277	+	0.481808i	$0.160020\pi$
$809$	18.9590	+	41.5145i	0.666564	+	1.45957i	−0.209713	+	0.977763i	$0.567253\pi$
$810$		0			0
$811$	−13.8622	+	30.3541i	−0.486769	+	1.06588i	0.493777	+	0.869589i	$0.335616\pi$
$811$	−13.8622	+	30.3541i	−0.486769	+	1.06588i	−0.980546	+	0.196288i	$0.937111\pi$
$812$		0			0
$813$	−0.717531	−	0.103165i	−0.0251649	−	0.00361817i
$814$		0			0
$815$	−45.3188	−	52.3006i	−1.58745	−	1.83201i
$816$		0			0
$817$	9.70934	−	6.23981i	0.339687	−	0.218303i
$818$		0			0
$819$	5.37042	+	18.2900i	0.187658	+	0.639104i
$820$		0			0
$821$	29.4360	+	25.5065i	1.02732	+	0.890182i	0.994013	−	0.109263i	$-0.0348491\pi$
$821$	29.4360	+	25.5065i	1.02732	+	0.890182i	0.0333119	+	0.999445i	$0.489395\pi$
$822$		0			0
$823$	10.3921	−	35.3923i	0.362246	−	1.23370i	−0.553809	−	0.832644i	$-0.686826\pi$
$823$	10.3921	−	35.3923i	0.362246	−	1.23370i	0.916055	−	0.401053i	$-0.131356\pi$
$824$		0			0
$825$	0.796580	−	0.114531i	0.0277334	−	0.00398746i
$826$		0			0
$827$		−	34.9852i		−	1.21655i	−0.793725	−	0.608277i	$-0.791861\pi$
$827$		−	34.9852i		−	1.21655i	0.793725	−	0.608277i	$-0.208139\pi$
$828$		0			0
$829$			8.72710i			0.303105i	0.988449	+	0.151552i	$0.0484272\pi$
$829$			8.72710i			0.303105i	−0.988449	+	0.151552i	$0.951573\pi$
$830$		0			0
$831$	0.367962	−	0.0529049i	0.0127645	−	0.00183525i
$832$		0			0
$833$	3.27811	−	11.1642i	0.113580	−	0.386817i
$834$		0			0
$835$	−14.7068	−	12.7435i	−0.508951	−	0.441008i
$836$		0			0
$837$	−0.256961	−	0.875130i	−0.00888188	−	0.0302489i
$838$		0			0
$839$	33.8567	−	21.7584i	1.16886	−	0.751183i	0.195557	−	0.980692i	$-0.437348\pi$
$839$	33.8567	−	21.7584i	1.16886	−	0.751183i	0.973307	+	0.229509i	$0.0737121\pi$
$840$		0			0
$841$	−13.0954	−	15.1129i	−0.451565	−	0.521133i
$842$		0			0
$843$	−0.477742	−	0.0686889i	−0.0164543	−	0.00236577i
$844$		0			0
$845$	5.51715	−	12.0809i	0.189796	−	0.415595i
$846$		0			0
$847$	−2.16911	−	4.74968i	−0.0745314	−	0.163201i
$848$		0			0
$849$	0.263978	−	0.410758i	0.00905970	−	0.0140972i
$850$		0			0
$851$	29.0759	+	27.3529i	0.996709	+	0.937646i
$852$		0			0
$853$	−0.784412	+	1.22057i	−0.0268578	+	0.0417915i	−0.854423	−	0.519578i	$-0.826089\pi$
$853$	−0.784412	+	1.22057i	−0.0268578	+	0.0417915i	0.827565	+	0.561370i	$0.189725\pi$
$854$		0			0
$855$	−14.5258	+	6.63371i	−0.496772	+	0.226868i
$856$		0			0
$857$	1.18687	−	2.59887i	0.0405426	−	0.0887758i	−0.888277	−	0.459308i	$-0.848097\pi$
$857$	1.18687	−	2.59887i	0.0405426	−	0.0887758i	0.928820	+	0.370532i	$0.120825\pi$
$858$		0			0
$859$	−4.01477	+	27.9234i	−0.136982	+	0.952733i	0.799162	+	0.601116i	$0.205277\pi$
$859$	−4.01477	+	27.9234i	−0.136982	+	0.952733i	−0.936144	+	0.351617i	$0.885632\pi$
$860$		0			0
$861$	0.258165	+	0.297939i	0.00879825	+	0.0101537i
$862$		0			0
$863$	−2.27225	−	3.53569i	−0.0773484	−	0.120356i	0.800424	−	0.599434i	$-0.204608\pi$
$863$	−2.27225	−	3.53569i	−0.0773484	−	0.120356i	−0.877773	+	0.479078i	$0.840971\pi$
$864$		0			0
$865$	11.1614	+	38.0121i	0.379498	+	1.29245i
$866$		0			0
$867$	0.0218619	−	0.0252300i	0.000742470	−	0.000856856i
$868$		0			0
$869$	13.8603	−	47.2040i	0.470180	−	1.60128i
$870$		0			0
$871$	5.86631	+	40.8011i	0.198772	+	1.38249i
$872$		0			0
$873$		−	25.8094i		−	0.873516i
$874$		0			0
$875$	29.5064			0.997499
$876$		0			0
$877$	17.3486	−	2.49436i	0.585821	−	0.0842284i	0.156970	−	0.987603i	$-0.449827\pi$
$877$	17.3486	−	2.49436i	0.585821	−	0.0842284i	0.428852	+	0.903375i	$0.358918\pi$
$878$		0			0
$879$	−0.0931647	−	0.0273556i	−0.00314237	−	0.000922683i
$880$		0			0
$881$	−11.9250	−	10.3330i	−0.401762	−	0.348129i	0.430422	−	0.902628i	$-0.358365\pi$
$881$	−11.9250	−	10.3330i	−0.401762	−	0.348129i	−0.832185	+	0.554499i	$0.812910\pi$
$882$		0			0
$883$	−33.7274	+	9.90327i	−1.13502	+	0.333271i	−0.794678	−	0.607031i	$-0.792360\pi$
$883$	−33.7274	+	9.90327i	−1.13502	+	0.333271i	−0.340340	+	0.940302i	$0.610542\pi$
$884$		0			0
$885$	−0.0139679	+	0.00897663i	−0.000469526	+	0.000301746i
$886$		0			0
$887$	1.60225	−	1.38835i	0.0537981	−	0.0466163i	−0.627547	−	0.778579i	$-0.715941\pi$
$887$	1.60225	−	1.38835i	0.0537981	−	0.0466163i	0.681345	+	0.731963i	$0.261395\pi$
$888$		0			0
$889$	−18.5691	−	2.66984i	−0.622788	−	0.0895434i
$890$		0			0
$891$	30.0868	+	13.7402i	1.00795	+	0.460314i
$892$		0			0
$893$	−1.94358	−	4.25585i	−0.0650394	−	0.142417i
$894$		0			0
$895$	28.6127	+	18.3883i	0.956418	+	0.614653i
$896$		0			0
$897$	0.0666393	−	0.358720i	0.00222502	−	0.0119773i
$898$		0			0
$899$	15.4887	+	9.95401i	0.516579	+	0.331985i
$900$		0			0
$901$	4.16641	−	1.90273i	0.138803	−	0.0633893i
$902$		0			0
$903$	0.376074	+	0.171747i	0.0125150	+	0.00571539i
$904$		0			0
$905$	5.94999	−	41.3831i	0.197784	−	1.37562i
$906$		0			0
$907$	9.75761	−	8.45502i	0.323996	−	0.280744i	−0.477641	−	0.878555i	$-0.658508\pi$
$907$	9.75761	−	8.45502i	0.323996	−	0.280744i	0.801637	+	0.597811i	$0.203963\pi$
$908$		0			0
$909$	21.2376	+	33.0463i	0.704406	+	1.09608i
$910$		0			0
$911$	43.0014	−	12.6263i	1.42470	−	0.418329i	0.523608	−	0.851959i	$-0.324586\pi$
$911$	43.0014	−	12.6263i	1.42470	−	0.418329i	0.901091	+	0.433630i	$0.142767\pi$
$912$		0			0
$913$	28.8782	−	33.3272i	0.955729	−	1.10297i
$914$		0			0
$915$	−0.400050	−	0.117465i	−0.0132253	−	0.00388329i
$916$		0			0
$917$	−5.80677	−	40.3870i	−0.191756	−	1.33369i
$918$		0			0
$919$	−7.35971			−0.242774			−0.121387	−	0.992605i	$-0.538734\pi$
$919$	−7.35971			−0.242774			−0.121387	+	0.992605i	$0.538734\pi$
$920$		0			0
$921$	−0.481315			−0.0158599
$922$		0			0
$923$	3.93418	+	27.3628i	0.129495	+	0.900659i
$924$		0			0
$925$	70.5473	+	20.7146i	2.31958	+	0.681091i
$926$		0			0
$927$	14.2782	−	16.4780i	0.468959	−	0.541207i
$928$		0			0
$929$	46.3387	−	13.6063i	1.52032	−	0.446408i	0.588252	−	0.808678i	$-0.299816\pi$
$929$	46.3387	−	13.6063i	1.52032	−	0.446408i	0.932073	+	0.362270i	$0.117998\pi$
$930$		0			0
$931$	2.10227	+	3.27120i	0.0688992	+	0.107209i
$932$		0			0
$933$	−0.225330	+	0.195249i	−0.00737696	+	0.00639217i
$934$		0			0
$935$	−8.33744	+	57.9882i	−0.272664	+	1.89642i
$936$		0			0
$937$	−7.72504	−	3.52791i	−0.252366	−	0.115252i	0.285216	−	0.958463i	$-0.407935\pi$
$937$	−7.72504	−	3.52791i	−0.252366	−	0.115252i	−0.537582	+	0.843212i	$0.680662\pi$
$938$		0			0
$939$	0.327001	−	0.149336i	0.0106713	−	0.00487341i
$940$		0			0
$941$	−0.781896	−	0.502494i	−0.0254891	−	0.0163808i	0.527834	−	0.849347i	$-0.323004\pi$
$941$	−0.781896	−	0.502494i	−0.0254891	−	0.0163808i	−0.553323	+	0.832967i	$0.686641\pi$
$942$		0			0
$943$	8.93342	+	35.7725i	0.290912	+	1.16491i
$944$		0			0
$945$	−0.962544	−	0.618589i	−0.0313115	−	0.0201227i
$946$		0			0
$947$	10.9088	+	23.8869i	0.354488	+	0.776220i	0.999923	+	0.0124053i	$0.00394882\pi$
$947$	10.9088	+	23.8869i	0.354488	+	0.776220i	−0.645435	+	0.763815i	$0.723324\pi$
$948$		0			0
$949$	−31.2725	−	14.2817i	−1.01515	−	0.463603i
$950$		0			0
$951$	−0.821256	−	0.118079i	−0.0266310	−	0.00382897i
$952$		0			0
$953$	27.6777	−	23.9829i	0.896568	−	0.776881i	−0.0789318	−	0.996880i	$-0.525151\pi$
$953$	27.6777	−	23.9829i	0.896568	−	0.776881i	0.975500	+	0.219999i	$0.0706055\pi$
$954$		0			0
$955$	−30.3330	+	19.4938i	−0.981552	+	0.630805i
$956$		0			0
$957$	0.262294	−	0.0770166i	0.00847877	−	0.00248959i
$958$		0			0
$959$	1.00274	+	0.868877i	0.0323801	+	0.0280575i
$960$		0			0
$961$	6.38356	+	1.87438i	0.205921	+	0.0604640i
$962$		0			0
$963$	−42.3646	+	6.09112i	−1.36518	+	0.196283i
$964$		0			0
$965$	−66.8667			−2.15251
$966$		0			0
$967$		−	26.6482i		−	0.856948i	−0.903554	−	0.428474i	$-0.859051\pi$
$967$		−	26.6482i		−	0.856948i	0.903554	−	0.428474i	$-0.140949\pi$
$968$		0			0
$969$	0.0216194	+	0.150366i	0.000694515	+	0.00483045i
$970$		0			0
$971$	11.5019	−	39.1718i	0.369113	−	1.25708i	−0.540400	−	0.841408i	$-0.681727\pi$
$971$	11.5019	−	39.1718i	0.369113	−	1.25708i	0.909513	−	0.415675i	$-0.136455\pi$
$972$		0			0
$973$	−9.26896	+	10.6970i	−0.297149	+	0.342929i
$974$		0			0
$975$	−0.189326	−	0.644787i	−0.00606330	−	0.0206497i
$976$		0			0
$977$	9.42838	+	14.6708i	0.301641	+	0.469362i	0.958677	−	0.284497i	$-0.0918266\pi$
$977$	9.42838	+	14.6708i	0.301641	+	0.469362i	−0.657036	+	0.753859i	$0.728190\pi$
$978$		0			0
$979$	10.8297	+	12.4982i	0.346119	+	0.399443i
$980$		0			0
$981$	0.248501	−	1.72836i	0.00793403	−	0.0551824i
$982$		0			0
$983$	21.7695	−	47.6685i	0.694338	−	1.52039i	−0.152366	−	0.988324i	$-0.548689\pi$
$983$	21.7695	−	47.6685i	0.694338	−	1.52039i	0.846704	−	0.532064i	$-0.178583\pi$
$984$		0			0
$985$	−17.2924	+	7.89718i	−0.550982	+	0.251625i
$986$		0			0
$987$	0.0906096	−	0.140991i	0.00288414	−	0.00448780i
$988$		0			0
$989$	24.1064	+	30.2332i	0.766540	+	0.961361i
$990$		0			0
$991$	−10.2459	+	15.9429i	−0.325472	+	0.506444i	−0.964974	−	0.262345i	$-0.915504\pi$
$991$	−10.2459	+	15.9429i	−0.325472	+	0.506444i	0.639503	+	0.768789i	$0.279140\pi$
$992$		0			0
$993$	0.0884163	+	0.193605i	0.00280581	+	0.00614386i
$994$		0			0
$995$	39.5180	−	86.5323i	1.25280	−	2.74326i
$996$		0			0
$997$	−31.1067	−	4.47247i	−0.985158	−	0.141644i	−0.369138	−	0.929375i	$-0.620347\pi$
$997$	−31.1067	−	4.47247i	−0.985158	−	0.141644i	−0.616020	+	0.787730i	$0.711256\pi$
$998$		0			0
$999$	−0.810221	−	0.935045i	−0.0256343	−	0.0295835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	736.2.r.a.527.11		220
4.3	odd	2		184.2.j.a.67.8	yes	220
8.3	odd	2	inner	736.2.r.a.527.12		220
8.5	even	2		184.2.j.a.67.15	yes	220
23.11	odd	22	inner	736.2.r.a.655.12		220
92.11	even	22		184.2.j.a.11.15	yes	220
184.11	even	22	inner	736.2.r.a.655.11		220
184.149	odd	22		184.2.j.a.11.8	✓	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
184.2.j.a.11.8	✓	220	184.149	odd	22
184.2.j.a.11.15	yes	220	92.11	even	22
184.2.j.a.67.8	yes	220	4.3	odd	2
184.2.j.a.67.15	yes	220	8.5	even	2
736.2.r.a.527.11		220	1.1	even	1	trivial
736.2.r.a.527.12		220	8.3	odd	2	inner
736.2.r.a.655.11		220	184.11	even	22	inner
736.2.r.a.655.12		220	23.11	odd	22	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:	\( N \)	\(=\)	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	736.r (of order \(22\), degree \(10\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.00352593 - 0.0245234i) q^{3} +(-3.56863 - 1.04785i) q^{5} +(-1.35535 + 1.56416i) q^{7} +(2.87789 - 0.845025i) q^{9} +O(q^{10})\)	\(q+(-0.00352593 - 0.0245234i) q^{3} +(-3.56863 - 1.04785i) q^{5} +(-1.35535 + 1.56416i) q^{7} +(2.87789 - 0.845025i) q^{9} +(1.98812 + 3.09358i) q^{11} +(2.32067 - 2.01087i) q^{13} +(-0.0131140 + 0.0912096i) q^{15} +(-3.89631 - 1.77939i) q^{17} +(1.30211 - 0.594653i) q^{19} +(0.0431373 + 0.0277227i) q^{21} +(2.42579 + 4.13709i) q^{23} +(7.43090 + 4.77555i) q^{25} +(-0.0617465 - 0.135206i) q^{27} +(2.72932 + 1.24644i) q^{29} +(6.07375 + 0.873274i) q^{31} +(0.0688551 - 0.0596633i) q^{33} +(6.47575 - 4.16171i) q^{35} +(7.98668 - 2.34510i) q^{37} +(-0.0574960 - 0.0498206i) q^{39} +(7.37673 + 2.16600i) q^{41} +(7.98064 - 1.14744i) q^{43} -11.1556 q^{45} -3.26843i q^{47} +(0.386588 + 2.68878i) q^{49} +(-0.0298984 + 0.101825i) q^{51} +(-0.700256 + 0.808138i) q^{53} +(-3.85329 - 13.1231i) q^{55} +(-0.0191741 - 0.0298354i) q^{57} +(0.117997 + 0.136175i) q^{59} +(-0.643931 + 4.47864i) q^{61} +(-2.57880 + 5.64678i) q^{63} +(-10.3887 + 4.74437i) q^{65} +(-7.25750 + 11.2929i) q^{67} +(0.0929024 - 0.0740756i) q^{69} +(-4.86718 + 7.57348i) q^{71} +(-4.65097 - 10.1842i) q^{73} +(0.0909118 - 0.199069i) q^{75} +(-7.53346 - 1.08315i) q^{77} +(-8.76095 - 10.1107i) q^{79} +(7.56663 - 4.86278i) q^{81} +(-3.37850 - 11.5061i) q^{83} +(12.0400 + 10.4327i) q^{85} +(0.0209435 - 0.0713271i) q^{87} +(4.45134 - 0.640006i) q^{89} +6.35534i q^{91} -0.152028i q^{93} +(-5.26985 + 0.757691i) q^{95} +(2.42428 - 8.25634i) q^{97} +(8.33575 + 7.22297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 18 q^{3} - 36 q^{9}+O(q^{10}) \) 220 * q + 18 * q^3 - 36 * q^9	\( 220 q + 18 q^{3} - 36 q^{9} + 22 q^{11} - 22 q^{17} + 22 q^{19} - 32 q^{25} + 18 q^{27} - 22 q^{33} - 2 q^{35} - 18 q^{41} + 22 q^{43} - 28 q^{49} + 22 q^{51} - 22 q^{57} + 6 q^{59} - 22 q^{65} + 22 q^{67} - 18 q^{73} - 14 q^{75} + 4 q^{81} + 22 q^{83} - 22 q^{89} - 22 q^{97} + 22 q^{99}+O(q^{100}) \) 220 * q + 18 * q^3 - 36 * q^9 + 22 * q^11 - 22 * q^17 + 22 * q^19 - 32 * q^25 + 18 * q^27 - 22 * q^33 - 2 * q^35 - 18 * q^41 + 22 * q^43 - 28 * q^49 + 22 * q^51 - 22 * q^57 + 6 * q^59 - 22 * q^65 + 22 * q^67 - 18 * q^73 - 14 * q^75 + 4 * q^81 + 22 * q^83 - 22 * q^89 - 22 * q^97 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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