LMFDB - Embedded newform 1323.2.i.d.521.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (of order $6$, degree $2$, 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.1
Character	$\chi$	$=$	1323.521
Dual form			1323.2.i.d.1097.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.17820i q^{2} +0.611843 q^{4} +(2.16601 - 3.75164i) q^{5} -3.07728i q^{8} +O(q^{10})$	\(q-1.17820i q^{2} +0.611843 q^{4} +(2.16601 - 3.75164i) q^{5} -3.07728i q^{8} +(-4.42019 - 2.55200i) q^{10} +(-1.87238 + 1.08102i) q^{11} +(2.25256 - 1.30052i) q^{13} -2.40196 q^{16} +(-0.585576 + 1.01425i) q^{17} +(2.09282 - 1.20829i) q^{19} +(1.32526 - 2.29541i) q^{20} +(1.27366 + 2.20604i) q^{22} +(-3.16186 - 1.82550i) q^{23} +(-6.88321 - 11.9221i) q^{25} +(-1.53227 - 2.65397i) q^{26} +(-0.589262 - 0.340210i) q^{29} +6.55550i q^{31} -3.32456i q^{32} +(1.19499 + 0.689926i) q^{34} +(2.55346 + 4.42272i) q^{37} +(-1.42361 - 2.46576i) q^{38} +(-11.5448 - 6.66541i) q^{40} +(3.68473 + 6.38214i) q^{41} +(-2.12577 + 3.68194i) q^{43} +(-1.14560 + 0.661414i) q^{44} +(-2.15081 + 3.72531i) q^{46} +7.14314 q^{47} +(-14.0466 + 8.10980i) q^{50} +(1.37821 - 0.795711i) q^{52} +(-2.79976 - 1.61644i) q^{53} +9.36601i q^{55} +(-0.400836 + 0.694269i) q^{58} +5.83621 q^{59} -7.17805i q^{61} +7.72370 q^{62} -8.72092 q^{64} -11.2677i q^{65} +6.65363 q^{67} +(-0.358281 + 0.620560i) q^{68} +1.95976i q^{71} +(10.3117 + 5.95345i) q^{73} +(5.21085 - 3.00849i) q^{74} +(1.28048 - 0.739283i) q^{76} -9.75404 q^{79} +(-5.20268 + 9.01130i) q^{80} +(7.51944 - 4.34135i) q^{82} +(-0.796736 + 1.37999i) q^{83} +(2.53673 + 4.39374i) q^{85} +(4.33806 + 2.50458i) q^{86} +(3.32660 + 5.76184i) q^{88} +(-3.04961 - 5.28207i) q^{89} +(-1.93456 - 1.11692i) q^{92} -8.41605i q^{94} -10.4687i q^{95} +(-2.36387 - 1.36478i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4}+O(q^{10}) $ 48 * q - 48 * q^4	$ 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) $ 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.17820i		−	0.833114i	−0.909110	−	0.416557i	$-0.863237\pi$
$2$		−	1.17820i		−	0.833114i	0.909110	−	0.416557i	$-0.136763\pi$
$3$		0			0
$3$		0			0
$4$	0.611843			0.305921
$5$	2.16601	−	3.75164i	0.968670	−	1.67778i	0.269254	−	0.963069i	$-0.413223\pi$
$5$	2.16601	−	3.75164i	0.968670	−	1.67778i	0.699415	−	0.714716i	$-0.253444\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	3.07728i		−	1.08798i
$9$		0			0
$10$	−4.42019	−	2.55200i	−1.39779	−	0.807012i
$11$	−1.87238	+	1.08102i	−0.564545	+	0.325940i	−0.754968	−	0.655762i	$-0.772347\pi$
$11$	−1.87238	+	1.08102i	−0.564545	+	0.325940i	0.190423	+	0.981702i	$0.439014\pi$
$12$		0			0
$13$	2.25256	−	1.30052i	0.624748	−	0.360698i	−0.153967	−	0.988076i	$-0.549205\pi$
$13$	2.25256	−	1.30052i	0.624748	−	0.360698i	0.778715	+	0.627378i	$0.215872\pi$
$14$		0			0
$15$		0			0
$16$	−2.40196			−0.600491
$17$	−0.585576	+	1.01425i	−0.142023	+	0.245991i	−0.928258	−	0.371936i	$-0.878694\pi$
$17$	−0.585576	+	1.01425i	−0.142023	+	0.245991i	0.786235	+	0.617927i	$0.212027\pi$
$18$		0			0
$19$	2.09282	−	1.20829i	0.480126	−	0.277201i	−0.240343	−	0.970688i	$-0.577260\pi$
$19$	2.09282	−	1.20829i	0.480126	−	0.277201i	0.720469	+	0.693487i	$0.243927\pi$
$20$	1.32526	−	2.29541i	0.296337	−	0.513270i
$21$		0			0
$22$	1.27366	+	2.20604i	0.271545	+	0.470330i
$23$	−3.16186	−	1.82550i	−0.659294	−	0.380644i	0.132714	−	0.991154i	$-0.457631\pi$
$23$	−3.16186	−	1.82550i	−0.659294	−	0.380644i	−0.792008	+	0.610511i	$0.790964\pi$
$24$		0			0
$25$	−6.88321	−	11.9221i	−1.37664	−	2.38441i
$26$	−1.53227	−	2.65397i	−0.300503	−	0.520486i
$27$		0			0
$28$		0			0
$29$	−0.589262	−	0.340210i	−0.109423	−	0.0631755i	0.444290	−	0.895883i	$-0.353456\pi$
$29$	−0.589262	−	0.340210i	−0.109423	−	0.0631755i	−0.553713	+	0.832708i	$0.686789\pi$
$30$		0			0
$31$			6.55550i			1.17740i	0.808350	+	0.588702i	$0.200361\pi$
$31$			6.55550i			1.17740i	−0.808350	+	0.588702i	$0.799639\pi$
$32$		−	3.32456i		−	0.587704i
$33$		0			0
$34$	1.19499	+	0.689926i	0.204939	+	0.118321i
$35$		0			0
$36$		0			0
$37$	2.55346	+	4.42272i	0.419786	+	0.727090i	0.995918	−	0.0902663i	$-0.0287718\pi$
$37$	2.55346	+	4.42272i	0.419786	+	0.727090i	−0.576132	+	0.817357i	$0.695439\pi$
$38$	−1.42361	−	2.46576i	−0.230940	−	0.399999i
$39$		0			0
$40$	−11.5448	−	6.66541i	−1.82540	−	1.05389i
$41$	3.68473	+	6.38214i	0.575458	+	0.996723i	0.995992	+	0.0894458i	$0.0285096\pi$
$41$	3.68473	+	6.38214i	0.575458	+	0.996723i	−0.420534	+	0.907277i	$0.638157\pi$
$42$		0			0
$43$	−2.12577	+	3.68194i	−0.324176	+	0.561490i	−0.981345	−	0.192253i	$-0.938420\pi$
$43$	−2.12577	+	3.68194i	−0.324176	+	0.561490i	0.657169	+	0.753743i	$0.271754\pi$
$44$	−1.14560	+	0.661414i	−0.172706	+	0.0997120i
$45$		0			0
$46$	−2.15081	+	3.72531i	−0.317120	+	0.549267i
$47$	7.14314			1.04193			0.520967	−	0.853577i	$-0.325572\pi$
$47$	7.14314			1.04193			0.520967	+	0.853577i	$0.325572\pi$
$48$		0			0
$49$		0			0
$50$	−14.0466	+	8.10980i	−1.98649	+	1.14690i
$51$		0			0
$52$	1.37821	−	0.795711i	0.191124	−	0.110345i
$53$	−2.79976	−	1.61644i	−0.384577	−	0.222036i	0.295231	−	0.955426i	$-0.404603\pi$
$53$	−2.79976	−	1.61644i	−0.384577	−	0.222036i	−0.679808	+	0.733390i	$0.737937\pi$
$54$		0			0
$55$			9.36601i			1.26291i
$56$		0			0
$57$		0			0
$58$	−0.400836	+	0.694269i	−0.0526324	+	0.0911619i
$59$	5.83621			0.759810			0.379905	−	0.925026i	$-0.375957\pi$
$59$	5.83621			0.759810			0.379905	+	0.925026i	$0.375957\pi$
$60$		0			0
$61$		−	7.17805i		−	0.919055i	−0.888163	−	0.459528i	$-0.848019\pi$
$61$		−	7.17805i		−	0.919055i	0.888163	−	0.459528i	$-0.151981\pi$
$62$	7.72370			0.980911
$63$		0			0
$64$	−8.72092			−1.09012
$65$		−	11.2677i		−	1.39759i
$66$		0			0
$67$	6.65363			0.812870			0.406435	−	0.913680i	$-0.366772\pi$
$67$	6.65363			0.812870			0.406435	+	0.913680i	$0.366772\pi$
$68$	−0.358281	+	0.620560i	−0.0434479	+	0.0752540i
$69$		0			0
$70$		0			0
$71$			1.95976i			0.232580i	0.993215	+	0.116290i	$0.0371003\pi$
$71$			1.95976i			0.232580i	−0.993215	+	0.116290i	$0.962900\pi$
$72$		0			0
$73$	10.3117	+	5.95345i	1.20689	+	0.696799i	0.962079	−	0.272771i	$-0.0879403\pi$
$73$	10.3117	+	5.95345i	1.20689	+	0.696799i	0.244812	+	0.969570i	$0.421274\pi$
$74$	5.21085	−	3.00849i	0.605749	−	0.349729i
$75$		0			0
$76$	1.28048	−	0.739283i	0.146881	−	0.0848016i
$77$		0			0
$78$		0			0
$79$	−9.75404			−1.09742			−0.548708	−	0.836014i	$-0.684880\pi$
$79$	−9.75404			−1.09742			−0.548708	+	0.836014i	$0.684880\pi$
$80$	−5.20268	+	9.01130i	−0.581677	+	1.00749i
$81$		0			0
$82$	7.51944	−	4.34135i	0.830384	−	0.479422i
$83$	−0.796736	+	1.37999i	−0.0874531	+	0.151473i	−0.906434	−	0.422348i	$-0.861206\pi$
$83$	−0.796736	+	1.37999i	−0.0874531	+	0.151473i	0.818981	+	0.573821i	$0.194539\pi$
$84$		0			0
$85$	2.53673	+	4.39374i	0.275147	+	0.476568i
$86$	4.33806	+	2.50458i	0.467785	+	0.270076i
$87$		0			0
$88$	3.32660	+	5.76184i	0.354617	+	0.614214i
$89$	−3.04961	−	5.28207i	−0.323258	−	0.559899i	0.657901	−	0.753105i	$-0.271445\pi$
$89$	−3.04961	−	5.28207i	−0.323258	−	0.559899i	−0.981158	+	0.193206i	$0.938111\pi$
$90$		0			0
$91$		0			0
$92$	−1.93456	−	1.11692i	−0.201692	−	0.116447i
$93$		0			0
$94$		−	8.41605i		−	0.868049i
$95$		−	10.4687i		−	1.07406i
$96$		0			0
$97$	−2.36387	−	1.36478i	−0.240014	−	0.138572i	0.375169	−	0.926956i	$-0.377585\pi$
$97$	−2.36387	−	1.36478i	−0.240014	−	0.138572i	−0.615183	+	0.788384i	$0.710918\pi$
$98$		0			0
$99$		0			0
$100$	−4.21144	−	7.29443i	−0.421144	−	0.729443i
$101$	−7.99849	−	13.8538i	−0.795880	−	1.37850i	−0.922279	−	0.386524i	$-0.873676\pi$
$101$	−7.99849	−	13.8538i	−0.795880	−	1.37850i	0.126400	−	0.991979i	$-0.459658\pi$
$102$		0			0
$103$	2.61251	+	1.50834i	0.257419	+	0.148621i	0.623156	−	0.782097i	$-0.285850\pi$
$103$	2.61251	+	1.50834i	0.257419	+	0.148621i	−0.365738	+	0.930718i	$0.619183\pi$
$104$	−4.00205	−	6.93175i	−0.392433	−	0.679714i
$105$		0			0
$106$	−1.90450	+	3.29868i	−0.184981	+	0.320397i
$107$	−10.2611	+	5.92422i	−0.991973	+	0.572716i	−0.905864	−	0.423569i	$-0.860777\pi$
$107$	−10.2611	+	5.92422i	−0.991973	+	0.572716i	−0.0861099	+	0.996286i	$0.527444\pi$
$108$		0			0
$109$	−3.58078	+	6.20210i	−0.342977	+	0.594053i	−0.984984	−	0.172645i	$-0.944769\pi$
$109$	−3.58078	+	6.20210i	−0.342977	+	0.594053i	0.642007	+	0.766699i	$0.278102\pi$
$110$	11.0350			1.05215
$111$		0			0
$112$		0			0
$113$	−2.46102	+	1.42087i	−0.231514	+	0.133664i	−0.611270	−	0.791422i	$-0.709341\pi$
$113$	−2.46102	+	1.42087i	−0.231514	+	0.133664i	0.379756	+	0.925086i	$0.376008\pi$
$114$		0			0
$115$	−13.6973	+	7.90812i	−1.27728	+	0.737436i
$116$	−0.360535	−	0.208155i	−0.0334749	−	0.0193267i
$117$		0			0
$118$		−	6.87623i		−	0.633008i
$119$		0			0
$120$		0			0
$121$	−3.16279	+	5.47811i	−0.287526	+	0.498010i
$122$	−8.45719			−0.765678
$123$		0			0
$124$			4.01094i			0.360193i
$125$	−37.9763			−3.39670
$126$		0			0
$127$	18.5344			1.64466			0.822332	−	0.569009i	$-0.192673\pi$
$127$	18.5344			1.64466			0.822332	+	0.569009i	$0.192673\pi$
$128$			3.62589i			0.320486i
$129$		0			0
$130$	−13.2757			−1.16435
$131$	−3.35221	+	5.80619i	−0.292884	+	0.507289i	−0.974490	−	0.224429i	$-0.927948\pi$
$131$	−3.35221	+	5.80619i	−0.292884	+	0.507289i	0.681607	+	0.731719i	$0.261282\pi$
$132$		0			0
$133$		0			0
$134$		−	7.83931i		−	0.677214i
$135$		0			0
$136$	3.12112	+	1.80198i	0.267634	+	0.154518i
$137$	11.8181	−	6.82316i	1.00969	−	0.582942i	0.0985856	−	0.995129i	$-0.468568\pi$
$137$	11.8181	−	6.82316i	1.00969	−	0.582942i	0.911099	+	0.412187i	$0.135235\pi$
$138$		0			0
$139$	7.74126	−	4.46942i	0.656605	−	0.379091i	−0.134377	−	0.990930i	$-0.542903\pi$
$139$	7.74126	−	4.46942i	0.656605	−	0.379091i	0.790982	+	0.611839i	$0.209570\pi$
$140$		0			0
$141$		0			0
$142$	2.30899			0.193766
$143$	−2.81177	+	4.87013i	−0.235132	+	0.407261i
$144$		0			0
$145$	−2.55269	+	1.47380i	−0.211990	+	0.122392i
$146$	7.01436	−	12.1492i	0.580513	−	1.00548i
$147$		0			0
$148$	1.56231	+	2.70601i	0.128421	+	0.222432i
$149$	−3.29003	−	1.89950i	−0.269530	−	0.155613i	0.359144	−	0.933282i	$-0.383069\pi$
$149$	−3.29003	−	1.89950i	−0.269530	−	0.155613i	−0.628674	+	0.777669i	$0.716402\pi$
$150$		0			0
$151$	1.91083	+	3.30965i	0.155501	+	0.269336i	0.933241	−	0.359250i	$-0.116967\pi$
$151$	1.91083	+	3.30965i	0.155501	+	0.269336i	−0.777740	+	0.628586i	$0.783634\pi$
$152$	−3.71824	−	6.44018i	−0.301589	−	0.522368i
$153$		0			0
$154$		0			0
$155$	24.5939	+	14.1993i	1.97543	+	1.14051i
$156$		0			0
$157$		−	21.4868i		−	1.71483i	−0.514622	−	0.857417i	$-0.672068\pi$
$157$		−	21.4868i		−	1.71483i	0.514622	−	0.857417i	$-0.327932\pi$
$158$			11.4922i			0.914272i
$159$		0			0
$160$	−12.4725	−	7.20102i	−0.986041	−	0.569291i
$161$		0			0
$162$		0			0
$163$	−6.25875	−	10.8405i	−0.490223	−	0.849092i	0.509713	−	0.860344i	$-0.329751\pi$
$163$	−6.25875	−	10.8405i	−0.490223	−	0.849092i	−0.999937	+	0.0112525i	$0.996418\pi$
$164$	2.25448	+	3.90487i	0.176045	+	0.304919i
$165$		0			0
$166$	1.62590	+	0.938715i	0.126194	+	0.0728584i
$167$	7.70819	+	13.3510i	0.596477	+	1.03313i	0.993337	+	0.115250i	$0.0367668\pi$
$167$	7.70819	+	13.3510i	0.596477	+	1.03313i	−0.396859	+	0.917880i	$0.629900\pi$
$168$		0			0
$169$	−3.11731	+	5.39935i	−0.239793	+	0.415334i
$170$	5.17671	−	2.98878i	0.397036	−	0.229229i
$171$		0			0
$172$	−1.30063	+	2.25277i	−0.0991725	+	0.171772i
$173$	−8.61474			−0.654967			−0.327483	−	0.944857i	$-0.606201\pi$
$173$	−8.61474			−0.654967			−0.327483	+	0.944857i	$0.606201\pi$
$174$		0			0
$175$		0			0
$176$	4.49739	−	2.59657i	0.339004	−	0.195724i
$177$		0			0
$178$	−6.22334	+	3.59305i	−0.466459	+	0.269310i
$179$	16.5744	+	9.56922i	1.23883	+	0.715237i	0.968854	−	0.247631i	$-0.0796521\pi$
$179$	16.5744	+	9.56922i	1.23883	+	0.715237i	0.269972	+	0.962868i	$0.412985\pi$
$180$		0			0
$181$		−	7.69817i		−	0.572200i	−0.958200	−	0.286100i	$-0.907641\pi$
$181$		−	7.69817i		−	0.572200i	0.958200	−	0.286100i	$-0.0923590\pi$
$182$		0			0
$183$		0			0
$184$	−5.61758	+	9.72993i	−0.414133	+	0.717300i
$185$	22.1233			1.62654
$186$		0			0
$187$		−	2.53208i		−	0.185164i
$188$	4.37047			0.318750
$189$		0			0
$190$	−12.3342			−0.894817
$191$			18.6141i			1.34687i	0.739248	+	0.673433i	$0.235181\pi$
$191$			18.6141i			1.34687i	−0.739248	+	0.673433i	$0.764819\pi$
$192$		0			0
$193$	18.1144			1.30390			0.651952	−	0.758260i	$-0.273950\pi$
$193$	18.1144			1.30390			0.651952	+	0.758260i	$0.273950\pi$
$194$	−1.60799	+	2.78511i	−0.115447	+	0.199959i
$195$		0			0
$196$		0			0
$197$		−	16.5945i		−	1.18231i	−0.806559	−	0.591154i	$-0.798672\pi$
$197$		−	16.5945i		−	1.18231i	0.806559	−	0.591154i	$-0.201328\pi$
$198$		0			0
$199$	2.35461	+	1.35943i	0.166914	+	0.0963677i	0.581130	−	0.813811i	$-0.302611\pi$
$199$	2.35461	+	1.35943i	0.166914	+	0.0963677i	−0.414216	+	0.910179i	$0.635944\pi$
$200$	−36.6875	+	21.1815i	−2.59420	+	1.49776i
$201$		0			0
$202$	−16.3225	+	9.42383i	−1.14845	+	0.663058i
$203$		0			0
$204$		0			0
$205$	31.9247			2.22972
$206$	1.77712	−	3.07807i	0.123818	−	0.214459i
$207$		0			0
$208$	−5.41057	+	3.12379i	−0.375155	+	0.216596i
$209$	−2.61237	+	4.52476i	−0.180702	+	0.312984i
$210$		0			0
$211$	−13.9445	−	24.1526i	−0.959979	−	1.66273i	−0.722539	−	0.691330i	$-0.757025\pi$
$211$	−13.9445	−	24.1526i	−0.959979	−	1.66273i	−0.237440	−	0.971402i	$-0.576308\pi$
$212$	−1.71301	−	0.989010i	−0.117650	−	0.0679255i
$213$		0			0
$214$	6.97992	+	12.0896i	0.477138	+	0.826427i
$215$	9.20887	+	15.9502i	0.628040	+	1.08780i
$216$		0			0
$217$		0			0
$218$	7.30732	+	4.21888i	0.494914	+	0.285739i
$219$		0			0
$220$			5.73052i			0.386352i
$221$			3.04621i			0.204910i
$222$		0			0
$223$	6.64349	+	3.83562i	0.444881	+	0.256852i	0.705666	−	0.708545i	$-0.250648\pi$
$223$	6.64349	+	3.83562i	0.444881	+	0.256852i	−0.260785	+	0.965397i	$0.583981\pi$
$224$		0			0
$225$		0			0
$226$	1.67407	+	2.89958i	0.111358	+	0.192877i
$227$	−1.16439	−	2.01677i	−0.0772829	−	0.133858i	0.824794	−	0.565434i	$-0.191291\pi$
$227$	−1.16439	−	2.01677i	−0.0772829	−	0.133858i	−0.902077	+	0.431576i	$0.857958\pi$
$228$		0			0
$229$	10.3653	+	5.98443i	0.684961	+	0.395463i	0.801722	−	0.597698i	$-0.203918\pi$
$229$	10.3653	+	5.98443i	0.684961	+	0.395463i	−0.116760	+	0.993160i	$0.537251\pi$
$230$	9.31735	+	16.1381i	0.614368	+	1.06412i
$231$		0			0
$232$	−1.04692	+	1.81332i	−0.0687337	+	0.119050i
$233$	−2.18913	+	1.26390i	−0.143415	+	0.0828007i	−0.569991	−	0.821651i	$-0.693053\pi$
$233$	−2.18913	+	1.26390i	−0.143415	+	0.0828007i	0.426576	+	0.904452i	$0.359720\pi$
$234$		0			0
$235$	15.4721	−	26.7985i	1.00929	−	1.74814i
$236$	3.57084			0.232442
$237$		0			0
$238$		0			0
$239$	−17.4587	+	10.0798i	−1.12931	+	0.652006i	−0.943761	−	0.330630i	$-0.892739\pi$
$239$	−17.4587	+	10.0798i	−1.12931	+	0.652006i	−0.185546	+	0.982636i	$0.559405\pi$
$240$		0			0
$241$	18.1254	−	10.4647i	1.16756	−	0.674091i	0.214455	−	0.976734i	$-0.431202\pi$
$241$	18.1254	−	10.4647i	1.16756	−	0.674091i	0.953104	+	0.302643i	$0.0978690\pi$
$242$	6.45432	+	3.72640i	0.414899	+	0.239542i
$243$		0			0
$244$		−	4.39184i		−	0.281159i
$245$		0			0
$246$		0			0
$247$	3.14280	−	5.44349i	0.199972	−	0.346361i
$248$	20.1731			1.28099
$249$		0			0
$250$			44.7437i			2.82984i
$251$	25.5747			1.61426			0.807130	−	0.590374i	$-0.201020\pi$
$251$	25.5747			1.61426			0.807130	+	0.590374i	$0.201020\pi$
$252$		0			0
$253$	7.89363			0.496268
$254$		−	21.8373i		−	1.37019i
$255$		0			0
$256$	−13.1698			−0.823114
$257$	−5.93725	+	10.2836i	−0.370355	+	0.641474i	−0.989620	−	0.143708i	$-0.954097\pi$
$257$	−5.93725	+	10.2836i	−0.370355	+	0.641474i	0.619265	+	0.785182i	$0.287431\pi$
$258$		0			0
$259$		0			0
$260$		−	6.89408i		−	0.427553i
$261$		0			0
$262$	6.84086	+	3.94957i	0.422630	+	0.244005i
$263$	19.3705	−	11.1836i	1.19444	−	0.689608i	0.235127	−	0.971965i	$-0.424450\pi$
$263$	19.3705	−	11.1836i	1.19444	−	0.689608i	0.959309	+	0.282357i	$0.0911162\pi$
$264$		0			0
$265$	−12.1286	+	7.00247i	−0.745056	+	0.430158i
$266$		0			0
$267$		0			0
$268$	4.07098			0.248674
$269$	2.11335	−	3.66043i	0.128853	−	0.223180i	−0.794379	−	0.607422i	$-0.792204\pi$
$269$	2.11335	−	3.66043i	0.128853	−	0.223180i	0.923232	+	0.384242i	$0.125537\pi$
$270$		0			0
$271$	−19.3941	+	11.1972i	−1.17811	+	0.680179i	−0.955576	−	0.294746i	$-0.904765\pi$
$271$	−19.3941	+	11.1972i	−1.17811	+	0.680179i	−0.222530	+	0.974926i	$0.571432\pi$
$272$	1.40653	−	2.43619i	0.0852836	−	0.147715i
$273$		0			0
$274$	−8.03905	−	13.9240i	−0.485657	−	0.841183i
$275$	25.7760	+	14.8818i	1.55435	+	0.897405i
$276$		0			0
$277$	−5.69230	−	9.85935i	−0.342017	−	0.592391i	0.642790	−	0.766042i	$-0.277777\pi$
$277$	−5.69230	−	9.85935i	−0.342017	−	0.592391i	−0.984807	+	0.173651i	$0.944443\pi$
$278$	−5.26587	−	9.12076i	−0.315826	−	0.547027i
$279$		0			0
$280$		0			0
$281$	0.702700	+	0.405704i	0.0419196	+	0.0242023i	0.520813	−	0.853671i	$-0.325629\pi$
$281$	0.702700	+	0.405704i	0.0419196	+	0.0242023i	−0.478894	+	0.877873i	$0.658962\pi$
$282$		0			0
$283$			18.3297i			1.08959i	0.838570	+	0.544794i	$0.183392\pi$
$283$			18.3297i			1.08959i	−0.838570	+	0.544794i	$0.816608\pi$
$284$			1.19906i			0.0711513i
$285$		0			0
$286$	5.73799	+	3.31283i	0.339294	+	0.195892i
$287$		0			0
$288$		0			0
$289$	7.81420	+	13.5346i	0.459659	+	0.796153i
$290$	1.73643	+	3.00759i	0.101967	+	0.176612i
$291$		0			0
$292$	6.30913	+	3.64258i	0.369214	+	0.213166i
$293$	−6.23639	−	10.8017i	−0.364334	−	0.631044i	0.624335	−	0.781156i	$-0.285370\pi$
$293$	−6.23639	−	10.8017i	−0.364334	−	0.631044i	−0.988669	+	0.150112i	$0.952037\pi$
$294$		0			0
$295$	12.6413	−	21.8954i	0.736004	−	1.27480i
$296$	13.6099	−	7.85769i	0.791061	−	0.456719i
$297$		0			0
$298$	−2.23800	+	3.87632i	−0.129644	+	0.224549i
$299$	−9.49639			−0.549190
$300$		0			0
$301$		0			0
$302$	3.89943	−	2.25134i	0.224387	−	0.129550i
$303$		0			0
$304$	−5.02688	+	2.90227i	−0.288311	+	0.166457i
$305$	−26.9295	−	15.5477i	−1.54198	−	0.890261i
$306$		0			0
$307$			21.3241i			1.21703i	0.793543	+	0.608514i	$0.208234\pi$
$307$			21.3241i			1.21703i	−0.793543	+	0.608514i	$0.791766\pi$
$308$		0			0
$309$		0			0
$310$	16.7296	−	28.9765i	0.950178	−	1.64576i
$311$	−7.84187			−0.444672			−0.222336	−	0.974970i	$-0.571368\pi$
$311$	−7.84187			−0.444672			−0.222336	+	0.974970i	$0.571368\pi$
$312$		0			0
$313$		−	9.90263i		−	0.559730i	−0.960039	−	0.279865i	$-0.909710\pi$
$313$		−	9.90263i		−	0.559730i	0.960039	−	0.279865i	$-0.0902897\pi$
$314$	−25.3158			−1.42865
$315$		0			0
$316$	−5.96794			−0.335723
$317$			24.0591i			1.35129i	0.737225	+	0.675647i	$0.236136\pi$
$317$			24.0591i			1.35129i	−0.737225	+	0.675647i	$0.763864\pi$
$318$		0			0
$319$	1.47110			0.0823657
$320$	−18.8896	+	32.7178i	−1.05596	+	1.82898i
$321$		0			0
$322$		0			0
$323$			2.83018i			0.157476i
$324$		0			0
$325$	−31.0097	−	17.9034i	−1.72011	−	0.993104i
$326$	−12.7723	+	7.37407i	−0.707390	+	0.408412i
$327$		0			0
$328$	19.6396	−	11.3389i	1.08442	−	0.626088i
$329$		0			0
$330$		0			0
$331$	−9.07371			−0.498736			−0.249368	−	0.968409i	$-0.580223\pi$
$331$	−9.07371			−0.498736			−0.249368	+	0.968409i	$0.580223\pi$
$332$	−0.487477	+	0.844335i	−0.0267538	+	0.0463389i
$333$		0			0
$334$	15.7301	−	9.08179i	0.860714	−	0.496934i
$335$	14.4118	−	24.9620i	0.787403	−	1.36382i
$336$		0			0
$337$	4.02012	+	6.96304i	0.218990	+	0.379301i	0.954499	−	0.298213i	$-0.0963906\pi$
$337$	4.02012	+	6.96304i	0.218990	+	0.379301i	−0.735510	+	0.677514i	$0.763057\pi$
$338$	6.36152	+	3.67282i	0.346021	+	0.199775i
$339$		0			0
$340$	1.55208	+	2.68828i	0.0841733	+	0.145792i
$341$	−7.08663	−	12.2744i	−0.383763	−	0.664696i
$342$		0			0
$343$		0			0
$344$	11.3303	+	6.54157i	0.610891	+	0.352698i
$345$		0			0
$346$			10.1499i			0.545662i
$347$			35.3736i			1.89896i	0.313832	+	0.949478i	$0.398387\pi$
$347$			35.3736i			1.89896i	−0.313832	+	0.949478i	$0.601613\pi$
$348$		0			0
$349$	21.1868	+	12.2322i	1.13411	+	0.654776i	0.944964	−	0.327174i	$-0.106096\pi$
$349$	21.1868	+	12.2322i	1.13411	+	0.654776i	0.189141	+	0.981950i	$0.439430\pi$
$350$		0			0
$351$		0			0
$352$	3.59391	+	6.22484i	0.191556	+	0.331785i
$353$	0.485949	+	0.841688i	0.0258644	+	0.0447985i	0.878668	−	0.477433i	$-0.158433\pi$
$353$	0.485949	+	0.841688i	0.0258644	+	0.0447985i	−0.852803	+	0.522232i	$0.825100\pi$
$354$		0			0
$355$	7.35231	+	4.24486i	0.390220	+	0.225294i
$356$	−1.86588	−	3.23180i	−0.0988914	−	0.171285i
$357$		0			0
$358$	11.2745	−	19.5279i	0.595874	−	1.03208i
$359$	13.7879	−	7.96048i	0.727700	−	0.420138i	−0.0898801	−	0.995953i	$-0.528648\pi$
$359$	13.7879	−	7.96048i	0.727700	−	0.420138i	0.817580	+	0.575815i	$0.195315\pi$
$360$		0			0
$361$	−6.58007	+	11.3970i	−0.346319	+	0.599843i
$362$	−9.06999			−0.476708
$363$		0			0
$364$		0			0
$365$	44.6704	−	25.7905i	2.33816	−	1.34994i
$366$		0			0
$367$	21.3983	−	12.3543i	1.11698	−	0.644891i	0.176355	−	0.984327i	$-0.443569\pi$
$367$	21.3983	−	12.3543i	1.11698	−	0.644891i	0.940629	+	0.339435i	$0.110236\pi$
$368$	7.59468	+	4.38479i	0.395900	+	0.228573i
$369$		0			0
$370$		−	26.0657i		−	1.35509i
$371$		0			0
$372$		0			0
$373$	4.71810	−	8.17200i	0.244294	−	0.423130i	−0.717639	−	0.696416i	$-0.754777\pi$
$373$	4.71810	−	8.17200i	0.244294	−	0.423130i	0.961933	+	0.273286i	$0.0881104\pi$
$374$	−2.98330			−0.154263
$375$		0			0
$376$		−	21.9814i		−	1.13360i
$377$	−1.76980			−0.0911492
$378$		0			0
$379$	20.8031			1.06858			0.534292	−	0.845300i	$-0.320578\pi$
$379$	20.8031			1.06858			0.534292	+	0.845300i	$0.320578\pi$
$380$		−	6.40518i		−	0.328579i
$381$		0			0
$382$	21.9311			1.12209
$383$	3.23008	−	5.59467i	0.165050	−	0.285874i	−0.771623	−	0.636080i	$-0.780555\pi$
$383$	3.23008	−	5.59467i	0.165050	−	0.285874i	0.936673	+	0.350205i	$0.113888\pi$
$384$		0			0
$385$		0			0
$386$		−	21.3424i		−	1.08630i
$387$		0			0
$388$	−1.44632	−	0.835031i	−0.0734255	−	0.0423923i
$389$	−0.0445846	+	0.0257409i	−0.00226053	+	0.00130512i	−0.501130	−	0.865372i	$-0.667082\pi$
$389$	−0.0445846	+	0.0257409i	−0.00226053	+	0.00130512i	0.498869	+	0.866677i	$0.333749\pi$
$390$		0			0
$391$	3.70303	−	2.13794i	0.187270	−	0.108120i
$392$		0			0
$393$		0			0
$394$	−19.5516			−0.984997
$395$	−21.1274	+	36.5937i	−1.06303	+	1.84123i
$396$		0			0
$397$	11.0099	−	6.35655i	0.552569	−	0.319026i	−0.197588	−	0.980285i	$-0.563311\pi$
$397$	11.0099	−	6.35655i	0.552569	−	0.319026i	0.750158	+	0.661259i	$0.229978\pi$
$398$	1.60169	−	2.77420i	0.0802853	−	0.139058i
$399$		0			0
$400$	16.5332	+	28.6364i	0.826660	+	1.43182i
$401$	−2.19725	−	1.26858i	−0.109725	−	0.0633500i	0.444133	−	0.895961i	$-0.353512\pi$
$401$	−2.19725	−	1.26858i	−0.109725	−	0.0633500i	−0.553858	+	0.832611i	$0.686845\pi$
$402$		0			0
$403$	8.52554	+	14.7667i	0.424687	+	0.735580i
$404$	−4.89382	−	8.47634i	−0.243477	−	0.421714i
$405$		0			0
$406$		0			0
$407$	−9.56210	−	5.52068i	−0.473976	−	0.273650i
$408$		0			0
$409$		−	0.0572333i		−	0.00283000i	−0.999999	−	0.00141500i	$-0.999550\pi$
$409$		−	0.0572333i		−	0.00283000i	0.999999	−	0.00141500i	$-0.000450409\pi$
$410$		−	37.6137i		−	1.85761i
$411$		0			0
$412$	1.59845	+	0.922864i	0.0787499	+	0.0454663i
$413$		0			0
$414$		0			0
$415$	3.45148	+	5.97813i	0.169426	+	0.293455i
$416$	−4.32364	−	7.48876i	−0.211984	−	0.367167i
$417$		0			0
$418$	5.33108	+	3.07790i	0.260752	+	0.150545i
$419$	−3.08007	−	5.33484i	−0.150471	−	0.260624i	0.780930	−	0.624619i	$-0.214746\pi$
$419$	−3.08007	−	5.33484i	−0.150471	−	0.260624i	−0.931401	+	0.363995i	$0.881412\pi$
$420$		0			0
$421$	15.0693	−	26.1007i	0.734431	−	1.27207i	−0.220542	−	0.975378i	$-0.570783\pi$
$421$	15.0693	−	26.1007i	0.734431	−	1.27207i	0.954973	−	0.296694i	$-0.0958842\pi$
$422$	−28.4566	+	16.4294i	−1.38525	+	0.799772i
$423$		0			0
$424$	−4.97424	+	8.61564i	−0.241571	+	0.418413i
$425$	16.1226			0.782059
$426$		0			0
$427$		0			0
$428$	−6.27815	+	3.62469i	−0.303466	+	0.175206i
$429$		0			0
$430$	18.7926	−	10.8499i	0.906258	−	0.523228i
$431$	−6.99003	−	4.03570i	−0.336698	−	0.194393i	0.322113	−	0.946701i	$-0.395607\pi$
$431$	−6.99003	−	4.03570i	−0.336698	−	0.194393i	−0.658811	+	0.752309i	$0.728940\pi$
$432$		0			0
$433$			28.4938i			1.36933i	0.728860	+	0.684663i	$0.240051\pi$
$433$			28.4938i			1.36933i	−0.728860	+	0.684663i	$0.759949\pi$
$434$		0			0
$435$		0			0
$436$	−2.19088	+	3.79471i	−0.104924	+	0.181734i
$437$	−8.82295			−0.422059
$438$		0			0
$439$		−	2.04460i		−	0.0975832i	−0.998809	−	0.0487916i	$-0.984463\pi$
$439$		−	2.04460i		−	0.0975832i	0.998809	−	0.0487916i	$-0.0155370\pi$
$440$	28.8218			1.37402
$441$		0			0
$442$	3.58904			0.170713
$443$		−	24.4016i		−	1.15935i	−0.814846	−	0.579677i	$-0.803179\pi$
$443$		−	24.4016i		−	1.15935i	0.814846	−	0.579677i	$-0.196821\pi$
$444$		0			0
$445$	−26.4219			−1.25252
$446$	4.51913	−	7.82737i	0.213987	−	0.370637i
$447$		0			0
$448$		0			0
$449$			0.293539i			0.0138529i	0.999976	+	0.00692647i	$0.00220478\pi$
$449$			0.293539i			0.0138529i	−0.999976	+	0.00692647i	$0.997795\pi$
$450$		0			0
$451$	−13.7984	−	7.96654i	−0.649744	−	0.375130i
$452$	−1.50576	+	0.869351i	−0.0708250	+	0.0408908i
$453$		0			0
$454$	−2.37616	+	1.37188i	−0.111519	+	0.0643855i
$455$		0			0
$456$		0			0
$457$	16.5494			0.774148			0.387074	−	0.922049i	$-0.373486\pi$
$457$	16.5494			0.774148			0.387074	+	0.922049i	$0.373486\pi$
$458$	7.05087	−	12.2125i	0.329465	−	0.570651i
$459$		0			0
$460$	−8.38057	+	4.83852i	−0.390746	+	0.225597i
$461$	−10.0560	+	17.4175i	−0.468354	+	0.811213i	−0.999346	−	0.0361638i	$-0.988486\pi$
$461$	−10.0560	+	17.4175i	−0.468354	+	0.811213i	0.530992	+	0.847377i	$0.321820\pi$
$462$		0			0
$463$	9.34602	+	16.1878i	0.434346	+	0.752310i	0.997242	−	0.0742181i	$-0.0236461\pi$
$463$	9.34602	+	16.1878i	0.434346	+	0.752310i	−0.562896	+	0.826528i	$0.690313\pi$
$464$	1.41538	+	0.817173i	0.0657076	+	0.0379363i
$465$		0			0
$466$	1.48912	+	2.57924i	0.0689824	+	0.119481i
$467$	14.6803	+	25.4270i	0.679322	+	1.17662i	0.975185	+	0.221390i	$0.0710593\pi$
$467$	14.6803	+	25.4270i	0.679322	+	1.17662i	−0.295864	+	0.955230i	$0.595607\pi$
$468$		0			0
$469$		0			0
$470$	−31.5740	−	18.2293i	−1.45640	−	0.840853i
$471$		0			0
$472$		−	17.9596i		−	0.826659i
$473$		−	9.19199i		−	0.422648i
$474$		0			0
$475$	−28.8106	−	16.6338i	−1.32192	−	0.763212i
$476$		0			0
$477$		0			0
$478$	11.8760	+	20.5698i	0.543195	+	0.940841i
$479$	−10.9660	−	18.9938i	−0.501051	−	0.867847i	−0.999999	−	0.00121455i	$-0.999613\pi$
$479$	−10.9660	−	18.9938i	−0.501051	−	0.867847i	0.498948	−	0.866632i	$-0.333720\pi$
$480$		0			0
$481$	11.5036	+	6.64163i	0.524521	+	0.302832i
$482$	−12.3295	−	21.3554i	−0.561594	−	0.972710i
$483$		0			0
$484$	−1.93513	+	3.35174i	−0.0879604	+	0.152352i
$485$	−10.2403	+	5.91226i	−0.464989	+	0.268462i
$486$		0			0
$487$	−0.538896	+	0.933395i	−0.0244197	+	0.0422962i	−0.877977	−	0.478703i	$-0.841107\pi$
$487$	−0.538896	+	0.933395i	−0.0244197	+	0.0422962i	0.853557	+	0.520999i	$0.174440\pi$
$488$	−22.0888			−0.999915
$489$		0			0
$490$		0			0
$491$	−16.3708	+	9.45168i	−0.738804	+	0.426549i	−0.821634	−	0.570015i	$-0.806937\pi$
$491$	−16.3708	+	9.45168i	−0.738804	+	0.426549i	0.0828305	+	0.996564i	$0.473604\pi$
$492$		0			0
$493$	0.690115	−	0.398438i	0.0310812	−	0.0179448i
$494$	−6.41353	−	3.70285i	−0.288558	−	0.166599i
$495$		0			0
$496$		−	15.7461i		−	0.707020i
$497$		0			0
$498$		0			0
$499$	8.34290	−	14.4503i	0.373479	−	0.646885i	−0.616619	−	0.787262i	$-0.711498\pi$
$499$	8.34290	−	14.4503i	0.373479	−	0.646885i	0.990098	+	0.140377i	$0.0448314\pi$
$500$	−23.2355			−1.03912
$501$		0			0
$502$		−	30.1321i		−	1.34486i
$503$	−21.2386			−0.946981			−0.473491	−	0.880799i	$-0.657006\pi$
$503$	−21.2386			−0.946981			−0.473491	+	0.880799i	$0.657006\pi$
$504$		0			0
$505$	−69.2993			−3.08378
$506$		−	9.30028i		−	0.413448i
$507$		0			0
$508$	11.3401			0.503138
$509$	5.72252	−	9.91170i	0.253646	−	0.439328i	−0.710881	−	0.703313i	$-0.751703\pi$
$509$	5.72252	−	9.91170i	0.253646	−	0.439328i	0.964527	+	0.263984i	$0.0850367\pi$
$510$		0			0
$511$		0			0
$512$			22.7685i			1.00623i
$513$		0			0
$514$	12.1162	+	6.99527i	0.534421	+	0.308548i
$515$	11.3175	−	6.53414i	0.498707	−	0.287929i
$516$		0			0
$517$	−13.3747	+	7.72188i	−0.588218	+	0.339608i
$518$		0			0
$519$		0			0
$520$	−34.6739			−1.52055
$521$	10.3999	−	18.0131i	0.455627	−	0.789169i	−0.543097	−	0.839670i	$-0.682748\pi$
$521$	10.3999	−	18.0131i	0.455627	−	0.789169i	0.998724	+	0.0505007i	$0.0160817\pi$
$522$		0			0
$523$	−12.9330	+	7.46690i	−0.565523	+	0.326505i	−0.755359	−	0.655311i	$-0.772538\pi$
$523$	−12.9330	+	7.46690i	−0.565523	+	0.326505i	0.189836	+	0.981816i	$0.439204\pi$
$524$	−2.05102	+	3.55248i	−0.0895994	+	0.155191i
$525$		0			0
$526$	−13.1765	−	22.8223i	−0.574522	−	0.995101i
$527$	−6.64890	−	3.83875i	−0.289631	−	0.167218i
$528$		0			0
$529$	−4.83508	−	8.37460i	−0.210221	−	0.364113i
$530$	8.25032	+	14.2900i	0.358371	+	0.620717i
$531$		0			0
$532$		0			0
$533$	16.6002	+	9.58410i	0.719033	+	0.415134i
$534$		0			0
$535$			51.3277i			2.21909i
$536$		−	20.4751i		−	0.884388i
$537$		0			0
$538$	−4.31272	−	2.48995i	−0.185934	−	0.107349i
$539$		0			0
$540$		0			0
$541$	−15.5838	−	26.9920i	−0.670002	−	1.16048i	−0.977903	−	0.209058i	$-0.932960\pi$
$541$	−15.5838	−	26.9920i	−0.670002	−	1.16048i	0.307902	−	0.951418i	$-0.400373\pi$
$542$	13.1925	+	22.8501i	0.566667	+	0.981496i
$543$		0			0
$544$	3.37192	+	1.94678i	0.144570	+	0.0834675i
$545$	15.5120	+	26.8676i	0.664462	+	1.15088i
$546$		0			0
$547$	−15.7410	+	27.2642i	−0.673035	+	1.16573i	0.304004	+	0.952671i	$0.401677\pi$
$547$	−15.7410	+	27.2642i	−0.673035	+	1.16573i	−0.977039	+	0.213061i	$0.931657\pi$
$548$	7.23079	−	4.17470i	0.308884	−	0.178334i
$549$		0			0
$550$	17.5337	−	30.3693i	0.747640	−	1.29495i
$551$	−1.64429			−0.0700492
$552$		0			0
$553$		0			0
$554$	−11.6163	+	6.70667i	−0.493529	+	0.284939i
$555$		0			0
$556$	4.73643	−	2.73458i	0.200870	−	0.115972i
$557$	23.5896	+	13.6194i	0.999522	+	0.577074i	0.908107	−	0.418738i	$-0.137528\pi$
$557$	23.5896	+	13.6194i	0.999522	+	0.577074i	0.0914153	+	0.995813i	$0.470861\pi$
$558$		0			0
$559$			11.0584i			0.467720i
$560$		0			0
$561$		0			0
$562$	0.478001	−	0.827922i	0.0201633	−	0.0349238i
$563$	28.3743			1.19583			0.597916	−	0.801559i	$-0.295996\pi$
$563$	28.3743			1.19583			0.597916	+	0.801559i	$0.295996\pi$
$564$		0			0
$565$			12.3105i			0.517907i
$566$	21.5961			0.907751
$567$		0			0
$568$	6.03071			0.253043
$569$			34.0193i			1.42616i	0.701081	+	0.713082i	$0.252701\pi$
$569$			34.0193i			1.42616i	−0.701081	+	0.713082i	$0.747299\pi$
$570$		0			0
$571$	−44.6910			−1.87026			−0.935130	−	0.354305i	$-0.884717\pi$
$571$	−44.6910			−1.87026			−0.935130	+	0.354305i	$0.884717\pi$
$572$	−1.72036	+	2.97975i	−0.0719319	+	0.124590i
$573$		0			0
$574$		0			0
$575$			50.2613i			2.09604i
$576$		0			0
$577$	−6.36301	−	3.67369i	−0.264896	−	0.152938i	0.361670	−	0.932306i	$-0.382207\pi$
$577$	−6.36301	−	3.67369i	−0.264896	−	0.152938i	−0.626566	+	0.779369i	$0.715540\pi$
$578$	15.9465	−	9.20670i	0.663286	−	0.382948i
$579$		0			0
$580$	−1.56185	+	0.901733i	−0.0648522	+	0.0374424i
$581$		0			0
$582$		0			0
$583$	6.98964			0.289481
$584$	18.3204	−	31.7319i	0.758104	−	1.31307i
$585$		0			0
$586$	−12.7266	+	7.34772i	−0.525732	+	0.303531i
$587$	−13.1328	+	22.7466i	−0.542048	+	0.938855i	0.456738	+	0.889601i	$0.349018\pi$
$587$	−13.1328	+	22.7466i	−0.542048	+	0.938855i	−0.998786	+	0.0492535i	$0.984316\pi$
$588$		0			0
$589$	7.92095	+	13.7195i	0.326377	+	0.565302i
$590$	−25.7971	−	14.8940i	−1.06205	−	0.613175i
$591$		0			0
$592$	−6.13331	−	10.6232i	−0.252078	−	0.436611i
$593$	4.56209	+	7.90178i	0.187343	+	0.324487i	0.944363	−	0.328904i	$-0.106679\pi$
$593$	4.56209	+	7.90178i	0.187343	+	0.324487i	−0.757021	+	0.653391i	$0.773346\pi$
$594$		0			0
$595$		0			0
$596$	−2.01298	−	1.16220i	−0.0824550	−	0.0476054i
$597$		0			0
$598$			11.1887i			0.457538i
$599$			23.2080i			0.948252i	0.880457	+	0.474126i	$0.157236\pi$
$599$			23.2080i			0.948252i	−0.880457	+	0.474126i	$0.842764\pi$
$600$		0			0
$601$	19.0021	+	10.9709i	0.775111	+	0.447510i	0.834695	−	0.550713i	$-0.185644\pi$
$601$	19.0021	+	10.9709i	0.775111	+	0.447510i	−0.0595840	+	0.998223i	$0.518977\pi$
$602$		0			0
$603$		0			0
$604$	1.16913	+	2.02499i	0.0475711	+	0.0823955i
$605$	13.7013	+	23.7313i	0.557036	+	0.964815i
$606$		0			0
$607$	−38.6289	−	22.3024i	−1.56790	−	0.905226i	−0.996414	−	0.0846136i	$-0.973034\pi$
$607$	−38.6289	−	22.3024i	−1.56790	−	0.905226i	−0.571484	−	0.820613i	$-0.693632\pi$
$608$	−4.01703	−	6.95770i	−0.162912	−	0.282172i
$609$		0			0
$610$	−18.3184	+	31.7283i	−0.741689	+	1.28464i
$611$	16.0903	−	9.28976i	0.650946	−	0.375824i
$612$		0			0
$613$	−5.82799	+	10.0944i	−0.235390	+	0.407708i	−0.959386	−	0.282097i	$-0.908970\pi$
$613$	−5.82799	+	10.0944i	−0.235390	+	0.407708i	0.723996	+	0.689804i	$0.242303\pi$
$614$	25.1240			1.01392
$615$		0			0
$616$		0			0
$617$	−36.6143	+	21.1393i	−1.47403	+	0.851034i	−0.999572	−	0.0292416i	$-0.990691\pi$
$617$	−36.6143	+	21.1393i	−1.47403	+	0.851034i	−0.474462	+	0.880276i	$0.657357\pi$
$618$		0			0
$619$	−30.0633	+	17.3571i	−1.20835	+	0.697640i	−0.962398	−	0.271643i	$-0.912433\pi$
$619$	−30.0633	+	17.3571i	−1.20835	+	0.697640i	−0.245949	+	0.969283i	$0.579100\pi$
$620$	15.0476	+	8.68773i	0.604326	+	0.348908i
$621$		0			0
$622$			9.23930i			0.370462i
$623$		0			0
$624$		0			0
$625$	−47.8410	+	82.8631i	−1.91364	+	3.31452i
$626$	−11.6673			−0.466319
$627$		0			0
$628$		−	13.1465i		−	0.524604i
$629$	−5.98098			−0.238477
$630$		0			0
$631$	−12.8860			−0.512982			−0.256491	−	0.966547i	$-0.582566\pi$
$631$	−12.8860			−0.512982			−0.256491	+	0.966547i	$0.582566\pi$
$632$			30.0159i			1.19397i
$633$		0			0
$634$	28.3465			1.12578
$635$	40.1457	−	69.5345i	1.59314	−	2.75939i
$636$		0			0
$637$		0			0
$638$		−	1.73325i		−	0.0686200i
$639$		0			0
$640$	13.6030	+	7.85371i	0.537707	+	0.310445i
$641$	−16.5666	+	9.56474i	−0.654342	+	0.377785i	−0.790118	−	0.612955i	$-0.789981\pi$
$641$	−16.5666	+	9.56474i	−0.654342	+	0.377785i	0.135776	+	0.990740i	$0.456647\pi$
$642$		0			0
$643$	9.77521	−	5.64372i	0.385497	−	0.222567i	−0.294710	−	0.955587i	$-0.595223\pi$
$643$	9.77521	−	5.64372i	0.385497	−	0.222567i	0.680207	+	0.733020i	$0.261890\pi$
$644$		0			0
$645$		0			0
$646$	3.33453			0.131195
$647$	2.54339	−	4.40528i	0.0999909	−	0.173189i	−0.811690	−	0.584089i	$-0.801452\pi$
$647$	2.54339	−	4.40528i	0.0999909	−	0.173189i	0.911681	+	0.410900i	$0.134785\pi$
$648$		0			0
$649$	−10.9276	+	6.30906i	−0.428946	+	0.247652i
$650$	−21.0939	+	36.5356i	−0.827369	+	1.43305i
$651$		0			0
$652$	−3.82937	−	6.63267i	−0.149970	−	0.259755i
$653$	−32.9044	−	18.9974i	−1.28765	−	0.743424i	−0.309414	−	0.950927i	$-0.600133\pi$
$653$	−32.9044	−	18.9974i	−1.28765	−	0.743424i	−0.978234	+	0.207503i	$0.933466\pi$
$654$		0			0
$655$	14.5218	+	25.1526i	0.567415	+	0.982792i
$656$	−8.85059	−	15.3297i	−0.345557	−	0.598523i
$657$		0			0
$658$		0			0
$659$	−9.97949	−	5.76166i	−0.388746	−	0.224442i	0.292871	−	0.956152i	$-0.405389\pi$
$659$	−9.97949	−	5.76166i	−0.388746	−	0.224442i	−0.681617	+	0.731710i	$0.738723\pi$
$660$		0			0
$661$		−	43.9858i		−	1.71085i	−0.517929	−	0.855424i	$-0.673297\pi$
$661$		−	43.9858i		−	1.71085i	0.517929	−	0.855424i	$-0.326703\pi$
$662$			10.6907i			0.415504i
$663$		0			0
$664$	4.24660	+	2.45178i	0.164800	+	0.0951473i
$665$		0			0
$666$		0			0
$667$	1.24211	+	2.15140i	0.0480947	+	0.0833025i
$668$	4.71620	+	8.16869i	0.182475	+	0.316056i
$669$		0			0
$670$	−29.4103	−	16.9800i	−1.13622	−	0.655996i
$671$	7.75962	+	13.4401i	0.299557	+	0.518848i
$672$		0			0
$673$	−21.9316	+	37.9866i	−0.845400	+	1.46428i	0.0398735	+	0.999205i	$0.487305\pi$
$673$	−21.9316	+	37.9866i	−0.845400	+	1.46428i	−0.885273	+	0.465071i	$0.846029\pi$
$674$	8.20387	−	4.73650i	0.316001	−	0.182443i
$675$		0			0
$676$	−1.90731	+	3.30355i	−0.0733579	+	0.127060i
$677$	1.47800			0.0568041			0.0284020	−	0.999597i	$-0.490958\pi$
$677$	1.47800			0.0568041			0.0284020	+	0.999597i	$0.490958\pi$
$678$		0			0
$679$		0			0
$680$	13.5208	−	7.80621i	0.518497	−	0.299355i
$681$		0			0
$682$	−14.4617	+	8.34948i	−0.553768	+	0.319718i
$683$	−8.94252	−	5.16296i	−0.342176	−	0.197555i	0.319058	−	0.947735i	$-0.396634\pi$
$683$	−8.94252	−	5.16296i	−0.342176	−	0.197555i	−0.661234	+	0.750180i	$0.729967\pi$
$684$		0			0
$685$		−	59.1162i		−	2.25871i
$686$		0			0
$687$		0			0
$688$	5.10601	−	8.84388i	0.194665	−	0.337170i
$689$	−8.40885			−0.320352
$690$		0			0
$691$		−	7.59984i		−	0.289112i	−0.989497	−	0.144556i	$-0.953825\pi$
$691$		−	7.59984i		−	0.289112i	0.989497	−	0.144556i	$-0.0461753\pi$
$692$	−5.27087			−0.200368
$693$		0			0
$694$	41.6773			1.58205
$695$		−	38.7232i		−	1.46886i
$696$		0			0
$697$	−8.63076			−0.326913
$698$	14.4120	−	24.9624i	0.545503	−	0.944839i
$699$		0			0
$700$		0			0
$701$		−	6.35907i		−	0.240179i	−0.992763	−	0.120089i	$-0.961682\pi$
$701$		−	6.35907i		−	0.240179i	0.992763	−	0.120089i	$-0.0383181\pi$
$702$		0			0
$703$	10.6879	+	6.17064i	0.403100	+	0.232730i
$704$	16.3289	−	9.42749i	0.615419	−	0.355312i
$705$		0			0
$706$	0.991677	−	0.572545i	0.0373223	−	0.0215480i
$707$		0			0
$708$		0			0
$709$	−47.6095			−1.78801			−0.894007	−	0.448054i	$-0.852117\pi$
$709$	−47.6095			−1.78801			−0.894007	+	0.448054i	$0.852117\pi$
$710$	5.00129	−	8.66249i	0.187695	−	0.325098i
$711$		0			0
$712$	−16.2544	+	9.38448i	−0.609159	+	0.351698i
$713$	11.9671	−	20.7276i	0.448171	−	0.776255i
$714$		0			0
$715$	12.1806	+	21.0975i	0.455530	+	0.789002i
$716$	10.1409	+	5.85486i	0.378983	+	0.218806i
$717$		0			0
$718$	−9.37904	−	16.2450i	−0.350023	−	0.606257i
$719$	−7.07350	−	12.2517i	−0.263797	−	0.456910i	0.703451	−	0.710744i	$-0.251642\pi$
$719$	−7.07350	−	12.2517i	−0.263797	−	0.456910i	−0.967248	+	0.253834i	$0.918308\pi$
$720$		0			0
$721$		0			0
$722$	13.4280	+	7.75264i	0.499737	+	0.288524i
$723$		0			0
$724$		−	4.71007i		−	0.175048i
$725$			9.36695i			0.347880i
$726$		0			0
$727$	−40.1828	−	23.1996i	−1.49030	−	0.860424i	−0.490360	−	0.871520i	$-0.663135\pi$
$727$	−40.1828	−	23.1996i	−1.49030	−	0.860424i	−0.999938	+	0.0110955i	$0.996468\pi$
$728$		0			0
$729$		0			0
$730$	−30.3864	−	52.6307i	−1.12465	−	1.94795i
$731$	−2.48960	−	4.31211i	−0.0920811	−	0.159489i
$732$		0			0
$733$	22.8893	+	13.2151i	0.845436	+	0.488112i	0.859108	−	0.511794i	$-0.171019\pi$
$733$	22.8893	+	13.2151i	0.845436	+	0.488112i	−0.0136726	+	0.999907i	$0.504352\pi$
$734$	−14.5559	−	25.2115i	−0.537268	−	0.930575i
$735$		0			0
$736$	−6.06899	+	10.5118i	−0.223706	+	0.387470i
$737$	−12.4581	+	7.19271i	−0.458902	+	0.264947i
$738$		0			0
$739$	23.1335	−	40.0684i	0.850979	−	1.47394i	−0.0293467	−	0.999569i	$-0.509343\pi$
$739$	23.1335	−	40.0684i	0.850979	−	1.47394i	0.880326	−	0.474370i	$-0.157324\pi$
$740$	13.5360			0.497592
$741$		0			0
$742$		0			0
$743$	36.5640	−	21.1102i	1.34140	−	0.774458i	0.354388	−	0.935098i	$-0.384689\pi$
$743$	36.5640	−	21.1102i	1.34140	−	0.774458i	0.987013	+	0.160640i	$0.0513558\pi$
$744$		0			0
$745$	−14.2525	+	8.22868i	−0.522171	+	0.301476i
$746$	−9.62825	−	5.55887i	−0.352515	−	0.203525i
$747$		0			0
$748$		−	1.54923i		−	0.0566456i
$749$		0			0
$750$		0			0
$751$	8.02320	−	13.8966i	0.292771	−	0.507094i	−0.681693	−	0.731638i	$-0.738756\pi$
$751$	8.02320	−	13.8966i	0.292771	−	0.507094i	0.974464	+	0.224544i	$0.0720894\pi$
$752$	−17.1575			−0.625671
$753$		0			0
$754$			2.08518i			0.0759376i
$755$	16.5555			0.602516
$756$		0			0
$757$	25.0149			0.909183			0.454591	−	0.890700i	$-0.349785\pi$
$757$	25.0149			0.909183			0.454591	+	0.890700i	$0.349785\pi$
$758$		−	24.5102i		−	0.890252i
$759$		0			0
$760$	−32.2150			−1.16856
$761$	3.00365	−	5.20247i	0.108882	−	0.188589i	−0.806436	−	0.591322i	$-0.798606\pi$
$761$	3.00365	−	5.20247i	0.108882	−	0.188589i	0.915318	+	0.402733i	$0.131940\pi$
$762$		0			0
$763$		0			0
$764$			11.3889i			0.412035i
$765$		0			0
$766$	−6.59165	−	3.80569i	−0.238166	−	0.137505i
$767$	13.1464	−	7.59008i	0.474689	−	0.274062i
$768$		0			0
$769$	−28.9946	+	16.7400i	−1.04557	+	0.603661i	−0.921406	−	0.388600i	$-0.872959\pi$
$769$	−28.9946	+	16.7400i	−1.04557	+	0.603661i	−0.124166	+	0.992262i	$0.539625\pi$
$770$		0			0
$771$		0			0
$772$	11.0832			0.398892
$773$	−18.1008	+	31.3515i	−0.651040	+	1.12763i	0.331831	+	0.943339i	$0.392334\pi$
$773$	−18.1008	+	31.3515i	−0.651040	+	1.12763i	−0.982871	+	0.184296i	$0.941000\pi$
$774$		0			0
$775$	78.1551	−	45.1229i	2.80741	−	1.62086i
$776$	−4.19980	+	7.27427i	−0.150764	+	0.261131i
$777$		0			0
$778$	0.0303280	+	0.0525296i	0.00108731	+	0.00188328i
$779$	15.4230	+	8.90445i	0.552585	+	0.319035i
$780$		0			0
$781$	−2.11854	−	3.66942i	−0.0758073	−	0.131302i
$782$	−2.51893	−	4.36291i	−0.0900766	−	0.156017i
$783$		0			0
$784$		0			0
$785$	−80.6108	−	46.5407i	−2.87712	−	1.66111i
$786$		0			0
$787$		−	16.3887i		−	0.584193i	−0.956389	−	0.292096i	$-0.905647\pi$
$787$		−	16.3887i		−	0.584193i	0.956389	−	0.292096i	$-0.0943528\pi$
$788$		−	10.1532i		−	0.361693i
$789$		0			0
$790$	43.1147	+	24.8923i	1.53395	+	0.885628i
$791$		0			0
$792$		0			0
$793$	−9.33517	−	16.1690i	−0.331502	−	0.574178i
$794$	−7.48929	−	12.9718i	−0.265785	−	0.460353i
$795$		0			0
$796$	1.44065	+	0.831760i	0.0510625	+	0.0294809i
$797$	−23.3328	−	40.4137i	−0.826492	−	1.43153i	−0.900774	−	0.434288i	$-0.857000\pi$
$797$	−23.3328	−	40.4137i	−0.826492	−	1.43153i	0.0742821	−	0.997237i	$-0.476333\pi$
$798$		0			0
$799$	−4.18285	+	7.24491i	−0.147979	+	0.256306i
$800$	−39.6356	+	22.8836i	−1.40133	+	0.809057i
$801$		0			0
$802$	−1.49464	+	2.58880i	−0.0527777	+	0.0914137i
$803$	−25.7432			−0.908459
$804$		0			0
$805$		0			0
$806$	17.3981	−	10.0448i	0.612822	−	0.353813i
$807$		0			0
$808$	−42.6319	+	24.6136i	−1.49979	+	0.865902i
$809$	−25.8925	−	14.9490i	−0.910330	−	0.525580i	−0.0297930	−	0.999556i	$-0.509485\pi$
$809$	−25.8925	−	14.9490i	−0.910330	−	0.525580i	−0.880537	+	0.473977i	$0.842818\pi$
$810$		0			0
$811$		−	25.3404i		−	0.889821i	−0.895575	−	0.444911i	$-0.853235\pi$
$811$		−	25.3404i		−	0.889821i	0.895575	−	0.444911i	$-0.146765\pi$
$812$		0			0
$813$		0			0
$814$	−6.50447	+	11.2661i	−0.227982	+	0.394876i
$815$	−54.2261			−1.89946
$816$		0			0
$817$			10.2742i			0.359448i
$818$	−0.0674323			−0.00235772
$819$		0			0
$820$	19.5329			0.682117
$821$			10.6580i			0.371968i	0.982553	+	0.185984i	$0.0595472\pi$
$821$			10.6580i			0.371968i	−0.982553	+	0.185984i	$0.940453\pi$
$822$		0			0
$823$	17.1048			0.596235			0.298118	−	0.954529i	$-0.403641\pi$
$823$	17.1048			0.596235			0.298118	+	0.954529i	$0.403641\pi$
$824$	4.64156	−	8.03943i	0.161697	−	0.280067i
$825$		0			0
$826$		0			0
$827$			18.3221i			0.637121i	0.947903	+	0.318560i	$0.103199\pi$
$827$			18.3221i			0.637121i	−0.947903	+	0.318560i	$0.896801\pi$
$828$		0			0
$829$	−6.69733	−	3.86670i	−0.232608	−	0.134296i	0.379167	−	0.925328i	$-0.376211\pi$
$829$	−6.69733	−	3.86670i	−0.232608	−	0.134296i	−0.611775	+	0.791032i	$0.709544\pi$
$830$	7.04344	−	4.06653i	0.244481	−	0.141151i
$831$		0			0
$832$	−19.6444	+	11.3417i	−0.681047	+	0.393203i
$833$		0			0
$834$		0			0
$835$	66.7841			2.31116
$836$	−1.59836	+	2.76844i	−0.0552805	+	0.0957486i
$837$		0			0
$838$	−6.28551	+	3.62894i	−0.217129	+	0.125360i
$839$	−9.73588	+	16.8630i	−0.336120	+	0.582177i	−0.983699	−	0.179821i	$-0.942448\pi$
$839$	−9.73588	+	16.8630i	−0.336120	+	0.582177i	0.647579	+	0.761998i	$0.275781\pi$
$840$		0			0
$841$	−14.2685	−	24.7138i	−0.492018	−	0.852200i
$842$	−30.7519	−	17.7546i	−1.05978	−	0.611865i
$843$		0			0
$844$	−8.53184	−	14.7776i	−0.293678	−	0.508665i
$845$	13.5043	+	23.3901i	0.464561	+	0.804643i
$846$		0			0
$847$		0			0
$848$	6.72493	+	3.88264i	0.230935	+	0.133330i
$849$		0			0
$850$		−	18.9956i		−	0.651545i
$851$		−	18.6454i		−	0.639155i
$852$		0			0
$853$	0.812274	+	0.468967i	0.0278117	+	0.0160571i	0.513841	−	0.857885i	$-0.328222\pi$
$853$	0.812274	+	0.468967i	0.0278117	+	0.0160571i	−0.486030	+	0.873942i	$0.661555\pi$
$854$		0			0
$855$		0			0
$856$	18.2305	+	31.5761i	0.623104	+	1.07925i
$857$	−9.00087	−	15.5900i	−0.307464	−	0.532543i	0.670343	−	0.742051i	$-0.266147\pi$
$857$	−9.00087	−	15.5900i	−0.307464	−	0.532543i	−0.977807	+	0.209509i	$0.932814\pi$
$858$		0			0
$859$	−23.1160	−	13.3460i	−0.788709	−	0.455361i	0.0507989	−	0.998709i	$-0.483823\pi$
$859$	−23.1160	−	13.3460i	−0.788709	−	0.455361i	−0.839508	+	0.543348i	$0.817157\pi$
$860$	5.63438	+	9.75903i	0.192131	+	0.332780i
$861$		0			0
$862$	−4.75486	+	8.23566i	−0.161951	+	0.280508i
$863$	24.0405	−	13.8798i	0.818348	−	0.472473i	−0.0314987	−	0.999504i	$-0.510028\pi$
$863$	24.0405	−	13.8798i	0.818348	−	0.472473i	0.849846	+	0.527031i	$0.176695\pi$
$864$		0			0
$865$	−18.6596	+	32.3194i	−0.634446	+	1.09889i
$866$	33.5715			1.14080
$867$		0			0
$868$		0			0
$869$	18.2633	−	10.5443i	0.619540	−	0.357692i
$870$		0			0
$871$	14.9877	−	8.65316i	0.507839	−	0.293201i
$872$	19.0856	+	11.0191i	0.646319	+	0.373152i
$873$		0			0
$874$			10.3952i			0.351623i
$875$		0			0
$876$		0			0
$877$	−6.90978	+	11.9681i	−0.233327	+	0.404134i	−0.958785	−	0.284132i	$-0.908295\pi$
$877$	−6.90978	+	11.9681i	−0.233327	+	0.404134i	0.725458	+	0.688266i	$0.241628\pi$
$878$	−2.40894			−0.0812979
$879$		0			0
$880$		−	22.4968i		−	0.758367i
$881$	43.9006			1.47905			0.739525	−	0.673129i	$-0.235050\pi$
$881$	43.9006			1.47905			0.739525	+	0.673129i	$0.235050\pi$
$882$		0			0
$883$	7.96743			0.268125			0.134063	−	0.990973i	$-0.457198\pi$
$883$	7.96743			0.268125			0.134063	+	0.990973i	$0.457198\pi$
$884$			1.86380i			0.0626863i
$885$		0			0
$886$	−28.7500			−0.965875
$887$	−10.6080	+	18.3736i	−0.356181	+	0.616924i	−0.987319	−	0.158747i	$-0.949255\pi$
$887$	−10.6080	+	18.3736i	−0.356181	+	0.616924i	0.631138	+	0.775670i	$0.282588\pi$
$888$		0			0
$889$		0			0
$890$			31.1303i			1.04349i
$891$		0			0
$892$	4.06477	+	2.34680i	0.136099	+	0.0785766i
$893$	14.9493	−	8.63098i	0.500259	−	0.288825i
$894$		0			0
$895$	71.8005	−	41.4541i	2.40003	−	1.38566i
$896$		0			0
$897$		0			0
$898$	0.345848			0.0115411
$899$	2.23025	−	3.86291i	0.0743830	−	0.128835i
$900$		0			0
$901$	3.27895	−	1.89310i	0.109238	−	0.0630684i
$902$	−9.38618	+	16.2573i	−0.312526	+	0.541310i
$903$		0			0
$904$	4.37242	+	7.57325i	0.145424	+	0.251883i
$905$	−28.8808	−	16.6743i	−0.960029	−	0.554273i
$906$		0			0
$907$	−1.88344	−	3.26221i	−0.0625385	−	0.108320i	0.833061	−	0.553181i	$-0.186586\pi$
$907$	−1.88344	−	3.26221i	−0.0625385	−	0.108320i	−0.895599	+	0.444861i	$0.853253\pi$
$908$	−0.712420	−	1.23395i	−0.0236425	−	0.0409500i
$909$		0			0
$910$		0			0
$911$	−40.0013	−	23.0947i	−1.32530	−	0.765163i	−0.340732	−	0.940160i	$-0.610675\pi$
$911$	−40.0013	−	23.0947i	−1.32530	−	0.765163i	−0.984569	+	0.174998i	$0.944008\pi$
$912$		0			0
$913$		−	3.44515i		−	0.114018i
$914$		−	19.4985i		−	0.644953i
$915$		0			0
$916$	6.34196	+	3.66153i	0.209544	+	0.120980i
$917$		0			0
$918$		0			0
$919$	−0.607610	−	1.05241i	−0.0200432	−	0.0347158i	0.855830	−	0.517257i	$-0.173047\pi$
$919$	−0.607610	−	1.05241i	−0.0200432	−	0.0347158i	−0.875873	+	0.482542i	$0.839714\pi$
$920$	24.3355	+	42.1503i	0.802316	+	1.38965i
$921$		0			0
$922$	20.5213	+	11.8480i	0.675833	+	0.390192i
$923$	2.54870	+	4.41447i	0.0838914	+	0.145304i
$924$		0			0
$925$	35.1520	−	60.8850i	1.15579	−	2.00189i
$926$	19.0725	−	11.0115i	0.626760	−	0.361860i
$927$		0			0
$928$	−1.13105	+	1.95903i	−0.0371285	+	0.0643084i
$929$	−18.8903			−0.619771			−0.309886	−	0.950774i	$-0.600291\pi$
$929$	−18.8903			−0.619771			−0.309886	+	0.950774i	$0.600291\pi$
$930$		0			0
$931$		0			0
$932$	−1.33941	+	0.773306i	−0.0438737	+	0.0253305i
$933$		0			0
$934$	29.9581	−	17.2963i	0.980258	−	0.565952i
$935$	−9.49945	−	5.48451i	−0.310665	−	0.179363i
$936$		0			0
$937$			27.0448i			0.883516i	0.897134	+	0.441758i	$0.145645\pi$
$937$			27.0448i			0.883516i	−0.897134	+	0.441758i	$0.854355\pi$
$938$		0			0
$939$		0			0
$940$	9.46650	−	16.3965i	0.308763	−	0.534793i
$941$	−16.3205			−0.532032			−0.266016	−	0.963969i	$-0.585707\pi$
$941$	−16.3205			−0.532032			−0.266016	+	0.963969i	$0.585707\pi$
$942$		0			0
$943$		−	26.9059i		−	0.876178i
$944$	−14.0184			−0.456259
$945$		0			0
$946$	−10.8300			−0.352114
$947$		−	28.7020i		−	0.932691i	−0.884603	−	0.466345i	$-0.845570\pi$
$947$		−	28.7020i		−	0.932691i	0.884603	−	0.466345i	$-0.154430\pi$
$948$		0			0
$949$	30.9703			1.00534
$950$	−19.5980	+	33.9447i	−0.635842	+	1.10131i
$951$		0			0
$952$		0			0
$953$			34.5757i			1.12002i	0.828486	+	0.560009i	$0.189202\pi$
$953$			34.5757i			1.12002i	−0.828486	+	0.560009i	$0.810798\pi$
$954$		0			0
$955$	69.8333	+	40.3183i	2.25975	+	1.30467i
$956$	−10.6820	+	6.16723i	−0.345479	+	0.199462i
$957$		0			0
$958$	−22.3785	+	12.9202i	−0.723015	+	0.417433i
$959$		0			0
$960$		0			0
$961$	−11.9746			−0.386278
$962$	7.82517	−	13.5536i	0.252294	−	0.436985i
$963$		0			0
$964$	11.0899	−	6.40275i	0.357181	−	0.206219i
$965$	39.2360	−	67.9588i	1.26305	−	2.18767i
$966$		0			0
$967$	−5.25000	−	9.09327i	−0.168829	−	0.292420i	0.769180	−	0.639033i	$-0.220665\pi$
$967$	−5.25000	−	9.09327i	−0.168829	−	0.292420i	−0.938008	+	0.346613i	$0.887332\pi$
$968$	16.8577	+	9.73277i	0.541826	+	0.312823i
$969$		0			0
$970$	6.96583	+	12.0652i	0.223659	+	0.387389i
$971$	−11.4156	−	19.7724i	−0.366345	−	0.634527i	0.622646	−	0.782503i	$-0.286058\pi$
$971$	−11.4156	−	19.7724i	−0.366345	−	0.634527i	−0.988991	+	0.147976i	$0.952724\pi$
$972$		0			0
$973$		0			0
$974$	1.09973	+	0.634927i	0.0352375	+	0.0203444i
$975$		0			0
$976$			17.2414i			0.551884i
$977$			10.2601i			0.328250i	0.986440	+	0.164125i	$0.0524800\pi$
$977$			10.2601i			0.328250i	−0.986440	+	0.164125i	$0.947520\pi$
$978$		0			0
$979$	11.4201	+	6.59337i	0.364987	+	0.210725i
$980$		0			0
$981$		0			0
$982$	11.1360	+	19.2881i	0.355363	+	0.615508i
$983$	16.9599	+	29.3754i	0.540937	+	0.936930i	0.998851	+	0.0479337i	$0.0152636\pi$
$983$	16.9599	+	29.3754i	0.540937	+	0.936930i	−0.457913	+	0.888997i	$0.651403\pi$
$984$		0			0
$985$	−62.2566	−	35.9438i	−1.98366	−	1.14527i
$986$	−0.469440	−	0.813095i	−0.0149500	−	0.0258942i
$987$		0			0
$988$	1.92290	−	3.33056i	0.0611756	−	0.105959i
$989$	13.4428	−	7.76119i	0.427455	−	0.246791i
$990$		0			0
$991$	−11.4278	+	19.7935i	−0.363015	+	0.628761i	−0.988456	−	0.151511i	$-0.951586\pi$
$991$	−11.4278	+	19.7935i	−0.363015	+	0.628761i	0.625440	+	0.780272i	$0.284919\pi$
$992$	21.7941			0.691964
$993$		0			0
$994$		0			0
$995$	10.2002	−	5.88910i	0.323369	−	0.186697i
$996$		0			0
$997$	5.65867	−	3.26704i	0.179212	−	0.103468i	−0.407710	−	0.913111i	$-0.633673\pi$
$997$	5.65867	−	3.26704i	0.179212	−	0.103468i	0.586922	+	0.809643i	$0.300339\pi$
$998$	−17.0254	−	9.82961i	−0.538929	−	0.311151i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.i.d.521.1		48
3.2	odd	2		441.2.i.d.227.17		48
7.2	even	3		1323.2.s.d.656.7		48
7.3	odd	6		1323.2.o.e.440.17		48
7.4	even	3		1323.2.o.e.440.18		48
7.5	odd	6		1323.2.s.d.656.8		48
7.6	odd	2	inner	1323.2.i.d.521.20		48
9.4	even	3		441.2.s.d.374.18		48
9.5	odd	6		1323.2.s.d.962.8		48
21.2	odd	6		441.2.s.d.362.17		48
21.5	even	6		441.2.s.d.362.18		48
21.11	odd	6		441.2.o.e.146.8	yes	48
21.17	even	6		441.2.o.e.146.7	✓	48
21.20	even	2		441.2.i.d.227.18		48
63.4	even	3		441.2.o.e.293.7	yes	48
63.5	even	6	inner	1323.2.i.d.1097.1		48
63.13	odd	6		441.2.s.d.374.17		48
63.23	odd	6	inner	1323.2.i.d.1097.20		48
63.31	odd	6		441.2.o.e.293.8	yes	48
63.32	odd	6		1323.2.o.e.881.17		48
63.40	odd	6		441.2.i.d.68.7		48
63.41	even	6		1323.2.s.d.962.7		48
63.58	even	3		441.2.i.d.68.8		48
63.59	even	6		1323.2.o.e.881.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.7		48	63.40	odd	6
441.2.i.d.68.8		48	63.58	even	3
441.2.i.d.227.17		48	3.2	odd	2
441.2.i.d.227.18		48	21.20	even	2
441.2.o.e.146.7	✓	48	21.17	even	6
441.2.o.e.146.8	yes	48	21.11	odd	6
441.2.o.e.293.7	yes	48	63.4	even	3
441.2.o.e.293.8	yes	48	63.31	odd	6
441.2.s.d.362.17		48	21.2	odd	6
441.2.s.d.362.18		48	21.5	even	6
441.2.s.d.374.17		48	63.13	odd	6
441.2.s.d.374.18		48	9.4	even	3
1323.2.i.d.521.1		48	1.1	even	1	trivial
1323.2.i.d.521.20		48	7.6	odd	2	inner
1323.2.i.d.1097.1		48	63.5	even	6	inner
1323.2.i.d.1097.20		48	63.23	odd	6	inner
1323.2.o.e.440.17		48	7.3	odd	6
1323.2.o.e.440.18		48	7.4	even	3
1323.2.o.e.881.17		48	63.32	odd	6
1323.2.o.e.881.18		48	63.59	even	6
1323.2.s.d.656.7		48	7.2	even	3
1323.2.s.d.656.8		48	7.5	odd	6
1323.2.s.d.962.7		48	63.41	even	6
1323.2.s.d.962.8		48	9.5	odd	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.17820i q^{2} +0.611843 q^{4} +(2.16601 - 3.75164i) q^{5} -3.07728i q^{8} +O(q^{10})\)	\(q-1.17820i q^{2} +0.611843 q^{4} +(2.16601 - 3.75164i) q^{5} -3.07728i q^{8} +(-4.42019 - 2.55200i) q^{10} +(-1.87238 + 1.08102i) q^{11} +(2.25256 - 1.30052i) q^{13} -2.40196 q^{16} +(-0.585576 + 1.01425i) q^{17} +(2.09282 - 1.20829i) q^{19} +(1.32526 - 2.29541i) q^{20} +(1.27366 + 2.20604i) q^{22} +(-3.16186 - 1.82550i) q^{23} +(-6.88321 - 11.9221i) q^{25} +(-1.53227 - 2.65397i) q^{26} +(-0.589262 - 0.340210i) q^{29} +6.55550i q^{31} -3.32456i q^{32} +(1.19499 + 0.689926i) q^{34} +(2.55346 + 4.42272i) q^{37} +(-1.42361 - 2.46576i) q^{38} +(-11.5448 - 6.66541i) q^{40} +(3.68473 + 6.38214i) q^{41} +(-2.12577 + 3.68194i) q^{43} +(-1.14560 + 0.661414i) q^{44} +(-2.15081 + 3.72531i) q^{46} +7.14314 q^{47} +(-14.0466 + 8.10980i) q^{50} +(1.37821 - 0.795711i) q^{52} +(-2.79976 - 1.61644i) q^{53} +9.36601i q^{55} +(-0.400836 + 0.694269i) q^{58} +5.83621 q^{59} -7.17805i q^{61} +7.72370 q^{62} -8.72092 q^{64} -11.2677i q^{65} +6.65363 q^{67} +(-0.358281 + 0.620560i) q^{68} +1.95976i q^{71} +(10.3117 + 5.95345i) q^{73} +(5.21085 - 3.00849i) q^{74} +(1.28048 - 0.739283i) q^{76} -9.75404 q^{79} +(-5.20268 + 9.01130i) q^{80} +(7.51944 - 4.34135i) q^{82} +(-0.796736 + 1.37999i) q^{83} +(2.53673 + 4.39374i) q^{85} +(4.33806 + 2.50458i) q^{86} +(3.32660 + 5.76184i) q^{88} +(-3.04961 - 5.28207i) q^{89} +(-1.93456 - 1.11692i) q^{92} -8.41605i q^{94} -10.4687i q^{95} +(-2.36387 - 1.36478i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4}+O(q^{10}) \) 48 * q - 48 * q^4	\( 48 q - 48 q^{4} - 24 q^{11} + 48 q^{16} - 48 q^{23} - 24 q^{25} + 96 q^{44} - 48 q^{50} + 48 q^{53} - 48 q^{64} - 168 q^{74} + 48 q^{79} - 24 q^{85} + 24 q^{86} + 144 q^{92}+O(q^{100}) \) 48 * q - 48 * q^4 - 24 * q^11 + 48 * q^16 - 48 * q^23 - 24 * q^25 + 96 * q^44 - 48 * q^50 + 48 * q^53 - 48 * q^64 - 168 * q^74 + 48 * q^79 - 24 * q^85 + 24 * q^86 + 144 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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