LMFDB - Embedded newform 1323.2.i.d.521.20

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			521.20
Character	$\chi$	$=$	1323.521
Dual form			1323.2.i.d.1097.20

$q$-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	$0.586777\pi$
$5$	−2.16601	+	3.75164i	−0.968670	+	1.67778i	−0.699415	+	0.714716i	$0.746556\pi$
$6$		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	−0.778715	−	0.627378i	$-0.784128\pi$
$13$	−2.25256	+	1.30052i	−0.624748	+	0.360698i	0.153967	+	0.988076i	$0.450795\pi$
$14$		0			0
$15$		0			0
$16$	−2.40196			−0.600491
$17$	0.585576	−	1.01425i	0.142023	−	0.245991i	−0.786235	−	0.617927i	$-0.787973\pi$
$17$	0.585576	−	1.01425i	0.142023	−	0.245991i	0.928258	+	0.371936i	$0.121306\pi$
$18$		0			0
$19$	−2.09282	+	1.20829i	−0.480126	+	0.277201i	−0.720469	−	0.693487i	$-0.756073\pi$
$19$	−2.09282	+	1.20829i	−0.480126	+	0.277201i	0.240343	+	0.970688i	$0.422740\pi$
$20$	−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	$-0.799639\pi$
$31$		−	6.55550i		−	1.17740i	0.808350	−	0.588702i	$-0.200361\pi$
$32$		−	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	$-0.971490\pi$
$41$	−3.68473	−	6.38214i	−0.575458	−	0.996723i	0.420534	−	0.907277i	$-0.361843\pi$
$42$		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	$-0.674428\pi$
$47$	−7.14314			−1.04193			−0.520967	+	0.853577i	$0.674428\pi$
$48$		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	$-0.624043\pi$
$59$	−5.83621			−0.759810			−0.379905	+	0.925026i	$0.624043\pi$
$60$		0			0
$61$			7.17805i			0.919055i	0.888163	+	0.459528i	$0.151981\pi$
$61$			7.17805i			0.919055i	−0.888163	+	0.459528i	$0.848019\pi$
$62$	−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	−0.244812	−	0.969570i	$-0.578726\pi$
$73$	−10.3117	−	5.95345i	−1.20689	−	0.696799i	−0.962079	+	0.272771i	$0.912060\pi$
$74$	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	−0.818981	−	0.573821i	$-0.805461\pi$
$83$	0.796736	−	1.37999i	0.0874531	−	0.151473i	0.906434	+	0.422348i	$0.138794\pi$
$84$		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	0.981158	−	0.193206i	$-0.0618886\pi$
$89$	3.04961	+	5.28207i	0.323258	+	0.559899i	−0.657901	+	0.753105i	$0.728555\pi$
$90$		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	0.615183	−	0.788384i	$-0.289082\pi$
$97$	2.36387	+	1.36478i	0.240014	+	0.138572i	−0.375169	+	0.926956i	$0.622415\pi$
$98$		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	$0.126324\pi$
$101$	7.99849	+	13.8538i	0.795880	+	1.37850i	−0.126400	+	0.991979i	$0.540342\pi$
$102$		0			0
$103$	−2.61251	−	1.50834i	−0.257419	−	0.148621i	0.365738	−	0.930718i	$-0.380817\pi$
$103$	−2.61251	−	1.50834i	−0.257419	−	0.148621i	−0.623156	+	0.782097i	$0.714150\pi$
$104$	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	−0.681607	−	0.731719i	$-0.738718\pi$
$131$	3.35221	−	5.80619i	0.292884	−	0.507289i	0.974490	+	0.224429i	$0.0720518\pi$
$132$		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	−0.790982	−	0.611839i	$-0.790430\pi$
$139$	−7.74126	+	4.46942i	−0.656605	+	0.379091i	0.134377	+	0.990930i	$0.457097\pi$
$140$		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	$0.327932\pi$
$157$			21.4868i			1.71483i	−0.514622	+	0.857417i	$0.672068\pi$
$158$			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	$-0.963233\pi$
$167$	−7.70819	−	13.3510i	−0.596477	−	1.03313i	0.396859	−	0.917880i	$-0.370100\pi$
$168$		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	$-0.393799\pi$
$173$	8.61474			0.654967			0.327483	+	0.944857i	$0.393799\pi$
$174$		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	$0.0923590\pi$
$181$			7.69817i			0.572200i	−0.958200	+	0.286100i	$0.907641\pi$
$182$		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	0.414216	−	0.910179i	$-0.364056\pi$
$199$	−2.35461	−	1.35943i	−0.166914	−	0.0963677i	−0.581130	+	0.813811i	$0.697389\pi$
$200$	−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	0.260785	−	0.965397i	$-0.416019\pi$
$223$	−6.64349	−	3.83562i	−0.444881	−	0.256852i	−0.705666	+	0.708545i	$0.749352\pi$
$224$		0			0
$225$		0			0
$226$	1.67407	+	2.89958i	0.111358	+	0.192877i
$227$	1.16439	+	2.01677i	0.0772829	+	0.133858i	0.902077	−	0.431576i	$-0.142042\pi$
$227$	1.16439	+	2.01677i	0.0772829	+	0.133858i	−0.824794	+	0.565434i	$0.808709\pi$
$228$		0			0
$229$	−10.3653	−	5.98443i	−0.684961	−	0.395463i	0.116760	−	0.993160i	$-0.462749\pi$
$229$	−10.3653	−	5.98443i	−0.684961	−	0.395463i	−0.801722	+	0.597698i	$0.796082\pi$
$230$	−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	−0.953104	−	0.302643i	$-0.902131\pi$
$241$	−18.1254	+	10.4647i	−1.16756	+	0.674091i	−0.214455	+	0.976734i	$0.568798\pi$
$242$	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	$-0.798980\pi$
$251$	−25.5747			−1.61426			−0.807130	+	0.590374i	$0.798980\pi$
$252$		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	−0.619265	−	0.785182i	$-0.712569\pi$
$257$	5.93725	−	10.2836i	0.370355	−	0.641474i	0.989620	+	0.143708i	$0.0459026\pi$
$258$		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	−0.923232	−	0.384242i	$-0.874463\pi$
$269$	−2.11335	+	3.66043i	−0.128853	+	0.223180i	0.794379	+	0.607422i	$0.207796\pi$
$270$		0			0
$271$	19.3941	−	11.1972i	1.17811	−	0.680179i	0.222530	−	0.974926i	$-0.428568\pi$
$271$	19.3941	−	11.1972i	1.17811	−	0.680179i	0.955576	+	0.294746i	$0.0952352\pi$
$272$	−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	$-0.816608\pi$
$283$		−	18.3297i		−	1.08959i	0.838570	−	0.544794i	$-0.183392\pi$
$284$			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	0.988669	−	0.150112i	$-0.0479634\pi$
$293$	6.23639	+	10.8017i	0.364334	+	0.631044i	−0.624335	+	0.781156i	$0.714630\pi$
$294$		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	$-0.791766\pi$
$307$		−	21.3241i		−	1.21703i	0.793543	−	0.608514i	$-0.208234\pi$
$308$		0			0
$309$		0			0
$310$	16.7296	−	28.9765i	0.950178	−	1.64576i
$311$	7.84187			0.444672			0.222336	−	0.974970i	$-0.428632\pi$
$311$	7.84187			0.444672			0.222336	+	0.974970i	$0.428632\pi$
$312$		0			0
$313$			9.90263i			0.559730i	0.960039	+	0.279865i	$0.0902897\pi$
$313$			9.90263i			0.559730i	−0.960039	+	0.279865i	$0.909710\pi$
$314$	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	−0.189141	−	0.981950i	$-0.560570\pi$
$349$	−21.1868	−	12.2322i	−1.13411	−	0.654776i	−0.944964	+	0.327174i	$0.893904\pi$
$350$		0			0
$351$		0			0
$352$	3.59391	+	6.22484i	0.191556	+	0.331785i
$353$	−0.485949	−	0.841688i	−0.0258644	−	0.0447985i	0.852803	−	0.522232i	$-0.174900\pi$
$353$	−0.485949	−	0.841688i	−0.0258644	−	0.0447985i	−0.878668	+	0.477433i	$0.841567\pi$
$354$		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	−0.940629	−	0.339435i	$-0.889764\pi$
$367$	−21.3983	+	12.3543i	−1.11698	+	0.644891i	−0.176355	+	0.984327i	$0.556431\pi$
$368$	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	−0.936673	−	0.350205i	$-0.886112\pi$
$383$	−3.23008	+	5.59467i	−0.165050	+	0.285874i	0.771623	+	0.636080i	$0.219445\pi$
$384$		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	−0.750158	−	0.661259i	$-0.770022\pi$
$397$	−11.0099	+	6.35655i	−0.552569	+	0.319026i	0.197588	+	0.980285i	$0.436689\pi$
$398$	−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	$0.000450409\pi$
$409$			0.0572333i			0.00283000i	−0.999999	+	0.00141500i	$0.999550\pi$
$410$		−	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	0.931401	−	0.363995i	$-0.118588\pi$
$419$	3.08007	+	5.33484i	0.150471	+	0.260624i	−0.780930	+	0.624619i	$0.785254\pi$
$420$		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	$-0.759949\pi$
$433$		−	28.4938i		−	1.36933i	0.728860	−	0.684663i	$-0.240051\pi$
$434$		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	$0.0155370\pi$
$439$			2.04460i			0.0975832i	−0.998809	+	0.0487916i	$0.984463\pi$
$440$	−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	−0.530992	−	0.847377i	$-0.678180\pi$
$461$	10.0560	−	17.4175i	0.468354	−	0.811213i	0.999346	+	0.0361638i	$0.0115138\pi$
$462$		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	$-0.928941\pi$
$467$	−14.6803	−	25.4270i	−0.679322	−	1.17662i	0.295864	−	0.955230i	$-0.404393\pi$
$468$		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	$0.000386605\pi$
$479$	10.9660	+	18.9938i	0.501051	+	0.867847i	−0.498948	+	0.866632i	$0.666280\pi$
$480$		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	$-0.342994\pi$
$503$	21.2386			0.946981			0.473491	+	0.880799i	$0.342994\pi$
$504$		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	−0.964527	−	0.263984i	$-0.914963\pi$
$509$	−5.72252	+	9.91170i	−0.253646	+	0.439328i	0.710881	+	0.703313i	$0.248297\pi$
$510$		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	−0.998724	−	0.0505007i	$-0.983918\pi$
$521$	−10.3999	+	18.0131i	−0.455627	+	0.789169i	0.543097	+	0.839670i	$0.317252\pi$
$522$		0			0
$523$	12.9330	−	7.46690i	0.565523	−	0.326505i	−0.189836	−	0.981816i	$-0.560796\pi$
$523$	12.9330	−	7.46690i	0.565523	−	0.326505i	0.755359	+	0.655311i	$0.227462\pi$
$524$	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	$-0.704004\pi$
$563$	−28.3743			−1.19583			−0.597916	+	0.801559i	$0.704004\pi$
$564$		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	0.626566	−	0.779369i	$-0.284460\pi$
$577$	6.36301	+	3.67369i	0.264896	+	0.152938i	−0.361670	+	0.932306i	$0.617793\pi$
$578$	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	$-0.650982\pi$
$587$	13.1328	−	22.7466i	0.542048	−	0.938855i	0.998786	−	0.0492535i	$-0.0156842\pi$
$588$		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	0.757021	−	0.653391i	$-0.226654\pi$
$593$	−4.56209	−	7.90178i	−0.187343	−	0.324487i	−0.944363	+	0.328904i	$0.893321\pi$
$594$		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	0.0595840	−	0.998223i	$-0.481023\pi$
$601$	−19.0021	−	10.9709i	−0.775111	−	0.447510i	−0.834695	+	0.550713i	$0.814356\pi$
$602$		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	$0.0269656\pi$
$607$	38.6289	+	22.3024i	1.56790	+	0.905226i	0.571484	+	0.820613i	$0.306368\pi$
$608$	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	0.245949	−	0.969283i	$-0.420900\pi$
$619$	30.0633	−	17.3571i	1.20835	−	0.697640i	0.962398	+	0.271643i	$0.0875670\pi$
$620$	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	−0.680207	−	0.733020i	$-0.738110\pi$
$643$	−9.77521	+	5.64372i	−0.385497	+	0.222567i	0.294710	+	0.955587i	$0.404777\pi$
$644$		0			0
$645$		0			0
$646$	3.33453			0.131195
$647$	−2.54339	+	4.40528i	−0.0999909	+	0.173189i	−0.911681	−	0.410900i	$-0.865215\pi$
$647$	−2.54339	+	4.40528i	−0.0999909	+	0.173189i	0.811690	+	0.584089i	$0.198548\pi$
$648$		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	$0.326703\pi$
$661$			43.9858i			1.71085i	−0.517929	+	0.855424i	$0.673297\pi$
$662$			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	$-0.509042\pi$
$677$	−1.47800			−0.0568041			−0.0284020	+	0.999597i	$0.509042\pi$
$678$		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	$0.0461753\pi$
$691$			7.59984i			0.289112i	−0.989497	+	0.144556i	$0.953825\pi$
$692$	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	0.967248	−	0.253834i	$-0.0816917\pi$
$719$	7.07350	+	12.2517i	0.263797	+	0.456910i	−0.703451	+	0.710744i	$0.748358\pi$
$720$		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	0.999938	−	0.0110955i	$-0.00353187\pi$
$727$	40.1828	+	23.1996i	1.49030	+	0.860424i	0.490360	+	0.871520i	$0.336865\pi$
$728$		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	0.0136726	−	0.999907i	$-0.495648\pi$
$733$	−22.8893	−	13.2151i	−0.845436	−	0.488112i	−0.859108	+	0.511794i	$0.828981\pi$
$734$	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	−0.915318	−	0.402733i	$-0.868060\pi$
$761$	−3.00365	+	5.20247i	−0.108882	+	0.188589i	0.806436	+	0.591322i	$0.201394\pi$
$762$		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	0.124166	−	0.992262i	$-0.460375\pi$
$769$	28.9946	−	16.7400i	1.04557	−	0.603661i	0.921406	+	0.388600i	$0.127041\pi$
$770$		0			0
$771$		0			0
$772$	11.0832			0.398892
$773$	18.1008	−	31.3515i	0.651040	−	1.12763i	−0.331831	−	0.943339i	$-0.607666\pi$
$773$	18.1008	−	31.3515i	0.651040	−	1.12763i	0.982871	−	0.184296i	$-0.0590004\pi$
$774$		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	$0.0943528\pi$
$787$			16.3887i			0.584193i	−0.956389	+	0.292096i	$0.905647\pi$
$788$		−	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	$0.143000\pi$
$797$	23.3328	+	40.4137i	0.826492	+	1.43153i	−0.0742821	+	0.997237i	$0.523667\pi$
$798$		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	$0.146765\pi$
$811$			25.3404i			0.889821i	−0.895575	+	0.444911i	$0.853235\pi$
$812$		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	0.611775	−	0.791032i	$-0.290456\pi$
$829$	6.69733	+	3.86670i	0.232608	+	0.134296i	−0.379167	+	0.925328i	$0.623789\pi$
$830$	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	−0.647579	−	0.761998i	$-0.724219\pi$
$839$	9.73588	−	16.8630i	0.336120	−	0.582177i	0.983699	+	0.179821i	$0.0575519\pi$
$840$		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	0.486030	−	0.873942i	$-0.338445\pi$
$853$	−0.812274	−	0.468967i	−0.0278117	−	0.0160571i	−0.513841	+	0.857885i	$0.671778\pi$
$854$		0			0
$855$		0			0
$856$	18.2305	+	31.5761i	0.623104	+	1.07925i
$857$	9.00087	+	15.5900i	0.307464	+	0.532543i	0.977807	−	0.209509i	$-0.0671864\pi$
$857$	9.00087	+	15.5900i	0.307464	+	0.532543i	−0.670343	+	0.742051i	$0.733853\pi$
$858$		0			0
$859$	23.1160	+	13.3460i	0.788709	+	0.455361i	0.839508	−	0.543348i	$-0.182843\pi$
$859$	23.1160	+	13.3460i	0.788709	+	0.455361i	−0.0507989	+	0.998709i	$0.516177\pi$
$860$	−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	$-0.764950\pi$
$881$	−43.9006			−1.47905			−0.739525	+	0.673129i	$0.764950\pi$
$882$		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	−0.631138	−	0.775670i	$-0.717412\pi$
$887$	10.6080	−	18.3736i	0.356181	−	0.616924i	0.987319	+	0.158747i	$0.0507453\pi$
$888$		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	$-0.399709\pi$
$929$	18.8903			0.619771			0.309886	+	0.950774i	$0.399709\pi$
$930$		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	$-0.854355\pi$
$937$		−	27.0448i		−	0.883516i	0.897134	−	0.441758i	$-0.145645\pi$
$938$		0			0
$939$		0			0
$940$	9.46650	−	16.3965i	0.308763	−	0.534793i
$941$	16.3205			0.532032			0.266016	−	0.963969i	$-0.414293\pi$
$941$	16.3205			0.532032			0.266016	+	0.963969i	$0.414293\pi$
$942$		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	0.988991	−	0.147976i	$-0.0472758\pi$
$971$	11.4156	+	19.7724i	0.366345	+	0.634527i	−0.622646	+	0.782503i	$0.713942\pi$
$972$		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	$-0.984736\pi$
$983$	−16.9599	−	29.3754i	−0.540937	−	0.936930i	0.457913	−	0.888997i	$-0.348597\pi$
$984$		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	−0.586922	−	0.809643i	$-0.699661\pi$
$997$	−5.65867	+	3.26704i	−0.179212	+	0.103468i	0.407710	+	0.913111i	$0.366327\pi$
$998$	−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.521.20		48
3.2	odd	2		441.2.i.d.227.18		48
7.2	even	3		1323.2.s.d.656.8		48
7.3	odd	6		1323.2.o.e.440.18		48
7.4	even	3		1323.2.o.e.440.17		48
7.5	odd	6		1323.2.s.d.656.7		48
7.6	odd	2	inner	1323.2.i.d.521.1		48
9.4	even	3		441.2.s.d.374.17		48
9.5	odd	6		1323.2.s.d.962.7		48
21.2	odd	6		441.2.s.d.362.18		48
21.5	even	6		441.2.s.d.362.17		48
21.11	odd	6		441.2.o.e.146.7	✓	48
21.17	even	6		441.2.o.e.146.8	yes	48
21.20	even	2		441.2.i.d.227.17		48
63.4	even	3		441.2.o.e.293.8	yes	48
63.5	even	6	inner	1323.2.i.d.1097.20		48
63.13	odd	6		441.2.s.d.374.18		48
63.23	odd	6	inner	1323.2.i.d.1097.1		48
63.31	odd	6		441.2.o.e.293.7	yes	48
63.32	odd	6		1323.2.o.e.881.18		48
63.40	odd	6		441.2.i.d.68.8		48
63.41	even	6		1323.2.s.d.962.8		48
63.58	even	3		441.2.i.d.68.7		48
63.59	even	6		1323.2.o.e.881.17		48

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