LMFDB - Embedded newform 1323.2.o.e.881.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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, 3]))

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (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			881.17
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.e.440.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02035 - 0.589100i) q^{2} +(-0.305921 + 0.529871i) q^{4} +(-2.16601 + 3.75164i) q^{5} +3.07728i q^{8} +O(q^{10})$	\(q+(1.02035 - 0.589100i) q^{2} +(-0.305921 + 0.529871i) q^{4} +(-2.16601 + 3.75164i) q^{5} +3.07728i q^{8} +5.10399i q^{10} +(1.87238 - 1.08102i) q^{11} +(-2.25256 - 1.30052i) q^{13} +(1.20098 + 2.08016i) q^{16} -1.17115 q^{17} +2.41658i q^{19} +(-1.32526 - 2.29541i) q^{20} +(1.27366 - 2.20604i) q^{22} +(3.16186 + 1.82550i) q^{23} +(-6.88321 - 11.9221i) q^{25} -3.06454 q^{26} +(-0.589262 + 0.340210i) q^{29} +(-5.67723 - 3.27775i) q^{31} +(-2.87915 - 1.66228i) q^{32} +(-1.19499 + 0.689926i) q^{34} -5.10692 q^{37} +(1.42361 + 2.46576i) q^{38} +(-11.5448 - 6.66541i) q^{40} +(-3.68473 + 6.38214i) q^{41} +(-2.12577 - 3.68194i) q^{43} +1.32283i q^{44} +4.30162 q^{46} +(3.57157 + 6.18614i) q^{47} +(-14.0466 - 8.10980i) q^{50} +(1.37821 - 0.795711i) q^{52} -3.23289i q^{53} +9.36601i q^{55} +(-0.400836 + 0.694269i) q^{58} +(2.91810 - 5.05430i) q^{59} +(-6.21638 + 3.58903i) q^{61} -7.72370 q^{62} -8.72092 q^{64} +(9.75814 - 5.63387i) q^{65} +(-3.32682 + 5.76221i) q^{67} +(0.358281 - 0.620560i) q^{68} -1.95976i q^{71} -11.9069i q^{73} +(-5.21085 + 3.00849i) q^{74} +(-1.28048 - 0.739283i) q^{76} +(4.87702 + 8.44725i) q^{79} -10.4054 q^{80} +8.68270i q^{82} +(0.796736 + 1.37999i) q^{83} +(2.53673 - 4.39374i) q^{85} +(-4.33806 - 2.50458i) q^{86} +(3.32660 + 5.76184i) q^{88} -6.09921 q^{89} +(-1.93456 + 1.11692i) q^{92} +(7.28851 + 4.20802i) q^{94} +(-9.06614 - 5.23434i) q^{95} +(2.36387 - 1.36478i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{4}+O(q^{10}) $ 48 * q + 24 * q^4	$ 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) $ 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.02035	−	0.589100i	0.721498	−	0.416557i	−0.0938059	−	0.995591i	$-0.529903\pi$
$2$	1.02035	−	0.589100i	0.721498	−	0.416557i	0.815304	+	0.579034i	$0.196570\pi$
$3$		0			0
$3$		0			0
$4$	−0.305921	+	0.529871i	−0.152961	+	0.264936i
$5$	−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
$10$			5.10399i			1.61402i
$11$	1.87238	−	1.08102i	0.564545	−	0.325940i	−0.190423	−	0.981702i	$-0.560986\pi$
$11$	1.87238	−	1.08102i	0.564545	−	0.325940i	0.754968	+	0.655762i	$0.227653\pi$
$12$		0			0
$13$	−2.25256	−	1.30052i	−0.624748	−	0.360698i	0.153967	−	0.988076i	$-0.450795\pi$
$13$	−2.25256	−	1.30052i	−0.624748	−	0.360698i	−0.778715	+	0.627378i	$0.784128\pi$
$14$		0			0
$15$		0			0
$16$	1.20098	+	2.08016i	0.300245	+	0.520040i
$17$	−1.17115			−0.284046			−0.142023	−	0.989863i	$-0.545361\pi$
$17$	−1.17115			−0.284046			−0.142023	+	0.989863i	$0.545361\pi$
$18$		0			0
$19$			2.41658i			0.554402i	0.960812	+	0.277201i	$0.0894067\pi$
$19$			2.41658i			0.554402i	−0.960812	+	0.277201i	$0.910593\pi$
$20$	−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	0.792008	−	0.610511i	$-0.209036\pi$
$23$	3.16186	+	1.82550i	0.659294	+	0.380644i	−0.132714	+	0.991154i	$0.542369\pi$
$24$		0			0
$25$	−6.88321	−	11.9221i	−1.37664	−	2.38441i
$26$	−3.06454			−0.601006
$27$		0			0
$28$		0			0
$29$	−0.589262	+	0.340210i	−0.109423	+	0.0631755i	−0.553713	−	0.832708i	$-0.686789\pi$
$29$	−0.589262	+	0.340210i	−0.109423	+	0.0631755i	0.444290	+	0.895883i	$0.353456\pi$
$30$		0			0
$31$	−5.67723	−	3.27775i	−1.01966	−	0.588702i	−0.105655	−	0.994403i	$-0.533694\pi$
$31$	−5.67723	−	3.27775i	−1.01966	−	0.588702i	−0.914006	+	0.405701i	$0.867027\pi$
$32$	−2.87915	−	1.66228i	−0.508967	−	0.293852i
$33$		0			0
$34$	−1.19499	+	0.689926i	−0.204939	+	0.118321i
$35$		0			0
$36$		0			0
$37$	−5.10692			−0.839572			−0.419786	−	0.907623i	$-0.637895\pi$
$37$	−5.10692			−0.839572			−0.419786	+	0.907623i	$0.637895\pi$
$38$	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	0.420534	+	0.907277i	$0.361843\pi$
$41$	−3.68473	+	6.38214i	−0.575458	+	0.996723i	−0.995992	+	0.0894458i	$0.971490\pi$
$42$		0			0
$43$	−2.12577	−	3.68194i	−0.324176	−	0.561490i	0.657169	−	0.753743i	$-0.271754\pi$
$43$	−2.12577	−	3.68194i	−0.324176	−	0.561490i	−0.981345	+	0.192253i	$0.938420\pi$
$44$			1.32283i			0.199424i
$45$		0			0
$46$	4.30162			0.634239
$47$	3.57157	+	6.18614i	0.520967	+	0.902341i	0.999703	+	0.0243819i	$0.00776176\pi$
$47$	3.57157	+	6.18614i	0.520967	+	0.902341i	−0.478736	+	0.877959i	$0.658905\pi$
$48$		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
$53$		−	3.23289i		−	0.444071i	−0.975039	−	0.222036i	$-0.928730\pi$
$53$		−	3.23289i		−	0.444071i	0.975039	−	0.222036i	$-0.0712702\pi$
$54$		0			0
$55$			9.36601i			1.26291i
$56$		0			0
$57$		0			0
$58$	−0.400836	+	0.694269i	−0.0526324	+	0.0911619i
$59$	2.91810	−	5.05430i	0.379905	−	0.658014i	−0.611143	−	0.791520i	$-0.709290\pi$
$59$	2.91810	−	5.05430i	0.379905	−	0.658014i	0.991048	+	0.133506i	$0.0426234\pi$
$60$		0			0
$61$	−6.21638	+	3.58903i	−0.795925	+	0.459528i	−0.842044	−	0.539408i	$-0.818648\pi$
$61$	−6.21638	+	3.58903i	−0.795925	+	0.459528i	0.0461190	+	0.998936i	$0.485315\pi$
$62$	−7.72370			−0.980911
$63$		0			0
$64$	−8.72092			−1.09012
$65$	9.75814	−	5.63387i	1.21035	−	0.698795i
$66$		0			0
$67$	−3.32682	+	5.76221i	−0.406435	+	0.703966i	−0.994487	−	0.104857i	$-0.966562\pi$
$67$	−3.32682	+	5.76221i	−0.406435	+	0.703966i	0.588052	+	0.808823i	$0.299895\pi$
$68$	0.358281	−	0.620560i	0.0434479	−	0.0752540i
$69$		0			0
$70$		0			0
$71$		−	1.95976i		−	0.232580i	−0.993215	−	0.116290i	$-0.962900\pi$
$71$		−	1.95976i		−	0.232580i	0.993215	−	0.116290i	$-0.0371003\pi$
$72$		0			0
$73$		−	11.9069i		−	1.39360i	−0.717266	−	0.696799i	$-0.754607\pi$
$73$		−	11.9069i		−	1.39360i	0.717266	−	0.696799i	$-0.245393\pi$
$74$	−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
$79$	4.87702	+	8.44725i	0.548708	+	0.950390i	0.998363	+	0.0571879i	$0.0182134\pi$
$79$	4.87702	+	8.44725i	0.548708	+	0.950390i	−0.449656	+	0.893202i	$0.648453\pi$
$80$	−10.4054			−1.16335
$81$		0			0
$82$			8.68270i			0.958844i
$83$	0.796736	+	1.37999i	0.0874531	+	0.151473i	0.906434	−	0.422348i	$-0.138794\pi$
$83$	0.796736	+	1.37999i	0.0874531	+	0.151473i	−0.818981	+	0.573821i	$0.805461\pi$
$84$		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
$89$	−6.09921			−0.646515			−0.323258	−	0.946311i	$-0.604778\pi$
$89$	−6.09921			−0.646515			−0.323258	+	0.946311i	$0.604778\pi$
$90$		0			0
$91$		0			0
$92$	−1.93456	+	1.11692i	−0.201692	+	0.116447i
$93$		0			0
$94$	7.28851	+	4.20802i	0.751753	+	0.434025i
$95$	−9.06614	−	5.23434i	−0.930166	−	0.537032i
$96$		0			0
$97$	2.36387	−	1.36478i	0.240014	−	0.138572i	−0.375169	−	0.926956i	$-0.622415\pi$
$97$	2.36387	−	1.36478i	0.240014	−	0.138572i	0.615183	+	0.788384i	$0.289082\pi$
$98$		0			0
$99$		0			0
$100$	8.42288			0.842288
$101$	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	0.623156	−	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
$107$			11.8484i			1.14543i	0.819754	+	0.572716i	$0.194110\pi$
$107$			11.8484i			1.14543i	−0.819754	+	0.572716i	$0.805890\pi$
$108$		0			0
$109$	7.16157			0.685954			0.342977	−	0.939344i	$-0.388565\pi$
$109$	7.16157			0.685954			0.342977	+	0.939344i	$0.388565\pi$
$110$	5.51752	+	9.55662i	0.526075	+	0.911188i
$111$		0			0
$112$		0			0
$113$	−2.46102	−	1.42087i	−0.231514	−	0.133664i	0.379756	−	0.925086i	$-0.376008\pi$
$113$	−2.46102	−	1.42087i	−0.231514	−	0.133664i	−0.611270	+	0.791422i	$0.709341\pi$
$114$		0			0
$115$	−13.6973	+	7.90812i	−1.27728	+	0.737436i
$116$		−	0.416310i		−	0.0386535i
$117$		0			0
$118$		−	6.87623i		−	0.633008i
$119$		0			0
$120$		0			0
$121$	−3.16279	+	5.47811i	−0.287526	+	0.498010i
$122$	−4.22859	+	7.32414i	−0.382839	+	0.663096i
$123$		0			0
$124$	3.47357	−	2.00547i	0.311936	−	0.180096i
$125$	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	$0.192673\pi$
$128$	−3.14011	+	1.81294i	−0.277549	+	0.160243i
$129$		0			0
$130$	6.63783	−	11.4971i	0.582176	−	1.00836i
$131$	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
$136$		−	3.60396i		−	0.309037i
$137$	−11.8181	+	6.82316i	−1.00969	+	0.582942i	−0.911099	−	0.412187i	$-0.864765\pi$
$137$	−11.8181	+	6.82316i	−1.00969	+	0.582942i	−0.0985856	+	0.995129i	$0.531432\pi$
$138$		0			0
$139$	−7.74126	−	4.46942i	−0.656605	−	0.379091i	0.134377	−	0.990930i	$-0.457097\pi$
$139$	−7.74126	−	4.46942i	−0.656605	−	0.379091i	−0.790982	+	0.611839i	$0.790430\pi$
$140$		0			0
$141$		0			0
$142$	−1.15449	−	1.99964i	−0.0968830	−	0.167806i
$143$	−5.62354			−0.470264
$144$		0			0
$145$		−	2.94760i		−	0.244785i
$146$	−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	0.628674	−	0.777669i	$-0.283598\pi$
$149$	3.29003	+	1.89950i	0.269530	+	0.155613i	−0.359144	+	0.933282i	$0.616931\pi$
$150$		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	$0.783634\pi$
$152$	−7.43648			−0.603178
$153$		0			0
$154$		0			0
$155$	24.5939	−	14.1993i	1.97543	−	1.14051i
$156$		0			0
$157$	18.6081	+	10.7434i	1.48509	+	0.857417i	0.999856	−	0.0169675i	$-0.00540117\pi$
$157$	18.6081	+	10.7434i	1.48509	+	0.857417i	0.485234	+	0.874384i	$0.338735\pi$
$158$	9.95256	+	5.74611i	0.791783	+	0.457136i
$159$		0			0
$160$	12.4725	−	7.20102i	0.986041	−	0.569291i
$161$		0			0
$162$		0			0
$163$	12.5175			0.980447			0.490223	−	0.871597i	$-0.336915\pi$
$163$	12.5175			0.980447			0.490223	+	0.871597i	$0.336915\pi$
$164$	−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	0.396859	+	0.917880i	$0.370100\pi$
$167$	−7.70819	+	13.3510i	−0.596477	+	1.03313i	−0.993337	+	0.115250i	$0.963233\pi$
$168$		0			0
$169$	−3.11731	−	5.39935i	−0.239793	−	0.415334i
$170$		−	5.97755i		−	0.458457i
$171$		0			0
$172$	2.60127			0.198345
$173$	−4.30737	−	7.46059i	−0.327483	−	0.567218i	0.654528	−	0.756037i	$-0.272867\pi$
$173$	−4.30737	−	7.46059i	−0.327483	−	0.567218i	−0.982012	+	0.188820i	$0.939534\pi$
$174$		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
$179$			19.1384i			1.43047i	0.698882	+	0.715237i	$0.253681\pi$
$179$			19.1384i			1.43047i	−0.698882	+	0.715237i	$0.746319\pi$
$180$		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
$185$	11.0616	−	19.1593i	0.813268	−	1.40862i
$186$		0			0
$187$	−2.19285	+	1.26604i	−0.160357	+	0.0925820i
$188$	−4.37047			−0.318750
$189$		0			0
$190$	−12.3342			−0.894817
$191$	−16.1203	+	9.30704i	−1.16642	+	0.673433i	−0.952834	−	0.303491i	$-0.901848\pi$
$191$	−16.1203	+	9.30704i	−1.16642	+	0.673433i	−0.213587	+	0.976924i	$0.568515\pi$
$192$		0			0
$193$	−9.05721	+	15.6875i	−0.651952	+	1.12921i	0.330696	+	0.943737i	$0.392716\pi$
$193$	−9.05721	+	15.6875i	−0.651952	+	1.12921i	−0.982649	+	0.185477i	$0.940617\pi$
$194$	1.60799	−	2.78511i	0.115447	−	0.199959i
$195$		0			0
$196$		0			0
$197$			16.5945i			1.18231i	0.806559	+	0.591154i	$0.201328\pi$
$197$			16.5945i			1.18231i	−0.806559	+	0.591154i	$0.798672\pi$
$198$		0			0
$199$		−	2.71887i		−	0.192735i	−0.995346	−	0.0963677i	$-0.969278\pi$
$199$		−	2.71887i		−	0.192735i	0.995346	−	0.0963677i	$-0.0307225\pi$
$200$	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
$205$	−15.9623	−	27.6476i	−1.11486	−	1.93099i
$206$	3.55425			0.247636
$207$		0			0
$208$		−	6.24759i		−	0.433192i
$209$	2.61237	+	4.52476i	0.180702	+	0.312984i
$210$		0			0
$211$	−13.9445	+	24.1526i	−0.959979	+	1.66273i	−0.237440	+	0.971402i	$0.576308\pi$
$211$	−13.9445	+	24.1526i	−0.959979	+	1.66273i	−0.722539	+	0.691330i	$0.757025\pi$
$212$	1.71301	+	0.989010i	0.117650	+	0.0679255i
$213$		0			0
$214$	6.97992	+	12.0896i	0.477138	+	0.826427i
$215$	18.4177			1.25608
$216$		0			0
$217$		0			0
$218$	7.30732	−	4.21888i	0.494914	−	0.285739i
$219$		0			0
$220$	−4.96278	−	2.86526i	−0.334590	−	0.193176i
$221$	2.63809	+	1.52310i	0.177457	+	0.102455i
$222$		0			0
$223$	−6.64349	+	3.83562i	−0.444881	+	0.256852i	−0.705666	−	0.708545i	$-0.749352\pi$
$223$	−6.64349	+	3.83562i	−0.444881	+	0.256852i	0.260785	+	0.965397i	$0.416019\pi$
$224$		0			0
$225$		0			0
$226$	−3.34815			−0.222715
$227$	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	0.801722	−	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
$233$			2.52779i			0.165601i	0.996566	+	0.0828007i	$0.0263865\pi$
$233$			2.52779i			0.165601i	−0.996566	+	0.0828007i	$0.973614\pi$
$234$		0			0
$235$	−30.9442			−2.01858
$236$	1.78542	+	3.09244i	0.116221	+	0.201301i
$237$		0			0
$238$		0			0
$239$	−17.4587	−	10.0798i	−1.12931	−	0.652006i	−0.185546	−	0.982636i	$-0.559405\pi$
$239$	−17.4587	−	10.0798i	−1.12931	−	0.652006i	−0.943761	+	0.330630i	$0.892739\pi$
$240$		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	$0.0978690\pi$
$242$			7.45280i			0.479084i
$243$		0			0
$244$		−	4.39184i		−	0.281159i
$245$		0			0
$246$		0			0
$247$	3.14280	−	5.44349i	0.199972	−	0.346361i
$248$	10.0865	−	17.4704i	0.640496	−	1.10937i
$249$		0			0
$250$	38.7492	−	22.3718i	2.45071	−	1.41492i
$251$	−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
$254$	18.9116	−	10.9186i	1.18662	−	0.685096i
$255$		0			0
$256$	6.58491	−	11.4054i	0.411557	−	0.712837i
$257$	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
$262$		−	7.89915i		−	0.488011i
$263$	−19.3705	+	11.1836i	−1.19444	+	0.689608i	−0.959309	−	0.282357i	$-0.908884\pi$
$263$	−19.3705	+	11.1836i	−1.19444	+	0.689608i	−0.235127	+	0.971965i	$0.575550\pi$
$264$		0			0
$265$	12.1286	+	7.00247i	0.745056	+	0.430158i
$266$		0			0
$267$		0			0
$268$	−2.03549	−	3.52557i	−0.124337	−	0.215358i
$269$	4.22669			0.257706			0.128853	−	0.991664i	$-0.458870\pi$
$269$	4.22669			0.257706			0.128853	+	0.991664i	$0.458870\pi$
$270$		0			0
$271$		−	22.3943i		−	1.36036i	−0.733046	−	0.680179i	$-0.761902\pi$
$271$		−	22.3943i		−	1.36036i	0.733046	−	0.680179i	$-0.238098\pi$
$272$	−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	$0.944443\pi$
$278$	−10.5317			−0.631652
$279$		0			0
$280$		0			0
$281$	0.702700	−	0.405704i	0.0419196	−	0.0242023i	−0.478894	−	0.877873i	$-0.658962\pi$
$281$	0.702700	−	0.405704i	0.0419196	−	0.0242023i	0.520813	+	0.853671i	$0.325629\pi$
$282$		0			0
$283$	−15.8740	−	9.16486i	−0.943611	−	0.544794i	−0.0525206	−	0.998620i	$-0.516726\pi$
$283$	−15.8740	−	9.16486i	−0.943611	−	0.544794i	−0.891090	+	0.453826i	$0.850059\pi$
$284$	1.03842	+	0.599532i	0.0616188	+	0.0355757i
$285$		0			0
$286$	−5.73799	+	3.31283i	−0.339294	+	0.195892i
$287$		0			0
$288$		0			0
$289$	−15.6284			−0.919318
$290$	−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	$-0.714630\pi$
$293$	6.23639	−	10.8017i	0.364334	−	0.631044i	0.988669	+	0.150112i	$0.0479634\pi$
$294$		0			0
$295$	12.6413	+	21.8954i	0.736004	+	1.27480i
$296$		−	15.7154i		−	0.913438i
$297$		0			0
$298$	4.47599			0.259287
$299$	−4.74819	−	8.22411i	−0.274595	−	0.475613i
$300$		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
$305$		−	31.0955i		−	1.78052i
$306$		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
$311$	−3.92094	+	6.79126i	−0.222336	+	0.385097i	−0.955517	−	0.294936i	$-0.904702\pi$
$311$	−3.92094	+	6.79126i	−0.222336	+	0.385097i	0.733181	+	0.680034i	$0.238035\pi$
$312$		0			0
$313$	−8.57593	+	4.95131i	−0.484740	+	0.279865i	−0.722390	−	0.691486i	$-0.756956\pi$
$313$	−8.57593	+	4.95131i	−0.484740	+	0.279865i	0.237650	+	0.971351i	$0.423623\pi$
$314$	25.3158			1.42865
$315$		0			0
$316$	−5.96794			−0.335723
$317$	−20.8358	+	12.0296i	−1.17025	+	0.675647i	−0.953740	−	0.300632i	$-0.902802\pi$
$317$	−20.8358	+	12.0296i	−1.17025	+	0.675647i	−0.216515	+	0.976279i	$0.569469\pi$
$318$		0			0
$319$	−0.735549	+	1.27401i	−0.0411828	+	0.0713308i
$320$	18.8896	−	32.7178i	1.05596	−	1.82898i
$321$		0			0
$322$		0			0
$323$		−	2.83018i		−	0.157476i
$324$		0			0
$325$			35.8069i			1.98621i
$326$	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
$331$	4.53686	+	7.85807i	0.249368	+	0.431918i	0.963351	−	0.268245i	$-0.0864437\pi$
$331$	4.53686	+	7.85807i	0.249368	+	0.431918i	−0.713982	+	0.700164i	$0.753110\pi$
$332$	−0.974954			−0.0535075
$333$		0			0
$334$			18.1636i			0.993867i
$335$	−14.4118	−	24.9620i	−0.787403	−	1.36382i
$336$		0			0
$337$	4.02012	−	6.96304i	0.218990	−	0.379301i	−0.735510	−	0.677514i	$-0.763057\pi$
$337$	4.02012	−	6.96304i	0.218990	−	0.379301i	0.954499	+	0.298213i	$0.0963906\pi$
$338$	−6.36152	−	3.67282i	−0.346021	−	0.199775i
$339$		0			0
$340$	1.55208	+	2.68828i	0.0841733	+	0.145792i
$341$	−14.1733			−0.767525
$342$		0			0
$343$		0			0
$344$	11.3303	−	6.54157i	0.610891	−	0.352698i
$345$		0			0
$346$	−8.79007	−	5.07495i	−0.472557	−	0.272831i
$347$	30.6345	+	17.6868i	1.64454	+	0.949478i	0.979189	+	0.202952i	$0.0650536\pi$
$347$	30.6345	+	17.6868i	1.64454	+	0.949478i	0.665356	+	0.746526i	$0.268280\pi$
$348$		0			0
$349$	−21.1868	+	12.2322i	−1.13411	+	0.654776i	−0.944964	−	0.327174i	$-0.893904\pi$
$349$	−21.1868	+	12.2322i	−1.13411	+	0.654776i	−0.189141	+	0.981950i	$0.560570\pi$
$350$		0			0
$351$		0			0
$352$	−7.18783			−0.383112
$353$	−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
$359$		−	15.9210i		−	0.840276i	−0.907460	−	0.420138i	$-0.861982\pi$
$359$		−	15.9210i		−	0.840276i	0.907460	−	0.420138i	$-0.138018\pi$
$360$		0			0
$361$	13.1601			0.692639
$362$	−4.53499	−	7.85484i	−0.238354	−	0.412841i
$363$		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	$0.110236\pi$
$368$			8.76958i			0.457146i
$369$		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	$0.0881104\pi$
$374$	−1.49165	+	2.58361i	−0.0771314	+	0.133595i
$375$		0			0
$376$	−19.0364	+	10.9907i	−0.981730	+	0.566802i
$377$	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	$0.320578\pi$
$380$	5.54705	−	3.20259i	0.284558	−	0.164289i
$381$		0			0
$382$	−10.9656	+	18.9929i	−0.561047	+	0.971761i
$383$	−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
$388$			1.67006i			0.0847845i
$389$	0.0445846	−	0.0257409i	0.00226053	−	0.00130512i	−0.498869	−	0.866677i	$-0.666251\pi$
$389$	0.0445846	−	0.0257409i	0.00226053	−	0.00130512i	0.501130	+	0.865372i	$0.332918\pi$
$390$		0			0
$391$	−3.70303	−	2.13794i	−0.187270	−	0.108120i
$392$		0			0
$393$		0			0
$394$	9.77582	+	16.9322i	0.492499	+	0.853033i
$395$	−42.2547			−2.12607
$396$		0			0
$397$			12.7131i			0.638052i	0.947746	+	0.319026i	$0.103356\pi$
$397$			12.7131i			0.638052i	−0.947746	+	0.319026i	$0.896644\pi$
$398$	−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	0.553858	−	0.832611i	$-0.313155\pi$
$401$	2.19725	+	1.26858i	0.109725	+	0.0633500i	−0.444133	+	0.895961i	$0.646488\pi$
$402$		0			0
$403$	8.52554	+	14.7667i	0.424687	+	0.735580i
$404$	−9.78764			−0.486953
$405$		0			0
$406$		0			0
$407$	−9.56210	+	5.52068i	−0.473976	+	0.273650i
$408$		0			0
$409$	0.0495655	+	0.0286167i	0.00245086	+	0.00141500i	0.501225	−	0.865317i	$-0.332883\pi$
$409$	0.0495655	+	0.0286167i	0.00245086	+	0.00141500i	−0.498774	+	0.866732i	$0.666216\pi$
$410$	−32.5744	−	18.8068i	−1.60873	−	0.928803i
$411$		0			0
$412$	−1.59845	+	0.922864i	−0.0787499	+	0.0454663i
$413$		0			0
$414$		0			0
$415$	−6.90295			−0.338853
$416$	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	$-0.785254\pi$
$419$	3.08007	−	5.33484i	0.150471	−	0.260624i	0.931401	+	0.363995i	$0.118588\pi$
$420$		0			0
$421$	15.0693	+	26.1007i	0.734431	+	1.27207i	0.954973	+	0.296694i	$0.0958842\pi$
$421$	15.0693	+	26.1007i	0.734431	+	1.27207i	−0.220542	+	0.975378i	$0.570783\pi$
$422$			32.8588i			1.59954i
$423$		0			0
$424$	9.94849			0.483141
$425$	8.06128	+	13.9626i	0.391030	+	0.677283i
$426$		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
$431$		−	8.07140i		−	0.388785i	−0.980924	−	0.194393i	$-0.937726\pi$
$431$		−	8.07140i		−	0.388785i	0.980924	−	0.194393i	$-0.0622736\pi$
$432$		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
$437$	−4.41147	+	7.64090i	−0.211029	+	0.365514i
$438$		0			0
$439$	−1.77067	+	1.02230i	−0.0845096	+	0.0487916i	−0.541659	−	0.840598i	$-0.682204\pi$
$439$	−1.77067	+	1.02230i	−0.0845096	+	0.0487916i	0.457150	+	0.889390i	$0.348870\pi$
$440$	−28.8218			−1.37402
$441$		0			0
$442$	3.58904			0.170713
$443$	21.1324	−	12.2008i	1.00403	−	0.579677i	0.0945924	−	0.995516i	$-0.469845\pi$
$443$	21.1324	−	12.2008i	1.00403	−	0.579677i	0.909438	+	0.415839i	$0.136512\pi$
$444$		0			0
$445$	13.2110	−	22.8821i	0.626260	−	1.08471i
$446$	−4.51913	+	7.82737i	−0.213987	+	0.370637i
$447$		0			0
$448$		0			0
$449$		−	0.293539i		−	0.0138529i	−0.999976	−	0.00692647i	$-0.997795\pi$
$449$		−	0.293539i		−	0.0138529i	0.999976	−	0.00692647i	$-0.00220478\pi$
$450$		0			0
$451$			15.9331i			0.750259i
$452$	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
$457$	−8.27470	−	14.3322i	−0.387074	−	0.670432i	0.604981	−	0.796240i	$-0.293181\pi$
$457$	−8.27470	−	14.3322i	−0.387074	−	0.670432i	−0.992055	+	0.125808i	$0.959848\pi$
$458$	14.1017			0.658931
$459$		0			0
$460$		−	9.67705i		−	0.451195i
$461$	10.0560	+	17.4175i	0.468354	+	0.811213i	0.999346	−	0.0361638i	$-0.0115138\pi$
$461$	10.0560	+	17.4175i	0.468354	+	0.811213i	−0.530992	+	0.847377i	$0.678180\pi$
$462$		0			0
$463$	9.34602	−	16.1878i	0.434346	−	0.752310i	−0.562896	−	0.826528i	$-0.690313\pi$
$463$	9.34602	−	16.1878i	0.434346	−	0.752310i	0.997242	+	0.0742181i	$0.0236461\pi$
$464$	−1.41538	−	0.817173i	−0.0657076	−	0.0379363i
$465$		0			0
$466$	1.48912	+	2.57924i	0.0689824	+	0.119481i
$467$	29.3605			1.35864			0.679322	−	0.733841i	$-0.262274\pi$
$467$	29.3605			1.35864			0.679322	+	0.733841i	$0.262274\pi$
$468$		0			0
$469$		0			0
$470$	−31.5740	+	18.2293i	−1.45640	+	0.840853i
$471$		0			0
$472$	15.5535	+	8.97981i	0.715907	+	0.413329i
$473$	−7.96050	−	4.59599i	−0.366024	−	0.211324i
$474$		0			0
$475$	28.8106	−	16.6338i	1.32192	−	0.763212i
$476$		0			0
$477$		0			0
$478$	−23.7520			−1.08639
$479$	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
$485$			11.8245i			0.536923i
$486$		0			0
$487$	1.07779			0.0488394			0.0244197	−	0.999702i	$-0.492226\pi$
$487$	1.07779			0.0488394			0.0244197	+	0.999702i	$0.492226\pi$
$488$	−11.0444	−	19.1295i	−0.499957	−	0.865952i
$489$		0			0
$490$		0			0
$491$	−16.3708	−	9.45168i	−0.738804	−	0.426549i	0.0828305	−	0.996564i	$-0.473604\pi$
$491$	−16.3708	−	9.45168i	−0.738804	−	0.426549i	−0.821634	+	0.570015i	$0.806937\pi$
$492$		0			0
$493$	0.690115	−	0.398438i	0.0310812	−	0.0179448i
$494$		−	7.40570i		−	0.333198i
$495$		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	$0.0448314\pi$
$500$	−11.6178	+	20.1225i	−0.519562	+	0.899908i
$501$		0			0
$502$	−26.0952	+	15.0661i	−1.16468	+	0.672431i
$503$	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
$506$	8.05428	−	4.65014i	0.358056	−	0.206724i
$507$		0			0
$508$	−5.67007	+	9.82085i	−0.251569	+	0.435730i
$509$	−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
$514$		−	13.9905i		−	0.617096i
$515$	−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
$520$	17.3370	+	30.0285i	0.760276	+	1.31684i
$521$	20.7998			0.911254			0.455627	−	0.890171i	$-0.349415\pi$
$521$	20.7998			0.911254			0.455627	+	0.890171i	$0.349415\pi$
$522$		0			0
$523$		−	14.9338i		−	0.653009i	−0.945196	−	0.326505i	$-0.894129\pi$
$523$		−	14.9338i		−	0.653009i	0.945196	−	0.326505i	$-0.105871\pi$
$524$	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
$530$	16.5006			0.716742
$531$		0			0
$532$		0			0
$533$	16.6002	−	9.58410i	0.719033	−	0.415134i
$534$		0			0
$535$	−44.4511	−	25.6639i	−1.92179	−	1.10955i
$536$	−17.7319	−	10.2375i	−0.765902	−	0.442194i
$537$		0			0
$538$	4.31272	−	2.48995i	0.185934	−	0.107349i
$539$		0			0
$540$		0			0
$541$	31.1677			1.34000			0.670002	−	0.742360i	$-0.266293\pi$
$541$	31.1677			1.34000			0.670002	+	0.742360i	$0.266293\pi$
$542$	−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	−0.977039	−	0.213061i	$-0.931657\pi$
$547$	−15.7410	−	27.2642i	−0.673035	−	1.16573i	0.304004	−	0.952671i	$-0.401677\pi$
$548$		−	8.34940i		−	0.356669i
$549$		0			0
$550$	−35.0674			−1.49528
$551$	−0.822146	−	1.42400i	−0.0350246	−	0.0606644i
$552$		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
$557$			27.2389i			1.15415i	0.816692	+	0.577074i	$0.195806\pi$
$557$			27.2389i			1.15415i	−0.816692	+	0.577074i	$0.804194\pi$
$558$		0			0
$559$			11.0584i			0.467720i
$560$		0			0
$561$		0			0
$562$	0.478001	−	0.827922i	0.0201633	−	0.0349238i
$563$	14.1871	−	24.5728i	0.597916	−	1.03562i	−0.395212	−	0.918590i	$-0.629329\pi$
$563$	14.1871	−	24.5728i	0.597916	−	1.03562i	0.993128	−	0.117031i	$-0.0373377\pi$
$564$		0			0
$565$	10.6612	−	6.15525i	0.448521	−	0.258953i
$566$	−21.5961			−0.907751
$567$		0			0
$568$	6.03071			0.253043
$569$	−29.4616	+	17.0097i	−1.23509	+	0.713082i	−0.968087	−	0.250613i	$-0.919368\pi$
$569$	−29.4616	+	17.0097i	−1.23509	+	0.713082i	−0.267007	+	0.963695i	$0.586035\pi$
$570$		0			0
$571$	22.3455	−	38.7035i	0.935130	−	1.61969i	0.160727	−	0.986999i	$-0.448616\pi$
$571$	22.3455	−	38.7035i	0.935130	−	1.61969i	0.774402	−	0.632693i	$-0.218051\pi$
$572$	1.72036	−	2.97975i	0.0719319	−	0.124590i
$573$		0			0
$574$		0			0
$575$		−	50.2613i		−	2.09604i
$576$		0			0
$577$			7.34738i			0.305875i	0.988236	+	0.152938i	$0.0488734\pi$
$577$			7.34738i			0.305875i	−0.988236	+	0.152938i	$0.951127\pi$
$578$	−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
$583$	−3.49482	−	6.05320i	−0.144741	−	0.250698i
$584$	36.6408			1.51621
$585$		0			0
$586$		−	14.6954i		−	0.607063i
$587$	13.1328	+	22.7466i	0.542048	+	0.938855i	0.998786	+	0.0492535i	$0.0156842\pi$
$587$	13.1328	+	22.7466i	0.542048	+	0.938855i	−0.456738	+	0.889601i	$0.650982\pi$
$588$		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
$593$	9.12418			0.374685			0.187343	−	0.982295i	$-0.440013\pi$
$593$	9.12418			0.374685			0.187343	+	0.982295i	$0.440013\pi$
$594$		0			0
$595$		0			0
$596$	−2.01298	+	1.16220i	−0.0824550	+	0.0476054i
$597$		0			0
$598$	−9.68966	−	5.59433i	−0.396240	−	0.228769i
$599$	20.0987	+	11.6040i	0.821210	+	0.474126i	0.850834	−	0.525435i	$-0.176097\pi$
$599$	20.0987	+	11.6040i	0.821210	+	0.474126i	−0.0296234	+	0.999561i	$0.509431\pi$
$600$		0			0
$601$	−19.0021	+	10.9709i	−0.775111	+	0.447510i	−0.834695	−	0.550713i	$-0.814356\pi$
$601$	−19.0021	+	10.9709i	−0.775111	+	0.447510i	0.0595840	+	0.998223i	$0.481023\pi$
$602$		0			0
$603$		0			0
$604$	−2.33825			−0.0951421
$605$	−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
$611$		−	18.5795i		−	0.751647i
$612$		0			0
$613$	11.6560			0.470780			0.235390	−	0.971901i	$-0.424363\pi$
$613$	11.6560			0.470780			0.235390	+	0.971901i	$0.424363\pi$
$614$	12.5620	+	21.7580i	0.506961	+	0.878083i
$615$		0			0
$616$		0			0
$617$	−36.6143	−	21.1393i	−1.47403	−	0.851034i	−0.474462	−	0.880276i	$-0.657357\pi$
$617$	−36.6143	−	21.1393i	−1.47403	−	0.851034i	−0.999572	+	0.0292416i	$0.990691\pi$
$618$		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	$0.579100\pi$
$620$			17.3755i			0.697815i
$621$		0			0
$622$			9.23930i			0.370462i
$623$		0			0
$624$		0			0
$625$	−47.8410	+	82.8631i	−1.91364	+	3.31452i
$626$	−5.83364	+	10.1042i	−0.233159	+	0.403844i
$627$		0			0
$628$	−11.3852	+	6.57327i	−0.454321	+	0.262302i
$629$	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	$0.582566\pi$
$632$	−25.9945	+	15.0079i	−1.03401	+	0.596984i
$633$		0			0
$634$	−14.1732	+	24.5488i	−0.562891	+	0.974956i
$635$	−40.1457	+	69.5345i	−1.59314	+	2.75939i
$636$		0			0
$637$		0			0
$638$			1.73325i			0.0686200i
$639$		0			0
$640$		−	15.7074i		−	0.620890i
$641$	16.5666	−	9.56474i	0.654342	−	0.377785i	−0.135776	−	0.990740i	$-0.543353\pi$
$641$	16.5666	−	9.56474i	0.654342	−	0.377785i	0.790118	+	0.612955i	$0.210019\pi$
$642$		0			0
$643$	−9.77521	−	5.64372i	−0.385497	−	0.222567i	0.294710	−	0.955587i	$-0.404777\pi$
$643$	−9.77521	−	5.64372i	−0.385497	−	0.222567i	−0.680207	+	0.733020i	$0.738110\pi$
$644$		0			0
$645$		0			0
$646$	−1.66726	−	2.88778i	−0.0655976	−	0.113618i
$647$	5.08677			0.199982			0.0999909	−	0.994988i	$-0.468119\pi$
$647$	5.08677			0.199982			0.0999909	+	0.994988i	$0.468119\pi$
$648$		0			0
$649$		−	12.6181i		−	0.495305i
$650$	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	0.978234	−	0.207503i	$-0.0665338\pi$
$653$	32.9044	+	18.9974i	1.28765	+	0.743424i	0.309414	+	0.950927i	$0.399867\pi$
$654$		0			0
$655$	14.5218	+	25.1526i	0.567415	+	0.982792i
$656$	−17.7012			−0.691115
$657$		0			0
$658$		0			0
$659$	−9.97949	+	5.76166i	−0.388746	+	0.224442i	−0.681617	−	0.731710i	$-0.738723\pi$
$659$	−9.97949	+	5.76166i	−0.388746	+	0.224442i	0.292871	+	0.956152i	$0.405389\pi$
$660$		0			0
$661$	38.0928	+	21.9929i	1.48164	+	0.855424i	0.999783	−	0.0208274i	$-0.00663005\pi$
$661$	38.0928	+	21.9929i	1.48164	+	0.855424i	0.481854	+	0.876251i	$0.339963\pi$
$662$	9.25838	+	5.34533i	0.359837	+	0.207752i
$663$		0			0
$664$	−4.24660	+	2.45178i	−0.164800	+	0.0951473i
$665$		0			0
$666$		0			0
$667$	−2.48422			−0.0961894
$668$	−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	−0.885273	−	0.465071i	$-0.846029\pi$
$673$	−21.9316	−	37.9866i	−0.845400	−	1.46428i	0.0398735	−	0.999205i	$-0.487305\pi$
$674$		−	9.47301i		−	0.364887i
$675$		0			0
$676$	3.81461			0.146716
$677$	0.738999	+	1.27998i	0.0284020	+	0.0491938i	0.879877	−	0.475201i	$-0.157625\pi$
$677$	0.738999	+	1.27998i	0.0284020	+	0.0491938i	−0.851475	+	0.524395i	$0.824291\pi$
$678$		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
$683$		−	10.3259i		−	0.395111i	−0.980292	−	0.197555i	$-0.936700\pi$
$683$		−	10.3259i		−	0.395111i	0.980292	−	0.197555i	$-0.0633002\pi$
$684$		0			0
$685$		−	59.1162i		−	2.25871i
$686$		0			0
$687$		0			0
$688$	5.10601	−	8.84388i	0.194665	−	0.337170i
$689$	−4.20442	+	7.28228i	−0.160176	+	0.277433i
$690$		0			0
$691$	−6.58166	+	3.79992i	−0.250378	+	0.144556i	−0.619937	−	0.784651i	$-0.712842\pi$
$691$	−6.58166	+	3.79992i	−0.250378	+	0.144556i	0.369559	+	0.929207i	$0.379509\pi$
$692$	5.27087			0.200368
$693$		0			0
$694$	41.6773			1.58205
$695$	33.5353	−	19.3616i	1.27207	−	0.734428i
$696$		0			0
$697$	4.31538	−	7.47446i	0.163457	−	0.283115i
$698$	−14.4120	+	24.9624i	−0.545503	+	0.944839i
$699$		0			0
$700$		0			0
$701$			6.35907i			0.240179i	0.992763	+	0.120089i	$0.0383181\pi$
$701$			6.35907i			0.240179i	−0.992763	+	0.120089i	$0.961682\pi$
$702$		0			0
$703$		−	12.3413i		−	0.465460i
$704$	−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
$709$	23.8048	+	41.2311i	0.894007	+	1.54847i	0.835029	+	0.550206i	$0.185451\pi$
$709$	23.8048	+	41.2311i	0.894007	+	1.54847i	0.0589776	+	0.998259i	$0.481216\pi$
$710$	10.0026			0.375390
$711$		0			0
$712$		−	18.7690i		−	0.703396i
$713$	−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
$719$	−14.1470			−0.527594			−0.263797	−	0.964578i	$-0.584975\pi$
$719$	−14.1470			−0.527594			−0.263797	+	0.964578i	$0.584975\pi$
$720$		0			0
$721$		0			0
$722$	13.4280	−	7.75264i	0.499737	−	0.288524i
$723$		0			0
$724$	4.07904	+	2.35503i	0.151596	+	0.0875241i
$725$	8.11202	+	4.68348i	0.301273	+	0.173940i
$726$		0			0
$727$	40.1828	−	23.1996i	1.49030	−	0.860424i	0.490360	−	0.871520i	$-0.336865\pi$
$727$	40.1828	−	23.1996i	1.49030	−	0.860424i	0.999938	+	0.0110955i	$0.00353187\pi$
$728$		0			0
$729$		0			0
$730$	60.7728			2.24930
$731$	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
$737$			14.3854i			0.529894i
$738$		0			0
$739$	−46.2670			−1.70196			−0.850979	−	0.525200i	$-0.823991\pi$
$739$	−46.2670			−1.70196			−0.850979	+	0.525200i	$0.823991\pi$
$740$	6.76798	+	11.7225i	0.248796	+	0.430927i
$741$		0			0
$742$		0			0
$743$	36.5640	+	21.1102i	1.34140	+	0.774458i	0.987013	−	0.160640i	$-0.0513558\pi$
$743$	36.5640	+	21.1102i	1.34140	+	0.774458i	0.354388	+	0.935098i	$0.384689\pi$
$744$		0			0
$745$	−14.2525	+	8.22868i	−0.522171	+	0.301476i
$746$		−	11.1177i		−	0.407050i
$747$		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	$0.0720894\pi$
$752$	−8.57877	+	14.8589i	−0.312836	+	0.541847i
$753$		0			0
$754$	1.80582	−	1.04259i	0.0657639	−	0.0379688i
$755$	−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	$0.349785\pi$
$758$	21.2265	−	12.2551i	0.770981	−	0.445126i
$759$		0			0
$760$	16.1075	−	27.8990i	0.584281	−	1.01200i
$761$	−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
$766$			7.61138i			0.275010i
$767$	−13.1464	+	7.59008i	−0.474689	+	0.274062i
$768$		0			0
$769$	28.9946	+	16.7400i	1.04557	+	0.603661i	0.921406	−	0.388600i	$-0.127041\pi$
$769$	28.9946	+	16.7400i	1.04557	+	0.603661i	0.124166	+	0.992262i	$0.460375\pi$
$770$		0			0
$771$		0			0
$772$	−5.54159	−	9.59831i	−0.199446	−	0.345451i
$773$	−36.2016			−1.30208			−0.651040	−	0.759043i	$-0.725667\pi$
$773$	−36.2016			−1.30208			−0.651040	+	0.759043i	$0.725667\pi$
$774$		0			0
$775$			90.2458i			3.24172i
$776$	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
$782$	−5.03785			−0.180153
$783$		0			0
$784$		0			0
$785$	−80.6108	+	46.5407i	−2.87712	+	1.66111i
$786$		0			0
$787$	14.1930	+	8.19433i	0.505926	+	0.292096i	0.731157	−	0.682209i	$-0.238981\pi$
$787$	14.1930	+	8.19433i	0.505926	+	0.292096i	−0.225232	+	0.974305i	$0.572314\pi$
$788$	−8.79294	−	5.07661i	−0.313236	−	0.180847i
$789$		0			0
$790$	−43.1147	+	24.8923i	−1.53395	+	0.885628i
$791$		0			0
$792$		0			0
$793$	18.6703			0.663004
$794$	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	−0.0742821	−	0.997237i	$-0.523667\pi$
$797$	23.3328	−	40.4137i	0.826492	−	1.43153i	0.900774	−	0.434288i	$-0.143000\pi$
$798$		0			0
$799$	−4.18285	−	7.24491i	−0.147979	−	0.256306i
$800$			45.7672i			1.61811i
$801$		0			0
$802$	2.98929			0.105555
$803$	−12.8716	−	22.2943i	−0.454229	−	0.786748i
$804$		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
$809$		−	29.8980i		−	1.05116i	−0.850744	−	0.525580i	$-0.823849\pi$
$809$		−	29.8980i		−	1.05116i	0.850744	−	0.525580i	$-0.176151\pi$
$810$		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
$815$	−27.1131	+	46.9612i	−0.949729	+	1.64498i
$816$		0			0
$817$	8.89769	−	5.13709i	0.311291	−	0.179724i
$818$	0.0674323			0.00235772
$819$		0			0
$820$	19.5329			0.682117
$821$	−9.23012	+	5.32901i	−0.322133	+	0.185984i	−0.652343	−	0.757924i	$-0.726214\pi$
$821$	−9.23012	+	5.32901i	−0.322133	+	0.185984i	0.330210	+	0.943908i	$0.392881\pi$
$822$		0			0
$823$	−8.55239	+	14.8132i	−0.298118	+	0.516355i	−0.975705	−	0.219087i	$-0.929692\pi$
$823$	−8.55239	+	14.8132i	−0.298118	+	0.516355i	0.677588	+	0.735442i	$0.263025\pi$
$824$	−4.64156	+	8.03943i	−0.161697	+	0.280067i
$825$		0			0
$826$		0			0
$827$		−	18.3221i		−	0.637121i	−0.947903	−	0.318560i	$-0.896801\pi$
$827$		−	18.3221i		−	0.637121i	0.947903	−	0.318560i	$-0.103199\pi$
$828$		0			0
$829$			7.73341i			0.268592i	0.990941	+	0.134296i	$0.0428774\pi$
$829$			7.73341i			0.268592i	−0.990941	+	0.134296i	$0.957123\pi$
$830$	−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
$835$	−33.3920	−	57.8367i	−1.15558	−	2.00152i
$836$	−3.19672			−0.110561
$837$		0			0
$838$		−	7.25788i		−	0.250719i
$839$	9.73588	+	16.8630i	0.336120	+	0.582177i	0.983699	−	0.179821i	$-0.0575519\pi$
$839$	9.73588	+	16.8630i	0.336120	+	0.582177i	−0.647579	+	0.761998i	$0.724219\pi$
$840$		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
$845$	27.0085			0.929122
$846$		0			0
$847$		0			0
$848$	6.72493	−	3.88264i	0.230935	−	0.133330i
$849$		0			0
$850$	16.4507	+	9.49781i	0.564254	+	0.325772i
$851$	−16.1474	−	9.32269i	−0.553525	−	0.319578i
$852$		0			0
$853$	−0.812274	+	0.468967i	−0.0278117	+	0.0160571i	−0.513841	−	0.857885i	$-0.671778\pi$
$853$	−0.812274	+	0.468967i	−0.0278117	+	0.0160571i	0.486030	+	0.873942i	$0.338445\pi$
$854$		0			0
$855$		0			0
$856$	−36.4609			−1.24621
$857$	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	0.0507989	−	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
$863$		−	27.7596i		−	0.944946i	−0.881345	−	0.472473i	$-0.843361\pi$
$863$		−	27.7596i		−	0.944946i	0.881345	−	0.472473i	$-0.156639\pi$
$864$		0			0
$865$	37.3193			1.26889
$866$	16.7857	+	29.0737i	0.570402	+	0.987966i
$867$		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
$872$			22.0381i			0.746305i
$873$		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	$0.241628\pi$
$878$	−1.20447	+	2.08621i	−0.0406490	+	0.0704061i
$879$		0			0
$880$	−19.4828	+	11.2484i	−0.656765	+	0.379184i
$881$	−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	$0.457198\pi$
$884$	−1.61410	+	0.931899i	−0.0542880	+	0.0313432i
$885$		0			0
$886$	14.3750	−	24.8982i	0.482937	−	0.836472i
$887$	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
$892$		−	4.69359i		−	0.157153i
$893$	−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
$898$	−0.172924	−	0.299513i	−0.00577054	−	0.00999487i
$899$	4.46050			0.148766
$900$		0			0
$901$			3.78621i			0.126137i
$902$	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	$0.853253\pi$
$908$	−1.42484			−0.0472850
$909$		0			0
$910$		0			0
$911$	−40.0013	+	23.0947i	−1.32530	+	0.765163i	−0.984569	−	0.174998i	$-0.944008\pi$
$911$	−40.0013	+	23.0947i	−1.32530	+	0.765163i	−0.340732	+	0.940160i	$0.610675\pi$
$912$		0			0
$913$	2.98359	+	1.72258i	0.0987423	+	0.0570089i
$914$	−16.8862	−	9.74926i	−0.558546	−	0.322477i
$915$		0			0
$916$	−6.34196	+	3.66153i	−0.209544	+	0.120980i
$917$		0			0
$918$		0			0
$919$	1.21522			0.0400864			0.0200432	−	0.999799i	$-0.493620\pi$
$919$	1.21522			0.0400864			0.0200432	+	0.999799i	$0.493620\pi$
$920$	−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
$926$		−	22.0230i		−	0.723720i
$927$		0			0
$928$	2.26210			0.0742570
$929$	−9.44516	−	16.3595i	−0.309886	−	0.536737i	0.668452	−	0.743756i	$-0.266957\pi$
$929$	−9.44516	−	16.3595i	−0.309886	−	0.536737i	−0.978337	+	0.207018i	$0.933624\pi$
$930$		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
$935$		−	10.9690i		−	0.358725i
$936$		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
$941$	−8.16024	+	14.1339i	−0.266016	+	0.460754i	−0.967829	−	0.251607i	$-0.919041\pi$
$941$	−8.16024	+	14.1339i	−0.266016	+	0.460754i	0.701813	+	0.712361i	$0.252374\pi$
$942$		0			0
$943$	−23.3012	+	13.4530i	−0.758793	+	0.438089i
$944$	14.0184			0.456259
$945$		0			0
$946$	−10.8300			−0.352114
$947$	24.8567	−	14.3510i	0.807734	−	0.466345i	−0.0384343	−	0.999261i	$-0.512237\pi$
$947$	24.8567	−	14.3510i	0.807734	−	0.466345i	0.846168	+	0.532916i	$0.178904\pi$
$948$		0			0
$949$	−15.4851	+	26.8210i	−0.502668	+	0.870647i
$950$	19.5980	−	33.9447i	0.635842	−	1.10131i
$951$		0			0
$952$		0			0
$953$		−	34.5757i		−	1.12002i	−0.828486	−	0.560009i	$-0.810798\pi$
$953$		−	34.5757i		−	1.12002i	0.828486	−	0.560009i	$-0.189202\pi$
$954$		0			0
$955$		−	80.6366i		−	2.60934i
$956$	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
$961$	5.98731	+	10.3703i	0.193139	+	0.334527i
$962$	15.6503			0.504587
$963$		0			0
$964$			12.8055i			0.412437i
$965$	−39.2360	−	67.9588i	−1.26305	−	2.18767i
$966$		0			0
$967$	−5.25000	+	9.09327i	−0.168829	+	0.292420i	−0.938008	−	0.346613i	$-0.887332\pi$
$967$	−5.25000	+	9.09327i	−0.168829	+	0.292420i	0.769180	+	0.639033i	$0.220665\pi$
$968$	−16.8577	−	9.73277i	−0.541826	−	0.312823i
$969$		0			0
$970$	6.96583	+	12.0652i	0.223659	+	0.387389i
$971$	−22.8312			−0.732689			−0.366345	−	0.930479i	$-0.619391\pi$
$971$	−22.8312			−0.732689			−0.366345	+	0.930479i	$0.619391\pi$
$972$		0			0
$973$		0			0
$974$	1.09973	−	0.634927i	0.0352375	−	0.0203444i
$975$		0			0
$976$	−14.9315	−	8.62071i	−0.477946	−	0.275942i
$977$	8.88551	+	5.13005i	0.284273	+	0.164125i	0.635356	−	0.772219i	$-0.280853\pi$
$977$	8.88551	+	5.13005i	0.284273	+	0.164125i	−0.351083	+	0.936344i	$0.614187\pi$
$978$		0			0
$979$	−11.4201	+	6.59337i	−0.364987	+	0.210725i
$980$		0			0
$981$		0			0
$982$	−22.2720			−0.710727
$983$	−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
$989$		−	15.5224i		−	0.493583i
$990$		0			0
$991$	22.8556			0.726031			0.363015	−	0.931783i	$-0.381747\pi$
$991$	22.8556			0.726031			0.363015	+	0.931783i	$0.381747\pi$
$992$	10.8971	+	18.8743i	0.345982	+	0.599259i
$993$		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	$0.300339\pi$
$998$		−	19.6592i		−	0.622302i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.e.881.17		48
3.2	odd	2		441.2.o.e.293.7	yes	48
7.2	even	3		1323.2.s.d.962.8		48
7.3	odd	6		1323.2.i.d.1097.1		48
7.4	even	3		1323.2.i.d.1097.20		48
7.5	odd	6		1323.2.s.d.962.7		48
7.6	odd	2	inner	1323.2.o.e.881.18		48
9.2	odd	6	inner	1323.2.o.e.440.18		48
9.7	even	3		441.2.o.e.146.8	yes	48
21.2	odd	6		441.2.s.d.374.18		48
21.5	even	6		441.2.s.d.374.17		48
21.11	odd	6		441.2.i.d.68.8		48
21.17	even	6		441.2.i.d.68.7		48
21.20	even	2		441.2.o.e.293.8	yes	48
63.2	odd	6		1323.2.i.d.521.1		48
63.11	odd	6		1323.2.s.d.656.7		48
63.16	even	3		441.2.i.d.227.17		48
63.20	even	6	inner	1323.2.o.e.440.17		48
63.25	even	3		441.2.s.d.362.17		48
63.34	odd	6		441.2.o.e.146.7	✓	48
63.38	even	6		1323.2.s.d.656.8		48
63.47	even	6		1323.2.i.d.521.20		48
63.52	odd	6		441.2.s.d.362.18		48
63.61	odd	6		441.2.i.d.227.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.i.d.68.7		48	21.17	even	6
441.2.i.d.68.8		48	21.11	odd	6
441.2.i.d.227.17		48	63.16	even	3
441.2.i.d.227.18		48	63.61	odd	6
441.2.o.e.146.7	✓	48	63.34	odd	6
441.2.o.e.146.8	yes	48	9.7	even	3
441.2.o.e.293.7	yes	48	3.2	odd	2
441.2.o.e.293.8	yes	48	21.20	even	2
441.2.s.d.362.17		48	63.25	even	3
441.2.s.d.362.18		48	63.52	odd	6
441.2.s.d.374.17		48	21.5	even	6
441.2.s.d.374.18		48	21.2	odd	6
1323.2.i.d.521.1		48	63.2	odd	6
1323.2.i.d.521.20		48	63.47	even	6
1323.2.i.d.1097.1		48	7.3	odd	6
1323.2.i.d.1097.20		48	7.4	even	3
1323.2.o.e.440.17		48	63.20	even	6	inner
1323.2.o.e.440.18		48	9.2	odd	6	inner
1323.2.o.e.881.17		48	1.1	even	1	trivial
1323.2.o.e.881.18		48	7.6	odd	2	inner
1323.2.s.d.656.7		48	63.11	odd	6
1323.2.s.d.656.8		48	63.38	even	6
1323.2.s.d.962.7		48	7.5	odd	6
1323.2.s.d.962.8		48	7.2	even	3

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.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.02035 - 0.589100i) q^{2} +(-0.305921 + 0.529871i) q^{4} +(-2.16601 + 3.75164i) q^{5} +3.07728i q^{8} +O(q^{10})\)	\(q+(1.02035 - 0.589100i) q^{2} +(-0.305921 + 0.529871i) q^{4} +(-2.16601 + 3.75164i) q^{5} +3.07728i q^{8} +5.10399i q^{10} +(1.87238 - 1.08102i) q^{11} +(-2.25256 - 1.30052i) q^{13} +(1.20098 + 2.08016i) q^{16} -1.17115 q^{17} +2.41658i q^{19} +(-1.32526 - 2.29541i) q^{20} +(1.27366 - 2.20604i) q^{22} +(3.16186 + 1.82550i) q^{23} +(-6.88321 - 11.9221i) q^{25} -3.06454 q^{26} +(-0.589262 + 0.340210i) q^{29} +(-5.67723 - 3.27775i) q^{31} +(-2.87915 - 1.66228i) q^{32} +(-1.19499 + 0.689926i) q^{34} -5.10692 q^{37} +(1.42361 + 2.46576i) q^{38} +(-11.5448 - 6.66541i) q^{40} +(-3.68473 + 6.38214i) q^{41} +(-2.12577 - 3.68194i) q^{43} +1.32283i q^{44} +4.30162 q^{46} +(3.57157 + 6.18614i) q^{47} +(-14.0466 - 8.10980i) q^{50} +(1.37821 - 0.795711i) q^{52} -3.23289i q^{53} +9.36601i q^{55} +(-0.400836 + 0.694269i) q^{58} +(2.91810 - 5.05430i) q^{59} +(-6.21638 + 3.58903i) q^{61} -7.72370 q^{62} -8.72092 q^{64} +(9.75814 - 5.63387i) q^{65} +(-3.32682 + 5.76221i) q^{67} +(0.358281 - 0.620560i) q^{68} -1.95976i q^{71} -11.9069i q^{73} +(-5.21085 + 3.00849i) q^{74} +(-1.28048 - 0.739283i) q^{76} +(4.87702 + 8.44725i) q^{79} -10.4054 q^{80} +8.68270i q^{82} +(0.796736 + 1.37999i) q^{83} +(2.53673 - 4.39374i) q^{85} +(-4.33806 - 2.50458i) q^{86} +(3.32660 + 5.76184i) q^{88} -6.09921 q^{89} +(-1.93456 + 1.11692i) q^{92} +(7.28851 + 4.20802i) q^{94} +(-9.06614 - 5.23434i) q^{95} +(2.36387 - 1.36478i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{4}+O(q^{10}) \) 48 * q + 24 * q^4	\( 48 q + 24 q^{4} + 24 q^{11} - 24 q^{16} + 48 q^{23} - 24 q^{25} - 120 q^{32} - 48 q^{50} - 48 q^{64} - 120 q^{65} + 168 q^{74} - 24 q^{79} - 24 q^{85} - 24 q^{86} + 144 q^{92} - 96 q^{95}+O(q^{100}) \) 48 * q + 24 * q^4 + 24 * q^11 - 24 * q^16 + 48 * q^23 - 24 * q^25 - 120 * q^32 - 48 * q^50 - 48 * q^64 - 120 * q^65 + 168 * q^74 - 24 * q^79 - 24 * q^85 - 24 * q^86 + 144 * q^92 - 96 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more