LMFDB - Embedded newform 532.2.cj.a.173.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [532,2,Mod(33,532)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(532, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 15, 7]))

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

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

chi := DirichletCharacter("532.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 532 = 2^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	532.cj (of order $18$, degree $6$, 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:	$4.24804138753$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			173.12
Character	$\chi$	$=$	532.173
Dual form			532.2.cj.a.409.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.438893 - 2.48909i) q^{3} +(-1.03151 - 0.181883i) q^{5} +(-2.55946 + 0.670193i) q^{7} +(-3.18386 - 1.15883i) q^{9} -2.06581 q^{11} +(-0.478089 + 0.401165i) q^{13} +(-0.905444 + 2.48769i) q^{15} +(-1.43338 - 3.93819i) q^{17} +(-3.76652 - 2.19394i) q^{19} +(0.544838 + 6.66487i) q^{21} +(-4.26093 + 3.57534i) q^{23} +(-3.66754 - 1.33487i) q^{25} +(-0.490573 + 0.849697i) q^{27} +(7.92909 - 1.39811i) q^{29} +(-0.252769 + 0.437809i) q^{31} +(-0.906671 + 5.14198i) q^{33} +(2.76200 - 0.225787i) q^{35} +(6.07450 + 3.50711i) q^{37} +(0.788704 + 1.36608i) q^{39} +(0.356481 + 0.299123i) q^{41} +(-8.38983 + 3.05365i) q^{43} +(3.07340 + 1.77443i) q^{45} +(0.662977 - 1.82152i) q^{47} +(6.10168 - 3.43066i) q^{49} +(-10.4316 + 1.83937i) q^{51} +(-0.276550 + 0.0487632i) q^{53} +(2.13090 + 0.375735i) q^{55} +(-7.11400 + 8.41229i) q^{57} +(6.12671 - 2.22994i) q^{59} +(-7.44630 - 8.87416i) q^{61} +(8.92560 + 0.832180i) q^{63} +(0.566118 - 0.326848i) q^{65} +(-3.76811 - 4.49065i) q^{67} +(7.02926 + 12.1750i) q^{69} +(-3.35917 - 9.22925i) q^{71} +(9.01173 + 1.58901i) q^{73} +(-4.93228 + 8.54296i) q^{75} +(5.28736 - 1.38449i) q^{77} +(-4.23127 - 11.6253i) q^{79} +(-5.88685 - 4.93965i) q^{81} +(4.36427 - 2.51971i) q^{83} +(0.762258 + 4.32298i) q^{85} -20.3498i q^{87} +(-2.04775 - 11.6134i) q^{89} +(0.954794 - 1.34718i) q^{91} +(0.978807 + 0.821317i) q^{93} +(3.48615 + 2.94813i) q^{95} +(1.08731 - 6.16646i) q^{97} +(6.57724 + 2.39392i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 6 q^{7} - 6 q^{11} + 6 q^{13} - 3 q^{15} + 27 q^{17} + 21 q^{19} - 3 q^{21} - 24 q^{23} + 12 q^{27} - 18 q^{29} + 33 q^{35} + 36 q^{37} - 18 q^{39} - 18 q^{41} - 48 q^{43} - 18 q^{45} - 18 q^{49}+ \cdots + 27 q^{99}+O(q^{100}) $ 78 * q + 6 * q^7 - 6 * q^11 + 6 * q^13 - 3 * q^15 + 27 * q^17 + 21 * q^19 - 3 * q^21 - 24 * q^23 + 12 * q^27 - 18 * q^29 + 33 * q^35 + 36 * q^37 - 18 * q^39 - 18 * q^41 - 48 * q^43 - 18 * q^45 - 18 * q^49 + 6 * q^53 - 18 * q^57 + 45 * q^59 + 39 * q^61 - 27 * q^63 - 18 * q^65 + 21 * q^67 + 6 * q^71 - 3 * q^73 - 21 * q^75 - 21 * q^77 + 36 * q^79 + 36 * q^81 - 18 * q^83 + 60 * q^85 - 21 * q^91 - 102 * q^93 + 60 * q^95 - 27 * q^97 + 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/532\mathbb{Z}\right)^\times$.

$n$	$267$	$381$	$477$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.438893	−	2.48909i	0.253395	−	1.43708i	−0.546763	−	0.837287i	$-0.684140\pi$
$3$	0.438893	−	2.48909i	0.253395	−	1.43708i	0.800158	−	0.599789i	$-0.204749\pi$
$4$		0			0
$5$	−1.03151	−	0.181883i	−0.461304	−	0.0813404i	−0.0618338	−	0.998086i	$-0.519695\pi$
$5$	−1.03151	−	0.181883i	−0.461304	−	0.0813404i	−0.399470	+	0.916746i	$0.630806\pi$
$6$		0			0
$7$	−2.55946	+	0.670193i	−0.967385	+	0.253309i
$7$	−2.55946	+	0.670193i	−0.967385	+	0.253309i
$8$		0			0
$9$	−3.18386	−	1.15883i	−1.06129	−	0.386276i
$10$		0			0
$11$	−2.06581			−0.622865			−0.311433	−	0.950268i	$-0.600809\pi$
$11$	−2.06581			−0.622865			−0.311433	+	0.950268i	$0.600809\pi$
$12$		0			0
$13$	−0.478089	+	0.401165i	−0.132598	+	0.111263i	−0.706675	−	0.707539i	$-0.749806\pi$
$13$	−0.478089	+	0.401165i	−0.132598	+	0.111263i	0.574077	+	0.818802i	$0.305361\pi$
$14$		0			0
$15$	−0.905444	+	2.48769i	−0.233785	+	0.642318i
$16$		0			0
$17$	−1.43338	−	3.93819i	−0.347647	−	0.955152i	−0.983109	−	0.183020i	$-0.941413\pi$
$17$	−1.43338	−	3.93819i	−0.347647	−	0.955152i	0.635462	−	0.772132i	$-0.280809\pi$
$18$		0			0
$19$	−3.76652	−	2.19394i	−0.864098	−	0.503324i
$19$	−3.76652	−	2.19394i	−0.864098	−	0.503324i
$20$		0			0
$21$	0.544838	+	6.66487i	0.118893	+	1.45439i
$22$		0			0
$23$	−4.26093	+	3.57534i	−0.888465	+	0.745511i	−0.967902	−	0.251329i	$-0.919132\pi$
$23$	−4.26093	+	3.57534i	−0.888465	+	0.745511i	0.0794364	+	0.996840i	$0.474688\pi$
$24$		0			0
$25$	−3.66754	−	1.33487i	−0.733507	−	0.266975i
$26$		0			0
$27$	−0.490573	+	0.849697i	−0.0944108	+	0.163524i
$28$		0			0
$29$	7.92909	−	1.39811i	1.47240	−	0.259623i	0.620861	−	0.783921i	$-0.286783\pi$
$29$	7.92909	−	1.39811i	1.47240	−	0.259623i	0.851535	+	0.524298i	$0.175672\pi$
$30$		0			0
$31$	−0.252769	+	0.437809i	−0.0453987	+	0.0786329i	−0.887832	−	0.460168i	$-0.847789\pi$
$31$	−0.252769	+	0.437809i	−0.0453987	+	0.0786329i	0.842433	+	0.538801i	$0.181122\pi$
$32$		0			0
$33$	−0.906671	+	5.14198i	−0.157831	+	0.895105i
$34$		0			0
$35$	2.76200	−	0.225787i	0.466863	−	0.0381651i
$36$		0			0
$37$	6.07450	+	3.50711i	0.998642	+	0.576566i	0.907846	−	0.419303i	$-0.137726\pi$
$37$	6.07450	+	3.50711i	0.998642	+	0.576566i	0.0907956	+	0.995870i	$0.471059\pi$
$38$		0			0
$39$	0.788704	+	1.36608i	0.126294	+	0.218747i
$40$		0			0
$41$	0.356481	+	0.299123i	0.0556730	+	0.0467152i	0.670200	−	0.742181i	$-0.266209\pi$
$41$	0.356481	+	0.299123i	0.0556730	+	0.0467152i	−0.614527	+	0.788896i	$0.710653\pi$
$42$		0			0
$43$	−8.38983	+	3.05365i	−1.27944	+	0.465677i	−0.890246	−	0.455480i	$-0.849468\pi$
$43$	−8.38983	+	3.05365i	−1.27944	+	0.465677i	−0.389191	+	0.921157i	$0.627245\pi$
$44$		0			0
$45$	3.07340	+	1.77443i	0.458156	+	0.264516i
$46$		0			0
$47$	0.662977	−	1.82152i	0.0967052	−	0.265695i	−0.881902	−	0.471433i	$-0.843737\pi$
$47$	0.662977	−	1.82152i	0.0967052	−	0.265695i	0.978607	+	0.205737i	$0.0659593\pi$
$48$		0			0
$49$	6.10168	−	3.43066i	0.871669	−	0.490095i
$50$		0			0
$51$	−10.4316	+	1.83937i	−1.46072	+	0.257564i
$52$		0			0
$53$	−0.276550	+	0.0487632i	−0.0379871	+	0.00669815i	−0.192609	−	0.981276i	$-0.561695\pi$
$53$	−0.276550	+	0.0487632i	−0.0379871	+	0.00669815i	0.154622	+	0.987974i	$0.450584\pi$
$54$		0			0
$55$	2.13090	+	0.375735i	0.287330	+	0.0506641i
$56$		0			0
$57$	−7.11400	+	8.41229i	−0.942273	+	1.11423i
$58$		0			0
$59$	6.12671	−	2.22994i	0.797630	−	0.290313i	0.0891257	−	0.996020i	$-0.471593\pi$
$59$	6.12671	−	2.22994i	0.797630	−	0.290313i	0.708504	+	0.705707i	$0.249370\pi$
$60$		0			0
$61$	−7.44630	−	8.87416i	−0.953402	−	1.13622i	−0.990583	−	0.136911i	$-0.956282\pi$
$61$	−7.44630	−	8.87416i	−0.953402	−	1.13622i	0.0371817	−	0.999309i	$-0.488162\pi$
$62$		0			0
$63$	8.92560	+	0.832180i	1.12452	+	0.104845i
$64$		0			0
$65$	0.566118	−	0.326848i	0.0702183	−	0.0405405i
$66$		0			0
$67$	−3.76811	−	4.49065i	−0.460347	−	0.548621i	0.485073	−	0.874474i	$-0.338793\pi$
$67$	−3.76811	−	4.49065i	−0.460347	−	0.548621i	−0.945420	+	0.325853i	$0.894349\pi$
$68$		0			0
$69$	7.02926	+	12.1750i	0.846223	+	1.46570i
$70$		0			0
$71$	−3.35917	−	9.22925i	−0.398661	−	1.09531i	−0.962937	−	0.269725i	$-0.913067\pi$
$71$	−3.35917	−	9.22925i	−0.398661	−	1.09531i	0.564277	−	0.825586i	$-0.309155\pi$
$72$		0			0
$73$	9.01173	+	1.58901i	1.05474	+	0.185980i	0.674023	−	0.738711i	$-0.264565\pi$
$73$	9.01173	+	1.58901i	1.05474	+	0.185980i	0.380720	+	0.924690i	$0.375676\pi$
$74$		0			0
$75$	−4.93228	+	8.54296i	−0.569530	+	0.986455i
$76$		0			0
$77$	5.28736	−	1.38449i	0.602551	−	0.157777i
$78$		0			0
$79$	−4.23127	−	11.6253i	−0.476055	−	1.30795i	−0.912816	−	0.408372i	$-0.866097\pi$
$79$	−4.23127	−	11.6253i	−0.476055	−	1.30795i	0.436761	−	0.899578i	$-0.356126\pi$
$80$		0			0
$81$	−5.88685	−	4.93965i	−0.654095	−	0.548850i
$82$		0			0
$83$	4.36427	−	2.51971i	0.479041	−	0.276574i	−0.240976	−	0.970531i	$-0.577468\pi$
$83$	4.36427	−	2.51971i	0.479041	−	0.276574i	0.720017	+	0.693957i	$0.244134\pi$
$84$		0			0
$85$	0.762258	+	4.32298i	0.0826785	+	0.468893i
$86$		0			0
$87$		−	20.3498i		−	2.18173i
$88$		0			0
$89$	−2.04775	−	11.6134i	−0.217061	−	1.23101i	−0.877294	−	0.479953i	$-0.840654\pi$
$89$	−2.04775	−	11.6134i	−0.217061	−	1.23101i	0.660234	−	0.751060i	$-0.270457\pi$
$90$		0			0
$91$	0.954794	−	1.34718i	0.100090	−	0.141223i
$92$		0			0
$93$	0.978807	+	0.821317i	0.101498	+	0.0851666i
$94$		0			0
$95$	3.48615	+	2.94813i	0.357672	+	0.302471i
$96$		0			0
$97$	1.08731	−	6.16646i	0.110400	−	0.626109i	−0.878525	−	0.477696i	$-0.841472\pi$
$97$	1.08731	−	6.16646i	0.110400	−	0.626109i	0.988925	−	0.148414i	$-0.0474167\pi$
$98$		0			0
$99$	6.57724	+	2.39392i	0.661038	+	0.240598i
$100$		0			0
$101$	0.920264	−	2.52841i	0.0915697	−	0.251586i	−0.885450	−	0.464735i	$-0.846150\pi$
$101$	0.920264	−	2.52841i	0.0915697	−	0.251586i	0.977020	+	0.213149i	$0.0683719\pi$
$102$		0			0
$103$	0.283136	+	0.490407i	0.0278983	+	0.0483212i	0.879637	−	0.475645i	$-0.157785\pi$
$103$	0.283136	+	0.490407i	0.0278983	+	0.0483212i	−0.851739	+	0.523966i	$0.824452\pi$
$104$		0			0
$105$	0.650219	−	6.97396i	0.0634549	−	0.680589i
$106$		0			0
$107$			8.20371i			0.793082i	0.918017	+	0.396541i	$0.129790\pi$
$107$			8.20371i			0.793082i	−0.918017	+	0.396541i	$0.870210\pi$
$108$		0			0
$109$	−4.40789	+	5.25312i	−0.422200	+	0.503158i	−0.934655	−	0.355556i	$-0.884292\pi$
$109$	−4.40789	+	5.25312i	−0.422200	+	0.503158i	0.512455	+	0.858714i	$0.328736\pi$
$110$		0			0
$111$	11.3956	−	13.5807i	1.08162	−	1.28903i
$112$		0			0
$113$			15.1147i			1.42187i	0.703258	+	0.710934i	$0.251728\pi$
$113$			15.1147i			1.42187i	−0.703258	+	0.710934i	$0.748272\pi$
$114$		0			0
$115$	5.04548	−	2.91301i	0.470493	−	0.271639i
$116$		0			0
$117$	1.98705	−	0.723227i	0.183703	−	0.0668624i
$118$		0			0
$119$	6.30804	+	9.11900i	0.578257	+	0.835938i
$120$		0			0
$121$	−6.73243			−0.612039
$122$		0			0
$123$	0.901001	−	0.756029i	0.0812405	−	0.0681689i
$124$		0			0
$125$	8.07577	+	4.66255i	0.722318	+	0.417031i
$126$		0			0
$127$	−5.91538	−	7.04967i	−0.524905	−	0.625557i	0.436828	−	0.899545i	$-0.356102\pi$
$127$	−5.91538	−	7.04967i	−0.524905	−	0.625557i	−0.961733	+	0.273988i	$0.911657\pi$
$128$		0			0
$129$	3.91856	+	22.2232i	0.345010	+	1.95665i
$130$		0			0
$131$	3.84891	−	4.58695i	0.336281	−	0.400764i	−0.571232	−	0.820789i	$-0.693534\pi$
$131$	3.84891	−	4.58695i	0.336281	−	0.400764i	0.907513	+	0.420025i	$0.137979\pi$
$132$		0			0
$133$	11.1106	+	3.09101i	0.963412	+	0.268024i
$134$		0			0
$135$	0.660575	−	0.787242i	0.0568532	−	0.0677550i
$136$		0			0
$137$	−0.521893	−	2.95980i	−0.0445883	−	0.252873i	0.954363	−	0.298647i	$-0.0965355\pi$
$137$	−0.521893	−	2.95980i	−0.0445883	−	0.252873i	−0.998952	+	0.0457747i	$0.985424\pi$
$138$		0			0
$139$	−2.27306	−	2.70893i	−0.192799	−	0.229768i	0.660982	−	0.750402i	$-0.270140\pi$
$139$	−2.27306	−	2.70893i	−0.192799	−	0.229768i	−0.853780	+	0.520634i	$0.825696\pi$
$140$		0			0
$141$	−4.24294	−	2.44966i	−0.357320	−	0.206299i
$142$		0			0
$143$	0.987642	−	0.828730i	0.0825908	−	0.0693019i
$144$		0			0
$145$	−8.43321			−0.700340
$146$		0			0
$147$	−5.86124	−	16.6933i	−0.483427	−	1.37684i
$148$		0			0
$149$	17.2125	−	6.26484i	1.41010	−	0.513235i	0.478943	−	0.877846i	$-0.341020\pi$
$149$	17.2125	−	6.26484i	1.41010	−	0.513235i	0.931160	+	0.364611i	$0.118798\pi$
$150$		0			0
$151$	8.62673	−	4.98064i	0.702033	−	0.405319i	−0.106071	−	0.994359i	$-0.533827\pi$
$151$	8.62673	−	4.98064i	0.702033	−	0.405319i	0.808104	+	0.589040i	$0.200494\pi$
$152$		0			0
$153$			14.1997i			1.14798i
$154$		0			0
$155$	0.340363	−	0.405629i	0.0273386	−	0.0325809i
$156$		0			0
$157$	−12.4810	+	14.8743i	−0.996094	+	1.18710i	−0.0137713	+	0.999905i	$0.504384\pi$
$157$	−12.4810	+	14.8743i	−0.996094	+	1.18710i	−0.982323	+	0.187194i	$0.940061\pi$
$158$		0			0
$159$			0.709759i			0.0562876i
$160$		0			0
$161$	8.50952	−	12.0066i	0.670644	−	0.946253i
$162$		0			0
$163$	−1.90963	−	3.30758i	−0.149574	−	0.259070i	0.781496	−	0.623910i	$-0.214457\pi$
$163$	−1.90963	−	3.30758i	−0.149574	−	0.259070i	−0.931070	+	0.364840i	$0.881124\pi$
$164$		0			0
$165$	1.87048	−	5.13909i	0.145616	−	0.400078i
$166$		0			0
$167$	19.0311	+	6.92674i	1.47267	+	0.536007i	0.948823	−	0.315807i	$-0.102275\pi$
$167$	19.0311	+	6.92674i	1.47267	+	0.536007i	0.523844	+	0.851814i	$0.324497\pi$
$168$		0			0
$169$	−2.18979	+	12.4189i	−0.168445	+	0.955301i
$170$		0			0
$171$	9.44965	+	11.3499i	0.722633	+	0.867951i
$172$		0			0
$173$	5.90128	+	4.95176i	0.448666	+	0.376476i	0.838941	−	0.544223i	$-0.183175\pi$
$173$	5.90128	+	4.95176i	0.448666	+	0.376476i	−0.390274	+	0.920699i	$0.627620\pi$
$174$		0			0
$175$	10.2815	+	0.958602i	0.777211	+	0.0724635i
$176$		0			0
$177$	−2.86154	−	16.2286i	−0.215087	−	1.21982i
$178$		0			0
$179$			16.3073i			1.21887i	0.792838	+	0.609433i	$0.208603\pi$
$179$			16.3073i			1.21887i	−0.792838	+	0.609433i	$0.791397\pi$
$180$		0			0
$181$	2.48116	+	14.0714i	0.184423	+	1.04592i	0.926694	+	0.375817i	$0.122638\pi$
$181$	2.48116	+	14.0714i	0.184423	+	1.04592i	−0.742271	+	0.670100i	$0.766251\pi$
$182$		0			0
$183$	−25.3567	+	14.6397i	−1.87442	+	1.08220i
$184$		0			0
$185$	−5.62801	−	4.72246i	−0.413780	−	0.347202i
$186$		0			0
$187$	2.96110	+	8.13555i	0.216537	+	0.594931i
$188$		0			0
$189$	0.686141	−	2.50354i	0.0499094	−	0.182106i
$190$		0			0
$191$	7.46171	−	12.9241i	0.539910	−	0.935152i	−0.458998	−	0.888437i	$-0.651792\pi$
$191$	7.46171	−	12.9241i	0.539910	−	0.935152i	0.998908	−	0.0467145i	$-0.0148751\pi$
$192$		0			0
$193$	−14.8844	−	2.62452i	−1.07140	−	0.188917i	−0.389992	−	0.920818i	$-0.627522\pi$
$193$	−14.8844	−	2.62452i	−1.07140	−	0.188917i	−0.681411	+	0.731901i	$0.738633\pi$
$194$		0			0
$195$	−0.565089	−	1.55257i	−0.0404669	−	0.111182i
$196$		0			0
$197$	5.94325	+	10.2940i	0.423439	+	0.733418i	0.996273	−	0.0862535i	$-0.0274895\pi$
$197$	5.94325	+	10.2940i	0.423439	+	0.733418i	−0.572834	+	0.819671i	$0.694156\pi$
$198$		0			0
$199$	−11.3910	−	13.5753i	−0.807489	−	0.962329i	0.192330	−	0.981330i	$-0.438396\pi$
$199$	−11.3910	−	13.5753i	−0.807489	−	0.962329i	−0.999819	+	0.0190018i	$0.993951\pi$
$200$		0			0
$201$	−12.8314	+	7.40823i	−0.905060	+	0.522536i
$202$		0			0
$203$	−19.3572	+	8.89244i	−1.35861	+	0.624127i
$204$		0			0
$205$	−0.313308	−	0.373385i	−0.0218823	−	0.0260784i
$206$		0			0
$207$	17.7094	−	6.44570i	1.23089	−	0.448007i
$208$		0			0
$209$	7.78091	+	4.53226i	0.538217	+	0.313503i
$210$		0			0
$211$	−5.35540	−	0.944301i	−0.368681	−	0.0650084i	−0.0137615	−	0.999905i	$-0.504381\pi$
$211$	−5.35540	−	0.944301i	−0.368681	−	0.0650084i	−0.354919	+	0.934897i	$0.615492\pi$
$212$		0			0
$213$	−24.4468	+	4.31062i	−1.67506	+	0.295359i
$214$		0			0
$215$	9.20958	−	1.62390i	0.628088	−	0.110749i
$216$		0			0
$217$	0.353537	−	1.28996i	0.0239996	−	0.0875682i
$218$		0			0
$219$	7.91038	−	21.7336i	0.534534	−	1.46862i
$220$		0			0
$221$	2.26515	+	1.30778i	0.152370	+	0.0879711i
$222$		0			0
$223$	4.20981	−	1.53225i	0.281910	−	0.102607i	−0.197195	−	0.980364i	$-0.563183\pi$
$223$	4.20981	−	1.53225i	0.281910	−	0.102607i	0.479105	+	0.877757i	$0.340961\pi$
$224$		0			0
$225$	10.1300	+	8.50010i	0.675335	+	0.566673i
$226$		0			0
$227$	−7.65938	−	13.2664i	−0.508371	−	0.880524i	−0.999953	−	0.00969273i	$-0.996915\pi$
$227$	−7.65938	−	13.2664i	−0.508371	−	0.880524i	0.491582	−	0.870831i	$-0.336419\pi$
$228$		0			0
$229$	18.9999	+	10.9696i	1.25555	+	0.724889i	0.972205	−	0.234130i	$-0.0752241\pi$
$229$	18.9999	+	10.9696i	1.25555	+	0.724889i	0.283340	+	0.959019i	$0.408557\pi$
$230$		0			0
$231$	−1.12553	−	13.7684i	−0.0740546	−	0.905891i
$232$		0			0
$233$	4.52413	−	25.6576i	0.296386	−	1.68089i	−0.365132	−	0.930956i	$-0.618976\pi$
$233$	4.52413	−	25.6576i	0.296386	−	1.68089i	0.661517	−	0.749930i	$-0.269913\pi$
$234$		0			0
$235$	−1.01517	+	1.75832i	−0.0662223	+	0.114700i
$236$		0			0
$237$	−30.7935	+	5.42973i	−2.00025	+	0.352699i
$238$		0			0
$239$	−3.58100	+	6.20247i	−0.231635	+	0.401204i	−0.958290	−	0.285799i	$-0.907741\pi$
$239$	−3.58100	+	6.20247i	−0.231635	+	0.401204i	0.726654	+	0.687003i	$0.241074\pi$
$240$		0			0
$241$	−23.9346	−	8.71148i	−1.54176	−	0.561156i	−0.575296	−	0.817946i	$-0.695113\pi$
$241$	−23.9346	−	8.71148i	−1.54176	−	0.561156i	−0.966467	+	0.256790i	$0.917335\pi$
$242$		0			0
$243$	−17.1337	+	14.3769i	−1.09913	+	0.922280i
$244$		0			0
$245$	−6.91791	+	2.42897i	−0.441969	+	0.155181i
$246$		0			0
$247$	2.68086	−	0.462095i	0.170579	−	0.0294024i
$248$		0			0
$249$	−4.35634	−	11.9689i	−0.276072	−	0.758500i
$250$		0			0
$251$	−9.01699	+	24.7740i	−0.569147	+	1.56372i	0.236692	+	0.971585i	$0.423937\pi$
$251$	−9.01699	+	24.7740i	−0.569147	+	1.56372i	−0.805839	+	0.592134i	$0.798285\pi$
$252$		0			0
$253$	8.80227	−	7.38598i	0.553394	−	0.464353i
$254$		0			0
$255$	11.0948			0.694786
$256$		0			0
$257$	7.45765	+	2.71436i	0.465195	+	0.169317i	0.563975	−	0.825792i	$-0.309272\pi$
$257$	7.45765	+	2.71436i	0.465195	+	0.169317i	−0.0987794	+	0.995109i	$0.531494\pi$
$258$		0			0
$259$	−17.8979	−	4.90524i	−1.11212	−	0.304797i
$260$		0			0
$261$	−26.8653	−	4.73707i	−1.66292	−	0.293217i
$262$		0			0
$263$	−4.47241	+	25.3643i	−0.275781	+	1.56403i	0.460691	+	0.887561i	$0.347602\pi$
$263$	−4.47241	+	25.3643i	−0.275781	+	1.56403i	−0.736471	+	0.676469i	$0.763509\pi$
$264$		0			0
$265$	0.294133			0.0180684
$266$		0			0
$267$	−29.8054			−1.82406
$268$		0			0
$269$	1.73604	−	9.84557i	0.105848	−	0.600295i	−0.885030	−	0.465534i	$-0.845862\pi$
$269$	1.73604	−	9.84557i	0.105848	−	0.600295i	0.990878	−	0.134761i	$-0.0430266\pi$
$270$		0			0
$271$	18.0444	+	3.18171i	1.09612	+	0.193275i	0.692333	−	0.721578i	$-0.256583\pi$
$271$	18.0444	+	3.18171i	1.09612	+	0.193275i	0.403786	+	0.914853i	$0.367694\pi$
$272$		0			0
$273$	−2.93419	−	2.96783i	−0.177585	−	0.179621i
$274$		0			0
$275$	7.57643	+	2.75760i	0.456876	+	0.166289i
$276$		0			0
$277$	−15.4531			−0.928489			−0.464244	−	0.885707i	$-0.653674\pi$
$277$	−15.4531			−0.928489			−0.464244	+	0.885707i	$0.653674\pi$
$278$		0			0
$279$	1.31213	−	1.10101i	0.0785550	−	0.0659155i
$280$		0			0
$281$	10.9992	−	30.2201i	0.656159	−	1.80278i	0.0625299	−	0.998043i	$-0.480083\pi$
$281$	10.9992	−	30.2201i	0.656159	−	1.80278i	0.593629	−	0.804739i	$-0.297695\pi$
$282$		0			0
$283$	1.00678	+	2.76610i	0.0598468	+	0.164428i	0.966013	−	0.258495i	$-0.0832265\pi$
$283$	1.00678	+	2.76610i	0.0598468	+	0.164428i	−0.906166	+	0.422922i	$0.861004\pi$
$284$		0			0
$285$	8.86820	−	7.38343i	0.525307	−	0.437356i
$286$		0			0
$287$	−1.11287	−	0.526683i	−0.0656906	−	0.0310891i
$288$		0			0
$289$	−0.432003	+	0.362493i	−0.0254119	+	0.0213231i
$290$		0			0
$291$	−14.8717	−	5.41284i	−0.871792	−	0.317306i
$292$		0			0
$293$	−0.297931	+	0.516031i	−0.0174053	+	0.0301468i	−0.874597	−	0.484851i	$-0.838874\pi$
$293$	−0.297931	+	0.516031i	−0.0174053	+	0.0301468i	0.857192	+	0.514998i	$0.172207\pi$
$294$		0			0
$295$	−6.72533	+	1.18586i	−0.391564	+	0.0690433i
$296$		0			0
$297$	1.01343	−	1.75531i	0.0588052	−	0.101854i
$298$		0			0
$299$	0.602804	−	3.41867i	0.0348610	−	0.197707i
$300$		0			0
$301$	19.4269	−	13.4385i	1.11975	−	0.774582i
$302$		0			0
$303$	−5.88953	−	3.40032i	−0.338345	−	0.195343i
$304$		0			0
$305$	6.06687	+	10.5081i	0.347388	+	0.601693i
$306$		0			0
$307$	−11.8485	−	9.94208i	−0.676230	−	0.567425i	0.238672	−	0.971100i	$-0.423288\pi$
$307$	−11.8485	−	9.94208i	−0.676230	−	0.567425i	−0.914902	+	0.403676i	$0.867732\pi$
$308$		0			0
$309$	1.34493	−	0.489516i	0.0765106	−	0.0278476i
$310$		0			0
$311$	−18.4345	−	10.6431i	−1.04532	−	0.603518i	−0.123987	−	0.992284i	$-0.539568\pi$
$311$	−18.4345	−	10.6431i	−1.04532	−	0.603518i	−0.921336	+	0.388766i	$0.872901\pi$
$312$		0			0
$313$	4.31080	−	11.8438i	0.243661	−	0.669452i	−0.756225	−	0.654312i	$-0.772958\pi$
$313$	4.31080	−	11.8438i	0.243661	−	0.669452i	0.999885	−	0.0151400i	$-0.00481940\pi$
$314$		0			0
$315$	−9.05546	−	2.48181i	−0.510218	−	0.139834i
$316$		0			0
$317$	−21.4507	+	3.78233i	−1.20479	+	0.212437i	−0.739768	−	0.672863i	$-0.765065\pi$
$317$	−21.4507	+	3.78233i	−1.20479	+	0.212437i	−0.465022	+	0.885299i	$0.653953\pi$
$318$		0			0
$319$	−16.3800	+	2.88824i	−0.917104	+	0.161710i
$320$		0			0
$321$	20.4198	+	3.60055i	1.13972	+	0.200963i
$322$		0			0
$323$	−3.24128	+	17.9780i	−0.180350	+	1.00032i
$324$		0			0
$325$	2.28891	−	0.833097i	0.126966	−	0.0462119i
$326$		0			0
$327$	11.1409	+	13.2772i	0.616093	+	0.734231i
$328$		0			0
$329$	−0.476098	+	5.10642i	−0.0262482	+	0.281526i
$330$		0			0
$331$	−18.0565	+	10.4249i	−0.992476	+	0.573006i	−0.906013	−	0.423249i	$-0.860890\pi$
$331$	−18.0565	+	10.4249i	−0.992476	+	0.573006i	−0.0864622	+	0.996255i	$0.527556\pi$
$332$		0			0
$333$	−15.2762	−	18.2055i	−0.837130	−	0.997653i
$334$		0			0
$335$	3.07006	+	5.31750i	0.167735	+	0.290526i
$336$		0			0
$337$	2.72493	+	7.48668i	0.148436	+	0.407825i	0.991520	−	0.129958i	$-0.0414842\pi$
$337$	2.72493	+	7.48668i	0.148436	+	0.407825i	−0.843083	+	0.537783i	$0.819262\pi$
$338$		0			0
$339$	37.6218	+	6.63373i	2.04333	+	0.360295i
$340$		0			0
$341$	0.522173	−	0.904431i	0.0282773	−	0.0489777i
$342$		0			0
$343$	−13.3178	+	12.8700i	−0.719094	+	0.694912i
$344$		0			0
$345$	−5.03631	−	13.8371i	−0.271146	−	0.744966i
$346$		0			0
$347$	5.96923	+	5.00878i	0.320445	+	0.268885i	0.788793	−	0.614659i	$-0.210706\pi$
$347$	5.96923	+	5.00878i	0.320445	+	0.268885i	−0.468348	+	0.883544i	$0.655151\pi$
$348$		0			0
$349$	3.31556	−	1.91424i	0.177478	−	0.102467i	−0.408629	−	0.912700i	$-0.633993\pi$
$349$	3.31556	−	1.91424i	0.177478	−	0.102467i	0.586107	+	0.810234i	$0.300660\pi$
$350$		0			0
$351$	−0.106331	−	0.603032i	−0.00567551	−	0.0321874i
$352$		0			0
$353$			19.7968i			1.05368i	0.849966	+	0.526838i	$0.176623\pi$
$353$			19.7968i			1.05368i	−0.849966	+	0.526838i	$0.823377\pi$
$354$		0			0
$355$	1.78637	+	10.1310i	0.0948108	+	0.537699i
$356$		0			0
$357$	25.4666	−	11.6990i	1.34783	−	0.619177i
$358$		0			0
$359$	14.2861	+	11.9875i	0.753992	+	0.632675i	0.936555	−	0.350519i	$-0.113995\pi$
$359$	14.2861	+	11.9875i	0.753992	+	0.632675i	−0.182563	+	0.983194i	$0.558439\pi$
$360$		0			0
$361$	9.37328	+	16.5270i	0.493331	+	0.869842i
$362$		0			0
$363$	−2.95482	+	16.7576i	−0.155088	+	0.879547i
$364$		0			0
$365$	−9.00665	−	3.27815i	−0.471430	−	0.171586i
$366$		0			0
$367$	−5.32417	+	14.6280i	−0.277920	+	0.763578i	0.719678	+	0.694308i	$0.244289\pi$
$367$	−5.32417	+	14.6280i	−0.277920	+	0.763578i	−0.997598	+	0.0692701i	$0.977933\pi$
$368$		0			0
$369$	−0.788352	−	1.36547i	−0.0410400	−	0.0710833i
$370$		0			0
$371$	0.675138	−	0.310149i	0.0350514	−	0.0161022i
$372$		0			0
$373$			6.33241i			0.327880i	0.986470	+	0.163940i	$0.0524203\pi$
$373$			6.33241i			0.327880i	−0.986470	+	0.163940i	$0.947580\pi$
$374$		0			0
$375$	15.1499	−	18.0549i	0.782337	−	0.932353i
$376$		0			0
$377$	−3.22994	+	3.84930i	−0.166350	+	0.198249i
$378$		0			0
$379$			18.3782i			0.944025i	0.881592	+	0.472012i	$0.156472\pi$
$379$			18.3782i			0.944025i	−0.881592	+	0.472012i	$0.843528\pi$
$380$		0			0
$381$	−20.1435	+	11.6298i	−1.03198	+	0.595815i
$382$		0			0
$383$	7.86029	−	2.86091i	0.401642	−	0.146186i	−0.133298	−	0.991076i	$-0.542557\pi$
$383$	7.86029	−	2.86091i	0.401642	−	0.146186i	0.534939	+	0.844890i	$0.320334\pi$
$384$		0			0
$385$	−5.70577	+	0.466434i	−0.290793	+	0.0237717i
$386$		0			0
$387$	30.2507			1.53773
$388$		0			0
$389$	5.96281	−	5.00339i	0.302327	−	0.253682i	−0.478985	−	0.877823i	$-0.658995\pi$
$389$	5.96281	−	5.00339i	0.302327	−	0.253682i	0.781312	+	0.624141i	$0.214551\pi$
$390$		0			0
$391$	20.1879	+	11.6555i	1.02095	+	0.589445i
$392$		0			0
$393$	−9.72807	−	11.5935i	−0.490716	−	0.584813i
$394$		0			0
$395$	2.25014	+	12.7612i	0.113217	+	0.642085i
$396$		0			0
$397$	−7.06339	+	8.41781i	−0.354501	+	0.422478i	−0.913594	−	0.406627i	$-0.866705\pi$
$397$	−7.06339	+	8.41781i	−0.354501	+	0.422478i	0.559093	+	0.829105i	$0.311149\pi$
$398$		0			0
$399$	12.5702	−	26.2987i	0.629295	−	1.31658i
$400$		0			0
$401$	11.3389	−	13.5131i	0.566236	−	0.674814i	−0.404618	−	0.914486i	$-0.632595\pi$
$401$	11.3389	−	13.5131i	0.566236	−	0.674814i	0.970854	+	0.239672i	$0.0770398\pi$
$402$		0			0
$403$	−0.0547873	−	0.310714i	−0.00272915	−	0.0154778i
$404$		0			0
$405$	5.17390	+	6.16601i	0.257093	+	0.306391i
$406$		0			0
$407$	−12.5488	−	7.24503i	−0.622019	−	0.359123i
$408$		0			0
$409$	19.9303	−	16.7235i	0.985492	−	0.826926i	0.000583372	−	1.00000i	$-0.499814\pi$
$409$	19.9303	−	16.7235i	0.985492	−	0.826926i	0.984909	+	0.173074i	$0.0553699\pi$
$410$		0			0
$411$	−7.59626			−0.374696
$412$		0			0
$413$	−14.1866	+	9.81352i	−0.698076	+	0.482892i
$414$		0			0
$415$	−4.96007	+	1.80532i	−0.243480	+	0.0886195i
$416$		0			0
$417$	−7.74040	+	4.46892i	−0.379049	+	0.218844i
$418$		0			0
$419$		−	9.89085i		−	0.483200i	−0.970376	−	0.241600i	$-0.922328\pi$
$419$		−	9.89085i		−	0.483200i	0.970376	−	0.241600i	$-0.0776721\pi$
$420$		0			0
$421$	18.5287	−	22.0816i	0.903033	−	1.07619i	−0.0937135	−	0.995599i	$-0.529874\pi$
$421$	18.5287	−	22.0816i	0.903033	−	1.07619i	0.996747	−	0.0805942i	$-0.0256818\pi$
$422$		0			0
$423$	−4.22165	+	5.03117i	−0.205264	+	0.244624i
$424$		0			0
$425$			16.3568i			0.793424i
$426$		0			0
$427$	25.0059	+	17.7226i	1.21012	+	0.857657i
$428$		0			0
$429$	−1.62931	−	2.82205i	−0.0786640	−	0.136250i
$430$		0			0
$431$	−9.96358	+	27.3747i	−0.479929	+	1.31859i	0.429625	+	0.903007i	$0.358646\pi$
$431$	−9.96358	+	27.3747i	−0.479929	+	1.31859i	−0.909554	+	0.415586i	$0.863577\pi$
$432$		0			0
$433$	8.88191	+	3.23275i	0.426838	+	0.155356i	0.546501	−	0.837458i	$-0.315959\pi$
$433$	8.88191	+	3.23275i	0.426838	+	0.155356i	−0.119664	+	0.992814i	$0.538182\pi$
$434$		0			0
$435$	−3.70128	+	20.9910i	−0.177463	+	1.00644i
$436$		0			0
$437$	23.8929	−	4.11838i	1.14295	−	0.197009i
$438$		0			0
$439$	−23.0781	−	19.3648i	−1.10146	−	0.924232i	−0.103934	−	0.994584i	$-0.533143\pi$
$439$	−23.0781	−	19.3648i	−1.10146	−	0.924232i	−0.997522	+	0.0703526i	$0.977588\pi$
$440$		0			0
$441$	−23.4024	+	3.85194i	−1.11440	+	0.183426i
$442$		0			0
$443$	−0.0551901	−	0.312998i	−0.00262216	−	0.0148710i	0.983469	−	0.181079i	$-0.0579589\pi$
$443$	−0.0551901	−	0.312998i	−0.00262216	−	0.0148710i	−0.986091	+	0.166208i	$0.946848\pi$
$444$		0			0
$445$			12.3517i			0.585527i
$446$		0			0
$447$	−8.03928	−	45.5930i	−0.380245	−	2.15648i
$448$		0			0
$449$	32.9104	−	19.0008i	1.55314	−	0.896705i	0.555256	−	0.831680i	$-0.312620\pi$
$449$	32.9104	−	19.0008i	1.55314	−	0.896705i	0.997884	−	0.0650256i	$-0.0207129\pi$
$450$		0			0
$451$	−0.736422	−	0.617931i	−0.0346767	−	0.0290972i
$452$		0			0
$453$	−8.61105	−	23.6587i	−0.404582	−	1.11158i
$454$		0			0
$455$	−1.22991	+	1.21596i	−0.0576588	+	0.0570053i
$456$		0			0
$457$	−10.7924	+	18.6930i	−0.504848	+	0.874423i	0.495136	+	0.868816i	$0.335118\pi$
$457$	−10.7924	+	18.6930i	−0.504848	+	0.874423i	−0.999984	+	0.00560743i	$0.998215\pi$
$458$		0			0
$459$	4.04945	+	0.714027i	0.189012	+	0.0333279i
$460$		0			0
$461$	−10.3049	−	28.3125i	−0.479948	−	1.31865i	−0.909537	−	0.415622i	$-0.863564\pi$
$461$	−10.3049	−	28.3125i	−0.479948	−	1.31865i	0.429589	−	0.903024i	$-0.358658\pi$
$462$		0			0
$463$	3.44849	+	5.97296i	0.160265	+	0.277587i	0.934964	−	0.354744i	$-0.115432\pi$
$463$	3.44849	+	5.97296i	0.160265	+	0.277587i	−0.774699	+	0.632330i	$0.782098\pi$
$464$		0			0
$465$	−0.860264	−	1.02522i	−0.0398938	−	0.0475436i
$466$		0			0
$467$	23.1417	−	13.3609i	1.07087	−	0.618267i	0.142451	−	0.989802i	$-0.454502\pi$
$467$	23.1417	−	13.3609i	1.07087	−	0.618267i	0.928419	+	0.371535i	$0.121168\pi$
$468$		0			0
$469$	12.6539	+	8.96830i	0.584304	+	0.414118i
$470$		0			0
$471$	31.5456	+	37.5946i	1.45355	+	1.73227i
$472$		0			0
$473$	17.3318	−	6.30826i	0.796917	−	0.290054i
$474$		0			0
$475$	10.8852	+	13.0742i	0.499447	+	0.599884i
$476$		0			0
$477$	0.937004	+	0.165219i	0.0429025	+	0.00756486i
$478$		0			0
$479$	−3.30821	+	0.583327i	−0.151156	+	0.0266529i	−0.248714	−	0.968577i	$-0.580008\pi$
$479$	−3.30821	+	0.583327i	−0.151156	+	0.0266529i	0.0975581	+	0.995230i	$0.468897\pi$
$480$		0			0
$481$	−4.31108	+	0.760161i	−0.196569	+	0.0346603i
$482$		0			0
$483$	−26.1507	−	26.4506i	−1.18990	−	1.20354i
$484$		0			0
$485$	−2.24314	+	6.16299i	−0.101856	+	0.279847i
$486$		0			0
$487$	8.27929	+	4.78005i	0.375170	+	0.216605i	0.675715	−	0.737163i	$-0.263835\pi$
$487$	8.27929	+	4.78005i	0.375170	+	0.216605i	−0.300545	+	0.953768i	$0.597168\pi$
$488$		0			0
$489$	−9.07099	+	3.30157i	−0.410204	+	0.149302i
$490$		0			0
$491$	−18.3565	−	15.4029i	−0.828416	−	0.695123i	0.126511	−	0.991965i	$-0.459622\pi$
$491$	−18.3565	−	15.4029i	−0.828416	−	0.695123i	−0.954927	+	0.296842i	$0.904067\pi$
$492$		0			0
$493$	−16.8715	−	29.2223i	−0.759853	−	1.31610i
$494$		0			0
$495$	−6.34907	−	3.66564i	−0.285369	−	0.164758i
$496$		0			0
$497$	14.7831	+	21.3706i	0.663111	+	0.958603i
$498$		0			0
$499$	4.92526	−	27.9325i	0.220485	−	1.25043i	−0.650646	−	0.759381i	$-0.725502\pi$
$499$	4.92526	−	27.9325i	0.220485	−	1.25043i	0.871131	−	0.491051i	$-0.163387\pi$
$500$		0			0
$501$	25.5939	−	44.3299i	1.14345	−	1.98051i
$502$		0			0
$503$	−2.04143	+	0.359959i	−0.0910227	+	0.0160498i	−0.218974	−	0.975731i	$-0.570271\pi$
$503$	−2.04143	+	0.359959i	−0.0910227	+	0.0160498i	0.127951	+	0.991780i	$0.459160\pi$
$504$		0			0
$505$	−1.40913	+	2.44069i	−0.0627056	+	0.108609i
$506$		0			0
$507$	29.9507	+	10.9012i	1.33016	+	0.484138i
$508$		0			0
$509$	−6.02661	+	5.05693i	−0.267125	+	0.224144i	−0.766505	−	0.642239i	$-0.778006\pi$
$509$	−6.02661	+	5.05693i	−0.267125	+	0.224144i	0.499380	+	0.866383i	$0.333561\pi$
$510$		0			0
$511$	−24.1301	+	1.97258i	−1.06745	+	0.0872619i
$512$		0			0
$513$	3.71193	−	2.12411i	0.163886	−	0.0937818i
$514$		0			0
$515$	−0.202861	−	0.557356i	−0.00893912	−	0.0245600i
$516$		0			0
$517$	−1.36959	+	3.76291i	−0.0602343	+	0.165492i
$518$		0			0
$519$	14.9154	−	12.5155i	0.654714	−	0.549370i
$520$		0			0
$521$	−2.38193			−0.104354			−0.0521772	−	0.998638i	$-0.516616\pi$
$521$	−2.38193			−0.104354			−0.0521772	+	0.998638i	$0.516616\pi$
$522$		0			0
$523$	−13.9841	−	5.08980i	−0.611482	−	0.222561i	0.0176696	−	0.999844i	$-0.494375\pi$
$523$	−13.9841	−	5.08980i	−0.611482	−	0.222561i	−0.629152	+	0.777283i	$0.716598\pi$
$524$		0			0
$525$	6.89855	−	25.1709i	0.301077	−	1.09855i
$526$		0			0
$527$	2.08649	+	0.367905i	0.0908890	+	0.0160262i
$528$		0			0
$529$	1.37853	−	7.81801i	0.0599359	−	0.339914i
$530$		0			0
$531$	−22.0907			−0.958654
$532$		0			0
$533$	−0.290427			−0.0125798
$534$		0			0
$535$	1.49211	−	8.46219i	0.0645096	−	0.365852i
$536$		0			0
$537$	40.5904	+	7.15717i	1.75160	+	0.308855i
$538$		0			0
$539$	−12.6049	+	7.08710i	−0.542932	+	0.305263i
$540$		0			0
$541$	33.1913	+	12.0806i	1.42700	+	0.519387i	0.936071	−	0.351810i	$-0.114434\pi$
$541$	33.1913	+	12.0806i	1.42700	+	0.519387i	0.490933	+	0.871197i	$0.336656\pi$
$542$		0			0
$543$	36.1139			1.54979
$544$		0			0
$545$	5.50223	−	4.61692i	0.235690	−	0.197767i
$546$		0			0
$547$	1.02493	−	2.81599i	0.0438231	−	0.120403i	−0.915851	−	0.401519i	$-0.868482\pi$
$547$	1.02493	−	2.81599i	0.0438231	−	0.120403i	0.959674	+	0.281116i	$0.0907046\pi$
$548$		0			0
$549$	13.4243	+	36.8831i	0.572937	+	1.57413i
$550$		0			0
$551$	−32.9324	−	12.1299i	−1.40297	−	0.516752i
$552$		0			0
$553$	18.6210	+	26.9188i	0.791844	+	1.14470i
$554$		0			0
$555$	−14.2247	+	11.9360i	−0.603806	+	0.506653i
$556$		0			0
$557$	−42.3181	−	15.4025i	−1.79307	−	0.652626i	−0.998995	−	0.0448121i	$-0.985731\pi$
$557$	−42.3181	−	15.4025i	−1.79307	−	0.652626i	−0.794080	−	0.607814i	$-0.792047\pi$
$558$		0			0
$559$	2.78607	−	4.82562i	0.117838	−	0.204102i
$560$		0			0
$561$	21.5497	−	3.79980i	0.909830	−	0.160428i
$562$		0			0
$563$	23.0136	−	39.8607i	0.969906	−	1.67993i	0.274093	−	0.961703i	$-0.411622\pi$
$563$	23.0136	−	39.8607i	0.969906	−	1.67993i	0.695813	−	0.718223i	$-0.255044\pi$
$564$		0			0
$565$	2.74910	−	15.5909i	0.115655	−	0.655914i
$566$		0			0
$567$	18.3777	+	8.69753i	0.771790	+	0.365262i
$568$		0			0
$569$	2.41070	+	1.39182i	0.101062	+	0.0583482i	0.549679	−	0.835376i	$-0.314750\pi$
$569$	2.41070	+	1.39182i	0.101062	+	0.0583482i	−0.448617	+	0.893724i	$0.648083\pi$
$570$		0			0
$571$	−17.1966	−	29.7853i	−0.719654	−	1.24648i	−0.961137	−	0.276072i	$-0.910967\pi$
$571$	−17.1966	−	29.7853i	−0.719654	−	1.24648i	0.241483	−	0.970405i	$-0.422366\pi$
$572$		0			0
$573$	−28.8942	−	24.2451i	−1.20707	−	1.01285i
$574$		0			0
$575$	20.3998	−	7.42490i	0.850728	−	0.309640i
$576$		0			0
$577$	−32.2628	−	18.6269i	−1.34312	−	0.775449i	−0.355854	−	0.934542i	$-0.615810\pi$
$577$	−32.2628	−	18.6269i	−1.34312	−	0.775449i	−0.987264	+	0.159092i	$0.949143\pi$
$578$		0			0
$579$	−13.0653	+	35.8967i	−0.542977	+	1.49182i
$580$		0			0
$581$	−9.48148	+	9.37400i	−0.393358	+	0.388899i
$582$		0			0
$583$	0.571300	−	0.100736i	0.0236608	−	0.00417204i
$584$		0			0
$585$	−2.18120	+	0.384604i	−0.0901815	+	0.0159014i
$586$		0			0
$587$	29.8277	+	5.25943i	1.23112	+	0.217080i	0.751107	−	0.660181i	$-0.229520\pi$
$587$	29.8277	+	5.25943i	1.23112	+	0.217080i	0.480015	+	0.877261i	$0.340631\pi$
$588$		0			0
$589$	1.91259	−	1.09446i	0.0788067	−	0.0450963i
$590$		0			0
$591$	28.2312	−	10.2753i	1.16127	−	0.422669i
$592$		0			0
$593$	−24.7872	−	29.5403i	−1.01789	−	1.21307i	−0.976852	−	0.213915i	$-0.931378\pi$
$593$	−24.7872	−	29.5403i	−1.01789	−	1.21307i	−0.0410368	−	0.999158i	$-0.513066\pi$
$594$		0			0
$595$	−4.84820	−	10.5536i	−0.198757	−	0.432657i
$596$		0			0
$597$	−38.7896	+	22.3952i	−1.58755	+	0.916574i
$598$		0			0
$599$	29.7680	+	35.4761i	1.21629	+	1.44951i	0.856238	+	0.516581i	$0.172795\pi$
$599$	29.7680	+	35.4761i	1.21629	+	1.44951i	0.360049	+	0.932934i	$0.382760\pi$
$600$		0			0
$601$	−7.57073	−	13.1129i	−0.308816	−	0.534886i	0.669287	−	0.743004i	$-0.266600\pi$
$601$	−7.57073	−	13.1129i	−0.308816	−	0.534886i	−0.978104	+	0.208118i	$0.933266\pi$
$602$		0			0
$603$	6.79321	+	18.6642i	0.276641	+	0.760065i
$604$		0			0
$605$	6.94455	+	1.22451i	0.282336	+	0.0497835i
$606$		0			0
$607$	16.4930	−	28.5668i	0.669432	−	1.15949i	−0.308631	−	0.951182i	$-0.599871\pi$
$607$	16.4930	−	28.5668i	0.669432	−	1.15949i	0.978063	−	0.208308i	$-0.0667957\pi$
$608$		0			0
$609$	13.6383	+	52.0846i	0.552652	+	2.11058i
$610$		0			0
$611$	0.413765	+	1.13681i	0.0167391	+	0.0459904i
$612$		0			0
$613$	−18.8170	−	15.7893i	−0.760010	−	0.637724i	0.178120	−	0.984009i	$-0.442999\pi$
$613$	−18.8170	−	15.7893i	−0.760010	−	0.637724i	−0.938129	+	0.346285i	$0.887443\pi$
$614$		0			0
$615$	−1.06690	+	0.615974i	−0.0430215	+	0.0248385i
$616$		0			0
$617$	−0.347381	−	1.97009i	−0.0139850	−	0.0793130i	0.977016	−	0.213164i	$-0.0683768\pi$
$617$	−0.347381	−	1.97009i	−0.0139850	−	0.0793130i	−0.991001	+	0.133851i	$0.957266\pi$
$618$		0			0
$619$		−	8.16127i		−	0.328029i	−0.986458	−	0.164015i	$-0.947556\pi$
$619$		−	8.16127i		−	0.328029i	0.986458	−	0.164015i	$-0.0524444\pi$
$620$		0			0
$621$	−0.947663	−	5.37447i	−0.0380284	−	0.215670i
$622$		0			0
$623$	13.0243	+	28.3515i	0.521808	+	1.13588i
$624$		0			0
$625$	7.46684	+	6.26542i	0.298673	+	0.250617i
$626$		0			0
$627$	14.6962	−	17.3782i	0.586909	−	0.694018i
$628$		0			0
$629$	5.10459	−	28.9496i	0.203533	−	1.15430i
$630$		0			0
$631$	24.0553	+	8.75542i	0.957627	+	0.348548i	0.773103	−	0.634280i	$-0.218703\pi$
$631$	24.0553	+	8.75542i	0.957627	+	0.348548i	0.184524	+	0.982828i	$0.440926\pi$
$632$		0			0
$633$	−4.70090	+	12.9156i	−0.186844	+	0.513349i
$634$		0			0
$635$	4.81955	+	8.34770i	0.191258	+	0.331268i
$636$		0			0
$637$	−1.54089	+	4.08794i	−0.0610522	+	0.161970i
$638$		0			0
$639$			33.2773i			1.31643i
$640$		0			0
$641$	−11.8758	+	14.1530i	−0.469064	+	0.559009i	−0.947765	−	0.318969i	$-0.896663\pi$
$641$	−11.8758	+	14.1530i	−0.469064	+	0.559009i	0.478701	+	0.877978i	$0.341108\pi$
$642$		0			0
$643$	9.26059	−	11.0363i	0.365202	−	0.435231i	−0.551883	−	0.833921i	$-0.686091\pi$
$643$	9.26059	−	11.0363i	0.365202	−	0.435231i	0.917086	+	0.398690i	$0.130535\pi$
$644$		0			0
$645$		−	23.6362i		−	0.930673i
$646$		0			0
$647$	−37.2079	+	21.4820i	−1.46279	+	0.844544i	−0.999140	−	0.0414724i	$-0.986795\pi$
$647$	−37.2079	+	21.4820i	−1.46279	+	0.844544i	−0.463654	+	0.886017i	$0.653462\pi$
$648$		0			0
$649$	−12.6566	+	4.60663i	−0.496816	+	0.180826i
$650$		0			0
$651$	−3.05566	−	1.44614i	−0.119761	−	0.0566787i
$652$		0			0
$653$	36.2183			1.41733			0.708666	−	0.705544i	$-0.249297\pi$
$653$	36.2183			1.41733			0.708666	+	0.705544i	$0.249297\pi$
$654$		0			0
$655$	−4.80447	+	4.03143i	−0.187726	+	0.157521i
$656$		0			0
$657$	−26.8507	−	15.5022i	−1.04754	−	0.604800i
$658$		0			0
$659$	20.4115	+	24.3255i	0.795118	+	0.947585i	0.999510	−	0.0313041i	$-0.00996604\pi$
$659$	20.4115	+	24.3255i	0.795118	+	0.947585i	−0.204392	+	0.978889i	$0.565522\pi$
$660$		0			0
$661$	7.91508	+	44.8887i	0.307861	+	1.74597i	0.609723	+	0.792615i	$0.291281\pi$
$661$	7.91508	+	44.8887i	0.307861	+	1.74597i	−0.301862	+	0.953352i	$0.597608\pi$
$662$		0			0
$663$	4.24935	−	5.06418i	0.165031	−	0.196676i
$664$		0			0
$665$	−10.8985	−	5.20922i	−0.422625	−	0.202005i
$666$		0			0
$667$	−28.7866	+	34.3065i	−1.11462	+	1.32835i
$668$		0			0
$669$	−1.96624	−	11.1511i	−0.0760192	−	0.431126i
$670$		0			0
$671$	15.3827	+	18.3323i	0.593841	+	0.707712i
$672$		0			0
$673$	−41.6004	−	24.0180i	−1.60358	−	0.925826i	−0.990764	−	0.135599i	$-0.956704\pi$
$673$	−41.6004	−	24.0180i	−1.60358	−	0.925826i	−0.612814	−	0.790227i	$-0.709963\pi$
$674$		0			0
$675$	2.93343	−	2.46144i	0.112908	−	0.0947409i
$676$		0			0
$677$	−20.1456			−0.774259			−0.387130	−	0.922025i	$-0.626533\pi$
$677$	−20.1456			−0.774259			−0.387130	+	0.922025i	$0.626533\pi$
$678$		0			0
$679$	1.34978	+	16.5115i	0.0517998	+	0.633654i
$680$		0			0
$681$	−36.3830	+	13.2423i	−1.39420	+	0.507447i
$682$		0			0
$683$	15.4155	−	8.90011i	0.589856	−	0.340553i	−0.175185	−	0.984536i	$-0.556052\pi$
$683$	15.4155	−	8.90011i	0.589856	−	0.340553i	0.765040	+	0.643982i	$0.222719\pi$
$684$		0			0
$685$			3.14798i			0.120278i
$686$		0			0
$687$	35.6431	−	42.4778i	1.35987	−	1.62063i
$688$		0			0
$689$	0.112654	−	0.134255i	0.00429176	−	0.00511472i
$690$		0			0
$691$			27.1326i			1.03217i	0.856536	+	0.516087i	$0.172612\pi$
$691$			27.1326i			1.03217i	−0.856536	+	0.516087i	$0.827388\pi$
$692$		0			0
$693$	−18.4386	−	1.71913i	−0.700424	−	0.0653042i
$694$		0			0
$695$	1.85197	+	3.20771i	0.0702494	+	0.121675i
$696$		0			0
$697$	0.667029	−	1.83265i	0.0252655	−	0.0694165i
$698$		0			0
$699$	−61.8785	−	22.5219i	−2.34046	−	0.851857i
$700$		0			0
$701$	−3.54939	+	20.1296i	−0.134059	+	0.760284i	0.841452	+	0.540332i	$0.181701\pi$
$701$	−3.54939	+	20.1296i	−0.134059	+	0.760284i	−0.975511	+	0.219952i	$0.929410\pi$
$702$		0			0
$703$	−15.1853	−	26.5367i	−0.572725	−	1.00085i
$704$		0			0
$705$	3.93107	+	3.29856i	0.148053	+	0.124231i
$706$		0			0
$707$	−0.660862	+	7.08811i	−0.0248543	+	0.266576i
$708$		0			0
$709$	3.71658	+	21.0778i	0.139579	+	0.791593i	0.971561	+	0.236790i	$0.0760952\pi$
$709$	3.71658	+	21.0778i	0.139579	+	0.791593i	−0.831982	+	0.554803i	$0.812794\pi$
$710$		0			0
$711$			41.9167i			1.57200i
$712$		0			0
$713$	−0.488287	−	2.76921i	−0.0182865	−	0.103708i
$714$		0			0
$715$	−1.16949	+	0.675207i	−0.0437365	+	0.0252513i
$716$		0			0
$717$	13.8668	+	11.6356i	0.517866	+	0.434541i
$718$		0			0
$719$	−11.1016	−	30.5014i	−0.414020	−	1.13751i	−0.955034	−	0.296497i	$-0.904182\pi$
$719$	−11.1016	−	30.5014i	−0.414020	−	1.13751i	0.541014	−	0.841014i	$-0.318041\pi$
$720$		0			0
$721$	−1.05334	−	1.06542i	−0.0392286	−	0.0396784i
$722$		0			0
$723$	−32.1884	+	55.7519i	−1.19710	+	2.07344i
$724$		0			0
$725$	−30.9465	−	5.45671i	−1.14933	−	0.202657i
$726$		0			0
$727$	−9.80057	−	26.9268i	−0.363483	−	0.998662i	−0.977789	−	0.209593i	$-0.932786\pi$
$727$	−9.80057	−	26.9268i	−0.363483	−	0.998662i	0.614306	−	0.789068i	$-0.289436\pi$
$728$		0			0
$729$	16.7384	+	28.9918i	0.619942	+	1.07377i
$730$		0			0
$731$	24.0517	+	28.6637i	0.889584	+	1.06016i
$732$		0			0
$733$	−12.1710	+	7.02692i	−0.449546	+	0.259545i	−0.707638	−	0.706575i	$-0.750239\pi$
$733$	−12.1710	+	7.02692i	−0.449546	+	0.259545i	0.258093	+	0.966120i	$0.416906\pi$
$734$		0			0
$735$	3.00969	+	18.2854i	0.111014	+	0.674465i
$736$		0			0
$737$	7.78419	+	9.27684i	0.286734	+	0.341717i
$738$		0			0
$739$	47.0311	−	17.1179i	1.73007	−	0.629693i	0.731432	−	0.681914i	$-0.238852\pi$
$739$	47.0311	−	17.1179i	1.73007	−	0.629693i	0.998636	+	0.0522208i	$0.0166300\pi$
$740$		0			0
$741$	0.0264175	−	6.87571i	0.000970471	−	0.252586i
$742$		0			0
$743$	−7.91373	−	1.39540i	−0.290326	−	0.0511924i	0.0265881	−	0.999646i	$-0.491536\pi$
$743$	−7.91373	−	1.39540i	−0.290326	−	0.0511924i	−0.316915	+	0.948454i	$0.602647\pi$
$744$		0			0
$745$	−18.8943	+	3.33157i	−0.692233	+	0.122059i
$746$		0			0
$747$	−16.8151	+	2.96496i	−0.615233	+	0.108482i
$748$		0			0
$749$	−5.49806	−	20.9971i	−0.200895	−	0.767216i
$750$		0			0
$751$	4.27218	−	11.7377i	0.155894	−	0.428316i	−0.837017	−	0.547177i	$-0.815702\pi$
$751$	4.27218	−	11.7377i	0.155894	−	0.428316i	0.992911	+	0.118862i	$0.0379245\pi$
$752$		0			0
$753$	57.7071	+	33.3172i	2.10296	+	1.21415i
$754$		0			0
$755$	−9.80443	+	3.56852i	−0.356820	+	0.129872i
$756$		0			0
$757$	−6.57900	−	5.52043i	−0.239118	−	0.200644i	0.515352	−	0.856979i	$-0.327661\pi$
$757$	−6.57900	−	5.52043i	−0.239118	−	0.200644i	−0.754469	+	0.656335i	$0.772106\pi$
$758$		0			0
$759$	−14.5211	−	25.1513i	−0.527083	−	0.912934i
$760$		0			0
$761$	−45.7925	−	26.4383i	−1.65998	−	0.958388i	−0.972723	−	0.231971i	$-0.925482\pi$
$761$	−45.7925	−	26.4383i	−1.65998	−	0.958388i	−0.687254	−	0.726417i	$-0.741184\pi$
$762$		0			0
$763$	7.76123	−	16.3993i	0.280975	−	0.593695i
$764$		0			0
$765$	2.58268	−	14.6471i	0.0933769	−	0.529567i
$766$		0			0
$767$	−2.03454	+	3.52393i	−0.0734630	+	0.127242i
$768$		0			0
$769$	14.3776	−	2.53516i	0.518469	−	0.0914201i	0.0917105	−	0.995786i	$-0.470767\pi$
$769$	14.3776	−	2.53516i	0.518469	−	0.0914201i	0.426758	+	0.904366i	$0.359655\pi$
$770$		0			0
$771$	10.0294	−	17.3714i	0.361200	−	0.625617i
$772$		0			0
$773$	−11.6988	−	4.25800i	−0.420775	−	0.153150i	0.122950	−	0.992413i	$-0.460764\pi$
$773$	−11.6988	−	4.25800i	−0.420775	−	0.153150i	−0.543725	+	0.839263i	$0.682987\pi$
$774$		0			0
$775$	1.51146	−	1.26827i	0.0542933	−	0.0455575i
$776$		0			0
$777$	−20.0648	+	42.3966i	−0.719822	+	1.52097i
$778$		0			0
$779$	−0.686434	−	1.90875i	−0.0245940	−	0.0683880i
$780$		0			0
$781$	6.93942	+	19.0659i	0.248312	+	0.682231i
$782$		0			0
$783$	−2.70182	+	7.42320i	−0.0965553	+	0.265284i
$784$		0			0
$785$	15.5797	−	13.0729i	0.556062	−	0.466591i
$786$		0			0
$787$	40.7012			1.45084			0.725421	−	0.688305i	$-0.241645\pi$
$787$	40.7012			1.45084			0.725421	+	0.688305i	$0.241645\pi$
$788$		0			0
$789$	61.1711	+	22.2644i	2.17775	+	0.792635i
$790$		0			0
$791$	−10.1297	−	38.6854i	−0.360172	−	1.37550i
$792$		0			0
$793$	7.12000	+	1.25545i	0.252839	+	0.0445823i
$794$		0			0
$795$	0.129093	−	0.732122i	0.00457845	−	0.0259657i
$796$		0			0
$797$	−42.3608			−1.50050			−0.750249	−	0.661155i	$-0.770066\pi$
$797$	−42.3608			−1.50050			−0.750249	+	0.661155i	$0.770066\pi$
$798$		0			0
$799$	−8.12378			−0.287399
$800$		0			0
$801$	−6.93816	+	39.3483i	−0.245148	+	1.39030i
$802$		0			0
$803$	−18.6165	−	3.28259i	−0.656963	−	0.115840i
$804$		0			0
$805$	−10.9614	+	10.8372i	−0.386339	+	0.381960i
$806$		0			0
$807$	−23.7446	−	8.64231i	−0.835848	−	0.304224i
$808$		0			0
$809$	−29.2965			−1.03001			−0.515005	−	0.857187i	$-0.672210\pi$
$809$	−29.2965			−1.03001			−0.515005	+	0.857187i	$0.672210\pi$
$810$		0			0
$811$	−14.8413	+	12.4533i	−0.521147	+	0.437294i	−0.865031	−	0.501718i	$-0.832702\pi$
$811$	−14.8413	+	12.4533i	−0.521147	+	0.437294i	0.343884	+	0.939012i	$0.388257\pi$
$812$		0			0
$813$	15.8391	−	43.5177i	0.555503	−	1.52623i
$814$		0			0
$815$	1.36821	+	3.75913i	0.0479263	+	0.131676i
$816$		0			0
$817$	38.2999	+	6.90514i	1.33994	+	0.241580i
$818$		0			0
$819$	−4.60108	+	3.18278i	−0.160775	+	0.111215i
$820$		0			0
$821$	1.30810	−	1.09762i	0.0456529	−	0.0383073i	−0.619676	−	0.784858i	$-0.712736\pi$
$821$	1.30810	−	1.09762i	0.0456529	−	0.0383073i	0.665329	+	0.746551i	$0.268291\pi$
$822$		0			0
$823$	29.9815	+	10.9124i	1.04509	+	0.380382i	0.806808	−	0.590814i	$-0.201193\pi$
$823$	29.9815	+	10.9124i	1.04509	+	0.380382i	0.238283	+	0.971196i	$0.423415\pi$
$824$		0			0
$825$	10.1891	−	17.6481i	0.354741	−	0.614429i
$826$		0			0
$827$	−11.2438	+	1.98259i	−0.390985	+	0.0689413i	−0.365685	−	0.930739i	$-0.619165\pi$
$827$	−11.2438	+	1.98259i	−0.390985	+	0.0689413i	−0.0253002	+	0.999680i	$0.508054\pi$
$828$		0			0
$829$	24.0471	−	41.6507i	0.835189	−	1.44659i	−0.0586880	−	0.998276i	$-0.518692\pi$
$829$	24.0471	−	41.6507i	0.835189	−	1.44659i	0.893877	−	0.448313i	$-0.147975\pi$
$830$		0			0
$831$	−6.78228	+	38.4642i	−0.235275	+	1.33431i
$832$		0			0
$833$	−22.2567	−	19.1121i	−0.771148	−	0.662196i
$834$		0			0
$835$	−18.3708	−	10.6064i	−0.635749	−	0.367050i
$836$		0			0
$837$	−0.248003	−	0.429555i	−0.00857225	−	0.0148476i
$838$		0			0
$839$	−38.5974	−	32.3870i	−1.33253	−	1.11812i	−0.983479	−	0.181020i	$-0.942060\pi$
$839$	−38.5974	−	32.3870i	−1.33253	−	1.11812i	−0.349050	−	0.937104i	$-0.613495\pi$
$840$		0			0
$841$	33.6647	−	12.2530i	1.16085	−	0.422516i
$842$		0			0
$843$	−70.3931	−	40.6415i	−2.42447	−	1.39977i
$844$		0			0
$845$	4.51757	−	12.4119i	0.155409	−	0.426983i
$846$		0			0
$847$	17.2314	−	4.51203i	0.592078	−	0.155035i
$848$		0			0
$849$	7.32694	−	1.29194i	0.251460	−	0.0443392i
$850$		0			0
$851$	−38.4222	+	6.77487i	−1.31710	+	0.232239i
$852$		0			0
$853$	−39.7702	−	7.01257i	−1.36171	−	0.240106i	−0.555391	−	0.831590i	$-0.687431\pi$
$853$	−39.7702	−	7.01257i	−1.36171	−	0.240106i	−0.806317	+	0.591484i	$0.798542\pi$
$854$		0			0
$855$	−7.68303	−	13.4263i	−0.262754	−	0.459169i
$856$		0			0
$857$	28.7141	−	10.4511i	0.980856	−	0.357002i	0.198683	−	0.980064i	$-0.436334\pi$
$857$	28.7141	−	10.4511i	0.980856	−	0.357002i	0.782173	+	0.623062i	$0.214111\pi$
$858$		0			0
$859$	30.6161	+	36.4868i	1.04461	+	1.24491i	0.968814	+	0.247791i	$0.0797045\pi$
$859$	30.6161	+	36.4868i	1.04461	+	1.24491i	0.0757934	+	0.997124i	$0.475851\pi$
$860$		0			0
$861$	−1.79939	+	2.53887i	−0.0613231	+	0.0865245i
$862$		0			0
$863$	−1.24770	+	0.720362i	−0.0424723	+	0.0245214i	−0.521086	−	0.853504i	$-0.674473\pi$
$863$	−1.24770	+	0.720362i	−0.0424723	+	0.0245214i	0.478613	+	0.878026i	$0.341140\pi$
$864$		0			0
$865$	−5.18658	−	6.18112i	−0.176349	−	0.210165i
$866$		0			0
$867$	0.712675	+	1.23439i	0.0242037	+	0.0419221i
$868$		0			0
$869$	8.74100	+	24.0157i	0.296518	+	0.814676i
$870$		0			0
$871$	3.60298	+	0.635303i	0.122082	+	0.0215264i
$872$		0			0
$873$	−10.6077	+	18.3731i	−0.359017	+	0.621836i
$874$		0			0
$875$	−23.7944	−	6.52128i	−0.804398	−	0.220460i
$876$		0			0
$877$	−2.43147	−	6.68041i	−0.0821050	−	0.225582i	0.891846	−	0.452338i	$-0.149410\pi$
$877$	−2.43147	−	6.68041i	−0.0821050	−	0.225582i	−0.973951	+	0.226757i	$0.927188\pi$
$878$		0			0
$879$	1.15369	+	0.968058i	0.0389129	+	0.0326518i
$880$		0			0
$881$	−24.1095	+	13.9196i	−0.812269	+	0.468964i	−0.847743	−	0.530407i	$-0.822039\pi$
$881$	−24.1095	+	13.9196i	−0.812269	+	0.468964i	0.0354739	+	0.999371i	$0.488706\pi$
$882$		0			0
$883$	−4.80697	−	27.2617i	−0.161767	−	0.917428i	−0.952335	−	0.305054i	$-0.901326\pi$
$883$	−4.80697	−	27.2617i	−0.161767	−	0.917428i	0.790568	−	0.612374i	$-0.209786\pi$
$884$		0			0
$885$			17.2604i			0.580203i
$886$		0			0
$887$	−7.31570	−	41.4894i	−0.245637	−	1.39308i	−0.819009	−	0.573781i	$-0.805476\pi$
$887$	−7.31570	−	41.4894i	−0.245637	−	1.39308i	0.573372	−	0.819295i	$-0.305635\pi$
$888$		0			0
$889$	19.8648	+	14.0789i	0.666245	+	0.472192i
$890$		0			0
$891$	12.1611	+	10.2044i	0.407413	+	0.341860i
$892$		0			0
$893$	−6.49341	+	5.40624i	−0.217294	+	0.180913i
$894$		0			0
$895$	2.96602	−	16.8211i	0.0991430	−	0.562268i
$896$		0			0
$897$	−8.24480	−	3.00086i	−0.275286	−	0.100196i
$898$		0			0
$899$	−1.39212	+	3.82483i	−0.0464300	+	0.127565i
$900$		0			0
$901$	0.588441	+	1.01921i	0.0196038	+	0.0339548i
$902$		0			0
$903$	−24.9233	−	54.2534i	−0.829394	−	1.80544i
$904$		0			0
$905$		−	14.9660i		−	0.497487i
$906$		0			0
$907$	1.18769	−	1.41543i	0.0394365	−	0.0469986i	−0.745966	−	0.665984i	$-0.768012\pi$
$907$	1.18769	−	1.41543i	0.0394365	−	0.0469986i	0.785402	+	0.618986i	$0.212456\pi$
$908$		0			0
$909$	−5.85998	+	6.98365i	−0.194363	+	0.231633i
$910$		0			0
$911$		−	30.5251i		−	1.01134i	−0.862727	−	0.505670i	$-0.831245\pi$
$911$		−	30.5251i		−	1.01134i	0.862727	−	0.505670i	$-0.168755\pi$
$912$		0			0
$913$	−9.01575	+	5.20524i	−0.298378	+	0.172268i
$914$		0			0
$915$	28.8183	−	10.4890i	0.952705	−	0.346756i
$916$		0			0
$917$	−6.77699	+	14.3196i	−0.223796	+	0.472876i
$918$		0			0
$919$	17.5512			0.578962			0.289481	−	0.957184i	$-0.406517\pi$
$919$	17.5512			0.578962			0.289481	+	0.957184i	$0.406517\pi$
$920$		0			0
$921$	−29.9470	+	25.1285i	−0.986786	+	0.828012i
$922$		0			0
$923$	5.30844	+	3.06483i	0.174729	+	0.100880i
$924$		0			0
$925$	−17.5969	−	20.9712i	−0.578582	−	0.689528i
$926$		0			0
$927$	−0.333168	−	1.88949i	−0.0109427	−	0.0620591i
$928$		0			0
$929$	14.7280	−	17.5522i	0.483211	−	0.575868i	−0.468267	−	0.883587i	$-0.655121\pi$
$929$	14.7280	−	17.5522i	0.483211	−	0.575868i	0.951477	+	0.307719i	$0.0995657\pi$
$930$		0			0
$931$	−30.5087	−	0.465056i	−0.999884	−	0.0152416i
$932$		0			0
$933$	−34.5825	+	41.2138i	−1.13218	+	1.34928i
$934$		0			0
$935$	−1.57468	−	8.93046i	−0.0514976	−	0.292057i
$936$		0			0
$937$	−24.2550	−	28.9060i	−0.792378	−	0.944319i	0.207044	−	0.978332i	$-0.433616\pi$
$937$	−24.2550	−	28.9060i	−0.792378	−	0.944319i	−0.999421	+	0.0340128i	$0.989171\pi$
$938$		0			0
$939$	−27.5883	−	15.9281i	−0.900311	−	0.519795i
$940$		0			0
$941$	−25.7387	+	21.5974i	−0.839058	+	0.704054i	−0.957352	−	0.288925i	$-0.906702\pi$
$941$	−25.7387	+	21.5974i	−0.839058	+	0.704054i	0.118293	+	0.992979i	$0.462258\pi$
$942$		0			0
$943$	−2.58841			−0.0842902
$944$		0			0
$945$	−1.16311	+	2.45763i	−0.0378360	+	0.0799467i
$946$		0			0
$947$	10.9463	−	3.98414i	0.355708	−	0.129467i	−0.157984	−	0.987442i	$-0.550500\pi$
$947$	10.9463	−	3.98414i	0.355708	−	0.129467i	0.513692	+	0.857975i	$0.328277\pi$
$948$		0			0
$949$	−4.94587	+	2.85550i	−0.160550	+	0.0926933i
$950$		0			0
$951$			55.0526i			1.78520i
$952$		0			0
$953$	9.62888	−	11.4752i	0.311910	−	0.371720i	−0.587201	−	0.809441i	$-0.699770\pi$
$953$	9.62888	−	11.4752i	0.311910	−	0.371720i	0.899111	+	0.437722i	$0.144214\pi$
$954$		0			0
$955$	−10.0475	+	11.9741i	−0.325128	+	0.387473i
$956$		0			0
$957$			42.0389i			1.35892i
$958$		0			0
$959$	3.31940	+	7.22572i	0.107189	+	0.233331i
$960$		0			0
$961$	15.3722	+	26.6255i	0.495878	+	0.858886i
$962$		0			0
$963$	9.50669	−	26.1194i	0.306349	−	0.841687i
$964$		0			0
$965$	14.8760	+	5.41443i	0.478876	+	0.174297i
$966$		0			0
$967$	−5.62252	+	31.8869i	−0.180808	+	1.02541i	0.750416	+	0.660966i	$0.229853\pi$
$967$	−5.62252	+	31.8869i	−0.180808	+	1.02541i	−0.931224	+	0.364448i	$0.881258\pi$
$968$		0			0
$969$	43.3263	+	15.9583i	1.39184	+	0.512653i
$970$		0			0
$971$	−46.9467	−	39.3930i	−1.50659	−	1.26418i	−0.870076	−	0.492917i	$-0.835931\pi$
$971$	−46.9467	−	39.3930i	−1.50659	−	1.26418i	−0.636516	−	0.771264i	$-0.719625\pi$
$972$		0			0
$973$	7.63332	+	5.41001i	0.244713	+	0.173437i
$974$		0			0
$975$	−1.06906	−	6.06295i	−0.0342374	−	0.194170i
$976$		0			0
$977$			58.3202i			1.86583i	0.360099	+	0.932914i	$0.382743\pi$
$977$			58.3202i			1.86583i	−0.360099	+	0.932914i	$0.617257\pi$
$978$		0			0
$979$	4.23026	+	23.9910i	0.135200	+	0.766755i
$980$		0			0
$981$	20.1216	−	11.6172i	0.642432	−	0.370908i
$982$		0			0
$983$	−26.7810	−	22.4720i	−0.854183	−	0.716744i	0.106524	−	0.994310i	$-0.466028\pi$
$983$	−26.7810	−	22.4720i	−0.854183	−	0.716744i	−0.960707	+	0.277566i	$0.910472\pi$
$984$		0			0
$985$	−4.25821	−	11.6993i	−0.135678	−	0.372771i
$986$		0			0
$987$	12.5014	+	3.42623i	0.397923	+	0.109058i
$988$		0			0
$989$	24.8306	−	43.0079i	0.789568	−	1.36757i
$990$		0			0
$991$	−43.2004	−	7.61740i	−1.37231	−	0.241975i	−0.561591	−	0.827415i	$-0.689811\pi$
$991$	−43.2004	−	7.61740i	−1.37231	−	0.241975i	−0.810716	+	0.585440i	$0.800922\pi$
$992$		0			0
$993$	18.0237	+	49.5197i	0.571965	+	1.57146i
$994$		0			0
$995$	9.28083	+	16.0749i	0.294222	+	0.509608i
$996$		0			0
$997$	16.0380	+	19.1134i	0.507930	+	0.605327i	0.957683	−	0.287826i	$-0.0929324\pi$
$997$	16.0380	+	19.1134i	0.507930	+	0.605327i	−0.449753	+	0.893153i	$0.648488\pi$
$998$		0			0
$999$	−5.95997	+	3.44099i	−0.188565	+	0.108868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	532.2.cj.a.173.12	yes	78
7.3	odd	6		532.2.bw.a.325.12	yes	78
19.10	odd	18		532.2.bw.a.257.12	✓	78
133.10	even	18	inner	532.2.cj.a.409.12	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
532.2.bw.a.257.12	✓	78	19.10	odd	18
532.2.bw.a.325.12	yes	78	7.3	odd	6
532.2.cj.a.173.12	yes	78	1.1	even	1	trivial
532.2.cj.a.409.12	yes	78	133.10	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 532 = 2^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	532.cj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.438893 - 2.48909i) q^{3} +(-1.03151 - 0.181883i) q^{5} +(-2.55946 + 0.670193i) q^{7} +(-3.18386 - 1.15883i) q^{9} -2.06581 q^{11} +(-0.478089 + 0.401165i) q^{13} +(-0.905444 + 2.48769i) q^{15} +(-1.43338 - 3.93819i) q^{17} +(-3.76652 - 2.19394i) q^{19} +(0.544838 + 6.66487i) q^{21} +(-4.26093 + 3.57534i) q^{23} +(-3.66754 - 1.33487i) q^{25} +(-0.490573 + 0.849697i) q^{27} +(7.92909 - 1.39811i) q^{29} +(-0.252769 + 0.437809i) q^{31} +(-0.906671 + 5.14198i) q^{33} +(2.76200 - 0.225787i) q^{35} +(6.07450 + 3.50711i) q^{37} +(0.788704 + 1.36608i) q^{39} +(0.356481 + 0.299123i) q^{41} +(-8.38983 + 3.05365i) q^{43} +(3.07340 + 1.77443i) q^{45} +(0.662977 - 1.82152i) q^{47} +(6.10168 - 3.43066i) q^{49} +(-10.4316 + 1.83937i) q^{51} +(-0.276550 + 0.0487632i) q^{53} +(2.13090 + 0.375735i) q^{55} +(-7.11400 + 8.41229i) q^{57} +(6.12671 - 2.22994i) q^{59} +(-7.44630 - 8.87416i) q^{61} +(8.92560 + 0.832180i) q^{63} +(0.566118 - 0.326848i) q^{65} +(-3.76811 - 4.49065i) q^{67} +(7.02926 + 12.1750i) q^{69} +(-3.35917 - 9.22925i) q^{71} +(9.01173 + 1.58901i) q^{73} +(-4.93228 + 8.54296i) q^{75} +(5.28736 - 1.38449i) q^{77} +(-4.23127 - 11.6253i) q^{79} +(-5.88685 - 4.93965i) q^{81} +(4.36427 - 2.51971i) q^{83} +(0.762258 + 4.32298i) q^{85} -20.3498i q^{87} +(-2.04775 - 11.6134i) q^{89} +(0.954794 - 1.34718i) q^{91} +(0.978807 + 0.821317i) q^{93} +(3.48615 + 2.94813i) q^{95} +(1.08731 - 6.16646i) q^{97} +(6.57724 + 2.39392i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 6 q^{7} - 6 q^{11} + 6 q^{13} - 3 q^{15} + 27 q^{17} + 21 q^{19} - 3 q^{21} - 24 q^{23} + 12 q^{27} - 18 q^{29} + 33 q^{35} + 36 q^{37} - 18 q^{39} - 18 q^{41} - 48 q^{43} - 18 q^{45} - 18 q^{49}+ \cdots + 27 q^{99}+O(q^{100}) \) 78 * q + 6 * q^7 - 6 * q^11 + 6 * q^13 - 3 * q^15 + 27 * q^17 + 21 * q^19 - 3 * q^21 - 24 * q^23 + 12 * q^27 - 18 * q^29 + 33 * q^35 + 36 * q^37 - 18 * q^39 - 18 * q^41 - 48 * q^43 - 18 * q^45 - 18 * q^49 + 6 * q^53 - 18 * q^57 + 45 * q^59 + 39 * q^61 - 27 * q^63 - 18 * q^65 + 21 * q^67 + 6 * q^71 - 3 * q^73 - 21 * q^75 - 21 * q^77 + 36 * q^79 + 36 * q^81 - 18 * q^83 + 60 * q^85 - 21 * q^91 - 102 * q^93 + 60 * q^95 - 27 * q^97 + 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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