LMFDB - Embedded newform 900.2.o.b.299.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(299,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("900.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.2
Character	$\chi$	$=$	900.299
Dual form			900.2.o.b.599.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38296 + 0.295692i) q^{2} +(-1.64850 - 0.531460i) q^{3} +(1.82513 - 0.817857i) q^{4} +(2.43695 + 0.247538i) q^{6} +(-2.08506 + 3.61144i) q^{7} +(-2.28224 + 1.67074i) q^{8} +(2.43510 + 1.75222i) q^{9} +(-3.22095 + 5.57886i) q^{11} +(-3.44339 + 0.378252i) q^{12} +(1.53691 - 0.887336i) q^{13} +(1.81568 - 5.61099i) q^{14} +(2.66222 - 2.98539i) q^{16} +0.950682 q^{17} +(-3.88575 - 1.70321i) q^{18} -2.19286i q^{19} +(5.35656 - 4.84532i) q^{21} +(2.80482 - 8.66772i) q^{22} +(1.74948 - 1.01006i) q^{23} +(4.65021 - 1.54129i) q^{24} +(-1.86310 + 1.68160i) q^{26} +(-3.08303 - 4.18270i) q^{27} +(-0.851880 + 8.29663i) q^{28} +(-5.65260 - 3.26353i) q^{29} +(2.46164 - 1.42123i) q^{31} +(-2.79898 + 4.91587i) q^{32} +(8.27468 - 7.48493i) q^{33} +(-1.31475 + 0.281109i) q^{34} +(5.87745 + 1.20647i) q^{36} +5.83599i q^{37} +(0.648412 + 3.03263i) q^{38} +(-3.00518 + 0.645966i) q^{39} +(-6.16222 + 3.55776i) q^{41} +(-5.97516 + 8.28476i) q^{42} +(2.65491 - 4.59844i) q^{43} +(-1.31596 + 12.8164i) q^{44} +(-2.12079 + 1.91418i) q^{46} +(-0.349867 - 0.201996i) q^{47} +(-5.97529 + 3.50656i) q^{48} +(-5.19498 - 8.99797i) q^{49} +(-1.56720 - 0.505249i) q^{51} +(2.07935 - 2.87648i) q^{52} -4.87844 q^{53} +(5.50048 + 4.87286i) q^{54} +(-1.27513 - 11.7258i) q^{56} +(-1.16542 + 3.61494i) q^{57} +(8.78229 + 2.84189i) q^{58} +(1.34391 + 2.32773i) q^{59} +(-2.04652 + 3.54468i) q^{61} +(-2.98409 + 2.69338i) q^{62} +(-11.4054 + 5.14072i) q^{63} +(2.41728 - 7.62606i) q^{64} +(-9.23028 + 12.7981i) q^{66} +(-5.44797 - 9.43616i) q^{67} +(1.73512 - 0.777522i) q^{68} +(-3.42083 + 0.735311i) q^{69} -2.23126 q^{71} +(-8.48500 + 0.0694119i) q^{72} -1.74662i q^{73} +(-1.72565 - 8.07091i) q^{74} +(-1.79345 - 4.00227i) q^{76} +(-13.4318 - 23.2645i) q^{77} +(3.96502 - 1.78195i) q^{78} +(-0.214428 - 0.123800i) q^{79} +(2.85943 + 8.53368i) q^{81} +(7.47008 - 6.74234i) q^{82} +(-10.1090 - 5.83641i) q^{83} +(5.81365 - 13.2243i) q^{84} +(-2.31191 + 7.14448i) q^{86} +(7.58387 + 8.38406i) q^{87} +(-1.96979 - 18.1137i) q^{88} -6.13881i q^{89} +7.40061i q^{91} +(2.36695 - 3.27433i) q^{92} +(-4.81334 + 1.03463i) q^{93} +(0.543580 + 0.175899i) q^{94} +(7.22670 - 6.61626i) q^{96} +(15.7357 + 9.08503i) q^{97} +(9.84505 + 10.9077i) q^{98} +(-17.6187 + 7.94125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} - 12 q^{8} - 4 q^{9} - 28 q^{12} + 30 q^{14} + 18 q^{18} - 4 q^{21} + 42 q^{22} + 28 q^{24} + 12 q^{29} + 48 q^{33} + 6 q^{34} + 42 q^{36} + 6 q^{38} - 60 q^{41} - 16 q^{42} - 12 q^{46} + 74 q^{48}+ \cdots - 84 q^{98}+O(q^{100}) $ 48 * q + 6 * q^6 - 12 * q^8 - 4 * q^9 - 28 * q^12 + 30 * q^14 + 18 * q^18 - 4 * q^21 + 42 * q^22 + 28 * q^24 + 12 * q^29 + 48 * q^33 + 6 * q^34 + 42 * q^36 + 6 * q^38 - 60 * q^41 - 16 * q^42 - 12 * q^46 + 74 * q^48 - 24 * q^49 + 90 * q^52 + 32 * q^54 - 42 * q^56 + 16 * q^57 - 84 * q^58 - 84 * q^62 + 48 * q^64 + 16 * q^66 - 6 * q^68 - 36 * q^69 + 80 * q^72 - 84 * q^74 + 6 * q^76 + 46 * q^78 - 50 * q^84 - 54 * q^86 - 114 * q^88 + 42 * q^92 + 24 * q^93 - 18 * q^94 - 18 * q^96 + 48 * q^97 - 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.38296	+	0.295692i	−0.977897	+	0.209086i
$2$	−1.38296	+	0.295692i	−0.977897	+	0.209086i
$3$	−1.64850	−	0.531460i	−0.951762	−	0.306838i
$3$	−1.64850	−	0.531460i	−0.951762	−	0.306838i
$4$	1.82513	−	0.817857i	0.912566	−	0.408928i
$5$		0			0
$5$		0			0
$6$	2.43695	+	0.247538i	0.994881	+	0.101057i
$7$	−2.08506	+	3.61144i	−0.788080	+	1.36499i	0.139062	+	0.990284i	$0.455591\pi$
$7$	−2.08506	+	3.61144i	−0.788080	+	1.36499i	−0.927142	+	0.374711i	$0.877742\pi$
$8$	−2.28224	+	1.67074i	−0.806895	+	0.590694i
$9$	2.43510	+	1.75222i	0.811700	+	0.584074i
$10$		0			0
$11$	−3.22095	+	5.57886i	−0.971154	+	1.68209i	−0.279071	+	0.960271i	$0.590026\pi$
$11$	−3.22095	+	5.57886i	−0.971154	+	1.68209i	−0.692083	+	0.721818i	$0.743307\pi$
$12$	−3.44339	+	0.378252i	−0.994021	+	0.109192i
$13$	1.53691	−	0.887336i	0.426262	−	0.246103i	−0.271491	−	0.962441i	$-0.587517\pi$
$13$	1.53691	−	0.887336i	0.426262	−	0.246103i	0.697753	+	0.716338i	$0.254183\pi$
$14$	1.81568	−	5.61099i	0.485261	−	1.49960i
$15$		0			0
$16$	2.66222	−	2.98539i	0.665555	−	0.746349i
$17$	0.950682			0.230574			0.115287	−	0.993332i	$-0.463221\pi$
$17$	0.950682			0.230574			0.115287	+	0.993332i	$0.463221\pi$
$18$	−3.88575	−	1.70321i	−0.915881	−	0.401450i
$19$		−	2.19286i		−	0.503078i	−0.967847	−	0.251539i	$-0.919063\pi$
$19$		−	2.19286i		−	0.503078i	0.967847	−	0.251539i	$-0.0809366\pi$
$20$		0			0
$21$	5.35656	−	4.84532i	1.16890	−	1.05734i
$22$	2.80482	−	8.66772i	0.597989	−	1.84796i
$23$	1.74948	−	1.01006i	0.364793	−	0.210613i	−0.306388	−	0.951907i	$-0.599121\pi$
$23$	1.74948	−	1.01006i	0.364793	−	0.210613i	0.671181	+	0.741293i	$0.265787\pi$
$24$	4.65021	−	1.54129i	0.949220	−	0.314614i
$25$		0			0
$26$	−1.86310	+	1.68160i	−0.365384	+	0.329788i
$27$	−3.08303	−	4.18270i	−0.593329	−	0.804960i
$28$	−0.851880	+	8.29663i	−0.160990	+	1.56792i
$29$	−5.65260	−	3.26353i	−1.04966	−	0.606022i	−0.127107	−	0.991889i	$-0.540569\pi$
$29$	−5.65260	−	3.26353i	−1.04966	−	0.606022i	−0.922555	+	0.385867i	$0.873902\pi$
$30$		0			0
$31$	2.46164	−	1.42123i	0.442124	−	0.255260i	−0.262374	−	0.964966i	$-0.584506\pi$
$31$	2.46164	−	1.42123i	0.442124	−	0.255260i	0.704498	+	0.709706i	$0.251172\pi$
$32$	−2.79898	+	4.91587i	−0.494794	+	0.869010i
$33$	8.27468	−	7.48493i	1.44044	−	1.30296i
$34$	−1.31475	+	0.281109i	−0.225478	+	0.0482097i
$35$		0			0
$36$	5.87745	+	1.20647i	0.979575	+	0.201079i
$37$			5.83599i			0.959431i	0.877424	+	0.479715i	$0.159260\pi$
$37$			5.83599i			0.959431i	−0.877424	+	0.479715i	$0.840740\pi$
$38$	0.648412	+	3.03263i	0.105186	+	0.491958i
$39$	−3.00518	+	0.645966i	−0.481214	+	0.103437i
$40$		0			0
$41$	−6.16222	+	3.55776i	−0.962378	+	0.555629i	−0.896904	−	0.442225i	$-0.854189\pi$
$41$	−6.16222	+	3.55776i	−0.962378	+	0.555629i	−0.0654736	+	0.997854i	$0.520856\pi$
$42$	−5.97516	+	8.28476i	−0.921988	+	1.27837i
$43$	2.65491	−	4.59844i	0.404870	−	0.701256i	−0.589436	−	0.807815i	$-0.700650\pi$
$43$	2.65491	−	4.59844i	0.404870	−	0.701256i	0.994306	+	0.106559i	$0.0339833\pi$
$44$	−1.31596	+	12.8164i	−0.198389	+	1.93215i
$45$		0			0
$46$	−2.12079	+	1.91418i	−0.312694	+	0.282231i
$47$	−0.349867	−	0.201996i	−0.0510334	−	0.0294641i	0.474266	−	0.880381i	$-0.342713\pi$
$47$	−0.349867	−	0.201996i	−0.0510334	−	0.0294641i	−0.525300	+	0.850917i	$0.676047\pi$
$48$	−5.97529	+	3.50656i	−0.862458	+	0.506128i
$49$	−5.19498	−	8.99797i	−0.742140	−	1.28542i
$50$		0			0
$51$	−1.56720	−	0.505249i	−0.219452	−	0.0707490i
$52$	2.07935	−	2.87648i	0.288354	−	0.398896i
$53$	−4.87844			−0.670106			−0.335053	−	0.942199i	$-0.608754\pi$
$53$	−4.87844			−0.670106			−0.335053	+	0.942199i	$0.608754\pi$
$54$	5.50048	+	4.87286i	0.748520	+	0.663112i
$55$		0			0
$56$	−1.27513	−	11.7258i	−0.170397	−	1.56692i
$57$	−1.16542	+	3.61494i	−0.154364	+	0.478810i
$58$	8.78229	+	2.84189i	1.15317	+	0.373159i
$59$	1.34391	+	2.32773i	0.174963	+	0.303045i	0.940148	−	0.340765i	$-0.110686\pi$
$59$	1.34391	+	2.32773i	0.174963	+	0.303045i	−0.765186	+	0.643810i	$0.777353\pi$
$60$		0			0
$61$	−2.04652	+	3.54468i	−0.262030	+	0.453849i	−0.966781	−	0.255605i	$-0.917725\pi$
$61$	−2.04652	+	3.54468i	−0.262030	+	0.453849i	0.704751	+	0.709454i	$0.251059\pi$
$62$	−2.98409	+	2.69338i	−0.378980	+	0.342060i
$63$	−11.4054	+	5.14072i	−1.43694	+	0.647669i
$64$	2.41728	−	7.62606i	0.302160	−	0.953257i
$65$		0			0
$66$	−9.23028	+	12.7981i	−1.13617	+	1.57534i
$67$	−5.44797	−	9.43616i	−0.665575	−	1.15281i	−0.979129	−	0.203240i	$-0.934853\pi$
$67$	−5.44797	−	9.43616i	−0.665575	−	1.15281i	0.313553	−	0.949571i	$-0.398480\pi$
$68$	1.73512	−	0.777522i	0.210414	−	0.0942883i
$69$	−3.42083	+	0.735311i	−0.411820	+	0.0885211i
$70$		0			0
$71$	−2.23126			−0.264802			−0.132401	−	0.991196i	$-0.542269\pi$
$71$	−2.23126			−0.264802			−0.132401	+	0.991196i	$0.542269\pi$
$72$	−8.48500	+	0.0694119i	−0.999967	+	0.00818027i
$73$		−	1.74662i		−	0.204426i	−0.994763	−	0.102213i	$-0.967408\pi$
$73$		−	1.74662i		−	0.204426i	0.994763	−	0.102213i	$-0.0325923\pi$
$74$	−1.72565	−	8.07091i	−0.200603	−	0.938225i
$75$		0			0
$76$	−1.79345	−	4.00227i	−0.205723	−	0.459092i
$77$	−13.4318	−	23.2645i	−1.53069	−	2.65124i
$78$	3.96502	−	1.78195i	0.448951	−	0.201766i
$79$	−0.214428	−	0.123800i	−0.0241250	−	0.0139286i	0.487889	−	0.872906i	$-0.337767\pi$
$79$	−0.214428	−	0.123800i	−0.0241250	−	0.0139286i	−0.512014	+	0.858977i	$0.671100\pi$
$80$		0			0
$81$	2.85943	+	8.53368i	0.317715	+	0.948186i
$82$	7.47008	−	6.74234i	0.824932	−	0.744567i
$83$	−10.1090	−	5.83641i	−1.10960	−	0.640629i	−0.170876	−	0.985293i	$-0.554660\pi$
$83$	−10.1090	−	5.83641i	−1.10960	−	0.640629i	−0.938726	+	0.344664i	$0.887993\pi$
$84$	5.81365	−	13.2243i	0.634321	−	1.44288i
$85$		0			0
$86$	−2.31191	+	7.14448i	−0.249299	+	0.770409i
$87$	7.58387	+	8.38406i	0.813076	+	0.898865i
$88$	−1.96979	−	18.1137i	−0.209981	−	1.93092i
$89$		−	6.13881i		−	0.650713i	−0.945591	−	0.325356i	$-0.894516\pi$
$89$		−	6.13881i		−	0.650713i	0.945591	−	0.325356i	$-0.105484\pi$
$90$		0			0
$91$			7.40061i			0.775794i
$92$	2.36695	−	3.27433i	0.246772	−	0.341373i
$93$	−4.81334	+	1.03463i	−0.499120	+	0.107286i
$94$	0.543580	+	0.175899i	0.0560660	+	0.0181426i
$95$		0			0
$96$	7.22670	−	6.61626i	0.737572	−	0.675269i
$97$	15.7357	+	9.08503i	1.59772	+	0.922446i	0.991925	+	0.126827i	$0.0404792\pi$
$97$	15.7357	+	9.08503i	1.59772	+	0.922446i	0.605798	+	0.795619i	$0.292854\pi$
$98$	9.84505	+	10.9077i	0.994500	+	1.10184i
$99$	−17.6187	+	7.94125i	−1.77075	+	0.798126i
$100$		0			0
$101$	−8.86799	−	5.11994i	−0.882398	−	0.509453i	−0.0109497	−	0.999940i	$-0.503485\pi$
$101$	−8.86799	−	5.11994i	−0.882398	−	0.509453i	−0.871448	+	0.490487i	$0.836819\pi$
$102$	2.31676	+	0.235330i	0.229394	+	0.0233011i
$103$	−4.82993	−	8.36568i	−0.475907	−	0.824295i	0.523712	−	0.851895i	$-0.324547\pi$
$103$	−4.82993	−	8.36568i	−0.475907	−	0.824295i	−0.999619	+	0.0276004i	$0.991213\pi$
$104$	−2.02510	+	4.59289i	−0.198578	+	0.450370i
$105$		0			0
$106$	6.74667	−	1.44252i	0.655295	−	0.140109i
$107$		−	3.23356i		−	0.312600i	−0.987710	−	0.156300i	$-0.950043\pi$
$107$		−	3.23356i		−	0.312600i	0.987710	−	0.156300i	$-0.0499567\pi$
$108$	−9.04778	−	5.11250i	−0.870623	−	0.491951i
$109$	−2.88351			−0.276190			−0.138095	−	0.990419i	$-0.544098\pi$
$109$	−2.88351			−0.276190			−0.138095	+	0.990419i	$0.544098\pi$
$110$		0			0
$111$	3.10159	−	9.62062i	0.294390	−	0.913149i
$112$	5.23066	+	15.8392i	0.494251	+	1.49666i
$113$	1.54411	+	2.67448i	0.145258	+	0.251594i	0.929469	−	0.368900i	$-0.120265\pi$
$113$	1.54411	+	2.67448i	0.145258	+	0.251594i	−0.784211	+	0.620494i	$0.786932\pi$
$114$	0.542817	−	5.34390i	0.0508395	−	0.500502i
$115$		0			0
$116$	−12.9858	−	1.33336i	−1.20571	−	0.123799i
$117$	5.29734	+	0.532257i	0.489739	+	0.0492072i
$118$	−2.54686	−	2.82176i	−0.234458	−	0.259764i
$119$	−1.98223	+	3.43333i	−0.181711	+	0.314732i
$120$		0			0
$121$	−15.2491	−	26.4122i	−1.38628	−	2.40111i
$122$	1.78211	−	5.50727i	0.161345	−	0.498605i
$123$	12.0492	−	2.58999i	1.08644	−	0.233532i
$124$	3.33046	−	4.60720i	0.299084	−	0.413739i
$125$		0			0
$126$	14.2531	−	10.4819i	1.26976	−	0.933798i
$127$	−2.16321			−0.191954			−0.0959771	−	0.995384i	$-0.530598\pi$
$127$	−2.16321			−0.191954			−0.0959771	+	0.995384i	$0.530598\pi$
$128$	−1.08803	+	11.2613i	−0.0961692	+	0.995365i
$129$	−6.82051	+	6.16955i	−0.600512	+	0.543199i
$130$		0			0
$131$	−0.957206	−	1.65793i	−0.0836315	−	0.144854i	0.821176	−	0.570675i	$-0.193319\pi$
$131$	−0.957206	−	1.65793i	−0.0836315	−	0.144854i	−0.904807	+	0.425821i	$0.859985\pi$
$132$	8.98078	−	20.4285i	0.781677	−	1.77807i
$133$	7.91939	+	4.57226i	0.686698	+	0.396465i
$134$	10.3245	+	11.4389i	0.891901	+	0.988168i
$135$		0			0
$136$	−2.16969	+	1.58834i	−0.186049	+	0.136199i
$137$	−5.83040	+	10.0986i	−0.498125	+	0.862778i	−0.999998	−	0.00216386i	$-0.999311\pi$
$137$	−5.83040	+	10.0986i	−0.498125	+	0.862778i	0.501873	+	0.864941i	$0.332645\pi$
$138$	4.51343	−	2.02841i	0.384209	−	0.172670i
$139$	−6.63468	+	3.83054i	−0.562747	+	0.324902i	−0.754247	−	0.656591i	$-0.771998\pi$
$139$	−6.63468	+	3.83054i	−0.562747	+	0.324902i	0.191501	+	0.981493i	$0.438665\pi$
$140$		0			0
$141$	0.469403	+	0.518931i	0.0395309	+	0.0437019i
$142$	3.08574	−	0.659766i	0.258949	−	0.0553663i
$143$			11.4323i			0.956014i
$144$	11.7139	−	2.60494i	0.976154	−	0.217078i
$145$		0			0
$146$	0.516460	+	2.41549i	0.0427425	+	0.199908i
$147$	3.78186	+	17.5941i	0.311923	+	1.45113i
$148$	4.77300	+	10.6515i	0.392338	+	0.875544i
$149$	3.02622	−	1.74719i	0.247918	−	0.143135i	−0.370893	−	0.928676i	$-0.620948\pi$
$149$	3.02622	−	1.74719i	0.247918	−	0.143135i	0.618810	+	0.785540i	$0.287615\pi$
$150$		0			0
$151$	−6.15927	−	3.55606i	−0.501234	−	0.289388i	0.227989	−	0.973664i	$-0.426785\pi$
$151$	−6.15927	−	3.55606i	−0.501234	−	0.289388i	−0.729223	+	0.684276i	$0.760118\pi$
$152$	3.66370	+	5.00465i	0.297165	+	0.405931i
$153$	2.31501	+	1.66581i	0.187157	+	0.134672i
$154$	25.4547	+	28.2022i	2.05120	+	2.27259i
$155$		0			0
$156$	−4.95654	+	3.63678i	−0.396841	+	0.291176i
$157$	2.73556	−	1.57938i	0.218321	−	0.126048i	−0.386851	−	0.922142i	$-0.626437\pi$
$157$	2.73556	−	1.57938i	0.218321	−	0.126048i	0.605173	+	0.796094i	$0.293104\pi$
$158$	0.333151	+	0.107805i	0.0265040	+	0.00857653i
$159$	8.04211	+	2.59270i	0.637781	+	0.205614i
$160$		0			0
$161$			8.42420i			0.663920i
$162$	−6.47781	−	10.9562i	−0.508945	−	0.860799i
$163$	−14.1062			−1.10488			−0.552442	−	0.833551i	$-0.686304\pi$
$163$	−14.1062			−1.10488			−0.552442	+	0.833551i	$0.686304\pi$
$164$	−8.33714	+	11.5332i	−0.651021	+	0.900592i
$165$		0			0
$166$	15.7060	+	5.08236i	1.21902	+	0.394468i
$167$	15.8767	−	9.16640i	1.22857	−	0.709317i	0.261842	−	0.965111i	$-0.415670\pi$
$167$	15.8767	−	9.16640i	1.22857	−	0.709317i	0.966731	+	0.255794i	$0.0823368\pi$
$168$	−4.12972	+	20.0076i	−0.318615	+	1.54362i
$169$	−4.92527	+	8.53082i	−0.378867	+	0.656217i
$170$		0			0
$171$	3.84239	−	5.33985i	0.293835	−	0.408348i
$172$	1.08470	−	10.5641i	0.0827076	−	0.805506i
$173$	3.94088	−	6.82580i	0.299620	−	0.518956i	−0.676429	−	0.736508i	$-0.736474\pi$
$173$	3.94088	−	6.82580i	0.299620	−	0.518956i	0.976049	+	0.217551i	$0.0698069\pi$
$174$	−12.9673	−	9.35229i	−0.983045	−	0.708995i
$175$		0			0
$176$	8.08020	+	24.4680i	0.609068	+	1.84434i
$177$	−0.978349	−	4.55150i	−0.0735372	−	0.342111i
$178$	1.81520	+	8.48970i	0.136055	+	0.636330i
$179$	9.84108			0.735557			0.367778	−	0.929914i	$-0.380119\pi$
$179$	9.84108			0.735557			0.367778	+	0.929914i	$0.380119\pi$
$180$		0			0
$181$	18.3215			1.36183			0.680913	−	0.732364i	$-0.261583\pi$
$181$	18.3215			1.36183			0.680913	+	0.732364i	$0.261583\pi$
$182$	−2.18830	−	10.2347i	−0.162207	−	0.758647i
$183$	5.25754	−	4.75575i	0.388648	−	0.351555i
$184$	−2.30520	+	5.22814i	−0.169941	+	0.385424i
$185$		0			0
$186$	6.35070	−	2.85411i	0.465656	−	0.209274i
$187$	−3.06210	+	5.30372i	−0.223923	+	0.387846i
$188$	−0.803758	−	0.0825282i	−0.0586201	−	0.00601898i
$189$	21.5338	−	2.41297i	1.56636	−	0.175518i
$190$		0			0
$191$	9.54024	−	16.5242i	0.690307	−	1.19565i	−0.281430	−	0.959582i	$-0.590809\pi$
$191$	9.54024	−	16.5242i	0.690307	−	1.19565i	0.971737	−	0.236066i	$-0.0758580\pi$
$192$	−8.03783	+	11.2869i	−0.580080	+	0.814559i
$193$	−11.2610	+	6.50154i	−0.810585	+	0.467991i	−0.847159	−	0.531340i	$-0.821689\pi$
$193$	−11.2610	+	6.50154i	−0.810585	+	0.467991i	0.0365742	+	0.999331i	$0.488355\pi$
$194$	−24.4482	−	7.91127i	−1.75528	−	0.567996i
$195$		0			0
$196$	−16.8406	−	12.1737i	−1.20290	−	0.869553i
$197$	−15.8462			−1.12899			−0.564496	−	0.825436i	$-0.690929\pi$
$197$	−15.8462			−1.12899			−0.564496	+	0.825436i	$0.690929\pi$
$198$	22.0178	−	16.1921i	1.56474	−	1.15072i
$199$		−	1.24563i		−	0.0883001i	−0.999025	−	0.0441500i	$-0.985942\pi$
$199$		−	1.24563i		−	0.0883001i	0.999025	−	0.0441500i	$-0.0140580\pi$
$200$		0			0
$201$	3.96604	+	18.4509i	0.279743	+	1.30142i
$202$	13.7780	+	4.45846i	0.969414	+	0.313696i
$203$	23.5721	−	13.6093i	1.65443	−	0.955188i
$204$	−3.27357	+	0.359597i	−0.229196	+	0.0251768i
$205$		0			0
$206$	9.15324	+	10.1412i	0.637736	+	0.706571i
$207$	6.03003	+	0.605874i	0.419116	+	0.0421112i
$208$	1.44255	−	6.95057i	0.100023	−	0.481935i
$209$	12.2337	+	7.06312i	0.846221	+	0.488566i
$210$		0			0
$211$	−14.1374	+	8.16221i	−0.973256	+	0.561910i	−0.900227	−	0.435420i	$-0.856600\pi$
$211$	−14.1374	+	8.16221i	−0.973256	+	0.561910i	−0.0730289	+	0.997330i	$0.523267\pi$
$212$	−8.90381	+	3.98987i	−0.611516	+	0.274025i
$213$	3.67824	+	1.18583i	0.252029	+	0.0812515i
$214$	0.956138	+	4.47188i	0.0653602	+	0.305691i
$215$		0			0
$216$	14.0244	+	4.39501i	0.954240	+	0.299043i
$217$			11.8534i			0.804662i
$218$	3.98776	−	0.852629i	0.270085	−	0.0577473i
$219$	−0.928257	+	2.87930i	−0.0627258	+	0.194565i
$220$		0			0
$221$	1.46111	−	0.843574i	0.0982851	−	0.0567449i
$222$	−1.44463	+	14.2220i	−0.0969571	+	0.954519i
$223$	−8.96287	+	15.5241i	−0.600198	+	1.03957i	0.392592	+	0.919713i	$0.371578\pi$
$223$	−8.96287	+	15.5241i	−0.600198	+	1.03957i	−0.992791	+	0.119861i	$0.961755\pi$
$224$	−11.9173	−	20.3582i	−0.796257	−	1.36024i
$225$		0			0
$226$	−2.92626	−	3.24211i	−0.194652	−	0.215662i
$227$	9.03303	+	5.21522i	0.599543	+	0.346146i	0.768862	−	0.639415i	$-0.220823\pi$
$227$	9.03303	+	5.21522i	0.599543	+	0.346146i	−0.169319	+	0.985561i	$0.554157\pi$
$228$	0.829455	+	7.55089i	0.0549320	+	0.500070i
$229$	−9.39388	−	16.2707i	−0.620765	−	1.07520i	−0.989344	−	0.145600i	$-0.953489\pi$
$229$	−9.39388	−	16.2707i	−0.620765	−	1.07520i	0.368578	−	0.929597i	$-0.379845\pi$
$230$		0			0
$231$	9.77813	+	45.4900i	0.643353	+	2.99302i
$232$	18.3531	−	1.99583i	1.20494	−	0.131033i
$233$	7.28693			0.477382			0.238691	−	0.971096i	$-0.423282\pi$
$233$	7.28693			0.477382			0.238691	+	0.971096i	$0.423282\pi$
$234$	−7.48337	+	0.830292i	−0.489203	+	0.0542779i
$235$		0			0
$236$	4.35657	+	3.14928i	0.283589	+	0.205001i
$237$	0.287689	+	0.318044i	0.0186874	+	0.0206592i
$238$	1.72613	−	5.33427i	0.111889	−	0.345769i
$239$	14.8408	+	25.7051i	0.959973	+	1.66272i	0.722553	+	0.691316i	$0.242969\pi$
$239$	14.8408	+	25.7051i	0.959973	+	1.66272i	0.237421	+	0.971407i	$0.423698\pi$
$240$		0			0
$241$	6.37517	−	11.0421i	0.410661	−	0.711285i	−0.584301	−	0.811537i	$-0.698631\pi$
$241$	6.37517	−	11.0421i	0.410661	−	0.711285i	0.994962	+	0.100251i	$0.0319647\pi$
$242$	28.8987	+	32.0179i	1.85768	+	2.05819i
$243$	−0.178469	−	15.5874i	−0.0114488	−	0.999934i
$244$	−0.836133	+	8.14327i	−0.0535279	+	0.521319i
$245$		0			0
$246$	−15.8977	+	7.14470i	−1.01360	+	0.455530i
$247$	−1.94581	−	3.37024i	−0.123809	−	0.214443i
$248$	−3.24357	+	7.35634i	−0.205967	+	0.467128i
$249$	13.5628	+	14.9938i	0.859507	+	0.950195i
$250$		0			0
$251$	−2.89830			−0.182939			−0.0914694	−	0.995808i	$-0.529156\pi$
$251$	−2.89830			−0.182939			−0.0914694	+	0.995808i	$0.529156\pi$
$252$	−16.6120	+	18.7105i	−1.04646	+	1.17865i
$253$			13.0135i			0.818151i
$254$	2.99163	−	0.639644i	0.187712	−	0.0401349i
$255$		0			0
$256$	−1.82517	−	15.8956i	−0.114073	−	0.993472i
$257$	4.98307	+	8.63093i	0.310835	+	0.538382i	0.978543	−	0.206041i	$-0.0660579\pi$
$257$	4.98307	+	8.63093i	0.310835	+	0.538382i	−0.667708	+	0.744423i	$0.732725\pi$
$258$	7.60818	−	10.5490i	0.473664	−	0.656751i
$259$	−21.0763	−	12.1684i	−1.30962	−	0.756108i
$260$		0			0
$261$	−8.04622	−	17.8516i	−0.498049	−	1.10499i
$262$	1.81401	+	2.00981i	0.112070	+	0.124166i
$263$	−1.05795	−	0.610808i	−0.0652360	−	0.0376640i	0.467027	−	0.884243i	$-0.345325\pi$
$263$	−1.05795	−	0.610808i	−0.0652360	−	0.0376640i	−0.532263	+	0.846579i	$0.678658\pi$
$264$	−6.37949	+	30.9073i	−0.392630	+	1.90221i
$265$		0			0
$266$	−12.3041	−	3.98154i	−0.754416	−	0.244124i
$267$	−3.26253	+	10.1198i	−0.199664	+	0.619323i
$268$	−17.6607	−	12.7666i	−1.07880	−	0.779843i
$269$		−	19.0910i		−	1.16400i	−0.813190	−	0.581998i	$-0.802271\pi$
$269$		−	19.0910i		−	1.16400i	0.813190	−	0.581998i	$-0.197729\pi$
$270$		0			0
$271$		−	12.0019i		−	0.729061i	−0.931191	−	0.364531i	$-0.881229\pi$
$271$		−	12.0019i		−	0.729061i	0.931191	−	0.364531i	$-0.118771\pi$
$272$	2.53092	−	2.83816i	0.153460	−	0.172089i
$273$	3.93312	−	12.1999i	0.238044	−	0.738371i
$274$	5.07713	−	15.6899i	0.306721	−	0.947859i
$275$		0			0
$276$	−5.64209	+	4.13979i	−0.339614	+	0.249186i
$277$	−20.8091	−	12.0141i	−1.25030	−	0.721860i	−0.279129	−	0.960254i	$-0.590046\pi$
$277$	−20.8091	−	12.0141i	−1.25030	−	0.721860i	−0.971169	+	0.238394i	$0.923379\pi$
$278$	8.04282	−	7.25928i	0.482376	−	0.435383i
$279$	8.48465	+	0.852506i	0.507963	+	0.0510382i
$280$		0			0
$281$	1.34110	+	0.774283i	0.0800031	+	0.0461898i	0.539468	−	0.842006i	$-0.318625\pi$
$281$	1.34110	+	0.774283i	0.0800031	+	0.0461898i	−0.459465	+	0.888196i	$0.651959\pi$
$282$	−0.802608	−	0.578860i	−0.0477946	−	0.0344706i
$283$	12.2787	+	21.2674i	0.729895	+	1.26422i	0.956927	+	0.290328i	$0.0937645\pi$
$283$	12.2787	+	21.2674i	0.729895	+	1.26422i	−0.227032	+	0.973887i	$0.572902\pi$
$284$	−4.07235	+	1.82485i	−0.241650	+	0.108285i
$285$		0			0
$286$	−3.38043	−	15.8103i	−0.199889	−	0.934884i
$287$		−	29.6726i		−	1.75152i
$288$	−15.4295	+	7.06620i	−0.909191	+	0.416380i
$289$	−16.0962			−0.946836
$290$		0			0
$291$	−21.1120	−	23.3396i	−1.23761	−	1.36819i
$292$	−1.42848	−	3.18781i	−0.0835956	−	0.186552i
$293$	−13.5844	−	23.5288i	−0.793607	−	1.37457i	−0.923720	−	0.383068i	$-0.874867\pi$
$293$	−13.5844	−	23.5288i	−0.793607	−	1.37457i	0.130113	−	0.991499i	$-0.458466\pi$
$294$	−10.4326	−	23.2136i	−0.608440	−	1.35384i
$295$		0			0
$296$	−9.75040	−	13.3192i	−0.566730	−	0.774160i
$297$	33.2649	−	3.72749i	1.93023	−	0.216291i
$298$	−3.66850	+	3.31111i	−0.212511	+	0.191808i
$299$	1.79253	−	3.10476i	0.103665	−	0.179553i
$300$		0			0
$301$	11.0713	+	19.1761i	0.638140	+	1.10529i
$302$	9.56949	+	3.09662i	0.550662	+	0.178191i
$303$	11.8978	+	13.1532i	0.683513	+	0.755631i
$304$	−6.54657	−	5.83789i	−0.375471	−	0.334826i
$305$		0			0
$306$	−3.69412	−	1.61921i	−0.211179	−	0.0925639i
$307$	−3.96646			−0.226378			−0.113189	−	0.993573i	$-0.536107\pi$
$307$	−3.96646			−0.226378			−0.113189	+	0.993573i	$0.536107\pi$
$308$	−43.5419	−	31.4756i	−2.48103	−	1.79349i
$309$	3.51611	+	16.3577i	0.200025	+	0.930559i
$310$		0			0
$311$	9.69205	+	16.7871i	0.549586	+	0.951911i	0.998303	+	0.0582368i	$0.0185478\pi$
$311$	9.69205	+	16.7871i	0.549586	+	0.951911i	−0.448717	+	0.893674i	$0.648119\pi$
$312$	5.77932	−	6.49512i	0.327189	−	0.367714i
$313$	−19.0268	−	10.9851i	−1.07546	−	0.620915i	−0.145789	−	0.989316i	$-0.546572\pi$
$313$	−19.0268	−	10.9851i	−1.07546	−	0.620915i	−0.929667	+	0.368400i	$0.879906\pi$
$314$	−3.31615	+	2.99309i	−0.187141	+	0.168910i
$315$		0			0
$316$	−0.492610	−	0.0505801i	−0.0277115	−	0.00284535i
$317$	13.3113	−	23.0559i	0.747640	−	1.29495i	−0.201311	−	0.979527i	$-0.564520\pi$
$317$	13.3113	−	23.0559i	0.747640	−	1.29495i	0.948951	−	0.315423i	$-0.102146\pi$
$318$	−11.8885	−	1.20760i	−0.666675	−	0.0677188i
$319$	36.4135	−	21.0234i	2.03877	−	1.17708i
$320$		0			0
$321$	−1.71851	+	5.33053i	−0.0959178	+	0.297521i
$322$	−2.49096	−	11.6503i	−0.138816	−	0.649245i
$323$		−	2.08472i		−	0.115997i
$324$	12.1982	+	13.2365i	0.677676	+	0.735360i
$325$		0			0
$326$	19.5083	−	4.17109i	1.08046	−	0.231015i
$327$	4.75346	+	1.53247i	0.262867	+	0.0847457i
$328$	8.11962	−	18.4151i	0.448331	−	1.01681i
$329$	1.45899	−	0.842349i	0.0804368	−	0.0464402i
$330$		0			0
$331$	28.7664	+	16.6083i	1.58115	+	0.912876i	0.994692	+	0.102894i	$0.0328101\pi$
$331$	28.7664	+	16.6083i	1.58115	+	0.912876i	0.586455	+	0.809982i	$0.300523\pi$
$332$	−23.2235	−	2.38454i	−1.27456	−	0.130869i
$333$	−10.2260	+	14.2112i	−0.560379	+	0.778770i
$334$	−19.2463	+	17.3713i	−1.05311	+	0.950516i
$335$		0			0
$336$	−0.204862	−	28.8908i	−0.0111761	−	1.57612i
$337$	−1.40051	+	0.808583i	−0.0762905	+	0.0440463i	−0.537660	−	0.843162i	$-0.680692\pi$
$337$	−1.40051	+	0.808583i	−0.0762905	+	0.0440463i	0.461370	+	0.887208i	$0.347358\pi$
$338$	4.28894	−	13.2541i	0.233288	−	0.720928i
$339$	−1.12409	−	5.22952i	−0.0610522	−	0.284028i
$340$		0			0
$341$			18.3109i			0.991588i
$342$	−3.73490	+	8.52093i	−0.201960	+	0.460759i
$343$	14.1366			0.763302
$344$	1.62363	+	14.9304i	0.0875401	+	0.804995i
$345$		0			0
$346$	−3.43173	+	10.6051i	−0.184491	+	0.570132i
$347$	−4.49117	+	2.59298i	−0.241099	+	0.139198i	−0.615682	−	0.787995i	$-0.711119\pi$
$347$	−4.49117	+	2.59298i	−0.241099	+	0.139198i	0.374583	+	0.927193i	$0.377786\pi$
$348$	20.6985	+	9.09950i	1.10956	+	0.487784i
$349$	−9.16716	+	15.8780i	−0.490707	+	0.849929i	−0.999943	−	0.0106977i	$-0.996595\pi$
$349$	−9.16716	+	15.8780i	−0.490707	+	0.849929i	0.509236	+	0.860627i	$0.329928\pi$
$350$		0			0
$351$	−8.44979	−	3.69275i	−0.451017	−	0.197104i
$352$	−18.4095	−	31.4489i	−0.981231	−	1.67623i
$353$	−5.34873	+	9.26426i	−0.284684	+	0.493087i	−0.972532	−	0.232767i	$-0.925222\pi$
$353$	−5.34873	+	9.26426i	−0.284684	+	0.493087i	0.687849	+	0.725854i	$0.258555\pi$
$354$	2.69885	+	6.00523i	0.143442	+	0.319174i
$355$		0			0
$356$	−5.02067	−	11.2041i	−0.266095	−	0.593819i
$357$	5.09238	−	4.60636i	0.269517	−	0.243794i
$358$	−13.6098	+	2.90992i	−0.719299	+	0.153794i
$359$	−15.1958			−0.802005			−0.401002	−	0.916077i	$-0.631338\pi$
$359$	−15.1958			−0.802005			−0.401002	+	0.916077i	$0.631338\pi$
$360$		0			0
$361$	14.1913			0.746913
$362$	−25.3378	+	5.41752i	−1.33173	+	0.284738i
$363$	11.1011	+	51.6448i	0.582656	+	2.71065i
$364$	6.05264	+	13.5071i	0.317244	+	0.707964i
$365$		0			0
$366$	−5.86471	+	8.13161i	−0.306553	+	0.425046i
$367$	−12.2791	+	21.2680i	−0.640964	+	1.11018i	0.344254	+	0.938877i	$0.388132\pi$
$367$	−12.2791	+	21.2680i	−0.640964	+	1.11018i	−0.985218	+	0.171306i	$0.945201\pi$
$368$	1.64207	−	7.91192i	0.0855987	−	0.412437i
$369$	−21.2396	−	2.13408i	−1.10569	−	0.111096i
$370$		0			0
$371$	10.1719	−	17.6182i	0.528097	−	0.914691i
$372$	−7.93880	+	5.82496i	−0.411608	+	0.302010i
$373$	16.1159	−	9.30451i	0.834449	−	0.481769i	−0.0209247	−	0.999781i	$-0.506661\pi$
$373$	16.1159	−	9.30451i	0.834449	−	0.481769i	0.855373	+	0.518012i	$0.173328\pi$
$374$	2.66649	−	8.24024i	0.137881	−	0.426093i
$375$		0			0
$376$	1.13596	−	0.123532i	0.0585829	−	0.00637067i
$377$	−11.5834			−0.596575
$378$	−29.0669	+	9.70441i	−1.49504	+	0.499141i
$379$		−	27.9052i		−	1.43339i	−0.697386	−	0.716696i	$-0.745653\pi$
$379$		−	27.9052i		−	1.43339i	0.697386	−	0.716696i	$-0.254347\pi$
$380$		0			0
$381$	3.56606	+	1.14966i	0.182695	+	0.0588989i
$382$	−8.30767	+	25.6732i	−0.425057	+	1.31355i
$383$	6.41061	−	3.70117i	0.327567	−	0.189121i	−0.327194	−	0.944957i	$-0.606103\pi$
$383$	6.41061	−	3.70117i	0.327567	−	0.189121i	0.654760	+	0.755837i	$0.272770\pi$
$384$	7.77853	−	17.9860i	0.396946	−	0.917842i
$385$		0			0
$386$	13.6510	−	12.3211i	0.694818	−	0.627129i
$387$	14.5225	−	6.54568i	0.738219	−	0.332735i
$388$	36.1501	+	3.71181i	1.83524	+	0.188439i
$389$	15.5362	+	8.96985i	0.787718	+	0.454789i	0.839159	−	0.543887i	$-0.183048\pi$
$389$	15.5362	+	8.96985i	0.787718	+	0.454789i	−0.0514403	+	0.998676i	$0.516381\pi$
$390$		0			0
$391$	1.66320	−	0.960250i	0.0841118	−	0.0485619i
$392$	26.8894	+	11.8561i	1.35812	+	0.598825i
$393$	0.696831	+	3.24181i	0.0351505	+	0.163528i
$394$	21.9145	−	4.68558i	1.10404	−	0.236056i
$395$		0			0
$396$	−25.6617	+	28.9034i	−1.28955	+	1.45245i
$397$			27.9101i			1.40077i	0.713768	+	0.700383i	$0.246987\pi$
$397$			27.9101i			1.40077i	−0.713768	+	0.700383i	$0.753013\pi$
$398$	0.368321	+	1.72265i	0.0184623	+	0.0863484i
$399$	−10.6251	−	11.7462i	−0.531922	−	0.588046i
$400$		0			0
$401$	3.46154	−	1.99852i	0.172861	−	0.0998015i	−0.411073	−	0.911602i	$-0.634846\pi$
$401$	3.46154	−	1.99852i	0.172861	−	0.0998015i	0.583934	+	0.811801i	$0.301513\pi$
$402$	−10.9406	−	24.3440i	−0.545669	−	1.21417i
$403$	2.52221	−	4.36860i	0.125640	−	0.217616i
$404$	−20.3726	−	2.09182i	−1.01358	−	0.104072i
$405$		0			0
$406$	−28.5749	+	25.7912i	−1.41815	+	1.27999i
$407$	−32.5581	−	18.7974i	−1.61385	−	0.931755i
$408$	4.42087	−	1.46527i	0.218866	−	0.0725418i
$409$	11.0645	+	19.1644i	0.547107	+	0.947616i	0.998471	+	0.0552767i	$0.0176041\pi$
$409$	11.0645	+	19.1644i	0.547107	+	0.947616i	−0.451364	+	0.892340i	$0.649063\pi$
$410$		0			0
$411$	14.9784	−	13.5488i	0.738829	−	0.668315i
$412$	−15.6572	−	11.3183i	−0.771374	−	0.557612i
$413$	−11.2086			−0.551539
$414$	−8.51841	+	0.945131i	−0.418657	+	0.0464507i
$415$		0			0
$416$	0.0602464	+	10.0389i	0.00295382	+	0.492196i
$417$	12.9730	−	2.78857i	0.635293	−	0.136557i
$418$	−19.0071	−	6.15058i	−0.929669	−	0.300835i
$419$	−15.8068	−	27.3783i	−0.772215	−	1.33752i	−0.936347	−	0.351077i	$-0.885816\pi$
$419$	−15.8068	−	27.3783i	−0.772215	−	1.33752i	0.164132	−	0.986438i	$-0.447518\pi$
$420$		0			0
$421$	−15.0283	+	26.0298i	−0.732435	+	1.26861i	0.223405	+	0.974726i	$0.428283\pi$
$421$	−15.0283	+	26.0298i	−0.732435	+	1.26861i	−0.955840	+	0.293889i	$0.905050\pi$
$422$	17.1379	−	15.4683i	0.834258	−	0.752984i
$423$	−0.498020	−	1.10493i	−0.0242146	−	0.0537233i
$424$	11.1338	−	8.15059i	0.540705	−	0.395828i
$425$		0			0
$426$	−5.43748	−	0.552322i	−0.263447	−	0.0267601i
$427$	−8.53425	−	14.7817i	−0.413001	−	0.715339i
$428$	−2.64459	−	5.90169i	−0.127831	−	0.285269i
$429$	6.07579	−	18.8461i	0.293342	−	0.909898i
$430$		0			0
$431$	−25.0832			−1.20822			−0.604108	−	0.796902i	$-0.706471\pi$
$431$	−25.0832			−1.20822			−0.604108	+	0.796902i	$0.706471\pi$
$432$	−20.6947	−	1.93120i	−0.995674	−	0.0929151i
$433$			29.4297i			1.41430i	0.707062	+	0.707151i	$0.250020\pi$
$433$			29.4297i			1.41430i	−0.707062	+	0.707151i	$0.749980\pi$
$434$	−3.50495	−	16.3927i	−0.168243	−	0.786877i
$435$		0			0
$436$	−5.26278	+	2.35830i	−0.252042	+	0.112942i
$437$	−2.21494	−	3.83638i	−0.105955	−	0.183519i
$438$	0.432354	−	4.25642i	0.0206587	−	0.203379i
$439$	24.8161	+	14.3276i	1.18441	+	0.683819i	0.957031	−	0.289987i	$-0.0936510\pi$
$439$	24.8161	+	14.3276i	1.18441	+	0.683819i	0.227379	+	0.973806i	$0.426984\pi$
$440$		0			0
$441$	3.11614	−	31.0137i	0.148388	−	1.47684i
$442$	−1.77122	+	1.59866i	−0.0842482	+	0.0760407i
$443$	−25.8577	−	14.9290i	−1.22854	−	0.709297i	−0.261814	−	0.965118i	$-0.584321\pi$
$443$	−25.8577	−	14.9290i	−1.22854	−	0.709297i	−0.966724	+	0.255822i	$0.917654\pi$
$444$	−2.20747	−	20.0956i	−0.104762	−	0.953694i
$445$		0			0
$446$	7.80489	−	24.1195i	0.369572	−	1.14209i
$447$	−5.91728	+	1.27193i	−0.279878	+	0.0601600i
$448$	22.5008	+	24.6307i	1.06306	+	1.16369i
$449$			14.7017i			0.693815i	0.937899	+	0.346908i	$0.112768\pi$
$449$			14.7017i			0.693815i	−0.937899	+	0.346908i	$0.887232\pi$
$450$		0			0
$451$		−	45.8375i		−	2.15841i
$452$	5.00556	+	3.61842i	0.235442	+	0.170196i
$453$	8.26365	+	9.13556i	0.388260	+	0.429226i
$454$	−14.0344	−	4.54143i	−0.658666	−	0.213140i
$455$		0			0
$456$	−3.37983	−	10.1973i	−0.158275	−	0.477531i
$457$	−7.64991	−	4.41668i	−0.357848	−	0.206604i	0.310288	−	0.950642i	$-0.399574\pi$
$457$	−7.64991	−	4.41668i	−0.357848	−	0.206604i	−0.668136	+	0.744039i	$0.732908\pi$
$458$	17.8024	+	19.7239i	0.831853	+	0.921639i
$459$	−2.93098	−	3.97641i	−0.136806	−	0.185603i
$460$		0			0
$461$	0.791004	+	0.456686i	0.0368407	+	0.0212700i	0.518307	−	0.855194i	$-0.326562\pi$
$461$	0.791004	+	0.456686i	0.0368407	+	0.0212700i	−0.481467	+	0.876464i	$0.659896\pi$
$462$	−26.9737	−	60.0194i	−1.25493	−	2.79235i
$463$	−3.93567	−	6.81678i	−0.182906	−	0.316803i	0.759963	−	0.649967i	$-0.225217\pi$
$463$	−3.93567	−	6.81678i	−0.182906	−	0.316803i	−0.942869	+	0.333164i	$0.891884\pi$
$464$	−24.7914	+	8.18701i	−1.15091	+	0.380072i
$465$		0			0
$466$	−10.0775	+	2.15468i	−0.466831	+	0.0998138i
$467$			28.6765i			1.32699i	0.748181	+	0.663495i	$0.230928\pi$
$467$			28.6765i			1.32699i	−0.748181	+	0.663495i	$0.769072\pi$
$468$	10.1037	−	3.36103i	0.467042	−	0.155364i
$469$	45.4375			2.09811
$470$		0			0
$471$	−5.34894	+	1.14976i	−0.246466	+	0.0529782i
$472$	−6.95616	−	3.06712i	−0.320183	−	0.141176i
$473$	17.1027	+	29.6227i	0.786383	+	1.36206i
$474$	−0.491905	−	0.354773i	−0.0225939	−	0.0162953i
$475$		0			0
$476$	−0.809867	+	7.88746i	−0.0371202	+	0.361521i
$477$	−11.8795	−	8.54812i	−0.543925	−	0.391391i
$478$	−28.1250	−	31.1607i	−1.28641	−	1.42526i
$479$	13.1909	−	22.8473i	0.602706	−	1.04392i	−0.389703	−	0.920941i	$-0.627422\pi$
$479$	13.1909	−	22.8473i	0.602706	−	1.04392i	0.992409	−	0.122977i	$-0.0392443\pi$
$480$		0			0
$481$	5.17848	+	8.96939i	0.236118	+	0.408969i
$482$	−5.55151	+	17.1558i	−0.252865	+	0.781427i
$483$	4.47712	−	13.8873i	0.203716	−	0.631893i
$484$	−49.4330	−	35.7342i	−2.24695	−	1.62428i
$485$		0			0
$486$	4.85589	+	21.5040i	0.220268	+	0.975439i
$487$	−7.87222			−0.356724			−0.178362	−	0.983965i	$-0.557080\pi$
$487$	−7.87222			−0.356724			−0.178362	+	0.983965i	$0.557080\pi$
$488$	−1.25156	−	11.5090i	−0.0566555	−	0.520989i
$489$	23.2541	+	7.49689i	1.05159	+	0.339021i
$490$		0			0
$491$	9.74699	+	16.8823i	0.439876	+	0.761887i	0.997679	−	0.0680859i	$-0.0216892\pi$
$491$	9.74699	+	16.8823i	0.439876	+	0.761887i	−0.557804	+	0.829973i	$0.688356\pi$
$492$	19.8732	−	14.5816i	0.895953	−	0.657390i
$493$	−5.37382	−	3.10258i	−0.242025	−	0.139733i
$494$	3.68752	+	4.08553i	0.165909	+	0.183817i
$495$		0			0
$496$	2.31050	−	11.1326i	0.103745	−	0.499868i
$497$	4.65233	−	8.05806i	0.208685	−	0.361454i
$498$	−23.1903	−	16.7254i	−1.03918	−	0.749482i
$499$	0.733058	−	0.423231i	0.0328162	−	0.0189464i	−0.483502	−	0.875343i	$-0.660635\pi$
$499$	0.733058	−	0.423231i	0.0328162	−	0.0189464i	0.516318	+	0.856397i	$0.327302\pi$
$500$		0			0
$501$	−31.0442	+	6.67299i	−1.38695	+	0.298127i
$502$	4.00822	−	0.857002i	0.178895	−	0.0382499i
$503$			18.5253i			0.826002i	0.910731	+	0.413001i	$0.135519\pi$
$503$			18.5253i			0.826002i	−0.910731	+	0.413001i	$0.864481\pi$
$504$	17.4411	−	30.7878i	0.776888	−	1.37140i
$505$		0			0
$506$	−3.84798	−	17.9971i	−0.171064	−	0.800068i
$507$	12.6531	−	11.4455i	0.561944	−	0.508311i
$508$	−3.94815	+	1.76920i	−0.175171	+	0.0784955i
$509$	23.6460	−	13.6520i	1.04809	−	0.605115i	0.125976	−	0.992033i	$-0.459794\pi$
$509$	23.6460	−	13.6520i	1.04809	−	0.605115i	0.922114	+	0.386918i	$0.126460\pi$
$510$		0			0
$511$	6.30779	+	3.64181i	0.279040	+	0.161104i
$512$	7.22431	+	21.4432i	0.319272	+	0.947663i
$513$	−9.17209	+	6.76066i	−0.404957	+	0.298490i
$514$	−9.44345	−	10.4627i	−0.416533	−	0.461491i
$515$		0			0
$516$	−7.40253	+	16.8385i	−0.325878	+	0.741272i
$517$	2.25381	−	1.30124i	0.0991226	−	0.0572285i
$518$	32.7457	+	10.5963i	1.43876	+	0.465574i
$519$	−10.1242	+	9.15792i	−0.444402	+	0.401988i
$520$		0			0
$521$		−	25.9868i		−	1.13850i	−0.822163	−	0.569252i	$-0.807233\pi$
$521$		−	25.9868i		−	1.13850i	0.822163	−	0.569252i	$-0.192767\pi$
$522$	16.4061	+	22.3088i	0.718078	+	0.976431i
$523$	−30.1683			−1.31917			−0.659584	−	0.751631i	$-0.729268\pi$
$523$	−30.1683			−1.31917			−0.659584	+	0.751631i	$0.729268\pi$
$524$	−3.10298	−	2.24308i	−0.135554	−	0.0979896i
$525$		0			0
$526$	1.64371	+	0.531893i	0.0716692	+	0.0231917i
$527$	2.34024	−	1.35114i	0.101942	−	0.0588564i
$528$	−0.316465	−	44.6297i	−0.0137724	−	1.94226i
$529$	−9.45954	+	16.3844i	−0.411284	+	0.712365i
$530$		0			0
$531$	−0.806130	+	8.02309i	−0.0349831	+	0.348173i
$532$	18.1934	+	1.86806i	0.788784	+	0.0809906i
$533$	−6.31386	+	10.9359i	−0.273484	+	0.473687i
$534$	1.51959	−	14.9600i	0.0657590	−	0.647381i
$535$		0			0
$536$	28.1989	+	12.4335i	1.21801	+	0.537046i
$537$	−16.2230	−	5.23014i	−0.700074	−	0.225697i
$538$	5.64504	+	26.4020i	0.243375	+	1.13827i
$539$	66.9311			2.88293
$540$		0			0
$541$	−34.2068			−1.47067			−0.735333	−	0.677706i	$-0.762974\pi$
$541$	−34.2068			−1.47067			−0.735333	+	0.677706i	$0.762974\pi$
$542$	3.54885	+	16.5980i	0.152436	+	0.712947i
$543$	−30.2030	−	9.73714i	−1.29613	−	0.417861i
$544$	−2.66094	+	4.67342i	−0.114087	+	0.200371i
$545$		0			0
$546$	−1.83193	+	18.0349i	−0.0783994	+	0.771823i
$547$	8.00761	−	13.8696i	0.342380	−	0.593020i	−0.642494	−	0.766291i	$-0.722100\pi$
$547$	8.00761	−	13.8696i	0.342380	−	0.593020i	0.984874	+	0.173270i	$0.0554335\pi$
$548$	−2.38209	+	23.1996i	−0.101758	+	0.991039i
$549$	−11.1945	+	5.04569i	−0.477771	+	0.215345i
$550$		0			0
$551$	−7.15648	+	12.3954i	−0.304876	+	0.528061i
$552$	6.57866	−	7.39347i	0.280007	−	0.314687i
$553$	0.894191	−	0.516261i	0.0380249	−	0.0219537i
$554$	32.3306	+	10.4619i	1.37359	+	0.444486i
$555$		0			0
$556$	−8.97635	+	12.4175i	−0.380682	+	0.526618i
$557$	−16.0344			−0.679401			−0.339701	−	0.940534i	$-0.610326\pi$
$557$	−16.0344			−0.679401			−0.339701	+	0.940534i	$0.610326\pi$
$558$	−11.9860	+	1.32986i	−0.507407	+	0.0562976i
$559$		−	9.42320i		−	0.398559i
$560$		0			0
$561$	7.86658	−	7.11579i	0.332127	−	0.300429i
$562$	−2.08363	−	0.674248i	−0.0878925	−	0.0284414i
$563$	3.87428	−	2.23682i	0.163282	−	0.0942707i	−0.416133	−	0.909304i	$-0.636615\pi$
$563$	3.87428	−	2.23682i	0.163282	−	0.0942707i	0.579414	+	0.815033i	$0.303281\pi$
$564$	1.28113	+	0.563213i	0.0539455	+	0.0237155i
$565$		0			0
$566$	−23.2695	−	25.7812i	−0.978092	−	1.08366i
$567$	−36.7809	−	7.46660i	−1.54465	−	0.313568i
$568$	5.09229	−	3.72785i	0.213668	−	0.156417i
$569$	−35.5461	−	20.5225i	−1.49017	−	0.860349i	−0.490232	−	0.871592i	$-0.663088\pi$
$569$	−35.5461	−	20.5225i	−1.49017	−	0.860349i	−0.999937	+	0.0112430i	$0.996421\pi$
$570$		0			0
$571$	−39.1877	+	22.6250i	−1.63995	+	0.946828i	−0.659107	+	0.752049i	$0.729065\pi$
$571$	−39.1877	+	22.6250i	−1.63995	+	0.946828i	−0.980847	+	0.194778i	$0.937601\pi$
$572$	9.34996	+	20.8654i	0.390941	+	0.872427i
$573$	−24.5090	+	22.1698i	−1.02388	+	0.926158i
$574$	8.77395	+	41.0359i	0.366218	+	1.71281i
$575$		0			0
$576$	19.2489	−	14.3346i	0.802036	−	0.597275i
$577$			27.1400i			1.12985i	0.825141	+	0.564927i	$0.191096\pi$
$577$			27.1400i			1.12985i	−0.825141	+	0.564927i	$0.808904\pi$
$578$	22.2603	−	4.75951i	0.925908	−	0.197970i
$579$	22.0191	−	4.73302i	0.915081	−	0.196698i
$580$		0			0
$581$	42.1556	−	24.3386i	1.74891	−	1.00973i
$582$	36.0983	+	26.0350i	1.49632	+	1.07918i
$583$	15.7132	−	27.2161i	0.650776	−	1.12718i
$584$	2.91814	+	3.98621i	0.120753	+	0.164950i
$585$		0			0
$586$	25.7438	+	28.5225i	1.06347	+	1.17825i
$587$	15.1886	+	8.76914i	0.626901	+	0.361941i	0.779551	−	0.626339i	$-0.215447\pi$
$587$	15.1886	+	8.76914i	0.626901	+	0.361941i	−0.152650	+	0.988280i	$0.548781\pi$
$588$	21.2918	+	29.0185i	0.878060	+	1.19670i
$589$	−3.11656	−	5.39805i	−0.128416	−	0.222423i
$590$		0			0
$591$	26.1224	+	8.42160i	1.07453	+	0.346418i
$592$	17.4227	+	15.5367i	0.716070	+	0.638554i
$593$	−15.6793			−0.643872			−0.321936	−	0.946761i	$-0.604334\pi$
$593$	−15.6793			−0.643872			−0.321936	+	0.946761i	$0.604334\pi$
$594$	−44.9018	+	14.9911i	−1.84234	+	0.615093i
$595$		0			0
$596$	4.09430	−	5.66387i	0.167709	−	0.232001i
$597$	−0.662000	+	2.05341i	−0.0270939	+	0.0840406i
$598$	−1.56094	+	4.82378i	−0.0638317	+	0.197259i
$599$	−3.60975	−	6.25226i	−0.147490	−	0.255461i	0.782809	−	0.622262i	$-0.213786\pi$
$599$	−3.60975	−	6.25226i	−0.147490	−	0.255461i	−0.930299	+	0.366801i	$0.880453\pi$
$600$		0			0
$601$	−22.9958	+	39.8299i	−0.938019	+	1.62470i	−0.168860	+	0.985640i	$0.554008\pi$
$601$	−22.9958	+	39.8299i	−0.938019	+	1.62470i	−0.769160	+	0.639057i	$0.779325\pi$
$602$	−20.9814	−	23.2460i	−0.855136	−	0.947436i
$603$	3.26789	−	32.5241i	0.133079	−	1.32448i
$604$	−14.1498	−	1.45287i	−0.575748	−	0.0591166i
$605$		0			0
$606$	−20.3435	−	14.6722i	−0.826397	−	0.596017i
$607$	1.07432	+	1.86077i	0.0436052	+	0.0755263i	0.887004	−	0.461761i	$-0.152782\pi$
$607$	1.07432	+	1.86077i	0.0436052	+	0.0755263i	−0.843399	+	0.537288i	$0.819449\pi$
$608$	10.7798	+	6.13778i	0.437180	+	0.248920i
$609$	−46.0913	+	9.90738i	−1.86772	+	0.401467i
$610$		0			0
$611$	−0.716953			−0.0290048
$612$	5.58758	+	1.14697i	0.225865	+	0.0463636i
$613$		−	44.8432i		−	1.81120i	−0.424131	−	0.905601i	$-0.639421\pi$
$613$		−	44.8432i		−	1.81120i	0.424131	−	0.905601i	$-0.360579\pi$
$614$	5.48544	−	1.17285i	0.221374	−	0.0473324i
$615$		0			0
$616$	69.5235	+	30.6544i	2.80118	+	1.23510i
$617$	17.2230	+	29.8311i	0.693371	+	1.20095i	0.970727	+	0.240186i	$0.0772085\pi$
$617$	17.2230	+	29.8311i	0.693371	+	1.20095i	−0.277356	+	0.960767i	$0.589458\pi$
$618$	−9.69947	−	21.5823i	−0.390170	−	0.868169i
$619$	11.0619	+	6.38657i	0.444614	+	0.256698i	0.705553	−	0.708657i	$-0.250699\pi$
$619$	11.0619	+	6.38657i	0.444614	+	0.256698i	−0.260939	+	0.965355i	$0.584032\pi$
$620$		0			0
$621$	−9.61850	−	4.20350i	−0.385977	−	0.168681i
$622$	−18.3675	−	20.3500i	−0.736469	−	0.815961i
$623$	22.1699	+	12.7998i	0.888219	+	0.512814i
$624$	−6.07199	+	10.6914i	−0.243074	+	0.427997i
$625$		0			0
$626$	29.5614	+	9.56586i	1.18151	+	0.382329i
$627$	−16.4134	−	18.1452i	−0.655490	−	0.724651i
$628$	3.70106	−	5.11987i	0.147688	−	0.204305i
$629$			5.54817i			0.221220i
$630$		0			0
$631$		−	12.9765i		−	0.516586i	−0.966067	−	0.258293i	$-0.916840\pi$
$631$		−	12.9765i		−	0.516586i	0.966067	−	0.258293i	$-0.0831600\pi$
$632$	0.696214	−	0.0757106i	0.0276939	−	0.00301160i
$633$	27.6433	−	5.94196i	1.09872	−	0.236172i
$634$	−11.5916	+	35.8214i	−0.460360	+	1.42265i
$635$		0			0
$636$	16.7984	−	1.84528i	0.666099	−	0.0731701i
$637$	−15.9684	−	9.21938i	−0.632693	−	0.365285i
$638$	−44.1419	+	39.8415i	−1.74759	+	1.57734i
$639$	−5.43335	−	3.90967i	−0.214940	−	0.154664i
$640$		0			0
$641$	26.4627	+	15.2782i	1.04521	+	0.603453i	0.921305	−	0.388840i	$-0.127124\pi$
$641$	26.4627	+	15.2782i	1.04521	+	0.603453i	0.123907	+	0.992294i	$0.460458\pi$
$642$	0.800430	−	7.88004i	0.0315904	−	0.311000i
$643$	3.08712	+	5.34706i	0.121744	+	0.210867i	0.920456	−	0.390847i	$-0.127818\pi$
$643$	3.08712	+	5.34706i	0.121744	+	0.210867i	−0.798711	+	0.601714i	$0.794485\pi$
$644$	6.88979	+	15.3753i	0.271496	+	0.605871i
$645$		0			0
$646$	0.616433	+	2.88307i	0.0242532	+	0.113433i
$647$			9.68580i			0.380788i	0.981708	+	0.190394i	$0.0609766\pi$
$647$			9.68580i			0.380788i	−0.981708	+	0.190394i	$0.939023\pi$
$648$	−20.7835	−	14.6986i	−0.816451	−	0.577415i
$649$	−17.3148			−0.679663
$650$		0			0
$651$	6.29961	−	19.5403i	0.246901	−	0.765846i
$652$	−25.7457	+	11.5369i	−1.00828	+	0.451819i
$653$	−8.17325	−	14.1565i	−0.319844	−	0.553986i	0.660611	−	0.750728i	$-0.270297\pi$
$653$	−8.17325	−	14.1565i	−0.319844	−	0.553986i	−0.980455	+	0.196742i	$0.936964\pi$
$654$	−7.02696	−	0.713777i	−0.274776	−	0.0279109i
$655$		0			0
$656$	−5.78387	+	27.8682i	−0.225822	+	1.08807i
$657$	3.06046	−	4.25319i	0.119400	−	0.165933i
$658$	−1.76864	+	1.59634i	−0.0689490	+	0.0622319i
$659$	−11.5429	+	19.9929i	−0.449648	+	0.778812i	−0.998363	−	0.0571968i	$-0.981784\pi$
$659$	−11.5429	+	19.9929i	−0.449648	+	0.778812i	0.548715	+	0.836009i	$0.315117\pi$
$660$		0			0
$661$	−9.23504	−	15.9956i	−0.359202	−	0.622155i	0.628626	−	0.777708i	$-0.283618\pi$
$661$	−9.23504	−	15.9956i	−0.359202	−	0.622155i	−0.987828	+	0.155552i	$0.950284\pi$
$662$	−44.6937	−	14.4626i	−1.73707	−	0.562104i
$663$	−2.85697	+	0.614108i	−0.110955	+	0.0238500i
$664$	32.8222	−	3.56929i	1.27375	−	0.138515i
$665$		0			0
$666$	9.93990	−	22.6772i	0.385163	−	0.878724i
$667$	−13.1855			−0.510545
$668$	21.4802	−	29.7147i	0.831095	−	1.14970i
$669$	23.0257	−	20.8281i	0.890227	−	0.805263i
$670$		0			0
$671$	−13.1835	−	22.8345i	−0.508943	−	0.881515i
$672$	8.82607	+	39.8941i	0.340473	+	1.53895i
$673$	26.2539	+	15.1577i	1.01201	+	0.584286i	0.911780	−	0.410678i	$-0.134708\pi$
$673$	26.2539	+	15.1577i	1.01201	+	0.584286i	0.100233	+	0.994964i	$0.468041\pi$
$674$	1.69775	−	1.53235i	0.0653948	−	0.0590240i
$675$		0			0
$676$	−2.01228	+	19.5980i	−0.0773956	+	0.753771i
$677$	−21.1946	+	36.7101i	−0.814573	+	1.41088i	0.0950610	+	0.995471i	$0.469695\pi$
$677$	−21.1946	+	36.7101i	−0.814573	+	1.41088i	−0.909634	+	0.415410i	$0.863638\pi$
$678$	3.10089	+	6.89981i	0.119089	+	0.264985i
$679$	−65.6200	+	37.8857i	−2.51827	+	1.45392i
$680$		0			0
$681$	−12.1193	−	13.3980i	−0.464411	−	0.513412i
$682$	−5.41437	−	25.3231i	−0.207327	−	0.969671i
$683$			20.7847i			0.795303i	0.917536	+	0.397652i	$0.130175\pi$
$683$			20.7847i			0.795303i	−0.917536	+	0.397652i	$0.869825\pi$
$684$	2.64564	−	12.8885i	0.101158	−	0.492802i
$685$		0			0
$686$	−19.5502	+	4.18006i	−0.746431	+	0.159595i
$687$	6.83860	+	31.8147i	0.260909	+	1.21381i
$688$	−6.66021	−	20.1680i	−0.253918	−	0.768899i
$689$	−7.49773	+	4.32882i	−0.285641	+	0.164915i
$690$		0			0
$691$	36.9591	+	21.3383i	1.40599	+	0.811748i	0.994998	−	0.0998910i	$-0.0318494\pi$
$691$	36.9591	+	21.3383i	1.40599	+	0.811748i	0.410991	+	0.911639i	$0.365183\pi$
$692$	1.61010	−	15.6811i	0.0612068	−	0.596105i
$693$	8.05688	−	80.1870i	0.306056	−	3.04605i
$694$	5.44437	−	4.91398i	0.206665	−	0.186532i
$695$		0			0
$696$	−31.3158	−	6.46382i	−1.18702	−	0.245010i
$697$	−5.85831	+	3.38230i	−0.221899	+	0.128114i
$698$	7.98279	−	24.6692i	0.302153	−	0.933743i
$699$	−12.0125	−	3.87271i	−0.454354	−	0.146479i
$700$		0			0
$701$		−	26.5424i		−	1.00249i	−0.865305	−	0.501247i	$-0.832875\pi$
$701$		−	26.5424i		−	1.00249i	0.865305	−	0.501247i	$-0.167125\pi$
$702$	12.7776	+	2.60838i	0.482260	+	0.0984468i
$703$	12.7975			0.482668
$704$	34.7587	+	38.0488i	1.31002	+	1.43402i
$705$		0			0
$706$	4.65768	−	14.3936i	0.175294	−	0.541712i
$707$	36.9806	−	21.3508i	1.39080	−	0.802979i
$708$	−5.50809	−	7.50694i	−0.207007	−	0.282128i
$709$	23.1270	−	40.0571i	0.868553	−	1.50438i	0.00507739	−	0.999987i	$-0.498384\pi$
$709$	23.1270	−	40.0571i	0.868553	−	1.50438i	0.863476	−	0.504391i	$-0.168283\pi$
$710$		0			0
$711$	−0.305228	−	0.677191i	−0.0114470	−	0.0253966i
$712$	10.2563	+	14.0103i	0.384372	+	0.525057i
$713$	2.87107	−	4.97283i	0.107522	−	0.186234i
$714$	−5.68048	+	7.87617i	−0.212587	+	0.294758i
$715$		0			0
$716$	17.9613	−	8.04859i	0.671244	−	0.300790i
$717$	−10.8039	−	50.2621i	−0.403479	−	1.87707i
$718$	21.0151	−	4.49328i	0.784278	−	0.167688i
$719$	−44.9992			−1.67819			−0.839094	−	0.543986i	$-0.816914\pi$
$719$	−44.9992			−1.67819			−0.839094	+	0.543986i	$0.816914\pi$
$720$		0			0
$721$	40.2828			1.50021
$722$	−19.6260	+	4.19626i	−0.730404	+	0.156169i
$723$	−16.3779	+	14.8148i	−0.609101	+	0.550968i
$724$	33.4392	−	14.9844i	1.24276	−	0.556890i
$725$		0			0
$726$	−30.6232	−	68.1399i	−1.13654	−	2.52891i
$727$	−17.8289	+	30.8806i	−0.661237	+	1.14530i	0.319054	+	0.947737i	$0.396635\pi$
$727$	−17.8289	+	30.8806i	−0.661237	+	1.14530i	−0.980291	+	0.197560i	$0.936698\pi$
$728$	−12.3645	−	16.8900i	−0.458257	−	0.625985i
$729$	−7.98989	+	25.7907i	−0.295922	+	0.955212i
$730$		0			0
$731$	2.52398	−	4.37166i	0.0933526	−	0.161692i
$732$	5.70618	−	12.9798i	0.210907	−	0.479747i
$733$	−40.8238	+	23.5696i	−1.50786	+	0.870563i	−0.507902	+	0.861415i	$0.669579\pi$
$733$	−40.8238	+	23.5696i	−1.50786	+	0.870563i	−0.999958	+	0.00914815i	$0.997088\pi$
$734$	10.6927	−	33.0436i	0.394674	−	1.21966i
$735$		0			0
$736$	0.0685791	+	11.4274i	0.00252786	+	0.421219i
$737$	70.1906			2.58551
$738$	30.0045	−	3.32904i	1.10448	−	0.122544i
$739$			40.9282i			1.50557i	0.658268	+	0.752784i	$0.271289\pi$
$739$			40.9282i			1.50557i	−0.658268	+	0.752784i	$0.728711\pi$
$740$		0			0
$741$	1.41652	+	6.58995i	0.0520370	+	0.242088i
$742$	−8.85769	+	27.3729i	−0.325176	+	1.00489i
$743$	−29.3195	+	16.9276i	−1.07563	+	0.621014i	−0.929714	−	0.368283i	$-0.879946\pi$
$743$	−29.3195	+	16.9276i	−1.07563	+	0.621014i	−0.145915	+	0.989297i	$0.546613\pi$
$744$	9.25662	−	10.4031i	0.339364	−	0.381396i
$745$		0			0
$746$	−19.5363	+	17.6331i	−0.715274	+	0.645592i
$747$	−14.3896	−	31.9254i	−0.526490	−	1.16809i
$748$	−1.25106	+	12.1843i	−0.0457434	+	0.445504i
$749$	11.6778	+	6.74219i	0.426698	+	0.246354i
$750$		0			0
$751$	5.93626	−	3.42730i	0.216617	−	0.125064i	−0.387766	−	0.921758i	$-0.626753\pi$
$751$	5.93626	−	3.42730i	0.216617	−	0.125064i	0.604383	+	0.796694i	$0.293420\pi$
$752$	−1.53446	+	0.506734i	−0.0559561	+	0.0184787i
$753$	4.77784	+	1.54033i	0.174114	+	0.0561327i
$754$	16.0193	−	3.42511i	0.583389	−	0.124735i
$755$		0			0
$756$	37.3287	−	22.0156i	1.35763	−	0.800699i
$757$		−	40.8568i		−	1.48497i	−0.669865	−	0.742483i	$-0.733648\pi$
$757$		−	40.8568i		−	1.48497i	0.669865	−	0.742483i	$-0.266352\pi$
$758$	8.25133	+	38.5916i	0.299702	+	1.40171i
$759$	6.91615	−	21.4527i	0.251040	−	0.778685i
$760$		0			0
$761$	−24.1632	+	13.9506i	−0.875916	+	0.505710i	−0.869310	−	0.494268i	$-0.835436\pi$
$761$	−24.1632	+	13.9506i	−0.875916	+	0.505710i	−0.00660605	+	0.999978i	$0.502103\pi$
$762$	−5.27165	−	0.535477i	−0.190972	−	0.0193983i
$763$	6.01230	−	10.4136i	0.217660	−	0.376998i
$764$	3.89779	−	37.9614i	0.141017	−	1.37339i
$765$		0			0
$766$	−7.77118	+	7.01411i	−0.280784	+	0.253430i
$767$	4.13095	+	2.38501i	0.149160	+	0.0861176i
$768$	−5.43906	+	27.1738i	−0.196265	+	0.980551i
$769$	3.06170	+	5.30302i	0.110408	+	0.191232i	0.915935	−	0.401327i	$-0.131451\pi$
$769$	3.06170	+	5.30302i	0.110408	+	0.191232i	−0.805527	+	0.592559i	$0.798118\pi$
$770$		0			0
$771$	−3.62759	−	16.8764i	−0.130645	−	0.607788i
$772$	−15.2355	+	21.0761i	−0.548337	+	0.758544i
$773$	14.8193			0.533012			0.266506	−	0.963833i	$-0.414131\pi$
$773$	14.8193			0.533012			0.266506	+	0.963833i	$0.414131\pi$
$774$	−18.1484	+	13.3466i	−0.652332	+	0.479732i
$775$		0			0
$776$	−51.0915	+	5.55600i	−1.83408	+	0.199449i
$777$	28.2772	+	31.2608i	1.01444	+	1.12148i
$778$	−24.1382	−	7.81097i	−0.865398	−	0.280037i
$779$	7.80169	+	13.5129i	0.279525	+	0.484151i
$780$		0			0
$781$	7.18680	−	12.4479i	0.257164	−	0.445421i
$782$	−2.01620	+	1.81978i	−0.0720991	+	0.0650751i
$783$	3.77676	+	33.7047i	0.134971	+	1.20451i
$784$	−40.6927	−	8.44551i	−1.45331	−	0.301625i
$785$		0			0
$786$	−1.92226	−	4.27724i	−0.0685648	−	0.152564i
$787$	−7.86353	−	13.6200i	−0.280305	−	0.485502i	0.691155	−	0.722707i	$-0.257102\pi$
$787$	−7.86353	−	13.6200i	−0.280305	−	0.485502i	−0.971460	+	0.237205i	$0.923769\pi$
$788$	−28.9214	+	12.9599i	−1.03028	+	0.461677i
$789$	1.41941	+	1.56918i	0.0505324	+	0.0558641i
$790$		0			0
$791$	−12.8783			−0.457900
$792$	26.9425	−	47.5601i	0.957362	−	1.68998i
$793$			7.26380i			0.257945i
$794$	−8.25277	−	38.5984i	−0.292880	−	1.36980i
$795$		0			0
$796$	−1.01874	−	2.27343i	−0.0361084	−	0.0805797i
$797$	21.6839	+	37.5576i	0.768083	+	1.33036i	0.938601	+	0.345005i	$0.112123\pi$
$797$	21.6839	+	37.5576i	0.768083	+	1.33036i	−0.170517	+	0.985355i	$0.554544\pi$
$798$	18.1673	+	13.1027i	0.643117	+	0.463831i
$799$	−0.332613	−	0.192034i	−0.0117670	−	0.00679367i
$800$		0			0
$801$	10.7566	−	14.9486i	0.380064	−	0.528184i
$802$	−4.19622	+	3.78742i	−0.148174	+	0.133738i
$803$	9.74412	+	5.62577i	0.343863	+	0.198529i
$804$	22.3287	+	30.4317i	0.787473	+	1.07324i
$805$		0			0
$806$	−2.19635	+	6.78738i	−0.0773632	+	0.239075i
$807$	−10.1461	+	31.4715i	−0.357159	+	1.10785i
$808$	28.7930	−	3.13113i	1.01293	−	0.110153i
$809$			0.395982i			0.0139220i	0.999976	+	0.00696100i	$0.00221577\pi$
$809$			0.395982i			0.0139220i	−0.999976	+	0.00696100i	$0.997784\pi$
$810$		0			0
$811$			45.9241i			1.61261i	0.591498	+	0.806307i	$0.298537\pi$
$811$			45.9241i			1.61261i	−0.591498	+	0.806307i	$0.701463\pi$
$812$	31.8916	−	44.1174i	1.11918	−	1.54822i
$813$	−6.37851	+	19.7851i	−0.223704	+	0.693893i
$814$	50.5847	+	16.3689i	1.77299	+	0.573729i
$815$		0			0
$816$	−5.68060	+	3.33362i	−0.198861	+	0.116700i
$817$	−10.0838	−	5.82186i	−0.352786	−	0.203681i
$818$	−20.9685	−	23.2318i	−0.733147	−	0.812279i
$819$	−12.9675	+	18.0212i	−0.453121	+	0.629712i
$820$		0			0
$821$	29.4827	+	17.0219i	1.02895	+	0.594067i	0.916685	−	0.399610i	$-0.130855\pi$
$821$	29.4827	+	17.0219i	1.02895	+	0.594067i	0.112270	+	0.993678i	$0.464188\pi$
$822$	−16.7082	+	23.1664i	−0.582764	+	0.808022i
$823$	−5.25672	−	9.10490i	−0.183238	−	0.317377i	0.759744	−	0.650223i	$-0.225324\pi$
$823$	−5.25672	−	9.10490i	−0.183238	−	0.317377i	−0.942981	+	0.332846i	$0.891991\pi$
$824$	24.9999	+	11.0230i	0.870914	+	0.384004i
$825$		0			0
$826$	15.5010	−	3.31429i	0.539348	−	0.115319i
$827$			40.8826i			1.42163i	0.703381	+	0.710813i	$0.251673\pi$
$827$			40.8826i			1.42163i	−0.703381	+	0.710813i	$0.748327\pi$
$828$	11.5011	−	3.82590i	0.399692	−	0.132959i
$829$	−24.0184			−0.834194			−0.417097	−	0.908862i	$-0.636952\pi$
$829$	−24.0184			−0.834194			−0.417097	+	0.908862i	$0.636952\pi$
$830$		0			0
$831$	27.9188	+	30.8645i	0.968491	+	1.07068i
$832$	−3.05173	−	13.8655i	−0.105800	−	0.480700i
$833$	−4.93877	−	8.55420i	−0.171118	−	0.296386i
$834$	−17.1166	+	7.69249i	−0.592699	+	0.266369i
$835$		0			0
$836$	28.1047	+	2.88573i	0.972021	+	0.0998050i
$837$	−13.5339	−	5.91461i	−0.467799	−	0.204439i
$838$	29.9557	+	33.1890i	1.03480	+	1.14649i
$839$	−17.0952	+	29.6098i	−0.590192	+	1.02224i	0.404014	+	0.914753i	$0.367615\pi$
$839$	−17.0952	+	29.6098i	−0.590192	+	1.02224i	−0.994206	+	0.107490i	$0.965719\pi$
$840$		0			0
$841$	6.80125	+	11.7801i	0.234526	+	0.406211i
$842$	13.0867	−	40.4418i	0.450997	−	1.39372i
$843$	−1.79930	−	1.98914i	−0.0619711	−	0.0685098i
$844$	−19.1271	+	26.4595i	−0.658380	+	0.910772i
$845$		0			0
$846$	1.01546	+	1.38080i	0.0349122	+	0.0474730i
$847$	127.181			4.37000
$848$	−12.9875	+	14.5641i	−0.445992	+	0.500133i
$849$	−8.93873	−	41.5850i	−0.306776	−	1.42719i
$850$		0			0
$851$	5.89473	+	10.2100i	0.202069	+	0.349993i
$852$	7.68311	−	0.843979i	0.263219	−	0.0289143i
$853$	21.4327	+	12.3742i	0.733840	+	0.423683i	0.819825	−	0.572614i	$-0.194070\pi$
$853$	21.4327	+	12.3742i	0.733840	+	0.423683i	−0.0859851	+	0.996296i	$0.527404\pi$
$854$	16.1733	+	17.9190i	0.553440	+	0.613176i
$855$		0			0
$856$	5.40243	+	7.37979i	0.184651	+	0.252236i
$857$	−5.33556	+	9.24145i	−0.182259	+	0.315682i	−0.942649	−	0.333784i	$-0.891674\pi$
$857$	−5.33556	+	9.24145i	−0.182259	+	0.315682i	0.760390	+	0.649466i	$0.225008\pi$
$858$	−2.82992	+	27.8599i	−0.0966118	+	0.951120i
$859$	−20.6204	+	11.9052i	−0.703560	+	0.406200i	−0.808672	−	0.588260i	$-0.799813\pi$
$859$	−20.6204	+	11.9052i	−0.703560	+	0.406200i	0.105112	+	0.994460i	$0.466480\pi$
$860$		0			0
$861$	−15.7698	+	48.9153i	−0.537434	+	1.66703i
$862$	34.6890	−	7.41690i	1.18151	−	0.252621i
$863$		−	53.1072i		−	1.80779i	−0.427753	−	0.903896i	$-0.640695\pi$
$863$		−	53.1072i		−	1.80779i	0.427753	−	0.903896i	$-0.359305\pi$
$864$	29.1909	−	3.44848i	0.993094	−	0.117320i
$865$		0			0
$866$	−8.70212	−	40.7000i	−0.295710	−	1.38304i
$867$	26.5346	+	8.55449i	0.901162	+	0.290526i
$868$	9.69439	+	21.6340i	0.329049	+	0.734307i
$869$	1.38132	−	0.797508i	0.0468582	−	0.0270536i
$870$		0			0
$871$	−16.7461	−	9.66836i	−0.567419	−	0.327600i
$872$	6.58087	−	4.81758i	0.222856	−	0.163144i
$873$	22.3991	+	49.6955i	0.758095	+	1.68194i
$874$	4.19754	+	4.65061i	0.141984	+	0.157309i
$875$		0			0
$876$	0.660661	+	6.01428i	0.0223217	+	0.203204i
$877$	35.8774	−	20.7138i	1.21149	−	0.699456i	0.248409	−	0.968655i	$-0.420092\pi$
$877$	35.8774	−	20.7138i	1.21149	−	0.699456i	0.963085	+	0.269199i	$0.0867590\pi$
$878$	−38.5562	−	12.4765i	−1.30121	−	0.421062i
$879$	9.88920	+	46.0068i	0.333554	+	1.55177i
$880$		0			0
$881$		−	18.8579i		−	0.635340i	−0.948201	−	0.317670i	$-0.897100\pi$
$881$		−	18.8579i		−	0.635340i	0.948201	−	0.317670i	$-0.102900\pi$
$882$	4.86101	+	43.8120i	0.163679	+	1.47523i
$883$	36.0305			1.21252			0.606261	−	0.795266i	$-0.292669\pi$
$883$	36.0305			1.21252			0.606261	+	0.795266i	$0.292669\pi$
$884$	1.97680	−	2.73462i	0.0664871	−	0.0919751i
$885$		0			0
$886$	40.1745	+	13.0002i	1.34969	+	0.436750i
$887$	16.7456	−	9.66809i	0.562263	−	0.324623i	−0.191790	−	0.981436i	$-0.561429\pi$
$887$	16.7456	−	9.66809i	0.562263	−	0.324623i	0.754053	+	0.656813i	$0.228096\pi$
$888$	8.99493	+	27.1386i	0.301850	+	0.910711i
$889$	4.51044	−	7.81231i	0.151275	−	0.262016i
$890$		0			0
$891$	−56.8183	−	11.5342i	−1.90348	−	0.386411i
$892$	−3.66190	+	35.6640i	−0.122609	+	1.19412i
$893$	−0.442950	+	0.767212i	−0.0148228	+	0.0256738i
$894$	7.80724	−	3.50871i	0.261113	−	0.117349i
$895$		0			0
$896$	−38.4007	−	27.4098i	−1.28288	−	0.915698i
$897$	−4.60505	+	4.16553i	−0.153758	+	0.139083i
$898$	−4.34716	−	20.3318i	−0.145067	−	0.678480i
$899$	−18.5529			−0.618774
$900$		0			0
$901$	−4.63785			−0.154509
$902$	13.5538	+	63.3913i	0.451291	+	2.11070i
$903$	−8.05975	−	37.4957i	−0.268212	−	1.24778i
$904$	−7.99240	−	3.52402i	−0.265823	−	0.117207i
$905$		0			0
$906$	−14.1296	−	10.1906i	−0.469424	−	0.338559i
$907$	8.55508	−	14.8178i	0.284067	−	0.492018i	−0.688316	−	0.725411i	$-0.741650\pi$
$907$	8.55508	−	14.8178i	0.284067	−	0.492018i	0.972382	+	0.233393i	$0.0749829\pi$
$908$	20.7518	+	2.13075i	0.688672	+	0.0707114i
$909$	−12.6232	−	28.0063i	−0.418685	−	0.928909i
$910$		0			0
$911$	5.66416	−	9.81062i	0.187662	−	0.325040i	−0.756808	−	0.653637i	$-0.773242\pi$
$911$	5.66416	−	9.81062i	0.187662	−	0.325040i	0.944470	+	0.328597i	$0.106576\pi$
$912$	7.68941	+	13.1030i	0.254622	+	0.433883i
$913$	65.1210	−	37.5976i	2.15519	−	1.24430i
$914$	11.8855	+	3.84606i	0.393136	+	0.127216i
$915$		0			0
$916$	−30.4522	−	22.0133i	−1.00617	−	0.727340i
$917$	7.98334			0.263633
$918$	5.22920	+	4.63254i	0.172589	+	0.152896i
$919$		−	33.3567i		−	1.10034i	−0.835054	−	0.550169i	$-0.814563\pi$
$919$		−	33.3567i		−	1.10034i	0.835054	−	0.550169i	$-0.185437\pi$
$920$		0			0
$921$	6.53871	+	2.10801i	0.215458	+	0.0694615i
$922$	−1.22896	−	0.397684i	−0.0404737	−	0.0130970i
$923$	−3.42925	+	1.97988i	−0.112875	+	0.0651685i
$924$	55.0507	+	75.0282i	1.81104	+	2.46825i
$925$		0			0
$926$	7.45853	+	8.26357i	0.245102	+	0.271558i
$927$	2.89717	−	28.8344i	0.0951555	−	0.947045i
$928$	31.8646	−	18.6529i	1.04601	−	0.612311i
$929$	9.08679	+	5.24626i	0.298128	+	0.172124i	0.641602	−	0.767038i	$-0.278270\pi$
$929$	9.08679	+	5.24626i	0.298128	+	0.172124i	−0.343474	+	0.939162i	$0.611604\pi$
$930$		0			0
$931$	−19.7313	+	11.3919i	−0.646668	+	0.373354i
$932$	13.2996	−	5.95966i	0.435643	−	0.195215i
$933$	−7.05566	−	32.8245i	−0.230992	−	1.07463i
$934$	−8.47940	−	39.6583i	−0.277454	−	1.29766i
$935$		0			0
$936$	−12.9791	+	7.63572i	−0.424235	+	0.249581i
$937$		−	29.4458i		−	0.961952i	−0.876734	−	0.480976i	$-0.840282\pi$
$937$		−	29.4458i		−	0.961952i	0.876734	−	0.480976i	$-0.159718\pi$
$938$	−62.8380	+	13.4355i	−2.05173	+	0.438684i
$939$	25.5275	+	28.2209i	0.833058	+	0.920955i
$940$		0			0
$941$	−31.2128	+	18.0207i	−1.01751	+	0.587459i	−0.913382	−	0.407105i	$-0.866538\pi$
$941$	−31.2128	+	18.0207i	−1.01751	+	0.587459i	−0.104128	+	0.994564i	$0.533205\pi$
$942$	7.05738	−	3.17171i	0.229942	−	0.103340i
$943$	−7.18714	+	12.4485i	−0.234045	+	0.405379i
$944$	10.5270	+	2.18481i	0.342624	+	0.0711095i
$945$		0			0
$946$	−32.4115	−	35.9098i	−1.05379	−	1.16753i
$947$	−10.5418	−	6.08631i	−0.342562	−	0.197778i	0.318842	−	0.947808i	$-0.396706\pi$
$947$	−10.5418	−	6.08631i	−0.342562	−	0.197778i	−0.661405	+	0.750029i	$0.730039\pi$
$948$	0.785186	+	0.345184i	0.0255016	+	0.0112110i
$949$	−1.54984	−	2.68439i	−0.0503098	−	0.0871391i
$950$		0			0
$951$	−34.1971	+	30.9332i	−1.10892	+	1.00308i
$952$	−1.21225	−	11.1475i	−0.0392891	−	0.361292i
$953$	25.0300			0.810801			0.405400	−	0.914139i	$-0.367132\pi$
$953$	25.0300			0.810801			0.405400	+	0.914139i	$0.367132\pi$
$954$	18.9564	+	8.30900i	0.613737	+	0.269014i
$955$		0			0
$956$	48.1096	+	34.7775i	1.55597	+	1.12478i
$957$	−71.2007	+	15.3047i	−2.30159	+	0.494730i
$958$	−11.4866	+	35.4972i	−0.371117	+	1.14686i
$959$	−24.3135	−	42.1122i	−0.785124	−	1.35988i
$960$		0			0
$961$	−11.4602	+	19.8497i	−0.369684	+	0.640312i
$962$	−9.81379	−	10.8730i	−0.316409	−	0.350561i
$963$	5.66592	−	7.87406i	0.182582	−	0.253738i
$964$	2.60466	−	25.3673i	0.0838905	−	0.817026i
$965$		0			0
$966$	−2.08531	+	20.5293i	−0.0670937	+	0.660521i
$967$	1.37768	+	2.38621i	0.0443032	+	0.0767353i	0.887327	−	0.461141i	$-0.152560\pi$
$967$	1.37768	+	2.38621i	0.0443032	+	0.0767353i	−0.843023	+	0.537877i	$0.819227\pi$
$968$	78.9299	+	34.8019i	2.53690	+	1.11857i
$969$	−1.10794	+	3.43665i	−0.0355923	+	0.110401i
$970$		0			0
$971$	33.6700			1.08052			0.540261	−	0.841497i	$-0.318325\pi$
$971$	33.6700			1.08052			0.540261	+	0.841497i	$0.318325\pi$
$972$	−13.0740	−	28.3032i	−0.419349	−	0.907825i
$973$		−	31.9476i		−	1.02419i
$974$	10.8869	−	2.32775i	0.348840	−	0.0745859i
$975$		0			0
$976$	5.13397	+	15.5464i	0.164334	+	0.497627i
$977$	−28.0375	−	48.5624i	−0.897000	−	1.55365i	−0.831309	−	0.555810i	$-0.812408\pi$
$977$	−28.0375	−	48.5624i	−0.897000	−	1.55365i	−0.0656907	−	0.997840i	$-0.520925\pi$
$978$	−34.3762	−	3.49182i	−1.09923	−	0.111656i
$979$	34.2475	+	19.7728i	1.09456	+	0.631942i
$980$		0			0
$981$	−7.02163	−	5.05255i	−0.224183	−	0.161315i
$982$	−18.4716	−	20.4654i	−0.589453	−	0.653076i
$983$	13.0365	+	7.52662i	0.415799	+	0.240062i	0.693278	−	0.720670i	$-0.256166\pi$
$983$	13.0365	+	7.52662i	0.415799	+	0.240062i	−0.277479	+	0.960732i	$0.589499\pi$
$984$	−23.1721	+	26.0421i	−0.738699	+	0.830191i
$985$		0			0
$986$	8.34917	+	2.70173i	0.265892	+	0.0860407i
$987$	−2.85282	+	0.613217i	−0.0908063	+	0.0195189i
$988$	−6.30773	−	4.55974i	−0.200676	−	0.145065i
$989$		−	10.7265i		−	0.341084i
$990$		0			0
$991$		−	32.4096i		−	1.02953i	−0.857333	−	0.514763i	$-0.827880\pi$
$991$		−	32.4096i		−	1.02953i	0.857333	−	0.514763i	$-0.172120\pi$
$992$	0.0964955	+	16.0791i	0.00306373	+	0.510511i
$993$	−38.5948	−	42.6670i	−1.22477	−	1.35400i
$994$	−4.05126	+	12.5196i	−0.128498	+	0.397098i
$995$		0			0
$996$	37.0167	+	16.2733i	1.17292	+	0.515639i
$997$	−38.2349	−	22.0749i	−1.21091	−	0.699120i	−0.247954	−	0.968772i	$-0.579758\pi$
$997$	−38.2349	−	22.0749i	−1.21091	−	0.699120i	−0.962958	+	0.269652i	$0.913091\pi$
$998$	−0.888641	+	0.802069i	−0.0281294	+	0.0253891i
$999$	24.4102	−	17.9925i	0.772303	−	0.569258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.o.b.299.2		48
4.3	odd	2	inner	900.2.o.b.299.15		48
5.2	odd	4		180.2.q.a.11.10	yes	48
5.3	odd	4		900.2.r.f.551.15		48
5.4	even	2		900.2.o.c.299.23		48
9.5	odd	6		900.2.o.c.599.10		48
15.2	even	4		540.2.q.a.251.15		48
20.3	even	4		900.2.r.f.551.22		48
20.7	even	4		180.2.q.a.11.3	✓	48
20.19	odd	2		900.2.o.c.299.10		48
36.23	even	6		900.2.o.c.599.23		48
45.2	even	12		1620.2.e.b.971.37		48
45.7	odd	12		1620.2.e.b.971.12		48
45.14	odd	6	inner	900.2.o.b.599.15		48
45.22	odd	12		540.2.q.a.71.22		48
45.23	even	12		900.2.r.f.851.22		48
45.32	even	12		180.2.q.a.131.3	yes	48
60.47	odd	4		540.2.q.a.251.22		48
180.7	even	12		1620.2.e.b.971.38		48
180.23	odd	12		900.2.r.f.851.15		48
180.47	odd	12		1620.2.e.b.971.11		48
180.59	even	6	inner	900.2.o.b.599.2		48
180.67	even	12		540.2.q.a.71.15		48
180.167	odd	12		180.2.q.a.131.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.3	✓	48	20.7	even	4
180.2.q.a.11.10	yes	48	5.2	odd	4
180.2.q.a.131.3	yes	48	45.32	even	12
180.2.q.a.131.10	yes	48	180.167	odd	12
540.2.q.a.71.15		48	180.67	even	12
540.2.q.a.71.22		48	45.22	odd	12
540.2.q.a.251.15		48	15.2	even	4
540.2.q.a.251.22		48	60.47	odd	4
900.2.o.b.299.2		48	1.1	even	1	trivial
900.2.o.b.299.15		48	4.3	odd	2	inner
900.2.o.b.599.2		48	180.59	even	6	inner
900.2.o.b.599.15		48	45.14	odd	6	inner
900.2.o.c.299.10		48	20.19	odd	2
900.2.o.c.299.23		48	5.4	even	2
900.2.o.c.599.10		48	9.5	odd	6
900.2.o.c.599.23		48	36.23	even	6
900.2.r.f.551.15		48	5.3	odd	4
900.2.r.f.551.22		48	20.3	even	4
900.2.r.f.851.15		48	180.23	odd	12
900.2.r.f.851.22		48	45.23	even	12
1620.2.e.b.971.11		48	180.47	odd	12
1620.2.e.b.971.12		48	45.7	odd	12
1620.2.e.b.971.37		48	45.2	even	12
1620.2.e.b.971.38		48	180.7	even	12

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.38296 + 0.295692i) q^{2} +(-1.64850 - 0.531460i) q^{3} +(1.82513 - 0.817857i) q^{4} +(2.43695 + 0.247538i) q^{6} +(-2.08506 + 3.61144i) q^{7} +(-2.28224 + 1.67074i) q^{8} +(2.43510 + 1.75222i) q^{9} +(-3.22095 + 5.57886i) q^{11} +(-3.44339 + 0.378252i) q^{12} +(1.53691 - 0.887336i) q^{13} +(1.81568 - 5.61099i) q^{14} +(2.66222 - 2.98539i) q^{16} +0.950682 q^{17} +(-3.88575 - 1.70321i) q^{18} -2.19286i q^{19} +(5.35656 - 4.84532i) q^{21} +(2.80482 - 8.66772i) q^{22} +(1.74948 - 1.01006i) q^{23} +(4.65021 - 1.54129i) q^{24} +(-1.86310 + 1.68160i) q^{26} +(-3.08303 - 4.18270i) q^{27} +(-0.851880 + 8.29663i) q^{28} +(-5.65260 - 3.26353i) q^{29} +(2.46164 - 1.42123i) q^{31} +(-2.79898 + 4.91587i) q^{32} +(8.27468 - 7.48493i) q^{33} +(-1.31475 + 0.281109i) q^{34} +(5.87745 + 1.20647i) q^{36} +5.83599i q^{37} +(0.648412 + 3.03263i) q^{38} +(-3.00518 + 0.645966i) q^{39} +(-6.16222 + 3.55776i) q^{41} +(-5.97516 + 8.28476i) q^{42} +(2.65491 - 4.59844i) q^{43} +(-1.31596 + 12.8164i) q^{44} +(-2.12079 + 1.91418i) q^{46} +(-0.349867 - 0.201996i) q^{47} +(-5.97529 + 3.50656i) q^{48} +(-5.19498 - 8.99797i) q^{49} +(-1.56720 - 0.505249i) q^{51} +(2.07935 - 2.87648i) q^{52} -4.87844 q^{53} +(5.50048 + 4.87286i) q^{54} +(-1.27513 - 11.7258i) q^{56} +(-1.16542 + 3.61494i) q^{57} +(8.78229 + 2.84189i) q^{58} +(1.34391 + 2.32773i) q^{59} +(-2.04652 + 3.54468i) q^{61} +(-2.98409 + 2.69338i) q^{62} +(-11.4054 + 5.14072i) q^{63} +(2.41728 - 7.62606i) q^{64} +(-9.23028 + 12.7981i) q^{66} +(-5.44797 - 9.43616i) q^{67} +(1.73512 - 0.777522i) q^{68} +(-3.42083 + 0.735311i) q^{69} -2.23126 q^{71} +(-8.48500 + 0.0694119i) q^{72} -1.74662i q^{73} +(-1.72565 - 8.07091i) q^{74} +(-1.79345 - 4.00227i) q^{76} +(-13.4318 - 23.2645i) q^{77} +(3.96502 - 1.78195i) q^{78} +(-0.214428 - 0.123800i) q^{79} +(2.85943 + 8.53368i) q^{81} +(7.47008 - 6.74234i) q^{82} +(-10.1090 - 5.83641i) q^{83} +(5.81365 - 13.2243i) q^{84} +(-2.31191 + 7.14448i) q^{86} +(7.58387 + 8.38406i) q^{87} +(-1.96979 - 18.1137i) q^{88} -6.13881i q^{89} +7.40061i q^{91} +(2.36695 - 3.27433i) q^{92} +(-4.81334 + 1.03463i) q^{93} +(0.543580 + 0.175899i) q^{94} +(7.22670 - 6.61626i) q^{96} +(15.7357 + 9.08503i) q^{97} +(9.84505 + 10.9077i) q^{98} +(-17.6187 + 7.94125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} - 12 q^{8} - 4 q^{9} - 28 q^{12} + 30 q^{14} + 18 q^{18} - 4 q^{21} + 42 q^{22} + 28 q^{24} + 12 q^{29} + 48 q^{33} + 6 q^{34} + 42 q^{36} + 6 q^{38} - 60 q^{41} - 16 q^{42} - 12 q^{46} + 74 q^{48}+ \cdots - 84 q^{98}+O(q^{100}) \) 48 * q + 6 * q^6 - 12 * q^8 - 4 * q^9 - 28 * q^12 + 30 * q^14 + 18 * q^18 - 4 * q^21 + 42 * q^22 + 28 * q^24 + 12 * q^29 + 48 * q^33 + 6 * q^34 + 42 * q^36 + 6 * q^38 - 60 * q^41 - 16 * q^42 - 12 * q^46 + 74 * q^48 - 24 * q^49 + 90 * q^52 + 32 * q^54 - 42 * q^56 + 16 * q^57 - 84 * q^58 - 84 * q^62 + 48 * q^64 + 16 * q^66 - 6 * q^68 - 36 * q^69 + 80 * q^72 - 84 * q^74 + 6 * q^76 + 46 * q^78 - 50 * q^84 - 54 * q^86 - 114 * q^88 + 42 * q^92 + 24 * q^93 - 18 * q^94 - 18 * q^96 + 48 * q^97 - 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more