LMFDB - Embedded newform 735.2.y.i.263.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(128,735)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("735.128"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.7
Character	$\chi$	$=$	735.263
Dual form			735.2.y.i.422.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0799329 - 0.298314i) q^{2} +(-0.540759 + 1.64547i) q^{3} +(1.64945 + 0.952310i) q^{4} +(-0.596180 - 2.15513i) q^{5} +(0.447643 + 0.292843i) q^{6} +(0.852694 - 0.852694i) q^{8} +(-2.41516 - 1.77961i) q^{9} +(-0.690558 + 0.00558322i) q^{10} +(0.660315 + 0.381233i) q^{11} +(-2.45895 + 2.19915i) q^{12} +(2.27077 + 2.27077i) q^{13} +(3.86859 + 0.184406i) q^{15} +(1.71841 + 2.97637i) q^{16} +(4.69471 - 1.25794i) q^{17} +(-0.723932 + 0.578226i) q^{18} +(1.41761 - 0.818455i) q^{19} +(1.06898 - 4.12252i) q^{20} +(0.166508 - 0.166508i) q^{22} +(7.39003 + 1.98015i) q^{23} +(0.941983 + 1.86419i) q^{24} +(-4.28914 + 2.56969i) q^{25} +(0.858909 - 0.495891i) q^{26} +(4.23432 - 3.01174i) q^{27} -4.94251 q^{29} +(0.364238 - 1.13931i) q^{30} +(-2.96413 + 5.13403i) q^{31} +(3.35485 - 0.898930i) q^{32} +(-0.984380 + 0.880375i) q^{33} -1.50105i q^{34} +(-2.28894 - 5.23535i) q^{36} +(3.41587 + 0.915280i) q^{37} +(-0.130843 - 0.488313i) q^{38} +(-4.96442 + 2.50855i) q^{39} +(-2.34602 - 1.32930i) q^{40} -4.35963i q^{41} +(2.69037 + 2.69037i) q^{43} +(0.726104 + 1.25765i) q^{44} +(-2.39541 + 6.26594i) q^{45} +(1.18141 - 2.04627i) q^{46} +(-1.10971 + 4.14148i) q^{47} +(-5.82678 + 1.21809i) q^{48} +(0.423730 + 1.48491i) q^{50} +(-0.468795 + 8.40527i) q^{51} +(1.58304 + 5.90798i) q^{52} +(-1.79889 - 6.71354i) q^{53} +(-0.559982 - 1.50389i) q^{54} +(0.427939 - 1.65035i) q^{55} +(0.580162 + 2.77522i) q^{57} +(-0.395069 + 1.47442i) q^{58} +(-3.84501 + 6.65975i) q^{59} +(6.20543 + 3.98826i) q^{60} +(2.19699 + 3.80529i) q^{61} +(1.29462 + 1.29462i) q^{62} +5.80098i q^{64} +(3.54000 - 6.24757i) q^{65} +(0.183944 + 0.364025i) q^{66} +(0.0126297 + 0.0471345i) q^{67} +(8.94164 + 2.39591i) q^{68} +(-7.25451 + 11.0893i) q^{69} -12.4172i q^{71} +(-3.57685 + 0.541931i) q^{72} +(1.34043 - 0.359168i) q^{73} +(0.546081 - 0.945840i) q^{74} +(-1.90896 - 8.44724i) q^{75} +3.11769 q^{76} +(0.351513 + 1.68147i) q^{78} +(3.66808 - 2.11777i) q^{79} +(5.38997 - 5.47784i) q^{80} +(2.66599 + 8.59607i) q^{81} +(-1.30054 - 0.348478i) q^{82} +(5.05351 - 5.05351i) q^{83} +(-5.50993 - 9.36774i) q^{85} +(1.01762 - 0.587525i) q^{86} +(2.67271 - 8.13276i) q^{87} +(0.888122 - 0.237971i) q^{88} +(0.453600 + 0.785658i) q^{89} +(1.67774 + 1.21544i) q^{90} +(10.3038 + 10.3038i) q^{92} +(-6.84502 - 7.65367i) q^{93} +(1.14676 + 0.662081i) q^{94} +(-2.60902 - 2.56717i) q^{95} +(-0.335002 + 6.00642i) q^{96} +(-3.73061 + 3.73061i) q^{97} +(-0.916321 - 2.09584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{3} + 24 q^{6} + 8 q^{10} + 10 q^{12} + 16 q^{13} + 4 q^{15} - 8 q^{16} + 14 q^{18} - 8 q^{22} + 4 q^{25} - 40 q^{27} + 40 q^{30} + 24 q^{31} + 4 q^{33} + 8 q^{36} + 4 q^{37} + 16 q^{40} + 16 q^{43}+ \cdots + 120 q^{97}+O(q^{100}) $ 48 * q + 2 * q^3 + 24 * q^6 + 8 * q^10 + 10 * q^12 + 16 * q^13 + 4 * q^15 - 8 * q^16 + 14 * q^18 - 8 * q^22 + 4 * q^25 - 40 * q^27 + 40 * q^30 + 24 * q^31 + 4 * q^33 + 8 * q^36 + 4 * q^37 + 16 * q^40 + 16 * q^43 - 40 * q^45 - 32 * q^46 - 44 * q^48 + 8 * q^51 - 36 * q^52 + 40 * q^55 - 88 * q^57 + 56 * q^58 - 50 * q^60 + 8 * q^61 - 76 * q^66 + 12 * q^67 - 34 * q^72 - 52 * q^73 - 6 * q^75 - 64 * q^76 - 120 * q^78 + 20 * q^81 - 104 * q^82 - 24 * q^85 + 46 * q^87 + 84 * q^90 - 44 * q^93 - 12 * q^96 + 120 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.0799329	−	0.298314i	0.0565211	−	0.210940i	−0.931890	−	0.362741i	$-0.881841\pi$
$2$	0.0799329	−	0.298314i	0.0565211	−	0.210940i	0.988411	+	0.151802i	$0.0485075\pi$
$3$	−0.540759	+	1.64547i	−0.312207	+	0.950014i
$3$	−0.540759	+	1.64547i	−0.312207	+	0.950014i
$4$	1.64945	+	0.952310i	0.824725	+	0.476155i
$5$	−0.596180	−	2.15513i	−0.266620	−	0.963802i
$5$	−0.596180	−	2.15513i	−0.266620	−	0.963802i
$6$	0.447643	+	0.292843i	0.182749	+	0.119553i
$7$		0			0
$7$		0			0
$8$	0.852694	−	0.852694i	0.301473	−	0.301473i
$9$	−2.41516	−	1.77961i	−0.805053	−	0.593203i
$10$	−0.690558	+	0.00558322i	−0.218374	+	0.00176557i
$11$	0.660315	+	0.381233i	0.199092	+	0.114946i	0.596232	−	0.802812i	$-0.296664\pi$
$11$	0.660315	+	0.381233i	0.199092	+	0.114946i	−0.397140	+	0.917758i	$0.629997\pi$
$12$	−2.45895	+	2.19915i	−0.709839	+	0.634841i
$13$	2.27077	+	2.27077i	0.629797	+	0.629797i	0.948017	−	0.318220i	$-0.103085\pi$
$13$	2.27077	+	2.27077i	0.629797	+	0.629797i	−0.318220	+	0.948017i	$0.603085\pi$
$14$		0			0
$15$	3.86859	+	0.184406i	0.998866	+	0.0476133i
$16$	1.71841	+	2.97637i	0.429602	+	0.744092i
$17$	4.69471	−	1.25794i	1.13864	−	0.305096i	0.360233	−	0.932862i	$-0.382697\pi$
$17$	4.69471	−	1.25794i	1.13864	−	0.305096i	0.778402	+	0.627766i	$0.216030\pi$
$18$	−0.723932	+	0.578226i	−0.170632	+	0.136289i
$19$	1.41761	−	0.818455i	0.325221	−	0.187767i	−0.328496	−	0.944505i	$-0.606542\pi$
$19$	1.41761	−	0.818455i	0.325221	−	0.187767i	0.653717	+	0.756739i	$0.273209\pi$
$20$	1.06898	−	4.12252i	0.239031	−	0.921823i
$21$		0			0
$22$	0.166508	−	0.166508i	0.0354996	−	0.0354996i
$23$	7.39003	+	1.98015i	1.54093	+	0.412890i	0.926566	−	0.376133i	$-0.122747\pi$
$23$	7.39003	+	1.98015i	1.54093	+	0.412890i	0.614363	+	0.789024i	$0.289413\pi$
$24$	0.941983	+	1.86419i	0.192281	+	0.380525i
$25$	−4.28914	+	2.56969i	−0.857828	+	0.513937i
$26$	0.858909	−	0.495891i	0.168446	−	0.0972523i
$27$	4.23432	−	3.01174i	0.814894	−	0.579610i
$28$		0			0
$29$	−4.94251			−0.917801			−0.458900	−	0.888488i	$-0.651757\pi$
$29$	−4.94251			−0.917801			−0.458900	+	0.888488i	$0.651757\pi$
$30$	0.364238	−	1.13931i	0.0665005	−	0.208009i
$31$	−2.96413	+	5.13403i	−0.532374	+	0.922099i	0.466911	+	0.884304i	$0.345367\pi$
$31$	−2.96413	+	5.13403i	−0.532374	+	0.922099i	−0.999286	+	0.0377949i	$0.987967\pi$
$32$	3.35485	−	0.898930i	0.593060	−	0.158910i
$33$	−0.984380	+	0.880375i	−0.171358	+	0.153254i
$34$		−	1.50105i		−	0.257428i
$35$		0			0
$36$	−2.28894	−	5.23535i	−0.381491	−	0.872559i
$37$	3.41587	+	0.915280i	0.561566	+	0.150471i	0.528426	−	0.848980i	$-0.322783\pi$
$37$	3.41587	+	0.915280i	0.561566	+	0.150471i	0.0331401	+	0.999451i	$0.489449\pi$
$38$	−0.130843	−	0.488313i	−0.0212255	−	0.0792148i
$39$	−4.96442	+	2.50855i	−0.794943	+	0.401689i
$40$	−2.34602	−	1.32930i	−0.370939	−	0.210181i
$41$		−	4.35963i		−	0.680860i	−0.940270	−	0.340430i	$-0.889427\pi$
$41$		−	4.35963i		−	0.680860i	0.940270	−	0.340430i	$-0.110573\pi$
$42$		0			0
$43$	2.69037	+	2.69037i	0.410277	+	0.410277i	0.881835	−	0.471558i	$-0.156308\pi$
$43$	2.69037	+	2.69037i	0.410277	+	0.410277i	−0.471558	+	0.881835i	$0.656308\pi$
$44$	0.726104	+	1.25765i	0.109464	+	0.189598i
$45$	−2.39541	+	6.26594i	−0.357087	+	0.934071i
$46$	1.18141	−	2.04627i	0.174190	−	0.301706i
$47$	−1.10971	+	4.14148i	−0.161867	+	0.604097i	0.836552	+	0.547888i	$0.184568\pi$
$47$	−1.10971	+	4.14148i	−0.161867	+	0.604097i	−0.998419	+	0.0562089i	$0.982099\pi$
$48$	−5.82678	+	1.21809i	−0.841023	+	0.175817i
$49$		0			0
$50$	0.423730	+	1.48491i	0.0599244	+	0.209998i
$51$	−0.468795	+	8.40527i	−0.0656444	+	1.17697i
$52$	1.58304	+	5.90798i	0.219528	+	0.819290i
$53$	−1.79889	−	6.71354i	−0.247096	−	0.922176i	−0.972318	−	0.233661i	$-0.924929\pi$
$53$	−1.79889	−	6.71354i	−0.247096	−	0.922176i	0.725222	−	0.688515i	$-0.241737\pi$
$54$	−0.559982	−	1.50389i	−0.0762039	−	0.204654i
$55$	0.427939	−	1.65035i	0.0577032	−	0.222533i
$56$		0			0
$57$	0.580162	+	2.77522i	0.0768444	+	0.367587i
$58$	−0.395069	+	1.47442i	−0.0518751	+	0.193601i
$59$	−3.84501	+	6.65975i	−0.500577	+	0.867026i	0.499422	+	0.866359i	$0.333546\pi$
$59$	−3.84501	+	6.65975i	−0.500577	+	0.867026i	−1.00000		0.000666931i	$0.999788\pi$
$60$	6.20543	+	3.98826i	0.801118	+	0.514883i
$61$	2.19699	+	3.80529i	0.281295	+	0.487218i	0.971704	−	0.236202i	$-0.0759026\pi$
$61$	2.19699	+	3.80529i	0.281295	+	0.487218i	−0.690409	+	0.723420i	$0.742569\pi$
$62$	1.29462	+	1.29462i	0.164417	+	0.164417i
$63$		0			0
$64$			5.80098i			0.725122i
$65$	3.54000	−	6.24757i	0.439083	−	0.774916i
$66$	0.183944	+	0.364025i	0.0226419	+	0.0448084i
$67$	0.0126297	+	0.0471345i	0.00154296	+	0.00575840i	0.966693	−	0.255939i	$-0.0823845\pi$
$67$	0.0126297	+	0.0471345i	0.00154296	+	0.00575840i	−0.965150	+	0.261697i	$0.915718\pi$
$68$	8.94164	+	2.39591i	1.08433	+	0.290546i
$69$	−7.25451	+	11.0893i	−0.873341	+	1.33500i
$70$		0			0
$71$		−	12.4172i		−	1.47365i	−0.676082	−	0.736826i	$-0.736324\pi$
$71$		−	12.4172i		−	1.47365i	0.676082	−	0.736826i	$-0.263676\pi$
$72$	−3.57685	+	0.541931i	−0.421536	+	0.0638672i
$73$	1.34043	−	0.359168i	0.156886	−	0.0420374i	−0.179521	−	0.983754i	$-0.557455\pi$
$73$	1.34043	−	0.359168i	0.156886	−	0.0420374i	0.336407	+	0.941717i	$0.390788\pi$
$74$	0.546081	−	0.945840i	0.0634806	−	0.109952i
$75$	−1.90896	−	8.44724i	−0.220428	−	0.975403i
$76$	3.11769			0.357624
$77$		0			0
$78$	0.351513	+	1.68147i	0.0398010	+	0.190389i
$79$	3.66808	−	2.11777i	0.412692	−	0.238268i	−0.279254	−	0.960217i	$-0.590087\pi$
$79$	3.66808	−	2.11777i	0.412692	−	0.238268i	0.691946	+	0.721950i	$0.256754\pi$
$80$	5.38997	−	5.47784i	0.602617	−	0.612441i
$81$	2.66599	+	8.59607i	0.296221	+	0.955119i
$82$	−1.30054	−	0.348478i	−0.143620	−	0.0384830i
$83$	5.05351	−	5.05351i	0.554695	−	0.554695i	−0.373097	−	0.927792i	$-0.621704\pi$
$83$	5.05351	−	5.05351i	0.554695	−	0.554695i	0.927792	+	0.373097i	$0.121704\pi$
$84$		0			0
$85$	−5.50993	−	9.36774i	−0.597635	−	1.01607i
$86$	1.01762	−	0.587525i	0.109733	−	0.0633544i
$87$	2.67271	−	8.13276i	0.286544	−	0.871924i
$88$	0.888122	−	0.237971i	0.0946741	−	0.0253678i
$89$	0.453600	+	0.785658i	0.0480815	+	0.0832796i	0.889065	−	0.457782i	$-0.151356\pi$
$89$	0.453600	+	0.785658i	0.0480815	+	0.0832796i	−0.840983	+	0.541061i	$0.818023\pi$
$90$	1.67774	+	1.21544i	0.176850	+	0.128118i
$91$		0			0
$92$	10.3038	+	10.3038i	1.07424	+	1.07424i
$93$	−6.84502	−	7.65367i	−0.709796	−	0.793649i
$94$	1.14676	+	0.662081i	0.118279	+	0.0682884i
$95$	−2.60902	−	2.56717i	−0.267680	−	0.263386i
$96$	−0.335002	+	6.00642i	−0.0341910	+	0.613028i
$97$	−3.73061	+	3.73061i	−0.378786	+	0.378786i	−0.870664	−	0.491878i	$-0.836311\pi$
$97$	−3.73061	+	3.73061i	−0.378786	+	0.378786i	0.491878	+	0.870664i	$0.336311\pi$
$98$		0			0
$99$	−0.916321	−	2.09584i	−0.0920937	−	0.210640i
$100$	−9.52185	+	0.153980i	−0.952185	+	0.0153980i
$101$	−16.4444	−	9.49420i	−1.63628	−	0.944708i	−0.982098	−	0.188373i	$-0.939679\pi$
$101$	−16.4444	−	9.49420i	−1.63628	−	0.944708i	−0.654185	−	0.756335i	$-0.726988\pi$
$102$	2.46993	+	0.811705i	0.244560	+	0.0803708i
$103$	3.26921	−	12.2009i	0.322125	−	1.20219i	−0.595046	−	0.803692i	$-0.702866\pi$
$103$	3.26921	−	12.2009i	0.322125	−	1.20219i	0.917171	−	0.398494i	$-0.130467\pi$
$104$	3.87254			0.379733
$105$		0			0
$106$	−2.14653			−0.208490
$107$	−0.564395	+	2.10635i	−0.0545621	+	0.203629i	−0.987826	−	0.155563i	$-0.950281\pi$
$107$	−0.564395	+	2.10635i	−0.0545621	+	0.203629i	0.933264	+	0.359192i	$0.116948\pi$
$108$	9.85240	−	0.935331i	0.948047	−	0.0900023i
$109$	−2.04357	−	1.17986i	−0.195739	−	0.113010i	0.398928	−	0.916982i	$-0.369382\pi$
$109$	−2.04357	−	1.17986i	−0.195739	−	0.113010i	−0.594666	+	0.803973i	$0.702716\pi$
$110$	−0.458114	−	0.259577i	−0.0436795	−	0.0247497i
$111$	−3.35323	+	5.12578i	−0.318275	+	0.486517i
$112$		0			0
$113$	−11.9386	+	11.9386i	−1.12309	+	1.12309i	−0.131814	+	0.991274i	$0.542080\pi$
$113$	−11.9386	+	11.9386i	−1.12309	+	1.12309i	−0.991274	+	0.131814i	$0.957920\pi$
$114$	0.874260	+	0.0487609i	0.0818819	+	0.00456688i
$115$	−0.138311	−	17.1070i	−0.0128976	−	1.59523i
$116$	−8.15242	−	4.70680i	−0.756933	−	0.437015i
$117$	−1.44319	−	9.52533i	−0.133423	−	0.880617i
$118$	1.67935	+	1.67935i	0.154597	+	0.154597i
$119$		0			0
$120$	3.45597	−	3.14148i	0.315485	−	0.286777i
$121$	−5.20932	−	9.02281i	−0.473575	−	0.820256i
$122$	1.31078	−	0.351223i	0.118673	−	0.0317983i
$123$	7.17366	+	2.35751i	0.646827	+	0.212570i
$124$	−9.77837	+	5.64555i	−0.878124	+	0.506985i
$125$	8.09510	+	7.71164i	0.724048	+	0.689750i
$126$		0			0
$127$	4.46126	−	4.46126i	0.395873	−	0.395873i	−0.480901	−	0.876775i	$-0.659691\pi$
$127$	4.46126	−	4.46126i	0.395873	−	0.395873i	0.876775	+	0.480901i	$0.159691\pi$
$128$	8.44022	+	2.26155i	0.746017	+	0.199895i
$129$	−5.88177	+	2.97209i	−0.517861	+	0.261678i
$130$	−1.58077	−	1.55542i	−0.138643	−	0.136419i
$131$	−1.86149	+	1.07473i	−0.162639	+	0.0938999i	−0.579111	−	0.815249i	$-0.696600\pi$
$131$	−1.86149	+	1.07473i	−0.162639	+	0.0938999i	0.416471	+	0.909149i	$0.363267\pi$
$132$	−2.46207	+	0.514699i	−0.214296	+	0.0447988i
$133$		0			0
$134$	0.0150704			0.00130188
$135$	−9.01509	−	7.32994i	−0.775896	−	0.630861i
$136$	2.93051	−	5.07580i	0.251289	−	0.435246i
$137$	−8.51678	+	2.28207i	−0.727638	+	0.194970i	−0.603577	−	0.797305i	$-0.706258\pi$
$137$	−8.51678	+	2.28207i	−0.727638	+	0.194970i	−0.124061	+	0.992275i	$0.539592\pi$
$138$	2.72822	+	3.05052i	0.232241	+	0.259678i
$139$		−	10.3626i		−	0.878941i	−0.898257	−	0.439471i	$-0.855166\pi$
$139$		−	10.3626i		−	0.878941i	0.898257	−	0.439471i	$-0.144834\pi$
$140$		0			0
$141$	−6.21461	−	4.06553i	−0.523364	−	0.342380i
$142$	−3.70423	−	0.992544i	−0.310852	−	0.0832925i
$143$	0.633730	+	2.36511i	0.0529951	+	0.197780i
$144$	1.14654	−	10.2465i	0.0955452	−	0.853875i
$145$	2.94663	+	10.6517i	0.244704	+	0.884578i
$146$		−	0.428578i		−	0.0354694i
$147$		0			0
$148$	4.76267	+	4.76267i	0.391489	+	0.391489i
$149$	8.72716	+	15.1159i	0.714957	+	1.23834i	0.962976	+	0.269586i	$0.0868870\pi$
$149$	8.72716	+	15.1159i	0.714957	+	1.23834i	−0.248019	+	0.968755i	$0.579780\pi$
$150$	−2.67252	−	0.105744i	−0.218210	−	0.00863393i
$151$	7.60786	−	13.1772i	0.619119	−	1.07235i	−0.370528	−	0.928821i	$-0.620823\pi$
$151$	7.60786	−	13.1772i	0.619119	−	1.07235i	0.989647	−	0.143524i	$-0.0458434\pi$
$152$	0.510892	−	1.90668i	0.0414388	−	0.154652i
$153$	−13.5771	−	5.31661i	−1.09765	−	0.429823i
$154$		0			0
$155$	12.8316	+	3.32727i	1.03066	+	0.267253i
$156$	−10.5775	−	0.589947i	−0.846875	−	0.0472336i
$157$	−2.36469	−	8.82516i	−0.188723	−	0.704324i	−0.993803	−	0.111158i	$-0.964544\pi$
$157$	−2.36469	−	8.82516i	−0.188723	−	0.704324i	0.805080	−	0.593167i	$-0.202122\pi$
$158$	−0.338559	−	1.26352i	−0.0269343	−	0.100520i
$159$	12.0197	+	0.670387i	0.953225	+	0.0531652i
$160$	−3.93740	−	6.69421i	−0.311279	−	0.529223i
$161$		0			0
$162$	2.77743	−	0.108192i	0.218215	−	0.00850040i
$163$	0.700710	−	2.61508i	0.0548838	−	0.204829i	−0.933039	−	0.359775i	$-0.882854\pi$
$163$	0.700710	−	2.61508i	0.0548838	−	0.204829i	0.987923	+	0.154946i	$0.0495202\pi$
$164$	4.15172	−	7.19099i	0.324195	−	0.561522i
$165$	2.48419	+	1.59660i	0.193394	+	0.124295i
$166$	−1.10359	−	1.91147i	−0.0856551	−	0.148359i
$167$	−3.85551	−	3.85551i	−0.298348	−	0.298348i	0.542018	−	0.840367i	$-0.317660\pi$
$167$	−3.85551	−	3.85551i	−0.298348	−	0.298348i	−0.840367	+	0.542018i	$0.817660\pi$
$168$		0			0
$169$		−	2.68725i		−	0.206712i
$170$	−3.23495	+	0.894896i	−0.248109	+	0.0686354i
$171$	−4.88027	−	0.546083i	−0.373204	−	0.0417600i
$172$	1.87556	+	6.99969i	0.143010	+	0.533721i
$173$	−1.27815	−	0.342481i	−0.0971763	−	0.0260383i	0.209903	−	0.977722i	$-0.432685\pi$
$173$	−1.27815	−	0.342481i	−0.0971763	−	0.0260383i	−0.307080	+	0.951684i	$0.599352\pi$
$174$	−2.21248	−	1.44738i	−0.167727	−	0.109726i
$175$		0			0
$176$			2.62045i			0.197524i
$177$	−8.87921	−	9.92818i	−0.667403	−	0.746247i
$178$	0.270630	−	0.0725151i	0.0202846	−	0.00543524i
$179$	0.120836	−	0.209294i	0.00903168	−	0.0156433i	−0.861474	−	0.507801i	$-0.830458\pi$
$179$	0.120836	−	0.209294i	0.00903168	−	0.0156433i	0.870506	+	0.492158i	$0.163792\pi$
$180$	−9.91822	+	8.05418i	−0.739261	+	0.600323i
$181$	−18.6864			−1.38895			−0.694475	−	0.719517i	$-0.744363\pi$
$181$	−18.6864			−1.38895			−0.694475	+	0.719517i	$0.744363\pi$
$182$		0			0
$183$	−7.44955	+	1.55734i	−0.550686	+	0.115122i
$184$	7.98990	−	4.61297i	0.589023	−	0.340073i
$185$	−0.0639312	−	7.90730i	−0.00470032	−	0.581357i
$186$	−2.83034	+	1.43018i	−0.207530	+	0.104866i
$187$	3.57956	+	0.959140i	0.261763	+	0.0701393i
$188$	−5.77437	+	5.77437i	−0.421140	+	0.421140i
$189$		0			0
$190$	−0.974370	+	0.573106i	−0.0706882	+	0.0415775i
$191$	−12.3330	+	7.12049i	−0.892388	+	0.515220i	−0.874723	−	0.484624i	$-0.838957\pi$
$191$	−12.3330	+	7.12049i	−0.892388	+	0.515220i	−0.0176651	+	0.999844i	$0.505623\pi$
$192$	−9.54535	−	3.13693i	−0.688876	−	0.226388i
$193$	−6.58385	+	1.76414i	−0.473916	+	0.126985i	−0.487868	−	0.872917i	$-0.662225\pi$
$193$	−6.58385	+	1.76414i	−0.473916	+	0.126985i	0.0139523	+	0.999903i	$0.495559\pi$
$194$	0.814694	+	1.41109i	0.0584916	+	0.101310i
$195$	8.36592	+	9.20340i	0.599096	+	0.659069i
$196$		0			0
$197$	−7.65626	−	7.65626i	−0.545486	−	0.545486i	0.379646	−	0.925132i	$-0.376046\pi$
$197$	−7.65626	−	7.65626i	−0.545486	−	0.545486i	−0.925132	+	0.379646i	$0.876046\pi$
$198$	−0.698462	+	0.105824i	−0.0496375	+	0.00752061i
$199$	14.1855	+	8.19000i	1.00558	+	0.580573i	0.909895	−	0.414838i	$-0.136162\pi$
$199$	14.1855	+	8.19000i	1.00558	+	0.580573i	0.0956874	+	0.995411i	$0.469495\pi$
$200$	−1.46617	+	5.84848i	−0.103674	+	0.413550i
$201$	−0.0843881	−	0.00470666i	−0.00595228	−	0.000331982i
$202$	−4.14670	+	4.14670i	−0.291761	+	0.291761i
$203$		0			0
$204$	−8.77767	+	13.4176i	−0.614560	+	0.939421i
$205$	−9.39556	+	2.59913i	−0.656214	+	0.181531i
$206$	−3.37836	−	1.95050i	−0.235382	−	0.135898i
$207$	−14.3242	−	17.9337i	−0.995601	−	1.24648i
$208$	−2.85654	+	10.6607i	−0.198065	+	0.739189i
$209$	1.24809			0.0863321
$210$		0			0
$211$	−25.5028			−1.75568			−0.877842	−	0.478950i	$-0.841018\pi$
$211$	−25.5028			−1.75568			−0.877842	+	0.478950i	$0.841018\pi$
$212$	3.42620	−	12.7867i	0.235312	−	0.878197i
$213$	20.4322	+	6.71472i	1.39999	+	0.460085i
$214$	0.583239	+	0.336733i	0.0398694	+	0.0230186i
$215$	4.19414	−	7.40203i	0.286038	−	0.504814i
$216$	1.04248	−	6.17867i	0.0709320	−	0.420405i
$217$		0			0
$218$	−0.515316	+	0.515316i	−0.0349016	+	0.0349016i
$219$	−0.133850	+	2.39987i	−0.00904475	+	0.162168i
$220$	2.27750	−	2.31463i	0.153549	−	0.156052i
$221$	13.5171	+	7.80410i	0.909258	+	0.524960i
$222$	1.26106	+	1.41003i	0.0846365	+	0.0946352i
$223$	15.4546	+	15.4546i	1.03491	+	1.03491i	0.999368	+	0.0355465i	$0.0113172\pi$
$223$	15.4546	+	15.4546i	1.03491	+	1.03491i	0.0355465	+	0.999368i	$0.488683\pi$
$224$		0			0
$225$	14.9320	+	1.42678i	0.995466	+	0.0951186i
$226$	2.60716	+	4.51573i	0.173426	+	0.300382i
$227$	−12.4101	+	3.32527i	−0.823686	+	0.220706i	−0.645957	−	0.763374i	$-0.723542\pi$
$227$	−12.4101	+	3.32527i	−0.823686	+	0.220706i	−0.177728	+	0.984080i	$0.556875\pi$
$228$	−1.68592	+	5.13008i	−0.111653	+	0.339748i
$229$	13.2508	−	7.65038i	0.875641	−	0.505551i	0.00642204	−	0.999979i	$-0.497956\pi$
$229$	13.2508	−	7.65038i	0.875641	−	0.505551i	0.869219	+	0.494428i	$0.164622\pi$
$230$	−5.11430	−	1.32615i	−0.337227	−	0.0874438i
$231$		0			0
$232$	−4.21445	+	4.21445i	−0.276692	+	0.276692i
$233$	−6.62761	−	1.77586i	−0.434189	−	0.116341i	0.0351029	−	0.999384i	$-0.488824\pi$
$233$	−6.62761	−	1.77586i	−0.434189	−	0.116341i	−0.469292	+	0.883043i	$0.655491\pi$
$234$	−2.95690	−	0.330865i	−0.193298	−	0.0216293i
$235$	9.58699	−	0.0775117i	0.625387	−	0.00505630i
$236$	−12.6843	+	7.32328i	−0.825677	+	0.476705i
$237$	1.50118	+	7.18093i	0.0975122	+	0.466452i
$238$		0			0
$239$	−18.7082			−1.21013			−0.605067	−	0.796174i	$-0.706854\pi$
$239$	−18.7082			−1.21013			−0.605067	+	0.796174i	$0.706854\pi$
$240$	6.09896	+	11.8312i	0.393686	+	0.763703i
$241$	−0.986063	+	1.70791i	−0.0635179	+	0.110016i	−0.896036	−	0.443982i	$-0.853565\pi$
$241$	−0.986063	+	1.70791i	−0.0635179	+	0.110016i	0.832518	+	0.553998i	$0.186899\pi$
$242$	−3.10802	+	0.832793i	−0.199791	+	0.0535339i
$243$	−15.5863	−	0.261589i	−0.999859	−	0.0167810i
$244$			8.36885i			0.535761i
$245$		0			0
$246$	1.27669	−	1.95156i	0.0813987	−	0.124427i
$247$	5.07757	+	1.36053i	0.323078	+	0.0865685i
$248$	1.85026	+	6.90525i	0.117491	+	0.438484i
$249$	5.58268	+	11.0481i	0.353788	+	0.700148i
$250$	2.94755	−	1.79847i	0.186420	−	0.113745i
$251$		−	17.9016i		−	1.12994i	−0.825112	−	0.564970i	$-0.808888\pi$
$251$		−	17.9016i		−	1.12994i	0.825112	−	0.564970i	$-0.191112\pi$
$252$		0			0
$253$	4.12485	+	4.12485i	0.259327	+	0.259327i
$254$	−0.974254	−	1.68746i	−0.0611301	−	0.105881i
$255$	18.3939	−	4.00074i	1.15187	−	0.250536i
$256$	−4.45168	+	7.71053i	−0.278230	+	0.481908i
$257$	5.10358	−	19.0468i	0.318353	−	1.18811i	−0.602475	−	0.798138i	$-0.705819\pi$
$257$	5.10358	−	19.0468i	0.318353	−	1.18811i	0.920827	−	0.389971i	$-0.127515\pi$
$258$	0.416467	+	1.99218i	0.0259281	+	0.124028i
$259$		0			0
$260$	11.7887	−	6.93387i	0.731102	−	0.430021i
$261$	11.9369	+	8.79573i	0.738879	+	0.544442i
$262$	0.171813	+	0.641215i	0.0106147	+	0.0396144i
$263$	−1.43607	−	5.35948i	−0.0885517	−	0.330480i	0.907411	−	0.420244i	$-0.138055\pi$
$263$	−1.43607	−	5.35948i	−0.0885517	−	0.330480i	−0.995963	+	0.0897640i	$0.971389\pi$
$264$	−0.0886842	+	1.59006i	−0.00545813	+	0.0978617i
$265$	−13.3961	+	7.87931i	−0.822914	+	0.484022i
$266$		0			0
$267$	−1.53807	+	0.321534i	−0.0941281	+	0.0196776i
$268$	−0.0240547	+	0.0897733i	−0.00146937	+	0.00548378i
$269$	−5.02321	+	8.70045i	−0.306270	+	0.530476i	−0.977543	−	0.210734i	$-0.932414\pi$
$269$	−5.02321	+	8.70045i	−0.306270	+	0.530476i	0.671273	+	0.741210i	$0.265748\pi$
$270$	−2.90723	+	2.10342i	−0.176928	+	0.128010i
$271$	−2.82028	−	4.88486i	−0.171320	−	0.296734i	0.767562	−	0.640975i	$-0.221470\pi$
$271$	−2.82028	−	4.88486i	−0.171320	−	0.296734i	−0.938881	+	0.344241i	$0.888136\pi$
$272$	11.8115	+	11.8115i	0.716180	+	0.716180i
$273$		0			0
$274$			2.72309i			0.164508i
$275$	−3.81183	+	0.0616420i	−0.229862	+	0.00371715i
$276$	−22.5264	+	11.3827i	−1.35593	+	0.685158i
$277$	2.91038	+	10.8617i	0.174868	+	0.652615i	0.996574	+	0.0827040i	$0.0263556\pi$
$277$	2.91038	+	10.8617i	0.174868	+	0.652615i	−0.821707	+	0.569911i	$0.806978\pi$
$278$	−3.09130	−	0.828310i	−0.185404	−	0.0496787i
$279$	16.2954	−	7.12451i	0.975581	−	0.426533i
$280$		0			0
$281$		−	1.92831i		−	0.115033i	−0.998345	−	0.0575167i	$-0.981682\pi$
$281$		−	1.92831i		−	0.115033i	0.998345	−	0.0575167i	$-0.0183183\pi$
$282$	−1.70956	+	1.52893i	−0.101803	+	0.0910466i
$283$	−25.4667	+	6.82379i	−1.51384	+	0.405632i	−0.917709	−	0.397254i	$-0.869963\pi$
$283$	−25.4667	+	6.82379i	−1.51384	+	0.405632i	−0.596132	+	0.802887i	$0.703296\pi$
$284$	11.8250	−	20.4816i	0.701687	−	1.21536i
$285$	5.63507	−	2.90485i	0.333793	−	0.172069i
$286$	0.756201			0.0447151
$287$		0			0
$288$	−9.70225	−	3.79926i	−0.571710	−	0.223874i
$289$	5.73548	−	3.31138i	0.337381	−	0.194787i
$290$	3.41309	−	0.0275951i	0.200424	−	0.00162044i
$291$	−4.12126	−	8.15598i	−0.241592	−	0.478112i
$292$	2.55301	+	0.684078i	0.149404	+	0.0400326i
$293$	−7.83332	+	7.83332i	−0.457627	+	0.457627i	−0.897876	−	0.440249i	$-0.854890\pi$
$293$	−7.83332	+	7.83332i	−0.457627	+	0.457627i	0.440249	+	0.897876i	$0.354890\pi$
$294$		0			0
$295$	16.6449	+	4.31607i	0.969105	+	0.251291i
$296$	3.69315	−	2.13224i	0.214660	−	0.123934i
$297$	3.94416	−	0.374436i	0.228863	−	0.0217270i
$298$	5.20686	−	1.39517i	0.301625	−	0.0808203i
$299$	12.2846	+	21.2775i	0.710435	+	1.23051i
$300$	4.89566	−	15.7512i	0.282651	−	0.909397i
$301$		0			0
$302$	−3.32282	−	3.32282i	−0.191207	−	0.191207i
$303$	24.5149	−	21.9248i	1.40835	−	1.25955i
$304$	4.87205	+	2.81288i	0.279431	+	0.161330i
$305$	6.89109	−	7.00343i	0.394583	−	0.401015i
$306$	−2.67128	+	3.62527i	−0.152707	+	0.207243i
$307$	17.0769	−	17.0769i	0.974628	−	0.974628i	−0.0250576	−	0.999686i	$-0.507977\pi$
$307$	17.0769	−	17.0769i	0.974628	−	0.974628i	0.999686	+	0.0250576i	$0.00797691\pi$
$308$		0			0
$309$	18.3083	+	11.9771i	1.04152	+	0.681354i
$310$	2.01824	−	3.56190i	0.114628	−	0.202302i
$311$	20.4797	+	11.8240i	1.16130	+	0.670475i	0.951615	−	0.307294i	$-0.0994235\pi$
$311$	20.4797	+	11.8240i	1.16130	+	0.670475i	0.209683	+	0.977769i	$0.432757\pi$
$312$	−2.09411	+	6.37215i	−0.118556	+	0.360752i
$313$	3.20409	−	11.9578i	0.181106	−	0.675895i	−0.814325	−	0.580409i	$-0.802893\pi$
$313$	3.20409	−	11.9578i	0.181106	−	0.675895i	0.995431	−	0.0954864i	$-0.0304406\pi$
$314$	−2.82168			−0.159237
$315$		0			0
$316$	8.06709			0.453809
$317$	1.13684	−	4.24276i	0.0638515	−	0.238297i	−0.926623	−	0.375991i	$-0.877302\pi$
$317$	1.13684	−	4.24276i	0.0638515	−	0.238297i	0.990475	+	0.137694i	$0.0439691\pi$
$318$	1.16076	−	3.53206i	0.0650920	−	0.198068i
$319$	−3.26361	−	1.88425i	−0.182727	−	0.105498i
$320$	12.5018	−	3.45843i	0.698874	−	0.193332i
$321$	−3.16074	−	2.06772i	−0.176415	−	0.115409i
$322$		0			0
$323$	5.62568	−	5.62568i	0.313021	−	0.313021i
$324$	−3.78871	+	16.7176i	−0.210484	+	0.928758i
$325$	−15.5748	−	3.90447i	−0.863933	−	0.216581i
$326$	−0.724106	−	0.418063i	−0.0401045	−	0.0231543i
$327$	3.04650	−	2.72462i	0.168472	−	0.150672i
$328$	−3.71743	−	3.71743i	−0.205261	−	0.205261i
$329$		0			0
$330$	0.674856	−	0.613446i	0.0371496	−	0.0337691i
$331$	3.10933	+	5.38552i	0.170904	+	0.296015i	0.938736	−	0.344636i	$-0.111998\pi$
$331$	3.10933	+	5.38552i	0.170904	+	0.296015i	−0.767832	+	0.640651i	$0.778664\pi$
$332$	13.1480	−	3.52300i	0.721591	−	0.193350i
$333$	−6.62103	−	8.28946i	−0.362830	−	0.454259i
$334$	−1.45833	+	0.841970i	−0.0797965	+	0.0460705i
$335$	0.0940513	−	0.0553192i	0.00513857	−	0.00302241i
$336$		0			0
$337$	15.0501	−	15.0501i	0.819833	−	0.819833i	−0.166250	−	0.986084i	$-0.553166\pi$
$337$	15.0501	−	15.0501i	0.819833	−	0.819833i	0.986084	+	0.166250i	$0.0531659\pi$
$338$	−0.801644	−	0.214800i	−0.0436037	−	0.0116836i
$339$	−13.1887	−	26.1005i	−0.716313	−	1.41759i
$340$	−0.167351	−	20.6988i	−0.00907590	−	1.12255i
$341$	−3.91452	+	2.26005i	−0.211983	+	0.122389i
$342$	−0.552999	+	1.41220i	−0.0299027	+	0.0763632i
$343$		0			0
$344$	4.58812			0.247375
$345$	28.2239	+	9.02317i	1.51952	+	0.485791i
$346$	−0.204333	+	0.353916i	−0.0109850	+	0.0190266i
$347$	18.6057	−	4.98539i	0.998808	−	0.267630i	0.277862	−	0.960621i	$-0.410374\pi$
$347$	18.6057	−	4.98539i	0.998808	−	0.267630i	0.720946	+	0.692991i	$0.243708\pi$
$348$	12.1534	−	10.8693i	0.651491	−	0.582657i
$349$		−	9.24369i		−	0.494803i	−0.968913	−	0.247402i	$-0.920423\pi$
$349$		−	9.24369i		−	0.494803i	0.968913	−	0.247402i	$-0.0795767\pi$
$350$		0			0
$351$	16.4541	+	2.77618i	0.878254	+	0.148182i
$352$	2.55796	+	0.685404i	0.136340	+	0.0365321i
$353$	3.05649	+	11.4070i	0.162681	+	0.607132i	0.998325	+	0.0578609i	$0.0184280\pi$
$353$	3.05649	+	11.4070i	0.162681	+	0.607132i	−0.835644	+	0.549271i	$0.814905\pi$
$354$	−3.67145	+	1.85520i	−0.195135	+	0.0986029i
$355$	−26.7607	+	7.40290i	−1.42031	+	0.392905i
$356$			1.72787i			0.0915769i
$357$		0			0
$358$	−0.0527764	−	0.0527764i	−0.00278932	−	0.00278932i
$359$	−6.98129	−	12.0920i	−0.368459	−	0.638189i	0.620866	−	0.783917i	$-0.286781\pi$
$359$	−6.98129	−	12.0920i	−0.368459	−	0.638189i	−0.989325	+	0.145728i	$0.953448\pi$
$360$	3.30038	+	7.38548i	0.173945	+	0.389249i
$361$	−8.16026	+	14.1340i	−0.429487	+	0.743894i
$362$	−1.49366	+	5.57441i	−0.0785050	+	0.292985i
$363$	17.6638	−	3.69263i	0.927108	−	0.193813i
$364$		0			0
$365$	−1.57319	−	2.67467i	−0.0823446	−	0.139999i
$366$	−0.130889	+	2.34678i	−0.00684170	+	0.122668i
$367$	3.90370	+	14.5688i	0.203771	+	0.760485i	0.989821	+	0.142321i	$0.0454565\pi$
$367$	3.90370	+	14.5688i	0.203771	+	0.760485i	−0.786049	+	0.618164i	$0.787877\pi$
$368$	6.80542	+	25.3982i	0.354757	+	1.32397i
$369$	−7.75844	+	10.5292i	−0.403888	+	0.548129i
$370$	−2.36397	−	0.612982i	−0.122897	−	0.0318674i
$371$		0			0
$372$	−4.00185	−	19.1429i	−0.207486	−	0.992515i
$373$	−9.01635	+	33.6495i	−0.466849	+	1.74230i	0.183837	+	0.982957i	$0.441148\pi$
$373$	−9.01635	+	33.6495i	−0.466849	+	1.74230i	−0.650686	+	0.759347i	$0.725519\pi$
$374$	0.572249	−	0.991165i	0.0295903	−	0.0512519i
$375$	−17.0668	+	9.15013i	−0.881325	+	0.472511i
$376$	2.58517	+	4.47765i	0.133320	+	0.230917i
$377$	−11.2233	−	11.2233i	−0.578028	−	0.578028i
$378$		0			0
$379$		−	19.0602i		−	0.979056i	−0.871988	−	0.489528i	$-0.837169\pi$
$379$		−	19.0602i		−	0.979056i	0.871988	−	0.489528i	$-0.162831\pi$
$380$	−1.85871	−	6.71902i	−0.0953496	−	0.344678i
$381$	4.92842	+	9.75335i	0.252491	+	0.499680i
$382$	1.13832	+	4.24828i	0.0582417	+	0.217361i
$383$	−9.81007	−	2.62860i	−0.501271	−	0.134315i	−0.000681261	−	1.00000i	$-0.500217\pi$
$383$	−9.81007	−	2.62860i	−0.501271	−	0.134315i	−0.500590	+	0.865685i	$0.666884\pi$
$384$	−8.28544	+	12.6652i	−0.422815	+	0.646318i
$385$		0			0
$386$			2.10507i			0.107145i
$387$	−1.70987	−	11.2855i	−0.0869174	−	0.573672i
$388$	−9.70615	+	2.60076i	−0.492755	+	0.132033i
$389$	−18.6290	+	32.2664i	−0.944528	+	1.63597i	−0.187835	+	0.982201i	$0.560147\pi$
$389$	−18.6290	+	32.2664i	−0.944528	+	1.63597i	−0.756693	+	0.653770i	$0.773186\pi$
$390$	3.41421	−	1.76001i	0.172885	−	0.0891218i
$391$	37.1850			1.88053
$392$		0			0
$393$	−0.761825	−	3.64421i	−0.0384290	−	0.183826i
$394$	−2.89595	+	1.67198i	−0.145896	+	0.0842331i
$395$	−6.75090	−	6.64261i	−0.339675	−	0.334226i
$396$	0.484465	−	4.32960i	0.0243453	−	0.217571i
$397$	−8.58658	−	2.30077i	−0.430948	−	0.115472i	0.0368231	−	0.999322i	$-0.488276\pi$
$397$	−8.58658	−	2.30077i	−0.430948	−	0.115472i	−0.467771	+	0.883850i	$0.654943\pi$
$398$	3.57708	−	3.57708i	0.179303	−	0.179303i
$399$		0			0
$400$	−15.0188	−	8.35029i	−0.750941	−	0.417514i
$401$	−4.02832	+	2.32575i	−0.201165	+	0.116142i	−0.597199	−	0.802093i	$-0.703720\pi$
$401$	−4.02832	+	2.32575i	−0.201165	+	0.116142i	0.396034	+	0.918236i	$0.370386\pi$
$402$	−0.00814945	+	0.0247979i	−0.000406458	+	0.00123681i
$403$	−18.3890	+	4.92733i	−0.916023	+	0.245448i
$404$	−18.0828	−	31.3204i	−0.899655	−	1.55825i
$405$	16.9362	−	10.8704i	0.841567	−	0.540152i
$406$		0			0
$407$	1.90662	+	1.90662i	0.0945074	+	0.0945074i
$408$	6.76738	+	7.56686i	0.335035	+	0.374615i
$409$	23.0006	+	13.2794i	1.13731	+	0.656626i	0.945763	−	0.324858i	$-0.105317\pi$
$409$	23.0006	+	13.2794i	1.13731	+	0.656626i	0.191546	+	0.981484i	$0.438650\pi$
$410$	0.0243408	+	3.01058i	0.00120211	+	0.148682i
$411$	0.850451	−	15.2482i	0.0419497	−	0.752137i
$412$	17.0114	−	17.0114i	0.838091	−	0.838091i
$413$		0			0
$414$	−6.49486	+	2.83961i	−0.319205	+	0.139559i
$415$	−13.9038	−	7.87815i	−0.682508	−	0.386723i
$416$	9.65934	+	5.57682i	0.473588	+	0.273426i
$417$	17.0513	+	5.60365i	0.835007	+	0.274412i
$418$	0.0997634	−	0.372322i	0.00487959	−	0.0182109i
$419$	−25.8278			−1.26177			−0.630885	−	0.775876i	$-0.717308\pi$
$419$	−25.8278			−1.26177			−0.630885	+	0.775876i	$0.717308\pi$
$420$		0			0
$421$	0.432430			0.0210753			0.0105377	−	0.999944i	$-0.496646\pi$
$421$	0.432430			0.0210753			0.0105377	+	0.999944i	$0.496646\pi$
$422$	−2.03851	+	7.60783i	−0.0992332	+	0.370343i
$423$	10.0503	−	8.02749i	0.488664	−	0.390310i
$424$	−7.25850	−	4.19070i	−0.352504	−	0.203518i
$425$	−16.9038	+	17.4594i	−0.819952	+	0.846908i
$426$	3.63630	−	5.55847i	0.176179	−	0.269309i
$427$		0			0
$428$	−2.93684	+	2.93684i	−0.141957	+	0.141957i
$429$	−4.23442	−	0.236170i	−0.204440	−	0.0114024i
$430$	−1.87288	−	1.84283i	−0.0903181	−	0.0888694i
$431$	14.1264	+	8.15586i	0.680443	+	0.392854i	0.800022	−	0.599971i	$-0.204821\pi$
$431$	14.1264	+	8.15586i	0.680443	+	0.392854i	−0.119579	+	0.992825i	$0.538154\pi$
$432$	16.2403	+	7.42749i	0.781363	+	0.357355i
$433$	0.514238	+	0.514238i	0.0247127	+	0.0247127i	0.719355	−	0.694642i	$-0.244437\pi$
$433$	0.514238	+	0.514238i	0.0247127	+	0.0247127i	−0.694642	+	0.719355i	$0.744437\pi$
$434$		0			0
$435$	−19.1205	−	0.911426i	−0.916760	−	0.0436995i
$436$	−2.24718	−	3.89223i	−0.107620	−	0.186404i
$437$	12.0968	−	3.24133i	0.578669	−	0.155054i
$438$	0.705214	+	0.231758i	0.0336964	+	0.0110738i
$439$	−13.2487	+	7.64917i	−0.632328	+	0.365075i	−0.781653	−	0.623713i	$-0.785623\pi$
$439$	−13.2487	+	7.64917i	−0.632328	+	0.365075i	0.149325	+	0.988788i	$0.452290\pi$
$440$	−1.04234	−	1.77214i	−0.0496916	−	0.0844835i
$441$		0			0
$442$	3.40853	−	3.40853i	0.162127	−	0.162127i
$443$	−8.81439	−	2.36181i	−0.418784	−	0.112213i	0.0432723	−	0.999063i	$-0.486222\pi$
$443$	−8.81439	−	2.36181i	−0.418784	−	0.112213i	−0.462057	+	0.886850i	$0.652888\pi$
$444$	−10.4123	+	5.26139i	−0.494146	+	0.249695i
$445$	1.42276	−	1.44596i	0.0674455	−	0.0685450i
$446$	5.84564	−	3.37498i	0.276799	−	0.159810i
$447$	−29.5921	+	6.18625i	−1.39966	+	0.292600i
$448$		0			0
$449$	9.40891			0.444034			0.222017	−	0.975043i	$-0.428736\pi$
$449$	9.40891			0.444034			0.222017	+	0.975043i	$0.428736\pi$
$450$	1.61919	−	4.34037i	0.0763291	−	0.204607i
$451$	1.66204	−	2.87873i	0.0782622	−	0.135554i
$452$	−31.0613	+	8.32286i	−1.46100	+	0.391474i
$453$	17.5687	+	19.6442i	0.825450	+	0.922966i
$454$			3.96789i			0.186222i
$455$		0			0
$456$	2.86111	+	1.87171i	0.133984	+	0.0876509i
$457$	33.3520	+	8.93665i	1.56014	+	0.418039i	0.932708	−	0.360631i	$-0.117439\pi$
$457$	33.3520	+	8.93665i	1.56014	+	0.418039i	0.627434	+	0.778670i	$0.284105\pi$
$458$	−1.22303	−	4.56443i	−0.0571486	−	0.213282i
$459$	16.0903	−	19.4658i	0.751031	−	0.908585i
$460$	16.0630	−	28.3488i	0.748942	−	1.32177i
$461$			36.9326i			1.72012i	0.510192	+	0.860061i	$0.329574\pi$
$461$			36.9326i			1.72012i	−0.510192	+	0.860061i	$0.670426\pi$
$462$		0			0
$463$	26.3687	+	26.3687i	1.22546	+	1.22546i	0.965664	+	0.259794i	$0.0836548\pi$
$463$	26.3687	+	26.3687i	1.22546	+	1.22546i	0.259794	+	0.965664i	$0.416345\pi$
$464$	−8.49325	−	14.7107i	−0.394289	−	0.682929i
$465$	−12.4138	+	19.3149i	−0.575675	+	0.895705i
$466$	−1.05953	+	1.83516i	−0.0490817	+	0.0850120i
$467$	−2.63979	+	9.85183i	−0.122155	+	0.455888i	−0.999722	−	0.0235650i	$-0.992498\pi$
$467$	−2.63979	+	9.85183i	−0.122155	+	0.455888i	0.877567	+	0.479453i	$0.159165\pi$
$468$	6.69060	−	17.0859i	0.309273	−	0.789797i
$469$		0			0
$470$	0.743194	−	2.86613i	0.0342810	−	0.132205i
$471$	15.8003	+	0.881244i	0.728039	+	0.0406056i
$472$	2.40011	+	8.95734i	0.110474	+	0.412295i
$473$	0.750833	+	2.80215i	0.0345233	+	0.128843i
$474$	2.26216	+	0.126170i	0.103905	+	0.00579517i
$475$	−3.97713	+	7.15327i	−0.182483	+	0.328215i
$476$		0			0
$477$	−7.60287	+	19.4156i	−0.348112	+	0.888979i
$478$	−1.49540	+	5.58092i	−0.0683981	+	0.255265i
$479$	−6.85350	+	11.8706i	−0.313144	+	0.542382i	−0.979041	−	0.203662i	$-0.934716\pi$
$479$	−6.85350	+	11.8706i	−0.313144	+	0.542382i	0.665897	+	0.746044i	$0.268049\pi$
$480$	13.1443	−	2.85894i	0.599953	−	0.130492i
$481$	5.67825	+	9.83503i	0.258906	+	0.448439i
$482$	0.430674	+	0.430674i	0.0196167	+	0.0196167i
$483$		0			0
$484$		−	19.8436i		−	0.901980i
$485$	10.2641	+	5.81582i	0.466067	+	0.264083i
$486$	−1.32389	+	4.62869i	−0.0600529	+	0.209961i
$487$	−5.91662	−	22.0811i	−0.268108	−	1.00059i	−0.960321	−	0.278898i	$-0.910031\pi$
$487$	−5.91662	−	22.0811i	−0.268108	−	1.00059i	0.692213	−	0.721693i	$-0.256636\pi$
$488$	5.11811	+	1.37139i	0.231686	+	0.0620800i
$489$	3.92413	+	2.56713i	0.177455	+	0.116090i
$490$		0			0
$491$		−	23.7476i		−	1.07172i	−0.844308	−	0.535858i	$-0.819988\pi$
$491$		−	23.7476i		−	1.07172i	0.844308	−	0.535858i	$-0.180012\pi$
$492$	9.58750	+	10.7201i	0.432238	+	0.483301i
$493$	−23.2037	+	6.21740i	−1.04504	+	0.280018i
$494$	0.811730	−	1.40596i	0.0365215	−	0.0632570i
$495$	−3.97051	+	3.22429i	−0.178461	+	0.144921i
$496$	−20.3744			−0.914836
$497$		0			0
$498$	3.74205	−	0.782280i	0.167685	−	0.0350548i
$499$	−2.80187	+	1.61766i	−0.125429	+	0.0724165i	−0.561402	−	0.827543i	$-0.689738\pi$
$499$	−2.80187	+	1.61766i	−0.125429	+	0.0724165i	0.435973	+	0.899960i	$0.356404\pi$
$500$	6.00859	+	20.4290i	0.268712	+	0.913612i
$501$	8.42904	−	4.25924i	0.376582	−	0.190289i
$502$	−5.34029	−	1.43093i	−0.238349	−	0.0638654i
$503$	2.62851	−	2.62851i	0.117199	−	0.117199i	−0.646075	−	0.763274i	$-0.723591\pi$
$503$	2.62851	−	2.62851i	0.117199	−	0.117199i	0.763274	+	0.646075i	$0.223591\pi$
$504$		0			0
$505$	−10.6573	+	41.1001i	−0.474246	+	1.82893i
$506$	1.56021	−	0.900788i	0.0693598	−	0.0400449i
$507$	4.42180	+	1.45316i	0.196379	+	0.0645369i
$508$	11.6071	−	3.11012i	0.514983	−	0.137989i
$509$	−6.91189	−	11.9717i	−0.306364	−	0.530638i	0.671200	−	0.741276i	$-0.265779\pi$
$509$	−6.91189	−	11.9717i	−0.306364	−	0.530638i	−0.977564	+	0.210638i	$0.932446\pi$
$510$	0.276802	−	5.80694i	0.0122570	−	0.257136i
$511$		0			0
$512$	14.3017	+	14.3017i	0.632050	+	0.632050i
$513$	3.53762	−	7.73506i	0.156190	−	0.341511i
$514$	−5.27399	−	3.04494i	−0.232626	−	0.134306i
$515$	−28.2434	+	0.228350i	−1.24455	+	0.0100623i
$516$	−12.5320	−	0.698960i	−0.551691	−	0.0307700i
$517$	−2.31162	+	2.31162i	−0.101665	+	0.101665i
$518$		0			0
$519$	1.25472	−	1.91797i	0.0550759	−	0.0841895i
$520$	−2.30873	−	8.34580i	−0.101244	−	0.365988i
$521$	−9.49156	−	5.47996i	−0.415833	−	0.240081i	0.277460	−	0.960737i	$-0.410507\pi$
$521$	−9.49156	−	5.47996i	−0.415833	−	0.240081i	−0.693293	+	0.720656i	$0.743841\pi$
$522$	3.57804	−	2.85789i	0.156607	−	0.125086i
$523$	−3.54814	+	13.2418i	−0.155149	+	0.579026i	0.843943	+	0.536433i	$0.180229\pi$
$523$	−3.54814	+	13.2418i	−0.155149	+	0.579026i	−0.999093	+	0.0425929i	$0.986438\pi$
$524$	−4.09392			−0.178844
$525$		0			0
$526$	−1.71360			−0.0747163
$527$	−7.45743	+	27.8315i	−0.324851	+	1.21236i
$528$	−4.31189	−	1.41703i	−0.187651	−	0.0616685i
$529$	30.7730	+	17.7668i	1.33796	+	0.772469i
$530$	1.27972	+	4.62605i	0.0555875	+	0.200943i
$531$	21.1381	−	9.24175i	0.917313	−	0.401058i
$532$		0			0
$533$	9.89970	−	9.89970i	0.428804	−	0.428804i
$534$	−0.0270240	+	0.484527i	−0.00116944	+	0.0209676i
$535$	4.87593	−	0.0394223i	0.210805	−	0.00170438i
$536$	0.0509605	+	0.0294221i	0.00220116	+	0.00127084i
$537$	0.279044	+	0.312009i	0.0120416	+	0.0134642i
$538$	2.19394	+	2.19394i	0.0945876	+	0.0945876i
$539$		0			0
$540$	−7.88956	−	20.6755i	−0.339513	−	0.889733i
$541$	−3.53276	−	6.11892i	−0.151885	−	0.263073i	0.780035	−	0.625735i	$-0.215201\pi$
$541$	−3.53276	−	6.11892i	−0.151885	−	0.263073i	−0.931920	+	0.362663i	$0.881868\pi$
$542$	−1.68265	+	0.450866i	−0.0722762	+	0.0193663i
$543$	10.1048	−	30.7480i	0.433640	−	1.31952i
$544$	14.6193	−	8.44044i	0.626796	−	0.361881i
$545$	−1.32440	+	5.10756i	−0.0567312	+	0.218784i
$546$		0			0
$547$	−19.7665	+	19.7665i	−0.845154	+	0.845154i	−0.989524	−	0.144370i	$-0.953885\pi$
$547$	−19.7665	+	19.7665i	−0.845154	+	0.845154i	0.144370	+	0.989524i	$0.453885\pi$
$548$	−16.2212	−	4.34647i	−0.692937	−	0.185672i
$549$	1.46586	−	13.1002i	0.0625612	−	0.559101i
$550$	−0.286302	+	1.14205i	−0.0122080	+	0.0486971i
$551$	−7.00653	+	4.04522i	−0.298488	+	0.172332i
$552$	3.26991	+	15.6417i	0.139176	+	0.665753i
$553$		0			0
$554$	3.47282			0.147546
$555$	13.0458	+	4.17075i	0.553764	+	0.177038i
$556$	9.86837	−	17.0925i	0.418512	−	0.724884i
$557$	42.2902	−	11.3316i	1.79189	−	0.480137i	0.799228	−	0.601028i	$-0.205242\pi$
$557$	42.2902	−	11.3316i	1.79189	−	0.480137i	0.992666	+	0.120891i	$0.0385751\pi$
$558$	−0.822798	−	5.43063i	−0.0348318	−	0.229897i
$559$			12.2184i			0.516783i
$560$		0			0
$561$	−3.51392	+	5.37140i	−0.148358	+	0.226781i
$562$	−0.575242	−	0.154136i	−0.0242651	−	0.00650182i
$563$	−2.87110	−	10.7151i	−0.121002	−	0.451587i	0.878663	−	0.477442i	$-0.158436\pi$
$563$	−2.87110	−	10.7151i	−0.121002	−	0.451587i	−0.999666	+	0.0258549i	$0.991769\pi$
$564$	−6.37903	−	12.6241i	−0.268606	−	0.531571i
$565$	32.8467	+	18.6116i	1.38187	+	0.782997i
$566$			8.14252i			0.342256i
$567$		0			0
$568$	−10.5881	−	10.5881i	−0.444266	−	0.444266i
$569$	−6.90318	−	11.9567i	−0.289396	−	0.501249i	0.684269	−	0.729229i	$-0.260121\pi$
$569$	−6.90318	−	11.9567i	−0.289396	−	0.501249i	−0.973666	+	0.227980i	$0.926788\pi$
$570$	−0.416131	−	1.91321i	−0.0174298	−	0.0801356i
$571$	6.56260	−	11.3668i	0.274636	−	0.475684i	−0.695407	−	0.718616i	$-0.744776\pi$
$571$	6.56260	−	11.3668i	0.274636	−	0.475684i	0.970043	+	0.242932i	$0.0781092\pi$
$572$	−1.20701	+	4.50464i	−0.0504678	+	0.188348i
$573$	−5.04736	−	24.1442i	−0.210857	−	1.00864i
$574$		0			0
$575$	−36.7852	+	10.4969i	−1.53405	+	0.437752i
$576$	10.3235	−	14.0103i	0.430144	−	0.583762i
$577$	3.94772	+	14.7331i	0.164346	+	0.613347i	0.998123	+	0.0612453i	$0.0195072\pi$
$577$	3.94772	+	14.7331i	0.164346	+	0.613347i	−0.833777	+	0.552101i	$0.813826\pi$
$578$	−0.529377	−	1.97566i	−0.0220192	−	0.0821767i
$579$	0.657437	−	11.7875i	0.0273221	−	0.489873i
$580$	−5.28344	+	20.3756i	−0.219383	+	0.846050i
$581$		0			0
$582$	−2.76247	+	0.577496i	−0.114508	+	0.0239380i
$583$	1.37159	−	5.11885i	0.0568055	−	0.212001i
$584$	0.836718	−	1.44924i	0.0346236	−	0.0599699i
$585$	−19.6679	+	8.78907i	−0.813167	+	0.363383i
$586$	1.71065	+	2.96293i	0.0706662	+	0.122397i
$587$	5.54217	+	5.54217i	0.228750	+	0.228750i	0.812170	−	0.583421i	$-0.198286\pi$
$587$	5.54217	+	5.54217i	0.228750	+	0.228750i	−0.583421	+	0.812170i	$0.698286\pi$
$588$		0			0
$589$			9.70404i			0.399848i
$590$	2.61802	−	4.62041i	0.107782	−	0.190219i
$591$	16.7384	−	8.45798i	0.688524	−	0.347915i
$592$	3.14565	+	11.7397i	0.129285	+	0.482499i
$593$	8.37814	+	2.24492i	0.344049	+	0.0921877i	0.426706	−	0.904390i	$-0.359674\pi$
$593$	8.37814	+	2.24492i	0.344049	+	0.0921877i	−0.0826570	+	0.996578i	$0.526341\pi$
$594$	0.203568	−	1.20653i	0.00835252	−	0.0495043i
$595$		0			0
$596$			33.2438i			1.36172i
$597$	−21.1473	+	18.9130i	−0.865503	+	0.774058i
$598$	7.32931	−	1.96388i	0.299718	−	0.0803091i
$599$	−7.93869	+	13.7502i	−0.324366	+	0.561819i	−0.981384	−	0.192056i	$-0.938484\pi$
$599$	−7.93869	+	13.7502i	−0.324366	+	0.561819i	0.657018	+	0.753875i	$0.271818\pi$
$600$	−8.83067	−	5.57515i	−0.360511	−	0.227605i
$601$	−41.5249			−1.69384			−0.846919	−	0.531722i	$-0.821545\pi$
$601$	−41.5249			−1.69384			−0.846919	+	0.531722i	$0.821545\pi$
$602$		0			0
$603$	0.0533783	−	0.136313i	0.00217373	−	0.00555110i
$604$	25.0976	−	14.4901i	1.02120	−	0.589593i
$605$	−16.3396	+	16.6060i	−0.664299	+	0.675129i
$606$	−4.58092	−	9.06565i	−0.186087	−	0.368267i
$607$	−14.7681	−	3.95710i	−0.599418	−	0.160614i	−0.0536641	−	0.998559i	$-0.517090\pi$
$607$	−14.7681	−	3.95710i	−0.599418	−	0.160614i	−0.545754	+	0.837945i	$0.683757\pi$
$608$	4.02013	−	4.02013i	0.163038	−	0.163038i
$609$		0			0
$610$	−1.53839	−	2.61551i	−0.0622877	−	0.105899i
$611$	−11.9242	+	6.88444i	−0.482402	+	0.278515i
$612$	−17.3317	−	21.6991i	−0.700593	−	0.877135i
$613$	−29.7879	+	7.98165i	−1.20312	+	0.322376i	−0.804060	−	0.594548i	$-0.797331\pi$
$613$	−29.7879	+	7.98165i	−1.20312	+	0.322376i	−0.399063	+	0.916924i	$0.630664\pi$
$614$	−3.72926	−	6.45927i	−0.150501	−	0.260675i
$615$	0.803941	−	16.8656i	0.0324180	−	0.680088i
$616$		0			0
$617$	−13.2098	−	13.2098i	−0.531808	−	0.531808i	0.389302	−	0.921110i	$-0.372716\pi$
$617$	−13.2098	−	13.2098i	−0.531808	−	0.531808i	−0.921110	+	0.389302i	$0.872716\pi$
$618$	5.03637	−	4.50426i	0.202593	−	0.181188i
$619$	14.7495	+	8.51561i	0.592831	+	0.342271i	0.766216	−	0.642583i	$-0.222137\pi$
$619$	14.7495	+	8.51561i	0.592831	+	0.342271i	−0.173385	+	0.984854i	$0.555471\pi$
$620$	17.9965	+	17.7079i	0.722758	+	0.711165i
$621$	37.2554	−	13.8723i	1.49501	−	0.556675i
$622$	5.16425	−	5.16425i	0.207068	−	0.207068i
$623$		0			0
$624$	−15.9973	−	10.4652i	−0.640403	−	0.418945i
$625$	11.7934	−	22.0435i	0.471736	−	0.881740i
$626$	−3.31107	−	1.91165i	−0.132337	−	0.0764047i
$627$	−0.674915	+	2.05370i	−0.0269535	+	0.0820167i
$628$	4.50384	−	16.8086i	0.179723	−	0.670735i
$629$	17.1879			0.685327
$630$		0			0
$631$	6.51082			0.259191			0.129596	−	0.991567i	$-0.458632\pi$
$631$	6.51082			0.259191			0.129596	+	0.991567i	$0.458632\pi$
$632$	1.32194	−	4.93356i	0.0525841	−	0.196247i
$633$	13.7909	−	41.9641i	0.548138	−	1.66792i
$634$	−1.17480	−	0.678272i	−0.0466573	−	0.0269376i
$635$	−12.2743	−	6.95487i	−0.487091	−	0.275996i
$636$	19.1875	+	12.5523i	0.760834	+	0.497730i
$637$		0			0
$638$	−0.822967	+	0.822967i	−0.0325816	+	0.0325816i
$639$	−22.0978	+	29.9896i	−0.874174	+	1.18637i
$640$	−0.157967	−	19.5380i	−0.00624418	−	0.772308i
$641$	−36.6801	−	21.1773i	−1.44878	−	0.836451i	−0.450367	−	0.892843i	$-0.648707\pi$
$641$	−36.6801	−	21.1773i	−1.44878	−	0.836451i	−0.998409	+	0.0563924i	$0.982040\pi$
$642$	−0.869478	+	0.777613i	−0.0343155	+	0.0306899i
$643$	−11.2098	−	11.2098i	−0.442072	−	0.442072i	0.450636	−	0.892708i	$-0.351197\pi$
$643$	−11.2098	−	11.2098i	−0.442072	−	0.442072i	−0.892708	+	0.450636i	$0.851197\pi$
$644$		0			0
$645$	9.91181	+	10.9040i	0.390277	+	0.429347i
$646$	−1.22854	−	2.12790i	−0.0483363	−	0.0837209i
$647$	−22.9610	+	6.15237i	−0.902689	+	0.241875i	−0.680171	−	0.733054i	$-0.738094\pi$
$647$	−22.9610	+	6.15237i	−0.902689	+	0.241875i	−0.222518	+	0.974929i	$0.571428\pi$
$648$	9.60309	+	5.05655i	0.377245	+	0.198640i
$649$	−5.07783	+	2.93169i	−0.199322	+	0.115079i
$650$	−2.40969	+	4.33408i	−0.0945160	+	0.169996i
$651$		0			0
$652$	3.64616	−	3.64616i	0.142794	−	0.142794i
$653$	−21.0505	−	5.64046i	−0.823769	−	0.220728i	−0.177775	−	0.984071i	$-0.556890\pi$
$653$	−21.0505	−	5.64046i	−0.823769	−	0.220728i	−0.645994	+	0.763343i	$0.723557\pi$
$654$	−0.569277	−	1.12660i	−0.0222605	−	0.0440535i
$655$	3.42597	+	3.37102i	0.133864	+	0.131717i
$656$	12.9759	−	7.49163i	0.506623	−	0.292499i
$657$	−3.87653	−	1.51800i	−0.151238	−	0.0592227i
$658$		0			0
$659$	42.6184			1.66018			0.830088	−	0.557632i	$-0.188290\pi$
$659$	42.6184			1.66018			0.830088	+	0.557632i	$0.188290\pi$
$660$	2.57708	+	4.99923i	0.100313	+	0.194595i
$661$	22.7467	−	39.3985i	0.884744	−	1.53242i	0.0387381	−	0.999249i	$-0.487666\pi$
$661$	22.7467	−	39.3985i	0.884744	−	1.53242i	0.846006	−	0.533173i	$-0.179000\pi$
$662$	1.85511	−	0.497076i	0.0721010	−	0.0193194i
$663$	−20.1509	+	18.0219i	−0.782597	+	0.699911i
$664$		−	8.61819i		−	0.334451i
$665$		0			0
$666$	−3.00210	+	1.31254i	−0.116329	+	0.0508601i
$667$	−36.5253	−	9.78693i	−1.41427	−	0.378951i
$668$	−2.68783	−	10.0311i	−0.103995	−	0.388115i
$669$	−33.7873	+	17.0729i	−1.30629	+	0.660075i
$670$	−0.00898467	−	0.0324786i	−0.000347108	−	0.00125476i
$671$			3.35026i			0.129335i
$672$		0			0
$673$	−32.1249	−	32.1249i	−1.23832	−	1.23832i	−0.960686	−	0.277636i	$-0.910449\pi$
$673$	−32.1249	−	32.1249i	−1.23832	−	1.23832i	−0.277636	−	0.960686i	$-0.589551\pi$
$674$	−3.28666	−	5.69266i	−0.126597	−	0.219273i
$675$	−10.4223	+	23.7986i	−0.401156	+	0.916010i
$676$	2.55910	−	4.43248i	0.0984268	−	0.170480i
$677$	−11.0202	+	41.1280i	−0.423542	+	1.58068i	0.343545	+	0.939136i	$0.388372\pi$
$677$	−11.0202	+	41.1280i	−0.423542	+	1.58068i	−0.767087	+	0.641543i	$0.778295\pi$
$678$	−8.84036	+	1.84809i	−0.339512	+	0.0709753i
$679$		0			0
$680$	−12.6861	−	3.28953i	−0.486489	−	0.126148i
$681$	1.23922	−	22.2186i	0.0474870	−	0.851419i
$682$	0.361305	+	1.34841i	0.0138351	+	0.0516332i
$683$	0.603360	+	2.25177i	0.0230869	+	0.0861617i	0.976508	−	0.215481i	$-0.0691318\pi$
$683$	0.603360	+	2.25177i	0.0230869	+	0.0861617i	−0.953421	+	0.301642i	$0.902465\pi$
$684$	−7.52972	−	5.54827i	−0.287906	−	0.212143i
$685$	9.99568	+	16.9942i	0.381915	+	0.649316i
$686$		0			0
$687$	5.42298	+	25.9409i	0.206899	+	0.989708i
$688$	−3.38438	+	12.6307i	−0.129028	+	0.481540i
$689$	11.1600	−	19.3297i	0.425163	−	0.736404i
$690$	4.94775	−	7.69832i	0.188358	−	0.293070i
$691$	−8.27824	−	14.3383i	−0.314919	−	0.545456i	0.664501	−	0.747287i	$-0.268644\pi$
$691$	−8.27824	−	14.3383i	−0.314919	−	0.545456i	−0.979420	+	0.201831i	$0.935311\pi$
$692$	−1.78210	−	1.78210i	−0.0677454	−	0.0677454i
$693$		0			0
$694$		−	5.94884i		−	0.225815i
$695$	−22.3326	+	6.17796i	−0.847125	+	0.234343i
$696$	−4.65576	−	9.21376i	−0.176476	−	0.349247i
$697$	−5.48418	−	20.4672i	−0.207728	−	0.775252i
$698$	−2.75752	−	0.738875i	−0.104374	−	0.0279668i
$699$	6.50607	−	9.94523i	0.246082	−	0.376163i
$700$		0			0
$701$			26.5973i			1.00457i	0.864703	+	0.502284i	$0.167507\pi$
$701$			26.5973i			1.00457i	−0.864703	+	0.502284i	$0.832493\pi$
$702$	2.14340	−	4.68657i	0.0808973	−	0.176883i
$703$	5.59148	−	1.49823i	0.210886	−	0.0565069i
$704$	−2.21152	+	3.83047i	−0.0833500	+	0.144366i
$705$	−5.05671	+	15.8171i	−0.190447	+	0.595705i
$706$	3.64717			0.137263
$707$		0			0
$708$	−5.19111	−	24.8318i	−0.195094	−	0.933235i
$709$	−13.7850	+	7.95880i	−0.517708	+	0.298899i	−0.735997	−	0.676985i	$-0.763286\pi$
$709$	−13.7850	+	7.95880i	−0.517708	+	0.298899i	0.218288	+	0.975884i	$0.429953\pi$
$710$	0.0693280	+	8.57481i	0.00260184	+	0.321807i
$711$	−12.6278	−	1.41300i	−0.473580	−	0.0529917i
$712$	1.05671	+	0.283144i	0.0396018	+	0.0106113i
$713$	−32.0712	+	32.0712i	−1.20108	+	1.20108i
$714$		0			0
$715$	4.71930	−	2.77580i	0.176492	−	0.103809i
$716$	0.398625	−	0.230146i	0.0148973	−	0.00860096i
$717$	10.1166	−	30.7839i	0.377813	−	1.14964i
$718$	−4.16523	+	1.11607i	−0.155445	+	0.0416514i
$719$	10.6906	+	18.5167i	0.398694	+	0.690558i	0.993565	−	0.113263i	$-0.0361302\pi$
$719$	10.6906	+	18.5167i	0.398694	+	0.690558i	−0.594871	+	0.803821i	$0.702797\pi$
$720$	−22.7660	+	3.63782i	−0.848440	+	0.135573i
$721$		0			0
$722$	3.56409	+	3.56409i	0.132642	+	0.132642i
$723$	−2.27710	−	2.54611i	−0.0846862	−	0.0946907i
$724$	−30.8223	−	17.7952i	−1.14550	−	0.661355i
$725$	21.1991	−	12.7007i	0.787315	−	0.471692i
$726$	0.310355	−	5.56451i	0.0115183	−	0.206518i
$727$	−7.43836	+	7.43836i	−0.275873	+	0.275873i	−0.831459	−	0.555586i	$-0.812494\pi$
$727$	−7.43836	+	7.43836i	−0.275873	+	0.275873i	0.555586	+	0.831459i	$0.312494\pi$
$728$		0			0
$729$	8.85885	−	25.5053i	0.328106	−	0.944641i
$730$	−0.923641	+	0.255510i	−0.0341855	+	0.00945685i
$731$	16.0148	+	9.24617i	0.592330	+	0.341982i
$732$	−13.7707	−	4.52553i	−0.508980	−	0.167268i
$733$	−9.45077	+	35.2708i	−0.349072	+	1.30276i	0.538710	+	0.842491i	$0.318912\pi$
$733$	−9.45077	+	35.2708i	−0.349072	+	1.30276i	−0.887782	+	0.460264i	$0.847755\pi$
$734$	4.65810			0.171934
$735$		0			0
$736$	26.5725			0.979475
$737$	−0.00962968	+	0.0359385i	−0.000354714	+	0.00132381i
$738$	2.52085	+	3.15608i	0.0927939	+	0.116177i
$739$	33.2198	+	19.1794i	1.22201	+	0.705527i	0.965346	−	0.260974i	$-0.0840437\pi$
$739$	33.2198	+	19.1794i	1.22201	+	0.705527i	0.256663	+	0.966501i	$0.417377\pi$
$740$	7.42475	−	13.1036i	0.272939	−	0.481697i
$741$	−4.98446	+	7.61928i	−0.183109	+	0.279901i
$742$		0			0
$743$	30.8182	−	30.8182i	1.13061	−	1.13061i	0.140534	−	0.990076i	$-0.455118\pi$
$743$	30.8182	−	30.8182i	1.13061	−	1.13061i	0.990076	−	0.140534i	$-0.0448819\pi$
$744$	−12.3630	−	0.689531i	−0.453248	−	0.0252794i
$745$	27.3737	−	27.8199i	1.00289	−	1.01924i
$746$	9.31740	+	5.37940i	0.341134	+	0.196954i
$747$	−21.1983	+	3.21177i	−0.775605	+	0.117512i
$748$	4.99090	+	4.99090i	0.182485	+	0.182485i
$749$		0			0
$750$	1.36541	+	5.82265i	0.0498578	+	0.212613i
$751$	−19.9356	−	34.5294i	−0.727459	−	1.26000i	−0.957954	−	0.286923i	$-0.907368\pi$
$751$	−19.9356	−	34.5294i	−0.727459	−	1.26000i	0.230495	−	0.973074i	$-0.425966\pi$
$752$	−14.2335	+	3.81385i	−0.519042	+	0.139077i
$753$	29.4566	+	9.68045i	1.07346	+	0.352775i
$754$	−4.24517	+	2.45095i	−0.154600	+	0.0892583i
$755$	−32.9342	−	8.53991i	−1.19860	−	0.310799i
$756$		0			0
$757$	0.798673	−	0.798673i	0.0290283	−	0.0290283i	−0.692444	−	0.721472i	$-0.743466\pi$
$757$	0.798673	−	0.798673i	0.0290283	−	0.0290283i	0.721472	+	0.692444i	$0.243466\pi$
$758$	−5.68591	−	1.52354i	−0.206522	−	0.0553373i
$759$	−9.01787	+	4.55678i	−0.327328	+	0.165401i
$760$	−4.41371	+	0.0356852i	−0.160102	+	0.00129444i
$761$	37.3941	−	21.5895i	1.35554	−	0.782619i	0.366518	−	0.930411i	$-0.380550\pi$
$761$	37.3941	−	21.5895i	1.35554	−	0.782619i	0.989019	+	0.147791i	$0.0472164\pi$
$762$	3.30350	−	0.690601i	0.119673	−	0.0250178i
$763$		0			0
$764$	−27.1236			−0.981299
$765$	−3.36355	+	32.4301i	−0.121610	+	1.17251i
$766$	−1.56829	+	2.71637i	−0.0566648	+	0.0981463i
$767$	−23.8538	+	6.39162i	−0.861312	+	0.230788i
$768$	−10.2802	−	11.4946i	−0.370954	−	0.414777i
$769$		−	44.1875i		−	1.59344i	−0.604348	−	0.796720i	$-0.706566\pi$
$769$		−	44.1875i		−	1.59344i	0.604348	−	0.796720i	$-0.293434\pi$
$770$		0			0
$771$	28.5812	+	18.6975i	1.02933	+	0.673376i
$772$	−12.5397	−	3.36001i	−0.451315	−	0.120929i
$773$	−5.66214	−	21.1314i	−0.203653	−	0.760043i	−0.989856	−	0.142075i	$-0.954623\pi$
$773$	−5.66214	−	21.1314i	−0.203653	−	0.760043i	0.786203	−	0.617968i	$-0.212044\pi$
$774$	−3.50328	−	0.392003i	−0.125923	−	0.0140903i
$775$	−0.479274	−	29.6375i	−0.0172160	−	1.06461i
$776$			6.36214i			0.228388i
$777$		0			0
$778$	8.13643	+	8.13643i	0.291705	+	0.291705i
$779$	−3.56817	−	6.18024i	−0.127843	−	0.221430i
$780$	5.03467	+	23.1475i	0.180270	+	0.828813i
$781$	4.73385	−	8.19927i	0.169391	−	0.293393i
$782$	2.97231	−	11.0928i	0.106289	−	0.396678i
$783$	−20.9281	+	14.8856i	−0.747911	+	0.531966i
$784$		0			0
$785$	−17.6095	+	10.3576i	−0.628512	+	0.369679i
$786$	−1.14801	−	0.0640291i	−0.0409482	−	0.00228384i
$787$	−0.0780372	−	0.291239i	−0.00278173	−	0.0103815i	0.964521	−	0.264006i	$-0.0850439\pi$
$787$	−0.0780372	−	0.291239i	−0.00278173	−	0.0103815i	−0.967303	+	0.253625i	$0.918377\pi$
$788$	−5.33748	−	19.9197i	−0.190140	−	0.709612i
$789$	9.59544	+	0.535176i	0.341607	+	0.0190528i
$790$	−2.52120	+	1.48292i	−0.0897003	+	0.0527600i
$791$		0			0
$792$	−2.56845	−	1.00577i	−0.0912659	−	0.0357385i
$793$	−3.65209	+	13.6298i	−0.129689	+	0.484007i
$794$	−1.37270	+	2.37759i	−0.0487153	+	0.0843774i
$795$	−5.72115	−	26.3037i	−0.202908	−	0.932895i
$796$	15.5988	+	27.0180i	0.552886	+	0.957626i
$797$	−8.45240	−	8.45240i	−0.299399	−	0.299399i	0.541379	−	0.840779i	$-0.317902\pi$
$797$	−8.45240	−	8.45240i	−0.299399	−	0.299399i	−0.840779	+	0.541379i	$0.817902\pi$
$798$		0			0
$799$			20.8390i			0.737231i
$800$	−12.0795	+	12.4766i	−0.427073	+	0.441113i
$801$	0.302647	−	2.70472i	0.0106935	−	0.0955665i
$802$	0.371808	+	1.38761i	0.0131290	+	0.0489981i
$803$	1.02203	+	0.273853i	0.0360668	+	0.00966407i
$804$	−0.134712	−	0.0881271i	−0.00475092	−	0.00310800i
$805$		0			0
$806$			5.87955i			0.207098i
$807$	−11.6000	−	12.9704i	−0.408340	−	0.456579i
$808$	−22.1177	+	5.92642i	−0.778098	+	0.208491i
$809$	18.5676	−	32.1600i	0.652801	−	1.13068i	−0.329640	−	0.944107i	$-0.606927\pi$
$809$	18.5676	−	32.1600i	0.652801	−	1.13068i	0.982440	−	0.186577i	$-0.0597394\pi$
$810$	−1.88902	−	5.92120i	−0.0663732	−	0.208050i
$811$	−23.5491			−0.826921			−0.413461	−	0.910522i	$-0.635680\pi$
$811$	−23.5491			−0.826921			−0.413461	+	0.910522i	$0.635680\pi$
$812$		0			0
$813$	9.56300	−	1.99915i	0.335389	−	0.0701134i
$814$	0.721171	−	0.416368i	0.0252770	−	0.0145937i
$815$	−6.05359	+	0.0489438i	−0.212048	+	0.00171442i
$816$	−25.8228	+	13.0484i	−0.903977	+	0.456784i
$817$	6.01583	+	1.61194i	0.210467	+	0.0563945i
$818$	5.79994	−	5.79994i	0.202790	−	0.202790i
$819$		0			0
$820$	−17.9727	−	4.66036i	−0.627633	−	0.162747i
$821$	35.4996	−	20.4957i	1.23895	−	0.715306i	0.270067	−	0.962842i	$-0.412954\pi$
$821$	35.4996	−	20.4957i	1.23895	−	0.715306i	0.968879	+	0.247536i	$0.0796208\pi$
$822$	−4.48076	−	1.47253i	−0.156285	−	0.0513605i
$823$	24.8888	−	6.66893i	0.867568	−	0.232464i	0.202532	−	0.979276i	$-0.435083\pi$
$823$	24.8888	−	6.66893i	0.867568	−	0.232464i	0.665036	+	0.746812i	$0.268416\pi$
$824$	−7.61596	−	13.1912i	−0.265315	−	0.459538i
$825$	1.95985	−	6.30560i	0.0682333	−	0.219533i
$826$		0			0
$827$	−19.5668	−	19.5668i	−0.680404	−	0.680404i	0.279687	−	0.960091i	$-0.409769\pi$
$827$	−19.5668	−	19.5668i	−0.680404	−	0.680404i	−0.960091	+	0.279687i	$0.909769\pi$
$828$	−6.54857	−	43.2219i	−0.227579	−	1.50206i
$829$	−21.9279	−	12.6601i	−0.761588	−	0.439703i	0.0682778	−	0.997666i	$-0.478250\pi$
$829$	−21.9279	−	12.6601i	−0.761588	−	0.439703i	−0.829866	+	0.557963i	$0.811583\pi$
$830$	−3.46153	+	3.51796i	−0.120151	+	0.122110i
$831$	−19.4464	−	1.08460i	−0.674588	−	0.0376245i
$832$	−13.1727	+	13.1727i	−0.456680	+	0.456680i
$833$		0			0
$834$	3.03461	−	4.63873i	0.105080	−	0.160626i
$835$	−6.01053	+	10.6077i	−0.208003	+	0.367094i
$836$	2.05866	+	1.18857i	0.0712002	+	0.0411075i
$837$	2.91129	+	30.6663i	0.100629	+	1.05998i
$838$	−2.06449	+	7.70479i	−0.0713167	+	0.266157i
$839$	50.7484			1.75203			0.876014	−	0.482286i	$-0.160193\pi$
$839$	50.7484			1.75203			0.876014	+	0.482286i	$0.160193\pi$
$840$		0			0
$841$	−4.57160			−0.157641
$842$	0.0345654	−	0.129000i	0.00119120	−	0.00444563i
$843$	3.17299	+	1.04275i	0.109283	+	0.0359143i
$844$	−42.0656	−	24.2866i	−1.44796	−	0.835978i
$845$	−5.79137	+	1.60209i	−0.199229	+	0.0551134i
$846$	−1.59136	−	3.63981i	−0.0547120	−	0.125139i
$847$		0			0
$848$	16.8908	−	16.8908i	0.580031	−	0.580031i
$849$	2.54300	−	45.5948i	0.0872757	−	1.56481i
$850$	3.85723	+	6.43820i	0.132302	+	0.220829i
$851$	23.4310	+	13.5279i	0.803204	+	0.463730i
$852$	27.3074	+	30.5334i	0.935535	+	1.04606i
$853$	18.8448	+	18.8448i	0.645233	+	0.645233i	0.951837	−	0.306604i	$-0.0991928\pi$
$853$	18.8448	+	18.8448i	0.645233	+	0.645233i	−0.306604	+	0.951837i	$0.599193\pi$
$854$		0			0
$855$	1.73265	+	10.8432i	0.0592552	+	0.370829i
$856$	1.31482	+	2.27733i	0.0449395	+	0.0778375i
$857$	12.0212	−	3.22108i	0.410637	−	0.110030i	−0.0475860	−	0.998867i	$-0.515153\pi$
$857$	12.0212	−	3.22108i	0.410637	−	0.110030i	0.458223	+	0.888837i	$0.348486\pi$
$858$	−0.408922	+	1.24431i	−0.0139604	+	0.0424800i
$859$	−3.33705	+	1.92665i	−0.113859	+	0.0657364i	−0.555848	−	0.831284i	$-0.687606\pi$
$859$	−3.33705	+	1.92665i	−0.113859	+	0.0657364i	0.441989	+	0.897020i	$0.354273\pi$
$860$	13.9670	−	8.21515i	0.476272	−	0.280134i
$861$		0			0
$862$	3.56217	−	3.56217i	0.121328	−	0.121328i
$863$	48.2127	+	12.9186i	1.64118	+	0.439753i	0.957125	−	0.289676i	$-0.0935477\pi$
$863$	48.2127	+	12.9186i	1.64118	+	0.439753i	0.684056	+	0.729429i	$0.260214\pi$
$864$	11.4982	−	13.9103i	0.391175	−	0.473238i
$865$	0.0239219	+	2.95877i	0.000813368	+	0.100601i
$866$	0.194509	−	0.112300i	0.00660967	−	0.00381610i
$867$	2.34727	+	11.2282i	0.0797176	+	0.381331i
$868$		0			0
$869$	3.22945			0.109552
$870$	−1.80025	+	5.63107i	−0.0610343	+	0.190911i
$871$	−0.0783524	+	0.135710i	−0.00265487	+	0.00459837i
$872$	−2.74860	+	0.736484i	−0.0930793	+	0.0249405i
$873$	15.6491	−	2.37100i	0.529640	−	0.0802461i
$874$		−	3.86774i		−	0.130828i
$875$		0			0
$876$	−2.50620	+	3.83099i	−0.0846765	+	0.129437i
$877$	43.6713	+	11.7017i	1.47467	+	0.395138i	0.904531	−	0.426408i	$-0.140221\pi$
$877$	43.6713	+	11.7017i	1.47467	+	0.395138i	0.570143	+	0.821546i	$0.306888\pi$
$878$	1.22284	+	4.56370i	0.0412689	+	0.154018i
$879$	−8.65357	−	17.1254i	−0.291878	−	0.577627i
$880$	5.64741	−	1.56226i	0.190374	−	0.0526639i
$881$		−	25.2055i		−	0.849195i	−0.905382	−	0.424597i	$-0.860416\pi$
$881$		−	25.2055i		−	0.849195i	0.905382	−	0.424597i	$-0.139584\pi$
$882$		0			0
$883$	−14.2942	−	14.2942i	−0.481039	−	0.481039i	0.424424	−	0.905463i	$-0.360476\pi$
$883$	−14.2942	−	14.2942i	−0.481039	−	0.481039i	−0.905463	+	0.424424i	$0.860476\pi$
$884$	14.8638	+	25.7449i	0.499925	+	0.865895i
$885$	−16.1029	+	25.0548i	−0.541292	+	0.842208i
$886$	−1.40912	+	2.44067i	−0.0473403	+	0.0819958i
$887$	10.0709	−	37.5853i	0.338149	−	1.26199i	−0.562266	−	0.826957i	$-0.690070\pi$
$887$	10.0709	−	37.5853i	0.338149	−	1.26199i	0.900415	−	0.435033i	$-0.143263\pi$
$888$	1.51144	+	7.23000i	0.0507206	+	0.242623i
$889$		0			0
$890$	−0.317623	−	0.540010i	−0.0106468	−	0.0181012i
$891$	−1.51671	+	6.69248i	−0.0508118	+	0.224207i
$892$	10.7740	+	40.2091i	0.360740	+	1.34630i
$893$	1.81649	+	6.77923i	0.0607865	+	0.226858i
$894$	−0.519936	+	9.32220i	−0.0173893	+	0.311781i
$895$	−0.523094	−	0.135639i	−0.0174851	−	0.00453393i
$896$		0			0
$897$	−41.6545	+	8.70792i	−1.39080	+	0.290749i
$898$	0.752081	−	2.80681i	0.0250973	−	0.0936643i
$899$	14.6503	−	25.3750i	0.488613	−	0.846303i
$900$	23.2708	+	16.5733i	0.775694	+	0.552443i
$901$	−16.8905	−	29.2553i	−0.562705	−	0.974634i
$902$	−0.725914	−	0.725914i	−0.0241703	−	0.0241703i
$903$		0			0
$904$			20.3599i			0.677161i
$905$	11.1405	+	40.2716i	0.370322	+	1.33867i
$906$	7.26446	−	3.67077i	0.241345	−	0.121953i
$907$	0.623721	+	2.32776i	0.0207103	+	0.0772920i	0.975508	−	0.219966i	$-0.0705946\pi$
$907$	0.623721	+	2.32776i	0.0207103	+	0.0772920i	−0.954797	+	0.297258i	$0.903928\pi$
$908$	−23.6365	−	6.33337i	−0.784404	−	0.210180i
$909$	22.8200	+	52.1946i	0.756891	+	1.73119i
$910$		0			0
$911$			19.3662i			0.641631i	0.947142	+	0.320815i	$0.103957\pi$
$911$			19.3662i			0.641631i	−0.947142	+	0.320815i	$0.896043\pi$
$912$	−7.26312	+	6.49574i	−0.240506	+	0.215095i
$913$	5.26347	−	1.41034i	0.174196	−	0.0466755i
$914$	5.33185	−	9.23503i	0.176362	−	0.305468i
$915$	7.79753	+	15.1263i	0.257778	+	0.500059i
$916$	29.1421			0.962883
$917$		0			0
$918$	−4.52077	−	6.35591i	−0.149208	−	0.209776i
$919$	29.5591	−	17.0659i	0.975063	−	0.562953i	0.0742872	−	0.997237i	$-0.476332\pi$
$919$	29.5591	−	17.0659i	0.975063	−	0.562953i	0.900776	+	0.434284i	$0.142998\pi$
$920$	−14.7050	−	14.4691i	−0.484808	−	0.477031i
$921$	18.8650	+	37.3340i	0.621625	+	1.23020i
$922$	11.0175	+	2.95213i	0.362842	+	0.0972231i
$923$	28.1966	−	28.1966i	0.928102	−	0.928102i
$924$		0			0
$925$	−17.0031	+	4.85196i	−0.559059	+	0.159531i
$926$	9.97388	−	5.75842i	0.327762	−	0.189233i
$927$	−29.6084	+	23.6491i	−0.972467	+	0.776738i
$928$	−16.5814	+	4.44297i	−0.544311	+	0.145848i
$929$	9.86232	+	17.0820i	0.323572	+	0.560443i	0.981222	−	0.192880i	$-0.0617828\pi$
$929$	9.86232	+	17.0820i	0.323572	+	0.560443i	−0.657650	+	0.753323i	$0.728450\pi$
$930$	4.76962	+	5.24709i	0.156402	+	0.172059i
$931$		0			0
$932$	−9.24073	−	9.24073i	−0.302690	−	0.302690i
$933$	−30.5306	+	27.3049i	−0.999527	+	0.893922i
$934$	2.72793	+	1.57497i	0.0892606	+	0.0515346i
$935$	−0.0669948	−	8.28622i	−0.00219096	−	0.270988i
$936$	−9.35279	−	6.89159i	−0.305706	−	0.225259i
$937$	17.3041	−	17.3041i	0.565300	−	0.565300i	−0.365508	−	0.930808i	$-0.619105\pi$
$937$	17.3041	−	17.3041i	0.565300	−	0.565300i	0.930808	+	0.365508i	$0.119105\pi$
$938$		0			0
$939$	17.9436	+	11.7385i	0.585568	+	0.383072i
$940$	15.8871	+	9.00194i	0.518179	+	0.293611i
$941$	3.89269	+	2.24744i	0.126898	+	0.0732646i	0.562105	−	0.827066i	$-0.309992\pi$
$941$	3.89269	+	2.24744i	0.126898	+	0.0732646i	−0.435207	+	0.900330i	$0.643325\pi$
$942$	1.52585	−	4.64300i	0.0497149	−	0.151277i
$943$	8.63274	−	32.2178i	0.281121	−	1.04916i
$944$	−26.4292			−0.860196
$945$		0			0
$946$	0.895935			0.0291294
$947$	3.88234	−	14.4891i	0.126159	−	0.470832i	−0.873719	−	0.486431i	$-0.838299\pi$
$947$	3.88234	−	14.4891i	0.126159	−	0.470832i	0.999878	+	0.0155984i	$0.00496534\pi$
$948$	−4.36235	+	13.2742i	−0.141683	+	0.431125i
$949$	3.85939	+	2.22822i	0.125281	+	0.0723311i
$950$	1.81602	+	1.75822i	0.0589193	+	0.0570440i
$951$	6.36658	+	4.16495i	0.206451	+	0.135058i
$952$		0			0
$953$	−21.6181	+	21.6181i	−0.700277	+	0.700277i	−0.964470	−	0.264193i	$-0.914895\pi$
$953$	−21.6181	+	21.6181i	−0.700277	+	0.700277i	0.264193	+	0.964470i	$0.414895\pi$
$954$	5.18422	+	3.81999i	0.167845	+	0.123677i
$955$	22.6983	+	22.3342i	0.734499	+	0.722717i
$956$	−30.8583	−	17.8160i	−0.998028	−	0.576212i
$957$	4.86531	−	4.35126i	0.157273	−	0.140656i
$958$	2.99334	+	2.99334i	0.0967106	+	0.0967106i
$959$		0			0
$960$	−1.06973	+	22.4416i	−0.0345255	+	0.724300i
$961$	−2.07218	−	3.58912i	−0.0668444	−	0.115778i
$962$	3.38780	−	0.907759i	0.109227	−	0.0292673i
$963$	5.11158	−	4.08277i	0.164718	−	0.131565i
$964$	−3.25292	+	1.87807i	−0.104769	+	0.0604887i
$965$	7.72710	+	13.1373i	0.248744	+	0.422904i
$966$		0			0
$967$	16.1911	−	16.1911i	0.520672	−	0.520672i	−0.397102	−	0.917774i	$-0.629984\pi$
$967$	16.1911	−	16.1911i	0.520672	−	0.520672i	0.917774	+	0.397102i	$0.129984\pi$
$968$	−12.1357	−	3.25174i	−0.390055	−	0.104515i
$969$	6.21477	+	12.2990i	0.199647	+	0.395102i
$970$	2.55538	−	2.59703i	0.0820482	−	0.0833857i
$971$	15.8437	−	9.14738i	0.508450	−	0.293553i	−0.223747	−	0.974647i	$-0.571829\pi$
$971$	15.8437	−	9.14738i	0.508450	−	0.293553i	0.732196	+	0.681094i	$0.238495\pi$
$972$	−25.4596	−	15.2744i	−0.816618	−	0.489928i
$973$		0			0
$974$	−7.06004			−0.226218
$975$	14.8469	−	23.5165i	0.475481	−	0.753131i
$976$	−7.55064	+	13.0781i	−0.241690	+	0.418619i
$977$	14.3951	−	3.85716i	0.460540	−	0.123401i	−0.0210868	−	0.999778i	$-0.506713\pi$
$977$	14.3951	−	3.85716i	0.460540	−	0.123401i	0.481627	+	0.876376i	$0.340046\pi$
$978$	1.07948	−	0.965425i	0.0345179	−	0.0308709i
$979$			0.691709i			0.0221071i
$980$		0			0
$981$	2.83587	+	6.48630i	0.0905423	+	0.207092i
$982$	−7.08425	−	1.89822i	−0.226067	−	0.0605746i
$983$	−3.04352	−	11.3586i	−0.0970733	−	0.362283i	0.900252	−	0.435368i	$-0.143382\pi$
$983$	−3.04352	−	11.3586i	−0.0970733	−	0.362283i	−0.997326	+	0.0730860i	$0.976715\pi$
$984$	8.12717	−	4.10670i	0.259085	−	0.130917i
$985$	−11.9357	+	21.0647i	−0.380303	+	0.671178i
$986$			7.41895i			0.236267i
$987$		0			0
$988$	7.07955	+	7.07955i	0.225230	+	0.225230i
$989$	14.5546	+	25.2092i	0.462808	+	0.801607i
$990$	0.644474	+	1.44218i	0.0204827	+	0.0458356i
$991$	−5.02003	+	8.69495i	−0.159467	+	0.276204i	−0.934676	−	0.355499i	$-0.884311\pi$
$991$	−5.02003	+	8.69495i	−0.159467	+	0.276204i	0.775210	+	0.631704i	$0.217644\pi$
$992$	−5.32910	+	19.8885i	−0.169199	+	0.631459i
$993$	−10.5431	+	2.20405i	−0.334576	+	0.0699434i
$994$		0			0
$995$	9.19337	−	35.4542i	0.291449	−	1.12397i
$996$	−1.31291	+	23.5398i	−0.0416010	+	0.745887i
$997$	3.64290	+	13.5955i	0.115372	+	0.430574i	0.999314	−	0.0370216i	$-0.0117870\pi$
$997$	3.64290	+	13.5955i	0.115372	+	0.430574i	−0.883943	+	0.467596i	$0.845120\pi$
$998$	0.258609	+	0.965142i	0.00818612	+	0.0305510i
$999$	17.2205	−	6.41213i	0.544831	−	0.202871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.y.i.263.7		48
3.2	odd	2	inner	735.2.y.i.263.6		48
5.2	odd	4	inner	735.2.y.i.557.7		48
7.2	even	3	inner	735.2.y.i.128.6		48
7.3	odd	6		735.2.j.g.638.7		24
7.4	even	3		735.2.j.e.638.7		24
7.5	odd	6		105.2.x.a.23.6	yes	48
7.6	odd	2		105.2.x.a.53.7	yes	48
15.2	even	4	inner	735.2.y.i.557.6		48
21.2	odd	6	inner	735.2.y.i.128.7		48
21.5	even	6		105.2.x.a.23.7	yes	48
21.11	odd	6		735.2.j.e.638.6		24
21.17	even	6		735.2.j.g.638.6		24
21.20	even	2		105.2.x.a.53.6	yes	48
35.2	odd	12	inner	735.2.y.i.422.6		48
35.12	even	12		105.2.x.a.2.6	✓	48
35.13	even	4		525.2.bf.f.32.6		48
35.17	even	12		735.2.j.g.197.6		24
35.19	odd	6		525.2.bf.f.443.7		48
35.27	even	4		105.2.x.a.32.7	yes	48
35.32	odd	12		735.2.j.e.197.6		24
35.33	even	12		525.2.bf.f.107.7		48
35.34	odd	2		525.2.bf.f.368.6		48
105.2	even	12	inner	735.2.y.i.422.7		48
105.17	odd	12		735.2.j.g.197.7		24
105.32	even	12		735.2.j.e.197.7		24
105.47	odd	12		105.2.x.a.2.7	yes	48
105.62	odd	4		105.2.x.a.32.6	yes	48
105.68	odd	12		525.2.bf.f.107.6		48
105.83	odd	4		525.2.bf.f.32.7		48
105.89	even	6		525.2.bf.f.443.6		48
105.104	even	2		525.2.bf.f.368.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.x.a.2.6	✓	48	35.12	even	12
105.2.x.a.2.7	yes	48	105.47	odd	12
105.2.x.a.23.6	yes	48	7.5	odd	6
105.2.x.a.23.7	yes	48	21.5	even	6
105.2.x.a.32.6	yes	48	105.62	odd	4
105.2.x.a.32.7	yes	48	35.27	even	4
105.2.x.a.53.6	yes	48	21.20	even	2
105.2.x.a.53.7	yes	48	7.6	odd	2
525.2.bf.f.32.6		48	35.13	even	4
525.2.bf.f.32.7		48	105.83	odd	4
525.2.bf.f.107.6		48	105.68	odd	12
525.2.bf.f.107.7		48	35.33	even	12
525.2.bf.f.368.6		48	35.34	odd	2
525.2.bf.f.368.7		48	105.104	even	2
525.2.bf.f.443.6		48	105.89	even	6
525.2.bf.f.443.7		48	35.19	odd	6
735.2.j.e.197.6		24	35.32	odd	12
735.2.j.e.197.7		24	105.32	even	12
735.2.j.e.638.6		24	21.11	odd	6
735.2.j.e.638.7		24	7.4	even	3
735.2.j.g.197.6		24	35.17	even	12
735.2.j.g.197.7		24	105.17	odd	12
735.2.j.g.638.6		24	21.17	even	6
735.2.j.g.638.7		24	7.3	odd	6
735.2.y.i.128.6		48	7.2	even	3	inner
735.2.y.i.128.7		48	21.2	odd	6	inner
735.2.y.i.263.6		48	3.2	odd	2	inner
735.2.y.i.263.7		48	1.1	even	1	trivial
735.2.y.i.422.6		48	35.2	odd	12	inner
735.2.y.i.422.7		48	105.2	even	12	inner
735.2.y.i.557.6		48	15.2	even	4	inner
735.2.y.i.557.7		48	5.2	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0799329 - 0.298314i) q^{2} +(-0.540759 + 1.64547i) q^{3} +(1.64945 + 0.952310i) q^{4} +(-0.596180 - 2.15513i) q^{5} +(0.447643 + 0.292843i) q^{6} +(0.852694 - 0.852694i) q^{8} +(-2.41516 - 1.77961i) q^{9} +(-0.690558 + 0.00558322i) q^{10} +(0.660315 + 0.381233i) q^{11} +(-2.45895 + 2.19915i) q^{12} +(2.27077 + 2.27077i) q^{13} +(3.86859 + 0.184406i) q^{15} +(1.71841 + 2.97637i) q^{16} +(4.69471 - 1.25794i) q^{17} +(-0.723932 + 0.578226i) q^{18} +(1.41761 - 0.818455i) q^{19} +(1.06898 - 4.12252i) q^{20} +(0.166508 - 0.166508i) q^{22} +(7.39003 + 1.98015i) q^{23} +(0.941983 + 1.86419i) q^{24} +(-4.28914 + 2.56969i) q^{25} +(0.858909 - 0.495891i) q^{26} +(4.23432 - 3.01174i) q^{27} -4.94251 q^{29} +(0.364238 - 1.13931i) q^{30} +(-2.96413 + 5.13403i) q^{31} +(3.35485 - 0.898930i) q^{32} +(-0.984380 + 0.880375i) q^{33} -1.50105i q^{34} +(-2.28894 - 5.23535i) q^{36} +(3.41587 + 0.915280i) q^{37} +(-0.130843 - 0.488313i) q^{38} +(-4.96442 + 2.50855i) q^{39} +(-2.34602 - 1.32930i) q^{40} -4.35963i q^{41} +(2.69037 + 2.69037i) q^{43} +(0.726104 + 1.25765i) q^{44} +(-2.39541 + 6.26594i) q^{45} +(1.18141 - 2.04627i) q^{46} +(-1.10971 + 4.14148i) q^{47} +(-5.82678 + 1.21809i) q^{48} +(0.423730 + 1.48491i) q^{50} +(-0.468795 + 8.40527i) q^{51} +(1.58304 + 5.90798i) q^{52} +(-1.79889 - 6.71354i) q^{53} +(-0.559982 - 1.50389i) q^{54} +(0.427939 - 1.65035i) q^{55} +(0.580162 + 2.77522i) q^{57} +(-0.395069 + 1.47442i) q^{58} +(-3.84501 + 6.65975i) q^{59} +(6.20543 + 3.98826i) q^{60} +(2.19699 + 3.80529i) q^{61} +(1.29462 + 1.29462i) q^{62} +5.80098i q^{64} +(3.54000 - 6.24757i) q^{65} +(0.183944 + 0.364025i) q^{66} +(0.0126297 + 0.0471345i) q^{67} +(8.94164 + 2.39591i) q^{68} +(-7.25451 + 11.0893i) q^{69} -12.4172i q^{71} +(-3.57685 + 0.541931i) q^{72} +(1.34043 - 0.359168i) q^{73} +(0.546081 - 0.945840i) q^{74} +(-1.90896 - 8.44724i) q^{75} +3.11769 q^{76} +(0.351513 + 1.68147i) q^{78} +(3.66808 - 2.11777i) q^{79} +(5.38997 - 5.47784i) q^{80} +(2.66599 + 8.59607i) q^{81} +(-1.30054 - 0.348478i) q^{82} +(5.05351 - 5.05351i) q^{83} +(-5.50993 - 9.36774i) q^{85} +(1.01762 - 0.587525i) q^{86} +(2.67271 - 8.13276i) q^{87} +(0.888122 - 0.237971i) q^{88} +(0.453600 + 0.785658i) q^{89} +(1.67774 + 1.21544i) q^{90} +(10.3038 + 10.3038i) q^{92} +(-6.84502 - 7.65367i) q^{93} +(1.14676 + 0.662081i) q^{94} +(-2.60902 - 2.56717i) q^{95} +(-0.335002 + 6.00642i) q^{96} +(-3.73061 + 3.73061i) q^{97} +(-0.916321 - 2.09584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{3} + 24 q^{6} + 8 q^{10} + 10 q^{12} + 16 q^{13} + 4 q^{15} - 8 q^{16} + 14 q^{18} - 8 q^{22} + 4 q^{25} - 40 q^{27} + 40 q^{30} + 24 q^{31} + 4 q^{33} + 8 q^{36} + 4 q^{37} + 16 q^{40} + 16 q^{43}+ \cdots + 120 q^{97}+O(q^{100}) \) 48 * q + 2 * q^3 + 24 * q^6 + 8 * q^10 + 10 * q^12 + 16 * q^13 + 4 * q^15 - 8 * q^16 + 14 * q^18 - 8 * q^22 + 4 * q^25 - 40 * q^27 + 40 * q^30 + 24 * q^31 + 4 * q^33 + 8 * q^36 + 4 * q^37 + 16 * q^40 + 16 * q^43 - 40 * q^45 - 32 * q^46 - 44 * q^48 + 8 * q^51 - 36 * q^52 + 40 * q^55 - 88 * q^57 + 56 * q^58 - 50 * q^60 + 8 * q^61 - 76 * q^66 + 12 * q^67 - 34 * q^72 - 52 * q^73 - 6 * q^75 - 64 * q^76 - 120 * q^78 + 20 * q^81 - 104 * q^82 - 24 * q^85 + 46 * q^87 + 84 * q^90 - 44 * q^93 - 12 * q^96 + 120 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more