LMFDB - Embedded newform 525.2.bf.f.368.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [525,2,Mod(32,525)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(525, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("525.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$525 = 3 \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	525.bf (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,2,0,0,-24,12,0,0,0,0,10,16,0,0,-8,0,-14,0,0,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces)

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

Self dual:	no
Analytic conductor:	$4.19214610612$
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			368.7
Character	$\chi$	$=$	525.368
Dual form			525.2.bf.f.107.7

$q$ -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} +(-1.29105 - 1.15464i) q^{3} +(1.64945 + 0.952310i) q^{4} +(-0.447643 + 0.292843i) q^{6} +(2.46856 + 0.951942i) q^{7} +(0.852694 - 0.852694i) q^{8} +(0.333606 + 2.98139i) q^{9} +(-0.660315 - 0.381233i) q^{11} +(-1.02994 - 3.13400i) q^{12} +(2.27077 + 2.27077i) q^{13} +(0.481297 - 0.660315i) q^{14} +(1.71841 + 2.97637i) q^{16} +(-4.69471 + 1.25794i) q^{17} +(0.916057 + 0.138792i) q^{18} +(-1.41761 + 0.818455i) q^{19} +(-2.08788 - 4.07931i) q^{21} +(-0.166508 + 0.166508i) q^{22} +(7.39003 + 1.98015i) q^{23} +(-2.08542 + 0.116312i) q^{24} +(0.858909 - 0.495891i) q^{26} +(3.01174 - 4.23432i) q^{27} +(3.16523 + 3.92102i) q^{28} +4.94251 q^{29} +(2.96413 - 5.13403i) q^{31} +(3.35485 - 0.898930i) q^{32} +(0.412310 + 1.25462i) q^{33} +1.50105i q^{34} +(-2.28894 + 5.23535i) q^{36} +(-3.41587 - 0.915280i) q^{37} +(0.130843 + 0.488313i) q^{38} +(-0.309745 - 5.55358i) q^{39} -4.35963i q^{41} +(-1.38380 + 0.296773i) q^{42} +(-2.69037 - 2.69037i) q^{43} +(-0.726104 - 1.25765i) q^{44} +(1.18141 - 2.04627i) q^{46} +(1.10971 - 4.14148i) q^{47} +(1.21809 - 5.82678i) q^{48} +(5.18761 + 4.69986i) q^{49} +(7.51357 + 3.79665i) q^{51} +(1.58304 + 5.90798i) q^{52} +(-1.79889 - 6.71354i) q^{53} +(-1.02242 - 1.23690i) q^{54} +(2.91664 - 1.29321i) q^{56} +(2.77522 + 0.580162i) q^{57} +(0.395069 - 1.47442i) q^{58} +(-3.84501 + 6.65975i) q^{59} +(-2.19699 - 3.80529i) q^{61} +(-1.29462 - 1.29462i) q^{62} +(-2.01458 + 7.67733i) q^{63} +5.80098i q^{64} +(0.407227 - 0.0227126i) q^{66} +(-0.0126297 - 0.0471345i) q^{67} +(-8.94164 - 2.39591i) q^{68} +(-7.25451 - 11.0893i) q^{69} +12.4172i q^{71} +(2.82668 + 2.25775i) q^{72} +(1.34043 - 0.359168i) q^{73} +(-0.546081 + 0.945840i) q^{74} -3.11769 q^{76} +(-1.26712 - 1.56968i) q^{77} +(-1.68147 - 0.351513i) q^{78} +(3.66808 - 2.11777i) q^{79} +(-8.77741 + 1.98922i) q^{81} +(-1.30054 - 0.348478i) q^{82} +(-5.05351 + 5.05351i) q^{83} +(0.440911 - 8.71692i) q^{84} +(-1.01762 + 0.587525i) q^{86} +(-6.38101 - 5.70683i) q^{87} +(-0.888122 + 0.237971i) q^{88} +(0.453600 + 0.785658i) q^{89} +(3.44389 + 7.76716i) q^{91} +(10.3038 + 10.3038i) q^{92} +(-9.75480 + 3.20576i) q^{93} +(-1.14676 - 0.662081i) q^{94} +(-5.36921 - 2.71309i) q^{96} +(-3.73061 + 3.73061i) q^{97} +(1.81669 - 1.17186i) q^{98} +(0.916321 - 2.09584i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$48 q + 2 q^{3} - 24 q^{6} + 12 q^{7} + 10 q^{12} + 16 q^{13} - 8 q^{16} - 14 q^{18} - 28 q^{21} + 8 q^{22} - 40 q^{27} + 60 q^{28} - 24 q^{31} + 4 q^{33} + 8 q^{36} - 4 q^{37} - 14 q^{42} - 16 q^{43} - 32 q^{46}+ \cdots + 120 q^{97}+O(q^{100})$ 48 * q + 2 * q^3 - 24 * q^6 + 12 * q^7 + 10 * q^12 + 16 * q^13 - 8 * q^16 - 14 * q^18 - 28 * q^21 + 8 * q^22 - 40 * q^27 + 60 * q^28 - 24 * q^31 + 4 * q^33 + 8 * q^36 - 4 * q^37 - 14 * q^42 - 16 * q^43 - 32 * q^46 - 44 * q^48 + 8 * q^51 - 36 * q^52 + 88 * q^57 - 56 * q^58 - 8 * q^61 - 44 * q^63 + 76 * q^66 - 12 * q^67 + 34 * q^72 - 52 * q^73 + 64 * q^76 + 120 * q^78 + 20 * q^81 - 104 * q^82 + 46 * q^87 + 72 * q^91 + 44 * q^93 + 12 * q^96 + 120 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$ .

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.0799329	−	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	$0.0485075\pi$
$3$	−1.29105	−	1.15464i	−0.745386	−	0.666633i
$3$	−1.29105	−	1.15464i	−0.745386	−	0.666633i
$4$	1.64945	+	0.952310i	0.824725	+	0.476155i
$5$		0			0
$5$		0			0
$6$	−0.447643	+	0.292843i	−0.182749	+	0.119553i
$7$	2.46856	+	0.951942i	0.933029	+	0.359800i
$7$	2.46856	+	0.951942i	0.933029	+	0.359800i
$8$	0.852694	−	0.852694i	0.301473	−	0.301473i
$9$	0.333606	+	2.98139i	0.111202	+	0.993798i
$10$		0			0
$11$	−0.660315	−	0.381233i	−0.199092	−	0.114946i	0.397140	−	0.917758i	$-0.370003\pi$
$11$	−0.660315	−	0.381233i	−0.199092	−	0.114946i	−0.596232	+	0.802812i	$0.703336\pi$
$12$	−1.02994	−	3.13400i	−0.297318	−	0.904708i
$13$	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	$0.603085\pi$
$14$	0.481297	−	0.660315i	0.128632	−	0.176477i
$15$		0			0
$16$	1.71841	+	2.97637i	0.429602	+	0.744092i
$17$	−4.69471	+	1.25794i	−1.13864	+	0.305096i	−0.778402	−	0.627766i	$-0.783970\pi$
$17$	−4.69471	+	1.25794i	−1.13864	+	0.305096i	−0.360233	+	0.932862i	$0.617303\pi$
$18$	0.916057	+	0.138792i	0.215917	+	0.0327136i
$19$	−1.41761	+	0.818455i	−0.325221	+	0.187767i	−0.653717	−	0.756739i	$-0.726791\pi$
$19$	−1.41761	+	0.818455i	−0.325221	+	0.187767i	0.328496	+	0.944505i	$0.393458\pi$
$20$		0			0
$21$	−2.08788	−	4.07931i	−0.455613	−	0.890178i
$22$	−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	$0.289413\pi$
$24$	−2.08542	+	0.116312i	−0.425685	+	0.0237422i
$25$		0			0
$26$	0.858909	−	0.495891i	0.168446	−	0.0972523i
$27$	3.01174	−	4.23432i	0.579610	−	0.814894i
$28$	3.16523	+	3.92102i	0.598172	+	0.741003i
$29$	4.94251			0.917801			0.458900	−	0.888488i	$-0.348243\pi$
$29$	4.94251			0.917801			0.458900	+	0.888488i	$0.348243\pi$
$30$		0			0
$31$	2.96413	−	5.13403i	0.532374	−	0.922099i	−0.466911	−	0.884304i	$-0.654633\pi$
$31$	2.96413	−	5.13403i	0.532374	−	0.922099i	0.999286	−	0.0377949i	$-0.0120334\pi$
$32$	3.35485	−	0.898930i	0.593060	−	0.158910i
$33$	0.412310	+	1.25462i	0.0717740	+	0.218401i
$34$			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	−0.0331401	−	0.999451i	$-0.510551\pi$
$37$	−3.41587	−	0.915280i	−0.561566	−	0.150471i	−0.528426	+	0.848980i	$0.677217\pi$
$38$	0.130843	+	0.488313i	0.0212255	+	0.0792148i
$39$	−0.309745	−	5.55358i	−0.0495990	−	0.889285i
$40$		0			0
$41$		−	4.35963i		−	0.680860i	−0.940270	−	0.340430i	$-0.889427\pi$
$41$		−	4.35963i		−	0.680860i	0.940270	−	0.340430i	$-0.110573\pi$
$42$	−1.38380	+	0.296773i	−0.213526	+	0.0457930i
$43$	−2.69037	−	2.69037i	−0.410277	−	0.410277i	0.471558	−	0.881835i	$-0.343692\pi$
$43$	−2.69037	−	2.69037i	−0.410277	−	0.410277i	−0.881835	+	0.471558i	$0.843692\pi$
$44$	−0.726104	−	1.25765i	−0.109464	−	0.189598i
$45$		0			0
$46$	1.18141	−	2.04627i	0.174190	−	0.301706i
$47$	1.10971	−	4.14148i	0.161867	−	0.604097i	−0.836552	−	0.547888i	$-0.815432\pi$
$47$	1.10971	−	4.14148i	0.161867	−	0.604097i	0.998419	−	0.0562089i	$-0.0179013\pi$
$48$	1.21809	−	5.82678i	0.175817	−	0.841023i
$49$	5.18761	+	4.69986i	0.741088	+	0.671408i
$50$		0			0
$51$	7.51357	+	3.79665i	1.05211	+	0.531637i
$52$	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	$-0.241737\pi$
$54$	−1.02242	−	1.23690i	−0.139133	−	0.168321i
$55$		0			0
$56$	2.91664	−	1.29321i	0.389753	−	0.172813i
$57$	2.77522	+	0.580162i	0.367587	+	0.0768444i
$58$	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	$0.999788\pi$
$60$		0			0
$61$	−2.19699	−	3.80529i	−0.281295	−	0.487218i	0.690409	−	0.723420i	$-0.257431\pi$
$61$	−2.19699	−	3.80529i	−0.281295	−	0.487218i	−0.971704	+	0.236202i	$0.924097\pi$
$62$	−1.29462	−	1.29462i	−0.164417	−	0.164417i
$63$	−2.01458	+	7.67733i	−0.253814	+	0.967253i
$64$			5.80098i			0.725122i
$65$		0			0
$66$	0.407227	−	0.0227126i	0.0501261	−	0.00279573i
$67$	−0.0126297	−	0.0471345i	−0.00154296	−	0.00575840i	0.965150	−	0.261697i	$-0.0842821\pi$
$67$	−0.0126297	−	0.0471345i	−0.00154296	−	0.00575840i	−0.966693	+	0.255939i	$0.917615\pi$
$68$	−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	$0.263676\pi$
$71$			12.4172i			1.47365i	−0.676082	+	0.736826i	$0.736324\pi$
$72$	2.82668	+	2.25775i	0.333127	+	0.266079i
$73$	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
$75$		0			0
$76$	−3.11769			−0.357624
$77$	−1.26712	−	1.56968i	−0.144401	−	0.178882i
$78$	−1.68147	−	0.351513i	−0.190389	−	0.0398010i
$79$	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	$0.256754\pi$
$80$		0			0
$81$	−8.77741	+	1.98922i	−0.975268	+	0.221025i
$82$	−1.30054	−	0.348478i	−0.143620	−	0.0384830i
$83$	−5.05351	+	5.05351i	−0.554695	+	0.554695i	−0.927792	−	0.373097i	$-0.878296\pi$
$83$	−5.05351	+	5.05351i	−0.554695	+	0.554695i	0.373097	+	0.927792i	$0.378296\pi$
$84$	0.440911	−	8.71692i	0.0481074	−	0.951094i
$85$		0			0
$86$	−1.01762	+	0.587525i	−0.109733	+	0.0633544i
$87$	−6.38101	−	5.70683i	−0.684116	−	0.611836i
$88$	−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	$0.818023\pi$
$90$		0			0
$91$	3.44389	+	7.76716i	0.361018	+	0.814220i
$92$	10.3038	+	10.3038i	1.07424	+	1.07424i
$93$	−9.75480	+	3.20576i	−1.01153	+	0.332422i
$94$	−1.14676	−	0.662081i	−0.118279	−	0.0682884i
$95$		0			0
$96$	−5.36921	−	2.71309i	−0.547993	−	0.276904i
$97$	−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	$0.336311\pi$
$98$	1.81669	−	1.17186i	0.183514	−	0.118376i
$99$	0.916321	−	2.09584i	0.0920937	−	0.210640i
$100$		0			0
$101$	−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	$-0.726988\pi$
$102$	1.73317	−	1.93792i	0.171610	−	0.191883i
$103$	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	$0.116948\pi$
$108$	9.00009	−	4.11618i	0.866034	−	0.396079i
$109$	−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			0
$111$	3.35323	+	5.12578i	0.318275	+	0.486517i
$112$	1.40867	+	8.98318i	0.133107	+	0.848831i
$113$	−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	$0.957920\pi$
$114$	0.394902	−	0.781512i	0.0369859	−	0.0731953i
$115$		0			0
$116$	8.15242	+	4.70680i	0.756933	+	0.437015i
$117$	−6.01250	+	7.52759i	−0.555856	+	0.695925i
$118$	1.67935	+	1.67935i	0.154597	+	0.154597i
$119$	−12.7867	−	1.36378i	−1.17215	−	0.125017i
$120$		0			0
$121$	−5.20932	−	9.02281i	−0.473575	−	0.820256i
$122$	−1.31078	+	0.351223i	−0.118673	+	0.0317983i
$123$	−5.03381	+	5.62849i	−0.453884	+	0.507504i
$124$	9.77837	−	5.64555i	0.878124	−	0.506985i
$125$		0			0
$126$	2.12922	+	1.21465i	0.189686	+	0.108210i
$127$	−4.46126	+	4.46126i	−0.395873	+	0.395873i	−0.876775	−	0.480901i	$-0.840309\pi$
$127$	−4.46126	+	4.46126i	−0.395873	+	0.395873i	0.480901	+	0.876775i	$0.340309\pi$
$128$	8.44022	+	2.26155i	0.746017	+	0.199895i
$129$	0.366982	+	6.57980i	0.0323109	+	0.579319i
$130$		0			0
$131$	−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	$0.363267\pi$
$132$	−0.514699	+	2.46207i	−0.0447988	+	0.214296i
$133$	−4.27857	+	0.670931i	−0.370999	+	0.0581771i
$134$	−0.0150704			−0.00130188
$135$		0			0
$136$	−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	$0.539592\pi$
$138$	−3.88797	+	1.27772i	−0.330966	+	0.108767i
$139$			10.3626i			0.878941i	0.898257	+	0.439471i	$0.144834\pi$
$139$			10.3626i			0.878941i	−0.898257	+	0.439471i	$0.855166\pi$
$140$		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
$144$	−8.30046	+	6.11618i	−0.691705	+	0.509682i
$145$		0			0
$146$		−	0.428578i		−	0.0354694i
$147$	−1.27081	−	12.0576i	−0.104814	−	0.994492i
$148$	−4.76267	−	4.76267i	−0.391489	−	0.391489i
$149$	−8.72716	−	15.1159i	−0.714957	−	1.23834i	−0.962976	−	0.269586i	$-0.913113\pi$
$149$	−8.72716	−	15.1159i	−0.714957	−	1.23834i	0.248019	−	0.968755i	$-0.420220\pi$
$150$		0			0
$151$	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
$153$	−5.31661	−	13.5771i	−0.429823	−	1.09765i
$154$	−0.569541	+	0.252530i	−0.0458949	+	0.0203494i
$155$		0			0
$156$	4.77782	−	9.45533i	0.382532	−	0.757032i
$157$	−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
$159$	−5.42929	+	10.7446i	−0.430570	+	0.852100i
$160$		0			0
$161$	16.3578	+	11.9230i	1.28917	+	0.939665i
$162$	−0.108192	+	2.77743i	−0.00850040	+	0.218215i
$163$	−0.700710	+	2.61508i	−0.0548838	+	0.204829i	−0.987923	−	0.154946i	$-0.950480\pi$
$163$	−0.700710	+	2.61508i	−0.0548838	+	0.204829i	0.933039	+	0.359775i	$0.117146\pi$
$164$	4.15172	−	7.19099i	0.324195	−	0.561522i
$165$		0			0
$166$	1.10359	+	1.91147i	0.0856551	+	0.148359i
$167$	3.85551	+	3.85551i	0.298348	+	0.298348i	0.840367	−	0.542018i	$-0.182340\pi$
$167$	3.85551	+	3.85551i	0.298348	+	0.298348i	−0.542018	+	0.840367i	$0.682340\pi$
$168$	−5.25872	−	1.69808i	−0.405719	−	0.131010i
$169$		−	2.68725i		−	0.206712i
$170$		0			0
$171$	−2.91306	−	3.95340i	−0.222767	−	0.302324i
$172$	−1.87556	−	6.99969i	−0.143010	−	0.533721i
$173$	1.27815	+	0.342481i	0.0971763	+	0.0260383i	0.307080	−	0.951684i	$-0.400648\pi$
$173$	1.27815	+	0.342481i	0.0971763	+	0.0260383i	−0.209903	+	0.977722i	$0.567315\pi$
$174$	−2.21248	+	1.44738i	−0.167727	+	0.109726i
$175$		0			0
$176$		−	2.62045i		−	0.197524i
$177$	12.6537	−	4.15845i	0.951111	−	0.312568i
$178$	0.270630	−	0.0725151i	0.0202846	−	0.00543524i
$179$	−0.120836	+	0.209294i	−0.00903168	+	0.0156433i	−0.870506	−	0.492158i	$-0.836208\pi$
$179$	−0.120836	+	0.209294i	−0.00903168	+	0.0156433i	0.861474	+	0.507801i	$0.169542\pi$
$180$		0			0
$181$	18.6864			1.38895			0.694475	−	0.719517i	$-0.255637\pi$
$181$	18.6864			1.38895			0.694475	+	0.719517i	$0.255637\pi$
$182$	2.59233	−	0.406508i	0.192156	−	0.0301324i
$183$	−1.55734	+	7.44955i	−0.115122	+	0.550686i
$184$	7.98990	−	4.61297i	0.589023	−	0.340073i
$185$		0			0
$186$	0.176594	+	3.16624i	0.0129485	+	0.232160i
$187$	3.57956	+	0.959140i	0.261763	+	0.0701393i
$188$	5.77437	−	5.77437i	0.421140	−	0.421140i
$189$	11.4655	−	7.58568i	0.833992	−	0.551777i
$190$		0			0
$191$	12.3330	−	7.12049i	0.892388	−	0.515220i	0.0176651	−	0.999844i	$-0.494377\pi$
$191$	12.3330	−	7.12049i	0.892388	−	0.515220i	0.874723	+	0.484624i	$0.161043\pi$
$192$	6.69805	−	7.48934i	0.483390	−	0.540496i
$193$	6.58385	−	1.76414i	0.473916	−	0.126985i	−0.0139523	−	0.999903i	$-0.504441\pi$
$193$	6.58385	−	1.76414i	0.473916	−	0.126985i	0.487868	+	0.872917i	$0.337775\pi$
$194$	0.814694	+	1.41109i	0.0584916	+	0.101310i
$195$		0			0
$196$	4.08099	+	12.6924i	0.291499	+	0.906599i
$197$	−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	$0.876046\pi$
$198$	−0.551974	−	0.440878i	−0.0392271	−	0.0313318i
$199$	−14.1855	−	8.19000i	−1.00558	−	0.580573i	−0.0956874	−	0.995411i	$-0.530505\pi$
$199$	−14.1855	−	8.19000i	−1.00558	−	0.580573i	−0.909895	+	0.414838i	$0.863838\pi$
$200$		0			0
$201$	−0.0381180	+	0.0754356i	−0.00268864	+	0.00532082i
$202$	−4.14670	+	4.14670i	−0.291761	+	0.291761i
$203$	12.2009	+	4.70498i	0.856335	+	0.330225i
$204$	8.77767	+	13.4176i	0.614560	+	0.939421i
$205$		0			0
$206$	−3.37836	−	1.95050i	−0.235382	−	0.135898i
$207$	−3.43826	+	22.6932i	−0.238975	+	1.57729i
$208$	−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
$213$	14.3374	−	16.0312i	0.982385	−	1.09844i
$214$	0.583239	+	0.336733i	0.0398694	+	0.0230186i
$215$		0			0
$216$	−1.04248	−	6.17867i	−0.0709320	−	0.420405i
$217$	12.2044	−	9.85200i	0.828492	−	0.668797i
$218$	−0.515316	+	0.515316i	−0.0349016	+	0.0349016i
$219$	−2.14527	−	1.08402i	−0.144964	−	0.0732510i
$220$		0			0
$221$	−13.5171	−	7.80410i	−0.909258	−	0.524960i
$222$	1.79712	−	0.590596i	0.120615	−	0.0396382i
$223$	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	$0.488683\pi$
$224$	9.13740	+	0.974557i	0.610518	+	0.0651154i
$225$		0			0
$226$	2.60716	+	4.51573i	0.173426	+	0.300382i
$227$	12.4101	−	3.32527i	0.823686	−	0.220706i	0.177728	−	0.984080i	$-0.443125\pi$
$227$	12.4101	−	3.32527i	0.823686	−	0.220706i	0.645957	+	0.763374i	$0.276458\pi$
$228$	4.02509	+	3.59982i	0.266568	+	0.238404i
$229$	−13.2508	+	7.65038i	−0.875641	+	0.505551i	−0.869219	−	0.494428i	$-0.835378\pi$
$229$	−13.2508	+	7.65038i	−0.875641	+	0.505551i	−0.00642204	+	0.999979i	$0.502044\pi$
$230$		0			0
$231$	−0.176508	+	3.48960i	−0.0116134	+	0.229599i
$232$	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	$0.655491\pi$
$234$	1.76498	+	2.39531i	0.115381	+	0.156587i
$235$		0			0
$236$	−12.6843	+	7.32328i	−0.825677	+	0.476705i
$237$	−7.18093	−	1.50118i	−0.466452	−	0.0975122i
$238$	−1.42891	+	3.70543i	−0.0926225	+	0.240188i
$239$	18.7082			1.21013			0.605067	−	0.796174i	$-0.293146\pi$
$239$	18.7082			1.21013			0.605067	+	0.796174i	$0.293146\pi$
$240$		0			0
$241$	0.986063	−	1.70791i	0.0635179	−	0.110016i	−0.832518	−	0.553998i	$-0.813101\pi$
$241$	0.986063	−	1.70791i	0.0635179	−	0.110016i	0.896036	+	0.443982i	$0.146435\pi$
$242$	−3.10802	+	0.832793i	−0.199791	+	0.0535339i
$243$	13.6289	+	7.56659i	0.874294	+	0.485397i
$244$		−	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
$249$	12.3593	−	0.689328i	0.783240	−	0.0436844i
$250$		0			0
$251$		−	17.9016i		−	1.12994i	−0.825112	−	0.564970i	$-0.808888\pi$
$251$		−	17.9016i		−	1.12994i	0.825112	−	0.564970i	$-0.191112\pi$
$252$	−10.6342	+	10.7449i	−0.669889	+	0.676863i
$253$	−4.12485	−	4.12485i	−0.259327	−	0.259327i
$254$	0.974254	+	1.68746i	0.0611301	+	0.105881i
$255$		0			0
$256$	−4.45168	+	7.71053i	−0.278230	+	0.481908i
$257$	−5.10358	+	19.0468i	−0.318353	+	1.18811i	0.602475	+	0.798138i	$0.294181\pi$
$257$	−5.10358	+	19.0468i	−0.318353	+	1.18811i	−0.920827	+	0.389971i	$0.872485\pi$
$258$	1.99218	+	0.416467i	0.124028	+	0.0259281i
$259$	−7.56100	−	5.51114i	−0.469818	−	0.342445i
$260$		0			0
$261$	1.64885	+	14.7356i	0.102061	+	0.912109i
$262$	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	$0.971389\pi$
$264$	1.42138	+	0.718230i	0.0874798	+	0.0442040i
$265$		0			0
$266$	−0.141851	+	1.32999i	−0.00869744	+	0.0815467i
$267$	0.321534	−	1.53807i	0.0196776	−	0.0941281i
$268$	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	$0.265748\pi$
$270$		0			0
$271$	2.82028	+	4.88486i	0.171320	+	0.296734i	0.938881	−	0.344241i	$-0.111864\pi$
$271$	2.82028	+	4.88486i	0.171320	+	0.296734i	−0.767562	+	0.640975i	$0.778530\pi$
$272$	−11.8115	−	11.8115i	−0.716180	−	0.716180i
$273$	4.52206	−	14.0042i	0.273688	−	0.847575i
$274$			2.72309i			0.164508i
$275$		0			0
$276$	−1.40549	−	25.1998i	−0.0846007	−	1.51685i
$277$	−2.91038	−	10.8617i	−0.174868	−	0.652615i	−0.996574	−	0.0827040i	$-0.973644\pi$
$277$	−2.91038	−	10.8617i	−0.174868	−	0.652615i	0.821707	−	0.569911i	$-0.193022\pi$
$278$	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	$0.0183183\pi$
$281$			1.92831i			0.115033i	−0.998345	+	0.0575167i	$0.981682\pi$
$282$	0.716052	+	2.17887i	0.0426403	+	0.129750i
$283$	−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
$285$		0			0
$286$	−0.756201			−0.0447151
$287$	4.15012	−	10.7620i	0.244974	−	0.635263i
$288$	3.79926	+	9.70225i	0.223874	+	0.571710i
$289$	5.73548	−	3.31138i	0.337381	−	0.194787i
$290$		0			0
$291$	9.12392	−	0.508877i	0.534853	−	0.0298309i
$292$	2.55301	+	0.684078i	0.149404	+	0.0400326i
$293$	7.83332	−	7.83332i	0.457627	−	0.457627i	−0.440249	−	0.897876i	$-0.645110\pi$
$293$	7.83332	−	7.83332i	0.457627	−	0.457627i	0.897876	+	0.440249i	$0.145110\pi$
$294$	−3.69852	−	0.584698i	−0.215702	−	0.0341003i
$295$		0			0
$296$	−3.69315	+	2.13224i	−0.214660	+	0.123934i
$297$	−3.60296	+	1.64781i	−0.209065	+	0.0956155i
$298$	−5.20686	+	1.39517i	−0.301625	+	0.0808203i
$299$	12.2846	+	21.2775i	0.710435	+	1.23051i
$300$		0			0
$301$	−4.08027	−	9.20242i	−0.235183	−	0.530418i
$302$	−3.32282	−	3.32282i	−0.191207	−	0.191207i
$303$	10.2681	+	31.2449i	0.589890	+	1.79497i
$304$	−4.87205	−	2.81288i	−0.279431	−	0.161330i
$305$		0			0
$306$	−4.47522	+	0.500759i	−0.255831	+	0.0286265i
$307$	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	$0.00797691\pi$
$308$	−0.595226	−	3.79579i	−0.0339161	−	0.216285i
$309$	−18.3083	+	11.9771i	−1.04152	+	0.681354i
$310$		0			0
$311$	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	$0.432757\pi$
$312$	−4.99963	−	4.47139i	−0.283048	−	0.253143i
$313$	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	$0.0439691\pi$
$318$	2.77127	+	2.47848i	0.155405	+	0.138986i
$319$	−3.26361	−	1.88425i	−0.182727	−	0.105498i
$320$		0			0
$321$	3.16074	−	2.06772i	0.176415	−	0.115409i
$322$	4.86432	−	3.92671i	0.271078	−	0.218827i
$323$	5.62568	−	5.62568i	0.313021	−	0.313021i
$324$	−16.3723	−	5.07770i	−0.909570	−	0.282094i
$325$		0			0
$326$	0.724106	+	0.418063i	0.0401045	+	0.0231543i
$327$	1.27604	+	3.88284i	0.0705650	+	0.214722i
$328$	−3.71743	−	3.71743i	−0.205261	−	0.205261i
$329$	6.68183	−	9.16713i	0.368381	−	0.505400i
$330$		0			0
$331$	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
$333$	1.58925	−	10.4894i	0.0870906	−	0.574815i
$334$	1.45833	−	0.841970i	0.0797965	−	0.0460705i
$335$		0			0
$336$	8.55370	−	13.2242i	0.466642	−	0.721440i
$337$	−15.0501	+	15.0501i	−0.819833	+	0.819833i	−0.986084	−	0.166250i	$-0.946834\pi$
$337$	−15.0501	+	15.0501i	−0.819833	+	0.819833i	0.166250	+	0.986084i	$0.446834\pi$
$338$	−0.801644	−	0.214800i	−0.0436037	−	0.0116836i
$339$	29.1981	−	1.62849i	1.58582	−	0.0884476i
$340$		0			0
$341$	−3.91452	+	2.26005i	−0.211983	+	0.122389i
$342$	−1.41220	+	0.552999i	−0.0763632	+	0.0299027i
$343$	8.33197	+	16.5402i	0.449884	+	0.893087i
$344$	−4.58812			−0.247375
$345$		0			0
$346$	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	$0.243708\pi$
$348$	−5.09049	−	15.4898i	−0.272879	−	0.830342i
$349$			9.24369i			0.494803i	0.968913	+	0.247402i	$0.0795767\pi$
$349$			9.24369i			0.494803i	−0.968913	+	0.247402i	$0.920423\pi$
$350$		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	$-0.981572\pi$
$353$	−3.05649	−	11.4070i	−0.162681	−	0.607132i	0.835644	−	0.549271i	$-0.185095\pi$
$354$	−0.229073	−	4.10717i	−0.0121751	−	0.218294i
$355$		0			0
$356$			1.72787i			0.0915769i
$357$	14.9335	+	16.5247i	0.790367	+	0.874582i
$358$	0.0527764	+	0.0527764i	0.00278932	+	0.00278932i
$359$	6.98129	+	12.0920i	0.368459	+	0.638189i	0.989325	−	0.145728i	$-0.0465523\pi$
$359$	6.98129	+	12.0920i	0.368459	+	0.638189i	−0.620866	+	0.783917i	$0.713219\pi$
$360$		0			0
$361$	−8.16026	+	14.1340i	−0.429487	+	0.743894i
$362$	1.49366	−	5.57441i	0.0785050	−	0.292985i
$363$	−3.69263	+	17.6638i	−0.193813	+	0.927108i
$364$	−1.71622	+	16.0912i	−0.0899544	+	0.843408i
$365$		0			0
$366$	2.09782	+	1.06004i	0.109655	+	0.0554091i
$367$	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
$369$	12.9978	−	1.45440i	0.676638	−	0.0757130i
$370$		0			0
$371$	1.95023	−	18.2852i	0.101251	−	0.949323i
$372$	−19.1429	−	4.00185i	−0.992515	−	0.207486i
$373$	9.01635	−	33.6495i	0.466849	−	1.74230i	−0.183837	−	0.982957i	$-0.558852\pi$
$373$	9.01635	−	33.6495i	0.466849	−	1.74230i	0.650686	−	0.759347i	$-0.274481\pi$
$374$	0.572249	−	0.991165i	0.0295903	−	0.0512519i
$375$		0			0
$376$	−2.58517	−	4.47765i	−0.133320	−	0.230917i
$377$	11.2233	+	11.2233i	0.578028	+	0.578028i
$378$	−1.34644	−	4.02666i	−0.0692535	−	0.207109i
$379$		−	19.0602i		−	0.979056i	−0.871988	−	0.489528i	$-0.837169\pi$
$379$		−	19.0602i		−	0.979056i	0.871988	−	0.489528i	$-0.162831\pi$
$380$		0			0
$381$	10.9109	−	0.608542i	0.558980	−	0.0311765i
$382$	−1.13832	−	4.24828i	−0.0582417	−	0.217361i
$383$	9.81007	+	2.62860i	0.501271	+	0.134315i	0.500590	−	0.865685i	$-0.333116\pi$
$383$	9.81007	+	2.62860i	0.501271	+	0.134315i	0.000681261		1.00000i	$0.499783\pi$
$384$	−8.28544	−	12.6652i	−0.422815	−	0.646318i
$385$		0			0
$386$		−	2.10507i		−	0.107145i
$387$	7.12352	−	8.91857i	0.362109	−	0.453356i
$388$	−9.70615	+	2.60076i	−0.492755	+	0.132033i
$389$	18.6290	−	32.2664i	0.944528	−	1.63597i	0.187835	−	0.982201i	$-0.439853\pi$
$389$	18.6290	−	32.2664i	0.944528	−	1.63597i	0.756693	−	0.653770i	$-0.226814\pi$
$390$		0			0
$391$	−37.1850			−1.88053
$392$	8.43099	−	0.415908i	0.425829	−	0.0210065i
$393$	3.64421	+	0.761825i	0.183826	+	0.0384290i
$394$	−2.89595	+	1.67198i	−0.145896	+	0.0842331i
$395$		0			0
$396$	3.50731	−	2.58436i	0.176249	−	0.129869i
$397$	−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
$399$	6.29852	+	4.07401i	0.315321	+	0.203956i
$400$		0			0
$401$	4.02832	−	2.32575i	0.201165	−	0.116142i	−0.396034	−	0.918236i	$-0.629614\pi$
$401$	4.02832	−	2.32575i	0.201165	−	0.116142i	0.597199	+	0.802093i	$0.296280\pi$
$402$	0.0194566	+	0.0174009i	0.000970407	+	0.000867878i
$403$	18.3890	−	4.92733i	0.916023	−	0.245448i
$404$	−18.0828	−	31.3204i	−0.899655	−	1.55825i
$405$		0			0
$406$	2.37881	−	3.26361i	0.118059	−	0.161970i
$407$	1.90662	+	1.90662i	0.0945074	+	0.0945074i
$408$	9.64415	−	3.16940i	0.477457	−	0.156909i
$409$	−23.0006	−	13.2794i	−1.13731	−	0.656626i	−0.191546	−	0.981484i	$-0.561350\pi$
$409$	−23.0006	−	13.2794i	−1.13731	−	0.656626i	−0.945763	+	0.324858i	$0.894683\pi$
$410$		0			0
$411$	13.6305	+	6.88758i	0.672345	+	0.339739i
$412$	17.0114	−	17.0114i	0.838091	−	0.838091i
$413$	−15.8313	+	12.7798i	−0.779009	+	0.628853i
$414$	6.49486	+	2.83961i	0.319205	+	0.139559i
$415$		0			0
$416$	9.65934	+	5.57682i	0.473588	+	0.273426i
$417$	11.9650	−	13.3786i	0.585931	−	0.655151i
$418$	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
$423$	12.7176	+	1.92685i	0.618350	+	0.0936866i
$424$	−7.25850	−	4.19070i	−0.352504	−	0.203518i
$425$		0			0
$426$	−3.63630	−	5.55847i	−0.176179	−	0.269309i
$427$	−1.80099	−	11.4850i	−0.0871558	−	0.555799i
$428$	−2.93684	+	2.93684i	−0.141957	+	0.141957i
$429$	−1.91268	+	3.78520i	−0.0923451	+	0.182751i
$430$		0			0
$431$	−14.1264	−	8.15586i	−0.680443	−	0.392854i	0.119579	−	0.992825i	$-0.461846\pi$
$431$	−14.1264	−	8.15586i	−0.680443	−	0.392854i	−0.800022	+	0.599971i	$0.795179\pi$
$432$	17.7783	+	1.68777i	0.855358	+	0.0812029i
$433$	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	$0.744437\pi$
$434$	−1.96345	−	4.42825i	−0.0942486	−	0.212563i
$435$		0			0
$436$	−2.24718	−	3.89223i	−0.107620	−	0.186404i
$437$	−12.0968	+	3.24133i	−0.578669	+	0.155054i
$438$	−0.494855	+	0.553315i	−0.0236451	+	0.0264384i
$439$	13.2487	−	7.64917i	0.632328	−	0.365075i	−0.149325	−	0.988788i	$-0.547710\pi$
$439$	13.2487	−	7.64917i	0.632328	−	0.365075i	0.781653	+	0.623713i	$0.214377\pi$
$440$		0			0
$441$	−12.2815	+	17.0342i	−0.584834	+	0.811153i
$442$	−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	$0.652888\pi$
$444$	0.649656	+	11.6480i	0.0308313	+	0.552791i
$445$		0			0
$446$	5.84564	−	3.37498i	0.276799	−	0.159810i
$447$	−6.18625	+	29.5921i	−0.292600	+	1.39966i
$448$	−5.52219	+	14.3201i	−0.260899	+	0.676560i
$449$	−9.40891			−0.444034			−0.222017	−	0.975043i	$-0.571264\pi$
$449$	−9.40891			−0.444034			−0.222017	+	0.975043i	$0.571264\pi$
$450$		0			0
$451$	−1.66204	+	2.87873i	−0.0782622	+	0.135554i
$452$	−31.0613	+	8.32286i	−1.46100	+	0.391474i
$453$	−25.0370	+	8.22804i	−1.17634	+	0.386587i
$454$		−	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	−0.627434	−	0.778670i	$-0.715895\pi$
$457$	−33.3520	−	8.93665i	−1.56014	−	0.418039i	−0.932708	+	0.360631i	$0.882561\pi$
$458$	1.22303	+	4.56443i	0.0571486	+	0.213282i
$459$	−8.81272	+	23.6675i	−0.411343	+	1.10470i
$460$		0			0
$461$			36.9326i			1.72012i	0.510192	+	0.860061i	$0.329574\pi$
$461$			36.9326i			1.72012i	−0.510192	+	0.860061i	$0.670426\pi$
$462$	1.02689	+	0.331588i	0.0477751	+	0.0154269i
$463$	−26.3687	−	26.3687i	−1.22546	−	1.22546i	−0.965664	−	0.259794i	$-0.916345\pi$
$463$	−26.3687	−	26.3687i	−1.22546	−	1.22546i	−0.259794	−	0.965664i	$-0.583655\pi$
$464$	8.49325	+	14.7107i	0.394289	+	0.682929i
$465$		0			0
$466$	−1.05953	+	1.83516i	−0.0490817	+	0.0850120i
$467$	2.63979	−	9.85183i	0.122155	−	0.455888i	−0.877567	−	0.479453i	$-0.840835\pi$
$467$	2.63979	−	9.85183i	0.122155	−	0.455888i	0.999722	+	0.0235650i	$0.00750166\pi$
$468$	−17.0859	+	6.69060i	−0.789797	+	0.309273i
$469$	0.0136922	−	0.128377i	0.000632247	−	0.00592791i
$470$		0			0
$471$	−7.13696	+	14.1241i	−0.328854	+	0.650803i
$472$	2.40011	+	8.95734i	0.110474	+	0.412295i
$473$	0.750833	+	2.80215i	0.0345233	+	0.128843i
$474$	−1.02182	+	2.02218i	−0.0469336	+	0.0928817i
$475$		0			0
$476$	−19.7923	−	14.4264i	−0.907177	−	0.661232i
$477$	19.4156	−	7.60287i	0.888979	−	0.348112i
$478$	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	$0.268049\pi$
$480$		0			0
$481$	−5.67825	−	9.83503i	−0.258906	−	0.448439i
$482$	−0.430674	−	0.430674i	−0.0196167	−	0.0196167i
$483$	−7.35185	−	34.2805i	−0.334521	−	1.55982i
$484$		−	19.8436i		−	0.901980i
$485$		0			0
$486$	3.34661	−	3.46087i	0.151805	−	0.156988i
$487$	5.91662	+	22.0811i	0.268108	+	1.00059i	0.960321	+	0.278898i	$0.0899692\pi$
$487$	5.91662	+	22.0811i	0.268108	+	1.00059i	−0.692213	+	0.721693i	$0.743364\pi$
$488$	−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	$0.180012\pi$
$491$			23.7476i			1.07172i	−0.844308	+	0.535858i	$0.819988\pi$
$492$	−13.6631	+	4.49016i	−0.615980	+	0.202432i
$493$	−23.2037	+	6.21740i	−1.04504	+	0.280018i
$494$	−0.811730	+	1.40596i	−0.0365215	+	0.0632570i
$495$		0			0
$496$	20.3744			0.914836
$497$	−11.8205	+	30.6527i	−0.530220	+	1.37496i
$498$	0.782280	−	3.74205i	0.0350548	−	0.167685i
$499$	−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	$0.356404\pi$
$500$		0			0
$501$	−0.525914	−	9.42938i	−0.0234961	−	0.421274i
$502$	−5.34029	−	1.43093i	−0.238349	−	0.0638654i
$503$	−2.62851	+	2.62851i	−0.117199	+	0.117199i	−0.763274	−	0.646075i	$-0.776409\pi$
$503$	−2.62851	+	2.62851i	−0.117199	+	0.117199i	0.646075	+	0.763274i	$0.276409\pi$
$504$	4.82859	+	8.26424i	0.215083	+	0.368118i
$505$		0			0
$506$	−1.56021	+	0.900788i	−0.0693598	+	0.0400449i
$507$	−3.10281	+	3.46937i	−0.137801	+	0.154080i
$508$	−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			0
$511$	3.65085	+	0.389385i	0.161504	+	0.0172254i
$512$	14.3017	+	14.3017i	0.632050	+	0.632050i
$513$	−0.803863	+	8.46757i	−0.0354914	+	0.373852i
$514$	5.27399	+	3.04494i	0.232626	+	0.134306i
$515$		0			0
$516$	−5.66069	+	11.2025i	−0.249198	+	0.493164i
$517$	−2.31162	+	2.31162i	−0.101665	+	0.101665i
$518$	−2.24842	+	1.81503i	−0.0987899	+	0.0797478i
$519$	−1.25472	−	1.91797i	−0.0550759	−	0.0841895i
$520$		0			0
$521$	−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	$0.743841\pi$
$522$	4.52762	+	0.685982i	0.198168	+	0.0300246i
$523$	−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
$528$	−3.02569	+	3.38313i	−0.131676	+	0.147232i
$529$	30.7730	+	17.7668i	1.33796	+	0.772469i
$530$		0			0
$531$	−21.1381	−	9.24175i	−0.917313	−	0.401058i
$532$	−7.69622	−	2.96786i	−0.333674	−	0.128673i
$533$	9.89970	−	9.89970i	0.428804	−	0.428804i
$534$	−0.433125	−	0.218860i	−0.0187432	−	0.00947101i
$535$		0			0
$536$	−0.0509605	−	0.0294221i	−0.00220116	−	0.00127084i
$537$	0.397664	−	0.130686i	0.0171605	−	0.00563952i
$538$	2.19394	+	2.19394i	0.0945876	+	0.0945876i
$539$	−1.63372	−	5.08108i	−0.0703692	−	0.218857i
$540$		0			0
$541$	−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
$543$	−24.1250	−	21.5761i	−1.03530	−	0.925919i
$544$	−14.6193	+	8.44044i	−0.626796	+	0.361881i
$545$		0			0
$546$	−3.81619	−	2.46839i	−0.163318	−	0.105637i
$547$	19.7665	−	19.7665i	0.845154	−	0.845154i	−0.144370	−	0.989524i	$-0.546115\pi$
$547$	19.7665	−	19.7665i	0.845154	−	0.845154i	0.989524	+	0.144370i	$0.0461154\pi$
$548$	−16.2212	−	4.34647i	−0.692937	−	0.185672i
$549$	10.6121	−	7.81955i	0.452915	−	0.333730i
$550$		0			0
$551$	−7.00653	+	4.04522i	−0.298488	+	0.172332i
$552$	−15.6417	−	3.26991i	−0.665753	−	0.139176i
$553$	11.0709	−	1.73605i	0.470782	−	0.0738242i
$554$	−3.47282			−0.147546
$555$		0			0
$556$	−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	$0.0385751\pi$
$558$	3.42788	−	4.29166i	0.145114	−	0.181681i
$559$		−	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	0.999666	−	0.0258549i	$-0.00823079\pi$
$563$	2.87110	+	10.7151i	0.121002	+	0.451587i	−0.878663	+	0.477442i	$0.841564\pi$
$564$	−14.1223	+	0.787658i	−0.594657	+	0.0331664i
$565$		0			0
$566$			8.14252i			0.342256i
$567$	−23.5612	−	3.44507i	−0.989479	−	0.144679i
$568$	10.5881	+	10.5881i	0.444266	+	0.444266i
$569$	6.90318	+	11.9567i	0.289396	+	0.501249i	0.973666	−	0.227980i	$-0.0732121\pi$
$569$	6.90318	+	11.9567i	0.289396	+	0.501249i	−0.684269	+	0.729229i	$0.739879\pi$
$570$		0			0
$571$	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
$573$	−24.1442	−	5.04736i	−1.00864	−	0.210857i
$574$	−2.87873	−	2.09828i	−0.120156	−	0.0875804i
$575$		0			0
$576$	−17.2950	+	1.93524i	−0.720625	+	0.0806350i
$577$	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
$579$	−10.5370	−	5.32440i	−0.437903	−	0.221275i
$580$		0			0
$581$	−17.2856	+	7.66426i	−0.717126	+	0.317967i
$582$	0.577496	−	2.76247i	0.0239380	−	0.114508i
$583$	−1.37159	+	5.11885i	−0.0568055	+	0.212001i
$584$	0.836718	−	1.44924i	0.0346236	−	0.0599699i
$585$		0			0
$586$	−1.71065	−	2.96293i	−0.0706662	−	0.122397i
$587$	−5.54217	−	5.54217i	−0.228750	−	0.228750i	0.583421	−	0.812170i	$-0.301714\pi$
$587$	−5.54217	−	5.54217i	−0.228750	−	0.228750i	−0.812170	+	0.583421i	$0.801714\pi$
$588$	9.38642	−	21.0986i	0.387089	−	0.870090i
$589$			9.70404i			0.399848i
$590$		0			0
$591$	1.04436	+	18.7248i	0.0429591	+	0.770237i
$592$	−3.14565	−	11.7397i	−0.129285	−	0.482499i
$593$	−8.37814	−	2.24492i	−0.344049	−	0.0921877i	0.0826570	−	0.996578i	$-0.473659\pi$
$593$	−8.37814	−	2.24492i	−0.344049	−	0.0921877i	−0.426706	+	0.904390i	$0.640326\pi$
$594$	0.203568	+	1.20653i	0.00835252	+	0.0495043i
$595$		0			0
$596$		−	33.2438i		−	1.36172i
$597$	8.85763	+	26.9528i	0.362519	+	1.10311i
$598$	7.32931	−	1.96388i	0.299718	−	0.0803091i
$599$	7.93869	−	13.7502i	0.324366	−	0.561819i	−0.657018	−	0.753875i	$-0.728182\pi$
$599$	7.93869	−	13.7502i	0.324366	−	0.561819i	0.981384	+	0.192056i	$0.0615157\pi$
$600$		0			0
$601$	41.5249			1.69384			0.846919	−	0.531722i	$-0.178455\pi$
$601$	41.5249			1.69384			0.846919	+	0.531722i	$0.178455\pi$
$602$	−3.07135	+	0.481625i	−0.125179	+	0.0196296i
$603$	0.136313	−	0.0533783i	0.00555110	−	0.00217373i
$604$	25.0976	−	14.4901i	1.02120	−	0.589593i
$605$		0			0
$606$	10.1415	−	0.565634i	0.411972	−	0.0229773i
$607$	−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
$609$	−10.3194	−	20.1620i	−0.418162	−	0.817006i
$610$		0			0
$611$	11.9242	−	6.88444i	0.482402	−	0.278515i
$612$	4.16015	−	27.4578i	0.168164	−	1.10992i
$613$	29.7879	−	7.98165i	1.20312	−	0.322376i	0.399063	−	0.916924i	$-0.369336\pi$
$613$	29.7879	−	7.98165i	1.20312	−	0.322376i	0.804060	+	0.594548i	$0.202669\pi$
$614$	−3.72926	−	6.45927i	−0.150501	−	0.260675i
$615$		0			0
$616$	−2.41892	−	0.257992i	−0.0974611	−	0.0103948i
$617$	−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	$0.872716\pi$
$618$	2.10950	+	6.41899i	0.0848566	+	0.258210i
$619$	−14.7495	−	8.51561i	−0.592831	−	0.342271i	0.173385	−	0.984854i	$-0.444529\pi$
$619$	−14.7495	−	8.51561i	−0.592831	−	0.342271i	−0.766216	+	0.642583i	$0.777863\pi$
$620$		0			0
$621$	30.6414	−	25.3280i	1.22960	−	1.01638i
$622$	5.16425	−	5.16425i	0.207068	−	0.207068i
$623$	0.371840	+	2.37125i	0.0148974	+	0.0950020i
$624$	15.9973	−	10.4652i	0.640403	−	0.418945i
$625$		0			0
$626$	−3.31107	−	1.91165i	−0.132337	−	0.0764047i
$627$	−1.61134	−	1.44110i	−0.0643508	−	0.0575518i
$628$	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
$633$	32.9253	+	29.4466i	1.30866	+	1.17040i
$634$	−1.17480	−	0.678272i	−0.0466573	−	0.0269376i
$635$		0			0
$636$	−19.1875	+	12.5523i	−0.760834	+	0.497730i
$637$	1.10758	+	22.4521i	0.0438840	+	0.889586i
$638$	−0.822967	+	0.822967i	−0.0325816	+	0.0325816i
$639$	−37.0206	+	4.14246i	−1.46451	+	0.163873i
$640$		0			0
$641$	36.6801	+	21.1773i	1.44878	+	0.836451i	0.998409	−	0.0563924i	$-0.0179598\pi$
$641$	36.6801	+	21.1773i	1.44878	+	0.836451i	0.450367	+	0.892843i	$0.351293\pi$
$642$	−0.364183	−	1.10817i	−0.0143732	−	0.0437360i
$643$	−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	$0.851197\pi$
$644$	15.6269	+	35.2441i	0.615787	+	1.38881i
$645$		0			0
$646$	−1.22854	−	2.12790i	−0.0483363	−	0.0837209i
$647$	22.9610	−	6.15237i	0.902689	−	0.241875i	0.222518	−	0.974929i	$-0.428572\pi$
$647$	22.9610	−	6.15237i	0.902689	−	0.241875i	0.680171	+	0.733054i	$0.261906\pi$
$648$	−5.78825	+	9.18064i	−0.227384	+	0.360650i
$649$	5.07783	−	2.93169i	0.199322	−	0.115079i
$650$		0			0
$651$	−27.1320	−	1.37237i	−1.06339	−	0.0537874i
$652$	−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	$0.723557\pi$
$654$	1.26030	−	0.0702921i	0.0492817	−	0.00274864i
$655$		0			0
$656$	12.9759	−	7.49163i	0.506623	−	0.292499i
$657$	1.51800	+	3.87653i	0.0592227	+	0.151238i
$658$	−2.20058	−	2.72604i	−0.0857876	−	0.106272i
$659$	−42.6184			−1.66018			−0.830088	−	0.557632i	$-0.811710\pi$
$659$	−42.6184			−1.66018			−0.830088	+	0.557632i	$0.811710\pi$
$660$		0			0
$661$	−22.7467	+	39.3985i	−0.884744	+	1.53242i	−0.0387381	+	0.999249i	$0.512334\pi$
$661$	−22.7467	+	39.3985i	−0.884744	+	1.53242i	−0.846006	+	0.533173i	$0.821000\pi$
$662$	1.85511	−	0.497076i	0.0721010	−	0.0193194i
$663$	8.44027	+	25.6828i	0.327793	+	0.997439i
$664$			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
$669$	−2.10809	−	37.7971i	−0.0815035	−	1.46132i
$670$		0			0
$671$			3.35026i			0.129335i
$672$	−10.6715	−	11.8086i	−0.411664	−	0.455527i
$673$	32.1249	+	32.1249i	1.23832	+	1.23832i	0.960686	+	0.277636i	$0.0895508\pi$
$673$	32.1249	+	32.1249i	1.23832	+	1.23832i	0.277636	+	0.960686i	$0.410449\pi$
$674$	3.28666	+	5.69266i	0.126597	+	0.219273i
$675$		0			0
$676$	2.55910	−	4.43248i	0.0984268	−	0.170480i
$677$	11.0202	−	41.1280i	0.423542	−	1.58068i	−0.343545	−	0.939136i	$-0.611628\pi$
$677$	11.0202	−	41.1280i	0.423542	−	1.58068i	0.767087	−	0.641543i	$-0.221705\pi$
$678$	1.84809	−	8.84036i	0.0709753	−	0.339512i
$679$	−12.7606	+	5.65793i	−0.489706	+	0.217131i
$680$		0			0
$681$	−19.8615	−	10.0361i	−0.761094	−	0.384584i
$682$	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	$0.902465\pi$
$684$	−1.04008	−	9.29507i	−0.0397685	−	0.355406i
$685$		0			0
$686$	5.60017	−	1.16343i	0.213815	−	0.0444201i
$687$	25.9409	+	5.42298i	0.989708	+	0.206899i
$688$	3.38438	−	12.6307i	0.129028	−	0.481540i
$689$	11.1600	−	19.3297i	0.425163	−	0.736404i
$690$		0			0
$691$	8.27824	+	14.3383i	0.314919	+	0.545456i	0.979420	−	0.201831i	$-0.0646893\pi$
$691$	8.27824	+	14.3383i	0.314919	+	0.545456i	−0.664501	+	0.747287i	$0.731356\pi$
$692$	1.78210	+	1.78210i	0.0677454	+	0.0677454i
$693$	4.25711	−	4.30143i	0.161714	−	0.163398i
$694$		−	5.94884i		−	0.225815i
$695$		0			0
$696$	−10.3072	+	0.574875i	−0.390694	+	0.0217906i
$697$	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	$-0.832493\pi$
$701$		−	26.5973i		−	1.00457i	0.864703	−	0.502284i	$-0.167507\pi$
$702$	0.487050	−	5.13039i	0.0183825	−	0.193634i
$703$	5.59148	−	1.49823i	0.210886	−	0.0565069i
$704$	2.21152	−	3.83047i	0.0833500	−	0.144366i
$705$		0			0
$706$	−3.64717			−0.137263
$707$	−31.5562	−	39.0912i	−1.18679	−	1.47017i
$708$	24.8318	+	5.19111i	0.933235	+	0.195094i
$709$	−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			0
$711$	7.53760	+	10.2295i	0.282682	+	0.383636i
$712$	1.05671	+	0.283144i	0.0396018	+	0.0106113i
$713$	32.0712	−	32.0712i	1.20108	−	1.20108i
$714$	6.12324	−	3.13401i	0.229156	−	0.117287i
$715$		0			0
$716$	−0.398625	+	0.230146i	−0.0148973	+	0.00860096i
$717$	−24.1532	−	21.6013i	−0.902018	−	0.806715i
$718$	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	$0.702797\pi$
$720$		0			0
$721$	19.6848	−	27.0065i	0.733099	−	1.00577i
$722$	3.56409	+	3.56409i	0.132642	+	0.132642i
$723$	−3.24508	+	1.06644i	−0.120686	+	0.0396615i
$724$	30.8223	+	17.7952i	1.14550	+	0.661355i
$725$		0			0
$726$	4.97418	+	2.51348i	0.184609	+	0.0932840i
$727$	−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	$0.312494\pi$
$728$	9.55960	+	3.68643i	0.354302	+	0.136628i
$729$	−8.85885	−	25.5053i	−0.328106	−	0.944641i
$730$		0			0
$731$	16.0148	+	9.24617i	0.592330	+	0.341982i
$732$	−9.66302	+	10.8046i	−0.357156	+	0.399349i
$733$	−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
$738$	0.605083	−	3.99367i	0.0222734	−	0.147009i
$739$	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	$0.417377\pi$
$740$		0			0
$741$	4.98446	+	7.61928i	0.183109	+	0.279901i
$742$	−5.29885	−	2.04337i	−0.194527	−	0.0750146i
$743$	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	$-0.0448819\pi$
$744$	−5.58432	+	11.0514i	−0.204731	+	0.405164i
$745$		0			0
$746$	−9.31740	−	5.37940i	−0.341134	−	0.196954i
$747$	−16.7524	−	13.3806i	−0.612938	−	0.489571i
$748$	4.99090	+	4.99090i	0.182485	+	0.182485i
$749$	−3.39837	+	4.66239i	−0.124174	+	0.170360i
$750$		0			0
$751$	−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
$753$	−20.6699	+	23.1118i	−0.753254	+	0.842242i
$754$	4.24517	−	2.45095i	0.154600	−	0.0892583i
$755$		0			0
$756$	26.1357	−	1.59349i	0.950545	−	0.0579545i
$757$	−0.798673	+	0.798673i	−0.0290283	+	0.0290283i	−0.721472	−	0.692444i	$-0.756534\pi$
$757$	−0.798673	+	0.798673i	−0.0290283	+	0.0290283i	0.692444	+	0.721472i	$0.256534\pi$
$758$	−5.68591	−	1.52354i	−0.206522	−	0.0553373i
$759$	0.562653	+	10.0881i	0.0204230	+	0.366175i
$760$		0			0
$761$	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	$0.0472164\pi$
$762$	0.690601	−	3.30350i	0.0250178	−	0.119673i
$763$	−3.92153	−	4.85791i	−0.141969	−	0.175868i
$764$	27.1236			0.981299
$765$		0			0
$766$	1.56829	−	2.71637i	0.0566648	−	0.0981463i
$767$	−23.8538	+	6.39162i	−0.861312	+	0.230788i
$768$	14.6502	−	4.81457i	0.528644	−	0.173731i
$769$			44.1875i			1.59344i	0.604348	+	0.796720i	$0.293434\pi$
$769$			44.1875i			1.59344i	−0.604348	+	0.796720i	$0.706566\pi$
$770$		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	$0.0453773\pi$
$773$	5.66214	+	21.1314i	0.203653	+	0.760043i	−0.786203	+	0.617968i	$0.787956\pi$
$774$	−2.09113	−	2.83793i	−0.0751640	−	0.102007i
$775$		0			0
$776$			6.36214i			0.228388i
$777$	3.39822	+	15.8454i	0.121911	+	0.568450i
$778$	−8.13643	−	8.13643i	−0.291705	−	0.291705i
$779$	3.56817	+	6.18024i	0.127843	+	0.221430i
$780$		0			0
$781$	4.73385	−	8.19927i	0.169391	−	0.293393i
$782$	−2.97231	+	11.0928i	−0.106289	+	0.396678i
$783$	14.8856	−	20.9281i	0.531966	−	0.747911i
$784$	−5.07407	+	23.5165i	−0.181217	+	0.839876i
$785$		0			0
$786$	0.518555	−	1.02622i	0.0184962	−	0.0366041i
$787$	−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
$789$	−4.33425	+	8.57748i	−0.154303	+	0.305367i
$790$		0			0
$791$	−40.8360	+	18.1063i	−1.45196	+	0.643787i
$792$	−1.00577	−	2.56845i	−0.0357385	−	0.0912659i
$793$	3.65209	−	13.6298i	0.129689	−	0.484007i
$794$	−1.37270	+	2.37759i	−0.0487153	+	0.0843774i
$795$		0			0
$796$	−15.5988	−	27.0180i	−0.552886	−	0.957626i
$797$	8.45240	+	8.45240i	0.299399	+	0.299399i	0.840779	−	0.541379i	$-0.182098\pi$
$797$	8.45240	+	8.45240i	0.299399	+	0.299399i	−0.541379	+	0.840779i	$0.682098\pi$
$798$	1.71879	−	1.55329i	0.0608446	−	0.0549858i
$799$			20.8390i			0.737231i
$800$		0			0
$801$	−2.19103	+	1.61446i	−0.0774163	+	0.0570441i
$802$	−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
$807$	16.5311	−	5.43269i	0.581922	−	0.191240i
$808$	−22.1177	+	5.92642i	−0.778098	+	0.208491i
$809$	−18.5676	+	32.1600i	−0.652801	+	1.13068i	0.329640	+	0.944107i	$0.393073\pi$
$809$	−18.5676	+	32.1600i	−0.652801	+	1.13068i	−0.982440	+	0.186577i	$0.940261\pi$
$810$		0			0
$811$	23.5491			0.826921			0.413461	−	0.910522i	$-0.364320\pi$
$811$	23.5491			0.826921			0.413461	+	0.910522i	$0.364320\pi$
$812$	15.6442	+	19.3797i	0.549003	+	0.680093i
$813$	1.99915	−	9.56300i	0.0701134	−	0.335389i
$814$	0.721171	−	0.416368i	0.0252770	−	0.0145937i
$815$		0			0
$816$	1.61116	+	28.8874i	0.0564019	+	1.01126i
$817$	6.01583	+	1.61194i	0.210467	+	0.0563945i
$818$	−5.79994	+	5.79994i	−0.202790	+	0.202790i
$819$	−22.0081	+	12.8588i	−0.769024	+	0.449322i
$820$		0			0
$821$	−35.4996	+	20.4957i	−1.23895	+	0.715306i	−0.968879	−	0.247536i	$-0.920379\pi$
$821$	−35.4996	+	20.4957i	−1.23895	+	0.715306i	−0.270067	+	0.962842i	$0.587046\pi$
$822$	3.14419	−	3.51563i	0.109666	−	0.122622i
$823$	−24.8888	+	6.66893i	−0.867568	+	0.232464i	−0.665036	−	0.746812i	$-0.731584\pi$
$823$	−24.8888	+	6.66893i	−0.867568	+	0.232464i	−0.202532	+	0.979276i	$0.564917\pi$
$824$	−7.61596	−	13.1912i	−0.265315	−	0.459538i
$825$		0			0
$826$	2.54694	+	5.74423i	0.0886195	+	0.199867i
$827$	−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	$0.909769\pi$
$828$	−27.2822	+	34.1570i	−0.948121	+	1.18704i
$829$	21.9279	+	12.6601i	0.761588	+	0.439703i	0.829866	−	0.557963i	$-0.188417\pi$
$829$	21.9279	+	12.6601i	0.761588	+	0.439703i	−0.0682778	+	0.997666i	$0.521750\pi$
$830$		0			0
$831$	−8.78391	+	17.3834i	−0.304710	+	0.603023i
$832$	−13.1727	+	13.1727i	−0.456680	+	0.456680i
$833$	−30.2665	−	15.5388i	−1.04867	−	0.538386i
$834$	−3.03461	−	4.63873i	−0.105080	−	0.160626i
$835$		0			0
$836$	2.05866	+	1.18857i	0.0712002	+	0.0411075i
$837$	−12.8119	−	28.0134i	−0.442844	−	0.968286i
$838$	−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
$843$	2.22651	−	2.48954i	0.0766851	−	0.0857444i
$844$	−42.0656	−	24.2866i	−1.44796	−	0.835978i
$845$		0			0
$846$	1.59136	−	3.63981i	0.0547120	−	0.125139i
$847$	−4.27036	−	27.2324i	−0.146731	−	0.935715i
$848$	16.8908	−	16.8908i	0.580031	−	0.580031i
$849$	40.7578	+	20.5951i	1.39880	+	0.706823i
$850$		0			0
$851$	−23.4310	−	13.5279i	−0.803204	−	0.463730i
$852$	38.9155	−	12.7890i	1.33322	−	0.438143i
$853$	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	$0.599193\pi$
$854$	−3.57009	−	0.380772i	−0.122166	−	0.0130297i
$855$		0			0
$856$	1.31482	+	2.27733i	0.0449395	+	0.0778375i
$857$	−12.0212	+	3.22108i	−0.410637	+	0.110030i	−0.458223	−	0.888837i	$-0.651514\pi$
$857$	−12.0212	+	3.22108i	−0.410637	+	0.110030i	0.0475860	+	0.998867i	$0.484847\pi$
$858$	0.976291	+	0.873141i	0.0333300	+	0.0298085i
$859$	3.33705	−	1.92665i	0.113859	−	0.0657364i	−0.441989	−	0.897020i	$-0.645727\pi$
$859$	3.33705	−	1.92665i	0.113859	−	0.0657364i	0.555848	+	0.831284i	$0.312394\pi$
$860$		0			0
$861$	−17.7843	+	9.10240i	−0.606087	+	0.310209i
$862$	−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	$0.260214\pi$
$864$	6.29759	−	16.9128i	0.214248	−	0.575387i
$865$		0			0
$866$	0.194509	−	0.112300i	0.00660967	−	0.00381610i
$867$	−11.2282	−	2.34727i	−0.381331	−	0.0797176i
$868$	29.5128	−	4.62795i	1.00173	−	0.157083i
$869$	−3.22945			−0.109552
$870$		0			0
$871$	0.0783524	−	0.135710i	0.00265487	−	0.00459837i
$872$	−2.74860	+	0.736484i	−0.0930793	+	0.0249405i
$873$	−12.3670	−	9.87787i	−0.418559	−	0.334315i
$874$			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	−0.570143	−	0.821546i	$-0.693112\pi$
$877$	−43.6713	−	11.7017i	−1.47467	−	0.395138i	−0.904531	+	0.426408i	$0.859779\pi$
$878$	−1.22284	−	4.56370i	−0.0412689	−	0.154018i
$879$	−19.1579	+	1.06851i	−0.646179	+	0.0360399i
$880$		0			0
$881$		−	25.2055i		−	0.849195i	−0.905382	−	0.424597i	$-0.860416\pi$
$881$		−	25.2055i		−	0.849195i	0.905382	−	0.424597i	$-0.139584\pi$
$882$	4.09984	+	5.02534i	0.138049	+	0.169212i
$883$	14.2942	+	14.2942i	0.481039	+	0.481039i	0.905463	−	0.424424i	$-0.139524\pi$
$883$	14.2942	+	14.2942i	0.481039	+	0.481039i	−0.424424	+	0.905463i	$0.639524\pi$
$884$	−14.8638	−	25.7449i	−0.499925	−	0.865895i
$885$		0			0
$886$	−1.40912	+	2.44067i	−0.0473403	+	0.0819958i
$887$	−10.0709	+	37.5853i	−0.338149	+	1.26199i	0.562266	+	0.826957i	$0.309930\pi$
$887$	−10.0709	+	37.5853i	−0.338149	+	1.26199i	−0.900415	+	0.435033i	$0.856737\pi$
$888$	7.23000	+	1.51144i	0.242623	+	0.0507206i
$889$	−15.2598	+	6.76605i	−0.511796	+	0.226926i
$890$		0			0
$891$	6.55421	+	2.03273i	0.219574	+	0.0680989i
$892$	10.7740	+	40.2091i	0.360740	+	1.34630i
$893$	1.81649	+	6.77923i	0.0607865	+	0.226858i
$894$	8.33323	+	4.21082i	0.278705	+	0.140831i
$895$		0			0
$896$	18.6823	+	13.6174i	0.624133	+	0.454924i
$897$	8.70792	−	41.6545i	0.290749	−	1.39080i
$898$	−0.752081	+	2.80681i	−0.0250973	+	0.0936643i
$899$	14.6503	−	25.3750i	0.488613	−	0.846303i
$900$		0			0
$901$	16.8905	+	29.2553i	0.562705	+	0.974634i
$902$	0.725914	+	0.725914i	0.0241703	+	0.0241703i
$903$	−5.35767	+	16.5920i	−0.178292	+	0.552147i
$904$			20.3599i			0.677161i
$905$		0			0
$906$	0.453252	+	8.12659i	0.0150583	+	0.269988i
$907$	−0.623721	−	2.32776i	−0.0207103	−	0.0772920i	0.954797	−	0.297258i	$-0.0960721\pi$
$907$	−0.623721	−	2.32776i	−0.0207103	−	0.0772920i	−0.975508	+	0.219966i	$0.929405\pi$
$908$	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	$-0.896043\pi$
$911$		−	19.3662i		−	0.641631i	0.947142	−	0.320815i	$-0.103957\pi$
$912$	3.04218	+	9.25703i	0.100737	+	0.306531i
$913$	5.26347	−	1.41034i	0.174196	−	0.0466755i
$914$	−5.33185	+	9.23503i	−0.176362	+	0.305468i
$915$		0			0
$916$	−29.1421			−0.962883
$917$	−5.61830	+	0.881015i	−0.185533	+	0.0290937i
$918$	6.35591	+	4.52077i	0.209776	+	0.149208i
$919$	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	$0.142998\pi$
$920$		0			0
$921$	−41.7647	+	2.32938i	−1.37619	+	0.0767558i
$922$	11.0175	+	2.95213i	0.362842	+	0.0972231i
$923$	−28.1966	+	28.1966i	−0.928102	+	0.928102i
$924$	−3.61432	+	5.58782i	−0.118902	+	0.183826i
$925$		0			0
$926$	−9.97388	+	5.75842i	−0.327762	+	0.189233i
$927$	37.4662	+	5.67652i	1.23055	+	0.186441i
$928$	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	$0.728450\pi$
$930$		0			0
$931$	−11.2006	−	2.41672i	−0.367085	−	0.0792047i
$932$	−9.24073	−	9.24073i	−0.302690	−	0.302690i
$933$	−12.7878	−	38.9120i	−0.418655	−	1.27392i
$934$	−2.72793	−	1.57497i	−0.0892606	−	0.0515346i
$935$		0			0
$936$	1.29190	+	11.5456i	0.0422271	+	0.377378i
$937$	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	$0.119105\pi$
$938$	−0.0372022	−	0.0143461i	−0.00121470	−	0.000468418i
$939$	−17.9436	+	11.7385i	−0.585568	+	0.383072i
$940$		0			0
$941$	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	$0.643325\pi$
$942$	3.64292	+	3.25803i	0.118693	+	0.106152i
$943$	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	$0.00496534\pi$
$948$	−10.4150	−	9.31460i	−0.338263	−	0.302524i
$949$	3.85939	+	2.22822i	0.125281	+	0.0723311i
$950$		0			0
$951$	−6.36658	+	4.16495i	−0.206451	+	0.135058i
$952$	−12.0660	+	9.74025i	−0.391062	+	0.315683i
$953$	−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	$0.414895\pi$
$954$	−0.716096	−	6.39966i	−0.0231845	−	0.207197i
$955$		0			0
$956$	30.8583	+	17.8160i	0.998028	+	0.576212i
$957$	2.03785	+	6.20096i	0.0658743	+	0.200448i
$958$	2.99334	+	2.99334i	0.0967106	+	0.0967106i
$959$	−23.1966	−	2.47406i	−0.749058	−	0.0798915i
$960$		0			0
$961$	−2.07218	−	3.58912i	−0.0668444	−	0.115778i
$962$	−3.38780	+	0.907759i	−0.109227	+	0.0292673i
$963$	−6.46814	−	0.979992i	−0.208433	−	0.0315798i
$964$	3.25292	−	1.87807i	0.104769	−	0.0604887i
$965$		0			0
$966$	−10.8140	−	0.546985i	−0.347935	−	0.0175989i
$967$	−16.1911	+	16.1911i	−0.520672	+	0.520672i	−0.917774	−	0.397102i	$-0.870016\pi$
$967$	−16.1911	+	16.1911i	−0.520672	+	0.520672i	0.397102	+	0.917774i	$0.370016\pi$
$968$	−12.1357	−	3.25174i	−0.390055	−	0.104515i
$969$	−13.7587	+	0.767375i	−0.441992	+	0.0246517i
$970$		0			0
$971$	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	$0.238495\pi$
$972$	15.2744	+	25.4596i	0.489928	+	0.816618i
$973$	−9.86456	+	25.5807i	−0.316243	+	0.820078i
$974$	7.06004			0.226218
$975$		0			0
$976$	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	$0.340046\pi$
$978$	−0.452142	−	1.37582i	−0.0144579	−	0.0439939i
$979$		−	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	0.997326	−	0.0730860i	$-0.0232848\pi$
$983$	3.04352	+	11.3586i	0.0970733	+	0.362283i	−0.900252	+	0.435368i	$0.856618\pi$
$984$	0.507079	+	9.09168i	0.0161651	+	0.289832i
$985$		0			0
$986$			7.41895i			0.236267i
$987$	−19.2113	+	4.12008i	−0.611502	+	0.131144i
$988$	−7.07955	−	7.07955i	−0.225230	−	0.225230i
$989$	−14.5546	−	25.2092i	−0.462808	−	0.801607i
$990$		0			0
$991$	−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
$993$	2.20405	−	10.5431i	0.0699434	−	0.334576i
$994$	8.19927	+	5.97636i	0.260065	+	0.189559i
$995$		0			0
$996$	21.0425	+	10.6329i	0.666757	+	0.336916i
$997$	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
$999$	−14.1633	+	11.7073i	−0.448107	+	0.370402i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bf.f.368.7		48
3.2	odd	2	inner	525.2.bf.f.368.6		48
5.2	odd	4	inner	525.2.bf.f.32.7		48
5.3	odd	4		105.2.x.a.32.6	yes	48
5.4	even	2		105.2.x.a.53.6	yes	48
7.2	even	3	inner	525.2.bf.f.443.6		48
15.2	even	4	inner	525.2.bf.f.32.6		48
15.8	even	4		105.2.x.a.32.7	yes	48
15.14	odd	2		105.2.x.a.53.7	yes	48
21.2	odd	6	inner	525.2.bf.f.443.7		48
35.2	odd	12	inner	525.2.bf.f.107.6		48
35.3	even	12		735.2.j.e.197.7		24
35.4	even	6		735.2.j.g.638.6		24
35.9	even	6		105.2.x.a.23.7	yes	48
35.13	even	4		735.2.y.i.557.6		48
35.18	odd	12		735.2.j.g.197.7		24
35.19	odd	6		735.2.y.i.128.7		48
35.23	odd	12		105.2.x.a.2.7	yes	48
35.24	odd	6		735.2.j.e.638.6		24
35.33	even	12		735.2.y.i.422.7		48
35.34	odd	2		735.2.y.i.263.6		48
105.2	even	12	inner	525.2.bf.f.107.7		48
105.23	even	12		105.2.x.a.2.6	✓	48
105.38	odd	12		735.2.j.e.197.6		24
105.44	odd	6		105.2.x.a.23.6	yes	48
105.53	even	12		735.2.j.g.197.6		24
105.59	even	6		735.2.j.e.638.7		24
105.68	odd	12		735.2.y.i.422.6		48
105.74	odd	6		735.2.j.g.638.7		24
105.83	odd	4		735.2.y.i.557.7		48
105.89	even	6		735.2.y.i.128.6		48
105.104	even	2		735.2.y.i.263.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.x.a.2.6	✓	48	105.23	even	12
105.2.x.a.2.7	yes	48	35.23	odd	12
105.2.x.a.23.6	yes	48	105.44	odd	6
105.2.x.a.23.7	yes	48	35.9	even	6
105.2.x.a.32.6	yes	48	5.3	odd	4
105.2.x.a.32.7	yes	48	15.8	even	4
105.2.x.a.53.6	yes	48	5.4	even	2
105.2.x.a.53.7	yes	48	15.14	odd	2
525.2.bf.f.32.6		48	15.2	even	4	inner
525.2.bf.f.32.7		48	5.2	odd	4	inner
525.2.bf.f.107.6		48	35.2	odd	12	inner
525.2.bf.f.107.7		48	105.2	even	12	inner
525.2.bf.f.368.6		48	3.2	odd	2	inner
525.2.bf.f.368.7		48	1.1	even	1	trivial
525.2.bf.f.443.6		48	7.2	even	3	inner
525.2.bf.f.443.7		48	21.2	odd	6	inner
735.2.j.e.197.6		24	105.38	odd	12
735.2.j.e.197.7		24	35.3	even	12
735.2.j.e.638.6		24	35.24	odd	6
735.2.j.e.638.7		24	105.59	even	6
735.2.j.g.197.6		24	105.53	even	12
735.2.j.g.197.7		24	35.18	odd	12
735.2.j.g.638.6		24	35.4	even	6
735.2.j.g.638.7		24	105.74	odd	6
735.2.y.i.128.6		48	105.89	even	6
735.2.y.i.128.7		48	35.19	odd	6
735.2.y.i.263.6		48	35.34	odd	2
735.2.y.i.263.7		48	105.104	even	2
735.2.y.i.422.6		48	105.68	odd	12
735.2.y.i.422.7		48	35.33	even	12
735.2.y.i.557.6		48	35.13	even	4
735.2.y.i.557.7		48	105.83	odd	4

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	525.2.bf.f.368.7

Level	$525$
Weight	$2$
Character	525.368
Analytic conductor	$4.192$
Analytic rank	$0$
Dimension	$48$
Inner twists	$8$