LMFDB - Embedded newform 325.2.s.c.293.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(32,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.s (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.5
Character	$\chi$	$=$	325.293
Dual form			325.2.s.c.132.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0621297 + 0.107612i) q^{2} +(2.43488 - 0.652423i) q^{3} +(0.992280 + 1.71868i) q^{4} +(-0.0810697 + 0.302556i) q^{6} +(-2.27145 + 1.31142i) q^{7} -0.495119 q^{8} +(2.90489 - 1.67714i) q^{9} +(0.780655 + 2.91344i) q^{11} +(3.53738 + 3.53738i) q^{12} +(3.34618 - 1.34280i) q^{13} -0.325912i q^{14} +(-1.95380 + 3.38408i) q^{16} +(1.42727 - 5.32666i) q^{17} +0.416800i q^{18} +(-3.13682 - 0.840508i) q^{19} +(-4.67509 + 4.67509i) q^{21} +(-0.362023 - 0.0970037i) q^{22} +(-1.62278 - 6.05629i) q^{23} +(-1.20555 + 0.323027i) q^{24} +(-0.0633962 + 0.443516i) q^{26} +(0.631478 - 0.631478i) q^{27} +(-4.50782 - 2.60259i) q^{28} +(2.99096 + 1.72683i) q^{29} +(-6.63421 - 6.63421i) q^{31} +(-0.737897 - 1.27807i) q^{32} +(3.80159 + 6.58455i) q^{33} +(0.484535 + 0.484535i) q^{34} +(5.76492 + 3.32838i) q^{36} +(-1.89660 - 1.09500i) q^{37} +(0.285338 - 0.285338i) q^{38} +(7.27145 - 5.45267i) q^{39} +(8.78430 - 2.35375i) q^{41} +(-0.212633 - 0.793556i) q^{42} +(2.89597 + 0.775973i) q^{43} +(-4.23265 + 4.23265i) q^{44} +(0.752551 + 0.201645i) q^{46} +2.26395i q^{47} +(-2.54941 + 9.51451i) q^{48} +(-0.0603560 + 0.104540i) q^{49} -13.9009i q^{51} +(5.62818 + 4.41857i) q^{52} +(-5.63768 - 5.63768i) q^{53} +(0.0287210 + 0.107188i) q^{54} +(1.12464 - 0.649309i) q^{56} -8.18613 q^{57} +(-0.371655 + 0.214575i) q^{58} +(-3.33926 + 12.4623i) q^{59} +(2.79259 + 4.83692i) q^{61} +(1.12610 - 0.301738i) q^{62} +(-4.39886 + 7.61905i) q^{63} -7.63181 q^{64} -0.944768 q^{66} +(-3.96321 + 6.86447i) q^{67} +(10.5711 - 2.83251i) q^{68} +(-7.90252 - 13.6876i) q^{69} +(4.12887 - 15.4091i) q^{71} +(-1.43826 + 0.830383i) q^{72} -6.95689 q^{73} +(0.235671 - 0.136064i) q^{74} +(-1.66804 - 6.22520i) q^{76} +(-5.59396 - 5.59396i) q^{77} +(0.134998 + 1.12127i) q^{78} -5.90307i q^{79} +(-3.90583 + 6.76510i) q^{81} +(-0.292475 + 1.09153i) q^{82} +9.71444i q^{83} +(-12.6740 - 3.39598i) q^{84} +(-0.263430 + 0.263430i) q^{86} +(8.40925 + 2.25325i) q^{87} +(-0.386517 - 1.44250i) q^{88} +(12.3550 - 3.31051i) q^{89} +(-5.83969 + 7.43833i) q^{91} +(8.79857 - 8.79857i) q^{92} +(-20.4818 - 11.8252i) q^{93} +(-0.243628 - 0.140659i) q^{94} +(-2.63053 - 2.63053i) q^{96} +(-2.62855 - 4.55278i) q^{97} +(-0.00749980 - 0.0129900i) q^{98} +(7.15396 + 7.15396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{4} - 12 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{16} - 24 q^{19} + 32 q^{21} + 56 q^{24} + 76 q^{26} - 36 q^{29} + 8 q^{31} + 44 q^{34} - 60 q^{36} + 44 q^{39} - 52 q^{41} - 80 q^{44} - 60 q^{46}+ \cdots + 208 q^{99}+O(q^{100}) $ 40 * q - 24 * q^4 - 12 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^16 - 24 * q^19 + 32 * q^21 + 56 * q^24 + 76 * q^26 - 36 * q^29 + 8 * q^31 + 44 * q^34 - 60 * q^36 + 44 * q^39 - 52 * q^41 - 80 * q^44 - 60 * q^46 + 28 * q^49 - 68 * q^54 + 72 * q^56 - 72 * q^59 + 144 * q^64 + 24 * q^66 - 80 * q^69 - 52 * q^71 + 168 * q^74 + 8 * q^76 - 20 * q^81 - 248 * q^84 - 168 * q^86 + 60 * q^89 - 100 * q^91 - 156 * q^94 - 36 * q^96 + 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.0621297	+	0.107612i	−0.0439323	+	0.0760930i	−0.887155	−	0.461471i	$-0.847322\pi$
$2$	−0.0621297	+	0.107612i	−0.0439323	+	0.0760930i	0.843223	+	0.537564i	$0.180655\pi$
$3$	2.43488	−	0.652423i	1.40578	−	0.376677i	0.525361	−	0.850880i	$-0.323930\pi$
$3$	2.43488	−	0.652423i	1.40578	−	0.376677i	0.880415	+	0.474203i	$0.157264\pi$
$4$	0.992280	+	1.71868i	0.496140	+	0.859340i
$5$		0			0
$5$		0			0
$6$	−0.0810697	+	0.302556i	−0.0330966	+	0.123518i
$7$	−2.27145	+	1.31142i	−0.858526	+	0.495670i	−0.863518	−	0.504317i	$-0.831744\pi$
$7$	−2.27145	+	1.31142i	−0.858526	+	0.495670i	0.00499253	+	0.999988i	$0.498411\pi$
$8$	−0.495119			−0.175051
$9$	2.90489	−	1.67714i	0.968296	−	0.559046i
$10$		0			0
$11$	0.780655	+	2.91344i	0.235376	+	0.878436i	0.977979	+	0.208704i	$0.0669245\pi$
$11$	0.780655	+	2.91344i	0.235376	+	0.878436i	−0.742603	+	0.669732i	$0.766409\pi$
$12$	3.53738	+	3.53738i	1.02115	+	1.02115i
$13$	3.34618	−	1.34280i	0.928062	−	0.372425i
$13$	3.34618	−	1.34280i	0.928062	−	0.372425i
$14$		−	0.325912i		−	0.0871038i
$15$		0			0
$16$	−1.95380	+	3.38408i	−0.488450	+	0.846019i
$17$	1.42727	−	5.32666i	0.346165	−	1.29190i	−0.545081	−	0.838384i	$-0.683501\pi$
$17$	1.42727	−	5.32666i	0.346165	−	1.29190i	0.891246	−	0.453521i	$-0.149832\pi$
$18$			0.416800i			0.0982408i
$19$	−3.13682	−	0.840508i	−0.719636	−	0.192826i	−0.119626	−	0.992819i	$-0.538170\pi$
$19$	−3.13682	−	0.840508i	−0.719636	−	0.192826i	−0.600009	+	0.799993i	$0.704836\pi$
$20$		0			0
$21$	−4.67509	+	4.67509i	−1.02019	+	1.02019i
$22$	−0.362023	−	0.0970037i	−0.0771835	−	0.0206813i
$23$	−1.62278	−	6.05629i	−0.338373	−	1.26282i	−0.900166	−	0.435546i	$-0.856555\pi$
$23$	−1.62278	−	6.05629i	−0.338373	−	1.26282i	0.561794	−	0.827277i	$-0.310111\pi$
$24$	−1.20555	+	0.323027i	−0.246083	+	0.0659376i
$25$		0			0
$26$	−0.0633962	+	0.443516i	−0.0124330	+	0.0869806i
$27$	0.631478	−	0.631478i	0.121528	−	0.121528i
$28$	−4.50782	−	2.60259i	−0.851898	−	0.491843i
$29$	2.99096	+	1.72683i	0.555408	+	0.320665i	0.751300	−	0.659961i	$-0.229427\pi$
$29$	2.99096	+	1.72683i	0.555408	+	0.320665i	−0.195893	+	0.980625i	$0.562760\pi$
$30$		0			0
$31$	−6.63421	−	6.63421i	−1.19154	−	1.19154i	−0.976635	−	0.214905i	$-0.931056\pi$
$31$	−6.63421	−	6.63421i	−1.19154	−	1.19154i	−0.214905	−	0.976635i	$-0.568944\pi$
$32$	−0.737897	−	1.27807i	−0.130443	−	0.225934i
$33$	3.80159	+	6.58455i	0.661773	+	1.14622i
$34$	0.484535	+	0.484535i	0.0830971	+	0.0830971i
$35$		0			0
$36$	5.76492	+	3.32838i	0.960820	+	0.554730i
$37$	−1.89660	−	1.09500i	−0.311799	−	0.180017i	0.335932	−	0.941886i	$-0.390949\pi$
$37$	−1.89660	−	1.09500i	−0.311799	−	0.180017i	−0.647731	+	0.761869i	$0.724282\pi$
$38$	0.285338	−	0.285338i	0.0462880	−	0.0462880i
$39$	7.27145	−	5.45267i	1.16436	−	0.873125i
$40$		0			0
$41$	8.78430	−	2.35375i	1.37188	−	0.367593i	0.503713	−	0.863871i	$-0.331967\pi$
$41$	8.78430	−	2.35375i	1.37188	−	0.367593i	0.868164	+	0.496278i	$0.165300\pi$
$42$	−0.212633	−	0.793556i	−0.0328100	−	0.122448i
$43$	2.89597	+	0.775973i	0.441631	+	0.118335i	0.472781	−	0.881180i	$-0.343250\pi$
$43$	2.89597	+	0.775973i	0.441631	+	0.118335i	−0.0311497	+	0.999515i	$0.509917\pi$
$44$	−4.23265	+	4.23265i	−0.638095	+	0.638095i
$45$		0			0
$46$	0.752551	+	0.201645i	0.110958	+	0.0297310i
$47$			2.26395i			0.330231i	0.986274	+	0.165116i	$0.0527998\pi$
$47$			2.26395i			0.330231i	−0.986274	+	0.165116i	$0.947200\pi$
$48$	−2.54941	+	9.51451i	−0.367975	+	1.37330i
$49$	−0.0603560	+	0.104540i	−0.00862229	+	0.0149342i
$50$		0			0
$51$		−	13.9009i		−	1.94652i
$52$	5.62818	+	4.41857i	0.780488	+	0.612746i
$53$	−5.63768	−	5.63768i	−0.774395	−	0.774395i	0.204477	−	0.978871i	$-0.434451\pi$
$53$	−5.63768	−	5.63768i	−0.774395	−	0.774395i	−0.978871	+	0.204477i	$0.934451\pi$
$54$	0.0287210	+	0.107188i	0.00390843	+	0.0145865i
$55$		0			0
$56$	1.12464	−	0.649309i	0.150286	−	0.0867675i
$57$	−8.18613			−1.08428
$58$	−0.371655	+	0.214575i	−0.0488007	+	0.0281751i
$59$	−3.33926	+	12.4623i	−0.434734	+	1.62245i	0.306967	+	0.951720i	$0.400686\pi$
$59$	−3.33926	+	12.4623i	−0.434734	+	1.62245i	−0.741701	+	0.670730i	$0.765981\pi$
$60$		0			0
$61$	2.79259	+	4.83692i	0.357555	+	0.619304i	0.987552	−	0.157294i	$-0.0502771\pi$
$61$	2.79259	+	4.83692i	0.357555	+	0.619304i	−0.629997	+	0.776598i	$0.716944\pi$
$62$	1.12610	−	0.301738i	0.143015	−	0.0383208i
$63$	−4.39886	+	7.61905i	−0.554205	+	0.959911i
$64$	−7.63181			−0.953976
$65$		0			0
$66$	−0.944768			−0.116293
$67$	−3.96321	+	6.86447i	−0.484183	+	0.838629i	−0.999835	−	0.0181691i	$-0.994216\pi$
$67$	−3.96321	+	6.86447i	−0.484183	+	0.838629i	0.515652	+	0.856798i	$0.327550\pi$
$68$	10.5711	−	2.83251i	1.28193	−	0.343492i
$69$	−7.90252	−	13.6876i	−0.951352	−	1.64779i
$70$		0			0
$71$	4.12887	−	15.4091i	0.490006	−	1.82873i	−0.0663658	−	0.997795i	$-0.521140\pi$
$71$	4.12887	−	15.4091i	0.490006	−	1.82873i	0.556372	−	0.830933i	$-0.312193\pi$
$72$	−1.43826	+	0.830383i	−0.169501	+	0.0978615i
$73$	−6.95689			−0.814242			−0.407121	−	0.913374i	$-0.633467\pi$
$73$	−6.95689			−0.814242			−0.407121	+	0.913374i	$0.633467\pi$
$74$	0.235671	−	0.136064i	0.0273961	−	0.0158172i
$75$		0			0
$76$	−1.66804	−	6.22520i	−0.191337	−	0.714080i
$77$	−5.59396	−	5.59396i	−0.637491	−	0.637491i
$78$	0.134998	+	1.12127i	0.0152855	+	0.126958i
$79$		−	5.90307i		−	0.664147i	−0.943253	−	0.332074i	$-0.892252\pi$
$79$		−	5.90307i		−	0.664147i	0.943253	−	0.332074i	$-0.107748\pi$
$80$		0			0
$81$	−3.90583	+	6.76510i	−0.433981	+	0.751678i
$82$	−0.292475	+	1.09153i	−0.0322985	+	0.120539i
$83$			9.71444i			1.06630i	0.846021	+	0.533149i	$0.178992\pi$
$83$			9.71444i			1.06630i	−0.846021	+	0.533149i	$0.821008\pi$
$84$	−12.6740	−	3.39598i	−1.38284	−	0.370532i
$85$		0			0
$86$	−0.263430	+	0.263430i	−0.0284063	+	0.0284063i
$87$	8.40925	+	2.25325i	0.901566	+	0.241574i
$88$	−0.386517	−	1.44250i	−0.0412029	−	0.153771i
$89$	12.3550	−	3.31051i	1.30963	−	0.350913i	0.464544	−	0.885550i	$-0.346218\pi$
$89$	12.3550	−	3.31051i	1.30963	−	0.350913i	0.845082	+	0.534637i	$0.179552\pi$
$90$		0			0
$91$	−5.83969	+	7.43833i	−0.612166	+	0.779749i
$92$	8.79857	−	8.79857i	0.917314	−	0.917314i
$93$	−20.4818	−	11.8252i	−2.12386	−	1.22621i
$94$	−0.243628	−	0.140659i	−0.0251283	−	0.0145078i
$95$		0			0
$96$	−2.63053	−	2.63053i	−0.268478	−	0.268478i
$97$	−2.62855	−	4.55278i	−0.266888	−	0.462264i	0.701168	−	0.712996i	$-0.252662\pi$
$97$	−2.62855	−	4.55278i	−0.266888	−	0.462264i	−0.968057	+	0.250732i	$0.919329\pi$
$98$	−0.00749980	−	0.0129900i	−0.000757594	−	0.00131219i
$99$	7.15396	+	7.15396i	0.719000	+	0.719000i
$100$		0			0
$101$	−1.24767	−	0.720340i	−0.124147	−	0.0716765i	0.436640	−	0.899636i	$-0.356168\pi$
$101$	−1.24767	−	0.720340i	−0.124147	−	0.0716765i	−0.560788	+	0.827960i	$0.689502\pi$
$102$	1.49591	+	0.863661i	0.148117	+	0.0855152i
$103$	−2.90200	+	2.90200i	−0.285943	+	0.285943i	−0.835473	−	0.549531i	$-0.814806\pi$
$103$	−2.90200	+	2.90200i	−0.285943	+	0.285943i	0.549531	+	0.835473i	$0.314806\pi$
$104$	−1.65676	+	0.664844i	−0.162458	+	0.0651933i
$105$		0			0
$106$	0.956948	−	0.256414i	0.0929470	−	0.0249051i
$107$	−0.259465	−	0.968336i	−0.0250834	−	0.0936126i	0.952249	−	0.305321i	$-0.0987639\pi$
$107$	−0.259465	−	0.968336i	−0.0250834	−	0.0936126i	−0.977333	+	0.211709i	$0.932097\pi$
$108$	1.71191	+	0.458705i	0.164729	+	0.0441389i
$109$	−9.69976	+	9.69976i	−0.929068	+	0.929068i	−0.997646	−	0.0685774i	$-0.978154\pi$
$109$	−9.69976	+	9.69976i	−0.929068	+	0.929068i	0.0685774	+	0.997646i	$0.478154\pi$
$110$		0			0
$111$	−5.33239	−	1.42881i	−0.506128	−	0.135617i
$112$		−	10.2490i		−	0.968439i
$113$	−2.78387	+	10.3896i	−0.261885	+	0.977367i	0.702245	+	0.711935i	$0.252181\pi$
$113$	−2.78387	+	10.3896i	−0.261885	+	0.977367i	−0.964130	+	0.265432i	$0.914485\pi$
$114$	0.508602	−	0.880924i	0.0476349	−	0.0825061i
$115$		0			0
$116$			6.85401i			0.636378i
$117$	7.46821	−	9.51267i	0.690436	−	0.879447i
$118$	−1.13362	−	1.13362i	−0.104358	−	0.104358i
$119$	3.74351	+	13.9710i	0.343167	+	1.28072i
$120$		0			0
$121$	1.64755	−	0.951213i	0.149777	−	0.0864739i
$122$	−0.694012			−0.0628329
$123$	19.8530	−	11.4622i	1.79009	−	1.03351i
$124$	4.81909	−	17.9851i	0.432767	−	1.61511i
$125$		0			0
$126$	−0.546600	−	0.946739i	−0.0486950	−	0.0843422i
$127$	−5.30979	+	1.42275i	−0.471168	+	0.126249i	−0.486587	−	0.873632i	$-0.661758\pi$
$127$	−5.30979	+	1.42275i	−0.471168	+	0.126249i	0.0154193	+	0.999881i	$0.495092\pi$
$128$	1.94996	−	3.37742i	0.172353	−	0.298525i
$129$	7.55759			0.665408
$130$		0			0
$131$	1.87484			0.163806			0.0819028	−	0.996640i	$-0.473900\pi$
$131$	1.87484			0.163806			0.0819028	+	0.996640i	$0.473900\pi$
$132$	−7.54449	+	13.0674i	−0.656664	+	1.13737i
$133$	8.22737	−	2.20452i	0.713404	−	0.191156i
$134$	−0.492465	−	0.852975i	−0.0425425	−	0.0736858i
$135$		0			0
$136$	−0.706671	+	2.63733i	−0.0605965	+	0.226149i
$137$	−0.721267	+	0.416423i	−0.0616220	+	0.0355775i	−0.530494	−	0.847688i	$-0.677994\pi$
$137$	−0.721267	+	0.416423i	−0.0616220	+	0.0355775i	0.468872	+	0.883266i	$0.344660\pi$
$138$	1.96393			0.167180
$139$	12.2720	−	7.08524i	1.04090	−	0.600962i	0.120810	−	0.992676i	$-0.461451\pi$
$139$	12.2720	−	7.08524i	1.04090	−	0.600962i	0.920087	+	0.391713i	$0.128117\pi$
$140$		0			0
$141$	1.47705	+	5.51244i	0.124390	+	0.464231i
$142$	1.40168	+	1.40168i	0.117626	+	0.117626i
$143$	6.52437	+	8.70063i	0.545595	+	0.727584i
$144$			13.1072i			1.09226i
$145$		0			0
$146$	0.432229	−	0.748643i	0.0357716	−	0.0619582i
$147$	−0.0787553	+	0.293919i	−0.00649563	+	0.0242420i
$148$		−	4.34620i		−	0.357255i
$149$	0.0628459	+	0.0168395i	0.00514854	+	0.00137955i	0.261392	−	0.965233i	$-0.415818\pi$
$149$	0.0628459	+	0.0168395i	0.00514854	+	0.00137955i	−0.256244	+	0.966612i	$0.582485\pi$
$150$		0			0
$151$	0.503953	−	0.503953i	0.0410111	−	0.0410111i	−0.686304	−	0.727315i	$-0.740768\pi$
$151$	0.503953	−	0.503953i	0.0410111	−	0.0410111i	0.727315	+	0.686304i	$0.240768\pi$
$152$	1.55310	+	0.416152i	0.125973	+	0.0337543i
$153$	−4.78747	−	17.8671i	−0.387044	−	1.44447i
$154$	0.949528	−	0.254425i	0.0765151	−	0.0205022i
$155$		0			0
$156$	16.5867	+	7.08672i	1.32800	+	0.567392i
$157$	−11.7855	+	11.7855i	−0.940584	+	0.940584i	−0.998331	−	0.0577473i	$-0.981608\pi$
$157$	−11.7855	+	11.7855i	−0.940584	+	0.940584i	0.0577473	+	0.998331i	$0.481608\pi$
$158$	0.635240	+	0.366756i	0.0505370	+	0.0291775i
$159$	−17.4052	−	10.0489i	−1.38032	−	0.796929i
$160$		0			0
$161$	11.6284	+	11.6284i	0.916445	+	0.916445i
$162$	−0.485336	−	0.840627i	−0.0381316	−	0.0660459i
$163$	−1.98594	−	3.43975i	−0.155551	−	0.269422i	0.777709	−	0.628625i	$-0.216382\pi$
$163$	−1.98594	−	3.43975i	−0.155551	−	0.269422i	−0.933259	+	0.359203i	$0.883049\pi$
$164$	12.7618	+	12.7618i	0.996530	+	0.996530i
$165$		0			0
$166$	−1.04539	−	0.603555i	−0.0811379	−	0.0468450i
$167$	10.9692	+	6.33310i	0.848826	+	0.490070i	0.860254	−	0.509865i	$-0.170305\pi$
$167$	10.9692	+	6.33310i	0.848826	+	0.490070i	−0.0114288	+	0.999935i	$0.503638\pi$
$168$	2.31472	−	2.31472i	0.178585	−	0.178585i
$169$	9.39379	−	8.98647i	0.722600	−	0.691267i
$170$		0			0
$171$	−10.5218	+	2.81930i	−0.804619	+	0.215597i
$172$	1.53996	+	5.74722i	0.117421	+	0.438222i
$173$	23.6630	+	6.34047i	1.79906	+	0.482057i	0.993831	−	0.110905i	$-0.0353750\pi$
$173$	23.6630	+	6.34047i	1.79906	+	0.482057i	0.805230	+	0.592962i	$0.202042\pi$
$174$	−0.764940	+	0.764940i	−0.0579900	+	0.0579900i
$175$		0			0
$176$	−11.3846	−	3.05048i	−0.858143	−	0.229939i
$177$			32.5227i			2.44456i
$178$	−0.411362	+	1.53522i	−0.0308329	+	0.115070i
$179$	−6.48009	+	11.2238i	−0.484345	+	0.838910i	−0.999838	−	0.0179837i	$-0.994275\pi$
$179$	−6.48009	+	11.2238i	−0.484345	+	0.838910i	0.515493	+	0.856893i	$0.327609\pi$
$180$		0			0
$181$			10.2702i			0.763381i	0.924290	+	0.381691i	$0.124658\pi$
$181$			10.2702i			0.763381i	−0.924290	+	0.381691i	$0.875342\pi$
$182$	−0.437634	−	1.09056i	−0.0324396	−	0.0808377i
$183$	9.95533	+	9.95533i	0.735920	+	0.735920i
$184$	0.803468	+	2.99858i	0.0592324	+	0.221059i
$185$		0			0
$186$	2.54506	−	1.46939i	0.186613	−	0.107741i
$187$	16.6331			1.21633
$188$	−3.89101	+	2.24647i	−0.283781	+	0.163841i
$189$	−0.606236	+	2.26250i	−0.0440972	+	0.164573i
$190$		0			0
$191$	4.16282	+	7.21021i	0.301211	+	0.521712i	0.976410	−	0.215923i	$-0.0692759\pi$
$191$	4.16282	+	7.21021i	0.301211	+	0.521712i	−0.675200	+	0.737635i	$0.735943\pi$
$192$	−18.5825	+	4.97917i	−1.34108	+	0.359341i
$193$	−1.25060	+	2.16611i	−0.0900204	+	0.155920i	−0.907519	−	0.420010i	$-0.862027\pi$
$193$	−1.25060	+	2.16611i	−0.0900204	+	0.155920i	0.817499	+	0.575930i	$0.195360\pi$
$194$	0.653243			0.0469001
$195$		0			0
$196$	−0.239560			−0.0171114
$197$	9.79143	−	16.9593i	0.697611	−	1.20830i	−0.271682	−	0.962387i	$-0.587580\pi$
$197$	9.79143	−	16.9593i	0.697611	−	1.20830i	0.969293	−	0.245910i	$-0.0790868\pi$
$198$	−1.21432	+	0.325377i	−0.0862982	+	0.0231235i
$199$	−1.49761	−	2.59393i	−0.106163	−	0.183879i	0.808050	−	0.589114i	$-0.200523\pi$
$199$	−1.49761	−	2.59393i	−0.106163	−	0.183879i	−0.914213	+	0.405235i	$0.867190\pi$
$200$		0			0
$201$	−5.17137	+	19.2998i	−0.364760	+	1.36130i
$202$	0.155034	−	0.0895091i	0.0109082	−	0.00629784i
$203$	−9.05841			−0.635776
$204$	23.8913	−	13.7936i	1.67272	−	0.965747i
$205$		0			0
$206$	−0.131989	−	0.492590i	−0.00919611	−	0.0343204i
$207$	−14.8712	−	14.8712i	−1.03362	−	1.03362i
$208$	−1.99363	+	13.9473i	−0.138233	+	0.967069i
$209$		−	9.79509i		−	0.677541i
$210$		0			0
$211$	2.22460	−	3.85311i	0.153148	−	0.265259i	−0.779235	−	0.626731i	$-0.784392\pi$
$211$	2.22460	−	3.85311i	0.153148	−	0.265259i	0.932383	+	0.361472i	$0.117726\pi$
$212$	4.09521	−	15.2835i	0.281260	−	1.04968i
$213$		−	40.2131i		−	2.75536i
$214$	0.120325	+	0.0322410i	0.00822524	+	0.00220395i
$215$		0			0
$216$	−0.312657	+	0.312657i	−0.0212736	+	0.0212736i
$217$	23.7695	+	6.36902i	1.61358	+	0.432357i
$218$	−0.441165	−	1.64645i	−0.0298795	−	0.111512i
$219$	−16.9392	+	4.53883i	−1.14464	+	0.306706i
$220$		0			0
$221$	−2.37671	−	19.7405i	−0.159875	−	1.32789i
$222$	0.485057	−	0.485057i	0.0325549	−	0.0325549i
$223$	0.704652	+	0.406831i	0.0471870	+	0.0272434i	0.523408	−	0.852082i	$-0.324660\pi$
$223$	0.704652	+	0.406831i	0.0471870	+	0.0272434i	−0.476221	+	0.879326i	$0.657994\pi$
$224$	3.35219	+	1.93538i	0.223977	+	0.129313i
$225$		0			0
$226$	−0.945078	−	0.945078i	−0.0628656	−	0.0628656i
$227$	−12.1854	−	21.1058i	−0.808775	−	1.40084i	−0.913713	−	0.406360i	$-0.866798\pi$
$227$	−12.1854	−	21.1058i	−0.808775	−	1.40084i	0.104938	−	0.994479i	$-0.466535\pi$
$228$	−8.12293	−	14.0693i	−0.537954	−	0.931764i
$229$	−9.07194	−	9.07194i	−0.599491	−	0.599491i	0.340686	−	0.940177i	$-0.389341\pi$
$229$	−9.07194	−	9.07194i	−0.599491	−	0.599491i	−0.940177	+	0.340686i	$0.889341\pi$
$230$		0			0
$231$	−17.2702	−	9.97097i	−1.13630	−	0.656042i
$232$	−1.48088	−	0.854988i	−0.0972247	−	0.0561327i
$233$	3.41602	−	3.41602i	0.223791	−	0.223791i	−0.586302	−	0.810093i	$-0.699417\pi$
$233$	3.41602	−	3.41602i	0.223791	−	0.223791i	0.810093	+	0.586302i	$0.199417\pi$
$234$	0.559678	+	1.39469i	0.0365873	+	0.0911735i
$235$		0			0
$236$	−24.7321	+	6.62695i	−1.60992	+	0.431378i
$237$	−3.85130	−	14.3732i	−0.250169	−	0.933642i
$238$	−1.73602	−	0.465166i	−0.112530	−	0.0301523i
$239$	1.50535	−	1.50535i	0.0973730	−	0.0973730i	−0.656742	−	0.754115i	$-0.728066\pi$
$239$	1.50535	−	1.50535i	0.0973730	−	0.0973730i	0.754115	+	0.656742i	$0.228066\pi$
$240$		0			0
$241$	16.8894	+	4.52549i	1.08794	+	0.291513i	0.757845	−	0.652435i	$-0.226253\pi$
$241$	16.8894	+	4.52549i	1.08794	+	0.291513i	0.330095	+	0.943948i	$0.392919\pi$
$242$			0.236394i			0.0151960i
$243$	−5.78992	+	21.6083i	−0.371424	+	1.38617i
$244$	−5.54207	+	9.59915i	−0.354795	+	0.614522i
$245$		0			0
$246$			2.84856i			0.181618i
$247$	−11.6250	+	1.39962i	−0.739680	+	0.0890558i
$248$	3.28473	+	3.28473i	0.208580	+	0.208580i
$249$	6.33792	+	23.6535i	0.401650	+	1.49898i
$250$		0			0
$251$	−0.632462	+	0.365152i	−0.0399207	+	0.0230482i	−0.519828	−	0.854271i	$-0.674004\pi$
$251$	−0.632462	+	0.365152i	−0.0399207	+	0.0230482i	0.479907	+	0.877319i	$0.340670\pi$
$252$	−17.4596			−1.09985
$253$	16.3778	−	9.45574i	1.02966	−	0.594477i
$254$	0.176791	−	0.659791i	0.0110928	−	0.0413990i
$255$		0			0
$256$	−7.38951	−	12.7990i	−0.461844	−	0.799938i
$257$	14.8326	−	3.97438i	0.925232	−	0.247915i	0.235411	−	0.971896i	$-0.424356\pi$
$257$	14.8326	−	3.97438i	0.925232	−	0.247915i	0.689820	+	0.723981i	$0.257690\pi$
$258$	−0.469551	+	0.813286i	−0.0292329	+	0.0506329i
$259$	5.74404			0.356917
$260$		0			0
$261$	11.5845			0.717065
$262$	−0.116483	+	0.201755i	−0.00719636	+	0.0124645i
$263$	−24.6842	+	6.61411i	−1.52209	+	0.407844i	−0.920430	−	0.390907i	$-0.872161\pi$
$263$	−24.6842	+	6.61411i	−1.52209	+	0.407844i	−0.601663	+	0.798750i	$0.705495\pi$
$264$	−1.88224	−	3.26014i	−0.115844	−	0.200648i
$265$		0			0
$266$	−0.273932	+	1.02233i	−0.0167959	+	0.0626830i
$267$	27.9230	−	16.1213i	1.70886	−	0.986610i
$268$	−15.7304			−0.960889
$269$	−8.63715	+	4.98666i	−0.526617	+	0.304042i	−0.739638	−	0.673005i	$-0.765003\pi$
$269$	−8.63715	+	4.98666i	−0.526617	+	0.304042i	0.213021	+	0.977048i	$0.431670\pi$
$270$		0			0
$271$	2.45325	+	9.15564i	0.149024	+	0.556166i	0.999543	+	0.0302215i	$0.00962126\pi$
$271$	2.45325	+	9.15564i	0.149024	+	0.556166i	−0.850519	+	0.525944i	$0.823712\pi$
$272$	15.2372	+	15.2372i	0.923892	+	0.923892i
$273$	−9.36598	+	21.9214i	−0.566855	+	1.32674i
$274$		−	0.103489i		−	0.00625200i
$275$		0			0
$276$	15.6830	−	27.1638i	0.944007	−	1.63507i
$277$	−1.34713	+	5.02757i	−0.0809414	+	0.302077i	−0.994515	−	0.104597i	$-0.966645\pi$
$277$	−1.34713	+	5.02757i	−0.0809414	+	0.302077i	0.913573	+	0.406674i	$0.133312\pi$
$278$			1.76082i			0.105607i
$279$	−30.3981	−	8.14515i	−1.81989	−	0.487638i
$280$		0			0
$281$	18.7894	−	18.7894i	1.12088	−	1.12088i	0.129271	−	0.991609i	$-0.458736\pi$
$281$	18.7894	−	18.7894i	1.12088	−	1.12088i	0.991609	−	0.129271i	$-0.0412638\pi$
$282$	−0.684973	−	0.183538i	−0.0407895	−	0.0109295i
$283$	7.18567	+	26.8173i	0.427144	+	1.59412i	0.759197	+	0.650861i	$0.225592\pi$
$283$	7.18567	+	26.8173i	0.427144	+	1.59412i	−0.332053	+	0.943261i	$0.607741\pi$
$284$	30.5804	−	8.19398i	1.81461	−	0.486223i
$285$		0			0
$286$	−1.34165	+	0.161531i	−0.0793333	+	0.00955155i
$287$	−16.8663	+	16.8663i	−0.995586	+	0.995586i
$288$	−4.28701	−	2.47511i	−0.252615	−	0.145847i
$289$	−11.6138	−	6.70521i	−0.683162	−	0.394424i
$290$		0			0
$291$	−9.37052	−	9.37052i	−0.549310	−	0.549310i
$292$	−6.90318	−	11.9567i	−0.403978	−	0.699711i
$293$	−3.52420	−	6.10410i	−0.205886	−	0.356605i	0.744529	−	0.667591i	$-0.232674\pi$
$293$	−3.52420	−	6.10410i	−0.205886	−	0.356605i	−0.950415	+	0.310985i	$0.899341\pi$
$294$	−0.0267361	−	0.0267361i	−0.00155928	−	0.00155928i
$295$		0			0
$296$	0.939043	+	0.542157i	0.0545808	+	0.0315122i
$297$	2.33274	+	1.34681i	0.135359	+	0.0781498i
$298$	−0.00571673	+	0.00571673i	−0.000331161	+	0.000331161i
$299$	−13.5625	−	18.0864i	−0.784338	−	1.04596i
$300$		0			0
$301$	−7.59566	+	2.03525i	−0.437807	+	0.117310i
$302$	0.0229208	+	0.0855417i	0.00131895	+	0.00492237i
$303$	−3.50788	−	0.939933i	−0.201522	−	0.0539978i
$304$	8.97305	−	8.97305i	0.514640	−	0.514640i
$305$		0			0
$306$	2.22015	+	0.594888i	0.126918	+	0.0340075i
$307$			17.7175i			1.01119i	0.862770	+	0.505596i	$0.168727\pi$
$307$			17.7175i			1.01119i	−0.862770	+	0.505596i	$0.831273\pi$
$308$	4.06345	−	15.1650i	0.231537	−	0.864106i
$309$	−5.17268	+	8.95934i	−0.294263	+	0.509679i
$310$		0			0
$311$			18.1295i			1.02803i	0.857782	+	0.514014i	$0.171842\pi$
$311$			18.1295i			1.02803i	−0.857782	+	0.514014i	$0.828158\pi$
$312$	−3.60023	+	2.69972i	−0.203823	+	0.152841i
$313$	7.90286	+	7.90286i	0.446696	+	0.446696i	0.894255	−	0.447558i	$-0.147706\pi$
$313$	7.90286	+	7.90286i	0.446696	+	0.446696i	−0.447558	+	0.894255i	$0.647706\pi$
$314$	−0.536028	−	2.00049i	−0.0302498	−	0.112894i
$315$		0			0
$316$	10.1455	−	5.85750i	0.570728	−	0.329510i
$317$	−8.03345			−0.451203			−0.225602	−	0.974220i	$-0.572435\pi$
$317$	−8.03345			−0.451203			−0.225602	+	0.974220i	$0.572435\pi$
$318$	2.16276	−	1.24867i	0.121282	−	0.0700219i
$319$	−2.69612	+	10.0621i	−0.150954	+	0.563367i
$320$		0			0
$321$	−1.26353	−	2.18850i	−0.0705233	−	0.122150i
$322$	−1.97382	+	0.528884i	−0.109997	+	0.0294735i
$323$	−8.95420	+	15.5091i	−0.498225	+	0.862951i
$324$	−15.5027			−0.861262
$325$		0			0
$326$	0.493544			0.0273349
$327$	−17.2894	+	29.9461i	−0.956104	+	1.65602i
$328$	−4.34927	+	1.16538i	−0.240148	+	0.0643476i
$329$	−2.96899	−	5.14245i	−0.163686	−	0.283512i
$330$		0			0
$331$	3.42770	−	12.7924i	0.188403	−	0.703131i	−0.805473	−	0.592633i	$-0.798089\pi$
$331$	3.42770	−	12.7924i	0.188403	−	0.703131i	0.993876	−	0.110499i	$-0.0352448\pi$
$332$	−16.6960	+	9.63944i	−0.916312	+	0.529033i
$333$	−7.34588			−0.402552
$334$	−1.36303	+	0.786947i	−0.0745818	+	0.0430598i
$335$		0			0
$336$	−6.68668	−	24.9550i	−0.364788	−	1.36141i
$337$	−1.40596	−	1.40596i	−0.0765877	−	0.0765877i	0.667775	−	0.744363i	$-0.267247\pi$
$337$	−1.40596	−	1.40596i	−0.0765877	−	0.0765877i	−0.744363	+	0.667775i	$0.767247\pi$
$338$	0.383417	+	1.56921i	0.0208551	+	0.0853538i
$339$			27.1135i			1.47261i
$340$		0			0
$341$	14.1494	−	24.5074i	0.766232	−	1.32715i
$342$	0.350324	−	1.30743i	0.0189433	−	0.0706975i
$343$		−	18.6765i		−	1.00844i
$344$	−1.43385	−	0.384199i	−0.0773080	−	0.0207146i
$345$		0			0
$346$	−2.15248	+	2.15248i	−0.115718	+	0.115718i
$347$	4.58620	+	1.22887i	0.246200	+	0.0659692i	0.379809	−	0.925065i	$-0.375990\pi$
$347$	4.58620	+	1.22887i	0.246200	+	0.0659692i	−0.133608	+	0.991034i	$0.542656\pi$
$348$	4.47171	+	16.6887i	0.239709	+	0.894606i
$349$	−2.32494	+	0.622965i	−0.124451	+	0.0333466i	−0.320507	−	0.947246i	$-0.603853\pi$
$349$	−2.32494	+	0.622965i	−0.124451	+	0.0333466i	0.196056	+	0.980593i	$0.437187\pi$
$350$		0			0
$351$	1.26509	−	2.96099i	0.0675256	−	0.158046i
$352$	3.14756	−	3.14756i	0.167765	−	0.167765i
$353$	−4.58374	−	2.64643i	−0.243968	−	0.140855i	0.373031	−	0.927819i	$-0.378318\pi$
$353$	−4.58374	−	2.64643i	−0.243968	−	0.140855i	−0.616999	+	0.786964i	$0.711652\pi$
$354$	−3.49983	−	2.02063i	−0.186014	−	0.107395i
$355$		0			0
$356$	17.9493	+	17.9493i	0.951311	+	0.951311i
$357$	18.2300	+	31.5752i	0.964832	+	1.67114i
$358$	−0.805212	−	1.39467i	−0.0425568	−	0.0737105i
$359$	−0.976204	−	0.976204i	−0.0515221	−	0.0515221i	0.680876	−	0.732398i	$-0.261599\pi$
$359$	−0.976204	−	0.976204i	−0.0515221	−	0.0515221i	−0.732398	+	0.680876i	$0.761599\pi$
$360$		0			0
$361$	−7.32130	−	4.22696i	−0.385332	−	0.222471i
$362$	−1.10520	−	0.638087i	−0.0580880	−	0.0335371i
$363$	3.39099	−	3.39099i	0.177981	−	0.177981i
$364$	−18.5787	−	2.65564i	−0.973789	−	0.139194i
$365$		0			0
$366$	−1.68983	+	0.452790i	−0.0883290	+	0.0236677i
$367$	−7.60345	−	28.3765i	−0.396897	−	1.48124i	−0.818525	−	0.574471i	$-0.805208\pi$
$367$	−7.60345	−	28.3765i	−0.396897	−	1.48124i	0.421628	−	0.906769i	$-0.361459\pi$
$368$	23.6655	+	6.34116i	1.23365	+	0.330556i
$369$	21.5698	−	21.5698i	1.12288	−	1.12288i
$370$		0			0
$371$	20.1990	+	5.41232i	1.04868	+	0.280994i
$372$		−	46.9355i		−	2.43349i
$373$	−5.77365	+	21.5476i	−0.298949	+	1.11569i	0.639082	+	0.769139i	$0.279314\pi$
$373$	−5.77365	+	21.5476i	−0.298949	+	1.11569i	−0.938031	+	0.346552i	$0.887352\pi$
$374$	−1.03341	+	1.78992i	−0.0534364	+	0.0925546i
$375$		0			0
$376$		−	1.12093i		−	0.0578073i
$377$	12.3271	+	1.76203i	0.634877	+	0.0907493i
$378$	−0.205807	−	0.205807i	−0.0105856	−	0.0105856i
$379$	7.19049	+	26.8353i	0.369351	+	1.37844i	0.861426	+	0.507883i	$0.169572\pi$
$379$	7.19049	+	26.8353i	0.369351	+	1.37844i	−0.492075	+	0.870553i	$0.663762\pi$
$380$		0			0
$381$	−12.0004	+	6.92846i	−0.614801	+	0.354956i
$382$	−1.03454			−0.0529316
$383$	−3.00371	+	1.73419i	−0.153483	+	0.0886132i	−0.574774	−	0.818312i	$-0.694910\pi$
$383$	−3.00371	+	1.73419i	−0.153483	+	0.0886132i	0.421292	+	0.906925i	$0.361577\pi$
$384$	2.54439	−	9.49580i	0.129843	−	0.484580i
$385$		0			0
$386$	−0.155399	−	0.269159i	−0.00790961	−	0.0136998i
$387$	9.71388	−	2.60283i	0.493784	−	0.132309i
$388$	5.21651	−	9.03526i	0.264828	−	0.458696i
$389$	−15.9955			−0.811006			−0.405503	−	0.914094i	$-0.632904\pi$
$389$	−15.9955			−0.811006			−0.405503	+	0.914094i	$0.632904\pi$
$390$		0			0
$391$	−34.5759			−1.74858
$392$	0.0298834	−	0.0517596i	0.00150934	−	0.00261425i
$393$	4.56500	−	1.22319i	0.230274	−	0.0617017i
$394$	1.21668	+	2.10735i	0.0612953	+	0.106167i
$395$		0			0
$396$	−5.19663	+	19.3941i	−0.261140	+	0.974590i
$397$	9.72708	−	5.61593i	0.488188	−	0.281856i	−0.235634	−	0.971842i	$-0.575717\pi$
$397$	9.72708	−	5.61593i	0.488188	−	0.281856i	0.723823	+	0.689986i	$0.242383\pi$
$398$	0.372184			0.0186559
$399$	18.5944	−	10.7355i	0.930882	−	0.537445i
$400$		0			0
$401$	1.94255	+	7.24971i	0.0970065	+	0.362033i	0.997316	−	0.0732171i	$-0.0233266\pi$
$401$	1.94255	+	7.24971i	0.0970065	+	0.362033i	−0.900310	+	0.435250i	$0.856660\pi$
$402$	−1.75559	−	1.75559i	−0.0875610	−	0.0875610i
$403$	−31.1076	−	13.2908i	−1.54958	−	0.662064i
$404$		−	2.85912i		−	0.142246i
$405$		0			0
$406$	0.562796	−	0.974792i	0.0279311	−	0.0483781i
$407$	1.70964	−	6.38046i	0.0847437	−	0.316268i
$408$			6.88262i			0.340740i
$409$	36.5236	+	9.78648i	1.80598	+	0.483910i	0.994886	−	0.101008i	$-0.0322067\pi$
$409$	36.5236	+	9.78648i	1.80598	+	0.483910i	0.811092	+	0.584918i	$0.198873\pi$
$410$		0			0
$411$	−1.48451	+	1.48451i	−0.0732255	+	0.0732255i
$412$	−7.86720	−	2.10801i	−0.387589	−	0.103854i
$413$	−8.75834	−	32.6866i	−0.430970	−	1.60840i
$414$	2.52426	−	0.676374i	0.124061	−	0.0332420i
$415$		0			0
$416$	−4.18533	−	3.28582i	−0.205203	−	0.161100i
$417$	25.2582	−	25.2582i	1.23690	−	1.23690i
$418$	1.05407	+	0.608566i	0.0515561	+	0.0297659i
$419$	−2.07584	−	1.19849i	−0.101411	−	0.0585499i	0.448437	−	0.893815i	$-0.351981\pi$
$419$	−2.07584	−	1.19849i	−0.101411	−	0.0585499i	−0.549848	+	0.835265i	$0.685314\pi$
$420$		0			0
$421$	13.9343	+	13.9343i	0.679116	+	0.679116i	0.959800	−	0.280684i	$-0.0905614\pi$
$421$	13.9343	+	13.9343i	0.679116	+	0.679116i	−0.280684	+	0.959800i	$0.590561\pi$
$422$	0.276427	+	0.478786i	0.0134563	+	0.0233069i
$423$	3.79696	+	6.57653i	0.184614	+	0.319762i
$424$	2.79132	+	2.79132i	0.135559	+	0.135559i
$425$		0			0
$426$	4.32741	+	2.49843i	0.209663	+	0.121049i
$427$	−12.6865	−	7.32453i	−0.613941	−	0.354459i
$428$	1.40680	−	1.40680i	0.0680001	−	0.0680001i
$429$	21.5625	+	16.9283i	1.04105	+	0.817307i
$430$		0			0
$431$	−18.4142	+	4.93407i	−0.886981	+	0.237666i	−0.673417	−	0.739263i	$-0.735174\pi$
$431$	−18.4142	+	4.93407i	−0.886981	+	0.237666i	−0.213565	+	0.976929i	$0.568507\pi$
$432$	0.903190	+	3.37075i	0.0434548	+	0.162175i
$433$	−7.37884	−	1.97715i	−0.354604	−	0.0950159i	0.0771194	−	0.997022i	$-0.475428\pi$
$433$	−7.37884	−	1.97715i	−0.354604	−	0.0950159i	−0.431724	+	0.902006i	$0.642094\pi$
$434$	−2.16217	+	2.16217i	−0.103788	+	0.103788i
$435$		0			0
$436$	−26.2956	−	7.04590i	−1.25933	−	0.337437i
$437$			20.3614i			0.974020i
$438$	0.563993	−	2.10485i	0.0269486	−	0.100574i
$439$	−2.24892	+	3.89524i	−0.107335	+	0.185910i	−0.914690	−	0.404157i	$-0.867565\pi$
$439$	−2.24892	+	3.89524i	−0.107335	+	0.185910i	0.807355	+	0.590066i	$0.200898\pi$
$440$		0			0
$441$			0.404901i			0.0192810i
$442$	2.27197	+	0.970708i	0.108067	+	0.0461719i
$443$	−20.2178	−	20.2178i	−0.960576	−	0.960576i	0.0386758	−	0.999252i	$-0.487686\pi$
$443$	−20.2178	−	20.2178i	−0.960576	−	0.960576i	−0.999252	+	0.0386758i	$0.987686\pi$
$444$	−2.83556	−	10.5825i	−0.134570	−	0.502221i
$445$		0			0
$446$	−0.0875596	+	0.0505526i	−0.00414607	+	0.00239373i
$447$	0.164008			0.00775733
$448$	17.3352	−	10.0085i	0.819013	−	0.472858i
$449$	4.01450	−	14.9823i	0.189456	−	0.707059i	−0.804177	−	0.594390i	$-0.797393\pi$
$449$	4.01450	−	14.9823i	0.189456	−	0.707059i	0.993633	−	0.112669i	$-0.0359399\pi$
$450$		0			0
$451$	13.7150	+	23.7551i	0.645814	+	1.11858i
$452$	−20.6187	+	5.52476i	−0.969822	+	0.259863i
$453$	0.898272	−	1.55585i	0.0422045	−	0.0731004i
$454$	3.02831			0.142125
$455$		0			0
$456$	4.05311			0.189804
$457$	2.26685	−	3.92630i	0.106039	−	0.183665i	−0.808123	−	0.589013i	$-0.799517\pi$
$457$	2.26685	−	3.92630i	0.106039	−	0.183665i	0.914162	+	0.405349i	$0.132850\pi$
$458$	1.53989	−	0.412611i	0.0719541	−	0.0192800i
$459$	−2.46238	−	4.26496i	−0.114934	−	0.199071i
$460$		0			0
$461$	1.41111	−	5.26633i	0.0657219	−	0.245278i	−0.925248	−	0.379363i	$-0.876143\pi$
$461$	1.41111	−	5.26633i	0.0657219	−	0.245278i	0.990970	+	0.134086i	$0.0428097\pi$
$462$	2.14599	−	1.23899i	0.0998404	−	0.0576429i
$463$	34.6785			1.61165			0.805824	−	0.592155i	$-0.201723\pi$
$463$	34.6785			1.61165			0.805824	+	0.592155i	$0.201723\pi$
$464$	−11.6875	+	6.74777i	−0.542577	+	0.313257i
$465$		0			0
$466$	0.155368	+	0.579840i	0.00719727	+	0.0268606i
$467$	0.351988	+	0.351988i	0.0162881	+	0.0162881i	0.715204	−	0.698916i	$-0.246334\pi$
$467$	0.351988	+	0.351988i	0.0162881	+	0.0162881i	−0.698916	+	0.715204i	$0.746334\pi$
$468$	23.7598	+	3.39623i	1.09830	+	0.156991i
$469$		−	20.7897i		−	0.959979i
$470$		0			0
$471$	−21.0071	+	36.3853i	−0.967954	+	1.67655i
$472$	1.65333	−	6.17031i	0.0761007	−	0.284012i
$473$			9.04301i			0.415798i
$474$	1.78601	+	0.478560i	0.0820342	+	0.0219810i
$475$		0			0
$476$	−20.2970	+	20.2970i	−0.930312	+	0.930312i
$477$	−25.8320	−	6.92166i	−1.18277	−	0.316921i
$478$	0.0684665	+	0.255520i	0.00313158	+	0.0116872i
$479$	−16.9065	+	4.53008i	−0.772478	+	0.206985i	−0.623466	−	0.781851i	$-0.714276\pi$
$479$	−16.9065	+	4.53008i	−0.772478	+	0.206985i	−0.149012	+	0.988835i	$0.547609\pi$
$480$		0			0
$481$	−7.81673	−	1.11732i	−0.356412	−	0.0509456i
$482$	−1.53633	+	1.53633i	−0.0699778	+	0.0699778i
$483$	35.9003	+	20.7271i	1.63352	+	0.943114i
$484$	3.26966	+	1.88774i	0.148621	+	0.0858063i
$485$		0			0
$486$	−1.96558	−	1.96558i	−0.0891605	−	0.0891605i
$487$	3.59243	+	6.22227i	0.162788	+	0.281958i	0.935868	−	0.352352i	$-0.114618\pi$
$487$	3.59243	+	6.22227i	0.162788	+	0.281958i	−0.773079	+	0.634309i	$0.781285\pi$
$488$	−1.38267	−	2.39485i	−0.0625904	−	0.108410i
$489$	−7.07969	−	7.07969i	−0.320155	−	0.320155i
$490$		0			0
$491$	−10.4598	−	6.03895i	−0.472042	−	0.272534i	0.245052	−	0.969510i	$-0.421195\pi$
$491$	−10.4598	−	6.03895i	−0.472042	−	0.272534i	−0.717094	+	0.696976i	$0.754528\pi$
$492$	39.3995	+	22.7473i	1.77627	+	1.02553i
$493$	13.4672	−	13.4672i	0.606531	−	0.606531i
$494$	0.571641	−	1.33794i	0.0257193	−	0.0601969i
$495$		0			0
$496$	35.4126	−	9.48878i	1.59007	−	0.426059i
$497$	10.8294	+	40.4157i	0.485763	+	1.81289i
$498$	−2.93916	−	0.787547i	−0.131707	−	0.0352908i
$499$	−26.4464	+	26.4464i	−1.18390	+	1.18390i	−0.205177	+	0.978725i	$0.565777\pi$
$499$	−26.4464	+	26.4464i	−1.18390	+	1.18390i	−0.978725	+	0.205177i	$0.934223\pi$
$500$		0			0
$501$	30.8406	+	8.26372i	1.37786	+	0.369196i
$502$		−	0.0907472i		−	0.00405025i
$503$	6.61654	−	24.6933i	0.295017	−	1.10102i	−0.646187	−	0.763179i	$-0.723637\pi$
$503$	6.61654	−	24.6933i	0.295017	−	1.10102i	0.941204	−	0.337839i	$-0.109696\pi$
$504$	2.17796	−	3.77234i	0.0970141	−	0.168033i
$505$		0			0
$506$			2.34993i			0.104467i
$507$	17.0097	−	28.0097i	0.755429	−	1.24395i
$508$	−7.71406	−	7.71406i	−0.342256	−	0.342256i
$509$	−2.29966	−	8.58245i	−0.101931	−	0.380410i	0.896048	−	0.443957i	$-0.146426\pi$
$509$	−2.29966	−	8.58245i	−0.101931	−	0.380410i	−0.997979	+	0.0635463i	$0.979759\pi$
$510$		0			0
$511$	15.8022	−	9.12340i	0.699048	−	0.403596i
$512$	9.63626			0.425866
$513$	−2.51160	+	1.45007i	−0.110890	+	0.0640222i
$514$	−0.493854	+	1.84309i	−0.0217830	+	0.0812952i
$515$		0			0
$516$	7.49924	+	12.9891i	0.330136	+	0.571812i
$517$	−6.59590	+	1.76737i	−0.290087	+	0.0777286i
$518$	−0.356875	+	0.618126i	−0.0156802	+	0.0271589i
$519$	61.7530			2.71066
$520$		0			0
$521$	−25.8875			−1.13415			−0.567076	−	0.823666i	$-0.691925\pi$
$521$	−25.8875			−1.13415			−0.567076	+	0.823666i	$0.691925\pi$
$522$	−0.719744	+	1.24663i	−0.0315024	+	0.0545637i
$523$	1.16769	−	0.312883i	0.0510597	−	0.0136814i	−0.233199	−	0.972429i	$-0.574919\pi$
$523$	1.16769	−	0.312883i	0.0510597	−	0.0136814i	0.284258	+	0.958748i	$0.408253\pi$
$524$	1.86037	+	3.22225i	0.0812704	+	0.140765i
$525$		0			0
$526$	0.821866	−	3.06724i	0.0358350	−	0.133738i
$527$	−44.8070	+	25.8694i	−1.95183	+	1.12689i
$528$	−29.7102			−1.29297
$529$	−14.1266	+	8.15602i	−0.614202	+	0.354610i
$530$		0			0
$531$	11.2008	+	41.8019i	0.486073	+	1.81405i
$532$	11.9527	+	11.9527i	0.518216	+	0.518216i
$533$	26.2332	−	19.6716i	1.13629	−	0.852070i
$534$			4.00646i			0.173376i
$535$		0			0
$536$	1.96226	−	3.39873i	0.0847566	−	0.146803i
$537$	−8.45552	+	31.5564i	−0.364883	+	1.36176i
$538$		−	1.23928i		−	0.0534291i
$539$	−0.351688	−	0.0942344i	−0.0151483	−	0.00405896i
$540$		0			0
$541$	1.85241	−	1.85241i	0.0796411	−	0.0796411i	−0.666164	−	0.745805i	$-0.732065\pi$
$541$	1.85241	−	1.85241i	0.0796411	−	0.0796411i	0.745805	+	0.666164i	$0.232065\pi$
$542$	−1.13767	−	0.304839i	−0.0488673	−	0.0130940i
$543$	6.70054	+	25.0068i	0.287548	+	1.07314i
$544$	−7.86105	+	2.10636i	−0.337040	+	0.0903095i
$545$		0			0
$546$	−1.77709	−	2.36986i	−0.0760525	−	0.101421i
$547$	−13.8446	+	13.8446i	−0.591954	+	0.591954i	−0.938159	−	0.346205i	$-0.887470\pi$
$547$	−13.8446	+	13.8446i	−0.591954	+	0.591954i	0.346205	+	0.938159i	$0.387470\pi$
$548$	−1.43140	−	0.826417i	−0.0611462	−	0.0353028i
$549$	16.2243	+	9.36713i	0.692438	+	0.399779i
$550$		0			0
$551$	−7.93069	−	7.93069i	−0.337859	−	0.337859i
$552$	3.91269	+	6.77698i	0.166535	+	0.288447i
$553$	7.74140	+	13.4085i	0.329198	+	0.570187i
$554$	−0.457329	−	0.457329i	−0.0194300	−	0.0194300i
$555$		0			0
$556$	24.3545	+	14.0611i	1.03286	+	0.596323i
$557$	−29.0126	−	16.7504i	−1.22930	−	0.709738i	−0.262418	−	0.964954i	$-0.584520\pi$
$557$	−29.0126	−	16.7504i	−1.22930	−	0.709738i	−0.966884	+	0.255216i	$0.917853\pi$
$558$	2.76514	−	2.76514i	0.117058	−	0.117058i
$559$	10.7324	−	1.29216i	0.453932	−	0.0546524i
$560$		0			0
$561$	40.4996	−	10.8518i	1.70989	−	0.458165i
$562$	0.854581	+	3.18934i	0.0360483	+	0.134534i
$563$	−16.5085	−	4.42343i	−0.695748	−	0.186425i	−0.106423	−	0.994321i	$-0.533940\pi$
$563$	−16.5085	−	4.42343i	−0.695748	−	0.186425i	−0.589325	+	0.807896i	$0.700606\pi$
$564$	−8.00847	+	8.00847i	−0.337217	+	0.337217i
$565$		0			0
$566$	−3.33230	−	0.892887i	−0.140067	−	0.0375308i
$567$		−	20.4887i		−	0.860446i
$568$	−2.04428	+	7.62936i	−0.0857761	+	0.320121i
$569$	22.0925	−	38.2653i	0.926165	−	1.60416i	0.136488	−	0.990642i	$-0.456418\pi$
$569$	22.0925	−	38.2653i	0.926165	−	1.60416i	0.789677	−	0.613523i	$-0.210248\pi$
$570$		0			0
$571$		−	37.9123i		−	1.58658i	−0.608844	−	0.793290i	$-0.708367\pi$
$571$		−	37.9123i		−	1.58658i	0.608844	−	0.793290i	$-0.291633\pi$
$572$	−8.47960	+	19.8468i	−0.354550	+	0.829835i
$573$	14.8400	+	14.8400i	0.619952	+	0.619952i
$574$	−0.767115	−	2.86291i	−0.0320188	−	0.119496i
$575$		0			0
$576$	−22.1696	+	12.7996i	−0.923731	+	0.533316i
$577$	16.9069			0.703843			0.351921	−	0.936030i	$-0.385528\pi$
$577$	16.9069			0.703843			0.351921	+	0.936030i	$0.385528\pi$
$578$	1.44312	−	0.833185i	0.0600258	−	0.0346559i
$579$	−1.63184	+	6.09012i	−0.0678171	+	0.253097i
$580$		0			0
$581$	−12.7397	−	22.0658i	−0.528532	−	0.915445i
$582$	1.59057	−	0.426191i	0.0659311	−	0.0176662i
$583$	12.0240	−	20.8261i	0.497982	−	0.862531i
$584$	3.44449			0.142534
$585$		0			0
$586$	0.875831			0.0361802
$587$	15.0303	−	26.0333i	0.620368	−	1.07451i	−0.369049	−	0.929410i	$-0.620317\pi$
$587$	15.0303	−	26.0333i	0.620368	−	1.07451i	0.989417	−	0.145099i	$-0.0463500\pi$
$588$	−0.583299	+	0.156295i	−0.0240549	+	0.00644548i
$589$	15.2342	+	26.3864i	0.627715	+	1.08723i
$590$		0			0
$591$	12.7763	−	47.6818i	0.525547	−	1.96137i
$592$	7.41115	−	4.27883i	0.304596	−	0.175859i
$593$	−5.10110			−0.209477			−0.104739	−	0.994500i	$-0.533401\pi$
$593$	−5.10110			−0.209477			−0.104739	+	0.994500i	$0.533401\pi$
$594$	−0.289865	+	0.167354i	−0.0118933	+	0.00686661i
$595$		0			0
$596$	0.0334190	+	0.124721i	0.00136890	+	0.00510879i
$597$	−5.33883	−	5.33883i	−0.218504	−	0.218504i
$598$	2.78894	−	0.335782i	0.114048	−	0.0137311i
$599$		−	33.5536i		−	1.37096i	−0.728091	−	0.685480i	$-0.759592\pi$
$599$		−	33.5536i		−	1.37096i	0.728091	−	0.685480i	$-0.240408\pi$
$600$		0			0
$601$	−23.6229	+	40.9160i	−0.963597	+	1.66900i	−0.250259	+	0.968179i	$0.580516\pi$
$601$	−23.6229	+	40.9160i	−0.963597	+	1.66900i	−0.713338	+	0.700820i	$0.752817\pi$
$602$	0.252899	−	0.943833i	0.0103074	−	0.0384677i
$603$			26.5874i			1.08272i
$604$	1.36620	+	0.366071i	0.0555897	+	0.0148952i
$605$		0			0
$606$	0.319091	−	0.319091i	0.0129622	−	0.0129622i
$607$	−3.18128	−	0.852422i	−0.129124	−	0.0345987i	0.193678	−	0.981065i	$-0.437958\pi$
$607$	−3.18128	−	0.852422i	−0.129124	−	0.0345987i	−0.322802	+	0.946466i	$0.604625\pi$
$608$	1.24042	+	4.62930i	0.0503055	+	0.187743i
$609$	−22.0561	+	5.90992i	−0.893758	+	0.239482i
$610$		0			0
$611$	3.04003	+	7.57558i	0.122986	+	0.306475i
$612$	25.9573	−	25.9573i	1.04926	−	1.04926i
$613$	−2.67402	−	1.54384i	−0.108003	−	0.0623553i	0.445026	−	0.895518i	$-0.353195\pi$
$613$	−2.67402	−	1.54384i	−0.108003	−	0.0623553i	−0.553028	+	0.833162i	$0.686528\pi$
$614$	−1.90661	−	1.10078i	−0.0769447	−	0.0444241i
$615$		0			0
$616$	2.76968	+	2.76968i	0.111593	+	0.111593i
$617$	−13.7837	−	23.8740i	−0.554909	−	0.961131i	−0.997911	−	0.0646098i	$-0.979420\pi$
$617$	−13.7837	−	23.8740i	−0.554909	−	0.961131i	0.443002	−	0.896521i	$-0.353914\pi$
$618$	−0.642754	−	1.11328i	−0.0258554	−	0.0447828i
$619$	13.0430	+	13.0430i	0.524244	+	0.524244i	0.918850	−	0.394606i	$-0.129119\pi$
$619$	13.0430	+	13.0430i	0.524244	+	0.524244i	−0.394606	+	0.918850i	$0.629119\pi$
$620$		0			0
$621$	−4.84916	−	2.79967i	−0.194590	−	0.112347i
$622$	−1.95094	−	1.12638i	−0.0782257	−	0.0451636i
$623$	−23.7222	+	23.7222i	−0.950410	+	0.950410i
$624$	4.24529	+	35.2606i	0.169948	+	1.41155i
$625$		0			0
$626$	−1.34144	+	0.359439i	−0.0536149	+	0.0143661i
$627$	−6.39054	−	23.8498i	−0.255214	−	0.952470i
$628$	−31.9500	−	8.56097i	−1.27494	−	0.341620i
$629$	−8.53968	+	8.53968i	−0.340499	+	0.340499i
$630$		0			0
$631$	−23.7377	−	6.36049i	−0.944982	−	0.253207i	−0.246750	−	0.969079i	$-0.579363\pi$
$631$	−23.7377	−	6.36049i	−0.944982	−	0.253207i	−0.698232	+	0.715872i	$0.746029\pi$
$632$			2.92272i			0.116260i
$633$	2.90276	−	10.8332i	0.115374	−	0.430582i
$634$	0.499116	−	0.864494i	0.0198224	−	0.0343334i
$635$		0			0
$636$		−	39.8853i		−	1.58155i
$637$	−0.0615863	+	0.430854i	−0.00244014	+	0.0170711i
$638$	−0.915287	−	0.915287i	−0.0362366	−	0.0362366i
$639$	−13.8494	−	51.6865i	−0.547872	−	2.04469i
$640$		0			0
$641$	−28.0502	+	16.1948i	−1.10792	+	0.639656i	−0.938289	−	0.345852i	$-0.887590\pi$
$641$	−28.0502	+	16.1948i	−1.10792	+	0.639656i	−0.169628	+	0.985508i	$0.554257\pi$
$642$	0.314011			0.0123930
$643$	−29.2730	+	16.9008i	−1.15441	+	0.666501i	−0.949959	−	0.312375i	$-0.898876\pi$
$643$	−29.2730	+	16.9008i	−1.15441	+	0.666501i	−0.204455	+	0.978876i	$0.565542\pi$
$644$	−8.44685	+	31.5241i	−0.332853	+	1.24222i
$645$		0			0
$646$	−1.11264	−	1.92716i	−0.0437764	−	0.0758229i
$647$	32.5598	−	8.72438i	1.28006	−	0.342991i	0.446183	−	0.894942i	$-0.352783\pi$
$647$	32.5598	−	8.72438i	1.28006	−	0.342991i	0.833877	+	0.551951i	$0.186116\pi$
$648$	1.93385	−	3.34953i	0.0759689	−	0.131582i
$649$	−38.9149			−1.52755
$650$		0			0
$651$	62.0311			2.43119
$652$	3.94122	−	6.82639i	0.154350	−	0.267342i
$653$	17.1323	−	4.59060i	0.670441	−	0.179644i	0.0924873	−	0.995714i	$-0.470518\pi$
$653$	17.1323	−	4.59060i	0.670441	−	0.179644i	0.577953	+	0.816070i	$0.303852\pi$
$654$	−2.14837	−	3.72108i	−0.0840077	−	0.145506i
$655$		0			0
$656$	−9.19748	+	34.3255i	−0.359101	+	1.34018i
$657$	−20.2090	+	11.6677i	−0.788427	+	0.455199i
$658$	0.737850			0.0287644
$659$	−11.6311	+	6.71522i	−0.453084	+	0.261588i	−0.709132	−	0.705076i	$-0.750913\pi$
$659$	−11.6311	+	6.71522i	−0.453084	+	0.261588i	0.256048	+	0.966664i	$0.417579\pi$
$660$		0			0
$661$	−9.25257	−	34.5311i	−0.359883	−	1.34310i	−0.874226	−	0.485518i	$-0.838631\pi$
$661$	−9.25257	−	34.5311i	−0.359883	−	1.34310i	0.514343	−	0.857585i	$-0.328036\pi$
$662$	1.16365	+	1.16365i	0.0452264	+	0.0452264i
$663$	−18.6661	−	46.5150i	−0.724933	−	1.80649i
$664$		−	4.80980i		−	0.186657i
$665$		0			0
$666$	0.456398	−	0.790504i	0.0176850	−	0.0306314i
$667$	5.60453	−	20.9164i	0.217008	−	0.809886i
$668$			25.1368i			0.972573i
$669$	1.98117	+	0.530852i	0.0765963	+	0.0205239i
$670$		0			0
$671$	−11.9120	+	11.9120i	−0.459859	+	0.459859i
$672$	9.42484	+	2.52538i	0.363571	+	0.0974186i
$673$	−12.1457	−	45.3283i	−0.468181	−	1.74728i	−0.646120	−	0.763235i	$-0.723610\pi$
$673$	−12.1457	−	45.3283i	−0.468181	−	1.74728i	0.177939	−	0.984042i	$-0.443057\pi$
$674$	0.238650	−	0.0639462i	0.00919247	−	0.00246311i
$675$		0			0
$676$	24.7661	+	7.22783i	0.952543	+	0.277993i
$677$	−11.2472	+	11.2472i	−0.432266	+	0.432266i	−0.889398	−	0.457133i	$-0.848876\pi$
$677$	−11.2472	+	11.2472i	−0.432266	+	0.432266i	0.457133	+	0.889398i	$0.348876\pi$
$678$	−2.91774	−	1.68456i	−0.112055	−	0.0646950i
$679$	11.9412	+	6.89426i	0.458261	+	0.264577i
$680$		0			0
$681$	−43.4399	−	43.4399i	−1.66462	−	1.66462i
$682$	1.75819	+	3.04528i	0.0673247	+	0.116610i
$683$	7.99498	+	13.8477i	0.305919	+	0.529868i	0.977466	−	0.211095i	$-0.0677029\pi$
$683$	7.99498	+	13.8477i	0.305919	+	0.529868i	−0.671546	+	0.740963i	$0.734370\pi$
$684$	−15.2860	−	15.2860i	−0.584474	−	0.584474i
$685$		0			0
$686$	2.00981	+	1.16036i	0.0767349	+	0.0443029i
$687$	−28.0078	−	16.1703i	−1.06856	−	0.616936i
$688$	−8.28409	+	8.28409i	−0.315828	+	0.315828i
$689$	−26.4349	−	11.2944i	−1.00709	−	0.430283i
$690$		0			0
$691$	13.8396	−	3.70831i	0.526483	−	0.141071i	0.0142191	−	0.999899i	$-0.495474\pi$
$691$	13.8396	−	3.70831i	0.526483	−	0.141071i	0.512264	+	0.858828i	$0.328807\pi$
$692$	12.5830	+	46.9605i	0.478335	+	1.78517i
$693$	−25.6317	−	6.86799i	−0.973667	−	0.260893i
$694$	−0.417180	+	0.417180i	−0.0158359	+	0.0158359i
$695$		0			0
$696$	−4.16358	−	1.11563i	−0.157820	−	0.0422877i
$697$		−	50.1504i		−	1.89958i
$698$	0.0774093	−	0.288895i	0.00292999	−	0.0109349i
$699$	6.08889	−	10.5463i	0.230303	−	0.398897i
$700$		0			0
$701$		−	2.47832i		−	0.0936050i	−0.998904	−	0.0468025i	$-0.985097\pi$
$701$		−	2.47832i		−	0.0936050i	0.998904	−	0.0468025i	$-0.0149031\pi$
$702$	0.240037	+	0.320104i	0.00905962	+	0.0120815i
$703$	5.02894	+	5.02894i	0.189670	+	0.189670i
$704$	−5.95781	−	22.2348i	−0.224543	−	0.838007i
$705$		0			0
$706$	0.569573	−	0.328843i	0.0214362	−	0.0123762i
$707$	3.77867			0.142112
$708$	−55.8961	+	32.2716i	−2.10070	+	1.21284i
$709$	2.01972	−	7.53768i	0.0758520	−	0.283084i	−0.917573	−	0.397567i	$-0.869855\pi$
$709$	2.01972	−	7.53768i	0.0758520	−	0.283084i	0.993425	+	0.114483i	$0.0365213\pi$
$710$		0			0
$711$	−9.90026	−	17.1477i	−0.371289	−	0.643091i
$712$	−6.11719	+	1.63910i	−0.229251	+	0.0614277i
$713$	−29.4129	+	50.9446i	−1.10152	+	1.90789i
$714$	−4.53049			−0.169549
$715$		0			0
$716$	−25.7203			−0.961211
$717$	2.68322	−	4.64747i	0.100207	−	0.173563i
$718$	0.165702	−	0.0443998i	0.00618396	−	0.00165699i
$719$	−16.7165	−	28.9539i	−0.623421	−	1.07980i	−0.988844	−	0.148955i	$-0.952409\pi$
$719$	−16.7165	−	28.9539i	−0.623421	−	1.07980i	0.365423	−	0.930842i	$-0.380924\pi$
$720$		0			0
$721$	2.78600	−	10.3975i	0.103756	−	0.387222i
$722$	0.909741	−	0.525239i	0.0338571	−	0.0195474i
$723$	44.0760			1.63921
$724$	−17.6513	+	10.1910i	−0.656004	+	0.378744i
$725$		0			0
$726$	0.154229	+	0.575591i	0.00572398	+	0.0213622i
$727$	22.0118	+	22.0118i	0.816374	+	0.816374i	0.985581	−	0.169207i	$-0.0541206\pi$
$727$	22.0118	+	22.0118i	0.816374	+	0.816374i	−0.169207	+	0.985581i	$0.554121\pi$
$728$	2.89134	−	3.68286i	0.107160	−	0.136496i
$729$			32.9560i			1.22059i
$730$		0			0
$731$	8.26668	−	14.3183i	0.305754	−	0.529582i
$732$	−7.23155	+	26.9885i	−0.267286	+	0.997524i
$733$			32.5431i			1.20201i	0.799246	+	0.601004i	$0.205232\pi$
$733$			32.5431i			1.20201i	−0.799246	+	0.601004i	$0.794768\pi$
$734$	3.52604	+	0.944800i	0.130149	+	0.0348732i
$735$		0			0
$736$	−6.54295	+	6.54295i	−0.241176	+	0.241176i
$737$	−23.0931	−	6.18779i	−0.850647	−	0.227930i
$738$	0.981041	+	3.66130i	0.0361126	+	0.134774i
$739$	34.8599	−	9.34069i	1.28234	−	0.343603i	0.447595	−	0.894236i	$-0.352280\pi$
$739$	34.8599	−	9.34069i	1.28234	−	0.343603i	0.834747	+	0.550633i	$0.185614\pi$
$740$		0			0
$741$	−27.3922	+	10.9923i	−1.00628	+	0.403813i
$742$	−1.83739	+	1.83739i	−0.0674527	+	0.0674527i
$743$	−4.30370	−	2.48474i	−0.157887	−	0.0911563i	0.418975	−	0.907998i	$-0.362390\pi$
$743$	−4.30370	−	2.48474i	−0.157887	−	0.0911563i	−0.576862	+	0.816842i	$0.695723\pi$
$744$	10.1409	+	5.85487i	0.371784	+	0.214650i
$745$		0			0
$746$	−1.96006	−	1.96006i	−0.0717628	−	0.0717628i
$747$	16.2925	+	28.2194i	0.596110	+	1.03249i
$748$	16.5047	+	28.5870i	0.603472	+	1.04524i
$749$	1.85926	+	1.85926i	0.0679357	+	0.0679357i
$750$		0			0
$751$	21.9475	+	12.6714i	0.800876	+	0.462386i	0.843778	−	0.536693i	$-0.180327\pi$
$751$	21.9475	+	12.6714i	0.800876	+	0.462386i	−0.0429011	+	0.999079i	$0.513660\pi$
$752$	−7.66139	−	4.42331i	−0.279382	−	0.161301i
$753$	−1.30173	+	1.30173i	−0.0474378	+	0.0474378i
$754$	−0.955493	+	1.21706i	−0.0347970	+	0.0443229i
$755$		0			0
$756$	−4.49007	+	1.20311i	−0.163302	+	0.0437567i
$757$	−9.11581	−	34.0207i	−0.331320	−	1.23650i	−0.907804	−	0.419394i	$-0.862242\pi$
$757$	−9.11581	−	34.0207i	−0.331320	−	1.23650i	0.576484	−	0.817108i	$-0.304424\pi$
$758$	−3.33454	−	0.893486i	−0.121116	−	0.0324529i
$759$	33.7088	−	33.7088i	1.22355	−	1.22355i
$760$		0			0
$761$	−3.10639	−	0.832355i	−0.112607	−	0.0301728i	0.202076	−	0.979370i	$-0.435231\pi$
$761$	−3.10639	−	0.832355i	−0.112607	−	0.0301728i	−0.314682	+	0.949197i	$0.601898\pi$
$762$		−	1.72185i		−	0.0623761i
$763$	9.31202	−	34.7529i	0.337118	−	1.25814i
$764$	−8.26136	+	14.3091i	−0.298885	+	0.517685i
$765$		0			0
$766$		−	0.430980i		−	0.0155719i
$767$	5.56056	+	46.1849i	0.200780	+	1.66764i
$768$	−26.3429	−	26.3429i	−0.950568	−	0.950568i
$769$	−7.34107	−	27.3973i	−0.264726	−	0.987970i	−0.962418	−	0.271573i	$-0.912456\pi$
$769$	−7.34107	−	27.3973i	−0.264726	−	0.987970i	0.697692	−	0.716398i	$-0.254210\pi$
$770$		0			0
$771$	33.5225	−	19.3542i	1.20728	−	0.697026i
$772$	−4.96379			−0.178651
$773$	−24.8703	+	14.3589i	−0.894524	+	0.516454i	−0.875420	−	0.483364i	$-0.839415\pi$
$773$	−24.8703	+	14.3589i	−0.894524	+	0.516454i	−0.0191044	+	0.999817i	$0.506081\pi$
$774$	−0.323426	+	1.20704i	−0.0116253	+	0.0433862i
$775$		0			0
$776$	1.30144	+	2.25417i	0.0467191	+	0.0809198i
$777$	13.9860	−	3.74754i	0.501745	−	0.134442i
$778$	0.993798	−	1.72131i	0.0356294	−	0.0617119i
$779$	−29.5331			−1.05813
$780$		0			0
$781$	48.1169			1.72176
$782$	2.14819	−	3.72078i	0.0768192	−	0.133055i
$783$	2.97919	−	0.798270i	0.106467	−	0.0285279i
$784$	−0.235847	−	0.408499i	−0.00842310	−	0.0145892i
$785$		0			0
$786$	−0.151993	+	0.567244i	−0.00542140	+	0.0202329i
$787$	−0.450435	+	0.260059i	−0.0160563	+	0.00927010i	−0.508007	−	0.861353i	$-0.669617\pi$
$787$	−0.450435	+	0.260059i	−0.0160563	+	0.00927010i	0.491950	+	0.870623i	$0.336284\pi$
$788$	38.8634			1.38445
$789$	−55.7878	+	32.2091i	−1.98610	+	1.14667i
$790$		0			0
$791$	−7.30165	−	27.2501i	−0.259617	−	0.968903i
$792$	−3.54206	−	3.54206i	−0.125862	−	0.125862i
$793$	15.8395	+	12.4353i	0.562477	+	0.441590i
$794$			1.39567i			0.0495303i
$795$		0			0
$796$	2.97209	−	5.14782i	0.105343	−	0.182459i
$797$	−1.03627	+	3.86739i	−0.0367064	+	0.136990i	−0.981847	−	0.189672i	$-0.939257\pi$
$797$	−1.03627	+	3.86739i	−0.0367064	+	0.136990i	0.945141	+	0.326663i	$0.105924\pi$
$798$			2.66796i			0.0944448i
$799$	12.0593	+	3.23128i	0.426628	+	0.114315i
$800$		0			0
$801$	30.3377	−	30.3377i	1.07193	−	1.07193i
$802$	−0.900844	−	0.241380i	−0.0318099	−	0.00852344i
$803$	−5.43093	−	20.2685i	−0.191653	−	0.715260i
$804$	−38.3016	+	10.2629i	−1.35079	+	0.361944i
$805$		0			0
$806$	3.36296	−	2.52179i	0.118455	−	0.0888264i
$807$	−17.7770	+	17.7770i	−0.625779	+	0.625779i
$808$	0.617743	+	0.356654i	0.0217321	+	0.0125471i
$809$	39.9699	+	23.0766i	1.40527	+	0.811331i	0.994927	−	0.100602i	$-0.0320769\pi$
$809$	39.9699	+	23.0766i	1.40527	+	0.811331i	0.410339	+	0.911933i	$0.365410\pi$
$810$		0			0
$811$	−13.0967	−	13.0967i	−0.459888	−	0.459888i	0.438731	−	0.898618i	$-0.355428\pi$
$811$	−13.0967	−	13.0967i	−0.459888	−	0.459888i	−0.898618	+	0.438731i	$0.855428\pi$
$812$	−8.98848	−	15.5685i	−0.315434	−	0.546347i
$813$	11.9467	+	20.6923i	0.418989	+	0.725710i
$814$	0.580393	+	0.580393i	0.0203428	+	0.0203428i
$815$		0			0
$816$	47.0419	+	27.1596i	1.64679	+	0.950777i
$817$	−8.43192	−	4.86817i	−0.294996	−	0.170316i
$818$	−3.32234	+	3.32234i	−0.116163	+	0.116163i
$819$	−4.48853	+	31.4015i	−0.156842	+	1.09726i
$820$		0			0
$821$	19.0466	−	5.10353i	0.664733	−	0.178115i	0.0893517	−	0.996000i	$-0.471520\pi$
$821$	19.0466	−	5.10353i	0.664733	−	0.178115i	0.575381	+	0.817886i	$0.304854\pi$
$822$	−0.0675186	−	0.251983i	−0.00235498	−	0.00878892i
$823$	5.46939	+	1.46552i	0.190651	+	0.0510848i	0.352881	−	0.935668i	$-0.385202\pi$
$823$	5.46939	+	1.46552i	0.190651	+	0.0510848i	−0.162230	+	0.986753i	$0.551869\pi$
$824$	1.43684	−	1.43684i	0.0500545	−	0.0500545i
$825$		0			0
$826$	4.06161	+	1.08831i	0.141322	+	0.0378670i
$827$			37.5355i			1.30524i	0.757687	+	0.652618i	$0.226329\pi$
$827$			37.5355i			1.30524i	−0.757687	+	0.652618i	$0.773671\pi$
$828$	10.8024	−	40.3153i	0.375411	−	1.40105i
$829$	19.0247	−	32.9518i	0.660756	−	1.14446i	−0.319661	−	0.947532i	$-0.603569\pi$
$829$	19.0247	−	32.9518i	0.660756	−	1.14446i	0.980417	−	0.196932i	$-0.0630977\pi$
$830$		0			0
$831$			13.1204i			0.455142i
$832$	−25.5374	+	10.2480i	−0.885350	+	0.355284i
$833$	0.470703	+	0.470703i	0.0163089	+	0.0163089i
$834$	1.14880	+	4.28737i	0.0397796	+	0.148459i
$835$		0			0
$836$	16.8346	−	9.71947i	0.582237	−	0.336155i
$837$	−8.37872			−0.289611
$838$	0.257942	−	0.148923i	0.00891047	−	0.00514446i
$839$	0.986990	−	3.68350i	0.0340747	−	0.127168i	−0.946793	−	0.321842i	$-0.895698\pi$
$839$	0.986990	−	3.68350i	0.0340747	−	0.127168i	0.980868	+	0.194673i	$0.0623647\pi$
$840$		0			0
$841$	−8.53610	−	14.7850i	−0.294348	−	0.509826i
$842$	−2.36523	+	0.633761i	−0.0815111	+	0.0218408i
$843$	33.4912	−	58.0084i	1.15350	−	1.99792i
$844$	8.82969			0.303930
$845$		0			0
$846$	−0.943616			−0.0324422
$847$	−2.49488	+	4.32126i	−0.0857251	+	0.148480i
$848$	30.0932	−	8.06346i	1.03341	−	0.276900i
$849$	34.9924	+	60.6086i	1.20094	+	2.08008i
$850$		0			0
$851$	−3.55389	+	13.2633i	−0.121826	+	0.454660i
$852$	69.1134	−	39.9027i	2.36779	−	1.36704i
$853$	15.1949			0.520263			0.260132	−	0.965573i	$-0.416234\pi$
$853$	15.1949			0.520263			0.260132	+	0.965573i	$0.416234\pi$
$854$	1.57641	−	0.910141i	0.0539437	−	0.0311444i
$855$		0			0
$856$	0.128466	+	0.479442i	0.00439088	+	0.0163870i
$857$	−21.7961	−	21.7961i	−0.744542	−	0.744542i	0.228906	−	0.973448i	$-0.426485\pi$
$857$	−21.7961	−	21.7961i	−0.744542	−	0.744542i	−0.973448	+	0.228906i	$0.926485\pi$
$858$	−3.16136	+	1.26863i	−0.107927	+	0.0433103i
$859$			19.9625i			0.681113i	0.940224	+	0.340557i	$0.110615\pi$
$859$			19.9625i			0.681113i	−0.940224	+	0.340557i	$0.889385\pi$
$860$		0			0
$861$	−30.0634	+	52.0713i	−1.02456	+	1.77459i
$862$	0.613105	−	2.28814i	0.0208824	−	0.0779343i
$863$			45.8868i			1.56201i	0.624527	+	0.781003i	$0.285292\pi$
$863$			45.8868i			1.56201i	−0.624527	+	0.781003i	$0.714708\pi$
$864$	−1.27304	−	0.341111i	−0.0433098	−	0.0116048i
$865$		0			0
$866$	0.671210	−	0.671210i	0.0228086	−	0.0228086i
$867$	−32.6527	−	8.74926i	−1.10894	−	0.297141i
$868$	12.6397	+	47.1720i	0.429019	+	1.60112i
$869$	17.1983	−	4.60826i	0.583411	−	0.156324i
$870$		0			0
$871$	−4.04399	+	28.2915i	−0.137025	+	0.958621i
$872$	4.80254	−	4.80254i	0.162634	−	0.162634i
$873$	−15.2713	−	8.81687i	−0.516854	−	0.298406i
$874$	−2.19113	−	1.26505i	−0.0741161	−	0.0427910i
$875$		0			0
$876$	−24.6092	−	24.6092i	−0.831467	−	0.831467i
$877$	17.6180	+	30.5152i	0.594916	+	1.03042i	0.993559	+	0.113318i	$0.0361480\pi$
$877$	17.6180	+	30.5152i	0.594916	+	1.03042i	−0.398643	+	0.917106i	$0.630519\pi$
$878$	−0.279449	−	0.484020i	−0.00943096	−	0.0163349i
$879$	−12.5635	−	12.5635i	−0.423755	−	0.423755i
$880$		0			0
$881$	−19.2802	−	11.1314i	−0.649566	−	0.375027i	0.138724	−	0.990331i	$-0.455700\pi$
$881$	−19.2802	−	11.1314i	−0.649566	−	0.375027i	−0.788290	+	0.615304i	$0.789033\pi$
$882$	−0.0435722	−	0.0251564i	−0.00146715	−	0.000847060i
$883$	−11.0289	+	11.0289i	−0.371151	+	0.371151i	−0.867896	−	0.496745i	$-0.834528\pi$
$883$	−11.0289	+	11.0289i	−0.371151	+	0.371151i	0.496745	+	0.867896i	$0.334528\pi$
$884$	31.5692	−	23.6729i	1.06179	−	0.796205i
$885$		0			0
$886$	3.43180	−	0.919547i	0.115293	−	0.0308928i
$887$	4.57003	+	17.0556i	0.153447	+	0.572671i	0.999233	+	0.0391497i	$0.0124649\pi$
$887$	4.57003	+	17.0556i	0.153447	+	0.572671i	−0.845787	+	0.533521i	$0.820868\pi$
$888$	2.64017	+	0.707431i	0.0885983	+	0.0237398i
$889$	10.1951	−	10.1951i	0.341932	−	0.341932i
$890$		0			0
$891$	−22.7588	−	6.09821i	−0.762450	−	0.204298i
$892$			1.61476i			0.0540662i
$893$	1.90287	−	7.10161i	0.0636771	−	0.237646i
$894$	−0.0101898	+	0.0176492i	−0.000340798	+	0.000590279i
$895$		0			0
$896$			10.2288i			0.341722i
$897$	−44.8229	−	35.1895i	−1.49659	−	1.17494i
$898$	1.36285	+	1.36285i	0.0454790	+	0.0454790i
$899$	−8.38650	−	31.2989i	−0.279706	−	1.04388i
$900$		0			0
$901$	−38.0765	+	21.9835i	−1.26851	+	0.732376i
$902$	−3.40844			−0.113489
$903$	−17.1666	+	9.91117i	−0.571270	+	0.329823i
$904$	1.37835	−	5.14407i	0.0458432	−	0.171089i
$905$		0			0
$906$	0.111619	+	0.193329i	0.00370829	+	0.00642294i
$907$	53.6498	−	14.3754i	1.78141	−	0.477328i	0.790573	−	0.612367i	$-0.209783\pi$
$907$	53.6498	−	14.3754i	1.78141	−	0.477328i	0.990840	+	0.135039i	$0.0431160\pi$
$908$	24.1827	−	41.8856i	0.802531	−	1.39002i
$909$	−4.83244			−0.160282
$910$		0			0
$911$	−15.2824			−0.506330			−0.253165	−	0.967423i	$-0.581472\pi$
$911$	−15.2824			−0.506330			−0.253165	+	0.967423i	$0.581472\pi$
$912$	15.9940	−	27.7025i	0.529616	−	0.917321i
$913$	−28.3025	+	7.58363i	−0.936675	+	0.250981i
$914$	0.281678	+	0.487880i	0.00931706	+	0.0161376i
$915$		0			0
$916$	6.58985	−	24.5937i	0.217735	−	0.812597i
$917$	−4.25860	+	2.45870i	−0.140631	+	0.0811935i
$918$	0.611947			0.0201973
$919$	15.6355	−	9.02717i	0.515768	−	0.297779i	−0.219433	−	0.975628i	$-0.570421\pi$
$919$	15.6355	−	9.02717i	0.515768	−	0.297779i	0.735202	+	0.677848i	$0.237087\pi$
$920$		0			0
$921$	11.5593	+	43.1400i	0.380893	+	1.42151i
$922$	0.479048	+	0.479048i	0.0157766	+	0.0157766i
$923$	−6.87543	−	57.1059i	−0.226307	−	1.87966i
$924$		−	39.5760i		−	1.30195i
$925$		0			0
$926$	−2.15457	+	3.73182i	−0.0708035	+	0.122635i
$927$	−3.56293	+	13.2970i	−0.117022	+	0.436732i
$928$		−	5.09690i		−	0.167314i
$929$	40.3925	+	10.8231i	1.32524	+	0.355096i	0.850937	−	0.525268i	$-0.176035\pi$
$929$	40.3925	+	10.8231i	1.32524	+	0.355096i	0.474299	+	0.880364i	$0.342702\pi$
$930$		0			0
$931$	0.277192	−	0.277192i	0.00908461	−	0.00908461i
$932$	9.26069	+	2.48139i	0.303344	+	0.0812808i
$933$	11.8281	+	44.1430i	0.387234	+	1.44518i
$934$	−0.0597469	+	0.0160091i	−0.00195498	+	0.000523835i
$935$		0			0
$936$	−3.69765	+	4.70990i	−0.120862	+	0.153948i
$937$	10.8603	−	10.8603i	0.354791	−	0.354791i	−0.507098	−	0.861889i	$-0.669282\pi$
$937$	10.8603	−	10.8603i	0.354791	−	0.354791i	0.861889	+	0.507098i	$0.169282\pi$
$938$	2.23722	+	1.29166i	0.0730477	+	0.0421741i
$939$	24.3985	+	14.0865i	0.796215	+	0.459695i
$940$		0			0
$941$	33.9949	+	33.9949i	1.10820	+	1.10820i	0.993387	+	0.114815i	$0.0366274\pi$
$941$	33.9949	+	33.9949i	1.10820	+	1.10820i	0.114815	+	0.993387i	$0.463373\pi$
$942$	−2.61033	−	4.52122i	−0.0850490	−	0.147309i
$943$	−28.5099	−	49.3806i	−0.928411	−	1.60805i
$944$	−35.6491	−	35.6491i	−1.16028	−	1.16028i
$945$		0			0
$946$	−0.973134	−	0.561839i	−0.0316393	−	0.0182670i
$947$	40.6489	+	23.4687i	1.32091	+	0.762629i	0.983874	−	0.178862i	$-0.0572416\pi$
$947$	40.6489	+	23.4687i	1.32091	+	0.762629i	0.337038	+	0.941491i	$0.390575\pi$
$948$	20.8814	−	20.8814i	0.678197	−	0.678197i
$949$	−23.2790	+	9.34169i	−0.755668	+	0.303244i
$950$		0			0
$951$	−19.5605	+	5.24121i	−0.634291	+	0.169958i
$952$	−1.85348	−	6.91729i	−0.0600717	−	0.224191i
$953$	3.06703	+	0.821808i	0.0993508	+	0.0266210i	0.308152	−	0.951337i	$-0.400289\pi$
$953$	3.06703	+	0.821808i	0.0993508	+	0.0266210i	−0.208801	+	0.977958i	$0.566956\pi$
$954$	2.34979	−	2.34979i	0.0760771	−	0.0760771i
$955$		0			0
$956$	4.08094	+	1.09349i	0.131987	+	0.0353658i
$957$			26.2589i			0.848829i
$958$	0.562905	−	2.10079i	0.0181866	−	0.0678735i
$959$	1.09221	−	1.89177i	0.0352694	−	0.0610883i
$960$		0			0
$961$			57.0256i			1.83953i
$962$	0.605888	−	0.771753i	0.0195346	−	0.0248823i
$963$	−2.37775	−	2.37775i	−0.0766219	−	0.0766219i
$964$	8.98111	+	33.5179i	0.289262	+	1.07954i
$965$		0			0
$966$	−4.46095	+	2.57553i	−0.143529	+	0.0828664i
$967$	18.3290			0.589421			0.294711	−	0.955587i	$-0.404777\pi$
$967$	18.3290			0.589421			0.294711	+	0.955587i	$0.404777\pi$
$968$	−0.815733	+	0.470964i	−0.0262187	+	0.0151374i
$969$	−11.6839	+	43.6047i	−0.375339	+	1.40079i
$970$		0			0
$971$	11.2202	+	19.4339i	0.360073	+	0.623664i	0.987972	−	0.154630i	$-0.0494185\pi$
$971$	11.2202	+	19.4339i	0.360073	+	0.623664i	−0.627900	+	0.778294i	$0.716085\pi$
$972$	−42.8829	+	11.4904i	−1.37547	+	0.368556i
$973$	−18.5835	+	32.1875i	−0.595758	+	1.03188i
$974$	−0.892786			−0.0286067
$975$		0			0
$976$	−21.8247			−0.698590
$977$	21.2868	−	36.8699i	0.681026	−	1.17957i	−0.293642	−	0.955915i	$-0.594867\pi$
$977$	21.2868	−	36.8699i	0.681026	−	1.17957i	0.974668	−	0.223656i	$-0.0717993\pi$
$978$	1.20172	−	0.321999i	0.0384267	−	0.0102964i
$979$	19.2900	+	33.4112i	0.616510	+	1.06783i
$980$		0			0
$981$	−11.9089	+	44.4445i	−0.380221	+	1.41900i
$982$	1.29972	−	0.750396i	0.0414758	−	0.0239461i
$983$	2.26298			0.0721778			0.0360889	−	0.999349i	$-0.488510\pi$
$983$	2.26298			0.0721778			0.0360889	+	0.999349i	$0.488510\pi$
$984$	−9.82961	+	5.67513i	−0.313357	+	0.180917i
$985$		0			0
$986$	0.612515	+	2.28594i	0.0195065	+	0.0727991i
$987$	−10.5842	−	10.5842i	−0.336898	−	0.336898i
$988$	−13.9407	−	18.5908i	−0.443514	−	0.591452i
$989$		−	18.7981i		−	0.597743i
$990$		0			0
$991$	2.17856	−	3.77337i	0.0692042	−	0.119865i	−0.829347	−	0.558734i	$-0.811287\pi$
$991$	2.17856	−	3.77337i	0.0692042	−	0.119865i	0.898551	+	0.438869i	$0.144621\pi$
$992$	−3.58366	+	13.3744i	−0.113781	+	0.424637i
$993$		−	33.3841i		−	1.05941i
$994$	−5.02203	−	1.34565i	−0.159289	−	0.0426814i
$995$		0			0
$996$	−34.3637	+	34.3637i	−1.08886	+	1.08886i
$997$	−10.8817	−	2.91575i	−0.344627	−	0.0923426i	0.0823538	−	0.996603i	$-0.473756\pi$
$997$	−10.8817	−	2.91575i	−0.344627	−	0.0923426i	−0.426981	+	0.904261i	$0.640423\pi$
$998$	−1.20284	−	4.48905i	−0.0380751	−	0.142098i
$999$	−1.88913	+	0.506192i	−0.0597695	+	0.0160152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.s.c.293.5	yes	40
5.2	odd	4		325.2.x.c.7.5	yes	40
5.3	odd	4		325.2.x.c.7.6	yes	40
5.4	even	2	inner	325.2.s.c.293.6	yes	40
13.2	odd	12		325.2.x.c.93.5	yes	40
65.2	even	12	inner	325.2.s.c.132.5	✓	40
65.28	even	12	inner	325.2.s.c.132.6	yes	40
65.54	odd	12		325.2.x.c.93.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.2.s.c.132.5	✓	40	65.2	even	12	inner
325.2.s.c.132.6	yes	40	65.28	even	12	inner
325.2.s.c.293.5	yes	40	1.1	even	1	trivial
325.2.s.c.293.6	yes	40	5.4	even	2	inner
325.2.x.c.7.5	yes	40	5.2	odd	4
325.2.x.c.7.6	yes	40	5.3	odd	4
325.2.x.c.93.5	yes	40	13.2	odd	12
325.2.x.c.93.6	yes	40	65.54	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.s (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0621297 + 0.107612i) q^{2} +(2.43488 - 0.652423i) q^{3} +(0.992280 + 1.71868i) q^{4} +(-0.0810697 + 0.302556i) q^{6} +(-2.27145 + 1.31142i) q^{7} -0.495119 q^{8} +(2.90489 - 1.67714i) q^{9} +(0.780655 + 2.91344i) q^{11} +(3.53738 + 3.53738i) q^{12} +(3.34618 - 1.34280i) q^{13} -0.325912i q^{14} +(-1.95380 + 3.38408i) q^{16} +(1.42727 - 5.32666i) q^{17} +0.416800i q^{18} +(-3.13682 - 0.840508i) q^{19} +(-4.67509 + 4.67509i) q^{21} +(-0.362023 - 0.0970037i) q^{22} +(-1.62278 - 6.05629i) q^{23} +(-1.20555 + 0.323027i) q^{24} +(-0.0633962 + 0.443516i) q^{26} +(0.631478 - 0.631478i) q^{27} +(-4.50782 - 2.60259i) q^{28} +(2.99096 + 1.72683i) q^{29} +(-6.63421 - 6.63421i) q^{31} +(-0.737897 - 1.27807i) q^{32} +(3.80159 + 6.58455i) q^{33} +(0.484535 + 0.484535i) q^{34} +(5.76492 + 3.32838i) q^{36} +(-1.89660 - 1.09500i) q^{37} +(0.285338 - 0.285338i) q^{38} +(7.27145 - 5.45267i) q^{39} +(8.78430 - 2.35375i) q^{41} +(-0.212633 - 0.793556i) q^{42} +(2.89597 + 0.775973i) q^{43} +(-4.23265 + 4.23265i) q^{44} +(0.752551 + 0.201645i) q^{46} +2.26395i q^{47} +(-2.54941 + 9.51451i) q^{48} +(-0.0603560 + 0.104540i) q^{49} -13.9009i q^{51} +(5.62818 + 4.41857i) q^{52} +(-5.63768 - 5.63768i) q^{53} +(0.0287210 + 0.107188i) q^{54} +(1.12464 - 0.649309i) q^{56} -8.18613 q^{57} +(-0.371655 + 0.214575i) q^{58} +(-3.33926 + 12.4623i) q^{59} +(2.79259 + 4.83692i) q^{61} +(1.12610 - 0.301738i) q^{62} +(-4.39886 + 7.61905i) q^{63} -7.63181 q^{64} -0.944768 q^{66} +(-3.96321 + 6.86447i) q^{67} +(10.5711 - 2.83251i) q^{68} +(-7.90252 - 13.6876i) q^{69} +(4.12887 - 15.4091i) q^{71} +(-1.43826 + 0.830383i) q^{72} -6.95689 q^{73} +(0.235671 - 0.136064i) q^{74} +(-1.66804 - 6.22520i) q^{76} +(-5.59396 - 5.59396i) q^{77} +(0.134998 + 1.12127i) q^{78} -5.90307i q^{79} +(-3.90583 + 6.76510i) q^{81} +(-0.292475 + 1.09153i) q^{82} +9.71444i q^{83} +(-12.6740 - 3.39598i) q^{84} +(-0.263430 + 0.263430i) q^{86} +(8.40925 + 2.25325i) q^{87} +(-0.386517 - 1.44250i) q^{88} +(12.3550 - 3.31051i) q^{89} +(-5.83969 + 7.43833i) q^{91} +(8.79857 - 8.79857i) q^{92} +(-20.4818 - 11.8252i) q^{93} +(-0.243628 - 0.140659i) q^{94} +(-2.63053 - 2.63053i) q^{96} +(-2.62855 - 4.55278i) q^{97} +(-0.00749980 - 0.0129900i) q^{98} +(7.15396 + 7.15396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{4} - 12 q^{6} + 24 q^{9} + 8 q^{11} - 32 q^{16} - 24 q^{19} + 32 q^{21} + 56 q^{24} + 76 q^{26} - 36 q^{29} + 8 q^{31} + 44 q^{34} - 60 q^{36} + 44 q^{39} - 52 q^{41} - 80 q^{44} - 60 q^{46}+ \cdots + 208 q^{99}+O(q^{100}) \) 40 * q - 24 * q^4 - 12 * q^6 + 24 * q^9 + 8 * q^11 - 32 * q^16 - 24 * q^19 + 32 * q^21 + 56 * q^24 + 76 * q^26 - 36 * q^29 + 8 * q^31 + 44 * q^34 - 60 * q^36 + 44 * q^39 - 52 * q^41 - 80 * q^44 - 60 * q^46 + 28 * q^49 - 68 * q^54 + 72 * q^56 - 72 * q^59 + 144 * q^64 + 24 * q^66 - 80 * q^69 - 52 * q^71 + 168 * q^74 + 8 * q^76 - 20 * q^81 - 248 * q^84 - 168 * q^86 + 60 * q^89 - 100 * q^91 - 156 * q^94 - 36 * q^96 + 208 * q^99

Introduction

L-functions

Modular forms

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