LMFDB - Embedded newform 325.2.x.c.7.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(7,325)] 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, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.x (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			7.5
Character	$\chi$	$=$	325.7
Dual form			325.2.x.c.93.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.107612 - 0.0621297i) q^{2} +(-0.652423 - 2.43488i) q^{3} +(-0.992280 - 1.71868i) q^{4} +(-0.0810697 + 0.302556i) q^{6} +(-1.31142 - 2.27145i) q^{7} +0.495119i q^{8} +(-2.90489 + 1.67714i) q^{9} +(0.780655 + 2.91344i) q^{11} +(-3.53738 + 3.53738i) q^{12} +(-1.34280 - 3.34618i) q^{13} +0.325912i q^{14} +(-1.95380 + 3.38408i) q^{16} +(5.32666 + 1.42727i) q^{17} +0.416800 q^{18} +(3.13682 + 0.840508i) q^{19} +(-4.67509 + 4.67509i) q^{21} +(0.0970037 - 0.362023i) q^{22} +(-6.05629 + 1.62278i) q^{23} +(1.20555 - 0.323027i) q^{24} +(-0.0633962 + 0.443516i) q^{26} +(0.631478 + 0.631478i) q^{27} +(-2.60259 + 4.50782i) q^{28} +(-2.99096 - 1.72683i) q^{29} +(-6.63421 - 6.63421i) q^{31} +(1.27807 - 0.737897i) q^{32} +(6.58455 - 3.80159i) q^{33} +(-0.484535 - 0.484535i) q^{34} +(5.76492 + 3.32838i) q^{36} +(1.09500 - 1.89660i) q^{37} +(-0.285338 - 0.285338i) q^{38} +(-7.27145 + 5.45267i) q^{39} +(8.78430 - 2.35375i) q^{41} +(0.793556 - 0.212633i) q^{42} +(0.775973 - 2.89597i) q^{43} +(4.23265 - 4.23265i) q^{44} +(0.752551 + 0.201645i) q^{46} -2.26395 q^{47} +(9.51451 + 2.54941i) q^{48} +(0.0603560 - 0.104540i) q^{49} -13.9009i q^{51} +(-4.41857 + 5.62818i) q^{52} +(-5.63768 + 5.63768i) q^{53} +(-0.0287210 - 0.107188i) q^{54} +(1.12464 - 0.649309i) q^{56} -8.18613i q^{57} +(0.214575 + 0.371655i) q^{58} +(3.33926 - 12.4623i) q^{59} +(2.79259 + 4.83692i) q^{61} +(0.301738 + 1.12610i) q^{62} +(7.61905 + 4.39886i) q^{63} +7.63181 q^{64} -0.944768 q^{66} +(-6.86447 - 3.96321i) q^{67} +(-2.83251 - 10.5711i) q^{68} +(7.90252 + 13.6876i) q^{69} +(4.12887 - 15.4091i) q^{71} +(-0.830383 - 1.43826i) q^{72} +6.95689i q^{73} +(-0.235671 + 0.136064i) q^{74} +(-1.66804 - 6.22520i) q^{76} +(5.59396 - 5.59396i) q^{77} +(1.12127 - 0.134998i) q^{78} +5.90307i q^{79} +(-3.90583 + 6.76510i) q^{81} +(-1.09153 - 0.292475i) q^{82} +9.71444 q^{83} +(12.6740 + 3.39598i) q^{84} +(-0.263430 + 0.263430i) q^{86} +(-2.25325 + 8.40925i) q^{87} +(-1.44250 + 0.386517i) q^{88} +(-12.3550 + 3.31051i) q^{89} +(-5.83969 + 7.43833i) q^{91} +(8.79857 + 8.79857i) q^{92} +(-11.8252 + 20.4818i) q^{93} +(0.243628 + 0.140659i) q^{94} +(-2.63053 - 2.63053i) q^{96} +(4.55278 - 2.62855i) q^{97} +(-0.0129900 + 0.00749980i) 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 $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.107612	−	0.0621297i	−0.0760930	−	0.0439323i	0.461471	−	0.887155i	$-0.347322\pi$
$2$	−0.107612	−	0.0621297i	−0.0760930	−	0.0439323i	−0.537564	+	0.843223i	$0.680655\pi$
$3$	−0.652423	−	2.43488i	−0.376677	−	1.40578i	−0.850880	−	0.525361i	$-0.823930\pi$
$3$	−0.652423	−	2.43488i	−0.376677	−	1.40578i	0.474203	−	0.880415i	$-0.342736\pi$
$4$	−0.992280	−	1.71868i	−0.496140	−	0.859340i
$5$		0			0
$5$		0			0
$6$	−0.0810697	+	0.302556i	−0.0330966	+	0.123518i
$7$	−1.31142	−	2.27145i	−0.495670	−	0.858526i	0.504317	−	0.863518i	$-0.331744\pi$
$7$	−1.31142	−	2.27145i	−0.495670	−	0.858526i	−0.999988	+	0.00499253i	$0.998411\pi$
$8$			0.495119i			0.175051i
$9$	−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
$13$	−1.34280	−	3.34618i	−0.372425	−	0.928062i
$13$	−1.34280	−	3.34618i	−0.372425	−	0.928062i
$14$			0.325912i			0.0871038i
$15$		0			0
$16$	−1.95380	+	3.38408i	−0.488450	+	0.846019i
$17$	5.32666	+	1.42727i	1.29190	+	0.346165i	0.838384	−	0.545081i	$-0.183501\pi$
$17$	5.32666	+	1.42727i	1.29190	+	0.346165i	0.453521	+	0.891246i	$0.350168\pi$
$18$	0.416800			0.0982408
$19$	3.13682	+	0.840508i	0.719636	+	0.192826i	0.600009	−	0.799993i	$-0.295164\pi$
$19$	3.13682	+	0.840508i	0.719636	+	0.192826i	0.119626	+	0.992819i	$0.461830\pi$
$20$		0			0
$21$	−4.67509	+	4.67509i	−1.02019	+	1.02019i
$22$	0.0970037	−	0.362023i	0.0206813	−	0.0771835i
$23$	−6.05629	+	1.62278i	−1.26282	+	0.338373i	−0.827277	−	0.561794i	$-0.810111\pi$
$23$	−6.05629	+	1.62278i	−1.26282	+	0.338373i	−0.435546	+	0.900166i	$0.643445\pi$
$24$	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
$28$	−2.60259	+	4.50782i	−0.491843	+	0.851898i
$29$	−2.99096	−	1.72683i	−0.555408	−	0.320665i	0.195893	−	0.980625i	$-0.437240\pi$
$29$	−2.99096	−	1.72683i	−0.555408	−	0.320665i	−0.751300	+	0.659961i	$0.770573\pi$
$30$		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	$-0.568944\pi$
$32$	1.27807	−	0.737897i	0.225934	−	0.130443i
$33$	6.58455	−	3.80159i	1.14622	−	0.661773i
$34$	−0.484535	−	0.484535i	−0.0830971	−	0.0830971i
$35$		0			0
$36$	5.76492	+	3.32838i	0.960820	+	0.554730i
$37$	1.09500	−	1.89660i	0.180017	−	0.311799i	−0.761869	−	0.647731i	$-0.775718\pi$
$37$	1.09500	−	1.89660i	0.180017	−	0.311799i	0.941886	+	0.335932i	$0.109051\pi$
$38$	−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	$0.165300\pi$
$42$	0.793556	−	0.212633i	0.122448	−	0.0328100i
$43$	0.775973	−	2.89597i	0.118335	−	0.441631i	−0.881180	−	0.472781i	$-0.843250\pi$
$43$	0.775973	−	2.89597i	0.118335	−	0.441631i	0.999515	+	0.0311497i	$0.00991687\pi$
$44$	4.23265	−	4.23265i	0.638095	−	0.638095i
$45$		0			0
$46$	0.752551	+	0.201645i	0.110958	+	0.0297310i
$47$	−2.26395			−0.330231			−0.165116	−	0.986274i	$-0.552800\pi$
$47$	−2.26395			−0.330231			−0.165116	+	0.986274i	$0.552800\pi$
$48$	9.51451	+	2.54941i	1.37330	+	0.367975i
$49$	0.0603560	−	0.104540i	0.00862229	−	0.0149342i
$50$		0			0
$51$		−	13.9009i		−	1.94652i
$52$	−4.41857	+	5.62818i	−0.612746	+	0.780488i
$53$	−5.63768	+	5.63768i	−0.774395	+	0.774395i	−0.978871	−	0.204477i	$-0.934451\pi$
$53$	−5.63768	+	5.63768i	−0.774395	+	0.774395i	0.204477	+	0.978871i	$0.434451\pi$
$54$	−0.0287210	−	0.107188i	−0.00390843	−	0.0145865i
$55$		0			0
$56$	1.12464	−	0.649309i	0.150286	−	0.0867675i
$57$		−	8.18613i		−	1.08428i
$58$	0.214575	+	0.371655i	0.0281751	+	0.0488007i
$59$	3.33926	−	12.4623i	0.434734	−	1.62245i	−0.306967	−	0.951720i	$-0.599314\pi$
$59$	3.33926	−	12.4623i	0.434734	−	1.62245i	0.741701	−	0.670730i	$-0.234019\pi$
$60$		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	$0.716944\pi$
$62$	0.301738	+	1.12610i	0.0383208	+	0.143015i
$63$	7.61905	+	4.39886i	0.959911	+	0.554205i
$64$	7.63181			0.953976
$65$		0			0
$66$	−0.944768			−0.116293
$67$	−6.86447	−	3.96321i	−0.838629	−	0.484183i	0.0181691	−	0.999835i	$-0.494216\pi$
$67$	−6.86447	−	3.96321i	−0.838629	−	0.484183i	−0.856798	+	0.515652i	$0.827550\pi$
$68$	−2.83251	−	10.5711i	−0.343492	−	1.28193i
$69$	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	$-0.312193\pi$
$72$	−0.830383	−	1.43826i	−0.0978615	−	0.169501i
$73$			6.95689i			0.814242i	0.913374	+	0.407121i	$0.133467\pi$
$73$			6.95689i			0.814242i	−0.913374	+	0.407121i	$0.866533\pi$
$74$	−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
$78$	1.12127	−	0.134998i	0.126958	−	0.0152855i
$79$			5.90307i			0.664147i	0.943253	+	0.332074i	$0.107748\pi$
$79$			5.90307i			0.664147i	−0.943253	+	0.332074i	$0.892252\pi$
$80$		0			0
$81$	−3.90583	+	6.76510i	−0.433981	+	0.751678i
$82$	−1.09153	−	0.292475i	−0.120539	−	0.0322985i
$83$	9.71444			1.06630			0.533149	−	0.846021i	$-0.321008\pi$
$83$	9.71444			1.06630			0.533149	+	0.846021i	$0.321008\pi$
$84$	12.6740	+	3.39598i	1.38284	+	0.370532i
$85$		0			0
$86$	−0.263430	+	0.263430i	−0.0284063	+	0.0284063i
$87$	−2.25325	+	8.40925i	−0.241574	+	0.901566i
$88$	−1.44250	+	0.386517i	−0.153771	+	0.0412029i
$89$	−12.3550	+	3.31051i	−1.30963	+	0.350913i	−0.845082	−	0.534637i	$-0.820448\pi$
$89$	−12.3550	+	3.31051i	−1.30963	+	0.350913i	−0.464544	+	0.885550i	$0.653782\pi$
$90$		0			0
$91$	−5.83969	+	7.43833i	−0.612166	+	0.779749i
$92$	8.79857	+	8.79857i	0.917314	+	0.917314i
$93$	−11.8252	+	20.4818i	−1.22621	+	2.12386i
$94$	0.243628	+	0.140659i	0.0251283	+	0.0145078i
$95$		0			0
$96$	−2.63053	−	2.63053i	−0.268478	−	0.268478i
$97$	4.55278	−	2.62855i	0.462264	−	0.266888i	−0.250732	−	0.968057i	$-0.580671\pi$
$97$	4.55278	−	2.62855i	0.462264	−	0.266888i	0.712996	+	0.701168i	$0.247338\pi$
$98$	−0.0129900	+	0.00749980i	−0.00131219	+	0.000757594i
$99$	−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	$0.689502\pi$
$102$	−0.863661	+	1.49591i	−0.0855152	+	0.148117i
$103$	2.90200	+	2.90200i	0.285943	+	0.285943i	0.835473	−	0.549531i	$-0.185194\pi$
$103$	2.90200	+	2.90200i	0.285943	+	0.285943i	−0.549531	+	0.835473i	$0.685194\pi$
$104$	1.65676	−	0.664844i	0.162458	−	0.0651933i
$105$		0			0
$106$	0.956948	−	0.256414i	0.0929470	−	0.0249051i
$107$	0.968336	−	0.259465i	0.0936126	−	0.0250834i	−0.211709	−	0.977333i	$-0.567903\pi$
$107$	0.968336	−	0.259465i	0.0936126	−	0.0250834i	0.305321	+	0.952249i	$0.401236\pi$
$108$	0.458705	−	1.71191i	0.0441389	−	0.164729i
$109$	9.69976	−	9.69976i	0.929068	−	0.929068i	−0.0685774	−	0.997646i	$-0.521846\pi$
$109$	9.69976	−	9.69976i	0.929068	−	0.929068i	0.997646	+	0.0685774i	$0.0218460\pi$
$110$		0			0
$111$	−5.33239	−	1.42881i	−0.506128	−	0.135617i
$112$	10.2490			0.968439
$113$	10.3896	+	2.78387i	0.977367	+	0.261885i	0.711935	−	0.702245i	$-0.247819\pi$
$113$	10.3896	+	2.78387i	0.977367	+	0.261885i	0.265432	+	0.964130i	$0.414485\pi$
$114$	−0.508602	+	0.880924i	−0.0476349	+	0.0825061i
$115$		0			0
$116$			6.85401i			0.636378i
$117$	9.51267	+	7.46821i	0.879447	+	0.690436i
$118$	−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
$122$		−	0.694012i		−	0.0628329i
$123$	−11.4622	−	19.8530i	−1.03351	−	1.79009i
$124$	−4.81909	+	17.9851i	−0.432767	+	1.61511i
$125$		0			0
$126$	−0.546600	−	0.946739i	−0.0486950	−	0.0843422i
$127$	−1.42275	−	5.30979i	−0.126249	−	0.471168i	0.873632	−	0.486587i	$-0.161758\pi$
$127$	−1.42275	−	5.30979i	−0.126249	−	0.471168i	−0.999881	+	0.0154193i	$0.995092\pi$
$128$	−3.37742	−	1.94996i	−0.298525	−	0.172353i
$129$	−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	$0.473900\pi$
$132$	−13.0674	−	7.54449i	−1.13737	−	0.656664i
$133$	−2.20452	−	8.22737i	−0.191156	−	0.713404i
$134$	0.492465	+	0.852975i	0.0425425	+	0.0736858i
$135$		0			0
$136$	−0.706671	+	2.63733i	−0.0605965	+	0.226149i
$137$	−0.416423	−	0.721267i	−0.0355775	−	0.0616220i	0.847688	−	0.530494i	$-0.177994\pi$
$137$	−0.416423	−	0.721267i	−0.0355775	−	0.0616220i	−0.883266	+	0.468872i	$0.844660\pi$
$138$		−	1.96393i		−	0.167180i
$139$	−12.2720	+	7.08524i	−1.04090	+	0.600962i	−0.920087	−	0.391713i	$-0.871883\pi$
$139$	−12.2720	+	7.08524i	−1.04090	+	0.600962i	−0.120810	+	0.992676i	$0.538549\pi$
$140$		0			0
$141$	1.47705	+	5.51244i	0.124390	+	0.464231i
$142$	−1.40168	+	1.40168i	−0.117626	+	0.117626i
$143$	8.70063	−	6.52437i	0.727584	−	0.545595i
$144$		−	13.1072i		−	1.09226i
$145$		0			0
$146$	0.432229	−	0.748643i	0.0357716	−	0.0619582i
$147$	−0.293919	−	0.0787553i	−0.0242420	−	0.00649563i
$148$	−4.34620			−0.357255
$149$	−0.0628459	−	0.0168395i	−0.00514854	−	0.00137955i	0.256244	−	0.966612i	$-0.417515\pi$
$149$	−0.0628459	−	0.0168395i	−0.00514854	−	0.00137955i	−0.261392	+	0.965233i	$0.584182\pi$
$150$		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	$0.240768\pi$
$152$	−0.416152	+	1.55310i	−0.0337543	+	0.125973i
$153$	−17.8671	+	4.78747i	−1.44447	+	0.387044i
$154$	−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	0.0577473	−	0.998331i	$-0.481608\pi$
$157$	−11.7855	−	11.7855i	−0.940584	−	0.940584i	−0.998331	+	0.0577473i	$0.981608\pi$
$158$	0.366756	−	0.635240i	0.0291775	−	0.0505370i
$159$	17.4052	+	10.0489i	1.38032	+	0.796929i
$160$		0			0
$161$	11.6284	+	11.6284i	0.916445	+	0.916445i
$162$	0.840627	−	0.485336i	0.0660459	−	0.0381316i
$163$	−3.43975	+	1.98594i	−0.269422	+	0.155551i	−0.628625	−	0.777709i	$-0.716382\pi$
$163$	−3.43975	+	1.98594i	−0.269422	+	0.155551i	0.359203	+	0.933259i	$0.383049\pi$
$164$	−12.7618	−	12.7618i	−0.996530	−	0.996530i
$165$		0			0
$166$	−1.04539	−	0.603555i	−0.0811379	−	0.0468450i
$167$	−6.33310	+	10.9692i	−0.490070	+	0.848826i	−0.999935	−	0.0114288i	$-0.996362\pi$
$167$	−6.33310	+	10.9692i	−0.490070	+	0.848826i	0.509865	+	0.860254i	$0.329695\pi$
$168$	−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
$172$	−5.74722	+	1.53996i	−0.438222	+	0.117421i
$173$	6.34047	−	23.6630i	0.482057	−	1.79906i	−0.110905	−	0.993831i	$-0.535375\pi$
$173$	6.34047	−	23.6630i	0.482057	−	1.79906i	0.592962	−	0.805230i	$-0.297958\pi$
$174$	0.764940	−	0.764940i	0.0579900	−	0.0579900i
$175$		0			0
$176$	−11.3846	−	3.05048i	−0.858143	−	0.229939i
$177$	−32.5227			−2.44456
$178$	1.53522	+	0.411362i	0.115070	+	0.0308329i
$179$	6.48009	−	11.2238i	0.484345	−	0.838910i	−0.515493	−	0.856893i	$-0.672391\pi$
$179$	6.48009	−	11.2238i	0.484345	−	0.838910i	0.999838	+	0.0179837i	$0.00572470\pi$
$180$		0			0
$181$			10.2702i			0.763381i	0.924290	+	0.381691i	$0.124658\pi$
$181$			10.2702i			0.763381i	−0.924290	+	0.381691i	$0.875342\pi$
$182$	1.09056	−	0.437634i	0.0808377	−	0.0324396i
$183$	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
$187$			16.6331i			1.21633i
$188$	2.24647	+	3.89101i	0.163841	+	0.283781i
$189$	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	$0.735943\pi$
$192$	−4.97917	−	18.5825i	−0.359341	−	1.34108i
$193$	2.16611	+	1.25060i	0.155920	+	0.0900204i	0.575930	−	0.817499i	$-0.304640\pi$
$193$	2.16611	+	1.25060i	0.155920	+	0.0900204i	−0.420010	+	0.907519i	$0.637973\pi$
$194$	−0.653243			−0.0469001
$195$		0			0
$196$	−0.239560			−0.0171114
$197$	16.9593	+	9.79143i	1.20830	+	0.697611i	0.962387	−	0.271682i	$-0.0875799\pi$
$197$	16.9593	+	9.79143i	1.20830	+	0.697611i	0.245910	+	0.969293i	$0.420913\pi$
$198$	0.325377	+	1.21432i	0.0231235	+	0.0862982i
$199$	1.49761	+	2.59393i	0.106163	+	0.183879i	0.914213	−	0.405235i	$-0.132810\pi$
$199$	1.49761	+	2.59393i	0.106163	+	0.183879i	−0.808050	+	0.589114i	$0.799477\pi$
$200$		0			0
$201$	−5.17137	+	19.2998i	−0.364760	+	1.36130i
$202$	0.0895091	+	0.155034i	0.00629784	+	0.0109082i
$203$			9.05841i			0.635776i
$204$	−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
$208$	13.9473	+	1.99363i	0.967069	+	0.138233i
$209$			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	$0.117726\pi$
$212$	15.2835	+	4.09521i	1.04968	+	0.281260i
$213$	−40.2131			−2.75536
$214$	−0.120325	−	0.0322410i	−0.00822524	−	0.00220395i
$215$		0			0
$216$	−0.312657	+	0.312657i	−0.0212736	+	0.0212736i
$217$	−6.36902	+	23.7695i	−0.432357	+	1.61358i
$218$	−1.64645	+	0.441165i	−0.111512	+	0.0298795i
$219$	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
$223$	0.406831	−	0.704652i	0.0272434	−	0.0471870i	−0.852082	−	0.523408i	$-0.824660\pi$
$223$	0.406831	−	0.704652i	0.0272434	−	0.0471870i	0.879326	+	0.476221i	$0.157994\pi$
$224$	−3.35219	−	1.93538i	−0.223977	−	0.129313i
$225$		0			0
$226$	−0.945078	−	0.945078i	−0.0628656	−	0.0628656i
$227$	21.1058	−	12.1854i	1.40084	−	0.808775i	0.406360	−	0.913713i	$-0.366798\pi$
$227$	21.1058	−	12.1854i	1.40084	−	0.808775i	0.994479	+	0.104938i	$0.0334646\pi$
$228$	−14.0693	+	8.12293i	−0.931764	+	0.537954i
$229$	9.07194	+	9.07194i	0.599491	+	0.599491i	0.940177	−	0.340686i	$-0.110659\pi$
$229$	9.07194	+	9.07194i	0.599491	+	0.599491i	−0.340686	+	0.940177i	$0.610659\pi$
$230$		0			0
$231$	−17.2702	−	9.97097i	−1.13630	−	0.656042i
$232$	0.854988	−	1.48088i	0.0561327	−	0.0972247i
$233$	−3.41602	−	3.41602i	−0.223791	−	0.223791i	0.586302	−	0.810093i	$-0.300583\pi$
$233$	−3.41602	−	3.41602i	−0.223791	−	0.223791i	−0.810093	+	0.586302i	$0.800583\pi$
$234$	−0.559678	−	1.39469i	−0.0365873	−	0.0911735i
$235$		0			0
$236$	−24.7321	+	6.62695i	−1.60992	+	0.431378i
$237$	14.3732	−	3.85130i	0.933642	−	0.250169i
$238$	−0.465166	+	1.73602i	−0.0301523	+	0.112530i
$239$	−1.50535	+	1.50535i	−0.0973730	+	0.0973730i	−0.754115	−	0.656742i	$-0.771934\pi$
$239$	−1.50535	+	1.50535i	−0.0973730	+	0.0973730i	0.656742	+	0.754115i	$0.271934\pi$
$240$		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	$0.392919\pi$
$242$	−0.236394			−0.0151960
$243$	21.6083	+	5.78992i	1.38617	+	0.371424i
$244$	5.54207	−	9.59915i	0.354795	−	0.614522i
$245$		0			0
$246$			2.84856i			0.181618i
$247$	−1.39962	−	11.6250i	−0.0890558	−	0.739680i
$248$	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	$0.340670\pi$
$252$		−	17.4596i		−	1.09985i
$253$	−9.45574	−	16.3778i	−0.594477	−	1.02966i
$254$	−0.176791	+	0.659791i	−0.0110928	+	0.0413990i
$255$		0			0
$256$	−7.38951	−	12.7990i	−0.461844	−	0.799938i
$257$	3.97438	+	14.8326i	0.247915	+	0.925232i	0.971896	+	0.235411i	$0.0756437\pi$
$257$	3.97438	+	14.8326i	0.247915	+	0.925232i	−0.723981	+	0.689820i	$0.757690\pi$
$258$	0.813286	+	0.469551i	0.0506329	+	0.0292329i
$259$	−5.74404			−0.356917
$260$		0			0
$261$	11.5845			0.717065
$262$	−0.201755	−	0.116483i	−0.0124645	−	0.00719636i
$263$	6.61411	+	24.6842i	0.407844	+	1.52209i	0.798750	+	0.601663i	$0.205495\pi$
$263$	6.61411	+	24.6842i	0.407844	+	1.52209i	−0.390907	+	0.920430i	$0.627839\pi$
$264$	1.88224	+	3.26014i	0.115844	+	0.200648i
$265$		0			0
$266$	−0.273932	+	1.02233i	−0.0167959	+	0.0626830i
$267$	16.1213	+	27.9230i	0.986610	+	1.70886i
$268$			15.7304i			0.960889i
$269$	8.63715	−	4.98666i	0.526617	−	0.304042i	−0.213021	−	0.977048i	$-0.568330\pi$
$269$	8.63715	−	4.98666i	0.526617	−	0.304042i	0.739638	+	0.673005i	$0.234997\pi$
$270$		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
$273$	21.9214	+	9.36598i	1.32674	+	0.566855i
$274$			0.103489i			0.00625200i
$275$		0			0
$276$	15.6830	−	27.1638i	0.944007	−	1.63507i
$277$	−5.02757	−	1.34713i	−0.302077	−	0.0809414i	0.104597	−	0.994515i	$-0.466645\pi$
$277$	−5.02757	−	1.34713i	−0.302077	−	0.0809414i	−0.406674	+	0.913573i	$0.633312\pi$
$278$	1.76082			0.105607
$279$	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	$-0.0412638\pi$
$282$	0.183538	−	0.684973i	0.0109295	−	0.0407895i
$283$	26.8173	−	7.18567i	1.59412	−	0.427144i	0.650861	−	0.759197i	$-0.274408\pi$
$283$	26.8173	−	7.18567i	1.59412	−	0.427144i	0.943261	+	0.332053i	$0.107741\pi$
$284$	−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
$288$	−2.47511	+	4.28701i	−0.145847	+	0.252615i
$289$	11.6138	+	6.70521i	0.683162	+	0.394424i
$290$		0			0
$291$	−9.37052	−	9.37052i	−0.549310	−	0.549310i
$292$	11.9567	−	6.90318i	0.699711	−	0.403978i
$293$	−6.10410	+	3.52420i	−0.356605	+	0.205886i	−0.667591	−	0.744529i	$-0.732674\pi$
$293$	−6.10410	+	3.52420i	−0.356605	+	0.205886i	0.310985	+	0.950415i	$0.399341\pi$
$294$	0.0267361	+	0.0267361i	0.00155928	+	0.00155928i
$295$		0			0
$296$	0.939043	+	0.542157i	0.0545808	+	0.0315122i
$297$	−1.34681	+	2.33274i	−0.0781498	+	0.135359i
$298$	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
$302$	−0.0855417	+	0.0229208i	−0.00492237	+	0.00131895i
$303$	−0.939933	+	3.50788i	−0.0539978	+	0.201522i
$304$	−8.97305	+	8.97305i	−0.514640	+	0.514640i
$305$		0			0
$306$	2.22015	+	0.594888i	0.126918	+	0.0340075i
$307$	−17.7175			−1.01119			−0.505596	−	0.862770i	$-0.668727\pi$
$307$	−17.7175			−1.01119			−0.505596	+	0.862770i	$0.668727\pi$
$308$	−15.1650	−	4.06345i	−0.864106	−	0.231537i
$309$	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	$0.828158\pi$
$312$	−2.69972	−	3.60023i	−0.152841	−	0.203823i
$313$	7.90286	−	7.90286i	0.446696	−	0.446696i	−0.447558	−	0.894255i	$-0.647706\pi$
$313$	7.90286	−	7.90286i	0.446696	−	0.446696i	0.894255	+	0.447558i	$0.147706\pi$
$314$	0.536028	+	2.00049i	0.0302498	+	0.112894i
$315$		0			0
$316$	10.1455	−	5.85750i	0.570728	−	0.329510i
$317$		−	8.03345i		−	0.451203i	−0.974220	−	0.225602i	$-0.927565\pi$
$317$		−	8.03345i		−	0.451203i	0.974220	−	0.225602i	$-0.0724348\pi$
$318$	−1.24867	−	2.16276i	−0.0700219	−	0.121282i
$319$	2.69612	−	10.0621i	0.150954	−	0.563367i
$320$		0			0
$321$	−1.26353	−	2.18850i	−0.0705233	−	0.122150i
$322$	−0.528884	−	1.97382i	−0.0294735	−	0.109997i
$323$	15.5091	+	8.95420i	0.862951	+	0.498225i
$324$	15.5027			0.861262
$325$		0			0
$326$	0.493544			0.0273349
$327$	−29.9461	−	17.2894i	−1.65602	−	0.956104i
$328$	1.16538	+	4.34927i	0.0643476	+	0.240148i
$329$	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	$-0.0352448\pi$
$332$	−9.63944	−	16.6960i	−0.529033	−	0.916312i
$333$			7.34588i			0.402552i
$334$	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	$-0.732753\pi$
$337$	1.40596	−	1.40596i	0.0765877	−	0.0765877i	0.744363	+	0.667775i	$0.232753\pi$
$338$	1.56921	−	0.383417i	0.0853538	−	0.0208551i
$339$		−	27.1135i		−	1.47261i
$340$		0			0
$341$	14.1494	−	24.5074i	0.766232	−	1.32715i
$342$	1.30743	+	0.350324i	0.0706975	+	0.0189433i
$343$	−18.6765			−1.00844
$344$	1.43385	+	0.384199i	0.0773080	+	0.0207146i
$345$		0			0
$346$	−2.15248	+	2.15248i	−0.115718	+	0.115718i
$347$	−1.22887	+	4.58620i	−0.0659692	+	0.246200i	−0.991034	−	0.133608i	$-0.957344\pi$
$347$	−1.22887	+	4.58620i	−0.0659692	+	0.246200i	0.925065	+	0.379809i	$0.124010\pi$
$348$	16.6887	−	4.47171i	0.894606	−	0.239709i
$349$	2.32494	−	0.622965i	0.124451	−	0.0333466i	−0.196056	−	0.980593i	$-0.562813\pi$
$349$	2.32494	−	0.622965i	0.124451	−	0.0333466i	0.320507	+	0.947246i	$0.396147\pi$
$350$		0			0
$351$	1.26509	−	2.96099i	0.0675256	−	0.158046i
$352$	3.14756	+	3.14756i	0.167765	+	0.167765i
$353$	−2.64643	+	4.58374i	−0.140855	+	0.243968i	−0.927819	−	0.373031i	$-0.878318\pi$
$353$	−2.64643	+	4.58374i	−0.140855	+	0.243968i	0.786964	+	0.616999i	$0.211652\pi$
$354$	3.49983	+	2.02063i	0.186014	+	0.107395i
$355$		0			0
$356$	17.9493	+	17.9493i	0.951311	+	0.951311i
$357$	−31.5752	+	18.2300i	−1.67114	+	0.964832i
$358$	−1.39467	+	0.805212i	−0.0737105	+	0.0425568i
$359$	0.976204	+	0.976204i	0.0515221	+	0.0515221i	0.732398	−	0.680876i	$-0.238401\pi$
$359$	0.976204	+	0.976204i	0.0515221	+	0.0515221i	−0.680876	+	0.732398i	$0.738401\pi$
$360$		0			0
$361$	−7.32130	−	4.22696i	−0.385332	−	0.222471i
$362$	0.638087	−	1.10520i	0.0335371	−	0.0580880i
$363$	−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
$367$	28.3765	−	7.60345i	1.48124	−	0.396897i	0.574471	−	0.818525i	$-0.305208\pi$
$367$	28.3765	−	7.60345i	1.48124	−	0.396897i	0.906769	+	0.421628i	$0.138541\pi$
$368$	6.34116	−	23.6655i	0.330556	−	1.23365i
$369$	−21.5698	+	21.5698i	−1.12288	+	1.12288i
$370$		0			0
$371$	20.1990	+	5.41232i	1.04868	+	0.280994i
$372$	46.9355			2.43349
$373$	21.5476	+	5.77365i	1.11569	+	0.298949i	0.769139	−	0.639082i	$-0.220686\pi$
$373$	21.5476	+	5.77365i	1.11569	+	0.298949i	0.346552	+	0.938031i	$0.387352\pi$
$374$	1.03341	−	1.78992i	0.0534364	−	0.0925546i
$375$		0			0
$376$		−	1.12093i		−	0.0578073i
$377$	−1.76203	+	12.3271i	−0.0907493	+	0.634877i
$378$	−0.205807	+	0.205807i	−0.0105856	+	0.0105856i
$379$	−7.19049	−	26.8353i	−0.369351	−	1.37844i	−0.861426	−	0.507883i	$-0.830428\pi$
$379$	−7.19049	−	26.8353i	−0.369351	−	1.37844i	0.492075	−	0.870553i	$-0.336238\pi$
$380$		0			0
$381$	−12.0004	+	6.92846i	−0.614801	+	0.354956i
$382$		−	1.03454i		−	0.0529316i
$383$	1.73419	+	3.00371i	0.0886132	+	0.153483i	0.906925	−	0.421292i	$-0.138423\pi$
$383$	1.73419	+	3.00371i	0.0886132	+	0.153483i	−0.818312	+	0.574774i	$0.805090\pi$
$384$	−2.54439	+	9.49580i	−0.129843	+	0.484580i
$385$		0			0
$386$	−0.155399	−	0.269159i	−0.00790961	−	0.0136998i
$387$	2.60283	+	9.71388i	0.132309	+	0.493784i
$388$	−9.03526	−	5.21651i	−0.458696	−	0.264828i
$389$	15.9955			0.811006			0.405503	−	0.914094i	$-0.367096\pi$
$389$	15.9955			0.811006			0.405503	+	0.914094i	$0.367096\pi$
$390$		0			0
$391$	−34.5759			−1.74858
$392$	0.0517596	+	0.0298834i	0.00261425	+	0.00150934i
$393$	−1.22319	−	4.56500i	−0.0617017	−	0.230274i
$394$	−1.21668	−	2.10735i	−0.0612953	−	0.106167i
$395$		0			0
$396$	−5.19663	+	19.3941i	−0.261140	+	0.974590i
$397$	5.61593	+	9.72708i	0.281856	+	0.488188i	0.971842	−	0.235634i	$-0.0757167\pi$
$397$	5.61593	+	9.72708i	0.281856	+	0.488188i	−0.689986	+	0.723823i	$0.742383\pi$
$398$		−	0.372184i		−	0.0186559i
$399$	−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
$403$	−13.2908	+	31.1076i	−0.662064	+	1.54958i
$404$			2.85912i			0.142246i
$405$		0			0
$406$	0.562796	−	0.974792i	0.0279311	−	0.0483781i
$407$	6.38046	+	1.70964i	0.316268	+	0.0847437i
$408$	6.88262			0.340740
$409$	−36.5236	−	9.78648i	−1.80598	−	0.483910i	−0.811092	−	0.584918i	$-0.801127\pi$
$409$	−36.5236	−	9.78648i	−1.80598	−	0.483910i	−0.994886	+	0.101008i	$0.967793\pi$
$410$		0			0
$411$	−1.48451	+	1.48451i	−0.0732255	+	0.0732255i
$412$	2.10801	−	7.86720i	0.103854	−	0.387589i
$413$	−32.6866	+	8.75834i	−1.60840	+	0.430970i
$414$	−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
$418$	0.608566	−	1.05407i	0.0297659	−	0.0515561i
$419$	2.07584	+	1.19849i	0.101411	+	0.0585499i	0.549848	−	0.835265i	$-0.314686\pi$
$419$	2.07584	+	1.19849i	0.101411	+	0.0585499i	−0.448437	+	0.893815i	$0.648019\pi$
$420$		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	$0.590561\pi$
$422$	−0.478786	+	0.276427i	−0.0233069	+	0.0134563i
$423$	6.57653	−	3.79696i	0.319762	−	0.184614i
$424$	−2.79132	−	2.79132i	−0.135559	−	0.135559i
$425$		0			0
$426$	4.32741	+	2.49843i	0.209663	+	0.121049i
$427$	7.32453	−	12.6865i	0.354459	−	0.613941i
$428$	−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	$0.568507\pi$
$432$	−3.37075	+	0.903190i	−0.162175	+	0.0434548i
$433$	−1.97715	+	7.37884i	−0.0950159	+	0.354604i	−0.997022	−	0.0771194i	$-0.975428\pi$
$433$	−1.97715	+	7.37884i	−0.0950159	+	0.354604i	0.902006	+	0.431724i	$0.142094\pi$
$434$	2.16217	−	2.16217i	0.103788	−	0.103788i
$435$		0			0
$436$	−26.2956	−	7.04590i	−1.25933	−	0.337437i
$437$	−20.3614			−0.974020
$438$	−2.10485	−	0.563993i	−0.100574	−	0.0269486i
$439$	2.24892	−	3.89524i	0.107335	−	0.185910i	−0.807355	−	0.590066i	$-0.799102\pi$
$439$	2.24892	−	3.89524i	0.107335	−	0.185910i	0.914690	+	0.404157i	$0.132435\pi$
$440$		0			0
$441$			0.404901i			0.0192810i
$442$	−0.970708	+	2.27197i	−0.0461719	+	0.108067i
$443$	−20.2178	+	20.2178i	−0.960576	+	0.960576i	−0.999252	−	0.0386758i	$-0.987686\pi$
$443$	−20.2178	+	20.2178i	−0.960576	+	0.960576i	0.0386758	+	0.999252i	$0.487686\pi$
$444$	2.83556	+	10.5825i	0.134570	+	0.502221i
$445$		0			0
$446$	−0.0875596	+	0.0505526i	−0.00414607	+	0.00239373i
$447$			0.164008i			0.00775733i
$448$	−10.0085	−	17.3352i	−0.472858	−	0.819013i
$449$	−4.01450	+	14.9823i	−0.189456	+	0.707059i	0.804177	+	0.594390i	$0.202607\pi$
$449$	−4.01450	+	14.9823i	−0.189456	+	0.707059i	−0.993633	+	0.112669i	$0.964060\pi$
$450$		0			0
$451$	13.7150	+	23.7551i	0.645814	+	1.11858i
$452$	−5.52476	−	20.6187i	−0.259863	−	0.969822i
$453$	−1.55585	−	0.898272i	−0.0731004	−	0.0422045i
$454$	−3.02831			−0.142125
$455$		0			0
$456$	4.05311			0.189804
$457$	3.92630	+	2.26685i	0.183665	+	0.106039i	0.589013	−	0.808123i	$-0.299517\pi$
$457$	3.92630	+	2.26685i	0.183665	+	0.106039i	−0.405349	+	0.914162i	$0.632850\pi$
$458$	−0.412611	−	1.53989i	−0.0192800	−	0.0719541i
$459$	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	$0.0428097\pi$
$462$	1.23899	+	2.14599i	0.0576429	+	0.0998404i
$463$		−	34.6785i		−	1.61165i	−0.592155	−	0.805824i	$-0.701723\pi$
$463$		−	34.6785i		−	1.61165i	0.592155	−	0.805824i	$-0.298277\pi$
$464$	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	$-0.753666\pi$
$467$	−0.351988	+	0.351988i	−0.0162881	+	0.0162881i	0.698916	+	0.715204i	$0.253666\pi$
$468$	3.39623	−	23.7598i	0.156991	−	1.09830i
$469$			20.7897i			0.959979i
$470$		0			0
$471$	−21.0071	+	36.3853i	−0.967954	+	1.67655i
$472$	6.17031	+	1.65333i	0.284012	+	0.0761007i
$473$	9.04301			0.415798
$474$	−1.78601	−	0.478560i	−0.0820342	−	0.0219810i
$475$		0			0
$476$	−20.2970	+	20.2970i	−0.930312	+	0.930312i
$477$	6.92166	−	25.8320i	0.316921	−	1.18277i
$478$	0.255520	−	0.0684665i	0.0116872	−	0.00313158i
$479$	16.9065	−	4.53008i	0.772478	−	0.206985i	0.149012	−	0.988835i	$-0.452391\pi$
$479$	16.9065	−	4.53008i	0.772478	−	0.206985i	0.623466	+	0.781851i	$0.285724\pi$
$480$		0			0
$481$	−7.81673	−	1.11732i	−0.356412	−	0.0509456i
$482$	−1.53633	−	1.53633i	−0.0699778	−	0.0699778i
$483$	20.7271	−	35.9003i	0.943114	−	1.63352i
$484$	−3.26966	−	1.88774i	−0.148621	−	0.0858063i
$485$		0			0
$486$	−1.96558	−	1.96558i	−0.0891605	−	0.0891605i
$487$	−6.22227	+	3.59243i	−0.281958	+	0.162788i	−0.634309	−	0.773079i	$-0.718715\pi$
$487$	−6.22227	+	3.59243i	−0.281958	+	0.162788i	0.352352	+	0.935868i	$0.385382\pi$
$488$	−2.39485	+	1.38267i	−0.108410	+	0.0625904i
$489$	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	$0.754528\pi$
$492$	−22.7473	+	39.3995i	−1.02553	+	1.77627i
$493$	−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
$497$	−40.4157	+	10.8294i	−1.81289	+	0.485763i
$498$	−0.787547	+	2.93916i	−0.0352908	+	0.131707i
$499$	26.4464	−	26.4464i	1.18390	−	1.18390i	0.205177	−	0.978725i	$-0.434223\pi$
$499$	26.4464	−	26.4464i	1.18390	−	1.18390i	0.978725	−	0.205177i	$-0.0657770\pi$
$500$		0			0
$501$	30.8406	+	8.26372i	1.37786	+	0.369196i
$502$	0.0907472			0.00405025
$503$	−24.6933	−	6.61654i	−1.10102	−	0.295017i	−0.337839	−	0.941204i	$-0.609696\pi$
$503$	−24.6933	−	6.61654i	−1.10102	−	0.295017i	−0.763179	+	0.646187i	$0.776363\pi$
$504$	−2.17796	+	3.77234i	−0.0970141	+	0.168033i
$505$		0			0
$506$			2.34993i			0.104467i
$507$	28.0097	+	17.0097i	1.24395	+	0.755429i
$508$	−7.71406	+	7.71406i	−0.342256	+	0.342256i
$509$	2.29966	+	8.58245i	0.101931	+	0.380410i	0.997979	−	0.0635463i	$-0.0202411\pi$
$509$	2.29966	+	8.58245i	0.101931	+	0.380410i	−0.896048	+	0.443957i	$0.853574\pi$
$510$		0			0
$511$	15.8022	−	9.12340i	0.699048	−	0.403596i
$512$			9.63626i			0.425866i
$513$	1.45007	+	2.51160i	0.0640222	+	0.110890i
$514$	0.493854	−	1.84309i	0.0217830	−	0.0812952i
$515$		0			0
$516$	7.49924	+	12.9891i	0.330136	+	0.571812i
$517$	−1.76737	−	6.59590i	−0.0777286	−	0.290087i
$518$	0.618126	+	0.356875i	0.0271589	+	0.0156802i
$519$	−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	$0.691925\pi$
$522$	−1.24663	−	0.719744i	−0.0545637	−	0.0315024i
$523$	−0.312883	−	1.16769i	−0.0136814	−	0.0510597i	0.958748	−	0.284258i	$-0.0917474\pi$
$523$	−0.312883	−	1.16769i	−0.0136814	−	0.0510597i	−0.972429	+	0.233199i	$0.925081\pi$
$524$	−1.86037	−	3.22225i	−0.0812704	−	0.140765i
$525$		0			0
$526$	0.821866	−	3.06724i	0.0358350	−	0.133738i
$527$	−25.8694	−	44.8070i	−1.12689	−	1.95183i
$528$			29.7102i			1.29297i
$529$	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
$533$	−19.6716	−	26.2332i	−0.852070	−	1.13629i
$534$		−	4.00646i		−	0.173376i
$535$		0			0
$536$	1.96226	−	3.39873i	0.0847566	−	0.146803i
$537$	−31.5564	−	8.45552i	−1.36176	−	0.364883i
$538$	−1.23928			−0.0534291
$539$	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	$0.232065\pi$
$542$	0.304839	−	1.13767i	0.0130940	−	0.0488673i
$543$	25.0068	−	6.70054i	1.07314	−	0.287548i
$544$	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	0.346205	−	0.938159i	$-0.387470\pi$
$547$	−13.8446	−	13.8446i	−0.591954	−	0.591954i	−0.938159	+	0.346205i	$0.887470\pi$
$548$	−0.826417	+	1.43140i	−0.0353028	+	0.0611462i
$549$	−16.2243	−	9.36713i	−0.692438	−	0.399779i
$550$		0			0
$551$	−7.93069	−	7.93069i	−0.337859	−	0.337859i
$552$	−6.77698	+	3.91269i	−0.288447	+	0.166535i
$553$	13.4085	−	7.74140i	0.570187	−	0.329198i
$554$	0.457329	+	0.457329i	0.0194300	+	0.0194300i
$555$		0			0
$556$	24.3545	+	14.0611i	1.03286	+	0.596323i
$557$	16.7504	−	29.0126i	0.709738	−	1.22930i	−0.255216	−	0.966884i	$-0.582147\pi$
$557$	16.7504	−	29.0126i	0.709738	−	1.22930i	0.964954	−	0.262418i	$-0.0845201\pi$
$558$	−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
$562$	−3.18934	+	0.854581i	−0.134534	+	0.0360483i
$563$	−4.42343	+	16.5085i	−0.186425	+	0.695748i	0.807896	+	0.589325i	$0.200606\pi$
$563$	−4.42343	+	16.5085i	−0.186425	+	0.695748i	−0.994321	+	0.106423i	$0.966060\pi$
$564$	8.00847	−	8.00847i	0.337217	−	0.337217i
$565$		0			0
$566$	−3.33230	−	0.892887i	−0.140067	−	0.0375308i
$567$	20.4887			0.860446
$568$	7.62936	+	2.04428i	0.320121	+	0.0857761i
$569$	−22.0925	+	38.2653i	−0.926165	+	1.60416i	−0.136488	+	0.990642i	$0.543582\pi$
$569$	−22.0925	+	38.2653i	−0.926165	+	1.60416i	−0.789677	+	0.613523i	$0.789752\pi$
$570$		0			0
$571$		−	37.9123i		−	1.58658i	−0.608844	−	0.793290i	$-0.708367\pi$
$571$		−	37.9123i		−	1.58658i	0.608844	−	0.793290i	$-0.291633\pi$
$572$	−19.8468	−	8.47960i	−0.829835	−	0.354550i
$573$	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
$577$			16.9069i			0.703843i	0.936030	+	0.351921i	$0.114472\pi$
$577$			16.9069i			0.703843i	−0.936030	+	0.351921i	$0.885528\pi$
$578$	−0.833185	−	1.44312i	−0.0346559	−	0.0600258i
$579$	1.63184	−	6.09012i	0.0678171	−	0.253097i
$580$		0			0
$581$	−12.7397	−	22.0658i	−0.528532	−	0.915445i
$582$	0.426191	+	1.59057i	0.0176662	+	0.0659311i
$583$	−20.8261	−	12.0240i	−0.862531	−	0.497982i
$584$	−3.44449			−0.142534
$585$		0			0
$586$	0.875831			0.0361802
$587$	26.0333	+	15.0303i	1.07451	+	0.620368i	0.929410	−	0.369049i	$-0.120317\pi$
$587$	26.0333	+	15.0303i	1.07451	+	0.620368i	0.145099	+	0.989417i	$0.453650\pi$
$588$	0.156295	+	0.583299i	0.00644548	+	0.0240549i
$589$	−15.2342	−	26.3864i	−0.627715	−	1.08723i
$590$		0			0
$591$	12.7763	−	47.6818i	0.525547	−	1.96137i
$592$	4.27883	+	7.41115i	0.175859	+	0.304596i
$593$			5.10110i			0.209477i	0.994500	+	0.104739i	$0.0334006\pi$
$593$			5.10110i			0.209477i	−0.994500	+	0.104739i	$0.966599\pi$
$594$	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
$598$	−0.335782	−	2.78894i	−0.0137311	−	0.114048i
$599$			33.5536i			1.37096i	0.728091	+	0.685480i	$0.240408\pi$
$599$			33.5536i			1.37096i	−0.728091	+	0.685480i	$0.759592\pi$
$600$		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	$0.752817\pi$
$602$	0.943833	+	0.252899i	0.0384677	+	0.0103074i
$603$	26.5874			1.08272
$604$	−1.36620	−	0.366071i	−0.0555897	−	0.0148952i
$605$		0			0
$606$	0.319091	−	0.319091i	0.0129622	−	0.0129622i
$607$	0.852422	−	3.18128i	0.0345987	−	0.129124i	−0.946466	−	0.322802i	$-0.895375\pi$
$607$	0.852422	−	3.18128i	0.0345987	−	0.129124i	0.981065	+	0.193678i	$0.0620418\pi$
$608$	4.62930	−	1.24042i	0.187743	−	0.0503055i
$609$	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
$613$	−1.54384	+	2.67402i	−0.0623553	+	0.108003i	−0.895518	−	0.445026i	$-0.853195\pi$
$613$	−1.54384	+	2.67402i	−0.0623553	+	0.108003i	0.833162	+	0.553028i	$0.186528\pi$
$614$	1.90661	+	1.10078i	0.0769447	+	0.0444241i
$615$		0			0
$616$	2.76968	+	2.76968i	0.111593	+	0.111593i
$617$	23.8740	−	13.7837i	0.961131	−	0.554909i	0.0646098	−	0.997911i	$-0.479420\pi$
$617$	23.8740	−	13.7837i	0.961131	−	0.554909i	0.896521	+	0.443002i	$0.146086\pi$
$618$	−1.11328	+	0.642754i	−0.0447828	+	0.0258554i
$619$	−13.0430	−	13.0430i	−0.524244	−	0.524244i	0.394606	−	0.918850i	$-0.370881\pi$
$619$	−13.0430	−	13.0430i	−0.524244	−	0.524244i	−0.918850	+	0.394606i	$0.870881\pi$
$620$		0			0
$621$	−4.84916	−	2.79967i	−0.194590	−	0.112347i
$622$	1.12638	−	1.95094i	0.0451636	−	0.0782257i
$623$	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
$627$	23.8498	−	6.39054i	0.952470	−	0.255214i
$628$	−8.56097	+	31.9500i	−0.341620	+	1.27494i
$629$	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	$0.746029\pi$
$632$	−2.92272			−0.116260
$633$	−10.8332	−	2.90276i	−0.430582	−	0.115374i
$634$	−0.499116	+	0.864494i	−0.0198224	+	0.0343334i
$635$		0			0
$636$		−	39.8853i		−	1.58155i
$637$	−0.430854	−	0.0615863i	−0.0170711	−	0.00244014i
$638$	−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	$0.554257\pi$
$642$			0.314011i			0.0123930i
$643$	16.9008	+	29.2730i	0.666501	+	1.15441i	0.978876	+	0.204455i	$0.0655422\pi$
$643$	16.9008	+	29.2730i	0.666501	+	1.15441i	−0.312375	+	0.949959i	$0.601124\pi$
$644$	8.44685	−	31.5241i	0.332853	−	1.24222i
$645$		0			0
$646$	−1.11264	−	1.92716i	−0.0437764	−	0.0758229i
$647$	8.72438	+	32.5598i	0.342991	+	1.28006i	0.894942	+	0.446183i	$0.147217\pi$
$647$	8.72438	+	32.5598i	0.342991	+	1.28006i	−0.551951	+	0.833877i	$0.686116\pi$
$648$	−3.34953	−	1.93385i	−0.131582	−	0.0759689i
$649$	38.9149			1.52755
$650$		0			0
$651$	62.0311			2.43119
$652$	6.82639	+	3.94122i	0.267342	+	0.154350i
$653$	−4.59060	−	17.1323i	−0.179644	−	0.670441i	−0.995714	−	0.0924873i	$-0.970518\pi$
$653$	−4.59060	−	17.1323i	−0.179644	−	0.670441i	0.816070	−	0.577953i	$-0.196148\pi$
$654$	2.14837	+	3.72108i	0.0840077	+	0.145506i
$655$		0			0
$656$	−9.19748	+	34.3255i	−0.359101	+	1.34018i
$657$	−11.6677	−	20.2090i	−0.455199	−	0.788427i
$658$		−	0.737850i		−	0.0287644i
$659$	11.6311	−	6.71522i	0.453084	−	0.261588i	−0.256048	−	0.966664i	$-0.582421\pi$
$659$	11.6311	−	6.71522i	0.453084	−	0.261588i	0.709132	+	0.705076i	$0.249087\pi$
$660$		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
$663$	−46.5150	+	18.6661i	−1.80649	+	0.724933i
$664$			4.80980i			0.186657i
$665$		0			0
$666$	0.456398	−	0.790504i	0.0176850	−	0.0306314i
$667$	20.9164	+	5.60453i	0.809886	+	0.217008i
$668$	25.1368			0.972573
$669$	−1.98117	−	0.530852i	−0.0765963	−	0.0205239i
$670$		0			0
$671$	−11.9120	+	11.9120i	−0.459859	+	0.459859i
$672$	−2.52538	+	9.42484i	−0.0974186	+	0.363571i
$673$	−45.3283	+	12.1457i	−1.74728	+	0.468181i	−0.984042	−	0.177939i	$-0.943057\pi$
$673$	−45.3283	+	12.1457i	−1.74728	+	0.468181i	−0.763235	+	0.646120i	$0.776390\pi$
$674$	−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	0.457133	−	0.889398i	$-0.348876\pi$
$677$	−11.2472	−	11.2472i	−0.432266	−	0.432266i	−0.889398	+	0.457133i	$0.848876\pi$
$678$	−1.68456	+	2.91774i	−0.0646950	+	0.112055i
$679$	−11.9412	−	6.89426i	−0.458261	−	0.264577i
$680$		0			0
$681$	−43.4399	−	43.4399i	−1.66462	−	1.66462i
$682$	−3.04528	+	1.75819i	−0.116610	+	0.0673247i
$683$	13.8477	−	7.99498i	0.529868	−	0.305919i	−0.211095	−	0.977466i	$-0.567703\pi$
$683$	13.8477	−	7.99498i	0.529868	−	0.305919i	0.740963	+	0.671546i	$0.234370\pi$
$684$	15.2860	+	15.2860i	0.584474	+	0.584474i
$685$		0			0
$686$	2.00981	+	1.16036i	0.0767349	+	0.0443029i
$687$	16.1703	−	28.0078i	0.616936	−	1.06856i
$688$	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	$0.328807\pi$
$692$	−46.9605	+	12.5830i	−1.78517	+	0.478335i
$693$	−6.86799	+	25.6317i	−0.260893	+	0.973667i
$694$	0.417180	−	0.417180i	0.0158359	−	0.0158359i
$695$		0			0
$696$	−4.16358	−	1.11563i	−0.157820	−	0.0422877i
$697$	50.1504			1.89958
$698$	−0.288895	−	0.0774093i	−0.0109349	−	0.00292999i
$699$	−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	$-0.0149031\pi$
$702$	−0.320104	+	0.240037i	−0.0120815	+	0.00905962i
$703$	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
$707$			3.77867i			0.142112i
$708$	32.2716	+	55.8961i	1.21284	+	2.10070i
$709$	−2.01972	+	7.53768i	−0.0758520	+	0.283084i	−0.993425	−	0.114483i	$-0.963479\pi$
$709$	−2.01972	+	7.53768i	−0.0758520	+	0.283084i	0.917573	+	0.397567i	$0.130145\pi$
$710$		0			0
$711$	−9.90026	−	17.1477i	−0.371289	−	0.643091i
$712$	−1.63910	−	6.11719i	−0.0614277	−	0.229251i
$713$	50.9446	+	29.4129i	1.90789	+	1.10152i
$714$	4.53049			0.169549
$715$		0			0
$716$	−25.7203			−0.961211
$717$	4.64747	+	2.68322i	0.173563	+	0.100207i
$718$	−0.0443998	−	0.165702i	−0.00165699	−	0.00618396i
$719$	16.7165	+	28.9539i	0.623421	+	1.07980i	0.988844	+	0.148955i	$0.0475910\pi$
$719$	16.7165	+	28.9539i	0.623421	+	1.07980i	−0.365423	+	0.930842i	$0.619076\pi$
$720$		0			0
$721$	2.78600	−	10.3975i	0.103756	−	0.387222i
$722$	0.525239	+	0.909741i	0.0195474	+	0.0338571i
$723$		−	44.0760i		−	1.63921i
$724$	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	$-0.945879\pi$
$727$	−22.0118	+	22.0118i	−0.816374	+	0.816374i	0.169207	+	0.985581i	$0.445879\pi$
$728$	−3.68286	−	2.89134i	−0.136496	−	0.107160i
$729$		−	32.9560i		−	1.22059i
$730$		0			0
$731$	8.26668	−	14.3183i	0.305754	−	0.529582i
$732$	−26.9885	−	7.23155i	−0.997524	−	0.267286i
$733$	32.5431			1.20201			0.601004	−	0.799246i	$-0.294768\pi$
$733$	32.5431			1.20201			0.601004	+	0.799246i	$0.294768\pi$
$734$	−3.52604	−	0.944800i	−0.130149	−	0.0348732i
$735$		0			0
$736$	−6.54295	+	6.54295i	−0.241176	+	0.241176i
$737$	6.18779	−	23.0931i	0.227930	−	0.850647i
$738$	3.66130	−	0.981041i	0.134774	−	0.0361126i
$739$	−34.8599	+	9.34069i	−1.28234	+	0.343603i	−0.834747	−	0.550633i	$-0.814386\pi$
$739$	−34.8599	+	9.34069i	−1.28234	+	0.343603i	−0.447595	+	0.894236i	$0.647720\pi$
$740$		0			0
$741$	−27.3922	+	10.9923i	−1.00628	+	0.403813i
$742$	−1.83739	−	1.83739i	−0.0674527	−	0.0674527i
$743$	−2.48474	+	4.30370i	−0.0911563	+	0.157887i	−0.907998	−	0.418975i	$-0.862390\pi$
$743$	−2.48474	+	4.30370i	−0.0911563	+	0.157887i	0.816842	+	0.576862i	$0.195723\pi$
$744$	−10.1409	−	5.85487i	−0.371784	−	0.214650i
$745$		0			0
$746$	−1.96006	−	1.96006i	−0.0717628	−	0.0717628i
$747$	−28.2194	+	16.2925i	−1.03249	+	0.596110i
$748$	28.5870	−	16.5047i	1.04524	−	0.603472i
$749$	−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	$0.513660\pi$
$752$	4.42331	−	7.66139i	0.161301	−	0.279382i
$753$	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
$757$	34.0207	−	9.11581i	1.23650	−	0.331320i	0.419394	−	0.907804i	$-0.362242\pi$
$757$	34.0207	−	9.11581i	1.23650	−	0.331320i	0.817108	+	0.576484i	$0.195576\pi$
$758$	−0.893486	+	3.33454i	−0.0324529	+	0.121116i
$759$	−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	$0.601898\pi$
$762$	1.72185			0.0623761
$763$	−34.7529	−	9.31202i	−1.25814	−	0.337118i
$764$	8.26136	−	14.3091i	0.298885	−	0.517685i
$765$		0			0
$766$		−	0.430980i		−	0.0155719i
$767$	−46.1849	+	5.56056i	−1.66764	+	0.200780i
$768$	−26.3429	+	26.3429i	−0.950568	+	0.950568i
$769$	7.34107	+	27.3973i	0.264726	+	0.987970i	0.962418	+	0.271573i	$0.0875437\pi$
$769$	7.34107	+	27.3973i	0.264726	+	0.987970i	−0.697692	+	0.716398i	$0.745790\pi$
$770$		0			0
$771$	33.5225	−	19.3542i	1.20728	−	0.697026i
$772$		−	4.96379i		−	0.178651i
$773$	14.3589	+	24.8703i	0.516454	+	0.894524i	0.999817	+	0.0191044i	$0.00608150\pi$
$773$	14.3589	+	24.8703i	0.516454	+	0.894524i	−0.483364	+	0.875420i	$0.660585\pi$
$774$	0.323426	−	1.20704i	0.0116253	−	0.0433862i
$775$		0			0
$776$	1.30144	+	2.25417i	0.0467191	+	0.0809198i
$777$	3.74754	+	13.9860i	0.134442	+	0.501745i
$778$	−1.72131	−	0.993798i	−0.0617119	−	0.0356294i
$779$	29.5331			1.05813
$780$		0			0
$781$	48.1169			1.72176
$782$	3.72078	+	2.14819i	0.133055	+	0.0768192i
$783$	−0.798270	−	2.97919i	−0.0285279	−	0.106467i
$784$	0.235847	+	0.408499i	0.00842310	+	0.0145892i
$785$		0			0
$786$	−0.151993	+	0.567244i	−0.00542140	+	0.0202329i
$787$	−0.260059	−	0.450435i	−0.00927010	−	0.0160563i	0.861353	−	0.508007i	$-0.169617\pi$
$787$	−0.260059	−	0.450435i	−0.00927010	−	0.0160563i	−0.870623	+	0.491950i	$0.836284\pi$
$788$		−	38.8634i		−	1.38445i
$789$	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
$793$	12.4353	−	15.8395i	0.441590	−	0.562477i
$794$		−	1.39567i		−	0.0495303i
$795$		0			0
$796$	2.97209	−	5.14782i	0.105343	−	0.182459i
$797$	−3.86739	−	1.03627i	−0.136990	−	0.0367064i	0.189672	−	0.981847i	$-0.439257\pi$
$797$	−3.86739	−	1.03627i	−0.136990	−	0.0367064i	−0.326663	+	0.945141i	$0.605924\pi$
$798$	2.66796			0.0944448
$799$	−12.0593	−	3.23128i	−0.426628	−	0.114315i
$800$		0			0
$801$	30.3377	−	30.3377i	1.07193	−	1.07193i
$802$	0.241380	−	0.900844i	0.00852344	−	0.0318099i
$803$	−20.2685	+	5.43093i	−0.715260	+	0.191653i
$804$	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
$808$	0.356654	−	0.617743i	0.0125471	−	0.0217321i
$809$	−39.9699	−	23.0766i	−1.40527	−	0.811331i	−0.410339	−	0.911933i	$-0.634590\pi$
$809$	−39.9699	−	23.0766i	−1.40527	−	0.811331i	−0.994927	+	0.100602i	$0.967923\pi$
$810$		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	$0.855428\pi$
$812$	15.5685	−	8.98848i	0.546347	−	0.315434i
$813$	20.6923	−	11.9467i	0.725710	−	0.418989i
$814$	−0.580393	−	0.580393i	−0.0203428	−	0.0203428i
$815$		0			0
$816$	47.0419	+	27.1596i	1.64679	+	0.950777i
$817$	4.86817	−	8.43192i	0.170316	−	0.294996i
$818$	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	$0.304854\pi$
$822$	0.251983	−	0.0675186i	0.00878892	−	0.00235498i
$823$	1.46552	−	5.46939i	0.0510848	−	0.190651i	−0.935668	−	0.352881i	$-0.885202\pi$
$823$	1.46552	−	5.46939i	0.0510848	−	0.190651i	0.986753	+	0.162230i	$0.0518687\pi$
$824$	−1.43684	+	1.43684i	−0.0500545	+	0.0500545i
$825$		0			0
$826$	4.06161	+	1.08831i	0.141322	+	0.0378670i
$827$	−37.5355			−1.30524			−0.652618	−	0.757687i	$-0.726329\pi$
$827$	−37.5355			−1.30524			−0.652618	+	0.757687i	$0.726329\pi$
$828$	−40.3153	−	10.8024i	−1.40105	−	0.375411i
$829$	−19.0247	+	32.9518i	−0.660756	+	1.14446i	0.319661	+	0.947532i	$0.396431\pi$
$829$	−19.0247	+	32.9518i	−0.660756	+	1.14446i	−0.980417	+	0.196932i	$0.936902\pi$
$830$		0			0
$831$			13.1204i			0.455142i
$832$	−10.2480	−	25.5374i	−0.355284	−	0.885350i
$833$	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
$837$		−	8.37872i		−	0.289611i
$838$	−0.148923	−	0.257942i	−0.00514446	−	0.00891047i
$839$	−0.986990	+	3.68350i	−0.0340747	+	0.127168i	−0.980868	−	0.194673i	$-0.937635\pi$
$839$	−0.986990	+	3.68350i	−0.0340747	+	0.127168i	0.946793	+	0.321842i	$0.104302\pi$
$840$		0			0
$841$	−8.53610	−	14.7850i	−0.294348	−	0.509826i
$842$	−0.633761	−	2.36523i	−0.0218408	−	0.0815111i
$843$	−58.0084	−	33.4912i	−1.99792	−	1.15350i
$844$	−8.82969			−0.303930
$845$		0			0
$846$	−0.943616			−0.0324422
$847$	−4.32126	−	2.49488i	−0.148480	−	0.0857251i
$848$	−8.06346	−	30.0932i	−0.276900	−	1.03341i
$849$	−34.9924	−	60.6086i	−1.20094	−	2.08008i
$850$		0			0
$851$	−3.55389	+	13.2633i	−0.121826	+	0.454660i
$852$	39.9027	+	69.1134i	1.36704	+	2.36779i
$853$		−	15.1949i		−	0.520263i	−0.965573	−	0.260132i	$-0.916234\pi$
$853$		−	15.1949i		−	0.520263i	0.965573	−	0.260132i	$-0.0837660\pi$
$854$	−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	$-0.573515\pi$
$857$	21.7961	−	21.7961i	0.744542	−	0.744542i	0.973448	+	0.228906i	$0.0735150\pi$
$858$	1.26863	+	3.16136i	0.0433103	+	0.107927i
$859$		−	19.9625i		−	0.681113i	−0.940224	−	0.340557i	$-0.889385\pi$
$859$		−	19.9625i		−	0.681113i	0.940224	−	0.340557i	$-0.110615\pi$
$860$		0			0
$861$	−30.0634	+	52.0713i	−1.02456	+	1.77459i
$862$	2.28814	+	0.613105i	0.0779343	+	0.0208824i
$863$	45.8868			1.56201			0.781003	−	0.624527i	$-0.214708\pi$
$863$	45.8868			1.56201			0.781003	+	0.624527i	$0.214708\pi$
$864$	1.27304	+	0.341111i	0.0433098	+	0.0116048i
$865$		0			0
$866$	0.671210	−	0.671210i	0.0228086	−	0.0228086i
$867$	8.74926	−	32.6527i	0.297141	−	1.10894i
$868$	47.1720	−	12.6397i	1.60112	−	0.429019i
$869$	−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
$873$	−8.81687	+	15.2713i	−0.298406	+	0.516854i
$874$	2.19113	+	1.26505i	0.0741161	+	0.0427910i
$875$		0			0
$876$	−24.6092	−	24.6092i	−0.831467	−	0.831467i
$877$	−30.5152	+	17.6180i	−1.03042	+	0.594916i	−0.917106	−	0.398643i	$-0.869481\pi$
$877$	−30.5152	+	17.6180i	−1.03042	+	0.594916i	−0.113318	+	0.993559i	$0.536148\pi$
$878$	−0.484020	+	0.279449i	−0.0163349	+	0.00943096i
$879$	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	$0.789033\pi$
$882$	0.0251564	−	0.0435722i	0.000847060	−	0.00146715i
$883$	11.0289	+	11.0289i	0.371151	+	0.371151i	0.867896	−	0.496745i	$-0.165472\pi$
$883$	11.0289	+	11.0289i	0.371151	+	0.371151i	−0.496745	+	0.867896i	$0.665472\pi$
$884$	−31.5692	+	23.6729i	−1.06179	+	0.796205i
$885$		0			0
$886$	3.43180	−	0.919547i	0.115293	−	0.0308928i
$887$	−17.0556	+	4.57003i	−0.572671	+	0.153447i	−0.533521	−	0.845787i	$-0.679132\pi$
$887$	−17.0556	+	4.57003i	−0.572671	+	0.153447i	−0.0391497	+	0.999233i	$0.512465\pi$
$888$	0.707431	−	2.64017i	0.0237398	−	0.0885983i
$889$	−10.1951	+	10.1951i	−0.341932	+	0.341932i
$890$		0			0
$891$	−22.7588	−	6.09821i	−0.762450	−	0.204298i
$892$	−1.61476			−0.0540662
$893$	−7.10161	−	1.90287i	−0.237646	−	0.0636771i
$894$	0.0101898	−	0.0176492i	0.000340798	−	0.000590279i
$895$		0			0
$896$			10.2288i			0.341722i
$897$	35.1895	−	44.8229i	1.17494	−	1.49659i
$898$	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
$902$		−	3.40844i		−	0.113489i
$903$	9.91117	+	17.1666i	0.329823	+	0.571270i
$904$	−1.37835	+	5.14407i	−0.0458432	+	0.171089i
$905$		0			0
$906$	0.111619	+	0.193329i	0.00370829	+	0.00642294i
$907$	14.3754	+	53.6498i	0.477328	+	1.78141i	0.612367	+	0.790573i	$0.290217\pi$
$907$	14.3754	+	53.6498i	0.477328	+	1.78141i	−0.135039	+	0.990840i	$0.543116\pi$
$908$	−41.8856	−	24.1827i	−1.39002	−	0.802531i
$909$	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	$0.581472\pi$
$912$	27.7025	+	15.9940i	0.917321	+	0.529616i
$913$	7.58363	+	28.3025i	0.250981	+	0.936675i
$914$	−0.281678	−	0.487880i	−0.00931706	−	0.0161376i
$915$		0			0
$916$	6.58985	−	24.5937i	0.217735	−	0.812597i
$917$	−2.45870	−	4.25860i	−0.0811935	−	0.140631i
$918$		−	0.611947i		−	0.0201973i
$919$	−15.6355	+	9.02717i	−0.515768	+	0.297779i	−0.735202	−	0.677848i	$-0.762913\pi$
$919$	−15.6355	+	9.02717i	−0.515768	+	0.297779i	0.219433	+	0.975628i	$0.429579\pi$
$920$		0			0
$921$	11.5593	+	43.1400i	0.380893	+	1.42151i
$922$	−0.479048	+	0.479048i	−0.0157766	+	0.0157766i
$923$	−57.1059	+	6.87543i	−1.87966	+	0.226307i
$924$			39.5760i			1.30195i
$925$		0			0
$926$	−2.15457	+	3.73182i	−0.0708035	+	0.122635i
$927$	−13.2970	−	3.56293i	−0.436732	−	0.117022i
$928$	−5.09690			−0.167314
$929$	−40.3925	−	10.8231i	−1.32524	−	0.355096i	−0.474299	−	0.880364i	$-0.657298\pi$
$929$	−40.3925	−	10.8231i	−1.32524	−	0.355096i	−0.850937	+	0.525268i	$0.823965\pi$
$930$		0			0
$931$	0.277192	−	0.277192i	0.00908461	−	0.00908461i
$932$	−2.48139	+	9.26069i	−0.0812808	+	0.303344i
$933$	44.1430	−	11.8281i	1.44518	−	0.387234i
$934$	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	0.861889	−	0.507098i	$-0.169282\pi$
$937$	10.8603	+	10.8603i	0.354791	+	0.354791i	−0.507098	+	0.861889i	$0.669282\pi$
$938$	1.29166	−	2.23722i	0.0421741	−	0.0730477i
$939$	−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	$0.463373\pi$
$942$	4.52122	−	2.61033i	0.147309	−	0.0850490i
$943$	−49.3806	+	28.5099i	−1.60805	+	0.928411i
$944$	35.6491	+	35.6491i	1.16028	+	1.16028i
$945$		0			0
$946$	−0.973134	−	0.561839i	−0.0316393	−	0.0182670i
$947$	−23.4687	+	40.6489i	−0.762629	+	1.32091i	0.178862	+	0.983874i	$0.442758\pi$
$947$	−23.4687	+	40.6489i	−0.762629	+	1.32091i	−0.941491	+	0.337038i	$0.890575\pi$
$948$	−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
$952$	6.91729	−	1.85348i	0.224191	−	0.0600717i
$953$	0.821808	−	3.06703i	0.0266210	−	0.0993508i	−0.951337	−	0.308152i	$-0.900289\pi$
$953$	0.821808	−	3.06703i	0.0266210	−	0.0993508i	0.977958	+	0.208801i	$0.0669561\pi$
$954$	−2.34979	+	2.34979i	−0.0760771	+	0.0760771i
$955$		0			0
$956$	4.08094	+	1.09349i	0.131987	+	0.0353658i
$957$	−26.2589			−0.848829
$958$	−2.10079	−	0.562905i	−0.0678735	−	0.0181866i
$959$	−1.09221	+	1.89177i	−0.0352694	+	0.0610883i
$960$		0			0
$961$			57.0256i			1.83953i
$962$	0.771753	+	0.605888i	0.0248823	+	0.0195346i
$963$	−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
$967$			18.3290i			0.589421i	0.955587	+	0.294711i	$0.0952233\pi$
$967$			18.3290i			0.589421i	−0.955587	+	0.294711i	$0.904777\pi$
$968$	0.470964	+	0.815733i	0.0151374	+	0.0262187i
$969$	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	$0.716085\pi$
$972$	−11.4904	−	42.8829i	−0.368556	−	1.37547i
$973$	32.1875	+	18.5835i	1.03188	+	0.595758i
$974$	0.892786			0.0286067
$975$		0			0
$976$	−21.8247			−0.698590
$977$	36.8699	+	21.2868i	1.17957	+	0.681026i	0.955915	−	0.293642i	$-0.0948674\pi$
$977$	36.8699	+	21.2868i	1.17957	+	0.681026i	0.223656	+	0.974668i	$0.428201\pi$
$978$	−0.321999	−	1.20172i	−0.0102964	−	0.0384267i
$979$	−19.2900	−	33.4112i	−0.616510	−	1.06783i
$980$		0			0
$981$	−11.9089	+	44.4445i	−0.380221	+	1.41900i
$982$	0.750396	+	1.29972i	0.0239461	+	0.0414758i
$983$		−	2.26298i		−	0.0721778i	−0.999349	−	0.0360889i	$-0.988510\pi$
$983$		−	2.26298i		−	0.0721778i	0.999349	−	0.0360889i	$-0.0114899\pi$
$984$	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
$988$	−18.5908	+	13.9407i	−0.591452	+	0.443514i
$989$			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	$0.144621\pi$
$992$	−13.3744	−	3.58366i	−0.424637	−	0.113781i
$993$	−33.3841			−1.05941
$994$	5.02203	+	1.34565i	0.159289	+	0.0426814i
$995$		0			0
$996$	−34.3637	+	34.3637i	−1.08886	+	1.08886i
$997$	2.91575	−	10.8817i	0.0923426	−	0.344627i	−0.904261	−	0.426981i	$-0.859577\pi$
$997$	2.91575	−	10.8817i	0.0923426	−	0.344627i	0.996603	+	0.0823538i	$0.0262437\pi$
$998$	−4.48905	+	1.20284i	−0.142098	+	0.0380751i
$999$	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.x.c.7.5	yes	40
5.2	odd	4		325.2.s.c.293.6	yes	40
5.3	odd	4		325.2.s.c.293.5	yes	40
5.4	even	2	inner	325.2.x.c.7.6	yes	40
13.2	odd	12		325.2.s.c.132.5	✓	40
65.2	even	12	inner	325.2.x.c.93.6	yes	40
65.28	even	12	inner	325.2.x.c.93.5	yes	40
65.54	odd	12		325.2.s.c.132.6	yes	40

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Varieties

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Database

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