LMFDB - Embedded newform 875.2.bb.b.768.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			768.9
Character	$\chi$	$=$	875.768
Dual form			875.2.bb.b.507.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.000791762 + 0.000514176i) q^{2} +(2.48892 - 0.955405i) q^{3} +(-0.813473 + 1.82709i) q^{4} +(-0.00147938 + 0.00203619i) q^{6} +(-2.21008 + 1.45449i) q^{7} +(-0.000590739 - 0.00372978i) q^{8} +(3.05247 - 2.74845i) q^{9} +(-3.30773 + 3.67360i) q^{11} +(-0.279054 + 5.32467i) q^{12} +(2.45874 + 4.82554i) q^{13} +(0.00100199 - 0.00228798i) q^{14} +(-2.67652 - 2.97258i) q^{16} +(-0.599995 + 0.485867i) q^{17} +(-0.00100364 + 0.00374563i) q^{18} +(-0.883861 + 0.393520i) q^{19} +(-4.11107 + 5.73163i) q^{21} +(0.000730053 - 0.00460937i) q^{22} +(1.49430 + 2.30102i) q^{23} +(-0.00503375 - 0.00871871i) q^{24} +(-0.00442791 - 0.00255646i) q^{26} +(1.34044 - 2.63077i) q^{27} +(-0.859653 - 5.22120i) q^{28} +(-2.32212 - 3.19613i) q^{29} +(8.98125 + 0.943968i) q^{31} +(0.0109428 + 0.00293211i) q^{32} +(-4.72287 + 12.3035i) q^{33} +(0.000225232 - 0.000693194i) q^{34} +(2.53857 + 7.81292i) q^{36} +(2.11384 + 0.110782i) q^{37} +(0.000497468 - 0.000766034i) q^{38} +(10.7299 + 9.66128i) q^{39} +(6.23478 + 2.02580i) q^{41} +(0.000307917 - 0.00665190i) q^{42} +(-2.74386 - 2.74386i) q^{43} +(-4.02126 - 9.03189i) q^{44} +(-0.00236626 - 0.00105353i) q^{46} +(-2.81832 + 3.48033i) q^{47} +(-9.50164 - 4.84133i) q^{48} +(2.76889 - 6.42909i) q^{49} +(-1.02914 + 1.78252i) q^{51} +(-10.8168 + 0.566885i) q^{52} +(0.0828569 + 0.215850i) q^{53} +(0.000291366 + 0.00277217i) q^{54} +(0.00673052 + 0.00738387i) q^{56} +(-1.82388 + 1.82388i) q^{57} +(0.00348194 + 0.00133659i) q^{58} +(-4.31794 + 0.917807i) q^{59} +(2.52960 - 11.9008i) q^{61} +(-0.00759638 + 0.00387055i) q^{62} +(-2.74858 + 10.5141i) q^{63} +(7.60843 - 2.47213i) q^{64} +(-0.00258678 - 0.0121698i) q^{66} +(0.453546 + 0.560082i) q^{67} +(-0.399642 - 1.49149i) q^{68} +(5.91760 + 4.29939i) q^{69} +(3.49220 - 2.53723i) q^{71} +(-0.0120543 - 0.00976140i) q^{72} +(0.0425173 + 0.811278i) q^{73} +(-0.00173062 + 0.000999174i) q^{74} -1.93501i q^{76} +(1.96710 - 12.9300i) q^{77} +(-0.0134631 - 0.00213235i) q^{78} +(4.91609 - 0.516702i) q^{79} +(-0.465251 + 4.42657i) q^{81} +(-0.00597808 + 0.00160182i) q^{82} +(-13.2310 + 2.09559i) q^{83} +(-7.12797 - 12.1738i) q^{84} +(0.00358331 + 0.000761656i) q^{86} +(-8.83316 - 5.73632i) q^{87} +(0.0156557 + 0.0101669i) q^{88} +(11.3525 + 2.41304i) q^{89} +(-12.4527 - 7.08861i) q^{91} +(-5.41975 + 0.858405i) q^{92} +(23.2555 - 6.23128i) q^{93} +(0.000441932 - 0.00420470i) q^{94} +(0.0300370 - 0.00315702i) q^{96} +(13.4877 + 2.13624i) q^{97} +(0.00111338 + 0.00651401i) q^{98} +20.3047i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) $ 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.000791762	0	0.000514176i	−0.000559860	0	0.000363577i	−0.544919	−	0.838489i	$-0.683440\pi$
$2$	−0.000791762	0	0.000514176i	−0.000559860	0	0.000363577i	0.544359	+	0.838852i	$0.316773\pi$
$3$	2.48892	−	0.955405i	1.43698	−	0.551603i	0.489663	−	0.871912i	$-0.337120\pi$
$3$	2.48892	−	0.955405i	1.43698	−	0.551603i	0.947313	+	0.320309i	$0.103787\pi$
$4$	−0.813473	+	1.82709i	−0.406736	+	0.913545i
$5$		0			0
$5$		0			0
$6$	−0.00147938	+	0.00203619i	−0.000603955	+	0.000831273i
$7$	−2.21008	+	1.45449i	−0.835331	+	0.549747i
$7$	−2.21008	+	1.45449i	−0.835331	+	0.549747i
$8$	−0.000590739	−	0.00372978i	−0.000208858	−	0.00131868i
$9$	3.05247	−	2.74845i	1.01749	−	0.916151i
$10$		0			0
$11$	−3.30773	+	3.67360i	−0.997317	+	1.10763i	−0.00312730	+	0.999995i	$0.500995\pi$
$11$	−3.30773	+	3.67360i	−0.997317	+	1.10763i	−0.994190	+	0.107638i	$0.965671\pi$
$12$	−0.279054	+	5.32467i	−0.0805560	+	1.53710i
$13$	2.45874	+	4.82554i	0.681931	+	1.33836i	0.929258	+	0.369432i	$0.120448\pi$
$13$	2.45874	+	4.82554i	0.681931	+	1.33836i	−0.247327	+	0.968932i	$0.579552\pi$
$14$	0.00100199	−	0.00228798i	0.000267793	−	0.000611489i
$15$		0			0
$16$	−2.67652	−	2.97258i	−0.669130	−	0.743144i
$17$	−0.599995	+	0.485867i	−0.145520	+	0.117840i	−0.699316	−	0.714812i	$-0.746512\pi$
$17$	−0.599995	+	0.485867i	−0.145520	+	0.117840i	0.553796	+	0.832652i	$0.313179\pi$
$18$	−0.00100364	+	0.00374563i	−0.000236560	+	0.000882852i
$19$	−0.883861	+	0.393520i	−0.202772	+	0.0902797i	−0.505610	−	0.862762i	$-0.668732\pi$
$19$	−0.883861	+	0.393520i	−0.202772	+	0.0902797i	0.302838	+	0.953042i	$0.402066\pi$
$20$		0			0
$21$	−4.11107	+	5.73163i	−0.897108	+	1.25074i
$22$	0.000730053	−	0.00460937i	0.000155648	−	0.000982722i
$23$	1.49430	+	2.30102i	0.311584	+	0.479797i	0.959419	−	0.281983i	$-0.0909923\pi$
$23$	1.49430	+	2.30102i	0.311584	+	0.479797i	−0.647836	+	0.761780i	$0.724326\pi$
$24$	−0.00503375	−	0.00871871i	−0.00102751	−	0.00177970i
$25$		0			0
$26$	−0.00442791	−	0.00255646i	−0.000868385	−	0.000501362i
$27$	1.34044	−	2.63077i	0.257968	−	0.506292i
$28$	−0.859653	−	5.22120i	−0.162459	−	0.986715i
$29$	−2.32212	−	3.19613i	−0.431207	−	0.593506i	0.537023	−	0.843568i	$-0.319549\pi$
$29$	−2.32212	−	3.19613i	−0.431207	−	0.593506i	−0.968230	+	0.250062i	$0.919549\pi$
$30$		0			0
$31$	8.98125	+	0.943968i	1.61308	+	0.169542i	0.867697	−	0.497094i	$-0.165600\pi$
$31$	8.98125	+	0.943968i	1.61308	+	0.169542i	0.745384	+	0.666635i	$0.232266\pi$
$32$	0.0109428	+	0.00293211i	0.00193443	+	0.000518329i
$33$	−4.72287	+	12.3035i	−0.822147	+	2.14177i
$34$	0.000225232	0	0.000693194i	3.86270e−5	0	0.000118882i
$35$		0			0
$36$	2.53857	+	7.81292i	0.423095	+	1.30215i
$37$	2.11384	+	0.110782i	0.347513	+	0.0182124i	0.225294	−	0.974291i	$-0.427666\pi$
$37$	2.11384	+	0.110782i	0.347513	+	0.0182124i	0.122219	+	0.992503i	$0.460999\pi$
$38$	0.000497468	0	0.000766034i	8.07000e−5	0	0.000124267i
$39$	10.7299	+	9.66128i	1.71816	+	1.54704i
$40$		0			0
$41$	6.23478	+	2.02580i	0.973710	+	0.316377i	0.752313	−	0.658806i	$-0.228938\pi$
$41$	6.23478	+	2.02580i	0.973710	+	0.316377i	0.221397	+	0.975184i	$0.428938\pi$
$42$	0.000307917	−	0.00665190i	4.75127e−5	−	0.00102641i
$43$	−2.74386	−	2.74386i	−0.418435	−	0.418435i	0.466229	−	0.884664i	$-0.345612\pi$
$43$	−2.74386	−	2.74386i	−0.418435	−	0.418435i	−0.884664	+	0.466229i	$0.845612\pi$
$44$	−4.02126	−	9.03189i	−0.606227	−	1.36161i
$45$		0			0
$46$	−0.00236626	−	0.00105353i	−0.000348887	−	0.000155334i
$47$	−2.81832	+	3.48033i	−0.411094	+	0.507659i	−0.940072	−	0.340977i	$-0.889242\pi$
$47$	−2.81832	+	3.48033i	−0.411094	+	0.507659i	0.528978	+	0.848636i	$0.322575\pi$
$48$	−9.50164	−	4.84133i	−1.37144	−	0.698786i
$49$	2.76889	−	6.42909i	0.395556	−	0.918442i
$50$		0			0
$51$	−1.02914	+	1.78252i	−0.144108	+	0.249603i
$52$	−10.8168	+	0.566885i	−1.50002	+	0.0786128i
$53$	0.0828569	+	0.215850i	0.0113813	+	0.0296492i	0.939153	−	0.343498i	$-0.111612\pi$
$53$	0.0828569	+	0.215850i	0.0113813	+	0.0296492i	−0.927772	+	0.373147i	$0.878279\pi$
$54$	0.000291366		0.00277217i	3.96499e−5		0.000377244i
$55$		0			0
$56$	0.00673052	+	0.00738387i	0.000899403	+	0.000986712i
$57$	−1.82388	+	1.82388i	−0.241579	+	0.241579i
$58$	0.00348194	+	0.00133659i	0.000457201	+	0.000175503i
$59$	−4.31794	+	0.917807i	−0.562148	+	0.119488i	−0.480217	−	0.877150i	$-0.659442\pi$
$59$	−4.31794	+	0.917807i	−0.562148	+	0.119488i	−0.0819313	+	0.996638i	$0.526109\pi$
$60$		0			0
$61$	2.52960	−	11.9008i	0.323882	−	1.52374i	−0.451511	−	0.892265i	$-0.649115\pi$
$61$	2.52960	−	11.9008i	0.323882	−	1.52374i	0.775393	−	0.631479i	$-0.217552\pi$
$62$	−0.00759638	+	0.00387055i	−0.000964741	+	0.000491560i
$63$	−2.74858	+	10.5141i	−0.346289	+	1.32465i
$64$	7.60843	−	2.47213i	0.951054	−	0.309016i
$65$		0			0
$66$	−0.00258678	−	0.0121698i	−0.000318410	−	0.00149800i
$67$	0.453546	+	0.560082i	0.0554094	+	0.0684249i	0.804097	−	0.594498i	$-0.202649\pi$
$67$	0.453546	+	0.560082i	0.0554094	+	0.0684249i	−0.748688	+	0.662923i	$0.769316\pi$
$68$	−0.399642	−	1.49149i	−0.0484637	−	0.180869i
$69$	5.91760	+	4.29939i	0.712396	+	0.517586i
$70$		0			0
$71$	3.49220	−	2.53723i	0.414447	−	0.301114i	−0.360952	−	0.932584i	$-0.617548\pi$
$71$	3.49220	−	2.53723i	0.414447	−	0.301114i	0.775400	+	0.631471i	$0.217548\pi$
$72$	−0.0120543	−	0.00976140i	−0.00142062	−	0.00115039i
$73$	0.0425173	+	0.811278i	0.00497627	+	0.0949529i	0.999988	−	0.00480033i	$-0.00152800\pi$
$73$	0.0425173	+	0.811278i	0.00497627	+	0.0949529i	−0.995012	+	0.0997532i	$0.968195\pi$
$74$	−0.00173062		0.000999174i	−0.000201181		0.000116152i
$75$		0			0
$76$		−	1.93501i		−	0.221961i
$77$	1.96710	−	12.9300i	0.224172	−	1.47351i
$78$	−0.0134631	−	0.00213235i	−0.00152440	−	0.000241441i
$79$	4.91609	−	0.516702i	0.553104	−	0.0581335i	0.176146	−	0.984364i	$-0.443637\pi$
$79$	4.91609	−	0.516702i	0.553104	−	0.0581335i	0.376958	+	0.926231i	$0.376970\pi$
$80$		0			0
$81$	−0.465251	+	4.42657i	−0.0516946	+	0.491841i
$82$	−0.00597808	+	0.00160182i	−0.000660169	+	0.000176892i
$83$	−13.2310	+	2.09559i	−1.45229	+	0.230020i	−0.832186	−	0.554497i	$-0.812911\pi$
$83$	−13.2310	+	2.09559i	−1.45229	+	0.230020i	−0.620106	+	0.784518i	$0.712911\pi$
$84$	−7.12797	−	12.1738i	−0.777725	−	1.32827i
$85$		0			0
$86$	0.00358331		0.000761656i	0.000386398		8.21315e-5i
$87$	−8.83316	−	5.73632i	−0.947014	−	0.614998i
$88$	0.0156557	+	0.0101669i	0.00166891	+	0.00108380i
$89$	11.3525	+	2.41304i	1.20336	+	0.255782i	0.765604	−	0.643312i	$-0.222440\pi$
$89$	11.3525	+	2.41304i	1.20336	+	0.255782i	0.437755	+	0.899094i	$0.355774\pi$
$90$		0			0
$91$	−12.4527	−	7.08861i	−1.30540	−	0.743088i
$92$	−5.41975	+	0.858405i	−0.565048	+	0.0894949i
$93$	23.2555	−	6.23128i	2.41148	−	0.646154i
$94$	0.000441932	−	0.00420470i	4.55818e−5	−	0.000433682i
$95$		0			0
$96$	0.0300370	−	0.00315702i	0.00306564	−	0.000322212i
$97$	13.4877	+	2.13624i	1.36947	+	0.216902i	0.797472	−	0.603355i	$-0.206170\pi$
$97$	13.4877	+	2.13624i	1.36947	+	0.216902i	0.571994	+	0.820258i	$0.306170\pi$
$98$	0.00111338	+	0.00651401i	0.000112468	+	0.000658014i
$99$			20.3047i			2.04070i
$100$		0			0
$101$	−10.5363	+	6.08311i	−1.04840	+	0.605292i	−0.922200	−	0.386713i	$-0.873610\pi$
$101$	−10.5363	+	6.08311i	−1.04840	+	0.605292i	−0.126197	+	0.992005i	$0.540277\pi$
$102$	−0.000101697	−	0.00194049i	−1.00695e−5	−	0.000192137i
$103$	−3.05353	−	2.47270i	−0.300873	−	0.243642i	0.466980	−	0.884268i	$-0.345342\pi$
$103$	−3.05353	−	2.47270i	−0.300873	−	0.243642i	−0.767854	+	0.640625i	$0.778675\pi$
$104$	0.0165457	−	0.0120212i	0.00162244	−	0.00117877i
$105$		0			0
$106$	−0.000176588	0	0.000128298i	−1.71517e−5	0	1.24614e-5i
$107$	0.0184739	+	0.0689457i	0.00178594	+	0.00666523i	0.966813	−	0.255485i	$-0.0822351\pi$
$107$	0.0184739	+	0.0689457i	0.00178594	+	0.00666523i	−0.965027	+	0.262150i	$0.915568\pi$
$108$	3.71624	+	4.58917i	0.357595	+	0.441593i
$109$	−2.03134	−	9.55668i	−0.194567	−	0.915364i	−0.961748	−	0.273934i	$-0.911675\pi$
$109$	−2.03134	−	9.55668i	−0.194567	−	0.915364i	0.767182	−	0.641430i	$-0.221658\pi$
$110$		0			0
$111$	5.36702	−	1.74385i	0.509415	−	0.165519i
$112$	10.2389	+	2.67664i	0.967486	+	0.252919i
$113$	15.3761	−	7.83452i	1.44646	−	0.737009i	0.458068	−	0.888917i	$-0.348542\pi$
$113$	15.3761	−	7.83452i	1.44646	−	0.737009i	0.988395	+	0.151908i	$0.0485417\pi$
$114$	0.000506284	−	0.00238188i	4.74178e−5	−	0.000223083i
$115$		0			0
$116$	7.72859	−	1.64276i	0.717582	−	0.152527i
$117$	20.7680	+	7.97208i	1.92000	+	0.737019i
$118$	0.00294687	−	0.00294687i	0.000271281	−	0.000271281i
$119$	0.619347	−	1.94649i	0.0567754	−	0.178435i
$120$		0			0
$121$	−1.40449	−	13.3628i	−0.127681	−	1.21480i
$122$	0.00411628	+	0.0107233i	0.000372670	+	0.000970840i
$123$	17.4533	−	0.914689i	1.57371	−	0.0824748i
$124$	−9.03072	+	15.6417i	−0.810983	+	1.40466i
$125$		0			0
$126$	−0.00322987	−	0.00973791i	−0.000287740	−	0.000867522i
$127$	15.6443	+	7.97116i	1.38821	+	0.707326i	0.978760	−	0.205009i	$-0.0657223\pi$
$127$	15.6443	+	7.97116i	1.38821	+	0.707326i	0.409445	+	0.912335i	$0.365722\pi$
$128$	−0.0190119	+	0.0234777i	−0.00168043	+	0.00207515i
$129$	−9.45073	−	4.20774i	−0.832091	−	0.370471i
$130$		0			0
$131$	1.18007	+	2.65048i	0.103103	+	0.231573i	0.957730	−	0.287670i	$-0.0928806\pi$
$131$	1.18007	+	2.65048i	0.103103	+	0.231573i	−0.854627	+	0.519243i	$0.826214\pi$
$132$	−18.6377	−	18.6377i	−1.62220	−	1.62220i
$133$	1.38103	−	2.15528i	0.119750	−	0.186887i
$134$	−0.000647081	0	0.000210249i	−5.58993e−5	0	1.81628e-5i
$135$		0			0
$136$	0.00216662	+	0.00195083i	0.000185786	+	0.000167282i
$137$	−11.3105	+	17.4167i	−0.966323	+	1.48801i	−0.0960872	+	0.995373i	$0.530633\pi$
$137$	−11.3105	+	17.4167i	−0.966323	+	1.48801i	−0.870236	+	0.492635i	$0.836034\pi$
$138$	−0.00689598		0.000361403i	−0.000587025		3.07647e-5i
$139$	−0.653905	−	2.01251i	−0.0554635	−	0.170699i	0.919487	−	0.393120i	$-0.128604\pi$
$139$	−0.653905	−	2.01251i	−0.0554635	−	0.170699i	−0.974951	+	0.222421i	$0.928604\pi$
$140$		0			0
$141$	−3.68943	+	11.3549i	−0.310706	+	0.956254i
$142$	−0.00146040	+	0.00380448i	−0.000122554	+	0.000319265i
$143$	−25.8600	−	6.92916i	−2.16252	−	0.579445i
$144$	−16.3400	−	1.71740i	−1.36166	−	0.143117i
$145$		0			0
$146$	−0.000450803	0	0.000620477i	−3.73087e−5	0	5.13511e-5i
$147$	0.749156	−	18.6469i	0.0617893	−	1.53797i
$148$	−1.92196	+	3.77206i	−0.157984	+	0.310062i
$149$	−9.34465	−	5.39514i	−0.765543	−	0.441987i	0.0657390	−	0.997837i	$-0.479060\pi$
$149$	−9.34465	−	5.39514i	−0.765543	−	0.441987i	−0.831283	+	0.555850i	$0.812393\pi$
$150$		0			0
$151$	−3.46356	−	5.99906i	−0.281861	−	0.488197i	0.689982	−	0.723826i	$-0.257618\pi$
$151$	−3.46356	−	5.99906i	−0.281861	−	0.488197i	−0.971843	+	0.235629i	$0.924285\pi$
$152$	0.00198987	+	0.00306414i	0.000161400	+	0.000248534i
$153$	−0.496084	+	3.13215i	−0.0401060	+	0.253219i
$154$	0.00509083	+	0.0112489i	0.000410231	+	0.000906465i
$155$		0			0
$156$	−26.3805	+	11.7454i	−2.11213	+	0.940382i
$157$	−4.51732	+	16.8589i	−0.360521	+	1.34548i	0.512871	+	0.858466i	$0.328582\pi$
$157$	−4.51732	+	16.8589i	−0.360521	+	1.34548i	−0.873392	+	0.487018i	$0.838085\pi$
$158$	−0.00362670	+	0.00293684i	−0.000288525	+	0.000233643i
$159$	0.412447	+	0.458069i	0.0327092	+	0.0363273i
$160$		0			0
$161$	−6.64935	−	2.91199i	−0.524042	−	0.229497i
$162$	−0.00190767	−	0.00374401i	−0.000149880	−	0.000294157i
$163$	−0.422192	+	8.05590i	−0.0330686	+	0.630987i	0.930949	+	0.365149i	$0.118982\pi$
$163$	−0.422192	+	8.05590i	−0.0330686	+	0.630987i	−0.964018	+	0.265838i	$0.914351\pi$
$164$	−8.77315	+	9.74357i	−0.685068	+	0.760845i
$165$		0			0
$166$	0.00939831	−	0.00846227i	0.000729450	−	0.000656800i
$167$	0.835336	+	5.27411i	0.0646403	+	0.408123i	0.998699	+	0.0510020i	$0.0162415\pi$
$167$	0.835336	+	5.27411i	0.0646403	+	0.408123i	−0.934058	+	0.357121i	$0.883759\pi$
$168$	0.0238063	+	0.0119475i	0.00183669	+	0.000921767i
$169$	−9.59926	+	13.2122i	−0.738405	+	1.01633i
$170$		0			0
$171$	−1.61638	+	3.63046i	−0.123608	+	0.277628i
$172$	7.24534	−	2.78122i	0.552452	−	0.212066i
$173$	3.20860	−	2.08369i	0.243945	−	0.158420i	−0.416876	−	0.908963i	$-0.636875\pi$
$173$	3.20860	−	2.08369i	0.243945	−	0.158420i	0.660821	+	0.750544i	$0.270208\pi$
$174$	0.00994323			0.000753795
$175$		0			0
$176$	19.7733			1.49047
$177$	−9.87012	+	6.40973i	−0.741884	+	0.481785i
$178$	−0.0102292	+	0.00392661i	−0.000766709	+	0.000294312i
$179$	3.19136	−	7.16790i	0.238533	−	0.535754i	−0.754122	−	0.656735i	$-0.771937\pi$
$179$	3.19136	−	7.16790i	0.238533	−	0.535754i	0.992655	+	0.120980i	$0.0386038\pi$
$180$		0			0
$181$	13.0808	−	18.0042i	0.972287	−	1.33824i	0.0314040	−	0.999507i	$-0.490002\pi$
$181$	13.0808	−	18.0042i	0.972287	−	1.33824i	0.940883	−	0.338732i	$-0.109998\pi$
$182$	0.0135044		0.000790403i	0.00100101		5.85885e-5i
$183$	−5.07415	−	32.0369i	−0.375092	−	2.36824i
$184$	0.00769957	−	0.00693272i	0.000567620	−	0.000511087i
$185$		0			0
$186$	−0.0152088	+	0.0168911i	−0.00111516	+	0.00123851i
$187$	0.199740	−	3.81126i	0.0146064	−	0.278707i
$188$	−4.06626	−	7.98048i	−0.296562	−	0.582036i
$189$	0.863952	+	7.76387i	0.0628432	+	0.564738i
$190$		0			0
$191$	6.97036	+	7.74137i	0.504357	+	0.560146i	0.940527	−	0.339719i	$-0.110332\pi$
$191$	6.97036	+	7.74137i	0.504357	+	0.560146i	−0.436170	+	0.899864i	$0.643665\pi$
$192$	16.5749	−	13.4221i	1.19619	−	0.968653i
$193$	−1.73551	+	6.47700i	−0.124925	+	0.466225i	−0.999837	−	0.0180564i	$-0.994252\pi$
$193$	−1.73551	+	6.47700i	−0.124925	+	0.466225i	0.874912	+	0.484281i	$0.160919\pi$
$194$	−0.0117774	+	0.00524365i	−0.000845571	+	0.000376472i
$195$		0			0
$196$	9.49411	+	10.2889i	0.678151	+	0.734922i
$197$	3.93688	−	24.8565i	0.280491	−	1.77095i	−0.297318	−	0.954779i	$-0.596092\pi$
$197$	3.93688	−	24.8565i	0.280491	−	1.77095i	0.577809	−	0.816172i	$-0.303908\pi$
$198$	−0.0104402	−	0.0160765i	−0.000741952	−	0.00114251i
$199$	0.330685	+	0.572764i	0.0234417	+	0.0406022i	0.877508	−	0.479562i	$-0.159204\pi$
$199$	0.330685	+	0.572764i	0.0234417	+	0.0406022i	−0.854067	+	0.520164i	$0.825871\pi$
$200$		0			0
$201$	1.66394	+	0.960678i	0.117365	+	0.0677610i
$202$	0.00521442	−	0.0102339i	0.000366885	−	0.000720052i
$203$	9.78082	+	3.68618i	0.686479	+	0.258719i
$204$	−2.41965	−	3.33036i	−0.169409	−	0.233172i
$205$		0			0
$206$	0.00368907		0.000387737i	0.000257030		2.70149e-5i
$207$	10.8856	+	2.91678i	0.756599	+	0.202730i
$208$	7.76343	−	20.2244i	0.538297	−	1.40231i
$209$	1.47793	−	4.54861i	0.102231	−	0.314634i
$210$		0			0
$211$	1.58569	+	4.88026i	0.109164	+	0.335971i	0.990685	−	0.136173i	$-0.0434803\pi$
$211$	1.58569	+	4.88026i	0.109164	+	0.335971i	−0.881521	+	0.472144i	$0.843480\pi$
$212$	−0.461778	−	0.0242008i	−0.0317151	−	0.00166212i
$213$	6.26770	−	9.65141i	0.429456	−	0.661304i
$214$	−5.00772e−5	0	4.50897e-5i	−3.42321e−6	0	3.08227e-6i
$215$		0			0
$216$	−0.0106040	−	0.00344546i	−0.000721513	−	0.000234434i
$217$	−21.2223	+	10.9769i	−1.44066	+	0.745163i
$218$	0.00652215	+	0.00652215i	0.000441736	+	0.000441736i
$219$	0.880921	+	1.97858i	0.0595271	+	0.133700i
$220$		0			0
$221$	−3.81980	−	1.70068i	−0.256948	−	0.114400i
$222$	−0.00335275	+	0.00414030i	−0.000225022	+	0.000277879i
$223$	6.06675	+	3.09117i	0.406260	+	0.207000i	0.645165	−	0.764043i	$-0.276789\pi$
$223$	6.06675	+	3.09117i	0.406260	+	0.207000i	−0.238905	+	0.971043i	$0.576789\pi$
$224$	−0.0284492	+	0.00943602i	−0.00190084	+	0.000630471i
$225$		0			0
$226$	−0.00814589	+	0.0141091i	−0.000541857	+	0.000938523i
$227$	4.02433	−	0.210906i	0.267104	−	0.0139983i	0.0816864	−	0.996658i	$-0.473969\pi$
$227$	4.02433	−	0.210906i	0.267104	−	0.0139983i	0.185418	+	0.982660i	$0.440636\pi$
$228$	−1.84872	−	4.81608i	−0.122434	−	0.318953i
$229$	−1.47332	−	14.0177i	−0.0973599	−	0.926317i	−0.928770	−	0.370657i	$-0.879132\pi$
$229$	−1.47332	−	14.0177i	−0.0973599	−	0.926317i	0.831410	−	0.555660i	$-0.187534\pi$
$230$		0			0
$231$	−7.45746	−	34.0611i	−0.490665	−	2.24106i
$232$	−0.0105491	+	0.0105491i	−0.000692580	+	0.000692580i
$233$	6.54499	+	2.51239i	0.428777	+	0.164592i	0.563179	−	0.826335i	$-0.309578\pi$
$233$	6.54499	+	2.51239i	0.428777	+	0.164592i	−0.134402	+	0.990927i	$0.542911\pi$
$234$	−0.0205424	+	0.00436641i	−0.00134290	+	0.000285441i
$235$		0			0
$236$	1.83561	−	8.63588i	0.119488	−	0.562148i
$237$	11.7421	−	5.98289i	0.762730	−	0.388630i
$238$	0.000510465		0.00185961i	3.30885e−5		0.000120541i
$239$	6.46280	−	2.09989i	0.418044	−	0.135831i	−0.0924397	−	0.995718i	$-0.529467\pi$
$239$	6.46280	−	2.09989i	0.418044	−	0.135831i	0.510483	+	0.859888i	$0.329467\pi$
$240$		0			0
$241$	−3.23241	−	15.2073i	−0.208218	−	0.979588i	−0.950793	−	0.309826i	$-0.899729\pi$
$241$	−3.23241	−	15.2073i	−0.208218	−	0.979588i	0.742576	−	0.669762i	$-0.233604\pi$
$242$	0.00798286	+	0.00985802i	0.000513158	+	0.000633697i
$243$	5.36375	+	20.0178i	0.344084	+	1.28414i
$244$	19.6861	+	14.3028i	1.26027	+	0.915643i
$245$		0			0
$246$	−0.0133486	+	0.00969829i	−0.000851073	+	0.000618340i
$247$	−4.07213	−	3.29754i	−0.259103	−	0.209818i
$248$	−0.00178478	−	0.0340557i	−0.000113334	−	0.00216254i
$249$	−30.9287	+	17.8567i	−1.96003	+	1.13162i
$250$		0			0
$251$		−	19.2636i		−	1.21591i	−0.793972	−	0.607955i	$-0.791990\pi$
$251$		−	19.2636i		−	1.21591i	0.793972	−	0.607955i	$-0.208010\pi$
$252$	−16.9743	−	13.5748i	−1.06928	−	0.855134i
$253$	−13.3958	−	2.12169i	−0.842187	−	0.133389i
$254$	−0.0164851	+	0.00173266i	−0.00103437	+	0.000108717i
$255$		0			0
$256$	−1.67245	+	15.9123i	−0.104528	+	0.994517i
$257$	−4.39708	+	1.17819i	−0.274282	+	0.0734937i	−0.393338	−	0.919394i	$-0.628680\pi$
$257$	−4.39708	+	1.17819i	−0.274282	+	0.0734937i	0.119056	+	0.992888i	$0.462013\pi$
$258$	0.00964625	−	0.00152782i	0.000600549	−	9.51176e-5i
$259$	−4.83289	+	2.82973i	−0.300301	+	0.175831i
$260$		0			0
$261$	−15.8726	−	3.37383i	−0.982489	−	0.208835i
$262$	−0.00229715	−	0.00149178i	−0.000141918	−	9.21627e-5i
$263$	−22.5479	−	14.6428i	−1.39036	−	0.902913i	−0.390520	−	0.920595i	$-0.627705\pi$
$263$	−22.5479	−	14.6428i	−1.39036	−	0.902913i	−0.999844	+	0.0176819i	$0.994371\pi$
$264$	0.0486793	+	0.0103471i	0.00299601	+	0.000636821i
$265$		0			0
$266$	1.47479e−5		0.00241656i	9.04251e−7		0.000148169i
$267$	30.5608	−	4.84035i	1.87029	−	0.296225i
$268$	−1.39227	+	0.373057i	−0.0850463	+	0.0227881i
$269$	0.982072	−	9.34379i	0.0598780	−	0.569701i	−0.922917	−	0.385000i	$-0.874202\pi$
$269$	0.982072	−	9.34379i	0.0598780	−	0.569701i	0.982795	−	0.184701i	$-0.0591317\pi$
$270$		0			0
$271$	16.2015	−	1.70285i	0.984174	−	0.103441i	0.401251	−	0.915968i	$-0.368576\pi$
$271$	16.2015	−	1.70285i	0.984174	−	0.103441i	0.582923	+	0.812527i	$0.301909\pi$
$272$	3.05017	+	0.483100i	0.184944	+	0.0292923i
$273$	−37.7663	−	5.74555i	−2.28572	−	0.347737i
$274$		−	0.0196055i		−	0.00118441i
$275$		0			0
$276$	−12.6692	+	7.31456i	−0.762595	+	0.440285i
$277$	−0.919673	−	17.5484i	−0.0552578	−	1.05438i	−0.875763	−	0.482742i	$-0.839641\pi$
$277$	−0.919673	−	17.5484i	−0.0552578	−	1.05438i	0.820505	−	0.571640i	$-0.193692\pi$
$278$	0.00155252	+	0.00125721i	9.31141e−5	+	7.54023e-5i
$279$	30.0094	−	21.8031i	1.79662	−	1.30532i
$280$		0			0
$281$	−16.5863	−	12.0506i	−0.989455	−	0.718881i	−0.0296530	−	0.999560i	$-0.509440\pi$
$281$	−16.5863	−	12.0506i	−0.989455	−	0.718881i	−0.959802	+	0.280679i	$0.909440\pi$
$282$	−0.00291726	−	0.0108874i	−0.000173721	−	0.000648334i
$283$	12.8041	+	15.8117i	0.761125	+	0.939911i	0.999511	−	0.0312595i	$-0.00995182\pi$
$283$	12.8041	+	15.8117i	0.761125	+	0.939911i	−0.238386	+	0.971170i	$0.576618\pi$
$284$	1.79494	+	8.44452i	0.106510	+	0.501090i
$285$		0			0
$286$	0.0240377	−	0.00781033i	0.00142138	−	0.000461835i
$287$	−16.7259	+	4.59127i	−0.987298	+	0.271014i
$288$	0.0414613	−	0.0211256i	0.00244313	−	0.00124484i
$289$	−3.41057	+	16.0455i	−0.200622	+	0.943851i
$290$		0			0
$291$	35.6107	−	7.56928i	2.08753	−	0.443719i
$292$	−1.51686	−	0.582270i	−0.0887678	−	0.0340748i
$293$	−1.07980	+	1.07980i	−0.0630827	+	0.0630827i	−0.737944	−	0.674862i	$-0.764203\pi$
$293$	−1.07980	+	1.07980i	−0.0630827	+	0.0630827i	0.674862	+	0.737944i	$0.264203\pi$
$294$	0.00899463	+	0.0151491i	0.000524577	+	0.000883513i
$295$		0			0
$296$	−0.000835537	−	0.00794960i	−4.85646e−5	−	0.000462061i
$297$	5.23058	+	13.6261i	0.303509	+	0.790668i
$298$	0.0101728		0.000533133i	0.000589294		3.08836e-5i
$299$	−7.42959	+	12.8684i	−0.429665	+	0.744201i
$300$		0			0
$301$	10.0551	+	2.07322i	0.579565	+	0.119498i
$302$	0.00582689	+	0.00296895i	0.000335300	+	0.000170844i
$303$	−20.4120	+	25.2067i	−1.17264	+	1.44809i
$304$	3.53544	+	1.57408i	0.202771	+	0.0902796i
$305$		0			0
$306$	−0.00121770	−	0.00273499i	−6.96111e−5	−	0.000156349i
$307$	4.76575	+	4.76575i	0.271996	+	0.271996i	0.829903	−	0.557908i	$-0.188396\pi$
$307$	4.76575	+	4.76575i	0.271996	+	0.271996i	−0.557908	+	0.829903i	$0.688396\pi$
$308$	22.0241	+	14.1123i	1.25494	+	0.804123i
$309$	−9.96241	−	3.23698i	−0.566742	−	0.184146i
$310$		0			0
$311$	−15.4894	−	13.9467i	−0.878324	−	0.790847i	0.100631	−	0.994924i	$-0.467914\pi$
$311$	−15.4894	−	13.9467i	−0.878324	−	0.790847i	−0.978955	+	0.204077i	$0.934581\pi$
$312$	0.0296958	−	0.0457276i	0.00168119	−	0.00258881i
$313$	−3.53873	−	0.185457i	−0.200021	−	0.0104826i	−0.0479375	−	0.998850i	$-0.515265\pi$
$313$	−3.53873	−	0.185457i	−0.200021	−	0.0104826i	−0.152083	+	0.988368i	$0.548598\pi$
$314$	−0.00509178	−	0.0156709i	−0.000287346	−	0.000884360i
$315$		0			0
$316$	−3.05505	+	9.40247i	−0.171860	+	0.528930i
$317$	−4.35221	+	11.3379i	−0.244444	+	0.636799i	−0.999829	−	0.0184820i	$-0.994117\pi$
$317$	−4.35221	+	11.3379i	−0.244444	+	0.636799i	0.755385	+	0.655281i	$0.227450\pi$
$318$	−0.000562088	0	0.000150611i	−3.15204e−5	0	8.44585e-6i
$319$	19.4222	+	2.04136i	1.08744	+	0.114294i
$320$		0			0
$321$	0.111851	+	0.153950i	0.00624292	+	0.00859265i
$322$	0.00676198	−	0.00111334i	0.000376830	−	6.20438e-5i
$323$	0.339114	−	0.665549i	0.0188688	−	0.0370321i
$324$	−7.70927	−	4.45095i	−0.428293	−	0.247275i
$325$		0			0
$326$	−0.00380788	−	0.00659544i	−0.000210899	−	0.000365287i
$327$	−14.1863	−	21.8450i	−0.784506	−	1.20803i
$328$	0.00387267	−	0.0244511i	0.000213832	−	0.00135008i
$329$	1.16658	−	11.7910i	0.0643157	−	0.650061i
$330$		0			0
$331$	3.09687	−	1.37881i	0.170219	−	0.0757865i	−0.319858	−	0.947465i	$-0.603635\pi$
$331$	3.09687	−	1.37881i	0.170219	−	0.0757865i	0.490077	+	0.871679i	$0.336969\pi$
$332$	6.93424	−	25.8789i	0.380566	−	1.42029i
$333$	6.75691	−	5.47164i	0.370276	−	0.299844i
$334$	−0.00337321	−	0.00374633i	−0.000184574	−	0.000204990i
$335$		0			0
$336$	28.0411	−	3.12037i	1.52977	−	0.170230i
$337$	13.9648	+	27.4074i	0.760710	+	1.49298i	0.866819	+	0.498623i	$0.166161\pi$
$337$	13.9648	+	27.4074i	0.760710	+	1.49298i	−0.106109	+	0.994354i	$0.533839\pi$
$338$	0.000806905	−	0.0153967i	4.38898e−5	−	0.000837468i
$339$	30.7847	−	34.1899i	1.67199	−	1.85694i
$340$		0			0
$341$	−33.1753	+	29.8712i	−1.79654	+	1.61762i
$342$	−0.000586903	−	0.00370556i	−3.17361e−5	−	0.000200374i
$343$	3.23160	+	18.2361i	0.174490	+	0.984659i
$344$	−0.00861308	+	0.0118549i	−0.000464386	+	0.000639173i
$345$		0			0
$346$	−0.00146906	+	0.00329957i	−7.89773e−5	+	0.000177386i
$347$	9.62635	−	3.69521i	0.516769	−	0.198369i	−0.0859843	−	0.996296i	$-0.527403\pi$
$347$	9.62635	−	3.69521i	0.516769	−	0.198369i	0.602754	+	0.797927i	$0.294070\pi$
$348$	17.6663	−	11.4726i	0.947014	−	0.614998i
$349$	2.01795			0.108019			0.0540093	−	0.998540i	$-0.482800\pi$
$349$	2.01795			0.108019			0.0540093	+	0.998540i	$0.482800\pi$
$350$		0			0
$351$	15.9907			0.853519
$352$	−0.0469672	+	0.0305008i	−0.00250336	+	0.00162570i
$353$	18.5248	−	7.11099i	0.985973	−	0.378480i	0.188658	−	0.982043i	$-0.439586\pi$
$353$	18.5248	−	7.11099i	0.985973	−	0.378480i	0.797315	+	0.603563i	$0.206253\pi$
$354$	0.00451905	−	0.0101500i	0.000240185	−	0.000539464i
$355$		0			0
$356$	−13.6438	+	18.7790i	−0.723118	+	0.995287i
$357$	−0.318188	−	5.43638i	−0.0168403	−	0.287724i
$358$	0.00115877	+	0.00731619i	6.12429e−5	+	0.000386673i
$359$	−9.63173	+	8.67245i	−0.508343	+	0.457715i	−0.882948	−	0.469470i	$-0.844445\pi$
$359$	−9.63173	+	8.67245i	−0.508343	+	0.457715i	0.374605	+	0.927185i	$0.377778\pi$
$360$		0			0
$361$	−12.0871	+	13.4241i	−0.636165	+	0.706533i
$362$	−0.00109956	+	0.0209808i	−5.77915e−5	+	0.00110273i
$363$	−16.2626	−	31.9171i	−0.853563	−	1.67521i
$364$	23.0815	−	16.9859i	1.20980	−	0.890301i
$365$		0			0
$366$	0.0204901	+	0.0227566i	0.00107104	+	0.00118951i
$367$	−3.12627	+	2.53160i	−0.163190	+	0.132148i	−0.707437	−	0.706776i	$-0.750149\pi$
$367$	−3.12627	+	2.53160i	−0.163190	+	0.132148i	0.544247	+	0.838925i	$0.316815\pi$
$368$	2.84044	−	10.6007i	0.148068	−	0.552598i
$369$	24.5993	−	10.9523i	1.28059	−	0.570155i
$370$		0			0
$371$	−0.497072	−	0.356530i	−0.0258067	−	0.0185101i
$372$	−7.53257	+	47.5588i	−0.390546	+	2.46581i
$373$	6.95498	+	10.7097i	0.360115	+	0.554529i	0.971571	−	0.236750i	$-0.0760822\pi$
$373$	6.95498	+	10.7097i	0.360115	+	0.554529i	−0.611455	+	0.791279i	$0.709416\pi$
$374$	0.00180151	+	0.00312031i	9.31540e−5	+	0.000161347i
$375$		0			0
$376$	0.0146458	+	0.00845573i	0.000755297	+	0.000436071i
$377$	9.71355	−	19.0639i	0.500274	−	0.981842i
$378$	−0.00467604	−	0.00570291i	−0.000240510	−	0.000293326i
$379$	18.7383	+	25.7910i	0.962519	+	1.32479i	0.945736	+	0.324935i	$0.105342\pi$
$379$	18.7383	+	25.7910i	0.962519	+	1.32479i	0.0167829	+	0.999859i	$0.494658\pi$
$380$		0			0
$381$	46.5530	+	4.89292i	2.38498	+	0.250672i
$382$	−0.00949929	−	0.00254533i	−0.000486026	−	0.000130230i
$383$	7.99829	−	20.8363i	0.408694	−	1.06468i	−0.562585	−	0.826739i	$-0.690193\pi$
$383$	7.99829	−	20.8363i	0.408694	−	1.06468i	0.971279	−	0.237944i	$-0.0764735\pi$
$384$	−0.0248882	+	0.0765980i	−0.00127007	+	0.00390887i
$385$		0			0
$386$	−0.00195621	−	0.00602060i	−9.95685e−5	−	0.000306440i
$387$	−15.9169	−	0.834170i	−0.809102	−	0.0424032i
$388$	−14.8750	+	22.9054i	−0.755162	+	1.16285i
$389$	−11.1057	−	9.99966i	−0.563083	−	0.507003i	0.337710	−	0.941250i	$-0.390348\pi$
$389$	−11.1057	−	9.99966i	−0.563083	−	0.507003i	−0.900794	+	0.434248i	$0.857014\pi$
$390$		0			0
$391$	−2.01457	−	0.654572i	−0.101881	−	0.0331031i
$392$	−0.0256148	−	0.00652945i	−0.00129374	−	0.000329787i
$393$	5.46937	+	5.46937i	0.275893	+	0.275893i
$394$	0.00966353	+	0.0217047i	0.000486842	+	0.00109346i
$395$		0			0
$396$	−37.0985	−	16.5173i	−1.86427	−	0.830026i
$397$	−4.41649	+	5.45391i	−0.221657	+	0.273724i	−0.875828	−	0.482623i	$-0.839684\pi$
$397$	−4.41649	+	5.45391i	−0.221657	+	0.273724i	0.654171	+	0.756347i	$0.273018\pi$
$398$	−0.000556326	0	0.000283462i	−2.78861e−5	0	1.42087e-5i
$399$	1.37810	−	6.68375i	0.0689912	−	0.334606i
$400$		0			0
$401$	−3.16906	+	5.48898i	−0.158255	+	0.274106i	−0.934240	−	0.356646i	$-0.883920\pi$
$401$	−3.16906	+	5.48898i	−0.158255	+	0.274106i	0.775984	+	0.630752i	$0.217254\pi$
$402$	−0.00181140		9.49316e-5i	−9.03446e−5		4.73476e-6i
$403$	17.5274	+	45.6604i	0.873101	+	2.27451i
$404$	−2.54343	−	24.1991i	−0.126540	−	1.20395i
$405$		0			0
$406$	−0.00963942	+	0.00211049i	−0.000478396	+	0.000104742i
$407$	−7.39898	+	7.39898i	−0.366754	+	0.366754i
$408$	0.00725635	+	0.00278545i	0.000359243	+	0.000137900i
$409$	−6.62164	+	1.40747i	−0.327419	+	0.0695951i	−0.368689	−	0.929553i	$-0.620193\pi$
$409$	−6.62164	+	1.40747i	−0.327419	+	0.0695951i	0.0412694	+	0.999148i	$0.486860\pi$
$410$		0			0
$411$	−11.5110	+	54.1548i	−0.567793	+	2.67126i
$412$	7.00181	−	3.56760i	0.344954	−	0.175763i
$413$	8.20805	−	8.30885i	0.403892	−	0.408852i
$414$	−0.0101185	+	0.00328770i	−0.000497298	+	0.000161582i
$415$		0			0
$416$	0.0127564	+	0.0600142i	0.000625434	+	0.00294244i
$417$	−3.55028	−	4.38423i	−0.173858	−	0.214697i
$418$	0.00116862	+	0.00436133i	5.71589e−5	+	0.000213320i
$419$	−21.9666	−	15.9597i	−1.07314	−	0.779681i	−0.0966645	−	0.995317i	$-0.530817\pi$
$419$	−21.9666	−	15.9597i	−1.07314	−	0.779681i	−0.976474	+	0.215636i	$0.930817\pi$
$420$		0			0
$421$	14.9220	−	10.8415i	0.727255	−	0.528382i	−0.161439	−	0.986883i	$-0.551613\pi$
$421$	14.9220	−	10.8415i	0.727255	−	0.528382i	0.888694	+	0.458501i	$0.151613\pi$
$422$	−0.00376480	−	0.00304868i	−0.000183268	−	0.000148407i
$423$	0.962710	+	18.3696i	0.0468086	+	0.893161i
$424$	0.000756124	0	0.000436548i	3.67206e−5	0	2.12007e-5i
$425$		0			0
$426$			0.0108643i			0.000526378i
$427$	11.7191	+	29.9810i	0.567125	+	1.45088i
$428$	−0.140998	−	0.0223319i	−0.00681540	−	0.00107945i
$429$	−70.9834	+	7.46066i	−3.42711	+	0.360204i
$430$		0			0
$431$	−2.30867	+	21.9655i	−0.111205	+	1.05804i	0.786545	+	0.617533i	$0.211868\pi$
$431$	−2.30867	+	21.9655i	−0.111205	+	1.05804i	−0.897749	+	0.440507i	$0.854799\pi$
$432$	−11.4079	+	3.05673i	−0.548862	+	0.147067i
$433$	−1.19136	+	0.188692i	−0.0572529	+	0.00906797i	−0.184995	−	0.982739i	$-0.559227\pi$
$433$	−1.19136	+	0.188692i	−0.0572529	+	0.00906797i	0.127742	+	0.991807i	$0.459227\pi$
$434$	0.0111589	−	0.0196031i	0.000535645	−	0.000940979i
$435$		0			0
$436$	19.1134	+	4.06267i	0.915364	+	0.194567i
$437$	−2.22626	−	1.44575i	−0.106496	−	0.0691595i
$438$	−0.00171482	−	0.00111362i	−8.19372e−5	−	5.32106e-5i
$439$	−25.4760	−	5.41509i	−1.21590	−	0.258448i	−0.445076	−	0.895493i	$-0.646823\pi$
$439$	−25.4760	−	5.41509i	−1.21590	−	0.258448i	−0.770827	+	0.637044i	$0.780157\pi$
$440$		0			0
$441$	−9.21810	−	27.2348i	−0.438957	−	1.29689i
$442$	0.00389882		0.000617513i	0.000185448		2.93721e-5i
$443$	3.65513	−	0.979388i	0.173660	−	0.0465321i	−0.170941	−	0.985281i	$-0.554681\pi$
$443$	3.65513	−	0.979388i	0.173660	−	0.0465321i	0.344601	+	0.938749i	$0.388014\pi$
$444$	−1.17975	+	11.2246i	−0.0559886	+	0.532696i
$445$		0			0
$446$	−0.00639283		0.000671913i	−0.000302709		3.18160e-5i
$447$	−28.4126	−	4.50011i	−1.34387	−	0.212848i
$448$	−13.2195	+	16.5300i	−0.624564	+	0.780970i
$449$			17.0058i			0.802554i	0.915957	+	0.401277i	$0.131433\pi$
$449$			17.0058i			0.802554i	−0.915957	+	0.401277i	$0.868567\pi$
$450$		0			0
$451$	−28.0650	+	16.2033i	−1.32153	+	0.762984i
$452$	1.80632	+	34.4667i	0.0849623	+	1.62118i
$453$	−14.3520	−	11.6221i	−0.674318	−	0.546052i
$454$	−0.00307787	+	0.00223620i	−0.000144452	+	0.000104950i
$455$		0			0
$456$	0.00788012	+	0.00572524i	0.000369020	+	0.000268109i
$457$	0.357319	+	1.33353i	0.0167147	+	0.0623800i	0.973779	−	0.227494i	$-0.0730532\pi$
$457$	0.357319	+	1.33353i	0.0167147	+	0.0623800i	−0.957065	+	0.289874i	$0.906387\pi$
$458$	0.00837410	+	0.0103412i	0.000391296	+	0.000483210i
$459$	0.473943	+	2.22973i	0.0221218	+	0.104075i
$460$		0			0
$461$	33.9089	−	11.0177i	1.57930	−	0.513145i	0.617421	−	0.786633i	$-0.288177\pi$
$461$	33.9089	−	11.0177i	1.57930	−	0.513145i	0.961875	+	0.273488i	$0.0881775\pi$
$462$	0.0234179	+	0.0231338i	0.00108950	+	0.00107628i
$463$	4.47206	−	2.27863i	0.207834	−	0.105897i	−0.346975	−	0.937874i	$-0.612791\pi$
$463$	4.47206	−	2.27863i	0.207834	−	0.105897i	0.554809	+	0.831977i	$0.312791\pi$
$464$	−3.28552	+	15.4572i	−0.152527	+	0.717581i
$465$		0			0
$466$	−0.00647388	+	0.00137607i	−0.000299897	+	6.37451e-5i
$467$	−17.9268	−	6.88146i	−0.829554	−	0.318436i	−0.0937207	−	0.995599i	$-0.529876\pi$
$467$	−17.9268	−	6.88146i	−0.829554	−	0.318436i	−0.735833	+	0.677163i	$0.763209\pi$
$468$	−31.4599	+	31.4599i	−1.45423	+	1.45423i
$469$	−1.81701	−	0.578146i	−0.0839016	−	0.0266963i
$470$		0			0
$471$	4.86382	+	46.2761i	0.224113	+	2.13229i
$472$	0.00597399	+	0.0155628i	0.000274975	+	0.000716335i
$473$	19.1558	−	1.00391i	0.880784	−	0.0461600i
$474$	−0.00622067	+	0.0107745i	−0.000285725	+	0.000494890i
$475$		0			0
$476$	3.05260	+	2.71502i	0.139916	+	0.124443i
$477$	0.846170	+	0.431145i	0.0387435	+	0.0197408i
$478$	−0.00403728	+	0.00498563i	−0.000184661	+	0.000228037i
$479$	31.2095	+	13.8953i	1.42600	+	0.634894i	0.967285	−	0.253691i	$-0.0816446\pi$
$479$	31.2095	+	13.8953i	1.42600	+	0.634894i	0.458711	+	0.888585i	$0.348311\pi$
$480$		0			0
$481$	4.66280	+	10.4728i	0.212605	+	0.477519i
$482$	0.0103785	+	0.0103785i	0.000472729	+	0.000472729i
$483$	−19.3318	−	0.894872i	−0.879628	−	0.0407181i
$484$	25.5576	+	8.30417i	1.16171	+	0.377462i
$485$		0			0
$486$	−0.0145395	−	0.0130914i	−0.000659524	−	0.000593838i
$487$	−14.0720	+	21.6689i	−0.637661	+	0.981913i	0.361118	+	0.932520i	$0.382395\pi$
$487$	−14.0720	+	21.6689i	−0.637661	+	0.981913i	−0.998779	+	0.0493924i	$0.984272\pi$
$488$	−0.0458818	−	0.00240456i	−0.00207697	−	0.000108849i
$489$	6.64585	+	20.4538i	0.300536	+	0.924954i
$490$		0			0
$491$	−11.4055	+	35.1024i	−0.514721	+	1.58415i	0.269068	+	0.963121i	$0.413284\pi$
$491$	−11.4055	+	35.1024i	−0.514721	+	1.58415i	−0.783789	+	0.621027i	$0.786716\pi$
$492$	−12.5266	+	32.6328i	−0.564742	+	1.47120i
$493$	2.94615	+	0.789419i	0.132688	+	0.0355537i
$494$	0.00491967		0.000517079i	0.000221347		2.32645e-5i
$495$		0			0
$496$	−21.2325	−	29.2240i	−0.953366	−	1.31220i
$497$	−4.02764	+	10.6869i	−0.180664	+	0.479371i
$498$	0.0153067	−	0.0300411i	0.000685909	−	0.00134617i
$499$	31.2169	+	18.0231i	1.39746	+	0.806823i	0.994126	−	0.108231i	$-0.0345185\pi$
$499$	31.2169	+	18.0231i	1.39746	+	0.806823i	0.403333	+	0.915053i	$0.367852\pi$
$500$		0			0
$501$	7.11799	+	12.3287i	0.318008	+	0.550807i
$502$	0.00990490	+	0.0152522i	0.000442077	+	0.000680739i
$503$	3.12995	−	19.7617i	0.139558	−	0.881132i	−0.814206	−	0.580576i	$-0.802828\pi$
$503$	3.12995	−	19.7617i	0.139558	−	0.881132i	0.953764	−	0.300557i	$-0.0971724\pi$
$504$	0.0408389	+	0.00404052i	0.00181911	+	0.000179979i
$505$		0			0
$506$	0.0116972	−	0.00520793i	0.000520004	−	0.000231521i
$507$	−11.2687	+	42.0554i	−0.500460	+	1.86774i
$508$	−27.2902	+	22.0992i	−1.21081	+	0.980493i
$509$	13.7494	+	15.2702i	0.609431	+	0.676842i	0.966331	−	0.257301i	$-0.0828331\pi$
$509$	13.7494	+	15.2702i	0.609431	+	0.676842i	−0.356900	+	0.934142i	$0.616166\pi$
$510$		0			0
$511$	−1.27397	−	1.73115i	−0.0563569	−	0.0765814i
$512$	−0.0342878	−	0.0672935i	−0.00151532	−	0.00297398i
$513$	−0.149505	+	2.85272i	−0.00660080	+	0.125951i
$514$	0.00287564	−	0.00319372i	0.000126839	−	0.000140869i
$515$		0			0
$516$	15.3758	−	13.8445i	0.676883	−	0.609468i
$517$	−3.46313	−	21.8654i	−0.152308	−	0.961638i
$518$	0.00237151	−	0.00472543i	0.000104198	−	0.000207623i
$519$	5.99516	−	8.25163i	0.263158	−	0.362206i
$520$		0			0
$521$	−7.95687	+	17.8714i	−0.348597	+	0.782961i	0.651116	+	0.758979i	$0.274301\pi$
$521$	−7.95687	+	17.8714i	−0.348597	+	0.782961i	−0.999712	+	0.0239826i	$0.992365\pi$
$522$	0.0143021	−	0.00549005i	0.000625984	−	0.000240293i
$523$	2.11708	−	1.37485i	0.0925733	−	0.0601178i	−0.497522	−	0.867451i	$-0.665757\pi$
$523$	2.11708	−	1.37485i	0.0925733	−	0.0601178i	0.590096	+	0.807333i	$0.299090\pi$
$524$	−5.80262			−0.253488
$525$		0			0
$526$	0.0253815			0.00110669
$527$	−5.84735	+	3.79732i	−0.254715	+	0.165414i
$528$	49.2140	−	18.8915i	2.14176	−	0.822146i
$529$	6.29317	−	14.1347i	0.273616	−	0.614552i
$530$		0			0
$531$	−10.6578	+	14.6692i	−0.462510	+	0.636591i
$532$	2.81446	+	4.27653i	0.122022	+	0.185411i
$533$	5.55409	+	35.0671i	0.240574	+	1.51893i
$534$	−0.0217080	+	0.0195460i	−0.000939399	+	0.000845839i
$535$		0			0
$536$	0.00182106	−	0.00202249i	7.86576e−5	−	8.73581e-5i
$537$	1.09476	−	20.8893i	0.0472426	−	0.901442i
$538$	0.00402679	+	0.00790301i	0.000173607	+	0.000340723i
$539$	14.4592	+	31.4375i	0.622801	+	1.35411i
$540$		0			0
$541$	8.08881	+	8.98354i	0.347765	+	0.386232i	0.891497	−	0.453027i	$-0.149656\pi$
$541$	8.08881	+	8.98354i	0.347765	+	0.386232i	−0.543732	+	0.839259i	$0.682989\pi$
$542$	−0.0119522	+	0.00967870i	−0.000513391	+	0.000415736i
$543$	15.3557	−	57.3083i	0.658976	−	2.45933i
$544$	−0.00799024	+	0.00355748i	−0.000342579	+	0.000152526i
$545$		0			0
$546$	0.0328561	−	0.0148694i	0.00140611	−	0.000636352i
$547$	4.09571	−	25.8593i	0.175120	−	1.10566i	−0.730917	−	0.682466i	$-0.760907\pi$
$547$	4.09571	−	25.8593i	0.175120	−	1.10566i	0.906037	−	0.423198i	$-0.139093\pi$
$548$	−22.6210	−	34.8333i	−0.966323	−	1.48801i
$549$	−24.9873	−	43.2793i	−1.06643	−	1.84712i
$550$		0			0
$551$	3.31017	+	1.91113i	0.141018	+	0.0814168i
$552$	0.0125400	−	0.0246112i	0.000533738	−	0.00104752i
$553$	−10.1134	+	8.29238i	−0.430066	+	0.352628i
$554$	0.00975113	+	0.0134213i	0.000414286	+	0.000570216i
$555$		0			0
$556$	4.20898	+	0.442381i	0.178500	+	0.0187611i
$557$	−30.0108	−	8.04137i	−1.27160	−	0.340724i	−0.440955	−	0.897529i	$-0.645360\pi$
$557$	−30.0108	−	8.04137i	−1.27160	−	0.340724i	−0.830643	+	0.556806i	$0.812027\pi$
$558$	−0.0125497	+	0.0326930i	−0.000531270	+	0.00138401i
$559$	6.49418	−	19.9870i	0.274675	−	0.845362i
$560$		0			0
$561$	−3.14416	−	9.67674i	−0.132747	−	0.408552i
$562$	0.0193285	+	0.00101297i	0.000815325	+	4.27294e-5i
$563$	−16.7885	+	25.8520i	−0.707550	+	1.08953i	0.283876	+	0.958861i	$0.408380\pi$
$563$	−16.7885	+	25.8520i	−0.707550	+	1.08953i	−0.991426	+	0.130670i	$0.958287\pi$
$564$	−17.7452	−	15.9778i	−0.747206	−	0.672787i
$565$		0			0
$566$	−0.0182678	−	0.00593557i	−0.000767854	−	0.000249491i
$567$	−5.41017	−	10.4598i	−0.227206	−	0.439269i
$568$	−0.0115263	−	0.0115263i	−0.000483632	−	0.000483632i
$569$	−10.2970	−	23.1274i	−0.431672	−	0.969552i	−0.990147	−	0.140030i	$-0.955280\pi$
$569$	−10.2970	−	23.1274i	−0.431672	−	0.969552i	0.558475	−	0.829521i	$-0.311387\pi$
$570$		0			0
$571$	−16.6441	−	7.41042i	−0.696533	−	0.310117i	0.0277541	−	0.999615i	$-0.491164\pi$
$571$	−16.6441	−	7.41042i	−0.696533	−	0.310117i	−0.724287	+	0.689498i	$0.757831\pi$
$572$	33.6966	−	41.6118i	1.40892	−	1.73988i
$573$	24.7448	+	12.6081i	1.03373	+	0.526711i
$574$	0.0108822	−	0.0122352i	0.000454214	−	0.000510689i
$575$		0			0
$576$	16.4300	−	28.4575i	0.684581	−	1.18573i
$577$	13.3242	−	0.698293i	0.554695	−	0.0290703i	0.227070	−	0.973878i	$-0.427085\pi$
$577$	13.3242	−	0.698293i	0.554695	−	0.0290703i	0.327625	+	0.944808i	$0.393752\pi$
$578$	−0.00554984	−	0.0144578i	−0.000230843	−	0.000601366i
$579$	1.86863	+	17.7788i	0.0776576	+	0.738863i
$580$		0			0
$581$	26.1936	−	23.8758i	1.08669	−	0.990536i
$582$	−0.0243032	+	0.0243032i	−0.00100740	+	0.00100740i
$583$	−1.06701	−	0.409588i	−0.0441912	−	0.0169634i
$584$	0.00300077		0.000637833i	0.000124173		2.63937e-5i
$585$		0			0
$586$	0.000299738	−	0.00141015i	1.23820e−5	−	5.82529e-5i
$587$	32.5308	−	16.5752i	1.34269	−	0.684134i	0.372852	−	0.927891i	$-0.378380\pi$
$587$	32.5308	−	16.5752i	1.34269	−	0.684134i	0.969836	+	0.243757i	$0.0783800\pi$
$588$	33.4601	+	16.5375i	1.37987	+	0.681995i
$589$	−8.30965	+	2.69997i	−0.342393	+	0.111250i
$590$		0			0
$591$	−13.9494	−	65.6270i	−0.573803	−	2.69953i
$592$	−5.32843	−	6.58006i	−0.218997	−	0.270439i
$593$	5.46046	+	20.3787i	0.224234	+	0.836854i	0.982710	+	0.185152i	$0.0592778\pi$
$593$	5.46046	+	20.3787i	0.224234	+	0.836854i	−0.758476	+	0.651701i	$0.774056\pi$
$594$	−0.0111476	−	0.00809920i	−0.000457391	−	0.000332314i
$595$		0			0
$596$	17.4590	−	12.6847i	0.715149	−	0.519586i
$597$	1.37027	+	1.10962i	0.0560814	+	0.0454138i
$598$	−0.000734173	−	0.0140089i	−3.00226e−5	−	0.000572865i
$599$	33.8887	−	19.5656i	1.38465	−	0.799430i	0.391947	−	0.919988i	$-0.371802\pi$
$599$	33.8887	−	19.5656i	1.38465	−	0.799430i	0.992706	+	0.120558i	$0.0384684\pi$
$600$		0			0
$601$		−	16.9750i		−	0.692423i	−0.938157	−	0.346211i	$-0.887468\pi$
$601$		−	16.9750i		−	0.692423i	0.938157	−	0.346211i	$-0.112532\pi$
$602$	−0.00902722	+	0.00352858i	−0.000367922	+	0.000143814i
$603$	2.92379	+	0.463083i	0.119066	+	0.0188582i
$604$	13.7783	−	1.44816i	0.560633	−	0.0589249i
$605$		0			0
$606$	0.00320075	−	0.0304531i	0.000130022	−	0.00123707i
$607$	−4.36034	+	1.16835i	−0.176981	+	0.0474218i	−0.346221	−	0.938153i	$-0.612535\pi$
$607$	−4.36034	+	1.16835i	−0.176981	+	0.0474218i	0.169240	+	0.985575i	$0.445869\pi$
$608$	−0.0108257	+	0.00171463i	−0.000439042	+	6.95374e-5i
$609$	27.8654	−	0.170058i	1.12916	−	0.00689111i
$610$		0			0
$611$	−23.7240	−	5.04269i	−0.959770	−	0.204005i
$612$	−5.31917	−	3.45431i	−0.215015	−	0.139632i
$613$	−11.7002	−	7.59818i	−0.472565	−	0.306888i	0.286294	−	0.958142i	$-0.407577\pi$
$613$	−11.7002	−	7.59818i	−0.472565	−	0.306888i	−0.758860	+	0.651254i	$0.774243\pi$
$614$	−0.00622377	−	0.00132290i	−0.000251171	−	5.33880e-5i
$615$		0			0
$616$	−0.0493882		0.000301408i	−0.00198991		1.21441e-5i
$617$	11.6768	−	1.84942i	0.470090	−	0.0744549i	0.0831047	−	0.996541i	$-0.473516\pi$
$617$	11.6768	−	1.84942i	0.470090	−	0.0744549i	0.386985	+	0.922086i	$0.373516\pi$
$618$	0.00955223	−	0.00255951i	0.000384247	−	0.000102959i
$619$	−3.96510	+	37.7254i	−0.159371	+	1.51631i	0.563955	+	0.825806i	$0.309279\pi$
$619$	−3.96510	+	37.7254i	−0.159371	+	1.51631i	−0.723326	+	0.690507i	$0.757387\pi$
$620$		0			0
$621$	8.05649	−	0.846771i	0.323296	−	0.0339798i
$622$	0.0194350	+	0.00307820i	0.000779273	+	0.000123425i
$623$	−28.5996	+	11.1791i	−1.14582	+	0.447881i
$624$		−	57.7541i		−	2.31202i
$625$		0			0
$626$	0.00289719	−	0.00167269i	0.000115795	−	6.68542e-5i
$627$	−0.667315	−	12.7331i	−0.0266500	−	0.508512i
$628$	−27.1279	−	21.9678i	−1.08252	−	0.876609i
$629$	−1.32212	+	0.960577i	−0.0527164	+	0.0383007i
$630$		0			0
$631$	16.6746	+	12.1148i	0.663803	+	0.482281i	0.867945	−	0.496660i	$-0.165440\pi$
$631$	16.6746	+	12.1148i	0.663803	+	0.482281i	−0.204142	+	0.978941i	$0.565440\pi$
$632$	−0.00483131	−	0.0180307i	−0.000192179	−	0.000717222i
$633$	8.60928	+	10.6316i	0.342188	+	0.422567i
$634$	−0.00238376	−	0.0112147i	−9.46712e−5	−	0.000445393i
$635$		0			0
$636$	−1.17245	+	0.380952i	−0.0464906	+	0.0151057i
$637$	37.8318	−	2.44603i	1.49895	−	0.0969151i
$638$	−0.0164274	+	0.00837018i	−0.000650367	+	0.000331379i
$639$	3.68636	−	17.3429i	0.145830	−	0.686076i
$640$		0			0
$641$	15.7402	−	3.34568i	0.621701	−	0.132147i	0.113717	−	0.993513i	$-0.463724\pi$
$641$	15.7402	−	3.34568i	0.621701	−	0.132147i	0.507984	+	0.861367i	$0.330391\pi$
$642$	−0.000167717	0	6.43805e-5i	−6.61926e−6	0	2.54089e-6i
$643$	9.53067	−	9.53067i	0.375853	−	0.375853i	−0.493751	−	0.869604i	$-0.664374\pi$
$643$	9.53067	−	9.53067i	0.375853	−	0.375853i	0.869604	+	0.493751i	$0.164374\pi$
$644$	10.7295	−	9.78014i	0.422803	−	0.385392i
$645$		0			0
$646$	7.37117e−5	0	0.000701320i	2.90015e−6	0	2.75931e-5i
$647$	1.58915	+	4.13988i	0.0624760	+	0.162755i	0.961265	−	0.275626i	$-0.0888852\pi$
$647$	1.58915	+	4.13988i	0.0624760	+	0.162755i	−0.898789	+	0.438382i	$0.855552\pi$
$648$	0.0167850		0.000879662i	0.000659375		3.45564e-5i
$649$	10.9109	−	18.8983i	0.428291	−	0.741822i
$650$		0			0
$651$	−42.3330	+	47.5965i	−1.65916	+	1.86546i
$652$	−14.3754	−	7.32464i	−0.562985	−	0.286855i
$653$	1.75843	−	2.17147i	0.0688125	−	0.0849764i	−0.741577	−	0.670867i	$-0.765922\pi$
$653$	1.75843	−	2.17147i	0.0688125	−	0.0849764i	0.810390	+	0.585891i	$0.199255\pi$
$654$	0.0224644	+	0.0100018i	0.000878427	+	0.000391101i
$655$		0			0
$656$	−10.6657	−	23.9555i	−0.416424	−	0.935304i
$657$	2.35954	+	2.35954i	0.0920545	+	0.0920545i
$658$	0.00513901	+	0.00993552i	0.000200340	+	0.000387327i
$659$	−24.9611	−	8.11036i	−0.972347	−	0.315935i	−0.220584	−	0.975368i	$-0.570796\pi$
$659$	−24.9611	−	8.11036i	−0.972347	−	0.315935i	−0.751763	+	0.659433i	$0.770796\pi$
$660$		0			0
$661$	−13.5294	−	12.1819i	−0.526233	−	0.473823i	0.362670	−	0.931918i	$-0.381865\pi$
$661$	−13.5294	−	12.1819i	−0.526233	−	0.473823i	−0.888903	+	0.458095i	$0.848532\pi$
$662$	−0.00174303	+	0.00268403i	−6.77447e−5	+	0.000104318i
$663$	−11.1320	−	0.583404i	−0.432331	−	0.0226575i
$664$	0.0156321	+	0.0481108i	0.000606645	+	0.00186706i
$665$		0			0
$666$	−0.00253648	+	0.00780647i	−9.82865e−5	+	0.000302495i
$667$	3.88441	−	10.1192i	0.150405	−	0.391818i
$668$	−10.3158	−	2.76411i	−0.399130	−	0.106947i
$669$	18.0530	+	1.89744i	0.697968	+	0.0733593i
$670$		0			0
$671$	35.3517	+	48.6574i	1.36474	+	1.87840i
$672$	−0.0617923	+	0.0506659i	−0.00238369	+	0.00195448i
$673$	−1.13223	+	2.22212i	−0.0436441	+	0.0856564i	−0.911799	−	0.410638i	$-0.865306\pi$
$673$	−1.13223	+	2.22212i	−0.0436441	+	0.0856564i	0.868155	+	0.496294i	$0.165306\pi$
$674$	−0.0251490	−	0.0145198i	−0.000968704	−	0.000559281i
$675$		0			0
$676$	−16.3312	−	28.2865i	−0.628124	−	1.08794i
$677$	21.6166	+	33.2867i	0.830795	+	1.27931i	0.957807	+	0.287411i	$0.0927945\pi$
$677$	21.6166	+	33.2867i	0.830795	+	1.27931i	−0.127012	+	0.991901i	$0.540539\pi$
$678$	−0.00679453	+	0.0428990i	−0.000260942	+	0.00164753i
$679$	−32.9160	+	14.8965i	−1.26320	+	0.571675i
$680$		0			0
$681$	9.81472	−	4.36980i	0.376101	−	0.167451i
$682$	0.0109079	−	0.0407088i	0.000417685	−	0.00155882i
$683$	−14.6160	+	11.8358i	−0.559265	+	0.452884i	−0.866802	−	0.498652i	$-0.833828\pi$
$683$	−14.6160	+	11.8358i	−0.559265	+	0.452884i	0.307537	+	0.951536i	$0.400495\pi$
$684$	−5.31829	−	5.90656i	−0.203350	−	0.225843i
$685$		0			0
$686$	−0.0119352	−	0.0127771i	−0.000455690	−	0.000487831i
$687$	−17.0596	−	33.4813i	−0.650864	−	1.27739i
$688$	−0.812338	+	15.5003i	−0.0309701	+	0.590944i
$689$	−0.837868	+	0.930546i	−0.0319202	+	0.0354510i
$690$		0			0
$691$	4.41599	−	3.97618i	0.167992	−	0.151261i	−0.580847	−	0.814013i	$-0.697278\pi$
$691$	4.41599	−	3.97618i	0.167992	−	0.151261i	0.748839	+	0.662752i	$0.230612\pi$
$692$	1.19698	+	7.55742i	0.0455023	+	0.287290i
$693$	−29.5330	−	44.8750i	−1.12187	−	1.70466i
$694$	−0.00572179	+	0.00787536i	−0.000217196	+	0.000298945i
$695$		0			0
$696$	−0.0161771	+	0.0363344i	−0.000613192	+	0.00137725i
$697$	−4.72511	+	1.81380i	−0.178976	+	0.0687026i
$698$	−0.00159774	+	0.00103758i	−6.04753e−5	+	3.92731e-5i
$699$	18.6903			0.706931
$700$		0			0
$701$	−14.1559			−0.534661			−0.267331	−	0.963605i	$-0.586142\pi$
$701$	−14.1559			−0.534661			−0.267331	+	0.963605i	$0.586142\pi$
$702$	−0.0126608	+	0.00822202i	−0.000477851	+	0.000310320i
$703$	−1.91194	+	0.733924i	−0.0721101	+	0.0276805i
$704$	−16.0850	+	36.1275i	−0.606226	+	1.36161i
$705$		0			0
$706$	−0.0110109	+	0.0151552i	−0.000414400	+	0.000570373i
$707$	14.4381	−	28.7691i	0.543001	−	1.08197i
$708$	−3.68208	−	23.2477i	−0.138381	−	0.873704i
$709$	31.6569	−	28.5040i	1.18890	−	1.07049i	0.192892	−	0.981220i	$-0.438213\pi$
$709$	31.6569	−	28.5040i	1.18890	−	1.07049i	0.996007	−	0.0892700i	$-0.0284534\pi$
$710$		0			0
$711$	13.5861	−	15.0889i	0.509518	−	0.565877i
$712$	0.00229377	−	0.0437676i	8.59625e−5	−	0.00164026i
$713$	11.2486	+	22.0767i	0.421264	+	0.826777i
$714$	0.00304719	+	0.00414072i	0.000114038	+	0.000154962i
$715$		0			0
$716$	10.5003	+	11.6618i	0.392415	+	0.435822i
$717$	14.0791	−	11.4010i	0.525794	−	0.425780i
$718$	0.00316687	−	0.0118189i	0.000118187	−	0.000441078i
$719$	−26.2400	+	11.6828i	−0.978588	+	0.435695i	−0.832772	−	0.553616i	$-0.813247\pi$
$719$	−26.2400	+	11.6828i	−0.978588	+	0.435695i	−0.145816	+	0.989312i	$0.546581\pi$
$720$		0			0
$721$	10.3451	+	1.02352i	0.385270	+	0.0381179i
$722$	0.00266777	−	0.0168436i	9.92840e−5	−	0.000626854i
$723$	−22.5743	−	34.7614i	−0.839548	−	1.29279i
$724$	22.2544	+	38.5457i	0.827076	+	1.43254i
$725$		0			0
$726$	0.0292871	+	0.0169089i	0.00108695	+	0.000627548i
$727$	−1.89366	+	3.71652i	−0.0702320	+	0.137838i	−0.923453	−	0.383711i	$-0.874646\pi$
$727$	−1.89366	+	3.71652i	−0.0702320	+	0.137838i	0.853221	+	0.521549i	$0.174646\pi$
$728$	−0.0190826	+	0.0506334i	−0.000707249	+	0.00187660i
$729$	24.6264	+	33.8953i	0.912088	+	1.25538i
$730$		0			0
$731$	2.97945	+	0.313153i	0.110199	+	0.0115824i
$732$	62.6621	+	16.7902i	2.31606	+	0.620585i
$733$	−4.51696	+	11.7671i	−0.166838	+	0.434627i	−0.991355	−	0.131210i	$-0.958114\pi$
$733$	−4.51696	+	11.7671i	−0.166838	+	0.434627i	0.824517	+	0.565837i	$0.191447\pi$
$734$	0.00117357	−	0.00361188i	4.33172e−5	−	0.000133317i
$735$		0			0
$736$	0.00960498	+	0.0295611i	0.000354044	+	0.00108964i
$737$	−3.55773	−	0.186453i	−0.131051	−	0.00686807i
$738$	−0.0138454	+	0.0213200i	−0.000509655	+	0.000784800i
$739$	12.3469	+	11.1172i	0.454189	+	0.408954i	0.864217	−	0.503119i	$-0.167814\pi$
$739$	12.3469	+	11.1172i	0.454189	+	0.408954i	−0.410028	+	0.912073i	$0.634481\pi$
$740$		0			0
$741$	−13.2857	−	4.31678i	−0.488061	−	0.158581i
$742$	0.000576882	0	2.67039e-5i	2.11780e−5	0	9.80332e-7i
$743$	−2.71850	−	2.71850i	−0.0997323	−	0.0997323i	0.655480	−	0.755212i	$-0.272466\pi$
$743$	−2.71850	−	2.71850i	−0.0997323	−	0.0997323i	−0.755212	+	0.655480i	$0.772466\pi$
$744$	−0.0369792	−	0.0830566i	−0.00135572	−	0.00304500i
$745$		0			0
$746$	−0.0110134	−	0.00490347i	−0.000403229	−	0.000179529i
$747$	−34.6276	+	42.7615i	−1.26696	+	1.56456i
$748$	6.80103	+	3.46530i	0.248670	+	0.126704i
$749$	−0.141110	−	0.125505i	−0.00515605	−	0.00458586i
$750$		0			0
$751$	5.06756	−	8.77727i	0.184918	−	0.320287i	−0.758631	−	0.651521i	$-0.774131\pi$
$751$	5.06756	−	8.77727i	0.184918	−	0.320287i	0.943549	+	0.331233i	$0.107465\pi$
$752$	17.8888	−	0.937514i	0.652338	−	0.0341876i
$753$	−18.4046	−	47.9455i	−0.670700	−	1.74723i
$754$	0.00211139	+	0.0200886i	7.68924e−5	+	0.000731582i
$755$		0			0
$756$	−14.8881	−	4.73718i	−0.541475	−	0.172290i
$757$	28.7244	−	28.7244i	1.04401	−	1.04401i	0.0450200	−	0.998986i	$-0.485665\pi$
$757$	28.7244	−	28.7244i	1.04401	−	1.04401i	0.998986	−	0.0450200i	$-0.0143352\pi$
$758$	−0.0280973	−	0.0107856i	−0.00102054	−	0.000391749i
$759$	−35.3681	+	7.51772i	−1.28378	+	0.272876i
$760$		0			0
$761$	6.51041	−	30.6291i	0.236002	−	1.11030i	−0.687343	−	0.726333i	$-0.741223\pi$
$761$	6.51041	−	30.6291i	0.236002	−	1.11030i	0.923345	−	0.383971i	$-0.125444\pi$
$762$	−0.0393747	+	0.0200624i	−0.00142639	+	0.000726784i
$763$	18.3896	+	18.1665i	0.665746	+	0.657670i
$764$	−19.8144	+	6.43808i	−0.716859	+	0.232922i
$765$		0			0
$766$	0.00438077	+	0.0206099i	0.000158284	+	0.000744666i
$767$	−15.0456	−	18.5798i	−0.543265	−	0.670877i
$768$	11.0401	+	41.2022i	0.398375	+	1.48676i
$769$	−19.4789	−	14.1523i	−0.702429	−	0.510344i	0.178294	−	0.983977i	$-0.442942\pi$
$769$	−19.4789	−	14.1523i	−0.702429	−	0.510344i	−0.880722	+	0.473633i	$0.842942\pi$
$770$		0			0
$771$	−9.81830	+	7.13341i	−0.353597	+	0.256904i
$772$	−10.4223	−	8.43979i	−0.375106	−	0.303755i
$773$	−2.02881	−	38.7120i	−0.0729712	−	1.39237i	−0.752436	−	0.658665i	$-0.771121\pi$
$773$	−2.02881	−	38.7120i	−0.0729712	−	1.39237i	0.679465	−	0.733708i	$-0.262212\pi$
$774$	0.0130313	−	0.00752363i	0.000468401	−	0.000270431i
$775$		0			0
$776$		−	0.0515680i		−	0.00185118i
$777$	−9.32511	+	11.6603i	−0.334536	+	0.418312i
$778$	0.0139347	+	0.00220704i	0.000499583	+	7.91261e-5i
$779$	−6.30788	+	0.662984i	−0.226003	+	0.0237539i
$780$		0			0
$781$	−2.23046	+	21.2214i	−0.0798121	+	0.759362i
$782$	0.00193162		0.000517577i	6.90747e−5		1.85085e-5i
$783$	−11.5209	+	1.82474i	−0.411725	+	0.0652108i
$784$	−26.5220	+	8.97684i	−0.947213	+	0.320601i
$785$		0			0
$786$	−0.00714266	−	0.00151822i	−0.000254770	−	5.41531e-5i
$787$	−32.7767	−	21.2854i	−1.16836	−	0.758744i	−0.193402	−	0.981120i	$-0.561952\pi$
$787$	−32.7767	−	21.2854i	−1.16836	−	0.758744i	−0.974961	+	0.222375i	$0.928619\pi$
$788$	42.2125	+	27.4131i	1.50376	+	0.976551i
$789$	−70.1096	−	14.9023i	−2.49597	−	0.530535i
$790$		0			0
$791$	−22.5871	+	39.6794i	−0.803106	+	1.41084i
$792$	0.0757320	−	0.0119948i	0.00269102	−	0.000426215i
$793$	63.6475	−	17.0543i	2.26019	−	0.605616i
$794$	0.000692537	−	0.00658905i	2.45772e−5	−	0.000233837i
$795$		0			0
$796$	−1.31550	+	0.138264i	−0.0466265	+	0.00490064i
$797$	−16.8476	−	2.66839i	−0.596771	−	0.0945193i	−0.149261	−	0.988798i	$-0.547689\pi$
$797$	−16.8476	−	2.66839i	−0.596771	−	0.0945193i	−0.447511	+	0.894279i	$0.647689\pi$
$798$	0.00234550	+	0.00600052i	8.30298e−5	+	0.000212416i
$799$		−	3.45751i		−	0.122318i
$800$		0			0
$801$	41.2852	−	23.8360i	1.45874	−	0.842203i
$802$	−0.000313158	−	0.00597542i	−1.10580e−5	−	0.000210999i
$803$	−3.12095	−	2.52729i	−0.110136	−	0.0891863i
$804$	−3.10882	+	2.25869i	−0.109640	+	0.0796578i
$805$		0			0
$806$	−0.0373550	−	0.0271400i	−0.00131577	−	0.000955965i
$807$	−6.48281	−	24.1942i	−0.228206	−	0.851675i
$808$	0.0289128	+	0.0357044i	0.00101715	+	0.00125608i
$809$	6.74829	+	31.7482i	0.237257	+	1.11621i	0.921930	+	0.387357i	$0.126612\pi$
$809$	6.74829	+	31.7482i	0.237257	+	1.11621i	−0.684673	+	0.728851i	$0.740055\pi$
$810$		0			0
$811$	−28.6458	+	9.30758i	−1.00589	+	0.326833i	−0.765216	−	0.643773i	$-0.777368\pi$
$811$	−28.6458	+	9.30758i	−1.00589	+	0.326833i	−0.240673	+	0.970606i	$0.577368\pi$
$812$	−14.6914	+	14.8718i	−0.515567	+	0.521899i
$813$	38.6974	−	19.7173i	1.35718	−	0.691516i
$814$	0.00205385	−	0.00966261i	7.19874e−5	−	0.000338674i
$815$		0			0
$816$	8.05318	−	1.71176i	0.281918	−	0.0599235i
$817$	3.50495	+	1.34543i	0.122623	+	0.0470705i
$818$	0.00451907	−	0.00451907i	0.000158006	−	0.000158006i
$819$	−57.4942	+	12.5880i	−2.00901	+	0.439860i
$820$		0			0
$821$	−3.33657	−	31.7454i	−0.116447	−	1.10792i	−0.884179	−	0.467149i	$-0.845281\pi$
$821$	−3.33657	−	31.7454i	−0.116447	−	1.10792i	0.767731	−	0.640772i	$-0.221385\pi$
$822$	−0.0187312	−	0.0487963i	−0.000653324	−	0.00170197i
$823$	18.3358	−	0.960940i	0.639147	−	0.0334963i	0.269990	−	0.962863i	$-0.412980\pi$
$823$	18.3358	−	0.960940i	0.639147	−	0.0334963i	0.369157	+	0.929367i	$0.379646\pi$
$824$	−0.00741878	+	0.0128497i	−0.000258446	+	0.000447641i
$825$		0			0
$826$	−0.00222661	+	0.0107990i	−7.74736e−5	+	0.000375746i
$827$	−27.0035	−	13.7590i	−0.939005	−	0.478447i	−0.0836537	−	0.996495i	$-0.526659\pi$
$827$	−27.0035	−	13.7590i	−0.939005	−	0.478447i	−0.855352	+	0.518048i	$0.826659\pi$
$828$	−14.1843	+	17.5162i	−0.492940	+	0.608730i
$829$	−17.6268	−	7.84795i	−0.612203	−	0.272570i	0.0771228	−	0.997022i	$-0.475427\pi$
$829$	−17.6268	−	7.84795i	−0.612203	−	0.272570i	−0.689326	+	0.724451i	$0.742093\pi$
$830$		0			0
$831$	−19.0548	−	42.7978i	−0.661005	−	1.48464i
$832$	30.6365	+	30.6365i	1.06213	+	1.06213i
$833$	1.46236	+	5.20274i	0.0506677	+	0.180264i
$834$	0.00506524	+	0.00164580i	0.000175395	+	5.69893e-5i
$835$		0			0
$836$	7.10846	+	6.40049i	0.245851	+	0.221366i
$837$	14.5222	−	22.3623i	0.501961	−	0.772953i
$838$	0.0255984	+	0.00134155i	0.000884281	+	4.63432e-5i
$839$	−9.65006	−	29.6998i	−0.333157	−	1.02535i	−0.967623	−	0.252401i	$-0.918780\pi$
$839$	−9.65006	−	29.6998i	−0.333157	−	1.02535i	0.634465	−	0.772951i	$-0.281220\pi$
$840$		0			0
$841$	4.13852	−	12.7371i	0.142708	−	0.439209i
$842$	−0.00624026	+	0.0162564i	−0.000215054	+	0.000560234i
$843$	−52.7951	−	14.1464i	−1.81836	−	0.487228i
$844$	−10.2066	−	1.07276i	−0.351325	−	0.0369258i
$845$		0			0
$846$	−0.0102075	−	0.0140494i	−0.000350939	−	0.000483027i
$847$	22.5402	+	27.4901i	0.774490	+	0.944570i
$848$	0.419861	−	0.824024i	0.0144181	−	0.0282971i
$849$	46.9750	+	27.1210i	1.61218	+	0.930790i
$850$		0			0
$851$	2.90381	+	5.02954i	0.0995413	+	0.172411i
$852$	12.5354	+	19.3028i	0.429455	+	0.661303i
$853$	−1.34957	+	8.52083i	−0.0462083	+	0.291748i	−0.999961	−	0.00884499i	$-0.997185\pi$
$853$	−1.34957	+	8.52083i	−0.0462083	+	0.291748i	0.953753	+	0.300593i	$0.0971845\pi$
$854$	−0.0246942	−	0.0177122i	−0.000845020	−	0.000606098i
$855$		0			0
$856$	0.000246239	0	0.000109633i	8.41627e−6	0	3.74717e-6i
$857$	9.78746	−	36.5273i	0.334333	−	1.24775i	−0.570257	−	0.821466i	$-0.693156\pi$
$857$	9.78746	−	36.5273i	0.334333	−	1.24775i	0.904590	−	0.426282i	$-0.140177\pi$
$858$	0.0523658	−	0.0424050i	0.00178774	−	0.00144768i
$859$	1.84494	+	2.04902i	0.0629487	+	0.0699116i	0.773797	−	0.633434i	$-0.218355\pi$
$859$	1.84494	+	2.04902i	0.0629487	+	0.0699116i	−0.710848	+	0.703346i	$0.751689\pi$
$860$		0			0
$861$	−37.2428	+	27.4073i	−1.26923	+	0.934037i
$862$	−0.00946622	−	0.0185785i	−0.000322421	−	0.000632786i
$863$	−1.58361	+	30.2171i	−0.0539068	+	1.02860i	0.829057	+	0.559163i	$0.188878\pi$
$863$	−1.58361	+	30.2171i	−0.0539068	+	1.02860i	−0.882964	+	0.469440i	$0.844456\pi$
$864$	0.0223819	−	0.0248576i	0.000761447	−	0.000845673i
$865$		0			0
$866$	0.000846249	0	0.000761966i	2.87567e−5	0	2.58927e-5i
$867$	6.84131	+	43.1943i	0.232343	+	1.46696i
$868$	−2.79211	−	47.7044i	−0.0947704	−	1.61919i
$869$	−14.3629	+	19.7689i	−0.487229	+	0.670613i
$870$		0			0
$871$	−1.58755	+	3.56570i	−0.0537921	+	0.120819i
$872$	−0.0344443	+	0.0132219i	−0.00116643	+	0.000447751i
$873$	47.0421	−	30.5495i	1.59213	−	1.03394i
$874$	0.00250603			8.47678e−5
$875$		0			0
$876$	−4.33165			−0.146353
$877$	7.77982	−	5.05228i	0.262706	−	0.170603i	−0.406565	−	0.913622i	$-0.633273\pi$
$877$	7.77982	−	5.05228i	0.262706	−	0.170603i	0.669271	+	0.743019i	$0.266607\pi$
$878$	0.0229552	−	0.00881169i	0.000774702	−	0.000297380i
$879$	−1.65589	+	3.71918i	−0.0558517	+	0.125445i
$880$		0			0
$881$	−2.03919	+	2.80671i	−0.0687022	+	0.0945604i	−0.841985	−	0.539500i	$-0.818613\pi$
$881$	−2.03919	+	2.80671i	−0.0687022	+	0.0945604i	0.773283	+	0.634061i	$0.218613\pi$
$882$	0.0213020	+	0.0168237i	0.000717276	+	0.000566484i
$883$	−8.05760	−	50.8737i	−0.271160	−	1.71204i	−0.628288	−	0.777981i	$-0.716244\pi$
$883$	−8.05760	−	50.8737i	−0.271160	−	1.71204i	0.357128	−	0.934056i	$-0.383756\pi$
$884$	6.21461	−	5.59566i	0.209020	−	0.188202i
$885$		0			0
$886$	−0.00239041	+	0.00265482i	−8.03074e−5	+	8.91904e-5i
$887$	−0.773181	+	14.7532i	−0.0259609	+	0.495363i	0.954446	+	0.298382i	$0.0964470\pi$
$887$	−0.773181	+	14.7532i	−0.0259609	+	0.495363i	−0.980407	+	0.196981i	$0.936886\pi$
$888$	−0.00967467	−	0.0189876i	−0.000324661	−	0.000637183i
$889$	−46.1691	+	5.13763i	−1.54846	+	0.172310i
$890$		0			0
$891$	−14.7225	−	16.3510i	−0.493223	−	0.547780i
$892$	−10.5830	+	8.56993i	−0.354344	+	0.286942i
$893$	1.12142	−	4.18519i	0.0375269	−	0.140052i
$894$	0.0248098	−	0.0110461i	0.000829765	−	0.000369435i
$895$		0			0
$896$	0.00786954	−	0.0795401i	0.000262903	−	0.00265725i
$897$	−6.19706	+	39.1267i	−0.206914	+	1.30640i
$898$	−0.00874398	−	0.0134645i	−0.000291790	−	0.000449318i
$899$	−17.8385	−	30.8972i	−0.594948	−	1.03048i
$900$		0			0
$901$	−0.154588	−	0.0892513i	−0.00515007	−	0.00297339i
$902$	0.0138894	−	0.0272595i	0.000462467	−	0.000907642i
$903$	27.0070	−	4.44660i	0.898736	−	0.147974i
$904$	−0.0383043	−	0.0527213i	−0.00127398	−	0.00175348i
$905$		0			0
$906$	0.0173392	+	0.00182242i	0.000576056	+	6.05459e-5i
$907$	−9.81060	−	2.62874i	−0.325755	−	0.0872859i	0.0922352	−	0.995737i	$-0.470599\pi$
$907$	−9.81060	−	2.62874i	−0.325755	−	0.0872859i	−0.417991	+	0.908451i	$0.637266\pi$
$908$	−2.88834	+	7.52439i	−0.0958530	+	0.249706i
$909$	−15.4424	+	47.5269i	−0.512193	+	1.57637i
$910$		0			0
$911$	−14.3699	−	44.2260i	−0.476096	−	1.46527i	−0.844474	−	0.535596i	$-0.820087\pi$
$911$	−14.3699	−	44.2260i	−0.476096	−	1.46527i	0.368378	−	0.929676i	$-0.379913\pi$
$912$	10.3033	+	0.539973i	0.341176	+	0.0178803i
$913$	36.0662	−	55.5371i	1.19362	−	1.83801i
$914$	−0.000968582	0	0.000872115i	−3.20378e−5	0	2.88470e-5i
$915$		0			0
$916$	26.8102	+	8.71115i	0.885832	+	0.287824i
$917$	−6.46315	−	4.14136i	−0.213432	−	0.136760i
$918$	−0.00152172	−	0.00152172i	−5.02243e−5	−	5.02243e-5i
$919$	−8.94502	−	20.0908i	−0.295069	−	0.662736i	0.703794	−	0.710404i	$-0.251488\pi$
$919$	−8.94502	−	20.0908i	−0.295069	−	0.662736i	−0.998863	+	0.0476680i	$0.984821\pi$
$920$		0			0
$921$	16.4148	+	7.30832i	0.540885	+	0.240817i
$922$	−0.0211828	+	0.0261585i	−0.000697617	+	0.000861486i
$923$	20.8299	+	10.6134i	0.685624	+	0.349343i
$924$	68.2992	+	14.0823i	2.24688	+	0.463275i
$925$		0			0
$926$	−0.00236919	+	0.00410356i	−7.78565e−5	+	0.000134851i
$927$	−16.1169	+	0.844651i	−0.529348	+	0.0277420i
$928$	−0.0160391	−	0.0417832i	−0.000526509	−	0.00137160i
$929$	3.41889	+	32.5285i	0.112170	+	1.06723i	0.895329	+	0.445405i	$0.146940\pi$
$929$	3.41889	+	32.5285i	0.112170	+	1.06723i	−0.783159	+	0.621821i	$0.786393\pi$
$930$		0			0
$931$	0.0826604	+	6.77204i	0.00270909	+	0.221945i
$932$	−9.91453	+	9.91453i	−0.324761	+	0.324761i
$933$	−51.8766	−	19.9136i	−1.69836	−	0.651941i
$934$	0.0177320	−	0.00376906i	0.000580210	−	0.000123328i
$935$		0			0
$936$	0.0174656	−	0.0821694i	0.000570882	−	0.00268579i
$937$	−25.9243	+	13.2091i	−0.846910	+	0.431522i	−0.822898	−	0.568190i	$-0.807644\pi$
$937$	−25.9243	+	13.2091i	−0.846910	+	0.431522i	−0.0240121	+	0.999712i	$0.507644\pi$
$938$	0.00173591		0.000476508i	5.66794e−5		1.55585e-5i
$939$	−8.98478	+	2.91933i	−0.293207	+	0.0952688i
$940$		0			0
$941$	3.68978	+	17.3591i	0.120283	+	0.565889i	0.996472	+	0.0839213i	$0.0267444\pi$
$941$	3.68978	+	17.3591i	0.120283	+	0.565889i	−0.876189	+	0.481968i	$0.839922\pi$
$942$	−0.0276451	−	0.0341388i	−0.000900725	−	0.00111230i
$943$	4.65523	+	17.3736i	0.151595	+	0.565761i
$944$	14.2853	+	10.3789i	0.464947	+	0.337804i
$945$		0			0
$946$	−0.0146506	+	0.0106443i	−0.000476333	+	0.000346076i
$947$	8.65161	+	7.00594i	0.281140	+	0.227662i	0.759510	−	0.650496i	$-0.225439\pi$
$947$	8.65161	+	7.00594i	0.281140	+	0.227662i	−0.478370	+	0.878158i	$0.658772\pi$
$948$	1.37941	+	26.3208i	0.0448012	+	0.854858i
$949$	−3.81032	+	2.19989i	−0.123688	+	0.0714114i
$950$		0			0
$951$			32.3772i			1.04990i
$952$	−0.00762586	−	0.00116016i	−0.000247156	−	3.76009e-5i
$953$	−0.974249	−	0.154306i	−0.0315590	−	0.00499846i	0.140635	−	0.990062i	$-0.455086\pi$
$953$	−0.974249	−	0.154306i	−0.0315590	−	0.00499846i	−0.172194	+	0.985063i	$0.555086\pi$
$954$	−0.000891650	0	9.37162e-5i	−2.88682e−5	0	3.03417e-6i
$955$		0			0
$956$	−1.42062	+	13.5163i	−0.0459462	+	0.437149i
$957$	50.2907	−	13.4753i	1.62567	−	0.435596i
$958$	−0.0318551	+	0.00504535i	−0.00102919	+	0.000163008i
$959$	−0.335310	−	54.9433i	−0.0108277	−	1.77421i
$960$		0			0
$961$	49.4493	+	10.5108i	1.59514	+	0.339057i
$962$	−0.00907670	−	0.00589448i	−0.000292644	−	0.000190046i
$963$	0.245885	+	0.159680i	0.00792354	+	0.00514561i
$964$	30.4146	+	6.46482i	0.979588	+	0.208218i
$965$		0			0
$966$	0.0157663	−	0.00923143i	0.000507273	−	0.000297016i
$967$	−38.3926	+	6.08079i	−1.23462	+	0.195545i	−0.739427	−	0.673237i	$-0.764903\pi$
$967$	−38.3926	+	6.08079i	−1.23462	+	0.195545i	−0.495195	+	0.868782i	$0.664903\pi$
$968$	−0.0490107	+	0.0131324i	−0.00157526	+	0.000422090i
$969$	0.208157	−	1.98049i	0.00668698	−	0.0636224i
$970$		0			0
$971$	−32.8377	+	3.45138i	−1.05381	+	0.110760i	−0.615558	−	0.788092i	$-0.711069\pi$
$971$	−32.8377	+	3.45138i	−1.05381	+	0.110760i	−0.438253	+	0.898852i	$0.644403\pi$
$972$	−40.9375	−	6.48387i	−1.31307	−	0.207970i
$973$	4.37237	+	3.49671i	0.140172	+	0.112099i
$974$		−	0.0243921i		−	0.000781573i
$975$		0			0
$976$	−42.1466	+	24.3334i	−1.34908	+	0.778892i
$977$	0.446582	+	8.52128i	0.0142874	+	0.272620i	0.996427	+	0.0844639i	$0.0269178\pi$
$977$	0.446582	+	8.52128i	0.0142874	+	0.272620i	−0.982139	+	0.188156i	$0.939749\pi$
$978$	−0.0157788	−	0.0127774i	−0.000504550	−	0.000408577i
$979$	−46.4154	+	33.7228i	−1.48344	+	1.07778i
$980$		0			0
$981$	−32.4667	−	23.5884i	−1.03658	−	0.753120i
$982$	−0.00901840	−	0.0336571i	−0.000287789	−	0.00107404i
$983$	−22.9338	−	28.3209i	−0.731475	−	0.903297i	0.266694	−	0.963781i	$-0.414069\pi$
$983$	−22.9338	−	28.3209i	−0.731475	−	0.903297i	−0.998169	+	0.0604846i	$0.980735\pi$
$984$	−0.0137219	−	0.0645566i	−0.000437439	−	0.00205799i
$985$		0			0
$986$	−0.00273855		0.000889809i	−8.72133e−5		2.83373e-5i
$987$	−8.36169	−	30.4614i	−0.266156	−	0.969598i
$988$	9.33748	−	4.75768i	0.297065	−	0.151362i
$989$	2.21353	−	10.4138i	0.0703862	−	0.331141i
$990$		0			0
$991$	17.4728	−	3.71396i	0.555041	−	0.117978i	0.0781527	−	0.996941i	$-0.475098\pi$
$991$	17.4728	−	3.71396i	0.555041	−	0.117978i	0.476889	+	0.878964i	$0.341764\pi$
$992$	0.0955121	+	0.0366637i	0.00303251	+	0.00116407i
$993$	6.39051	−	6.39051i	0.202797	−	0.202797i
$994$	−0.00230599	−	0.0105324i	−7.31416e−5	−	0.000334066i
$995$		0			0
$996$	−7.46613	−	71.0355i	−0.236574	−	2.25085i
$997$	−16.8264	−	43.8344i	−0.532898	−	1.38825i	−0.890760	−	0.454473i	$-0.849827\pi$
$997$	−16.8264	−	43.8344i	−0.532898	−	1.38825i	0.357862	−	0.933775i	$-0.383506\pi$
$998$	−0.0339833	+	0.00178099i	−0.00107572	+	5.63763e-5i
$999$	3.12493	−	5.41253i	0.0988683	−	0.171245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.768.9		288
5.2	odd	4		175.2.x.a.117.9	yes	288
5.3	odd	4		875.2.bb.c.607.10		288
5.4	even	2		875.2.bb.a.768.10		288
7.3	odd	6	inner	875.2.bb.b.143.9		288
25.3	odd	20		875.2.bb.a.257.10		288
25.4	even	10		875.2.bb.c.243.9		288
25.21	even	5		175.2.x.a.103.10	yes	288
25.22	odd	20	inner	875.2.bb.b.257.9		288
35.3	even	12		875.2.bb.c.857.9		288
35.17	even	12		175.2.x.a.17.10	yes	288
35.24	odd	6		875.2.bb.a.143.10		288
175.3	even	60		875.2.bb.a.507.10		288
175.122	even	60	inner	875.2.bb.b.507.9		288
175.129	odd	30		875.2.bb.c.493.10		288
175.171	odd	30		175.2.x.a.3.9	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.9	✓	288	175.171	odd	30
175.2.x.a.17.10	yes	288	35.17	even	12
175.2.x.a.103.10	yes	288	25.21	even	5
175.2.x.a.117.9	yes	288	5.2	odd	4
875.2.bb.a.143.10		288	35.24	odd	6
875.2.bb.a.257.10		288	25.3	odd	20
875.2.bb.a.507.10		288	175.3	even	60
875.2.bb.a.768.10		288	5.4	even	2
875.2.bb.b.143.9		288	7.3	odd	6	inner
875.2.bb.b.257.9		288	25.22	odd	20	inner
875.2.bb.b.507.9		288	175.122	even	60	inner
875.2.bb.b.768.9		288	1.1	even	1	trivial
875.2.bb.c.243.9		288	25.4	even	10
875.2.bb.c.493.10		288	175.129	odd	30
875.2.bb.c.607.10		288	5.3	odd	4
875.2.bb.c.857.9		288	35.3	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.000791762 + 0.000514176i) q^{2} +(2.48892 - 0.955405i) q^{3} +(-0.813473 + 1.82709i) q^{4} +(-0.00147938 + 0.00203619i) q^{6} +(-2.21008 + 1.45449i) q^{7} +(-0.000590739 - 0.00372978i) q^{8} +(3.05247 - 2.74845i) q^{9} +(-3.30773 + 3.67360i) q^{11} +(-0.279054 + 5.32467i) q^{12} +(2.45874 + 4.82554i) q^{13} +(0.00100199 - 0.00228798i) q^{14} +(-2.67652 - 2.97258i) q^{16} +(-0.599995 + 0.485867i) q^{17} +(-0.00100364 + 0.00374563i) q^{18} +(-0.883861 + 0.393520i) q^{19} +(-4.11107 + 5.73163i) q^{21} +(0.000730053 - 0.00460937i) q^{22} +(1.49430 + 2.30102i) q^{23} +(-0.00503375 - 0.00871871i) q^{24} +(-0.00442791 - 0.00255646i) q^{26} +(1.34044 - 2.63077i) q^{27} +(-0.859653 - 5.22120i) q^{28} +(-2.32212 - 3.19613i) q^{29} +(8.98125 + 0.943968i) q^{31} +(0.0109428 + 0.00293211i) q^{32} +(-4.72287 + 12.3035i) q^{33} +(0.000225232 - 0.000693194i) q^{34} +(2.53857 + 7.81292i) q^{36} +(2.11384 + 0.110782i) q^{37} +(0.000497468 - 0.000766034i) q^{38} +(10.7299 + 9.66128i) q^{39} +(6.23478 + 2.02580i) q^{41} +(0.000307917 - 0.00665190i) q^{42} +(-2.74386 - 2.74386i) q^{43} +(-4.02126 - 9.03189i) q^{44} +(-0.00236626 - 0.00105353i) q^{46} +(-2.81832 + 3.48033i) q^{47} +(-9.50164 - 4.84133i) q^{48} +(2.76889 - 6.42909i) q^{49} +(-1.02914 + 1.78252i) q^{51} +(-10.8168 + 0.566885i) q^{52} +(0.0828569 + 0.215850i) q^{53} +(0.000291366 + 0.00277217i) q^{54} +(0.00673052 + 0.00738387i) q^{56} +(-1.82388 + 1.82388i) q^{57} +(0.00348194 + 0.00133659i) q^{58} +(-4.31794 + 0.917807i) q^{59} +(2.52960 - 11.9008i) q^{61} +(-0.00759638 + 0.00387055i) q^{62} +(-2.74858 + 10.5141i) q^{63} +(7.60843 - 2.47213i) q^{64} +(-0.00258678 - 0.0121698i) q^{66} +(0.453546 + 0.560082i) q^{67} +(-0.399642 - 1.49149i) q^{68} +(5.91760 + 4.29939i) q^{69} +(3.49220 - 2.53723i) q^{71} +(-0.0120543 - 0.00976140i) q^{72} +(0.0425173 + 0.811278i) q^{73} +(-0.00173062 + 0.000999174i) q^{74} -1.93501i q^{76} +(1.96710 - 12.9300i) q^{77} +(-0.0134631 - 0.00213235i) q^{78} +(4.91609 - 0.516702i) q^{79} +(-0.465251 + 4.42657i) q^{81} +(-0.00597808 + 0.00160182i) q^{82} +(-13.2310 + 2.09559i) q^{83} +(-7.12797 - 12.1738i) q^{84} +(0.00358331 + 0.000761656i) q^{86} +(-8.83316 - 5.73632i) q^{87} +(0.0156557 + 0.0101669i) q^{88} +(11.3525 + 2.41304i) q^{89} +(-12.4527 - 7.08861i) q^{91} +(-5.41975 + 0.858405i) q^{92} +(23.2555 - 6.23128i) q^{93} +(0.000441932 - 0.00420470i) q^{94} +(0.0300370 - 0.00315702i) q^{96} +(13.4877 + 2.13624i) q^{97} +(0.00111338 + 0.00651401i) q^{98} +20.3047i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) \) 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

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