LMFDB - Embedded newform 475.2.n.b.39.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.17
Character	$\chi$	$=$	475.39
Dual form			475.2.n.b.134.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.861798 + 1.18616i) q^{2} +(0.988821 + 0.321288i) q^{3} +(-0.0462526 + 0.142351i) q^{4} +(1.82580 + 1.29092i) q^{5} +(0.471065 + 1.44979i) q^{6} +2.09401i q^{7} +(2.58012 - 0.838333i) q^{8} +(-1.55251 - 1.12796i) q^{9} +O(q^{10})$	\(q+(0.861798 + 1.18616i) q^{2} +(0.988821 + 0.321288i) q^{3} +(-0.0462526 + 0.142351i) q^{4} +(1.82580 + 1.29092i) q^{5} +(0.471065 + 1.44979i) q^{6} +2.09401i q^{7} +(2.58012 - 0.838333i) q^{8} +(-1.55251 - 1.12796i) q^{9} +(0.0422287 + 3.27820i) q^{10} +(-4.61229 + 3.35102i) q^{11} +(-0.0914711 + 0.125899i) q^{12} +(2.20447 - 3.03420i) q^{13} +(-2.48383 + 1.80461i) q^{14} +(1.39063 + 1.86309i) q^{15} +(3.46013 + 2.51393i) q^{16} +(2.51704 - 0.817835i) q^{17} -2.81360i q^{18} +(0.309017 + 0.951057i) q^{19} +(-0.268211 + 0.200195i) q^{20} +(-0.672779 + 2.07060i) q^{21} +(-7.94972 - 2.58302i) q^{22} +(-1.95581 - 2.69195i) q^{23} +2.82063 q^{24} +(1.66706 + 4.71390i) q^{25} +5.49886 q^{26} +(-3.00613 - 4.13758i) q^{27} +(-0.298084 - 0.0968533i) q^{28} +(1.14814 - 3.53361i) q^{29} +(-1.01149 + 3.25512i) q^{30} +(-1.33250 - 4.10102i) q^{31} +0.844962i q^{32} +(-5.63737 + 1.83169i) q^{33} +(3.13926 + 2.28081i) q^{34} +(-2.70319 + 3.82323i) q^{35} +(0.232374 - 0.168830i) q^{36} +(-0.118683 + 0.163353i) q^{37} +(-0.861798 + 1.18616i) q^{38} +(3.15468 - 2.29201i) q^{39} +(5.79300 + 1.80010i) q^{40} +(0.194906 + 0.141608i) q^{41} +(-3.03587 + 0.986413i) q^{42} +9.59241i q^{43} +(-0.263691 - 0.811556i) q^{44} +(-1.37846 - 4.06359i) q^{45} +(1.50757 - 4.63983i) q^{46} +(-6.77067 - 2.19992i) q^{47} +(2.61375 + 3.59752i) q^{48} +2.61513 q^{49} +(-4.15479 + 6.03984i) q^{50} +2.75166 q^{51} +(0.329958 + 0.454148i) q^{52} +(1.14518 + 0.372093i) q^{53} +(2.31717 - 7.13151i) q^{54} +(-12.7470 + 0.164202i) q^{55} +(1.75548 + 5.40280i) q^{56} +1.03971i q^{57} +(5.18090 - 1.68338i) q^{58} +(-11.1086 - 8.07090i) q^{59} +(-0.329533 + 0.111785i) q^{60} +(1.87481 - 1.36213i) q^{61} +(3.71613 - 5.11482i) q^{62} +(2.36197 - 3.25097i) q^{63} +(5.91799 - 4.29967i) q^{64} +(7.94182 - 2.69403i) q^{65} +(-7.03096 - 5.10829i) q^{66} +(-6.61137 + 2.14817i) q^{67} +0.396129i q^{68} +(-1.06906 - 3.29023i) q^{69} +(-6.86458 + 0.0884271i) q^{70} +(3.77186 - 11.6086i) q^{71} +(-4.95128 - 1.60877i) q^{72} +(-3.72518 - 5.12727i) q^{73} -0.296043 q^{74} +(0.133909 + 5.19682i) q^{75} -0.149676 q^{76} +(-7.01707 - 9.65817i) q^{77} +(5.43739 + 1.76672i) q^{78} +(-3.10913 + 9.56892i) q^{79} +(3.07221 + 9.05666i) q^{80} +(0.135846 + 0.418092i) q^{81} +0.353227i q^{82} +(8.61217 - 2.79826i) q^{83} +(-0.263634 - 0.191541i) q^{84} +(5.65135 + 1.75609i) q^{85} +(-11.3782 + 8.26672i) q^{86} +(2.27061 - 3.12522i) q^{87} +(-9.09100 + 12.5127i) q^{88} +(-2.97960 + 2.16480i) q^{89} +(3.63213 - 5.13707i) q^{90} +(6.35363 + 4.61618i) q^{91} +(0.473662 - 0.153902i) q^{92} -4.48330i q^{93} +(-3.22548 - 9.92701i) q^{94} +(-0.663533 + 2.13535i) q^{95} +(-0.271476 + 0.835517i) q^{96} +(3.65745 + 1.18838i) q^{97} +(2.25371 + 3.10197i) q^{98} +10.9405 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) $ 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9	$ 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) $ 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9 + 28 * q^10 - 15 * q^11 - 85 * q^12 + 10 * q^14 - 10 * q^15 - 42 * q^16 + 20 * q^17 - 24 * q^19 - 16 * q^21 - 35 * q^23 - 24 * q^24 - 8 * q^25 + 28 * q^26 + 15 * q^27 + 30 * q^28 + 28 * q^29 - 64 * q^30 - 8 * q^31 + 25 * q^33 - 8 * q^34 + 33 * q^35 - 42 * q^36 - 55 * q^37 - 6 * q^39 - 48 * q^40 - 27 * q^41 + 210 * q^42 - 4 * q^44 + 15 * q^45 + 10 * q^46 - 115 * q^48 - 150 * q^49 + 9 * q^50 + 60 * q^51 - 5 * q^52 + 40 * q^53 + 47 * q^54 + 33 * q^55 - 12 * q^56 + 60 * q^58 + 25 * q^59 + 170 * q^60 + 26 * q^61 - 110 * q^62 - 30 * q^63 + 62 * q^64 - 15 * q^65 - 41 * q^66 + 35 * q^67 + 14 * q^69 - 20 * q^70 - 38 * q^71 - 60 * q^73 + 6 * q^74 - 151 * q^75 - 104 * q^76 + 115 * q^78 + 8 * q^79 - 63 * q^80 - 67 * q^81 + 160 * q^83 + 18 * q^84 - 8 * q^85 - 10 * q^87 - 120 * q^88 + 76 * q^89 + 108 * q^90 - 8 * q^91 + 85 * q^92 + 58 * q^94 + q^95 - 6 * q^96 - 10 * q^97 + 10 * q^98 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	0.861798	+	1.18616i	0.609383	+	0.838744i	0.996527	−	0.0832758i	$-0.0265383\pi$
$2$	0.861798	+	1.18616i	0.609383	+	0.838744i	−0.387144	+	0.922019i	$0.626538\pi$
$3$	0.988821	+	0.321288i	0.570896	+	0.185495i	0.580218	−	0.814461i	$-0.302967\pi$
$3$	0.988821	+	0.321288i	0.570896	+	0.185495i	−0.00932190	+	0.999957i	$0.502967\pi$
$4$	−0.0462526	+	0.142351i	−0.0231263	+	0.0711754i
$5$	1.82580	+	1.29092i	0.816521	+	0.577316i
$5$	1.82580	+	1.29092i	0.816521	+	0.577316i
$6$	0.471065	+	1.44979i	0.192311	+	0.591873i
$7$			2.09401i			0.791461i	0.918367	+	0.395730i	$0.129508\pi$
$7$			2.09401i			0.791461i	−0.918367	+	0.395730i	$0.870492\pi$
$8$	2.58012	−	0.838333i	0.912212	−	0.296395i
$9$	−1.55251	−	1.12796i	−0.517503	−	0.375988i
$10$	0.0422287	+	3.27820i	0.0133539	+	1.03666i
$11$	−4.61229	+	3.35102i	−1.39066	+	1.01037i	−0.394864	+	0.918739i	$0.629208\pi$
$11$	−4.61229	+	3.35102i	−1.39066	+	1.01037i	−0.995793	+	0.0916321i	$0.970792\pi$
$12$	−0.0914711	+	0.125899i	−0.0264054	+	0.0363439i
$13$	2.20447	−	3.03420i	0.611411	−	0.841535i	−0.385282	−	0.922799i	$-0.625896\pi$
$13$	2.20447	−	3.03420i	0.611411	−	0.841535i	0.996693	+	0.0812642i	$0.0258957\pi$
$14$	−2.48383	+	1.80461i	−0.663832	+	0.482302i
$15$	1.39063	+	1.86309i	0.359059	+	0.481048i
$16$	3.46013	+	2.51393i	0.865031	+	0.628482i
$17$	2.51704	−	0.817835i	0.610471	−	0.198354i	0.0125661	−	0.999921i	$-0.496000\pi$
$17$	2.51704	−	0.817835i	0.610471	−	0.198354i	0.597905	+	0.801567i	$0.296000\pi$
$18$		−	2.81360i		−	0.663173i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	−0.268211	+	0.200195i	−0.0599738	+	0.0447650i
$21$	−0.672779	+	2.07060i	−0.146812	+	0.451842i
$22$	−7.94972	−	2.58302i	−1.69489	−	0.550702i
$23$	−1.95581	−	2.69195i	−0.407815	−	0.561310i	0.554869	−	0.831938i	$-0.312769\pi$
$23$	−1.95581	−	2.69195i	−0.407815	−	0.561310i	−0.962684	+	0.270628i	$0.912769\pi$
$24$	2.82063			0.575758
$25$	1.66706	+	4.71390i	0.333413	+	0.942781i
$26$	5.49886			1.07842
$27$	−3.00613	−	4.13758i	−0.578530	−	0.796278i
$28$	−0.298084	−	0.0968533i	−0.0563325	−	0.0183035i
$29$	1.14814	−	3.53361i	0.213204	−	0.656175i	−0.786072	−	0.618135i	$-0.787889\pi$
$29$	1.14814	−	3.53361i	0.213204	−	0.656175i	0.999276	−	0.0380399i	$-0.0121114\pi$
$30$	−1.01149	+	3.25512i	−0.184672	+	0.594301i
$31$	−1.33250	−	4.10102i	−0.239325	−	0.736566i	−0.996518	−	0.0833750i	$-0.973430\pi$
$31$	−1.33250	−	4.10102i	−0.239325	−	0.736566i	0.757194	−	0.653191i	$-0.226570\pi$
$32$			0.844962i			0.149370i
$33$	−5.63737	+	1.83169i	−0.981340	+	0.318857i
$34$	3.13926	+	2.28081i	0.538379	+	0.391155i
$35$	−2.70319	+	3.82323i	−0.456923	+	0.646244i
$36$	0.232374	−	0.168830i	0.0387290	−	0.0281383i
$37$	−0.118683	+	0.163353i	−0.0195113	+	0.0268550i	−0.818661	−	0.574277i	$-0.805283\pi$
$37$	−0.118683	+	0.163353i	−0.0195113	+	0.0268550i	0.799150	+	0.601132i	$0.205283\pi$
$38$	−0.861798	+	1.18616i	−0.139802	+	0.192421i
$39$	3.15468	−	2.29201i	0.505153	−	0.367015i
$40$	5.79300	+	1.80010i	0.915954	+	0.284621i
$41$	0.194906	+	0.141608i	0.0304392	+	0.0221154i	0.602901	−	0.797816i	$-0.294011\pi$
$41$	0.194906	+	0.141608i	0.0304392	+	0.0221154i	−0.572462	+	0.819932i	$0.694011\pi$
$42$	−3.03587	+	0.986413i	−0.468444	+	0.152207i
$43$			9.59241i			1.46283i	0.681933	+	0.731414i	$0.261139\pi$
$43$			9.59241i			1.46283i	−0.681933	+	0.731414i	$0.738861\pi$
$44$	−0.263691	−	0.811556i	−0.0397529	−	0.122347i
$45$	−1.37846	−	4.06359i	−0.205488	−	0.605765i
$46$	1.50757	−	4.63983i	0.222279	−	0.684105i
$47$	−6.77067	−	2.19992i	−0.987604	−	0.320892i	−0.229702	−	0.973261i	$-0.573775\pi$
$47$	−6.77067	−	2.19992i	−0.987604	−	0.320892i	−0.757902	+	0.652369i	$0.773775\pi$
$48$	2.61375	+	3.59752i	0.377263	+	0.519257i
$49$	2.61513			0.373590
$50$	−4.15479	+	6.03984i	−0.587575	+	0.854162i
$51$	2.75166			0.385309
$52$	0.329958	+	0.454148i	0.0457569	+	0.0629790i
$53$	1.14518	+	0.372093i	0.157303	+	0.0511109i	0.386610	−	0.922243i	$-0.373646\pi$
$53$	1.14518	+	0.372093i	0.157303	+	0.0511109i	−0.229307	+	0.973354i	$0.573646\pi$
$54$	2.31717	−	7.13151i	0.315327	−	0.970476i
$55$	−12.7470	+	0.164202i	−1.71880	+	0.0221410i
$56$	1.75548	+	5.40280i	0.234585	+	0.721979i
$57$			1.03971i			0.137713i
$58$	5.18090	−	1.68338i	0.680285	−	0.221038i
$59$	−11.1086	−	8.07090i	−1.44622	−	1.05074i	−0.986696	−	0.162578i	$-0.948019\pi$
$59$	−11.1086	−	8.07090i	−1.44622	−	1.05074i	−0.459526	−	0.888164i	$-0.651981\pi$
$60$	−0.329533	+	0.111785i	−0.0425425	+	0.0144313i
$61$	1.87481	−	1.36213i	0.240045	−	0.174403i	−0.461258	−	0.887266i	$-0.652602\pi$
$61$	1.87481	−	1.36213i	0.240045	−	0.174403i	0.701304	+	0.712863i	$0.252602\pi$
$62$	3.71613	−	5.11482i	0.471949	−	0.649582i
$63$	2.36197	−	3.25097i	0.297580	−	0.409583i
$64$	5.91799	−	4.29967i	0.739748	−	0.537459i
$65$	7.94182	−	2.69403i	0.985061	−	0.334154i
$66$	−7.03096	−	5.10829i	−0.865451	−	0.628787i
$67$	−6.61137	+	2.14817i	−0.807708	+	0.262440i	−0.683627	−	0.729832i	$-0.739598\pi$
$67$	−6.61137	+	2.14817i	−0.807708	+	0.262440i	−0.124081	+	0.992272i	$0.539598\pi$
$68$			0.396129i			0.0480377i
$69$	−1.06906	−	3.29023i	−0.128700	−	0.396097i
$70$	−6.86458	+	0.0884271i	−0.820474	+	0.0105691i
$71$	3.77186	−	11.6086i	0.447637	−	1.37769i	−0.431929	−	0.901908i	$-0.642167\pi$
$71$	3.77186	−	11.6086i	0.447637	−	1.37769i	0.879566	−	0.475777i	$-0.157833\pi$
$72$	−4.95128	−	1.60877i	−0.583513	−	0.189595i
$73$	−3.72518	−	5.12727i	−0.435999	−	0.600101i	0.533318	−	0.845915i	$-0.320945\pi$
$73$	−3.72518	−	5.12727i	−0.435999	−	0.600101i	−0.969317	+	0.245814i	$0.920945\pi$
$74$	−0.296043			−0.0344144
$75$	0.133909	+	5.19682i	0.0154625	+	0.600077i
$76$	−0.149676			−0.0171691
$77$	−7.01707	−	9.65817i	−0.799669	−	1.10065i
$78$	5.43739	+	1.76672i	0.615663	+	0.200041i
$79$	−3.10913	+	9.56892i	−0.349805	+	1.07659i	0.609156	+	0.793050i	$0.291508\pi$
$79$	−3.10913	+	9.56892i	−0.349805	+	1.07659i	−0.958961	+	0.283538i	$0.908492\pi$
$80$	3.07221	+	9.05666i	0.343483	+	1.01257i
$81$	0.135846	+	0.418092i	0.0150940	+	0.0464546i
$82$			0.353227i			0.0390075i
$83$	8.61217	−	2.79826i	0.945308	−	0.307149i	0.204501	−	0.978866i	$-0.434443\pi$
$83$	8.61217	−	2.79826i	0.945308	−	0.307149i	0.740808	+	0.671717i	$0.234443\pi$
$84$	−0.263634	−	0.191541i	−0.0287648	−	0.0208989i
$85$	5.65135	+	1.75609i	0.612975	+	0.190474i
$86$	−11.3782	+	8.26672i	−1.22694	+	0.891423i
$87$	2.27061	−	3.12522i	0.243435	−	0.335059i
$88$	−9.09100	+	12.5127i	−0.969104	+	1.33386i
$89$	−2.97960	+	2.16480i	−0.315837	+	0.229469i	−0.734397	−	0.678720i	$-0.762535\pi$
$89$	−2.97960	+	2.16480i	−0.315837	+	0.229469i	0.418560	+	0.908189i	$0.362535\pi$
$90$	3.63213	−	5.13707i	0.382860	−	0.541495i
$91$	6.35363	+	4.61618i	0.666042	+	0.483908i
$92$	0.473662	−	0.153902i	0.0493827	−	0.0160454i
$93$		−	4.48330i		−	0.464896i
$94$	−3.22548	−	9.92701i	−0.332683	−	1.02389i
$95$	−0.663533	+	2.13535i	−0.0680771	+	0.219082i
$96$	−0.271476	+	0.835517i	−0.0277074	+	0.0852746i
$97$	3.65745	+	1.18838i	0.371358	+	0.120661i	0.488749	−	0.872424i	$-0.337453\pi$
$97$	3.65745	+	1.18838i	0.371358	+	0.120661i	−0.117392	+	0.993086i	$0.537453\pi$
$98$	2.25371	+	3.10197i	0.227659	+	0.313346i
$99$	10.9405			1.09956
$100$	−0.748134	+	0.0192776i	−0.0748134	+	0.00192776i
$101$	−4.87656			−0.485236			−0.242618	−	0.970122i	$-0.578006\pi$
$101$	−4.87656			−0.485236			−0.242618	+	0.970122i	$0.578006\pi$
$102$	2.37137	+	3.26392i	0.234801	+	0.323176i
$103$	3.85024	+	1.25102i	0.379376	+	0.123267i	0.492496	−	0.870315i	$-0.336085\pi$
$103$	3.85024	+	1.25102i	0.379376	+	0.123267i	−0.113120	+	0.993581i	$0.536085\pi$
$104$	3.14415	−	9.67669i	0.308309	−	0.948877i
$105$	−3.90133	+	2.91199i	−0.380731	+	0.284181i
$106$	0.545554	+	1.67904i	0.0529889	+	0.163083i
$107$		−	15.2213i		−	1.47150i	−0.677252	−	0.735751i	$-0.736829\pi$
$107$		−	15.2213i		−	1.47150i	0.677252	−	0.735751i	$-0.263171\pi$
$108$	0.728029	−	0.236551i	0.0700546	−	0.0227621i
$109$	8.36858	+	6.08013i	0.801564	+	0.582371i	0.911373	−	0.411582i	$-0.135024\pi$
$109$	8.36858	+	6.08013i	0.801564	+	0.582371i	−0.109808	+	0.993953i	$0.535024\pi$
$110$	−11.1801	−	14.9785i	−1.06598	−	1.42814i
$111$	−0.169839	+	0.123395i	−0.0161204	+	0.0117122i
$112$	−5.26418	+	7.24553i	−0.497419	+	0.684638i
$113$	5.74663	−	7.90956i	0.540598	−	0.744069i	−0.448101	−	0.893983i	$-0.647900\pi$
$113$	5.74663	−	7.90956i	0.540598	−	0.744069i	0.988699	+	0.149914i	$0.0478997\pi$
$114$	−1.23326	+	0.896018i	−0.115506	+	0.0839198i
$115$	−0.0958362	−	7.43974i	−0.00893677	−	0.693759i
$116$	0.449908	+	0.326877i	0.0417729	+	0.0303498i
$117$	−6.84493	+	2.22405i	−0.632814	+	0.205614i
$118$		−	20.1321i		−	1.85331i
$119$	1.71255	+	5.27069i	0.156989	+	0.483164i
$120$	5.14989	+	3.64120i	0.470119	+	0.332394i
$121$	6.64466	−	20.4502i	0.604060	−	1.85910i
$122$	3.23142	+	1.04995i	0.292559	+	0.0950582i
$123$	0.147231	+	0.202646i	0.0132753	+	0.0182719i
$124$	0.645416			0.0579600
$125$	−3.04154	+	10.7587i	−0.272044	+	0.962285i
$126$	5.89171			0.524875
$127$	−1.26302	−	1.73840i	−0.112075	−	0.154258i	0.749295	−	0.662237i	$-0.230393\pi$
$127$	−1.26302	−	1.73840i	−0.112075	−	0.154258i	−0.861369	+	0.507979i	$0.830393\pi$
$128$	11.8074	+	3.83647i	1.04364	+	0.339099i
$129$	−3.08192	+	9.48518i	−0.271348	+	0.835124i
$130$	10.0398	+	7.09857i	0.880549	+	0.622586i
$131$	6.74126	+	20.7475i	0.588987	+	1.81271i	0.582634	+	0.812734i	$0.302022\pi$
$131$	6.74126	+	20.7475i	0.588987	+	1.81271i	0.00635226	+	0.999980i	$0.497978\pi$
$132$		−	0.887205i		−	0.0772213i
$133$	−1.99152	+	0.647084i	−0.172687	+	0.0561093i
$134$	−8.24574	−	5.99088i	−0.712323	−	0.517533i
$135$	−0.147302	−	11.4350i	−0.0126778	−	0.984172i
$136$	5.80865	−	4.22023i	0.498087	−	0.361882i
$137$	−10.4279	+	14.3528i	−0.890916	+	1.22624i	0.0823601	+	0.996603i	$0.473754\pi$
$137$	−10.4279	+	14.3528i	−0.890916	+	1.22624i	−0.973276	+	0.229638i	$0.926246\pi$
$138$	2.98144	−	4.10360i	0.253797	−	0.349321i
$139$	8.85263	−	6.43181i	0.750870	−	0.545539i	−0.145226	−	0.989398i	$-0.546391\pi$
$139$	8.85263	−	6.43181i	0.750870	−	0.545539i	0.896097	+	0.443859i	$0.146391\pi$
$140$	−0.419211	−	0.561636i	−0.0354298	−	0.0474669i
$141$	−5.98818	−	4.35067i	−0.504295	−	0.366392i
$142$	17.0202	−	5.53021i	1.42831	−	0.464085i
$143$			21.3818i			1.78804i
$144$	−2.53626	−	7.80579i	−0.211355	−	0.650483i
$145$	6.65787	−	4.96950i	0.552906	−	0.412694i
$146$	2.87142	−	8.83733i	0.237641	−	0.731383i
$147$	2.58590	+	0.840209i	0.213281	+	0.0692993i
$148$	−0.0177640	−	0.0244501i	−0.00146019	−	0.00200978i
$149$	−18.3059			−1.49968			−0.749841	−	0.661619i	$-0.769870\pi$
$149$	−18.3059			−1.49968			−0.749841	+	0.661619i	$0.769870\pi$
$150$	−6.04887	+	4.63744i	−0.493888	+	0.378646i
$151$	12.9194			1.05137			0.525684	−	0.850680i	$-0.323809\pi$
$151$	12.9194			1.05137			0.525684	+	0.850680i	$0.323809\pi$
$152$	1.59460	+	2.19478i	0.129339	+	0.178021i
$153$	−4.83021	−	1.56943i	−0.390499	−	0.126881i
$154$	5.40886	−	16.6468i	0.435859	−	1.34143i
$155$	2.86120	−	9.20779i	0.229817	−	0.739587i
$156$	0.180357	+	0.555082i	0.0144401	+	0.0444422i
$157$			7.77574i			0.620571i	0.950643	+	0.310286i	$0.100425\pi$
$157$			7.77574i			0.620571i	−0.950643	+	0.310286i	$0.899575\pi$
$158$	−14.0297	+	4.55854i	−1.11615	+	0.362658i
$159$	1.01283	+	0.735866i	0.0803229	+	0.0583580i
$160$	−1.09078	+	1.54273i	−0.0862335	+	0.121963i
$161$	5.63696	−	4.09549i	0.444254	−	0.322770i
$162$	−0.378853	+	0.521446i	−0.0297655	+	0.0409687i
$163$	−3.05559	+	4.20566i	−0.239333	+	0.329413i	−0.911740	−	0.410768i	$-0.865260\pi$
$163$	−3.05559	+	4.20566i	−0.239333	+	0.329413i	0.672407	+	0.740182i	$0.265260\pi$
$164$	−0.0291729	+	0.0211953i	−0.00227802	+	0.00165508i
$165$	−12.6573	−	3.93308i	−0.985366	−	0.306190i
$166$	10.7411	+	7.80389i	0.833674	+	0.605700i
$167$	−14.9091	+	4.84427i	−1.15370	+	0.374861i	−0.822537	−	0.568711i	$-0.807442\pi$
$167$	−14.9091	+	4.84427i	−1.15370	+	0.374861i	−0.331167	+	0.943572i	$0.607442\pi$
$168$			5.90642i			0.455690i
$169$	−0.329428	−	1.01388i	−0.0253406	−	0.0779904i
$170$	2.78732	+	8.21682i	0.213777	+	0.630201i
$171$	0.593006	−	1.82508i	0.0453483	−	0.139568i
$172$	−1.36549	−	0.443674i	−0.104117	−	0.0338298i
$173$	0.342764	+	0.471775i	0.0260599	+	0.0358684i	0.821848	−	0.569707i	$-0.192943\pi$
$173$	0.342764	+	0.471775i	0.0260599	+	0.0358684i	−0.795788	+	0.605575i	$0.792943\pi$
$174$	5.66383			0.429374
$175$	−9.87095	+	3.49084i	−0.746174	+	0.263883i
$176$	−24.3833			−1.83796
$177$	−8.39138	−	11.5497i	−0.630735	−	0.868132i
$178$	−5.13562	−	1.66866i	−0.384931	−	0.125072i
$179$	−4.90611	+	15.0994i	−0.366700	+	1.12859i	0.582210	+	0.813038i	$0.302188\pi$
$179$	−4.90611	+	15.0994i	−0.366700	+	1.12859i	−0.948910	+	0.315547i	$0.897812\pi$
$180$	0.642213	−	0.00827277i	0.0478677	−	0.000616616i
$181$	−3.85361	−	11.8602i	−0.286436	−	0.881561i	−0.985964	−	0.166955i	$-0.946606\pi$
$181$	−3.85361	−	11.8602i	−0.286436	−	0.881561i	0.699528	−	0.714605i	$-0.253394\pi$
$182$			11.5147i			0.853523i
$183$	2.29149	−	0.744551i	0.169392	−	0.0550388i
$184$	−7.30299	−	5.30593i	−0.538384	−	0.391159i
$185$	−0.427566	+	0.145039i	−0.0314352	+	0.0106635i
$186$	5.31792	−	3.86369i	0.389929	−	0.283300i
$187$	−8.86871	+	12.2067i	−0.648545	+	0.892645i
$188$	0.626322	−	0.862059i	0.0456792	−	0.0628721i
$189$	8.66413	−	6.29486i	0.630223	−	0.457883i
$190$	−3.10470	+	1.05318i	−0.225239	+	0.0764058i
$191$	5.63440	+	4.09363i	0.407691	+	0.296205i	0.772666	−	0.634812i	$-0.218923\pi$
$191$	5.63440	+	4.09363i	0.407691	+	0.296205i	−0.364975	+	0.931017i	$0.618923\pi$
$192$	7.23326	−	2.35023i	0.522016	−	0.169613i
$193$		−	0.0419440i		−	0.00301920i	−0.999999	−	0.00150960i	$-0.999519\pi$
$193$		−	0.0419440i		−	0.00301920i	0.999999	−	0.00150960i	$-0.000480521\pi$
$194$	1.74237	+	5.36247i	0.125095	+	0.385003i
$195$	8.71860	−	0.112310i	0.624352	−	0.00804268i
$196$	−0.120957	+	0.372266i	−0.00863976	+	0.0265904i
$197$	−11.1902	−	3.63592i	−0.797270	−	0.259049i	−0.118073	−	0.993005i	$-0.537672\pi$
$197$	−11.1902	−	3.63592i	−0.797270	−	0.259049i	−0.679197	+	0.733956i	$0.737672\pi$
$198$	9.42846	+	12.9772i	0.670051	+	0.922246i
$199$	−12.2791			−0.870446			−0.435223	−	0.900323i	$-0.643330\pi$
$199$	−12.2791			−0.870446			−0.435223	+	0.900323i	$0.643330\pi$
$200$	8.25305	+	10.7649i	0.583579	+	0.761194i
$201$	−7.22765			−0.509799
$202$	−4.20261	−	5.78439i	−0.295694	−	0.406988i
$203$	7.39940	+	2.40421i	0.519336	+	0.168743i
$204$	−0.127271	+	0.391701i	−0.00891078	+	0.0274246i
$205$	0.173055	+	0.510154i	0.0120867	+	0.0356307i
$206$	1.83422	+	5.64514i	0.127796	+	0.393315i
$207$			6.38536i			0.443813i
$208$	15.2555	−	4.95681i	1.05778	−	0.343693i
$209$	−4.61229	−	3.35102i	−0.319039	−	0.231795i
$210$	−6.81625	−	2.11806i	−0.470366	−	0.146160i
$211$	−5.74862	+	4.17661i	−0.395751	+	0.287530i	−0.767808	−	0.640680i	$-0.778653\pi$
$211$	−5.74862	+	4.17661i	−0.395751	+	0.287530i	0.372057	+	0.928210i	$0.378653\pi$
$212$	−0.105935	+	0.145808i	−0.00727567	+	0.0100141i
$213$	7.45938	−	10.2670i	0.511109	−	0.703481i
$214$	18.0550	−	13.1177i	1.23421	−	0.896708i
$215$	−12.3830	+	17.5138i	−0.844514	+	1.19443i
$216$	−11.2249	−	8.15534i	−0.763755	−	0.554900i
$217$	8.58758	−	2.79027i	0.582963	−	0.189416i
$218$			15.1663i			1.02719i
$219$	−2.03621	−	6.26680i	−0.137594	−	0.423471i
$220$	0.566207	−	1.82214i	0.0381737	−	0.122849i
$221$	3.06727	−	9.44008i	0.206327	−	0.635008i
$222$	−0.292734	−	0.0951151i	−0.0196470	−	0.00638371i
$223$	6.08093	+	8.36968i	0.407209	+	0.560475i	0.962535	−	0.271158i	$-0.0874064\pi$
$223$	6.08093	+	8.36968i	0.407209	+	0.560475i	−0.555326	+	0.831633i	$0.687406\pi$
$224$	−1.76936			−0.118220
$225$	2.72898	−	9.19877i	0.181932	−	0.613251i
$226$	14.3345			0.953514
$227$	−5.47829	−	7.54022i	−0.363607	−	0.500462i	0.587542	−	0.809193i	$-0.300096\pi$
$227$	−5.47829	−	7.54022i	−0.363607	−	0.500462i	−0.951149	+	0.308732i	$0.900096\pi$
$228$	−0.148003	−	0.0480892i	−0.00980176	−	0.00318478i
$229$	−4.74269	+	14.5965i	−0.313406	+	0.964563i	0.663000	+	0.748619i	$0.269283\pi$
$229$	−4.74269	+	14.5965i	−0.313406	+	0.964563i	−0.976406	+	0.215944i	$0.930717\pi$
$230$	8.74215	−	6.52523i	0.576440	−	0.430261i
$231$	−3.83558	−	11.8047i	−0.252363	−	0.776692i
$232$		−	10.0797i		−	0.661763i
$233$	−9.83863	+	3.19677i	−0.644550	+	0.209427i	−0.613010	−	0.790075i	$-0.710041\pi$
$233$	−9.83863	+	3.19677i	−0.644550	+	0.209427i	−0.0315406	+	0.999502i	$0.510041\pi$
$234$	−8.53703	−	6.20252i	−0.558083	−	0.405471i
$235$	−9.52195	−	12.7570i	−0.621143	−	0.832175i
$236$	1.66270	−	1.20802i	0.108233	−	0.0786357i
$237$	−6.14875	+	8.46303i	−0.399404	+	0.549733i
$238$	−4.77603	+	6.57364i	−0.309584	+	0.426106i
$239$	3.25831	−	2.36730i	0.210763	−	0.153128i	−0.477396	−	0.878688i	$-0.658419\pi$
$239$	3.25831	−	2.36730i	0.210763	−	0.153128i	0.688159	+	0.725560i	$0.258419\pi$
$240$	0.128076	+	9.94248i	0.00826724	+	0.641784i
$241$	11.2719	+	8.18955i	0.726090	+	0.527535i	0.888324	−	0.459217i	$-0.151870\pi$
$241$	11.2719	+	8.18955i	0.726090	+	0.527535i	−0.162234	+	0.986752i	$0.551870\pi$
$242$	29.9836	−	9.74225i	1.92742	−	0.626255i
$243$			15.8001i			1.01357i
$244$	0.107186	+	0.329884i	0.00686186	+	0.0211186i
$245$	4.77470	+	3.37592i	0.305044	+	0.215680i
$246$	−0.113488	+	0.349279i	−0.00723570	+	0.0222692i
$247$	3.56691	+	1.15896i	0.226957	+	0.0737429i
$248$	−6.87605	−	9.46407i	−0.436629	−	0.600969i
$249$	9.41494			0.596648
$250$	−15.3827	+	5.66403i	−0.972889	+	0.358225i
$251$	9.33869			0.589453			0.294726	−	0.955582i	$-0.404772\pi$
$251$	9.33869			0.589453			0.294726	+	0.955582i	$0.404772\pi$
$252$	0.353531	+	0.486593i	0.0222703	+	0.0306525i
$253$	18.0416	+	5.86206i	1.13426	+	0.368544i
$254$	0.973554	−	2.99629i	0.0610862	−	0.188004i
$255$	5.02397	+	3.55217i	0.314613	+	0.222445i
$256$	1.10400	+	3.39776i	0.0690000	+	0.212360i
$257$			11.0373i			0.688485i	0.938881	+	0.344243i	$0.111864\pi$
$257$			11.0373i			0.688485i	−0.938881	+	0.344243i	$0.888136\pi$
$258$	−13.9070	+	4.51864i	−0.865809	+	0.281319i
$259$	−0.342062	−	0.248523i	−0.0212547	−	0.0154424i
$260$	0.0161682	+	1.25513i	0.00100271	+	0.0778399i
$261$	−5.76828	+	4.19090i	−0.357048	+	0.259410i
$262$	−18.8003	+	25.8763i	−1.16148	+	1.59865i
$263$	−14.2559	+	19.6215i	−0.879054	+	1.20991i	0.0976277	+	0.995223i	$0.468875\pi$
$263$	−14.2559	+	19.6215i	−0.879054	+	1.20991i	−0.976682	+	0.214691i	$0.931125\pi$
$264$	−13.0095	+	9.45199i	−0.800682	+	0.581730i
$265$	1.61053	+	2.15770i	0.0989341	+	0.132547i
$266$	−2.48383	−	1.80461i	−0.152294	−	0.110648i
$267$	−3.64181	+	1.18330i	−0.222875	+	0.0724166i
$268$		−	1.04049i		−	0.0635582i
$269$	6.36609	+	19.5928i	0.388148	+	1.19460i	0.934171	+	0.356825i	$0.116141\pi$
$269$	6.36609	+	19.5928i	0.388148	+	1.19460i	−0.546024	+	0.837770i	$0.683859\pi$
$270$	13.4369	−	10.0294i	0.817742	−	0.610371i
$271$	6.07429	−	18.6947i	0.368987	−	1.13562i	−0.578460	−	0.815711i	$-0.696346\pi$
$271$	6.07429	−	18.6947i	0.368987	−	1.13562i	0.947447	−	0.319914i	$-0.103654\pi$
$272$	10.7652	+	3.49784i	0.652739	+	0.212088i
$273$	4.79948	+	6.60592i	0.290478	+	0.399809i
$274$	−26.0115			−1.57141
$275$	−23.4854	−	16.1555i	−1.41622	−	0.974214i
$276$	0.517814			0.0311687
$277$	−1.65856	−	2.28281i	−0.0996532	−	0.137161i	0.756278	−	0.654250i	$-0.227016\pi$
$277$	−1.65856	−	2.28281i	−0.0996532	−	0.137161i	−0.855932	+	0.517089i	$0.827016\pi$
$278$	15.2584	+	4.95774i	0.915135	+	0.297345i
$279$	−2.55708	+	7.86989i	−0.153089	+	0.471158i
$280$	−3.76943	+	12.1306i	−0.225266	+	0.724941i
$281$	5.05754	+	15.5655i	0.301707	+	0.928560i	0.980885	+	0.194586i	$0.0623364\pi$
$281$	5.05754	+	15.5655i	0.301707	+	0.928560i	−0.679178	+	0.733974i	$0.737664\pi$
$282$		−	10.8523i		−	0.646248i
$283$	−21.2251	+	6.89647i	−1.26170	+	0.409952i	−0.862101	−	0.506736i	$-0.830852\pi$
$283$	−21.2251	+	6.89647i	−1.26170	+	0.409952i	−0.399603	+	0.916688i	$0.630852\pi$
$284$	1.47803	+	1.07385i	0.0877051	+	0.0637215i
$285$	−1.34218	+	1.89830i	−0.0795037	+	0.112445i
$286$	−25.3623	+	18.4268i	−1.49971	+	1.08960i
$287$	−0.296527	+	0.408135i	−0.0175035	+	0.0240914i
$288$	0.953087	−	1.31181i	0.0561612	−	0.0772993i
$289$	−8.08667	+	5.87531i	−0.475686	+	0.345606i
$290$	11.6324	+	3.61461i	0.683076	+	0.212257i
$291$	3.23475	+	2.35019i	0.189625	+	0.137770i
$292$	0.902170	−	0.293133i	0.0527955	−	0.0171543i
$293$			9.93267i			0.580273i	0.956985	+	0.290136i	$0.0937007\pi$
$293$			9.93267i			0.580273i	−0.956985	+	0.290136i	$0.906299\pi$
$294$	1.23190	+	3.79139i	0.0718456	+	0.221118i
$295$	−9.86325	−	29.0762i	−0.574261	−	1.69288i
$296$	−0.169272	+	0.520966i	−0.00983874	+	0.0302805i
$297$	27.7303	+	9.01011i	1.60907	+	0.522820i
$298$	−15.7760	−	21.7138i	−0.913880	−	1.25785i
$299$	−12.4794			−0.721704
$300$	−0.745965	−	0.221304i	−0.0430683	−	0.0127770i
$301$	−20.0866			−1.15777
$302$	11.1339	+	15.3246i	0.640686	+	0.881829i
$303$	−4.82205	−	1.56678i	−0.277019	−	0.0900090i
$304$	−1.32165	+	4.06762i	−0.0758018	+	0.233294i
$305$	5.18143	−	0.0667454i	0.296688	−	0.00382183i
$306$	−2.30106	−	7.08195i	−0.131543	−	0.404848i
$307$			24.9200i			1.42226i	0.703060	+	0.711130i	$0.251816\pi$
$307$			24.9200i			1.42226i	−0.703060	+	0.711130i	$0.748184\pi$
$308$	1.69941	−	0.552170i	0.0968326	−	0.0314628i
$309$	3.40526	+	2.47407i	0.193719	+	0.140745i
$310$	13.3877	−	4.54139i	0.760371	−	0.257934i
$311$	28.2750	−	20.5430i	1.60333	−	1.16489i	0.722603	−	0.691263i	$-0.242945\pi$
$311$	28.2750	−	20.5430i	1.60333	−	1.16489i	0.880727	−	0.473624i	$-0.157055\pi$
$312$	6.21800	−	8.55834i	0.352025	−	0.484521i
$313$	17.8041	−	24.5052i	1.00635	−	1.38512i	0.0849971	−	0.996381i	$-0.472912\pi$
$313$	17.8041	−	24.5052i	1.00635	−	1.38512i	0.921349	−	0.388736i	$-0.127088\pi$
$314$	−9.22329	+	6.70111i	−0.520500	+	0.378166i
$315$	8.50920	−	2.88650i	0.479439	−	0.162636i
$316$	−1.21834	−	0.885175i	−0.0685369	−	0.0497950i
$317$	29.7930	−	9.68033i	1.67334	−	0.543701i	0.689740	−	0.724058i	$-0.257725\pi$
$317$	29.7930	−	9.68033i	1.67334	−	0.543701i	0.983601	+	0.180356i	$0.0577250\pi$
$318$			1.83555i			0.102933i
$319$	6.54566	+	20.1455i	0.366486	+	1.12793i
$320$	16.3556	−	0.210687i	0.914304	−	0.0117777i
$321$	4.89043	−	15.0512i	0.272957	−	0.840075i
$322$	9.71583	+	3.15687i	0.541442	+	0.175925i
$323$	1.55561	+	2.14112i	0.0865567	+	0.119135i
$324$	−0.0657989			−0.00365549
$325$	17.9779	+	5.33348i	0.997235	+	0.295848i
$326$	−7.62190			−0.422138
$327$	6.32156	+	8.70088i	0.349583	+	0.481160i
$328$	0.621596	+	0.201969i	0.0343219	+	0.0111519i
$329$	4.60666	−	14.1778i	0.253973	−	0.781650i
$330$	−6.24271	−	18.4031i	−0.343650	−	1.01306i
$331$	0.313173	+	0.963847i	0.0172135	+	0.0529778i	0.959294	−	0.282408i	$-0.0911333\pi$
$331$	0.313173	+	0.963847i	0.0172135	+	0.0529778i	−0.942081	+	0.335386i	$0.891133\pi$
$332$			1.35538i			0.0743859i
$333$	0.368512	−	0.119737i	0.0201943	−	0.00656154i
$334$	−18.5948	−	13.5099i	−1.01746	−	0.739228i
$335$	−14.8441	−	4.61263i	−0.811021	−	0.252015i
$336$	−7.53324	+	5.47322i	−0.410972	+	0.298588i
$337$	4.90226	−	6.74738i	0.267043	−	0.367553i	−0.654346	−	0.756196i	$-0.727056\pi$
$337$	4.90226	−	6.74738i	0.267043	−	0.367553i	0.921389	+	0.388642i	$0.127056\pi$
$338$	0.918721	−	1.26451i	0.0499718	−	0.0687803i
$339$	8.22363	−	5.97482i	0.446647	−	0.324508i
$340$	−0.511370	+	0.723251i	−0.0277329	+	0.0392238i
$341$	19.8885	+	14.4499i	1.07702	+	0.782503i
$342$	2.67590	−	0.869452i	0.144696	−	0.0470146i
$343$			20.1342i			1.08714i
$344$	8.04164	+	24.7496i	0.433576	+	1.33441i
$345$	2.29553	−	7.38736i	0.123587	−	0.397722i
$346$	−0.264208	+	0.813149i	−0.0142039	+	0.0437151i
$347$	−10.0795	−	3.27504i	−0.541097	−	0.175813i	0.0257011	−	0.999670i	$-0.491818\pi$
$347$	−10.0795	−	3.27504i	−0.541097	−	0.175813i	−0.566798	+	0.823856i	$0.691818\pi$
$348$	0.339857	+	0.467773i	0.0182182	+	0.0250752i
$349$	34.7378			1.85947			0.929735	−	0.368229i	$-0.120036\pi$
$349$	34.7378			1.85947			0.929735	+	0.368229i	$0.120036\pi$
$350$	−12.6475	−	8.70015i	−0.676036	−	0.465043i
$351$	−19.1812			−1.02381
$352$	−2.83149	−	3.89721i	−0.150919	−	0.207722i
$353$	−28.0030	−	9.09871i	−1.49045	−	0.484276i	−0.553232	−	0.833027i	$-0.686606\pi$
$353$	−28.0030	−	9.09871i	−1.49045	−	0.484276i	−0.937215	+	0.348752i	$0.886606\pi$
$354$	6.46821	−	19.9071i	0.343781	−	1.05805i
$355$	21.8724	−	16.3257i	1.16086	−	0.866481i
$356$	−0.170347	−	0.524276i	−0.00902840	−	0.0277866i
$357$			5.76200i			0.304957i
$358$	−22.1385	+	7.19322i	−1.17005	+	0.380174i
$359$	18.4009	+	13.3690i	0.971160	+	0.705589i	0.955716	−	0.294292i	$-0.0950838\pi$
$359$	18.4009	+	13.3690i	0.971160	+	0.705589i	0.0154442	+	0.999881i	$0.495084\pi$
$360$	−6.96323	−	9.32897i	−0.366995	−	0.491680i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	10.7471	−	14.7921i	0.564854	−	0.777455i
$363$	13.1408	−	18.0867i	0.689711	−	0.949305i
$364$	−0.950989	+	0.690934i	−0.0498454	+	0.0362148i
$365$	−0.182536	−	14.1702i	−0.00955438	−	0.741704i
$366$	2.85796	+	2.07643i	0.149388	+	0.108537i
$367$	26.2911	−	8.54249i	1.37238	−	0.445914i	0.472225	−	0.881478i	$-0.343451\pi$
$367$	26.2911	−	8.54249i	1.37238	−	0.445914i	0.900158	+	0.435564i	$0.143451\pi$
$368$		−	14.2312i		−	0.741855i
$369$	−0.142865	−	0.439694i	−0.00743727	−	0.0228896i
$370$	−0.540515	−	0.382168i	−0.0281000	−	0.0198680i
$371$	−0.779165	+	2.39802i	−0.0404522	+	0.124499i
$372$	0.638201	+	0.207364i	0.0330892	+	0.0107513i
$373$	−22.3140	−	30.7126i	−1.15537	−	1.59024i	−0.727006	−	0.686631i	$-0.759089\pi$
$373$	−22.3140	−	30.7126i	−1.15537	−	1.59024i	−0.428368	−	0.903605i	$-0.640911\pi$
$374$	−22.1222			−1.14391
$375$	−6.46417	+	9.66119i	−0.333808	+	0.498902i
$376$	−19.3134			−0.996015
$377$	−8.19062	−	11.2734i	−0.421839	−	0.580611i
$378$	14.9334	+	4.85217i	0.768094	+	0.249569i
$379$	−9.47232	+	29.1528i	−0.486560	+	1.49748i	0.343148	+	0.939281i	$0.388507\pi$
$379$	−9.47232	+	29.1528i	−0.486560	+	1.49748i	−0.829708	+	0.558197i	$0.811493\pi$
$380$	−0.273279	−	0.193220i	−0.0140189	−	0.00991198i
$381$	−0.690375	−	2.12476i	−0.0353690	−	0.108855i
$382$			10.2112i			0.522450i
$383$	−13.3703	+	4.34427i	−0.683189	+	0.221982i	−0.629991	−	0.776602i	$-0.716941\pi$
$383$	−13.3703	+	4.34427i	−0.683189	+	0.221982i	−0.0531980	+	0.998584i	$0.516941\pi$
$384$	10.4428	+	7.58716i	0.532908	+	0.387181i
$385$	−0.343841	−	26.6923i	−0.0175238	−	1.36037i
$386$	0.0497525	−	0.0361473i	0.00253233	−	0.00183985i
$387$	10.8199	−	14.8923i	0.550006	−	0.757018i
$388$	−0.338333	+	0.465675i	−0.0171763	+	0.0236411i
$389$	−26.4005	+	19.1811i	−1.33856	+	0.972519i	−0.339062	+	0.940764i	$0.610110\pi$
$389$	−26.4005	+	19.1811i	−1.33856	+	0.972519i	−0.999496	+	0.0317548i	$0.989890\pi$
$390$	7.64688	+	10.2449i	0.387215	+	0.518770i
$391$	−7.12442	−	5.17620i	−0.360298	−	0.261771i
$392$	6.74736	−	2.19235i	0.340793	−	0.110730i
$393$			22.6814i			1.14413i
$394$	−5.33091	−	16.4068i	−0.268567	−	0.826565i
$395$	−18.0293	+	13.4573i	−0.907154	+	0.677109i
$396$	−0.506024	+	1.55738i	−0.0254287	+	0.0782614i
$397$	−27.0585	−	8.79185i	−1.35803	−	0.441250i	−0.462644	−	0.886544i	$-0.653099\pi$
$397$	−27.0585	−	8.79185i	−1.35803	−	0.441250i	−0.895385	+	0.445294i	$0.853099\pi$
$398$	−10.5821	−	14.5651i	−0.530435	−	0.730081i
$399$	−2.17716			−0.108994
$400$	−6.08217	+	20.5016i	−0.304108	+	1.02508i
$401$	24.3439			1.21568			0.607839	−	0.794061i	$-0.292037\pi$
$401$	24.3439			1.21568			0.607839	+	0.794061i	$0.292037\pi$
$402$	−6.22877	−	8.57316i	−0.310663	−	0.427591i
$403$	−15.3808	−	4.99752i	−0.766171	−	0.248944i
$404$	0.225553	−	0.694182i	0.0112217	−	0.0345368i
$405$	−0.291694	+	0.938716i	−0.0144944	+	0.0466452i
$406$	3.52500	+	10.8488i	0.174943	+	0.538419i
$407$		−	1.15114i		−	0.0570598i
$408$	7.09962	−	2.30681i	0.351484	−	0.114204i
$409$	9.27135	+	6.73603i	0.458439	+	0.333075i	0.792919	−	0.609328i	$-0.208561\pi$
$409$	9.27135	+	6.73603i	0.458439	+	0.333075i	−0.334480	+	0.942403i	$0.608561\pi$
$410$	−0.455988	+	0.644921i	−0.0225196	+	0.0318504i
$411$	−14.9227	+	10.8420i	−0.736083	+	0.534795i
$412$	−0.356167	+	0.490222i	−0.0175471	+	0.0241515i
$413$	16.9005	−	23.2616i	0.831621	−	1.14463i
$414$	−7.57407	+	5.50289i	−0.372245	+	0.270452i
$415$	19.3364	+	6.00854i	0.949186	+	0.294948i
$416$	2.56378	+	1.86270i	0.125700	+	0.0913262i
$417$	10.8201	−	3.51567i	0.529864	−	0.172163i
$418$		−	8.35883i		−	0.408844i
$419$	−2.22991	−	6.86294i	−0.108938	−	0.335277i	0.881697	−	0.471817i	$-0.156402\pi$
$419$	−2.22991	−	6.86294i	−0.108938	−	0.335277i	−0.990635	+	0.136540i	$0.956402\pi$
$420$	−0.234078	−	0.690045i	−0.0114218	−	0.0336707i
$421$	6.73237	−	20.7201i	0.328116	−	1.00984i	−0.641899	−	0.766789i	$-0.721853\pi$
$421$	6.73237	−	20.7201i	0.328116	−	1.00984i	0.970015	−	0.243047i	$-0.0781469\pi$
$422$	−9.90829	−	3.21940i	−0.482328	−	0.156718i
$423$	8.03010	+	11.0525i	0.390437	+	0.537390i
$424$	3.26665			0.158643
$425$	8.05126	+	10.5017i	0.390543	+	0.509407i
$426$	18.6068			0.901501
$427$	2.85232	+	3.92588i	0.138033	+	0.189986i
$428$	2.16677	+	0.704026i	0.104735	+	0.0340304i
$429$	−6.86972	+	21.1428i	−0.331673	+	1.02078i
$430$	−31.4458	+	0.405075i	−1.51645	+	0.0195344i
$431$	10.9090	+	33.5744i	0.525468	+	1.61722i	0.763389	+	0.645939i	$0.223534\pi$
$431$	10.9090	+	33.5744i	0.525468	+	1.61722i	−0.237921	+	0.971284i	$0.576466\pi$
$432$		−	21.8737i		−	1.05240i
$433$	30.3817	−	9.87160i	1.46005	−	0.474399i	0.531965	−	0.846767i	$-0.321454\pi$
$433$	30.3817	−	9.87160i	1.46005	−	0.474399i	0.928085	+	0.372368i	$0.121454\pi$
$434$	10.7105	+	7.78161i	0.514119	+	0.373529i
$435$	8.18008	−	2.77486i	0.392205	−	0.133044i
$436$	−1.25258	+	0.910052i	−0.0599877	+	0.0435836i
$437$	1.95581	−	2.69195i	0.0935593	−	0.128773i
$438$	5.67865	−	7.81599i	0.271336	−	0.373462i
$439$	31.6545	−	22.9983i	1.51079	−	1.09765i	0.544961	−	0.838461i	$-0.316544\pi$
$439$	31.6545	−	22.9983i	1.51079	−	1.09765i	0.965826	−	0.259190i	$-0.0834556\pi$
$440$	−32.7512	+	11.1099i	−1.56135	+	0.529643i
$441$	−4.06002	−	2.94977i	−0.193334	−	0.140465i
$442$	13.8408	−	4.49716i	0.658341	−	0.213908i
$443$		−	31.4698i		−	1.49518i	−0.664163	−	0.747588i	$-0.731212\pi$
$443$		−	31.4698i		−	1.49518i	0.664163	−	0.747588i	$-0.268788\pi$
$444$	−0.00970994	−	0.0298841i	−0.000460813	−	0.00141824i
$445$	−8.23472	+	0.106077i	−0.390363	+	0.00502852i
$446$	−4.68727	+	14.4259i	−0.221949	+	0.683088i
$447$	−18.1013	−	5.88147i	−0.856162	−	0.278184i
$448$	9.00354	+	12.3923i	0.425377	+	0.585482i
$449$	−18.5805			−0.876867			−0.438433	−	0.898764i	$-0.644466\pi$
$449$	−18.5805			−0.876867			−0.438433	+	0.898764i	$0.644466\pi$
$450$	13.2631	−	4.69046i	0.625227	−	0.221110i
$451$	−1.37349			−0.0646753
$452$	0.860136	+	1.18388i	0.0404574	+	0.0556848i
$453$	12.7750	+	4.15085i	0.600223	+	0.195024i
$454$	4.22275	−	12.9963i	0.198183	−	0.609946i
$455$	5.64132	+	16.6302i	0.264469	+	0.779637i
$456$	0.871622	+	2.68258i	0.0408174	+	0.125623i
$457$			12.0466i			0.563514i	0.959486	+	0.281757i	$0.0909172\pi$
$457$			12.0466i			0.563514i	−0.959486	+	0.281757i	$0.909083\pi$
$458$	−21.4010	+	6.95362i	−1.00000	+	0.324921i
$459$	−10.9504	−	7.95593i	−0.511121	−	0.371351i
$460$	1.06349	+	0.330465i	0.0495853	+	0.0154080i
$461$	17.0663	−	12.3994i	0.794858	−	0.577498i	−0.114543	−	0.993418i	$-0.536540\pi$
$461$	17.0663	−	12.3994i	0.794858	−	0.577498i	0.909401	+	0.415920i	$0.136540\pi$
$462$	10.6968	−	14.7229i	0.497660	−	0.684970i
$463$	−14.3431	+	19.7416i	−0.666581	+	0.917470i	−0.999677	−	0.0254227i	$-0.991907\pi$
$463$	−14.3431	+	19.7416i	−0.666581	+	0.917470i	0.333096	+	0.942893i	$0.391907\pi$
$464$	12.8559	−	9.34039i	0.596822	−	0.433617i
$465$	5.78757	−	8.18559i	0.268392	−	0.379597i
$466$	−12.2708	−	8.91525i	−0.568433	−	0.412991i
$467$	−17.8706	+	5.80652i	−0.826954	+	0.268694i	−0.691762	−	0.722126i	$-0.743165\pi$
$467$	−17.8706	+	5.80652i	−0.826954	+	0.268694i	−0.135192	+	0.990819i	$0.543165\pi$
$468$		−	1.07725i		−	0.0497959i
$469$	−4.49828	−	13.8443i	−0.207711	−	0.639269i
$470$	6.92588	−	22.2885i	0.319467	−	1.02809i
$471$	−2.49825	+	7.68881i	−0.115113	+	0.354282i
$472$	−35.4278	−	11.5112i	−1.63070	−	0.529845i
$473$	−32.1444	−	44.2430i	−1.47800	−	2.03429i
$474$	−15.3375			−0.704475
$475$	−3.96804	+	3.04215i	−0.182066	+	0.139583i
$476$	−0.829498			−0.0380200
$477$	−1.35820	−	1.86940i	−0.0621877	−	0.0855941i
$478$	5.61601	+	1.82475i	0.256870	+	0.0834622i
$479$	8.29318	−	25.5238i	0.378925	−	1.16621i	−0.561867	−	0.827227i	$-0.689917\pi$
$479$	8.29318	−	25.5238i	0.378925	−	1.16621i	0.940792	−	0.338984i	$-0.110083\pi$
$480$	−1.57424	+	1.17503i	−0.0718540	+	0.0536326i
$481$	0.234012	+	0.720214i	0.0106700	+	0.0328389i
$482$			20.4281i			0.930474i
$483$	6.88977	−	2.23862i	0.313496	−	0.101861i
$484$	2.60376	+	1.89174i	0.118353	+	0.0859884i
$485$	5.14366	+	6.89120i	0.233562	+	0.312913i
$486$	−18.7414	+	13.6165i	−0.850129	+	0.617655i
$487$	−2.51876	+	3.46677i	−0.114136	+	0.157095i	−0.862263	−	0.506461i	$-0.830953\pi$
$487$	−2.51876	+	3.46677i	−0.114136	+	0.157095i	0.748127	+	0.663556i	$0.230953\pi$
$488$	3.69533	−	5.08619i	0.167280	−	0.230241i
$489$	−4.37266	+	3.17693i	−0.197739	+	0.143666i
$490$	0.110433	+	8.57293i	0.00498888	+	0.387285i
$491$	−15.4105	−	11.1964i	−0.695464	−	0.505284i	0.182988	−	0.983115i	$-0.441423\pi$
$491$	−15.4105	−	11.1964i	−0.695464	−	0.505284i	−0.878452	+	0.477831i	$0.841423\pi$
$492$	−0.0356566	+	0.0115855i	−0.00160752	+	0.000522315i
$493$		−	9.83321i		−	0.442866i
$494$	1.69924	+	5.22973i	0.0764525	+	0.235297i
$495$	19.9750	+	14.1232i	0.897811	+	0.634792i
$496$	5.69905	−	17.5399i	0.255895	−	0.787564i
$497$	24.3085	+	7.89830i	1.09038	+	0.354287i
$498$	8.11377	+	11.1677i	0.363587	+	0.500434i
$499$	16.7151			0.748269			0.374135	−	0.927374i	$-0.377940\pi$
$499$	16.7151			0.748269			0.374135	+	0.927374i	$0.377940\pi$
$500$	−1.39083	−	0.930583i	−0.0621996	−	0.0416169i
$501$	−16.2989			−0.728180
$502$	8.04806	+	11.0772i	0.359202	+	0.494400i
$503$	−31.5842	−	10.2623i	−1.40827	−	0.457575i	−0.496416	−	0.868085i	$-0.665351\pi$
$503$	−31.5842	−	10.2623i	−1.40827	−	0.457575i	−0.911856	+	0.410510i	$0.865351\pi$
$504$	3.36877	−	10.3680i	0.150057	−	0.461828i
$505$	−8.90360	−	6.29524i	−0.396205	−	0.280134i
$506$	8.59481	+	26.4521i	0.382086	+	1.17594i
$507$		−	1.10838i		−	0.0492250i
$508$	0.305880	−	0.0993864i	0.0135712	−	0.00440956i
$509$	10.4238	+	7.57336i	0.462029	+	0.335683i	0.794327	−	0.607491i	$-0.207824\pi$
$509$	10.4238	+	7.57336i	0.462029	+	0.335683i	−0.332298	+	0.943174i	$0.607824\pi$
$510$	0.116199	+	9.02049i	0.00514537	+	0.399434i
$511$	10.7365	−	7.80055i	0.474956	−	0.345076i
$512$	11.5159	−	15.8503i	0.508936	−	0.700490i
$513$	3.00613	−	4.13758i	0.132724	−	0.182679i
$514$	−13.0920	+	9.51188i	−0.577462	+	0.419551i
$515$	5.41479	+	7.25445i	0.238604	+	0.319669i
$516$	−1.20768	−	0.877428i	−0.0531650	−	0.0386266i
$517$	38.6003	−	12.5420i	1.69764	−	0.551596i
$518$		−	0.619917i		−	0.0272376i
$519$	0.187357	+	0.576627i	0.00822408	+	0.0253111i
$520$	18.2324	−	13.6088i	0.799542	−	0.596786i
$521$	−8.18506	+	25.1910i	−0.358594	+	1.10364i	0.595302	+	0.803502i	$0.297032\pi$
$521$	−8.18506	+	25.1910i	−0.358594	+	1.10364i	−0.953896	+	0.300137i	$0.902968\pi$
$522$	−9.94218	−	3.23041i	−0.435157	−	0.141391i
$523$	4.15785	+	5.72279i	0.181810	+	0.250240i	0.890188	−	0.455593i	$-0.150573\pi$
$523$	4.15785	+	5.72279i	0.181810	+	0.250240i	−0.708378	+	0.705833i	$0.750573\pi$
$524$	−3.26522			−0.142642
$525$	−10.8822	+	0.280407i	−0.474937	+	0.0122380i
$526$	−35.5600			−1.55049
$527$	−6.70792	−	9.23266i	−0.292202	−	0.402181i
$528$	−24.1108	−	7.83406i	−1.04929	−	0.340934i
$529$	3.68602	−	11.3444i	0.160262	−	0.493235i
$530$	−1.17144	+	3.76985i	−0.0508839	+	0.163752i
$531$	8.14258	+	25.0603i	0.353358	+	1.08752i
$532$		−	0.313424i		−	0.0135886i
$533$	0.859331	−	0.279214i	0.0372217	−	0.0120941i
$534$	−4.54209	−	3.30002i	−0.196555	−	0.142806i
$535$	19.6495	−	27.7911i	0.849522	−	1.20151i
$536$	−15.2573	+	11.0851i	−0.659014	+	0.478802i
$537$	−9.70253	+	13.3544i	−0.418695	+	0.576284i
$538$	−17.7540	+	24.4363i	−0.765429	+	1.05352i
$539$	−12.0617	+	8.76337i	−0.519536	+	0.377465i
$540$	1.63460	+	0.507932i	0.0703420	+	0.0218579i
$541$	7.09415	+	5.15420i	0.305001	+	0.221597i	0.729749	−	0.683715i	$-0.239637\pi$
$541$	7.09415	+	5.15420i	0.305001	+	0.221597i	−0.424747	+	0.905312i	$0.639637\pi$
$542$	27.4098	−	8.90598i	1.17735	−	0.382545i
$543$		−	12.9657i		−	0.556412i
$544$	0.691040	+	2.12680i	0.0296281	+	0.0911859i
$545$	7.43037	+	21.9042i	0.318282	+	0.938274i
$546$	−3.69951	+	11.3859i	−0.158325	+	0.487273i
$547$	−19.7700	−	6.42367i	−0.845306	−	0.274656i	−0.145827	−	0.989310i	$-0.546584\pi$
$547$	−19.7700	−	6.42367i	−0.845306	−	0.274656i	−0.699479	+	0.714654i	$0.746584\pi$
$548$	−1.56081	−	2.14827i	−0.0666746	−	0.0917697i
$549$	−4.44710			−0.189798
$550$	−1.07658	−	41.7803i	−0.0459054	−	1.78152i
$551$	3.71546			0.158284
$552$	−5.51662	−	7.59298i	−0.234803	−	0.323179i
$553$	−20.0374	−	6.51054i	−0.852077	−	0.276857i
$554$	1.27844	−	3.93464i	0.0543159	−	0.167167i
$555$	−0.469385	+	0.00604646i	−0.0199243	+	0.000256658i
$556$	0.506117	+	1.55767i	0.0214641	+	0.0660598i
$557$			19.2118i			0.814030i	0.913421	+	0.407015i	$0.133430\pi$
$557$			19.2118i			0.814030i	−0.913421	+	0.407015i	$0.866570\pi$
$558$	−11.5387	+	3.74914i	−0.488470	+	0.158714i
$559$	29.1053	+	21.1462i	1.23102	+	0.894389i
$560$	−18.9647	+	6.43323i	−0.801405	+	0.271854i
$561$	−12.6914	+	9.22088i	−0.535833	+	0.389306i
$562$	−14.1046	+	19.4134i	−0.594968	+	0.818904i
$563$	23.3727	−	32.1698i	0.985044	−	1.35580i	0.0509763	−	0.998700i	$-0.483767\pi$
$563$	23.3727	−	32.1698i	0.985044	−	1.35580i	0.934067	−	0.357097i	$-0.116233\pi$
$564$	0.896289	−	0.651192i	0.0377406	−	0.0274201i
$565$	20.7028	−	7.02282i	0.870972	−	0.295452i
$566$	−26.4721	−	19.2331i	−1.11271	−	0.808428i
$567$	−0.875487	+	0.284463i	−0.0367670	+	0.0119463i
$568$		−	33.1136i		−	1.38942i
$569$	−11.5931	−	35.6798i	−0.486007	−	1.49578i	−0.830516	−	0.556994i	$-0.811955\pi$
$569$	−11.5931	−	35.6798i	−0.486007	−	1.49578i	0.344509	−	0.938783i	$-0.388045\pi$
$570$	−3.40837	+	0.0439055i	−0.142761	+	0.00183900i
$571$	12.0639	−	37.1290i	0.504860	−	1.55380i	−0.296146	−	0.955143i	$-0.595702\pi$
$571$	12.0639	−	37.1290i	0.504860	−	1.55380i	0.801006	−	0.598656i	$-0.204298\pi$
$572$	−3.04372	−	0.988965i	−0.127264	−	0.0413507i
$573$	4.25618	+	5.85813i	0.177805	+	0.244727i
$574$	−0.739661			−0.0308729
$575$	9.42911	−	13.7072i	0.393221	−	0.571628i
$576$	−14.0376			−0.584900
$577$	−8.29410	−	11.4159i	−0.345288	−	0.475248i	0.600689	−	0.799483i	$-0.294893\pi$
$577$	−8.29410	−	11.4159i	−0.345288	−	0.475248i	−0.945977	+	0.324235i	$0.894893\pi$
$578$	−13.9381	−	4.52878i	−0.579750	−	0.188372i
$579$	0.0134761	−	0.0414752i	0.000560047	−	0.00172365i
$580$	0.399468	+	1.17760i	0.0165870	+	0.0488974i
$581$	5.85958	+	18.0339i	0.243097	+	0.748174i
$582$			5.86233i			0.243001i
$583$	−6.52881	+	2.12134i	−0.270396	+	0.0878569i
$584$	−13.9098	−	10.1060i	−0.575591	−	0.418191i
$585$	−15.3685	−	4.77557i	−0.635410	−	0.197446i
$586$	−11.7818	+	8.55995i	−0.486700	+	0.353608i
$587$	−2.34922	+	3.23343i	−0.0969629	+	0.133458i	−0.854742	−	0.519053i	$-0.826285\pi$
$587$	−2.34922	+	3.23343i	−0.0969629	+	0.133458i	0.757779	+	0.652511i	$0.226285\pi$
$588$	−0.239209	+	0.329243i	−0.00986481	+	0.0135777i
$589$	3.48854	−	2.53457i	0.143743	−	0.104435i
$590$	25.9889	−	36.7572i	1.06995	−	1.51327i
$591$	−9.89695	−	7.19055i	−0.407106	−	0.295780i
$592$	−0.821314	+	0.266861i	−0.0337558	+	0.0109679i
$593$		−	28.7485i		−	1.18056i	−0.807198	−	0.590281i	$-0.799017\pi$
$593$		−	28.7485i		−	1.18056i	0.807198	−	0.590281i	$-0.200983\pi$
$594$	13.2104	+	40.6575i	0.542030	+	1.66820i
$595$	−3.67726	+	11.8340i	−0.150753	+	0.485146i
$596$	0.846697	−	2.60587i	0.0346821	−	0.106740i
$597$	−12.1419	−	3.94514i	−0.496934	−	0.161464i
$598$	−10.7547	−	14.8026i	−0.439794	−	0.605325i
$599$	15.4594			0.631655			0.315827	−	0.948817i	$-0.397718\pi$
$599$	15.4594			0.631655			0.315827	+	0.948817i	$0.397718\pi$
$600$	4.70217	+	13.2962i	0.191965	+	0.542814i
$601$	−18.2512			−0.744482			−0.372241	−	0.928136i	$-0.621410\pi$
$601$	−18.2512			−0.744482			−0.372241	+	0.928136i	$0.621410\pi$
$602$	−17.3106	−	23.8260i	−0.705526	−	0.971073i
$603$	12.6873	+	4.12234i	0.516666	+	0.167875i
$604$	−0.597557	+	1.83909i	−0.0243143	+	0.0748316i
$605$	38.5312	−	28.7601i	1.56652	−	1.16926i
$606$	−2.29717	−	7.06997i	−0.0933163	−	0.287198i
$607$			37.5613i			1.52457i	0.647244	+	0.762283i	$0.275921\pi$
$607$			37.5613i			1.52457i	−0.647244	+	0.762283i	$0.724079\pi$
$608$	−0.803607	+	0.261108i	−0.0325906	+	0.0105893i
$609$	6.54425	+	4.75467i	0.265186	+	0.192669i
$610$	4.54451	+	6.08850i	0.184002	+	0.246516i
$611$	−21.6008	+	15.6939i	−0.873874	+	0.634906i
$612$	0.446819	−	0.614994i	0.0180616	−	0.0248597i
$613$	13.4572	−	18.5223i	0.543533	−	0.748109i	−0.445584	−	0.895240i	$-0.647004\pi$
$613$	13.4572	−	18.5223i	0.543533	−	0.748109i	0.989117	+	0.147131i	$0.0470039\pi$
$614$	−29.5592	+	21.4760i	−1.19291	+	0.866701i
$615$	0.00721440	+	0.560052i	0.000290913	+	0.0225835i
$616$	−26.2017	−	19.0366i	−1.05570	−	0.767008i
$617$	1.60060	−	0.520067i	0.0644377	−	0.0209371i	−0.276621	−	0.960979i	$-0.589215\pi$
$617$	1.60060	−	0.520067i	0.0644377	−	0.0209371i	0.341058	+	0.940042i	$0.389215\pi$
$618$			6.17134i			0.248248i
$619$	9.81686	+	30.2132i	0.394573	+	1.21437i	0.929293	+	0.369342i	$0.120417\pi$
$619$	9.81686	+	30.2132i	0.394573	+	1.21437i	−0.534720	+	0.845029i	$0.679583\pi$
$620$	1.17840	+	0.833179i	0.0473256	+	0.0334613i
$621$	−5.25872	+	16.1847i	−0.211025	+	0.649469i
$622$	48.7347	+	15.8349i	1.95408	+	0.634920i
$623$	−4.53311	−	6.23930i	−0.181615	−	0.249972i
$624$	16.6775			0.667636
$625$	−19.4418	+	15.7168i	−0.777672	+	0.628670i
$626$	44.4107			1.77501
$627$	−3.48409	−	4.79543i	−0.139141	−	0.191511i
$628$	−1.10688	−	0.359648i	−0.0441694	−	0.0143515i
$629$	−0.165133	+	0.508228i	−0.00658429	+	0.0202644i
$630$	10.7571	+	7.60571i	0.428572	+	0.303019i
$631$	−3.65422	−	11.2465i	−0.145472	−	0.447718i	0.851599	−	0.524194i	$-0.175633\pi$
$631$	−3.65422	−	11.2465i	−0.145472	−	0.447718i	−0.997071	+	0.0764758i	$0.975633\pi$
$632$			27.2955i			1.08576i
$633$	−7.02625	+	2.28297i	−0.279268	+	0.0907398i
$634$	37.1580	+	26.9968i	1.47573	+	1.07218i
$635$	−0.0618888	−	4.80441i	−0.00245598	−	0.190657i
$636$	−0.151597	+	0.110142i	−0.00601123	+	0.00436741i
$637$	5.76499	−	7.93482i	0.228417	−	0.314389i
$638$	−18.2548	+	25.1255i	−0.722713	+	0.994729i
$639$	−18.9499	+	13.7679i	−0.749647	+	0.544650i
$640$	16.6054	+	22.2470i	0.656386	+	0.879391i
$641$	−17.5787	−	12.7717i	−0.694317	−	0.504451i	0.183759	−	0.982971i	$-0.441173\pi$
$641$	−17.5787	−	12.7717i	−0.694317	−	0.504451i	−0.878077	+	0.478520i	$0.841173\pi$
$642$	22.0677	−	7.17023i	0.870943	−	0.282986i
$643$			1.51037i			0.0595632i	0.999556	+	0.0297816i	$0.00948118\pi$
$643$			1.51037i			0.0595632i	−0.999556	+	0.0297816i	$0.990519\pi$
$644$	0.322272	+	0.991852i	0.0126993	+	0.0390845i
$645$	−17.8715	+	13.3395i	−0.703691	+	0.525242i
$646$	−1.19909	+	3.69042i	−0.0471776	+	0.145198i
$647$	−0.556648	−	0.180866i	−0.0218841	−	0.00711057i	0.298054	−	0.954549i	$-0.403662\pi$
$647$	−0.556648	−	0.180866i	−0.0218841	−	0.00711057i	−0.319939	+	0.947438i	$0.603662\pi$
$648$	0.701000	+	0.964844i	0.0275379	+	0.0379026i
$649$	78.2820			3.07284
$650$	9.16695	+	25.9211i	0.359557	+	1.01671i
$651$	9.38806			0.367947
$652$	−0.457351	−	0.629489i	−0.0179112	−	0.0246527i
$653$	18.1093	+	5.88406i	0.708671	+	0.230261i	0.641104	−	0.767454i	$-0.278477\pi$
$653$	18.1093	+	5.88406i	0.708671	+	0.230261i	0.0675665	+	0.997715i	$0.478477\pi$
$654$	−4.87275	+	14.9968i	−0.190540	+	0.586421i
$655$	−14.4751	+	46.5830i	−0.565589	+	1.82015i
$656$	0.318408	+	0.979960i	0.0124318	+	0.0382610i
$657$			12.1620i			0.474485i
$658$	20.7872	−	6.75418i	0.810371	−	0.263305i
$659$	−24.9777	−	18.1474i	−0.972995	−	0.706922i	−0.0168626	−	0.999858i	$-0.505368\pi$
$659$	−24.9777	−	18.1474i	−0.972995	−	0.706922i	−0.956132	+	0.292936i	$0.905368\pi$
$660$	1.14531	−	1.61986i	0.0445811	−	0.0630528i
$661$	−28.2160	+	20.5002i	−1.09748	+	0.797364i	−0.980646	−	0.195788i	$-0.937274\pi$
$661$	−28.2160	+	20.5002i	−1.09748	+	0.797364i	−0.116831	+	0.993152i	$0.537274\pi$
$662$	−0.873388	+	1.20212i	−0.0339452	+	0.0467215i
$663$	6.06596	−	8.34908i	0.235582	−	0.324251i
$664$	19.8746	−	14.4397i	0.771283	−	0.560370i
$665$	−4.47144	−	1.38944i	−0.173395	−	0.0538803i
$666$	0.459610	+	0.333926i	0.0178095	+	0.0129394i
$667$	−11.7578	+	3.82035i	−0.455265	+	0.147925i
$668$		−	2.34639i		−	0.0907845i
$669$	3.32388	+	10.2298i	0.128509	+	0.395509i
$670$	−7.32131	−	21.5827i	−0.282847	−	0.833812i
$671$	−4.08265	+	12.5651i	−0.157609	+	0.485070i
$672$	−1.74958	−	0.568473i	−0.0674915	−	0.0219293i
$673$	−20.5613	−	28.3002i	−0.792579	−	1.09089i	−0.993782	−	0.111342i	$-0.964485\pi$
$673$	−20.5613	−	28.3002i	−0.792579	−	1.09089i	0.201203	−	0.979550i	$-0.435515\pi$
$674$	12.2282			0.471014
$675$	14.4928	−	21.0682i	0.557826	−	0.810916i
$676$	0.159563			0.00613704
$677$	7.38445	+	10.1638i	0.283807	+	0.390627i	0.926990	−	0.375085i	$-0.122387\pi$
$677$	7.38445	+	10.1638i	0.283807	+	0.390627i	−0.643183	+	0.765713i	$0.722387\pi$
$678$	14.1742	+	4.60548i	0.544357	+	0.176872i
$679$	−2.48847	+	7.65873i	−0.0954988	+	0.293915i
$680$	16.0534	−	0.206794i	0.615619	−	0.00793019i
$681$	−2.99447	−	9.21603i	−0.114748	−	0.353159i
$682$			36.0439i			1.38019i
$683$	47.1212	−	15.3106i	1.80304	−	0.585844i	0.803092	−	0.595855i	$-0.203187\pi$
$683$	47.1212	−	15.3106i	1.80304	−	0.585844i	0.999950	+	0.0100115i	$0.00318683\pi$
$684$	0.232374	+	0.168830i	0.00888505	+	0.00645536i
$685$	−37.5675	+	12.7437i	−1.43538	+	0.486911i
$686$	−23.8824	+	17.3516i	−0.911834	+	0.662486i
$687$	−9.37934	+	12.9096i	−0.357844	+	0.492530i
$688$	−24.1146	+	33.1909i	−0.919362	+	1.26539i
$689$	3.65353	−	2.65444i	0.139188	−	0.101126i
$690$	10.7409	−	3.64354i	0.408899	−	0.138707i
$691$	−5.06726	−	3.68158i	−0.192768	−	0.140054i	0.487215	−	0.873282i	$-0.338013\pi$
$691$	−5.06726	−	3.68158i	−0.192768	−	0.140054i	−0.679983	+	0.733228i	$0.738013\pi$
$692$	−0.0830113	+	0.0269720i	−0.00315561	+	0.00102532i
$693$			22.9094i			0.870256i
$694$	−4.80179	−	14.7784i	−0.182273	−	0.560980i
$695$	24.4660	−	0.315163i	0.928050	−	0.0119548i
$696$	3.23847	−	9.96699i	0.122754	−	0.377798i
$697$	0.606398	+	0.197031i	0.0229689	+	0.00746306i
$698$	29.9369	+	41.2046i	1.13313	+	1.55962i
$699$	−10.7557			−0.406819
$700$	−0.0403675	−	1.56660i	−0.00152575	−	0.0592119i
$701$	6.49885			0.245458			0.122729	−	0.992440i	$-0.460835\pi$
$701$	6.49885			0.245458			0.122729	+	0.992440i	$0.460835\pi$
$702$	−16.5303	−	22.7520i	−0.623895	−	0.858718i
$703$	−0.192033	−	0.0623952i	−0.00724265	−	0.00235328i
$704$	−12.8872	+	39.6626i	−0.485703	+	1.49484i
$705$	−5.31684	−	15.6737i	−0.200244	−	0.590305i
$706$	−13.3403	−	41.0573i	−0.502070	−	1.54521i
$707$		−	10.2116i		−	0.384045i
$708$	2.03224	−	0.660315i	0.0763762	−	0.0248161i
$709$	−21.8949	−	15.9076i	−0.822282	−	0.597423i	0.0950835	−	0.995469i	$-0.469688\pi$
$709$	−21.8949	−	15.9076i	−0.822282	−	0.597423i	−0.917365	+	0.398047i	$0.869688\pi$
$710$	38.2145	+	11.8747i	1.43417	+	0.445649i
$711$	15.6204	−	11.3489i	0.585809	−	0.425615i
$712$	−5.87290	+	8.08335i	−0.220096	+	0.302936i
$713$	−8.43361	+	11.6079i	−0.315841	+	0.434718i
$714$	−6.83466	+	4.96567i	−0.255781	+	0.185836i
$715$	−27.6022	+	39.0389i	−1.03226	+	1.45997i
$716$	−1.92250	−	1.39678i	−0.0718471	−	0.0522000i
$717$	3.98247	−	1.29398i	0.148728	−	0.0483247i
$718$			33.3478i			1.24453i
$719$	5.94709	+	18.3033i	0.221789	+	0.682597i	0.998602	+	0.0528648i	$0.0168352\pi$
$719$	5.94709	+	18.3033i	0.221789	+	0.682597i	−0.776813	+	0.629732i	$0.783165\pi$
$720$	5.44595	−	17.5259i	0.202959	−	0.653151i
$721$	−2.61964	+	8.06244i	−0.0975606	+	0.300261i
$722$	−1.39442	−	0.453074i	−0.0518949	−	0.0168617i
$723$	8.51474	+	11.7195i	0.316667	+	0.435854i
$724$	1.86655			0.0693696
$725$	18.5711	−	0.478533i	0.689714	−	0.0177723i
$726$	32.7784			1.21652
$727$	−3.52196	−	4.84757i	−0.130622	−	0.179786i	0.738696	−	0.674039i	$-0.235442\pi$
$727$	−3.52196	−	4.84757i	−0.130622	−	0.179786i	−0.869318	+	0.494252i	$0.835442\pi$
$728$	20.2631	+	6.58387i	0.750999	+	0.244014i
$729$	−4.66882	+	14.3692i	−0.172919	+	0.532191i
$730$	16.6509	−	12.4284i	0.616277	−	0.459996i
$731$	7.84501	+	24.1445i	0.290158	+	0.893015i
$732$			0.360633i			0.0133294i
$733$	37.4986	−	12.1840i	1.38504	−	0.450028i	0.480719	−	0.876874i	$-0.340376\pi$
$733$	37.4986	−	12.1840i	1.38504	−	0.450028i	0.904324	+	0.426847i	$0.140376\pi$
$734$	32.7904	+	23.8236i	1.21031	+	0.879345i
$735$	3.63668	+	4.87223i	0.134141	+	0.179715i
$736$	2.27459	−	1.65259i	0.0838426	−	0.0609152i
$737$	23.2950	−	32.0628i	0.858083	−	1.18105i
$738$	0.398428	−	0.548389i	0.0146663	−	0.0201865i
$739$	11.8912	−	8.63949i	0.437426	−	0.317809i	−0.347185	−	0.937797i	$-0.612862\pi$
$739$	11.8912	−	8.63949i	0.437426	−	0.317809i	0.784612	+	0.619988i	$0.212862\pi$
$740$	−0.000870449	−	0.0675727i	−3.19983e−5	−	0.00248402i
$741$	3.15468	+	2.29201i	0.115890	+	0.0841990i
$742$	−3.51593	+	1.14239i	−0.129074	+	0.0419386i
$743$		−	30.5140i		−	1.11945i	−0.828678	−	0.559726i	$-0.810906\pi$
$743$		−	30.5140i		−	1.11945i	0.828678	−	0.559726i	$-0.189094\pi$
$744$	−3.75850	−	11.5675i	−0.137793	−	0.424084i
$745$	−33.4229	−	23.6315i	−1.22452	−	0.865790i
$746$	17.1999	−	52.9360i	0.629735	−	1.93812i
$747$	−16.5268	−	5.36989i	−0.604684	−	0.196474i
$748$	−1.32744	−	1.82706i	−0.0485359	−	0.0668040i
$749$	31.8736			1.16464
$750$	−17.0306	+	0.658436i	−0.621868	+	0.0240427i
$751$	7.04590			0.257108			0.128554	−	0.991702i	$-0.458966\pi$
$751$	7.04590			0.257108			0.128554	+	0.991702i	$0.458966\pi$
$752$	−17.8969	−	24.6330i	−0.652634	−	0.898273i
$753$	9.23429	+	3.00040i	0.336516	+	0.109341i
$754$	6.31346	−	19.4308i	0.229923	−	0.707629i
$755$	23.5883	+	16.6779i	0.858465	+	0.606972i
$756$	0.495340	+	1.52450i	0.0180153	+	0.0554455i
$757$			28.1118i			1.02174i	0.859658	+	0.510870i	$0.170677\pi$
$757$			28.1118i			1.02174i	−0.859658	+	0.510870i	$0.829323\pi$
$758$	−42.7432	+	13.8881i	−1.55250	+	0.504438i
$759$	15.9565	+	11.5931i	0.579183	+	0.420801i
$760$	0.0781367	+	6.06573i	0.00283431	+	0.220027i
$761$	−21.9963	+	15.9813i	−0.797367	+	0.579321i	−0.910140	−	0.414300i	$-0.864027\pi$
$761$	−21.9963	+	15.9813i	−0.797367	+	0.579321i	0.112774	+	0.993621i	$0.464027\pi$
$762$	1.92534	−	2.65001i	0.0697478	−	0.0959996i
$763$	−12.7318	+	17.5239i	−0.460923	+	0.634407i
$764$	−0.843337	+	0.612720i	−0.0305109	+	0.0221674i
$765$	−6.79297	−	9.10086i	−0.245601	−	0.329042i
$766$	−16.6755	−	12.1154i	−0.602509	−	0.437749i
$767$	−48.9774	+	15.9137i	−1.76847	+	0.574611i
$768$			3.71448i			0.134035i
$769$	4.09594	+	12.6060i	0.147703	+	0.454584i	0.997349	−	0.0727703i	$-0.0231840\pi$
$769$	4.09594	+	12.6060i	0.147703	+	0.454584i	−0.849645	+	0.527355i	$0.823184\pi$
$770$	31.3651	−	23.4112i	1.13032	−	0.843682i
$771$	−3.54613	+	10.9139i	−0.127711	+	0.393054i
$772$	0.00597077	+	0.00194002i	0.000214893	+	6.98229e-5i
$773$	8.79155	+	12.1005i	0.316210	+	0.435226i	0.937305	−	0.348509i	$-0.113312\pi$
$773$	8.79155	+	12.1005i	0.316210	+	0.435226i	−0.621095	+	0.783735i	$0.713312\pi$
$774$	26.9893			0.970109
$775$	17.1105	−	13.1180i	0.614626	−	0.471211i
$776$	10.4329			0.374520
$777$	−0.258391	−	0.355645i	−0.00926973	−	0.0127587i
$778$	−45.5037	−	14.7851i	−1.63139	−	0.530070i
$779$	−0.0744475	+	0.229126i	−0.00266736	+	0.00820929i
$780$	−0.387270	+	1.24629i	−0.0138665	+	0.0446245i
$781$	21.5037	+	66.1817i	0.769464	+	2.36817i
$782$		−	12.9116i		−	0.461716i
$783$	−18.0720	+	5.87196i	−0.645842	+	0.209847i
$784$	9.04868	+	6.57425i	0.323167	+	0.234795i
$785$	−10.0378	+	14.1969i	−0.358266	+	0.506710i
$786$	−26.9038	+	19.5468i	−0.959628	+	0.697211i
$787$	−16.4377	+	22.6245i	−0.585940	+	0.806477i	−0.994331	−	0.106330i	$-0.966090\pi$
$787$	−16.4377	+	22.6245i	−0.585940	+	0.806477i	0.408391	+	0.912807i	$0.366090\pi$
$788$	1.03515	−	1.42477i	0.0368758	−	0.0507552i
$789$	−20.4007	+	14.8219i	−0.726282	+	0.527675i
$790$	−31.5001	−	9.78827i	−1.12072	−	0.348251i
$791$	16.5627	+	12.0335i	0.588901	+	0.427862i
$792$	28.2277	−	9.17174i	1.00303	−	0.325904i
$793$		−	8.69134i		−	0.308639i
$794$	−12.8904	−	39.6726i	−0.457464	−	1.40793i
$795$	0.899284	+	2.65103i	0.0318943	+	0.0940222i
$796$	0.567942	−	1.74795i	0.0201302	−	0.0619543i
$797$	41.0061	+	13.3237i	1.45251	+	0.471949i	0.925773	−	0.378079i	$-0.123415\pi$
$797$	41.0061	+	13.3237i	1.45251	+	0.471949i	0.526737	+	0.850028i	$0.323415\pi$
$798$	−1.87627	−	2.58246i	−0.0664192	−	0.0914182i
$799$	−18.8412			−0.666554
$800$	−3.98307	+	1.40861i	−0.140823	+	0.0498018i
$801$	7.06767			0.249724
$802$	20.9795	+	28.8758i	0.740813	+	1.01964i
$803$	34.3632	+	11.1653i	1.21265	+	0.394014i
$804$	0.334297	−	1.02886i	0.0117898	−	0.0362851i
$805$	15.5789	−	0.200682i	0.549083	−	0.00707310i
$806$	−7.32725	−	22.5510i	−0.258091	−	0.794324i
$807$			21.4191i			0.753990i
$808$	−12.5821	+	4.08818i	−0.442638	+	0.143822i
$809$	−37.1355	−	26.9806i	−1.30562	−	0.948586i	−0.305623	−	0.952153i	$-0.598865\pi$
$809$	−37.1355	−	26.9806i	−1.30562	−	0.948586i	−0.999994	+	0.00356703i	$0.998865\pi$
$810$	−1.36485	+	0.462986i	−0.0479560	+	0.0162677i
$811$	−7.30988	+	5.31094i	−0.256685	+	0.186492i	−0.708684	−	0.705526i	$-0.750711\pi$
$811$	−7.30988	+	5.31094i	−0.256685	+	0.186492i	0.452000	+	0.892018i	$0.350711\pi$
$812$	−0.684483	+	0.942110i	−0.0240206	+	0.0330616i
$813$	12.0128	−	16.5342i	0.421306	−	0.579878i
$814$	1.36544	−	0.992049i	0.0478586	−	0.0347713i
$815$	−11.0081	+	3.73417i	−0.385595	+	0.130802i
$816$	9.52109	+	6.91747i	0.333305	+	0.242160i
$817$	−9.12292	+	2.96422i	−0.319171	+	0.103705i
$818$			16.8024i			0.587483i
$819$	−4.65718	−	14.3333i	−0.162735	−	0.500847i
$820$	−0.0806252	+	0.00103859i	−0.00281555	+	3.62690e-5i
$821$	−0.868336	+	2.67246i	−0.0303051	+	0.0932696i	−0.965065	−	0.262010i	$-0.915615\pi$
$821$	−0.868336	+	2.67246i	−0.0303051	+	0.0932696i	0.934760	+	0.355280i	$0.115615\pi$
$822$	−25.7207	−	8.35716i	−0.897112	−	0.291489i
$823$	8.75277	+	12.0472i	0.305102	+	0.419938i	0.933846	−	0.357675i	$-0.116430\pi$
$823$	8.75277	+	12.0472i	0.305102	+	0.419938i	−0.628744	+	0.777613i	$0.716430\pi$
$824$	10.9829			0.382606
$825$	−18.0323	−	23.5205i	−0.627803	−	0.818878i
$826$	42.1569			1.46682
$827$	−24.7498	−	34.0652i	−0.860636	−	1.18456i	−0.981418	−	0.191885i	$-0.938540\pi$
$827$	−24.7498	−	34.0652i	−0.860636	−	1.18456i	0.120782	−	0.992679i	$-0.461460\pi$
$828$	−0.908961	−	0.295339i	−0.0315886	−	0.0102638i
$829$	−12.1301	+	37.3326i	−0.421295	+	1.29661i	0.485202	+	0.874402i	$0.338746\pi$
$829$	−12.1301	+	37.3326i	−0.421295	+	1.29661i	−0.906497	+	0.422211i	$0.861254\pi$
$830$	9.53695	+	28.1142i	0.331032	+	0.975860i
$831$	−0.906581	−	2.79017i	−0.0314489	−	0.0967899i
$832$		−	27.4348i		−	0.951132i
$833$	6.58238	−	2.13875i	0.228066	−	0.0741031i
$834$	13.4949	+	9.80464i	0.467291	+	0.339507i
$835$	−33.4746	−	10.4018i	−1.15844	−	0.359970i
$836$	0.690351	−	0.501569i	0.0238763	−	0.0173471i
$837$	−12.9626	+	17.8415i	−0.448054	+	0.616694i
$838$	6.21884	−	8.55950i	0.214826	−	0.295683i
$839$	−3.78691	+	2.75135i	−0.130739	+	0.0949873i	−0.651233	−	0.758878i	$-0.725748\pi$
$839$	−3.78691	+	2.75135i	−0.130739	+	0.0949873i	0.520494	+	0.853865i	$0.325748\pi$
$840$	−7.62470	+	10.7839i	−0.263077	+	0.372080i
$841$	12.2933	+	8.93162i	0.423908	+	0.307987i
$842$	30.3794	−	9.87085i	1.04694	−	0.340172i
$843$			17.0164i			0.586077i
$844$	−0.328656	−	1.01150i	−0.0113128	−	0.0348172i
$845$	0.707361	−	2.27640i	0.0243340	−	0.0783104i
$846$	−6.18972	+	19.0500i	−0.212807	+	0.654952i
$847$	42.8228	+	13.9140i	1.47141	+	0.478089i
$848$	3.02706	+	4.16640i	0.103950	+	0.143075i
$849$	−23.2036			−0.796346
$850$	−5.51816	+	18.6004i	−0.189271	+	0.637989i
$851$	0.671858			0.0230310
$852$	1.11649	+	1.53672i	0.0382505	+	0.0526473i
$853$	−0.835168	−	0.271363i	−0.0285956	−	0.00929128i	0.294684	−	0.955595i	$-0.404786\pi$
$853$	−0.835168	−	0.271363i	−0.0285956	−	0.00929128i	−0.323280	+	0.946303i	$0.604786\pi$
$854$	−2.19861	+	6.76662i	−0.0752348	+	0.231549i
$855$	3.43874	−	2.56671i	0.117602	−	0.0877796i
$856$	−12.7606	−	39.2729i	−0.436147	−	1.34232i
$857$		−	44.7799i		−	1.52965i	−0.644237	−	0.764826i	$-0.722825\pi$
$857$		−	44.7799i		−	1.52965i	0.644237	−	0.764826i	$-0.277175\pi$
$858$	−30.9991	+	10.0722i	−1.05829	+	0.343860i
$859$	−11.5316	−	8.37820i	−0.393453	−	0.285861i	0.373416	−	0.927664i	$-0.378186\pi$
$859$	−11.5316	−	8.37820i	−0.393453	−	0.285861i	−0.766869	+	0.641803i	$0.778186\pi$
$860$	−1.92036	−	2.57279i	−0.0654836	−	0.0877314i
$861$	−0.424341	+	0.308302i	−0.0144615	+	0.0105069i
$862$	−30.4234	+	41.8742i	−1.03622	+	1.42624i
$863$	−15.5316	+	21.3775i	−0.528703	+	0.727698i	−0.986932	−	0.161137i	$-0.948484\pi$
$863$	−15.5316	+	21.3775i	−0.528703	+	0.727698i	0.458229	+	0.888834i	$0.348484\pi$
$864$	3.49610	−	2.54007i	0.118940	−	0.0864148i
$865$	0.0167957	+	1.30385i	0.000571070	+	0.0443321i
$866$	37.8922	+	27.5303i	1.28763	+	0.935517i
$867$	−9.88393	+	3.21148i	−0.335676	+	0.109068i
$868$			1.35151i			0.0458731i
$869$	−17.7255	−	54.5534i	−0.601295	−	1.85060i
$870$	10.3410	+	7.31154i	0.350593	+	0.247884i
$871$	−8.05664	+	24.7958i	−0.272989	+	0.840173i
$872$	26.6891	+	8.67183i	0.903808	+	0.293665i
$873$	−4.33778	−	5.97044i	−0.146812	−	0.202069i
$874$	4.87860			0.165021
$875$	−22.5287	−	6.36902i	−0.761610	−	0.215312i
$876$	0.986264			0.0333228
$877$	−17.0865	−	23.5176i	−0.576971	−	0.794132i	0.416388	−	0.909187i	$-0.363296\pi$
$877$	−17.0865	−	23.5176i	−0.576971	−	0.794132i	−0.993359	+	0.115054i	$0.963296\pi$
$878$	54.5596	+	17.7275i	1.84130	+	0.598273i
$879$	−3.19124	+	9.82164i	−0.107638	+	0.331276i
$880$	−44.5190	−	31.4769i	−1.50073	−	1.06108i
$881$	−5.47454	−	16.8489i	−0.184442	−	0.567654i	0.815496	−	0.578762i	$-0.196464\pi$
$881$	−5.47454	−	16.8489i	−0.184442	−	0.567654i	−0.999938	+	0.0111085i	$0.996464\pi$
$882$		−	7.35795i		−	0.247755i
$883$	27.8054	−	9.03453i	0.935727	−	0.304036i	0.198824	−	0.980035i	$-0.436288\pi$
$883$	27.8054	−	9.03453i	0.935727	−	0.304036i	0.736902	+	0.675999i	$0.236288\pi$
$884$	1.20193	+	0.873256i	0.0404254	+	0.0293708i
$885$	−0.411183	−	31.9201i	−0.0138218	−	1.07298i
$886$	37.3283	−	27.1206i	1.25407	−	0.911135i
$887$	27.2799	−	37.5475i	0.915969	−	1.26072i	−0.0491182	−	0.998793i	$-0.515641\pi$
$887$	27.2799	−	37.5475i	0.915969	−	1.26072i	0.965087	−	0.261930i	$-0.0843589\pi$
$888$	−0.334760	+	0.460757i	−0.0112338	+	0.0154620i
$889$	3.64022	−	2.64477i	0.122089	−	0.0887028i
$890$	−7.22248	−	9.67630i	−0.242098	−	0.324350i
$891$	−2.02760	−	1.47313i	−0.0679270	−	0.0493519i
$892$	−1.47269	+	0.478506i	−0.0493093	+	0.0160216i
$893$		−	7.11911i		−	0.238232i
$894$	−8.62328	−	26.5397i	−0.288406	−	0.887621i
$895$	−28.4497	+	21.2351i	−0.950968	+	0.709812i
$896$	−8.03359	+	24.7248i	−0.268383	+	0.825999i
$897$	−12.3399	−	4.00949i	−0.412018	−	0.133873i
$898$	−16.0126	−	22.0395i	−0.534348	−	0.735466i
$899$	−16.0213			−0.534341
$900$	1.18323	+	0.813940i	0.0394410	+	0.0271313i
$901$	3.18678			0.106167
$902$	−1.18367	−	1.62919i	−0.0394120	−	0.0542460i
$903$	−19.8620	−	6.45357i	−0.660967	−	0.214761i
$904$	8.19618	−	25.2252i	0.272601	−	0.838979i
$905$	8.27462	−	26.6290i	0.275058	−	0.885177i
$906$	6.08589	+	18.7304i	0.202190	+	0.622277i
$907$		−	35.6857i		−	1.18492i	−0.805598	−	0.592462i	$-0.798156\pi$
$907$		−	35.6857i		−	1.18492i	0.805598	−	0.592462i	$-0.201844\pi$
$908$	1.32674	−	0.431084i	0.0440295	−	0.0143060i
$909$	7.57090	+	5.50058i	0.251111	+	0.182443i
$910$	−14.8645	+	21.0234i	−0.492752	+	0.696919i
$911$	1.16708	−	0.847932i	0.0386670	−	0.0280932i	−0.568284	−	0.822833i	$-0.692392\pi$
$911$	1.16708	−	0.847932i	0.0386670	−	0.0280932i	0.606951	+	0.794739i	$0.292392\pi$
$912$	−2.61375	+	3.59752i	−0.0865500	+	0.119126i
$913$	−30.3448	+	41.7660i	−1.00426	+	1.38225i
$914$	−14.2892	+	10.3817i	−0.472644	+	0.343396i
$915$	5.14495	+	1.59873i	0.170087	+	0.0528524i
$916$	−1.85846	−	1.35025i	−0.0614053	−	0.0446135i
$917$	−43.4453	+	14.1162i	−1.43469	+	0.466160i
$918$		−	19.8453i		−	0.654994i
$919$	3.51481	+	10.8175i	0.115943	+	0.356835i	0.992143	−	0.125113i	$-0.0399293\pi$
$919$	3.51481	+	10.8175i	0.115943	+	0.356835i	−0.876200	+	0.481948i	$0.839929\pi$
$920$	−6.48425	−	19.1151i	−0.213779	−	0.630206i
$921$	−8.00649	+	24.6414i	−0.263823	+	0.811963i
$922$	29.4154	+	9.55766i	0.968746	+	0.314765i
$923$	−26.9078	−	37.0354i	−0.885680	−	1.21903i
$924$	1.85781			0.0611176
$925$	−0.967881	−	0.287140i	−0.0318237	−	0.00944109i
$926$	−35.7776			−1.17573
$927$	−4.56643	−	6.28515i	−0.149981	−	0.206431i
$928$	2.98577	+	0.970134i	0.0980126	+	0.0318462i
$929$	7.48994	−	23.0517i	0.245737	−	0.756301i	−0.749777	−	0.661690i	$-0.769839\pi$
$929$	7.48994	−	23.0517i	0.245737	−	0.756301i	0.995514	−	0.0946106i	$-0.0301606\pi$
$930$	14.6971	−	0.189324i	0.481938	−	0.00620816i
$931$	0.808120	+	2.48714i	0.0264851	+	0.0815127i
$932$		−	1.54840i		−	0.0507194i
$933$	34.5592	−	11.2290i	1.13142	−	0.367619i
$934$	−22.2883	−	16.1934i	−0.729297	−	0.529865i
$935$	−31.9504	+	10.8382i	−1.04489	+	0.354448i
$936$	−15.7963	+	11.4767i	−0.516317	+	0.375126i
$937$	22.8199	−	31.4089i	0.745493	−	1.02608i	−0.252791	−	0.967521i	$-0.581348\pi$
$937$	22.8199	−	31.4089i	0.745493	−	1.02608i	0.998284	−	0.0585621i	$-0.0186516\pi$
$938$	12.5450	−	17.2666i	0.409607	−	0.563776i
$939$	25.4783	−	18.5111i	0.831452	−	0.604085i
$940$	2.25638	−	0.765413i	0.0735951	−	0.0249650i
$941$	−17.8374	−	12.9596i	−0.581483	−	0.422472i	0.257776	−	0.966205i	$-0.417010\pi$
$941$	−17.8374	−	12.9596i	−0.581483	−	0.422472i	−0.839258	+	0.543733i	$0.817010\pi$
$942$	−11.2732	+	3.66287i	−0.367300	+	0.119343i
$943$		−	0.801635i		−	0.0261048i
$944$	−18.1476	−	55.8527i	−0.590655	−	1.81785i
$945$	23.9451	−	0.308452i	0.778933	−	0.0100339i
$946$	24.7774	−	76.2570i	0.805582	−	2.47933i
$947$	−4.74456	−	1.54160i	−0.154178	−	0.0500953i	0.230911	−	0.972975i	$-0.425829\pi$
$947$	−4.74456	−	1.54160i	−0.154178	−	0.0500953i	−0.385089	+	0.922879i	$0.625829\pi$
$948$	−0.920323	−	1.26672i	−0.0298907	−	0.0411410i
$949$	−23.7692			−0.771580
$950$	−7.02813	−	2.08502i	−0.228023	−	0.0676471i
$951$	32.5701			1.05616
$952$	8.83719	+	12.1634i	0.286415	+	0.394217i
$953$	−13.2318	−	4.29927i	−0.428620	−	0.139267i	0.0867592	−	0.996229i	$-0.472349\pi$
$953$	−13.2318	−	4.29927i	−0.428620	−	0.139267i	−0.515379	+	0.856962i	$0.672349\pi$
$954$	1.04692	−	3.22209i	0.0338953	−	0.104319i
$955$	5.00273	+	14.7477i	0.161884	+	0.477224i
$956$	0.186282	+	0.573317i	0.00602479	+	0.0185424i
$957$			22.0233i			0.711912i
$958$	37.4224	−	12.1593i	1.20906	−	0.392848i
$959$	−30.0548	−	21.8361i	−0.970521	−	0.705125i
$960$	16.2404	+	5.04651i	0.524157	+	0.162875i
$961$	10.0367	−	7.29209i	0.323764	−	0.235229i
$962$	−0.652620	+	0.898254i	−0.0210413	+	0.0289609i
$963$	−17.1691	+	23.6313i	−0.553267	+	0.761507i
$964$	−1.68715	+	1.22578i	−0.0543393	+	0.0394798i
$965$	0.0541463	−	0.0765813i	0.00174303	−	0.00246524i
$966$	8.59296	+	6.24315i	0.276474	+	0.200870i
$967$	−2.78461	+	0.904776i	−0.0895471	+	0.0290956i	−0.353448	−	0.935454i	$-0.614991\pi$
$967$	−2.78461	+	0.904776i	−0.0895471	+	0.0290956i	0.263901	+	0.964550i	$0.414991\pi$
$968$		−	58.3344i		−	1.87494i
$969$	0.850310	+	2.61698i	0.0273159	+	0.0840696i
$970$	−3.74129	+	12.0400i	−0.120126	+	0.386582i
$971$	−4.56450	+	14.0481i	−0.146482	+	0.450824i	−0.997199	−	0.0747998i	$-0.976168\pi$
$971$	−4.56450	+	14.0481i	−0.146482	+	0.450824i	0.850717	+	0.525624i	$0.176168\pi$
$972$	−2.24915	−	0.730794i	−0.0721416	−	0.0234402i
$973$	13.4683	+	18.5375i	0.431773	+	0.594284i
$974$	−6.28282			−0.201315
$975$	16.0634	+	11.0499i	0.514439	+	0.353881i
$976$	9.91140			0.317256
$977$	−28.3862	−	39.0703i	−0.908156	−	1.24997i	−0.967792	−	0.251749i	$-0.918994\pi$
$977$	−28.3862	−	39.0703i	−0.908156	−	1.24997i	0.0596363	−	0.998220i	$-0.481006\pi$
$978$	−7.53670	−	2.44882i	−0.240997	−	0.0783047i
$979$	6.48845	−	19.9694i	0.207372	−	0.638224i
$980$	−0.701407	+	0.523537i	−0.0224056	+	0.0167238i
$981$	−6.13413	−	18.8789i	−0.195848	−	0.602757i
$982$		−	27.9283i		−	0.891228i
$983$	−32.1255	+	10.4382i	−1.02464	+	0.332927i	−0.772671	−	0.634807i	$-0.781080\pi$
$983$	−32.1255	+	10.4382i	−1.02464	+	0.332927i	−0.251973	+	0.967734i	$0.581080\pi$
$984$	0.549758	+	0.399422i	0.0175256	+	0.0127331i
$985$	−15.7374	−	21.0841i	−0.501435	−	0.671795i
$986$	11.6638	−	8.47424i	0.371451	−	0.269875i
$987$	9.11033	−	12.5393i	0.289985	−	0.399130i
$988$	−0.329958	+	0.454148i	−0.0104974	+	0.0144484i
$989$	25.8223	−	18.7610i	0.821100	−	0.596564i
$990$	0.462001	+	35.8650i	0.0146833	+	1.13986i
$991$	−10.7036	−	7.77661i	−0.340010	−	0.247032i	0.404656	−	0.914469i	$-0.367391\pi$
$991$	−10.7036	−	7.77661i	−0.340010	−	0.247032i	−0.744666	+	0.667437i	$0.767391\pi$
$992$	3.46521	−	1.12592i	0.110021	−	0.0357478i
$993$			1.05369i			0.0334379i
$994$	11.5803	+	35.6405i	0.367305	+	1.13045i
$995$	−22.4192	−	15.8514i	−0.710737	−	0.502522i
$996$	−0.435465	+	1.34022i	−0.0137982	+	0.0424666i
$997$	29.5865	+	9.61323i	0.937013	+	0.304454i	0.737427	−	0.675427i	$-0.236040\pi$
$997$	29.5865	+	9.61323i	0.937013	+	0.304454i	0.199585	+	0.979880i	$0.436040\pi$
$998$	14.4050	+	19.8268i	0.455982	+	0.627606i
$999$	1.03266			0.0326720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.b.39.17	✓	96
25.9	even	10	inner	475.2.n.b.134.17	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.b.39.17	✓	96	1.1	even	1	trivial
475.2.n.b.134.17	yes	96	25.9	even	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.861798 + 1.18616i) q^{2} +(0.988821 + 0.321288i) q^{3} +(-0.0462526 + 0.142351i) q^{4} +(1.82580 + 1.29092i) q^{5} +(0.471065 + 1.44979i) q^{6} +2.09401i q^{7} +(2.58012 - 0.838333i) q^{8} +(-1.55251 - 1.12796i) q^{9} +O(q^{10})\)	\(q+(0.861798 + 1.18616i) q^{2} +(0.988821 + 0.321288i) q^{3} +(-0.0462526 + 0.142351i) q^{4} +(1.82580 + 1.29092i) q^{5} +(0.471065 + 1.44979i) q^{6} +2.09401i q^{7} +(2.58012 - 0.838333i) q^{8} +(-1.55251 - 1.12796i) q^{9} +(0.0422287 + 3.27820i) q^{10} +(-4.61229 + 3.35102i) q^{11} +(-0.0914711 + 0.125899i) q^{12} +(2.20447 - 3.03420i) q^{13} +(-2.48383 + 1.80461i) q^{14} +(1.39063 + 1.86309i) q^{15} +(3.46013 + 2.51393i) q^{16} +(2.51704 - 0.817835i) q^{17} -2.81360i q^{18} +(0.309017 + 0.951057i) q^{19} +(-0.268211 + 0.200195i) q^{20} +(-0.672779 + 2.07060i) q^{21} +(-7.94972 - 2.58302i) q^{22} +(-1.95581 - 2.69195i) q^{23} +2.82063 q^{24} +(1.66706 + 4.71390i) q^{25} +5.49886 q^{26} +(-3.00613 - 4.13758i) q^{27} +(-0.298084 - 0.0968533i) q^{28} +(1.14814 - 3.53361i) q^{29} +(-1.01149 + 3.25512i) q^{30} +(-1.33250 - 4.10102i) q^{31} +0.844962i q^{32} +(-5.63737 + 1.83169i) q^{33} +(3.13926 + 2.28081i) q^{34} +(-2.70319 + 3.82323i) q^{35} +(0.232374 - 0.168830i) q^{36} +(-0.118683 + 0.163353i) q^{37} +(-0.861798 + 1.18616i) q^{38} +(3.15468 - 2.29201i) q^{39} +(5.79300 + 1.80010i) q^{40} +(0.194906 + 0.141608i) q^{41} +(-3.03587 + 0.986413i) q^{42} +9.59241i q^{43} +(-0.263691 - 0.811556i) q^{44} +(-1.37846 - 4.06359i) q^{45} +(1.50757 - 4.63983i) q^{46} +(-6.77067 - 2.19992i) q^{47} +(2.61375 + 3.59752i) q^{48} +2.61513 q^{49} +(-4.15479 + 6.03984i) q^{50} +2.75166 q^{51} +(0.329958 + 0.454148i) q^{52} +(1.14518 + 0.372093i) q^{53} +(2.31717 - 7.13151i) q^{54} +(-12.7470 + 0.164202i) q^{55} +(1.75548 + 5.40280i) q^{56} +1.03971i q^{57} +(5.18090 - 1.68338i) q^{58} +(-11.1086 - 8.07090i) q^{59} +(-0.329533 + 0.111785i) q^{60} +(1.87481 - 1.36213i) q^{61} +(3.71613 - 5.11482i) q^{62} +(2.36197 - 3.25097i) q^{63} +(5.91799 - 4.29967i) q^{64} +(7.94182 - 2.69403i) q^{65} +(-7.03096 - 5.10829i) q^{66} +(-6.61137 + 2.14817i) q^{67} +0.396129i q^{68} +(-1.06906 - 3.29023i) q^{69} +(-6.86458 + 0.0884271i) q^{70} +(3.77186 - 11.6086i) q^{71} +(-4.95128 - 1.60877i) q^{72} +(-3.72518 - 5.12727i) q^{73} -0.296043 q^{74} +(0.133909 + 5.19682i) q^{75} -0.149676 q^{76} +(-7.01707 - 9.65817i) q^{77} +(5.43739 + 1.76672i) q^{78} +(-3.10913 + 9.56892i) q^{79} +(3.07221 + 9.05666i) q^{80} +(0.135846 + 0.418092i) q^{81} +0.353227i q^{82} +(8.61217 - 2.79826i) q^{83} +(-0.263634 - 0.191541i) q^{84} +(5.65135 + 1.75609i) q^{85} +(-11.3782 + 8.26672i) q^{86} +(2.27061 - 3.12522i) q^{87} +(-9.09100 + 12.5127i) q^{88} +(-2.97960 + 2.16480i) q^{89} +(3.63213 - 5.13707i) q^{90} +(6.35363 + 4.61618i) q^{91} +(0.473662 - 0.153902i) q^{92} -4.48330i q^{93} +(-3.22548 - 9.92701i) q^{94} +(-0.663533 + 2.13535i) q^{95} +(-0.271476 + 0.835517i) q^{96} +(3.65745 + 1.18838i) q^{97} +(2.25371 + 3.10197i) q^{98} +10.9405 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) \) 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9	\( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) \) 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9 + 28 * q^10 - 15 * q^11 - 85 * q^12 + 10 * q^14 - 10 * q^15 - 42 * q^16 + 20 * q^17 - 24 * q^19 - 16 * q^21 - 35 * q^23 - 24 * q^24 - 8 * q^25 + 28 * q^26 + 15 * q^27 + 30 * q^28 + 28 * q^29 - 64 * q^30 - 8 * q^31 + 25 * q^33 - 8 * q^34 + 33 * q^35 - 42 * q^36 - 55 * q^37 - 6 * q^39 - 48 * q^40 - 27 * q^41 + 210 * q^42 - 4 * q^44 + 15 * q^45 + 10 * q^46 - 115 * q^48 - 150 * q^49 + 9 * q^50 + 60 * q^51 - 5 * q^52 + 40 * q^53 + 47 * q^54 + 33 * q^55 - 12 * q^56 + 60 * q^58 + 25 * q^59 + 170 * q^60 + 26 * q^61 - 110 * q^62 - 30 * q^63 + 62 * q^64 - 15 * q^65 - 41 * q^66 + 35 * q^67 + 14 * q^69 - 20 * q^70 - 38 * q^71 - 60 * q^73 + 6 * q^74 - 151 * q^75 - 104 * q^76 + 115 * q^78 + 8 * q^79 - 63 * q^80 - 67 * q^81 + 160 * q^83 + 18 * q^84 - 8 * q^85 - 10 * q^87 - 120 * q^88 + 76 * q^89 + 108 * q^90 - 8 * q^91 + 85 * q^92 + 58 * q^94 + q^95 - 6 * q^96 - 10 * q^97 + 10 * q^98 - 112 * q^99

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