LMFDB - Embedded newform 525.2.z.b.64.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(64,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 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("525.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.z (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			64.5
Character	$\chi$	$=$	525.64
Dual form			525.2.z.b.484.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12883 - 1.55370i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.521699 + 1.60562i) q^{4} +(-1.49468 - 1.66311i) q^{5} +(-0.593462 - 1.82649i) q^{6} -1.00000i q^{7} +(-0.569402 + 0.185010i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.12883 - 1.55370i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.521699 + 1.60562i) q^{4} +(-1.49468 - 1.66311i) q^{5} +(-0.593462 - 1.82649i) q^{6} -1.00000i q^{7} +(-0.569402 + 0.185010i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.896746 + 4.19966i) q^{10} +(-4.02724 + 2.92596i) q^{11} +(-0.992330 + 1.36583i) q^{12} +(-3.67441 + 5.05739i) q^{13} +(-1.55370 + 1.12883i) q^{14} +(-0.907591 - 2.04359i) q^{15} +(3.66186 + 2.66050i) q^{16} +(2.43800 - 0.792156i) q^{17} -1.92048i q^{18} +(-1.39736 - 4.30064i) q^{19} +(3.45010 - 1.53224i) q^{20} +(0.309017 - 0.951057i) q^{21} +(9.09215 + 2.95422i) q^{22} +(-5.38371 - 7.41004i) q^{23} -0.598705 q^{24} +(-0.531888 + 4.97163i) q^{25} +12.0055 q^{26} +(0.587785 + 0.809017i) q^{27} +(1.60562 + 0.521699i) q^{28} +(-2.38574 + 7.34255i) q^{29} +(-2.15062 + 3.71700i) q^{30} +(1.52256 + 4.68595i) q^{31} -7.49529i q^{32} +(-4.73430 + 1.53827i) q^{33} +(-3.98287 - 2.89373i) q^{34} +(-1.66311 + 1.49468i) q^{35} +(-1.36583 + 0.992330i) q^{36} +(2.00003 - 2.75281i) q^{37} +(-5.10453 + 7.02579i) q^{38} +(-5.05739 + 3.67441i) q^{39} +(1.15876 + 0.670450i) q^{40} +(-1.71666 - 1.24722i) q^{41} +(-1.82649 + 0.593462i) q^{42} +2.54032i q^{43} +(-2.59699 - 7.99270i) q^{44} +(-0.231665 - 2.22403i) q^{45} +(-5.43570 + 16.7294i) q^{46} +(-7.05369 - 2.29188i) q^{47} +(2.66050 + 3.66186i) q^{48} -1.00000 q^{49} +(8.32485 - 4.78573i) q^{50} +2.56347 q^{51} +(-6.20333 - 8.53816i) q^{52} +(-1.84509 - 0.599507i) q^{53} +(0.593462 - 1.82649i) q^{54} +(10.8856 + 2.32439i) q^{55} +(0.185010 + 0.569402i) q^{56} -4.52196i q^{57} +(14.1012 - 4.58177i) q^{58} +(6.96560 + 5.06081i) q^{59} +(3.75473 - 0.391109i) q^{60} +(-4.59755 + 3.34031i) q^{61} +(5.56186 - 7.65524i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-4.32173 + 3.13992i) q^{64} +(13.9031 - 1.44820i) q^{65} +(7.73424 + 5.61926i) q^{66} +(-5.49881 + 1.78667i) q^{67} +4.32779i q^{68} +(-2.83038 - 8.71102i) q^{69} +(4.19966 + 0.896746i) q^{70} +(1.36688 - 4.20684i) q^{71} +(-0.569402 - 0.185010i) q^{72} +(-8.49380 - 11.6907i) q^{73} -6.53474 q^{74} +(-2.04217 + 4.56394i) q^{75} +7.63422 q^{76} +(2.92596 + 4.02724i) q^{77} +(11.4179 + 3.70990i) q^{78} +(0.527506 - 1.62350i) q^{79} +(-1.04859 - 10.0667i) q^{80} +(0.309017 + 0.951057i) q^{81} +4.07508i q^{82} +(9.49283 - 3.08441i) q^{83} +(1.36583 + 0.992330i) q^{84} +(-4.96147 - 2.87066i) q^{85} +(3.94690 - 2.86759i) q^{86} +(-4.53794 + 6.24594i) q^{87} +(1.75179 - 2.41113i) q^{88} +(-12.6619 + 9.19943i) q^{89} +(-3.19398 + 2.87050i) q^{90} +(5.05739 + 3.67441i) q^{91} +(14.7064 - 4.77840i) q^{92} +4.92710i q^{93} +(4.40152 + 13.5465i) q^{94} +(-5.06385 + 8.75204i) q^{95} +(2.31617 - 7.12844i) q^{96} +(-4.76576 - 1.54849i) q^{97} +(1.12883 + 1.55370i) q^{98} -4.97794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	$ 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) $ 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$	$1$

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 $

$2$	−1.12883	−	1.55370i	−0.798204	−	1.09863i	−0.993038	−	0.117798i	$-0.962417\pi$
$2$	−1.12883	−	1.55370i	−0.798204	−	1.09863i	0.194833	−	0.980836i	$-0.437583\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.521699	+	1.60562i	−0.260849	+	0.802812i
$5$	−1.49468	−	1.66311i	−0.668439	−	0.743767i
$5$	−1.49468	−	1.66311i	−0.668439	−	0.743767i
$6$	−0.593462	−	1.82649i	−0.242280	−	0.745660i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−0.569402	+	0.185010i	−0.201314	+	0.0654109i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−0.896746	+	4.19966i	−0.283576	+	1.32805i
$11$	−4.02724	+	2.92596i	−1.21426	+	0.882211i	−0.995611	−	0.0935933i	$-0.970165\pi$
$11$	−4.02724	+	2.92596i	−1.21426	+	0.882211i	−0.218648	+	0.975804i	$0.570165\pi$
$12$	−0.992330	+	1.36583i	−0.286461	+	0.394280i
$13$	−3.67441	+	5.05739i	−1.01910	+	1.40267i	−0.106264	+	0.994338i	$0.533889\pi$
$13$	−3.67441	+	5.05739i	−1.01910	+	1.40267i	−0.912834	+	0.408330i	$0.866111\pi$
$14$	−1.55370	+	1.12883i	−0.415245	+	0.301693i
$15$	−0.907591	−	2.04359i	−0.234339	−	0.527654i
$16$	3.66186	+	2.66050i	0.915465	+	0.665124i
$17$	2.43800	−	0.792156i	0.591303	−	0.192126i	0.00194520	−	0.999998i	$-0.499381\pi$
$17$	2.43800	−	0.792156i	0.591303	−	0.192126i	0.589358	+	0.807872i	$0.299381\pi$
$18$		−	1.92048i		−	0.452662i
$19$	−1.39736	−	4.30064i	−0.320577	−	0.986635i	−0.973398	−	0.229122i	$-0.926414\pi$
$19$	−1.39736	−	4.30064i	−0.320577	−	0.986635i	0.652821	−	0.757513i	$-0.273586\pi$
$20$	3.45010	−	1.53224i	0.771467	−	0.342620i
$21$	0.309017	−	0.951057i	0.0674330	−	0.207538i
$22$	9.09215	+	2.95422i	1.93845	+	0.629841i
$23$	−5.38371	−	7.41004i	−1.12258	−	1.54510i	−0.801447	−	0.598065i	$-0.795936\pi$
$23$	−5.38371	−	7.41004i	−1.12258	−	1.54510i	−0.321133	−	0.947034i	$-0.604064\pi$
$24$	−0.598705			−0.122210
$25$	−0.531888	+	4.97163i	−0.106378	+	0.994326i
$26$	12.0055			2.35447
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	1.60562	+	0.521699i	0.303434	+	0.0985918i
$29$	−2.38574	+	7.34255i	−0.443020	+	1.36348i	0.441620	+	0.897202i	$0.354404\pi$
$29$	−2.38574	+	7.34255i	−0.443020	+	1.36348i	−0.884640	+	0.466274i	$0.845596\pi$
$30$	−2.15062	+	3.71700i	−0.392648	+	0.678628i
$31$	1.52256	+	4.68595i	0.273459	+	0.841621i	0.989623	+	0.143689i	$0.0458964\pi$
$31$	1.52256	+	4.68595i	0.273459	+	0.841621i	−0.716164	+	0.697932i	$0.754104\pi$
$32$		−	7.49529i		−	1.32499i
$33$	−4.73430	+	1.53827i	−0.824137	+	0.267778i
$34$	−3.98287	−	2.89373i	−0.683057	−	0.496270i
$35$	−1.66311	+	1.49468i	−0.281117	+	0.252646i
$36$	−1.36583	+	0.992330i	−0.227638	+	0.165388i
$37$	2.00003	−	2.75281i	0.328803	−	0.452559i	−0.612326	−	0.790605i	$-0.709766\pi$
$37$	2.00003	−	2.75281i	0.328803	−	0.452559i	0.941129	+	0.338046i	$0.109766\pi$
$38$	−5.10453	+	7.02579i	−0.828064	+	1.13973i
$39$	−5.05739	+	3.67441i	−0.809831	+	0.588377i
$40$	1.15876	+	0.670450i	0.183217	+	0.106007i
$41$	−1.71666	−	1.24722i	−0.268097	−	0.194784i	0.445612	−	0.895226i	$-0.352986\pi$
$41$	−1.71666	−	1.24722i	−0.268097	−	0.194784i	−0.713709	+	0.700442i	$0.752986\pi$
$42$	−1.82649	+	0.593462i	−0.281833	+	0.0915731i
$43$			2.54032i			0.387395i	0.981061	+	0.193698i	$0.0620481\pi$
$43$			2.54032i			0.387395i	−0.981061	+	0.193698i	$0.937952\pi$
$44$	−2.59699	−	7.99270i	−0.391510	−	1.20495i
$45$	−0.231665	−	2.22403i	−0.0345346	−	0.331540i
$46$	−5.43570	+	16.7294i	−0.801450	+	2.46661i
$47$	−7.05369	−	2.29188i	−1.02889	−	0.334305i	−0.254537	−	0.967063i	$-0.581923\pi$
$47$	−7.05369	−	2.29188i	−1.02889	−	0.334305i	−0.774350	+	0.632758i	$0.781923\pi$
$48$	2.66050	+	3.66186i	0.384010	+	0.528544i
$49$	−1.00000			−0.142857
$50$	8.32485	−	4.78573i	1.17731	−	0.676805i
$51$	2.56347			0.358958
$52$	−6.20333	−	8.53816i	−0.860248	−	1.18403i
$53$	−1.84509	−	0.599507i	−0.253443	−	0.0823487i	0.179540	−	0.983751i	$-0.442539\pi$
$53$	−1.84509	−	0.599507i	−0.253443	−	0.0823487i	−0.432983	+	0.901402i	$0.642539\pi$
$54$	0.593462	−	1.82649i	0.0807599	−	0.248553i
$55$	10.8856	+	2.32439i	1.46782	+	0.313421i
$56$	0.185010	+	0.569402i	0.0247230	+	0.0760896i
$57$		−	4.52196i		−	0.598949i
$58$	14.1012	−	4.58177i	1.85158	−	0.601616i
$59$	6.96560	+	5.06081i	0.906845	+	0.658861i	0.940215	−	0.340582i	$-0.110624\pi$
$59$	6.96560	+	5.06081i	0.906845	+	0.658861i	−0.0333703	+	0.999443i	$0.510624\pi$
$60$	3.75473	−	0.391109i	0.484734	−	0.0504920i
$61$	−4.59755	+	3.34031i	−0.588655	+	0.427683i	−0.841834	−	0.539736i	$-0.818524\pi$
$61$	−4.59755	+	3.34031i	−0.588655	+	0.427683i	0.253179	+	0.967420i	$0.418524\pi$
$62$	5.56186	−	7.65524i	0.706357	−	0.972217i
$63$	0.587785	−	0.809017i	0.0740540	−	0.101927i
$64$	−4.32173	+	3.13992i	−0.540216	+	0.392490i
$65$	13.9031	−	1.44820i	1.72446	−	0.179628i
$66$	7.73424	+	5.61926i	0.952020	+	0.691683i
$67$	−5.49881	+	1.78667i	−0.671787	+	0.218277i	−0.624996	−	0.780628i	$-0.714899\pi$
$67$	−5.49881	+	1.78667i	−0.671787	+	0.218277i	−0.0467908	+	0.998905i	$0.514899\pi$
$68$			4.32779i			0.524821i
$69$	−2.83038	−	8.71102i	−0.340738	−	1.04868i
$70$	4.19966	+	0.896746i	0.501955	+	0.107182i
$71$	1.36688	−	4.20684i	0.162219	−	0.499260i	−0.836601	−	0.547812i	$-0.815461\pi$
$71$	1.36688	−	4.20684i	0.162219	−	0.499260i	0.998821	+	0.0485526i	$0.0154608\pi$
$72$	−0.569402	−	0.185010i	−0.0671047	−	0.0218036i
$73$	−8.49380	−	11.6907i	−0.994124	−	1.36829i	−0.928862	−	0.370426i	$-0.879212\pi$
$73$	−8.49380	−	11.6907i	−0.994124	−	1.36829i	−0.0652621	−	0.997868i	$-0.520788\pi$
$74$	−6.53474			−0.759648
$75$	−2.04217	+	4.56394i	−0.235810	+	0.526998i
$76$	7.63422			0.875705
$77$	2.92596	+	4.02724i	0.333444	+	0.458947i
$78$	11.4179	+	3.70990i	1.29282	+	0.420063i
$79$	0.527506	−	1.62350i	0.0593491	−	0.182658i	−0.916987	−	0.398918i	$-0.869386\pi$
$79$	0.527506	−	1.62350i	0.0593491	−	0.182658i	0.976336	+	0.216260i	$0.0693859\pi$
$80$	−1.04859	−	10.0667i	−0.117236	−	1.12549i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$			4.07508i			0.450017i
$83$	9.49283	−	3.08441i	1.04197	−	0.338558i	0.262460	−	0.964943i	$-0.415466\pi$
$83$	9.49283	−	3.08441i	1.04197	−	0.338558i	0.779514	+	0.626385i	$0.215466\pi$
$84$	1.36583	+	0.992330i	0.149024	+	0.108272i
$85$	−4.96147	−	2.87066i	−0.538147	−	0.311367i
$86$	3.94690	−	2.86759i	0.425606	−	0.309221i
$87$	−4.53794	+	6.24594i	−0.486519	+	0.669635i
$88$	1.75179	−	2.41113i	0.186741	−	0.257027i
$89$	−12.6619	+	9.19943i	−1.34216	+	0.975138i	−0.342800	+	0.939408i	$0.611375\pi$
$89$	−12.6619	+	9.19943i	−1.34216	+	0.975138i	−0.999362	+	0.0357293i	$0.988625\pi$
$90$	−3.19398	+	2.87050i	−0.336675	+	0.302577i
$91$	5.05739	+	3.67441i	0.530159	+	0.385183i
$92$	14.7064	−	4.77840i	1.53325	−	0.498183i
$93$			4.92710i			0.510916i
$94$	4.40152	+	13.5465i	0.453982	+	1.39721i
$95$	−5.06385	+	8.75204i	−0.519540	+	0.897940i
$96$	2.31617	−	7.12844i	0.236393	−	0.727543i
$97$	−4.76576	−	1.54849i	−0.483889	−	0.157225i	0.0569057	−	0.998380i	$-0.481877\pi$
$97$	−4.76576	−	1.54849i	−0.483889	−	0.157225i	−0.540795	+	0.841154i	$0.681877\pi$
$98$	1.12883	+	1.55370i	0.114029	+	0.156948i
$99$	−4.97794			−0.500302
$100$	−7.70508	−	3.44771i	−0.770508	−	0.344771i
$101$	−2.39950			−0.238759			−0.119380	−	0.992849i	$-0.538091\pi$
$101$	−2.39950			−0.238759			−0.119380	+	0.992849i	$0.538091\pi$
$102$	−2.89373	−	3.98287i	−0.286521	−	0.394363i
$103$	7.32653	+	2.38053i	0.721904	+	0.234561i	0.646849	−	0.762619i	$-0.276087\pi$
$103$	7.32653	+	2.38053i	0.721904	+	0.234561i	0.0750555	+	0.997179i	$0.476087\pi$
$104$	1.15655	−	3.55949i	0.113409	−	0.349037i
$105$	−2.04359	+	0.907591i	−0.199434	+	0.0885718i
$106$	1.15134	+	3.54347i	0.111828	+	0.344172i
$107$		−	1.46647i		−	0.141769i	−0.997485	−	0.0708846i	$-0.977418\pi$
$107$		−	1.46647i		−	0.141769i	0.997485	−	0.0708846i	$-0.0225822\pi$
$108$	−1.60562	+	0.521699i	−0.154501	+	0.0502005i
$109$	−14.2238	−	10.3342i	−1.36240	−	0.989839i	−0.998288	−	0.0584820i	$-0.981374\pi$
$109$	−14.2238	−	10.3342i	−1.36240	−	0.989839i	−0.364108	−	0.931357i	$-0.618626\pi$
$110$	−8.67662	−	19.5369i	−0.827283	−	1.86277i
$111$	2.75281	−	2.00003i	0.261285	−	0.189835i
$112$	2.66050	−	3.66186i	0.251393	−	0.346013i
$113$	0.710558	−	0.977999i	0.0668437	−	0.0920024i	−0.774286	−	0.632835i	$-0.781891\pi$
$113$	0.710558	−	0.977999i	0.0668437	−	0.0920024i	0.841130	+	0.540833i	$0.181891\pi$
$114$	−7.02579	+	5.10453i	−0.658025	+	0.478083i
$115$	−4.27683	+	20.0293i	−0.398816	+	1.86774i
$116$	−10.5447	−	7.66120i	−0.979054	−	0.711324i
$117$	−5.94532	+	1.93175i	−0.549645	+	0.178591i
$118$		−	16.5353i		−	1.52220i
$119$	−0.792156	−	2.43800i	−0.0726168	−	0.223492i
$120$	0.894870	+	0.995714i	0.0816901	+	0.0908958i
$121$	4.25823	−	13.1055i	0.387112	−	1.19141i
$122$	10.3797	+	3.37257i	0.939734	+	0.305338i
$123$	−1.24722	−	1.71666i	−0.112458	−	0.154786i
$124$	−8.31818			−0.746995
$125$	9.06338	−	6.54638i	0.810653	−	0.585526i
$126$	−1.92048			−0.171090
$127$	−12.9079	−	17.7662i	−1.14539	−	1.57649i	−0.754837	−	0.655913i	$-0.772284\pi$
$127$	−12.9079	−	17.7662i	−1.14539	−	1.57649i	−0.390552	−	0.920581i	$-0.627716\pi$
$128$	−4.49988	−	1.46210i	−0.397737	−	0.129233i
$129$	−0.785002	+	2.41599i	−0.0691156	+	0.212716i
$130$	−17.9443	−	19.9665i	−1.57382	−	1.75117i
$131$	3.39059	+	10.4352i	0.296237	+	0.911725i	0.982803	+	0.184657i	$0.0591175\pi$
$131$	3.39059	+	10.4352i	0.296237	+	0.911725i	−0.686566	+	0.727068i	$0.740883\pi$
$132$		−	8.40403i		−	0.731477i
$133$	−4.30064	+	1.39736i	−0.372913	+	0.121167i
$134$	8.98319	+	6.52667i	0.776029	+	0.563818i
$135$	0.466938	−	2.18677i	0.0401876	−	0.188207i
$136$	−1.24165	+	0.902111i	−0.106471	+	0.0773554i
$137$	10.2899	−	14.1628i	0.879125	−	1.21001i	−0.0975375	−	0.995232i	$-0.531097\pi$
$137$	10.2899	−	14.1628i	0.879125	−	1.21001i	0.976662	−	0.214780i	$-0.0689034\pi$
$138$	−10.3393	+	14.2308i	−0.880141	+	1.21141i
$139$	−1.32616	+	0.963513i	−0.112484	+	0.0817241i	−0.642605	−	0.766198i	$-0.722146\pi$
$139$	−1.32616	+	0.963513i	−0.112484	+	0.0817241i	0.530121	+	0.847922i	$0.322146\pi$
$140$	−1.53224	−	3.45010i	−0.129498	−	0.291587i
$141$	−6.00023	−	4.35942i	−0.505310	−	0.367129i
$142$	−8.07916	+	2.62508i	−0.677988	+	0.220292i
$143$		−	31.1185i		−	2.60226i
$144$	1.39871	+	4.30477i	0.116559	+	0.358731i
$145$	15.7774	−	7.00698i	1.31024	−	0.581898i
$146$	−8.57583	+	26.3937i	−0.709740	+	2.18436i
$147$	−0.951057	−	0.309017i	−0.0784418	−	0.0254873i
$148$	3.37656	+	4.64743i	0.277551	+	0.382017i
$149$	−11.0273			−0.903393			−0.451697	−	0.892172i	$-0.649181\pi$
$149$	−11.0273			−0.903393			−0.451697	+	0.892172i	$0.649181\pi$
$150$	9.39627	−	1.97898i	0.767202	−	0.161583i
$151$	1.27095			0.103429			0.0517144	−	0.998662i	$-0.483531\pi$
$151$	1.27095			0.103429			0.0517144	+	0.998662i	$0.483531\pi$
$152$	1.59132	+	2.19027i	0.129073	+	0.177654i
$153$	2.43800	+	0.792156i	0.197101	+	0.0640420i
$154$	2.95422	−	9.09215i	0.238058	−	0.732666i
$155$	5.51753	−	9.53616i	0.443179	−	0.765962i
$156$	−3.26129	−	10.0372i	−0.261112	−	0.803620i
$157$			7.48945i			0.597723i	0.954296	+	0.298861i	$0.0966069\pi$
$157$			7.48945i			0.597723i	−0.954296	+	0.298861i	$0.903393\pi$
$158$	−3.11790	+	1.01307i	−0.248047	+	0.0805952i
$159$	−1.56953	−	1.14033i	−0.124472	−	0.0904341i
$160$	−12.4655	+	11.2030i	−0.985485	+	0.885677i
$161$	−7.41004	+	5.38371i	−0.583993	+	0.424295i
$162$	1.12883	−	1.55370i	0.0886894	−	0.122070i
$163$	11.9949	−	16.5096i	0.939514	−	1.29313i	−0.0165170	−	0.999864i	$-0.505258\pi$
$163$	11.9949	−	16.5096i	0.939514	−	1.29313i	0.956031	−	0.293266i	$-0.0947422\pi$
$164$	2.89815	−	2.10563i	0.226308	−	0.164422i
$165$	9.63457	+	5.57447i	0.750050	+	0.433972i
$166$	−15.5081	−	11.2673i	−1.20366	−	0.874509i
$167$	−23.4781	+	7.62851i	−1.81679	+	0.590312i	−0.816885	+	0.576801i	$0.804301\pi$
$167$	−23.4781	+	7.62851i	−1.81679	+	0.590312i	−0.999909	+	0.0135110i	$0.995699\pi$
$168$			0.598705i			0.0461911i
$169$	−8.05870	−	24.8021i	−0.619900	−	1.90786i
$170$	1.14051	+	10.9491i	0.0874731	+	0.839761i
$171$	1.39736	−	4.30064i	0.106859	−	0.328878i
$172$	−4.07880	−	1.32528i	−0.311006	−	0.101052i
$173$	7.57149	+	10.4213i	0.575650	+	0.792314i	0.993210	−	0.116335i	$-0.0371146\pi$
$173$	7.57149	+	10.4213i	0.575650	+	0.792314i	−0.417560	+	0.908649i	$0.637115\pi$
$174$	14.8269			1.12403
$175$	4.97163	+	0.531888i	0.375820	+	0.0402070i
$176$	−22.5317			−1.69839
$177$	5.06081	+	6.96560i	0.380394	+	0.523567i
$178$	28.5864	+	9.28827i	2.14264	+	0.696185i
$179$	−0.155674	+	0.479116i	−0.0116356	+	0.0358108i	−0.956706	−	0.291057i	$-0.905993\pi$
$179$	−0.155674	+	0.479116i	−0.0116356	+	0.0358108i	0.945070	+	0.326868i	$0.105993\pi$
$180$	3.69182	+	0.788309i	0.275172	+	0.0587571i
$181$	2.14826	+	6.61166i	0.159679	+	0.491441i	0.998605	−	0.0528046i	$-0.0168160\pi$
$181$	2.14826	+	6.61166i	0.159679	+	0.491441i	−0.838926	+	0.544245i	$0.816816\pi$
$182$		−	12.0055i		−	0.889905i
$183$	−5.40474	+	1.75611i	−0.399530	+	0.129815i
$184$	4.43643	+	3.22325i	0.327058	+	0.237621i
$185$	−7.56763	+	0.788277i	−0.556383	+	0.0579553i
$186$	7.65524	−	5.56186i	0.561310	−	0.407815i
$187$	−7.50061	+	10.3237i	−0.548499	+	0.754944i
$188$	7.35980	−	10.1299i	0.536769	−	0.738799i
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	19.3143	−	2.01186i	1.40121	−	0.145956i
$191$	−5.54195	−	4.02646i	−0.401001	−	0.291345i	0.368947	−	0.929450i	$-0.379718\pi$
$191$	−5.54195	−	4.02646i	−0.401001	−	0.291345i	−0.769949	+	0.638106i	$0.779718\pi$
$192$	−5.08049	+	1.65075i	−0.366653	+	0.119133i
$193$			4.66004i			0.335437i	0.985835	+	0.167719i	$0.0536400\pi$
$193$			4.66004i			0.335437i	−0.985835	+	0.167719i	$0.946360\pi$
$194$	2.97384	+	9.15255i	0.213510	+	0.657115i
$195$	13.6701	+	2.91896i	0.978938	+	0.209031i
$196$	0.521699	−	1.60562i	0.0372642	−	0.114687i
$197$	5.11243	+	1.66113i	0.364245	+	0.118351i	0.485421	−	0.874281i	$-0.338666\pi$
$197$	5.11243	+	1.66113i	0.364245	+	0.118351i	−0.121175	+	0.992631i	$0.538666\pi$
$198$	5.61926	+	7.73424i	0.399343	+	0.549649i
$199$	6.42630			0.455548			0.227774	−	0.973714i	$-0.426855\pi$
$199$	6.42630			0.455548			0.227774	+	0.973714i	$0.426855\pi$
$200$	−0.616943	−	2.92926i	−0.0436245	−	0.207130i
$201$	−5.78179			−0.407816
$202$	2.70863	+	3.72811i	0.190579	+	0.262309i
$203$	7.34255	+	2.38574i	0.515346	+	0.167446i
$204$	−1.33736	+	4.11597i	−0.0936339	+	0.288175i
$205$	0.491571	+	4.71919i	0.0343328	+	0.329602i
$206$	−4.57177	−	14.0705i	−0.318530	−	0.980336i
$207$		−	9.15931i		−	0.636616i
$208$	−26.9104	+	8.74370i	−1.86590	+	0.606267i
$209$	18.2110	+	13.2311i	1.25968	+	0.915213i
$210$	3.71700	+	2.15062i	0.256497	+	0.148407i
$211$	5.93382	−	4.31117i	0.408501	−	0.296793i	−0.364494	−	0.931206i	$-0.618758\pi$
$211$	5.93382	−	4.31117i	0.408501	−	0.296793i	0.772995	+	0.634413i	$0.218758\pi$
$212$	1.92517	−	2.64976i	0.132221	−	0.181987i
$213$	2.59997	−	3.57855i	0.178147	−	0.245198i
$214$	−2.27846	+	1.65540i	−0.155752	+	0.113161i
$215$	4.22484	−	3.79696i	0.288132	−	0.258950i
$216$	−0.484363	−	0.351910i	−0.0329567	−	0.0239444i
$217$	4.68595	−	1.52256i	0.318103	−	0.103358i
$218$			33.7652i			2.28687i
$219$	−4.46545	−	13.7433i	−0.301747	−	0.928683i
$220$	−9.41111	+	16.2656i	−0.634497	+	1.09663i
$221$	−4.95199	+	15.2407i	−0.333107	+	1.02520i
$222$	−6.21491	−	2.01935i	−0.417117	−	0.135530i
$223$	−2.18214	−	3.00345i	−0.146127	−	0.201126i	0.729679	−	0.683790i	$-0.239669\pi$
$223$	−2.18214	−	3.00345i	−0.146127	−	0.201126i	−0.875806	+	0.482663i	$0.839669\pi$
$224$	−7.49529			−0.500800
$225$	−3.35256	+	3.70950i	−0.223504	+	0.247300i
$226$	−2.32162			−0.154432
$227$	6.93829	+	9.54974i	0.460511	+	0.633838i	0.974615	−	0.223889i	$-0.0718754\pi$
$227$	6.93829	+	9.54974i	0.460511	+	0.633838i	−0.514104	+	0.857728i	$0.671875\pi$
$228$	7.26057	+	2.35910i	0.480843	+	0.156235i
$229$	2.76251	−	8.50213i	0.182552	−	0.561837i	−0.817346	−	0.576148i	$-0.804555\pi$
$229$	2.76251	−	8.50213i	0.182552	−	0.561837i	0.999898	+	0.0143107i	$0.00455538\pi$
$230$	35.9474	−	15.9648i	2.37030	−	1.05269i
$231$	1.53827	+	4.73430i	0.101211	+	0.311494i
$232$		−	4.62225i		−	0.303465i
$233$	−11.1697	+	3.62924i	−0.731749	+	0.237760i	−0.651110	−	0.758984i	$-0.725696\pi$
$233$	−11.1697	+	3.62924i	−0.731749	+	0.237760i	−0.0806392	+	0.996743i	$0.525696\pi$
$234$	9.71263	+	7.05664i	0.634935	+	0.461307i
$235$	6.73132	+	15.1567i	0.439103	+	0.988714i
$236$	−11.7597	+	8.54392i	−0.765491	+	0.556162i
$237$	1.00338	−	1.38103i	0.0651763	−	0.0897075i
$238$	−2.89373	+	3.98287i	−0.187572	+	0.258171i
$239$	8.27896	−	6.01502i	0.535522	−	0.389079i	−0.286897	−	0.957961i	$-0.592624\pi$
$239$	8.27896	−	6.01502i	0.535522	−	0.389079i	0.822419	+	0.568882i	$0.192624\pi$
$240$	2.11351	−	9.89800i	0.136426	−	0.638913i
$241$	7.49034	+	5.44205i	0.482495	+	0.350553i	0.802291	−	0.596933i	$-0.203614\pi$
$241$	7.49034	+	5.44205i	0.482495	+	0.350553i	−0.319796	+	0.947487i	$0.603614\pi$
$242$	−25.1688	+	8.17785i	−1.61791	+	0.525692i
$243$			1.00000i			0.0641500i
$244$	−2.96475	−	9.12457i	−0.189799	−	0.584140i
$245$	1.49468	+	1.66311i	0.0954913	+	0.106252i
$246$	−1.25927	+	3.87563i	−0.0802881	+	0.247101i
$247$	26.8845	+	8.73531i	1.71062	+	0.555814i
$248$	−1.73389	−	2.38650i	−0.110102	−	0.151543i
$249$	9.98135			0.632542
$250$	−20.4022	−	6.69204i	−1.29035	−	0.423242i
$251$	22.2035			1.40147			0.700735	−	0.713421i	$-0.252855\pi$
$251$	22.2035			1.40147			0.700735	+	0.713421i	$0.252855\pi$
$252$	0.992330	+	1.36583i	0.0625109	+	0.0860389i
$253$	43.3630	+	14.0895i	2.72621	+	0.885798i
$254$	−13.0325	+	40.1100i	−0.817734	+	2.51673i
$255$	−3.83156	−	4.26334i	−0.239941	−	0.266981i
$256$	6.10944	+	18.8029i	0.381840	+	1.17518i
$257$			16.0393i			1.00050i	0.865880	+	0.500252i	$0.166759\pi$
$257$			16.0393i			1.00050i	−0.865880	+	0.500252i	$0.833241\pi$
$258$	4.63986	−	1.50758i	0.288865	−	0.0938580i
$259$	−2.75281	−	2.00003i	−0.171051	−	0.124276i
$260$	−4.92794	+	23.0786i	−0.305618	+	1.43128i
$261$	−6.24594	+	4.53794i	−0.386614	+	0.280892i
$262$	12.3857	−	17.0475i	0.765194	−	1.05320i
$263$	−14.6792	+	20.2041i	−0.905156	+	1.24584i	0.0636379	+	0.997973i	$0.479730\pi$
$263$	−14.6792	+	20.2041i	−0.905156	+	1.24584i	−0.968794	+	0.247867i	$0.920270\pi$
$264$	2.41113	−	1.75179i	0.148395	−	0.107815i
$265$	1.76077	+	3.96467i	0.108163	+	0.243548i
$266$	7.02579	+	5.10453i	0.430779	+	0.312979i
$267$	−14.8850	+	4.83643i	−0.910947	+	0.295984i
$268$		−	9.76113i		−	0.596256i
$269$	−1.05507	−	3.24717i	−0.0643287	−	0.197983i	0.913726	−	0.406330i	$-0.133192\pi$
$269$	−1.05507	−	3.24717i	−0.0643287	−	0.197983i	−0.978055	+	0.208347i	$0.933192\pi$
$270$	−3.92469	+	1.74301i	−0.238849	+	0.106076i
$271$	3.84361	−	11.8294i	0.233483	−	0.718586i	−0.763836	−	0.645410i	$-0.776687\pi$
$271$	3.84361	−	11.8294i	0.233483	−	0.718586i	0.997319	−	0.0731759i	$-0.0233134\pi$
$272$	11.0352	+	3.58554i	0.669105	+	0.217405i
$273$	3.67441	+	5.05739i	0.222385	+	0.306087i
$274$	−33.6204			−2.03108
$275$	−12.4048	−	21.5782i	−0.748035	−	1.30122i
$276$	15.4632			0.930777
$277$	−12.0376	−	16.5684i	−0.723271	−	0.995498i	−0.999409	−	0.0343795i	$-0.989055\pi$
$277$	−12.0376	−	16.5684i	−0.723271	−	0.995498i	0.276137	−	0.961118i	$-0.410945\pi$
$278$	2.99403	+	0.972818i	0.179570	+	0.0583457i
$279$	−1.52256	+	4.68595i	−0.0911531	+	0.280540i
$280$	0.670450	−	1.15876i	0.0400671	−	0.0692494i
$281$	−1.09792	−	3.37906i	−0.0654965	−	0.201578i	0.912953	−	0.408066i	$-0.133797\pi$
$281$	−1.09792	−	3.37906i	−0.0654965	−	0.201578i	−0.978449	+	0.206488i	$0.933797\pi$
$282$			14.2436i			0.848195i
$283$	−5.82450	+	1.89249i	−0.346231	+	0.112497i	−0.476970	−	0.878920i	$-0.658265\pi$
$283$	−5.82450	+	1.89249i	−0.346231	+	0.112497i	0.130739	+	0.991417i	$0.458265\pi$
$284$	6.04149	+	4.38940i	0.358497	+	0.260463i
$285$	−7.52053	+	6.75887i	−0.445478	+	0.400361i
$286$	−48.3489	+	35.1276i	−2.85893	+	2.07714i
$287$	−1.24722	+	1.71666i	−0.0736213	+	0.101331i
$288$	4.40562	−	6.06381i	0.259604	−	0.357314i
$289$	−8.43693	+	6.12979i	−0.496290	+	0.360576i
$290$	−28.6968	−	16.6037i	−1.68513	−	0.975002i
$291$	−4.05400	−	2.94540i	−0.237649	−	0.172662i
$292$	23.2021	−	7.53882i	1.35780	−	0.441176i
$293$			27.0353i			1.57942i	0.613481	+	0.789710i	$0.289769\pi$
$293$			27.0353i			1.57942i	−0.613481	+	0.789710i	$0.710231\pi$
$294$	0.593462	+	1.82649i	0.0346114	+	0.106523i
$295$	−1.99463	−	19.1489i	−0.116132	−	1.11489i
$296$	−0.629526	+	1.93748i	−0.0365904	+	0.112614i
$297$	−4.73430	−	1.53827i	−0.274712	−	0.0892594i
$298$	12.4480	+	17.1332i	0.721092	+	0.992499i
$299$	57.2574			3.31128
$300$	−6.26257	−	5.65996i	−0.361570	−	0.326778i
$301$	2.54032			0.146422
$302$	−1.43469	−	1.97469i	−0.0825573	−	0.113630i
$303$	−2.28206	−	0.741486i	−0.131101	−	0.0425973i
$304$	6.32490	−	19.4660i	0.362758	−	1.11645i
$305$	12.4272	+	2.65355i	0.711577	+	0.151942i
$306$	−1.52132	−	4.68215i	−0.0869682	−	0.267660i
$307$			20.1943i			1.15255i	0.817255	+	0.576276i	$0.195495\pi$
$307$			20.1943i			1.15255i	−0.817255	+	0.576276i	$0.804505\pi$
$308$	−7.99270	+	2.59699i	−0.455427	+	0.147977i
$309$	6.23232	+	4.52804i	0.354544	+	0.257591i
$310$	−21.0447	+	2.19211i	−1.19526	+	0.124503i
$311$	18.5862	−	13.5037i	1.05393	−	0.765724i	0.0809727	−	0.996716i	$-0.474197\pi$
$311$	18.5862	−	13.5037i	1.05393	−	0.765724i	0.972955	+	0.230993i	$0.0741973\pi$
$312$	2.19989	−	3.02789i	0.124544	−	0.171420i
$313$	11.4401	−	15.7460i	0.646633	−	0.890014i	−0.352314	−	0.935882i	$-0.614605\pi$
$313$	11.4401	−	15.7460i	0.646633	−	0.890014i	0.998948	+	0.0458675i	$0.0146052\pi$
$314$	11.6364	−	8.45432i	0.656679	−	0.477105i
$315$	−2.22403	+	0.231665i	−0.125310	+	0.0130528i
$316$	2.33153	+	1.69395i	0.131159	+	0.0952923i
$317$	−28.3298	+	9.20491i	−1.59116	+	0.516999i	−0.964901	−	0.262615i	$-0.915415\pi$
$317$	−28.3298	+	9.20491i	−1.59116	+	0.516999i	−0.626260	+	0.779615i	$0.715415\pi$
$318$			3.72583i			0.208934i
$319$	−11.8761	−	36.5508i	−0.664932	−	2.04645i
$320$	11.6816	+	2.49436i	0.653022	+	0.139439i
$321$	0.453165	−	1.39470i	0.0252932	−	0.0778445i
$322$	16.7294	+	5.43570i	0.932291	+	0.302920i
$323$	−6.81356	−	9.37806i	−0.379116	−	0.521809i
$324$	−1.68825			−0.0937918
$325$	−23.1891	−	20.9578i	−1.28630	−	1.16253i
$326$	−39.1912			−2.17060
$327$	−10.3342	−	14.2238i	−0.571484	−	0.786580i
$328$	1.20822	+	0.392574i	0.0667126	+	0.0216762i
$329$	−2.29188	+	7.05369i	−0.126356	+	0.388882i
$330$	−2.21473	−	21.2619i	−0.121917	−	1.17043i
$331$	5.06032	+	15.5741i	0.278140	+	0.856028i	0.988371	+	0.152059i	$0.0485905\pi$
$331$	5.06032	+	15.5741i	0.278140	+	0.856028i	−0.710231	+	0.703969i	$0.751409\pi$
$332$			16.8510i			0.924821i
$333$	3.23612	−	1.05148i	0.177338	−	0.0576207i
$334$	38.3553	+	27.8668i	2.09871	+	1.52480i
$335$	11.1904	+	6.47465i	0.611396	+	0.353748i
$336$	3.66186	−	2.66050i	0.199771	−	0.145142i
$337$	−10.4396	+	14.3689i	−0.568684	+	0.782726i	−0.992398	−	0.123070i	$-0.960726\pi$
$337$	−10.4396	+	14.3689i	−0.568684	+	0.782726i	0.423714	+	0.905796i	$0.360726\pi$
$338$	−29.4382	+	40.5183i	−1.60123	+	2.20390i
$339$	0.977999	−	0.710558i	0.0531176	−	0.0385922i
$340$	7.19760	−	6.46864i	0.390344	−	0.350811i
$341$	−19.8426	−	14.4165i	−1.07454	−	0.780697i
$342$	−8.25931	+	2.68361i	−0.446612	+	0.145113i
$343$			1.00000i			0.0539949i
$344$	−0.469985	−	1.44646i	−0.0253399	−	0.0779881i
$345$	−10.2569	+	17.7274i	−0.552213	+	0.954411i
$346$	7.64461	−	23.5277i	0.410977	−	1.26486i
$347$	19.6201	+	6.37496i	1.05326	+	0.342226i	0.783948	−	0.620826i	$-0.213203\pi$
$347$	19.6201	+	6.37496i	1.05326	+	0.342226i	0.269315	+	0.963052i	$0.413203\pi$
$348$	−7.66120	−	10.5447i	−0.410683	−	0.565257i
$349$	−2.63045			−0.140805			−0.0704024	−	0.997519i	$-0.522428\pi$
$349$	−2.63045			−0.140805			−0.0704024	+	0.997519i	$0.522428\pi$
$350$	−4.78573	−	8.32485i	−0.255808	−	0.444982i
$351$	−6.25128			−0.333669
$352$	21.9309	+	30.1853i	1.16892	+	1.60888i
$353$	−7.62832	−	2.47859i	−0.406015	−	0.131922i	0.0988878	−	0.995099i	$-0.468472\pi$
$353$	−7.62832	−	2.47859i	−0.406015	−	0.131922i	−0.504902	+	0.863176i	$0.668472\pi$
$354$	5.10968	−	15.7260i	0.271577	−	0.835827i
$355$	−9.03949	+	4.01457i	−0.479766	+	0.213071i
$356$	−8.16511	−	25.1296i	−0.432750	−	1.33187i
$357$		−	2.56347i		−	0.135673i
$358$	0.920134	−	0.298970i	0.0486306	−	0.0158010i
$359$	10.1097	+	7.34512i	0.533569	+	0.387660i	0.821691	−	0.569933i	$-0.193031\pi$
$359$	10.1097	+	7.34512i	0.533569	+	0.387660i	−0.288122	+	0.957594i	$0.593031\pi$
$360$	0.543379	+	1.22351i	0.0286386	+	0.0644846i
$361$	−1.17157	+	0.851197i	−0.0616617	+	0.0447998i
$362$	7.84753	−	10.8012i	0.412457	−	0.567699i
$363$	8.09963	−	11.1482i	0.425120	−	0.585128i
$364$	−8.53816	+	6.20333i	−0.447521	+	0.325143i
$365$	−6.74749	+	31.6000i	−0.353180	+	1.65402i
$366$	8.82951	+	6.41501i	0.461526	+	0.335318i
$367$	−6.31517	+	2.05192i	−0.329649	+	0.107110i	−0.469165	−	0.883110i	$-0.655445\pi$
$367$	−6.31517	+	2.05192i	−0.329649	+	0.107110i	0.139516	+	0.990220i	$0.455445\pi$
$368$		−	41.4579i		−	2.16114i
$369$	−0.655704	−	2.01805i	−0.0341346	−	0.105056i
$370$	9.76732	+	10.8680i	0.507779	+	0.565001i
$371$	−0.599507	+	1.84509i	−0.0311249	+	0.0957925i
$372$	−7.91106	−	2.57046i	−0.410170	−	0.133272i
$373$	4.64247	+	6.38982i	0.240378	+	0.330852i	0.912113	−	0.409940i	$-0.134450\pi$
$373$	4.64247	+	6.38982i	0.240378	+	0.330852i	−0.671734	+	0.740792i	$0.734450\pi$
$374$	24.5069			1.26722
$375$	10.6427	−	3.42524i	0.549588	−	0.176879i
$376$	4.44041			0.228997
$377$	−28.3680	−	39.0451i	−1.46102	−	2.01093i
$378$	−1.82649	−	0.593462i	−0.0939444	−	0.0305244i
$379$	7.46580	−	22.9774i	0.383492	−	1.18027i	−0.554076	−	0.832466i	$-0.686928\pi$
$379$	7.46580	−	22.9774i	0.383492	−	1.18027i	0.937568	−	0.347802i	$-0.113072\pi$
$380$	−11.4107	−	12.6966i	−0.585355	−	0.651320i
$381$	−6.78608	−	20.8854i	−0.347661	−	1.06999i
$382$			13.1557i			0.673106i
$383$	4.42693	−	1.43840i	0.226206	−	0.0734987i	−0.193721	−	0.981057i	$-0.562056\pi$
$383$	4.42693	−	1.43840i	0.226206	−	0.0734987i	0.419927	+	0.907558i	$0.362056\pi$
$384$	−3.82783	−	2.78108i	−0.195338	−	0.141921i
$385$	2.32439	−	10.8856i	0.118462	−	0.554783i
$386$	7.24032	−	5.26040i	0.368523	−	0.267747i
$387$	−1.49316	+	2.05516i	−0.0759017	+	0.104470i
$388$	4.97258	−	6.84417i	0.252444	−	0.347460i
$389$	6.34542	−	4.61022i	0.321726	−	0.233747i	−0.415186	−	0.909737i	$-0.636283\pi$
$389$	6.34542	−	4.61022i	0.321726	−	0.233747i	0.736911	+	0.675989i	$0.236283\pi$
$390$	−10.8961	−	24.5343i	−0.551744	−	1.24234i
$391$	−18.9954	−	13.8010i	−0.960639	−	0.697945i
$392$	0.569402	−	0.185010i	0.0287592	−	0.00934442i
$393$			10.9722i			0.553474i
$394$	−3.19017	−	9.81833i	−0.160718	−	0.494640i
$395$	−3.48851	+	1.54930i	−0.175526	+	0.0779537i
$396$	2.59699	−	7.99270i	0.130503	−	0.401648i
$397$	−1.10842	−	0.360146i	−0.0556298	−	0.0180752i	0.281070	−	0.959687i	$-0.409311\pi$
$397$	−1.10842	−	0.360146i	−0.0556298	−	0.0180752i	−0.336700	+	0.941612i	$0.609311\pi$
$398$	−7.25420	−	9.98455i	−0.363620	−	0.500481i
$399$	−4.52196			−0.226381
$400$	−15.1747	+	16.7903i	−0.758735	+	0.839516i
$401$	25.9705			1.29690			0.648451	−	0.761256i	$-0.275417\pi$
$401$	25.9705			1.29690			0.648451	+	0.761256i	$0.275417\pi$
$402$	6.52667	+	8.98319i	0.325521	+	0.448041i
$403$	−29.2932	−	9.51793i	−1.45920	−	0.474122i
$404$	1.25182	−	3.85269i	0.0622802	−	0.191679i
$405$	1.11983	−	1.93545i	0.0556450	−	0.0961734i
$406$	−4.58177	−	14.1012i	−0.227389	−	0.699832i
$407$			16.9382i			0.839597i
$408$	−1.45965	+	0.474268i	−0.0722632	+	0.0234797i
$409$	22.3717	+	16.2540i	1.10621	+	0.803709i	0.982063	−	0.188554i	$-0.0603802\pi$
$409$	22.3717	+	16.2540i	1.10621	+	0.803709i	0.124148	+	0.992264i	$0.460380\pi$
$410$	6.77732	−	6.09092i	0.334708	−	0.300809i
$411$	14.1628	−	10.2899i	0.698601	−	0.507563i
$412$	−7.64448	+	10.5217i	−0.376616	+	0.518368i
$413$	5.06081	−	6.96560i	0.249026	−	0.342755i
$414$	−14.2308	+	10.3393i	−0.699408	+	0.508150i
$415$	−19.3184	−	11.1775i	−0.948304	−	0.548680i
$416$	37.9066	+	27.5408i	1.85852	+	1.35030i
$417$	−1.55900	+	0.506549i	−0.0763444	+	0.0248058i
$418$		−	43.2302i		−	2.11446i
$419$	4.07006	+	12.5263i	0.198835	+	0.611952i	0.999910	+	0.0133883i	$0.00426176\pi$
$419$	4.07006	+	12.5263i	0.198835	+	0.611952i	−0.801075	+	0.598564i	$0.795738\pi$
$420$	−0.391109	−	3.75473i	−0.0190842	−	0.183212i
$421$	−0.993831	+	3.05870i	−0.0484364	+	0.149072i	−0.972349	−	0.233531i	$-0.924972\pi$
$421$	−0.993831	+	3.05870i	−0.0484364	+	0.149072i	0.923913	+	0.382602i	$0.124972\pi$
$422$	−13.3966	−	4.35281i	−0.652134	−	0.211891i
$423$	−4.35942	−	6.00023i	−0.211962	−	0.291741i
$424$	1.16152			0.0564082
$425$	2.64156	+	12.5422i	0.128134	+	0.608386i
$426$	−8.49493			−0.411581
$427$	3.34031	+	4.59755i	0.161649	+	0.222491i
$428$	2.35460	+	0.765057i	0.113814	+	0.0369804i
$429$	9.61615	−	29.5955i	0.464272	−	1.42888i
$430$	−10.6685	−	2.27802i	−0.514479	−	0.109856i
$431$	6.88680	+	21.1954i	0.331725	+	1.02095i	0.968313	+	0.249741i	$0.0803455\pi$
$431$	6.88680	+	21.1954i	0.331725	+	1.02095i	−0.636587	+	0.771205i	$0.719654\pi$
$432$			4.52631i			0.217772i
$433$	−4.89869	+	1.59168i	−0.235416	+	0.0764912i	−0.424349	−	0.905499i	$-0.639497\pi$
$433$	−4.89869	+	1.59168i	−0.235416	+	0.0764912i	0.188933	+	0.981990i	$0.439497\pi$
$434$	−7.65524	−	5.56186i	−0.367463	−	0.266978i
$435$	17.1705	−	1.78855i	0.823261	−	0.0857544i
$436$	24.0134	−	17.4468i	1.15003	−	0.835549i
$437$	−24.3449	+	33.5079i	−1.16458	+	1.60290i
$438$	−16.3122	+	22.4518i	−0.779427	+	1.07279i
$439$	−15.7999	+	11.4793i	−0.754088	+	0.547877i	−0.897091	−	0.441845i	$-0.854324\pi$
$439$	−15.7999	+	11.4793i	−0.754088	+	0.547877i	0.143004	+	0.989722i	$0.454324\pi$
$440$	−6.62833	+	0.690436i	−0.315993	+	0.0329152i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	29.2694	−	9.51021i	1.39220	−	0.452354i
$443$		−	36.9512i		−	1.75560i	−0.479023	−	0.877802i	$-0.659009\pi$
$443$		−	36.9512i		−	1.75560i	0.479023	−	0.877802i	$-0.340991\pi$
$444$	1.77516	+	5.46339i	0.0842455	+	0.259281i
$445$	34.2252	+	7.30805i	1.62243	+	0.346435i
$446$	−2.20321	+	6.78079i	−0.104325	+	0.321080i
$447$	−10.4876	−	3.40763i	−0.496047	−	0.161175i
$448$	3.13992	+	4.32173i	0.148347	+	0.204182i
$449$	−24.9129			−1.17571			−0.587856	−	0.808966i	$-0.700028\pi$
$449$	−24.9129			−1.17571			−0.587856	+	0.808966i	$0.700028\pi$
$450$	9.54793	+	1.02148i	0.450094	+	0.0481531i
$451$	10.5627			0.497379
$452$	1.19960	+	1.65111i	0.0564245	+	0.0776617i
$453$	1.20875	+	0.392747i	0.0567920	+	0.0184528i
$454$	7.00530	−	21.5601i	0.328775	−	1.01187i
$455$	−1.44820	−	13.9031i	−0.0678928	−	0.651786i
$456$	0.836608	+	2.57482i	0.0391778	+	0.120577i
$457$			28.6984i			1.34246i	0.741251	+	0.671228i	$0.234233\pi$
$457$			28.6984i			1.34246i	−0.741251	+	0.671228i	$0.765767\pi$
$458$	−16.3282	+	5.30535i	−0.762967	+	0.247903i
$459$	2.07389	+	1.50677i	0.0968009	+	0.0703300i
$460$	−29.9283	−	17.3162i	−1.39542	−	0.807374i
$461$	−10.2123	+	7.41970i	−0.475636	+	0.345570i	−0.799634	−	0.600488i	$-0.794973\pi$
$461$	−10.2123	+	7.41970i	−0.475636	+	0.345570i	0.323998	+	0.946058i	$0.394973\pi$
$462$	5.61926	−	7.73424i	0.261432	−	0.359830i
$463$	−21.0019	+	28.9066i	−0.976041	+	1.34340i	−0.0371052	+	0.999311i	$0.511814\pi$
$463$	−21.0019	+	28.9066i	−0.976041	+	1.34340i	−0.938935	+	0.344093i	$0.888186\pi$
$464$	−28.2711	+	20.5401i	−1.31245	+	0.953552i
$465$	8.19432	−	7.36441i	0.380002	−	0.341516i
$466$	18.2474	+	13.2575i	0.845296	+	0.614143i
$467$	4.58959	−	1.49125i	0.212381	−	0.0690067i	−0.200894	−	0.979613i	$-0.564385\pi$
$467$	4.58959	−	1.49125i	0.212381	−	0.0690067i	0.413275	+	0.910606i	$0.364385\pi$
$468$		−	10.5537i		−	0.487847i
$469$	1.78667	+	5.49881i	0.0825009	+	0.253912i
$470$	15.9505	−	27.5678i	0.735741	−	1.27161i
$471$	−2.31437	+	7.12289i	−0.106640	+	0.328205i
$472$	−4.90253	−	1.59293i	−0.225657	−	0.0733205i
$473$	−7.43288	−	10.2305i	−0.341764	−	0.470398i
$474$	−3.27835			−0.150580
$475$	22.1244	−	4.65971i	1.01514	−	0.213802i
$476$	4.32779			0.198364
$477$	−1.14033	−	1.56953i	−0.0522122	−	0.0718639i
$478$	−18.6911	−	6.07311i	−0.854911	−	0.277778i
$479$	3.31953	−	10.2165i	0.151673	−	0.466803i	−0.846135	−	0.532968i	$-0.821077\pi$
$479$	3.31953	−	10.2165i	0.151673	−	0.466803i	0.997809	+	0.0661656i	$0.0210766\pi$
$480$	−15.3173	+	6.80265i	−0.699137	+	0.310497i
$481$	6.57309	+	20.2299i	0.299707	+	0.922404i
$482$		−	17.7809i		−	0.809899i
$483$	−8.71102	+	2.83038i	−0.396365	+	0.128787i
$484$	18.8210	+	13.6742i	0.855498	+	0.621556i
$485$	4.54795	+	10.2405i	0.206512	+	0.464996i
$486$	1.55370	−	1.12883i	0.0704774	−	0.0512048i
$487$	9.02734	−	12.4251i	0.409068	−	0.563033i	−0.553923	−	0.832568i	$-0.686870\pi$
$487$	9.02734	−	12.4251i	0.409068	−	0.563033i	0.962991	+	0.269535i	$0.0868698\pi$
$488$	1.99986	−	2.75257i	0.0905295	−	0.124603i
$489$	16.5096	−	11.9949i	0.746589	−	0.542429i
$490$	0.896746	−	4.19966i	0.0405109	−	0.189721i
$491$	−15.7098	−	11.4138i	−0.708971	−	0.515098i	0.173870	−	0.984769i	$-0.444373\pi$
$491$	−15.7098	−	11.4138i	−0.708971	−	0.515098i	−0.882842	+	0.469671i	$0.844373\pi$
$492$	3.40698	−	1.10699i	0.153599	−	0.0499072i
$493$			19.7910i			0.891344i
$494$	−16.7760	−	51.6312i	−0.754788	−	2.32300i
$495$	7.44041	+	8.27888i	0.334422	+	0.372108i
$496$	−6.89156	+	21.2100i	−0.309440	+	0.952359i
$497$	−4.20684	−	1.36688i	−0.188702	−	0.0613131i
$498$	−11.2673	−	15.5081i	−0.504898	−	0.694932i
$499$	−14.6431			−0.655513			−0.327757	−	0.944762i	$-0.606293\pi$
$499$	−14.6431			−0.655513			−0.327757	+	0.944762i	$0.606293\pi$
$500$	5.78268	+	17.9676i	0.258609	+	0.803536i
$501$	−24.6864			−1.10291
$502$	−25.0640	−	34.4976i	−1.11866	−	1.53970i
$503$	−3.29841	−	1.07172i	−0.147069	−	0.0477855i	0.234558	−	0.972102i	$-0.424636\pi$
$503$	−3.29841	−	1.07172i	−0.147069	−	0.0477855i	−0.381626	+	0.924317i	$0.624636\pi$
$504$	−0.185010	+	0.569402i	−0.00824100	+	0.0253632i
$505$	3.58648	+	3.99064i	0.159596	+	0.177581i
$506$	−27.0586	−	83.2778i	−1.20290	−	3.70215i
$507$		−	26.0785i		−	1.15819i
$508$	35.2598	−	11.4566i	1.56440	−	0.508305i
$509$	−24.0395	−	17.4657i	−1.06553	−	0.774154i	−0.0904275	−	0.995903i	$-0.528823\pi$
$509$	−24.0395	−	17.4657i	−1.06553	−	0.774154i	−0.975104	+	0.221749i	$0.928823\pi$
$510$	−2.29878	+	10.7657i	−0.101792	+	0.476713i
$511$	−11.6907	+	8.49380i	−0.517167	+	0.375744i
$512$	16.7555	−	23.0619i	0.740495	−	1.01920i
$513$	2.65794	−	3.65834i	0.117351	−	0.161520i
$514$	24.9203	−	18.1057i	1.09919	−	0.798606i
$515$	−6.99169	−	15.7430i	−0.308091	−	0.693718i
$516$	−3.46963	−	2.52084i	−0.152742	−	0.110974i
$517$	35.1129	−	11.4089i	1.54426	−	0.501761i
$518$			6.53474i			0.287120i
$519$	3.98057	+	12.2509i	0.174728	+	0.537756i
$520$	−7.64851	+	3.39682i	−0.335409	+	0.148960i
$521$	−7.79338	+	23.9855i	−0.341434	+	1.05083i	0.622031	+	0.782992i	$0.286308\pi$
$521$	−7.79338	+	23.9855i	−0.341434	+	1.05083i	−0.963465	+	0.267833i	$0.913692\pi$
$522$	14.1012	+	4.58177i	0.617194	+	0.200539i
$523$	16.4856	+	22.6905i	0.720866	+	0.992187i	0.999495	+	0.0317877i	$0.0101201\pi$
$523$	16.4856	+	22.6905i	0.720866	+	0.992187i	−0.278629	+	0.960399i	$0.589880\pi$
$524$	−18.5238			−0.809217
$525$	4.56394	+	2.04217i	0.199187	+	0.0891278i
$526$	47.9615			2.09122
$527$	7.42400	+	10.2183i	0.323395	+	0.445114i
$528$	−21.4289	−	6.96268i	−0.932574	−	0.303012i
$529$	−18.8169	+	57.9126i	−0.818128	+	2.51794i
$530$	4.17231	−	7.21115i	0.181233	−	0.313233i
$531$	2.66062	+	8.18856i	0.115461	+	0.355353i
$532$		−	7.63422i		−	0.330985i
$533$	12.6154	−	4.09899i	0.546434	−	0.177547i
$534$	24.3170	+	17.6673i	1.05230	+	0.764541i
$535$	−2.43891	+	2.19190i	−0.105443	+	0.0947641i
$536$	2.80048	−	2.03467i	0.120962	−	0.0878844i
$537$	−0.296110	+	0.407561i	−0.0127781	+	0.0175875i
$538$	−3.85414	+	5.30477i	−0.166164	+	0.228705i
$539$	4.02724	−	2.92596i	0.173466	−	0.126030i
$540$	3.26753	+	1.89056i	0.140612	+	0.0813569i
$541$	−4.58684	−	3.33254i	−0.197204	−	0.143277i	0.484801	−	0.874624i	$-0.338892\pi$
$541$	−4.58684	−	3.33254i	−0.197204	−	0.143277i	−0.682005	+	0.731347i	$0.738892\pi$
$542$	−22.7182	+	7.38159i	−0.975830	+	0.317066i
$543$			6.95191i			0.298335i
$544$	−5.93743	−	18.2735i	−0.254565	−	0.783472i
$545$	4.07305	+	39.1022i	0.174470	+	1.67495i
$546$	3.70990	−	11.4179i	0.158769	−	0.488640i
$547$	2.06080	+	0.669594i	0.0881134	+	0.0286298i	0.352742	−	0.935721i	$-0.385249\pi$
$547$	2.06080	+	0.669594i	0.0881134	+	0.0286298i	−0.264629	+	0.964350i	$0.585249\pi$
$548$	17.3719	+	23.9104i	0.742093	+	1.02140i
$549$	−5.68288			−0.242539
$550$	−19.5233	+	43.6315i	−0.832476	+	1.86045i
$551$	34.9114			1.48728
$552$	3.22325	+	4.43643i	0.137191	+	0.188827i
$553$	−1.62350	−	0.527506i	−0.0690381	−	0.0224318i
$554$	−12.1539	+	37.4058i	−0.516369	+	1.58922i
$555$	−7.44083	−	1.58883i	−0.315846	−	0.0674421i
$556$	−0.855182	−	2.63198i	−0.0362678	−	0.111621i
$557$		−	3.95107i		−	0.167412i	−0.996490	−	0.0837061i	$-0.973324\pi$
$557$		−	3.95107i		−	0.167412i	0.996490	−	0.0837061i	$-0.0266757\pi$
$558$	8.99928	−	2.92404i	0.380970	−	0.123785i
$559$	−12.8474	−	9.33418i	−0.543387	−	0.394794i
$560$	−10.0667	+	1.04859i	−0.425394	+	0.0443109i
$561$	−10.3237	+	7.50061i	−0.435867	+	0.316676i
$562$	−4.01068	+	5.52023i	−0.169180	+	0.232857i
$563$	12.5095	−	17.2178i	0.527211	−	0.725644i	−0.459491	−	0.888182i	$-0.651968\pi$
$563$	12.5095	−	17.2178i	0.527211	−	0.725644i	0.986702	+	0.162539i	$0.0519682\pi$
$564$	10.1299	−	7.35980i	0.426546	−	0.309904i
$565$	−2.68858	+	0.280054i	−0.113109	+	0.0117819i
$566$	9.51525	+	6.91324i	0.399956	+	0.290585i
$567$	0.951057	−	0.309017i	0.0399406	−	0.0129775i
$568$			2.64827i			0.111119i
$569$	8.25859	+	25.4173i	0.346218	+	1.06555i	0.960928	+	0.276797i	$0.0892730\pi$
$569$	8.25859	+	25.4173i	0.346218	+	1.06555i	−0.614710	+	0.788753i	$0.710727\pi$
$570$	18.9907	+	4.05505i	0.795432	+	0.169847i
$571$	11.4847	−	35.3463i	0.480620	−	1.47920i	−0.357606	−	0.933873i	$-0.616407\pi$
$571$	11.4847	−	35.3463i	0.480620	−	1.47920i	0.838226	−	0.545323i	$-0.183593\pi$
$572$	49.9646	+	16.2345i	2.08913	+	0.678798i
$573$	−4.02646	−	5.54195i	−0.168208	−	0.231518i
$574$	4.07508			0.170091
$575$	39.7035	−	22.8245i	1.65575	−	0.951847i
$576$	−5.34195			−0.222581
$577$	18.7873	+	25.8584i	0.782123	+	1.07650i	0.995044	+	0.0994312i	$0.0317023\pi$
$577$	18.7873	+	25.8584i	0.782123	+	1.07650i	−0.212921	+	0.977069i	$0.568298\pi$
$578$	19.0477	+	6.18899i	0.792282	+	0.257428i
$579$	−1.44003	+	4.43196i	−0.0598457	+	0.184186i
$580$	3.01952	+	28.9881i	0.125379	+	1.20366i
$581$	−3.08441	−	9.49283i	−0.127963	−	0.393829i
$582$			9.62356i			0.398910i
$583$	9.18477	−	2.98431i	0.380394	−	0.123598i
$584$	6.99929	+	5.08528i	0.289633	+	0.210430i
$585$	12.0991	+	7.00040i	0.500234	+	0.289431i
$586$	42.0048	−	30.5183i	1.73520	−	1.26070i
$587$	−5.95260	+	8.19305i	−0.245690	+	0.338163i	−0.913996	−	0.405723i	$-0.867020\pi$
$587$	−5.95260	+	8.19305i	−0.245690	+	0.338163i	0.668306	+	0.743886i	$0.267020\pi$
$588$	0.992330	−	1.36583i	0.0409230	−	0.0563257i
$589$	18.0250	−	13.0959i	0.742708	−	0.539609i
$590$	−27.5000	+	24.7149i	−1.13216	+	1.01750i
$591$	4.34889	+	3.15965i	0.178889	+	0.129971i
$592$	14.6477	−	4.75932i	0.602016	−	0.195607i
$593$			6.03022i			0.247631i	0.992305	+	0.123816i	$0.0395132\pi$
$593$			6.03022i			0.247631i	−0.992305	+	0.123816i	$0.960487\pi$
$594$	2.95422	+	9.09215i	0.121213	+	0.373055i
$595$	−2.87066	+	4.96147i	−0.117686	+	0.203401i
$596$	5.75294	−	17.7057i	0.235650	−	0.725255i
$597$	6.11177	+	1.98583i	0.250138	+	0.0812748i
$598$	−64.6340	−	88.9610i	−2.64308	−	3.63789i
$599$	1.95208			0.0797598			0.0398799	−	0.999204i	$-0.487302\pi$
$599$	1.95208			0.0797598			0.0398799	+	0.999204i	$0.487302\pi$
$600$	0.318444	−	2.97654i	0.0130004	−	0.121517i
$601$	−40.2867			−1.64333			−0.821664	−	0.569972i	$-0.806954\pi$
$601$	−40.2867			−1.64333			−0.821664	+	0.569972i	$0.806954\pi$
$602$	−2.86759	−	3.94690i	−0.116874	−	0.160864i
$603$	−5.49881	−	1.78667i	−0.223929	−	0.0727589i
$604$	−0.663055	+	2.04067i	−0.0269793	+	0.0830339i
$605$	−28.1606	+	12.5065i	−1.14489	+	0.508463i
$606$	1.42401	+	4.38266i	0.0578465	+	0.178033i
$607$			29.5172i			1.19806i	0.800725	+	0.599032i	$0.204448\pi$
$607$			29.5172i			1.19806i	−0.800725	+	0.599032i	$0.795552\pi$
$608$	−32.2345	+	10.4736i	−1.30728	+	0.424762i
$609$	6.24594	+	4.53794i	0.253098	+	0.183887i
$610$	−9.90533	−	22.3035i	−0.401055	−	0.903043i
$611$	37.5091	−	27.2520i	1.51746	−	1.10250i
$612$	−2.54381	+	3.50125i	−0.102827	+	0.141530i
$613$	1.44245	−	1.98536i	0.0582599	−	0.0801879i	−0.778893	−	0.627157i	$-0.784218\pi$
$613$	1.44245	−	1.98536i	0.0582599	−	0.0801879i	0.837153	+	0.546969i	$0.184218\pi$
$614$	31.3760	−	22.7960i	1.26623	−	0.919972i
$615$	−0.990798	+	4.64012i	−0.0399528	+	0.187108i
$616$	−2.41113	−	1.75179i	−0.0971471	−	0.0705815i
$617$	1.08060	−	0.351107i	0.0435031	−	0.0141350i	−0.287185	−	0.957875i	$-0.592719\pi$
$617$	1.08060	−	0.351107i	0.0435031	−	0.0141350i	0.330688	+	0.943740i	$0.392719\pi$
$618$		−	14.7946i		−	0.595125i
$619$	−3.75438	−	11.5548i	−0.150901	−	0.464426i	0.846821	−	0.531877i	$-0.178513\pi$
$619$	−3.75438	−	11.5548i	−0.150901	−	0.464426i	−0.997723	+	0.0674512i	$0.978513\pi$
$620$	12.4330	+	13.8341i	0.499321	+	0.555590i
$621$	2.83038	−	8.71102i	0.113579	−	0.349561i
$622$	−41.9614	−	13.6341i	−1.68250	−	0.546677i
$623$	9.19943	+	12.6619i	0.368567	+	0.507289i
$624$	−28.2952			−1.13272
$625$	−24.4342	−	5.28870i	−0.977368	−	0.211548i
$626$	−37.3785			−1.49395
$627$	13.2311	+	18.2110i	0.528399	+	0.727278i
$628$	−12.0252	−	3.90724i	−0.479859	−	0.155916i
$629$	2.69543	−	8.29569i	0.107474	−	0.330771i
$630$	2.87050	+	3.19398i	0.114363	+	0.127251i
$631$	−8.09980	−	24.9286i	−0.322448	−	0.992393i	−0.972579	−	0.232571i	$-0.925286\pi$
$631$	−8.09980	−	24.9286i	−0.322448	−	0.992393i	0.650131	−	0.759822i	$-0.274714\pi$
$632$			1.02202i			0.0406536i
$633$	6.97562	−	2.26652i	0.277256	−	0.0900859i
$634$	46.2813	+	33.6253i	1.83806	+	1.33543i
$635$	−10.2541	+	48.0219i	−0.406920	+	1.90569i
$636$	2.64976	−	1.92517i	0.105070	−	0.0763378i
$637$	3.67441	−	5.05739i	0.145585	−	0.200381i
$638$	−43.3830	+	59.7115i	−1.71755	+	2.36400i
$639$	3.57855	−	2.59997i	0.141565	−	0.102853i
$640$	4.29423	+	9.66917i	0.169744	+	0.382208i
$641$	2.16716	+	1.57454i	0.0855978	+	0.0621905i	0.629761	−	0.776789i	$-0.283153\pi$
$641$	2.16716	+	1.57454i	0.0855978	+	0.0621905i	−0.544163	+	0.838979i	$0.683153\pi$
$642$	−2.67849	+	0.870295i	−0.105712	+	0.0343478i
$643$		−	29.3951i		−	1.15923i	−0.814891	−	0.579614i	$-0.803203\pi$
$643$		−	29.3951i		−	1.15923i	0.814891	−	0.579614i	$-0.196797\pi$
$644$	−4.77840	−	14.7064i	−0.188295	−	0.579513i
$645$	5.19139	−	2.30557i	0.204411	−	0.0907818i
$646$	−6.87936	+	21.1725i	−0.270665	+	0.833020i
$647$	−4.91541	−	1.59711i	−0.193245	−	0.0627891i	0.210796	−	0.977530i	$-0.432395\pi$
$647$	−4.91541	−	1.59711i	−0.193245	−	0.0627891i	−0.404041	+	0.914741i	$0.632395\pi$
$648$	−0.351910	−	0.484363i	−0.0138243	−	0.0190276i
$649$	−42.8599			−1.68240
$650$	−6.38557	+	59.6868i	−0.250463	+	2.34111i
$651$	4.92710			0.193108
$652$	20.2504	+	27.8723i	0.793068	+	1.09157i
$653$	17.7191	+	5.75729i	0.693403	+	0.225300i	0.634454	−	0.772961i	$-0.281225\pi$
$653$	17.7191	+	5.75729i	0.693403	+	0.225300i	0.0589489	+	0.998261i	$0.481225\pi$
$654$	−10.4340	+	32.1126i	−0.408003	+	1.25570i
$655$	12.2870	−	21.2361i	0.480094	−	0.829764i
$656$	−2.96792	−	9.13432i	−0.115878	−	0.356635i
$657$		−	14.4505i		−	0.563768i
$658$	13.5465	−	4.40152i	0.528097	−	0.171589i
$659$	−20.6427	−	14.9978i	−0.804126	−	0.584232i	0.107996	−	0.994151i	$-0.465557\pi$
$659$	−20.6427	−	14.9978i	−0.804126	−	0.584232i	−0.912122	+	0.409920i	$0.865557\pi$
$660$	−13.9768	+	12.5613i	−0.544048	+	0.488948i
$661$	14.8618	−	10.7977i	0.578057	−	0.419983i	−0.259966	−	0.965618i	$-0.583711\pi$
$661$	14.8618	−	10.7977i	0.578057	−	0.419983i	0.838023	+	0.545635i	$0.183711\pi$
$662$	18.4852	−	25.4427i	0.718449	−	0.988860i
$663$	−9.41924	+	12.9645i	−0.365813	+	0.503498i
$664$	−4.83459	+	3.51254i	−0.187619	+	0.136313i
$665$	8.75204	+	5.06385i	0.339389	+	0.196368i
$666$	−5.28672	−	3.84103i	−0.204856	−	0.148837i
$667$	67.2526	−	21.8517i	2.60403	−	0.846102i
$668$		−	41.6769i		−	1.61253i
$669$	−1.14722	−	3.53077i	−0.0443540	−	0.136508i
$670$	−2.57237	−	24.6953i	−0.0993793	−	0.954063i
$671$	8.74180	−	26.9045i	0.337473	−	1.03864i
$672$	−7.12844	−	2.31617i	−0.274986	−	0.0893482i
$673$	−6.23794	−	8.58579i	−0.240455	−	0.330958i	0.671685	−	0.740837i	$-0.265571\pi$
$673$	−6.23794	−	8.58579i	−0.240455	−	0.330958i	−0.912140	+	0.409879i	$0.865571\pi$
$674$	34.1097			1.31386
$675$	−4.33477	+	2.49194i	−0.166845	+	0.0959150i
$676$	44.0271			1.69335
$677$	12.0755	+	16.6205i	0.464099	+	0.638778i	0.975353	−	0.220652i	$-0.0708186\pi$
$677$	12.0755	+	16.6205i	0.464099	+	0.638778i	−0.511253	+	0.859430i	$0.670819\pi$
$678$	−2.20799	−	0.717420i	−0.0847974	−	0.0275523i
$679$	−1.54849	+	4.76576i	−0.0594255	+	0.182893i
$680$	3.35617	+	0.716639i	0.128703	+	0.0274818i
$681$	3.64768	+	11.2264i	0.139779	+	0.430196i
$682$			47.1033i			1.80368i
$683$	22.1360	−	7.19243i	0.847011	−	0.275211i	0.146817	−	0.989164i	$-0.453097\pi$
$683$	22.1360	−	7.19243i	0.847011	−	0.275211i	0.700194	+	0.713953i	$0.253097\pi$
$684$	6.17621	+	4.48728i	0.236153	+	0.171575i
$685$	−38.9344	+	4.05558i	−1.48761	+	0.154956i
$686$	1.55370	−	1.12883i	0.0593207	−	0.0430990i
$687$	5.25461	−	7.23235i	0.200476	−	0.275931i
$688$	−6.75852	+	9.30230i	−0.257666	+	0.354647i
$689$	9.81158	−	7.12853i	0.373791	−	0.271575i
$690$	39.1214	−	4.07506i	1.48933	−	0.155135i
$691$	9.83654	+	7.14666i	0.374200	+	0.271872i	0.758950	−	0.651149i	$-0.225713\pi$
$691$	9.83654	+	7.14666i	0.374200	+	0.271872i	−0.384751	+	0.923021i	$0.625713\pi$
$692$	−20.6827	+	6.72021i	−0.786237	+	0.255464i
$693$			4.97794i			0.189096i
$694$	−12.2430	−	37.6801i	−0.464738	−	1.43032i
$695$	3.58461	+	0.765417i	0.135972	+	0.0290339i
$696$	1.42835	−	4.39602i	0.0541416	−	0.166631i
$697$	−5.17321	−	1.68088i	−0.195949	−	0.0636678i
$698$	2.96934	+	4.08694i	0.112391	+	0.154693i
$699$	−11.7445			−0.444217
$700$	−3.44771	+	7.70508i	−0.130311	+	0.291225i
$701$	18.4194			0.695689			0.347845	−	0.937552i	$-0.386914\pi$
$701$	18.4194			0.695689			0.347845	+	0.937552i	$0.386914\pi$
$702$	7.05664	+	9.71263i	0.266336	+	0.366580i
$703$	−14.6336	−	4.75475i	−0.551917	−	0.179329i
$704$	8.21735	−	25.2904i	0.309703	−	0.953168i
$705$	1.71819	+	16.4950i	0.0647107	+	0.621237i
$706$	4.76009	+	14.6501i	0.179148	+	0.551362i
$707$			2.39950i			0.0902425i
$708$	−13.8244	+	4.49181i	−0.519551	+	0.168812i
$709$	−25.8359	−	18.7709i	−0.970287	−	0.704954i	−0.0147697	−	0.999891i	$-0.504702\pi$
$709$	−25.8359	−	18.7709i	−0.970287	−	0.704954i	−0.955517	+	0.294936i	$0.904702\pi$
$710$	16.4415	+	9.51291i	0.617039	+	0.357013i
$711$	1.38103	−	1.00338i	0.0517926	−	0.0376296i
$712$	5.50774	−	7.58076i	0.206411	−	0.284101i
$713$	26.5260	−	36.5100i	0.993408	−	1.36731i
$714$	−3.98287	+	2.89373i	−0.149055	+	0.108295i
$715$	−51.7536	+	46.5121i	−1.93548	+	1.73945i
$716$	−0.688065	−	0.499909i	−0.0257142	−	0.0186825i
$717$	9.73251	−	3.16228i	0.363467	−	0.118098i
$718$		−	23.9988i		−	0.895629i
$719$	−9.24388	−	28.4497i	−0.344739	−	1.06100i	−0.961724	−	0.274022i	$-0.911646\pi$
$719$	−9.24388	−	28.4497i	−0.344739	−	1.06100i	0.616985	−	0.786975i	$-0.288354\pi$
$720$	5.06871	−	8.76045i	0.188900	−	0.326483i
$721$	2.38053	−	7.32653i	0.0886557	−	0.272854i
$722$	2.64501	+	0.859417i	0.0984372	+	0.0319842i
$723$	5.44205	+	7.49034i	0.202392	+	0.278569i
$724$	−11.7366			−0.436187
$725$	−35.2355	−	15.7664i	−1.30861	−	0.585550i
$726$	−26.4641			−0.982174
$727$	3.91678	+	5.39098i	0.145265	+	0.199940i	0.875449	−	0.483310i	$-0.160566\pi$
$727$	3.91678	+	5.39098i	0.145265	+	0.199940i	−0.730184	+	0.683251i	$0.760566\pi$
$728$	−3.55949	−	1.15655i	−0.131924	−	0.0428646i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	56.7137	−	25.1874i	2.09907	−	0.932229i
$731$	2.01233	+	6.19331i	0.0744287	+	0.229068i
$732$		−	9.59414i		−	0.354609i
$733$	−40.2045	+	13.0632i	−1.48499	+	0.482501i	−0.935598	−	0.353067i	$-0.885139\pi$
$733$	−40.2045	+	13.0632i	−1.48499	+	0.482501i	−0.549387	+	0.835568i	$0.685139\pi$
$734$	10.3168	+	7.49562i	0.380802	+	0.276668i
$735$	0.907591	+	2.04359i	0.0334770	+	0.0753791i
$736$	−55.5403	+	40.3524i	−2.04724	+	1.48741i
$737$	16.9173	−	23.2847i	0.623157	−	0.857702i
$738$	−2.39527	+	3.29681i	−0.0881712	+	0.121357i
$739$	−22.5271	+	16.3669i	−0.828674	+	0.602067i	−0.919184	−	0.393829i	$-0.871150\pi$
$739$	−22.5271	+	16.3669i	−0.828674	+	0.602067i	0.0905097	+	0.995896i	$0.471150\pi$
$740$	2.68235	−	12.5620i	0.0986050	−	0.461789i
$741$	22.8693	+	16.6155i	0.840126	+	0.610387i
$742$	3.54347	−	1.15134i	0.130085	−	0.0422671i
$743$		−	33.5461i		−	1.23069i	−0.788259	−	0.615343i	$-0.789018\pi$
$743$		−	33.5461i		−	1.23069i	0.788259	−	0.615343i	$-0.210982\pi$
$744$	−0.911562	−	2.80550i	−0.0334195	−	0.102855i
$745$	16.4823	+	18.3397i	0.603864	+	0.671914i
$746$	4.68731	−	14.4260i	0.171615	−	0.528175i
$747$	9.49283	+	3.08441i	0.347324	+	0.112853i
$748$	−12.6629	−	17.4290i	−0.463003	−	0.637269i
$749$	−1.46647			−0.0535837
$750$	−17.3357	−	12.6691i	−0.633009	−	0.462611i
$751$	−26.4908			−0.966663			−0.483331	−	0.875438i	$-0.660573\pi$
$751$	−26.4908			−0.966663			−0.483331	+	0.875438i	$0.660573\pi$
$752$	−19.7321	−	27.1589i	−0.719555	−	0.990382i
$753$	21.1168	+	6.86125i	0.769538	+	0.250038i
$754$	−28.6419	+	88.1508i	−1.04308	+	3.21026i
$755$	−1.89966	−	2.11374i	−0.0691359	−	0.0769269i
$756$	0.521699	+	1.60562i	0.0189740	+	0.0583960i
$757$		−	30.4084i		−	1.10521i	−0.833442	−	0.552606i	$-0.813633\pi$
$757$		−	30.4084i		−	1.10521i	0.833442	−	0.552606i	$-0.186367\pi$
$758$	−44.1276	+	14.3379i	−1.60279	+	0.520777i
$759$	36.8867	+	26.7998i	1.33890	+	0.972770i
$760$	1.26415	−	5.92029i	0.0458556	−	0.214752i
$761$	41.0097	−	29.7953i	1.48660	−	1.08008i	0.511246	−	0.859434i	$-0.329184\pi$
$761$	41.0097	−	29.7953i	1.48660	−	1.08008i	0.975354	−	0.220644i	$-0.0708159\pi$
$762$	−24.7894	+	34.1196i	−0.898024	+	1.23602i
$763$	−10.3342	+	14.2238i	−0.374124	+	0.514937i
$764$	9.35621	−	6.79769i	0.338496	−	0.245932i
$765$	−2.32658	−	5.23869i	−0.0841178	−	0.189405i
$766$	−7.23210	−	5.25443i	−0.261306	−	0.189850i
$767$	−51.1890	+	16.6323i	−1.84833	+	0.600558i
$768$			19.7706i			0.713409i
$769$	−1.57520	−	4.84797i	−0.0568033	−	0.174822i	0.918629	−	0.395120i	$-0.129297\pi$
$769$	−1.57520	−	4.84797i	−0.0568033	−	0.174822i	−0.975433	+	0.220298i	$0.929297\pi$
$770$	−19.5369	+	8.67662i	−0.704060	+	0.312684i
$771$	−4.95641	+	15.2543i	−0.178501	+	0.549369i
$772$	−7.48228	−	2.43114i	−0.269293	−	0.0874986i
$773$	−13.3969	−	18.4392i	−0.481852	−	0.663213i	0.497007	−	0.867746i	$-0.334432\pi$
$773$	−13.3969	−	18.4392i	−0.481852	−	0.663213i	−0.978860	+	0.204534i	$0.934432\pi$
$774$	4.87864			0.175359
$775$	−24.1066	+	5.07719i	−0.865935	+	0.182378i
$776$	3.00012			0.107698
$777$	−2.00003	−	2.75281i	−0.0717507	−	0.0987564i
$778$	−14.3258	−	4.65474i	−0.513606	−	0.166881i
$779$	−2.96507	+	9.12555i	−0.106235	+	0.326957i
$780$	−11.8184	+	20.4263i	−0.423168	+	0.731377i
$781$	6.80427	+	20.9414i	0.243476	+	0.749342i
$782$			45.0922i			1.61249i
$783$	−7.34255	+	2.38574i	−0.262401	+	0.0852593i
$784$	−3.66186	−	2.66050i	−0.130781	−	0.0950178i
$785$	12.4558	−	11.1943i	0.444566	−	0.399542i
$786$	17.0475	−	12.3857i	0.608065	−	0.441785i
$787$	−19.8253	+	27.2872i	−0.706697	+	0.972685i	0.293165	+	0.956062i	$0.405291\pi$
$787$	−19.8253	+	27.2872i	−0.706697	+	0.972685i	−0.999862	+	0.0166229i	$0.994709\pi$
$788$	−5.33430	+	7.34203i	−0.190026	+	0.261549i
$789$	−20.2041	+	14.6792i	−0.719286	+	0.522592i
$790$	6.34509	+	3.67121i	0.225748	+	0.130616i
$791$	−0.977999	−	0.710558i	−0.0347736	−	0.0252645i
$792$	2.83445	−	0.920969i	0.100718	−	0.0327252i
$793$		−	35.5253i		−	1.26154i
$794$	0.691654	+	2.12869i	0.0245459	+	0.0755445i
$795$	0.449441	+	4.31473i	0.0159400	+	0.153028i
$796$	−3.35259	+	10.3182i	−0.118829	+	0.365719i
$797$	−34.5991	−	11.2419i	−1.22556	−	0.398210i	−0.376459	−	0.926433i	$-0.622858\pi$
$797$	−34.5991	−	11.2419i	−1.22556	−	0.398210i	−0.849106	+	0.528223i	$0.822858\pi$
$798$	5.10453	+	7.02579i	0.180698	+	0.248710i
$799$	−19.0125			−0.672612
$800$	37.2638	+	3.98665i	1.31747	+	0.140949i
$801$	−15.6510			−0.553001
$802$	−29.3163	−	40.3504i	−1.03519	−	1.42482i
$803$	68.4131	+	22.2288i	2.41425	+	0.784436i
$804$	3.01635	−	9.28339i	0.106379	−	0.327400i
$805$	20.0293	+	4.27683i	0.705941	+	0.150738i
$806$	18.2790	+	56.2570i	0.643851	+	1.98157i
$807$		−	3.41427i		−	0.120188i
$808$	1.36628	−	0.443932i	0.0480656	−	0.0156175i
$809$	2.63619	+	1.91531i	0.0926836	+	0.0673386i	0.633162	−	0.774019i	$-0.281757\pi$
$809$	2.63619	+	1.91531i	0.0926836	+	0.0673386i	−0.540478	+	0.841358i	$0.681757\pi$
$810$	−4.27122	+	0.444909i	−0.150075	+	0.0156325i
$811$	−15.4432	+	11.2201i	−0.542284	+	0.393993i	−0.824933	−	0.565231i	$-0.808787\pi$
$811$	−15.4432	+	11.2201i	−0.542284	+	0.393993i	0.282648	+	0.959224i	$0.408787\pi$
$812$	−7.66120	+	10.5447i	−0.268855	+	0.370048i
$813$	7.31098	−	10.0627i	0.256407	−	0.352914i
$814$	26.3170	−	19.1204i	0.922410	−	0.670170i
$815$	−45.3858	+	4.72758i	−1.58979	+	0.165600i
$816$	9.38707	+	6.82010i	0.328613	+	0.238751i
$817$	10.9250	−	3.54975i	0.382218	−	0.124190i
$818$		−	53.1071i		−	1.85685i
$819$	1.93175	+	5.94532i	0.0675009	+	0.207746i
$820$	−7.83369	−	1.67272i	−0.273564	−	0.0584138i
$821$	6.21578	−	19.1302i	0.216932	−	0.667649i	−0.782079	−	0.623180i	$-0.785840\pi$
$821$	6.21578	−	19.1302i	0.216932	−	0.667649i	0.999011	−	0.0444687i	$-0.0141595\pi$
$822$	−31.9749	−	10.3893i	−1.11525	−	0.362367i
$823$	−25.0147	−	34.4297i	−0.871956	−	1.20015i	−0.978584	−	0.205846i	$-0.934005\pi$
$823$	−25.0147	−	34.4297i	−0.871956	−	1.20015i	0.106628	−	0.994299i	$-0.465995\pi$
$824$	−4.61216			−0.160672
$825$	−5.12958	−	24.3554i	−0.178589	−	0.847946i
$826$	−16.5353			−0.575336
$827$	8.66147	+	11.9215i	0.301189	+	0.414551i	0.932608	−	0.360891i	$-0.117527\pi$
$827$	8.66147	+	11.9215i	0.301189	+	0.414551i	−0.631419	+	0.775442i	$0.717527\pi$
$828$	14.7064	+	4.77840i	0.511083	+	0.166061i
$829$	−3.35472	+	10.3248i	−0.116514	+	0.358594i	−0.992260	−	0.124179i	$-0.960370\pi$
$829$	−3.35472	+	10.3248i	−0.116514	+	0.358594i	0.875746	+	0.482773i	$0.160370\pi$
$830$	4.44079	+	42.6325i	0.154142	+	1.47980i
$831$	−6.32856	−	19.4773i	−0.219535	−	0.675660i
$832$		−	33.3940i		−	1.15773i
$833$	−2.43800	+	0.792156i	−0.0844719	+	0.0274466i
$834$	2.54687	+	1.85041i	0.0881909	+	0.0640745i
$835$	47.7793	+	27.6447i	1.65347	+	0.956683i
$836$	−30.7448	+	22.3374i	−1.06333	+	0.772556i
$837$	−2.89607	+	3.98610i	−0.100103	+	0.137780i
$838$	14.8678	−	20.4638i	0.513600	−	0.706910i
$839$	5.89103	−	4.28009i	0.203381	−	0.147765i	−0.481433	−	0.876483i	$-0.659883\pi$
$839$	5.89103	−	4.28009i	0.203381	−	0.147765i	0.684814	+	0.728718i	$0.259883\pi$
$840$	0.995714	−	0.894870i	0.0343554	−	0.0308759i
$841$	−24.7597	−	17.9890i	−0.853784	−	0.620311i
$842$	5.87418	−	1.90864i	0.202438	−	0.0657759i
$843$		−	3.55295i		−	0.122370i
$844$	3.82645	+	11.7766i	0.131712	+	0.405368i
$845$	−29.2036	+	50.4737i	−1.00463	+	1.73635i
$846$	−4.40152	+	13.5465i	−0.151327	+	0.465738i
$847$	−13.1055	−	4.25823i	−0.450309	−	0.146314i
$848$	−5.16149	−	7.10418i	−0.177246	−	0.243959i
$849$	−6.12424			−0.210183
$850$	16.5050	−	18.2622i	0.566116	−	0.626389i
$851$	−31.1660			−1.06836
$852$	4.38940	+	6.04149i	0.150378	+	0.206978i
$853$	24.9315	+	8.10074i	0.853639	+	0.277364i	0.702970	−	0.711220i	$-0.251857\pi$
$853$	24.9315	+	8.10074i	0.853639	+	0.277364i	0.150670	+	0.988584i	$0.451857\pi$
$854$	3.37257	−	10.3797i	0.115407	−	0.355186i
$855$	−9.24106	+	4.10409i	−0.316037	+	0.140357i
$856$	0.271312	+	0.835013i	0.00927326	+	0.0285401i
$857$			37.1084i			1.26760i	0.773497	+	0.633799i	$0.218506\pi$
$857$			37.1084i			1.26760i	−0.773497	+	0.633799i	$0.781494\pi$
$858$	−56.8376	+	18.4676i	−1.94040	+	0.630475i
$859$	1.72420	+	1.25271i	0.0588290	+	0.0427418i	0.616811	−	0.787111i	$-0.288424\pi$
$859$	1.72420	+	1.25271i	0.0588290	+	0.0427418i	−0.557982	+	0.829853i	$0.688424\pi$
$860$	3.89239	+	8.76437i	0.132729	+	0.298863i
$861$	−1.71666	+	1.24722i	−0.0585035	+	0.0425053i
$862$	25.1573	−	34.6261i	0.856861	−	1.17937i
$863$	−11.7725	+	16.2035i	−0.400741	+	0.551573i	−0.960930	−	0.276792i	$-0.910729\pi$
$863$	−11.7725	+	16.2035i	−0.400741	+	0.551573i	0.560189	+	0.828365i	$0.310729\pi$
$864$	6.06381	−	4.40562i	0.206295	−	0.149882i
$865$	6.01481	−	28.1687i	0.204510	−	0.957763i
$866$	8.00279	+	5.81437i	0.271946	+	0.197580i
$867$	−9.91821	+	3.22262i	−0.336840	+	0.109446i
$868$			8.31818i			0.282338i
$869$	2.62590	+	8.08167i	0.0890774	+	0.274152i
$870$	−22.1614	−	24.6588i	−0.751343	−	0.836013i
$871$	11.1690	−	34.3746i	0.378447	−	1.16474i
$872$	10.0110	+	3.25278i	0.339016	+	0.110153i
$873$	−2.94540	−	4.05400i	−0.0996867	−	0.137207i
$874$	79.5426			2.69057
$875$	−6.54638	−	9.06338i	−0.221308	−	0.306398i
$876$	24.3961			0.824269
$877$	−23.6382	−	32.5352i	−0.798205	−	1.09863i	−0.993038	−	0.117798i	$-0.962416\pi$
$877$	−23.6382	−	32.5352i	−0.798205	−	1.09863i	0.194833	−	0.980836i	$-0.437584\pi$
$878$	35.6708	+	11.5902i	1.20383	+	0.391149i
$879$	−8.35437	+	25.7121i	−0.281786	+	0.867248i
$880$	33.6776	+	37.4728i	1.13527	+	1.26321i
$881$	7.02531	+	21.6217i	0.236689	+	0.728453i	0.996893	+	0.0787685i	$0.0250988\pi$
$881$	7.02531	+	21.6217i	0.236689	+	0.728453i	−0.760204	+	0.649684i	$0.774901\pi$
$882$			1.92048i			0.0646660i
$883$	−18.4638	+	5.99924i	−0.621355	+	0.201891i	−0.602742	−	0.797936i	$-0.705925\pi$
$883$	−18.4638	+	5.99924i	−0.621355	+	0.201891i	−0.0186134	+	0.999827i	$0.505925\pi$
$884$	−21.8873	−	15.9021i	−0.736150	−	0.534844i
$885$	4.02032	−	18.8280i	0.135142	−	0.632897i
$886$	−57.4112	+	41.7117i	−1.92877	+	1.40133i
$887$	15.2961	−	21.0533i	0.513593	−	0.706900i	−0.470927	−	0.882172i	$-0.656080\pi$
$887$	15.2961	−	21.0533i	0.513593	−	0.706900i	0.984520	+	0.175272i	$0.0560805\pi$
$888$	−1.19743	+	1.64812i	−0.0401831	+	0.0553073i
$889$	−17.7662	+	12.9079i	−0.595858	+	0.432916i
$890$	−27.2799	−	61.4253i	−0.914424	−	2.05898i
$891$	−4.02724	−	2.92596i	−0.134918	−	0.0980234i
$892$	5.96084	−	1.93679i	0.199584	−	0.0648486i
$893$			33.5380i			1.12231i
$894$	6.54429	+	20.1413i	0.218874	+	0.673625i
$895$	1.02951	−	0.457219i	0.0344126	−	0.0152832i
$896$	−1.46210	+	4.49988i	−0.0488453	+	0.150330i
$897$	54.4550	+	17.6935i	1.81820	+	0.590769i
$898$	28.1225	+	38.7072i	0.938458	+	1.29168i
$899$	−38.0392			−1.26868
$900$	−4.20703	−	7.31818i	−0.140234	−	0.243939i
$901$	−4.97325			−0.165683
$902$	−11.9235	−	16.4113i	−0.397010	−	0.546437i
$903$	2.41599	+	0.785002i	0.0803991	+	0.0261232i
$904$	−0.223654	+	0.688335i	−0.00743861	+	0.0228937i
$905$	7.78499	−	13.4551i	0.258782	−	0.447262i
$906$	−0.754263	−	2.32138i	−0.0250587	−	0.0771228i
$907$		−	14.0934i		−	0.467965i	−0.972241	−	0.233983i	$-0.924824\pi$
$907$		−	14.0934i		−	0.467965i	0.972241	−	0.233983i	$-0.0751759\pi$
$908$	−18.9530	+	6.15820i	−0.628977	+	0.204367i
$909$	−1.94124	−	1.41039i	−0.0643867	−	0.0467797i
$910$	−19.9665	+	17.9443i	−0.661882	+	0.594848i
$911$	47.9909	−	34.8674i	1.59001	−	1.15521i	0.686082	−	0.727524i	$-0.259329\pi$
$911$	47.9909	−	34.8674i	1.59001	−	1.15521i	0.903928	−	0.427685i	$-0.140671\pi$
$912$	12.0307	−	16.5588i	0.398375	−	0.548316i
$913$	−29.2050	+	40.1973i	−0.966546	+	1.33034i
$914$	44.5888	−	32.3957i	1.47487	−	1.07155i
$915$	10.9989	+	6.36388i	0.363614	+	0.210383i
$916$	12.2100	+	8.87111i	0.403431	+	0.293110i
$917$	10.4352	−	3.39059i	0.344600	−	0.111967i
$918$		−	4.92310i		−	0.162486i
$919$	18.3222	+	56.3899i	0.604393	+	1.86013i	0.500909	+	0.865500i	$0.332999\pi$
$919$	18.3222	+	56.3899i	0.604393	+	1.86013i	0.103484	+	0.994631i	$0.467001\pi$
$920$	−1.27039	−	12.1960i	−0.0418834	−	0.402090i
$921$	−6.24039	+	19.2060i	−0.205628	+	0.632858i
$922$	23.0560	+	7.49135i	0.759309	+	0.246715i
$923$	16.2531	+	22.3705i	0.534978	+	0.736334i
$924$	−8.40403			−0.276472
$925$	12.6221	+	11.4076i	0.415014	+	0.375080i
$926$	68.6199			2.25499
$927$	4.52804	+	6.23232i	0.148720	+	0.204696i
$928$	55.0345	+	17.8818i	1.80660	+	0.586998i
$929$	−2.38406	+	7.33737i	−0.0782184	+	0.240731i	−0.982518	−	0.186166i	$-0.940394\pi$
$929$	−2.38406	+	7.33737i	−0.0782184	+	0.240731i	0.904300	+	0.426898i	$0.140394\pi$
$930$	−20.6921	−	4.41836i	−0.678521	−	0.144884i
$931$	1.39736	+	4.30064i	0.0457967	+	0.140948i
$932$		−	19.8276i		−	0.649476i
$933$	21.8494	−	7.09931i	0.715318	−	0.232421i
$934$	−7.49783	−	5.44749i	−0.245336	−	0.178247i
$935$	28.3805	−	2.95623i	0.928141	−	0.0966792i
$936$	3.02789	−	2.19989i	0.0989696	−	0.0719056i
$937$	−5.32468	+	7.32879i	−0.173950	+	0.239421i	−0.887086	−	0.461604i	$-0.847274\pi$
$937$	−5.32468	+	7.32879i	−0.173950	+	0.239421i	0.713136	+	0.701025i	$0.247274\pi$
$938$	6.52667	−	8.98319i	0.213103	−	0.293312i
$939$	15.7460	−	11.4401i	0.513850	−	0.373334i
$940$	−27.8477	+	2.90073i	−0.908291	+	0.0946115i
$941$	−9.61060	−	6.98251i	−0.313297	−	0.227623i	0.420013	−	0.907518i	$-0.362025\pi$
$941$	−9.61060	−	6.98251i	−0.313297	−	0.227623i	−0.733310	+	0.679895i	$0.762025\pi$
$942$	13.6794	−	4.44470i	0.445698	−	0.144816i
$943$			19.4352i			0.632896i
$944$	12.0428	+	37.0639i	0.391960	+	1.20633i
$945$	−2.18677	−	0.466938i	−0.0711357	−	0.0151895i
$946$	−7.50466	+	23.0970i	−0.243998	+	0.750947i
$947$	−27.4043	−	8.90421i	−0.890521	−	0.289348i	−0.172202	−	0.985062i	$-0.555088\pi$
$947$	−27.4043	−	8.90421i	−0.890521	−	0.289348i	−0.718319	+	0.695714i	$0.755088\pi$
$948$	1.69395	+	2.33153i	0.0550170	+	0.0757244i
$949$	90.3342			2.93237
$950$	−32.2146	−	29.1148i	−1.04518	−	0.944608i
$951$	−29.7877			−0.965933
$952$	0.902111	+	1.24165i	0.0292376	+	0.0402421i
$953$	−0.325239	−	0.105676i	−0.0105355	−	0.00342319i	0.303744	−	0.952754i	$-0.401763\pi$
$953$	−0.325239	−	0.105676i	−0.0105355	−	0.00342319i	−0.314280	+	0.949330i	$0.601763\pi$
$954$	−1.15134	+	3.54347i	−0.0372761	+	0.114724i
$955$	1.58696	+	15.2351i	0.0513528	+	0.492998i
$956$	5.33873	+	16.4309i	0.172667	+	0.531414i
$957$		−	38.4318i		−	1.24232i
$958$	−19.6206	+	6.37511i	−0.633911	+	0.205970i
$959$	−14.1628	−	10.2899i	−0.457341	−	0.332278i
$960$	10.3391	+	5.98209i	0.333692	+	0.193071i
$961$	5.43960	−	3.95210i	0.175471	−	0.127487i
$962$	24.0113	−	33.0488i	0.774156	−	1.06553i
$963$	0.861971	−	1.18640i	0.0277766	−	0.0382312i
$964$	−12.6456	+	9.18756i	−0.407287	+	0.295911i
$965$	7.75018	−	6.96525i	0.249487	−	0.224219i
$966$	14.2308	+	10.3393i	0.457870	+	0.332662i
$967$	7.37243	−	2.39545i	0.237081	−	0.0770324i	−0.188066	−	0.982156i	$-0.560222\pi$
$967$	7.37243	−	2.39545i	0.237081	−	0.0770324i	0.425148	+	0.905124i	$0.360222\pi$
$968$			8.25010i			0.265168i
$969$	−3.58210	−	11.0246i	−0.115074	−	0.354160i
$970$	10.7768	−	18.6259i	0.346022	−	0.598043i
$971$	−6.37891	+	19.6323i	−0.204709	+	0.630030i	0.795016	+	0.606588i	$0.207462\pi$
$971$	−6.37891	+	19.6323i	−0.204709	+	0.630030i	−0.999725	+	0.0234415i	$0.992538\pi$
$972$	−1.60562	−	0.521699i	−0.0515004	−	0.0167335i
$973$	0.963513	+	1.32616i	0.0308888	+	0.0425148i
$974$	−29.4952			−0.945087
$975$	−15.5778	−	27.0979i	−0.498890	−	0.867826i
$976$	−25.7225			−0.823356
$977$	−12.2466	−	16.8560i	−0.391803	−	0.539270i	0.566860	−	0.823814i	$-0.308158\pi$
$977$	−12.2466	−	16.8560i	−0.391803	−	0.539270i	−0.958663	+	0.284544i	$0.908158\pi$
$978$	−37.2731	−	12.1107i	−1.19186	−	0.387259i
$979$	24.0755	−	74.0966i	0.769455	−	2.36814i
$980$	−3.45010	+	1.53224i	−0.110210	+	0.0489457i
$981$	−5.43302	−	16.7211i	−0.173463	−	0.533864i
$982$			37.2926i			1.19005i
$983$	36.4522	−	11.8440i	1.16265	−	0.377767i	0.336753	−	0.941593i	$-0.390671\pi$
$983$	36.4522	−	11.8440i	1.16265	−	0.377767i	0.825893	+	0.563827i	$0.190671\pi$
$984$	1.02777	+	0.746719i	0.0327641	+	0.0238045i
$985$	−4.87878	−	10.9854i	−0.155451	−	0.350024i
$986$	30.7494	−	22.3407i	0.979260	−	0.711474i
$987$	−4.35942	+	6.00023i	−0.138762	+	0.190989i
$988$	−28.0512	+	38.6092i	−0.892429	+	1.22832i
$989$	18.8239	−	13.6763i	0.598564	−	0.434882i
$990$	4.46395	−	20.9056i	0.141874	−	0.664425i
$991$	13.8138	+	10.0363i	0.438810	+	0.318814i	0.785162	−	0.619290i	$-0.212580\pi$
$991$	13.8138	+	10.0363i	0.438810	+	0.318814i	−0.346352	+	0.938105i	$0.612580\pi$
$992$	35.1225	−	11.4120i	1.11514	−	0.362331i
$993$			16.3755i			0.519662i
$994$	2.62508	+	8.07916i	0.0832624	+	0.256255i
$995$	−9.60523	−	10.6877i	−0.304506	−	0.338821i
$996$	−5.20726	+	16.0263i	−0.164998	+	0.507813i
$997$	−11.3331	−	3.68235i	−0.358923	−	0.116621i	0.124004	−	0.992282i	$-0.460426\pi$
$997$	−11.3331	−	3.68235i	−0.358923	−	0.116621i	−0.482927	+	0.875661i	$0.660426\pi$
$998$	16.5295	+	22.7510i	0.523233	+	0.720169i
$999$	3.40266			0.107655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.z.b.64.5	✓	72
25.9	even	10	inner	525.2.z.b.484.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.z.b.64.5	✓	72	1.1	even	1	trivial
525.2.z.b.484.5	yes	72	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12883 - 1.55370i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.521699 + 1.60562i) q^{4} +(-1.49468 - 1.66311i) q^{5} +(-0.593462 - 1.82649i) q^{6} -1.00000i q^{7} +(-0.569402 + 0.185010i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.12883 - 1.55370i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.521699 + 1.60562i) q^{4} +(-1.49468 - 1.66311i) q^{5} +(-0.593462 - 1.82649i) q^{6} -1.00000i q^{7} +(-0.569402 + 0.185010i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.896746 + 4.19966i) q^{10} +(-4.02724 + 2.92596i) q^{11} +(-0.992330 + 1.36583i) q^{12} +(-3.67441 + 5.05739i) q^{13} +(-1.55370 + 1.12883i) q^{14} +(-0.907591 - 2.04359i) q^{15} +(3.66186 + 2.66050i) q^{16} +(2.43800 - 0.792156i) q^{17} -1.92048i q^{18} +(-1.39736 - 4.30064i) q^{19} +(3.45010 - 1.53224i) q^{20} +(0.309017 - 0.951057i) q^{21} +(9.09215 + 2.95422i) q^{22} +(-5.38371 - 7.41004i) q^{23} -0.598705 q^{24} +(-0.531888 + 4.97163i) q^{25} +12.0055 q^{26} +(0.587785 + 0.809017i) q^{27} +(1.60562 + 0.521699i) q^{28} +(-2.38574 + 7.34255i) q^{29} +(-2.15062 + 3.71700i) q^{30} +(1.52256 + 4.68595i) q^{31} -7.49529i q^{32} +(-4.73430 + 1.53827i) q^{33} +(-3.98287 - 2.89373i) q^{34} +(-1.66311 + 1.49468i) q^{35} +(-1.36583 + 0.992330i) q^{36} +(2.00003 - 2.75281i) q^{37} +(-5.10453 + 7.02579i) q^{38} +(-5.05739 + 3.67441i) q^{39} +(1.15876 + 0.670450i) q^{40} +(-1.71666 - 1.24722i) q^{41} +(-1.82649 + 0.593462i) q^{42} +2.54032i q^{43} +(-2.59699 - 7.99270i) q^{44} +(-0.231665 - 2.22403i) q^{45} +(-5.43570 + 16.7294i) q^{46} +(-7.05369 - 2.29188i) q^{47} +(2.66050 + 3.66186i) q^{48} -1.00000 q^{49} +(8.32485 - 4.78573i) q^{50} +2.56347 q^{51} +(-6.20333 - 8.53816i) q^{52} +(-1.84509 - 0.599507i) q^{53} +(0.593462 - 1.82649i) q^{54} +(10.8856 + 2.32439i) q^{55} +(0.185010 + 0.569402i) q^{56} -4.52196i q^{57} +(14.1012 - 4.58177i) q^{58} +(6.96560 + 5.06081i) q^{59} +(3.75473 - 0.391109i) q^{60} +(-4.59755 + 3.34031i) q^{61} +(5.56186 - 7.65524i) q^{62} +(0.587785 - 0.809017i) q^{63} +(-4.32173 + 3.13992i) q^{64} +(13.9031 - 1.44820i) q^{65} +(7.73424 + 5.61926i) q^{66} +(-5.49881 + 1.78667i) q^{67} +4.32779i q^{68} +(-2.83038 - 8.71102i) q^{69} +(4.19966 + 0.896746i) q^{70} +(1.36688 - 4.20684i) q^{71} +(-0.569402 - 0.185010i) q^{72} +(-8.49380 - 11.6907i) q^{73} -6.53474 q^{74} +(-2.04217 + 4.56394i) q^{75} +7.63422 q^{76} +(2.92596 + 4.02724i) q^{77} +(11.4179 + 3.70990i) q^{78} +(0.527506 - 1.62350i) q^{79} +(-1.04859 - 10.0667i) q^{80} +(0.309017 + 0.951057i) q^{81} +4.07508i q^{82} +(9.49283 - 3.08441i) q^{83} +(1.36583 + 0.992330i) q^{84} +(-4.96147 - 2.87066i) q^{85} +(3.94690 - 2.86759i) q^{86} +(-4.53794 + 6.24594i) q^{87} +(1.75179 - 2.41113i) q^{88} +(-12.6619 + 9.19943i) q^{89} +(-3.19398 + 2.87050i) q^{90} +(5.05739 + 3.67441i) q^{91} +(14.7064 - 4.77840i) q^{92} +4.92710i q^{93} +(4.40152 + 13.5465i) q^{94} +(-5.06385 + 8.75204i) q^{95} +(2.31617 - 7.12844i) q^{96} +(-4.76576 - 1.54849i) q^{97} +(1.12883 + 1.55370i) q^{98} -4.97794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9	\( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) \) 72 * q + 24 * q^4 - 2 * q^5 + 18 * q^9 - 28 * q^10 - 12 * q^11 - 20 * q^13 - 24 * q^16 + 10 * q^19 + 10 * q^20 - 18 * q^21 + 50 * q^22 - 10 * q^23 + 12 * q^25 + 36 * q^26 + 20 * q^28 - 2 * q^29 + 10 * q^30 - 16 * q^31 - 10 * q^33 + 24 * q^34 - 10 * q^35 - 24 * q^36 + 10 * q^37 - 100 * q^38 + 16 * q^39 - 14 * q^40 - 16 * q^41 - 18 * q^44 + 2 * q^45 - 44 * q^46 + 20 * q^47 - 72 * q^49 + 86 * q^50 + 32 * q^51 - 80 * q^52 + 70 * q^53 + 46 * q^55 - 40 * q^58 + 44 * q^59 - 62 * q^60 + 4 * q^61 - 50 * q^62 + 48 * q^64 + 38 * q^65 - 16 * q^66 - 20 * q^67 + 4 * q^69 + 10 * q^70 - 8 * q^71 - 20 * q^73 - 116 * q^74 - 8 * q^75 + 92 * q^76 + 20 * q^77 + 90 * q^78 + 28 * q^79 + 114 * q^80 - 18 * q^81 + 30 * q^83 + 24 * q^84 - 122 * q^85 + 40 * q^86 - 40 * q^87 - 270 * q^88 + 2 * q^89 - 12 * q^90 - 16 * q^91 - 100 * q^92 + 22 * q^94 + 116 * q^95 + 10 * q^96 + 190 * q^97 - 48 * q^99

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