LMFDB - Embedded newform 315.2.t.c.131.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (of order $6$, degree $2$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.4
Character	$\chi$	$=$	315.131
Dual form			315.2.t.c.101.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71080i q^{2} +(1.72161 - 0.189893i) q^{3} -0.926832 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.324870 - 2.94533i) q^{6} +(1.44091 + 2.21896i) q^{7} -1.83597i q^{8} +(2.92788 - 0.653845i) q^{9} +O(q^{10})$	\(q-1.71080i q^{2} +(1.72161 - 0.189893i) q^{3} -0.926832 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.324870 - 2.94533i) q^{6} +(1.44091 + 2.21896i) q^{7} -1.83597i q^{8} +(2.92788 - 0.653845i) q^{9} +(-1.48159 + 0.855399i) q^{10} +(-0.497227 - 0.287074i) q^{11} +(-1.59564 + 0.175999i) q^{12} +(-0.130417 - 0.0752961i) q^{13} +(3.79620 - 2.46510i) q^{14} +(-1.02526 - 1.39601i) q^{15} -4.99465 q^{16} +(-0.586913 - 1.01656i) q^{17} +(-1.11860 - 5.00901i) q^{18} +(0.00148739 + 0.000858744i) q^{19} +(0.463416 + 0.802660i) q^{20} +(2.90205 + 3.54657i) q^{21} +(-0.491126 + 0.850655i) q^{22} +(-6.46683 + 3.73363i) q^{23} +(-0.348640 - 3.16083i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.128816 + 0.223117i) q^{26} +(4.91651 - 1.68165i) q^{27} +(-1.33548 - 2.05660i) q^{28} +(5.81941 - 3.35984i) q^{29} +(-2.38829 + 1.75401i) q^{30} +6.63760i q^{31} +4.87288i q^{32} +(-0.910544 - 0.399809i) q^{33} +(-1.73914 + 1.00409i) q^{34} +(1.20122 - 2.35734i) q^{35} +(-2.71365 + 0.606004i) q^{36} +(-0.718409 + 1.24432i) q^{37} +(0.00146914 - 0.00254462i) q^{38} +(-0.238825 - 0.104865i) q^{39} +(-1.59000 + 0.917987i) q^{40} +(-5.37138 + 9.30350i) q^{41} +(6.06746 - 4.96481i) q^{42} +(-3.00541 - 5.20553i) q^{43} +(0.460846 + 0.266069i) q^{44} +(-2.03019 - 2.20870i) q^{45} +(6.38748 + 11.0634i) q^{46} -8.44431 q^{47} +(-8.59883 + 0.948451i) q^{48} +(-2.84758 + 6.39463i) q^{49} +(1.48159 + 0.855399i) q^{50} +(-1.20347 - 1.63867i) q^{51} +(0.120874 + 0.0697868i) q^{52} +(9.60845 - 5.54744i) q^{53} +(-2.87697 - 8.41115i) q^{54} +0.574148i q^{55} +(4.07396 - 2.64547i) q^{56} +(0.00272377 + 0.00119598i) q^{57} +(-5.74801 - 9.95584i) q^{58} +10.2693 q^{59} +(0.950241 + 1.29387i) q^{60} +7.35365i q^{61} +11.3556 q^{62} +(5.66966 + 5.55472i) q^{63} -1.65277 q^{64} +0.150592i q^{65} +(-0.683993 + 1.55776i) q^{66} -8.20281 q^{67} +(0.543970 + 0.942183i) q^{68} +(-10.4244 + 7.65586i) q^{69} +(-4.03294 - 2.05505i) q^{70} +0.0708560i q^{71} +(-1.20044 - 5.37552i) q^{72} +(10.2405 - 5.91235i) q^{73} +(2.12878 + 1.22905i) q^{74} +(-0.696352 + 1.58590i) q^{75} +(-0.00137856 - 0.000795911i) q^{76} +(-0.0794513 - 1.51697i) q^{77} +(-0.179403 + 0.408581i) q^{78} +3.31080 q^{79} +(2.49732 + 4.32549i) q^{80} +(8.14497 - 3.82876i) q^{81} +(15.9164 + 9.18935i) q^{82} +(4.47627 + 7.75313i) q^{83} +(-2.68971 - 3.28707i) q^{84} +(-0.586913 + 1.01656i) q^{85} +(-8.90561 + 5.14166i) q^{86} +(9.38075 - 6.88940i) q^{87} +(-0.527061 + 0.912896i) q^{88} +(0.699730 - 1.21197i) q^{89} +(-3.77864 + 3.47324i) q^{90} +(-0.0208391 - 0.397884i) q^{91} +(5.99366 - 3.46044i) q^{92} +(1.26044 + 11.4274i) q^{93} +14.4465i q^{94} -0.00171749i q^{95} +(0.925329 + 8.38920i) q^{96} +(14.9143 - 8.61076i) q^{97} +(10.9399 + 4.87163i) q^{98} +(-1.64352 - 0.515409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.71080i		−	1.20972i	−0.796333	−	0.604859i	$-0.793230\pi$
$2$		−	1.71080i		−	1.20972i	0.796333	−	0.604859i	$-0.206770\pi$
$3$	1.72161	−	0.189893i	0.993972	−	0.109635i
$3$	1.72161	−	0.189893i	0.993972	−	0.109635i
$4$	−0.926832			−0.463416
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.324870	−	2.94533i	−0.132627	−	1.20242i
$7$	1.44091	+	2.21896i	0.544611	+	0.838688i
$7$	1.44091	+	2.21896i	0.544611	+	0.838688i
$8$		−	1.83597i		−	0.649115i
$9$	2.92788	−	0.653845i	0.975960	−	0.217948i
$10$	−1.48159	+	0.855399i	−0.468521	+	0.270501i
$11$	−0.497227	−	0.287074i	−0.149920	−	0.0865561i	0.423164	−	0.906053i	$-0.360920\pi$
$11$	−0.497227	−	0.287074i	−0.149920	−	0.0865561i	−0.573083	+	0.819497i	$0.694253\pi$
$12$	−1.59564	+	0.175999i	−0.460622	+	0.0508066i
$13$	−0.130417	−	0.0752961i	−0.0361711	−	0.0208834i	0.481805	−	0.876278i	$-0.339981\pi$
$13$	−0.130417	−	0.0752961i	−0.0361711	−	0.0208834i	−0.517976	+	0.855395i	$0.673315\pi$
$14$	3.79620	−	2.46510i	1.01458	−	0.658826i
$15$	−1.02526	−	1.39601i	−0.264720	−	0.360449i
$16$	−4.99465			−1.24866
$17$	−0.586913	−	1.01656i	−0.142347	−	0.246553i	0.786033	−	0.618185i	$-0.212132\pi$
$17$	−0.586913	−	1.01656i	−0.142347	−	0.246553i	−0.928380	+	0.371632i	$0.878798\pi$
$18$	−1.11860	−	5.00901i	−0.263656	−	1.18064i
$19$	0.00148739		0.000858744i	0.000341230		0.000197009i	0.500171	−	0.865927i	$-0.333271\pi$
$19$	0.00148739		0.000858744i	0.000341230		0.000197009i	−0.499829	+	0.866124i	$0.666604\pi$
$20$	0.463416	+	0.802660i	0.103623	+	0.179480i
$21$	2.90205	+	3.54657i	0.633278	+	0.773924i
$22$	−0.491126	+	0.850655i	−0.104708	+	0.181360i
$23$	−6.46683	+	3.73363i	−1.34843	+	0.778515i	−0.988027	−	0.154283i	$-0.950693\pi$
$23$	−6.46683	+	3.73363i	−1.34843	+	0.778515i	−0.360401	+	0.932798i	$0.617360\pi$
$24$	−0.348640	−	3.16083i	−0.0711658	−	0.645202i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.128816	+	0.223117i	−0.0252630	+	0.0437568i
$27$	4.91651	−	1.68165i	0.946182	−	0.323634i
$28$	−1.33548	−	2.05660i	−0.252382	−	0.388661i
$29$	5.81941	−	3.35984i	1.08064	−	0.623906i	0.149569	−	0.988751i	$-0.452211\pi$
$29$	5.81941	−	3.35984i	1.08064	−	0.623906i	0.931068	+	0.364845i	$0.118878\pi$
$30$	−2.38829	+	1.75401i	−0.436041	+	0.320237i
$31$			6.63760i			1.19215i	0.802930	+	0.596074i	$0.203273\pi$
$31$			6.63760i			1.19215i	−0.802930	+	0.596074i	$0.796727\pi$
$32$			4.87288i			0.861412i
$33$	−0.910544	−	0.399809i	−0.158505	−	0.0695979i
$34$	−1.73914	+	1.00409i	−0.298259	+	0.172200i
$35$	1.20122	−	2.35734i	0.203044	−	0.398464i
$36$	−2.71365	+	0.606004i	−0.452275	+	0.101001i
$37$	−0.718409	+	1.24432i	−0.118106	+	0.204565i	−0.919017	−	0.394218i	$-0.871015\pi$
$37$	−0.718409	+	1.24432i	−0.118106	+	0.204565i	0.800911	+	0.598783i	$0.204349\pi$
$38$	0.00146914	−	0.00254462i	0.000238326	−	0.000412792i
$39$	−0.238825	−	0.104865i	−0.0382426	−	0.0167919i
$40$	−1.59000	+	0.917987i	−0.251401	+	0.145147i
$41$	−5.37138	+	9.30350i	−0.838869	+	1.45296i	0.0519726	+	0.998649i	$0.483449\pi$
$41$	−5.37138	+	9.30350i	−0.838869	+	1.45296i	−0.890841	+	0.454315i	$0.849884\pi$
$42$	6.06746	−	4.96481i	0.936230	−	0.766088i
$43$	−3.00541	−	5.20553i	−0.458321	−	0.793836i	0.540551	−	0.841311i	$-0.318216\pi$
$43$	−3.00541	−	5.20553i	−0.458321	−	0.793836i	−0.998872	+	0.0474753i	$0.984882\pi$
$44$	0.460846	+	0.266069i	0.0694751	+	0.0401115i
$45$	−2.03019	−	2.20870i	−0.302642	−	0.329253i
$46$	6.38748	+	11.0634i	0.941783	+	1.63122i
$47$	−8.44431			−1.23173			−0.615864	−	0.787852i	$-0.711193\pi$
$47$	−8.44431			−1.23173			−0.615864	+	0.787852i	$0.711193\pi$
$48$	−8.59883	+	0.948451i	−1.24113	+	0.136897i
$49$	−2.84758	+	6.39463i	−0.406797	+	0.913519i
$50$	1.48159	+	0.855399i	0.209529	+	0.120972i
$51$	−1.20347	−	1.63867i	−0.168520	−	0.229460i
$52$	0.120874	+	0.0697868i	0.0167622	+	0.00967769i
$53$	9.60845	−	5.54744i	1.31982	−	0.762000i	0.336123	−	0.941818i	$-0.390884\pi$
$53$	9.60845	−	5.54744i	1.31982	−	0.762000i	0.983700	+	0.179818i	$0.0575509\pi$
$54$	−2.87697	−	8.41115i	−0.391506	−	1.14461i
$55$			0.574148i			0.0774181i
$56$	4.07396	−	2.64547i	0.544405	−	0.353516i
$57$	0.00272377	+	0.00119598i	0.000360772	+	0.000158411i
$58$	−5.74801	−	9.95584i	−0.754750	−	1.30727i
$59$	10.2693			1.33695			0.668475	−	0.743735i	$-0.266947\pi$
$59$	10.2693			1.33695			0.668475	+	0.743735i	$0.266947\pi$
$60$	0.950241	+	1.29387i	0.122676	+	0.167038i
$61$			7.35365i			0.941538i	0.882256	+	0.470769i	$0.156023\pi$
$61$			7.35365i			0.941538i	−0.882256	+	0.470769i	$0.843977\pi$
$62$	11.3556			1.44216
$63$	5.66966	+	5.55472i	0.714310	+	0.699829i
$64$	−1.65277			−0.206596
$65$			0.150592i			0.0186787i
$66$	−0.683993	+	1.55776i	−0.0841938	+	0.191747i
$67$	−8.20281			−1.00213			−0.501066	−	0.865409i	$-0.667059\pi$
$67$	−8.20281			−1.00213			−0.501066	+	0.865409i	$0.667059\pi$
$68$	0.543970	+	0.942183i	0.0659660	+	0.114257i
$69$	−10.4244	+	7.65586i	−1.25495	+	0.921657i
$70$	−4.03294	−	2.05505i	−0.482028	−	0.245626i
$71$			0.0708560i			0.00840906i	0.999991	+	0.00420453i	$0.00133835\pi$
$71$			0.0708560i			0.00840906i	−0.999991	+	0.00420453i	$0.998662\pi$
$72$	−1.20044	−	5.37552i	−0.141474	−	0.633511i
$73$	10.2405	−	5.91235i	1.19856	−	0.691989i	0.238326	−	0.971185i	$-0.423401\pi$
$73$	10.2405	−	5.91235i	1.19856	−	0.691989i	0.960234	+	0.279197i	$0.0900681\pi$
$74$	2.12878	+	1.22905i	0.247466	+	0.142874i
$75$	−0.696352	+	1.58590i	−0.0804078	+	0.183124i
$76$	−0.00137856		0.000795911i	−0.000158132		9.12973e-5i
$77$	−0.0794513	−	1.51697i	−0.00905431	−	0.172875i
$78$	−0.179403	+	0.408581i	−0.0203134	+	0.0462627i
$79$	3.31080			0.372494			0.186247	−	0.982503i	$-0.440368\pi$
$79$	3.31080			0.372494			0.186247	+	0.982503i	$0.440368\pi$
$80$	2.49732	+	4.32549i	0.279209	+	0.483605i
$81$	8.14497	−	3.82876i	0.904997	−	0.425418i
$82$	15.9164	+	9.18935i	1.75767	+	1.01479i
$83$	4.47627	+	7.75313i	0.491334	+	0.851016i	0.999950	−	0.00997747i	$-0.00317598\pi$
$83$	4.47627	+	7.75313i	0.491334	+	0.851016i	−0.508616	+	0.860994i	$0.669843\pi$
$84$	−2.68971	−	3.28707i	−0.293471	−	0.358649i
$85$	−0.586913	+	1.01656i	−0.0636597	+	0.110262i
$86$	−8.90561	+	5.14166i	−0.960317	+	0.554439i
$87$	9.38075	−	6.88940i	1.00572	−	0.738621i
$88$	−0.527061	+	0.912896i	−0.0561849	+	0.0973151i
$89$	0.699730	−	1.21197i	0.0741713	−	0.128468i	−0.826554	−	0.562857i	$-0.809702\pi$
$89$	0.699730	−	1.21197i	0.0741713	−	0.128468i	0.900726	+	0.434389i	$0.143036\pi$
$90$	−3.77864	+	3.47324i	−0.398303	+	0.366112i
$91$	−0.0208391	−	0.397884i	−0.00218453	−	0.0417096i
$92$	5.99366	−	3.46044i	0.624883	−	0.360776i
$93$	1.26044	+	11.4274i	0.130701	+	1.18496i
$94$			14.4465i			1.49004i
$95$		−	0.00171749i		−	0.000176211i
$96$	0.925329	+	8.38920i	0.0944410	+	0.856220i
$97$	14.9143	−	8.61076i	1.51432	−	0.874291i	0.514457	−	0.857516i	$-0.327994\pi$
$97$	14.9143	−	8.61076i	1.51432	−	0.874291i	0.999859	−	0.0167742i	$-0.00533965\pi$
$98$	10.9399	+	4.87163i	1.10510	+	0.492109i
$99$	−1.64352	−	0.515409i	−0.165180	−	0.0518006i
$100$	0.463416	−	0.802660i	0.0463416	−	0.0802660i
$101$	−6.67484	+	11.5612i	−0.664171	+	1.15038i	0.315338	+	0.948979i	$0.397882\pi$
$101$	−6.67484	+	11.5612i	−0.664171	+	1.15038i	−0.979509	+	0.201399i	$0.935451\pi$
$102$	−2.80344	+	2.05890i	−0.277582	+	0.203862i
$103$	−3.84810	+	2.22170i	−0.379165	+	0.218911i	−0.677455	−	0.735564i	$-0.736917\pi$
$103$	−3.84810	+	2.22170i	−0.379165	+	0.218911i	0.298290	+	0.954475i	$0.403584\pi$
$104$	−0.138242	+	0.239442i	−0.0135557	+	0.0234792i
$105$	1.62039	−	4.28653i	0.158134	−	0.418322i
$106$	−9.49056	−	16.4381i	−0.921805	−	1.59661i
$107$	−5.21803	−	3.01263i	−0.504446	−	0.291242i	0.226102	−	0.974104i	$-0.427402\pi$
$107$	−5.21803	−	3.01263i	−0.504446	−	0.291242i	−0.730548	+	0.682862i	$0.760735\pi$
$108$	−4.55677	+	1.55861i	−0.438476	+	0.149977i
$109$	2.58035	+	4.46930i	0.247153	+	0.428082i	0.962735	−	0.270447i	$-0.0871716\pi$
$109$	2.58035	+	4.46930i	0.247153	+	0.428082i	−0.715582	+	0.698529i	$0.753838\pi$
$110$	0.982252			0.0936541
$111$	−1.00053	+	2.27866i	−0.0949662	+	0.216280i
$112$	−7.19682	−	11.0829i	−0.680035	−	1.04724i
$113$	−7.32830	−	4.23100i	−0.689389	−	0.398019i	0.113994	−	0.993481i	$-0.463635\pi$
$113$	−7.32830	−	4.23100i	−0.689389	−	0.398019i	−0.803383	+	0.595463i	$0.796969\pi$
$114$	0.00204608	−	0.00465983i	0.000191633	−	0.000436433i
$115$	6.46683	+	3.73363i	0.603035	+	0.348162i
$116$	−5.39361	+	3.11400i	−0.500785	+	0.289128i
$117$	−0.431076	−	0.135186i	−0.0398530	−	0.0124979i
$118$		−	17.5687i		−	1.61733i
$119$	1.41003	−	2.76711i	0.129257	−	0.253661i
$120$	−2.56304	+	1.88235i	−0.233973	+	0.171834i
$121$	−5.33518	−	9.24080i	−0.485016	−	0.840072i
$122$	12.5806			1.13899
$123$	−7.48075	+	17.0370i	−0.674516	+	1.53617i
$124$		−	6.15193i		−	0.552460i
$125$	1.00000			0.0894427
$126$	9.50301	−	9.69964i	0.846596	−	0.864113i
$127$	−6.42212			−0.569871			−0.284936	−	0.958547i	$-0.591972\pi$
$127$	−6.42212			−0.569871			−0.284936	+	0.958547i	$0.591972\pi$
$128$			12.5733i			1.11134i
$129$	−6.16265	−	8.39118i	−0.542591	−	0.738803i
$130$	0.257633			0.0225959
$131$	−6.67485	−	11.5612i	−0.583185	−	1.01011i	−0.995099	−	0.0988828i	$-0.968473\pi$
$131$	−6.67485	−	11.5612i	−0.583185	−	1.01011i	0.411915	−	0.911222i	$-0.364860\pi$
$132$	0.843921	+	0.370556i	0.0734539	+	0.0322528i
$133$	0.000237668		0.00453783i	2.06084e−5		0.000393480i
$134$			14.0334i			1.21230i
$135$	−3.91461	−	3.41699i	−0.336916	−	0.294088i
$136$	−1.86639	+	1.07756i	−0.160041	+	0.0923998i
$137$	−15.8371	−	9.14358i	−1.35306	−	0.781189i	−0.364382	−	0.931250i	$-0.618720\pi$
$137$	−15.8371	−	9.14358i	−1.35306	−	0.781189i	−0.988677	+	0.150061i	$0.952053\pi$
$138$	13.0976	+	17.8340i	1.11494	+	1.51813i
$139$	4.60943	+	2.66125i	0.390967	+	0.225725i	0.682579	−	0.730812i	$-0.260858\pi$
$139$	4.60943	+	2.66125i	0.390967	+	0.225725i	−0.291612	+	0.956537i	$0.594192\pi$
$140$	−1.11333	+	2.18486i	−0.0940937	+	0.184654i
$141$	−14.5378	+	1.60352i	−1.22430	+	0.135041i
$142$	0.121220			0.0101726
$143$	0.0432311	+	0.0748785i	0.00361517	+	0.00626166i
$144$	−14.6237	+	3.26572i	−1.21864	+	0.272144i
$145$	−5.81941	−	3.35984i	−0.483276	−	0.279019i
$146$	−10.1148	−	17.5194i	−0.837111	−	1.44992i
$147$	−3.68812	+	11.5498i	−0.304191	+	0.952611i
$148$	0.665844	−	1.15328i	0.0547320	−	0.0947987i
$149$	0.627546	−	0.362314i	0.0514106	−	0.0296819i	−0.474074	−	0.880485i	$-0.657217\pi$
$149$	0.627546	−	0.362314i	0.0514106	−	0.0296819i	0.525485	+	0.850803i	$0.323884\pi$
$150$	2.71316	+	1.19132i	0.221529	+	0.0972708i
$151$	1.93186	−	3.34608i	0.157213	−	0.272300i	−0.776650	−	0.629933i	$-0.783083\pi$
$151$	1.93186	−	3.34608i	0.157213	−	0.272300i	0.933863	+	0.357632i	$0.116416\pi$
$152$	0.00157663	−	0.00273081i	0.000127882	−	0.000221498i
$153$	−2.38309	−	2.59263i	−0.192661	−	0.209601i
$154$	−2.59524	+	0.135925i	−0.209130	+	0.0109532i
$155$	5.74833	−	3.31880i	0.461717	−	0.266572i
$156$	0.221350	+	0.0971924i	0.0177222	+	0.00778162i
$157$		−	6.55283i		−	0.522972i	−0.965207	−	0.261486i	$-0.915787\pi$
$157$		−	6.55283i		−	0.522972i	0.965207	−	0.261486i	$-0.0842126\pi$
$158$		−	5.66411i		−	0.450612i
$159$	15.4886	−	11.3751i	1.22832	−	0.902105i
$160$	4.22004	−	2.43644i	0.333624	−	0.192618i
$161$	−17.6029	−	8.96984i	−1.38730	−	0.706922i
$162$	−6.55024	−	13.9344i	−0.514635	−	1.09479i
$163$	9.53391	−	16.5132i	0.746753	−	1.29341i	−0.202618	−	0.979258i	$-0.564945\pi$
$163$	9.53391	−	16.5132i	0.746753	−	1.29341i	0.949371	−	0.314157i	$-0.101722\pi$
$164$	4.97836	−	8.62278i	0.388745	−	0.673326i
$165$	0.109027	+	0.988459i	0.00848774	+	0.0769515i
$166$	13.2640	−	7.65799i	1.02949	−	0.594376i
$167$	−3.03835	+	5.26258i	−0.235115	+	0.407231i	−0.959306	−	0.282368i	$-0.908880\pi$
$167$	−3.03835	+	5.26258i	−0.235115	+	0.407231i	0.724191	+	0.689599i	$0.242213\pi$
$168$	6.51141	−	5.32808i	0.502366	−	0.411070i
$169$	−6.48866	−	11.2387i	−0.499128	−	0.864515i
$170$	1.73914	+	1.00409i	0.133386	+	0.0770102i
$171$	0.00491638	+	0.00154178i	0.000375965	+	0.000117903i
$172$	2.78551	+	4.82465i	0.212393	+	0.367876i
$173$	−19.6507			−1.49401			−0.747006	−	0.664817i	$-0.768509\pi$
$173$	−19.6507			−1.49401			−0.747006	+	0.664817i	$0.768509\pi$
$174$	−11.7864	−	16.0486i	−0.893523	−	1.21664i
$175$	−2.64213	+	0.138381i	−0.199726	+	0.0104606i
$176$	2.48347	+	1.43383i	0.187199	+	0.108079i
$177$	17.6797	−	1.95007i	1.32889	−	0.146577i
$178$	−2.07343	−	1.19710i	−0.155410	−	0.0897263i
$179$	−11.5181	+	6.64999i	−0.860905	+	0.497044i	−0.864315	−	0.502951i	$-0.832248\pi$
$179$	−11.5181	+	6.64999i	−0.860905	+	0.497044i	0.00341036	+	0.999994i	$0.498914\pi$
$180$	1.88164	+	2.04709i	0.140249	+	0.152581i
$181$			7.87417i			0.585282i	0.956222	+	0.292641i	$0.0945341\pi$
$181$			7.87417i			0.585282i	−0.956222	+	0.292641i	$0.905466\pi$
$182$	−0.680700	+	0.0356515i	−0.0504568	+	0.00264267i
$183$	1.39641	+	12.6601i	0.103226	+	0.935862i
$184$	6.85484	+	11.8729i	0.505346	+	0.875285i
$185$	1.43682			0.105637
$186$	19.5499	−	2.15635i	1.43347	−	0.158111i
$187$			0.673950i			0.0492841i
$188$	7.82645			0.570803
$189$	10.8157	+	8.48644i	0.786730	+	0.617297i
$190$	−0.00293828			−0.000213165
$191$		−	6.63671i		−	0.480215i	−0.970746	−	0.240108i	$-0.922817\pi$
$191$		−	6.63671i		−	0.480215i	0.970746	−	0.240108i	$-0.0771827\pi$
$192$	−2.84543	+	0.313850i	−0.205351	+	0.0226502i
$193$	−10.8444			−0.780600			−0.390300	−	0.920688i	$-0.627629\pi$
$193$	−10.8444			−0.780600			−0.390300	+	0.920688i	$0.627629\pi$
$194$	−14.7313	−	25.5153i	−1.05764	−	1.83189i
$195$	0.0285965	+	0.259261i	0.00204784	+	0.0185661i
$196$	2.63922	−	5.92675i	0.188516	−	0.423339i
$197$		−	11.0578i		−	0.787838i	−0.919145	−	0.393919i	$-0.871119\pi$
$197$		−	11.0578i		−	0.787838i	0.919145	−	0.393919i	$-0.128881\pi$
$198$	−0.881762	+	2.81174i	−0.0626641	+	0.199821i
$199$	0.779269	−	0.449911i	0.0552409	−	0.0318933i	−0.472125	−	0.881532i	$-0.656513\pi$
$199$	0.779269	−	0.449911i	0.0552409	−	0.0318933i	0.527366	+	0.849638i	$0.323180\pi$
$200$	1.59000	+	0.917987i	0.112430	+	0.0649115i
$201$	−14.1220	+	1.55766i	−0.996092	+	0.109869i
$202$	19.7788	+	11.4193i	1.39163	+	0.803459i
$203$	15.8406	+	8.07183i	1.11179	+	0.566532i
$204$	1.11542	+	1.51878i	0.0780949	+	0.106336i
$205$	10.7428			0.750307
$206$	3.80088	+	6.58333i	0.264820	+	0.458682i
$207$	−16.4929	+	15.1599i	−1.14634	+	1.05369i
$208$	0.651385	+	0.376077i	0.0451654	+	0.0260763i
$209$	−0.000493046	0	0.000853981i	−3.41047e−5	0	5.90711e-5i
$210$	−7.33339	−	2.77217i	−0.506052	−	0.191298i
$211$	−9.71550	+	16.8277i	−0.668842	+	1.15847i	0.309386	+	0.950937i	$0.399877\pi$
$211$	−9.71550	+	16.8277i	−0.668842	+	1.15847i	−0.978228	+	0.207532i	$0.933457\pi$
$212$	−8.90542	+	5.14155i	−0.611627	+	0.353123i
$213$	0.0134551	+	0.121986i	0.000921927	+	0.00835837i
$214$	−5.15400	+	8.92699i	−0.352320	+	0.610237i
$215$	−3.00541	+	5.20553i	−0.204968	+	0.355014i
$216$	−3.08747	−	9.02659i	−0.210076	−	0.614181i
$217$	−14.7286	+	9.56416i	−0.999840	+	0.649257i
$218$	7.64608	−	4.41447i	0.517858	−	0.298985i
$219$	16.5074	−	12.1234i	1.11547	−	0.819221i
$220$		−	0.532139i		−	0.0358768i
$221$			0.176769i			0.0118908i
$222$	3.89832	+	1.71171i	0.261638	+	0.114882i
$223$	−2.12653	+	1.22775i	−0.142403	+	0.0822164i	−0.569509	−	0.821985i	$-0.692867\pi$
$223$	−2.12653	+	1.22775i	−0.142403	+	0.0822164i	0.427106	+	0.904202i	$0.359533\pi$
$224$	−10.8127	+	7.02137i	−0.722457	+	0.469135i
$225$	−0.897694	+	2.86254i	−0.0598463	+	0.190836i
$226$	−7.23839	+	12.5373i	−0.481490	+	0.833966i
$227$	0.929028	−	1.60912i	0.0616618	−	0.106801i	−0.833547	−	0.552449i	$-0.813693\pi$
$227$	0.929028	−	1.60912i	0.0616618	−	0.106801i	0.895208	+	0.445648i	$0.147027\pi$
$228$	−0.00252448	−	0.00110847i	−0.000167188	−	7.34102e-5i
$229$	23.5639	−	13.6046i	1.55715	−	0.899019i	0.559619	−	0.828750i	$-0.310948\pi$
$229$	23.5639	−	13.6046i	1.55715	−	0.899019i	0.997528	−	0.0702690i	$-0.0223858\pi$
$230$	6.38748	−	11.0634i	0.421178	−	0.729502i
$231$	−0.424848	−	2.59655i	−0.0279529	−	0.170840i
$232$	−6.16858	−	10.6843i	−0.404987	−	0.701458i
$233$	−4.27773	−	2.46975i	−0.280244	−	0.161799i	0.353290	−	0.935514i	$-0.385063\pi$
$233$	−4.27773	−	2.46975i	−0.280244	−	0.161799i	−0.633534	+	0.773715i	$0.718396\pi$
$234$	−0.231276	+	0.737485i	−0.0151190	+	0.0482109i
$235$	4.22215	+	7.31298i	0.275423	+	0.477046i
$236$	−9.51792			−0.619564
$237$	5.69990	−	0.628699i	0.370248	−	0.0408384i
$238$	−4.73397	−	2.41227i	−0.306858	−	0.156364i
$239$	16.7127	+	9.64908i	1.08105	+	0.624147i	0.931181	−	0.364558i	$-0.118780\pi$
$239$	16.7127	+	9.64908i	1.08105	+	0.624147i	0.149874	+	0.988705i	$0.452113\pi$
$240$	5.12080	+	6.97258i	0.330546	+	0.450078i
$241$	14.8776	+	8.58961i	0.958353	+	0.553305i	0.895666	−	0.444728i	$-0.146700\pi$
$241$	14.8776	+	8.58961i	0.958353	+	0.553305i	0.0626870	+	0.998033i	$0.480033\pi$
$242$	−15.8091	+	9.12741i	−1.01625	+	0.586732i
$243$	13.2954	−	8.13831i	0.852901	−	0.522073i
$244$		−	6.81559i		−	0.436324i
$245$	6.96170	−	0.731242i	0.444767	−	0.0467173i
$246$	29.1469	+	12.7981i	1.85834	+	0.815974i
$247$	−0.000129320	0	0.000223989i	−8.22845e−6	0	1.42521e-5i
$248$	12.1865			0.773841
$249$	9.17866	+	12.4978i	0.581674	+	0.792019i
$250$		−	1.71080i		−	0.108200i
$251$	−14.8491			−0.937268			−0.468634	−	0.883392i	$-0.655254\pi$
$251$	−14.8491			−0.937268			−0.468634	+	0.883392i	$0.655254\pi$
$252$	−5.25482	−	5.14829i	−0.331023	−	0.324312i
$253$	4.28731			0.269541
$254$			10.9870i			0.689383i
$255$	−0.817397	+	1.86158i	−0.0511874	+	0.116576i
$256$	18.2049			1.13781
$257$	−6.95267	−	12.0424i	−0.433695	−	0.751182i	0.563493	−	0.826121i	$-0.309457\pi$
$257$	−6.95267	−	12.0424i	−0.433695	−	0.751182i	−0.997188	+	0.0749386i	$0.976124\pi$
$258$	−14.3556	+	10.5430i	−0.893742	+	0.656382i
$259$	−3.79626	+	0.198828i	−0.235888	+	0.0123546i
$260$		−	0.139574i		−	0.00865599i
$261$	14.8417	−	13.6422i	0.918680	−	0.844431i
$262$	−19.7789	+	11.4193i	−1.22194	+	0.705488i
$263$	3.25213	+	1.87762i	0.200535	+	0.115779i	0.596905	−	0.802312i	$-0.296397\pi$
$263$	3.25213	+	1.87762i	0.200535	+	0.115779i	−0.396370	+	0.918091i	$0.629730\pi$
$264$	−0.734040	+	1.67174i	−0.0451771	+	0.102888i
$265$	−9.60845	−	5.54744i	−0.590243	−	0.340777i
$266$	0.00776331		0.000406602i	0.000475999		2.49304e-5i
$267$	0.974518	−	2.21941i	0.0596395	−	0.135826i
$268$	7.60262			0.464404
$269$	−11.2443	−	19.4757i	−0.685578	−	1.18746i	−0.973255	−	0.229729i	$-0.926216\pi$
$269$	−11.2443	−	19.4757i	−0.685578	−	1.18746i	0.287677	−	0.957728i	$-0.407117\pi$
$270$	−5.84579	+	6.69710i	−0.355763	+	0.407573i
$271$	19.6597	+	11.3506i	1.19424	+	0.689497i	0.959266	−	0.282504i	$-0.0911650\pi$
$271$	19.6597	+	11.3506i	1.19424	+	0.689497i	0.234978	+	0.972001i	$0.424498\pi$
$272$	2.93142	+	5.07738i	0.177744	+	0.307861i
$273$	−0.111432	−	0.681044i	−0.00674420	−	0.0412187i
$274$	−15.6428	+	27.0942i	−0.945017	+	1.63682i
$275$	0.497227	−	0.287074i	0.0299839	−	0.0173112i
$276$	9.66163	−	7.09569i	0.581562	−	0.427110i
$277$	12.2471	−	21.2126i	0.735856	−	1.27454i	−0.218491	−	0.975839i	$-0.570114\pi$
$277$	12.2471	−	21.2126i	0.735856	−	1.27454i	0.954347	−	0.298700i	$-0.0965531\pi$
$278$	4.55287	−	7.88580i	0.273063	−	0.472959i
$279$	4.33996	+	19.4341i	0.259827	+	1.16349i
$280$	−4.32802	−	2.20542i	−0.258649	−	0.131799i
$281$	13.9234	−	8.03869i	0.830602	−	0.479548i	−0.0234571	−	0.999725i	$-0.507467\pi$
$281$	13.9234	−	8.03869i	0.830602	−	0.479548i	0.854059	+	0.520177i	$0.174134\pi$
$282$	2.74330	+	24.8712i	0.163361	+	1.48106i
$283$			5.19267i			0.308672i	0.988018	+	0.154336i	$0.0493238\pi$
$283$			5.19267i			0.308672i	−0.988018	+	0.154336i	$0.950676\pi$
$284$		−	0.0656715i		−	0.00389689i
$285$	−0.000326140	−	0.00295684i	−1.93189e−5	−	0.000175148i
$286$	0.128102	−	0.0739597i	0.00757483	−	0.00437333i
$287$	−28.3838	+	1.48660i	−1.67544	+	0.0877509i
$288$	3.18611	+	14.2672i	0.187743	+	0.840704i
$289$	7.81107	−	13.5292i	0.459474	−	0.795833i
$290$	−5.74801	+	9.95584i	−0.337535	+	0.584627i
$291$	24.0414	−	17.6565i	1.40933	−	1.03504i
$292$	−9.49122	+	5.47976i	−0.555431	+	0.320678i
$293$	−1.24041	+	2.14845i	−0.0724655	+	0.125514i	−0.899981	−	0.435928i	$-0.856420\pi$
$293$	−1.24041	+	2.14845i	−0.0724655	+	0.125514i	0.827516	+	0.561442i	$0.189753\pi$
$294$	19.7594	+	6.30963i	1.15239	+	0.367985i
$295$	−5.13465	−	8.89348i	−0.298951	−	0.517799i
$296$	2.28454	+	1.31898i	0.132786	+	0.0766642i
$297$	−2.92738	−	0.575240i	−0.169864	−	0.0333788i
$298$	−0.619846	−	1.07360i	−0.0359067	−	0.0621923i
$299$	1.12451			0.0650321
$300$	0.645401	−	1.46987i	0.0372623	−	0.0848628i
$301$	7.22035	−	14.1696i	0.416174	−	0.816721i
$302$	−5.72448	−	3.30503i	−0.329407	−	0.190183i
$303$	−9.29608	+	21.1713i	−0.534046	+	1.21626i
$304$	−0.00742898	−	0.00428912i	−0.000426081	−	0.000245998i
$305$	6.36845	−	3.67682i	0.364656	−	0.210534i
$306$	−4.43546	+	4.07698i	−0.253559	+	0.233066i
$307$			16.2261i			0.926071i	0.886340	+	0.463035i	$0.153240\pi$
$307$			16.2261i			0.926071i	−0.886340	+	0.463035i	$0.846760\pi$
$308$	0.0736379	+	1.40598i	0.00419591	+	0.0801131i
$309$	−6.20304	+	4.55563i	−0.352879	+	0.259161i
$310$	−5.67779	−	9.83423i	−0.322477	−	0.558547i
$311$	15.8182			0.896971			0.448485	−	0.893790i	$-0.351964\pi$
$311$	15.8182			0.896971			0.448485	+	0.893790i	$0.351964\pi$
$312$	−0.192530	+	0.438476i	−0.0108999	+	0.0248238i
$313$		−	30.3024i		−	1.71279i	−0.516320	−	0.856396i	$-0.672698\pi$
$313$		−	30.3024i		−	1.71279i	0.516320	−	0.856396i	$-0.327302\pi$
$314$	−11.2106			−0.632649
$315$	1.97570	−	7.68743i	0.111318	−	0.433138i
$316$	−3.06855			−0.172620
$317$			26.5814i			1.49296i	0.665409	+	0.746479i	$0.268257\pi$
$317$			26.5814i			1.49296i	−0.665409	+	0.746479i	$0.731743\pi$
$318$	−19.4605	−	26.4979i	−1.09129	−	1.48593i
$319$	−3.85809			−0.216012
$320$	0.826385	+	1.43134i	0.0461963	+	0.0800144i
$321$	−9.55548	−	4.19570i	−0.533335	−	0.234181i
$322$	−15.3456	+	30.1150i	−0.855176	+	1.67824i
$323$		−	0.00201603i		−	0.000112175i
$324$	−7.54902	+	3.54862i	−0.419390	+	0.197145i
$325$	0.130417	−	0.0752961i	0.00723422	−	0.00417668i
$326$	−28.2508	−	16.3106i	−1.56467	−	0.903360i
$327$	5.29105	+	7.20441i	0.292596	+	0.398405i
$328$	17.0810	+	9.86172i	0.943140	+	0.544522i
$329$	−12.1675	−	18.7376i	−0.670814	−	1.03304i
$330$	1.69105	−	0.186523i	0.0930895	−	0.0102678i
$331$	−13.0517			−0.717388			−0.358694	−	0.933455i	$-0.616778\pi$
$331$	−13.0517			−0.717388			−0.358694	+	0.933455i	$0.616778\pi$
$332$	−4.14875	−	7.18584i	−0.227692	−	0.394374i
$333$	−1.28982	+	4.11295i	−0.0706819	+	0.225388i
$334$	9.00322	+	5.19801i	0.492634	+	0.284423i
$335$	4.10141	+	7.10384i	0.224084	+	0.388124i
$336$	−14.4947	−	17.7138i	−0.790750	−	0.966370i
$337$	12.2635	−	21.2411i	0.668038	−	1.15708i	−0.310414	−	0.950601i	$-0.600468\pi$
$337$	12.2635	−	21.2411i	0.668038	−	1.15708i	0.978452	−	0.206474i	$-0.0661989\pi$
$338$	−19.2271	+	11.1008i	−1.04582	+	0.603803i
$339$	−13.4199	−	5.89253i	−0.728870	−	0.320038i
$340$	0.543970	−	0.942183i	0.0295009	−	0.0510971i
$341$	1.90548	−	3.30039i	0.103188	−	0.178726i
$342$	0.00263767	−	0.00841094i	0.000142629	−	0.000454811i
$343$	−18.2925	+	2.89540i	−0.987704	+	0.156337i
$344$	−9.55722	+	5.51787i	−0.515291	+	0.297503i
$345$	11.8424	+	5.19984i	0.637571	+	0.279950i
$346$			33.6183i			1.80733i
$347$			19.6841i			1.05670i	0.849027	+	0.528350i	$0.177189\pi$
$347$			19.6841i			1.05670i	−0.849027	+	0.528350i	$0.822811\pi$
$348$	−8.69437	+	6.38531i	−0.466067	+	0.342289i
$349$	−25.4274	+	14.6805i	−1.36110	+	0.785831i	−0.989770	−	0.142671i	$-0.954431\pi$
$349$	−25.4274	+	14.6805i	−1.36110	+	0.785831i	−0.371329	+	0.928501i	$0.621098\pi$
$350$	0.236742	+	4.52015i	0.0126544	+	0.241612i
$351$	−0.767816	−	0.150878i	−0.0409830	−	0.00805330i
$352$	1.39888	−	2.42293i	0.0745605	−	0.129143i
$353$	−7.65735	+	13.2629i	−0.407560	+	0.705914i	−0.994616	−	0.103632i	$-0.966953\pi$
$353$	−7.65735	+	13.2629i	−0.407560	+	0.705914i	0.587056	+	0.809546i	$0.300287\pi$
$354$	−3.33618	−	30.2465i	−0.177316	−	1.60758i
$355$	0.0613631	−	0.0354280i	0.00325681	−	0.00188032i
$356$	−0.648532	+	1.12329i	−0.0343721	+	0.0595343i
$357$	1.90206	−	5.03164i	0.100668	−	0.266303i
$358$	11.3768	+	19.7052i	0.601282	+	1.04145i
$359$	2.96529	+	1.71201i	0.156502	+	0.0903564i	0.576206	−	0.817305i	$-0.304533\pi$
$359$	2.96529	+	1.71201i	0.156502	+	0.0903564i	−0.419704	+	0.907661i	$0.637866\pi$
$360$	−4.05511	+	3.72737i	−0.213723	+	0.196450i
$361$	−9.50000	−	16.4545i	−0.500000	−	0.866025i
$362$	13.4711			0.708026
$363$	−10.9399	−	14.8959i	−0.574194	−	0.781834i
$364$	0.0193144	+	0.368772i	0.00101235	+	0.0193289i
$365$	−10.2405	−	5.91235i	−0.536012	−	0.309467i
$366$	21.6589	−	2.38898i	1.13213	−	0.124874i
$367$	−0.562857	−	0.324966i	−0.0293809	−	0.0169631i	0.485238	−	0.874382i	$-0.338733\pi$
$367$	−0.562857	−	0.324966i	−0.0293809	−	0.0169631i	−0.514619	+	0.857419i	$0.672066\pi$
$368$	32.2995	−	18.6481i	1.68373	−	0.972102i
$369$	−9.64371	+	30.7516i	−0.502032	+	1.60086i
$370$		−	2.45811i		−	0.127791i
$371$	26.1544	+	13.3274i	1.35787	+	0.691926i
$372$	−1.16821	−	10.5912i	−0.0605690	−	0.549130i
$373$	−8.83032	−	15.2946i	−0.457217	−	0.791923i	0.541596	−	0.840639i	$-0.317820\pi$
$373$	−8.83032	−	15.2946i	−0.457217	−	0.791923i	−0.998813	+	0.0487163i	$0.984487\pi$
$374$	1.15299			0.0596199
$375$	1.72161	−	0.189893i	0.0889036	−	0.00980606i
$376$			15.5035i			0.799534i
$377$	−1.01193			−0.0521171
$378$	14.5186	−	18.5036i	0.746755	−	0.951721i
$379$	34.7390			1.78442			0.892210	−	0.451620i	$-0.149154\pi$
$379$	34.7390			1.78442			0.892210	+	0.451620i	$0.149154\pi$
$380$			0.00159182i			8.16588e-5i
$381$	−11.0564	+	1.21952i	−0.566436	+	0.0624779i
$382$	−11.3541			−0.580925
$383$	1.22112	+	2.11505i	0.0623965	+	0.108074i	0.895536	−	0.444989i	$-0.146792\pi$
$383$	1.22112	+	2.11505i	0.0623965	+	0.108074i	−0.833140	+	0.553063i	$0.813459\pi$
$384$	2.38759	+	21.6464i	0.121841	+	1.10464i
$385$	−1.27401	+	0.827294i	−0.0649297	+	0.0421628i
$386$			18.5527i			0.944306i
$387$	−12.2031	−	13.2761i	−0.620319	−	0.674862i
$388$	−13.8230	+	7.98073i	−0.701758	+	0.405160i
$389$	13.8071	+	7.97152i	0.700047	+	0.404172i	0.807365	−	0.590052i	$-0.200893\pi$
$389$	13.8071	+	7.97152i	0.700047	+	0.404172i	−0.107318	+	0.994225i	$0.534226\pi$
$390$	0.443543	−	0.0489228i	0.0224597	−	0.00247730i
$391$	7.59094	+	4.38263i	0.383890	+	0.221639i
$392$	11.7404	+	5.22808i	0.592979	+	0.264058i
$393$	−13.6869	−	18.6363i	−0.690412	−	0.940079i
$394$	−18.9177			−0.953061
$395$	−1.65540	−	2.86723i	−0.0832921	−	0.144266i
$396$	1.52327	+	0.477698i	0.0765472	+	0.0240052i
$397$	12.0664	+	6.96657i	0.605598	+	0.349642i	0.771241	−	0.636544i	$-0.219637\pi$
$397$	12.0664	+	6.96657i	0.605598	+	0.349642i	−0.165643	+	0.986186i	$0.552970\pi$
$398$	−0.769707	−	1.33317i	−0.0385819	−	0.0668258i
$399$	0.00127088	+	0.00776724i	6.36233e−5	+	0.000388848i
$400$	2.49732	−	4.32549i	0.124866	−	0.216275i
$401$	24.7488	−	14.2887i	1.23590	−	0.713545i	0.267643	−	0.963518i	$-0.413755\pi$
$401$	24.7488	−	14.2887i	1.23590	−	0.713545i	0.968253	+	0.249973i	$0.0804219\pi$
$402$	2.66484	+	24.1600i	0.132910	+	1.20499i
$403$	0.499785	−	0.865653i	0.0248961	−	0.0431213i
$404$	6.18645	−	10.7152i	0.307787	−	0.533104i
$405$	−7.38829	−	5.13937i	−0.367127	−	0.255378i
$406$	13.8093	−	27.1000i	0.685343	−	1.34495i
$407$	0.714425	−	0.412473i	0.0354127	−	0.0204455i
$408$	−3.00857	+	2.20955i	−0.148946	+	0.109389i
$409$		−	34.5754i		−	1.70964i	−0.518921	−	0.854822i	$-0.673666\pi$
$409$		−	34.5754i		−	1.70964i	0.518921	−	0.854822i	$-0.326334\pi$
$410$		−	18.3787i		−	0.907659i
$411$	−29.0017	−	12.7343i	−1.43055	−	0.628137i
$412$	3.56654	−	2.05914i	0.175711	−	0.101447i
$413$	14.7971	+	22.7872i	0.728118	+	1.12128i
$414$	25.9356	+	28.2160i	1.27466	+	1.38674i
$415$	4.47627	−	7.75313i	0.219731	−	0.380586i
$416$	0.366909	−	0.635505i	0.0179892	−	0.0311582i
$417$	8.44099	+	3.70634i	0.413357	+	0.181500i
$418$	−0.00146099		0.000843503i	−7.14594e−5		4.12571e-5i
$419$	3.74166	−	6.48074i	0.182792	−	0.316605i	−0.760038	−	0.649878i	$-0.774820\pi$
$419$	3.74166	−	6.48074i	0.182792	−	0.316605i	0.942830	+	0.333273i	$0.108153\pi$
$420$	−1.50183	+	3.97289i	−0.0732819	+	0.193857i
$421$	4.74302	+	8.21515i	0.231161	+	0.400382i	0.958150	−	0.286267i	$-0.0924144\pi$
$421$	4.74302	+	8.21515i	0.231161	+	0.400382i	−0.726989	+	0.686649i	$0.759081\pi$
$422$	28.7889	+	16.6213i	1.40142	+	0.809110i
$423$	−24.7239	+	5.52127i	−1.20212	+	0.268453i
$424$	−10.1850	−	17.6409i	−0.494626	−	0.856717i
$425$	1.17383			0.0569390
$426$	0.208694	−	0.0230189i	0.0101113	−	0.00111527i
$427$	−16.3175	+	10.5959i	−0.789657	+	0.512772i
$428$	4.83623	+	2.79220i	0.233768	+	0.134966i
$429$	0.0886461	+	0.120702i	0.00427987	+	0.00582756i
$430$	8.90561	+	5.14166i	0.429467	+	0.247953i
$431$	25.2973	−	14.6054i	1.21853	−	0.703519i	0.253927	−	0.967223i	$-0.418278\pi$
$431$	25.2973	−	14.6054i	1.21853	−	0.703519i	0.964603	+	0.263705i	$0.0849445\pi$
$432$	−24.5562	+	8.39925i	−1.18146	+	0.404109i
$433$			12.2560i			0.588987i	0.955654	+	0.294493i	$0.0951509\pi$
$433$			12.2560i			0.588987i	−0.955654	+	0.294493i	$0.904849\pi$
$434$	16.3623	+	25.1976i	0.785418	+	1.20952i
$435$	−10.6568	−	4.67926i	−0.510953	−	0.224354i
$436$	−2.39155	−	4.14229i	−0.114535	−	0.198380i
$437$	−0.0128249			−0.000613499
$438$	−20.7406	−	28.2409i	−0.991026	−	1.34940i
$439$			0.752043i			0.0358931i	0.999839	+	0.0179465i	$0.00571287\pi$
$439$			0.752043i			0.0358931i	−0.999839	+	0.0179465i	$0.994287\pi$
$440$	1.05412			0.0502533
$441$	−4.15627	+	20.5846i	−0.197918	+	0.980219i
$442$	0.302416			0.0143845
$443$		−	29.1093i		−	1.38303i	−0.722364	−	0.691513i	$-0.756945\pi$
$443$		−	29.1093i		−	1.38303i	0.722364	−	0.691513i	$-0.243055\pi$
$444$	0.927324	−	2.11193i	0.0440089	−	0.100228i
$445$	−1.39946			−0.0663408
$446$	2.10044	+	3.63807i	0.0994587	+	0.172267i
$447$	1.01159	−	0.742930i	0.0478465	−	0.0351394i
$448$	−2.38149	−	3.66743i	−0.112515	−	0.173270i
$449$			33.1131i			1.56270i	0.624091	+	0.781352i	$0.285469\pi$
$449$			33.1131i			1.56270i	−0.624091	+	0.781352i	$0.714531\pi$
$450$	4.89723	+	1.53577i	0.230858	+	0.0723971i
$451$	5.34159	−	3.08397i	0.251526	−	0.145218i
$452$	6.79210	+	3.92142i	0.319474	+	0.184448i
$453$	2.69051	−	6.12750i	0.126411	−	0.287895i
$454$	−2.75289	−	1.58938i	−0.129199	−	0.0745933i
$455$	−0.334158	+	0.216989i	−0.0156656	+	0.0101726i
$456$	0.00219578	−	0.00500078i	0.000102827	−	0.000234183i
$457$	22.4720			1.05119			0.525597	−	0.850734i	$-0.323842\pi$
$457$	22.4720			1.05119			0.525597	+	0.850734i	$0.323842\pi$
$458$	−23.2748	−	40.3131i	−1.08756	−	1.88371i
$459$	−4.59507	−	4.01096i	−0.214479	−	0.187216i
$460$	−5.99366	−	3.46044i	−0.279456	−	0.161344i
$461$	−4.42868	−	7.67071i	−0.206264	−	0.357260i	0.744270	−	0.667878i	$-0.232797\pi$
$461$	−4.42868	−	7.67071i	−0.206264	−	0.357260i	−0.950535	+	0.310618i	$0.899464\pi$
$462$	−4.44217	+	0.726829i	−0.206669	+	0.0338151i
$463$	−18.4035	+	31.8758i	−0.855283	+	1.48139i	0.0210995	+	0.999777i	$0.493283\pi$
$463$	−18.4035	+	31.8758i	−0.855283	+	1.48139i	−0.876382	+	0.481616i	$0.840050\pi$
$464$	−29.0659	+	16.7812i	−1.34935	+	0.779048i
$465$	9.26616	−	6.80525i	0.429708	−	0.315586i
$466$	−4.22525	+	7.31834i	−0.195731	+	0.339016i
$467$	−6.27600	+	10.8703i	−0.290418	+	0.503020i	−0.973909	−	0.226940i	$-0.927128\pi$
$467$	−6.27600	+	10.8703i	−0.290418	+	0.503020i	0.683490	+	0.729960i	$0.260461\pi$
$468$	0.399535	+	0.125294i	0.0184685	+	0.00579174i
$469$	−11.8195	−	18.2017i	−0.545773	−	0.840477i
$470$	12.5110	−	7.22325i	0.577091	−	0.333184i
$471$	−1.24434	−	11.2814i	−0.0573361	−	0.519820i
$472$		−	18.8542i		−	0.867835i
$473$			3.45111i			0.158682i
$474$	−1.07558	−	9.75138i	−0.0494029	−	0.447896i
$475$	−0.00148739		0.000858744i	−6.82461e−5		3.94019e-5i
$476$	−1.30686	+	2.56465i	−0.0598998	+	0.117550i
$477$	24.5052	−	22.5247i	1.12202	−	1.03133i
$478$	16.5076	−	28.5921i	0.755041	−	1.30777i
$479$	−8.98952	+	15.5703i	−0.410741	+	0.711425i	−0.994971	−	0.100163i	$-0.968063\pi$
$479$	−8.98952	+	15.5703i	−0.410741	+	0.711425i	0.584230	+	0.811588i	$0.301397\pi$
$480$	6.80260	−	4.99596i	0.310495	−	0.228033i
$481$	0.187385	−	0.108187i	0.00854402	−	0.00493289i
$482$	14.6951	−	25.4526i	0.669343	−	1.15934i
$483$	−32.0086	−	12.0999i	−1.45644	−	0.550564i
$484$	4.94481	+	8.56466i	0.224764	+	0.389303i
$485$	−14.9143	−	8.61076i	−0.677223	−	0.390995i
$486$	−13.9230	−	22.7458i	−0.631560	−	1.03177i
$487$	−1.00935	−	1.74825i	−0.0457382	−	0.0792208i	0.842250	−	0.539087i	$-0.181231\pi$
$487$	−1.00935	−	1.74825i	−0.0457382	−	0.0792208i	−0.887988	+	0.459866i	$0.847897\pi$
$488$	13.5011			0.611167
$489$	13.2779	−	30.2397i	0.600448	−	1.36749i
$490$	−1.25101	−	11.9101i	−0.0565147	−	0.538042i
$491$	29.4591	+	17.0082i	1.32947	+	0.767570i	0.985218	−	0.171307i	$-0.0547989\pi$
$491$	29.4591	+	17.0082i	1.32947	+	0.767570i	0.344253	+	0.938877i	$0.388132\pi$
$492$	6.93339	−	15.7904i	0.312581	−	0.711887i
$493$	−6.83098	−	3.94387i	−0.307652	−	0.177623i
$494$	−0.000383200	0	0.000221241i	−1.72410e−5	0	9.95409e-6i
$495$	0.375404	+	1.68104i	0.0168732	+	0.0755570i
$496$		−	33.1524i		−	1.48859i
$497$	−0.157227	+	0.102097i	−0.00705258	+	0.00457967i
$498$	21.3813	−	15.7028i	0.958119	−	0.703661i
$499$	−16.7461	−	29.0052i	−0.749660	−	1.29845i	−0.947986	−	0.318313i	$-0.896884\pi$
$499$	−16.7461	−	29.0052i	−0.749660	−	1.29845i	0.198325	−	0.980136i	$-0.436450\pi$
$500$	−0.926832			−0.0414492
$501$	−4.23153	+	9.63708i	−0.189051	+	0.430553i
$502$			25.4039i			1.13383i
$503$	28.8478			1.28626			0.643129	−	0.765758i	$-0.277636\pi$
$503$	28.8478			1.28626			0.643129	+	0.765758i	$0.277636\pi$
$504$	10.1983	−	10.4094i	0.454270	−	0.463669i
$505$	13.3497			0.594053
$506$		−	7.33472i		−	0.326068i
$507$	−13.3051	−	18.1165i	−0.590900	−	0.804581i
$508$	5.95223			0.264087
$509$	−4.54361	−	7.86976i	−0.201392	−	0.348821i	0.747585	−	0.664166i	$-0.231213\pi$
$509$	−4.54361	−	7.86976i	−0.201392	−	0.348821i	−0.948977	+	0.315345i	$0.897880\pi$
$510$	3.18478	+	1.39840i	0.141025	+	0.0619223i
$511$	27.8749	+	14.2041i	1.23311	+	0.628353i
$512$		−	5.99824i		−	0.265087i
$513$	0.00875687	+	0.00172075i	0.000386625	+	7.59731e-5i
$514$	−20.6021	+	11.8946i	−0.908718	+	0.524649i
$515$	3.84810	+	2.22170i	0.169568	+	0.0978999i
$516$	5.71174	+	7.77721i	0.251445	+	0.342373i
$517$	4.19874	+	2.42414i	0.184660	+	0.106614i
$518$	0.340155	+	6.49463i	0.0149456	+	0.285358i
$519$	−33.8308	+	3.73153i	−1.48501	+	0.163796i
$520$	0.276484			0.0121246
$521$	5.10354	+	8.83959i	0.223590	+	0.387269i	0.955896	−	0.293707i	$-0.0948890\pi$
$521$	5.10354	+	8.83959i	0.223590	+	0.387269i	−0.732305	+	0.680976i	$0.761556\pi$
$522$	−23.3391	−	25.3912i	−1.02152	−	1.11134i
$523$	−29.5981	−	17.0885i	−1.29423	−	0.747226i	−0.314832	−	0.949147i	$-0.601948\pi$
$523$	−29.5981	−	17.0885i	−1.29423	−	0.747226i	−0.979402	+	0.201921i	$0.935282\pi$
$524$	6.18646	+	10.7153i	0.270257	+	0.468099i
$525$	−4.52244	+	0.739962i	−0.197375	+	0.0322946i
$526$	3.21223	−	5.56374i	0.140060	−	0.242591i
$527$	6.74754	−	3.89569i	0.293927	−	0.169699i
$528$	4.54785	+	1.99691i	0.197920	+	0.0869042i
$529$	16.3799	−	28.3709i	0.712171	−	1.23352i
$530$	−9.49056	+	16.4381i	−0.412244	+	0.714027i
$531$	30.0673	−	6.71454i	1.30481	−	0.291386i
$532$	−0.000220278	−	0.00420580i	−9.55027e−6	−	0.000182345i
$533$	1.40104	−	0.808888i	0.0606856	−	0.0350368i
$534$	−3.79697	−	1.66720i	−0.164311	−	0.0721470i
$535$			6.02526i			0.260495i
$536$			15.0602i			0.650500i
$537$	−18.5669	+	13.6359i	−0.801222	+	0.588433i
$538$	−33.3190	+	19.2368i	−1.43649	+	0.829356i
$539$	3.25163	−	2.36212i	0.140057	−	0.101744i
$540$	3.62818	+	3.16698i	0.156132	+	0.136285i
$541$	−21.3930	+	37.0537i	−0.919756	+	1.59306i	−0.119970	+	0.992778i	$0.538280\pi$
$541$	−21.3930	+	37.0537i	−0.919756	+	1.59306i	−0.799786	+	0.600286i	$0.795054\pi$
$542$	19.4185	−	33.6338i	0.834096	−	1.44470i
$543$	1.49525	+	13.5562i	0.0641674	+	0.581754i
$544$	4.95360	−	2.85996i	0.212384	−	0.122620i
$545$	2.58035	−	4.46930i	0.110530	−	0.191444i
$546$	−1.16513	+	0.190638i	−0.0498629	+	0.00815857i
$547$	17.5337	+	30.3692i	0.749685	+	1.29849i	0.947973	+	0.318350i	$0.103129\pi$
$547$	17.5337	+	30.3692i	0.749685	+	1.29849i	−0.198288	+	0.980144i	$0.563538\pi$
$548$	14.6784	+	8.47456i	0.627029	+	0.362015i
$549$	4.80815	+	21.5306i	0.205207	+	0.918904i
$550$	−0.491126	−	0.850655i	−0.0209417	−	0.0362721i
$551$	0.0115410			0.000491662
$552$	14.0560	+	19.1389i	0.598261	+	0.814605i
$553$	4.77055	+	7.34653i	0.202864	+	0.312406i
$554$	−36.2904	−	20.9523i	−1.54183	−	0.890177i
$555$	2.47364	−	0.272842i	0.105000	−	0.0115815i
$556$	−4.27216	−	2.46653i	−0.181180	−	0.104604i
$557$	22.7389	−	13.1283i	0.963477	−	0.556263i	0.0662353	−	0.997804i	$-0.478901\pi$
$557$	22.7389	−	13.1283i	0.963477	−	0.556263i	0.897241	+	0.441541i	$0.145568\pi$
$558$	33.2478	−	7.42480i	1.40749	−	0.314317i
$559$			0.905184i			0.0382852i
$560$	−5.99969	+	11.7741i	−0.253533	+	0.497546i
$561$	0.127979	+	1.16028i	0.00540327	+	0.0489871i
$562$	−13.7526	−	23.8202i	−0.580118	−	1.00479i
$563$	39.1292			1.64910			0.824550	−	0.565789i	$-0.191428\pi$
$563$	39.1292			1.64910			0.824550	+	0.565789i	$0.191428\pi$
$564$	13.4741	−	1.48619i	0.567362	−	0.0625800i
$565$			8.46200i			0.355999i
$566$	8.88361			0.373406
$567$	20.2320	+	12.5565i	0.849665	+	0.527323i
$568$	0.130090			0.00545845
$569$			10.0112i			0.419693i	0.977734	+	0.209846i	$0.0672964\pi$
$569$			10.0112i			0.419693i	−0.977734	+	0.209846i	$0.932704\pi$
$570$	−0.00505857		0.000557960i	−0.000211880		2.33704e-5i
$571$	−17.1913			−0.719435			−0.359717	−	0.933061i	$-0.617127\pi$
$571$	−17.1913			−0.719435			−0.359717	+	0.933061i	$0.617127\pi$
$572$	−0.0400680	−	0.0693998i	−0.00167533	−	0.00290175i
$573$	−1.26027	−	11.4258i	−0.0526484	−	0.477320i
$574$	2.54326	+	48.5589i	0.106154	+	2.02681i
$575$		−	7.46725i		−	0.311406i
$576$	−4.83912	+	1.08066i	−0.201630	+	0.0450273i
$577$	−21.9901	+	12.6960i	−0.915458	+	0.528540i	−0.882183	−	0.470906i	$-0.843927\pi$
$577$	−21.9901	+	12.6960i	−0.915458	+	0.528540i	−0.0332750	+	0.999446i	$0.510594\pi$
$578$	−23.1457	−	13.3632i	−0.962733	−	0.555834i
$579$	−18.6699	+	2.05929i	−0.775895	+	0.0855811i
$580$	5.39361	+	3.11400i	0.223958	+	0.129302i
$581$	−10.7540	+	21.1042i	−0.446151	+	0.875550i
$582$	−30.2067	−	41.1301i	−1.25211	−	1.70490i
$583$	−6.37011			−0.263823
$584$	−10.8549	−	18.8013i	−0.449180	−	0.778003i
$585$	0.0984640	+	0.440916i	0.00407098	+	0.0182296i
$586$	3.67557	+	2.12209i	0.151836	+	0.0876628i
$587$	2.12974	+	3.68882i	0.0879038	+	0.152254i	0.906625	−	0.421938i	$-0.138650\pi$
$587$	2.12974	+	3.68882i	0.0879038	+	0.152254i	−0.818721	+	0.574191i	$0.805317\pi$
$588$	3.41826	−	10.7047i	0.140967	−	0.441455i
$589$	−0.00570000	+	0.00987268i	−0.000234864	+	0.000406797i
$590$	−15.2150	+	8.78436i	−0.626390	+	0.361646i
$591$	−2.09981	−	19.0373i	−0.0863747	−	0.783089i
$592$	3.58820	−	6.21494i	0.147474	−	0.255433i
$593$	−16.9948	+	29.4359i	−0.697894	+	1.20879i	0.271301	+	0.962494i	$0.412546\pi$
$593$	−16.9948	+	29.4359i	−0.697894	+	1.20879i	−0.969195	+	0.246293i	$0.920787\pi$
$594$	−0.984119	+	5.00816i	−0.0403789	+	0.205487i
$595$	−3.10140	+	0.162435i	−0.127145	+	0.00665920i
$596$	−0.581630	+	0.335804i	−0.0238245	+	0.0137551i
$597$	1.25616	−	0.922549i	0.0514113	−	0.0377574i
$598$		−	1.92381i		−	0.0786704i
$599$			0.484474i			0.0197951i	0.999951	+	0.00989753i	$0.00315053\pi$
$599$			0.484474i			0.0197951i	−0.999951	+	0.00989753i	$0.996849\pi$
$600$	2.91168	+	1.27849i	0.118869	+	0.0521939i
$601$	−33.2908	+	19.2204i	−1.35796	+	0.784018i	−0.989349	−	0.145565i	$-0.953500\pi$
$601$	−33.2908	+	19.2204i	−1.35796	+	0.784018i	−0.368611	+	0.929584i	$0.620167\pi$
$602$	−24.2413	−	12.3526i	−0.988002	−	0.503453i
$603$	−24.0169	+	5.36337i	−0.978042	+	0.218413i
$604$	−1.79051	+	3.10126i	−0.0728549	+	0.126188i
$605$	−5.33518	+	9.24080i	−0.216906	+	0.375692i
$606$	36.2199	+	15.9037i	1.47133	+	0.646044i
$607$	4.62788	−	2.67191i	0.187840	−	0.108449i	−0.403131	−	0.915142i	$-0.632078\pi$
$607$	4.62788	−	2.67191i	0.187840	−	0.108449i	0.590971	+	0.806693i	$0.298745\pi$
$608$	−0.00418456	+	0.00724787i	−0.000169706	+	0.000293940i
$609$	28.8041	+	10.8885i	1.16720	+	0.441225i
$610$	−6.29030	−	10.8951i	−0.254687	−	0.441131i
$611$	1.10128	+	0.635823i	0.0445530	+	0.0257227i
$612$	2.20872	+	2.40293i	0.0892822	+	0.0971326i
$613$	22.9643	+	39.7754i	0.927520	+	1.60651i	0.787457	+	0.616370i	$0.211397\pi$
$613$	22.9643	+	39.7754i	0.927520	+	1.60651i	0.140064	+	0.990142i	$0.455269\pi$
$614$	27.7595			1.12028
$615$	18.4948	−	2.03998i	0.745784	−	0.0822599i
$616$	−2.78513	+	0.145871i	−0.112216	+	0.00587729i
$617$	−34.3802	−	19.8494i	−1.38409	−	0.799107i	−0.391452	−	0.920199i	$-0.628027\pi$
$617$	−34.3802	−	19.8494i	−1.38409	−	0.799107i	−0.992641	+	0.121092i	$0.961360\pi$
$618$	7.79377	+	10.6122i	0.313511	+	0.426883i
$619$	−30.9739	−	17.8828i	−1.24494	−	0.718769i	−0.274848	−	0.961488i	$-0.588627\pi$
$619$	−30.9739	−	17.8828i	−1.24494	−	0.718769i	−0.970097	+	0.242719i	$0.921961\pi$
$620$	−5.32773	+	3.07597i	−0.213967	+	0.123534i
$621$	−25.5156	+	29.2314i	−1.02390	+	1.17301i
$622$		−	27.0618i		−	1.08508i
$623$	3.69756	−	0.193659i	0.148140	−	0.00775878i
$624$	1.19285	+	0.523765i	0.0477520	+	0.0209674i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−51.8413			−2.07199
$627$	−0.00101100	−	0.00137660i	−4.03754e−5	−	5.49760e-5i
$628$			6.07337i			0.242354i
$629$	1.68657			0.0672481
$630$	−13.1516	−	3.38003i	−0.523974	−	0.134664i
$631$	−42.2092			−1.68032			−0.840162	−	0.542336i	$-0.817540\pi$
$631$	−42.2092			−1.68032			−0.840162	+	0.542336i	$0.817540\pi$
$632$		−	6.07854i		−	0.241791i
$633$	−13.5308	+	30.8157i	−0.537802	+	1.22481i
$634$	45.4754			1.80606
$635$	3.21106	+	5.56172i	0.127427	+	0.220710i
$636$	−14.3553	+	10.5428i	−0.569225	+	0.418050i
$637$	0.852862	−	0.619555i	0.0337916	−	0.0245477i
$638$			6.60042i			0.261313i
$639$	0.0463288	+	0.207458i	0.00183274	+	0.00820690i
$640$	10.8888	−	6.28666i	0.430418	−	0.248502i
$641$	−14.3626	−	8.29223i	−0.567287	−	0.327524i	0.188778	−	0.982020i	$-0.439547\pi$
$641$	−14.3626	−	8.29223i	−0.567287	−	0.327524i	−0.756065	+	0.654496i	$0.772881\pi$
$642$	−7.17800	+	16.3475i	−0.283293	+	0.645185i
$643$	16.8290	+	9.71622i	0.663670	+	0.383170i	0.793674	−	0.608343i	$-0.208166\pi$
$643$	16.8290	+	9.71622i	0.663670	+	0.383170i	−0.130004	+	0.991514i	$0.541499\pi$
$644$	16.3149	+	8.31353i	0.642897	+	0.327599i
$645$	−4.18565	+	9.53260i	−0.164810	+	0.375346i
$646$	−0.00344903			−0.000135700
$647$	12.3390	+	21.3718i	0.485098	+	0.840214i	0.999853	−	0.0171232i	$-0.00545074\pi$
$647$	12.3390	+	21.3718i	0.485098	+	0.840214i	−0.514756	+	0.857337i	$0.672117\pi$
$648$	−7.02951	−	14.9540i	−0.276145	−	0.587447i
$649$	−5.10618	−	2.94805i	−0.200435	−	0.115721i
$650$	−0.128816	−	0.223117i	−0.00505260	−	0.00875135i
$651$	−23.5407	+	19.2626i	−0.922632	+	0.754961i
$652$	−8.83633	+	15.3050i	−0.346057	+	0.599389i
$653$	−20.7763	+	11.9952i	−0.813038	+	0.469407i	−0.848010	−	0.529981i	$-0.822199\pi$
$653$	−20.7763	+	11.9952i	−0.813038	+	0.469407i	0.0349721	+	0.999388i	$0.488866\pi$
$654$	12.3253	−	9.05193i	0.481957	−	0.353958i
$655$	−6.67485	+	11.5612i	−0.260808	+	0.451733i
$656$	26.8281	−	46.4677i	1.04746	−	1.81426i
$657$	26.1172	−	24.0064i	1.01893	−	0.936578i
$658$	−32.0562	+	20.8161i	−1.24968	+	0.811495i
$659$	5.35052	−	3.08912i	0.208427	−	0.120335i	−0.392153	−	0.919900i	$-0.628270\pi$
$659$	5.35052	−	3.08912i	0.208427	−	0.120335i	0.600580	+	0.799565i	$0.294936\pi$
$660$	−0.101050	−	0.916135i	−0.00393335	−	0.0356605i
$661$		−	12.0667i		−	0.469339i	−0.972075	−	0.234670i	$-0.924599\pi$
$661$		−	12.0667i		−	0.469339i	0.972075	−	0.234670i	$-0.0754008\pi$
$662$			22.3289i			0.867837i
$663$	0.0335673	+	0.304327i	0.00130365	+	0.0118191i
$664$	14.2345	−	8.21832i	0.552407	−	0.318933i
$665$	0.00381104	−	0.00247474i	0.000147786	−	9.59663e-5i
$666$	7.03643	+	2.20663i	0.272656	+	0.0855051i
$667$	−25.0888	+	43.4550i	−0.971441	+	1.68259i
$668$	2.81604	−	4.87753i	0.108956	−	0.188717i
$669$	−3.42791	+	2.51753i	−0.132531	+	0.0973332i
$670$	12.1532	−	7.01668i	0.469521	−	0.271078i
$671$	2.11104	−	3.65643i	0.0814959	−	0.141155i
$672$	−17.2820	+	14.1413i	−0.666668	+	0.545514i
$673$	21.8014	+	37.7611i	0.840382	+	1.45558i	0.889572	+	0.456794i	$0.151003\pi$
$673$	21.8014	+	37.7611i	0.840382	+	1.45558i	−0.0491906	+	0.998789i	$0.515664\pi$
$674$	−36.3392	−	20.9805i	−1.39973	−	0.808137i
$675$	−1.00190	+	5.09865i	−0.0385632	+	0.196247i
$676$	6.01390	+	10.4164i	0.231304	+	0.400630i
$677$	−14.1862			−0.545218			−0.272609	−	0.962125i	$-0.587887\pi$
$677$	−14.1862			−0.545218			−0.272609	+	0.962125i	$0.587887\pi$
$678$	−10.0809	+	22.9588i	−0.387156	+	0.881727i
$679$	40.5970	+	20.6869i	1.55797	+	0.793891i
$680$	1.86639	+	1.07756i	0.0715726	+	0.0413225i
$681$	1.29386	−	2.94670i	0.0495809	−	0.112918i
$682$	−5.64631	−	3.25990i	−0.216208	−	0.124828i
$683$	35.8109	−	20.6754i	1.37026	−	0.791123i	0.379303	−	0.925272i	$-0.376164\pi$
$683$	35.8109	−	20.6754i	1.37026	−	0.791123i	0.990961	+	0.134150i	$0.0428303\pi$
$684$	−0.00455666	−	0.00142897i	−0.000174228	−	5.46380e-5i
$685$			18.2872i			0.698716i
$686$	4.95345	+	31.2948i	0.189124	+	1.19484i
$687$	37.9844	−	27.8965i	1.44920	−	1.06432i
$688$	15.0110	+	25.9998i	0.572288	+	0.991233i
$689$	−1.67080			−0.0636525
$690$	8.89588	−	20.2599i	0.338660	−	0.771280i
$691$		−	14.3851i		−	0.547234i	−0.961839	−	0.273617i	$-0.911780\pi$
$691$		−	14.3851i		−	0.547234i	0.961839	−	0.273617i	$-0.0882201\pi$
$692$	18.2129			0.692349
$693$	−1.22449	−	4.38957i	−0.0465145	−	0.166746i
$694$	33.6756			1.27831
$695$		−	5.32251i		−	0.201894i
$696$	−12.6488	−	17.2228i	−0.479450	−	0.652829i
$697$	12.6101			0.477643
$698$	25.1154	+	43.5012i	0.950633	+	1.64654i
$699$	−7.83358	−	3.43963i	−0.296293	−	0.130099i
$700$	2.44881	−	0.128256i	0.0925563	−	0.00484762i
$701$		−	18.3839i		−	0.694349i	−0.937801	−	0.347174i	$-0.887141\pi$
$701$		−	18.3839i		−	0.694349i	0.937801	−	0.347174i	$-0.112859\pi$
$702$	−0.258123	+	1.31358i	−0.00974221	+	0.0495778i
$703$	−0.00213711	+	0.00123386i	−8.06025e−5	+	4.65359e-5i
$704$	0.821802	+	0.474468i	0.0309728	+	0.0178822i
$705$	8.65759	+	11.7883i	0.326064	+	0.443975i
$706$	22.6902	+	13.1002i	0.853956	+	0.493032i
$707$	−35.2716	+	1.84734i	−1.32652	+	0.0694765i
$708$	−16.3861	+	1.80739i	−0.615829	+	0.0679259i
$709$	16.5609			0.621959			0.310980	−	0.950417i	$-0.399343\pi$
$709$	16.5609			0.621959			0.310980	+	0.950417i	$0.399343\pi$
$710$	−0.0606101	−	0.104980i	−0.00227466	−	0.00393982i
$711$	9.69362	−	2.16475i	0.363539	−	0.0811844i
$712$	−2.22514	−	1.28469i	−0.0833908	−	0.0481457i
$713$	−24.7823	−	42.9242i	−0.928105	−	1.60752i
$714$	−8.60812	−	3.25404i	−0.322151	−	0.121780i
$715$	0.0432311	−	0.0748785i	0.00161675	−	0.00280030i
$716$	10.6754	−	6.16342i	0.398957	−	0.230338i
$717$	30.6050	+	13.4383i	1.14297	+	0.501863i
$718$	2.92890	−	5.07301i	0.109306	−	0.189323i
$719$	−16.2728	+	28.1854i	−0.606875	+	1.05114i	0.384878	+	0.922968i	$0.374244\pi$
$719$	−16.2728	+	28.1854i	−0.606875	+	1.05114i	−0.991752	+	0.128170i	$0.959090\pi$
$720$	10.1401	+	11.0317i	0.377898	+	0.411126i
$721$	−10.4746	−	5.33752i	−0.390095	−	0.198780i
$722$	−28.1503	+	16.2526i	−1.04765	+	0.604859i
$723$	27.2446	+	11.9628i	1.01324	+	0.444901i
$724$		−	7.29803i		−	0.271229i
$725$			6.71968i			0.249563i
$726$	−25.4839	+	18.7159i	−0.945798	+	0.694612i
$727$	1.88292	−	1.08711i	0.0698338	−	0.0403185i	−0.464677	−	0.885480i	$-0.653829\pi$
$727$	1.88292	−	1.08711i	0.0698338	−	0.0403185i	0.534510	+	0.845162i	$0.320496\pi$
$728$	−0.730505	+	0.0382601i	−0.0270743	+	0.00141801i
$729$	21.3441	−	16.5357i	0.790522	−	0.612434i
$730$	−10.1148	+	17.5194i	−0.374367	+	0.648423i
$731$	−3.52784	+	6.11039i	−0.130482	+	0.226001i
$732$	−1.29424	−	11.7338i	−0.0478364	−	0.433693i
$733$	10.2701	−	5.92943i	0.379334	−	0.219009i	−0.298195	−	0.954505i	$-0.596384\pi$
$733$	10.2701	−	5.92943i	0.379334	−	0.219009i	0.677528	+	0.735497i	$0.263051\pi$
$734$	−0.555951	+	0.962936i	−0.0205205	+	0.0355426i
$735$	11.8465	−	2.58089i	0.436964	−	0.0951977i
$736$	−18.1935	−	31.5121i	−0.670622	−	1.16155i
$737$	4.07866	+	2.35481i	0.150239	+	0.0867407i
$738$	52.6098	+	16.4984i	1.93659	+	0.607316i
$739$	−9.10025	−	15.7621i	−0.334758	−	0.579818i	0.648680	−	0.761061i	$-0.275321\pi$
$739$	−9.10025	−	15.7621i	−0.334758	−	0.579818i	−0.983438	+	0.181243i	$0.941988\pi$
$740$	−1.33169			−0.0489538
$741$	−0.000265173	0	0.000361065i	−9.74137e−6	0	1.32640e-5i
$742$	22.8006	−	44.7450i	0.837035	−	1.64264i
$743$	8.54475	+	4.93331i	0.313476	+	0.180986i	0.648481	−	0.761231i	$-0.275405\pi$
$743$	8.54475	+	4.93331i	0.313476	+	0.180986i	−0.335005	+	0.942216i	$0.608738\pi$
$744$	20.9803	−	2.31413i	0.769176	−	0.0848401i
$745$	−0.627546	−	0.362314i	−0.0229915	−	0.0132742i
$746$	−26.1659	+	15.1069i	−0.958002	+	0.553103i
$747$	18.1753	+	19.7734i	0.665000	+	0.723472i
$748$		−	0.624639i		−	0.0228390i
$749$	−0.833782	−	15.9195i	−0.0304657	−	0.581686i
$750$	−0.324870	−	2.94533i	−0.0118626	−	0.107548i
$751$	−4.06281	−	7.03699i	−0.148254	−	0.256783i	0.782328	−	0.622866i	$-0.214032\pi$
$751$	−4.06281	−	7.03699i	−0.148254	−	0.256783i	−0.930582	+	0.366083i	$0.880699\pi$
$752$	42.1763			1.53801
$753$	−25.5644	+	2.81975i	−0.931618	+	0.102757i
$754$			1.73121i			0.0630470i
$755$	−3.86372			−0.140615
$756$	−10.0244	−	7.86550i	−0.364583	−	0.286065i
$757$	27.0462			0.983009			0.491505	−	0.870875i	$-0.336447\pi$
$757$	27.0462			0.983009			0.491505	+	0.870875i	$0.336447\pi$
$758$		−	59.4314i		−	2.15864i
$759$	7.38108	−	0.814132i	0.267916	−	0.0295511i
$760$	−0.00315327			−0.000114381
$761$	2.94228	+	5.09618i	0.106658	+	0.184736i	0.914414	−	0.404780i	$-0.132652\pi$
$761$	2.94228	+	5.09618i	0.106658	+	0.184736i	−0.807757	+	0.589516i	$0.799318\pi$
$762$	2.08635	+	18.9153i	0.0755806	+	0.685228i
$763$	−6.19916	+	12.1656i	−0.224425	+	0.440423i
$764$			6.15111i			0.222539i
$765$	−1.05374	+	3.36013i	−0.0380979	+	0.121486i
$766$	3.61842	−	2.08910i	0.130739	−	0.0754822i
$767$	−1.33929	−	0.773239i	−0.0483589	−	0.0279200i
$768$	31.3417	−	3.45699i	1.13095	−	0.124743i
$769$	−37.1384	−	21.4419i	−1.33925	−	0.773214i	−0.352550	−	0.935793i	$-0.614686\pi$
$769$	−37.1384	−	21.4419i	−1.33925	−	0.773214i	−0.986696	+	0.162579i	$0.948019\pi$
$770$	1.41533	+	2.17958i	0.0510051	+	0.0785466i
$771$	−14.2565	−	19.4120i	−0.513437	−	0.699106i
$772$	10.0510			0.361742
$773$	4.16275	+	7.21009i	0.149724	+	0.259329i	0.931125	−	0.364700i	$-0.118828\pi$
$773$	4.16275	+	7.21009i	0.149724	+	0.259329i	−0.781402	+	0.624028i	$0.785495\pi$
$774$	−22.7127	+	20.8771i	−0.816392	+	0.750410i
$775$	−5.74833	−	3.31880i	−0.206486	−	0.119215i
$776$	−15.8091	−	27.3822i	−0.567515	−	0.982965i
$777$	−6.49792	+	1.06319i	−0.233112	+	0.0381417i
$778$	13.6377	−	23.6211i	0.488934	−	0.846859i
$779$	−0.0159787	+	0.00922528i	−0.000572495	+	0.000330530i
$780$	−0.0265041	−	0.240291i	−0.000949000	−	0.00860381i
$781$	0.0203409	−	0.0352315i	0.000727855	−	0.00126068i
$782$	7.49780	−	12.9866i	0.268121	−	0.464399i
$783$	22.9611	−	26.3049i	0.820563	−	0.940060i
$784$	14.2226	−	31.9389i	0.507951	−	1.14068i
$785$	−5.67491	+	3.27641i	−0.202546	+	0.116940i
$786$	−31.8830	+	23.4155i	−1.13723	+	0.835203i
$787$			23.3597i			0.832683i	0.909208	+	0.416341i	$0.136688\pi$
$787$			23.3597i			0.832683i	−0.909208	+	0.416341i	$0.863312\pi$
$788$			10.2487i			0.365097i
$789$	5.95545	+	2.61497i	0.212020	+	0.0930953i
$790$	−4.90526	+	2.83205i	−0.174521	+	0.100760i
$791$	−1.17098	−	22.3577i	−0.0416353	−	0.794948i
$792$	−0.946279	+	3.01747i	−0.0336246	+	0.107221i
$793$	0.553701	−	0.959038i	0.0196625	−	0.0340564i
$794$	11.9184	−	20.6433i	0.422968	−	0.732602i
$795$	−17.5954	−	7.72595i	−0.624046	−	0.274011i
$796$	−0.722251	+	0.416992i	−0.0255995	+	0.0147799i
$797$	−5.30395	+	9.18672i	−0.187876	+	0.325410i	−0.944542	−	0.328391i	$-0.893494\pi$
$797$	−5.30395	+	9.18672i	−0.187876	+	0.325410i	0.756666	+	0.653802i	$0.226827\pi$
$798$	0.0132882	−	0.00217421i	0.000470396	−	7.69663e-5i
$799$	4.95608	+	8.58418i	0.175333	+	0.303686i
$800$	−4.22004	−	2.43644i	−0.149201	−	0.0861412i
$801$	1.25629	−	4.00602i	0.0443887	−	0.141546i
$802$	−24.4451	−	42.3402i	−0.863187	−	1.49508i
$803$	−6.78914			−0.239583
$804$	13.0888	−	1.44369i	0.461605	−	0.0509150i
$805$	1.03333	+	19.7295i	0.0364200	+	0.695372i
$806$	−1.48096	−	0.855032i	−0.0521645	−	0.0301172i
$807$	−23.0566	−	31.3944i	−0.811632	−	1.10513i
$808$	21.2260	+	12.2548i	0.746728	+	0.431124i
$809$	15.8894	−	9.17377i	0.558643	−	0.322533i	−0.193958	−	0.981010i	$-0.562132\pi$
$809$	15.8894	−	9.17377i	0.558643	−	0.322533i	0.752601	+	0.658477i	$0.228799\pi$
$810$	−8.79243	+	12.6399i	−0.308935	+	0.444120i
$811$			0.983192i			0.0345245i	0.999851	+	0.0172623i	$0.00549502\pi$
$811$			0.983192i			0.0345245i	−0.999851	+	0.0172623i	$0.994505\pi$
$812$	−14.6816	−	7.48123i	−0.515221	−	0.262540i
$813$	36.0018	+	15.8080i	1.26264	+	0.554410i
$814$	−0.705659	−	1.22224i	−0.0247333	−	0.0428394i
$815$	−19.0678			−0.667917
$816$	6.01093	+	8.18460i	0.210425	+	0.286518i
$817$		−	0.0103235i		−	0.000361175i
$818$	−59.1516			−2.06819
$819$	−0.321169	−	1.15133i	−0.0112226	−	0.0402308i
$820$	−9.95673			−0.347704
$821$			31.8244i			1.11068i	0.831624	+	0.555340i	$0.187412\pi$
$821$			31.8244i			1.11068i	−0.831624	+	0.555340i	$0.812588\pi$
$822$	−21.7858	+	49.6160i	−0.759868	+	1.73056i
$823$	8.51136			0.296687			0.148344	−	0.988936i	$-0.452606\pi$
$823$	8.51136			0.296687			0.148344	+	0.988936i	$0.452606\pi$
$824$	4.07899	+	7.06502i	0.142098	+	0.246122i
$825$	0.801517	−	0.588650i	0.0279053	−	0.0204942i
$826$	38.9843	−	25.3149i	1.35644	−	0.880817i
$827$			34.2983i			1.19267i	0.802736	+	0.596334i	$0.203377\pi$
$827$			34.2983i			1.19267i	−0.802736	+	0.596334i	$0.796623\pi$
$828$	15.2861	−	14.0507i	0.531230	−	0.488295i
$829$	−16.1048	+	9.29811i	−0.559343	+	0.322937i	−0.752882	−	0.658156i	$-0.771337\pi$
$829$	−16.1048	+	9.29811i	−0.559343	+	0.322937i	0.193539	+	0.981093i	$0.438003\pi$
$830$	−13.2640	−	7.65799i	−0.460401	−	0.265813i
$831$	17.0566	−	38.8454i	0.591686	−	1.34753i
$832$	0.215549	+	0.124447i	0.00747281	+	0.00431443i
$833$	8.17183	−	0.858351i	0.283137	−	0.0297401i
$834$	6.34080	−	14.4408i	0.219564	−	0.500045i
$835$	6.07671			0.210293
$836$	0.000456971	0	0.000791497i	1.58047e−5	0	2.73745e-5i
$837$	11.1621	+	32.6338i	0.385819	+	1.12799i
$838$	−11.0872	−	6.40122i	−0.383003	−	0.221127i
$839$	−19.7247	−	34.1643i	−0.680974	−	1.17948i	−0.974684	−	0.223587i	$-0.928223\pi$
$839$	−19.7247	−	34.1643i	−0.680974	−	1.17948i	0.293710	−	0.955895i	$-0.405110\pi$
$840$	−7.86996	−	2.97500i	−0.271539	−	0.102647i
$841$	8.07704	−	13.9898i	0.278518	−	0.482408i
$842$	14.0545	−	8.11435i	0.484349	−	0.279639i
$843$	22.4442	−	16.4835i	0.773019	−	0.567720i
$844$	9.00463	−	15.5965i	0.309952	−	0.536853i
$845$	−6.48866	+	11.2387i	−0.223217	+	0.386623i
$846$	9.44578	+	42.2977i	0.324752	+	1.45422i
$847$	12.8175	−	25.1537i	0.440414	−	0.864291i
$848$	−47.9908	+	27.7075i	−1.64801	+	0.951480i
$849$	0.986054	+	8.93975i	0.0338413	+	0.306811i
$850$		−	2.00818i		−	0.0688800i
$851$		−	10.7291i		−	0.367788i
$852$	−0.0124706	−	0.113061i	−0.000427236	−	0.00387340i
$853$	−23.0814	+	13.3260i	−0.790291	+	0.456275i	−0.840065	−	0.542486i	$-0.817483\pi$
$853$	−23.0814	+	13.3260i	−0.790291	+	0.456275i	0.0497738	+	0.998761i	$0.484150\pi$
$854$	18.1275	+	27.9159i	0.620310	+	0.955262i
$855$	−0.00112297	−	0.00502860i	−3.84048e−5	−	0.000171975i
$856$	−5.53111	+	9.58017i	−0.189049	+	0.327443i
$857$	6.96617	−	12.0658i	0.237960	−	0.412159i	−0.722169	−	0.691717i	$-0.756855\pi$
$857$	6.96617	−	12.0658i	0.237960	−	0.412159i	0.960129	+	0.279558i	$0.0901880\pi$
$858$	0.206497	−	0.151656i	0.00704970	−	0.00517744i
$859$	−15.3456	+	8.85980i	−0.523586	+	0.302292i	−0.738401	−	0.674362i	$-0.764419\pi$
$859$	−15.3456	+	8.85980i	−0.523586	+	0.302292i	0.214815	+	0.976655i	$0.431085\pi$
$860$	2.78551	−	4.82465i	0.0949852	−	0.164519i
$861$	−48.5835	+	7.94923i	−1.65572	+	0.270909i
$862$	−24.9869	−	43.2787i	−0.851059	−	1.47408i
$863$	−31.5079	−	18.1911i	−1.07254	−	0.619233i	−0.143668	−	0.989626i	$-0.545890\pi$
$863$	−31.5079	−	18.1911i	−1.07254	−	0.619233i	−0.928875	+	0.370393i	$0.879223\pi$
$864$	8.19449	+	23.9576i	0.278782	+	0.815053i
$865$	9.82533	+	17.0180i	0.334071	+	0.578628i
$866$	20.9676			0.712507
$867$	10.8785	−	24.7752i	0.369453	−	0.841410i
$868$	13.6509	−	8.86436i	0.463342	−	0.300876i
$869$	−1.64622	−	0.950444i	−0.0558441	−	0.0322416i
$870$	−8.00528	+	18.2316i	−0.271404	+	0.618109i
$871$	1.06978	+	0.617640i	0.0362482	+	0.0209279i
$872$	8.20553	−	4.73747i	0.277874	−	0.160431i
$873$	38.0371	−	34.9629i	1.28736	−	1.18332i
$874$			0.0219409i			0.000742160i
$875$	1.44091	+	2.21896i	0.0487115	+	0.0750146i
$876$	−15.2996	+	11.2363i	−0.516926	+	0.379640i
$877$	12.2495	+	21.2167i	0.413635	+	0.716437i	0.995284	−	0.0970027i	$-0.0309255\pi$
$877$	12.2495	+	21.2167i	0.413635	+	0.716437i	−0.581649	+	0.813440i	$0.697592\pi$
$878$	1.28659			0.0434205
$879$	−1.72752	+	3.93434i	−0.0582679	+	0.132702i
$880$		−	2.86767i		−	0.0966691i
$881$	23.4938			0.791527			0.395763	−	0.918353i	$-0.370480\pi$
$881$	23.4938			0.791527			0.395763	+	0.918353i	$0.370480\pi$
$882$	35.2161	+	7.11054i	1.18579	+	0.239424i
$883$	26.9871			0.908189			0.454094	−	0.890954i	$-0.349963\pi$
$883$	26.9871			0.908189			0.454094	+	0.890954i	$0.349963\pi$
$884$		−	0.163835i		−	0.00551037i
$885$	−10.5287	−	14.3361i	−0.353918	−	0.481902i
$886$	−49.8002			−1.67307
$887$	−7.70367	−	13.3431i	−0.258664	−	0.448019i	0.707220	−	0.706993i	$-0.249949\pi$
$887$	−7.70367	−	13.3431i	−0.258664	−	0.448019i	−0.965884	+	0.258974i	$0.916615\pi$
$888$	4.18356	+	1.83695i	0.140391	+	0.0616440i
$889$	−9.25368	−	14.2504i	−0.310358	−	0.477945i
$890$			2.39420i			0.0802536i
$891$	−5.14904	−	0.434448i	−0.172499	−	0.0145546i
$892$	1.97094	−	1.13792i	0.0659918	−	0.0381004i
$893$	−0.0125600	−	0.00725150i	−0.000420303	−	0.000242662i
$894$	−1.27100	−	1.73062i	−0.0425087	−	0.0578807i
$895$	11.5181	+	6.64999i	0.385008	+	0.222285i
$896$	−27.8997	+	18.1170i	−0.932064	+	0.605246i
$897$	1.93597	−	0.213537i	0.0646401	−	0.00712980i
$898$	56.6498			1.89043
$899$	22.3013	+	38.6269i	0.743788	+	1.28828i
$900$	0.832011	−	2.65309i	0.0277337	−	0.0884365i
$901$	−11.2787	−	6.51174i	−0.375747	−	0.216937i
$902$	−5.27605	−	9.13839i	−0.175673	−	0.304275i
$903$	9.73991	−	25.7656i	0.324124	−	0.857425i
$904$	−7.76801	+	13.4546i	−0.258360	+	0.447493i
$905$	6.81923	−	3.93708i	0.226679	−	0.130873i
$906$	−10.4829	−	4.60293i	−0.348272	−	0.152922i
$907$	6.57369	−	11.3860i	0.218276	−	0.378065i	−0.736005	−	0.676976i	$-0.763290\pi$
$907$	6.57369	−	11.3860i	0.218276	−	0.378065i	0.954281	+	0.298911i	$0.0966234\pi$
$908$	−0.861053	+	1.49139i	−0.0285750	+	0.0494934i
$909$	−11.9839	+	38.2140i	−0.397482	+	1.26748i
$910$	0.371225	+	0.571677i	0.0123060	+	0.0189509i
$911$	−18.4987	+	10.6802i	−0.612889	+	0.353852i	−0.774095	−	0.633069i	$-0.781795\pi$
$911$	−18.4987	+	10.6802i	−0.612889	+	0.353852i	0.161206	+	0.986921i	$0.448462\pi$
$912$	−0.0136043	−	0.00597348i	−0.000450483	−	0.000197802i
$913$		−	5.14008i		−	0.170112i
$914$		−	38.4450i		−	1.27165i
$915$	10.2658	−	7.53938i	0.339376	−	0.249244i
$916$	−21.8398	+	12.6092i	−0.721606	+	0.416620i
$917$	16.0360	−	31.4698i	0.529555	−	1.03923i
$918$	−6.86194	+	7.86124i	−0.226478	+	0.259460i
$919$	−12.2951	+	21.2957i	−0.405576	+	0.702479i	−0.994388	−	0.105791i	$-0.966263\pi$
$919$	−12.2951	+	21.2957i	−0.405576	+	0.702479i	0.588812	+	0.808270i	$0.299596\pi$
$920$	6.85484	−	11.8729i	0.225998	−	0.391439i
$921$	3.08123	+	27.9350i	0.101530	+	0.920488i
$922$	−13.1230	+	7.57659i	−0.432184	+	0.249522i
$923$	0.00533518	−	0.00924080i	0.000175610	−	0.000304165i
$924$	0.393762	+	2.40657i	0.0129538	+	0.0791702i
$925$	−0.718409	−	1.24432i	−0.0236211	−	0.0409130i
$926$	54.5330	+	31.4847i	1.79207	+	1.03465i
$927$	−9.81413	+	9.02094i	−0.322338	+	0.296287i
$928$	16.3721	+	28.3573i	0.537441	+	0.930875i
$929$	11.8156			0.387658			0.193829	−	0.981035i	$-0.437909\pi$
$929$	11.8156			0.387658			0.193829	+	0.981035i	$0.437909\pi$
$930$	−11.6424	−	15.8525i	−0.381769	−	0.519825i
$931$	−0.00972680	+	0.00706596i	−0.000318783	+	0.000231578i
$932$	3.96474	+	2.28904i	0.129869	+	0.0749801i
$933$	27.2329	−	3.00378i	0.891564	−	0.0983394i
$934$	18.5970	+	10.7370i	0.608511	+	0.351324i
$935$	0.583658	−	0.336975i	0.0190877	−	0.0110203i
$936$	−0.248198	+	0.791446i	−0.00811259	+	0.0258692i
$937$		−	45.3542i		−	1.48166i	−0.671694	−	0.740829i	$-0.734433\pi$
$937$		−	45.3542i		−	1.48166i	0.671694	−	0.740829i	$-0.265567\pi$
$938$	−31.1395	+	20.2208i	−1.01674	+	0.660231i
$939$	−5.75422	−	52.1689i	−0.187782	−	1.70247i
$940$	−3.91322	−	6.77790i	−0.127635	−	0.221071i
$941$	10.0589			0.327910			0.163955	−	0.986468i	$-0.447575\pi$
$941$	10.0589			0.327910			0.163955	+	0.986468i	$0.447575\pi$
$942$	−19.3002	+	2.12881i	−0.628835	+	0.0693605i
$943$		−	80.2189i		−	2.61229i
$944$	−51.2916			−1.66940
$945$	1.94160	−	13.6099i	0.0631601	−	0.442731i
$946$	5.90415			0.191960
$947$		−	15.5358i		−	0.504844i	−0.967617	−	0.252422i	$-0.918773\pi$
$947$		−	15.5358i		−	0.504844i	0.967617	−	0.252422i	$-0.0812272\pi$
$948$	−5.28285	+	0.582698i	−0.171579	+	0.0189251i
$949$	−1.78071			−0.0578043
$950$	0.00146914	+	0.00254462i	4.76651e−5	+	8.25584e-5i
$951$	5.04763	+	45.7627i	0.163681	+	1.48396i
$952$	−5.08035	−	2.58878i	−0.164655	−	0.0839027i
$953$		−	31.4136i		−	1.01759i	−0.860889	−	0.508793i	$-0.830092\pi$
$953$		−	31.4136i		−	1.01759i	0.860889	−	0.508793i	$-0.169908\pi$
$954$	−38.5352	−	41.9235i	−1.24762	−	1.35732i
$955$	−5.74756	+	3.31835i	−0.185987	+	0.107379i
$956$	−15.4899	−	8.94307i	−0.500978	−	0.289240i
$957$	−6.64213	+	0.732626i	−0.214710	+	0.0236824i
$958$	26.6376	+	15.3793i	0.860623	+	0.496881i
$959$	−2.53060	−	48.3170i	−0.0817172	−	1.56024i
$960$	1.69452	+	2.30729i	0.0546902	+	0.0744673i
$961$	−13.0577			−0.421216
$962$	−0.185086	−	0.320578i	−0.00596740	−	0.0103358i
$963$	−17.2476	−	5.40884i	−0.555795	−	0.174297i
$964$	−13.7891	−	7.96112i	−0.444116	−	0.256410i
$965$	5.42222	+	9.39156i	0.174548	+	0.302325i
$966$	−20.7005	+	54.7602i	−0.666027	+	1.76188i
$967$	−13.5686	+	23.5016i	−0.436338	+	0.755760i	−0.997404	−	0.0720113i	$-0.977058\pi$
$967$	−13.5686	+	23.5016i	−0.436338	+	0.755760i	0.561065	+	0.827771i	$0.310392\pi$
$968$	−16.9659	+	9.79525i	−0.545304	+	0.314831i
$969$	−0.000382832	−	0.00347082i	−1.22983e−5	−	0.000111499i
$970$	−14.7313	+	25.5153i	−0.472993	+	0.819248i
$971$	24.3180	−	42.1200i	0.780402	−	1.35170i	−0.151306	−	0.988487i	$-0.548348\pi$
$971$	24.3180	−	42.1200i	0.780402	−	1.35170i	0.931708	−	0.363209i	$-0.118319\pi$
$972$	−12.3226	+	7.54284i	−0.395248	+	0.241937i
$973$	0.736535	+	14.0628i	0.0236122	+	0.450831i
$974$	−2.99091	+	1.72680i	−0.0958348	+	0.0553302i
$975$	0.210228	−	0.154396i	0.00673270	−	0.00494462i
$976$		−	36.7289i		−	1.17566i
$977$			57.6595i			1.84469i	0.386367	+	0.922345i	$0.373730\pi$
$977$			57.6595i			1.84469i	−0.386367	+	0.922345i	$0.626270\pi$
$978$	−51.7341	−	22.7158i	−1.65427	−	0.726373i
$979$	−0.695850	+	0.401749i	−0.0222395	+	0.0128400i
$980$	−6.45232	+	0.677738i	−0.206112	+	0.0216495i
$981$	10.4772	+	11.3984i	0.334511	+	0.363924i
$982$	29.0976	−	50.3986i	0.928543	−	1.60828i
$983$	−5.22542	+	9.05069i	−0.166665	+	0.288672i	−0.937245	−	0.348671i	$-0.886633\pi$
$983$	−5.22542	+	9.05069i	−0.166665	+	0.288672i	0.770580	+	0.637343i	$0.219966\pi$
$984$	31.2795	+	13.7345i	0.997154	+	0.437839i
$985$	−9.57636	+	5.52892i	−0.305128	+	0.176166i
$986$	−6.74716	+	11.6864i	−0.214873	+	0.372172i
$987$	−24.5058	−	29.9483i	−0.780027	−	0.953265i
$988$	0.000119858	0	0.000207600i	3.81319e−6	0	6.60464e-6i
$989$	38.8710	+	22.4422i	1.23603	+	0.713620i
$990$	2.87592	−	0.642241i	0.0914026	−	0.0204117i
$991$	−1.42712	−	2.47185i	−0.0453341	−	0.0785209i	0.842468	−	0.538746i	$-0.181102\pi$
$991$	−1.42712	−	2.47185i	−0.0453341	−	0.0785209i	−0.887802	+	0.460225i	$0.847769\pi$
$992$	−32.3442			−1.02693
$993$	−22.4700	+	2.47844i	−0.713063	+	0.0786509i
$994$	0.174667	+	0.268983i	0.00554010	+	0.00853163i
$995$	−0.779269	−	0.449911i	−0.0247045	−	0.0142631i
$996$	−8.50707	−	11.5834i	−0.269557	−	0.367034i
$997$	7.06298	+	4.07781i	0.223687	+	0.129146i	0.607656	−	0.794200i	$-0.292110\pi$
$997$	7.06298	+	4.07781i	0.223687	+	0.129146i	−0.383969	+	0.923346i	$0.625443\pi$
$998$	−49.6220	+	28.6493i	−1.57076	+	0.906877i
$999$	−1.43955	+	7.32583i	−0.0455453	+	0.231779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.c.131.4	yes	32
3.2	odd	2		945.2.t.c.341.13		32
7.3	odd	6		315.2.be.c.311.13	yes	32
9.2	odd	6		315.2.be.c.236.13	yes	32
9.7	even	3		945.2.be.c.656.4		32
21.17	even	6		945.2.be.c.206.4		32
63.38	even	6	inner	315.2.t.c.101.13	✓	32
63.52	odd	6		945.2.t.c.521.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.13	✓	32	63.38	even	6	inner
315.2.t.c.131.4	yes	32	1.1	even	1	trivial
315.2.be.c.236.13	yes	32	9.2	odd	6
315.2.be.c.311.13	yes	32	7.3	odd	6
945.2.t.c.341.13		32	3.2	odd	2
945.2.t.c.521.4		32	63.52	odd	6
945.2.be.c.206.4		32	21.17	even	6
945.2.be.c.656.4		32	9.7	even	3

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.71080i q^{2} +(1.72161 - 0.189893i) q^{3} -0.926832 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.324870 - 2.94533i) q^{6} +(1.44091 + 2.21896i) q^{7} -1.83597i q^{8} +(2.92788 - 0.653845i) q^{9} +O(q^{10})\)	\(q-1.71080i q^{2} +(1.72161 - 0.189893i) q^{3} -0.926832 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.324870 - 2.94533i) q^{6} +(1.44091 + 2.21896i) q^{7} -1.83597i q^{8} +(2.92788 - 0.653845i) q^{9} +(-1.48159 + 0.855399i) q^{10} +(-0.497227 - 0.287074i) q^{11} +(-1.59564 + 0.175999i) q^{12} +(-0.130417 - 0.0752961i) q^{13} +(3.79620 - 2.46510i) q^{14} +(-1.02526 - 1.39601i) q^{15} -4.99465 q^{16} +(-0.586913 - 1.01656i) q^{17} +(-1.11860 - 5.00901i) q^{18} +(0.00148739 + 0.000858744i) q^{19} +(0.463416 + 0.802660i) q^{20} +(2.90205 + 3.54657i) q^{21} +(-0.491126 + 0.850655i) q^{22} +(-6.46683 + 3.73363i) q^{23} +(-0.348640 - 3.16083i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.128816 + 0.223117i) q^{26} +(4.91651 - 1.68165i) q^{27} +(-1.33548 - 2.05660i) q^{28} +(5.81941 - 3.35984i) q^{29} +(-2.38829 + 1.75401i) q^{30} +6.63760i q^{31} +4.87288i q^{32} +(-0.910544 - 0.399809i) q^{33} +(-1.73914 + 1.00409i) q^{34} +(1.20122 - 2.35734i) q^{35} +(-2.71365 + 0.606004i) q^{36} +(-0.718409 + 1.24432i) q^{37} +(0.00146914 - 0.00254462i) q^{38} +(-0.238825 - 0.104865i) q^{39} +(-1.59000 + 0.917987i) q^{40} +(-5.37138 + 9.30350i) q^{41} +(6.06746 - 4.96481i) q^{42} +(-3.00541 - 5.20553i) q^{43} +(0.460846 + 0.266069i) q^{44} +(-2.03019 - 2.20870i) q^{45} +(6.38748 + 11.0634i) q^{46} -8.44431 q^{47} +(-8.59883 + 0.948451i) q^{48} +(-2.84758 + 6.39463i) q^{49} +(1.48159 + 0.855399i) q^{50} +(-1.20347 - 1.63867i) q^{51} +(0.120874 + 0.0697868i) q^{52} +(9.60845 - 5.54744i) q^{53} +(-2.87697 - 8.41115i) q^{54} +0.574148i q^{55} +(4.07396 - 2.64547i) q^{56} +(0.00272377 + 0.00119598i) q^{57} +(-5.74801 - 9.95584i) q^{58} +10.2693 q^{59} +(0.950241 + 1.29387i) q^{60} +7.35365i q^{61} +11.3556 q^{62} +(5.66966 + 5.55472i) q^{63} -1.65277 q^{64} +0.150592i q^{65} +(-0.683993 + 1.55776i) q^{66} -8.20281 q^{67} +(0.543970 + 0.942183i) q^{68} +(-10.4244 + 7.65586i) q^{69} +(-4.03294 - 2.05505i) q^{70} +0.0708560i q^{71} +(-1.20044 - 5.37552i) q^{72} +(10.2405 - 5.91235i) q^{73} +(2.12878 + 1.22905i) q^{74} +(-0.696352 + 1.58590i) q^{75} +(-0.00137856 - 0.000795911i) q^{76} +(-0.0794513 - 1.51697i) q^{77} +(-0.179403 + 0.408581i) q^{78} +3.31080 q^{79} +(2.49732 + 4.32549i) q^{80} +(8.14497 - 3.82876i) q^{81} +(15.9164 + 9.18935i) q^{82} +(4.47627 + 7.75313i) q^{83} +(-2.68971 - 3.28707i) q^{84} +(-0.586913 + 1.01656i) q^{85} +(-8.90561 + 5.14166i) q^{86} +(9.38075 - 6.88940i) q^{87} +(-0.527061 + 0.912896i) q^{88} +(0.699730 - 1.21197i) q^{89} +(-3.77864 + 3.47324i) q^{90} +(-0.0208391 - 0.397884i) q^{91} +(5.99366 - 3.46044i) q^{92} +(1.26044 + 11.4274i) q^{93} +14.4465i q^{94} -0.00171749i q^{95} +(0.925329 + 8.38920i) q^{96} +(14.9143 - 8.61076i) q^{97} +(10.9399 + 4.87163i) q^{98} +(-1.64352 - 0.515409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

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