LMFDB - Embedded newform 731.2.e.b.307.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (of order $3$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.11
Character	$\chi$	$=$	731.307
Dual form			731.2.e.b.681.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.09472 q^{2} +(0.124885 - 0.216307i) q^{3} -0.801596 q^{4} +(-1.31747 + 2.28193i) q^{5} +(-0.136714 + 0.236795i) q^{6} +(0.589522 + 1.02108i) q^{7} +3.06695 q^{8} +(1.46881 + 2.54405i) q^{9} +O(q^{10})$	\(q-1.09472 q^{2} +(0.124885 - 0.216307i) q^{3} -0.801596 q^{4} +(-1.31747 + 2.28193i) q^{5} +(-0.136714 + 0.236795i) q^{6} +(0.589522 + 1.02108i) q^{7} +3.06695 q^{8} +(1.46881 + 2.54405i) q^{9} +(1.44226 - 2.49806i) q^{10} +1.55975 q^{11} +(-0.100107 + 0.173391i) q^{12} +(-1.03437 - 1.79158i) q^{13} +(-0.645360 - 1.11780i) q^{14} +(0.329065 + 0.569957i) q^{15} -1.75425 q^{16} +(-0.500000 - 0.866025i) q^{17} +(-1.60793 - 2.78501i) q^{18} +(-0.307833 + 0.533182i) q^{19} +(1.05608 - 1.82918i) q^{20} +0.294490 q^{21} -1.70748 q^{22} +(-0.480197 + 0.831725i) q^{23} +(0.383016 - 0.663403i) q^{24} +(-0.971464 - 1.68263i) q^{25} +(1.13234 + 1.96127i) q^{26} +1.48304 q^{27} +(-0.472559 - 0.818496i) q^{28} +(-3.26474 - 5.65469i) q^{29} +(-0.360232 - 0.623941i) q^{30} +(-5.14718 + 8.91517i) q^{31} -4.21350 q^{32} +(0.194789 - 0.337384i) q^{33} +(0.547358 + 0.948052i) q^{34} -3.10672 q^{35} +(-1.17739 - 2.03930i) q^{36} +(-4.65816 + 8.06818i) q^{37} +(0.336989 - 0.583683i) q^{38} -0.516707 q^{39} +(-4.04062 + 6.99857i) q^{40} +6.98957 q^{41} -0.322383 q^{42} +(3.49286 + 5.54977i) q^{43} -1.25029 q^{44} -7.74045 q^{45} +(0.525679 - 0.910503i) q^{46} -10.6446 q^{47} +(-0.219080 + 0.379457i) q^{48} +(2.80493 - 4.85828i) q^{49} +(1.06348 + 1.84200i) q^{50} -0.249770 q^{51} +(0.829144 + 1.43612i) q^{52} +(-5.40158 + 9.35582i) q^{53} -1.62350 q^{54} +(-2.05492 + 3.55923i) q^{55} +(1.80804 + 3.13161i) q^{56} +(0.0768873 + 0.133173i) q^{57} +(3.57396 + 6.19028i) q^{58} -5.74771 q^{59} +(-0.263777 - 0.456875i) q^{60} +(3.93921 + 6.82292i) q^{61} +(5.63470 - 9.75959i) q^{62} +(-1.73179 + 2.99955i) q^{63} +8.12109 q^{64} +5.45100 q^{65} +(-0.213238 + 0.369340i) q^{66} +(6.87317 - 11.9047i) q^{67} +(0.400798 + 0.694202i) q^{68} +(0.119939 + 0.207740i) q^{69} +3.40097 q^{70} +(-5.58215 - 9.66857i) q^{71} +(4.50476 + 7.80248i) q^{72} +(0.540369 + 0.935947i) q^{73} +(5.09937 - 8.83237i) q^{74} -0.485285 q^{75} +(0.246757 - 0.427396i) q^{76} +(0.919505 + 1.59263i) q^{77} +0.565648 q^{78} +(-5.53693 - 9.59024i) q^{79} +(2.31118 - 4.00308i) q^{80} +(-4.22121 + 7.31136i) q^{81} -7.65159 q^{82} +(-5.20374 + 9.01313i) q^{83} -0.236062 q^{84} +2.63494 q^{85} +(-3.82369 - 6.07542i) q^{86} -1.63086 q^{87} +4.78367 q^{88} +(-3.51840 + 6.09404i) q^{89} +8.47360 q^{90} +(1.21957 - 2.11235i) q^{91} +(0.384924 - 0.666707i) q^{92} +(1.28561 + 2.22674i) q^{93} +11.6528 q^{94} +(-0.811122 - 1.40490i) q^{95} +(-0.526202 + 0.911409i) q^{96} +7.75256 q^{97} +(-3.07060 + 5.31843i) q^{98} +(2.29097 + 3.96807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) $ 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.09472			−0.774081			−0.387041	−	0.922063i	$-0.626503\pi$
$2$	−1.09472			−0.774081			−0.387041	+	0.922063i	$0.626503\pi$
$3$	0.124885	−	0.216307i	0.0721023	−	0.124885i	−0.827720	−	0.561141i	$-0.810363\pi$
$3$	0.124885	−	0.216307i	0.0721023	−	0.124885i	0.899823	+	0.436256i	$0.143696\pi$
$4$	−0.801596			−0.400798
$5$	−1.31747	+	2.28193i	−0.589191	+	1.02051i	0.405147	+	0.914251i	$0.367220\pi$
$5$	−1.31747	+	2.28193i	−0.589191	+	1.02051i	−0.994339	+	0.106258i	$0.966113\pi$
$6$	−0.136714	+	0.236795i	−0.0558131	+	0.0966711i
$7$	0.589522	+	1.02108i	0.222819	+	0.385933i	0.955663	−	0.294463i	$-0.0951409\pi$
$7$	0.589522	+	1.02108i	0.222819	+	0.385933i	−0.732844	+	0.680396i	$0.761808\pi$
$8$	3.06695			1.08433
$9$	1.46881	+	2.54405i	0.489603	+	0.848016i
$10$	1.44226	−	2.49806i	0.456082	−	0.789957i
$11$	1.55975			0.470281			0.235141	−	0.971961i	$-0.424445\pi$
$11$	1.55975			0.470281			0.235141	+	0.971961i	$0.424445\pi$
$12$	−0.100107	+	0.173391i	−0.0288985	+	0.0500536i
$13$	−1.03437	−	1.79158i	−0.286882	−	0.496894i	0.686182	−	0.727430i	$-0.259285\pi$
$13$	−1.03437	−	1.79158i	−0.286882	−	0.496894i	−0.973064	+	0.230536i	$0.925952\pi$
$14$	−0.645360	−	1.11780i	−0.172480	−	0.298744i
$15$	0.329065	+	0.569957i	0.0849641	+	0.147162i
$16$	−1.75425			−0.438563
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i
$18$	−1.60793	−	2.78501i	−0.378992	−	0.656434i
$19$	−0.307833	+	0.533182i	−0.0706216	+	0.122320i	−0.899174	−	0.437591i	$-0.855832\pi$
$19$	−0.307833	+	0.533182i	−0.0706216	+	0.122320i	0.828552	+	0.559912i	$0.189165\pi$
$20$	1.05608	−	1.82918i	0.236147	−	0.409018i
$21$	0.294490			0.0642629
$22$	−1.70748			−0.364036
$23$	−0.480197	+	0.831725i	−0.100128	+	0.173427i	−0.911737	−	0.410774i	$-0.865259\pi$
$23$	−0.480197	+	0.831725i	−0.100128	+	0.173427i	0.811609	+	0.584201i	$0.198592\pi$
$24$	0.383016	−	0.663403i	0.0781828	−	0.135417i
$25$	−0.971464	−	1.68263i	−0.194293	−	0.336525i
$26$	1.13234	+	1.96127i	0.222070	+	0.384636i
$27$	1.48304			0.285411
$28$	−0.472559	−	0.818496i	−0.0893052	−	0.154681i
$29$	−3.26474	−	5.65469i	−0.606246	−	1.05005i	−0.991853	−	0.127386i	$-0.959341\pi$
$29$	−3.26474	−	5.65469i	−0.606246	−	1.05005i	0.385607	−	0.922663i	$-0.373992\pi$
$30$	−0.360232	−	0.623941i	−0.0657692	−	0.113916i
$31$	−5.14718	+	8.91517i	−0.924460	+	1.60121i	−0.132033	+	0.991245i	$0.542151\pi$
$31$	−5.14718	+	8.91517i	−0.924460	+	1.60121i	−0.792427	+	0.609967i	$0.791183\pi$
$32$	−4.21350			−0.744848
$33$	0.194789	−	0.337384i	0.0339084	−	0.0587310i
$34$	0.547358	+	0.948052i	0.0938712	+	0.162590i
$35$	−3.10672			−0.525131
$36$	−1.17739	−	2.03930i	−0.196232	−	0.339883i
$37$	−4.65816	+	8.06818i	−0.765797	+	1.32640i	0.174026	+	0.984741i	$0.444322\pi$
$37$	−4.65816	+	8.06818i	−0.765797	+	1.32640i	−0.939824	+	0.341659i	$0.889011\pi$
$38$	0.336989	−	0.583683i	0.0546669	−	0.0946859i
$39$	−0.516707			−0.0827394
$40$	−4.04062	+	6.99857i	−0.638879	+	1.10657i
$41$	6.98957			1.09159			0.545793	−	0.837920i	$-0.316228\pi$
$41$	6.98957			1.09159			0.545793	+	0.837920i	$0.316228\pi$
$42$	−0.322383			−0.0497447
$43$	3.49286	+	5.54977i	0.532656	+	0.846332i
$43$	3.49286	+	5.54977i	0.532656	+	0.846332i
$44$	−1.25029			−0.188488
$45$	−7.74045			−1.15388
$46$	0.525679	−	0.910503i	0.0775072	−	0.134246i
$47$	−10.6446			−1.55267			−0.776334	−	0.630321i	$-0.782923\pi$
$47$	−10.6446			−1.55267			−0.776334	+	0.630321i	$0.782923\pi$
$48$	−0.219080	+	0.379457i	−0.0316214	+	0.0547699i
$49$	2.80493	−	4.85828i	0.400704	−	0.694039i
$50$	1.06348	+	1.84200i	0.150399	+	0.260498i
$51$	−0.249770			−0.0349748
$52$	0.829144	+	1.43612i	0.114982	+	0.199154i
$53$	−5.40158	+	9.35582i	−0.741965	+	1.28512i	0.209635	+	0.977780i	$0.432772\pi$
$53$	−5.40158	+	9.35582i	−0.741965	+	1.28512i	−0.951600	+	0.307341i	$0.900561\pi$
$54$	−1.62350			−0.220931
$55$	−2.05492	+	3.55923i	−0.277086	+	0.479926i
$56$	1.80804	+	3.13161i	0.241609	+	0.418479i
$57$	0.0768873	+	0.133173i	0.0101840	+	0.0176392i
$58$	3.57396	+	6.19028i	0.469284	+	0.812824i
$59$	−5.74771			−0.748288			−0.374144	−	0.927371i	$-0.622063\pi$
$59$	−5.74771			−0.748288			−0.374144	+	0.927371i	$0.622063\pi$
$60$	−0.263777	−	0.456875i	−0.0340534	−	0.0589823i
$61$	3.93921	+	6.82292i	0.504365	+	0.873585i	0.999987	+	0.00504730i	$0.00160661\pi$
$61$	3.93921	+	6.82292i	0.504365	+	0.873585i	−0.495623	+	0.868538i	$0.665060\pi$
$62$	5.63470	−	9.75959i	0.715608	−	1.23947i
$63$	−1.73179	+	2.99955i	−0.218185	+	0.377908i
$64$	8.12109			1.01514
$65$	5.45100			0.676113
$66$	−0.213238	+	0.369340i	−0.0262478	+	0.0454626i
$67$	6.87317	−	11.9047i	0.839692	−	1.45439i	−0.0504607	−	0.998726i	$-0.516069\pi$
$67$	6.87317	−	11.9047i	0.839692	−	1.45439i	0.890152	−	0.455663i	$-0.150598\pi$
$68$	0.400798	+	0.694202i	0.0486039	+	0.0841844i
$69$	0.119939	+	0.207740i	0.0144389	+	0.0250089i
$70$	3.40097			0.406494
$71$	−5.58215	−	9.66857i	−0.662479	−	1.14745i	−0.979962	−	0.199184i	$-0.936171\pi$
$71$	−5.58215	−	9.66857i	−0.662479	−	1.14745i	0.317483	−	0.948264i	$-0.397162\pi$
$72$	4.50476	+	7.80248i	0.530892	+	0.919531i
$73$	0.540369	+	0.935947i	0.0632455	+	0.109544i	0.895914	−	0.444227i	$-0.146522\pi$
$73$	0.540369	+	0.935947i	0.0632455	+	0.109544i	−0.832669	+	0.553771i	$0.813188\pi$
$74$	5.09937	−	8.83237i	0.592790	−	1.02674i
$75$	−0.485285			−0.0560359
$76$	0.246757	−	0.427396i	0.0283050	−	0.0490257i
$77$	0.919505	+	1.59263i	0.104787	+	0.181497i
$78$	0.565648			0.0640470
$79$	−5.53693	−	9.59024i	−0.622953	−	1.07899i	−0.988933	−	0.148363i	$-0.952599\pi$
$79$	−5.53693	−	9.59024i	−0.622953	−	1.07899i	0.365980	−	0.930623i	$-0.380734\pi$
$80$	2.31118	−	4.00308i	0.258398	−	0.447558i
$81$	−4.22121	+	7.31136i	−0.469024	+	0.812373i
$82$	−7.65159			−0.844977
$83$	−5.20374	+	9.01313i	−0.571184	+	0.989320i	0.425261	+	0.905071i	$0.360182\pi$
$83$	−5.20374	+	9.01313i	−0.571184	+	0.989320i	−0.996445	+	0.0842491i	$0.973151\pi$
$84$	−0.236062			−0.0257564
$85$	2.63494			0.285800
$86$	−3.82369	−	6.07542i	−0.412319	−	0.655130i
$87$	−1.63086			−0.174847
$88$	4.78367			0.509941
$89$	−3.51840	+	6.09404i	−0.372949	+	0.645967i	−0.990018	−	0.140942i	$-0.954987\pi$
$89$	−3.51840	+	6.09404i	−0.372949	+	0.645967i	0.617068	+	0.786910i	$0.288320\pi$
$90$	8.47360			0.893196
$91$	1.21957	−	2.11235i	0.127845	−	0.221434i
$92$	0.384924	−	0.666707i	0.0401311	−	0.0695090i
$93$	1.28561	+	2.22674i	0.133311	+	0.230902i
$94$	11.6528			1.20189
$95$	−0.811122	−	1.40490i	−0.0832193	−	0.144140i
$96$	−0.526202	+	0.911409i	−0.0537053	+	0.0930203i
$97$	7.75256			0.787153			0.393576	−	0.919292i	$-0.371238\pi$
$97$	7.75256			0.787153			0.393576	+	0.919292i	$0.371238\pi$
$98$	−3.07060	+	5.31843i	−0.310177	+	0.537243i
$99$	2.29097	+	3.96807i	0.230251	+	0.398806i
$100$	0.778722	+	1.34879i	0.0778722	+	0.134879i
$101$	−2.41807	−	4.18822i	−0.240607	−	0.416744i	0.720280	−	0.693683i	$-0.244013\pi$
$101$	−2.41807	−	4.18822i	−0.240607	−	0.416744i	−0.960887	+	0.276940i	$0.910680\pi$
$102$	0.273427			0.0270733
$103$	−6.86693	−	11.8939i	−0.676619	−	1.17194i	−0.975993	−	0.217802i	$-0.930111\pi$
$103$	−6.86693	−	11.8939i	−0.676619	−	1.17194i	0.299374	−	0.954136i	$-0.403222\pi$
$104$	−3.17236	−	5.49468i	−0.311075	−	0.538798i
$105$	−0.387982	+	0.672004i	−0.0378632	+	0.0655809i
$106$	5.91320	−	10.2420i	0.574341	−	0.994788i
$107$	−9.23427			−0.892710			−0.446355	−	0.894856i	$-0.647278\pi$
$107$	−9.23427			−0.892710			−0.446355	+	0.894856i	$0.647278\pi$
$108$	−1.18880			−0.114392
$109$	−9.22157	+	15.9722i	−0.883266	+	1.52986i	−0.0355772	+	0.999367i	$0.511327\pi$
$109$	−9.22157	+	15.9722i	−0.883266	+	1.52986i	−0.847689	+	0.530494i	$0.822006\pi$
$110$	2.24956	−	3.89635i	0.214487	−	0.371502i
$111$	1.16347	+	2.01519i	0.110432	+	0.191273i
$112$	−1.03417	−	1.79124i	−0.0977200	−	0.169256i
$113$	−1.16009			−0.109132			−0.0545662	−	0.998510i	$-0.517378\pi$
$113$	−1.16009			−0.109132			−0.0545662	+	0.998510i	$0.517378\pi$
$114$	−0.0841698	−	0.145786i	−0.00788322	−	0.0136541i
$115$	−1.26529	−	2.19155i	−0.117989	−	0.204363i
$116$	2.61700	+	4.53278i	0.242982	+	0.420858i
$117$	3.03857	−	5.26296i	0.280916	−	0.486561i
$118$	6.29212			0.579236
$119$	0.589522	−	1.02108i	0.0540414	−	0.0936025i
$120$	1.00923	+	1.74803i	0.0921293	+	0.159573i
$121$	−8.56719			−0.778836
$122$	−4.31232	−	7.46916i	−0.390419	−	0.676226i
$123$	0.872891	−	1.51189i	0.0787059	−	0.136323i
$124$	4.12595	−	7.14636i	0.370522	−	0.641762i
$125$	−8.05521			−0.720480
$126$	1.89582	−	3.28365i	0.168893	−	0.292531i
$127$	6.88778			0.611192			0.305596	−	0.952161i	$-0.401144\pi$
$127$	6.88778			0.611192			0.305596	+	0.952161i	$0.401144\pi$
$128$	−0.463298			−0.0409501
$129$	1.63666	−	0.0624475i	0.144100	−	0.00549819i
$130$	−5.96730			−0.523367
$131$	14.8510			1.29754			0.648770	−	0.760984i	$-0.275284\pi$
$131$	14.8510			1.29754			0.648770	+	0.760984i	$0.275284\pi$
$132$	−0.156142	+	0.270446i	−0.0135904	+	0.0235393i
$133$	−0.725897			−0.0629432
$134$	−7.52418	+	13.0323i	−0.649990	+	1.12582i
$135$	−1.95386	+	3.38418i	−0.168161	+	0.291264i
$136$	−1.53348	−	2.65606i	−0.131495	−	0.227755i
$137$	−8.73498			−0.746279			−0.373140	−	0.927775i	$-0.621719\pi$
$137$	−8.73498			−0.746279			−0.373140	+	0.927775i	$0.621719\pi$
$138$	−0.131299	−	0.227416i	−0.0111769	−	0.0193589i
$139$	−5.42639	+	9.39878i	−0.460260	+	0.797194i	−0.998974	−	0.0452949i	$-0.985577\pi$
$139$	−5.42639	+	9.39878i	−0.460260	+	0.797194i	0.538713	+	0.842489i	$0.318911\pi$
$140$	2.49033			0.210471
$141$	−1.32934	+	2.30249i	−0.111951	+	0.193905i
$142$	6.11087	+	10.5843i	0.512813	+	0.888218i
$143$	−1.61335	−	2.79440i	−0.134915	−	0.233680i
$144$	−2.57666	−	4.46291i	−0.214722	−	0.371909i
$145$	17.2048			1.42878
$146$	−0.591551	−	1.02460i	−0.0489571	−	0.0847962i
$147$	−0.700586	−	1.21345i	−0.0577833	−	0.100084i
$148$	3.73396	−	6.46742i	0.306930	−	0.531618i
$149$	5.22593	−	9.05157i	0.428124	−	0.741533i	−0.568582	−	0.822627i	$-0.692508\pi$
$149$	5.22593	−	9.05157i	0.428124	−	0.741533i	0.996707	+	0.0810932i	$0.0258411\pi$
$150$	0.531249			0.0433763
$151$	5.31871			0.432831			0.216415	−	0.976301i	$-0.430563\pi$
$151$	5.31871			0.432831			0.216415	+	0.976301i	$0.430563\pi$
$152$	−0.944108	+	1.63524i	−0.0765773	+	0.132636i
$153$	1.46881	−	2.54405i	0.118746	−	0.205674i
$154$	−1.00660	−	1.74348i	−0.0811139	−	0.140493i
$155$	−13.5625	−	23.4910i	−1.08937	−	1.88684i
$156$	0.414190			0.0331618
$157$	1.08116	+	1.87263i	0.0862862	+	0.149452i	0.905939	−	0.423409i	$-0.139167\pi$
$157$	1.08116	+	1.87263i	0.0862862	+	0.149452i	−0.819652	+	0.572861i	$0.805833\pi$
$158$	6.06137	+	10.4986i	0.482216	+	0.835223i
$159$	1.34915	+	2.33680i	0.106995	+	0.185320i
$160$	5.55116	−	9.61490i	0.438858	−	0.760124i
$161$	−1.13235			−0.0892414
$162$	4.62103	−	8.00386i	0.363063	−	0.628843i
$163$	3.78459	+	6.55511i	0.296432	+	0.513435i	0.975317	−	0.220809i	$-0.0708698\pi$
$163$	3.78459	+	6.55511i	0.296432	+	0.513435i	−0.678885	+	0.734245i	$0.737536\pi$
$164$	−5.60281			−0.437506
$165$	0.513257	+	0.888988i	0.0399570	+	0.0692076i
$166$	5.69662	−	9.86683i	0.442143	−	0.765814i
$167$	1.42552	−	2.46908i	0.110310	−	0.191063i	−0.805585	−	0.592480i	$-0.798149\pi$
$167$	1.42552	−	2.46908i	0.110310	−	0.191063i	0.915895	+	0.401417i	$0.131482\pi$
$168$	0.903186			0.0696823
$169$	4.36017	−	7.55203i	0.335398	−	0.580926i
$170$	−2.88452			−0.221232
$171$	−1.80859			−0.138306
$172$	−2.79986	−	4.44867i	−0.213487	−	0.339208i
$173$	16.1028			1.22427			0.612135	−	0.790753i	$-0.290311\pi$
$173$	16.1028			1.22427			0.612135	+	0.790753i	$0.290311\pi$
$174$	1.78533			0.135346
$175$	1.14540	−	1.98389i	0.0865841	−	0.149968i
$176$	−2.73619			−0.206248
$177$	−0.717802	+	1.24327i	−0.0539533	+	0.0934499i
$178$	3.85165	−	6.67125i	0.288693	−	0.500031i
$179$	9.76440	+	16.9124i	0.729826	+	1.26410i	0.956957	+	0.290231i	$0.0937321\pi$
$179$	9.76440	+	16.9124i	0.729826	+	1.26410i	−0.227131	+	0.973864i	$0.572935\pi$
$180$	6.20471			0.462472
$181$	9.70292	+	16.8059i	0.721212	+	1.24918i	0.960514	+	0.278231i	$0.0897481\pi$
$181$	9.70292	+	16.8059i	0.721212	+	1.24918i	−0.239302	+	0.970945i	$0.576919\pi$
$182$	−1.33508	+	2.31242i	−0.0989626	+	0.171408i
$183$	1.96779			0.145463
$184$	−1.47274	+	2.55086i	−0.108572	+	0.188052i
$185$	−12.2740	−	21.2592i	−0.902402	−	1.56301i
$186$	−1.40738	−	2.43765i	−0.103194	−	0.178737i
$187$	−0.779873	−	1.35078i	−0.0570300	−	0.0987788i
$188$	8.53263			0.622306
$189$	0.874283	+	1.51430i	0.0635948	+	0.110149i
$190$	0.887948	+	1.53797i	0.0644185	+	0.111576i
$191$	9.31164	−	16.1282i	0.673766	−	1.16700i	−0.303061	−	0.952971i	$-0.598009\pi$
$191$	9.31164	−	16.1282i	0.673766	−	1.16700i	0.976828	−	0.214027i	$-0.0686579\pi$
$192$	1.01420	−	1.75665i	0.0731937	−	0.126775i
$193$	−0.801043			−0.0576604			−0.0288302	−	0.999584i	$-0.509178\pi$
$193$	−0.801043			−0.0576604			−0.0288302	+	0.999584i	$0.509178\pi$
$194$	−8.48685			−0.609320
$195$	0.680747	−	1.17909i	0.0487493	−	0.0844363i
$196$	−2.24842	+	3.89437i	−0.160601	+	0.278169i
$197$	−10.7296	−	18.5842i	−0.764453	−	1.32407i	−0.940535	−	0.339696i	$-0.889676\pi$
$197$	−10.7296	−	18.5842i	−0.764453	−	1.32407i	0.176082	−	0.984376i	$-0.443658\pi$
$198$	−2.50796	−	4.34391i	−0.178233	−	0.308708i
$199$	20.6478			1.46369			0.731843	−	0.681473i	$-0.238660\pi$
$199$	20.6478			1.46369			0.731843	+	0.681473i	$0.238660\pi$
$200$	−2.97944	−	5.16053i	−0.210678	−	0.364905i
$201$	−1.71671	−	2.97343i	−0.121087	−	0.209730i
$202$	2.64710	+	4.58491i	0.186249	+	0.322593i
$203$	3.84927	−	6.66713i	0.270166	−	0.467941i
$204$	0.200214			0.0140178
$205$	−9.20856	+	15.9497i	−0.643153	+	1.11397i
$206$	7.51734	+	13.0204i	0.523758	+	0.907176i
$207$	−2.82127			−0.196092
$208$	1.81454	+	3.14288i	0.125816	+	0.217919i
$209$	−0.480141	+	0.831628i	−0.0332120	+	0.0575249i
$210$	0.424730	−	0.735654i	0.0293092	−	0.0507650i
$211$	14.6788			1.01053			0.505263	−	0.862965i	$-0.331395\pi$
$211$	14.6788			1.01053			0.505263	+	0.862965i	$0.331395\pi$
$212$	4.32989	−	7.49958i	0.297378	−	0.515074i
$213$	−2.78850			−0.191065
$214$	10.1089			0.691031
$215$	−17.2659	+	0.658789i	−1.17753	+	0.0449290i
$216$	4.54840			0.309480
$217$	−12.1375			−0.823947
$218$	10.0950	−	17.4851i	0.683720	−	1.18424i
$219$	0.269936			0.0182406
$220$	1.64722	−	2.85306i	0.111055	−	0.192353i
$221$	−1.03437	+	1.79158i	−0.0695791	+	0.120514i
$222$	−1.27367	−	2.20606i	−0.0854830	−	0.148061i
$223$	20.8228			1.39440			0.697199	−	0.716878i	$-0.254429\pi$
$223$	20.8228			1.39440			0.697199	+	0.716878i	$0.254429\pi$
$224$	−2.48395	−	4.30233i	−0.165966	−	0.287461i
$225$	2.85379	−	4.94291i	0.190253	−	0.329527i
$226$	1.26997			0.0844773
$227$	−11.1671	+	19.3419i	−0.741185	+	1.28377i	0.210771	+	0.977535i	$0.432403\pi$
$227$	−11.1671	+	19.3419i	−0.741185	+	1.28377i	−0.951956	+	0.306235i	$0.900931\pi$
$228$	−0.0616325	−	0.106751i	−0.00408171	−	0.00706973i
$229$	4.15043	+	7.18875i	0.274268	+	0.475046i	0.969950	−	0.243304i	$-0.0782312\pi$
$229$	4.15043	+	7.18875i	0.274268	+	0.475046i	−0.695682	+	0.718350i	$0.744898\pi$
$230$	1.38513	+	2.39912i	0.0913331	+	0.158194i
$231$	0.459329			0.0302216
$232$	−10.0128	−	17.3427i	−0.657372	−	1.13860i
$233$	12.0778	+	20.9193i	0.791241	+	1.37047i	0.925199	+	0.379482i	$0.123898\pi$
$233$	12.0778	+	20.9193i	0.791241	+	1.37047i	−0.133958	+	0.990987i	$0.542769\pi$
$234$	−3.32638	+	5.76145i	−0.217452	+	0.376638i
$235$	14.0239	−	24.2901i	0.914819	−	1.58451i
$236$	4.60734			0.299912
$237$	−2.76591			−0.179665
$238$	−0.645360	+	1.11780i	−0.0418325	+	0.0724560i
$239$	7.80357	−	13.5162i	0.504771	−	0.874289i	−0.495214	−	0.868771i	$-0.664910\pi$
$239$	7.80357	−	13.5162i	0.504771	−	0.874289i	0.999985	−	0.00551769i	$-0.00175634\pi$
$240$	−0.577263	−	0.999848i	−0.0372621	−	0.0645399i
$241$	12.2423	+	21.2042i	0.788593	+	1.36588i	0.926829	+	0.375484i	$0.122523\pi$
$241$	12.2423	+	21.2042i	0.788593	+	1.36588i	−0.138236	+	0.990399i	$0.544143\pi$
$242$	9.37865			0.602882
$243$	3.27889	+	5.67920i	0.210341	+	0.364321i
$244$	−3.15766	−	5.46922i	−0.202148	−	0.350131i
$245$	7.39082	+	12.8013i	0.472182	+	0.817844i
$246$	−0.955568	+	1.65509i	−0.0609248	+	0.105525i
$247$	1.27365			0.0810403
$248$	−15.7861	+	27.3424i	−1.00242	+	1.73624i
$249$	1.29974	+	2.25121i	0.0823674	+	0.142665i
$250$	8.81817			0.557710
$251$	4.15161	+	7.19079i	0.262047	+	0.453879i	0.966786	−	0.255588i	$-0.0822691\pi$
$251$	4.15161	+	7.19079i	0.262047	+	0.453879i	−0.704739	+	0.709467i	$0.748936\pi$
$252$	1.38820	−	2.40443i	0.0874481	−	0.151465i
$253$	−0.748985	+	1.29728i	−0.0470883	+	0.0815593i
$254$	−7.54017			−0.473112
$255$	0.329065	−	0.569957i	0.0206068	−	0.0356921i
$256$	−15.7350			−0.983438
$257$	−15.8203			−0.986841			−0.493420	−	0.869791i	$-0.664254\pi$
$257$	−15.8203			−0.986841			−0.493420	+	0.869791i	$0.664254\pi$
$258$	−1.79168	+	0.0683623i	−0.111545	+	0.00425605i
$259$	−10.9844			−0.682535
$260$	−4.36950			−0.270985
$261$	9.59054	−	16.6113i	0.593640	−	1.02821i
$262$	−16.2577			−1.00440
$263$	−3.19406	+	5.53227i	−0.196954	+	0.341134i	−0.947539	−	0.319639i	$-0.896438\pi$
$263$	−3.19406	+	5.53227i	−0.196954	+	0.341134i	0.750585	+	0.660773i	$0.229772\pi$
$264$	0.597408	−	1.03474i	0.0367679	−	0.0636839i
$265$	−14.2329	−	24.6521i	−0.874318	−	1.51436i
$266$	0.794651			0.0487232
$267$	0.878789	+	1.52211i	0.0537810	+	0.0931515i
$268$	−5.50951	+	9.54275i	−0.336547	+	0.582916i
$269$	11.4301			0.696903			0.348452	−	0.937327i	$-0.386708\pi$
$269$	11.4301			0.696903			0.348452	+	0.937327i	$0.386708\pi$
$270$	2.13892	−	3.70472i	0.130171	−	0.225462i
$271$	14.3052	+	24.7774i	0.868981	+	1.50512i	0.863039	+	0.505137i	$0.168558\pi$
$271$	14.3052	+	24.7774i	0.868981	+	1.50512i	0.00594216	+	0.999982i	$0.498109\pi$
$272$	0.877126	+	1.51923i	0.0531836	+	0.0921167i
$273$	−0.304611	−	0.527601i	−0.0184359	−	0.0319319i
$274$	9.56232			0.577681
$275$	−1.51524	−	2.62447i	−0.0913723	−	0.158261i
$276$	−0.0961423	−	0.166523i	−0.00578708	−	0.0100235i
$277$	3.88331	−	6.72609i	0.233325	−	0.404131i	−0.725459	−	0.688265i	$-0.758373\pi$
$277$	3.88331	−	6.72609i	0.233325	−	0.404131i	0.958785	+	0.284134i	$0.0917059\pi$
$278$	5.94036	−	10.2890i	0.356279	−	0.617093i
$279$	−30.2408			−1.81047
$280$	−9.52815			−0.569416
$281$	1.41702	−	2.45435i	0.0845324	−	0.146414i	−0.820659	−	0.571418i	$-0.806394\pi$
$281$	1.41702	−	2.45435i	0.0845324	−	0.146414i	0.905192	+	0.425003i	$0.139727\pi$
$282$	1.45526	−	2.52058i	0.0866592	−	0.150098i
$283$	−6.67702	−	11.5649i	−0.396908	−	0.687464i	0.596435	−	0.802661i	$-0.296583\pi$
$283$	−6.67702	−	11.5649i	−0.396908	−	0.687464i	−0.993343	+	0.115197i	$0.963250\pi$
$284$	4.47463	+	7.75028i	0.265520	+	0.459895i
$285$	−0.405187			−0.0240012
$286$	1.76616	+	3.05908i	0.104435	+	0.180887i
$287$	4.12051	+	7.13692i	0.243226	+	0.421279i
$288$	−6.18882	−	10.7193i	−0.364679	−	0.631643i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	−18.8344			−1.10599
$291$	0.968177	−	1.67693i	0.0567555	−	0.0983035i
$292$	−0.433158	−	0.750251i	−0.0253486	−	0.0439051i
$293$	6.54169			0.382170			0.191085	−	0.981574i	$-0.438799\pi$
$293$	6.54169			0.382170			0.191085	+	0.981574i	$0.438799\pi$
$294$	0.766943	+	1.32838i	0.0447290	+	0.0774729i
$295$	7.57245	−	13.1159i	0.440885	−	0.763635i
$296$	−14.2864	+	24.7447i	−0.830378	+	1.43826i
$297$	2.31316			0.134223
$298$	−5.72091	+	9.90890i	−0.331403	+	0.574007i
$299$	1.98680			0.114900
$300$	0.389002			0.0224591
$301$	−3.60765	+	6.83821i	−0.207942	+	0.394148i
$302$	−5.82248			−0.335046
$303$	−1.20792			−0.0693933
$304$	0.540016	−	0.935336i	0.0309721	−	0.0536452i
$305$	−20.7592			−1.18867
$306$	−1.60793	+	2.78501i	−0.0919191	+	0.159209i
$307$	−6.19425	+	10.7288i	−0.353525	+	0.612323i	−0.986864	−	0.161551i	$-0.948350\pi$
$307$	−6.19425	+	10.7288i	−0.353525	+	0.612323i	0.633340	+	0.773874i	$0.281684\pi$
$308$	−0.737071	−	1.27665i	−0.0419985	−	0.0727436i
$309$	−3.43030			−0.195143
$310$	14.8471	+	25.7160i	0.843260	+	1.46057i
$311$	1.79921	−	3.11632i	0.102024	−	0.176710i	−0.810495	−	0.585746i	$-0.800802\pi$
$311$	1.79921	−	3.11632i	0.102024	−	0.176710i	0.912518	+	0.409036i	$0.134135\pi$
$312$	−1.58472			−0.0897169
$313$	3.59444	−	6.22575i	0.203170	−	0.351900i	−0.746378	−	0.665522i	$-0.768209\pi$
$313$	3.59444	−	6.22575i	0.203170	−	0.351900i	0.949548	+	0.313622i	$0.101542\pi$
$314$	−1.18357	−	2.05000i	−0.0667926	−	0.115688i
$315$	−4.56317	−	7.90364i	−0.257105	−	0.445320i
$316$	4.43838	+	7.68749i	0.249678	+	0.432455i
$317$	−34.9460			−1.96276			−0.981382	−	0.192066i	$-0.938481\pi$
$317$	−34.9460			−1.96276			−0.981382	+	0.192066i	$0.938481\pi$
$318$	−1.47694	−	2.55813i	−0.0828226	−	0.143453i
$319$	−5.09216	−	8.81988i	−0.285106	−	0.493818i
$320$	−10.6993	+	18.5317i	−0.598110	+	1.03596i
$321$	−1.15322	+	1.99744i	−0.0643665	+	0.111486i
$322$	1.23960			0.0690801
$323$	0.615665			0.0342565
$324$	3.38371	−	5.86075i	0.187984	−	0.325597i
$325$	−2.00970	+	3.48091i	−0.111478	+	0.193086i
$326$	−4.14306	−	7.17598i	−0.229463	−	0.397441i
$327$	2.30327	+	3.98938i	0.127371	+	0.220613i
$328$	21.4367			1.18364
$329$	−6.27521	−	10.8690i	−0.345963	−	0.599226i
$330$	−0.561871	−	0.973189i	−0.0309300	−	0.0535723i
$331$	−13.0028	−	22.5215i	−0.714697	−	1.23789i	−0.963076	−	0.269229i	$-0.913231\pi$
$331$	−13.0028	−	22.5215i	−0.714697	−	1.23789i	0.248379	−	0.968663i	$-0.420102\pi$
$332$	4.17129	−	7.22489i	0.228929	−	0.396517i
$333$	−27.3678			−1.49975
$334$	−1.56054	+	2.70294i	−0.0853892	+	0.147898i
$335$	18.1104	+	31.3682i	0.989478	+	1.71383i
$336$	−0.516609			−0.0281834
$337$	6.15200	+	10.6556i	0.335121	+	0.580447i	0.983508	−	0.180864i	$-0.0578895\pi$
$337$	6.15200	+	10.6556i	0.335121	+	0.580447i	−0.648387	+	0.761311i	$0.724556\pi$
$338$	−4.77315	+	8.26734i	−0.259625	+	0.449684i
$339$	−0.144878	+	0.250936i	−0.00786869	+	0.0136290i
$340$	−2.11216			−0.114548
$341$	−8.02829	+	13.9054i	−0.434756	+	0.753020i
$342$	1.97989			0.107060
$343$	14.8676			0.802774
$344$	10.7124	+	17.0209i	0.577576	+	0.917704i
$345$	−0.632063			−0.0340291
$346$	−17.6280			−0.947685
$347$	7.98831	−	13.8362i	0.428835	−	0.742764i	−0.567935	−	0.823073i	$-0.692258\pi$
$347$	7.98831	−	13.8362i	0.428835	−	0.742764i	0.996770	+	0.0803097i	$0.0255909\pi$
$348$	1.30729			0.0700783
$349$	−0.588715	+	1.01968i	−0.0315132	+	0.0545825i	−0.881352	−	0.472460i	$-0.843366\pi$
$349$	−0.588715	+	1.01968i	−0.0315132	+	0.0545825i	0.849839	+	0.527043i	$0.176699\pi$
$350$	−1.25389	+	2.17180i	−0.0670232	+	0.116088i
$351$	−1.53400	−	2.65697i	−0.0818791	−	0.141819i
$352$	−6.57199			−0.350288
$353$	−13.4259	−	23.2543i	−0.714587	−	1.23770i	−0.963119	−	0.269077i	$-0.913282\pi$
$353$	−13.4259	−	23.2543i	−0.714587	−	1.23770i	0.248532	−	0.968624i	$-0.420052\pi$
$354$	0.785790	−	1.36103i	0.0417643	−	0.0723378i
$355$	29.4173			1.56131
$356$	2.82033	−	4.88496i	0.149477	−	0.258902i
$357$	−0.147245	−	0.255036i	−0.00779302	−	0.0134979i
$358$	−10.6893	−	18.5143i	−0.564944	−	0.978513i
$359$	−11.6448	−	20.1693i	−0.614587	−	1.06450i	−0.990457	−	0.137823i	$-0.955989\pi$
$359$	−11.6448	−	20.1693i	−0.614587	−	1.06450i	0.375870	−	0.926672i	$-0.377344\pi$
$360$	−23.7396			−1.25119
$361$	9.31048	+	16.1262i	0.490025	+	0.848748i
$362$	−10.6219	−	18.3978i	−0.558277	−	0.966964i
$363$	−1.06991	+	1.85314i	−0.0561559	+	0.0972648i
$364$	−0.977598	+	1.69325i	−0.0512401	+	0.0887504i
$365$	−2.84769			−0.149055
$366$	−2.15418			−0.112601
$367$	−8.69112	+	15.0535i	−0.453673	+	0.785785i	−0.998611	−	0.0526918i	$-0.983220\pi$
$367$	−8.69112	+	15.0535i	−0.453673	+	0.785785i	0.544938	+	0.838476i	$0.316553\pi$
$368$	0.842386	−	1.45906i	0.0439124	−	0.0760585i
$369$	10.2663	+	17.7818i	0.534444	+	0.925683i
$370$	13.4366	+	23.2728i	0.698533	+	1.20989i
$371$	−12.7374			−0.661294
$372$	−1.03054	−	1.78495i	−0.0534309	−	0.0925451i
$373$	7.46804	+	12.9350i	0.386681	+	0.669751i	0.992001	−	0.126232i	$-0.0402882\pi$
$373$	7.46804	+	12.9350i	0.386681	+	0.669751i	−0.605320	+	0.795982i	$0.706955\pi$
$374$	0.853740	+	1.47872i	0.0441458	+	0.0764628i
$375$	−1.00597	+	1.74240i	−0.0519483	+	0.0899770i
$376$	−32.6464			−1.68361
$377$	−6.75387	+	11.6981i	−0.347842	+	0.602480i
$378$	−0.957092	−	1.65773i	−0.0492275	−	0.0852646i
$379$	−32.8924			−1.68957			−0.844783	−	0.535109i	$-0.820271\pi$
$379$	−32.8924			−1.68957			−0.844783	+	0.535109i	$0.820271\pi$
$380$	0.650192	+	1.12617i	0.0333541	+	0.0577710i
$381$	0.860180	−	1.48987i	0.0440683	−	0.0763286i
$382$	−10.1936	+	17.6558i	−0.521550	+	0.903351i
$383$	16.5767			0.847029			0.423515	−	0.905889i	$-0.360796\pi$
$383$	16.5767			0.847029			0.423515	+	0.905889i	$0.360796\pi$
$384$	−0.0578589	+	0.100215i	−0.00295260	+	0.00511405i
$385$	−4.84569			−0.246959
$386$	0.876915			0.0446338
$387$	−8.98855	+	17.0375i	−0.456914	+	0.866067i
$388$	−6.21442			−0.315489
$389$	−13.7663			−0.697977			−0.348989	−	0.937127i	$-0.613475\pi$
$389$	−13.7663			−0.697977			−0.348989	+	0.937127i	$0.613475\pi$
$390$	−0.745225	+	1.29077i	−0.0377359	+	0.0653606i
$391$	0.960393			0.0485692
$392$	8.60258	−	14.9001i	0.434496	−	0.752569i
$393$	1.85467	−	3.21238i	0.0935557	−	0.162043i
$394$	11.7459	+	20.3445i	0.591749	+	1.02494i
$395$	29.1790			1.46815
$396$	−1.83643	−	3.18079i	−0.0922840	−	0.159841i
$397$	−10.9765	+	19.0118i	−0.550894	+	0.954176i	0.447316	+	0.894376i	$0.352380\pi$
$397$	−10.9765	+	19.0118i	−0.550894	+	0.954176i	−0.998210	+	0.0598005i	$0.980954\pi$
$398$	−22.6035			−1.13301
$399$	−0.0906535	+	0.157017i	−0.00453835	+	0.00786066i
$400$	1.70419	+	2.95175i	0.0852097	+	0.147588i
$401$	7.99439	+	13.8467i	0.399221	+	0.691471i	0.993630	−	0.112692i	$-0.0359474\pi$
$401$	7.99439	+	13.8467i	0.399221	+	0.691471i	−0.594409	+	0.804163i	$0.702614\pi$
$402$	1.87931	+	3.25506i	0.0937315	+	0.162348i
$403$	21.2963			1.06084
$404$	1.93832	+	3.35726i	0.0964348	+	0.167030i
$405$	−11.1227	−	19.2650i	−0.552689	−	0.957286i
$406$	−4.21386	+	7.29862i	−0.209130	+	0.362224i
$407$	−7.26555	+	12.5843i	−0.360140	+	0.623781i
$408$	−0.766032			−0.0379242
$409$	25.2615			1.24910			0.624550	−	0.780985i	$-0.285282\pi$
$409$	25.2615			1.24910			0.624550	+	0.780985i	$0.285282\pi$
$410$	10.0808	−	17.4604i	0.497853	−	0.862307i
$411$	−1.09087	+	1.88944i	−0.0538085	+	0.0931990i
$412$	5.50450	+	9.53408i	0.271187	+	0.469710i
$413$	−3.38841	−	5.86889i	−0.166733	−	0.288789i
$414$	3.08849			0.151791
$415$	−13.7116	−	23.7491i	−0.673074	−	1.16580i
$416$	4.35830	+	7.54880i	0.213683	+	0.370110i
$417$	1.35535	+	2.34753i	0.0663717	+	0.114959i
$418$	0.525618	−	0.910397i	0.0257088	−	0.0445290i
$419$	17.0722			0.834032			0.417016	−	0.908899i	$-0.363076\pi$
$419$	17.0722			0.834032			0.417016	+	0.908899i	$0.363076\pi$
$420$	0.311005	−	0.538676i	0.0151755	−	0.0262847i
$421$	−14.3595	−	24.8713i	−0.699837	−	1.21215i	−0.968523	−	0.248925i	$-0.919923\pi$
$421$	−14.3595	−	24.8713i	−0.699837	−	1.21215i	0.268686	−	0.963228i	$-0.413411\pi$
$422$	−16.0691			−0.782230
$423$	−15.6348	−	27.0803i	−0.760190	−	1.31669i
$424$	−16.5664	+	28.6939i	−0.804536	+	1.39350i
$425$	−0.971464	+	1.68263i	−0.0471229	+	0.0816193i
$426$	3.05262			0.147900
$427$	−4.64451	+	8.04453i	−0.224764	+	0.389302i
$428$	7.40215			0.357796
$429$	−0.805932			−0.0389108
$430$	18.9013	−	0.721187i	0.911501	−	0.0347787i
$431$	29.0199			1.39784			0.698919	−	0.715201i	$-0.253665\pi$
$431$	29.0199			1.39784			0.698919	+	0.715201i	$0.253665\pi$
$432$	−2.60162			−0.125171
$433$	−13.5940	+	23.5455i	−0.653287	+	1.13153i	0.329033	+	0.944318i	$0.393277\pi$
$433$	−13.5940	+	23.5455i	−0.653287	+	1.13153i	−0.982320	+	0.187208i	$0.940056\pi$
$434$	13.2871			0.637802
$435$	2.14862	−	3.72152i	0.103018	−	0.178433i
$436$	7.39197	−	12.8033i	0.354011	−	0.613165i
$437$	−0.295640	−	0.512064i	−0.0141424	−	0.0244953i
$438$	−0.295503			−0.0141197
$439$	5.94372	+	10.2948i	0.283678	+	0.491345i	0.972288	−	0.233787i	$-0.0751119\pi$
$439$	5.94372	+	10.2948i	0.283678	+	0.491345i	−0.688610	+	0.725132i	$0.741779\pi$
$440$	−6.30235	+	10.9160i	−0.300453	+	0.520399i
$441$	16.4796			0.784742
$442$	1.13234	−	1.96127i	0.0538599	−	0.0932880i
$443$	15.3366	+	26.5638i	0.728666	+	1.26209i	0.957447	+	0.288608i	$0.0931926\pi$
$443$	15.3366	+	26.5638i	0.728666	+	1.26209i	−0.228781	+	0.973478i	$0.573474\pi$
$444$	−0.932631	−	1.61536i	−0.0442607	−	0.0766618i
$445$	−9.27078	−	16.0575i	−0.439477	−	0.761197i
$446$	−22.7951			−1.07938
$447$	−1.30528	−	2.26081i	−0.0617375	−	0.106933i
$448$	4.78756	+	8.29231i	0.226191	+	0.391775i
$449$	13.9142	−	24.1002i	0.656654	−	1.13736i	−0.324823	−	0.945775i	$-0.605305\pi$
$449$	13.9142	−	24.1002i	0.656654	−	1.13736i	0.981476	−	0.191583i	$-0.0613621\pi$
$450$	−3.12409	+	5.41108i	−0.147271	+	0.255081i
$451$	10.9019			0.513353
$452$	0.929925			0.0437400
$453$	0.664227	−	1.15047i	0.0312081	−	0.0540540i
$454$	12.2248	−	21.1739i	0.573738	−	0.993743i
$455$	3.21349	+	5.56592i	0.150651	+	0.260934i
$456$	0.235810	+	0.408434i	0.0110428	+	0.0191267i
$457$	18.6475			0.872291			0.436146	−	0.899876i	$-0.356343\pi$
$457$	18.6475			0.872291			0.436146	+	0.899876i	$0.356343\pi$
$458$	−4.54354	−	7.86964i	−0.212306	−	0.367724i
$459$	−0.741518	−	1.28435i	−0.0346111	−	0.0599482i
$460$	1.01425	+	1.75674i	0.0472897	+	0.0819082i
$461$	−5.49976	+	9.52586i	−0.256149	+	0.443664i	−0.965207	−	0.261487i	$-0.915787\pi$
$461$	−5.49976	+	9.52586i	−0.256149	+	0.443664i	0.709058	+	0.705150i	$0.249121\pi$
$462$	−0.502835			−0.0233940
$463$	2.18152	−	3.77851i	0.101384	−	0.175602i	−0.810871	−	0.585225i	$-0.801006\pi$
$463$	2.18152	−	3.77851i	0.101384	−	0.175602i	0.912255	+	0.409623i	$0.134340\pi$
$464$	5.72717	+	9.91976i	0.265877	+	0.460513i
$465$	−6.77502			−0.314184
$466$	−13.2217	−	22.9007i	−0.612485	−	1.06085i
$467$	−8.59413	+	14.8855i	−0.397689	+	0.688818i	−0.993440	−	0.114351i	$-0.963521\pi$
$467$	−8.59413	+	14.8855i	−0.397689	+	0.688818i	0.595751	+	0.803169i	$0.296854\pi$
$468$	−2.43571	+	4.21877i	−0.112591	+	0.195013i
$469$	16.2076			0.748396
$470$	−15.3522	+	26.5908i	−0.708144	+	1.22654i
$471$	0.540084			0.0248857
$472$	−17.6280			−0.811393
$473$	5.44797	+	8.65623i	0.250498	+	0.398014i
$474$	3.02789			0.139076
$475$	1.19619			0.0548851
$476$	−0.472559	+	0.818496i	−0.0216597	+	0.0375157i
$477$	−31.7355			−1.45307
$478$	−8.54269	+	14.7964i	−0.390734	+	0.676771i
$479$	0.156690	−	0.271395i	0.00715935	−	0.0124004i	−0.862424	−	0.506187i	$-0.831054\pi$
$479$	0.156690	−	0.271395i	0.00715935	−	0.0124004i	0.869583	+	0.493787i	$0.164388\pi$
$480$	−1.38651	−	2.40151i	−0.0632854	−	0.109613i
$481$	19.2730			0.878774
$482$	−13.4018	−	23.2126i	−0.610435	−	1.05730i
$483$	−0.141413	+	0.244934i	−0.00643451	+	0.0111449i
$484$	6.86742			0.312156
$485$	−10.2138	+	17.6908i	−0.463784	+	0.803297i
$486$	−3.58945	−	6.21711i	−0.162821	−	0.282014i
$487$	1.02327	+	1.77235i	0.0463686	+	0.0803128i	0.888278	−	0.459306i	$-0.151902\pi$
$487$	1.02327	+	1.77235i	0.0463686	+	0.0803128i	−0.841910	+	0.539619i	$0.818568\pi$
$488$	12.0814	+	20.9256i	0.546899	+	0.947256i
$489$	1.89055			0.0854938
$490$	−8.09086	−	14.0138i	−0.365508	−	0.633078i
$491$	−3.66088	−	6.34083i	−0.165213	−	0.286157i	0.771518	−	0.636208i	$-0.219498\pi$
$491$	−3.66088	−	6.34083i	−0.165213	−	0.286157i	−0.936731	+	0.350050i	$0.886165\pi$
$492$	−0.699706	+	1.21193i	−0.0315452	+	0.0546378i
$493$	−3.26474	+	5.65469i	−0.147036	+	0.254674i
$494$	−1.39428			−0.0627318
$495$	−12.0731			−0.542647
$496$	9.02945	−	15.6395i	0.405434	−	0.702233i
$497$	6.58160	−	11.3997i	0.295225	−	0.511345i
$498$	−1.42284	−	2.46444i	−0.0637591	−	0.110434i
$499$	6.15907	+	10.6678i	0.275718	+	0.477557i	0.970316	−	0.241841i	$-0.0777511\pi$
$499$	6.15907	+	10.6678i	0.275718	+	0.477557i	−0.694598	+	0.719398i	$0.744418\pi$
$500$	6.45702			0.288767
$501$	−0.356053	−	0.616701i	−0.0159073	−	0.0275522i
$502$	−4.54483	−	7.87188i	−0.202846	−	0.351339i
$503$	−9.60007	−	16.6278i	−0.428046	−	0.741397i	0.568654	−	0.822577i	$-0.307465\pi$
$503$	−9.60007	−	16.6278i	−0.428046	−	0.741397i	−0.996699	+	0.0811799i	$0.974131\pi$
$504$	−5.31132	+	9.19947i	−0.236585	+	0.409777i
$505$	12.7430			0.567054
$506$	0.819926	−	1.42015i	0.0364502	−	0.0631335i
$507$	−1.08904	−	1.88627i	−0.0483659	−	0.0837722i
$508$	−5.52122			−0.244964
$509$	8.54933	+	14.8079i	0.378943	+	0.656348i	0.990909	−	0.134536i	$-0.0429545\pi$
$509$	8.54933	+	14.8079i	0.378943	+	0.656348i	−0.611966	+	0.790884i	$0.709621\pi$
$510$	−0.360232	+	0.623941i	−0.0159514	+	0.0276286i
$511$	−0.637120	+	1.10352i	−0.0281845	+	0.0488170i
$512$	18.1520			0.802211
$513$	−0.456527	+	0.790728i	−0.0201562	+	0.0349115i
$514$	17.3187			0.763895
$515$	36.1880			1.59463
$516$	−1.31194	+	0.0500576i	−0.0577549	+	0.00220366i
$517$	−16.6028			−0.730191
$518$	12.0248			0.528338
$519$	2.01099	−	3.48314i	0.0882727	−	0.152893i
$520$	16.7180			0.733131
$521$	−0.811375	+	1.40534i	−0.0355470	+	0.0615692i	−0.883252	−	0.468899i	$-0.844651\pi$
$521$	−0.811375	+	1.40534i	−0.0355470	+	0.0615692i	0.847705	+	0.530469i	$0.177984\pi$
$522$	−10.4989	+	18.1847i	−0.459525	+	0.795921i
$523$	−17.5521	−	30.4012i	−0.767501	−	1.32935i	−0.938914	−	0.344152i	$-0.888167\pi$
$523$	−17.5521	−	30.4012i	−0.767501	−	1.32935i	0.171413	−	0.985199i	$-0.445167\pi$
$524$	−11.9045			−0.520052
$525$	−0.286086	−	0.495516i	−0.0124858	−	0.0216261i
$526$	3.49659	−	6.05626i	0.152458	−	0.264066i
$527$	10.2944			0.448429
$528$	−0.341709	+	0.591857i	−0.0148710	+	0.0257573i
$529$	11.0388	+	19.1198i	0.479949	+	0.831296i
$530$	15.5810	+	26.9870i	0.676794	+	1.17224i
$531$	−8.44228	−	14.6225i	−0.366364	−	0.634561i
$532$	0.581876			0.0252275
$533$	−7.22978	−	12.5223i	−0.313156	−	0.542403i
$534$	−0.962025	−	1.66628i	−0.0416309	−	0.0721068i
$535$	12.1659	−	21.0719i	0.525977	−	0.911019i
$536$	21.0797	−	36.5111i	0.910504	−	1.57704i
$537$	4.87770			0.210488
$538$	−12.5127			−0.539460
$539$	4.37497	−	7.57768i	0.188443	−	0.326394i
$540$	1.56621	−	2.71275i	0.0673987	−	0.116738i
$541$	10.6011	+	18.3617i	0.455779	+	0.789432i	0.998733	−	0.0503308i	$-0.0160276\pi$
$541$	10.6011	+	18.3617i	0.455779	+	0.789432i	−0.542954	+	0.839762i	$0.682694\pi$
$542$	−15.6602	−	27.1242i	−0.672662	−	1.16509i
$543$	4.84699			0.208004
$544$	2.10675	+	3.64900i	0.0903261	+	0.156449i
$545$	−24.2983	−	42.0859i	−1.04083	−	1.80276i
$546$	0.333462	+	0.577573i	0.0142709	+	0.0247179i
$547$	17.6184	−	30.5159i	0.753308	−	1.30477i	−0.192903	−	0.981218i	$-0.561790\pi$
$547$	17.6184	−	30.5159i	0.753308	−	1.30477i	0.946211	−	0.323550i	$-0.104876\pi$
$548$	7.00192			0.299107
$549$	−11.5719	+	20.0431i	−0.493876	+	0.855419i
$550$	1.65876	+	2.87305i	0.0707296	+	0.122507i
$551$	4.01997			0.171256
$552$	0.367846	+	0.637128i	0.0156566	+	0.0271180i
$553$	6.52829	−	11.3073i	0.277611	−	0.480836i
$554$	−4.25112	+	7.36316i	−0.180613	+	0.312831i
$555$	−6.13135			−0.260261
$556$	4.34977	−	7.53402i	0.184471	−	0.319514i
$557$	−35.5615			−1.50679			−0.753395	−	0.657568i	$-0.771585\pi$
$557$	−35.5615			−1.50679			−0.753395	+	0.657568i	$0.771585\pi$
$558$	33.1052			1.40145
$559$	6.32994	−	11.9982i	0.267728	−	0.507471i
$560$	5.44997			0.230303
$561$	−0.389577			−0.0164480
$562$	−1.55124	+	2.68682i	−0.0654350	+	0.113337i
$563$	12.5711			0.529810			0.264905	−	0.964275i	$-0.414659\pi$
$563$	12.5711			0.529810			0.264905	+	0.964275i	$0.414659\pi$
$564$	1.06560	−	1.84567i	0.0448697	−	0.0777166i
$565$	1.52839	−	2.64725i	0.0642998	−	0.111371i
$566$	7.30945	+	12.6603i	0.307239	+	0.532154i
$567$	−9.95400			−0.418029
$568$	−17.1202	−	29.6530i	−0.718347	−	1.24421i
$569$	−5.06689	+	8.77611i	−0.212415	+	0.367914i	−0.952470	−	0.304633i	$-0.901466\pi$
$569$	−5.06689	+	8.77611i	−0.212415	+	0.367914i	0.740055	+	0.672547i	$0.234800\pi$
$570$	0.443565			0.0185789
$571$	6.78642	−	11.7544i	0.284003	−	0.491907i	−0.688364	−	0.725365i	$-0.741671\pi$
$571$	6.78642	−	11.7544i	0.284003	−	0.491907i	0.972367	+	0.233458i	$0.0750041\pi$
$572$	1.29325	+	2.23998i	0.0540737	+	0.0936584i
$573$	−2.32577	−	4.02834i	−0.0971602	−	0.168286i
$574$	−4.51079	−	7.81291i	−0.188277	−	0.326105i
$575$	1.86598			0.0778166
$576$	11.9283	+	20.6605i	0.497013	+	0.860852i
$577$	−20.1966	−	34.9815i	−0.840795	−	1.45630i	−0.889224	−	0.457472i	$-0.848755\pi$
$577$	−20.1966	−	34.9815i	−0.840795	−	1.45630i	0.0484293	−	0.998827i	$-0.484578\pi$
$578$	0.547358	−	0.948052i	0.0227671	−	0.0394338i
$579$	−0.100038	+	0.173271i	−0.00415744	+	0.00720091i
$580$	−13.7913			−0.572652
$581$	−12.2709			−0.509082
$582$	−1.05988	+	1.83577i	−0.0439334	+	0.0760949i
$583$	−8.42510	+	14.5927i	−0.348932	+	0.604368i
$584$	1.65729	+	2.87051i	0.0685790	+	0.118782i
$585$	8.00647	+	13.8676i	0.331027	+	0.573355i
$586$	−7.16130			−0.295831
$587$	−9.85358	−	17.0669i	−0.406701	−	0.704426i	0.587817	−	0.808994i	$-0.299987\pi$
$587$	−9.85358	−	17.0669i	−0.406701	−	0.704426i	−0.994518	+	0.104568i	$0.966654\pi$
$588$	0.561587	+	0.972697i	0.0231594	+	0.0401133i
$589$	−3.16894	−	5.48876i	−0.130574	−	0.226160i
$590$	−8.28969	+	14.3582i	−0.341281	+	0.591116i
$591$	−5.35987			−0.220475
$592$	8.17160	−	14.1536i	0.335851	−	0.581710i
$593$	−1.63876	−	2.83842i	−0.0672959	−	0.116560i	0.830414	−	0.557146i	$-0.188104\pi$
$593$	−1.63876	−	2.83842i	−0.0672959	−	0.116560i	−0.897710	+	0.440587i	$0.854770\pi$
$594$	−2.53226			−0.103900
$595$	1.55336	+	2.69050i	0.0636815	+	0.110300i
$596$	−4.18908	+	7.25570i	−0.171591	+	0.297205i
$597$	2.57860	−	4.46627i	0.105535	−	0.182792i
$598$	−2.17498			−0.0889416
$599$	12.3835	−	21.4489i	0.505978	−	0.876380i	−0.493998	−	0.869463i	$-0.664465\pi$
$599$	12.3835	−	21.4489i	0.505978	−	0.876380i	0.999976	−	0.00691665i	$-0.00220165\pi$
$600$	−1.48835			−0.0607615
$601$	23.6370			0.964173			0.482087	−	0.876124i	$-0.339879\pi$
$601$	23.6370			0.964173			0.482087	+	0.876124i	$0.339879\pi$
$602$	3.94936	−	7.48590i	0.160964	−	0.305103i
$603$	40.3815			1.64446
$604$	−4.26346			−0.173478
$605$	11.2870	−	19.5497i	0.458883	−	0.794809i
$606$	1.32233			0.0537161
$607$	9.89625	−	17.1408i	0.401676	−	0.695724i	−0.592252	−	0.805753i	$-0.701761\pi$
$607$	9.89625	−	17.1408i	0.401676	−	0.695724i	0.993928	+	0.110029i	$0.0350943\pi$
$608$	1.29705	−	2.24656i	0.0526024	−	0.0911100i
$609$	−0.961431	−	1.66525i	−0.0389592	−	0.0674793i
$610$	22.7255			0.920127
$611$	11.0104	+	19.0705i	0.445432	+	0.771512i
$612$	−1.17739	+	2.03930i	−0.0475932	+	0.0824338i
$613$	−24.4937			−0.989290			−0.494645	−	0.869095i	$-0.664702\pi$
$613$	−24.4937			−0.989290			−0.494645	+	0.869095i	$0.664702\pi$
$614$	6.78095	−	11.7450i	0.273657	−	0.473988i
$615$	2.30002	+	3.98375i	0.0927457	+	0.160640i
$616$	2.82008	+	4.88452i	0.113624	+	0.196803i
$617$	−6.48566	−	11.2335i	−0.261103	−	0.452243i	0.705432	−	0.708777i	$-0.250753\pi$
$617$	−6.48566	−	11.2335i	−0.261103	−	0.452243i	−0.966535	+	0.256534i	$0.917419\pi$
$618$	3.75521			0.151057
$619$	19.1037	+	33.0887i	0.767844	+	1.32995i	0.938730	+	0.344654i	$0.112004\pi$
$619$	19.1037	+	33.0887i	0.767844	+	1.32995i	−0.170885	+	0.985291i	$0.554663\pi$
$620$	10.8717	+	18.8303i	0.436616	+	0.756242i
$621$	−0.712149	+	1.23348i	−0.0285776	+	0.0494978i
$622$	−1.96962	+	3.41148i	−0.0789746	+	0.136788i
$623$	−8.29670			−0.332400
$624$	0.906435			0.0362864
$625$	15.4698	−	26.7945i	0.618793	−	1.07178i
$626$	−3.93489	+	6.81543i	−0.157270	+	0.272400i
$627$	0.119925	+	0.207716i	0.00478933	+	0.00829536i
$628$	−0.866656	−	1.50109i	−0.0345833	−	0.0599001i
$629$	9.31633			0.371466
$630$	4.99538	+	8.65225i	0.199021	+	0.344714i
$631$	17.8027	+	30.8352i	0.708716	+	1.22753i	0.965334	+	0.261019i	$0.0840585\pi$
$631$	17.8027	+	30.8352i	0.708716	+	1.22753i	−0.256618	+	0.966513i	$0.582608\pi$
$632$	−16.9815	−	29.4128i	−0.675488	−	1.16998i
$633$	1.83315	−	3.17512i	0.0728613	−	0.126200i
$634$	38.2560			1.51934
$635$	−9.07446	+	15.7174i	−0.360109	+	0.623727i
$636$	−1.08147	−	1.87317i	−0.0428833	−	0.0742760i
$637$	−11.6053			−0.459819
$638$	5.57447	+	9.65527i	0.220695	+	0.382256i
$639$	16.3982	−	28.4025i	0.648703	−	1.12359i
$640$	0.610382	−	1.05721i	0.0241275	−	0.0417900i
$641$	41.6563			1.64533			0.822663	−	0.568529i	$-0.192487\pi$
$641$	41.6563			1.64533			0.822663	+	0.568529i	$0.192487\pi$
$642$	1.26245	−	2.18663i	0.0498249	−	0.0862993i
$643$	−16.8302			−0.663718			−0.331859	−	0.943329i	$-0.607676\pi$
$643$	−16.8302			−0.663718			−0.331859	+	0.943329i	$0.607676\pi$
$644$	0.907684			0.0357678
$645$	−2.01375	+	3.81701i	−0.0792914	+	0.150295i
$646$	−0.673979			−0.0265173
$647$	21.9103			0.861384			0.430692	−	0.902499i	$-0.358270\pi$
$647$	21.9103			0.861384			0.430692	+	0.902499i	$0.358270\pi$
$648$	−12.9463	+	22.4236i	−0.508577	+	0.880882i
$649$	−8.96497			−0.351906
$650$	2.20005	−	3.81060i	0.0862932	−	0.149464i
$651$	−1.51579	+	2.62543i	−0.0594085	+	0.102899i
$652$	−3.03371	−	5.25454i	−0.118809	−	0.205784i
$653$	7.13544			0.279231			0.139616	−	0.990206i	$-0.455413\pi$
$653$	7.13544			0.279231			0.139616	+	0.990206i	$0.455413\pi$
$654$	−2.52143	−	4.36724i	−0.0985955	−	0.170772i
$655$	−19.5658	+	33.8890i	−0.764500	+	1.32415i
$656$	−12.2615			−0.478730
$657$	−1.58740	+	2.74945i	−0.0619303	+	0.107266i
$658$	6.86957	+	11.8984i	0.267804	+	0.463850i
$659$	−18.7068	−	32.4011i	−0.728713	−	1.26217i	−0.957427	−	0.288675i	$-0.906785\pi$
$659$	−18.7068	−	32.4011i	−0.728713	−	1.26217i	0.228714	−	0.973494i	$-0.426548\pi$
$660$	−0.411425	−	0.712609i	−0.0160147	−	0.0277383i
$661$	−36.3440			−1.41362			−0.706808	−	0.707405i	$-0.749866\pi$
$661$	−36.3440			−1.41362			−0.706808	+	0.707405i	$0.749866\pi$
$662$	14.2344	+	24.6546i	0.553234	+	0.958229i
$663$	0.258354	+	0.447482i	0.0100336	+	0.0173787i
$664$	−15.9596	+	27.6429i	−0.619353	+	1.07275i
$665$	0.956349	−	1.65644i	0.0370856	−	0.0642342i
$666$	29.9600			1.16093
$667$	6.27086			0.242809
$668$	−1.14269	+	1.97920i	−0.0442121	+	0.0765777i
$669$	2.60045	−	4.50412i	0.100539	−	0.174139i
$670$	−19.8258	−	34.3393i	−0.765937	−	1.32664i
$671$	6.14417	+	10.6420i	0.237193	+	0.410831i
$672$	−1.24083			−0.0478661
$673$	14.8062	+	25.6451i	0.570738	+	0.988546i	0.996490	+	0.0837069i	$0.0266760\pi$
$673$	14.8062	+	25.6451i	0.570738	+	0.988546i	−0.425753	+	0.904839i	$0.639991\pi$
$674$	−6.73470	−	11.6648i	−0.259411	−	0.449313i
$675$	−1.44072	−	2.49540i	−0.0554532	−	0.0960478i
$676$	−3.49509	+	6.05368i	−0.134427	+	0.232834i
$677$	−45.3213			−1.74184			−0.870920	−	0.491426i	$-0.836476\pi$
$677$	−45.3213			−1.74184			−0.870920	+	0.491426i	$0.836476\pi$
$678$	0.158600	−	0.274704i	0.00609101	−	0.0105499i
$679$	4.57031	+	7.91600i	0.175392	+	0.303788i
$680$	8.08125			0.309902
$681$	2.78920	+	4.83103i	0.106882	+	0.185126i
$682$	8.78870	−	15.2225i	0.336537	−	0.582899i
$683$	9.65401	−	16.7212i	0.369400	−	0.639820i	−0.620072	−	0.784545i	$-0.712896\pi$
$683$	9.65401	−	16.7212i	0.369400	−	0.639820i	0.989472	+	0.144725i	$0.0462298\pi$
$684$	1.44976			0.0554328
$685$	11.5081	−	19.9326i	0.439701	−	0.761585i
$686$	−16.2758			−0.621412
$687$	2.07330			0.0791014
$688$	−6.12736	−	9.73570i	−0.233603	−	0.371170i
$689$	22.3489			0.851425
$690$	0.691930			0.0263413
$691$	−3.86898	+	6.70127i	−0.147183	+	0.254929i	−0.930185	−	0.367090i	$-0.880354\pi$
$691$	−3.86898	+	6.70127i	−0.147183	+	0.254929i	0.783002	+	0.622019i	$0.213687\pi$
$692$	−12.9079			−0.490685
$693$	−2.70115	+	4.67853i	−0.102608	+	0.177723i
$694$	−8.74493	+	15.1467i	−0.331953	+	0.574960i
$695$	−14.2982	−	24.7653i	−0.542363	−	0.939400i
$696$	−5.00179			−0.189592
$697$	−3.49478	−	6.05314i	−0.132374	−	0.229279i
$698$	0.644476	−	1.11627i	0.0243938	−	0.0422513i
$699$	6.03332			0.228201
$700$	−0.918148	+	1.59028i	−0.0347027	+	0.0601069i
$701$	10.5396	+	18.2551i	0.398076	+	0.689487i	0.993488	−	0.113933i	$-0.0363449\pi$
$701$	10.5396	+	18.2551i	0.398076	+	0.689487i	−0.595413	+	0.803420i	$0.703012\pi$
$702$	1.67930	+	2.90863i	0.0633811	+	0.109779i
$703$	−2.86787	−	4.96730i	−0.108164	−	0.187345i
$704$	12.6668			0.477399
$705$	−3.50275	−	6.06694i	−0.131921	−	0.228494i
$706$	14.6975	+	25.4568i	0.553148	+	0.958081i
$707$	2.85101	−	4.93810i	0.107223	−	0.185716i
$708$	0.575387	−	0.996600i	0.0216244	−	0.0374545i
$709$	16.8959			0.634537			0.317269	−	0.948336i	$-0.397234\pi$
$709$	16.8959			0.634537			0.317269	+	0.948336i	$0.397234\pi$
$710$	−32.2036			−1.20858
$711$	16.2654	−	28.1724i	0.609999	−	1.05655i
$712$	−10.7908	+	18.6901i	−0.404401	+	0.700443i
$713$	−4.94331	−	8.56207i	−0.185129	−	0.320652i
$714$	0.161191	+	0.279192i	0.00603244	+	0.0104485i
$715$	8.50217			0.317963
$716$	−7.82710	−	13.5569i	−0.292513	−	0.506647i
$717$	−1.94910	−	3.37593i	−0.0727903	−	0.126076i
$718$	12.7477	+	22.0797i	0.475740	+	0.824006i
$719$	−5.98408	+	10.3647i	−0.223168	+	0.386539i	−0.955768	−	0.294120i	$-0.904973\pi$
$719$	−5.98408	+	10.3647i	−0.223168	+	0.386539i	0.732600	+	0.680659i	$0.238307\pi$
$720$	13.5787			0.506049
$721$	8.09642	−	14.0234i	0.301526	−	0.522259i
$722$	−10.1923	−	17.6536i	−0.379319	−	0.657000i
$723$	6.11549			0.227438
$724$	−7.77782	−	13.4716i	−0.289060	−	0.500667i
$725$	−6.34315	+	10.9867i	−0.235579	+	0.408034i
$726$	1.17125	−	2.02867i	0.0434692	−	0.0752909i
$727$	1.24308			0.0461034			0.0230517	−	0.999734i	$-0.492662\pi$
$727$	1.24308			0.0461034			0.0230517	+	0.999734i	$0.492662\pi$
$728$	3.74035	−	6.47848i	0.138627	−	0.240108i
$729$	−23.6893			−0.877383
$730$	3.11741			0.115380
$731$	3.05981	−	5.79979i	0.113171	−	0.214513i
$732$	−1.57737			−0.0583014
$733$	−36.2534			−1.33905			−0.669524	−	0.742790i	$-0.733502\pi$
$733$	−36.2534			−1.33905			−0.669524	+	0.742790i	$0.733502\pi$
$734$	9.51432	−	16.4793i	0.351180	−	0.608261i
$735$	3.69201			0.136182
$736$	2.02331	−	3.50447i	0.0745801	−	0.129176i
$737$	10.7204	−	18.5683i	0.394891	−	0.683972i
$738$	−11.2387	−	19.4660i	−0.413703	−	0.716554i
$739$	25.5326			0.939233			0.469617	−	0.882870i	$-0.344392\pi$
$739$	25.5326			0.939233			0.469617	+	0.882870i	$0.344392\pi$
$740$	9.83879	+	17.0413i	0.361681	+	0.626450i
$741$	0.159059	−	0.275499i	0.00584319	−	0.0101207i
$742$	13.9439			0.511895
$743$	−2.54431	+	4.40688i	−0.0933418	+	0.161673i	−0.908915	−	0.416981i	$-0.863088\pi$
$743$	−2.54431	+	4.40688i	−0.0933418	+	0.161673i	0.815574	+	0.578653i	$0.196422\pi$
$744$	3.94290	+	6.82931i	0.144554	+	0.250375i
$745$	13.7700	+	23.8504i	0.504494	+	0.873810i
$746$	−8.17539	−	14.1602i	−0.299322	−	0.518442i
$747$	−30.5731			−1.11861
$748$	0.625143	+	1.08278i	0.0228575	+	0.0395903i
$749$	−5.44381	−	9.42895i	−0.198912	−	0.344526i
$750$	1.10126	−	1.90743i	0.0402122	−	0.0696496i
$751$	0.801592	−	1.38840i	0.0292505	−	0.0506633i	−0.851030	−	0.525118i	$-0.824021\pi$
$751$	0.801592	−	1.38840i	0.0292505	−	0.0506633i	0.880280	+	0.474454i	$0.157355\pi$
$752$	18.6732			0.680943
$753$	2.07389			0.0755768
$754$	7.39358	−	12.8060i	0.269258	−	0.466369i
$755$	−7.00725	+	12.1369i	−0.255020	+	0.441708i
$756$	−0.700822	−	1.21386i	−0.0254886	−	0.0441476i
$757$	9.78156	+	16.9422i	0.355517	+	0.615773i	0.987206	−	0.159448i	$-0.0509715\pi$
$757$	9.78156	+	16.9422i	0.355517	+	0.615773i	−0.631689	+	0.775222i	$0.717638\pi$
$758$	36.0078			1.30786
$759$	0.187074	+	0.324021i	0.00679035	+	0.0117612i
$760$	−2.48767	−	4.30877i	−0.0902374	−	0.156296i
$761$	10.1535	+	17.5864i	0.368064	+	0.637505i	0.989263	−	0.146148i	$-0.0466874\pi$
$761$	10.1535	+	17.5864i	0.368064	+	0.637505i	−0.621199	+	0.783653i	$0.713354\pi$
$762$	−0.941653	+	1.63099i	−0.0341125	+	0.0590846i
$763$	−21.7453			−0.787232
$764$	−7.46417	+	12.9283i	−0.270044	+	0.467730i
$765$	3.87023	+	6.70343i	0.139928	+	0.242363i
$766$	−18.1468			−0.655670
$767$	5.94524	+	10.2975i	0.214670	+	0.371820i
$768$	−1.96506	+	3.40359i	−0.0709081	+	0.122816i
$769$	−22.8369	+	39.5547i	−0.823521	+	1.42638i	0.0795239	+	0.996833i	$0.474660\pi$
$769$	−22.8369	+	39.5547i	−0.823521	+	1.42638i	−0.903045	+	0.429547i	$0.858673\pi$
$770$	5.30466			0.191167
$771$	−1.97571	+	3.42203i	−0.0711535	+	0.123241i
$772$	0.642113			0.0231101
$773$	9.28069			0.333803			0.166902	−	0.985974i	$-0.446624\pi$
$773$	9.28069			0.333803			0.166902	+	0.985974i	$0.446624\pi$
$774$	9.83991	−	18.6513i	0.353688	−	0.670407i
$775$	20.0012			0.718464
$776$	23.7767			0.853535
$777$	−1.37178	+	2.37600i	−0.0492124	+	0.0852384i
$778$	15.0702			0.540291
$779$	−2.15162	+	3.72671i	−0.0770897	+	0.133523i
$780$	−0.545684	+	0.945153i	−0.0195386	+	0.0338419i
$781$	−8.70674	−	15.0805i	−0.311551	−	0.539623i
$782$	−1.05136			−0.0375965
$783$	−4.84172	−	8.38611i	−0.173029	−	0.299695i
$784$	−4.92055	+	8.52264i	−0.175734	+	0.304380i
$785$	−5.69761			−0.203356
$786$	−2.03034	+	3.51665i	−0.0724197	+	0.125435i
$787$	−12.3239	−	21.3456i	−0.439299	−	0.760889i	0.558336	−	0.829615i	$-0.311440\pi$
$787$	−12.3239	−	21.3456i	−0.439299	−	0.760889i	−0.997636	+	0.0687259i	$0.978107\pi$
$788$	8.60081	+	14.8970i	0.306391	+	0.530685i
$789$	0.797778	+	1.38179i	0.0284017	+	0.0491931i
$790$	−31.9427			−1.13647
$791$	−0.683900	−	1.18455i	−0.0243167	−	0.0421178i
$792$	7.02629	+	12.1699i	0.249668	+	0.432438i
$793$	8.14919	−	14.1148i	0.289386	−	0.501232i
$794$	12.0161	−	20.8126i	0.426437	−	0.738610i
$795$	−7.10988			−0.252161
$796$	−16.5512			−0.586642
$797$	3.03031	−	5.24865i	0.107339	−	0.185917i	−0.807352	−	0.590070i	$-0.799100\pi$
$797$	3.03031	−	5.24865i	0.107339	−	0.185917i	0.914691	+	0.404153i	$0.132434\pi$
$798$	0.0992399	−	0.171889i	0.00351306	−	0.00608479i
$799$	5.32228	+	9.21846i	0.188289	+	0.326126i
$800$	4.09326	+	7.08974i	0.144719	+	0.250660i
$801$	−20.6714			−0.730388
$802$	−8.75159	−	15.1582i	−0.309029	−	0.535255i
$803$	0.842839	+	1.45984i	0.0297431	+	0.0515166i
$804$	1.37611	+	2.38349i	0.0485316	+	0.0840592i
$805$	1.49183	−	2.58393i	0.0525803	−	0.0910717i
$806$	−23.3134			−0.821179
$807$	1.42744	−	2.47240i	0.0502483	−	0.0870327i
$808$	−7.41611	−	12.8451i	−0.260898	−	0.451888i
$809$	1.24830			0.0438879			0.0219440	−	0.999759i	$-0.493014\pi$
$809$	1.24830			0.0438879			0.0219440	+	0.999759i	$0.493014\pi$
$810$	12.1762	+	21.0897i	0.427827	+	0.741018i
$811$	23.1286	−	40.0599i	0.812155	−	1.40669i	−0.0991981	−	0.995068i	$-0.531628\pi$
$811$	23.1286	−	40.0599i	0.812155	−	1.40669i	0.911353	−	0.411626i	$-0.135039\pi$
$812$	−3.08556	+	5.34435i	−0.108282	+	0.187550i
$813$	7.14603			0.250622
$814$	7.95372	−	13.7762i	0.278778	−	0.482857i
$815$	−19.9444			−0.698621
$816$	0.438159			0.0153386
$817$	−4.03425	+	0.153929i	−0.141141	+	0.00538528i
$818$	−27.6542			−0.966906
$819$	7.16523			0.250373
$820$	7.38154	−	12.7852i	0.257775	−	0.446479i
$821$	50.9798			1.77921			0.889604	−	0.456732i	$-0.150980\pi$
$821$	50.9798			1.77921			0.889604	+	0.456732i	$0.150980\pi$
$822$	1.19419	−	2.06840i	0.0416521	−	0.0721436i
$823$	−1.21967	+	2.11253i	−0.0425151	+	0.0736382i	−0.886500	−	0.462729i	$-0.846870\pi$
$823$	−1.21967	+	2.11253i	−0.0425151	+	0.0736382i	0.843985	+	0.536367i	$0.180204\pi$
$824$	−21.0606	−	36.4780i	−0.733679	−	1.27077i
$825$	−0.756921			−0.0263526
$826$	3.70934	+	6.42477i	0.129065	+	0.223546i
$827$	−2.42543	+	4.20097i	−0.0843405	+	0.146082i	−0.905110	−	0.425177i	$-0.860212\pi$
$827$	−2.42543	+	4.20097i	−0.0843405	+	0.146082i	0.820769	+	0.571260i	$0.193545\pi$
$828$	2.26151			0.0785931
$829$	−2.44310	+	4.23157i	−0.0848522	+	0.146968i	−0.905328	−	0.424713i	$-0.860375\pi$
$829$	−2.44310	+	4.23157i	−0.0848522	+	0.146968i	0.820476	+	0.571681i	$0.193708\pi$
$830$	15.0103	+	25.9985i	0.521014	+	0.902422i
$831$	−0.969933	−	1.67997i	−0.0336466	−	0.0582776i
$832$	−8.40019	−	14.5496i	−0.291224	−	0.504415i
$833$	−5.60985			−0.194370
$834$	−1.48372	−	2.56988i	−0.0513771	−	0.0889877i
$835$	3.75617	+	6.50588i	0.129988	+	0.225145i
$836$	0.384879	−	0.666630i	0.0133113	−	0.0230559i
$837$	−7.63345	+	13.2215i	−0.263851	+	0.457003i
$838$	−18.6892			−0.645609
$839$	34.2067			1.18095			0.590473	−	0.807058i	$-0.298941\pi$
$839$	34.2067			1.18095			0.590473	+	0.807058i	$0.298941\pi$
$840$	−1.18992	+	2.06101i	−0.0410562	+	0.0711115i
$841$	−6.81701	+	11.8074i	−0.235069	+	0.407152i
$842$	15.7195	+	27.2270i	0.541731	+	0.938306i
$843$	−0.353929	−	0.613023i	−0.0121900	−	0.0211136i
$844$	−11.7664			−0.405017
$845$	11.4888	+	19.8992i	0.395227	+	0.684553i
$846$	17.1157	+	29.6452i	0.588449	+	1.01922i
$847$	−5.05055	−	8.74781i	−0.173539	−	0.300578i
$848$	9.47574	−	16.4125i	0.325398	−	0.563606i
$849$	−3.33544			−0.114472
$850$	1.06348	−	1.84200i	0.0364770	−	0.0631800i
$851$	−4.47367	−	7.74862i	−0.153355	−	0.265619i
$852$	2.23525			0.0765785
$853$	18.1085	+	31.3649i	0.620024	+	1.07391i	0.989481	+	0.144665i	$0.0462104\pi$
$853$	18.1085	+	31.3649i	0.620024	+	1.07391i	−0.369457	+	0.929248i	$0.620456\pi$
$854$	5.08442	−	8.80648i	0.173985	−	0.301351i
$855$	2.38276	−	4.12707i	0.0814888	−	0.141143i
$856$	−28.3211			−0.967994
$857$	9.49241	−	16.4413i	0.324255	−	0.561626i	−0.657107	−	0.753798i	$-0.728220\pi$
$857$	9.49241	−	16.4413i	0.324255	−	0.561626i	0.981361	+	0.192172i	$0.0615532\pi$
$858$	0.882267			0.0301201
$859$	−29.9113			−1.02056			−0.510280	−	0.860008i	$-0.670458\pi$
$859$	−29.9113			−1.02056			−0.510280	+	0.860008i	$0.670458\pi$
$860$	13.8403	−	0.528082i	0.471950	−	0.0180075i
$861$	2.05836			0.0701486
$862$	−31.7685			−1.08204
$863$	4.68592	−	8.11625i	0.159511	−	0.276280i	−0.775182	−	0.631738i	$-0.782342\pi$
$863$	4.68592	−	8.11625i	0.159511	−	0.276280i	0.934692	+	0.355458i	$0.115675\pi$
$864$	−6.24877			−0.212587
$865$	−21.2149	+	36.7454i	−0.721330	+	1.24938i
$866$	14.8816	−	25.7757i	0.505698	−	0.875894i
$867$	0.124885	+	0.216307i	0.00424131	+	0.00734617i
$868$	9.72937			0.330236
$869$	−8.63620	−	14.9583i	−0.292963	−	0.507427i
$870$	−2.35213	+	4.07401i	−0.0797446	+	0.138122i
$871$	−28.4375			−0.963569
$872$	−28.2821	+	48.9860i	−0.957753	+	1.65888i
$873$	11.3870	+	19.7229i	0.385392	+	0.667519i
$874$	0.323642	+	0.560565i	0.0109474	+	0.0189614i
$875$	−4.74873	−	8.22504i	−0.160536	−	0.278057i
$876$	−0.216379			−0.00731078
$877$	16.6772	+	28.8857i	0.563148	+	0.975401i	0.997219	+	0.0745224i	$0.0237432\pi$
$877$	16.6772	+	28.8857i	0.563148	+	0.975401i	−0.434071	+	0.900879i	$0.642923\pi$
$878$	−6.50669	−	11.2699i	−0.219590	−	0.380341i
$879$	0.816959	−	1.41501i	0.0275553	−	0.0477272i
$880$	3.60485	−	6.24379i	0.121520	−	0.210478i
$881$	20.2817			0.683308			0.341654	−	0.939826i	$-0.389013\pi$
$881$	20.2817			0.683308			0.341654	+	0.939826i	$0.389013\pi$
$882$	−18.0405			−0.607455
$883$	9.76083	−	16.9062i	0.328478	−	0.568941i	−0.653732	−	0.756726i	$-0.726798\pi$
$883$	9.76083	−	16.9062i	0.328478	−	0.568941i	0.982210	+	0.187786i	$0.0601310\pi$
$884$	0.829144	−	1.43612i	0.0278871	−	0.0483019i
$885$	−1.89137	−	3.27595i	−0.0635777	−	0.110120i
$886$	−16.7893	−	29.0799i	−0.564047	−	0.976958i
$887$	35.8671			1.20430			0.602150	−	0.798383i	$-0.294311\pi$
$887$	35.8671			1.20430			0.602150	+	0.798383i	$0.294311\pi$
$888$	3.56830	+	6.18048i	0.119744	+	0.207403i
$889$	4.06050	+	7.03299i	0.136185	+	0.235879i
$890$	10.1489	+	17.5784i	0.340191	+	0.589228i
$891$	−6.58402	+	11.4039i	−0.220573	+	0.382044i
$892$	−16.6915			−0.558872
$893$	3.27674	−	5.67549i	0.109652	−	0.189923i
$894$	1.42891	+	2.47494i	0.0477899	+	0.0827745i
$895$	−51.4573			−1.72003
$896$	−0.273124	−	0.473065i	−0.00912445	−	0.0158040i
$897$	0.248121	−	0.429758i	0.00828452	−	0.0143492i
$898$	−15.2322	+	26.3829i	−0.508304	+	0.880408i
$899$	67.2167			2.24180
$900$	−2.28758	+	3.96221i	−0.0762528	+	0.132074i
$901$	10.8032			0.359906
$902$	−11.9345			−0.397377
$903$	1.02861	+	1.63435i	0.0342300	+	0.0543878i
$904$	−3.55795			−0.118336
$905$	−51.1333			−1.69973
$906$	−0.727140	+	1.25944i	−0.0241576	+	0.0418422i
$907$	18.5756			0.616791			0.308396	−	0.951258i	$-0.400208\pi$
$907$	18.5756			0.616791			0.308396	+	0.951258i	$0.400208\pi$
$908$	8.95148	−	15.5044i	0.297065	−	0.514532i
$909$	7.10336	−	12.3034i	0.235604	−	0.408077i
$910$	−3.51786	−	6.09311i	−0.116616	−	0.201984i
$911$	−5.62453			−0.186349			−0.0931745	−	0.995650i	$-0.529701\pi$
$911$	−5.62453			−0.186349			−0.0931745	+	0.995650i	$0.529701\pi$
$912$	−0.134880	−	0.233619i	−0.00446631	−	0.00773588i
$913$	−8.11651	+	14.0582i	−0.268617	+	0.465259i
$914$	−20.4137			−0.675224
$915$	−2.59251	+	4.49036i	−0.0857058	+	0.148447i
$916$	−3.32696	−	5.76247i	−0.109926	−	0.190397i
$917$	8.75502	+	15.1641i	0.289116	+	0.500764i
$918$	0.811752	+	1.40600i	0.0267918	+	0.0464048i
$919$	−7.82808			−0.258225			−0.129112	−	0.991630i	$-0.541213\pi$
$919$	−7.82808			−0.258225			−0.129112	+	0.991630i	$0.541213\pi$
$920$	−3.88059	−	6.72138i	−0.127939	−	0.221597i
$921$	1.54714	+	2.67972i	0.0509799	+	0.0882998i
$922$	6.02068	−	10.4281i	0.198280	−	0.343432i
$923$	−11.5480	+	20.0017i	−0.380107	+	0.658364i
$924$	−0.368196			−0.0121128
$925$	18.1010			0.595156
$926$	−2.38815	+	4.13639i	−0.0784794	+	0.135930i
$927$	20.1724	−	34.9396i	0.662549	−	1.14757i
$928$	13.7560	+	23.8260i	0.451561	+	0.782127i
$929$	23.1238	+	40.0517i	0.758668	+	1.31405i	0.943530	+	0.331288i	$0.107483\pi$
$929$	23.1238	+	40.0517i	0.758668	+	1.31405i	−0.184862	+	0.982765i	$0.559184\pi$
$930$	7.41672			0.243204
$931$	1.72690	+	2.99107i	0.0565967	+	0.0980284i
$932$	−9.68149	−	16.7688i	−0.317128	−	0.549281i
$933$	−0.449387	−	0.778361i	−0.0147123	−	0.0254824i
$934$	9.40814	−	16.2954i	0.307844	−	0.533201i
$935$	4.10984			0.134406
$936$	9.31916	−	16.1413i	0.304606	−	0.527594i
$937$	1.73906	+	3.01213i	0.0568125	+	0.0984021i	0.893033	−	0.449991i	$-0.148573\pi$
$937$	1.73906	+	3.01213i	0.0568125	+	0.0984021i	−0.836220	+	0.548393i	$0.815240\pi$
$938$	−17.7427			−0.579319
$939$	−0.897782	−	1.55500i	−0.0292980	−	0.0507457i
$940$	−11.2415	+	19.4709i	−0.366657	+	0.635069i
$941$	0.339030	−	0.587217i	0.0110521	−	0.0191427i	−0.860446	−	0.509541i	$-0.829815\pi$
$941$	0.339030	−	0.587217i	0.0110521	−	0.0191427i	0.871499	+	0.490398i	$0.163149\pi$
$942$	−0.591239			−0.0192636
$943$	−3.35637	+	5.81340i	−0.109298	+	0.189310i
$944$	10.0829			0.328172
$945$	−4.60737			−0.149878
$946$	−5.96399	−	9.47612i	−0.193906	−	0.308095i
$947$	−29.3284			−0.953044			−0.476522	−	0.879163i	$-0.658103\pi$
$947$	−29.3284			−0.953044			−0.476522	+	0.879163i	$0.658103\pi$
$948$	2.21714			0.0720095
$949$	1.11788	−	1.93623i	0.0362879	−	0.0628526i
$950$	−1.30949			−0.0424856
$951$	−4.36423	+	7.55907i	−0.141520	+	0.245120i
$952$	1.80804	−	3.13161i	0.0585988	−	0.101496i
$953$	−29.9641	−	51.8994i	−0.970634	−	1.68119i	−0.693649	−	0.720313i	$-0.743998\pi$
$953$	−29.9641	−	51.8994i	−0.970634	−	1.68119i	−0.276985	−	0.960874i	$-0.589335\pi$
$954$	34.7414			1.12480
$955$	24.5356	+	42.4970i	0.793955	+	1.37517i
$956$	−6.25531	+	10.8345i	−0.202311	+	0.350413i
$957$	−2.54374			−0.0822273
$958$	−0.171531	+	0.297101i	−0.00554192	+	0.00959889i
$959$	−5.14946	−	8.91913i	−0.166285	−	0.288014i
$960$	2.67236	+	4.62867i	0.0862502	+	0.149390i
$961$	−37.4869	−	64.9291i	−1.20925	−	2.09449i
$962$	−21.0985			−0.680242
$963$	−13.5634	−	23.4924i	−0.437073	−	0.757033i
$964$	−9.81334	−	16.9972i	−0.316066	−	0.547443i
$965$	1.05535	−	1.82792i	0.0339730	−	0.0588429i
$966$	0.154807	−	0.268134i	0.00498084	−	0.00862706i
$967$	−51.9363			−1.67016			−0.835080	−	0.550129i	$-0.814579\pi$
$967$	−51.9363			−1.67016			−0.835080	+	0.550129i	$0.814579\pi$
$968$	−26.2752			−0.844516
$969$	0.0768873	−	0.133173i	0.00246998	−	0.00427812i
$970$	11.1812	−	19.3664i	0.359006	−	0.621817i
$971$	0.509278	+	0.882095i	0.0163435	+	0.0283078i	0.874081	−	0.485779i	$-0.161464\pi$
$971$	0.509278	+	0.882095i	0.0163435	+	0.0283078i	−0.857738	+	0.514087i	$0.828131\pi$
$972$	−2.62834	−	4.55242i	−0.0843041	−	0.146019i
$973$	−12.7959			−0.410218
$974$	−1.12019	−	1.94022i	−0.0358931	−	0.0621687i
$975$	0.501963	+	0.869425i	0.0160757	+	0.0278439i
$976$	−6.91038	−	11.9691i	−0.221196	−	0.383122i
$977$	−10.7466	+	18.6137i	−0.343815	+	0.595505i	−0.985138	−	0.171766i	$-0.945053\pi$
$977$	−10.7466	+	18.6137i	−0.343815	+	0.595505i	0.641323	+	0.767271i	$0.278386\pi$
$978$	−2.06962			−0.0661791
$979$	−5.48781	+	9.50516i	−0.175391	+	0.303786i
$980$	−5.92445	−	10.2615i	−0.189250	−	0.327790i
$981$	−54.1788			−1.72980
$982$	4.00762	+	6.94141i	0.127888	+	0.221509i
$983$	2.47716	−	4.29056i	0.0790091	−	0.136848i	−0.823814	−	0.566861i	$-0.808158\pi$
$983$	2.47716	−	4.29056i	0.0790091	−	0.136848i	0.902823	+	0.430013i	$0.141491\pi$
$984$	2.67712	−	4.63690i	0.0853433	−	0.147819i
$985$	56.5439			1.80164
$986$	3.57396	−	6.19028i	0.113818	−	0.197139i
$987$	−3.13471			−0.0997790
$988$	−1.02095			−0.0324808
$989$	−6.29314	+	0.240118i	−0.200110	+	0.00763530i
$990$	13.2167			0.420053
$991$	26.8684			0.853502			0.426751	−	0.904369i	$-0.359658\pi$
$991$	26.8684			0.853502			0.426751	+	0.904369i	$0.359658\pi$
$992$	21.6876	−	37.5640i	0.688582	−	1.19266i
$993$	−6.49540			−0.206125
$994$	−7.20499	+	12.4794i	−0.228528	+	0.395823i
$995$	−27.2029	+	47.1169i	−0.862391	+	1.49371i
$996$	−1.04186	−	1.80456i	−0.0330127	−	0.0571796i
$997$	−14.4281			−0.456941			−0.228471	−	0.973551i	$-0.573372\pi$
$997$	−14.4281			−0.456941			−0.228471	+	0.973551i	$0.573372\pi$
$998$	−6.74244	−	11.6782i	−0.213428	−	0.369668i
$999$	−6.90823	+	11.9654i	−0.218567	+	0.378569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.b.307.11	✓	58
43.36	even	3	inner	731.2.e.b.681.11	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.b.307.11	✓	58	1.1	even	1	trivial
731.2.e.b.681.11	yes	58	43.36	even	3	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.09472 q^{2} +(0.124885 - 0.216307i) q^{3} -0.801596 q^{4} +(-1.31747 + 2.28193i) q^{5} +(-0.136714 + 0.236795i) q^{6} +(0.589522 + 1.02108i) q^{7} +3.06695 q^{8} +(1.46881 + 2.54405i) q^{9} +O(q^{10})\)	\(q-1.09472 q^{2} +(0.124885 - 0.216307i) q^{3} -0.801596 q^{4} +(-1.31747 + 2.28193i) q^{5} +(-0.136714 + 0.236795i) q^{6} +(0.589522 + 1.02108i) q^{7} +3.06695 q^{8} +(1.46881 + 2.54405i) q^{9} +(1.44226 - 2.49806i) q^{10} +1.55975 q^{11} +(-0.100107 + 0.173391i) q^{12} +(-1.03437 - 1.79158i) q^{13} +(-0.645360 - 1.11780i) q^{14} +(0.329065 + 0.569957i) q^{15} -1.75425 q^{16} +(-0.500000 - 0.866025i) q^{17} +(-1.60793 - 2.78501i) q^{18} +(-0.307833 + 0.533182i) q^{19} +(1.05608 - 1.82918i) q^{20} +0.294490 q^{21} -1.70748 q^{22} +(-0.480197 + 0.831725i) q^{23} +(0.383016 - 0.663403i) q^{24} +(-0.971464 - 1.68263i) q^{25} +(1.13234 + 1.96127i) q^{26} +1.48304 q^{27} +(-0.472559 - 0.818496i) q^{28} +(-3.26474 - 5.65469i) q^{29} +(-0.360232 - 0.623941i) q^{30} +(-5.14718 + 8.91517i) q^{31} -4.21350 q^{32} +(0.194789 - 0.337384i) q^{33} +(0.547358 + 0.948052i) q^{34} -3.10672 q^{35} +(-1.17739 - 2.03930i) q^{36} +(-4.65816 + 8.06818i) q^{37} +(0.336989 - 0.583683i) q^{38} -0.516707 q^{39} +(-4.04062 + 6.99857i) q^{40} +6.98957 q^{41} -0.322383 q^{42} +(3.49286 + 5.54977i) q^{43} -1.25029 q^{44} -7.74045 q^{45} +(0.525679 - 0.910503i) q^{46} -10.6446 q^{47} +(-0.219080 + 0.379457i) q^{48} +(2.80493 - 4.85828i) q^{49} +(1.06348 + 1.84200i) q^{50} -0.249770 q^{51} +(0.829144 + 1.43612i) q^{52} +(-5.40158 + 9.35582i) q^{53} -1.62350 q^{54} +(-2.05492 + 3.55923i) q^{55} +(1.80804 + 3.13161i) q^{56} +(0.0768873 + 0.133173i) q^{57} +(3.57396 + 6.19028i) q^{58} -5.74771 q^{59} +(-0.263777 - 0.456875i) q^{60} +(3.93921 + 6.82292i) q^{61} +(5.63470 - 9.75959i) q^{62} +(-1.73179 + 2.99955i) q^{63} +8.12109 q^{64} +5.45100 q^{65} +(-0.213238 + 0.369340i) q^{66} +(6.87317 - 11.9047i) q^{67} +(0.400798 + 0.694202i) q^{68} +(0.119939 + 0.207740i) q^{69} +3.40097 q^{70} +(-5.58215 - 9.66857i) q^{71} +(4.50476 + 7.80248i) q^{72} +(0.540369 + 0.935947i) q^{73} +(5.09937 - 8.83237i) q^{74} -0.485285 q^{75} +(0.246757 - 0.427396i) q^{76} +(0.919505 + 1.59263i) q^{77} +0.565648 q^{78} +(-5.53693 - 9.59024i) q^{79} +(2.31118 - 4.00308i) q^{80} +(-4.22121 + 7.31136i) q^{81} -7.65159 q^{82} +(-5.20374 + 9.01313i) q^{83} -0.236062 q^{84} +2.63494 q^{85} +(-3.82369 - 6.07542i) q^{86} -1.63086 q^{87} +4.78367 q^{88} +(-3.51840 + 6.09404i) q^{89} +8.47360 q^{90} +(1.21957 - 2.11235i) q^{91} +(0.384924 - 0.666707i) q^{92} +(1.28561 + 2.22674i) q^{93} +11.6528 q^{94} +(-0.811122 - 1.40490i) q^{95} +(-0.526202 + 0.911409i) q^{96} +7.75256 q^{97} +(-3.07060 + 5.31843i) q^{98} +(2.29097 + 3.96807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9}+O(q^{10}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9	\( 58 q + 2 q^{2} - 5 q^{3} + 54 q^{4} - 3 q^{5} - 8 q^{6} - 13 q^{7} + 12 q^{8} - 30 q^{9} + 4 q^{10} - 8 q^{12} + 2 q^{13} + 5 q^{14} - 5 q^{15} + 30 q^{16} - 29 q^{17} + 16 q^{18} - 4 q^{19} - 7 q^{20} - 26 q^{21} - 10 q^{22} + 5 q^{23} - 28 q^{24} - 24 q^{25} - 8 q^{26} + 28 q^{27} - 25 q^{28} + 10 q^{29} - 5 q^{30} + 3 q^{31} + 16 q^{32} - 23 q^{33} - q^{34} - 26 q^{35} - 39 q^{36} - 16 q^{37} + q^{38} + 130 q^{39} + 15 q^{40} - 22 q^{41} + 112 q^{42} + 7 q^{43} + 24 q^{44} + 2 q^{45} - 61 q^{46} + 12 q^{47} + 22 q^{48} - 36 q^{49} - 17 q^{50} + 10 q^{51} - 35 q^{52} - 10 q^{53} - 10 q^{54} - 20 q^{55} - 4 q^{56} + 9 q^{57} - 17 q^{58} - 36 q^{59} + 22 q^{60} - 35 q^{61} + 3 q^{62} - 22 q^{63} + 28 q^{64} - 28 q^{65} + 14 q^{66} - 17 q^{67} - 27 q^{68} - 23 q^{69} + 10 q^{70} - 6 q^{71} + 17 q^{72} - 14 q^{73} + 21 q^{74} + 70 q^{75} - 44 q^{76} - 11 q^{77} - 184 q^{78} - 10 q^{79} + 8 q^{80} - 13 q^{81} + 184 q^{82} + 9 q^{83} - 36 q^{84} + 6 q^{85} - 76 q^{86} + 8 q^{87} + 50 q^{88} - 54 q^{89} - 34 q^{90} - 23 q^{91} - 66 q^{92} + 96 q^{94} - 3 q^{95} - 60 q^{96} + 36 q^{97} - 16 q^{98} + 20 q^{99}+O(q^{100}) \) 58 * q + 2 * q^2 - 5 * q^3 + 54 * q^4 - 3 * q^5 - 8 * q^6 - 13 * q^7 + 12 * q^8 - 30 * q^9 + 4 * q^10 - 8 * q^12 + 2 * q^13 + 5 * q^14 - 5 * q^15 + 30 * q^16 - 29 * q^17 + 16 * q^18 - 4 * q^19 - 7 * q^20 - 26 * q^21 - 10 * q^22 + 5 * q^23 - 28 * q^24 - 24 * q^25 - 8 * q^26 + 28 * q^27 - 25 * q^28 + 10 * q^29 - 5 * q^30 + 3 * q^31 + 16 * q^32 - 23 * q^33 - q^34 - 26 * q^35 - 39 * q^36 - 16 * q^37 + q^38 + 130 * q^39 + 15 * q^40 - 22 * q^41 + 112 * q^42 + 7 * q^43 + 24 * q^44 + 2 * q^45 - 61 * q^46 + 12 * q^47 + 22 * q^48 - 36 * q^49 - 17 * q^50 + 10 * q^51 - 35 * q^52 - 10 * q^53 - 10 * q^54 - 20 * q^55 - 4 * q^56 + 9 * q^57 - 17 * q^58 - 36 * q^59 + 22 * q^60 - 35 * q^61 + 3 * q^62 - 22 * q^63 + 28 * q^64 - 28 * q^65 + 14 * q^66 - 17 * q^67 - 27 * q^68 - 23 * q^69 + 10 * q^70 - 6 * q^71 + 17 * q^72 - 14 * q^73 + 21 * q^74 + 70 * q^75 - 44 * q^76 - 11 * q^77 - 184 * q^78 - 10 * q^79 + 8 * q^80 - 13 * q^81 + 184 * q^82 + 9 * q^83 - 36 * q^84 + 6 * q^85 - 76 * q^86 + 8 * q^87 + 50 * q^88 - 54 * q^89 - 34 * q^90 - 23 * q^91 - 66 * q^92 + 96 * q^94 - 3 * q^95 - 60 * q^96 + 36 * q^97 - 16 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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