LMFDB - Embedded newform 731.2.e.a.681.17

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			681.17
Character	$\chi$	$=$	731.681
Dual form			731.2.e.a.307.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.469159 q^{2} +(1.22299 + 2.11828i) q^{3} -1.77989 q^{4} +(-1.20485 - 2.08687i) q^{5} +(0.573775 + 0.993808i) q^{6} +(1.21565 - 2.10557i) q^{7} -1.77337 q^{8} +(-1.49139 + 2.58317i) q^{9} +O(q^{10})$	\(q+0.469159 q^{2} +(1.22299 + 2.11828i) q^{3} -1.77989 q^{4} +(-1.20485 - 2.08687i) q^{5} +(0.573775 + 0.993808i) q^{6} +(1.21565 - 2.10557i) q^{7} -1.77337 q^{8} +(-1.49139 + 2.58317i) q^{9} +(-0.565268 - 0.979072i) q^{10} +5.54536 q^{11} +(-2.17678 - 3.77030i) q^{12} +(0.602228 - 1.04309i) q^{13} +(0.570332 - 0.987844i) q^{14} +(2.94704 - 5.10443i) q^{15} +2.72779 q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.699701 + 1.21192i) q^{18} +(-0.840542 - 1.45586i) q^{19} +(2.14451 + 3.71440i) q^{20} +5.94689 q^{21} +2.60165 q^{22} +(4.22810 + 7.32328i) q^{23} +(-2.16881 - 3.75648i) q^{24} +(-0.403346 + 0.698616i) q^{25} +(0.282540 - 0.489374i) q^{26} +0.0420982 q^{27} +(-2.16372 + 3.74767i) q^{28} +(1.18338 - 2.04967i) q^{29} +(1.38263 - 2.39479i) q^{30} +(1.47298 + 2.55127i) q^{31} +4.82650 q^{32} +(6.78191 + 11.7466i) q^{33} +(0.234579 - 0.406303i) q^{34} -5.85872 q^{35} +(2.65452 - 4.59776i) q^{36} +(-5.14856 - 8.91757i) q^{37} +(-0.394348 - 0.683030i) q^{38} +2.94607 q^{39} +(2.13665 + 3.70079i) q^{40} -8.54362 q^{41} +2.79004 q^{42} +(6.14525 - 2.28821i) q^{43} -9.87013 q^{44} +7.18765 q^{45} +(1.98365 + 3.43578i) q^{46} +0.538653 q^{47} +(3.33605 + 5.77821i) q^{48} +(0.544396 + 0.942922i) q^{49} +(-0.189233 + 0.327762i) q^{50} +2.44597 q^{51} +(-1.07190 + 1.85658i) q^{52} +(-6.43981 - 11.1541i) q^{53} +0.0197508 q^{54} +(-6.68135 - 11.5724i) q^{55} +(-2.15579 + 3.73394i) q^{56} +(2.05594 - 3.56100i) q^{57} +(0.555193 - 0.961622i) q^{58} +8.86543 q^{59} +(-5.24541 + 9.08532i) q^{60} +(-3.02182 + 5.23394i) q^{61} +(0.691059 + 1.19695i) q^{62} +(3.62602 + 6.28046i) q^{63} -3.19118 q^{64} -2.90239 q^{65} +(3.18179 + 5.51102i) q^{66} +(3.11456 + 5.39458i) q^{67} +(-0.889945 + 1.54143i) q^{68} +(-10.3418 + 17.9125i) q^{69} -2.74867 q^{70} +(3.37073 - 5.83827i) q^{71} +(2.64479 - 4.58091i) q^{72} +(-3.31308 + 5.73843i) q^{73} +(-2.41549 - 4.18376i) q^{74} -1.97315 q^{75} +(1.49607 + 2.59127i) q^{76} +(6.74121 - 11.6761i) q^{77} +1.38217 q^{78} +(-3.85283 + 6.67329i) q^{79} +(-3.28659 - 5.69254i) q^{80} +(4.52567 + 7.83869i) q^{81} -4.00832 q^{82} +(0.342282 + 0.592849i) q^{83} -10.5848 q^{84} -2.40971 q^{85} +(2.88310 - 1.07354i) q^{86} +5.78903 q^{87} -9.83397 q^{88} +(1.77324 + 3.07133i) q^{89} +3.37215 q^{90} +(-1.46419 - 2.53606i) q^{91} +(-7.52555 - 13.0346i) q^{92} +(-3.60286 + 6.24034i) q^{93} +0.252714 q^{94} +(-2.02546 + 3.50820i) q^{95} +(5.90275 + 10.2239i) q^{96} -1.52535 q^{97} +(0.255408 + 0.442380i) q^{98} +(-8.27032 + 14.3246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) $ 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.469159			0.331745			0.165873	−	0.986147i	$-0.446956\pi$
$2$	0.469159			0.331745			0.165873	+	0.986147i	$0.446956\pi$
$3$	1.22299	+	2.11828i	0.706092	+	1.22299i	0.966296	+	0.257433i	$0.0828768\pi$
$3$	1.22299	+	2.11828i	0.706092	+	1.22299i	−0.260204	+	0.965554i	$0.583790\pi$
$4$	−1.77989			−0.889945
$5$	−1.20485	−	2.08687i	−0.538827	−	0.933276i	−0.998968	−	0.0454297i	$-0.985534\pi$
$5$	−1.20485	−	2.08687i	−0.538827	−	0.933276i	0.460140	−	0.887846i	$-0.347799\pi$
$6$	0.573775	+	0.993808i	0.234243	+	0.405720i
$7$	1.21565	−	2.10557i	0.459472	−	0.795829i	−0.539461	−	0.842011i	$-0.681372\pi$
$7$	1.21565	−	2.10557i	0.459472	−	0.795829i	0.998933	+	0.0461817i	$0.0147053\pi$
$8$	−1.77337			−0.626980
$9$	−1.49139	+	2.58317i	−0.497131	+	0.861057i
$10$	−0.565268	−	0.979072i	−0.178753	−	0.309610i
$11$	5.54536			1.67199			0.835995	−	0.548737i	$-0.184891\pi$
$11$	5.54536			1.67199			0.835995	+	0.548737i	$0.184891\pi$
$12$	−2.17678	−	3.77030i	−0.628383	−	1.08839i
$13$	0.602228	−	1.04309i	0.167028	−	0.289301i	−0.770346	−	0.637627i	$-0.779916\pi$
$13$	0.602228	−	1.04309i	0.167028	−	0.289301i	0.937374	+	0.348326i	$0.113250\pi$
$14$	0.570332	−	0.987844i	0.152428	−	0.264013i
$15$	2.94704	−	5.10443i	0.760923	−	1.31796i
$16$	2.72779			0.681947
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$17$	0.500000	−	0.866025i	0.121268	−	0.210042i
$18$	−0.699701	+	1.21192i	−0.164921	+	0.285652i
$19$	−0.840542	−	1.45586i	−0.192834	−	0.333998i	0.753355	−	0.657615i	$-0.228434\pi$
$19$	−0.840542	−	1.45586i	−0.192834	−	0.333998i	−0.946188	+	0.323617i	$0.895101\pi$
$20$	2.14451	+	3.71440i	0.479526	+	0.830564i
$21$	5.94689			1.29772
$22$	2.60165			0.554675
$23$	4.22810	+	7.32328i	0.881619	+	1.52701i	0.849540	+	0.527524i	$0.176879\pi$
$23$	4.22810	+	7.32328i	0.881619	+	1.52701i	0.0320787	+	0.999485i	$0.489787\pi$
$24$	−2.16881	−	3.75648i	−0.442706	−	0.766789i
$25$	−0.403346	+	0.698616i	−0.0806692	+	0.139723i
$26$	0.282540	−	0.489374i	0.0554107	−	0.0959742i
$27$	0.0420982			0.00810181
$28$	−2.16372	+	3.74767i	−0.408905	+	0.708244i
$29$	1.18338	−	2.04967i	0.219748	−	0.380615i	−0.734983	−	0.678086i	$-0.762810\pi$
$29$	1.18338	−	2.04967i	0.219748	−	0.380615i	0.954731	+	0.297471i	$0.0961431\pi$
$30$	1.38263	−	2.39479i	0.252433	−	0.437226i
$31$	1.47298	+	2.55127i	0.264554	+	0.458221i	0.967447	−	0.253075i	$-0.0814418\pi$
$31$	1.47298	+	2.55127i	0.264554	+	0.458221i	−0.702892	+	0.711296i	$0.748109\pi$
$32$	4.82650			0.853213
$33$	6.78191	+	11.7466i	1.18058	+	2.04482i
$34$	0.234579	−	0.406303i	0.0402300	−	0.0696805i
$35$	−5.85872			−0.990304
$36$	2.65452	−	4.59776i	0.442420	−	0.766293i
$37$	−5.14856	−	8.91757i	−0.846418	−	1.46604i	−0.884384	−	0.466760i	$-0.845421\pi$
$37$	−5.14856	−	8.91757i	−0.846418	−	1.46604i	0.0379657	−	0.999279i	$-0.487912\pi$
$38$	−0.394348	−	0.683030i	−0.0639717	−	0.110802i
$39$	2.94607			0.471748
$40$	2.13665	+	3.70079i	0.337834	+	0.585146i
$41$	−8.54362			−1.33429			−0.667145	−	0.744928i	$-0.732484\pi$
$41$	−8.54362			−1.33429			−0.667145	+	0.744928i	$0.732484\pi$
$42$	2.79004			0.430512
$43$	6.14525	−	2.28821i	0.937142	−	0.348949i
$43$	6.14525	−	2.28821i	0.937142	−	0.348949i
$44$	−9.87013			−1.48798
$45$	7.18765			1.07147
$46$	1.98365	+	3.43578i	0.292473	+	0.506578i
$47$	0.538653			0.0785707			0.0392853	−	0.999228i	$-0.487492\pi$
$47$	0.538653			0.0785707			0.0392853	+	0.999228i	$0.487492\pi$
$48$	3.33605	+	5.77821i	0.481517	+	0.834013i
$49$	0.544396	+	0.942922i	0.0777709	+	0.134703i
$50$	−0.189233	+	0.327762i	−0.0267616	+	0.0463525i
$51$	2.44597			0.342505
$52$	−1.07190	+	1.85658i	−0.148646	+	0.257462i
$53$	−6.43981	−	11.1541i	−0.884577	−	1.53213i	−0.846198	−	0.532868i	$-0.821114\pi$
$53$	−6.43981	−	11.1541i	−0.884577	−	1.53213i	−0.0383783	−	0.999263i	$-0.512219\pi$
$54$	0.0197508			0.00268774
$55$	−6.68135	−	11.5724i	−0.900913	−	1.56043i
$56$	−2.15579	+	3.73394i	−0.288080	+	0.498969i
$57$	2.05594	−	3.56100i	0.272317	−	0.471666i
$58$	0.555193	−	0.961622i	0.0729004	−	0.126267i
$59$	8.86543			1.15418			0.577090	−	0.816680i	$-0.304188\pi$
$59$	8.86543			1.15418			0.577090	+	0.816680i	$0.304188\pi$
$60$	−5.24541	+	9.08532i	−0.677180	+	1.17291i
$61$	−3.02182	+	5.23394i	−0.386904	+	0.670138i	−0.992031	−	0.125991i	$-0.959789\pi$
$61$	−3.02182	+	5.23394i	−0.386904	+	0.670138i	0.605127	+	0.796129i	$0.293122\pi$
$62$	0.691059	+	1.19695i	0.0877646	+	0.152013i
$63$	3.62602	+	6.28046i	0.456836	+	0.791263i
$64$	−3.19118			−0.398898
$65$	−2.90239			−0.359997
$66$	3.18179	+	5.51102i	0.391651	+	0.678360i
$67$	3.11456	+	5.39458i	0.380504	+	0.659053i	0.991134	−	0.132863i	$-0.0424171\pi$
$67$	3.11456	+	5.39458i	0.380504	+	0.659053i	−0.610630	+	0.791916i	$0.709084\pi$
$68$	−0.889945	+	1.54143i	−0.107922	+	0.186926i
$69$	−10.3418	+	17.9125i	−1.24501	+	2.15642i
$70$	−2.74867			−0.328529
$71$	3.37073	−	5.83827i	0.400032	−	0.692875i	−0.593697	−	0.804688i	$-0.702332\pi$
$71$	3.37073	−	5.83827i	0.400032	−	0.692875i	0.993729	+	0.111813i	$0.0356657\pi$
$72$	2.64479	−	4.58091i	0.311692	−	0.539866i
$73$	−3.31308	+	5.73843i	−0.387767	+	0.671632i	−0.992149	−	0.125063i	$-0.960087\pi$
$73$	−3.31308	+	5.73843i	−0.387767	+	0.671632i	0.604382	+	0.796695i	$0.293420\pi$
$74$	−2.41549	−	4.18376i	−0.280795	−	0.486352i
$75$	−1.97315			−0.227840
$76$	1.49607	+	2.59127i	0.171611	+	0.297240i
$77$	6.74121	−	11.6761i	0.768232	−	1.33062i
$78$	1.38217			0.156500
$79$	−3.85283	+	6.67329i	−0.433477	+	0.750804i	−0.997170	−	0.0751801i	$-0.976047\pi$
$79$	−3.85283	+	6.67329i	−0.433477	+	0.750804i	0.563693	+	0.825984i	$0.309380\pi$
$80$	−3.28659	−	5.69254i	−0.367452	−	0.636445i
$81$	4.52567	+	7.83869i	0.502852	+	0.870965i
$82$	−4.00832			−0.442644
$83$	0.342282	+	0.592849i	0.0375703	+	0.0650736i	0.884199	−	0.467110i	$-0.154705\pi$
$83$	0.342282	+	0.592849i	0.0375703	+	0.0650736i	−0.846629	+	0.532184i	$0.821372\pi$
$84$	−10.5848			−1.15490
$85$	−2.40971			−0.261370
$86$	2.88310	−	1.07354i	0.310892	−	0.115762i
$87$	5.78903			0.620649
$88$	−9.83397			−1.04830
$89$	1.77324	+	3.07133i	0.187963	+	0.325561i	0.944571	−	0.328308i	$-0.106478\pi$
$89$	1.77324	+	3.07133i	0.187963	+	0.325561i	−0.756608	+	0.653869i	$0.773145\pi$
$90$	3.37215			0.355456
$91$	−1.46419	−	2.53606i	−0.153489	−	0.265851i
$92$	−7.52555	−	13.0346i	−0.784593	−	1.35895i
$93$	−3.60286	+	6.24034i	−0.373599	+	0.647093i
$94$	0.252714			0.0260654
$95$	−2.02546	+	3.50820i	−0.207808	+	0.359934i
$96$	5.90275	+	10.2239i	0.602447	+	1.04347i
$97$	−1.52535			−0.154876			−0.0774380	−	0.996997i	$-0.524674\pi$
$97$	−1.52535			−0.154876			−0.0774380	+	0.996997i	$0.524674\pi$
$98$	0.255408	+	0.442380i	0.0258001	+	0.0446872i
$99$	−8.27032	+	14.3246i	−0.831199	+	1.43968i
$100$	0.717912	−	1.24346i	0.0717912	−	0.124346i
$101$	6.88312	−	11.9219i	0.684896	−	1.18627i	−0.288574	−	0.957458i	$-0.593181\pi$
$101$	6.88312	−	11.9219i	0.684896	−	1.18627i	0.973470	−	0.228817i	$-0.0734856\pi$
$102$	1.14755			0.113624
$103$	−1.50457	+	2.60599i	−0.148249	+	0.256775i	−0.930581	−	0.366087i	$-0.880697\pi$
$103$	−1.50457	+	2.60599i	−0.148249	+	0.256775i	0.782331	+	0.622863i	$0.214031\pi$
$104$	−1.06797	+	1.84978i	−0.104723	+	0.181386i
$105$	−7.16513	−	12.4104i	−0.699246	−	1.21113i
$106$	−3.02130	−	5.23304i	−0.293454	−	0.508277i
$107$	9.76720			0.944231			0.472115	−	0.881537i	$-0.343491\pi$
$107$	9.76720			0.944231			0.472115	+	0.881537i	$0.343491\pi$
$108$	−0.0749302			−0.00721017
$109$	−7.15752	−	12.3972i	−0.685566	−	1.18743i	−0.973259	−	0.229712i	$-0.926222\pi$
$109$	−7.15752	−	12.3972i	−0.685566	−	1.18743i	0.287693	−	0.957723i	$-0.407112\pi$
$110$	−3.13461	−	5.42931i	−0.298874	−	0.517665i
$111$	12.5932	−	21.8121i	1.19530	−	2.07032i
$112$	3.31603	−	5.74354i	0.313336	−	0.542713i
$113$	−15.0764			−1.41827			−0.709136	−	0.705072i	$-0.750915\pi$
$113$	−15.0764			−1.41827			−0.709136	+	0.705072i	$0.750915\pi$
$114$	0.964564	−	1.67067i	0.0903397	−	0.156473i
$115$	10.1885	−	17.6470i	0.950080	−	1.64559i
$116$	−2.10629	+	3.64819i	−0.195564	+	0.338726i
$117$	1.79632	+	3.11131i	0.166070	+	0.287641i
$118$	4.15929			0.382894
$119$	−1.21565	−	2.10557i	−0.111438	−	0.193017i
$120$	−5.22619	+	9.05203i	−0.477084	+	0.826333i
$121$	19.7510			1.79555
$122$	−1.41771	+	2.45555i	−0.128354	+	0.222315i
$123$	−10.4487	−	18.0977i	−0.942131	−	1.63182i
$124$	−2.62173	−	4.54098i	−0.235439	−	0.407792i
$125$	−10.1046			−0.903787
$126$	1.70118	+	2.94653i	0.151553	+	0.262498i
$127$	2.61546			0.232084			0.116042	−	0.993244i	$-0.462979\pi$
$127$	2.61546			0.232084			0.116042	+	0.993244i	$0.462979\pi$
$128$	−11.1502			−0.985546
$129$	12.3626	+	10.2189i	1.08847	+	0.899722i
$130$	−1.36168			−0.119427
$131$	−8.75682			−0.765087			−0.382544	−	0.923937i	$-0.624952\pi$
$131$	−8.75682			−0.765087			−0.382544	+	0.923937i	$0.624952\pi$
$132$	−12.0710	−	20.9077i	−1.05065	−	1.81978i
$133$	−4.08722			−0.354407
$134$	1.46122	+	2.53091i	0.126231	+	0.218638i
$135$	−0.0507222	−	0.0878535i	−0.00436547	−	0.00756122i
$136$	−0.886684	+	1.53578i	−0.0760325	+	0.131692i
$137$	−16.2222			−1.38596			−0.692978	−	0.720958i	$-0.743702\pi$
$137$	−16.2222			−1.38596			−0.692978	+	0.720958i	$0.743702\pi$
$138$	−4.85195	+	8.40383i	−0.413026	+	0.715381i
$139$	9.02148	+	15.6257i	0.765192	+	1.32535i	0.940145	+	0.340775i	$0.110689\pi$
$139$	9.02148	+	15.6257i	0.765192	+	1.32535i	−0.174953	+	0.984577i	$0.555977\pi$
$140$	10.4279			0.881316
$141$	0.658766	+	1.14102i	0.0554781	+	0.0960909i
$142$	1.58141	−	2.73908i	0.132709	−	0.229858i
$143$	3.33957	−	5.78431i	0.279269	−	0.483708i
$144$	−4.06821	+	7.04634i	−0.339017	+	0.587195i
$145$	−5.70320			−0.473625
$146$	−1.55436	+	2.69223i	−0.128640	+	0.222811i
$147$	−1.33158	+	2.30636i	−0.109827	+	0.190226i
$148$	9.16387	+	15.8723i	0.753266	+	1.30469i
$149$	−0.214832	−	0.372100i	−0.0175997	−	0.0304837i	0.857091	−	0.515164i	$-0.172269\pi$
$149$	−0.214832	−	0.372100i	−0.0175997	−	0.0304837i	−0.874691	+	0.484681i	$0.838936\pi$
$150$	−0.925720			−0.0755847
$151$	−19.7277			−1.60542			−0.802710	−	0.596369i	$-0.796610\pi$
$151$	−19.7277			−1.60542			−0.802710	+	0.596369i	$0.796610\pi$
$152$	1.49059	+	2.58178i	0.120903	+	0.209410i
$153$	1.49139	+	2.58317i	0.120572	+	0.208837i
$154$	3.16270	−	5.47795i	0.254858	−	0.441426i
$155$	3.54944	−	6.14781i	0.285098	−	0.493804i
$156$	−5.24368			−0.419830
$157$	−4.18820	+	7.25417i	−0.334255	+	0.578946i	−0.983341	−	0.181768i	$-0.941818\pi$
$157$	−4.18820	+	7.25417i	−0.334255	+	0.578946i	0.649087	+	0.760714i	$0.275151\pi$
$158$	−1.80759	+	3.13083i	−0.143804	+	0.249076i
$159$	15.7516	−	27.2826i	1.24918	−	2.16365i
$160$	−5.81523	−	10.0723i	−0.459734	−	0.796283i
$161$	20.5595			1.62032
$162$	2.12326	+	3.67759i	0.166819	+	0.288939i
$163$	3.83561	−	6.64346i	0.300428	−	0.520356i	−0.675805	−	0.737080i	$-0.736204\pi$
$163$	3.83561	−	6.64346i	0.300428	−	0.520356i	0.976233	+	0.216724i	$0.0695372\pi$
$164$	15.2067			1.18744
$165$	16.3424	−	28.3059i	1.27225	−	2.20361i
$166$	0.160584	+	0.278140i	0.0124638	+	0.0215879i
$167$	2.08907	+	3.61838i	0.161657	+	0.279998i	0.935463	−	0.353424i	$-0.114983\pi$
$167$	2.08907	+	3.61838i	0.161657	+	0.279998i	−0.773806	+	0.633423i	$0.781649\pi$
$168$	−10.5460			−0.813644
$169$	5.77464	+	10.0020i	0.444203	+	0.769383i
$170$	−1.13054			−0.0867081
$171$	5.01432			0.383455
$172$	−10.9379	+	4.07277i	−0.834005	+	0.310546i
$173$	20.8642			1.58628			0.793139	−	0.609040i	$-0.208445\pi$
$173$	20.8642			1.58628			0.793139	+	0.609040i	$0.208445\pi$
$174$	2.71598			0.205898
$175$	0.980655	+	1.69854i	0.0741305	+	0.128398i
$176$	15.1266			1.14021
$177$	10.8423	+	18.7794i	0.814957	+	1.41155i
$178$	0.831929	+	1.44094i	0.0623557	+	0.108003i
$179$	−9.91290	+	17.1696i	−0.740925	+	1.28332i	0.211150	+	0.977454i	$0.432279\pi$
$179$	−9.91290	+	17.1696i	−0.740925	+	1.28332i	−0.952075	+	0.305865i	$0.901054\pi$
$180$	−12.7932			−0.953551
$181$	−6.84309	+	11.8526i	−0.508643	+	0.880995i	0.491307	+	0.870986i	$0.336519\pi$
$181$	−6.84309	+	11.8526i	−0.508643	+	0.880995i	−0.999950	+	0.0100089i	$0.996814\pi$
$182$	−0.686940	−	1.18981i	−0.0509194	−	0.0881949i
$183$	−14.7826			−1.09276
$184$	−7.49797	−	12.9869i	−0.552758	−	0.957405i
$185$	−12.4065	+	21.4887i	−0.912146	+	1.57988i
$186$	−1.69031	+	2.92771i	−0.123940	+	0.214670i
$187$	2.77268	−	4.80242i	0.202759	−	0.351188i
$188$	−0.958744			−0.0699236
$189$	0.0511767	−	0.0886406i	0.00372256	−	0.00644765i
$190$	−0.950263	+	1.64590i	−0.0689393	+	0.119406i
$191$	−0.298921	−	0.517747i	−0.0216292	−	0.0374628i	0.855008	−	0.518614i	$-0.173552\pi$
$191$	−0.298921	−	0.517747i	−0.0216292	−	0.0374628i	−0.876637	+	0.481152i	$0.840219\pi$
$192$	−3.90277	−	6.75980i	−0.281658	−	0.487847i
$193$	−1.24993			−0.0899717			−0.0449859	−	0.998988i	$-0.514324\pi$
$193$	−1.24993			−0.0899717			−0.0449859	+	0.998988i	$0.514324\pi$
$194$	−0.715632			−0.0513794
$195$	−3.54958	−	6.14805i	−0.254191	−	0.440271i
$196$	−0.968966	−	1.67830i	−0.0692118	−	0.119878i
$197$	−2.05471	+	3.55887i	−0.146392	+	0.253559i	−0.929892	−	0.367834i	$-0.880100\pi$
$197$	−2.05471	+	3.55887i	−0.146392	+	0.253559i	0.783499	+	0.621393i	$0.213433\pi$
$198$	−3.88009	+	6.72052i	−0.275746	+	0.477607i
$199$	12.1525			0.861464			0.430732	−	0.902480i	$-0.358255\pi$
$199$	12.1525			0.861464			0.430732	+	0.902480i	$0.358255\pi$
$200$	0.715281	−	1.23890i	0.0505780	−	0.0876037i
$201$	−7.61814	+	13.1950i	−0.537342	+	0.930704i
$202$	3.22927	−	5.59327i	0.227211	−	0.393541i
$203$	−2.87715	−	4.98337i	−0.201936	−	0.349764i
$204$	−4.35356			−0.304811
$205$	10.2938	+	17.8294i	0.718951	+	1.24526i
$206$	−0.705881	+	1.22262i	−0.0491810	+	0.0851841i
$207$	−25.2230			−1.75312
$208$	1.64275	−	2.84533i	0.113904	−	0.197288i
$209$	−4.66111	−	8.07328i	−0.322416	−	0.558441i
$210$	−3.36159	−	5.82244i	−0.231971	−	0.401786i
$211$	−20.2554			−1.39444			−0.697218	−	0.716859i	$-0.745579\pi$
$211$	−20.2554			−1.39444			−0.697218	+	0.716859i	$0.745579\pi$
$212$	11.4622	+	19.8530i	0.787224	+	1.36351i
$213$	16.4894			1.12984
$214$	4.58237			0.313244
$215$	−12.1793	−	10.0674i	−0.830623	−	0.686588i
$216$	−0.0746557			−0.00507968
$217$	7.16248			0.486221
$218$	−3.35801	−	5.81625i	−0.227433	−	0.393926i
$219$	−16.2074			−1.09520
$220$	11.8921	+	20.5977i	0.801763	+	1.38869i
$221$	−0.602228	−	1.04309i	−0.0405102	−	0.0701658i
$222$	5.90823	−	10.2334i	0.396535	−	0.686818i
$223$	−19.7621			−1.32337			−0.661684	−	0.749783i	$-0.730158\pi$
$223$	−19.7621			−1.32337			−0.661684	+	0.749783i	$0.730158\pi$
$224$	5.86733	−	10.1625i	0.392028	−	0.679012i
$225$	−1.20310	−	2.08382i	−0.0802064	−	0.138922i
$226$	−7.07324			−0.470505
$227$	10.7636	+	18.6431i	0.714404	+	1.23738i	0.963189	+	0.268825i	$0.0866353\pi$
$227$	10.7636	+	18.6431i	0.714404	+	1.23738i	−0.248785	+	0.968559i	$0.580031\pi$
$228$	−3.65936	+	6.33819i	−0.242347	+	0.419757i
$229$	−12.2775	+	21.2653i	−0.811321	+	1.40525i	0.100619	+	0.994925i	$0.467918\pi$
$229$	−12.2775	+	21.2653i	−0.811321	+	1.40525i	−0.911940	+	0.410324i	$0.865416\pi$
$230$	4.78001	−	8.27923i	0.315185	−	0.545916i
$231$	32.9777			2.16977
$232$	−2.09857	+	3.63483i	−0.137778	+	0.238638i
$233$	1.93026	−	3.34331i	0.126455	−	0.219027i	−0.795845	−	0.605500i	$-0.792973\pi$
$233$	1.93026	−	3.34331i	0.126455	−	0.219027i	0.922301	+	0.386472i	$0.126307\pi$
$234$	0.842758	+	1.45970i	0.0550928	+	0.0954236i
$235$	−0.648999	−	1.12410i	−0.0423360	−	0.0733281i
$236$	−15.7795			−1.02716
$237$	−18.8478			−1.22430
$238$	−0.570332	−	0.987844i	−0.0369691	−	0.0640324i
$239$	−12.6429	−	21.8982i	−0.817802	−	1.41647i	−0.907298	−	0.420487i	$-0.861859\pi$
$239$	−12.6429	−	21.8982i	−0.817802	−	1.41647i	0.0894966	−	0.995987i	$-0.471474\pi$
$240$	8.03891	−	13.9238i	0.518909	−	0.898777i
$241$	5.40172	−	9.35605i	0.347955	−	0.602676i	−0.637931	−	0.770094i	$-0.720209\pi$
$241$	5.40172	−	9.35605i	0.347955	−	0.602676i	0.985886	+	0.167418i	$0.0535428\pi$
$242$	9.26637			0.595665
$243$	−11.0065	+	19.0639i	−0.706069	+	1.22295i
$244$	5.37850	−	9.31584i	0.344323	−	0.596386i
$245$	1.31184	−	2.27217i	0.0838102	−	0.145163i
$246$	−4.90212	−	8.49072i	−0.312548	−	0.541348i
$247$	−2.02479			−0.128834
$248$	−2.61213	−	4.52434i	−0.165870	−	0.287296i
$249$	−0.837212	+	1.45009i	−0.0530561	+	0.0918959i
$250$	−4.74068			−0.299827
$251$	−3.07673	+	5.32906i	−0.194202	+	0.336367i	−0.946638	−	0.322297i	$-0.895545\pi$
$251$	−3.07673	+	5.32906i	−0.194202	+	0.336367i	0.752437	+	0.658664i	$0.228878\pi$
$252$	−6.45392	−	11.1785i	−0.406559	−	0.704181i
$253$	23.4463	+	40.6102i	1.47406	+	2.55314i
$254$	1.22706			0.0769929
$255$	−2.94704	−	5.10443i	−0.184551	−	0.319652i
$256$	1.15116			0.0719475
$257$	−3.37336			−0.210425			−0.105212	−	0.994450i	$-0.533552\pi$
$257$	−3.37336			−0.210425			−0.105212	+	0.994450i	$0.533552\pi$
$258$	5.80003	+	4.79427i	0.361094	+	0.298478i
$259$	−25.0354			−1.55562
$260$	5.16593			0.320377
$261$	3.52977	+	6.11374i	0.218487	+	0.378431i
$262$	−4.10834			−0.253814
$263$	5.74822	+	9.95622i	0.354451	+	0.613927i	0.987024	−	0.160574i	$-0.0513346\pi$
$263$	5.74822	+	9.95622i	0.354451	+	0.613927i	−0.632573	+	0.774501i	$0.718001\pi$
$264$	−12.0268	−	20.8311i	−0.740199	−	1.28206i
$265$	−15.5181	+	26.8781i	−0.953268	+	1.65111i
$266$	−1.91755			−0.117573
$267$	−4.33729	+	7.51240i	−0.265438	+	0.459752i
$268$	−5.54358	−	9.60176i	−0.338628	−	0.586521i
$269$	18.5934			1.13366			0.566829	−	0.823835i	$-0.308170\pi$
$269$	18.5934			1.13366			0.566829	+	0.823835i	$0.308170\pi$
$270$	−0.0237968	−	0.0412172i	−0.00144823	−	0.00250840i
$271$	−9.35483	+	16.2030i	−0.568265	+	0.984265i	0.428472	+	0.903555i	$0.359052\pi$
$271$	−9.35483	+	16.2030i	−0.568265	+	0.984265i	−0.996738	+	0.0807097i	$0.974281\pi$
$272$	1.36389	−	2.36233i	0.0826982	−	0.143238i
$273$	3.58138	−	6.20314i	0.216755	−	0.375431i
$274$	−7.61079			−0.459785
$275$	−2.23670	+	3.87408i	−0.134878	+	0.233616i
$276$	18.4073	−	31.8824i	1.10799	−	1.91909i
$277$	2.34852	+	4.06775i	0.141109	+	0.244408i	0.927914	−	0.372793i	$-0.121600\pi$
$277$	2.34852	+	4.06775i	0.141109	+	0.244408i	−0.786806	+	0.617201i	$0.788267\pi$
$278$	4.23251	+	7.33092i	0.253849	+	0.439679i
$279$	−8.78715			−0.526073
$280$	10.3897			0.620901
$281$	−12.3267	−	21.3505i	−0.735352	−	1.27367i	−0.954569	−	0.297990i	$-0.903684\pi$
$281$	−12.3267	−	21.3505i	−0.735352	−	1.27367i	0.219217	−	0.975676i	$-0.429650\pi$
$282$	0.309066	+	0.535318i	0.0184046	+	0.0318777i
$283$	−2.63158	+	4.55803i	−0.156431	+	0.270947i	−0.933579	−	0.358371i	$-0.883332\pi$
$283$	−2.63158	+	4.55803i	−0.156431	+	0.270947i	0.777148	+	0.629318i	$0.216666\pi$
$284$	−5.99952	+	10.3915i	−0.356006	+	0.616621i
$285$	−9.90845			−0.586926
$286$	1.56679	−	2.71376i	0.0926462	−	0.160468i
$287$	−10.3860	+	17.9892i	−0.613069	+	1.06187i
$288$	−7.19822	+	12.4677i	−0.424159	+	0.734665i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−2.67571			−0.157123
$291$	−1.86549	−	3.23112i	−0.109357	−	0.189411i
$292$	5.89692	−	10.2138i	0.345091	−	0.597716i
$293$	−29.6786			−1.73384			−0.866921	−	0.498445i	$-0.833905\pi$
$293$	−29.6786			−1.73384			−0.866921	+	0.498445i	$0.833905\pi$
$294$	−0.624722	+	1.08205i	−0.0364345	+	0.0631065i
$295$	−10.6815	−	18.5010i	−0.621904	−	1.07717i
$296$	9.13030	+	15.8141i	0.530688	+	0.919178i
$297$	0.233450			0.0135461
$298$	−0.100790	−	0.174574i	−0.00583863	−	0.0101128i
$299$	10.1851			0.589020
$300$	3.51199			0.202765
$301$	2.65248	−	15.7209i	0.152886	−	0.906137i
$302$	−9.25544			−0.532591
$303$	33.6718			1.93440
$304$	−2.29282	−	3.97128i	−0.131502	−	0.227769i
$305$	14.5634			0.833898
$306$	0.699701	+	1.21192i	0.0399992	+	0.0692807i
$307$	7.62297	+	13.2034i	0.435066	+	0.753556i	0.997301	−	0.0734215i	$-0.0233918\pi$
$307$	7.62297	+	13.2034i	0.435066	+	0.753556i	−0.562235	+	0.826977i	$0.690058\pi$
$308$	−11.9986	+	20.7822i	−0.683685	+	1.18418i
$309$	−7.36026			−0.418711
$310$	1.66525	−	2.88430i	0.0945799	−	0.163817i
$311$	−0.131831	−	0.228338i	−0.00747546	−	0.0129479i	0.862263	−	0.506460i	$-0.169046\pi$
$311$	−0.131831	−	0.228338i	−0.00747546	−	0.0129479i	−0.869739	+	0.493512i	$0.835713\pi$
$312$	−5.22446			−0.295777
$313$	2.53402	+	4.38905i	0.143231	+	0.248084i	0.928712	−	0.370803i	$-0.120917\pi$
$313$	2.53402	+	4.38905i	0.143231	+	0.248084i	−0.785480	+	0.618887i	$0.787584\pi$
$314$	−1.96493	+	3.40336i	−0.110887	+	0.192063i
$315$	8.73766	−	15.1341i	0.492311	−	0.852708i
$316$	6.85761	−	11.8777i	0.385771	−	0.668175i
$317$	27.9509			1.56988			0.784938	−	0.619574i	$-0.212695\pi$
$317$	27.9509			1.56988			0.784938	+	0.619574i	$0.212695\pi$
$318$	7.39001	−	12.7999i	0.414411	−	0.717781i
$319$	6.56227	−	11.3662i	0.367417	−	0.636384i
$320$	3.84491	+	6.65958i	0.214937	+	0.372282i
$321$	11.9452	+	20.6896i	0.666714	+	1.15478i
$322$	9.64568			0.537533
$323$	−1.68108			−0.0935381
$324$	−8.05519	−	13.9520i	−0.447511	−	0.775111i
$325$	0.485813	+	0.841452i	0.0269480	+	0.0466754i
$326$	1.79951	−	3.11684i	0.0996655	−	0.172626i
$327$	17.5071	−	30.3232i	0.968145	−	1.67688i
$328$	15.1510			0.836574
$329$	0.654813	−	1.13417i	0.0361010	−	0.0625288i
$330$	7.66719	−	13.2800i	0.422065	−	0.731037i
$331$	−9.04798	+	15.6716i	−0.497322	+	0.861387i	−0.999995	−	0.00308935i	$-0.999017\pi$
$331$	−9.04798	+	15.6716i	−0.497322	+	0.861387i	0.502673	+	0.864477i	$0.332350\pi$
$332$	−0.609223	−	1.05521i	−0.0334355	−	0.0579120i
$333$	30.7141			1.68312
$334$	0.980106	+	1.69759i	0.0536290	+	0.0928882i
$335$	7.50518	−	12.9994i	0.410052	−	0.710231i
$336$	16.2219			0.884975
$337$	−5.30362	+	9.18613i	−0.288906	+	0.500400i	−0.973549	−	0.228478i	$-0.926625\pi$
$337$	−5.30362	+	9.18613i	−0.288906	+	0.500400i	0.684643	+	0.728879i	$0.259958\pi$
$338$	2.70922	+	4.69251i	0.147362	+	0.255239i
$339$	−18.4383	−	31.9361i	−1.00143	−	1.73453i
$340$	4.28902			0.232605
$341$	8.16818	+	14.1477i	0.442332	+	0.766141i
$342$	2.35251			0.127209
$343$	19.6663			1.06188
$344$	−10.8978	+	4.05785i	−0.587569	+	0.218784i
$345$	49.8415			2.68338
$346$	9.78864			0.526241
$347$	0.847047	+	1.46713i	0.0454719	+	0.0787596i	0.887866	−	0.460103i	$-0.152188\pi$
$347$	0.847047	+	1.46713i	0.0454719	+	0.0787596i	−0.842394	+	0.538863i	$0.818854\pi$
$348$	−10.3038			−0.552344
$349$	−2.05372	−	3.55715i	−0.109933	−	0.190410i	0.805810	−	0.592174i	$-0.201730\pi$
$349$	−2.05372	−	3.55715i	−0.109933	−	0.190410i	−0.915743	+	0.401765i	$0.868397\pi$
$350$	0.460083	+	0.796887i	0.0245925	+	0.0425954i
$351$	0.0253527	−	0.0439122i	0.00135323	−	0.00234386i
$352$	26.7647			1.42656
$353$	−0.239974	+	0.415647i	−0.0127725	+	0.0221227i	−0.872341	−	0.488898i	$-0.837399\pi$
$353$	−0.239974	+	0.415647i	−0.0127725	+	0.0221227i	0.859568	+	0.511021i	$0.170732\pi$
$354$	5.08676	+	8.81053i	0.270358	+	0.468274i
$355$	−16.2449			−0.862192
$356$	−3.15617	−	5.46664i	−0.167276	−	0.289731i
$357$	2.97345	−	5.15016i	0.157371	−	0.272575i
$358$	−4.65072	+	8.05529i	−0.245798	+	0.425735i
$359$	13.6448	−	23.6335i	0.720146	−	1.24733i	−0.240795	−	0.970576i	$-0.577408\pi$
$359$	13.6448	−	23.6335i	0.720146	−	1.24733i	0.960941	−	0.276753i	$-0.0892584\pi$
$360$	−12.7464			−0.671792
$361$	8.08698	−	14.0071i	0.425630	−	0.737213i
$362$	−3.21050	+	5.56074i	−0.168740	+	0.292266i
$363$	24.1553	+	41.8381i	1.26782	+	2.19593i
$364$	2.60611	+	4.51391i	0.136597	+	0.236593i
$365$	15.9671			0.835758
$366$	−6.93538			−0.362518
$367$	2.33913	+	4.05150i	0.122102	+	0.211487i	0.920596	−	0.390515i	$-0.127703\pi$
$367$	2.33913	+	4.05150i	0.122102	+	0.211487i	−0.798495	+	0.602002i	$0.794370\pi$
$368$	11.5334	+	19.9764i	0.601218	+	1.04134i
$369$	12.7419	−	22.0696i	0.663317	−	1.14890i
$370$	−5.82063	+	10.0816i	−0.302600	+	0.524119i
$371$	−31.3142			−1.62575
$372$	6.41270	−	11.1071i	0.332483	−	0.575877i
$373$	−0.198338	+	0.343532i	−0.0102696	+	0.0177874i	−0.871115	−	0.491080i	$-0.836602\pi$
$373$	−0.198338	+	0.343532i	−0.0102696	+	0.0177874i	0.860845	+	0.508867i	$0.169936\pi$
$374$	1.30083	−	2.25310i	0.0672642	−	0.116505i
$375$	−12.3579	−	21.4044i	−0.638157	−	1.10532i
$376$	−0.955231			−0.0492623
$377$	−1.42533	−	2.46874i	−0.0734081	−	0.127147i
$378$	0.0240100	−	0.0415865i	0.00123494	−	0.00213898i
$379$	−9.16932			−0.470996			−0.235498	−	0.971875i	$-0.575672\pi$
$379$	−9.16932			−0.470996			−0.235498	+	0.971875i	$0.575672\pi$
$380$	3.60510	−	6.24421i	0.184938	−	0.320321i
$381$	3.19867	+	5.54026i	0.163873	+	0.283836i
$382$	−0.140242	−	0.242905i	−0.00717538	−	0.0124281i
$383$	32.4990			1.66062			0.830312	−	0.557299i	$-0.188162\pi$
$383$	32.4990			1.66062			0.830312	+	0.557299i	$0.188162\pi$
$384$	−13.6365	−	23.6191i	−0.695886	−	1.20531i
$385$	−32.4887			−1.65578
$386$	−0.586414			−0.0298477
$387$	−3.25414	+	19.2869i	−0.165417	+	0.980406i
$388$	2.71496			0.137831
$389$	25.6446			1.30023			0.650116	−	0.759835i	$-0.274720\pi$
$389$	25.6446			1.30023			0.650116	+	0.759835i	$0.274720\pi$
$390$	−1.66532	−	2.88441i	−0.0843266	−	0.146058i
$391$	8.45619			0.427648
$392$	−0.965416	−	1.67215i	−0.0487608	−	0.0844563i
$393$	−10.7095	−	18.5494i	−0.540222	−	0.935692i
$394$	−0.963987	+	1.66967i	−0.0485650	+	0.0841170i
$395$	18.5684			0.934277
$396$	14.7203	−	25.4962i	0.739721	−	1.28123i
$397$	−4.52898	−	7.84443i	−0.227303	−	0.393701i	0.729705	−	0.683762i	$-0.239657\pi$
$397$	−4.52898	−	7.84443i	−0.227303	−	0.393701i	−0.957008	+	0.290062i	$0.906324\pi$
$398$	5.70143			0.285787
$399$	−4.99861	−	8.65785i	−0.250244	−	0.433435i
$400$	−1.10024	+	1.90568i	−0.0550122	+	0.0952839i
$401$	4.68840	−	8.12055i	0.234128	−	0.405521i	−0.724891	−	0.688863i	$-0.758110\pi$
$401$	4.68840	−	8.12055i	0.234128	−	0.405521i	0.959019	+	0.283343i	$0.0914433\pi$
$402$	−3.57412	+	6.19055i	−0.178261	+	0.308757i
$403$	3.54827			0.176752
$404$	−12.2512	+	21.2197i	−0.609520	+	1.05572i
$405$	10.9055	−	18.8889i	0.541901	−	0.938599i
$406$	−1.34984	−	2.33799i	−0.0669914	−	0.116032i
$407$	−28.5506	−	49.4511i	−1.41520	−	2.45120i
$408$	−4.33761			−0.214744
$409$	−12.2302			−0.604745			−0.302373	−	0.953190i	$-0.597779\pi$
$409$	−12.2302			−0.604745			−0.302373	+	0.953190i	$0.597779\pi$
$410$	4.82943	+	8.36483i	0.238509	+	0.413109i
$411$	−19.8395	−	34.3631i	−0.978613	−	1.69501i
$412$	2.67796	−	4.63837i	0.131934	−	0.228516i
$413$	10.7772	−	18.6667i	0.530314	−	0.918530i
$414$	−11.8336			−0.581590
$415$	0.824799	−	1.42859i	0.0404878	−	0.0701269i
$416$	2.90665	−	5.03447i	0.142510	−	0.246835i
$417$	−22.0663	+	38.2200i	−1.08059	+	1.87164i
$418$	−2.18680	−	3.78765i	−0.106960	−	0.185260i
$419$	6.27652			0.306628			0.153314	−	0.988178i	$-0.451005\pi$
$419$	6.27652			0.306628			0.153314	+	0.988178i	$0.451005\pi$
$420$	12.7532	+	22.0891i	0.622290	+	1.07784i
$421$	−7.91138	+	13.7029i	−0.385577	+	0.667839i	−0.991849	−	0.127418i	$-0.959331\pi$
$421$	−7.91138	+	13.7029i	−0.385577	+	0.667839i	0.606272	+	0.795257i	$0.292664\pi$
$422$	−9.50298			−0.462598
$423$	−0.803345	+	1.39143i	−0.0390599	+	0.0676538i
$424$	11.4202	+	19.7803i	0.554612	+	0.960616i
$425$	0.403346	+	0.698616i	0.0195652	+	0.0338879i
$426$	7.73616			0.374818
$427$	7.34694	+	12.7253i	0.355543	+	0.615819i
$428$	−17.3845			−0.840313
$429$	16.3370			0.788758
$430$	−5.71404	−	4.72319i	−0.275555	−	0.227772i
$431$	23.7291			1.14299			0.571496	−	0.820605i	$-0.306363\pi$
$431$	23.7291			1.14299			0.571496	+	0.820605i	$0.306363\pi$
$432$	0.114835			0.00552501
$433$	−8.27790	−	14.3377i	−0.397811	−	0.689028i	0.595645	−	0.803248i	$-0.296897\pi$
$433$	−8.27790	−	14.3377i	−0.397811	−	0.689028i	−0.993456	+	0.114220i	$0.963563\pi$
$434$	3.36034			0.161302
$435$	−6.97494	−	12.0809i	−0.334423	−	0.579237i
$436$	12.7396	+	22.0656i	0.610116	+	1.05675i
$437$	7.10779	−	12.3111i	0.340012	−	0.588917i
$438$	−7.60386			−0.363326
$439$	−14.8563	+	25.7318i	−0.709052	+	1.22811i	0.256158	+	0.966635i	$0.417543\pi$
$439$	−14.8563	+	25.7318i	−0.709052	+	1.22811i	−0.965209	+	0.261479i	$0.915790\pi$
$440$	11.8485	+	20.5222i	0.564855	+	0.978357i
$441$	−3.24764			−0.154649
$442$	−0.282540	−	0.489374i	−0.0134391	−	0.0232772i
$443$	−17.5183	+	30.3426i	−0.832320	+	1.44162i	0.0638732	+	0.997958i	$0.479655\pi$
$443$	−17.5183	+	30.3426i	−0.832320	+	1.44162i	−0.896194	+	0.443663i	$0.853679\pi$
$444$	−22.4146	+	38.8232i	−1.06375	+	1.84247i
$445$	4.27298	−	7.40102i	0.202559	−	0.350842i
$446$	−9.27156			−0.439021
$447$	0.525474	−	0.910148i	0.0248541	−	0.0430485i
$448$	−3.87936	+	6.71924i	−0.183282	+	0.317454i
$449$	5.41794	+	9.38414i	0.255688	+	0.442865i	0.965082	−	0.261947i	$-0.0843646\pi$
$449$	5.41794	+	9.38414i	0.255688	+	0.442865i	−0.709394	+	0.704812i	$0.751031\pi$
$450$	−0.564443	−	0.977644i	−0.0266081	−	0.0460866i
$451$	−47.3775			−2.23092
$452$	26.8344			1.26218
$453$	−24.1268	−	41.7888i	−1.13357	−	1.96341i
$454$	5.04983	+	8.74656i	0.237000	+	0.410496i
$455$	−3.52828	+	6.11116i	−0.165408	+	0.286496i
$456$	−3.64595	+	6.31497i	−0.170737	+	0.295725i
$457$	9.02952			0.422383			0.211192	−	0.977445i	$-0.432266\pi$
$457$	9.02952			0.422383			0.211192	+	0.977445i	$0.432266\pi$
$458$	−5.76010	+	9.97679i	−0.269152	+	0.466185i
$459$	0.0210491	−	0.0364581i	0.000982489	−	0.00170172i
$460$	−18.1344	+	31.4097i	−0.845519	+	1.46448i
$461$	−15.0723	−	26.1060i	−0.701988	−	1.21588i	−0.967768	−	0.251845i	$-0.918963\pi$
$461$	−15.0723	−	26.1060i	−0.701988	−	1.21588i	0.265779	−	0.964034i	$-0.414371\pi$
$462$	15.4718			0.719811
$463$	18.7387	+	32.4564i	0.870863	+	1.50838i	0.861106	+	0.508426i	$0.169772\pi$
$463$	18.7387	+	32.4564i	0.870863	+	1.50838i	0.00975673	+	0.999952i	$0.496894\pi$
$464$	3.22801	−	5.59108i	0.149857	−	0.259559i
$465$	17.3637			0.805222
$466$	0.905598	−	1.56854i	0.0419510	−	0.0726613i
$467$	3.17399	+	5.49751i	0.146875	+	0.254394i	0.930071	−	0.367380i	$-0.119745\pi$
$467$	3.17399	+	5.49751i	0.146875	+	0.254394i	−0.783196	+	0.621775i	$0.786412\pi$
$468$	−3.19725	−	5.53780i	−0.147793	−	0.255985i
$469$	15.1449			0.699324
$470$	−0.304483	−	0.527381i	−0.0140448	−	0.0243263i
$471$	−20.4884			−0.944058
$472$	−15.7217			−0.723649
$473$	34.0776	−	12.6890i	1.56689	−	0.583440i
$474$	−8.84263			−0.406155
$475$	1.35612			0.0622230
$476$	2.16372	+	3.74767i	0.0991740	+	0.171774i
$477$	38.4172			1.75900
$478$	−5.93153	−	10.2737i	−0.271302	−	0.469909i
$479$	−0.819851	−	1.42002i	−0.0374599	−	0.0648825i	0.846688	−	0.532090i	$-0.178593\pi$
$479$	−0.819851	−	1.42002i	−0.0374599	−	0.0648825i	−0.884148	+	0.467208i	$0.845260\pi$
$480$	14.2239	−	24.6365i	0.649229	−	1.12450i
$481$	−12.4024			−0.565502
$482$	2.53426	−	4.38947i	0.115432	−	0.199935i
$483$	25.1440	+	43.5507i	1.14409	+	1.98163i
$484$	−35.1547			−1.59794
$485$	1.83783	+	3.18321i	0.0834514	+	0.144542i
$486$	−5.16381	+	8.94397i	−0.234235	+	0.405707i
$487$	12.5725	−	21.7762i	0.569714	−	0.986774i	−0.426880	−	0.904308i	$-0.640387\pi$
$487$	12.5725	−	21.7762i	0.569714	−	0.986774i	0.996594	−	0.0824653i	$-0.0262794\pi$
$488$	5.35880	−	9.28171i	0.242581	−	0.420163i
$489$	18.7636			0.848518
$490$	0.615460	−	1.06601i	0.0278036	−	0.0481573i
$491$	4.75429	−	8.23468i	0.214558	−	0.371626i	−0.738578	−	0.674169i	$-0.764502\pi$
$491$	4.75429	−	8.23468i	0.214558	−	0.371626i	0.953136	+	0.302543i	$0.0978355\pi$
$492$	18.5976	+	32.2120i	0.838445	+	1.45223i
$493$	−1.18338	−	2.04967i	−0.0532967	−	0.0923127i
$494$	−0.949949			−0.0427402
$495$	39.8581			1.79149
$496$	4.01797	+	6.95932i	0.180412	+	0.312483i
$497$	−8.19524	−	14.1946i	−0.367607	−	0.636714i
$498$	−0.392785	+	0.680324i	−0.0176011	+	0.0304860i
$499$	−1.89983	+	3.29060i	−0.0850480	+	0.147308i	−0.905412	−	0.424535i	$-0.860438\pi$
$499$	−1.89983	+	3.29060i	−0.0850480	+	0.147308i	0.820364	+	0.571842i	$0.193771\pi$
$500$	17.9852			0.804321
$501$	−5.10981	+	8.85046i	−0.228290	+	0.395409i
$502$	−1.44348	+	2.50017i	−0.0644255	+	0.111588i
$503$	−6.39530	+	11.0770i	−0.285152	+	0.493898i	−0.972646	−	0.232292i	$-0.925378\pi$
$503$	−6.39530	+	11.0770i	−0.285152	+	0.493898i	0.687494	+	0.726190i	$0.258711\pi$
$504$	−6.43028	−	11.1376i	−0.286427	−	0.496107i
$505$	−33.1726			−1.47616
$506$	11.0000	+	19.0526i	0.489012	+	0.846993i
$507$	−14.1246	+	24.4646i	−0.627297	+	1.08651i
$508$	−4.65523			−0.206542
$509$	12.0725	−	20.9103i	0.535106	−	0.926831i	−0.464052	−	0.885808i	$-0.653605\pi$
$509$	12.0725	−	20.9103i	0.535106	−	0.926831i	0.999158	−	0.0410228i	$-0.0130616\pi$
$510$	−1.38263	−	2.39479i	−0.0612239	−	0.106043i
$511$	8.05509	+	13.9518i	0.356336	+	0.617192i
$512$	22.8404			1.00941
$513$	−0.0353854	−	0.0612892i	−0.00156230	−	0.00270599i
$514$	−1.58264			−0.0698074
$515$	7.25113			0.319523
$516$	−22.0041	−	18.1885i	−0.968677	−	0.800703i
$517$	2.98703			0.131369
$518$	−11.7456			−0.516070
$519$	25.5167	+	44.1962i	1.12006	+	1.94000i
$520$	5.14700			0.225711
$521$	−21.6857	−	37.5607i	−0.950066	−	1.64556i	−0.745276	−	0.666757i	$-0.767682\pi$
$521$	−21.6857	−	37.5607i	−0.950066	−	1.64556i	−0.204790	−	0.978806i	$-0.565651\pi$
$522$	1.65602	+	2.86832i	0.0724822	+	0.125543i
$523$	1.49321	−	2.58631i	0.0652933	−	0.113091i	−0.831531	−	0.555479i	$-0.812535\pi$
$523$	1.49321	−	2.58631i	0.0652933	−	0.113091i	0.896824	+	0.442387i	$0.145868\pi$
$524$	15.5862			0.680886
$525$	−2.39866	+	4.15459i	−0.104686	+	0.181321i
$526$	2.69683	+	4.67105i	0.117587	+	0.203667i
$527$	2.94595			0.128328
$528$	18.4996	+	32.0423i	0.805092	+	1.39446i
$529$	−24.2536	+	42.0085i	−1.05450	+	1.82646i
$530$	−7.28044	+	12.6101i	−0.316242	+	0.547747i
$531$	−13.2219	+	22.9009i	−0.573779	+	0.993815i
$532$	7.27480			0.315402
$533$	−5.14521	+	8.91176i	−0.222864	+	0.386011i
$534$	−2.03488	+	3.52451i	−0.0880577	+	0.152520i
$535$	−11.7680	−	20.3829i	−0.508777	−	0.881228i
$536$	−5.52327	−	9.56658i	−0.238569	−	0.413213i
$537$	−48.4934			−2.09264
$538$	8.72325			0.376086
$539$	3.01888	+	5.22885i	0.130032	+	0.225222i
$540$	0.0902800	+	0.156370i	0.00388503	+	0.00672907i
$541$	1.69442	−	2.93483i	0.0728489	−	0.126178i	−0.827300	−	0.561761i	$-0.810124\pi$
$541$	1.69442	−	2.93483i	0.0728489	−	0.126178i	0.900149	+	0.435582i	$0.143458\pi$
$542$	−4.38890	+	7.60180i	−0.188519	+	0.326525i
$543$	−33.4760			−1.43659
$544$	2.41325	−	4.17987i	0.103467	−	0.179211i
$545$	−17.2475	+	29.8736i	−0.738803	+	1.27964i
$546$	1.68024	−	2.91026i	0.0719075	−	0.124547i
$547$	−6.71750	−	11.6350i	−0.287219	−	0.497479i	0.685926	−	0.727672i	$-0.259398\pi$
$547$	−6.71750	−	11.6350i	−0.287219	−	0.497479i	−0.973145	+	0.230193i	$0.926064\pi$
$548$	28.8737			1.23343
$549$	−9.01345	−	15.6117i	−0.384685	−	0.666293i
$550$	−1.04937	+	1.81756i	−0.0447452	+	0.0775009i
$551$	−3.97872			−0.169499
$552$	18.3398	−	31.7655i	0.780596	−	1.35203i
$553$	9.36737	+	16.2248i	0.398341	+	0.689947i
$554$	1.10183	+	1.90842i	0.0468122	+	0.0810811i
$555$	−60.6921			−2.57624
$556$	−16.0572	−	27.8120i	−0.680979	−	1.17949i
$557$	2.04567			0.0866776			0.0433388	−	0.999060i	$-0.486201\pi$
$557$	2.04567			0.0866776			0.0433388	+	0.999060i	$0.486201\pi$
$558$	−4.12257			−0.174522
$559$	1.31403	−	7.78807i	0.0555775	−	0.329400i
$560$	−15.9813			−0.675335
$561$	13.5638			0.572665
$562$	−5.78320	−	10.0168i	−0.243949	−	0.422533i
$563$	9.26283			0.390382			0.195191	−	0.980765i	$-0.437467\pi$
$563$	9.26283			0.390382			0.195191	+	0.980765i	$0.437467\pi$
$564$	−1.17253	−	2.03088i	−0.0493725	−	0.0855156i
$565$	18.1649	+	31.4625i	0.764203	+	1.32364i
$566$	−1.23463	+	2.13844i	−0.0518953	+	0.0898853i
$567$	22.0065			0.924186
$568$	−5.97754	+	10.3534i	−0.250812	+	0.434419i
$569$	−21.1653	−	36.6595i	−0.887297	−	1.53684i	−0.843058	−	0.537823i	$-0.819247\pi$
$569$	−21.1653	−	36.6595i	−0.887297	−	1.53684i	−0.0442397	−	0.999021i	$-0.514087\pi$
$570$	−4.64864			−0.194710
$571$	2.78784	+	4.82869i	0.116668	+	0.202074i	0.918445	−	0.395548i	$-0.129445\pi$
$571$	2.78784	+	4.82869i	0.116668	+	0.202074i	−0.801778	+	0.597623i	$0.796112\pi$
$572$	−5.94407	+	10.2954i	−0.248534	+	0.430474i
$573$	0.731154	−	1.26640i	0.0305444	−	0.0529044i
$574$	−4.87270	+	8.43977i	−0.203383	+	0.352269i
$575$	−6.82155			−0.284478
$576$	4.75931	−	8.24337i	0.198305	−	0.343474i
$577$	0.504170	−	0.873248i	0.0209889	−	0.0363538i	−0.855340	−	0.518067i	$-0.826652\pi$
$577$	0.504170	−	0.873248i	0.0209889	−	0.0363538i	0.876329	+	0.481713i	$0.159985\pi$
$578$	−0.234579	−	0.406303i	−0.00975722	−	0.0169000i
$579$	−1.52864	−	2.64769i	−0.0635283	−	0.110034i
$580$	10.1511			0.421500
$581$	1.66438			0.0690500
$582$	−0.875209	−	1.51591i	−0.0362786	−	0.0628363i
$583$	−35.7111	−	61.8534i	−1.47900	−	2.56171i
$584$	5.87532	−	10.1763i	0.243122	−	0.421100i
$585$	4.32860	−	7.49736i	0.178966	−	0.309978i
$586$	−13.9240			−0.575194
$587$	14.3255	−	24.8125i	0.591276	−	1.02412i	−0.402784	−	0.915295i	$-0.631958\pi$
$587$	14.3255	−	24.8125i	0.591276	−	1.02412i	0.994061	−	0.108826i	$-0.0347091\pi$
$588$	2.37007	−	4.10507i	0.0977398	−	0.169290i
$589$	2.47620	−	4.28890i	0.102030	−	0.176721i
$590$	−5.01134	−	8.67990i	−0.206314	−	0.357346i
$591$	−10.0516			−0.413466
$592$	−14.0442	−	24.3252i	−0.577213	−	0.999761i
$593$	−0.412859	+	0.715093i	−0.0169541	+	0.0293653i	−0.874378	−	0.485245i	$-0.838730\pi$
$593$	−0.412859	+	0.715093i	−0.0169541	+	0.0293653i	0.857424	+	0.514611i	$0.172064\pi$
$594$	0.109525			0.00449387
$595$	−2.92936	+	5.07380i	−0.120092	+	0.208005i
$596$	0.382378	+	0.662298i	0.0156628	+	0.0271288i
$597$	14.8623	+	25.7422i	0.608273	+	1.05356i
$598$	4.77843			0.195405
$599$	−6.81784	−	11.8088i	−0.278569	−	0.482496i	0.692460	−	0.721456i	$-0.256527\pi$
$599$	−6.81784	−	11.8088i	−0.278569	−	0.482496i	−0.971029	+	0.238960i	$0.923194\pi$
$600$	3.49912			0.142851
$601$	−20.8449			−0.850281			−0.425141	−	0.905127i	$-0.639775\pi$
$601$	−20.8449			−0.850281			−0.425141	+	0.905127i	$0.639775\pi$
$602$	1.24443	−	7.37559i	0.0507193	−	0.300607i
$603$	−18.5802			−0.756643
$604$	35.1132			1.42874
$605$	−23.7971	−	41.2178i	−0.967490	−	1.67574i
$606$	15.7974			0.641727
$607$	−9.51473	−	16.4800i	−0.386191	−	0.668902i	0.605743	−	0.795661i	$-0.292876\pi$
$607$	−9.51473	−	16.4800i	−0.386191	−	0.668902i	−0.991934	+	0.126758i	$0.959543\pi$
$608$	−4.05688	−	7.02672i	−0.164528	−	0.284971i
$609$	7.03743	−	12.1892i	0.285171	−	0.493931i
$610$	6.83255			0.276642
$611$	0.324392	−	0.561863i	0.0131235	−	0.0227306i
$612$	−2.65452	−	4.59776i	−0.107303	−	0.185853i
$613$	−11.8513			−0.478668			−0.239334	−	0.970937i	$-0.576929\pi$
$613$	−11.8513			−0.478668			−0.239334	+	0.970937i	$0.576929\pi$
$614$	3.57638	+	6.19447i	0.144331	+	0.249989i
$615$	−25.1784	+	43.6103i	−1.01529	+	1.75854i
$616$	−11.9547	+	20.7061i	−0.481667	+	0.834271i
$617$	17.9486	−	31.0879i	0.722584	−	1.25155i	−0.237377	−	0.971418i	$-0.576288\pi$
$617$	17.9486	−	31.0879i	0.722584	−	1.25155i	0.959961	−	0.280134i	$-0.0903790\pi$
$618$	−3.45313			−0.138905
$619$	−8.58500	+	14.8697i	−0.345060	+	0.597662i	−0.985365	−	0.170459i	$-0.945475\pi$
$619$	−8.58500	+	14.8697i	−0.345060	+	0.597662i	0.640304	+	0.768121i	$0.278808\pi$
$620$	−6.31762	+	10.9424i	−0.253722	+	0.439459i
$621$	0.177995	+	0.308297i	0.00714271	+	0.0123715i
$622$	−0.0618497	−	0.107127i	−0.00247995	−	0.00429540i
$623$	8.62253			0.345454
$624$	8.03625			0.321707
$625$	14.1914	+	24.5801i	0.567654	+	0.983206i
$626$	1.18886	+	2.05916i	0.0475163	+	0.0823007i
$627$	11.4010	−	19.7470i	0.455310	−	0.788621i
$628$	7.45453	−	12.9116i	0.297468	−	0.515230i
$629$	−10.2971			−0.410573
$630$	4.09935	−	7.10028i	0.163322	−	0.282882i
$631$	12.8843	−	22.3163i	0.512916	−	0.888397i	−0.486972	−	0.873418i	$-0.661899\pi$
$631$	12.8843	−	22.3163i	0.512916	−	0.888397i	0.999888	−	0.0149789i	$-0.00476810\pi$
$632$	6.83248	−	11.8342i	0.271782	−	0.470740i
$633$	−24.7720	−	42.9064i	−0.984600	−	1.70538i
$634$	13.1134			0.520799
$635$	−3.15124	−	5.45811i	−0.125053	−	0.216599i
$636$	−28.0361	+	48.5600i	−1.11171	+	1.92553i
$637$	1.31140			0.0519597
$638$	3.07875	−	5.33254i	0.121889	−	0.211117i
$639$	10.0542	+	17.4143i	0.397737	+	0.688900i
$640$	13.4343	+	23.2689i	0.531039	+	0.919786i
$641$	41.5637			1.64167			0.820833	−	0.571168i	$-0.193510\pi$
$641$	41.5637			1.64167			0.820833	+	0.571168i	$0.193510\pi$
$642$	5.60417	+	9.70671i	0.221179	+	0.383093i
$643$	11.9280			0.470396			0.235198	−	0.971947i	$-0.424426\pi$
$643$	11.9280			0.470396			0.235198	+	0.971947i	$0.424426\pi$
$644$	−36.5937			−1.44199
$645$	6.43029	−	38.1114i	0.253192	−	1.50064i
$646$	−0.788696			−0.0310308
$647$	−46.0062			−1.80869			−0.904345	−	0.426802i	$-0.859640\pi$
$647$	−46.0062			−1.80869			−0.904345	+	0.426802i	$0.859640\pi$
$648$	−8.02568	−	13.9009i	−0.315278	−	0.546078i
$649$	49.1620			1.92978
$650$	0.227923	+	0.394775i	0.00893988	+	0.0154843i
$651$	8.75963	+	15.1721i	0.343317	+	0.594642i
$652$	−6.82696	+	11.8246i	−0.267364	+	0.463088i
$653$	−39.3376			−1.53940			−0.769701	−	0.638405i	$-0.779594\pi$
$653$	−39.3376			−1.53940			−0.769701	+	0.638405i	$0.779594\pi$
$654$	8.21361	−	14.2264i	0.321177	−	0.556296i
$655$	10.5507	+	18.2743i	0.412250	+	0.714038i
$656$	−23.3052			−0.909915
$657$	−9.88223	−	17.1165i	−0.385542	−	0.667779i
$658$	0.307211	−	0.532106i	0.0119763	−	0.0207436i
$659$	−14.6725	+	25.4136i	−0.571560	+	0.989971i	0.424846	+	0.905266i	$0.360328\pi$
$659$	−14.6725	+	25.4136i	−0.571560	+	0.989971i	−0.996406	+	0.0847057i	$0.973005\pi$
$660$	−29.0877	+	50.3814i	−1.13224	+	1.96109i
$661$	30.9953			1.20558			0.602789	−	0.797901i	$-0.294056\pi$
$661$	30.9953			1.20558			0.602789	+	0.797901i	$0.294056\pi$
$662$	−4.24494	+	7.35245i	−0.164984	+	0.285761i
$663$	1.47303	−	2.55137i	0.0572079	−	0.0990870i
$664$	−0.606991	−	1.05134i	−0.0235558	−	0.0407999i
$665$	4.92450	+	8.52948i	0.190964	+	0.330759i
$666$	14.4098			0.558369
$667$	20.0138			0.774936
$668$	−3.71832	−	6.44031i	−0.143866	−	0.249183i
$669$	−24.1688	−	41.8616i	−0.934419	−	1.61846i
$670$	3.52112	−	6.09876i	0.136033	−	0.235616i
$671$	−16.7571	+	29.0241i	−0.646900	+	1.12046i
$672$	28.7027			1.10723
$673$	−10.8069	+	18.7181i	−0.416575	+	0.721530i	−0.995592	−	0.0937858i	$-0.970103\pi$
$673$	−10.8069	+	18.7181i	−0.416575	+	0.721530i	0.579017	+	0.815315i	$0.303436\pi$
$674$	−2.48824	+	4.30975i	−0.0958433	+	0.166006i
$675$	−0.0169802	+	0.0294105i	−0.000653567	+	0.00113201i
$676$	−10.2782	−	17.8024i	−0.395317	−	0.684708i
$677$	19.8967			0.764690			0.382345	−	0.924020i	$-0.375117\pi$
$677$	19.8967			0.764690			0.382345	+	0.924020i	$0.375117\pi$
$678$	−8.65048	−	14.9831i	−0.332220	−	0.575422i
$679$	−1.85429	+	3.21173i	−0.0711612	+	0.123255i
$680$	4.27330			0.163874
$681$	−26.3274	+	45.6004i	−1.00887	+	1.74741i
$682$	3.83217	+	6.63752i	0.146742	+	0.254164i
$683$	−1.69346	−	2.93316i	−0.0647986	−	0.112234i	0.831806	−	0.555066i	$-0.187307\pi$
$683$	−1.69346	−	2.93316i	−0.0647986	−	0.112234i	−0.896605	+	0.442832i	$0.853974\pi$
$684$	−8.92494			−0.341254
$685$	19.5454	+	33.8536i	0.746791	+	1.29348i
$686$	9.22660			0.352273
$687$	−60.0610			−2.29147
$688$	16.7629	−	6.24176i	0.639081	−	0.237965i
$689$	−15.5129			−0.590996
$690$	23.3836			0.890198
$691$	3.12067	+	5.40517i	0.118716	+	0.205622i	0.919259	−	0.393653i	$-0.128789\pi$
$691$	3.12067	+	5.40517i	0.118716	+	0.205622i	−0.800543	+	0.599275i	$0.795456\pi$
$692$	−37.1361			−1.41170
$693$	20.1076	+	34.8274i	0.763825	+	1.32298i
$694$	0.397400	+	0.688316i	0.0150851	+	0.0261281i
$695$	21.7391	−	37.6533i	0.824613	−	1.42827i
$696$	−10.2661			−0.389135
$697$	−4.27181	+	7.39899i	−0.161806	+	0.280257i
$698$	−0.963521	−	1.66887i	−0.0364698	−	0.0631676i
$699$	9.44273			0.357157
$700$	−1.74546	−	3.02322i	−0.0659721	−	0.114267i
$701$	19.0390	−	32.9765i	0.719092	−	1.24550i	−0.242267	−	0.970210i	$-0.577891\pi$
$701$	19.0390	−	32.9765i	0.719092	−	1.24550i	0.961360	−	0.275295i	$-0.0887756\pi$
$702$	0.0118945	−	0.0206018i	0.000448927	−	0.000777565i
$703$	−8.65517	+	14.9912i	−0.326436	+	0.565403i
$704$	−17.6963			−0.666953
$705$	1.58743	−	2.74952i	0.0597862	−	0.103553i
$706$	−0.112586	+	0.195004i	−0.00423723	+	0.00733909i
$707$	−16.7349	−	28.9857i	−0.629381	−	1.09012i
$708$	−19.2981	−	33.4253i	−0.725267	−	1.25620i
$709$	17.9802			0.675260			0.337630	−	0.941279i	$-0.390375\pi$
$709$	17.9802			0.675260			0.337630	+	0.941279i	$0.390375\pi$
$710$	−7.62145			−0.286028
$711$	−11.4922	−	19.9050i	−0.430990	−	0.746497i
$712$	−3.14460	−	5.44661i	−0.117849	−	0.204120i
$713$	−12.4558	+	21.5740i	−0.466472	+	0.807953i
$714$	1.39502	−	2.41624i	0.0522072	−	0.0904256i
$715$	−16.0948			−0.601911
$716$	17.6439	−	30.5601i	0.659382	−	1.14208i
$717$	30.9242	−	53.5623i	1.15489	−	2.00032i
$718$	6.40158	−	11.0879i	0.238905	−	0.413796i
$719$	5.14116	+	8.90475i	0.191733	+	0.332091i	0.945825	−	0.324678i	$-0.105256\pi$
$719$	5.14116	+	8.90475i	0.191733	+	0.332091i	−0.754092	+	0.656769i	$0.771923\pi$
$720$	19.6064			0.730687
$721$	3.65805	+	6.33593i	0.136233	+	0.235962i
$722$	3.79408	−	6.57153i	0.141201	−	0.244567i
$723$	26.4249			0.982753
$724$	12.1799	−	21.0963i	0.452664	−	0.784037i
$725$	0.954623	+	1.65346i	0.0354538	+	0.0614078i
$726$	11.3327	+	19.6287i	0.420594	+	0.728490i
$727$	5.44852			0.202074			0.101037	−	0.994883i	$-0.467784\pi$
$727$	5.44852			0.202074			0.101037	+	0.994883i	$0.467784\pi$
$728$	2.59656	+	4.49737i	0.0962348	+	0.166684i
$729$	−26.6893			−0.988493
$730$	7.49112			0.277259
$731$	1.09097	−	6.46605i	0.0403511	−	0.239155i
$732$	26.3114			0.972496
$733$	−40.6409			−1.50111			−0.750553	−	0.660811i	$-0.770213\pi$
$733$	−40.6409			−1.50111			−0.750553	+	0.660811i	$0.770213\pi$
$734$	1.09743	+	1.90080i	0.0405067	+	0.0701597i
$735$	6.41744			0.236711
$736$	20.4069	+	35.3458i	0.752209	+	1.30286i
$737$	17.2714	+	29.9149i	0.636199	+	1.10193i
$738$	5.97798	−	10.3542i	0.220052	−	0.381142i
$739$	−22.4700			−0.826571			−0.413286	−	0.910601i	$-0.635619\pi$
$739$	−22.4700			−0.826571			−0.413286	+	0.910601i	$0.635619\pi$
$740$	22.0823	−	38.2476i	0.811760	−	1.40601i
$741$	−2.47629	−	4.28907i	−0.0909689	−	0.157563i
$742$	−14.6913			−0.539336
$743$	−9.62588	−	16.6725i	−0.353139	−	0.611655i	0.633658	−	0.773613i	$-0.281553\pi$
$743$	−9.62588	−	16.6725i	−0.353139	−	0.611655i	−0.986798	+	0.161958i	$0.948219\pi$
$744$	6.38920	−	11.0664i	0.234239	−	0.405715i
$745$	−0.517683	+	0.896653i	−0.0189664	+	0.0328508i
$746$	−0.0930521	+	0.161171i	−0.00340688	+	0.00590089i
$747$	−2.04191			−0.0747095
$748$	−4.93507	+	8.54779i	−0.180444	+	0.312538i
$749$	11.8735	−	20.5655i	0.433848	−	0.751446i
$750$	−5.79779	−	10.0421i	−0.211706	−	0.366685i
$751$	13.1719	+	22.8144i	0.480649	+	0.832508i	0.999753	−	0.0222023i	$-0.00706779\pi$
$751$	13.1719	+	22.8144i	0.480649	+	0.832508i	−0.519104	+	0.854711i	$0.673734\pi$
$752$	1.46933			0.0535810
$753$	−15.0512			−0.548497
$754$	−0.668705	−	1.15823i	−0.0243528	−	0.0421803i
$755$	23.7690	+	41.1692i	0.865044	+	1.49830i
$756$	−0.0910889	+	0.157771i	−0.00331287	+	0.00573806i
$757$	6.61142	−	11.4513i	0.240296	−	0.416205i	−0.720503	−	0.693452i	$-0.756089\pi$
$757$	6.61142	−	11.4513i	0.240296	−	0.416205i	0.960799	+	0.277247i	$0.0894222\pi$
$758$	−4.30187			−0.156251
$759$	−57.3491	+	99.3316i	−2.08164	+	3.60551i
$760$	3.59189	−	6.22134i	0.130292	−	0.225672i
$761$	−19.0528	+	33.0004i	−0.690663	+	1.19626i	0.280958	+	0.959720i	$0.409348\pi$
$761$	−19.0528	+	33.0004i	−0.690663	+	1.19626i	−0.971621	+	0.236544i	$0.923985\pi$
$762$	1.50068	+	2.59926i	0.0543640	+	0.0941613i
$763$	−34.8041			−1.25999
$764$	0.532047	+	0.921532i	0.0192488	+	0.0333399i
$765$	3.59382	−	6.22469i	0.129935	−	0.225054i
$766$	15.2472			0.550904
$767$	5.33901	−	9.24743i	0.192780	−	0.333905i
$768$	1.40785	+	2.43848i	0.0508016	+	0.0879909i
$769$	21.8734	+	37.8858i	0.788774	+	1.36620i	0.926718	+	0.375757i	$0.122617\pi$
$769$	21.8734	+	37.8858i	0.788774	+	1.36620i	−0.137944	+	0.990440i	$0.544049\pi$
$770$	−15.2424			−0.549296
$771$	−4.12558	−	7.14572i	−0.148579	−	0.257347i
$772$	2.22473			0.0800699
$773$	29.0683			1.04551			0.522757	−	0.852482i	$-0.324904\pi$
$773$	29.0683			1.04551			0.522757	+	0.852482i	$0.324904\pi$
$774$	−1.52671	+	9.04860i	−0.0548764	+	0.325245i
$775$	−2.37648			−0.0853656
$776$	2.70501			0.0971042
$777$	−30.6179	−	53.0318i	−1.09841	−	1.90251i
$778$	12.0314			0.431346
$779$	7.18128	+	12.4383i	0.257296	+	0.445650i
$780$	6.31786	+	10.9429i	0.226216	+	0.391817i
$781$	18.6919	−	32.3753i	0.668849	−	1.15848i
$782$	3.96730			0.141870
$783$	0.0498182	−	0.0862877i	0.00178036	−	0.00308367i
$784$	1.48500	+	2.57209i	0.0530357	+	0.0918605i
$785$	20.1847			0.720422
$786$	−5.02445	−	8.70260i	−0.179216	−	0.310411i
$787$	17.7839	−	30.8025i	0.633926	−	1.09799i	−0.352816	−	0.935693i	$-0.614776\pi$
$787$	17.7839	−	30.8025i	0.633926	−	1.09799i	0.986742	−	0.162299i	$-0.0518909\pi$
$788$	3.65716	−	6.33439i	0.130281	−	0.225653i
$789$	−14.0600	+	24.3526i	−0.500549	+	0.866977i
$790$	8.71152			0.309942
$791$	−18.3277	+	31.7444i	−0.651656	+	1.12870i
$792$	14.6663	−	25.4028i	0.521145	−	0.902650i
$793$	3.63965	+	6.30405i	0.129248	+	0.223863i
$794$	−2.12481	−	3.68028i	−0.0754067	−	0.130608i
$795$	−75.9136			−2.69238
$796$	−21.6300			−0.766656
$797$	25.8269	+	44.7335i	0.914836	+	1.58454i	0.807141	+	0.590358i	$0.201013\pi$
$797$	25.8269	+	44.7335i	0.914836	+	1.58454i	0.107694	+	0.994184i	$0.465653\pi$
$798$	−2.34514	−	4.06191i	−0.0830172	−	0.143790i
$799$	0.269327	−	0.466487i	0.00952809	−	0.0165031i
$800$	−1.94675	+	3.37187i	−0.0688281	+	0.119214i
$801$	−10.5784			−0.373769
$802$	2.19960	−	3.80983i	0.0776707	−	0.134530i
$803$	−18.3722	+	31.8217i	−0.648342	+	1.12296i
$804$	13.5594	−	23.4857i	0.478205	−	0.828275i
$805$	−24.7712	−	42.9050i	−0.873071	−	1.51220i
$806$	1.66470			0.0586366
$807$	22.7395	+	39.3859i	0.800467	+	1.38645i
$808$	−12.2063	+	21.1419i	−0.429416	+	0.743771i
$809$	−45.0977			−1.58555			−0.792776	−	0.609513i	$-0.791365\pi$
$809$	−45.0977			−1.58555			−0.792776	+	0.609513i	$0.791365\pi$
$810$	5.11643	−	8.86192i	0.179773	−	0.311376i
$811$	−3.42694	−	5.93564i	−0.120336	−	0.208428i	0.799564	−	0.600581i	$-0.205064\pi$
$811$	−3.42694	−	5.93564i	−0.120336	−	0.208428i	−0.919900	+	0.392152i	$0.871731\pi$
$812$	5.12101	+	8.86984i	0.179712	+	0.311271i
$813$	−45.7633			−1.60499
$814$	−13.3948	−	23.2004i	−0.469487	−	0.813175i
$815$	−18.4854			−0.647515
$816$	6.67210			0.233570
$817$	−8.49667	−	7.02329i	−0.297261	−	0.245714i
$818$	−5.73791			−0.200621
$819$	8.73477			0.305217
$820$	−18.3219	−	31.7344i	−0.639827	−	1.10821i
$821$	−51.4623			−1.79605			−0.898023	−	0.439949i	$-0.854996\pi$
$821$	−51.4623			−1.79605			−0.898023	+	0.439949i	$0.854996\pi$
$822$	−9.30790	−	16.1218i	−0.324650	−	0.562311i
$823$	−4.30066	−	7.44896i	−0.149911	−	0.259654i	0.781283	−	0.624177i	$-0.214566\pi$
$823$	−4.30066	−	7.44896i	−0.149911	−	0.259654i	−0.931195	+	0.364523i	$0.881232\pi$
$824$	2.66815	−	4.62137i	0.0929495	−	0.160993i
$825$	−10.9418			−0.380945
$826$	5.05624	−	8.75766i	0.175929	−	0.304718i
$827$	18.6216	+	32.2536i	0.647537	+	1.12157i	0.983709	+	0.179766i	$0.0575341\pi$
$827$	18.6216	+	32.2536i	0.647537	+	1.12157i	−0.336173	+	0.941800i	$0.609133\pi$
$828$	44.8942			1.56018
$829$	19.1151	+	33.1084i	0.663896	+	1.14990i	0.979583	+	0.201038i	$0.0644314\pi$
$829$	19.1151	+	33.1084i	0.663896	+	1.14990i	−0.315688	+	0.948863i	$0.602235\pi$
$830$	0.386961	−	0.670237i	0.0134316	−	0.0232643i
$831$	−5.74442	+	9.94962i	−0.199272	+	0.345149i
$832$	−1.92182	+	3.32869i	−0.0666271	+	0.115401i
$833$	1.08879			0.0377244
$834$	−10.3526	+	17.9312i	−0.358481	+	0.620908i
$835$	5.03405	−	8.71923i	0.174211	−	0.301741i
$836$	8.29627	+	14.3696i	0.286932	+	0.496981i
$837$	0.0620097	+	0.107404i	0.00214337	+	0.00371242i
$838$	2.94468			0.101722
$839$	−33.6280			−1.16097			−0.580484	−	0.814272i	$-0.697137\pi$
$839$	−33.6280			−1.16097			−0.580484	+	0.814272i	$0.697137\pi$
$840$	12.7064	+	22.0082i	0.438413	+	0.759354i
$841$	11.6992	+	20.2637i	0.403422	+	0.698747i
$842$	−3.71169	+	6.42884i	−0.127913	+	0.221552i
$843$	30.1509	−	52.2229i	1.03845	−	1.79865i
$844$	36.0523			1.24097
$845$	13.9152	−	24.1018i	0.478698	−	0.829129i
$846$	−0.376896	+	0.652803i	−0.0129580	+	0.0224438i
$847$	24.0103	−	41.5871i	0.825004	−	1.42895i
$848$	−17.5665	−	30.4260i	−0.603234	−	1.04483i
$849$	−12.8735			−0.441819
$850$	0.189233	+	0.327762i	0.00649065	+	0.0112421i
$851$	43.5372	−	75.4087i	1.49244	−	2.58498i
$852$	−29.3494			−1.00549
$853$	22.9994	−	39.8361i	0.787483	−	1.36396i	−0.140021	−	0.990149i	$-0.544717\pi$
$853$	22.9994	−	39.8361i	0.787483	−	1.36396i	0.927504	−	0.373813i	$-0.121950\pi$
$854$	3.44688	+	5.97017i	0.117950	+	0.204295i
$855$	−6.04152	−	10.4642i	−0.206616	−	0.357869i
$856$	−17.3208			−0.592014
$857$	17.8415	+	30.9024i	0.609454	+	1.05561i	0.991330	+	0.131392i	$0.0419447\pi$
$857$	17.8415	+	30.9024i	0.609454	+	1.05561i	−0.381876	+	0.924213i	$0.624722\pi$
$858$	7.66465			0.261667
$859$	−12.4093			−0.423400			−0.211700	−	0.977335i	$-0.567900\pi$
$859$	−12.4093			−0.423400			−0.211700	+	0.977335i	$0.567900\pi$
$860$	21.6779	+	17.9188i	0.739209	+	0.611026i
$861$	−50.8080			−1.73153
$862$	11.1327			0.379182
$863$	22.5922	+	39.1309i	0.769049	+	1.33203i	0.938079	+	0.346421i	$0.112603\pi$
$863$	22.5922	+	39.1309i	0.769049	+	1.33203i	−0.169030	+	0.985611i	$0.554064\pi$
$864$	0.203187			0.00691257
$865$	−25.1384	−	43.5409i	−0.854730	−	1.48044i
$866$	−3.88365	−	6.72668i	−0.131972	−	0.228582i
$867$	1.22299	−	2.11828i	0.0415348	−	0.0719404i
$868$	−12.7484			−0.432710
$869$	−21.3653	+	37.0058i	−0.724769	+	1.25534i
$870$	−3.27235	−	5.66788i	−0.110943	−	0.192159i
$871$	7.50270			0.254219
$872$	12.6929	+	21.9848i	0.429836	+	0.744498i
$873$	2.27490	−	3.94024i	0.0769937	−	0.133357i
$874$	3.33468	−	5.77584i	0.112797	−	0.195371i
$875$	−12.2837	+	21.2760i	−0.415265	+	0.719260i
$876$	28.8474			0.974665
$877$	−16.2756	+	28.1902i	−0.549589	+	0.951916i	0.448713	+	0.893676i	$0.351882\pi$
$877$	−16.2756	+	28.1902i	−0.549589	+	0.951916i	−0.998303	+	0.0582406i	$0.981451\pi$
$878$	−6.96996	+	12.0723i	−0.235225	+	0.407421i
$879$	−36.2966	−	62.8675i	−1.22425	−	2.12047i
$880$	−18.2253	−	31.5672i	−0.614375	−	1.06413i
$881$	−28.3797			−0.956136			−0.478068	−	0.878323i	$-0.658663\pi$
$881$	−28.3797			−0.956136			−0.478068	+	0.878323i	$0.658663\pi$
$882$	−1.52366			−0.0513042
$883$	−0.684752	−	1.18603i	−0.0230437	−	0.0399129i	0.854274	−	0.519824i	$-0.174002\pi$
$883$	−0.684752	−	1.18603i	−0.0230437	−	0.0399129i	−0.877317	+	0.479911i	$0.840669\pi$
$884$	1.07190	+	1.85658i	0.0360519	+	0.0624437i
$885$	26.1268	−	45.2529i	0.878242	−	1.52116i
$886$	−8.21887	+	14.2355i	−0.276118	+	0.478251i
$887$	−10.2116			−0.342871			−0.171435	−	0.985195i	$-0.554841\pi$
$887$	−10.2116			−0.342871			−0.171435	+	0.985195i	$0.554841\pi$
$888$	−22.3325	+	38.6810i	−0.749428	+	1.29805i
$889$	3.17948	−	5.50701i	0.106636	−	0.184699i
$890$	2.00471	−	3.47225i	0.0671979	−	0.116390i
$891$	25.0965	+	43.4684i	0.840763	+	1.45624i
$892$	35.1743			1.17772
$893$	−0.452761	−	0.784205i	−0.0151511	−	0.0262424i
$894$	0.246531	−	0.427004i	0.00824522	−	0.0142811i
$895$	47.7744			1.59692
$896$	−13.5547	+	23.4774i	−0.452831	+	0.784326i
$897$	12.4563	+	21.5749i	0.415902	+	0.720364i
$898$	2.54187	+	4.40265i	0.0848234	+	0.146918i
$899$	6.97236			0.232541
$900$	2.14138	+	3.70898i	0.0713793	+	0.123633i
$901$	−12.8796			−0.429083
$902$	−22.2276			−0.740097
$903$	36.5451	−	13.6078i	1.21615	−	0.452838i
$904$	26.7361			0.889229
$905$	32.9797			1.09628
$906$	−11.3193	−	19.6056i	−0.376058	−	0.651352i
$907$	−35.1531			−1.16724			−0.583620	−	0.812027i	$-0.698364\pi$
$907$	−35.1531			−1.16724			−0.583620	+	0.812027i	$0.698364\pi$
$908$	−19.1580	−	33.1826i	−0.635780	−	1.10120i
$909$	20.5309	+	35.5605i	0.680966	+	1.17947i
$910$	−1.65532	+	2.86711i	−0.0548735	+	0.0950436i
$911$	−31.5815			−1.04634			−0.523172	−	0.852227i	$-0.675251\pi$
$911$	−31.5815			−1.04634			−0.523172	+	0.852227i	$0.675251\pi$
$912$	5.60818	−	9.71366i	0.185706	−	0.321651i
$913$	1.89807	+	3.28756i	0.0628171	+	0.108802i
$914$	4.23628			0.140124
$915$	17.8108	+	30.8493i	0.588808	+	1.01985i
$916$	21.8526	−	37.8499i	0.722031	−	1.25059i
$917$	−10.6452	+	18.4381i	−0.351536	+	0.608879i
$918$	0.00987538	−	0.0171047i	0.000325936	−	0.000564538i
$919$	−30.7650			−1.01484			−0.507422	−	0.861697i	$-0.669402\pi$
$919$	−30.7650			−1.01484			−0.507422	+	0.861697i	$0.669402\pi$
$920$	−18.0679	+	31.2946i	−0.595682	+	1.03175i
$921$	−18.6456	+	32.2951i	−0.614393	+	1.06416i
$922$	−7.07131	−	12.2479i	−0.232881	−	0.403362i
$923$	−4.05989	−	7.03194i	−0.133633	−	0.231459i
$924$	−58.6966			−1.93098
$925$	8.30661			0.273120
$926$	8.79144	+	15.2272i	0.288905	+	0.500397i
$927$	−4.48781	−	7.77311i	−0.147399	−	0.255302i
$928$	5.71159	−	9.89276i	0.187492	−	0.324746i
$929$	25.1444	−	43.5513i	0.824960	−	1.42887i	−0.0769899	−	0.997032i	$-0.524531\pi$
$929$	25.1444	−	43.5513i	0.824960	−	1.42887i	0.901950	−	0.431841i	$-0.142136\pi$
$930$	8.14632			0.267128
$931$	0.915177	−	1.58513i	0.0299937	−	0.0519506i
$932$	−3.43565	+	5.95072i	−0.112538	+	0.194922i
$933$	0.322456	−	0.558509i	0.0105567	−	0.0182848i
$934$	1.48910	+	2.57920i	0.0487250	+	0.0843942i
$935$	−13.3627			−0.437007
$936$	−3.18553	−	5.51751i	−0.104122	−	0.180345i
$937$	23.4901	−	40.6860i	0.767387	−	1.32915i	−0.171589	−	0.985169i	$-0.554890\pi$
$937$	23.4901	−	40.6860i	0.767387	−	1.32915i	0.938975	−	0.343984i	$-0.111777\pi$
$938$	7.10534			0.231998
$939$	−6.19815	+	10.7355i	−0.202269	+	0.350340i
$940$	1.15515	+	2.00077i	0.0376767	+	0.0652580i
$941$	−0.812658	−	1.40757i	−0.0264919	−	0.0458853i	0.852476	−	0.522767i	$-0.175100\pi$
$941$	−0.812658	−	1.40757i	−0.0264919	−	0.0458853i	−0.878967	+	0.476882i	$0.841767\pi$
$942$	−9.61233			−0.313187
$943$	−36.1233	−	62.5673i	−1.17634	−	2.03747i
$944$	24.1830			0.787090
$945$	−0.246642			−0.00802325
$946$	15.9878	−	5.95314i	0.519809	−	0.193553i
$947$	−22.9001			−0.744154			−0.372077	−	0.928202i	$-0.621354\pi$
$947$	−22.9001			−0.744154			−0.372077	+	0.928202i	$0.621354\pi$
$948$	33.5471			1.08956
$949$	3.99046	+	6.91168i	0.129536	+	0.224363i
$950$	0.636235			0.0206422
$951$	34.1835	+	59.2076i	1.10848	+	1.91994i
$952$	2.15579	+	3.73394i	0.0698697	+	0.121018i
$953$	17.7604	−	30.7619i	0.575316	−	0.996476i	−0.420691	−	0.907204i	$-0.638212\pi$
$953$	17.7604	−	30.7619i	0.575316	−	0.996476i	0.996007	−	0.0892725i	$-0.0284542\pi$
$954$	18.0238			0.583541
$955$	−0.720313	+	1.24762i	−0.0233088	+	0.0403720i
$956$	22.5030	+	38.9763i	0.727799	+	1.26058i
$957$	32.1023			1.03772
$958$	−0.384640	−	0.666216i	−0.0124272	−	0.0215245i
$959$	−19.7205	+	34.1569i	−0.636808	+	1.10298i
$960$	−9.40454	+	16.2891i	−0.303530	+	0.525730i
$961$	11.1607	−	19.3309i	0.360022	−	0.623577i
$962$	−5.81871			−0.187603
$963$	−14.5667	+	25.2303i	−0.469407	+	0.813036i
$964$	−9.61446	+	16.6527i	−0.309661	+	0.536348i
$965$	1.50598	+	2.60843i	0.0484792	+	0.0839684i
$966$	11.7965	+	20.4322i	0.379547	+	0.657395i
$967$	−43.3224			−1.39315			−0.696577	−	0.717482i	$-0.745294\pi$
$967$	−43.3224			−1.39315			−0.696577	+	0.717482i	$0.745294\pi$
$968$	−35.0259			−1.12577
$969$	−2.05594	−	3.56100i	−0.0660465	−	0.114396i
$970$	0.862232	+	1.49343i	0.0276846	+	0.0479512i
$971$	−6.41141	+	11.1049i	−0.205752	+	0.356373i	−0.950372	−	0.311116i	$-0.899297\pi$
$971$	−6.41141	+	11.1049i	−0.205752	+	0.356373i	0.744620	+	0.667489i	$0.232631\pi$
$972$	19.5904	−	33.9316i	0.628362	−	1.08836i
$973$	43.8678			1.40634
$974$	5.89849	−	10.2165i	0.189000	−	0.327358i
$975$	−1.18828	+	2.05817i	−0.0380556	+	0.0659142i
$976$	−8.24288	+	14.2771i	−0.263848	+	0.456999i
$977$	−18.5000	−	32.0429i	−0.591866	−	1.02514i	−0.993981	−	0.109553i	$-0.965058\pi$
$977$	−18.5000	−	32.0429i	−0.591866	−	1.02514i	0.402115	−	0.915589i	$-0.368275\pi$
$978$	8.80310			0.281492
$979$	9.83323	+	17.0317i	0.314272	+	0.544334i
$980$	−2.33492	+	4.04421i	−0.0745864	+	0.129187i
$981$	42.6987			1.36327
$982$	2.23052	−	3.86337i	0.0711787	−	0.123285i
$983$	−19.2644	−	33.3669i	−0.614438	−	1.06424i	−0.990483	−	0.137636i	$-0.956050\pi$
$983$	−19.2644	−	33.3669i	−0.614438	−	1.06424i	0.376045	−	0.926601i	$-0.377284\pi$
$984$	18.5295	+	32.0940i	0.590698	+	1.02312i
$985$	9.90252			0.315521
$986$	−0.555193	−	0.961622i	−0.0176809	−	0.0306243i
$987$	3.20331			0.101963
$988$	3.60391			0.114656
$989$	42.7399	+	35.3286i	1.35905	+	1.12338i
$990$	18.6998			0.594318
$991$	−31.3741			−0.996631			−0.498316	−	0.866996i	$-0.666048\pi$
$991$	−31.3741			−0.996631			−0.498316	+	0.866996i	$0.666048\pi$
$992$	7.10932	+	12.3137i	0.225721	+	0.390961i
$993$	−44.2623			−1.40462
$994$	−3.84487	−	6.65951i	−0.121952	−	0.211227i
$995$	−14.6419	−	25.3606i	−0.464180	−	0.803984i
$996$	1.49014	−	2.58101i	0.0472170	−	0.0817823i
$997$	24.9932			0.791542			0.395771	−	0.918349i	$-0.370477\pi$
$997$	24.9932			0.791542			0.395771	+	0.918349i	$0.370477\pi$
$998$	−0.891321	+	1.54381i	−0.0282143	+	0.0488686i
$999$	−0.216745	−	0.375414i	−0.00685752	−	0.0118776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.681.17	yes	58
43.6	even	3	inner	731.2.e.a.307.17	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.17	✓	58	43.6	even	3	inner
731.2.e.a.681.17	yes	58	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+0.469159 q^{2} +(1.22299 + 2.11828i) q^{3} -1.77989 q^{4} +(-1.20485 - 2.08687i) q^{5} +(0.573775 + 0.993808i) q^{6} +(1.21565 - 2.10557i) q^{7} -1.77337 q^{8} +(-1.49139 + 2.58317i) q^{9} +O(q^{10})\)	\(q+0.469159 q^{2} +(1.22299 + 2.11828i) q^{3} -1.77989 q^{4} +(-1.20485 - 2.08687i) q^{5} +(0.573775 + 0.993808i) q^{6} +(1.21565 - 2.10557i) q^{7} -1.77337 q^{8} +(-1.49139 + 2.58317i) q^{9} +(-0.565268 - 0.979072i) q^{10} +5.54536 q^{11} +(-2.17678 - 3.77030i) q^{12} +(0.602228 - 1.04309i) q^{13} +(0.570332 - 0.987844i) q^{14} +(2.94704 - 5.10443i) q^{15} +2.72779 q^{16} +(0.500000 - 0.866025i) q^{17} +(-0.699701 + 1.21192i) q^{18} +(-0.840542 - 1.45586i) q^{19} +(2.14451 + 3.71440i) q^{20} +5.94689 q^{21} +2.60165 q^{22} +(4.22810 + 7.32328i) q^{23} +(-2.16881 - 3.75648i) q^{24} +(-0.403346 + 0.698616i) q^{25} +(0.282540 - 0.489374i) q^{26} +0.0420982 q^{27} +(-2.16372 + 3.74767i) q^{28} +(1.18338 - 2.04967i) q^{29} +(1.38263 - 2.39479i) q^{30} +(1.47298 + 2.55127i) q^{31} +4.82650 q^{32} +(6.78191 + 11.7466i) q^{33} +(0.234579 - 0.406303i) q^{34} -5.85872 q^{35} +(2.65452 - 4.59776i) q^{36} +(-5.14856 - 8.91757i) q^{37} +(-0.394348 - 0.683030i) q^{38} +2.94607 q^{39} +(2.13665 + 3.70079i) q^{40} -8.54362 q^{41} +2.79004 q^{42} +(6.14525 - 2.28821i) q^{43} -9.87013 q^{44} +7.18765 q^{45} +(1.98365 + 3.43578i) q^{46} +0.538653 q^{47} +(3.33605 + 5.77821i) q^{48} +(0.544396 + 0.942922i) q^{49} +(-0.189233 + 0.327762i) q^{50} +2.44597 q^{51} +(-1.07190 + 1.85658i) q^{52} +(-6.43981 - 11.1541i) q^{53} +0.0197508 q^{54} +(-6.68135 - 11.5724i) q^{55} +(-2.15579 + 3.73394i) q^{56} +(2.05594 - 3.56100i) q^{57} +(0.555193 - 0.961622i) q^{58} +8.86543 q^{59} +(-5.24541 + 9.08532i) q^{60} +(-3.02182 + 5.23394i) q^{61} +(0.691059 + 1.19695i) q^{62} +(3.62602 + 6.28046i) q^{63} -3.19118 q^{64} -2.90239 q^{65} +(3.18179 + 5.51102i) q^{66} +(3.11456 + 5.39458i) q^{67} +(-0.889945 + 1.54143i) q^{68} +(-10.3418 + 17.9125i) q^{69} -2.74867 q^{70} +(3.37073 - 5.83827i) q^{71} +(2.64479 - 4.58091i) q^{72} +(-3.31308 + 5.73843i) q^{73} +(-2.41549 - 4.18376i) q^{74} -1.97315 q^{75} +(1.49607 + 2.59127i) q^{76} +(6.74121 - 11.6761i) q^{77} +1.38217 q^{78} +(-3.85283 + 6.67329i) q^{79} +(-3.28659 - 5.69254i) q^{80} +(4.52567 + 7.83869i) q^{81} -4.00832 q^{82} +(0.342282 + 0.592849i) q^{83} -10.5848 q^{84} -2.40971 q^{85} +(2.88310 - 1.07354i) q^{86} +5.78903 q^{87} -9.83397 q^{88} +(1.77324 + 3.07133i) q^{89} +3.37215 q^{90} +(-1.46419 - 2.53606i) q^{91} +(-7.52555 - 13.0346i) q^{92} +(-3.60286 + 6.24034i) q^{93} +0.252714 q^{94} +(-2.02546 + 3.50820i) q^{95} +(5.90275 + 10.2239i) q^{96} -1.52535 q^{97} +(0.255408 + 0.442380i) q^{98} +(-8.27032 + 14.3246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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