LMFDB - Embedded newform 231.4.j.b.190.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,4,Mod(64,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	231.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.6294412113$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.2
Character	$\chi$	$=$	231.190
Dual form			231.4.j.b.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.18050 + 2.31077i) q^{2} +(-0.927051 - 2.85317i) q^{3} +(2.30381 - 7.09039i) q^{4} +(-0.314127 - 0.228227i) q^{5} +(9.54151 + 6.93232i) q^{6} +(-2.16312 + 6.65740i) q^{7} +(-0.661756 - 2.03668i) q^{8} +(-7.28115 + 5.29007i) q^{9} +1.52646 q^{10} +(31.6266 + 18.1868i) q^{11} -22.3658 q^{12} +(-12.0427 + 8.74950i) q^{13} +(-8.50391 - 26.1724i) q^{14} +(-0.359958 + 1.10784i) q^{15} +(55.0626 + 40.0053i) q^{16} +(-54.1331 - 39.3300i) q^{17} +(10.9336 - 33.6502i) q^{18} +(29.6070 + 91.1210i) q^{19} +(-2.34191 + 1.70149i) q^{20} +21.0000 q^{21} +(-142.614 + 15.2386i) q^{22} -182.733 q^{23} +(-5.19750 + 3.77620i) q^{24} +(-38.5805 - 118.739i) q^{25} +(18.0836 - 55.6557i) q^{26} +(21.8435 + 15.8702i) q^{27} +(42.2201 + 30.6747i) q^{28} +(85.6286 - 263.538i) q^{29} +(-1.41511 - 4.35526i) q^{30} +(108.829 - 79.0691i) q^{31} -250.438 q^{32} +(22.5706 - 107.096i) q^{33} +263.053 q^{34} +(2.19889 - 1.59759i) q^{35} +(20.7343 + 63.8135i) q^{36} +(-2.05555 + 6.32632i) q^{37} +(-304.725 - 221.396i) q^{38} +(36.1280 + 26.2485i) q^{39} +(-0.256949 + 0.790806i) q^{40} +(4.26003 + 13.1110i) q^{41} +(-66.7906 + 48.5262i) q^{42} +316.055 q^{43} +(201.813 - 182.346i) q^{44} +3.49455 q^{45} +(581.183 - 422.254i) q^{46} +(-148.623 - 457.414i) q^{47} +(63.0961 - 194.190i) q^{48} +(-39.6418 - 28.8015i) q^{49} +(397.084 + 288.498i) q^{50} +(-62.0310 + 190.912i) q^{51} +(34.2934 + 105.544i) q^{52} +(237.949 - 172.880i) q^{53} -106.146 q^{54} +(-5.78406 - 12.9310i) q^{55} +14.9904 q^{56} +(232.537 - 168.948i) q^{57} +(336.633 + 1036.05i) q^{58} +(235.920 - 726.088i) q^{59} +(7.02572 + 5.10448i) q^{60} +(52.0276 + 37.8003i) q^{61} +(-163.421 + 502.959i) q^{62} +(-19.4681 - 59.9166i) q^{63} +(356.018 - 258.663i) q^{64} +5.77980 q^{65} +(175.689 + 392.775i) q^{66} -524.204 q^{67} +(-403.577 + 293.216i) q^{68} +(169.403 + 521.368i) q^{69} +(-3.30192 + 10.1623i) q^{70} +(-761.041 - 552.929i) q^{71} +(15.5925 + 11.3286i) q^{72} +(329.395 - 1013.77i) q^{73} +(-8.08101 - 24.8708i) q^{74} +(-303.015 + 220.154i) q^{75} +714.292 q^{76} +(-189.489 + 171.210i) q^{77} -175.559 q^{78} +(-245.167 + 178.124i) q^{79} +(-8.16638 - 25.1335i) q^{80} +(25.0304 - 77.0356i) q^{81} +(-43.8456 - 31.8557i) q^{82} +(125.746 + 91.3596i) q^{83} +(48.3799 - 148.898i) q^{84} +(8.02853 + 24.7093i) q^{85} +(-1005.21 + 730.330i) q^{86} -831.299 q^{87} +(16.1115 - 76.4483i) q^{88} -1405.10 q^{89} +(-11.1144 + 8.07510i) q^{90} +(-32.1992 - 99.0989i) q^{91} +(-420.981 + 1295.65i) q^{92} +(-326.488 - 237.207i) q^{93} +(1529.67 + 1111.37i) q^{94} +(11.4959 - 35.3807i) q^{95} +(232.169 + 714.542i) q^{96} +(-506.716 + 368.151i) q^{97} +192.635 q^{98} +(-326.487 + 34.8859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} + 27 q^{3} - 44 q^{4} - 16 q^{5} + 18 q^{6} + 63 q^{7} + 135 q^{8} - 81 q^{9} - 260 q^{10} - 29 q^{11} - 498 q^{12} - 4 q^{13} - 63 q^{14} + 18 q^{15} - 456 q^{16} + 130 q^{17} + 81 q^{18}+ \cdots + 1764 q^{99}+O(q^{100}) $ 36 * q - 6 * q^2 + 27 * q^3 - 44 * q^4 - 16 * q^5 + 18 * q^6 + 63 * q^7 + 135 * q^8 - 81 * q^9 - 260 * q^10 - 29 * q^11 - 498 * q^12 - 4 * q^13 - 63 * q^14 + 18 * q^15 - 456 * q^16 + 130 * q^17 + 81 * q^18 + 310 * q^19 + 136 * q^20 + 756 * q^21 - 318 * q^22 + 498 * q^23 + 135 * q^24 - 1183 * q^25 + 65 * q^26 + 243 * q^27 + 273 * q^28 - 276 * q^29 - 165 * q^30 - 68 * q^31 - 2986 * q^32 + 207 * q^33 - 774 * q^34 + 112 * q^35 - 396 * q^36 + 607 * q^37 - 550 * q^38 + 12 * q^39 + 1938 * q^40 + 1242 * q^41 - 126 * q^42 - 334 * q^43 + 1358 * q^44 + 396 * q^45 + 2052 * q^46 - 1532 * q^47 - 27 * q^48 - 441 * q^49 - 1117 * q^50 + 952 * q^52 + 369 * q^53 + 162 * q^54 - 702 * q^55 + 1260 * q^56 + 660 * q^57 + 257 * q^58 - 198 * q^59 - 408 * q^60 + 1754 * q^61 + 3553 * q^62 + 567 * q^63 - 5453 * q^64 - 2344 * q^65 + 1179 * q^66 - 1250 * q^67 + 9267 * q^68 - 9 * q^69 - 385 * q^70 - 853 * q^71 - 405 * q^72 + 1458 * q^73 - 1444 * q^74 - 2331 * q^75 - 2284 * q^76 + 483 * q^77 - 4530 * q^78 + 3653 * q^79 - 8057 * q^80 - 729 * q^81 - 2483 * q^82 + 2922 * q^83 - 924 * q^84 - 3170 * q^85 - 4626 * q^86 + 1578 * q^87 + 16631 * q^88 + 4596 * q^89 + 675 * q^90 - 742 * q^91 - 228 * q^92 + 204 * q^93 - 11483 * q^94 + 2610 * q^95 - 2412 * q^96 - 2022 * q^97 - 294 * q^98 + 1764 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−3.18050	+	2.31077i	−1.12448	+	0.816981i	−0.984882	−	0.173227i	$-0.944580\pi$
$2$	−3.18050	+	2.31077i	−1.12448	+	0.816981i	−0.139596	+	0.990209i	$0.544580\pi$
$3$	−0.927051	−	2.85317i	−0.178411	−	0.549093i
$3$	−0.927051	−	2.85317i	−0.178411	−	0.549093i
$4$	2.30381	−	7.09039i	0.287976	−	0.886299i
$5$	−0.314127	−	0.228227i	−0.0280964	−	0.0204132i	0.573648	−	0.819102i	$-0.305528\pi$
$5$	−0.314127	−	0.228227i	−0.0280964	−	0.0204132i	−0.601745	+	0.798688i	$0.705528\pi$
$6$	9.54151	+	6.93232i	0.649218	+	0.471684i
$7$	−2.16312	+	6.65740i	−0.116797	+	0.359466i
$7$	−2.16312	+	6.65740i	−0.116797	+	0.359466i
$8$	−0.661756	−	2.03668i	−0.0292458	−	0.0900092i
$9$	−7.28115	+	5.29007i	−0.269672	+	0.195928i
$10$	1.52646			0.0482710
$11$	31.6266	+	18.1868i	0.866888	+	0.498502i
$11$	31.6266	+	18.1868i	0.866888	+	0.498502i
$12$	−22.3658			−0.538038
$13$	−12.0427	+	8.74950i	−0.256926	+	0.186667i	−0.708791	−	0.705419i	$-0.750759\pi$
$13$	−12.0427	+	8.74950i	−0.256926	+	0.186667i	0.451865	+	0.892086i	$0.350759\pi$
$14$	−8.50391	−	26.1724i	−0.162340	−	0.499633i
$15$	−0.359958	+	1.10784i	−0.00619605	+	0.0190695i
$16$	55.0626	+	40.0053i	0.860353	+	0.625083i
$17$	−54.1331	−	39.3300i	−0.772306	−	0.561113i	0.130354	−	0.991468i	$-0.458389\pi$
$17$	−54.1331	−	39.3300i	−0.772306	−	0.561113i	−0.902660	+	0.430354i	$0.858389\pi$
$18$	10.9336	−	33.6502i	0.143171	−	0.440634i
$19$	29.6070	+	91.1210i	0.357490	+	1.10024i	0.954551	+	0.298046i	$0.0963350\pi$
$19$	29.6070	+	91.1210i	0.357490	+	1.10024i	−0.597061	+	0.802196i	$0.703665\pi$
$20$	−2.34191	+	1.70149i	−0.0261833	+	0.0190233i
$21$	21.0000			0.218218
$22$	−142.614	+	15.2386i	−1.38206	+	0.147677i
$23$	−182.733			−1.65663			−0.828314	−	0.560264i	$-0.810700\pi$
$23$	−182.733			−1.65663			−0.828314	+	0.560264i	$0.810700\pi$
$24$	−5.19750	+	3.77620i	−0.0442056	+	0.0321173i
$25$	−38.5805	−	118.739i	−0.308644	−	0.949909i
$26$	18.0836	−	55.6557i	0.136403	−	0.419807i
$27$	21.8435	+	15.8702i	0.155695	+	0.113119i
$28$	42.2201	+	30.6747i	0.284959	+	0.207035i
$29$	85.6286	−	263.538i	0.548304	−	1.68751i	−0.164697	−	0.986344i	$-0.552665\pi$
$29$	85.6286	−	263.538i	0.548304	−	1.68751i	0.713001	−	0.701163i	$-0.247335\pi$
$30$	−1.41511	−	4.35526i	−0.00861209	−	0.0265053i
$31$	108.829	−	79.0691i	0.630526	−	0.458104i	−0.226056	−	0.974114i	$-0.572583\pi$
$31$	108.829	−	79.0691i	0.630526	−	0.458104i	0.856582	+	0.516010i	$0.172583\pi$
$32$	−250.438			−1.38349
$33$	22.5706	−	107.096i	0.119061	−	0.564940i
$34$	263.053			1.32686
$35$	2.19889	−	1.59759i	0.0106194	−	0.00771548i
$36$	20.7343	+	63.8135i	0.0959919	+	0.295433i
$37$	−2.05555	+	6.32632i	−0.00913324	+	0.0281092i	−0.955519	−	0.294929i	$-0.904704\pi$
$37$	−2.05555	+	6.32632i	−0.00913324	+	0.0281092i	0.946386	+	0.323038i	$0.104704\pi$
$38$	−304.725	−	221.396i	−1.30087	−	0.945135i
$39$	36.1280	+	26.2485i	0.148336	+	0.107772i
$40$	−0.256949	+	0.790806i	−0.00101568	+	0.00312594i
$41$	4.26003	+	13.1110i	0.0162269	+	0.0499414i	0.958842	−	0.283940i	$-0.0916416\pi$
$41$	4.26003	+	13.1110i	0.0162269	+	0.0499414i	−0.942615	+	0.333881i	$0.891642\pi$
$42$	−66.7906	+	48.5262i	−0.245381	+	0.178280i
$43$	316.055			1.12088			0.560441	−	0.828195i	$-0.310632\pi$
$43$	316.055			1.12088			0.560441	+	0.828195i	$0.310632\pi$
$44$	201.813	−	182.346i	0.691465	−	0.624765i
$45$	3.49455			0.0115764
$46$	581.183	−	422.254i	1.86284	−	1.35343i
$47$	−148.623	−	457.414i	−0.461252	−	1.41959i	−0.863636	−	0.504117i	$-0.831818\pi$
$47$	−148.623	−	457.414i	−0.461252	−	1.41959i	0.402384	−	0.915471i	$-0.368182\pi$
$48$	63.0961	−	194.190i	0.189732	−	0.583935i
$49$	−39.6418	−	28.8015i	−0.115574	−	0.0839693i
$50$	397.084	+	288.498i	1.12312	+	0.815996i
$51$	−62.0310	+	190.912i	−0.170315	+	0.524177i
$52$	34.2934	+	105.544i	0.0914546	+	0.281468i
$53$	237.949	−	172.880i	0.616695	−	0.448055i	−0.235070	−	0.971978i	$-0.575532\pi$
$53$	237.949	−	172.880i	0.616695	−	0.448055i	0.851766	+	0.523923i	$0.175532\pi$
$54$	−106.146			−0.267492
$55$	−5.78406	−	12.9310i	−0.0141804	−	0.0317021i
$56$	14.9904			0.0357710
$57$	232.537	−	168.948i	0.540355	−	0.392591i
$58$	336.633	+	1036.05i	0.762105	+	2.34552i
$59$	235.920	−	726.088i	0.520580	−	1.60218i	−0.252315	−	0.967645i	$-0.581192\pi$
$59$	235.920	−	726.088i	0.520580	−	1.60218i	0.772894	−	0.634535i	$-0.218808\pi$
$60$	7.02572	+	5.10448i	0.0151169	+	0.0109831i
$61$	52.0276	+	37.8003i	0.109204	+	0.0793415i	0.641047	−	0.767502i	$-0.278500\pi$
$61$	52.0276	+	37.8003i	0.109204	+	0.0793415i	−0.531843	+	0.846843i	$0.678500\pi$
$62$	−163.421	+	502.959i	−0.334750	+	1.03026i
$63$	−19.4681	−	59.9166i	−0.0389325	−	0.119822i
$64$	356.018	−	258.663i	0.695349	−	0.505200i
$65$	5.77980			0.0110292
$66$	175.689	+	392.775i	0.327664	+	0.732534i
$67$	−524.204			−0.955846			−0.477923	−	0.878402i	$-0.658610\pi$
$67$	−524.204			−0.955846			−0.477923	+	0.878402i	$0.658610\pi$
$68$	−403.577	+	293.216i	−0.719720	+	0.522907i
$69$	169.403	+	521.368i	0.295561	+	0.909642i
$70$	−3.30192	+	10.1623i	−0.00563793	+	0.0173518i
$71$	−761.041	−	552.929i	−1.27210	−	0.924233i	−0.272814	−	0.962067i	$-0.587954\pi$
$71$	−761.041	−	552.929i	−1.27210	−	0.924233i	−0.999284	+	0.0378339i	$0.987954\pi$
$72$	15.5925	+	11.3286i	0.0255221	+	0.0185429i
$73$	329.395	−	1013.77i	0.528120	−	1.62539i	−0.229941	−	0.973205i	$-0.573853\pi$
$73$	329.395	−	1013.77i	0.528120	−	1.62539i	0.758062	−	0.652183i	$-0.226147\pi$
$74$	−8.08101	−	24.8708i	−0.0126946	−	0.0390699i
$75$	−303.015	+	220.154i	−0.466523	+	0.338949i
$76$	714.292			1.07809
$77$	−189.489	+	171.210i	−0.280445	+	0.253393i
$78$	−175.559			−0.254849
$79$	−245.167	+	178.124i	−0.349157	+	0.253678i	−0.748515	−	0.663117i	$-0.769233\pi$
$79$	−245.167	+	178.124i	−0.349157	+	0.253678i	0.399358	+	0.916795i	$0.369233\pi$
$80$	−8.16638	−	25.1335i	−0.0114129	−	0.0351252i
$81$	25.0304	−	77.0356i	0.0343352	−	0.105673i
$82$	−43.8456	−	31.8557i	−0.0590480	−	0.0429009i
$83$	125.746	+	91.3596i	0.166294	+	0.120820i	0.667820	−	0.744323i	$-0.267228\pi$
$83$	125.746	+	91.3596i	0.166294	+	0.120820i	−0.501526	+	0.865143i	$0.667228\pi$
$84$	48.3799	−	148.898i	0.0628415	−	0.193406i
$85$	8.02853	+	24.7093i	0.0102449	+	0.0315306i
$86$	−1005.21	+	730.330i	−1.26041	+	0.915739i
$87$	−831.299			−1.02442
$88$	16.1115	−	76.4483i	0.0195170	−	0.0926070i
$89$	−1405.10			−1.67348			−0.836742	−	0.547598i	$-0.815542\pi$
$89$	−1405.10			−1.67348			−0.836742	+	0.547598i	$0.815542\pi$
$90$	−11.1144	+	8.07510i	−0.0130174	+	0.00945767i
$91$	−32.1992	−	99.0989i	−0.0370922	−	0.114158i
$92$	−420.981	+	1295.65i	−0.477069	+	1.46827i
$93$	−326.488	−	237.207i	−0.364034	−	0.264486i
$94$	1529.67	+	1111.37i	1.67844	+	1.21946i
$95$	11.4959	−	35.3807i	0.0124153	−	0.0382104i
$96$	232.169	+	714.542i	0.246829	+	0.759663i
$97$	−506.716	+	368.151i	−0.530404	+	0.385361i	−0.820509	−	0.571634i	$-0.806310\pi$
$97$	−506.716	+	368.151i	−0.530404	+	0.385361i	0.290105	+	0.956995i	$0.406310\pi$
$98$	192.635			0.198562
$99$	−326.487	+	34.8859i	−0.331447	+	0.0354158i
$100$	−930.785			−0.930785
$101$	−331.197	+	240.629i	−0.326291	+	0.237064i	−0.738855	−	0.673864i	$-0.764633\pi$
$101$	−331.197	+	240.629i	−0.326291	+	0.237064i	0.412564	+	0.910928i	$0.364633\pi$
$102$	−243.864	−	750.536i	−0.236727	−	0.728570i
$103$	469.849	−	1446.05i	0.449472	−	1.38333i	−0.428033	−	0.903763i	$-0.640793\pi$
$103$	469.849	−	1446.05i	0.449472	−	1.38333i	0.877505	−	0.479568i	$-0.159207\pi$
$104$	25.7892	+	18.7369i	0.0243158	+	0.0176664i
$105$	−6.59668	−	4.79277i	−0.00613114	−	0.00445453i
$106$	−357.312	+	1099.69i	−0.327408	+	1.00766i
$107$	496.228	+	1527.23i	0.448338	+	1.37984i	0.878782	+	0.477224i	$0.158357\pi$
$107$	496.228	+	1527.23i	0.448338	+	1.37984i	−0.430444	+	0.902617i	$0.641643\pi$
$108$	162.849	−	118.317i	0.145094	−	0.105417i
$109$	−1294.98			−1.13795			−0.568975	−	0.822355i	$-0.692660\pi$
$109$	−1294.98			−1.13795			−0.568975	+	0.822355i	$0.692660\pi$
$110$	48.2768	+	27.7615i	0.0418456	+	0.0240632i
$111$	19.9557			0.0170640
$112$	−385.438	+	280.037i	−0.325183	+	0.236259i
$113$	399.244	+	1228.75i	0.332369	+	1.02293i	0.968003	+	0.250937i	$0.0807387\pi$
$113$	399.244	+	1228.75i	0.332369	+	1.02293i	−0.635634	+	0.771990i	$0.719261\pi$
$114$	−349.184	+	1074.68i	−0.286878	+	0.882919i
$115$	57.4014	+	41.7046i	0.0465453	+	0.0338172i
$116$	−1671.31	−	1214.28i	−1.33774	−	0.971922i
$117$	41.3990	−	127.413i	0.0327123	−	0.100678i
$118$	927.478	+	2854.48i	0.723570	+	2.22692i
$119$	378.932	−	275.310i	0.291904	−	0.212081i
$120$	2.49451			0.00189764
$121$	669.481	+	1150.37i	0.502991	+	0.864292i
$122$	−252.822			−0.187618
$123$	33.4587	−	24.3092i	0.0245274	−	0.0178202i
$124$	−309.909	−	953.801i	−0.224441	−	0.690757i
$125$	−29.9784	+	92.2641i	−0.0214508	+	0.0660188i
$126$	200.372	+	145.579i	0.141671	+	0.102930i
$127$	−484.617	−	352.095i	−0.338604	−	0.246011i	0.405468	−	0.914109i	$-0.367108\pi$
$127$	−484.617	−	352.095i	−0.338604	−	0.246011i	−0.744073	+	0.668099i	$0.767108\pi$
$128$	84.5084	−	260.090i	0.0583559	−	0.179601i
$129$	−292.999	−	901.758i	−0.199978	−	0.615468i
$130$	−18.3827	+	13.3558i	−0.0124021	+	0.00901063i
$131$	2602.02			1.73542			0.867709	−	0.497072i	$-0.165592\pi$
$131$	2602.02			1.73542			0.867709	+	0.497072i	$0.165592\pi$
$132$	−707.355	−	406.763i	−0.466419	−	0.268213i
$133$	−670.672			−0.437253
$134$	1667.23	−	1211.32i	1.07483	−	0.780908i
$135$	−3.23962	−	9.97053i	−0.00206535	−	0.00635650i
$136$	−44.2796	+	136.278i	−0.0279187	+	0.0859249i
$137$	−2128.20	−	1546.23i	−1.32719	−	0.964258i	−0.999813	−	0.0193637i	$-0.993836\pi$
$137$	−2128.20	−	1546.23i	−1.32719	−	0.964258i	−0.327375	−	0.944894i	$-0.606164\pi$
$138$	−1743.55	−	1266.76i	−1.07551	−	0.781405i
$139$	894.928	−	2754.30i	0.546092	−	1.68070i	−0.172287	−	0.985047i	$-0.555116\pi$
$139$	894.928	−	2754.30i	0.546092	−	1.68070i	0.718379	−	0.695652i	$-0.244884\pi$
$140$	−6.26170	−	19.2715i	−0.00378007	−	0.0116339i
$141$	−1167.30	+	848.091i	−0.697193	+	0.506540i
$142$	3698.19			2.18553
$143$	−539.993	+	57.6995i	−0.315780	+	0.0337418i
$144$	−612.550			−0.354485
$145$	−87.0447	+	63.2417i	−0.0498529	+	0.0362202i
$146$	1294.96	+	3985.47i	0.734051	+	2.25918i
$147$	−45.4255	+	139.805i	−0.0254873	+	0.0784418i
$148$	40.1205	+	29.1492i	0.0222830	+	0.0161895i
$149$	2027.01	+	1472.71i	1.11449	+	0.809726i	0.983365	−	0.181639i	$-0.0581403\pi$
$149$	2027.01	+	1472.71i	1.11449	+	0.809726i	0.131127	+	0.991366i	$0.458140\pi$
$150$	455.017	−	1400.40i	0.247680	−	0.762281i
$151$	127.086	+	391.130i	0.0684908	+	0.210793i	0.979444	−	0.201717i	$-0.0646521\pi$
$151$	127.086	+	391.130i	0.0684908	+	0.210793i	−0.910953	+	0.412510i	$0.864652\pi$
$152$	165.991	−	120.600i	0.0885768	−	0.0643548i
$153$	602.210			0.318208
$154$	207.041	−	982.401i	0.108337	−	0.514053i
$155$	−52.2319			−0.0270669
$156$	269.344	−	195.690i	0.138236	−	0.100434i
$157$	377.626	+	1162.21i	0.191961	+	0.590794i	0.999999	+	0.00166353i	$0.000529520\pi$
$157$	377.626	+	1162.21i	0.191961	+	0.590794i	−0.808038	+	0.589130i	$0.799470\pi$
$158$	368.150	−	1133.05i	0.185370	−	0.570510i
$159$	−713.848	−	518.641i	−0.356049	−	0.258685i
$160$	78.6694	+	57.1567i	0.0388710	+	0.0282415i
$161$	395.273	−	1216.53i	0.193490	−	0.595501i
$162$	98.4024	+	302.851i	0.0477236	+	0.146878i
$163$	−1298.76	+	943.606i	−0.624092	+	0.453429i	−0.854348	−	0.519701i	$-0.826043\pi$
$163$	−1298.76	+	943.606i	−0.624092	+	0.453429i	0.230257	+	0.973130i	$0.426043\pi$
$164$	102.776			0.0489360
$165$	−31.5322	+	28.4906i	−0.0148775	+	0.0134424i
$166$	−611.046			−0.285701
$167$	562.696	−	408.822i	0.260735	−	0.189435i	−0.449736	−	0.893161i	$-0.648482\pi$
$167$	562.696	−	408.822i	0.260735	−	0.189435i	0.710471	+	0.703727i	$0.248482\pi$
$168$	−13.8969	−	42.7702i	−0.00638195	−	0.0196416i
$169$	−610.439	+	1878.74i	−0.277851	+	0.855137i
$170$	−82.6323	−	60.0359i	−0.0372800	−	0.0270855i
$171$	−697.610	−	506.843i	−0.311974	−	0.226662i
$172$	728.129	−	2240.95i	0.322787	−	0.993435i
$173$	−1154.66	−	3553.67i	−0.507438	−	1.56173i	−0.796632	−	0.604464i	$-0.793387\pi$
$173$	−1154.66	−	3553.67i	−0.507438	−	1.56173i	0.289194	−	0.957271i	$-0.406613\pi$
$174$	2643.95	−	1920.94i	1.15194	−	0.836933i
$175$	873.945			0.377509
$176$	1013.87	+	2266.64i	0.434225	+	0.970765i
$177$	−2290.36			−0.972623
$178$	4468.92	−	3246.86i	1.88180	−	1.36720i
$179$	516.265	+	1588.90i	0.215572	+	0.663464i	0.999112	+	0.0421224i	$0.0134120\pi$
$179$	516.265	+	1588.90i	0.215572	+	0.663464i	−0.783540	+	0.621341i	$0.786588\pi$
$180$	8.05076	−	24.7777i	0.00333371	−	0.0102601i
$181$	1795.19	+	1304.28i	0.737212	+	0.535616i	0.891837	−	0.452358i	$-0.149417\pi$
$181$	1795.19	+	1304.28i	0.737212	+	0.535616i	−0.154625	+	0.987973i	$0.549417\pi$
$182$	331.405	+	240.780i	0.134974	+	0.0980647i
$183$	59.6184	−	183.486i	0.0240826	−	0.0741186i
$184$	120.925	+	372.168i	0.0484494	+	0.149112i
$185$	2.08954	−	1.51814i	0.000830411	−	0.000603329i
$186$	1586.53			0.625429
$187$	−996.758	−	2228.38i	−0.389787	−	0.871419i
$188$	−3585.64			−1.39101
$189$	−152.904	+	111.091i	−0.0588473	+	0.0427551i
$190$	45.1941	+	139.093i	0.0172564	+	0.0531098i
$191$	1176.89	−	3622.10i	0.445847	−	1.37218i	−0.435705	−	0.900089i	$-0.643501\pi$
$191$	1176.89	−	3622.10i	0.445847	−	1.37218i	0.881552	−	0.472087i	$-0.156499\pi$
$192$	−1068.06	−	775.988i	−0.401460	−	0.291678i
$193$	−2674.92	−	1943.44i	−0.997640	−	0.724828i	−0.0360594	−	0.999350i	$-0.511481\pi$
$193$	−2674.92	−	1943.44i	−0.997640	−	0.724828i	−0.961581	+	0.274521i	$0.911481\pi$
$194$	760.900	−	2341.81i	0.281595	−	0.866660i
$195$	−5.35817	−	16.4908i	−0.00196773	−	0.00605604i
$196$	−295.541	+	214.723i	−0.107704	+	0.0782518i
$197$	2606.14			0.942538			0.471269	−	0.881990i	$-0.343796\pi$
$197$	2606.14			0.942538			0.471269	+	0.881990i	$0.343796\pi$
$198$	957.781	−	865.392i	0.343770	−	0.310610i
$199$	−553.258			−0.197082			−0.0985412	−	0.995133i	$-0.531418\pi$
$199$	−553.258			−0.197082			−0.0985412	+	0.995133i	$0.531418\pi$
$200$	−216.301	+	157.152i	−0.0764741	+	0.0555617i
$201$	485.964	+	1495.64i	0.170533	+	0.524848i
$202$	497.336	−	1530.64i	0.173230	−	0.533147i
$203$	1569.25	+	1140.13i	0.542560	+	0.394193i
$204$	1210.73	+	879.648i	0.415530	+	0.301900i
$205$	1.65410	−	5.09079i	0.000563547	−	0.00173442i
$206$	1847.13	+	5684.87i	0.624735	+	1.92274i
$207$	1330.51	−	966.669i	0.446747	−	0.324581i
$208$	−1013.13			−0.337729
$209$	−720.831	+	3420.30i	−0.238569	+	1.13200i
$210$	32.0558			0.0105336
$211$	−1365.65	+	992.200i	−0.445568	+	0.323724i	−0.787844	−	0.615875i	$-0.788802\pi$
$211$	−1365.65	+	992.200i	−0.445568	+	0.323724i	0.342275	+	0.939600i	$0.388802\pi$
$212$	−677.599	−	2085.44i	−0.219517	−	0.675605i
$213$	−872.075	+	2683.97i	−0.280533	+	0.863393i
$214$	−5107.34	−	3710.70i	−1.63145	−	1.18532i
$215$	−99.2815	−	72.1322i	−0.0314927	−	0.0228808i
$216$	17.8674	−	54.9902i	0.00562835	−	0.0173223i
$217$	290.983	+	895.555i	0.0910288	+	0.280158i
$218$	4118.69	−	2992.40i	1.27960	−	0.929684i
$219$	−3197.84			−0.986711
$220$	−105.011	+	11.2207i	−0.0321812	+	0.00343863i
$221$	996.024			0.303167
$222$	−63.4691	+	46.1130i	−0.0191881	+	0.0139410i
$223$	114.395	+	352.072i	0.0343519	+	0.105724i	0.966762	−	0.255677i	$-0.0822984\pi$
$223$	114.395	+	352.072i	0.0343519	+	0.105724i	−0.932410	+	0.361401i	$0.882298\pi$
$224$	541.727	−	1667.26i	0.161588	−	0.497316i
$225$	909.046	+	660.461i	0.269347	+	0.195692i
$226$	−4109.15	−	2985.47i	−1.20945	−	0.878720i
$227$	−283.313	+	871.946i	−0.0828375	+	0.254948i	−0.983894	−	0.178755i	$-0.942793\pi$
$227$	−283.313	+	871.946i	−0.0828375	+	0.254948i	0.901056	+	0.433702i	$0.142793\pi$
$228$	−662.185	−	2038.00i	−0.192343	−	0.591972i
$229$	3336.96	−	2424.44i	0.962936	−	0.699614i	0.00910553	−	0.999959i	$-0.497102\pi$
$229$	3336.96	−	2424.44i	0.962936	−	0.699614i	0.953831	+	0.300344i	$0.0971016\pi$
$230$	−278.935			−0.0799672
$231$	664.158	+	381.923i	0.189171	+	0.108782i
$232$	−593.406			−0.167927
$233$	−497.199	+	361.236i	−0.139796	+	0.101568i	−0.655486	−	0.755208i	$-0.727536\pi$
$233$	−497.199	+	361.236i	−0.139796	+	0.101568i	0.515689	+	0.856776i	$0.327536\pi$
$234$	162.753	+	500.901i	0.0454678	+	0.139936i
$235$	−57.7076	+	177.606i	−0.0160189	+	0.0493010i
$236$	−4604.73	−	3345.53i	−1.27010	−	0.922778i
$237$	735.501	+	534.372i	0.201586	+	0.146461i
$238$	−569.016	+	1751.25i	−0.154974	+	0.476961i
$239$	217.228	+	668.558i	0.0587920	+	0.180943i	0.976140	−	0.217144i	$-0.0696741\pi$
$239$	217.228	+	668.558i	0.0587920	+	0.180943i	−0.917348	+	0.398087i	$0.869674\pi$
$240$	−64.1396	+	46.6001i	−0.0172508	+	0.0125334i
$241$	4927.95			1.31717			0.658584	−	0.752507i	$-0.271156\pi$
$241$	4927.95			1.31717			0.658584	+	0.752507i	$0.271156\pi$
$242$	−4787.54	−	2111.75i	−1.27171	−	0.560943i
$243$	−243.000			−0.0641500
$244$	387.880	−	281.812i	0.101768	−	0.0739391i
$245$	5.87932	+	18.0947i	0.00153313	+	0.00471847i
$246$	−50.2426	+	154.631i	−0.0130218	+	0.0400768i
$247$	−1153.81	−	838.293i	−0.297228	−	0.215948i
$248$	−233.056	−	169.325i	−0.0596738	−	0.0433555i
$249$	144.092	−	443.469i	0.0366725	−	0.112866i
$250$	−117.855	−	362.720i	−0.0298152	−	0.0917616i
$251$	−739.112	+	536.996i	−0.185866	+	0.135039i	−0.676827	−	0.736142i	$-0.736646\pi$
$251$	−739.112	+	536.996i	−0.185866	+	0.135039i	0.490961	+	0.871181i	$0.336646\pi$
$252$	−469.682			−0.117410
$253$	−5779.22	−	3323.33i	−1.43611	−	0.825833i
$254$	2354.94			0.581739
$255$	63.0569	−	45.8135i	0.0154854	−	0.0112508i
$256$	1420.13	+	4370.70i	0.346710	+	1.06706i
$257$	−912.178	+	2807.40i	−0.221401	+	0.681403i	0.777236	+	0.629210i	$0.216621\pi$
$257$	−912.178	+	2807.40i	−0.221401	+	0.681403i	−0.998637	+	0.0521935i	$0.983379\pi$
$258$	3015.64	+	2190.99i	0.727696	+	0.528702i
$259$	−37.6704	−	27.3692i	−0.00903756	−	0.00656617i
$260$	13.3155	−	40.9810i	0.00317614	−	0.00977514i
$261$	770.657	+	2371.84i	0.182768	+	0.562502i
$262$	−8275.74	+	6012.68i	−1.95144	+	1.41780i
$263$	−300.554			−0.0704676			−0.0352338	−	0.999379i	$-0.511218\pi$
$263$	−300.554			−0.0704676			−0.0352338	+	0.999379i	$0.511218\pi$
$264$	−233.056	+	24.9026i	−0.0543319	+	0.00580548i
$265$	−114.202			−0.0264732
$266$	2133.08	−	1549.77i	0.491682	−	0.357228i
$267$	1302.60	+	4008.98i	0.298568	+	0.918898i
$268$	−1207.66	+	3716.81i	−0.275261	+	0.847165i
$269$	−5439.27	−	3951.86i	−1.23286	−	0.895722i	−0.235755	−	0.971813i	$-0.575756\pi$
$269$	−5439.27	−	3951.86i	−1.23286	−	0.895722i	−0.997101	+	0.0760907i	$0.975756\pi$
$270$	33.3433	+	24.2253i	0.00751558	+	0.00546039i
$271$	−190.546	+	586.439i	−0.0427115	+	0.131452i	−0.970138	−	0.242552i	$-0.922016\pi$
$271$	−190.546	+	586.439i	−0.0427115	+	0.131452i	0.927427	+	0.374004i	$0.122016\pi$
$272$	−1407.30	−	4331.22i	−0.313713	−	0.965511i
$273$	−252.896	+	183.740i	−0.0560657	+	0.0407341i
$274$	10341.7			2.28017
$275$	939.305	−	4456.95i	0.205972	−	0.977325i
$276$	4086.97			0.891329
$277$	−3417.06	+	2482.64i	−0.741196	+	0.538510i	−0.893085	−	0.449887i	$-0.851464\pi$
$277$	−3417.06	+	2482.64i	−0.741196	+	0.538510i	0.151890	+	0.988397i	$0.451464\pi$
$278$	3518.25	+	10828.1i	0.759030	+	2.33606i
$279$	−374.122	+	1151.43i	−0.0802798	+	0.247076i
$280$	−4.70890	−	3.42122i	−0.00100504	−	0.000730203i
$281$	−657.102	−	477.413i	−0.139500	−	0.101352i	0.515847	−	0.856681i	$-0.327477\pi$
$281$	−657.102	−	477.413i	−0.139500	−	0.101352i	−0.655346	+	0.755328i	$0.727477\pi$
$282$	1752.85	−	5394.72i	0.370144	−	1.13919i
$283$	−776.158	−	2388.77i	−0.163031	−	0.501758i	0.835855	−	0.548951i	$-0.184973\pi$
$283$	−776.158	−	2388.77i	−0.163031	−	0.501758i	−0.998886	+	0.0471925i	$0.984973\pi$
$284$	−5673.77	+	4122.23i	−1.18548	+	0.861301i
$285$	−111.605			−0.0231961
$286$	1584.12	−	1431.32i	0.327521	−	0.295928i
$287$	−96.5002			−0.0198475
$288$	1823.48	−	1324.83i	0.373088	−	0.271064i
$289$	−134.656	−	414.430i	−0.0274082	−	0.0843537i
$290$	130.709	−	402.281i	0.0264672	−	0.0814577i
$291$	1520.15	+	1104.45i	0.306229	+	0.222488i
$292$	−6429.19	−	4671.08i	−1.28849	−	0.936145i
$293$	−2640.27	+	8125.92i	−0.526438	+	1.62021i	0.235016	+	0.971992i	$0.424486\pi$
$293$	−2640.27	+	8125.92i	−0.526438	+	1.62021i	−0.761454	+	0.648219i	$0.775514\pi$
$294$	−178.582	−	549.619i	−0.0354256	−	0.109029i
$295$	−239.822	+	174.241i	−0.0473321	+	0.0343888i
$296$	14.2449			0.00279720
$297$	402.206	+	899.183i	0.0785803	+	0.175676i
$298$	−9850.03			−1.91475
$299$	2200.59	−	1598.82i	0.425630	−	0.309238i
$300$	862.886	+	2655.69i	0.166062	+	0.511088i
$301$	−683.664	+	2104.10i	−0.130916	+	0.402918i
$302$	−1308.01	−	950.326i	−0.249230	−	0.181076i
$303$	993.592	+	721.886i	0.188384	+	0.136869i
$304$	−2015.09	+	6201.80i	−0.380175	+	1.17006i
$305$	−7.71626	−	23.7482i	−0.00144863	−	0.00445842i
$306$	−1915.33	+	1391.57i	−0.357818	+	0.259970i
$307$	1418.70			0.263745			0.131872	−	0.991267i	$-0.457901\pi$
$307$	1418.70			0.263745			0.131872	+	0.991267i	$0.457901\pi$
$308$	777.403	+	1737.98i	0.143820	+	0.321529i
$309$	−4561.39			−0.839768
$310$	166.124	−	120.696i	0.0304361	−	0.0221132i
$311$	1829.36	+	5630.19i	0.333548	+	1.02656i	0.967433	+	0.253129i	$0.0814596\pi$
$311$	1829.36	+	5630.19i	0.333548	+	1.02656i	−0.633884	+	0.773428i	$0.718540\pi$
$312$	29.5518	−	90.9511i	0.00536231	−	0.0165035i
$313$	5264.79	+	3825.10i	0.950747	+	0.690758i	0.950983	−	0.309242i	$-0.100075\pi$
$313$	5264.79	+	3825.10i	0.950747	+	0.690758i	−0.000236743		1.00000i	$0.500075\pi$
$314$	−3886.65	−	2823.81i	−0.698523	−	0.507507i
$315$	−7.55912	+	23.2646i	−0.00135209	+	0.00416130i
$316$	698.152	+	2148.69i	0.124285	+	0.382511i
$317$	4560.18	−	3313.16i	0.807966	−	0.587022i	−0.105274	−	0.994443i	$-0.533572\pi$
$317$	4560.18	−	3313.16i	0.807966	−	0.587022i	0.913240	+	0.407422i	$0.133572\pi$
$318$	3468.86			0.611710
$319$	7501.04	−	6777.48i	1.31654	−	1.18955i
$320$	−170.869			−0.0298496
$321$	3897.42	−	2831.64i	0.677673	−	0.492358i
$322$	1553.94	+	4782.55i	0.268938	+	0.827705i
$323$	1981.07	−	6097.11i	0.341268	−	1.05032i
$324$	−488.547	−	354.950i	−0.0837701	−	0.0608625i
$325$	1503.52	+	1092.37i	0.256616	+	0.186442i
$326$	1950.26	−	6002.29i	0.331334	−	1.01974i
$327$	1200.51	+	3694.80i	0.203023	+	0.624840i
$328$	23.8838	−	17.3526i	0.00402062	−	0.00292115i
$329$	3366.67			0.564166
$330$	34.4531	−	163.478i	0.00574722	−	0.0272703i
$331$	−1611.98			−0.267681			−0.133841	−	0.991003i	$-0.542731\pi$
$331$	−1611.98			−0.267681			−0.133841	+	0.991003i	$0.542731\pi$
$332$	937.469	−	681.111i	0.154971	−	0.112593i
$333$	−18.4999	−	56.9369i	−0.00304441	−	0.00936974i
$334$	−844.961	+	2600.52i	−0.138426	+	0.426031i
$335$	164.667	+	119.637i	0.0268558	+	0.0195119i
$336$	1156.31	+	840.111i	0.187744	+	0.136404i
$337$	−894.066	+	2751.65i	−0.144519	+	0.444783i	−0.996949	−	0.0780582i	$-0.975128\pi$
$337$	−894.066	+	2751.65i	−0.144519	+	0.444783i	0.852430	+	0.522841i	$0.175128\pi$
$338$	−2399.83	−	7385.91i	−0.386194	−	1.18858i
$339$	3135.70	−	2278.22i	0.502384	−	0.365003i
$340$	193.695			0.0308958
$341$	4879.91	−	521.429i	0.774961	−	0.0828064i
$342$	3389.95			0.535987
$343$	277.493	−	201.610i	0.0436828	−	0.0317374i
$344$	−209.151	−	643.701i	−0.0327810	−	0.100890i
$345$	65.7762	−	202.438i	0.0102646	−	0.0315910i
$346$	11884.1	+	8634.30i	1.84651	+	1.34157i
$347$	123.176	+	89.4928i	0.0190561	+	0.0138450i	0.597273	−	0.802038i	$-0.296251\pi$
$347$	123.176	+	89.4928i	0.0190561	+	0.0138450i	−0.578216	+	0.815883i	$0.696251\pi$
$348$	−1915.15	+	5894.24i	−0.295009	+	0.907943i
$349$	−1539.33	−	4737.58i	−0.236099	−	0.726638i	−0.996974	−	0.0777394i	$-0.975230\pi$
$349$	−1539.33	−	4737.58i	−0.236099	−	0.726638i	0.760875	−	0.648899i	$-0.224770\pi$
$350$	−2779.58	+	2019.49i	−0.424500	+	0.308417i
$351$	−401.910			−0.0611178
$352$	−7920.50	−	4554.66i	−1.19933	−	0.689671i
$353$	−48.4448			−0.00730441			−0.00365221	−	0.999993i	$-0.501163\pi$
$353$	−48.4448			−0.00730441			−0.00365221	+	0.999993i	$0.501163\pi$
$354$	7284.51	−	5292.51i	1.09369	−	0.794614i
$355$	112.871	+	347.380i	0.0168748	+	0.0519353i
$356$	−3237.07	+	9962.69i	−0.481923	+	1.48321i
$357$	−1136.80	−	825.930i	−0.168531	−	0.122445i
$358$	−5313.57	−	3860.54i	−0.784444	−	0.569932i
$359$	1716.46	−	5282.71i	0.252343	−	0.776632i	−0.741998	−	0.670402i	$-0.766122\pi$
$359$	1716.46	−	5282.71i	0.252343	−	0.776632i	0.994342	−	0.106231i	$-0.0338782\pi$
$360$	−2.31254	−	7.11726i	−0.000338559	−	0.00104198i
$361$	−1877.42	+	1364.02i	−0.273716	+	0.198866i
$362$	−8723.50			−1.26657
$363$	2661.56	−	2976.60i	0.384837	−	0.430388i
$364$	−776.831			−0.111860
$365$	−334.843	+	243.277i	−0.0480177	+	0.0348869i
$366$	234.379	+	721.344i	0.0334732	+	0.103020i
$367$	1819.19	−	5598.89i	0.258749	−	0.796349i	−0.734318	−	0.678805i	$-0.762498\pi$
$367$	1819.19	−	5598.89i	0.258749	−	0.796349i	0.993068	−	0.117543i	$-0.0375019\pi$
$368$	−10061.7	−	7310.28i	−1.42528	−	1.03553i
$369$	−100.376	−	72.9275i	−0.0141609	−	0.0102885i
$370$	−3.13772	+	9.65690i	−0.000440871	+	0.00135686i
$371$	636.220	+	1958.08i	0.0890320	+	0.274012i
$372$	−2434.06	+	1768.44i	−0.339247	+	0.246477i
$373$	−739.031			−0.102589			−0.0512943	−	0.998684i	$-0.516335\pi$
$373$	−739.031			−0.102589			−0.0512943	+	0.998684i	$0.516335\pi$
$374$	8319.48	+	4784.10i	1.15024	+	0.661443i
$375$	291.037			0.0400775
$376$	−833.251	+	605.392i	−0.114286	+	0.0830338i
$377$	1274.63	+	3922.90i	0.174129	+	0.535914i
$378$	229.606	−	706.653i	0.0312424	−	0.0961543i
$379$	−5336.37	−	3877.10i	−0.723248	−	0.525470i	0.164172	−	0.986432i	$-0.447505\pi$
$379$	−5336.37	−	3877.10i	−0.723248	−	0.525470i	−0.887420	+	0.460961i	$0.847505\pi$
$380$	−224.379	−	163.021i	−0.0302905	−	0.0220073i
$381$	−555.321	+	1709.10i	−0.0746718	+	0.229816i
$382$	4626.73	+	14239.6i	0.619697	+	1.90723i
$383$	5400.70	−	3923.84i	0.720529	−	0.523495i	−0.166024	−	0.986122i	$-0.553093\pi$
$383$	5400.70	−	3923.84i	0.720529	−	0.523495i	0.886553	+	0.462626i	$0.153093\pi$
$384$	−820.425			−0.109029
$385$	98.5985	−	10.5355i	0.0130521	−	0.00139464i
$386$	12998.4			1.71400
$387$	−2301.24	+	1671.95i	−0.302271	+	0.219612i
$388$	1442.96	+	4440.96i	0.188801	+	0.581071i
$389$	−1945.36	+	5987.21i	−0.253557	+	0.780369i	0.740553	+	0.671998i	$0.234564\pi$
$389$	−1945.36	+	5987.21i	−0.253557	+	0.780369i	−0.994110	+	0.108371i	$0.965436\pi$
$390$	55.1481	+	40.0674i	0.00716033	+	0.00520229i
$391$	9891.90	+	7186.89i	1.27942	+	0.929556i
$392$	−32.4260	+	99.7971i	−0.00417797	+	0.0128585i
$393$	−2412.21	−	7424.01i	−0.309618	−	0.952905i
$394$	−8288.84	+	6022.20i	−1.05986	+	0.770035i
$395$	117.666			0.0149885
$396$	−504.809	+	2395.29i	−0.0640596	+	0.303960i
$397$	−6513.10			−0.823383			−0.411692	−	0.911323i	$-0.635062\pi$
$397$	−6513.10			−0.823383			−0.411692	+	0.911323i	$0.635062\pi$
$398$	1759.64	−	1278.45i	0.221615	−	0.161013i
$399$	621.747	+	1913.54i	0.0780108	+	0.240092i
$400$	2625.83	−	8081.48i	0.328229	−	1.01019i
$401$	−4318.89	−	3137.86i	−0.537844	−	0.390766i	0.285440	−	0.958397i	$-0.407860\pi$
$401$	−4318.89	−	3137.86i	−0.537844	−	0.390766i	−0.823284	+	0.567630i	$0.807860\pi$
$402$	−5001.70	−	3633.95i	−0.620552	−	0.450858i
$403$	−618.778	+	1904.40i	−0.0764852	+	0.235397i
$404$	943.138	+	2902.68i	0.116146	+	0.357460i
$405$	−25.4443	+	18.4864i	−0.00312182	+	0.00226814i
$406$	−7625.58			−0.932145
$407$	−180.065	+	162.696i	−0.0219300	+	0.0198146i
$408$	429.875			0.0521617
$409$	−3452.60	+	2508.46i	−0.417408	+	0.303265i	−0.776594	−	0.630001i	$-0.783054\pi$
$409$	−3452.60	+	2508.46i	−0.417408	+	0.303265i	0.359186	+	0.933266i	$0.383054\pi$
$410$	6.50278	+	20.0135i	0.000783291	+	0.00241072i
$411$	−2438.70	+	7505.56i	−0.292682	+	0.900783i
$412$	−9170.58	−	6662.82i	−1.09661	−	0.796732i
$413$	4323.53	+	3141.23i	0.515126	+	0.374261i
$414$	−1997.93	+	6148.99i	−0.237181	+	0.729967i
$415$	−18.6495	−	57.3971i	−0.00220594	−	0.00678919i
$416$	3015.94	−	2191.21i	0.355453	−	0.258252i
$417$	−8688.14			−1.02029
$418$	−5610.94	−	12544.0i	−0.656555	−	1.46781i
$419$	−12586.1			−1.46748			−0.733739	−	0.679431i	$-0.762227\pi$
$419$	−12586.1			−1.46748			−0.733739	+	0.679431i	$0.762227\pi$
$420$	−49.1800	+	35.7314i	−0.00571367	+	0.00415122i
$421$	−845.901	−	2603.42i	−0.0979257	−	0.301384i	0.890079	−	0.455805i	$-0.150649\pi$
$421$	−845.901	−	2603.42i	−0.0979257	−	0.301384i	−0.988005	+	0.154421i	$0.950649\pi$
$422$	2050.69	−	6311.39i	0.236555	−	0.728042i
$423$	3501.89	+	2544.27i	0.402524	+	0.292451i
$424$	−509.565	−	370.221i	−0.0583648	−	0.0424045i
$425$	−2581.51	+	7945.07i	−0.294639	+	0.906806i
$426$	−3428.41	−	10551.5i	−0.389922	−	1.20006i
$427$	−364.193	+	264.602i	−0.0412753	+	0.0299883i
$428$	11971.9			1.35206
$429$	665.228	+	1487.20i	0.0748660	+	0.167373i
$430$	482.446			0.0541061
$431$	−8803.18	+	6395.88i	−0.983838	+	0.714800i	−0.958563	−	0.284880i	$-0.908046\pi$
$431$	−8803.18	+	6395.88i	−0.983838	+	0.714800i	−0.0252751	+	0.999681i	$0.508046\pi$
$432$	567.865	+	1747.71i	0.0632440	+	0.194645i
$433$	2146.21	−	6605.34i	0.238199	−	0.733101i	−0.758482	−	0.651694i	$-0.774059\pi$
$433$	2146.21	−	6605.34i	0.238199	−	0.733101i	0.996681	−	0.0814068i	$-0.0259413\pi$
$434$	−2994.90	−	2175.92i	−0.331243	−	0.240662i
$435$	261.134	+	189.725i	0.0287826	+	0.0209118i
$436$	−2983.38	+	9181.91i	−0.327702	+	1.00856i
$437$	−5410.18	−	16650.8i	−0.592228	−	1.82269i
$438$	10170.7	−	7389.47i	1.10953	−	0.806124i
$439$	10602.2			1.15266			0.576330	−	0.817217i	$-0.304484\pi$
$439$	10602.2			1.15266			0.576330	+	0.817217i	$0.304484\pi$
$440$	−22.5086	+	20.3374i	−0.00243877	+	0.00220352i
$441$	441.000			0.0476190
$442$	−3167.86	+	2301.59i	−0.340904	+	0.247682i
$443$	380.999	+	1172.60i	0.0408619	+	0.125760i	0.969407	−	0.245461i	$-0.0789393\pi$
$443$	380.999	+	1172.60i	0.0408619	+	0.125760i	−0.928545	+	0.371221i	$0.878939\pi$
$444$	45.9740	−	141.493i	0.00491403	−	0.0151238i
$445$	441.380	+	320.681i	0.0470189	+	0.0341612i
$446$	−1177.39	−	855.427i	−0.125003	−	0.0908198i
$447$	2322.75	−	7148.69i	0.245777	−	0.756424i
$448$	951.909	+	2929.67i	0.100387	+	0.308960i
$449$	−14265.5	+	10364.5i	−1.49940	+	1.08938i	−0.528777	+	0.848761i	$0.677349\pi$
$449$	−14265.5	+	10364.5i	−1.49940	+	1.08938i	−0.970620	+	0.240616i	$0.922651\pi$
$450$	−4417.40			−0.462752
$451$	−103.717	+	492.133i	−0.0108289	+	0.0513828i
$452$	9632.08			1.00233
$453$	998.146	−	725.196i	0.103525	−	0.0752156i
$454$	−1113.79	−	3427.90i	−0.115138	−	0.354360i
$455$	−12.5024	+	38.4784i	−0.00128818	+	0.00396461i
$456$	−497.974	−	361.799i	−0.0511399	−	0.0371553i
$457$	−4326.69	−	3143.52i	−0.442875	−	0.321768i	0.343901	−	0.939006i	$-0.388251\pi$
$457$	−4326.69	−	3143.52i	−0.442875	−	0.321768i	−0.786776	+	0.617238i	$0.788251\pi$
$458$	−5010.88	+	15421.9i	−0.511229	+	1.57340i
$459$	−558.279	−	1718.21i	−0.0567718	−	0.174726i
$460$	427.943	−	310.919i	0.0433760	−	0.0315145i
$461$	−2417.13			−0.244202			−0.122101	−	0.992518i	$-0.538963\pi$
$461$	−2417.13			−0.244202			−0.122101	+	0.992518i	$0.538963\pi$
$462$	−2994.89	+	320.011i	−0.301591	+	0.0322257i
$463$	3451.65			0.346462			0.173231	−	0.984881i	$-0.444579\pi$
$463$	3451.65			0.346462			0.173231	+	0.984881i	$0.444579\pi$
$464$	15257.8	−	11085.5i	1.52657	−	1.10912i
$465$	48.4217	+	149.027i	0.00482903	+	0.0148622i
$466$	746.609	−	2297.83i	0.0742189	−	0.228422i
$467$	3622.20	+	2631.68i	0.358920	+	0.260770i	0.752601	−	0.658476i	$-0.228799\pi$
$467$	3622.20	+	2631.68i	0.358920	+	0.260770i	−0.393682	+	0.919247i	$0.628799\pi$
$468$	−808.032	−	587.069i	−0.0798104	−	0.0579857i
$469$	1133.92	−	3489.83i	0.111640	−	0.343594i
$470$	−226.867	−	698.225i	−0.0222651	−	0.0685250i
$471$	2965.91	−	2154.86i	0.290153	−	0.210808i
$472$	−1634.93			−0.159436
$473$	9995.73	+	5748.02i	0.971679	+	0.558762i
$474$	−3574.08			−0.346335
$475$	9677.34	−	7031.00i	0.934793	−	0.679167i
$476$	−1079.07	−	3321.03i	−0.103906	−	0.319789i
$477$	−817.997	+	2517.54i	−0.0785189	+	0.241656i
$478$	−2235.78	−	1624.39i	−0.213938	−	0.155435i
$479$	10708.6	+	7780.24i	1.02148	+	0.742147i	0.966585	−	0.256346i	$-0.0825185\pi$
$479$	10708.6	+	7780.24i	1.02148	+	0.742147i	0.0548920	+	0.998492i	$0.482519\pi$
$480$	90.1472	−	277.444i	0.00857216	−	0.0263824i
$481$	−30.5979	−	94.1707i	−0.00290051	−	0.00892685i
$482$	−15673.4	+	11387.4i	−1.48113	+	1.07610i
$483$	−3837.39			−0.361506
$484$	9698.94	−	2096.65i	0.910870	−	0.196905i
$485$	243.195			0.0227689
$486$	772.863	−	561.518i	0.0721353	−	0.0524094i
$487$	−4486.34	−	13807.5i	−0.417444	−	1.28476i	−0.910046	−	0.414507i	$-0.863954\pi$
$487$	−4486.34	−	13807.5i	−0.417444	−	1.28476i	0.492602	−	0.870255i	$-0.336046\pi$
$488$	42.5573	−	130.978i	0.00394770	−	0.0121498i
$489$	3896.29	+	2830.82i	0.360319	+	0.261787i
$490$	−60.5118	−	43.9644i	−0.00557887	−	0.00405329i
$491$	−1074.84	+	3308.01i	−0.0987917	+	0.304049i	−0.988223	−	0.153019i	$-0.951100\pi$
$491$	−1074.84	+	3308.01i	−0.0987917	+	0.304049i	0.889432	+	0.457068i	$0.151100\pi$
$492$	−95.2791	−	293.239i	−0.00873071	−	0.0268704i
$493$	−15000.3	+	10898.3i	−1.37034	+	0.995611i
$494$	5606.80			0.510652
$495$	110.521	+	63.5546i	0.0100354	+	0.00577084i
$496$	9155.60			0.828827
$497$	5327.29	−	3870.50i	0.480808	−	0.349327i
$498$	566.471	+	1743.42i	0.0509722	+	0.156876i
$499$	3875.36	−	11927.1i	0.347665	−	1.07000i	−0.612476	−	0.790489i	$-0.709827\pi$
$499$	3875.36	−	11927.1i	0.347665	−	1.07000i	0.960142	−	0.279514i	$-0.0901735\pi$
$500$	585.124	+	425.117i	0.0523351	+	0.0380236i
$501$	−1688.09	−	1226.47i	−0.150535	−	0.109370i
$502$	1109.87	−	3415.84i	0.0986774	−	0.303698i
$503$	1952.16	+	6008.12i	0.173046	+	0.532582i	0.999539	−	0.0303657i	$-0.00966718\pi$
$503$	1952.16	+	6008.12i	0.173046	+	0.532582i	−0.826492	+	0.562948i	$0.809667\pi$
$504$	−109.147	+	79.3003i	−0.00964646	+	0.00700856i
$505$	158.956			0.0140068
$506$	26060.3	−	2784.60i	2.28957	−	0.244645i
$507$	5926.26			0.519121
$508$	−3612.95	+	2624.96i	−0.315549	+	0.229260i
$509$	1557.01	+	4791.98i	0.135586	+	0.417290i	0.995681	−	0.0928438i	$-0.0295957\pi$
$509$	1557.01	+	4791.98i	0.135586	+	0.417290i	−0.860095	+	0.510134i	$0.829596\pi$
$510$	−94.6881	+	291.420i	−0.00822130	+	0.0253026i
$511$	6036.57	+	4385.83i	0.522588	+	0.379682i
$512$	−12846.4	−	9333.48i	−1.10886	−	0.805635i
$513$	−799.389	+	2460.27i	−0.0687990	+	0.211742i
$514$	−3586.07	−	11036.8i	−0.307733	−	0.947104i
$515$	−477.619	+	347.011i	−0.0408668	+	0.0296915i
$516$	−7068.82			−0.603077
$517$	3618.46	−	17169.4i	0.307814	−	1.46056i
$518$	183.055			0.0155270
$519$	−9068.78	+	6588.86i	−0.767005	+	0.557262i
$520$	−3.82482	−	11.7716i	−0.000322557	−	0.000992727i
$521$	2797.13	−	8608.69i	0.235210	−	0.723903i	−0.761883	−	0.647715i	$-0.775725\pi$
$521$	2797.13	−	8608.69i	0.235210	−	0.723903i	0.997093	−	0.0761885i	$-0.0242751\pi$
$522$	−7931.85	−	5762.83i	−0.665073	−	0.483203i
$523$	−5524.27	−	4013.61i	−0.461872	−	0.335570i	0.332393	−	0.943141i	$-0.392144\pi$
$523$	−5524.27	−	4013.61i	−0.461872	−	0.335570i	−0.794265	+	0.607571i	$0.792144\pi$
$524$	5994.56	−	18449.4i	0.499758	−	1.53810i
$525$	−810.191	−	2493.51i	−0.0673517	−	0.207287i
$526$	955.914	−	694.512i	0.0792392	−	0.0575707i
$527$	−9001.05			−0.744007
$528$	5527.20	−	4994.04i	0.455569	−	0.411625i
$529$	21224.3			1.74442
$530$	363.221	−	263.896i	0.0297685	−	0.0216281i
$531$	2123.28	+	6534.79i	0.173527	+	0.534060i
$532$	−1545.10	+	4755.33i	−0.125918	+	0.387537i
$533$	−166.017	−	120.618i	−0.0134915	−	0.00980218i
$534$	−13406.8	−	9740.58i	−1.08646	−	0.789356i
$535$	192.677	−	592.998i	0.0155704	−	0.0479206i
$536$	346.895	+	1067.63i	0.0279544	+	0.0860349i
$537$	4054.80	−	2945.98i	0.325843	−	0.236739i
$538$	26431.5			2.11811
$539$	−729.929	−	1631.85i	−0.0583307	−	0.130406i
$540$	−78.1584			−0.00622852
$541$	−8290.22	+	6023.20i	−0.658826	+	0.478665i	−0.866266	−	0.499583i	$-0.833487\pi$
$541$	−8290.22	+	6023.20i	−0.658826	+	0.478665i	0.207441	+	0.978248i	$0.433487\pi$
$542$	−749.095	−	2305.48i	−0.0593661	−	0.182710i
$543$	2057.10	−	6331.11i	0.162576	−	0.500357i
$544$	13557.0	+	9849.73i	1.06848	+	0.776293i
$545$	406.789	+	295.549i	0.0319723	+	0.0232293i
$546$	379.756	−	1168.77i	0.0297657	−	0.0916093i
$547$	−3235.99	−	9959.34i	−0.252945	−	0.778484i	−0.994228	−	0.107291i	$-0.965782\pi$
$547$	−3235.99	−	9959.34i	−0.252945	−	0.778484i	0.741283	−	0.671193i	$-0.234218\pi$
$548$	−15866.3	+	11527.6i	−1.23682	+	0.898601i
$549$	−578.787			−0.0449946
$550$	7311.54	+	16345.9i	0.566846	+	1.26726i
$551$	26549.0			2.05268
$552$	949.754	−	690.037i	0.0732323	−	0.0532064i
$553$	−655.518	−	2017.48i	−0.0504077	−	0.155139i
$554$	5131.16	−	15792.1i	0.393506	−	1.21109i
$555$	−6.26862	−	4.55442i	−0.000479438	−	0.000348332i
$556$	−17467.3	−	12690.8i	−1.33234	−	0.968001i
$557$	545.170	−	1677.86i	0.0414714	−	0.127636i	−0.928177	−	0.372138i	$-0.878625\pi$
$557$	545.170	−	1677.86i	0.0414714	−	0.127636i	0.969649	+	0.244503i	$0.0786247\pi$
$558$	−1470.79	−	4526.63i	−0.111583	−	0.343419i
$559$	−3806.14	+	2765.32i	−0.287983	+	0.209232i
$560$	184.989			0.0139593
$561$	−5433.90	+	4909.74i	−0.408948	+	0.369500i
$562$	3193.11			0.239667
$563$	1282.99	−	932.147i	0.0960419	−	0.0697785i	−0.538728	−	0.842480i	$-0.681095\pi$
$563$	1282.99	−	932.147i	0.0960419	−	0.0697785i	0.634770	+	0.772701i	$0.281095\pi$
$564$	3324.07	+	10230.4i	0.248171	+	0.763792i
$565$	155.020	−	477.102i	0.0115429	−	0.0355253i
$566$	7988.48	+	5803.97i	0.593252	+	0.431023i
$567$	458.713	+	333.274i	0.0339755	+	0.0246847i
$568$	−622.513	+	1915.90i	−0.0459860	+	0.141530i
$569$	3366.83	+	10362.0i	0.248058	+	0.763444i	0.995118	+	0.0986879i	$0.0314645\pi$
$569$	3366.83	+	10362.0i	0.248058	+	0.763444i	−0.747060	+	0.664756i	$0.768535\pi$
$570$	354.959	−	257.893i	0.0260835	−	0.0189508i
$571$	12988.6			0.951938			0.475969	−	0.879462i	$-0.342097\pi$
$571$	12988.6			0.951938			0.475969	+	0.879462i	$0.342097\pi$
$572$	−834.928	+	3961.69i	−0.0610317	+	0.289592i
$573$	−11425.5			−0.832996
$574$	306.919	−	222.990i	0.0223181	−	0.0162150i
$575$	7049.93	+	21697.5i	0.511309	+	1.57365i
$576$	−1223.88	+	3766.72i	−0.0885332	+	0.272477i
$577$	−7502.37	−	5450.79i	−0.541296	−	0.393274i	0.283270	−	0.959040i	$-0.408581\pi$
$577$	−7502.37	−	5450.79i	−0.541296	−	0.393274i	−0.824566	+	0.565766i	$0.808581\pi$
$578$	1385.93	+	1006.94i	0.0997353	+	0.0724619i
$579$	−3065.18	+	9433.65i	−0.220008	+	0.677114i
$580$	247.874	+	762.877i	0.0177455	+	0.0546151i
$581$	−880.220	+	639.517i	−0.0628532	+	0.0456655i
$582$	−7386.97			−0.526116
$583$	10669.7	−	1140.08i	0.757963	−	0.0809900i
$584$	−2282.71			−0.161745
$585$	−42.0836	+	30.5755i	−0.00297426	+	0.00216093i
$586$	−10379.8	−	31945.6i	−0.731713	−	2.25198i
$587$	125.459	−	386.124i	0.00882157	−	0.0271500i	−0.946549	−	0.322561i	$-0.895456\pi$
$587$	125.459	−	386.124i	0.00882157	−	0.0271500i	0.955370	+	0.295411i	$0.0954564\pi$
$588$	886.622	+	644.169i	0.0621831	+	0.0451787i
$589$	10427.0	+	7575.63i	0.729432	+	0.529963i
$590$	360.124	−	1108.35i	0.0251289	−	0.0773389i
$591$	−2416.03	−	7435.76i	−0.168159	−	0.517541i
$592$	−366.270	+	266.111i	−0.0254284	+	0.0184748i
$593$	−23675.5			−1.63952			−0.819761	−	0.572706i	$-0.805894\pi$
$593$	−23675.5			−1.63952			−0.819761	+	0.572706i	$0.805894\pi$
$594$	−3357.02	−	1930.45i	−0.231886	−	0.133346i
$595$	−181.866			−0.0125307
$596$	15111.9	−	10979.5i	1.03861	−	0.754592i
$597$	512.898	+	1578.54i	0.0351617	+	0.108217i
$598$	−3304.47	+	10170.1i	−0.225970	+	0.695463i
$599$	−14032.5	−	10195.2i	−0.957183	−	0.695434i	−0.00468834	−	0.999989i	$-0.501492\pi$
$599$	−14032.5	−	10195.2i	−0.957183	−	0.695434i	−0.952495	+	0.304555i	$0.901492\pi$
$600$	648.904	+	471.456i	0.0441523	+	0.0320785i
$601$	−3332.97	+	10257.8i	−0.226214	+	0.696215i	0.771952	+	0.635681i	$0.219281\pi$
$601$	−3332.97	+	10257.8i	−0.226214	+	0.696215i	−0.998166	+	0.0605346i	$0.980719\pi$
$602$	−2687.70	−	8271.89i	−0.181964	−	0.560029i
$603$	3816.81	−	2773.07i	0.257765	−	0.187277i
$604$	3066.05			0.206549
$605$	52.2435	−	514.157i	0.00351075	−	0.0345512i
$606$	−4828.24			−0.323653
$607$	21404.9	−	15551.5i	1.43130	−	1.03990i	0.441521	−	0.897251i	$-0.354439\pi$
$607$	21404.9	−	15551.5i	1.43130	−	1.03990i	0.989774	−	0.142646i	$-0.0455611\pi$
$608$	−7414.72	−	22820.2i	−0.494583	−	1.52217i
$609$	1798.20	−	5534.29i	0.119650	−	0.368244i
$610$	79.4183	+	57.7008i	0.00527140	+	0.00382990i
$611$	5791.95	+	4208.10i	0.383498	+	0.278628i
$612$	1387.38	−	4269.90i	0.0916361	−	0.282027i
$613$	6716.27	+	20670.6i	0.442525	+	1.36195i	0.885176	+	0.465257i	$0.154038\pi$
$613$	6716.27	+	20670.6i	0.442525	+	1.36195i	−0.442651	+	0.896694i	$0.645962\pi$
$614$	−4512.19	+	3278.30i	−0.296575	+	0.215474i
$615$	−16.0583			−0.00105290
$616$	474.095	+	272.628i	0.0310095	+	0.0178319i
$617$	−23209.3			−1.51438			−0.757188	−	0.653196i	$-0.773428\pi$
$617$	−23209.3			−1.51438			−0.757188	+	0.653196i	$0.773428\pi$
$618$	14507.5	−	10540.3i	0.944301	−	0.686074i
$619$	−3287.43	−	10117.7i	−0.213462	−	0.656969i	−0.999259	−	0.0384845i	$-0.987747\pi$
$619$	−3287.43	−	10117.7i	−0.213462	−	0.656969i	0.785797	−	0.618484i	$-0.212253\pi$
$620$	−120.332	+	370.345i	−0.00779462	+	0.0239894i
$621$	−3991.52	−	2900.01i	−0.257929	−	0.187397i
$622$	−18828.4	−	13679.6i	−1.21375	−	0.881838i
$623$	3039.39	−	9354.29i	0.195459	−	0.601560i
$624$	939.219	+	2890.62i	0.0602546	+	0.185445i
$625$	−12595.2	+	9150.93i	−0.806091	+	0.585659i
$626$	−25583.6			−1.63343
$627$	10427.0	−	1114.14i	0.664135	−	0.0709643i
$628$	9110.51			0.578900
$629$	360.087	−	261.619i	0.0228261	−	0.0165841i
$630$	−29.7173	−	91.4605i	−0.00187931	−	0.00578393i
$631$	888.940	−	2735.88i	0.0560826	−	0.172605i	−0.919091	−	0.394044i	$-0.871076\pi$
$631$	888.940	−	2735.88i	0.0560826	−	0.172605i	0.975174	+	0.221440i	$0.0710756\pi$
$632$	525.022	+	381.451i	0.0330447	+	0.0240084i
$633$	4096.94	+	2976.60i	0.257249	+	0.186902i
$634$	−6847.71	+	21075.1i	−0.428954	+	1.32019i
$635$	71.8739	+	221.205i	0.00449170	+	0.0138240i
$636$	−5321.93	+	3866.61i	−0.331806	+	0.241071i
$637$	729.392			0.0453682
$638$	−8195.88	+	38889.0i	−0.508586	+	2.41321i
$639$	8466.28			0.524133
$640$	−85.9060	+	62.4144i	−0.00530583	+	0.00385491i
$641$	452.598	+	1392.95i	0.0278885	+	0.0858321i	0.964032	−	0.265786i	$-0.0856315\pi$
$641$	452.598	+	1392.95i	0.0278885	+	0.0858321i	−0.936143	+	0.351618i	$0.885632\pi$
$642$	−5852.49	+	18012.1i	−0.359781	+	1.10729i
$643$	18381.9	+	13355.3i	1.12739	+	0.819098i	0.985313	−	0.170757i	$-0.0546213\pi$
$643$	18381.9	+	13355.3i	1.12739	+	0.819098i	0.142079	+	0.989855i	$0.454621\pi$
$644$	−7715.00	−	5605.28i	−0.472071	−	0.342980i
$645$	−113.766	+	350.137i	−0.00694504	+	0.0213746i
$646$	7788.22	+	23969.7i	0.474340	+	1.45987i
$647$	−1371.70	+	996.599i	−0.0833495	+	0.0605569i	−0.628680	−	0.777664i	$-0.716404\pi$
$647$	−1371.70	+	996.599i	−0.0833495	+	0.0605569i	0.545330	+	0.838221i	$0.316404\pi$
$648$	−173.460			−0.0105157
$649$	20666.6	−	18673.0i	1.24997	−	1.12940i
$650$	−7306.16			−0.440878
$651$	2285.41	−	1660.45i	0.137592	−	0.0999665i
$652$	3698.44	+	11382.6i	0.222150	+	0.683708i
$653$	−8376.01	+	25778.7i	−0.501958	+	1.54487i	0.303867	+	0.952714i	$0.401722\pi$
$653$	−8376.01	+	25778.7i	−0.501958	+	1.54487i	−0.805825	+	0.592154i	$0.798278\pi$
$654$	−12356.1	−	8977.21i	−0.738777	−	0.536753i
$655$	−817.367	−	593.852i	−0.0487590	−	0.0354255i
$656$	−289.942	+	892.350i	−0.0172566	+	0.0531104i
$657$	2964.56	+	9123.97i	0.176040	+	0.541796i
$658$	−10707.7	+	7779.61i	−0.634392	+	0.460913i
$659$	−14244.0			−0.841984			−0.420992	−	0.907064i	$-0.638318\pi$
$659$	−14244.0			−0.841984			−0.420992	+	0.907064i	$0.638318\pi$
$660$	129.365	+	289.213i	0.00762960	+	0.0170570i
$661$	10808.3			0.635995			0.317998	−	0.948092i	$-0.396990\pi$
$661$	10808.3			0.635995			0.317998	+	0.948092i	$0.396990\pi$
$662$	5126.91	−	3724.92i	0.301002	−	0.218691i
$663$	−923.365	−	2841.83i	−0.0540883	−	0.166467i
$664$	102.857	−	316.561i	0.00601148	−	0.0185014i
$665$	210.677	+	153.066i	0.0122852	+	0.00892575i
$666$	190.407	+	138.339i	0.0110783	+	0.00804884i
$667$	−15647.2	+	48157.0i	−0.908336	+	2.79557i
$668$	−1602.37	−	4931.58i	−0.0928106	−	0.285642i
$669$	898.472	−	652.778i	0.0519237	−	0.0377248i
$670$	−800.178			−0.0461397
$671$	957.990	+	2141.71i	0.0551159	+	0.123219i
$672$	−5259.20			−0.301902
$673$	−9366.80	+	6805.38i	−0.536498	+	0.389789i	−0.822783	−	0.568356i	$-0.807580\pi$
$673$	−9366.80	+	6805.38i	−0.536498	+	0.389789i	0.286285	+	0.958145i	$0.407580\pi$
$674$	−3514.86	−	10817.6i	−0.200871	−	0.618218i
$675$	1041.67	−	3205.94i	0.0593986	−	0.182810i
$676$	11914.6	+	8656.49i	0.677893	+	0.492518i
$677$	−4800.02	−	3487.42i	−0.272496	−	0.197980i	0.443142	−	0.896452i	$-0.353864\pi$
$677$	−4800.02	−	3487.42i	−0.272496	−	0.197980i	−0.715638	+	0.698472i	$0.753864\pi$
$678$	−4708.67	+	14491.8i	−0.266719	+	0.820876i
$679$	−1354.84	−	4169.76i	−0.0765742	−	0.235671i
$680$	45.0118	−	32.7030i	0.00253842	−	0.00184427i
$681$	2750.46			0.154769
$682$	−14315.7	+	12934.8i	−0.803776	+	0.726243i
$683$	18836.2			1.05527			0.527634	−	0.849472i	$-0.323079\pi$
$683$	18836.2			1.05527			0.527634	+	0.849472i	$0.323079\pi$
$684$	−5200.87	+	3778.65i	−0.290731	+	0.211229i
$685$	315.636	+	971.427i	0.0176056	+	0.0541844i
$686$	−416.692	+	1282.45i	−0.0231915	+	0.0713761i
$687$	−10010.9	−	7273.33i	−0.555952	−	0.403922i
$688$	17402.8	+	12643.9i	0.964353	+	0.700643i
$689$	−1352.93	+	4163.88i	−0.0748075	+	0.230234i
$690$	258.587	+	795.850i	0.0142670	+	0.0439094i
$691$	1871.96	−	1360.06i	0.103057	−	0.0748755i	−0.535063	−	0.844812i	$-0.679712\pi$
$691$	1871.96	−	1360.06i	0.103057	−	0.0748755i	0.638120	+	0.769937i	$0.279712\pi$
$692$	−27857.0			−1.53029
$693$	473.982	−	2249.02i	0.0259813	−	0.123280i
$694$	−598.560			−0.0327393
$695$	−909.728	+	660.956i	−0.0496517	+	0.0360741i
$696$	550.117	+	1693.09i	0.0299600	+	0.0922073i
$697$	285.048	−	877.287i	0.0154906	−	0.0476752i
$698$	15843.3	+	11510.8i	0.859138	+	0.624200i
$699$	1491.60	+	1083.71i	0.0807115	+	0.0586404i
$700$	2013.40	−	6196.61i	0.108713	−	0.334585i
$701$	−7236.56	−	22271.8i	−0.389902	−	1.19999i	−0.932861	−	0.360235i	$-0.882696\pi$
$701$	−7236.56	−	22271.8i	−0.389902	−	1.19999i	0.542960	−	0.839759i	$-0.317304\pi$
$702$	1278.28	−	928.721i	0.0687256	−	0.0499321i
$703$	−637.320			−0.0341920
$704$	15963.9	−	1705.78i	0.854633	−	0.0913195i
$705$	560.238			0.0299287
$706$	154.079	−	111.945i	0.00821365	−	0.00596757i
$707$	−885.542	−	2725.42i	−0.0471064	−	0.144979i
$708$	−5276.55	+	16239.6i	−0.280092	+	0.862034i
$709$	30041.2	+	21826.2i	1.59129	+	1.15614i	0.902076	+	0.431576i	$0.142042\pi$
$709$	30041.2	+	21826.2i	1.59129	+	1.15614i	0.689210	+	0.724561i	$0.257958\pi$
$710$	−1161.70	−	844.026i	−0.0614055	−	0.0446137i
$711$	842.809	−	2593.90i	0.0444554	−	0.136820i
$712$	929.832	+	2861.73i	0.0489423	+	0.150629i
$713$	−19886.7	+	14448.5i	−1.04455	+	0.758908i
$714$	5524.12			0.289545
$715$	182.795	+	105.116i	0.00956106	+	0.00549807i
$716$	12455.3			0.650107
$717$	1706.13	−	1239.57i	0.0888655	−	0.0645645i
$718$	6747.94	+	20768.0i	0.350740	+	1.07947i
$719$	−3958.87	+	12184.1i	−0.205342	+	0.631978i	0.794357	+	0.607451i	$0.207808\pi$
$719$	−3958.87	+	12184.1i	−0.205342	+	0.631978i	−0.999699	+	0.0245268i	$0.992192\pi$
$720$	192.419	+	139.800i	0.00995975	+	0.00723618i
$721$	8610.56	+	6255.94i	0.444763	+	0.323139i
$722$	2819.19	−	8676.57i	0.145318	−	0.447242i
$723$	−4568.46	−	14060.3i	−0.234997	−	0.723247i
$724$	13383.6	−	9723.77i	0.687015	−	0.499145i
$725$	−34595.7			−1.77221
$726$	−1586.88	+	15617.3i	−0.0811221	+	0.798366i
$727$	−31765.2			−1.62050			−0.810251	−	0.586084i	$-0.800669\pi$
$727$	−31765.2			−1.62050			−0.810251	+	0.586084i	$0.800669\pi$
$728$	−180.524	+	131.159i	−0.00919049	+	0.00667728i
$729$	225.273	+	693.320i	0.0114451	+	0.0352243i
$730$	502.810	−	1547.49i	0.0254929	−	0.0784591i
$731$	−17109.0	−	12430.4i	−0.865664	−	0.628941i
$732$	−1163.64	−	845.435i	−0.0587560	−	0.0426888i
$733$	3704.92	−	11402.6i	0.186691	−	0.574574i	−0.813283	−	0.581869i	$-0.802322\pi$
$733$	3704.92	−	11402.6i	0.186691	−	0.574574i	0.999973	+	0.00729415i	$0.00232182\pi$
$734$	7151.82	+	22011.0i	0.359644	+	1.10687i
$735$	46.1767	−	33.5494i	0.00231735	−	0.00168366i
$736$	45763.3			2.29192
$737$	−16578.8	−	9533.59i	−0.828612	−	0.476491i
$738$	487.765			0.0243291
$739$	−26826.4	+	19490.5i	−1.33535	+	0.970191i	−0.335753	+	0.941950i	$0.608991\pi$
$739$	−26826.4	+	19490.5i	−1.33535	+	0.970191i	−0.999601	+	0.0282412i	$0.991009\pi$
$740$	−5.95031	−	18.3132i	−0.000295591	−	0.000909737i
$741$	−1322.15	+	4069.16i	−0.0655471	+	0.201733i
$742$	−6548.18	−	4757.53i	−0.323978	−	0.235384i
$743$	10551.1	+	7665.81i	0.520971	+	0.378508i	0.816970	−	0.576681i	$-0.195652\pi$
$743$	10551.1	+	7665.81i	0.520971	+	0.378508i	−0.295998	+	0.955188i	$0.595652\pi$
$744$	−267.059	+	821.923i	−0.0131597	+	0.0405015i
$745$	−300.628	−	925.238i	−0.0147841	−	0.0455008i
$746$	2350.49	−	1707.73i	0.115359	−	0.0838130i
$747$	−1398.87			−0.0685168
$748$	−18096.4	+	1933.64i	−0.884587	+	0.0945201i
$749$	−11240.8			−0.548370
$750$	−925.643	+	672.519i	−0.0450663	+	0.0327426i
$751$	−4187.61	−	12888.1i	−0.203473	−	0.626225i	−0.999773	−	0.0213229i	$-0.993212\pi$
$751$	−4187.61	−	12888.1i	−0.203473	−	0.626225i	0.796300	−	0.604902i	$-0.206788\pi$
$752$	10115.4	−	31132.1i	0.490520	−	1.50967i
$753$	2217.34	+	1610.99i	0.107310	+	0.0779651i
$754$	−13118.9	−	9531.43i	−0.633636	−	0.460364i
$755$	49.3453	−	151.869i	0.00237862	−	0.00732065i
$756$	435.419	+	1340.08i	0.0209472	+	0.0644687i
$757$	25769.2	−	18722.4i	1.23725	−	0.898914i	0.239836	−	0.970813i	$-0.422906\pi$
$757$	25769.2	−	18722.4i	1.23725	−	0.898914i	0.997412	+	0.0718998i	$0.0229062\pi$
$758$	25931.4			1.24258
$759$	−4124.38	+	19570.0i	−0.197241	+	0.935896i
$760$	−79.6666			−0.00380238
$761$	−14833.0	+	10776.8i	−0.706566	+	0.513350i	−0.882064	−	0.471130i	$-0.843846\pi$
$761$	−14833.0	+	10776.8i	−0.706566	+	0.513350i	0.175498	+	0.984480i	$0.443846\pi$
$762$	−2183.14	−	6719.03i	−0.103789	−	0.319429i
$763$	2801.20	−	8621.19i	0.132910	−	0.409054i
$764$	−22970.7	−	16689.2i	−1.08776	−	0.790307i
$765$	−189.171	−	137.441i	−0.00894050	−	0.00649565i
$766$	−8109.85	+	24959.6i	−0.382534	+	1.17732i
$767$	3511.80	+	10808.2i	0.165324	+	0.508816i
$768$	11153.8	−	8103.72i	0.524060	−	0.380752i
$769$	−2603.81			−0.122101			−0.0610507	−	0.998135i	$-0.519445\pi$
$769$	−2603.81			−0.122101			−0.0610507	+	0.998135i	$0.519445\pi$
$770$	−289.248	+	261.347i	−0.0135374	+	0.0122315i
$771$	8855.61			0.413654
$772$	−19942.2	+	14488.9i	−0.929710	+	0.675474i
$773$	−9961.64	−	30658.8i	−0.463513	−	1.42655i	−0.860843	−	0.508870i	$-0.830063\pi$
$773$	−9961.64	−	30658.8i	−0.463513	−	1.42655i	0.397331	−	0.917676i	$-0.369937\pi$
$774$	3455.62	−	10635.3i	0.160477	−	0.493899i
$775$	−13587.2	−	9871.71i	−0.629765	−	0.457551i
$776$	1085.13	+	788.390i	0.0501981	+	0.0364711i
$777$	−43.1665	+	132.853i	−0.00199304	+	0.00613393i
$778$	−7647.84	−	23537.6i	−0.352427	−	1.08466i
$779$	−1068.56	+	776.356i	−0.0491466	+	0.0357071i
$780$	−129.270			−0.00593412
$781$	−14013.1	−	31328.1i	−0.642034	−	1.43535i
$782$	−48068.5			−2.19811
$783$	6052.82	−	4397.63i	0.276258	−	0.200713i
$784$	−1030.57	−	3171.77i	−0.0469465	−	0.144486i
$785$	146.626	−	451.267i	0.00666661	−	0.0205177i
$786$	24827.2	+	18038.0i	1.12666	+	0.818570i
$787$	−1465.91	−	1065.05i	−0.0663965	−	0.0482399i	0.554092	−	0.832455i	$-0.313066\pi$
$787$	−1465.91	−	1065.05i	−0.0663965	−	0.0482399i	−0.620488	+	0.784216i	$0.713066\pi$
$788$	6004.05	−	18478.6i	0.271428	−	0.835370i
$789$	278.629	+	857.532i	0.0125722	+	0.0386932i
$790$	−374.238	+	271.900i	−0.0168542	+	0.0122453i
$791$	−9043.87			−0.406527
$792$	287.106	+	641.863i	0.0128812	+	0.0287975i
$793$	−957.285			−0.0428678
$794$	20714.9	−	15050.3i	0.925876	−	0.672689i
$795$	105.871	+	325.839i	0.00472311	+	0.0145362i
$796$	−1274.60	+	3922.81i	−0.0567550	+	0.174674i
$797$	−1742.97	−	1266.34i	−0.0774646	−	0.0562813i	0.548379	−	0.836230i	$-0.315245\pi$
$797$	−1742.97	−	1266.34i	−0.0774646	−	0.0562813i	−0.625844	+	0.779949i	$0.715245\pi$
$798$	−6399.23	−	4649.31i	−0.283872	−	0.206245i
$799$	−9944.67	+	30606.5i	−0.440322	+	1.35517i
$800$	9662.03	+	29736.7i	0.427005	+	1.31419i
$801$	10230.7	−	7433.06i	0.451292	−	0.327883i
$802$	20987.1			0.924042
$803$	28854.9	−	26071.6i	1.26808	−	1.14576i
$804$	11724.3			0.514282
$805$	−401.810	+	291.932i	−0.0175925	+	0.0127817i
$806$	−2432.61	−	7486.82i	−0.106309	−	0.327186i
$807$	−6232.85	+	19182.7i	−0.271879	+	0.836759i
$808$	709.255	+	515.304i	0.0308806	+	0.0224360i
$809$	15174.5	+	11024.9i	0.659466	+	0.479130i	0.866483	−	0.499207i	$-0.166375\pi$
$809$	15174.5	+	11024.9i	0.659466	+	0.479130i	−0.207017	+	0.978337i	$0.566375\pi$
$810$	38.2080	−	117.592i	0.00165740	−	0.00510094i
$811$	−7977.05	−	24550.8i	−0.345391	−	1.06300i	−0.961374	−	0.275245i	$-0.911241\pi$
$811$	−7977.05	−	24550.8i	−0.345391	−	1.06300i	0.615983	−	0.787759i	$-0.288759\pi$
$812$	11699.2	−	8499.96i	0.505617	−	0.367352i
$813$	1849.85			0.0797998
$814$	196.745	−	933.546i	0.00847164	−	0.0401975i
$815$	623.333			0.0267907
$816$	−11053.1	+	8030.53i	−0.474185	+	0.344516i
$817$	9357.44	+	28799.2i	0.400704	+	1.23324i
$818$	5184.52	−	15956.3i	0.221605	−	0.682029i
$819$	758.687	+	551.219i	0.0323696	+	0.0235179i
$820$	−32.2849	−	23.4564i	−0.00137492	−	0.000998941i
$821$	4403.66	−	13553.1i	0.187197	−	0.576134i	−0.812782	−	0.582568i	$-0.802048\pi$
$821$	4403.66	−	13553.1i	0.187197	−	0.576134i	0.999979	+	0.00643416i	$0.00204807\pi$
$822$	−9587.33	−	29506.8i	−0.406808	−	1.25203i
$823$	16814.0	−	12216.1i	0.712149	−	0.517406i	−0.171718	−	0.985146i	$-0.554932\pi$
$823$	16814.0	−	12216.1i	0.712149	−	0.517406i	0.883866	+	0.467740i	$0.154932\pi$
$824$	−3256.05			−0.137658
$825$	−13587.2	+	1451.83i	−0.573390	+	0.0612680i
$826$	−21009.7			−0.885012
$827$	−17707.4	+	12865.2i	−0.744556	+	0.540951i	−0.894135	−	0.447798i	$-0.852208\pi$
$827$	−17707.4	+	12865.2i	−0.744556	+	0.540951i	0.149579	+	0.988750i	$0.452208\pi$
$828$	−3788.83	−	11660.8i	−0.159023	−	0.489422i
$829$	7028.33	−	21631.0i	0.294456	−	0.906243i	−0.688947	−	0.724811i	$-0.741927\pi$
$829$	7028.33	−	21631.0i	0.294456	−	0.906243i	0.983404	−	0.181432i	$-0.0580731\pi$
$830$	191.946	+	139.457i	0.00802718	+	0.00583208i
$831$	10251.2	+	7447.92i	0.427930	+	0.310909i
$832$	−2024.24	+	6229.97i	−0.0843484	+	0.259598i
$833$	1013.17	+	3118.23i	0.0421421	+	0.129700i
$834$	27632.7	−	20076.3i	1.14729	−	0.833556i
$835$	−270.063			−0.0111927
$836$	22590.6	+	12990.7i	0.934585	+	0.537431i
$837$	3632.05			0.149990
$838$	40030.3	−	29083.7i	1.65015	−	1.19890i
$839$	3148.03	+	9688.65i	0.129538	+	0.398676i	0.994700	−	0.102815i	$-0.0327850\pi$
$839$	3148.03	+	9688.65i	0.129538	+	0.398676i	−0.865163	+	0.501491i	$0.832785\pi$
$840$	−5.39592	+	16.6069i	−0.000221639	+	0.000682135i
$841$	−42388.7	−	30797.2i	−1.73803	−	1.26275i
$842$	8706.29	+	6325.49i	0.356340	+	0.258897i
$843$	−752.972	+	2317.41i	−0.0307636	+	0.0946807i
$844$	3888.90	+	11968.8i	0.158603	+	0.488131i
$845$	620.534	−	450.844i	0.0252627	−	0.0183545i
$846$	−17017.0			−0.691557
$847$	−9106.65	+	1968.61i	−0.369431	+	0.0798609i
$848$	20018.2			0.810647
$849$	−6096.03	+	4429.02i	−0.246425	+	0.179038i
$850$	−10148.7	−	31234.6i	−0.409528	−	1.26040i
$851$	375.616	−	1156.03i	0.0151304	−	0.0465665i
$852$	17021.3	+	12366.7i	0.684437	+	0.497273i
$853$	−8157.44	−	5926.73i	−0.327439	−	0.237898i	0.411904	−	0.911227i	$-0.364864\pi$
$853$	−8157.44	−	5926.73i	−0.327439	−	0.237898i	−0.739343	+	0.673329i	$0.764864\pi$
$854$	546.884	−	1683.14i	0.0219133	−	0.0674423i
$855$	103.463	+	318.427i	0.00413844	+	0.0127368i
$856$	2782.09	−	2021.31i	0.111086	−	0.0807090i
$857$	9943.59			0.396344			0.198172	−	0.980167i	$-0.436500\pi$
$857$	9943.59			0.396344			0.198172	+	0.980167i	$0.436500\pi$
$858$	−5552.35	−	3192.86i	−0.220925	−	0.127043i
$859$	29111.5			1.15631			0.578156	−	0.815926i	$-0.303773\pi$
$859$	29111.5			1.15631			0.578156	+	0.815926i	$0.303773\pi$
$860$	−740.171	+	537.765i	−0.0293484	+	0.0213228i
$861$	89.4606	+	275.331i	0.00354101	+	0.0108981i
$862$	13219.1	−	40684.3i	0.522326	−	1.60755i
$863$	3456.52	+	2511.31i	0.136340	+	0.0990567i	0.653865	−	0.756611i	$-0.273147\pi$
$863$	3456.52	+	2511.31i	0.136340	+	0.0990567i	−0.517525	+	0.855668i	$0.673147\pi$
$864$	−5470.43	−	3974.50i	−0.215403	−	0.156499i
$865$	−448.333	+	1379.83i	−0.0176229	+	0.0542376i
$866$	8437.42	+	25967.7i	0.331080	+	1.01896i
$867$	−1057.60	+	768.395i	−0.0414281	+	0.0300993i
$868$	7020.20			0.274517
$869$	−10993.3	+	1174.66i	−0.429139	+	0.0458545i
$870$	−1268.95			−0.0494499
$871$	6312.81	−	4586.52i	0.245581	−	0.178425i
$872$	856.961	+	2637.45i	0.0332802	+	0.102426i
$873$	1741.93	−	5361.12i	0.0675321	−	0.207842i
$874$	55683.3	+	40456.3i	2.15505	+	1.56574i
$875$	−549.392	−	399.156i	−0.0212261	−	0.0154217i
$876$	−7367.20	+	22673.9i	−0.284149	+	0.874520i
$877$	4307.73	+	13257.8i	0.165863	+	0.510474i	0.999099	−	0.0424439i	$-0.0135144\pi$
$877$	4307.73	+	13257.8i	0.165863	+	0.510474i	−0.833236	+	0.552918i	$0.813514\pi$
$878$	−33720.5	+	24499.4i	−1.29614	+	0.941701i
$879$	25632.3			0.983568
$880$	198.824	−	943.408i	0.00761630	−	0.0361389i
$881$	19223.0			0.735117			0.367559	−	0.930000i	$-0.380194\pi$
$881$	19223.0			0.735117			0.367559	+	0.930000i	$0.380194\pi$
$882$	−1402.60	+	1019.05i	−0.0535466	+	0.0389039i
$883$	−14455.0	−	44488.0i	−0.550907	−	1.69552i	−0.706515	−	0.707698i	$-0.749734\pi$
$883$	−14455.0	−	44488.0i	−0.550907	−	1.69552i	0.155608	−	0.987819i	$-0.450266\pi$
$884$	2294.65	−	7062.20i	0.0873047	−	0.268696i
$885$	719.466	+	522.723i	0.0273272	+	0.0198544i
$886$	−3921.37	−	2849.04i	−0.148692	−	0.108031i
$887$	14944.9	−	45995.6i	0.565726	−	1.74113i	−0.100057	−	0.994982i	$-0.531902\pi$
$887$	14944.9	−	45995.6i	0.565726	−	1.74113i	0.665783	−	0.746145i	$-0.268098\pi$
$888$	−13.2058	−	40.6432i	−0.000499051	−	0.00153592i
$889$	3392.32	−	2464.66i	0.127980	−	0.0929832i
$890$	−2144.83			−0.0807808
$891$	2192.66	−	1981.15i	0.0824430	−	0.0744905i
$892$	2759.87			0.103596
$893$	37279.7	−	27085.3i	1.39700	−	1.01498i
$894$	9131.48	+	28103.8i	0.341613	+	1.05138i
$895$	200.457	−	616.943i	0.00748663	−	0.0230415i
$896$	1548.72	+	1125.21i	0.0577446	+	0.0419539i
$897$	−6601.77	−	4796.47i	−0.245738	−	0.178539i
$898$	21421.5	−	65928.5i	0.796040	−	2.44996i
$899$	−11518.8	−	35451.2i	−0.427333	−	1.31520i
$900$	6777.19	−	4923.92i	0.251007	−	0.182367i
$901$	−19680.3			−0.727688
$902$	−807.334	−	1804.90i	−0.0298019	−	0.0666259i
$903$	6637.15			0.244596
$904$	2238.36	−	1626.26i	0.0823525	−	0.0598326i
$905$	−266.246	−	819.421i	−0.00977936	−	0.0300978i
$906$	−1498.85	+	4612.98i	−0.0549623	+	0.169157i
$907$	−10984.7	−	7980.86i	−0.402140	−	0.292172i	0.368272	−	0.929718i	$-0.379950\pi$
$907$	−10984.7	−	7980.86i	−0.402140	−	0.292172i	−0.770412	+	0.637546i	$0.779950\pi$
$908$	5529.74	+	4017.59i	0.202104	+	0.146837i
$909$	1138.55	−	3504.11i	0.0415440	−	0.127859i
$910$	−49.1509	−	151.271i	−0.00179048	−	0.00551053i
$911$	18030.8	−	13100.1i	0.655747	−	0.476428i	−0.209477	−	0.977814i	$-0.567176\pi$
$911$	18030.8	−	13100.1i	0.655747	−	0.476428i	0.865224	+	0.501385i	$0.167176\pi$
$912$	19562.9			0.710297
$913$	2315.37	+	5176.30i	0.0839294	+	0.187635i
$914$	21025.0			0.760881
$915$	−60.6043	+	44.0316i	−0.00218964	+	0.00159086i
$916$	−9502.53	−	29245.8i	−0.342765	−	1.05492i
$917$	−5628.48	+	17322.7i	−0.202692	+	0.623823i
$918$	5745.99	+	4174.71i	0.206586	+	0.150094i
$919$	2251.50	+	1635.81i	0.0808164	+	0.0587165i	0.627460	−	0.778649i	$-0.284095\pi$
$919$	2251.50	+	1635.81i	0.0808164	+	0.0587165i	−0.546643	+	0.837365i	$0.684095\pi$
$920$	46.9530	−	144.506i	0.00168260	−	0.00517851i
$921$	−1315.21	−	4047.80i	−0.0470550	−	0.144820i
$922$	7687.69	−	5585.43i	0.274599	−	0.199508i
$923$	14002.8			0.499358
$924$	4238.07	−	3829.26i	0.150890	−	0.136335i
$925$	830.483			0.0295201
$926$	−10978.0	+	7975.98i	−0.389589	+	0.283053i
$927$	4228.64	+	13014.4i	0.149824	+	0.461110i
$928$	−21444.6	+	65999.8i	−0.758572	+	2.33464i
$929$	32862.8	+	23876.2i	1.16060	+	0.843222i	0.989853	−	0.142094i	$-0.0453834\pi$
$929$	32862.8	+	23876.2i	1.16060	+	0.843222i	0.170742	+	0.985316i	$0.445383\pi$
$930$	−498.372	−	362.088i	−0.0175723	−	0.0127670i
$931$	1450.74	−	4464.93i	0.0510700	−	0.157177i
$932$	1415.85	+	4357.55i	0.0497616	+	0.153151i
$933$	14368.0	−	10439.0i	0.504166	−	0.366298i
$934$	−17601.6			−0.616642
$935$	−195.468	+	927.483i	−0.00683687	+	0.0324406i
$936$	−286.895			−0.0100186
$937$	−35218.4	+	25587.7i	−1.22789	+	0.892116i	−0.996730	−	0.0807995i	$-0.974253\pi$
$937$	−35218.4	+	25587.7i	−1.22789	+	0.892116i	−0.231162	+	0.972915i	$0.574253\pi$
$938$	4457.78	+	13719.6i	0.155172	+	0.477572i
$939$	6032.92	−	18567.4i	0.209666	−	0.645287i
$940$	1126.35	+	818.339i	0.0390823	+	0.0283950i
$941$	24069.5	+	17487.5i	0.833841	+	0.605821i	0.920643	−	0.390405i	$-0.127665\pi$
$941$	24069.5	+	17487.5i	0.833841	+	0.605821i	−0.0868024	+	0.996226i	$0.527665\pi$
$942$	−4453.70	+	13707.1i	−0.154044	+	0.474099i
$943$	−778.447	−	2395.81i	−0.0268820	−	0.0827343i
$944$	42037.7	−	30542.2i	1.44938	−	1.05303i
$945$	73.3855			0.00252617
$946$	−45073.8	+	4816.24i	−1.54913	+	0.165528i
$947$	−32581.5			−1.11801			−0.559005	−	0.829164i	$-0.688817\pi$
$947$	−32581.5			−1.11801			−0.559005	+	0.829164i	$0.688817\pi$
$948$	5483.36	−	3983.89i	0.187860	−	0.136488i
$949$	4903.23	+	15090.6i	0.167719	+	0.516186i
$950$	−14531.8	+	44724.2i	−0.496288	+	1.52742i
$951$	−13680.5	−	9939.49i	−0.466479	−	0.338917i
$952$	−811.478	−	589.573i	−0.0276262	−	0.0200716i
$953$	−9650.93	+	29702.5i	−0.328042	+	1.00961i	0.642006	+	0.766699i	$0.278102\pi$
$953$	−9650.93	+	29702.5i	−0.328042	+	1.00961i	−0.970049	+	0.242911i	$0.921898\pi$
$954$	−3215.81	−	9897.24i	−0.109136	−	0.335886i
$955$	−1196.35	+	869.202i	−0.0405373	+	0.0294520i
$956$	5240.79			0.177300
$957$	−26291.2	−	15118.7i	−0.888059	−	0.510676i
$958$	−52037.0			−1.75495
$959$	14897.4	−	10823.6i	0.501630	−	0.364455i
$960$	158.404	+	487.518i	0.00532549	+	0.0163902i
$961$	−3614.04	+	11122.9i	−0.121313	+	0.373364i
$962$	314.924	+	228.806i	0.0105546	+	0.00766839i
$963$	−11692.3	−	8494.93i	−0.391254	−	0.284263i
$964$	11353.1	−	34941.1i	0.379312	−	1.16740i
$965$	396.719	+	1220.98i	0.0132340	+	0.0407302i
$966$	12204.8	−	8867.34i	0.406505	−	0.295344i
$967$	27196.2			0.904418			0.452209	−	0.891912i	$-0.350636\pi$
$967$	27196.2			0.904418			0.452209	+	0.891912i	$0.350636\pi$
$968$	1899.90	−	2124.78i	0.0630838	−	0.0705507i
$969$	−19232.6			−0.637607
$970$	−773.484	+	561.969i	−0.0256032	+	0.0186018i
$971$	−2716.04	−	8359.12i	−0.0897652	−	0.276269i	0.896089	−	0.443875i	$-0.146396\pi$
$971$	−2716.04	−	8359.12i	−0.0897652	−	0.276269i	−0.985854	+	0.167606i	$0.946396\pi$
$972$	−559.825	+	1722.96i	−0.0184737	+	0.0568561i
$973$	16400.7	+	11915.8i	0.540371	+	0.392603i
$974$	46174.9	+	33548.0i	1.51903	+	1.10364i
$975$	1722.88	−	5302.47i	0.0565910	−	0.174169i
$976$	1352.56	+	4162.76i	0.0443591	+	0.136523i
$977$	49048.9	−	35636.1i	1.60616	−	1.16694i	0.731989	−	0.681316i	$-0.238592\pi$
$977$	49048.9	−	35636.1i	1.60616	−	1.16694i	0.874167	−	0.485625i	$-0.161408\pi$
$978$	−18933.5			−0.619047
$979$	−44438.4	−	25554.2i	−1.45072	−	0.834235i
$980$	141.843			0.00462348
$981$	9428.95	−	6850.53i	0.306874	−	0.222957i
$982$	−4225.53	−	13004.8i	−0.137314	−	0.422608i
$983$	3438.45	−	10582.5i	0.111566	−	0.343365i	−0.879649	−	0.475623i	$-0.842223\pi$
$983$	3438.45	−	10582.5i	0.111566	−	0.343365i	0.991215	+	0.132258i	$0.0422227\pi$
$984$	−71.6514	−	52.0578i	−0.00232130	−	0.00168653i
$985$	−818.661	−	594.792i	−0.0264819	−	0.0192402i
$986$	22524.9	−	69324.4i	0.727523	−	2.23909i
$987$	−3121.08	−	9605.68i	−0.100653	−	0.309779i
$988$	−8601.98	+	6249.70i	−0.276989	+	0.201244i
$989$	−57753.6			−1.85688
$990$	−498.371	+	53.2521i	−0.0159993	+	0.00170956i
$991$	−46992.9			−1.50633			−0.753167	−	0.657829i	$-0.771475\pi$
$991$	−46992.9			−1.50633			−0.753167	+	0.657829i	$0.771475\pi$
$992$	−27255.0	+	19801.9i	−0.872325	+	0.633781i
$993$	1494.39	+	4599.26i	0.0477573	+	0.146982i
$994$	−7999.61	+	24620.3i	−0.255264	+	0.785622i
$995$	173.793	+	126.268i	0.00553731	+	0.00402309i
$996$	−2812.41	−	2043.33i	−0.0894724	−	0.0650055i
$997$	−12243.7	+	37682.3i	−0.388929	+	1.19700i	0.544660	+	0.838657i	$0.316659\pi$
$997$	−12243.7	+	37682.3i	−0.388929	+	1.19700i	−0.933589	+	0.358345i	$0.883341\pi$
$998$	15235.3	+	46889.4i	0.483231	+	1.48723i
$999$	−145.300	+	105.567i	−0.00460170	+	0.00334333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.4.j.b.190.2	yes	36
11.4	even	5	inner	231.4.j.b.169.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.j.b.169.2	✓	36	11.4	even	5	inner
231.4.j.b.190.2	yes	36	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.18050 + 2.31077i) q^{2} +(-0.927051 - 2.85317i) q^{3} +(2.30381 - 7.09039i) q^{4} +(-0.314127 - 0.228227i) q^{5} +(9.54151 + 6.93232i) q^{6} +(-2.16312 + 6.65740i) q^{7} +(-0.661756 - 2.03668i) q^{8} +(-7.28115 + 5.29007i) q^{9} +1.52646 q^{10} +(31.6266 + 18.1868i) q^{11} -22.3658 q^{12} +(-12.0427 + 8.74950i) q^{13} +(-8.50391 - 26.1724i) q^{14} +(-0.359958 + 1.10784i) q^{15} +(55.0626 + 40.0053i) q^{16} +(-54.1331 - 39.3300i) q^{17} +(10.9336 - 33.6502i) q^{18} +(29.6070 + 91.1210i) q^{19} +(-2.34191 + 1.70149i) q^{20} +21.0000 q^{21} +(-142.614 + 15.2386i) q^{22} -182.733 q^{23} +(-5.19750 + 3.77620i) q^{24} +(-38.5805 - 118.739i) q^{25} +(18.0836 - 55.6557i) q^{26} +(21.8435 + 15.8702i) q^{27} +(42.2201 + 30.6747i) q^{28} +(85.6286 - 263.538i) q^{29} +(-1.41511 - 4.35526i) q^{30} +(108.829 - 79.0691i) q^{31} -250.438 q^{32} +(22.5706 - 107.096i) q^{33} +263.053 q^{34} +(2.19889 - 1.59759i) q^{35} +(20.7343 + 63.8135i) q^{36} +(-2.05555 + 6.32632i) q^{37} +(-304.725 - 221.396i) q^{38} +(36.1280 + 26.2485i) q^{39} +(-0.256949 + 0.790806i) q^{40} +(4.26003 + 13.1110i) q^{41} +(-66.7906 + 48.5262i) q^{42} +316.055 q^{43} +(201.813 - 182.346i) q^{44} +3.49455 q^{45} +(581.183 - 422.254i) q^{46} +(-148.623 - 457.414i) q^{47} +(63.0961 - 194.190i) q^{48} +(-39.6418 - 28.8015i) q^{49} +(397.084 + 288.498i) q^{50} +(-62.0310 + 190.912i) q^{51} +(34.2934 + 105.544i) q^{52} +(237.949 - 172.880i) q^{53} -106.146 q^{54} +(-5.78406 - 12.9310i) q^{55} +14.9904 q^{56} +(232.537 - 168.948i) q^{57} +(336.633 + 1036.05i) q^{58} +(235.920 - 726.088i) q^{59} +(7.02572 + 5.10448i) q^{60} +(52.0276 + 37.8003i) q^{61} +(-163.421 + 502.959i) q^{62} +(-19.4681 - 59.9166i) q^{63} +(356.018 - 258.663i) q^{64} +5.77980 q^{65} +(175.689 + 392.775i) q^{66} -524.204 q^{67} +(-403.577 + 293.216i) q^{68} +(169.403 + 521.368i) q^{69} +(-3.30192 + 10.1623i) q^{70} +(-761.041 - 552.929i) q^{71} +(15.5925 + 11.3286i) q^{72} +(329.395 - 1013.77i) q^{73} +(-8.08101 - 24.8708i) q^{74} +(-303.015 + 220.154i) q^{75} +714.292 q^{76} +(-189.489 + 171.210i) q^{77} -175.559 q^{78} +(-245.167 + 178.124i) q^{79} +(-8.16638 - 25.1335i) q^{80} +(25.0304 - 77.0356i) q^{81} +(-43.8456 - 31.8557i) q^{82} +(125.746 + 91.3596i) q^{83} +(48.3799 - 148.898i) q^{84} +(8.02853 + 24.7093i) q^{85} +(-1005.21 + 730.330i) q^{86} -831.299 q^{87} +(16.1115 - 76.4483i) q^{88} -1405.10 q^{89} +(-11.1144 + 8.07510i) q^{90} +(-32.1992 - 99.0989i) q^{91} +(-420.981 + 1295.65i) q^{92} +(-326.488 - 237.207i) q^{93} +(1529.67 + 1111.37i) q^{94} +(11.4959 - 35.3807i) q^{95} +(232.169 + 714.542i) q^{96} +(-506.716 + 368.151i) q^{97} +192.635 q^{98} +(-326.487 + 34.8859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} + 27 q^{3} - 44 q^{4} - 16 q^{5} + 18 q^{6} + 63 q^{7} + 135 q^{8} - 81 q^{9} - 260 q^{10} - 29 q^{11} - 498 q^{12} - 4 q^{13} - 63 q^{14} + 18 q^{15} - 456 q^{16} + 130 q^{17} + 81 q^{18}+ \cdots + 1764 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 27 * q^3 - 44 * q^4 - 16 * q^5 + 18 * q^6 + 63 * q^7 + 135 * q^8 - 81 * q^9 - 260 * q^10 - 29 * q^11 - 498 * q^12 - 4 * q^13 - 63 * q^14 + 18 * q^15 - 456 * q^16 + 130 * q^17 + 81 * q^18 + 310 * q^19 + 136 * q^20 + 756 * q^21 - 318 * q^22 + 498 * q^23 + 135 * q^24 - 1183 * q^25 + 65 * q^26 + 243 * q^27 + 273 * q^28 - 276 * q^29 - 165 * q^30 - 68 * q^31 - 2986 * q^32 + 207 * q^33 - 774 * q^34 + 112 * q^35 - 396 * q^36 + 607 * q^37 - 550 * q^38 + 12 * q^39 + 1938 * q^40 + 1242 * q^41 - 126 * q^42 - 334 * q^43 + 1358 * q^44 + 396 * q^45 + 2052 * q^46 - 1532 * q^47 - 27 * q^48 - 441 * q^49 - 1117 * q^50 + 952 * q^52 + 369 * q^53 + 162 * q^54 - 702 * q^55 + 1260 * q^56 + 660 * q^57 + 257 * q^58 - 198 * q^59 - 408 * q^60 + 1754 * q^61 + 3553 * q^62 + 567 * q^63 - 5453 * q^64 - 2344 * q^65 + 1179 * q^66 - 1250 * q^67 + 9267 * q^68 - 9 * q^69 - 385 * q^70 - 853 * q^71 - 405 * q^72 + 1458 * q^73 - 1444 * q^74 - 2331 * q^75 - 2284 * q^76 + 483 * q^77 - 4530 * q^78 + 3653 * q^79 - 8057 * q^80 - 729 * q^81 - 2483 * q^82 + 2922 * q^83 - 924 * q^84 - 3170 * q^85 - 4626 * q^86 + 1578 * q^87 + 16631 * q^88 + 4596 * q^89 + 675 * q^90 - 742 * q^91 - 228 * q^92 + 204 * q^93 - 11483 * q^94 + 2610 * q^95 - 2412 * q^96 - 2022 * q^97 - 294 * q^98 + 1764 * q^99

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