LMFDB - Embedded newform 221.2.m.c.205.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [221,2,Mod(69,221)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("221.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(221, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 221 = 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	221.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.76469388467$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.3
Character	$\chi$	$=$	221.205
Dual form			221.2.m.c.69.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60408 + 0.926118i) q^{2} +(0.634338 + 1.09871i) q^{3} +(0.715389 - 1.23909i) q^{4} +4.17850i q^{5} +(-2.03506 - 1.17494i) q^{6} +(3.61684 + 2.08819i) q^{7} -1.05433i q^{8} +(0.695230 - 1.20417i) q^{9} +(-3.86978 - 6.70266i) q^{10} +(-2.19777 + 1.26888i) q^{11} +1.81520 q^{12} +(1.81069 - 3.11792i) q^{13} -7.73563 q^{14} +(-4.59094 + 2.65058i) q^{15} +(2.40721 + 4.16942i) q^{16} +(-0.500000 + 0.866025i) q^{17} +2.57546i q^{18} +(0.0120062 + 0.00693178i) q^{19} +(5.17753 + 2.98925i) q^{20} +5.29846i q^{21} +(2.35027 - 4.07079i) q^{22} +(-2.94311 - 5.09761i) q^{23} +(1.15840 - 0.668803i) q^{24} -12.4598 q^{25} +(-0.0169419 + 6.67831i) q^{26} +5.57007 q^{27} +(5.17490 - 2.98773i) q^{28} +(-0.596941 - 1.03393i) q^{29} +(4.90950 - 8.50350i) q^{30} -2.28280i q^{31} +(-5.89659 - 3.40440i) q^{32} +(-2.78826 - 1.60980i) q^{33} -1.85224i q^{34} +(-8.72548 + 15.1130i) q^{35} +(-0.994720 - 1.72291i) q^{36} +(-1.25038 + 0.721908i) q^{37} -0.0256786 q^{38} +(4.57426 + 0.0116042i) q^{39} +4.40552 q^{40} +(7.17652 - 4.14337i) q^{41} +(-4.90700 - 8.49918i) q^{42} +(2.03042 - 3.51679i) q^{43} +3.63098i q^{44} +(5.03164 + 2.90502i) q^{45} +(9.44197 + 5.45133i) q^{46} -1.97614i q^{47} +(-3.05398 + 5.28964i) q^{48} +(5.22104 + 9.04311i) q^{49} +(19.9866 - 11.5393i) q^{50} -1.26868 q^{51} +(-2.56803 - 4.47413i) q^{52} -6.25632 q^{53} +(-8.93486 + 5.15855i) q^{54} +(-5.30202 - 9.18336i) q^{55} +(2.20164 - 3.81336i) q^{56} +0.0175884i q^{57} +(1.91509 + 1.10568i) q^{58} +(11.9610 + 6.90567i) q^{59} +7.58478i q^{60} +(2.92222 - 5.06143i) q^{61} +(2.11415 + 3.66181i) q^{62} +(5.02908 - 2.90354i) q^{63} +2.98264 q^{64} +(13.0282 + 7.56596i) q^{65} +5.96346 q^{66} +(0.770695 - 0.444961i) q^{67} +(0.715389 + 1.23909i) q^{68} +(3.73385 - 6.46721i) q^{69} -32.3233i q^{70} +(4.74753 + 2.74099i) q^{71} +(-1.26960 - 0.733004i) q^{72} +6.60599i q^{73} +(1.33714 - 2.31600i) q^{74} +(-7.90374 - 13.6897i) q^{75} +(0.0171782 - 0.00991784i) q^{76} -10.5986 q^{77} +(-7.34825 + 4.21769i) q^{78} -5.49114 q^{79} +(-17.4219 + 10.0585i) q^{80} +(1.44762 + 2.50735i) q^{81} +(-7.67450 + 13.2926i) q^{82} +6.31349i q^{83} +(6.56528 + 3.79047i) q^{84} +(-3.61868 - 2.08925i) q^{85} +7.52163i q^{86} +(0.757325 - 1.31173i) q^{87} +(1.33782 + 2.31718i) q^{88} +(-8.58966 + 4.95924i) q^{89} -10.7616 q^{90} +(13.0598 - 7.49596i) q^{91} -8.42186 q^{92} +(2.50813 - 1.44807i) q^{93} +(1.83014 + 3.16990i) q^{94} +(-0.0289644 + 0.0501678i) q^{95} -8.63816i q^{96} +(-14.2922 - 8.25160i) q^{97} +(-16.7500 - 9.67060i) q^{98} +3.52866i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{3} + 14 q^{4} - 9 q^{6} - 3 q^{7} - 14 q^{9} + q^{10} + 6 q^{11} - 18 q^{12} + q^{13} - 12 q^{14} + 3 q^{15} - 24 q^{16} - 11 q^{17} + 3 q^{19} + 12 q^{20} - 11 q^{22} + 3 q^{23} + 57 q^{24}+ \cdots + 18 q^{98}+O(q^{100}) $ 22 * q - 3 * q^3 + 14 * q^4 - 9 * q^6 - 3 * q^7 - 14 * q^9 + q^10 + 6 * q^11 - 18 * q^12 + q^13 - 12 * q^14 + 3 * q^15 - 24 * q^16 - 11 * q^17 + 3 * q^19 + 12 * q^20 - 11 * q^22 + 3 * q^23 + 57 * q^24 - 48 * q^25 - 33 * q^26 + 6 * q^27 - 6 * q^28 - 15 * q^29 + 34 * q^30 + 33 * q^32 + 36 * q^33 - 6 * q^35 - 3 * q^36 + 12 * q^37 - 44 * q^38 - 17 * q^39 - 18 * q^40 - 9 * q^41 - 48 * q^42 + 42 * q^43 + 3 * q^45 + 48 * q^46 - 16 * q^48 + 22 * q^49 + 102 * q^50 + 6 * q^51 - 9 * q^52 - 16 * q^53 + 45 * q^54 - 38 * q^55 + 44 * q^56 - 93 * q^58 + 45 * q^59 + q^61 - 18 * q^62 + 27 * q^63 - 26 * q^64 + 18 * q^65 - 76 * q^66 - 21 * q^67 + 14 * q^68 - 9 * q^69 + 6 * q^71 + 57 * q^72 + 4 * q^74 + 27 * q^75 + 99 * q^76 - 22 * q^77 - 41 * q^78 + 52 * q^79 + 63 * q^80 - 75 * q^81 + 14 * q^82 - 126 * q^84 - 3 * q^85 - 31 * q^87 + 53 * q^88 - 3 * q^89 - 4 * q^90 + 11 * q^91 - 92 * q^92 + 66 * q^93 - 17 * q^94 + 9 * q^95 - 60 * q^97 + 18 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/221\mathbb{Z}\right)^\times$.

$n$	$105$	$171$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.60408	+	0.926118i	−1.13426	+	0.654864i	−0.945002	−	0.327063i	$-0.893941\pi$
$2$	−1.60408	+	0.926118i	−1.13426	+	0.654864i	−0.189256	+	0.981928i	$0.560608\pi$
$3$	0.634338	+	1.09871i	0.366235	+	0.634338i	0.988974	−	0.148092i	$-0.0473132\pi$
$3$	0.634338	+	1.09871i	0.366235	+	0.634338i	−0.622738	+	0.782430i	$0.713980\pi$
$4$	0.715389	−	1.23909i	0.357695	−	0.619545i
$5$			4.17850i			1.86868i	0.356383	+	0.934340i	$0.384010\pi$
$5$			4.17850i			1.86868i	−0.356383	+	0.934340i	$0.615990\pi$
$6$	−2.03506	−	1.17494i	−0.830811	−	0.479669i
$7$	3.61684	+	2.08819i	1.36704	+	0.789260i	0.990549	−	0.137161i	$-0.0437976\pi$
$7$	3.61684	+	2.08819i	1.36704	+	0.789260i	0.376490	+	0.926421i	$0.377131\pi$
$8$		−	1.05433i		−	0.372763i
$9$	0.695230	−	1.20417i	0.231743	−	0.401391i
$10$	−3.86978	−	6.70266i	−1.22373	−	2.11957i
$11$	−2.19777	+	1.26888i	−0.662652	+	0.382582i	−0.793287	−	0.608848i	$-0.791632\pi$
$11$	−2.19777	+	1.26888i	−0.662652	+	0.382582i	0.130635	+	0.991431i	$0.458298\pi$
$12$	1.81520			0.524002
$13$	1.81069	−	3.11792i	0.502195	−	0.864754i
$13$	1.81069	−	3.11792i	0.502195	−	0.864754i
$14$	−7.73563			−2.06743
$15$	−4.59094	+	2.65058i	−1.18538	+	0.684377i
$16$	2.40721	+	4.16942i	0.601804	+	1.04235i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i
$18$			2.57546i			0.607042i
$19$	0.0120062	+	0.00693178i	0.00275441	+	0.00159026i	0.501377	−	0.865229i	$-0.332827\pi$
$19$	0.0120062	+	0.00693178i	0.00275441	+	0.00159026i	−0.498622	+	0.866819i	$0.666160\pi$
$20$	5.17753	+	2.98925i	1.15773	+	0.668417i
$21$			5.29846i			1.15622i
$22$	2.35027	−	4.07079i	0.501079	−	0.867894i
$23$	−2.94311	−	5.09761i	−0.613680	−	1.06292i	−0.990615	−	0.136685i	$-0.956355\pi$
$23$	−2.94311	−	5.09761i	−0.613680	−	1.06292i	0.376935	−	0.926240i	$-0.376978\pi$
$24$	1.15840	−	0.668803i	0.236458	−	0.136519i
$25$	−12.4598			−2.49196
$26$	−0.0169419	+	6.67831i	−0.00332258	+	1.30972i
$27$	5.57007			1.07196
$28$	5.17490	−	2.98773i	0.977965	−	0.564628i
$29$	−0.596941	−	1.03393i	−0.110849	−	0.191996i	0.805264	−	0.592917i	$-0.202024\pi$
$29$	−0.596941	−	1.03393i	−0.110849	−	0.191996i	−0.916113	+	0.400920i	$0.868690\pi$
$30$	4.90950	−	8.50350i	0.896348	−	1.55252i
$31$		−	2.28280i		−	0.410004i	−0.978762	−	0.205002i	$-0.934280\pi$
$31$		−	2.28280i		−	0.410004i	0.978762	−	0.205002i	$-0.0657200\pi$
$32$	−5.89659	−	3.40440i	−1.04238	−	0.601818i
$33$	−2.78826	−	1.60980i	−0.485373	−	0.280230i
$34$		−	1.85224i		−	0.317656i
$35$	−8.72548	+	15.1130i	−1.47487	+	2.55456i
$36$	−0.994720	−	1.72291i	−0.165787	−	0.287151i
$37$	−1.25038	+	0.721908i	−0.205561	+	0.118681i	−0.599247	−	0.800564i	$-0.704533\pi$
$37$	−1.25038	+	0.721908i	−0.205561	+	0.118681i	0.393686	+	0.919245i	$0.371200\pi$
$38$	−0.0256786			−0.00416562
$39$	4.57426	+	0.0116042i	0.732468	+	0.00185816i
$40$	4.40552			0.696574
$41$	7.17652	−	4.14337i	1.12078	−	0.647085i	0.179184	−	0.983816i	$-0.442654\pi$
$41$	7.17652	−	4.14337i	1.12078	−	0.647085i	0.941601	+	0.336730i	$0.109321\pi$
$42$	−4.90700	−	8.49918i	−0.757167	−	1.31145i
$43$	2.03042	−	3.51679i	0.309636	−	0.536305i	−0.668647	−	0.743580i	$-0.733126\pi$
$43$	2.03042	−	3.51679i	0.309636	−	0.536305i	0.978283	+	0.207275i	$0.0664595\pi$
$44$			3.63098i			0.547391i
$45$	5.03164	+	2.90502i	0.750072	+	0.433054i
$46$	9.44197	+	5.45133i	1.39214	+	0.803754i
$47$		−	1.97614i		−	0.288250i	−0.989559	−	0.144125i	$-0.953963\pi$
$47$		−	1.97614i		−	0.288250i	0.989559	−	0.144125i	$-0.0460367\pi$
$48$	−3.05398	+	5.28964i	−0.440804	+	0.763494i
$49$	5.22104	+	9.04311i	0.745863	+	1.29187i
$50$	19.9866	−	11.5393i	2.82653	−	1.63190i
$51$	−1.26868			−0.177650
$52$	−2.56803	−	4.47413i	−0.356122	−	0.620451i
$53$	−6.25632			−0.859372			−0.429686	−	0.902978i	$-0.641376\pi$
$53$	−6.25632			−0.859372			−0.429686	+	0.902978i	$0.641376\pi$
$54$	−8.93486	+	5.15855i	−1.21588	+	0.701989i
$55$	−5.30202	−	9.18336i	−0.714924	−	1.23828i
$56$	2.20164	−	3.81336i	0.294207	−	0.509581i
$57$			0.0175884i			0.00232964i
$58$	1.91509	+	1.10568i	0.251463	+	0.145182i
$59$	11.9610	+	6.90567i	1.55719	+	0.899042i	0.997524	+	0.0703207i	$0.0224023\pi$
$59$	11.9610	+	6.90567i	1.55719	+	0.899042i	0.559662	+	0.828721i	$0.310931\pi$
$60$			7.58478i			0.979191i
$61$	2.92222	−	5.06143i	0.374152	−	0.648050i	−0.616048	−	0.787709i	$-0.711267\pi$
$61$	2.92222	−	5.06143i	0.374152	−	0.648050i	0.990200	+	0.139659i	$0.0446006\pi$
$62$	2.11415	+	3.66181i	0.268497	+	0.465050i
$63$	5.02908	−	2.90354i	0.633604	−	0.365812i
$64$	2.98264			0.372830
$65$	13.0282	+	7.56596i	1.61595	+	0.938442i
$66$	5.96346			0.734051
$67$	0.770695	−	0.444961i	0.0941554	−	0.0543606i	−0.452183	−	0.891925i	$-0.649355\pi$
$67$	0.770695	−	0.444961i	0.0941554	−	0.0543606i	0.546338	+	0.837565i	$0.316021\pi$
$68$	0.715389	+	1.23909i	0.0867537	+	0.150262i
$69$	3.73385	−	6.46721i	0.449502	−	0.778561i
$70$		−	32.3233i		−	3.86337i
$71$	4.74753	+	2.74099i	0.563428	+	0.325295i	0.754520	−	0.656277i	$-0.227870\pi$
$71$	4.74753	+	2.74099i	0.563428	+	0.325295i	−0.191092	+	0.981572i	$0.561203\pi$
$72$	−1.26960	−	0.733004i	−0.149624	−	0.0863853i
$73$			6.60599i			0.773172i	0.922253	+	0.386586i	$0.126346\pi$
$73$			6.60599i			0.773172i	−0.922253	+	0.386586i	$0.873654\pi$
$74$	1.33714	−	2.31600i	0.155440	−	0.269230i
$75$	−7.90374	−	13.6897i	−0.912646	−	1.58075i
$76$	0.0171782	−	0.00991784i	0.00197048	−	0.00113765i
$77$	−10.5986			−1.20783
$78$	−7.34825	+	4.21769i	−0.832025	+	0.477560i
$79$	−5.49114			−0.617802			−0.308901	−	0.951094i	$-0.599961\pi$
$79$	−5.49114			−0.617802			−0.308901	+	0.951094i	$0.599961\pi$
$80$	−17.4219	+	10.0585i	−1.94783	+	1.12458i
$81$	1.44762	+	2.50735i	0.160847	+	0.278595i
$82$	−7.67450	+	13.2926i	−0.847506	+	1.46792i
$83$			6.31349i			0.692996i	0.938051	+	0.346498i	$0.112629\pi$
$83$			6.31349i			0.692996i	−0.938051	+	0.346498i	$0.887371\pi$
$84$	6.56528	+	3.79047i	0.716331	+	0.413574i
$85$	−3.61868	−	2.08925i	−0.392501	−	0.226611i
$86$			7.52163i			0.811078i
$87$	0.757325	−	1.31173i	0.0811938	−	0.140632i
$88$	1.33782	+	2.31718i	0.142612	+	0.247012i
$89$	−8.58966	+	4.95924i	−0.910502	+	0.525678i	−0.880593	−	0.473874i	$-0.842855\pi$
$89$	−8.58966	+	4.95924i	−0.910502	+	0.525678i	−0.0299091	+	0.999553i	$0.509522\pi$
$90$	−10.7616			−1.13437
$91$	13.0598	−	7.49596i	1.36904	−	0.785790i
$92$	−8.42186			−0.878040
$93$	2.50813	−	1.44807i	0.260081	−	0.150158i
$94$	1.83014	+	3.16990i	0.188765	+	0.326950i
$95$	−0.0289644	+	0.0501678i	−0.00297169	+	0.00514711i
$96$		−	8.63816i		−	0.881628i
$97$	−14.2922	−	8.25160i	−1.45115	−	0.837824i	−0.452606	−	0.891711i	$-0.649506\pi$
$97$	−14.2922	−	8.25160i	−1.45115	−	0.837824i	−0.998547	+	0.0538871i	$0.982839\pi$
$98$	−16.7500	−	9.67060i	−1.69200	−	0.976878i
$99$			3.52866i			0.354644i
$100$	−8.91363	+	15.4389i	−0.891363	+	1.54389i
$101$	2.68197	+	4.64531i	0.266866	+	0.462225i	0.968051	−	0.250754i	$-0.0806786\pi$
$101$	2.68197	+	4.64531i	0.266866	+	0.462225i	−0.701185	+	0.712979i	$0.747345\pi$
$102$	2.03506	−	1.17494i	0.201501	−	0.116337i
$103$	−9.27817			−0.914206			−0.457103	−	0.889414i	$-0.651113\pi$
$103$	−9.27817			−0.914206			−0.457103	+	0.889414i	$0.651113\pi$
$104$	−3.28732	−	1.90907i	−0.322348	−	0.187200i
$105$	−22.1396			−2.16060
$106$	10.0357	−	5.79409i	0.974750	−	0.562772i
$107$	4.93108	+	8.54087i	0.476705	+	0.825678i	0.999644	−	0.0266929i	$-0.00849761\pi$
$107$	4.93108	+	8.54087i	0.476705	+	0.825678i	−0.522939	+	0.852370i	$0.675164\pi$
$108$	3.98477	−	6.90183i	0.383435	−	0.664128i
$109$			1.76854i			0.169395i	0.996407	+	0.0846977i	$0.0269924\pi$
$109$			1.76854i			0.169395i	−0.996407	+	0.0846977i	$0.973008\pi$
$110$	17.0098	+	9.82059i	1.62182	+	0.936356i
$111$	−1.58633	−	0.915868i	−0.150568	−	0.0869303i
$112$			20.1069i			1.89992i
$113$	10.1648	−	17.6060i	0.956228	−	1.65624i	0.224696	−	0.974429i	$-0.427861\pi$
$113$	10.1648	−	17.6060i	0.956228	−	1.65624i	0.731532	−	0.681807i	$-0.238805\pi$
$114$	−0.0162889	−	0.0282132i	−0.00152560	−	0.00264241i
$115$	21.3003	−	12.2978i	1.98627	−	1.14677i
$116$	−1.70818			−0.158601
$117$	−2.49567	−	4.34806i	−0.230724	−	0.401978i
$118$	−25.5819			−2.35500
$119$	−3.61684	+	2.08819i	−0.331556	+	0.191424i
$120$	2.79459	+	4.84037i	0.255110	+	0.441864i
$121$	−2.27988	+	3.94886i	−0.207262	+	0.358988i
$122$			10.8253i			0.980074i
$123$	9.10469	+	5.25659i	0.820942	+	0.473971i
$124$	−2.82860	−	1.63309i	−0.254016	−	0.146656i
$125$		−	31.1708i		−	2.78800i
$126$	−5.37804	+	9.31504i	−0.479114	+	0.829850i
$127$	6.55897	+	11.3605i	0.582014	+	1.00808i	0.995240	+	0.0974497i	$0.0310685\pi$
$127$	6.55897	+	11.3605i	0.582014	+	1.00808i	−0.413226	+	0.910628i	$0.635598\pi$
$128$	7.00878	−	4.04652i	0.619494	−	0.357665i
$129$	5.15189			0.453598
$130$	−27.9053	−	0.0707916i	−2.44746	−	0.00620883i
$131$	7.98543			0.697691			0.348845	−	0.937180i	$-0.386574\pi$
$131$	7.98543			0.697691			0.348845	+	0.937180i	$0.386574\pi$
$132$	−3.98938	+	2.30327i	−0.347231	+	0.200474i
$133$	0.0289497	+	0.0501424i	0.00251026	+	0.00434789i
$134$	−0.824173	+	1.42751i	−0.0711977	+	0.123318i
$135$			23.2745i			2.00315i
$136$	0.913079	+	0.527166i	0.0782958	+	0.0452041i
$137$	−15.7504	−	9.09352i	−1.34565	−	0.776912i	−0.358020	−	0.933714i	$-0.616548\pi$
$137$	−15.7504	−	9.09352i	−1.34565	−	0.776912i	−0.987630	+	0.156802i	$0.949881\pi$
$138$			13.8319i			1.17745i
$139$	1.28370	−	2.22343i	0.108882	−	0.188589i	−0.806436	−	0.591322i	$-0.798606\pi$
$139$	1.28370	−	2.22343i	0.108882	−	0.188589i	0.915318	+	0.402733i	$0.131940\pi$
$140$	12.4842	+	21.6233i	1.05511	+	1.82750i
$141$	2.17120	−	1.25354i	0.182848	−	0.105567i
$142$	−10.1539			−0.852097
$143$	−0.0232122	+	9.15001i	−0.00194110	+	0.765162i
$144$	6.69427			0.557856
$145$	4.32028	−	2.49432i	0.358780	−	0.207142i
$146$	−6.11793	−	10.5966i	−0.506323	−	0.876977i
$147$	−6.62381	+	11.4728i	−0.546323	+	0.946259i
$148$			2.06578i			0.169806i
$149$	−10.6354	−	6.14033i	−0.871283	−	0.503036i	−0.00350877	−	0.999994i	$-0.501117\pi$
$149$	−10.6354	−	6.14033i	−0.871283	−	0.503036i	−0.867774	+	0.496958i	$0.834450\pi$
$150$	25.3565	+	14.6396i	2.07035	+	1.19532i
$151$			15.7390i			1.28082i	0.768031	+	0.640412i	$0.221237\pi$
$151$			15.7390i			1.28082i	−0.768031	+	0.640412i	$0.778763\pi$
$152$	0.00730840	−	0.0126585i	0.000592790	−	0.00102674i
$153$	0.695230	+	1.20417i	0.0562060	+	0.0973517i
$154$	17.0011	−	9.81560i	1.36999	−	0.790963i
$155$	9.53868			0.766165
$156$	3.28676	−	5.65962i	0.263151	−	0.453133i
$157$	−3.90178			−0.311396			−0.155698	−	0.987805i	$-0.549763\pi$
$157$	−3.90178			−0.311396			−0.155698	+	0.987805i	$0.549763\pi$
$158$	8.80825	−	5.08545i	0.700747	−	0.404577i
$159$	−3.96862	−	6.87386i	−0.314732	−	0.545132i
$160$	14.2253	−	24.6389i	1.12461	−	1.94787i
$161$		−	24.5830i		−	1.93741i
$162$	−4.64421	−	2.68133i	−0.364883	−	0.210665i
$163$	7.61680	+	4.39756i	0.596594	+	0.344443i	0.767700	−	0.640809i	$-0.221401\pi$
$163$	7.61680	+	4.39756i	0.596594	+	0.344443i	−0.171107	+	0.985252i	$0.554734\pi$
$164$		−	11.8565i		−	0.925836i
$165$	6.72654	−	11.6507i	0.523661	−	0.907007i
$166$	−5.84704	−	10.1274i	−0.453818	−	0.786037i
$167$	−8.26280	+	4.77053i	−0.639395	+	0.369155i	−0.784381	−	0.620279i	$-0.787019\pi$
$167$	−8.26280	+	4.77053i	−0.639395	+	0.369155i	0.144986	+	0.989434i	$0.453686\pi$
$168$	5.58634			0.430996
$169$	−6.44280	−	11.2912i	−0.495600	−	0.868551i
$170$	7.73956			0.593597
$171$	0.0166941	−	0.00963837i	0.00127663	−	0.000737064i
$172$	−2.90508	−	5.03175i	−0.221510	−	0.383667i
$173$	9.67784	−	16.7625i	0.735793	−	1.27443i	−0.218582	−	0.975819i	$-0.570143\pi$
$173$	9.67784	−	16.7625i	0.735793	−	1.27443i	0.954375	−	0.298612i	$-0.0965236\pi$
$174$			2.80549i			0.212684i
$175$	−45.0652	−	26.0184i	−3.40661	−	1.96681i
$176$	−10.5810	−	6.10894i	−0.797573	−	0.460479i
$177$			17.5221i			1.31704i
$178$	9.18568	−	15.9101i	0.688496	−	1.19251i
$179$	8.31496	+	14.4019i	0.621490	+	1.07645i	0.989209	+	0.146515i	$0.0468055\pi$
$179$	8.31496	+	14.4019i	0.621490	+	1.07645i	−0.367719	+	0.929937i	$0.619861\pi$
$180$	7.19916	−	4.15644i	0.536593	−	0.309802i
$181$	8.55872			0.636165			0.318082	−	0.948063i	$-0.396961\pi$
$181$	8.55872			0.636165			0.318082	+	0.948063i	$0.396961\pi$
$182$	−14.0068	+	24.1190i	−1.03826	+	1.78782i
$183$	7.41470			0.548110
$184$	−5.37457	+	3.10301i	−0.396219	+	0.228757i
$185$	−3.01649	−	5.22471i	−0.221777	−	0.384129i
$186$	−2.68217	+	4.64565i	−0.196666	+	0.340635i
$187$		−	2.53776i		−	0.185580i
$188$	−2.44862	−	1.41371i	−0.178584	−	0.103105i
$189$	20.1461	+	11.6313i	1.46541	+	0.846056i
$190$		−	0.107298i		−	0.00778421i
$191$	11.8393	−	20.5063i	0.856661	−	1.48378i	−0.0184340	−	0.999830i	$-0.505868\pi$
$191$	11.8393	−	20.5063i	0.856661	−	1.48378i	0.875095	−	0.483951i	$-0.160799\pi$
$192$	1.89200	+	3.27704i	0.136543	+	0.236500i
$193$	−3.07145	+	1.77330i	−0.221088	+	0.127645i	−0.606454	−	0.795119i	$-0.707409\pi$
$193$	−3.07145	+	1.77330i	−0.221088	+	0.127645i	0.385366	+	0.922764i	$0.374075\pi$
$194$	30.5678			2.19464
$195$	−0.0484882	+	19.1135i	−0.00347231	+	1.36875i
$196$	14.9403			1.06717
$197$	−21.3905	+	12.3498i	−1.52401	+	0.879889i	−0.524417	+	0.851462i	$0.675717\pi$
$197$	−21.3905	+	12.3498i	−1.52401	+	0.879889i	−0.999596	+	0.0284271i	$0.990950\pi$
$198$	−3.26796	−	5.66027i	−0.232244	−	0.402258i
$199$	1.39834	−	2.42199i	0.0991256	−	0.171691i	−0.812197	−	0.583383i	$-0.801729\pi$
$199$	1.39834	−	2.42199i	0.0991256	−	0.171691i	0.911323	+	0.411692i	$0.135062\pi$
$200$			13.1368i			0.928912i
$201$	0.977763	+	0.564511i	0.0689661	+	0.0398176i
$202$	−8.60420	−	4.96764i	−0.605390	−	0.349522i
$203$		−	4.98610i		−	0.349955i
$204$	−0.907598	+	1.57201i	−0.0635445	+	0.110062i
$205$	17.3130	+	29.9871i	1.20920	+	2.09439i
$206$	14.8830	−	8.59269i	1.03695	−	0.598681i
$207$	−8.18454			−0.568865
$208$	17.3586	+	0.0440362i	1.20360	+	0.00305336i
$209$	−0.0351824			−0.00243362
$210$	35.5138	−	20.5039i	2.45068	−	1.41490i
$211$	−1.33306	−	2.30893i	−0.0917718	−	0.158953i	0.816485	−	0.577367i	$-0.195920\pi$
$211$	−1.33306	−	2.30893i	−0.0917718	−	0.158953i	−0.908257	+	0.418413i	$0.862586\pi$
$212$	−4.47571	+	7.75215i	−0.307393	+	0.532420i
$213$			6.95485i			0.476538i
$214$	−15.8197	−	9.13352i	−1.08141	−	0.624354i
$215$	14.6949	+	8.48410i	1.00218	+	0.578611i
$216$		−	5.87271i		−	0.399587i
$217$	4.76692	−	8.25654i	0.323599	−	0.560491i
$218$	−1.63788	−	2.83688i	−0.110931	−	0.192138i
$219$	−7.25804	+	4.19043i	−0.490453	+	0.283163i
$220$	−15.1720			−1.02290
$221$	1.79485	+	3.12706i	0.120735	+	0.210349i
$222$	3.39281			0.227710
$223$	12.7839	−	7.38079i	0.856073	−	0.494254i	−0.00662215	−	0.999978i	$-0.502108\pi$
$223$	12.7839	−	7.38079i	0.856073	−	0.494254i	0.862695	+	0.505724i	$0.168775\pi$
$224$	−14.2180	−	24.6264i	−0.949982	−	1.64542i
$225$	−8.66245	+	15.0038i	−0.577496	+	1.00025i
$226$			37.6554i			2.50480i
$227$	0.504518	+	0.291284i	0.0334860	+	0.0193332i	0.516650	−	0.856197i	$-0.327179\pi$
$227$	0.504518	+	0.291284i	0.0334860	+	0.0193332i	−0.483164	+	0.875530i	$0.660512\pi$
$228$	0.0217936	+	0.0125825i	0.00144332	+	0.000833299i
$229$			3.90401i			0.257984i	0.991646	+	0.128992i	$0.0411741\pi$
$229$			3.90401i			0.257984i	−0.991646	+	0.128992i	$0.958826\pi$
$230$	−22.7783	+	39.4532i	−1.50196	+	2.60147i
$231$	−6.72313	−	11.6448i	−0.442349	−	0.766171i
$232$	−1.09011	+	0.629374i	−0.0715691	+	0.0413204i
$233$	−9.47292			−0.620592			−0.310296	−	0.950640i	$-0.600428\pi$
$233$	−9.47292			−0.620592			−0.310296	+	0.950640i	$0.600428\pi$
$234$	8.03007	+	4.66336i	0.524942	+	0.304854i
$235$	8.25730			0.538647
$236$	17.1135	−	9.88049i	1.11399	−	0.643165i
$237$	−3.48324	−	6.03315i	−0.226261	−	0.391895i
$238$	3.86781	−	6.69925i	0.250713	−	0.434248i
$239$		−	9.79998i		−	0.633908i	−0.948441	−	0.316954i	$-0.897340\pi$
$239$		−	9.79998i		−	0.633908i	0.948441	−	0.316954i	$-0.102660\pi$
$240$	−22.1027	−	12.7610i	−1.42673	−	0.823721i
$241$	10.2235	+	5.90252i	0.658552	+	0.380215i	0.791725	−	0.610878i	$-0.209183\pi$
$241$	10.2235	+	5.90252i	0.658552	+	0.380215i	−0.133173	+	0.991093i	$0.542517\pi$
$242$		−	8.44574i		−	0.542913i
$243$	6.51855	−	11.2905i	0.418165	−	0.724283i
$244$	−4.18105	−	7.24179i	−0.267664	−	0.463608i
$245$	−37.7866	+	21.8161i	−2.41410	+	1.39378i
$246$	−19.4729			−1.24155
$247$	0.0433522	−	0.0248830i	0.00275844	−	0.00158327i
$248$	−2.40683			−0.152834
$249$	−6.93667	+	4.00489i	−0.439594	+	0.253800i
$250$	28.8679	+	50.0006i	1.82577	+	3.16232i
$251$	−7.05010	+	12.2111i	−0.444999	+	0.770760i	−0.998052	−	0.0623855i	$-0.980129\pi$
$251$	−7.05010	+	12.2111i	−0.444999	+	0.770760i	0.553054	+	0.833146i	$0.313462\pi$
$252$		−	8.30865i		−	0.523396i
$253$	12.9365	+	7.46891i	0.813312	+	0.469566i
$254$	−21.0423	−	12.1488i	−1.32031	−	0.762281i
$255$		−	5.30116i		−	0.331971i
$256$	−10.4778	+	18.1480i	−0.654859	+	1.13425i
$257$	−12.0069	−	20.7966i	−0.748971	−	1.29726i	−0.948316	−	0.317327i	$-0.897215\pi$
$257$	−12.0069	−	20.7966i	−0.748971	−	1.29726i	0.199345	−	0.979929i	$-0.436119\pi$
$258$	−8.26406	+	4.77126i	−0.514498	+	0.297045i
$259$	−6.02991			−0.374681
$260$	18.6951	−	10.7305i	1.15942	−	0.665478i
$261$	−1.66005			−0.102754
$262$	−12.8093	+	7.39546i	−0.791361	+	0.456893i
$263$	−13.3444	−	23.1131i	−0.822848	−	1.42521i	−0.903553	−	0.428477i	$-0.859050\pi$
$263$	−13.3444	−	23.1131i	−0.822848	−	1.42521i	0.0807046	−	0.996738i	$-0.474283\pi$
$264$	−1.69726	+	2.93975i	−0.104459	+	0.180929i
$265$		−	26.1420i		−	1.60589i
$266$	−0.0928755	−	0.0536217i	−0.00569456	−	0.00328776i
$267$	−10.8975	−	6.29167i	−0.666916	−	0.385044i
$268$		−	1.27328i		−	0.0777780i
$269$	4.56476	−	7.90639i	0.278318	−	0.482061i	−0.692649	−	0.721275i	$-0.743556\pi$
$269$	4.56476	−	7.90639i	0.278318	−	0.482061i	0.970967	+	0.239214i	$0.0768897\pi$
$270$	−21.5550	−	37.3343i	−1.31179	−	2.27209i
$271$	1.44834	−	0.836200i	0.0879804	−	0.0507955i	−0.455364	−	0.890305i	$-0.650491\pi$
$271$	1.44834	−	0.836200i	0.0879804	−	0.0507955i	0.543345	+	0.839510i	$0.317158\pi$
$272$	−4.81443			−0.291918
$273$	16.5202	+	9.59388i	0.999846	+	0.580648i
$274$	33.6867			2.03509
$275$	27.3838	−	15.8100i	1.65131	−	0.953382i
$276$	−5.34231	−	9.25315i	−0.321569	−	0.556974i
$277$	5.72788	−	9.92098i	0.344155	−	0.596094i	−0.641045	−	0.767503i	$-0.721499\pi$
$277$	5.72788	−	9.92098i	0.344155	−	0.596094i	0.985200	+	0.171410i	$0.0548321\pi$
$278$			4.75542i			0.285211i
$279$	−2.74889	−	1.58707i	−0.164572	−	0.0950156i
$280$	15.9341	+	9.19955i	0.952244	+	0.549778i
$281$		−	8.91674i		−	0.531928i	−0.963983	−	0.265964i	$-0.914310\pi$
$281$		−	8.91674i		−	0.531928i	0.963983	−	0.265964i	$-0.0856902\pi$
$282$	−2.32186	+	4.02157i	−0.138265	+	0.239481i
$283$	7.33922	+	12.7119i	0.436271	+	0.755644i	0.997398	−	0.0720858i	$-0.0229655\pi$
$283$	7.33922	+	12.7119i	0.436271	+	0.755644i	−0.561127	+	0.827730i	$0.689632\pi$
$284$	6.79266	−	3.92174i	0.403070	−	0.232713i
$285$	−0.0734929			−0.00435335
$286$	−8.43675	−	14.6989i	−0.498876	−	0.869163i
$287$	34.6085			2.04288
$288$	−8.19898	+	4.73368i	−0.483129	+	0.278935i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	−4.62006	+	8.00218i	−0.271299	+	0.469904i
$291$		−	20.9372i		−	1.22736i
$292$	8.18542	+	4.72585i	0.479015	+	0.276560i
$293$	−15.0523	−	8.69044i	−0.879364	−	0.507701i	−0.00891521	−	0.999960i	$-0.502838\pi$
$293$	−15.0523	−	8.69044i	−0.879364	−	0.507701i	−0.870449	+	0.492259i	$0.836171\pi$
$294$		−	24.5377i		−	1.43107i
$295$	−28.8553	+	49.9789i	−1.68002	+	2.90988i
$296$	0.761131	+	1.31832i	0.0442398	+	0.0766256i
$297$	−12.2417	+	7.06777i	−0.710337	+	0.410113i
$298$	22.7467			1.31768
$299$	−21.2230	−	0.0538395i	−1.22736	−	0.00311362i
$300$	−22.6170			−1.30579
$301$	14.6874	−	8.47978i	0.846569	−	0.488767i
$302$	−14.5762	−	25.2467i	−0.838767	−	1.45279i
$303$	−3.40255	+	5.89339i	−0.195471	+	0.338566i
$304$			0.0667452i			0.00382810i
$305$	21.1492	+	12.2105i	1.21100	+	0.699170i
$306$	−2.23041	−	1.28773i	−0.127504	−	0.0736146i
$307$		−	28.7329i		−	1.63987i	−0.572454	−	0.819937i	$-0.694009\pi$
$307$		−	28.7329i		−	1.63987i	0.572454	−	0.819937i	$-0.305991\pi$
$308$	−7.58216	+	13.1327i	−0.432034	+	0.748304i
$309$	−5.88550	−	10.1940i	−0.334814	−	0.579916i
$310$	−15.3008	+	8.83395i	−0.869029	+	0.501734i
$311$	−3.09676			−0.175601			−0.0878006	−	0.996138i	$-0.527984\pi$
$311$	−3.09676			−0.175601			−0.0878006	+	0.996138i	$0.527984\pi$
$312$	0.0122347	−	4.82279i	0.000692654	−	0.273037i
$313$	−5.53672			−0.312954			−0.156477	−	0.987682i	$-0.550014\pi$
$313$	−5.53672			−0.312954			−0.156477	+	0.987682i	$0.550014\pi$
$314$	6.25879	−	3.61351i	0.353204	−	0.203922i
$315$	12.1324	+	21.0140i	0.683585	+	1.18400i
$316$	−3.92831	+	6.80403i	−0.220984	+	0.382756i
$317$			9.70763i			0.545235i	0.962123	+	0.272617i	$0.0878893\pi$
$317$			9.70763i			0.545235i	−0.962123	+	0.272617i	$0.912111\pi$
$318$	12.7320	+	7.35083i	0.713976	+	0.412214i
$319$	2.62388	+	1.51490i	0.146909	+	0.0848179i
$320$			12.4629i			0.696700i
$321$	−6.25594	+	10.8356i	−0.349173	+	0.604785i
$322$	22.7668	+	39.4332i	1.26874	+	2.19753i
$323$	−0.0120062	+	0.00693178i	−0.000668043	+	0.000385695i
$324$	4.14245			0.230136
$325$	−22.5609	+	38.8487i	−1.25145	+	2.15494i
$326$	−16.2906			−0.902255
$327$	−1.94310	+	1.12185i	−0.107454	+	0.0620386i
$328$	−4.36849	−	7.56644i	−0.241209	−	0.417787i
$329$	4.12655	−	7.14740i	0.227504	−	0.394049i
$330$			24.9183i			1.37171i
$331$	−4.50690	−	2.60206i	−0.247721	−	0.143022i	0.370999	−	0.928633i	$-0.379015\pi$
$331$	−4.50690	−	2.60206i	−0.247721	−	0.143022i	−0.618720	+	0.785611i	$0.712349\pi$
$332$	7.82299	+	4.51661i	0.429342	+	0.247881i
$333$			2.00757i			0.110014i
$334$	8.83615	−	15.3047i	0.483493	−	0.837434i
$335$	1.85927	+	3.22035i	0.101583	+	0.175946i
$336$	−22.0915	+	12.7545i	−1.20519	+	0.695817i
$337$	10.2731			0.559612			0.279806	−	0.960057i	$-0.409730\pi$
$337$	10.2731			0.559612			0.279806	+	0.960057i	$0.409730\pi$
$338$	20.7917	+	12.1452i	1.13092	+	0.660611i
$339$	25.7918			1.40082
$340$	−5.17753	+	2.98925i	−0.280791	+	0.162115i
$341$	2.89661	+	5.01707i	0.156860	+	0.271690i
$342$	−0.0178525	+	0.0309215i	−0.000965354	+	0.00167204i
$343$			14.3754i			0.776200i
$344$	−3.70786	−	2.14074i	−0.199915	−	0.115421i
$345$	27.0232	+	15.6019i	1.45488	+	0.839976i
$346$			35.8513i			1.92738i
$347$	10.1994	−	17.6659i	0.547533	−	0.948355i	−0.450910	−	0.892569i	$-0.648900\pi$
$347$	10.1994	−	17.6659i	0.547533	−	0.948355i	0.998443	−	0.0557853i	$-0.0177662\pi$
$348$	−1.08356	−	1.87679i	−0.0580852	−	0.100606i
$349$	−26.8134	+	15.4807i	−1.43529	+	0.828663i	−0.997517	−	0.0704238i	$-0.977565\pi$
$349$	−26.8134	+	15.4807i	−1.43529	+	0.828663i	−0.437770	+	0.899087i	$0.644232\pi$
$350$	96.3846			5.15197
$351$	10.0857	−	17.3670i	0.538334	−	0.926983i
$352$	17.2791			0.920980
$353$	−6.43153	+	3.71325i	−0.342316	+	0.197636i	−0.661296	−	0.750125i	$-0.729993\pi$
$353$	−6.43153	+	3.71325i	−0.342316	+	0.197636i	0.318980	+	0.947761i	$0.396660\pi$
$354$	−16.2276	−	28.1070i	−0.862485	−	1.49387i
$355$	−11.4532	+	19.8375i	−0.607873	+	1.05287i
$356$			14.1911i			0.752129i
$357$	−4.58860	−	2.64923i	−0.242855	−	0.140212i
$358$	−26.6758	−	15.4013i	−1.40986	−	0.813983i
$359$			29.9429i			1.58033i	0.612897	+	0.790163i	$0.290004\pi$
$359$			29.9429i			1.58033i	−0.612897	+	0.790163i	$0.709996\pi$
$360$	3.06285	−	5.30502i	0.161426	−	0.279599i
$361$	−9.49990	−	16.4543i	−0.499995	−	0.866017i
$362$	−13.7289	+	7.92639i	−0.721575	+	0.416602i
$363$	−5.78485			−0.303626
$364$	0.0546559	−	21.5448i	0.00286475	−	1.12925i
$365$	−27.6031			−1.44481
$366$	−11.8938	+	6.86688i	−0.621699	+	0.358938i
$367$	−8.99642	−	15.5823i	−0.469609	−	0.813387i	0.529787	−	0.848131i	$-0.322272\pi$
$367$	−8.99642	−	15.5823i	−0.469609	−	0.813387i	−0.999396	+	0.0347437i	$0.988939\pi$
$368$	14.1694	−	24.5421i	0.738630	−	1.27934i
$369$		−	11.5224i		−	0.599831i
$370$	9.67740	+	5.58725i	0.503104	+	0.290467i
$371$	−22.6281	−	13.0644i	−1.17479	−	0.678268i
$372$		−	4.14373i		−	0.214843i
$373$	−6.95230	+	12.0417i	−0.359976	+	0.623497i	−0.987956	−	0.154732i	$-0.950549\pi$
$373$	−6.95230	+	12.0417i	−0.359976	+	0.623497i	0.627980	+	0.778229i	$0.283882\pi$
$374$	2.35027	+	4.07079i	0.121530	+	0.210495i
$375$	34.2476	−	19.7729i	1.76854	−	1.02107i
$376$	−2.08351			−0.107449
$377$	−4.30459	−	0.0109201i	−0.221698	−	0.000562414i
$378$	−43.0880			−2.21621
$379$	0.990182	−	0.571682i	0.0508623	−	0.0293653i	−0.474353	−	0.880335i	$-0.657318\pi$
$379$	0.990182	−	0.571682i	0.0508623	−	0.0293653i	0.525216	+	0.850969i	$0.323985\pi$
$380$	0.0414417	+	0.0717791i	0.00212591	+	0.00368219i
$381$	−8.32120	+	14.4127i	−0.426308	+	0.738388i
$382$			43.8583i			2.24399i
$383$	−9.04558	−	5.22247i	−0.462207	−	0.266856i	0.250765	−	0.968048i	$-0.419318\pi$
$383$	−9.04558	−	5.22247i	−0.462207	−	0.266856i	−0.712972	+	0.701193i	$0.752651\pi$
$384$	8.89187	+	5.13373i	0.453761	+	0.261979i
$385$		−	44.2864i		−	2.25704i
$386$	3.28457	−	5.68905i	0.167180	−	0.289565i
$387$	−2.82322	−	4.88995i	−0.143512	−	0.248570i
$388$	−20.4490	+	11.8062i	−1.03814	+	0.599370i
$389$	14.3527			0.727712			0.363856	−	0.931455i	$-0.381460\pi$
$389$	14.3527			0.727712			0.363856	+	0.931455i	$0.381460\pi$
$390$	−17.6236	−	30.7046i	−0.892406	−	1.55479i
$391$	5.88621			0.297678
$392$	9.53444	−	5.50471i	0.481562	−	0.278030i
$393$	5.06547	+	8.77364i	0.255519	+	0.442572i
$394$	22.8748	−	39.6203i	1.15242	−	1.99604i
$395$		−	22.9447i		−	1.15447i
$396$	4.37233	+	2.52437i	0.219718	+	0.126854i
$397$	−14.7152	−	8.49584i	−0.738536	−	0.426394i	0.0830006	−	0.996549i	$-0.473550\pi$
$397$	−14.7152	−	8.49584i	−0.738536	−	0.426394i	−0.821537	+	0.570155i	$0.806883\pi$
$398$			5.18011i			0.259655i
$399$	−0.0367278	+	0.0636144i	−0.00183869	+	0.00318470i
$400$	−29.9935	−	51.9502i	−1.49967	−	2.59751i
$401$	34.0499	−	19.6587i	1.70037	−	0.981710i	0.754993	−	0.655732i	$-0.227640\pi$
$401$	34.0499	−	19.6587i	1.70037	−	0.981710i	0.945378	−	0.325977i	$-0.105693\pi$
$402$	−2.09122			−0.104300
$403$	−7.11759	−	4.13345i	−0.354552	−	0.205902i
$404$	7.67461			0.381826
$405$	−10.4770	+	6.04887i	−0.520604	+	0.300571i
$406$	4.61771	+	7.99811i	0.229173	+	0.396940i
$407$	1.83203	−	3.17317i	0.0908105	−	0.157288i
$408$			1.33761i			0.0662214i
$409$	−0.798855	−	0.461219i	−0.0395009	−	0.0228058i	0.480120	−	0.877203i	$-0.340593\pi$
$409$	−0.798855	−	0.461219i	−0.0395009	−	0.0228058i	−0.519620	+	0.854397i	$0.673927\pi$
$410$	−55.5431	−	32.0679i	−2.74308	−	1.58372i
$411$		−	23.0735i		−	1.13813i
$412$	−6.63751	+	11.4965i	−0.327007	+	0.566392i
$413$	28.8407	+	49.9535i	1.41916	+	2.45805i
$414$	13.1287	−	7.57985i	0.645240	−	0.372529i
$415$	−26.3809			−1.29499
$416$	−21.2915	+	12.2208i	−1.04390	+	0.599172i
$417$	3.25719			0.159505
$418$	0.0564356	−	0.0325831i	0.00276035	−	0.00159369i
$419$	17.3160	+	29.9922i	0.845942	+	1.46521i	0.884801	+	0.465969i	$0.154294\pi$
$419$	17.3160	+	29.9922i	0.845942	+	1.46521i	−0.0388590	+	0.999245i	$0.512372\pi$
$420$	−15.8384	+	27.4330i	−0.772837	+	1.33859i
$421$			21.4058i			1.04326i	0.853173	+	0.521628i	$0.174675\pi$
$421$			21.4058i			1.04326i	−0.853173	+	0.521628i	$0.825325\pi$
$422$	4.27669	+	2.46915i	0.208186	+	0.120196i
$423$	−2.37962	−	1.37387i	−0.115701	−	0.0668000i
$424$			6.59624i			0.320342i
$425$	6.22991	−	10.7905i	0.302195	−	0.523417i
$426$	−6.44101	−	11.1562i	−0.312068	−	0.540518i
$427$	21.1384	−	12.2043i	1.02296	−	0.590606i
$428$	14.1106			0.682060
$429$	−10.0679	+	5.77870i	−0.486082	+	0.278998i
$430$	−31.4291			−1.51565
$431$	−11.9017	+	6.87148i	−0.573287	+	0.330987i	−0.758461	−	0.651718i	$-0.774048\pi$
$431$	−11.9017	+	6.87148i	−0.573287	+	0.330987i	0.185174	+	0.982706i	$0.440715\pi$
$432$	13.4084	+	23.2240i	0.645110	+	1.11736i
$433$	−6.92966	+	12.0025i	−0.333018	+	0.576804i	−0.983102	−	0.183058i	$-0.941400\pi$
$433$	−6.92966	+	12.0025i	−0.333018	+	0.576804i	0.650084	+	0.759862i	$0.274734\pi$
$434$			17.6589i			0.847655i
$435$	5.48104	+	3.16448i	0.262796	+	0.151725i
$436$	2.19138	+	1.26519i	0.104948	+	0.0605918i
$437$		−	0.0816038i		−	0.00390364i
$438$	7.76167	−	13.4436i	0.370867	−	0.642360i
$439$	6.01309	+	10.4150i	0.286989	+	0.497079i	0.973090	−	0.230427i	$-0.0740124\pi$
$439$	6.01309	+	10.4150i	0.286989	+	0.497079i	−0.686101	+	0.727507i	$0.740679\pi$
$440$	−9.68232	+	5.59009i	−0.461586	+	0.266497i
$441$	14.5193			0.691395
$442$	−5.77512	−	3.35383i	−0.274694	−	0.159525i
$443$	14.9271			0.709206			0.354603	−	0.935017i	$-0.384616\pi$
$443$	14.9271			0.709206			0.354603	+	0.935017i	$0.384616\pi$
$444$	−2.26969	+	1.31040i	−0.107715	+	0.0621890i
$445$	−20.7222	−	35.8918i	−0.982325	−	1.70144i
$446$	−13.6710	+	23.6788i	−0.647339	+	1.12122i
$447$		−	15.5802i		−	0.736918i
$448$	10.7877	+	6.22830i	0.509673	+	0.294260i
$449$	12.4157	+	7.16820i	0.585933	+	0.338288i	0.763488	−	0.645822i	$-0.223485\pi$
$449$	12.4157	+	7.16820i	0.585933	+	0.338288i	−0.177555	+	0.984111i	$0.556819\pi$
$450$		−	32.0898i		−	1.51273i
$451$	−10.5149	+	18.2123i	−0.495127	+	0.857585i
$452$	−14.5436	−	25.1903i	−0.684075	−	1.18485i
$453$	−17.2926	+	9.98387i	−0.812476	+	0.469083i
$454$	−1.07905			−0.0506424
$455$	31.3218	+	54.5702i	1.46839	+	2.55829i
$456$	0.0185440			0.000868402
$457$	−3.96756	+	2.29067i	−0.185595	+	0.107153i	−0.589919	−	0.807463i	$-0.700840\pi$
$457$	−3.96756	+	2.29067i	−0.185595	+	0.107153i	0.404324	+	0.914616i	$0.367507\pi$
$458$	−3.61557	−	6.26235i	−0.168944	−	0.292620i
$459$	−2.78504	+	4.82382i	−0.129994	+	0.225157i
$460$		−	35.1907i		−	1.64078i
$461$	21.5881	+	12.4639i	1.00546	+	0.580503i	0.909859	−	0.414917i	$-0.136189\pi$
$461$	21.5881	+	12.4639i	1.00546	+	0.580503i	0.0956008	+	0.995420i	$0.469523\pi$
$462$	21.5689	+	12.4528i	1.00348	+	0.579357i
$463$		−	6.20674i		−	0.288452i	−0.989545	−	0.144226i	$-0.953931\pi$
$463$		−	6.20674i		−	0.288452i	0.989545	−	0.144226i	$-0.0460692\pi$
$464$	2.87393	−	4.97779i	0.133419	−	0.231088i
$465$	6.05075	+	10.4802i	0.280597	+	0.486008i
$466$	15.1954	−	8.77304i	0.703911	−	0.406403i
$467$	−1.38949			−0.0642982			−0.0321491	−	0.999483i	$-0.510235\pi$
$467$	−1.38949			−0.0642982			−0.0321491	+	0.999483i	$0.510235\pi$
$468$	−7.17301	−	0.0181969i	−0.331572	−	0.000841150i
$469$	3.71665			0.171619
$470$	−13.2454	+	7.64724i	−0.610965	+	0.352741i
$471$	−2.47505	−	4.28691i	−0.114044	−	0.197531i
$472$	7.28087	−	12.6108i	0.335129	−	0.580461i
$473$			10.3054i			0.473845i
$474$	11.1748	+	6.45179i	0.513277	+	0.296340i
$475$	−0.149595	−	0.0863688i	−0.00686389	−	0.00396287i
$476$			5.97546i			0.273885i
$477$	−4.34958	+	7.53370i	−0.199154	+	0.344944i
$478$	9.07594	+	15.7200i	0.415124	+	0.719015i
$479$	−12.3432	+	7.12635i	−0.563975	+	0.325611i	−0.754739	−	0.656025i	$-0.772237\pi$
$479$	−12.3432	+	7.12635i	−0.563975	+	0.325611i	0.190764	+	0.981636i	$0.438903\pi$
$480$	36.0945			1.64748
$481$	−0.0132062	+	5.20574i	−0.000602150	+	0.237361i
$482$	−21.8657			−0.995957
$483$	27.0095	−	15.5939i	1.22897	−	0.709549i
$484$	3.26200	+	5.64995i	0.148273	+	0.256816i
$485$	34.4793	−	59.7199i	1.56562	−	2.71174i
$486$			24.1478i			1.09537i
$487$	11.0641	+	6.38786i	0.501362	+	0.289462i	0.729276	−	0.684220i	$-0.239857\pi$
$487$	11.0641	+	6.38786i	0.501362	+	0.289462i	−0.227914	+	0.973681i	$0.573190\pi$
$488$	−5.33643	−	3.08099i	−0.241569	−	0.139470i
$489$			11.1582i			0.504589i
$490$	40.4086	−	69.9897i	1.82547	−	3.16181i
$491$	−10.7614	−	18.6394i	−0.485657	−	0.841183i	0.514207	−	0.857666i	$-0.328086\pi$
$491$	−10.7614	−	18.6394i	−0.485657	−	0.841183i	−0.999864	+	0.0164833i	$0.994753\pi$
$492$	13.0268	−	7.52102i	0.587293	−	0.339074i
$493$	1.19388			0.0537697
$494$	−0.0464960	+	0.0800637i	−0.00209195	+	0.00360224i
$495$	−14.7445			−0.662716
$496$	9.51796	−	5.49520i	0.427369	−	0.246742i
$497$	11.4474	+	19.8274i	0.513485	+	0.889382i
$498$	7.41800	−	12.8484i	0.332409	−	0.575749i
$499$		−	12.7574i		−	0.571102i	−0.958364	−	0.285551i	$-0.907823\pi$
$499$		−	12.7574i		−	0.571102i	0.958364	−	0.285551i	$-0.0921765\pi$
$500$	−38.6235	−	22.2993i	−1.72730	−	0.997254i
$501$	−10.4828	−	6.05226i	−0.468338	−	0.270395i
$502$		−	26.1169i		−	1.16565i
$503$	−2.47008	+	4.27830i	−0.110135	+	0.190760i	−0.915825	−	0.401578i	$-0.868462\pi$
$503$	−2.47008	+	4.27830i	−0.110135	+	0.190760i	0.805689	+	0.592338i	$0.201795\pi$
$504$	−3.06130	−	5.30232i	−0.136361	−	0.236184i
$505$	−19.4104	+	11.2066i	−0.863751	+	0.498687i
$506$	−27.6684			−1.23001
$507$	8.31876	−	14.2412i	0.369449	−	0.632472i
$508$	18.7689			0.832733
$509$	0.396937	−	0.229172i	0.0175939	−	0.0101579i	−0.491177	−	0.871060i	$-0.663433\pi$
$509$	0.396937	−	0.229172i	0.0175939	−	0.0101579i	0.508771	+	0.860902i	$0.330100\pi$
$510$	4.90950	+	8.50350i	0.217396	+	0.376541i
$511$	−13.7945	+	23.8928i	−0.610234	+	1.05696i
$512$		−	22.6285i		−	1.00005i
$513$	0.0668754	+	0.0386105i	0.00295262	+	0.00170470i
$514$	38.5202	+	22.2397i	1.69905	+	0.980949i
$515$		−	38.7688i		−	1.70836i
$516$	3.68561	−	6.38366i	0.162250	−	0.281025i
$517$	2.50749	+	4.34310i	0.110279	+	0.191009i
$518$	9.67248	−	5.58441i	0.424985	−	0.245365i
$519$	24.5561			1.07789
$520$	7.97704	−	13.7360i	0.349816	−	0.602366i
$521$	−3.24552			−0.142189			−0.0710945	−	0.997470i	$-0.522649\pi$
$521$	−3.24552			−0.142189			−0.0710945	+	0.997470i	$0.522649\pi$
$522$	2.66285	−	1.53740i	0.116550	−	0.0672901i
$523$	14.2553	+	24.6908i	0.623339	+	1.07966i	0.988859	+	0.148852i	$0.0475578\pi$
$523$	14.2553	+	24.6908i	0.623339	+	1.07966i	−0.365520	+	0.930803i	$0.619109\pi$
$524$	5.71269	−	9.89468i	0.249560	−	0.432251i
$525$		−	66.0179i		−	2.88126i
$526$	42.8109	+	24.7169i	1.86664	+	1.07771i
$527$	1.97697	+	1.14140i	0.0861180	+	0.0497202i
$528$		−	15.5005i		−	0.674575i
$529$	−5.82374	+	10.0870i	−0.253206	+	0.438566i
$530$	24.2106	+	41.9340i	1.05164	+	1.82150i
$531$	16.6313	−	9.60206i	0.721735	−	0.416694i
$532$	0.0828412			0.00359162
$533$	0.0757964	−	29.8782i	0.00328311	−	1.29417i
$534$	23.3073			1.00861
$535$	−35.6880	+	20.6045i	−1.54293	+	0.890809i
$536$	−0.469137	−	0.812569i	−0.0202636	−	0.0350976i
$537$	−10.5490	+	18.2714i	−0.455223	+	0.788469i
$538$			16.9100i			0.729043i
$539$	−22.9493	−	13.2498i	−0.988495	−	0.570708i
$540$	28.8392	+	16.6503i	1.24104	+	0.716517i
$541$			17.1419i			0.736987i	0.929630	+	0.368493i	$0.120126\pi$
$541$			17.1419i			0.736987i	−0.929630	+	0.368493i	$0.879874\pi$
$542$	−1.54884	+	2.68267i	−0.0665284	+	0.115231i
$543$	5.42912	+	9.40352i	0.232986	+	0.403544i
$544$	5.89659	−	3.40440i	0.252814	−	0.145962i
$545$	−7.38983			−0.316546
$546$	−35.3848	−	0.0897660i	−1.51433	−	0.00384163i
$547$	33.5688			1.43530			0.717649	−	0.696405i	$-0.245218\pi$
$547$	33.5688			1.43530			0.717649	+	0.696405i	$0.245218\pi$
$548$	−22.5354	+	13.0108i	−0.962664	+	0.555794i
$549$	−4.06323	−	7.03772i	−0.173414	−	0.300362i
$550$	−29.2839	+	50.7213i	−1.24867	+	2.16276i
$551$		−	0.0165515i		−	0.000705116i
$552$	−6.81859	−	3.93672i	−0.290219	−	0.167558i
$553$	−19.8606	−	11.4665i	−0.844559	−	0.487607i
$554$			21.2188i			0.901499i
$555$	3.82695	−	6.62847i	0.162445	−	0.281363i
$556$	−1.83669	−	3.18124i	−0.0778929	−	0.134914i
$557$	−20.7476	+	11.9787i	−0.879106	+	0.507552i	−0.870363	−	0.492410i	$-0.836116\pi$
$557$	−20.7476	+	11.9787i	−0.879106	+	0.507552i	−0.00874233	+	0.999962i	$0.502783\pi$
$558$	5.87927			0.248889
$559$	−7.28859	−	12.6985i	−0.308274	−	0.537089i
$560$	−84.0164			−3.55034
$561$	2.78826	−	1.60980i	0.117720	−	0.0679658i
$562$	8.25795	+	14.3032i	0.348341	+	0.603344i
$563$	6.75274	−	11.6961i	0.284594	−	0.492931i	−0.687917	−	0.725790i	$-0.741475\pi$
$563$	6.75274	−	11.6961i	0.284594	−	0.492931i	0.972511	+	0.232858i	$0.0748079\pi$
$564$		−	3.58708i		−	0.151043i
$565$	73.5667	+	42.4738i	3.09497	+	1.78688i
$566$	−23.5454	−	13.5940i	−0.989688	−	0.571397i
$567$			12.0916i			0.507799i
$568$	2.88991	−	5.00547i	0.121258	−	0.210025i
$569$	−0.781149	−	1.35299i	−0.0327475	−	0.0567203i	0.849187	−	0.528092i	$-0.177092\pi$
$569$	−0.781149	−	1.35299i	−0.0327475	−	0.0567203i	−0.881935	+	0.471372i	$0.843759\pi$
$570$	0.117889	−	0.0680631i	0.00493782	−	0.00285085i
$571$	−43.1615			−1.80625			−0.903127	−	0.429374i	$-0.858734\pi$
$571$	−43.1615			−1.80625			−0.903127	+	0.429374i	$0.858734\pi$
$572$	11.3211	+	6.57458i	0.473358	+	0.274897i
$573$	30.0405			1.25496
$574$	−55.5149	+	32.0516i	−2.31715	+	1.33781i
$575$	36.6706	+	63.5153i	1.52927	+	2.64877i
$576$	2.07362	−	3.59162i	0.0864008	−	0.149651i
$577$		−	19.8752i		−	0.827416i	−0.910410	−	0.413708i	$-0.864233\pi$
$577$		−	19.8752i		−	0.827416i	0.910410	−	0.413708i	$-0.135767\pi$
$578$	1.60408	+	0.926118i	0.0667211	+	0.0385214i
$579$	−3.89668	−	2.24975i	−0.161940	−	0.0934963i
$580$		−	7.13763i		−	0.296374i
$581$	−13.1838	+	22.8349i	−0.546954	+	0.947352i
$582$	19.3903	+	33.5851i	0.803756	+	1.39215i
$583$	13.7499	−	7.93853i	0.569465	−	0.328781i
$584$	6.96491			0.288210
$585$	18.1683	−	10.4281i	0.751168	−	0.431150i
$586$	32.1935			1.32990
$587$	7.51416	−	4.33830i	0.310143	−	0.179061i	−0.336848	−	0.941559i	$-0.609361\pi$
$587$	7.51416	−	4.33830i	0.310143	−	0.179061i	0.646990	+	0.762498i	$0.276027\pi$
$588$	9.47721	+	16.4150i	0.390834	+	0.676944i
$589$	0.0158239	−	0.0274078i	0.000652012	−	0.00112932i
$590$		−	106.894i		−	4.40074i
$591$	−27.1377	−	15.6679i	−1.11629	−	0.644493i
$592$	−6.01987	−	3.47558i	−0.247415	−	0.142845i
$593$		−	20.2739i		−	0.832548i	−0.909239	−	0.416274i	$-0.863336\pi$
$593$		−	20.2739i		−	0.832548i	0.909239	−	0.416274i	$-0.136664\pi$
$594$	13.0912	−	22.6746i	0.537137	−	0.930349i
$595$	−8.72548	−	15.1130i	−0.357710	−	0.619571i
$596$	−15.2169	+	8.78546i	−0.623307	+	0.359866i
$597$	3.54808			0.145213
$598$	34.0933	−	19.5686i	1.39418	−	0.800220i
$599$	−31.1545			−1.27294			−0.636470	−	0.771301i	$-0.719606\pi$
$599$	−31.1545			−1.27294			−0.636470	+	0.771301i	$0.719606\pi$
$600$	−14.4335	+	8.33317i	−0.589244	+	0.340200i
$601$	3.16795	+	5.48705i	0.129223	+	0.223822i	0.923376	−	0.383897i	$-0.125418\pi$
$601$	3.16795	+	5.48705i	0.129223	+	0.223822i	−0.794152	+	0.607719i	$0.792085\pi$
$602$	−15.7066	+	27.2046i	−0.640152	+	1.10878i
$603$		−	1.23740i		−	0.0503909i
$604$	19.5021	+	11.2595i	0.793529	+	0.458144i
$605$	−16.5003	−	9.52646i	−0.670833	−	0.387306i
$606$		−	12.6047i		−	0.512029i
$607$	−14.8197	+	25.6685i	−0.601514	+	1.04185i	0.391079	+	0.920357i	$0.372102\pi$
$607$	−14.8197	+	25.6685i	−0.601514	+	1.04185i	−0.992592	+	0.121495i	$0.961231\pi$
$608$	−0.0471971	−	0.0817478i	−0.00191409	−	0.00331531i
$609$	5.47825	−	3.16287i	0.221990	−	0.128166i
$610$	−45.2334			−1.83145
$611$	−6.16144	−	3.57818i	−0.249265	−	0.144758i
$612$	1.98944			0.0804184
$613$	2.26678	−	1.30873i	0.0915545	−	0.0528590i	−0.453524	−	0.891244i	$-0.649833\pi$
$613$	2.26678	−	1.30873i	0.0915545	−	0.0528590i	0.545078	+	0.838385i	$0.316500\pi$
$614$	26.6101	+	46.0900i	1.07389	+	1.86004i
$615$	−21.9647	+	38.0439i	−0.885700	+	1.53408i
$616$			11.1745i			0.450233i
$617$	3.26063	+	1.88253i	0.131268	+	0.0757876i	0.564196	−	0.825641i	$-0.309186\pi$
$617$	3.26063	+	1.88253i	0.131268	+	0.0757876i	−0.432928	+	0.901429i	$0.642520\pi$
$618$	18.8817	+	10.9013i	0.759532	+	0.438516i
$619$		−	32.7936i		−	1.31809i	−0.752106	−	0.659043i	$-0.770962\pi$
$619$		−	32.7936i		−	1.31809i	0.752106	−	0.659043i	$-0.229038\pi$
$620$	6.82387	−	11.8193i	0.274053	−	0.474674i
$621$	−16.3933	−	28.3940i	−0.657841	−	1.13941i
$622$	4.96746	−	2.86797i	0.199177	−	0.114995i
$623$	−41.4233			−1.65959
$624$	10.9629	+	19.0999i	0.438865	+	0.764610i
$625$	67.9481			2.71792
$626$	8.88136	−	5.12766i	0.354971	−	0.204942i
$627$	−0.0223176	−	0.0386552i	−0.000891278	−	0.00154374i
$628$	−2.79129	+	4.83466i	−0.111385	+	0.192924i
$629$		−	1.44382i		−	0.0575687i
$630$	−38.9229	−	22.4721i	−1.55072	−	0.895311i
$631$	9.43453	+	5.44703i	0.375583	+	0.216843i	0.675895	−	0.736998i	$-0.263757\pi$
$631$	9.43453	+	5.44703i	0.375583	+	0.216843i	−0.300312	+	0.953841i	$0.597091\pi$
$632$			5.78949i			0.230294i
$633$	1.69122	−	2.92929i	0.0672202	−	0.116429i
$634$	−8.99041	−	15.5718i	−0.357055	−	0.618437i
$635$	−47.4696	+	27.4066i	−1.88378	+	1.08760i
$636$	−11.3564			−0.450312
$637$	37.6494	+	0.0955108i	1.49172	+	0.00378428i
$638$	−5.61189			−0.222177
$639$	6.60125	−	3.81123i	0.261141	−	0.150770i
$640$	16.9084	+	29.2862i	0.668362	+	1.15764i
$641$	−11.8944	+	20.6016i	−0.469799	+	0.813715i	−0.999404	−	0.0345291i	$-0.989007\pi$
$641$	−11.8944	+	20.6016i	−0.469799	+	0.813715i	0.529605	+	0.848244i	$0.322340\pi$
$642$		−	23.1750i		−	0.914643i
$643$	−27.7501	−	16.0215i	−1.09436	−	0.631828i	−0.159625	−	0.987178i	$-0.551029\pi$
$643$	−27.7501	−	16.0215i	−1.09436	−	0.631828i	−0.934733	+	0.355350i	$0.884362\pi$
$644$	−30.4606	−	17.5864i	−1.20031	−	0.693002i
$645$			21.5271i			0.847630i
$646$	0.0128393	−	0.0222383i	0.000505155	−	0.000874955i
$647$	0.282650	+	0.489564i	0.0111121	+	0.0192468i	0.871528	−	0.490346i	$-0.163129\pi$
$647$	0.282650	+	0.489564i	0.0111121	+	0.0192468i	−0.860416	+	0.509593i	$0.829796\pi$
$648$	2.64358	−	1.52627i	0.103850	−	0.0599576i
$649$	−35.0499			−1.37583
$650$	0.211093	−	83.2106i	0.00827974	−	3.26379i
$651$	12.0954			0.474054
$652$	10.8979	−	6.29193i	0.426797	−	0.246411i
$653$	23.4408	+	40.6007i	0.917311	+	1.58883i	0.803482	+	0.595329i	$0.202978\pi$
$653$	23.4408	+	40.6007i	0.917311	+	1.58883i	0.113830	+	0.993500i	$0.463688\pi$
$654$	2.07793	−	3.59909i	0.0812537	−	0.140735i
$655$			33.3671i			1.30376i
$656$	34.5509	+	19.9480i	1.34899	+	0.778837i
$657$	7.95476	+	4.59268i	0.310345	+	0.179178i
$658$			15.2867i			0.595938i
$659$	−4.92895	+	8.53719i	−0.192005	+	0.332562i	−0.945914	−	0.324416i	$-0.894832\pi$
$659$	−4.92895	+	8.53719i	−0.192005	+	0.332562i	0.753910	+	0.656978i	$0.228166\pi$
$660$	−9.62420	−	16.6696i	−0.374621	−	0.648863i
$661$	−15.5819	+	8.99619i	−0.606064	+	0.349911i	−0.771424	−	0.636322i	$-0.780455\pi$
$661$	−15.5819	+	8.99619i	−0.606064	+	0.349911i	0.165359	+	0.986233i	$0.447122\pi$
$662$	9.63925			0.374640
$663$	−2.29718	+	3.95563i	−0.0892151	+	0.153624i
$664$	6.65652			0.258323
$665$	−0.209520	+	0.120966i	−0.00812482	+	0.00469087i
$666$	−1.85925	−	3.22031i	−0.0720443	−	0.124784i
$667$	−3.51372	+	6.08594i	−0.136052	+	0.235649i
$668$			13.6512i			0.528179i
$669$	16.2186	+	9.36383i	0.627048	+	0.362027i
$670$	−5.96484	−	3.44380i	−0.230442	−	0.133046i
$671$			14.8318i			0.572575i
$672$	18.0381	−	31.2429i	0.695834	−	1.20522i
$673$	−8.79373	−	15.2312i	−0.338973	−	0.587119i	0.645267	−	0.763957i	$-0.276746\pi$
$673$	−8.79373	−	15.2312i	−0.338973	−	0.587119i	−0.984240	+	0.176839i	$0.943413\pi$
$674$	−16.4789	+	9.51411i	−0.634744	+	0.366470i
$675$	−69.4021			−2.67129
$676$	−18.5999	−	0.0943709i	−0.715380	−	0.00362965i
$677$	11.6062			0.446062			0.223031	−	0.974811i	$-0.428405\pi$
$677$	11.6062			0.446062			0.223031	+	0.974811i	$0.428405\pi$
$678$	−41.3722	+	23.8862i	−1.58889	+	0.917346i
$679$	−34.4618	−	59.6895i	−1.32252	−	2.29067i
$680$	−2.20276	+	3.81529i	−0.0844720	+	0.146310i
$681$			0.739089i			0.0283220i
$682$	−9.29280	−	5.36520i	−0.355840	−	0.205444i
$683$	16.7233	+	9.65523i	0.639901	+	0.369447i	0.784576	−	0.620032i	$-0.212880\pi$
$683$	16.7233	+	9.65523i	0.639901	+	0.369447i	−0.144675	+	0.989479i	$0.546214\pi$
$684$		−	0.0275807i		−	0.00105458i
$685$	37.9972	−	65.8131i	1.45180	−	2.51459i
$686$	−13.3133	−	23.0594i	−0.508306	−	0.880412i
$687$	−4.28935	+	2.47646i	−0.163649	+	0.0944828i
$688$	19.5506			0.745360
$689$	−11.3283	+	19.5067i	−0.431573	+	0.743145i
$690$	−57.7967			−2.20028
$691$	−12.1454	+	7.01217i	−0.462034	+	0.266755i	−0.712899	−	0.701267i	$-0.752618\pi$
$691$	−12.1454	+	7.01217i	−0.462034	+	0.266755i	0.250865	+	0.968022i	$0.419285\pi$
$692$	−13.8469	−	23.9835i	−0.526378	−	0.911714i
$693$	−7.36850	+	12.7626i	−0.279906	+	0.484812i
$694$			37.7834i			1.43424i
$695$	9.29059	+	5.36392i	0.352412	+	0.203465i
$696$	−1.38299	−	0.798472i	−0.0524223	−	0.0302660i
$697$			8.28674i			0.313883i
$698$	28.6739	−	49.6647i	1.08532	−	1.87984i
$699$	−6.00904	−	10.4080i	−0.227283	−	0.393665i
$700$	−64.4784	+	37.2266i	−2.43705	+	1.40703i
$701$	6.47008			0.244372			0.122186	−	0.992507i	$-0.461010\pi$
$701$	6.47008			0.244372			0.122186	+	0.992507i	$0.461010\pi$
$702$	−0.0943675	+	37.1987i	−0.00356167	+	1.40397i
$703$	−0.0200164			−0.000754934
$704$	−6.55515	+	3.78462i	−0.247056	+	0.142638i
$705$	5.23792	+	9.07235i	0.197272	+	0.341684i
$706$	6.87781	−	11.9127i	0.258850	−	0.448341i
$707$			22.4018i			0.842506i
$708$	21.7115	+	12.5351i	0.815968	+	0.471099i
$709$	−11.7104	−	6.76101i	−0.439794	−	0.253915i	0.263716	−	0.964600i	$-0.415052\pi$
$709$	−11.7104	−	6.76101i	−0.439794	−	0.253915i	−0.703510	+	0.710685i	$0.748385\pi$
$710$		−	42.4281i		−	1.59230i
$711$	−3.81761	+	6.61229i	−0.143172	+	0.247980i
$712$	5.22869	+	9.05635i	0.195953	+	0.339401i
$713$	−11.6368	+	6.71853i	−0.435803	+	0.251611i
$714$	9.81401			0.367280
$715$	−38.2333	−	0.0969921i	−1.42984	−	0.00362730i
$716$	23.7937			0.889214
$717$	10.7673	−	6.21650i	0.402112	−	0.232159i
$718$	−27.7307	−	48.0309i	−1.03490	−	1.79250i
$719$	−21.6262	+	37.4577i	−0.806523	+	1.39694i	0.108736	+	0.994071i	$0.465320\pi$
$719$	−21.6262	+	37.4577i	−0.806523	+	1.39694i	−0.915258	+	0.402868i	$0.868014\pi$
$720$			27.9720i			1.04245i
$721$	−33.5577	−	19.3746i	−1.24975	−	0.721546i
$722$	30.4773	+	17.5961i	1.13425	+	0.654858i
$723$			14.9768i			0.556993i
$724$	6.12282	−	10.6050i	0.227553	−	0.394133i
$725$	7.43778	+	12.8826i	0.276232	+	0.478448i
$726$	9.27939	−	5.35746i	0.344390	−	0.198834i
$727$	−28.9856			−1.07502			−0.537508	−	0.843258i	$-0.680634\pi$
$727$	−28.9856			−1.07502			−0.537508	+	0.843258i	$0.680634\pi$
$728$	−7.90323	−	13.7693i	−0.292913	−	0.510326i
$729$	25.2256			0.934281
$730$	44.2777	−	25.5637i	1.63879	−	0.946156i
$731$	2.03042	+	3.51679i	0.0750977	+	0.130073i
$732$	5.30439	−	9.18748i	0.196056	−	0.339579i
$733$			15.4987i			0.572456i	0.958162	+	0.286228i	$0.0924015\pi$
$733$			15.4987i			0.572456i	−0.958162	+	0.286228i	$0.907599\pi$
$734$	28.8620	+	16.6635i	1.06532	+	0.615061i
$735$	−47.9390	−	27.6776i	−1.76826	−	1.02090i
$736$			40.0780i			1.47729i
$737$	−1.12921	+	1.95584i	−0.0415948	+	0.0720444i
$738$	10.6711	+	18.4829i	0.392808	+	0.680363i
$739$	14.2301	−	8.21577i	0.523464	−	0.302222i	−0.214887	−	0.976639i	$-0.568938\pi$
$739$	14.2301	−	8.21577i	0.523464	−	0.302222i	0.738351	+	0.674417i	$0.235605\pi$
$740$	−8.63186			−0.317313
$741$	0.0548391	+	0.0318471i	0.00201456	+	0.00116993i
$742$	48.3966			1.77669
$743$	−6.87161	+	3.96732i	−0.252095	+	0.145547i	−0.620723	−	0.784030i	$-0.713161\pi$
$743$	−6.87161	+	3.96732i	−0.252095	+	0.145547i	0.368628	+	0.929577i	$0.379828\pi$
$744$	−1.52675	−	2.64440i	−0.0559732	−	0.0969485i
$745$	25.6573	−	44.4398i	0.940013	−	1.62815i
$746$		−	25.7546i		−	0.942943i
$747$	7.60255	+	4.38933i	0.278163	+	0.160597i
$748$	−3.14452	−	1.81549i	−0.114975	−	0.0663809i
$749$			41.1880i			1.50498i
$750$	−36.6240	+	63.4346i	−1.33732	+	2.31630i
$751$	−5.30349	−	9.18591i	−0.193527	−	0.335198i	0.752890	−	0.658147i	$-0.228659\pi$
$751$	−5.30349	−	9.18591i	−0.193527	−	0.335198i	−0.946417	+	0.322948i	$0.895326\pi$
$752$	8.23936	−	4.75700i	0.300459	−	0.173470i
$753$	−17.8886			−0.651897
$754$	6.91503	−	3.96904i	0.251831	−	0.144544i
$755$	−65.7655			−2.39345
$756$	28.8246	−	16.6419i	1.04834	−	0.605260i
$757$	−17.7648	−	30.7695i	−0.645672	−	1.11834i	−0.984146	−	0.177361i	$-0.943244\pi$
$757$	−17.7648	−	30.7695i	−0.645672	−	1.11834i	0.338473	−	0.940976i	$-0.390089\pi$
$758$	−1.05889	+	1.83405i	−0.0384606	+	0.0666158i
$759$			18.9512i			0.687887i
$760$	0.0528936	+	0.0305381i	0.00191865	+	0.00110773i
$761$	−7.23231	−	4.17558i	−0.262171	−	0.151365i	0.363153	−	0.931729i	$-0.381700\pi$
$761$	−7.23231	−	4.17558i	−0.262171	−	0.151365i	−0.625325	+	0.780365i	$0.715033\pi$
$762$		−	30.8257i		−	1.11670i
$763$	−3.69304	+	6.39653i	−0.133697	+	0.231570i
$764$	−16.9394	−	29.3399i	−0.612846	−	1.06148i
$765$	−5.03164	+	2.90502i	−0.181919	+	0.105031i
$766$	19.3465			0.699017
$767$	43.1889	−	24.7893i	1.55946	−	0.895089i
$768$	−26.5857			−0.959331
$769$	41.9528	−	24.2215i	1.51286	−	0.873448i	0.512969	−	0.858407i	$-0.328545\pi$
$769$	41.9528	−	24.2215i	1.51286	−	0.873448i	0.999887	−	0.0150409i	$-0.00478784\pi$
$770$	41.0144	+	71.0391i	1.47806	+	2.56007i
$771$	15.2329	−	26.3842i	0.548599	−	0.950202i
$772$			5.07441i			0.182632i
$773$	−41.1885	−	23.7802i	−1.48145	−	0.855314i	−0.481669	−	0.876353i	$-0.659969\pi$
$773$	−41.1885	−	23.7802i	−1.48145	−	0.855314i	−0.999779	+	0.0210385i	$0.993303\pi$
$774$	9.05735	+	5.22926i	0.325560	+	0.187962i
$775$			28.4433i			1.02171i
$776$	−8.69993	+	15.0687i	−0.312309	+	0.540936i
$777$	−3.82500	−	6.62510i	−0.137221	−	0.237674i
$778$	−23.0230	+	13.2923i	−0.825413	+	0.476553i
$779$	0.114884			0.00411614
$780$	23.6487	+	13.7337i	0.846760	+	0.491745i
$781$	−13.9120			−0.497809
$782$	−9.44197	+	5.45133i	−0.337644	+	0.194939i
$783$	−3.32501	−	5.75908i	−0.118826	−	0.205813i
$784$	−25.1363	+	43.5374i	−0.897727	+	1.55491i
$785$		−	16.3036i		−	0.581900i
$786$	−16.2509	−	9.38244i	−0.579649	−	0.334661i
$787$	39.4634	+	22.7842i	1.40672	+	0.812170i	0.995070	−	0.0991725i	$-0.0316195\pi$
$787$	39.4634	+	22.7842i	1.40672	+	0.812170i	0.411649	+	0.911342i	$0.364953\pi$
$788$			35.3397i			1.25893i
$789$	16.9297	−	29.3230i	0.602712	−	1.04393i
$790$	21.2495	+	36.8052i	0.756024	+	1.30947i
$791$	73.5293	−	42.4522i	2.61440	−	1.50943i
$792$	3.72038			0.132198
$793$	−10.4899	−	18.2759i	−0.372506	−	0.648997i
$794$	31.4726			1.11692
$795$	28.7224	−	16.5829i	1.01868	−	0.588134i
$796$	−2.00071	−	3.46534i	−0.0709134	−	0.122826i
$797$	8.12627	−	14.0751i	0.287847	−	0.498566i	−0.685448	−	0.728121i	$-0.740394\pi$
$797$	8.12627	−	14.0751i	0.287847	−	0.498566i	0.973296	+	0.229555i	$0.0737272\pi$
$798$		−	0.136057i		−	0.00481637i
$799$	1.71139	+	0.988071i	0.0605446	+	0.0349554i
$800$	73.4705	+	42.4182i	2.59757	+	1.49971i
$801$			13.7913i			0.487290i
$802$	−36.4126	+	63.0685i	−1.28577	+	2.22702i
$803$	−8.38222	−	14.5184i	−0.295802	−	0.512344i
$804$	1.39896	−	0.807691i	0.0493376	−	0.0284851i
$805$	102.720			3.62040
$806$	15.2453	+	0.0386750i	0.536992	+	0.00136227i
$807$	11.5824			0.407720
$808$	4.89770	−	2.82769i	0.172300	−	0.0994776i
$809$	6.30089	+	10.9135i	0.221528	+	0.383697i	0.955272	−	0.295729i	$-0.0955624\pi$
$809$	6.30089	+	10.9135i	0.221528	+	0.383697i	−0.733744	+	0.679426i	$0.762229\pi$
$810$	11.2039	−	19.4058i	0.393666	−	0.681850i
$811$		−	19.5583i		−	0.686787i	−0.939192	−	0.343393i	$-0.888424\pi$
$811$		−	19.5583i		−	0.686787i	0.939192	−	0.343393i	$-0.111576\pi$
$812$	−6.17823	−	3.56700i	−0.216813	−	0.125177i
$813$	1.83748	+	1.06087i	0.0644431	+	0.0372062i
$814$			6.78671i			0.237874i
$815$	−18.3752	+	31.8267i	−0.643655	+	1.11484i
$816$	−3.05398	−	5.28964i	−0.106911	−	0.185175i
$817$	0.0487552	−	0.0281488i	0.00170573	−	0.000984803i
$818$	1.70857			0.0597389
$819$	0.0531157	−	20.9377i	0.00185601	−	0.731621i
$820$	49.5423			1.73009
$821$	−24.4514	+	14.1170i	−0.853359	+	0.492687i	−0.861783	−	0.507278i	$-0.830652\pi$
$821$	−24.4514	+	14.1170i	−0.853359	+	0.492687i	0.00842392	+	0.999965i	$0.497319\pi$
$822$	21.3687	+	37.0118i	0.745321	+	1.29093i
$823$	22.6965	−	39.3115i	0.791151	−	1.37031i	−0.134103	−	0.990967i	$-0.542815\pi$
$823$	22.6965	−	39.3115i	0.791151	−	1.37031i	0.925255	−	0.379347i	$-0.123851\pi$
$824$			9.78228i			0.340782i
$825$	34.7412	+	20.0578i	1.20953	+	0.698324i
$826$	−92.5256	−	53.4197i	−3.21938	−	1.85871i
$827$			6.36972i			0.221497i	0.993848	+	0.110748i	$0.0353248\pi$
$827$			6.36972i			0.221497i	−0.993848	+	0.110748i	$0.964675\pi$
$828$	−5.85513	+	10.1414i	−0.203480	+	0.352438i
$829$	−19.6758	−	34.0794i	−0.683368	−	1.18363i	−0.973947	−	0.226777i	$-0.927181\pi$
$829$	−19.6758	−	34.0794i	−0.683368	−	1.18363i	0.290579	−	0.956851i	$-0.406152\pi$
$830$	42.3172	−	24.4318i	1.46885	−	0.848041i
$831$	14.5336			0.504167
$832$	5.40064	−	9.29961i	0.187233	−	0.322406i
$833$	−10.4421			−0.361797
$834$	−5.22481	+	3.01655i	−0.180920	+	0.104454i
$835$	−19.9336	−	34.5261i	−0.689832	−	1.19482i
$836$	−0.0251691	+	0.0435942i	−0.000870493	+	0.00150774i
$837$		−	12.7154i		−	0.439508i
$838$	−55.5526	−	32.0733i	−1.91903	−	1.10795i
$839$	11.0210	+	6.36297i	0.380487	+	0.219674i	0.678030	−	0.735034i	$-0.262834\pi$
$839$	11.0210	+	6.36297i	0.380487	+	0.219674i	−0.297543	+	0.954708i	$0.596167\pi$
$840$			23.3425i			0.805393i
$841$	13.7873	−	23.8803i	0.475425	−	0.823460i
$842$	−19.8243	−	34.3367i	−0.683191	−	1.18332i
$843$	9.79687	−	5.65623i	0.337422	−	0.194811i
$844$	−3.81463			−0.131305
$845$	47.1801	−	26.9212i	1.62304	−	0.926117i
$846$	5.08948			0.174980
$847$	−16.4919	+	9.52162i	−0.566669	+	0.327167i
$848$	−15.0603	−	26.0852i	−0.517173	−	0.895770i
$849$	−9.31109	+	16.1273i	−0.319556	+	0.553487i
$850$			23.0785i			0.791587i
$851$	7.36001	+	4.24930i	0.252298	+	0.145664i
$852$	8.61769	+	4.97542i	0.295237	+	0.170455i
$853$			33.2736i			1.13927i	0.821899	+	0.569633i	$0.192914\pi$
$853$			33.2736i			1.13927i	−0.821899	+	0.569633i	$0.807086\pi$
$854$	−22.6052	+	39.1533i	−0.773534	+	1.33980i
$855$	0.0402739	+	0.0697564i	0.00137734	+	0.00238562i
$856$	9.00492	−	5.19899i	0.307782	−	0.177698i
$857$	25.1673			0.859698			0.429849	−	0.902901i	$-0.358567\pi$
$857$	25.1673			0.859698			0.429849	+	0.902901i	$0.358567\pi$
$858$	10.7980	−	18.5936i	0.368637	−	0.634774i
$859$	−32.5072			−1.10913			−0.554566	−	0.832140i	$-0.687116\pi$
$859$	−32.5072			−1.10913			−0.554566	+	0.832140i	$0.687116\pi$
$860$	21.0251	−	12.1389i	0.716951	−	0.413932i
$861$	21.9535	+	38.0246i	0.748173	+	1.29587i
$862$	12.7276	−	22.0448i	0.433504	−	0.750850i
$863$		−	2.99739i		−	0.102032i	−0.998698	−	0.0510162i	$-0.983754\pi$
$863$		−	2.99739i		−	0.102032i	0.998698	−	0.0510162i	$-0.0162460\pi$
$864$	−32.8444	−	18.9627i	−1.11739	−	0.645126i
$865$	70.0421	+	40.4388i	2.38150	+	1.37496i
$866$		−	25.6707i		−	0.872327i
$867$	0.634338	−	1.09871i	0.0215433	−	0.0373140i
$868$	−6.82040	−	11.8133i	−0.231500	−	0.400969i
$869$	12.0683	−	6.96761i	0.409388	−	0.236360i
$870$	−11.7227			−0.397438
$871$	0.00813986	−	3.20865i	0.000275809	−	0.108721i
$872$	1.86463			0.0631443
$873$	−19.8727	+	11.4735i	−0.672590	+	0.388320i
$874$	0.0755748	+	0.130899i	0.00255636	+	0.00442774i
$875$	65.0905	−	112.740i	2.20046	−	3.81131i
$876$			11.9912i			0.405144i
$877$	−39.6583	−	22.8967i	−1.33916	−	0.773167i	−0.352481	−	0.935819i	$-0.614662\pi$
$877$	−39.6583	−	22.8967i	−1.33916	−	0.773167i	−0.986683	+	0.162652i	$0.947995\pi$
$878$	−19.2910	−	11.1377i	−0.651039	−	0.375878i
$879$		−	22.0507i		−	0.743752i
$880$	25.5262	−	44.2127i	0.860488	−	1.49041i
$881$	−1.78238	−	3.08718i	−0.0600500	−	0.104010i	0.834438	−	0.551103i	$-0.185793\pi$
$881$	−1.78238	−	3.08718i	−0.0600500	−	0.104010i	−0.894488	+	0.447093i	$0.852459\pi$
$882$	−23.2902	+	13.4466i	−0.784221	+	0.452770i
$883$	33.8940			1.14062			0.570312	−	0.821428i	$-0.306822\pi$
$883$	33.8940			1.14062			0.570312	+	0.821428i	$0.306822\pi$
$884$	5.15873	+	0.0130869i	0.173507	+	0.000440161i
$885$	−73.2161			−2.46113
$886$	−23.9443	+	13.8242i	−0.804423	+	0.464434i
$887$	0.328781	+	0.569466i	0.0110394	+	0.0191208i	0.871492	−	0.490409i	$-0.163153\pi$
$887$	0.328781	+	0.569466i	0.0110394	+	0.0191208i	−0.860453	+	0.509530i	$0.829819\pi$
$888$	−0.965629	+	1.67252i	−0.0324044	+	0.0561260i
$889$			54.7854i			1.83744i
$890$	66.4802	+	38.3823i	2.22842	+	1.28658i
$891$	−6.36306	−	3.67372i	−0.213171	−	0.123074i
$892$		−	21.1205i		−	0.707168i
$893$	0.0136982	−	0.0237260i	0.000458392	−	0.000793959i
$894$	14.4291	+	24.9919i	0.482581	+	0.835855i
$895$	−60.1784	+	34.7440i	−2.01154	+	1.16137i
$896$	33.7996			1.12916
$897$	−13.4034	−	23.3520i	−0.447526	−	0.779699i
$898$	−26.5544			−0.886132
$899$	−2.36026	+	1.36270i	−0.0787192	+	0.0454486i
$900$	12.3940	+	21.4671i	0.413135	+	0.715570i
$901$	3.12816	−	5.41813i	0.104214	−	0.180504i
$902$		−	38.9521i		−	1.29696i
$903$	18.6336	+	10.7581i	0.620087	+	0.358007i
$904$	−18.5626	−	10.7171i	−0.617383	−	0.356446i
$905$			35.7626i			1.18879i
$906$	18.4925	−	32.0299i	0.614372	−	1.06412i
$907$	19.4929	+	33.7627i	0.647252	+	1.12107i	0.983777	+	0.179398i	$0.0574151\pi$
$907$	19.4929	+	33.7627i	0.647252	+	1.12107i	−0.336525	+	0.941675i	$0.609252\pi$
$908$	0.721854	−	0.416762i	0.0239556	−	0.0138307i
$909$	7.45834			0.247378
$910$	−100.781	−	58.5275i	−3.34087	−	1.94017i
$911$	40.1276			1.32949			0.664743	−	0.747072i	$-0.268541\pi$
$911$	40.1276			1.32949			0.664743	+	0.747072i	$0.268541\pi$
$912$	−0.0733333	+	0.0423390i	−0.00242831	+	0.00140198i
$913$	−8.01108	−	13.8756i	−0.265128	−	0.459215i
$914$	4.24287	−	7.34886i	0.140342	−	0.243079i
$915$			30.9823i			1.02424i
$916$	4.83742	+	2.79288i	0.159833	+	0.0922795i
$917$	28.8821	+	16.6751i	0.953770	+	0.550659i
$918$		−	10.3171i		−	0.340515i
$919$	9.61009	−	16.6452i	0.317008	−	0.549073i	−0.662855	−	0.748748i	$-0.730655\pi$
$919$	9.61009	−	16.6452i	0.317008	−	0.549073i	0.979862	+	0.199675i	$0.0639886\pi$
$920$	−12.9659	−	22.4576i	−0.427474	−	0.740406i
$921$	31.5690	−	18.2264i	1.04023	−	0.600580i
$922$	−46.1722			−1.52060
$923$	17.1425	−	9.83931i	0.564251	−	0.323865i
$924$	−19.2386			−0.632904
$925$	15.5795	−	8.99485i	0.512252	−	0.295749i
$926$	5.74818	+	9.95613i	0.188897	+	0.327179i
$927$	−6.45047	+	11.1725i	−0.211861	+	0.366954i
$928$			8.12890i			0.266844i
$929$	25.6944	+	14.8347i	0.843006	+	0.486710i	0.858285	−	0.513173i	$-0.171530\pi$
$929$	25.6944	+	14.8347i	0.843006	+	0.486710i	−0.0152787	+	0.999883i	$0.504864\pi$
$930$	−19.4118	−	11.2074i	−0.636539	−	0.367506i
$931$			0.144765i			0.00474447i
$932$	−6.77683	+	11.7378i	−0.221982	+	0.384485i
$933$	−1.96439	−	3.40243i	−0.0643114	−	0.111391i
$934$	2.22887	−	1.28684i	0.0729307	−	0.0421066i
$935$	10.6040			0.346789
$936$	−4.58430	+	2.63126i	−0.149842	+	0.0860055i
$937$	22.1392			0.723255			0.361627	−	0.932323i	$-0.382221\pi$
$937$	22.1392			0.723255			0.361627	+	0.932323i	$0.382221\pi$
$938$	−5.96181	+	3.44205i	−0.194660	+	0.112387i
$939$	−3.51215	−	6.08323i	−0.114615	−	0.198519i
$940$	5.90718	−	10.2315i	0.192671	−	0.333716i
$941$		−	58.7706i		−	1.91587i	−0.286989	−	0.957934i	$-0.592654\pi$
$941$		−	58.7706i		−	1.91587i	0.286989	−	0.957934i	$-0.407346\pi$
$942$	7.94038	+	4.58438i	0.258711	+	0.149367i
$943$	−42.2425	−	24.3887i	−1.37561	−	0.794207i
$944$			66.4937i			2.16419i
$945$	−48.6015	+	84.1803i	−1.58101	+	2.73839i
$946$	−9.54406	−	16.5308i	−0.310304	−	0.537463i
$947$	−18.2875	+	10.5583i	−0.594264	+	0.343098i	−0.766782	−	0.641908i	$-0.778143\pi$
$947$	−18.2875	+	10.5583i	−0.594264	+	0.343098i	0.172518	+	0.985006i	$0.444810\pi$
$948$	−9.96750			−0.323729
$949$	20.5969	+	11.9614i	0.668604	+	0.388284i
$950$	0.319951			0.0103806
$951$	−10.6658	+	6.15792i	−0.345863	+	0.199684i
$952$	2.20164	+	3.81336i	0.0713556	+	0.123592i
$953$	−11.3396	+	19.6407i	−0.367324	+	0.636224i	−0.989146	−	0.146934i	$-0.953059\pi$
$953$	−11.3396	+	19.6407i	−0.367324	+	0.636224i	0.621822	+	0.783159i	$0.286393\pi$
$954$		−	16.1129i		−	0.521675i
$955$	85.6853	+	49.4704i	2.77271	+	1.60083i
$956$	−12.1431	−	7.01080i	−0.392735	−	0.226745i
$957$			3.84382i			0.124253i
$958$	13.1997	−	22.8625i	0.426462	−	0.738654i
$959$	−37.9779	−	65.7797i	−1.22637	−	2.12414i
$960$	−13.6931	+	7.90572i	−0.441943	+	0.255156i
$961$	25.7888			0.831897
$962$	−4.79994	−	8.36267i	−0.154756	−	0.269623i
$963$	13.7129			0.441893
$964$	14.6275	−	8.44521i	0.471121	−	0.272002i
$965$	−7.40974	−	12.8340i	−0.238528	−	0.413142i
$966$	−28.8837	+	50.0280i	−0.929316	+	1.60962i
$967$		−	53.9101i		−	1.73363i	−0.498628	−	0.866816i	$-0.666163\pi$
$967$		−	53.9101i		−	1.73363i	0.498628	−	0.866816i	$-0.333837\pi$
$968$	4.16341	+	2.40375i	0.133817	+	0.0772594i
$969$	−0.0152320	−	0.00879419i	−0.000489322	−	0.000282510i
$970$			127.728i			4.10109i
$971$	−17.4100	+	30.1551i	−0.558715	+	0.967722i	0.438889	+	0.898541i	$0.355372\pi$
$971$	−17.4100	+	30.1551i	−0.558715	+	0.967722i	−0.997604	+	0.0691812i	$0.977961\pi$
$972$	−9.32660	−	16.1541i	−0.299151	−	0.518144i
$973$	9.28587	−	5.36120i	0.297691	−	0.171872i
$974$	−23.6637			−0.758232
$975$	−56.9945	−	0.144587i	−1.82529	−	0.00463048i
$976$	28.1376			0.900663
$977$	−47.6503	+	27.5109i	−1.52447	+	0.880151i	−0.524887	+	0.851172i	$0.675892\pi$
$977$	−47.6503	+	27.5109i	−1.52447	+	0.880151i	−0.999580	+	0.0289796i	$0.990774\pi$
$978$	−10.3338	−	17.8986i	−0.330438	−	0.572335i
$979$	12.5854	−	21.7985i	0.402230	−	0.696684i
$980$			62.4280i			1.99419i
$981$	2.12963	+	1.22954i	0.0679938	+	0.0392562i
$982$	34.5245	+	19.9327i	1.10172	+	0.636079i
$983$		−	58.1472i		−	1.85461i	−0.374308	−	0.927304i	$-0.622120\pi$
$983$		−	58.1472i		−	1.85461i	0.374308	−	0.927304i	$-0.377880\pi$
$984$	5.54220	−	9.59937i	0.176679	−	0.306017i
$985$	−51.6037	−	89.3802i	−1.64423	−	2.84789i
$986$	−1.91509	+	1.10568i	−0.0609888	+	0.0352119i
$987$	10.4705			0.333280
$988$	0.000181431	−	0.0715184i	5.77210e−6	−	0.00227530i
$989$	−23.9029			−0.760069
$990$	23.6514	−	13.6551i	0.751691	−	0.433989i
$991$	−16.3160	−	28.2602i	−0.518295	−	0.897714i	−0.999774	−	0.0212561i	$-0.993233\pi$
$991$	−16.3160	−	28.2602i	−0.518295	−	0.897714i	0.481479	−	0.876458i	$-0.340100\pi$
$992$	−7.77157	+	13.4608i	−0.246748	+	0.427379i
$993$		−	6.60234i		−	0.209519i
$994$	−36.7251	−	21.2033i	−1.16485	−	0.672526i
$995$	10.1203	+	5.84295i	0.320835	+	0.185234i
$996$			11.4602i			0.363131i
$997$	31.1040	−	53.8737i	0.985073	−	1.70620i	0.343462	−	0.939167i	$-0.388400\pi$
$997$	31.1040	−	53.8737i	0.985073	−	1.70620i	0.641611	−	0.767030i	$-0.278266\pi$
$998$	11.8149	+	20.4640i	0.373994	+	0.647777i
$999$	−6.96472	+	4.02108i	−0.220354	+	0.127221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	221.2.m.c.205.3	yes	22
13.2	odd	12		2873.2.a.x.1.6		22
13.4	even	6	inner	221.2.m.c.69.3	✓	22
13.11	odd	12		2873.2.a.x.1.17		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
221.2.m.c.69.3	✓	22	13.4	even	6	inner
221.2.m.c.205.3	yes	22	1.1	even	1	trivial
2873.2.a.x.1.6		22	13.2	odd	12
2873.2.a.x.1.17		22	13.11	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 221 = 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	221.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60408 + 0.926118i) q^{2} +(0.634338 + 1.09871i) q^{3} +(0.715389 - 1.23909i) q^{4} +4.17850i q^{5} +(-2.03506 - 1.17494i) q^{6} +(3.61684 + 2.08819i) q^{7} -1.05433i q^{8} +(0.695230 - 1.20417i) q^{9} +(-3.86978 - 6.70266i) q^{10} +(-2.19777 + 1.26888i) q^{11} +1.81520 q^{12} +(1.81069 - 3.11792i) q^{13} -7.73563 q^{14} +(-4.59094 + 2.65058i) q^{15} +(2.40721 + 4.16942i) q^{16} +(-0.500000 + 0.866025i) q^{17} +2.57546i q^{18} +(0.0120062 + 0.00693178i) q^{19} +(5.17753 + 2.98925i) q^{20} +5.29846i q^{21} +(2.35027 - 4.07079i) q^{22} +(-2.94311 - 5.09761i) q^{23} +(1.15840 - 0.668803i) q^{24} -12.4598 q^{25} +(-0.0169419 + 6.67831i) q^{26} +5.57007 q^{27} +(5.17490 - 2.98773i) q^{28} +(-0.596941 - 1.03393i) q^{29} +(4.90950 - 8.50350i) q^{30} -2.28280i q^{31} +(-5.89659 - 3.40440i) q^{32} +(-2.78826 - 1.60980i) q^{33} -1.85224i q^{34} +(-8.72548 + 15.1130i) q^{35} +(-0.994720 - 1.72291i) q^{36} +(-1.25038 + 0.721908i) q^{37} -0.0256786 q^{38} +(4.57426 + 0.0116042i) q^{39} +4.40552 q^{40} +(7.17652 - 4.14337i) q^{41} +(-4.90700 - 8.49918i) q^{42} +(2.03042 - 3.51679i) q^{43} +3.63098i q^{44} +(5.03164 + 2.90502i) q^{45} +(9.44197 + 5.45133i) q^{46} -1.97614i q^{47} +(-3.05398 + 5.28964i) q^{48} +(5.22104 + 9.04311i) q^{49} +(19.9866 - 11.5393i) q^{50} -1.26868 q^{51} +(-2.56803 - 4.47413i) q^{52} -6.25632 q^{53} +(-8.93486 + 5.15855i) q^{54} +(-5.30202 - 9.18336i) q^{55} +(2.20164 - 3.81336i) q^{56} +0.0175884i q^{57} +(1.91509 + 1.10568i) q^{58} +(11.9610 + 6.90567i) q^{59} +7.58478i q^{60} +(2.92222 - 5.06143i) q^{61} +(2.11415 + 3.66181i) q^{62} +(5.02908 - 2.90354i) q^{63} +2.98264 q^{64} +(13.0282 + 7.56596i) q^{65} +5.96346 q^{66} +(0.770695 - 0.444961i) q^{67} +(0.715389 + 1.23909i) q^{68} +(3.73385 - 6.46721i) q^{69} -32.3233i q^{70} +(4.74753 + 2.74099i) q^{71} +(-1.26960 - 0.733004i) q^{72} +6.60599i q^{73} +(1.33714 - 2.31600i) q^{74} +(-7.90374 - 13.6897i) q^{75} +(0.0171782 - 0.00991784i) q^{76} -10.5986 q^{77} +(-7.34825 + 4.21769i) q^{78} -5.49114 q^{79} +(-17.4219 + 10.0585i) q^{80} +(1.44762 + 2.50735i) q^{81} +(-7.67450 + 13.2926i) q^{82} +6.31349i q^{83} +(6.56528 + 3.79047i) q^{84} +(-3.61868 - 2.08925i) q^{85} +7.52163i q^{86} +(0.757325 - 1.31173i) q^{87} +(1.33782 + 2.31718i) q^{88} +(-8.58966 + 4.95924i) q^{89} -10.7616 q^{90} +(13.0598 - 7.49596i) q^{91} -8.42186 q^{92} +(2.50813 - 1.44807i) q^{93} +(1.83014 + 3.16990i) q^{94} +(-0.0289644 + 0.0501678i) q^{95} -8.63816i q^{96} +(-14.2922 - 8.25160i) q^{97} +(-16.7500 - 9.67060i) q^{98} +3.52866i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{3} + 14 q^{4} - 9 q^{6} - 3 q^{7} - 14 q^{9} + q^{10} + 6 q^{11} - 18 q^{12} + q^{13} - 12 q^{14} + 3 q^{15} - 24 q^{16} - 11 q^{17} + 3 q^{19} + 12 q^{20} - 11 q^{22} + 3 q^{23} + 57 q^{24}+ \cdots + 18 q^{98}+O(q^{100}) \) 22 * q - 3 * q^3 + 14 * q^4 - 9 * q^6 - 3 * q^7 - 14 * q^9 + q^10 + 6 * q^11 - 18 * q^12 + q^13 - 12 * q^14 + 3 * q^15 - 24 * q^16 - 11 * q^17 + 3 * q^19 + 12 * q^20 - 11 * q^22 + 3 * q^23 + 57 * q^24 - 48 * q^25 - 33 * q^26 + 6 * q^27 - 6 * q^28 - 15 * q^29 + 34 * q^30 + 33 * q^32 + 36 * q^33 - 6 * q^35 - 3 * q^36 + 12 * q^37 - 44 * q^38 - 17 * q^39 - 18 * q^40 - 9 * q^41 - 48 * q^42 + 42 * q^43 + 3 * q^45 + 48 * q^46 - 16 * q^48 + 22 * q^49 + 102 * q^50 + 6 * q^51 - 9 * q^52 - 16 * q^53 + 45 * q^54 - 38 * q^55 + 44 * q^56 - 93 * q^58 + 45 * q^59 + q^61 - 18 * q^62 + 27 * q^63 - 26 * q^64 + 18 * q^65 - 76 * q^66 - 21 * q^67 + 14 * q^68 - 9 * q^69 + 6 * q^71 + 57 * q^72 + 4 * q^74 + 27 * q^75 + 99 * q^76 - 22 * q^77 - 41 * q^78 + 52 * q^79 + 63 * q^80 - 75 * q^81 + 14 * q^82 - 126 * q^84 - 3 * q^85 - 31 * q^87 + 53 * q^88 - 3 * q^89 - 4 * q^90 + 11 * q^91 - 92 * q^92 + 66 * q^93 - 17 * q^94 + 9 * q^95 - 60 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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