LMFDB - Embedded newform 58.3.f.a.39.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [58,3,Mod(3,58)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("58.3"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	58.f (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] 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:	$1.58038553329$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			39.2
Character	$\chi$	$=$	58.39
Dual form			58.3.f.a.3.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19745 + 0.752407i) q^{2} +(3.88561 + 1.35964i) q^{3} +(0.867767 - 1.80194i) q^{4} +(0.590885 + 0.134866i) q^{5} +(-5.67582 + 1.29547i) q^{6} +(0.570217 - 0.274602i) q^{7} +(0.316683 + 2.81064i) q^{8} +(6.21291 + 4.95463i) q^{9} +(-0.809028 + 0.283091i) q^{10} +(-1.17390 + 10.4186i) q^{11} +(5.82179 - 5.82179i) q^{12} +(4.14659 - 3.30680i) q^{13} +(-0.476193 + 0.757857i) q^{14} +(2.11258 + 1.32742i) q^{15} +(-2.49396 - 3.12733i) q^{16} +(-17.9446 - 17.9446i) q^{17} +(-11.1675 - 1.25828i) q^{18} +(-9.71346 - 27.7595i) q^{19} +(0.755770 - 0.947706i) q^{20} +(2.58900 - 0.291711i) q^{21} +(-6.43336 - 13.3590i) q^{22} +(3.53861 + 15.5037i) q^{23} +(-2.59094 + 11.3516i) q^{24} +(-22.1933 - 10.6877i) q^{25} +(-2.47727 + 7.07964i) q^{26} +(-2.30711 - 3.67175i) q^{27} -1.26579i q^{28} +(14.0029 + 25.3953i) q^{29} -3.52847 q^{30} +(37.2787 - 23.4237i) q^{31} +(5.33941 + 1.86834i) q^{32} +(-18.7268 + 38.8867i) q^{33} +(34.9895 + 7.98612i) q^{34} +(0.373967 - 0.0853555i) q^{35} +(14.3193 - 6.89581i) q^{36} +(3.11221 + 27.6217i) q^{37} +(32.5178 + 25.9321i) q^{38} +(20.6081 - 7.21108i) q^{39} +(-0.191936 + 1.70348i) q^{40} +(-11.3284 + 11.3284i) q^{41} +(-2.88071 + 2.29729i) q^{42} +(7.60867 - 12.1091i) q^{43} +(17.7550 + 11.1562i) q^{44} +(3.00290 + 3.76552i) q^{45} +(-15.9024 - 15.9024i) q^{46} +(-49.6702 - 5.59649i) q^{47} +(-5.43854 - 15.5425i) q^{48} +(-30.3013 + 37.9966i) q^{49} +(34.6168 - 3.90038i) q^{50} +(-45.3278 - 94.1241i) q^{51} +(-2.36036 - 10.3414i) q^{52} +(-17.7861 + 77.9259i) q^{53} +(5.52530 + 2.66085i) q^{54} +(-2.09875 + 5.99789i) q^{55} +(0.952387 + 1.51571i) q^{56} -121.069i q^{57} +(-35.8753 - 19.8737i) q^{58} +96.3972 q^{59} +(4.22517 - 2.65485i) q^{60} +(-29.9934 - 10.4951i) q^{61} +(-27.0151 + 56.0975i) q^{62} +(4.90326 + 1.11914i) q^{63} +(-7.79942 + 1.78017i) q^{64} +(2.89613 - 1.39470i) q^{65} +(-6.83418 - 60.6550i) q^{66} +(69.1612 + 55.1543i) q^{67} +(-47.9069 + 16.7633i) q^{68} +(-7.32965 + 65.0524i) q^{69} +(-0.383584 + 0.383584i) q^{70} +(48.7878 - 38.9069i) q^{71} +(-11.9582 + 19.0313i) q^{72} +(68.8428 + 43.2568i) q^{73} +(-24.5094 - 30.7339i) q^{74} +(-71.7031 - 71.7031i) q^{75} +(-58.4498 - 6.58572i) q^{76} +(2.19160 + 6.26323i) q^{77} +(-19.2515 + 24.1406i) q^{78} +(-26.4998 + 2.98581i) q^{79} +(-1.05187 - 2.18424i) q^{80} +(-19.8869 - 87.1302i) q^{81} +(5.04160 - 22.0887i) q^{82} +(-29.2488 - 14.0855i) q^{83} +(1.72101 - 4.91836i) q^{84} +(-8.18310 - 13.0233i) q^{85} +20.2249i q^{86} +(19.8814 + 117.715i) q^{87} -29.6548 q^{88} +(-95.4740 + 59.9903i) q^{89} +(-6.42903 - 2.24962i) q^{90} +(1.45640 - 3.02425i) q^{91} +(31.0073 + 7.07721i) q^{92} +(176.698 - 40.3302i) q^{93} +(63.6883 - 30.6707i) q^{94} +(-1.99574 - 17.7127i) q^{95} +(18.2066 + 14.5193i) q^{96} +(9.22461 - 3.22783i) q^{97} +(7.69532 - 68.2978i) q^{98} +(-58.9137 + 58.9137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 4 q^{3} + 28 q^{5} + 34 q^{7} + 8 q^{8} + 4 q^{10} - 44 q^{11} + 8 q^{12} - 36 q^{14} - 90 q^{15} + 16 q^{16} + 32 q^{17} - 16 q^{18} - 56 q^{19} + 36 q^{20} - 168 q^{21} - 84 q^{22} + 68 q^{23}+ \cdots + 132 q^{99}+O(q^{100}) $ 24 * q - 4 * q^2 - 4 * q^3 + 28 * q^5 + 34 * q^7 + 8 * q^8 + 4 * q^10 - 44 * q^11 + 8 * q^12 - 36 * q^14 - 90 * q^15 + 16 * q^16 + 32 * q^17 - 16 * q^18 - 56 * q^19 + 36 * q^20 - 168 * q^21 - 84 * q^22 + 68 * q^23 - 40 * q^24 - 84 * q^25 - 96 * q^26 - 28 * q^27 + 144 * q^29 - 40 * q^30 + 106 * q^31 + 16 * q^32 + 98 * q^33 + 84 * q^34 + 196 * q^35 + 80 * q^36 - 262 * q^37 + 280 * q^38 + 458 * q^39 + 8 * q^40 + 116 * q^41 + 308 * q^42 - 212 * q^43 - 24 * q^44 + 14 * q^45 - 16 * q^46 - 238 * q^47 + 16 * q^48 + 188 * q^49 - 196 * q^50 - 462 * q^51 + 32 * q^52 - 126 * q^53 - 56 * q^54 - 96 * q^55 + 72 * q^56 - 24 * q^58 - 48 * q^59 - 180 * q^60 + 268 * q^61 - 56 * q^62 + 28 * q^63 + 376 * q^65 - 108 * q^66 + 490 * q^67 - 64 * q^68 - 328 * q^69 - 72 * q^70 - 14 * q^71 - 88 * q^72 - 552 * q^73 - 188 * q^74 - 356 * q^75 - 420 * q^76 - 186 * q^77 - 316 * q^78 - 358 * q^79 - 20 * q^81 + 288 * q^82 - 448 * q^83 - 140 * q^84 - 420 * q^85 + 606 * q^87 - 48 * q^88 + 314 * q^89 + 308 * q^90 - 182 * q^91 + 112 * q^92 + 1428 * q^93 + 336 * q^94 + 510 * q^95 + 424 * q^97 + 244 * q^98 + 132 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/58\mathbb{Z}\right)^\times$.

$n$	$31$
$\chi(n)$	$e\left(\frac{23}{28}\right)$

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 $

$2$	−1.19745	+	0.752407i	−0.598724	+	0.376203i
$2$	−1.19745	+	0.752407i	−0.598724	+	0.376203i
$3$	3.88561	+	1.35964i	1.29520	+	0.453212i	0.887881	−	0.460072i	$-0.152176\pi$
$3$	3.88561	+	1.35964i	1.29520	+	0.453212i	0.407323	+	0.913284i	$0.366462\pi$
$4$	0.867767	−	1.80194i	0.216942	−	0.450484i
$5$	0.590885	+	0.134866i	0.118177	+	0.0269731i	0.281200	−	0.959649i	$-0.409267\pi$
$5$	0.590885	+	0.134866i	0.118177	+	0.0269731i	−0.163023	+	0.986622i	$0.552125\pi$
$6$	−5.67582	+	1.29547i	−0.945971	+	0.215912i
$7$	0.570217	−	0.274602i	0.0814596	−	0.0392289i	−0.392710	−	0.919662i	$-0.628463\pi$
$7$	0.570217	−	0.274602i	0.0814596	−	0.0392289i	0.474170	+	0.880433i	$0.342748\pi$
$8$	0.316683	+	2.81064i	0.0395854	+	0.351330i
$9$	6.21291	+	4.95463i	0.690323	+	0.550514i
$10$	−0.809028	+	0.283091i	−0.0809028	+	0.0283091i
$11$	−1.17390	+	10.4186i	−0.106718	+	0.947148i	0.820250	+	0.572006i	$0.193835\pi$
$11$	−1.17390	+	10.4186i	−0.106718	+	0.947148i	−0.926967	+	0.375142i	$0.877594\pi$
$12$	5.82179	−	5.82179i	0.485149	−	0.485149i
$13$	4.14659	−	3.30680i	0.318969	−	0.254369i	−0.450896	−	0.892577i	$-0.648895\pi$
$13$	4.14659	−	3.30680i	0.318969	−	0.254369i	0.769864	+	0.638208i	$0.220324\pi$
$14$	−0.476193	+	0.757857i	−0.0340138	+	0.0541327i
$15$	2.11258	+	1.32742i	0.140839	+	0.0884949i
$16$	−2.49396	−	3.12733i	−0.155872	−	0.195458i
$17$	−17.9446	−	17.9446i	−1.05557	−	1.05557i	−0.998362	−	0.0572046i	$-0.981781\pi$
$17$	−17.9446	−	17.9446i	−1.05557	−	1.05557i	−0.0572046	−	0.998362i	$-0.518219\pi$
$18$	−11.1675	−	1.25828i	−0.620419	−	0.0699044i
$19$	−9.71346	−	27.7595i	−0.511235	−	1.46102i	−0.853336	−	0.521361i	$-0.825424\pi$
$19$	−9.71346	−	27.7595i	−0.511235	−	1.46102i	0.342102	−	0.939663i	$-0.388861\pi$
$20$	0.755770	−	0.947706i	0.0377885	−	0.0473853i
$21$	2.58900	−	0.291711i	0.123286	−	0.0138910i
$22$	−6.43336	−	13.3590i	−0.292426	−	0.607228i
$23$	3.53861	+	15.5037i	0.153852	+	0.674072i	0.991744	+	0.128235i	$0.0409311\pi$
$23$	3.53861	+	15.5037i	0.153852	+	0.674072i	−0.837891	+	0.545837i	$0.816212\pi$
$24$	−2.59094	+	11.3516i	−0.107956	+	0.472985i
$25$	−22.1933	−	10.6877i	−0.887731	−	0.427509i
$26$	−2.47727	+	7.07964i	−0.0952798	+	0.272294i
$27$	−2.30711	−	3.67175i	−0.0854487	−	0.135991i
$28$		−	1.26579i		−	0.0452067i
$29$	14.0029	+	25.3953i	0.482857	+	0.875699i
$29$	14.0029	+	25.3953i	0.482857	+	0.875699i
$30$	−3.52847			−0.117616
$31$	37.2787	−	23.4237i	1.20254	−	0.755605i	0.226671	−	0.973971i	$-0.427216\pi$
$31$	37.2787	−	23.4237i	1.20254	−	0.755605i	0.975867	+	0.218367i	$0.0700729\pi$
$32$	5.33941	+	1.86834i	0.166857	+	0.0583856i
$33$	−18.7268	+	38.8867i	−0.567480	+	1.17838i
$34$	34.9895	+	7.98612i	1.02910	+	0.234886i
$35$	0.373967	−	0.0853555i	0.0106848	−	0.00243873i
$36$	14.3193	−	6.89581i	0.397758	−	0.191550i
$37$	3.11221	+	27.6217i	0.0841139	+	0.746531i	0.963000	+	0.269500i	$0.0868585\pi$
$37$	3.11221	+	27.6217i	0.0841139	+	0.746531i	−0.878886	+	0.477031i	$0.841713\pi$
$38$	32.5178	+	25.9321i	0.855731	+	0.682423i
$39$	20.6081	−	7.21108i	0.528413	−	0.184900i
$40$	−0.191936	+	1.70348i	−0.00479839	+	0.0425869i
$41$	−11.3284	+	11.3284i	−0.276302	+	0.276302i	−0.831631	−	0.555329i	$-0.812592\pi$
$41$	−11.3284	+	11.3284i	−0.276302	+	0.276302i	0.555329	+	0.831631i	$0.312592\pi$
$42$	−2.88071	+	2.29729i	−0.0685884	+	0.0546974i
$43$	7.60867	−	12.1091i	0.176946	−	0.281608i	−0.746462	−	0.665428i	$-0.768249\pi$
$43$	7.60867	−	12.1091i	0.176946	−	0.281608i	0.923408	+	0.383820i	$0.125392\pi$
$44$	17.7550	+	11.1562i	0.403524	+	0.253551i
$45$	3.00290	+	3.76552i	0.0667312	+	0.0836783i
$46$	−15.9024	−	15.9024i	−0.345703	−	0.345703i
$47$	−49.6702	−	5.59649i	−1.05681	−	0.119074i	−0.433583	−	0.901113i	$-0.642751\pi$
$47$	−49.6702	−	5.59649i	−1.05681	−	0.119074i	−0.623229	+	0.782039i	$0.714180\pi$
$48$	−5.43854	−	15.5425i	−0.113303	−	0.323801i
$49$	−30.3013	+	37.9966i	−0.618393	+	0.775440i
$50$	34.6168	−	3.90038i	0.692336	−	0.0780076i
$51$	−45.3278	−	94.1241i	−0.888780	−	1.84557i
$52$	−2.36036	−	10.3414i	−0.0453916	−	0.198874i
$53$	−17.7861	+	77.9259i	−0.335587	+	1.47030i	0.472549	+	0.881304i	$0.343334\pi$
$53$	−17.7861	+	77.9259i	−0.335587	+	1.47030i	−0.808136	+	0.588996i	$0.799523\pi$
$54$	5.52530	+	2.66085i	0.102320	+	0.0492749i
$55$	−2.09875	+	5.99789i	−0.0381591	+	0.109053i
$56$	0.952387	+	1.51571i	0.0170069	+	0.0270663i
$57$		−	121.069i		−	2.12402i
$58$	−35.8753	−	19.8737i	−0.618540	−	0.342650i
$59$	96.3972			1.63385			0.816925	−	0.576744i	$-0.195677\pi$
$59$	96.3972			1.63385			0.816925	+	0.576744i	$0.195677\pi$
$60$	4.22517	−	2.65485i	0.0704194	−	0.0442475i
$61$	−29.9934	−	10.4951i	−0.491695	−	0.172051i	0.0730317	−	0.997330i	$-0.476733\pi$
$61$	−29.9934	−	10.4951i	−0.491695	−	0.172051i	−0.564726	+	0.825278i	$0.691018\pi$
$62$	−27.0151	+	56.0975i	−0.435728	+	0.904798i
$63$	4.90326	+	1.11914i	0.0778295	+	0.0177641i
$64$	−7.79942	+	1.78017i	−0.121866	+	0.0278151i
$65$	2.89613	−	1.39470i	0.0445559	−	0.0214570i
$66$	−6.83418	−	60.6550i	−0.103548	−	0.919016i
$67$	69.1612	+	55.1543i	1.03226	+	0.823198i	0.984451	−	0.175659i	$-0.0562056\pi$
$67$	69.1612	+	55.1543i	1.03226	+	0.823198i	0.0478063	+	0.998857i	$0.484777\pi$
$68$	−47.9069	+	16.7633i	−0.704513	+	0.246520i
$69$	−7.32965	+	65.0524i	−0.106227	+	0.942789i
$70$	−0.383584	+	0.383584i	−0.00547978	+	0.00547978i
$71$	48.7878	−	38.9069i	0.687152	−	0.547985i	−0.216485	−	0.976286i	$-0.569459\pi$
$71$	48.7878	−	38.9069i	0.687152	−	0.547985i	0.903636	+	0.428301i	$0.140888\pi$
$72$	−11.9582	+	19.0313i	−0.166086	+	0.264324i
$73$	68.8428	+	43.2568i	0.943052	+	0.592559i	0.913427	−	0.407002i	$-0.133426\pi$
$73$	68.8428	+	43.2568i	0.943052	+	0.592559i	0.0296248	+	0.999561i	$0.490569\pi$
$74$	−24.5094	−	30.7339i	−0.331209	−	0.415323i
$75$	−71.7031	−	71.7031i	−0.956041	−	0.956041i
$76$	−58.4498	−	6.58572i	−0.769077	−	0.0866542i
$77$	2.19160	+	6.26323i	0.0284623	+	0.0813407i
$78$	−19.2515	+	24.1406i	−0.246814	+	0.309495i
$79$	−26.4998	+	2.98581i	−0.335440	+	0.0377951i	−0.278078	−	0.960558i	$-0.589698\pi$
$79$	−26.4998	+	2.98581i	−0.335440	+	0.0377951i	−0.0573621	+	0.998353i	$0.518269\pi$
$80$	−1.05187	−	2.18424i	−0.0131484	−	0.0273030i
$81$	−19.8869	−	87.1302i	−0.245517	−	1.07568i
$82$	5.04160	−	22.0887i	0.0614829	−	0.269374i
$83$	−29.2488	−	14.0855i	−0.352395	−	0.169704i	0.249308	−	0.968424i	$-0.419797\pi$
$83$	−29.2488	−	14.0855i	−0.352395	−	0.169704i	−0.601703	+	0.798720i	$0.705511\pi$
$84$	1.72101	−	4.91836i	0.0204882	−	0.0585519i
$85$	−8.18310	−	13.0233i	−0.0962718	−	0.153216i
$86$			20.2249i			0.235173i
$87$	19.8814	+	117.715i	0.228522	+	1.35305i
$88$	−29.6548			−0.336986
$89$	−95.4740	+	59.9903i	−1.07274	+	0.674048i	−0.948042	−	0.318146i	$-0.896940\pi$
$89$	−95.4740	+	59.9903i	−1.07274	+	0.674048i	−0.124700	+	0.992194i	$0.539797\pi$
$90$	−6.42903	−	2.24962i	−0.0714337	−	0.0249957i
$91$	1.45640	−	3.02425i	0.0160044	−	0.0332336i
$92$	31.0073	+	7.07721i	0.337036	+	0.0769262i
$93$	176.698	−	40.3302i	1.89998	−	0.433658i
$94$	63.6883	−	30.6707i	0.677536	−	0.326284i
$95$	−1.99574	−	17.7127i	−0.0210078	−	0.186449i
$96$	18.2066	+	14.5193i	0.189652	+	0.151243i
$97$	9.22461	−	3.22783i	0.0950990	−	0.0332766i	−0.282310	−	0.959323i	$-0.591101\pi$
$97$	9.22461	−	3.22783i	0.0950990	−	0.0332766i	0.377409	+	0.926047i	$0.376815\pi$
$98$	7.69532	−	68.2978i	0.0785237	−	0.696917i
$99$	−58.9137	+	58.9137i	−0.595088	+	0.595088i
$100$	−38.5172	+	30.7164i	−0.385172	+	0.307164i
$101$	61.0316	−	97.1312i	0.604273	−	0.961695i	−0.394805	−	0.918765i	$-0.629188\pi$
$101$	61.0316	−	97.1312i	0.604273	−	0.961695i	0.999078	−	0.0429303i	$-0.0136693\pi$
$102$	125.097	+	78.6039i	1.22644	+	0.770626i
$103$	80.1755	+	100.537i	0.778403	+	0.976087i	1.00000		0.000948181i	$0.000301815\pi$
$103$	80.1755	+	100.537i	0.778403	+	0.976087i	−0.221596	+	0.975138i	$0.571127\pi$
$104$	10.6074	+	10.6074i	0.101994	+	0.101994i
$105$	1.56914	+	0.176800i	0.0149442	+	0.00168381i
$106$	−37.3341	−	106.695i	−0.352208	−	1.00655i
$107$	−1.31273	+	1.64612i	−0.0122685	+	0.0153843i	−0.787928	−	0.615767i	$-0.788846\pi$
$107$	−1.31273	+	1.64612i	−0.0122685	+	0.0153843i	0.775659	+	0.631152i	$0.217417\pi$
$108$	−8.61830	+	0.971050i	−0.0797991	+	0.00899120i
$109$	−8.47574	−	17.6001i	−0.0777591	−	0.161468i	0.858465	−	0.512872i	$-0.171419\pi$
$109$	−8.47574	−	17.6001i	−0.0777591	−	0.161468i	−0.936224	+	0.351404i	$0.885704\pi$
$110$	−1.99971	−	8.76128i	−0.0181791	−	0.0796480i
$111$	−25.4625	+	111.559i	−0.229392	+	1.00503i
$112$	−2.28087	−	1.09841i	−0.0203649	−	0.00980722i
$113$	13.7498	−	39.2946i	0.121680	−	0.347740i	−0.866891	−	0.498497i	$-0.833885\pi$
$113$	13.7498	−	39.2946i	0.121680	−	0.347740i	0.988571	+	0.150757i	$0.0481711\pi$
$114$	91.0934	+	144.974i	0.799065	+	1.27170i
$115$			9.63811i			0.0838097i
$116$	57.9119	−	3.19510i	0.499241	−	0.0275439i
$117$	42.1463			0.360225
$118$	−115.431	+	72.5299i	−0.978226	+	0.614660i
$119$	−15.1600	−	5.30471i	−0.127395	−	0.0445774i
$120$	−3.06189	+	6.35809i	−0.0255158	+	0.0529841i
$121$	10.7966	+	2.46425i	0.0892278	+	0.0203657i
$122$	43.8121	−	9.99984i	0.359116	−	0.0819659i
$123$	−59.4202	+	28.6152i	−0.483091	+	0.232644i
$124$	−9.85891	−	87.5002i	−0.0795073	−	0.705647i
$125$	−23.5186	−	18.7554i	−0.188149	−	0.150044i
$126$	−6.71345	+	2.34914i	−0.0532813	+	0.0186439i
$127$	−15.5206	+	137.749i	−0.122209	+	1.08464i	0.771575	+	0.636138i	$0.219469\pi$
$127$	−15.5206	+	137.749i	−0.122209	+	1.08464i	−0.893784	+	0.448497i	$0.851959\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	46.0284	−	36.7064i	0.356809	−	0.284546i
$130$	−2.41858	+	3.84916i	−0.0186045	+	0.0296089i
$131$	−160.486	−	100.840i	−1.22509	−	0.769773i	−0.245228	−	0.969466i	$-0.578863\pi$
$131$	−160.486	−	100.840i	−1.22509	−	0.769773i	−0.979859	+	0.199693i	$0.936006\pi$
$132$	53.8208	+	67.4892i	0.407734	+	0.511282i
$133$	−13.1616	−	13.1616i	−0.0989593	−	0.0989593i
$134$	−124.315	−	14.0070i	−0.927728	−	0.104530i
$135$	−0.868046	−	2.48073i	−0.00642997	−	0.0183758i
$136$	44.7532	−	56.1187i	0.329068	−	0.412638i
$137$	−16.9537	+	1.91022i	−0.123749	+	0.0139432i	−0.173622	−	0.984812i	$-0.555547\pi$
$137$	−16.9537	+	1.91022i	−0.123749	+	0.0139432i	0.0498725	+	0.998756i	$0.484118\pi$
$138$	−40.1690	−	83.4118i	−0.291080	−	0.604434i
$139$	−41.1605	−	180.336i	−0.296119	−	1.29738i	−0.875854	−	0.482576i	$-0.839701\pi$
$139$	−41.1605	−	180.336i	−0.296119	−	1.29738i	0.579736	−	0.814805i	$-0.303156\pi$
$140$	0.170711	−	0.747934i	0.00121936	−	0.00534239i
$141$	−185.390	−	89.2791i	−1.31482	−	0.633185i
$142$	−29.1470	+	83.2973i	−0.205261	+	0.586601i
$143$	29.5846	+	47.0836i	0.206885	+	0.329256i
$144$		−	31.7864i		−	0.220739i
$145$	4.84913	+	16.8942i	0.0334423	+	0.116512i
$146$	−114.982			−0.787551
$147$	−169.401	+	106.441i	−1.15238	+	0.724091i
$148$	52.4732	+	18.3612i	0.354549	+	0.124062i
$149$	113.376	−	235.427i	0.760910	−	1.58005i	−0.0526839	−	0.998611i	$-0.516778\pi$
$149$	113.376	−	235.427i	0.760910	−	1.58005i	0.813594	−	0.581434i	$-0.197508\pi$
$150$	139.811	+	31.9109i	0.932071	+	0.212739i
$151$	266.261	−	60.7723i	1.76332	−	0.402466i	0.786680	−	0.617361i	$-0.211798\pi$
$151$	266.261	−	60.7723i	1.76332	−	0.402466i	0.976637	+	0.214896i	$0.0689411\pi$
$152$	74.9458	−	36.0920i	0.493065	−	0.237447i
$153$	−22.5794	−	200.397i	−0.147578	−	1.30979i
$154$	−7.33683	−	5.85093i	−0.0476417	−	0.0379930i
$155$	25.1865	−	8.81313i	0.162493	−	0.0568589i
$156$	4.88911	−	43.3920i	0.0313404	−	0.278154i
$157$	−114.963	+	114.963i	−0.732247	+	0.732247i	−0.971065	−	0.238817i	$-0.923240\pi$
$157$	−114.963	+	114.963i	−0.732247	+	0.732247i	0.238817	+	0.971065i	$0.423240\pi$
$158$	29.4856	−	23.5140i	0.186618	−	0.148823i
$159$	−175.061	+	278.608i	−1.10101	+	1.75225i
$160$	2.90300	+	1.82408i	0.0181438	+	0.0114005i
$161$	6.27511	+	7.86874i	0.0389758	+	0.0488741i
$162$	89.3709	+	89.3709i	0.551672	+	0.551672i
$163$	−110.207	−	12.4173i	−0.676115	−	0.0761799i	−0.232771	−	0.972532i	$-0.574779\pi$
$163$	−110.207	−	12.4173i	−0.676115	−	0.0761799i	−0.443344	+	0.896352i	$0.646208\pi$
$164$	10.5826	+	30.2434i	0.0645282	+	0.184411i
$165$	−16.3099	+	20.4520i	−0.0988478	+	0.123951i
$166$	45.6219	−	5.14036i	0.274831	−	0.0309660i
$167$	−42.9913	−	89.2723i	−0.257433	−	0.534564i	0.731694	−	0.681634i	$-0.238730\pi$
$167$	−42.9913	−	89.2723i	−0.257433	−	0.534564i	−0.989126	+	0.147069i	$0.953016\pi$
$168$	1.63979	+	7.18438i	0.00976064	+	0.0427642i
$169$	−31.3467	+	137.339i	−0.185484	+	0.812657i
$170$	19.5977	+	9.43775i	0.115281	+	0.0555162i
$171$	77.1890	−	220.594i	0.451398	−	1.29002i
$172$	−15.2173	−	24.2183i	−0.0884729	−	0.140804i
$173$			56.9956i			0.329454i	0.986339	+	0.164727i	$0.0526744\pi$
$173$			56.9956i			0.329454i	−0.986339	+	0.164727i	$0.947326\pi$
$174$	−112.377	−	125.999i	−0.645842	−	0.724131i
$175$	−15.5898			−0.0890848
$176$	35.5101	−	22.3125i	0.201762	−	0.126775i
$177$	374.562	+	131.065i	2.11617	+	0.740480i
$178$	69.1881	−	143.671i	0.388697	−	0.807138i
$179$	−81.6499	−	18.6360i	−0.456145	−	0.104112i	−0.0117259	−	0.999931i	$-0.503733\pi$
$179$	−81.6499	−	18.6360i	−0.456145	−	0.104112i	−0.444419	+	0.895819i	$0.646590\pi$
$180$	9.39106	−	2.14345i	0.0521726	−	0.0119080i
$181$	−210.518	+	101.380i	−1.16308	+	0.560110i	−0.912938	−	0.408099i	$-0.866192\pi$
$181$	−210.518	+	101.380i	−1.16308	+	0.560110i	−0.250143	+	0.968209i	$0.580478\pi$
$182$	0.531501	+	4.71720i	0.00292033	+	0.0259187i
$183$	−102.273	−	81.5601i	−0.558870	−	0.445684i
$184$	−42.4546	+	14.8555i	−0.230732	+	0.0807365i
$185$	−1.88625	+	16.7410i	−0.0101960	+	0.0904916i
$186$	−181.242	+	181.242i	−0.974422	+	0.974422i
$187$	208.024	−	165.893i	1.11243	−	0.887130i
$188$	−53.1867	+	84.6461i	−0.282908	+	0.450245i
$189$	−2.32383	−	1.46016i	−0.0122954	−	0.00772570i
$190$	15.7169	+	19.7084i	0.0827206	+	0.103728i
$191$	75.3943	+	75.3943i	0.394735	+	0.394735i	0.876371	−	0.481636i	$-0.159957\pi$
$191$	75.3943	+	75.3943i	0.394735	+	0.394735i	−0.481636	+	0.876371i	$0.659957\pi$
$192$	−32.7259	−	3.68733i	−0.170448	−	0.0192048i
$193$	48.4523	+	138.469i	0.251048	+	0.717455i	0.998582	+	0.0532312i	$0.0169520\pi$
$193$	48.4523	+	138.469i	0.251048	+	0.717455i	−0.747534	+	0.664224i	$0.768762\pi$
$194$	−8.61735	+	10.8058i	−0.0444193	+	0.0557001i
$195$	13.1495	−	1.48160i	0.0674335	−	0.00759793i
$196$	42.1730	+	87.5732i	0.215168	+	0.446802i
$197$	−11.9316	−	52.2756i	−0.0605663	−	0.265358i	0.935574	−	0.353130i	$-0.114883\pi$
$197$	−11.9316	−	52.2756i	−0.0605663	−	0.265358i	−0.996141	+	0.0877715i	$0.972025\pi$
$198$	26.2191	−	114.873i	0.132420	−	0.580168i
$199$	271.898	+	130.939i	1.36632	+	0.657985i	0.966036	−	0.258407i	$-0.0831975\pi$
$199$	271.898	+	130.939i	1.36632	+	0.657985i	0.400283	+	0.916392i	$0.368912\pi$
$200$	23.0111	−	65.7620i	0.115056	−	0.328810i
$201$	193.744	+	308.342i	0.963902	+	1.53404i
$202$			162.230i			0.803120i
$203$	14.9583	+	10.6356i	0.0736860	+	0.0523921i
$204$	−208.940			−1.02421
$205$	−8.22158	+	5.16596i	−0.0401052	+	0.0251998i
$206$	−171.651	−	60.0632i	−0.833256	−	0.291569i
$207$	−54.8298	+	113.855i	−0.264878	+	0.550025i
$208$	−20.6829	−	4.72073i	−0.0994368	−	0.0226958i
$209$	300.618	−	68.6141i	1.43836	−	0.328297i
$210$	−2.01200	+	0.968926i	−0.00958093	+	0.00461393i
$211$	5.75069	+	51.0388i	0.0272544	+	0.241890i	0.999952	+	0.00981283i	$0.00312357\pi$
$211$	5.75069	+	51.0388i	0.0272544	+	0.241890i	−0.972697	+	0.232077i	$0.925448\pi$
$212$	124.983	+	99.6710i	0.589545	+	0.470146i
$213$	242.470	−	84.8438i	1.13836	−	0.398328i
$214$	0.333382	−	2.95885i	0.00155786	−	0.0138264i
$215$	6.12896	−	6.12896i	0.0285068	−	0.0285068i
$216$	9.58935	−	7.64725i	0.0443952	−	0.0354040i
$217$	14.8247	−	23.5934i	0.0683167	−	0.108725i
$218$	23.3917	+	14.6980i	0.107301	+	0.0674218i
$219$	208.683	+	261.680i	0.952891	+	1.19489i
$220$	8.98660	+	8.98660i	0.0408482	+	0.0408482i
$221$	−133.748	−	15.0698i	−0.605196	−	0.0681892i
$222$	−53.4474	−	152.744i	−0.240754	−	0.688036i
$223$	89.6584	−	112.428i	0.402055	−	0.504162i	−0.539050	−	0.842273i	$-0.681217\pi$
$223$	89.6584	−	112.428i	0.402055	−	0.504162i	0.941106	+	0.338112i	$0.109788\pi$
$224$	3.55767	−	0.400853i	0.0158825	−	0.00178952i
$225$	−84.9311	−	176.361i	−0.377471	−	0.783828i
$226$	13.1009	+	57.3988i	0.0579686	+	0.253977i
$227$	−36.2066	+	158.631i	−0.159500	+	0.698817i	0.830414	+	0.557147i	$0.188104\pi$
$227$	−36.2066	+	158.631i	−0.159500	+	0.698817i	−0.989914	+	0.141669i	$0.954753\pi$
$228$	−218.159	−	105.060i	−0.956839	−	0.460790i
$229$	109.296	−	312.349i	0.477273	−	1.36397i	−0.413907	−	0.910319i	$-0.635836\pi$
$229$	109.296	−	312.349i	0.477273	−	1.36397i	0.891180	−	0.453649i	$-0.149878\pi$
$230$	−7.25178	−	11.5411i	−0.0315295	−	0.0501789i
$231$			27.3163i			0.118252i
$232$	−66.9426	+	47.3993i	−0.288546	+	0.204307i
$233$	−350.697			−1.50514			−0.752569	−	0.658514i	$-0.771185\pi$
$233$	−350.697			−1.50514			−0.752569	+	0.658514i	$0.771185\pi$
$234$	−50.4681	+	31.7112i	−0.215676	+	0.135518i
$235$	−28.5946	−	10.0057i	−0.121679	−	0.0425774i
$236$	83.6503	−	173.702i	0.354451	−	0.736024i
$237$	−107.028	−	24.4284i	−0.451593	−	0.103073i
$238$	22.1446	−	5.05436i	0.0930445	−	0.0212368i
$239$	−76.0526	+	36.6250i	−0.318212	+	0.153243i	−0.586171	−	0.810188i	$-0.699365\pi$
$239$	−76.0526	+	36.6250i	−0.318212	+	0.153243i	0.267959	+	0.963430i	$0.413651\pi$
$240$	−1.11741	−	9.91728i	−0.00465587	−	0.0413220i
$241$	−204.018	−	162.699i	−0.846546	−	0.675098i	0.100941	−	0.994892i	$-0.467815\pi$
$241$	−204.018	−	162.699i	−0.846546	−	0.675098i	−0.947487	+	0.319794i	$0.896386\pi$
$242$	−14.7824	+	5.17260i	−0.0610845	+	0.0213744i
$243$	36.8227	−	326.811i	0.151534	−	1.34490i
$244$	−44.9389	+	44.9389i	−0.184176	+	0.184176i
$245$	−23.0290	+	18.3650i	−0.0939959	+	0.0749592i
$246$	49.6223	−	78.9734i	0.201717	−	0.321030i
$247$	−132.073	−	82.9867i	−0.534707	−	0.335979i
$248$	77.6413	+	97.3591i	0.313070	+	0.392577i
$249$	−94.4984	−	94.4984i	−0.379511	−	0.379511i
$250$	42.2740	+	4.76314i	0.169096	+	0.0190526i
$251$	−99.2323	−	283.590i	−0.395348	−	1.12984i	−0.953836	−	0.300327i	$-0.902904\pi$
$251$	−99.2323	−	283.590i	−0.395348	−	1.12984i	0.558488	−	0.829512i	$-0.311382\pi$
$252$	6.27150	−	7.86422i	0.0248869	−	0.0312072i
$253$	−165.681	+	18.6677i	−0.654864	+	0.0737855i
$254$	−85.0581	−	176.625i	−0.334874	−	0.695373i
$255$	−14.0894	−	61.7297i	−0.0552525	−	0.242077i
$256$	−3.56033	+	15.5988i	−0.0139076	+	0.0609330i
$257$	266.252	+	128.220i	1.03600	+	0.498912i	0.873003	−	0.487714i	$-0.162169\pi$
$257$	266.252	+	128.220i	1.03600	+	0.498912i	0.162998	+	0.986626i	$0.447884\pi$
$258$	−27.4985	+	78.5861i	−0.106583	+	0.304597i
$259$	9.35960	+	14.8957i	0.0361375	+	0.0575124i
$260$		−	6.42893i		−	0.0247266i
$261$	−38.8257	+	227.158i	−0.148757	+	0.870335i
$262$	268.047			1.02308
$263$	−206.939	+	130.028i	−0.786840	+	0.494404i	−0.864535	−	0.502573i	$-0.832387\pi$
$263$	−206.939	+	130.028i	−0.786840	+	0.494404i	0.0776947	+	0.996977i	$0.475244\pi$
$264$	−115.227	−	40.3197i	−0.436466	−	0.152726i
$265$	−21.0191	+	43.6465i	−0.0793172	+	0.164704i
$266$	25.6632	+	5.85746i	0.0964782	+	0.0220205i
$267$	−452.540	+	103.289i	−1.69491	+	0.386851i
$268$	159.400	−	76.7632i	0.594778	−	0.286430i
$269$	4.46857	+	39.6596i	0.0166118	+	0.147434i	0.999280	−	0.0379392i	$-0.0120793\pi$
$269$	4.46857	+	39.6596i	0.0166118	+	0.147434i	−0.982668	+	0.185373i	$0.940651\pi$
$270$	2.90596	+	2.31743i	0.0107628	+	0.00858306i
$271$	−270.375	+	94.6084i	−0.997695	+	0.349109i	−0.779231	−	0.626736i	$-0.784390\pi$
$271$	−270.375	+	94.6084i	−0.997695	+	0.349109i	−0.218464	+	0.975845i	$0.570105\pi$
$272$	−11.3655	+	100.872i	−0.0417851	+	0.370853i
$273$	9.77091	−	9.77091i	0.0357909	−	0.0357909i
$274$	18.8639	−	15.0434i	0.0688463	−	0.0549031i
$275$	137.404	−	218.677i	0.499651	−	0.795189i
$276$	110.860	+	69.6580i	0.401667	+	0.252384i
$277$	−200.401	−	251.295i	−0.723471	−	0.907204i	0.275058	−	0.961428i	$-0.411303\pi$
$277$	−200.401	−	251.295i	−0.723471	−	0.907204i	−0.998529	+	0.0542241i	$0.982731\pi$
$278$	184.974	+	184.974i	0.665372	+	0.665372i
$279$	347.665	+	39.1724i	1.24611	+	0.140403i
$280$	0.358333	+	1.02406i	0.00127976	+	0.00365735i
$281$	−103.685	+	130.017i	−0.368985	+	0.462692i	−0.931312	−	0.364223i	$-0.881335\pi$
$281$	−103.685	+	130.017i	−0.368985	+	0.462692i	0.562327	+	0.826915i	$0.309906\pi$
$282$	289.169	−	32.5816i	1.02542	−	0.115537i
$283$	106.044	+	220.203i	0.374715	+	0.778104i	0.999997	−	0.00229456i	$-0.000730381\pi$
$283$	106.044	+	220.203i	0.374715	+	0.778104i	−0.625282	+	0.780399i	$0.715016\pi$
$284$	−27.7715	−	121.675i	−0.0977868	−	0.428432i
$285$	16.3281	−	71.5380i	0.0572915	−	0.251011i
$286$	−70.8521	−	34.1206i	−0.247735	−	0.119303i
$287$	−3.34884	+	9.57043i	−0.0116684	+	0.0333464i
$288$	23.9163	+	38.0626i	0.0830428	+	0.132162i
$289$			355.020i			1.22844i
$290$	−18.5179	−	16.5814i	−0.0638548	−	0.0571773i
$291$	40.2319			0.138254
$292$	137.686	−	86.5136i	0.471526	−	0.296279i
$293$	274.103	+	95.9127i	0.935504	+	0.327347i	0.754624	−	0.656158i	$-0.227820\pi$
$293$	274.103	+	95.9127i	0.935504	+	0.327347i	0.180881	+	0.983505i	$0.442105\pi$
$294$	122.761	−	254.916i	0.417555	−	0.867062i
$295$	56.9596	+	13.0007i	0.193083	+	0.0440700i
$296$	−76.6490	+	17.4946i	−0.258949	+	0.0591035i
$297$	40.9629	−	19.7267i	0.137922	−	0.0664199i
$298$	41.3753	+	367.216i	0.138843	+	1.23227i
$299$	65.9406	+	52.5859i	0.220537	+	0.175872i
$300$	−191.426	+	66.9829i	−0.638087	+	0.223276i
$301$	1.01340	−	8.99419i	0.00336678	−	0.0298810i
$302$	−273.108	+	273.108i	−0.904332	+	0.904332i
$303$	369.208	−	294.434i	1.21851	−	0.971729i
$304$	−62.5879	+	99.6081i	−0.205881	+	0.327658i
$305$	−16.3072	−	10.2465i	−0.0534662	−	0.0335951i
$306$	177.818	+	222.977i	0.581105	+	0.728682i
$307$	−228.861	−	228.861i	−0.745475	−	0.745475i	0.228151	−	0.973626i	$-0.426732\pi$
$307$	−228.861	−	228.861i	−0.745475	−	0.745475i	−0.973626	+	0.228151i	$0.926732\pi$
$308$	13.1878	+	1.48590i	0.0428174	+	0.00482436i
$309$	174.838	+	499.657i	0.565818	+	1.61701i
$310$	−23.5284	+	29.5037i	−0.0758982	+	0.0951734i
$311$	551.927	−	62.1872i	1.77468	−	0.199959i	0.836942	−	0.547291i	$-0.184341\pi$
$311$	551.927	−	62.1872i	1.77468	−	0.199959i	0.937742	+	0.347333i	$0.112912\pi$
$312$	26.7940	+	55.6384i	0.0858783	+	0.178328i
$313$	−74.4604	−	326.232i	−0.237893	−	1.04228i	−0.942900	−	0.333075i	$-0.891914\pi$
$313$	−74.4604	−	326.232i	−0.237893	−	1.04228i	0.705008	−	0.709200i	$-0.250944\pi$
$314$	51.1633	−	224.161i	0.162940	−	0.713888i
$315$	2.74633	+	1.32256i	0.00871850	+	0.00419861i
$316$	−17.6154	+	50.3420i	−0.0557450	+	0.159310i
$317$	−323.887	−	515.463i	−1.02173	−	1.62607i	−0.747334	−	0.664449i	$-0.768666\pi$
$317$	−323.887	−	515.463i	−1.02173	−	1.62607i	−0.274392	−	0.961618i	$-0.588476\pi$
$318$		−	465.335i		−	1.46332i
$319$	−281.022	+	116.079i	−0.880946	+	0.363884i
$320$	−4.84864			−0.0151520
$321$	−7.33889	+	4.61133i	−0.0228626	+	0.0143655i
$322$	−13.4346	−	4.70098i	−0.0417224	−	0.0145993i
$323$	−323.829	+	672.438i	−1.00257	+	2.08185i
$324$	−174.260	−	39.7738i	−0.537841	−	0.122759i
$325$	−127.368	+	29.0710i	−0.391903	+	0.0894493i
$326$	141.310	−	68.0512i	0.433466	−	0.208746i
$327$	−9.00380	−	79.9109i	−0.0275346	−	0.244376i
$328$	−35.4275	−	28.2525i	−0.108011	−	0.0861357i
$329$	−29.8596	+	10.4483i	−0.0907586	+	0.0317578i
$330$	4.14206	−	36.7618i	0.0125517	−	0.111400i
$331$	449.162	−	449.162i	1.35698	−	1.35698i	0.479371	−	0.877612i	$-0.340865\pi$
$331$	449.162	−	449.162i	1.35698	−	1.35698i	0.877612	−	0.479371i	$-0.159135\pi$
$332$	−50.7623	+	40.4816i	−0.152898	+	0.121932i
$333$	−117.519	+	187.031i	−0.352911	+	0.561654i
$334$	118.649	+	74.5521i	0.355236	+	0.223210i
$335$	33.4279	+	41.9173i	0.0997848	+	0.125126i
$336$	−7.36914	−	7.36914i	−0.0219320	−	0.0219320i
$337$	−529.655	−	59.6778i	−1.57168	−	0.177085i	−0.717309	−	0.696755i	$-0.754627\pi$
$337$	−529.655	−	59.6778i	−1.57168	−	0.177085i	−0.854367	+	0.519669i	$0.826055\pi$
$338$	−65.7987	−	188.042i	−0.194671	−	0.556337i
$339$	106.853	−	133.989i	0.315200	−	0.395248i
$340$	−30.5683	+	3.44422i	−0.0899067	+	0.0101300i
$341$	200.282	+	415.890i	0.587337	+	1.21962i
$342$	73.5462	+	322.227i	0.215047	+	0.942184i
$343$	−13.7451	+	60.2213i	−0.0400732	+	0.175572i
$344$	36.4440	+	17.5505i	0.105942	+	0.0510189i
$345$	−13.1043	+	37.4500i	−0.0379835	+	0.108551i
$346$	−42.8839	−	68.2493i	−0.123942	−	0.197252i
$347$		−	264.538i		−	0.762358i	−0.924501	−	0.381179i	$-0.875518\pi$
$347$		−	264.538i		−	0.762358i	0.924501	−	0.381179i	$-0.124482\pi$
$348$	229.368	+	66.3242i	0.659102	+	0.190587i
$349$	516.984			1.48133			0.740664	−	0.671875i	$-0.234511\pi$
$349$	516.984			1.48133			0.740664	+	0.671875i	$0.234511\pi$
$350$	18.6680	−	11.7299i	0.0533373	−	0.0335140i
$351$	−21.7084	−	7.59609i	−0.0618473	−	0.0216413i
$352$	−25.7335	+	53.4361i	−0.0731064	+	0.151807i
$353$	537.052	+	122.579i	1.52139	+	0.347248i	0.899874	−	0.436151i	$-0.143659\pi$
$353$	537.052	+	122.579i	1.52139	+	0.347248i	0.621519	+	0.783399i	$0.286516\pi$
$354$	−547.133	+	124.880i	−1.54557	+	0.352767i
$355$	34.0752	−	16.4097i	0.0959864	−	0.0462246i
$356$	25.2495	+	224.096i	0.0709257	+	0.629483i
$357$	−51.6934	−	41.2241i	−0.144799	−	0.115474i
$358$	111.793	−	39.1182i	0.312272	−	0.109269i
$359$	−15.3889	+	136.581i	−0.0428661	+	0.380447i	0.953902	+	0.300117i	$0.0970259\pi$
$359$	−15.3889	+	136.581i	−0.0428661	+	0.380447i	−0.996768	+	0.0803297i	$0.974403\pi$
$360$	−9.63257	+	9.63257i	−0.0267571	+	0.0267571i
$361$	−393.995	+	314.201i	−1.09140	+	0.870362i
$362$	175.805	−	279.792i	0.485650	−	0.772907i
$363$	38.6008	+	24.2545i	0.106338	+	0.0668168i
$364$	−4.18570	−	5.24870i	−0.0114992	−	0.0144195i
$365$	34.8443	+	34.8443i	0.0954639	+	0.0954639i
$366$	183.833	+	20.7130i	0.502277	+	0.0565930i
$367$	−94.2784	−	269.432i	−0.256889	−	0.734148i	−0.998027	−	0.0627941i	$-0.979999\pi$
$367$	−94.2784	−	269.432i	−0.256889	−	0.734148i	0.741137	−	0.671354i	$-0.234287\pi$
$368$	39.6598	−	49.7319i	0.107771	−	0.135141i
$369$	−126.510	+	14.2543i	−0.342846	+	0.0386294i
$370$	−10.3373	−	21.4657i	−0.0279387	−	0.0580153i
$371$	11.2567	+	49.3188i	0.0303415	+	0.132935i
$372$	80.6605	−	353.397i	0.216829	−	0.949991i
$373$	−53.5103	−	25.7692i	−0.143459	−	0.0690863i	0.360777	−	0.932652i	$-0.382512\pi$
$373$	−53.5103	−	25.7692i	−0.143459	−	0.0690863i	−0.504236	+	0.863566i	$0.668226\pi$
$374$	−124.278	+	355.167i	−0.332295	+	0.949645i
$375$	−65.8836	−	104.853i	−0.175690	−	0.279608i
$376$		−	141.377i		−	0.376004i
$377$	142.041	+	58.9992i	0.376767	+	0.156497i
$378$	3.88129			0.0102680
$379$	484.836	−	304.643i	1.27925	−	0.803807i	0.291012	−	0.956719i	$-0.406008\pi$
$379$	484.836	−	304.643i	1.27925	−	0.803807i	0.988240	+	0.152913i	$0.0488653\pi$
$380$	−33.6489	−	11.7743i	−0.0885498	−	0.0309849i
$381$	−247.595	+	514.136i	−0.649856	+	1.34944i
$382$	−147.008	−	33.5536i	−0.384838	−	0.0878367i
$383$	−318.548	+	72.7065i	−0.831718	+	0.189834i	−0.617121	−	0.786868i	$-0.711701\pi$
$383$	−318.548	+	72.7065i	−0.831718	+	0.189834i	−0.214597	+	0.976703i	$0.568844\pi$
$384$	41.9620	−	20.2078i	0.109276	−	0.0526246i
$385$	0.450289	+	3.99642i	0.00116958	+	0.0103803i
$386$	−162.204	−	129.353i	−0.420218	−	0.335112i
$387$	107.268	−	37.5348i	0.277179	−	0.0969891i
$388$	2.18847	−	19.4232i	0.00564038	−	0.0500597i
$389$	35.1177	−	35.1177i	0.0902768	−	0.0902768i	−0.660526	−	0.750803i	$-0.729667\pi$
$389$	35.1177	−	35.1177i	0.0902768	−	0.0902768i	0.750803	+	0.660526i	$0.229667\pi$
$390$	−14.6311	+	11.6679i	−0.0375157	+	0.0299178i
$391$	214.708	−	341.706i	0.549126	−	0.873930i
$392$	−116.391	−	73.1331i	−0.296915	−	0.186564i
$393$	−486.482	−	610.029i	−1.23787	−	1.55224i
$394$	53.6199	+	53.6199i	0.136091	+	0.136091i
$395$	−16.0610	−	1.80964i	−0.0406608	−	0.00458137i
$396$	55.0355	+	157.282i	0.138978	+	0.397178i
$397$	−209.688	+	262.941i	−0.528183	+	0.662320i	−0.972324	−	0.233637i	$-0.924937\pi$
$397$	−209.688	+	262.941i	−0.528183	+	0.662320i	0.444141	+	0.895957i	$0.353509\pi$
$398$	−424.103	+	47.7849i	−1.06558	+	0.120063i
$399$	−33.2459	−	69.0358i	−0.0833230	−	0.173022i
$400$	21.9251	+	96.0603i	0.0548128	+	0.240151i
$401$	−44.1776	+	193.554i	−0.110168	+	0.482680i	0.889500	+	0.456935i	$0.151053\pi$
$401$	−44.1776	+	193.554i	−0.110168	+	0.482680i	−0.999669	+	0.0257446i	$0.991804\pi$
$402$	−463.998	−	223.450i	−1.15422	−	0.555845i
$403$	77.1219	−	220.402i	0.191369	−	0.546902i
$404$	−122.063	−	194.262i	−0.302137	−	0.480848i
$405$		−	54.1660i		−	0.133743i
$406$	−25.9141	−	1.48089i	−0.0638277	−	0.00364750i
$407$	−291.433			−0.716052
$408$	250.195	−	157.208i	0.613222	−	0.385313i
$409$	203.575	+	71.2340i	0.497739	+	0.174166i	0.567461	−	0.823400i	$-0.307926\pi$
$409$	203.575	+	71.2340i	0.497739	+	0.174166i	−0.0697224	+	0.997566i	$0.522211\pi$
$410$	5.95801	−	12.3719i	0.0145317	−	0.0301755i
$411$	−68.4726	−	15.6284i	−0.166600	−	0.0380254i
$412$	250.735	−	57.2286i	0.608580	−	0.138904i
$413$	54.9673	−	26.4709i	0.133093	−	0.0640941i
$414$	−20.0096	−	177.590i	−0.0483324	−	0.428962i
$415$	−15.3830	−	12.2675i	−0.0370675	−	0.0295603i
$416$	28.3186	−	9.90910i	0.0680735	−	0.0238199i
$417$	85.2572	−	756.679i	0.204454	−	1.81458i
$418$	−308.349	+	308.349i	−0.737677	+	0.737677i
$419$	−309.408	+	246.745i	−0.738444	+	0.588889i	−0.918805	−	0.394711i	$-0.870845\pi$
$419$	−309.408	+	246.745i	−0.738444	+	0.588889i	0.180361	+	0.983600i	$0.442273\pi$
$420$	1.68024	−	2.67408i	0.00400056	−	0.00636685i
$421$	180.587	+	113.470i	0.428948	+	0.269526i	0.729156	−	0.684348i	$-0.239913\pi$
$421$	180.587	+	113.470i	0.428948	+	0.269526i	−0.300208	+	0.953874i	$0.597056\pi$
$422$	−45.2881	−	56.7894i	−0.107318	−	0.134572i
$423$	−280.868	−	280.868i	−0.663990	−	0.663990i
$424$	−224.655	−	25.3125i	−0.529846	−	0.0596993i
$425$	206.463	+	590.037i	0.485795	+	1.38832i
$426$	−226.508	+	284.032i	−0.531709	+	0.666742i
$427$	−19.9847	+	2.25174i	−0.0468026	+	0.00527339i
$428$	1.82705	+	3.79391i	0.00426881	+	0.00886428i
$429$	50.9378	+	223.173i	0.118736	+	0.520217i
$430$	−2.72764	+	11.9506i	−0.00634335	+	0.0277920i
$431$	591.546	+	284.874i	1.37250	+	0.660960i	0.967386	−	0.253307i	$-0.0815184\pi$
$431$	591.546	+	284.874i	1.37250	+	0.660960i	0.405112	+	0.914267i	$0.367233\pi$
$432$	−5.72891	+	16.3723i	−0.0132614	+	0.0378988i
$433$	−128.532	−	204.557i	−0.296840	−	0.472419i	0.664689	−	0.747120i	$-0.268564\pi$
$433$	−128.532	−	204.557i	−0.296840	−	0.472419i	−0.961530	+	0.274701i	$0.911421\pi$
$434$			39.4061i			0.0907976i
$435$	−4.12808	+	72.2374i	−0.00948984	+	0.166063i
$436$	−39.0692			−0.0896082
$437$	396.001	−	248.824i	0.906181	−	0.569391i
$438$	−446.777	−	156.334i	−1.02004	−	0.356927i
$439$	175.887	−	365.234i	0.400655	−	0.831968i	−0.598861	−	0.800853i	$-0.704380\pi$
$439$	175.887	−	365.234i	0.400655	−	0.831968i	0.999516	−	0.0311151i	$-0.00990586\pi$
$440$	−17.5226	−	3.99941i	−0.0398240	−	0.00908957i
$441$	−376.518	+	85.9378i	−0.853782	+	0.194870i
$442$	171.495	−	82.5879i	0.387999	−	0.186850i
$443$	69.2861	+	614.931i	0.156402	+	1.38811i	0.789365	+	0.613924i	$0.210410\pi$
$443$	69.2861	+	614.931i	0.156402	+	1.38811i	−0.632963	+	0.774182i	$0.718162\pi$
$444$	178.926	+	142.689i	0.402987	+	0.321371i
$445$	−64.5048	+	22.5712i	−0.144955	+	0.0507218i
$446$	−22.7697	+	202.086i	−0.0510531	+	0.453109i
$447$	760.628	−	760.628i	1.70163	−	1.70163i
$448$	−3.95853	+	3.15682i	−0.00883600	+	0.00704647i
$449$	187.287	−	298.066i	0.417120	−	0.663843i	−0.570394	−	0.821371i	$-0.693210\pi$
$449$	187.287	−	298.066i	0.417120	−	0.663843i	0.987515	+	0.157528i	$0.0503524\pi$
$450$	234.396	+	147.281i	0.520880	+	0.327291i
$451$	−104.728	−	131.324i	−0.232212	−	0.291185i
$452$	−58.8749	−	58.8749i	−0.130254	−	0.130254i
$453$	1117.22	+	125.880i	2.46626	+	0.277881i
$454$	−75.9998	−	217.195i	−0.167401	−	0.478403i
$455$	1.26844	−	1.59057i	0.00278777	−	0.00349575i
$456$	340.283	−	38.3406i	0.746234	−	0.0840804i
$457$	−131.860	−	273.810i	−0.288534	−	0.599148i	0.705439	−	0.708771i	$-0.250750\pi$
$457$	−131.860	−	273.810i	−0.288534	−	0.599148i	−0.993973	+	0.109623i	$0.965036\pi$
$458$	104.138	+	456.256i	0.227375	+	0.996193i
$459$	−24.4879	+	107.289i	−0.0533506	+	0.233744i
$460$	17.3673	+	8.36364i	0.0377549	+	0.0181818i
$461$	−160.473	+	458.605i	−0.348097	+	0.994804i	0.628141	+	0.778100i	$0.283816\pi$
$461$	−160.473	+	458.605i	−0.348097	+	0.994804i	−0.976237	+	0.216704i	$0.930469\pi$
$462$	−20.5530	−	32.7099i	−0.0444869	−	0.0708005i
$463$			601.923i			1.30005i	0.759913	+	0.650025i	$0.225242\pi$
$463$			601.923i			1.30005i	−0.759913	+	0.650025i	$0.774758\pi$
$464$	44.4967	−	107.126i	0.0958981	−	0.230876i
$465$	109.848			0.236231
$466$	419.942	−	263.867i	0.901162	−	0.566238i
$467$	119.448	+	41.7968i	0.255778	+	0.0895007i	0.455122	−	0.890429i	$-0.349595\pi$
$467$	119.448	+	41.7968i	0.255778	+	0.0895007i	−0.199344	+	0.979930i	$0.563881\pi$
$468$	36.5732	−	75.9451i	0.0781479	−	0.162276i
$469$	54.5824	+	12.4581i	0.116380	+	0.0265631i
$470$	41.7689	−	9.53348i	0.0888700	−	0.0202840i
$471$	−603.009	+	290.394i	−1.28027	+	0.616547i
$472$	30.5274	+	270.938i	0.0646766	+	0.574021i
$473$	117.229	+	93.4868i	0.247841	+	0.197646i
$474$	146.540	−	51.2766i	0.309156	−	0.108179i
$475$	−81.1119	+	719.888i	−0.170762	+	1.51555i
$476$	−22.7141	+	22.7141i	−0.0477187	+	0.0477187i
$477$	−496.597	+	396.023i	−1.04108	+	0.830237i
$478$	63.5122	−	101.079i	0.132871	−	0.211462i
$479$	−385.075	−	241.959i	−0.803914	−	0.505133i	0.0663041	−	0.997799i	$-0.478879\pi$
$479$	−385.075	−	241.959i	−0.803914	−	0.505133i	−0.870218	+	0.492667i	$0.836022\pi$
$480$	8.79987	+	11.0347i	0.0183331	+	0.0229889i
$481$	104.244	+	104.244i	0.216724	+	0.216724i
$482$	366.716	+	41.3190i	0.760822	+	0.0857241i
$483$	13.6840	+	39.1067i	0.0283313	+	0.0809663i
$484$	13.8093	−	17.3163i	0.0285317	−	0.0357776i
$485$	5.88600	−	0.663193i	0.0121361	−	0.00136741i
$486$	201.801	+	419.045i	0.415229	+	0.862232i
$487$	119.746	+	524.642i	0.245885	+	1.07729i	0.935558	+	0.353173i	$0.114897\pi$
$487$	119.746	+	524.642i	0.245885	+	1.07729i	−0.689673	+	0.724121i	$0.742246\pi$
$488$	19.9997	−	87.6243i	0.0409829	−	0.179558i
$489$	−411.338	−	198.090i	−0.841182	−	0.405092i
$490$	13.7581	−	39.3183i	0.0280777	−	0.0802415i
$491$	130.381	+	207.501i	0.265543	+	0.422609i	0.952706	−	0.303895i	$-0.0982871\pi$
$491$	130.381	+	207.501i	0.265543	+	0.422609i	−0.687163	+	0.726503i	$0.741144\pi$
$492$			131.903i			0.268095i
$493$	204.433	−	706.985i	0.414671	−	1.43405i
$494$	220.590			0.446538
$495$	−42.7567	+	26.8658i	−0.0863771	+	0.0542743i
$496$	−166.225	−	58.1647i	−0.335131	−	0.117268i
$497$	17.1357	−	35.5826i	0.0344782	−	0.0715948i
$498$	184.258	+	42.0557i	0.369996	+	0.0844492i
$499$	−429.603	+	98.0540i	−0.860927	+	0.196501i	−0.630119	−	0.776498i	$-0.716994\pi$
$499$	−429.603	+	98.0540i	−0.860927	+	0.196501i	−0.230808	+	0.972999i	$0.574137\pi$
$500$	−54.2048	+	26.1037i	−0.108410	+	0.0522073i
$501$	−45.6697	−	405.330i	−0.0911571	−	0.809042i
$502$	332.201	+	264.921i	0.661754	+	0.527731i
$503$	−370.450	+	129.626i	−0.736481	+	0.257706i	−0.672348	−	0.740235i	$-0.734714\pi$
$503$	−370.450	+	129.626i	−0.736481	+	0.257706i	−0.0641334	+	0.997941i	$0.520428\pi$
$504$	−1.59271	+	14.1357i	−0.00316014	+	0.0280471i
$505$	49.1623	−	49.1623i	0.0973511	−	0.0973511i
$506$	184.348	−	147.013i	0.364325	−	0.290539i
$507$	−308.532	+	491.026i	−0.608545	+	0.968493i
$508$	234.746	+	147.501i	0.462099	+	0.290356i
$509$	−586.959	−	736.023i	−1.15316	−	1.44602i	−0.874102	−	0.485743i	$-0.838549\pi$
$509$	−586.959	−	736.023i	−1.15316	−	1.44602i	−0.279058	−	0.960274i	$-0.590022\pi$
$510$	63.3172	+	63.3172i	0.124151	+	0.124151i
$511$	51.1337	+	5.76139i	0.100066	+	0.0112747i
$512$	−7.47336	−	21.3576i	−0.0145964	−	0.0417141i
$513$	−79.5158	+	99.7096i	−0.155002	+	0.194366i
$514$	−415.298	+	46.7928i	−0.807972	+	0.0910366i
$515$	33.8155	+	70.2187i	0.0656612	+	0.136347i
$516$	−26.2007	−	114.793i	−0.0507766	−	0.222467i
$517$	116.615	−	510.925i	0.225562	−	0.988250i
$518$	−22.4153	−	10.7946i	−0.0432728	−	0.0208391i
$519$	−77.4933	+	221.463i	−0.149313	+	0.426711i
$520$	4.83717	+	7.69831i	0.00930225	+	0.0148044i
$521$		−	676.178i		−	1.29785i	−0.760854	−	0.648924i	$-0.775219\pi$
$521$		−	676.178i		−	1.29785i	0.760854	−	0.648924i	$-0.224781\pi$
$522$	−124.423	−	301.222i	−0.238359	−	0.577054i
$523$	105.295			0.201329			0.100664	−	0.994920i	$-0.467903\pi$
$523$	105.295			0.201329			0.100664	+	0.994920i	$0.467903\pi$
$524$	−320.973	+	201.680i	−0.612543	+	0.384886i
$525$	−60.5761	−	21.1965i	−0.115383	−	0.0403743i
$526$	149.965	−	311.405i	0.285104	−	0.592024i
$527$	−1089.28	−	248.622i	−2.06695	−	0.471768i
$528$	168.315	−	38.4169i	0.318779	−	0.0727592i
$529$	248.771	−	119.802i	0.470267	−	0.226468i
$530$	−7.67070	−	68.0794i	−0.0144730	−	0.128452i
$531$	598.907	+	477.612i	1.12788	+	0.899458i
$532$	−35.1375	+	12.2952i	−0.0660480	+	0.0231112i
$533$	−9.51351	+	84.4348i	−0.0178490	+	0.158414i
$534$	464.178	−	464.178i	0.869247	−	0.869247i
$535$	−0.997679	+	0.795622i	−0.00186482	+	0.00148714i
$536$	−133.117	+	211.854i	−0.248352	+	0.395250i
$537$	−291.922	−	183.427i	−0.543616	−	0.341576i
$538$	−35.1911	−	44.1282i	−0.0654109	−	0.0820227i
$539$	−360.302	−	360.302i	−0.668463	−	0.668463i
$540$	−5.22339	−	0.588534i	−0.00967294	−	0.00108988i
$541$	101.517	+	290.118i	0.187646	+	0.536262i	0.998821	−	0.0485417i	$-0.0154574\pi$
$541$	101.517	+	290.118i	0.187646	+	0.536262i	−0.811175	+	0.584803i	$0.801172\pi$
$542$	252.577	−	316.721i	0.466009	−	0.584356i
$543$	−955.830	+	107.696i	−1.76028	+	0.198336i
$544$	−62.2871	−	129.341i	−0.114498	−	0.237758i
$545$	−2.63454	−	11.5427i	−0.00483403	−	0.0211792i
$546$	−4.34846	+	19.0519i	−0.00796422	+	0.0348935i
$547$	310.899	+	149.721i	0.568371	+	0.273713i	0.695920	−	0.718119i	$-0.254997\pi$
$547$	310.899	+	149.721i	0.568371	+	0.273713i	−0.127549	+	0.991832i	$0.540711\pi$
$548$	−11.2697	+	32.2071i	−0.0205652	+	0.0587720i
$549$	−134.347	−	213.811i	−0.244711	−	0.389456i
$550$			365.238i			0.664069i
$551$	568.943	−	635.388i	1.03256	−	1.15315i
$552$	−185.160			−0.335435
$553$	−14.2907	+	8.97946i	−0.0258422	+	0.0162377i
$554$	429.047	+	150.130i	0.774453	+	0.270993i
$555$	−30.0908	+	62.4843i	−0.0542177	+	0.112584i
$556$	−360.672	−	82.3210i	−0.648690	−	0.148059i
$557$	781.572	−	178.389i	1.40318	−	0.320267i	0.547083	−	0.837079i	$-0.315738\pi$
$557$	781.572	−	178.389i	1.40318	−	0.320267i	0.856099	+	0.516811i	$0.172881\pi$
$558$	−445.785	+	214.679i	−0.798897	+	0.384729i
$559$	−8.49238	−	75.3720i	−0.0151921	−	0.134834i
$560$	−1.19959	−	0.956644i	−0.00214213	−	0.00170829i
$561$	1033.85	−	361.761i	1.84288	−	0.644851i
$562$	26.3318	−	233.701i	0.0468537	−	0.415839i
$563$	224.904	−	224.904i	0.399474	−	0.399474i	−0.478574	−	0.878047i	$-0.658846\pi$
$563$	224.904	−	224.904i	0.399474	−	0.399474i	0.878047	+	0.478574i	$0.158846\pi$
$564$	−321.751	+	256.588i	−0.570480	+	0.454943i
$565$	13.4240	−	21.3642i	0.0237594	−	0.0378128i
$566$	−292.665	−	183.894i	−0.517077	−	0.324901i
$567$	−35.2660	−	44.2221i	−0.0621975	−	0.0779932i
$568$	124.804	+	124.804i	0.219725	+	0.219725i
$569$	−119.690	−	13.4858i	−0.210352	−	0.0237009i	0.00615973	−	0.999981i	$-0.498039\pi$
$569$	−119.690	−	13.4858i	−0.210352	−	0.0237009i	−0.216511	+	0.976280i	$0.569468\pi$
$570$	34.2737	+	97.9485i	0.0601292	+	0.171839i
$571$	−25.0372	+	31.3956i	−0.0438479	+	0.0549835i	−0.803272	−	0.595612i	$-0.796909\pi$
$571$	−25.0372	+	31.3956i	−0.0438479	+	0.0549835i	0.759424	+	0.650596i	$0.225481\pi$
$572$	110.514	−	12.4520i	0.193207	−	0.0217692i
$573$	190.445	+	395.462i	0.332364	+	0.690161i
$574$	−3.19080	−	13.9798i	−0.00555888	−	0.0243550i
$575$	87.1653	−	381.896i	0.151592	−	0.664167i
$576$	−57.2772	−	27.5832i	−0.0994395	−	0.0478876i
$577$	−173.017	+	494.454i	−0.299856	+	0.856939i	0.691101	+	0.722758i	$0.257126\pi$
$577$	−173.017	+	494.454i	−0.299856	+	0.856939i	−0.990957	+	0.134181i	$0.957160\pi$
$578$	−267.120	−	425.119i	−0.462145	−	0.735499i
$579$			603.914i			1.04303i
$580$	34.6502	+	5.92239i	0.0597417	+	0.0102110i
$581$	−20.5460			−0.0353632
$582$	−48.1757	+	30.2708i	−0.0827761	+	0.0520117i
$583$	−791.002	−	276.784i	−1.35678	−	0.474757i
$584$	−99.7780	+	207.191i	−0.170853	+	0.354779i
$585$	24.9036	+	5.68409i	0.0425703	+	0.00971640i
$586$	−400.389	+	91.3863i	−0.683258	+	0.155949i
$587$	−168.729	+	81.2556i	−0.287443	+	0.138425i	−0.572049	−	0.820219i	$-0.693851\pi$
$587$	−168.729	+	81.2556i	−0.287443	+	0.138425i	0.284606	+	0.958644i	$0.408137\pi$
$588$	44.8005	+	397.616i	0.0761913	+	0.676217i
$589$	−1012.34	−	807.310i	−1.71874	−	1.37065i
$590$	−77.9880	+	27.2892i	−0.132183	+	0.0462529i
$591$	24.7143	−	219.345i	0.0418177	−	0.371143i
$592$	78.6202	−	78.6202i	0.132804	−	0.132804i
$593$	143.119	−	114.134i	0.241348	−	0.192468i	−0.495344	−	0.868697i	$-0.664958\pi$
$593$	143.119	−	114.134i	0.241348	−	0.192468i	0.736692	+	0.676228i	$0.236387\pi$
$594$	−34.2085	+	54.4425i	−0.0575900	+	0.0916540i
$595$	−8.24238	−	5.17903i	−0.0138527	−	0.00870425i
$596$	−325.841	−	408.591i	−0.546713	−	0.685556i
$597$	878.460	+	878.460i	1.47146	+	1.47146i
$598$	−118.526	−	13.3547i	−0.198205	−	0.0223323i
$599$	−185.143	−	529.108i	−0.309087	−	0.883319i	−0.988721	−	0.149768i	$-0.952147\pi$
$599$	−185.143	−	529.108i	−0.309087	−	0.883319i	0.679635	−	0.733551i	$-0.262138\pi$
$600$	178.825	−	224.239i	0.298041	−	0.373732i
$601$	−377.843	+	42.5727i	−0.628690	+	0.0708364i	−0.420560	−	0.907265i	$-0.638166\pi$
$601$	−377.843	+	42.5727i	−0.628690	+	0.0708364i	−0.208130	+	0.978101i	$0.566738\pi$
$602$	5.55380	+	11.5326i	0.00922557	+	0.0191571i
$603$	156.424	+	685.337i	0.259409	+	1.13655i
$604$	121.545	−	532.522i	0.201233	−	0.881658i
$605$	6.04718	+	2.91217i	0.00999535	+	0.00481350i
$606$	−220.574	+	630.364i	−0.363984	+	1.04021i
$607$	295.220	+	469.840i	0.486359	+	0.774036i	0.996279	−	0.0861859i	$-0.0274679\pi$
$607$	295.220	+	469.840i	0.486359	+	0.774036i	−0.509920	+	0.860222i	$0.670325\pi$
$608$		−	166.367i		−	0.273630i
$609$	43.6615	+	61.6636i	0.0716938	+	0.101254i
$610$	27.2366			0.0446501
$611$	−224.468	+	141.043i	−0.367379	+	0.230839i
$612$	−380.697	−	133.212i	−0.622055	−	0.217666i
$613$	−3.86981	+	8.03575i	−0.00631291	+	0.0131089i	−0.904101	−	0.427318i	$-0.859459\pi$
$613$	−3.86981	+	8.03575i	−0.00631291	+	0.0131089i	0.897789	+	0.440427i	$0.145173\pi$
$614$	446.245	+	101.853i	0.726784	+	0.165884i
$615$	−38.9697	+	8.89458i	−0.0633654	+	0.0144627i
$616$	−16.9097	+	8.14327i	−0.0274508	+	0.0132196i
$617$	−73.2937	−	650.499i	−0.118790	−	1.05429i	−0.901761	−	0.432235i	$-0.857725\pi$
$617$	−73.2937	−	650.499i	−0.118790	−	1.05429i	0.782971	−	0.622059i	$-0.213704\pi$
$618$	−585.305	−	466.765i	−0.947095	−	0.755283i
$619$	148.640	−	52.0115i	0.240130	−	0.0840251i	−0.207531	−	0.978228i	$-0.566543\pi$
$619$	148.640	−	52.0115i	0.240130	−	0.0840251i	0.447661	+	0.894203i	$0.352257\pi$
$620$	5.97529	−	53.0322i	0.00963757	−	0.0855358i
$621$	48.7616	−	48.7616i	0.0785211	−	0.0785211i
$622$	−614.114	+	489.740i	−0.987322	+	0.787363i
$623$	−37.9674	+	60.4248i	−0.0609429	+	0.0969901i
$624$	−73.9472	−	46.4641i	−0.118505	−	0.0744617i
$625$	372.588	+	467.211i	0.596141	+	0.747537i
$626$	334.622	+	334.622i	0.534540	+	0.534540i
$627$	1261.38	+	142.123i	2.01176	+	0.226671i
$628$	107.395	+	306.917i	0.171011	+	0.488721i
$629$	439.813	−	551.508i	0.699226	−	0.876802i
$630$	−4.28369	+	0.482656i	−0.00679951	+	0.000766121i
$631$	461.348	+	958.000i	0.731138	+	1.51822i	0.850846	+	0.525415i	$0.176090\pi$
$631$	461.348	+	958.000i	0.731138	+	1.51822i	−0.119708	+	0.992809i	$0.538196\pi$
$632$	−16.7841	−	73.5359i	−0.0265571	−	0.116354i
$633$	−47.0491	+	206.136i	−0.0743272	+	0.325649i
$634$	775.676	+	373.546i	1.22346	+	0.589189i
$635$	−27.7484	+	79.3005i	−0.0436983	+	0.124883i
$636$	350.121	+	557.215i	0.550505	+	0.876124i
$637$			257.756i			0.404641i
$638$	249.170	−	350.442i	0.390549	−	0.549281i
$639$	495.883			0.776030
$640$	5.80600	−	3.64815i	0.00907188	−	0.00570024i
$641$	−208.547	−	72.9738i	−0.325347	−	0.113844i	0.162664	−	0.986682i	$-0.447991\pi$
$641$	−208.547	−	72.9738i	−0.325347	−	0.113844i	−0.488010	+	0.872838i	$0.662277\pi$
$642$	5.31835	−	11.0437i	0.00828404	−	0.0172020i
$643$	295.512	+	67.4487i	0.459583	+	0.104897i	0.446043	−	0.895011i	$-0.352833\pi$
$643$	295.512	+	67.4487i	0.459583	+	0.104897i	0.0135402	+	0.999908i	$0.495690\pi$
$644$	19.6243	−	4.47912i	0.0304725	−	0.00695516i
$645$	32.1479	−	15.4816i	0.0498417	−	0.0240025i
$646$	−118.178	−	1048.86i	−0.182939	−	1.62362i
$647$	−157.641	−	125.715i	−0.243650	−	0.194304i	0.494049	−	0.869434i	$-0.335516\pi$
$647$	−157.641	−	125.715i	−0.243650	−	0.194304i	−0.737699	+	0.675130i	$0.764088\pi$
$648$	238.594	−	83.4876i	0.368201	−	0.128839i
$649$	−113.160	+	1004.33i	−0.174361	+	1.54750i
$650$	130.644	−	130.644i	0.200991	−	0.200991i
$651$	89.6816	−	71.5187i	0.137760	−	0.109860i
$652$	−118.009	+	187.810i	−0.180995	+	0.288053i
$653$	−784.860	−	493.160i	−1.20193	−	0.755222i	−0.226174	−	0.974087i	$-0.572622\pi$
$653$	−784.860	−	493.160i	−1.20193	−	0.755222i	−0.975755	+	0.218865i	$0.929765\pi$
$654$	70.9071	+	88.9147i	0.108421	+	0.135955i
$655$	−81.2290	−	81.2290i	−0.124014	−	0.124014i
$656$	63.6800	+	7.17502i	0.0970732	+	0.0109375i
$657$	213.393	+	609.841i	0.324798	+	0.928221i
$658$	27.8939	−	34.9779i	0.0423920	−	0.0531579i
$659$	175.691	−	19.7957i	0.266603	−	0.0300389i	0.0223490	−	0.999750i	$-0.492886\pi$
$659$	175.691	−	19.7957i	0.266603	−	0.0300389i	0.244254	+	0.969711i	$0.421457\pi$
$660$	22.7000	+	47.1369i	0.0343939	+	0.0714196i
$661$	51.6619	+	226.345i	0.0781572	+	0.342429i	0.998855	−	0.0478482i	$-0.0152364\pi$
$661$	51.6619	+	226.345i	0.0781572	+	0.342429i	−0.920697	+	0.390277i	$0.872379\pi$
$662$	−199.896	+	875.800i	−0.301957	+	1.32296i
$663$	−499.205	−	240.405i	−0.752949	−	0.362601i
$664$	30.3266	−	86.6685i	0.0456726	−	0.130525i
$665$	−6.00194	−	9.55203i	−0.00902547	−	0.0143639i
$666$		−	312.382i		−	0.469042i
$667$	−344.169	+	306.959i	−0.515995	+	0.460209i
$668$	−198.169			−0.296661
$669$	501.239	−	314.949i	0.749236	−	0.470776i
$670$	−71.5671	−	25.0424i	−0.106817	−	0.0373767i
$671$	144.554	−	300.170i	0.215431	−	0.447347i
$672$	14.3688	+	3.27958i	0.0213821	+	0.00488032i
$673$	1119.59	−	255.540i	1.66358	−	0.379702i	0.715723	−	0.698385i	$-0.246098\pi$
$673$	1119.59	−	255.540i	1.66358	−	0.379702i	0.947862	+	0.318683i	$0.103240\pi$
$674$	679.137	−	327.055i	1.00762	−	0.485245i
$675$	11.9598	+	106.146i	0.0177182	+	0.157253i
$676$	220.275	+	175.663i	0.325850	+	0.259857i
$677$	−268.974	+	94.1180i	−0.397303	+	0.139022i	−0.521533	−	0.853231i	$-0.674640\pi$
$677$	−268.974	+	94.1180i	−0.397303	+	0.139022i	0.124230	+	0.992253i	$0.460354\pi$
$678$	−27.1364	+	240.842i	−0.0400241	+	0.355224i
$679$	4.37366	−	4.37366i	0.00644132	−	0.00644132i
$680$	34.0125	−	27.1240i	0.0500184	−	0.0398883i
$681$	−356.366	+	567.153i	−0.523298	+	0.832823i
$682$	−552.746	−	347.313i	−0.810477	−	0.509257i
$683$	389.520	+	488.442i	0.570307	+	0.715143i	0.980426	−	0.196890i	$-0.0630841\pi$
$683$	389.520	+	488.442i	0.570307	+	0.715143i	−0.410119	+	0.912032i	$0.634513\pi$
$684$	−330.514	−	330.514i	−0.483207	−	0.483207i
$685$	−10.2753	−	1.15775i	−0.0150004	−	0.00169014i
$686$	−28.8519	−	82.4539i	−0.0420581	−	0.120195i
$687$	849.361	−	1065.06i	1.23633	−	1.55031i
$688$	−56.8449	+	6.40488i	−0.0826234	+	0.00930943i
$689$	183.934	+	381.942i	0.266957	+	0.554342i
$690$	−12.4859	−	54.7042i	−0.0180955	−	0.0792815i
$691$	162.656	−	712.644i	0.235393	−	1.03132i	−0.709696	−	0.704508i	$-0.751168\pi$
$691$	162.656	−	712.644i	0.235393	−	1.03132i	0.945088	−	0.326815i	$-0.105975\pi$
$692$	102.703	+	49.4590i	0.148414	+	0.0714725i
$693$	−17.4158	+	49.7715i	−0.0251310	+	0.0718203i
$694$	199.040	+	316.771i	0.286802	+	0.456442i
$695$		−	112.109i		−	0.161308i
$696$	−324.559	+	93.1579i	−0.466320	+	0.133848i
$697$	406.567			0.583310
$698$	−619.061	+	388.982i	−0.886908	+	0.557281i
$699$	−1362.67	−	476.820i	−1.94946	−	0.682146i
$700$	−13.5284	+	28.0919i	−0.0193262	+	0.0401313i
$701$	−665.125	−	151.811i	−0.948824	−	0.216563i	−0.280014	−	0.959996i	$-0.590339\pi$
$701$	−665.125	−	151.811i	−0.948824	−	0.216563i	−0.668810	+	0.743433i	$0.733196\pi$
$702$	31.7100	−	7.23761i	0.0451710	−	0.0103100i
$703$	736.532	−	354.695i	1.04770	−	0.504545i
$704$	−9.39118	−	83.3490i	−0.0133397	−	0.118393i
$705$	−97.5035	−	77.7564i	−0.138303	−	0.110293i
$706$	−735.321	+	257.300i	−1.04153	+	0.364447i
$707$	8.12882	−	72.1453i	0.0114976	−	0.102044i
$708$	561.204	−	561.204i	0.792661	−	0.792661i
$709$	−1025.09	+	817.484i	−1.44583	+	1.15301i	−0.485465	+	0.874256i	$0.661350\pi$
$709$	−1025.09	+	817.484i	−1.44583	+	1.15301i	−0.960363	+	0.278753i	$0.910079\pi$
$710$	−28.4565	+	45.2882i	−0.0400795	+	0.0637862i
$711$	−179.434	−	112.746i	−0.252369	−	0.158574i
$712$	−198.846	−	249.345i	−0.279279	−	0.350204i
$713$	495.068	+	495.068i	0.694345	+	0.694345i
$714$	92.9174	+	10.4693i	0.130136	+	0.0146629i
$715$	11.1311	+	31.8109i	0.0155680	+	0.0444908i
$716$	−104.434	+	130.956i	−0.145858	+	0.182900i
$717$	−345.308	+	38.9068i	−0.481601	+	0.0542634i
$718$	−84.3367	−	175.127i	−0.117461	−	0.243909i
$719$	−53.0938	−	232.619i	−0.0738440	−	0.323532i	0.924492	−	0.381202i	$-0.124490\pi$
$719$	−53.0938	−	232.619i	−0.0738440	−	0.323532i	−0.998336	+	0.0576706i	$0.981633\pi$
$720$	4.28690	−	18.7821i	0.00595402	−	0.0260863i
$721$	73.3251	+	35.3115i	0.101699	+	0.0489757i
$722$	235.382	−	672.684i	0.326014	−	0.931696i
$723$	−571.523	−	909.574i	−0.790488	−	1.25805i
$724$			467.314i			0.645461i
$725$	−39.3519	−	713.263i	−0.0542784	−	0.983810i
$726$	−64.4717			−0.0888041
$727$	−348.342	+	218.878i	−0.479150	+	0.301070i	−0.749867	−	0.661589i	$-0.769882\pi$
$727$	−348.342	+	218.878i	−0.479150	+	0.301070i	0.270716	+	0.962659i	$0.412739\pi$
$728$	8.96132	+	3.13570i	0.0123095	+	0.00430728i
$729$	238.433	−	495.112i	0.327069	−	0.679166i
$730$	−67.9414	−	15.5072i	−0.0930704	−	0.0212427i
$731$	−353.829	+	80.7591i	−0.484034	+	0.110478i
$732$	−235.716	+	113.515i	−0.322016	+	0.155075i
$733$	86.8431	+	770.754i	0.118476	+	1.05151i	0.902474	+	0.430743i	$0.141749\pi$
$733$	86.8431	+	770.754i	0.118476	+	1.05151i	−0.783998	+	0.620763i	$0.786823\pi$
$734$	315.616	+	251.696i	0.429995	+	0.342910i
$735$	−114.451	+	40.0483i	−0.155716	+	0.0544875i
$736$	−10.0720	+	89.3917i	−0.0136848	+	0.121456i
$737$	−655.820	+	655.820i	−0.889850	+	0.889850i
$738$	140.764	−	112.256i	0.190738	−	0.152108i
$739$	168.604	−	268.332i	0.228152	−	0.363102i	−0.712956	−	0.701209i	$-0.752644\pi$
$739$	168.604	−	268.332i	0.228152	−	0.363102i	0.941107	+	0.338108i	$0.109787\pi$
$740$	28.5293	+	17.9262i	0.0385531	+	0.0242245i
$741$	−400.352	−	502.025i	−0.540286	−	0.677497i
$742$	−50.5871	−	50.5871i	−0.0681767	−	0.0681767i
$743$	325.292	+	36.6516i	0.437809	+	0.0493292i	0.328119	−	0.944637i	$-0.393585\pi$
$743$	325.292	+	36.6516i	0.437809	+	0.0493292i	0.109691	+	0.993966i	$0.465014\pi$
$744$	169.311	+	483.864i	0.227569	+	0.650355i
$745$	98.7429	−	123.820i	0.132541	−	0.166201i
$746$	83.4648	−	9.40422i	0.111883	−	0.0126062i
$747$	−111.932	−	232.429i	−0.149842	−	0.311149i
$748$	−118.413	−	518.802i	−0.158307	−	0.693586i
$749$	−0.296516	+	1.29912i	−0.000395883	+	0.00173448i
$750$	157.784	+	75.9850i	0.210379	+	0.101313i
$751$	51.6713	−	147.668i	0.0688033	−	0.196629i	−0.904348	−	0.426797i	$-0.859642\pi$
$751$	51.6713	−	147.668i	0.0688033	−	0.196629i	0.973151	+	0.230168i	$0.0739276\pi$
$752$	106.373	+	169.292i	0.141454	+	0.225123i
$753$		−	1236.84i		−	1.64255i
$754$	−214.478	+	36.2242i	−0.284454	+	0.0480427i
$755$	165.526			0.219239
$756$	−4.64765	+	2.92031i	−0.00614769	+	0.00386285i
$757$	−178.230	−	62.3653i	−0.235442	−	0.0823848i	0.209979	−	0.977706i	$-0.432660\pi$
$757$	−178.230	−	62.3653i	−0.235442	−	0.0823848i	−0.445421	+	0.895321i	$0.646946\pi$
$758$	−351.351	+	729.588i	−0.463524	+	0.962518i
$759$	−669.153	−	152.730i	−0.881624	−	0.201225i
$760$	49.1519	−	11.2186i	0.0646736	−	0.0147613i
$761$	−929.953	+	447.842i	−1.22201	+	0.588491i	−0.929872	−	0.367884i	$-0.880082\pi$
$761$	−929.953	+	447.842i	−1.22201	+	0.588491i	−0.292142	+	0.956375i	$0.594368\pi$
$762$	−90.3574	−	801.944i	−0.118579	−	1.05242i
$763$	−9.66602	−	7.70839i	−0.0126684	−	0.0101027i
$764$	201.281	−	70.4311i	0.263456	−	0.0921874i
$765$	13.6849	−	121.457i	0.0178888	−	0.158767i
$766$	326.740	−	326.740i	0.426553	−	0.426553i
$767$	399.720	−	318.766i	0.521147	−	0.415601i
$768$	−35.0428	+	55.7703i	−0.0456287	+	0.0726176i
$769$	676.317	+	424.958i	0.879476	+	0.552611i	0.894395	−	0.447277i	$-0.147606\pi$
$769$	676.317	+	424.958i	0.879476	+	0.552611i	−0.0149194	+	0.999889i	$0.504749\pi$
$770$	−3.54613	−	4.44671i	−0.00460537	−	0.00577495i
$771$	860.221	+	860.221i	1.11572	+	1.11572i
$772$	291.557	+	32.8506i	0.377665	+	0.0425526i
$773$	80.8270	+	230.990i	0.104563	+	0.298823i	0.984264	−	0.176703i	$-0.0565433\pi$
$773$	80.8270	+	230.990i	0.104563	+	0.298823i	−0.879701	+	0.475527i	$0.842258\pi$
$774$	−100.207	+	125.655i	−0.129466	+	0.162345i
$775$	−1077.68	+	121.426i	−1.39056	+	0.156678i
$776$	11.9936	+	24.9049i	0.0154556	+	0.0320939i
$777$	16.1151	+	70.6047i	0.0207401	+	0.0908683i
$778$	−15.6288	+	68.4744i	−0.0200885	+	0.0880133i
$779$	424.507	+	204.432i	0.544939	+	0.262429i
$780$	8.74100	−	24.9803i	0.0112064	−	0.0320261i
$781$	348.085	+	553.974i	0.445691	+	0.709314i
$782$			570.724i			0.729826i
$783$	60.9389	−	110.005i	0.0778275	−	0.140491i
$784$	194.398			0.247956
$785$	−83.4343	+	52.4253i	−0.106286	+	0.0667838i
$786$	1041.53	+	364.446i	1.32510	+	0.463672i
$787$	402.867	−	836.561i	0.511902	−	1.06297i	−0.471556	−	0.881836i	$-0.656307\pi$
$787$	402.867	−	836.561i	0.511902	−	1.06297i	0.983458	−	0.181139i	$-0.0579783\pi$
$788$	−104.551	−	23.8631i	−0.132679	−	0.0302831i
$789$	−980.876	+	223.879i	−1.24319	+	0.283750i
$790$	20.5938	−	9.91746i	0.0260681	−	0.0125538i
$791$	−2.95002	−	26.1822i	−0.00372949	−	0.0331001i
$792$	−184.242	−	146.928i	−0.232629	−	0.185516i
$793$	−159.076	+	55.6629i	−0.200600	+	0.0701929i
$794$	53.2526	−	472.630i	0.0670687	−	0.595251i
$795$	−141.015	+	141.015i	−0.177378	+	0.177378i
$796$	471.888	−	376.318i	0.592824	−	0.472761i
$797$	162.325	−	258.339i	0.203671	−	0.324140i	−0.729233	−	0.684265i	$-0.760123\pi$
$797$	162.325	−	258.339i	0.203671	−	0.324140i	0.932904	+	0.360125i	$0.117266\pi$
$798$	91.7533	+	57.6524i	0.114979	+	0.0722461i
$799$	790.887	+	991.741i	0.989846	+	1.24123i
$800$	−98.5307	−	98.5307i	−0.123163	−	0.123163i
$801$	−890.401	−	100.324i	−1.11161	−	0.125249i
$802$	−92.7314	−	265.011i	−0.115625	−	0.330438i
$803$	−531.491	+	666.468i	−0.661881	+	0.829973i
$804$	723.738	−	81.5457i	0.900172	−	0.101425i
$805$	2.64664	+	5.49581i	0.00328776	+	0.00682710i
$806$	73.4823	+	321.947i	0.0911690	+	0.399438i
$807$	−36.5595	+	160.178i	−0.0453030	+	0.198485i
$808$	292.329	+	140.778i	0.361793	+	0.174230i
$809$	185.166	−	529.175i	0.228883	−	0.654110i	−0.770969	−	0.636873i	$-0.780227\pi$
$809$	185.166	−	529.175i	0.228883	−	0.654110i	0.999851	−	0.0172364i	$-0.00548680\pi$
$810$	40.7548	+	64.8610i	0.0503146	+	0.0800753i
$811$		−	146.787i		−	0.180996i	−0.995897	−	0.0904978i	$-0.971154\pi$
$811$		−	146.787i		−	0.180996i	0.995897	−	0.0904978i	$-0.0288458\pi$
$812$	32.1450	−	17.7246i	0.0395874	−	0.0218284i
$813$	−1179.21			−1.45044
$814$	348.976	−	219.276i	0.428718	−	0.269381i
$815$	−63.4448	−	22.2003i	−0.0778464	−	0.0272396i
$816$	−181.311	+	376.496i	−0.222195	+	0.461393i
$817$	−410.050	−	93.5911i	−0.501897	−	0.114555i
$818$	−297.368	+	67.8723i	−0.363530	+	0.0829734i
$819$	24.0326	−	11.5735i	0.0293438	−	0.0141312i
$820$	2.17432	+	19.2976i	0.00265161	+	0.0235337i
$821$	368.638	+	293.979i	0.449011	+	0.358074i	0.821737	−	0.569867i	$-0.193005\pi$
$821$	368.638	+	293.979i	0.449011	+	0.358074i	−0.372726	+	0.927941i	$0.621577\pi$
$822$	93.7514	−	32.8050i	0.114053	−	0.0399088i
$823$	64.6347	−	573.649i	0.0785355	−	0.697022i	−0.891326	−	0.453364i	$-0.850224\pi$
$823$	64.6347	−	573.649i	0.0785355	−	0.697022i	0.969861	−	0.243658i	$-0.0783475\pi$
$824$	−257.183	+	257.183i	−0.312115	+	0.312115i
$825$	831.220	−	662.875i	1.00754	−	0.803485i
$826$	−45.9037	+	73.0553i	−0.0555735	+	0.0884447i
$827$	429.027	+	269.576i	0.518775	+	0.325968i	0.765840	−	0.643031i	$-0.222323\pi$
$827$	429.027	+	269.576i	0.518775	+	0.325968i	−0.247065	+	0.968999i	$0.579466\pi$
$828$	157.581	+	197.600i	0.190315	+	0.238647i
$829$	−1113.40	−	1113.40i	−1.34306	−	1.34306i	−0.892997	−	0.450062i	$-0.851402\pi$
$829$	−1113.40	−	1113.40i	−1.34306	−	1.34306i	−0.450062	−	0.892997i	$-0.648598\pi$
$830$	27.6506	+	3.11547i	0.0333139	+	0.00375358i
$831$	−437.012	−	1248.91i	−0.525887	−	1.50290i
$832$	−26.4544	+	33.1727i	−0.0317961	+	0.0398711i
$833$	1225.58	−	138.090i	1.47128	−	0.165774i
$834$	467.239	+	970.232i	0.560239	+	1.16335i
$835$	−13.3631	−	58.5477i	−0.0160037	−	0.0701170i
$836$	137.228	−	601.236i	0.164149	−	0.719182i
$837$	−172.012	−	82.8368i	−0.205511	−	0.0989686i
$838$	184.848	−	528.265i	0.220582	−	0.630388i
$839$	−214.741	−	341.758i	−0.255949	−	0.407340i	0.693890	−	0.720081i	$-0.255896\pi$
$839$	−214.741	−	341.758i	−0.255949	−	0.407340i	−0.949838	+	0.312741i	$0.898753\pi$
$840$			4.46629i			0.00531702i
$841$	−448.840	+	711.213i	−0.533698	+	0.845675i
$842$	−301.620			−0.358218
$843$	−579.654	+	364.221i	−0.687608	+	0.432053i
$844$	96.9589	+	33.9274i	0.114880	+	0.0401983i
$845$	−37.0446	+	76.9239i	−0.0438398	+	0.0910342i
$846$	547.652	+	124.998i	0.647342	+	0.147752i
$847$	6.83307	−	1.55960i	0.00806738	−	0.00184133i
$848$	288.058	−	138.721i	0.339691	−	0.163586i
$849$	112.651	+	999.808i	0.132687	+	1.17763i
$850$	−691.177	−	551.195i	−0.813150	−	0.648465i
$851$	−417.224	+	145.993i	−0.490275	+	0.171555i
$852$	57.5240	−	510.540i	0.0675165	−	0.599225i
$853$	252.617	−	252.617i	0.296151	−	0.296151i	−0.543353	−	0.839504i	$-0.682846\pi$
$853$	252.617	−	252.617i	0.296151	−	0.296151i	0.839504	+	0.543353i	$0.182846\pi$
$854$	22.2365	−	17.7330i	0.0260380	−	0.0207646i
$855$	75.3603	−	119.935i	0.0881407	−	0.140275i
$856$	−5.04236	−	3.16833i	−0.00589061	−	0.00370132i
$857$	447.832	+	561.564i	0.522558	+	0.655267i	0.971150	−	0.238470i	$-0.0766458\pi$
$857$	447.832	+	561.564i	0.522558	+	0.655267i	−0.448592	+	0.893737i	$0.648074\pi$
$858$	−228.912	−	228.912i	−0.266798	−	0.266798i
$859$	9.13149	+	1.02887i	0.0106304	+	0.00119776i	0.117278	−	0.993099i	$-0.462583\pi$
$859$	9.13149	+	1.02887i	0.0106304	+	0.00119776i	−0.106648	+	0.994297i	$0.534012\pi$
$860$	−5.72549	−	16.3625i	−0.00665754	−	0.0190262i
$861$	−26.0246	+	32.6338i	−0.0302260	+	0.0379022i
$862$	−922.687	+	103.962i	−1.07040	+	0.120605i
$863$	−250.994	−	521.195i	−0.290839	−	0.603934i	0.703439	−	0.710756i	$-0.251647\pi$
$863$	−250.994	−	521.195i	−0.290839	−	0.603934i	−0.994278	+	0.106822i	$0.965933\pi$
$864$	−5.45855	−	23.9155i	−0.00631776	−	0.0276799i
$865$	−7.68675	+	33.6779i	−0.00888642	+	0.0389339i
$866$	307.821	+	148.239i	0.355451	+	0.171176i
$867$	−482.698	+	1379.47i	−0.556745	+	1.59109i
$868$	−29.6495	−	47.1868i	−0.0341584	−	0.0543627i
$869$		−	279.596i		−	0.321745i
$870$	−49.4087	−	89.6065i	−0.0567916	−	0.102996i
$871$	469.167			0.538654
$872$	46.7833	−	29.3959i	0.0536506	−	0.0337109i
$873$	73.3043	+	25.6503i	0.0839683	+	0.0293818i
$874$	−286.974	+	595.908i	−0.328346	+	0.681817i
$875$	−18.5610	−	4.23642i	−0.0212126	−	0.00484163i
$876$	652.620	−	148.956i	0.745000	−	0.170041i
$877$	184.643	−	88.9193i	0.210539	−	0.101390i	−0.325642	−	0.945493i	$-0.605581\pi$
$877$	184.643	−	88.9193i	0.210539	−	0.101390i	0.536182	+	0.844103i	$0.319866\pi$
$878$	64.1884	+	569.688i	0.0731075	+	0.648847i
$879$	934.651	+	745.360i	1.06331	+	0.847963i
$880$	23.9916	−	8.39501i	0.0272631	−	0.00953978i
$881$	−91.6821	+	813.701i	−0.104066	+	0.923611i	0.827853	+	0.560945i	$0.189562\pi$
$881$	−91.6821	+	813.701i	−0.104066	+	0.923611i	−0.931919	+	0.362666i	$0.881867\pi$
$882$	386.201	−	386.201i	0.437869	−	0.437869i
$883$	1043.02	−	831.777i	1.18122	−	0.941990i	0.182071	−	0.983285i	$-0.441720\pi$
$883$	1043.02	−	831.777i	1.18122	−	0.941990i	0.999147	+	0.0412952i	$0.0131484\pi$
$884$	−143.217	+	227.929i	−0.162011	+	0.257838i
$885$	203.647	+	127.960i	0.230110	+	0.144587i
$886$	−545.645	−	684.217i	−0.615852	−	0.772254i
$887$	651.784	+	651.784i	0.734818	+	0.734818i	0.971570	−	0.236752i	$-0.0760829\pi$
$887$	651.784	+	651.784i	0.734818	+	0.734818i	−0.236752	+	0.971570i	$0.576083\pi$
$888$	−321.615	−	36.2373i	−0.362179	−	0.0408078i
$889$	28.9760	+	82.8087i	0.0325939	+	0.0931481i
$890$	60.2584	−	75.5617i	0.0677061	−	0.0849008i
$891$	931.122	−	104.912i	1.04503	−	0.117747i
$892$	−124.786	−	259.120i	−0.139894	−	0.290493i
$893$	327.114	+	1433.18i	0.366309	+	1.60490i
$894$	−338.511	+	1483.12i	−0.378648	+	1.65897i
$895$	−45.7323	−	22.0235i	−0.0510976	−	0.0246073i
$896$	2.36492	−	6.75855i	0.00263942	−	0.00754303i
$897$	184.722	+	293.983i	0.205933	+	0.327741i
$898$			497.835i			0.554381i
$899$	1116.86	+	618.703i	1.24234	+	0.688212i
$900$	−391.492			−0.434991
$901$	1717.52	−	1079.19i	1.90624	−	1.19777i
$902$	224.216	+	78.4564i	0.248576	+	0.0869805i
$903$	16.1665	−	33.5701i	0.0179031	−	0.0371762i
$904$	114.798	+	26.2018i	0.126988	+	0.0289843i
$905$	−138.064	+	31.5123i	−0.152557	+	0.0348202i
$906$	−1432.52	+	689.866i	−1.58115	+	0.761441i
$907$	−5.04374	−	44.7644i	−0.00556090	−	0.0493544i	0.990625	−	0.136607i	$-0.0436198\pi$
$907$	−5.04374	−	44.7644i	−0.00556090	−	0.0493544i	−0.996186	+	0.0872528i	$0.972191\pi$
$908$	254.425	+	202.897i	0.280204	+	0.223455i
$909$	860.433	−	301.079i	0.946571	−	0.331219i
$910$	−0.322132	+	2.85900i	−0.000353991	+	0.00314176i
$911$	−629.031	+	629.031i	−0.690484	+	0.690484i	−0.962338	−	0.271854i	$-0.912363\pi$
$911$	−629.031	+	629.031i	−0.690484	+	0.690484i	0.271854	+	0.962338i	$0.412363\pi$
$912$	−378.623	+	301.942i	−0.415157	+	0.331077i
$913$	181.086	−	288.197i	0.198342	−	0.315659i
$914$	363.913	+	228.661i	0.398154	+	0.250177i
$915$	−49.4320	−	61.9858i	−0.0540240	−	0.0677440i
$916$	−467.990	−	467.990i	−0.510906	−	0.510906i
$917$	−119.203	−	13.4309i	−0.129992	−	0.0146466i
$918$	−51.4016	−	146.897i	−0.0559931	−	0.160019i
$919$	−978.302	+	1226.75i	−1.06453	+	1.33488i	−0.125096	+	0.992145i	$0.539924\pi$
$919$	−978.302	+	1226.75i	−1.06453	+	1.33488i	−0.939433	+	0.342732i	$0.888648\pi$
$920$	−27.0893	+	3.05223i	−0.0294449	+	0.00331764i
$921$	−578.097	−	1200.43i	−0.627684	−	1.30340i
$922$	−152.899	−	669.896i	−0.165835	−	0.726569i
$923$	73.6456	−	322.662i	0.0797894	−	0.349580i
$924$	49.2222	+	23.7042i	0.0532708	+	0.0256539i
$925$	226.142	−	646.277i	0.244478	−	0.698678i
$926$	−452.891	−	720.772i	−0.489083	−	0.778371i
$927$			1021.87i			1.10234i
$928$	27.3200	+	161.758i	0.0294397	+	0.174308i
$929$	−628.319			−0.676339			−0.338170	−	0.941085i	$-0.609808\pi$
$929$	−628.319			−0.676339			−0.338170	+	0.941085i	$0.609808\pi$
$930$	−131.537	+	82.6500i	−0.141437	+	0.0888710i
$931$	1349.09	+	472.069i	1.44908	+	0.507055i
$932$	−304.323	+	631.934i	−0.326527	+	0.678041i
$933$	2229.13	+	508.784i	2.38920	+	0.545320i
$934$	−174.482	+	39.8243i	−0.186811	+	0.0426384i
$935$	145.291	−	69.9686i	0.155392	−	0.0748327i
$936$	13.3470	+	118.458i	0.0142597	+	0.126558i
$937$	−541.116	−	431.526i	−0.577498	−	0.460540i	0.290660	−	0.956826i	$-0.406125\pi$
$937$	−541.116	−	431.526i	−0.577498	−	0.460540i	−0.868159	+	0.496287i	$0.834696\pi$
$938$	−74.7332	+	26.1503i	−0.0796729	+	0.0278787i
$939$	154.232	−	1368.85i	0.164252	−	1.45778i
$940$	−42.8431	+	42.8431i	−0.0455777	+	0.0455777i
$941$	−948.976	+	756.783i	−1.00848	+	0.804233i	−0.980727	−	0.195382i	$-0.937405\pi$
$941$	−948.976	+	756.783i	−1.00848	+	0.804233i	−0.0277487	+	0.999615i	$0.508834\pi$
$942$	503.578	−	801.439i	0.534584	−	0.850785i
$943$	−215.718	−	135.545i	−0.228757	−	0.143738i
$944$	−240.411	−	301.465i	−0.254672	−	0.319349i
$945$	−1.17619	−	1.17619i	−0.00124464	−	0.00124464i
$946$	−210.715	−	23.7419i	−0.222744	−	0.0250972i
$947$	−245.263	−	700.923i	−0.258990	−	0.740151i	−0.997804	−	0.0662410i	$-0.978899\pi$
$947$	−245.263	−	700.923i	−0.258990	−	0.740151i	0.738814	−	0.673910i	$-0.235386\pi$
$948$	−136.893	+	171.659i	−0.144402	+	0.181075i
$949$	428.504	−	48.2808i	0.451532	−	0.0508755i
$950$	−444.521	−	923.058i	−0.467917	−	0.971640i
$951$	−557.658	−	2443.26i	−0.586391	−	2.56915i
$952$	10.1087	−	44.2892i	0.0106184	−	0.0465223i
$953$	−1359.77	−	654.831i	−1.42683	−	0.687126i	−0.448426	−	0.893820i	$-0.648015\pi$
$953$	−1359.77	−	654.831i	−1.42683	−	0.687126i	−0.978406	+	0.206694i	$0.933729\pi$
$954$	296.679	−	847.861i	0.310985	−	0.888743i
$955$	34.3813	+	54.7175i	0.0360013	+	0.0572958i
$956$			168.824i			0.176594i
$957$	−1249.77	+	68.9517i	−1.30592	+	0.0720499i
$958$	643.159			0.671356
$959$	−9.14272	+	5.74475i	−0.00953359	+	0.00599035i
$960$	−18.8400	−	6.59239i	−0.0196250	−	0.00686707i
$961$	424.066	−	880.581i	0.441275	−	0.916318i
$962$	−203.261	−	46.3931i	−0.211290	−	0.0482256i
$963$	−16.3118	+	3.72306i	−0.0169385	+	0.00386611i
$964$	−470.213	+	226.442i	−0.487772	+	0.234899i
$965$	9.95507	+	88.3537i	0.0103161	+	0.0915582i
$966$	−45.8101	−	36.5324i	−0.0474225	−	0.0378182i
$967$	−482.598	+	168.868i	−0.499068	+	0.174631i	−0.568062	−	0.822986i	$-0.692307\pi$
$967$	−482.598	+	168.868i	−0.499068	+	0.174631i	0.0689944	+	0.997617i	$0.478021\pi$
$968$	−3.50702	+	31.1257i	−0.00362295	+	0.0321546i
$969$	−2172.55	+	2172.55i	−2.24205	+	2.24205i
$970$	−6.54920	+	5.22281i	−0.00675175	+	0.00538434i
$971$	138.977	−	221.181i	0.143128	−	0.227787i	−0.767465	−	0.641090i	$-0.778482\pi$
$971$	138.977	−	221.181i	0.143128	−	0.227787i	0.910593	+	0.413304i	$0.135625\pi$
$972$	−556.939	−	349.948i	−0.572983	−	0.360029i
$973$	−72.9910	−	91.5278i	−0.0750165	−	0.0940677i
$974$	−538.134	−	538.134i	−0.552499	−	0.552499i
$975$	−534.431	−	60.2159i	−0.548134	−	0.0617599i
$976$	41.9805	+	119.974i	0.0430129	+	0.122924i
$977$	−584.650	+	733.128i	−0.598414	+	0.750387i	−0.985130	−	0.171812i	$-0.945038\pi$
$977$	−584.650	+	733.128i	−0.598414	+	0.750387i	0.386716	+	0.922199i	$0.373609\pi$
$978$	641.600	−	72.2910i	0.656033	−	0.0739172i
$979$	−512.940	−	1065.13i	−0.523943	−	1.08798i
$980$	13.1088	+	57.4334i	0.0133763	+	0.0586055i
$981$	34.5427	−	151.342i	0.0352118	−	0.154273i
$982$	−312.250	−	150.372i	−0.317974	−	0.153128i
$983$	−36.9543	+	105.609i	−0.0375934	+	0.107436i	−0.961150	−	0.276026i	$-0.910982\pi$
$983$	−36.9543	+	105.609i	−0.0375934	+	0.107436i	0.923557	+	0.383462i	$0.125268\pi$
$984$	−99.2446	−	157.947i	−0.100858	−	0.160515i
$985$		−	32.4980i		−	0.0329929i
$986$	287.143	+	1000.40i	0.291220	+	1.01460i
$987$	−130.229			−0.131944
$988$	−264.145	+	165.973i	−0.267353	+	0.167989i
$989$	214.660	+	75.1127i	0.217047	+	0.0759482i
$990$	30.9849	−	64.3408i	0.0312979	−	0.0649908i
$991$	118.719	+	27.0969i	0.119797	+	0.0273430i	0.281999	−	0.959415i	$-0.409002\pi$
$991$	118.719	+	27.0969i	0.119797	+	0.0273430i	−0.162202	+	0.986758i	$0.551860\pi$
$992$	242.810	−	55.4197i	0.244768	−	0.0558667i
$993$	2355.96	−	1134.57i	2.37257	−	1.14257i
$994$	6.25350	+	55.5014i	0.00629125	+	0.0558364i
$995$	143.001	+	114.039i	0.143720	+	0.114613i
$996$	−252.283	+	88.2776i	−0.253296	+	0.0886321i
$997$	−90.6930	+	804.923i	−0.0909659	+	0.807345i	0.862544	+	0.505983i	$0.168870\pi$
$997$	−90.6930	+	804.923i	−0.0909659	+	0.807345i	−0.953510	+	0.301362i	$0.902559\pi$
$998$	440.651	−	440.651i	0.441534	−	0.441534i
$999$	94.2396	−	75.1536i	0.0943340	−	0.0752288i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.3.f.a.39.2	yes	24
29.3	odd	28	inner	58.3.f.a.3.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.3.f.a.3.2	✓	24	29.3	odd	28	inner
58.3.f.a.39.2	yes	24	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	58.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19745 + 0.752407i) q^{2} +(3.88561 + 1.35964i) q^{3} +(0.867767 - 1.80194i) q^{4} +(0.590885 + 0.134866i) q^{5} +(-5.67582 + 1.29547i) q^{6} +(0.570217 - 0.274602i) q^{7} +(0.316683 + 2.81064i) q^{8} +(6.21291 + 4.95463i) q^{9} +(-0.809028 + 0.283091i) q^{10} +(-1.17390 + 10.4186i) q^{11} +(5.82179 - 5.82179i) q^{12} +(4.14659 - 3.30680i) q^{13} +(-0.476193 + 0.757857i) q^{14} +(2.11258 + 1.32742i) q^{15} +(-2.49396 - 3.12733i) q^{16} +(-17.9446 - 17.9446i) q^{17} +(-11.1675 - 1.25828i) q^{18} +(-9.71346 - 27.7595i) q^{19} +(0.755770 - 0.947706i) q^{20} +(2.58900 - 0.291711i) q^{21} +(-6.43336 - 13.3590i) q^{22} +(3.53861 + 15.5037i) q^{23} +(-2.59094 + 11.3516i) q^{24} +(-22.1933 - 10.6877i) q^{25} +(-2.47727 + 7.07964i) q^{26} +(-2.30711 - 3.67175i) q^{27} -1.26579i q^{28} +(14.0029 + 25.3953i) q^{29} -3.52847 q^{30} +(37.2787 - 23.4237i) q^{31} +(5.33941 + 1.86834i) q^{32} +(-18.7268 + 38.8867i) q^{33} +(34.9895 + 7.98612i) q^{34} +(0.373967 - 0.0853555i) q^{35} +(14.3193 - 6.89581i) q^{36} +(3.11221 + 27.6217i) q^{37} +(32.5178 + 25.9321i) q^{38} +(20.6081 - 7.21108i) q^{39} +(-0.191936 + 1.70348i) q^{40} +(-11.3284 + 11.3284i) q^{41} +(-2.88071 + 2.29729i) q^{42} +(7.60867 - 12.1091i) q^{43} +(17.7550 + 11.1562i) q^{44} +(3.00290 + 3.76552i) q^{45} +(-15.9024 - 15.9024i) q^{46} +(-49.6702 - 5.59649i) q^{47} +(-5.43854 - 15.5425i) q^{48} +(-30.3013 + 37.9966i) q^{49} +(34.6168 - 3.90038i) q^{50} +(-45.3278 - 94.1241i) q^{51} +(-2.36036 - 10.3414i) q^{52} +(-17.7861 + 77.9259i) q^{53} +(5.52530 + 2.66085i) q^{54} +(-2.09875 + 5.99789i) q^{55} +(0.952387 + 1.51571i) q^{56} -121.069i q^{57} +(-35.8753 - 19.8737i) q^{58} +96.3972 q^{59} +(4.22517 - 2.65485i) q^{60} +(-29.9934 - 10.4951i) q^{61} +(-27.0151 + 56.0975i) q^{62} +(4.90326 + 1.11914i) q^{63} +(-7.79942 + 1.78017i) q^{64} +(2.89613 - 1.39470i) q^{65} +(-6.83418 - 60.6550i) q^{66} +(69.1612 + 55.1543i) q^{67} +(-47.9069 + 16.7633i) q^{68} +(-7.32965 + 65.0524i) q^{69} +(-0.383584 + 0.383584i) q^{70} +(48.7878 - 38.9069i) q^{71} +(-11.9582 + 19.0313i) q^{72} +(68.8428 + 43.2568i) q^{73} +(-24.5094 - 30.7339i) q^{74} +(-71.7031 - 71.7031i) q^{75} +(-58.4498 - 6.58572i) q^{76} +(2.19160 + 6.26323i) q^{77} +(-19.2515 + 24.1406i) q^{78} +(-26.4998 + 2.98581i) q^{79} +(-1.05187 - 2.18424i) q^{80} +(-19.8869 - 87.1302i) q^{81} +(5.04160 - 22.0887i) q^{82} +(-29.2488 - 14.0855i) q^{83} +(1.72101 - 4.91836i) q^{84} +(-8.18310 - 13.0233i) q^{85} +20.2249i q^{86} +(19.8814 + 117.715i) q^{87} -29.6548 q^{88} +(-95.4740 + 59.9903i) q^{89} +(-6.42903 - 2.24962i) q^{90} +(1.45640 - 3.02425i) q^{91} +(31.0073 + 7.07721i) q^{92} +(176.698 - 40.3302i) q^{93} +(63.6883 - 30.6707i) q^{94} +(-1.99574 - 17.7127i) q^{95} +(18.2066 + 14.5193i) q^{96} +(9.22461 - 3.22783i) q^{97} +(7.69532 - 68.2978i) q^{98} +(-58.9137 + 58.9137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 4 q^{3} + 28 q^{5} + 34 q^{7} + 8 q^{8} + 4 q^{10} - 44 q^{11} + 8 q^{12} - 36 q^{14} - 90 q^{15} + 16 q^{16} + 32 q^{17} - 16 q^{18} - 56 q^{19} + 36 q^{20} - 168 q^{21} - 84 q^{22} + 68 q^{23}+ \cdots + 132 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 - 4 * q^3 + 28 * q^5 + 34 * q^7 + 8 * q^8 + 4 * q^10 - 44 * q^11 + 8 * q^12 - 36 * q^14 - 90 * q^15 + 16 * q^16 + 32 * q^17 - 16 * q^18 - 56 * q^19 + 36 * q^20 - 168 * q^21 - 84 * q^22 + 68 * q^23 - 40 * q^24 - 84 * q^25 - 96 * q^26 - 28 * q^27 + 144 * q^29 - 40 * q^30 + 106 * q^31 + 16 * q^32 + 98 * q^33 + 84 * q^34 + 196 * q^35 + 80 * q^36 - 262 * q^37 + 280 * q^38 + 458 * q^39 + 8 * q^40 + 116 * q^41 + 308 * q^42 - 212 * q^43 - 24 * q^44 + 14 * q^45 - 16 * q^46 - 238 * q^47 + 16 * q^48 + 188 * q^49 - 196 * q^50 - 462 * q^51 + 32 * q^52 - 126 * q^53 - 56 * q^54 - 96 * q^55 + 72 * q^56 - 24 * q^58 - 48 * q^59 - 180 * q^60 + 268 * q^61 - 56 * q^62 + 28 * q^63 + 376 * q^65 - 108 * q^66 + 490 * q^67 - 64 * q^68 - 328 * q^69 - 72 * q^70 - 14 * q^71 - 88 * q^72 - 552 * q^73 - 188 * q^74 - 356 * q^75 - 420 * q^76 - 186 * q^77 - 316 * q^78 - 358 * q^79 - 20 * q^81 + 288 * q^82 - 448 * q^83 - 140 * q^84 - 420 * q^85 + 606 * q^87 - 48 * q^88 + 314 * q^89 + 308 * q^90 - 182 * q^91 + 112 * q^92 + 1428 * q^93 + 336 * q^94 + 510 * q^95 + 424 * q^97 + 244 * q^98 + 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more