LMFDB - Embedded newform 861.2.i.f.739.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(247,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("861.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			739.7
Character	$\chi$	$=$	861.739
Dual form			861.2.i.f.247.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.220740 + 0.382333i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.902547 - 1.56326i) q^{4} +(1.91947 + 3.32462i) q^{5} -0.441481 q^{6} +(-2.64147 - 0.150533i) q^{7} +1.67988 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.220740 + 0.382333i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.902547 - 1.56326i) q^{4} +(1.91947 + 3.32462i) q^{5} -0.441481 q^{6} +(-2.64147 - 0.150533i) q^{7} +1.67988 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.847410 + 1.46776i) q^{10} +(-1.22781 + 2.12664i) q^{11} +(0.902547 + 1.56326i) q^{12} -6.48554 q^{13} +(-0.525524 - 1.04315i) q^{14} -3.83895 q^{15} +(-1.43428 - 2.48424i) q^{16} +(-2.53649 + 4.39333i) q^{17} +(0.220740 - 0.382333i) q^{18} +(2.49196 + 4.31620i) q^{19} +6.92966 q^{20} +(1.45110 - 2.21231i) q^{21} -1.08411 q^{22} +(1.04972 + 1.81817i) q^{23} +(-0.839938 + 1.45481i) q^{24} +(-4.86875 + 8.43293i) q^{25} +(-1.43162 - 2.47964i) q^{26} +1.00000 q^{27} +(-2.61937 + 3.99343i) q^{28} +2.32836 q^{29} +(-0.847410 - 1.46776i) q^{30} +(1.24773 - 2.16112i) q^{31} +(2.31308 - 4.00637i) q^{32} +(-1.22781 - 2.12664i) q^{33} -2.23962 q^{34} +(-4.56976 - 9.07083i) q^{35} -1.80509 q^{36} +(-4.60573 - 7.97737i) q^{37} +(-1.10015 + 1.90552i) q^{38} +(3.24277 - 5.61664i) q^{39} +(3.22448 + 5.58495i) q^{40} +1.00000 q^{41} +(1.16616 + 0.0664574i) q^{42} +7.53119 q^{43} +(2.21632 + 3.83878i) q^{44} +(1.91947 - 3.32462i) q^{45} +(-0.463433 + 0.802689i) q^{46} +(2.29835 + 3.98086i) q^{47} +2.86856 q^{48} +(6.95468 + 0.795256i) q^{49} -4.29892 q^{50} +(-2.53649 - 4.39333i) q^{51} +(-5.85351 + 10.1386i) q^{52} +(-2.46128 + 4.26306i) q^{53} +(0.220740 + 0.382333i) q^{54} -9.42703 q^{55} +(-4.43733 - 0.252877i) q^{56} -4.98391 q^{57} +(0.513962 + 0.890209i) q^{58} +(-3.84738 + 6.66386i) q^{59} +(-3.46483 + 6.00126i) q^{60} +(5.66875 + 9.81857i) q^{61} +1.10169 q^{62} +(1.19037 + 2.36284i) q^{63} -3.69475 q^{64} +(-12.4488 - 21.5620i) q^{65} +(0.542056 - 0.938869i) q^{66} +(-0.242801 + 0.420543i) q^{67} +(4.57861 + 7.93038i) q^{68} -2.09945 q^{69} +(2.45935 - 3.74947i) q^{70} -1.75931 q^{71} +(-0.839938 - 1.45481i) q^{72} +(-4.83324 + 8.37142i) q^{73} +(2.03334 - 3.52185i) q^{74} +(-4.86875 - 8.43293i) q^{75} +8.99644 q^{76} +(3.56336 - 5.43261i) q^{77} +2.86324 q^{78} +(-0.0360553 - 0.0624496i) q^{79} +(5.50612 - 9.53688i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.220740 + 0.382333i) q^{82} +7.72291 q^{83} +(-2.14873 - 4.26516i) q^{84} -19.4749 q^{85} +(1.66244 + 2.87942i) q^{86} +(-1.16418 + 2.01642i) q^{87} +(-2.06258 + 3.57249i) q^{88} +(-5.03404 - 8.71920i) q^{89} +1.69482 q^{90} +(17.1313 + 0.976288i) q^{91} +3.78970 q^{92} +(1.24773 + 2.16112i) q^{93} +(-1.01468 + 1.75747i) q^{94} +(-9.56649 + 16.5696i) q^{95} +(2.31308 + 4.00637i) q^{96} +0.164606 q^{97} +(1.23113 + 2.83455i) q^{98} +2.45563 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 4 q^{2} - 13 q^{3} - 12 q^{4} + 8 q^{5} - 8 q^{6} + 5 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) $ 26 * q + 4 * q^2 - 13 * q^3 - 12 * q^4 + 8 * q^5 - 8 * q^6 + 5 * q^7 - 24 * q^8 - 13 * q^9	\( 26 q + 4 q^{2} - 13 q^{3} - 12 q^{4} + 8 q^{5} - 8 q^{6} + 5 q^{7} - 24 q^{8} - 13 q^{9} + q^{10} + 10 q^{11} - 12 q^{12} - 32 q^{13} - 18 q^{14} - 16 q^{15} - 26 q^{16} + 12 q^{17} + 4 q^{18} + 11 q^{19} - 12 q^{20} - 4 q^{21} + 2 q^{22} + 15 q^{23} + 12 q^{24} - 15 q^{25} + 18 q^{26} + 26 q^{27} - 55 q^{28} - 16 q^{29} + q^{30} + 9 q^{31} + 23 q^{32} + 10 q^{33} + 14 q^{34} - 10 q^{35} + 24 q^{36} + 2 q^{37} + 20 q^{38} + 16 q^{39} + 49 q^{40} + 26 q^{41} + 12 q^{42} - 14 q^{43} + 22 q^{44} + 8 q^{45} + 4 q^{46} + 26 q^{47} + 52 q^{48} - 7 q^{49} - 30 q^{50} + 12 q^{51} + 24 q^{52} - 4 q^{53} + 4 q^{54} - 2 q^{55} + 9 q^{56} - 22 q^{57} - 39 q^{58} - 3 q^{59} + 6 q^{60} + 28 q^{61} - 14 q^{62} - q^{63} + 4 q^{64} + 20 q^{65} - q^{66} - 7 q^{67} + 55 q^{68} - 30 q^{69} + 8 q^{70} - 80 q^{71} + 12 q^{72} - 2 q^{73} - q^{74} - 15 q^{75} + 52 q^{76} + 28 q^{77} - 36 q^{78} - 13 q^{79} + 22 q^{80} - 13 q^{81} + 4 q^{82} - 28 q^{83} + 11 q^{84} + 96 q^{85} + 49 q^{86} + 8 q^{87} - 20 q^{88} + 35 q^{89} - 2 q^{90} + 4 q^{91} - 210 q^{92} + 9 q^{93} - 2 q^{94} - 7 q^{95} + 23 q^{96} - 128 q^{97} - 17 q^{98} - 20 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 - 13 * q^3 - 12 * q^4 + 8 * q^5 - 8 * q^6 + 5 * q^7 - 24 * q^8 - 13 * q^9 + q^10 + 10 * q^11 - 12 * q^12 - 32 * q^13 - 18 * q^14 - 16 * q^15 - 26 * q^16 + 12 * q^17 + 4 * q^18 + 11 * q^19 - 12 * q^20 - 4 * q^21 + 2 * q^22 + 15 * q^23 + 12 * q^24 - 15 * q^25 + 18 * q^26 + 26 * q^27 - 55 * q^28 - 16 * q^29 + q^30 + 9 * q^31 + 23 * q^32 + 10 * q^33 + 14 * q^34 - 10 * q^35 + 24 * q^36 + 2 * q^37 + 20 * q^38 + 16 * q^39 + 49 * q^40 + 26 * q^41 + 12 * q^42 - 14 * q^43 + 22 * q^44 + 8 * q^45 + 4 * q^46 + 26 * q^47 + 52 * q^48 - 7 * q^49 - 30 * q^50 + 12 * q^51 + 24 * q^52 - 4 * q^53 + 4 * q^54 - 2 * q^55 + 9 * q^56 - 22 * q^57 - 39 * q^58 - 3 * q^59 + 6 * q^60 + 28 * q^61 - 14 * q^62 - q^63 + 4 * q^64 + 20 * q^65 - q^66 - 7 * q^67 + 55 * q^68 - 30 * q^69 + 8 * q^70 - 80 * q^71 + 12 * q^72 - 2 * q^73 - q^74 - 15 * q^75 + 52 * q^76 + 28 * q^77 - 36 * q^78 - 13 * q^79 + 22 * q^80 - 13 * q^81 + 4 * q^82 - 28 * q^83 + 11 * q^84 + 96 * q^85 + 49 * q^86 + 8 * q^87 - 20 * q^88 + 35 * q^89 - 2 * q^90 + 4 * q^91 - 210 * q^92 + 9 * q^93 - 2 * q^94 - 7 * q^95 + 23 * q^96 - 128 * q^97 - 17 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.220740	+	0.382333i	0.156087	+	0.270351i	0.933454	−	0.358696i	$-0.116779\pi$
$2$	0.220740	+	0.382333i	0.156087	+	0.270351i	−0.777367	+	0.629047i	$0.783445\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.902547	−	1.56326i	0.451274	−	0.781629i
$5$	1.91947	+	3.32462i	0.858414	+	1.48682i	0.873441	+	0.486930i	$0.161883\pi$
$5$	1.91947	+	3.32462i	0.858414	+	1.48682i	−0.0150265	+	0.999887i	$0.504783\pi$
$6$	−0.441481			−0.180234
$7$	−2.64147	−	0.150533i	−0.998380	−	0.0568961i
$7$	−2.64147	−	0.150533i	−0.998380	−	0.0568961i
$8$	1.67988			0.593926
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.847410	+	1.46776i	−0.267975	+	0.464146i
$11$	−1.22781	+	2.12664i	−0.370200	+	0.641205i	−0.989596	−	0.143873i	$-0.954044\pi$
$11$	−1.22781	+	2.12664i	−0.370200	+	0.641205i	0.619396	+	0.785079i	$0.287378\pi$
$12$	0.902547	+	1.56326i	0.260543	+	0.451274i
$13$	−6.48554			−1.79877			−0.899383	−	0.437162i	$-0.855984\pi$
$13$	−6.48554			−1.79877			−0.899383	+	0.437162i	$0.855984\pi$
$14$	−0.525524	−	1.04315i	−0.140452	−	0.278793i
$15$	−3.83895			−0.991212
$16$	−1.43428	−	2.48424i	−0.358570	−	0.621061i
$17$	−2.53649	+	4.39333i	−0.615189	+	1.06554i	0.375162	+	0.926959i	$0.377587\pi$
$17$	−2.53649	+	4.39333i	−0.615189	+	1.06554i	−0.990351	+	0.138580i	$0.955746\pi$
$18$	0.220740	−	0.382333i	0.0520290	−	0.0901168i
$19$	2.49196	+	4.31620i	0.571694	+	0.990203i	0.996392	+	0.0848681i	$0.0270469\pi$
$19$	2.49196	+	4.31620i	0.571694	+	0.990203i	−0.424698	+	0.905335i	$0.639620\pi$
$20$	6.92966			1.54952
$21$	1.45110	−	2.21231i	0.316656	−	0.482766i
$22$	−1.08411			−0.231134
$23$	1.04972	+	1.81817i	0.218882	+	0.379116i	0.954467	−	0.298318i	$-0.0964255\pi$
$23$	1.04972	+	1.81817i	0.218882	+	0.379116i	−0.735584	+	0.677433i	$0.763092\pi$
$24$	−0.839938	+	1.45481i	−0.171452	+	0.296963i
$25$	−4.86875	+	8.43293i	−0.973751	+	1.68659i
$26$	−1.43162	−	2.47964i	−0.280764	−	0.486297i
$27$	1.00000			0.192450
$28$	−2.61937	+	3.99343i	−0.495014	+	0.754687i
$29$	2.32836			0.432365			0.216183	−	0.976353i	$-0.430639\pi$
$29$	2.32836			0.432365			0.216183	+	0.976353i	$0.430639\pi$
$30$	−0.847410	−	1.46776i	−0.154715	−	0.267975i
$31$	1.24773	−	2.16112i	0.224098	−	0.388149i	−0.731950	−	0.681358i	$-0.761390\pi$
$31$	1.24773	−	2.16112i	0.224098	−	0.388149i	0.956048	+	0.293209i	$0.0947231\pi$
$32$	2.31308	−	4.00637i	0.408899	−	0.708234i
$33$	−1.22781	−	2.12664i	−0.213735	−	0.370200i
$34$	−2.23962			−0.384092
$35$	−4.56976	−	9.07083i	−0.772430	−	1.53325i
$36$	−1.80509			−0.300849
$37$	−4.60573	−	7.97737i	−0.757178	−	1.31147i	−0.944284	−	0.329131i	$-0.893244\pi$
$37$	−4.60573	−	7.97737i	−0.757178	−	1.31147i	0.187106	−	0.982340i	$-0.440089\pi$
$38$	−1.10015	+	1.90552i	−0.178468	+	0.309116i
$39$	3.24277	−	5.61664i	0.519259	−	0.899383i
$40$	3.22448	+	5.58495i	0.509834	+	0.883059i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	1.16616	+	0.0664574i	0.179942	+	0.0102546i
$43$	7.53119			1.14850			0.574248	−	0.818682i	$-0.305295\pi$
$43$	7.53119			1.14850			0.574248	+	0.818682i	$0.305295\pi$
$44$	2.21632	+	3.83878i	0.334123	+	0.578718i
$45$	1.91947	−	3.32462i	0.286138	−	0.495606i
$46$	−0.463433	+	0.802689i	−0.0683294	+	0.118350i
$47$	2.29835	+	3.98086i	0.335249	+	0.580668i	0.983533	−	0.180731i	$-0.0578464\pi$
$47$	2.29835	+	3.98086i	0.335249	+	0.580668i	−0.648284	+	0.761399i	$0.724513\pi$
$48$	2.86856			0.414041
$49$	6.95468	+	0.795256i	0.993526	+	0.113608i
$50$	−4.29892			−0.607959
$51$	−2.53649	−	4.39333i	−0.355180	−	0.615189i
$52$	−5.85351	+	10.1386i	−0.811736	+	1.40597i
$53$	−2.46128	+	4.26306i	−0.338083	+	0.585576i	−0.984072	−	0.177770i	$-0.943112\pi$
$53$	−2.46128	+	4.26306i	−0.338083	+	0.585576i	0.645989	+	0.763346i	$0.276445\pi$
$54$	0.220740	+	0.382333i	0.0300389	+	0.0520290i
$55$	−9.42703			−1.27114
$56$	−4.43733	−	0.252877i	−0.592964	−	0.0337921i
$57$	−4.98391			−0.660135
$58$	0.513962	+	0.890209i	0.0674866	+	0.116890i
$59$	−3.84738	+	6.66386i	−0.500886	+	0.867561i	0.499113	+	0.866537i	$0.333659\pi$
$59$	−3.84738	+	6.66386i	−0.500886	+	0.867561i	−0.999999	+	0.00102383i	$0.999674\pi$
$60$	−3.46483	+	6.00126i	−0.447308	+	0.774760i
$61$	5.66875	+	9.81857i	0.725809	+	1.25714i	0.958640	+	0.284621i	$0.0918679\pi$
$61$	5.66875	+	9.81857i	0.725809	+	1.25714i	−0.232831	+	0.972517i	$0.574799\pi$
$62$	1.10169			0.139915
$63$	1.19037	+	2.36284i	0.149972	+	0.297690i
$64$	−3.69475			−0.461844
$65$	−12.4488	−	21.5620i	−1.54409	−	2.67444i
$66$	0.542056	−	0.938869i	0.0667225	−	0.115567i
$67$	−0.242801	+	0.420543i	−0.0296628	+	0.0513775i	−0.880476	−	0.474091i	$-0.842777\pi$
$67$	−0.242801	+	0.420543i	−0.0296628	+	0.0513775i	0.850813	+	0.525469i	$0.176110\pi$
$68$	4.57861	+	7.93038i	0.555238	+	0.961700i
$69$	−2.09945			−0.252744
$70$	2.45935	−	3.74947i	0.293949	−	0.448147i
$71$	−1.75931			−0.208792			−0.104396	−	0.994536i	$-0.533291\pi$
$71$	−1.75931			−0.208792			−0.104396	+	0.994536i	$0.533291\pi$
$72$	−0.839938	−	1.45481i	−0.0989876	−	0.171452i
$73$	−4.83324	+	8.37142i	−0.565688	+	0.979800i	0.431297	+	0.902210i	$0.358056\pi$
$73$	−4.83324	+	8.37142i	−0.565688	+	0.979800i	−0.996985	+	0.0775905i	$0.975277\pi$
$74$	2.03334	−	3.52185i	0.236371	−	0.409407i
$75$	−4.86875	−	8.43293i	−0.562195	−	0.973751i
$76$	8.99644			1.03196
$77$	3.56336	−	5.43261i	0.406082	−	0.619104i
$78$	2.86324			0.324198
$79$	−0.0360553	−	0.0624496i	−0.00405654	−	0.00702613i	0.863990	−	0.503509i	$-0.167958\pi$
$79$	−0.0360553	−	0.0624496i	−0.00405654	−	0.00702613i	−0.868047	+	0.496483i	$0.834625\pi$
$80$	5.50612	−	9.53688i	0.615603	−	1.06626i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.220740	+	0.382333i	0.0243767	+	0.0422217i
$83$	7.72291			0.847699			0.423849	−	0.905733i	$-0.360679\pi$
$83$	7.72291			0.847699			0.423849	+	0.905733i	$0.360679\pi$
$84$	−2.14873	−	4.26516i	−0.234445	−	0.465367i
$85$	−19.4749			−2.11235
$86$	1.66244	+	2.87942i	0.179265	+	0.310496i
$87$	−1.16418	+	2.01642i	−0.124813	+	0.216183i
$88$	−2.06258	+	3.57249i	−0.219871	+	0.380828i
$89$	−5.03404	−	8.71920i	−0.533607	−	0.924234i	−0.999229	−	0.0392506i	$-0.987503\pi$
$89$	−5.03404	−	8.71920i	−0.533607	−	0.924234i	0.465623	−	0.884983i	$-0.345830\pi$
$90$	1.69482			0.178650
$91$	17.1313	+	0.976288i	1.79585	+	0.102343i
$92$	3.78970			0.395104
$93$	1.24773	+	2.16112i	0.129383	+	0.224098i
$94$	−1.01468	+	1.75747i	−0.104656	+	0.181269i
$95$	−9.56649	+	16.5696i	−0.981501	+	1.70001i
$96$	2.31308	+	4.00637i	0.236078	+	0.408899i
$97$	0.164606			0.0167132			0.00835661	−	0.999965i	$-0.497340\pi$
$97$	0.164606			0.0167132			0.00835661	+	0.999965i	$0.497340\pi$
$98$	1.23113	+	2.83455i	0.124362	+	0.286333i
$99$	2.45563			0.246800
$100$	8.78856	+	15.2222i	0.878856	+	1.52222i
$101$	9.00196	−	15.5919i	0.895729	−	1.55145i	0.0628286	−	0.998024i	$-0.479988\pi$
$101$	9.00196	−	15.5919i	0.895729	−	1.55145i	0.832900	−	0.553423i	$-0.186679\pi$
$102$	1.11981	−	1.93957i	0.110878	−	0.192046i
$103$	−3.66830	−	6.35367i	−0.361448	−	0.626046i	0.626751	−	0.779219i	$-0.284384\pi$
$103$	−3.66830	−	6.35367i	−0.361448	−	0.626046i	−0.988199	+	0.153173i	$0.951051\pi$
$104$	−10.8949			−1.06833
$105$	10.1404	+	0.577888i	0.989606	+	0.0563961i
$106$	−2.17321			−0.211081
$107$	2.36888	+	4.10302i	0.229008	+	0.396654i	0.957515	−	0.288385i	$-0.0931183\pi$
$107$	2.36888	+	4.10302i	0.229008	+	0.396654i	−0.728506	+	0.685039i	$0.759785\pi$
$108$	0.902547	−	1.56326i	0.0868477	−	0.150425i
$109$	6.06366	−	10.5026i	0.580793	−	1.00596i	−0.414592	−	0.910007i	$-0.636076\pi$
$109$	6.06366	−	10.5026i	0.580793	−	1.00596i	0.995386	−	0.0959564i	$-0.0305909\pi$
$110$	−2.08092	−	3.60427i	−0.198408	−	0.343653i
$111$	9.21147			0.874314
$112$	3.41464	+	6.77795i	0.322653	+	0.640456i
$113$	−17.0681			−1.60563			−0.802816	−	0.596227i	$-0.796666\pi$
$113$	−17.0681			−1.60563			−0.802816	+	0.596227i	$0.796666\pi$
$114$	−1.10015	−	1.90552i	−0.103039	−	0.178468i
$115$	−4.02983	+	6.97987i	−0.375784	+	0.650877i
$116$	2.10145	−	3.63982i	0.195115	−	0.337949i
$117$	3.24277	+	5.61664i	0.299794	+	0.519259i
$118$	−3.39709			−0.312727
$119$	7.36140	−	11.2230i	0.674818	−	1.02881i
$120$	−6.44895			−0.588706
$121$	2.48494	+	4.30405i	0.225904	+	0.391277i
$122$	−2.50264	+	4.33471i	−0.226579	+	0.392446i
$123$	−0.500000	+	0.866025i	−0.0450835	+	0.0780869i
$124$	−2.25226	−	3.90103i	−0.202259	−	0.350323i
$125$	−18.1870			−1.62670
$126$	−0.640632	+	0.976692i	−0.0570720	+	0.0870106i
$127$	16.8227			1.49277			0.746386	−	0.665513i	$-0.231787\pi$
$127$	16.8227			1.49277			0.746386	+	0.665513i	$0.231787\pi$
$128$	−5.44174	−	9.42538i	−0.480987	−	0.833094i
$129$	−3.76559	+	6.52220i	−0.331542	+	0.574248i
$130$	5.49591	−	9.51920i	0.482023	−	0.834889i
$131$	4.97030	+	8.60880i	0.434257	+	0.752155i	0.997235	−	0.0743172i	$-0.0236777\pi$
$131$	4.97030	+	8.60880i	0.434257	+	0.752155i	−0.562978	+	0.826472i	$0.690344\pi$
$132$	−4.43264			−0.385812
$133$	−5.93269	−	11.7762i	−0.514429	−	1.02113i
$134$	−0.214383			−0.0185199
$135$	1.91947	+	3.32462i	0.165202	+	0.286138i
$136$	−4.26099	+	7.38025i	−0.365377	+	0.632851i
$137$	−4.42149	+	7.65824i	−0.377753	+	0.654288i	−0.990735	−	0.135809i	$-0.956637\pi$
$137$	−4.42149	+	7.65824i	−0.377753	+	0.654288i	0.612982	+	0.790097i	$0.289970\pi$
$138$	−0.463433	−	0.802689i	−0.0394500	−	0.0683294i
$139$	8.03584			0.681591			0.340795	−	0.940137i	$-0.389304\pi$
$139$	8.03584			0.681591			0.340795	+	0.940137i	$0.389304\pi$
$140$	−18.3045	−	1.04314i	−1.54701	−	0.0881617i
$141$	−4.59670			−0.387112
$142$	−0.388351	−	0.672643i	−0.0325897	−	0.0564470i
$143$	7.96304	−	13.7924i	0.665903	−	1.15338i
$144$	−1.43428	+	2.48424i	−0.119523	+	0.207020i
$145$	4.46922	+	7.74092i	0.371149	+	0.642848i
$146$	−4.26756			−0.353186
$147$	−4.16605	+	5.62530i	−0.343610	+	0.463967i
$148$	−16.6276			−1.36678
$149$	8.13081	+	14.0830i	0.666102	+	1.15372i	0.978985	+	0.203931i	$0.0653719\pi$
$149$	8.13081	+	14.0830i	0.666102	+	1.15372i	−0.312883	+	0.949792i	$0.601295\pi$
$150$	2.14946	−	3.72297i	0.175503	−	0.303979i
$151$	10.2768	−	17.7999i	0.836313	−	1.44854i	−0.0566447	−	0.998394i	$-0.518040\pi$
$151$	10.2768	−	17.7999i	0.836313	−	1.44854i	0.892957	−	0.450141i	$-0.148626\pi$
$152$	4.18618	+	7.25067i	0.339544	+	0.588107i
$153$	5.07298			0.410126
$154$	2.86365	+	0.163195i	0.230759	+	0.0131506i
$155$	9.57990			0.769476
$156$	−5.85351	−	10.1386i	−0.468656	−	0.811736i
$157$	4.23147	−	7.32912i	0.337708	−	0.584927i	−0.646293	−	0.763089i	$-0.723682\pi$
$157$	4.23147	−	7.32912i	0.337708	−	0.584927i	0.984001	+	0.178162i	$0.0570151\pi$
$158$	0.0159177	−	0.0275703i	0.00126634	−	0.00219337i
$159$	−2.46128	−	4.26306i	−0.195192	−	0.338083i
$160$	17.7596			1.40402
$161$	−2.49911	−	4.96066i	−0.196958	−	0.390955i
$162$	−0.441481			−0.0346860
$163$	5.25382	+	9.09988i	0.411511	+	0.712758i	0.995055	−	0.0993236i	$-0.0316679\pi$
$163$	5.25382	+	9.09988i	0.411511	+	0.712758i	−0.583544	+	0.812081i	$0.698335\pi$
$164$	0.902547	−	1.56326i	0.0704771	−	0.122070i
$165$	4.71351	−	8.16405i	0.366947	−	0.635570i
$166$	1.70476	+	2.95272i	0.132315	+	0.229176i
$167$	19.6572			1.52112			0.760561	−	0.649266i	$-0.224924\pi$
$167$	19.6572			1.52112			0.760561	+	0.649266i	$0.224924\pi$
$168$	2.43766	−	3.71640i	0.188070	−	0.286727i
$169$	29.0622			2.23556
$170$	−4.29890	−	7.44591i	−0.329710	−	0.571075i
$171$	2.49196	−	4.31620i	0.190565	−	0.330068i
$172$	6.79725	−	11.7732i	0.518286	−	0.897697i
$173$	−7.05505	−	12.2197i	−0.536385	−	0.929046i	−0.999095	−	0.0425366i	$-0.986456\pi$
$173$	−7.05505	−	12.2197i	−0.536385	−	0.929046i	0.462710	−	0.886510i	$-0.346877\pi$
$174$	−1.02792			−0.0779268
$175$	14.1301	−	21.5424i	1.06813	−	1.62845i
$176$	7.04411			0.530970
$177$	−3.84738	−	6.66386i	−0.289187	−	0.500886i
$178$	2.22243	−	3.84936i	0.166578	−	0.288522i
$179$	4.25763	−	7.37443i	0.318230	−	0.551191i	−0.661889	−	0.749602i	$-0.730245\pi$
$179$	4.25763	−	7.37443i	0.318230	−	0.551191i	0.980119	+	0.198411i	$0.0635782\pi$
$180$	−3.46483	−	6.00126i	−0.258253	−	0.447308i
$181$	−19.7965			−1.47146			−0.735731	−	0.677274i	$-0.763161\pi$
$181$	−19.7965			−1.47146			−0.735731	+	0.677274i	$0.763161\pi$
$182$	3.40831	+	6.76539i	0.252641	+	0.501484i
$183$	−11.3375			−0.838093
$184$	1.76340	+	3.05431i	0.130000	+	0.225166i
$185$	17.6812	−	30.6247i	1.29995	−	2.25157i
$186$	−0.550846	+	0.954094i	−0.0403900	+	0.0699576i
$187$	−6.22868	−	10.7884i	−0.455486	−	0.788926i
$188$	8.29747			0.605156
$189$	−2.64147	−	0.150533i	−0.192138	−	0.0109497i
$190$	−8.44683			−0.612798
$191$	4.71686	+	8.16984i	0.341300	+	0.591149i	0.984674	−	0.174403i	$-0.0557995\pi$
$191$	4.71686	+	8.16984i	0.341300	+	0.591149i	−0.643375	+	0.765552i	$0.722466\pi$
$192$	1.84738	−	3.19975i	0.133323	−	0.230922i
$193$	−10.4033	+	18.0191i	−0.748846	+	1.29704i	0.199530	+	0.979892i	$0.436059\pi$
$193$	−10.4033	+	18.0191i	−0.748846	+	1.29704i	−0.948376	+	0.317148i	$0.897275\pi$
$194$	0.0363352	+	0.0629344i	0.00260871	+	0.00451843i
$195$	24.8976			1.78296
$196$	7.52012	−	10.1542i	0.537151	−	0.725300i
$197$	−8.77318			−0.625063			−0.312532	−	0.949907i	$-0.601177\pi$
$197$	−8.77318			−0.625063			−0.312532	+	0.949907i	$0.601177\pi$
$198$	0.542056	+	0.938869i	0.0385223	+	0.0667225i
$199$	−11.6230	+	20.1317i	−0.823935	+	1.42710i	0.0787951	+	0.996891i	$0.474893\pi$
$199$	−11.6230	+	20.1317i	−0.823935	+	1.42710i	−0.902730	+	0.430207i	$0.858441\pi$
$200$	−8.17890	+	14.1663i	−0.578335	+	1.00171i
$201$	−0.242801	−	0.420543i	−0.0171258	−	0.0296628i
$202$	7.94838			0.559246
$203$	−6.15028	−	0.350495i	−0.431665	−	0.0245999i
$204$	−9.15721			−0.641133
$205$	1.91947	+	3.32462i	0.134062	+	0.232202i
$206$	1.61948	−	2.80502i	0.112835	−	0.195435i
$207$	1.04972	−	1.81817i	0.0729608	−	0.126372i
$208$	9.30207	+	16.1117i	0.644983	+	1.11714i
$209$	−12.2386			−0.846565
$210$	2.01746	+	4.00459i	0.139218	+	0.276343i
$211$	0.435591			0.0299873			0.0149937	−	0.999888i	$-0.495227\pi$
$211$	0.435591			0.0299873			0.0149937	+	0.999888i	$0.495227\pi$
$212$	4.44284	+	7.69523i	0.305136	+	0.528510i
$213$	0.879656	−	1.52361i	0.0602730	−	0.104396i
$214$	−1.04581	+	1.81140i	−0.0714904	+	0.123825i
$215$	14.4559	+	25.0384i	0.985885	+	1.70760i
$216$	1.67988			0.114301
$217$	−3.62114	+	5.52071i	−0.245819	+	0.374770i
$218$	5.35398			0.362617
$219$	−4.83324	−	8.37142i	−0.326600	−	0.565688i
$220$	−8.50834	+	14.7369i	−0.573632	+	0.993560i
$221$	16.4505	−	28.4931i	1.10658	−	1.91666i
$222$	2.03334	+	3.52185i	0.136469	+	0.236371i
$223$	2.80695			0.187967			0.0939836	−	0.995574i	$-0.470040\pi$
$223$	2.80695			0.187967			0.0939836	+	0.995574i	$0.470040\pi$
$224$	−6.71302	+	10.2345i	−0.448532	+	0.683822i
$225$	9.73751			0.649167
$226$	−3.76762	−	6.52570i	−0.250618	−	0.434083i
$227$	6.10066	−	10.5666i	0.404915	−	0.701333i	−0.589397	−	0.807844i	$-0.700635\pi$
$227$	6.10066	−	10.5666i	0.404915	−	0.701333i	0.994312	+	0.106511i	$0.0339679\pi$
$228$	−4.49822	+	7.79114i	−0.297902	+	0.515981i
$229$	−6.72140	−	11.6418i	−0.444163	−	0.769312i	0.553831	−	0.832629i	$-0.313165\pi$
$229$	−6.72140	−	11.6418i	−0.444163	−	0.769312i	−0.997993	+	0.0633168i	$0.979832\pi$
$230$	−3.55818			−0.234620
$231$	2.92310	+	5.80227i	0.192326	+	0.381761i
$232$	3.91135			0.256793
$233$	6.09980	+	10.5652i	0.399611	+	0.692147i	0.993678	−	0.112269i	$-0.0358118\pi$
$233$	6.09980	+	10.5652i	0.399611	+	0.692147i	−0.594067	+	0.804416i	$0.702478\pi$
$234$	−1.43162	+	2.47964i	−0.0935879	+	0.162099i
$235$	−8.82324	+	15.2823i	−0.575564	+	0.996907i
$236$	6.94489	+	12.0289i	0.452074	+	0.783015i
$237$	0.0721106			0.00468409
$238$	5.91589	+	0.337137i	0.383470	+	0.0218534i
$239$	1.85661			0.120094			0.0600470	−	0.998196i	$-0.480875\pi$
$239$	1.85661			0.120094			0.0600470	+	0.998196i	$0.480875\pi$
$240$	5.50612	+	9.53688i	0.355418	+	0.615603i
$241$	1.41597	−	2.45253i	0.0912105	−	0.157981i	−0.816810	−	0.576906i	$-0.804260\pi$
$241$	1.41597	−	2.45253i	0.0912105	−	0.157981i	0.908021	+	0.418925i	$0.137593\pi$
$242$	−1.09705	+	1.90015i	−0.0705213	+	0.122146i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	20.4653			1.31015
$245$	10.7054	+	24.6482i	0.683942	+	1.57471i
$246$	−0.441481			−0.0281478
$247$	−16.1617	−	27.9929i	−1.02834	−	1.78114i
$248$	2.09602	−	3.63042i	0.133098	−	0.230532i
$249$	−3.86145	+	6.68823i	−0.244710	+	0.423849i
$250$	−4.01461	−	6.95351i	−0.253906	−	0.439778i
$251$	0.705533			0.0445328			0.0222664	−	0.999752i	$-0.492912\pi$
$251$	0.705533			0.0445328			0.0222664	+	0.999752i	$0.492912\pi$
$252$	4.76810	+	0.271726i	0.300362	+	0.0171172i
$253$	−5.15546			−0.324121
$254$	3.71344	+	6.43188i	0.233002	+	0.403572i
$255$	9.73745	−	16.8658i	0.609783	−	1.05617i
$256$	−1.29233	+	2.23838i	−0.0807707	+	0.139899i
$257$	14.8279	+	25.6827i	0.924939	+	1.60204i	0.791659	+	0.610963i	$0.209218\pi$
$257$	14.8279	+	25.6827i	0.924939	+	1.60204i	0.133280	+	0.991078i	$0.457449\pi$
$258$	−3.32487			−0.206998
$259$	10.9650	+	21.7653i	0.681334	+	1.35243i
$260$	−44.9426			−2.78722
$261$	−1.16418	−	2.01642i	−0.0720609	−	0.124813i
$262$	−2.19429	+	3.80062i	−0.135564	+	0.234803i
$263$	10.9138	−	18.9033i	0.672975	−	1.16563i	−0.304082	−	0.952646i	$-0.598350\pi$
$263$	10.9138	−	18.9033i	0.672975	−	1.16563i	0.977056	−	0.212981i	$-0.0683171\pi$
$264$	−2.06258	−	3.57249i	−0.126943	−	0.219871i
$265$	−18.8974			−1.16086
$266$	3.19285	−	4.86775i	0.195766	−	0.298461i
$267$	10.0681			0.616156
$268$	0.438278	+	0.759120i	0.0267721	+	0.0463706i
$269$	13.8188	−	23.9349i	0.842548	−	1.45934i	−0.0451853	−	0.998979i	$-0.514388\pi$
$269$	13.8188	−	23.9349i	0.842548	−	1.45934i	0.887734	−	0.460358i	$-0.152279\pi$
$270$	−0.847410	+	1.46776i	−0.0515717	+	0.0893248i
$271$	9.79996	+	16.9740i	0.595305	+	1.03110i	0.993504	+	0.113799i	$0.0363021\pi$
$271$	9.79996	+	16.9740i	0.595305	+	1.03110i	−0.398199	+	0.917299i	$0.630365\pi$
$272$	14.5521			0.882353
$273$	−9.41116	+	14.3480i	−0.569589	+	0.868382i
$274$	−3.90400			−0.235849
$275$	−11.9559	−	20.7081i	−0.720965	−	1.24875i
$276$	−1.89485	+	3.28198i	−0.114057	+	0.197552i
$277$	−9.91489	+	17.1731i	−0.595728	+	1.03183i	0.397716	+	0.917509i	$0.369803\pi$
$277$	−9.91489	+	17.1731i	−0.595728	+	1.03183i	−0.993444	+	0.114323i	$0.963530\pi$
$278$	1.77383	+	3.07237i	0.106387	+	0.184268i
$279$	−2.49545			−0.149399
$280$	−7.67662	−	15.2379i	−0.458766	−	0.910636i
$281$	9.72421			0.580098			0.290049	−	0.957012i	$-0.406328\pi$
$281$	9.72421			0.580098			0.290049	+	0.957012i	$0.406328\pi$
$282$	−1.01468	−	1.75747i	−0.0604231	−	0.104656i
$283$	7.53792	−	13.0561i	0.448083	−	0.776102i	−0.550178	−	0.835047i	$-0.685440\pi$
$283$	7.53792	−	13.0561i	0.448083	−	0.776102i	0.998261	+	0.0589450i	$0.0187737\pi$
$284$	−1.58786	+	2.75026i	−0.0942223	+	0.163198i
$285$	−9.56649	−	16.5696i	−0.566670	−	0.981501i
$286$	7.03106			0.415755
$287$	−2.64147	−	0.150533i	−0.155921	−	0.00888569i
$288$	−4.62616			−0.272599
$289$	−4.36757	−	7.56486i	−0.256916	−	0.444992i
$290$	−1.97307	+	3.41746i	−0.115863	+	0.200680i
$291$	−0.0823030	+	0.142553i	−0.00482469	+	0.00835661i
$292$	8.72446	+	15.1112i	0.510560	+	0.884316i
$293$	−17.7092			−1.03458			−0.517290	−	0.855810i	$-0.673059\pi$
$293$	−17.7092			−1.03458			−0.517290	+	0.855810i	$0.673059\pi$
$294$	−3.07036	−	0.351090i	−0.179067	−	0.0204760i
$295$	−29.5398			−1.71987
$296$	−7.73706	−	13.4010i	−0.449707	−	0.778916i
$297$	−1.22781	+	2.12664i	−0.0712450	+	0.123400i
$298$	−3.58960	+	6.21736i	−0.207940	+	0.360162i
$299$	−6.80802	−	11.7918i	−0.393718	−	0.681940i
$300$	−17.5771			−1.01482
$301$	−19.8934	−	1.13369i	−1.14663	−	0.0653450i
$302$	9.07400			0.522150
$303$	9.00196	+	15.5919i	0.517149	+	0.895729i
$304$	7.14832	−	12.3813i	0.409984	−	0.710114i
$305$	−21.7620	+	37.6930i	−1.24609	+	2.15829i
$306$	1.11981	+	1.93957i	0.0640154	+	0.110878i
$307$	−24.2710			−1.38522			−0.692610	−	0.721312i	$-0.743539\pi$
$307$	−24.2710			−1.38522			−0.692610	+	0.721312i	$0.743539\pi$
$308$	−5.27647	−	10.4736i	−0.300655	−	0.596791i
$309$	7.33659			0.417364
$310$	2.11467	+	3.66271i	0.120105	+	0.208028i
$311$	−2.97798	+	5.15802i	−0.168866	+	0.292484i	−0.938021	−	0.346577i	$-0.887344\pi$
$311$	−2.97798	+	5.15802i	−0.168866	+	0.292484i	0.769155	+	0.639062i	$0.220677\pi$
$312$	5.44745	−	9.43526i	0.308401	−	0.534166i
$313$	−14.2722	−	24.7203i	−0.806715	−	1.39727i	−0.915127	−	0.403165i	$-0.867910\pi$
$313$	−14.2722	−	24.7203i	−0.806715	−	1.39727i	0.108412	−	0.994106i	$-0.465423\pi$
$314$	3.73622			0.210847
$315$	−5.57069	+	8.49294i	−0.313873	+	0.478523i
$316$	−0.130166			−0.00732243
$317$	9.68080	+	16.7676i	0.543728	+	0.941764i	0.998686	+	0.0512512i	$0.0163209\pi$
$317$	9.68080	+	16.7676i	0.543728	+	0.941764i	−0.454958	+	0.890513i	$0.650346\pi$
$318$	1.08661	−	1.88206i	0.0609339	−	0.105541i
$319$	−2.85879	+	4.95157i	−0.160062	+	0.277235i
$320$	−7.09198	−	12.2837i	−0.396454	−	0.686678i
$321$	−4.73776			−0.264436
$322$	1.34497	−	2.05051i	0.0749524	−	0.114271i
$323$	−25.2833			−1.40680
$324$	0.902547	+	1.56326i	0.0501415	+	0.0868477i
$325$	31.5765	−	54.6921i	1.75155	−	3.03377i
$326$	−2.31946	+	4.01742i	−0.128463	+	0.222504i
$327$	6.06366	+	10.5026i	0.335321	+	0.580793i
$328$	1.67988			0.0927556
$329$	−5.47176	−	10.8613i	−0.301668	−	0.598801i
$330$	4.16185			0.229102
$331$	7.48935	+	12.9719i	0.411652	+	0.713002i	0.995071	−	0.0991694i	$-0.0316186\pi$
$331$	7.48935	+	12.9719i	0.411652	+	0.713002i	−0.583419	+	0.812172i	$0.698285\pi$
$332$	6.97029	−	12.0729i	0.382544	−	0.662586i
$333$	−4.60573	+	7.97737i	−0.252393	+	0.437157i
$334$	4.33914	+	7.51561i	0.237427	+	0.411236i
$335$	−1.86420			−0.101852
$336$	−7.57720	−	0.431813i	−0.413370	−	0.0235573i
$337$	−16.4667			−0.896999			−0.448500	−	0.893783i	$-0.648041\pi$
$337$	−16.4667			−0.896999			−0.448500	+	0.893783i	$0.648041\pi$
$338$	6.41520	+	11.1115i	0.348941	+	0.604384i
$339$	8.53405	−	14.7814i	0.463506	−	0.802816i
$340$	−17.5770	+	30.4443i	−0.953248	+	1.65107i
$341$	3.06395	+	5.30692i	0.165922	+	0.287386i
$342$	2.20030			0.118979
$343$	−18.2508	−	3.14755i	−0.985452	−	0.169952i
$344$	12.6515			0.682121
$345$	−4.02983	−	6.97987i	−0.216959	−	0.375784i
$346$	3.11467	−	5.39476i	0.167445	−	0.290024i
$347$	9.32273	−	16.1474i	0.500470	−	0.866840i	−0.499529	−	0.866297i	$-0.666494\pi$
$347$	9.32273	−	16.1474i	0.500470	−	0.866840i	1.00000		0.000543204i	$-0.000172907\pi$
$348$	2.10145	+	3.63982i	0.112650	+	0.195115i
$349$	13.1818			0.705605			0.352802	−	0.935698i	$-0.385229\pi$
$349$	13.1818			0.705605			0.352802	+	0.935698i	$0.385229\pi$
$350$	11.3554	+	0.647129i	0.606974	+	0.0345905i
$351$	−6.48554			−0.346173
$352$	5.68007	+	9.83817i	0.302749	+	0.524376i
$353$	13.2529	−	22.9546i	0.705378	−	1.22175i	−0.261176	−	0.965291i	$-0.584110\pi$
$353$	13.2529	−	22.9546i	0.705378	−	1.22175i	0.966555	−	0.256460i	$-0.0825563\pi$
$354$	1.69854	−	2.94196i	0.0902766	−	0.156364i
$355$	−3.37695	−	5.84905i	−0.179230	−	0.310435i
$356$	−18.1738			−0.963211
$357$	6.03871	+	11.9867i	0.319603	+	0.634401i
$358$	3.75932			0.198686
$359$	11.3065	+	19.5835i	0.596736	+	1.03358i	0.993299	+	0.115570i	$0.0368695\pi$
$359$	11.3065	+	19.5835i	0.596736	+	1.03358i	−0.396563	+	0.918007i	$0.629797\pi$
$360$	3.22448	−	5.58495i	0.169945	−	0.294353i
$361$	−2.91969	+	5.05706i	−0.153668	+	0.266161i
$362$	−4.36988	−	7.56886i	−0.229676	−	0.397810i
$363$	−4.96988			−0.260851
$364$	16.9880	−	25.8995i	0.890415	−	1.35751i
$365$	−37.1091			−1.94238
$366$	−2.50264	−	4.33471i	−0.130815	−	0.226579i
$367$	−8.54575	+	14.8017i	−0.446084	+	0.772641i	−0.998127	−	0.0611751i	$-0.980515\pi$
$367$	−8.54575	+	14.8017i	−0.446084	+	0.772641i	0.552043	+	0.833816i	$0.313849\pi$
$368$	3.01119	−	5.21554i	0.156969	−	0.271879i
$369$	−0.500000	−	0.866025i	−0.0260290	−	0.0450835i
$370$	15.6118			0.811618
$371$	7.14311	−	10.8902i	0.370852	−	0.565392i
$372$	4.50452			0.233549
$373$	−7.51134	−	13.0100i	−0.388923	−	0.673634i	0.603382	−	0.797452i	$-0.293819\pi$
$373$	−7.51134	−	13.0100i	−0.388923	−	0.673634i	−0.992305	+	0.123818i	$0.960486\pi$
$374$	2.74984	−	4.76287i	0.142191	−	0.246282i
$375$	9.09351	−	15.7504i	0.469587	−	0.813349i
$376$	3.86094	+	6.68734i	0.199113	+	0.344873i
$377$	−15.1007			−0.777724
$378$	−0.525524	−	1.04315i	−0.0270300	−	0.0536538i
$379$	−28.7158			−1.47503			−0.737516	−	0.675330i	$-0.764001\pi$
$379$	−28.7158			−1.47503			−0.737516	+	0.675330i	$0.764001\pi$
$380$	17.2684	+	29.9098i	0.885851	+	1.53434i
$381$	−8.41134	+	14.5689i	−0.430926	+	0.746386i
$382$	−2.08240	+	3.60682i	−0.106545	+	0.184541i
$383$	16.3802	+	28.3714i	0.836991	+	1.44971i	0.892399	+	0.451247i	$0.149020\pi$
$383$	16.3802	+	28.3714i	0.836991	+	1.44971i	−0.0554087	+	0.998464i	$0.517646\pi$
$384$	10.8835			0.555396
$385$	24.9012	+	1.41908i	1.26908	+	0.0723230i
$386$	−9.18571			−0.467541
$387$	−3.76559	−	6.52220i	−0.191416	−	0.331542i
$388$	0.148565	−	0.257322i	0.00754224	−	0.0130635i
$389$	2.73534	−	4.73774i	0.138687	−	0.240213i	−0.788313	−	0.615275i	$-0.789045\pi$
$389$	2.73534	−	4.73774i	0.138687	−	0.240213i	0.927000	+	0.375062i	$0.122378\pi$
$390$	5.49591	+	9.51920i	0.278296	+	0.482023i
$391$	−10.6505			−0.538617
$392$	11.6830	+	1.33593i	0.590080	+	0.0674747i
$393$	−9.94059			−0.501436
$394$	−1.93659	−	3.35428i	−0.0975642	−	0.168986i
$395$	0.138414	−	0.239741i	0.00696438	−	0.0120627i
$396$	2.21632	−	3.83878i	0.111374	−	0.192906i
$397$	3.66714	+	6.35167i	0.184048	+	0.318781i	0.943255	−	0.332068i	$-0.107746\pi$
$397$	3.66714	+	6.35167i	0.184048	+	0.318781i	−0.759207	+	0.650849i	$0.774413\pi$
$398$	−10.2627			−0.514422
$399$	13.1648	+	0.750244i	0.659066	+	0.0375592i
$400$	27.9326			1.39663
$401$	−5.01155	−	8.68026i	−0.250265	−	0.433471i	0.713334	−	0.700824i	$-0.247184\pi$
$401$	−5.01155	−	8.68026i	−0.250265	−	0.433471i	−0.963599	+	0.267353i	$0.913851\pi$
$402$	0.107192	−	0.185661i	0.00534624	−	0.00925995i
$403$	−8.09217	+	14.0161i	−0.403100	+	0.698189i
$404$	−16.2494	−	28.1448i	−0.808438	−	1.40026i
$405$	−3.83895			−0.190759
$406$	−1.22361	−	2.42882i	−0.0607266	−	0.120541i
$407$	22.6200			1.12123
$408$	−4.26099	−	7.38025i	−0.210950	−	0.365377i
$409$	0.575518	−	0.996826i	0.0284575	−	0.0492899i	−0.851446	−	0.524442i	$-0.824274\pi$
$409$	0.575518	−	0.996826i	0.0284575	−	0.0492899i	0.879903	+	0.475153i	$0.157607\pi$
$410$	−0.847410	+	1.46776i	−0.0418506	+	0.0724874i
$411$	−4.42149	−	7.65824i	−0.218096	−	0.377753i
$412$	−13.2432			−0.652448
$413$	11.1659	−	17.0232i	0.549436	−	0.837657i
$414$	0.926865			0.0455529
$415$	14.8239	+	25.6758i	0.727677	+	1.26037i
$416$	−15.0016	+	25.9835i	−0.735513	+	1.27395i
$417$	−4.01792	+	6.95924i	−0.196758	+	0.340795i
$418$	−2.70156	−	4.67924i	−0.132138	−	0.228869i
$419$	−12.9283			−0.631589			−0.315795	−	0.948828i	$-0.602271\pi$
$419$	−12.9283			−0.631589			−0.315795	+	0.948828i	$0.602271\pi$
$420$	10.0556	−	15.3306i	0.490664	−	0.748055i
$421$	−0.825751			−0.0402447			−0.0201223	−	0.999798i	$-0.506406\pi$
$421$	−0.825751			−0.0402447			−0.0201223	+	0.999798i	$0.506406\pi$
$422$	0.0961525	+	0.166541i	0.00468063	+	0.00810709i
$423$	2.29835	−	3.98086i	0.111750	−	0.193556i
$424$	−4.13464	+	7.16141i	−0.200796	+	0.347789i
$425$	−24.6991	−	42.7801i	−1.19808	−	2.07514i
$426$	0.776702			0.0376313
$427$	−13.4958	−	26.7887i	−0.653107	−	1.29640i
$428$	8.55211			0.413382
$429$	7.96304	+	13.7924i	0.384459	+	0.665903i
$430$	−6.38200	+	11.0540i	−0.307768	+	0.533069i
$431$	−0.465776	+	0.806747i	−0.0224356	+	0.0388596i	−0.877025	−	0.480444i	$-0.840475\pi$
$431$	−0.465776	+	0.806747i	−0.0224356	+	0.0388596i	0.854590	+	0.519304i	$0.173809\pi$
$432$	−1.43428	−	2.48424i	−0.0690068	−	0.119523i
$433$	−19.1576			−0.920654			−0.460327	−	0.887749i	$-0.652268\pi$
$433$	−19.1576			−0.920654			−0.460327	+	0.887749i	$0.652268\pi$
$434$	−2.91008	−	0.165841i	−0.139688	−	0.00796063i
$435$	−8.93844			−0.428565
$436$	−10.9455	−	18.9581i	−0.524194	−	0.907930i
$437$	−5.23173	+	9.06162i	−0.250268	+	0.433476i
$438$	2.13378	−	3.69582i	0.101956	−	0.176593i
$439$	15.4438	+	26.7495i	0.737094	+	1.27668i	0.953798	+	0.300448i	$0.0971361\pi$
$439$	15.4438	+	26.7495i	0.737094	+	1.27668i	−0.216704	+	0.976237i	$0.569531\pi$
$440$	−15.8362			−0.754963
$441$	−2.78863	−	6.42056i	−0.132792	−	0.305741i
$442$	14.5252			0.690892
$443$	−5.84510	−	10.1240i	−0.277709	−	0.481006i	0.693106	−	0.720836i	$-0.256242\pi$
$443$	−5.84510	−	10.1240i	−0.277709	−	0.481006i	−0.970815	+	0.239829i	$0.922909\pi$
$444$	8.31379	−	14.3999i	0.394555	−	0.683389i
$445$	19.3254	−	33.4726i	0.916111	−	1.58675i
$446$	0.619606	+	1.07319i	0.0293392	+	0.0508170i
$447$	−16.2616			−0.769149
$448$	9.75957	+	0.556183i	0.461096	+	0.0262772i
$449$	−1.25766			−0.0593529			−0.0296764	−	0.999560i	$-0.509448\pi$
$449$	−1.25766			−0.0593529			−0.0296764	+	0.999560i	$0.509448\pi$
$450$	2.14946	+	3.72297i	0.101326	+	0.175503i
$451$	−1.22781	+	2.12664i	−0.0578155	+	0.100139i
$452$	−15.4048	+	26.6818i	−0.724579	+	1.25501i
$453$	10.2768	+	17.7999i	0.482845	+	0.836313i
$454$	5.38664			0.252808
$455$	29.6373	+	58.8292i	1.38942	+	2.75796i
$456$	−8.37235			−0.392071
$457$	−4.04171	−	7.00045i	−0.189063	−	0.327467i	0.755875	−	0.654716i	$-0.227212\pi$
$457$	−4.04171	−	7.00045i	−0.189063	−	0.327467i	−0.944938	+	0.327249i	$0.893878\pi$
$458$	2.96737	−	5.13963i	0.138656	−	0.240159i
$459$	−2.53649	+	4.39333i	−0.118393	+	0.205063i
$460$	7.27423	+	12.5993i	0.339163	+	0.587447i
$461$	23.9297			1.11452			0.557259	−	0.830339i	$-0.311853\pi$
$461$	23.9297			1.11452			0.557259	+	0.830339i	$0.311853\pi$
$462$	−1.57315	+	2.39839i	−0.0731897	+	0.111583i
$463$	6.07473			0.282317			0.141158	−	0.989987i	$-0.454917\pi$
$463$	6.07473			0.282317			0.141158	+	0.989987i	$0.454917\pi$
$464$	−3.33951	−	5.78421i	−0.155033	−	0.268525i
$465$	−4.78995	+	8.29644i	−0.222129	+	0.384738i
$466$	−2.69294	+	4.66431i	−0.124748	+	0.216070i
$467$	12.5236	+	21.6915i	0.579522	+	1.00376i	0.995534	+	0.0944023i	$0.0300940\pi$
$467$	12.5236	+	21.6915i	0.579522	+	1.00376i	−0.416012	+	0.909359i	$0.636573\pi$
$468$	11.7070			0.541157
$469$	0.704655	−	1.07430i	0.0325379	−	0.0496066i
$470$	−7.79057			−0.359352
$471$	4.23147	+	7.32912i	0.194976	+	0.337708i
$472$	−6.46312	+	11.1945i	−0.297489	+	0.515267i
$473$	−9.24690	+	16.0161i	−0.425173	+	0.736421i
$474$	0.0159177	+	0.0275703i	0.000731125	+	0.00126634i
$475$	−48.5309			−2.22675
$476$	−10.9004	−	21.6371i	−0.499621	−	0.991733i
$477$	4.92256			0.225388
$478$	0.409828	+	0.709843i	0.0187451	+	0.0324675i
$479$	−3.33086	+	5.76923i	−0.152191	+	0.263603i	−0.932033	−	0.362374i	$-0.881966\pi$
$479$	−3.33086	+	5.76923i	−0.152191	+	0.263603i	0.779842	+	0.625977i	$0.215300\pi$
$480$	−8.87979	+	15.3803i	−0.405305	+	0.702009i
$481$	29.8707	+	51.7375i	1.36199	+	2.35903i
$482$	1.25024			0.0569470
$483$	5.54562	+	0.316036i	0.252334	+	0.0143801i
$484$	8.97111			0.407778
$485$	0.315957	+	0.547253i	0.0143469	+	0.0248495i
$486$	0.220740	−	0.382333i	0.0100130	−	0.0173430i
$487$	−0.0180603	+	0.0312814i	−0.000818392	+	0.00141750i	−0.866434	−	0.499291i	$-0.833594\pi$
$487$	−0.0180603	+	0.0312814i	−0.000818392	+	0.00141750i	0.865616	+	0.500709i	$0.166927\pi$
$488$	9.52280	+	16.4940i	0.431077	+	0.746647i
$489$	−10.5076			−0.475172
$490$	−7.06071	+	9.53387i	−0.318970	+	0.430696i
$491$	−29.1555			−1.31577			−0.657885	−	0.753119i	$-0.728549\pi$
$491$	−29.1555			−1.31577			−0.657885	+	0.753119i	$0.728549\pi$
$492$	0.902547	+	1.56326i	0.0406900	+	0.0704771i
$493$	−5.90586	+	10.2292i	−0.265987	+	0.460702i
$494$	7.13507	−	12.3583i	0.321022	−	0.556026i
$495$	4.71351	+	8.16405i	0.211857	+	0.366947i
$496$	−7.15834			−0.321419
$497$	4.64716	+	0.264834i	0.208454	+	0.0118795i
$498$	−3.40951			−0.152784
$499$	−21.0446	−	36.4503i	−0.942085	−	1.63174i	−0.761484	−	0.648183i	$-0.775529\pi$
$499$	−21.0446	−	36.4503i	−0.942085	−	1.63174i	−0.180601	−	0.983556i	$-0.557804\pi$
$500$	−16.4147	+	28.4310i	−0.734086	+	1.27147i
$501$	−9.82861	+	17.0237i	−0.439110	+	0.760561i
$502$	0.155739	+	0.269749i	0.00695099	+	0.0120395i
$503$	−9.50491			−0.423803			−0.211901	−	0.977291i	$-0.567966\pi$
$503$	−9.50491			−0.423803			−0.211901	+	0.977291i	$0.567966\pi$
$504$	1.99967	+	3.96928i	0.0890723	+	0.176806i
$505$	69.1161			3.07563
$506$	−1.13802	−	1.97111i	−0.0505911	−	0.0876263i
$507$	−14.5311	+	25.1686i	−0.645350	+	1.11778i
$508$	15.1833	−	26.2982i	0.673649	−	1.16679i
$509$	−8.21728	−	14.2328i	−0.364225	−	0.630856i	0.624427	−	0.781083i	$-0.285333\pi$
$509$	−8.21728	−	14.2328i	−0.364225	−	0.630856i	−0.988651	+	0.150228i	$0.951999\pi$
$510$	8.59779			0.380717
$511$	14.0270	−	21.3852i	0.620518	−	0.946028i
$512$	−22.9081			−1.01240
$513$	2.49196	+	4.31620i	0.110023	+	0.190565i
$514$	−6.54623	+	11.3384i	−0.288742	+	0.500115i
$515$	14.0824	−	24.3914i	0.620544	−	1.07481i
$516$	6.79725	+	11.7732i	0.299232	+	0.518286i
$517$	−11.2878			−0.496436
$518$	−5.90116	+	8.99676i	−0.259282	+	0.395295i
$519$	14.1101			0.619364
$520$	−20.9125	−	36.2215i	−0.917072	−	1.58842i
$521$	−12.4387	+	21.5445i	−0.544951	+	0.943882i	0.453659	+	0.891175i	$0.350118\pi$
$521$	−12.4387	+	21.5445i	−0.544951	+	0.943882i	−0.998610	+	0.0527070i	$0.983215\pi$
$522$	0.513962	−	0.890209i	0.0224955	−	0.0389634i
$523$	−20.3141	−	35.1851i	−0.888275	−	1.53854i	−0.841913	−	0.539613i	$-0.818571\pi$
$523$	−20.3141	−	35.1851i	−0.888275	−	1.53854i	−0.0463615	−	0.998925i	$-0.514763\pi$
$524$	17.9437			0.783875
$525$	11.5912	+	23.0082i	0.505882	+	1.00416i
$526$	9.63648			0.420170
$527$	6.32969	+	10.9633i	0.275726	+	0.477571i
$528$	−3.52206	+	6.10038i	−0.153278	+	0.265485i
$529$	9.29616	−	16.1014i	0.404181	−	0.700062i
$530$	−4.17142	−	7.22512i	−0.181195	−	0.313839i
$531$	7.69476			0.333924
$532$	−23.7638	−	1.35426i	−1.03029	−	0.0587147i
$533$	−6.48554			−0.280920
$534$	2.22243	+	3.84936i	0.0961739	+	0.166578i
$535$	−9.09401	+	15.7513i	−0.393168	+	0.680987i
$536$	−0.407875	+	0.706460i	−0.0176175	+	0.0305144i
$537$	4.25763	+	7.37443i	0.183730	+	0.318230i
$538$	12.2015			0.526043
$539$	−10.2303	+	13.8137i	−0.440649	+	0.594996i
$540$	6.92966			0.298205
$541$	8.40676	+	14.5609i	0.361435	+	0.626024i	0.988197	−	0.153187i	$-0.0489536\pi$
$541$	8.40676	+	14.5609i	0.361435	+	0.626024i	−0.626762	+	0.779210i	$0.715620\pi$
$542$	−4.32649	+	7.49370i	−0.185839	+	0.321882i
$543$	9.89825	−	17.1443i	0.424774	−	0.735731i
$544$	11.7342	+	20.3243i	0.503101	+	0.871396i
$545$	46.5561			1.99425
$546$	−7.56315	−	0.431012i	−0.323673	−	0.0184456i
$547$	−12.1076			−0.517683			−0.258842	−	0.965920i	$-0.583341\pi$
$547$	−12.1076			−0.517683			−0.258842	+	0.965920i	$0.583341\pi$
$548$	7.98121	+	13.8239i	0.340940	+	0.590526i
$549$	5.66875	−	9.81857i	0.241936	−	0.419046i
$550$	5.27828	−	9.14224i	0.225066	−	0.389827i
$551$	5.80217	+	10.0496i	0.247181	+	0.428129i
$552$	−3.52681			−0.150111
$553$	0.0858381	+	0.170386i	0.00365021	+	0.00724555i
$554$	−8.75446			−0.371942
$555$	17.6812	+	30.6247i	0.750524	+	1.29995i
$556$	7.25272	−	12.5621i	0.307584	−	0.532751i
$557$	−22.3992	+	38.7966i	−0.949085	+	1.64386i	−0.201728	+	0.979442i	$0.564656\pi$
$557$	−22.3992	+	38.7966i	−0.949085	+	1.64386i	−0.747357	+	0.664423i	$0.768678\pi$
$558$	−0.550846	−	0.954094i	−0.0233192	−	0.0403900i
$559$	−48.8438			−2.06587
$560$	−15.9798	+	24.3625i	−0.675271	+	1.02950i
$561$	12.4574			0.525950
$562$	2.14652	+	3.71789i	0.0905457	+	0.156830i
$563$	−21.8126	+	37.7805i	−0.919292	+	1.59226i	−0.118798	+	0.992918i	$0.537904\pi$
$563$	−21.8126	+	37.7805i	−0.919292	+	1.59226i	−0.800493	+	0.599342i	$0.795429\pi$
$564$	−4.14874	+	7.18582i	−0.174693	+	0.302578i
$565$	−32.7617	−	56.7450i	−1.37830	−	2.38728i
$566$	6.65569			0.279759
$567$	1.45110	−	2.21231i	0.0609404	−	0.0929083i
$568$	−2.95542			−0.124007
$569$	−18.9697	−	32.8565i	−0.795251	−	1.37742i	−0.922680	−	0.385568i	$-0.874006\pi$
$569$	−18.9697	−	32.8565i	−0.795251	−	1.37742i	0.127428	−	0.991848i	$-0.459328\pi$
$570$	4.22342	−	7.31517i	0.176899	−	0.306399i
$571$	0.351385	−	0.608616i	0.0147050	−	0.0254698i	−0.858579	−	0.512681i	$-0.828652\pi$
$571$	0.351385	−	0.608616i	0.0147050	−	0.0254698i	0.873284	+	0.487211i	$0.161986\pi$
$572$	−14.3740	−	24.8966i	−0.601009	−	1.04098i
$573$	−9.43371			−0.394099
$574$	−0.525524	−	1.04315i	−0.0219349	−	0.0435402i
$575$	−20.4434			−0.852548
$576$	1.84738	+	3.19975i	0.0769741	+	0.133323i
$577$	6.12903	−	10.6158i	0.255155	−	0.441941i	−0.709783	−	0.704421i	$-0.751207\pi$
$577$	6.12903	−	10.6158i	0.255155	−	0.441941i	0.964938	+	0.262480i	$0.0845403\pi$
$578$	1.92820	−	3.33974i	0.0802025	−	0.138915i
$579$	−10.4033	−	18.0191i	−0.432347	−	0.748846i
$580$	16.1347			0.669958
$581$	−20.3998	−	1.16255i	−0.846326	−	0.0482308i
$582$	−0.0726704			−0.00301228
$583$	−6.04399	−	10.4685i	−0.250316	−	0.433561i
$584$	−8.11924	+	14.0629i	−0.335977	+	0.581929i
$585$	−12.4488	+	21.5620i	−0.514695	+	0.891478i
$586$	−3.90913	−	6.77080i	−0.161484	−	0.279699i
$587$	−11.5743			−0.477722			−0.238861	−	0.971054i	$-0.576774\pi$
$587$	−11.5743			−0.477722			−0.238861	+	0.971054i	$0.576774\pi$
$588$	5.03374	+	11.5897i	0.207588	+	0.477952i
$589$	12.4371			0.512462
$590$	−6.52062	−	11.2940i	−0.268450	−	0.464968i
$591$	4.38659	−	7.59780i	0.180440	−	0.312532i
$592$	−13.2118	+	22.8835i	−0.543002	+	0.940508i
$593$	13.5129	+	23.4049i	0.554906	+	0.961126i	0.997911	+	0.0646065i	$0.0205792\pi$
$593$	13.5129	+	23.4049i	0.554906	+	0.961126i	−0.443005	+	0.896519i	$0.646087\pi$
$594$	−1.08411			−0.0444817
$595$	51.4423	+	2.93162i	2.10893	+	0.120185i
$596$	29.3538			1.20238
$597$	−11.6230	−	20.1317i	−0.475699	−	0.823935i
$598$	3.00561	−	5.20587i	0.122909	−	0.212884i
$599$	4.59385	−	7.95677i	0.187699	−	0.325105i	−0.756783	−	0.653666i	$-0.773230\pi$
$599$	4.59385	−	7.95677i	0.187699	−	0.325105i	0.944483	+	0.328561i	$0.106564\pi$
$600$	−8.17890	−	14.1663i	−0.333902	−	0.578335i
$601$	3.35483			0.136846			0.0684231	−	0.997656i	$-0.478203\pi$
$601$	3.35483			0.136846			0.0684231	+	0.997656i	$0.478203\pi$
$602$	−3.95782	−	7.85615i	−0.161309	−	0.320193i
$603$	0.485601			0.0197752
$604$	−18.5506	−	32.1305i	−0.754812	−	1.30737i
$605$	−9.53956	+	16.5230i	−0.387838	+	0.671755i
$606$	−3.97419	+	6.88350i	−0.161440	+	0.279623i
$607$	10.7811	+	18.6733i	0.437589	+	0.757927i	0.997503	−	0.0706239i	$-0.0224990\pi$
$607$	10.7811	+	18.6733i	0.437589	+	0.757927i	−0.559914	+	0.828551i	$0.689166\pi$
$608$	23.0564			0.935060
$609$	3.37868	−	5.15105i	0.136911	−	0.208731i
$610$	−19.2150			−0.777994
$611$	−14.9060	−	25.8180i	−0.603033	−	1.04448i
$612$	4.57861	−	7.93038i	0.185079	−	0.320567i
$613$	1.79747	−	3.11330i	0.0725990	−	0.125745i	−0.827441	−	0.561553i	$-0.810204\pi$
$613$	1.79747	−	3.11330i	0.0725990	−	0.125745i	0.900040	+	0.435808i	$0.143537\pi$
$614$	−5.35759	−	9.27962i	−0.216215	−	0.374495i
$615$	−3.83895			−0.154801
$616$	5.98600	−	9.12611i	0.241183	−	0.367702i
$617$	−13.0715			−0.526240			−0.263120	−	0.964763i	$-0.584752\pi$
$617$	−13.0715			−0.526240			−0.263120	+	0.964763i	$0.584752\pi$
$618$	1.61948	+	2.80502i	0.0651451	+	0.112835i
$619$	0.611991	−	1.06000i	0.0245980	−	0.0426050i	−0.853464	−	0.521151i	$-0.825503\pi$
$619$	0.611991	−	1.06000i	0.0245980	−	0.0426050i	0.878062	+	0.478546i	$0.158836\pi$
$620$	8.64631	−	14.9759i	0.347244	−	0.601445i
$621$	1.04972	+	1.81817i	0.0421240	+	0.0729608i
$622$	−2.62944			−0.105431
$623$	11.9847	+	23.7893i	0.480157	+	0.953097i
$624$	−18.6041			−0.744762
$625$	−10.5657	−	18.3004i	−0.422630	−	0.732016i
$626$	6.30092	−	10.9135i	0.251835	−	0.436192i
$627$	6.11932	−	10.5990i	0.244382	−	0.423282i
$628$	−7.63820	−	13.2298i	−0.304797	−	0.527925i
$629$	46.7296			1.86323
$630$	−4.47681	−	0.255126i	−0.178360	−	0.0101645i
$631$	42.3951			1.68772			0.843862	−	0.536561i	$-0.180277\pi$
$631$	42.3951			1.68772			0.843862	+	0.536561i	$0.180277\pi$
$632$	−0.0605684	−	0.104908i	−0.00240928	−	0.00417300i
$633$	−0.217796	+	0.377233i	−0.00865660	+	0.0149937i
$634$	−4.27388	+	7.40258i	−0.169738	+	0.293994i
$635$	32.2907	+	55.9291i	1.28142	+	2.21948i
$636$	−8.88568			−0.352340
$637$	−45.1049	−	5.15766i	−1.78712	−	0.204354i
$638$	−2.52420			−0.0999341
$639$	0.879656	+	1.52361i	0.0347986	+	0.0602730i
$640$	20.8906	−	36.1835i	0.825772	−	1.43028i
$641$	−7.07827	+	12.2599i	−0.279575	+	0.484238i	−0.971279	−	0.237943i	$-0.923527\pi$
$641$	−7.07827	+	12.2599i	−0.279575	+	0.484238i	0.691704	+	0.722181i	$0.256860\pi$
$642$	−1.04581	−	1.81140i	−0.0412750	−	0.0714904i
$643$	−28.9883			−1.14319			−0.571594	−	0.820537i	$-0.693675\pi$
$643$	−28.9883			−1.14319			−0.571594	+	0.820537i	$0.693675\pi$
$644$	−10.0104	−	0.570475i	−0.394464	−	0.0224799i
$645$	−28.9118			−1.13840
$646$	−5.58104	−	9.66665i	−0.219583	−	0.380329i
$647$	1.79691	−	3.11235i	0.0706440	−	0.122359i	−0.828540	−	0.559930i	$-0.810828\pi$
$647$	1.79691	−	3.11235i	0.0706440	−	0.122359i	0.899184	+	0.437571i	$0.144161\pi$
$648$	−0.839938	+	1.45481i	−0.0329959	+	0.0571505i
$649$	−9.44774	−	16.3640i	−0.370856	−	0.642342i
$650$	27.8808			1.09358
$651$	−2.97050	−	5.89636i	−0.116423	−	0.231096i
$652$	18.9673			0.742816
$653$	−3.60816	−	6.24952i	−0.141198	−	0.244562i	0.786750	−	0.617272i	$-0.211762\pi$
$653$	−3.60816	−	6.24952i	−0.141198	−	0.244562i	−0.927948	+	0.372709i	$0.878429\pi$
$654$	−2.67699	+	4.63668i	−0.104679	+	0.181309i
$655$	−19.0807	+	33.0487i	−0.745544	+	1.29132i
$656$	−1.43428	−	2.48424i	−0.0559992	−	0.0969934i
$657$	9.66648			0.377125
$658$	2.94479	−	4.48956i	0.114800	−	0.175021i
$659$	34.6958			1.35156			0.675779	−	0.737105i	$-0.263808\pi$
$659$	34.6958			1.35156			0.675779	+	0.737105i	$0.263808\pi$
$660$	−8.50834	−	14.7369i	−0.331187	−	0.573632i
$661$	1.12404	−	1.94689i	0.0437199	−	0.0757251i	−0.843337	−	0.537384i	$-0.819412\pi$
$661$	1.12404	−	1.94689i	0.0437199	−	0.0757251i	0.887057	+	0.461659i	$0.152746\pi$
$662$	−3.30640	+	5.72686i	−0.128507	+	0.222581i
$663$	16.4505	+	28.4931i	0.638885	+	1.10658i
$664$	12.9735			0.503470
$665$	27.7638	−	42.3281i	1.07663	−	1.64141i
$666$	−4.06668			−0.157581
$667$	2.44413	+	4.23336i	0.0946372	+	0.163916i
$668$	17.7416	−	30.7293i	0.686442	−	1.18895i
$669$	−1.40347	+	2.43089i	−0.0542614	+	0.0939836i
$670$	−0.411503	−	0.712744i	−0.0158978	−	0.0275357i
$671$	−27.8407			−1.07478
$672$	−5.50683	−	10.9309i	−0.212431	−	0.421668i
$673$	43.3411			1.67068			0.835338	−	0.549737i	$-0.185272\pi$
$673$	43.3411			1.67068			0.835338	+	0.549737i	$0.185272\pi$
$674$	−3.63487	−	6.29577i	−0.140010	−	0.242504i
$675$	−4.86875	+	8.43293i	−0.187398	+	0.324584i
$676$	26.2300	−	45.4318i	1.00885	−	1.74738i
$677$	−2.42205	−	4.19512i	−0.0930871	−	0.161232i	0.815722	−	0.578445i	$-0.196340\pi$
$677$	−2.42205	−	4.19512i	−0.0930871	−	0.161232i	−0.908809	+	0.417213i	$0.863007\pi$
$678$	7.53523			0.289389
$679$	−0.434801	−	0.0247787i	−0.0166861	−	0.000950918i
$680$	−32.7154			−1.25458
$681$	6.10066	+	10.5666i	0.233778	+	0.404915i
$682$	−1.35267	+	2.34290i	−0.0517966	+	0.0897143i
$683$	19.5403	−	33.8448i	0.747690	−	1.29504i	−0.201237	−	0.979543i	$-0.564496\pi$
$683$	19.5403	−	33.8448i	0.747690	−	1.29504i	0.948927	−	0.315495i	$-0.102170\pi$
$684$	−4.49822	−	7.79114i	−0.171994	−	0.297902i
$685$	−33.9477			−1.29708
$686$	−2.82528	−	7.67269i	−0.107870	−	0.292945i
$687$	13.4428			0.512875
$688$	−10.8018	−	18.7093i	−0.411816	−	0.713286i
$689$	15.9627	−	27.6482i	0.608131	−	1.05331i
$690$	1.77909	−	3.08148i	0.0677289	−	0.117310i
$691$	−6.14156	−	10.6375i	−0.233636	−	0.404669i	0.725240	−	0.688497i	$-0.241729\pi$
$691$	−6.14156	−	10.6375i	−0.233636	−	0.404669i	−0.958875	+	0.283828i	$0.908396\pi$
$692$	−25.4701			−0.968226
$693$	−6.48646	−	0.369653i	−0.246400	−	0.0140420i
$694$	8.23161			0.312468
$695$	15.4246	+	26.7161i	0.585087	+	1.01340i
$696$	−1.95568	+	3.38733i	−0.0741297	+	0.128396i
$697$	−2.53649	+	4.39333i	−0.0960765	+	0.166409i
$698$	2.90975	+	5.03983i	0.110136	+	0.190761i
$699$	−12.1996			−0.461431
$700$	−20.9232	−	41.5320i	−0.790824	−	1.56976i
$701$	42.2313			1.59505			0.797527	−	0.603283i	$-0.206141\pi$
$701$	42.2313			1.59505			0.797527	+	0.603283i	$0.206141\pi$
$702$	−1.43162	−	2.47964i	−0.0540330	−	0.0935879i
$703$	22.9546	−	39.7585i	0.865748	−	1.49952i
$704$	4.53647	−	7.85740i	0.170975	−	0.296137i
$705$	−8.82324	−	15.2823i	−0.332302	−	0.575564i
$706$	11.7018			0.440401
$707$	−26.1255	+	39.8303i	−0.982549	+	1.49797i
$708$	−13.8898			−0.522010
$709$	−6.93929	−	12.0192i	−0.260611	−	0.451391i	0.705794	−	0.708417i	$-0.250591\pi$
$709$	−6.93929	−	12.0192i	−0.260611	−	0.451391i	−0.966404	+	0.257027i	$0.917257\pi$
$710$	1.49086	−	2.58224i	0.0559509	−	0.0969098i
$711$	−0.0360553	+	0.0624496i	−0.00135218	+	0.00234204i
$712$	−8.45655	−	14.6472i	−0.316923	−	0.548926i
$713$	5.23907			0.196205
$714$	−3.24991	+	4.95474i	−0.121625	+	0.185426i
$715$	61.1394			2.28648
$716$	−7.68543	−	13.3115i	−0.287218	−	0.497476i
$717$	−0.928304	+	1.60787i	−0.0346681	+	0.0600470i
$718$	−4.99162	+	8.64573i	−0.186285	+	0.322656i
$719$	−14.1815	−	24.5631i	−0.528882	−	0.916050i	−0.999433	−	0.0336772i	$-0.989278\pi$
$719$	−14.1815	−	24.5631i	−0.528882	−	0.916050i	0.470551	−	0.882373i	$-0.344055\pi$
$720$	−11.0122			−0.410402
$721$	8.73324	+	17.3352i	0.325243	+	0.645597i
$722$	−2.57798			−0.0959424
$723$	1.41597	+	2.45253i	0.0526604	+	0.0912105i
$724$	−17.8673	+	30.9470i	−0.664032	+	1.15014i
$725$	−11.3362	+	19.6349i	−0.421016	+	0.729221i
$726$	−1.09705	−	1.90015i	−0.0407155	−	0.0705213i
$727$	32.5233			1.20622			0.603112	−	0.797657i	$-0.293927\pi$
$727$	32.5233			1.20622			0.603112	+	0.797657i	$0.293927\pi$
$728$	28.7785	+	1.64004i	1.06660	+	0.0607840i
$729$	1.00000			0.0370370
$730$	−8.19147	−	14.1880i	−0.303180	−	0.525123i
$731$	−19.1028	+	33.0870i	−0.706542	+	1.22377i
$732$	−10.2326	+	17.7234i	−0.378209	+	0.655077i
$733$	16.5273	+	28.6262i	0.610450	+	1.05733i	0.991165	+	0.132638i	$0.0423449\pi$
$733$	16.5273	+	28.6262i	0.610450	+	1.05733i	−0.380714	+	0.924693i	$0.624322\pi$
$734$	−7.54556			−0.278512
$735$	−26.6986	−	3.05294i	−0.984794	−	0.112610i
$736$	9.71238			0.358003
$737$	−0.596228	−	1.03270i	−0.0219623	−	0.0380399i
$738$	0.220740	−	0.382333i	0.00812556	−	0.0140739i
$739$	−1.07157	+	1.85601i	−0.0394183	+	0.0682744i	−0.885061	−	0.465474i	$-0.845884\pi$
$739$	−1.07157	+	1.85601i	−0.0394183	+	0.0682744i	0.845643	+	0.533749i	$0.179217\pi$
$740$	−31.9162	−	55.2805i	−1.17326	−	2.03215i
$741$	32.3234			1.18743
$742$	5.74047	+	0.327140i	0.210739	+	0.0120097i
$743$	−13.2245			−0.485161			−0.242580	−	0.970131i	$-0.577994\pi$
$743$	−13.2245			−0.485161			−0.242580	+	0.970131i	$0.577994\pi$
$744$	2.09602	+	3.63042i	0.0768439	+	0.133098i
$745$	−31.2138	+	54.0638i	−1.14358	+	1.98074i
$746$	3.31611	−	5.74367i	0.121411	−	0.210291i
$747$	−3.86145	−	6.68823i	−0.141283	−	0.244710i
$748$	−22.4867			−0.822196
$749$	−5.63968	−	11.1946i	−0.206069	−	0.409041i
$750$	8.02922			0.293186
$751$	−7.39068	−	12.8010i	−0.269690	−	0.467116i	0.699092	−	0.715032i	$-0.253588\pi$
$751$	−7.39068	−	12.8010i	−0.269690	−	0.467116i	−0.968782	+	0.247916i	$0.920254\pi$
$752$	6.59294	−	11.4193i	0.240420	−	0.416420i
$753$	−0.352766	+	0.611009i	−0.0128555	+	0.0222664i
$754$	−3.33332	−	5.77349i	−0.121392	−	0.210258i
$755$	78.9040			2.87161
$756$	−2.61937	+	3.99343i	−0.0952656	+	0.145240i
$757$	9.71165			0.352976			0.176488	−	0.984303i	$-0.443526\pi$
$757$	9.71165			0.352976			0.176488	+	0.984303i	$0.443526\pi$
$758$	−6.33873	−	10.9790i	−0.230233	−	0.398775i
$759$	2.57773	−	4.46476i	0.0935657	−	0.162061i
$760$	−16.0705	+	27.8349i	−0.582938	+	1.00968i
$761$	4.35187	+	7.53766i	0.157755	+	0.273240i	0.934059	−	0.357119i	$-0.116241\pi$
$761$	4.35187	+	7.53766i	0.157755	+	0.273240i	−0.776304	+	0.630359i	$0.782908\pi$
$762$	−7.42689			−0.269048
$763$	−17.5979	+	26.8294i	−0.637088	+	0.971289i
$764$	17.0287			0.616079
$765$	9.73745	+	16.8658i	0.352058	+	0.609783i
$766$	−7.23155	+	12.5254i	−0.261287	+	0.452562i
$767$	24.9523	−	43.2187i	0.900977	−	1.56054i
$768$	−1.29233	−	2.23838i	−0.0466330	−	0.0807707i
$769$	−18.3947			−0.663331			−0.331665	−	0.943397i	$-0.607611\pi$
$769$	−18.3947			−0.663331			−0.331665	+	0.943397i	$0.607611\pi$
$770$	4.95413	+	9.83380i	0.178534	+	0.354385i
$771$	−29.6558			−1.06803
$772$	18.7790	+	32.5261i	0.675869	+	1.17064i
$773$	5.17129	−	8.95694i	0.185998	−	0.322159i	−0.757914	−	0.652354i	$-0.773781\pi$
$773$	5.17129	−	8.95694i	0.185998	−	0.322159i	0.943912	+	0.330196i	$0.107115\pi$
$774$	1.66244	−	2.87942i	0.0597550	−	0.103499i
$775$	12.1497	+	21.0439i	0.436431	+	0.755921i
$776$	0.276518			0.00992641
$777$	−24.3318	−	1.38663i	−0.872898	−	0.0497451i
$778$	2.41520			0.0865890
$779$	2.49196	+	4.31620i	0.0892836	+	0.154644i
$780$	22.4713	−	38.9214i	0.804602	−	1.39361i
$781$	2.16011	−	3.74142i	0.0772947	−	0.133878i
$782$	−2.35098	−	4.07203i	−0.0840710	−	0.145615i
$783$	2.32836			0.0832087
$784$	−7.99934	−	18.4177i	−0.285691	−	0.657776i
$785$	32.4888			1.15957
$786$	−2.19429	−	3.80062i	−0.0782677	−	0.135564i
$787$	−19.0397	+	32.9777i	−0.678692	+	1.17553i	0.296683	+	0.954976i	$0.404119\pi$
$787$	−19.0397	+	32.9777i	−0.678692	+	1.17553i	−0.975375	+	0.220553i	$0.929214\pi$
$788$	−7.91821	+	13.7148i	−0.282075	+	0.488568i
$789$	10.9138	+	18.9033i	0.388542	+	0.672975i
$790$	0.122214			0.00434819
$791$	45.0848	+	2.56931i	1.60303	+	0.0913542i
$792$	4.12515			0.146581
$793$	−36.7649	−	63.6787i	−1.30556	−	2.26130i
$794$	−1.61897	+	2.80414i	−0.0574551	+	0.0995151i
$795$	9.44872	−	16.3657i	0.335111	−	0.580430i
$796$	20.9807	+	36.3396i	0.743641	+	1.28802i
$797$	−1.39186			−0.0493023			−0.0246512	−	0.999696i	$-0.507848\pi$
$797$	−1.39186			−0.0493023			−0.0246512	+	0.999696i	$0.507848\pi$
$798$	2.61917	+	5.19896i	0.0927175	+	0.184041i
$799$	−23.3190			−0.824966
$800$	22.5236	+	39.0121i	0.796331	+	1.37929i
$801$	−5.03404	+	8.71920i	−0.177869	+	0.308078i
$802$	2.21250	−	3.83217i	0.0781262	−	0.135318i
$803$	−11.8686	−	20.5571i	−0.418835	−	0.725444i
$804$	−0.876556			−0.0309137
$805$	11.6954	−	17.8305i	0.412207	−	0.628442i
$806$	−7.14507			−0.251674
$807$	13.8188	+	23.9349i	0.486445	+	0.842548i
$808$	15.1222	−	26.1924i	0.531996	−	0.921444i
$809$	9.35232	−	16.1987i	0.328810	−	0.569515i	−0.653466	−	0.756956i	$-0.726686\pi$
$809$	9.35232	−	16.1987i	0.328810	−	0.569515i	0.982276	+	0.187440i	$0.0600191\pi$
$810$	−0.847410	−	1.46776i	−0.0297749	−	0.0515717i
$811$	−8.66059			−0.304114			−0.152057	−	0.988372i	$-0.548590\pi$
$811$	−8.66059			−0.304114			−0.152057	+	0.988372i	$0.548590\pi$
$812$	−6.09883	+	9.29813i	−0.214027	+	0.326300i
$813$	−19.5999			−0.687399
$814$	4.99313	+	8.64836i	0.175009	+	0.303125i
$815$	−20.1691	+	34.9340i	−0.706494	+	1.22368i
$816$	−7.27607	+	12.6025i	−0.254713	+	0.441177i
$817$	18.7674	+	32.5061i	0.656588	+	1.13724i
$818$	0.508160			0.0177674
$819$	−7.72017	−	15.3243i	−0.269765	−	0.535475i
$820$	6.92966			0.241994
$821$	5.34478	+	9.25743i	0.186534	+	0.323087i	0.944092	−	0.329681i	$-0.106941\pi$
$821$	5.34478	+	9.25743i	0.186534	+	0.323087i	−0.757558	+	0.652768i	$0.773608\pi$
$822$	1.95200	−	3.38097i	0.0680839	−	0.117925i
$823$	−5.69207	+	9.85896i	−0.198413	+	0.343662i	−0.948014	−	0.318228i	$-0.896912\pi$
$823$	−5.69207	+	9.85896i	−0.198413	+	0.343662i	0.749601	+	0.661890i	$0.230245\pi$
$824$	−6.16228	−	10.6734i	−0.214673	−	0.371825i
$825$	23.9117			0.832499
$826$	8.97329	+	0.511374i	0.312221	+	0.0177930i
$827$	23.5344			0.818371			0.409185	−	0.912451i	$-0.365813\pi$
$827$	23.5344			0.818371			0.409185	+	0.912451i	$0.365813\pi$
$828$	−1.89485	−	3.28198i	−0.0658506	−	0.114057i
$829$	−14.4841	+	25.0872i	−0.503054	+	0.871314i	0.496940	+	0.867785i	$0.334457\pi$
$829$	−14.4841	+	25.0872i	−0.503054	+	0.871314i	−0.999994	+	0.00352952i	$0.998877\pi$
$830$	−6.54447	+	11.3353i	−0.227162	+	0.393456i
$831$	−9.91489	−	17.1731i	−0.343944	−	0.595728i
$832$	23.9625			0.830749
$833$	−21.1343	+	28.5371i	−0.732260	+	0.988750i
$834$	−3.54767			−0.122846
$835$	37.7315	+	65.3529i	1.30575	+	2.26163i
$836$	−11.0460	+	19.1322i	−0.382032	+	0.661700i
$837$	1.24773	−	2.16112i	0.0431277	−	0.0746993i
$838$	−2.85380	−	4.94292i	−0.0985828	−	0.170750i
$839$	−13.1731			−0.454786			−0.227393	−	0.973803i	$-0.573020\pi$
$839$	−13.1731			−0.454786			−0.227393	+	0.973803i	$0.573020\pi$
$840$	17.0347	+	0.970780i	0.587752	+	0.0334951i
$841$	−23.5787			−0.813060
$842$	−0.182277	−	0.315712i	−0.00628167	−	0.0108802i
$843$	−4.86210	+	8.42141i	−0.167460	+	0.290049i
$844$	0.393142	−	0.680942i	0.0135325	−	0.0234390i
$845$	55.7842	+	96.6210i	1.91903	+	3.32386i
$846$	2.02935			0.0697706
$847$	−5.91599	−	11.7431i	−0.203276	−	0.403496i
$848$	14.1206			0.484905
$849$	7.53792	+	13.0561i	0.258701	+	0.448083i
$850$	10.9042	−	18.8866i	0.374010	−	0.647804i
$851$	9.66950	−	16.7481i	0.331466	−	0.574116i
$852$	−1.58786	−	2.75026i	−0.0543993	−	0.0942223i
$853$	25.8416			0.884799			0.442399	−	0.896818i	$-0.354127\pi$
$853$	25.8416			0.884799			0.442399	+	0.896818i	$0.354127\pi$
$854$	7.26316	−	11.0732i	0.248540	−	0.378919i
$855$	19.1330			0.654334
$856$	3.97943	+	6.89257i	0.136014	+	0.235583i
$857$	19.6505	−	34.0356i	0.671248	−	1.16264i	−0.306302	−	0.951934i	$-0.599092\pi$
$857$	19.6505	−	34.0356i	0.671248	−	1.16264i	0.977550	−	0.210701i	$-0.0675748\pi$
$858$	−3.51553	+	6.08907i	−0.120018	+	0.207878i
$859$	−19.3649	−	33.5410i	−0.660723	−	1.14441i	−0.980426	−	0.196888i	$-0.936917\pi$
$859$	−19.3649	−	33.5410i	−0.660723	−	1.14441i	0.319703	−	0.947518i	$-0.396417\pi$
$860$	52.1886			1.77962
$861$	1.45110	−	2.21231i	0.0494533	−	0.0753953i
$862$	−0.411262			−0.0140076
$863$	21.7126	+	37.6073i	0.739104	+	1.28017i	0.952899	+	0.303287i	$0.0980842\pi$
$863$	21.7126	+	37.6073i	0.739104	+	1.28017i	−0.213795	+	0.976879i	$0.568582\pi$
$864$	2.31308	−	4.00637i	0.0786926	−	0.136300i
$865$	27.0839	−	46.9108i	0.920882	−	1.59501i
$866$	−4.22885	−	7.32458i	−0.143702	−	0.248899i
$867$	8.73515			0.296661
$868$	5.36204	+	10.6435i	0.181999	+	0.361263i
$869$	0.177077			0.00600692
$870$	−1.97307	−	3.41746i	−0.0668935	−	0.115863i
$871$	1.57469	−	2.72745i	0.0533564	−	0.0924160i
$872$	10.1862	−	17.6430i	0.344948	−	0.597468i
$873$	−0.0823030	−	0.142553i	−0.00278554	−	0.00482469i
$874$	−4.61941			−0.156254
$875$	48.0404	+	2.73775i	1.62406	+	0.0925528i
$876$	−17.4489			−0.589544
$877$	7.48270	+	12.9604i	0.252673	+	0.437642i	0.964261	−	0.264955i	$-0.0853570\pi$
$877$	7.48270	+	12.9604i	0.252673	+	0.437642i	−0.711588	+	0.702597i	$0.752024\pi$
$878$	−6.81816	+	11.8094i	−0.230102	+	0.398548i
$879$	8.85458	−	15.3366i	0.298658	−	0.517290i
$880$	13.5210	+	23.4190i	0.455792	+	0.789456i
$881$	−23.9505			−0.806914			−0.403457	−	0.914999i	$-0.632192\pi$
$881$	−23.9505			−0.806914			−0.403457	+	0.914999i	$0.632192\pi$
$882$	1.83923	−	2.48346i	0.0619301	−	0.0836225i
$883$	−12.9604			−0.436152			−0.218076	−	0.975932i	$-0.569978\pi$
$883$	−12.9604			−0.436152			−0.218076	+	0.975932i	$0.569978\pi$
$884$	−29.6947	−	51.4328i	−0.998742	−	1.72987i
$885$	14.7699	−	25.5822i	0.496484	−	0.859936i
$886$	2.58050	−	4.46956i	0.0866936	−	0.150158i
$887$	−6.95141	−	12.0402i	−0.233406	−	0.404270i	0.725403	−	0.688325i	$-0.241654\pi$
$887$	−6.95141	−	12.0402i	−0.233406	−	0.404270i	−0.958808	+	0.284055i	$0.908320\pi$
$888$	15.4741			0.519277
$889$	−44.4366	−	2.53237i	−1.49035	−	0.0849330i
$890$	17.0636			0.571972
$891$	−1.22781	−	2.12664i	−0.0411333	−	0.0712450i
$892$	2.53340	−	4.38798i	0.0848246	−	0.146921i
$893$	−11.4548	+	19.8402i	−0.383319	+	0.663928i
$894$	−3.58960	−	6.21736i	−0.120054	−	0.207940i
$895$	32.6896			1.09269
$896$	12.9553	+	25.7160i	0.432808	+	0.859110i
$897$	13.6160			0.454627
$898$	−0.277617	−	0.480847i	−0.00926421	−	0.0160461i
$899$	2.90515	−	5.03187i	0.0968922	−	0.167822i
$900$	8.78856	−	15.2222i	0.292952	−	0.507408i
$901$	−12.4860	−	21.6264i	−0.415970	−	0.720481i
$902$	−1.08411			−0.0360970
$903$	10.9285	−	16.6613i	0.363677	−	0.554454i
$904$	−28.6723			−0.953626
$905$	−37.9988	−	65.8159i	−1.26312	−	2.18779i
$906$	−4.53700	+	7.85831i	−0.150732	+	0.261075i
$907$	18.4828	−	32.0132i	0.613712	−	1.06298i	−0.376896	−	0.926255i	$-0.623009\pi$
$907$	18.4828	−	32.0132i	0.613712	−	1.06298i	0.990609	−	0.136726i	$-0.0436579\pi$
$908$	−11.0123	−	19.0738i	−0.365455	−	0.632986i
$909$	−18.0039			−0.597152
$910$	−15.9502	+	24.3173i	−0.528744	+	0.806111i
$911$	−13.9918			−0.463568			−0.231784	−	0.972767i	$-0.574456\pi$
$911$	−13.9918			−0.463568			−0.231784	+	0.972767i	$0.574456\pi$
$912$	7.14832	+	12.3813i	0.236705	+	0.409984i
$913$	−9.48230	+	16.4238i	−0.313818	+	0.543549i
$914$	1.78434	−	3.09056i	0.0590206	−	0.102227i
$915$	−21.7620	−	37.6930i	−0.719431	−	1.24609i
$916$	−24.2655			−0.801756
$917$	−11.8330	−	23.4881i	−0.390759	−	0.775644i
$918$	−2.23962			−0.0739186
$919$	−18.5747	−	32.1723i	−0.612723	−	1.06127i	−0.990779	−	0.135485i	$-0.956741\pi$
$919$	−18.5747	−	32.1723i	−0.612723	−	1.06127i	0.378056	−	0.925783i	$-0.376593\pi$
$920$	−6.76962	+	11.7253i	−0.223188	+	0.386572i
$921$	12.1355	−	21.0193i	0.399879	−	0.692610i
$922$	5.28225	+	9.14913i	0.173962	+	0.301310i
$923$	11.4101			0.375567
$924$	11.7087	+	0.667259i	0.385187	+	0.0219512i
$925$	89.6967			2.94921
$926$	1.34094	+	2.32257i	0.0440659	+	0.0763244i
$927$	−3.66830	+	6.35367i	−0.120483	+	0.208682i
$928$	5.38568	−	9.32828i	0.176794	−	0.306216i
$929$	13.9728	+	24.2016i	0.458433	+	0.794029i	0.998878	−	0.0473498i	$-0.0150775\pi$
$929$	13.9728	+	24.2016i	0.458433	+	0.794029i	−0.540445	+	0.841379i	$0.681744\pi$
$930$	−4.22934			−0.138685
$931$	13.8983	+	31.9995i	0.455498	+	1.04874i
$932$	22.0214			0.721336
$933$	−2.97798	−	5.15802i	−0.0974948	−	0.168866i
$934$	−5.52891	+	9.57636i	−0.180912	+	0.313348i
$935$	23.9116	−	41.4161i	0.781992	−	1.35445i
$936$	5.44745	+	9.43526i	0.178055	+	0.308401i
$937$	14.7129			0.480649			0.240324	−	0.970693i	$-0.422746\pi$
$937$	14.7129			0.480649			0.240324	+	0.970693i	$0.422746\pi$
$938$	0.566286	+	0.0322718i	0.0184899	+	0.00105371i
$939$	28.5445			0.931514
$940$	15.9268	+	27.5860i	0.519474	+	0.899756i
$941$	−17.2798	+	29.9294i	−0.563305	+	0.975672i	0.433901	+	0.900961i	$0.357137\pi$
$941$	−17.2798	+	29.9294i	−0.563305	+	0.975672i	−0.997205	+	0.0747114i	$0.976196\pi$
$942$	−1.86811	+	3.23566i	−0.0608663	+	0.105424i
$943$	1.04972	+	1.81817i	0.0341837	+	0.0592079i
$944$	22.0729			0.718411
$945$	−4.56976	−	9.07083i	−0.148654	−	0.295074i
$946$	−8.16465			−0.265456
$947$	16.0064	+	27.7238i	0.520137	+	0.900903i	0.999726	+	0.0234102i	$0.00745237\pi$
$947$	16.0064	+	27.7238i	0.520137	+	0.900903i	−0.479589	+	0.877493i	$0.659214\pi$
$948$	0.0650832	−	0.112727i	0.00211380	−	0.00366122i
$949$	31.3462	−	54.2932i	1.01754	−	1.76243i
$950$	−10.7127	−	18.5550i	−0.347567	−	0.602003i
$951$	−19.3616			−0.627843
$952$	12.3662	−	18.8533i	0.400792	−	0.611037i
$953$	−30.5471			−0.989519			−0.494759	−	0.869030i	$-0.664744\pi$
$953$	−30.5471			−0.989519			−0.494759	+	0.869030i	$0.664744\pi$
$954$	1.08661	+	1.88206i	0.0351802	+	0.0609339i
$955$	−18.1078	+	31.3636i	−0.585953	+	1.01490i
$956$	1.67568	−	2.90236i	0.0541952	−	0.0938689i
$957$	−2.85879	−	4.95157i	−0.0924116	−	0.160062i
$958$	−2.94102			−0.0950201
$959$	12.8320	−	19.5634i	0.414368	−	0.631735i
$960$	14.1840			0.457785
$961$	12.3864	+	21.4538i	0.399560	+	0.692058i
$962$	−13.1873	+	22.8411i	−0.425176	+	0.736427i
$963$	2.36888	−	4.10302i	0.0763361	−	0.132218i
$964$	−2.55596	−	4.42704i	−0.0823218	−	0.142585i
$965$	−79.8755			−2.57128
$966$	1.10331	+	2.19004i	0.0354984	+	0.0704633i
$967$	18.5581			0.596789			0.298395	−	0.954443i	$-0.403549\pi$
$967$	18.5581			0.596789			0.298395	+	0.954443i	$0.403549\pi$
$968$	4.17439	+	7.23026i	0.134170	+	0.232389i
$969$	12.6417	−	21.8960i	0.406108	−	0.703400i
$970$	−0.139489	+	0.241602i	−0.00447872	+	0.00775736i
$971$	12.9702	+	22.4651i	0.416234	+	0.720939i	0.995557	−	0.0941595i	$-0.0300164\pi$
$971$	12.9702	+	22.4651i	0.416234	+	0.720939i	−0.579323	+	0.815098i	$0.696683\pi$
$972$	−1.80509			−0.0578984
$973$	−21.2264	−	1.20966i	−0.680487	−	0.0387799i
$974$	−0.0159466			−0.000510961
$975$	31.5765	+	54.6921i	1.01126	+	1.75155i
$976$	16.2611	−	28.1651i	0.520507	−	0.901544i
$977$	3.21822	−	5.57413i	0.102960	−	0.178332i	−0.809943	−	0.586509i	$-0.800502\pi$
$977$	3.21822	−	5.57413i	0.102960	−	0.178332i	0.912903	+	0.408177i	$0.133835\pi$
$978$	−2.31946	−	4.01742i	−0.0741681	−	0.128463i
$979$	24.7235			0.790165
$980$	48.1936	+	5.51085i	1.53949	+	0.176038i
$981$	−12.1273			−0.387196
$982$	−6.43579	−	11.1471i	−0.205374	−	0.355719i
$983$	1.22634	−	2.12409i	0.0391142	−	0.0677478i	−0.845806	−	0.533491i	$-0.820880\pi$
$983$	1.22634	−	2.12409i	0.0391142	−	0.0677478i	0.884920	+	0.465743i	$0.154213\pi$
$984$	−0.839938	+	1.45481i	−0.0267762	+	0.0463778i
$985$	−16.8399	−	29.1675i	−0.536563	−	0.929355i
$986$	−5.21464			−0.166068
$987$	12.1420	+	0.691955i	0.386485	+	0.0220252i
$988$	−58.3468			−1.85626
$989$	7.90566	+	13.6930i	0.251386	+	0.435412i
$990$	−2.08092	+	3.60427i	−0.0661361	+	0.114551i
$991$	−8.29257	+	14.3632i	−0.263422	+	0.456261i	−0.967149	−	0.254210i	$-0.918185\pi$
$991$	−8.29257	+	14.3632i	−0.263422	+	0.456261i	0.703727	+	0.710471i	$0.251518\pi$
$992$	−5.77218	−	9.99771i	−0.183267	−	0.317428i
$993$	−14.9787			−0.475335
$994$	0.924560	+	1.83522i	0.0293253	+	0.0582098i
$995$	−89.2404			−2.82911
$996$	6.97029	+	12.0729i	0.220862	+	0.382544i
$997$	3.36615	−	5.83035i	0.106607	−	0.184649i	−0.807787	−	0.589475i	$-0.799335\pi$
$997$	3.36615	−	5.83035i	0.106607	−	0.184649i	0.914394	+	0.404826i	$0.132668\pi$
$998$	9.29078	−	16.0921i	0.294094	−	0.509386i
$999$	−4.60573	−	7.97737i	−0.145719	−	0.252393i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.i.f.739.7	yes	26
7.2	even	3	inner	861.2.i.f.247.7	✓	26
7.3	odd	6		6027.2.a.bh.1.7		13
7.4	even	3		6027.2.a.bi.1.7		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.f.247.7	✓	26	7.2	even	3	inner
861.2.i.f.739.7	yes	26	1.1	even	1	trivial
6027.2.a.bh.1.7		13	7.3	odd	6
6027.2.a.bi.1.7		13	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.220740 + 0.382333i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.902547 - 1.56326i) q^{4} +(1.91947 + 3.32462i) q^{5} -0.441481 q^{6} +(-2.64147 - 0.150533i) q^{7} +1.67988 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.220740 + 0.382333i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.902547 - 1.56326i) q^{4} +(1.91947 + 3.32462i) q^{5} -0.441481 q^{6} +(-2.64147 - 0.150533i) q^{7} +1.67988 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.847410 + 1.46776i) q^{10} +(-1.22781 + 2.12664i) q^{11} +(0.902547 + 1.56326i) q^{12} -6.48554 q^{13} +(-0.525524 - 1.04315i) q^{14} -3.83895 q^{15} +(-1.43428 - 2.48424i) q^{16} +(-2.53649 + 4.39333i) q^{17} +(0.220740 - 0.382333i) q^{18} +(2.49196 + 4.31620i) q^{19} +6.92966 q^{20} +(1.45110 - 2.21231i) q^{21} -1.08411 q^{22} +(1.04972 + 1.81817i) q^{23} +(-0.839938 + 1.45481i) q^{24} +(-4.86875 + 8.43293i) q^{25} +(-1.43162 - 2.47964i) q^{26} +1.00000 q^{27} +(-2.61937 + 3.99343i) q^{28} +2.32836 q^{29} +(-0.847410 - 1.46776i) q^{30} +(1.24773 - 2.16112i) q^{31} +(2.31308 - 4.00637i) q^{32} +(-1.22781 - 2.12664i) q^{33} -2.23962 q^{34} +(-4.56976 - 9.07083i) q^{35} -1.80509 q^{36} +(-4.60573 - 7.97737i) q^{37} +(-1.10015 + 1.90552i) q^{38} +(3.24277 - 5.61664i) q^{39} +(3.22448 + 5.58495i) q^{40} +1.00000 q^{41} +(1.16616 + 0.0664574i) q^{42} +7.53119 q^{43} +(2.21632 + 3.83878i) q^{44} +(1.91947 - 3.32462i) q^{45} +(-0.463433 + 0.802689i) q^{46} +(2.29835 + 3.98086i) q^{47} +2.86856 q^{48} +(6.95468 + 0.795256i) q^{49} -4.29892 q^{50} +(-2.53649 - 4.39333i) q^{51} +(-5.85351 + 10.1386i) q^{52} +(-2.46128 + 4.26306i) q^{53} +(0.220740 + 0.382333i) q^{54} -9.42703 q^{55} +(-4.43733 - 0.252877i) q^{56} -4.98391 q^{57} +(0.513962 + 0.890209i) q^{58} +(-3.84738 + 6.66386i) q^{59} +(-3.46483 + 6.00126i) q^{60} +(5.66875 + 9.81857i) q^{61} +1.10169 q^{62} +(1.19037 + 2.36284i) q^{63} -3.69475 q^{64} +(-12.4488 - 21.5620i) q^{65} +(0.542056 - 0.938869i) q^{66} +(-0.242801 + 0.420543i) q^{67} +(4.57861 + 7.93038i) q^{68} -2.09945 q^{69} +(2.45935 - 3.74947i) q^{70} -1.75931 q^{71} +(-0.839938 - 1.45481i) q^{72} +(-4.83324 + 8.37142i) q^{73} +(2.03334 - 3.52185i) q^{74} +(-4.86875 - 8.43293i) q^{75} +8.99644 q^{76} +(3.56336 - 5.43261i) q^{77} +2.86324 q^{78} +(-0.0360553 - 0.0624496i) q^{79} +(5.50612 - 9.53688i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.220740 + 0.382333i) q^{82} +7.72291 q^{83} +(-2.14873 - 4.26516i) q^{84} -19.4749 q^{85} +(1.66244 + 2.87942i) q^{86} +(-1.16418 + 2.01642i) q^{87} +(-2.06258 + 3.57249i) q^{88} +(-5.03404 - 8.71920i) q^{89} +1.69482 q^{90} +(17.1313 + 0.976288i) q^{91} +3.78970 q^{92} +(1.24773 + 2.16112i) q^{93} +(-1.01468 + 1.75747i) q^{94} +(-9.56649 + 16.5696i) q^{95} +(2.31308 + 4.00637i) q^{96} +0.164606 q^{97} +(1.23113 + 2.83455i) q^{98} +2.45563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 4 q^{2} - 13 q^{3} - 12 q^{4} + 8 q^{5} - 8 q^{6} + 5 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) \) 26 * q + 4 * q^2 - 13 * q^3 - 12 * q^4 + 8 * q^5 - 8 * q^6 + 5 * q^7 - 24 * q^8 - 13 * q^9	\( 26 q + 4 q^{2} - 13 q^{3} - 12 q^{4} + 8 q^{5} - 8 q^{6} + 5 q^{7} - 24 q^{8} - 13 q^{9} + q^{10} + 10 q^{11} - 12 q^{12} - 32 q^{13} - 18 q^{14} - 16 q^{15} - 26 q^{16} + 12 q^{17} + 4 q^{18} + 11 q^{19} - 12 q^{20} - 4 q^{21} + 2 q^{22} + 15 q^{23} + 12 q^{24} - 15 q^{25} + 18 q^{26} + 26 q^{27} - 55 q^{28} - 16 q^{29} + q^{30} + 9 q^{31} + 23 q^{32} + 10 q^{33} + 14 q^{34} - 10 q^{35} + 24 q^{36} + 2 q^{37} + 20 q^{38} + 16 q^{39} + 49 q^{40} + 26 q^{41} + 12 q^{42} - 14 q^{43} + 22 q^{44} + 8 q^{45} + 4 q^{46} + 26 q^{47} + 52 q^{48} - 7 q^{49} - 30 q^{50} + 12 q^{51} + 24 q^{52} - 4 q^{53} + 4 q^{54} - 2 q^{55} + 9 q^{56} - 22 q^{57} - 39 q^{58} - 3 q^{59} + 6 q^{60} + 28 q^{61} - 14 q^{62} - q^{63} + 4 q^{64} + 20 q^{65} - q^{66} - 7 q^{67} + 55 q^{68} - 30 q^{69} + 8 q^{70} - 80 q^{71} + 12 q^{72} - 2 q^{73} - q^{74} - 15 q^{75} + 52 q^{76} + 28 q^{77} - 36 q^{78} - 13 q^{79} + 22 q^{80} - 13 q^{81} + 4 q^{82} - 28 q^{83} + 11 q^{84} + 96 q^{85} + 49 q^{86} + 8 q^{87} - 20 q^{88} + 35 q^{89} - 2 q^{90} + 4 q^{91} - 210 q^{92} + 9 q^{93} - 2 q^{94} - 7 q^{95} + 23 q^{96} - 128 q^{97} - 17 q^{98} - 20 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 - 13 * q^3 - 12 * q^4 + 8 * q^5 - 8 * q^6 + 5 * q^7 - 24 * q^8 - 13 * q^9 + q^10 + 10 * q^11 - 12 * q^12 - 32 * q^13 - 18 * q^14 - 16 * q^15 - 26 * q^16 + 12 * q^17 + 4 * q^18 + 11 * q^19 - 12 * q^20 - 4 * q^21 + 2 * q^22 + 15 * q^23 + 12 * q^24 - 15 * q^25 + 18 * q^26 + 26 * q^27 - 55 * q^28 - 16 * q^29 + q^30 + 9 * q^31 + 23 * q^32 + 10 * q^33 + 14 * q^34 - 10 * q^35 + 24 * q^36 + 2 * q^37 + 20 * q^38 + 16 * q^39 + 49 * q^40 + 26 * q^41 + 12 * q^42 - 14 * q^43 + 22 * q^44 + 8 * q^45 + 4 * q^46 + 26 * q^47 + 52 * q^48 - 7 * q^49 - 30 * q^50 + 12 * q^51 + 24 * q^52 - 4 * q^53 + 4 * q^54 - 2 * q^55 + 9 * q^56 - 22 * q^57 - 39 * q^58 - 3 * q^59 + 6 * q^60 + 28 * q^61 - 14 * q^62 - q^63 + 4 * q^64 + 20 * q^65 - q^66 - 7 * q^67 + 55 * q^68 - 30 * q^69 + 8 * q^70 - 80 * q^71 + 12 * q^72 - 2 * q^73 - q^74 - 15 * q^75 + 52 * q^76 + 28 * q^77 - 36 * q^78 - 13 * q^79 + 22 * q^80 - 13 * q^81 + 4 * q^82 - 28 * q^83 + 11 * q^84 + 96 * q^85 + 49 * q^86 + 8 * q^87 - 20 * q^88 + 35 * q^89 - 2 * q^90 + 4 * q^91 - 210 * q^92 + 9 * q^93 - 2 * q^94 - 7 * q^95 + 23 * q^96 - 128 * q^97 - 17 * q^98 - 20 * q^99

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