LMFDB - Embedded newform 61.2.g.a.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(3,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("61.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.g (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 17x^{14} + 111x^{12} + 361x^{10} + 624x^{8} + 558x^{6} + 229x^{4} + 34x^{2} + 1 $ x^16 + 17x^14 + 111x^12 + 361x^10 + 624x^8 + 558x^6 + 229x^4 + 34*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			27.1
Root			$1.85647i$ of defining polynomial
Character	$\chi$	$=$	61.27
Dual form			61.2.g.a.52.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09120 - 1.50191i) q^{2} +(2.38911 - 1.73579i) q^{3} +(-0.446986 + 1.37568i) q^{4} +(-1.04459 + 3.21492i) q^{5} +(-5.21402 - 1.69414i) q^{6} +(-0.380995 + 0.524395i) q^{7} +(-0.977305 + 0.317546i) q^{8} +(1.76783 - 5.44082i) q^{9} +O(q^{10})$	\(q+(-1.09120 - 1.50191i) q^{2} +(2.38911 - 1.73579i) q^{3} +(-0.446986 + 1.37568i) q^{4} +(-1.04459 + 3.21492i) q^{5} +(-5.21402 - 1.69414i) q^{6} +(-0.380995 + 0.524395i) q^{7} +(-0.977305 + 0.317546i) q^{8} +(1.76783 - 5.44082i) q^{9} +(5.96841 - 1.93925i) q^{10} +1.99452i q^{11} +(1.32000 + 4.06253i) q^{12} -3.16903 q^{13} +1.20334 q^{14} +(3.08479 + 9.49401i) q^{15} +(3.88381 + 2.82176i) q^{16} +(-1.97448 - 0.641547i) q^{17} +(-10.1007 + 3.28192i) q^{18} +(6.52771 - 4.74266i) q^{19} +(-3.95579 - 2.87405i) q^{20} +1.91417i q^{21} +(2.99560 - 2.17643i) q^{22} +(-1.69695 - 0.551371i) q^{23} +(-1.78370 + 2.45505i) q^{24} +(-5.19948 - 3.77765i) q^{25} +(3.45806 + 4.75962i) q^{26} +(-2.48291 - 7.64161i) q^{27} +(-0.551101 - 0.758525i) q^{28} -4.71399i q^{29} +(10.8931 - 14.9930i) q^{30} +(-3.45198 + 4.75125i) q^{31} -6.85708i q^{32} +(3.46208 + 4.76514i) q^{33} +(1.19101 + 3.66556i) q^{34} +(-1.28791 - 1.77265i) q^{35} +(6.69464 + 4.86394i) q^{36} +(0.671864 - 0.924742i) q^{37} +(-14.2461 - 4.62885i) q^{38} +(-7.57117 + 5.50078i) q^{39} -3.47367i q^{40} +(-0.608514 - 0.442111i) q^{41} +(2.87491 - 2.08875i) q^{42} +(-7.92050 + 2.57353i) q^{43} +(-2.74383 - 0.891524i) q^{44} +(15.6452 + 11.3669i) q^{45} +(1.02360 + 3.15033i) q^{46} -0.0653651 q^{47} +14.1768 q^{48} +(2.03329 + 6.25781i) q^{49} +11.9314i q^{50} +(-5.83084 + 1.89456i) q^{51} +(1.41651 - 4.35958i) q^{52} +(8.91212 - 2.89572i) q^{53} +(-8.76768 + 12.0677i) q^{54} +(-6.41224 - 2.08346i) q^{55} +(0.205829 - 0.633477i) q^{56} +(7.36316 - 22.6615i) q^{57} +(-7.08001 + 5.14393i) q^{58} +(3.23616 + 4.45419i) q^{59} -14.4396 q^{60} +(-6.96193 - 3.53999i) q^{61} +10.9028 q^{62} +(2.17961 + 2.99997i) q^{63} +(-2.53111 + 1.83896i) q^{64} +(3.31035 - 10.1882i) q^{65} +(3.37900 - 10.3995i) q^{66} +(-2.94629 - 0.957308i) q^{67} +(1.76513 - 2.42949i) q^{68} +(-5.01126 + 1.62826i) q^{69} +(-1.25700 + 3.86865i) q^{70} +(2.91741 - 0.947925i) q^{71} +5.87871i q^{72} +(1.61021 + 4.95571i) q^{73} -2.12203 q^{74} -18.9793 q^{75} +(3.60659 + 11.0999i) q^{76} +(-1.04592 - 0.759904i) q^{77} +(16.5234 + 5.36878i) q^{78} +(10.2090 - 3.31711i) q^{79} +(-13.1287 + 9.53859i) q^{80} +(-5.31146 - 3.85900i) q^{81} +1.39637i q^{82} +(0.991530 - 0.720388i) q^{83} +(-2.63328 - 0.855605i) q^{84} +(4.12505 - 5.67765i) q^{85} +(12.5081 + 9.08767i) q^{86} +(-8.18249 - 11.2622i) q^{87} +(-0.633352 - 1.94926i) q^{88} +(-4.86460 - 6.69554i) q^{89} -35.9013i q^{90} +(1.20739 - 1.66183i) q^{91} +(1.51702 - 2.08800i) q^{92} +17.3432i q^{93} +(0.0713268 + 0.0981729i) q^{94} +(8.42850 + 25.9402i) q^{95} +(-11.9024 - 16.3823i) q^{96} +(6.74067 + 4.89738i) q^{97} +(7.17997 - 9.88238i) q^{98} +(10.8519 + 3.52598i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	$ 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) $ 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−1.09120	−	1.50191i	−0.771598	−	1.06201i	−0.996160	−	0.0875542i	$-0.972095\pi$
$2$	−1.09120	−	1.50191i	−0.771598	−	1.06201i	0.224561	−	0.974460i	$-0.427905\pi$
$3$	2.38911	−	1.73579i	1.37935	−	1.00216i	0.382414	−	0.923991i	$-0.375093\pi$
$3$	2.38911	−	1.73579i	1.37935	−	1.00216i	0.996940	−	0.0781680i	$-0.0249070\pi$
$4$	−0.446986	+	1.37568i	−0.223493	+	0.687840i
$5$	−1.04459	+	3.21492i	−0.467156	+	1.43776i	0.389095	+	0.921198i	$0.372788\pi$
$5$	−1.04459	+	3.21492i	−0.467156	+	1.43776i	−0.856251	+	0.516560i	$0.827212\pi$
$6$	−5.21402	−	1.69414i	−2.12861	−	0.691629i
$7$	−0.380995	+	0.524395i	−0.144003	+	0.198203i	−0.874926	−	0.484257i	$-0.839090\pi$
$7$	−0.380995	+	0.524395i	−0.144003	+	0.198203i	0.730923	+	0.682460i	$0.239090\pi$
$8$	−0.977305	+	0.317546i	−0.345529	+	0.112269i
$9$	1.76783	−	5.44082i	0.589277	−	1.81361i
$10$	5.96841	−	1.93925i	1.88738	−	0.613246i
$11$			1.99452i			0.601372i	0.953723	+	0.300686i	$0.0972155\pi$
$11$			1.99452i			0.601372i	−0.953723	+	0.300686i	$0.902784\pi$
$12$	1.32000	+	4.06253i	0.381050	+	1.17275i
$13$	−3.16903			−0.878932			−0.439466	−	0.898259i	$-0.644832\pi$
$13$	−3.16903			−0.878932			−0.439466	+	0.898259i	$0.644832\pi$
$14$	1.20334			0.321606
$15$	3.08479	+	9.49401i	0.796489	+	2.45134i
$16$	3.88381	+	2.82176i	0.970954	+	0.705439i
$17$	−1.97448	−	0.641547i	−0.478882	−	0.155598i	0.0596224	−	0.998221i	$-0.481010\pi$
$17$	−1.97448	−	0.641547i	−0.478882	−	0.155598i	−0.538504	+	0.842623i	$0.681010\pi$
$18$	−10.1007	+	3.28192i	−2.38076	+	0.773557i
$19$	6.52771	−	4.74266i	1.49756	−	1.08804i	0.526219	−	0.850349i	$-0.323609\pi$
$19$	6.52771	−	4.74266i	1.49756	−	1.08804i	0.971341	−	0.237691i	$-0.0763906\pi$
$20$	−3.95579	−	2.87405i	−0.884542	−	0.642658i
$21$			1.91417i			0.417705i
$22$	2.99560	−	2.17643i	0.638665	−	0.464017i
$23$	−1.69695	−	0.551371i	−0.353838	−	0.114969i	0.126704	−	0.991941i	$-0.459560\pi$
$23$	−1.69695	−	0.551371i	−0.353838	−	0.114969i	−0.480542	+	0.876972i	$0.659560\pi$
$24$	−1.78370	+	2.45505i	−0.364096	+	0.501135i
$25$	−5.19948	−	3.77765i	−1.03990	−	0.755529i
$26$	3.45806	+	4.75962i	0.678182	+	0.933438i
$27$	−2.48291	−	7.64161i	−0.477836	−	1.47063i
$28$	−0.551101	−	0.758525i	−0.104148	−	0.143348i
$29$		−	4.71399i		−	0.875365i	−0.899130	−	0.437683i	$-0.855799\pi$
$29$		−	4.71399i		−	0.875365i	0.899130	−	0.437683i	$-0.144201\pi$
$30$	10.8931	−	14.9930i	1.98879	−	2.73733i
$31$	−3.45198	+	4.75125i	−0.619995	+	0.853350i	−0.997353	−	0.0727180i	$-0.976833\pi$
$31$	−3.45198	+	4.75125i	−0.619995	+	0.853350i	0.377358	+	0.926068i	$0.376833\pi$
$32$		−	6.85708i		−	1.21217i
$33$	3.46208	+	4.76514i	0.602670	+	0.829504i
$34$	1.19101	+	3.66556i	0.204257	+	0.628638i
$35$	−1.28791	−	1.77265i	−0.217696	−	0.299633i
$36$	6.69464	+	4.86394i	1.11577	+	0.810657i
$37$	0.671864	−	0.924742i	0.110454	−	0.152027i	−0.750211	−	0.661198i	$-0.770048\pi$
$37$	0.671864	−	0.924742i	0.110454	−	0.152027i	0.860665	+	0.509172i	$0.170048\pi$
$38$	−14.2461	−	4.62885i	−2.31103	−	0.750899i
$39$	−7.57117	+	5.50078i	−1.21236	+	0.880829i
$40$		−	3.47367i		−	0.549235i
$41$	−0.608514	−	0.442111i	−0.0950339	−	0.0690462i	0.539254	−	0.842143i	$-0.318706\pi$
$41$	−0.608514	−	0.442111i	−0.0950339	−	0.0690462i	−0.634287	+	0.773097i	$0.718706\pi$
$42$	2.87491	−	2.08875i	0.443609	−	0.322301i
$43$	−7.92050	+	2.57353i	−1.20786	+	0.392459i	−0.842649	−	0.538464i	$-0.819005\pi$
$43$	−7.92050	+	2.57353i	−1.20786	+	0.392459i	−0.365216	+	0.930923i	$0.619005\pi$
$44$	−2.74383	−	0.891524i	−0.413648	−	0.134402i
$45$	15.6452	+	11.3669i	2.33225	+	1.69448i
$46$	1.02360	+	3.15033i	0.150922	+	0.464490i
$47$	−0.0653651			−0.00953448			−0.00476724	−	0.999989i	$-0.501517\pi$
$47$	−0.0653651			−0.00953448			−0.00476724	+	0.999989i	$0.501517\pi$
$48$	14.1768			2.04625
$49$	2.03329	+	6.25781i	0.290469	+	0.893973i
$50$			11.9314i			1.68735i
$51$	−5.83084	+	1.89456i	−0.816481	+	0.265291i
$52$	1.41651	−	4.35958i	0.196435	−	0.604565i
$53$	8.91212	−	2.89572i	1.22417	−	0.397758i	0.375573	−	0.926793i	$-0.377446\pi$
$53$	8.91212	−	2.89572i	1.22417	−	0.397758i	0.848600	+	0.529035i	$0.177446\pi$
$54$	−8.76768	+	12.0677i	−1.19313	+	1.64220i
$55$	−6.41224	−	2.08346i	−0.864627	−	0.280934i
$56$	0.205829	−	0.633477i	0.0275051	−	0.0846520i
$57$	7.36316	−	22.6615i	0.975274	−	3.00159i
$58$	−7.08001	+	5.14393i	−0.929650	+	0.675431i
$59$	3.23616	+	4.45419i	0.421312	+	0.579886i	0.965932	−	0.258797i	$-0.0833260\pi$
$59$	3.23616	+	4.45419i	0.421312	+	0.579886i	−0.544620	+	0.838683i	$0.683326\pi$
$60$	−14.4396			−1.86414
$61$	−6.96193	−	3.53999i	−0.891384	−	0.453250i
$61$	−6.96193	−	3.53999i	−0.891384	−	0.453250i
$62$	10.9028			1.38466
$63$	2.17961	+	2.99997i	0.274605	+	0.377961i
$64$	−2.53111	+	1.83896i	−0.316389	+	0.229870i
$65$	3.31035	−	10.1882i	0.410598	−	1.26369i
$66$	3.37900	−	10.3995i	0.415926	−	1.28009i
$67$	−2.94629	−	0.957308i	−0.359947	−	0.116954i	0.123460	−	0.992350i	$-0.460601\pi$
$67$	−2.94629	−	0.957308i	−0.359947	−	0.116954i	−0.483407	+	0.875396i	$0.660601\pi$
$68$	1.76513	−	2.42949i	0.214053	−	0.294619i
$69$	−5.01126	+	1.62826i	−0.603284	+	0.196019i
$70$	−1.25700	+	3.86865i	−0.150240	+	0.462392i
$71$	2.91741	−	0.947925i	0.346233	−	0.112498i	−0.130738	−	0.991417i	$-0.541735\pi$
$71$	2.91741	−	0.947925i	0.346233	−	0.112498i	0.476971	+	0.878919i	$0.341735\pi$
$72$			5.87871i			0.692813i
$73$	1.61021	+	4.95571i	0.188461	+	0.580022i	0.999991	−	0.00428843i	$-0.00136505\pi$
$73$	1.61021	+	4.95571i	0.188461	+	0.580022i	−0.811530	+	0.584310i	$0.801365\pi$
$74$	−2.12203			−0.246680
$75$	−18.9793			−2.19155
$76$	3.60659	+	11.0999i	0.413704	+	1.27325i
$77$	−1.04592	−	0.759904i	−0.119193	−	0.0865991i
$78$	16.5234	+	5.36878i	1.87091	+	0.607894i
$79$	10.2090	−	3.31711i	1.14860	−	0.373204i	0.327986	−	0.944682i	$-0.393630\pi$
$79$	10.2090	−	3.31711i	1.14860	−	0.373204i	0.820617	+	0.571479i	$0.193630\pi$
$80$	−13.1287	+	9.53859i	−1.46784	+	1.06645i
$81$	−5.31146	−	3.85900i	−0.590162	−	0.428778i
$82$			1.39637i			0.154203i
$83$	0.991530	−	0.720388i	0.108835	−	0.0790729i	−0.532037	−	0.846721i	$-0.678573\pi$
$83$	0.991530	−	0.720388i	0.108835	−	0.0790729i	0.640871	+	0.767648i	$0.278573\pi$
$84$	−2.63328	−	0.855605i	−0.287315	−	0.0933542i
$85$	4.12505	−	5.67765i	0.447425	−	0.615827i
$86$	12.5081	+	9.08767i	1.34878	+	0.979949i
$87$	−8.18249	−	11.2622i	−0.877255	−	1.20744i
$88$	−0.633352	−	1.94926i	−0.0675156	−	0.207792i
$89$	−4.86460	−	6.69554i	−0.515646	−	0.709726i	0.469212	−	0.883085i	$-0.344538\pi$
$89$	−4.86460	−	6.69554i	−0.515646	−	0.709726i	−0.984859	+	0.173359i	$0.944538\pi$
$90$		−	35.9013i		−	3.78433i
$91$	1.20739	−	1.66183i	0.126569	−	0.174207i
$92$	1.51702	−	2.08800i	0.158160	−	0.217689i
$93$			17.3432i			1.79840i
$94$	0.0713268	+	0.0981729i	0.00735679	+	0.0101258i
$95$	8.42850	+	25.9402i	0.864745	+	2.66141i
$96$	−11.9024	−	16.3823i	−1.21479	−	1.67201i
$97$	6.74067	+	4.89738i	0.684411	+	0.497254i	0.874818	−	0.484451i	$-0.160981\pi$
$97$	6.74067	+	4.89738i	0.684411	+	0.497254i	−0.190407	+	0.981705i	$0.560981\pi$
$98$	7.17997	−	9.88238i	0.725286	−	0.998271i
$99$	10.8519	+	3.52598i	1.09065	+	0.354374i
$100$	7.52093	−	5.46428i	0.752093	−	0.546428i
$101$		−	1.81333i		−	0.180433i	−0.995922	−	0.0902165i	$-0.971244\pi$
$101$		−	1.81333i		−	0.180433i	0.995922	−	0.0902165i	$-0.0287559\pi$
$102$	9.20810	+	6.69008i	0.911738	+	0.662417i
$103$	4.45208	−	3.23462i	0.438676	−	0.318717i	−0.346432	−	0.938075i	$-0.612607\pi$
$103$	4.45208	−	3.23462i	0.438676	−	0.318717i	0.785109	+	0.619358i	$0.212607\pi$
$104$	3.09711	−	1.00631i	0.303697	−	0.0986770i
$105$	−6.15390	−	1.99952i	−0.600559	−	0.195134i
$106$	−14.0741	−	10.2254i	−1.36699	−	0.993180i
$107$	−0.309196	−	0.951609i	−0.0298911	−	0.0919955i	0.934998	−	0.354653i	$-0.115401\pi$
$107$	−0.309196	−	0.951609i	−0.0298911	−	0.0919955i	−0.964889	+	0.262658i	$0.915401\pi$
$108$	11.6222			1.11835
$109$	−10.1528			−0.972464			−0.486232	−	0.873830i	$-0.661629\pi$
$109$	−10.1528			−0.972464			−0.486232	+	0.873830i	$0.661629\pi$
$110$	3.86789	+	11.9041i	0.368789	+	1.13501i
$111$		−	3.37553i		−	0.320391i
$112$	−2.95943	+	0.961577i	−0.279640	+	0.0908605i
$113$	2.96773	−	9.13375i	0.279181	−	0.859231i	−0.708902	−	0.705307i	$-0.750809\pi$
$113$	2.96773	−	9.13375i	0.279181	−	0.859231i	0.988083	−	0.153924i	$-0.0491909\pi$
$114$	−42.0703	+	13.6695i	−3.94025	+	1.28026i
$115$	3.54523	−	4.87959i	0.330595	−	0.455025i
$116$	6.48494	+	2.10709i	0.602112	+	0.195638i
$117$	−5.60231	+	17.2421i	−0.517934	+	1.59404i
$118$	3.15850	−	9.72087i	0.290764	−	0.894879i
$119$	1.08869	−	0.790981i	0.0998002	−	0.0725091i
$120$	−6.02956	−	8.29898i	−0.550421	−	0.757589i
$121$	7.02188			0.638352
$122$	2.28012	+	14.3191i	0.206432	+	1.29639i
$123$	−2.22122			−0.200281
$124$	−4.99321	−	6.87257i	−0.448404	−	0.617175i
$125$	3.90230	−	2.83519i	0.349032	−	0.253587i
$126$	2.12730	−	6.54716i	0.189515	−	0.583268i
$127$	0.634767	−	1.95361i	0.0563265	−	0.173355i	−0.918935	−	0.394408i	$-0.870950\pi$
$127$	0.634767	−	1.95361i	0.0563265	−	0.173355i	0.975262	+	0.221053i	$0.0709495\pi$
$128$	−7.51900	−	2.44307i	−0.664592	−	0.215939i
$129$	−14.4558	+	19.8968i	−1.27277	+	1.75181i
$130$	−18.9141	+	6.14556i	−1.65887	+	0.539001i
$131$	−6.08890	+	18.7397i	−0.531990	+	1.63730i	0.218075	+	0.975932i	$0.430022\pi$
$131$	−6.08890	+	18.7397i	−0.531990	+	1.63730i	−0.750065	+	0.661364i	$0.769978\pi$
$132$	−8.10281	+	2.63276i	−0.705259	+	0.229153i
$133$			5.23003i			0.453501i
$134$	1.77721	+	5.46970i	0.153528	+	0.472510i
$135$	27.1608			2.33763
$136$	2.13339			0.182937
$137$	−1.08235	−	3.33113i	−0.0924713	−	0.284597i	0.894115	−	0.447837i	$-0.147806\pi$
$137$	−1.08235	−	3.33113i	−0.0924713	−	0.284597i	−0.986586	+	0.163240i	$0.947806\pi$
$138$	7.91381	+	5.74972i	0.673668	+	0.489449i
$139$	4.41220	+	1.43361i	0.374238	+	0.121597i	0.490096	−	0.871669i	$-0.336962\pi$
$139$	4.41220	+	1.43361i	0.374238	+	0.121597i	−0.115858	+	0.993266i	$0.536962\pi$
$140$	3.01428	−	0.979398i	0.254753	−	0.0827742i
$141$	−0.156165	+	0.113460i	−0.0131514	+	0.00955507i
$142$	−4.60720	−	3.34733i	−0.386627	−	0.280901i
$143$		−	6.32071i		−	0.528564i
$144$	22.2186	−	16.1428i	1.85155	−	1.34523i
$145$	15.1551	+	4.92419i	1.25856	+	0.408932i
$146$	5.68599	−	7.82609i	0.470576	−	0.647692i
$147$	15.7200	+	11.4212i	1.29656	+	0.942009i
$148$	0.971836	+	1.33762i	0.0798844	+	0.109952i
$149$	−5.90174	−	18.1637i	−0.483490	−	1.48803i	−0.834156	−	0.551528i	$-0.814045\pi$
$149$	−5.90174	−	18.1637i	−0.483490	−	1.48803i	0.350667	−	0.936500i	$-0.385955\pi$
$150$	20.7104	+	28.5054i	1.69099	+	2.32745i
$151$			14.8545i			1.20885i	0.796664	+	0.604423i	$0.206596\pi$
$151$			14.8545i			1.20885i	−0.796664	+	0.604423i	$0.793404\pi$
$152$	−4.87355	+	6.70787i	−0.395297	+	0.544080i
$153$	−6.98109	+	9.60865i	−0.564388	+	0.776813i
$154$			2.40009i			0.193405i
$155$	−11.6690	−	16.0610i	−0.937276	−	1.29005i
$156$	−4.18311	−	12.8743i	−0.334917	−	1.03077i
$157$	−5.86799	−	8.07659i	−0.468316	−	0.644582i	0.507891	−	0.861421i	$-0.330425\pi$
$157$	−5.86799	−	8.07659i	−0.468316	−	0.644582i	−0.976207	+	0.216839i	$0.930425\pi$
$158$	−16.1221	−	11.7134i	−1.28261	−	0.931869i
$159$	16.2657	−	22.3878i	1.28995	−	1.77547i
$160$	22.0450	+	7.16285i	1.74281	+	0.566273i
$161$	0.935665	−	0.679800i	0.0737407	−	0.0535758i
$162$			12.1883i			0.957605i
$163$	−19.2154	−	13.9608i	−1.50507	−	1.09349i	−0.968309	−	0.249757i	$-0.919649\pi$
$163$	−19.2154	−	13.9608i	−1.50507	−	1.09349i	−0.536756	−	0.843737i	$-0.680351\pi$
$164$	0.880201	−	0.639504i	0.0687322	−	0.0499368i
$165$	−18.9360	+	6.15269i	−1.47417	+	0.478986i
$166$	−2.16392	−	0.703102i	−0.167953	−	0.0545713i
$167$	8.41684	+	6.11519i	0.651315	+	0.473208i	0.863719	−	0.503974i	$-0.168129\pi$
$167$	8.41684	+	6.11519i	0.651315	+	0.473208i	−0.212404	+	0.977182i	$0.568129\pi$
$168$	−0.607835	−	1.87072i	−0.0468955	−	0.144329i
$169$	−2.95723			−0.227479
$170$	−13.0286			−0.999250
$171$	−14.2641	−	43.9003i	−1.09080	−	3.35714i
$172$		−	12.0464i		−	0.918530i
$173$	15.1752	−	4.93072i	1.15375	−	0.374876i	0.331194	−	0.943563i	$-0.392548\pi$
$173$	15.1752	−	4.93072i	1.15375	−	0.374876i	0.822554	+	0.568687i	$0.192548\pi$
$174$	−7.98614	+	24.5788i	−0.605428	+	1.86332i
$175$	3.96196	−	1.28732i	0.299496	−	0.0973121i
$176$	−5.62806	+	7.74636i	−0.424231	+	0.583904i
$177$	15.4631	+	5.02426i	1.16228	+	0.377647i
$178$	−4.74786	+	14.6124i	−0.355867	+	1.09525i
$179$	−4.34140	+	13.3615i	−0.324492	+	0.998682i	0.647178	+	0.762339i	$0.275949\pi$
$179$	−4.34140	+	13.3615i	−0.324492	+	0.998682i	−0.971670	+	0.236343i	$0.924051\pi$
$180$	−22.6304	+	16.4419i	−1.68677	+	1.22551i
$181$	6.78088	+	9.33308i	0.504019	+	0.693723i	0.982896	−	0.184159i	$-0.0589562\pi$
$181$	6.78088	+	9.33308i	0.504019	+	0.693723i	−0.478877	+	0.877882i	$0.658956\pi$
$182$	−3.81343			−0.282670
$183$	−22.7775	+	3.62701i	−1.68376	+	0.268116i
$184$	1.83352			0.135169
$185$	2.27115	+	3.12597i	0.166978	+	0.229826i
$186$	26.0480	−	18.9250i	1.90993	−	1.38765i
$187$	1.27958	−	3.93815i	0.0935722	−	0.287986i
$188$	0.0292173	−	0.0899216i	0.00213089	−	0.00655820i
$189$	4.95320	+	1.60939i	0.360292	+	0.117066i
$190$	29.7628	−	40.9650i	2.15922	−	2.97191i
$191$	17.5805	−	5.71226i	1.27208	−	0.413325i	0.406298	−	0.913741i	$-0.366820\pi$
$191$	17.5805	−	5.71226i	1.27208	−	0.413325i	0.865785	+	0.500416i	$0.166820\pi$
$192$	−2.85506	+	8.78697i	−0.206046	+	0.634145i
$193$	−19.7470	+	6.41618i	−1.42142	+	0.461847i	−0.916053	−	0.401058i	$-0.868642\pi$
$193$	−19.7470	+	6.41618i	−1.42142	+	0.461847i	−0.505366	+	0.862905i	$0.668642\pi$
$194$		−	15.4680i		−	1.11053i
$195$	−9.77580	−	30.0868i	−0.700060	−	2.15456i
$196$	−9.51760			−0.679829
$197$	−10.9269			−0.778512			−0.389256	−	0.921130i	$-0.627268\pi$
$197$	−10.9269			−0.778512			−0.389256	+	0.921130i	$0.627268\pi$
$198$	−6.54587	−	20.1461i	−0.465195	−	1.43172i
$199$	15.6016	+	11.3353i	1.10597	+	0.803535i	0.982024	−	0.188754i	$-0.0604448\pi$
$199$	15.6016	+	11.3353i	1.10597	+	0.803535i	0.123947	+	0.992289i	$0.460445\pi$
$200$	6.28106	+	2.04084i	0.444138	+	0.144309i
$201$	−8.70070	+	2.82703i	−0.613700	+	0.199403i
$202$	−2.72347	+	1.97871i	−0.191622	+	0.139222i
$203$	2.47199	+	1.79601i	0.173500	+	0.126055i
$204$		−	8.86822i		−	0.620899i
$205$	2.05700	−	1.49450i	0.143667	−	0.104380i
$206$	−9.71626	−	3.15700i	−0.676964	−	0.219959i
$207$	−5.99983	+	8.25805i	−0.417017	+	0.573974i
$208$	−12.3079	−	8.94224i	−0.853402	−	0.620033i
$209$	9.45935	+	13.0197i	0.654317	+	0.900590i
$210$	3.71205	+	11.4245i	0.256156	+	0.788367i
$211$	1.91405	+	2.63447i	0.131769	+	0.181364i	0.869803	−	0.493399i	$-0.164246\pi$
$211$	1.91405	+	2.63447i	0.131769	+	0.181364i	−0.738034	+	0.674763i	$0.764246\pi$
$212$			13.5546i			0.930932i
$213$	5.32462	−	7.32872i	0.364837	−	0.502155i
$214$	−1.09184	+	1.50279i	−0.0746365	+	0.102728i
$215$		−	28.1521i		−	1.91996i
$216$	4.85312	+	6.67974i	0.330213	+	0.454499i
$217$	−1.17634	−	3.62041i	−0.0798553	−	0.245769i
$218$	11.0788	+	15.2487i	0.750352	+	1.03277i
$219$	12.4490	+	9.04476i	0.841228	+	0.611188i
$220$	5.73236	−	7.88992i	0.386476	−	0.531938i
$221$	6.25719	+	2.03308i	0.420904	+	0.136760i
$222$	−5.06975	+	3.68339i	−0.340260	+	0.247213i
$223$			19.1357i			1.28142i	0.767782	+	0.640712i	$0.221361\pi$
$223$			19.1357i			1.28142i	−0.767782	+	0.640712i	$0.778639\pi$
$224$	3.59582	+	2.61251i	0.240256	+	0.174556i
$225$	−29.7453	+	21.6112i	−1.98302	+	1.44075i
$226$	−16.9565	+	5.50951i	−1.12793	+	0.366487i
$227$	27.7372	+	9.01235i	1.84098	+	0.598170i	0.998204	+	0.0599050i	$0.0190798\pi$
$227$	27.7372	+	9.01235i	1.84098	+	0.598170i	0.842775	+	0.538266i	$0.180920\pi$
$228$	27.8837	+	20.2587i	1.84665	+	1.34167i
$229$	−1.52092	−	4.68090i	−0.100505	−	0.309323i	0.888144	−	0.459565i	$-0.151995\pi$
$229$	−1.52092	−	4.68090i	−0.100505	−	0.309323i	−0.988649	+	0.150242i	$0.951995\pi$
$230$	−11.1973			−0.738329
$231$	−3.81785			−0.251196
$232$	1.49691	+	4.60700i	0.0982767	+	0.302464i
$233$			12.4757i			0.817311i	0.912689	+	0.408656i	$0.134002\pi$
$233$			12.4757i			0.817311i	−0.912689	+	0.408656i	$0.865998\pi$
$234$	32.0095	−	10.4005i	2.09253	−	0.679903i
$235$	0.0682799	−	0.210144i	0.00445409	−	0.0137083i
$236$	−7.57406	+	2.46096i	−0.493029	+	0.160195i
$237$	18.6326	−	25.6456i	1.21032	−	1.66586i
$238$	−2.37597	−	0.772000i	−0.154011	−	0.0500413i
$239$	−0.356672	+	1.09772i	−0.0230712	+	0.0710057i	−0.961929	−	0.273299i	$-0.911885\pi$
$239$	−0.356672	+	1.09772i	−0.0230712	+	0.0710057i	0.938858	+	0.344304i	$0.111885\pi$
$240$	−14.8090	+	45.5775i	−0.955918	+	2.94201i
$241$	1.23981	−	0.900772i	0.0798630	−	0.0580238i	−0.547137	−	0.837043i	$-0.684282\pi$
$241$	1.23981	−	0.900772i	0.0798630	−	0.0580238i	0.627000	+	0.779019i	$0.284282\pi$
$242$	−7.66231	−	10.5463i	−0.492552	−	0.677939i
$243$	4.71651			0.302564
$244$	7.98179	−	7.99506i	0.510981	−	0.511832i
$245$	−22.2423			−1.42101
$246$	2.42381	+	3.33608i	0.154536	+	0.212701i
$247$	−20.6865	+	15.0296i	−1.31625	+	0.956313i
$248$	1.86490	−	5.73958i	0.118421	−	0.364464i
$249$	1.11843	−	3.44218i	0.0708777	−	0.218139i
$250$	−8.51641	−	2.76715i	−0.538625	−	0.175010i
$251$	−4.61811	+	6.35629i	−0.291493	+	0.401205i	−0.929498	−	0.368826i	$-0.879760\pi$
$251$	−4.61811	+	6.35629i	−0.291493	+	0.401205i	0.638006	+	0.770032i	$0.279760\pi$
$252$	−5.10125	+	1.65750i	−0.321349	+	0.104413i
$253$	1.09972	−	3.38460i	0.0691390	−	0.212788i
$254$	−3.62682	+	1.17843i	−0.227567	+	0.0739410i
$255$		−	20.7248i		−	1.29783i
$256$	6.46909	+	19.9098i	0.404318	+	1.24436i
$257$	−30.3098			−1.89068			−0.945338	−	0.326093i	$-0.894268\pi$
$257$	−30.3098			−1.89068			−0.945338	+	0.326093i	$0.894268\pi$
$258$	45.6575			2.84251
$259$	0.228953	+	0.704645i	0.0142264	+	0.0437845i
$260$	12.5360	+	9.10796i	0.777452	+	0.564852i
$261$	−25.6480	−	8.33353i	−1.58757	−	0.515833i
$262$	34.7897	−	11.3039i	2.14931	−	0.698354i
$263$	−8.62794	+	6.26856i	−0.532021	+	0.386536i	−0.821113	−	0.570765i	$-0.806647\pi$
$263$	−8.62794	+	6.26856i	−0.532021	+	0.386536i	0.289092	+	0.957301i	$0.406647\pi$
$264$	−4.89665	−	3.55763i	−0.301368	−	0.218957i
$265$			31.6766i			1.94588i
$266$	7.85506	−	5.70703i	0.481625	−	0.349921i
$267$	−23.2441	−	7.55247i	−1.42252	−	0.462204i
$268$	2.63390	−	3.62525i	0.160891	−	0.221448i
$269$	−21.5298	−	15.6423i	−1.31270	−	0.953730i	−0.999992	−	0.00387939i	$-0.998765\pi$
$269$	−21.5298	−	15.6423i	−1.31270	−	0.953730i	−0.312704	−	0.949851i	$-0.601235\pi$
$270$	−29.6380	−	40.7933i	−1.80371	−	2.48260i
$271$	−0.933834	−	2.87405i	−0.0567264	−	0.174586i	0.918679	−	0.395006i	$-0.129257\pi$
$271$	−0.933834	−	2.87405i	−0.0567264	−	0.174586i	−0.975405	+	0.220420i	$0.929257\pi$
$272$	−5.85822	−	8.06315i	−0.355207	−	0.488900i
$273$		−	6.06606i		−	0.367134i
$274$	−3.82201	+	5.26054i	−0.230896	+	0.317801i
$275$	7.53460	−	10.3705i	0.454354	−	0.625364i
$276$		−	7.62170i		−	0.458772i
$277$	−8.92783	−	12.2881i	−0.536421	−	0.738321i	0.451671	−	0.892185i	$-0.350828\pi$
$277$	−8.92783	−	12.2881i	−0.536421	−	0.738321i	−0.988092	+	0.153864i	$0.950828\pi$
$278$	−2.66145	−	8.19111i	−0.159623	−	0.491270i
$279$	19.7482	+	27.1810i	1.18229	+	1.62729i
$280$	1.82157	+	1.32345i	0.108860	+	0.0790913i
$281$	−2.28965	+	3.15144i	−0.136589	+	0.187999i	−0.871832	−	0.489805i	$-0.837068\pi$
$281$	−2.28965	+	3.15144i	−0.136589	+	0.187999i	0.735243	+	0.677804i	$0.237068\pi$
$282$	0.340815	+	0.110738i	0.0202952	+	0.00659432i
$283$	3.82440	−	2.77859i	0.227337	−	0.165170i	−0.468286	−	0.883577i	$-0.655128\pi$
$283$	3.82440	−	2.77859i	0.227337	−	0.165170i	0.695623	+	0.718407i	$0.255128\pi$
$284$			4.43714i			0.263296i
$285$	65.1634	+	47.3440i	3.85995	+	2.80442i
$286$	−9.49317	+	6.89719i	−0.561343	+	0.407839i
$287$	0.463682	−	0.150659i	0.0273703	−	0.00889314i
$288$	−37.3081	−	12.1221i	−2.19840	−	0.714304i
$289$	−10.2663	−	7.45891i	−0.603900	−	0.438759i
$290$	−9.14161	−	28.1350i	−0.536814	−	1.65214i
$291$	24.6050			1.44237
$292$	−7.53722			−0.441082
$293$	−2.15245	−	6.62457i	−0.125748	−	0.387011i	0.868289	−	0.496059i	$-0.165220\pi$
$293$	−2.15245	−	6.62457i	−0.125748	−	0.387011i	−0.994037	+	0.109047i	$0.965220\pi$
$294$		−	36.0730i		−	2.10382i
$295$	−17.7004	+	5.75119i	−1.03055	+	0.334847i
$296$	−0.362969	+	1.11710i	−0.0210971	+	0.0649303i
$297$	15.2414	−	4.95222i	0.884394	−	0.287357i
$298$	−20.8403	+	28.6842i	−1.20725	+	1.66163i
$299$	5.37768	+	1.74731i	0.310999	+	0.101050i
$300$	8.48350	−	26.1095i	0.489795	−	1.50743i
$301$	1.66813	−	5.13397i	0.0961493	−	0.295917i
$302$	22.3103	−	16.2094i	1.28381	−	0.932744i
$303$	−3.14756	−	4.33224i	−0.180823	−	0.248881i
$304$	38.7350			2.22161
$305$	18.6532	−	18.6842i	1.06808	−	1.06986i
$306$	22.0492			1.26047
$307$	−8.10704	−	11.1584i	−0.462693	−	0.636842i	0.512371	−	0.858764i	$-0.328767\pi$
$307$	−8.10704	−	11.1584i	−0.462693	−	0.636842i	−0.975065	+	0.221921i	$0.928767\pi$
$308$	1.51290	−	1.09918i	0.0862053	−	0.0626318i
$309$	5.02188	−	15.4557i	0.285685	−	0.879247i
$310$	−11.3890	+	35.0517i	−0.646850	+	1.99080i
$311$	−11.1358	−	3.61823i	−0.631452	−	0.205171i	−0.0242337	−	0.999706i	$-0.507715\pi$
$311$	−11.1358	−	3.61823i	−0.631452	−	0.205171i	−0.607218	+	0.794535i	$0.707715\pi$
$312$	5.65259	−	7.78013i	0.320015	−	0.440463i
$313$	30.0602	−	9.76717i	1.69911	−	0.552073i	0.710645	−	0.703551i	$-0.248403\pi$
$313$	30.0602	−	9.76717i	1.69911	−	0.552073i	0.988461	+	0.151478i	$0.0484032\pi$
$314$	−5.72718	+	17.6264i	−0.323203	+	0.994717i
$315$	−11.9215	+	3.87352i	−0.671699	+	0.218248i
$316$			15.5270i			0.873464i
$317$	5.37131	+	16.5312i	0.301683	+	0.928484i	0.980894	+	0.194541i	$0.0623218\pi$
$317$	5.37131	+	16.5312i	0.301683	+	0.928484i	−0.679212	+	0.733942i	$0.737678\pi$
$318$	−51.3737			−2.88089
$319$	9.40216			0.526420
$320$	−3.26814	−	10.0583i	−0.182695	−	0.562276i
$321$	−2.39050	−	1.73680i	−0.133425	−	0.0969386i
$322$	−2.04200	−	0.663487i	−0.113796	−	0.0369747i
$323$	−15.9315	+	5.17645i	−0.886451	+	0.288025i
$324$	7.68290	−	5.58195i	0.426828	−	0.310109i
$325$	16.4773	+	11.9715i	0.913998	+	0.664058i
$326$			44.0940i			2.44214i
$327$	−24.2562	+	17.6232i	−1.34137	+	0.974564i
$328$	0.735094	+	0.238847i	0.0405888	+	0.0131881i
$329$	0.0249038	−	0.0342772i	0.00137299	−	0.00188976i
$330$	29.9039	+	21.7264i	1.64615	+	1.19600i
$331$	−11.8521	−	16.3131i	−0.651452	−	0.896647i	0.347709	−	0.937603i	$-0.386960\pi$
$331$	−11.8521	−	16.3131i	−0.651452	−	0.896647i	−0.999161	+	0.0409556i	$0.986960\pi$
$332$	0.547825	+	1.68603i	0.0300658	+	0.0925330i
$333$	−3.84362	−	5.29028i	−0.210629	−	0.289906i
$334$		−	19.3143i		−	1.05683i
$335$	6.15535	−	8.47211i	0.336303	−	0.462881i
$336$	−5.40131	+	7.43427i	−0.294666	+	0.405572i
$337$			35.3366i			1.92491i	0.271446	+	0.962454i	$0.412498\pi$
$337$			35.3366i			1.92491i	−0.271446	+	0.962454i	$0.587502\pi$
$338$	3.22695	+	4.44151i	0.175523	+	0.241586i
$339$	−8.76403	−	26.9729i	−0.475997	−	1.46497i
$340$	5.96679	+	8.21258i	0.323595	+	0.445390i
$341$	−9.47648	−	6.88507i	−0.513180	−	0.372847i
$342$	−50.3695	+	69.3277i	−2.72367	+	3.74881i
$343$	−8.37148	−	2.72006i	−0.452018	−	0.146869i
$344$	6.92353	−	5.03024i	0.373292	−	0.271212i
$345$		−	17.8117i		−	0.958948i
$346$	−23.9648	−	17.4114i	−1.28835	−	0.936044i
$347$	−10.2926	+	7.47804i	−0.552538	+	0.401442i	−0.828720	−	0.559663i	$-0.810931\pi$
$347$	−10.2926	+	7.47804i	−0.552538	+	0.401442i	0.276183	+	0.961105i	$0.410931\pi$
$348$	19.1507	−	6.22244i	1.02659	−	0.333558i
$349$	7.26041	+	2.35905i	0.388641	+	0.126277i	0.496818	−	0.867855i	$-0.334502\pi$
$349$	7.26041	+	2.35905i	0.388641	+	0.126277i	−0.108178	+	0.994132i	$0.534502\pi$
$350$	−6.25675	−	4.54580i	−0.334437	−	0.242983i
$351$	7.86842	+	24.2165i	0.419985	+	1.29258i
$352$	13.6766			0.728965
$353$	7.75100			0.412544			0.206272	−	0.978495i	$-0.433867\pi$
$353$	7.75100			0.412544			0.206272	+	0.978495i	$0.433867\pi$
$354$	−9.32738	−	28.7067i	−0.495745	−	1.52575i
$355$			10.3695i			0.550354i
$356$	11.3853	−	3.69932i	0.603422	−	0.196064i
$357$	1.22803	−	3.77948i	0.0649941	−	0.200031i
$358$	24.8051	−	8.05967i	1.31099	−	0.425967i
$359$	17.3472	−	23.8764i	0.915552	−	1.26015i	−0.0496828	−	0.998765i	$-0.515821\pi$
$359$	17.3472	−	23.8764i	0.915552	−	1.26015i	0.965235	−	0.261384i	$-0.0841790\pi$
$360$	−18.8996	−	6.14086i	−0.996097	−	0.323652i
$361$	14.2469	−	43.8473i	0.749835	−	2.30775i
$362$	6.61816	−	20.3686i	0.347843	−	1.07055i
$363$	16.7760	−	12.1885i	0.880514	−	0.639731i
$364$	1.74646	+	2.40379i	0.0915392	+	0.125993i
$365$	−17.6142			−0.921972
$366$	30.3024	+	30.2521i	1.58393	+	1.58130i
$367$	18.0729			0.943397			0.471698	−	0.881760i	$-0.343641\pi$
$367$	18.0729			0.943397			0.471698	+	0.881760i	$0.343641\pi$
$368$	−5.03479	−	6.92979i	−0.262456	−	0.361240i
$369$	−3.48120	+	2.52924i	−0.181224	+	0.131667i
$370$	2.21665	−	6.82215i	0.115238	−	0.354667i
$371$	−1.87697	+	5.77673i	−0.0974475	+	0.299913i
$372$	−23.8587	−	7.75216i	−1.23702	−	0.401931i
$373$	5.33134	−	7.33796i	0.276046	−	0.379945i	−0.648373	−	0.761323i	$-0.724550\pi$
$373$	5.33134	−	7.33796i	0.276046	−	0.379945i	0.924419	+	0.381378i	$0.124550\pi$
$374$	−7.31104	+	2.37550i	−0.378045	+	0.122834i
$375$	4.40173	−	13.5471i	0.227305	−	0.699572i
$376$	0.0638817	−	0.0207564i	0.00329444	−	0.00107043i
$377$			14.9388i			0.769386i
$378$	−2.98779	−	9.19546i	−0.153675	−	0.472963i
$379$	8.84314			0.454242			0.227121	−	0.973867i	$-0.427069\pi$
$379$	8.84314			0.454242			0.227121	+	0.973867i	$0.427069\pi$
$380$	−39.4529			−2.02389
$381$	−1.87453	−	5.76922i	−0.0960353	−	0.295566i
$382$	−27.7633	−	20.1712i	−1.42049	−	1.03205i
$383$	15.9258	+	5.17462i	0.813773	+	0.264411i	0.686195	−	0.727418i	$-0.259280\pi$
$383$	15.9258	+	5.17462i	0.813773	+	0.264411i	0.127578	+	0.991829i	$0.459280\pi$
$384$	−22.2044	+	7.21465i	−1.13311	+	0.368171i
$385$	3.53559	−	2.56876i	0.180191	−	0.130916i
$386$	31.1846	+	22.6569i	1.58725	+	1.15321i
$387$			47.6436i			2.42186i
$388$	−9.75022	+	7.08395i	−0.494992	+	0.359633i
$389$	−24.4822	−	7.95475i	−1.24130	−	0.403322i	−0.386502	−	0.922289i	$-0.626317\pi$
$389$	−24.4822	−	7.95475i	−1.24130	−	0.403322i	−0.854794	+	0.518967i	$0.826317\pi$
$390$	−34.5204	+	47.5133i	−1.74801	+	2.40593i
$391$	2.99685	+	2.17734i	0.151557	+	0.110113i
$392$	−3.97428	−	5.47013i	−0.200731	−	0.276283i
$393$	17.9812	+	55.3403i	0.907029	+	2.79155i
$394$	11.9235	+	16.4113i	0.600698	+	0.826790i
$395$			36.2862i			1.82576i
$396$	−9.70125	+	13.3526i	−0.487506	+	0.670994i
$397$	−7.55830	+	10.4031i	−0.379340	+	0.522117i	−0.955410	−	0.295284i	$-0.904586\pi$
$397$	−7.55830	+	10.4031i	−0.379340	+	0.522117i	0.576069	+	0.817401i	$0.304586\pi$
$398$		−	35.8014i		−	1.79456i
$399$	9.07824	+	12.4951i	0.454480	+	0.625538i
$400$	−9.53423	−	29.3434i	−0.476712	−	1.46717i
$401$	−3.66149	−	5.03961i	−0.182846	−	0.251666i	0.707748	−	0.706465i	$-0.249711\pi$
$401$	−3.66149	−	5.03961i	−0.182846	−	0.251666i	−0.890594	+	0.454799i	$0.849711\pi$
$402$	13.7402	+	9.98285i	0.685299	+	0.497899i
$403$	10.9395	−	15.0569i	0.544933	−	0.750036i
$404$	2.49456	+	0.810532i	0.124109	+	0.0403255i
$405$	17.9547	−	13.0449i	0.892176	−	0.648204i
$406$		−	5.67253i		−	0.281523i
$407$	1.84442	+	1.34005i	0.0914245	+	0.0664238i
$408$	5.09690	−	3.70312i	0.252334	−	0.183332i
$409$	13.4486	−	4.36970i	0.664989	−	0.216068i	0.0429772	−	0.999076i	$-0.486316\pi$
$409$	13.4486	−	4.36970i	0.664989	−	0.216068i	0.622011	+	0.783008i	$0.286316\pi$
$410$	−4.48923	−	1.45864i	−0.221707	−	0.0720370i
$411$	−8.36799	−	6.07970i	−0.412763	−	0.299890i
$412$	2.45979	+	7.57047i	0.121185	+	0.372970i
$413$	−3.56872			−0.175605
$414$	18.9499			0.931338
$415$	1.28025	+	3.94021i	0.0628450	+	0.193417i
$416$			21.7303i			1.06542i
$417$	13.0297	−	4.23360i	0.638066	−	0.207320i
$418$	9.23235	−	28.4143i	0.451569	−	1.38979i
$419$	−24.4427	+	7.94192i	−1.19410	+	0.387988i	−0.837589	−	0.546301i	$-0.816035\pi$
$419$	−24.4427	+	7.94192i	−1.19410	+	0.387988i	−0.356516	+	0.934289i	$0.616035\pi$
$420$	5.50141	−	7.57204i	0.268441	−	0.369478i
$421$	−32.2332	−	10.4732i	−1.57095	−	0.510433i	−0.611246	−	0.791441i	$-0.709331\pi$
$421$	−32.2332	−	10.4732i	−1.57095	−	0.510433i	−0.959705	+	0.281008i	$0.909331\pi$
$422$	1.86812	−	5.74949i	0.0909388	−	0.279881i
$423$	−0.115554	+	0.355640i	−0.00561845	+	0.0172918i
$424$	−7.79033	+	5.66001i	−0.378332	+	0.274874i
$425$	7.84274	+	10.7946i	0.380429	+	0.523615i
$426$	−16.8174			−0.814804
$427$	4.50882	−	2.30208i	0.218197	−	0.111405i
$428$	1.44732			0.0699587
$429$	−10.9714	−	15.1009i	−0.529706	−	0.729077i
$430$	−42.2821	+	30.7197i	−2.03902	+	1.48144i
$431$	−7.46758	+	22.9829i	−0.359701	+	1.10705i	0.593533	+	0.804810i	$0.297733\pi$
$431$	−7.46758	+	22.9829i	−0.359701	+	1.10705i	−0.953233	+	0.302235i	$0.902267\pi$
$432$	11.9196	−	36.6848i	0.573482	−	1.76500i
$433$	10.7927	+	3.50677i	0.518666	+	0.168525i	0.556640	−	0.830754i	$-0.312090\pi$
$433$	10.7927	+	3.50677i	0.518666	+	0.168525i	−0.0379740	+	0.999279i	$0.512090\pi$
$434$	−4.15391	+	5.71737i	−0.199394	+	0.274443i
$435$	44.7546	−	14.5417i	2.14582	−	0.697219i
$436$	4.53817	−	13.9670i	0.217339	−	0.668900i
$437$	−13.6921	+	4.44884i	−0.654984	+	0.212817i
$438$		−	28.5671i		−	1.36499i
$439$	−5.39505	−	16.6043i	−0.257492	−	0.792478i	−0.993328	−	0.115319i	$-0.963211\pi$
$439$	−5.39505	−	16.6043i	−0.257492	−	0.792478i	0.735837	−	0.677159i	$-0.236789\pi$
$440$	6.92831			0.330294
$441$	37.6422			1.79248
$442$	−3.77436	−	11.6163i	−0.179528	−	0.552530i
$443$	−1.10282	−	0.801245i	−0.0523965	−	0.0380683i	0.561279	−	0.827627i	$-0.310310\pi$
$443$	−1.10282	−	0.801245i	−0.0523965	−	0.0380683i	−0.613675	+	0.789559i	$0.710310\pi$
$444$	4.64365	+	1.50881i	0.220378	+	0.0716051i
$445$	26.6072	−	8.64520i	1.26130	−	0.409822i
$446$	28.7402	−	20.8810i	1.36089	−	0.988744i
$447$	−45.6283	−	33.1509i	−2.15814	−	1.56798i
$448$		−	2.02794i		−	0.0958111i
$449$	−2.33456	+	1.69616i	−0.110175	+	0.0800467i	−0.641508	−	0.767116i	$-0.721691\pi$
$449$	−2.33456	+	1.69616i	−0.110175	+	0.0800467i	0.531334	+	0.847163i	$0.321691\pi$
$450$	64.9165	+	21.0926i	3.06019	+	0.994317i
$451$	0.881801	−	1.21370i	0.0415224	−	0.0571507i
$452$	11.2386	+	8.16531i	0.528619	+	0.384064i
$453$	25.7844	+	35.4892i	1.21146	+	1.66743i
$454$	−16.7311	−	51.4932i	−0.785231	−	2.41669i
$455$	4.08142	+	5.61759i	0.191340	+	0.263357i
$456$			24.4853i			1.14663i
$457$	6.52841	−	8.98558i	0.305386	−	0.420328i	−0.628549	−	0.777770i	$-0.716351\pi$
$457$	6.52841	−	8.98558i	0.305386	−	0.420328i	0.933935	+	0.357442i	$0.116351\pi$
$458$	−5.37068	+	7.39211i	−0.250955	+	0.345411i
$459$			16.6811i			0.778607i
$460$	5.12810	+	7.05822i	0.239099	+	0.329091i
$461$	7.40615	+	22.7938i	0.344939	+	1.06161i	0.961617	+	0.274397i	$0.0884782\pi$
$461$	7.40615	+	22.7938i	0.344939	+	1.06161i	−0.616678	+	0.787216i	$0.711522\pi$
$462$	4.16606	+	5.73409i	0.193822	+	0.266774i
$463$	12.0111	+	8.72655i	0.558201	+	0.405557i	0.830800	−	0.556571i	$-0.187883\pi$
$463$	12.0111	+	8.72655i	0.558201	+	0.405557i	−0.272599	+	0.962128i	$0.587883\pi$
$464$	13.3017	−	18.3082i	0.617517	−	0.849939i
$465$	−55.7570	−	18.1166i	−2.58567	−	0.840135i
$466$	18.7375	−	13.6136i	0.867996	−	0.630636i
$467$		−	30.5953i		−	1.41578i	−0.706322	−	0.707890i	$-0.749647\pi$
$467$		−	30.5953i		−	1.41578i	0.706322	−	0.707890i	$-0.250353\pi$
$468$	−21.2155	−	15.4140i	−0.980689	−	0.712512i
$469$	1.62453	−	1.18029i	0.0750139	−	0.0545008i
$470$	−0.390126	+	0.126760i	−0.0179952	+	0.00584698i
$471$	−28.0385	−	9.11027i	−1.29195	−	0.419779i
$472$	−4.57712	−	3.32547i	−0.210679	−	0.153067i
$473$	−5.13296	−	15.7976i	−0.236014	−	0.726376i
$474$	−58.8496			−2.70305
$475$	−51.8568			−2.37935
$476$	0.601507	+	1.85125i	0.0275700	+	0.0848519i
$477$		−	53.6084i		−	2.45456i
$478$	2.03789	−	0.662150i	0.0932108	−	0.0302860i
$479$	−7.86283	+	24.1993i	−0.359262	+	1.10569i	0.594235	+	0.804291i	$0.297455\pi$
$479$	−7.86283	+	24.1993i	−0.359262	+	1.10569i	−0.953497	+	0.301402i	$0.902545\pi$
$480$	65.1011	−	21.1526i	2.97145	−	0.965481i
$481$	−2.12916	+	2.93054i	−0.0970814	+	0.133621i
$482$	−2.70577	−	0.879157i	−0.123244	−	0.0400445i
$483$	1.05542	−	3.24824i	0.0480231	−	0.147800i
$484$	−3.13868	+	9.65986i	−0.142667	+	0.439085i
$485$	−22.7860	+	16.5550i	−1.03466	+	0.751723i
$486$	−5.14668	−	7.08380i	−0.233458	−	0.321328i
$487$	−28.5228			−1.29249			−0.646245	−	0.763130i	$-0.723662\pi$
$487$	−28.5228			−1.29249			−0.646245	+	0.763130i	$0.723662\pi$
$488$	7.92804	+	1.24892i	0.358885	+	0.0565361i
$489$	−70.1407			−3.17187
$490$	24.2710	+	33.4061i	1.09645	+	1.50913i
$491$	19.7030	−	14.3151i	0.889183	−	0.646030i	−0.0464815	−	0.998919i	$-0.514801\pi$
$491$	19.7030	−	14.3151i	0.889183	−	0.646030i	0.935665	+	0.352890i	$0.114801\pi$
$492$	0.992854	−	3.05569i	0.0447613	−	0.137761i
$493$	−3.02424	+	9.30767i	−0.136205	+	0.419196i
$494$	45.1465	+	14.6690i	2.03124	+	0.659989i
$495$	−22.6715	+	31.2047i	−1.01901	+	1.40255i
$496$	−26.8137	+	8.71231i	−1.20397	+	0.391194i
$497$	−0.614434	+	1.89103i	−0.0275611	+	0.0848244i
$498$	−6.39029	+	2.07633i	−0.286356	+	0.0930426i
$499$		−	7.03020i		−	0.314715i	−0.987542	−	0.157358i	$-0.949702\pi$
$499$		−	7.03020i		−	0.314715i	0.987542	−	0.157358i	$-0.0502975\pi$
$500$	2.15604	+	6.63560i	0.0964210	+	0.296753i
$501$	30.7235			1.37262
$502$	14.5859			0.651001
$503$	4.10793	+	12.6429i	0.183164	+	0.563720i	0.999912	−	0.0132743i	$-0.00422547\pi$
$503$	4.10793	+	12.6429i	0.183164	+	0.563720i	−0.816748	+	0.576994i	$0.804225\pi$
$504$	−3.08277	−	2.23976i	−0.137317	−	0.0997669i
$505$	5.82972	+	1.89419i	0.259419	+	0.0842903i
$506$	−6.28340	+	2.04160i	−0.279331	+	0.0907602i
$507$	−7.06515	+	5.13314i	−0.313775	+	0.227971i
$508$	2.40382	+	1.74647i	0.106652	+	0.0774873i
$509$		−	27.7249i		−	1.22889i	−0.788961	−	0.614443i	$-0.789381\pi$
$509$		−	27.7249i		−	1.22889i	0.788961	−	0.614443i	$-0.210619\pi$
$510$	−31.1268	+	22.6150i	−1.37832	+	1.00141i
$511$	−3.21223	−	1.04372i	−0.142101	−	0.0461713i
$512$	13.5497	−	18.6496i	0.598819	−	0.824204i
$513$	−52.4493	−	38.1066i	−2.31569	−	1.68245i
$514$	33.0742	+	45.5228i	1.45884	+	2.00792i
$515$	5.74847	+	17.6920i	0.253308	+	0.779601i
$516$	−20.9100	−	28.7802i	−0.920513	−	1.26698i
$517$		−	0.130372i		−	0.00573377i
$518$	0.808482	−	1.11278i	0.0355227	−	0.0488927i
$519$	27.6965	−	38.1210i	1.21574	−	1.67333i
$520$			11.0082i			0.482740i
$521$	24.9596	+	34.3539i	1.09350	+	1.50507i	0.843732	+	0.536764i	$0.180354\pi$
$521$	24.9596	+	34.3539i	1.09350	+	1.50507i	0.249766	+	0.968306i	$0.419646\pi$
$522$	15.4709	+	47.6147i	0.677145	+	2.08404i
$523$	10.8349	+	14.9130i	0.473779	+	0.652101i	0.977294	−	0.211886i	$-0.0679604\pi$
$523$	10.8349	+	14.9130i	0.473779	+	0.652101i	−0.503516	+	0.863986i	$0.667960\pi$
$524$	−23.0582	−	16.7528i	−1.00730	−	0.731848i
$525$	7.23104	−	9.95268i	0.315589	−	0.434370i
$526$	18.8297	+	6.11814i	0.821014	+	0.266764i
$527$	9.86402	−	7.16663i	0.429684	−	0.312183i
$528$			28.2760i			1.23056i
$529$	−16.0318	−	11.6478i	−0.697034	−	0.506425i
$530$	47.5756	−	34.5657i	2.06655	−	1.50144i
$531$	29.9554	−	9.73311i	1.29996	−	0.422381i
$532$	−7.19485	−	2.33775i	−0.311936	−	0.101354i
$533$	1.92840	+	1.40107i	0.0835283	+	0.0606869i
$534$	14.0209	+	43.1520i	0.606745	+	1.86737i
$535$	3.38233			0.146231
$536$	3.18341			0.137503
$537$	12.8206	+	39.4578i	0.553250	+	1.70273i
$538$			49.4050i			2.13000i
$539$	−12.4814	+	4.05544i	−0.537610	+	0.174680i
$540$	−12.1405	+	37.3646i	−0.522444	+	1.60792i
$541$	−26.2719	+	8.53627i	−1.12952	+	0.367003i	−0.813393	−	0.581715i	$-0.802382\pi$
$541$	−26.2719	+	8.53627i	−1.12952	+	0.367003i	−0.316126	+	0.948717i	$0.602382\pi$
$542$	−3.29757	+	4.53871i	−0.141643	+	0.194954i
$543$	32.4006	+	10.5276i	1.39044	+	0.451782i
$544$	−4.39914	+	13.5392i	−0.188611	+	0.580486i
$545$	10.6056	−	32.6406i	0.454292	−	1.39817i
$546$	−9.11070	+	6.61931i	−0.389902	+	0.283280i
$547$	−13.6963	−	18.8514i	−0.585612	−	0.806026i	0.408684	−	0.912676i	$-0.365988\pi$
$547$	−13.6963	−	18.8514i	−0.585612	−	0.806026i	−0.994297	+	0.106649i	$0.965988\pi$
$548$	5.06636			0.216424
$549$	−31.5680	+	31.6205i	−1.34729	+	1.34953i
$550$	−23.7974			−1.01472
$551$	−22.3568	−	30.7715i	−0.952433	−	1.31091i
$552$	4.38048	−	3.18260i	0.186446	−	0.135461i
$553$	−2.15011	+	6.61736i	−0.0914320	+	0.281399i
$554$	−8.71360	+	26.8177i	−0.370205	+	1.13937i
$555$	10.8521	+	3.52605i	0.460645	+	0.149673i
$556$	−3.94438	+	5.42897i	−0.167279	+	0.230240i
$557$	16.6235	−	5.40131i	0.704362	−	0.228861i	0.0651319	−	0.997877i	$-0.479253\pi$
$557$	16.6235	−	5.40131i	0.704362	−	0.228861i	0.639230	+	0.769016i	$0.279253\pi$
$558$	19.2743	−	59.3202i	0.815946	−	2.51122i
$559$	25.1003	−	8.15559i	1.06163	−	0.344945i
$560$		−	10.5188i		−	0.444501i
$561$	−3.77874	−	11.6298i	−0.159538	−	0.491009i
$562$	7.23167			0.305050
$563$	11.3956			0.480266			0.240133	−	0.970740i	$-0.422809\pi$
$563$	11.3956			0.480266			0.240133	+	0.970740i	$0.422809\pi$
$564$	−0.0862817	−	0.265548i	−0.00363311	−	0.0111816i
$565$	26.2642	+	19.0821i	1.10494	+	0.802789i
$566$	−8.34641	−	2.71191i	−0.350826	−	0.113990i
$567$	4.04728	−	1.31504i	0.169970	−	0.0552266i
$568$	−2.55019	+	1.85282i	−0.107004	+	0.0777427i
$569$	20.0899	+	14.5962i	0.842214	+	0.611904i	0.922988	−	0.384828i	$-0.125739\pi$
$569$	20.0899	+	14.5962i	0.842214	+	0.611904i	−0.0807746	+	0.996732i	$0.525739\pi$
$570$		−	149.532i		−	6.26320i
$571$	−3.73659	+	2.71479i	−0.156371	+	0.113610i	−0.663220	−	0.748425i	$-0.730810\pi$
$571$	−3.73659	+	2.71479i	−0.156371	+	0.113610i	0.506848	+	0.862035i	$0.330810\pi$
$572$	8.69528	+	2.82527i	0.363568	+	0.118130i
$573$	32.0865	−	44.1633i	1.34043	−	1.84495i
$574$	−0.732250	−	0.532011i	−0.0305635	−	0.0222057i
$575$	6.74036	+	9.27731i	0.281092	+	0.386890i
$576$	5.53089	+	17.0223i	0.230454	+	0.709263i
$577$	−13.0718	−	17.9917i	−0.544184	−	0.749005i	0.445024	−	0.895518i	$-0.353195\pi$
$577$	−13.0718	−	17.9917i	−0.544184	−	0.749005i	−0.989209	+	0.146513i	$0.953195\pi$
$578$			23.5583i			0.979896i
$579$	−36.0406	+	49.6056i	−1.49779	+	2.06154i
$580$	−13.5482	+	18.6476i	−0.562560	+	0.774298i
$581$			0.794418i			0.0329580i
$582$	−26.8491	−	36.9547i	−1.11293	−	1.53182i
$583$	5.77559	+	17.7754i	0.239200	+	0.736183i
$584$	−3.14733	−	4.33193i	−0.130237	−	0.179256i
$585$	−49.5801	−	36.0220i	−2.04988	−	1.48933i
$586$	−7.60077	+	10.4616i	−0.313985	+	0.432163i
$587$	27.4460	+	8.91775i	1.13282	+	0.368075i	0.814646	−	0.579958i	$-0.196931\pi$
$587$	27.4460	+	8.91775i	1.13282	+	0.368075i	0.318172	+	0.948033i	$0.396931\pi$
$588$	−22.7386	+	16.5206i	−0.937724	+	0.681297i
$589$			47.3864i			1.95252i
$590$	27.9525	+	20.3087i	1.15079	+	0.836096i
$591$	−26.1056	+	18.9669i	−1.07384	+	0.780193i
$592$	5.21879	−	1.69569i	0.214491	−	0.0696924i
$593$	−7.87972	−	2.56028i	−0.323581	−	0.105138i	0.142722	−	0.989763i	$-0.454414\pi$
$593$	−7.87972	−	2.56028i	−0.323581	−	0.105138i	−0.466303	+	0.884625i	$0.654414\pi$
$594$	−24.0693	−	17.4874i	−0.987574	−	0.717515i
$595$	1.40570	+	4.32631i	0.0576283	+	0.177362i
$596$	27.6254			1.13158
$597$	56.9497			2.33080
$598$	−3.24383	−	9.98349i	−0.132650	−	0.408255i
$599$			28.3090i			1.15667i	0.815798	+	0.578336i	$0.196298\pi$
$599$			28.3090i			1.15667i	−0.815798	+	0.578336i	$0.803702\pi$
$600$	18.5486	−	6.02681i	0.757244	−	0.246043i
$601$	12.4485	−	38.3127i	0.507787	−	1.56281i	−0.288247	−	0.957556i	$-0.593073\pi$
$601$	12.4485	−	38.3127i	0.507787	−	1.56281i	0.796034	−	0.605251i	$-0.206927\pi$
$602$	−9.53106	+	3.09683i	−0.388457	+	0.126217i
$603$	−10.4171	+	14.3379i	−0.424217	+	0.583884i
$604$	−20.4351	−	6.63977i	−0.831493	−	0.270168i
$605$	−7.33500	+	22.5748i	−0.298210	+	0.917796i
$606$	−3.07203	+	9.45473i	−0.124793	+	0.384072i
$607$	−14.1953	+	10.3135i	−0.576169	+	0.418611i	−0.837341	−	0.546681i	$-0.815891\pi$
$607$	−14.1953	+	10.3135i	−0.576169	+	0.418611i	0.261172	+	0.965292i	$0.415891\pi$
$608$	−32.5208	−	44.7610i	−1.31889	−	1.81530i
$609$	9.02335			0.365645
$610$	−48.4166	−	7.62719i	−1.96033	−	0.308816i
$611$	0.207144			0.00838016
$612$	−10.0980	−	13.8987i	−0.408187	−	0.561821i
$613$	−18.0552	+	13.1179i	−0.729242	+	0.529825i	−0.889323	−	0.457279i	$-0.848824\pi$
$613$	−18.0552	+	13.1179i	−0.729242	+	0.529825i	0.160082	+	0.987104i	$0.448824\pi$
$614$	−7.91250	+	24.3522i	−0.319322	+	0.982773i
$615$	2.32027	−	7.14106i	0.0935623	−	0.287955i
$616$	1.26349	+	0.410531i	0.0509073	+	0.0165408i
$617$	5.77670	−	7.95094i	0.232561	−	0.320093i	−0.676748	−	0.736215i	$-0.736611\pi$
$617$	5.77670	−	7.95094i	0.232561	−	0.320093i	0.909309	+	0.416122i	$0.136611\pi$
$618$	−28.6931	+	9.32296i	−1.15421	+	0.375024i
$619$	8.24434	−	25.3735i	0.331368	−	1.01985i	−0.637116	−	0.770768i	$-0.719873\pi$
$619$	8.24434	−	25.3735i	0.331368	−	1.01985i	0.968484	−	0.249077i	$-0.0801274\pi$
$620$	27.3107	−	8.87378i	1.09682	−	0.356379i
$621$			14.3364i			0.575300i
$622$	6.71714	+	20.6732i	0.269333	+	0.828920i
$623$	5.36450			0.214924
$624$	−44.9269			−1.79851
$625$	−4.89153	−	15.0546i	−0.195661	−	0.602184i
$626$	−47.4713	−	34.4900i	−1.89734	−	1.37850i
$627$	45.1988	+	14.6860i	1.80507	+	0.586502i
$628$	13.7337	−	4.46236i	0.548035	−	0.178067i
$629$	−1.91985	+	1.39485i	−0.0765494	+	0.0556164i
$630$	18.8265	+	13.6782i	0.750065	+	0.544954i
$631$		−	39.3047i		−	1.56469i	−0.622842	−	0.782347i	$-0.714022\pi$
$631$		−	39.3047i		−	1.56469i	0.622842	−	0.782347i	$-0.285978\pi$
$632$	−8.92398	+	6.48365i	−0.354977	+	0.257906i
$633$	9.14578	+	2.97164i	0.363512	+	0.118112i
$634$	18.9672	−	26.1061i	0.753285	−	1.03681i
$635$	5.61765	+	4.08146i	0.222929	+	0.161968i
$636$	23.5279	+	32.3834i	0.932942	+	1.28408i
$637$	−6.44355	−	19.8312i	−0.255303	−	0.785741i
$638$	−10.2597	−	14.1212i	−0.406185	−	0.559065i
$639$		−	17.5489i		−	0.694224i
$640$	15.7086	−	21.6210i	0.620936	−	0.854646i
$641$	10.0517	−	13.8350i	0.397019	−	0.546450i	−0.562974	−	0.826475i	$-0.690343\pi$
$641$	10.0517	−	13.8350i	0.397019	−	0.546450i	0.959993	+	0.280025i	$0.0903427\pi$
$642$			5.48553i			0.216496i
$643$	6.90429	+	9.50293i	0.272278	+	0.374759i	0.923157	−	0.384423i	$-0.125599\pi$
$643$	6.90429	+	9.50293i	0.272278	+	0.374759i	−0.650879	+	0.759182i	$0.725599\pi$
$644$	0.516959	+	1.59104i	0.0203710	+	0.0626956i
$645$	−48.8662	−	67.2585i	−1.92410	−	2.64830i
$646$	25.1591	+	18.2791i	0.989871	+	0.719183i
$647$	−13.5159	+	18.6030i	−0.531364	+	0.731360i	−0.987338	−	0.158633i	$-0.949291\pi$
$647$	−13.5159	+	18.6030i	−0.531364	+	0.731360i	0.455973	+	0.889993i	$0.349291\pi$
$648$	6.41632	+	2.08479i	0.252057	+	0.0818983i
$649$	−8.88399	+	6.45460i	−0.348727	+	0.253365i
$650$		−	37.8109i		−	1.48307i
$651$	−9.09468	−	6.60767i	−0.356449	−	0.258975i
$652$	27.7946	−	20.1940i	1.08852	−	0.790857i
$653$	−4.71580	+	1.53225i	−0.184543	+	0.0599618i	−0.399831	−	0.916589i	$-0.630931\pi$
$653$	−4.71580	+	1.53225i	−0.184543	+	0.0599618i	0.215288	+	0.976551i	$0.430931\pi$
$654$	52.9370	+	17.2003i	2.07000	+	0.672584i
$655$	−53.8863	−	39.1507i	−2.10551	−	1.52975i
$656$	−1.11583	−	3.43416i	−0.0435657	−	0.134081i
$657$	29.8097			1.16299
$658$	−0.0786565			−0.00306635
$659$	−6.55590	−	20.1770i	−0.255382	−	0.785984i	−0.993754	−	0.111591i	$-0.964405\pi$
$659$	−6.55590	−	20.1770i	−0.255382	−	0.785984i	0.738373	−	0.674393i	$-0.235595\pi$
$660$		−	28.8001i		−	1.12104i
$661$	−2.53902	+	0.824979i	−0.0987566	+	0.0320880i	−0.357979	−	0.933730i	$-0.616534\pi$
$661$	−2.53902	+	0.824979i	−0.0987566	+	0.0320880i	0.259222	+	0.965818i	$0.416534\pi$
$662$	−11.5677	+	35.6018i	−0.449592	+	1.38370i
$663$	18.4781	−	6.00391i	0.717631	−	0.233172i
$664$	−0.740270	+	1.01889i	−0.0287281	+	0.0395408i
$665$	−16.8142	−	5.46325i	−0.652025	−	0.211856i
$666$	−3.75138	+	11.5456i	−0.145363	+	0.447382i
$667$	−2.59916	+	7.99938i	−0.100640	+	0.309737i
$668$	−12.1748	+	8.84548i	−0.471056	+	0.342242i
$669$	33.2156	+	45.7174i	1.28419	+	1.76754i
$670$	−19.4411			−0.751076
$671$	7.06060	−	13.8857i	0.272572	−	0.536053i
$672$	13.1256			0.506330
$673$	1.97543	+	2.71894i	0.0761472	+	0.104808i	0.845392	−	0.534147i	$-0.179367\pi$
$673$	1.97543	+	2.71894i	0.0761472	+	0.104808i	−0.769244	+	0.638955i	$0.779367\pi$
$674$	53.0726	−	38.5595i	2.04428	−	1.48526i
$675$	−15.9574	+	49.1120i	−0.614203	+	1.89032i
$676$	1.32184	−	4.06821i	0.0508400	−	0.156470i
$677$	42.6046	+	13.8431i	1.63743	+	0.532032i	0.975962	−	0.217943i	$-0.0699346\pi$
$677$	42.6046	+	13.8431i	1.63743	+	0.532032i	0.661466	+	0.749975i	$0.269935\pi$
$678$	−30.9477	+	42.5958i	−1.18854	+	1.63588i
$679$	−5.13633	+	1.66889i	−0.197114	+	0.0640463i
$680$	−2.22852	+	6.85868i	−0.0854599	+	0.263019i
$681$	81.9107	−	26.6144i	3.13882	−	1.01987i
$682$			21.7459i			0.832693i
$683$	4.92754	+	15.1654i	0.188547	+	0.580289i	0.999991	−	0.00414117i	$-0.00131818\pi$
$683$	4.92754	+	15.1654i	0.188547	+	0.580289i	−0.811444	+	0.584430i	$0.801318\pi$
$684$	66.7687			2.55296
$685$	11.8399			0.452381
$686$	5.04971	+	15.5414i	0.192799	+	0.593373i
$687$	−11.7587	−	8.54320i	−0.448622	−	0.325943i
$688$	−38.0236	−	12.3546i	−1.44964	−	0.471016i
$689$	−28.2428	+	9.17664i	−1.07596	+	0.349602i
$690$	−26.7516	+	19.4362i	−1.01842	+	0.739923i
$691$	−31.5050	−	22.8897i	−1.19851	−	0.870766i	−0.204369	−	0.978894i	$-0.565514\pi$
$691$	−31.5050	−	22.8897i	−1.19851	−	0.870766i	−0.994137	+	0.108128i	$0.965514\pi$
$692$			23.0802i			0.877377i
$693$	−5.98351	+	4.34728i	−0.227295	+	0.165139i
$694$	22.4628	+	7.29859i	0.852674	+	0.277051i
$695$	−9.21789	+	12.6873i	−0.349655	+	0.481258i
$696$	11.5731	+	8.40832i	0.438676	+	0.318717i
$697$	0.917863	+	1.26333i	0.0347665	+	0.0478520i
$698$	−4.37950	−	13.4787i	−0.165767	−	0.510177i
$699$	21.6552	+	29.8059i	0.819076	+	1.12736i
$700$			6.02580i			0.227754i
$701$	−15.4704	+	21.2932i	−0.584309	+	0.804232i	−0.994160	−	0.107920i	$-0.965581\pi$
$701$	−15.4704	+	21.2932i	−0.584309	+	0.804232i	0.409851	+	0.912153i	$0.365581\pi$
$702$	27.7851	−	38.2429i	1.04868	−	1.44338i
$703$		−	9.22287i		−	0.347847i
$704$	−3.66785	−	5.04837i	−0.138237	−	0.190267i
$705$	−0.201638	−	0.620577i	−0.00759411	−	0.0233723i
$706$	−8.45793	−	11.6413i	−0.318318	−	0.438127i
$707$	0.950901	+	0.690870i	0.0357623	+	0.0259828i
$708$	−13.8236	+	19.0265i	−0.519521	+	0.715060i
$709$	9.49601	+	3.08544i	0.356630	+	0.115876i	0.481852	−	0.876253i	$-0.339964\pi$
$709$	9.49601	+	3.08544i	0.356630	+	0.115876i	−0.125222	+	0.992129i	$0.539964\pi$
$710$	15.5740	−	11.3152i	0.584483	−	0.424652i
$711$		−	61.4095i		−	2.30304i
$712$	6.88034	+	4.99886i	0.257851	+	0.187340i
$713$	8.47753	−	6.15929i	0.317486	−	0.230667i
$714$	−7.01649	+	2.27980i	−0.262586	+	0.0853192i
$715$	20.3206	+	6.60257i	0.759948	+	0.246922i
$716$	−16.4406	−	11.9448i	−0.614412	−	0.446397i
$717$	1.05329	+	3.24169i	0.0393358	+	0.121063i
$718$	−54.7897			−2.04473
$719$	−6.60710			−0.246403			−0.123202	−	0.992382i	$-0.539316\pi$
$719$	−6.60710			−0.246403			−0.123202	+	0.992382i	$0.539316\pi$
$720$	28.6884	+	88.2938i	1.06915	+	3.29051i
$721$			3.56702i			0.132843i
$722$	−81.4012	+	26.4489i	−3.02944	+	0.984324i
$723$	1.39848	−	4.30409i	0.0520102	−	0.160071i
$724$	−15.8703	+	5.15657i	−0.589815	+	0.191643i
$725$	−17.8078	+	24.5103i	−0.661364	+	0.910290i
$726$	−36.6122	−	11.8960i	−1.35881	−	0.441503i
$727$	−8.65029	+	26.6229i	−0.320821	+	0.987387i	0.652470	+	0.757814i	$0.273733\pi$
$727$	−8.65029	+	26.6229i	−0.320821	+	0.987387i	−0.973292	+	0.229573i	$0.926267\pi$
$728$	−0.652280	+	2.00751i	−0.0241751	+	0.0744033i
$729$	27.2026	−	19.7639i	1.00751	−	0.731995i
$730$	19.2208	+	26.4551i	0.711392	+	0.979147i
$731$	17.2899			0.639490
$732$	5.19161	−	32.9558i	0.191888	−	1.21808i
$733$	−27.9235			−1.03138			−0.515690	−	0.856776i	$-0.672464\pi$
$733$	−27.9235			−1.03138			−0.515690	+	0.856776i	$0.672464\pi$
$734$	−19.7212	−	27.1439i	−0.727924	−	1.00190i
$735$	−53.1394	+	38.6081i	−1.96008	+	1.42408i
$736$	−3.78079	+	11.6361i	−0.139362	+	0.428912i
$737$	1.90937	−	5.87645i	0.0703327	−	0.216462i
$738$	7.59740	+	2.46855i	0.279664	+	0.0908684i
$739$	17.3291	−	23.8514i	0.637461	−	0.877390i	−0.361016	−	0.932560i	$-0.617570\pi$
$739$	17.3291	−	23.8514i	0.637461	−	0.877390i	0.998477	+	0.0551700i	$0.0175701\pi$
$740$	−5.31551	+	1.72711i	−0.195402	+	0.0634900i
$741$	−23.3341	+	71.8150i	−0.857199	+	2.63819i
$742$	10.7243	−	3.48454i	0.393702	−	0.127921i
$743$			8.88260i			0.325871i	0.986637	+	0.162935i	$0.0520962\pi$
$743$			8.88260i			0.325871i	−0.986637	+	0.162935i	$0.947904\pi$
$744$	−5.50725	−	16.9496i	−0.201906	−	0.621402i
$745$	64.5598			2.36529
$746$	−16.8386			−0.616504
$747$	−2.16665	−	6.66826i	−0.0792736	−	0.243979i
$748$	4.84568	+	3.52059i	0.177176	+	0.128726i
$749$	0.616821	+	0.200417i	0.0225382	+	0.00732309i
$750$	−25.1499	+	8.17168i	−0.918343	+	0.298388i
$751$	36.3614	−	26.4181i	1.32685	−	0.964010i	0.327026	−	0.945015i	$-0.393954\pi$
$751$	36.3614	−	26.4181i	1.32685	−	0.964010i	0.999820	−	0.0189944i	$-0.00604647\pi$
$752$	−0.253866	−	0.184444i	−0.00925754	−	0.00672600i
$753$			23.2020i			0.845526i
$754$	22.4368	−	16.3013i	0.817099	−	0.593657i
$755$	−47.7562	−	15.5169i	−1.73803	−	0.564719i
$756$	−4.42802	+	6.09465i	−0.161046	+	0.221660i
$757$	18.9021	+	13.7332i	0.687009	+	0.499141i	0.875676	−	0.482900i	$-0.160416\pi$
$757$	18.9021	+	13.7332i	0.687009	+	0.499141i	−0.188666	+	0.982041i	$0.560416\pi$
$758$	−9.64968	−	13.2816i	−0.350492	−	0.482411i
$759$	−3.24759	−	9.99507i	−0.117880	−	0.362798i
$760$	−16.4744	−	22.6751i	−0.597590	−	0.822512i
$761$		−	22.0846i		−	0.800566i	−0.916392	−	0.400283i	$-0.868912\pi$
$761$		−	22.0846i		−	0.800566i	0.916392	−	0.400283i	$-0.131088\pi$
$762$	−6.61938	+	9.11079i	−0.239795	+	0.330049i
$763$	3.86818	−	5.32409i	0.140037	−	0.192745i
$764$			26.7385i			0.967365i
$765$	−23.5987	−	32.4808i	−0.853212	−	1.17435i
$766$	−9.60652	−	29.5658i	−0.347098	−	1.06826i
$767$	−10.2555	−	14.1155i	−0.370304	−	0.509680i
$768$	50.0146	+	36.3377i	1.80475	+	1.31123i
$769$	−4.07999	+	5.61563i	−0.147128	+	0.202505i	−0.876220	−	0.481911i	$-0.839943\pi$
$769$	−4.07999	+	5.61563i	−0.147128	+	0.202505i	0.729092	+	0.684416i	$0.239943\pi$
$770$	−7.71611	−	2.50712i	−0.278069	−	0.0903502i
$771$	−72.4135	+	52.6115i	−2.60791	+	1.89476i
$772$		−	30.0335i		−	1.08093i
$773$	−17.4946	−	12.7106i	−0.629236	−	0.457167i	0.226899	−	0.973918i	$-0.427141\pi$
$773$	−17.4946	−	12.7106i	−0.629236	−	0.457167i	−0.856135	+	0.516751i	$0.827141\pi$
$774$	71.5566	−	51.9889i	2.57205	−	1.86870i
$775$	35.8971	−	11.6637i	1.28946	−	0.418971i
$776$	−8.14283	−	2.64577i	−0.292311	−	0.0949775i
$777$	1.77011	+	1.28606i	0.0635023	+	0.0461372i
$778$	14.7677	+	45.4504i	0.529449	+	1.62948i
$779$	−6.06899			−0.217444
$780$	45.7595			1.63845
$781$	1.89066	+	5.81885i	0.0676531	+	0.208215i
$782$		−	6.87694i		−	0.245919i
$783$	−36.0224	+	11.7044i	−1.28734	+	0.418281i
$784$	−9.76111	+	30.0416i	−0.348611	+	1.07291i
$785$	32.0953	−	10.4284i	1.14553	−	0.372205i
$786$	63.4953	−	87.3938i	2.26480	−	3.11723i
$787$	30.3750	+	9.86944i	1.08275	+	0.351808i	0.795442	−	0.606030i	$-0.207239\pi$
$787$	30.3750	+	9.86944i	1.08275	+	0.351808i	0.287311	+	0.957837i	$0.407239\pi$
$788$	4.88418	−	15.0320i	0.173992	−	0.535492i
$789$	−9.73219	+	29.9526i	−0.346475	+	1.06634i
$790$	54.4988	−	39.5957i	1.93898	−	1.40875i
$791$	3.65900	+	5.03618i	0.130099	+	0.179066i
$792$	−11.7252			−0.416638
$793$	22.0626	+	11.2184i	0.783465	+	0.398376i
$794$	23.8722			0.847194
$795$	54.9840	+	75.6790i	1.95008	+	2.68406i
$796$	−22.5674	+	16.3962i	−0.799881	+	0.581147i
$797$	15.8324	−	48.7272i	0.560813	−	1.72601i	−0.119262	−	0.992863i	$-0.538053\pi$
$797$	15.8324	−	48.7272i	0.560813	−	1.72601i	0.680075	−	0.733142i	$-0.261947\pi$
$798$	8.86039	−	27.2695i	0.313654	−	0.965329i
$799$	0.129062	+	0.0419348i	0.00456589	+	0.00148355i
$800$	−25.9036	+	35.6533i	−0.915831	+	1.26053i
$801$	−45.0291	+	14.6308i	−1.59102	+	0.516955i
$802$	−3.57363	+	10.9985i	−0.126189	+	0.388370i
$803$	−9.88428	+	3.21160i	−0.348809	+	0.113335i
$804$		−	13.2330i		−	0.466693i
$805$	1.20812	+	3.71821i	0.0425806	+	0.131050i
$806$	−34.5513			−1.21702
$807$	−78.5890			−2.76646
$808$	0.575815	+	1.77218i	0.0202571	+	0.0623449i
$809$	−17.5511	−	12.7516i	−0.617065	−	0.448324i	0.234830	−	0.972036i	$-0.424547\pi$
$809$	−17.5511	−	12.7516i	−0.617065	−	0.448324i	−0.851895	+	0.523713i	$0.824547\pi$
$810$	−39.1845	−	12.7318i	−1.37680	−	0.447351i
$811$	24.8962	−	8.08926i	0.874224	−	0.284052i	0.162667	−	0.986681i	$-0.447990\pi$
$811$	24.8962	−	8.08926i	0.874224	−	0.284052i	0.711557	+	0.702629i	$0.247990\pi$
$812$	−3.57568	+	2.59788i	−0.125482	+	0.0911678i
$813$	−7.21978	−	5.24548i	−0.253209	−	0.183967i
$814$		−	4.23243i		−	0.148347i
$815$	64.9552	−	47.1927i	2.27528	−	1.65309i
$816$	−27.9919	−	9.09511i	−0.979912	−	0.318393i
$817$	−39.4974	+	54.3635i	−1.38184	+	1.90194i
$818$	−21.2381	−	15.4304i	−0.742571	−	0.539510i
$819$	−6.90724	−	9.50700i	−0.241359	−	0.332202i
$820$	1.13650	+	3.49780i	0.0396885	+	0.122149i
$821$	20.9046	+	28.7727i	0.729576	+	1.00418i	0.999151	+	0.0411957i	$0.0131167\pi$
$821$	20.9046	+	28.7727i	0.729576	+	1.00418i	−0.269575	+	0.962979i	$0.586883\pi$
$822$			19.2022i			0.669754i
$823$	27.0662	−	37.2534i	0.943467	−	1.29857i	−0.0109014	−	0.999941i	$-0.503470\pi$
$823$	27.0662	−	37.2534i	0.943467	−	1.29857i	0.954369	−	0.298631i	$-0.0965299\pi$
$824$	−3.32390	+	4.57495i	−0.115793	+	0.159376i
$825$		−	37.8548i		−	1.31793i
$826$	3.89420	+	5.35991i	0.135497	+	0.186495i
$827$	−7.46209	−	22.9659i	−0.259482	−	0.798604i	−0.992913	−	0.118840i	$-0.962082\pi$
$827$	−7.46209	−	22.9659i	−0.259482	−	0.798604i	0.733431	−	0.679764i	$-0.237918\pi$
$828$	−8.67861	−	11.9451i	−0.301602	−	0.415120i
$829$	−39.2811	−	28.5394i	−1.36429	−	0.991213i	−0.998159	−	0.0606487i	$-0.980683\pi$
$829$	−39.2811	−	28.5394i	−1.36429	−	0.991213i	−0.366128	−	0.930564i	$-0.619317\pi$
$830$	4.52084	−	6.22240i	0.156921	−	0.215983i
$831$	−42.6592	−	13.8608i	−1.47983	−	0.480826i
$832$	8.02118	−	5.82773i	0.278084	−	0.202040i
$833$		−	13.6604i		−	0.473304i
$834$	−20.5765	−	14.9497i	−0.712508	−	0.517667i
$835$	−28.4521	+	20.6716i	−0.984624	+	0.715371i
$836$	−22.1391	+	7.19343i	−0.765697	+	0.248790i
$837$	44.8782	+	14.5818i	1.55122	+	0.504021i
$838$	38.6001	+	28.0446i	1.33342	+	0.968785i
$839$	−2.00788	−	6.17962i	−0.0693197	−	0.213344i	0.910395	−	0.413739i	$-0.135777\pi$
$839$	−2.00788	−	6.17962i	−0.0693197	−	0.213344i	−0.979715	+	0.200395i	$0.935777\pi$
$840$	6.64918			0.229418
$841$	6.77833			0.233736
$842$	19.4432	+	59.8400i	0.670056	+	2.06222i
$843$			11.5035i			0.396201i
$844$	−4.47974	+	1.45556i	−0.154199	+	0.0501023i
$845$	3.08910	−	9.50728i	0.106268	−	0.327060i
$846$	0.660235	−	0.214523i	0.0226993	−	0.00737546i
$847$	−2.67530	+	3.68224i	−0.0919245	+	0.126523i
$848$	42.7840	+	13.9014i	1.46921	+	0.477375i
$849$	4.31387	−	13.2767i	0.148051	−	0.455656i
$850$	7.65454	−	23.5582i	0.262548	−	0.808041i
$851$	−1.64999	+	1.19879i	−0.0565611	+	0.0410940i
$852$	7.70194	+	10.6008i	0.263864	+	0.363178i
$853$	18.0361			0.617544			0.308772	−	0.951136i	$-0.400082\pi$
$853$	18.0361			0.617544			0.308772	+	0.951136i	$0.400082\pi$
$854$	−8.37757	−	4.25982i	−0.286675	−	0.145768i
$855$	156.036			5.33633
$856$	0.604358	+	0.831828i	0.0206565	+	0.0284313i
$857$	−11.0489	+	8.02751i	−0.377424	+	0.274215i	−0.760283	−	0.649592i	$-0.774940\pi$
$857$	−11.0489	+	8.02751i	−0.377424	+	0.274215i	0.382859	+	0.923807i	$0.374940\pi$
$858$	−10.7082	+	32.9563i	−0.365570	+	1.12511i
$859$	−4.03727	+	12.4254i	−0.137750	+	0.423950i	−0.996008	−	0.0892684i	$-0.971547\pi$
$859$	−4.03727	+	12.4254i	−0.137750	+	0.423950i	0.858258	+	0.513219i	$0.171547\pi$
$860$	38.7283	+	12.5836i	1.32062	+	0.429097i
$861$	0.846274	−	1.16480i	0.0288410	−	0.0396962i
$862$	42.6670	−	13.8633i	1.45324	−	0.472187i
$863$	7.95333	−	24.4778i	0.270735	−	0.833235i	−0.719582	−	0.694407i	$-0.755667\pi$
$863$	7.95333	−	24.4778i	0.270735	−	0.833235i	0.990317	−	0.138828i	$-0.0443334\pi$
$864$	−52.3991	+	17.0255i	−1.78265	+	0.579219i
$865$			53.9377i			1.83394i
$866$	−6.51021	−	20.0364i	−0.221226	−	0.680864i
$867$	−37.4744			−1.27270
$868$	5.50633			0.186897
$869$	6.61605	+	20.3621i	0.224434	+	0.690737i
$870$	−70.6768	−	51.3497i	−2.39617	−	1.74092i
$871$	9.33689	+	3.03374i	0.316369	+	0.102794i
$872$	9.92240	−	3.22398i	0.336015	−	0.109178i
$873$	38.5622	−	28.0171i	1.30513	−	0.948234i
$874$	21.6227	+	15.7098i	0.731399	+	0.531393i
$875$			3.12654i			0.105696i
$876$	−18.0072	+	13.0830i	−0.608408	+	0.442035i
$877$	2.13649	+	0.694189i	0.0721443	+	0.0234411i	0.344867	−	0.938652i	$-0.387924\pi$
$877$	2.13649	+	0.694189i	0.0721443	+	0.0234411i	−0.272722	+	0.962093i	$0.587924\pi$
$878$	−19.0511	+	26.2216i	−0.642943	+	0.884935i
$879$	−16.6413	−	12.0906i	−0.561298	−	0.407807i
$880$	−19.0249	−	26.1856i	−0.641330	−	0.882716i
$881$	11.2527	+	34.6323i	0.379114	+	1.16679i	0.940661	+	0.339347i	$0.110206\pi$
$881$	11.2527	+	34.6323i	0.379114	+	1.16679i	−0.561548	+	0.827444i	$0.689794\pi$
$882$	−41.0753	−	56.5353i	−1.38308	−	1.90364i
$883$		−	35.1903i		−	1.18425i	−0.805847	−	0.592123i	$-0.798290\pi$
$883$		−	35.1903i		−	1.18425i	0.805847	−	0.592123i	$-0.201710\pi$
$884$	−5.59375	+	7.69914i	−0.188138	+	0.258950i
$885$	−32.3052	+	44.4644i	−1.08593	+	1.49465i
$886$			2.53066i			0.0850193i
$887$	2.23307	+	3.07355i	0.0749790	+	0.103200i	0.844859	−	0.534989i	$-0.179684\pi$
$887$	2.23307	+	3.07355i	0.0749790	+	0.103200i	−0.769880	+	0.638188i	$0.779684\pi$
$888$	1.07188	+	3.29892i	0.0359701	+	0.110704i
$889$	0.782622	+	1.07719i	0.0262483	+	0.0361277i
$890$	−42.0183	−	30.5281i	−1.40846	−	1.02330i
$891$	7.69687	−	10.5938i	0.257855	−	0.354907i
$892$	−26.3247	−	8.55340i	−0.881415	−	0.286389i
$893$	−0.426685	+	0.310005i	−0.0142785	+	0.0103739i
$894$			104.704i			3.50183i
$895$	−38.4211	−	27.9146i	−1.28428	−	0.933081i
$896$	4.14584	−	3.01213i	0.138503	−	0.100628i
$897$	15.8808	−	5.16000i	0.530246	−	0.172287i
$898$	5.09497	+	1.65546i	0.170022	+	0.0552433i
$899$	22.3973	+	16.2726i	0.746993	+	0.542722i
$900$	−16.4344	−	50.5800i	−0.547814	−	1.68600i
$901$	−19.4545			−0.648124
$902$	−2.78509			−0.0927335
$903$	−4.92616	−	15.1612i	−0.163932	−	0.504532i
$904$			9.86885i			0.328233i
$905$	−37.0884	+	12.0508i	−1.23286	+	0.400581i
$906$	25.1656	−	77.4519i	0.836073	−	2.57317i
$907$	39.7501	−	12.9156i	1.31988	−	0.428855i	0.437425	−	0.899255i	$-0.355890\pi$
$907$	39.7501	−	12.9156i	1.31988	−	0.428855i	0.882453	+	0.470400i	$0.155890\pi$
$908$	−24.7962	+	34.1291i	−0.822892	+	1.13261i
$909$	−9.86600	−	3.20566i	−0.327235	−	0.106325i
$910$	3.98348	−	12.2599i	0.132051	−	0.406411i
$911$	4.50075	−	13.8519i	0.149116	−	0.458933i	−0.848401	−	0.529354i	$-0.822434\pi$
$911$	4.50075	−	13.8519i	0.149116	−	0.458933i	0.997517	+	0.0704210i	$0.0224343\pi$
$912$	92.5423	−	67.2359i	3.06438	−	2.22640i
$913$	1.43683	+	1.97763i	0.0475522	+	0.0654500i
$914$	−20.6194			−0.682030
$915$	12.1326	−	77.0167i	0.401093	−	2.54609i
$916$	7.11925			0.235227
$917$	−7.50717	−	10.3327i	−0.247909	−	0.341217i
$918$	25.0536	−	18.2025i	0.826892	−	0.600772i
$919$	−8.56687	+	26.3661i	−0.282595	+	0.869738i	0.704514	+	0.709690i	$0.251165\pi$
$919$	−8.56687	+	26.3661i	−0.282595	+	0.869738i	−0.987109	+	0.160048i	$0.948835\pi$
$920$	−1.91528	+	5.89462i	−0.0631449	+	0.194340i
$921$	−38.7372	−	12.5865i	−1.27644	−	0.414739i
$922$	26.1527	−	35.9961i	0.861293	−	1.18547i
$923$	−9.24538	+	3.00401i	−0.304315	+	0.0988780i
$924$	1.70652	−	5.25214i	0.0561405	−	0.172783i
$925$	−6.98670	+	2.27012i	−0.229721	+	0.0746409i
$926$		−	27.5620i		−	0.905745i
$927$	−9.72850	−	29.9412i	−0.319526	−	0.983399i
$928$	−32.3242			−1.06109
$929$	−21.3678			−0.701056			−0.350528	−	0.936552i	$-0.613998\pi$
$929$	−21.3678			−0.701056			−0.350528	+	0.936552i	$0.613998\pi$
$930$	33.6328	+	103.511i	1.10286	+	3.39427i
$931$	42.9514	+	31.2060i	1.40767	+	1.02274i
$932$	−17.1626	−	5.57647i	−0.562180	−	0.182663i
$933$	−32.8851	+	10.6850i	−1.07661	+	0.349812i
$934$	−45.9515	+	33.3857i	−1.50358	+	1.09241i
$935$	11.3242	+	8.22751i	0.370341	+	0.269068i
$936$		−	18.6298i		−	0.608935i
$937$	−37.9973	+	27.6066i	−1.24132	+	0.901870i	−0.997685	−	0.0679982i	$-0.978339\pi$
$937$	−37.9973	+	27.6066i	−1.24132	+	0.901870i	−0.243632	+	0.969868i	$0.578339\pi$
$938$	−3.54539	−	1.15197i	−0.115761	−	0.0376131i
$939$	54.8635	−	75.5131i	1.79040	−	2.46428i
$940$	0.258571	+	0.187863i	0.00843365	+	0.00612741i
$941$	−21.7238	−	29.9002i	−0.708176	−	0.974720i	−0.999834	−	0.0181978i	$-0.994207\pi$
$941$	−21.7238	−	29.9002i	−0.708176	−	0.974720i	0.291659	−	0.956522i	$-0.405793\pi$
$942$	16.9129	+	52.0527i	0.551053	+	1.69597i
$943$	0.788848	+	1.08576i	0.0256884	+	0.0353571i
$944$			26.4309i			0.860253i
$945$	−10.3481	+	14.2430i	−0.336625	+	0.463325i
$946$	−18.1256	+	24.9477i	−0.589313	+	0.811120i
$947$		−	20.4153i		−	0.663409i	−0.943383	−	0.331704i	$-0.892376\pi$
$947$		−	20.4153i		−	0.663409i	0.943383	−	0.331704i	$-0.107624\pi$
$948$	26.9517	+	37.0958i	0.875350	+	1.20482i
$949$	−5.10280	−	15.7048i	−0.165644	−	0.509800i
$950$	56.5864	+	77.8845i	1.83591	+	2.52691i
$951$	41.5273	+	30.1714i	1.34662	+	0.978373i
$952$	−0.812811	+	1.11874i	−0.0263434	+	0.0362585i
$953$	−56.8386	−	18.4680i	−1.84118	−	0.598236i	−0.998179	−	0.0603292i	$-0.980785\pi$
$953$	−56.8386	−	18.4680i	−1.84118	−	0.598236i	−0.843004	−	0.537907i	$-0.819215\pi$
$954$	−80.5152	+	58.4977i	−2.60678	+	1.89393i
$955$			62.4871i			2.02203i
$956$	−1.35069	−	0.981333i	−0.0436844	−	0.0317386i
$957$	22.4628	−	16.3202i	0.726119	−	0.527556i
$958$	44.9252	−	14.5971i	1.45147	−	0.471611i
$959$	2.15920	+	0.701566i	0.0697241	+	0.0226547i
$960$	−25.2671	−	18.3576i	−0.815491	−	0.592489i
$961$	−1.07865	−	3.31973i	−0.0347950	−	0.107088i
$962$	6.72477			0.216815
$963$	−5.72414			−0.184458
$964$	0.684999	+	2.10821i	0.0220623	+	0.0679009i
$965$		−	70.1873i		−	2.25941i
$966$	−6.03025	+	1.95935i	−0.194020	+	0.0630409i
$967$	−0.891611	+	2.74410i	−0.0286723	+	0.0882442i	−0.964369	−	0.264562i	$-0.914773\pi$
$967$	−0.891611	+	2.74410i	−0.0286723	+	0.0882442i	0.935696	+	0.352806i	$0.114773\pi$
$968$	−6.86251	+	2.22977i	−0.220570	+	0.0716674i
$969$	−29.0768	+	40.0208i	−0.934082	+	1.28565i
$970$	49.7283	+	16.1577i	1.59668	+	0.518793i
$971$	−13.0870	+	40.2777i	−0.419983	+	1.29257i	0.487735	+	0.872992i	$0.337823\pi$
$971$	−13.0870	+	40.2777i	−0.419983	+	1.29257i	−0.907718	+	0.419582i	$0.862177\pi$
$972$	−2.10821	+	6.48841i	−0.0676210	+	0.208116i
$973$	−2.43280	+	1.76754i	−0.0779921	+	0.0566646i
$974$	31.1242	+	42.8388i	0.997283	+	1.37264i
$975$	60.1462			1.92622
$976$	−17.0498	−	33.3935i	−0.545752	−	1.06890i
$977$	5.24295			0.167737			0.0838684	−	0.996477i	$-0.473272\pi$
$977$	5.24295			0.167737			0.0838684	+	0.996477i	$0.473272\pi$
$978$	76.5379	+	105.345i	2.44741	+	3.36857i
$979$	13.3544	−	9.70256i	0.426809	−	0.310095i
$980$	9.94201	−	30.5984i	0.317586	−	0.977429i
$981$	−17.9485	+	55.2397i	−0.573051	+	1.76367i
$982$	−43.0000	−	13.9715i	−1.37219	−	0.445850i
$983$	−15.1730	+	20.8839i	−0.483944	+	0.666092i	−0.979257	−	0.202623i	$-0.935054\pi$
$983$	−15.1730	+	20.8839i	−0.483944	+	0.666092i	0.495313	+	0.868715i	$0.335054\pi$
$984$	2.17081	−	0.705339i	0.0692029	−	0.0224854i
$985$	11.4142	−	35.1293i	0.363686	−	1.11931i
$986$	17.2794	−	5.61442i	0.550288	−	0.178799i
$987$		−	0.125120i		−	0.00398260i
$988$	−11.4294	−	35.1761i	−0.363618	−	1.11910i
$989$	14.8596			0.472509
$990$	71.6060			2.27579
$991$	−2.36555	−	7.28043i	−0.0751443	−	0.231270i	0.906428	−	0.422360i	$-0.138798\pi$
$991$	−2.36555	−	7.28043i	−0.0751443	−	0.231270i	−0.981573	+	0.191089i	$0.938798\pi$
$992$	32.5797	+	23.6705i	1.03441	+	0.751540i
$993$	−56.6321	−	18.4009i	−1.79717	−	0.583935i
$994$	3.51064	−	1.14068i	0.111351	−	0.0361801i
$995$	−52.7394	+	38.3174i	−1.67195	+	1.21474i
$996$	4.23541	+	3.07721i	0.134204	+	0.0975050i
$997$			33.0522i			1.04677i	0.852095	+	0.523387i	$0.175332\pi$
$997$			33.0522i			1.04677i	−0.852095	+	0.523387i	$0.824668\pi$
$998$	−10.5588	+	7.67139i	−0.334232	+	0.242834i
$999$	−8.73470	−	2.83808i	−0.276354	−	0.0897927i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.g.a.27.1	✓	16
3.2	odd	2		549.2.y.b.271.4		16
4.3	odd	2		976.2.bd.b.881.1		16
61.28	odd	20		3721.2.a.k.1.2		16
61.33	odd	20		3721.2.a.k.1.15		16
61.52	even	10	inner	61.2.g.a.52.1	yes	16
183.113	odd	10		549.2.y.b.235.4		16
244.235	odd	10		976.2.bd.b.113.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.g.a.27.1	✓	16	1.1	even	1	trivial
61.2.g.a.52.1	yes	16	61.52	even	10	inner
549.2.y.b.235.4		16	183.113	odd	10
549.2.y.b.271.4		16	3.2	odd	2
976.2.bd.b.113.1		16	244.235	odd	10
976.2.bd.b.881.1		16	4.3	odd	2
3721.2.a.k.1.2		16	61.28	odd	20
3721.2.a.k.1.15		16	61.33	odd	20

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.g (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09120 - 1.50191i) q^{2} +(2.38911 - 1.73579i) q^{3} +(-0.446986 + 1.37568i) q^{4} +(-1.04459 + 3.21492i) q^{5} +(-5.21402 - 1.69414i) q^{6} +(-0.380995 + 0.524395i) q^{7} +(-0.977305 + 0.317546i) q^{8} +(1.76783 - 5.44082i) q^{9} +O(q^{10})\)	\(q+(-1.09120 - 1.50191i) q^{2} +(2.38911 - 1.73579i) q^{3} +(-0.446986 + 1.37568i) q^{4} +(-1.04459 + 3.21492i) q^{5} +(-5.21402 - 1.69414i) q^{6} +(-0.380995 + 0.524395i) q^{7} +(-0.977305 + 0.317546i) q^{8} +(1.76783 - 5.44082i) q^{9} +(5.96841 - 1.93925i) q^{10} +1.99452i q^{11} +(1.32000 + 4.06253i) q^{12} -3.16903 q^{13} +1.20334 q^{14} +(3.08479 + 9.49401i) q^{15} +(3.88381 + 2.82176i) q^{16} +(-1.97448 - 0.641547i) q^{17} +(-10.1007 + 3.28192i) q^{18} +(6.52771 - 4.74266i) q^{19} +(-3.95579 - 2.87405i) q^{20} +1.91417i q^{21} +(2.99560 - 2.17643i) q^{22} +(-1.69695 - 0.551371i) q^{23} +(-1.78370 + 2.45505i) q^{24} +(-5.19948 - 3.77765i) q^{25} +(3.45806 + 4.75962i) q^{26} +(-2.48291 - 7.64161i) q^{27} +(-0.551101 - 0.758525i) q^{28} -4.71399i q^{29} +(10.8931 - 14.9930i) q^{30} +(-3.45198 + 4.75125i) q^{31} -6.85708i q^{32} +(3.46208 + 4.76514i) q^{33} +(1.19101 + 3.66556i) q^{34} +(-1.28791 - 1.77265i) q^{35} +(6.69464 + 4.86394i) q^{36} +(0.671864 - 0.924742i) q^{37} +(-14.2461 - 4.62885i) q^{38} +(-7.57117 + 5.50078i) q^{39} -3.47367i q^{40} +(-0.608514 - 0.442111i) q^{41} +(2.87491 - 2.08875i) q^{42} +(-7.92050 + 2.57353i) q^{43} +(-2.74383 - 0.891524i) q^{44} +(15.6452 + 11.3669i) q^{45} +(1.02360 + 3.15033i) q^{46} -0.0653651 q^{47} +14.1768 q^{48} +(2.03329 + 6.25781i) q^{49} +11.9314i q^{50} +(-5.83084 + 1.89456i) q^{51} +(1.41651 - 4.35958i) q^{52} +(8.91212 - 2.89572i) q^{53} +(-8.76768 + 12.0677i) q^{54} +(-6.41224 - 2.08346i) q^{55} +(0.205829 - 0.633477i) q^{56} +(7.36316 - 22.6615i) q^{57} +(-7.08001 + 5.14393i) q^{58} +(3.23616 + 4.45419i) q^{59} -14.4396 q^{60} +(-6.96193 - 3.53999i) q^{61} +10.9028 q^{62} +(2.17961 + 2.99997i) q^{63} +(-2.53111 + 1.83896i) q^{64} +(3.31035 - 10.1882i) q^{65} +(3.37900 - 10.3995i) q^{66} +(-2.94629 - 0.957308i) q^{67} +(1.76513 - 2.42949i) q^{68} +(-5.01126 + 1.62826i) q^{69} +(-1.25700 + 3.86865i) q^{70} +(2.91741 - 0.947925i) q^{71} +5.87871i q^{72} +(1.61021 + 4.95571i) q^{73} -2.12203 q^{74} -18.9793 q^{75} +(3.60659 + 11.0999i) q^{76} +(-1.04592 - 0.759904i) q^{77} +(16.5234 + 5.36878i) q^{78} +(10.2090 - 3.31711i) q^{79} +(-13.1287 + 9.53859i) q^{80} +(-5.31146 - 3.85900i) q^{81} +1.39637i q^{82} +(0.991530 - 0.720388i) q^{83} +(-2.63328 - 0.855605i) q^{84} +(4.12505 - 5.67765i) q^{85} +(12.5081 + 9.08767i) q^{86} +(-8.18249 - 11.2622i) q^{87} +(-0.633352 - 1.94926i) q^{88} +(-4.86460 - 6.69554i) q^{89} -35.9013i q^{90} +(1.20739 - 1.66183i) q^{91} +(1.51702 - 2.08800i) q^{92} +17.3432i q^{93} +(0.0713268 + 0.0981729i) q^{94} +(8.42850 + 25.9402i) q^{95} +(-11.9024 - 16.3823i) q^{96} +(6.74067 + 4.89738i) q^{97} +(7.17997 - 9.88238i) q^{98} +(10.8519 + 3.52598i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9	\( 16 q - 5 q^{2} - q^{3} + 3 q^{4} - 15 q^{6} + 10 q^{7} - 5 q^{8} + q^{9} - 5 q^{10} - 12 q^{13} - 18 q^{14} - 13 q^{15} + 19 q^{16} - 10 q^{18} + 3 q^{19} - 13 q^{20} + 19 q^{22} - 15 q^{23} + 10 q^{24} - 2 q^{25} + 10 q^{26} - 4 q^{27} + 35 q^{28} + 45 q^{30} - 15 q^{31} + 25 q^{33} - 14 q^{34} + 10 q^{35} + 37 q^{36} - 5 q^{37} - 15 q^{38} - 3 q^{39} + 12 q^{41} - 15 q^{42} - 25 q^{43} - 50 q^{44} + 36 q^{45} + 27 q^{46} + 6 q^{47} - 20 q^{48} - 30 q^{49} + 50 q^{51} - 46 q^{52} - 20 q^{53} - 20 q^{54} + 20 q^{55} - 28 q^{56} - 11 q^{57} - 41 q^{58} + 5 q^{59} + 14 q^{60} - 53 q^{61} + 16 q^{62} - 5 q^{63} + 17 q^{64} + 20 q^{65} + 13 q^{66} - 55 q^{67} + 80 q^{68} - 15 q^{69} - 17 q^{70} - 50 q^{71} - 11 q^{73} + 24 q^{74} - 88 q^{75} - 19 q^{76} + 63 q^{77} + 50 q^{78} + 40 q^{79} - 49 q^{80} - 19 q^{81} + 31 q^{83} - 25 q^{84} + 55 q^{85} + 35 q^{86} + 25 q^{87} + 27 q^{88} + 60 q^{89} - 15 q^{91} - 5 q^{92} + 65 q^{94} + 48 q^{95} - 25 q^{96} + 45 q^{97} + 10 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 5 * q^2 - q^3 + 3 * q^4 - 15 * q^6 + 10 * q^7 - 5 * q^8 + q^9 - 5 * q^10 - 12 * q^13 - 18 * q^14 - 13 * q^15 + 19 * q^16 - 10 * q^18 + 3 * q^19 - 13 * q^20 + 19 * q^22 - 15 * q^23 + 10 * q^24 - 2 * q^25 + 10 * q^26 - 4 * q^27 + 35 * q^28 + 45 * q^30 - 15 * q^31 + 25 * q^33 - 14 * q^34 + 10 * q^35 + 37 * q^36 - 5 * q^37 - 15 * q^38 - 3 * q^39 + 12 * q^41 - 15 * q^42 - 25 * q^43 - 50 * q^44 + 36 * q^45 + 27 * q^46 + 6 * q^47 - 20 * q^48 - 30 * q^49 + 50 * q^51 - 46 * q^52 - 20 * q^53 - 20 * q^54 + 20 * q^55 - 28 * q^56 - 11 * q^57 - 41 * q^58 + 5 * q^59 + 14 * q^60 - 53 * q^61 + 16 * q^62 - 5 * q^63 + 17 * q^64 + 20 * q^65 + 13 * q^66 - 55 * q^67 + 80 * q^68 - 15 * q^69 - 17 * q^70 - 50 * q^71 - 11 * q^73 + 24 * q^74 - 88 * q^75 - 19 * q^76 + 63 * q^77 + 50 * q^78 + 40 * q^79 - 49 * q^80 - 19 * q^81 + 31 * q^83 - 25 * q^84 + 55 * q^85 + 35 * q^86 + 25 * q^87 + 27 * q^88 + 60 * q^89 - 15 * q^91 - 5 * q^92 + 65 * q^94 + 48 * q^95 - 25 * q^96 + 45 * q^97 + 10 * q^98 - 5 * q^99

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