LMFDB - Embedded newform 261.2.x.a.2.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(2,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([14, 3]))

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

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

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			2.6
Character	$\chi$	$=$	261.2
Dual form			261.2.x.a.131.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45392 - 1.07304i) q^{2} +(1.56552 + 0.741045i) q^{3} +(0.372954 + 1.20909i) q^{4} +(0.540145 - 1.37627i) q^{5} +(-1.48097 - 2.75729i) q^{6} +(3.98072 + 1.22789i) q^{7} +(-0.438482 + 1.25311i) q^{8} +(1.90171 + 2.32024i) q^{9} +O(q^{10})$	\(q+(-1.45392 - 1.07304i) q^{2} +(1.56552 + 0.741045i) q^{3} +(0.372954 + 1.20909i) q^{4} +(0.540145 - 1.37627i) q^{5} +(-1.48097 - 2.75729i) q^{6} +(3.98072 + 1.22789i) q^{7} +(-0.438482 + 1.25311i) q^{8} +(1.90171 + 2.32024i) q^{9} +(-2.26212 + 1.42138i) q^{10} +(-1.17345 - 0.222029i) q^{11} +(-0.312121 + 2.16923i) q^{12} +(-1.95303 + 0.146359i) q^{13} +(-4.47007 - 6.05673i) q^{14} +(1.86548 - 1.75430i) q^{15} +(4.07304 - 2.77695i) q^{16} +(0.644767 + 0.644767i) q^{17} +(-0.275212 - 5.41405i) q^{18} +(0.737125 + 1.17313i) q^{19} +(1.86548 + 0.139798i) q^{20} +(5.32197 + 4.87218i) q^{21} +(1.46786 + 1.58197i) q^{22} +(0.731034 - 4.85009i) q^{23} +(-1.61506 + 1.63683i) q^{24} +(2.06291 + 1.91410i) q^{25} +(2.99660 + 1.88289i) q^{26} +(1.25776 + 5.04163i) q^{27} +5.27099i q^{28} +(0.245280 - 5.37958i) q^{29} +(-4.59470 + 0.548873i) q^{30} +(-3.09460 - 7.09290i) q^{31} +(-6.24829 - 0.233795i) q^{32} +(-1.67253 - 1.21717i) q^{33} +(-0.245578 - 1.62930i) q^{34} +(3.84007 - 4.81529i) q^{35} +(-2.09613 + 3.16467i) q^{36} +(1.98669 + 0.695173i) q^{37} +(0.187094 - 2.49660i) q^{38} +(-3.16597 - 1.21815i) q^{39} +(1.48777 + 1.28033i) q^{40} +(-1.55989 - 0.417970i) q^{41} +(-2.50968 - 12.7945i) q^{42} +(-9.57671 - 4.17828i) q^{43} +(-0.169191 - 1.50161i) q^{44} +(4.22046 - 1.36399i) q^{45} +(-6.26721 + 6.26721i) q^{46} +(-1.80509 + 9.54012i) q^{47} +(8.43427 - 1.32907i) q^{48} +(8.55474 + 5.83252i) q^{49} +(-0.945395 - 4.99653i) q^{50} +(0.531594 + 1.48720i) q^{51} +(-0.905353 - 2.30680i) q^{52} +(-1.72461 + 1.37533i) q^{53} +(3.58121 - 8.67975i) q^{54} +(-0.939404 + 1.49505i) q^{55} +(-3.28415 + 4.44987i) q^{56} +(0.284644 + 2.38280i) q^{57} +(-6.12913 + 7.55828i) q^{58} +(2.83866 - 1.63890i) q^{59} +(2.81684 + 1.60126i) q^{60} +(-12.0227 + 6.35417i) q^{61} +(-3.11168 + 13.6331i) q^{62} +(4.72116 + 11.5713i) q^{63} +(1.12539 + 0.897471i) q^{64} +(-0.853490 + 2.76695i) q^{65} +(1.12565 + 3.56436i) q^{66} +(-5.01615 + 7.35734i) q^{67} +(-0.539111 + 1.02005i) q^{68} +(4.73858 - 7.05118i) q^{69} +(-10.7502 + 2.88050i) q^{70} +(-2.90138 - 1.39723i) q^{71} +(-3.74138 + 1.36566i) q^{72} +(11.3062 - 1.27390i) q^{73} +(-2.14254 - 3.14253i) q^{74} +(1.81109 + 4.52527i) q^{75} +(-1.14350 + 1.32877i) q^{76} +(-4.39855 - 2.32470i) q^{77} +(3.29593 + 5.16832i) q^{78} +(-1.45848 - 1.69478i) q^{79} +(-1.62179 - 7.10554i) q^{80} +(-1.76703 + 8.82483i) q^{81} +(1.81945 + 2.28152i) q^{82} +(-4.71675 + 5.08345i) q^{83} +(-3.90604 + 8.25184i) q^{84} +(1.23564 - 0.539103i) q^{85} +(9.44031 + 16.3511i) q^{86} +(4.37050 - 8.24007i) q^{87} +(0.792763 - 1.37311i) q^{88} +(-1.56439 + 13.8843i) q^{89} +(-7.59983 - 2.54561i) q^{90} +(-7.95418 - 1.81549i) q^{91} +(6.13683 - 0.924978i) q^{92} +(0.411497 - 13.3973i) q^{93} +(12.8614 - 11.9336i) q^{94} +(2.01269 - 0.380822i) q^{95} +(-9.60858 - 4.99628i) q^{96} +(-0.726683 - 19.4210i) q^{97} +(-6.17937 - 17.6596i) q^{98} +(-1.71640 - 3.14492i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.45392	−	1.07304i	−1.02808	−	0.758755i	−0.0572068	−	0.998362i	$-0.518219\pi$
$2$	−1.45392	−	1.07304i	−1.02808	−	0.758755i	−0.970870	+	0.239607i	$0.922981\pi$
$3$	1.56552	+	0.741045i	0.903853	+	0.427842i
$3$	1.56552	+	0.741045i	0.903853	+	0.427842i
$4$	0.372954	+	1.20909i	0.186477	+	0.604544i
$5$	0.540145	−	1.37627i	0.241560	−	0.615485i	−0.757753	−	0.652541i	$-0.773703\pi$
$5$	0.540145	−	1.37627i	0.241560	−	0.615485i	0.999313	+	0.0370564i	$0.0117981\pi$
$6$	−1.48097	−	2.75729i	−0.604603	−	1.12566i
$7$	3.98072	+	1.22789i	1.50457	+	0.464099i	0.934037	−	0.357176i	$-0.116260\pi$
$7$	3.98072	+	1.22789i	1.50457	+	0.464099i	0.570533	+	0.821274i	$0.306737\pi$
$8$	−0.438482	+	1.25311i	−0.155027	+	0.443041i
$9$	1.90171	+	2.32024i	0.633902	+	0.773414i
$10$	−2.26212	+	1.42138i	−0.715345	+	0.449481i
$11$	−1.17345	−	0.222029i	−0.353809	−	0.0669443i	0.00596912	−	0.999982i	$-0.498100\pi$
$11$	−1.17345	−	0.222029i	−0.353809	−	0.0669443i	−0.359778	+	0.933038i	$0.617148\pi$
$12$	−0.312121	+	2.16923i	−0.0901016	+	0.626202i
$13$	−1.95303	+	0.146359i	−0.541673	+	0.0405928i	−0.342758	−	0.939424i	$-0.611361\pi$
$13$	−1.95303	+	0.146359i	−0.541673	+	0.0405928i	−0.198916	+	0.980017i	$0.563742\pi$
$14$	−4.47007	−	6.05673i	−1.19468	−	1.61873i
$15$	1.86548	−	1.75430i	0.481665	−	0.452958i
$16$	4.07304	−	2.77695i	1.01826	−	0.694238i
$17$	0.644767	+	0.644767i	0.156379	+	0.156379i	0.780960	−	0.624581i	$-0.214730\pi$
$17$	0.644767	+	0.644767i	0.156379	+	0.156379i	−0.624581	+	0.780960i	$0.714730\pi$
$18$	−0.275212	−	5.41405i	−0.0648681	−	1.27610i
$19$	0.737125	+	1.17313i	0.169108	+	0.269134i	0.920517	−	0.390703i	$-0.127768\pi$
$19$	0.737125	+	1.17313i	0.169108	+	0.269134i	−0.751409	+	0.659837i	$0.770625\pi$
$20$	1.86548	+	0.139798i	0.417133	+	0.0312598i
$21$	5.32197	+	4.87218i	1.16135	+	1.06320i
$22$	1.46786	+	1.58197i	0.312948	+	0.337278i
$23$	0.731034	−	4.85009i	0.152431	−	1.01131i	−0.773548	−	0.633738i	$-0.781520\pi$
$23$	0.731034	−	4.85009i	0.152431	−	1.01131i	0.925979	−	0.377576i	$-0.123242\pi$
$24$	−1.61506	+	1.63683i	−0.329673	+	0.334117i
$25$	2.06291	+	1.91410i	0.412581	+	0.382820i
$26$	2.99660	+	1.88289i	0.587682	+	0.369265i
$27$	1.25776	+	5.04163i	0.242055	+	0.970262i
$28$			5.27099i			0.996123i
$29$	0.245280	−	5.37958i	0.0455474	−	0.998962i
$29$	0.245280	−	5.37958i	0.0455474	−	0.998962i
$30$	−4.59470	+	0.548873i	−0.838873	+	0.100210i
$31$	−3.09460	−	7.09290i	−0.555807	−	1.27392i	−0.936968	−	0.349414i	$-0.886381\pi$
$31$	−3.09460	−	7.09290i	−0.555807	−	1.27392i	0.381162	−	0.924508i	$-0.375524\pi$
$32$	−6.24829	−	0.233795i	−1.10455	−	0.0413295i
$33$	−1.67253	−	1.21717i	−0.291150	−	0.211882i
$34$	−0.245578	−	1.62930i	−0.0421162	−	0.279423i
$35$	3.84007	−	4.81529i	0.649090	−	0.813933i
$36$	−2.09613	+	3.16467i	−0.349354	+	0.527446i
$37$	1.98669	+	0.695173i	0.326610	+	0.114286i	0.488603	−	0.872506i	$-0.337507\pi$
$37$	1.98669	+	0.695173i	0.326610	+	0.114286i	−0.161993	+	0.986792i	$0.551792\pi$
$38$	0.187094	−	2.49660i	0.0303507	−	0.405002i
$39$	−3.16597	−	1.21815i	−0.506961	−	0.195061i
$40$	1.48777	+	1.28033i	0.235237	+	0.202438i
$41$	−1.55989	−	0.417970i	−0.243613	−	0.0652760i	0.134946	−	0.990853i	$-0.456914\pi$
$41$	−1.55989	−	0.417970i	−0.243613	−	0.0652760i	−0.378560	+	0.925577i	$0.623580\pi$
$42$	−2.50968	−	12.7945i	−0.387251	−	1.97423i
$43$	−9.57671	−	4.17828i	−1.46044	−	0.637181i	−0.488529	−	0.872548i	$-0.662466\pi$
$43$	−9.57671	−	4.17828i	−1.46044	−	0.637181i	−0.971907	+	0.235367i	$0.924371\pi$
$44$	−0.169191	−	1.50161i	−0.0255065	−	0.226377i
$45$	4.22046	−	1.36399i	0.629150	−	0.203331i
$46$	−6.26721	+	6.26721i	−0.924050	+	0.924050i
$47$	−1.80509	+	9.54012i	−0.263299	+	1.39157i	0.562123	+	0.827053i	$0.309985\pi$
$47$	−1.80509	+	9.54012i	−0.263299	+	1.39157i	−0.825422	+	0.564516i	$0.809063\pi$
$48$	8.43427	−	1.32907i	1.21738	−	0.191834i
$49$	8.55474	+	5.83252i	1.22211	+	0.833218i
$50$	−0.945395	−	4.99653i	−0.133699	−	0.706616i
$51$	0.531594	+	1.48720i	0.0744381	+	0.208249i
$52$	−0.905353	−	2.30680i	−0.125550	−	0.319896i
$53$	−1.72461	+	1.37533i	−0.236893	+	0.188916i	−0.734740	−	0.678349i	$-0.762696\pi$
$53$	−1.72461	+	1.37533i	−0.236893	+	0.188916i	0.497846	+	0.867265i	$0.334124\pi$
$54$	3.58121	−	8.67975i	0.487340	−	1.18116i
$55$	−0.939404	+	1.49505i	−0.126669	+	0.201593i
$56$	−3.28415	+	4.44987i	−0.438863	+	0.594638i
$57$	0.284644	+	2.38280i	0.0377020	+	0.315609i
$58$	−6.12913	+	7.55828i	−0.804794	+	0.992450i
$59$	2.83866	−	1.63890i	0.369562	−	0.213367i	−0.303705	−	0.952766i	$-0.598224\pi$
$59$	2.83866	−	1.63890i	0.369562	−	0.213367i	0.673267	+	0.739399i	$0.264890\pi$
$60$	2.81684	+	1.60126i	0.363653	+	0.206722i
$61$	−12.0227	+	6.35417i	−1.53935	+	0.813568i	−0.999601	−	0.0282602i	$-0.991003\pi$
$61$	−12.0227	+	6.35417i	−1.53935	+	0.813568i	−0.539745	+	0.841828i	$0.681479\pi$
$62$	−3.11168	+	13.6331i	−0.395183	+	1.73141i
$63$	4.72116	+	11.5713i	0.594810	+	1.45785i
$64$	1.12539	+	0.897471i	0.140674	+	0.112184i
$65$	−0.853490	+	2.76695i	−0.105862	+	0.343197i
$66$	1.12565	+	3.56436i	0.138558	+	0.438743i
$67$	−5.01615	+	7.35734i	−0.612820	+	0.898842i	−0.999729	−	0.0232759i	$-0.992590\pi$
$67$	−5.01615	+	7.35734i	−0.612820	+	0.898842i	0.386909	+	0.922118i	$0.373543\pi$
$68$	−0.539111	+	1.02005i	−0.0653769	+	0.123699i
$69$	4.73858	−	7.05118i	0.570458	−	0.848863i
$70$	−10.7502	+	2.88050i	−1.28489	+	0.344285i
$71$	−2.90138	−	1.39723i	−0.344330	−	0.165821i	0.253723	−	0.967277i	$-0.418345\pi$
$71$	−2.90138	−	1.39723i	−0.344330	−	0.165821i	−0.598054	+	0.801456i	$0.704059\pi$
$72$	−3.74138	+	1.36566i	−0.440925	+	0.160945i
$73$	11.3062	−	1.27390i	1.32329	−	0.149099i	0.578109	−	0.815960i	$-0.303791\pi$
$73$	11.3062	−	1.27390i	1.32329	−	0.149099i	0.745183	+	0.666860i	$0.232362\pi$
$74$	−2.14254	−	3.14253i	−0.249065	−	0.365312i
$75$	1.81109	+	4.52527i	0.209127	+	0.522533i
$76$	−1.14350	+	1.32877i	−0.131169	+	0.152421i
$77$	−4.39855	−	2.32470i	−0.501262	−	0.264925i
$78$	3.29593	+	5.16832i	0.373191	+	0.585197i
$79$	−1.45848	−	1.69478i	−0.164092	−	0.190678i	0.669906	−	0.742446i	$-0.266334\pi$
$79$	−1.45848	−	1.69478i	−0.164092	−	0.190678i	−0.833998	+	0.551768i	$0.813953\pi$
$80$	−1.62179	−	7.10554i	−0.181322	−	0.794424i
$81$	−1.76703	+	8.82483i	−0.196337	+	0.980536i
$82$	1.81945	+	2.28152i	0.200925	+	0.251952i
$83$	−4.71675	+	5.08345i	−0.517730	+	0.557981i	−0.936751	−	0.349996i	$-0.886183\pi$
$83$	−4.71675	+	5.08345i	−0.517730	+	0.557981i	0.419021	+	0.907977i	$0.362373\pi$
$84$	−3.90604	+	8.25184i	−0.426184	+	0.900349i
$85$	1.23564	−	0.539103i	0.134024	−	0.0584740i
$86$	9.44031	+	16.3511i	1.01797	+	1.76318i
$87$	4.37050	−	8.24007i	0.468567	−	0.883428i
$88$	0.792763	−	1.37311i	0.0845089	−	0.146374i
$89$	−1.56439	+	13.8843i	−0.165825	+	1.47173i	0.584893	+	0.811110i	$0.301136\pi$
$89$	−1.56439	+	13.8843i	−0.165825	+	1.47173i	−0.750718	+	0.660623i	$0.770292\pi$
$90$	−7.59983	−	2.54561i	−0.801093	−	0.268331i
$91$	−7.95418	−	1.81549i	−0.833825	−	0.190315i
$92$	6.13683	−	0.924978i	0.639809	−	0.0964357i
$93$	0.411497	−	13.3973i	0.0426703	−	1.38924i
$94$	12.8614	−	11.9336i	1.32655	−	1.23086i
$95$	2.01269	−	0.380822i	0.206498	−	0.0390715i
$96$	−9.60858	−	4.99628i	−0.980671	−	0.509930i
$97$	−0.726683	−	19.4210i	−0.0737835	−	1.97190i	−0.199679	−	0.979861i	$-0.563990\pi$
$97$	−0.726683	−	19.4210i	−0.0737835	−	1.97190i	0.125896	−	0.992043i	$-0.459820\pi$
$98$	−6.17937	−	17.6596i	−0.624210	−	1.78389i
$99$	−1.71640	−	3.14492i	−0.172504	−	0.316077i
$100$	−1.54494	+	3.20811i	−0.154494	+	0.320811i
$101$	−3.84006	+	8.80151i	−0.382100	+	0.875783i	0.614144	+	0.789194i	$0.289501\pi$
$101$	−3.84006	+	8.80151i	−0.382100	+	0.875783i	−0.996244	+	0.0865890i	$0.972403\pi$
$102$	0.822928	−	2.73269i	0.0814821	−	0.270576i
$103$	−0.900880	−	12.0214i	−0.0887663	−	1.18450i	−0.846663	−	0.532129i	$-0.821392\pi$
$103$	−0.900880	−	12.0214i	−0.0887663	−	1.18450i	0.757897	−	0.652375i	$-0.226227\pi$
$104$	0.672964	−	2.51154i	0.0659896	−	0.246276i
$105$	9.58005	−	4.69277i	0.934917	−	0.457968i
$106$	3.98323	−	0.149042i	0.386886	−	0.0144762i
$107$	4.23965	+	8.80372i	0.409862	+	0.851088i	0.999070	+	0.0431065i	$0.0137255\pi$
$107$	4.23965	+	8.80372i	0.409862	+	0.851088i	−0.589208	+	0.807981i	$0.700560\pi$
$108$	−5.62669	+	3.40104i	−0.541429	+	0.327265i
$109$	−3.88850	+	0.887525i	−0.372451	+	0.0850095i	−0.404649	−	0.914472i	$-0.632606\pi$
$109$	−3.88850	+	0.887525i	−0.372451	+	0.0850095i	0.0321983	+	0.999481i	$0.489749\pi$
$110$	2.97007	−	1.16567i	0.283185	−	0.111142i
$111$	2.59505	+	2.56053i	0.246311	+	0.243035i
$112$	19.6234	−	6.05302i	1.85424	−	0.571957i
$113$	0.287530	−	7.68439i	0.0270485	−	0.722887i	−0.918120	−	0.396303i	$-0.870293\pi$
$113$	0.287530	−	7.68439i	0.0270485	−	0.722887i	0.945168	−	0.326584i	$-0.105898\pi$
$114$	2.14299	−	3.76983i	0.200710	−	0.353077i
$115$	−6.28015	−	3.62585i	−0.585627	−	0.338112i
$116$	6.59586	−	1.70977i	0.612410	−	0.158748i
$117$	−4.05368	−	4.25317i	−0.374763	−	0.393206i
$118$	−5.88580	−	0.663170i	−0.541832	−	0.0610498i
$119$	1.77493	+	3.35834i	0.162708	+	0.307858i
$120$	1.38035	+	3.10688i	0.126008	+	0.283618i
$121$	−8.91192	−	3.49767i	−0.810175	−	0.317970i
$122$	24.2983	+	3.66238i	2.19986	+	0.331576i
$123$	−2.13230	−	1.81029i	−0.192263	−	0.163228i
$124$	7.42180	−	6.38697i	0.666497	−	0.573567i
$125$	10.4088	−	5.01263i	0.930995	−	0.448344i
$126$	5.55232	−	21.8898i	0.494640	−	1.95009i
$127$	2.85191	−	0.997928i	0.253066	−	0.0885518i	−0.200765	−	0.979640i	$-0.564343\pi$
$127$	2.85191	−	0.997928i	0.253066	−	0.0885518i	0.453831	+	0.891088i	$0.350057\pi$
$128$	2.56341	+	9.56678i	0.226576	+	0.845592i
$129$	−11.8962	−	13.6380i	−1.04741	−	1.20075i
$130$	4.20995	−	3.10709i	0.369237	−	0.272510i
$131$	−17.2948	+	12.7641i	−1.51105	+	1.11521i	−0.551322	+	0.834293i	$0.685876\pi$
$131$	−17.2948	+	12.7641i	−1.51105	+	1.11521i	−0.959732	+	0.280916i	$0.909362\pi$
$132$	0.847890	−	2.47618i	0.0737994	−	0.215524i
$133$	1.49382	+	5.57500i	0.129530	+	0.483414i
$134$	15.1878	−	5.31444i	1.31203	−	0.459098i
$135$	7.61800	+	0.992204i	0.655653	+	0.0853953i
$136$	−1.09068	+	0.525244i	−0.0935252	+	0.0450393i
$137$	13.0338	−	11.2165i	1.11356	−	0.958293i	0.114175	−	0.993461i	$-0.463578\pi$
$137$	13.0338	−	11.2165i	1.11356	−	0.958293i	0.999381	+	0.0351678i	$0.0111966\pi$
$138$	−14.4557	+	5.16716i	−1.23055	+	0.439858i
$139$	2.47835	+	0.373551i	0.210211	+	0.0316842i	0.253303	−	0.967387i	$-0.418483\pi$
$139$	2.47835	+	0.373551i	0.210211	+	0.0316842i	−0.0430925	+	0.999071i	$0.513721\pi$
$140$	7.25428	+	2.84710i	0.613099	+	0.240623i
$141$	−9.89555	+	13.5976i	−0.833356	+	1.14512i
$142$	2.71909	+	5.14476i	0.228181	+	0.431739i
$143$	2.32428	+	0.261884i	0.194366	+	0.0218998i
$144$	14.1889	+	4.16949i	1.18241	+	0.347457i
$145$	−7.27124	−	3.24332i	−0.603844	−	0.269343i
$146$	−17.8053	−	10.2799i	−1.47358	−	0.850769i
$147$	9.07046	+	15.4704i	0.748119	+	1.27598i
$148$	−0.0995808	+	2.66135i	−0.00818549	+	0.218762i
$149$	−6.71953	+	2.07270i	−0.550486	+	0.169802i	−0.557506	−	0.830173i	$-0.688242\pi$
$149$	−6.71953	+	2.07270i	−0.550486	+	0.169802i	0.00702021	+	0.999975i	$0.497765\pi$
$150$	2.22262	−	8.52275i	0.181476	−	0.695880i
$151$	4.82051	−	1.89191i	0.392288	−	0.153962i	−0.160995	−	0.986955i	$-0.551470\pi$
$151$	4.82051	−	1.89191i	0.392288	−	0.153962i	0.553282	+	0.832994i	$0.313375\pi$
$152$	−1.79327	+	0.409303i	−0.145454	+	0.0331988i
$153$	−0.269858	+	2.72217i	−0.0218167	+	0.220074i
$154$	3.90064	+	8.09976i	0.314323	+	0.652698i
$155$	−11.4333	+	0.427802i	−0.918341	+	0.0343619i
$156$	0.292095	−	4.28225i	0.0233863	−	0.342855i
$157$	1.80884	−	6.75069i	0.144361	−	0.538764i	−0.855422	−	0.517932i	$-0.826702\pi$
$157$	1.80884	−	6.75069i	0.144361	−	0.538764i	0.999783	−	0.0208315i	$-0.00663134\pi$
$158$	0.301939	+	4.02909i	0.0240209	+	0.320537i
$159$	−3.71909	+	0.875094i	−0.294943	+	0.0693995i
$160$	−3.69675	+	8.47303i	−0.292253	+	0.669852i
$161$	8.86541	−	18.4092i	0.698692	−	1.45085i
$162$	12.0385	−	10.9345i	0.945837	−	0.859095i
$163$	3.12027	+	8.91721i	0.244398	+	0.698449i	0.999101	+	0.0423833i	$0.0134951\pi$
$163$	3.12027	+	8.91721i	0.244398	+	0.698449i	−0.754703	+	0.656066i	$0.772219\pi$
$164$	−0.0764034	−	2.04192i	−0.00596611	−	0.159448i
$165$	−2.57856	+	1.64440i	−0.200740	+	0.128016i
$166$	12.3125	−	2.32966i	0.955637	−	0.180816i
$167$	6.53615	−	6.06467i	0.505783	−	0.469298i	−0.385524	−	0.922698i	$-0.625979\pi$
$167$	6.53615	−	6.06467i	0.505783	−	0.469298i	0.891307	+	0.453400i	$0.149789\pi$
$168$	−8.43895	+	4.53265i	−0.651080	+	0.349702i
$169$	−9.06189	+	1.36586i	−0.697069	+	0.105066i
$170$	−2.37500	−	0.542078i	−0.182154	−	0.0415755i
$171$	−1.32014	+	3.94125i	−0.100954	+	0.301395i
$172$	1.48023	−	13.1374i	0.112866	−	1.00172i
$173$	6.50967	−	11.2751i	0.494921	−	0.857228i	−0.505062	−	0.863083i	$-0.668530\pi$
$173$	6.50967	−	11.2751i	0.494921	−	0.857228i	0.999983	+	0.00585481i	$0.00186366\pi$
$174$	−15.1963	+	7.29068i	−1.15203	+	0.552705i
$175$	5.86155	+	10.1525i	0.443092	+	0.767458i
$176$	−5.39608	+	2.35428i	−0.406745	+	0.177461i
$177$	5.65848	−	0.462159i	0.425318	−	0.0347380i
$178$	17.1729	−	18.5080i	1.28717	−	1.38723i
$179$	−8.73442	−	10.9526i	−0.652841	−	0.818637i	0.339702	−	0.940533i	$-0.389674\pi$
$179$	−8.73442	−	10.9526i	−0.652841	−	0.818637i	−0.992543	+	0.121897i	$0.961102\pi$
$180$	3.22322	+	4.59421i	0.240245	+	0.342432i
$181$	−3.69268	−	16.1787i	−0.274475	−	1.20255i	−0.904669	−	0.426116i	$-0.859882\pi$
$181$	−3.69268	−	16.1787i	−0.274475	−	1.20255i	0.630194	−	0.776438i	$-0.282975\pi$
$182$	9.61665	+	11.1747i	0.712833	+	0.828327i
$183$	−23.5305	+	1.03824i	−1.73942	+	0.0767488i
$184$	5.75715	+	3.04274i	0.424422	+	0.224314i
$185$	2.02984	−	2.35872i	0.149237	−	0.173417i
$186$	−14.9742	+	19.0371i	−1.09796	+	1.39587i
$187$	−0.613446	−	0.899759i	−0.0448596	−	0.0657969i
$188$	−12.2081	+	1.37552i	−0.890364	+	0.100320i
$189$	−1.18379	+	21.6137i	−0.0861084	+	1.57217i
$190$	−3.33493	−	1.60602i	−0.241941	−	0.116513i
$191$	13.2484	−	3.54990i	0.958621	−	0.256862i	0.254605	−	0.967045i	$-0.418055\pi$
$191$	13.2484	−	3.54990i	0.958621	−	0.256862i	0.704017	+	0.710183i	$0.251388\pi$
$192$	1.09676	+	2.23898i	0.0791518	+	0.161584i
$193$	−6.48331	+	12.2670i	−0.466679	+	0.882999i	0.532649	+	0.846336i	$0.321197\pi$
$193$	−6.48331	+	12.2670i	−0.466679	+	0.882999i	−0.999328	+	0.0366627i	$0.988327\pi$
$194$	−19.7830	+	29.0164i	−1.42034	+	2.08325i
$195$	−3.38659	+	3.69923i	−0.242518	+	0.264908i
$196$	−3.86151	+	12.5187i	−0.275822	+	0.894193i
$197$	20.1266	+	16.0505i	1.43396	+	1.14355i	0.965607	+	0.260008i	$0.0837251\pi$
$197$	20.1266	+	16.0505i	1.43396	+	1.14355i	0.468356	+	0.883540i	$0.344846\pi$
$198$	−0.879129	+	6.41423i	−0.0624770	+	0.455840i
$199$	−3.24670	+	14.2247i	−0.230152	+	1.00836i	0.719361	+	0.694637i	$0.244435\pi$
$199$	−3.24670	+	14.2247i	−0.230152	+	1.00836i	−0.949513	+	0.313727i	$0.898422\pi$
$200$	−3.30312	+	1.74575i	−0.233566	+	0.123443i
$201$	−13.3050	+	7.80087i	−0.938462	+	0.550231i
$202$	15.0275	−	8.67615i	1.05733	−	0.610452i
$203$	7.58191	−	21.1134i	0.532146	−	1.48187i
$204$	−1.59989	+	1.19740i	−0.112015	+	0.0838348i
$205$	−1.41780	+	1.92105i	−0.0990236	+	0.134172i
$206$	−11.5897	+	18.4448i	−0.807490	+	1.28511i
$207$	12.6436	−	7.52727i	0.878790	−	0.523181i
$208$	−7.54834	+	6.01960i	−0.523383	+	0.417384i
$209$	−0.604512	−	1.54027i	−0.0418150	−	0.106543i
$210$	−18.9642	−	3.45687i	−1.30865	−	0.238547i
$211$	0.894469	+	4.72738i	0.0615778	+	0.325446i	0.999787	−	0.0206212i	$-0.00656439\pi$
$211$	0.894469	+	4.72738i	0.0615778	+	0.325446i	−0.938210	+	0.346068i	$0.887517\pi$
$212$	−2.30610	−	1.57227i	−0.158383	−	0.107984i
$213$	−3.50676	−	4.33744i	−0.240279	−	0.297197i
$214$	3.28265	−	17.3492i	0.224397	−	1.18597i
$215$	−10.9232	+	10.9232i	−0.744958	+	0.744958i
$216$	−6.86922	−	0.634559i	−0.467391	−	0.0431763i
$217$	−3.60944	−	32.0347i	−0.245025	−	2.17466i
$218$	6.60592	+	2.88213i	0.447409	+	0.195203i
$219$	18.6441	+	6.38409i	1.25985	+	0.431397i
$220$	−2.15801	−	0.578236i	−0.145493	−	0.0389847i
$221$	−1.35362	−	1.16488i	−0.0910542	−	0.0783584i
$222$	−1.02543	−	6.50741i	−0.0688227	−	0.436749i
$223$	−0.881694	+	11.7654i	−0.0590426	+	0.787868i	0.886574	+	0.462586i	$0.153078\pi$
$223$	−0.881694	+	11.7654i	−0.0590426	+	0.787868i	−0.945617	+	0.325282i	$0.894541\pi$
$224$	−24.5856	−	8.60288i	−1.64270	−	0.574804i
$225$	−0.518127	+	8.42649i	−0.0345418	+	0.561766i
$226$	−8.66372	+	10.8640i	−0.576302	+	0.722660i
$227$	−1.86152	−	12.3504i	−0.123553	−	0.819724i	−0.961665	−	0.274225i	$-0.911579\pi$
$227$	−1.86152	−	12.3504i	−0.123553	−	0.819724i	0.838112	−	0.545498i	$-0.183660\pi$
$228$	−2.77485	+	1.23283i	−0.183769	+	0.0816465i
$229$	−4.32739	−	0.161919i	−0.285962	−	0.0106999i	−0.105974	−	0.994369i	$-0.533796\pi$
$229$	−4.32739	−	0.161919i	−0.285962	−	0.0106999i	−0.179987	+	0.983669i	$0.557606\pi$
$230$	5.24015	+	12.0106i	0.345525	+	0.791953i
$231$	−5.16331	−	6.89889i	−0.339721	−	0.453914i
$232$	6.63364	+	2.66621i	0.435520	+	0.175045i
$233$		−	5.82234i		−	0.381434i	−0.981645	−	0.190717i	$-0.938919\pi$
$233$		−	5.82234i		−	0.381434i	0.981645	−	0.190717i	$-0.0610813\pi$
$234$	1.32990	+	10.5335i	0.0869380	+	0.688599i
$235$	12.1547	+	7.63732i	0.792887	+	0.498204i
$236$	3.04027	+	2.82096i	0.197905	+	0.183629i
$237$	−1.02737	−	3.73402i	−0.0667347	−	0.242550i
$238$	1.02303	−	6.78733i	0.0663129	−	0.439957i
$239$	14.4285	+	15.5503i	0.933304	+	1.00586i	0.999967	+	0.00808683i	$0.00257415\pi$
$239$	14.4285	+	15.5503i	0.933304	+	1.00586i	−0.0666634	+	0.997776i	$0.521235\pi$
$240$	2.72657	−	12.3257i	0.176000	−	0.795620i
$241$	14.8889	+	1.11577i	0.959076	+	0.0718728i	0.545060	−	0.838397i	$-0.316507\pi$
$241$	14.8889	+	1.11577i	0.959076	+	0.0718728i	0.414016	+	0.910270i	$0.364126\pi$
$242$	9.20407	+	14.6482i	0.591660	+	0.941622i
$243$	−9.30592	+	12.5060i	−0.596975	+	0.802260i
$244$	−12.1667	−	12.1667i	−0.778891	−	0.778891i
$245$	12.6479	−	8.62319i	0.808045	−	0.550916i
$246$	1.15768	+	4.92006i	0.0738109	+	0.313691i
$247$	−1.61133	−	2.18327i	−0.102526	−	0.138918i
$248$	10.2451	−	0.767764i	0.650565	−	0.0487531i
$249$	−11.1512	+	4.46291i	−0.706680	+	0.282826i
$250$	−20.5124	−	3.88115i	−1.29732	−	0.245466i
$251$	−13.4376	+	8.44338i	−0.848171	+	0.532941i	−0.884576	−	0.466396i	$-0.845552\pi$
$251$	−13.4376	+	8.44338i	−0.848171	+	0.532941i	0.0364050	+	0.999337i	$0.488409\pi$
$252$	−12.2300	+	10.0239i	−0.770415	+	0.631444i
$253$	−1.93469	+	5.52903i	−0.121633	+	0.347607i
$254$	−5.21727	−	1.60932i	−0.327361	−	0.100977i
$255$	2.33392	+	0.0716860i	0.146155	+	0.00448915i
$256$	7.59033	−	19.3398i	0.474395	−	1.20874i
$257$	−2.96902	−	9.62532i	−0.185202	−	0.600411i	−0.999792	−	0.0203741i	$-0.993514\pi$
$257$	−2.96902	−	9.62532i	−0.185202	−	0.600411i	0.814590	−	0.580037i	$-0.196962\pi$
$258$	2.66210	+	32.5937i	0.165735	+	2.02919i
$259$	7.05486	+	5.20673i	0.438368	+	0.323530i
$260$	−3.66379			−0.227219
$261$	12.9484	−	9.66126i	0.801483	−	0.598017i
$262$	38.8417			2.39965
$263$	−15.1496	−	11.1809i	−0.934167	−	0.689446i	0.0164334	−	0.999865i	$-0.494769\pi$
$263$	−15.1496	−	11.1809i	−0.934167	−	0.689446i	−0.950600	+	0.310419i	$0.899531\pi$
$264$	2.25862	−	1.56215i	0.139008	−	0.0961438i
$265$	0.961282	+	3.11640i	0.0590511	+	0.191439i
$266$	3.81032	−	9.70854i	0.233626	−	0.595269i
$267$	−12.7380	+	20.5769i	−0.779551	+	1.25928i
$268$	−10.7665	−	3.32102i	−0.657667	−	0.202863i
$269$	10.2258	−	29.2238i	0.623480	−	1.78180i	−4.47955e−5	−	1.00000i	$-0.500014\pi$
$269$	10.2258	−	29.2238i	0.623480	−	1.78180i	0.623525	−	0.781804i	$-0.285700\pi$
$270$	−10.0113	−	9.61701i	−0.609267	−	0.585273i
$271$	−1.24565	+	0.782691i	−0.0756676	+	0.0475451i	−0.569335	−	0.822106i	$-0.692799\pi$
$271$	−1.24565	+	0.782691i	−0.0756676	+	0.0475451i	0.493667	+	0.869651i	$0.335656\pi$
$272$	4.41665	+	0.835675i	0.267798	+	0.0506702i
$273$	−11.1071	−	8.73659i	−0.672231	−	0.528763i
$274$	−30.9860	+	2.32208i	−1.87193	+	0.140282i
$275$	−1.99574	−	2.70413i	−0.120347	−	0.163065i
$276$	10.2928	+	3.09959i	0.619553	+	0.186574i
$277$	23.4679	−	16.0002i	1.41005	−	0.961356i	0.411294	−	0.911503i	$-0.365077\pi$
$277$	23.4679	−	16.0002i	1.41005	−	0.961356i	0.998757	−	0.0498531i	$-0.0158753\pi$
$278$	−3.20249	−	3.20249i	−0.192072	−	0.192072i
$279$	10.5722	−	20.6688i	0.632942	−	1.23741i
$280$	4.35028	+	6.92344i	0.259979	+	0.413755i
$281$	−24.7958	−	1.85819i	−1.47920	−	0.110850i	−0.689472	−	0.724313i	$-0.742157\pi$
$281$	−24.7958	−	1.85819i	−1.47920	−	0.110850i	−0.789724	+	0.613462i	$0.789776\pi$
$282$	28.9781	−	9.15147i	1.72562	−	0.544962i
$283$	9.20801	+	9.92387i	0.547359	+	0.589913i	0.944773	−	0.327727i	$-0.106283\pi$
$283$	9.20801	+	9.92387i	0.547359	+	0.589913i	−0.397413	+	0.917640i	$0.630092\pi$
$284$	0.607293	−	4.02913i	0.0360362	−	0.239085i
$285$	3.43311	+	0.895310i	0.203360	+	0.0530336i
$286$	−3.09831	−	2.87481i	−0.183207	−	0.169991i
$287$	−5.69625	−	3.57919i	−0.336239	−	0.211273i
$288$	−11.3400	−	14.9422i	−0.668213	−	0.880475i
$289$		−	16.1686i		−	0.951091i
$290$	7.09159	+	12.5179i	0.416432	+	0.735075i
$291$	13.2542	−	30.9425i	0.776975	−	1.81388i
$292$	5.75696	+	13.1951i	0.336901	+	0.772185i
$293$	5.22611	+	0.195547i	0.305313	+	0.0114240i	0.189609	−	0.981860i	$-0.439278\pi$
$293$	5.22611	+	0.195547i	0.305313	+	0.0114240i	0.115704	+	0.993284i	$0.463088\pi$
$294$	3.41264	−	32.2257i	0.199029	−	1.87944i
$295$	−0.722278	−	4.79200i	−0.0420526	−	0.279001i
$296$	−1.74226	+	2.18472i	−0.101267	+	0.126984i
$297$	−0.356526	−	6.19537i	−0.0206878	−	0.359492i
$298$	11.9938	+	4.19680i	0.694780	+	0.243114i
$299$	−0.717875	+	9.57937i	−0.0415158	+	0.553989i
$300$	−4.79599	+	3.87749i	−0.276897	+	0.223867i
$301$	−32.9917	−	28.3917i	−1.90161	−	1.63647i
$302$	−9.03874	−	2.42192i	−0.520121	−	0.139366i
$303$	−12.5340	+	10.9333i	−0.720060	+	0.628101i
$304$	6.26006	+	2.73124i	0.359039	+	0.156647i
$305$	2.25104	+	19.9786i	0.128894	+	1.14397i
$306$	3.31335	−	3.66825i	0.189412	−	0.209700i
$307$	−19.7283	+	19.7283i	−1.12595	+	1.12595i	−0.135123	+	0.990829i	$0.543143\pi$
$307$	−19.7283	+	19.7283i	−1.12595	+	1.12595i	−0.990829	+	0.135123i	$0.956857\pi$
$308$	1.17031	−	6.18525i	0.0666847	−	0.352437i
$309$	7.49805	−	19.4873i	0.426549	−	1.10860i
$310$	17.0821	+	11.6464i	0.970197	+	0.661469i
$311$	0.830496	+	4.38928i	0.0470931	+	0.248893i	0.998200	−	0.0599679i	$-0.0190998\pi$
$311$	0.830496	+	4.38928i	0.0470931	+	0.248893i	−0.951107	+	0.308861i	$0.900052\pi$
$312$	2.91470	−	3.43316i	0.165012	−	0.194365i
$313$	9.60917	+	24.4838i	0.543142	+	1.38390i	0.894249	+	0.447569i	$0.147710\pi$
$313$	9.60917	+	24.4838i	0.543142	+	1.38390i	−0.351107	+	0.936335i	$0.614195\pi$
$314$	−9.87368	+	7.87400i	−0.557204	+	0.444355i
$315$	18.4753	−	0.247386i	1.04097	−	0.0139386i
$316$	1.50520	−	2.39551i	0.0846739	−	0.134758i
$317$	12.8625	−	17.4281i	0.722432	−	0.978861i	−0.277404	−	0.960753i	$-0.589474\pi$
$317$	12.8625	−	17.4281i	0.722432	−	0.978861i	0.999836	−	0.0181072i	$-0.00576401\pi$
$318$	6.34628	+	2.71842i	0.355881	+	0.152442i
$319$	−1.48225	+	6.25821i	−0.0829898	+	0.350393i
$320$	1.84303	−	1.06408i	0.103029	−	0.0594837i
$321$	0.113303	+	16.9242i	0.00632396	+	0.944615i
$322$	−32.6435	+	17.2526i	−1.81915	+	0.961448i
$323$	−0.281120	+	1.23167i	−0.0156419	+	0.0685318i
$324$	−11.3290	+	1.15476i	−0.629390	+	0.0641532i
$325$	−4.30907	−	3.43637i	−0.239024	−	0.190615i
$326$	5.03192	−	16.3131i	0.278692	−	0.903498i
$327$	−6.74522	−	1.49211i	−0.373012	−	0.0825141i
$328$	1.20774	−	1.77144i	0.0666865	−	0.0978111i
$329$	−18.8998	+	35.7601i	−1.04198	+	1.97152i
$330$	5.51352	+	0.376081i	0.303509	+	0.0207026i
$331$	−18.5409	+	4.96801i	−1.01910	+	0.273066i	−0.729426	−	0.684060i	$-0.760213\pi$
$331$	−18.5409	+	4.96801i	−1.01910	+	0.273066i	−0.289672	+	0.957126i	$0.593546\pi$
$332$	−7.90547	−	3.80707i	−0.433869	−	0.208940i
$333$	2.16513	+	5.93162i	0.118648	+	0.325051i
$334$	−16.0107	+	1.80397i	−0.876066	+	0.0987089i
$335$	7.41621	+	10.8776i	0.405191	+	0.594306i
$336$	35.2064	+	5.06570i	1.92067	+	0.276357i
$337$	−16.8815	+	19.6167i	−0.919594	+	1.06859i	0.0778381	+	0.996966i	$0.475198\pi$
$337$	−16.8815	+	19.6167i	−0.919594	+	1.06859i	−0.997432	+	0.0716214i	$0.977183\pi$
$338$	14.6409	+	7.73794i	0.796359	+	0.420888i
$339$	6.14461	−	11.8170i	0.333730	−	0.641811i
$340$	1.11266	+	1.29293i	0.0603425	+	0.0701192i
$341$	2.05653	+	9.01027i	0.111368	+	0.487933i
$342$	6.14851	−	4.31370i	0.332474	−	0.233258i
$343$	8.71102	+	10.9233i	0.470351	+	0.589801i
$344$	9.43505	−	10.1686i	0.508704	−	0.548252i
$345$	−7.14479	−	10.3302i	−0.384662	−	0.556160i
$346$	−21.5632	+	9.40791i	−1.15924	+	0.505773i
$347$	−9.17952	−	15.8994i	−0.492783	−	0.853524i	0.507183	−	0.861838i	$-0.330687\pi$
$347$	−9.17952	−	15.8994i	−0.492783	−	0.853524i	−0.999965	+	0.00831406i	$0.997354\pi$
$348$	11.5930	+	2.21115i	0.621448	+	0.118530i
$349$	−11.1289	+	19.2758i	−0.595717	+	1.03181i	0.397728	+	0.917503i	$0.369799\pi$
$349$	−11.1289	+	19.2758i	−0.595717	+	1.03181i	−0.993445	+	0.114309i	$0.963535\pi$
$350$	2.37184	−	21.0506i	0.126780	−	1.12520i
$351$	−3.19433	−	9.66238i	−0.170501	−	0.515740i
$352$	7.28016	+	1.66165i	0.388034	+	0.0885662i
$353$	5.59379	−	0.843129i	0.297728	−	0.0448752i	0.00152015	−	0.999999i	$-0.499516\pi$
$353$	5.59379	−	0.843129i	0.297728	−	0.0448752i	0.296207	+	0.955124i	$0.404278\pi$
$354$	−8.72290	−	5.39985i	−0.463617	−	0.286999i
$355$	−3.49012	+	3.23836i	−0.185237	+	0.171874i
$356$	−17.3708	+	3.28673i	−0.920650	+	0.174196i
$357$	0.290015	+	6.57285i	0.0153492	+	0.347872i
$358$	0.946532	+	25.2966i	0.0500258	+	1.33697i
$359$	−0.497235	−	1.42102i	−0.0262431	−	0.0749984i	0.930017	−	0.367518i	$-0.119792\pi$
$359$	−0.497235	−	1.42102i	−0.0262431	−	0.0749984i	−0.956260	+	0.292519i	$0.905506\pi$
$360$	−0.141372	+	5.88678i	−0.00745098	+	0.310261i
$361$	7.41092	−	15.3889i	0.390048	−	0.809943i
$362$	−11.9916	+	27.4849i	−0.630262	+	1.44458i
$363$	−11.3599	−	12.0798i	−0.596238	−	0.634025i
$364$	−0.771459	−	10.2944i	−0.0404354	−	0.539573i
$365$	4.35376	−	16.2484i	0.227886	−	0.850482i
$366$	35.3255	+	23.7397i	1.84649	+	1.24089i
$367$	18.9422	−	0.708767i	0.988774	−	0.0369973i	0.461892	−	0.886936i	$-0.347171\pi$
$367$	18.9422	−	0.708767i	0.988774	−	0.0369973i	0.526882	+	0.849939i	$0.323361\pi$
$368$	−10.4909	−	21.7847i	−0.546878	−	1.13560i
$369$	−1.99665	−	4.41417i	−0.103942	−	0.229792i
$370$	−5.48224	+	1.25128i	−0.285008	+	0.0650512i
$371$	−8.55394	+	3.35717i	−0.444098	+	0.174296i
$372$	16.3520	−	4.49905i	0.847812	−	0.233265i
$373$	−3.01313	+	0.929429i	−0.156014	+	0.0481240i	−0.371778	−	0.928321i	$-0.621252\pi$
$373$	−3.01313	+	0.929429i	−0.156014	+	0.0481240i	0.215764	+	0.976445i	$0.430776\pi$
$374$	−0.0735787	+	1.96643i	−0.00380466	+	0.101682i
$375$	20.0098	−	0.133961i	1.03330	−	0.00691771i
$376$	−11.1633	−	6.44514i	−0.575704	−	0.332383i
$377$	0.308312	+	10.5424i	0.0158789	+	0.542960i
$378$	24.9136	−	30.1543i	1.28141	−	1.55097i
$379$	23.1016	+	2.60293i	1.18665	+	0.133704i	0.683142	−	0.730286i	$-0.260613\pi$
$379$	23.1016	+	2.60293i	1.18665	+	0.133704i	0.503510	+	0.863989i	$0.332042\pi$
$380$	1.21109	+	2.29149i	0.0621275	+	0.117551i
$381$	5.20424	+	0.551120i	0.266621	+	0.0282347i
$382$	−23.0713	−	9.05483i	−1.18043	−	0.463285i
$383$	1.82140	+	0.274532i	0.0930691	+	0.0140279i	0.195412	−	0.980721i	$-0.437396\pi$
$383$	1.82140	+	0.274532i	0.0930691	+	0.0140279i	−0.102343	+	0.994749i	$0.532634\pi$
$384$	−3.07634	+	16.8766i	−0.156989	+	0.861230i
$385$	−5.57526	+	4.79790i	−0.284142	+	0.244524i
$386$	22.5892	−	10.8784i	1.14976	−	0.553696i
$387$	−8.51748	−	30.1661i	−0.432968	−	1.53343i
$388$	23.2107	−	8.12177i	1.17834	−	0.412321i
$389$	5.55796	+	20.7426i	0.281800	+	1.05169i	0.951146	+	0.308741i	$0.0999076\pi$
$389$	5.55796	+	20.7426i	0.281800	+	1.05169i	−0.669346	+	0.742951i	$0.733426\pi$
$390$	8.89326	−	1.74444i	0.450328	−	0.0883333i
$391$	3.59852	−	2.65583i	0.181985	−	0.134311i
$392$	−11.0599	+	8.16257i	−0.558609	+	0.412272i
$393$	−36.5342	+	7.16630i	−1.84290	+	0.361492i
$394$	−12.0397	−	44.9328i	−0.606551	−	2.26368i
$395$	−3.12026	+	1.09183i	−0.156997	+	0.0549358i
$396$	3.16235	−	3.24819i	0.158914	−	0.163228i
$397$	22.6706	−	10.9176i	1.13780	−	0.547937i	0.232454	−	0.972607i	$-0.425324\pi$
$397$	22.6706	−	10.9176i	1.13780	−	0.547937i	0.905348	+	0.424671i	$0.139610\pi$
$398$	19.9842	−	17.1978i	1.00172	−	0.862046i
$399$	−1.79273	+	9.83476i	−0.0897485	+	0.492354i
$400$	13.7177	+	2.06760i	0.685883	+	0.103380i
$401$	20.2058	+	7.93018i	1.00903	+	0.396014i	0.811544	−	0.584292i	$-0.198628\pi$
$401$	20.2058	+	7.93018i	1.00903	+	0.396014i	0.197484	+	0.980306i	$0.436723\pi$
$402$	27.7151	+	2.93498i	1.38230	+	0.146383i
$403$	7.08197	+	13.3997i	0.352778	+	0.667488i
$404$	−12.0740	−	1.36041i	−0.600703	−	0.0676829i
$405$	11.1909	+	7.19859i	0.556078	+	0.357701i
$406$	−33.6791	+	22.5615i	−1.67146	+	1.11971i
$407$	−2.17694	−	1.25686i	−0.107907	−	0.0623000i
$408$	−2.09671	+	0.0140370i	−0.103803	+	0.000694934i
$409$	0.133250	−	3.56118i	0.00658878	−	0.176089i	−0.992120	−	0.125290i	$-0.960014\pi$
$409$	0.133250	−	3.56118i	0.00658878	−	0.176089i	0.998709	−	0.0507986i	$-0.0161767\pi$
$410$	4.12274	−	1.27170i	0.203608	−	0.0628047i
$411$	28.7167	−	7.90104i	1.41649	−	0.389730i
$412$	14.1990	−	5.57268i	0.699532	−	0.274546i
$413$	13.3123	−	3.03845i	0.655056	−	0.149512i
$414$	−26.4598	−	2.62305i	−1.30043	−	0.128916i
$415$	4.44845	+	9.23730i	0.218366	+	0.453441i
$416$	12.2373	−	0.457889i	0.599985	−	0.0224498i
$417$	3.60309	+	2.42137i	0.176444	+	0.118575i
$418$	−0.773864	+	2.88810i	−0.0378509	+	0.141262i
$419$	−1.30605	−	17.4280i	−0.0638046	−	0.851413i	−0.933672	−	0.358128i	$-0.883415\pi$
$419$	−1.30605	−	17.4280i	−0.0638046	−	0.851413i	0.869868	−	0.493285i	$-0.164204\pi$
$420$	9.24690	+	9.83293i	0.451202	+	0.479798i
$421$	3.30394	−	7.57272i	0.161024	−	0.369072i	−0.817281	−	0.576239i	$-0.804520\pi$
$421$	3.30394	−	7.57272i	0.161024	−	0.369072i	0.978306	+	0.207167i	$0.0664245\pi$
$422$	3.77219	−	7.83304i	0.183627	−	0.381306i
$423$	−25.5681	+	13.9543i	−1.24316	+	0.678479i
$424$	−0.967229	−	2.76418i	−0.0469728	−	0.134240i
$425$	0.0959471	+	2.56424i	0.00465412	+	0.124384i
$426$	0.444285	+	10.0692i	0.0215257	+	0.487854i
$427$	−55.6611	+	10.5317i	−2.69363	+	0.509662i
$428$	−9.06328	+	8.40949i	−0.438090	+	0.406488i
$429$	3.44464	+	2.13238i	0.166309	+	0.102952i
$430$	27.6026	−	4.16042i	1.33112	−	0.200633i
$431$	−8.95113	−	2.04304i	−0.431161	−	0.0984097i	0.00143206	−	0.999999i	$-0.499544\pi$
$431$	−8.95113	−	2.04304i	−0.431161	−	0.0984097i	−0.432593	+	0.901589i	$0.642401\pi$
$432$	19.1233	+	17.0420i	0.920068	+	0.819935i
$433$	4.54734	−	40.3587i	0.218531	−	1.93952i	−0.107602	−	0.994194i	$-0.534317\pi$
$433$	4.54734	−	40.3587i	0.218531	−	1.93952i	0.326134	−	0.945324i	$-0.394254\pi$
$434$	−29.1267	+	50.4489i	−1.39813	+	2.42163i
$435$	−8.97983	−	10.4658i	−0.430550	−	0.501797i
$436$	−2.52333	−	4.37053i	−0.120846	−	0.209311i
$437$	6.22864	−	2.71753i	0.297956	−	0.129997i
$438$	−20.2567	−	29.2879i	−0.967901	−	1.39943i
$439$	−4.99942	+	5.38810i	−0.238610	+	0.257160i	−0.840992	−	0.541048i	$-0.818028\pi$
$439$	−4.99942	+	5.38810i	−0.238610	+	0.257160i	0.602382	+	0.798208i	$0.294218\pi$
$440$	−1.46155	−	1.83273i	−0.0696768	−	0.0873719i
$441$	2.73574	+	30.9408i	0.130273	+	1.47337i
$442$	0.718084	+	3.14613i	0.0341558	+	0.149646i
$443$	−11.1037	−	12.9027i	−0.527552	−	0.613027i	0.429456	−	0.903088i	$-0.358705\pi$
$443$	−11.1037	−	12.9027i	−0.527552	−	0.613027i	−0.957008	+	0.290061i	$0.906324\pi$
$444$	−2.12808	+	4.09261i	−0.100994	+	0.194227i
$445$	18.2635	+	9.65254i	0.865773	+	0.457574i
$446$	13.9067	−	16.1598i	0.658499	−	0.765190i
$447$	−12.0555	−	1.73462i	−0.570207	−	0.0820447i
$448$	3.37788	+	4.95444i	0.159590	+	0.234075i
$449$	31.3107	−	3.52787i	1.47764	−	0.166491i	0.663947	−	0.747780i	$-0.268880\pi$
$449$	31.3107	−	3.52787i	1.47764	−	0.166491i	0.813697	+	0.581289i	$0.197451\pi$
$450$	9.79529	−	11.6955i	0.461755	−	0.551330i
$451$	1.73765	+	0.836808i	0.0818227	+	0.0394037i
$452$	9.39835	−	2.51828i	0.442061	−	0.118450i
$453$	8.94860	+	0.610390i	0.420442	+	0.0286786i
$454$	−10.5460	+	19.9540i	−0.494947	+	0.936486i
$455$	−6.79501	+	9.96644i	−0.318555	+	0.467234i
$456$	−3.11072	−	0.688124i	−0.145673	−	0.0322244i
$457$	4.37422	−	14.1809i	0.204617	−	0.663353i	−0.793856	−	0.608106i	$-0.791929\pi$
$457$	4.37422	−	14.1809i	0.204617	−	0.663353i	0.998473	−	0.0552462i	$-0.0175944\pi$
$458$	6.11793	+	4.87889i	0.285872	+	0.227975i
$459$	−2.43972	+	4.06164i	−0.113876	+	0.189581i
$460$	2.04176	−	8.94553i	0.0951975	−	0.417088i
$461$	10.6024	−	5.60355i	0.493805	−	0.260983i	−0.201776	−	0.979432i	$-0.564671\pi$
$461$	10.6024	−	5.60355i	0.493805	−	0.260983i	0.695580	+	0.718448i	$0.255147\pi$
$462$	0.104243	+	15.5709i	0.00484983	+	0.724423i
$463$	7.15961	−	4.13360i	0.332735	−	0.192105i	−0.324320	−	0.945948i	$-0.605135\pi$
$463$	7.15961	−	4.13360i	0.332735	−	0.192105i	0.657055	+	0.753843i	$0.271802\pi$
$464$	−13.9398	−	22.5924i	−0.647138	−	1.04882i
$465$	−18.2160	−	7.80282i	−0.844747	−	0.361847i
$466$	−6.24762	+	8.46522i	−0.289415	+	0.392144i
$467$	−12.3243	+	19.6140i	−0.570300	+	0.907627i	0.429690	+	0.902977i	$0.358623\pi$
$467$	−12.3243	+	19.6140i	−0.570300	+	0.907627i	−0.999989	+	0.00465004i	$0.998520\pi$
$468$	3.63062	−	6.48749i	0.167826	−	0.299885i
$469$	−29.0019	+	23.1282i	−1.33918	+	1.06796i
$470$	−9.47684	−	24.1466i	−0.437134	−	1.11380i
$471$	7.83434	−	9.22790i	0.360987	−	0.425199i
$472$	0.809022	+	4.27578i	0.0372382	+	0.196809i
$473$	10.3101	+	7.02931i	0.474059	+	0.323208i
$474$	−2.51304	+	6.53137i	−0.115428	+	0.299996i
$475$	−0.724862	+	3.83099i	−0.0332589	+	0.175778i
$476$	−3.39856	+	3.39856i	−0.155773	+	0.155773i
$477$	−6.47080	−	1.38604i	−0.296277	−	0.0634623i
$478$	−4.29185	−	38.0912i	−0.196305	−	1.74225i
$479$	8.63182	+	3.76603i	0.394398	+	0.172074i	0.587726	−	0.809060i	$-0.300023\pi$
$479$	8.63182	+	3.76603i	0.394398	+	0.172074i	−0.193328	+	0.981134i	$0.561928\pi$
$480$	−12.0662	+	10.5252i	−0.550745	+	0.480410i
$481$	−3.98182	−	1.06692i	−0.181555	−	0.0486476i
$482$	−20.4500	−	17.5986i	−0.931470	−	0.801595i
$483$	27.5210	−	22.2503i	1.25225	−	1.01243i
$484$	0.905254	−	12.0798i	0.0411479	−	0.549080i
$485$	−27.1210	−	9.49004i	−1.23150	−	0.430921i
$486$	26.9495	−	8.19707i	1.22245	−	0.371827i
$487$	−2.76574	+	3.46813i	−0.125328	+	0.157156i	−0.840536	−	0.541755i	$-0.817760\pi$
$487$	−2.76574	+	3.46813i	−0.125328	+	0.157156i	0.715209	+	0.698911i	$0.246332\pi$
$488$	−2.69074	−	17.8519i	−0.121804	−	0.808118i
$489$	−1.72321	+	16.2723i	−0.0779263	+	0.735860i
$490$	−27.6421	−	1.03429i	−1.24874	−	0.0467246i
$491$	−9.80344	−	22.4697i	−0.442423	−	1.01404i	−0.984766	−	0.173887i	$-0.944367\pi$
$491$	−9.80344	−	22.4697i	−0.442423	−	1.01404i	0.542342	−	0.840158i	$-0.317538\pi$
$492$	1.39355	−	3.25329i	0.0628259	−	0.146670i
$493$	3.62672	−	3.31042i	0.163339	−	0.149094i
$494$			4.90332i			0.220611i
$495$	−5.25535	+	0.663507i	−0.236211	+	0.0298224i
$496$	−32.3011	−	20.2961i	−1.45036	−	0.911322i
$497$	−9.83393	−	9.12455i	−0.441112	−	0.409292i
$498$	21.0019	+	5.47701i	0.941117	+	0.245431i
$499$	−0.487598	+	3.23500i	−0.0218279	+	0.144819i	−0.997090	−	0.0762329i	$-0.975711\pi$
$499$	−0.487598	+	3.23500i	−0.0218279	+	0.144819i	0.975262	+	0.221051i	$0.0709489\pi$
$500$	9.94274	+	10.7157i	0.444653	+	0.479222i
$501$	14.7267	−	4.65077i	0.657939	−	0.207781i
$502$	28.5972	+	2.14307i	1.27636	+	0.0956497i
$503$	14.7520	+	23.4776i	0.657757	+	1.04682i	0.994451	+	0.105201i	$0.0335485\pi$
$503$	14.7520	+	23.4776i	0.657757	+	1.04682i	−0.336694	+	0.941614i	$0.609309\pi$
$504$	−16.5703	+	0.842314i	−0.738098	+	0.0375197i
$505$	10.0390	+	10.0390i	0.446731	+	0.446731i
$506$	8.74577	−	5.96277i	0.388797	−	0.265077i
$507$	−15.1987	−	4.57699i	−0.674999	−	0.203271i
$508$	2.27022	+	3.07604i	0.100725	+	0.136477i
$509$	18.3658	−	1.37633i	0.814051	−	0.0610047i	0.338804	−	0.940857i	$-0.389978\pi$
$509$	18.3658	−	1.37633i	0.814051	−	0.0610047i	0.475247	+	0.879852i	$0.342359\pi$
$510$	−3.31640	−	2.60861i	−0.146853	−	0.115511i
$511$	46.5711	+	8.81172i	2.06018	+	0.389808i
$512$	−15.0158	+	9.43507i	−0.663612	+	0.416975i
$513$	−4.98736	+	5.19182i	−0.220197	+	0.229225i
$514$	−6.01166	+	17.1803i	−0.265163	+	0.757792i
$515$	−17.0313	−	5.25345i	−0.750487	−	0.231494i
$516$	12.0527	−	19.4699i	0.530592	−	0.857117i
$517$	4.23636	−	10.7941i	0.186315	−	0.474723i
$518$	−4.67017	−	15.1403i	−0.205196	−	0.665228i
$519$	18.5464	−	12.8274i	0.814095	−	0.563061i
$520$	−3.09304	−	2.28277i	−0.135639	−	0.100106i
$521$	−0.0962244			−0.00421567			−0.00210783	−	0.999998i	$-0.500671\pi$
$521$	−0.0962244			−0.00421567			−0.00210783	+	0.999998i	$0.500671\pi$
$522$	−29.1928	+	0.152565i	−1.27773	+	0.00667761i
$523$	2.47443			0.108199			0.0540997	−	0.998536i	$-0.482771\pi$
$523$	2.47443			0.108199			0.0540997	+	0.998536i	$0.482771\pi$
$524$	−21.8832	−	16.1505i	−0.955970	−	0.705538i
$525$	1.65292	+	20.2376i	0.0721392	+	0.883243i
$526$	10.0287	+	32.5124i	0.437274	+	1.41761i
$527$	2.57797	−	6.56856i	0.112298	−	0.286131i
$528$	−10.1923	−	0.313055i	−0.443563	−	0.0136240i
$529$	−1.01079	−	0.311788i	−0.0439475	−	0.0135560i
$530$	1.94640	−	5.56249i	0.0845462	−	0.241619i
$531$	9.20095	+	3.46967i	0.399287	+	0.150571i
$532$	−6.18354	+	3.88538i	−0.268091	+	0.168453i
$533$	3.10768	+	0.588005i	0.134609	+	0.0254693i
$534$	40.5998	−	16.2488i	1.75693	−	0.703153i
$535$	14.4063	−	1.07960i	0.622838	−	0.0466753i
$536$	−7.02006	−	9.51184i	−0.303220	−	0.410849i
$537$	−5.55753	−	23.6191i	−0.239825	−	1.01924i
$538$	−46.2258	+	31.5163i	−1.99294	+	1.35876i
$539$	−8.74358	−	8.74358i	−0.376613	−	0.376613i
$540$	1.64150	+	9.58088i	0.0706390	+	0.412295i
$541$	11.1019	+	17.6685i	0.477307	+	0.759630i	0.995411	−	0.0956873i	$-0.0305049\pi$
$541$	11.1019	+	17.6685i	0.477307	+	0.759630i	−0.518104	+	0.855318i	$0.673362\pi$
$542$	2.65093	+	0.198660i	0.113867	+	0.00853317i
$543$	6.20817	−	28.0645i	0.266418	−	1.20436i
$544$	−3.87795	−	4.17944i	−0.166266	−	0.179192i
$545$	−0.878882	+	5.83100i	−0.0376472	+	0.249773i
$546$	6.77407	+	24.6207i	0.289903	+	1.05367i
$547$	5.62423	+	5.21852i	0.240475	+	0.223128i	0.791198	−	0.611560i	$-0.209458\pi$
$547$	5.62423	+	5.21852i	0.240475	+	0.223128i	−0.550723	+	0.834688i	$0.685648\pi$
$548$	18.4228	+	11.5758i	0.786983	+	0.494494i
$549$	−37.6068	−	15.8117i	−1.60502	−	0.674829i
$550$			6.07309i			0.258958i
$551$	6.49173	−	3.67768i	0.276557	−	0.156674i
$552$	6.75812	+	9.02977i	0.287645	+	0.384333i
$553$	−3.72479	−	8.53731i	−0.158394	−	0.363043i
$554$	−51.2893	−	1.91911i	−2.17907	−	0.0815352i
$555$	4.92568	−	2.18842i	0.209083	−	0.0928933i
$556$	0.472655	+	3.13586i	0.0200450	+	0.132990i
$557$	1.71296	−	2.14799i	0.0725805	−	0.0910131i	−0.744216	−	0.667939i	$-0.767177\pi$
$557$	1.71296	−	2.14799i	0.0725805	−	0.0910131i	0.816796	+	0.576926i	$0.195748\pi$
$558$	−37.5497	+	18.7064i	−1.58960	+	0.791905i
$559$	19.3152	+	6.75866i	0.816944	+	0.285861i
$560$	2.26891	−	30.2765i	0.0958791	−	1.27942i
$561$	−0.293599	−	1.86318i	−0.0123958	−	0.0786636i
$562$	34.0573	+	29.3086i	1.43662	+	1.23631i
$563$	30.8497	+	8.26615i	1.30016	+	0.348377i	0.841510	−	0.540241i	$-0.181667\pi$
$563$	30.8497	+	8.26615i	1.30016	+	0.348377i	0.458649	+	0.888618i	$0.348334\pi$
$564$	−20.1313	−	6.89332i	−0.847680	−	0.290261i
$565$	−10.4205	−	4.54640i	−0.438392	−	0.191269i
$566$	−2.73898	−	24.3091i	−0.115128	−	1.02179i
$567$	−17.8700	+	32.9594i	−0.750468	+	1.38417i
$568$	3.02308	−	3.02308i	0.126846	−	0.126846i
$569$	−2.75302	+	14.5501i	−0.115413	+	0.609970i	0.876328	+	0.481714i	$0.159986\pi$
$569$	−2.75302	+	14.5501i	−0.115413	+	0.609970i	−0.991741	+	0.128256i	$0.959062\pi$
$570$	−4.03077	−	4.98558i	−0.168830	−	0.208823i
$571$	5.51851	+	3.76246i	0.230942	+	0.157454i	0.673263	−	0.739403i	$-0.264892\pi$
$571$	5.51851	+	3.76246i	0.230942	+	0.157454i	−0.442320	+	0.896857i	$0.645845\pi$
$572$	0.550211	+	2.90793i	0.0230055	+	0.121587i
$573$	23.3713	+	4.26022i	0.976349	+	0.177973i
$574$	4.44127	+	11.3162i	0.185375	+	0.472328i
$575$	10.7916	−	8.60602i	0.450041	−	0.358896i
$576$	0.0578172	+	4.31791i	0.00240905	+	0.179913i
$577$	0.0563047	−	0.0896085i	0.00234400	−	0.00373045i	−0.845550	−	0.533896i	$-0.820727\pi$
$577$	0.0563047	−	0.0896085i	0.00234400	−	0.00373045i	0.847894	+	0.530166i	$0.177870\pi$
$578$	−17.3495	+	23.5078i	−0.721645	+	0.977795i
$579$	−19.2401	+	14.3998i	−0.799593	+	0.598437i
$580$	1.20962	−	10.0012i	0.0502267	−	0.415277i
$581$	−25.0180	+	14.4441i	−1.03792	+	0.599243i
$582$	−52.4731	+	30.7656i	−2.17508	+	1.27527i
$583$	2.32911	−	1.23097i	0.0964618	−	0.0509816i
$584$	−3.36123	+	14.7265i	−0.139089	+	0.609387i
$585$	−8.04307	+	3.28161i	−0.332540	+	0.135678i
$586$	−7.38852	−	5.89215i	−0.305217	−	0.243402i
$587$	−10.1262	+	32.8284i	−0.417953	+	1.35497i	0.464917	+	0.885354i	$0.346084\pi$
$587$	−10.1262	+	32.8284i	−0.417953	+	1.35497i	−0.882870	+	0.469617i	$0.844392\pi$
$588$	−15.3222	+	16.7367i	−0.631876	+	0.690211i
$589$	6.03977	−	8.85872i	0.248865	−	0.365017i
$590$	−4.09188	+	7.74222i	−0.168460	+	0.318742i
$591$	19.6145	+	40.0420i	0.806834	+	1.64711i
$592$	10.0223	−	2.68548i	0.411915	−	0.110372i
$593$	−16.3551	−	7.87622i	−0.671625	−	0.323437i	0.0668067	−	0.997766i	$-0.478719\pi$
$593$	−16.3551	−	7.87622i	−0.671625	−	0.323437i	−0.738432	+	0.674328i	$0.764433\pi$
$594$	−6.12953	+	9.39014i	−0.251498	+	0.385282i
$595$	5.58069	−	0.628792i	0.228786	−	0.0257780i
$596$	−5.01216	−	7.35149i	−0.205306	−	0.301129i
$597$	−15.6239	+	19.8631i	−0.639445	+	0.812944i
$598$	11.3228	−	13.1573i	0.463024	−	0.538043i
$599$	−42.0334	−	22.2153i	−1.71744	−	0.907693i	−0.969910	−	0.243465i	$-0.921716\pi$
$599$	−42.0334	−	22.2153i	−1.71744	−	0.907693i	−0.747530	−	0.664229i	$-0.768760\pi$
$600$	−6.46478	+	0.285247i	−0.263924	+	0.0116451i
$601$	6.64656	+	7.72344i	0.271119	+	0.315046i	0.876982	−	0.480523i	$-0.159553\pi$
$601$	6.64656	+	7.72344i	0.271119	+	0.315046i	−0.605863	+	0.795569i	$0.707172\pi$
$602$	17.5019	+	76.6808i	0.713324	+	3.12528i
$603$	−26.6100	+	2.35282i	−1.08364	+	0.0958142i
$604$	4.08532	+	5.12283i	0.166229	+	0.208445i
$605$	−9.62745	+	10.3759i	−0.391412	+	0.421841i
$606$	29.9553	−	2.44661i	1.21685	−	0.0993868i
$607$	17.6481	−	7.69979i	0.716314	−	0.312525i	−0.00994028	−	0.999951i	$-0.503164\pi$
$607$	17.6481	−	7.69979i	0.716314	−	0.312525i	0.726255	+	0.687426i	$0.241259\pi$
$608$	−4.33150	−	7.50239i	−0.175666	−	0.304262i
$609$	27.5156	−	27.4349i	1.11499	−	1.11172i
$610$	18.1650	−	31.4627i	0.735480	−	1.27389i
$611$	2.12911	−	18.8963i	0.0861344	−	0.764464i
$612$	−3.39199	+	0.688964i	−0.137113	+	0.0278497i
$613$	30.1829	+	6.88905i	1.21908	+	0.278246i	0.783205	−	0.621763i	$-0.213583\pi$
$613$	30.1829	+	6.88905i	1.21908	+	0.278246i	0.435871	+	0.900009i	$0.356441\pi$
$614$	49.8526	−	7.51407i	2.01189	−	0.303243i
$615$	−3.64319	+	1.95679i	−0.146907	+	0.0789055i
$616$	4.84179	−	4.49253i	0.195081	−	0.181009i
$617$	−33.4918	+	6.33700i	−1.34833	+	0.255118i	−0.809413	−	0.587240i	$-0.800214\pi$
$617$	−33.4918	+	6.33700i	−1.34833	+	0.255118i	−0.538918	+	0.842358i	$0.681167\pi$
$618$	−31.8123	+	20.2873i	−1.27968	+	0.816075i
$619$	1.08158	+	28.9058i	0.0434724	+	1.16182i	0.834843	+	0.550488i	$0.185558\pi$
$619$	1.08158	+	28.9058i	0.0434724	+	1.16182i	−0.791371	+	0.611336i	$0.790632\pi$
$620$	−4.78133	−	13.6643i	−0.192023	−	0.548770i
$621$	25.3718	−	2.41463i	1.01814	−	0.0968956i
$622$	3.50240	−	7.27282i	0.140434	−	0.291613i
$623$	−23.2758	+	53.3486i	−0.932524	+	2.13737i
$624$	−16.2779	+	3.83015i	−0.651636	+	0.153329i
$625$	−0.224935	−	3.00154i	−0.00899739	−	0.120062i
$626$	12.3011	−	45.9085i	0.491652	−	1.83487i
$627$	0.195035	−	2.85930i	0.00778893	−	0.114189i
$628$	8.83679	−	0.330649i	0.352626	−	0.0131944i
$629$	0.832728	+	1.72918i	0.0332030	+	0.0689468i
$630$	−27.1271	−	19.4651i	−1.08077	−	0.775508i
$631$	−41.4545	+	9.46172i	−1.65028	+	0.376665i	−0.943656	−	0.330928i	$-0.892638\pi$
$631$	−41.4545	+	9.46172i	−1.65028	+	0.376665i	−0.706621	+	0.707592i	$0.749781\pi$
$632$	2.76326	−	1.08450i	0.109917	−	0.0431392i
$633$	−2.10289	+	8.06365i	−0.0835825	+	0.320501i
$634$	−37.4022	+	11.5370i	−1.48543	+	0.458195i
$635$	0.167032	−	4.46402i	0.00662845	−	0.177149i
$636$	−2.44512	−	4.17034i	−0.0969552	−	0.165365i
$637$	−17.5613	−	10.1390i	−0.695805	−	0.401723i
$638$	8.87039	−	7.50843i	0.351182	−	0.297261i
$639$	−2.27566	−	9.38902i	−0.0900236	−	0.371424i
$640$	14.5510	+	1.63951i	0.575181	+	0.0648073i
$641$	6.21164	+	11.7530i	0.245345	+	0.464215i	0.975776	−	0.218771i	$-0.0702047\pi$
$641$	6.21164	+	11.7530i	0.245345	+	0.464215i	−0.730431	+	0.682986i	$0.760681\pi$
$642$	17.9956	−	24.7280i	0.710230	−	0.975935i
$643$	4.63788	+	1.82023i	0.182900	+	0.0717830i	0.455024	−	0.890479i	$-0.349631\pi$
$643$	4.63788	+	1.82023i	0.182900	+	0.0717830i	−0.272124	+	0.962262i	$0.587726\pi$
$644$	25.5648	+	3.85327i	1.00739	+	0.151840i
$645$	−25.1951	+	9.00593i	−0.992058	+	0.354608i
$646$	1.73036	−	1.48909i	0.0680800	−	0.0585876i
$647$	20.1139	−	9.68636i	0.790760	−	0.380810i	0.00550698	−	0.999985i	$-0.498247\pi$
$647$	20.1139	−	9.68636i	0.790760	−	0.380810i	0.785253	+	0.619175i	$0.212533\pi$
$648$	−10.2837	−	6.08381i	−0.403980	−	0.238995i
$649$	−3.69492	+	1.29291i	−0.145038	+	0.0507510i
$650$	2.57768	+	9.62002i	0.101105	+	0.377328i
$651$	18.0885	−	52.8257i	0.708943	−	2.07040i
$652$	−9.61797	+	7.09839i	−0.376669	+	0.277994i
$653$	7.00358	−	5.16888i	0.274071	−	0.202274i	−0.448109	−	0.893979i	$-0.647902\pi$
$653$	7.00358	−	5.16888i	0.274071	−	0.202274i	0.722180	+	0.691705i	$0.243140\pi$
$654$	8.20591	+	9.40732i	0.320876	+	0.367855i
$655$	8.22517	+	30.6967i	0.321384	+	1.19942i
$656$	−7.51416	+	2.62932i	−0.293379	+	0.102658i
$657$	24.4568	+	23.8105i	0.954152	+	0.928938i
$658$	65.8508	−	31.7121i	2.56713	−	1.23627i
$659$	16.1663	−	13.9122i	0.629749	−	0.541943i	−0.278466	−	0.960446i	$-0.589826\pi$
$659$	16.1663	−	13.9122i	0.629749	−	0.541943i	0.908215	+	0.418503i	$0.137445\pi$
$660$	−2.94990	−	2.50442i	−0.114825	−	0.0974844i
$661$	−31.4616	−	4.74208i	−1.22372	−	0.184445i	−0.494774	−	0.869022i	$-0.664749\pi$
$661$	−31.4616	−	4.74208i	−1.22372	−	0.184445i	−0.728941	+	0.684576i	$0.759987\pi$
$662$	32.2878	+	12.6720i	1.25490	+	0.492512i
$663$	−1.25589	−	2.82674i	−0.0487745	−	0.109781i
$664$	−4.30190	−	8.13960i	−0.166946	−	0.315878i
$665$	8.47956	+	0.955417i	0.328823	+	0.0370495i
$666$	3.21694	−	10.9474i	0.124654	−	0.424202i
$667$	−25.9121	−	5.12228i	−1.00332	−	0.198336i
$668$	9.77040	+	5.64095i	0.378028	+	0.218255i
$669$	−10.0990	+	17.7656i	−0.390449	+	0.686857i
$670$	0.889524	−	23.7730i	0.0343653	−	0.918433i
$671$	15.5188	−	4.78693i	0.599098	−	0.184797i
$672$	−32.1142	−	31.6870i	−1.23883	−	1.22235i
$673$	−6.92054	+	2.71611i	−0.266767	+	0.104698i	−0.494955	−	0.868919i	$-0.664815\pi$
$673$	−6.92054	+	2.71611i	−0.266767	+	0.104698i	0.228187	+	0.973617i	$0.426720\pi$
$674$	45.5938	−	10.4065i	1.75621	−	0.400843i
$675$	−7.05555	+	12.8079i	−0.271568	+	0.492976i
$676$	−5.03112	−	10.4472i	−0.193505	−	0.401816i
$677$	2.89976	−	0.108501i	0.111447	−	0.00417004i	0.0183903	−	0.999831i	$-0.494146\pi$
$677$	2.89976	−	0.108501i	0.111447	−	0.00417004i	0.0930564	+	0.995661i	$0.470336\pi$
$678$	−21.6139	+	10.5875i	−0.830077	+	0.406612i
$679$	20.9541	−	78.2019i	0.804146	−	3.00111i
$680$	0.133750	+	1.78478i	0.00512910	+	0.0684430i
$681$	6.23794	−	20.7142i	0.239038	−	0.793771i
$682$	6.67836	−	15.3070i	0.255727	−	0.586134i
$683$	−13.3783	+	27.7803i	−0.511907	+	1.06299i	0.471550	+	0.881840i	$0.343695\pi$
$683$	−13.3783	+	27.7803i	−0.511907	+	1.06299i	−0.983456	+	0.181146i	$0.942019\pi$
$684$	−5.25768	−	0.126264i	−0.201032	−	0.00482784i
$685$	−8.39677	−	23.9966i	−0.320824	−	0.916862i
$686$	−0.943997	−	25.2289i	−0.0360420	−	0.963242i
$687$	−6.65462	−	3.46028i	−0.253890	−	0.132018i
$688$	−50.6092	+	9.57578i	−1.92946	+	0.365073i
$689$	3.16692	−	2.93848i	0.120650	−	0.111947i
$690$	−0.696797	+	22.6860i	−0.0265266	+	0.863639i
$691$	−14.2857	+	2.15323i	−0.543455	+	0.0819126i	−0.415032	−	0.909807i	$-0.636230\pi$
$691$	−14.2857	+	2.15323i	−0.543455	+	0.0819126i	−0.128423	+	0.991720i	$0.540991\pi$
$692$	16.0604	+	3.66568i	0.610524	+	0.139348i
$693$	−2.97088	−	14.6266i	−0.112854	−	0.555619i
$694$	−3.71443	+	32.9665i	−0.140998	+	1.25139i
$695$	1.85277	−	3.20910i	0.0702797	−	0.121728i
$696$	8.40932	+	9.08983i	0.318754	+	0.344549i
$697$	−0.736270	−	1.27526i	−0.0278882	−	0.0483038i
$698$	36.8643	−	16.0837i	1.39534	−	0.608779i
$699$	4.31462	−	9.11499i	0.163194	−	0.344761i
$700$	−10.0892	+	10.8736i	−0.381336	+	0.410982i
$701$	9.54881	+	11.9738i	0.360653	+	0.452245i	0.928744	−	0.370721i	$-0.120889\pi$
$701$	9.54881	+	11.9738i	0.360653	+	0.452245i	−0.568091	+	0.822966i	$0.692318\pi$
$702$	−5.72384	+	17.4760i	−0.216033	+	0.659588i
$703$	0.648913	+	2.84307i	0.0244742	+	0.107229i
$704$	−1.12133	−	1.30301i	−0.0422617	−	0.0491090i
$705$	13.3689	+	20.9636i	0.503501	+	0.789534i
$706$	−9.03764	−	4.77653i	−0.340136	−	0.179767i
$707$	−26.0935	+	30.3212i	−0.981346	+	1.14035i
$708$	2.66915	+	6.66924i	0.100313	+	0.250645i
$709$	12.5668	+	18.4321i	0.471956	+	0.692233i	0.986227	−	0.165395i	$-0.0528899\pi$
$709$	12.5668	+	18.4321i	0.471956	+	0.692233i	−0.514271	+	0.857628i	$0.671938\pi$
$710$	8.54926	−	0.963270i	0.320848	−	0.0361509i
$711$	1.15871	−	6.60700i	0.0434550	−	0.247782i
$712$	−16.7126	−	8.04836i	−0.626331	−	0.301625i
$713$	−36.6635	+	9.82395i	−1.37306	+	0.367910i
$714$	6.63128	−	9.86760i	0.248170	−	0.369286i
$715$	1.61587	−	3.05738i	0.0604301	−	0.114339i
$716$	9.98514	−	14.6455i	0.373162	−	0.547328i
$717$	11.0647	+	35.0364i	0.413219	+	1.30846i
$718$	−0.801870	+	2.59960i	−0.0299255	+	0.0970162i
$719$	−8.40651	−	6.70397i	−0.313510	−	0.250016i	0.454074	−	0.890964i	$-0.349970\pi$
$719$	−8.40651	−	6.70397i	−0.313510	−	0.250016i	−0.767584	+	0.640948i	$0.778541\pi$
$720$	13.4024	−	17.2756i	0.499478	−	0.643823i
$721$	11.1748	−	48.9600i	0.416171	−	1.82337i
$722$	−27.2878	+	14.4220i	−1.01555	+	0.536733i
$723$	22.4820	+	12.7801i	0.836114	+	0.475296i
$724$	18.1843	−	10.4987i	0.675813	−	0.390181i
$725$	10.8030	−	10.6281i	0.401214	−	0.394717i
$726$	3.55419	+	29.7527i	0.131908	+	1.10423i
$727$	19.7439	−	26.7521i	0.732262	−	0.992180i	−0.267330	−	0.963605i	$-0.586141\pi$
$727$	19.7439	−	26.7521i	0.732262	−	0.992180i	0.999592	−	0.0285746i	$-0.00909682\pi$
$728$	5.76277	−	9.17140i	0.213582	−	0.339915i
$729$	−23.8361	+	12.6823i	−0.882819	+	0.469714i
$730$	−23.7653	+	18.9522i	−0.879592	+	0.701451i
$731$	−3.48073	−	8.86876i	−0.128740	−	0.328023i
$732$	−10.0311	−	28.0632i	−0.370761	−	1.03725i
$733$	2.79310	+	14.7619i	0.103165	+	0.545242i	0.995571	+	0.0940087i	$0.0299682\pi$
$733$	2.79310	+	14.7619i	0.103165	+	0.545242i	−0.892406	+	0.451233i	$0.850984\pi$
$734$	−28.3010	−	19.2953i	−1.04461	−	0.712201i
$735$	26.1907	−	4.12712i	0.966059	−	0.152231i
$736$	−5.70164	+	30.1339i	−0.210165	+	1.11075i
$737$	7.51975	−	7.51975i	0.276993	−	0.276993i
$738$	−1.83361	+	8.56034i	−0.0674963	+	0.315110i
$739$	−4.65545	−	41.3182i	−0.171253	−	1.51992i	−0.725883	−	0.687818i	$-0.758569\pi$
$739$	−4.65545	−	41.3182i	−0.171253	−	1.51992i	0.554630	−	0.832097i	$-0.312860\pi$
$740$	3.60894	+	1.57457i	0.132667	+	0.0578822i
$741$	−0.904663	−	4.61202i	−0.0332336	−	0.169427i
$742$	16.0391	+	4.29767i	0.588815	+	0.157773i
$743$	19.6467	+	16.9074i	0.720769	+	0.620272i	0.934226	−	0.356681i	$-0.116092\pi$
$743$	19.6467	+	16.9074i	0.720769	+	0.620272i	−0.213458	+	0.976952i	$0.568473\pi$
$744$	16.6079	+	6.39013i	0.608874	+	0.234274i
$745$	−0.776931	+	10.3674i	−0.0284645	+	0.379833i
$746$	5.37817	+	1.88190i	0.196909	+	0.0689014i
$747$	−20.7647	−	1.27678i	−0.759740	−	0.0467148i
$748$	0.859101	−	1.07728i	0.0314119	−	0.0393892i
$749$	6.06686	+	40.2510i	0.221678	+	1.47074i
$750$	−29.2364	−	21.2766i	−1.06756	−	0.776912i
$751$	36.9327	+	1.38192i	1.34769	+	0.0504271i	0.701458	−	0.712711i	$-0.252533\pi$
$751$	36.9327	+	1.38192i	1.34769	+	0.0504271i	0.646236	+	0.763138i	$0.276342\pi$
$752$	19.1402	+	43.8699i	0.697973	+	1.59977i
$753$	−27.2937	+	3.26044i	−0.994637	+	0.118817i
$754$	10.8642	−	15.6586i	0.395649	−	0.570253i
$755$		−	7.65621i		−	0.278638i
$756$	−26.5744	+	6.62961i	−0.966501	+	0.241117i
$757$	26.7809	+	16.8276i	0.973369	+	0.611608i	0.922049	−	0.387074i	$-0.126514\pi$
$757$	26.7809	+	16.8276i	0.973369	+	0.611608i	0.0513201	+	0.998682i	$0.483657\pi$
$758$	−30.7949	−	28.5735i	−1.11852	−	1.03784i
$759$	−7.12606	+	7.22212i	−0.258660	+	0.262146i
$760$	−0.405317	+	2.68910i	−0.0147024	+	0.0975440i
$761$	33.8806	+	36.5146i	1.22817	+	1.32365i	0.929285	+	0.369365i	$0.120425\pi$
$761$	33.8806	+	36.5146i	1.22817	+	1.32365i	0.298886	+	0.954289i	$0.403385\pi$
$762$	−6.97517	−	6.38565i	−0.252684	−	0.231328i
$763$	−16.5688	−	1.24166i	−0.599831	−	0.0449511i
$764$	9.23320	+	14.6945i	0.334045	+	0.531630i
$765$	3.60067	+	1.84176i	0.130182	+	0.0665890i
$766$	−2.35358	−	2.35358i	−0.0850384	−	0.0850384i
$767$	−5.30413	+	3.61629i	−0.191521	+	0.130577i
$768$	26.2145	−	24.6521i	0.945934	−	0.889557i
$769$	18.9826	+	25.7205i	0.684529	+	0.927504i	0.999769	−	0.0215080i	$-0.00684674\pi$
$769$	18.9826	+	25.7205i	0.684529	+	0.927504i	−0.315239	+	0.949012i	$0.602085\pi$
$770$	13.2543	−	0.993275i	0.477653	−	0.0357952i
$771$	2.48474	−	17.2688i	0.0894856	−	0.621921i
$772$	−17.2499	−	3.26385i	−0.620837	−	0.117469i
$773$	8.77107	−	5.51123i	0.315473	−	0.198225i	−0.364982	−	0.931015i	$-0.618925\pi$
$773$	8.77107	−	5.51123i	0.315473	−	0.198225i	0.680455	+	0.732789i	$0.261782\pi$
$774$	−19.9858	+	52.9988i	−0.718374	+	1.90500i
$775$	7.19264	−	20.5554i	0.258367	−	0.738371i
$776$	24.6553	+	7.60515i	0.885073	+	0.273009i
$777$	7.18611	+	13.3792i	0.257800	+	0.479976i
$778$	14.1768	−	36.1220i	0.508264	−	1.29504i
$779$	−0.659499	−	2.13804i	−0.0236290	−	0.0766034i
$780$	−5.73574	−	2.71504i	−0.205373	−	0.0972139i
$781$	3.09440	+	2.28377i	0.110726	+	0.0817198i
$782$	−8.08178			−0.289004
$783$	27.4303	−	5.52958i	0.980281	−	0.197611i
$784$	51.0404			1.82287
$785$	−8.31371	−	6.13579i	−0.296729	−	0.218996i
$786$	60.8075	+	28.7835i	2.16893	+	1.02667i
$787$	−4.12627	−	13.3770i	−0.147086	−	0.476840i	0.851809	−	0.523853i	$-0.175506\pi$
$787$	−4.12627	−	13.3770i	−0.147086	−	0.476840i	−0.998894	+	0.0470134i	$0.985030\pi$
$788$	−11.9001	+	30.3210i	−0.423923	+	1.08014i
$789$	−15.4315	−	28.7305i	−0.549375	−	1.02283i
$790$	5.70819	+	1.76074i	0.203088	+	0.0626444i
$791$	10.5802	−	30.2364i	0.376187	−	1.07508i
$792$	4.69354	−	0.771842i	0.166778	−	0.0274262i
$793$	22.5507	−	14.1695i	0.800798	−	0.503175i
$794$	−44.6762	−	8.45319i	−1.58550	−	0.299992i
$795$	−0.804485	+	5.59114i	−0.0285322	+	0.198297i
$796$	−18.4098	+	1.37963i	−0.652519	+	0.0488995i
$797$	22.2496	+	30.1472i	0.788122	+	1.06787i	0.995968	+	0.0897062i	$0.0285928\pi$
$797$	22.2496	+	30.1472i	0.788122	+	1.06787i	−0.207846	+	0.978162i	$0.566645\pi$
$798$	13.1596	−	12.3753i	0.465844	−	0.438080i
$799$	−7.31501	+	4.98729i	−0.258786	+	0.176438i
$800$	−12.4421	−	12.4421i	−0.439896	−	0.439896i
$801$	−35.1899	+	22.7741i	−1.24337	+	0.804683i
$802$	−20.8682	−	33.2115i	−0.736880	−	1.17274i
$803$	−13.5501	−	1.01544i	−0.478174	−	0.0358342i
$804$	−14.3941	−	13.1775i	−0.507641	−	0.464736i
$805$	−20.5474	−	22.1448i	−0.724200	−	0.780502i
$806$	4.08186	−	27.0814i	0.143777	−	0.953901i
$807$	37.6649	−	38.1726i	1.32587	−	1.34374i
$808$	−9.34545	−	8.67131i	−0.328772	−	0.305056i
$809$	7.23293	+	4.54475i	0.254296	+	0.159785i	0.653148	−	0.757231i	$-0.273448\pi$
$809$	7.23293	+	4.54475i	0.254296	+	0.159785i	−0.398851	+	0.917016i	$0.630591\pi$
$810$	−8.54622	−	22.4744i	−0.300284	−	0.789671i
$811$		−	13.0907i		−	0.459676i	−0.973229	−	0.229838i	$-0.926180\pi$
$811$		−	13.0907i		−	0.459676i	0.973229	−	0.229838i	$-0.0738196\pi$
$812$	28.3557	+	1.29287i	0.995089	+	0.0453708i
$813$	−2.53009	+	0.302239i	−0.0887343	+	0.0106000i
$814$	1.81643	+	4.16331i	0.0636660	+	0.145924i
$815$	13.9578	+	0.522266i	0.488922	+	0.0182942i
$816$	6.29508	+	4.58120i	0.220372	+	0.160374i
$817$	−2.15758	−	14.3146i	−0.0754843	−	0.500805i
$818$	−4.01503	+	5.03468i	−0.140382	+	0.176034i
$819$	−10.9141	−	21.9081i	−0.381371	−	0.765533i
$820$	−2.85150	−	0.997783i	−0.0995787	−	0.0348441i
$821$	1.04367	−	13.9267i	0.0364242	−	0.486047i	−0.948925	−	0.315500i	$-0.897828\pi$
$821$	1.04367	−	13.9267i	0.0364242	−	0.486047i	0.985350	−	0.170546i	$-0.0545533\pi$
$822$	−50.2299	−	19.3267i	−1.75197	−	0.674097i
$823$	36.4760	+	31.3901i	1.27147	+	1.09419i	0.990934	+	0.134349i	$0.0428945\pi$
$823$	36.4760	+	31.3901i	1.27147	+	1.09419i	0.280540	+	0.959842i	$0.409486\pi$
$824$	15.4591	+	4.14227i	0.538545	+	0.144303i
$825$	−1.12049	−	5.71229i	−0.0390103	−	0.198877i
$826$	−22.6154	−	9.86701i	−0.786891	−	0.343317i
$827$	−5.70009	−	50.5897i	−0.198212	−	1.75918i	−0.561478	−	0.827492i	$-0.689767\pi$
$827$	−5.70009	−	50.5897i	−0.198212	−	1.75918i	0.363266	−	0.931685i	$-0.381662\pi$
$828$	13.8166	+	12.4799i	0.480161	+	0.433706i
$829$	1.63661	−	1.63661i	0.0568417	−	0.0568417i	−0.678115	−	0.734956i	$-0.737203\pi$
$829$	1.63661	−	1.63661i	0.0568417	−	0.0568417i	0.734956	+	0.678115i	$0.237203\pi$
$830$	3.44432	−	18.2037i	0.119554	−	0.631858i
$831$	48.5963	−	7.65778i	1.68579	−	0.265646i
$832$	−2.32928	−	1.58808i	−0.0807533	−	0.0550567i
$833$	1.75520	+	9.27643i	0.0608139	+	0.321409i
$834$	−2.64037	−	7.38674i	−0.0914285	−	0.255782i
$835$	−4.81612	−	12.2713i	−0.166669	−	0.424665i
$836$	1.63687	−	1.30536i	0.0566123	−	0.0451468i
$837$	31.8675	−	24.5230i	1.10150	−	0.847638i
$838$	−16.8021	+	26.7404i	−0.580418	+	0.923730i
$839$	−9.30141	+	12.6030i	−0.321120	+	0.435103i	−0.935188	−	0.354150i	$-0.884770\pi$
$839$	−9.30141	+	12.6030i	−0.321120	+	0.435103i	0.614068	+	0.789253i	$0.289532\pi$
$840$	1.67988	+	14.0625i	0.0579613	+	0.485204i
$841$	−28.8797	−	2.63901i	−0.995851	−	0.0910002i
$842$	−12.9295	+	7.46486i	−0.445581	+	0.257256i
$843$	−37.4414	−	21.2839i	−1.28955	−	0.733055i
$844$	−5.38223	+	2.84459i	−0.185264	+	0.0979148i
$845$	−3.01494	+	13.2093i	−0.103717	+	0.454415i
$846$	52.1475	+	7.14728i	1.79287	+	0.245729i
$847$	−31.1811	−	24.8661i	−1.07140	−	0.854409i
$848$	−3.20518	+	10.3909i	−0.110066	+	0.356826i
$849$	7.06128	+	22.3596i	0.242343	+	0.767378i
$850$	2.61204	−	3.83116i	0.0895922	−	0.131408i
$851$	4.82399	−	9.12744i	0.165364	−	0.312885i
$852$	3.93649	−	5.85765i	0.134862	−	0.200680i
$853$	−45.9729	+	12.3184i	−1.57408	+	0.421774i	−0.937087	−	0.349095i	$-0.886489\pi$
$853$	−45.9729	+	12.3184i	−1.57408	+	0.421774i	−0.636994	+	0.770869i	$0.719822\pi$
$854$	92.2277	+	44.4145i	3.15597	+	1.51983i
$855$	4.71114	+	3.94572i	0.161118	+	0.134941i
$856$	−12.8910	+	1.45247i	−0.440606	+	0.0496444i
$857$	4.15389	+	6.09263i	0.141894	+	0.208120i	0.890607	−	0.454774i	$-0.150280\pi$
$857$	4.15389	+	6.09263i	0.141894	+	0.208120i	−0.748713	+	0.662895i	$0.769328\pi$
$858$	−2.72010	−	6.79656i	−0.0928627	−	0.232031i
$859$	13.3647	−	15.5301i	0.455999	−	0.529881i	−0.482161	−	0.876083i	$-0.660148\pi$
$859$	13.3647	−	15.5301i	0.455999	−	0.529881i	0.938160	+	0.346202i	$0.112529\pi$
$860$	−17.2810	−	9.13329i	−0.589278	−	0.311442i
$861$	−6.26525	−	9.82447i	−0.213519	−	0.334817i
$862$	10.8220	+	12.5754i	0.368598	+	0.428318i
$863$	0.634317	+	2.77912i	0.0215924	+	0.0946025i	0.984576	−	0.174958i	$-0.0559789\pi$
$863$	0.634317	+	2.77912i	0.0215924	+	0.0946025i	−0.962984	+	0.269560i	$0.913122\pi$
$864$	−6.68012	−	31.7957i	−0.227262	−	1.08171i
$865$	−12.0013	−	15.0492i	−0.408058	−	0.511688i
$866$	−49.9181	+	53.7989i	−1.69629	+	1.82816i
$867$	11.9816	−	25.3122i	0.406917	−	0.859647i
$868$	37.3866	−	16.3116i	1.26898	−	0.553652i
$869$	1.33516	+	2.31257i	0.0452923	+	0.0784486i
$870$	1.82571	+	24.8522i	0.0618975	+	0.842567i
$871$	8.71988	−	15.1033i	0.295462	−	0.511755i
$872$	0.592871	−	5.26188i	0.0200771	−	0.178190i
$873$	43.6795	−	38.6191i	1.47833	−	1.30706i
$874$	−11.9720	−	2.73252i	−0.404958	−	0.0924290i
$875$	47.5896	−	7.17298i	1.60882	−	0.242491i
$876$	−0.765519	+	24.9234i	−0.0258645	+	0.842082i
$877$	−7.21525	+	6.69477i	−0.243642	+	0.226066i	−0.792536	−	0.609825i	$-0.791240\pi$
$877$	−7.21525	+	6.69477i	−0.243642	+	0.226066i	0.548894	+	0.835892i	$0.315049\pi$
$878$	13.0504	−	2.46927i	0.440430	−	0.0833339i
$879$	8.03667	+	4.17892i	0.271070	+	0.140951i
$880$	0.325460	+	8.69809i	0.0109712	+	0.293213i
$881$	−3.06148	−	8.74922i	−0.103144	−	0.294769i	0.880734	−	0.473612i	$-0.157050\pi$
$881$	−3.06148	−	8.74922i	−0.103144	−	0.294769i	−0.983878	+	0.178843i	$0.942764\pi$
$882$	29.2232	−	47.9210i	0.983997	−	1.61358i
$883$	−11.1562	+	23.1661i	−0.375436	+	0.779600i	−0.999999	−	0.00137403i	$-0.999563\pi$
$883$	−11.1562	+	23.1661i	−0.375436	+	0.779600i	0.624563	+	0.780974i	$0.285277\pi$
$884$	0.903608	−	2.07109i	0.0303916	−	0.0696583i
$885$	2.42035	−	8.03721i	0.0813590	−	0.270168i
$886$	2.29872	+	30.6742i	0.0772269	+	1.03052i
$887$	−1.77098	+	6.60938i	−0.0594636	+	0.221921i	−0.989263	−	0.146145i	$-0.953313\pi$
$887$	−1.77098	+	6.60938i	−0.0594636	+	0.221921i	0.929800	+	0.368066i	$0.119980\pi$
$888$	−4.34651	+	2.12913i	−0.145859	+	0.0714490i
$889$	12.5780	−	0.470636i	0.421853	−	0.0157846i
$890$	−16.1961	−	33.6315i	−0.542894	−	1.12733i
$891$	4.03290	−	9.96317i	0.135107	−	0.333779i
$892$	−14.5542	+	3.32191i	−0.487311	+	0.111226i
$893$	−12.5224	+	4.91466i	−0.419045	+	0.164463i
$894$	15.6665	+	15.4581i	0.523965	+	0.516996i
$895$	−19.7916	+	6.10489i	−0.661559	+	0.204064i
$896$	−1.54273	+	41.2303i	−0.0515389	+	1.37741i
$897$	−8.22259	+	14.4647i	−0.274544	+	0.482963i
$898$	−49.3088	−	28.4685i	−1.64546	−	0.950005i
$899$	−38.9158	+	14.9079i	−1.29792	+	0.497206i
$900$	−10.3816	+	2.51624i	−0.346054	+	0.0838745i
$901$	−1.99874	−	0.225204i	−0.0665876	−	0.00750262i
$902$	−1.62847	−	3.08122i	−0.0542222	−	0.102593i
$903$	−30.6097	−	68.8961i	−1.01863	−	2.29272i
$904$	9.50330	+	3.72977i	0.316075	+	0.124050i
$905$	−24.2608	−	3.65672i	−0.806456	−	0.121554i
$906$	−12.3556	−	10.4897i	−0.410486	−	0.348496i
$907$	25.5402	−	21.9792i	0.848050	−	0.729806i	−0.116646	−	0.993174i	$-0.537214\pi$
$907$	25.5402	−	21.9792i	0.848050	−	0.729806i	0.964696	+	0.263368i	$0.0848332\pi$
$908$	14.2384	−	6.85687i	0.472519	−	0.227553i
$909$	−27.7243	+	7.82802i	−0.919557	+	0.259639i
$910$	20.5738	−	7.19909i	0.682015	−	0.238647i
$911$	−13.1500	−	49.0766i	−0.435680	−	1.62598i	−0.739433	−	0.673230i	$-0.764906\pi$
$911$	−13.1500	−	49.0766i	−0.435680	−	1.62598i	0.303752	−	0.952751i	$-0.401760\pi$
$912$	7.77628	+	8.91479i	0.257498	+	0.295198i
$913$	6.66355	−	4.91792i	0.220531	−	0.162759i
$914$	−21.5764	+	15.9241i	−0.713684	+	0.526723i
$915$	−11.2810	+	32.9450i	−0.372937	+	1.08913i
$916$	−1.41814	−	5.29258i	−0.0468568	−	0.174872i
$917$	−84.5187	+	29.5744i	−2.79105	+	0.976632i
$918$	7.90546	−	3.28737i	0.260919	−	0.108500i
$919$	−23.4464	+	11.2912i	−0.773426	+	0.372462i	−0.778597	−	0.627524i	$-0.784068\pi$
$919$	−23.4464	+	11.2912i	−0.773426	+	0.372462i	0.00517083	+	0.999987i	$0.498354\pi$
$920$	7.29731	−	6.27984i	0.240585	−	0.207040i
$921$	−45.5045	+	16.2655i	−1.49943	+	0.535966i
$922$	−21.4279	−	3.22974i	−0.705691	−	0.106366i
$923$	5.87098	+	2.30419i	0.193246	+	0.0758433i
$924$	6.41569	−	8.81588i	0.211061	−	0.290021i
$925$	2.76773	+	5.23680i	0.0910024	+	0.172185i
$926$	−14.8450	−	1.67263i	−0.487838	−	0.0549661i
$927$	26.1793	−	24.9514i	0.859842	−	0.819512i
$928$	−2.79030	+	33.5558i	−0.0915960	+	1.10152i
$929$	33.6789	+	19.4445i	1.10497	+	0.637954i	0.937522	−	0.347927i	$-0.113114\pi$
$929$	33.6789	+	19.4445i	1.10497	+	0.637954i	0.167447	+	0.985881i	$0.446448\pi$
$930$	18.1119	+	30.8912i	0.593911	+	1.01296i
$931$	−0.536382	+	14.3351i	−0.0175792	+	0.469814i
$932$	7.03973	−	2.17147i	0.230594	−	0.0711288i
$933$	−1.95249	+	7.48694i	−0.0639217	+	0.245111i
$934$	38.9651	−	15.2927i	1.27498	−	0.500392i
$935$	−1.56966	+	0.358264i	−0.0513333	+	0.0117165i
$936$	7.10715	−	3.21476i	0.232304	−	0.105078i
$937$	24.5085	+	50.8924i	0.800657	+	1.66258i	0.747748	+	0.663983i	$0.231135\pi$
$937$	24.5085	+	50.8924i	0.800657	+	1.66258i	0.0529094	+	0.998599i	$0.483151\pi$
$938$	66.9840	−	2.50636i	2.18710	−	0.0818356i
$939$	−3.10022	+	45.4507i	−0.101172	+	1.48323i
$940$	−4.70104	+	17.5445i	−0.153331	+	0.572239i
$941$	0.482708	+	6.44129i	0.0157358	+	0.209980i	0.999529	+	0.0306754i	$0.00976580\pi$
$941$	0.482708	+	6.44129i	0.0157358	+	0.209980i	−0.983794	+	0.179305i	$0.942615\pi$
$942$	−21.2924	+	5.01006i	−0.693745	+	0.163237i
$943$	−3.16752	+	7.26004i	−0.103149	+	0.236419i
$944$	7.01083	−	14.5581i	0.228183	−	0.473827i
$945$	29.1068	+	13.3037i	0.946844	+	0.432771i
$946$	−7.44733	−	21.2832i	−0.242133	−	0.691978i
$947$	−0.406524	−	10.8646i	−0.0132103	−	0.353051i	−0.990191	−	0.139723i	$-0.955379\pi$
$947$	−0.406524	−	10.8646i	−0.0132103	−	0.353051i	0.976980	−	0.213329i	$-0.0684306\pi$
$948$	4.13159	−	2.63480i	0.134188	−	0.0855742i
$949$	−21.8949	+	4.14274i	−0.710740	+	0.134479i
$950$	5.16470	−	4.79214i	0.167565	−	0.155478i
$951$	33.0516	−	17.7523i	1.07177	−	0.575659i
$952$	−4.98664	+	0.751615i	−0.161618	+	0.0243600i
$953$	−22.7690	−	5.19687i	−0.737559	−	0.168343i	−0.162793	−	0.986660i	$-0.552050\pi$
$953$	−22.7690	−	5.19687i	−0.737559	−	0.168343i	−0.574767	+	0.818317i	$0.694907\pi$
$954$	7.92075	+	8.95862i	0.256444	+	0.290046i
$955$	2.27045	−	20.1508i	0.0734700	−	0.652064i
$956$	−13.4204	+	23.2449i	−0.434048	+	0.751794i
$957$	−6.95810	+	8.69894i	−0.224923	+	0.281197i
$958$	−8.50888	−	14.7378i	−0.274909	−	0.476157i
$959$	65.6567	−	28.6457i	2.12017	−	0.925019i
$960$	3.67383	−	0.300062i	0.118572	−	0.00968445i
$961$	−19.6473	+	21.1748i	−0.633785	+	0.683058i
$962$	4.64439	+	5.82388i	0.149741	+	0.187769i
$963$	−12.3642	+	26.5791i	−0.398430	+	0.856499i
$964$	4.20381	+	18.4181i	0.135396	+	0.593207i
$965$	13.3807	+	15.5487i	0.430742	+	0.500531i
$966$	−63.8889	+	2.81898i	−2.05559	+	0.0906992i
$967$	16.0634	+	8.48975i	0.516564	+	0.273012i	0.705167	−	0.709041i	$-0.250872\pi$
$967$	16.0634	+	8.48975i	0.516564	+	0.273012i	−0.188603	+	0.982053i	$0.560396\pi$
$968$	8.29068	−	9.63394i	0.266472	−	0.309647i
$969$	−1.35282	+	1.71988i	−0.0434589	+	0.0552504i
$970$	29.2485	+	42.8997i	0.939114	+	1.37743i
$971$	−30.9999	+	3.49285i	−0.994833	+	0.112091i	−0.594344	−	0.804211i	$-0.702588\pi$
$971$	−30.9999	+	3.49285i	−0.994833	+	0.112091i	−0.400489	+	0.916302i	$0.631160\pi$
$972$	−18.5915	−	6.58751i	−0.596324	−	0.211295i
$973$	9.40693	+	4.53014i	0.301572	+	0.145230i
$974$	7.74260	−	2.07462i	0.248089	−	0.0664753i
$975$	−4.19943	−	8.57292i	−0.134489	−	0.274553i
$976$	−31.3236	+	59.2672i	−1.00264	+	1.89710i
$977$	−27.8609	+	40.8645i	−0.891350	+	1.30737i	0.0596634	+	0.998219i	$0.480997\pi$
$977$	−27.8609	+	40.8645i	−0.891350	+	1.30737i	−0.951013	+	0.309151i	$0.899955\pi$
$978$	19.9663	−	21.8096i	0.638452	−	0.697393i
$979$	4.91845	−	15.9452i	0.157194	−	0.509611i
$980$	15.1433	+	12.0764i	0.483735	+	0.385766i
$981$	−9.45405	−	7.33445i	−0.301845	−	0.234171i
$982$	−9.85754	+	43.1887i	−0.314567	+	1.37821i
$983$	13.1812	−	6.96647i	0.420415	−	0.222196i	−0.243662	−	0.969860i	$-0.578349\pi$
$983$	13.1812	−	6.96647i	0.420415	−	0.222196i	0.664077	+	0.747664i	$0.268825\pi$
$984$	3.20346	−	1.87822i	0.102123	−	0.0598756i
$985$	32.9610	−	19.0300i	1.05022	−	0.606347i
$986$	−8.82518	+	0.921468i	−0.281051	+	0.0293455i
$987$	−56.0878	+	41.9776i	−1.78529	+	1.33616i
$988$	2.03882	−	2.76250i	0.0648634	−	0.0878867i
$989$	−27.2659	+	43.3935i	−0.867006	+	1.37983i
$990$	8.35284	+	4.67453i	0.265471	+	0.148566i
$991$	−25.7999	+	20.5748i	−0.819562	+	0.653579i	−0.940769	−	0.339049i	$-0.889895\pi$
$991$	−25.7999	+	20.5748i	−0.819562	+	0.653579i	0.121207	+	0.992627i	$0.461323\pi$
$992$	17.6777	+	45.0420i	0.561267	+	1.43009i
$993$	−32.7076	−	5.96209i	−1.03794	−	0.189201i
$994$	4.50672	+	23.8186i	0.142944	+	0.755480i
$995$	17.8233	+	12.1517i	0.565037	+	0.385236i
$996$	−9.55496	−	11.8184i	−0.302760	−	0.374479i
$997$	5.42624	−	28.6784i	0.171851	−	0.908253i	−0.785399	−	0.618990i	$-0.787542\pi$
$997$	5.42624	−	28.6784i	0.171851	−	0.908253i	0.957250	−	0.289263i	$-0.0934101\pi$
$998$	4.18022	−	4.18022i	0.132323	−	0.132323i
$999$	−1.00604	+	10.8905i	−0.0318296	+	0.344561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.2.6	✓	672
3.2	odd	2		783.2.be.a.89.23		672
9.4	even	3		783.2.be.a.611.23		672
9.5	odd	6	inner	261.2.x.a.176.6	yes	672
29.15	odd	28	inner	261.2.x.a.218.6	yes	672
87.44	even	28		783.2.be.a.305.23		672
261.131	even	84	inner	261.2.x.a.131.6	yes	672
261.247	odd	84		783.2.be.a.44.23		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.2.6	✓	672	1.1	even	1	trivial
261.2.x.a.131.6	yes	672	261.131	even	84	inner
261.2.x.a.176.6	yes	672	9.5	odd	6	inner
261.2.x.a.218.6	yes	672	29.15	odd	28	inner
783.2.be.a.44.23		672	261.247	odd	84
783.2.be.a.89.23		672	3.2	odd	2
783.2.be.a.305.23		672	87.44	even	28
783.2.be.a.611.23		672	9.4	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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.45392 - 1.07304i) q^{2} +(1.56552 + 0.741045i) q^{3} +(0.372954 + 1.20909i) q^{4} +(0.540145 - 1.37627i) q^{5} +(-1.48097 - 2.75729i) q^{6} +(3.98072 + 1.22789i) q^{7} +(-0.438482 + 1.25311i) q^{8} +(1.90171 + 2.32024i) q^{9} +O(q^{10})\)	\(q+(-1.45392 - 1.07304i) q^{2} +(1.56552 + 0.741045i) q^{3} +(0.372954 + 1.20909i) q^{4} +(0.540145 - 1.37627i) q^{5} +(-1.48097 - 2.75729i) q^{6} +(3.98072 + 1.22789i) q^{7} +(-0.438482 + 1.25311i) q^{8} +(1.90171 + 2.32024i) q^{9} +(-2.26212 + 1.42138i) q^{10} +(-1.17345 - 0.222029i) q^{11} +(-0.312121 + 2.16923i) q^{12} +(-1.95303 + 0.146359i) q^{13} +(-4.47007 - 6.05673i) q^{14} +(1.86548 - 1.75430i) q^{15} +(4.07304 - 2.77695i) q^{16} +(0.644767 + 0.644767i) q^{17} +(-0.275212 - 5.41405i) q^{18} +(0.737125 + 1.17313i) q^{19} +(1.86548 + 0.139798i) q^{20} +(5.32197 + 4.87218i) q^{21} +(1.46786 + 1.58197i) q^{22} +(0.731034 - 4.85009i) q^{23} +(-1.61506 + 1.63683i) q^{24} +(2.06291 + 1.91410i) q^{25} +(2.99660 + 1.88289i) q^{26} +(1.25776 + 5.04163i) q^{27} +5.27099i q^{28} +(0.245280 - 5.37958i) q^{29} +(-4.59470 + 0.548873i) q^{30} +(-3.09460 - 7.09290i) q^{31} +(-6.24829 - 0.233795i) q^{32} +(-1.67253 - 1.21717i) q^{33} +(-0.245578 - 1.62930i) q^{34} +(3.84007 - 4.81529i) q^{35} +(-2.09613 + 3.16467i) q^{36} +(1.98669 + 0.695173i) q^{37} +(0.187094 - 2.49660i) q^{38} +(-3.16597 - 1.21815i) q^{39} +(1.48777 + 1.28033i) q^{40} +(-1.55989 - 0.417970i) q^{41} +(-2.50968 - 12.7945i) q^{42} +(-9.57671 - 4.17828i) q^{43} +(-0.169191 - 1.50161i) q^{44} +(4.22046 - 1.36399i) q^{45} +(-6.26721 + 6.26721i) q^{46} +(-1.80509 + 9.54012i) q^{47} +(8.43427 - 1.32907i) q^{48} +(8.55474 + 5.83252i) q^{49} +(-0.945395 - 4.99653i) q^{50} +(0.531594 + 1.48720i) q^{51} +(-0.905353 - 2.30680i) q^{52} +(-1.72461 + 1.37533i) q^{53} +(3.58121 - 8.67975i) q^{54} +(-0.939404 + 1.49505i) q^{55} +(-3.28415 + 4.44987i) q^{56} +(0.284644 + 2.38280i) q^{57} +(-6.12913 + 7.55828i) q^{58} +(2.83866 - 1.63890i) q^{59} +(2.81684 + 1.60126i) q^{60} +(-12.0227 + 6.35417i) q^{61} +(-3.11168 + 13.6331i) q^{62} +(4.72116 + 11.5713i) q^{63} +(1.12539 + 0.897471i) q^{64} +(-0.853490 + 2.76695i) q^{65} +(1.12565 + 3.56436i) q^{66} +(-5.01615 + 7.35734i) q^{67} +(-0.539111 + 1.02005i) q^{68} +(4.73858 - 7.05118i) q^{69} +(-10.7502 + 2.88050i) q^{70} +(-2.90138 - 1.39723i) q^{71} +(-3.74138 + 1.36566i) q^{72} +(11.3062 - 1.27390i) q^{73} +(-2.14254 - 3.14253i) q^{74} +(1.81109 + 4.52527i) q^{75} +(-1.14350 + 1.32877i) q^{76} +(-4.39855 - 2.32470i) q^{77} +(3.29593 + 5.16832i) q^{78} +(-1.45848 - 1.69478i) q^{79} +(-1.62179 - 7.10554i) q^{80} +(-1.76703 + 8.82483i) q^{81} +(1.81945 + 2.28152i) q^{82} +(-4.71675 + 5.08345i) q^{83} +(-3.90604 + 8.25184i) q^{84} +(1.23564 - 0.539103i) q^{85} +(9.44031 + 16.3511i) q^{86} +(4.37050 - 8.24007i) q^{87} +(0.792763 - 1.37311i) q^{88} +(-1.56439 + 13.8843i) q^{89} +(-7.59983 - 2.54561i) q^{90} +(-7.95418 - 1.81549i) q^{91} +(6.13683 - 0.924978i) q^{92} +(0.411497 - 13.3973i) q^{93} +(12.8614 - 11.9336i) q^{94} +(2.01269 - 0.380822i) q^{95} +(-9.60858 - 4.99628i) q^{96} +(-0.726683 - 19.4210i) q^{97} +(-6.17937 - 17.6596i) q^{98} +(-1.71640 - 3.14492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

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