LMFDB - Embedded newform 195.2.k.a.112.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(112,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("195.112");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			112.13
Character	$\chi$	$=$	195.112
Dual form			195.2.k.a.148.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.21780i q^{2} +(0.707107 - 0.707107i) q^{3} -2.91862 q^{4} +(1.59963 - 1.56243i) q^{5} +(1.56822 + 1.56822i) q^{6} +4.11325 q^{7} -2.03732i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+2.21780i q^{2} +(0.707107 - 0.707107i) q^{3} -2.91862 q^{4} +(1.59963 - 1.56243i) q^{5} +(1.56822 + 1.56822i) q^{6} +4.11325 q^{7} -2.03732i q^{8} -1.00000i q^{9} +(3.46515 + 3.54765i) q^{10} +(-2.59303 + 2.59303i) q^{11} +(-2.06378 + 2.06378i) q^{12} +(-3.29198 - 1.47066i) q^{13} +9.12235i q^{14} +(0.0263025 - 2.23591i) q^{15} -1.31889 q^{16} +(-1.98080 + 1.98080i) q^{17} +2.21780 q^{18} +(2.76089 - 2.76089i) q^{19} +(-4.66871 + 4.56015i) q^{20} +(2.90851 - 2.90851i) q^{21} +(-5.75081 - 5.75081i) q^{22} +(-1.53954 - 1.53954i) q^{23} +(-1.44060 - 1.44060i) q^{24} +(0.117620 - 4.99862i) q^{25} +(3.26162 - 7.30095i) q^{26} +(-0.707107 - 0.707107i) q^{27} -12.0050 q^{28} +8.40712i q^{29} +(4.95880 + 0.0583336i) q^{30} +(2.11332 + 2.11332i) q^{31} -6.99966i q^{32} +3.66710i q^{33} +(-4.39301 - 4.39301i) q^{34} +(6.57967 - 6.42667i) q^{35} +2.91862i q^{36} -7.83564 q^{37} +(6.12310 + 6.12310i) q^{38} +(-3.36770 + 1.28787i) q^{39} +(-3.18317 - 3.25895i) q^{40} +(1.65250 + 1.65250i) q^{41} +(6.45048 + 6.45048i) q^{42} +(-1.27192 - 1.27192i) q^{43} +(7.56807 - 7.56807i) q^{44} +(-1.56243 - 1.59963i) q^{45} +(3.41439 - 3.41439i) q^{46} -6.35092 q^{47} +(-0.932593 + 0.932593i) q^{48} +9.91882 q^{49} +(11.0859 + 0.260858i) q^{50} +2.80127i q^{51} +(9.60806 + 4.29230i) q^{52} +(5.31987 - 5.31987i) q^{53} +(1.56822 - 1.56822i) q^{54} +(-0.0964538 + 8.19931i) q^{55} -8.38000i q^{56} -3.90449i q^{57} -18.6453 q^{58} +(-6.51015 - 6.51015i) q^{59} +(-0.0767671 + 6.52579i) q^{60} +7.84876 q^{61} +(-4.68691 + 4.68691i) q^{62} -4.11325i q^{63} +12.8861 q^{64} +(-7.56375 + 2.79099i) q^{65} -8.13287 q^{66} -12.3496i q^{67} +(5.78120 - 5.78120i) q^{68} -2.17724 q^{69} +(14.2530 + 14.5924i) q^{70} +(-7.75627 - 7.75627i) q^{71} -2.03732 q^{72} -5.27944i q^{73} -17.3779i q^{74} +(-3.45139 - 3.61773i) q^{75} +(-8.05801 + 8.05801i) q^{76} +(-10.6658 + 10.6658i) q^{77} +(-2.85624 - 7.46887i) q^{78} +8.45538i q^{79} +(-2.10973 + 2.06067i) q^{80} -1.00000 q^{81} +(-3.66491 + 3.66491i) q^{82} +4.49388 q^{83} +(-8.48883 + 8.48883i) q^{84} +(-0.0736805 + 6.26340i) q^{85} +(2.82085 - 2.82085i) q^{86} +(5.94473 + 5.94473i) q^{87} +(5.28283 + 5.28283i) q^{88} +(8.91884 + 8.91884i) q^{89} +(3.54765 - 3.46515i) q^{90} +(-13.5408 - 6.04919i) q^{91} +(4.49334 + 4.49334i) q^{92} +2.98868 q^{93} -14.0850i q^{94} +(0.102698 - 8.73011i) q^{95} +(-4.94951 - 4.94951i) q^{96} +17.6029i q^{97} +21.9979i q^{98} +(2.59303 + 2.59303i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{4} + 8 q^{5}+O(q^{10}) $ 28 * q - 28 * q^4 + 8 * q^5	$ 28 q - 28 q^{4} + 8 q^{5} - 8 q^{11} + 8 q^{12} - 12 q^{13} + 4 q^{15} + 28 q^{16} - 28 q^{17} - 4 q^{18} + 8 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{25} - 16 q^{31} + 28 q^{34} + 32 q^{37} + 8 q^{39} - 48 q^{40} + 4 q^{41} + 40 q^{44} - 4 q^{45} - 16 q^{46} - 24 q^{47} - 16 q^{48} - 28 q^{49} - 32 q^{50} + 52 q^{52} + 20 q^{53} - 8 q^{55} - 8 q^{58} + 32 q^{59} - 12 q^{60} + 8 q^{61} + 72 q^{62} - 28 q^{64} - 8 q^{65} + 16 q^{66} + 60 q^{68} + 8 q^{69} + 64 q^{70} + 40 q^{71} + 12 q^{72} - 16 q^{75} - 40 q^{76} - 48 q^{77} + 8 q^{78} - 32 q^{80} - 28 q^{81} + 4 q^{82} - 104 q^{83} - 32 q^{84} - 4 q^{85} + 16 q^{86} - 24 q^{87} + 72 q^{88} - 36 q^{89} - 12 q^{90} - 56 q^{91} - 32 q^{92} + 56 q^{95} + 8 q^{99}+O(q^{100}) $ 28 * q - 28 * q^4 + 8 * q^5 - 8 * q^11 + 8 * q^12 - 12 * q^13 + 4 * q^15 + 28 * q^16 - 28 * q^17 - 4 * q^18 + 8 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^25 - 16 * q^31 + 28 * q^34 + 32 * q^37 + 8 * q^39 - 48 * q^40 + 4 * q^41 + 40 * q^44 - 4 * q^45 - 16 * q^46 - 24 * q^47 - 16 * q^48 - 28 * q^49 - 32 * q^50 + 52 * q^52 + 20 * q^53 - 8 * q^55 - 8 * q^58 + 32 * q^59 - 12 * q^60 + 8 * q^61 + 72 * q^62 - 28 * q^64 - 8 * q^65 + 16 * q^66 + 60 * q^68 + 8 * q^69 + 64 * q^70 + 40 * q^71 + 12 * q^72 - 16 * q^75 - 40 * q^76 - 48 * q^77 + 8 * q^78 - 32 * q^80 - 28 * q^81 + 4 * q^82 - 104 * q^83 - 32 * q^84 - 4 * q^85 + 16 * q^86 - 24 * q^87 + 72 * q^88 - 36 * q^89 - 12 * q^90 - 56 * q^91 - 32 * q^92 + 56 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			2.21780i			1.56822i	0.620622	+	0.784110i	$0.286880\pi$
$2$			2.21780i			1.56822i	−0.620622	+	0.784110i	$0.713120\pi$
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−2.91862			−1.45931
$5$	1.59963	−	1.56243i	0.715375	−	0.698740i
$5$	1.59963	−	1.56243i	0.715375	−	0.698740i
$6$	1.56822	+	1.56822i	0.640223	+	0.640223i
$7$	4.11325			1.55466			0.777331	−	0.629092i	$-0.216573\pi$
$7$	4.11325			1.55466			0.777331	+	0.629092i	$0.216573\pi$
$8$		−	2.03732i		−	0.720301i
$9$		−	1.00000i		−	0.333333i
$10$	3.46515	+	3.54765i	1.09578	+	1.12187i
$11$	−2.59303	+	2.59303i	−0.781827	+	0.781827i	−0.980139	−	0.198312i	$-0.936454\pi$
$11$	−2.59303	+	2.59303i	−0.781827	+	0.781827i	0.198312	+	0.980139i	$0.436454\pi$
$12$	−2.06378	+	2.06378i	−0.595761	+	0.595761i
$13$	−3.29198	−	1.47066i	−0.913032	−	0.407887i
$13$	−3.29198	−	1.47066i	−0.913032	−	0.407887i
$14$			9.12235i			2.43805i
$15$	0.0263025	−	2.23591i	0.00679128	−	0.577310i
$16$	−1.31889			−0.329721
$17$	−1.98080	+	1.98080i	−0.480414	+	0.480414i	−0.905264	−	0.424850i	$-0.860327\pi$
$17$	−1.98080	+	1.98080i	−0.480414	+	0.480414i	0.424850	+	0.905264i	$0.360327\pi$
$18$	2.21780			0.522740
$19$	2.76089	−	2.76089i	0.633393	−	0.633393i	−0.315525	−	0.948917i	$-0.602181\pi$
$19$	2.76089	−	2.76089i	0.633393	−	0.633393i	0.948917	+	0.315525i	$0.102181\pi$
$20$	−4.66871	+	4.56015i	−1.04396	+	1.01968i
$21$	2.90851	−	2.90851i	0.634688	−	0.634688i
$22$	−5.75081	−	5.75081i	−1.22608	−	1.22608i
$23$	−1.53954	−	1.53954i	−0.321017	−	0.321017i	0.528140	−	0.849157i	$-0.322890\pi$
$23$	−1.53954	−	1.53954i	−0.321017	−	0.321017i	−0.849157	+	0.528140i	$0.822890\pi$
$24$	−1.44060	−	1.44060i	−0.294062	−	0.294062i
$25$	0.117620	−	4.99862i	0.0235241	−	0.999723i
$26$	3.26162	−	7.30095i	0.639657	−	1.43183i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−12.0050			−2.26874
$29$			8.40712i			1.56116i	0.625054	+	0.780582i	$0.285077\pi$
$29$			8.40712i			1.56116i	−0.625054	+	0.780582i	$0.714923\pi$
$30$	4.95880	+	0.0583336i	0.905349	+	0.0106502i
$31$	2.11332	+	2.11332i	0.379563	+	0.379563i	0.870944	−	0.491381i	$-0.163508\pi$
$31$	2.11332	+	2.11332i	0.379563	+	0.379563i	−0.491381	+	0.870944i	$0.663508\pi$
$32$		−	6.99966i		−	1.23738i
$33$			3.66710i			0.638359i
$34$	−4.39301	−	4.39301i	−0.753395	−	0.753395i
$35$	6.57967	−	6.42667i	1.11217	−	1.08631i
$36$			2.91862i			0.486437i
$37$	−7.83564			−1.28817			−0.644086	−	0.764953i	$-0.722762\pi$
$37$	−7.83564			−1.28817			−0.644086	+	0.764953i	$0.722762\pi$
$38$	6.12310	+	6.12310i	0.993299	+	0.993299i
$39$	−3.36770	+	1.28787i	−0.539263	+	0.206225i
$40$	−3.18317	−	3.25895i	−0.503304	−	0.515286i
$41$	1.65250	+	1.65250i	0.258077	+	0.258077i	0.824272	−	0.566195i	$-0.191585\pi$
$41$	1.65250	+	1.65250i	0.258077	+	0.258077i	−0.566195	+	0.824272i	$0.691585\pi$
$42$	6.45048	+	6.45048i	0.995330	+	0.995330i
$43$	−1.27192	−	1.27192i	−0.193965	−	0.193965i	0.603442	−	0.797407i	$-0.293796\pi$
$43$	−1.27192	−	1.27192i	−0.193965	−	0.193965i	−0.797407	+	0.603442i	$0.793796\pi$
$44$	7.56807	−	7.56807i	1.14093	−	1.14093i
$45$	−1.56243	−	1.59963i	−0.232913	−	0.238458i
$46$	3.41439	−	3.41439i	0.503425	−	0.503425i
$47$	−6.35092			−0.926376			−0.463188	−	0.886260i	$-0.653295\pi$
$47$	−6.35092			−0.926376			−0.463188	+	0.886260i	$0.653295\pi$
$48$	−0.932593	+	0.932593i	−0.134608	+	0.134608i
$49$	9.91882			1.41697
$50$	11.0859	+	0.260858i	1.56779	+	0.0368909i
$51$			2.80127i			0.392257i
$52$	9.60806	+	4.29230i	1.33240	+	0.595235i
$53$	5.31987	−	5.31987i	0.730740	−	0.730740i	−0.240027	−	0.970766i	$-0.577156\pi$
$53$	5.31987	−	5.31987i	0.730740	−	0.730740i	0.970766	+	0.240027i	$0.0771562\pi$
$54$	1.56822	−	1.56822i	0.213408	−	0.213408i
$55$	−0.0964538	+	8.19931i	−0.0130058	+	1.10559i
$56$		−	8.38000i		−	1.11983i
$57$		−	3.90449i		−	0.517163i
$58$	−18.6453			−2.44825
$59$	−6.51015	−	6.51015i	−0.847550	−	0.847550i	0.142277	−	0.989827i	$-0.454558\pi$
$59$	−6.51015	−	6.51015i	−0.847550	−	0.847550i	−0.989827	+	0.142277i	$0.954558\pi$
$60$	−0.0767671	+	6.52579i	−0.00991059	+	0.842476i
$61$	7.84876			1.00493			0.502465	−	0.864597i	$-0.332426\pi$
$61$	7.84876			1.00493			0.502465	+	0.864597i	$0.332426\pi$
$62$	−4.68691	+	4.68691i	−0.595238	+	0.595238i
$63$		−	4.11325i		−	0.518221i
$64$	12.8861			1.61076
$65$	−7.56375	+	2.79099i	−0.938168	+	0.346180i
$66$	−8.13287			−1.00109
$67$		−	12.3496i		−	1.50874i	−0.656447	−	0.754372i	$-0.727942\pi$
$67$		−	12.3496i		−	1.50874i	0.656447	−	0.754372i	$-0.272058\pi$
$68$	5.78120	−	5.78120i	0.701074	−	0.701074i
$69$	−2.17724			−0.262109
$70$	14.2530	+	14.5924i	1.70356	+	1.74412i
$71$	−7.75627	−	7.75627i	−0.920500	−	0.920500i	0.0765650	−	0.997065i	$-0.475605\pi$
$71$	−7.75627	−	7.75627i	−0.920500	−	0.920500i	−0.997065	+	0.0765650i	$0.975605\pi$
$72$	−2.03732			−0.240100
$73$		−	5.27944i		−	0.617912i	−0.951076	−	0.308956i	$-0.900020\pi$
$73$		−	5.27944i		−	0.617912i	0.951076	−	0.308956i	$-0.0999796\pi$
$74$		−	17.3779i		−	2.02014i
$75$	−3.45139	−	3.61773i	−0.398532	−	0.417739i
$76$	−8.05801	+	8.05801i	−0.924317	+	0.924317i
$77$	−10.6658	+	10.6658i	−1.21548	+	1.21548i
$78$	−2.85624	−	7.46887i	−0.323405	−	0.845683i
$79$			8.45538i			0.951305i	0.879633	+	0.475653i	$0.157788\pi$
$79$			8.45538i			0.951305i	−0.879633	+	0.475653i	$0.842212\pi$
$80$	−2.10973	+	2.06067i	−0.235874	+	0.230390i
$81$	−1.00000			−0.111111
$82$	−3.66491	+	3.66491i	−0.404722	+	0.404722i
$83$	4.49388			0.493267			0.246634	−	0.969109i	$-0.420676\pi$
$83$	4.49388			0.493267			0.246634	+	0.969109i	$0.420676\pi$
$84$	−8.48883	+	8.48883i	−0.926208	+	0.926208i
$85$	−0.0736805	+	6.26340i	−0.00799177	+	0.679361i
$86$	2.82085	−	2.82085i	0.304180	−	0.304180i
$87$	5.94473	+	5.94473i	0.637342	+	0.637342i
$88$	5.28283	+	5.28283i	0.563151	+	0.563151i
$89$	8.91884	+	8.91884i	0.945395	+	0.945395i	0.998584	−	0.0531890i	$-0.0169386\pi$
$89$	8.91884	+	8.91884i	0.945395	+	0.945395i	−0.0531890	+	0.998584i	$0.516939\pi$
$90$	3.54765	−	3.46515i	0.373955	−	0.365259i
$91$	−13.5408	−	6.04919i	−1.41946	−	0.634127i
$92$	4.49334	+	4.49334i	0.468464	+	0.468464i
$93$	2.98868			0.309912
$94$		−	14.0850i		−	1.45276i
$95$	0.102698	−	8.73011i	0.0105366	−	0.895691i
$96$	−4.94951	−	4.94951i	−0.505157	−	0.505157i
$97$			17.6029i			1.78730i	0.448765	+	0.893650i	$0.351864\pi$
$97$			17.6029i			1.78730i	−0.448765	+	0.893650i	$0.648136\pi$
$98$			21.9979i			2.22213i
$99$	2.59303	+	2.59303i	0.260609	+	0.260609i
$100$	−0.343289	+	14.5891i	−0.0343289	+	1.45891i
$101$			4.66632i			0.464316i	0.972678	+	0.232158i	$0.0745787\pi$
$101$			4.66632i			0.464316i	−0.972678	+	0.232158i	$0.925421\pi$
$102$	−6.21265			−0.615144
$103$	2.08089	+	2.08089i	0.205036	+	0.205036i	0.802154	−	0.597118i	$-0.203687\pi$
$103$	2.08089	+	2.08089i	0.205036	+	0.205036i	−0.597118	+	0.802154i	$0.703687\pi$
$104$	−2.99620	+	6.70683i	−0.293802	+	0.657658i
$105$	0.108189	−	9.19687i	0.0105581	−	0.897522i
$106$	11.7984	+	11.7984i	1.14596	+	1.14596i
$107$	1.71214	+	1.71214i	0.165519	+	0.165519i	0.785006	−	0.619488i	$-0.212660\pi$
$107$	1.71214	+	1.71214i	0.165519	+	0.165519i	−0.619488	+	0.785006i	$0.712660\pi$
$108$	2.06378	+	2.06378i	0.198587	+	0.198587i
$109$	−4.77725	+	4.77725i	−0.457578	+	0.457578i	−0.897860	−	0.440282i	$-0.854879\pi$
$109$	−4.77725	+	4.77725i	−0.457578	+	0.457578i	0.440282	+	0.897860i	$0.354879\pi$
$110$	−18.1844	−	0.213915i	−1.73381	−	0.0203960i
$111$	−5.54064	+	5.54064i	−0.525894	+	0.525894i
$112$	−5.42490			−0.512605
$113$	−1.95021	+	1.95021i	−0.183460	+	0.183460i	−0.792862	−	0.609402i	$-0.791410\pi$
$113$	−1.95021	+	1.95021i	−0.183460	+	0.183460i	0.609402	+	0.792862i	$0.291410\pi$
$114$	8.65938			0.811025
$115$	−4.86812	−	0.0572669i	−0.453955	−	0.00534017i
$116$		−	24.5372i		−	2.27822i
$117$	−1.47066	+	3.29198i	−0.135962	+	0.304344i
$118$	14.4382	−	14.4382i	1.32914	−	1.32914i
$119$	−8.14752	+	8.14752i	−0.746882	+	0.746882i
$120$	−4.55527	−	0.0535866i	−0.415837	−	0.00489177i
$121$		−	2.44759i		−	0.222508i
$122$			17.4070i			1.57595i
$123$	2.33699			0.210719
$124$	−6.16798	−	6.16798i	−0.553901	−	0.553901i
$125$	−7.62184	−	8.17970i	−0.681718	−	0.731615i
$126$	9.12235			0.812684
$127$	4.33250	−	4.33250i	0.384447	−	0.384447i	−0.488254	−	0.872701i	$-0.662366\pi$
$127$	4.33250	−	4.33250i	0.384447	−	0.384447i	0.872701	+	0.488254i	$0.162366\pi$
$128$			14.5793i			1.28864i
$129$	−1.79876			−0.158372
$130$	−6.18985	−	16.7749i	−0.542886	−	1.47125i
$131$	−11.7646			−1.02788			−0.513939	−	0.857827i	$-0.671814\pi$
$131$	−11.7646			−1.02788			−0.513939	+	0.857827i	$0.671814\pi$
$132$		−	10.7029i		−	0.931565i
$133$	11.3562	−	11.3562i	0.984712	−	0.984712i
$134$	27.3889			2.36604
$135$	−2.23591	−	0.0263025i	−0.192437	−	0.00226376i
$136$	4.03552	+	4.03552i	0.346043	+	0.346043i
$137$	12.3668			1.05657			0.528286	−	0.849067i	$-0.322835\pi$
$137$	12.3668			1.05657			0.528286	+	0.849067i	$0.322835\pi$
$138$		−	4.82868i		−	0.411045i
$139$			15.1730i			1.28695i	0.765466	+	0.643477i	$0.222509\pi$
$139$			15.1730i			1.28695i	−0.765466	+	0.643477i	$0.777491\pi$
$140$	−19.2036	+	18.7570i	−1.62300	+	1.58526i
$141$	−4.49078	+	4.49078i	−0.378192	+	0.378192i
$142$	17.2018	−	17.2018i	1.44355	−	1.44355i
$143$	12.3497	−	4.72275i	1.03273	−	0.394936i
$144$			1.31889i			0.109907i
$145$	13.1355	+	13.4483i	1.09085	+	1.11682i
$146$	11.7087			0.969022
$147$	7.01366	−	7.01366i	0.578477	−	0.578477i
$148$	22.8693			1.87984
$149$	6.53739	−	6.53739i	0.535564	−	0.535564i	−0.386659	−	0.922223i	$-0.626371\pi$
$149$	6.53739	−	6.53739i	0.535564	−	0.535564i	0.922223	+	0.386659i	$0.126371\pi$
$150$	8.02338	−	7.65447i	0.655106	−	0.624985i
$151$	2.56165	−	2.56165i	0.208464	−	0.208464i	−0.595150	−	0.803614i	$-0.702907\pi$
$151$	2.56165	−	2.56165i	0.208464	−	0.208464i	0.803614	+	0.595150i	$0.202907\pi$
$152$	−5.62483	−	5.62483i	−0.456234	−	0.456234i
$153$	1.98080	+	1.98080i	0.160138	+	0.160138i
$154$	−23.6545	−	23.6545i	−1.90613	−	1.90613i
$155$	6.68243	+	0.0786099i	0.536746	+	0.00631410i
$156$	9.82904	−	3.75881i	0.786953	−	0.300946i
$157$	−2.92797	−	2.92797i	−0.233678	−	0.233678i	0.580548	−	0.814226i	$-0.302838\pi$
$157$	−2.92797	−	2.92797i	−0.233678	−	0.233678i	−0.814226	+	0.580548i	$0.802838\pi$
$158$	−18.7523			−1.49185
$159$		−	7.52343i		−	0.596646i
$160$	−10.9365	−	11.1969i	−0.864605	−	0.885189i
$161$	−6.33252	−	6.33252i	−0.499073	−	0.499073i
$162$		−	2.21780i		−	0.174247i
$163$		−	8.49438i		−	0.665331i	−0.943045	−	0.332666i	$-0.892052\pi$
$163$		−	8.49438i		−	0.665331i	0.943045	−	0.332666i	$-0.107948\pi$
$164$	−4.82302	−	4.82302i	−0.376615	−	0.376615i
$165$	5.72958	+	5.86599i	0.446047	+	0.456667i
$166$			9.96651i			0.773551i
$167$	13.2559			1.02577			0.512886	−	0.858457i	$-0.328576\pi$
$167$	13.2559			1.02577			0.512886	+	0.858457i	$0.328576\pi$
$168$	−5.92556	−	5.92556i	−0.457167	−	0.457167i
$169$	8.67432	+	9.68277i	0.667256	+	0.744829i
$170$	−13.8910	−	0.163408i	−1.06539	−	0.0125329i
$171$	−2.76089	−	2.76089i	−0.211131	−	0.211131i
$172$	3.71224	+	3.71224i	0.283056	+	0.283056i
$173$	−7.94523	−	7.94523i	−0.604065	−	0.604065i	0.337324	−	0.941389i	$-0.390478\pi$
$173$	−7.94523	−	7.94523i	−0.604065	−	0.604065i	−0.941389	+	0.337324i	$0.890478\pi$
$174$	−13.1842	+	13.1842i	−0.999493	+	0.999493i
$175$	0.483802	−	20.5606i	0.0365720	−	1.55423i
$176$	3.41991	−	3.41991i	0.257785	−	0.257785i
$177$	−9.20675			−0.692022
$178$	−19.7802	+	19.7802i	−1.48259	+	1.48259i
$179$	1.37631			0.102870			0.0514350	−	0.998676i	$-0.483621\pi$
$179$	1.37631			0.102870			0.0514350	+	0.998676i	$0.483621\pi$
$180$	4.56015	+	4.66871i	0.339893	+	0.347985i
$181$			23.4687i			1.74442i	0.489136	+	0.872208i	$0.337312\pi$
$181$			23.4687i			1.74442i	−0.489136	+	0.872208i	$0.662688\pi$
$182$	13.4159	−	30.0306i	0.994450	−	2.22602i
$183$	5.54991	−	5.54991i	0.410261	−	0.410261i
$184$	−3.13654	+	3.13654i	−0.231229	+	0.231229i
$185$	−12.5341	+	12.2427i	−0.921527	+	0.900098i
$186$			6.62829i			0.486010i
$187$		−	10.2725i		−	0.751202i
$188$	18.5359			1.35187
$189$	−2.90851	−	2.90851i	−0.211563	−	0.211563i
$190$	19.3616	+	0.227763i	1.40464	+	0.0165237i
$191$	−2.92479			−0.211630			−0.105815	−	0.994386i	$-0.533745\pi$
$191$	−2.92479			−0.211630			−0.105815	+	0.994386i	$0.533745\pi$
$192$	9.11181	−	9.11181i	0.657589	−	0.657589i
$193$			20.6977i			1.48985i	0.667146	+	0.744927i	$0.267516\pi$
$193$			20.6977i			1.48985i	−0.667146	+	0.744927i	$0.732484\pi$
$194$	−39.0396			−2.80288
$195$	−3.37485	+	7.32191i	−0.241678	+	0.524333i
$196$	−28.9493			−2.06781
$197$		−	6.16201i		−	0.439025i	−0.975610	−	0.219513i	$-0.929553\pi$
$197$		−	6.16201i		−	0.439025i	0.975610	−	0.219513i	$-0.0704467\pi$
$198$	−5.75081	+	5.75081i	−0.408692	+	0.408692i
$199$	23.2876			1.65081			0.825407	−	0.564538i	$-0.190946\pi$
$199$	23.2876			1.65081			0.825407	+	0.564538i	$0.190946\pi$
$200$	−10.1838	−	0.239630i	−0.720102	−	0.0169444i
$201$	−8.73248	−	8.73248i	−0.615942	−	0.615942i
$202$	−10.3489			−0.728150
$203$			34.5806i			2.42708i
$204$		−	8.17586i		−	0.572424i
$205$	5.22530	+	0.0614687i	0.364951	+	0.00429316i
$206$	−4.61499	+	4.61499i	−0.321542	+	0.321542i
$207$	−1.53954	+	1.53954i	−0.107006	+	0.107006i
$208$	4.34175	+	1.93963i	0.301046	+	0.134489i
$209$			14.3182i			0.990407i
$210$	20.3968	+	0.239941i	1.40751	+	0.0165575i
$211$	11.6786			0.803990			0.401995	−	0.915642i	$-0.368317\pi$
$211$	11.6786			0.803990			0.401995	+	0.915642i	$0.368317\pi$
$212$	−15.5267	+	15.5267i	−1.06638	+	1.06638i
$213$	−10.9690			−0.751585
$214$	−3.79718	+	3.79718i	−0.259570	+	0.259570i
$215$	−4.02187	−	0.0473119i	−0.274289	−	0.00322665i
$216$	−1.44060	+	1.44060i	−0.0980206	+	0.0980206i
$217$	8.69260	+	8.69260i	0.590092	+	0.590092i
$218$	−10.5950	−	10.5950i	−0.717583	−	0.717583i
$219$	−3.73313	−	3.73313i	−0.252262	−	0.252262i
$220$	0.281512	−	23.9307i	0.0189796	−	1.61341i
$221$	9.43384	−	3.60768i	0.634588	−	0.242679i
$222$	−12.2880	−	12.2880i	−0.824717	−	0.824717i
$223$	−16.7954			−1.12470			−0.562351	−	0.826898i	$-0.690103\pi$
$223$	−16.7954			−1.12470			−0.562351	+	0.826898i	$0.690103\pi$
$224$		−	28.7913i		−	1.92370i
$225$	−4.99862	−	0.117620i	−0.333241	−	0.00784135i
$226$	−4.32517	−	4.32517i	−0.287706	−	0.287706i
$227$		−	22.2305i		−	1.47549i	−0.675078	−	0.737746i	$-0.735890\pi$
$227$		−	22.2305i		−	1.47549i	0.675078	−	0.737746i	$-0.264110\pi$
$228$			11.3957i			0.754702i
$229$	1.99942	+	1.99942i	0.132125	+	0.132125i	0.770077	−	0.637951i	$-0.220218\pi$
$229$	1.99942	+	1.99942i	0.132125	+	0.132125i	−0.637951	+	0.770077i	$0.720218\pi$
$230$	0.127006	−	10.7965i	0.00837456	−	0.711901i
$231$			15.0837i			0.992433i
$232$	17.1280			1.12451
$233$	−7.60402	−	7.60402i	−0.498156	−	0.498156i	0.412708	−	0.910863i	$-0.364583\pi$
$233$	−7.60402	−	7.60402i	−0.498156	−	0.498156i	−0.910863	+	0.412708i	$0.864583\pi$
$234$	−7.30095	−	3.26162i	−0.477278	−	0.213219i
$235$	−10.1591	+	9.92287i	−0.662707	+	0.647296i
$236$	19.0007	+	19.0007i	1.23684	+	1.23684i
$237$	5.97886	+	5.97886i	0.388369	+	0.388369i
$238$	−18.0695	−	18.0695i	−1.17127	−	1.17127i
$239$	17.2164	−	17.2164i	1.11363	−	1.11363i	0.120979	−	0.992655i	$-0.461397\pi$
$239$	17.2164	−	17.2164i	1.11363	−	1.11363i	0.992655	−	0.120979i	$-0.0386034\pi$
$240$	−0.0346900	+	2.94891i	−0.00223923	+	0.190351i
$241$	10.2155	−	10.2155i	0.658040	−	0.658040i	−0.296876	−	0.954916i	$-0.595945\pi$
$241$	10.2155	−	10.2155i	0.658040	−	0.658040i	0.954916	+	0.296876i	$0.0959447\pi$
$242$	5.42825			0.348941
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−22.9076			−1.46651
$245$	15.8664	−	15.4975i	1.01367	−	0.990097i
$246$			5.18296i			0.330454i
$247$	−13.1492	+	5.02849i	−0.836661	+	0.319955i
$248$	4.30550	−	4.30550i	0.273400	−	0.273400i
$249$	3.17765	−	3.17765i	0.201376	−	0.201376i
$250$	18.1409	−	16.9037i	1.14733	−	1.06908i
$251$			18.7574i			1.18396i	0.805954	+	0.591978i	$0.201653\pi$
$251$			18.7574i			1.18396i	−0.805954	+	0.591978i	$0.798347\pi$
$252$			12.0050i			0.756245i
$253$	7.98415			0.501959
$254$	9.60860	+	9.60860i	0.602897	+	0.602897i
$255$	4.37679	+	4.48099i	0.274085	+	0.280611i
$256$	−6.56189			−0.410118
$257$	1.40078	−	1.40078i	0.0873784	−	0.0873784i	−0.662067	−	0.749445i	$-0.730320\pi$
$257$	1.40078	−	1.40078i	0.0873784	−	0.0873784i	0.749445	+	0.662067i	$0.230320\pi$
$258$		−	3.98928i		−	0.248362i
$259$	−32.2300			−2.00267
$260$	22.0757	−	8.14585i	1.36908	−	0.505184i
$261$	8.40712			0.520388
$262$		−	26.0915i		−	1.61194i
$263$	15.8782	−	15.8782i	0.979092	−	0.979092i	−0.0206938	−	0.999786i	$-0.506587\pi$
$263$	15.8782	−	15.8782i	0.979092	−	0.979092i	0.999786	+	0.0206938i	$0.00658750\pi$
$264$	7.47105			0.459811
$265$	0.197885	−	16.8217i	0.0121560	−	1.03335i
$266$	25.1859	+	25.1859i	1.54424	+	1.54424i
$267$	12.6131			0.771912
$268$			36.0438i			2.20173i
$269$		−	0.349269i		−	0.0212953i	−0.999943	−	0.0106477i	$-0.996611\pi$
$269$		−	0.349269i		−	0.0212953i	0.999943	−	0.0106477i	$-0.00338932\pi$
$270$	0.0583336	−	4.95880i	0.00355007	−	0.301783i
$271$	8.52139	−	8.52139i	0.517637	−	0.517637i	−0.399218	−	0.916856i	$-0.630719\pi$
$271$	8.52139	−	8.52139i	0.517637	−	0.517637i	0.916856	+	0.399218i	$0.130719\pi$
$272$	2.61245	−	2.61245i	0.158403	−	0.158403i
$273$	−13.8522	+	5.29734i	−0.838372	+	0.320609i
$274$			27.4272i			1.65694i
$275$	12.6566	+	13.2665i	0.763219	+	0.800003i
$276$	6.35455			0.382499
$277$	−5.27671	+	5.27671i	−0.317047	+	0.317047i	−0.847632	−	0.530585i	$-0.821972\pi$
$277$	−5.27671	+	5.27671i	−0.317047	+	0.317047i	0.530585	+	0.847632i	$0.321972\pi$
$278$	−33.6505			−2.01823
$279$	2.11332	−	2.11332i	0.126521	−	0.126521i
$280$	−13.0932	−	13.4049i	−0.782467	−	0.801095i
$281$	−5.98480	+	5.98480i	−0.357023	+	0.357023i	−0.862714	−	0.505691i	$-0.831237\pi$
$281$	−5.98480	+	5.98480i	−0.357023	+	0.357023i	0.505691	+	0.862714i	$0.331237\pi$
$282$	−9.95963	−	9.95963i	−0.593087	−	0.593087i
$283$	−2.56174	−	2.56174i	−0.152280	−	0.152280i	0.626856	−	0.779135i	$-0.284342\pi$
$283$	−2.56174	−	2.56174i	−0.152280	−	0.152280i	−0.779135	+	0.626856i	$0.784342\pi$
$284$	22.6376	+	22.6376i	1.34330	+	1.34330i
$285$	−6.10050	−	6.24574i	−0.361363	−	0.369966i
$286$	10.4741	+	27.3891i	0.619346	+	1.61955i
$287$	6.79714	+	6.79714i	0.401223	+	0.401223i
$288$	−6.99966			−0.412459
$289$			9.15288i			0.538404i
$290$	−29.8255	+	29.1320i	−1.75142	+	1.71069i
$291$	12.4471	+	12.4471i	0.729662	+	0.729662i
$292$			15.4087i			0.901727i
$293$		−	5.91537i		−	0.345579i	−0.984959	−	0.172790i	$-0.944722\pi$
$293$		−	5.91537i		−	0.345579i	0.984959	−	0.172790i	$-0.0552781\pi$
$294$	15.5549	+	15.5549i	0.907179	+	0.907179i
$295$	−20.5855	−	0.242161i	−1.19853	−	0.0140991i
$296$			15.9637i			0.927872i
$297$	3.66710			0.212786
$298$	14.4986	+	14.4986i	0.839882	+	0.839882i
$299$	2.80401	+	7.33229i	0.162160	+	0.424037i
$300$	10.0733	+	10.5588i	0.581582	+	0.609611i
$301$	−5.23170	−	5.23170i	−0.301550	−	0.301550i
$302$	5.68122	+	5.68122i	0.326918	+	0.326918i
$303$	3.29959	+	3.29959i	0.189556	+	0.189556i
$304$	−3.64130	+	3.64130i	−0.208843	+	0.208843i
$305$	12.5551	−	12.2631i	0.718903	−	0.702186i
$306$	−4.39301	+	4.39301i	−0.251132	+	0.251132i
$307$	−2.81730			−0.160792			−0.0803960	−	0.996763i	$-0.525618\pi$
$307$	−2.81730			−0.160792			−0.0803960	+	0.996763i	$0.525618\pi$
$308$	31.1294	−	31.1294i	1.77376	−	1.77376i
$309$	2.94282			0.167411
$310$	−0.174341	+	14.8203i	−0.00990189	+	0.841735i
$311$		−	9.18067i		−	0.520588i	−0.965529	−	0.260294i	$-0.916180\pi$
$311$		−	9.18067i		−	0.520588i	0.965529	−	0.260294i	$-0.0838195\pi$
$312$	2.62381	+	6.86108i	0.148544	+	0.388432i
$313$	16.4881	−	16.4881i	0.931960	−	0.931960i	−0.0658683	−	0.997828i	$-0.520982\pi$
$313$	16.4881	−	16.4881i	0.931960	−	0.931960i	0.997828	+	0.0658683i	$0.0209817\pi$
$314$	6.49365	−	6.49365i	0.366458	−	0.366458i
$315$	−6.42667	−	6.57967i	−0.362102	−	0.370722i
$316$		−	24.6781i		−	1.38825i
$317$			13.3835i			0.751695i	0.926682	+	0.375847i	$0.122648\pi$
$317$			13.3835i			0.751695i	−0.926682	+	0.375847i	$0.877352\pi$
$318$	16.6854			0.935672
$319$	−21.7999	−	21.7999i	−1.22056	−	1.22056i
$320$	20.6129	−	20.1336i	1.15230	−	1.12550i
$321$	2.42133			0.135145
$322$	14.0442	−	14.0442i	0.782655	−	0.782655i
$323$			10.9376i			0.608582i
$324$	2.91862			0.162146
$325$	−7.73846	+	16.2824i	−0.429253	+	0.903184i
$326$	18.8388			1.04339
$327$			6.75606i			0.373611i
$328$	3.36667	−	3.36667i	0.185893	−	0.185893i
$329$	−26.1229			−1.44020
$330$	−13.0096	+	12.7071i	−0.716153	+	0.699500i
$331$	−13.7828	−	13.7828i	−0.757572	−	0.757572i	0.218308	−	0.975880i	$-0.429946\pi$
$331$	−13.7828	−	13.7828i	−0.757572	−	0.757572i	−0.975880	+	0.218308i	$0.929946\pi$
$332$	−13.1159			−0.719831
$333$			7.83564i			0.429391i
$334$			29.3989i			1.60863i
$335$	−19.2954	−	19.7548i	−1.05422	−	1.07932i
$336$	−3.83599	+	3.83599i	−0.209270	+	0.209270i
$337$	−24.8025	+	24.8025i	−1.35108	+	1.35108i	−0.466618	+	0.884459i	$0.654528\pi$
$337$	−24.8025	+	24.8025i	−1.35108	+	1.35108i	−0.884459	+	0.466618i	$0.845472\pi$
$338$	−21.4744	+	19.2379i	−1.16805	+	1.04640i
$339$			2.75801i			0.149795i
$340$	0.215046	−	18.2805i	0.0116625	−	0.991400i
$341$	−10.9598			−0.593506
$342$	6.12310	−	6.12310i	0.331100	−	0.331100i
$343$	12.0058			0.648254
$344$	−2.59130	+	2.59130i	−0.139713	+	0.139713i
$345$	−3.48278	+	3.40179i	−0.187506	+	0.183146i
$346$	17.6209	−	17.6209i	0.947306	−	0.947306i
$347$	2.24725	+	2.24725i	0.120639	+	0.120639i	0.764849	−	0.644210i	$-0.222814\pi$
$347$	2.24725	+	2.24725i	0.120639	+	0.120639i	−0.644210	+	0.764849i	$0.722814\pi$
$348$	−17.3504	−	17.3504i	−0.930081	−	0.930081i
$349$	−19.2780	−	19.2780i	−1.03193	−	1.03193i	−0.999473	−	0.0324525i	$-0.989668\pi$
$349$	−19.2780	−	19.2780i	−1.03193	−	1.03193i	−0.0324525	−	0.999473i	$-0.510332\pi$
$350$	45.5991	+	1.07297i	2.43738	+	0.0573529i
$351$	1.28787	+	3.36770i	0.0687415	+	0.179754i
$352$	18.1503	+	18.1503i	0.967415	+	0.967415i
$353$	20.5850			1.09563			0.547814	−	0.836600i	$-0.315460\pi$
$353$	20.5850			1.09563			0.547814	+	0.836600i	$0.315460\pi$
$354$		−	20.4187i		−	1.08524i
$355$	−24.5258	−	0.288513i	−1.30169	−	0.0153127i
$356$	−26.0307	−	26.0307i	−1.37963	−	1.37963i
$357$			11.5223i			0.609826i
$358$			3.05237i			0.161323i
$359$	−10.6029	−	10.6029i	−0.559602	−	0.559602i	0.369592	−	0.929194i	$-0.379497\pi$
$359$	−10.6029	−	10.6029i	−0.559602	−	0.559602i	−0.929194	+	0.369592i	$0.879497\pi$
$360$	−3.25895	+	3.18317i	−0.171762	+	0.167768i
$361$			3.75492i			0.197627i
$362$	−52.0488			−2.73563
$363$	−1.73071	−	1.73071i	−0.0908385	−	0.0908385i
$364$	39.5204	+	17.6553i	2.07143	+	0.925389i
$365$	−8.24877	−	8.44515i	−0.431760	−	0.442039i
$366$	12.3086	+	12.3086i	0.643380	+	0.643380i
$367$	−1.02534	−	1.02534i	−0.0535221	−	0.0535221i	0.679839	−	0.733361i	$-0.262050\pi$
$367$	−1.02534	−	1.02534i	−0.0535221	−	0.0535221i	−0.733361	+	0.679839i	$0.762050\pi$
$368$	2.03048	+	2.03048i	0.105846	+	0.105846i
$369$	1.65250	−	1.65250i	0.0860257	−	0.0860257i
$370$	−27.1517	−	27.7981i	−1.41155	−	1.44516i
$371$	21.8819	−	21.8819i	1.13605	−	1.13605i
$372$	−8.72284			−0.452258
$373$	8.41567	−	8.41567i	0.435747	−	0.435747i	−0.454831	−	0.890578i	$-0.650300\pi$
$373$	8.41567	−	8.41567i	0.435747	−	0.435747i	0.890578	+	0.454831i	$0.150300\pi$
$374$	22.7824			1.17805
$375$	−11.1734	−	0.394465i	−0.576991	−	0.0203701i
$376$			12.9388i			0.667270i
$377$	12.3640	−	27.6761i	0.636779	−	1.42539i
$378$	6.45048	−	6.45048i	0.331777	−	0.331777i
$379$	5.03557	−	5.03557i	0.258660	−	0.258660i	−0.565849	−	0.824509i	$-0.691452\pi$
$379$	5.03557	−	5.03557i	0.258660	−	0.258660i	0.824509	+	0.565849i	$0.191452\pi$
$380$	−0.299737	+	25.4799i	−0.0153762	+	1.30709i
$381$		−	6.12708i		−	0.313900i
$382$		−	6.48659i		−	0.331883i
$383$	−0.483559			−0.0247087			−0.0123543	−	0.999924i	$-0.503933\pi$
$383$	−0.483559			−0.0247087			−0.0123543	+	0.999924i	$0.503933\pi$
$384$	10.3091	+	10.3091i	0.526086	+	0.526086i
$385$	−0.396739	+	33.7258i	−0.0202197	+	1.71883i
$386$	−45.9033			−2.33642
$387$	−1.27192	+	1.27192i	−0.0646551	+	0.0646551i
$388$		−	51.3761i		−	2.60823i
$389$	−17.5944			−0.892070			−0.446035	−	0.895015i	$-0.647164\pi$
$389$	−17.5944			−0.892070			−0.446035	+	0.895015i	$0.647164\pi$
$390$	−16.2385	−	7.48474i	−0.822269	−	0.379004i
$391$	6.09905			0.308442
$392$		−	20.2078i		−	1.02065i
$393$	−8.31883	+	8.31883i	−0.419629	+	0.419629i
$394$	13.6661			0.688488
$395$	13.2110	+	13.5255i	0.664715	+	0.680540i
$396$	−7.56807	−	7.56807i	−0.380310	−	0.380310i
$397$	−9.63810			−0.483722			−0.241861	−	0.970311i	$-0.577758\pi$
$397$	−9.63810			−0.483722			−0.241861	+	0.970311i	$0.577758\pi$
$398$			51.6472i			2.58884i
$399$		−	16.0602i		−	0.804014i
$400$	−0.155128	+	6.59260i	−0.00775638	+	0.329630i
$401$	−16.8784	+	16.8784i	−0.842865	+	0.842865i	−0.989231	−	0.146365i	$-0.953243\pi$
$401$	−16.8784	+	16.8784i	−0.842865	+	0.842865i	0.146365	+	0.989231i	$0.453243\pi$
$402$	19.3669	−	19.3669i	0.965932	−	0.965932i
$403$	−3.84904	−	10.0650i	−0.191734	−	0.501372i
$404$		−	13.6192i		−	0.677582i
$405$	−1.59963	+	1.56243i	−0.0794862	+	0.0776378i
$406$	−76.6927			−3.80620
$407$	20.3180	−	20.3180i	1.00713	−	1.00713i
$408$	5.70709			0.282543
$409$	3.65546	−	3.65546i	0.180751	−	0.180751i	−0.610932	−	0.791683i	$-0.709205\pi$
$409$	3.65546	−	3.65546i	0.180751	−	0.180751i	0.791683	+	0.610932i	$0.209205\pi$
$410$	−0.136325	+	11.5887i	−0.00673261	+	0.572323i
$411$	8.74468	−	8.74468i	0.431343	−	0.431343i
$412$	−6.07334	−	6.07334i	−0.299212	−	0.299212i
$413$	−26.7779	−	26.7779i	−1.31765	−	1.31765i
$414$	−3.41439	−	3.41439i	−0.167808	−	0.167808i
$415$	7.18853	−	7.02137i	0.352871	−	0.344666i
$416$	−10.2941	+	23.0428i	−0.504710	+	1.12976i
$417$	10.7289	+	10.7289i	0.525397	+	0.525397i
$418$	−31.7548			−1.55318
$419$			33.9420i			1.65818i	0.559117	+	0.829089i	$0.311140\pi$
$419$			33.9420i			1.65818i	−0.559117	+	0.829089i	$0.688860\pi$
$420$	−0.315762	+	26.8422i	−0.0154076	+	1.30976i
$421$	−19.7073	−	19.7073i	−0.960474	−	0.960474i	0.0387742	−	0.999248i	$-0.487655\pi$
$421$	−19.7073	−	19.7073i	−0.960474	−	0.960474i	−0.999248	+	0.0387742i	$0.987655\pi$
$422$			25.9008i			1.26083i
$423$			6.35092i			0.308792i
$424$	−10.8383	−	10.8383i	−0.526353	−	0.526353i
$425$	9.66827	+	10.1342i	0.468980	+	0.491583i
$426$		−	24.3271i		−	1.17865i
$427$	32.2839			1.56233
$428$	−4.99709	−	4.99709i	−0.241543	−	0.241543i
$429$	5.39305	−	12.0720i	0.260379	−	0.582843i
$430$	0.104928	−	8.91969i	0.00506009	−	0.430146i
$431$	10.7665	+	10.7665i	0.518606	+	0.518606i	0.917150	−	0.398543i	$-0.130484\pi$
$431$	10.7665	+	10.7665i	0.518606	+	0.518606i	−0.398543	+	0.917150i	$0.630484\pi$
$432$	0.932593	+	0.932593i	0.0448694	+	0.0448694i
$433$	11.8525	+	11.8525i	0.569594	+	0.569594i	0.932015	−	0.362421i	$-0.118050\pi$
$433$	11.8525	+	11.8525i	0.569594	+	0.569594i	−0.362421	+	0.932015i	$0.618050\pi$
$434$	−19.2784	+	19.2784i	−0.925394	+	0.925394i
$435$	18.7976	+	0.221129i	0.901276	+	0.0106023i
$436$	13.9430	−	13.9430i	0.667749	−	0.667749i
$437$	−8.50103			−0.406659
$438$	8.27933	−	8.27933i	0.395602	−	0.395602i
$439$	2.02222			0.0965152			0.0482576	−	0.998835i	$-0.484633\pi$
$439$	2.02222			0.0965152			0.0482576	+	0.998835i	$0.484633\pi$
$440$	16.7046	+	0.196507i	0.796361	+	0.00936812i
$441$		−	9.91882i		−	0.472325i
$442$	8.00110	+	20.9223i	0.380573	+	0.995174i
$443$	0.127396	−	0.127396i	0.00605277	−	0.00605277i	−0.704074	−	0.710127i	$-0.748638\pi$
$443$	0.127396	−	0.127396i	0.00605277	−	0.00605277i	0.710127	+	0.704074i	$0.248638\pi$
$444$	16.1710	−	16.1710i	0.767443	−	0.767443i
$445$	28.2019	+	0.331758i	1.33690	+	0.0157268i
$446$		−	37.2488i		−	1.76378i
$447$		−	9.24527i		−	0.437286i
$448$	53.0035			2.50418
$449$	24.8640	+	24.8640i	1.17341	+	1.17341i	0.981392	+	0.192014i	$0.0615019\pi$
$449$	24.8640	+	24.8640i	1.17341	+	1.17341i	0.192014	+	0.981392i	$0.438498\pi$
$450$	0.260858	−	11.0859i	0.0122970	−	0.522595i
$451$	−8.56996			−0.403544
$452$	5.69192	−	5.69192i	0.267726	−	0.267726i
$453$		−	3.62272i		−	0.170210i
$454$	49.3028			2.31390
$455$	−31.1116	+	11.4800i	−1.45853	+	0.538193i
$456$	−7.95470			−0.372513
$457$			32.3018i			1.51101i	0.655140	+	0.755507i	$0.272610\pi$
$457$			32.3018i			1.51101i	−0.655140	+	0.755507i	$0.727390\pi$
$458$	−4.43430	+	4.43430i	−0.207201	+	0.207201i
$459$	2.80127			0.130752
$460$	14.2082	+	0.167141i	0.662462	+	0.00779297i
$461$	−14.5631	−	14.5631i	−0.678272	−	0.678272i	0.281337	−	0.959609i	$-0.409222\pi$
$461$	−14.5631	−	14.5631i	−0.678272	−	0.678272i	−0.959609	+	0.281337i	$0.909222\pi$
$462$	−33.4525			−1.55635
$463$		−	13.2720i		−	0.616800i	−0.951257	−	0.308400i	$-0.900206\pi$
$463$		−	13.2720i		−	0.616800i	0.951257	−	0.308400i	$-0.0997935\pi$
$464$		−	11.0880i		−	0.514749i
$465$	4.78078	−	4.66961i	0.221703	−	0.216548i
$466$	16.8642	−	16.8642i	0.781217	−	0.781217i
$467$	−21.6107	+	21.6107i	−1.00002	+	1.00002i	−2.29542e−5		1.00000i	$0.500007\pi$
$467$	−21.6107	+	21.6107i	−1.00002	+	1.00002i	−1.00000		2.29542e-5i	$0.999993\pi$
$468$	4.29230	−	9.60806i	0.198412	−	0.444133i
$469$		−	50.7970i		−	2.34559i
$470$	−22.0069	−	22.5308i	−1.01510	−	1.03927i
$471$	−4.14078			−0.190797
$472$	−13.2633	+	13.2633i	−0.610491	+	0.610491i
$473$	6.59622			0.303295
$474$	−13.2599	+	13.2599i	−0.609047	+	0.609047i
$475$	−13.4759	−	14.1254i	−0.618317	−	0.648117i
$476$	23.7795	−	23.7795i	1.08993	−	1.08993i
$477$	−5.31987	−	5.31987i	−0.243580	−	0.243580i
$478$	38.1824	+	38.1824i	1.74642	+	1.74642i
$479$	−13.5992	−	13.5992i	−0.621361	−	0.621361i	0.324518	−	0.945879i	$-0.394798\pi$
$479$	−13.5992	−	13.5992i	−0.621361	−	0.621361i	−0.945879	+	0.324518i	$0.894798\pi$
$480$	−15.6506	−	0.184109i	−0.714350	−	0.00840337i
$481$	25.7948	+	11.5236i	1.17614	+	0.525429i
$482$	22.6560	+	22.6560i	1.03195	+	1.03195i
$483$	−8.95554			−0.407491
$484$			7.14359i			0.324708i
$485$	27.5032	+	28.1580i	1.24886	+	1.27859i
$486$	−1.56822	−	1.56822i	−0.0711359	−	0.0711359i
$487$			16.1028i			0.729687i	0.931069	+	0.364844i	$0.118878\pi$
$487$			16.1028i			0.729687i	−0.931069	+	0.364844i	$0.881122\pi$
$488$		−	15.9904i		−	0.723853i
$489$	−6.00644	−	6.00644i	−0.271620	−	0.271620i
$490$	34.3702	+	35.1885i	1.55269	+	1.58965i
$491$		−	20.7163i		−	0.934915i	−0.884016	−	0.467457i	$-0.845170\pi$
$491$		−	20.7163i		−	0.934915i	0.884016	−	0.467457i	$-0.154830\pi$
$492$	−6.82079			−0.307505
$493$	−16.6528	−	16.6528i	−0.750005	−	0.750005i
$494$	−11.1522	−	29.1622i	−0.501760	−	1.31207i
$495$	8.19931	+	0.0964538i	0.368531	+	0.00433528i
$496$	−2.78722	−	2.78722i	−0.125150	−	0.125150i
$497$	−31.9035	−	31.9035i	−1.43107	−	1.43107i
$498$	7.04739	+	7.04739i	0.315801	+	0.315801i
$499$	4.09738	−	4.09738i	0.183424	−	0.183424i	−0.609422	−	0.792846i	$-0.708599\pi$
$499$	4.09738	−	4.09738i	0.183424	−	0.183424i	0.792846	+	0.609422i	$0.208599\pi$
$500$	22.2453	+	23.8735i	0.994840	+	1.06765i
$501$	9.37333	−	9.37333i	0.418769	−	0.418769i
$502$	−41.6001			−1.85670
$503$	−23.4993	+	23.4993i	−1.04778	+	1.04778i	−0.0489821	+	0.998800i	$0.515598\pi$
$503$	−23.4993	+	23.4993i	−1.04778	+	1.04778i	−0.998800	+	0.0489821i	$0.984402\pi$
$504$	−8.38000			−0.373275
$505$	7.29080	+	7.46438i	0.324436	+	0.332160i
$506$			17.7072i			0.787182i
$507$	12.9804	+	0.713080i	0.576481	+	0.0316690i
$508$	−12.6449	+	12.6449i	−0.561028	+	0.561028i
$509$	13.7959	−	13.7959i	0.611492	−	0.611492i	−0.331843	−	0.943335i	$-0.607670\pi$
$509$	13.7959	−	13.7959i	0.611492	−	0.611492i	0.943335	+	0.331843i	$0.107670\pi$
$510$	−9.93793	+	9.70684i	−0.440059	+	0.429826i
$511$		−	21.7157i		−	0.960645i
$512$			14.6057i			0.645488i
$513$	−3.90449			−0.172388
$514$	3.10665	+	3.10665i	0.137029	+	0.137029i
$515$	6.57990	+	0.0774037i	0.289945	+	0.00341081i
$516$	5.24990			0.231114
$517$	16.4681	−	16.4681i	0.724266	−	0.724266i
$518$		−	71.4795i		−	3.14063i
$519$	−11.2362			−0.493217
$520$	5.68614	+	15.4098i	0.249354	+	0.675764i
$521$	−20.4402			−0.895503			−0.447752	−	0.894158i	$-0.647775\pi$
$521$	−20.4402			−0.895503			−0.447752	+	0.894158i	$0.647775\pi$
$522$			18.6453i			0.816082i
$523$	1.95338	−	1.95338i	0.0854154	−	0.0854154i	−0.663108	−	0.748524i	$-0.730763\pi$
$523$	1.95338	−	1.95338i	0.0854154	−	0.0854154i	0.748524	+	0.663108i	$0.230763\pi$
$524$	34.3364			1.49999
$525$	−14.1964	−	14.8806i	−0.619582	−	0.649443i
$526$	35.2146	+	35.2146i	1.53543	+	1.53543i
$527$	−8.37211			−0.364695
$528$		−	4.83648i		−	0.210481i
$529$		−	18.2596i		−	0.793896i
$530$	37.3072	+	0.438869i	1.62052	+	0.0190632i
$531$	−6.51015	+	6.51015i	−0.282517	+	0.282517i
$532$	−33.1446	+	33.1446i	−1.43700	+	1.43700i
$533$	−3.00974	−	7.87027i	−0.130366	−	0.340899i
$534$			27.9734i			1.21053i
$535$	5.41388	+	0.0636871i	0.234063	+	0.00275343i
$536$	−25.1601			−1.08675
$537$	0.973196	−	0.973196i	0.0419965	−	0.0419965i
$538$	0.774608			0.0333957
$539$	−25.7198	+	25.7198i	−1.10783	+	1.10783i
$540$	6.52579	+	0.0767671i	0.280825	+	0.00330353i
$541$	28.9135	−	28.9135i	1.24309	−	1.24309i	0.284374	−	0.958714i	$-0.408214\pi$
$541$	28.9135	−	28.9135i	1.24309	−	1.24309i	0.958714	−	0.284374i	$-0.0917856\pi$
$542$	18.8987	+	18.8987i	0.811769	+	0.811769i
$543$	16.5949	+	16.5949i	0.712155	+	0.712155i
$544$	13.8649	+	13.8649i	0.594453	+	0.594453i
$545$	−0.177701	+	15.1060i	−0.00761189	+	0.647068i
$546$	−11.7484	−	30.7213i	−0.502786	−	1.31475i
$547$	−21.7628	−	21.7628i	−0.930509	−	0.930509i	0.0672284	−	0.997738i	$-0.478584\pi$
$547$	−21.7628	−	21.7628i	−0.930509	−	0.930509i	−0.997738	+	0.0672284i	$0.978584\pi$
$548$	−36.0942			−1.54187
$549$		−	7.84876i		−	0.334977i
$550$	−29.4225	+	28.0697i	−1.25458	+	1.19690i
$551$	23.2112	+	23.2112i	0.988830	+	0.988830i
$552$			4.43574i			0.188798i
$553$			34.7791i			1.47896i
$554$	−11.7027	−	11.7027i	−0.497199	−	0.497199i
$555$	−0.206097	+	17.5198i	−0.00874834	+	0.743675i
$556$		−	44.2842i		−	1.87807i
$557$	37.6115			1.59365			0.796825	−	0.604210i	$-0.206511\pi$
$557$	37.6115			1.59365			0.796825	+	0.604210i	$0.206511\pi$
$558$	4.68691	+	4.68691i	0.198413	+	0.198413i
$559$	2.31657	+	6.05768i	0.0979805	+	0.256212i
$560$	−8.67783	+	8.47604i	−0.366705	+	0.358178i
$561$	−7.26378	−	7.26378i	−0.306677	−	0.306677i
$562$	−13.2731	−	13.2731i	−0.559890	−	0.559890i
$563$	27.8463	+	27.8463i	1.17358	+	1.17358i	0.981349	+	0.192234i	$0.0615733\pi$
$563$	27.8463	+	27.8463i	1.17358	+	1.17358i	0.192234	+	0.981349i	$0.438427\pi$
$564$	13.1069	−	13.1069i	0.551899	−	0.551899i
$565$	−0.0725426	+	6.16667i	−0.00305189	+	0.259434i
$566$	5.68142	−	5.68142i	0.238808	−	0.238808i
$567$	−4.11325			−0.172740
$568$	−15.8020	+	15.8020i	−0.663037	+	0.663037i
$569$	1.85521			0.0777743			0.0388872	−	0.999244i	$-0.487619\pi$
$569$	1.85521			0.0777743			0.0388872	+	0.999244i	$0.487619\pi$
$570$	13.8518	−	13.5297i	0.580187	−	0.566696i
$571$			33.3973i			1.39763i	0.715302	+	0.698816i	$0.246289\pi$
$571$			33.3973i			1.39763i	−0.715302	+	0.698816i	$0.753711\pi$
$572$	−36.0440	+	13.7839i	−1.50708	+	0.576335i
$573$	−2.06814	+	2.06814i	−0.0863977	+	0.0863977i
$574$	−15.0747	+	15.0747i	−0.629205	+	0.629205i
$575$	−7.87666	+	7.51450i	−0.328480	+	0.313376i
$576$		−	12.8861i		−	0.536919i
$577$		−	17.7281i		−	0.738030i	−0.929423	−	0.369015i	$-0.879695\pi$
$577$		−	17.7281i		−	0.738030i	0.929423	−	0.369015i	$-0.120305\pi$
$578$	−20.2992			−0.844336
$579$	14.6355	+	14.6355i	0.608230	+	0.608230i
$580$	−38.3377	−	39.2504i	−1.59189	−	1.62979i
$581$	18.4844			0.766864
$582$	−27.6051	+	27.6051i	−1.14427	+	1.14427i
$583$			27.5891i			1.14262i
$584$	−10.7559			−0.445083
$585$	2.79099	+	7.56375i	0.115393	+	0.312723i
$586$	13.1191			0.541944
$587$		−	33.3826i		−	1.37785i	−0.724834	−	0.688924i	$-0.758083\pi$
$587$		−	33.3826i		−	1.37785i	0.724834	−	0.688924i	$-0.241917\pi$
$588$	−20.4702	+	20.4702i	−0.844179	+	0.844179i
$589$	11.6693			0.480825
$590$	0.537063	−	45.6544i	0.0221105	−	1.87956i
$591$	−4.35720	−	4.35720i	−0.179231	−	0.179231i
$592$	10.3343			0.424738
$593$		−	26.1087i		−	1.07216i	−0.844169	−	0.536078i	$-0.819905\pi$
$593$		−	26.1087i		−	1.07216i	0.844169	−	0.536078i	$-0.180095\pi$
$594$			8.13287i			0.333696i
$595$	−0.303066	+	25.7629i	−0.0124245	+	1.05618i
$596$	−19.0802	+	19.0802i	−0.781555	+	0.781555i
$597$	16.4668	−	16.4668i	0.673942	−	0.673942i
$598$	−16.2615	+	6.21872i	−0.664984	+	0.254302i
$599$		−	1.98183i		−	0.0809755i	−0.999180	−	0.0404877i	$-0.987109\pi$
$599$		−	1.98183i		−	0.0809755i	0.999180	−	0.0404877i	$-0.0128912\pi$
$600$	−7.37046	+	7.03158i	−0.300898	+	0.287063i
$601$	−7.83403			−0.319557			−0.159778	−	0.987153i	$-0.551078\pi$
$601$	−7.83403			−0.319557			−0.159778	+	0.987153i	$0.551078\pi$
$602$	11.6029	−	11.6029i	0.472897	−	0.472897i
$603$	−12.3496			−0.502914
$604$	−7.47650	+	7.47650i	−0.304214	+	0.304214i
$605$	−3.82419	−	3.91523i	−0.155475	−	0.159177i
$606$	−7.31781	+	7.31781i	−0.297266	+	0.297266i
$607$	15.2335	+	15.2335i	0.618309	+	0.618309i	0.945098	−	0.326788i	$-0.105966\pi$
$607$	15.2335	+	15.2335i	0.618309	+	0.618309i	−0.326788	+	0.945098i	$0.605966\pi$
$608$	−19.3253	−	19.3253i	−0.783745	−	0.783745i
$609$	24.4522	+	24.4522i	0.990852	+	0.990852i
$610$	27.1972	+	27.8447i	1.10118	+	1.12740i
$611$	20.9071	+	9.34003i	0.845811	+	0.377857i
$612$	−5.78120	−	5.78120i	−0.233691	−	0.233691i
$613$	−34.9526			−1.41172			−0.705862	−	0.708349i	$-0.749440\pi$
$613$	−34.9526			−1.41172			−0.705862	+	0.708349i	$0.749440\pi$
$614$		−	6.24821i		−	0.252157i
$615$	3.73831	−	3.65138i	0.150743	−	0.147238i
$616$	21.7296	+	21.7296i	0.875510	+	0.875510i
$617$			12.6145i			0.507842i	0.967225	+	0.253921i	$0.0817204\pi$
$617$			12.6145i			0.507842i	−0.967225	+	0.253921i	$0.918280\pi$
$618$			6.52658i			0.262538i
$619$	−21.5568	−	21.5568i	−0.866442	−	0.866442i	0.125635	−	0.992077i	$-0.459903\pi$
$619$	−21.5568	−	21.5568i	−0.866442	−	0.866442i	−0.992077	+	0.125635i	$0.959903\pi$
$620$	−19.5035	−	0.229433i	−0.783280	−	0.00921423i
$621$			2.17724i			0.0873697i
$622$	20.3609			0.816396
$623$	36.6854	+	36.6854i	1.46977	+	1.46977i
$624$	4.44161	−	1.69855i	0.177807	−	0.0679966i
$625$	−24.9723	−	1.17588i	−0.998893	−	0.0470351i
$626$	36.5672	+	36.5672i	1.46152	+	1.46152i
$627$	10.1245	+	10.1245i	0.404332	+	0.404332i
$628$	8.54565	+	8.54565i	0.341009	+	0.341009i
$629$	15.5208	−	15.5208i	0.618856	−	0.618856i
$630$	14.5924	−	14.2530i	0.581374	−	0.567855i
$631$	−25.2174	+	25.2174i	−1.00389	+	1.00389i	−0.00389463	+	0.999992i	$0.501240\pi$
$631$	−25.2174	+	25.2174i	−1.00389	+	1.00389i	−0.999992	+	0.00389463i	$0.998760\pi$
$632$	17.2263			0.685226
$633$	8.25804	−	8.25804i	0.328228	−	0.328228i
$634$	−29.6820			−1.17882
$635$	0.161158	−	13.6996i	0.00639534	−	0.543653i
$636$			21.9580i			0.870693i
$637$	−32.6526	−	14.5872i	−1.29374	−	0.577966i
$638$	48.3478	−	48.3478i	1.91411	−	1.91411i
$639$	−7.75627	+	7.75627i	−0.306833	+	0.306833i
$640$	22.7792	+	23.3215i	0.900427	+	0.921863i
$641$			15.3670i			0.606961i	0.952838	+	0.303481i	$0.0981487\pi$
$641$			15.3670i			0.606961i	−0.952838	+	0.303481i	$0.901851\pi$
$642$			5.37002i			0.211938i
$643$	5.80970			0.229112			0.114556	−	0.993417i	$-0.463455\pi$
$643$	5.80970			0.229112			0.114556	+	0.993417i	$0.463455\pi$
$644$	18.4822	+	18.4822i	0.728302	+	0.728302i
$645$	−2.87735	+	2.81044i	−0.113295	+	0.110661i
$646$	−24.2573			−0.954389
$647$	−21.0666	+	21.0666i	−0.828212	+	0.828212i	−0.987269	−	0.159057i	$-0.949155\pi$
$647$	−21.0666	+	21.0666i	−0.828212	+	0.828212i	0.159057	+	0.987269i	$0.449155\pi$
$648$			2.03732i			0.0800335i
$649$	33.7620			1.32528
$650$	−36.1110	−	17.1623i	−1.41639	−	0.673162i
$651$	12.2932			0.481808
$652$			24.7919i			0.970926i
$653$	−9.40721	+	9.40721i	−0.368132	+	0.368132i	−0.866796	−	0.498663i	$-0.833824\pi$
$653$	−9.40721	+	9.40721i	−0.368132	+	0.368132i	0.498663	+	0.866796i	$0.333824\pi$
$654$	−14.9836			−0.585904
$655$	−18.8190	+	18.3814i	−0.735319	+	0.718220i
$656$	−2.17946	−	2.17946i	−0.0850935	−	0.0850935i
$657$	−5.27944			−0.205971
$658$		−	57.9353i		−	2.25855i
$659$		−	2.27833i		−	0.0887510i	−0.999015	−	0.0443755i	$-0.985870\pi$
$659$		−	2.27833i		−	0.0887510i	0.999015	−	0.0443755i	$-0.0141298\pi$
$660$	−16.7225	−	17.1206i	−0.650922	−	0.666419i
$661$	22.0600	−	22.0600i	0.858036	−	0.858036i	−0.133071	−	0.991107i	$-0.542484\pi$
$661$	22.0600	−	22.0600i	0.858036	−	0.858036i	0.991107	+	0.133071i	$0.0424837\pi$
$662$	30.5675	−	30.5675i	1.18804	−	1.18804i
$663$	4.11972	−	9.22174i	0.159996	−	0.358143i
$664$		−	9.15547i		−	0.355301i
$665$	0.422423	−	35.9091i	0.0163808	−	1.39250i
$666$	−17.3779			−0.673379
$667$	12.9431	−	12.9431i	0.501160	−	0.501160i
$668$	−38.6889			−1.49692
$669$	−11.8761	+	11.8761i	−0.459158	+	0.459158i
$670$	43.8121	−	42.7933i	1.69261	−	1.65325i
$671$	−20.3521	+	20.3521i	−0.785682	+	0.785682i
$672$	−20.3586	−	20.3586i	−0.785348	−	0.785348i
$673$	−24.7463	−	24.7463i	−0.953900	−	0.953900i	0.0450834	−	0.998983i	$-0.485645\pi$
$673$	−24.7463	−	24.7463i	−0.953900	−	0.953900i	−0.998983	+	0.0450834i	$0.985645\pi$
$674$	−55.0069	−	55.0069i	−2.11879	−	2.11879i
$675$	−3.61773	+	3.45139i	−0.139246	+	0.132844i
$676$	−25.3171	−	28.2604i	−0.973734	−	1.08694i
$677$	−11.5334	−	11.5334i	−0.443265	−	0.443265i	0.449843	−	0.893108i	$-0.351480\pi$
$677$	−11.5334	−	11.5334i	−0.443265	−	0.443265i	−0.893108	+	0.449843i	$0.851480\pi$
$678$	−6.11671			−0.234911
$679$			72.4049i			2.77865i
$680$	12.7605	+	0.150111i	0.489345	+	0.00575648i
$681$	−15.7194	−	15.7194i	−0.602367	−	0.602367i
$682$		−	24.3066i		−	0.930747i
$683$		−	33.8458i		−	1.29507i	−0.762035	−	0.647536i	$-0.775800\pi$
$683$		−	33.8458i		−	1.29507i	0.762035	−	0.647536i	$-0.224200\pi$
$684$	8.05801	+	8.05801i	0.308106	+	0.308106i
$685$	19.7824	−	19.3223i	0.755845	−	0.738269i
$686$			26.6265i			1.01660i
$687$	2.82760			0.107880
$688$	1.67751	+	1.67751i	0.0639545	+	0.0639545i
$689$	−25.3366	+	9.68921i	−0.965248	+	0.369129i
$690$	−7.54448	−	7.72409i	−0.287213	−	0.294051i
$691$	13.6461	+	13.6461i	0.519121	+	0.519121i	0.917305	−	0.398185i	$-0.130360\pi$
$691$	13.6461	+	13.6461i	0.519121	+	0.519121i	−0.398185	+	0.917305i	$0.630360\pi$
$692$	23.1891	+	23.1891i	0.881518	+	0.881518i
$693$	10.6658	+	10.6658i	0.405159	+	0.405159i
$694$	−4.98395	+	4.98395i	−0.189188	+	0.189188i
$695$	23.7067	+	24.2711i	0.899246	+	0.920655i
$696$	12.1113	−	12.1113i	0.459079	−	0.459079i
$697$	−6.54654			−0.247968
$698$	42.7546	−	42.7546i	1.61829	−	1.61829i
$699$	−10.7537			−0.406742
$700$	−1.41203	+	60.0085i	−0.0533699	+	2.26811i
$701$		−	36.0430i		−	1.36133i	−0.732597	−	0.680663i	$-0.761692\pi$
$701$		−	36.0430i		−	1.36133i	0.732597	−	0.680663i	$-0.238308\pi$
$702$	−7.46887	+	2.85624i	−0.281894	+	0.107802i
$703$	−21.6334	+	21.6334i	−0.815919	+	0.815919i
$704$	−33.4139	+	33.4139i	−1.25933	+	1.25933i
$705$	−0.167045	+	14.2001i	−0.00629128	+	0.534807i
$706$			45.6533i			1.71819i
$707$			19.1937i			0.721855i
$708$	26.8710			1.00988
$709$	11.7237	+	11.7237i	0.440292	+	0.440292i	0.892110	−	0.451818i	$-0.149224\pi$
$709$	11.7237	+	11.7237i	0.440292	+	0.440292i	−0.451818	+	0.892110i	$0.649224\pi$
$710$	0.639863	−	54.3932i	0.0240136	−	2.04134i
$711$	8.45538			0.317102
$712$	18.1705	−	18.1705i	0.680970	−	0.680970i
$713$		−	6.50708i		−	0.243692i
$714$	−25.5542			−0.956341
$715$	12.3759	−	26.8501i	0.462833	−	1.00414i
$716$	−4.01692			−0.150119
$717$		−	24.3476i		−	0.909279i
$718$	23.5152	−	23.5152i	0.877578	−	0.877578i
$719$	15.7258			0.586474			0.293237	−	0.956040i	$-0.405267\pi$
$719$	15.7258			0.586474			0.293237	+	0.956040i	$0.405267\pi$
$720$	2.06067	+	2.10973i	0.0767965	+	0.0786248i
$721$	8.55922	+	8.55922i	0.318762	+	0.318762i
$722$	−8.32765			−0.309923
$723$		−	14.4469i		−	0.537288i
$724$		−	68.4963i		−	2.54565i
$725$	42.0240	+	0.988848i	1.56073	+	0.0367249i
$726$	3.83835	−	3.83835i	0.142455	−	0.142455i
$727$	29.7923	−	29.7923i	1.10494	−	1.10494i	0.111131	−	0.993806i	$-0.464553\pi$
$727$	29.7923	−	29.7923i	1.10494	−	1.10494i	0.993806	−	0.111131i	$-0.0354474\pi$
$728$	−12.3241	+	27.5868i	−0.456763	+	1.02244i
$729$			1.00000i			0.0370370i
$730$	18.7296	−	18.2941i	0.693214	−	0.677095i
$731$	5.03881			0.186367
$732$	−16.1981	+	16.1981i	−0.598699	+	0.598699i
$733$	21.4923			0.793836			0.396918	−	0.917854i	$-0.370080\pi$
$733$	21.4923			0.793836			0.396918	+	0.917854i	$0.370080\pi$
$734$	2.27399	−	2.27399i	0.0839344	−	0.0839344i
$735$	0.260890	−	22.1776i	0.00962307	−	0.818034i
$736$	−10.7763	+	10.7763i	−0.397219	+	0.397219i
$737$	32.0229	+	32.0229i	1.17958	+	1.17958i
$738$	3.66491	+	3.66491i	0.134907	+	0.134907i
$739$	0.314385	+	0.314385i	0.0115649	+	0.0115649i	0.712866	−	0.701301i	$-0.247397\pi$
$739$	0.314385	+	0.314385i	0.0115649	+	0.0115649i	−0.701301	+	0.712866i	$0.747397\pi$
$740$	36.5824	−	35.7317i	1.34479	−	1.31352i
$741$	−5.74218	+	12.8535i	−0.210944	+	0.472186i
$742$	48.5297	+	48.5297i	1.78158	+	1.78158i
$743$	−22.1368			−0.812122			−0.406061	−	0.913846i	$-0.633098\pi$
$743$	−22.1368			−0.812122			−0.406061	+	0.913846i	$0.633098\pi$
$744$		−	6.08890i		−	0.223230i
$745$	0.243174	−	20.6716i	0.00890920	−	0.757350i
$746$	18.6642	+	18.6642i	0.683347	+	0.683347i
$747$		−	4.49388i		−	0.164422i
$748$			29.9816i			1.09624i
$749$	7.04245	+	7.04245i	0.257326	+	0.257326i
$750$	0.874843	−	24.7803i	0.0319448	−	0.904848i
$751$			0.516848i			0.0188600i	0.999956	+	0.00943002i	$0.00300171\pi$
$751$			0.516848i			0.0188600i	−0.999956	+	0.00943002i	$0.996998\pi$
$752$	8.37613			0.305446
$753$	13.2635	+	13.2635i	0.483348	+	0.483348i
$754$	61.3800	+	27.4209i	2.23533	+	0.998609i
$755$	0.0952867	−	8.10010i	0.00346784	−	0.294793i
$756$	8.48883	+	8.48883i	0.308736	+	0.308736i
$757$	−24.0375	−	24.0375i	−0.873657	−	0.873657i	0.119212	−	0.992869i	$-0.461963\pi$
$757$	−24.0375	−	24.0375i	−0.873657	−	0.873657i	−0.992869	+	0.119212i	$0.961963\pi$
$758$	11.1679	+	11.1679i	0.405635	+	0.405635i
$759$	5.64565	−	5.64565i	0.204924	−	0.204924i
$760$	−17.7860	−	0.209229i	−0.645167	−	0.00758952i
$761$	−36.2711	+	36.2711i	−1.31483	+	1.31483i	−0.397015	+	0.917812i	$0.629954\pi$
$761$	−36.2711	+	36.2711i	−1.31483	+	1.31483i	−0.917812	+	0.397015i	$0.870046\pi$
$762$	13.5886			0.492264
$763$	−19.6500	+	19.6500i	−0.711379	+	0.711379i
$764$	8.53636			0.308835
$765$	6.26340	+	0.0736805i	0.226454	+	0.00266392i
$766$		−	1.07243i		−	0.0387486i
$767$	11.8571	+	31.0055i	0.428136	+	1.11955i
$768$	−4.63995	+	4.63995i	−0.167430	+	0.167430i
$769$	−5.51342	+	5.51342i	−0.198819	+	0.198819i	−0.799494	−	0.600675i	$-0.794899\pi$
$769$	−5.51342	+	5.51342i	−0.198819	+	0.198819i	0.600675	+	0.799494i	$0.294899\pi$
$770$	−74.7970	−	0.879886i	−2.69550	−	0.0317089i
$771$		−	1.98101i		−	0.0713442i
$772$		−	60.4088i		−	2.17416i
$773$	−37.1946			−1.33780			−0.668899	−	0.743353i	$-0.733234\pi$
$773$	−37.1946			−1.33780			−0.668899	+	0.743353i	$0.733234\pi$
$774$	−2.82085	−	2.82085i	−0.101393	−	0.101393i
$775$	10.8122	−	10.3151i	0.388387	−	0.370529i
$776$	35.8627			1.28739
$777$	−22.7900	+	22.7900i	−0.817587	+	0.817587i
$778$		−	39.0208i		−	1.39896i
$779$	9.12476			0.326928
$780$	9.84992	−	21.3699i	0.352684	−	0.765165i
$781$	40.2244			1.43934
$782$			13.5264i			0.483705i
$783$	5.94473	−	5.94473i	0.212447	−	0.212447i
$784$	−13.0818			−0.467207
$785$	−9.25843	−	0.108913i	−0.330447	−	0.00388727i
$786$	−18.4495	−	18.4495i	−0.658071	−	0.658071i
$787$	−16.6120			−0.592154			−0.296077	−	0.955164i	$-0.595679\pi$
$787$	−16.6120			−0.592154			−0.296077	+	0.955164i	$0.595679\pi$
$788$			17.9846i			0.640674i
$789$		−	22.4552i		−	0.799425i
$790$	−29.9967	+	29.2992i	−1.06724	+	1.04242i
$791$	−8.02169	+	8.02169i	−0.285219	+	0.285219i
$792$	5.28283	−	5.28283i	0.187717	−	0.187717i
$793$	−25.8380	−	11.5428i	−0.917534	−	0.409899i
$794$		−	21.3753i		−	0.758582i
$795$	−11.7548	−	12.0347i	−0.416901	−	0.426826i
$796$	−67.9677			−2.40905
$797$	−23.0821	+	23.0821i	−0.817611	+	0.817611i	−0.985761	−	0.168150i	$-0.946221\pi$
$797$	−23.0821	+	23.0821i	−0.817611	+	0.817611i	0.168150	+	0.985761i	$0.446221\pi$
$798$	35.6182			1.26087
$799$	12.5799	−	12.5799i	0.445044	−	0.445044i
$800$	−34.9886	−	0.823302i	−1.23703	−	0.0291081i
$801$	8.91884	−	8.91884i	0.315132	−	0.315132i
$802$	−37.4328	−	37.4328i	−1.32180	−	1.32180i
$803$	13.6897	+	13.6897i	0.483101	+	0.483101i
$804$	25.4868	+	25.4868i	0.898851	+	0.898851i
$805$	−20.0238	−	0.235553i	−0.705746	−	0.00830216i
$806$	22.3221	−	8.53639i	0.786262	−	0.300681i
$807$	−0.246971	−	0.246971i	−0.00869377	−	0.00869377i
$808$	9.50678			0.334448
$809$		−	10.9372i		−	0.384533i	−0.981343	−	0.192267i	$-0.938416\pi$
$809$		−	10.9372i		−	0.384533i	0.981343	−	0.192267i	$-0.0615838\pi$
$810$	−3.46515	−	3.54765i	−0.121753	−	0.124652i
$811$	17.0726	+	17.0726i	0.599501	+	0.599501i	0.940180	−	0.340679i	$-0.110657\pi$
$811$	17.0726	+	17.0726i	0.599501	+	0.599501i	−0.340679	+	0.940180i	$0.610657\pi$
$812$		−	100.928i		−	3.54187i
$813$		−	12.0511i		−	0.422649i
$814$	45.0613	+	45.0613i	1.57940	+	1.57940i
$815$	−13.2719	−	13.5879i	−0.464894	−	0.475962i
$816$		−	3.69456i		−	0.129335i
$817$	−7.02325			−0.245712
$818$	8.10707	+	8.10707i	0.283457	+	0.283457i
$819$	−6.04919	+	13.5408i	−0.211376	+	0.473152i
$820$	−15.2507	−	0.179404i	−0.532577	−	0.00626506i
$821$	−7.58466	−	7.58466i	−0.264706	−	0.264706i	0.562256	−	0.826963i	$-0.309933\pi$
$821$	−7.58466	−	7.58466i	−0.264706	−	0.264706i	−0.826963	+	0.562256i	$0.809933\pi$
$822$	19.3939	+	19.3939i	0.676441	+	0.676441i
$823$	−20.2348	−	20.2348i	−0.705341	−	0.705341i	0.260211	−	0.965552i	$-0.416208\pi$
$823$	−20.2348	−	20.2348i	−0.705341	−	0.705341i	−0.965552	+	0.260211i	$0.916208\pi$
$824$	4.23944	−	4.23944i	0.147688	−	0.147688i
$825$	18.3304	+	0.431325i	0.638183	+	0.0150168i
$826$	59.3879	−	59.3879i	2.06637	−	2.06637i
$827$	−0.322011			−0.0111974			−0.00559871	−	0.999984i	$-0.501782\pi$
$827$	−0.322011			−0.0111974			−0.00559871	+	0.999984i	$0.501782\pi$
$828$	4.49334	−	4.49334i	0.156155	−	0.156155i
$829$	−2.29166			−0.0795925			−0.0397963	−	0.999208i	$-0.512671\pi$
$829$	−2.29166			−0.0795925			−0.0397963	+	0.999208i	$0.512671\pi$
$830$	15.5720	+	15.9427i	0.540511	+	0.553380i
$831$			7.46240i			0.258868i
$832$	−42.4207	−	18.9510i	−1.47067	−	0.657007i
$833$	−19.6472	+	19.6472i	−0.680735	+	0.680735i
$834$	−23.7945	+	23.7945i	−0.823937	+	0.823937i
$835$	21.2045	−	20.7114i	0.733812	−	0.716748i
$836$		−	41.7893i		−	1.44531i
$837$		−	2.98868i		−	0.103304i
$838$	−75.2766			−2.60039
$839$	−0.488256	−	0.488256i	−0.0168565	−	0.0168565i	0.698628	−	0.715485i	$-0.253794\pi$
$839$	−0.488256	−	0.488256i	−0.0168565	−	0.0168565i	−0.715485	+	0.698628i	$0.753794\pi$
$840$	−18.7370	−	0.220415i	−0.646487	−	0.00760505i
$841$	−41.6797			−1.43723
$842$	43.7067	−	43.7067i	1.50623	−	1.50623i
$843$			8.46378i			0.291508i
$844$	−34.0855			−1.17327
$845$	29.0044	+	1.93580i	0.997780	+	0.0665937i
$846$	−14.0850			−0.484254
$847$		−	10.0675i		−	0.345925i
$848$	−7.01629	+	7.01629i	−0.240940	+	0.240940i
$849$	−3.62285			−0.124336
$850$	−22.4757	+	21.4423i	−0.770909	+	0.735463i
$851$	12.0633	+	12.0633i	0.413525	+	0.413525i
$852$	32.0144			1.09680
$853$			2.53904i			0.0869352i	0.999055	+	0.0434676i	$0.0138405\pi$
$853$			2.53904i			0.0869352i	−0.999055	+	0.0434676i	$0.986159\pi$
$854$			71.5992i			2.45007i
$855$	−8.73011	−	0.102698i	−0.298564	−	0.00351220i
$856$	3.48817	−	3.48817i	0.119223	−	0.119223i
$857$	3.15552	−	3.15552i	0.107791	−	0.107791i	−0.651155	−	0.758945i	$-0.725715\pi$
$857$	3.15552	−	3.15552i	0.107791	−	0.107791i	0.758945	+	0.651155i	$0.225715\pi$
$858$	26.7733	+	11.9607i	0.914025	+	0.408331i
$859$		−	36.8208i		−	1.25631i	−0.778088	−	0.628155i	$-0.783810\pi$
$859$		−	36.8208i		−	1.25631i	0.778088	−	0.628155i	$-0.216190\pi$
$860$	11.7383	+	0.138086i	0.400274	+	0.00470868i
$861$	9.61261			0.327597
$862$	−23.8780	+	23.8780i	−0.813288	+	0.813288i
$863$	−11.3029			−0.384754			−0.192377	−	0.981321i	$-0.561620\pi$
$863$	−11.3029			−0.384754			−0.192377	+	0.981321i	$0.561620\pi$
$864$	−4.94951	+	4.94951i	−0.168386	+	0.168386i
$865$	−25.1233	−	0.295542i	−0.854217	−	0.0100487i
$866$	−26.2864	+	26.2864i	−0.893248	+	0.893248i
$867$	6.47206	+	6.47206i	0.219803	+	0.219803i
$868$	−25.3704	−	25.3704i	−0.861129	−	0.861129i
$869$	−21.9250	−	21.9250i	−0.743756	−	0.743756i
$870$	−0.490418	+	41.6893i	−0.0166267	+	1.41340i
$871$	−18.1620	+	40.6547i	−0.615397	+	1.37753i
$872$	9.73279	+	9.73279i	0.329594	+	0.329594i
$873$	17.6029			0.595767
$874$		−	18.8536i		−	0.637731i
$875$	−31.3505	−	33.6451i	−1.05984	−	1.13741i
$876$	10.8956	+	10.8956i	0.368128	+	0.368128i
$877$			11.1316i			0.375889i	0.982180	+	0.187944i	$0.0601824\pi$
$877$			11.1316i			0.375889i	−0.982180	+	0.187944i	$0.939818\pi$
$878$			4.48487i			0.151357i
$879$	−4.18280	−	4.18280i	−0.141082	−	0.141082i
$880$	0.127212	−	10.8139i	0.00428830	−	0.364538i
$881$		−	25.7462i		−	0.867410i	−0.901055	−	0.433705i	$-0.857206\pi$
$881$		−	25.7462i		−	0.867410i	0.901055	−	0.433705i	$-0.142794\pi$
$882$	21.9979			0.740709
$883$	−3.65379	−	3.65379i	−0.122960	−	0.122960i	0.642949	−	0.765909i	$-0.277711\pi$
$883$	−3.65379	−	3.65379i	−0.122960	−	0.122960i	−0.765909	+	0.642949i	$0.777711\pi$
$884$	−27.5338	+	10.5295i	−0.926062	+	0.354144i
$885$	−14.7274	+	14.3849i	−0.495055	+	0.483543i
$886$	0.282539	+	0.282539i	0.00949208	+	0.00949208i
$887$	−9.40170	−	9.40170i	−0.315678	−	0.315678i	0.531426	−	0.847105i	$-0.321656\pi$
$887$	−9.40170	−	9.40170i	−0.315678	−	0.315678i	−0.847105	+	0.531426i	$0.821656\pi$
$888$	11.2880	+	11.2880i	0.378802	+	0.378802i
$889$	17.8206	−	17.8206i	0.597685	−	0.597685i
$890$	−0.735771	+	62.5461i	−0.0246631	+	2.09655i
$891$	2.59303	−	2.59303i	0.0868697	−	0.0868697i
$892$	49.0194			1.64129
$893$	−17.5342	+	17.5342i	−0.586760	+	0.586760i
$894$	20.5041			0.685761
$895$	2.20158	−	2.15038i	0.0735907	−	0.0718794i
$896$			59.9684i			2.00340i
$897$	7.16745	+	3.20198i	0.239314	+	0.106911i
$898$	−55.1434	+	55.1434i	−1.84016	+	1.84016i
$899$	−17.7669	+	17.7669i	−0.592560	+	0.592560i
$900$	14.5891	+	0.343289i	0.486303	+	0.0114430i
$901$			21.0752i			0.702115i
$902$		−	19.0064i		−	0.632845i
$903$	−7.39875			−0.246215
$904$	3.97320	+	3.97320i	0.132147	+	0.132147i
$905$	36.6682	+	37.5412i	1.21889	+	1.24791i
$906$	8.03446			0.266927
$907$	0.772139	−	0.772139i	0.0256384	−	0.0256384i	−0.694171	−	0.719810i	$-0.744229\pi$
$907$	0.772139	−	0.772139i	0.0256384	−	0.0256384i	0.719810	+	0.694171i	$0.244229\pi$
$908$			64.8825i			2.15320i
$909$	4.66632			0.154772
$910$	−25.4604	−	68.9992i	−0.844004	−	2.28730i
$911$	−6.21262			−0.205833			−0.102917	−	0.994690i	$-0.532818\pi$
$911$	−6.21262			−0.205833			−0.102917	+	0.994690i	$0.532818\pi$
$912$			5.14958i			0.170520i
$913$	−11.6528	+	11.6528i	−0.385650	+	0.385650i
$914$	−71.6388			−2.36960
$915$	0.206442	−	17.5491i	0.00682477	−	0.580157i
$916$	−5.83555	−	5.83555i	−0.192812	−	0.192812i
$917$	−48.3907			−1.59800
$918$			6.21265i			0.205048i
$919$		−	29.9003i		−	0.986320i	−0.869939	−	0.493160i	$-0.835842\pi$
$919$		−	29.9003i		−	0.986320i	0.869939	−	0.493160i	$-0.164158\pi$
$920$	−0.116671	+	9.91792i	−0.00384653	+	0.326984i
$921$	−1.99213	+	1.99213i	−0.0656431	+	0.0656431i
$922$	32.2980	−	32.2980i	1.06368	−	1.06368i
$923$	14.1267	+	36.9403i	0.464986	+	1.21591i
$924$		−	44.0236i		−	1.44827i
$925$	−0.921631	+	39.1674i	−0.0303030	+	1.28782i
$926$	29.4345			0.967278
$927$	2.08089	−	2.08089i	0.0683454	−	0.0683454i
$928$	58.8470			1.93175
$929$	−16.4364	+	16.4364i	−0.539260	+	0.539260i	−0.923312	−	0.384052i	$-0.874528\pi$
$929$	−16.4364	+	16.4364i	−0.539260	+	0.539260i	0.384052	+	0.923312i	$0.374528\pi$
$930$	10.3562	+	10.6028i	0.339595	+	0.347680i
$931$	27.3848	−	27.3848i	0.897501	−	0.897501i
$932$	22.1933	+	22.1933i	0.726964	+	0.726964i
$933$	−6.49171	−	6.49171i	−0.212529	−	0.212529i
$934$	−47.9281	−	47.9281i	−1.56826	−	1.56826i
$935$	−16.0501	−	16.4322i	−0.524895	−	0.537391i
$936$	6.70683	+	2.99620i	0.219219	+	0.0979339i
$937$	15.7357	+	15.7357i	0.514064	+	0.514064i	0.915769	−	0.401705i	$-0.131582\pi$
$937$	15.7357	+	15.7357i	0.514064	+	0.514064i	−0.401705	+	0.915769i	$0.631582\pi$
$938$	112.657			3.67839
$939$		−	23.3176i		−	0.760942i
$940$	29.6506	−	28.9611i	0.967096	−	0.944607i
$941$	−6.42421	−	6.42421i	−0.209423	−	0.209423i	0.594599	−	0.804022i	$-0.297311\pi$
$941$	−6.42421	−	6.42421i	−0.209423	−	0.209423i	−0.804022	+	0.594599i	$0.797311\pi$
$942$		−	9.18341i		−	0.299212i
$943$		−	5.08819i		−	0.165694i
$944$	8.58615	+	8.58615i	0.279455	+	0.279455i
$945$	−9.19687	−	0.108189i	−0.299174	−	0.00351938i
$946$			14.6291i			0.475633i
$947$	−12.4887			−0.405827			−0.202914	−	0.979197i	$-0.565041\pi$
$947$	−12.4887			−0.405827			−0.202914	+	0.979197i	$0.565041\pi$
$948$	−17.4500	−	17.4500i	−0.566751	−	0.566751i
$949$	−7.76426	+	17.3799i	−0.252039	+	0.564174i
$950$	31.3272	−	29.8868i	1.01639	−	0.969657i
$951$	9.46360	+	9.46360i	0.306878	+	0.306878i
$952$	16.5991	+	16.5991i	0.537980	+	0.537980i
$953$	30.2555	+	30.2555i	0.980072	+	0.980072i	0.999805	−	0.0197332i	$-0.00628169\pi$
$953$	30.2555	+	30.2555i	0.980072	+	0.980072i	−0.0197332	+	0.999805i	$0.506282\pi$
$954$	11.7984	−	11.7984i	0.381987	−	0.381987i
$955$	−4.67858	+	4.56978i	−0.151395	+	0.147875i
$956$	−50.2481	+	50.2481i	−1.62514	+	1.62514i
$957$	−30.8297			−0.996583
$958$	30.1602	−	30.1602i	0.974431	−	0.974431i
$959$	50.8679			1.64261
$960$	0.338936	−	28.8121i	0.0109391	−	0.929906i
$961$		−	22.0678i		−	0.711864i
$962$	−25.5569	+	57.2077i	−0.823988	+	1.84445i
$963$	1.71214	−	1.71214i	0.0551729	−	0.0551729i
$964$	−29.8153	+	29.8153i	−0.960286	+	0.960286i
$965$	32.3387	+	33.1086i	1.04102	+	1.06580i
$966$		−	19.8616i		−	0.639035i
$967$			35.6086i			1.14510i	0.819871	+	0.572548i	$0.194045\pi$
$967$			35.6086i			1.14510i	−0.819871	+	0.572548i	$0.805955\pi$
$968$	−4.98652			−0.160273
$969$	7.73402	+	7.73402i	0.248452	+	0.248452i
$970$	−62.4488	+	60.9966i	−2.00511	+	1.95848i
$971$	−28.4165			−0.911929			−0.455964	−	0.889998i	$-0.650706\pi$
$971$	−28.4165			−0.911929			−0.455964	+	0.889998i	$0.650706\pi$
$972$	2.06378	−	2.06378i	0.0661957	−	0.0661957i
$973$			62.4102i			2.00078i
$974$	−35.7127			−1.14431
$975$	6.04147	+	16.9853i	0.193482	+	0.543965i
$976$	−10.3516			−0.331347
$977$		−	42.8927i		−	1.37226i	−0.727479	−	0.686130i	$-0.759308\pi$
$977$		−	42.8927i		−	1.37226i	0.727479	−	0.686130i	$-0.240692\pi$
$978$	13.3211	−	13.3211i	0.425960	−	0.425960i
$979$	−46.2536			−1.47827
$980$	−46.3081	+	45.2313i	−1.47926	+	1.44486i
$981$	4.77725	+	4.77725i	0.152526	+	0.152526i
$982$	45.9446			1.46615
$983$		−	39.1642i		−	1.24914i	−0.780967	−	0.624572i	$-0.785273\pi$
$983$		−	39.1642i		−	1.24914i	0.780967	−	0.624572i	$-0.214727\pi$
$984$		−	4.76119i		−	0.151781i
$985$	−9.62772	−	9.85693i	−0.306765	−	0.314068i
$986$	36.9326	−	36.9326i	1.17617	−	1.17617i
$987$	−18.4717	+	18.4717i	−0.587960	+	0.587960i
$988$	38.3774	−	14.6763i	1.22095	−	0.466914i
$989$			3.91633i			0.124532i
$990$	−0.213915	+	18.1844i	−0.00679867	+	0.577938i
$991$	7.60282			0.241512			0.120756	−	0.992682i	$-0.461468\pi$
$991$	7.60282			0.241512			0.120756	+	0.992682i	$0.461468\pi$
$992$	14.7925	−	14.7925i	0.469662	−	0.469662i
$993$	−19.4918			−0.618555
$994$	70.7554	−	70.7554i	2.24422	−	2.24422i
$995$	37.2515	−	36.3853i	1.18095	−	1.15349i
$996$	−9.27437	+	9.27437i	−0.293870	+	0.293870i
$997$	−1.06259	−	1.06259i	−0.0336527	−	0.0336527i	0.690080	−	0.723733i	$-0.257575\pi$
$997$	−1.06259	−	1.06259i	−0.0336527	−	0.0336527i	−0.723733	+	0.690080i	$0.757575\pi$
$998$	9.08715	+	9.08715i	0.287649	+	0.287649i
$999$	5.54064	+	5.54064i	0.175298	+	0.175298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.k.a.112.13	✓	28
3.2	odd	2		585.2.n.g.307.2		28
5.2	odd	4		975.2.t.d.268.2		28
5.3	odd	4		195.2.t.a.73.13	yes	28
5.4	even	2		975.2.k.d.307.2		28
13.5	odd	4		195.2.t.a.187.13	yes	28
15.8	even	4		585.2.w.g.73.2		28
39.5	even	4		585.2.w.g.577.2		28
65.18	even	4	inner	195.2.k.a.148.2	yes	28
65.44	odd	4		975.2.t.d.382.2		28
65.57	even	4		975.2.k.d.343.13		28
195.83	odd	4		585.2.n.g.343.13		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.13	✓	28	1.1	even	1	trivial
195.2.k.a.148.2	yes	28	65.18	even	4	inner
195.2.t.a.73.13	yes	28	5.3	odd	4
195.2.t.a.187.13	yes	28	13.5	odd	4
585.2.n.g.307.2		28	3.2	odd	2
585.2.n.g.343.13		28	195.83	odd	4
585.2.w.g.73.2		28	15.8	even	4
585.2.w.g.577.2		28	39.5	even	4
975.2.k.d.307.2		28	5.4	even	2
975.2.k.d.343.13		28	65.57	even	4
975.2.t.d.268.2		28	5.2	odd	4
975.2.t.d.382.2		28	65.44	odd	4

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.21780i q^{2} +(0.707107 - 0.707107i) q^{3} -2.91862 q^{4} +(1.59963 - 1.56243i) q^{5} +(1.56822 + 1.56822i) q^{6} +4.11325 q^{7} -2.03732i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+2.21780i q^{2} +(0.707107 - 0.707107i) q^{3} -2.91862 q^{4} +(1.59963 - 1.56243i) q^{5} +(1.56822 + 1.56822i) q^{6} +4.11325 q^{7} -2.03732i q^{8} -1.00000i q^{9} +(3.46515 + 3.54765i) q^{10} +(-2.59303 + 2.59303i) q^{11} +(-2.06378 + 2.06378i) q^{12} +(-3.29198 - 1.47066i) q^{13} +9.12235i q^{14} +(0.0263025 - 2.23591i) q^{15} -1.31889 q^{16} +(-1.98080 + 1.98080i) q^{17} +2.21780 q^{18} +(2.76089 - 2.76089i) q^{19} +(-4.66871 + 4.56015i) q^{20} +(2.90851 - 2.90851i) q^{21} +(-5.75081 - 5.75081i) q^{22} +(-1.53954 - 1.53954i) q^{23} +(-1.44060 - 1.44060i) q^{24} +(0.117620 - 4.99862i) q^{25} +(3.26162 - 7.30095i) q^{26} +(-0.707107 - 0.707107i) q^{27} -12.0050 q^{28} +8.40712i q^{29} +(4.95880 + 0.0583336i) q^{30} +(2.11332 + 2.11332i) q^{31} -6.99966i q^{32} +3.66710i q^{33} +(-4.39301 - 4.39301i) q^{34} +(6.57967 - 6.42667i) q^{35} +2.91862i q^{36} -7.83564 q^{37} +(6.12310 + 6.12310i) q^{38} +(-3.36770 + 1.28787i) q^{39} +(-3.18317 - 3.25895i) q^{40} +(1.65250 + 1.65250i) q^{41} +(6.45048 + 6.45048i) q^{42} +(-1.27192 - 1.27192i) q^{43} +(7.56807 - 7.56807i) q^{44} +(-1.56243 - 1.59963i) q^{45} +(3.41439 - 3.41439i) q^{46} -6.35092 q^{47} +(-0.932593 + 0.932593i) q^{48} +9.91882 q^{49} +(11.0859 + 0.260858i) q^{50} +2.80127i q^{51} +(9.60806 + 4.29230i) q^{52} +(5.31987 - 5.31987i) q^{53} +(1.56822 - 1.56822i) q^{54} +(-0.0964538 + 8.19931i) q^{55} -8.38000i q^{56} -3.90449i q^{57} -18.6453 q^{58} +(-6.51015 - 6.51015i) q^{59} +(-0.0767671 + 6.52579i) q^{60} +7.84876 q^{61} +(-4.68691 + 4.68691i) q^{62} -4.11325i q^{63} +12.8861 q^{64} +(-7.56375 + 2.79099i) q^{65} -8.13287 q^{66} -12.3496i q^{67} +(5.78120 - 5.78120i) q^{68} -2.17724 q^{69} +(14.2530 + 14.5924i) q^{70} +(-7.75627 - 7.75627i) q^{71} -2.03732 q^{72} -5.27944i q^{73} -17.3779i q^{74} +(-3.45139 - 3.61773i) q^{75} +(-8.05801 + 8.05801i) q^{76} +(-10.6658 + 10.6658i) q^{77} +(-2.85624 - 7.46887i) q^{78} +8.45538i q^{79} +(-2.10973 + 2.06067i) q^{80} -1.00000 q^{81} +(-3.66491 + 3.66491i) q^{82} +4.49388 q^{83} +(-8.48883 + 8.48883i) q^{84} +(-0.0736805 + 6.26340i) q^{85} +(2.82085 - 2.82085i) q^{86} +(5.94473 + 5.94473i) q^{87} +(5.28283 + 5.28283i) q^{88} +(8.91884 + 8.91884i) q^{89} +(3.54765 - 3.46515i) q^{90} +(-13.5408 - 6.04919i) q^{91} +(4.49334 + 4.49334i) q^{92} +2.98868 q^{93} -14.0850i q^{94} +(0.102698 - 8.73011i) q^{95} +(-4.94951 - 4.94951i) q^{96} +17.6029i q^{97} +21.9979i q^{98} +(2.59303 + 2.59303i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{4} + 8 q^{5}+O(q^{10}) \) 28 * q - 28 * q^4 + 8 * q^5	\( 28 q - 28 q^{4} + 8 q^{5} - 8 q^{11} + 8 q^{12} - 12 q^{13} + 4 q^{15} + 28 q^{16} - 28 q^{17} - 4 q^{18} + 8 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{25} - 16 q^{31} + 28 q^{34} + 32 q^{37} + 8 q^{39} - 48 q^{40} + 4 q^{41} + 40 q^{44} - 4 q^{45} - 16 q^{46} - 24 q^{47} - 16 q^{48} - 28 q^{49} - 32 q^{50} + 52 q^{52} + 20 q^{53} - 8 q^{55} - 8 q^{58} + 32 q^{59} - 12 q^{60} + 8 q^{61} + 72 q^{62} - 28 q^{64} - 8 q^{65} + 16 q^{66} + 60 q^{68} + 8 q^{69} + 64 q^{70} + 40 q^{71} + 12 q^{72} - 16 q^{75} - 40 q^{76} - 48 q^{77} + 8 q^{78} - 32 q^{80} - 28 q^{81} + 4 q^{82} - 104 q^{83} - 32 q^{84} - 4 q^{85} + 16 q^{86} - 24 q^{87} + 72 q^{88} - 36 q^{89} - 12 q^{90} - 56 q^{91} - 32 q^{92} + 56 q^{95} + 8 q^{99}+O(q^{100}) \) 28 * q - 28 * q^4 + 8 * q^5 - 8 * q^11 + 8 * q^12 - 12 * q^13 + 4 * q^15 + 28 * q^16 - 28 * q^17 - 4 * q^18 + 8 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^25 - 16 * q^31 + 28 * q^34 + 32 * q^37 + 8 * q^39 - 48 * q^40 + 4 * q^41 + 40 * q^44 - 4 * q^45 - 16 * q^46 - 24 * q^47 - 16 * q^48 - 28 * q^49 - 32 * q^50 + 52 * q^52 + 20 * q^53 - 8 * q^55 - 8 * q^58 + 32 * q^59 - 12 * q^60 + 8 * q^61 + 72 * q^62 - 28 * q^64 - 8 * q^65 + 16 * q^66 + 60 * q^68 + 8 * q^69 + 64 * q^70 + 40 * q^71 + 12 * q^72 - 16 * q^75 - 40 * q^76 - 48 * q^77 + 8 * q^78 - 32 * q^80 - 28 * q^81 + 4 * q^82 - 104 * q^83 - 32 * q^84 - 4 * q^85 + 16 * q^86 - 24 * q^87 + 72 * q^88 - 36 * q^89 - 12 * q^90 - 56 * q^91 - 32 * q^92 + 56 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

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