LMFDB - Embedded newform 195.2.bb.c.166.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(121,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("195.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.bb (of order $6$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			166.2
Root			$0.500000 - 1.56488i$ of defining polynomial
Character	$\chi$	$=$	195.166
Dual form			195.2.bb.c.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.260797 - 0.150571i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.954656 + 1.65351i) q^{4} +1.00000i q^{5} +(-0.260797 - 0.150571i) q^{6} +(2.97125 + 1.71545i) q^{7} +1.17726i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.260797 - 0.150571i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.954656 + 1.65351i) q^{4} +1.00000i q^{5} +(-0.260797 - 0.150571i) q^{6} +(2.97125 + 1.71545i) q^{7} +1.17726i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.150571 + 0.260797i) q^{10} +(2.28749 - 1.32068i) q^{11} +1.90931 q^{12} +(0.572034 + 3.55988i) q^{13} +1.03319 q^{14} +(0.866025 - 0.500000i) q^{15} +(-1.73205 - 3.00000i) q^{16} +(0.0403455 - 0.0698805i) q^{17} +0.301143i q^{18} +(0.824892 + 0.476251i) q^{19} +(-1.65351 - 0.954656i) q^{20} -3.43091i q^{21} +(0.397714 - 0.688861i) q^{22} +(0.110226 + 0.190917i) q^{23} +(1.01954 - 0.588631i) q^{24} -1.00000 q^{25} +(0.685202 + 0.842277i) q^{26} +1.00000 q^{27} +(-5.67305 + 3.27534i) q^{28} +(-4.82362 - 8.35476i) q^{29} +(0.150571 - 0.260797i) q^{30} +1.57498i q^{31} +(-2.94251 - 1.69886i) q^{32} +(-2.28749 - 1.32068i) q^{33} -0.0242995i q^{34} +(-1.71545 + 2.97125i) q^{35} +(-0.954656 - 1.65351i) q^{36} +(-2.47841 + 1.43091i) q^{37} +0.286840 q^{38} +(2.79693 - 2.27534i) q^{39} -1.17726 q^{40} +(6.89590 - 3.98135i) q^{41} +(-0.516597 - 0.894772i) q^{42} +(-4.46704 + 7.73715i) q^{43} +5.04319i q^{44} +(-0.866025 - 0.500000i) q^{45} +(0.0574933 + 0.0331938i) q^{46} -8.52159i q^{47} +(-1.73205 + 3.00000i) q^{48} +(2.38556 + 4.13192i) q^{49} +(-0.260797 + 0.150571i) q^{50} -0.0806910 q^{51} +(-6.43241 - 2.45260i) q^{52} +5.28273 q^{53} +(0.260797 - 0.150571i) q^{54} +(1.32068 + 2.28749i) q^{55} +(-2.01954 + 3.49794i) q^{56} -0.952503i q^{57} +(-2.51598 - 1.45260i) q^{58} +(-8.37841 - 4.83728i) q^{59} +1.90931i q^{60} +(6.49373 - 11.2475i) q^{61} +(0.237147 + 0.410750i) q^{62} +(-2.97125 + 1.71545i) q^{63} +5.90501 q^{64} +(-3.55988 + 0.572034i) q^{65} -0.795428 q^{66} +(2.17001 - 1.25286i) q^{67} +(0.0770322 + 0.133424i) q^{68} +(0.110226 - 0.190917i) q^{69} +1.03319i q^{70} +(4.58363 + 2.64636i) q^{71} +(-1.01954 - 0.588631i) q^{72} -14.3591i q^{73} +(-0.430908 + 0.746354i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-1.57498 + 0.909313i) q^{76} +9.06228 q^{77} +(0.386832 - 1.01454i) q^{78} +11.8661 q^{79} +(3.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.19895 - 2.07665i) q^{82} +9.58956i q^{83} +(5.67305 + 3.27534i) q^{84} +(0.0698805 + 0.0403455i) q^{85} +2.69044i q^{86} +(-4.82362 + 8.35476i) q^{87} +(1.55479 + 2.69297i) q^{88} +(-9.17319 + 5.29614i) q^{89} -0.301143 q^{90} +(-4.40716 + 11.5586i) q^{91} -0.420912 q^{92} +(1.36397 - 0.787488i) q^{93} +(-1.28311 - 2.22241i) q^{94} +(-0.476251 + 0.824892i) q^{95} +3.39771i q^{96} +(-4.05202 - 2.33943i) q^{97} +(1.24430 + 0.718396i) q^{98} +2.64136i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{6} + 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 6 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^6 + 6 * q^7 - 4 * q^9	$ 8 q + 6 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{6} + 6 q^{7} - 4 q^{9} + 2 q^{10} + 12 q^{11} - 8 q^{12} + 6 q^{13} - 4 q^{14} - 2 q^{17} + 12 q^{19} + 4 q^{23} - 12 q^{24} - 8 q^{25} - 4 q^{26} + 8 q^{27} - 12 q^{28} - 6 q^{29} + 2 q^{30} + 12 q^{32} - 12 q^{33} - 6 q^{35} + 4 q^{36} - 12 q^{37} - 16 q^{38} - 30 q^{41} + 2 q^{42} + 6 q^{43} + 36 q^{46} - 8 q^{49} - 6 q^{50} + 4 q^{51} - 20 q^{52} - 32 q^{53} + 6 q^{54} - 8 q^{55} + 4 q^{56} + 12 q^{58} - 30 q^{59} - 30 q^{62} - 6 q^{63} + 32 q^{64} - 6 q^{65} + 30 q^{67} + 16 q^{68} + 4 q^{69} + 18 q^{71} + 12 q^{72} + 12 q^{74} + 4 q^{75} - 8 q^{77} + 14 q^{78} + 56 q^{79} + 24 q^{80} - 4 q^{81} - 24 q^{82} + 12 q^{84} + 6 q^{85} - 6 q^{87} + 8 q^{88} - 18 q^{89} - 4 q^{90} - 16 q^{91} + 40 q^{92} - 24 q^{93} - 16 q^{94} - 6 q^{97} - 12 q^{98}+O(q^{100}) $ 8 * q + 6 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^6 + 6 * q^7 - 4 * q^9 + 2 * q^10 + 12 * q^11 - 8 * q^12 + 6 * q^13 - 4 * q^14 - 2 * q^17 + 12 * q^19 + 4 * q^23 - 12 * q^24 - 8 * q^25 - 4 * q^26 + 8 * q^27 - 12 * q^28 - 6 * q^29 + 2 * q^30 + 12 * q^32 - 12 * q^33 - 6 * q^35 + 4 * q^36 - 12 * q^37 - 16 * q^38 - 30 * q^41 + 2 * q^42 + 6 * q^43 + 36 * q^46 - 8 * q^49 - 6 * q^50 + 4 * q^51 - 20 * q^52 - 32 * q^53 + 6 * q^54 - 8 * q^55 + 4 * q^56 + 12 * q^58 - 30 * q^59 - 30 * q^62 - 6 * q^63 + 32 * q^64 - 6 * q^65 + 30 * q^67 + 16 * q^68 + 4 * q^69 + 18 * q^71 + 12 * q^72 + 12 * q^74 + 4 * q^75 - 8 * q^77 + 14 * q^78 + 56 * q^79 + 24 * q^80 - 4 * q^81 - 24 * q^82 + 12 * q^84 + 6 * q^85 - 6 * q^87 + 8 * q^88 - 18 * q^89 - 4 * q^90 - 16 * q^91 + 40 * q^92 - 24 * q^93 - 16 * q^94 - 6 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.260797	−	0.150571i	0.184412	−	0.106470i	−0.404952	−	0.914338i	$-0.632712\pi$
$2$	0.260797	−	0.150571i	0.184412	−	0.106470i	0.589364	+	0.807868i	$0.299378\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.954656	+	1.65351i	−0.477328	+	0.826757i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.260797	−	0.150571i	−0.106470	−	0.0614706i
$7$	2.97125	+	1.71545i	1.12303	+	0.648381i	0.942172	−	0.335129i	$-0.108780\pi$
$7$	2.97125	+	1.71545i	1.12303	+	0.648381i	0.180856	+	0.983510i	$0.442113\pi$
$8$			1.17726i			0.416225i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.150571	+	0.260797i	0.0476149	+	0.0824714i
$11$	2.28749	−	1.32068i	0.689704	−	0.398201i	−0.113797	−	0.993504i	$-0.536301\pi$
$11$	2.28749	−	1.32068i	0.689704	−	0.398201i	0.803501	+	0.595303i	$0.202968\pi$
$12$	1.90931			0.551171
$13$	0.572034	+	3.55988i	0.158654	+	0.987334i
$13$	0.572034	+	3.55988i	0.158654	+	0.987334i
$14$	1.03319			0.276133
$15$	0.866025	−	0.500000i	0.223607	−	0.129099i
$16$	−1.73205	−	3.00000i	−0.433013	−	0.750000i
$17$	0.0403455	−	0.0698805i	0.00978522	−	0.0169485i	−0.861091	−	0.508450i	$-0.830219\pi$
$17$	0.0403455	−	0.0698805i	0.00978522	−	0.0169485i	0.870877	+	0.491502i	$0.163552\pi$
$18$			0.301143i			0.0709801i
$19$	0.824892	+	0.476251i	0.189243	+	0.109260i	0.591628	−	0.806211i	$-0.298485\pi$
$19$	0.824892	+	0.476251i	0.189243	+	0.109260i	−0.402385	+	0.915471i	$0.631819\pi$
$20$	−1.65351	−	0.954656i	−0.369737	−	0.213468i
$21$		−	3.43091i		−	0.748685i
$22$	0.397714	−	0.688861i	0.0847929	−	0.146866i
$23$	0.110226	+	0.190917i	0.0229837	+	0.0398089i	0.877288	−	0.479963i	$-0.159350\pi$
$23$	0.110226	+	0.190917i	0.0229837	+	0.0398089i	−0.854305	+	0.519772i	$0.826017\pi$
$24$	1.01954	−	0.588631i	0.208113	−	0.120154i
$25$	−1.00000			−0.200000
$26$	0.685202	+	0.842277i	0.134379	+	0.165184i
$27$	1.00000			0.192450
$28$	−5.67305	+	3.27534i	−1.07211	+	0.618981i
$29$	−4.82362	−	8.35476i	−0.895724	−	1.55144i	−0.832905	−	0.553415i	$-0.813324\pi$
$29$	−4.82362	−	8.35476i	−0.895724	−	1.55144i	−0.0628190	−	0.998025i	$-0.520009\pi$
$30$	0.150571	−	0.260797i	0.0274905	−	0.0476149i
$31$			1.57498i			0.282874i	0.989947	+	0.141437i	$0.0451723\pi$
$31$			1.57498i			0.282874i	−0.989947	+	0.141437i	$0.954828\pi$
$32$	−2.94251	−	1.69886i	−0.520167	−	0.300318i
$33$	−2.28749	−	1.32068i	−0.398201	−	0.229901i
$34$		−	0.0242995i		−	0.00416734i
$35$	−1.71545	+	2.97125i	−0.289965	+	0.502233i
$36$	−0.954656	−	1.65351i	−0.159109	−	0.275586i
$37$	−2.47841	+	1.43091i	−0.407447	+	0.235240i	−0.689692	−	0.724103i	$-0.742254\pi$
$37$	−2.47841	+	1.43091i	−0.407447	+	0.235240i	0.282245	+	0.959342i	$0.408921\pi$
$38$	0.286840			0.0465315
$39$	2.79693	−	2.27534i	0.447868	−	0.364346i
$40$	−1.17726			−0.186141
$41$	6.89590	−	3.98135i	1.07696	−	0.621782i	0.146884	−	0.989154i	$-0.453076\pi$
$41$	6.89590	−	3.98135i	1.07696	−	0.621782i	0.930074	+	0.367372i	$0.119742\pi$
$42$	−0.516597	−	0.894772i	−0.0797126	−	0.138066i
$43$	−4.46704	+	7.73715i	−0.681218	+	1.17990i	0.293392	+	0.955992i	$0.405216\pi$
$43$	−4.46704	+	7.73715i	−0.681218	+	1.17990i	−0.974609	+	0.223911i	$0.928117\pi$
$44$			5.04319i			0.760289i
$45$	−0.866025	−	0.500000i	−0.129099	−	0.0745356i
$46$	0.0574933	+	0.0331938i	0.00847693	+	0.00489416i
$47$		−	8.52159i		−	1.24300i	−0.783413	−	0.621501i	$-0.786523\pi$
$47$		−	8.52159i		−	1.24300i	0.783413	−	0.621501i	$-0.213477\pi$
$48$	−1.73205	+	3.00000i	−0.250000	+	0.433013i
$49$	2.38556	+	4.13192i	0.340795	+	0.590274i
$50$	−0.260797	+	0.150571i	−0.0368823	+	0.0212940i
$51$	−0.0806910			−0.0112990
$52$	−6.43241	−	2.45260i	−0.892015	−	0.340114i
$53$	5.28273			0.725638			0.362819	−	0.931860i	$-0.381814\pi$
$53$	5.28273			0.725638			0.362819	+	0.931860i	$0.381814\pi$
$54$	0.260797	−	0.150571i	0.0354900	−	0.0204902i
$55$	1.32068	+	2.28749i	0.178081	+	0.308445i
$56$	−2.01954	+	3.49794i	−0.269872	+	0.467432i
$57$		−	0.952503i		−	0.126162i
$58$	−2.51598	−	1.45260i	−0.330364	−	0.190736i
$59$	−8.37841	−	4.83728i	−1.09078	−	0.629760i	−0.156993	−	0.987600i	$-0.550180\pi$
$59$	−8.37841	−	4.83728i	−1.09078	−	0.629760i	−0.933783	+	0.357840i	$0.883513\pi$
$60$			1.90931i			0.246491i
$61$	6.49373	−	11.2475i	0.831437	−	1.44009i	−0.0654609	−	0.997855i	$-0.520852\pi$
$61$	6.49373	−	11.2475i	0.831437	−	1.44009i	0.896898	−	0.442237i	$-0.145815\pi$
$62$	0.237147	+	0.410750i	0.0301176	+	0.0521653i
$63$	−2.97125	+	1.71545i	−0.374343	+	0.216127i
$64$	5.90501			0.738126
$65$	−3.55988	+	0.572034i	−0.441549	+	0.0709521i
$66$	−0.795428			−0.0979104
$67$	2.17001	−	1.25286i	0.265109	−	0.153061i	−0.361554	−	0.932351i	$-0.617754\pi$
$67$	2.17001	−	1.25286i	0.265109	−	0.153061i	0.626663	+	0.779290i	$0.284420\pi$
$68$	0.0770322	+	0.133424i	0.00934153	+	0.0161800i
$69$	0.110226	−	0.190917i	0.0132696	−	0.0229837i
$70$			1.03319i			0.123490i
$71$	4.58363	+	2.64636i	0.543977	+	0.314065i	0.746689	−	0.665173i	$-0.231642\pi$
$71$	4.58363	+	2.64636i	0.543977	+	0.314065i	−0.202712	+	0.979238i	$0.564976\pi$
$72$	−1.01954	−	0.588631i	−0.120154	−	0.0693708i
$73$		−	14.3591i		−	1.68061i	−0.542116	−	0.840303i	$-0.682377\pi$
$73$		−	14.3591i		−	1.68061i	0.542116	−	0.840303i	$-0.317623\pi$
$74$	−0.430908	+	0.746354i	−0.0500920	+	0.0867619i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−1.57498	+	0.909313i	−0.180662	+	0.104305i
$77$	9.06228			1.03274
$78$	0.386832	−	1.01454i	0.0438001	−	0.114874i
$79$	11.8661			1.33504			0.667522	−	0.744590i	$-0.267355\pi$
$79$	11.8661			1.33504			0.667522	+	0.744590i	$0.267355\pi$
$80$	3.00000	−	1.73205i	0.335410	−	0.193649i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.19895	−	2.07665i	0.132402	−	0.229328i
$83$			9.58956i			1.05259i	0.850302	+	0.526295i	$0.176419\pi$
$83$			9.58956i			1.05259i	−0.850302	+	0.526295i	$0.823581\pi$
$84$	5.67305	+	3.27534i	0.618981	+	0.357369i
$85$	0.0698805	+	0.0403455i	0.00757960	+	0.00437608i
$86$			2.69044i			0.290117i
$87$	−4.82362	+	8.35476i	−0.517147	+	0.895724i
$88$	1.55479	+	2.69297i	0.165741	+	0.287072i
$89$	−9.17319	+	5.29614i	−0.972356	+	0.561390i	−0.899954	−	0.435985i	$-0.856400\pi$
$89$	−9.17319	+	5.29614i	−0.972356	+	0.561390i	−0.0724026	+	0.997375i	$0.523067\pi$
$90$	−0.301143			−0.0317433
$91$	−4.40716	+	11.5586i	−0.461996	+	1.21167i
$92$	−0.420912			−0.0438831
$93$	1.36397	−	0.787488i	0.141437	−	0.0816587i
$94$	−1.28311	−	2.22241i	−0.132343	−	0.229224i
$95$	−0.476251	+	0.824892i	−0.0488624	+	0.0846321i
$96$			3.39771i			0.346778i
$97$	−4.05202	−	2.33943i	−0.411420	−	0.237533i	0.279980	−	0.960006i	$-0.409672\pi$
$97$	−4.05202	−	2.33943i	−0.411420	−	0.237533i	−0.691400	+	0.722473i	$0.743006\pi$
$98$	1.24430	+	0.718396i	0.125693	+	0.0725689i
$99$			2.64136i			0.265467i
$100$	0.954656	−	1.65351i	0.0954656	−	0.165351i
$101$	−3.40137	−	5.89135i	−0.338449	−	0.586211i	0.645692	−	0.763598i	$-0.276569\pi$
$101$	−3.40137	−	5.89135i	−0.338449	−	0.586211i	−0.984141	+	0.177387i	$0.943236\pi$
$102$	−0.0210440	+	0.0121498i	−0.00208367	+	0.00120301i
$103$	4.67456			0.460598			0.230299	−	0.973120i	$-0.426030\pi$
$103$	4.67456			0.460598			0.230299	+	0.973120i	$0.426030\pi$
$104$	−4.19092	+	0.673434i	−0.410953	+	0.0660357i
$105$	3.43091			0.334822
$106$	1.37772	−	0.795428i	0.133816	−	0.0772588i
$107$	6.66217	+	11.5392i	0.644056	+	1.11554i	0.984519	+	0.175280i	$0.0560831\pi$
$107$	6.66217	+	11.5392i	0.644056	+	1.11554i	−0.340462	+	0.940258i	$0.610584\pi$
$108$	−0.954656	+	1.65351i	−0.0918619	+	0.159109i
$109$		−	5.12976i		−	0.491342i	−0.969353	−	0.245671i	$-0.920992\pi$
$109$		−	5.12976i		−	0.491342i	0.969353	−	0.245671i	$-0.0790083\pi$
$110$	0.688861	+	0.397714i	0.0656803	+	0.0379205i
$111$	2.47841	+	1.43091i	0.235240	+	0.135816i
$112$		−	11.8850i		−	1.12303i
$113$	−4.08658	+	7.07816i	−0.384433	+	0.665857i	−0.991690	−	0.128648i	$-0.958936\pi$
$113$	−4.08658	+	7.07816i	−0.384433	+	0.665857i	0.607258	+	0.794505i	$0.292270\pi$
$114$	−0.143420	−	0.248410i	−0.0134325	−	0.0232658i
$115$	−0.190917	+	0.110226i	−0.0178031	+	0.0102786i
$116$	18.4196			1.71022
$117$	−3.36897	−	1.28455i	−0.311461	−	0.118756i
$118$	−2.91342			−0.268203
$119$	0.239753	−	0.138422i	0.0219782	−	0.0126891i
$120$	0.588631	+	1.01954i	0.0537344	+	0.0930707i
$121$	−2.01160	+	3.48419i	−0.182873	+	0.316745i
$122$		−	3.91108i		−	0.354093i
$123$	−6.89590	−	3.98135i	−0.621782	−	0.358986i
$124$	−2.60424	−	1.50356i	−0.233868	−	0.135024i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.516597	+	0.894772i	−0.0460221	+	0.0797126i
$127$	10.4744	+	18.1422i	0.929456	+	1.60986i	0.784234	+	0.620465i	$0.213056\pi$
$127$	10.4744	+	18.1422i	0.929456	+	1.60986i	0.145222	+	0.989399i	$0.453610\pi$
$128$	7.42502	−	4.28684i	0.656286	−	0.378907i
$129$	8.93409			0.786603
$130$	−0.842277	+	0.685202i	−0.0738726	+	0.0600962i
$131$	−17.0250			−1.48748			−0.743739	−	0.668470i	$-0.766950\pi$
$131$	−17.0250			−1.48748			−0.743739	+	0.668470i	$0.766950\pi$
$132$	4.36753	−	2.52159i	0.380145	−	0.219477i
$133$	1.63397	+	2.83013i	0.141684	+	0.245403i
$134$	0.377289	−	0.653484i	0.0325928	−	0.0564524i
$135$			1.00000i			0.0860663i
$136$	0.0822676	+	0.0474972i	0.00705439	+	0.00407285i
$137$	12.9233	+	7.46126i	1.10411	+	0.637458i	0.937297	−	0.348530i	$-0.113319\pi$
$137$	12.9233	+	7.46126i	1.10411	+	0.637458i	0.166813	+	0.985989i	$0.446653\pi$
$138$		−	0.0663876i		−	0.00565128i
$139$	4.05479	−	7.02310i	0.343923	−	0.595692i	−0.641235	−	0.767345i	$-0.721578\pi$
$139$	4.05479	−	7.02310i	0.343923	−	0.595692i	0.985157	+	0.171653i	$0.0549109\pi$
$140$	−3.27534	−	5.67305i	−0.276817	−	0.479460i
$141$	−7.37992	+	4.26080i	−0.621501	+	0.358824i
$142$	1.59387			0.133754
$143$	6.01000	+	7.38772i	0.502581	+	0.617792i
$144$	3.46410			0.288675
$145$	8.35476	−	4.82362i	0.693825	−	0.400580i
$146$	−2.16207	−	3.74482i	−0.178934	−	0.309923i
$147$	2.38556	−	4.13192i	0.196758	−	0.340795i
$148$		−	5.46410i		−	0.449146i
$149$	−18.8471	−	10.8814i	−1.54401	−	0.891435i	−0.998580	−	0.0532800i	$-0.983032\pi$
$149$	−18.8471	−	10.8814i	−1.54401	−	0.891435i	−0.545432	−	0.838155i	$-0.683634\pi$
$150$	0.260797	+	0.150571i	0.0212940	+	0.0122941i
$151$		−	14.1688i		−	1.15304i	−0.817082	−	0.576522i	$-0.804409\pi$
$151$		−	14.1688i		−	1.15304i	0.817082	−	0.576522i	$-0.195591\pi$
$152$	−0.560673	+	0.971114i	−0.0454766	+	0.0787677i
$153$	0.0403455	+	0.0698805i	0.00326174	+	0.00564950i
$154$	2.36342	−	1.36452i	0.190450	−	0.109956i
$155$	−1.57498			−0.126505
$156$	1.09219	+	6.79693i	0.0874454	+	0.544190i
$157$	−6.03449			−0.481605			−0.240802	−	0.970574i	$-0.577411\pi$
$157$	−6.03449			−0.481605			−0.240802	+	0.970574i	$0.577411\pi$
$158$	3.09465	−	1.78670i	0.246198	−	0.142142i
$159$	−2.64136	−	4.57498i	−0.209474	−	0.362819i
$160$	1.69886	−	2.94251i	0.134306	−	0.232626i
$161$			0.756350i			0.0596088i
$162$	−0.260797	−	0.150571i	−0.0204902	−	0.0118300i
$163$	−17.7138	−	10.2271i	−1.38745	−	0.801045i	−0.394423	−	0.918929i	$-0.629055\pi$
$163$	−17.7138	−	10.2271i	−1.38745	−	0.801045i	−0.993027	+	0.117885i	$0.962389\pi$
$164$			15.2033i			1.18718i
$165$	1.32068	−	2.28749i	0.102815	−	0.178081i
$166$	1.44391	+	2.50093i	0.112069	+	0.194110i
$167$	−14.6704	+	8.46999i	−1.13523	+	0.655427i	−0.945246	−	0.326359i	$-0.894178\pi$
$167$	−14.6704	+	8.46999i	−1.13523	+	0.655427i	−0.189987	+	0.981787i	$0.560845\pi$
$168$	4.03908			0.311622
$169$	−12.3456	+	4.07275i	−0.949658	+	0.313289i
$170$	0.0242995			0.00186369
$171$	−0.824892	+	0.476251i	−0.0630810	+	0.0364199i
$172$	−8.52898	−	14.7726i	−0.650329	−	1.12640i
$173$	9.40534	−	16.2905i	0.715075	−	1.23855i	−0.247856	−	0.968797i	$-0.579726\pi$
$173$	9.40534	−	16.2905i	0.715075	−	1.23855i	0.962931	−	0.269749i	$-0.0869407\pi$
$174$			2.90520i			0.220243i
$175$	−2.97125	−	1.71545i	−0.224606	−	0.129676i
$176$	−7.92409	−	4.57498i	−0.597301	−	0.344852i
$177$			9.67456i			0.727184i
$178$	−1.59490	+	2.76244i	−0.119543	+	0.207054i
$179$	5.13842	+	8.90001i	0.384064	+	0.665218i	0.991639	−	0.129044i	$-0.0411910\pi$
$179$	5.13842	+	8.90001i	0.384064	+	0.665218i	−0.607575	+	0.794262i	$0.707858\pi$
$180$	1.65351	−	0.954656i	0.123246	−	0.0711559i
$181$	−15.0970			−1.12215			−0.561077	−	0.827763i	$-0.689613\pi$
$181$	−15.0970			−1.12215			−0.561077	+	0.827763i	$0.689613\pi$
$182$	0.591022	+	3.67805i	0.0438095	+	0.272635i
$183$	−12.9875			−0.960061
$184$	−0.224759	+	0.129765i	−0.0165695	+	0.00956639i
$185$	−1.43091	−	2.47841i	−0.105202	−	0.182216i
$186$	0.237147	−	0.410750i	0.0173884	−	0.0301176i
$187$		−	0.213134i		−	0.0155859i
$188$	14.0906	+	8.13520i	1.02766	+	0.593320i
$189$	2.97125	+	1.71545i	0.216127	+	0.124781i
$190$			0.286840i			0.0208095i
$191$	−5.75659	+	9.97070i	−0.416532	+	0.721455i	−0.995588	−	0.0938332i	$-0.970088\pi$
$191$	−5.75659	+	9.97070i	−0.416532	+	0.721455i	0.579056	+	0.815288i	$0.303421\pi$
$192$	−2.95250	−	5.11388i	−0.213079	−	0.369063i
$193$	14.6819	−	8.47659i	1.05682	−	0.610158i	0.132273	−	0.991213i	$-0.457773\pi$
$193$	14.6819	−	8.47659i	1.05682	−	0.610158i	0.924552	+	0.381055i	$0.124439\pi$
$194$	−1.40901			−0.101161
$195$	2.27534	+	2.79693i	0.162940	+	0.200293i
$196$	−9.10958			−0.650684
$197$	−10.1868	+	5.88135i	−0.725780	+	0.419029i	−0.816876	−	0.576813i	$-0.804296\pi$
$197$	−10.1868	+	5.88135i	−0.725780	+	0.419029i	0.0910965	+	0.995842i	$0.470963\pi$
$198$	0.397714	+	0.688861i	0.0282643	+	0.0489552i
$199$	4.15724	−	7.20056i	0.294699	−	0.510434i	−0.680216	−	0.733012i	$-0.738114\pi$
$199$	4.15724	−	7.20056i	0.294699	−	0.510434i	0.974915	+	0.222578i	$0.0714472\pi$
$200$		−	1.17726i		−	0.0832450i
$201$	−2.17001	−	1.25286i	−0.153061	−	0.0883697i
$202$	−1.77414	−	1.02430i	−0.124828	−	0.0720695i
$203$		−	33.0988i		−	2.32308i
$204$	0.0770322	−	0.133424i	0.00539333	−	0.00934153i
$205$	3.98135	+	6.89590i	0.278069	+	0.481630i
$206$	1.21911	−	0.703855i	0.0849396	−	0.0490399i
$207$	−0.220452			−0.0153225
$208$	9.68886	−	7.88200i	0.671802	−	0.546519i
$209$	2.51591			0.174029
$210$	0.894772	−	0.516597i	0.0617451	−	0.0356486i
$211$	8.21775	+	14.2336i	0.565733	+	0.979878i	0.996981	+	0.0776450i	$0.0247401\pi$
$211$	8.21775	+	14.2336i	0.565733	+	0.979878i	−0.431248	+	0.902233i	$0.641927\pi$
$212$	−5.04319	+	8.73506i	−0.346368	+	0.599926i
$213$		−	5.29272i		−	0.362651i
$214$	3.47495	+	2.00627i	0.237543	+	0.137146i
$215$	−7.73715	−	4.46704i	−0.527669	−	0.304650i
$216$			1.17726i			0.0801025i
$217$	−2.70180	+	4.67965i	−0.183410	+	0.317676i
$218$	−0.772396	−	1.33783i	−0.0523133	−	0.0906093i
$219$	−12.4354	+	7.17956i	−0.840303	+	0.485149i
$220$	−5.04319			−0.340012
$221$	0.271845	+	0.103651i	0.0182863	+	0.00697234i
$222$	0.861816			0.0578413
$223$	−1.97139	+	1.13818i	−0.132014	+	0.0762185i	−0.564553	−	0.825397i	$-0.690951\pi$
$223$	−1.97139	+	1.13818i	−0.132014	+	0.0762185i	0.432538	+	0.901615i	$0.357618\pi$
$224$	−5.82862	−	10.0955i	−0.389441	−	0.674532i
$225$	0.500000	−	0.866025i	0.0333333	−	0.0577350i
$226$			2.46129i			0.163722i
$227$	−17.0113	−	9.82147i	−1.12908	−	0.651874i	−0.185376	−	0.982668i	$-0.559350\pi$
$227$	−17.0113	−	9.82147i	−1.12908	−	0.651874i	−0.943703	+	0.330794i	$0.892684\pi$
$228$	1.57498	+	0.909313i	0.104305	+	0.0602207i
$229$			6.38800i			0.422131i	0.977472	+	0.211065i	$0.0676933\pi$
$229$			6.38800i			0.422131i	−0.977472	+	0.211065i	$0.932307\pi$
$230$	−0.0331938	+	0.0574933i	−0.00218873	+	0.00379100i
$231$	−4.53114	−	7.84816i	−0.298127	−	0.516371i
$232$	9.83574	−	5.67867i	0.645748	−	0.372823i
$233$	20.0391			1.31280			0.656402	−	0.754411i	$-0.272078\pi$
$233$	20.0391			1.31280			0.656402	+	0.754411i	$0.272078\pi$
$234$	−1.07203	+	0.172264i	−0.0700811	+	0.0112613i
$235$	8.52159			0.555888
$236$	15.9970	−	9.23588i	1.04132	−	0.601204i
$237$	−5.93306	−	10.2764i	−0.385394	−	0.667522i
$238$	0.0416847	−	0.0722001i	0.00270202	−	0.00468004i
$239$			4.47998i			0.289786i	0.989447	+	0.144893i	$0.0462838\pi$
$239$			4.47998i			0.289786i	−0.989447	+	0.144893i	$0.953716\pi$
$240$	−3.00000	−	1.73205i	−0.193649	−	0.111803i
$241$	−0.535517	−	0.309181i	−0.0344957	−	0.0199161i	0.482653	−	0.875812i	$-0.339673\pi$
$241$	−0.535517	−	0.309181i	−0.0344957	−	0.0199161i	−0.517149	+	0.855896i	$0.673007\pi$
$242$			1.21156i			0.0778819i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	12.3986	+	21.4750i	0.793737	+	1.37479i
$245$	−4.13192	+	2.38556i	−0.263979	+	0.152408i
$246$	−2.39791			−0.152885
$247$	−1.22353	+	3.20895i	−0.0778516	+	0.204181i
$248$	−1.85416			−0.117739
$249$	8.30480	−	4.79478i	0.526295	−	0.303857i
$250$	−0.150571	−	0.260797i	−0.00952298	−	0.0164943i
$251$	−9.01543	+	15.6152i	−0.569049	+	0.985621i	0.427612	+	0.903963i	$0.359355\pi$
$251$	−9.01543	+	15.6152i	−0.569049	+	0.985621i	−0.996660	+	0.0816587i	$0.973978\pi$
$252$		−	6.55068i		−	0.412654i
$253$	0.504281	+	0.291147i	0.0317039	+	0.0183042i
$254$	5.46341	+	3.15430i	0.342805	+	0.197918i
$255$		−	0.0806910i		−	0.00505307i
$256$	−4.61405	+	7.99178i	−0.288378	+	0.499486i
$257$	−3.80193	−	6.58514i	−0.237158	−	0.410770i	0.722740	−	0.691120i	$-0.242883\pi$
$257$	−3.80193	−	6.58514i	−0.237158	−	0.410770i	−0.959898	+	0.280351i	$0.909549\pi$
$258$	2.32999	−	1.34522i	0.145059	−	0.0837497i
$259$	−9.81863			−0.610100
$260$	2.45260	−	6.43241i	0.152104	−	0.398921i
$261$	9.64725			0.597150
$262$	−4.44007	+	2.56347i	−0.274308	+	0.158372i
$263$	−1.48713	−	2.57579i	−0.0917006	−	0.158830i	0.816526	−	0.577308i	$-0.195897\pi$
$263$	−1.48713	−	2.57579i	−0.0917006	−	0.158830i	−0.908227	+	0.418478i	$0.862564\pi$
$264$	1.55479	−	2.69297i	0.0956906	−	0.165741i
$265$			5.28273i			0.324515i
$266$	0.852273	+	0.492060i	0.0522562	+	0.0301701i
$267$	9.17319	+	5.29614i	0.561390	+	0.324119i
$268$			4.78419i			0.292241i
$269$	14.0536	−	24.3416i	0.856864	−	1.48413i	−0.0180404	−	0.999837i	$-0.505743\pi$
$269$	14.0536	−	24.3416i	0.856864	−	1.48413i	0.874905	−	0.484295i	$-0.160924\pi$
$270$	0.150571	+	0.260797i	0.00916349	+	0.0158716i
$271$	16.3350	−	9.43101i	0.992279	−	0.572893i	0.0863245	−	0.996267i	$-0.472488\pi$
$271$	16.3350	−	9.43101i	0.992279	−	0.572893i	0.905955	+	0.423374i	$0.139154\pi$
$272$	−0.279522			−0.0169485
$273$	12.2136	−	1.96260i	0.739203	−	0.118782i
$274$	4.49381			0.271481
$275$	−2.28749	+	1.32068i	−0.137941	+	0.0796401i
$276$	0.210456	+	0.364520i	0.0126680	+	0.0219415i
$277$	−10.7668	+	18.6487i	−0.646916	+	1.12049i	0.336940	+	0.941526i	$0.390608\pi$
$277$	−10.7668	+	18.6487i	−0.646916	+	1.12049i	−0.983856	+	0.178965i	$0.942725\pi$
$278$		−	2.44214i		−	0.146470i
$279$	−1.36397	−	0.787488i	−0.0816587	−	0.0471457i
$280$	−3.49794	−	2.01954i	−0.209042	−	0.120691i
$281$			18.5104i			1.10424i	0.833766	+	0.552118i	$0.186180\pi$
$281$			18.5104i			1.10424i	−0.833766	+	0.552118i	$0.813820\pi$
$282$	−1.28311	+	2.22241i	−0.0764080	+	0.132343i
$283$	5.07672	+	8.79313i	0.301780	+	0.522698i	0.976539	−	0.215340i	$-0.0690860\pi$
$283$	5.07672	+	8.79313i	0.301780	+	0.522698i	−0.674760	+	0.738038i	$0.735753\pi$
$284$	−8.75159	+	5.05273i	−0.519311	+	0.299825i
$285$	0.952503			0.0564214
$286$	2.67977	+	1.02176i	0.158458	+	0.0604182i
$287$	27.3193			1.61261
$288$	2.94251	−	1.69886i	0.173389	−	0.100106i
$289$	8.49674	+	14.7168i	0.499808	+	0.865694i
$290$	1.45260	−	2.51598i	0.0852996	−	0.147743i
$291$			4.67886i			0.274280i
$292$	23.7430	+	13.7080i	1.38945	+	0.802201i
$293$	14.6080	+	8.43395i	0.853410	+	0.492716i	0.861800	−	0.507248i	$-0.169337\pi$
$293$	14.6080	+	8.43395i	0.853410	+	0.492716i	−0.00838997	+	0.999965i	$0.502671\pi$
$294$		−	1.43679i		−	0.0837954i
$295$	4.83728	−	8.37841i	0.281637	−	0.487810i
$296$	−1.68455	−	2.91773i	−0.0979127	−	0.169590i
$297$	2.28749	−	1.32068i	0.132734	−	0.0766337i
$298$	−6.55369			−0.379645
$299$	−0.616589	+	0.501603i	−0.0356583	+	0.0290084i
$300$	−1.90931			−0.110234
$301$	−26.5454	+	15.3260i	−1.53005	+	0.883377i
$302$	−2.13342	−	3.69520i	−0.122765	−	0.212635i
$303$	−3.40137	+	5.89135i	−0.195404	+	0.338449i
$304$		−	3.29957i		−	0.189243i
$305$	11.2475	+	6.49373i	0.644029	+	0.371830i
$306$	0.0210440	+	0.0121498i	0.00120301	+	0.000694556i
$307$			6.94155i			0.396175i	0.980184	+	0.198088i	$0.0634730\pi$
$307$			6.94155i			0.396175i	−0.980184	+	0.198088i	$0.936527\pi$
$308$	−8.65136	+	14.9846i	−0.492957	+	0.853827i
$309$	−2.33728	−	4.04829i	−0.132963	−	0.230299i
$310$	−0.410750	+	0.237147i	−0.0233290	+	0.0134690i
$311$	13.9341			0.790130			0.395065	−	0.918653i	$-0.370722\pi$
$311$	13.9341			0.790130			0.395065	+	0.918653i	$0.370722\pi$
$312$	2.67867	+	3.29272i	0.151650	+	0.186414i
$313$	−9.02908			−0.510354			−0.255177	−	0.966894i	$-0.582134\pi$
$313$	−9.02908			−0.510354			−0.255177	+	0.966894i	$0.582134\pi$
$314$	−1.57378	+	0.908622i	−0.0888135	+	0.0512765i
$315$	−1.71545	−	2.97125i	−0.0966549	−	0.167411i
$316$	−11.3281	+	19.6208i	−0.637254	+	1.10376i
$317$			0.496821i			0.0279042i	0.999903	+	0.0139521i	$0.00444124\pi$
$317$			0.496821i			0.0279042i	−0.999903	+	0.0139521i	$0.995559\pi$
$318$	−1.37772	−	0.795428i	−0.0772588	−	0.0446054i
$319$	−22.0680	−	12.7409i	−1.23557	−	0.713356i
$320$			5.90501i			0.330100i
$321$	6.66217	−	11.5392i	0.371846	−	0.644056i
$322$	0.113885	+	0.197254i	0.00634655	+	0.0109925i
$323$	0.0665613	−	0.0384292i	0.00370357	−	0.00213826i
$324$	1.90931			0.106073
$325$	−0.572034	−	3.55988i	−0.0317307	−	0.197467i
$326$	−6.15961			−0.341149
$327$	−4.44251	+	2.56488i	−0.245671	+	0.141838i
$328$	4.68709	+	8.11828i	0.258801	+	0.448257i
$329$	14.6184	−	25.3198i	0.805939	−	1.39593i
$330$		−	0.795428i		−	0.0437869i
$331$	22.5350	+	13.0106i	1.23863	+	0.715126i	0.968815	−	0.247786i	$-0.0797028\pi$
$331$	22.5350	+	13.0106i	1.23863	+	0.715126i	0.269819	+	0.962911i	$0.413036\pi$
$332$	−15.8565	−	9.15473i	−0.870237	−	0.502431i
$333$		−	2.86182i		−	0.156827i
$334$	−2.55068	+	4.41790i	−0.139567	+	0.241737i
$335$	1.25286	+	2.17001i	0.0684509	+	0.118560i
$336$	−10.2927	+	5.94251i	−0.561514	+	0.324190i
$337$	−1.60276			−0.0873079			−0.0436540	−	0.999047i	$-0.513900\pi$
$337$	−1.60276			−0.0873079			−0.0436540	+	0.999047i	$0.513900\pi$
$338$	−2.60645	+	2.92105i	−0.141772	+	0.158884i
$339$	8.17315			0.443905
$340$	−0.133424	+	0.0770322i	−0.00723592	+	0.00417766i
$341$	2.08004	+	3.60274i	0.112641	+	0.195099i
$342$	−0.143420	+	0.248410i	−0.00775525	+	0.0134325i
$343$		−	7.64705i		−	0.412902i
$344$	−9.10865	−	5.25888i	−0.491105	−	0.283540i
$345$	0.190917	+	0.110226i	0.0102786	+	0.00593437i
$346$		−	5.66470i		−	0.304536i
$347$	15.4789	−	26.8102i	0.830950	−	1.43925i	−0.0663361	−	0.997797i	$-0.521131\pi$
$347$	15.4789	−	26.8102i	0.830950	−	1.43925i	0.897286	−	0.441450i	$-0.145536\pi$
$348$	−9.20981	−	15.9519i	−0.493697	−	0.855109i
$349$	−14.1851	+	8.18979i	−0.759313	+	0.438389i	−0.829049	−	0.559176i	$-0.811118\pi$
$349$	−14.1851	+	8.18979i	−0.759313	+	0.438389i	0.0697363	+	0.997565i	$0.477784\pi$
$350$	−1.03319			−0.0552265
$351$	0.572034	+	3.55988i	0.0305329	+	0.190013i
$352$	−8.97460			−0.478348
$353$	−17.6768	+	10.2057i	−0.940840	+	0.543194i	−0.890224	−	0.455524i	$-0.849452\pi$
$353$	−17.6768	+	10.2057i	−0.940840	+	0.543194i	−0.0506166	+	0.998718i	$0.516119\pi$
$354$	1.45671	+	2.52310i	0.0774234	+	0.134101i
$355$	−2.64636	+	4.58363i	−0.140454	+	0.243274i
$356$		−	20.2240i		−	1.07187i
$357$	−0.239753	−	0.138422i	−0.0126891	−	0.00732605i
$358$	2.68017	+	1.54740i	0.141652	+	0.0817826i
$359$			27.7823i			1.46629i	0.680071	+	0.733146i	$0.261949\pi$
$359$			27.7823i			1.46629i	−0.680071	+	0.733146i	$0.738051\pi$
$360$	0.588631	−	1.01954i	0.0310236	−	0.0537344i
$361$	−9.04637	−	15.6688i	−0.476125	−	0.824672i
$362$	−3.93727	+	2.27318i	−0.206938	+	0.119476i
$363$	4.02320			0.211163
$364$	−14.9050	−	18.3218i	−0.781235	−	0.960324i
$365$	14.3591			0.751590
$366$	−3.38710	+	1.95554i	−0.177046	+	0.102218i
$367$	−2.83998	−	4.91900i	−0.148246	−	0.256769i	0.782333	−	0.622860i	$-0.214029\pi$
$367$	−2.83998	−	4.91900i	−0.148246	−	0.256769i	−0.930579	+	0.366091i	$0.880696\pi$
$368$	0.381834	−	0.661356i	0.0199045	−	0.0344756i
$369$			7.96269i			0.414521i
$370$	−0.746354	−	0.430908i	−0.0388011	−	0.0224018i
$371$	15.6963	+	9.06228i	0.814912	+	0.470490i
$372$			3.00712i			0.155912i
$373$	1.99014	−	3.44703i	0.103046	−	0.178480i	−0.809892	−	0.586579i	$-0.800475\pi$
$373$	1.99014	−	3.44703i	0.103046	−	0.178480i	0.912938	+	0.408098i	$0.133808\pi$
$374$	−0.0320920	−	0.0555849i	−0.00165944	−	0.00287423i
$375$	−0.866025	+	0.500000i	−0.0447214	+	0.0258199i
$376$	10.0322			0.517369
$377$	26.9827	−	21.9508i	1.38968	−	1.13052i
$378$	1.03319			0.0531418
$379$	23.5846	−	13.6166i	1.21146	−	0.699437i	0.248383	−	0.968662i	$-0.420101\pi$
$379$	23.5846	−	13.6166i	1.21146	−	0.699437i	0.963077	+	0.269225i	$0.0867675\pi$
$380$	−0.909313	−	1.57498i	−0.0466468	−	0.0807946i
$381$	10.4744	−	18.1422i	0.536621	−	0.929456i
$382$			3.46711i			0.177393i
$383$	−10.4776	−	6.04924i	−0.535380	−	0.309102i	0.207825	−	0.978166i	$-0.433362\pi$
$383$	−10.4776	−	6.04924i	−0.535380	−	0.309102i	−0.743204	+	0.669064i	$0.766695\pi$
$384$	−7.42502	−	4.28684i	−0.378907	−	0.218762i
$385$			9.06228i			0.461856i
$386$	2.55266	−	4.42134i	0.129927	−	0.225041i
$387$	−4.46704	−	7.73715i	−0.227073	−	0.393301i
$388$	7.73657	−	4.46671i	0.392765	−	0.226763i
$389$	−38.7373			−1.96406			−0.982030	−	0.188726i	$-0.939564\pi$
$389$	−38.7373			−1.96406			−0.982030	+	0.188726i	$0.939564\pi$
$390$	1.01454	+	0.386832i	0.0513733	+	0.0195880i
$391$	0.0177885			0.000899603
$392$	−4.86435	+	2.80843i	−0.245687	+	0.141847i
$393$	8.51248	+	14.7441i	0.429398	+	0.743739i
$394$	−1.77113	+	3.06768i	−0.0892282	+	0.154548i
$395$			11.8661i			0.597049i
$396$	−4.36753	−	2.52159i	−0.219477	−	0.126715i
$397$	2.32709	+	1.34354i	0.116793	+	0.0674306i	0.557259	−	0.830339i	$-0.311853\pi$
$397$	2.32709	+	1.34354i	0.116793	+	0.0674306i	−0.440465	+	0.897770i	$0.645187\pi$
$398$		−	2.50385i		−	0.125507i
$399$	1.63397	−	2.83013i	0.0818010	−	0.141684i
$400$	1.73205	+	3.00000i	0.0866025	+	0.150000i
$401$	−5.93978	+	3.42933i	−0.296618	+	0.171253i	−0.640923	−	0.767605i	$-0.721448\pi$
$401$	−5.93978	+	3.42933i	−0.296618	+	0.171253i	0.344304	+	0.938858i	$0.388115\pi$
$402$	−0.754578			−0.0376350
$403$	−5.60673	+	0.900940i	−0.279291	+	0.0448790i
$404$	12.9886			0.646206
$405$	0.866025	−	0.500000i	0.0430331	−	0.0248452i
$406$	−4.98374	−	8.63209i	−0.247339	−	0.428403i
$407$	−3.77955	+	6.54637i	−0.187345	+	0.324491i
$408$		−	0.0949945i		−	0.00470293i
$409$	0.360959	+	0.208400i	0.0178483	+	0.0103047i	0.508898	−	0.860827i	$-0.330053\pi$
$409$	0.360959	+	0.208400i	0.0178483	+	0.0103047i	−0.491049	+	0.871132i	$0.663387\pi$
$410$	2.07665	+	1.19895i	0.102558	+	0.0592122i
$411$		−	14.9225i		−	0.736073i
$412$	−4.46260	+	7.72944i	−0.219856	+	0.380802i
$413$	−16.5963	−	28.7456i	−0.816648	−	1.41448i
$414$	−0.0574933	+	0.0331938i	−0.00282564	+	0.00163139i
$415$	−9.58956			−0.470733
$416$	4.36452	−	11.4468i	0.213988	−	0.561225i
$417$	−8.10958			−0.397128
$418$	0.656142	−	0.378824i	0.0320930	−	0.0185289i
$419$	5.31726	+	9.20977i	0.259765	+	0.449926i	0.966179	−	0.257873i	$-0.0830215\pi$
$419$	5.31726	+	9.20977i	0.259765	+	0.449926i	−0.706414	+	0.707799i	$0.749688\pi$
$420$	−3.27534	+	5.67305i	−0.159820	+	0.276817i
$421$		−	26.1373i		−	1.27385i	−0.770925	−	0.636926i	$-0.780205\pi$
$421$		−	26.1373i		−	1.27385i	0.770925	−	0.636926i	$-0.219795\pi$
$422$	4.28634	+	2.47472i	0.208656	+	0.120467i
$423$	7.37992	+	4.26080i	0.358824	+	0.207167i
$424$			6.21915i			0.302029i
$425$	−0.0403455	+	0.0698805i	−0.00195704	+	0.00338970i
$426$	−0.796933	−	1.38033i	−0.0386115	−	0.0668772i
$427$	38.5891	−	22.2794i	1.86746	−	1.07818i
$428$	−25.4403			−1.22971
$429$	3.39295	−	8.89867i	0.163813	−	0.429632i
$430$	−2.69044			−0.129744
$431$	−14.6870	+	8.47953i	−0.707447	+	0.408445i	−0.810115	−	0.586271i	$-0.800595\pi$
$431$	−14.6870	+	8.47953i	−0.707447	+	0.408445i	0.102668	+	0.994716i	$0.467262\pi$
$432$	−1.73205	−	3.00000i	−0.0833333	−	0.144338i
$433$	−17.9671	+	31.1200i	−0.863446	+	1.49553i	0.00513654	+	0.999987i	$0.498365\pi$
$433$	−17.9671	+	31.1200i	−0.863446	+	1.49553i	−0.868582	+	0.495545i	$0.834968\pi$
$434$			1.62726i			0.0781108i
$435$	−8.35476	−	4.82362i	−0.400580	−	0.231275i
$436$	8.48214	+	4.89716i	0.406221	+	0.234532i
$437$			0.209981i			0.0100448i
$438$	−2.16207	+	3.74482i	−0.103308	+	0.178934i
$439$	1.89125	+	3.27575i	0.0902646	+	0.156343i	0.907622	−	0.419787i	$-0.137895\pi$
$439$	1.89125	+	3.27575i	0.0902646	+	0.156343i	−0.817358	+	0.576130i	$0.804562\pi$
$440$	−2.69297	+	1.55479i	−0.128382	+	0.0741216i
$441$	−4.77113			−0.227197
$442$	0.0865035	−	0.0139002i	0.00411455	−	0.000661163i
$443$	−33.5683			−1.59488			−0.797440	−	0.603399i	$-0.793813\pi$
$443$	−33.5683			−1.59488			−0.797440	+	0.603399i	$0.793813\pi$
$444$	−4.73205	+	2.73205i	−0.224573	+	0.129657i
$445$	−5.29614	−	9.17319i	−0.251061	−	0.434851i
$446$	−0.342756	+	0.593671i	−0.0162300	+	0.0281111i
$447$			21.7627i			1.02934i
$448$	17.5453	+	10.1298i	0.828936	+	0.478586i
$449$	15.2743	+	8.81863i	0.720839	+	0.416177i	0.815061	−	0.579374i	$-0.196703\pi$
$449$	15.2743	+	8.81863i	0.720839	+	0.416177i	−0.0942223	+	0.995551i	$0.530036\pi$
$450$		−	0.301143i		−	0.0141960i
$451$	10.5162	−	18.2146i	0.495188	−	0.857691i
$452$	−7.80255	−	13.5144i	−0.367001	−	0.635665i
$453$	−12.2706	+	7.08442i	−0.576522	+	0.332855i
$454$	−5.91533			−0.277620
$455$	−11.5586	−	4.40716i	−0.541876	−	0.206611i
$456$	1.12135			0.0525118
$457$	−18.2930	+	10.5615i	−0.855710	+	0.494044i	−0.862573	−	0.505932i	$-0.831149\pi$
$457$	−18.2930	+	10.5615i	−0.855710	+	0.494044i	0.00686344	+	0.999976i	$0.497815\pi$
$458$	0.961850	+	1.66597i	0.0449443	+	0.0778458i
$459$	0.0403455	−	0.0698805i	0.00188317	−	0.00326174i
$460$		−	0.420912i		−	0.0196251i
$461$	−20.8786	−	12.0543i	−0.972413	−	0.561423i	−0.0724423	−	0.997373i	$-0.523079\pi$
$461$	−20.8786	−	12.0543i	−0.972413	−	0.561423i	−0.899971	+	0.435949i	$0.856413\pi$
$462$	−2.36342	−	1.36452i	−0.109956	−	0.0634832i
$463$		−	19.0861i		−	0.887006i	−0.896273	−	0.443503i	$-0.853736\pi$
$463$		−	19.0861i		−	0.887006i	0.896273	−	0.443503i	$-0.146264\pi$
$464$	−16.7095	+	28.9417i	−0.775720	+	1.34359i
$465$	0.787488	+	1.36397i	0.0365189	+	0.0632526i
$466$	5.22614	−	3.01731i	0.242096	−	0.139774i
$467$	−13.7080			−0.634332			−0.317166	−	0.948370i	$-0.602731\pi$
$467$	−13.7080			−0.634332			−0.317166	+	0.948370i	$0.602731\pi$
$468$	5.34022	−	4.34433i	0.246852	−	0.200817i
$469$	8.59688			0.396967
$470$	2.22241	−	1.28311i	0.102512	−	0.0591854i
$471$	3.01725	+	5.22602i	0.139027	+	0.240802i
$472$	5.69474	−	9.86359i	0.262122	−	0.454008i
$473$			23.5982i			1.08505i
$474$	−3.09465	−	1.78670i	−0.142142	−	0.0820658i
$475$	−0.824892	−	0.476251i	−0.0378486	−	0.0218519i
$476$			0.528581i			0.0242275i
$477$	−2.64136	+	4.57498i	−0.120940	+	0.209474i
$478$	0.674557	+	1.16837i	0.0308535	+	0.0534399i
$479$	30.3652	−	17.5314i	1.38742	−	0.801029i	0.394399	−	0.918939i	$-0.370953\pi$
$479$	30.3652	−	17.5314i	1.38742	−	0.801029i	0.993024	+	0.117910i	$0.0376196\pi$
$480$	−3.39771			−0.155084
$481$	−6.51160	−	8.00431i	−0.296903	−	0.364965i
$482$	−0.186215			−0.00848187
$483$	0.655019	−	0.378175i	0.0298044	−	0.0172076i
$484$	−3.84077	−	6.65241i	−0.174581	−	0.302382i
$485$	2.33943	−	4.05202i	0.106228	−	0.183993i
$486$			0.301143i			0.0136601i
$487$	−2.61331	−	1.50880i	−0.118420	−	0.0683701i	0.439620	−	0.898184i	$-0.355113\pi$
$487$	−2.61331	−	1.50880i	−0.118420	−	0.0683701i	−0.558040	+	0.829814i	$0.688447\pi$
$488$	13.2412	+	7.64483i	0.599402	+	0.346065i
$489$			20.4541i			0.924967i
$490$	−0.718396	+	1.24430i	−0.0324538	+	0.0562117i
$491$	1.10047	+	1.90607i	0.0496634	+	0.0860195i	0.889788	−	0.456373i	$-0.150852\pi$
$491$	1.10047	+	1.90607i	0.0496634	+	0.0860195i	−0.840125	+	0.542393i	$0.817518\pi$
$492$	13.1664	−	7.60164i	0.593588	−	0.342708i
$493$	−0.778446			−0.0350595
$494$	0.164082	+	1.02112i	0.00738240	+	0.0459422i
$495$	−2.64136			−0.118720
$496$	4.72493	−	2.72794i	0.212156	−	0.122488i
$497$	9.07942	+	15.7260i	0.407268	+	0.705409i
$498$	1.44391	−	2.50093i	0.0647033	−	0.112069i
$499$		−	8.68475i		−	0.388783i	−0.980924	−	0.194391i	$-0.937727\pi$
$499$		−	8.68475i		−	0.388783i	0.980924	−	0.194391i	$-0.0622732\pi$
$500$	1.65351	+	0.954656i	0.0739474	+	0.0426935i
$501$	14.6704	+	8.46999i	0.655427	+	0.378411i
$502$			5.42986i			0.242347i
$503$	−7.93251	+	13.7395i	−0.353693	+	0.612615i	−0.986893	−	0.161373i	$-0.948408\pi$
$503$	−7.93251	+	13.7395i	−0.353693	+	0.612615i	0.633200	+	0.773988i	$0.281741\pi$
$504$	−2.01954	−	3.49794i	−0.0899574	−	0.155811i
$505$	5.89135	−	3.40137i	0.262162	−	0.151359i
$506$	0.175354			0.00779542
$507$	9.69988	+	8.65519i	0.430787	+	0.384390i
$508$	−39.9979			−1.77462
$509$	36.9324	−	21.3229i	1.63700	−	0.945122i	0.655141	−	0.755506i	$-0.272609\pi$
$509$	36.9324	−	21.3229i	1.63700	−	0.945122i	0.981858	−	0.189616i	$-0.0607242\pi$
$510$	−0.0121498	−	0.0210440i	−0.000538001	−	0.000931845i
$511$	24.6324	−	42.6646i	1.08967	−	1.88737i
$512$			19.9263i			0.880628i
$513$	0.824892	+	0.476251i	0.0364199	+	0.0210270i
$514$	−1.98307	−	1.14492i	−0.0874694	−	0.0505005i
$515$			4.67456i			0.205986i
$516$	−8.52898	+	14.7726i	−0.375468	+	0.650329i
$517$	−11.2543	−	19.4930i	−0.494964	−	0.857303i
$518$	−2.56067	+	1.47841i	−0.112509	+	0.0649574i
$519$	−18.8107			−0.825697
$520$	−0.673434	−	4.19092i	−0.0295320	−	0.183784i
$521$	−5.40996			−0.237015			−0.118507	−	0.992953i	$-0.537811\pi$
$521$	−5.40996			−0.237015			−0.118507	+	0.992953i	$0.537811\pi$
$522$	2.51598	−	1.45260i	0.110121	−	0.0635786i
$523$	8.80021	+	15.2424i	0.384806	+	0.666504i	0.991742	−	0.128247i	$-0.0409349\pi$
$523$	8.80021	+	15.2424i	0.384806	+	0.666504i	−0.606936	+	0.794751i	$0.707602\pi$
$524$	16.2530	−	28.1510i	0.710015	−	1.22978i
$525$			3.43091i			0.149737i
$526$	−0.775681	−	0.447840i	−0.0338213	−	0.0195267i
$527$	0.110060	+	0.0635432i	0.00479429	+	0.00276799i
$528$			9.14995i			0.398201i
$529$	11.4757	−	19.8765i	0.498943	−	0.864195i
$530$	0.795428	+	1.37772i	0.0345512	+	0.0598444i
$531$	8.37841	−	4.83728i	0.363592	−	0.209920i
$532$	−6.23954			−0.270518
$533$	18.1178	+	22.2711i	0.784770	+	0.964669i
$534$	3.18979			0.138036
$535$	−11.5392	+	6.66217i	−0.498884	+	0.288031i
$536$	1.47494	+	2.55467i	0.0637078	+	0.110345i
$537$	5.13842	−	8.90001i	0.221739	−	0.384064i
$538$		−	8.46430i		−	0.364922i
$539$	10.9139	+	6.30114i	0.470095	+	0.271409i
$540$	−1.65351	−	0.954656i	−0.0711559	−	0.0410819i
$541$		−	2.26288i		−	0.0972887i	−0.998816	−	0.0486444i	$-0.984510\pi$
$541$		−	2.26288i		−	0.0972887i	0.998816	−	0.0486444i	$-0.0154901\pi$
$542$	2.84008	−	4.91916i	0.121992	−	0.211296i
$543$	7.54852	+	13.0744i	0.323938	+	0.561077i
$544$	−0.237434	+	0.137082i	−0.0101799	+	0.00587736i
$545$	5.12976			0.219735
$546$	2.88977	−	2.35087i	0.123671	−	0.100608i
$547$	0.320033			0.0136836			0.00684182	−	0.999977i	$-0.497822\pi$
$547$	0.320033			0.0136836			0.00684182	+	0.999977i	$0.497822\pi$
$548$	−24.6746	+	14.2459i	−1.05405	+	0.608554i
$549$	6.49373	+	11.2475i	0.277146	+	0.480031i
$550$	−0.397714	+	0.688861i	−0.0169586	+	0.0293731i
$551$		−	9.18903i		−	0.391466i
$552$	0.224759	+	0.129765i	0.00956639	+	0.00552316i
$553$	35.2573	+	20.3558i	1.49929	+	0.865616i
$554$			6.48471i			0.275509i
$555$	−1.43091	+	2.47841i	−0.0607387	+	0.105202i
$556$	7.74186	+	13.4093i	0.328328	+	0.568681i
$557$	−13.8305	+	7.98505i	−0.586017	+	0.338337i	−0.763521	−	0.645783i	$-0.776531\pi$
$557$	−13.8305	+	7.98505i	−0.586017	+	0.338337i	0.177504	+	0.984120i	$0.443198\pi$
$558$	−0.474293			−0.0200784
$559$	−30.0986	−	11.4762i	−1.27304	−	0.485394i
$560$	11.8850			0.502233
$561$	−0.184580	+	0.106567i	−0.00779296	+	0.00449927i
$562$	2.78713	+	4.82746i	0.117568	+	0.203634i
$563$	6.15426	−	10.6595i	0.259371	−	0.449244i	−0.706702	−	0.707511i	$-0.749818\pi$
$563$	6.15426	−	10.6595i	0.259371	−	0.449244i	0.966074	+	0.258267i	$0.0831514\pi$
$564$		−	16.2704i		−	0.685107i
$565$	−7.07816	−	4.08658i	−0.297780	−	0.171924i
$566$	2.64799	+	1.52882i	0.111303	+	0.0642610i
$567$		−	3.43091i		−	0.144085i
$568$	−3.11546	+	5.39614i	−0.130722	+	0.226417i
$569$	13.8416	+	23.9743i	0.580269	+	1.00506i	0.995447	+	0.0953158i	$0.0303861\pi$
$569$	13.8416	+	23.9743i	0.580269	+	1.00506i	−0.415178	+	0.909740i	$0.636281\pi$
$570$	0.248410	−	0.143420i	0.0104048	−	0.00600719i
$571$	−19.9502			−0.834892			−0.417446	−	0.908702i	$-0.637075\pi$
$571$	−19.9502			−0.834892			−0.417446	+	0.908702i	$0.637075\pi$
$572$	−17.9532	+	2.88488i	−0.750660	+	0.120623i
$573$	11.5132			0.480970
$574$	7.12480	−	4.11350i	0.297383	−	0.171694i
$575$	−0.110226	−	0.190917i	−0.00459674	−	0.00796179i
$576$	−2.95250	+	5.11388i	−0.123021	+	0.213079i
$577$		−	24.1623i		−	1.00589i	−0.864318	−	0.502946i	$-0.832250\pi$
$577$		−	24.1623i		−	1.00589i	0.864318	−	0.502946i	$-0.167750\pi$
$578$	4.43186	+	2.55873i	0.184341	+	0.106429i
$579$	−14.6819	−	8.47659i	−0.610158	−	0.352275i
$580$			18.4196i			0.764833i
$581$	−16.4504	+	28.4930i	−0.682480	+	1.18209i
$582$	0.704504	+	1.22024i	0.0292026	+	0.0505804i
$583$	12.0842	−	6.97680i	0.500475	−	0.288950i
$584$	16.9044			0.699511
$585$	1.28455	−	3.36897i	0.0531094	−	0.139290i
$586$	5.07965			0.209838
$587$	9.55436	−	5.51622i	0.394351	−	0.227679i	−0.289693	−	0.957120i	$-0.593553\pi$
$587$	9.55436	−	5.51622i	0.394351	−	0.227679i	0.684044	+	0.729441i	$0.260220\pi$
$588$	4.55479	+	7.88913i	0.187836	+	0.325342i
$589$	−0.750085	+	1.29918i	−0.0309067	+	0.0535320i
$590$		−	2.91342i		−	0.119944i
$591$	10.1868	+	5.88135i	0.419029	+	0.241927i
$592$	8.58545	+	4.95681i	0.352860	+	0.203724i
$593$			1.72909i			0.0710053i	0.999370	+	0.0355027i	$0.0113032\pi$
$593$			1.72909i			0.0710053i	−0.999370	+	0.0355027i	$0.988697\pi$
$594$	0.397714	−	0.688861i	0.0163184	−	0.0282643i
$595$	0.138422	+	0.239753i	0.00567474	+	0.00982893i
$596$	35.9849	−	20.7759i	1.47400	−	0.851014i
$597$	−8.31449			−0.340289
$598$	−0.0852779	+	0.223658i	−0.00348727	+	0.00914604i
$599$	15.5218			0.634203			0.317102	−	0.948392i	$-0.397290\pi$
$599$	15.5218			0.634203			0.317102	+	0.948392i	$0.397290\pi$
$600$	−1.01954	+	0.588631i	−0.0416225	+	0.0240308i
$601$	7.39125	+	12.8020i	0.301495	+	0.522206i	0.976475	−	0.215631i	$-0.0691808\pi$
$601$	7.39125	+	12.8020i	0.301495	+	0.522206i	−0.674979	+	0.737837i	$0.735848\pi$
$602$	−4.61532	+	7.99397i	−0.188106	+	0.325810i
$603$			2.50571i			0.102041i
$604$	23.4284	+	13.5264i	0.953287	+	0.550380i
$605$	−3.48419	−	2.01160i	−0.141653	−	0.0817831i
$606$			2.04860i			0.0832186i
$607$	12.4674	−	21.5941i	0.506035	−	0.876479i	−0.493940	−	0.869496i	$-0.664444\pi$
$607$	12.4674	−	21.5941i	0.506035	−	0.876479i	0.999976	−	0.00698303i	$-0.00222279\pi$
$608$	−1.61817	−	2.80275i	−0.0656253	−	0.113666i
$609$	−28.6644	+	16.5494i	−1.16154	+	0.670616i
$610$	3.91108			0.158355
$611$	30.3359	−	4.87464i	1.22726	−	0.197207i
$612$	−0.154064			−0.00622768
$613$	−25.5334	+	14.7417i	−1.03129	+	0.595413i	−0.917353	−	0.398075i	$-0.869678\pi$
$613$	−25.5334	+	14.7417i	−1.03129	+	0.595413i	−0.113933	+	0.993488i	$0.536345\pi$
$614$	1.04520	+	1.81034i	0.0421808	+	0.0730593i
$615$	3.98135	−	6.89590i	0.160543	−	0.278069i
$616$			10.6687i			0.429853i
$617$	14.0182	+	8.09339i	0.564350	+	0.325827i	0.754890	−	0.655852i	$-0.227690\pi$
$617$	14.0182	+	8.09339i	0.564350	+	0.325827i	−0.190540	+	0.981679i	$0.561024\pi$
$618$	−1.21911	−	0.703855i	−0.0490399	−	0.0283132i
$619$			39.3442i			1.58138i	0.612218	+	0.790689i	$0.290278\pi$
$619$			39.3442i			1.58138i	−0.612218	+	0.790689i	$0.709722\pi$
$620$	1.50356	−	2.60424i	0.0603845	−	0.104589i
$621$	0.110226	+	0.190917i	0.00442322	+	0.00766124i
$622$	3.63397	−	2.09808i	0.145709	−	0.0841252i
$623$	−36.3412			−1.45598
$624$	−11.6704	−	4.44980i	−0.467192	−	0.178134i
$625$	1.00000			0.0400000
$626$	−2.35476	+	1.35952i	−0.0941152	+	0.0543374i
$627$	−1.25795	−	2.17884i	−0.0502378	−	0.0870144i
$628$	5.76087	−	9.97811i	0.229884	−	0.398170i
$629$			0.230923i			0.00920750i
$630$	−0.894772	−	0.516597i	−0.0356486	−	0.0205817i
$631$	18.1035	+	10.4520i	0.720688	+	0.416090i	0.815006	−	0.579453i	$-0.196734\pi$
$631$	18.1035	+	10.4520i	0.720688	+	0.416090i	−0.0943177	+	0.995542i	$0.530067\pi$
$632$			13.9695i			0.555678i
$633$	8.21775	−	14.2336i	0.326626	−	0.565733i
$634$	0.0748070	+	0.129570i	0.00297097	+	0.00514586i
$635$	−18.1422	+	10.4744i	−0.719953	+	0.415665i
$636$	10.0864			0.399951
$637$	−13.3445	+	10.8559i	−0.528729	+	0.430128i
$638$	−7.67369			−0.303804
$639$	−4.58363	+	2.64636i	−0.181326	+	0.104688i
$640$	4.28684	+	7.42502i	0.169452	+	0.293500i
$641$	6.91708	−	11.9807i	0.273208	−	0.473211i	−0.696473	−	0.717583i	$-0.745248\pi$
$641$	6.91708	−	11.9807i	0.273208	−	0.473211i	0.969682	+	0.244372i	$0.0785818\pi$
$642$		−	4.01253i		−	0.158362i
$643$	0.133542	+	0.0771004i	0.00526638	+	0.00304054i	0.502631	−	0.864501i	$-0.332365\pi$
$643$	0.133542	+	0.0771004i	0.00526638	+	0.00304054i	−0.497364	+	0.867542i	$0.665699\pi$
$644$	−1.25064	−	0.722055i	−0.0492819	−	0.0284529i
$645$			8.93409i			0.351779i
$646$	0.0115727	−	0.0200445i	0.000455321	−	0.000788640i
$647$	−6.69998	−	11.6047i	−0.263403	−	0.456228i	0.703741	−	0.710457i	$-0.251512\pi$
$647$	−6.69998	−	11.6047i	−0.263403	−	0.456228i	−0.967144	+	0.254229i	$0.918178\pi$
$648$	1.01954	−	0.588631i	0.0400513	−	0.0231236i
$649$	−25.5540			−1.00308
$650$	−0.685202	−	0.842277i	−0.0268758	−	0.0330368i
$651$	5.40360			0.211784
$652$	33.8211	−	19.5266i	1.32454	−	0.764722i
$653$	2.67870	+	4.63964i	0.104826	+	0.181563i	0.913667	−	0.406464i	$-0.133238\pi$
$653$	2.67870	+	4.63964i	0.104826	+	0.181563i	−0.808841	+	0.588027i	$0.799905\pi$
$654$	−0.772396	+	1.33783i	−0.0302031	+	0.0523133i
$655$		−	17.0250i		−	0.665221i
$656$	−23.8881	−	13.7918i	−0.932673	−	0.538479i
$657$	12.4354	+	7.17956i	0.485149	+	0.280101i
$658$		−	8.80446i		−	0.343234i
$659$	6.44138	−	11.1568i	0.250920	−	0.434607i	−0.712859	−	0.701307i	$-0.752600\pi$
$659$	6.44138	−	11.1568i	0.250920	−	0.434607i	0.963780	+	0.266700i	$0.0859334\pi$
$660$	2.52159	+	4.36753i	0.0981529	+	0.170006i
$661$	−5.28132	+	3.04917i	−0.205420	+	0.118599i	−0.599181	−	0.800614i	$-0.704507\pi$
$661$	−5.28132	+	3.04917i	−0.205420	+	0.118599i	0.393761	+	0.919213i	$0.371174\pi$
$662$	7.83608			0.304558
$663$	−0.0461580	−	0.287251i	−0.00179263	−	0.0111559i
$664$	−11.2894			−0.438115
$665$	−2.83013	+	1.63397i	−0.109748	+	0.0633628i
$666$	−0.430908	−	0.746354i	−0.0166973	−	0.0289206i
$667$	1.06338	−	1.84182i	0.0411741	−	0.0713157i
$668$		−	32.3437i		−	1.25142i
$669$	1.97139	+	1.13818i	0.0762185	+	0.0440047i
$670$	0.653484	+	0.377289i	0.0252463	+	0.0145760i
$671$		−	34.3046i		−	1.32432i
$672$	−5.82862	+	10.0955i	−0.224844	+	0.389441i
$673$	−10.3388	−	17.9073i	−0.398531	−	0.690276i	0.595014	−	0.803715i	$-0.297146\pi$
$673$	−10.3388	−	17.9073i	−0.398531	−	0.690276i	−0.993545	+	0.113440i	$0.963813\pi$
$674$	−0.417996	+	0.241330i	−0.0161006	+	0.00929569i
$675$	−1.00000			−0.0384900
$676$	5.05141	−	24.3016i	0.194285	−	0.934678i
$677$	−25.5159			−0.980656			−0.490328	−	0.871538i	$-0.663123\pi$
$677$	−25.5159			−0.980656			−0.490328	+	0.871538i	$0.663123\pi$
$678$	2.13154	−	1.23064i	0.0818612	−	0.0472626i
$679$	−8.02638	−	13.9021i	−0.308024	−	0.533513i
$680$	−0.0474972	+	0.0822676i	−0.00182144	+	0.00315482i
$681$			19.6429i			0.752719i
$682$	1.08494	+	0.626390i	0.0415445	+	0.0239857i
$683$	−1.38625	−	0.800355i	−0.0530436	−	0.0306247i	0.473244	−	0.880932i	$-0.343083\pi$
$683$	−1.38625	−	0.800355i	−0.0530436	−	0.0306247i	−0.526287	+	0.850307i	$0.676416\pi$
$684$		−	1.81863i		−	0.0695369i
$685$	−7.46126	+	12.9233i	−0.285080	+	0.493773i
$686$	−1.15143	−	1.99433i	−0.0439617	−	0.0761439i
$687$	5.53217	−	3.19400i	0.211065	−	0.121859i
$688$	30.9486			1.17990
$689$	3.02190	+	18.8059i	0.115125	+	0.716448i
$690$	0.0663876			0.00252733
$691$	−22.8052	+	13.1666i	−0.867551	+	0.500881i	−0.866534	−	0.499119i	$-0.833657\pi$
$691$	−22.8052	+	13.1666i	−0.867551	+	0.500881i	−0.00101729	+	0.999999i	$0.500324\pi$
$692$	17.9577	+	31.1037i	0.682651	+	1.18239i
$693$	−4.53114	+	7.84816i	−0.172124	+	0.298127i
$694$		−	9.32271i		−	0.353885i
$695$	7.02310	+	4.05479i	0.266401	+	0.153807i
$696$	−9.83574	−	5.67867i	−0.372823	−	0.215249i
$697$		−	0.642518i		−	0.0243371i
$698$	−2.46630	+	4.27175i	−0.0933507	+	0.161688i
$699$	−10.0195	−	17.3544i	−0.378974	−	0.656402i
$700$	5.67305	−	3.27534i	0.214421	−	0.123796i
$701$	−39.3777			−1.48728			−0.743638	−	0.668582i	$-0.766901\pi$
$701$	−39.3777			−1.48728			−0.743638	+	0.668582i	$0.766901\pi$
$702$	0.685202	+	0.842277i	0.0258613	+	0.0317897i
$703$	−2.72589			−0.102809
$704$	13.5076	−	7.79863i	0.509088	−	0.293922i
$705$	−4.26080	−	7.37992i	−0.160471	−	0.277944i
$706$	−3.07337	+	5.32324i	−0.115668	+	0.200343i
$707$		−	23.3396i		−	0.877776i
$708$	−15.9970	−	9.23588i	−0.601204	−	0.347106i
$709$	−15.5842	−	8.99756i	−0.585278	−	0.337911i	0.177950	−	0.984040i	$-0.443053\pi$
$709$	−15.5842	−	8.99756i	−0.585278	−	0.337911i	−0.763228	+	0.646129i	$0.776387\pi$
$710$			1.59387i			0.0598167i
$711$	−5.93306	+	10.2764i	−0.222507	+	0.385394i
$712$	−6.23495	−	10.7993i	−0.233665	−	0.404719i
$713$	−0.300690	+	0.173603i	−0.0112609	+	0.00650149i
$714$	−0.0833695			−0.00312002
$715$	−7.38772	+	6.01000i	−0.276285	+	0.224761i
$716$	−19.6217			−0.733298
$717$	3.87978	−	2.23999i	0.144893	−	0.0836540i
$718$	4.18322	+	7.24555i	0.156116	+	0.270401i
$719$	−10.1016	+	17.4964i	−0.376725	+	0.652507i	−0.990584	−	0.136909i	$-0.956283\pi$
$719$	−10.1016	+	17.4964i	−0.376725	+	0.652507i	0.613859	+	0.789416i	$0.289616\pi$
$720$			3.46410i			0.129099i
$721$	13.8893	+	8.01899i	0.517264	+	0.298643i
$722$	−4.71854	−	2.72425i	−0.175606	−	0.101386i
$723$			0.618361i			0.0229971i
$724$	14.4125	−	24.9632i	0.535636	−	0.927749i
$725$	4.82362	+	8.35476i	0.179145	+	0.310288i
$726$	1.04924	−	0.605779i	0.0389409	−	0.0224826i
$727$	−21.8795			−0.811466			−0.405733	−	0.913992i	$-0.632984\pi$
$727$	−21.8795			−0.811466			−0.405733	+	0.913992i	$0.632984\pi$
$728$	−13.6075	−	5.18838i	−0.504328	−	0.192294i
$729$	1.00000			0.0370370
$730$	3.74482	−	2.16207i	0.138602	−	0.0800219i
$731$	0.360450	+	0.624318i	0.0133317	+	0.0230912i
$732$	12.3986	−	21.4750i	0.458264	−	0.793737i
$733$		−	26.2697i		−	0.970294i	−0.874433	−	0.485147i	$-0.838766\pi$
$733$		−	26.2697i		−	0.970294i	0.874433	−	0.485147i	$-0.161234\pi$
$734$	−1.48132	−	0.855241i	−0.0546766	−	0.0315675i
$735$	4.13192	+	2.38556i	0.152408	+	0.0879929i
$736$		−	0.749033i		−	0.0276097i
$737$	3.30925	−	5.73179i	0.121898	−	0.211133i
$738$	1.19895	+	2.07665i	0.0441341	+	0.0764426i
$739$	−36.1172	+	20.8523i	−1.32859	+	0.767064i	−0.985082	−	0.172084i	$-0.944950\pi$
$739$	−36.1172	+	20.8523i	−1.32859	+	0.767064i	−0.343512	+	0.939148i	$0.611617\pi$
$740$	5.46410			0.200864
$741$	3.39080	−	0.544864i	0.124564	−	0.0200161i
$742$	5.45808			0.200372
$743$	−9.06081	+	5.23126i	−0.332409	+	0.191916i	−0.656910	−	0.753969i	$-0.728137\pi$
$743$	−9.06081	+	5.23126i	−0.332409	+	0.191916i	0.324501	+	0.945885i	$0.394804\pi$
$744$	0.927080	+	1.60575i	0.0339884	+	0.0588696i
$745$	10.8814	−	18.8471i	0.398662	−	0.690503i
$746$		−	1.19864i		−	0.0438852i
$747$	−8.30480	−	4.79478i	−0.303857	−	0.175432i
$748$	0.352420	+	0.203470i	0.0128858	+	0.00743960i
$749$			45.7146i			1.67037i
$750$	−0.150571	+	0.260797i	−0.00549809	+	0.00952298i
$751$	14.3155	+	24.7952i	0.522381	+	0.904791i	0.999661	+	0.0260396i	$0.00828961\pi$
$751$	14.3155	+	24.7952i	0.522381	+	0.904791i	−0.477279	+	0.878752i	$0.658377\pi$
$752$	−25.5648	+	14.7598i	−0.932252	+	0.538236i
$753$	18.0309			0.657081
$754$	3.73186	−	9.78753i	0.135906	−	0.356441i
$755$	14.1688			0.515657
$756$	−5.67305	+	3.27534i	−0.206327	+	0.119123i
$757$	4.66717	+	8.08377i	0.169631	+	0.293810i	0.938290	−	0.345849i	$-0.112409\pi$
$757$	4.66717	+	8.08377i	0.169631	+	0.293810i	−0.768659	+	0.639659i	$0.779076\pi$
$758$	4.10054	−	7.10234i	0.148938	−	0.257969i
$759$		−	0.582294i		−	0.0211359i
$760$	−0.971114	−	0.560673i	−0.0352260	−	0.0203377i
$761$	0.754600	+	0.435668i	0.0273542	+	0.0157930i	0.513615	−	0.858021i	$-0.328306\pi$
$761$	0.754600	+	0.435668i	0.0273542	+	0.0157930i	−0.486261	+	0.873814i	$0.661639\pi$
$762$		−	6.30860i		−	0.228537i
$763$	8.79988	−	15.2418i	0.318577	−	0.551791i
$764$	−10.9911	−	19.0372i	−0.397645	−	0.688741i
$765$	−0.0698805	+	0.0403455i	−0.00252653	+	0.00145869i
$766$	−3.64337			−0.131640
$767$	12.4274	−	32.5933i	0.448728	−	1.17687i
$768$	9.22811			0.332991
$769$	−30.0008	+	17.3209i	−1.08186	+	0.624609i	−0.931396	−	0.364007i	$-0.881408\pi$
$769$	−30.0008	+	17.3209i	−1.08186	+	0.624609i	−0.150459	+	0.988616i	$0.548075\pi$
$770$	1.36452	+	2.36342i	0.0491739	+	0.0851717i
$771$	−3.80193	+	6.58514i	−0.136923	+	0.237158i
$772$			32.3689i			1.16498i
$773$	23.3874	+	13.5027i	0.841187	+	0.485659i	0.857667	−	0.514205i	$-0.171913\pi$
$773$	23.3874	+	13.5027i	0.841187	+	0.485659i	−0.0164808	+	0.999864i	$0.505246\pi$
$774$	−2.32999	−	1.34522i	−0.0837497	−	0.0483529i
$775$		−	1.57498i		−	0.0565748i
$776$	2.75413	−	4.77028i	0.0988673	−	0.171243i
$777$	4.90931	+	8.50318i	0.176121	+	0.305050i
$778$	−10.1026	+	5.83273i	−0.362195	+	0.209114i
$779$	7.58449			0.271742
$780$	−6.79693	+	1.09219i	−0.243369	+	0.0391068i
$781$	13.9800			0.500244
$782$	0.00463919	−	0.00267844i	0.000165897	−	9.57808e-5i
$783$	−4.82362	−	8.35476i	−0.172382	−	0.298575i
$784$	8.26384	−	14.3134i	0.295137	−	0.511192i
$785$		−	6.03449i		−	0.215380i
$786$	4.44007	+	2.56347i	0.158372	+	0.0914361i
$787$	−21.0283	−	12.1407i	−0.749577	−	0.432768i	0.0759643	−	0.997111i	$-0.475796\pi$
$787$	−21.0283	−	12.1407i	−0.749577	−	0.432768i	−0.825541	+	0.564342i	$0.809130\pi$
$788$		−	22.4587i		−	0.800058i
$789$	−1.48713	+	2.57579i	−0.0529434	+	0.0917006i
$790$	1.78670	+	3.09465i	0.0635679	+	0.110103i
$791$	−24.2845	+	14.0207i	−0.863457	+	0.498517i
$792$	−3.10958			−0.110494
$793$	43.7544	+	16.6830i	1.55376	+	0.592431i
$794$	0.809198			0.0287174
$795$	4.57498	−	2.64136i	0.162258	−	0.0936795i
$796$	7.93748	+	13.7481i	0.281336	+	0.487289i
$797$	−5.49209	+	9.51258i	−0.194540	+	0.336953i	−0.946750	−	0.321971i	$-0.895655\pi$
$797$	−5.49209	+	9.51258i	−0.194540	+	0.336953i	0.752210	+	0.658924i	$0.228988\pi$
$798$		−	0.984120i		−	0.0348375i
$799$	−0.595493	−	0.343808i	−0.0210670	−	0.0121631i
$800$	2.94251	+	1.69886i	0.104033	+	0.0600637i
$801$		−	10.5923i		−	0.374260i
$802$	−1.03272	+	1.78872i	−0.0364666	+	0.0631620i
$803$	−18.9638	−	32.8463i	−0.669219	−	1.15912i
$804$	4.14323	−	2.39210i	0.146121	−	0.0843628i
$805$	−0.756350			−0.0266578
$806$	−1.32657	+	1.07918i	−0.0467263	+	0.0380124i
$807$	−28.1072			−0.989422
$808$	6.93566	−	4.00431i	0.243996	−	0.140871i
$809$	−25.3218	−	43.8587i	−0.890267	−	1.54199i	−0.839555	−	0.543275i	$-0.817184\pi$
$809$	−25.3218	−	43.8587i	−0.890267	−	1.54199i	−0.0507123	−	0.998713i	$-0.516149\pi$
$810$	0.150571	−	0.260797i	0.00529054	−	0.00916349i
$811$		−	7.67073i		−	0.269356i	−0.990889	−	0.134678i	$-0.957000\pi$
$811$		−	7.67073i		−	0.269356i	0.990889	−	0.134678i	$-0.0430000\pi$
$812$	54.7293	+	31.5980i	1.92062	+	1.10887i
$813$	−16.3350	−	9.43101i	−0.572893	−	0.330760i
$814$			2.27637i			0.0797867i
$815$	10.2271	−	17.7138i	0.358238	−	0.620486i
$816$	0.139761	+	0.242073i	0.00489261	+	0.00847425i
$817$	−7.36965	+	4.25487i	−0.257832	+	0.148859i
$818$	0.125516			0.00438857
$819$	−7.80648	−	9.59602i	−0.272780	−	0.335312i
$820$	−15.2033			−0.530921
$821$	−30.3041	+	17.4961i	−1.05762	+	0.610617i	−0.924773	−	0.380520i	$-0.875745\pi$
$821$	−30.3041	+	17.4961i	−1.05762	+	0.610617i	−0.132846	+	0.991137i	$0.542412\pi$
$822$	−2.24691	−	3.89175i	−0.0783698	−	0.135741i
$823$	−8.10657	+	14.0410i	−0.282577	+	0.489438i	−0.972019	−	0.234903i	$-0.924523\pi$
$823$	−8.10657	+	14.0410i	−0.282577	+	0.489438i	0.689442	+	0.724341i	$0.257856\pi$
$824$			5.50318i			0.191712i
$825$	2.28749	+	1.32068i	0.0796401	+	0.0459802i
$826$	−8.65652	−	4.99785i	−0.301199	−	0.173897i
$827$		−	26.9634i		−	0.937611i	−0.883301	−	0.468805i	$-0.844685\pi$
$827$		−	26.9634i		−	0.937611i	0.883301	−	0.468805i	$-0.155315\pi$
$828$	0.210456	−	0.364520i	0.00731385	−	0.0126680i
$829$	1.08254	+	1.87501i	0.0375981	+	0.0651219i	0.884212	−	0.467086i	$-0.154696\pi$
$829$	1.08254	+	1.87501i	0.0375981	+	0.0651219i	−0.846614	+	0.532207i	$0.821363\pi$
$830$	−2.50093	+	1.44391i	−0.0868086	+	0.0501190i
$831$	21.5336			0.746994
$832$	3.37786	+	21.0211i	0.117106	+	0.728777i
$833$	0.384987			0.0133390
$834$	−2.11496	+	1.22107i	−0.0732350	+	0.0422822i
$835$	−8.46999	−	14.6704i	−0.293116	−	0.507692i
$836$	−2.40183	+	4.16008i	−0.0830689	+	0.143880i
$837$			1.57498i			0.0544391i
$838$	2.77346	+	1.60126i	0.0958074	+	0.0553145i
$839$	−6.71524	−	3.87705i	−0.231836	−	0.133851i	0.379583	−	0.925158i	$-0.376068\pi$
$839$	−6.71524	−	3.87705i	−0.231836	−	0.133851i	−0.611419	+	0.791307i	$0.709401\pi$
$840$			4.03908i			0.139361i
$841$	−32.0347	+	55.4857i	−1.10464	+	1.91330i
$842$	−3.93553	−	6.81654i	−0.135627	−	0.234913i
$843$	16.0304	−	9.25518i	0.552118	−	0.318765i
$844$	−31.3805			−1.08016
$845$	−4.07275	−	12.3456i	−0.140107	−	0.424700i
$846$	2.56622			0.0882284
$847$	−11.9539	+	6.90161i	−0.410742	+	0.237142i
$848$	−9.14995	−	15.8482i	−0.314211	−	0.544229i
$849$	5.07672	−	8.79313i	0.174233	−	0.301780i
$850$			0.0242995i			0.000833467i
$851$	−0.546369	−	0.315446i	−0.0187293	−	0.0108134i
$852$	8.75159	+	5.05273i	0.299825	+	0.173104i
$853$		−	14.4459i		−	0.494618i	−0.968937	−	0.247309i	$-0.920454\pi$
$853$		−	14.4459i		−	0.494618i	0.968937	−	0.247309i	$-0.0795462\pi$
$854$	6.70929	−	11.6208i	0.229587	−	0.397656i
$855$	−0.476251	−	0.824892i	−0.0162875	−	0.0282107i
$856$	−13.5847	+	7.84312i	−0.464315	+	0.268072i
$857$	1.52830			0.0522058			0.0261029	−	0.999659i	$-0.491690\pi$
$857$	1.52830			0.0522058			0.0261029	+	0.999659i	$0.491690\pi$
$858$	−0.455012	−	2.83163i	−0.0155339	−	0.0966703i
$859$	49.1152			1.67579			0.837894	−	0.545833i	$-0.183787\pi$
$859$	49.1152			1.67579			0.837894	+	0.545833i	$0.183787\pi$
$860$	14.7726	−	8.52898i	0.503743	−	0.290836i
$861$	−13.6596	−	23.6592i	−0.465519	−	0.806303i
$862$	−2.55355	+	4.42288i	−0.0869743	+	0.150644i
$863$		−	9.73540i		−	0.331397i	−0.986176	−	0.165698i	$-0.947012\pi$
$863$		−	9.73540i		−	0.331397i	0.986176	−	0.165698i	$-0.0529878\pi$
$864$	−2.94251	−	1.69886i	−0.100106	−	0.0577963i
$865$	16.2905	+	9.40534i	0.553895	+	0.319791i
$866$			10.8214i			0.367725i
$867$	8.49674	−	14.7168i	0.288565	−	0.499808i
$868$	−5.15858	−	8.93492i	−0.175094	−	0.303271i
$869$	27.1436	−	15.6714i	0.920784	−	0.531615i
$870$	−2.90520			−0.0984955
$871$	5.70135	+	7.00832i	0.193183	+	0.237468i
$872$	6.03908			0.204509
$873$	4.05202	−	2.33943i	0.137140	−	0.0791778i
$874$	0.0316172	+	0.0547625i	0.00106947	+	0.00185237i
$875$	1.71545	−	2.97125i	0.0579929	−	0.100447i
$876$		−	27.4160i		−	0.926302i
$877$	−42.3637	−	24.4587i	−1.43052	−	0.825911i	−0.433360	−	0.901221i	$-0.642672\pi$
$877$	−42.3637	−	24.4587i	−1.43052	−	0.825911i	−0.997160	+	0.0753094i	$0.976006\pi$
$878$	0.986468	+	0.569538i	0.0332917	+	0.0192210i
$879$		−	16.8679i		−	0.568940i
$880$	4.57498	−	7.92409i	0.154222	−	0.267121i
$881$	0.353227	+	0.611807i	0.0119005	+	0.0206123i	0.871914	−	0.489658i	$-0.162879\pi$
$881$	0.353227	+	0.611807i	0.0119005	+	0.0206123i	−0.860014	+	0.510271i	$0.829545\pi$
$882$	−1.24430	+	0.718396i	−0.0418977	+	0.0241896i
$883$	6.46965			0.217721			0.108860	−	0.994057i	$-0.465280\pi$
$883$	6.46965			0.217721			0.108860	+	0.994057i	$0.465280\pi$
$884$	−0.430908	+	0.350549i	−0.0144930	+	0.0117902i
$885$	−9.67456			−0.325207
$886$	−8.75453	+	5.05443i	−0.294114	+	0.169807i
$887$	20.8317	+	36.0815i	0.699459	+	1.21150i	0.968654	+	0.248413i	$0.0799089\pi$
$887$	20.8317	+	36.0815i	0.699459	+	1.21150i	−0.269196	+	0.963086i	$0.586758\pi$
$888$	−1.68455	+	2.91773i	−0.0565299	+	0.0979127i
$889$			71.8736i			2.41056i
$890$	−2.76244	−	1.59490i	−0.0925973	−	0.0534611i
$891$	−2.28749	−	1.32068i	−0.0766337	−	0.0442445i
$892$		−	4.34630i		−	0.145525i
$893$	4.05842	−	7.02939i	0.135810	−	0.235230i
$894$	3.27684	+	5.67566i	0.109594	+	0.189822i
$895$	−8.90001	+	5.13842i	−0.297494	+	0.171758i
$896$	29.4155			0.982703
$897$	0.742695	+	0.283181i	0.0247979	+	0.00945513i
$898$	5.31133			0.177242
$899$	13.1586	−	7.59709i	0.438862	−	0.253377i
$900$	0.954656	+	1.65351i	0.0318219	+	0.0551171i
$901$	0.213134	−	0.369159i	0.00710053	−	0.0122985i
$902$		−	6.33375i		−	0.210891i
$903$	26.5454	+	15.3260i	0.883377	+	0.510018i
$904$	−8.33284	−	4.81097i	−0.277146	−	0.160010i
$905$		−	15.0970i		−	0.501843i
$906$	−2.13342	+	3.69520i	−0.0708783	+	0.122765i
$907$	25.1044	+	43.4822i	0.833579	+	1.44380i	0.895182	+	0.445701i	$0.147045\pi$
$907$	25.1044	+	43.4822i	0.833579	+	1.44380i	−0.0616030	+	0.998101i	$0.519621\pi$
$908$	32.4799	−	18.7523i	1.07788	−	0.622316i
$909$	6.80275			0.225633
$910$	−3.67805	+	0.591022i	−0.121926	+	0.0195922i
$911$	6.06993			0.201106			0.100553	−	0.994932i	$-0.467939\pi$
$911$	6.06993			0.201106			0.100553	+	0.994932i	$0.467939\pi$
$912$	−2.85751	+	1.64978i	−0.0946216	+	0.0546298i
$913$	12.6648	+	21.9360i	0.419142	+	0.725976i
$914$	−3.18051	+	5.50880i	−0.105202	+	0.182215i
$915$		−	12.9875i		−	0.429352i
$916$	−10.5626	−	6.09834i	−0.348999	−	0.201495i
$917$	−50.5855	−	29.2056i	−1.67048	−	0.964452i
$918$		−	0.0242995i		−	0.000802004i
$919$	9.61032	−	16.6456i	0.317015	−	0.549087i	−0.662849	−	0.748754i	$-0.730653\pi$
$919$	9.61032	−	16.6456i	0.317015	−	0.549087i	0.979864	+	0.199667i	$0.0639860\pi$
$920$	−0.129765	−	0.224759i	−0.00427822	−	0.00741010i
$921$	6.01156	−	3.47077i	0.198088	−	0.114366i
$922$	−7.26012			−0.239099
$923$	−6.79875	+	17.8310i	−0.223783	+	0.586915i
$924$	17.3027			0.569218
$925$	2.47841	−	1.43091i	0.0814895	−	0.0470480i
$926$	−2.87382	−	4.97760i	−0.0944396	−	0.163574i
$927$	−2.33728	+	4.04829i	−0.0767663	+	0.132963i
$928$			32.7786i			1.07601i
$929$	−5.33864	−	3.08227i	−0.175155	−	0.101126i	0.409859	−	0.912149i	$-0.365578\pi$
$929$	−5.33864	−	3.08227i	−0.175155	−	0.101126i	−0.585014	+	0.811023i	$0.698911\pi$
$930$	0.410750	+	0.237147i	0.0134690	+	0.00777634i
$931$			4.54451i			0.148940i
$932$	−19.1304	+	33.1349i	−0.626638	+	1.08537i
$933$	−6.96704	−	12.0673i	−0.228091	−	0.395065i
$934$	−3.57502	+	2.06404i	−0.116978	+	0.0675374i
$935$	0.213134			0.00697024
$936$	1.51225	−	3.96616i	0.0494294	−	0.129638i
$937$	7.89678			0.257977			0.128988	−	0.991646i	$-0.458827\pi$
$937$	7.89678			0.257977			0.128988	+	0.991646i	$0.458827\pi$
$938$	2.24204	−	1.29444i	0.0732053	−	0.0422651i
$939$	4.51454	+	7.81941i	0.147326	+	0.255177i
$940$	−8.13520	+	14.0906i	−0.265341	+	0.459584i
$941$			38.9659i			1.27025i	0.772409	+	0.635126i	$0.219052\pi$
$941$			38.9659i			1.27025i	−0.772409	+	0.635126i	$0.780948\pi$
$942$	1.57378	+	0.908622i	0.0512765	+	0.0296045i
$943$	1.52021	+	0.877696i	0.0495050	+	0.0285817i
$944$			33.5137i			1.09078i
$945$	−1.71545	+	2.97125i	−0.0558037	+	0.0966549i
$946$	3.55321	+	6.15434i	0.115525	+	0.200095i
$947$	−17.5175	+	10.1137i	−0.569243	+	0.328652i	−0.756847	−	0.653592i	$-0.773261\pi$
$947$	−17.5175	+	10.1137i	−0.569243	+	0.328652i	0.187604	+	0.982245i	$0.439928\pi$
$948$	22.6561			0.735837
$949$	51.1168	−	8.21390i	1.65932	−	0.266635i
$950$	−0.286840			−0.00930630
$951$	0.430259	−	0.248410i	0.0139521	−	0.00805526i
$952$	0.162959	+	0.282253i	0.00528152	+	0.00914786i
$953$	−7.18379	+	12.4427i	−0.232706	+	0.403059i	−0.958604	−	0.284744i	$-0.908091\pi$
$953$	−7.18379	+	12.4427i	−0.232706	+	0.403059i	0.725898	+	0.687803i	$0.241425\pi$
$954$			1.59086i			0.0515059i
$955$	−9.97070	−	5.75659i	−0.322644	−	0.186279i
$956$	−7.40771	−	4.27684i	−0.239582	−	0.138323i
$957$			25.4819i			0.823713i
$958$	5.27945	−	9.14428i	0.170571	−	0.295438i
$959$	25.5989	+	44.3386i	0.826631	+	1.43177i
$960$	5.11388	−	2.95250i	0.165050	−	0.0952916i
$961$	28.5195			0.919982
$962$	−2.90343	−	1.10704i	−0.0936103	−	0.0356925i
$963$	−13.3243			−0.429371
$964$	1.02247	−	0.590323i	0.0329315	−	0.0190130i
$965$	8.47659	+	14.6819i	0.272871	+	0.472626i
$966$	0.113885	−	0.197254i	0.00366418	−	0.00634655i
$967$		−	3.30779i		−	0.106371i	−0.998585	−	0.0531857i	$-0.983062\pi$
$967$		−	3.30779i		−	0.106371i	0.998585	−	0.0531857i	$-0.0169375\pi$
$968$	−4.10181	−	2.36818i	−0.131837	−	0.0761162i
$969$	−0.0665613	−	0.0384292i	−0.00213826	−	0.00123452i
$970$		−	1.40901i		−	0.0452405i
$971$	14.6341	−	25.3469i	0.469630	−	0.813422i	−0.529767	−	0.848143i	$-0.677721\pi$
$971$	14.6341	−	25.3469i	0.469630	−	0.813422i	0.999397	+	0.0347206i	$0.0110541\pi$
$972$	−0.954656	−	1.65351i	−0.0306206	−	0.0530365i
$973$	24.0956	−	13.9116i	0.772470	−	0.445986i
$974$	−0.908727			−0.0291175
$975$	−2.79693	+	2.27534i	−0.0895736	+	0.0728691i
$976$	−44.9899			−1.44009
$977$	43.8512	−	25.3175i	1.40292	−	0.809979i	0.408232	−	0.912878i	$-0.366145\pi$
$977$	43.8512	−	25.3175i	1.40292	−	0.809979i	0.994692	+	0.102900i	$0.0328120\pi$
$978$	3.07981	+	5.33438i	0.0984813	+	0.170575i
$979$	−13.9890	+	24.2297i	−0.447092	+	0.774386i
$980$		−	9.10958i		−	0.290995i
$981$	4.44251	+	2.56488i	0.141838	+	0.0818904i
$982$	0.573998	+	0.331398i	0.0183170	+	0.0105753i
$983$			29.1032i			0.928248i	0.885770	+	0.464124i	$0.153631\pi$
$983$			29.1032i			0.928248i	−0.885770	+	0.464124i	$0.846369\pi$
$984$	4.68709	−	8.11828i	0.149419	−	0.258801i
$985$	−5.88135	−	10.1868i	−0.187396	−	0.324579i
$986$	−0.203017	+	0.117212i	−0.00646537	+	0.00373278i
$987$	−29.2368			−0.930618
$988$	−4.13799	−	5.08658i	−0.131647	−	0.161826i
$989$	−1.96954			−0.0626276
$990$	−0.688861	+	0.397714i	−0.0218934	+	0.0126402i
$991$	−9.67671	−	16.7606i	−0.307391	−	0.532417i	0.670400	−	0.742000i	$-0.266123\pi$
$991$	−9.67671	−	16.7606i	−0.307391	−	0.532417i	−0.977791	+	0.209583i	$0.932789\pi$
$992$	2.67566	−	4.63438i	0.0849523	−	0.147142i
$993$		−	26.0211i		−	0.825756i
$994$	4.73578	+	2.73420i	0.150210	+	0.0867237i
$995$	7.20056	+	4.15724i	0.228273	+	0.131793i
$996$			18.3095i			0.580158i
$997$	−30.8483	+	53.4309i	−0.976976	+	1.69217i	−0.303723	+	0.952760i	$0.598230\pi$
$997$	−30.8483	+	53.4309i	−0.976976	+	1.69217i	−0.673253	+	0.739412i	$0.735104\pi$
$998$	−1.30768	−	2.26496i	−0.0413937	−	0.0716961i
$999$	−2.47841	+	1.43091i	−0.0784133	+	0.0452719i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.bb.c.166.2	yes	8
3.2	odd	2		585.2.bu.b.361.3		8
5.2	odd	4		975.2.w.j.49.2		8
5.3	odd	4		975.2.w.g.49.3		8
5.4	even	2		975.2.bc.i.751.3		8
13.2	odd	12		2535.2.a.bl.1.2		4
13.4	even	6	inner	195.2.bb.c.121.2	✓	8
13.11	odd	12		2535.2.a.bi.1.3		4
39.2	even	12		7605.2.a.cg.1.3		4
39.11	even	12		7605.2.a.ck.1.2		4
39.17	odd	6		585.2.bu.b.316.3		8
65.4	even	6		975.2.bc.i.901.3		8
65.17	odd	12		975.2.w.g.199.3		8
65.43	odd	12		975.2.w.j.199.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.c.121.2	✓	8	13.4	even	6	inner
195.2.bb.c.166.2	yes	8	1.1	even	1	trivial
585.2.bu.b.316.3		8	39.17	odd	6
585.2.bu.b.361.3		8	3.2	odd	2
975.2.w.g.49.3		8	5.3	odd	4
975.2.w.g.199.3		8	65.17	odd	12
975.2.w.j.49.2		8	5.2	odd	4
975.2.w.j.199.2		8	65.43	odd	12
975.2.bc.i.751.3		8	5.4	even	2
975.2.bc.i.901.3		8	65.4	even	6
2535.2.a.bi.1.3		4	13.11	odd	12
2535.2.a.bl.1.2		4	13.2	odd	12
7605.2.a.cg.1.3		4	39.2	even	12
7605.2.a.ck.1.2		4	39.11	even	12

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.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.260797 - 0.150571i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.954656 + 1.65351i) q^{4} +1.00000i q^{5} +(-0.260797 - 0.150571i) q^{6} +(2.97125 + 1.71545i) q^{7} +1.17726i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.260797 - 0.150571i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.954656 + 1.65351i) q^{4} +1.00000i q^{5} +(-0.260797 - 0.150571i) q^{6} +(2.97125 + 1.71545i) q^{7} +1.17726i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.150571 + 0.260797i) q^{10} +(2.28749 - 1.32068i) q^{11} +1.90931 q^{12} +(0.572034 + 3.55988i) q^{13} +1.03319 q^{14} +(0.866025 - 0.500000i) q^{15} +(-1.73205 - 3.00000i) q^{16} +(0.0403455 - 0.0698805i) q^{17} +0.301143i q^{18} +(0.824892 + 0.476251i) q^{19} +(-1.65351 - 0.954656i) q^{20} -3.43091i q^{21} +(0.397714 - 0.688861i) q^{22} +(0.110226 + 0.190917i) q^{23} +(1.01954 - 0.588631i) q^{24} -1.00000 q^{25} +(0.685202 + 0.842277i) q^{26} +1.00000 q^{27} +(-5.67305 + 3.27534i) q^{28} +(-4.82362 - 8.35476i) q^{29} +(0.150571 - 0.260797i) q^{30} +1.57498i q^{31} +(-2.94251 - 1.69886i) q^{32} +(-2.28749 - 1.32068i) q^{33} -0.0242995i q^{34} +(-1.71545 + 2.97125i) q^{35} +(-0.954656 - 1.65351i) q^{36} +(-2.47841 + 1.43091i) q^{37} +0.286840 q^{38} +(2.79693 - 2.27534i) q^{39} -1.17726 q^{40} +(6.89590 - 3.98135i) q^{41} +(-0.516597 - 0.894772i) q^{42} +(-4.46704 + 7.73715i) q^{43} +5.04319i q^{44} +(-0.866025 - 0.500000i) q^{45} +(0.0574933 + 0.0331938i) q^{46} -8.52159i q^{47} +(-1.73205 + 3.00000i) q^{48} +(2.38556 + 4.13192i) q^{49} +(-0.260797 + 0.150571i) q^{50} -0.0806910 q^{51} +(-6.43241 - 2.45260i) q^{52} +5.28273 q^{53} +(0.260797 - 0.150571i) q^{54} +(1.32068 + 2.28749i) q^{55} +(-2.01954 + 3.49794i) q^{56} -0.952503i q^{57} +(-2.51598 - 1.45260i) q^{58} +(-8.37841 - 4.83728i) q^{59} +1.90931i q^{60} +(6.49373 - 11.2475i) q^{61} +(0.237147 + 0.410750i) q^{62} +(-2.97125 + 1.71545i) q^{63} +5.90501 q^{64} +(-3.55988 + 0.572034i) q^{65} -0.795428 q^{66} +(2.17001 - 1.25286i) q^{67} +(0.0770322 + 0.133424i) q^{68} +(0.110226 - 0.190917i) q^{69} +1.03319i q^{70} +(4.58363 + 2.64636i) q^{71} +(-1.01954 - 0.588631i) q^{72} -14.3591i q^{73} +(-0.430908 + 0.746354i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-1.57498 + 0.909313i) q^{76} +9.06228 q^{77} +(0.386832 - 1.01454i) q^{78} +11.8661 q^{79} +(3.00000 - 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.19895 - 2.07665i) q^{82} +9.58956i q^{83} +(5.67305 + 3.27534i) q^{84} +(0.0698805 + 0.0403455i) q^{85} +2.69044i q^{86} +(-4.82362 + 8.35476i) q^{87} +(1.55479 + 2.69297i) q^{88} +(-9.17319 + 5.29614i) q^{89} -0.301143 q^{90} +(-4.40716 + 11.5586i) q^{91} -0.420912 q^{92} +(1.36397 - 0.787488i) q^{93} +(-1.28311 - 2.22241i) q^{94} +(-0.476251 + 0.824892i) q^{95} +3.39771i q^{96} +(-4.05202 - 2.33943i) q^{97} +(1.24430 + 0.718396i) q^{98} +2.64136i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{6} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 6 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^6 + 6 * q^7 - 4 * q^9	\( 8 q + 6 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{6} + 6 q^{7} - 4 q^{9} + 2 q^{10} + 12 q^{11} - 8 q^{12} + 6 q^{13} - 4 q^{14} - 2 q^{17} + 12 q^{19} + 4 q^{23} - 12 q^{24} - 8 q^{25} - 4 q^{26} + 8 q^{27} - 12 q^{28} - 6 q^{29} + 2 q^{30} + 12 q^{32} - 12 q^{33} - 6 q^{35} + 4 q^{36} - 12 q^{37} - 16 q^{38} - 30 q^{41} + 2 q^{42} + 6 q^{43} + 36 q^{46} - 8 q^{49} - 6 q^{50} + 4 q^{51} - 20 q^{52} - 32 q^{53} + 6 q^{54} - 8 q^{55} + 4 q^{56} + 12 q^{58} - 30 q^{59} - 30 q^{62} - 6 q^{63} + 32 q^{64} - 6 q^{65} + 30 q^{67} + 16 q^{68} + 4 q^{69} + 18 q^{71} + 12 q^{72} + 12 q^{74} + 4 q^{75} - 8 q^{77} + 14 q^{78} + 56 q^{79} + 24 q^{80} - 4 q^{81} - 24 q^{82} + 12 q^{84} + 6 q^{85} - 6 q^{87} + 8 q^{88} - 18 q^{89} - 4 q^{90} - 16 q^{91} + 40 q^{92} - 24 q^{93} - 16 q^{94} - 6 q^{97} - 12 q^{98}+O(q^{100}) \) 8 * q + 6 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^6 + 6 * q^7 - 4 * q^9 + 2 * q^10 + 12 * q^11 - 8 * q^12 + 6 * q^13 - 4 * q^14 - 2 * q^17 + 12 * q^19 + 4 * q^23 - 12 * q^24 - 8 * q^25 - 4 * q^26 + 8 * q^27 - 12 * q^28 - 6 * q^29 + 2 * q^30 + 12 * q^32 - 12 * q^33 - 6 * q^35 + 4 * q^36 - 12 * q^37 - 16 * q^38 - 30 * q^41 + 2 * q^42 + 6 * q^43 + 36 * q^46 - 8 * q^49 - 6 * q^50 + 4 * q^51 - 20 * q^52 - 32 * q^53 + 6 * q^54 - 8 * q^55 + 4 * q^56 + 12 * q^58 - 30 * q^59 - 30 * q^62 - 6 * q^63 + 32 * q^64 - 6 * q^65 + 30 * q^67 + 16 * q^68 + 4 * q^69 + 18 * q^71 + 12 * q^72 + 12 * q^74 + 4 * q^75 - 8 * q^77 + 14 * q^78 + 56 * q^79 + 24 * q^80 - 4 * q^81 - 24 * q^82 + 12 * q^84 + 6 * q^85 - 6 * q^87 + 8 * q^88 - 18 * q^89 - 4 * q^90 - 16 * q^91 + 40 * q^92 - 24 * q^93 - 16 * q^94 - 6 * q^97 - 12 * q^98

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