LMFDB - Embedded newform 798.2.be.a.607.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(493,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("798.493");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.be (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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			607.2
Character	$\chi$	$=$	798.607
Dual form			798.2.be.a.493.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.81074 - 1.62278i) q^{5} +1.00000i q^{6} +(2.61522 + 0.400774i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.81074 - 1.62278i) q^{5} +1.00000i q^{6} +(2.61522 + 0.400774i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.62278 + 2.81074i) q^{10} +(2.06663 + 3.57950i) q^{11} +(0.500000 - 0.866025i) q^{12} -2.67370 q^{13} +(-2.06446 - 1.65469i) q^{14} +3.24556i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.12164 + 1.22493i) q^{17} +(0.866025 - 0.500000i) q^{18} +(1.61619 + 4.04820i) q^{19} -3.24556i q^{20} +(-0.960530 - 2.46523i) q^{21} -4.13326i q^{22} +(-2.24167 + 3.88269i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(2.76684 + 4.79230i) q^{25} +(2.31549 + 1.33685i) q^{26} +1.00000 q^{27} +(0.960530 + 2.46523i) q^{28} -8.43515i q^{29} +(1.62278 - 2.81074i) q^{30} +(0.831683 + 1.44052i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.06663 - 3.57950i) q^{33} +2.44985 q^{34} +(-6.70034 - 5.37040i) q^{35} -1.00000 q^{36} +(9.75396 + 5.63145i) q^{37} +(0.624436 - 4.31394i) q^{38} +(1.33685 + 2.31549i) q^{39} +(-1.62278 + 2.81074i) q^{40} -6.53220 q^{41} +(-0.400774 + 2.61522i) q^{42} +11.0930 q^{43} +(-2.06663 + 3.57950i) q^{44} +(2.81074 - 1.62278i) q^{45} +(3.88269 - 2.24167i) q^{46} +(9.65673 + 5.57531i) q^{47} +1.00000 q^{48} +(6.67876 + 2.09623i) q^{49} -5.53367i q^{50} +(2.12164 + 1.22493i) q^{51} +(-1.33685 - 2.31549i) q^{52} +(8.72415 - 5.03689i) q^{53} +(-0.866025 - 0.500000i) q^{54} -13.4147i q^{55} +(0.400774 - 2.61522i) q^{56} +(2.69775 - 3.42376i) q^{57} +(-4.21757 + 7.30505i) q^{58} +(3.12287 + 5.40896i) q^{59} +(-2.81074 + 1.62278i) q^{60} +(-10.5360 - 6.08297i) q^{61} -1.66337i q^{62} +(-1.65469 + 2.06446i) q^{63} -1.00000 q^{64} +(7.51506 + 4.33882i) q^{65} +(-3.57950 + 2.06663i) q^{66} +(-7.27683 + 4.20128i) q^{67} +(-2.12164 - 1.22493i) q^{68} +4.48334 q^{69} +(3.11746 + 8.00107i) q^{70} +8.08098i q^{71} +(0.866025 + 0.500000i) q^{72} +(-3.98840 + 2.30270i) q^{73} +(-5.63145 - 9.75396i) q^{74} +(2.76684 - 4.79230i) q^{75} +(-2.69775 + 3.42376i) q^{76} +(3.97011 + 10.1894i) q^{77} -2.67370i q^{78} +(4.73594 + 2.73430i) q^{79} +(2.81074 - 1.62278i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.65705 + 3.26610i) q^{82} -14.0898i q^{83} +(1.65469 - 2.06446i) q^{84} +7.95116 q^{85} +(-9.60686 - 5.54652i) q^{86} +(-7.30505 + 4.21757i) q^{87} +(3.57950 - 2.06663i) q^{88} +(-5.38710 + 9.33073i) q^{89} -3.24556 q^{90} +(-6.99230 - 1.07155i) q^{91} -4.48334 q^{92} +(0.831683 - 1.44052i) q^{93} +(-5.57531 - 9.65673i) q^{94} +(2.02664 - 14.0012i) q^{95} +(-0.866025 - 0.500000i) q^{96} +5.90991 q^{97} +(-4.73586 - 5.15477i) q^{98} -4.13326 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 14 q^{3} + 14 q^{4} - 6 q^{5} - 2 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q - 14 * q^3 + 14 * q^4 - 6 * q^5 - 2 * q^7 - 14 * q^9	$ 28 q - 14 q^{3} + 14 q^{4} - 6 q^{5} - 2 q^{7} - 14 q^{9} - 4 q^{10} + 6 q^{11} + 14 q^{12} + 8 q^{13} + 4 q^{14} - 14 q^{16} - 12 q^{17} + 6 q^{19} + 4 q^{21} + 6 q^{23} + 20 q^{25} + 12 q^{26} + 28 q^{27} - 4 q^{28} - 4 q^{30} + 4 q^{31} + 6 q^{33} + 8 q^{34} - 10 q^{35} - 28 q^{36} + 12 q^{37} - 24 q^{38} - 4 q^{39} + 4 q^{40} + 40 q^{41} - 8 q^{42} + 52 q^{43} - 6 q^{44} + 6 q^{45} + 36 q^{46} - 6 q^{47} + 28 q^{48} + 18 q^{49} + 12 q^{51} + 4 q^{52} + 36 q^{53} + 8 q^{56} - 12 q^{57} + 4 q^{58} + 32 q^{59} - 6 q^{60} + 6 q^{61} - 2 q^{63} - 28 q^{64} - 60 q^{65} - 12 q^{67} - 12 q^{68} - 12 q^{69} - 12 q^{70} + 30 q^{73} + 12 q^{74} + 20 q^{75} + 12 q^{76} + 28 q^{77} - 36 q^{79} + 6 q^{80} - 14 q^{81} + 2 q^{84} + 64 q^{85} - 24 q^{86} + 16 q^{89} + 8 q^{90} - 20 q^{91} + 12 q^{92} + 4 q^{93} + 14 q^{95} - 16 q^{97} - 8 q^{98} - 12 q^{99}+O(q^{100}) $ 28 * q - 14 * q^3 + 14 * q^4 - 6 * q^5 - 2 * q^7 - 14 * q^9 - 4 * q^10 + 6 * q^11 + 14 * q^12 + 8 * q^13 + 4 * q^14 - 14 * q^16 - 12 * q^17 + 6 * q^19 + 4 * q^21 + 6 * q^23 + 20 * q^25 + 12 * q^26 + 28 * q^27 - 4 * q^28 - 4 * q^30 + 4 * q^31 + 6 * q^33 + 8 * q^34 - 10 * q^35 - 28 * q^36 + 12 * q^37 - 24 * q^38 - 4 * q^39 + 4 * q^40 + 40 * q^41 - 8 * q^42 + 52 * q^43 - 6 * q^44 + 6 * q^45 + 36 * q^46 - 6 * q^47 + 28 * q^48 + 18 * q^49 + 12 * q^51 + 4 * q^52 + 36 * q^53 + 8 * q^56 - 12 * q^57 + 4 * q^58 + 32 * q^59 - 6 * q^60 + 6 * q^61 - 2 * q^63 - 28 * q^64 - 60 * q^65 - 12 * q^67 - 12 * q^68 - 12 * q^69 - 12 * q^70 + 30 * q^73 + 12 * q^74 + 20 * q^75 + 12 * q^76 + 28 * q^77 - 36 * q^79 + 6 * q^80 - 14 * q^81 + 2 * q^84 + 64 * q^85 - 24 * q^86 + 16 * q^89 + 8 * q^90 - 20 * q^91 + 12 * q^92 + 4 * q^93 + 14 * q^95 - 16 * q^97 - 8 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.81074	−	1.62278i	−1.25700	−	0.725730i	−0.284511	−	0.958673i	$-0.591831\pi$
$5$	−2.81074	−	1.62278i	−1.25700	−	0.725730i	−0.972490	+	0.232943i	$0.925164\pi$
$6$			1.00000i			0.408248i
$7$	2.61522	+	0.400774i	0.988461	+	0.151478i
$7$	2.61522	+	0.400774i	0.988461	+	0.151478i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.62278	+	2.81074i	0.513168	+	0.888834i
$11$	2.06663	+	3.57950i	0.623112	+	1.07926i	0.988903	+	0.148564i	$0.0474651\pi$
$11$	2.06663	+	3.57950i	0.623112	+	1.07926i	−0.365791	+	0.930697i	$0.619202\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−2.67370			−0.741550			−0.370775	−	0.928723i	$-0.620908\pi$
$13$	−2.67370			−0.741550			−0.370775	+	0.928723i	$0.620908\pi$
$14$	−2.06446	−	1.65469i	−0.551750	−	0.442235i
$15$			3.24556i			0.838001i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.12164	+	1.22493i	−0.514572	+	0.297089i	−0.734711	−	0.678380i	$-0.762682\pi$
$17$	−2.12164	+	1.22493i	−0.514572	+	0.297089i	0.220139	+	0.975469i	$0.429349\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	1.61619	+	4.04820i	0.370780	+	0.928721i
$19$	1.61619	+	4.04820i	0.370780	+	0.928721i
$20$		−	3.24556i		−	0.725730i
$21$	−0.960530	−	2.46523i	−0.209605	−	0.537958i
$22$		−	4.13326i		−	0.881213i
$23$	−2.24167	+	3.88269i	−0.467421	+	0.809596i	−0.999307	−	0.0372195i	$-0.988150\pi$
$23$	−2.24167	+	3.88269i	−0.467421	+	0.809596i	0.531887	+	0.846816i	$0.321483\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	2.76684	+	4.79230i	0.553367	+	0.958461i
$26$	2.31549	+	1.33685i	0.454105	+	0.262177i
$27$	1.00000			0.192450
$28$	0.960530	+	2.46523i	0.181523	+	0.465886i
$29$		−	8.43515i		−	1.56637i	−0.621790	−	0.783184i	$-0.713594\pi$
$29$		−	8.43515i		−	1.56637i	0.621790	−	0.783184i	$-0.286406\pi$
$30$	1.62278	−	2.81074i	0.296278	−	0.513168i
$31$	0.831683	+	1.44052i	0.149375	+	0.258725i	0.930997	−	0.365028i	$-0.118941\pi$
$31$	0.831683	+	1.44052i	0.149375	+	0.258725i	−0.781622	+	0.623753i	$0.785607\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	2.06663	−	3.57950i	0.359754	−	0.623112i
$34$	2.44985			0.420147
$35$	−6.70034	−	5.37040i	−1.13256	−	0.907764i
$36$	−1.00000			−0.166667
$37$	9.75396	+	5.63145i	1.60354	+	0.925805i	0.990771	+	0.135544i	$0.0432782\pi$
$37$	9.75396	+	5.63145i	1.60354	+	0.925805i	0.612770	+	0.790261i	$0.290055\pi$
$38$	0.624436	−	4.31394i	0.101297	−	0.699814i
$39$	1.33685	+	2.31549i	0.214067	+	0.370775i
$40$	−1.62278	+	2.81074i	−0.256584	+	0.444417i
$41$	−6.53220			−1.02016			−0.510079	−	0.860127i	$-0.670384\pi$
$41$	−6.53220			−1.02016			−0.510079	+	0.860127i	$0.670384\pi$
$42$	−0.400774	+	2.61522i	−0.0618408	+	0.403537i
$43$	11.0930			1.69167			0.845837	−	0.533441i	$-0.179102\pi$
$43$	11.0930			1.69167			0.845837	+	0.533441i	$0.179102\pi$
$44$	−2.06663	+	3.57950i	−0.311556	+	0.539631i
$45$	2.81074	−	1.62278i	0.419000	−	0.241910i
$46$	3.88269	−	2.24167i	0.572471	−	0.330516i
$47$	9.65673	+	5.57531i	1.40858	+	0.813243i	0.995251	−	0.0973395i	$-0.0310333\pi$
$47$	9.65673	+	5.57531i	1.40858	+	0.813243i	0.413327	+	0.910583i	$0.364367\pi$
$48$	1.00000			0.144338
$49$	6.67876	+	2.09623i	0.954109	+	0.299461i
$50$		−	5.53367i		−	0.782580i
$51$	2.12164	+	1.22493i	0.297089	+	0.171524i
$52$	−1.33685	−	2.31549i	−0.185387	−	0.321100i
$53$	8.72415	−	5.03689i	1.19835	−	0.691870i	0.238166	−	0.971225i	$-0.423454\pi$
$53$	8.72415	−	5.03689i	1.19835	−	0.691870i	0.960188	+	0.279355i	$0.0901205\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		−	13.4147i		−	1.80884i
$56$	0.400774	−	2.61522i	0.0535557	−	0.349474i
$57$	2.69775	−	3.42376i	0.357325	−	0.453489i
$58$	−4.21757	+	7.30505i	−0.553795	+	0.959200i
$59$	3.12287	+	5.40896i	0.406563	+	0.704187i	0.994502	−	0.104718i	$-0.0333940\pi$
$59$	3.12287	+	5.40896i	0.406563	+	0.704187i	−0.587939	+	0.808905i	$0.700061\pi$
$60$	−2.81074	+	1.62278i	−0.362865	+	0.209500i
$61$	−10.5360	−	6.08297i	−1.34900	−	0.778844i	−0.360890	−	0.932608i	$-0.617527\pi$
$61$	−10.5360	−	6.08297i	−1.34900	−	0.778844i	−0.988108	+	0.153764i	$0.950860\pi$
$62$		−	1.66337i		−	0.211248i
$63$	−1.65469	+	2.06446i	−0.208472	+	0.260098i
$64$	−1.00000			−0.125000
$65$	7.51506	+	4.33882i	0.932129	+	0.538165i
$66$	−3.57950	+	2.06663i	−0.440606	+	0.254384i
$67$	−7.27683	+	4.20128i	−0.889006	+	0.513268i	−0.873617	−	0.486614i	$-0.838232\pi$
$67$	−7.27683	+	4.20128i	−0.889006	+	0.513268i	−0.0153889	+	0.999882i	$0.504899\pi$
$68$	−2.12164	−	1.22493i	−0.257286	−	0.148544i
$69$	4.48334			0.539731
$70$	3.11746	+	8.00107i	0.372608	+	0.956311i
$71$			8.08098i			0.959036i	0.877532	+	0.479518i	$0.159188\pi$
$71$			8.08098i			0.959036i	−0.877532	+	0.479518i	$0.840812\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−3.98840	+	2.30270i	−0.466806	+	0.269511i	−0.714902	−	0.699225i	$-0.753529\pi$
$73$	−3.98840	+	2.30270i	−0.466806	+	0.269511i	0.248095	+	0.968736i	$0.420195\pi$
$74$	−5.63145	−	9.75396i	−0.654643	−	1.13388i
$75$	2.76684	−	4.79230i	0.319487	−	0.553367i
$76$	−2.69775	+	3.42376i	−0.309453	+	0.392733i
$77$	3.97011	+	10.1894i	0.452436	+	1.16120i
$78$		−	2.67370i		−	0.302736i
$79$	4.73594	+	2.73430i	0.532835	+	0.307632i	0.742170	−	0.670212i	$-0.233797\pi$
$79$	4.73594	+	2.73430i	0.532835	+	0.307632i	−0.209335	+	0.977844i	$0.567130\pi$
$80$	2.81074	−	1.62278i	0.314250	−	0.181432i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.65705	+	3.26610i	0.624717	+	0.360681i
$83$		−	14.0898i		−	1.54655i	−0.634070	−	0.773276i	$-0.718617\pi$
$83$		−	14.0898i		−	1.54655i	0.634070	−	0.773276i	$-0.281383\pi$
$84$	1.65469	−	2.06446i	0.180542	−	0.225251i
$85$	7.95116			0.862424
$86$	−9.60686	−	5.54652i	−1.03593	−	0.598097i
$87$	−7.30505	+	4.21757i	−0.783184	+	0.452171i
$88$	3.57950	−	2.06663i	0.381576	−	0.220303i
$89$	−5.38710	+	9.33073i	−0.571031	+	0.989055i	0.425429	+	0.904992i	$0.360123\pi$
$89$	−5.38710	+	9.33073i	−0.571031	+	0.989055i	−0.996460	+	0.0840637i	$0.973210\pi$
$90$	−3.24556			−0.342112
$91$	−6.99230	−	1.07155i	−0.732993	−	0.112329i
$92$	−4.48334			−0.467421
$93$	0.831683	−	1.44052i	0.0862415	−	0.149375i
$94$	−5.57531	−	9.65673i	−0.575050	−	0.996015i
$95$	2.02664	−	14.0012i	0.207929	−	1.43649i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	5.90991			0.600060			0.300030	−	0.953930i	$-0.403003\pi$
$97$	5.90991			0.600060			0.300030	+	0.953930i	$0.403003\pi$
$98$	−4.73586	−	5.15477i	−0.478394	−	0.520710i
$99$	−4.13326			−0.415408
$100$	−2.76684	+	4.79230i	−0.276684	+	0.479230i
$101$	12.5236	−	7.23050i	1.24614	−	0.719462i	0.275806	−	0.961213i	$-0.411055\pi$
$101$	12.5236	−	7.23050i	1.24614	−	0.719462i	0.970338	+	0.241752i	$0.0777220\pi$
$102$	−1.22493	−	2.12164i	−0.121286	−	0.210073i
$103$	0.804019	−	1.39260i	0.0792223	−	0.137217i	−0.823692	−	0.567037i	$-0.808090\pi$
$103$	0.804019	−	1.39260i	0.0792223	−	0.137217i	0.902915	+	0.429820i	$0.141423\pi$
$104$			2.67370i			0.262177i
$105$	−1.30074	+	8.48786i	−0.126939	+	0.828331i
$106$	−10.0738			−0.978452
$107$	6.95800	+	4.01720i	0.672655	+	0.388357i	0.797082	−	0.603871i	$-0.206376\pi$
$107$	6.95800	+	4.01720i	0.672655	+	0.388357i	−0.124427	+	0.992229i	$0.539709\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−5.60373	+	3.23532i	−0.536740	+	0.309887i	−0.743757	−	0.668450i	$-0.766958\pi$
$109$	−5.60373	+	3.23532i	−0.536740	+	0.309887i	0.207016	+	0.978337i	$0.433625\pi$
$110$	−6.70737	+	11.6175i	−0.639523	+	1.10769i
$111$		−	11.2629i		−	1.06903i
$112$	−1.65469	+	2.06446i	−0.156354	+	0.195073i
$113$			17.3265i			1.62994i	0.579501	+	0.814972i	$0.303248\pi$
$113$			17.3265i			1.62994i	−0.579501	+	0.814972i	$0.696752\pi$
$114$	−4.04820	+	1.61619i	−0.379149	+	0.151370i
$115$	12.6015	−	7.27548i	1.17510	−	0.678442i
$116$	7.30505	−	4.21757i	0.678257	−	0.391592i
$117$	1.33685	−	2.31549i	0.123592	−	0.214067i
$118$		−	6.24573i		−	0.574966i
$119$	−6.03947	+	2.35316i	−0.553637	+	0.215714i
$120$	3.24556			0.296278
$121$	−3.04190	+	5.26872i	−0.276536	+	0.478975i
$122$	6.08297	+	10.5360i	0.550726	+	0.953885i
$123$	3.26610	+	5.65705i	0.294494	+	0.510079i
$124$	−0.831683	+	1.44052i	−0.0746873	+	0.129362i
$125$		−	1.73208i		−	0.154922i
$126$	2.46523	−	0.960530i	0.219621	−	0.0855708i
$127$		−	17.0052i		−	1.50897i	−0.656317	−	0.754485i	$-0.727887\pi$
$127$		−	17.0052i		−	1.50897i	0.656317	−	0.754485i	$-0.272113\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−5.54652	−	9.60686i	−0.488344	−	0.845837i
$130$	−4.33882	−	7.51506i	−0.380540	−	0.659115i
$131$	−8.03326	−	4.63800i	−0.701869	−	0.405224i	0.106174	−	0.994348i	$-0.466140\pi$
$131$	−8.03326	−	4.63800i	−0.701869	−	0.405224i	−0.808043	+	0.589123i	$0.799473\pi$
$132$	4.13326			0.359754
$133$	2.60429	+	11.2347i	0.225820	+	0.974169i
$134$	8.40256			0.725871
$135$	−2.81074	−	1.62278i	−0.241910	−	0.139667i
$136$	1.22493	+	2.12164i	0.105037	+	0.181929i
$137$	3.59761	+	6.23124i	0.307365	+	0.532371i	0.977785	−	0.209610i	$-0.0672196\pi$
$137$	3.59761	+	6.23124i	0.307365	+	0.532371i	−0.670420	+	0.741981i	$0.733886\pi$
$138$	−3.88269	−	2.24167i	−0.330516	−	0.190824i
$139$			15.9417i			1.35216i	0.736828	+	0.676081i	$0.236323\pi$
$139$			15.9417i			1.35216i	−0.736828	+	0.676081i	$0.763677\pi$
$140$	1.30074	−	8.48786i	0.109932	−	0.717355i
$141$		−	11.1506i		−	0.939052i
$142$	4.04049	−	6.99833i	0.339070	−	0.587287i
$143$	−5.52553	−	9.57050i	−0.462068	−	0.800326i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−13.6884	+	23.7090i	−1.13676	+	1.96893i
$146$	4.60540			0.381146
$147$	−1.52399	−	6.83209i	−0.125697	−	0.563501i
$148$			11.2629i			0.925805i
$149$	0.186849	−	0.323631i	0.0153072	−	0.0265129i	−0.858270	−	0.513198i	$-0.828461\pi$
$149$	0.186849	−	0.323631i	0.0153072	−	0.0265129i	0.873578	+	0.486685i	$0.161794\pi$
$150$	−4.79230	+	2.76684i	−0.391290	+	0.225911i
$151$	−2.99302	+	1.72802i	−0.243569	+	0.140625i	−0.616816	−	0.787107i	$-0.711578\pi$
$151$	−2.99302	+	1.72802i	−0.243569	+	0.140625i	0.373247	+	0.927732i	$0.378244\pi$
$152$	4.04820	−	1.61619i	0.328352	−	0.131091i
$153$		−	2.44985i		−	0.198059i
$154$	1.65650	−	10.8094i	0.133485	−	0.871044i
$155$		−	5.39856i		−	0.433623i
$156$	−1.33685	+	2.31549i	−0.107033	+	0.185387i
$157$	−2.24178	+	1.29429i	−0.178914	+	0.103296i	−0.586782	−	0.809745i	$-0.699606\pi$
$157$	−2.24178	+	1.29429i	−0.178914	+	0.103296i	0.407868	+	0.913041i	$0.366272\pi$
$158$	−2.73430	−	4.73594i	−0.217529	−	0.376771i
$159$	−8.72415	−	5.03689i	−0.691870	−	0.399451i
$160$	−3.24556			−0.256584
$161$	−7.41854	+	9.25568i	−0.584663	+	0.729450i
$162$			1.00000i			0.0785674i
$163$	6.82563	−	11.8223i	0.534625	−	0.925997i	−0.464557	−	0.885543i	$-0.653786\pi$
$163$	6.82563	−	11.8223i	0.534625	−	0.925997i	0.999181	−	0.0404539i	$-0.0128804\pi$
$164$	−3.26610	−	5.65705i	−0.255040	−	0.441742i
$165$	−11.6175	+	6.70737i	−0.904421	+	0.522168i
$166$	−7.04488	+	12.2021i	−0.546788	+	0.947065i
$167$	11.4230			0.883936			0.441968	−	0.897031i	$-0.354281\pi$
$167$	11.4230			0.883936			0.441968	+	0.897031i	$0.354281\pi$
$168$	−2.46523	+	0.960530i	−0.190197	+	0.0741065i
$169$	−5.85135			−0.450104
$170$	−6.88590	−	3.97558i	−0.528125	−	0.304913i
$171$	−4.31394	−	0.624436i	−0.329895	−	0.0477518i
$172$	5.54652	+	9.60686i	0.422919	+	0.732516i
$173$	−5.95502	+	10.3144i	−0.452752	+	0.784189i	−0.998556	−	0.0537241i	$-0.982891\pi$
$173$	−5.95502	+	10.3144i	−0.452752	+	0.784189i	0.545804	+	0.837913i	$0.316224\pi$
$174$	8.43515			0.639467
$175$	5.31526	+	13.6418i	0.401796	+	1.03122i
$176$	−4.13326			−0.311556
$177$	3.12287	−	5.40896i	0.234729	−	0.406563i
$178$	9.33073	−	5.38710i	0.699368	−	0.403780i
$179$	−13.9559	+	8.05746i	−1.04312	+	0.602243i	−0.920714	−	0.390238i	$-0.872393\pi$
$179$	−13.9559	+	8.05746i	−1.04312	+	0.602243i	−0.122401	+	0.992481i	$0.539059\pi$
$180$	2.81074	+	1.62278i	0.209500	+	0.120955i
$181$	5.23735			0.389289			0.194644	−	0.980874i	$-0.437645\pi$
$181$	5.23735			0.389289			0.194644	+	0.980874i	$0.437645\pi$
$182$	5.51974	+	4.42414i	0.409150	+	0.327939i
$183$			12.1659i			0.899332i
$184$	3.88269	+	2.24167i	0.286235	+	0.165258i
$185$	−18.2772	−	31.6571i	−1.34377	−	2.32748i
$186$	−1.44052	+	0.831683i	−0.105624	+	0.0609820i
$187$	−8.76926	−	5.06294i	−0.641272	−	0.370239i
$188$			11.1506i			0.813243i
$189$	2.61522	+	0.400774i	0.190229	+	0.0291520i
$190$	−8.75571	+	11.1120i	−0.635206	+	0.806152i
$191$	−10.8765	+	18.8387i	−0.786999	+	1.36312i	0.140798	+	0.990038i	$0.455033\pi$
$191$	−10.8765	+	18.8387i	−0.786999	+	1.36312i	−0.927797	+	0.373085i	$0.878300\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−19.7137	+	11.3817i	−1.41902	+	0.819273i	−0.996213	−	0.0869459i	$-0.972289\pi$
$193$	−19.7137	+	11.3817i	−1.41902	+	0.819273i	−0.422809	+	0.906219i	$0.638956\pi$
$194$	−5.11813	−	2.95496i	−0.367460	−	0.212153i
$195$		−	8.67765i		−	0.621419i
$196$	1.52399	+	6.83209i	0.108857	+	0.488006i
$197$	−7.61179			−0.542318			−0.271159	−	0.962535i	$-0.587407\pi$
$197$	−7.61179			−0.542318			−0.271159	+	0.962535i	$0.587407\pi$
$198$	3.57950	+	2.06663i	0.254384	+	0.146869i
$199$	−3.81618	+	2.20327i	−0.270522	+	0.156186i	−0.629125	−	0.777304i	$-0.716587\pi$
$199$	−3.81618	+	2.20327i	−0.270522	+	0.156186i	0.358603	+	0.933490i	$0.383253\pi$
$200$	4.79230	−	2.76684i	0.338867	−	0.195645i
$201$	7.27683	+	4.20128i	0.513268	+	0.296335i
$202$	−14.4610			−1.01747
$203$	3.38059	−	22.0598i	0.237271	−	1.54829i
$204$			2.44985i			0.171524i
$205$	18.3603	+	10.6003i	1.28234	+	0.740359i
$206$	−1.39260	+	0.804019i	−0.0970271	+	0.0560186i
$207$	−2.24167	−	3.88269i	−0.155807	−	0.269865i
$208$	1.33685	−	2.31549i	0.0926937	−	0.160550i
$209$	−11.1505	+	14.1513i	−0.771295	+	0.978865i
$210$	5.37040	−	6.70034i	0.370593	−	0.462367i
$211$		−	9.92538i		−	0.683292i	−0.939829	−	0.341646i	$-0.889016\pi$
$211$		−	9.92538i		−	0.683292i	0.939829	−	0.341646i	$-0.110984\pi$
$212$	8.72415	+	5.03689i	0.599177	+	0.345935i
$213$	6.99833	−	4.04049i	0.479518	−	0.276850i
$214$	−4.01720	−	6.95800i	−0.274610	−	0.475639i
$215$	−31.1797	−	18.0016i	−2.12644	−	1.22770i
$216$		−	1.00000i		−	0.0680414i
$217$	1.59771	+	4.10059i	0.108460	+	0.278366i
$218$	6.47064			0.438247
$219$	3.98840	+	2.30270i	0.269511	+	0.155602i
$220$	11.6175	−	6.70737i	0.783252	−	0.452211i
$221$	5.67261	−	3.27508i	0.381581	−	0.220306i
$222$	−5.63145	+	9.75396i	−0.377958	+	0.654643i
$223$	−2.27240			−0.152171			−0.0760856	−	0.997101i	$-0.524242\pi$
$223$	−2.27240			−0.152171			−0.0760856	+	0.997101i	$0.524242\pi$
$224$	2.46523	−	0.960530i	0.164715	−	0.0641781i
$225$	−5.53367			−0.368912
$226$	8.66327	−	15.0052i	0.576272	−	0.998132i
$227$	8.20350	+	14.2089i	0.544485	+	0.943076i	0.998639	+	0.0521527i	$0.0166083\pi$
$227$	8.20350	+	14.2089i	0.544485	+	0.943076i	−0.454154	+	0.890923i	$0.650058\pi$
$228$	4.31394	+	0.624436i	0.285698	+	0.0413543i
$229$	8.11773	+	4.68677i	0.536435	+	0.309711i	0.743633	−	0.668588i	$-0.233101\pi$
$229$	8.11773	+	4.68677i	0.536435	+	0.309711i	−0.207198	+	0.978299i	$0.566434\pi$
$230$	−14.5510			−0.959462
$231$	6.83926	−	8.53294i	0.449990	−	0.561426i
$232$	−8.43515			−0.553795
$233$	6.22587	−	10.7835i	0.407870	−	0.706452i	−0.586781	−	0.809746i	$-0.699605\pi$
$233$	6.22587	−	10.7835i	0.407870	−	0.706452i	0.994651	+	0.103294i	$0.0329382\pi$
$234$	−2.31549	+	1.33685i	−0.151368	+	0.0873925i
$235$	−18.0950	−	31.3415i	−1.18039	−	2.04449i
$236$	−3.12287	+	5.40896i	−0.203281	+	0.352093i
$237$		−	5.46859i		−	0.355223i
$238$	6.40691	+	0.981839i	0.415298	+	0.0636432i
$239$	−11.3168			−0.732023			−0.366012	−	0.930610i	$-0.619277\pi$
$239$	−11.3168			−0.732023			−0.366012	+	0.930610i	$0.619277\pi$
$240$	−2.81074	−	1.62278i	−0.181432	−	0.104750i
$241$	2.14036	+	3.70722i	0.137873	+	0.238803i	0.926691	−	0.375824i	$-0.122640\pi$
$241$	2.14036	+	3.70722i	0.137873	+	0.238803i	−0.788818	+	0.614626i	$0.789307\pi$
$242$	5.26872	−	3.04190i	0.338686	−	0.195541i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		−	12.1659i		−	0.778844i
$245$	−15.3705	−	16.7301i	−0.981987	−	1.06885i
$246$		−	6.53220i		−	0.416478i
$247$	−4.32121	−	10.8237i	−0.274952	−	0.688693i
$248$	1.44052	−	0.831683i	0.0914729	−	0.0528119i
$249$	−12.2021	+	7.04488i	−0.773276	+	0.446451i
$250$	−0.866038	+	1.50002i	−0.0547730	+	0.0948697i
$251$		−	7.12640i		−	0.449814i	−0.974380	−	0.224907i	$-0.927792\pi$
$251$		−	7.12640i		−	0.449814i	0.974380	−	0.224907i	$-0.0722079\pi$
$252$	−2.61522	−	0.400774i	−0.164743	−	0.0252464i
$253$	−18.5308			−1.16502
$254$	−8.50262	+	14.7270i	−0.533502	+	0.924052i
$255$	−3.97558	−	6.88590i	−0.248960	−	0.431212i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	4.74391	−	8.21669i	0.295917	−	0.512543i	−0.679281	−	0.733878i	$-0.737708\pi$
$257$	4.74391	−	8.21669i	0.295917	−	0.512543i	0.975198	+	0.221336i	$0.0710416\pi$
$258$			11.0930i			0.690623i
$259$	23.2518	+	18.6366i	1.44480	+	1.15802i
$260$			8.67765i			0.538165i
$261$	7.30505	+	4.21757i	0.452171	+	0.261061i
$262$	4.63800	+	8.03326i	0.286537	+	0.496296i
$263$	8.19288	+	14.1905i	0.505194	+	0.875022i	0.999982	+	0.00600830i	$0.00191251\pi$
$263$	8.19288	+	14.1905i	0.505194	+	0.875022i	−0.494788	+	0.869014i	$0.664754\pi$
$264$	−3.57950	−	2.06663i	−0.220303	−	0.127192i
$265$	−32.6951			−2.00844
$266$	3.36195	−	11.0316i	0.206135	−	0.676394i
$267$	10.7742			0.659370
$268$	−7.27683	−	4.20128i	−0.444503	−	0.256634i
$269$	11.3597	+	19.6756i	0.692614	+	1.19964i	0.970978	+	0.239167i	$0.0768743\pi$
$269$	11.3597	+	19.6756i	0.692614	+	1.19964i	−0.278365	+	0.960475i	$0.589792\pi$
$270$	1.62278	+	2.81074i	0.0987593	+	0.171056i
$271$	−4.12943	−	2.38413i	−0.250845	−	0.144825i	0.369306	−	0.929308i	$-0.379595\pi$
$271$	−4.12943	−	2.38413i	−0.250845	−	0.144825i	−0.620151	+	0.784482i	$0.712929\pi$
$272$		−	2.44985i		−	0.148544i
$273$	2.56816	+	6.59129i	0.155432	+	0.398923i
$274$		−	7.19522i		−	0.434679i
$275$	−11.4360	+	19.8078i	−0.689619	+	1.19446i
$276$	2.24167	+	3.88269i	0.134933	+	0.233710i
$277$	−0.361704	−	0.626490i	−0.0217327	−	0.0376421i	0.854955	−	0.518703i	$-0.173585\pi$
$277$	−0.361704	−	0.626490i	−0.0217327	−	0.0376421i	−0.876687	+	0.481061i	$0.840252\pi$
$278$	7.97087	−	13.8060i	0.478061	−	0.828026i
$279$	−1.66337			−0.0995831
$280$	−5.37040	+	6.70034i	−0.320943	+	0.400422i
$281$		−	0.876797i		−	0.0523053i	−0.999658	−	0.0261527i	$-0.991674\pi$
$281$		−	0.876797i		−	0.0523053i	0.999658	−	0.0261527i	$-0.00832560\pi$
$282$	−5.57531	+	9.65673i	−0.332005	+	0.575050i
$283$	−13.1301	+	7.58065i	−0.780502	+	0.450623i	−0.836608	−	0.547802i	$-0.815465\pi$
$283$	−13.1301	+	7.58065i	−0.780502	+	0.450623i	0.0561062	+	0.998425i	$0.482131\pi$
$284$	−6.99833	+	4.04049i	−0.415275	+	0.239759i
$285$	−13.1387	+	5.24546i	−0.778268	+	0.310714i
$286$			11.0511i			0.653463i
$287$	−17.0832	−	2.61794i	−1.00839	−	0.154532i
$288$			1.00000i			0.0589256i
$289$	−5.49911	+	9.52473i	−0.323477	+	0.560278i
$290$	23.7090	−	13.6884i	1.39224	−	0.803810i
$291$	−2.95496	−	5.11813i	−0.173223	−	0.300030i
$292$	−3.98840	−	2.30270i	−0.233403	−	0.134755i
$293$	14.9827			0.875299			0.437649	−	0.899146i	$-0.355811\pi$
$293$	14.9827			0.875299			0.437649	+	0.899146i	$0.355811\pi$
$294$	−2.09623	+	6.67876i	−0.122254	+	0.389513i
$295$		−	20.2709i		−	1.18022i
$296$	5.63145	−	9.75396i	0.327322	−	0.566938i
$297$	2.06663	+	3.57950i	0.119918	+	0.207704i
$298$	−0.323631	+	0.186849i	−0.0187474	+	0.0108238i
$299$	5.99354	−	10.3811i	0.346616	−	0.600356i
$300$	5.53367			0.319487
$301$	29.0108	+	4.44581i	1.67215	+	0.256252i
$302$	3.45605			0.198873
$303$	−12.5236	−	7.23050i	−0.719462	−	0.415381i
$304$	−4.31394	−	0.624436i	−0.247421	−	0.0358138i
$305$	19.7426	+	34.1953i	1.13046	+	1.95802i
$306$	−1.22493	+	2.12164i	−0.0700244	+	0.121286i
$307$	30.9323			1.76540			0.882700	−	0.469936i	$-0.155723\pi$
$307$	30.9323			1.76540			0.882700	+	0.469936i	$0.155723\pi$
$308$	−6.83926	+	8.53294i	−0.389703	+	0.486209i
$309$	−1.60804			−0.0914781
$310$	−2.69928	+	4.67529i	−0.153309	+	0.265539i
$311$	12.0428	−	6.95294i	0.682887	−	0.394265i	−0.118055	−	0.993007i	$-0.537666\pi$
$311$	12.0428	−	6.95294i	0.682887	−	0.394265i	0.800942	+	0.598742i	$0.204332\pi$
$312$	2.31549	−	1.33685i	0.131089	−	0.0756841i
$313$	3.08265	+	1.77977i	0.174242	+	0.100598i	0.584584	−	0.811333i	$-0.301258\pi$
$313$	3.08265	+	1.77977i	0.174242	+	0.100598i	−0.410343	+	0.911931i	$0.634591\pi$
$314$	2.58859			0.146083
$315$	8.00107	−	3.11746i	0.450809	−	0.175649i
$316$			5.46859i			0.307632i
$317$	4.08784	+	2.36011i	0.229596	+	0.132557i	0.610386	−	0.792104i	$-0.291015\pi$
$317$	4.08784	+	2.36011i	0.229596	+	0.132557i	−0.380790	+	0.924662i	$0.624348\pi$
$318$	5.03689	+	8.72415i	0.282455	+	0.489226i
$319$	30.1936	−	17.4323i	1.69052	−	0.976022i
$320$	2.81074	+	1.62278i	0.157125	+	0.0907162i
$321$		−	8.03440i		−	0.448437i
$322$	11.0525	−	4.30638i	0.615931	−	0.239985i
$323$	−8.38772	−	6.60909i	−0.466705	−	0.367740i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−7.39768	−	12.8132i	−0.410350	−	0.710746i
$326$	−11.8223	+	6.82563i	−0.654779	+	0.378037i
$327$	5.60373	+	3.23532i	0.309887	+	0.178913i
$328$			6.53220i			0.360681i
$329$	23.0200	+	18.4508i	1.26914	+	1.01723i
$330$	13.4147			0.738457
$331$	−24.6345	−	14.2227i	−1.35403	−	0.781751i	−0.365220	−	0.930921i	$-0.619006\pi$
$331$	−24.6345	−	14.2227i	−1.35403	−	0.781751i	−0.988812	+	0.149170i	$0.952340\pi$
$332$	12.2021	−	7.04488i	0.669676	−	0.386638i
$333$	−9.75396	+	5.63145i	−0.534514	+	0.308602i
$334$	−9.89258	−	5.71148i	−0.541298	−	0.312518i
$335$	27.2710			1.48998
$336$	2.61522	+	0.400774i	0.142672	+	0.0218640i
$337$		−	16.1819i		−	0.881485i	−0.897634	−	0.440742i	$-0.854715\pi$
$337$		−	16.1819i		−	0.881485i	0.897634	−	0.440742i	$-0.145285\pi$
$338$	5.06742	+	2.92568i	0.275631	+	0.159136i
$339$	15.0052	−	8.66327i	0.814972	−	0.470524i
$340$	3.97558	+	6.88590i	0.215606	+	0.373441i
$341$	−3.43756	+	5.95403i	−0.186154	+	0.322429i
$342$	3.42376	+	2.69775i	0.185136	+	0.145877i
$343$	16.6263	+	8.15877i	0.897737	+	0.440532i
$344$		−	11.0930i		−	0.598097i
$345$	−12.6015	−	7.27548i	−0.678442	−	0.391699i
$346$	10.3144	−	5.95502i	0.554505	−	0.320144i
$347$	0.202254	+	0.350314i	0.0108575	+	0.0188058i	0.871403	−	0.490568i	$-0.163211\pi$
$347$	0.202254	+	0.350314i	0.0108575	+	0.0188058i	−0.860546	+	0.509373i	$0.829877\pi$
$348$	−7.30505	−	4.21757i	−0.391592	−	0.226086i
$349$		−	23.8691i		−	1.27768i	−0.769339	−	0.638841i	$-0.779414\pi$
$349$		−	23.8691i		−	1.27768i	0.769339	−	0.638841i	$-0.220586\pi$
$350$	2.21776	−	14.4718i	0.118544	−	0.773549i
$351$	−2.67370			−0.142711
$352$	3.57950	+	2.06663i	0.190788	+	0.110152i
$353$	21.1765	−	12.2263i	1.12711	−	0.650738i	0.183904	−	0.982944i	$-0.441126\pi$
$353$	21.1765	−	12.2263i	1.12711	−	0.650738i	0.943207	+	0.332206i	$0.107793\pi$
$354$	−5.40896	+	3.12287i	−0.287483	+	0.165978i
$355$	13.1137	−	22.7135i	0.696001	−	1.20551i
$356$	−10.7742			−0.571031
$357$	5.05763	+	4.05375i	0.267678	+	0.214547i
$358$	16.1149			0.851700
$359$	−6.29910	+	10.9104i	−0.332454	+	0.575827i	−0.982992	−	0.183646i	$-0.941210\pi$
$359$	−6.29910	+	10.9104i	−0.332454	+	0.575827i	0.650538	+	0.759473i	$0.274543\pi$
$360$	−1.62278	−	2.81074i	−0.0855281	−	0.148139i
$361$	−13.7758	+	13.0853i	−0.725044	+	0.688702i
$362$	−4.53568	−	2.61867i	−0.238390	−	0.137634i
$363$	6.08380			0.319317
$364$	−2.56816	−	6.59129i	−0.134608	−	0.345477i
$365$	14.9471			0.782368
$366$	6.08297	−	10.5360i	0.317962	−	0.550726i
$367$	4.55901	−	2.63215i	0.237978	−	0.137397i	−0.376269	−	0.926511i	$-0.622793\pi$
$367$	4.55901	−	2.63215i	0.237978	−	0.137397i	0.614247	+	0.789114i	$0.289460\pi$
$368$	−2.24167	−	3.88269i	−0.116855	−	0.202399i
$369$	3.26610	−	5.65705i	0.170026	−	0.294494i
$370$			36.5545i			1.90038i
$371$	24.8342	−	9.67616i	1.28933	−	0.502361i
$372$	1.66337			0.0862415
$373$	14.0672	+	8.12173i	0.728374	+	0.420527i	0.817827	−	0.575464i	$-0.195179\pi$
$373$	14.0672	+	8.12173i	0.728374	+	0.420527i	−0.0894529	+	0.995991i	$0.528512\pi$
$374$	5.06294	+	8.76926i	0.261798	+	0.453448i
$375$	−1.50002	+	0.866038i	−0.0774608	+	0.0447220i
$376$	5.57531	−	9.65673i	0.287525	−	0.498008i
$377$			22.5530i			1.16154i
$378$	−2.06446	−	1.65469i	−0.106184	−	0.0851081i
$379$		−	3.03506i		−	0.155901i	−0.996957	−	0.0779504i	$-0.975162\pi$
$379$		−	3.03506i		−	0.155901i	0.996957	−	0.0779504i	$-0.0248376\pi$
$380$	13.1387	−	5.24546i	0.674000	−	0.269086i
$381$	−14.7270	+	8.50262i	−0.754485	+	0.435602i
$382$	18.8387	−	10.8765i	0.963873	−	0.556493i
$383$	−10.0764	+	17.4529i	−0.514882	+	0.891801i	0.484969	+	0.874531i	$0.338831\pi$
$383$	−10.0764	+	17.4529i	−0.514882	+	0.891801i	−0.999851	+	0.0172701i	$0.994502\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	5.37628	−	35.0825i	0.274001	−	1.78797i
$386$	22.7634			1.15863
$387$	−5.54652	+	9.60686i	−0.281946	+	0.488344i
$388$	2.95496	+	5.11813i	0.150015	+	0.259834i
$389$	−4.10781	−	7.11493i	−0.208274	−	0.360741i	0.742897	−	0.669406i	$-0.233451\pi$
$389$	−4.10781	−	7.11493i	−0.208274	−	0.360741i	−0.951171	+	0.308665i	$0.900118\pi$
$390$	−4.33882	+	7.51506i	−0.219705	+	0.380540i
$391$		−	10.9835i		−	0.555461i
$392$	2.09623	−	6.67876i	0.105875	−	0.337328i
$393$			9.27601i			0.467913i
$394$	6.59201	+	3.80590i	0.332101	+	0.191738i
$395$	−8.87433	−	15.3708i	−0.446516	−	0.773389i
$396$	−2.06663	−	3.57950i	−0.103852	−	0.179877i
$397$	7.88789	+	4.55408i	0.395882	+	0.228563i	0.684706	−	0.728820i	$-0.259931\pi$
$397$	7.88789	+	4.55408i	0.395882	+	0.228563i	−0.288824	+	0.957382i	$0.593264\pi$
$398$	4.40654			0.220880
$399$	8.42736	−	7.87271i	0.421896	−	0.394129i
$400$	−5.53367			−0.276684
$401$	10.8318	+	6.25373i	0.540913	+	0.312296i	0.745449	−	0.666563i	$-0.232235\pi$
$401$	10.8318	+	6.25373i	0.540913	+	0.312296i	−0.204536	+	0.978859i	$0.565568\pi$
$402$	−4.20128	−	7.27683i	−0.209541	−	0.362935i
$403$	−2.22367	−	3.85151i	−0.110769	−	0.191857i
$404$	12.5236	+	7.23050i	0.623072	+	0.359731i
$405$			3.24556i			0.161273i
$406$	−13.9576	+	17.4140i	−0.692702	+	0.864244i
$407$			46.5525i			2.30752i
$408$	1.22493	−	2.12164i	0.0606429	−	0.105037i
$409$	−7.31022	−	12.6617i	−0.361467	−	0.626079i	0.626736	−	0.779232i	$-0.284391\pi$
$409$	−7.31022	−	12.6617i	−0.361467	−	0.626079i	−0.988202	+	0.153153i	$0.951057\pi$
$410$	−10.6003	−	18.3603i	−0.523513	−	0.906751i
$411$	3.59761	−	6.23124i	0.177457	−	0.307365i
$412$	1.60804			0.0792223
$413$	5.99921	+	15.3972i	0.295202	+	0.757647i
$414$			4.48334i			0.220344i
$415$	−22.8646	+	39.6026i	−1.12238	+	1.94402i
$416$	−2.31549	+	1.33685i	−0.113526	+	0.0655444i
$417$	13.8060	−	7.97087i	0.676081	−	0.390335i
$418$	16.7322	−	6.68014i	0.818401	−	0.326736i
$419$			6.18841i			0.302324i	0.988509	+	0.151162i	$0.0483015\pi$
$419$			6.18841i			0.302324i	−0.988509	+	0.151162i	$0.951699\pi$
$420$	−8.00107	+	3.11746i	−0.390412	+	0.152116i
$421$		−	30.2999i		−	1.47673i	−0.674403	−	0.738364i	$-0.735599\pi$
$421$		−	30.2999i		−	1.47673i	0.674403	−	0.738364i	$-0.264401\pi$
$422$	−4.96269	+	8.59563i	−0.241580	+	0.418429i
$423$	−9.65673	+	5.57531i	−0.469526	+	0.271081i
$424$	−5.03689	−	8.72415i	−0.244613	−	0.423682i
$425$	−11.7404	−	6.77835i	−0.569495	−	0.328798i
$426$	−8.08098			−0.391525
$427$	−25.1161	−	20.1309i	−1.21545	−	0.974201i
$428$			8.03440i			0.388357i
$429$	−5.52553	+	9.57050i	−0.266775	+	0.462068i
$430$	18.0016	+	31.1797i	0.868114	+	1.50362i
$431$	−12.1625	+	7.02204i	−0.585848	+	0.338240i	−0.763454	−	0.645862i	$-0.776498\pi$
$431$	−12.1625	+	7.02204i	−0.585848	+	0.338240i	0.177606	+	0.984102i	$0.443165\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−3.28827			−0.158024			−0.0790120	−	0.996874i	$-0.525177\pi$
$433$	−3.28827			−0.158024			−0.0790120	+	0.996874i	$0.525177\pi$
$434$	0.666635	−	4.35007i	0.0319995	−	0.208810i
$435$	27.3768			1.31262
$436$	−5.60373	−	3.23532i	−0.268370	−	0.154944i
$437$	−19.3409	−	2.79956i	−0.925199	−	0.133921i
$438$	−2.30270	−	3.98840i	−0.110027	−	0.190573i
$439$	−1.68735	+	2.92258i	−0.0805329	+	0.139487i	−0.903479	−	0.428632i	$-0.858996\pi$
$439$	−1.68735	+	2.92258i	−0.0805329	+	0.139487i	0.822946	+	0.568120i	$0.192329\pi$
$440$	−13.4147			−0.639523
$441$	−5.15477	+	4.73586i	−0.245465	+	0.225517i
$442$	−6.55017			−0.311560
$443$	0.0952864	−	0.165041i	0.00452719	−	0.00784133i	−0.863753	−	0.503916i	$-0.831892\pi$
$443$	0.0952864	−	0.165041i	0.00452719	−	0.00784133i	0.868280	+	0.496074i	$0.165226\pi$
$444$	9.75396	−	5.63145i	0.462903	−	0.267257i
$445$	30.2835	−	17.4842i	1.43557	−	0.828829i
$446$	1.96796	+	1.13620i	0.0931855	+	0.0538007i
$447$	−0.373697			−0.0176753
$448$	−2.61522	−	0.400774i	−0.123558	−	0.0189348i
$449$		−	31.7726i		−	1.49944i	−0.661754	−	0.749721i	$-0.730188\pi$
$449$		−	31.7726i		−	1.49944i	0.661754	−	0.749721i	$-0.269812\pi$
$450$	4.79230	+	2.76684i	0.225911	+	0.130430i
$451$	−13.4996	−	23.3820i	−0.635673	−	1.10102i
$452$	−15.0052	+	8.66327i	−0.705786	+	0.407486i
$453$	2.99302	+	1.72802i	0.140625	+	0.0811896i
$454$		−	16.4070i		−	0.770018i
$455$	17.9147	+	14.3588i	0.839852	+	0.673152i
$456$	−3.42376	−	2.69775i	−0.160332	−	0.126334i
$457$	−13.2053	+	22.8722i	−0.617716	+	1.06992i	0.372185	+	0.928158i	$0.378609\pi$
$457$	−13.2053	+	22.8722i	−0.617716	+	1.06992i	−0.989901	+	0.141757i	$0.954725\pi$
$458$	−4.68677	−	8.11773i	−0.218999	−	0.379317i
$459$	−2.12164	+	1.22493i	−0.0990295	+	0.0571747i
$460$	12.6015	+	7.27548i	0.587548	+	0.339221i
$461$		−	19.7480i		−	0.919757i	−0.887982	−	0.459878i	$-0.847893\pi$
$461$		−	19.7480i		−	0.919757i	0.887982	−	0.459878i	$-0.152107\pi$
$462$	−10.1894	+	3.97011i	−0.474056	+	0.184706i
$463$	24.1178			1.12085			0.560424	−	0.828206i	$-0.310638\pi$
$463$	24.1178			1.12085			0.560424	+	0.828206i	$0.310638\pi$
$464$	7.30505	+	4.21757i	0.339129	+	0.195796i
$465$	−4.67529	+	2.69928i	−0.216811	+	0.125176i
$466$	−10.7835	+	6.22587i	−0.499537	+	0.288408i
$467$	−26.1755	−	15.1124i	−1.21126	−	0.699319i	−0.248224	−	0.968703i	$-0.579847\pi$
$467$	−26.1755	−	15.1124i	−1.21126	−	0.699319i	−0.963033	+	0.269383i	$0.913180\pi$
$468$	2.67370			0.123592
$469$	−20.7143	+	8.07091i	−0.956497	+	0.372680i
$470$			36.1901i			1.66932i
$471$	2.24178	+	1.29429i	0.103296	+	0.0596379i
$472$	5.40896	−	3.12287i	0.248968	−	0.143742i
$473$	22.9252	+	39.7076i	1.05410	+	1.82576i
$474$	−2.73430	+	4.73594i	−0.125590	+	0.217529i
$475$	−14.9285	+	18.9460i	−0.684965	+	0.869302i
$476$	−5.05763	−	4.05375i	−0.231816	−	0.185803i
$477$			10.0738i			0.461247i
$478$	9.80064	+	5.65840i	0.448271	+	0.258809i
$479$	3.14967	−	1.81846i	0.143912	−	0.0830877i	−0.426315	−	0.904575i	$-0.640188\pi$
$479$	3.14967	−	1.81846i	0.143912	−	0.0830877i	0.570227	+	0.821487i	$0.306855\pi$
$480$	1.62278	+	2.81074i	0.0740695	+	0.128292i
$481$	−26.0791	−	15.0568i	−1.18911	−	0.686531i
$482$		−	4.28072i		−	0.194982i
$483$	11.7249	+	1.79681i	0.533503	+	0.0817576i
$484$	−6.08380			−0.276536
$485$	−16.6112	−	9.59049i	−0.754277	−	0.435482i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−14.2336	+	8.21775i	−0.644985	+	0.372382i	−0.786532	−	0.617549i	$-0.788126\pi$
$487$	−14.2336	+	8.21775i	−0.644985	+	0.372382i	0.141548	+	0.989931i	$0.454792\pi$
$488$	−6.08297	+	10.5360i	−0.275363	+	0.476943i
$489$	−13.6513			−0.617332
$490$	4.94622	+	22.1740i	0.223447	+	1.00172i
$491$	8.96423			0.404550			0.202275	−	0.979329i	$-0.435167\pi$
$491$	8.96423			0.404550			0.202275	+	0.979329i	$0.435167\pi$
$492$	−3.26610	+	5.65705i	−0.147247	+	0.255040i
$493$	10.3324	+	17.8963i	0.465350	+	0.806010i
$494$	−1.66955	+	11.5342i	−0.0751166	+	0.518947i
$495$	11.6175	+	6.70737i	0.522168	+	0.301474i
$496$	−1.66337			−0.0746873
$497$	−3.23865	+	21.1335i	−0.145273	+	0.947969i
$498$	14.0898			0.631377
$499$	12.1657	−	21.0716i	0.544610	−	0.943292i	−0.454021	−	0.890991i	$-0.650011\pi$
$499$	12.1657	−	21.0716i	0.544610	−	0.943292i	0.998631	−	0.0523014i	$-0.0166556\pi$
$500$	1.50002	−	0.866038i	0.0670830	−	0.0387304i
$501$	−5.71148	−	9.89258i	−0.255170	−	0.441968i
$502$	−3.56320	+	6.17164i	−0.159033	+	0.275454i
$503$		−	5.97658i		−	0.266482i	−0.991084	−	0.133241i	$-0.957461\pi$
$503$		−	5.97658i		−	0.266482i	0.991084	−	0.133241i	$-0.0425385\pi$
$504$	2.06446	+	1.65469i	0.0919584	+	0.0737058i
$505$	−46.9341			−2.08854
$506$	16.0481	+	9.26539i	0.713427	+	0.411897i
$507$	2.92568	+	5.06742i	0.129934	+	0.225052i
$508$	14.7270	−	8.50262i	0.653403	−	0.377243i
$509$	−6.08102	+	10.5326i	−0.269537	+	0.466851i	−0.968742	−	0.248070i	$-0.920204\pi$
$509$	−6.08102	+	10.5326i	−0.269537	+	0.466851i	0.699206	+	0.714921i	$0.253537\pi$
$510$			7.95116i			0.352083i
$511$	−11.3534	+	4.42363i	−0.502245	+	0.195690i
$512$			1.00000i			0.0441942i
$513$	1.61619	+	4.04820i	0.0713567	+	0.178732i
$514$	−8.21669	+	4.74391i	−0.362422	+	0.209245i
$515$	−4.51977	+	2.60949i	−0.199165	+	0.114988i
$516$	5.54652	−	9.60686i	0.244172	−	0.422919i
$517$			46.0884i			2.02697i
$518$	−10.8184	−	27.7657i	−0.475331	−	1.21996i
$519$	11.9100			0.522792
$520$	4.33882	−	7.51506i	0.190270	−	0.329557i
$521$	−20.3791	−	35.2976i	−0.892824	−	1.54642i	−0.836475	−	0.548006i	$-0.815387\pi$
$521$	−20.3791	−	35.2976i	−0.892824	−	1.54642i	−0.0563496	−	0.998411i	$-0.517946\pi$
$522$	−4.21757	−	7.30505i	−0.184598	−	0.319733i
$523$	1.81149	−	3.13760i	0.0792110	−	0.137198i	−0.823699	−	0.567028i	$-0.808093\pi$
$523$	1.81149	−	3.13760i	0.0792110	−	0.137198i	0.902910	+	0.429830i	$0.141427\pi$
$524$		−	9.27601i		−	0.405224i
$525$	9.15652	−	11.4241i	0.399623	−	0.498587i
$526$		−	16.3858i		−	0.714453i
$527$	−3.52906	−	2.03750i	−0.153728	−	0.0887550i
$528$	2.06663	+	3.57950i	0.0899384	+	0.155778i
$529$	1.44983	+	2.51118i	0.0630361	+	0.109182i
$530$	28.3148	+	16.3475i	1.22991	+	0.710092i
$531$	−6.24573			−0.271042
$532$	−8.42736	+	7.87271i	−0.365372	+	0.341325i
$533$	17.4651			0.756498
$534$	−9.33073	−	5.38710i	−0.403780	−	0.233123i
$535$	−13.0381	−	22.5826i	−0.563685	−	0.976331i
$536$	4.20128	+	7.27683i	0.181468	+	0.314311i
$537$	13.9559	+	8.05746i	0.602243	+	0.347705i
$538$		−	22.7194i		−	0.979504i
$539$	6.29906	+	28.2388i	0.271320	+	1.21633i
$540$		−	3.24556i		−	0.139667i
$541$	18.3787	−	31.8329i	0.790163	−	1.36860i	−0.135702	−	0.990750i	$-0.543329\pi$
$541$	18.3787	−	31.8329i	0.790163	−	1.36860i	0.925866	−	0.377853i	$-0.123338\pi$
$542$	2.38413	+	4.12943i	0.102407	+	0.177374i
$543$	−2.61867	−	4.53568i	−0.112378	−	0.194644i
$544$	−1.22493	+	2.12164i	−0.0525183	+	0.0909644i
$545$	21.0008			0.899578
$546$	1.07155	−	6.99230i	0.0458581	−	0.299243i
$547$		−	16.6946i		−	0.713811i	−0.934140	−	0.356906i	$-0.883832\pi$
$547$		−	16.6946i		−	0.713811i	0.934140	−	0.356906i	$-0.116168\pi$
$548$	−3.59761	+	6.23124i	−0.153682	+	0.266186i
$549$	10.5360	−	6.08297i	0.449666	−	0.259615i
$550$	19.8078	−	11.4360i	0.844608	−	0.487635i
$551$	34.1472	−	13.6328i	1.45472	−	0.580778i
$552$		−	4.48334i		−	0.190824i
$553$	11.2897	+	9.04883i	0.480087	+	0.384796i
$554$			0.723409i			0.0307347i
$555$	−18.2772	+	31.6571i	−0.775825	+	1.34377i
$556$	−13.8060	+	7.97087i	−0.585503	+	0.338040i
$557$	−10.0088	−	17.3358i	−0.424087	−	0.734540i	0.572248	−	0.820081i	$-0.306072\pi$
$557$	−10.0088	−	17.3358i	−0.424087	−	0.734540i	−0.996335	+	0.0855405i	$0.972738\pi$
$558$	1.44052	+	0.831683i	0.0609820	+	0.0352080i
$559$	−29.6594			−1.25446
$560$	8.00107	−	3.11746i	0.338107	−	0.131737i
$561$			10.1259i			0.427515i
$562$	−0.438399	+	0.759329i	−0.0184927	+	0.0320304i
$563$	−10.9978	−	19.0487i	−0.463501	−	0.802807i	0.535632	−	0.844452i	$-0.320074\pi$
$563$	−10.9978	−	19.0487i	−0.463501	−	0.802807i	−0.999132	+	0.0416448i	$0.986740\pi$
$564$	9.65673	−	5.57531i	0.406622	−	0.234763i
$565$	28.1172	−	48.7004i	1.18290	−	2.04884i
$566$	15.1613			0.637277
$567$	−0.960530	−	2.46523i	−0.0403385	−	0.103530i
$568$	8.08098			0.339070
$569$	18.0677	+	10.4314i	0.757436	+	0.437306i	0.828374	−	0.560175i	$-0.189266\pi$
$569$	18.0677	+	10.4314i	0.757436	+	0.437306i	−0.0709385	+	0.997481i	$0.522599\pi$
$570$	14.0012	+	2.02664i	0.586444	+	0.0848868i
$571$	1.70601	+	2.95490i	0.0713944	+	0.123659i	0.899513	−	0.436895i	$-0.143922\pi$
$571$	1.70601	+	2.95490i	0.0713944	+	0.123659i	−0.828118	+	0.560553i	$0.810588\pi$
$572$	5.52553	−	9.57050i	0.231034	−	0.400163i
$573$	21.7531			0.908749
$574$	13.4855	+	10.8088i	0.562873	+	0.451150i
$575$	−24.8093			−1.03462
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−15.1914	+	8.77073i	−0.632425	+	0.365130i	−0.781690	−	0.623667i	$-0.785642\pi$
$577$	−15.1914	+	8.77073i	−0.632425	+	0.365130i	0.149266	+	0.988797i	$0.452309\pi$
$578$	9.52473	−	5.49911i	0.396177	−	0.228733i
$579$	19.7137	+	11.3817i	0.819273	+	0.473007i
$580$	−27.3768			−1.13676
$581$	5.64681	−	36.8478i	0.234269	−	1.52870i
$582$			5.90991i			0.244974i
$583$	36.0591	+	20.8187i	1.49342	+	0.862224i
$584$	2.30270	+	3.98840i	0.0952865	+	0.165041i
$585$	−7.51506	+	4.33882i	−0.310710	+	0.179388i
$586$	−12.9754	−	7.49135i	−0.536009	−	0.309465i
$587$		−	24.3952i		−	1.00690i	−0.864025	−	0.503448i	$-0.832065\pi$
$587$		−	24.3952i		−	1.00690i	0.864025	−	0.503448i	$-0.167935\pi$
$588$	5.15477	−	4.73586i	0.212579	−	0.195304i
$589$	−4.48734	+	5.69497i	−0.184898	+	0.234657i
$590$	−10.1355	+	17.5551i	−0.417270	+	0.722733i
$591$	3.80590	+	6.59201i	0.156554	+	0.271159i
$592$	−9.75396	+	5.63145i	−0.400885	+	0.231451i
$593$	25.3516	+	14.6368i	1.04107	+	0.601060i	0.920135	−	0.391600i	$-0.128078\pi$
$593$	25.3516	+	14.6368i	1.04107	+	0.601060i	0.120932	+	0.992661i	$0.461412\pi$
$594$		−	4.13326i		−	0.169590i
$595$	20.7940	+	3.18662i	0.852472	+	0.130639i
$596$	0.373697			0.0153072
$597$	3.81618	+	2.20327i	0.156186	+	0.0901739i
$598$	−10.3811	+	5.99354i	−0.424516	+	0.245094i
$599$	20.4835	−	11.8261i	0.836932	−	0.483203i	−0.0192881	−	0.999814i	$-0.506140\pi$
$599$	20.4835	−	11.8261i	0.836932	−	0.483203i	0.856220	+	0.516611i	$0.172807\pi$
$600$	−4.79230	−	2.76684i	−0.195645	−	0.112956i
$601$	−39.7085			−1.61974			−0.809871	−	0.586608i	$-0.800463\pi$
$601$	−39.7085			−1.61974			−0.809871	+	0.586608i	$0.800463\pi$
$602$	−22.9012	−	18.3556i	−0.933382	−	0.748117i
$603$		−	8.40256i		−	0.342179i
$604$	−2.99302	−	1.72802i	−0.121784	−	0.0703123i
$605$	17.1000	−	9.87267i	0.695213	−	0.401381i
$606$	7.23050	+	12.5236i	0.293719	+	0.508736i
$607$	16.0136	−	27.7364i	0.649972	−	1.12578i	−0.333157	−	0.942871i	$-0.608114\pi$
$607$	16.0136	−	27.7364i	0.649972	−	1.12578i	0.983129	−	0.182914i	$-0.0585528\pi$
$608$	3.42376	+	2.69775i	0.138852	+	0.109408i
$609$	−20.7946	+	8.10221i	−0.842641	+	0.328318i
$610$		−	39.4853i		−	1.59871i
$611$	−25.8191	−	14.9067i	−1.04453	−	0.603060i
$612$	2.12164	−	1.22493i	0.0857621	−	0.0495148i
$613$	−17.5523	−	30.4015i	−0.708932	−	1.22791i	−0.965254	−	0.261314i	$-0.915844\pi$
$613$	−17.5523	−	30.4015i	−0.708932	−	1.22791i	0.256322	−	0.966591i	$-0.417489\pi$
$614$	−26.7882	−	15.4662i	−1.08108	−	0.624163i
$615$		−	21.2007i		−	0.854893i
$616$	10.1894	−	3.97011i	0.410544	−	0.159960i
$617$	9.38501			0.377826			0.188913	−	0.981994i	$-0.439504\pi$
$617$	9.38501			0.377826			0.188913	+	0.981994i	$0.439504\pi$
$618$	1.39260	+	0.804019i	0.0560186	+	0.0323424i
$619$	1.60684	−	0.927707i	0.0645842	−	0.0372877i	−0.467360	−	0.884067i	$-0.654795\pi$
$619$	1.60684	−	0.927707i	0.0645842	−	0.0372877i	0.531944	+	0.846779i	$0.321462\pi$
$620$	4.67529	−	2.69928i	0.187764	−	0.108406i
$621$	−2.24167	+	3.88269i	−0.0899551	+	0.155807i
$622$	−13.9059			−0.557575
$623$	−17.8280	+	22.2429i	−0.714263	+	0.891143i
$624$	−2.67370			−0.107033
$625$	11.0234	−	19.0931i	0.440936	−	0.763724i
$626$	−1.77977	−	3.08265i	−0.0711338	−	0.123207i
$627$	17.8306	+	2.58095i	0.712086	+	0.103073i
$628$	−2.24178	−	1.29429i	−0.0894569	−	0.0516480i
$629$	−27.5925			−1.10018
$630$	−8.48786	−	1.30074i	−0.338165	−	0.0518227i
$631$	44.2947			1.76334			0.881672	−	0.471863i	$-0.156418\pi$
$631$	44.2947			1.76334			0.881672	+	0.471863i	$0.156418\pi$
$632$	2.73430	−	4.73594i	0.108764	−	0.188386i
$633$	−8.59563	+	4.96269i	−0.341646	+	0.197249i
$634$	−2.36011	−	4.08784i	−0.0937321	−	0.162349i
$635$	−27.5958	+	47.7973i	−1.09510	+	1.89678i
$636$		−	10.0738i		−	0.399451i
$637$	−17.8570	−	5.60467i	−0.707519	−	0.222065i
$638$	−34.8646			−1.38030
$639$	−6.99833	−	4.04049i	−0.276850	−	0.159839i
$640$	−1.62278	−	2.81074i	−0.0641461	−	0.111104i
$641$	−35.5752	+	20.5393i	−1.40514	+	0.811255i	−0.994914	−	0.100731i	$-0.967882\pi$
$641$	−35.5752	+	20.5393i	−1.40514	+	0.811255i	−0.410222	+	0.911986i	$0.634549\pi$
$642$	−4.01720	+	6.95800i	−0.158546	+	0.274610i
$643$			35.4962i			1.39983i	0.714225	+	0.699916i	$0.246779\pi$
$643$			35.4962i			1.39983i	−0.714225	+	0.699916i	$0.753221\pi$
$644$	−11.7249	−	1.79681i	−0.462027	−	0.0708042i
$645$			36.0032i			1.41762i
$646$	3.95944	+	9.91750i	0.155782	+	0.390199i
$647$	−25.1836	+	14.5398i	−0.990070	+	0.571617i	−0.905295	−	0.424783i	$-0.860351\pi$
$647$	−25.1836	+	14.5398i	−0.990070	+	0.571617i	−0.0847751	+	0.996400i	$0.527017\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−12.9076	+	22.3566i	−0.506668	+	0.877574i
$650$			14.7954i			0.580322i
$651$	2.75236	−	3.43395i	0.107873	−	0.134587i
$652$	13.6513			0.534625
$653$	−2.34277	+	4.05779i	−0.0916796	+	0.158794i	−0.908218	−	0.418497i	$-0.862557\pi$
$653$	−2.34277	+	4.05779i	−0.0916796	+	0.158794i	0.816538	+	0.577291i	$0.195890\pi$
$654$	−3.23532	−	5.60373i	−0.126511	−	0.219123i
$655$	15.0529	+	26.0724i	0.588167	+	1.01873i
$656$	3.26610	−	5.65705i	0.127520	−	0.220871i
$657$		−	4.60540i		−	0.179674i
$658$	−10.7105	−	27.4889i	−0.417539	−	1.07163i
$659$			39.6664i			1.54518i	0.634903	+	0.772592i	$0.281040\pi$
$659$			39.6664i			1.54518i	−0.634903	+	0.772592i	$0.718960\pi$
$660$	−11.6175	−	6.70737i	−0.452211	−	0.261084i
$661$	9.36430	+	16.2194i	0.364229	+	0.630863i	0.988652	−	0.150223i	$-0.0479992\pi$
$661$	9.36430	+	16.2194i	0.364229	+	0.630863i	−0.624423	+	0.781086i	$0.714666\pi$
$662$	14.2227	+	24.6345i	0.552781	+	0.957445i
$663$	−5.67261	−	3.27508i	−0.220306	−	0.127194i
$664$	−14.0898			−0.546788
$665$	10.9114	−	35.8039i	0.423127	−	1.38842i
$666$	11.2629			0.436429
$667$	32.7510	+	18.9088i	1.26813	+	0.732152i
$668$	5.71148	+	9.89258i	0.220984	+	0.382755i
$669$	1.13620	+	1.96796i	0.0439281	+	0.0760856i
$670$	−23.6174	−	13.6355i	−0.912420	−	0.526786i
$671$		−	50.2849i		−	1.94123i
$672$	−2.06446	−	1.65469i	−0.0796383	−	0.0638311i
$673$		−	30.0770i		−	1.15938i	−0.814837	−	0.579691i	$-0.803173\pi$
$673$		−	30.0770i		−	1.15938i	0.814837	−	0.579691i	$-0.196827\pi$
$674$	−8.09095	+	14.0139i	−0.311652	+	0.539797i
$675$	2.76684	+	4.79230i	0.106496	+	0.184456i
$676$	−2.92568	−	5.06742i	−0.112526	−	0.194901i
$677$	9.13801	−	15.8275i	0.351202	−	0.608300i	−0.635258	−	0.772300i	$-0.719106\pi$
$677$	9.13801	−	15.8275i	0.351202	−	0.608300i	0.986460	+	0.164000i	$0.0524396\pi$
$678$	−17.3265			−0.665422
$679$	15.4557	+	2.36854i	0.593136	+	0.0908963i
$680$		−	7.95116i		−	0.304913i
$681$	8.20350	−	14.2089i	0.314359	−	0.544485i
$682$	5.95403	−	3.43756i	0.227991	−	0.131631i
$683$	−14.4265	+	8.32913i	−0.552014	+	0.318705i	−0.749934	−	0.661513i	$-0.769915\pi$
$683$	−14.4265	+	8.32913i	−0.552014	+	0.318705i	0.197920	+	0.980218i	$0.436581\pi$
$684$	−1.61619	−	4.04820i	−0.0617967	−	0.154787i
$685$		−	23.3525i		−	0.892254i
$686$	−10.3194	−	15.3789i	−0.393998	−	0.587168i
$687$		−	9.37355i		−	0.357623i
$688$	−5.54652	+	9.60686i	−0.211459	+	0.366258i
$689$	−23.3257	+	13.4671i	−0.888639	+	0.513056i
$690$	7.27548	+	12.6015i	0.276973	+	0.479731i
$691$	−34.5167	−	19.9282i	−1.31308	−	0.758105i	−0.330472	−	0.943816i	$-0.607208\pi$
$691$	−34.5167	−	19.9282i	−1.31308	−	0.758105i	−0.982605	+	0.185710i	$0.940541\pi$
$692$	−11.9100			−0.452752
$693$	−10.8094	−	1.65650i	−0.410614	−	0.0629253i
$694$		−	0.404507i		−	0.0153549i
$695$	25.8700	−	44.8081i	0.981304	−	1.69967i
$696$	4.21757	+	7.30505i	0.159867	+	0.276897i
$697$	13.8590	−	8.00147i	0.524945	−	0.303077i
$698$	−11.9345	+	20.6712i	−0.451729	+	0.782417i
$699$	−12.4517			−0.470968
$700$	−9.15652	+	11.4241i	−0.346084	+	0.431789i
$701$	26.0232			0.982881			0.491441	−	0.870911i	$-0.336471\pi$
$701$	26.0232			0.982881			0.491441	+	0.870911i	$0.336471\pi$
$702$	2.31549	+	1.33685i	0.0873925	+	0.0504561i
$703$	−7.03296	+	48.5875i	−0.265253	+	1.83251i
$704$	−2.06663	−	3.57950i	−0.0778890	−	0.134908i
$705$	−18.0950	+	31.3415i	−0.681498	+	1.18039i
$706$	−24.4525			−0.920283
$707$	35.6498	−	13.8902i	1.34075	−	0.522395i
$708$	6.24573			0.234729
$709$	−2.81510	+	4.87590i	−0.105723	+	0.183118i	−0.914033	−	0.405639i	$-0.867049\pi$
$709$	−2.81510	+	4.87590i	−0.105723	+	0.183118i	0.808310	+	0.588757i	$0.200382\pi$
$710$	−22.7135	+	13.1137i	−0.852424	+	0.492147i
$711$	−4.73594	+	2.73430i	−0.177612	+	0.102544i
$712$	9.33073	+	5.38710i	0.349684	+	0.201890i
$713$	−7.45744			−0.279283
$714$	−2.35316	−	6.03947i	−0.0880647	−	0.226021i
$715$			35.8669i			1.34135i
$716$	−13.9559	−	8.05746i	−0.521558	−	0.301121i
$717$	5.65840	+	9.80064i	0.211317	+	0.366012i
$718$	10.9104	−	6.29910i	0.407171	−	0.235080i
$719$	−5.80034	−	3.34883i	−0.216316	−	0.124890i	0.387927	−	0.921690i	$-0.373191\pi$
$719$	−5.80034	−	3.34883i	−0.216316	−	0.124890i	−0.604243	+	0.796800i	$0.706525\pi$
$720$			3.24556i			0.120955i
$721$	2.66081	−	3.31973i	0.0990936	−	0.123633i
$722$	18.4729	−	4.44432i	0.687490	−	0.165400i
$723$	2.14036	−	3.70722i	0.0796009	−	0.137873i
$724$	2.61867	+	4.53568i	0.0973222	+	0.168567i
$725$	40.4238	−	23.3387i	1.50130	−	0.866777i
$726$	−5.26872	−	3.04190i	−0.195541	−	0.112895i
$727$		−	3.03772i		−	0.112663i	−0.998412	−	0.0563314i	$-0.982060\pi$
$727$		−	3.03772i		−	0.112663i	0.998412	−	0.0563314i	$-0.0179403\pi$
$728$	−1.07155	+	6.99230i	−0.0397142	+	0.259152i
$729$	1.00000			0.0370370
$730$	−12.9446	−	7.47356i	−0.479101	−	0.276609i
$731$	−23.5354	+	13.5882i	−0.870489	+	0.502577i
$732$	−10.5360	+	6.08297i	−0.389422	+	0.224833i
$733$	−19.9712	−	11.5304i	−0.737655	−	0.425885i	0.0835613	−	0.996503i	$-0.473371\pi$
$733$	−19.9712	−	11.5304i	−0.737655	−	0.425885i	−0.821216	+	0.570618i	$0.806704\pi$
$734$	−5.26429			−0.194309
$735$	−6.80344	+	21.6763i	−0.250949	+	0.799544i
$736$			4.48334i			0.165258i
$737$	−30.0770	−	17.3650i	−1.10790	−	0.639647i
$738$	−5.65705	+	3.26610i	−0.208239	+	0.120227i
$739$	1.56893	+	2.71747i	0.0577140	+	0.0999637i	0.893439	−	0.449185i	$-0.148286\pi$
$739$	1.56893	+	2.71747i	0.0577140	+	0.0999637i	−0.835725	+	0.549148i	$0.814952\pi$
$740$	18.2772	−	31.6571i	0.671884	−	1.16374i
$741$	−7.21296	+	9.15410i	−0.264975	+	0.336284i
$742$	−26.3452	−	4.03731i	−0.967161	−	0.148214i
$743$			13.0208i			0.477686i	0.971058	+	0.238843i	$0.0767682\pi$
$743$			13.0208i			0.477686i	−0.971058	+	0.238843i	$0.923232\pi$
$744$	−1.44052	−	0.831683i	−0.0528119	−	0.0304910i
$745$	−1.05037	+	0.606429i	−0.0384824	+	0.0222178i
$746$	−8.12173	−	14.0672i	−0.297358	−	0.515038i
$747$	12.2021	+	7.04488i	0.446451	+	0.257759i
$748$		−	10.1259i		−	0.370239i
$749$	16.5867	+	13.2945i	0.606065	+	0.485769i
$750$	1.73208			0.0632464
$751$	3.78757	+	2.18675i	0.138210	+	0.0797958i	0.567511	−	0.823366i	$-0.307907\pi$
$751$	3.78757	+	2.18675i	0.138210	+	0.0797958i	−0.429300	+	0.903162i	$0.641240\pi$
$752$	−9.65673	+	5.57531i	−0.352145	+	0.203311i
$753$	−6.17164	+	3.56320i	−0.224907	+	0.129850i
$754$	11.2765	−	19.5315i	0.410666	−	0.711295i
$755$	11.2168			0.408222
$756$	0.960530	+	2.46523i	0.0349341	+	0.0896597i
$757$	−16.4922			−0.599420			−0.299710	−	0.954030i	$-0.596890\pi$
$757$	−16.4922			−0.599420			−0.299710	+	0.954030i	$0.596890\pi$
$758$	−1.51753	+	2.62844i	−0.0551192	+	0.0954693i
$759$	9.26539	+	16.0481i	0.336313	+	0.582510i
$760$	−14.0012	−	2.02664i	−0.507876	−	0.0735141i
$761$	−31.5222	−	18.1994i	−1.14268	−	0.659727i	−0.195588	−	0.980686i	$-0.562661\pi$
$761$	−31.5222	−	18.1994i	−1.14268	−	0.659727i	−0.947093	+	0.320959i	$0.895995\pi$
$762$	17.0052			0.616035
$763$	−15.9516	+	6.21524i	−0.577488	+	0.225007i
$764$	−21.7531			−0.786999
$765$	−3.97558	+	6.88590i	−0.143737	+	0.248960i
$766$	17.4529	−	10.0764i	0.630599	−	0.364076i
$767$	−8.34959	−	14.4619i	−0.301486	−	0.522190i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$			43.3047i			1.56161i	0.624776	+	0.780804i	$0.285190\pi$
$769$			43.3047i			1.56161i	−0.624776	+	0.780804i	$0.714810\pi$
$770$	−22.1972	+	27.6942i	−0.799933	+	0.998030i
$771$	−9.48781			−0.341695
$772$	−19.7137	−	11.3817i	−0.709511	−	0.409636i
$773$	−2.47575	−	4.28812i	−0.0890465	−	0.154233i	0.818062	−	0.575130i	$-0.195049\pi$
$773$	−2.47575	−	4.28812i	−0.0890465	−	0.154233i	−0.907108	+	0.420897i	$0.861715\pi$
$774$	9.60686	−	5.54652i	0.345312	−	0.199366i
$775$	−4.60226	+	7.97136i	−0.165318	+	0.286340i
$776$		−	5.90991i		−	0.212153i
$777$	4.51388	−	29.4550i	0.161935	−	1.05669i
$778$			8.21562i			0.294544i
$779$	−10.5573	−	26.4437i	−0.378255	−	0.947442i
$780$	7.51506	−	4.33882i	0.269082	−	0.155355i
$781$	−28.9259	+	16.7004i	−1.03505	+	0.597587i
$782$	−5.49177	+	9.51202i	−0.196385	+	0.340149i
$783$		−	8.43515i		−	0.301448i
$784$	−5.15477	+	4.73586i	−0.184099	+	0.169138i
$785$	8.40143			0.299860
$786$	4.63800	−	8.03326i	0.165432	−	0.286537i
$787$	23.7387	+	41.1166i	0.846192	+	1.46565i	0.884582	+	0.466385i	$0.154444\pi$
$787$	23.7387	+	41.1166i	0.846192	+	1.46565i	−0.0383896	+	0.999263i	$0.512223\pi$
$788$	−3.80590	−	6.59201i	−0.135579	−	0.234831i
$789$	8.19288	−	14.1905i	0.291674	−	0.505194i
$790$			17.7487i			0.631469i
$791$	−6.94403	+	45.3127i	−0.246901	+	1.61113i
$792$			4.13326i			0.146869i
$793$	28.1701	+	16.2640i	1.00035	+	0.577552i
$794$	−4.55408	−	7.88789i	−0.161618	−	0.279931i
$795$	16.3475	+	28.3148i	0.579787	+	1.00422i
$796$	−3.81618	−	2.20327i	−0.135261	−	0.0780929i
$797$	−33.4874			−1.18618			−0.593092	−	0.805135i	$-0.702093\pi$
$797$	−33.4874			−1.18618			−0.593092	+	0.805135i	$0.702093\pi$
$798$	−11.2347	+	2.60429i	−0.397703	+	0.0921908i
$799$	−27.3174			−0.966421
$800$	4.79230	+	2.76684i	0.169434	+	0.0978225i
$801$	−5.38710	−	9.33073i	−0.190344	−	0.329685i
$802$	−6.25373	−	10.8318i	−0.220827	−	0.382483i
$803$	−16.4851	−	9.51765i	−0.581745	−	0.335871i
$804$			8.40256i			0.296335i
$805$	35.8715	−	13.9766i	1.26431	−	0.492611i
$806$			4.44734i			0.156651i
$807$	11.3597	−	19.6756i	0.399881	−	0.692614i
$808$	−7.23050	−	12.5236i	−0.254368	−	0.440578i
$809$	2.08613	+	3.61329i	0.0733445	+	0.127036i	0.900365	−	0.435135i	$-0.143299\pi$
$809$	2.08613	+	3.61329i	0.0733445	+	0.127036i	−0.827021	+	0.562172i	$0.809966\pi$
$810$	1.62278	−	2.81074i	0.0570187	−	0.0987593i
$811$	6.50641			0.228471			0.114236	−	0.993454i	$-0.463558\pi$
$811$	6.50641			0.228471			0.114236	+	0.993454i	$0.463558\pi$
$812$	20.7946	−	8.10221i	0.729748	−	0.284332i
$813$			4.76825i			0.167230i
$814$	23.2762	−	40.3156i	0.815831	−	1.41306i
$815$	−38.3702	+	22.1530i	−1.34405	+	0.775986i
$816$	−2.12164	+	1.22493i	−0.0742721	+	0.0428810i
$817$	17.9285	+	44.9069i	0.627239	+	1.57109i
$818$			14.6204i			0.511191i
$819$	4.42414	−	5.51974i	0.154592	−	0.192875i
$820$			21.2007i			0.740359i
$821$	−1.08931	+	1.88674i	−0.0380172	+	0.0658477i	−0.884408	−	0.466715i	$-0.845437\pi$
$821$	−1.08931	+	1.88674i	−0.0380172	+	0.0658477i	0.846391	+	0.532562i	$0.178771\pi$
$822$	−6.23124	+	3.59761i	−0.217340	+	0.125481i
$823$	−14.9284	−	25.8567i	−0.520370	−	0.901308i	−0.999720	−	0.0236837i	$-0.992461\pi$
$823$	−14.9284	−	25.8567i	−0.520370	−	0.901308i	0.479349	−	0.877624i	$-0.340873\pi$
$824$	−1.39260	−	0.804019i	−0.0485136	−	0.0280093i
$825$	22.8721			0.796304
$826$	2.50313	−	16.3340i	0.0870950	−	0.568331i
$827$		−	6.40901i		−	0.222863i	−0.993772	−	0.111431i	$-0.964456\pi$
$827$		−	6.40901i		−	0.222863i	0.993772	−	0.111431i	$-0.0355436\pi$
$828$	2.24167	−	3.88269i	0.0779034	−	0.134933i
$829$	−5.29249	−	9.16687i	−0.183816	−	0.318379i	0.759361	−	0.650670i	$-0.225512\pi$
$829$	−5.29249	−	9.16687i	−0.183816	−	0.318379i	−0.943177	+	0.332291i	$0.892178\pi$
$830$	39.6026	−	22.8646i	1.37463	−	0.793641i
$831$	−0.361704	+	0.626490i	−0.0125474	+	0.0217327i
$832$	2.67370			0.0926937
$833$	−16.7376	+	3.73356i	−0.579924	+	0.129360i
$834$	−15.9417			−0.552018
$835$	−32.1070	−	18.5370i	−1.11111	−	0.641499i
$836$	−17.8306	−	2.58095i	−0.616685	−	0.0892641i
$837$	0.831683	+	1.44052i	0.0287472	+	0.0497916i
$838$	3.09421	−	5.35932i	0.106888	−	0.185135i
$839$	42.2297			1.45793			0.728966	−	0.684550i	$-0.240001\pi$
$839$	42.2297			1.45793			0.728966	+	0.684550i	$0.240001\pi$
$840$	8.48786	+	1.30074i	0.292859	+	0.0448797i
$841$	−42.1517			−1.45351
$842$	−15.1500	+	26.2405i	−0.522102	+	0.904307i
$843$	−0.759329	+	0.438399i	−0.0261527	+	0.0150993i
$844$	8.59563	−	4.96269i	0.295874	−	0.170823i
$845$	16.4466	+	9.49546i	0.565781	+	0.326654i
$846$	11.1506			0.383366
$847$	−10.0668	+	12.5598i	−0.345900	+	0.431559i
$848$			10.0738i			0.345935i
$849$	13.1301	+	7.58065i	0.450623	+	0.260167i
$850$	6.77835	+	11.7404i	0.232495	+	0.402694i
$851$	−43.7303	+	25.2477i	−1.49906	+	0.865481i
$852$	6.99833	+	4.04049i	0.239759	+	0.138425i
$853$		−	7.50394i		−	0.256930i	−0.991714	−	0.128465i	$-0.958995\pi$
$853$		−	7.50394i		−	0.256930i	0.991714	−	0.128465i	$-0.0410050\pi$
$854$	11.6857	+	29.9919i	0.399878	+	1.02630i
$855$	11.1120	+	8.75571i	0.380024	+	0.299439i
$856$	4.01720	−	6.95800i	0.137305	−	0.237819i
$857$	9.76221	+	16.9086i	0.333471	+	0.577588i	0.983190	−	0.182586i	$-0.0584469\pi$
$857$	9.76221	+	16.9086i	0.333471	+	0.577588i	−0.649719	+	0.760174i	$0.725114\pi$
$858$	9.57050	−	5.52553i	0.326732	−	0.188639i
$859$	−17.6941	−	10.2157i	−0.603713	−	0.348554i	0.166788	−	0.985993i	$-0.446661\pi$
$859$	−17.6941	−	10.2157i	−0.603713	−	0.348554i	−0.770501	+	0.637439i	$0.779994\pi$
$860$		−	36.0032i		−	1.22770i
$861$	6.27437	+	16.1034i	0.213830	+	0.548803i
$862$	14.0441			0.478343
$863$	−40.8912	−	23.6085i	−1.39195	−	0.803644i	−0.398420	−	0.917203i	$-0.630441\pi$
$863$	−40.8912	−	23.6085i	−1.39195	−	0.803644i	−0.993531	+	0.113559i	$0.963775\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	33.4760	−	19.3274i	1.13822	−	0.657151i
$866$	2.84772	+	1.64413i	0.0967696	+	0.0558699i
$867$	10.9982			0.373519
$868$	−2.75236	+	3.43395i	−0.0934211	+	0.116556i
$869$			22.6031i			0.766757i
$870$	−23.7090	−	13.6884i	−0.803810	−	0.464080i
$871$	19.4560	−	11.2329i	0.659242	−	0.380614i
$872$	3.23532	+	5.60373i	0.109562	+	0.189766i
$873$	−2.95496	+	5.11813i	−0.100010	+	0.173223i
$874$	15.3499	+	12.0949i	0.519218	+	0.409117i
$875$	0.694172	−	4.52976i	0.0234673	−	0.153134i
$876$			4.60540i			0.155602i
$877$	11.8333	+	6.83193i	0.399581	+	0.230698i	0.686303	−	0.727316i	$-0.259232\pi$
$877$	11.8333	+	6.83193i	0.399581	+	0.230698i	−0.286722	+	0.958014i	$0.592566\pi$
$878$	2.92258	−	1.68735i	0.0986323	−	0.0569454i
$879$	−7.49135	−	12.9754i	−0.252677	−	0.437649i
$880$	11.6175	+	6.70737i	0.391626	+	0.226105i
$881$		−	23.1442i		−	0.779748i	−0.920868	−	0.389874i	$-0.872519\pi$
$881$		−	23.1442i		−	0.779748i	0.920868	−	0.389874i	$-0.127481\pi$
$882$	6.83209	−	1.52399i	0.230048	−	0.0513155i
$883$	−52.2983			−1.75998			−0.879989	−	0.474994i	$-0.842450\pi$
$883$	−52.2983			−1.75998			−0.879989	+	0.474994i	$0.842450\pi$
$884$	5.67261	+	3.27508i	0.190791	+	0.110153i
$885$	−17.5551	+	10.1355i	−0.590109	+	0.340700i
$886$	−0.165041	+	0.0952864i	−0.00554465	+	0.00320121i
$887$	6.02310	−	10.4323i	0.202236	−	0.350283i	−0.747013	−	0.664810i	$-0.768513\pi$
$887$	6.02310	−	10.4323i	0.202236	−	0.350283i	0.949248	+	0.314527i	$0.101846\pi$
$888$	−11.2629			−0.377958
$889$	6.81526	−	44.4724i	0.228577	−	1.49156i
$890$	−34.9683			−1.17214
$891$	2.06663	−	3.57950i	0.0692346	−	0.119918i
$892$	−1.13620	−	1.96796i	−0.0380428	−	0.0658921i
$893$	−6.96285	+	48.1031i	−0.233003	+	1.60971i
$894$	0.323631	+	0.186849i	0.0108238	+	0.00624915i
$895$	52.3020			1.74826
$896$	2.06446	+	1.65469i	0.0689688	+	0.0552794i
$897$	−11.9871			−0.400237
$898$	−15.8863	+	27.5159i	−0.530133	+	0.918217i
$899$	12.1510	−	7.01537i	0.405258	−	0.233976i
$900$	−2.76684	−	4.79230i	−0.0922279	−	0.159743i
$901$	−12.3396	+	21.3729i	−0.411093	+	0.712034i
$902$			26.9993i			0.898977i
$903$	−10.6552	−	27.3470i	−0.354583	−	0.910050i
$904$	17.3265			0.576272
$905$	−14.7208	−	8.49907i	−0.489337	−	0.282519i
$906$	−1.72802	−	2.99302i	−0.0574097	−	0.0994366i
$907$	−11.4445	+	6.60746i	−0.380007	+	0.219397i	−0.677821	−	0.735227i	$-0.737076\pi$
$907$	−11.4445	+	6.60746i	−0.380007	+	0.219397i	0.297814	+	0.954624i	$0.403742\pi$
$908$	−8.20350	+	14.2089i	−0.272243	+	0.471538i
$909$			14.4610i			0.479641i
$910$	−8.33514	−	21.3924i	−0.276307	−	0.709152i
$911$		−	9.35547i		−	0.309961i	−0.987918	−	0.154980i	$-0.950469\pi$
$911$		−	9.35547i		−	0.309961i	0.987918	−	0.154980i	$-0.0495314\pi$
$912$	1.61619	+	4.04820i	0.0535175	+	0.134049i
$913$	50.4343	−	29.1183i	1.66913	−	0.963674i
$914$	22.8722	−	13.2053i	0.756545	−	0.436791i
$915$	19.7426	−	34.1953i	0.652672	−	1.13046i
$916$			9.37355i			0.309711i
$917$	−19.1499	−	15.3489i	−0.632387	−	0.506866i
$918$	2.44985			0.0808573
$919$	16.5539	−	28.6721i	0.546061	−	0.945806i	−0.452478	−	0.891776i	$-0.649460\pi$
$919$	16.5539	−	28.6721i	0.546061	−	0.945806i	0.998539	−	0.0540303i	$-0.0172067\pi$
$920$	−7.27548	−	12.6015i	−0.239865	−	0.415459i
$921$	−15.4662	−	26.7882i	−0.509627	−	0.882700i
$922$	−9.87401	+	17.1023i	−0.325183	+	0.563234i
$923$		−	21.6061i		−	0.711173i
$924$	10.8094	+	1.65650i	0.355602	+	0.0544949i
$925$			62.3253i			2.04924i
$926$	−20.8866	−	12.0589i	−0.686377	−	0.396280i
$927$	0.804019	+	1.39260i	0.0264074	+	0.0457390i
$928$	−4.21757	−	7.30505i	−0.138449	−	0.239800i
$929$	14.4811	+	8.36069i	0.475111	+	0.274305i	0.718377	−	0.695654i	$-0.244885\pi$
$929$	14.4811	+	8.36069i	0.475111	+	0.274305i	−0.243266	+	0.969960i	$0.578219\pi$
$930$	5.39856			0.177026
$931$	2.30822	+	30.4249i	0.0756488	+	0.997135i
$932$	12.4517			0.407870
$933$	−12.0428	−	6.95294i	−0.394265	−	0.227629i
$934$	15.1124	+	26.1755i	0.494494	+	0.856488i
$935$	16.4321	+	28.4612i	0.537386	+	0.930781i
$936$	−2.31549	−	1.33685i	−0.0756841	−	0.0436962i
$937$			12.9638i			0.423509i	0.977323	+	0.211755i	$0.0679177\pi$
$937$			12.9638i			0.423509i	−0.977323	+	0.211755i	$0.932082\pi$
$938$	21.9745	+	3.36753i	0.717494	+	0.109954i
$939$		−	3.55954i		−	0.116161i
$940$	18.0950	−	31.3415i	0.590195	−	1.02225i
$941$	−12.7744	−	22.1259i	−0.416433	−	0.721282i	0.579145	−	0.815225i	$-0.303386\pi$
$941$	−12.7744	−	22.1259i	−0.416433	−	0.721282i	−0.995578	+	0.0939420i	$0.970053\pi$
$942$	−1.29429	−	2.24178i	−0.0421704	−	0.0730413i
$943$	14.6430	−	25.3625i	0.476843	−	0.825916i
$944$	−6.24573			−0.203281
$945$	−6.70034	−	5.37040i	−0.217962	−	0.174699i
$946$		−	45.8504i		−	1.49073i
$947$	14.6899	−	25.4437i	0.477358	−	0.826809i	−0.522305	−	0.852759i	$-0.674928\pi$
$947$	14.6899	−	25.4437i	0.477358	−	0.826809i	0.999663	+	0.0259499i	$0.00826105\pi$
$948$	4.73594	−	2.73430i	0.153816	−	0.0888058i
$949$	10.6638	−	6.15672i	0.346160	−	0.199856i
$950$	22.4014	−	8.94349i	0.726798	−	0.290165i
$951$		−	4.72023i		−	0.153064i
$952$	2.35316	+	6.03947i	0.0762663	+	0.195740i
$953$		−	43.7248i		−	1.41638i	−0.706020	−	0.708192i	$-0.749511\pi$
$953$		−	43.7248i		−	1.41638i	0.706020	−	0.708192i	$-0.250489\pi$
$954$	5.03689	−	8.72415i	0.163075	−	0.282455i
$955$	61.1423	−	35.3005i	1.97852	−	1.14230i
$956$	−5.65840	−	9.80064i	−0.183006	−	0.316975i
$957$	−30.1936	−	17.4323i	−0.976022	−	0.563507i
$958$	−3.63693			−0.117504
$959$	6.91122	+	17.7379i	0.223175	+	0.572787i
$960$		−	3.24556i		−	0.104750i
$961$	14.1166	−	24.4507i	0.455374	−	0.788732i
$962$	15.0568	+	26.0791i	0.485450	+	0.840825i
$963$	−6.95800	+	4.01720i	−0.224218	+	0.129452i
$964$	−2.14036	+	3.70722i	−0.0689364	+	0.119401i
$965$	73.8800			2.37828
$966$	−9.25568	−	7.41854i	−0.297797	−	0.238688i
$967$	32.7590			1.05346			0.526729	−	0.850034i	$-0.323418\pi$
$967$	32.7590			1.05346			0.526729	+	0.850034i	$0.323418\pi$
$968$	5.26872	+	3.04190i	0.169343	+	0.0977703i
$969$	−1.52978	+	10.5685i	−0.0491435	+	0.339510i
$970$	9.59049	+	16.6112i	0.307932	+	0.533354i
$971$	7.84757	−	13.5924i	0.251841	−	0.436201i	−0.712192	−	0.701985i	$-0.752297\pi$
$971$	7.84757	−	13.5924i	0.251841	−	0.436201i	0.964033	+	0.265784i	$0.0856308\pi$
$972$	−1.00000			−0.0320750
$973$	−6.38904	+	41.6912i	−0.204823	+	1.33656i
$974$	16.4355			0.526628
$975$	−7.39768	+	12.8132i	−0.236915	+	0.410350i
$976$	10.5360	−	6.08297i	0.337249	−	0.194711i
$977$	38.7331	−	22.3626i	1.23918	−	0.715443i	0.270256	−	0.962789i	$-0.412892\pi$
$977$	38.7331	−	22.3626i	1.23918	−	0.715443i	0.968927	+	0.247346i	$0.0795584\pi$
$978$	11.8223	+	6.82563i	0.378037	+	0.218260i
$979$	−44.5325			−1.42327
$980$	6.80344	−	21.6763i	0.217328	−	0.692425i
$981$		−	6.47064i		−	0.206591i
$982$	−7.76325	−	4.48211i	−0.247735	−	0.143030i
$983$	1.82659	+	3.16375i	0.0582593	+	0.100908i	0.893684	−	0.448697i	$-0.148112\pi$
$983$	1.82659	+	3.16375i	0.0582593	+	0.100908i	−0.835425	+	0.549605i	$0.814778\pi$
$984$	5.65705	−	3.26610i	0.180340	−	0.104119i
$985$	21.3948	+	12.3523i	0.681694	+	0.393576i
$986$		−	20.6649i		−	0.658104i
$987$	4.46889	−	29.1614i	0.142246	−	0.928216i
$988$	7.21296	−	9.15410i	0.229475	−	0.291231i
$989$	−24.8670	+	43.0708i	−0.790723	+	1.36957i
$990$	−6.70737	−	11.6175i	−0.213174	−	0.369228i
$991$	−26.0739	+	15.0538i	−0.828265	+	0.478199i	−0.853258	−	0.521489i	$-0.825377\pi$
$991$	−26.0739	+	15.0538i	−0.828265	+	0.478199i	0.0249935	+	0.999688i	$0.492043\pi$
$992$	1.44052	+	0.831683i	0.0457365	+	0.0264060i
$993$			28.4454i			0.902688i
$994$	13.3715	−	16.6829i	0.424119	−	0.529148i
$995$	14.3017			0.453395
$996$	−12.2021	−	7.04488i	−0.386638	−	0.223225i
$997$	−38.2630	+	22.0912i	−1.21180	+	0.699634i	−0.963151	−	0.268959i	$-0.913320\pi$
$997$	−38.2630	+	22.0912i	−1.21180	+	0.699634i	−0.248650	+	0.968593i	$0.579987\pi$
$998$	−21.0716	+	12.1657i	−0.667008	+	0.385097i
$999$	9.75396	+	5.63145i	0.308602	+	0.178171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.be.a.607.2	yes	28
7.3	odd	6		798.2.be.b.493.9	yes	28
19.18	odd	2		798.2.be.b.607.9	yes	28
133.94	even	6	inner	798.2.be.a.493.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.be.a.493.2	✓	28	133.94	even	6	inner
798.2.be.a.607.2	yes	28	1.1	even	1	trivial
798.2.be.b.493.9	yes	28	7.3	odd	6
798.2.be.b.607.9	yes	28	19.18	odd	2

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.81074 - 1.62278i) q^{5} +1.00000i q^{6} +(2.61522 + 0.400774i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.81074 - 1.62278i) q^{5} +1.00000i q^{6} +(2.61522 + 0.400774i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.62278 + 2.81074i) q^{10} +(2.06663 + 3.57950i) q^{11} +(0.500000 - 0.866025i) q^{12} -2.67370 q^{13} +(-2.06446 - 1.65469i) q^{14} +3.24556i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.12164 + 1.22493i) q^{17} +(0.866025 - 0.500000i) q^{18} +(1.61619 + 4.04820i) q^{19} -3.24556i q^{20} +(-0.960530 - 2.46523i) q^{21} -4.13326i q^{22} +(-2.24167 + 3.88269i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(2.76684 + 4.79230i) q^{25} +(2.31549 + 1.33685i) q^{26} +1.00000 q^{27} +(0.960530 + 2.46523i) q^{28} -8.43515i q^{29} +(1.62278 - 2.81074i) q^{30} +(0.831683 + 1.44052i) q^{31} +(0.866025 - 0.500000i) q^{32} +(2.06663 - 3.57950i) q^{33} +2.44985 q^{34} +(-6.70034 - 5.37040i) q^{35} -1.00000 q^{36} +(9.75396 + 5.63145i) q^{37} +(0.624436 - 4.31394i) q^{38} +(1.33685 + 2.31549i) q^{39} +(-1.62278 + 2.81074i) q^{40} -6.53220 q^{41} +(-0.400774 + 2.61522i) q^{42} +11.0930 q^{43} +(-2.06663 + 3.57950i) q^{44} +(2.81074 - 1.62278i) q^{45} +(3.88269 - 2.24167i) q^{46} +(9.65673 + 5.57531i) q^{47} +1.00000 q^{48} +(6.67876 + 2.09623i) q^{49} -5.53367i q^{50} +(2.12164 + 1.22493i) q^{51} +(-1.33685 - 2.31549i) q^{52} +(8.72415 - 5.03689i) q^{53} +(-0.866025 - 0.500000i) q^{54} -13.4147i q^{55} +(0.400774 - 2.61522i) q^{56} +(2.69775 - 3.42376i) q^{57} +(-4.21757 + 7.30505i) q^{58} +(3.12287 + 5.40896i) q^{59} +(-2.81074 + 1.62278i) q^{60} +(-10.5360 - 6.08297i) q^{61} -1.66337i q^{62} +(-1.65469 + 2.06446i) q^{63} -1.00000 q^{64} +(7.51506 + 4.33882i) q^{65} +(-3.57950 + 2.06663i) q^{66} +(-7.27683 + 4.20128i) q^{67} +(-2.12164 - 1.22493i) q^{68} +4.48334 q^{69} +(3.11746 + 8.00107i) q^{70} +8.08098i q^{71} +(0.866025 + 0.500000i) q^{72} +(-3.98840 + 2.30270i) q^{73} +(-5.63145 - 9.75396i) q^{74} +(2.76684 - 4.79230i) q^{75} +(-2.69775 + 3.42376i) q^{76} +(3.97011 + 10.1894i) q^{77} -2.67370i q^{78} +(4.73594 + 2.73430i) q^{79} +(2.81074 - 1.62278i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.65705 + 3.26610i) q^{82} -14.0898i q^{83} +(1.65469 - 2.06446i) q^{84} +7.95116 q^{85} +(-9.60686 - 5.54652i) q^{86} +(-7.30505 + 4.21757i) q^{87} +(3.57950 - 2.06663i) q^{88} +(-5.38710 + 9.33073i) q^{89} -3.24556 q^{90} +(-6.99230 - 1.07155i) q^{91} -4.48334 q^{92} +(0.831683 - 1.44052i) q^{93} +(-5.57531 - 9.65673i) q^{94} +(2.02664 - 14.0012i) q^{95} +(-0.866025 - 0.500000i) q^{96} +5.90991 q^{97} +(-4.73586 - 5.15477i) q^{98} -4.13326 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 14 q^{3} + 14 q^{4} - 6 q^{5} - 2 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q - 14 * q^3 + 14 * q^4 - 6 * q^5 - 2 * q^7 - 14 * q^9	\( 28 q - 14 q^{3} + 14 q^{4} - 6 q^{5} - 2 q^{7} - 14 q^{9} - 4 q^{10} + 6 q^{11} + 14 q^{12} + 8 q^{13} + 4 q^{14} - 14 q^{16} - 12 q^{17} + 6 q^{19} + 4 q^{21} + 6 q^{23} + 20 q^{25} + 12 q^{26} + 28 q^{27} - 4 q^{28} - 4 q^{30} + 4 q^{31} + 6 q^{33} + 8 q^{34} - 10 q^{35} - 28 q^{36} + 12 q^{37} - 24 q^{38} - 4 q^{39} + 4 q^{40} + 40 q^{41} - 8 q^{42} + 52 q^{43} - 6 q^{44} + 6 q^{45} + 36 q^{46} - 6 q^{47} + 28 q^{48} + 18 q^{49} + 12 q^{51} + 4 q^{52} + 36 q^{53} + 8 q^{56} - 12 q^{57} + 4 q^{58} + 32 q^{59} - 6 q^{60} + 6 q^{61} - 2 q^{63} - 28 q^{64} - 60 q^{65} - 12 q^{67} - 12 q^{68} - 12 q^{69} - 12 q^{70} + 30 q^{73} + 12 q^{74} + 20 q^{75} + 12 q^{76} + 28 q^{77} - 36 q^{79} + 6 q^{80} - 14 q^{81} + 2 q^{84} + 64 q^{85} - 24 q^{86} + 16 q^{89} + 8 q^{90} - 20 q^{91} + 12 q^{92} + 4 q^{93} + 14 q^{95} - 16 q^{97} - 8 q^{98} - 12 q^{99}+O(q^{100}) \) 28 * q - 14 * q^3 + 14 * q^4 - 6 * q^5 - 2 * q^7 - 14 * q^9 - 4 * q^10 + 6 * q^11 + 14 * q^12 + 8 * q^13 + 4 * q^14 - 14 * q^16 - 12 * q^17 + 6 * q^19 + 4 * q^21 + 6 * q^23 + 20 * q^25 + 12 * q^26 + 28 * q^27 - 4 * q^28 - 4 * q^30 + 4 * q^31 + 6 * q^33 + 8 * q^34 - 10 * q^35 - 28 * q^36 + 12 * q^37 - 24 * q^38 - 4 * q^39 + 4 * q^40 + 40 * q^41 - 8 * q^42 + 52 * q^43 - 6 * q^44 + 6 * q^45 + 36 * q^46 - 6 * q^47 + 28 * q^48 + 18 * q^49 + 12 * q^51 + 4 * q^52 + 36 * q^53 + 8 * q^56 - 12 * q^57 + 4 * q^58 + 32 * q^59 - 6 * q^60 + 6 * q^61 - 2 * q^63 - 28 * q^64 - 60 * q^65 - 12 * q^67 - 12 * q^68 - 12 * q^69 - 12 * q^70 + 30 * q^73 + 12 * q^74 + 20 * q^75 + 12 * q^76 + 28 * q^77 - 36 * q^79 + 6 * q^80 - 14 * q^81 + 2 * q^84 + 64 * q^85 - 24 * q^86 + 16 * q^89 + 8 * q^90 - 20 * q^91 + 12 * q^92 + 4 * q^93 + 14 * q^95 - 16 * q^97 - 8 * q^98 - 12 * q^99

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