LMFDB - Embedded newform 770.2.i.m.331.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(221,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("770.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.i (of order $3$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 12x^{8} - 6x^{7} + 113x^{6} - 43x^{5} + 381x^{4} - 75x^{3} + 982x^{2} - 217x + 49 $ x^10 + 12x^8 - 6x^7 + 113x^6 - 43x^5 + 381x^4 - 75x^3 + 982x^2 - 217x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.4
Root			$-0.922461 + 1.59775i$ of defining polynomial
Character	$\chi$	$=$	770.331
Dual form			770.2.i.m.221.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.922461 + 1.59775i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.84492 q^{6} +(2.59682 - 0.506486i) q^{7} +1.00000 q^{8} +(-0.201870 + 0.349648i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.922461 + 1.59775i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.84492 q^{6} +(2.59682 - 0.506486i) q^{7} +1.00000 q^{8} +(-0.201870 + 0.349648i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.922461 - 1.59775i) q^{12} +4.07034 q^{13} +(-0.859780 + 2.50215i) q^{14} -1.84492 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.51928 + 6.09557i) q^{17} +(-0.201870 - 0.349648i) q^{18} +(1.22059 - 2.11413i) q^{19} +1.00000 q^{20} +(3.20470 + 3.68185i) q^{21} +1.00000 q^{22} +(-2.78224 + 4.81898i) q^{23} +(0.922461 + 1.59775i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.03517 + 3.52502i) q^{26} +4.78990 q^{27} +(-1.73704 - 1.99567i) q^{28} +0.245482 q^{29} +(0.922461 - 1.59775i) q^{30} +(-2.22059 - 3.84618i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.922461 - 1.59775i) q^{33} -7.03856 q^{34} +(-0.859780 + 2.50215i) q^{35} +0.403739 q^{36} +(-2.79972 + 4.84926i) q^{37} +(1.22059 + 2.11413i) q^{38} +(3.75473 + 6.50338i) q^{39} +(-0.500000 + 0.866025i) q^{40} -8.26604 q^{41} +(-4.79093 + 0.934427i) q^{42} -1.56448 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.201870 - 0.349648i) q^{45} +(-2.78224 - 4.81898i) q^{46} +(2.44118 - 4.22825i) q^{47} -1.84492 q^{48} +(6.48694 - 2.63050i) q^{49} +1.00000 q^{50} +(-6.49280 + 11.2459i) q^{51} +(-2.03517 - 3.52502i) q^{52} +(-2.77165 - 4.80064i) q^{53} +(-2.39495 + 4.14818i) q^{54} +1.00000 q^{55} +(2.59682 - 0.506486i) q^{56} +4.50379 q^{57} +(-0.122741 + 0.212594i) q^{58} +(2.15847 + 3.73858i) q^{59} +(0.922461 + 1.59775i) q^{60} +(-1.92729 + 3.33816i) q^{61} +4.44118 q^{62} +(-0.347127 + 1.01022i) q^{63} +1.00000 q^{64} +(-2.03517 + 3.52502i) q^{65} +(0.922461 + 1.59775i) q^{66} +(1.34492 + 2.32947i) q^{67} +(3.51928 - 6.09557i) q^{68} -10.2660 q^{69} +(-1.73704 - 1.99567i) q^{70} +10.6878 q^{71} +(-0.201870 + 0.349648i) q^{72} +(-8.38775 - 14.5280i) q^{73} +(-2.79972 - 4.84926i) q^{74} +(0.922461 - 1.59775i) q^{75} -2.44118 q^{76} +(-1.73704 - 1.99567i) q^{77} -7.50946 q^{78} +(-5.25094 + 9.09489i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.02411 + 8.70201i) q^{81} +(4.13302 - 7.15860i) q^{82} -10.8228 q^{83} +(1.58623 - 4.61628i) q^{84} -7.03856 q^{85} +(0.782242 - 1.35488i) q^{86} +(0.226448 + 0.392219i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-1.23601 + 2.14083i) q^{89} +0.403739 q^{90} +(10.5699 - 2.06157i) q^{91} +5.56448 q^{92} +(4.09682 - 7.09590i) q^{93} +(2.44118 + 4.22825i) q^{94} +(1.22059 + 2.11413i) q^{95} +(0.922461 - 1.59775i) q^{96} +6.25751 q^{97} +(-0.965389 + 6.93311i) q^{98} +0.403739 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9	$ 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9} - 5 q^{10} - 5 q^{11} - 2 q^{13} + 3 q^{14} - 5 q^{16} - 9 q^{18} - 4 q^{19} + 10 q^{20} + 2 q^{21} + 10 q^{22} - 7 q^{23} - 5 q^{25} + q^{26} - 18 q^{27} - 3 q^{28} + 8 q^{29} - 6 q^{31} - 5 q^{32} + 3 q^{35} + 18 q^{36} - 16 q^{37} - 4 q^{38} - 7 q^{39} - 5 q^{40} - 2 q^{41} + 11 q^{42} + 26 q^{43} - 5 q^{44} - 9 q^{45} - 7 q^{46} - 8 q^{47} + 14 q^{49} + 10 q^{50} - 13 q^{51} + q^{52} - 4 q^{53} + 9 q^{54} + 10 q^{55} + 30 q^{57} - 4 q^{58} - 9 q^{59} - 2 q^{61} + 12 q^{62} + 25 q^{63} + 10 q^{64} + q^{65} - 5 q^{67} - 22 q^{69} - 3 q^{70} + 56 q^{71} - 9 q^{72} + q^{73} - 16 q^{74} + 8 q^{76} - 3 q^{77} + 14 q^{78} - 23 q^{79} - 5 q^{80} + 7 q^{81} + q^{82} - 46 q^{83} - 13 q^{84} - 13 q^{86} - 15 q^{87} - 5 q^{88} + 9 q^{89} + 18 q^{90} + 29 q^{91} + 14 q^{92} + 15 q^{93} - 8 q^{94} - 4 q^{95} - 26 q^{97} - 19 q^{98} + 18 q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9 - 5 * q^10 - 5 * q^11 - 2 * q^13 + 3 * q^14 - 5 * q^16 - 9 * q^18 - 4 * q^19 + 10 * q^20 + 2 * q^21 + 10 * q^22 - 7 * q^23 - 5 * q^25 + q^26 - 18 * q^27 - 3 * q^28 + 8 * q^29 - 6 * q^31 - 5 * q^32 + 3 * q^35 + 18 * q^36 - 16 * q^37 - 4 * q^38 - 7 * q^39 - 5 * q^40 - 2 * q^41 + 11 * q^42 + 26 * q^43 - 5 * q^44 - 9 * q^45 - 7 * q^46 - 8 * q^47 + 14 * q^49 + 10 * q^50 - 13 * q^51 + q^52 - 4 * q^53 + 9 * q^54 + 10 * q^55 + 30 * q^57 - 4 * q^58 - 9 * q^59 - 2 * q^61 + 12 * q^62 + 25 * q^63 + 10 * q^64 + q^65 - 5 * q^67 - 22 * q^69 - 3 * q^70 + 56 * q^71 - 9 * q^72 + q^73 - 16 * q^74 + 8 * q^76 - 3 * q^77 + 14 * q^78 - 23 * q^79 - 5 * q^80 + 7 * q^81 + q^82 - 46 * q^83 - 13 * q^84 - 13 * q^86 - 15 * q^87 - 5 * q^88 + 9 * q^89 + 18 * q^90 + 29 * q^91 + 14 * q^92 + 15 * q^93 - 8 * q^94 - 4 * q^95 - 26 * q^97 - 19 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.922461	+	1.59775i	0.532583	+	0.922461i	0.999276	+	0.0380418i	$0.0121120\pi$
$3$	0.922461	+	1.59775i	0.532583	+	0.922461i	−0.466693	+	0.884419i	$0.654555\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.84492			−0.753186
$7$	2.59682	−	0.506486i	0.981506	−	0.191434i
$7$	2.59682	−	0.506486i	0.981506	−	0.191434i
$8$	1.00000			0.353553
$9$	−0.201870	+	0.349648i	−0.0672899	+	0.116549i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	0.922461	−	1.59775i	0.266292	−	0.461231i
$13$	4.07034			1.12891			0.564455	−	0.825464i	$-0.309087\pi$
$13$	4.07034			1.12891			0.564455	+	0.825464i	$0.309087\pi$
$14$	−0.859780	+	2.50215i	−0.229786	+	0.668729i
$15$	−1.84492			−0.476357
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.51928	+	6.09557i	0.853551	+	1.47839i	0.877983	+	0.478692i	$0.158889\pi$
$17$	3.51928	+	6.09557i	0.853551	+	1.47839i	−0.0244318	+	0.999701i	$0.507778\pi$
$18$	−0.201870	−	0.349648i	−0.0475811	−	0.0824129i
$19$	1.22059	−	2.11413i	0.280023	−	0.485014i	−0.691367	−	0.722504i	$-0.742991\pi$
$19$	1.22059	−	2.11413i	0.280023	−	0.485014i	0.971390	+	0.237490i	$0.0763246\pi$
$20$	1.00000			0.223607
$21$	3.20470	+	3.68185i	0.699324	+	0.803447i
$22$	1.00000			0.213201
$23$	−2.78224	+	4.81898i	−0.580137	+	1.00483i	0.415325	+	0.909673i	$0.363668\pi$
$23$	−2.78224	+	4.81898i	−0.580137	+	1.00483i	−0.995463	+	0.0951545i	$0.969665\pi$
$24$	0.922461	+	1.59775i	0.188297	+	0.326139i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.03517	+	3.52502i	−0.399130	+	0.691313i
$27$	4.78990			0.921817
$28$	−1.73704	−	1.99567i	−0.328270	−	0.377146i
$29$	0.245482			0.0455849			0.0227924	−	0.999740i	$-0.492744\pi$
$29$	0.245482			0.0455849			0.0227924	+	0.999740i	$0.492744\pi$
$30$	0.922461	−	1.59775i	0.168418	−	0.291708i
$31$	−2.22059	−	3.84618i	−0.398830	−	0.690794i	0.594752	−	0.803909i	$-0.297250\pi$
$31$	−2.22059	−	3.84618i	−0.398830	−	0.690794i	−0.993582	+	0.113115i	$0.963917\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.922461	−	1.59775i	0.160580	−	0.278133i
$34$	−7.03856			−1.20710
$35$	−0.859780	+	2.50215i	−0.145329	+	0.422941i
$36$	0.403739			0.0672899
$37$	−2.79972	+	4.84926i	−0.460271	+	0.797213i	−0.998974	−	0.0452827i	$-0.985581\pi$
$37$	−2.79972	+	4.84926i	−0.460271	+	0.797213i	0.538703	+	0.842496i	$0.318914\pi$
$38$	1.22059	+	2.11413i	0.198006	+	0.342957i
$39$	3.75473	+	6.50338i	0.601238	+	1.04137i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−8.26604			−1.29094			−0.645469	−	0.763786i	$-0.723338\pi$
$41$	−8.26604			−1.29094			−0.645469	+	0.763786i	$0.723338\pi$
$42$	−4.79093	+	0.934427i	−0.739257	+	0.144185i
$43$	−1.56448			−0.238581			−0.119291	−	0.992859i	$-0.538062\pi$
$43$	−1.56448			−0.238581			−0.119291	+	0.992859i	$0.538062\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	−0.201870	−	0.349648i	−0.0300929	−	0.0521225i
$46$	−2.78224	−	4.81898i	−0.410219	−	0.710520i
$47$	2.44118	−	4.22825i	0.356083	−	0.616754i	−0.631220	−	0.775604i	$-0.717445\pi$
$47$	2.44118	−	4.22825i	0.356083	−	0.616754i	0.987303	+	0.158850i	$0.0507786\pi$
$48$	−1.84492			−0.266292
$49$	6.48694	−	2.63050i	0.926706	−	0.375786i
$50$	1.00000			0.141421
$51$	−6.49280	+	11.2459i	−0.909174	+	1.57474i
$52$	−2.03517	−	3.52502i	−0.282227	−	0.488832i
$53$	−2.77165	−	4.80064i	−0.380715	−	0.659418i	0.610449	−	0.792055i	$-0.290989\pi$
$53$	−2.77165	−	4.80064i	−0.380715	−	0.659418i	−0.991165	+	0.132637i	$0.957656\pi$
$54$	−2.39495	+	4.14818i	−0.325911	+	0.564495i
$55$	1.00000			0.134840
$56$	2.59682	−	0.506486i	0.347015	−	0.0676820i
$57$	4.50379			0.596542
$58$	−0.122741	+	0.212594i	−0.0161167	+	0.0279149i
$59$	2.15847	+	3.73858i	0.281009	+	0.486722i	0.971633	−	0.236492i	$-0.0759977\pi$
$59$	2.15847	+	3.73858i	0.281009	+	0.486722i	−0.690625	+	0.723213i	$0.742664\pi$
$60$	0.922461	+	1.59775i	0.119089	+	0.206269i
$61$	−1.92729	+	3.33816i	−0.246764	+	0.427407i	−0.962626	−	0.270834i	$-0.912700\pi$
$61$	−1.92729	+	3.33816i	−0.246764	+	0.427407i	0.715862	+	0.698242i	$0.246034\pi$
$62$	4.44118			0.564031
$63$	−0.347127	+	1.01022i	−0.0437339	+	0.127275i
$64$	1.00000			0.125000
$65$	−2.03517	+	3.52502i	−0.252432	+	0.437225i
$66$	0.922461	+	1.59775i	0.113547	+	0.196669i
$67$	1.34492	+	2.32947i	0.164308	+	0.284591i	0.936409	−	0.350909i	$-0.114127\pi$
$67$	1.34492	+	2.32947i	0.164308	+	0.284591i	−0.772101	+	0.635500i	$0.780794\pi$
$68$	3.51928	−	6.09557i	0.426775	−	0.739197i
$69$	−10.2660			−1.23589
$70$	−1.73704	−	1.99567i	−0.207616	−	0.238528i
$71$	10.6878			1.26841			0.634203	−	0.773166i	$-0.281328\pi$
$71$	10.6878			1.26841			0.634203	+	0.773166i	$0.281328\pi$
$72$	−0.201870	+	0.349648i	−0.0237906	+	0.0412065i
$73$	−8.38775	−	14.5280i	−0.981712	−	1.70038i	−0.655723	−	0.755001i	$-0.727636\pi$
$73$	−8.38775	−	14.5280i	−0.981712	−	1.70038i	−0.325989	−	0.945374i	$-0.605697\pi$
$74$	−2.79972	−	4.84926i	−0.325461	−	0.563715i
$75$	0.922461	−	1.59775i	0.106517	−	0.184492i
$76$	−2.44118			−0.280023
$77$	−1.73704	−	1.99567i	−0.197954	−	0.227428i
$78$	−7.50946			−0.850279
$79$	−5.25094	+	9.09489i	−0.590776	+	1.02325i	0.403352	+	0.915045i	$0.367845\pi$
$79$	−5.25094	+	9.09489i	−0.590776	+	1.02325i	−0.994128	+	0.108210i	$0.965488\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	5.02411	+	8.70201i	0.558234	+	0.966890i
$82$	4.13302	−	7.15860i	0.456416	−	0.790535i
$83$	−10.8228			−1.18796			−0.593978	−	0.804481i	$-0.702443\pi$
$83$	−10.8228			−1.18796			−0.593978	+	0.804481i	$0.702443\pi$
$84$	1.58623	−	4.61628i	0.173072	−	0.503678i
$85$	−7.03856			−0.763439
$86$	0.782242	−	1.35488i	0.0843513	−	0.146101i
$87$	0.226448	+	0.392219i	0.0242778	+	0.0420503i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−1.23601	+	2.14083i	−0.131017	+	0.226927i	−0.924069	−	0.382226i	$-0.875157\pi$
$89$	−1.23601	+	2.14083i	−0.131017	+	0.226927i	0.793052	+	0.609154i	$0.208491\pi$
$90$	0.403739			0.0425578
$91$	10.5699	−	2.06157i	1.10803	−	0.216111i
$92$	5.56448			0.580137
$93$	4.09682	−	7.09590i	0.424820	−	0.735811i
$94$	2.44118	+	4.22825i	0.251789	+	0.436111i
$95$	1.22059	+	2.11413i	0.125230	+	0.216905i
$96$	0.922461	−	1.59775i	0.0941483	−	0.163070i
$97$	6.25751			0.635354			0.317677	−	0.948199i	$-0.397097\pi$
$97$	6.25751			0.635354			0.317677	+	0.948199i	$0.397097\pi$
$98$	−0.965389	+	6.93311i	−0.0975190	+	0.700350i
$99$	0.403739			0.0405773
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	0.725417	+	1.25646i	0.0721817	+	0.125022i	0.899857	−	0.436185i	$-0.143671\pi$
$101$	0.725417	+	1.25646i	0.0721817	+	0.125022i	−0.827676	+	0.561207i	$0.810337\pi$
$102$	−6.49280	−	11.2459i	−0.642883	−	1.11351i
$103$	2.81514	−	4.87596i	0.277384	−	0.480443i	−0.693350	−	0.720601i	$-0.743866\pi$
$103$	2.81514	−	4.87596i	0.277384	−	0.480443i	0.970734	+	0.240158i	$0.0771994\pi$
$104$	4.07034			0.399130
$105$	−4.79093	+	0.934427i	−0.467547	+	0.0911907i
$106$	5.54330			0.538413
$107$	−0.556825	+	0.964449i	−0.0538303	+	0.0932368i	−0.891685	−	0.452657i	$-0.850476\pi$
$107$	−0.556825	+	0.964449i	−0.0538303	+	0.0932368i	0.837855	+	0.545893i	$0.183810\pi$
$108$	−2.39495	−	4.14818i	−0.230454	−	0.399158i
$109$	−2.43305	−	4.21417i	−0.233044	−	0.403644i	0.725658	−	0.688055i	$-0.241535\pi$
$109$	−2.43305	−	4.21417i	−0.233044	−	0.403644i	−0.958702	+	0.284411i	$0.908202\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	−10.3305			−0.980531
$112$	−0.859780	+	2.50215i	−0.0812416	+	0.236431i
$113$	−1.37514			−0.129362			−0.0646812	−	0.997906i	$-0.520603\pi$
$113$	−1.37514			−0.129362			−0.0646812	+	0.997906i	$0.520603\pi$
$114$	−2.25190	+	3.90040i	−0.210909	+	0.365306i
$115$	−2.78224	−	4.81898i	−0.259445	−	0.449373i
$116$	−0.122741	−	0.212594i	−0.0113962	−	0.0197388i
$117$	−0.821678	+	1.42319i	−0.0759641	+	0.131574i
$118$	−4.31694			−0.397406
$119$	12.2263	+	14.0466i	1.12078	+	1.28765i
$120$	−1.84492			−0.168418
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−1.92729	−	3.33816i	−0.174488	−	0.302223i
$123$	−7.62510	−	13.2071i	−0.687532	−	1.19084i
$124$	−2.22059	+	3.84618i	−0.199415	+	0.345397i
$125$	1.00000			0.0894427
$126$	−0.701311	−	0.805730i	−0.0624777	−	0.0717801i
$127$	7.07887			0.628148			0.314074	−	0.949398i	$-0.398306\pi$
$127$	7.07887			0.628148			0.314074	+	0.949398i	$0.398306\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.44318	−	2.49965i	−0.127064	−	0.220082i
$130$	−2.03517	−	3.52502i	−0.178496	−	0.309164i
$131$	−1.17056	+	2.02748i	−0.102273	+	0.177141i	−0.912621	−	0.408807i	$-0.865945\pi$
$131$	−1.17056	+	2.02748i	−0.102273	+	0.177141i	0.810348	+	0.585949i	$0.199278\pi$
$132$	−1.84492			−0.160580
$133$	2.09888	−	6.10822i	0.181996	−	0.529650i
$134$	−2.68985			−0.232367
$135$	−2.39495	+	4.14818i	−0.206124	+	0.357018i
$136$	3.51928	+	6.09557i	0.301776	+	0.522691i
$137$	0.842648	+	1.45951i	0.0719923	+	0.124694i	0.899774	−	0.436355i	$-0.143731\pi$
$137$	0.842648	+	1.45951i	0.0719923	+	0.124694i	−0.827782	+	0.561050i	$0.810398\pi$
$138$	5.13302	−	8.89065i	0.436952	−	0.756823i
$139$	18.0803			1.53355			0.766776	−	0.641915i	$-0.221860\pi$
$139$	18.0803			1.53355			0.766776	+	0.641915i	$0.221860\pi$
$140$	2.59682	−	0.506486i	0.219471	−	0.0428059i
$141$	9.00759			0.758576
$142$	−5.34389	+	9.25589i	−0.448449	+	0.776737i
$143$	−2.03517	−	3.52502i	−0.170189	−	0.294777i
$144$	−0.201870	−	0.349648i	−0.0168225	−	0.0291374i
$145$	−0.122741	+	0.212594i	−0.0101931	+	0.0176550i
$146$	16.7755			1.38835
$147$	10.1868	+	7.93798i	0.840197	+	0.654713i
$148$	5.59944			0.460271
$149$	−5.67719	+	9.83318i	−0.465094	+	0.805566i	−0.999206	−	0.0398478i	$-0.987313\pi$
$149$	−5.67719	+	9.83318i	−0.465094	+	0.805566i	0.534112	+	0.845414i	$0.320646\pi$
$150$	0.922461	+	1.59775i	0.0753186	+	0.130456i
$151$	−6.73467	−	11.6648i	−0.548059	−	0.949267i	−0.998407	−	0.0564135i	$-0.982033\pi$
$151$	−6.73467	−	11.6648i	−0.548059	−	0.949267i	0.450348	−	0.892853i	$-0.351300\pi$
$152$	1.22059	−	2.11413i	0.0990031	−	0.171478i
$153$	−2.84174			−0.229741
$154$	2.59682	−	0.506486i	0.209258	−	0.0408138i
$155$	4.44118			0.356724
$156$	3.75473	−	6.50338i	0.300619	−	0.520687i
$157$	11.0105	+	19.0707i	0.878733	+	1.52201i	0.852732	+	0.522348i	$0.174944\pi$
$157$	11.0105	+	19.0707i	0.878733	+	1.52201i	0.0260006	+	0.999662i	$0.491723\pi$
$158$	−5.25094	−	9.09489i	−0.417742	−	0.723550i
$159$	5.11348	−	8.85681i	0.405525	−	0.702390i
$160$	1.00000			0.0790569
$161$	−4.78423	+	13.9232i	−0.377050	+	1.09730i
$162$	−10.0482			−0.789462
$163$	11.9687	−	20.7304i	0.937459	−	1.62373i	0.167271	−	0.985911i	$-0.446504\pi$
$163$	11.9687	−	20.7304i	0.937459	−	1.62373i	0.770188	−	0.637817i	$-0.220162\pi$
$164$	4.13302	+	7.15860i	0.322735	+	0.558993i
$165$	0.922461	+	1.59775i	0.0718135	+	0.124385i
$166$	5.41140	−	9.37282i	0.420006	−	0.727472i
$167$	0.482925			0.0373698			0.0186849	−	0.999825i	$-0.494052\pi$
$167$	0.482925			0.0373698			0.0186849	+	0.999825i	$0.494052\pi$
$168$	3.20470	+	3.68185i	0.247248	+	0.284061i
$169$	3.56766			0.274436
$170$	3.51928	−	6.09557i	0.269917	−	0.467509i
$171$	0.492801	+	0.853556i	0.0376854	+	0.0652730i
$172$	0.782242	+	1.35488i	0.0596454	+	0.103309i
$173$	−1.28065	+	2.21815i	−0.0973662	+	0.168643i	−0.910594	−	0.413303i	$-0.864375\pi$
$173$	−1.28065	+	2.21815i	−0.0973662	+	0.168643i	0.813228	+	0.581946i	$0.197708\pi$
$174$	−0.452896			−0.0343339
$175$	−1.73704	−	1.99567i	−0.131308	−	0.150858i
$176$	1.00000			0.0753778
$177$	−3.98221	+	6.89739i	−0.299321	+	0.518439i
$178$	−1.23601	−	2.14083i	−0.0926427	−	0.160462i
$179$	−7.09586	−	12.2904i	−0.530369	−	0.918627i	−0.999372	−	0.0354300i	$-0.988720\pi$
$179$	−7.09586	−	12.2904i	−0.530369	−	0.918627i	0.469003	−	0.883197i	$-0.344613\pi$
$180$	−0.201870	+	0.349648i	−0.0150465	+	0.0260613i
$181$	−13.7687			−1.02342			−0.511710	−	0.859158i	$-0.670988\pi$
$181$	−13.7687			−1.02342			−0.511710	+	0.859158i	$0.670988\pi$
$182$	−3.49960	+	10.1846i	−0.259407	+	0.754934i
$183$	−7.11139			−0.525689
$184$	−2.78224	+	4.81898i	−0.205110	+	0.355260i
$185$	−2.79972	−	4.84926i	−0.205840	−	0.356525i
$186$	4.09682	+	7.09590i	0.300393	+	0.520297i
$187$	3.51928	−	6.09557i	0.257355	−	0.445752i
$188$	−4.88237			−0.356083
$189$	12.4385	−	2.42602i	0.904768	−	0.176467i
$190$	−2.44118			−0.177102
$191$	9.19978	−	15.9345i	0.665673	−	1.15298i	−0.313430	−	0.949611i	$-0.601478\pi$
$191$	9.19978	−	15.9345i	0.665673	−	1.15298i	0.979102	−	0.203367i	$-0.0651886\pi$
$192$	0.922461	+	1.59775i	0.0665729	+	0.115308i
$193$	−8.09065	−	14.0134i	−0.582378	−	1.00871i	−0.995197	−	0.0978949i	$-0.968789\pi$
$193$	−8.09065	−	14.0134i	−0.582378	−	1.00871i	0.412819	−	0.910813i	$-0.364544\pi$
$194$	−3.12875	+	5.41916i	−0.224631	+	0.389073i
$195$	−7.50946			−0.537764
$196$	−5.52156	−	4.30261i	−0.394397	−	0.307329i
$197$	6.44628			0.459279			0.229639	−	0.973276i	$-0.426245\pi$
$197$	6.44628			0.459279			0.229639	+	0.973276i	$0.426245\pi$
$198$	−0.201870	+	0.349648i	−0.0143462	+	0.0248484i
$199$	−12.9335	−	22.4015i	−0.916832	−	1.58800i	−0.804196	−	0.594364i	$-0.797404\pi$
$199$	−12.9335	−	22.4015i	−0.916832	−	1.58800i	−0.112636	−	0.993636i	$-0.535929\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−2.48128	+	4.29770i	−0.175016	+	0.303136i
$202$	−1.45083			−0.102080
$203$	0.637473	−	0.124333i	0.0447418	−	0.00872648i
$204$	12.9856			0.909174
$205$	4.13302	−	7.15860i	0.288663	−	0.499978i
$206$	2.81514	+	4.87596i	0.196140	+	0.339724i
$207$	−1.12330	−	1.94561i	−0.0780747	−	0.135229i
$208$	−2.03517	+	3.52502i	−0.141114	+	0.244416i
$209$	−2.44118			−0.168860
$210$	1.58623	−	4.61628i	0.109460	−	0.318554i
$211$	17.9502			1.23574			0.617872	−	0.786279i	$-0.287995\pi$
$211$	17.9502			1.23574			0.617872	+	0.786279i	$0.287995\pi$
$212$	−2.77165	+	4.80064i	−0.190358	+	0.329709i
$213$	9.85907	+	17.0764i	0.675532	+	1.17006i
$214$	−0.556825	−	0.964449i	−0.0380638	−	0.0659284i
$215$	0.782242	−	1.35488i	0.0533484	−	0.0924022i
$216$	4.78990			0.325911
$217$	−7.71451	−	8.86313i	−0.523695	−	0.601669i
$218$	4.86611			0.329574
$219$	15.4748	−	26.8031i	1.04569	−	1.81118i
$220$	−0.500000	−	0.866025i	−0.0337100	−	0.0583874i
$221$	14.3247	+	24.8111i	0.963581	+	1.66897i
$222$	5.16527	−	8.94650i	0.346670	−	0.600450i
$223$	−7.50491			−0.502566			−0.251283	−	0.967914i	$-0.580852\pi$
$223$	−7.50491			−0.502566			−0.251283	+	0.967914i	$0.580852\pi$
$224$	−1.73704	−	1.99567i	−0.116061	−	0.133341i
$225$	0.403739			0.0269159
$226$	0.687571	−	1.19091i	0.0457365	−	0.0792180i
$227$	−12.5722	−	21.7757i	−0.834447	−	1.44530i	−0.894480	−	0.447108i	$-0.852454\pi$
$227$	−12.5722	−	21.7757i	−0.834447	−	1.44530i	0.0600329	−	0.998196i	$-0.480879\pi$
$228$	−2.25190	−	3.90040i	−0.149136	−	0.258310i
$229$	5.10006	−	8.83355i	0.337021	−	0.583738i	−0.646850	−	0.762617i	$-0.723914\pi$
$229$	5.10006	−	8.83355i	0.337021	−	0.583738i	0.983871	+	0.178880i	$0.0572473\pi$
$230$	5.56448			0.366911
$231$	1.58623	−	4.61628i	0.104366	−	0.303729i
$232$	0.245482			0.0161167
$233$	2.05003	−	3.55075i	0.134302	−	0.232617i	−0.791029	−	0.611779i	$-0.790454\pi$
$233$	2.05003	−	3.55075i	0.134302	−	0.232617i	0.925331	+	0.379161i	$0.123788\pi$
$234$	−0.821678	−	1.42319i	−0.0537148	−	0.0930367i
$235$	2.44118	+	4.22825i	0.159245	+	0.275821i
$236$	2.15847	−	3.73858i	0.140504	−	0.243361i
$237$	−19.3751			−1.25855
$238$	−18.2779	+	3.56493i	−1.18478	+	0.231080i
$239$	8.75260			0.566158			0.283079	−	0.959097i	$-0.408644\pi$
$239$	8.75260			0.566158			0.283079	+	0.959097i	$0.408644\pi$
$240$	0.922461	−	1.59775i	0.0595446	−	0.103134i
$241$	−12.8305	−	22.2231i	−0.826487	−	1.43152i	−0.900778	−	0.434280i	$-0.857003\pi$
$241$	−12.8305	−	22.2231i	−0.826487	−	1.43152i	0.0742911	−	0.997237i	$-0.476331\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	−2.08424	+	3.61000i	−0.133704	+	0.231582i
$244$	3.85457			0.246764
$245$	−0.965389	+	6.93311i	−0.0616764	+	0.442940i
$246$	15.2502			0.972318
$247$	4.96822	−	8.60521i	0.316120	−	0.547537i
$248$	−2.22059	−	3.84618i	−0.141008	−	0.244233i
$249$	−9.98361	−	17.2921i	−0.632686	−	1.09584i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	26.7900			1.69097			0.845485	−	0.533999i	$-0.179311\pi$
$251$	26.7900			1.69097			0.845485	+	0.533999i	$0.179311\pi$
$252$	1.04844	−	0.204488i	0.0660454	−	0.0128815i
$253$	5.56448			0.349836
$254$	−3.53944	+	6.13048i	−0.222084	+	0.384661i
$255$	−6.49280	−	11.2459i	−0.406595	−	0.704243i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.47429	−	16.4100i	0.590990	−	1.02362i	−0.403109	−	0.915152i	$-0.632071\pi$
$257$	9.47429	−	16.4100i	0.590990	−	1.02362i	0.994099	−	0.108473i	$-0.0345961\pi$
$258$	2.88635			0.179696
$259$	−4.81429	+	14.0107i	−0.299145	+	0.870580i
$260$	4.07034			0.252432
$261$	−0.0495554	+	0.0858324i	−0.00306740	+	0.00531290i
$262$	−1.17056	−	2.02748i	−0.0723177	−	0.125258i
$263$	−3.58451	−	6.20856i	−0.221031	−	0.382836i	0.734091	−	0.679051i	$-0.237609\pi$
$263$	−3.58451	−	6.20856i	−0.221031	−	0.382836i	−0.955121	+	0.296215i	$0.904275\pi$
$264$	0.922461	−	1.59775i	0.0567736	−	0.0983347i
$265$	5.54330			0.340522
$266$	4.24043	+	4.87179i	0.259998	+	0.298709i
$267$	−4.56068			−0.279109
$268$	1.34492	−	2.32947i	0.0821542	−	0.142295i
$269$	−1.08275	−	1.87537i	−0.0660162	−	0.114343i	0.831128	−	0.556081i	$-0.187696\pi$
$269$	−1.08275	−	1.87537i	−0.0660162	−	0.114343i	−0.897144	+	0.441738i	$0.854362\pi$
$270$	−2.39495	−	4.14818i	−0.145752	−	0.252450i
$271$	−11.8165	+	20.4668i	−0.717804	+	1.24327i	0.244065	+	0.969759i	$0.421519\pi$
$271$	−11.8165	+	20.4668i	−0.717804	+	1.24327i	−0.961868	+	0.273513i	$0.911814\pi$
$272$	−7.03856			−0.426775
$273$	13.0442	+	14.9864i	0.789473	+	0.907018i
$274$	−1.68530			−0.101812
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	5.13302	+	8.89065i	0.308972	+	0.535154i
$277$	10.3598	+	17.9438i	0.622462	+	1.07814i	0.989026	+	0.147743i	$0.0472009\pi$
$277$	10.3598	+	17.9438i	0.622462	+	1.07814i	−0.366563	+	0.930393i	$0.619466\pi$
$278$	−9.04015	+	15.6580i	−0.542192	+	0.939105i
$279$	1.79308			0.107349
$280$	−0.859780	+	2.50215i	−0.0513817	+	0.149532i
$281$	−12.9194			−0.770704			−0.385352	−	0.922770i	$-0.625920\pi$
$281$	−12.9194			−0.770704			−0.385352	+	0.922770i	$0.625920\pi$
$282$	−4.50379	+	7.80080i	−0.268197	+	0.464531i
$283$	−11.9164	−	20.6398i	−0.708355	−	1.22691i	−0.965467	−	0.260526i	$-0.916104\pi$
$283$	−11.9164	−	20.6398i	−0.708355	−	1.22691i	0.257112	−	0.966382i	$-0.417229\pi$
$284$	−5.34389	−	9.25589i	−0.317102	−	0.549236i
$285$	−2.25190	+	3.90040i	−0.133391	+	0.231040i
$286$	4.07034			0.240684
$287$	−21.4654	+	4.18663i	−1.26706	+	0.247129i
$288$	0.403739			0.0237906
$289$	−16.2707	+	28.1816i	−0.957099	+	1.65774i
$290$	−0.122741	−	0.212594i	−0.00720761	−	0.0124839i
$291$	5.77231	+	9.99793i	0.338379	+	0.586089i
$292$	−8.38775	+	14.5280i	−0.490856	+	0.850188i
$293$	4.36574			0.255049			0.127525	−	0.991835i	$-0.459297\pi$
$293$	4.36574			0.255049			0.127525	+	0.991835i	$0.459297\pi$
$294$	−11.9679	+	4.85308i	−0.697983	+	0.283037i
$295$	−4.31694			−0.251342
$296$	−2.79972	+	4.84926i	−0.162730	+	0.281857i
$297$	−2.39495	−	4.14818i	−0.138969	−	0.240702i
$298$	−5.67719	−	9.83318i	−0.328871	−	0.569621i
$299$	−11.3247	+	19.6149i	−0.654922	+	1.13436i
$300$	−1.84492			−0.106517
$301$	−4.06268	+	0.792388i	−0.234169	+	0.0456725i
$302$	13.4693			0.775073
$303$	−1.33834	+	2.31807i	−0.0768855	+	0.133170i
$304$	1.22059	+	2.11413i	0.0700057	+	0.121253i
$305$	−1.92729	−	3.33816i	−0.110356	−	0.191142i
$306$	1.42087	−	2.46102i	0.0812258	−	0.140687i
$307$	7.89233			0.450439			0.225220	−	0.974308i	$-0.427690\pi$
$307$	7.89233			0.450439			0.225220	+	0.974308i	$0.427690\pi$
$308$	−0.859780	+	2.50215i	−0.0489905	+	0.142573i
$309$	10.3874			0.590920
$310$	−2.22059	+	3.84618i	−0.126121	+	0.218448i
$311$	−13.3441	−	23.1127i	−0.756677	−	1.31060i	−0.944536	−	0.328407i	$-0.893488\pi$
$311$	−13.3441	−	23.1127i	−0.756677	−	1.31060i	0.187860	−	0.982196i	$-0.439845\pi$
$312$	3.75473	+	6.50338i	0.212570	+	0.368182i
$313$	−17.4831	+	30.2817i	−0.988205	+	1.71162i	−0.361484	+	0.932378i	$0.617730\pi$
$313$	−17.4831	+	30.2817i	−0.988205	+	1.71162i	−0.626721	+	0.779244i	$0.715603\pi$
$314$	−22.0210			−1.24272
$315$	−0.701311	−	0.805730i	−0.0395144	−	0.0453977i
$316$	10.5019			0.590776
$317$	−6.63000	+	11.4835i	−0.372378	+	0.644977i	−0.989931	−	0.141552i	$-0.954791\pi$
$317$	−6.63000	+	11.4835i	−0.372378	+	0.644977i	0.617553	+	0.786529i	$0.288124\pi$
$318$	5.11348	+	8.85681i	0.286750	+	0.496665i
$319$	−0.122741	−	0.212594i	−0.00687218	−	0.0119030i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−2.05460			−0.114676
$322$	−9.66573	−	11.1049i	−0.538650	−	0.618850i
$323$	17.1824			0.956055
$324$	5.02411	−	8.70201i	0.279117	−	0.483445i
$325$	−2.03517	−	3.52502i	−0.112891	−	0.195533i
$326$	11.9687	+	20.7304i	0.662884	+	1.14815i
$327$	4.48879	−	7.77482i	0.248231	−	0.429948i
$328$	−8.26604			−0.456416
$329$	4.19776	−	12.2164i	0.231430	−	0.673514i
$330$	−1.84492			−0.101560
$331$	−1.92987	+	3.34264i	−0.106075	+	0.183728i	−0.914177	−	0.405315i	$-0.867162\pi$
$331$	−1.92987	+	3.34264i	−0.106075	+	0.183728i	0.808102	+	0.589043i	$0.200495\pi$
$332$	5.41140	+	9.37282i	0.296989	+	0.514400i
$333$	−1.13036	−	1.95784i	−0.0619432	−	0.107289i
$334$	−0.241462	+	0.418225i	−0.0132122	+	0.0228843i
$335$	−2.68985			−0.146962
$336$	−4.79093	+	0.934427i	−0.261367	+	0.0509772i
$337$	−26.5188			−1.44457			−0.722286	−	0.691595i	$-0.756908\pi$
$337$	−26.5188			−1.44457			−0.722286	+	0.691595i	$0.756908\pi$
$338$	−1.78383	+	3.08969i	−0.0970276	+	0.168057i
$339$	−1.26851	−	2.19713i	−0.0688962	−	0.119332i
$340$	3.51928	+	6.09557i	0.190860	+	0.330579i
$341$	−2.22059	+	3.84618i	−0.120252	+	0.208282i
$342$	−0.985601			−0.0532952
$343$	15.5131	−	10.1165i	0.837629	−	0.546239i
$344$	−1.56448			−0.0843513
$345$	5.13302	−	8.89065i	0.276353	−	0.478657i
$346$	−1.28065	−	2.21815i	−0.0688483	−	0.119249i
$347$	11.2640	+	19.5099i	0.604686	+	1.04735i	0.992101	+	0.125441i	$0.0400347\pi$
$347$	11.2640	+	19.5099i	0.604686	+	1.04735i	−0.387415	+	0.921905i	$0.626632\pi$
$348$	0.226448	−	0.392219i	0.0121389	−	0.0210252i
$349$	−25.5154			−1.36581			−0.682905	−	0.730507i	$-0.739284\pi$
$349$	−25.5154			−1.36581			−0.682905	+	0.730507i	$0.739284\pi$
$350$	2.59682	−	0.506486i	0.138806	−	0.0270728i
$351$	19.4965			1.04065
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	6.40734	+	11.0978i	0.341029	+	0.590679i	0.984624	−	0.174687i	$-0.0558914\pi$
$353$	6.40734	+	11.0978i	0.341029	+	0.590679i	−0.643595	+	0.765366i	$0.722558\pi$
$354$	−3.98221	−	6.89739i	−0.211652	−	0.366592i
$355$	−5.34389	+	9.25589i	−0.283624	+	0.491252i
$356$	2.47202			0.131017
$357$	−11.1648	+	32.4920i	−0.590902	+	1.71966i
$358$	14.1917			0.750056
$359$	−13.4795	+	23.3472i	−0.711423	+	1.23222i	0.252901	+	0.967492i	$0.418615\pi$
$359$	−13.4795	+	23.3472i	−0.711423	+	1.23222i	−0.964323	+	0.264728i	$0.914718\pi$
$360$	−0.201870	−	0.349648i	−0.0106395	−	0.0184281i
$361$	6.52031	+	11.2935i	0.343174	+	0.594395i
$362$	6.88436	−	11.9241i	0.361834	−	0.626715i
$363$	−1.84492			−0.0968333
$364$	−7.07034	−	8.12305i	−0.370586	−	0.425764i
$365$	16.7755			0.878070
$366$	3.55569	−	6.15864i	0.185859	−	0.321917i
$367$	−7.51918	−	13.0236i	−0.392498	−	0.679827i	0.600280	−	0.799790i	$-0.295056\pi$
$367$	−7.51918	−	13.0236i	−0.392498	−	0.679827i	−0.992778	+	0.119963i	$0.961722\pi$
$368$	−2.78224	−	4.81898i	−0.145034	−	0.251207i
$369$	1.66866	−	2.89021i	0.0868671	−	0.150458i
$370$	5.59944			0.291101
$371$	−9.62893	−	11.0626i	−0.499909	−	0.574341i
$372$	−8.19364			−0.424820
$373$	−14.4139	+	24.9656i	−0.746324	+	1.29267i	0.203249	+	0.979127i	$0.434850\pi$
$373$	−14.4139	+	24.9656i	−0.746324	+	1.29267i	−0.949574	+	0.313545i	$0.898484\pi$
$374$	3.51928	+	6.09557i	0.181978	+	0.315195i
$375$	0.922461	+	1.59775i	0.0476357	+	0.0825074i
$376$	2.44118	−	4.22825i	0.125894	−	0.218056i
$377$	0.999196			0.0514612
$378$	−4.11826	+	11.9851i	−0.211821	+	0.616446i
$379$	28.7219			1.47535			0.737673	−	0.675158i	$-0.235925\pi$
$379$	28.7219			1.47535			0.737673	+	0.675158i	$0.235925\pi$
$380$	1.22059	−	2.11413i	0.0626150	−	0.108452i
$381$	6.52999	+	11.3103i	0.334541	+	0.579443i
$382$	9.19978	+	15.9345i	0.470702	+	0.815279i
$383$	−13.5810	+	23.5230i	−0.693956	+	1.20197i	0.276575	+	0.960992i	$0.410800\pi$
$383$	−13.5810	+	23.5230i	−0.693956	+	1.20197i	−0.970531	+	0.240975i	$0.922533\pi$
$384$	−1.84492			−0.0941483
$385$	2.59682	−	0.506486i	0.132346	−	0.0258129i
$386$	16.1813			0.823607
$387$	0.315822	−	0.547019i	0.0160541	−	0.0278065i
$388$	−3.12875	−	5.41916i	−0.158838	−	0.275116i
$389$	−4.81632	−	8.34212i	−0.244197	−	0.422962i	0.717708	−	0.696344i	$-0.245191\pi$
$389$	−4.81632	−	8.34212i	−0.244197	−	0.422962i	−0.961906	+	0.273382i	$0.911858\pi$
$390$	3.75473	−	6.50338i	0.190128	−	0.329312i
$391$	−39.1660			−1.98071
$392$	6.48694	−	2.63050i	0.327640	−	0.132861i
$393$	−4.31920			−0.217875
$394$	−3.22314	+	5.58265i	−0.162380	+	0.281250i
$395$	−5.25094	−	9.09489i	−0.264203	−	0.457613i
$396$	−0.201870	−	0.349648i	−0.0101443	−	0.0175705i
$397$	14.4685	−	25.0602i	0.726153	−	1.25773i	−0.232344	−	0.972634i	$-0.574640\pi$
$397$	14.4685	−	25.0602i	0.726153	−	1.25773i	0.958497	−	0.285101i	$-0.0920271\pi$
$398$	25.8670			1.29660
$399$	11.6955	−	2.28111i	0.585509	−	0.114198i
$400$	1.00000			0.0500000
$401$	16.3319	−	28.2876i	0.815575	−	1.41262i	−0.0933401	−	0.995634i	$-0.529754\pi$
$401$	16.3319	−	28.2876i	0.815575	−	1.41262i	0.908915	−	0.416982i	$-0.136912\pi$
$402$	−2.48128	−	4.29770i	−0.123755	−	0.214350i
$403$	−9.03856	−	15.6552i	−0.450243	−	0.779843i
$404$	0.725417	−	1.25646i	0.0360908	−	0.0625112i
$405$	−10.0482			−0.499300
$406$	−0.211061	+	0.614234i	−0.0104748	+	0.0304839i
$407$	5.59944			0.277554
$408$	−6.49280	+	11.2459i	−0.321442	+	0.556753i
$409$	−3.52505	−	6.10556i	−0.174302	−	0.301901i	0.765617	−	0.643296i	$-0.222434\pi$
$409$	−3.52505	−	6.10556i	−0.174302	−	0.301901i	−0.939920	+	0.341396i	$0.889100\pi$
$410$	4.13302	+	7.15860i	0.204115	+	0.353538i
$411$	−1.55462	+	2.69268i	−0.0766838	+	0.132820i
$412$	−5.63027			−0.277384
$413$	7.49869	+	8.61518i	0.368987	+	0.423925i
$414$	2.24660			0.110414
$415$	5.41140	−	9.37282i	0.265635	−	0.460093i
$416$	−2.03517	−	3.52502i	−0.0997824	−	0.172828i
$417$	16.6784	+	28.8878i	0.816744	+	1.41464i
$418$	1.22059	−	2.11413i	0.0597011	−	0.103405i
$419$	−7.83688			−0.382857			−0.191428	−	0.981507i	$-0.561312\pi$
$419$	−7.83688			−0.382857			−0.191428	+	0.981507i	$0.561312\pi$
$420$	3.20470	+	3.68185i	0.156373	+	0.179656i
$421$	−20.0754			−0.978414			−0.489207	−	0.872168i	$-0.662714\pi$
$421$	−20.0754			−0.978414			−0.489207	+	0.872168i	$0.662714\pi$
$422$	−8.97511	+	15.5453i	−0.436901	+	0.756736i
$423$	0.985601	+	1.70711i	0.0479216	+	0.0830026i
$424$	−2.77165	−	4.80064i	−0.134603	−	0.233140i
$425$	3.51928	−	6.09557i	0.170710	−	0.295679i
$426$	−19.7181			−0.955347
$427$	−3.31409	+	9.64474i	−0.160380	+	0.466742i
$428$	1.11365			0.0538303
$429$	3.75473	−	6.50338i	0.181280	−	0.313986i
$430$	0.782242	+	1.35488i	0.0377230	+	0.0653382i
$431$	15.4831	+	26.8176i	0.745796	+	1.29176i	0.949822	+	0.312792i	$0.101264\pi$
$431$	15.4831	+	26.8176i	0.745796	+	1.29176i	−0.204025	+	0.978966i	$0.565402\pi$
$432$	−2.39495	+	4.14818i	−0.115227	+	0.199579i
$433$	20.7038			0.994961			0.497480	−	0.867475i	$-0.334259\pi$
$433$	20.7038			0.994961			0.497480	+	0.867475i	$0.334259\pi$
$434$	11.5330	−	2.24940i	0.553599	−	0.107974i
$435$	−0.452896			−0.0217147
$436$	−2.43305	+	4.21417i	−0.116522	+	0.201822i
$437$	6.79196	+	11.7640i	0.324904	+	0.562750i
$438$	15.4748	+	26.8031i	0.739412	+	1.28070i
$439$	0.781959	−	1.35439i	0.0373209	−	0.0646416i	−0.846762	−	0.531972i	$-0.821451\pi$
$439$	0.781959	−	1.35439i	0.0373209	−	0.0646416i	0.884083	+	0.467331i	$0.154784\pi$
$440$	1.00000			0.0476731
$441$	−0.389765	+	2.79917i	−0.0185603	+	0.133294i
$442$	−28.6493			−1.36271
$443$	−10.3045	+	17.8480i	−0.489583	+	0.847983i	−0.999928	−	0.0119869i	$-0.996184\pi$
$443$	−10.3045	+	17.8480i	−0.489583	+	0.847983i	0.510345	+	0.859970i	$0.329518\pi$
$444$	5.16527	+	8.94650i	0.245133	+	0.424582i
$445$	−1.23601	−	2.14083i	−0.0585924	−	0.101485i
$446$	3.75246	−	6.49944i	0.177684	−	0.307758i
$447$	−20.9480			−0.990804
$448$	2.59682	−	0.506486i	0.122688	−	0.0239292i
$449$	−17.6929			−0.834979			−0.417489	−	0.908682i	$-0.637090\pi$
$449$	−17.6929			−0.834979			−0.417489	+	0.908682i	$0.637090\pi$
$450$	−0.201870	+	0.349648i	−0.00951622	+	0.0164826i
$451$	4.13302	+	7.15860i	0.194616	+	0.337085i
$452$	0.687571	+	1.19091i	0.0323406	+	0.0560156i
$453$	12.4249	−	21.5206i	0.583774	−	1.01113i
$454$	25.1444			1.18009
$455$	−3.49960	+	10.1846i	−0.164064	+	0.477462i
$456$	4.50379			0.210909
$457$	14.5770	−	25.2482i	0.681885	−	1.18106i	−0.292520	−	0.956259i	$-0.594494\pi$
$457$	14.5770	−	25.2482i	0.681885	−	1.18106i	0.974405	−	0.224800i	$-0.0721729\pi$
$458$	5.10006	+	8.83355i	0.238310	+	0.412765i
$459$	16.8570	+	29.1972i	0.786818	+	1.36281i
$460$	−2.78224	+	4.81898i	−0.129723	+	0.224686i
$461$	−39.8926			−1.85798			−0.928991	−	0.370103i	$-0.879322\pi$
$461$	−39.8926			−1.85798			−0.928991	+	0.370103i	$0.879322\pi$
$462$	3.20470	+	3.68185i	0.149096	+	0.171295i
$463$	−7.64734			−0.355402			−0.177701	−	0.984085i	$-0.556866\pi$
$463$	−7.64734			−0.355402			−0.177701	+	0.984085i	$0.556866\pi$
$464$	−0.122741	+	0.212594i	−0.00569811	+	0.00986942i
$465$	4.09682	+	7.09590i	0.189985	+	0.329064i
$466$	2.05003	+	3.55075i	0.0949657	+	0.164485i
$467$	11.8957	−	20.6040i	0.550468	−	0.953439i	−0.447772	−	0.894148i	$-0.647783\pi$
$467$	11.8957	−	20.6040i	0.550468	−	0.953439i	0.998241	−	0.0592915i	$-0.0188842\pi$
$468$	1.64336			0.0759641
$469$	4.67237	+	5.36804i	0.215750	+	0.247873i
$470$	−4.88237			−0.225207
$471$	−20.3135	+	35.1840i	−0.935997	+	1.62119i
$472$	2.15847	+	3.73858i	0.0993516	+	0.172082i
$473$	0.782242	+	1.35488i	0.0359675	+	0.0622976i
$474$	9.68757	−	16.7794i	0.444965	−	0.770702i
$475$	−2.44118			−0.112009
$476$	6.05162	−	17.6116i	0.277375	−	0.807225i
$477$	2.23805			0.102473
$478$	−4.37630	+	7.57997i	−0.200167	+	0.346700i
$479$	−18.6325	−	32.2725i	−0.851343	−	1.47457i	−0.879997	−	0.474980i	$-0.842455\pi$
$479$	−18.6325	−	32.2725i	−0.851343	−	1.47457i	0.0286539	−	0.999589i	$-0.490878\pi$
$480$	0.922461	+	1.59775i	0.0421044	+	0.0729270i
$481$	−11.3958	+	19.7381i	−0.519604	+	0.899981i
$482$	25.6610			1.16883
$483$	−26.6591	+	5.19960i	−1.21303	+	0.236590i
$484$	1.00000			0.0454545
$485$	−3.12875	+	5.41916i	−0.142069	+	0.246071i
$486$	−2.08424	−	3.61000i	−0.0945429	−	0.163753i
$487$	−10.4179	−	18.0444i	−0.472082	−	0.817670i	0.527408	−	0.849612i	$-0.323164\pi$
$487$	−10.4179	−	18.0444i	−0.472082	−	0.817670i	−0.999490	+	0.0319425i	$0.989831\pi$
$488$	−1.92729	+	3.33816i	−0.0872442	+	0.151111i
$489$	44.1626			1.99710
$490$	−5.52156	−	4.30261i	−0.249438	−	0.194372i
$491$	18.4851			0.834221			0.417110	−	0.908856i	$-0.363043\pi$
$491$	18.4851			0.834221			0.417110	+	0.908856i	$0.363043\pi$
$492$	−7.62510	+	13.2071i	−0.343766	+	0.595420i
$493$	0.863921	+	1.49635i	0.0389090	+	0.0673924i
$494$	4.96822	+	8.60521i	0.223531	+	0.387167i
$495$	−0.201870	+	0.349648i	−0.00907336	+	0.0157155i
$496$	4.44118			0.199415
$497$	27.7542	−	5.41321i	1.24495	−	0.242816i
$498$	19.9672			0.894752
$499$	10.8220	−	18.7442i	0.484459	−	0.839107i	−0.515382	−	0.856961i	$-0.672350\pi$
$499$	10.8220	−	18.7442i	0.484459	−	0.839107i	0.999841	+	0.0178533i	$0.00568320\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	0.445479	+	0.771593i	0.0199025	+	0.0344722i
$502$	−13.3950	+	23.2008i	−0.597848	+	1.03550i
$503$	−40.7938			−1.81890			−0.909452	−	0.415809i	$-0.863498\pi$
$503$	−40.7938			−1.81890			−0.909452	+	0.415809i	$0.863498\pi$
$504$	−0.347127	+	1.01022i	−0.0154623	+	0.0449987i
$505$	−1.45083			−0.0645613
$506$	−2.78224	+	4.81898i	−0.123686	+	0.214230i
$507$	3.29103	+	5.70023i	0.146160	+	0.253156i
$508$	−3.53944	−	6.13048i	−0.157037	−	0.271996i
$509$	−9.57669	+	16.5873i	−0.424479	+	0.735220i	−0.996372	−	0.0851089i	$-0.972876\pi$
$509$	−9.57669	+	16.5873i	−0.424479	+	0.735220i	0.571892	+	0.820329i	$0.306210\pi$
$510$	12.9856			0.575012
$511$	−29.1397	−	33.4783i	−1.28906	−	1.48099i
$512$	1.00000			0.0441942
$513$	5.84651	−	10.1265i	0.258130	−	0.447094i
$514$	9.47429	+	16.4100i	0.417893	+	0.723812i
$515$	2.81514	+	4.87596i	0.124050	+	0.214860i
$516$	−1.44318	+	2.49965i	−0.0635322	+	0.110041i
$517$	−4.88237			−0.214726
$518$	−9.72645	−	11.1746i	−0.427356	−	0.490985i
$519$	−4.72541			−0.207422
$520$	−2.03517	+	3.52502i	−0.0892481	+	0.154582i
$521$	−2.12171	−	3.67491i	−0.0929538	−	0.161001i	0.815799	−	0.578336i	$-0.196298\pi$
$521$	−2.12171	−	3.67491i	−0.0929538	−	0.161001i	−0.908753	+	0.417335i	$0.862964\pi$
$522$	−0.0495554	−	0.0858324i	−0.00216898	−	0.00375678i
$523$	−3.97028	+	6.87673i	−0.173608	+	0.300699i	−0.939679	−	0.342058i	$-0.888876\pi$
$523$	−3.97028	+	6.87673i	−0.173608	+	0.300699i	0.766070	+	0.642757i	$0.222209\pi$
$524$	2.34113			0.102273
$525$	1.58623	−	4.61628i	0.0692287	−	0.201471i
$526$	7.16902			0.312584
$527$	15.6298	−	27.0716i	0.680844	−	1.17926i
$528$	0.922461	+	1.59775i	0.0401450	+	0.0695331i
$529$	−3.98174	−	6.89657i	−0.173119	−	0.299851i
$530$	−2.77165	+	4.80064i	−0.120393	+	0.208526i
$531$	−1.74292			−0.0756362
$532$	−6.33931	+	1.23642i	−0.274844	+	0.0536058i
$533$	−33.6456			−1.45735
$534$	2.28034	−	3.94966i	0.0986799	−	0.170919i
$535$	−0.556825	−	0.964449i	−0.0240736	−	0.0416968i
$536$	1.34492	+	2.32947i	0.0580918	+	0.100618i
$537$	13.0913	−	22.6748i	0.564932	−	0.978490i
$538$	2.16549			0.0933610
$539$	−5.52156	−	4.30261i	−0.237830	−	0.185326i
$540$	4.78990			0.206124
$541$	−5.99486	+	10.3834i	−0.257739	+	0.446418i	−0.965636	−	0.259898i	$-0.916311\pi$
$541$	−5.99486	+	10.3834i	−0.257739	+	0.446418i	0.707897	+	0.706316i	$0.249644\pi$
$542$	−11.8165	−	20.4668i	−0.507564	−	0.879126i
$543$	−12.7011	−	21.9990i	−0.545057	−	0.944066i
$544$	3.51928	−	6.09557i	0.150888	−	0.261346i
$545$	4.86611			0.208441
$546$	−19.5007	+	3.80343i	−0.834554	+	0.162772i
$547$	−20.8228			−0.890318			−0.445159	−	0.895451i	$-0.646853\pi$
$547$	−20.8228			−0.890318			−0.445159	+	0.895451i	$0.646853\pi$
$548$	0.842648	−	1.45951i	0.0359961	−	0.0623471i
$549$	−0.778121	−	1.34775i	−0.0332094	−	0.0575204i
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$	0.299634	−	0.518980i	0.0127648	−	0.0221093i
$552$	−10.2660			−0.436952
$553$	−9.02930	+	26.2773i	−0.383965	+	1.11742i
$554$	−20.7197			−0.880295
$555$	5.16527	−	8.94650i	0.219253	−	0.379758i
$556$	−9.04015	−	15.6580i	−0.383388	−	0.664047i
$557$	9.40941	+	16.2976i	0.398689	+	0.690550i	0.993564	−	0.113268i	$-0.0361318\pi$
$557$	9.40941	+	16.2976i	0.398689	+	0.690550i	−0.594875	+	0.803818i	$0.702799\pi$
$558$	−0.896540	+	1.55285i	−0.0379536	+	0.0657375i
$559$	−6.36798			−0.269337
$560$	−1.73704	−	1.99567i	−0.0734033	−	0.0843324i
$561$	12.9856			0.548253
$562$	6.45968	−	11.1885i	0.272485	−	0.471958i
$563$	−9.31383	−	16.1320i	−0.392531	−	0.679884i	0.600252	−	0.799811i	$-0.295067\pi$
$563$	−9.31383	−	16.1320i	−0.392531	−	0.679884i	−0.992783	+	0.119927i	$0.961734\pi$
$564$	−4.50379	−	7.80080i	−0.189644	−	0.328473i
$565$	0.687571	−	1.19091i	0.0289263	−	0.0501018i
$566$	23.8328			1.00177
$567$	17.4541	+	20.0529i	0.733005	+	0.842143i
$568$	10.6878			0.448449
$569$	−15.0520	+	26.0708i	−0.631011	+	1.09294i	0.356335	+	0.934358i	$0.384026\pi$
$569$	−15.0520	+	26.0708i	−0.631011	+	1.09294i	−0.987345	+	0.158584i	$0.949307\pi$
$570$	−2.25190	−	3.90040i	−0.0943216	−	0.163370i
$571$	−14.6667	−	25.4035i	−0.613784	−	1.06311i	−0.990597	−	0.136816i	$-0.956313\pi$
$571$	−14.6667	−	25.4035i	−0.613784	−	1.06311i	0.376812	−	0.926290i	$-0.377020\pi$
$572$	−2.03517	+	3.52502i	−0.0850947	+	0.147388i
$573$	33.9458			1.41810
$574$	7.10698	−	20.6829i	0.296640	−	0.863288i
$575$	5.56448			0.232055
$576$	−0.201870	+	0.349648i	−0.00841123	+	0.0145687i
$577$	6.15529	+	10.6613i	0.256248	+	0.443835i	0.965234	−	0.261388i	$-0.0841803\pi$
$577$	6.15529	+	10.6613i	0.256248	+	0.443835i	−0.708986	+	0.705223i	$0.750847\pi$
$578$	−16.2707	−	28.1816i	−0.676771	−	1.17220i
$579$	14.9266	−	25.8537i	0.620329	−	1.07444i
$580$	0.245482			0.0101931
$581$	−28.1048	+	5.48159i	−1.16599	+	0.227415i
$582$	−11.5446			−0.478540
$583$	−2.77165	+	4.80064i	−0.114790	+	0.198822i
$584$	−8.38775	−	14.5280i	−0.347088	−	0.601173i
$585$	−0.821678	−	1.42319i	−0.0339722	−	0.0588416i
$586$	−2.18287	+	3.78084i	−0.0901736	+	0.156185i
$587$	38.0513			1.57055			0.785273	−	0.619149i	$-0.212523\pi$
$587$	38.0513			1.57055			0.785273	+	0.619149i	$0.212523\pi$
$588$	1.78107	−	12.7911i	0.0734500	−	0.527494i
$589$	−10.8417			−0.446726
$590$	2.15847	−	3.73858i	0.0888628	−	0.153915i
$591$	5.94645	+	10.2995i	0.244604	+	0.423667i
$592$	−2.79972	−	4.84926i	−0.115068	−	0.199303i
$593$	15.1367	−	26.2175i	0.621590	−	1.07662i	−0.367600	−	0.929984i	$-0.619821\pi$
$593$	15.1367	−	26.2175i	0.621590	−	1.07662i	0.989190	−	0.146641i	$-0.0468461\pi$
$594$	4.78990			0.196532
$595$	−18.2779	+	3.56493i	−0.749320	+	0.146148i
$596$	11.3544			0.465094
$597$	23.8613	−	41.3290i	0.976579	−	1.69148i
$598$	−11.3247	−	19.6149i	−0.463100	−	0.802113i
$599$	20.2420	+	35.0602i	0.827067	+	1.43252i	0.900330	+	0.435209i	$0.143325\pi$
$599$	20.2420	+	35.0602i	0.827067	+	1.43252i	−0.0732631	+	0.997313i	$0.523341\pi$
$600$	0.922461	−	1.59775i	0.0376593	−	0.0652279i
$601$	12.8207			0.522967			0.261484	−	0.965208i	$-0.415788\pi$
$601$	12.8207			0.522967			0.261484	+	0.965208i	$0.415788\pi$
$602$	1.34511	−	3.91458i	0.0548227	−	0.159546i
$603$	−1.08600			−0.0442252
$604$	−6.73467	+	11.6648i	−0.274030	+	0.474633i
$605$	−0.500000	−	0.866025i	−0.0203279	−	0.0352089i
$606$	−1.33834	−	2.31807i	−0.0543663	−	0.0941651i
$607$	17.2908	−	29.9486i	0.701813	−	1.21558i	−0.266016	−	0.963969i	$-0.585707\pi$
$607$	17.2908	−	29.9486i	0.701813	−	1.21558i	0.967829	−	0.251608i	$-0.0809592\pi$
$608$	−2.44118			−0.0990031
$609$	0.786697	+	0.903830i	0.0318786	+	0.0366250i
$610$	3.85457			0.156067
$611$	9.93644	−	17.2104i	0.401986	−	0.696259i
$612$	1.42087	+	2.46102i	0.0574353	+	0.0994809i
$613$	19.4685	+	33.7205i	0.786326	+	1.36196i	0.928203	+	0.372073i	$0.121353\pi$
$613$	19.4685	+	33.7205i	0.786326	+	1.36196i	−0.141877	+	0.989884i	$0.545314\pi$
$614$	−3.94617	+	6.83496i	−0.159254	+	0.275836i
$615$	15.2502			0.614948
$616$	−1.73704	−	1.99567i	−0.0699873	−	0.0804078i
$617$	−43.6232			−1.75621			−0.878103	−	0.478472i	$-0.841191\pi$
$617$	−43.6232			−1.75621			−0.878103	+	0.478472i	$0.841191\pi$
$618$	−5.19371	+	8.99577i	−0.208922	+	0.361863i
$619$	9.43663	+	16.3447i	0.379290	+	0.656950i	0.990959	−	0.134164i	$-0.0428348\pi$
$619$	9.43663	+	16.3447i	0.379290	+	0.656950i	−0.611669	+	0.791114i	$0.709501\pi$
$620$	−2.22059	−	3.84618i	−0.0891811	−	0.154466i
$621$	−13.3267	+	23.0825i	−0.534780	+	0.926267i
$622$	26.6883			1.07010
$623$	−2.12539	+	6.18537i	−0.0851520	+	0.247812i
$624$	−7.50946			−0.300619
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−17.4831	−	30.2817i	−0.698767	−	1.21030i
$627$	−2.25190	−	3.90040i	−0.0899321	−	0.155767i
$628$	11.0105	−	19.0707i	0.439366	−	0.761005i
$629$	−39.4120			−1.57146
$630$	1.04844	−	0.204488i	0.0417708	−	0.00814700i
$631$	−26.3275			−1.04808			−0.524041	−	0.851693i	$-0.675576\pi$
$631$	−26.3275			−1.04808			−0.524041	+	0.851693i	$0.675576\pi$
$632$	−5.25094	+	9.09489i	−0.208871	+	0.361775i
$633$	16.5584	+	28.6800i	0.658137	+	1.13993i
$634$	−6.63000	−	11.4835i	−0.263311	−	0.456068i
$635$	−3.53944	+	6.13048i	−0.140458	+	0.243281i
$636$	−10.2270			−0.405525
$637$	26.4041	−	10.7070i	1.04617	−	0.424229i
$638$	0.245482			0.00971873
$639$	−2.15754	+	3.73697i	−0.0853509	+	0.147832i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	3.64297	+	6.30980i	0.143889	+	0.249222i	0.928958	−	0.370186i	$-0.120706\pi$
$641$	3.64297	+	6.30980i	0.143889	+	0.249222i	−0.785069	+	0.619408i	$0.787373\pi$
$642$	1.02730	−	1.77933i	0.0405442	−	0.0702247i
$643$	29.7464			1.17308			0.586542	−	0.809919i	$-0.300489\pi$
$643$	29.7464			1.17308			0.586542	+	0.809919i	$0.300489\pi$
$644$	14.4500	−	2.81833i	0.569408	−	0.111058i
$645$	2.88635			0.113650
$646$	−8.59121	+	14.8804i	−0.338017	+	0.585462i
$647$	−9.34784	−	16.1909i	−0.367502	−	0.636531i	0.621673	−	0.783277i	$-0.286453\pi$
$647$	−9.34784	−	16.1909i	−0.367502	−	0.636531i	−0.989174	+	0.146746i	$0.953120\pi$
$648$	5.02411	+	8.70201i	0.197366	+	0.341847i
$649$	2.15847	−	3.73858i	0.0847273	−	0.146752i
$650$	4.07034			0.159652
$651$	7.04473	−	20.5018i	0.276105	−	0.803527i
$652$	−23.9374			−0.937459
$653$	23.9355	−	41.4575i	0.936667	−	1.62236i	0.165034	−	0.986288i	$-0.447227\pi$
$653$	23.9355	−	41.4575i	0.936667	−	1.62236i	0.771633	−	0.636068i	$-0.219440\pi$
$654$	4.48879	+	7.77482i	0.175526	+	0.304019i
$655$	−1.17056	−	2.02748i	−0.0457377	−	0.0792201i
$656$	4.13302	−	7.15860i	0.161367	−	0.279496i
$657$	6.77293			0.264237
$658$	8.48086	+	9.74359i	0.330618	+	0.379845i
$659$	17.5706			0.684455			0.342228	−	0.939617i	$-0.388819\pi$
$659$	17.5706			0.684455			0.342228	+	0.939617i	$0.388819\pi$
$660$	0.922461	−	1.59775i	0.0359068	−	0.0621923i
$661$	7.47415	+	12.9456i	0.290711	+	0.503526i	0.973978	−	0.226643i	$-0.0727750\pi$
$661$	7.47415	+	12.9456i	0.290711	+	0.503526i	−0.683267	+	0.730168i	$0.739442\pi$
$662$	−1.92987	−	3.34264i	−0.0750067	−	0.129915i
$663$	−26.4279	+	45.7745i	−1.02637	+	1.77773i
$664$	−10.8228			−0.420006
$665$	4.24043	+	4.87179i	0.164437	+	0.188920i
$666$	2.26071			0.0876009
$667$	−0.682991	+	1.18297i	−0.0264455	+	0.0458050i
$668$	−0.241462	−	0.418225i	−0.00934246	−	0.0161816i
$669$	−6.92299	−	11.9910i	−0.267658	−	0.463598i
$670$	1.34492	−	2.32947i	0.0519589	−	0.0899954i
$671$	3.85457			0.148804
$672$	1.58623	−	4.61628i	0.0611901	−	0.178077i
$673$	34.9020			1.34537			0.672686	−	0.739928i	$-0.265141\pi$
$673$	34.9020			1.34537			0.672686	+	0.739928i	$0.265141\pi$
$674$	13.2594	−	22.9660i	0.510733	−	0.884616i
$675$	−2.39495	−	4.14818i	−0.0921817	−	0.159663i
$676$	−1.78383	−	3.08969i	−0.0686089	−	0.118834i
$677$	0.981997	−	1.70087i	0.0377412	−	0.0653697i	−0.846538	−	0.532329i	$-0.821317\pi$
$677$	0.981997	−	1.70087i	0.0377412	−	0.0653697i	0.884279	+	0.466959i	$0.154650\pi$
$678$	2.53703			0.0974340
$679$	16.2496	−	3.16934i	0.623603	−	0.121628i
$680$	−7.03856			−0.269917
$681$	23.1948	−	40.1745i	0.888825	−	1.53949i
$682$	−2.22059	−	3.84618i	−0.0850309	−	0.147278i
$683$	3.94847	+	6.83895i	0.151084	+	0.261685i	0.931626	−	0.363418i	$-0.118390\pi$
$683$	3.94847	+	6.83895i	0.151084	+	0.261685i	−0.780542	+	0.625103i	$0.785057\pi$
$684$	0.492801	−	0.853556i	0.0188427	−	0.0326365i
$685$	−1.68530			−0.0643919
$686$	1.00458	+	18.4930i	0.0383550	+	0.706066i
$687$	18.8184			0.717967
$688$	0.782242	−	1.35488i	0.0298227	−	0.0516544i
$689$	−11.2816	−	19.5402i	−0.429793	−	0.744423i
$690$	5.13302	+	8.89065i	0.195411	+	0.338461i
$691$	9.32432	−	16.1502i	0.354714	−	0.614382i	−0.632355	−	0.774679i	$-0.717912\pi$
$691$	9.32432	−	16.1502i	0.354714	−	0.614382i	0.987069	+	0.160296i	$0.0512450\pi$
$692$	2.56130			0.0973662
$693$	1.04844	−	0.204488i	0.0398269	−	0.00776786i
$694$	−22.5281			−0.855155
$695$	−9.04015	+	15.6580i	−0.342912	+	0.593942i
$696$	0.226448	+	0.392219i	0.00858348	+	0.0148670i
$697$	−29.0905	−	50.3863i	−1.10188	−	1.90852i
$698$	12.7577	−	22.0970i	0.482887	−	0.836385i
$699$	7.56428			0.286107
$700$	−0.859780	+	2.50215i	−0.0324966	+	0.0945726i
$701$	−33.5712			−1.26797			−0.633984	−	0.773347i	$-0.718581\pi$
$701$	−33.5712			−1.26797			−0.633984	+	0.773347i	$0.718581\pi$
$702$	−9.74826	+	16.8845i	−0.367924	+	0.637264i
$703$	6.83463	+	11.8379i	0.257773	+	0.446476i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	−4.50379	+	7.80080i	−0.169623	+	0.293795i
$706$	−12.8147			−0.482287
$707$	2.52016	+	2.89538i	0.0947802	+	0.108892i
$708$	7.96442			0.299321
$709$	−2.19371	+	3.79962i	−0.0823865	+	0.142698i	−0.904275	−	0.426951i	$-0.859588\pi$
$709$	−2.19371	+	3.79962i	−0.0823865	+	0.142698i	0.821888	+	0.569649i	$0.192921\pi$
$710$	−5.34389	−	9.25589i	−0.200553	−	0.347367i
$711$	−2.12001	−	3.67196i	−0.0795065	−	0.137709i
$712$	−1.23601	+	2.14083i	−0.0463214	+	0.0802310i
$713$	24.7129			0.925505
$714$	−22.5565	−	25.9150i	−0.844156	−	0.969843i
$715$	4.07034			0.152222
$716$	−7.09586	+	12.2904i	−0.265185	+	0.459313i
$717$	8.07393	+	13.9845i	0.301526	+	0.522259i
$718$	−13.4795	−	23.3472i	−0.503052	−	0.871311i
$719$	−3.54071	+	6.13269i	−0.132046	+	0.228711i	−0.924465	−	0.381266i	$-0.875488\pi$
$719$	−3.54071	+	6.13269i	−0.132046	+	0.228711i	0.792419	+	0.609977i	$0.208821\pi$
$720$	0.403739			0.0150465
$721$	4.84080	−	14.0878i	0.180281	−	0.524658i
$722$	−13.0406			−0.485322
$723$	23.6713	−	40.9999i	0.880346	−	1.52480i
$724$	6.88436	+	11.9241i	0.255855	+	0.443154i
$725$	−0.122741	−	0.212594i	−0.00455849	−	0.00789554i
$726$	0.922461	−	1.59775i	0.0342357	−	0.0592981i
$727$	−19.3662			−0.718253			−0.359126	−	0.933289i	$-0.616925\pi$
$727$	−19.3662			−0.718253			−0.359126	+	0.933289i	$0.616925\pi$
$728$	10.5699	−	2.06157i	0.391748	−	0.0764068i
$729$	22.4541			0.831634
$730$	−8.38775	+	14.5280i	−0.310445	+	0.537706i
$731$	−5.50586	−	9.53642i	−0.203641	−	0.352717i
$732$	3.55569	+	6.15864i	0.131422	+	0.227630i
$733$	4.86003	−	8.41781i	0.179509	−	0.310919i	−0.762203	−	0.647338i	$-0.775882\pi$
$733$	4.86003	−	8.41781i	0.179509	−	0.310919i	0.941713	+	0.336419i	$0.109216\pi$
$734$	15.0384			0.555076
$735$	−11.9679	+	4.85308i	−0.441443	+	0.179008i
$736$	5.56448			0.205110
$737$	1.34492	−	2.32947i	0.0495409	−	0.0858073i
$738$	1.66866	+	2.89021i	0.0614243	+	0.106390i
$739$	0.110491	+	0.191376i	0.00406448	+	0.00703988i	0.868050	−	0.496476i	$-0.165373\pi$
$739$	0.110491	+	0.191376i	0.00406448	+	0.00703988i	−0.863986	+	0.503516i	$0.832040\pi$
$740$	−2.79972	+	4.84926i	−0.102920	+	0.178262i
$741$	18.3320			0.673442
$742$	14.3950	−	2.80760i	0.528455	−	0.103070i
$743$	8.78630			0.322338			0.161169	−	0.986927i	$-0.448474\pi$
$743$	8.78630			0.322338			0.161169	+	0.986927i	$0.448474\pi$
$744$	4.09682	−	7.09590i	0.150197	−	0.260148i
$745$	−5.67719	−	9.83318i	−0.207996	−	0.360260i
$746$	−14.4139	−	24.9656i	−0.527731	−	0.914057i
$747$	2.18479	−	3.78417i	0.0799374	−	0.138456i
$748$	−7.03856			−0.257355
$749$	−0.957494	+	2.78652i	−0.0349861	+	0.101817i
$750$	−1.84492			−0.0673670
$751$	13.0139	−	22.5408i	0.474885	−	0.822524i	−0.524702	−	0.851286i	$-0.675823\pi$
$751$	13.0139	−	22.5408i	0.474885	−	0.822524i	0.999586	+	0.0287619i	$0.00915646\pi$
$752$	2.44118	+	4.22825i	0.0890208	+	0.154189i
$753$	24.7128	+	42.8037i	0.900583	+	1.55985i
$754$	−0.499598	+	0.865329i	−0.0181943	+	0.0315134i
$755$	13.4693			0.490199
$756$	−8.32024	−	9.55905i	−0.302604	−	0.347659i
$757$	21.2327			0.771715			0.385858	−	0.922558i	$-0.373906\pi$
$757$	21.2327			0.771715			0.385858	+	0.922558i	$0.373906\pi$
$758$	−14.3610	+	24.8739i	−0.521613	+	0.903461i
$759$	5.13302	+	8.89065i	0.186317	+	0.322710i
$760$	1.22059	+	2.11413i	0.0442755	+	0.0766874i
$761$	−7.31015	+	12.6616i	−0.264993	+	0.458981i	−0.967562	−	0.252635i	$-0.918703\pi$
$761$	−7.31015	+	12.6616i	−0.264993	+	0.458981i	0.702569	+	0.711616i	$0.252036\pi$
$762$	−13.0600			−0.473113
$763$	−8.45262	−	9.71114i	−0.306005	−	0.351567i
$764$	−18.3996			−0.665673
$765$	1.42087	−	2.46102i	0.0513717	−	0.0889784i
$766$	−13.5810	−	23.5230i	−0.490701	−	0.849919i
$767$	8.78570	+	15.2173i	0.317233	+	0.549464i
$768$	0.922461	−	1.59775i	0.0332865	−	0.0576538i
$769$	3.64336			0.131383			0.0656914	−	0.997840i	$-0.479075\pi$
$769$	3.64336			0.131383			0.0656914	+	0.997840i	$0.479075\pi$
$770$	−0.859780	+	2.50215i	−0.0309843	+	0.0901714i
$771$	34.9587			1.25901
$772$	−8.09065	+	14.0134i	−0.291189	+	0.504354i
$773$	18.9758	+	32.8670i	0.682511	+	1.18214i	0.974212	+	0.225635i	$0.0724456\pi$
$773$	18.9758	+	32.8670i	0.682511	+	1.18214i	−0.291701	+	0.956510i	$0.594221\pi$
$774$	0.315822	+	0.547019i	0.0113520	+	0.0196622i
$775$	−2.22059	+	3.84618i	−0.0797660	+	0.138159i
$776$	6.25751			0.224631
$777$	−26.8265	+	5.23227i	−0.962397	+	0.187707i
$778$	9.63265			0.345347
$779$	−10.0895	+	17.4755i	−0.361492	+	0.626123i
$780$	3.75473	+	6.50338i	0.134441	+	0.232858i
$781$	−5.34389	−	9.25589i	−0.191219	−	0.331202i
$782$	19.5830	−	33.9187i	0.700286	−	1.21293i
$783$	1.17584			0.0420209
$784$	−0.965389	+	6.93311i	−0.0344782	+	0.247611i
$785$	−22.0210			−0.785963
$786$	2.15960	−	3.74054i	0.0770304	−	0.133421i
$787$	24.4931	+	42.4232i	0.873084	+	1.51223i	0.858790	+	0.512327i	$0.171217\pi$
$787$	24.4931	+	42.4232i	0.873084	+	1.51223i	0.0142935	+	0.999898i	$0.495450\pi$
$788$	−3.22314	−	5.58265i	−0.114820	−	0.198874i
$789$	6.61315	−	11.4543i	0.235434	−	0.407784i
$790$	10.5019			0.373640
$791$	−3.57099	+	0.696489i	−0.126970	+	0.0247643i
$792$	0.403739			0.0143462
$793$	−7.84471	+	13.5874i	−0.278574	+	0.482504i
$794$	14.4685	+	25.0602i	0.513468	+	0.889353i
$795$	5.11348	+	8.85681i	0.181356	+	0.314119i
$796$	−12.9335	+	22.4015i	−0.458416	+	0.794000i
$797$	−9.41664			−0.333555			−0.166777	−	0.985995i	$-0.553336\pi$
$797$	−9.41664			−0.333555			−0.166777	+	0.985995i	$0.553336\pi$
$798$	−3.87227	+	11.2692i	−0.137077	+	0.398925i
$799$	34.3648			1.21574
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−0.499025	−	0.864337i	−0.0176322	−	0.0305398i
$802$	16.3319	+	28.2876i	0.576698	+	0.998871i
$803$	−8.38775	+	14.5280i	−0.295997	+	0.512682i
$804$	4.96256			0.175016
$805$	−9.66573	−	11.1049i	−0.340672	−	0.391395i
$806$	18.0771			0.636740
$807$	1.99758	−	3.45992i	0.0703182	−	0.121795i
$808$	0.725417	+	1.25646i	0.0255201	+	0.0442021i
$809$	−10.8923	−	18.8659i	−0.382951	−	0.663291i	0.608531	−	0.793530i	$-0.291759\pi$
$809$	−10.8923	−	18.8659i	−0.382951	−	0.663291i	−0.991483	+	0.130239i	$0.958426\pi$
$810$	5.02411	−	8.70201i	0.176529	−	0.305757i
$811$	−9.61077			−0.337480			−0.168740	−	0.985661i	$-0.553970\pi$
$811$	−9.61077			−0.337480			−0.168740	+	0.985661i	$0.553970\pi$
$812$	−0.426412	−	0.489901i	−0.0149641	−	0.0171922i
$813$	−43.6012			−1.52916
$814$	−2.79972	+	4.84926i	−0.0981301	+	0.169966i
$815$	11.9687	+	20.7304i	0.419245	+	0.726153i
$816$	−6.49280	−	11.2459i	−0.227293	−	0.393684i
$817$	−1.90960	+	3.30752i	−0.0668083	+	0.115715i
$818$	7.05009			0.246501
$819$	−1.41292	+	4.11193i	−0.0493716	+	0.143682i
$820$	−8.26604			−0.288663
$821$	−24.7667	+	42.8972i	−0.864364	+	1.49712i	0.00331308	+	0.999995i	$0.498945\pi$
$821$	−24.7667	+	42.8972i	−0.864364	+	1.49712i	−0.867677	+	0.497128i	$0.834388\pi$
$822$	−1.55462	−	2.69268i	−0.0542236	−	0.0939180i
$823$	18.9085	+	32.7505i	0.659110	+	1.14161i	0.980847	+	0.194782i	$0.0624000\pi$
$823$	18.9085	+	32.7505i	0.659110	+	1.14161i	−0.321737	+	0.946829i	$0.604267\pi$
$824$	2.81514	−	4.87596i	0.0980699	−	0.169862i
$825$	−1.84492			−0.0642320
$826$	−11.2103	+	2.18647i	−0.390057	+	0.0760769i
$827$	51.9979			1.80814			0.904071	−	0.427382i	$-0.140564\pi$
$827$	51.9979			1.80814			0.904071	+	0.427382i	$0.140564\pi$
$828$	−1.12330	+	1.94561i	−0.0390374	+	0.0676147i
$829$	14.0318	+	24.3038i	0.487344	+	0.844104i	0.999894	−	0.0145530i	$-0.00463253\pi$
$829$	14.0318	+	24.3038i	0.487344	+	0.844104i	−0.512550	+	0.858657i	$0.671299\pi$
$830$	5.41140	+	9.37282i	0.187832	+	0.325335i
$831$	−19.1131	+	33.1049i	−0.663026	+	1.14839i
$832$	4.07034			0.141114
$833$	38.8638	+	30.2842i	1.34655	+	1.04928i
$834$	−33.3568			−1.15505
$835$	−0.241462	+	0.418225i	−0.00835615	+	0.0144733i
$836$	1.22059	+	2.11413i	0.0422150	+	0.0731186i
$837$	−10.6364	−	18.4228i	−0.367648	−	0.636785i
$838$	3.91844	−	6.78694i	0.135360	−	0.234451i
$839$	−5.50312			−0.189989			−0.0949943	−	0.995478i	$-0.530283\pi$
$839$	−5.50312			−0.189989			−0.0949943	+	0.995478i	$0.530283\pi$
$840$	−4.79093	+	0.934427i	−0.165303	+	0.0322408i
$841$	−28.9397			−0.997922
$842$	10.0377	−	17.3858i	0.345922	−	0.599154i
$843$	−11.9176	−	20.6419i	−0.410464	−	0.710945i
$844$	−8.97511	−	15.5453i	−0.308936	−	0.535093i
$845$	−1.78383	+	3.08969i	−0.0613657	+	0.106288i
$846$	−1.97120			−0.0677713
$847$	−0.859780	+	2.50215i	−0.0295424	+	0.0859751i
$848$	5.54330			0.190358
$849$	21.9848	−	38.0788i	0.754516	−	1.30686i
$850$	3.51928	+	6.09557i	0.120710	+	0.209076i
$851$	−15.5790	−	26.9836i	−0.534041	−	0.924986i
$852$	9.85907	−	17.0764i	0.337766	−	0.585028i
$853$	7.43723			0.254646			0.127323	−	0.991861i	$-0.459362\pi$
$853$	7.43723			0.254646			0.127323	+	0.991861i	$0.459362\pi$
$854$	−6.69554	−	7.69245i	−0.229117	−	0.263230i
$855$	−0.985601			−0.0337069
$856$	−0.556825	+	0.964449i	−0.0190319	+	0.0329642i
$857$	−5.76089	−	9.97815i	−0.196788	−	0.340847i	0.750697	−	0.660647i	$-0.229718\pi$
$857$	−5.76089	−	9.97815i	−0.196788	−	0.340847i	−0.947485	+	0.319800i	$0.896384\pi$
$858$	3.75473	+	6.50338i	0.128184	+	0.222022i
$859$	13.3213	−	23.0731i	0.454516	−	0.787245i	−0.544144	−	0.838992i	$-0.683146\pi$
$859$	13.3213	−	23.0731i	0.454516	−	0.787245i	0.998660	+	0.0517468i	$0.0164789\pi$
$860$	−1.56448			−0.0533484
$861$	−26.4902	−	30.4344i	−0.902784	−	1.03720i
$862$	−30.9663			−1.05472
$863$	11.0568	−	19.1510i	0.376378	−	0.651906i	−0.614154	−	0.789186i	$-0.710503\pi$
$863$	11.0568	−	19.1510i	0.376378	−	0.651906i	0.990532	+	0.137280i	$0.0438359\pi$
$864$	−2.39495	−	4.14818i	−0.0814779	−	0.141124i
$865$	−1.28065	−	2.21815i	−0.0435435	−	0.0754195i
$866$	−10.3519	+	17.9300i	−0.351772	+	0.609287i
$867$	−60.0363			−2.03894
$868$	−3.81844	+	11.1125i	−0.129606	+	0.377184i
$869$	10.5019			0.356252
$870$	0.226448	−	0.392219i	0.00767730	−	0.0132975i
$871$	5.47429	+	9.48175i	0.185489	+	0.321277i
$872$	−2.43305	−	4.21417i	−0.0823936	−	0.142710i
$873$	−1.26320	+	2.18793i	−0.0427529	+	0.0740501i
$874$	−13.5839			−0.459483
$875$	2.59682	−	0.506486i	0.0877885	−	0.0171223i
$876$	−30.9495			−1.04569
$877$	−23.2465	+	40.2641i	−0.784979	+	1.35962i	0.144033	+	0.989573i	$0.453993\pi$
$877$	−23.2465	+	40.2641i	−0.784979	+	1.35962i	−0.929012	+	0.370050i	$0.879341\pi$
$878$	0.781959	+	1.35439i	0.0263898	+	0.0457085i
$879$	4.02723	+	6.97536i	0.135835	+	0.235273i
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	7.86373			0.264936			0.132468	−	0.991187i	$-0.457710\pi$
$881$	7.86373			0.264936			0.132468	+	0.991187i	$0.457710\pi$
$882$	−2.22927	−	1.73713i	−0.0750634	−	0.0584922i
$883$	−28.7863			−0.968736			−0.484368	−	0.874864i	$-0.660950\pi$
$883$	−28.7863			−0.968736			−0.484368	+	0.874864i	$0.660950\pi$
$884$	14.3247	−	24.8111i	0.481791	−	0.834486i
$885$	−3.98221	−	6.89739i	−0.133860	−	0.231853i
$886$	−10.3045	−	17.8480i	−0.346188	−	0.599614i
$887$	14.7471	−	25.5427i	0.495158	−	0.857639i	−0.504826	−	0.863221i	$-0.668443\pi$
$887$	14.7471	−	25.5427i	0.495158	−	0.857639i	0.999984	+	0.00558182i	$0.00177676\pi$
$888$	−10.3305			−0.346670
$889$	18.3826	−	3.58535i	0.616531	−	0.120249i
$890$	2.47202			0.0828622
$891$	5.02411	−	8.70201i	0.168314	−	0.291528i
$892$	3.75246	+	6.49944i	0.125642	+	0.217617i
$893$	−5.95938	−	10.3219i	−0.199423	−	0.345411i
$894$	10.4740	−	18.1415i	0.350302	−	0.606741i
$895$	14.1917			0.474377
$896$	−0.859780	+	2.50215i	−0.0287232	+	0.0835911i
$897$	−41.7863			−1.39520
$898$	8.84644	−	15.3225i	0.295210	−	0.511318i
$899$	−0.545116	−	0.944168i	−0.0181806	−	0.0314898i
$900$	−0.201870	−	0.349648i	−0.00672899	−	0.0116549i
$901$	19.5084	−	33.7896i	0.649920	−	1.12569i
$902$	−8.26604			−0.275229
$903$	−5.01370	−	5.76020i	−0.166846	−	0.191687i
$904$	−1.37514			−0.0457365
$905$	6.88436	−	11.9241i	0.228844	−	0.396369i
$906$	12.4249	+	21.5206i	0.412791	+	0.714975i
$907$	19.7072	+	34.1339i	0.654367	+	1.13340i	0.982052	+	0.188609i	$0.0603980\pi$
$907$	19.7072	+	34.1339i	0.654367	+	1.13340i	−0.327686	+	0.944787i	$0.606269\pi$
$908$	−12.5722	+	21.7757i	−0.417224	+	0.722652i
$909$	−0.585758			−0.0194284
$910$	−7.07034	−	8.12305i	−0.234379	−	0.269276i
$911$	−22.5612			−0.747485			−0.373742	−	0.927533i	$-0.621926\pi$
$911$	−22.5612			−0.747485			−0.373742	+	0.927533i	$0.621926\pi$
$912$	−2.25190	+	3.90040i	−0.0745678	+	0.129155i
$913$	5.41140	+	9.37282i	0.179091	+	0.310195i
$914$	14.5770	+	25.2482i	0.482166	+	0.835135i
$915$	3.55569	−	6.15864i	0.117548	−	0.203598i
$916$	−10.2001			−0.337021
$917$	−2.01286	+	5.85787i	−0.0664704	+	0.193444i
$918$	−33.7140			−1.11273
$919$	−12.1096	+	20.9744i	−0.399459	+	0.691883i	−0.993659	−	0.112434i	$-0.964135\pi$
$919$	−12.1096	+	20.9744i	−0.399459	+	0.691883i	0.594201	+	0.804317i	$0.297469\pi$
$920$	−2.78224	−	4.81898i	−0.0917278	−	0.158877i
$921$	7.28037	+	12.6100i	0.239896	+	0.415513i
$922$	19.9463	−	34.5480i	0.656896	−	1.13778i
$923$	43.5029			1.43192
$924$	−4.79093	+	0.934427i	−0.157610	+	0.0307404i
$925$	5.59944			0.184108
$926$	3.82367	−	6.62279i	0.125654	−	0.217638i
$927$	1.13658	+	1.96862i	0.0373302	+	0.0646578i
$928$	−0.122741	−	0.212594i	−0.00402917	−	0.00697873i
$929$	−3.87520	+	6.71204i	−0.127141	+	0.220215i	−0.922568	−	0.385835i	$-0.873913\pi$
$929$	−3.87520	+	6.71204i	−0.127141	+	0.220215i	0.795427	+	0.606050i	$0.207247\pi$
$930$	−8.19364			−0.268680
$931$	2.35669	−	16.9250i	0.0772375	−	0.554694i
$932$	−4.10006			−0.134302
$933$	24.6189	−	42.6412i	0.805987	−	1.39601i
$934$	11.8957	+	20.6040i	0.389240	+	0.674183i
$935$	3.51928	+	6.09557i	0.115093	+	0.199347i
$936$	−0.821678	+	1.42319i	−0.0268574	+	0.0465183i
$937$	−4.62667			−0.151147			−0.0755733	−	0.997140i	$-0.524079\pi$
$937$	−4.62667			−0.151147			−0.0755733	+	0.997140i	$0.524079\pi$
$938$	−6.98504	+	1.36237i	−0.228070	+	0.0444829i
$939$	−64.5101			−2.10521
$940$	2.44118	−	4.22825i	0.0796226	−	0.137910i
$941$	−24.9906	−	43.2850i	−0.814671	−	1.41105i	−0.909564	−	0.415563i	$-0.863584\pi$
$941$	−24.9906	−	43.2850i	−0.814671	−	1.41105i	0.0948936	−	0.995487i	$-0.469749\pi$
$942$	−20.3135	−	35.1840i	−0.661850	−	1.14636i
$943$	22.9981	−	39.8339i	0.748922	−	1.29717i
$944$	−4.31694			−0.140504
$945$	−4.11826	+	11.9851i	−0.133967	+	0.389874i
$946$	−1.56448			−0.0508657
$947$	−2.09264	+	3.62456i	−0.0680018	+	0.117783i	−0.898022	−	0.439951i	$-0.854996\pi$
$947$	−2.09264	+	3.62456i	−0.0680018	+	0.117783i	0.830020	+	0.557734i	$0.188329\pi$
$948$	9.68757	+	16.7794i	0.314638	+	0.544968i
$949$	−34.1410	−	59.1339i	−1.10826	−	1.91957i
$950$	1.22059	−	2.11413i	0.0396012	−	0.0685913i
$951$	−24.4637			−0.793289
$952$	12.2263	+	14.0466i	0.396255	+	0.455254i
$953$	−27.0206			−0.875283			−0.437642	−	0.899149i	$-0.644186\pi$
$953$	−27.0206			−0.875283			−0.437642	+	0.899149i	$0.644186\pi$
$954$	−1.11902	+	1.93821i	−0.0362297	+	0.0627517i
$955$	9.19978	+	15.9345i	0.297698	+	0.515628i
$956$	−4.37630	−	7.57997i	−0.141540	−	0.245154i
$957$	0.226448	−	0.392219i	0.00732002	−	0.0126786i
$958$	37.2651			1.20398
$959$	2.92743	+	3.36329i	0.0945315	+	0.108606i
$960$	−1.84492			−0.0595446
$961$	5.63795	−	9.76521i	0.181869	−	0.315007i
$962$	−11.3958	−	19.7381i	−0.367416	−	0.636383i
$963$	−0.224812	−	0.389386i	−0.00724446	−	0.0125478i
$964$	−12.8305	+	22.2231i	−0.413243	+	0.715758i
$965$	16.1813			0.520895
$966$	8.82654	−	25.6872i	0.283989	−	0.826473i
$967$	−50.1754			−1.61353			−0.806766	−	0.590872i	$-0.798784\pi$
$967$	−50.1754			−1.61353			−0.806766	+	0.590872i	$0.798784\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$	15.8501	+	27.4532i	0.509179	+	0.881924i
$970$	−3.12875	−	5.41916i	−0.100458	−	0.173999i
$971$	12.2473	−	21.2130i	0.393035	−	0.680756i	−0.599813	−	0.800140i	$-0.704759\pi$
$971$	12.2473	−	21.2130i	0.393035	−	0.680756i	0.992848	+	0.119384i	$0.0380919\pi$
$972$	4.16847			0.133704
$973$	46.9513	−	9.15741i	1.50519	−	0.293573i
$974$	20.8359			0.667625
$975$	3.75473	−	6.50338i	0.120248	−	0.208275i
$976$	−1.92729	−	3.33816i	−0.0616909	−	0.106852i
$977$	−23.4106	−	40.5484i	−0.748973	−	1.29726i	−0.948316	−	0.317329i	$-0.897214\pi$
$977$	−23.4106	−	40.5484i	−0.748973	−	1.29726i	0.199343	−	0.979930i	$-0.436119\pi$
$978$	−22.0813	+	38.2459i	−0.706082	+	1.22297i
$979$	2.47202			0.0790060
$980$	6.48694	−	2.63050i	0.207218	−	0.0840284i
$981$	1.96464			0.0627260
$982$	−9.24255	+	16.0086i	−0.294942	+	0.510854i
$983$	−9.81832	−	17.0058i	−0.313156	−	0.542402i	0.665888	−	0.746052i	$-0.268053\pi$
$983$	−9.81832	−	17.0058i	−0.313156	−	0.542402i	−0.979044	+	0.203650i	$0.934719\pi$
$984$	−7.62510	−	13.2071i	−0.243079	−	0.421026i
$985$	−3.22314	+	5.58265i	−0.102698	+	0.177878i
$986$	−1.72784			−0.0550257
$987$	23.3911	−	4.56221i	0.744546	−	0.145217i
$988$	−9.93644			−0.316120
$989$	4.35277	−	7.53922i	0.138410	−	0.239733i
$990$	−0.201870	−	0.349648i	−0.00641584	−	0.0111126i
$991$	16.6389	+	28.8194i	0.528552	+	0.915479i	0.999446	+	0.0332891i	$0.0105982\pi$
$991$	16.6389	+	28.8194i	0.528552	+	0.915479i	−0.470894	+	0.882190i	$0.656068\pi$
$992$	−2.22059	+	3.84618i	−0.0705039	+	0.122116i
$993$	−7.12093			−0.225976
$994$	−9.18915	+	26.7425i	−0.291462	+	0.848220i
$995$	25.8670			0.820040
$996$	−9.98361	+	17.2921i	−0.316343	+	0.547922i
$997$	21.2629	+	36.8284i	0.673402	+	1.16637i	0.976933	+	0.213544i	$0.0685008\pi$
$997$	21.2629	+	36.8284i	0.673402	+	1.16637i	−0.303532	+	0.952821i	$0.598166\pi$
$998$	10.8220	+	18.7442i	0.342564	+	0.593339i
$999$	−13.4104	+	23.2275i	−0.424286	+	0.734884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.m.331.4	yes	10
7.2	even	3		5390.2.a.ci.1.2		5
7.4	even	3	inner	770.2.i.m.221.4	✓	10
7.5	odd	6		5390.2.a.ch.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.m.221.4	✓	10	7.4	even	3	inner
770.2.i.m.331.4	yes	10	1.1	even	1	trivial
5390.2.a.ch.1.4		5	7.5	odd	6
5390.2.a.ci.1.2		5	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.922461 + 1.59775i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.84492 q^{6} +(2.59682 - 0.506486i) q^{7} +1.00000 q^{8} +(-0.201870 + 0.349648i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.922461 + 1.59775i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.84492 q^{6} +(2.59682 - 0.506486i) q^{7} +1.00000 q^{8} +(-0.201870 + 0.349648i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(0.922461 - 1.59775i) q^{12} +4.07034 q^{13} +(-0.859780 + 2.50215i) q^{14} -1.84492 q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.51928 + 6.09557i) q^{17} +(-0.201870 - 0.349648i) q^{18} +(1.22059 - 2.11413i) q^{19} +1.00000 q^{20} +(3.20470 + 3.68185i) q^{21} +1.00000 q^{22} +(-2.78224 + 4.81898i) q^{23} +(0.922461 + 1.59775i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.03517 + 3.52502i) q^{26} +4.78990 q^{27} +(-1.73704 - 1.99567i) q^{28} +0.245482 q^{29} +(0.922461 - 1.59775i) q^{30} +(-2.22059 - 3.84618i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.922461 - 1.59775i) q^{33} -7.03856 q^{34} +(-0.859780 + 2.50215i) q^{35} +0.403739 q^{36} +(-2.79972 + 4.84926i) q^{37} +(1.22059 + 2.11413i) q^{38} +(3.75473 + 6.50338i) q^{39} +(-0.500000 + 0.866025i) q^{40} -8.26604 q^{41} +(-4.79093 + 0.934427i) q^{42} -1.56448 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-0.201870 - 0.349648i) q^{45} +(-2.78224 - 4.81898i) q^{46} +(2.44118 - 4.22825i) q^{47} -1.84492 q^{48} +(6.48694 - 2.63050i) q^{49} +1.00000 q^{50} +(-6.49280 + 11.2459i) q^{51} +(-2.03517 - 3.52502i) q^{52} +(-2.77165 - 4.80064i) q^{53} +(-2.39495 + 4.14818i) q^{54} +1.00000 q^{55} +(2.59682 - 0.506486i) q^{56} +4.50379 q^{57} +(-0.122741 + 0.212594i) q^{58} +(2.15847 + 3.73858i) q^{59} +(0.922461 + 1.59775i) q^{60} +(-1.92729 + 3.33816i) q^{61} +4.44118 q^{62} +(-0.347127 + 1.01022i) q^{63} +1.00000 q^{64} +(-2.03517 + 3.52502i) q^{65} +(0.922461 + 1.59775i) q^{66} +(1.34492 + 2.32947i) q^{67} +(3.51928 - 6.09557i) q^{68} -10.2660 q^{69} +(-1.73704 - 1.99567i) q^{70} +10.6878 q^{71} +(-0.201870 + 0.349648i) q^{72} +(-8.38775 - 14.5280i) q^{73} +(-2.79972 - 4.84926i) q^{74} +(0.922461 - 1.59775i) q^{75} -2.44118 q^{76} +(-1.73704 - 1.99567i) q^{77} -7.50946 q^{78} +(-5.25094 + 9.09489i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(5.02411 + 8.70201i) q^{81} +(4.13302 - 7.15860i) q^{82} -10.8228 q^{83} +(1.58623 - 4.61628i) q^{84} -7.03856 q^{85} +(0.782242 - 1.35488i) q^{86} +(0.226448 + 0.392219i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-1.23601 + 2.14083i) q^{89} +0.403739 q^{90} +(10.5699 - 2.06157i) q^{91} +5.56448 q^{92} +(4.09682 - 7.09590i) q^{93} +(2.44118 + 4.22825i) q^{94} +(1.22059 + 2.11413i) q^{95} +(0.922461 - 1.59775i) q^{96} +6.25751 q^{97} +(-0.965389 + 6.93311i) q^{98} +0.403739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9	\( 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9} - 5 q^{10} - 5 q^{11} - 2 q^{13} + 3 q^{14} - 5 q^{16} - 9 q^{18} - 4 q^{19} + 10 q^{20} + 2 q^{21} + 10 q^{22} - 7 q^{23} - 5 q^{25} + q^{26} - 18 q^{27} - 3 q^{28} + 8 q^{29} - 6 q^{31} - 5 q^{32} + 3 q^{35} + 18 q^{36} - 16 q^{37} - 4 q^{38} - 7 q^{39} - 5 q^{40} - 2 q^{41} + 11 q^{42} + 26 q^{43} - 5 q^{44} - 9 q^{45} - 7 q^{46} - 8 q^{47} + 14 q^{49} + 10 q^{50} - 13 q^{51} + q^{52} - 4 q^{53} + 9 q^{54} + 10 q^{55} + 30 q^{57} - 4 q^{58} - 9 q^{59} - 2 q^{61} + 12 q^{62} + 25 q^{63} + 10 q^{64} + q^{65} - 5 q^{67} - 22 q^{69} - 3 q^{70} + 56 q^{71} - 9 q^{72} + q^{73} - 16 q^{74} + 8 q^{76} - 3 q^{77} + 14 q^{78} - 23 q^{79} - 5 q^{80} + 7 q^{81} + q^{82} - 46 q^{83} - 13 q^{84} - 13 q^{86} - 15 q^{87} - 5 q^{88} + 9 q^{89} + 18 q^{90} + 29 q^{91} + 14 q^{92} + 15 q^{93} - 8 q^{94} - 4 q^{95} - 26 q^{97} - 19 q^{98} + 18 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9 - 5 * q^10 - 5 * q^11 - 2 * q^13 + 3 * q^14 - 5 * q^16 - 9 * q^18 - 4 * q^19 + 10 * q^20 + 2 * q^21 + 10 * q^22 - 7 * q^23 - 5 * q^25 + q^26 - 18 * q^27 - 3 * q^28 + 8 * q^29 - 6 * q^31 - 5 * q^32 + 3 * q^35 + 18 * q^36 - 16 * q^37 - 4 * q^38 - 7 * q^39 - 5 * q^40 - 2 * q^41 + 11 * q^42 + 26 * q^43 - 5 * q^44 - 9 * q^45 - 7 * q^46 - 8 * q^47 + 14 * q^49 + 10 * q^50 - 13 * q^51 + q^52 - 4 * q^53 + 9 * q^54 + 10 * q^55 + 30 * q^57 - 4 * q^58 - 9 * q^59 - 2 * q^61 + 12 * q^62 + 25 * q^63 + 10 * q^64 + q^65 - 5 * q^67 - 22 * q^69 - 3 * q^70 + 56 * q^71 - 9 * q^72 + q^73 - 16 * q^74 + 8 * q^76 - 3 * q^77 + 14 * q^78 - 23 * q^79 - 5 * q^80 + 7 * q^81 + q^82 - 46 * q^83 - 13 * q^84 - 13 * q^86 - 15 * q^87 - 5 * q^88 + 9 * q^89 + 18 * q^90 + 29 * q^91 + 14 * q^92 + 15 * q^93 - 8 * q^94 - 4 * q^95 - 26 * q^97 - 19 * q^98 + 18 * q^99

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