LMFDB - Embedded newform 414.2.e.e.277.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(139,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("414.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.e (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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 4x^{10} - 3x^{9} + 22x^{8} - 9x^{7} + 69x^{6} - 27x^{5} + 198x^{4} - 81x^{3} + 324x^{2} + 729 $ x^12 + 4x^10 - 3x^9 + 22x^8 - 9x^7 + 69x^6 - 27x^5 + 198x^4 - 81x^3 + 324*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.3
Root			$0.416383 - 1.68126i$ of defining polynomial
Character	$\chi$	$=$	414.277
Dual form			414.2.e.e.139.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.416383 + 1.68126i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.229999 - 0.398369i) q^{5} +(1.24782 + 1.20123i) q^{6} +(2.38325 - 4.12791i) q^{7} -1.00000 q^{8} +(-2.65325 - 1.40009i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.416383 + 1.68126i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.229999 - 0.398369i) q^{5} +(1.24782 + 1.20123i) q^{6} +(2.38325 - 4.12791i) q^{7} -1.00000 q^{8} +(-2.65325 - 1.40009i) q^{9} -0.459997 q^{10} +(0.173714 - 0.300881i) q^{11} +(1.66420 - 0.480030i) q^{12} +(-0.590096 - 1.02208i) q^{13} +(-2.38325 - 4.12791i) q^{14} +(0.765529 - 0.220813i) q^{15} +(-0.500000 + 0.866025i) q^{16} +3.30650 q^{17} +(-2.53914 + 1.59774i) q^{18} +3.47374 q^{19} +(-0.229999 + 0.398369i) q^{20} +(5.94773 + 5.72565i) q^{21} +(-0.173714 - 0.300881i) q^{22} +(0.500000 + 0.866025i) q^{23} +(0.416383 - 1.68126i) q^{24} +(2.39420 - 4.14688i) q^{25} -1.18019 q^{26} +(3.45868 - 3.87782i) q^{27} -4.76650 q^{28} +(1.32629 - 2.29720i) q^{29} +(0.191535 - 0.773373i) q^{30} +(-3.73831 - 6.47494i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.433526 + 0.417339i) q^{33} +(1.65325 - 2.86351i) q^{34} -2.19258 q^{35} +(0.114109 + 2.99783i) q^{36} -1.82382 q^{37} +(1.73687 - 3.00834i) q^{38} +(1.96408 - 0.566528i) q^{39} +(0.229999 + 0.398369i) q^{40} +(5.04230 + 8.73352i) q^{41} +(7.93242 - 2.28806i) q^{42} +(-5.09267 + 8.82077i) q^{43} -0.347427 q^{44} +(0.0524900 + 1.37899i) q^{45} +1.00000 q^{46} +(-3.49804 + 6.05878i) q^{47} +(-1.24782 - 1.20123i) q^{48} +(-7.85975 - 13.6135i) q^{49} +(-2.39420 - 4.14688i) q^{50} +(-1.37677 + 5.55908i) q^{51} +(-0.590096 + 1.02208i) q^{52} +0.836203 q^{53} +(-1.62895 - 4.93422i) q^{54} -0.159815 q^{55} +(-2.38325 + 4.12791i) q^{56} +(-1.44640 + 5.84024i) q^{57} +(-1.32629 - 2.29720i) q^{58} +(2.79724 + 4.84495i) q^{59} +(-0.573994 - 0.552561i) q^{60} +(-0.990767 + 1.71606i) q^{61} -7.47662 q^{62} +(-12.1028 + 7.61561i) q^{63} +1.00000 q^{64} +(-0.271443 + 0.470152i) q^{65} +(0.578189 - 0.166776i) q^{66} +(3.85000 + 6.66840i) q^{67} +(-1.65325 - 2.86351i) q^{68} +(-1.66420 + 0.480030i) q^{69} +(-1.09629 + 1.89883i) q^{70} -15.1020 q^{71} +(2.65325 + 1.40009i) q^{72} +5.28482 q^{73} +(-0.911910 + 1.57947i) q^{74} +(5.97506 + 5.75196i) q^{75} +(-1.73687 - 3.00834i) q^{76} +(-0.828005 - 1.43415i) q^{77} +(0.491412 - 1.98421i) q^{78} +(0.432876 - 0.749763i) q^{79} +0.459997 q^{80} +(5.07948 + 7.42960i) q^{81} +10.0846 q^{82} +(-4.69211 + 8.12698i) q^{83} +(1.98469 - 8.01371i) q^{84} +(-0.760491 - 1.31721i) q^{85} +(5.09267 + 8.82077i) q^{86} +(3.30993 + 3.18634i) q^{87} +(-0.173714 + 0.300881i) q^{88} -8.11127 q^{89} +(1.22049 + 0.644039i) q^{90} -5.62539 q^{91} +(0.500000 - 0.866025i) q^{92} +(12.4426 - 3.58900i) q^{93} +(3.49804 + 6.05878i) q^{94} +(-0.798954 - 1.38383i) q^{95} +(-1.66420 + 0.480030i) q^{96} +(8.80072 - 15.2433i) q^{97} -15.7195 q^{98} +(-0.882166 + 0.555097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9} + 10 q^{10} + 6 q^{11} - 6 q^{13} + 3 q^{14} + 7 q^{15} - 6 q^{16} - 8 q^{17} - 10 q^{18} + 4 q^{19} + 5 q^{20} + 17 q^{21} - 6 q^{22} + 6 q^{23} + q^{25} - 12 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} - q^{30} - 6 q^{31} + 6 q^{32} + 9 q^{33} - 4 q^{34} - 34 q^{35} - 2 q^{36} + 8 q^{37} + 2 q^{38} + 23 q^{39} - 5 q^{40} + 15 q^{41} + 7 q^{42} - 14 q^{43} - 12 q^{44} - 37 q^{45} + 12 q^{46} + 9 q^{47} - 5 q^{49} - q^{50} + 9 q^{51} - 6 q^{52} - 10 q^{53} - 9 q^{54} + 16 q^{55} + 3 q^{56} + 37 q^{57} - 12 q^{58} + 18 q^{59} - 8 q^{60} - 3 q^{61} - 12 q^{62} - 42 q^{63} + 12 q^{64} + 9 q^{65} + 3 q^{66} + 8 q^{67} + 4 q^{68} - 17 q^{70} - 18 q^{71} + 8 q^{72} - 32 q^{73} + 4 q^{74} + 34 q^{75} - 2 q^{76} - q^{77} + 22 q^{78} - 7 q^{79} - 10 q^{80} - 56 q^{81} + 30 q^{82} + 3 q^{83} - 10 q^{84} + 7 q^{85} + 14 q^{86} - 9 q^{87} - 6 q^{88} - 42 q^{89} - 17 q^{90} + 18 q^{91} + 6 q^{92} + 69 q^{93} - 9 q^{94} + 11 q^{95} + 13 q^{97} - 10 q^{98} - 60 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9 + 10 * q^10 + 6 * q^11 - 6 * q^13 + 3 * q^14 + 7 * q^15 - 6 * q^16 - 8 * q^17 - 10 * q^18 + 4 * q^19 + 5 * q^20 + 17 * q^21 - 6 * q^22 + 6 * q^23 + q^25 - 12 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 - q^30 - 6 * q^31 + 6 * q^32 + 9 * q^33 - 4 * q^34 - 34 * q^35 - 2 * q^36 + 8 * q^37 + 2 * q^38 + 23 * q^39 - 5 * q^40 + 15 * q^41 + 7 * q^42 - 14 * q^43 - 12 * q^44 - 37 * q^45 + 12 * q^46 + 9 * q^47 - 5 * q^49 - q^50 + 9 * q^51 - 6 * q^52 - 10 * q^53 - 9 * q^54 + 16 * q^55 + 3 * q^56 + 37 * q^57 - 12 * q^58 + 18 * q^59 - 8 * q^60 - 3 * q^61 - 12 * q^62 - 42 * q^63 + 12 * q^64 + 9 * q^65 + 3 * q^66 + 8 * q^67 + 4 * q^68 - 17 * q^70 - 18 * q^71 + 8 * q^72 - 32 * q^73 + 4 * q^74 + 34 * q^75 - 2 * q^76 - q^77 + 22 * q^78 - 7 * q^79 - 10 * q^80 - 56 * q^81 + 30 * q^82 + 3 * q^83 - 10 * q^84 + 7 * q^85 + 14 * q^86 - 9 * q^87 - 6 * q^88 - 42 * q^89 - 17 * q^90 + 18 * q^91 + 6 * q^92 + 69 * q^93 - 9 * q^94 + 11 * q^95 + 13 * q^97 - 10 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.416383	+	1.68126i	−0.240399	+	0.970674i
$3$	−0.416383	+	1.68126i	−0.240399	+	0.970674i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.229999	−	0.398369i	−0.102858	−	0.178156i	0.810003	−	0.586426i	$-0.199466\pi$
$5$	−0.229999	−	0.398369i	−0.102858	−	0.178156i	−0.912861	+	0.408270i	$0.866132\pi$
$6$	1.24782	+	1.20123i	0.509420	+	0.490399i
$7$	2.38325	−	4.12791i	0.900784	−	1.56020i	0.0743044	−	0.997236i	$-0.476326\pi$
$7$	2.38325	−	4.12791i	0.900784	−	1.56020i	0.826479	−	0.562967i	$-0.190340\pi$
$8$	−1.00000			−0.353553
$9$	−2.65325	−	1.40009i	−0.884417	−	0.466698i
$10$	−0.459997			−0.145464
$11$	0.173714	−	0.300881i	0.0523766	−	0.0907189i	−0.838648	−	0.544673i	$-0.816654\pi$
$11$	0.173714	−	0.300881i	0.0523766	−	0.0907189i	0.891025	+	0.453954i	$0.149987\pi$
$12$	1.66420	−	0.480030i	0.480414	−	0.138573i
$13$	−0.590096	−	1.02208i	−0.163663	−	0.283473i	0.772517	−	0.634995i	$-0.218998\pi$
$13$	−0.590096	−	1.02208i	−0.163663	−	0.283473i	−0.936180	+	0.351522i	$0.885664\pi$
$14$	−2.38325	−	4.12791i	−0.636950	−	1.10323i
$15$	0.765529	−	0.220813i	0.197659	−	0.0570136i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.30650			0.801944			0.400972	−	0.916090i	$-0.368672\pi$
$17$	3.30650			0.801944			0.400972	+	0.916090i	$0.368672\pi$
$18$	−2.53914	+	1.59774i	−0.598481	+	0.376590i
$19$	3.47374			0.796930			0.398465	−	0.917184i	$-0.369543\pi$
$19$	3.47374			0.796930			0.398465	+	0.917184i	$0.369543\pi$
$20$	−0.229999	+	0.398369i	−0.0514292	+	0.0890781i
$21$	5.94773	+	5.72565i	1.29790	+	1.24944i
$22$	−0.173714	−	0.300881i	−0.0370358	−	0.0641480i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	0.416383	−	1.68126i	0.0849938	−	0.343185i
$25$	2.39420	−	4.14688i	0.478840	−	0.829376i
$26$	−1.18019			−0.231455
$27$	3.45868	−	3.87782i	0.665624	−	0.746287i
$28$	−4.76650			−0.900784
$29$	1.32629	−	2.29720i	0.246285	−	0.426579i	−0.716207	−	0.697888i	$-0.754123\pi$
$29$	1.32629	−	2.29720i	0.246285	−	0.426579i	0.962492	+	0.271309i	$0.0874567\pi$
$30$	0.191535	−	0.773373i	0.0349693	−	0.141198i
$31$	−3.73831	−	6.47494i	−0.671420	−	1.16293i	−0.977502	−	0.210928i	$-0.932351\pi$
$31$	−3.73831	−	6.47494i	−0.671420	−	1.16293i	0.306081	−	0.952005i	$-0.400982\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.433526	+	0.417339i	0.0754673	+	0.0726493i
$34$	1.65325	−	2.86351i	0.283530	−	0.491089i
$35$	−2.19258			−0.370613
$36$	0.114109	+	2.99783i	0.0190182	+	0.499638i
$37$	−1.82382			−0.299834			−0.149917	−	0.988699i	$-0.547901\pi$
$37$	−1.82382			−0.299834			−0.149917	+	0.988699i	$0.547901\pi$
$38$	1.73687	−	3.00834i	0.281757	−	0.488018i
$39$	1.96408	−	0.566528i	0.314504	−	0.0907171i
$40$	0.229999	+	0.398369i	0.0363660	+	0.0629877i
$41$	5.04230	+	8.73352i	0.787475	+	1.36395i	0.927509	+	0.373800i	$0.121945\pi$
$41$	5.04230	+	8.73352i	0.787475	+	1.36395i	−0.140034	+	0.990147i	$0.544721\pi$
$42$	7.93242	−	2.28806i	1.22400	−	0.353056i
$43$	−5.09267	+	8.82077i	−0.776625	+	1.34515i	0.157251	+	0.987559i	$0.449737\pi$
$43$	−5.09267	+	8.82077i	−0.776625	+	1.34515i	−0.933876	+	0.357596i	$0.883597\pi$
$44$	−0.347427			−0.0523766
$45$	0.0524900	+	1.37899i	0.00782474	+	0.205568i
$46$	1.00000			0.147442
$47$	−3.49804	+	6.05878i	−0.510241	+	0.883763i	0.489689	+	0.871897i	$0.337110\pi$
$47$	−3.49804	+	6.05878i	−0.510241	+	0.883763i	−0.999930	+	0.0118660i	$0.996223\pi$
$48$	−1.24782	−	1.20123i	−0.180107	−	0.173382i
$49$	−7.85975	−	13.6135i	−1.12282	−	1.94478i
$50$	−2.39420	−	4.14688i	−0.338591	−	0.586457i
$51$	−1.37677	+	5.55908i	−0.192786	+	0.778427i
$52$	−0.590096	+	1.02208i	−0.0818316	+	0.141737i
$53$	0.836203			0.114861			0.0574307	−	0.998349i	$-0.481709\pi$
$53$	0.836203			0.114861			0.0574307	+	0.998349i	$0.481709\pi$
$54$	−1.62895	−	4.93422i	−0.221672	−	0.671462i
$55$	−0.159815			−0.0215495
$56$	−2.38325	+	4.12791i	−0.318475	+	0.551615i
$57$	−1.44640	+	5.84024i	−0.191581	+	0.773559i
$58$	−1.32629	−	2.29720i	−0.174150	−	0.301637i
$59$	2.79724	+	4.84495i	0.364169	+	0.630759i	0.988642	−	0.150287i	$-0.0480197\pi$
$59$	2.79724	+	4.84495i	0.364169	+	0.630759i	−0.624473	+	0.781046i	$0.714686\pi$
$60$	−0.573994	−	0.552561i	−0.0741023	−	0.0713353i
$61$	−0.990767	+	1.71606i	−0.126855	+	0.219719i	−0.922456	−	0.386101i	$-0.873822\pi$
$61$	−0.990767	+	1.71606i	−0.126855	+	0.219719i	0.795602	+	0.605820i	$0.207155\pi$
$62$	−7.47662			−0.949531
$63$	−12.1028	+	7.61561i	−1.52481	+	0.959476i
$64$	1.00000			0.125000
$65$	−0.271443	+	0.470152i	−0.0336683	+	0.0583152i
$66$	0.578189	−	0.166776i	0.0711701	−	0.0205287i
$67$	3.85000	+	6.66840i	0.470353	+	0.814675i	0.999425	−	0.0339018i	$-0.0107934\pi$
$67$	3.85000	+	6.66840i	0.470353	+	0.814675i	−0.529072	+	0.848577i	$0.677460\pi$
$68$	−1.65325	−	2.86351i	−0.200486	−	0.347252i
$69$	−1.66420	+	0.480030i	−0.200346	+	0.0577889i
$70$	−1.09629	+	1.89883i	−0.131031	+	0.226953i
$71$	−15.1020			−1.79228			−0.896139	−	0.443773i	$-0.853640\pi$
$71$	−15.1020			−1.79228			−0.896139	+	0.443773i	$0.853640\pi$
$72$	2.65325	+	1.40009i	0.312689	+	0.165003i
$73$	5.28482			0.618542			0.309271	−	0.950974i	$-0.399915\pi$
$73$	5.28482			0.618542			0.309271	+	0.950974i	$0.399915\pi$
$74$	−0.911910	+	1.57947i	−0.106007	+	0.183610i
$75$	5.97506	+	5.75196i	0.689941	+	0.664179i
$76$	−1.73687	−	3.00834i	−0.199232	−	0.345081i
$77$	−0.828005	−	1.43415i	−0.0943600	−	0.163436i
$78$	0.491412	−	1.98421i	0.0556414	−	0.224667i
$79$	0.432876	−	0.749763i	0.0487023	−	0.0843549i	−0.840647	−	0.541584i	$-0.817825\pi$
$79$	0.432876	−	0.749763i	0.0487023	−	0.0843549i	0.889349	+	0.457229i	$0.151158\pi$
$80$	0.459997			0.0514292
$81$	5.07948	+	7.42960i	0.564387	+	0.825511i
$82$	10.0846			1.11366
$83$	−4.69211	+	8.12698i	−0.515026	+	0.892052i	0.484821	+	0.874613i	$0.338885\pi$
$83$	−4.69211	+	8.12698i	−0.515026	+	0.892052i	−0.999848	+	0.0174389i	$0.994449\pi$
$84$	1.98469	−	8.01371i	0.216547	−	0.874367i
$85$	−0.760491	−	1.31721i	−0.0824868	−	0.142871i
$86$	5.09267	+	8.82077i	0.549157	+	0.951168i
$87$	3.30993	+	3.18634i	0.354862	+	0.341612i
$88$	−0.173714	+	0.300881i	−0.0185179	+	0.0320740i
$89$	−8.11127			−0.859793			−0.429896	−	0.902878i	$-0.641450\pi$
$89$	−8.11127			−0.859793			−0.429896	+	0.902878i	$0.641450\pi$
$90$	1.22049	+	0.644039i	0.128651	+	0.0678876i
$91$	−5.62539			−0.589701
$92$	0.500000	−	0.866025i	0.0521286	−	0.0902894i
$93$	12.4426	−	3.58900i	1.29024	−	0.372162i
$94$	3.49804	+	6.05878i	0.360795	+	0.624915i
$95$	−0.798954	−	1.38383i	−0.0819710	−	0.141978i
$96$	−1.66420	+	0.480030i	−0.169852	+	0.0489929i
$97$	8.80072	−	15.2433i	0.893577	−	1.54772i	0.0580217	−	0.998315i	$-0.481521\pi$
$97$	8.80072	−	15.2433i	0.893577	−	1.54772i	0.835556	−	0.549406i	$-0.185146\pi$
$98$	−15.7195			−1.58791
$99$	−0.882166	+	0.555097i	−0.0886611	+	0.0557893i
$100$	−4.78840			−0.478840
$101$	7.27000	−	12.5920i	0.723392	−	1.25295i	−0.236241	−	0.971695i	$-0.575915\pi$
$101$	7.27000	−	12.5920i	0.723392	−	1.25295i	0.959633	−	0.281257i	$-0.0907513\pi$
$102$	4.12592	+	3.97186i	0.408527	+	0.393273i
$103$	−2.80031	−	4.85028i	−0.275923	−	0.477912i	0.694445	−	0.719546i	$-0.255650\pi$
$103$	−2.80031	−	4.85028i	−0.275923	−	0.477912i	−0.970368	+	0.241634i	$0.922317\pi$
$104$	0.590096	+	1.02208i	0.0578637	+	0.100223i
$105$	0.912951	−	3.68628i	0.0890949	−	0.359744i
$106$	0.418102	−	0.724173i	0.0406096	−	0.0703379i
$107$	−5.98233			−0.578334			−0.289167	−	0.957279i	$-0.593378\pi$
$107$	−5.98233			−0.578334			−0.289167	+	0.957279i	$0.593378\pi$
$108$	−5.08763	−	1.05640i	−0.489558	−	0.101652i
$109$	5.45393			0.522392			0.261196	−	0.965286i	$-0.415883\pi$
$109$	5.45393			0.522392			0.261196	+	0.965286i	$0.415883\pi$
$110$	−0.0799077	+	0.138404i	−0.00761890	+	0.0131963i
$111$	0.759407	−	3.06631i	0.0720797	−	0.291041i
$112$	2.38325	+	4.12791i	0.225196	+	0.390051i
$113$	4.38801	+	7.60026i	0.412789	+	0.714972i	0.995194	−	0.0979273i	$-0.0312213\pi$
$113$	4.38801	+	7.60026i	0.412789	+	0.714972i	−0.582404	+	0.812899i	$0.697888\pi$
$114$	4.33460	+	4.17274i	0.405972	+	0.390813i
$115$	0.229999	−	0.398369i	0.0214475	−	0.0371481i
$116$	−2.65257			−0.246285
$117$	0.134671	+	3.53802i	0.0124503	+	0.327090i
$118$	5.59447			0.515013
$119$	7.88022	−	13.6489i	0.722378	−	1.25120i
$120$	−0.765529	+	0.220813i	−0.0698829	+	0.0201573i
$121$	5.43965	+	9.42175i	0.494513	+	0.856522i
$122$	0.990767	+	1.71606i	0.0896998	+	0.155365i
$123$	−16.7828	+	4.84092i	−1.51326	+	0.436491i
$124$	−3.73831	+	6.47494i	−0.335710	+	0.581467i
$125$	−4.50264			−0.402728
$126$	0.543902	+	14.2891i	0.0484546	+	1.27298i
$127$	−0.205400			−0.0182263			−0.00911317	−	0.999958i	$-0.502901\pi$
$127$	−0.205400			−0.0182263			−0.00911317	+	0.999958i	$0.502901\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−12.7095	−	12.2349i	−1.11901	−	1.07722i
$130$	0.271443	+	0.470152i	0.0238071	+	0.0412351i
$131$	9.16524	+	15.8747i	0.800771	+	1.38698i	0.919109	+	0.394002i	$0.128910\pi$
$131$	9.16524	+	15.8747i	0.800771	+	1.38698i	−0.118339	+	0.992973i	$0.537757\pi$
$132$	0.144663	−	0.584114i	0.0125913	−	0.0508406i
$133$	8.27878	−	14.3393i	0.717861	−	1.24337i
$134$	7.70001			0.665179
$135$	−2.34030	−	0.485940i	−0.201421	−	0.0418230i
$136$	−3.30650			−0.283530
$137$	−1.04018	+	1.80165i	−0.0888688	+	0.153925i	−0.907033	−	0.421059i	$-0.861659\pi$
$137$	−1.04018	+	1.80165i	−0.0888688	+	0.153925i	0.818164	+	0.574984i	$0.194992\pi$
$138$	−0.416383	+	1.68126i	−0.0354449	+	0.143118i
$139$	5.24536	+	9.08523i	0.444905	+	0.770599i	0.998046	−	0.0624893i	$-0.0199039\pi$
$139$	5.24536	+	9.08523i	0.444905	+	0.770599i	−0.553140	+	0.833088i	$0.686571\pi$
$140$	1.09629	+	1.89883i	0.0926532	+	0.160480i
$141$	−8.72984	−	8.40387i	−0.735185	−	0.707733i
$142$	−7.55100	+	13.0787i	−0.633666	+	1.09754i
$143$	−0.410031			−0.0342885
$144$	2.53914	−	1.59774i	0.211595	−	0.133145i
$145$	−1.22018			−0.101330
$146$	2.64241	−	4.57679i	0.218688	−	0.378778i
$147$	26.1605	−	7.54584i	2.15768	−	0.622371i
$148$	0.911910	+	1.57947i	0.0749585	+	0.129832i
$149$	10.4825	+	18.1561i	0.858756	+	1.48741i	0.873116	+	0.487512i	$0.162095\pi$
$149$	10.4825	+	18.1561i	0.858756	+	1.48741i	−0.0143603	+	0.999897i	$0.504571\pi$
$150$	7.96887	−	2.29858i	0.650656	−	0.187678i
$151$	−11.1890	+	19.3799i	−0.910548	+	1.57712i	−0.0972564	+	0.995259i	$0.531007\pi$
$151$	−11.1890	+	19.3799i	−0.910548	+	1.57712i	−0.813292	+	0.581856i	$0.802327\pi$
$152$	−3.47374			−0.281757
$153$	−8.77298	−	4.62941i	−0.709253	−	0.374266i
$154$	−1.65601			−0.133445
$155$	−1.71961	+	2.97845i	−0.138123	+	0.239235i
$156$	−1.47267	−	1.41768i	−0.117908	−	0.113505i
$157$	−1.53692	−	2.66203i	−0.122660	−	0.212453i	0.798156	−	0.602451i	$-0.205809\pi$
$157$	−1.53692	−	2.66203i	−0.122660	−	0.212453i	−0.920816	+	0.389998i	$0.872476\pi$
$158$	−0.432876	−	0.749763i	−0.0344377	−	0.0596479i
$159$	−0.348181	+	1.40587i	−0.0276125	+	0.111493i
$160$	0.229999	−	0.398369i	0.0181830	−	0.0314939i
$161$	4.76650			0.375653
$162$	8.97396	−	0.684160i	0.705061	−	0.0537527i
$163$	10.6473			0.833962			0.416981	−	0.908915i	$-0.363088\pi$
$163$	10.6473			0.833962			0.416981	+	0.908915i	$0.363088\pi$
$164$	5.04230	−	8.73352i	0.393738	−	0.681974i
$165$	0.0665444	−	0.268691i	0.00518047	−	0.0209176i
$166$	4.69211	+	8.12698i	0.364179	+	0.630776i
$167$	−11.0484	−	19.1365i	−0.854954	−	1.48082i	−0.876688	−	0.481060i	$-0.840252\pi$
$167$	−11.0484	−	19.1365i	−0.854954	−	1.48082i	0.0217341	−	0.999764i	$-0.493081\pi$
$168$	−5.94773	−	5.72565i	−0.458878	−	0.441743i
$169$	5.80357	−	10.0521i	0.446429	−	0.773237i
$170$	−1.52098			−0.116654
$171$	−9.21669	−	4.86355i	−0.704818	−	0.371925i
$172$	10.1853			0.776625
$173$	0.550564	−	0.953606i	0.0418586	−	0.0725013i	−0.844337	−	0.535812i	$-0.820005\pi$
$173$	0.550564	−	0.953606i	0.0418586	−	0.0725013i	0.886196	+	0.463311i	$0.153339\pi$
$174$	4.41442	−	1.27332i	0.334656	−	0.0965298i
$175$	−11.4120	−	19.7661i	−0.862663	−	1.49418i
$176$	0.173714	+	0.300881i	0.0130941	+	0.0226797i
$177$	−9.31033	+	2.68552i	−0.699808	+	0.201856i
$178$	−4.05563	+	7.02456i	−0.303983	+	0.526513i
$179$	18.0395			1.34834			0.674169	−	0.738577i	$-0.264502\pi$
$179$	18.0395			1.34834			0.674169	+	0.738577i	$0.264502\pi$
$180$	1.16800	−	0.734954i	0.0870574	−	0.0547802i
$181$	−1.57627			−0.117163			−0.0585816	−	0.998283i	$-0.518658\pi$
$181$	−1.57627			−0.117163			−0.0585816	+	0.998283i	$0.518658\pi$
$182$	−2.81269	+	4.87173i	−0.208491	+	0.361116i
$183$	−2.47260	−	2.38027i	−0.182780	−	0.175955i
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	0.419476	+	0.726554i	0.0308405	+	0.0534173i
$186$	3.11314	−	12.5701i	0.228266	−	0.921686i
$187$	0.574384	−	0.994862i	0.0420031	−	0.0727515i
$188$	6.99607			0.510241
$189$	−7.76439	−	23.5190i	−0.564776	−	1.71075i
$190$	−1.59791			−0.115924
$191$	5.12166	−	8.87097i	0.370590	−	0.641881i	−0.619066	−	0.785339i	$-0.712489\pi$
$191$	5.12166	−	8.87097i	0.370590	−	0.641881i	0.989656	+	0.143458i	$0.0458222\pi$
$192$	−0.416383	+	1.68126i	−0.0300498	+	0.121334i
$193$	5.85481	+	10.1408i	0.421439	+	0.729953i	0.996080	−	0.0884517i	$-0.0281919\pi$
$193$	5.85481	+	10.1408i	0.421439	+	0.729953i	−0.574642	+	0.818405i	$0.694859\pi$
$194$	−8.80072	−	15.2433i	−0.631855	−	1.09440i
$195$	−0.677423	−	0.652128i	−0.0485113	−	0.0466999i
$196$	−7.85975	+	13.6135i	−0.561411	+	0.972392i
$197$	−9.42228			−0.671310			−0.335655	−	0.941985i	$-0.608958\pi$
$197$	−9.42228			−0.671310			−0.335655	+	0.941985i	$0.608958\pi$
$198$	0.0396447	+	1.04153i	0.00281742	+	0.0740181i
$199$	−7.09412			−0.502889			−0.251445	−	0.967872i	$-0.580906\pi$
$199$	−7.09412			−0.502889			−0.251445	+	0.967872i	$0.580906\pi$
$200$	−2.39420	+	4.14688i	−0.169296	+	0.293229i
$201$	−12.8144	+	3.69624i	−0.903856	+	0.260713i
$202$	−7.27000	−	12.5920i	−0.511515	−	0.885970i
$203$	−6.32174	−	10.9496i	−0.443699	−	0.768510i
$204$	5.50269	−	1.58722i	0.385265	−	0.111128i
$205$	2.31944	−	4.01740i	0.161997	−	0.280587i
$206$	−5.60062			−0.390214
$207$	−0.114109	−	2.99783i	−0.00793114	−	0.208364i
$208$	1.18019			0.0818316
$209$	0.603435	−	1.04518i	0.0417405	−	0.0722966i
$210$	−2.73594	−	2.63378i	−0.188798	−	0.181748i
$211$	4.06155	+	7.03481i	0.279609	+	0.484296i	0.971287	−	0.237909i	$-0.0764620\pi$
$211$	4.06155	+	7.03481i	0.279609	+	0.484296i	−0.691679	+	0.722205i	$0.743129\pi$
$212$	−0.418102	−	0.724173i	−0.0287153	−	0.0497364i
$213$	6.28821	−	25.3904i	0.430861	−	1.73972i
$214$	−2.99117	+	5.18085i	−0.204472	+	0.354156i
$215$	4.68523			0.319530
$216$	−3.45868	+	3.87782i	−0.235334	+	0.263852i
$217$	−35.6373			−2.41922
$218$	2.72697	−	4.72325i	0.184694	−	0.319899i
$219$	−2.20051	+	8.88515i	−0.148697	+	0.600403i
$220$	0.0799077	+	0.138404i	0.00538738	+	0.00933121i
$221$	−1.95115	−	3.37950i	−0.131249	−	0.227330i
$222$	−2.27580	−	2.19082i	−0.152742	−	0.147038i
$223$	−6.08544	+	10.5403i	−0.407511	+	0.705830i	−0.994610	−	0.103685i	$-0.966937\pi$
$223$	−6.08544	+	10.5403i	−0.407511	+	0.705830i	0.587099	+	0.809515i	$0.300270\pi$
$224$	4.76650			0.318475
$225$	−12.1584	+	7.65060i	−0.810562	+	0.510040i
$226$	8.77602			0.583772
$227$	4.06803	−	7.04603i	0.270005	−	0.467662i	−0.698858	−	0.715260i	$-0.746308\pi$
$227$	4.06803	−	7.04603i	0.270005	−	0.467662i	0.968863	+	0.247599i	$0.0796415\pi$
$228$	5.78100	−	1.66750i	0.382856	−	0.110433i
$229$	8.61377	+	14.9195i	0.569214	+	0.985907i	0.996644	+	0.0818587i	$0.0260856\pi$
$229$	8.61377	+	14.9195i	0.569214	+	0.985907i	−0.427430	+	0.904048i	$0.640581\pi$
$230$	−0.229999	−	0.398369i	−0.0151657	−	0.0262677i
$231$	2.75594	−	0.794935i	0.181327	−	0.0523029i
$232$	−1.32629	+	2.29720i	−0.0870750	+	0.150818i
$233$	−5.13331			−0.336294			−0.168147	−	0.985762i	$-0.553778\pi$
$233$	−5.13331			−0.336294			−0.168147	+	0.985762i	$0.553778\pi$
$234$	3.13135	+	1.65238i	0.204703	+	0.108019i
$235$	3.21817			0.209930
$236$	2.79724	−	4.84495i	0.182085	−	0.315380i
$237$	1.08030	+	1.03996i	0.0701732	+	0.0675529i
$238$	−7.88022	−	13.6489i	−0.510799	−	0.884729i
$239$	9.07465	+	15.7178i	0.586990	+	1.01670i	0.994624	+	0.103552i	$0.0330207\pi$
$239$	9.07465	+	15.7178i	0.586990	+	1.01670i	−0.407634	+	0.913146i	$0.633646\pi$
$240$	−0.191535	+	0.773373i	−0.0123635	+	0.0499210i
$241$	13.4725	−	23.3350i	0.867839	−	1.50314i	0.00363866	−	0.999993i	$-0.498842\pi$
$241$	13.4725	−	23.3350i	0.867839	−	1.50314i	0.864200	−	0.503148i	$-0.167825\pi$
$242$	10.8793			0.699348
$243$	−14.6061	+	5.44635i	−0.936980	+	0.349384i
$244$	1.98153			0.126855
$245$	−3.61546	+	6.26217i	−0.230984	+	0.400075i
$246$	−4.19905	+	16.9548i	−0.267722	+	1.08100i
$247$	−2.04984	−	3.55042i	−0.130428	−	0.225908i
$248$	3.73831	+	6.47494i	0.237383	+	0.411159i
$249$	−11.7098	−	11.2726i	−0.742080	−	0.714371i
$250$	−2.25132	+	3.89940i	−0.142386	+	0.246620i
$251$	−6.60177			−0.416700			−0.208350	−	0.978054i	$-0.566809\pi$
$251$	−6.60177			−0.416700			−0.208350	+	0.978054i	$0.566809\pi$
$252$	12.6467	+	6.67354i	0.796668	+	0.420394i
$253$	0.347427			0.0218425
$254$	−0.102700	+	0.177882i	−0.00644399	+	0.0111613i
$255$	2.53122	−	0.730117i	0.158511	−	0.0457217i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.36680	−	11.0276i	−0.397150	−	0.687884i	0.596223	−	0.802819i	$-0.296667\pi$
$257$	−6.36680	−	11.0276i	−0.397150	−	0.687884i	−0.993373	+	0.114935i	$0.963334\pi$
$258$	−16.9505	+	4.88928i	−1.05529	+	0.304393i
$259$	−4.34662	+	7.52856i	−0.270086	+	0.467802i
$260$	0.542885			0.0336683
$261$	−6.73526	+	4.23811i	−0.416902	+	0.262333i
$262$	18.3305			1.13246
$263$	13.0617	−	22.6236i	0.805420	−	1.39503i	−0.110587	−	0.993866i	$-0.535273\pi$
$263$	13.0617	−	22.6236i	0.805420	−	1.39503i	0.916007	−	0.401162i	$-0.131394\pi$
$264$	−0.433526	−	0.417339i	−0.0266817	−	0.0256854i
$265$	−0.192325	−	0.333118i	−0.0118145	−	0.0204632i
$266$	−8.27878	−	14.3393i	−0.507605	−	0.879197i
$267$	3.37739	−	13.6371i	0.206693	−	0.834579i
$268$	3.85000	−	6.66840i	0.235176	−	0.407337i
$269$	5.60766			0.341905			0.170952	−	0.985279i	$-0.445316\pi$
$269$	5.60766			0.341905			0.170952	+	0.985279i	$0.445316\pi$
$270$	−1.59098	+	1.78379i	−0.0968243	+	0.108558i
$271$	30.8458			1.87375			0.936875	−	0.349665i	$-0.113705\pi$
$271$	30.8458			1.87375			0.936875	+	0.349665i	$0.113705\pi$
$272$	−1.65325	+	2.86351i	−0.100243	+	0.173626i
$273$	2.34231	−	9.45772i	0.141763	−	0.572407i
$274$	1.04018	+	1.80165i	0.0628397	+	0.108842i
$275$	−0.831810	−	1.44074i	−0.0501600	−	0.0868797i
$276$	1.24782	+	1.20123i	0.0751099	+	0.0723053i
$277$	7.33647	−	12.7071i	0.440806	−	0.763498i	−0.556944	−	0.830550i	$-0.688026\pi$
$277$	7.33647	−	12.7071i	0.440806	−	0.763498i	0.997749	+	0.0670522i	$0.0213594\pi$
$278$	10.4907			0.629191
$279$	0.853152	+	22.4136i	0.0510769	+	1.34187i
$280$	2.19258			0.131031
$281$	−4.00470	+	6.93634i	−0.238900	+	0.413787i	−0.960399	−	0.278629i	$-0.910120\pi$
$281$	−4.00470	+	6.93634i	−0.238900	+	0.413787i	0.721499	+	0.692416i	$0.243454\pi$
$282$	−11.6429	+	3.35833i	−0.693324	+	0.199986i
$283$	−7.10917	−	12.3134i	−0.422596	−	0.731958i	0.573597	−	0.819138i	$-0.305548\pi$
$283$	−7.10917	−	12.3134i	−0.422596	−	0.731958i	−0.996193	+	0.0871802i	$0.972214\pi$
$284$	7.55100	+	13.0787i	0.448070	+	0.776079i
$285$	2.65924	−	0.767045i	0.157520	−	0.0454358i
$286$	−0.205015	+	0.355097i	−0.0121228	+	0.0209973i
$287$	48.0682			2.83738
$288$	−0.114109	−	2.99783i	−0.00672395	−	0.176649i
$289$	−6.06705			−0.356885
$290$	−0.610088	+	1.05670i	−0.0358256	+	0.0620518i
$291$	21.9634	+	21.1433i	1.28752	+	1.23944i
$292$	−2.64241	−	4.57679i	−0.154635	−	0.267836i
$293$	−12.6386	−	21.8908i	−0.738357	−	1.27887i	−0.953235	−	0.302231i	$-0.902269\pi$
$293$	−12.6386	−	21.8908i	−0.738357	−	1.27887i	0.214878	−	0.976641i	$-0.431065\pi$
$294$	6.54533	−	26.4285i	0.381732	−	1.54134i
$295$	1.28672	−	2.22867i	0.0749158	−	0.129758i
$296$	1.82382			0.106007
$297$	−0.565941	−	1.71428i	−0.0328392	−	0.0994727i
$298$	20.9649			1.21446
$299$	0.590096	−	1.02208i	0.0341261	−	0.0591082i
$300$	1.99381	−	8.05054i	0.115113	−	0.464798i
$301$	24.2742	+	42.0442i	1.39914	+	2.42339i
$302$	11.1890	+	19.3799i	0.643855	+	1.11519i
$303$	18.1433	+	17.4658i	1.04231	+	1.00339i
$304$	−1.73687	+	3.00834i	−0.0996162	+	0.172540i
$305$	0.911500			0.0521923
$306$	−8.39568	+	5.28292i	−0.479949	+	0.302004i
$307$	−28.2454			−1.61205			−0.806024	−	0.591883i	$-0.798385\pi$
$307$	−28.2454			−1.61205			−0.806024	+	0.591883i	$0.798385\pi$
$308$	−0.828005	+	1.43415i	−0.0471800	+	0.0817181i
$309$	9.32057	−	2.68847i	0.530229	−	0.152942i
$310$	1.71961	+	2.97845i	0.0976674	+	0.169165i
$311$	0.0799903	+	0.138547i	0.00453583	+	0.00785630i	0.868284	−	0.496067i	$-0.165223\pi$
$311$	0.0799903	+	0.138547i	0.00453583	+	0.00785630i	−0.863749	+	0.503923i	$0.831890\pi$
$312$	−1.96408	+	0.566528i	−0.111194	+	0.0320734i
$313$	−16.4684	+	28.5241i	−0.930849	+	1.61228i	−0.148975	+	0.988841i	$0.547597\pi$
$313$	−16.4684	+	28.5241i	−0.930849	+	1.61228i	−0.781874	+	0.623437i	$0.785736\pi$
$314$	−3.07385			−0.173467
$315$	5.81745	+	3.06981i	0.327776	+	0.172964i
$316$	−0.865752			−0.0487023
$317$	2.58415	−	4.47587i	0.145140	−	0.251390i	−0.784285	−	0.620401i	$-0.786970\pi$
$317$	2.58415	−	4.47587i	0.145140	−	0.251390i	0.929425	+	0.369011i	$0.120303\pi$
$318$	1.04343	+	1.00447i	0.0585127	+	0.0563278i
$319$	−0.460788	−	0.798108i	−0.0257992	−	0.0446855i
$320$	−0.229999	−	0.398369i	−0.0128573	−	0.0222695i
$321$	2.49094	−	10.0578i	0.139031	−	0.561374i
$322$	2.38325	−	4.12791i	0.132813	−	0.230039i
$323$	11.4859			0.639093
$324$	3.89448	−	8.11376i	0.216360	−	0.450764i
$325$	−5.65124			−0.313474
$326$	5.32366	−	9.22084i	0.294850	−	0.510695i
$327$	−2.27092	+	9.16946i	−0.125582	+	0.507073i
$328$	−5.04230	−	8.73352i	−0.278415	−	0.482228i
$329$	16.6734	+	28.8792i	0.919234	+	1.59216i
$330$	−0.199421	−	0.191975i	−0.0109778	−	0.0105679i
$331$	3.39948	−	5.88807i	0.186852	−	0.323638i	−0.757347	−	0.653013i	$-0.773505\pi$
$331$	3.39948	−	5.88807i	0.186852	−	0.323638i	0.944199	+	0.329375i	$0.106838\pi$
$332$	9.38423			0.515026
$333$	4.83905	+	2.55352i	0.265178	+	0.139932i
$334$	−22.0969			−1.20909
$335$	1.77099	−	3.06745i	0.0967595	−	0.167592i
$336$	−7.93242	+	2.28806i	−0.432749	+	0.124824i
$337$	3.57823	+	6.19768i	0.194919	+	0.337609i	0.946874	−	0.321605i	$-0.104222\pi$
$337$	3.57823	+	6.19768i	0.194919	+	0.337609i	−0.751955	+	0.659214i	$0.770889\pi$
$338$	−5.80357	−	10.0521i	−0.315673	−	0.546761i
$339$	−14.6051	+	4.21276i	−0.793239	+	0.228806i
$340$	−0.760491	+	1.31721i	−0.0412434	+	0.0714357i
$341$	−2.59758			−0.140667
$342$	−8.82031	+	5.55011i	−0.476948	+	0.300116i
$343$	−41.5615			−2.24411
$344$	5.09267	−	8.82077i	0.274578	−	0.475584i
$345$	0.573994	+	0.552561i	0.0309028	+	0.0297489i
$346$	−0.550564	−	0.953606i	−0.0295985	−	0.0512662i
$347$	1.43008	+	2.47696i	0.0767705	+	0.132970i	0.901855	−	0.432039i	$-0.142206\pi$
$347$	1.43008	+	2.47696i	0.0767705	+	0.132970i	−0.825084	+	0.565010i	$0.808872\pi$
$348$	1.10449	−	4.45966i	0.0592066	−	0.239063i
$349$	5.11582	−	8.86086i	0.273844	−	0.474311i	−0.695999	−	0.718043i	$-0.745038\pi$
$349$	5.11582	−	8.86086i	0.273844	−	0.474311i	0.969843	+	0.243732i	$0.0783716\pi$
$350$	−22.8239			−1.21999
$351$	−6.00439	−	1.24675i	−0.320491	−	0.0665467i
$352$	0.347427			0.0185179
$353$	6.04977	−	10.4785i	0.321997	−	0.557715i	−0.658903	−	0.752228i	$-0.728979\pi$
$353$	6.04977	−	10.4785i	0.321997	−	0.557715i	0.980900	+	0.194513i	$0.0623126\pi$
$354$	−2.32944	+	9.40574i	−0.123808	+	0.499910i
$355$	3.47344	+	6.01617i	0.184351	+	0.319305i
$356$	4.05563	+	7.02456i	0.214948	+	0.372301i
$357$	19.6662	+	18.9319i	1.04084	+	1.00198i
$358$	9.01976	−	15.6227i	0.476709	−	0.825685i
$359$	−14.6702			−0.774263			−0.387132	−	0.922025i	$-0.626534\pi$
$359$	−14.6702			−0.774263			−0.387132	+	0.922025i	$0.626534\pi$
$360$	−0.0524900	−	1.37899i	−0.00276646	−	0.0726793i
$361$	−6.93316			−0.364903
$362$	−0.788134	+	1.36509i	−0.0414234	+	0.0717475i
$363$	−18.1054	+	5.22239i	−0.950285	+	0.274105i
$364$	2.81269	+	4.87173i	0.147425	+	0.255348i
$365$	−1.21550	−	2.10531i	−0.0636223	−	0.110197i
$366$	−3.29767	+	0.951196i	−0.172372	+	0.0497198i
$367$	−14.2292	+	24.6458i	−0.742760	+	1.28650i	0.208474	+	0.978028i	$0.433150\pi$
$367$	−14.2292	+	24.6458i	−0.742760	+	1.28650i	−0.951234	+	0.308471i	$0.900183\pi$
$368$	−1.00000			−0.0521286
$369$	−1.15075	−	30.2319i	−0.0599055	−	1.57381i
$370$	0.838952			0.0436150
$371$	1.99288	−	3.45177i	0.103465	−	0.179207i
$372$	−9.32947	−	8.98111i	−0.483711	−	0.465649i
$373$	15.9392	+	27.6076i	0.825302	+	1.42947i	0.901688	+	0.432387i	$0.142329\pi$
$373$	15.9392	+	27.6076i	0.825302	+	1.42947i	−0.0763855	+	0.997078i	$0.524338\pi$
$374$	−0.574384	−	0.994862i	−0.0297007	−	0.0514431i
$375$	1.87482	−	7.57009i	0.0968153	−	0.390918i
$376$	3.49804	−	6.05878i	0.180397	−	0.312458i
$377$	−3.13055			−0.161231
$378$	−24.2502	−	5.03532i	−1.24730	−	0.258989i
$379$	−35.1028			−1.80311			−0.901556	−	0.432663i	$-0.857574\pi$
$379$	−35.1028			−1.80311			−0.901556	+	0.432663i	$0.857574\pi$
$380$	−0.798954	+	1.38383i	−0.0409855	+	0.0709890i
$381$	0.0855252	−	0.345331i	0.00438159	−	0.0176918i
$382$	−5.12166	−	8.87097i	−0.262047	−	0.453878i
$383$	5.18398	+	8.97892i	0.264889	+	0.458802i	0.967535	−	0.252739i	$-0.0813313\pi$
$383$	5.18398	+	8.97892i	0.264889	+	0.458802i	−0.702645	+	0.711540i	$0.747998\pi$
$384$	1.24782	+	1.20123i	0.0636775	+	0.0612998i
$385$	−0.380880	+	0.659704i	−0.0194114	+	0.0336216i
$386$	11.7096			0.596004
$387$	25.8620	−	16.2735i	1.31464	−	0.827228i
$388$	−17.6014			−0.893577
$389$	−15.7506	+	27.2808i	−0.798585	+	1.38319i	0.121952	+	0.992536i	$0.461085\pi$
$389$	−15.7506	+	27.2808i	−0.798585	+	1.38319i	−0.920537	+	0.390655i	$0.872249\pi$
$390$	−0.903471	+	0.260601i	−0.0457490	+	0.0131961i
$391$	1.65325	+	2.86351i	0.0836085	+	0.144814i
$392$	7.85975	+	13.6135i	0.396978	+	0.687585i
$393$	−30.5056	+	8.79919i	−1.53881	+	0.443860i
$394$	−4.71114	+	8.15994i	−0.237344	+	0.411092i
$395$	−0.398243			−0.0200378
$396$	0.921811	+	0.486430i	0.0463227	+	0.0244440i
$397$	0.761736			0.0382305			0.0191152	−	0.999817i	$-0.493915\pi$
$397$	0.761736			0.0382305			0.0191152	+	0.999817i	$0.493915\pi$
$398$	−3.54706	+	6.14369i	−0.177798	+	0.307955i
$399$	20.6609	+	19.8894i	1.03434	+	0.995714i
$400$	2.39420	+	4.14688i	0.119710	+	0.207344i
$401$	2.01111	+	3.48335i	0.100430	+	0.173950i	0.911862	−	0.410497i	$-0.134645\pi$
$401$	2.01111	+	3.48335i	0.100430	+	0.173950i	−0.811432	+	0.584447i	$0.801311\pi$
$402$	−3.20615	+	12.9457i	−0.159908	+	0.645672i
$403$	−4.41192	+	7.64168i	−0.219774	+	0.380659i
$404$	−14.5400			−0.723392
$405$	1.79145	−	3.73230i	0.0890178	−	0.185460i
$406$	−12.6435			−0.627486
$407$	−0.316822	+	0.548752i	−0.0157043	+	0.0272006i
$408$	1.37677	−	5.55908i	0.0681603	−	0.275215i
$409$	−5.56843	−	9.64480i	−0.275341	−	0.476905i	0.694880	−	0.719126i	$-0.255457\pi$
$409$	−5.56843	−	9.64480i	−0.275341	−	0.476905i	−0.970221	+	0.242221i	$0.922124\pi$
$410$	−2.31944	−	4.01740i	−0.114549	−	0.198405i
$411$	−2.59592	−	2.49899i	−0.128047	−	0.123266i
$412$	−2.80031	+	4.85028i	−0.137961	+	0.238956i
$413$	26.6660			1.31215
$414$	−2.65325	−	1.40009i	−0.130400	−	0.0688108i
$415$	4.31672			0.211899
$416$	0.590096	−	1.02208i	0.0289319	−	0.0501114i
$417$	−17.4587	+	5.03586i	−0.854955	+	0.246607i
$418$	−0.603435	−	1.04518i	−0.0295150	−	0.0511214i
$419$	−6.06083	−	10.4977i	−0.296091	−	0.512845i	0.679147	−	0.734002i	$-0.262350\pi$
$419$	−6.06083	−	10.4977i	−0.296091	−	0.512845i	−0.975238	+	0.221157i	$0.929017\pi$
$420$	−3.64889	+	1.05250i	−0.178048	+	0.0513569i
$421$	−2.42944	+	4.20792i	−0.118404	+	0.205081i	−0.919135	−	0.393942i	$-0.871111\pi$
$421$	−2.42944	+	4.20792i	−0.118404	+	0.205081i	0.800731	+	0.599024i	$0.204444\pi$
$422$	8.12310			0.395426
$423$	17.7640	−	11.1779i	0.863716	−	0.543487i
$424$	−0.836203			−0.0406096
$425$	7.91643	−	13.7117i	0.384003	−	0.665113i
$426$	−18.8446	−	18.1409i	−0.913023	−	0.878931i
$427$	4.72249	+	8.17959i	0.228537	+	0.395838i
$428$	2.99117	+	5.18085i	0.144584	+	0.250426i
$429$	0.170730	−	0.689367i	0.00824291	−	0.0332830i
$430$	2.34261	−	4.05753i	0.112971	−	0.195671i
$431$	−20.4552			−0.985292			−0.492646	−	0.870230i	$-0.663970\pi$
$431$	−20.4552			−0.985292			−0.492646	+	0.870230i	$0.663970\pi$
$432$	1.62895	+	4.93422i	0.0783729	+	0.237398i
$433$	20.8268			1.00087			0.500436	−	0.865773i	$-0.333173\pi$
$433$	20.8268			1.00087			0.500436	+	0.865773i	$0.333173\pi$
$434$	−17.8186	+	30.8628i	−0.855322	+	1.48146i
$435$	0.508060	−	2.05143i	0.0243596	−	0.0983585i
$436$	−2.72697	−	4.72325i	−0.130598	−	0.226202i
$437$	1.73687	+	3.00834i	0.0830857	+	0.143909i
$438$	6.59451	+	6.34827i	0.315098	+	0.303332i
$439$	−5.59975	+	9.69906i	−0.267262	+	0.462911i	−0.968154	−	0.250357i	$-0.919452\pi$
$439$	−5.59975	+	9.69906i	−0.267262	+	0.462911i	0.700892	+	0.713267i	$0.252785\pi$
$440$	0.159815			0.00761890
$441$	1.79374	+	47.1244i	0.0854163	+	2.24402i
$442$	−3.90231			−0.185614
$443$	12.4842	−	21.6232i	0.593141	−	1.02735i	−0.400666	−	0.916224i	$-0.631221\pi$
$443$	12.4842	−	21.6232i	0.593141	−	1.02735i	0.993806	−	0.111125i	$-0.0354455\pi$
$444$	−3.03521	+	0.875489i	−0.144044	+	0.0415489i
$445$	1.86558	+	3.23128i	0.0884370	+	0.153177i
$446$	6.08544	+	10.5403i	0.288154	+	0.499097i
$447$	−34.8899	+	10.0638i	−1.65023	+	0.476001i
$448$	2.38325	−	4.12791i	0.112598	−	0.195025i
$449$	12.8742			0.607569			0.303785	−	0.952741i	$-0.401750\pi$
$449$	12.8742			0.607569			0.303785	+	0.952741i	$0.401750\pi$
$450$	0.546401	+	14.3548i	0.0257576	+	0.676692i
$451$	3.50366			0.164981
$452$	4.38801	−	7.60026i	0.206395	−	0.357486i
$453$	−27.9237	−	26.8811i	−1.31197	−	1.26298i
$454$	−4.06803	−	7.04603i	−0.190922	−	0.330687i
$455$	1.29383	+	2.24098i	0.0606557	+	0.105059i
$456$	1.44640	−	5.84024i	0.0677341	−	0.273494i
$457$	13.3157	−	23.0635i	0.622884	−	1.07887i	−0.366062	−	0.930590i	$-0.619294\pi$
$457$	13.3157	−	23.0635i	0.622884	−	1.07887i	0.988946	−	0.148276i	$-0.0473725\pi$
$458$	17.2275			0.804990
$459$	11.4361	−	12.8220i	0.533794	−	0.598481i
$460$	−0.459997			−0.0214475
$461$	−2.58862	+	4.48363i	−0.120564	+	0.208823i	−0.919990	−	0.391941i	$-0.871804\pi$
$461$	−2.58862	+	4.48363i	−0.120564	+	0.208823i	0.799426	+	0.600764i	$0.205137\pi$
$462$	0.689534	−	2.78418i	0.0320800	−	0.129532i
$463$	0.0666260	+	0.115400i	0.00309637	+	0.00536307i	0.867569	−	0.497316i	$-0.165681\pi$
$463$	0.0666260	+	0.115400i	0.00309637	+	0.00536307i	−0.864473	+	0.502679i	$0.832348\pi$
$464$	1.32629	+	2.29720i	0.0615713	+	0.106645i
$465$	−4.29153	−	4.13129i	−0.199015	−	0.191584i
$466$	−2.56665	+	4.44557i	−0.118898	+	0.205937i
$467$	−42.0261			−1.94474			−0.972369	−	0.233450i	$-0.924998\pi$
$467$	−42.0261			−1.94474			−0.972369	+	0.233450i	$0.924998\pi$
$468$	2.99668	−	1.88564i	0.138521	−	0.0871636i
$469$	36.7021			1.69474
$470$	1.60909	−	2.78702i	0.0742216	−	0.128556i
$471$	5.11551	−	1.47554i	0.235710	−	0.0679894i
$472$	−2.79724	−	4.84495i	−0.128753	−	0.223007i
$473$	1.76933	+	3.06457i	0.0813540	+	0.140909i
$474$	1.44079	−	0.415587i	0.0661775	−	0.0190885i
$475$	8.31682	−	14.4052i	0.381602	−	0.660954i
$476$	−15.7604			−0.722378
$477$	−2.21866	−	1.17076i	−0.101585	−	0.0536055i
$478$	18.1493			0.830130
$479$	0.272398	−	0.471807i	0.0124462	−	0.0215574i	−0.859735	−	0.510740i	$-0.829371\pi$
$479$	0.272398	−	0.471807i	0.0124462	−	0.0215574i	0.872181	+	0.489183i	$0.162705\pi$
$480$	0.573994	+	0.552561i	0.0261991	+	0.0252208i
$481$	1.07623	+	1.86408i	0.0490718	+	0.0849949i
$482$	−13.4725	−	23.3350i	−0.613655	−	1.06288i
$483$	−1.98469	+	8.01371i	−0.0903064	+	0.364636i
$484$	5.43965	−	9.42175i	0.247257	−	0.428261i
$485$	−8.09661			−0.367648
$486$	−2.58635	+	15.3724i	−0.117319	+	0.697306i
$487$	−9.33589			−0.423050			−0.211525	−	0.977373i	$-0.567843\pi$
$487$	−9.33589			−0.423050			−0.211525	+	0.977373i	$0.567843\pi$
$488$	0.990767	−	1.71606i	0.0448499	−	0.0776823i
$489$	−4.43336	+	17.9009i	−0.200483	+	0.809505i
$490$	3.61546	+	6.26217i	0.163330	+	0.282896i
$491$	−3.28790	−	5.69481i	−0.148381	−	0.257003i	0.782248	−	0.622967i	$-0.214073\pi$
$491$	−3.28790	−	5.69481i	−0.148381	−	0.257003i	−0.930629	+	0.365964i	$0.880739\pi$
$492$	12.5838	+	12.1139i	0.567320	+	0.546136i
$493$	4.38537	−	7.59568i	0.197507	−	0.342092i
$494$	−4.09968			−0.184453
$495$	0.424030	+	0.223756i	0.0190588	+	0.0100571i
$496$	7.47662			0.335710
$497$	−35.9918	+	62.3397i	−1.61445	+	2.79632i
$498$	−15.6173	+	4.50472i	−0.699826	+	0.201861i
$499$	3.91625	+	6.78315i	0.175315	+	0.303655i	0.940270	−	0.340429i	$-0.110572\pi$
$499$	3.91625	+	6.78315i	0.175315	+	0.303655i	−0.764955	+	0.644084i	$0.777239\pi$
$500$	2.25132	+	3.89940i	0.100682	+	0.174386i
$501$	36.7737	−	10.6072i	1.64293	−	0.473894i
$502$	−3.30088	+	5.71730i	−0.147326	+	0.255176i
$503$	−23.5608			−1.05052			−0.525262	−	0.850940i	$-0.676033\pi$
$503$	−23.5608			−1.05052			−0.525262	+	0.850940i	$0.676033\pi$
$504$	12.1028	−	7.61561i	0.539102	−	0.339226i
$505$	−6.68836			−0.297628
$506$	0.173714	−	0.300881i	0.00772251	−	0.0133758i
$507$	14.4836	+	13.9428i	0.643240	+	0.619222i
$508$	0.102700	+	0.177882i	0.00455659	+	0.00789224i
$509$	−5.96708	−	10.3353i	−0.264486	−	0.458104i	0.702943	−	0.711247i	$-0.251869\pi$
$509$	−5.96708	−	10.3353i	−0.264486	−	0.458104i	−0.967429	+	0.253143i	$0.918536\pi$
$510$	0.633310	−	2.55716i	0.0280435	−	0.113233i
$511$	12.5951	−	21.8153i	0.557172	−	0.965051i
$512$	−1.00000			−0.0441942
$513$	12.0146	−	13.4705i	0.530456	−	0.594738i
$514$	−12.7336			−0.561655
$515$	−1.28813	+	2.23111i	−0.0567620	+	0.0983147i
$516$	−4.24100	+	17.1242i	−0.186700	+	0.753850i
$517$	1.21531	+	2.10498i	0.0534494	+	0.0925770i
$518$	4.34662	+	7.52856i	0.190979	+	0.330786i
$519$	1.37401	+	1.32271i	0.0603124	+	0.0580603i
$520$	0.271443	−	0.470152i	0.0119035	−	0.0206175i
$521$	−31.5966			−1.38427			−0.692135	−	0.721768i	$-0.743330\pi$
$521$	−31.5966			−1.38427			−0.692135	+	0.721768i	$0.743330\pi$
$522$	0.302683	+	7.95196i	0.0132481	+	0.348048i
$523$	22.0276			0.963201			0.481601	−	0.876391i	$-0.340056\pi$
$523$	22.0276			0.963201			0.481601	+	0.876391i	$0.340056\pi$
$524$	9.16524	−	15.8747i	0.400385	−	0.693488i
$525$	37.9836	−	10.9562i	1.65774	−	0.478167i
$526$	−13.0617	−	22.6236i	−0.569518	−	0.986434i
$527$	−12.3607	−	21.4094i	−0.538442	−	0.932608i
$528$	−0.578189	+	0.166776i	−0.0251624	+	0.00725797i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−0.384651			−0.0167082
$531$	−0.638381	−	16.7713i	−0.0277034	−	0.727811i
$532$	−16.5576			−0.717861
$533$	5.95089	−	10.3072i	0.257762	−	0.446456i
$534$	−10.1214	−	9.74347i	−0.437996	−	0.421641i
$535$	1.37593	+	2.38318i	0.0594866	+	0.103034i
$536$	−3.85000	−	6.66840i	−0.166295	−	0.288031i
$537$	−7.51135	+	30.3291i	−0.324139	+	1.30880i
$538$	2.80383	−	4.85637i	0.120882	−	0.209373i
$539$	−5.46138			−0.235238
$540$	0.749313	+	2.26973i	0.0322453	+	0.0976735i
$541$	37.3422			1.60547			0.802734	−	0.596337i	$-0.203378\pi$
$541$	37.3422			1.60547			0.802734	+	0.596337i	$0.203378\pi$
$542$	15.4229	−	26.7133i	0.662471	−	1.14743i
$543$	0.656331	−	2.65011i	0.0281659	−	0.113727i
$544$	1.65325	+	2.86351i	0.0708825	+	0.122772i
$545$	−1.25440	−	2.17268i	−0.0537325	−	0.0930674i
$546$	−7.01947	−	6.75736i	−0.300406	−	0.289188i
$547$	−16.7235	+	28.9659i	−0.715045	+	1.23849i	0.247898	+	0.968786i	$0.420260\pi$
$547$	−16.7235	+	28.9659i	−0.715045	+	1.23849i	−0.962942	+	0.269707i	$0.913073\pi$
$548$	2.08036			0.0888688
$549$	5.03139	−	3.16597i	0.214735	−	0.135120i
$550$	−1.66362			−0.0709370
$551$	4.60717	−	7.97985i	0.196272	−	0.339953i
$552$	1.66420	−	0.480030i	0.0708332	−	0.0204315i
$553$	−2.06330	−	3.57374i	−0.0877405	−	0.151971i
$554$	−7.33647	−	12.7071i	−0.311697	−	0.539875i
$555$	−1.39619	+	0.402722i	−0.0592648	+	0.0170946i
$556$	5.24536	−	9.08523i	0.222453	−	0.385299i
$557$	−9.02717			−0.382493			−0.191247	−	0.981542i	$-0.561253\pi$
$557$	−9.02717			−0.382493			−0.191247	+	0.981542i	$0.561253\pi$
$558$	19.8373	+	10.4680i	0.839782	+	0.443144i
$559$	12.0207			0.508420
$560$	1.09629	−	1.89883i	0.0463266	−	0.0802401i
$561$	1.43346	+	1.37993i	0.0605205	+	0.0582607i
$562$	4.00470	+	6.93634i	0.168928	+	0.292592i
$563$	−19.6695	−	34.0685i	−0.828969	−	1.43582i	−0.898848	−	0.438261i	$-0.855595\pi$
$563$	−19.6695	−	34.0685i	−0.828969	−	1.43582i	0.0698791	−	0.997555i	$-0.477739\pi$
$564$	−2.91304	+	11.7622i	−0.122661	+	0.495278i
$565$	2.01847	−	3.49610i	0.0849178	−	0.147082i
$566$	−14.2183			−0.597641
$567$	42.7744	−	3.26105i	1.79635	−	0.136951i
$568$	15.1020			0.633666
$569$	−12.6936	+	21.9859i	−0.532142	+	0.921696i	0.467154	+	0.884176i	$0.345279\pi$
$569$	−12.6936	+	21.9859i	−0.532142	+	0.921696i	−0.999296	+	0.0375204i	$0.988054\pi$
$570$	0.665342	−	2.68650i	0.0278681	−	0.112525i
$571$	21.7198	+	37.6197i	0.908943	+	1.57434i	0.815535	+	0.578708i	$0.196443\pi$
$571$	21.7198	+	37.6197i	0.908943	+	1.57434i	0.0934089	+	0.995628i	$0.470224\pi$
$572$	0.205015	+	0.355097i	0.00857212	+	0.0148474i
$573$	12.7818	+	12.3045i	0.533968	+	0.514030i
$574$	24.0341	−	41.6283i	1.00316	−	1.73753i
$575$	4.78840			0.199690
$576$	−2.65325	−	1.40009i	−0.110552	−	0.0583372i
$577$	22.1179			0.920779			0.460389	−	0.887717i	$-0.347710\pi$
$577$	22.1179			0.920779			0.460389	+	0.887717i	$0.347710\pi$
$578$	−3.03352	+	5.25422i	−0.126178	+	0.218547i
$579$	−19.4872	+	5.62098i	−0.809860	+	0.233600i
$580$	0.610088	+	1.05670i	0.0253325	+	0.0438772i
$581$	22.3650	+	38.7372i	0.927855	+	1.60709i
$582$	29.2924	−	8.44922i	1.21421	−	0.350232i
$583$	0.145260	−	0.251597i	0.00601604	−	0.0104201i
$584$	−5.28482			−0.218688
$585$	1.37846	−	0.867387i	0.0569924	−	0.0358621i
$586$	−25.2773			−1.04419
$587$	15.0615	−	26.0873i	0.621656	−	1.07674i	−0.367521	−	0.930015i	$-0.619793\pi$
$587$	15.0615	−	26.0873i	0.621656	−	1.07674i	0.989177	−	0.146725i	$-0.0468732\pi$
$588$	−19.6151	−	18.8827i	−0.808914	−	0.778709i
$589$	−12.9859	−	22.4922i	−0.535075	−	0.926776i
$590$	−1.28672	−	2.22867i	−0.0529734	−	0.0917527i
$591$	3.92328	−	15.8413i	0.161382	−	0.651623i
$592$	0.911910	−	1.57947i	0.0374793	−	0.0649160i
$593$	−29.5709			−1.21433			−0.607166	−	0.794575i	$-0.707694\pi$
$593$	−29.5709			−1.21433			−0.607166	+	0.794575i	$0.707694\pi$
$594$	−1.76758	−	0.367021i	−0.0725248	−	0.0150591i
$595$	−7.24976			−0.297211
$596$	10.4825	−	18.1561i	0.429378	−	0.743704i
$597$	2.95387	−	11.9270i	0.120894	−	0.488141i
$598$	−0.590096	−	1.02208i	−0.0241308	−	0.0417958i
$599$	2.58136	+	4.47105i	0.105472	+	0.182682i	0.913931	−	0.405870i	$-0.133031\pi$
$599$	2.58136	+	4.47105i	0.105472	+	0.182682i	−0.808459	+	0.588552i	$0.799698\pi$
$600$	−5.97506	−	5.75196i	−0.243931	−	0.234823i
$601$	−1.63209	+	2.82687i	−0.0665744	+	0.115310i	−0.897391	−	0.441236i	$-0.854540\pi$
$601$	−1.63209	+	2.82687i	−0.0665744	+	0.115310i	0.830817	+	0.556546i	$0.187874\pi$
$602$	48.5484			1.97869
$603$	−0.878642	−	23.0833i	−0.0357811	−	0.940025i
$604$	22.3780			0.910548
$605$	2.50222	−	4.33398i	0.101730	−	0.176201i
$606$	24.1975	−	6.97964i	0.982956	−	0.283529i
$607$	−11.8767	−	20.5711i	−0.482061	−	0.834954i	0.517727	−	0.855546i	$-0.326778\pi$
$607$	−11.8767	−	20.5711i	−0.482061	−	0.834954i	−0.999788	+	0.0205916i	$0.993445\pi$
$608$	1.73687	+	3.00834i	0.0704393	+	0.122004i
$609$	21.0413	−	6.06926i	0.852637	−	0.245939i
$610$	0.455750	−	0.789382i	0.0184528	−	0.0319611i
$611$	8.25671			0.334031
$612$	0.377303	+	9.91233i	0.0152516	+	0.400682i
$613$	−32.8102			−1.32519			−0.662595	−	0.748978i	$-0.730545\pi$
$613$	−32.8102			−1.32519			−0.662595	+	0.748978i	$0.730545\pi$
$614$	−14.1227	+	24.4612i	−0.569945	+	0.987174i
$615$	5.78850	+	5.57236i	0.233415	+	0.224699i
$616$	0.828005	+	1.43415i	0.0333613	+	0.0577834i
$617$	11.9367	+	20.6750i	0.480555	+	0.832346i	0.999751	−	0.0223094i	$-0.00710189\pi$
$617$	11.9367	+	20.6750i	0.480555	+	0.832346i	−0.519196	+	0.854655i	$0.673769\pi$
$618$	2.33200	−	9.41608i	0.0938069	−	0.378770i
$619$	17.1325	−	29.6743i	0.688613	−	1.19271i	−0.283674	−	0.958921i	$-0.591553\pi$
$619$	17.1325	−	29.6743i	0.688613	−	1.19271i	0.972287	−	0.233791i	$-0.0751132\pi$
$620$	3.43922			0.138123
$621$	5.08763	+	1.05640i	0.204160	+	0.0423918i
$622$	0.159981			0.00641464
$623$	−19.3312	+	33.4826i	−0.774487	+	1.34145i
$624$	−0.491412	+	1.98421i	−0.0196722	+	0.0794319i
$625$	−10.9354	−	18.9407i	−0.437416	−	0.757627i
$626$	16.4684	+	28.5241i	0.658210	+	1.14005i
$627$	1.50596	+	1.44972i	0.0601421	+	0.0578964i
$628$	−1.53692	+	2.66203i	−0.0613300	+	0.106227i
$629$	−6.03046			−0.240450
$630$	5.56726	−	3.50316i	0.221805	−	0.139569i
$631$	7.12037			0.283457			0.141729	−	0.989906i	$-0.454734\pi$
$631$	7.12037			0.283457			0.141729	+	0.989906i	$0.454734\pi$
$632$	−0.432876	+	0.749763i	−0.0172189	+	0.0298240i
$633$	−13.5185	+	3.89933i	−0.537311	+	0.154985i
$634$	−2.58415	−	4.47587i	−0.102630	−	0.177760i
$635$	0.0472418	+	0.0818252i	0.00187473	+	0.00324713i
$636$	1.39161	−	0.401403i	0.0551810	−	0.0159167i
$637$	−9.27602	+	16.0665i	−0.367529	+	0.636580i
$638$	−0.921576			−0.0364855
$639$	40.0694	+	21.1442i	1.58512	+	0.836452i
$640$	−0.459997			−0.0181830
$641$	16.0180	−	27.7441i	0.632675	−	1.09582i	−0.354328	−	0.935121i	$-0.615290\pi$
$641$	16.0180	−	27.7441i	0.632675	−	1.09582i	0.987003	−	0.160704i	$-0.0513763\pi$
$642$	−7.46488	−	7.18614i	−0.294615	−	0.283614i
$643$	−11.0100	−	19.0699i	−0.434193	−	0.752045i	0.563036	−	0.826432i	$-0.309633\pi$
$643$	−11.0100	−	19.0699i	−0.434193	−	0.752045i	−0.997229	+	0.0743875i	$0.976300\pi$
$644$	−2.38325	−	4.12791i	−0.0939132	−	0.162662i
$645$	−1.95085	+	7.87708i	−0.0768146	+	0.310160i
$646$	5.74296	−	9.94709i	0.225954	−	0.391363i
$647$	45.2324			1.77827			0.889136	−	0.457644i	$-0.151307\pi$
$647$	45.2324			1.77827			0.889136	+	0.457644i	$0.151307\pi$
$648$	−5.07948	−	7.42960i	−0.199541	−	0.291862i
$649$	1.94367			0.0762957
$650$	−2.82562	+	4.89411i	−0.110830	+	0.191963i
$651$	14.8388	−	59.9154i	0.581577	−	2.34827i
$652$	−5.32366	−	9.22084i	−0.208490	−	0.361116i
$653$	−14.5869	−	25.2653i	−0.570830	−	0.988706i	−0.996481	−	0.0838189i	$-0.973288\pi$
$653$	−14.5869	−	25.2653i	−0.570830	−	0.988706i	0.425651	−	0.904887i	$-0.360045\pi$
$654$	6.80553	+	6.55141i	0.266117	+	0.256180i
$655$	4.21598	−	7.30230i	0.164732	−	0.285324i
$656$	−10.0846			−0.393738
$657$	−14.0220	−	7.39924i	−0.547049	−	0.288672i
$658$	33.3468			1.29999
$659$	−21.1435	+	36.6216i	−0.823633	+	1.42657i	0.0793273	+	0.996849i	$0.474723\pi$
$659$	−21.1435	+	36.6216i	−0.823633	+	1.42657i	−0.902960	+	0.429725i	$0.858611\pi$
$660$	−0.265965	+	0.0767163i	−0.0103527	+	0.00298618i
$661$	15.7745	+	27.3223i	0.613559	+	1.06271i	0.990636	+	0.136533i	$0.0435959\pi$
$661$	15.7745	+	27.3223i	0.613559	+	1.06271i	−0.377077	+	0.926182i	$0.623071\pi$
$662$	−3.39948	−	5.88807i	−0.132125	−	0.228846i
$663$	6.49423	−	1.87323i	0.252215	−	0.0727501i
$664$	4.69211	−	8.12698i	0.182089	−	0.315388i
$665$	−7.61643			−0.295352
$666$	4.63094	−	2.91398i	0.179445	−	0.112915i
$667$	2.65257			0.102708
$668$	−11.0484	+	19.1365i	−0.427477	+	0.740412i
$669$	−15.1871	−	14.6200i	−0.587166	−	0.565241i
$670$	−1.77099	−	3.06745i	−0.0684193	−	0.118506i
$671$	0.344219	+	0.596205i	0.0132884	+	0.0230162i
$672$	−1.98469	+	8.01371i	−0.0765610	+	0.309136i
$673$	−1.27946	+	2.21608i	−0.0493194	+	0.0854237i	−0.889631	−	0.456680i	$-0.849039\pi$
$673$	−1.27946	+	2.21608i	−0.0493194	+	0.0854237i	0.840312	+	0.542103i	$0.182372\pi$
$674$	7.15646			0.275657
$675$	−7.80007	−	23.6270i	−0.300225	−	0.909405i
$676$	−11.6071			−0.446429
$677$	−13.3573	+	23.1355i	−0.513363	+	0.889171i	0.486517	+	0.873671i	$0.338267\pi$
$677$	−13.3573	+	23.1355i	−0.513363	+	0.889171i	−0.999880	+	0.0154999i	$0.995066\pi$
$678$	−3.65418	+	14.7547i	−0.140338	+	0.566653i
$679$	−41.9486	−	72.6571i	−1.60984	−	2.78832i
$680$	0.760491	+	1.31721i	0.0291635	+	0.0505126i
$681$	10.1523	+	9.77325i	0.389038	+	0.374512i
$682$	−1.29879	+	2.24957i	−0.0497332	+	0.0861405i
$683$	−47.3370			−1.81130			−0.905651	−	0.424025i	$-0.860617\pi$
$683$	−47.3370			−1.81130			−0.905651	+	0.424025i	$0.860617\pi$
$684$	0.396386	+	10.4137i	0.0151562	+	0.398176i
$685$	0.956962			0.0365636
$686$	−20.7808	+	35.9933i	−0.793413	+	1.37423i
$687$	−28.6701	+	8.26974i	−1.09383	+	0.315510i
$688$	−5.09267	−	8.82077i	−0.194156	−	0.336289i
$689$	−0.493440	−	0.854664i	−0.0187986	−	0.0325601i
$690$	0.765529	−	0.220813i	0.0291432	−	0.00840619i
$691$	7.29606	−	12.6372i	0.277555	−	0.480740i	−0.693221	−	0.720725i	$-0.743809\pi$
$691$	7.29606	−	12.6372i	0.277555	−	0.480740i	0.970777	+	0.239985i	$0.0771425\pi$
$692$	−1.10113			−0.0418586
$693$	0.188966	+	4.96444i	0.00717823	+	0.188583i
$694$	2.86015			0.108570
$695$	2.41285	−	4.17918i	0.0915246	−	0.158525i
$696$	−3.30993	−	3.18634i	−0.125463	−	0.120778i
$697$	16.6724	+	28.8774i	0.631511	+	1.09381i
$698$	−5.11582	−	8.86086i	−0.193637	−	0.335389i
$699$	2.13742	−	8.63041i	0.0808447	−	0.326432i
$700$	−11.4120	+	19.7661i	−0.431331	+	0.747088i
$701$	17.4748			0.660012			0.330006	−	0.943979i	$-0.392949\pi$
$701$	17.4748			0.660012			0.330006	+	0.943979i	$0.392949\pi$
$702$	−4.08191	+	4.57658i	−0.154062	+	0.172732i
$703$	−6.33547			−0.238947
$704$	0.173714	−	0.300881i	0.00654707	−	0.0113399i
$705$	−1.33999	+	5.41058i	−0.0504670	+	0.203774i
$706$	−6.04977	−	10.4785i	−0.227686	−	0.394364i
$707$	−34.6524	−	60.0198i	−1.30324	−	2.25728i
$708$	6.98089	+	6.72023i	0.262358	+	0.252562i
$709$	8.21972	−	14.2370i	0.308698	−	0.534681i	−0.669380	−	0.742920i	$-0.733440\pi$
$709$	8.21972	−	14.2370i	0.308698	−	0.534681i	0.978078	+	0.208240i	$0.0667734\pi$
$710$	6.94688			0.260712
$711$	−2.19827	+	1.38324i	−0.0824414	+	0.0518756i
$712$	8.11127			0.303983
$713$	3.73831	−	6.47494i	0.140001	−	0.242488i
$714$	26.2286	−	7.56549i	0.981579	−	0.283131i
$715$	0.0943065	+	0.163344i	0.00352686	+	0.00610871i
$716$	−9.01976	−	15.6227i	−0.337084	−	0.583847i
$717$	−30.2041	+	8.71222i	−1.12799	+	0.325364i
$718$	−7.33510	+	12.7048i	−0.273743	+	0.474137i
$719$	29.7818			1.11068			0.555338	−	0.831625i	$-0.312589\pi$
$719$	29.7818			1.11068			0.555338	+	0.831625i	$0.312589\pi$
$720$	−1.22049	−	0.644039i	−0.0454849	−	0.0240019i
$721$	−26.6953			−0.994187
$722$	−3.46658	+	6.00429i	−0.129013	+	0.223457i
$723$	33.6225	+	32.3670i	1.25043	+	1.20374i
$724$	0.788134	+	1.36509i	0.0292908	+	0.0507331i
$725$	−6.35079	−	10.9999i	−0.235863	−	0.408526i
$726$	−4.52995	+	18.2909i	−0.168122	+	0.678839i
$727$	−16.7193	+	28.9587i	−0.620086	+	1.07402i	0.369383	+	0.929277i	$0.379569\pi$
$727$	−16.7193	+	28.9587i	−0.620086	+	1.07402i	−0.989469	+	0.144743i	$0.953764\pi$
$728$	5.62539			0.208491
$729$	−3.07501	−	26.8243i	−0.113889	−	0.993493i
$730$	−2.43100			−0.0899755
$731$	−16.8389	+	29.1659i	−0.622810	+	1.07874i
$732$	−0.825076	+	3.33147i	−0.0304957	+	0.123135i
$733$	−18.0411	−	31.2482i	−0.666365	−	1.15418i	−0.978913	−	0.204276i	$-0.934516\pi$
$733$	−18.0411	−	31.2482i	−0.666365	−	1.15418i	0.312548	−	0.949902i	$-0.398817\pi$
$734$	14.2292	+	24.6458i	0.525211	+	0.909692i
$735$	−9.02290	−	8.68599i	−0.332815	−	0.320387i
$736$	−0.500000	+	0.866025i	−0.0184302	+	0.0319221i
$737$	2.67519			0.0985419
$738$	−26.7570	−	14.1194i	−0.984938	−	0.519742i
$739$	−5.45311			−0.200596			−0.100298	−	0.994957i	$-0.531980\pi$
$739$	−5.45311			−0.200596			−0.100298	+	0.994957i	$0.531980\pi$
$740$	0.419476	−	0.726554i	0.0154202	−	0.0267086i
$741$	6.82269	−	1.96797i	0.250638	−	0.0722952i
$742$	−1.99288	−	3.45177i	−0.0731609	−	0.126718i
$743$	−20.9820	−	36.3419i	−0.769755	−	1.33325i	−0.937696	−	0.347457i	$-0.887045\pi$
$743$	−20.9820	−	36.3419i	−0.769755	−	1.33325i	0.167941	−	0.985797i	$-0.446288\pi$
$744$	−12.4426	+	3.58900i	−0.456168	+	0.131579i
$745$	4.82190	−	8.35177i	0.176661	−	0.305985i
$746$	31.8785			1.16715
$747$	23.8279	−	14.9935i	0.871817	−	0.548584i
$748$	−1.14877			−0.0420031
$749$	−14.2574	+	24.6945i	−0.520954	+	0.902318i
$750$	−5.61848	−	5.40869i	−0.205158	−	0.197497i
$751$	10.3338	+	17.8987i	0.377086	+	0.653133i	0.990637	−	0.136523i	$-0.0435926\pi$
$751$	10.3338	+	17.8987i	0.377086	+	0.653133i	−0.613551	+	0.789655i	$0.710259\pi$
$752$	−3.49804	−	6.05878i	−0.127560	−	0.220941i
$753$	2.74886	−	11.0993i	0.100174	−	0.404480i
$754$	−1.56527	+	2.71113i	−0.0570039	+	0.0987336i
$755$	10.2938			0.374630
$756$	−16.4858	+	18.4836i	−0.599583	+	0.672243i
$757$	−53.5319			−1.94565			−0.972825	−	0.231540i	$-0.925624\pi$
$757$	−53.5319			−1.94565			−0.972825	+	0.231540i	$0.925624\pi$
$758$	−17.5514	+	30.3999i	−0.637496	+	1.10418i
$759$	−0.144663	+	0.584114i	−0.00525092	+	0.0212020i
$760$	0.798954	+	1.38383i	0.0289811	+	0.0501968i
$761$	−20.7566	−	35.9515i	−0.752426	−	1.30324i	−0.946644	−	0.322281i	$-0.895550\pi$
$761$	−20.7566	−	35.9515i	−0.752426	−	1.30324i	0.194218	−	0.980958i	$-0.437783\pi$
$762$	−0.256303	−	0.246732i	−0.00928487	−	0.00893818i
$763$	12.9981	−	22.5133i	0.470562	−	0.815038i
$764$	−10.2433			−0.370590
$765$	0.173558	+	4.55964i	0.00627501	+	0.164854i
$766$	10.3680			0.374610
$767$	3.30128	−	5.71798i	0.119202	−	0.206464i
$768$	1.66420	−	0.480030i	0.0600517	−	0.0173216i
$769$	−23.4584	−	40.6311i	−0.845930	−	1.46519i	−0.884811	−	0.465950i	$-0.845713\pi$
$769$	−23.4584	−	40.6311i	−0.845930	−	1.46519i	0.0388813	−	0.999244i	$-0.487621\pi$
$770$	0.380880	+	0.659704i	0.0137260	+	0.0237741i
$771$	21.1913	−	6.11252i	0.763186	−	0.220137i
$772$	5.85481	−	10.1408i	0.210719	−	0.364977i
$773$	−3.59654			−0.129359			−0.0646793	−	0.997906i	$-0.520602\pi$
$773$	−3.59654			−0.129359			−0.0646793	+	0.997906i	$0.520602\pi$
$774$	−1.16224	−	30.5339i	−0.0417759	−	1.09752i
$775$	−35.8011			−1.28601
$776$	−8.80072	+	15.2433i	−0.315927	+	0.547202i
$777$	−10.8476	−	10.4425i	−0.389155	−	0.374624i
$778$	15.7506	+	27.2808i	0.564685	+	0.978063i
$779$	17.5156	+	30.3380i	0.627562	+	1.08697i
$780$	−0.226048	+	0.912730i	−0.00809382	+	0.0326810i
$781$	−2.62342	+	4.54390i	−0.0938734	+	0.162594i
$782$	3.30650			0.118240
$783$	−4.32091	−	13.0884i	−0.154417	−	0.467740i
$784$	15.7195			0.561411
$785$	−0.706981	+	1.22453i	−0.0252332	+	0.0437052i
$786$	−7.63250	+	30.8182i	−0.272242	+	1.09925i
$787$	18.2906	+	31.6803i	0.651991	+	1.12928i	0.982639	+	0.185528i	$0.0593994\pi$
$787$	18.2906	+	31.6803i	0.651991	+	1.12928i	−0.330648	+	0.943754i	$0.607267\pi$
$788$	4.71114	+	8.15994i	0.167827	+	0.290686i
$789$	32.5973	+	31.3802i	1.16050	+	1.11716i
$790$	−0.199122	+	0.344889i	−0.00708443	+	0.0122706i
$791$	41.8309			1.48734
$792$	0.882166	−	0.555097i	0.0313464	−	0.0197245i
$793$	2.33859			0.0830458
$794$	0.380868	−	0.659683i	0.0135165	−	0.0234113i
$795$	0.640137	−	0.184644i	0.0227033	−	0.00654866i
$796$	3.54706	+	6.14369i	0.125722	+	0.217757i
$797$	16.9127	+	29.2936i	0.599078	+	1.03763i	0.992958	+	0.118471i	$0.0377993\pi$
$797$	16.9127	+	29.2936i	0.599078	+	1.03763i	−0.393880	+	0.919162i	$0.628867\pi$
$798$	27.5551	−	7.94813i	0.975441	−	0.281361i
$799$	−11.5663	+	20.0334i	−0.409185	+	0.708729i
$800$	4.78840			0.169296
$801$	21.5212	+	11.3565i	0.760415	+	0.401263i
$802$	4.02223			0.142030
$803$	0.918045	−	1.59010i	0.0323971	−	0.0561134i
$804$	9.60822	+	9.24945i	0.338856	+	0.326203i
$805$	−1.09629	−	1.89883i	−0.0386391	−	0.0669248i
$806$	4.41192	+	7.64168i	0.155403	+	0.269167i
$807$	−2.33493	+	9.42791i	−0.0821935	+	0.331878i
$808$	−7.27000	+	12.5920i	−0.255758	+	0.442985i
$809$	32.1371			1.12988			0.564940	−	0.825132i	$-0.308899\pi$
$809$	32.1371			1.12988			0.564940	+	0.825132i	$0.308899\pi$
$810$	−2.33655	−	3.41759i	−0.0820979	−	0.120082i
$811$	49.0660			1.72294			0.861470	−	0.507809i	$-0.169544\pi$
$811$	49.0660			1.72294			0.861470	+	0.507809i	$0.169544\pi$
$812$	−6.32174	+	10.9496i	−0.221850	+	0.384255i
$813$	−12.8437	+	51.8597i	−0.450447	+	1.81880i
$814$	0.316822	+	0.548752i	0.0111046	+	0.0192337i
$815$	−2.44887	−	4.24156i	−0.0857800	−	0.148575i
$816$	−4.12592	−	3.97186i	−0.144436	−	0.139043i
$817$	−17.6906	+	30.6410i	−0.618916	+	1.07199i
$818$	−11.1369			−0.389391
$819$	14.9256	+	7.87606i	0.521541	+	0.275212i
$820$	−4.63889			−0.161997
$821$	22.2434	−	38.5267i	0.776300	−	1.34459i	−0.157761	−	0.987477i	$-0.550427\pi$
$821$	22.2434	−	38.5267i	0.776300	−	1.34459i	0.934061	−	0.357114i	$-0.116239\pi$
$822$	−3.46215	+	0.998639i	−0.120756	+	0.0348315i
$823$	11.9171	+	20.6410i	0.415404	+	0.719501i	0.995471	−	0.0950679i	$-0.0303068\pi$
$823$	11.9171	+	20.6410i	0.415404	+	0.719501i	−0.580067	+	0.814569i	$0.696973\pi$
$824$	2.80031	+	4.85028i	0.0975534	+	0.168967i
$825$	2.76860	−	0.798589i	0.0963903	−	0.0278033i
$826$	13.3330	−	23.0935i	0.463915	−	0.803525i
$827$	−12.8877			−0.448151			−0.224075	−	0.974572i	$-0.571936\pi$
$827$	−12.8877			−0.448151			−0.224075	+	0.974572i	$0.571936\pi$
$828$	−2.53914	+	1.59774i	−0.0882413	+	0.0555252i
$829$	0.994265			0.0345322			0.0172661	−	0.999851i	$-0.494504\pi$
$829$	0.994265			0.0345322			0.0172661	+	0.999851i	$0.494504\pi$
$830$	2.15836	−	3.73839i	0.0749177	−	0.129761i
$831$	18.3092	+	17.6255i	0.635139	+	0.611423i
$832$	−0.590096	−	1.02208i	−0.0204579	−	0.0354341i
$833$	−25.9883	−	45.0130i	−0.900441	−	1.55961i
$834$	−4.36815	+	17.6376i	−0.151257	+	0.610740i
$835$	−5.08225	+	8.80271i	−0.175879	+	0.304631i
$836$	−1.20687			−0.0417405
$837$	−38.0383	−	7.89828i	−1.31480	−	0.273004i
$838$	−12.1217			−0.418736
$839$	−7.83335	+	13.5678i	−0.270437	+	0.468411i	−0.968974	−	0.247163i	$-0.920502\pi$
$839$	−7.83335	+	13.5678i	−0.270437	+	0.468411i	0.698537	+	0.715574i	$0.253835\pi$
$840$	−0.912951	+	3.68628i	−0.0314998	+	0.127189i
$841$	10.9819	+	19.0213i	0.378687	+	0.655905i
$842$	2.42944	+	4.20792i	0.0837242	+	0.145015i
$843$	−9.99428	−	9.62109i	−0.344221	−	0.331368i
$844$	4.06155	−	7.03481i	0.139804	−	0.242148i
$845$	−5.33925			−0.183676
$846$	−0.798317	−	20.9730i	−0.0274467	−	0.721068i
$847$	51.8561			1.78180
$848$	−0.418102	+	0.724173i	−0.0143577	+	0.0248682i
$849$	23.6622	−	6.82523i	0.812084	−	0.234241i
$850$	−7.91643	−	13.7117i	−0.271531	−	0.470306i
$851$	−0.911910	−	1.57947i	−0.0312599	−	0.0541437i
$852$	−25.1328	+	7.24942i	−0.861035	+	0.248361i
$853$	17.9903	−	31.1601i	0.615975	−	1.06690i	−0.374237	−	0.927333i	$-0.622095\pi$
$853$	17.9903	−	31.1601i	0.615975	−	1.06690i	0.990213	−	0.139568i	$-0.0445712\pi$
$854$	9.44498			0.323200
$855$	0.182336	+	4.79026i	0.00623577	+	0.163823i
$856$	5.98233			0.204472
$857$	−14.3061	+	24.7789i	−0.488687	+	0.846431i	−0.999915	−	0.0130142i	$-0.995857\pi$
$857$	−14.3061	+	24.7789i	−0.488687	+	0.846431i	0.511228	+	0.859445i	$0.329191\pi$
$858$	−0.511645	−	0.492540i	−0.0174673	−	0.0168150i
$859$	9.22949	+	15.9859i	0.314906	+	0.545433i	0.979418	−	0.201845i	$-0.0646937\pi$
$859$	9.22949	+	15.9859i	0.314906	+	0.545433i	−0.664512	+	0.747278i	$0.731360\pi$
$860$	−2.34261	−	4.05753i	−0.0798825	−	0.138361i
$861$	−20.0148	+	80.8151i	−0.682102	+	2.75417i
$862$	−10.2276	+	17.7147i	−0.348353	+	0.603366i
$863$	−20.2738			−0.690129			−0.345064	−	0.938579i	$-0.612143\pi$
$863$	−20.2738			−0.690129			−0.345064	+	0.938579i	$0.612143\pi$
$864$	5.08763	+	1.05640i	0.173085	+	0.0359394i
$865$	−0.506516			−0.0172221
$866$	10.4134	−	18.0366i	0.353862	−	0.612907i
$867$	2.52621	−	10.2003i	0.0857947	−	0.346419i
$868$	17.8186	+	30.8628i	0.604804	+	1.04755i
$869$	−0.150393	−	0.260488i	−0.00510172	−	0.00883645i
$870$	−1.52256	−	1.46571i	−0.0516196	−	0.0496922i
$871$	4.54375	−	7.87000i	0.153959	−	0.266665i
$872$	−5.45393			−0.184694
$873$	−44.6925	+	28.1224i	−1.51261	+	0.951800i
$874$	3.47374			0.117501
$875$	−10.7309	+	18.5865i	−0.362771	+	0.628338i
$876$	8.79502	−	2.53688i	0.297156	−	0.0857131i
$877$	−24.3830	−	42.2326i	−0.823355	−	1.42609i	−0.903170	−	0.429283i	$-0.858766\pi$
$877$	−24.3830	−	42.2326i	−0.823355	−	1.42609i	0.0798146	−	0.996810i	$-0.474567\pi$
$878$	5.59975	+	9.69906i	0.188982	+	0.327327i
$879$	42.0665	−	12.1339i	1.41887	−	0.409265i
$880$	0.0799077	−	0.138404i	0.00269369	−	0.00466561i
$881$	−22.4592			−0.756671			−0.378335	−	0.925669i	$-0.623503\pi$
$881$	−22.4592			−0.756671			−0.378335	+	0.925669i	$0.623503\pi$
$882$	41.7078	+	22.0088i	1.40437	+	0.741074i
$883$	−1.78457			−0.0600556			−0.0300278	−	0.999549i	$-0.509560\pi$
$883$	−1.78457			−0.0600556			−0.0300278	+	0.999549i	$0.509560\pi$
$884$	−1.95115	+	3.37950i	−0.0656244	+	0.113665i
$885$	3.21119	+	3.09129i	0.107943	+	0.103912i
$886$	−12.4842	−	21.6232i	−0.419414	−	0.726446i
$887$	−25.1127	−	43.4966i	−0.843204	−	1.46047i	−0.887172	−	0.461439i	$-0.847333\pi$
$887$	−25.1127	−	43.4966i	−0.843204	−	1.46047i	0.0439686	−	0.999033i	$-0.486000\pi$
$888$	−0.759407	+	3.06631i	−0.0254840	+	0.102899i
$889$	−0.489521	+	0.847874i	−0.0164180	+	0.0284368i
$890$	3.73116			0.125069
$891$	3.11780	−	0.237696i	0.104450	−	0.00796311i
$892$	12.1709			0.407511
$893$	−12.1513	+	21.0466i	−0.406626	+	0.704297i
$894$	−8.72943	+	35.2474i	−0.291956	+	1.17885i
$895$	−4.14906	−	7.18639i	−0.138688	−	0.240215i
$896$	−2.38325	−	4.12791i	−0.0796188	−	0.137904i
$897$	1.47267	+	1.41768i	0.0491709	+	0.0473349i
$898$	6.43708	−	11.1494i	0.214808	−	0.372059i
$899$	−19.8323			−0.661443
$900$	12.7048	+	6.70421i	0.423494	+	0.223474i
$901$	2.76491			0.0921124
$902$	1.75183	−	3.03426i	0.0583296	−	0.101030i
$903$	−80.7944	+	23.3047i	−2.68867	+	0.775533i
$904$	−4.38801	−	7.60026i	−0.145943	−	0.252781i
$905$	0.362540	+	0.627937i	0.0120512	+	0.0208733i
$906$	−37.2415	+	10.7421i	−1.23727	+	0.356883i
$907$	0.627322	−	1.08655i	0.0208299	−	0.0360784i	−0.855423	−	0.517931i	$-0.826702\pi$
$907$	0.627322	−	1.08655i	0.0208299	−	0.0360784i	0.876252	+	0.481852i	$0.160036\pi$
$908$	−8.13606			−0.270005
$909$	−36.9191	+	23.2311i	−1.22453	+	0.770526i
$910$	2.58766			0.0857802
$911$	−0.424876	+	0.735908i	−0.0140768	+	0.0243817i	−0.872978	−	0.487760i	$-0.837814\pi$
$911$	−0.424876	+	0.735908i	−0.0140768	+	0.0243817i	0.858901	+	0.512141i	$0.171148\pi$
$912$	−4.33460	−	4.17274i	−0.143533	−	0.138173i
$913$	1.63017	+	2.82353i	0.0539507	+	0.0934453i
$914$	−13.3157	−	23.0635i	−0.440446	−	0.762874i
$915$	−0.379533	+	1.53247i	−0.0125470	+	0.0506617i
$916$	8.61377	−	14.9195i	0.284607	−	0.492954i
$917$	87.3722			2.88528
$918$	−5.38613	−	16.3150i	−0.177769	−	0.538475i
$919$	−11.9420			−0.393932			−0.196966	−	0.980410i	$-0.563109\pi$
$919$	−11.9420			−0.393932			−0.196966	+	0.980410i	$0.563109\pi$
$920$	−0.229999	+	0.398369i	−0.00758283	+	0.0131338i
$921$	11.7609	−	47.4877i	0.387534	−	1.56477i
$922$	2.58862	+	4.48363i	0.0852517	+	0.147660i
$923$	8.91164	+	15.4354i	0.293330	+	0.508063i
$924$	−2.06640	−	1.98924i	−0.0679797	−	0.0654413i
$925$	−4.36659	+	7.56316i	−0.143573	+	0.248675i
$926$	0.133252			0.00437893
$927$	0.639083	+	16.7897i	0.0209902	+	0.551446i
$928$	2.65257			0.0870750
$929$	−10.4109	+	18.0322i	−0.341570	+	0.591616i	−0.984724	−	0.174120i	$-0.944292\pi$
$929$	−10.4109	+	18.0322i	−0.341570	+	0.591616i	0.643155	+	0.765736i	$0.277625\pi$
$930$	−5.72356	+	1.65093i	−0.187683	+	0.0541362i
$931$	−27.3027	−	47.2897i	−0.894810	−	1.54986i
$932$	2.56665	+	4.44557i	0.0840735	+	0.145620i
$933$	−0.266240	+	0.0767956i	−0.00871631	+	0.00251417i
$934$	−21.0131	+	36.3957i	−0.687569	+	1.19090i
$935$	−0.528430			−0.0172815
$936$	−0.134671	−	3.53802i	−0.00440186	−	0.115644i
$937$	−26.4946			−0.865541			−0.432771	−	0.901504i	$-0.642464\pi$
$937$	−26.4946			−0.865541			−0.432771	+	0.901504i	$0.642464\pi$
$938$	18.3510	−	31.7849i	0.599183	−	1.03781i
$939$	−41.0992	−	39.5646i	−1.34122	−	1.29114i
$940$	−1.60909	−	2.78702i	−0.0524826	−	0.0909026i
$941$	20.6934	+	35.8420i	0.674586	+	1.16842i	0.976590	+	0.215110i	$0.0690111\pi$
$941$	20.6934	+	35.8420i	0.674586	+	1.16842i	−0.302004	+	0.953307i	$0.597656\pi$
$942$	1.27990	−	5.16793i	0.0417013	−	0.168380i
$943$	−5.04230	+	8.73352i	−0.164200	+	0.284403i
$944$	−5.59447			−0.182085
$945$	−7.58343	+	8.50242i	−0.246689	+	0.276584i
$946$	3.53866			0.115052
$947$	22.9033	−	39.6697i	0.744257	−	1.28909i	−0.206284	−	0.978492i	$-0.566137\pi$
$947$	22.9033	−	39.6697i	0.744257	−	1.28909i	0.950541	−	0.310599i	$-0.100530\pi$
$948$	0.360484	−	1.45555i	0.0117080	−	0.0472741i
$949$	−3.11855	−	5.40149i	−0.101233	−	0.175340i
$950$	−8.31682	−	14.4052i	−0.269833	−	0.467365i
$951$	6.44910	+	6.20829i	0.209126	+	0.201318i
$952$	−7.88022	+	13.6489i	−0.255399	+	0.442365i
$953$	33.1360			1.07338			0.536691	−	0.843779i	$-0.319674\pi$
$953$	33.1360			1.07338			0.536691	+	0.843779i	$0.319674\pi$
$954$	−2.12324	+	1.33603i	−0.0687424	+	0.0432556i
$955$	−4.71189			−0.152473
$956$	9.07465	−	15.7178i	0.293495	−	0.508349i
$957$	1.53369	−	0.442384i	0.0495771	−	0.0143003i
$958$	−0.272398	−	0.471807i	−0.00880077	−	0.0152434i
$959$	4.95803	+	8.58756i	0.160103	+	0.277307i
$960$	0.765529	−	0.220813i	0.0247073	−	0.00712670i
$961$	−12.4499	+	21.5639i	−0.401610	+	0.695609i
$962$	2.15246			0.0693980
$963$	15.8726	+	8.37582i	0.511488	+	0.269907i
$964$	−26.9450			−0.867839
$965$	2.69320	−	4.66476i	0.0866971	−	0.150164i
$966$	5.94773	+	5.72565i	0.191365	+	0.184220i
$967$	−4.17616	−	7.23333i	−0.134296	−	0.232608i	0.791032	−	0.611775i	$-0.209544\pi$
$967$	−4.17616	−	7.23333i	−0.134296	−	0.232608i	−0.925328	+	0.379167i	$0.876211\pi$
$968$	−5.43965	−	9.42175i	−0.174837	−	0.302826i
$969$	−4.78254	+	19.3108i	−0.153637	+	0.620351i
$970$	−4.04830	+	7.01187i	−0.129983	+	0.225138i
$971$	−40.3722			−1.29561			−0.647803	−	0.761808i	$-0.724312\pi$
$971$	−40.3722			−1.29561			−0.647803	+	0.761808i	$0.724312\pi$
$972$	12.0197	+	9.92605i	0.385533	+	0.318378i
$973$	50.0040			1.60305
$974$	−4.66795	+	8.08512i	−0.149571	+	0.259064i
$975$	2.35308	−	9.50118i	0.0753588	−	0.304281i
$976$	−0.990767	−	1.71606i	−0.0317137	−	0.0549297i
$977$	−11.4744	−	19.8743i	−0.367100	−	0.635835i	0.622011	−	0.783008i	$-0.286316\pi$
$977$	−11.4744	−	19.8743i	−0.367100	−	0.635835i	−0.989111	+	0.147173i	$0.952983\pi$
$978$	13.2859	+	12.7898i	0.424837	+	0.408974i
$979$	−1.40904	+	2.44052i	−0.0450330	+	0.0779995i
$980$	7.23093			0.230984
$981$	−14.4707	−	7.63601i	−0.462012	−	0.243799i
$982$	−6.57580			−0.209842
$983$	24.4491	−	42.3471i	0.779806	−	1.35066i	−0.152248	−	0.988342i	$-0.548651\pi$
$983$	24.4491	−	42.3471i	0.779806	−	1.35066i	0.932054	−	0.362321i	$-0.118015\pi$
$984$	16.7828	−	4.84092i	0.535017	−	0.154323i
$985$	2.16711	+	3.75355i	0.0690499	+	0.119598i
$986$	−4.38537	−	7.59568i	−0.139659	−	0.241896i
$987$	−55.4958	+	16.0075i	−1.76645	+	0.509523i
$988$	−2.04984	+	3.55042i	−0.0652141	+	0.112954i
$989$	−10.1853			−0.323875
$990$	0.405794	−	0.255343i	0.0128970	−	0.00811533i
$991$	9.89241			0.314243			0.157121	−	0.987579i	$-0.449779\pi$
$991$	9.89241			0.314243			0.157121	+	0.987579i	$0.449779\pi$
$992$	3.73831	−	6.47494i	0.118691	−	0.205580i
$993$	8.48388	+	8.16709i	0.269228	+	0.259175i
$994$	35.9918	+	62.3397i	1.14159	+	1.97730i
$995$	1.63164	+	2.82608i	0.0517264	+	0.0895928i
$996$	−3.90743	+	15.7773i	−0.123812	+	0.499923i
$997$	−27.3577	+	47.3850i	−0.866428	+	1.50070i	−0.000806169		1.00000i	$0.500257\pi$
$997$	−27.3577	+	47.3850i	−0.866428	+	1.50070i	−0.865622	+	0.500698i	$0.833077\pi$
$998$	7.83250			0.247934
$999$	−6.30802	+	7.07245i	−0.199577	+	0.223762i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.e.e.277.3	yes	12
3.2	odd	2		1242.2.e.e.829.4		12
9.2	odd	6		3726.2.a.x.1.3		6
9.4	even	3	inner	414.2.e.e.139.3	✓	12
9.5	odd	6		1242.2.e.e.415.4		12
9.7	even	3		3726.2.a.w.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.e.e.139.3	✓	12	9.4	even	3	inner
414.2.e.e.277.3	yes	12	1.1	even	1	trivial
1242.2.e.e.415.4		12	9.5	odd	6
1242.2.e.e.829.4		12	3.2	odd	2
3726.2.a.w.1.4		6	9.7	even	3
3726.2.a.x.1.3		6	9.2	odd	6

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.416383 + 1.68126i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.229999 - 0.398369i) q^{5} +(1.24782 + 1.20123i) q^{6} +(2.38325 - 4.12791i) q^{7} -1.00000 q^{8} +(-2.65325 - 1.40009i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.416383 + 1.68126i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.229999 - 0.398369i) q^{5} +(1.24782 + 1.20123i) q^{6} +(2.38325 - 4.12791i) q^{7} -1.00000 q^{8} +(-2.65325 - 1.40009i) q^{9} -0.459997 q^{10} +(0.173714 - 0.300881i) q^{11} +(1.66420 - 0.480030i) q^{12} +(-0.590096 - 1.02208i) q^{13} +(-2.38325 - 4.12791i) q^{14} +(0.765529 - 0.220813i) q^{15} +(-0.500000 + 0.866025i) q^{16} +3.30650 q^{17} +(-2.53914 + 1.59774i) q^{18} +3.47374 q^{19} +(-0.229999 + 0.398369i) q^{20} +(5.94773 + 5.72565i) q^{21} +(-0.173714 - 0.300881i) q^{22} +(0.500000 + 0.866025i) q^{23} +(0.416383 - 1.68126i) q^{24} +(2.39420 - 4.14688i) q^{25} -1.18019 q^{26} +(3.45868 - 3.87782i) q^{27} -4.76650 q^{28} +(1.32629 - 2.29720i) q^{29} +(0.191535 - 0.773373i) q^{30} +(-3.73831 - 6.47494i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.433526 + 0.417339i) q^{33} +(1.65325 - 2.86351i) q^{34} -2.19258 q^{35} +(0.114109 + 2.99783i) q^{36} -1.82382 q^{37} +(1.73687 - 3.00834i) q^{38} +(1.96408 - 0.566528i) q^{39} +(0.229999 + 0.398369i) q^{40} +(5.04230 + 8.73352i) q^{41} +(7.93242 - 2.28806i) q^{42} +(-5.09267 + 8.82077i) q^{43} -0.347427 q^{44} +(0.0524900 + 1.37899i) q^{45} +1.00000 q^{46} +(-3.49804 + 6.05878i) q^{47} +(-1.24782 - 1.20123i) q^{48} +(-7.85975 - 13.6135i) q^{49} +(-2.39420 - 4.14688i) q^{50} +(-1.37677 + 5.55908i) q^{51} +(-0.590096 + 1.02208i) q^{52} +0.836203 q^{53} +(-1.62895 - 4.93422i) q^{54} -0.159815 q^{55} +(-2.38325 + 4.12791i) q^{56} +(-1.44640 + 5.84024i) q^{57} +(-1.32629 - 2.29720i) q^{58} +(2.79724 + 4.84495i) q^{59} +(-0.573994 - 0.552561i) q^{60} +(-0.990767 + 1.71606i) q^{61} -7.47662 q^{62} +(-12.1028 + 7.61561i) q^{63} +1.00000 q^{64} +(-0.271443 + 0.470152i) q^{65} +(0.578189 - 0.166776i) q^{66} +(3.85000 + 6.66840i) q^{67} +(-1.65325 - 2.86351i) q^{68} +(-1.66420 + 0.480030i) q^{69} +(-1.09629 + 1.89883i) q^{70} -15.1020 q^{71} +(2.65325 + 1.40009i) q^{72} +5.28482 q^{73} +(-0.911910 + 1.57947i) q^{74} +(5.97506 + 5.75196i) q^{75} +(-1.73687 - 3.00834i) q^{76} +(-0.828005 - 1.43415i) q^{77} +(0.491412 - 1.98421i) q^{78} +(0.432876 - 0.749763i) q^{79} +0.459997 q^{80} +(5.07948 + 7.42960i) q^{81} +10.0846 q^{82} +(-4.69211 + 8.12698i) q^{83} +(1.98469 - 8.01371i) q^{84} +(-0.760491 - 1.31721i) q^{85} +(5.09267 + 8.82077i) q^{86} +(3.30993 + 3.18634i) q^{87} +(-0.173714 + 0.300881i) q^{88} -8.11127 q^{89} +(1.22049 + 0.644039i) q^{90} -5.62539 q^{91} +(0.500000 - 0.866025i) q^{92} +(12.4426 - 3.58900i) q^{93} +(3.49804 + 6.05878i) q^{94} +(-0.798954 - 1.38383i) q^{95} +(-1.66420 + 0.480030i) q^{96} +(8.80072 - 15.2433i) q^{97} -15.7195 q^{98} +(-0.882166 + 0.555097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} + 5 q^{5} - 3 q^{7} - 12 q^{8} - 8 q^{9} + 10 q^{10} + 6 q^{11} - 6 q^{13} + 3 q^{14} + 7 q^{15} - 6 q^{16} - 8 q^{17} - 10 q^{18} + 4 q^{19} + 5 q^{20} + 17 q^{21} - 6 q^{22} + 6 q^{23} + q^{25} - 12 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} - q^{30} - 6 q^{31} + 6 q^{32} + 9 q^{33} - 4 q^{34} - 34 q^{35} - 2 q^{36} + 8 q^{37} + 2 q^{38} + 23 q^{39} - 5 q^{40} + 15 q^{41} + 7 q^{42} - 14 q^{43} - 12 q^{44} - 37 q^{45} + 12 q^{46} + 9 q^{47} - 5 q^{49} - q^{50} + 9 q^{51} - 6 q^{52} - 10 q^{53} - 9 q^{54} + 16 q^{55} + 3 q^{56} + 37 q^{57} - 12 q^{58} + 18 q^{59} - 8 q^{60} - 3 q^{61} - 12 q^{62} - 42 q^{63} + 12 q^{64} + 9 q^{65} + 3 q^{66} + 8 q^{67} + 4 q^{68} - 17 q^{70} - 18 q^{71} + 8 q^{72} - 32 q^{73} + 4 q^{74} + 34 q^{75} - 2 q^{76} - q^{77} + 22 q^{78} - 7 q^{79} - 10 q^{80} - 56 q^{81} + 30 q^{82} + 3 q^{83} - 10 q^{84} + 7 q^{85} + 14 q^{86} - 9 q^{87} - 6 q^{88} - 42 q^{89} - 17 q^{90} + 18 q^{91} + 6 q^{92} + 69 q^{93} - 9 q^{94} + 11 q^{95} + 13 q^{97} - 10 q^{98} - 60 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 5 * q^5 - 3 * q^7 - 12 * q^8 - 8 * q^9 + 10 * q^10 + 6 * q^11 - 6 * q^13 + 3 * q^14 + 7 * q^15 - 6 * q^16 - 8 * q^17 - 10 * q^18 + 4 * q^19 + 5 * q^20 + 17 * q^21 - 6 * q^22 + 6 * q^23 + q^25 - 12 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 - q^30 - 6 * q^31 + 6 * q^32 + 9 * q^33 - 4 * q^34 - 34 * q^35 - 2 * q^36 + 8 * q^37 + 2 * q^38 + 23 * q^39 - 5 * q^40 + 15 * q^41 + 7 * q^42 - 14 * q^43 - 12 * q^44 - 37 * q^45 + 12 * q^46 + 9 * q^47 - 5 * q^49 - q^50 + 9 * q^51 - 6 * q^52 - 10 * q^53 - 9 * q^54 + 16 * q^55 + 3 * q^56 + 37 * q^57 - 12 * q^58 + 18 * q^59 - 8 * q^60 - 3 * q^61 - 12 * q^62 - 42 * q^63 + 12 * q^64 + 9 * q^65 + 3 * q^66 + 8 * q^67 + 4 * q^68 - 17 * q^70 - 18 * q^71 + 8 * q^72 - 32 * q^73 + 4 * q^74 + 34 * q^75 - 2 * q^76 - q^77 + 22 * q^78 - 7 * q^79 - 10 * q^80 - 56 * q^81 + 30 * q^82 + 3 * q^83 - 10 * q^84 + 7 * q^85 + 14 * q^86 - 9 * q^87 - 6 * q^88 - 42 * q^89 - 17 * q^90 + 18 * q^91 + 6 * q^92 + 69 * q^93 - 9 * q^94 + 11 * q^95 + 13 * q^97 - 10 * q^98 - 60 * q^99

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