LMFDB - Embedded newform 930.2.be.a.37.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.11
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.62734 - 1.53354i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.664038 + 2.47822i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.62734 - 1.53354i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.664038 + 2.47822i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.0663294 - 2.23508i) q^{10} +(-1.82901 - 1.05598i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-2.34239 + 0.627641i) q^{13} +(-2.22192 + 1.28282i) q^{14} +(-1.90247 + 1.17498i) q^{15} -1.00000 q^{16} +(-2.84018 - 0.761023i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-2.66665 + 1.53959i) q^{19} +(1.53354 - 1.62734i) q^{20} +(2.22192 + 1.28282i) q^{21} +(-0.546616 - 2.04000i) q^{22} +(-2.49783 - 2.49783i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.296503 + 4.99120i) q^{25} +(-2.10013 - 1.21251i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.47822 - 0.664038i) q^{28} +2.00914 q^{29} +(-2.17609 - 0.514413i) q^{30} +(-4.70519 + 2.97678i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.49338 + 1.49338i) q^{33} +(-1.47018 - 2.54643i) q^{34} +(4.88108 - 3.01460i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-0.454135 - 0.121685i) q^{37} +(-2.97427 - 0.796952i) q^{38} +2.42502i q^{39} +(2.23508 - 0.0663294i) q^{40} +(-2.76566 + 4.79027i) q^{41} +(0.664038 + 2.47822i) q^{42} +(0.779767 - 2.91013i) q^{43} +(1.05598 - 1.82901i) q^{44} +(0.642552 + 2.14176i) q^{45} -3.53246i q^{46} +(-4.35849 - 4.35849i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(0.361528 + 0.208728i) q^{49} +(-3.31965 + 3.73897i) q^{50} +(-1.47018 + 2.54643i) q^{51} +(-0.627641 - 2.34239i) q^{52} +(-0.255348 + 0.0684204i) q^{53} -1.00000 q^{54} +(1.35705 + 4.52332i) q^{55} +(-1.28282 - 2.22192i) q^{56} +(0.796952 + 2.97427i) q^{57} +(1.42068 + 1.42068i) q^{58} +(-3.84661 + 2.22084i) q^{59} +(-1.17498 - 1.90247i) q^{60} -5.24317i q^{61} +(-5.43197 - 1.22217i) q^{62} +(1.81419 - 1.81419i) q^{63} -1.00000i q^{64} +(4.77439 + 2.57076i) q^{65} -2.11196 q^{66} +(-4.43220 + 1.18760i) q^{67} +(0.761023 - 2.84018i) q^{68} +(-3.05920 + 1.76623i) q^{69} +(5.58309 + 1.31980i) q^{70} +(2.81229 - 4.87102i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-13.3326 + 3.57247i) q^{73} +(-0.235077 - 0.407166i) q^{74} +(4.89787 + 1.00542i) q^{75} +(-1.53959 - 2.66665i) q^{76} +(3.83150 - 3.83150i) q^{77} +(-1.71475 + 1.71475i) q^{78} +(1.55137 + 2.68705i) q^{79} +(1.62734 + 1.53354i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-5.34285 + 1.43161i) q^{82} +(2.20061 - 0.589652i) q^{83} +(-1.28282 + 2.22192i) q^{84} +(3.45489 + 5.59397i) q^{85} +(2.60915 - 1.50639i) q^{86} +(0.520003 - 1.94068i) q^{87} +(2.04000 - 0.546616i) q^{88} +15.0864 q^{89} +(-1.06010 + 1.96880i) q^{90} -6.22174i q^{91} +(2.49783 - 2.49783i) q^{92} +(1.65756 + 5.31531i) q^{93} -6.16383i q^{94} +(6.70059 + 1.58397i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(7.62570 + 7.62570i) q^{97} +(0.108046 + 0.403232i) q^{98} +(1.05598 + 1.82901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) $ 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$			1.00000i			0.500000i
$5$	−1.62734	−	1.53354i	−0.727771	−	0.685820i
$5$	−1.62734	−	1.53354i	−0.727771	−	0.685820i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−0.664038	+	2.47822i	−0.250983	+	0.936681i	0.719298	+	0.694701i	$0.244463\pi$
$7$	−0.664038	+	2.47822i	−0.250983	+	0.936681i	−0.970281	+	0.241980i	$0.922203\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−0.0663294	−	2.23508i	−0.0209752	−	0.706796i
$11$	−1.82901	−	1.05598i	−0.551469	−	0.318391i	0.198246	−	0.980152i	$-0.436476\pi$
$11$	−1.82901	−	1.05598i	−0.551469	−	0.318391i	−0.749714	+	0.661762i	$0.769809\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	−2.34239	+	0.627641i	−0.649662	+	0.174076i	−0.568576	−	0.822631i	$-0.692505\pi$
$13$	−2.34239	+	0.627641i	−0.649662	+	0.174076i	−0.0810858	+	0.996707i	$0.525839\pi$
$14$	−2.22192	+	1.28282i	−0.593832	+	0.342849i
$15$	−1.90247	+	1.17498i	−0.491217	+	0.303380i
$16$	−1.00000			−0.250000
$17$	−2.84018	−	0.761023i	−0.688844	−	0.184575i	−0.102616	−	0.994721i	$-0.532721\pi$
$17$	−2.84018	−	0.761023i	−0.688844	−	0.184575i	−0.586228	+	0.810146i	$0.699388\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	−2.66665	+	1.53959i	−0.611772	+	0.353207i	−0.773659	−	0.633603i	$-0.781575\pi$
$19$	−2.66665	+	1.53959i	−0.611772	+	0.353207i	0.161887	+	0.986809i	$0.448242\pi$
$20$	1.53354	−	1.62734i	0.342910	−	0.363885i
$21$	2.22192	+	1.28282i	0.484862	+	0.279935i
$22$	−0.546616	−	2.04000i	−0.116539	−	0.434930i
$23$	−2.49783	−	2.49783i	−0.520833	−	0.520833i	0.396990	−	0.917823i	$-0.370055\pi$
$23$	−2.49783	−	2.49783i	−0.520833	−	0.520833i	−0.917823	+	0.396990i	$0.870055\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	0.296503	+	4.99120i	0.0593007	+	0.998240i
$26$	−2.10013	−	1.21251i	−0.411869	−	0.237793i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−2.47822	−	0.664038i	−0.468340	−	0.125491i
$29$	2.00914			0.373088			0.186544	−	0.982447i	$-0.440271\pi$
$29$	2.00914			0.373088			0.186544	+	0.982447i	$0.440271\pi$
$30$	−2.17609	−	0.514413i	−0.397298	−	0.0939185i
$31$	−4.70519	+	2.97678i	−0.845076	+	0.534645i
$31$	−4.70519	+	2.97678i	−0.845076	+	0.534645i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.49338	+	1.49338i	−0.259965	+	0.259965i
$34$	−1.47018	−	2.54643i	−0.252134	−	0.436709i
$35$	4.88108	−	3.01460i	0.825053	−	0.509560i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−0.454135	−	0.121685i	−0.0746593	−	0.0200049i	0.221296	−	0.975207i	$-0.428971\pi$
$37$	−0.454135	−	0.121685i	−0.0746593	−	0.0200049i	−0.295955	+	0.955202i	$0.595638\pi$
$38$	−2.97427	−	0.796952i	−0.482490	−	0.129283i
$39$			2.42502i			0.388314i
$40$	2.23508	−	0.0663294i	0.353398	−	0.0104876i
$41$	−2.76566	+	4.79027i	−0.431924	+	0.748114i	−0.997039	−	0.0768981i	$-0.975498\pi$
$41$	−2.76566	+	4.79027i	−0.431924	+	0.748114i	0.565115	+	0.825012i	$0.308832\pi$
$42$	0.664038	+	2.47822i	0.102463	+	0.382398i
$43$	0.779767	−	2.91013i	0.118913	−	0.443790i	−0.880637	−	0.473792i	$-0.842885\pi$
$43$	0.779767	−	2.91013i	0.118913	−	0.443790i	0.999550	+	0.0300020i	$0.00955136\pi$
$44$	1.05598	−	1.82901i	0.159195	−	0.275734i
$45$	0.642552	+	2.14176i	0.0957859	+	0.319274i
$46$		−	3.53246i		−	0.520833i
$47$	−4.35849	−	4.35849i	−0.635751	−	0.635751i	0.313754	−	0.949504i	$-0.398413\pi$
$47$	−4.35849	−	4.35849i	−0.635751	−	0.635751i	−0.949504	+	0.313754i	$0.898413\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	0.361528	+	0.208728i	0.0516468	+	0.0298183i
$50$	−3.31965	+	3.73897i	−0.469470	+	0.528770i
$51$	−1.47018	+	2.54643i	−0.205867	+	0.356572i
$52$	−0.627641	−	2.34239i	−0.0870382	−	0.324831i
$53$	−0.255348	+	0.0684204i	−0.0350748	+	0.00939826i	−0.276314	−	0.961067i	$-0.589113\pi$
$53$	−0.255348	+	0.0684204i	−0.0350748	+	0.00939826i	0.241239	+	0.970466i	$0.422446\pi$
$54$	−1.00000			−0.136083
$55$	1.35705	+	4.52332i	0.182984	+	0.609924i
$56$	−1.28282	−	2.22192i	−0.171424	−	0.296916i
$57$	0.796952	+	2.97427i	0.105559	+	0.393951i
$58$	1.42068	+	1.42068i	0.186544	+	0.186544i
$59$	−3.84661	+	2.22084i	−0.500786	+	0.289129i	−0.729038	−	0.684473i	$-0.760032\pi$
$59$	−3.84661	+	2.22084i	−0.500786	+	0.289129i	0.228252	+	0.973602i	$0.426699\pi$
$60$	−1.17498	−	1.90247i	−0.151690	−	0.245608i
$61$		−	5.24317i		−	0.671319i	−0.941983	−	0.335659i	$-0.891041\pi$
$61$		−	5.24317i		−	0.671319i	0.941983	−	0.335659i	$-0.108959\pi$
$62$	−5.43197	−	1.22217i	−0.689861	−	0.155215i
$63$	1.81419	−	1.81419i	0.228566	−	0.228566i
$64$		−	1.00000i		−	0.125000i
$65$	4.77439	+	2.57076i	0.592190	+	0.318864i
$66$	−2.11196			−0.259965
$67$	−4.43220	+	1.18760i	−0.541479	+	0.145089i	−0.519184	−	0.854663i	$-0.673764\pi$
$67$	−4.43220	+	1.18760i	−0.541479	+	0.145089i	−0.0222951	+	0.999751i	$0.507097\pi$
$68$	0.761023	−	2.84018i	0.0922876	−	0.344422i
$69$	−3.05920	+	1.76623i	−0.368285	+	0.212629i
$70$	5.58309	+	1.31980i	0.667306	+	0.157747i
$71$	2.81229	−	4.87102i	0.333757	−	0.578084i	−0.649488	−	0.760372i	$-0.725017\pi$
$71$	2.81229	−	4.87102i	0.333757	−	0.578084i	0.983245	+	0.182288i	$0.0583502\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	−13.3326	+	3.57247i	−1.56047	+	0.418126i	−0.932812	−	0.360365i	$-0.882652\pi$
$73$	−13.3326	+	3.57247i	−1.56047	+	0.418126i	−0.627656	+	0.778491i	$0.715986\pi$
$74$	−0.235077	−	0.407166i	−0.0273272	−	0.0473321i
$75$	4.89787	+	1.00542i	0.565557	+	0.116096i
$76$	−1.53959	−	2.66665i	−0.176603	−	0.305886i
$77$	3.83150	−	3.83150i	0.436640	−	0.436640i
$78$	−1.71475	+	1.71475i	−0.194157	+	0.194157i
$79$	1.55137	+	2.68705i	0.174543	+	0.302317i	0.940003	−	0.341166i	$-0.110822\pi$
$79$	1.55137	+	2.68705i	0.174543	+	0.302317i	−0.765460	+	0.643483i	$0.777489\pi$
$80$	1.62734	+	1.53354i	0.181943	+	0.171455i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−5.34285	+	1.43161i	−0.590019	+	0.158095i
$83$	2.20061	−	0.589652i	0.241548	−	0.0647227i	−0.136014	−	0.990707i	$-0.543429\pi$
$83$	2.20061	−	0.589652i	0.241548	−	0.0647227i	0.377562	+	0.925984i	$0.376762\pi$
$84$	−1.28282	+	2.22192i	−0.139968	+	0.242431i
$85$	3.45489	+	5.59397i	0.374735	+	0.606751i
$86$	2.60915	−	1.50639i	0.281352	−	0.162439i
$87$	0.520003	−	1.94068i	0.0557502	−	0.208063i
$88$	2.04000	−	0.546616i	0.217465	−	0.0582695i
$89$	15.0864			1.59916			0.799580	−	0.600560i	$-0.205056\pi$
$89$	15.0864			1.59916			0.799580	+	0.600560i	$0.205056\pi$
$90$	−1.06010	+	1.96880i	−0.111744	+	0.207530i
$91$		−	6.22174i		−	0.652216i
$92$	2.49783	−	2.49783i	0.260417	−	0.260417i
$93$	1.65756	+	5.31531i	0.171881	+	0.551172i
$94$		−	6.16383i		−	0.635751i
$95$	6.70059	+	1.58397i	0.687466	+	0.162512i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	7.62570	+	7.62570i	0.774273	+	0.774273i	0.978850	−	0.204578i	$-0.0655821\pi$
$97$	7.62570	+	7.62570i	0.774273	+	0.774273i	−0.204578	+	0.978850i	$0.565582\pi$
$98$	0.108046	+	0.403232i	0.0109143	+	0.0407326i
$99$	1.05598	+	1.82901i	0.106130	+	0.183823i
$100$	−4.99120	+	0.296503i	−0.499120	+	0.0296503i
$101$	2.01603			0.200602			0.100301	−	0.994957i	$-0.468019\pi$
$101$	2.01603			0.200602			0.100301	+	0.994957i	$0.468019\pi$
$102$	−2.84018	+	0.761023i	−0.281219	+	0.0753525i
$103$	1.11516	+	4.16185i	0.109880	+	0.410079i	0.998853	−	0.0478810i	$-0.0152468\pi$
$103$	1.11516	+	4.16185i	0.109880	+	0.410079i	−0.888973	+	0.457960i	$0.848580\pi$
$104$	1.21251	−	2.10013i	0.118896	−	0.205935i
$105$	−1.64856	−	5.49499i	−0.160883	−	0.536257i
$106$	−0.228939	−	0.132178i	−0.0222365	−	0.0128383i
$107$	0.785626	−	2.93200i	0.0759493	−	0.283447i	−0.917498	−	0.397741i	$-0.869794\pi$
$107$	0.785626	−	2.93200i	0.0759493	−	0.283447i	0.993447	+	0.114295i	$0.0364608\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	20.3281i		−	1.94708i	−0.228512	−	0.973541i	$-0.573386\pi$
$109$		−	20.3281i		−	1.94708i	0.228512	−	0.973541i	$-0.426614\pi$
$110$	−2.23889	+	4.15804i	−0.213470	+	0.396454i
$111$	−0.235077	+	0.407166i	−0.0223126	+	0.0386465i
$112$	0.664038	−	2.47822i	0.0627457	−	0.234170i
$113$	2.05401	+	7.66567i	0.193225	+	0.721126i	0.992719	+	0.120452i	$0.0384344\pi$
$113$	2.05401	+	7.66567i	0.193225	+	0.721126i	−0.799494	+	0.600674i	$0.794899\pi$
$114$	−1.53959	+	2.66665i	−0.144196	+	0.249755i
$115$	0.234306	+	7.89535i	0.0218492	+	0.736246i
$116$			2.00914i			0.186544i
$117$	2.34239	+	0.627641i	0.216554	+	0.0580254i
$118$	−4.29033	−	1.14959i	−0.394957	−	0.105828i
$119$	3.77197	−	6.53324i	0.345776	−	0.598901i
$120$	0.514413	−	2.17609i	0.0469593	−	0.198649i
$121$	−3.26980	−	5.66347i	−0.297255	−	0.514861i
$122$	3.70748	−	3.70748i	0.335659	−	0.335659i
$123$	3.91124	+	3.91124i	0.352664	+	0.352664i
$124$	−2.97678	−	4.70519i	−0.267323	−	0.422538i
$125$	7.17170	−	8.57711i	0.641456	−	0.767160i
$126$	2.56565			0.228566
$127$	−5.17786	−	1.38740i	−0.459461	−	0.123112i	0.0216621	−	0.999765i	$-0.493104\pi$
$127$	−5.17786	−	1.38740i	−0.459461	−	0.123112i	−0.481123	+	0.876653i	$0.659771\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−2.60915	−	1.50639i	−0.229723	−	0.132631i
$130$	1.55820	+	5.19380i	0.136663	+	0.455527i
$131$	6.03036	+	10.4449i	0.526875	+	0.912575i	0.999510	+	0.0313162i	$0.00996990\pi$
$131$	6.03036	+	10.4449i	0.526875	+	0.912575i	−0.472634	+	0.881259i	$0.656697\pi$
$132$	−1.49338	−	1.49338i	−0.129982	−	0.129982i
$133$	−2.04470	−	7.63091i	−0.177298	−	0.661684i
$134$	−3.97380	−	2.29427i	−0.343284	−	0.198195i
$135$	2.23508	−	0.0663294i	0.192365	−	0.00570872i
$136$	2.54643	−	1.47018i	0.218355	−	0.126067i
$137$	−5.47027	−	20.4153i	−0.467357	−	1.74420i	−0.648955	−	0.760826i	$-0.724794\pi$
$137$	−5.47027	−	20.4153i	−0.467357	−	1.74420i	0.181599	−	0.983373i	$-0.441873\pi$
$138$	−3.41210	−	0.914269i	−0.290457	−	0.0778277i
$139$	1.84876			0.156810			0.0784048	−	0.996922i	$-0.475017\pi$
$139$	1.84876			0.156810			0.0784048	+	0.996922i	$0.475017\pi$
$140$	3.01460	+	4.88108i	0.254780	+	0.412526i
$141$	−5.33803	+	3.08192i	−0.449544	+	0.259544i
$142$	5.43292	−	1.45575i	0.455921	−	0.122164i
$143$	4.94704	+	1.32556i	0.413692	+	0.110849i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	−3.26956	−	3.08110i	−0.271522	−	0.255871i
$146$	−11.9537	−	6.90148i	−0.989297	−	0.571171i
$147$	0.295186	−	0.295186i	0.0243465	−	0.0243465i
$148$	0.121685	−	0.454135i	0.0100024	−	0.0373296i
$149$	13.0234	−	7.51908i	1.06692	−	0.615987i	0.139583	−	0.990210i	$-0.455424\pi$
$149$	13.0234	−	7.51908i	1.06692	−	0.615987i	0.927339	+	0.374223i	$0.122091\pi$
$150$	2.75238	+	4.17426i	0.224731	+	0.340826i
$151$		−	2.97324i		−	0.241958i	−0.992655	−	0.120979i	$-0.961397\pi$
$151$		−	2.97324i		−	0.241958i	0.992655	−	0.120979i	$-0.0386034\pi$
$152$	0.796952	−	2.97427i	0.0646413	−	0.241245i
$153$	2.07915	+	2.07915i	0.168090	+	0.168090i
$154$	5.41855			0.436640
$155$	12.2220	+	2.37135i	0.981693	+	0.190471i
$156$	−2.42502			−0.194157
$157$	10.7806	+	10.7806i	0.860382	+	0.860382i	0.991382	−	0.131000i	$-0.0418188\pi$
$157$	10.7806	+	10.7806i	0.860382	+	0.860382i	−0.131000	+	0.991382i	$0.541819\pi$
$158$	−0.803048	+	2.99702i	−0.0638871	+	0.238430i
$159$			0.264356i			0.0209648i
$160$	0.0663294	+	2.23508i	0.00524380	+	0.176699i
$161$	7.84884	−	4.53153i	0.618575	−	0.357134i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−5.29632	+	5.29632i	−0.414840	+	0.414840i	−0.883421	−	0.468581i	$-0.844766\pi$
$163$	−5.29632	+	5.29632i	−0.414840	+	0.414840i	0.468581	+	0.883421i	$0.344766\pi$
$164$	−4.79027	−	2.76566i	−0.374057	−	0.215962i
$165$	4.72042	−	0.140085i	0.367484	−	0.0109056i
$166$	1.97301	+	1.13912i	0.153135	+	0.0884128i
$167$	−11.9459	−	3.20089i	−0.924401	−	0.247692i	−0.234935	−	0.972011i	$-0.575488\pi$
$167$	−11.9459	−	3.20089i	−0.924401	−	0.247692i	−0.689466	+	0.724319i	$0.742155\pi$
$168$	−2.47822	+	0.664038i	−0.191199	+	0.0512317i
$169$	−6.16548	+	3.55964i	−0.474268	+	0.273819i
$170$	−1.51256	+	6.39851i	−0.116008	+	0.490743i
$171$	3.07919			0.235471
$172$	2.91013	+	0.779767i	0.221895	+	0.0594566i
$173$	5.65797	+	21.1158i	0.430168	+	1.60541i	0.752372	+	0.658738i	$0.228909\pi$
$173$	5.65797	+	21.1158i	0.430168	+	1.60541i	−0.322204	+	0.946670i	$0.604424\pi$
$174$	1.73997	−	1.00457i	0.131906	−	0.0761562i
$175$	−12.5662	−	2.57955i	−0.949916	−	0.194995i
$176$	1.82901	+	1.05598i	0.137867	+	0.0795976i
$177$	1.14959	+	4.29033i	0.0864086	+	0.322481i
$178$	10.6677	+	10.6677i	0.799580	+	0.799580i
$179$	0.614844	+	1.06494i	0.0459556	+	0.0795975i	0.888088	−	0.459673i	$-0.152033\pi$
$179$	0.614844	+	1.06494i	0.0459556	+	0.0795975i	−0.842133	+	0.539270i	$0.818700\pi$
$180$	−2.14176	+	0.642552i	−0.159637	+	0.0478930i
$181$	11.0006	+	6.35117i	0.817665	+	0.472079i	0.849611	−	0.527411i	$-0.176837\pi$
$181$	11.0006	+	6.35117i	0.817665	+	0.472079i	−0.0319456	+	0.999490i	$0.510170\pi$
$182$	4.39944	−	4.39944i	0.326108	−	0.326108i
$183$	−5.06451	−	1.35703i	−0.374379	−	0.100315i
$184$	3.53246			0.260417
$185$	0.552425	+	0.894458i	0.0406151	+	0.0657618i
$186$	−2.58642	+	4.93056i	−0.189646	+	0.361526i
$187$	4.39110	+	4.39110i	0.321109	+	0.321109i
$188$	4.35849	−	4.35849i	0.317875	−	0.317875i
$189$	−1.28282	−	2.22192i	−0.0933117	−	0.161621i
$190$	3.61800	+	5.85807i	0.262477	+	0.424989i
$191$	0.620187	−	1.07419i	0.0448751	−	0.0777260i	−0.842715	−	0.538359i	$-0.819044\pi$
$191$	0.620187	−	1.07419i	0.0448751	−	0.0777260i	0.887591	+	0.460633i	$0.152378\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−12.7245	−	3.40951i	−0.915927	−	0.245422i	−0.230084	−	0.973171i	$-0.573900\pi$
$193$	−12.7245	−	3.40951i	−0.915927	−	0.245422i	−0.685844	+	0.727749i	$0.740567\pi$
$194$			10.7844i			0.774273i
$195$	3.71887	−	3.94634i	0.266314	−	0.282603i
$196$	−0.208728	+	0.361528i	−0.0149092	+	0.0258234i
$197$	−6.85257	−	25.5741i	−0.488225	−	1.82208i	−0.565076	−	0.825039i	$-0.691153\pi$
$197$	−6.85257	−	25.5741i	−0.488225	−	1.82208i	0.0768508	−	0.997043i	$-0.475514\pi$
$198$	−0.546616	+	2.04000i	−0.0388463	+	0.144977i
$199$	−9.84497	+	17.0520i	−0.697891	+	1.20878i	0.271305	+	0.962493i	$0.412545\pi$
$199$	−9.84497	+	17.0520i	−0.697891	+	1.20878i	−0.969196	+	0.246290i	$0.920789\pi$
$200$	−3.73897	−	3.31965i	−0.264385	−	0.234735i
$201$			4.58855i			0.323651i
$202$	1.42555	+	1.42555i	0.100301	+	0.100301i
$203$	−1.33414	+	4.97910i	−0.0936386	+	0.349464i
$204$	−2.54643	−	1.47018i	−0.178286	−	0.102933i
$205$	11.8468	−	3.55416i	0.827413	−	0.248233i
$206$	−2.15433	+	3.73141i	−0.150099	+	0.259980i
$207$	0.914269	+	3.41210i	0.0635461	+	0.237157i
$208$	2.34239	−	0.627641i	0.162415	−	0.0435191i
$209$	6.50313			0.449831
$210$	2.71984	−	5.05126i	0.187687	−	0.348570i
$211$	9.50927	+	16.4705i	0.654645	+	1.13388i	0.981983	+	0.188971i	$0.0605153\pi$
$211$	9.50927	+	16.4705i	0.654645	+	1.13388i	−0.327337	+	0.944907i	$0.606151\pi$
$212$	−0.0684204	−	0.255348i	−0.00469913	−	0.0175374i
$213$	−3.97717	−	3.97717i	−0.272511	−	0.272511i
$214$	2.62876	−	1.51771i	0.179698	−	0.103749i
$215$	−5.73175	+	3.53998i	−0.390902	+	0.241425i
$216$		−	1.00000i		−	0.0680414i
$217$	−4.25271	−	13.6372i	−0.288692	−	0.925754i
$218$	14.3742	−	14.3742i	0.973541	−	0.973541i
$219$			13.8030i			0.932718i
$220$	−4.52332	+	1.35705i	−0.304962	+	0.0914920i
$221$	7.13044			0.479646
$222$	−0.454135	+	0.121685i	−0.0304795	+	0.00816696i
$223$	0.280902	−	1.04834i	0.0188106	−	0.0702020i	−0.955883	−	0.293749i	$-0.905097\pi$
$223$	0.280902	−	1.04834i	0.0188106	−	0.0702020i	0.974693	+	0.223547i	$0.0717636\pi$
$224$	2.22192	−	1.28282i	0.148458	−	0.0857122i
$225$	2.23882	−	4.47076i	0.149255	−	0.298051i
$226$	−3.96805	+	6.87286i	−0.263950	+	0.457176i
$227$	−18.8241	+	5.04390i	−1.24940	+	0.334776i	−0.822105	−	0.569337i	$-0.807200\pi$
$227$	−18.8241	+	5.04390i	−1.24940	+	0.334776i	−0.427295	+	0.904112i	$0.640533\pi$
$228$	−2.97427	+	0.796952i	−0.196976	+	0.0527794i
$229$	−6.53939	−	11.3265i	−0.432135	−	0.748479i	0.564922	−	0.825144i	$-0.308906\pi$
$229$	−6.53939	−	11.3265i	−0.432135	−	0.748479i	−0.997057	+	0.0766648i	$0.975573\pi$
$230$	−5.41718	+	5.74854i	−0.357198	+	0.379047i
$231$	−2.70928	−	4.69261i	−0.178257	−	0.308751i
$232$	−1.42068	+	1.42068i	−0.0932719	+	0.0932719i
$233$	−5.18083	+	5.18083i	−0.339407	+	0.339407i	−0.856144	−	0.516737i	$-0.827147\pi$
$233$	−5.18083	+	5.18083i	−0.339407	+	0.339407i	0.516737	+	0.856144i	$0.327147\pi$
$234$	1.21251	+	2.10013i	0.0792642	+	0.137290i
$235$	0.408843	+	13.7767i	0.0266700	+	0.898692i
$236$	−2.22084	−	3.84661i	−0.144564	−	0.250393i
$237$	2.99702	−	0.803048i	0.194677	−	0.0521636i
$238$	7.28689	−	1.95252i	0.472339	−	0.126563i
$239$	−2.37945	+	4.12133i	−0.153914	+	0.266587i	−0.932663	−	0.360749i	$-0.882521\pi$
$239$	−2.37945	+	4.12133i	−0.153914	+	0.266587i	0.778749	+	0.627335i	$0.215854\pi$
$240$	1.90247	−	1.17498i	0.122804	−	0.0758449i
$241$	4.07630	−	2.35345i	0.262577	−	0.151599i	−0.362932	−	0.931815i	$-0.618224\pi$
$241$	4.07630	−	2.35345i	0.262577	−	0.151599i	0.625510	+	0.780216i	$0.284891\pi$
$242$	1.69258	−	6.31678i	0.108803	−	0.406058i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	5.24317			0.335659
$245$	−0.268237	−	0.894090i	−0.0171370	−	0.0571213i
$246$			5.53132i			0.352664i
$247$	5.28003	−	5.28003i	0.335960	−	0.335960i
$248$	1.22217	−	5.43197i	0.0776077	−	0.344930i
$249$		−	2.27824i		−	0.144378i
$250$	11.1361	−	0.993773i	0.704308	−	0.0628517i
$251$	5.20426	−	3.00468i	0.328490	−	0.189654i	−0.326680	−	0.945135i	$-0.605930\pi$
$251$	5.20426	−	3.00468i	0.328490	−	0.189654i	0.655171	+	0.755481i	$0.272597\pi$
$252$	1.81419	+	1.81419i	0.114283	+	0.114283i
$253$	1.93090	+	7.20623i	0.121395	+	0.453052i
$254$	−2.68026	−	4.64234i	−0.168174	−	0.291286i
$255$	6.29755	−	1.88934i	0.394368	−	0.118315i
$256$	1.00000			0.0625000
$257$	−10.4409	+	2.79762i	−0.651283	+	0.174511i	−0.569309	−	0.822124i	$-0.692789\pi$
$257$	−10.4409	+	2.79762i	−0.651283	+	0.174511i	−0.0819740	+	0.996634i	$0.526122\pi$
$258$	−0.779767	−	2.91013i	−0.0485461	−	0.181177i
$259$	0.603126	−	1.04464i	0.0374764	−	0.0649110i
$260$	−2.57076	+	4.77439i	−0.159432	+	0.296095i
$261$	−1.73997	−	1.00457i	−0.107701	−	0.0621813i
$262$	−3.12155	+	11.6498i	−0.192850	+	0.719725i
$263$	−8.80074	−	8.80074i	−0.542677	−	0.542677i	0.381636	−	0.924313i	$-0.375361\pi$
$263$	−8.80074	−	8.80074i	−0.542677	−	0.542677i	−0.924313	+	0.381636i	$0.875361\pi$
$264$		−	2.11196i		−	0.129982i
$265$	0.520465	+	0.280244i	0.0319719	+	0.0172152i
$266$	3.95005	−	6.84169i	0.242193	−	0.419491i
$267$	3.90466	−	14.5724i	0.238961	−	0.891815i
$268$	−1.18760	−	4.43220i	−0.0725444	−	0.270739i
$269$	−2.96942	+	5.14319i	−0.181049	+	0.313586i	−0.942238	−	0.334944i	$-0.891283\pi$
$269$	−2.96942	+	5.14319i	−0.181049	+	0.313586i	0.761189	+	0.648530i	$0.224616\pi$
$270$	1.62734	+	1.53354i	0.0990371	+	0.0933283i
$271$			10.0800i			0.612318i	0.951980	+	0.306159i	$0.0990439\pi$
$271$			10.0800i			0.612318i	−0.951980	+	0.306159i	$0.900956\pi$
$272$	2.84018	+	0.761023i	0.172211	+	0.0461438i
$273$	−6.00974	−	1.61031i	−0.363726	−	0.0974601i
$274$	10.5678	−	18.3039i	0.638421	−	1.10578i
$275$	4.72831	−	9.44208i	0.285128	−	0.569379i
$276$	−1.76623	−	3.05920i	−0.106315	−	0.184142i
$277$	11.4671	−	11.4671i	0.688993	−	0.688993i	−0.273017	−	0.962009i	$-0.588021\pi$
$277$	11.4671	−	11.4671i	0.688993	−	0.688993i	0.962009	+	0.273017i	$0.0880214\pi$
$278$	1.30727	+	1.30727i	0.0784048	+	0.0784048i
$279$	5.56320	−	0.225374i	0.333060	−	0.0134928i
$280$	−1.31980	+	5.58309i	−0.0788733	+	0.333653i
$281$	15.0207			0.896058			0.448029	−	0.894019i	$-0.352126\pi$
$281$	15.0207			0.896058			0.448029	+	0.894019i	$0.352126\pi$
$282$	−5.95380	−	1.59532i	−0.354544	−	0.0949997i
$283$	−8.86983	+	8.86983i	−0.527257	+	0.527257i	−0.919753	−	0.392497i	$-0.871611\pi$
$283$	−8.86983	+	8.86983i	−0.527257	+	0.527257i	0.392497	+	0.919753i	$0.371611\pi$
$284$	4.87102	+	2.81229i	0.289042	+	0.166878i
$285$	3.26424	−	6.06231i	0.193357	−	0.359100i
$286$	2.56078	+	4.43539i	0.151422	+	0.262270i
$287$	−10.0349	−	10.0349i	−0.592338	−	0.592338i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	−7.23499	−	4.17712i	−0.425588	−	0.245713i
$290$	−0.133265	−	4.49059i	−0.00782558	−	0.263697i
$291$	9.33954	−	5.39219i	0.547493	−	0.316096i
$292$	−3.57247	−	13.3326i	−0.209063	−	0.780234i
$293$	−24.7417	−	6.62953i	−1.44543	−	0.387301i	−0.550997	−	0.834507i	$-0.685752\pi$
$293$	−24.7417	−	6.62953i	−1.44543	−	0.387301i	−0.894431	+	0.447206i	$0.852419\pi$
$294$	0.417456			0.0243465
$295$	9.66551	+	2.28486i	0.562748	+	0.133030i
$296$	0.407166	−	0.235077i	0.0236660	−	0.0136636i
$297$	2.04000	−	0.546616i	0.118373	−	0.0317179i
$298$	14.5258	+	3.89216i	0.841454	+	0.225467i
$299$	7.41863	+	4.28315i	0.429030	+	0.247701i
$300$	−1.00542	+	4.89787i	−0.0580478	+	0.282779i
$301$	6.69416	+	3.86487i	0.385845	+	0.222768i
$302$	2.10239	−	2.10239i	0.120979	−	0.120979i
$303$	0.521786	−	1.94733i	0.0299758	−	0.111871i
$304$	2.66665	−	1.53959i	0.152943	−	0.0883017i
$305$	−8.04061	+	8.53244i	−0.460404	+	0.488566i
$306$			2.94037i			0.168090i
$307$	−6.62457	+	24.7232i	−0.378084	+	1.41103i	0.470702	+	0.882293i	$0.344001\pi$
$307$	−6.62457	+	24.7232i	−0.378084	+	1.41103i	−0.848786	+	0.528737i	$0.822666\pi$
$308$	3.83150	+	3.83150i	0.218320	+	0.218320i
$309$	4.30866			0.245111
$310$	6.96545	+	10.3190i	0.395611	+	0.586082i
$311$	2.84327			0.161227			0.0806137	−	0.996745i	$-0.474312\pi$
$311$	2.84327			0.161227			0.0806137	+	0.996745i	$0.474312\pi$
$312$	−1.71475	−	1.71475i	−0.0970785	−	0.0970785i
$313$	−6.97882	+	26.0453i	−0.394466	+	1.47217i	0.428221	+	0.903674i	$0.359141\pi$
$313$	−6.97882	+	26.0453i	−0.394466	+	1.47217i	−0.822687	+	0.568495i	$0.807526\pi$
$314$			15.2460i			0.860382i
$315$	−5.73444	+	0.170178i	−0.323099	+	0.00958843i
$316$	−2.68705	+	1.55137i	−0.151158	+	0.0872714i
$317$	−0.464982	+	1.73533i	−0.0261160	+	0.0974661i	−0.977754	−	0.209756i	$-0.932733\pi$
$317$	−0.464982	+	1.73533i	−0.0261160	+	0.0974661i	0.951638	+	0.307222i	$0.0993996\pi$
$318$	−0.186928	+	0.186928i	−0.0104824	+	0.0104824i
$319$	−3.67474	−	2.12161i	−0.205746	−	0.118788i
$320$	−1.53354	+	1.62734i	−0.0857276	+	0.0909714i
$321$	−2.62876	−	1.51771i	−0.146723	−	0.0847105i
$322$	8.75424	+	2.34569i	0.487855	+	0.130720i
$323$	8.74543	−	2.34333i	0.486609	−	0.130386i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−3.82721	−	11.5052i	−0.212295	−	0.638196i
$326$	−7.49013			−0.414840
$327$	−19.6355	−	5.26131i	−1.08584	−	0.290951i
$328$	−1.43161	−	5.34285i	−0.0790475	−	0.295009i
$329$	13.6955	−	7.90711i	0.755058	−	0.435933i
$330$	3.43689	+	3.23878i	0.189195	+	0.178289i
$331$	20.5011	+	11.8363i	1.12684	+	0.650583i	0.943139	−	0.332399i	$-0.107858\pi$
$331$	20.5011	+	11.8363i	1.12684	+	0.650583i	0.183704	+	0.982982i	$0.441191\pi$
$332$	0.589652	+	2.20061i	0.0323613	+	0.120774i
$333$	0.332450	+	0.332450i	0.0182181	+	0.0182181i
$334$	−6.18365	−	10.7104i	−0.338354	−	0.586047i
$335$	9.03395	+	4.86431i	0.493577	+	0.265766i
$336$	−2.22192	−	1.28282i	−0.121215	−	0.0699838i
$337$	5.69489	−	5.69489i	0.310221	−	0.310221i	−0.534774	−	0.844995i	$-0.679603\pi$
$337$	5.69489	−	5.69489i	0.310221	−	0.310221i	0.844995	+	0.534774i	$0.179603\pi$
$338$	−6.87670	−	1.84261i	−0.374043	−	0.100225i
$339$	7.93609			0.431029
$340$	−5.59397	+	3.45489i	−0.303376	+	0.187367i
$341$	11.7493	−	0.475982i	0.636259	−	0.0257758i
$342$	2.17731	+	2.17731i	0.117736	+	0.117736i
$343$	−13.4566	+	13.4566i	−0.726591	+	0.726591i
$344$	1.50639	+	2.60915i	0.0812193	+	0.140676i
$345$	7.68697	+	1.81715i	0.413853	+	0.0978318i
$346$	−10.9304	+	18.9320i	−0.587620	+	1.01779i
$347$	−12.8853	−	3.45260i	−0.691717	−	0.185345i	−0.104200	−	0.994556i	$-0.533228\pi$
$347$	−12.8853	−	3.45260i	−0.691717	−	0.185345i	−0.587518	+	0.809211i	$0.699895\pi$
$348$	1.94068	+	0.520003i	0.104031	+	0.0278751i
$349$		−	7.09319i		−	0.379690i	−0.981814	−	0.189845i	$-0.939201\pi$
$349$		−	7.09319i		−	0.379690i	0.981814	−	0.189845i	$-0.0607985\pi$
$350$	−7.06163	−	10.7097i	−0.377460	−	0.572456i
$351$	1.21251	−	2.10013i	0.0647190	−	0.112097i
$352$	0.546616	+	2.04000i	0.0291348	+	0.108732i
$353$	3.74429	−	13.9739i	0.199288	−	0.743754i	−0.791827	−	0.610746i	$-0.790870\pi$
$353$	3.74429	−	13.9739i	0.199288	−	0.743754i	0.991115	−	0.133008i	$-0.0424636\pi$
$354$	−2.22084	+	3.84661i	−0.118036	+	0.204445i
$355$	−12.0465	+	3.61408i	−0.639360	+	0.191815i
$356$			15.0864i			0.799580i
$357$	−5.33437	−	5.33437i	−0.282325	−	0.282325i
$358$	−0.318267	+	1.18779i	−0.0168209	+	0.0627766i
$359$	−24.6267	−	14.2182i	−1.29975	−	0.750408i	−0.319385	−	0.947625i	$-0.603476\pi$
$359$	−24.6267	−	14.2182i	−1.29975	−	0.750408i	−0.980360	+	0.197217i	$0.936810\pi$
$360$	−1.96880	−	1.06010i	−0.103765	−	0.0558721i
$361$	−4.75931	+	8.24336i	−0.250490	+	0.433861i
$362$	3.28761	+	12.2695i	0.172793	+	0.644872i
$363$	−6.31678	+	1.69258i	−0.331545	+	0.0888372i
$364$	6.22174			0.326108
$365$	27.1753	+	14.6325i	1.42242	+	0.765901i
$366$	−2.62158	−	4.54072i	−0.137032	−	0.237347i
$367$	5.01820	+	18.7282i	0.261948	+	0.977603i	0.964092	+	0.265568i	$0.0855596\pi$
$367$	5.01820	+	18.7282i	0.261948	+	0.977603i	−0.702144	+	0.712035i	$0.747774\pi$
$368$	2.49783	+	2.49783i	0.130208	+	0.130208i
$369$	4.79027	−	2.76566i	0.249371	−	0.143975i
$370$	−0.241854	+	1.02310i	−0.0125734	+	0.0531885i
$371$		−	0.678244i		−	0.0352127i
$372$	−5.31531	+	1.65756i	−0.275586	+	0.0859403i
$373$	−11.7811	+	11.7811i	−0.610004	+	0.610004i	−0.942947	−	0.332943i	$-0.891958\pi$
$373$	−11.7811	+	11.7811i	−0.610004	+	0.610004i	0.332943	+	0.942947i	$0.391958\pi$
$374$			6.20995i			0.321109i
$375$	−6.42868	−	9.14725i	−0.331975	−	0.472362i
$376$	6.16383			0.317875
$377$	−4.70618	+	1.26102i	−0.242381	+	0.0649457i
$378$	0.664038	−	2.47822i	0.0341544	−	0.127466i
$379$	3.27940	−	1.89336i	0.168452	−	0.0972556i	−0.413404	−	0.910548i	$-0.635660\pi$
$379$	3.27940	−	1.89336i	0.168452	−	0.0972556i	0.581856	+	0.813292i	$0.302327\pi$
$380$	−1.58397	+	6.70059i	−0.0812561	+	0.343733i
$381$	−2.68026	+	4.64234i	−0.137314	+	0.237834i
$382$	1.19811	−	0.321032i	0.0613006	−	0.0164254i
$383$	−31.5083	+	8.44263i	−1.61000	+	0.431398i	−0.948043	−	0.318143i	$-0.896941\pi$
$383$	−31.5083	+	8.44263i	−1.61000	+	0.431398i	−0.661958	+	0.749541i	$0.730274\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−12.1109	+	0.359409i	−0.617230	+	0.0183172i
$386$	−6.58667	−	11.4084i	−0.335253	−	0.580675i
$387$	−2.13036	+	2.13036i	−0.108292	+	0.108292i
$388$	−7.62570	+	7.62570i	−0.387136	+	0.387136i
$389$	−1.14547	−	1.98401i	−0.0580775	−	0.100593i	0.835525	−	0.549453i	$-0.185164\pi$
$389$	−1.14547	−	1.98401i	−0.0580775	−	0.100593i	−0.893602	+	0.448859i	$0.851830\pi$
$390$	5.42012	−	0.160850i	0.274459	−	0.00814496i
$391$	5.19337	+	8.99518i	0.262640	+	0.454906i
$392$	−0.403232	+	0.108046i	−0.0203663	+	0.00545713i
$393$	11.6498	−	3.12155i	0.587653	−	0.157461i
$394$	13.2381	−	22.9291i	0.666928	−	1.15515i
$395$	1.59609	−	6.75185i	0.0803080	−	0.339722i
$396$	−1.82901	+	1.05598i	−0.0919114	+	0.0530651i
$397$	9.58684	−	35.7786i	0.481150	−	1.79568i	−0.115656	−	0.993289i	$-0.536897\pi$
$397$	9.58684	−	35.7786i	0.481150	−	1.79568i	0.596805	−	0.802386i	$-0.296436\pi$
$398$	−19.0190	+	5.09613i	−0.953337	+	0.255446i
$399$	−7.90010			−0.395500
$400$	−0.296503	−	4.99120i	−0.0148252	−	0.249560i
$401$			25.8609i			1.29143i	0.763578	+	0.645716i	$0.223441\pi$
$401$			25.8609i			1.29143i	−0.763578	+	0.645716i	$0.776559\pi$
$402$	−3.24459	+	3.24459i	−0.161826	+	0.161826i
$403$	9.15303	−	9.92594i	0.455945	−	0.494446i
$404$			2.01603i			0.100301i
$405$	0.514413	−	2.17609i	0.0255614	−	0.108131i
$406$	−4.46414	+	2.57737i	−0.221551	+	0.127913i
$407$	0.702122	+	0.702122i	0.0348029	+	0.0348029i
$408$	−0.761023	−	2.84018i	−0.0376762	−	0.140610i
$409$	3.80664	+	6.59330i	0.188226	+	0.326018i	0.944659	−	0.328054i	$-0.106393\pi$
$409$	3.80664	+	6.59330i	0.188226	+	0.326018i	−0.756433	+	0.654072i	$0.773059\pi$
$410$	10.8901	+	5.86375i	0.537823	+	0.289590i
$411$	−21.1355			−1.04254
$412$	−4.16185	+	1.11516i	−0.205040	+	0.0549402i
$413$	−2.94945	−	11.0075i	−0.145133	−	0.541643i
$414$	−1.76623	+	3.05920i	−0.0868056	+	0.150352i
$415$	−4.48541	−	2.41516i	−0.220180	−	0.118555i
$416$	2.10013	+	1.21251i	0.102967	+	0.0594482i
$417$	0.478493	−	1.78576i	0.0234319	−	0.0874491i
$418$	4.59841	+	4.59841i	0.224915	+	0.224915i
$419$			28.8316i			1.40851i	0.709945	+	0.704257i	$0.248720\pi$
$419$			28.8316i			1.40851i	−0.709945	+	0.704257i	$0.751280\pi$
$420$	5.49499	−	1.64856i	0.268128	−	0.0804415i
$421$	8.84047	−	15.3121i	0.430858	−	0.746268i	−0.566089	−	0.824344i	$-0.691544\pi$
$421$	8.84047	−	15.3121i	0.430858	−	0.746268i	0.996947	+	0.0780758i	$0.0248776\pi$
$422$	−4.92236	+	18.3705i	−0.239617	+	0.894262i
$423$	1.59532	+	5.95380i	0.0775670	+	0.289484i
$424$	0.132178	−	0.228939i	0.00641913	−	0.0111183i
$425$	2.95630	−	14.4015i	0.143401	−	0.698577i
$426$		−	5.62457i		−	0.272511i
$427$	12.9937	+	3.48166i	0.628811	+	0.168490i
$428$	2.93200	+	0.785626i	0.141723	+	0.0379747i
$429$	2.56078	−	4.43539i	0.123635	−	0.214143i
$430$	−6.55610	−	1.54982i	−0.316163	−	0.0747388i
$431$	−4.14497	−	7.17929i	−0.199656	−	0.345814i	0.748761	−	0.662840i	$-0.230649\pi$
$431$	−4.14497	−	7.17929i	−0.199656	−	0.345814i	−0.948417	+	0.317026i	$0.897316\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−19.4469	−	19.4469i	−0.934556	−	0.934556i	0.0634298	−	0.997986i	$-0.479796\pi$
$433$	−19.4469	−	19.4469i	−0.934556	−	0.934556i	−0.997986	+	0.0634298i	$0.979796\pi$
$434$	6.63584	−	12.6501i	0.318531	−	0.607223i
$435$	−3.82234	+	2.36071i	−0.183267	+	0.113187i
$436$	20.3281			0.973541
$437$	10.5065	+	2.81520i	0.502593	+	0.134669i
$438$	−9.76017	+	9.76017i	−0.466359	+	0.466359i
$439$	−31.7467	−	18.3290i	−1.51519	−	0.874793i	−0.999841	−	0.0178104i	$-0.994330\pi$
$439$	−31.7467	−	18.3290i	−1.51519	−	0.874793i	−0.515345	−	0.856983i	$-0.672336\pi$
$440$	−4.15804	−	2.23889i	−0.198227	−	0.106735i
$441$	−0.208728	−	0.361528i	−0.00993943	−	0.0172156i
$442$	5.04198	+	5.04198i	0.239823	+	0.239823i
$443$	0.106505	+	0.397481i	0.00506019	+	0.0188849i	0.968410	−	0.249364i	$-0.0802216\pi$
$443$	0.106505	+	0.397481i	0.00506019	+	0.0188849i	−0.963350	+	0.268249i	$0.913555\pi$
$444$	−0.407166	−	0.235077i	−0.0193232	−	0.0111563i
$445$	−24.5508	−	23.1357i	−1.16382	−	1.09674i
$446$	0.939916	−	0.542660i	0.0445063	−	0.0256957i
$447$	−3.89216	−	14.5258i	−0.184093	−	0.687044i
$448$	2.47822	+	0.664038i	0.117085	+	0.0313729i
$449$	5.53485			0.261206			0.130603	−	0.991435i	$-0.458309\pi$
$449$	5.53485			0.261206			0.130603	+	0.991435i	$0.458309\pi$
$450$	4.74439	−	1.57822i	0.223653	−	0.0743979i
$451$	10.1169	−	5.84098i	0.476385	−	0.275041i
$452$	−7.66567	+	2.05401i	−0.360563	+	0.0966126i
$453$	−2.87192	−	0.769530i	−0.134935	−	0.0361557i
$454$	−16.8772	−	9.74407i	−0.792088	−	0.457312i
$455$	−9.54130	+	10.1249i	−0.447303	+	0.474664i
$456$	−2.66665	−	1.53959i	−0.124877	−	0.0720980i
$457$	1.89032	−	1.89032i	0.0884254	−	0.0884254i	−0.661510	−	0.749936i	$-0.730084\pi$
$457$	1.89032	−	1.89032i	0.0884254	−	0.0884254i	0.749936	+	0.661510i	$0.230084\pi$
$458$	3.38504	−	12.6331i	0.158172	−	0.590307i
$459$	2.54643	−	1.47018i	0.118857	−	0.0686223i
$460$	−7.89535	+	0.234306i	−0.368123	+	0.0109246i
$461$		−	35.3344i		−	1.64569i	−0.568268	−	0.822844i	$-0.692386\pi$
$461$		−	35.3344i		−	1.64569i	0.568268	−	0.822844i	$-0.307614\pi$
$462$	1.40242	−	5.23392i	0.0652467	−	0.243504i
$463$	−22.9503	−	22.9503i	−1.06659	−	1.06659i	−0.997619	−	0.0689716i	$-0.978028\pi$
$463$	−22.9503	−	22.9503i	−1.06659	−	1.06659i	−0.0689716	−	0.997619i	$-0.521972\pi$
$464$	−2.00914			−0.0932719
$465$	5.45383	−	11.1918i	0.252915	−	0.519006i
$466$	−7.32679			−0.339407
$467$	−8.62417	−	8.62417i	−0.399079	−	0.399079i	0.478829	−	0.877908i	$-0.341061\pi$
$467$	−8.62417	−	8.62417i	−0.399079	−	0.399079i	−0.877908	+	0.478829i	$0.841061\pi$
$468$	−0.627641	+	2.34239i	−0.0290127	+	0.108277i
$469$		−	11.7726i		−	0.543608i
$470$	−9.45249	+	10.0307i	−0.436011	+	0.462681i
$471$	13.2034	−	7.62301i	0.608382	−	0.351250i
$472$	1.14959	−	4.29033i	0.0529142	−	0.197479i
$473$	−4.49925	+	4.49925i	−0.206876	+	0.206876i
$474$	2.68705	+	1.55137i	0.123420	+	0.0712568i
$475$	−8.47509	−	12.8533i	−0.388864	−	0.589750i
$476$	6.53324	+	3.77197i	0.299451	+	0.172888i
$477$	0.255348	+	0.0684204i	0.0116916	+	0.00313275i
$478$	−4.59674	+	1.23169i	−0.210250	+	0.0563364i
$479$	−29.4543	+	17.0054i	−1.34580	+	0.776998i	−0.987652	−	0.156666i	$-0.949925\pi$
$479$	−29.4543	+	17.0054i	−1.34580	+	0.776998i	−0.358149	+	0.933665i	$0.616592\pi$
$480$	2.17609	+	0.514413i	0.0993246	+	0.0234796i
$481$	1.14013			0.0519857
$482$	4.54652	+	1.21824i	0.207088	+	0.0554891i
$483$	−2.34569	−	8.75424i	−0.106733	−	0.398332i
$484$	5.66347	−	3.26980i	0.257430	−	0.148627i
$485$	−0.715320	−	24.1040i	−0.0324810	−	1.09451i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	6.79753	+	25.3687i	0.308026	+	1.14957i	0.930309	+	0.366775i	$0.119538\pi$
$487$	6.79753	+	25.3687i	0.308026	+	1.14957i	−0.622284	+	0.782792i	$0.713795\pi$
$488$	3.70748	+	3.70748i	0.167830	+	0.167830i
$489$	3.74507	+	6.48664i	0.169358	+	0.293336i
$490$	0.442545	−	0.821890i	0.0199921	−	0.0371292i
$491$	−5.25372	−	3.03324i	−0.237097	−	0.136888i	0.376745	−	0.926317i	$-0.377043\pi$
$491$	−5.25372	−	3.03324i	−0.237097	−	0.136888i	−0.613842	+	0.789429i	$0.710377\pi$
$492$	−3.91124	+	3.91124i	−0.176332	+	0.176332i
$493$	−5.70631	−	1.52900i	−0.256999	−	0.0688627i
$494$	7.46708			0.335960
$495$	1.08642	−	4.59583i	0.0488310	−	0.206567i
$496$	4.70519	−	2.97678i	0.211269	−	0.133661i
$497$	10.2040	+	10.2040i	0.457713	+	0.457713i
$498$	1.61096	−	1.61096i	0.0721888	−	0.0721888i
$499$	−2.78887	−	4.83046i	−0.124847	−	0.216241i	0.796826	−	0.604209i	$-0.206511\pi$
$499$	−2.78887	−	4.83046i	−0.124847	−	0.216241i	−0.921673	+	0.387967i	$0.873177\pi$
$500$	8.57711	+	7.17170i	0.383580	+	0.320728i
$501$	−6.18365	+	10.7104i	−0.276265	+	0.478505i
$502$	5.80460	+	1.55534i	0.259072	+	0.0694181i
$503$	−23.0337	−	6.17187i	−1.02702	−	0.275190i	−0.294297	−	0.955714i	$-0.595086\pi$
$503$	−23.0337	−	6.17187i	−1.02702	−	0.275190i	−0.732726	+	0.680524i	$0.761752\pi$
$504$			2.56565i			0.114283i
$505$	−3.28077	−	3.09166i	−0.145992	−	0.137577i
$506$	−3.73022	+	6.46093i	−0.165828	+	0.287223i
$507$	1.84261	+	6.87670i	0.0818330	+	0.305405i
$508$	1.38740	−	5.17786i	0.0615561	−	0.229730i
$509$	−1.67638	+	2.90358i	−0.0743044	+	0.128699i	−0.900784	−	0.434268i	$-0.857007\pi$
$509$	−1.67638	+	2.90358i	−0.0743044	+	0.128699i	0.826479	+	0.562967i	$0.190340\pi$
$510$	5.78900	+	3.11708i	0.256341	+	0.138027i
$511$		−	35.4135i		−	1.56660i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.796952	−	2.97427i	0.0351863	−	0.131317i
$514$	−9.36102	−	5.40458i	−0.412897	−	0.238386i
$515$	4.56761	−	8.48292i	0.201273	−	0.373802i
$516$	1.50639	−	2.60915i	0.0663153	−	0.114861i
$517$	3.36925	+	12.5742i	0.148180	+	0.553014i
$518$	1.16515	−	0.312201i	0.0511937	−	0.0137173i
$519$	21.8607			0.959580
$520$	−5.19380	+	1.55820i	−0.227763	+	0.0683316i
$521$	4.94530	+	8.56551i	0.216657	+	0.375262i	0.953784	−	0.300493i	$-0.0971512\pi$
$521$	4.94530	+	8.56551i	0.216657	+	0.375262i	−0.737127	+	0.675755i	$0.763818\pi$
$522$	−0.520003	−	1.94068i	−0.0227599	−	0.0849412i
$523$	12.5883	+	12.5883i	0.550448	+	0.550448i	0.926570	−	0.376122i	$-0.122743\pi$
$523$	12.5883	+	12.5883i	0.550448	+	0.550448i	−0.376122	+	0.926570i	$0.622743\pi$
$524$	−10.4449	+	6.03036i	−0.456288	+	0.263438i
$525$	−5.74402	+	11.4704i	−0.250690	+	0.500609i
$526$		−	12.4461i		−	0.542677i
$527$	15.6290	−	4.87382i	0.680808	−	0.212307i
$528$	1.49338	−	1.49338i	0.0649912	−	0.0649912i
$529$		−	10.5217i		−	0.457465i
$530$	0.169862	+	0.566187i	0.00737835	+	0.0245936i
$531$	4.44168			0.192752
$532$	7.63091	−	2.04470i	0.330842	−	0.0886489i
$533$	3.47169	−	12.9565i	0.150375	−	0.561209i
$534$	13.0652	−	7.54322i	0.565388	−	0.326427i
$535$	−5.77482	+	3.56658i	−0.249667	+	0.154197i
$536$	2.29427	−	3.97380i	0.0990975	−	0.171642i
$537$	1.18779	−	0.318267i	0.0512568	−	0.0137342i
$538$	−5.73648	+	1.53709i	−0.247317	+	0.0662685i
$539$	−0.440826	−	0.763533i	−0.0189877	−	0.0328877i
$540$	0.0663294	+	2.23508i	0.00285436	+	0.0961827i
$541$	−1.81372	−	3.14146i	−0.0779780	−	0.135062i	0.824399	−	0.566008i	$-0.191513\pi$
$541$	−1.81372	−	3.14146i	−0.0779780	−	0.135062i	−0.902377	+	0.430947i	$0.858180\pi$
$542$	−7.12765	+	7.12765i	−0.306159	+	0.306159i
$543$	8.98192	−	8.98192i	0.385451	−	0.385451i
$544$	1.47018	+	2.54643i	0.0630336	+	0.109177i
$545$	−31.1740	+	33.0809i	−1.33535	+	1.41703i
$546$	−3.11087	−	5.38819i	−0.133133	−	0.230593i
$547$	−18.0223	+	4.82907i	−0.770579	+	0.206476i	−0.622627	−	0.782519i	$-0.713935\pi$
$547$	−18.0223	+	4.82907i	−0.770579	+	0.206476i	−0.147952	+	0.988995i	$0.547268\pi$
$548$	20.4153	−	5.47027i	0.872100	−	0.233678i
$549$	−2.62158	+	4.54072i	−0.111886	+	0.193793i
$550$	10.0200	−	3.33314i	0.427253	−	0.142126i
$551$	−5.35768	+	3.09326i	−0.228245	+	0.131777i
$552$	0.914269	−	3.41210i	0.0389139	−	0.145229i
$553$	−7.68929	+	2.06034i	−0.326982	+	0.0876145i
$554$	16.2170			0.688993
$555$	1.00696	−	0.302099i	0.0427430	−	0.0128234i
$556$			1.84876i			0.0784048i
$557$	−4.92537	+	4.92537i	−0.208695	+	0.208695i	−0.803712	−	0.595018i	$-0.797145\pi$
$557$	−4.92537	+	4.92537i	−0.208695	+	0.208695i	0.595018	+	0.803712i	$0.297145\pi$
$558$	4.09314	+	3.77441i	0.173276	+	0.159784i
$559$			7.30607i			0.309014i
$560$	−4.88108	+	3.01460i	−0.206263	+	0.127390i
$561$	5.37797	−	3.10497i	0.227058	−	0.131092i
$562$	10.6212	+	10.6212i	0.448029	+	0.448029i
$563$	−5.77651	−	21.5582i	−0.243451	−	0.908572i	−0.974156	−	0.225878i	$-0.927475\pi$
$563$	−5.77651	−	21.5582i	−0.243451	−	0.908572i	0.730705	−	0.682694i	$-0.239192\pi$
$564$	−3.08192	−	5.33803i	−0.129772	−	0.224772i
$565$	8.41304	−	15.6246i	0.353939	−	0.657332i
$566$	−12.5438			−0.527257
$567$	−2.47822	+	0.664038i	−0.104076	+	0.0278870i
$568$	1.45575	+	5.43292i	0.0610818	+	0.227960i
$569$	−8.34734	+	14.4580i	−0.349939	+	0.606112i	−0.986238	−	0.165330i	$-0.947131\pi$
$569$	−8.34734	+	14.4580i	−0.349939	+	0.606112i	0.636299	+	0.771442i	$0.280464\pi$
$570$	6.59487	−	1.97854i	0.276229	−	0.0828717i
$571$	−27.1154	−	15.6551i	−1.13474	−	0.655144i	−0.189620	−	0.981858i	$-0.560726\pi$
$571$	−27.1154	−	15.6551i	−1.13474	−	0.655144i	−0.945124	+	0.326713i	$0.894059\pi$
$572$	−1.32556	+	4.94704i	−0.0554243	+	0.206846i
$573$	−0.877076	−	0.877076i	−0.0366404	−	0.0366404i
$574$		−	14.1914i		−	0.592338i
$575$	11.7266	−	13.2078i	0.489031	−	0.550803i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	6.54869	−	24.4400i	0.272625	−	1.01745i	−0.684791	−	0.728740i	$-0.740106\pi$
$577$	6.54869	−	24.4400i	0.272625	−	1.01745i	0.957416	−	0.288712i	$-0.0932270\pi$
$578$	−2.16224	−	8.06958i	−0.0899373	−	0.335650i
$579$	−6.58667	+	11.4084i	−0.273733	+	0.474119i
$580$	3.08110	−	3.26956i	0.127936	−	0.135761i
$581$			5.84516i			0.242498i
$582$	10.4169	+	2.79120i	0.431794	+	0.115699i
$583$	0.539287	+	0.144501i	0.0223350	+	0.00598464i
$584$	6.90148	−	11.9537i	0.285585	−	0.494648i
$585$	−2.84936	−	4.61354i	−0.117807	−	0.190746i
$586$	−12.8073	−	22.1828i	−0.529063	−	0.916365i
$587$	−7.95983	+	7.95983i	−0.328537	+	0.328537i	−0.852030	−	0.523493i	$-0.824629\pi$
$587$	−7.95983	+	7.95983i	−0.328537	+	0.328537i	0.523493	+	0.852030i	$0.324629\pi$
$588$	0.295186	+	0.295186i	0.0121733	+	0.0121733i
$589$	7.96407	−	15.1821i	0.328154	−	0.625568i
$590$	5.21891	+	8.45018i	0.214859	+	0.347889i
$591$	−26.4763			−1.08909
$592$	0.454135	+	0.121685i	0.0186648	+	0.00500122i
$593$	10.0957	−	10.0957i	0.414581	−	0.414581i	−0.468750	−	0.883331i	$-0.655295\pi$
$593$	10.0957	−	10.0957i	0.414581	−	0.414581i	0.883331	+	0.468750i	$0.155295\pi$
$594$	1.82901	+	1.05598i	0.0750454	+	0.0433275i
$595$	−16.1573	+	4.84737i	−0.662385	+	0.198723i
$596$	7.51908	+	13.0234i	0.307994	+	0.533461i
$597$	13.9229	+	13.9229i	0.569826	+	0.569826i
$598$	2.21712	+	8.27440i	0.0906648	+	0.338366i
$599$	−29.9808	−	17.3094i	−1.22498	−	0.707245i	−0.259008	−	0.965875i	$-0.583396\pi$
$599$	−29.9808	−	17.3094i	−1.22498	−	0.707245i	−0.965976	+	0.258630i	$0.916729\pi$
$600$	−4.17426	+	2.75238i	−0.170413	+	0.112365i
$601$	29.9479	−	17.2904i	1.22160	−	0.705291i	0.256341	−	0.966586i	$-0.417483\pi$
$601$	29.9479	−	17.2904i	1.22160	−	0.705291i	0.965259	+	0.261296i	$0.0841497\pi$
$602$	2.00061	+	7.46636i	0.0815386	+	0.304306i
$603$	4.43220	+	1.18760i	0.180493	+	0.0483629i
$604$	2.97324			0.120979
$605$	−3.36406	+	14.2308i	−0.136768	+	0.578564i
$606$	1.74593	−	1.00801i	0.0709236	−	0.0409478i
$607$	19.9143	−	5.33601i	0.808295	−	0.216582i	0.169072	−	0.985604i	$-0.445923\pi$
$607$	19.9143	−	5.33601i	0.808295	−	0.216582i	0.639223	+	0.769022i	$0.279256\pi$
$608$	2.97427	+	0.796952i	0.120622	+	0.0323207i
$609$	4.46414	+	2.57737i	0.180896	+	0.104440i
$610$	−11.7189	+	0.347776i	−0.474485	+	0.0140810i
$611$	12.9448	+	7.47370i	0.523692	+	0.302354i
$612$	−2.07915	+	2.07915i	−0.0840448	+	0.0840448i
$613$	−12.7098	+	47.4334i	−0.513342	+	1.91582i	−0.132483	+	0.991185i	$0.542295\pi$
$613$	−12.7098	+	47.4334i	−0.513342	+	1.91582i	−0.380859	+	0.924633i	$0.624372\pi$
$614$	−22.1662	+	12.7977i	−0.894557	+	0.516473i
$615$	−0.366889	−	12.3630i	−0.0147944	−	0.498523i
$616$			5.41855i			0.218320i
$617$	−6.30794	+	23.5416i	−0.253948	+	0.947747i	0.714724	+	0.699406i	$0.246552\pi$
$617$	−6.30794	+	23.5416i	−0.253948	+	0.947747i	−0.968673	+	0.248341i	$0.920115\pi$
$618$	3.04669	+	3.04669i	0.122556	+	0.122556i
$619$	−13.3823			−0.537881			−0.268941	−	0.963157i	$-0.586674\pi$
$619$	−13.3823			−0.537881			−0.268941	+	0.963157i	$0.586674\pi$
$620$	−2.37135	+	12.2220i	−0.0952357	+	0.490846i
$621$	3.53246			0.141753
$622$	2.01050	+	2.01050i	0.0806137	+	0.0806137i
$623$	−10.0180	+	37.3876i	−0.401362	+	1.49790i
$624$		−	2.42502i		−	0.0970785i
$625$	−24.8242	+	2.95982i	−0.992967	+	0.118393i
$626$	−23.3516	+	13.4821i	−0.933318	+	0.538851i
$627$	1.68313	−	6.28154i	0.0672179	−	0.250861i
$628$	−10.7806	+	10.7806i	−0.430191	+	0.430191i
$629$	1.19722	+	0.691214i	0.0477362	+	0.0275605i
$630$	−4.17519	−	3.93452i	−0.166344	−	0.156755i
$631$	10.5808	+	6.10885i	0.421216	+	0.243189i	0.695598	−	0.718432i	$-0.255140\pi$
$631$	10.5808	+	6.10885i	0.421216	+	0.243189i	−0.274381	+	0.961621i	$0.588473\pi$
$632$	−2.99702	−	0.803048i	−0.119215	−	0.0319435i
$633$	18.3705	−	4.92236i	0.730162	−	0.195646i
$634$	−1.55586	+	0.898275i	−0.0617910	+	0.0356751i
$635$	6.29852	+	10.1982i	0.249949	+	0.404705i
$636$	−0.264356			−0.0104824
$637$	−0.977845	−	0.262013i	−0.0387436	−	0.0103813i
$638$	−1.09823	−	4.09864i	−0.0434793	−	0.162267i
$639$	−4.87102	+	2.81229i	−0.192695	+	0.111252i
$640$	−2.23508	+	0.0663294i	−0.0883495	+	0.00262190i
$641$	17.9290	+	10.3513i	0.708151	+	0.408851i	0.810376	−	0.585910i	$-0.199263\pi$
$641$	17.9290	+	10.3513i	0.708151	+	0.408851i	−0.102225	+	0.994761i	$0.532596\pi$
$642$	−0.785626	−	2.93200i	−0.0310062	−	0.115717i
$643$	8.07803	+	8.07803i	0.318566	+	0.318566i	0.848216	−	0.529650i	$-0.177677\pi$
$643$	8.07803	+	8.07803i	0.318566	+	0.318566i	−0.529650	+	0.848216i	$0.677677\pi$
$644$	4.53153	+	7.84884i	0.178567	+	0.309287i
$645$	1.93587	+	6.45266i	0.0762248	+	0.254073i
$646$	7.84094	+	4.52697i	0.308498	+	0.178111i
$647$	0.114662	−	0.114662i	0.00450782	−	0.00450782i	−0.704849	−	0.709357i	$-0.748985\pi$
$647$	0.114662	−	0.114662i	0.00450782	−	0.00450782i	0.709357	+	0.704849i	$0.248985\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	9.38067			0.368223
$650$	5.42918	−	10.8417i	0.212950	−	0.425245i
$651$	−14.2732	+	0.578230i	−0.559411	+	0.0226626i
$652$	−5.29632	−	5.29632i	−0.207420	−	0.207420i
$653$	−14.2852	+	14.2852i	−0.559023	+	0.559023i	−0.929029	−	0.370006i	$-0.879356\pi$
$653$	−14.2852	+	14.2852i	−0.559023	+	0.559023i	0.370006	+	0.929029i	$0.379356\pi$
$654$	−10.1641	−	17.6047i	−0.397447	−	0.688398i
$655$	6.20420	−	26.2453i	0.242418	−	1.02549i
$656$	2.76566	−	4.79027i	0.107981	−	0.187028i
$657$	13.3326	+	3.57247i	0.520156	+	0.139375i
$658$	15.2754	+	4.09302i	0.595495	+	0.159563i
$659$			34.8022i			1.35570i	0.735199	+	0.677851i	$0.237089\pi$
$659$			34.8022i			1.35570i	−0.735199	+	0.677851i	$0.762911\pi$
$660$	0.140085	+	4.72042i	0.00545281	+	0.183742i
$661$	−1.64929	+	2.85665i	−0.0641498	+	0.111111i	−0.896317	−	0.443415i	$-0.853767\pi$
$661$	−1.64929	+	2.85665i	−0.0641498	+	0.111111i	0.832167	+	0.554525i	$0.187100\pi$
$662$	6.12693	+	22.8660i	0.238130	+	0.888713i
$663$	1.84549	−	6.88748i	0.0716731	−	0.267488i
$664$	−1.13912	+	1.97301i	−0.0442064	+	0.0765677i
$665$	−8.37489	+	15.5538i	−0.324764	+	0.603149i
$666$			0.470155i			0.0182181i
$667$	−5.01849	−	5.01849i	−0.194317	−	0.194317i
$668$	3.20089	−	11.9459i	0.123846	−	0.462200i
$669$	−0.939916	−	0.542660i	−0.0363392	−	0.0209805i
$670$	2.94838	+	9.82756i	0.113906	+	0.379672i
$671$	−5.53669	+	9.58983i	−0.213742	+	0.370211i
$672$	−0.664038	−	2.47822i	−0.0256158	−	0.0955996i
$673$	23.0845	−	6.18548i	0.889842	−	0.238433i	0.215194	−	0.976571i	$-0.430962\pi$
$673$	23.0845	−	6.18548i	0.889842	−	0.238433i	0.674649	+	0.738139i	$0.264295\pi$
$674$	8.05380			0.310221
$675$	−3.73897	−	3.31965i	−0.143913	−	0.127773i
$676$	−3.55964	−	6.16548i	−0.136909	−	0.237134i
$677$	11.4665	+	42.7937i	0.440694	+	1.64469i	0.727060	+	0.686574i	$0.240886\pi$
$677$	11.4665	+	42.7937i	0.440694	+	1.64469i	−0.286366	+	0.958120i	$0.592447\pi$
$678$	5.61166	+	5.61166i	0.215515	+	0.215515i
$679$	−23.9620	+	13.8344i	−0.919576	+	0.530917i
$680$	−6.39851	−	1.51256i	−0.245372	−	0.0580041i
$681$			19.4881i			0.746787i
$682$	8.64457	+	7.97143i	0.331018	+	0.305242i
$683$	24.3787	−	24.3787i	0.932824	−	0.932824i	−0.0650573	−	0.997882i	$-0.520723\pi$
$683$	24.3787	−	24.3787i	0.932824	−	0.932824i	0.997882	+	0.0650573i	$0.0207230\pi$
$684$			3.07919i			0.117736i
$685$	−22.4057	+	41.6117i	−0.856079	+	1.58990i
$686$	−19.0306			−0.726591
$687$	−12.6331	+	3.38504i	−0.481984	+	0.129147i
$688$	−0.779767	+	2.91013i	−0.0297283	+	0.110948i
$689$	0.555182	−	0.320534i	0.0211507	−	0.0122114i
$690$	4.15059	+	6.72042i	0.158010	+	0.255842i
$691$	16.1241	−	27.9278i	0.613390	−	1.06242i	−0.377275	−	0.926101i	$-0.623139\pi$
$691$	16.1241	−	27.9278i	0.613390	−	1.06242i	0.990665	−	0.136321i	$-0.0435278\pi$
$692$	−21.1158	+	5.65797i	−0.802704	+	0.215084i
$693$	−5.23392	+	1.40242i	−0.198820	+	0.0532737i
$694$	−6.66991	−	11.5526i	−0.253186	−	0.438531i
$695$	−3.00857	−	2.83514i	−0.114121	−	0.107543i
$696$	1.00457	+	1.73997i	0.0380781	+	0.0659532i
$697$	11.5005	−	11.5005i	0.435611	−	0.435611i
$698$	5.01564	−	5.01564i	0.189845	−	0.189845i
$699$	3.66340	+	6.34519i	0.138562	+	0.239997i
$700$	2.57955	−	12.5662i	0.0974977	−	0.474958i
$701$	11.6245	+	20.1342i	0.439051	+	0.760458i	0.997617	−	0.0690021i	$-0.0219815\pi$
$701$	11.6245	+	20.1342i	0.439051	+	0.760458i	−0.558566	+	0.829460i	$0.688648\pi$
$702$	2.34239	−	0.627641i	0.0884078	−	0.0236888i
$703$	1.39837	−	0.374691i	0.0527403	−	0.0141317i
$704$	−1.05598	+	1.82901i	−0.0397988	+	0.0689336i
$705$	13.4131	+	3.17076i	0.505165	+	0.119418i
$706$	12.5286	−	7.23340i	0.471521	−	0.272233i
$707$	−1.33872	+	4.99617i	−0.0503477	+	0.187900i
$708$	−4.29033	+	1.14959i	−0.161241	+	0.0432043i
$709$	−7.97508			−0.299510			−0.149755	−	0.988723i	$-0.547849\pi$
$709$	−7.97508			−0.299510			−0.149755	+	0.988723i	$0.547849\pi$
$710$	−11.0737	−	5.96260i	−0.415588	−	0.223773i
$711$		−	3.10274i		−	0.116362i
$712$	−10.6677	+	10.6677i	−0.399790	+	0.399790i
$713$	19.1882	+	4.31726i	0.718605	+	0.161683i
$714$		−	7.54394i		−	0.282325i
$715$	−6.01775	−	9.74363i	−0.225051	−	0.364391i
$716$	−1.06494	+	0.614844i	−0.0397987	+	0.0229778i
$717$	3.36505	+	3.36505i	0.125670	+	0.125670i
$718$	−7.35988	−	27.4675i	−0.274668	−	1.02508i
$719$	−9.99926	−	17.3192i	−0.372910	−	0.645898i	0.617102	−	0.786883i	$-0.288307\pi$
$719$	−9.99926	−	17.3192i	−0.372910	−	0.645898i	−0.990012	+	0.140985i	$0.954973\pi$
$720$	−0.642552	−	2.14176i	−0.0239465	−	0.0798186i
$721$	−11.0545			−0.411692
$722$	−9.19428	+	2.46360i	−0.342175	+	0.0916856i
$723$	−1.21824	−	4.54652i	−0.0453067	−	0.169087i
$724$	−6.35117	+	11.0006i	−0.236040	+	0.408832i
$725$	0.595716	+	10.0280i	0.0221244	+	0.372431i
$726$	−5.66347	−	3.26980i	−0.210191	−	0.121354i
$727$	0.435314	−	1.62461i	0.0161449	−	0.0602536i	−0.957383	−	0.288820i	$-0.906737\pi$
$727$	0.435314	−	1.62461i	0.0161449	−	0.0602536i	0.973528	+	0.228566i	$0.0734038\pi$
$728$	4.39944	+	4.39944i	0.163054	+	0.163054i
$729$		−	1.00000i		−	0.0370370i
$730$	8.86912	+	29.5626i	0.328261	+	1.09416i
$731$	−4.42935	+	7.67186i	−0.163825	+	0.283754i
$732$	1.35703	−	5.06451i	0.0501573	−	0.187190i
$733$	−0.664817	−	2.48113i	−0.0245556	−	0.0916426i	0.952561	−	0.304349i	$-0.0984389\pi$
$733$	−0.664817	−	2.48113i	−0.0245556	−	0.0916426i	−0.977116	+	0.212706i	$0.931772\pi$
$734$	−9.69442	+	16.7912i	−0.357828	+	0.619776i
$735$	−0.933050	+	0.0276896i	−0.0344161	+	0.00102135i
$736$			3.53246i			0.130208i
$737$	9.36064	+	2.50818i	0.344804	+	0.0923898i
$738$	5.34285	+	1.43161i	0.196673	+	0.0526984i
$739$	24.4483	−	42.3457i	0.899344	−	1.55771i	0.0710101	−	0.997476i	$-0.477378\pi$
$739$	24.4483	−	42.3457i	0.899344	−	1.55771i	0.828334	−	0.560234i	$-0.189289\pi$
$740$	−0.894458	+	0.552425i	−0.0328809	+	0.0203075i
$741$	−3.73354	−	6.46668i	−0.137155	−	0.237560i
$742$	0.479591	−	0.479591i	0.0176063	−	0.0176063i
$743$	−2.94210	−	2.94210i	−0.107935	−	0.107935i	0.651077	−	0.759012i	$-0.274318\pi$
$743$	−2.94210	−	2.94210i	−0.107935	−	0.107935i	−0.759012	+	0.651077i	$0.774318\pi$
$744$	−4.93056	−	2.58642i	−0.180763	−	0.0948228i
$745$	−32.7244	−	7.73583i	−1.19893	−	0.283419i
$746$	−16.6610			−0.610004
$747$	−2.20061	−	0.589652i	−0.0805161	−	0.0215742i
$748$	−4.39110	+	4.39110i	−0.160554	+	0.160554i
$749$	6.74446	+	3.89391i	0.246437	+	0.142281i
$750$	1.92232	−	11.0138i	0.0701932	−	0.402169i
$751$	22.2720	+	38.5763i	0.812718	+	1.40767i	0.910955	+	0.412505i	$0.135346\pi$
$751$	22.2720	+	38.5763i	0.812718	+	1.40767i	−0.0982377	+	0.995163i	$0.531321\pi$
$752$	4.35849	+	4.35849i	0.158938	+	0.158938i
$753$	−1.55534	−	5.80460i	−0.0566797	−	0.211531i
$754$	−4.21945	−	2.43610i	−0.153663	−	0.0887175i
$755$	−4.55958	+	4.83848i	−0.165940	+	0.176090i
$756$	2.22192	−	1.28282i	0.0808103	−	0.0466558i
$757$	10.4058	+	38.8348i	0.378204	+	1.41147i	0.848607	+	0.529023i	$0.177442\pi$
$757$	10.4058	+	38.8348i	0.378204	+	1.41147i	−0.470404	+	0.882451i	$0.655892\pi$
$758$	3.65770	+	0.980078i	0.132854	+	0.0355980i
$759$	7.46044			0.270797
$760$	−5.85807	+	3.61800i	−0.212495	+	0.131239i
$761$	−7.16374	+	4.13599i	−0.259685	+	0.149929i	−0.624191	−	0.781272i	$-0.714571\pi$
$761$	−7.16374	+	4.13599i	−0.259685	+	0.149929i	0.364506	+	0.931201i	$0.381238\pi$
$762$	−5.17786	+	1.38740i	−0.187574	+	0.0502603i
$763$	50.3777	+	13.4987i	1.82379	+	0.488684i
$764$	1.07419	+	0.620187i	0.0388630	+	0.0224376i
$765$	−0.195033	−	6.57196i	−0.00705142	−	0.237610i
$766$	−28.2496	−	16.3099i	−1.02070	−	0.589301i
$767$	7.61636	−	7.61636i	0.275011	−	0.275011i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	33.6902	−	19.4511i	1.21490	−	0.701423i	0.251078	−	0.967967i	$-0.419215\pi$
$769$	33.6902	−	19.4511i	1.21490	−	0.701423i	0.963823	+	0.266544i	$0.0858817\pi$
$770$	−8.81786	−	8.30957i	−0.317773	−	0.299456i
$771$			10.8092i			0.389283i
$772$	3.40951	−	12.7245i	0.122711	−	0.457964i
$773$	8.53801	+	8.53801i	0.307091	+	0.307091i	0.843780	−	0.536689i	$-0.180325\pi$
$773$	8.53801	+	8.53801i	0.307091	+	0.307091i	−0.536689	+	0.843780i	$0.680325\pi$
$774$	−3.01279			−0.108292
$775$	−16.2528	−	22.6019i	−0.583818	−	0.811884i
$776$	−10.7844			−0.387136
$777$	−0.852948	−	0.852948i	−0.0305994	−	0.0305994i
$778$	0.592937	−	2.21287i	0.0212578	−	0.0793353i
$779$		−	17.0320i		−	0.610234i
$780$	3.94634	+	3.71887i	0.141302	+	0.133157i
$781$	−10.2874	+	5.93945i	−0.368113	+	0.212530i
$782$	−2.68829	+	10.0328i	−0.0961329	+	0.358773i
$783$	−1.42068	+	1.42068i	−0.0507708	+	0.0507708i
$784$	−0.361528	−	0.208728i	−0.0129117	−	0.00745458i
$785$	−1.01126	−	34.0761i	−0.0360934	−	1.21623i
$786$	10.4449	+	6.03036i	0.372557	+	0.215096i
$787$	0.0758254	+	0.0203174i	0.00270288	+	0.000724236i	0.260170	−	0.965563i	$-0.416221\pi$
$787$	0.0758254	+	0.0203174i	0.00270288	+	0.000724236i	−0.257467	+	0.966287i	$0.582888\pi$
$788$	25.5741	−	6.85257i	0.911041	−	0.244113i
$789$	−10.7787	+	6.22306i	−0.383730	+	0.221547i
$790$	5.90289	−	3.64567i	0.210015	−	0.129707i
$791$	−20.3612			−0.723961
$792$	−2.04000	−	0.546616i	−0.0724883	−	0.0194232i
$793$	3.29083	+	12.2815i	0.116861	+	0.436130i
$794$	32.0782	−	18.5204i	1.13841	−	0.657263i
$795$	0.405401	−	0.430199i	0.0143781	−	0.0152576i
$796$	−17.0520	−	9.84497i	−0.604392	−	0.348946i
$797$	−10.1795	−	37.9905i	−0.360577	−	1.34569i	−0.873319	−	0.487149i	$-0.838037\pi$
$797$	−10.1795	−	37.9905i	−0.360577	−	1.34569i	0.512742	−	0.858543i	$-0.328630\pi$
$798$	−5.58622	−	5.58622i	−0.197750	−	0.197750i
$799$	9.06196	+	15.6958i	0.320589	+	0.555277i
$800$	3.31965	−	3.73897i	0.117367	−	0.132193i
$801$	−13.0652	−	7.54322i	−0.461638	−	0.266527i
$802$	−18.2864	+	18.2864i	−0.645716	+	0.645716i
$803$	28.1581	+	7.54493i	0.993676	+	0.266255i
$804$	−4.58855			−0.161826
$805$	−19.7220	−	4.66215i	−0.695111	−	0.164319i
$806$	13.4909	−	0.546536i	0.475196	−	0.0192509i
$807$	4.19940	+	4.19940i	0.147826	+	0.147826i
$808$	−1.42555	+	1.42555i	−0.0501506	+	0.0501506i
$809$	13.9949	+	24.2399i	0.492036	+	0.852231i	0.999958	−	0.00917186i	$-0.00291953\pi$
$809$	13.9949	+	24.2399i	0.492036	+	0.852231i	−0.507922	+	0.861403i	$0.669586\pi$
$810$	1.90247	−	1.17498i	0.0668462	−	0.0412848i
$811$	−11.8662	+	20.5529i	−0.416680	+	0.721710i	−0.995603	−	0.0936716i	$-0.970140\pi$
$811$	−11.8662	+	20.5529i	−0.416680	+	0.721710i	0.578924	+	0.815382i	$0.303473\pi$
$812$	−4.97910	−	1.33414i	−0.174732	−	0.0468193i
$813$	9.73655	+	2.60890i	0.341476	+	0.0914982i
$814$			0.992950i			0.0348029i
$815$	16.7411	−	0.496816i	0.586414	−	0.0174027i
$816$	1.47018	−	2.54643i	0.0514667	−	0.0891429i
$817$	2.40105	+	8.96083i	0.0840020	+	0.313500i
$818$	−1.97046	+	7.35387i	−0.0688956	+	0.257122i
$819$	−3.11087	+	5.38819i	−0.108703	+	0.188278i
$820$	3.55416	+	11.8468i	0.124117	+	0.413707i
$821$		−	16.0822i		−	0.561272i	−0.959814	−	0.280636i	$-0.909455\pi$
$821$		−	16.0822i		−	0.561272i	0.959814	−	0.280636i	$-0.0905454\pi$
$822$	−14.9451	−	14.9451i	−0.521269	−	0.521269i
$823$	9.76158	−	36.4307i	0.340267	−	1.26989i	−0.557778	−	0.829990i	$-0.688346\pi$
$823$	9.76158	−	36.4307i	0.340267	−	1.26989i	0.898045	−	0.439904i	$-0.144987\pi$
$824$	−3.73141	−	2.15433i	−0.129990	−	0.0750497i
$825$	−7.89657	−	7.01099i	−0.274923	−	0.244091i
$826$	5.69789	−	9.86904i	0.198255	−	0.343388i
$827$	3.67882	+	13.7295i	0.127925	+	0.477423i	0.999927	−	0.0120793i	$-0.00384507\pi$
$827$	3.67882	+	13.7295i	0.127925	+	0.477423i	−0.872002	+	0.489503i	$0.837178\pi$
$828$	−3.41210	+	0.914269i	−0.118579	+	0.0317730i
$829$	27.2191			0.945357			0.472679	−	0.881235i	$-0.343287\pi$
$829$	27.2191			0.945357			0.472679	+	0.881235i	$0.343287\pi$
$830$	−1.46389	−	4.87944i	−0.0508122	−	0.169368i
$831$	−8.10848	−	14.0443i	−0.281280	−	0.487191i
$832$	0.627641	+	2.34239i	0.0217595	+	0.0812077i
$833$	−0.867955	−	0.867955i	−0.0300729	−	0.0300729i
$834$	1.60107	−	0.924378i	0.0554405	−	0.0320086i
$835$	14.5314	+	23.5285i	0.502879	+	0.814236i
$836$			6.50313i			0.224915i
$837$	1.22217	−	5.43197i	0.0422443	−	0.187756i
$838$	−20.3870	+	20.3870i	−0.704257	+	0.704257i
$839$			39.8319i			1.37515i	0.726113	+	0.687575i	$0.241325\pi$
$839$			39.8319i			1.37515i	−0.726113	+	0.687575i	$0.758675\pi$
$840$	5.05126	+	2.71984i	0.174285	+	0.0938434i
$841$	−24.9634			−0.860806
$842$	17.0785	−	4.57616i	0.588563	−	0.157705i
$843$	3.88764	−	14.5089i	0.133897	−	0.499711i
$844$	−16.4705	+	9.50927i	−0.566939	+	0.327323i
$845$	15.4922	+	3.66225i	0.532949	+	0.125985i
$846$	−3.08192	+	5.33803i	−0.105958	+	0.183525i
$847$	16.2066	−	4.34255i	0.556866	−	0.149212i
$848$	0.255348	−	0.0684204i	0.00876870	−	0.00234957i
$849$	6.27192	+	10.8633i	0.215252	+	0.372827i
$850$	12.2738	−	8.09300i	0.420989	−	0.277588i
$851$	0.830403	+	1.43830i	0.0284658	+	0.0493043i
$852$	3.97717	−	3.97717i	0.136256	−	0.136256i
$853$	14.2347	−	14.2347i	0.487387	−	0.487387i	−0.420093	−	0.907481i	$-0.638003\pi$
$853$	14.2347	−	14.2347i	0.487387	−	0.487387i	0.907481	+	0.420093i	$0.138003\pi$
$854$	6.72606	+	11.6499i	0.230161	+	0.398650i
$855$	−5.01090	−	4.72206i	−0.171369	−	0.161491i
$856$	1.51771	+	2.62876i	0.0518744	+	0.0898490i
$857$	−24.3076	+	6.51321i	−0.830332	+	0.222487i	−0.648859	−	0.760909i	$-0.724753\pi$
$857$	−24.3076	+	6.51321i	−0.830332	+	0.222487i	−0.181474	+	0.983396i	$0.558087\pi$
$858$	4.94704	−	1.32556i	0.168889	−	0.0452537i
$859$	−4.00337	+	6.93404i	−0.136593	+	0.236586i	−0.926205	−	0.377020i	$-0.876949\pi$
$859$	−4.00337	+	6.93404i	−0.136593	+	0.236586i	0.789612	+	0.613607i	$0.210282\pi$
$860$	−3.53998	−	5.73175i	−0.120712	−	0.195451i
$861$	−12.2901	+	7.09571i	−0.418847	+	0.241821i
$862$	2.14559	−	8.00746i	0.0730792	−	0.272735i
$863$	25.4841	−	6.82843i	0.867487	−	0.232443i	0.202486	−	0.979285i	$-0.435098\pi$
$863$	25.4841	−	6.82843i	0.867487	−	0.232443i	0.665001	+	0.746843i	$0.268431\pi$
$864$	1.00000			0.0340207
$865$	23.1745	−	43.0395i	0.787958	−	1.46339i
$866$		−	27.5020i		−	0.934556i
$867$	−5.90735	+	5.90735i	−0.200624	+	0.200624i
$868$	13.6372	−	4.25271i	0.462877	−	0.144346i
$869$		−	6.55288i		−	0.222291i
$870$	−4.37207	−	1.03353i	−0.148227	−	0.0350399i
$871$	9.63654	−	5.56366i	0.326522	−	0.188517i
$872$	14.3742	+	14.3742i	0.486771	+	0.486771i
$873$	−2.79120	−	10.4169i	−0.0944678	−	0.352559i
$874$	5.43856	+	9.41986i	0.183962	+	0.318631i
$875$	16.4937	+	23.4686i	0.557589	+	0.793384i
$876$	−13.8030			−0.466359
$877$	5.02977	−	1.34772i	0.169843	−	0.0455094i	−0.172895	−	0.984940i	$-0.555312\pi$
$877$	5.02977	−	1.34772i	0.169843	−	0.0455094i	0.342738	+	0.939431i	$0.388646\pi$
$878$	−9.48776	−	35.4088i	−0.320197	−	1.19499i
$879$	−12.8073	+	22.1828i	−0.431978	+	0.748209i
$880$	−1.35705	−	4.52332i	−0.0457460	−	0.152481i
$881$	11.4685	+	6.62134i	0.386383	+	0.223078i	0.680592	−	0.732663i	$-0.261723\pi$
$881$	11.4685	+	6.62134i	0.386383	+	0.223078i	−0.294209	+	0.955741i	$0.595056\pi$
$882$	0.108046	−	0.403232i	0.00363809	−	0.0135775i
$883$	28.5351	+	28.5351i	0.960283	+	0.960283i	0.999241	−	0.0389579i	$-0.0124038\pi$
$883$	28.5351	+	28.5351i	0.960283	+	0.960283i	−0.0389579	+	0.999241i	$0.512404\pi$
$884$			7.13044i			0.239823i
$885$	4.70862	−	8.74480i	0.158279	−	0.293953i
$886$	−0.205751	+	0.356372i	−0.00691235	+	0.0119725i
$887$	12.7961	−	47.7558i	0.429652	−	1.60348i	−0.323898	−	0.946092i	$-0.604994\pi$
$887$	12.7961	−	47.7558i	0.429652	−	1.60348i	0.753550	−	0.657390i	$-0.228340\pi$
$888$	−0.121685	−	0.454135i	−0.00408348	−	0.0152398i
$889$	6.87659	−	11.9106i	0.230634	−	0.399469i
$890$	−1.00067	−	33.7195i	−0.0335427	−	1.13028i
$891$		−	2.11196i		−	0.0707535i
$892$	1.04834	+	0.280902i	0.0351010	+	0.00940529i
$893$	18.3329	+	4.91228i	0.613486	+	0.164383i
$894$	7.51908	−	13.0234i	0.251476	−	0.435569i
$895$	0.632568	−	2.67592i	0.0211444	−	0.0894460i
$896$	1.28282	+	2.22192i	0.0428561	+	0.0742290i
$897$	6.05728	−	6.05728i	0.202247	−	0.202247i
$898$	3.91373	+	3.91373i	0.130603	+	0.130603i
$899$	−9.45337	+	5.98076i	−0.315288	+	0.199470i
$900$	4.47076	+	2.23882i	0.149025	+	0.0746274i
$901$	0.777304			0.0258957
$902$	11.2839	+	3.02351i	0.375713	+	0.100672i
$903$	5.46576	−	5.46576i	0.181889	−	0.181889i
$904$	−6.87286	−	3.96805i	−0.228588	−	0.131975i
$905$	−8.16191	−	27.2054i	−0.271311	−	0.904337i
$906$	−1.48662	−	2.57490i	−0.0493896	−	0.0855452i
$907$	−0.108647	−	0.108647i	−0.00360755	−	0.00360755i	0.705301	−	0.708908i	$-0.250812\pi$
$907$	−0.108647	−	0.108647i	−0.00360755	−	0.00360755i	−0.708908	+	0.705301i	$0.750812\pi$
$908$	−5.04390	−	18.8241i	−0.167388	−	0.624700i
$909$	−1.74593	−	1.00801i	−0.0579089	−	0.0334337i
$910$	−13.9061	+	0.412684i	−0.460983	+	0.0136803i
$911$	35.0682	−	20.2466i	1.16186	−	0.670801i	0.210111	−	0.977677i	$-0.432617\pi$
$911$	35.0682	−	20.2466i	1.16186	−	0.670801i	0.951749	+	0.306877i	$0.0992840\pi$
$912$	−0.796952	−	2.97427i	−0.0263897	−	0.0984878i
$913$	−4.64761	−	1.24532i	−0.153813	−	0.0412142i
$914$	2.67332			0.0884254
$915$	6.16064	+	9.97499i	0.203665	+	0.329763i
$916$	11.3265	−	6.53939i	0.374240	−	0.216067i
$917$	−29.8892	+	8.00879i	−0.987028	+	0.264473i
$918$	2.84018	+	0.761023i	0.0937398	+	0.0251175i
$919$	42.1445	+	24.3322i	1.39022	+	0.802644i	0.993339	−	0.115226i	$-0.0367592\pi$
$919$	42.1445	+	24.3322i	1.39022	+	0.802644i	0.396881	+	0.917870i	$0.370093\pi$
$920$	−5.74854	−	5.41718i	−0.189524	−	0.178599i
$921$	22.1662	+	12.7977i	0.730403	+	0.421698i
$922$	24.9852	−	24.9852i	0.822844	−	0.822844i
$923$	−3.53021	+	13.1749i	−0.116198	+	0.433658i
$924$	4.69261	−	2.70928i	0.154375	−	0.0891287i
$925$	0.472702	−	2.30276i	0.0155423	−	0.0757142i
$926$		−	32.4566i		−	1.06659i
$927$	1.11516	−	4.16185i	0.0366268	−	0.136693i
$928$	−1.42068	−	1.42068i	−0.0466360	−	0.0466360i
$929$	5.04761			0.165607			0.0828034	−	0.996566i	$-0.473613\pi$
$929$	5.04761			0.165607			0.0828034	+	0.996566i	$0.473613\pi$
$930$	11.7702	−	4.05734i	0.385961	−	0.133045i
$931$	−1.28543			−0.0421281
$932$	−5.18083	−	5.18083i	−0.169704	−	0.169704i
$933$	0.735894	−	2.74639i	0.0240921	−	0.0899129i
$934$		−	12.1964i		−	0.399079i
$935$	−0.411902	−	13.8798i	−0.0134706	−	0.453916i
$936$	−2.10013	+	1.21251i	−0.0686448	+	0.0396321i
$937$	−0.635679	+	2.37239i	−0.0207667	+	0.0775025i	−0.975532	−	0.219859i	$-0.929440\pi$
$937$	−0.635679	+	2.37239i	−0.0207667	+	0.0775025i	0.954765	+	0.297362i	$0.0961068\pi$
$938$	8.32448	−	8.32448i	0.271804	−	0.271804i
$939$	23.3516	+	13.4821i	0.762051	+	0.439970i
$940$	−13.7767	+	0.408843i	−0.449346	+	0.0133350i
$941$	7.80370	+	4.50547i	0.254393	+	0.146874i	0.621774	−	0.783196i	$-0.286412\pi$
$941$	7.80370	+	4.50547i	0.254393	+	0.146874i	−0.367381	+	0.930071i	$0.619745\pi$
$942$	14.7265	+	3.94596i	0.479816	+	0.128566i
$943$	18.8734	−	5.05712i	0.614603	−	0.164682i
$944$	3.84661	−	2.22084i	0.125196	−	0.0722822i
$945$	−1.31980	+	5.58309i	−0.0429332	+	0.181618i
$946$	−6.36290			−0.206876
$947$	51.1879	+	13.7158i	1.66338	+	0.445702i	0.963315	−	0.268373i	$-0.0864860\pi$
$947$	51.1879	+	13.7158i	1.66338	+	0.445702i	0.700069	+	0.714076i	$0.253153\pi$
$948$	0.803048	+	2.99702i	0.0260818	+	0.0973386i
$949$	28.9880	−	16.7362i	0.940990	−	0.543281i
$950$	3.09587	−	15.0815i	0.100443	−	0.489307i
$951$	1.55586	+	0.898275i	0.0504522	+	0.0291286i
$952$	1.95252	+	7.28689i	0.0632814	+	0.236169i
$953$	30.9431	+	30.9431i	1.00235	+	1.00235i	0.999997	+	0.00234840i	$0.000747519\pi$
$953$	30.9431	+	30.9431i	1.00235	+	1.00235i	0.00234840	+	0.999997i	$0.499252\pi$
$954$	0.132178	+	0.228939i	0.00427942	+	0.00741218i
$955$	−2.65658	+	0.797004i	−0.0859649	+	0.0257904i
$956$	−4.12133	−	2.37945i	−0.133293	−	0.0769569i
$957$	−3.00042	+	3.00042i	−0.0969897	+	0.0969897i
$958$	−32.8520	−	8.80266i	−1.06140	−	0.284401i
$959$	54.2262			1.75106
$960$	1.17498	+	1.90247i	0.0379225	+	0.0614021i
$961$	13.2776	−	28.0126i	0.428308	−	0.903633i
$962$	0.806197	+	0.806197i	0.0259928	+	0.0259928i
$963$	−2.14637	+	2.14637i	−0.0691658	+	0.0691658i
$964$	2.35345	+	4.07630i	0.0757996	+	0.131289i
$965$	15.4785	+	25.0619i	0.498270	+	0.806773i
$966$	4.53153	−	7.84884i	0.145800	−	0.252532i
$967$	−29.1154	−	7.80144i	−0.936287	−	0.250877i	−0.241754	−	0.970338i	$-0.577723\pi$
$967$	−29.1154	−	7.80144i	−0.936287	−	0.250877i	−0.694534	+	0.719460i	$0.744389\pi$
$968$	6.31678	+	1.69258i	0.203029	+	0.0544014i
$969$		−	9.05393i		−	0.290854i
$970$	16.5383	−	17.5499i	0.531012	−	0.563493i
$971$	−8.90845	+	15.4299i	−0.285886	+	0.495168i	−0.972824	−	0.231548i	$-0.925621\pi$
$971$	−8.90845	+	15.4299i	−0.285886	+	0.495168i	0.686938	+	0.726716i	$0.258954\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	−1.22765	+	4.58163i	−0.0393565	+	0.146880i
$974$	−13.1318	+	22.7450i	−0.420771	+	0.728796i
$975$	−12.1038	+	0.719026i	−0.387630	+	0.0230273i
$976$			5.24317i			0.167830i
$977$	−11.4049	−	11.4049i	−0.364873	−	0.364873i	0.500730	−	0.865604i	$-0.333065\pi$
$977$	−11.4049	−	11.4049i	−0.364873	−	0.364873i	−0.865604	+	0.500730i	$0.833065\pi$
$978$	−1.93859	+	7.23491i	−0.0619892	+	0.231347i
$979$	−27.5933	−	15.9310i	−0.881886	−	0.509157i
$980$	0.894090	−	0.268237i	0.0285607	−	0.00856852i
$981$	−10.1641	+	17.6047i	−0.324514	+	0.562074i
$982$	−1.57012	−	5.85976i	−0.0501045	−	0.186993i
$983$	15.5219	−	4.15907i	0.495070	−	0.132654i	−0.00264088	−	0.999997i	$-0.500841\pi$
$983$	15.5219	−	4.15907i	0.495070	−	0.132654i	0.497711	+	0.867343i	$0.334174\pi$
$984$	−5.53132			−0.176332
$985$	−28.0675	+	52.1266i	−0.894305	+	1.66089i
$986$	−2.95380	−	5.11613i	−0.0940682	−	0.162931i
$987$	−4.09302	−	15.2754i	−0.130282	−	0.486220i
$988$	5.28003	+	5.28003i	0.167980	+	0.167980i
$989$	−9.21673	+	5.32128i	−0.293075	+	0.169207i
$990$	4.01796	−	2.48153i	0.127699	−	0.0788681i
$991$		−	20.7544i		−	0.659285i	−0.944106	−	0.329642i	$-0.893072\pi$
$991$		−	20.7544i		−	0.659285i	0.944106	−	0.329642i	$-0.106928\pi$
$992$	5.43197	+	1.22217i	0.172465	+	0.0388039i
$993$	16.7391	−	16.7391i	0.531199	−	0.531199i
$994$			14.4307i			0.457713i
$995$	42.1711	−	12.6518i	1.33691	−	0.401089i
$996$	2.27824			0.0721888
$997$	3.04075	−	0.814766i	0.0963014	−	0.0258039i	−0.210347	−	0.977627i	$-0.567459\pi$
$997$	3.04075	−	0.814766i	0.0963014	−	0.0258039i	0.306648	+	0.951823i	$0.400793\pi$
$998$	1.44362	−	5.38768i	0.0456971	−	0.170544i
$999$	0.407166	−	0.235077i	0.0128822	−	0.00743752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.11	✓	64
5.3	odd	4		930.2.be.b.223.16	yes	64
31.26	odd	6		930.2.be.b.367.16	yes	64
155.88	even	12	inner	930.2.be.a.553.11	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.11	✓	64	1.1	even	1	trivial
930.2.be.a.553.11	yes	64	155.88	even	12	inner
930.2.be.b.223.16	yes	64	5.3	odd	4
930.2.be.b.367.16	yes	64	31.26	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.62734 - 1.53354i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.664038 + 2.47822i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(-1.62734 - 1.53354i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-0.664038 + 2.47822i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.0663294 - 2.23508i) q^{10} +(-1.82901 - 1.05598i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-2.34239 + 0.627641i) q^{13} +(-2.22192 + 1.28282i) q^{14} +(-1.90247 + 1.17498i) q^{15} -1.00000 q^{16} +(-2.84018 - 0.761023i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-2.66665 + 1.53959i) q^{19} +(1.53354 - 1.62734i) q^{20} +(2.22192 + 1.28282i) q^{21} +(-0.546616 - 2.04000i) q^{22} +(-2.49783 - 2.49783i) q^{23} +(0.500000 + 0.866025i) q^{24} +(0.296503 + 4.99120i) q^{25} +(-2.10013 - 1.21251i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.47822 - 0.664038i) q^{28} +2.00914 q^{29} +(-2.17609 - 0.514413i) q^{30} +(-4.70519 + 2.97678i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.49338 + 1.49338i) q^{33} +(-1.47018 - 2.54643i) q^{34} +(4.88108 - 3.01460i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-0.454135 - 0.121685i) q^{37} +(-2.97427 - 0.796952i) q^{38} +2.42502i q^{39} +(2.23508 - 0.0663294i) q^{40} +(-2.76566 + 4.79027i) q^{41} +(0.664038 + 2.47822i) q^{42} +(0.779767 - 2.91013i) q^{43} +(1.05598 - 1.82901i) q^{44} +(0.642552 + 2.14176i) q^{45} -3.53246i q^{46} +(-4.35849 - 4.35849i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(0.361528 + 0.208728i) q^{49} +(-3.31965 + 3.73897i) q^{50} +(-1.47018 + 2.54643i) q^{51} +(-0.627641 - 2.34239i) q^{52} +(-0.255348 + 0.0684204i) q^{53} -1.00000 q^{54} +(1.35705 + 4.52332i) q^{55} +(-1.28282 - 2.22192i) q^{56} +(0.796952 + 2.97427i) q^{57} +(1.42068 + 1.42068i) q^{58} +(-3.84661 + 2.22084i) q^{59} +(-1.17498 - 1.90247i) q^{60} -5.24317i q^{61} +(-5.43197 - 1.22217i) q^{62} +(1.81419 - 1.81419i) q^{63} -1.00000i q^{64} +(4.77439 + 2.57076i) q^{65} -2.11196 q^{66} +(-4.43220 + 1.18760i) q^{67} +(0.761023 - 2.84018i) q^{68} +(-3.05920 + 1.76623i) q^{69} +(5.58309 + 1.31980i) q^{70} +(2.81229 - 4.87102i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-13.3326 + 3.57247i) q^{73} +(-0.235077 - 0.407166i) q^{74} +(4.89787 + 1.00542i) q^{75} +(-1.53959 - 2.66665i) q^{76} +(3.83150 - 3.83150i) q^{77} +(-1.71475 + 1.71475i) q^{78} +(1.55137 + 2.68705i) q^{79} +(1.62734 + 1.53354i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-5.34285 + 1.43161i) q^{82} +(2.20061 - 0.589652i) q^{83} +(-1.28282 + 2.22192i) q^{84} +(3.45489 + 5.59397i) q^{85} +(2.60915 - 1.50639i) q^{86} +(0.520003 - 1.94068i) q^{87} +(2.04000 - 0.546616i) q^{88} +15.0864 q^{89} +(-1.06010 + 1.96880i) q^{90} -6.22174i q^{91} +(2.49783 - 2.49783i) q^{92} +(1.65756 + 5.31531i) q^{93} -6.16383i q^{94} +(6.70059 + 1.58397i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(7.62570 + 7.62570i) q^{97} +(0.108046 + 0.403232i) q^{98} +(1.05598 + 1.82901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

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