LMFDB - Embedded newform 93.2.m.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(7,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 28]))

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

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

chi := DirichletCharacter("93.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.m (of order $15$, degree $8$, 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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7 x^{15} + 24 x^{14} - 36 x^{13} + 17 x^{12} + 18 x^{11} - 52 x^{10} + 59 x^{9} + 51 x^{8} + \cdots + 1 $ x^16 - 7x^15 + 24x^14 - 36x^13 + 17x^12 + 18x^11 - 52x^10 + 59x^9 + 51x^8 - 59x^7 - 52x^6 - 18x^5 + 17x^4 + 36x^3 + 24x^2 + 7*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			19.2
Root			$1.15747 + 0.246029i$ of defining polynomial
Character	$\chi$	$=$	93.19
Dual form			93.2.m.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.76635 + 1.28333i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.855032 + 2.63152i) q^{4} +(-0.272011 + 0.471137i) q^{5} +(-1.09167 - 1.89082i) q^{6} +(0.385694 - 0.428357i) q^{7} +(-0.517444 + 1.59253i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(1.76635 + 1.28333i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.855032 + 2.63152i) q^{4} +(-0.272011 + 0.471137i) q^{5} +(-1.09167 - 1.89082i) q^{6} +(0.385694 - 0.428357i) q^{7} +(-0.517444 + 1.59253i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-1.08509 + 0.483114i) q^{10} +(-4.22763 - 0.898610i) q^{11} +(0.289224 - 2.75178i) q^{12} +(-0.448690 - 4.26900i) q^{13} +(1.23100 - 0.261656i) q^{14} +(0.440123 - 0.319768i) q^{15} +(1.51927 - 1.10382i) q^{16} +(-0.117590 + 0.0249945i) q^{17} +(0.228220 + 2.17137i) q^{18} +(-0.0652913 + 0.621205i) q^{19} +(-1.47238 - 0.312964i) q^{20} +(-0.526577 + 0.234447i) q^{21} +(-6.31427 - 7.01270i) q^{22} +(-2.88935 + 8.89249i) q^{23} +(1.12045 - 1.24438i) q^{24} +(2.35202 + 4.07382i) q^{25} +(4.68600 - 8.11639i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.45701 + 0.648702i) q^{28} +(5.33477 + 3.87594i) q^{29} +1.18778 q^{30} +(-3.58077 - 4.26357i) q^{31} +7.44910 q^{32} +(3.49663 + 2.54045i) q^{33} +(-0.239781 - 0.106757i) q^{34} +(0.0969015 + 0.298232i) q^{35} +(-1.38347 + 2.39624i) q^{36} +(-0.992736 - 1.71947i) q^{37} +(-0.912539 + 1.01348i) q^{38} +(-1.32646 + 4.08243i) q^{39} +(-0.609549 - 0.676973i) q^{40} +(-5.07221 + 2.25829i) q^{41} +(-1.23100 - 0.261656i) q^{42} +(0.370707 - 3.52704i) q^{43} +(-1.25005 - 11.8934i) q^{44} +(-0.532134 + 0.113108i) q^{45} +(-16.5156 + 11.9993i) q^{46} +(2.68156 - 1.94827i) q^{47} +(-1.83689 + 0.390442i) q^{48} +(0.696970 + 6.63122i) q^{49} +(-1.07356 + 10.2142i) q^{50} +(0.117590 + 0.0249945i) q^{51} +(10.8503 - 4.83087i) q^{52} +(-3.45527 - 3.83747i) q^{53} +(0.674687 - 2.07647i) q^{54} +(1.57333 - 1.74736i) q^{55} +(0.482596 + 0.835880i) q^{56} +(0.312313 - 0.540943i) q^{57} +(4.44898 + 13.6926i) q^{58} +(-8.65421 - 3.85310i) q^{59} +(1.21779 + 0.884779i) q^{60} +12.2514 q^{61} +(-0.853338 - 12.1263i) q^{62} +0.576411 q^{63} +(10.1192 + 7.35203i) q^{64} +(2.13333 + 0.949821i) q^{65} +(2.91605 + 8.97467i) q^{66} +(1.98252 - 3.43383i) q^{67} +(-0.166316 - 0.288068i) q^{68} +(6.25645 - 6.94849i) q^{69} +(-0.211568 + 0.651140i) q^{70} +(0.374749 + 0.416201i) q^{71} +(-1.52972 + 0.681074i) q^{72} +(12.3871 + 2.63297i) q^{73} +(0.453125 - 4.31120i) q^{74} +(-0.491706 - 4.67827i) q^{75} +(-1.69054 + 0.359335i) q^{76} +(-2.01550 + 1.46434i) q^{77} +(-7.58210 + 5.50872i) q^{78} +(-13.0672 + 2.77752i) q^{79} +(0.106789 + 1.01603i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-11.8575 - 2.52038i) q^{82} +(6.20346 - 2.76196i) q^{83} +(-1.06719 - 1.18524i) q^{84} +(0.0202099 - 0.0621996i) q^{85} +(5.18116 - 5.75426i) q^{86} +(-3.29707 - 5.71070i) q^{87} +(3.61862 - 6.26764i) q^{88} +(-5.19694 - 15.9945i) q^{89} +(-1.08509 - 0.483114i) q^{90} +(-2.00171 - 1.45433i) q^{91} -25.8712 q^{92} +(1.53705 + 5.35140i) q^{93} +7.23684 q^{94} +(-0.274912 - 0.199736i) q^{95} +(-6.80509 - 3.02982i) q^{96} +(-3.46887 - 10.6761i) q^{97} +(-7.27896 + 12.6075i) q^{98} +(-2.16104 - 3.74303i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9	\( 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9} - 16 q^{10} + 10 q^{11} - 10 q^{12} + 3 q^{13} - 12 q^{14} - 8 q^{15} + 6 q^{16} + 3 q^{17} - 32 q^{19} - 10 q^{20} - 6 q^{21} - 9 q^{22} - 22 q^{23} + 20 q^{24} + 12 q^{25} + 18 q^{26} + 4 q^{27} + 30 q^{28} + 38 q^{29} - 2 q^{30} - 8 q^{31} + 10 q^{33} - 52 q^{34} + 3 q^{35} - 5 q^{36} - 8 q^{37} + 7 q^{38} + 6 q^{39} + 37 q^{40} - 40 q^{41} + 12 q^{42} + q^{43} + q^{45} - 7 q^{46} - 23 q^{47} + 18 q^{48} + 25 q^{49} - 21 q^{50} - 3 q^{51} - 45 q^{52} + 30 q^{53} - 5 q^{54} + 46 q^{55} - 6 q^{56} - 8 q^{57} + 48 q^{58} - 40 q^{59} + 15 q^{60} + 26 q^{61} + 40 q^{62} - 12 q^{63} + 38 q^{64} + 12 q^{65} + 12 q^{66} - 32 q^{67} + 15 q^{68} - 11 q^{69} + 33 q^{70} + 17 q^{71} + 5 q^{72} + 27 q^{73} - 70 q^{74} + 3 q^{75} - 15 q^{76} - 9 q^{77} - 9 q^{78} + 21 q^{80} + 2 q^{81} - 32 q^{82} - 17 q^{83} - 15 q^{84} - 64 q^{85} + 26 q^{86} - 6 q^{87} - 22 q^{88} - 43 q^{89} - 16 q^{90} - 140 q^{92} - q^{93} + 88 q^{94} - 2 q^{95} - 35 q^{96} + 12 q^{97} - 32 q^{98}+O(q^{100}) \) 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9 - 16 * q^10 + 10 * q^11 - 10 * q^12 + 3 * q^13 - 12 * q^14 - 8 * q^15 + 6 * q^16 + 3 * q^17 - 32 * q^19 - 10 * q^20 - 6 * q^21 - 9 * q^22 - 22 * q^23 + 20 * q^24 + 12 * q^25 + 18 * q^26 + 4 * q^27 + 30 * q^28 + 38 * q^29 - 2 * q^30 - 8 * q^31 + 10 * q^33 - 52 * q^34 + 3 * q^35 - 5 * q^36 - 8 * q^37 + 7 * q^38 + 6 * q^39 + 37 * q^40 - 40 * q^41 + 12 * q^42 + q^43 + q^45 - 7 * q^46 - 23 * q^47 + 18 * q^48 + 25 * q^49 - 21 * q^50 - 3 * q^51 - 45 * q^52 + 30 * q^53 - 5 * q^54 + 46 * q^55 - 6 * q^56 - 8 * q^57 + 48 * q^58 - 40 * q^59 + 15 * q^60 + 26 * q^61 + 40 * q^62 - 12 * q^63 + 38 * q^64 + 12 * q^65 + 12 * q^66 - 32 * q^67 + 15 * q^68 - 11 * q^69 + 33 * q^70 + 17 * q^71 + 5 * q^72 + 27 * q^73 - 70 * q^74 + 3 * q^75 - 15 * q^76 - 9 * q^77 - 9 * q^78 + 21 * q^80 + 2 * q^81 - 32 * q^82 - 17 * q^83 - 15 * q^84 - 64 * q^85 + 26 * q^86 - 6 * q^87 - 22 * q^88 - 43 * q^89 - 16 * q^90 - 140 * q^92 - q^93 + 88 * q^94 - 2 * q^95 - 35 * q^96 + 12 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	1.76635	+	1.28333i	1.24900	+	0.907452i	0.998163	−	0.0605777i	$-0.0192943\pi$
$2$	1.76635	+	1.28333i	1.24900	+	0.907452i	0.250837	+	0.968029i	$0.419294\pi$
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$4$	0.855032	+	2.63152i	0.427516	+	1.31576i
$5$	−0.272011	+	0.471137i	−0.121647	+	0.210699i	−0.920417	−	0.390937i	$-0.872151\pi$
$5$	−0.272011	+	0.471137i	−0.121647	+	0.210699i	0.798770	+	0.601636i	$0.205484\pi$
$6$	−1.09167	−	1.89082i	−0.445671	−	0.771925i
$7$	0.385694	−	0.428357i	0.145779	−	0.161904i	−0.665833	−	0.746101i	$-0.731924\pi$
$7$	0.385694	−	0.428357i	0.145779	−	0.161904i	0.811612	+	0.584197i	$0.198590\pi$
$8$	−0.517444	+	1.59253i	−0.182944	+	0.563044i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	−1.08509	+	0.483114i	−0.343136	+	0.152774i
$11$	−4.22763	−	0.898610i	−1.27468	−	0.270941i	−0.479621	−	0.877476i	$-0.659226\pi$
$11$	−4.22763	−	0.898610i	−1.27468	−	0.270941i	−0.795057	+	0.606535i	$0.792559\pi$
$12$	0.289224	−	2.75178i	0.0834918	−	0.794371i
$13$	−0.448690	−	4.26900i	−0.124444	−	1.18401i	−0.861350	−	0.508013i	$-0.830380\pi$
$13$	−0.448690	−	4.26900i	−0.124444	−	1.18401i	0.736905	−	0.675996i	$-0.236286\pi$
$14$	1.23100	−	0.261656i	0.328997	−	0.0699305i
$15$	0.440123	−	0.319768i	0.113639	−	0.0825637i
$16$	1.51927	−	1.10382i	0.379818	−	0.275954i
$17$	−0.117590	+	0.0249945i	−0.0285197	+	0.00606205i	−0.222149	−	0.975013i	$-0.571307\pi$
$17$	−0.117590	+	0.0249945i	−0.0285197	+	0.00606205i	0.193630	+	0.981075i	$0.437974\pi$
$18$	0.228220	+	2.17137i	0.0537921	+	0.511797i
$19$	−0.0652913	+	0.621205i	−0.0149788	+	0.142514i	−0.999455	−	0.0330027i	$-0.989493\pi$
$19$	−0.0652913	+	0.621205i	−0.0149788	+	0.142514i	0.984476	+	0.175517i	$0.0561597\pi$
$20$	−1.47238	−	0.312964i	−0.329235	−	0.0699810i
$21$	−0.526577	+	0.234447i	−0.114909	+	0.0511606i
$22$	−6.31427	−	7.01270i	−1.34621	−	1.49511i
$23$	−2.88935	+	8.89249i	−0.602470	+	1.85421i	−0.0891442	+	0.996019i	$0.528413\pi$
$23$	−2.88935	+	8.89249i	−0.602470	+	1.85421i	−0.513326	+	0.858194i	$0.671587\pi$
$24$	1.12045	−	1.24438i	0.228711	−	0.254009i
$25$	2.35202	+	4.07382i	0.470404	+	0.814764i
$26$	4.68600	−	8.11639i	0.919000	−	1.59175i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	1.45701	+	0.648702i	0.275349	+	0.122593i
$29$	5.33477	+	3.87594i	0.990643	+	0.719744i	0.960062	−	0.279788i	$-0.0902643\pi$
$29$	5.33477	+	3.87594i	0.990643	+	0.719744i	0.0305809	+	0.999532i	$0.490264\pi$
$30$	1.18778			0.216858
$31$	−3.58077	−	4.26357i	−0.643126	−	0.765760i
$31$	−3.58077	−	4.26357i	−0.643126	−	0.765760i
$32$	7.44910			1.31683
$33$	3.49663	+	2.54045i	0.608685	+	0.442236i
$34$	−0.239781	−	0.106757i	−0.0411221	−	0.0183088i
$35$	0.0969015	+	0.298232i	0.0163794	+	0.0504105i
$36$	−1.38347	+	2.39624i	−0.230578	+	0.399373i
$37$	−0.992736	−	1.71947i	−0.163205	−	0.282679i	0.772811	−	0.634636i	$-0.218850\pi$
$37$	−0.992736	−	1.71947i	−0.163205	−	0.282679i	−0.936016	+	0.351957i	$0.885516\pi$
$38$	−0.912539	+	1.01348i	−0.148033	+	0.164408i
$39$	−1.32646	+	4.08243i	−0.212404	+	0.653712i
$40$	−0.609549	−	0.676973i	−0.0963781	−	0.107039i
$41$	−5.07221	+	2.25829i	−0.792147	+	0.352686i	−0.762594	−	0.646877i	$-0.776075\pi$
$41$	−5.07221	+	2.25829i	−0.792147	+	0.352686i	−0.0295521	+	0.999563i	$0.509408\pi$
$42$	−1.23100	−	0.261656i	−0.189947	−	0.0403744i
$43$	0.370707	−	3.52704i	0.0565323	−	0.537869i	−0.929203	−	0.369569i	$-0.879505\pi$
$43$	0.370707	−	3.52704i	0.0565323	−	0.537869i	0.985736	−	0.168300i	$-0.0538279\pi$
$44$	−1.25005	−	11.8934i	−0.188452	−	1.79300i
$45$	−0.532134	+	0.113108i	−0.0793258	+	0.0168612i
$46$	−16.5156	+	11.9993i	−2.43509	+	1.76920i
$47$	2.68156	−	1.94827i	0.391145	−	0.284184i	−0.374779	−	0.927114i	$-0.622282\pi$
$47$	2.68156	−	1.94827i	0.391145	−	0.284184i	0.765925	+	0.642930i	$0.222282\pi$
$48$	−1.83689	+	0.390442i	−0.265132	+	0.0563555i
$49$	0.696970	+	6.63122i	0.0995671	+	0.947318i
$50$	−1.07356	+	10.2142i	−0.151824	+	1.44451i
$51$	0.117590	+	0.0249945i	0.0164659	+	0.00349993i
$52$	10.8503	−	4.83087i	1.50467	−	0.669921i
$53$	−3.45527	−	3.83747i	−0.474618	−	0.527117i	0.457530	−	0.889194i	$-0.348734\pi$
$53$	−3.45527	−	3.83747i	−0.474618	−	0.527117i	−0.932148	+	0.362078i	$0.882068\pi$
$54$	0.674687	−	2.07647i	0.0918132	−	0.282572i
$55$	1.57333	−	1.74736i	0.212148	−	0.235614i
$56$	0.482596	+	0.835880i	0.0644896	+	0.111699i
$57$	0.312313	−	0.540943i	0.0413669	−	0.0716496i
$58$	4.44898	+	13.6926i	0.584180	+	1.79792i
$59$	−8.65421	−	3.85310i	−1.12668	−	0.501631i	−0.243144	−	0.969990i	$-0.578179\pi$
$59$	−8.65421	−	3.85310i	−1.12668	−	0.501631i	−0.883538	+	0.468359i	$0.844845\pi$
$60$	1.21779	+	0.884779i	0.157216	+	0.114224i
$61$	12.2514			1.56863			0.784314	−	0.620365i	$-0.213015\pi$
$61$	12.2514			1.56863			0.784314	+	0.620365i	$0.213015\pi$
$62$	−0.853338	−	12.1263i	−0.108374	−	1.54004i
$63$	0.576411			0.0726209
$64$	10.1192	+	7.35203i	1.26490	+	0.919003i
$65$	2.13333	+	0.949821i	0.264607	+	0.117811i
$66$	2.91605	+	8.97467i	0.358941	+	1.10471i
$67$	1.98252	−	3.43383i	0.242204	−	0.419509i	−0.719138	−	0.694867i	$-0.755463\pi$
$67$	1.98252	−	3.43383i	0.242204	−	0.419509i	0.961342	+	0.275358i	$0.0887964\pi$
$68$	−0.166316	−	0.288068i	−0.0201688	−	0.0349334i
$69$	6.25645	−	6.94849i	0.753188	−	0.836500i
$70$	−0.211568	+	0.651140i	−0.0252872	+	0.0778261i
$71$	0.374749	+	0.416201i	0.0444745	+	0.0493940i	0.764972	−	0.644064i	$-0.222753\pi$
$71$	0.374749	+	0.416201i	0.0444745	+	0.0493940i	−0.720497	+	0.693458i	$0.756086\pi$
$72$	−1.52972	+	0.681074i	−0.180279	+	0.0802654i
$73$	12.3871	+	2.63297i	1.44981	+	0.308166i	0.864494	−	0.502643i	$-0.167639\pi$
$73$	12.3871	+	2.63297i	1.44981	+	0.308166i	0.585312	+	0.810808i	$0.300972\pi$
$74$	0.453125	−	4.31120i	0.0526747	−	0.501167i
$75$	−0.491706	−	4.67827i	−0.0567773	−	0.540200i
$76$	−1.69054	+	0.359335i	−0.193918	+	0.0412185i
$77$	−2.01550	+	1.46434i	−0.229687	+	0.166877i
$78$	−7.58210	+	5.50872i	−0.858504	+	0.623740i
$79$	−13.0672	+	2.77752i	−1.47017	+	0.312495i	−0.872251	−	0.489058i	$-0.837340\pi$
$79$	−13.0672	+	2.77752i	−1.47017	+	0.312495i	−0.597923	+	0.801554i	$0.704007\pi$
$80$	0.106789	+	1.01603i	0.0119394	+	0.113596i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−11.8575	−	2.52038i	−1.30944	−	0.278329i
$83$	6.20346	−	2.76196i	0.680918	−	0.303164i	−0.0369764	−	0.999316i	$-0.511773\pi$
$83$	6.20346	−	2.76196i	0.680918	−	0.303164i	0.717895	+	0.696152i	$0.245106\pi$
$84$	−1.06719	−	1.18524i	−0.116440	−	0.129320i
$85$	0.0202099	−	0.0621996i	0.00219207	−	0.00674650i
$86$	5.18116	−	5.75426i	0.558699	−	0.620498i
$87$	−3.29707	−	5.71070i	−0.353483	−	0.612251i
$88$	3.61862	−	6.26764i	0.385747	−	0.668133i
$89$	−5.19694	−	15.9945i	−0.550875	−	1.69542i	−0.706596	−	0.707618i	$-0.749770\pi$
$89$	−5.19694	−	15.9945i	−0.550875	−	1.69542i	0.155721	−	0.987801i	$-0.450230\pi$
$90$	−1.08509	−	0.483114i	−0.114379	−	0.0509247i
$91$	−2.00171	−	1.45433i	−0.209837	−	0.152455i
$92$	−25.8712			−2.69726
$93$	1.53705	+	5.35140i	0.159385	+	0.554914i
$94$	7.23684			0.746423
$95$	−0.274912	−	0.199736i	−0.0282054	−	0.0204924i
$96$	−6.80509	−	3.02982i	−0.694542	−	0.309230i
$97$	−3.46887	−	10.6761i	−0.352210	−	1.08399i	−0.957610	−	0.288069i	$-0.906987\pi$
$97$	−3.46887	−	10.6761i	−0.352210	−	1.08399i	0.605400	−	0.795922i	$-0.293013\pi$
$98$	−7.27896	+	12.6075i	−0.735286	+	1.27355i
$99$	−2.16104	−	3.74303i	−0.217192	−	0.376188i
$100$	−8.70927	+	9.67262i	−0.870927	+	0.967262i
$101$	−0.439522	+	1.35271i	−0.0437341	+	0.134600i	−0.970539	−	0.240942i	$-0.922543\pi$
$101$	−0.439522	+	1.35271i	−0.0437341	+	0.134600i	0.926805	+	0.375542i	$0.122543\pi$
$102$	0.175629	+	0.195056i	0.0173898	+	0.0193134i
$103$	−3.84029	+	1.70981i	−0.378395	+	0.168472i	−0.587116	−	0.809503i	$-0.699737\pi$
$103$	−3.84029	+	1.70981i	−0.378395	+	0.168472i	0.208721	+	0.977975i	$0.433070\pi$
$104$	7.03069	+	1.49442i	0.689416	+	0.146540i
$105$	0.0327780	−	0.311862i	0.00319881	−	0.0304346i
$106$	−1.17849	−	11.2126i	−0.114465	−	1.08906i
$107$	18.9572	−	4.02948i	1.83267	−	0.389545i	0.843594	−	0.536982i	$-0.180436\pi$
$107$	18.9572	−	4.02948i	1.83267	−	0.389545i	0.989071	+	0.147437i	$0.0471024\pi$
$108$	2.23850	−	1.62637i	0.215400	−	0.156497i
$109$	−10.7171	+	7.78644i	−1.02651	+	0.745805i	−0.967608	−	0.252458i	$-0.918761\pi$
$109$	−10.7171	+	7.78644i	−1.02651	+	0.745805i	−0.0589053	+	0.998264i	$0.518761\pi$
$110$	5.02149	−	1.06735i	0.478780	−	0.101768i
$111$	0.207538	+	1.97460i	0.0196987	+	0.187420i
$112$	0.113147	−	1.07652i	0.0106914	−	0.101722i
$113$	4.20774	+	0.894383i	0.395831	+	0.0841365i	0.401527	−	0.915847i	$-0.368480\pi$
$113$	4.20774	+	0.894383i	0.395831	+	0.0841365i	−0.00569564	+	0.999984i	$0.501813\pi$
$114$	1.24586	−	0.554694i	0.116686	−	0.0519519i
$115$	−3.40365	−	3.78013i	−0.317392	−	0.352499i
$116$	−5.63820	+	17.3526i	−0.523494	+	1.61115i
$117$	2.87226	−	3.18996i	0.265540	−	0.294912i
$118$	−10.3416	−	17.9122i	−0.952020	−	1.64895i
$119$	−0.0346471	+	0.0600106i	−0.00317610	+	0.00550116i
$120$	0.281501	+	0.866371i	0.0256974	+	0.0790885i
$121$	7.01633	+	3.12387i	0.637848	+	0.283988i
$122$	21.6402	+	15.7226i	1.95922	+	1.42345i
$123$	5.55223			0.500628
$124$	8.15799	−	13.0684i	0.732609	−	1.17357i
$125$	−5.27921			−0.472187
$126$	1.01814	+	0.739726i	0.0907035	+	0.0659000i
$127$	12.7961	+	5.69719i	1.13547	+	0.505544i	0.886390	−	0.462939i	$-0.153205\pi$
$127$	12.7961	+	5.69719i	1.13547	+	0.505544i	0.249080	+	0.968483i	$0.419872\pi$
$128$	3.83520	+	11.8035i	0.338987	+	1.04329i
$129$	−1.77324	+	3.07133i	−0.156125	+	0.270416i
$130$	2.54928	+	4.41549i	0.223587	+	0.387264i
$131$	−2.10129	+	2.33372i	−0.183591	+	0.203898i	−0.827914	−	0.560855i	$-0.810472\pi$
$131$	−2.10129	+	2.33372i	−0.183591	+	0.203898i	0.644323	+	0.764753i	$0.277139\pi$
$132$	−3.69551	+	11.3736i	−0.321653	+	0.989946i
$133$	0.240915	+	0.267563i	0.0208900	+	0.0232007i
$134$	7.90858	−	3.52113i	0.683197	−	0.304179i
$135$	0.532134	+	0.113108i	0.0457988	+	0.00973483i
$136$	0.0210417	−	0.200198i	0.00180431	−	0.0171669i
$137$	−0.239309	−	2.27687i	−0.0204455	−	0.194526i	0.979532	−	0.201290i	$-0.0645135\pi$
$137$	−0.239309	−	2.27687i	−0.0204455	−	0.194526i	−0.999977	+	0.00676430i	$0.997847\pi$
$138$	19.9683	−	4.24440i	1.69982	−	0.361307i
$139$	−13.7158	+	9.96510i	−1.16336	+	0.845228i	−0.990199	−	0.139666i	$-0.955397\pi$
$139$	−13.7158	+	9.96510i	−1.16336	+	0.845228i	−0.173158	+	0.984894i	$0.555397\pi$
$140$	−0.701949	+	0.509996i	−0.0593255	+	0.0431025i
$141$	−3.24215	+	0.689141i	−0.273039	+	0.0580362i
$142$	0.127816	+	1.21608i	0.0107261	+	0.102052i
$143$	−1.93927	+	18.4510i	−0.162170	+	1.54295i
$144$	1.83689	+	0.390442i	0.153074	+	0.0325368i
$145$	−3.27721	+	1.45911i	−0.272158	+	0.121172i
$146$	18.5011	+	20.5476i	1.53116	+	1.70053i
$147$	2.06045	−	6.34141i	0.169943	−	0.523030i
$148$	3.67599	−	4.08260i	0.302165	−	0.335588i
$149$	−5.00526	−	8.66937i	−0.410047	−	0.710222i	0.584848	−	0.811143i	$-0.301154\pi$
$149$	−5.00526	−	8.66937i	−0.410047	−	0.710222i	−0.994894	+	0.100921i	$0.967821\pi$
$150$	5.13524	−	8.89450i	0.419291	−	0.726233i
$151$	−1.93017	−	5.94046i	−0.157075	−	0.483428i	0.841290	−	0.540584i	$-0.181797\pi$
$151$	−1.93017	−	5.94046i	−0.157075	−	0.483428i	−0.998365	+	0.0571563i	$0.981797\pi$
$152$	−0.955503	−	0.425417i	−0.0775015	−	0.0345059i
$153$	−0.0972574	−	0.0706617i	−0.00786280	−	0.00571266i
$154$	−5.43931			−0.438312
$155$	2.98274	−	0.527296i	0.239579	−	0.0423534i
$156$	−11.8771			−0.950933
$157$	6.25331	+	4.54330i	0.499069	+	0.362595i	0.808661	−	0.588275i	$-0.200193\pi$
$157$	6.25331	+	4.54330i	0.499069	+	0.362595i	−0.309592	+	0.950869i	$0.600193\pi$
$158$	−26.6457	−	11.8635i	−2.11982	−	0.943805i
$159$	1.59571	+	4.91109i	0.126548	+	0.389474i
$160$	−2.02624	+	3.50954i	−0.160188	+	0.277454i
$161$	2.69475	+	4.66745i	0.212376	+	0.367847i
$162$	−1.46093	+	1.62253i	−0.114782	+	0.127478i
$163$	3.29115	−	10.1291i	0.257783	−	0.793373i	−0.735486	−	0.677540i	$-0.763046\pi$
$163$	3.29115	−	10.1291i	0.257783	−	0.793373i	0.993269	−	0.115833i	$-0.0369539\pi$
$164$	−10.2796	−	11.4167i	−0.802705	−	0.891494i
$165$	−2.14802	+	0.956361i	−0.167223	+	0.0744526i
$166$	14.5020	+	3.08250i	1.12557	+	0.239248i
$167$	−1.35749	+	12.9156i	−0.105045	+	0.999441i	0.807334	+	0.590095i	$0.200910\pi$
$167$	−1.35749	+	12.9156i	−0.105045	+	0.999441i	−0.912379	+	0.409346i	$0.865757\pi$
$168$	−0.100890	−	0.959904i	−0.00778383	−	0.0740582i
$169$	−5.30716	+	1.12807i	−0.408243	+	0.0867747i
$170$	0.115520	−	0.0839305i	0.00886002	−	0.00643718i
$171$	−0.505334	+	0.367146i	−0.0386438	+	0.0280764i
$172$	9.59844	−	2.04021i	0.731874	−	0.155565i
$173$	−0.284007	−	2.70215i	−0.0215927	−	0.205441i	0.978407	−	0.206690i	$-0.0662691\pi$
$173$	−0.284007	−	2.70215i	−0.0215927	−	0.205441i	−0.999999	+	0.00124914i	$0.999602\pi$
$174$	1.50492	−	14.3183i	0.114088	−	1.08547i
$175$	2.65221	+	0.563744i	0.200488	+	0.0426150i
$176$	−7.41481	+	3.30129i	−0.558912	+	0.248844i
$177$	6.33882	+	7.03997i	0.476455	+	0.529157i
$178$	11.3467	−	34.9214i	0.850468	−	2.61747i
$179$	−4.82179	+	5.35514i	−0.360397	+	0.400262i	−0.895888	−	0.444279i	$-0.853460\pi$
$179$	−4.82179	+	5.35514i	−0.360397	+	0.400262i	0.535491	+	0.844541i	$0.320127\pi$
$180$	−0.752638	−	1.30361i	−0.0560983	−	0.0971651i
$181$	−10.1723	+	17.6190i	−0.756102	+	1.30961i	0.188723	+	0.982030i	$0.439565\pi$
$181$	−10.1723	+	17.6190i	−0.756102	+	1.30961i	−0.944825	+	0.327577i	$0.893768\pi$
$182$	−1.66935	−	5.13772i	−0.123740	−	0.380833i
$183$	−11.1922	−	4.98308i	−0.827350	−	0.368360i
$184$	−12.6665	−	9.20274i	−0.933785	−	0.678435i
$185$	1.08014			0.0794135
$186$	−4.15264	+	11.4250i	−0.304487	+	0.837722i
$187$	0.519586			0.0379959
$188$	7.41971	+	5.39073i	0.541138	+	0.393160i
$189$	−0.526577	−	0.234447i	−0.0383029	−	0.0170535i
$190$	−0.229266	−	0.705607i	−0.0166327	−	0.0511901i
$191$	6.39185	−	11.0710i	0.462498	−	0.801070i	−0.536587	−	0.843845i	$-0.680287\pi$
$191$	6.39185	−	11.0710i	0.462498	−	0.801070i	0.999085	+	0.0427751i	$0.0136199\pi$
$192$	−6.25401	−	10.8323i	−0.451344	−	0.781751i
$193$	−11.0964	+	12.3238i	−0.798734	+	0.887084i	−0.995634	−	0.0933396i	$-0.970246\pi$
$193$	−11.0964	+	12.3238i	−0.798734	+	0.887084i	0.196900	+	0.980424i	$0.436912\pi$
$194$	7.57369	−	23.3094i	0.543759	−	1.67352i
$195$	−1.56257	−	1.73541i	−0.111898	−	0.124275i
$196$	−16.8542	+	7.50399i	−1.20387	+	0.535999i
$197$	3.08970	+	0.656736i	0.220132	+	0.0467905i	0.316657	−	0.948540i	$-0.397439\pi$
$197$	3.08970	+	0.656736i	0.220132	+	0.0467905i	−0.0965252	+	0.995331i	$0.530773\pi$
$198$	0.986385	−	9.38483i	0.0700994	−	0.666951i
$199$	0.917406	+	8.72854i	0.0650332	+	0.618750i	0.977694	+	0.210033i	$0.0673570\pi$
$199$	0.917406	+	8.72854i	0.0650332	+	0.618750i	−0.912661	+	0.408717i	$0.865976\pi$
$200$	−7.70472	+	1.63769i	−0.544806	+	0.115802i
$201$	−3.20779	+	2.33060i	−0.226260	+	0.164388i
$202$	−2.51233	+	1.82531i	−0.176767	+	0.128428i
$203$	3.71788	−	0.790259i	0.260944	−	0.0554653i
$204$	0.0347696	+	0.330810i	0.00243436	+	0.0231614i
$205$	0.315732	−	3.00399i	0.0220517	−	0.209808i
$206$	−8.97755	−	1.90824i	−0.625496	−	0.132953i
$207$	−8.54176	+	3.80304i	−0.593693	+	0.264329i
$208$	−5.39387	−	5.99050i	−0.373998	−	0.415367i
$209$	0.834248	−	2.56755i	0.0577061	−	0.177601i
$210$	0.458120	−	0.508794i	0.0316133	−	0.0351101i
$211$	−6.17467	−	10.6948i	−0.425082	−	0.736263i	0.571346	−	0.820709i	$-0.306421\pi$
$211$	−6.17467	−	10.6948i	−0.425082	−	0.736263i	−0.996428	+	0.0844461i	$0.973088\pi$
$212$	7.14399	−	12.3738i	0.490651	−	0.849833i
$213$	−0.173066	−	0.532643i	−0.0118583	−	0.0364961i
$214$	38.6563	+	17.2109i	2.64249	+	1.17651i
$215$	1.56088	+	1.13405i	0.106451	+	0.0773414i
$216$	1.67449			0.113934
$217$	−3.20741	−	0.110586i	−0.217733	−	0.00750709i
$218$	−28.9228			−1.95890
$219$	−10.2453	−	7.44364i	−0.692313	−	0.502995i
$220$	5.94345	+	2.64619i	0.400707	+	0.178406i
$221$	0.159463	+	0.490776i	0.0107266	+	0.0330132i
$222$	−2.16747	+	3.75417i	−0.145471	+	0.251964i
$223$	11.7632	+	20.3744i	0.787721	+	1.36437i	0.927360	+	0.374170i	$0.122072\pi$
$223$	11.7632	+	20.3744i	0.787721	+	1.36437i	−0.139639	+	0.990202i	$0.544594\pi$
$224$	2.87307	−	3.19087i	0.191965	−	0.213199i
$225$	−1.45363	+	4.47381i	−0.0969086	+	0.298254i
$226$	6.28457	+	6.97972i	0.418043	+	0.464284i
$227$	−3.39523	+	1.51166i	−0.225350	+	0.100332i	−0.516306	−	0.856404i	$-0.672693\pi$
$227$	−3.39523	+	1.51166i	−0.225350	+	0.100332i	0.290956	+	0.956736i	$0.406027\pi$
$228$	1.69054	+	0.359335i	0.111959	+	0.0237975i
$229$	0.540282	−	5.14044i	0.0357028	−	0.339690i	−0.962060	−	0.272838i	$-0.912038\pi$
$229$	0.540282	−	5.14044i	0.0357028	−	0.339690i	0.997763	−	0.0668520i	$-0.0212955\pi$
$230$	−1.16088	−	11.0450i	−0.0765462	−	0.728289i
$231$	2.43685	−	0.517968i	0.160333	−	0.0340798i
$232$	−8.93300	+	6.49020i	−0.586480	+	0.426103i
$233$	13.3708	−	9.71443i	0.875948	−	0.636413i	−0.0562286	−	0.998418i	$-0.517908\pi$
$233$	13.3708	−	9.71443i	0.875948	−	0.636413i	0.932176	+	0.362005i	$0.117908\pi$
$234$	9.16720	−	1.94855i	0.599278	−	0.127381i
$235$	0.188486	+	1.79333i	0.0122955	+	0.116984i
$236$	2.73988	−	26.0682i	0.178351	−	1.69690i
$237$	13.0672	+	2.77752i	0.848805	+	0.180419i
$238$	−0.138212	+	0.0615362i	−0.00895898	+	0.00398880i
$239$	9.09910	+	10.1056i	0.588572	+	0.653675i	0.961700	−	0.274104i	$-0.0883814\pi$
$239$	9.09910	+	10.1056i	0.588572	+	0.653675i	−0.373128	+	0.927780i	$0.621715\pi$
$240$	0.315701	−	0.971629i	0.0203784	−	0.0627184i
$241$	4.70863	−	5.22946i	0.303309	−	0.336859i	−0.572152	−	0.820148i	$-0.693891\pi$
$241$	4.70863	−	5.22946i	0.303309	−	0.336859i	0.875461	+	0.483289i	$0.160558\pi$
$242$	8.38435	+	14.5221i	0.538967	+	0.933517i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	10.4753	+	32.2397i	0.670613	+	2.06393i
$245$	−3.31380	−	1.47540i	−0.211711	−	0.0942597i
$246$	9.80720	+	7.12534i	0.625284	+	0.454295i
$247$	2.68122			0.170602
$248$	8.64272	−	3.49633i	0.548813	−	0.222017i
$249$	−6.79053			−0.430332
$250$	−9.32495	−	6.77497i	−0.589761	−	0.428487i
$251$	0.773256	+	0.344276i	0.0488075	+	0.0217305i	0.430995	−	0.902354i	$-0.358163\pi$
$251$	0.773256	+	0.344276i	0.0488075	+	0.0217305i	−0.382188	+	0.924085i	$0.624829\pi$
$252$	0.492849	+	1.51683i	0.0310466	+	0.0955516i
$253$	20.2060	−	34.9977i	1.27034	−	2.20029i
$254$	15.2910	+	26.4849i	0.959445	+	1.66181i
$255$	−0.0437615	+	0.0486021i	−0.00274045	+	0.00304358i
$256$	−0.643129	+	1.97935i	−0.0401955	+	0.123709i
$257$	−16.4264	−	18.2434i	−1.02465	−	1.13799i	−0.990351	−	0.138579i	$-0.955747\pi$
$257$	−16.4264	−	18.2434i	−1.02465	−	1.13799i	−0.0342998	−	0.999412i	$-0.510920\pi$
$258$	−7.07370	+	3.14941i	−0.440389	+	0.196074i
$259$	−1.11944	−	0.237944i	−0.0695585	−	0.0147851i
$260$	−0.675403	+	6.42603i	−0.0418867	+	0.398525i
$261$	0.689276	+	6.55802i	0.0426651	+	0.405931i
$262$	−6.70655	+	1.42552i	−0.414332	+	0.0880690i
$263$	5.22313	−	3.79483i	0.322072	−	0.233999i	−0.414987	−	0.909827i	$-0.636214\pi$
$263$	5.22313	−	3.79483i	0.322072	−	0.233999i	0.737059	+	0.675828i	$0.236214\pi$
$264$	−5.85506	+	4.25395i	−0.360354	+	0.261812i
$265$	2.74784	−	0.584072i	0.168799	−	0.0358793i
$266$	0.0821688	+	0.781784i	0.00503809	+	0.0479343i
$267$	−1.75792	+	16.7255i	−0.107583	+	1.02359i
$268$	10.7313	+	2.28101i	0.655519	+	0.139335i
$269$	−15.3532	+	6.83568i	−0.936100	+	0.416779i	−0.817347	−	0.576145i	$-0.804556\pi$
$269$	−15.3532	+	6.83568i	−0.936100	+	0.416779i	−0.118753	+	0.992924i	$0.537890\pi$
$270$	0.794780	+	0.882693i	0.0483688	+	0.0537190i
$271$	−5.69001	+	17.5121i	−0.345644	+	1.06378i	0.615595	+	0.788063i	$0.288916\pi$
$271$	−5.69001	+	17.5121i	−0.345644	+	1.06378i	−0.961238	+	0.275719i	$0.911084\pi$
$272$	−0.151061	+	0.167771i	−0.00915945	+	0.0101726i
$273$	1.23713	+	2.14277i	0.0748743	+	0.129686i
$274$	2.49927	−	4.32887i	0.150987	−	0.261517i
$275$	−6.28269	−	19.3361i	−0.378860	−	1.16601i
$276$	23.6345	+	10.5228i	1.42263	+	0.633396i
$277$	−10.1449	−	7.37069i	−0.609547	−	0.442862i	0.239708	−	0.970845i	$-0.422948\pi$
$277$	−10.1449	−	7.37069i	−0.609547	−	0.442862i	−0.849255	+	0.527983i	$0.822948\pi$
$278$	−37.0154			−2.22004
$279$	0.772447	−	5.51392i	0.0462452	−	0.330110i
$280$	−0.525085			−0.0313798
$281$	1.14013	+	0.828350i	0.0680142	+	0.0494152i	0.621273	−	0.783594i	$-0.286616\pi$
$281$	1.14013	+	0.828350i	0.0680142	+	0.0494152i	−0.553259	+	0.833010i	$0.686616\pi$
$282$	−6.61119	−	2.94349i	−0.393690	−	0.175282i
$283$	−9.87852	−	30.4030i	−0.587217	−	1.80727i	−0.590179	−	0.807273i	$-0.700943\pi$
$283$	−9.87852	−	30.4030i	−0.587217	−	1.80727i	0.00296144	−	0.999996i	$-0.499057\pi$
$284$	−0.774818	+	1.34202i	−0.0459770	+	0.0796344i
$285$	0.169905	+	0.294285i	0.0100643	+	0.0174319i
$286$	−27.1041	+	30.1022i	−1.60270	+	1.77998i
$287$	−0.988967	+	3.04373i	−0.0583769	+	0.179666i
$288$	4.98442	+	5.53576i	0.293710	+	0.326198i
$289$	−15.5171	+	6.90864i	−0.912769	+	0.406391i
$290$	−7.66124	−	1.62845i	−0.449883	−	0.0956257i
$291$	−1.17338	+	11.1640i	−0.0687849	+	0.654445i
$292$	3.66270	+	34.8483i	0.214343	+	2.03934i
$293$	−27.6152	+	5.86979i	−1.61330	+	0.342917i	−0.924246	−	0.381797i	$-0.875305\pi$
$293$	−27.6152	+	5.86979i	−1.61330	+	0.342917i	−0.689050	+	0.724714i	$0.741972\pi$
$294$	11.7776	−	8.55693i	0.686884	−	0.499050i
$295$	4.16938	−	3.02923i	0.242751	−	0.176369i
$296$	3.25199	−	0.691232i	0.189018	−	0.0401771i
$297$	0.451780	+	4.29840i	0.0262149	+	0.249418i
$298$	2.28460	−	21.7366i	0.132344	−	1.25917i
$299$	39.2585	+	8.34465i	2.27038	+	0.482584i
$300$	11.8905	−	5.29400i	0.686500	−	0.305649i
$301$	−1.36785	−	1.51915i	−0.0788417	−	0.0875626i
$302$	4.21421	−	12.9700i	0.242500	−	0.746339i
$303$	0.951720	−	1.05699i	0.0546749	−	0.0607226i
$304$	0.586500	+	1.01585i	0.0336381	+	0.0582629i
$305$	−3.33251	+	5.77207i	−0.190819	+	0.330508i
$306$	−0.0811087	−	0.249627i	−0.00463667	−	0.0142702i
$307$	7.95900	+	3.54358i	0.454244	+	0.202243i	0.621088	−	0.783741i	$-0.286691\pi$
$307$	7.95900	+	3.54358i	0.454244	+	0.202243i	−0.166844	+	0.985983i	$0.553358\pi$
$308$	−5.57676	−	4.05175i	−0.317765	−	0.230870i
$309$	4.20372			0.239141
$310$	5.94526	+	2.89644i	0.337668	+	0.164507i
$311$	26.5726			1.50679			0.753396	−	0.657567i	$-0.228414\pi$
$311$	26.5726			1.50679			0.753396	+	0.657567i	$0.228414\pi$
$312$	−5.81502	−	4.22486i	−0.329211	−	0.239186i
$313$	0.575297	+	0.256139i	0.0325177	+	0.0144778i	0.422931	−	0.906162i	$-0.361001\pi$
$313$	0.575297	+	0.256139i	0.0325177	+	0.0144778i	−0.390413	+	0.920640i	$0.627668\pi$
$314$	5.21500	+	16.0501i	0.294300	+	0.905761i
$315$	−0.156790	+	0.271568i	−0.00883412	+	0.0153011i
$316$	−18.4819	−	32.0117i	−1.03969	−	1.80080i
$317$	11.7477	−	13.0472i	0.659818	−	0.732802i	−0.316631	−	0.948549i	$-0.602552\pi$
$317$	11.7477	−	13.0472i	0.659818	−	0.732802i	0.976449	+	0.215746i	$0.0692184\pi$
$318$	−3.48396	+	10.7225i	−0.195371	+	0.601290i
$319$	−19.0705	−	21.1799i	−1.06774	−	1.18585i
$320$	−6.21634	+	2.76769i	−0.347504	+	0.154719i
$321$	−18.9572	−	4.02948i	−1.05809	−	0.224904i
$322$	−1.23000	+	11.7026i	−0.0685450	+	0.652162i
$323$	−0.00784911	−	0.0746793i	−0.000436736	−	0.00415527i
$324$	−2.70648	+	0.575279i	−0.150360	+	0.0319600i
$325$	16.3358	−	11.8687i	0.906148	−	0.658355i
$326$	18.8123	−	13.6680i	1.04192	−	0.756998i
$327$	12.9576	−	2.75422i	0.716557	−	0.152309i
$328$	−0.971814	−	9.24619i	−0.0536595	−	0.510536i
$329$	0.199708	−	1.90010i	0.0110103	−	0.104756i
$330$	−5.02149	−	1.06735i	−0.276424	−	0.0587557i
$331$	23.9416	−	10.6595i	1.31595	−	0.585898i	0.375812	−	0.926696i	$-0.377364\pi$
$331$	23.9416	−	10.6595i	1.31595	−	0.585898i	0.940137	+	0.340798i	$0.110697\pi$
$332$	12.5723	+	13.9629i	0.689994	+	0.766316i
$333$	0.613545	−	1.88830i	0.0336220	−	0.103478i
$334$	−18.9728	+	21.0714i	−1.03815	+	1.15298i
$335$	1.07854	+	1.86808i	0.0589267	+	0.102064i
$336$	−0.541227	+	0.937433i	−0.0295264	+	0.0511412i
$337$	0.562376	+	1.73081i	0.0306346	+	0.0942835i	0.965205	−	0.261495i	$-0.0842156\pi$
$337$	0.562376	+	1.73081i	0.0306346	+	0.0942835i	−0.934570	+	0.355779i	$0.884216\pi$
$338$	−10.8220	−	4.81826i	−0.588639	−	0.262079i
$339$	−3.48019	−	2.52850i	−0.189018	−	0.137329i
$340$	0.180959			0.00981390
$341$	11.3069	+	21.2425i	0.612302	+	1.15035i
$342$	−1.36377			−0.0737441
$343$	6.37363	+	4.63071i	0.344144	+	0.250035i
$344$	5.42510	+	2.41541i	0.292502	+	0.130230i
$345$	1.57187	+	4.83771i	0.0846265	+	0.260453i
$346$	2.96609	−	5.13742i	0.159458	−	0.276190i
$347$	−10.7444	−	18.6098i	−0.576787	−	0.999025i	−0.995845	−	0.0910652i	$-0.970973\pi$
$347$	−10.7444	−	18.6098i	−0.576787	−	0.999025i	0.419058	−	0.907960i	$-0.362361\pi$
$348$	12.2087	−	13.5591i	0.654454	−	0.726845i
$349$	1.45587	−	4.48070i	0.0779307	−	0.239846i	−0.904500	−	0.426474i	$-0.859756\pi$
$349$	1.45587	−	4.48070i	0.0779307	−	0.239846i	0.982431	+	0.186627i	$0.0597557\pi$
$350$	3.96126	+	4.39943i	0.211738	+	0.235159i
$351$	−3.92141	+	1.74592i	−0.209309	+	0.0931906i
$352$	−31.4920	−	6.69383i	−1.67853	−	0.356783i
$353$	1.04070	−	9.90156i	0.0553907	−	0.527007i	−0.931283	−	0.364296i	$-0.881310\pi$
$353$	1.04070	−	9.90156i	0.0553907	−	0.527007i	0.986674	−	0.162711i	$-0.0520237\pi$
$354$	2.16198	+	20.5699i	0.114908	+	1.09328i
$355$	−0.298023	+	0.0633468i	−0.0158174	+	0.00336210i
$356$	37.6464	−	27.3517i	1.99525	−	1.44964i
$357$	0.0560602	−	0.0407301i	0.00296702	−	0.00215567i
$358$	−15.3894	+	3.27112i	−0.813354	+	0.172884i
$359$	2.50730	+	23.8554i	0.132330	+	1.25904i	0.836087	+	0.548597i	$0.184838\pi$
$359$	2.50730	+	23.8554i	0.132330	+	1.25904i	−0.703756	+	0.710441i	$0.748495\pi$
$360$	0.0952209	−	0.905966i	0.00501858	−	0.0477486i
$361$	18.2032	+	3.86920i	0.958062	+	0.203642i
$362$	−40.5788	+	18.0669i	−2.13278	+	0.949573i
$363$	−5.13914	−	5.70759i	−0.269735	−	0.299571i
$364$	2.11557	−	6.51104i	0.110886	−	0.341271i
$365$	−4.60993	+	5.11984i	−0.241295	+	0.267985i
$366$	−13.3744	−	23.1652i	−0.699091	−	1.21086i
$367$	−8.25388	+	14.2961i	−0.430849	+	0.746252i	−0.996947	−	0.0780859i	$-0.975119\pi$
$367$	−8.25388	+	14.2961i	−0.430849	+	0.746252i	0.566098	+	0.824338i	$0.308452\pi$
$368$	5.42597	+	16.6994i	0.282848	+	0.870517i
$369$	−5.07221	−	2.25829i	−0.264049	−	0.117562i
$370$	1.90791	+	1.38618i	0.0991875	+	0.0720639i
$371$	−2.97648			−0.154531
$372$	−12.7681	+	8.62038i	−0.661994	+	0.446946i
$373$	−33.4166			−1.73024			−0.865122	−	0.501561i	$-0.832759\pi$
$373$	−33.4166			−1.73024			−0.865122	+	0.501561i	$0.832759\pi$
$374$	0.917772	+	0.666800i	0.0474569	+	0.0344794i
$375$	4.82280	+	2.14725i	0.249048	+	0.110883i
$376$	1.71511	+	5.27858i	0.0884503	+	0.272222i
$377$	14.1527	−	24.5133i	0.728903	−	1.26250i
$378$	−0.629248	−	1.08989i	−0.0323650	−	0.0560579i
$379$	18.9300	−	21.0239i	0.972368	−	1.07992i	−0.0244085	−	0.999702i	$-0.507770\pi$
$379$	18.9300	−	21.0239i	0.972368	−	1.07992i	0.996777	−	0.0802225i	$-0.0255631\pi$
$380$	0.290549	−	0.894217i	0.0149048	−	0.0458724i
$381$	−9.37256	−	10.4093i	−0.480171	−	0.533284i
$382$	25.4980	−	11.3525i	1.30459	−	0.580842i
$383$	19.0351	+	4.04604i	0.972649	+	0.206743i	0.666718	−	0.745310i	$-0.267699\pi$
$383$	19.0351	+	4.04604i	0.972649	+	0.206743i	0.305932	+	0.952053i	$0.401032\pi$
$384$	1.29730	−	12.3430i	0.0662025	−	0.629874i
$385$	−0.141669	−	1.34789i	−0.00722013	−	0.0686949i
$386$	−35.4156	+	7.52781i	−1.80260	+	0.383155i
$387$	2.86916	−	2.08456i	0.145847	−	0.105964i
$388$	25.1283	−	18.2568i	1.27569	−	0.926846i
$389$	−24.4704	+	5.20134i	−1.24070	+	0.263718i	−0.781098	−	0.624409i	$-0.785340\pi$
$389$	−24.4704	+	5.20134i	−1.24070	+	0.263718i	−0.459599	+	0.888127i	$0.652007\pi$
$390$	−0.532946	−	5.07064i	−0.0269868	−	0.256762i
$391$	0.117494	−	1.11788i	0.00594194	−	0.0565338i
$392$	−10.9211	−	2.32134i	−0.551597	−	0.117246i
$393$	2.86883	−	1.27729i	0.144713	−	0.0644306i
$394$	4.61469	+	5.12514i	0.232485	+	0.258201i
$395$	2.24583	−	6.91195i	0.113000	−	0.347778i
$396$	8.00208	−	8.88721i	0.402120	−	0.446599i
$397$	10.8434	+	18.7813i	0.544214	+	0.942605i	0.998656	+	0.0518293i	$0.0165052\pi$
$397$	10.8434	+	18.7813i	0.544214	+	0.942605i	−0.454442	+	0.890776i	$0.650161\pi$
$398$	−9.58114	+	16.5950i	−0.480259	+	0.831833i
$399$	−0.111259	−	0.342420i	−0.00556991	−	0.0171424i
$400$	8.07010	+	3.59304i	0.403505	+	0.179652i
$401$	−15.5334	−	11.2857i	−0.775703	−	0.563581i	0.127983	−	0.991776i	$-0.459150\pi$
$401$	−15.5334	−	11.2857i	−0.775703	−	0.563581i	−0.903686	+	0.428195i	$0.859150\pi$
$402$	−8.65702			−0.431773
$403$	−16.5946	+	17.1994i	−0.826634	+	0.856761i
$404$	−3.93548			−0.195798
$405$	−0.440123	−	0.319768i	−0.0218699	−	0.0158894i
$406$	7.58124	+	3.37539i	0.376251	+	0.167518i
$407$	2.65179	+	8.16136i	0.131444	+	0.404544i
$408$	−0.100651	+	0.174332i	−0.00498295	+	0.00863072i
$409$	−2.73332	−	4.73425i	−0.135154	−	0.234094i	0.790502	−	0.612459i	$-0.209820\pi$
$409$	−2.73332	−	4.73425i	−0.135154	−	0.234094i	−0.925656	+	0.378365i	$0.876486\pi$
$410$	4.41280	−	4.90091i	0.217933	−	0.242039i
$411$	−0.707467	+	2.17736i	−0.0348968	+	0.107401i
$412$	−7.78295	−	8.64385i	−0.383439	−	0.425852i
$413$	−4.98838	+	2.22097i	−0.245462	+	0.109287i
$414$	−19.9683	−	4.24440i	−0.981389	−	0.208601i
$415$	−0.386149	+	3.67396i	−0.0189553	+	0.180348i
$416$	−3.34234	−	31.8002i	−0.163872	−	1.55913i
$417$	16.5832	−	3.52486i	0.812081	−	0.172613i
$418$	4.76859	−	3.46459i	0.233240	−	0.169458i
$419$	−20.2779	+	14.7327i	−0.990638	+	0.719741i	−0.960061	−	0.279792i	$-0.909735\pi$
$419$	−20.2779	+	14.7327i	−0.990638	+	0.719741i	−0.0305774	+	0.999532i	$0.509735\pi$
$420$	0.848697	−	0.180396i	0.0414122	−	0.00880243i
$421$	3.02758	+	28.8055i	0.147555	+	1.40389i	0.778295	+	0.627899i	$0.216085\pi$
$421$	3.02758	+	28.8055i	0.147555	+	1.40389i	−0.630740	+	0.775995i	$0.717248\pi$
$422$	2.81837	−	26.8150i	0.137196	−	1.30533i
$423$	3.24215	+	0.689141i	0.157639	+	0.0335072i
$424$	7.89919	−	3.51695i	0.383619	−	0.170798i
$425$	−0.378396	−	0.420252i	−0.0183549	−	0.0203852i
$426$	0.377861	−	1.16294i	0.0183074	−	0.0563444i
$427$	4.72528	−	5.24796i	0.228672	−	0.253966i
$428$	26.8127	+	46.4409i	1.29604	+	2.24481i
$429$	9.27629	−	16.0670i	0.447864	−	0.775723i
$430$	1.30171	+	4.00626i	0.0627741	+	0.193199i
$431$	−25.2809	−	11.2558i	−1.21774	−	0.542171i	−0.305640	−	0.952147i	$-0.598870\pi$
$431$	−25.2809	−	11.2558i	−1.21774	−	0.542171i	−0.912096	+	0.409976i	$0.865537\pi$
$432$	−1.51927	−	1.10382i	−0.0730960	−	0.0531073i
$433$	−3.15532			−0.151635			−0.0758174	−	0.997122i	$-0.524157\pi$
$433$	−3.15532			−0.151635			−0.0758174	+	0.997122i	$0.524157\pi$
$434$	−5.52351	−	4.31151i	−0.265137	−	0.206959i
$435$	3.58736			0.172001
$436$	−29.6536	−	21.5446i	−1.42015	−	1.03180i
$437$	−5.33541	−	2.37548i	−0.255227	−	0.113635i
$438$	−8.54416	−	26.2962i	−0.408256	−	1.25648i
$439$	−9.89805	+	17.1439i	−0.472408	+	0.818235i	−0.999501	−	0.0315723i	$-0.989949\pi$
$439$	−9.89805	+	17.1439i	−0.472408	+	0.818235i	0.527093	+	0.849808i	$0.323282\pi$
$440$	1.96861	+	3.40973i	0.0938498	+	0.162553i
$441$	−4.46160	+	4.95510i	−0.212457	+	0.235957i
$442$	−0.348161	+	1.07153i	−0.0165603	+	0.0509674i
$443$	10.1441	+	11.2662i	0.481963	+	0.535274i	0.934260	−	0.356593i	$-0.116062\pi$
$443$	10.1441	+	11.2662i	0.481963	+	0.535274i	−0.452297	+	0.891868i	$0.649395\pi$
$444$	−5.01873	+	2.23448i	−0.238178	+	0.106044i
$445$	8.94924	+	1.90222i	0.424235	+	0.0901739i
$446$	−5.36920	+	51.0845i	−0.254239	+	2.41892i
$447$	1.04638	+	9.95568i	0.0494923	+	0.470888i
$448$	7.05220	−	1.49899i	0.333185	−	0.0708207i
$449$	11.3978	−	8.28096i	0.537894	−	0.390803i	−0.285408	−	0.958406i	$-0.592129\pi$
$449$	11.3978	−	8.28096i	0.537894	−	0.390803i	0.823302	+	0.567603i	$0.192129\pi$
$450$	−8.30900	+	6.03684i	−0.391690	+	0.284579i
$451$	23.4727	−	4.98929i	1.10529	−	0.234936i
$452$	1.24417	+	11.8375i	0.0585208	+	0.556788i
$453$	−0.652902	+	6.21195i	−0.0306760	+	0.291863i
$454$	−7.93714	−	1.68709i	−0.372508	−	0.0791791i
$455$	1.22968	−	0.547487i	0.0576481	−	0.0256666i
$456$	0.699863	+	0.777276i	0.0327741	+	0.0363993i
$457$	−3.14352	+	9.67475i	−0.147048	+	0.452566i	−0.997269	−	0.0738600i	$-0.976468\pi$
$457$	−3.14352	+	9.67475i	−0.147048	+	0.452566i	0.850221	+	0.526426i	$0.176468\pi$
$458$	7.55121	−	8.38647i	0.352845	−	0.391874i
$459$	0.0601084	+	0.104111i	0.00280562	+	0.00485948i
$460$	7.03725	−	12.1889i	0.328114	−	0.568309i
$461$	0.585718	+	1.80266i	0.0272796	+	0.0839580i	0.963769	−	0.266737i	$-0.0859454\pi$
$461$	0.585718	+	1.80266i	0.0272796	+	0.0839580i	−0.936490	+	0.350695i	$0.885945\pi$
$462$	4.96906	+	2.21237i	0.231182	+	0.102929i
$463$	19.5576	+	14.2094i	0.908917	+	0.660367i	0.940741	−	0.339126i	$-0.110131\pi$
$463$	19.5576	+	14.2094i	0.908917	+	0.660367i	−0.0318234	+	0.999494i	$0.510131\pi$
$464$	12.3833			0.574880
$465$	−2.93933	−	0.731479i	−0.136308	−	0.0339215i
$466$	36.0843			1.67157
$467$	17.6888	+	12.8517i	0.818541	+	0.594705i	0.916294	−	0.400506i	$-0.131166\pi$
$467$	17.6888	+	12.8517i	0.818541	+	0.594705i	−0.0977533	+	0.995211i	$0.531166\pi$
$468$	10.8503	+	4.83087i	0.501556	+	0.223307i
$469$	−0.706257	−	2.17364i	−0.0326119	−	0.100369i
$470$	−1.96850	+	3.40954i	−0.0908002	+	0.157270i
$471$	−3.86476	−	6.69396i	−0.178079	−	0.308441i
$472$	10.6143	−	11.7883i	0.488561	−	0.542602i
$473$	−4.73665	+	14.5779i	−0.217791	+	0.670292i
$474$	19.5168	+	21.6756i	0.896436	+	0.995593i
$475$	−2.68424	+	1.19510i	−0.123161	+	0.0548350i
$476$	−0.187543	−	0.0398635i	−0.00859603	−	0.00182714i
$477$	0.539766	−	5.13553i	0.0247142	−	0.235140i
$478$	3.10343	+	29.5272i	0.141948	+	1.35054i
$479$	−13.2053	+	2.80686i	−0.603363	+	0.128249i	−0.499458	−	0.866338i	$-0.666467\pi$
$479$	−13.2053	+	2.80686i	−0.603363	+	0.128249i	−0.103906	+	0.994587i	$0.533134\pi$
$480$	3.27852	−	2.38198i	0.149643	−	0.108722i
$481$	−6.89499	+	5.00951i	−0.314385	+	0.228414i
$482$	15.0282	−	3.19435i	0.684517	−	0.145499i
$483$	−0.563357	−	5.35998i	−0.0256336	−	0.243888i
$484$	−2.22133	+	21.1346i	−0.100970	+	0.960663i
$485$	5.97346	+	1.26970i	0.271241	+	0.0576540i
$486$	1.99457	−	0.888041i	0.0904757	−	0.0402824i
$487$	−20.5554	−	22.8291i	−0.931455	−	1.03449i	−0.999323	−	0.0367910i	$-0.988286\pi$
$487$	−20.5554	−	22.8291i	−0.931455	−	1.03449i	0.0678683	−	0.997694i	$-0.478380\pi$
$488$	−6.33940	+	19.5107i	−0.286971	+	0.883207i
$489$	−7.12649	+	7.91477i	−0.322271	+	0.357918i
$490$	−3.95991	−	6.85877i	−0.178891	−	0.309848i
$491$	−2.07639	+	3.59641i	−0.0937060	+	0.162304i	−0.909068	−	0.416648i	$-0.863205\pi$
$491$	−2.07639	+	3.59641i	−0.0937060	+	0.162304i	0.815362	+	0.578952i	$0.196538\pi$
$492$	4.74733	+	14.6108i	0.214026	+	0.658705i
$493$	−0.724192	−	0.322431i	−0.0326160	−	0.0145216i
$494$	4.73598	+	3.44089i	0.213082	+	0.154813i
$495$	2.35130			0.105683
$496$	−10.1464	−	2.52501i	−0.455585	−	0.113376i
$497$	0.322821			0.0144805
$498$	−11.9945	−	8.71450i	−0.537485	−	0.390506i
$499$	18.3950	+	8.19000i	0.823475	+	0.366635i	0.774821	−	0.632181i	$-0.217840\pi$
$499$	18.3950	+	8.19000i	0.823475	+	0.366635i	0.0486540	+	0.998816i	$0.484507\pi$
$500$	−4.51389	−	13.8923i	−0.201867	−	0.621284i
$501$	6.49338	−	11.2469i	0.290103	−	0.502473i
$502$	0.924023	+	1.60045i	0.0412412	+	0.0714318i
$503$	5.21162	−	5.78810i	0.232375	−	0.258078i	−0.615669	−	0.788005i	$-0.711114\pi$
$503$	5.21162	−	5.78810i	0.232375	−	0.258078i	0.848043	+	0.529927i	$0.177781\pi$
$504$	−0.298260	+	0.917951i	−0.0132856	+	0.0408888i
$505$	−0.517756	−	0.575027i	−0.0230399	−	0.0255884i
$506$	80.6045	−	35.8874i	3.58331	−	1.59539i
$507$	5.30716	+	1.12807i	0.235699	+	0.0500994i
$508$	−4.05118	+	38.5444i	−0.179742	+	1.71013i
$509$	2.03541	+	19.3656i	0.0902180	+	0.858367i	0.942258	+	0.334889i	$0.108699\pi$
$509$	2.03541	+	19.3656i	0.0902180	+	0.858367i	−0.852040	+	0.523477i	$0.824634\pi$
$510$	−0.139671	+	0.0296879i	−0.00618473	+	0.00131460i
$511$	5.90550	−	4.29060i	0.261244	−	0.189805i
$512$	16.4052	−	11.9191i	0.725014	−	0.526754i
$513$	0.610977	−	0.129867i	0.0269753	−	0.00573378i
$514$	−5.60255	−	53.3047i	−0.247118	−	2.35117i
$515$	0.239048	−	2.27439i	0.0105337	−	0.100221i
$516$	−9.59844	−	2.04021i	−0.422548	−	0.0898153i
$517$	−13.0874	+	5.82686i	−0.575581	+	0.256265i
$518$	−1.67196	−	1.85690i	−0.0734618	−	0.0815876i
$519$	−0.839609	+	2.58405i	−0.0368548	+	0.113427i
$520$	−2.61650	+	2.90592i	−0.114741	+	0.127433i
$521$	−9.25284	−	16.0264i	−0.405374	−	0.702129i	0.588991	−	0.808140i	$-0.299525\pi$
$521$	−9.25284	−	16.0264i	−0.405374	−	0.702129i	−0.994365	+	0.106011i	$0.966192\pi$
$522$	−7.19860	+	12.4683i	−0.315074	+	0.545725i
$523$	2.27973	+	7.01630i	0.0996858	+	0.306801i	0.988447	−	0.151570i	$-0.0484329\pi$
$523$	2.27973	+	7.01630i	0.0996858	+	0.306801i	−0.888761	+	0.458371i	$0.848433\pi$
$524$	−7.93789	−	3.53418i	−0.346768	−	0.154391i
$525$	−2.19362	−	1.59376i	−0.0957373	−	0.0695572i
$526$	14.0959			0.614611
$527$	0.527628	+	0.411853i	0.0229838	+	0.0179406i
$528$	8.11652			0.353226
$529$	−52.1207	−	37.8679i	−2.26612	−	1.64643i
$530$	5.60322	+	2.49471i	0.243388	+	0.108363i
$531$	−2.92738	−	9.00956i	−0.127038	−	0.390982i
$532$	−0.498107	+	0.862746i	−0.0215957	+	0.0374048i
$533$	11.9165	+	20.6400i	0.516162	+	0.894019i
$534$	−24.5695	+	27.2872i	−1.06323	+	1.18083i
$535$	−3.25814	+	10.0275i	−0.140862	+	0.433527i
$536$	4.44263	+	4.93405i	0.191893	+	0.213118i
$537$	6.58305	−	2.93096i	0.284080	−	0.126480i
$538$	−35.8916	−	7.62899i	−1.54740	−	0.328909i
$539$	3.01235	−	28.6606i	0.129751	−	1.23450i
$540$	0.157344	+	1.49703i	0.00677101	+	0.0644219i
$541$	18.1177	−	3.85103i	0.778940	−	0.165569i	0.198750	−	0.980050i	$-0.436312\pi$
$541$	18.1177	−	3.85103i	0.778940	−	0.165569i	0.580190	+	0.814481i	$0.302978\pi$
$542$	−32.5243	+	23.6303i	−1.39704	+	1.01501i
$543$	16.4591	−	11.9583i	0.706330	−	0.513179i
$544$	−0.875938	+	0.186186i	−0.0375555	+	0.00798267i
$545$	−0.753305	−	7.16722i	−0.0322680	−	0.307010i
$546$	−0.564675	+	5.37253i	−0.0241659	+	0.229923i
$547$	−32.8012	−	6.97211i	−1.40248	−	0.298106i	−0.556290	−	0.830989i	$-0.687775\pi$
$547$	−32.8012	−	6.97211i	−1.40248	−	0.298106i	−0.846189	+	0.532882i	$0.821109\pi$
$548$	5.78700	−	2.57654i	0.247209	−	0.110064i
$549$	8.19777	+	9.10454i	0.349872	+	0.388572i
$550$	13.7172	−	42.2172i	0.584903	−	1.80015i
$551$	−2.75607	+	3.06092i	−0.117412	+	0.130400i
$552$	7.82832	+	13.5590i	0.333195	+	0.577111i
$553$	−3.85017	+	6.66869i	−0.163726	+	0.283582i
$554$	−8.46042	−	26.0385i	−0.359449	−	1.10627i
$555$	−0.986757	−	0.439333i	−0.0418855	−	0.0186486i
$556$	−37.9507	−	27.5728i	−1.60947	−	1.16935i
$557$	3.07109			0.130126			0.0650631	−	0.997881i	$-0.479275\pi$
$557$	3.07109			0.130126			0.0650631	+	0.997881i	$0.479275\pi$
$558$	8.44060	−	8.74823i	0.357319	−	0.370342i
$559$	−15.2233			−0.643877
$560$	0.476413	+	0.346134i	0.0201321	+	0.0146268i
$561$	−0.474665	−	0.211335i	−0.0200404	−	0.00892256i
$562$	0.950818	+	2.92632i	0.0401078	+	0.123439i
$563$	−7.64253	+	13.2372i	−0.322094	+	0.557884i	−0.980920	−	0.194412i	$-0.937720\pi$
$563$	−7.64253	+	13.2372i	−0.322094	+	0.557884i	0.658826	+	0.752296i	$0.271053\pi$
$564$	−4.58563	−	7.94255i	−0.193090	−	0.334442i
$565$	−1.56593	+	1.73914i	−0.0658791	+	0.0731662i
$566$	21.5681	−	66.3798i	0.906575	−	2.79015i
$567$	0.385694	+	0.428357i	0.0161976	+	0.0179893i
$568$	−0.856725	+	0.381438i	−0.0359474	+	0.0160048i
$569$	−19.1548	−	4.07148i	−0.803010	−	0.170685i	−0.211916	−	0.977288i	$-0.567970\pi$
$569$	−19.1548	−	4.07148i	−0.803010	−	0.170685i	−0.591094	+	0.806603i	$0.701304\pi$
$570$	−0.0775517	+	0.737855i	−0.00324828	+	0.0309053i
$571$	−1.74331	−	16.5865i	−0.0729553	−	0.694123i	−0.968477	−	0.249104i	$-0.919864\pi$
$571$	−1.74331	−	16.5865i	−0.0729553	−	0.694123i	0.895521	−	0.445018i	$-0.146803\pi$
$572$	−50.2121	+	10.6729i	−2.09947	+	0.446257i
$573$	−10.3422	+	7.51407i	−0.432053	+	0.313905i
$574$	−5.65297	+	4.10713i	−0.235951	+	0.171428i
$575$	−43.0222	+	9.14465i	−1.79415	+	0.381358i
$576$	1.30744	+	12.4395i	0.0544768	+	0.518312i
$577$	−2.28265	+	21.7180i	−0.0950282	+	0.904133i	0.838324	+	0.545172i	$0.183536\pi$
$577$	−2.28265	+	21.7180i	−0.0950282	+	0.904133i	−0.933353	+	0.358961i	$0.883131\pi$
$578$	−36.2747	−	7.71043i	−1.50883	−	0.320711i
$579$	15.1496	−	6.74502i	0.629594	−	0.280313i
$580$	−6.64179	−	7.37646i	−0.275785	−	0.306291i
$581$	1.20953	−	3.72256i	0.0501799	−	0.154438i
$582$	−16.3997	+	18.2137i	−0.679789	+	0.754983i
$583$	11.1592	+	19.3283i	0.462167	+	0.800497i
$584$	−10.6027	+	18.3645i	−0.438745	+	0.759928i
$585$	0.721624	+	2.22093i	0.0298355	+	0.0918242i
$586$	−56.3110	−	25.0713i	−2.32619	−	1.03569i
$587$	−19.3085	−	14.0284i	−0.796946	−	0.579015i	0.113071	−	0.993587i	$-0.463931\pi$
$587$	−19.3085	−	14.0284i	−0.796946	−	0.579015i	−0.910017	+	0.414572i	$0.863931\pi$
$588$	18.4493			0.760835
$589$	2.88235	−	1.94602i	0.118765	−	0.0801844i
$590$	11.2521			0.463242
$591$	−2.55546	−	1.85665i	−0.105118	−	0.0763725i
$592$	−3.40621	−	1.51654i	−0.139994	−	0.0623296i
$593$	−2.46180	−	7.57665i	−0.101094	−	0.311136i	0.887700	−	0.460423i	$-0.152302\pi$
$593$	−2.46180	−	7.57665i	−0.101094	−	0.311136i	−0.988794	+	0.149287i	$0.952302\pi$
$594$	−4.71826	+	8.17227i	−0.193593	+	0.335312i
$595$	−0.0188488	−	0.0326471i	−0.000772725	−	0.00133840i
$596$	18.5339	−	20.5840i	0.759179	−	0.843154i
$597$	2.71212	−	8.34706i	0.111000	−	0.341622i
$598$	58.6354	+	65.1212i	2.39778	+	2.66301i
$599$	24.0844	−	10.7230i	0.984060	−	0.438132i	0.149328	−	0.988788i	$-0.452289\pi$
$599$	24.0844	−	10.7230i	0.984060	−	0.438132i	0.834732	+	0.550656i	$0.185622\pi$
$600$	7.70472	+	1.63769i	0.314544	+	0.0668583i
$601$	3.73546	−	35.5405i	0.152372	−	1.44973i	−0.604730	−	0.796431i	$-0.706719\pi$
$601$	3.73546	−	35.5405i	0.152372	−	1.44973i	0.757102	−	0.653296i	$-0.226614\pi$
$602$	−0.466534	−	4.43877i	−0.0190145	−	0.180911i
$603$	3.87840	−	0.824380i	0.157941	−	0.0335713i
$604$	13.9821	−	10.1586i	0.568922	−	0.413346i
$605$	−3.38029	+	2.45592i	−0.137428	+	0.0998474i
$606$	3.03754	−	0.645650i	0.123392	−	0.0262277i
$607$	−1.22455	−	11.6508i	−0.0497029	−	0.472892i	−0.990857	−	0.134915i	$-0.956924\pi$
$607$	−1.22455	−	11.6508i	−0.0497029	−	0.472892i	0.941154	−	0.337977i	$-0.109743\pi$
$608$	−0.486361	+	4.62742i	−0.0197245	+	0.187667i
$609$	−3.71788	−	0.790259i	−0.150656	−	0.0320229i
$610$	−13.2939	+	5.91881i	−0.538253	+	0.239645i
$611$	−9.52034	−	10.5734i	−0.385152	−	0.427754i
$612$	0.102789	−	0.316352i	0.00415501	−	0.0127878i
$613$	5.32853	−	5.91793i	0.215217	−	0.239023i	−0.625863	−	0.779933i	$-0.715253\pi$
$613$	5.32853	−	5.91793i	0.215217	−	0.239023i	0.841081	+	0.540910i	$0.181920\pi$
$614$	9.51083	+	16.4732i	0.383826	+	0.664806i
$615$	−1.51027	+	2.61586i	−0.0608998	+	0.105482i
$616$	−1.28910	−	3.96745i	−0.0519395	−	0.159853i
$617$	11.6393	+	5.18214i	0.468579	+	0.208625i	0.627423	−	0.778679i	$-0.284110\pi$
$617$	11.6393	+	5.18214i	0.468579	+	0.208625i	−0.158843	+	0.987304i	$0.550777\pi$
$618$	7.42525	+	5.39476i	0.298687	+	0.217009i
$619$	20.9025			0.840142			0.420071	−	0.907491i	$-0.362005\pi$
$619$	20.9025			0.840142			0.420071	+	0.907491i	$0.362005\pi$
$620$	3.93792	+	7.39826i	0.158151	+	0.297121i
$621$	9.35012			0.375207
$622$	46.9365	+	34.1014i	1.88198	+	1.36734i
$623$	−8.85580	−	3.94286i	−0.354800	−	0.157967i
$624$	2.49099	+	7.66648i	0.0997195	+	0.306905i
$625$	−10.3241	+	17.8819i	−0.412964	+	0.715275i
$626$	0.687466	+	1.19073i	0.0274767	+	0.0475910i
$627$	−1.80644	+	2.00626i	−0.0721423	+	0.0801221i
$628$	−6.60898	+	20.3404i	−0.263727	+	0.811669i
$629$	0.159713	+	0.177379i	0.00636817	+	0.00707257i
$630$	−0.625458	+	0.278472i	−0.0249189	+	0.0110946i
$631$	33.5699	+	7.13550i	1.33640	+	0.284060i	0.820036	−	0.572312i	$-0.193953\pi$
$631$	33.5699	+	7.13550i	1.33640	+	0.284060i	0.516360	+	0.856372i	$0.327287\pi$
$632$	2.33827	−	22.2471i	0.0930112	−	0.884942i
$633$	1.29086	+	12.2817i	0.0513070	+	0.488153i
$634$	37.4945	−	7.96970i	1.48910	−	0.316517i
$635$	−6.16483	+	4.47901i	−0.244644	+	0.177744i
$636$	−11.5592	+	8.39827i	−0.458353	+	0.333013i
$637$	27.9960	−	5.95073i	1.10924	−	0.235777i
$638$	−6.50437	−	61.8849i	−0.257510	−	2.45005i
$639$	−0.0585416	+	0.556986i	−0.00231587	+	0.0220340i
$640$	−6.60429	−	1.40378i	−0.261057	−	0.0554894i
$641$	28.2447	−	12.5754i	1.11560	−	0.496697i	0.235685	−	0.971830i	$-0.424267\pi$
$641$	28.2447	−	12.5754i	1.11560	−	0.496697i	0.879914	+	0.475133i	$0.157600\pi$
$642$	−28.3140	−	31.4459i	−1.11746	−	1.24107i
$643$	−8.87980	+	27.3292i	−0.350185	+	1.07776i	0.608564	+	0.793505i	$0.291746\pi$
$643$	−8.87980	+	27.3292i	−0.350185	+	1.07776i	−0.958749	+	0.284254i	$0.908254\pi$
$644$	−9.97837	+	11.0821i	−0.393203	+	0.436696i
$645$	−0.964679	−	1.67087i	−0.0379842	−	0.0657905i
$646$	0.0819739	−	0.141983i	0.00322522	−	0.00558624i
$647$	−8.68013	−	26.7147i	−0.341251	−	1.05026i	−0.963560	−	0.267492i	$-0.913805\pi$
$647$	−8.68013	−	26.7147i	−0.341251	−	1.05026i	0.622309	−	0.782772i	$-0.286195\pi$
$648$	−1.52972	−	0.681074i	−0.0600930	−	0.0267551i
$649$	33.1243	+	24.0662i	1.30024	+	0.944683i
$650$	44.0862			1.72920
$651$	2.88514	+	1.40560i	0.113077	+	0.0550897i
$652$	29.4690			1.15409
$653$	32.1184	+	23.3354i	1.25689	+	0.913185i	0.998601	−	0.0528825i	$-0.0168409\pi$
$653$	32.1184	+	23.3354i	1.25689	+	0.913185i	0.258290	+	0.966067i	$0.416841\pi$
$654$	26.4223	+	11.7640i	1.03319	+	0.460007i
$655$	−0.527927	−	1.62479i	−0.0206278	−	0.0634859i
$656$	−5.21333	+	9.02975i	−0.203546	+	0.352552i
$657$	6.33194	+	10.9672i	0.247033	+	0.427873i
$658$	2.79121	−	3.09995i	0.108813	−	0.120849i
$659$	−4.13934	+	12.7396i	−0.161246	+	0.496264i	−0.998740	−	0.0501825i	$-0.984020\pi$
$659$	−4.13934	+	12.7396i	−0.161246	+	0.496264i	0.837494	+	0.546446i	$0.184020\pi$
$660$	−4.35331	−	4.83484i	−0.169452	−	0.188196i
$661$	−4.52054	+	2.01267i	−0.175829	+	0.0782840i	−0.492763	−	0.870163i	$-0.664013\pi$
$661$	−4.52054	+	2.01267i	−0.175829	+	0.0782840i	0.316935	+	0.948447i	$0.397346\pi$
$662$	55.9689	+	11.8966i	2.17529	+	0.462373i
$663$	0.0539401	−	0.513206i	0.00209486	−	0.0199313i
$664$	1.18856	+	11.3084i	0.0461249	+	0.438849i
$665$	−0.191590	+	0.0407238i	−0.00742955	+	0.00157920i
$666$	3.50705	−	2.54802i	0.135895	−	0.0987337i
$667$	−49.8808	+	36.2405i	−1.93139	+	1.40324i
$668$	−35.1484	+	7.47101i	−1.35993	+	0.289062i
$669$	−2.45917	−	23.3975i	−0.0950772	−	0.904599i
$670$	−0.492288	+	4.68381i	−0.0190187	+	0.180951i
$671$	−51.7942	−	11.0092i	−1.99949	−	0.425006i
$672$	−3.92253	+	1.74642i	−0.151315	+	0.0673697i
$673$	26.3913	+	29.3105i	1.01731	+	1.12984i	0.991492	+	0.130171i	$0.0415525\pi$
$673$	26.3913	+	29.3105i	1.01731	+	1.12984i	0.0258183	+	0.999667i	$0.491781\pi$
$674$	−1.22785	+	3.77894i	−0.0472951	+	0.145559i
$675$	3.14762	−	3.49578i	0.121152	−	0.134553i
$676$	−7.50632	−	13.0013i	−0.288705	−	0.500051i
$677$	−15.2746	+	26.4563i	−0.587050	+	1.01680i	0.407567	+	0.913175i	$0.366377\pi$
$677$	−15.2746	+	26.4563i	−0.587050	+	1.01680i	−0.994617	+	0.103624i	$0.966956\pi$
$678$	−2.90233	−	8.93246i	−0.111463	−	0.343049i
$679$	−5.91109	−	2.63179i	−0.226847	−	0.100999i
$680$	0.0885973	+	0.0643697i	0.00339755	+	0.00246846i
$681$	3.71655			0.142418
$682$	−7.28921	+	52.0323i	−0.279118	+	1.99242i
$683$	4.13533			0.158234			0.0791170	−	0.996865i	$-0.474790\pi$
$683$	4.13533			0.158234			0.0791170	+	0.996865i	$0.474790\pi$
$684$	−1.39823	−	1.01587i	−0.0534626	−	0.0388428i
$685$	1.13781	+	0.506586i	0.0434735	+	0.0193557i
$686$	5.31534	+	16.3589i	0.202941	+	0.624587i
$687$	−2.58438	+	4.47627i	−0.0986001	+	0.170780i
$688$	−3.33000	−	5.76773i	−0.126955	−	0.219893i
$689$	−14.8318	+	16.4724i	−0.565047	+	0.627549i
$690$	−3.43191	+	10.5623i	−0.130650	+	0.402101i
$691$	−1.85230	−	2.05719i	−0.0704649	−	0.0782592i	0.706881	−	0.707332i	$-0.250101\pi$
$691$	−1.85230	−	2.05719i	−0.0704649	−	0.0782592i	−0.777346	+	0.629073i	$0.783435\pi$
$692$	6.86791	−	3.05779i	0.261079	−	0.116240i
$693$	−2.43685	−	0.517968i	−0.0925683	−	0.0196760i
$694$	4.90416	−	46.6600i	0.186159	−	1.77119i
$695$	−0.964081	−	9.17262i	−0.0365697	−	0.347937i
$696$	10.8005	−	2.29572i	0.409392	−	0.0870190i
$697$	0.539995	−	0.392330i	0.0204538	−	0.0148605i
$698$	8.32179	−	6.04613i	0.314984	−	0.228850i
$699$	−16.1660	+	3.43619i	−0.611455	+	0.129969i
$700$	0.784219	+	7.46135i	0.0296407	+	0.282012i
$701$	−2.10163	+	19.9957i	−0.0793776	+	0.755228i	0.880356	+	0.474314i	$0.157304\pi$
$701$	−2.10163	+	19.9957i	−0.0793776	+	0.755228i	−0.959733	+	0.280913i	$0.909363\pi$
$702$	−9.16720	−	1.94855i	−0.345993	−	0.0735432i
$703$	1.13296	−	0.504426i	0.0427304	−	0.0190248i
$704$	−36.1736	−	40.1748i	−1.36334	−	1.51415i
$705$	0.557222	−	1.71495i	0.0209862	−	0.0645888i
$706$	14.5452	−	16.1541i	0.547416	−	0.607967i
$707$	0.409921	+	0.710004i	0.0154167	+	0.0267025i
$708$	−13.1059	+	22.7001i	−0.492550	+	0.853122i
$709$	−15.0966	−	46.4626i	−0.566965	−	1.74494i	−0.662040	−	0.749469i	$-0.730309\pi$
$709$	−15.0966	−	46.4626i	−0.566965	−	1.74494i	0.0950750	−	0.995470i	$-0.469691\pi$
$710$	−0.607710	−	0.270570i	−0.0228069	−	0.0101543i
$711$	−10.8078	−	7.85229i	−0.405323	−	0.294484i
$712$	28.1609			1.05538
$713$	48.2599	−	19.5231i	1.80735	−	0.731145i
$714$	0.151292			0.00566198
$715$	−8.16542	−	5.93252i	−0.305369	−	0.221864i
$716$	−18.2149	−	8.10980i	−0.680723	−	0.303077i
$717$	−4.20214	−	12.9328i	−0.156932	−	0.482986i
$718$	−26.1856	+	45.3547i	−0.977236	+	1.69262i
$719$	4.66448	+	8.07911i	0.173956	+	0.301300i	0.939799	−	0.341727i	$-0.111012\pi$
$719$	4.66448	+	8.07911i	0.173956	+	0.301300i	−0.765844	+	0.643027i	$0.777678\pi$
$720$	−0.683604	+	0.759220i	−0.0254764	+	0.0282944i
$721$	−0.748770	+	2.30448i	−0.0278856	+	0.0858232i
$722$	27.1878	+	30.1951i	1.01182	+	1.12374i
$723$	−6.42856	+	2.86218i	−0.239081	+	0.106446i
$724$	−55.0622	−	11.7038i	−2.04637	−	0.434970i
$725$	−3.24238	+	30.8492i	−0.120419	+	1.14571i
$726$	−1.75281	−	16.6768i	−0.0650528	−	0.618936i
$727$	6.67182	−	1.41814i	0.247444	−	0.0525959i	−0.0825197	−	0.996589i	$-0.526297\pi$
$727$	6.67182	−	1.41814i	0.247444	−	0.0525959i	0.329964	+	0.943994i	$0.392963\pi$
$728$	3.35184	−	2.43525i	0.124227	−	0.0902565i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−14.7132	+	3.12739i	−0.544560	+	0.115750i
$731$	0.0445652	+	0.424010i	0.00164830	+	0.0156826i
$732$	3.54339	−	33.7131i	0.130967	−	1.24607i
$733$	7.46354	+	1.58642i	0.275672	+	0.0585959i	0.343673	−	0.939089i	$-0.388329\pi$
$733$	7.46354	+	1.58642i	0.275672	+	0.0585959i	−0.0680011	+	0.997685i	$0.521662\pi$
$734$	−32.9259	+	14.6596i	−1.21532	+	0.541095i
$735$	2.42721	+	2.69568i	0.0895288	+	0.0994318i
$736$	−21.5230	+	66.2410i	−0.793349	+	2.44168i
$737$	−11.4670	+	12.7354i	−0.422394	+	0.469116i
$738$	−6.06118	−	10.4983i	−0.223115	−	0.386447i
$739$	0.537519	−	0.931010i	0.0197730	−	0.0342478i	−0.855970	−	0.517026i	$-0.827039\pi$
$739$	0.537519	−	0.931010i	0.0197730	−	0.0342478i	0.875743	+	0.482778i	$0.160372\pi$
$740$	0.923554	+	2.84241i	0.0339505	+	0.104489i
$741$	−2.44942	−	1.09055i	−0.0899816	−	0.0400624i
$742$	−5.25752	−	3.81981i	−0.193010	−	0.140230i
$743$	1.15865			0.0425069			0.0212535	−	0.999774i	$-0.493234\pi$
$743$	1.15865			0.0425069			0.0212535	+	0.999774i	$0.493234\pi$
$744$	−9.31760	−	0.321256i	−0.341600	−	0.0117778i
$745$	5.44594			0.199524
$746$	−59.0255	−	42.8845i	−2.16108	−	1.57011i
$747$	6.20346	+	2.76196i	0.226973	+	0.101055i
$748$	0.444262	+	1.36730i	0.0162438	+	0.0499934i
$749$	5.58564	−	9.67461i	0.204095	−	0.353502i
$750$	5.76313	+	9.98204i	0.210440	+	0.364493i
$751$	34.3279	−	38.1250i	1.25264	−	1.39120i	0.364778	−	0.931095i	$-0.381145\pi$
$751$	34.3279	−	38.1250i	1.25264	−	1.39120i	0.887864	−	0.460105i	$-0.152188\pi$
$752$	1.92349	−	5.91989i	0.0701424	−	0.215876i
$753$	−0.566375	−	0.629023i	−0.0206398	−	0.0229229i
$754$	56.4574	−	25.1364i	2.05606	−	0.915415i
$755$	3.32380	+	0.706495i	0.120965	+	0.0257120i
$756$	0.166712	−	1.58616i	0.00606325	−	0.0576880i
$757$	−0.168110	−	1.59946i	−0.00611005	−	0.0581332i	0.991042	−	0.133550i	$-0.0426378\pi$
$757$	−0.168110	−	1.59946i	−0.00611005	−	0.0581332i	−0.997152	+	0.0754172i	$0.975971\pi$
$758$	60.4176	−	12.8422i	2.19447	−	0.466449i
$759$	−32.6939	+	23.7535i	−1.18671	+	0.862198i
$760$	0.460337	−	0.334454i	0.0166982	−	0.0121319i
$761$	52.8433	−	11.2322i	1.91557	−	0.407167i	0.915581	−	0.402134i	$-0.131731\pi$
$761$	52.8433	−	11.2322i	1.91557	−	0.407167i	0.999987	−	0.00503275i	$-0.00160198\pi$
$762$	−3.19670	−	30.4146i	−0.115804	−	1.10180i
$763$	−0.798154	+	7.59393i	−0.0288951	+	0.274919i
$764$	34.5988	+	7.35420i	1.25174	+	0.266066i
$765$	0.0597464	−	0.0266008i	0.00216013	−	0.000961754i
$766$	28.4303	+	31.5751i	1.02723	+	1.14085i
$767$	−12.5659	+	38.6737i	−0.453727	+	1.39643i
$768$	1.39260	−	1.54664i	0.0502511	−	0.0558095i
$769$	16.6782	+	28.8875i	0.601431	+	1.04171i	0.992605	+	0.121393i	$0.0387360\pi$
$769$	16.6782	+	28.8875i	0.601431	+	1.04171i	−0.391173	+	0.920317i	$0.627931\pi$
$770$	1.47955	−	2.56266i	0.0533194	−	0.0923519i
$771$	7.58602	+	23.3474i	0.273204	+	0.840835i
$772$	−41.9179	−	18.6631i	−1.50866	−	0.671698i
$773$	−20.0294	−	14.5522i	−0.720406	−	0.523406i	0.166108	−	0.986108i	$-0.446880\pi$
$773$	−20.0294	−	14.5522i	−0.720406	−	0.523406i	−0.886514	+	0.462702i	$0.846880\pi$
$774$	7.74312			0.278321
$775$	8.94697	−	24.6154i	0.321385	−	0.884212i
$776$	18.7969			0.674770
$777$	0.925878	+	0.672689i	0.0332157	+	0.0241326i
$778$	−49.8983	−	22.2162i	−1.78894	−	0.796488i
$779$	−1.07169	−	3.29833i	−0.0383974	−	0.118175i
$780$	3.23071	−	5.59576i	0.115678	−	0.200360i
$781$	−1.21030	−	2.09630i	−0.0433078	−	0.0750114i
$782$	1.64215	−	1.82379i	0.0587232	−	0.0652187i
$783$	2.03770	−	6.27140i	0.0728215	−	0.224122i
$784$	8.37853	+	9.30530i	0.299233	+	0.332332i
$785$	−3.84148	+	1.71034i	−0.137108	+	0.0610446i
$786$	6.70655	+	1.42552i	0.239215	+	0.0508467i
$787$	3.35812	−	31.9504i	0.119704	−	1.13891i	−0.755498	−	0.655151i	$-0.772605\pi$
$787$	3.35812	−	31.9504i	0.119704	−	1.13891i	0.875202	−	0.483757i	$-0.160728\pi$
$788$	0.913580	+	8.69213i	0.0325449	+	0.309644i
$789$	−6.31506	+	1.34231i	−0.224822	+	0.0477874i
$790$	12.8372	−	9.32680i	0.456729	−	0.331833i
$791$	2.00602	−	1.45746i	0.0713257	−	0.0518212i
$792$	7.07910	−	1.50471i	0.251545	−	0.0534675i
$793$	−5.49707	−	52.3012i	−0.195207	−	1.85727i
$794$	−4.94936	+	47.0900i	−0.175646	+	1.67116i
$795$	−2.74784	−	0.584072i	−0.0974559	−	0.0207149i
$796$	−22.1849	+	9.87735i	−0.786322	+	0.350093i
$797$	−4.17297	−	4.63455i	−0.147814	−	0.164164i	0.664691	−	0.747119i	$-0.268563\pi$
$797$	−4.17297	−	4.63455i	−0.147814	−	0.164164i	−0.812505	+	0.582954i	$0.801897\pi$
$798$	0.242915	−	0.747616i	0.00859911	−	0.0264653i
$799$	−0.266628	+	0.296120i	−0.00943261	+	0.0104760i
$800$	17.5204	+	30.3463i	0.619441	+	1.07290i
$801$	8.40883	−	14.5645i	0.297111	−	0.514612i
$802$	−12.9542	−	39.8691i	−0.457430	−	1.40783i
$803$	−50.0022	−	22.2624i	−1.76454	−	0.785624i
$804$	−8.87576	−	6.44862i	−0.313024	−	0.227425i
$805$	−2.93201			−0.103340
$806$	−51.3843	+	9.08385i	−1.80994	+	0.319965i
$807$	16.8062			0.591605
$808$	−1.92680	−	1.39990i	−0.0677847	−	0.0492485i
$809$	27.5543	+	12.2680i	0.968758	+	0.431319i	0.829235	−	0.558900i	$-0.188776\pi$
$809$	27.5543	+	12.2680i	0.968758	+	0.431319i	0.139523	+	0.990219i	$0.455443\pi$
$810$	−0.367044	−	1.12965i	−0.0128966	−	0.0396917i
$811$	−10.3277	+	17.8880i	−0.362653	+	0.628134i	−0.988397	−	0.151895i	$-0.951462\pi$
$811$	−10.3277	+	17.8880i	−0.362653	+	0.628134i	0.625744	+	0.780029i	$0.284796\pi$
$812$	5.25848	+	9.10795i	0.184536	+	0.319627i
$813$	12.3209	−	13.6837i	0.432112	−	0.479909i
$814$	−5.78973	+	17.8190i	−0.202930	+	0.624554i
$815$	3.87697	+	4.30581i	0.135804	+	0.150826i
$816$	0.206240	−	0.0918240i	0.00721985	−	0.00321448i
$817$	2.16681	+	0.460570i	0.0758072	+	0.0161133i
$818$	1.24760	−	11.8701i	0.0436213	−	0.415029i
$819$	−0.258630	−	2.46070i	−0.00903726	−	0.0859838i
$820$	8.17500	−	1.73765i	0.285483	−	0.0606814i
$821$	−26.1754	+	19.0175i	−0.913527	+	0.663716i	−0.941904	−	0.335881i	$-0.890966\pi$
$821$	−26.1754	+	19.0175i	−0.913527	+	0.663716i	0.0283775	+	0.999597i	$0.490966\pi$
$822$	−4.04391	+	2.93807i	−0.141048	+	0.102477i
$823$	−15.7061	+	3.33844i	−0.547481	+	0.116371i	−0.473344	−	0.880878i	$-0.656953\pi$
$823$	−15.7061	+	3.33844i	−0.547481	+	0.116371i	−0.0741363	+	0.997248i	$0.523620\pi$
$824$	−0.735783	−	7.00051i	−0.0256322	−	0.243874i
$825$	−2.12519	+	20.2198i	−0.0739896	+	0.703964i
$826$	−11.6615	−	2.47872i	−0.405755	−	0.0862458i
$827$	14.0249	−	6.24430i	0.487694	−	0.217136i	−0.148132	−	0.988968i	$-0.547326\pi$
$827$	14.0249	−	6.24430i	0.487694	−	0.217136i	0.635826	+	0.771832i	$0.280659\pi$
$828$	−17.3112	−	19.2261i	−0.601607	−	0.668152i
$829$	4.61694	−	14.2095i	0.160353	−	0.493516i	−0.838311	−	0.545192i	$-0.816457\pi$
$829$	4.61694	−	14.2095i	0.160353	−	0.493516i	0.998664	+	0.0516768i	$0.0164566\pi$
$830$	−5.39698	+	5.99395i	−0.187332	+	0.208053i
$831$	6.26989	+	10.8598i	0.217500	+	0.376721i
$832$	26.8454	−	46.4977i	0.930698	−	1.61202i
$833$	−0.247700	−	0.762344i	−0.00858231	−	0.0264136i
$834$	33.8153	+	15.0555i	1.17093	+	0.521330i
$835$	−5.71577	−	4.15275i	−0.197802	−	0.143712i
$836$	7.46986			0.258351
$837$	−2.94838	+	4.72304i	−0.101911	+	0.163252i
$838$	−54.7248			−1.89044
$839$	−2.94971	−	2.14309i	−0.101835	−	0.0739878i	0.535702	−	0.844407i	$-0.320047\pi$
$839$	−2.94971	−	2.14309i	−0.101835	−	0.0739878i	−0.637538	+	0.770419i	$0.720047\pi$
$840$	0.479689	+	0.213571i	0.0165508	+	0.00736891i
$841$	4.47541	+	13.7739i	0.154324	+	0.474962i
$842$	−31.6192	+	54.7660i	−1.08967	+	1.88736i
$843$	−0.704636	−	1.22047i	−0.0242690	−	0.0420351i
$844$	22.8641	−	25.3932i	0.787015	−	0.874069i
$845$	0.912129	−	2.80724i	0.0313782	−	0.0965721i
$846$	4.84239	+	5.37802i	0.166485	+	0.184900i
$847$	4.04429	−	1.80063i	0.138963	−	0.0618705i
$848$	−9.48535	−	2.01617i	−0.325728	−	0.0692357i
$849$	−3.34152	+	31.7924i	−0.114681	+	1.09111i
$850$	−0.129060	−	1.22792i	−0.00442671	−	0.0421173i
$851$	18.1587	−	3.85976i	0.622473	−	0.132311i
$852$	1.25368	−	0.910853i	0.0429504	−	0.0312053i
$853$	26.1967	−	19.0330i	0.896959	−	0.651679i	−0.0407242	−	0.999170i	$-0.512967\pi$
$853$	26.1967	−	19.0330i	0.896959	−	0.651679i	0.937683	+	0.347492i	$0.112967\pi$
$854$	15.0814	−	3.20565i	0.516074	−	0.109695i
$855$	−0.0355199	−	0.337949i	−0.00121475	−	0.0115576i
$856$	−3.39224	+	32.2750i	−0.115944	+	1.10314i
$857$	−2.49030	−	0.529329i	−0.0850669	−	0.0180815i	0.165182	−	0.986263i	$-0.447179\pi$
$857$	−2.49030	−	0.529329i	−0.0850669	−	0.0180815i	−0.250249	+	0.968182i	$0.580512\pi$
$858$	37.0045	−	16.4755i	1.26331	−	0.562463i
$859$	−12.2808	−	13.6392i	−0.419015	−	0.465363i	0.496271	−	0.868167i	$-0.334702\pi$
$859$	−12.2808	−	13.6392i	−0.419015	−	0.465363i	−0.915286	+	0.402804i	$0.868035\pi$
$860$	−1.64966	+	5.07714i	−0.0562530	+	0.173129i
$861$	2.14146	−	2.37833i	0.0729808	−	0.0810534i
$862$	−30.2100	−	52.3253i	−1.02896	−	1.78221i
$863$	4.06442	−	7.03977i	0.138354	−	0.239637i	−0.788520	−	0.615010i	$-0.789152\pi$
$863$	4.06442	−	7.03977i	0.138354	−	0.239637i	0.926874	+	0.375373i	$0.122485\pi$
$864$	−2.30190	−	7.08451i	−0.0783122	−	0.241020i
$865$	1.35033	+	0.601208i	0.0459127	+	0.0204417i
$866$	−5.57340	−	4.04931i	−0.189392	−	0.137601i
$867$	16.9855			0.576859
$868$	−2.45143	−	8.53492i	−0.0832069	−	0.289694i
$869$	57.7391			1.95867
$870$	6.33654	+	4.60377i	0.214829	+	0.156082i
$871$	−15.5486	−	6.92267i	−0.526844	−	0.234566i
$872$	−6.85463	−	21.0964i	−0.232127	−	0.714413i
$873$	5.61274	−	9.72155i	0.189963	−	0.329025i
$874$	−6.37569	−	11.0430i	−0.215661	−	0.373536i
$875$	−2.03616	+	2.26138i	−0.0688348	+	0.0764487i
$876$	10.8280	−	33.3252i	0.365845	−	1.12595i
$877$	−8.71039	−	9.67386i	−0.294129	−	0.326663i	0.577909	−	0.816101i	$-0.303869\pi$
$877$	−8.71039	−	9.67386i	−0.294129	−	0.326663i	−0.872038	+	0.489438i	$0.837202\pi$
$878$	−39.4848	+	17.5798i	−1.33255	+	0.593288i
$879$	27.6152	+	5.86979i	0.931437	+	0.197983i
$880$	0.461552	−	4.39138i	0.0155589	−	0.148033i
$881$	4.72550	+	44.9601i	0.159206	+	1.51474i	0.724166	+	0.689626i	$0.242225\pi$
$881$	4.72550	+	44.9601i	0.159206	+	1.51474i	−0.564960	+	0.825118i	$0.691108\pi$
$882$	−14.2398	+	3.02676i	−0.479479	+	0.101916i
$883$	22.2216	−	16.1449i	0.747815	−	0.543320i	−0.147334	−	0.989087i	$-0.547069\pi$
$883$	22.2216	−	16.1449i	0.747815	−	0.543320i	0.895149	+	0.445767i	$0.147069\pi$
$884$	−1.15514	+	0.839259i	−0.0388516	+	0.0282273i
$885$	−5.04102	+	1.07150i	−0.169452	+	0.0360181i
$886$	3.45986	+	32.9184i	0.116236	+	1.10592i
$887$	4.14774	−	39.4631i	0.139268	−	1.32504i	−0.672080	−	0.740478i	$-0.734599\pi$
$887$	4.14774	−	39.4631i	0.139268	−	1.32504i	0.811348	−	0.584564i	$-0.198734\pi$
$888$	−3.25199	−	0.691232i	−0.109130	−	0.0231962i
$889$	7.37581	−	3.28392i	0.247377	−	0.110139i
$890$	13.3663	+	14.8448i	0.448041	+	0.497600i
$891$	1.33559	−	4.11054i	0.0447441	−	0.137708i
$892$	−43.5577	+	48.3758i	−1.45842	+	1.61974i
$893$	1.03519	+	1.79300i	0.0346413	+	0.0600005i
$894$	−10.9281	+	18.9281i	−0.365492	+	0.633051i
$895$	−1.21142	−	3.72838i	−0.0404934	−	0.124626i
$896$	6.53533	+	2.90972i	0.218330	+	0.0972068i
$897$	−32.4704	−	23.5911i	−1.08415	−	0.787684i
$898$	30.7597			1.02646
$899$	−2.57727	−	36.6241i	−0.0859567	−	1.22148i
$900$	−13.0158			−0.433860
$901$	0.502220	+	0.364884i	0.0167314	+	0.0121561i
$902$	47.8641	+	21.3105i	1.59370	+	0.709561i
$903$	0.631700	+	1.94417i	0.0210217	+	0.0646980i
$904$	−3.60161	+	6.23816i	−0.119788	+	0.207478i
$905$	−5.53396	−	9.58510i	−0.183955	−	0.318619i
$906$	−9.12524	+	10.1346i	−0.303166	+	0.336700i
$907$	−10.2569	+	31.5674i	−0.340574	+	1.04818i	0.623337	+	0.781953i	$0.285777\pi$
$907$	−10.2569	+	31.5674i	−0.340574	+	1.04818i	−0.963911	+	0.266225i	$0.914223\pi$
$908$	−6.88098	−	7.64210i	−0.228353	−	0.253612i
$909$	−1.29936	+	0.578511i	−0.0430970	+	0.0191880i
$910$	2.87465	+	0.611026i	0.0952937	+	0.0202553i
$911$	2.72617	−	25.9378i	0.0903222	−	0.859358i	−0.851750	−	0.523948i	$-0.824459\pi$
$911$	2.72617	−	25.9378i	0.0903222	−	0.859358i	0.942072	−	0.335410i	$-0.108875\pi$
$912$	−0.122612	−	1.16657i	−0.00406009	−	0.0386292i
$913$	−28.7078	+	6.10204i	−0.950091	+	0.201948i
$914$	−17.9685	+	13.0549i	−0.594344	+	0.431816i
$915$	5.39211	−	3.91760i	0.178258	−	0.129512i
$916$	13.9891	−	2.97348i	0.462213	−	0.0982464i
$917$	0.189209	+	1.80020i	0.00624823	+	0.0594480i
$918$	−0.0274359	+	0.261035i	−0.000905520	+	0.00861545i
$919$	−36.9416	−	7.85219i	−1.21859	−	0.259020i	−0.446648	−	0.894710i	$-0.647382\pi$
$919$	−36.9416	−	7.85219i	−1.21859	−	0.259020i	−0.771944	+	0.635690i	$0.780716\pi$
$920$	7.78117	−	3.46440i	0.256538	−	0.114218i
$921$	−5.82961	−	6.47444i	−0.192092	−	0.213340i
$922$	−1.27882	+	3.93580i	−0.0421156	+	0.129619i
$923$	1.60862	−	1.78655i	0.0529483	−	0.0588050i
$924$	3.44663	+	5.96973i	0.113386	+	0.196390i
$925$	4.66987	−	8.08845i	0.153544	−	0.265947i
$926$	16.3102	+	50.1977i	0.535987	+	1.64960i
$927$	−3.84029	−	1.70981i	−0.126132	−	0.0561574i
$928$	39.7393	+	28.8723i	1.30451	+	0.947778i
$929$	−28.8820			−0.947588			−0.473794	−	0.880636i	$-0.657116\pi$
$929$	−28.8820			−0.947588			−0.473794	+	0.880636i	$0.657116\pi$
$930$	−4.25317	−	5.06419i	−0.139467	−	0.166061i
$931$	−4.16486			−0.136498
$932$	36.9961	+	26.8792i	1.21185	+	0.880459i
$933$	−24.2752	−	10.8080i	−0.794736	−	0.353839i
$934$	14.7517	+	45.4012i	0.482692	+	1.48557i
$935$	−0.141333	+	0.244796i	−0.00462208	+	0.00800568i
$936$	3.59388	+	6.22478i	0.117470	+	0.203463i
$937$	25.4923	−	28.3121i	0.832797	−	0.924914i	−0.165321	−	0.986240i	$-0.552866\pi$
$937$	25.4923	−	28.3121i	0.832797	−	0.924914i	0.998118	+	0.0613254i	$0.0195327\pi$
$938$	1.54199	−	4.74577i	0.0503479	−	0.154955i
$939$	−0.421379	−	0.467988i	−0.0137512	−	0.0152722i
$940$	−4.55801	+	2.02936i	−0.148666	+	0.0661904i
$941$	15.6300	+	3.32226i	0.509524	+	0.108303i	0.455498	−	0.890237i	$-0.349461\pi$
$941$	15.6300	+	3.32226i	0.509524	+	0.108303i	0.0540261	+	0.998540i	$0.482795\pi$
$942$	1.76403	−	16.7837i	0.0574753	−	0.546841i
$943$	−5.42649	−	51.6296i	−0.176711	−	1.68129i
$944$	−17.4012	+	3.69874i	−0.566361	+	0.120384i
$945$	0.253692	−	0.184318i	0.00825259	−	0.00599586i
$946$	−27.0749	+	19.6710i	−0.880279	+	0.639560i
$947$	−21.5063	+	4.57129i	−0.698859	+	0.148547i	−0.543622	−	0.839330i	$-0.682948\pi$
$947$	−21.5063	+	4.57129i	−0.698859	+	0.148547i	−0.155237	+	0.987877i	$0.549614\pi$
$948$	3.86378	+	36.7614i	0.125490	+	1.19395i
$949$	5.68216	−	54.0622i	0.184451	−	1.75493i
$950$	−6.27503	−	1.33380i	−0.203589	−	0.0432741i
$951$	−16.0388	+	7.14096i	−0.520095	+	0.231561i
$952$	−0.0776407	−	0.0862287i	−0.00251635	−	0.00279469i
$953$	1.43926	−	4.42957i	0.0466221	−	0.143488i	−0.925036	−	0.379880i	$-0.875965\pi$
$953$	1.43926	−	4.42957i	0.0466221	−	0.143488i	0.971658	+	0.236392i	$0.0759651\pi$
$954$	7.54401	−	8.37847i	0.244246	−	0.271263i
$955$	3.47731	+	6.02287i	0.112523	+	0.194896i
$956$	−18.8130	+	32.5850i	−0.608455	+	1.05388i
$957$	8.80710	+	27.1055i	0.284693	+	0.876195i
$958$	−26.9273	−	11.9888i	−0.869980	−	0.387340i
$959$	−1.06761	−	0.775666i	−0.0344750	−	0.0250476i
$960$	6.80463			0.219619
$961$	−5.35611	+	30.5338i	−0.172778	+	0.984961i
$962$	−18.6078			−0.599941
$963$	15.6794	+	11.3917i	0.505260	+	0.367093i
$964$	17.7874	+	7.91948i	0.572895	+	0.255069i
$965$	−2.78784	−	8.58010i	−0.0897439	−	0.276203i
$966$	5.88354	−	10.1906i	0.189300	−	0.327877i
$967$	−7.75084	−	13.4248i	−0.249250	−	0.431714i	0.714068	−	0.700077i	$-0.246851\pi$
$967$	−7.75084	−	13.4248i	−0.249250	−	0.431714i	−0.963318	+	0.268363i	$0.913517\pi$
$968$	−8.60542	+	9.55728i	−0.276589	+	0.307183i
$969$	−0.0232043	+	0.0714154i	−0.000745429	+	0.00229419i
$970$	8.92179	+	9.90865i	0.286462	+	0.318148i
$971$	6.98710	−	3.11086i	0.224227	−	0.0998321i	−0.291549	−	0.956556i	$-0.594171\pi$
$971$	6.98710	−	3.11086i	0.224227	−	0.0998321i	0.515775	+	0.856724i	$0.327504\pi$
$972$	2.70648	+	0.575279i	0.0868103	+	0.0184521i
$973$	−1.02148	+	9.71872i	−0.0327471	+	0.311568i
$974$	−7.01084	−	66.7036i	−0.224642	−	2.13732i
$975$	−19.7509	+	4.19819i	−0.632536	+	0.134450i
$976$	18.6132	−	13.5232i	0.595793	−	0.432869i
$977$	27.4317	−	19.9303i	0.877618	−	0.637627i	−0.0550023	−	0.998486i	$-0.517517\pi$
$977$	27.4317	−	19.9303i	0.877618	−	0.637627i	0.932620	+	0.360860i	$0.117517\pi$
$978$	−22.7452	+	4.83464i	−0.727311	+	0.154595i
$979$	7.59788	+	72.2890i	0.242829	+	2.31037i
$980$	1.04913	−	9.98182i	0.0335133	−	0.318858i
$981$	−12.9576	−	2.75422i	−0.413704	−	0.0879356i
$982$	−8.28301	+	3.68783i	−0.264321	+	0.117683i
$983$	1.65321	+	1.83608i	0.0527293	+	0.0585619i	0.768932	−	0.639330i	$-0.220788\pi$
$983$	1.65321	+	1.83608i	0.0527293	+	0.0585619i	−0.716203	+	0.697892i	$0.754122\pi$
$984$	−2.87297	+	8.84209i	−0.0915869	+	0.281876i
$985$	−1.14985	+	1.27703i	−0.0366371	+	0.0406896i
$986$	−0.865393	−	1.49890i	−0.0275597	−	0.0477348i
$987$	−0.955282	+	1.65460i	−0.0304070	+	0.0526664i
$988$	2.29253	+	7.05568i	0.0729351	+	0.224471i
$989$	30.2931	+	13.4874i	0.963264	+	0.428873i
$990$	4.15323	+	3.01750i	0.131998	+	0.0959024i
$991$	−3.74762			−0.119047			−0.0595235	−	0.998227i	$-0.518958\pi$
$991$	−3.74762			−0.119047			−0.0595235	+	0.998227i	$0.518958\pi$
$992$	−26.6735	−	31.7598i	−0.846886	−	1.00837i
$993$	−26.2073			−0.831665
$994$	0.570216	+	0.414286i	0.0180861	+	0.0131404i
$995$	−4.36188	−	1.94203i	−0.138281	−	0.0615666i
$996$	−5.80612	−	17.8694i	−0.183974	−	0.566214i
$997$	−9.52582	+	16.4992i	−0.301686	+	0.522535i	−0.976518	−	0.215436i	$-0.930883\pi$
$997$	−9.52582	+	16.4992i	−0.301686	+	0.522535i	0.674832	+	0.737971i	$0.264216\pi$
$998$	21.9816	+	38.0733i	0.695817	+	1.20519i
$999$	−1.32854	+	1.47549i	−0.0420332	+	0.0466826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.m.a.19.2	✓	16
3.2	odd	2		279.2.y.b.19.1		16
31.7	even	15		2883.2.a.m.1.2		8
31.18	even	15	inner	93.2.m.a.49.2	yes	16
31.24	odd	30		2883.2.a.n.1.2		8
93.38	odd	30		8649.2.a.bj.1.7		8
93.80	odd	30		279.2.y.b.235.1		16
93.86	even	30		8649.2.a.bi.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.a.19.2	✓	16	1.1	even	1	trivial
93.2.m.a.49.2	yes	16	31.18	even	15	inner
279.2.y.b.19.1		16	3.2	odd	2
279.2.y.b.235.1		16	93.80	odd	30
2883.2.a.m.1.2		8	31.7	even	15
2883.2.a.n.1.2		8	31.24	odd	30
8649.2.a.bi.1.7		8	93.86	even	30
8649.2.a.bj.1.7		8	93.38	odd	30

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.76635 + 1.28333i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.855032 + 2.63152i) q^{4} +(-0.272011 + 0.471137i) q^{5} +(-1.09167 - 1.89082i) q^{6} +(0.385694 - 0.428357i) q^{7} +(-0.517444 + 1.59253i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(1.76635 + 1.28333i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.855032 + 2.63152i) q^{4} +(-0.272011 + 0.471137i) q^{5} +(-1.09167 - 1.89082i) q^{6} +(0.385694 - 0.428357i) q^{7} +(-0.517444 + 1.59253i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-1.08509 + 0.483114i) q^{10} +(-4.22763 - 0.898610i) q^{11} +(0.289224 - 2.75178i) q^{12} +(-0.448690 - 4.26900i) q^{13} +(1.23100 - 0.261656i) q^{14} +(0.440123 - 0.319768i) q^{15} +(1.51927 - 1.10382i) q^{16} +(-0.117590 + 0.0249945i) q^{17} +(0.228220 + 2.17137i) q^{18} +(-0.0652913 + 0.621205i) q^{19} +(-1.47238 - 0.312964i) q^{20} +(-0.526577 + 0.234447i) q^{21} +(-6.31427 - 7.01270i) q^{22} +(-2.88935 + 8.89249i) q^{23} +(1.12045 - 1.24438i) q^{24} +(2.35202 + 4.07382i) q^{25} +(4.68600 - 8.11639i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.45701 + 0.648702i) q^{28} +(5.33477 + 3.87594i) q^{29} +1.18778 q^{30} +(-3.58077 - 4.26357i) q^{31} +7.44910 q^{32} +(3.49663 + 2.54045i) q^{33} +(-0.239781 - 0.106757i) q^{34} +(0.0969015 + 0.298232i) q^{35} +(-1.38347 + 2.39624i) q^{36} +(-0.992736 - 1.71947i) q^{37} +(-0.912539 + 1.01348i) q^{38} +(-1.32646 + 4.08243i) q^{39} +(-0.609549 - 0.676973i) q^{40} +(-5.07221 + 2.25829i) q^{41} +(-1.23100 - 0.261656i) q^{42} +(0.370707 - 3.52704i) q^{43} +(-1.25005 - 11.8934i) q^{44} +(-0.532134 + 0.113108i) q^{45} +(-16.5156 + 11.9993i) q^{46} +(2.68156 - 1.94827i) q^{47} +(-1.83689 + 0.390442i) q^{48} +(0.696970 + 6.63122i) q^{49} +(-1.07356 + 10.2142i) q^{50} +(0.117590 + 0.0249945i) q^{51} +(10.8503 - 4.83087i) q^{52} +(-3.45527 - 3.83747i) q^{53} +(0.674687 - 2.07647i) q^{54} +(1.57333 - 1.74736i) q^{55} +(0.482596 + 0.835880i) q^{56} +(0.312313 - 0.540943i) q^{57} +(4.44898 + 13.6926i) q^{58} +(-8.65421 - 3.85310i) q^{59} +(1.21779 + 0.884779i) q^{60} +12.2514 q^{61} +(-0.853338 - 12.1263i) q^{62} +0.576411 q^{63} +(10.1192 + 7.35203i) q^{64} +(2.13333 + 0.949821i) q^{65} +(2.91605 + 8.97467i) q^{66} +(1.98252 - 3.43383i) q^{67} +(-0.166316 - 0.288068i) q^{68} +(6.25645 - 6.94849i) q^{69} +(-0.211568 + 0.651140i) q^{70} +(0.374749 + 0.416201i) q^{71} +(-1.52972 + 0.681074i) q^{72} +(12.3871 + 2.63297i) q^{73} +(0.453125 - 4.31120i) q^{74} +(-0.491706 - 4.67827i) q^{75} +(-1.69054 + 0.359335i) q^{76} +(-2.01550 + 1.46434i) q^{77} +(-7.58210 + 5.50872i) q^{78} +(-13.0672 + 2.77752i) q^{79} +(0.106789 + 1.01603i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-11.8575 - 2.52038i) q^{82} +(6.20346 - 2.76196i) q^{83} +(-1.06719 - 1.18524i) q^{84} +(0.0202099 - 0.0621996i) q^{85} +(5.18116 - 5.75426i) q^{86} +(-3.29707 - 5.71070i) q^{87} +(3.61862 - 6.26764i) q^{88} +(-5.19694 - 15.9945i) q^{89} +(-1.08509 - 0.483114i) q^{90} +(-2.00171 - 1.45433i) q^{91} -25.8712 q^{92} +(1.53705 + 5.35140i) q^{93} +7.23684 q^{94} +(-0.274912 - 0.199736i) q^{95} +(-6.80509 - 3.02982i) q^{96} +(-3.46887 - 10.6761i) q^{97} +(-7.27896 + 12.6075i) q^{98} +(-2.16104 - 3.74303i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9	\( 16 q - 2 q^{3} + 6 q^{5} - 5 q^{6} - 9 q^{7} + 10 q^{8} + 2 q^{9} - 16 q^{10} + 10 q^{11} - 10 q^{12} + 3 q^{13} - 12 q^{14} - 8 q^{15} + 6 q^{16} + 3 q^{17} - 32 q^{19} - 10 q^{20} - 6 q^{21} - 9 q^{22} - 22 q^{23} + 20 q^{24} + 12 q^{25} + 18 q^{26} + 4 q^{27} + 30 q^{28} + 38 q^{29} - 2 q^{30} - 8 q^{31} + 10 q^{33} - 52 q^{34} + 3 q^{35} - 5 q^{36} - 8 q^{37} + 7 q^{38} + 6 q^{39} + 37 q^{40} - 40 q^{41} + 12 q^{42} + q^{43} + q^{45} - 7 q^{46} - 23 q^{47} + 18 q^{48} + 25 q^{49} - 21 q^{50} - 3 q^{51} - 45 q^{52} + 30 q^{53} - 5 q^{54} + 46 q^{55} - 6 q^{56} - 8 q^{57} + 48 q^{58} - 40 q^{59} + 15 q^{60} + 26 q^{61} + 40 q^{62} - 12 q^{63} + 38 q^{64} + 12 q^{65} + 12 q^{66} - 32 q^{67} + 15 q^{68} - 11 q^{69} + 33 q^{70} + 17 q^{71} + 5 q^{72} + 27 q^{73} - 70 q^{74} + 3 q^{75} - 15 q^{76} - 9 q^{77} - 9 q^{78} + 21 q^{80} + 2 q^{81} - 32 q^{82} - 17 q^{83} - 15 q^{84} - 64 q^{85} + 26 q^{86} - 6 q^{87} - 22 q^{88} - 43 q^{89} - 16 q^{90} - 140 q^{92} - q^{93} + 88 q^{94} - 2 q^{95} - 35 q^{96} + 12 q^{97} - 32 q^{98}+O(q^{100}) \) 16 * q - 2 * q^3 + 6 * q^5 - 5 * q^6 - 9 * q^7 + 10 * q^8 + 2 * q^9 - 16 * q^10 + 10 * q^11 - 10 * q^12 + 3 * q^13 - 12 * q^14 - 8 * q^15 + 6 * q^16 + 3 * q^17 - 32 * q^19 - 10 * q^20 - 6 * q^21 - 9 * q^22 - 22 * q^23 + 20 * q^24 + 12 * q^25 + 18 * q^26 + 4 * q^27 + 30 * q^28 + 38 * q^29 - 2 * q^30 - 8 * q^31 + 10 * q^33 - 52 * q^34 + 3 * q^35 - 5 * q^36 - 8 * q^37 + 7 * q^38 + 6 * q^39 + 37 * q^40 - 40 * q^41 + 12 * q^42 + q^43 + q^45 - 7 * q^46 - 23 * q^47 + 18 * q^48 + 25 * q^49 - 21 * q^50 - 3 * q^51 - 45 * q^52 + 30 * q^53 - 5 * q^54 + 46 * q^55 - 6 * q^56 - 8 * q^57 + 48 * q^58 - 40 * q^59 + 15 * q^60 + 26 * q^61 + 40 * q^62 - 12 * q^63 + 38 * q^64 + 12 * q^65 + 12 * q^66 - 32 * q^67 + 15 * q^68 - 11 * q^69 + 33 * q^70 + 17 * q^71 + 5 * q^72 + 27 * q^73 - 70 * q^74 + 3 * q^75 - 15 * q^76 - 9 * q^77 - 9 * q^78 + 21 * q^80 + 2 * q^81 - 32 * q^82 - 17 * q^83 - 15 * q^84 - 64 * q^85 + 26 * q^86 - 6 * q^87 - 22 * q^88 - 43 * q^89 - 16 * q^90 - 140 * q^92 - q^93 + 88 * q^94 - 2 * q^95 - 35 * q^96 + 12 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more