LMFDB - Embedded newform 930.2.bg.d.691.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (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:	$7.42608738798$
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} + 21x^{14} + 167x^{12} + 653x^{10} + 1350x^{8} + 1472x^{6} + 777x^{4} + 149x^{2} + 1 $ x^16 + 21x^14 + 167x^12 + 653x^10 + 1350x^8 + 1472x^6 + 777x^4 + 149*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			691.2
Root			$1.38019i$ of defining polynomial
Character	$\chi$	$=$	930.691
Dual form			930.2.bg.d.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.69481 - 1.19981i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.69481 - 1.19981i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.978148 - 0.207912i) q^{10} +(-0.511450 + 4.86612i) q^{11} +(0.669131 + 0.743145i) q^{12} +(-3.88437 + 4.31403i) q^{13} +(-0.308342 - 2.93368i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.454946 + 4.32852i) q^{17} +(0.669131 - 0.743145i) q^{18} +(-2.85224 - 3.16773i) q^{19} +(0.104528 - 0.994522i) q^{20} +(-2.88538 + 0.613306i) q^{21} +(4.46991 + 1.99013i) q^{22} +(0.665173 - 0.483276i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.90255 + 5.02736i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.88538 - 0.613306i) q^{28} +(-1.37169 + 4.22164i) q^{29} -1.00000 q^{30} +(-4.43934 + 3.36039i) q^{31} +1.00000 q^{32} +(1.51200 - 4.65345i) q^{33} +(4.25725 + 0.904907i) q^{34} +(2.38647 + 1.73387i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.22730 - 2.12574i) q^{37} +(-3.89408 + 1.73376i) q^{38} +(4.69642 - 3.41215i) q^{39} +(-0.913545 - 0.406737i) q^{40} +(3.37116 - 0.716562i) q^{41} +(-0.308342 + 2.93368i) q^{42} +(4.18463 + 4.64750i) q^{43} +(3.27400 - 3.63615i) q^{44} +(0.104528 + 0.994522i) q^{45} +(-0.254073 - 0.781958i) q^{46} +(-1.31524 - 4.04788i) q^{47} +(-0.104528 - 0.994522i) q^{48} +(1.13856 - 1.26450i) q^{49} +(0.669131 + 0.743145i) q^{50} +(0.454946 - 4.32852i) q^{51} +(5.67824 - 1.20695i) q^{52} +(10.5453 + 4.69509i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-4.46991 + 1.99013i) q^{55} +(-1.47492 + 2.55464i) q^{56} +(2.13130 + 3.69152i) q^{57} +(3.59114 + 2.60912i) q^{58} +(11.3426 + 2.41095i) q^{59} +(-0.309017 + 0.951057i) q^{60} -3.69305 q^{61} +(1.82409 + 5.26048i) q^{62} +2.94984 q^{63} +(0.309017 - 0.951057i) q^{64} +(-5.67824 - 1.20695i) q^{65} +(-3.95846 - 2.87599i) q^{66} +(7.38101 + 12.7843i) q^{67} +(2.17618 - 3.76926i) q^{68} +(-0.751116 + 0.334418i) q^{69} +(2.38647 - 1.73387i) q^{70} +(-4.97553 - 2.21525i) q^{71} +(-0.978148 + 0.207912i) q^{72} +(-0.565177 + 5.37730i) q^{73} +(-1.64245 - 1.82412i) q^{74} +(0.669131 - 0.743145i) q^{75} +(0.445564 + 4.23925i) q^{76} +(4.46015 + 13.7269i) q^{77} +(-1.79387 - 5.52098i) q^{78} +(-0.418690 - 3.98357i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(0.360255 - 3.42759i) q^{82} +(12.6178 - 2.68200i) q^{83} +(2.69481 + 1.19981i) q^{84} +(-3.52114 + 2.55825i) q^{85} +(5.71316 - 2.54366i) q^{86} +(2.21945 - 3.84419i) q^{87} +(-2.44646 - 4.23740i) q^{88} +(-13.2932 - 9.65806i) q^{89} +(0.978148 + 0.207912i) q^{90} +(-5.29164 + 16.2860i) q^{91} -0.822199 q^{92} +(5.04100 - 2.36397i) q^{93} -4.25619 q^{94} +(1.31722 - 4.05398i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-15.0500 - 10.9345i) q^{97} +(-0.850779 - 1.47359i) q^{98} +(-2.44646 + 4.23740i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{15}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	2.69481	−	1.19981i	1.01854	−	0.453485i	0.171600	−	0.985167i	$-0.445106\pi$
$7$	2.69481	−	1.19981i	1.01854	−	0.453485i	0.846944	+	0.531682i	$0.178440\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	0.978148	−	0.207912i	0.309317	−	0.0657474i
$11$	−0.511450	+	4.86612i	−0.154208	+	1.46719i	0.594396	+	0.804173i	$0.297391\pi$
$11$	−0.511450	+	4.86612i	−0.154208	+	1.46719i	−0.748604	+	0.663018i	$0.769275\pi$
$12$	0.669131	+	0.743145i	0.193161	+	0.214527i
$13$	−3.88437	+	4.31403i	−1.07733	+	1.19650i	−0.0977989	+	0.995206i	$0.531180\pi$
$13$	−3.88437	+	4.31403i	−1.07733	+	1.19650i	−0.979532	+	0.201291i	$0.935486\pi$
$14$	−0.308342	−	2.93368i	−0.0824079	−	0.784059i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.454946	+	4.32852i	0.110341	+	1.04982i	0.899885	+	0.436127i	$0.143650\pi$
$17$	0.454946	+	4.32852i	0.110341	+	1.04982i	−0.789545	+	0.613693i	$0.789683\pi$
$18$	0.669131	−	0.743145i	0.157716	−	0.175161i
$19$	−2.85224	−	3.16773i	−0.654349	−	0.726728i	0.321078	−	0.947053i	$-0.395955\pi$
$19$	−2.85224	−	3.16773i	−0.654349	−	0.726728i	−0.975427	+	0.220325i	$0.929288\pi$
$20$	0.104528	−	0.994522i	0.0233733	−	0.222382i
$21$	−2.88538	+	0.613306i	−0.629641	+	0.133834i
$22$	4.46991	+	1.99013i	0.952987	+	0.424297i
$23$	0.665173	−	0.483276i	0.138698	−	0.100770i	−0.516273	−	0.856424i	$-0.672681\pi$
$23$	0.665173	−	0.483276i	0.138698	−	0.100770i	0.654971	+	0.755654i	$0.272681\pi$
$24$	0.913545	−	0.406737i	0.186477	−	0.0830248i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.90255	+	5.02736i	0.569237	+	0.985947i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−2.88538	−	0.613306i	−0.545285	−	0.115904i
$29$	−1.37169	+	4.22164i	−0.254717	+	0.783938i	0.739168	+	0.673521i	$0.235219\pi$
$29$	−1.37169	+	4.22164i	−0.254717	+	0.783938i	−0.993885	+	0.110418i	$0.964781\pi$
$30$	−1.00000			−0.182574
$31$	−4.43934	+	3.36039i	−0.797330	+	0.603544i
$31$	−4.43934	+	3.36039i	−0.797330	+	0.603544i
$32$	1.00000			0.176777
$33$	1.51200	−	4.65345i	0.263205	−	0.810061i
$34$	4.25725	+	0.904907i	0.730113	+	0.155190i
$35$	2.38647	+	1.73387i	0.403387	+	0.293078i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	1.22730	−	2.12574i	0.201767	−	0.349470i	−0.747331	−	0.664452i	$-0.768665\pi$
$37$	1.22730	−	2.12574i	0.201767	−	0.349470i	0.949098	+	0.314982i	$0.101998\pi$
$38$	−3.89408	+	1.73376i	−0.631704	+	0.281253i
$39$	4.69642	−	3.41215i	0.752030	−	0.546382i
$40$	−0.913545	−	0.406737i	−0.144444	−	0.0643107i
$41$	3.37116	−	0.716562i	0.526487	−	0.111908i	0.0630025	−	0.998013i	$-0.479932\pi$
$41$	3.37116	−	0.716562i	0.526487	−	0.111908i	0.463484	+	0.886105i	$0.346599\pi$
$42$	−0.308342	+	2.93368i	−0.0475782	+	0.452677i
$43$	4.18463	+	4.64750i	0.638150	+	0.708737i	0.972288	−	0.233787i	$-0.0751119\pi$
$43$	4.18463	+	4.64750i	0.638150	+	0.708737i	−0.334138	+	0.942524i	$0.608445\pi$
$44$	3.27400	−	3.63615i	0.493575	−	0.548170i
$45$	0.104528	+	0.994522i	0.0155822	+	0.148255i
$46$	−0.254073	−	0.781958i	−0.0374611	−	0.115293i
$47$	−1.31524	−	4.04788i	−0.191847	−	0.590444i	−0.999999	−	0.00147008i	$-0.999532\pi$
$47$	−1.31524	−	4.04788i	−0.191847	−	0.590444i	0.808152	−	0.588974i	$-0.200468\pi$
$48$	−0.104528	−	0.994522i	−0.0150874	−	0.143547i
$49$	1.13856	−	1.26450i	0.162652	−	0.180643i
$50$	0.669131	+	0.743145i	0.0946294	+	0.105097i
$51$	0.454946	−	4.32852i	0.0637051	−	0.606114i
$52$	5.67824	−	1.20695i	0.787431	−	0.167374i
$53$	10.5453	+	4.69509i	1.44852	+	0.644921i	0.972157	−	0.234331i	$-0.0752899\pi$
$53$	10.5453	+	4.69509i	1.44852	+	0.644921i	0.476358	+	0.879251i	$0.341957\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	−4.46991	+	1.99013i	−0.602722	+	0.268349i
$56$	−1.47492	+	2.55464i	−0.197094	+	0.341378i
$57$	2.13130	+	3.69152i	0.282298	+	0.488954i
$58$	3.59114	+	2.60912i	0.471540	+	0.342594i
$59$	11.3426	+	2.41095i	1.47669	+	0.313879i	0.874715	−	0.484638i	$-0.161049\pi$
$59$	11.3426	+	2.41095i	1.47669	+	0.313879i	0.601972	+	0.798517i	$0.294382\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	−3.69305			−0.472847			−0.236423	−	0.971650i	$-0.575975\pi$
$61$	−3.69305			−0.472847			−0.236423	+	0.971650i	$0.575975\pi$
$62$	1.82409	+	5.26048i	0.231660	+	0.668082i
$63$	2.94984			0.371645
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−5.67824	−	1.20695i	−0.704300	−	0.149704i
$66$	−3.95846	−	2.87599i	−0.487252	−	0.354010i
$67$	7.38101	+	12.7843i	0.901734	+	1.56185i	0.825243	+	0.564778i	$0.191038\pi$
$67$	7.38101	+	12.7843i	0.901734	+	1.56185i	0.0764908	+	0.997070i	$0.475628\pi$
$68$	2.17618	−	3.76926i	0.263901	−	0.457089i
$69$	−0.751116	+	0.334418i	−0.0904237	+	0.0402592i
$70$	2.38647	−	1.73387i	0.285238	−	0.207237i
$71$	−4.97553	−	2.21525i	−0.590487	−	0.262902i	0.0896662	−	0.995972i	$-0.471420\pi$
$71$	−4.97553	−	2.21525i	−0.590487	−	0.262902i	−0.680153	+	0.733070i	$0.738087\pi$
$72$	−0.978148	+	0.207912i	−0.115276	+	0.0245026i
$73$	−0.565177	+	5.37730i	−0.0661490	+	0.629366i	0.910349	+	0.413841i	$0.135813\pi$
$73$	−0.565177	+	5.37730i	−0.0661490	+	0.629366i	−0.976498	+	0.215525i	$0.930854\pi$
$74$	−1.64245	−	1.82412i	−0.190931	−	0.212050i
$75$	0.669131	−	0.743145i	0.0772645	−	0.0858110i
$76$	0.445564	+	4.23925i	0.0511097	+	0.486276i
$77$	4.46015	+	13.7269i	0.508281	+	1.56433i
$78$	−1.79387	−	5.52098i	−0.203116	−	0.625128i
$79$	−0.418690	−	3.98357i	−0.0471063	−	0.448187i	−0.992499	−	0.122253i	$-0.960988\pi$
$79$	−0.418690	−	3.98357i	−0.0471063	−	0.448187i	0.945393	−	0.325934i	$-0.105679\pi$
$80$	−0.669131	+	0.743145i	−0.0748111	+	0.0830861i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	0.360255	−	3.42759i	0.0397835	−	0.378514i
$83$	12.6178	−	2.68200i	1.38499	−	0.294388i	0.545656	−	0.838009i	$-0.316281\pi$
$83$	12.6178	−	2.68200i	1.38499	−	0.294388i	0.839331	+	0.543621i	$0.182947\pi$
$84$	2.69481	+	1.19981i	0.294028	+	0.130910i
$85$	−3.52114	+	2.55825i	−0.381921	+	0.277482i
$86$	5.71316	−	2.54366i	0.616065	−	0.274290i
$87$	2.21945	−	3.84419i	0.237950	−	0.412141i
$88$	−2.44646	−	4.23740i	−0.260794	−	0.451708i
$89$	−13.2932	−	9.65806i	−1.40907	−	1.02375i	−0.993456	−	0.114213i	$-0.963565\pi$
$89$	−13.2932	−	9.65806i	−1.40907	−	1.02375i	−0.415618	−	0.909539i	$-0.636435\pi$
$90$	0.978148	+	0.207912i	0.103106	+	0.0219158i
$91$	−5.29164	+	16.2860i	−0.554715	+	1.70724i
$92$	−0.822199			−0.0857201
$93$	5.04100	−	2.36397i	0.522727	−	0.245132i
$94$	−4.25619			−0.438993
$95$	1.31722	−	4.05398i	0.135144	−	0.415929i
$96$	−0.978148	−	0.207912i	−0.0998318	−	0.0212199i
$97$	−15.0500	−	10.9345i	−1.52810	−	1.11023i	−0.957283	−	0.289154i	$-0.906626\pi$
$97$	−15.0500	−	10.9345i	−1.52810	−	1.11023i	−0.570818	−	0.821076i	$-0.693374\pi$
$98$	−0.850779	−	1.47359i	−0.0859416	−	0.148855i
$99$	−2.44646	+	4.23740i	−0.245879	+	0.425874i
$100$	0.913545	−	0.406737i	0.0913545	−	0.0406737i
$101$	10.9391	−	7.94773i	1.08848	−	0.790829i	0.109340	−	0.994004i	$-0.465126\pi$
$101$	10.9391	−	7.94773i	1.08848	−	0.790829i	0.979142	+	0.203176i	$0.0651263\pi$
$102$	−3.97608	−	1.77027i	−0.393691	−	0.175282i
$103$	−1.04187	+	0.221456i	−0.102658	+	0.0218207i	−0.258954	−	0.965890i	$-0.583378\pi$
$103$	−1.04187	+	0.221456i	−0.102658	+	0.0218207i	0.156296	+	0.987710i	$0.450045\pi$
$104$	0.606798	−	5.77330i	0.0595015	−	0.566119i
$105$	−1.97383	−	2.19216i	−0.192626	−	0.213933i
$106$	7.72399	−	8.57836i	0.750220	−	0.833204i
$107$	−0.381052	−	3.62547i	−0.0368377	−	0.350487i	−0.997379	−	0.0723509i	$-0.976950\pi$
$107$	−0.381052	−	3.62547i	−0.0368377	−	0.350487i	0.960542	−	0.278137i	$-0.0897168\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	−3.69983	−	11.3869i	−0.354380	−	1.09067i	−0.956368	−	0.292164i	$-0.905625\pi$
$109$	−3.69983	−	11.3869i	−0.354380	−	1.09067i	0.601989	−	0.798504i	$-0.294375\pi$
$110$	0.511450	+	4.86612i	0.0487648	+	0.463966i
$111$	−1.64245	+	1.82412i	−0.155894	+	0.173138i
$112$	1.97383	+	2.19216i	0.186509	+	0.207140i
$113$	0.549992	−	5.23282i	0.0517389	−	0.492263i	−0.937714	−	0.347408i	$-0.887062\pi$
$113$	0.549992	−	5.23282i	0.0517389	−	0.492263i	0.989453	−	0.144855i	$-0.0462715\pi$
$114$	4.16946	−	0.886246i	0.390505	−	0.0830045i
$115$	0.751116	+	0.334418i	0.0700419	+	0.0311847i
$116$	3.59114	−	2.60912i	0.333429	−	0.242250i
$117$	−5.30322	+	2.36115i	−0.490283	+	0.218288i
$118$	5.79802	−	10.0425i	0.533751	−	0.924484i
$119$	6.41939	+	11.1187i	0.588464	+	1.01925i
$120$	0.809017	+	0.587785i	0.0738528	+	0.0536572i
$121$	−12.6579	−	2.69052i	−1.15072	−	0.244593i
$122$	−1.14122	+	3.51230i	−0.103321	+	0.317989i
$123$	−3.44647			−0.310758
$124$	5.56669	−	0.109233i	0.499904	−	0.00980943i
$125$	−1.00000			−0.0894427
$126$	0.911551	−	2.80546i	0.0812074	−	0.249931i
$127$	4.45786	+	0.947547i	0.395571	+	0.0840812i	0.401402	−	0.915902i	$-0.368523\pi$
$127$	4.45786	+	0.947547i	0.395571	+	0.0840812i	−0.00583155	+	0.999983i	$0.501856\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−3.12691	−	5.41597i	−0.275309	−	0.476850i
$130$	−2.90255	+	5.02736i	−0.254570	+	0.440929i
$131$	1.38390	−	0.616153i	0.120912	−	0.0538335i	−0.345389	−	0.938460i	$-0.612253\pi$
$131$	1.38390	−	0.616153i	0.120912	−	0.0538335i	0.466301	+	0.884626i	$0.345586\pi$
$132$	−3.95846	+	2.87599i	−0.344540	+	0.250323i
$133$	−11.4869	−	5.11431i	−0.996043	−	0.443467i
$134$	14.4394	−	3.06920i	1.24738	−	0.265138i
$135$	0.104528	−	0.994522i	0.00899638	−	0.0855948i
$136$	−2.91230	−	3.23444i	−0.249728	−	0.277351i
$137$	−8.16686	+	9.07021i	−0.697742	+	0.774921i	−0.983015	−	0.183526i	$-0.941249\pi$
$137$	−8.16686	+	9.07021i	−0.697742	+	0.774921i	0.285273	+	0.958446i	$0.407916\pi$
$138$	0.0859432	+	0.817695i	0.00731597	+	0.0696068i
$139$	−4.40009	−	13.5421i	−0.373211	−	1.14862i	−0.944678	−	0.327999i	$-0.893626\pi$
$139$	−4.40009	−	13.5421i	−0.373211	−	1.14862i	0.571467	−	0.820625i	$-0.306374\pi$
$140$	−0.911551	−	2.80546i	−0.0770401	−	0.237105i
$141$	0.444893	+	4.23288i	0.0374668	+	0.356473i
$142$	−3.64435	+	4.04746i	−0.305827	+	0.339655i
$143$	−19.0059	−	21.1082i	−1.58936	−	1.76516i
$144$	−0.104528	+	0.994522i	−0.00871071	+	0.0828768i
$145$	−4.34189	+	0.922897i	−0.360574	+	0.0766425i
$146$	4.93947	+	2.19919i	0.408793	+	0.182007i
$147$	−1.37659	+	1.00015i	−0.113539	+	0.0824910i
$148$	−2.24239	+	0.998375i	−0.184323	+	0.0820659i
$149$	−8.53681	+	14.7862i	−0.699363	+	1.21133i	0.269325	+	0.963049i	$0.413199\pi$
$149$	−8.53681	+	14.7862i	−0.699363	+	1.21133i	−0.968688	+	0.248282i	$0.920134\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−2.98000	−	2.16510i	−0.242509	−	0.176193i	0.459891	−	0.887975i	$-0.347888\pi$
$151$	−2.98000	−	2.16510i	−0.242509	−	0.176193i	−0.702400	+	0.711782i	$0.747888\pi$
$152$	4.16946	+	0.886246i	0.338188	+	0.0718840i
$153$	−1.34495	+	4.13934i	−0.108733	+	0.334646i
$154$	14.4333			1.16307
$155$	−5.12986	−	2.16439i	−0.412040	−	0.173848i
$156$	−5.80510			−0.464780
$157$	−5.31302	+	16.3518i	−0.424025	+	1.30502i	0.479899	+	0.877324i	$0.340673\pi$
$157$	−5.31302	+	16.3518i	−0.424025	+	1.30502i	−0.903924	+	0.427692i	$0.859327\pi$
$158$	−3.91798	−	0.832793i	−0.311698	−	0.0662534i
$159$	−9.33874	−	6.78499i	−0.740611	−	0.538085i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	1.21268	−	2.10042i	0.0955724	−	0.165536i
$162$	0.913545	−	0.406737i	0.0717749	−	0.0319562i
$163$	9.70537	−	7.05137i	0.760183	−	0.552306i	−0.138783	−	0.990323i	$-0.544319\pi$
$163$	9.70537	−	7.05137i	0.760183	−	0.552306i	0.898967	+	0.438017i	$0.144319\pi$
$164$	−3.14851	−	1.40181i	−0.245857	−	0.109463i
$165$	4.78600	−	1.01730i	0.372590	−	0.0791964i
$166$	1.34839	−	12.8291i	0.104655	−	0.995727i
$167$	10.8786	+	12.0819i	0.841811	+	0.934926i	0.998610	−	0.0527044i	$-0.0167841\pi$
$167$	10.8786	+	12.0819i	0.841811	+	0.934926i	−0.156799	+	0.987631i	$0.550117\pi$
$168$	1.97383	−	2.19216i	0.152284	−	0.169129i
$169$	−2.16365	−	20.5858i	−0.166435	−	1.58352i
$170$	1.34495	+	4.13934i	0.103153	+	0.317473i
$171$	−1.31722	−	4.05398i	−0.100730	−	0.310016i
$172$	−0.653703	−	6.21957i	−0.0498444	−	0.474238i
$173$	−15.6781	+	17.4123i	−1.19199	+	1.32384i	−0.258164	+	0.966101i	$0.583118\pi$
$173$	−15.6781	+	17.4123i	−1.19199	+	1.32384i	−0.933823	+	0.357735i	$0.883549\pi$
$174$	−2.97020	−	3.29874i	−0.225170	−	0.250077i
$175$	−0.308342	+	2.93368i	−0.0233085	+	0.221765i
$176$	−4.78600	+	1.01730i	−0.360758	+	0.0766816i
$177$	−10.5935	−	4.71654i	−0.796257	−	0.354517i
$178$	−13.2932	+	9.65806i	−0.996366	+	0.723902i
$179$	11.3812	−	5.06723i	0.850670	−	0.378743i	0.0653720	−	0.997861i	$-0.479177\pi$
$179$	11.3812	−	5.06723i	0.850670	−	0.378743i	0.785298	+	0.619118i	$0.212510\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	1.22884	+	2.12842i	0.0913390	+	0.158204i	0.908075	−	0.418808i	$-0.137552\pi$
$181$	1.22884	+	2.12842i	0.0913390	+	0.158204i	−0.816736	+	0.577012i	$0.804219\pi$
$182$	13.8537	+	10.0653i	1.02690	+	0.746090i
$183$	3.61235	+	0.767828i	0.267032	+	0.0567595i
$184$	−0.254073	+	0.781958i	−0.0187305	+	0.0576467i
$185$	2.45460			0.180466
$186$	−0.690513	−	5.52478i	−0.0506308	−	0.405097i
$187$	−21.2958			−1.55730
$188$	−1.31524	+	4.04788i	−0.0959234	+	0.295222i
$189$	−2.88538	−	0.613306i	−0.209880	−	0.0446115i
$190$	−3.44852	−	2.50550i	−0.250182	−	0.181768i
$191$	11.3202	+	19.6072i	0.819101	+	1.41873i	0.906345	+	0.422538i	$0.138861\pi$
$191$	11.3202	+	19.6072i	0.819101	+	1.41873i	−0.0872437	+	0.996187i	$0.527806\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−2.56031	+	1.13992i	−0.184295	+	0.0820536i	−0.496810	−	0.867859i	$-0.665495\pi$
$193$	−2.56031	+	1.13992i	−0.184295	+	0.0820536i	0.312515	+	0.949913i	$0.398829\pi$
$194$	−15.0500	+	10.9345i	−1.08053	+	0.785051i
$195$	5.30322	+	2.36115i	0.379772	+	0.169085i
$196$	−1.66437	+	0.353774i	−0.118884	+	0.0252696i
$197$	−1.30429	+	12.4095i	−0.0929271	+	0.884143i	0.844405	+	0.535705i	$0.179954\pi$
$197$	−1.30429	+	12.4095i	−0.0929271	+	0.884143i	−0.937332	+	0.348437i	$0.886712\pi$
$198$	3.27400	+	3.63615i	0.232673	+	0.258410i
$199$	1.24552	−	1.38329i	0.0882927	−	0.0980590i	−0.697379	−	0.716702i	$-0.745651\pi$
$199$	1.24552	−	1.38329i	0.0882927	−	0.0980590i	0.785672	+	0.618643i	$0.212317\pi$
$200$	−0.104528	−	0.994522i	−0.00739128	−	0.0703233i
$201$	−4.56171	−	14.0395i	−0.321758	−	0.990271i
$202$	−4.17837	−	12.8597i	−0.293989	−	0.904805i
$203$	1.36870	+	13.0223i	0.0960638	+	0.913986i
$204$	−2.91230	+	3.23444i	−0.203902	+	0.226456i
$205$	2.30614	+	2.56123i	0.161068	+	0.178884i
$206$	−0.111338	+	1.05931i	−0.00775728	+	0.0738056i
$207$	0.804232	−	0.170945i	0.0558980	−	0.0118815i
$208$	−5.30322	−	2.36115i	−0.367712	−	0.163716i
$209$	16.8733	−	12.2592i	1.16715	−	0.847987i
$210$	−2.69481	+	1.19981i	−0.185960	+	0.0827946i
$211$	−4.53973	+	7.86305i	−0.312528	+	0.541314i	−0.978909	−	0.204297i	$-0.934509\pi$
$211$	−4.53973	+	7.86305i	−0.312528	+	0.541314i	0.666381	+	0.745611i	$0.267842\pi$
$212$	−5.77166	−	9.99681i	−0.396399	−	0.686584i
$213$	4.40623	+	3.20131i	0.301910	+	0.219350i
$214$	−3.56578	−	0.757930i	−0.243752	−	0.0518110i
$215$	−1.93254	+	5.94774i	−0.131798	+	0.405633i
$216$	1.00000			0.0680414
$217$	−7.93138	+	14.3820i	−0.538417	+	0.976313i
$218$	−11.9729			−0.810907
$219$	1.67083	−	5.14229i	0.112904	−	0.347484i
$220$	4.78600	+	1.01730i	0.322672	+	0.0685861i
$221$	−20.4405	−	14.8509i	−1.37498	−	0.998981i
$222$	1.22730	+	2.12574i	0.0823709	+	0.142671i
$223$	13.7115	−	23.7490i	0.918188	−	1.59035i	0.116023	−	0.993246i	$-0.462985\pi$
$223$	13.7115	−	23.7490i	0.918188	−	1.59035i	0.802165	−	0.597103i	$-0.203681\pi$
$224$	2.69481	−	1.19981i	0.180055	−	0.0801656i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−4.80676	−	2.14011i	−0.319741	−	0.142358i
$227$	24.7416	−	5.25898i	1.64216	−	0.349051i	0.708081	−	0.706131i	$-0.249561\pi$
$227$	24.7416	−	5.25898i	1.64216	−	0.349051i	0.934074	+	0.357080i	$0.116228\pi$
$228$	0.445564	−	4.23925i	0.0295082	−	0.280751i
$229$	−10.6925	−	11.8752i	−0.706577	−	0.784733i	0.277832	−	0.960630i	$-0.410384\pi$
$229$	−10.6925	−	11.8752i	−0.706577	−	0.784733i	−0.984409	+	0.175896i	$0.943718\pi$
$230$	0.550158	−	0.611013i	0.0362764	−	0.0402890i
$231$	−1.50869	−	14.3543i	−0.0992648	−	0.944442i
$232$	−1.37169	−	4.22164i	−0.0900561	−	0.277164i
$233$	7.22755	+	22.2441i	0.473492	+	1.45726i	0.847980	+	0.530028i	$0.177818\pi$
$233$	7.22755	+	22.2441i	0.473492	+	1.45726i	−0.374488	+	0.927232i	$0.622182\pi$
$234$	0.606798	+	5.77330i	0.0396676	+	0.377412i
$235$	2.84795	−	3.16297i	0.185780	−	0.206329i
$236$	−7.75927	−	8.61754i	−0.505085	−	0.560954i
$237$	−0.418690	+	3.98357i	−0.0271968	+	0.258761i
$238$	12.5582	−	2.66933i	0.814028	−	0.173027i
$239$	−17.3165	−	7.70980i	−1.12011	−	0.498706i	−0.238718	−	0.971089i	$-0.576727\pi$
$239$	−17.3165	−	7.70980i	−1.12011	−	0.498706i	−0.881393	+	0.472383i	$0.843394\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	−2.37761	+	1.05858i	−0.153156	+	0.0681893i	−0.481883	−	0.876236i	$-0.660047\pi$
$241$	−2.37761	+	1.05858i	−0.153156	+	0.0681893i	0.328727	+	0.944425i	$0.393380\pi$
$242$	−6.47035	+	11.2070i	−0.415930	+	0.720411i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	2.98774	+	2.17072i	0.191270	+	0.138966i
$245$	1.66437	+	0.353774i	0.106333	+	0.0226018i
$246$	−1.06502	+	3.27779i	−0.0679031	+	0.208984i
$247$	24.7449			1.57448
$248$	1.61632	−	5.32799i	0.102636	−	0.338328i
$249$	−12.8997			−0.817486
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−11.5848	−	2.46243i	−0.731228	−	0.155427i	−0.172772	−	0.984962i	$-0.555273\pi$
$251$	−11.5848	−	2.46243i	−0.731228	−	0.155427i	−0.558455	+	0.829534i	$0.688606\pi$
$252$	−2.38647	−	1.73387i	−0.150334	−	0.109224i
$253$	2.01148	+	3.48398i	0.126461	+	0.219036i
$254$	2.27872	−	3.94687i	0.142980	−	0.247648i
$255$	3.97608	−	1.77027i	0.248992	−	0.110858i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	4.71384	+	2.09874i	0.294042	+	0.130916i	0.548456	−	0.836180i	$-0.315216\pi$
$257$	4.71384	+	2.09874i	0.294042	+	0.130916i	−0.254414	+	0.967095i	$0.581883\pi$
$258$	−6.11717	+	1.30024i	−0.380838	+	0.0809496i
$259$	0.756856	−	7.20101i	0.0470288	−	0.447449i
$260$	3.88437	+	4.31403i	0.240898	+	0.267545i
$261$	−2.97020	+	3.29874i	−0.183851	+	0.204187i
$262$	−0.158347	−	1.50657i	−0.00978270	−	0.0930762i
$263$	−1.79078	−	5.51145i	−0.110424	−	0.339850i	0.880541	−	0.473970i	$-0.157179\pi$
$263$	−1.79078	−	5.51145i	−0.110424	−	0.339850i	−0.990965	+	0.134119i	$0.957179\pi$
$264$	1.51200	+	4.65345i	0.0930569	+	0.286400i
$265$	1.20661	+	11.4801i	0.0741212	+	0.705216i
$266$	−8.41365	+	9.34431i	−0.515874	+	0.572936i
$267$	10.9947	+	12.2108i	0.672863	+	0.747290i
$268$	1.54305	−	14.6811i	0.0942568	−	0.896794i
$269$	16.8303	−	3.57739i	1.02616	−	0.218118i	0.336069	−	0.941838i	$-0.390903\pi$
$269$	16.8303	−	3.57739i	1.02616	−	0.218118i	0.690094	+	0.723720i	$0.257569\pi$
$270$	−0.913545	−	0.406737i	−0.0555966	−	0.0247532i
$271$	9.98472	−	7.25432i	0.606528	−	0.440669i	−0.241662	−	0.970361i	$-0.577692\pi$
$271$	9.98472	−	7.25432i	0.606528	−	0.440669i	0.848190	+	0.529692i	$0.177692\pi$
$272$	−3.97608	+	1.77027i	−0.241085	+	0.107338i
$273$	8.56206	−	14.8299i	0.518199	−	0.897548i
$274$	6.10259	+	10.5700i	0.368671	+	0.638557i
$275$	−3.95846	−	2.87599i	−0.238704	−	0.173429i
$276$	0.804232	+	0.170945i	0.0484091	+	0.0102897i
$277$	2.33943	−	7.20004i	0.140563	−	0.432608i	−0.855851	−	0.517223i	$-0.826966\pi$
$277$	2.33943	−	7.20004i	0.140563	−	0.432608i	0.996414	+	0.0846145i	$0.0269659\pi$
$278$	−14.2390			−0.853998
$279$	−5.42234	+	1.26423i	−0.324627	+	0.0756873i
$280$	−2.94984			−0.176287
$281$	6.11018	−	18.8052i	0.364503	−	1.12182i	−0.585789	−	0.810463i	$-0.699215\pi$
$281$	6.11018	−	18.8052i	0.364503	−	1.12182i	0.950292	−	0.311360i	$-0.100785\pi$
$282$	4.16319	+	0.884912i	0.247914	+	0.0526958i
$283$	20.9494	+	15.2207i	1.24532	+	0.904775i	0.997941	−	0.0641453i	$-0.0204321\pi$
$283$	20.9494	+	15.2207i	1.24532	+	0.904775i	0.247375	+	0.968920i	$0.420432\pi$
$284$	2.72320	+	4.71672i	0.161592	+	0.279886i
$285$	−2.13130	+	3.69152i	−0.126247	+	0.218667i
$286$	−25.9483	+	11.5529i	−1.53435	+	0.683138i
$287$	8.22491	−	5.97575i	0.485501	−	0.352737i
$288$	0.913545	+	0.406737i	0.0538312	+	0.0239672i
$289$	−1.90060	+	0.403985i	−0.111800	+	0.0237638i
$290$	−0.463991	+	4.41457i	−0.0272465	+	0.259233i
$291$	12.4478	+	13.8246i	0.729701	+	0.810415i
$292$	3.61794	−	4.01813i	0.211724	−	0.235143i
$293$	−1.21248	−	11.5360i	−0.0708338	−	0.673939i	−0.971112	−	0.238624i	$-0.923304\pi$
$293$	−1.21248	−	11.5360i	−0.0708338	−	0.673939i	0.900278	−	0.435315i	$-0.143363\pi$
$294$	0.525810	+	1.61828i	0.0306659	+	0.0943799i
$295$	3.58338	+	11.0285i	0.208632	+	0.642104i
$296$	0.256575	+	2.44115i	0.0149131	+	0.141889i
$297$	3.27400	−	3.63615i	0.189977	−	0.210991i
$298$	11.4245	+	12.6882i	0.661802	+	0.735006i
$299$	−0.498909	+	4.74680i	−0.0288526	+	0.274515i
$300$	−0.978148	+	0.207912i	−0.0564734	+	0.0120038i
$301$	16.8529	+	7.50339i	0.971385	+	0.432488i
$302$	−2.98000	+	2.16510i	−0.171480	+	0.124587i
$303$	−12.3525	+	5.49968i	−0.709632	+	0.315949i
$304$	2.13130	−	3.69152i	0.122239	−	0.211723i
$305$	−1.84653	−	3.19828i	−0.105732	−	0.183133i
$306$	3.52114	+	2.55825i	0.201290	+	0.146246i
$307$	−28.1726	−	5.98827i	−1.60789	−	0.341768i	−0.685516	−	0.728057i	$-0.740423\pi$
$307$	−28.1726	−	5.98827i	−1.60789	−	0.341768i	−0.922378	+	0.386289i	$0.873757\pi$
$308$	4.46015	−	13.7269i	0.254141	−	0.782164i
$309$	1.06514			0.0605940
$310$	−3.64367	+	4.20995i	−0.206946	+	0.239109i
$311$	17.0480			0.966703			0.483351	−	0.875426i	$-0.339419\pi$
$311$	17.0480			0.966703			0.483351	+	0.875426i	$0.339419\pi$
$312$	−1.79387	+	5.52098i	−0.101558	+	0.312564i
$313$	4.19008	+	0.890628i	0.236837	+	0.0503413i	0.324801	−	0.945782i	$-0.394703\pi$
$313$	4.19008	+	0.890628i	0.236837	+	0.0503413i	−0.0879638	+	0.996124i	$0.528036\pi$
$314$	13.9097	+	10.1060i	0.784968	+	0.570313i
$315$	1.47492	+	2.55464i	0.0831023	+	0.143937i
$316$	−2.00276	+	3.46887i	−0.112664	+	0.195139i
$317$	−15.1206	+	6.73214i	−0.849259	+	0.378114i	−0.784757	−	0.619803i	$-0.787212\pi$
$317$	−15.1206	+	6.73214i	−0.849259	+	0.378114i	−0.0645016	+	0.997918i	$0.520546\pi$
$318$	−9.33874	+	6.78499i	−0.523691	+	0.380484i
$319$	−19.8414	−	8.83398i	−1.11091	−	0.494608i
$320$	0.978148	−	0.207912i	0.0546801	−	0.0116226i
$321$	−0.381052	+	3.62547i	−0.0212683	+	0.202354i
$322$	−1.62288	−	1.80239i	−0.0904395	−	0.100443i
$323$	12.4140	−	13.7871i	0.690732	−	0.767136i
$324$	−0.104528	−	0.994522i	−0.00580714	−	0.0552512i
$325$	−1.79387	−	5.52098i	−0.0995063	−	0.306249i
$326$	−3.70712	−	11.4093i	−0.205319	−	0.631905i
$327$	1.25151	+	11.9073i	0.0692086	+	0.658476i
$328$	−2.30614	+	2.56123i	−0.127335	+	0.141420i
$329$	−8.40099	−	9.33025i	−0.463162	−	0.514393i
$330$	0.511450	−	4.86612i	0.0281544	−	0.267871i
$331$	−15.1478	+	3.21977i	−0.832600	+	0.176975i	−0.604442	−	0.796649i	$-0.706604\pi$
$331$	−15.1478	+	3.21977i	−0.832600	+	0.176975i	−0.228158	+	0.973624i	$0.573270\pi$
$332$	−11.7845	−	5.24679i	−0.646757	−	0.287955i
$333$	1.98581	−	1.44278i	0.108822	−	0.0790637i
$334$	14.8523	−	6.61265i	0.812679	−	0.361828i
$335$	−7.38101	+	12.7843i	−0.403268	+	0.698480i
$336$	−1.47492	−	2.55464i	−0.0804635	−	0.139367i
$337$	7.06808	+	5.13526i	0.385023	+	0.279735i	0.763413	−	0.645911i	$-0.223522\pi$
$337$	7.06808	+	5.13526i	0.385023	+	0.279735i	−0.378390	+	0.925646i	$0.623522\pi$
$338$	−20.2469	−	4.30360i	−1.10128	−	0.234085i
$339$	−1.62594	+	5.00413i	−0.0883089	+	0.271787i
$340$	4.35236			0.236040
$341$	−14.0816	−	23.3210i	−0.762559	−	1.26291i
$342$	−4.26261			−0.230495
$343$	−4.82980	+	14.8646i	−0.260785	+	0.802613i
$344$	−6.11717	−	1.30024i	−0.329816	−	0.0701044i
$345$	−0.665173	−	0.483276i	−0.0358117	−	0.0260187i
$346$	11.7153	+	20.2915i	0.629819	+	1.09088i
$347$	−9.79109	+	16.9587i	−0.525614	+	0.910389i	0.473941	+	0.880556i	$0.342831\pi$
$347$	−9.79109	+	16.9587i	−0.525614	+	0.910389i	−0.999555	+	0.0298329i	$0.990502\pi$
$348$	−4.05513	+	1.80546i	−0.217378	+	0.0967828i
$349$	−2.57971	+	1.87427i	−0.138089	+	0.100327i	−0.654685	−	0.755902i	$-0.727199\pi$
$349$	−2.57971	+	1.87427i	−0.138089	+	0.100327i	0.516596	+	0.856229i	$0.327199\pi$
$350$	2.69481	+	1.19981i	0.144044	+	0.0641324i
$351$	5.67824	−	1.20695i	0.303082	−	0.0644221i
$352$	−0.511450	+	4.86612i	−0.0272604	+	0.259365i
$353$	−14.9608	−	16.6157i	−0.796283	−	0.884362i	0.199136	−	0.979972i	$-0.436187\pi$
$353$	−14.9608	−	16.6157i	−0.796283	−	0.884362i	−0.995419	+	0.0956099i	$0.969520\pi$
$354$	−7.75927	+	8.61754i	−0.412400	+	0.458017i
$355$	−0.569303	−	5.41656i	−0.0302155	−	0.287481i
$356$	5.07754	+	15.6271i	0.269109	+	0.828233i
$357$	−3.96740	−	12.2104i	−0.209977	−	0.646243i
$358$	−1.30224	−	12.3900i	−0.0688257	−	0.654832i
$359$	−3.02920	+	3.36427i	−0.159875	+	0.177559i	−0.817760	−	0.575559i	$-0.804785\pi$
$359$	−3.02920	+	3.36427i	−0.159875	+	0.177559i	0.657885	+	0.753118i	$0.271451\pi$
$360$	−0.669131	−	0.743145i	−0.0352663	−	0.0391672i
$361$	0.0867789	−	0.825646i	0.00456731	−	0.0434551i
$362$	2.40398	−	0.510981i	0.126350	−	0.0268566i
$363$	11.8219	+	5.26345i	0.620490	+	0.276260i
$364$	13.8537	−	10.0653i	0.726131	−	0.527565i
$365$	−4.93947	+	2.19919i	−0.258544	+	0.115111i
$366$	1.84653	−	3.19828i	0.0965194	−	0.167177i
$367$	−7.25572	−	12.5673i	−0.378746	−	0.656007i	0.612134	−	0.790754i	$-0.290311\pi$
$367$	−7.25572	−	12.5673i	−0.378746	−	0.656007i	−0.990880	+	0.134747i	$0.956978\pi$
$368$	0.665173	+	0.483276i	0.0346745	+	0.0251925i
$369$	3.37116	+	0.716562i	0.175496	+	0.0373027i
$370$	0.758513	−	2.33446i	0.0394332	−	0.121363i
$371$	34.0510			1.76784
$372$	−5.46776	−	1.05053i	−0.283490	−	0.0544677i
$373$	23.2235			1.20247			0.601234	−	0.799073i	$-0.294676\pi$
$373$	23.2235			1.20247			0.601234	+	0.799073i	$0.294676\pi$
$374$	−6.58076	+	20.2535i	−0.340283	+	1.04728i
$375$	0.978148	+	0.207912i	0.0505113	+	0.0107365i
$376$	3.44333	+	2.50173i	0.177576	+	0.129017i
$377$	−12.8841	−	22.3159i	−0.663565	−	1.14933i
$378$	−1.47492	+	2.55464i	−0.0758617	+	0.131396i
$379$	5.64016	−	2.51116i	0.289715	−	0.128990i	−0.256733	−	0.966482i	$-0.582646\pi$
$379$	5.64016	−	2.51116i	0.289715	−	0.128990i	0.546448	+	0.837493i	$0.315979\pi$
$380$	−3.44852	+	2.50550i	−0.176905	+	0.128529i
$381$	−4.16344	−	1.85368i	−0.213299	−	0.0949670i
$382$	22.1457	−	4.70721i	1.13307	−	0.240842i
$383$	−1.19046	+	11.3264i	−0.0608295	+	0.578754i	0.921076	+	0.389383i	$0.127312\pi$
$383$	−1.19046	+	11.3264i	−0.0608295	+	0.578754i	−0.981906	+	0.189371i	$0.939355\pi$
$384$	0.669131	+	0.743145i	0.0341464	+	0.0379235i
$385$	−9.65779	+	10.7261i	−0.492207	+	0.546651i
$386$	0.292953	+	2.78726i	0.0149109	+	0.141868i
$387$	1.93254	+	5.94774i	0.0982365	+	0.302341i
$388$	5.74861	+	17.6924i	0.291841	+	0.898195i
$389$	0.171371	+	1.63048i	0.00868884	+	0.0826688i	0.998007	−	0.0631038i	$-0.0200999\pi$
$389$	0.171371	+	1.63048i	0.00868884	+	0.0826688i	−0.989318	+	0.145773i	$0.953433\pi$
$390$	3.88437	−	4.31403i	0.196693	−	0.218449i
$391$	2.39449	+	2.65935i	0.121094	+	0.134489i
$392$	−0.177861	+	1.69224i	−0.00898335	+	0.0854708i
$393$	−1.48176	+	0.314959i	−0.0747452	+	0.0158876i
$394$	11.3991	+	5.07521i	0.574279	+	0.255686i
$395$	3.24053	−	2.35438i	0.163049	−	0.118462i
$396$	4.46991	−	1.99013i	0.224621	−	0.100008i
$397$	18.1622	−	31.4578i	0.911533	−	1.57882i	0.0996346	−	0.995024i	$-0.468233\pi$
$397$	18.1622	−	31.4578i	0.911533	−	1.57882i	0.811899	−	0.583798i	$-0.198434\pi$
$398$	−0.930702	−	1.61202i	−0.0466519	−	0.0808034i
$399$	10.1726	+	7.39081i	0.509266	+	0.370004i
$400$	−0.978148	−	0.207912i	−0.0489074	−	0.0103956i
$401$	6.46635	−	19.9014i	0.322914	−	0.993828i	−0.649459	−	0.760397i	$-0.725005\pi$
$401$	6.46635	−	19.9014i	0.322914	−	0.993828i	0.972373	−	0.233431i	$-0.0749954\pi$
$402$	−14.7620			−0.736262
$403$	2.74722	−	32.2045i	0.136849	−	1.60422i
$404$	−13.5215			−0.672719
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	12.8079	+	2.72240i	0.635645	+	0.135110i
$407$	9.71642	+	7.05939i	0.481625	+	0.349921i
$408$	2.17618	+	3.76926i	0.107737	+	0.186606i
$409$	−7.43905	+	12.8848i	−0.367837	+	0.637113i	−0.989227	−	0.146389i	$-0.953235\pi$
$409$	−7.43905	+	12.8848i	−0.367837	+	0.637113i	0.621390	+	0.783501i	$0.286568\pi$
$410$	3.14851	−	1.40181i	0.155494	−	0.0692303i
$411$	9.87420	−	7.17402i	0.487058	−	0.353868i
$412$	0.973058	+	0.433233i	0.0479391	+	0.0213439i
$413$	33.4590	−	7.11193i	1.64641	−	0.349955i
$414$	0.0859432	−	0.817695i	0.00422388	−	0.0401875i
$415$	8.63160	+	9.58636i	0.423708	+	0.470576i
$416$	−3.88437	+	4.31403i	−0.190447	+	0.211513i
$417$	1.48838	+	14.1610i	0.0728862	+	0.693466i
$418$	−6.44504	−	19.8358i	−0.315237	−	0.970201i
$419$	−3.93134	−	12.0994i	−0.192058	−	0.591095i	−0.999998	−	0.00183017i	$-0.999417\pi$
$419$	−3.93134	−	12.0994i	−0.192058	−	0.591095i	0.807940	−	0.589265i	$-0.200583\pi$
$420$	0.308342	+	2.93368i	0.0150456	+	0.143149i
$421$	−15.6390	+	17.3689i	−0.762197	+	0.846506i	−0.991935	−	0.126747i	$-0.959547\pi$
$421$	−15.6390	+	17.3689i	−0.762197	+	0.846506i	0.229738	+	0.973253i	$0.426213\pi$
$422$	6.07535	+	6.74736i	0.295743	+	0.328456i
$423$	0.444893	−	4.23288i	0.0216315	−	0.205810i
$424$	−11.2911	+	2.39999i	−0.548343	+	0.116554i
$425$	−3.97608	−	1.77027i	−0.192868	−	0.0858705i
$426$	4.40623	−	3.20131i	0.213482	−	0.155104i
$427$	−9.95208	+	4.43095i	−0.481615	+	0.214429i
$428$	−1.82272	+	3.15704i	−0.0881045	+	0.152601i
$429$	14.2020	+	24.5985i	0.685677	+	1.18763i
$430$	5.05945	+	3.67591i	0.243988	+	0.177268i
$431$	17.3778	+	3.69377i	0.837061	+	0.177923i	0.606448	−	0.795123i	$-0.292594\pi$
$431$	17.3778	+	3.69377i	0.837061	+	0.177923i	0.230612	+	0.973046i	$0.425927\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	18.0135			0.865672			0.432836	−	0.901473i	$-0.357513\pi$
$433$	18.0135			0.865672			0.432836	+	0.901473i	$0.357513\pi$
$434$	11.2272	+	11.9875i	0.538921	+	0.575417i
$435$	4.43889			0.212829
$436$	−3.69983	+	11.3869i	−0.177190	+	0.545334i
$437$	−3.42812	−	0.728670i	−0.163989	−	0.0348570i
$438$	−4.37429	−	3.17811i	−0.209012	−	0.151856i
$439$	−10.0054	−	17.3299i	−0.477534	−	0.827113i	0.522134	−	0.852863i	$-0.325136\pi$
$439$	−10.0054	−	17.3299i	−0.477534	−	0.827113i	−0.999668	+	0.0257501i	$0.991803\pi$
$440$	2.44646	−	4.23740i	0.116630	−	0.202010i
$441$	1.55445	−	0.692086i	0.0740214	−	0.0329565i
$442$	−20.4405	+	14.8509i	−0.972257	+	0.706386i
$443$	4.31206	+	1.91985i	0.204872	+	0.0912149i	0.506608	−	0.862177i	$-0.330899\pi$
$443$	4.31206	+	1.91985i	0.204872	+	0.0912149i	−0.301736	+	0.953392i	$0.597566\pi$
$444$	2.40096	−	0.510340i	0.113944	−	0.0242196i
$445$	1.71754	−	16.3413i	0.0814190	−	0.774650i
$446$	−18.3495	−	20.3792i	−0.868876	−	0.964984i
$447$	11.4245	−	12.6882i	0.540359	−	0.600130i
$448$	−0.308342	−	2.93368i	−0.0145678	−	0.138603i
$449$	−5.30908	−	16.3397i	−0.250551	−	0.771116i	−0.994674	−	0.103074i	$-0.967132\pi$
$449$	−5.30908	−	16.3397i	−0.250551	−	0.771116i	0.744123	−	0.668043i	$-0.232868\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	1.76270	+	16.7710i	0.0830022	+	0.789713i
$452$	−3.52073	+	3.91017i	−0.165601	+	0.183919i
$453$	2.46473	+	2.73736i	0.115803	+	0.128613i
$454$	2.64397	−	25.1557i	0.124088	−	1.18062i
$455$	−16.7499	+	3.56030i	−0.785248	+	0.166910i
$456$	−3.89408	−	1.73376i	−0.182357	−	0.0811907i
$457$	18.8636	−	13.7052i	0.882402	−	0.641102i	−0.0514840	−	0.998674i	$-0.516395\pi$
$457$	18.8636	−	13.7052i	0.882402	−	0.641102i	0.933886	+	0.357571i	$0.116395\pi$
$458$	−14.5981	+	6.49950i	−0.682125	+	0.303702i
$459$	2.17618	−	3.76926i	0.101575	−	0.175934i
$460$	−0.411099	−	0.712045i	−0.0191676	−	0.0331993i
$461$	9.12865	+	6.63235i	0.425164	+	0.308900i	0.779712	−	0.626138i	$-0.215365\pi$
$461$	9.12865	+	6.63235i	0.425164	+	0.308900i	−0.354548	+	0.935038i	$0.615365\pi$
$462$	−14.1179	−	3.00086i	−0.656826	−	0.139613i
$463$	6.36870	−	19.6009i	0.295979	−	0.910929i	−0.686912	−	0.726740i	$-0.741034\pi$
$463$	6.36870	−	19.6009i	0.295979	−	0.910929i	0.982891	−	0.184188i	$-0.0589657\pi$
$464$	−4.43889			−0.206070
$465$	4.56775	+	3.18365i	0.211825	+	0.147638i
$466$	23.3888			1.08347
$467$	−8.80929	+	27.1122i	−0.407645	+	1.25460i	0.511021	+	0.859568i	$0.329268\pi$
$467$	−8.80929	+	27.1122i	−0.407645	+	1.25460i	−0.918666	+	0.395035i	$0.870732\pi$
$468$	5.67824	+	1.20695i	0.262477	+	0.0557912i
$469$	35.2291	+	25.5955i	1.62673	+	1.18189i
$470$	−2.12810	−	3.68597i	−0.0981618	−	0.170021i
$471$	8.59665	−	14.8898i	0.396113	−	0.686087i
$472$	−10.5935	+	4.71654i	−0.487606	+	0.217096i
$473$	−24.7555	+	17.9859i	−1.13826	+	0.826994i
$474$	3.65922	+	1.62919i	0.168073	+	0.0748311i
$475$	4.16946	−	0.886246i	0.191308	−	0.0406637i
$476$	1.34202	−	12.7684i	0.0615113	−	0.585241i
$477$	7.72399	+	8.57836i	0.353657	+	0.392776i
$478$	−12.6835	+	14.0865i	−0.580132	+	0.644302i
$479$	−0.524685	−	4.99204i	−0.0239735	−	0.228092i	−0.999948	−	0.0102072i	$-0.996751\pi$
$479$	−0.524685	−	4.99204i	−0.0239735	−	0.228092i	0.975974	−	0.217885i	$-0.0699158\pi$
$480$	−0.309017	−	0.951057i	−0.0141046	−	0.0434096i
$481$	4.40324	+	13.5518i	0.200771	+	0.617908i
$482$	0.272048	+	2.58837i	0.0123915	+	0.117897i
$483$	−1.62288	+	1.80239i	−0.0738436	+	0.0820116i
$484$	8.65902	+	9.61681i	0.393592	+	0.437128i
$485$	1.94453	−	18.5010i	0.0882966	−	0.840086i
$486$	−0.978148	+	0.207912i	−0.0443697	+	0.00943107i
$487$	23.9381	+	10.6579i	1.08474	+	0.482957i	0.869666	−	0.493641i	$-0.164334\pi$
$487$	23.9381	+	10.6579i	1.08474	+	0.482957i	0.215074	+	0.976598i	$0.431001\pi$
$488$	2.98774	−	2.17072i	0.135249	−	0.0982639i
$489$	−10.9593	+	4.87942i	−0.495599	+	0.220655i
$490$	0.850779	−	1.47359i	0.0384343	−	0.0665701i
$491$	5.79776	+	10.0420i	0.261649	+	0.453190i	0.966680	−	0.255987i	$-0.0824003\pi$
$491$	5.79776	+	10.0420i	0.261649	+	0.453190i	−0.705031	+	0.709176i	$0.749067\pi$
$492$	2.78826	+	2.02579i	0.125704	+	0.0913295i
$493$	−18.8975	−	4.01678i	−0.851100	−	0.180907i
$494$	7.64658	−	23.5338i	0.344036	−	1.05883i
$495$	−4.89292			−0.219921
$496$	−4.56775	−	3.18365i	−0.205098	−	0.142950i
$497$	−16.0660			−0.720658
$498$	−3.98623	+	12.2684i	−0.178627	+	0.549758i
$499$	−16.1795	−	3.43907i	−0.724296	−	0.153954i	−0.169011	−	0.985614i	$-0.554057\pi$
$499$	−16.1795	−	3.43907i	−0.724296	−	0.153954i	−0.555285	+	0.831660i	$0.687391\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−8.12891	−	14.0797i	−0.363173	−	0.629034i
$502$	−5.92182	+	10.2569i	−0.264304	+	0.457788i
$503$	21.9486	−	9.77214i	0.978639	−	0.435718i	0.145849	−	0.989307i	$-0.453409\pi$
$503$	21.9486	−	9.77214i	0.978639	−	0.435718i	0.832790	+	0.553589i	$0.186742\pi$
$504$	−2.38647	+	1.73387i	−0.106302	+	0.0772328i
$505$	12.3525	+	5.49968i	0.549679	+	0.244733i
$506$	3.93504	−	0.836419i	0.174934	−	0.0371834i
$507$	−2.16365	+	20.5858i	−0.0960913	+	0.914247i
$508$	−3.04953	−	3.38684i	−0.135301	−	0.150267i
$509$	−17.3799	+	19.3023i	−0.770350	+	0.855561i	−0.992850	−	0.119372i	$-0.961912\pi$
$509$	−17.3799	+	19.3023i	−0.770350	+	0.855561i	0.222499	+	0.974933i	$0.428578\pi$
$510$	−0.454946	−	4.32852i	−0.0201453	−	0.191670i
$511$	4.92868	+	15.1689i	0.218032	+	0.671034i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	0.445564	+	4.23925i	0.0196721	+	0.187168i
$514$	3.45268	−	3.83459i	0.152291	−	0.169136i
$515$	−0.712721	−	0.791557i	−0.0314062	−	0.0348802i
$516$	−0.653703	+	6.21957i	−0.0287777	+	0.273801i
$517$	20.3701	−	4.32981i	0.895878	−	0.190425i
$518$	−6.61468	−	2.94505i	−0.290633	−	0.129398i
$519$	18.9558	−	13.7722i	0.832066	−	0.604531i
$520$	5.30322	−	2.36115i	0.232562	−	0.103543i
$521$	−1.30016	+	2.25194i	−0.0569608	+	0.0986591i	−0.893100	−	0.449859i	$-0.851474\pi$
$521$	−1.30016	+	2.25194i	−0.0569608	+	0.0986591i	0.836139	+	0.548518i	$0.184808\pi$
$522$	2.21945	+	3.84419i	0.0971425	+	0.168256i
$523$	−16.2502	−	11.8065i	−0.710573	−	0.516262i	0.172785	−	0.984960i	$-0.444723\pi$
$523$	−16.2502	−	11.8065i	−0.710573	−	0.516262i	−0.883359	+	0.468698i	$0.844723\pi$
$524$	−1.48176	−	0.314959i	−0.0647312	−	0.0137590i
$525$	0.911551	−	2.80546i	0.0397833	−	0.122441i
$526$	−5.79508			−0.252677
$527$	−16.5652	−	17.6870i	−0.721591	−	0.770457i
$528$	4.89292			0.212937
$529$	−6.89849	+	21.2314i	−0.299934	+	0.923103i
$530$	11.2911	+	2.39999i	0.490453	+	0.104249i
$531$	9.38140	+	6.81598i	0.407118	+	0.295789i
$532$	6.28700	+	10.8894i	0.272576	+	0.472116i
$533$	−10.0036	+	17.3267i	−0.433302	+	0.750502i
$534$	15.0107	−	6.68320i	0.649577	−	0.289210i
$535$	2.94922	−	2.14274i	0.127506	−	0.0926386i
$536$	−13.4858	−	6.00425i	−0.582497	−	0.259344i
$537$	−12.1860	+	2.59022i	−0.525865	+	0.111776i
$538$	1.79855	−	17.1121i	0.0775410	−	0.737753i
$539$	5.57091	+	6.18712i	0.239956	+	0.266498i
$540$	−0.669131	+	0.743145i	−0.0287948	+	0.0319799i
$541$	−1.97893	−	18.8282i	−0.0850807	−	0.809488i	−0.950976	−	0.309264i	$-0.899917\pi$
$541$	−1.97893	−	18.8282i	−0.0850807	−	0.809488i	0.865896	−	0.500225i	$-0.166749\pi$
$542$	−3.81382	−	11.7377i	−0.163818	−	0.504179i
$543$	−0.759466	−	2.33739i	−0.0325918	−	0.100307i
$544$	0.454946	+	4.32852i	0.0195056	+	0.185584i
$545$	8.01144	−	8.89760i	0.343172	−	0.381131i
$546$	−11.4583	−	12.7257i	−0.490369	−	0.544610i
$547$	3.83840	−	36.5199i	0.164118	−	1.56148i	−0.533993	−	0.845489i	$-0.679309\pi$
$547$	3.83840	−	36.5199i	0.164118	−	1.56148i	0.698111	−	0.715990i	$-0.254024\pi$
$548$	11.9385	−	2.53760i	0.509986	−	0.108401i
$549$	−3.37377	−	1.50210i	−0.143989	−	0.0641080i
$550$	−3.95846	+	2.87599i	−0.168789	+	0.122633i
$551$	17.2854	−	7.69596i	0.736384	−	0.327859i
$552$	0.411099	−	0.712045i	0.0174976	−	0.0303066i
$553$	−5.90781	−	10.2326i	−0.251226	−	0.435136i
$554$	−6.12472	−	4.44987i	−0.260214	−	0.189057i
$555$	−2.40096	−	0.510340i	−0.101915	−	0.0216627i
$556$	−4.40009	+	13.5421i	−0.186605	+	0.574312i
$557$	20.7067			0.877372			0.438686	−	0.898640i	$-0.355444\pi$
$557$	20.7067			0.877372			0.438686	+	0.898640i	$0.355444\pi$
$558$	−0.473243	+	5.54762i	−0.0200340	+	0.234849i
$559$	−36.3041			−1.53550
$560$	−0.911551	+	2.80546i	−0.0385201	+	0.118553i
$561$	20.8304	+	4.42764i	0.879461	+	0.186935i
$562$	−15.9967	−	11.6223i	−0.674778	−	0.490255i
$563$	5.57846	+	9.66217i	0.235104	+	0.407212i	0.959303	−	0.282379i	$-0.0911236\pi$
$563$	5.57846	+	9.66217i	0.235104	+	0.407212i	−0.724199	+	0.689591i	$0.757790\pi$
$564$	2.12810	−	3.68597i	0.0896090	−	0.155207i
$565$	4.80676	−	2.14011i	0.202222	−	0.0900349i
$566$	20.9494	−	15.2207i	0.880571	−	0.639772i
$567$	2.69481	+	1.19981i	0.113172	+	0.0503872i
$568$	5.32738	−	1.13237i	0.223532	−	0.0475132i
$569$	2.25468	−	21.4518i	0.0945210	−	0.899307i	−0.839805	−	0.542888i	$-0.817331\pi$
$569$	2.25468	−	21.4518i	0.0945210	−	0.899307i	0.934326	−	0.356419i	$-0.116003\pi$
$570$	2.85224	+	3.16773i	0.119467	+	0.132682i
$571$	−9.39333	+	10.4323i	−0.393099	+	0.436580i	−0.906911	−	0.421322i	$-0.861566\pi$
$571$	−9.39333	+	10.4323i	−0.393099	+	0.436580i	0.513812	+	0.857903i	$0.328233\pi$
$572$	2.96902	+	28.2483i	0.124141	+	1.18112i
$573$	−6.99627	−	21.5323i	−0.292273	−	0.899525i
$574$	−3.14164	−	9.66896i	−0.131129	−	0.403575i
$575$	0.0859432	+	0.817695i	0.00358408	+	0.0341002i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	25.4625	+	28.2790i	1.06002	+	1.17727i	0.983632	+	0.180190i	$0.0576712\pi$
$577$	25.4625	+	28.2790i	1.06002	+	1.17727i	0.0763852	+	0.997078i	$0.475662\pi$
$578$	−0.203105	+	1.93241i	−0.00844805	+	0.0803778i
$579$	2.74137	−	0.582695i	0.113927	−	0.0242160i
$580$	4.05513	+	1.80546i	0.168380	+	0.0749676i
$581$	30.7848	−	22.3665i	1.27717	−	0.927917i
$582$	16.9946	−	7.56647i	0.704448	−	0.313640i
$583$	−28.2403	+	48.9136i	−1.16959	+	2.02580i
$584$	−2.70346	−	4.68253i	−0.111870	−	0.193765i
$585$	−4.69642	−	3.41215i	−0.194173	−	0.141075i
$586$	−11.3460	−	2.41168i	−0.468701	−	0.0996254i
$587$	−0.183523	+	0.564824i	−0.00757479	+	0.0233128i	−0.954772	−	0.297337i	$-0.903901\pi$
$587$	−0.183523	+	0.564824i	−0.00757479	+	0.0233128i	0.947198	+	0.320650i	$0.103901\pi$
$588$	1.70156			0.0701711
$589$	23.3069	+	4.47801i	0.960344	+	0.184513i
$590$	11.5960			0.477402
$591$	3.85588	−	11.8672i	0.158610	−	0.488150i
$592$	2.40096	+	0.510340i	0.0986788	+	0.0209748i
$593$	23.1309	+	16.8056i	0.949871	+	0.690121i	0.950776	−	0.309878i	$-0.100288\pi$
$593$	23.1309	+	16.8056i	0.949871	+	0.690121i	−0.000905676		1.00000i	$0.500288\pi$
$594$	−2.44646	−	4.23740i	−0.100380	−	0.173862i
$595$	−6.41939	+	11.1187i	−0.263169	+	0.455822i
$596$	15.5975	−	6.94447i	0.638900	−	0.284456i
$597$	−1.50591	+	1.09411i	−0.0616327	+	0.0447788i
$598$	4.36030	+	1.94133i	0.178306	+	0.0793870i
$599$	36.0099	−	7.65414i	1.47132	−	0.312740i	0.598637	−	0.801020i	$-0.295709\pi$
$599$	36.0099	−	7.65414i	1.47132	−	0.312740i	0.872687	+	0.488280i	$0.162376\pi$
$600$	−0.104528	+	0.994522i	−0.00426736	+	0.0406012i
$601$	18.1413	+	20.1479i	0.739998	+	0.821851i	0.989196	−	0.146602i	$-0.0468336\pi$
$601$	18.1413	+	20.1479i	0.739998	+	0.821851i	−0.249198	+	0.968453i	$0.580167\pi$
$602$	12.3440	−	13.7094i	0.503103	−	0.558753i
$603$	1.54305	+	14.6811i	0.0628379	+	0.597863i
$604$	1.13826	+	3.50320i	0.0463151	+	0.142543i
$605$	−3.99889	−	12.3073i	−0.162578	−	0.500364i
$606$	1.41338	+	13.4474i	0.0574146	+	0.546264i
$607$	−8.63941	+	9.59504i	−0.350663	+	0.389451i	−0.892511	−	0.451026i	$-0.851058\pi$
$607$	−8.63941	+	9.59504i	−0.350663	+	0.389451i	0.541848	+	0.840477i	$0.317725\pi$
$608$	−2.85224	−	3.16773i	−0.115674	−	0.128469i
$609$	1.36870	−	13.0223i	0.0554624	−	0.527690i
$610$	−3.61235	+	0.767828i	−0.146260	+	0.0310885i
$611$	22.5715	+	10.0495i	0.913147	+	0.406559i
$612$	3.52114	−	2.55825i	0.142333	−	0.103411i
$613$	−26.7628	+	11.9156i	−1.08094	+	0.481265i	−0.868388	−	0.495885i	$-0.834844\pi$
$613$	−26.7628	+	11.9156i	−1.08094	+	0.481265i	−0.212551	+	0.977150i	$0.568177\pi$
$614$	−14.4010	+	24.9432i	−0.581176	+	1.00663i
$615$	−1.72324	−	2.98473i	−0.0694876	−	0.120356i
$616$	−11.6768	−	8.48371i	−0.470472	−	0.341818i
$617$	9.97659	+	2.12059i	0.401643	+	0.0853718i	0.404304	−	0.914625i	$-0.367514\pi$
$617$	9.97659	+	2.12059i	0.401643	+	0.0853718i	−0.00266139	+	0.999996i	$0.500847\pi$
$618$	0.329148	−	1.01301i	0.0132403	−	0.0407493i
$619$	13.1417			0.528208			0.264104	−	0.964494i	$-0.414924\pi$
$619$	13.1417			0.528208			0.264104	+	0.964494i	$0.414924\pi$
$620$	2.87795	+	4.76628i	0.115581	+	0.191418i
$621$	−0.822199			−0.0329937
$622$	5.26812	−	16.2136i	0.211232	−	0.650106i
$623$	−47.4104	−	10.0774i	−1.89946	−	0.403743i
$624$	4.69642	+	3.41215i	0.188007	+	0.136595i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.14184	−	3.70978i	0.0856053	−	0.148273i
$627$	−19.0535	+	8.48314i	−0.760922	+	0.338784i
$628$	13.9097	−	10.1060i	0.555056	−	0.403272i
$629$	9.75968	+	4.34529i	0.389144	+	0.173258i
$630$	2.88538	−	0.613306i	0.114956	−	0.0244347i
$631$	−4.56362	+	43.4199i	−0.181675	+	1.72852i	0.401228	+	0.915978i	$0.368583\pi$
$631$	−4.56362	+	43.4199i	−0.181675	+	1.72852i	−0.582903	+	0.812542i	$0.698083\pi$
$632$	2.68021	+	2.97668i	0.106613	+	0.118406i
$633$	6.07535	−	6.74736i	0.241473	−	0.268183i
$634$	1.73011	+	16.4609i	0.0687115	+	0.653746i
$635$	1.40833	+	4.33439i	0.0558878	+	0.172005i
$636$	3.56708	+	10.9784i	0.141444	+	0.435320i
$637$	1.03250	+	9.82360i	0.0409092	+	0.389225i
$638$	−14.5330	+	16.1405i	−0.575365	+	0.639008i
$639$	−3.64435	−	4.04746i	−0.144168	−	0.160115i
$640$	0.104528	−	0.994522i	0.00413185	−	0.0393119i
$641$	−19.4373	+	4.13152i	−0.767727	+	0.163185i	−0.575096	−	0.818086i	$-0.695035\pi$
$641$	−19.4373	+	4.13152i	−0.767727	+	0.163185i	−0.192631	+	0.981271i	$0.561702\pi$
$642$	3.33028	+	1.48273i	0.131436	+	0.0585189i
$643$	30.1948	−	21.9378i	1.19077	−	0.865143i	0.197422	−	0.980319i	$-0.436743\pi$
$643$	30.1948	−	21.9378i	1.19077	−	0.865143i	0.993345	+	0.115176i	$0.0367432\pi$
$644$	−2.21567	+	0.986481i	−0.0873097	+	0.0388728i
$645$	3.12691	−	5.41597i	0.123122	−	0.213254i
$646$	−9.27620	−	16.0669i	−0.364967	−	0.632142i
$647$	−36.1053	−	26.2320i	−1.41945	−	1.03129i	−0.991863	−	0.127312i	$-0.959365\pi$
$647$	−36.1053	−	26.2320i	−1.41945	−	1.03129i	−0.427583	−	0.903976i	$-0.640635\pi$
$648$	−0.978148	−	0.207912i	−0.0384253	−	0.00816754i
$649$	−17.5332	+	53.9616i	−0.688237	+	2.11818i
$650$	−5.80510			−0.227695
$651$	10.7482	−	12.4187i	0.421257	−	0.486726i
$652$	−11.9965			−0.469819
$653$	−3.34151	+	10.2841i	−0.130763	+	0.402448i	−0.994907	−	0.100797i	$-0.967861\pi$
$653$	−3.34151	+	10.2841i	−0.130763	+	0.402448i	0.864144	+	0.503245i	$0.167861\pi$
$654$	11.7113	+	2.48931i	0.457947	+	0.0973396i
$655$	1.22555	+	0.890417i	0.0478864	+	0.0347915i
$656$	1.72324	+	2.98473i	0.0672811	+	0.116534i
$657$	−2.70346	+	4.68253i	−0.105472	+	0.182683i
$658$	−11.4696	+	5.10662i	−0.447133	+	0.199077i
$659$	−2.27381	+	1.65202i	−0.0885750	+	0.0643535i	−0.631191	−	0.775627i	$-0.717434\pi$
$659$	−2.27381	+	1.65202i	−0.0885750	+	0.0643535i	0.542616	+	0.839981i	$0.317434\pi$
$660$	−4.46991	−	1.99013i	−0.173991	−	0.0774657i
$661$	−31.7689	+	6.75268i	−1.23567	+	0.262649i	−0.779019	−	0.627000i	$-0.784283\pi$
$661$	−31.7689	+	6.75268i	−1.23567	+	0.262649i	−0.456646	+	0.889649i	$0.650949\pi$
$662$	−1.61875	+	15.4014i	−0.0629146	+	0.598593i
$663$	16.9062	+	18.7762i	0.656582	+	0.729208i
$664$	−8.63160	+	9.58636i	−0.334971	+	0.372023i
$665$	−1.31434	−	12.5051i	−0.0509680	−	0.484928i
$666$	−0.758513	−	2.33446i	−0.0293918	−	0.0904586i
$667$	1.12780	+	3.47102i	0.0436688	+	0.134399i
$668$	−1.69940	−	16.1688i	−0.0657519	−	0.625588i
$669$	−18.3495	+	20.3792i	−0.709434	+	0.787906i
$670$	9.87772	+	10.9703i	0.381609	+	0.423820i
$671$	1.88881	−	17.9708i	0.0729167	−	0.693756i
$672$	−2.88538	+	0.613306i	−0.111306	+	0.0236588i
$673$	32.1686	+	14.3224i	1.24001	+	0.552087i	0.918726	−	0.394897i	$-0.129220\pi$
$673$	32.1686	+	14.3224i	1.24001	+	0.552087i	0.321282	+	0.946984i	$0.395886\pi$
$674$	7.06808	−	5.13526i	0.272252	−	0.197803i
$675$	0.913545	−	0.406737i	0.0351624	−	0.0156553i
$676$	−10.3496	+	17.9260i	−0.398061	+	0.689462i
$677$	−17.5830	−	30.4547i	−0.675770	−	1.17047i	−0.976243	−	0.216678i	$-0.930478\pi$
$677$	−17.5830	−	30.4547i	−0.675770	−	1.17047i	0.300473	−	0.953790i	$-0.402856\pi$
$678$	4.25676	+	3.09272i	0.163480	+	0.118775i
$679$	−53.6764	−	11.4093i	−2.05991	−	0.437847i
$680$	1.34495	−	4.13934i	0.0515766	−	0.158737i
$681$	−25.2943			−0.969280
$682$	−26.5311	+	6.18576i	−1.01593	+	0.236865i
$683$	13.2917			0.508593			0.254297	−	0.967126i	$-0.418156\pi$
$683$	13.2917			0.508593			0.254297	+	0.967126i	$0.418156\pi$
$684$	−1.31722	+	4.05398i	−0.0503651	+	0.155008i
$685$	−11.9385	−	2.53760i	−0.456145	−	0.0969567i
$686$	12.6446	+	9.18682i	0.482772	+	0.350755i
$687$	7.98981	+	13.8388i	0.304830	+	0.527981i
$688$	−3.12691	+	5.41597i	−0.119212	+	0.206482i
$689$	−61.2168	+	27.2555i	−2.33217	+	1.03835i
$690$	−0.665173	+	0.483276i	−0.0253227	+	0.0183980i
$691$	22.8208	+	10.1605i	0.868144	+	0.386523i	0.791961	−	0.610571i	$-0.209060\pi$
$691$	22.8208	+	10.1605i	0.868144	+	0.386523i	0.0761825	+	0.997094i	$0.475727\pi$
$692$	22.9186	−	4.87150i	0.871235	−	0.185187i
$693$	−1.50869	+	14.3543i	−0.0573106	+	0.545274i
$694$	13.1030	+	14.5524i	0.497385	+	0.552402i
$695$	9.52774	−	10.5816i	0.361408	−	0.401384i
$696$	0.463991	+	4.41457i	0.0175875	+	0.167334i
$697$	4.63535	+	14.2661i	0.175576	+	0.540369i
$698$	0.985361	+	3.03263i	0.0372965	+	0.114787i
$699$	−2.44480	−	23.2607i	−0.0924708	−	0.879801i
$700$	1.97383	−	2.19216i	0.0746037	−	0.0828558i
$701$	21.7392	+	24.1438i	0.821078	+	0.911899i	0.997373	−	0.0724382i	$-0.0230780\pi$
$701$	21.7392	+	24.1438i	0.821078	+	0.911899i	−0.176295	+	0.984337i	$0.556411\pi$
$702$	0.606798	−	5.77330i	0.0229021	−	0.217899i
$703$	−10.2343	+	2.17538i	−0.385996	+	0.0820459i
$704$	4.46991	+	1.99013i	0.168466	+	0.0750059i
$705$	−3.44333	+	2.50173i	−0.129683	+	0.0942205i
$706$	−20.4256	+	9.09405i	−0.768726	+	0.342259i
$707$	19.9431	−	34.5425i	0.750038	−	1.29910i
$708$	5.79802	+	10.0425i	0.217903	+	0.377419i
$709$	19.3197	+	14.0366i	0.725568	+	0.527156i	0.888158	−	0.459537i	$-0.151985\pi$
$709$	19.3197	+	14.0366i	0.725568	+	0.527156i	−0.162590	+	0.986694i	$0.551985\pi$
$710$	−5.32738	−	1.13237i	−0.199933	−	0.0424971i
$711$	1.23777	−	3.80947i	0.0464200	−	0.142866i
$712$	16.4313			0.615788
$713$	−1.32893	+	4.38067i	−0.0497689	+	0.164057i
$714$	−12.8388			−0.480479
$715$	8.77729	−	27.0137i	0.328252	−	1.01026i
$716$	−12.1860	−	2.59022i	−0.455413	−	0.0968010i
$717$	15.3351	+	11.1416i	0.572701	+	0.416092i
$718$	2.26354	+	3.92056i	0.0844744	+	0.146314i
$719$	−3.98185	+	6.89677i	−0.148498	+	0.257206i	−0.930673	−	0.365853i	$-0.880777\pi$
$719$	−3.98185	+	6.89677i	−0.148498	+	0.257206i	0.782175	+	0.623059i	$0.214111\pi$
$720$	−0.913545	+	0.406737i	−0.0340458	+	0.0151582i
$721$	−2.54194	+	1.84682i	−0.0946667	+	0.0687794i
$722$	−0.758420	−	0.337670i	−0.0282255	−	0.0125668i
$723$	2.54575	−	0.541116i	0.0946775	−	0.0201243i
$724$	0.256898	−	2.44422i	0.00954753	−	0.0908387i
$725$	−2.97020	−	3.29874i	−0.110310	−	0.122512i
$726$	8.65902	−	9.61681i	0.321366	−	0.356913i
$727$	−4.67534	−	44.4829i	−0.173399	−	1.64978i	−0.642245	−	0.766499i	$-0.721997\pi$
$727$	−4.67534	−	44.4829i	−0.173399	−	1.64978i	0.468846	−	0.883280i	$-0.344670\pi$
$728$	−5.29164	−	16.2860i	−0.196121	−	0.603599i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.565177	+	5.37730i	0.0209181	+	0.199023i
$731$	−18.2130	+	20.2276i	−0.673633	+	0.748145i
$732$	−2.47113	−	2.74447i	−0.0913357	−	0.101439i
$733$	0.849497	−	8.08242i	0.0313769	−	0.298531i	−0.967568	−	0.252610i	$-0.918711\pi$
$733$	0.849497	−	8.08242i	0.0313769	−	0.298531i	0.998945	−	0.0459211i	$-0.0146223\pi$
$734$	−14.1943	+	3.01710i	−0.523923	+	0.111363i
$735$	−1.55445	−	0.692086i	−0.0573368	−	0.0255280i
$736$	0.665173	−	0.483276i	0.0245186	−	0.0178138i
$737$	−65.9848	+	29.3783i	−2.43058	+	1.08217i
$738$	1.72324	−	2.98473i	0.0634332	−	0.109870i
$739$	19.0488	+	32.9936i	0.700723	+	1.21369i	0.968213	+	0.250127i	$0.0804725\pi$
$739$	19.0488	+	32.9936i	0.700723	+	1.21369i	−0.267490	+	0.963561i	$0.586194\pi$
$740$	−1.98581	−	1.44278i	−0.0729999	−	0.0530375i
$741$	−24.2041	−	5.14474i	−0.889160	−	0.188997i
$742$	10.5223	−	32.3844i	0.386287	−	1.18887i
$743$	−10.2168			−0.374818			−0.187409	−	0.982282i	$-0.560009\pi$
$743$	−10.2168			−0.374818			−0.187409	+	0.982282i	$0.560009\pi$
$744$	−2.68875	+	4.87551i	−0.0985743	+	0.178745i
$745$	−17.0736			−0.625529
$746$	7.17646	−	22.0869i	0.262749	−	0.808658i
$747$	12.6178	+	2.68200i	0.461662	+	0.0981293i
$748$	17.2286	+	12.5173i	0.629942	+	0.457679i
$749$	−5.37673	−	9.31278i	−0.196462	−	0.340281i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	48.4279	−	21.5615i	1.76716	−	0.786790i	0.780258	−	0.625458i	$-0.215088\pi$
$751$	48.4279	−	21.5615i	1.76716	−	0.786790i	0.986900	−	0.161332i	$-0.0515789\pi$
$752$	3.44333	−	2.50173i	0.125565	−	0.0912286i
$753$	10.8197	+	4.81724i	0.394292	+	0.175550i
$754$	−25.2051	+	5.35751i	−0.917916	+	0.195109i
$755$	0.385029	−	3.66331i	0.0140126	−	0.133321i
$756$	1.97383	+	2.19216i	0.0717874	+	0.0797280i
$757$	25.9239	−	28.7914i	0.942219	−	1.04644i	−0.0566262	−	0.998395i	$-0.518034\pi$
$757$	25.9239	−	28.7914i	0.942219	−	1.04644i	0.998845	−	0.0480447i	$-0.0152990\pi$
$758$	−0.645351	−	6.14010i	−0.0234402	−	0.223019i
$759$	−1.24316	−	3.82606i	−0.0451239	−	0.138877i
$760$	1.31722	+	4.05398i	0.0477805	+	0.147053i
$761$	3.21951	+	30.6316i	0.116707	+	1.11040i	0.883478	+	0.468474i	$0.155196\pi$
$761$	3.21951	+	30.6316i	0.116707	+	1.11040i	−0.766770	+	0.641922i	$0.778137\pi$
$762$	−3.04953	+	3.38684i	−0.110473	+	0.122692i
$763$	−23.6325	−	26.2465i	−0.855552	−	0.950187i
$764$	2.36657	−	22.5164i	0.0856194	−	0.814614i
$765$	−4.25725	+	0.904907i	−0.153921	+	0.0327170i
$766$	10.4042	+	4.63225i	0.375919	+	0.167370i
$767$	−54.4600	+	39.5675i	−1.96643	+	1.42870i
$768$	0.913545	−	0.406737i	0.0329647	−	0.0146768i
$769$	1.52821	−	2.64694i	0.0551087	−	0.0954510i	−0.837155	−	0.546966i	$-0.815783\pi$
$769$	1.52821	−	2.64694i	0.0551087	−	0.0954510i	0.892264	+	0.451515i	$0.149116\pi$
$770$	7.21667	+	12.4996i	0.260071	+	0.450456i
$771$	−4.17448	−	3.03294i	−0.150340	−	0.109229i
$772$	2.74137	+	0.582695i	0.0986639	+	0.0209717i
$773$	2.87845	−	8.85894i	0.103530	−	0.318634i	−0.885852	−	0.463967i	$-0.846425\pi$
$773$	2.87845	−	8.85894i	0.103530	−	0.318634i	0.989383	+	0.145333i	$0.0464255\pi$
$774$	6.25383			0.224789
$775$	−0.690513	−	5.52478i	−0.0248039	−	0.198456i
$776$	18.6029			0.667805
$777$	−2.23749	+	6.88629i	−0.0802695	+	0.247044i
$778$	1.60364	+	0.340864i	0.0574932	+	0.0122206i
$779$	−11.8852	−	8.63513i	−0.425833	−	0.309386i
$780$	−2.90255	−	5.02736i	−0.103928	−	0.180009i
$781$	13.3244	−	23.0785i	0.476784	−	0.825815i
$782$	3.26913	−	1.45551i	0.116904	−	0.0520489i
$783$	3.59114	−	2.60912i	0.128337	−	0.0932422i
$784$	1.55445	+	0.692086i	0.0555161	+	0.0247174i
$785$	−16.8176	+	3.57469i	−0.600245	+	0.127586i
$786$	−0.158347	+	1.50657i	−0.00564805	+	0.0537376i
$787$	6.20669	+	6.89323i	0.221245	+	0.245717i	0.843541	−	0.537065i	$-0.180467\pi$
$787$	6.20669	+	6.89323i	0.221245	+	0.245717i	−0.622297	+	0.782782i	$0.713800\pi$
$788$	8.34934	−	9.27288i	0.297433	−	0.330333i
$789$	0.605750	+	5.76333i	0.0215653	+	0.205180i
$790$	−1.23777	−	3.80947i	−0.0440379	−	0.135535i
$791$	−4.79626	−	14.7614i	−0.170535	−	0.524854i
$792$	−0.511450	−	4.86612i	−0.0181736	−	0.172910i
$793$	14.3452	−	15.9319i	0.509412	−	0.565759i
$794$	−24.3057	−	26.9943i	−0.862578	−	0.957990i
$795$	1.20661	−	11.4801i	0.0427939	−	0.407157i
$796$	−1.82073	+	0.387008i	−0.0645340	+	0.0137171i
$797$	−19.9191	−	8.86857i	−0.705572	−	0.314141i	0.0223988	−	0.999749i	$-0.492870\pi$
$797$	−19.9191	−	8.86857i	−0.705572	−	0.314141i	−0.727971	+	0.685608i	$0.759536\pi$
$798$	10.1726	−	7.39081i	0.360106	−	0.261632i
$799$	16.9230	−	7.53459i	0.598692	−	0.266555i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−8.21563	−	14.2299i	−0.290285	−	0.502789i
$802$	−16.9291	−	12.2997i	−0.597789	−	0.434319i
$803$	−25.8775	−	5.50044i	−0.913198	−	0.194106i
$804$	−4.56171	+	14.0395i	−0.160879	+	0.495135i
$805$	2.42536			0.0854825
$806$	−29.7793	−	12.5645i	−1.04893	−	0.442565i
$807$	−17.2063			−0.605691
$808$	−4.17837	+	12.8597i	−0.146994	+	0.452402i
$809$	−10.6121	−	2.25568i	−0.373103	−	0.0793054i	0.0175440	−	0.999846i	$-0.494415\pi$
$809$	−10.6121	−	2.25568i	−0.373103	−	0.0793054i	−0.390647	+	0.920541i	$0.627749\pi$
$810$	0.809017	+	0.587785i	0.0284260	+	0.0206527i
$811$	−2.81237	−	4.87117i	−0.0987557	−	0.171050i	0.812414	−	0.583081i	$-0.198153\pi$
$811$	−2.81237	−	4.87117i	−0.0987557	−	0.171050i	−0.911170	+	0.412031i	$0.864820\pi$
$812$	6.54701	−	11.3398i	0.229755	−	0.397947i
$813$	−11.2748	+	5.01986i	−0.395424	+	0.176054i
$814$	9.71642	−	7.05939i	0.340560	−	0.247432i
$815$	10.9593	+	4.87942i	0.383889	+	0.170918i
$816$	4.25725	−	0.904907i	0.149034	−	0.0316781i
$817$	2.78648	−	26.5116i	0.0974865	−	0.927522i
$818$	9.95539	+	11.0566i	0.348082	+	0.386584i
$819$	−11.4583	+	12.7257i	−0.400384	+	0.444672i
$820$	−0.360255	−	3.42759i	−0.0125806	−	0.119697i
$821$	−4.10594	−	12.6368i	−0.143298	−	0.441027i	0.853490	−	0.521109i	$-0.174482\pi$
$821$	−4.10594	−	12.6368i	−0.143298	−	0.441027i	−0.996788	+	0.0800826i	$0.974482\pi$
$822$	−3.77161	−	11.6078i	−0.131550	−	0.404869i
$823$	4.98212	+	47.4017i	0.173666	+	1.65232i	0.640489	+	0.767967i	$0.278732\pi$
$823$	4.98212	+	47.4017i	0.173666	+	1.65232i	−0.466823	+	0.884351i	$0.654602\pi$
$824$	0.712721	−	0.791557i	0.0248288	−	0.0275752i
$825$	3.27400	+	3.63615i	0.113986	+	0.126595i
$826$	3.57555	−	34.0191i	0.124409	−	1.18368i
$827$	11.5239	−	2.44948i	0.400725	−	0.0851767i	−0.00314069	−	0.999995i	$-0.501000\pi$
$827$	11.5239	−	2.44948i	0.400725	−	0.0851767i	0.403865	+	0.914818i	$0.367666\pi$
$828$	−0.751116	−	0.334418i	−0.0261031	−	0.0116218i
$829$	41.9221	−	30.4582i	1.45601	−	1.05786i	0.471635	−	0.881794i	$-0.343664\pi$
$829$	41.9221	−	30.4582i	1.45601	−	1.05786i	0.984379	−	0.176062i	$-0.0563359\pi$
$830$	11.7845	−	5.24679i	0.409045	−	0.182119i
$831$	−3.78528	+	6.55630i	−0.131310	+	0.227436i
$832$	2.90255	+	5.02736i	0.100628	+	0.174292i
$833$	5.99141	+	4.35302i	0.207590	+	0.150823i
$834$	13.9278	+	2.96045i	0.482281	+	0.102512i
$835$	−5.02394	+	15.4621i	−0.173861	+	0.535088i
$836$	−20.8566			−0.721341
$837$	5.56669	−	0.109233i	0.192413	−	0.00377565i
$838$	−12.7221			−0.439477
$839$	1.19326	−	3.67246i	0.0411958	−	0.126788i	−0.928343	−	0.371724i	$-0.878767\pi$
$839$	1.19326	−	3.67246i	0.0411958	−	0.126788i	0.969539	+	0.244936i	$0.0787669\pi$
$840$	2.88538	+	0.613306i	0.0995550	+	0.0211611i
$841$	7.52082	+	5.46419i	0.259339	+	0.188420i
$842$	11.6860	+	20.2408i	0.402728	+	0.697545i
$843$	−9.88648	+	17.1239i	−0.340508	+	0.589778i
$844$	8.29450	−	3.69295i	0.285509	−	0.127117i
$845$	16.7460	−	12.1667i	0.576080	−	0.418546i
$846$	−3.88823	−	1.73115i	−0.133680	−	0.0595182i
$847$	−37.3388	+	7.93661i	−1.28298	+	0.272705i
$848$	−1.20661	+	11.4801i	−0.0414350	+	0.394228i
$849$	−17.3271	−	19.2437i	−0.594664	−	0.660442i
$850$	−2.91230	+	3.23444i	−0.0998910	+	0.110940i
$851$	−0.210956	−	2.00711i	−0.00723148	−	0.0688029i
$852$	−1.68303	−	5.17983i	−0.0576596	−	0.177458i
$853$	−7.38492	−	22.7285i	−0.252855	−	0.778207i	−0.994245	−	0.107133i	$-0.965833\pi$
$853$	−7.38492	−	22.7285i	−0.252855	−	0.778207i	0.741390	−	0.671075i	$-0.234167\pi$
$854$	1.13872	+	10.8342i	0.0389663	+	0.370740i
$855$	2.85224	−	3.16773i	0.0975445	−	0.108334i
$856$	2.43928	+	2.70909i	0.0833727	+	0.0925948i
$857$	3.05621	−	29.0779i	0.104398	−	0.993282i	−0.809440	−	0.587203i	$-0.800229\pi$
$857$	3.05621	−	29.0779i	0.104398	−	0.993282i	0.913838	−	0.406079i	$-0.133104\pi$
$858$	27.7832	−	5.90550i	0.948503	−	0.201611i
$859$	−43.4148	−	19.3295i	−1.48129	−	0.659514i	−0.502540	−	0.864554i	$-0.667601\pi$
$859$	−43.4148	−	19.3295i	−1.48129	−	0.659514i	−0.978754	+	0.205040i	$0.934268\pi$
$860$	5.05945	−	3.67591i	0.172526	−	0.125347i
$861$	−9.28760	+	4.13511i	−0.316521	+	0.140924i
$862$	8.88303	−	15.3859i	0.302557	−	0.524044i
$863$	−13.9438	−	24.1514i	−0.474653	−	0.822123i	0.524926	−	0.851148i	$-0.324093\pi$
$863$	−13.9438	−	24.1514i	−0.474653	−	0.822123i	−0.999579	+	0.0290249i	$0.990760\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−22.9186	−	4.87150i	−0.779256	−	0.165636i
$866$	5.56646	−	17.1318i	0.189156	−	0.582163i
$867$	1.94306			0.0659897
$868$	14.8701	−	6.97333i	0.504725	−	0.236690i
$869$	19.5987			0.664839
$870$	1.37169	−	4.22164i	0.0465047	−	0.143127i
$871$	−83.8223	−	17.8170i	−2.84021	−	0.603706i
$872$	9.68628	+	7.03750i	0.328019	+	0.238320i
$873$	−9.30144	−	16.1106i	−0.314806	−	0.545260i
$874$	−1.75235	+	3.03517i	−0.0592743	+	0.102666i
$875$	−2.69481	+	1.19981i	−0.0911013	+	0.0405609i
$876$	−4.37429	+	3.17811i	−0.147794	+	0.107378i
$877$	−7.37151	−	3.28201i	−0.248918	−	0.110825i	0.278485	−	0.960440i	$-0.410168\pi$
$877$	−7.37151	−	3.28201i	−0.248918	−	0.110825i	−0.527403	+	0.849615i	$0.676834\pi$
$878$	−19.5736	+	4.16050i	−0.660577	+	0.140410i
$879$	−1.21248	+	11.5360i	−0.0408959	+	0.389099i
$880$	−3.27400	−	3.63615i	−0.110367	−	0.122575i
$881$	5.66619	−	6.29294i	0.190899	−	0.212015i	−0.640096	−	0.768295i	$-0.721105\pi$
$881$	5.66619	−	6.29294i	0.190899	−	0.212015i	0.830995	+	0.556281i	$0.187772\pi$
$882$	−0.177861	−	1.69224i	−0.00598890	−	0.0569806i
$883$	10.4646	+	32.2068i	0.352163	+	1.08385i	0.957636	+	0.287980i	$0.0929837\pi$
$883$	10.4646	+	32.2068i	0.352163	+	1.08385i	−0.605474	+	0.795865i	$0.707016\pi$
$884$	7.80759	+	24.0293i	0.262598	+	0.808193i
$885$	−1.21212	−	11.5325i	−0.0407449	−	0.387661i
$886$	3.15839	−	3.50774i	0.106108	−	0.117845i
$887$	−8.01978	−	8.90687i	−0.269278	−	0.299064i	0.593306	−	0.804977i	$-0.297822\pi$
$887$	−8.01978	−	8.90687i	−0.269278	−	0.299064i	−0.862584	+	0.505913i	$0.831156\pi$
$888$	0.256575	−	2.44115i	0.00861011	−	0.0819197i
$889$	13.1500	−	2.79511i	0.441036	−	0.0937450i
$890$	−15.0107	−	6.68320i	−0.503160	−	0.224021i
$891$	−3.95846	+	2.87599i	−0.132613	+	0.0963492i
$892$	−25.0521	+	11.1539i	−0.838807	+	0.373461i
$893$	−9.07124	+	15.7118i	−0.303557	+	0.525777i
$894$	−8.53681	−	14.7862i	−0.285514	−	0.494524i
$895$	10.0789	+	7.32278i	0.336902	+	0.244774i
$896$	−2.88538	−	0.613306i	−0.0963938	−	0.0204891i
$897$	1.47492	−	4.53934i	0.0492462	−	0.151564i
$898$	−17.1805			−0.573322
$899$	−8.09694	−	23.3507i	−0.270048	−	0.778790i
$900$	1.00000			0.0333333
$901$	−15.5252	+	47.7818i	−0.517221	+	1.59184i
$902$	16.4948	+	3.50608i	0.549218	+	0.116740i
$903$	−14.9246	−	10.8433i	−0.496659	−	0.360844i
$904$	2.63082	+	4.55672i	0.0874999	+	0.151554i
$905$	−1.22884	+	2.12842i	−0.0408481	+	0.0707509i
$906$	3.36503	−	1.49821i	0.111796	−	0.0497747i
$907$	−11.9040	+	8.64874i	−0.395265	+	0.287177i	−0.767609	−	0.640918i	$-0.778554\pi$
$907$	−11.9040	+	8.64874i	−0.395265	+	0.287177i	0.372345	+	0.928094i	$0.378554\pi$
$908$	−23.1075	−	10.2881i	−0.766849	−	0.341423i
$909$	13.2260	−	2.81127i	0.438679	−	0.0932441i
$910$	−1.78996	+	17.0303i	−0.0593365	+	0.564549i
$911$	10.9192	+	12.1270i	0.361769	+	0.401785i	0.896361	−	0.443325i	$-0.146201\pi$
$911$	10.9192	+	12.1270i	0.361769	+	0.401785i	−0.534592	+	0.845110i	$0.679535\pi$
$912$	−2.85224	+	3.16773i	−0.0944471	+	0.104894i
$913$	6.59756	+	62.7716i	0.218347	+	2.07744i
$914$	−7.20525	−	22.1755i	−0.238329	−	0.733500i
$915$	1.14122	+	3.51230i	0.0377274	+	0.116113i
$916$	1.67032	+	15.8921i	0.0551891	+	0.525089i
$917$	2.99009	−	3.32083i	0.0987415	−	0.109664i
$918$	−2.91230	−	3.23444i	−0.0961202	−	0.106752i
$919$	0.123789	−	1.17777i	0.00408342	−	0.0388512i	−0.992290	−	0.123934i	$-0.960449\pi$
$919$	0.123789	−	1.17777i	0.00408342	−	0.0388512i	0.996374	+	0.0850829i	$0.0271155\pi$
$920$	−0.804232	+	0.170945i	−0.0265147	+	0.00563588i
$921$	26.3119	+	11.7148i	0.867007	+	0.386016i
$922$	9.12865	−	6.63235i	0.300636	−	0.218425i
$923$	28.8834	−	12.8597i	0.950710	−	0.423283i
$924$	−7.21667	+	12.4996i	−0.237411	+	0.411208i
$925$	1.22730	+	2.12574i	0.0403533	+	0.0698940i
$926$	−16.6735	−	12.1140i	−0.547925	−	0.398090i
$927$	−1.04187	−	0.221456i	−0.0342195	−	0.00727357i
$928$	−1.37169	+	4.22164i	−0.0450280	+	0.138582i
$929$	43.7759			1.43624			0.718121	−	0.695919i	$-0.245003\pi$
$929$	43.7759			1.43624			0.718121	+	0.695919i	$0.245003\pi$
$930$	4.43934	−	3.36039i	0.145572	−	0.110192i
$931$	−7.25307			−0.237710
$932$	7.22755	−	22.2441i	0.236746	−	0.728630i
$933$	−16.6754	−	3.54448i	−0.545930	−	0.116041i
$934$	23.0630	+	16.7563i	0.754645	+	0.548282i
$935$	−10.6479	−	18.4427i	−0.348223	−	0.603140i
$936$	2.90255	−	5.02736i	0.0948728	−	0.164325i
$937$	41.2086	−	18.3473i	1.34623	−	0.599379i	0.398121	−	0.917333i	$-0.369663\pi$
$937$	41.2086	−	18.3473i	1.34623	−	0.599379i	0.948106	+	0.317954i	$0.102996\pi$
$938$	35.2291	−	25.5955i	1.15027	−	0.835721i
$939$	−3.91334	−	1.74233i	−0.127707	−	0.0568589i
$940$	−4.16319	+	0.884912i	−0.135788	+	0.0288627i
$941$	−3.95397	+	37.6195i	−0.128896	+	1.22636i	0.718549	+	0.695476i	$0.244807\pi$
$941$	−3.95397	+	37.6195i	−0.128896	+	1.22636i	−0.847445	+	0.530884i	$0.821860\pi$
$942$	−11.5046	−	12.7771i	−0.374839	−	0.416301i
$943$	1.89611	−	2.10584i	0.0617457	−	0.0685756i
$944$	1.21212	+	11.5325i	0.0394510	+	0.375352i
$945$	−0.911551	−	2.80546i	−0.0296527	−	0.0912618i
$946$	9.45576	+	29.1018i	0.307433	+	0.946183i
$947$	−1.24343	−	11.8305i	−0.0404061	−	0.384438i	−0.995972	−	0.0896617i	$-0.971421\pi$
$947$	−1.24343	−	11.8305i	−0.0404061	−	0.384438i	0.955566	−	0.294777i	$-0.0952453\pi$
$948$	2.68021	−	2.97668i	0.0870492	−	0.0966779i
$949$	−21.0025	−	23.3256i	−0.681770	−	0.757182i
$950$	0.445564	−	4.23925i	0.0144560	−	0.137540i
$951$	16.1899	−	3.44127i	0.524993	−	0.111591i
$952$	−11.7288	−	5.22200i	−0.380133	−	0.169246i
$953$	−10.1174	+	7.35070i	−0.327734	+	0.238113i	−0.739468	−	0.673191i	$-0.764923\pi$
$953$	−10.1174	+	7.35070i	−0.327734	+	0.238113i	0.411735	+	0.911304i	$0.364923\pi$
$954$	10.5453	−	4.69509i	0.341418	−	0.152009i
$955$	−11.3202	+	19.6072i	−0.366313	+	0.634473i
$956$	9.47763	+	16.4157i	0.306529	+	0.530923i
$957$	17.5712	+	12.7662i	0.567995	+	0.412673i
$958$	−4.90985	−	1.04362i	−0.158630	−	0.0337179i
$959$	−11.1256	+	34.2412i	−0.359266	+	1.10571i
$960$	−1.00000			−0.0322749
$961$	8.41554	−	29.8359i	0.271469	−	0.962447i
$962$	14.2492			0.459412
$963$	1.12650	−	3.46702i	0.0363011	−	0.111723i
$964$	2.54575	+	0.541116i	0.0819931	+	0.0174282i
$965$	−2.26736	−	1.64733i	−0.0729889	−	0.0530295i
$966$	1.21268	+	2.10042i	0.0390173	+	0.0675799i
$967$	18.2718	−	31.6477i	0.587581	−	1.01772i	−0.406967	−	0.913443i	$-0.633414\pi$
$967$	18.2718	−	31.6477i	0.587581	−	1.01772i	0.994548	−	0.104277i	$-0.0332529\pi$
$968$	11.8219	−	5.26345i	0.379971	−	0.169174i
$969$	−15.0092	+	10.9048i	−0.482165	+	0.350314i
$970$	−16.9946	−	7.56647i	−0.545663	−	0.242945i
$971$	7.25552	−	1.54221i	0.232841	−	0.0494919i	−0.0900134	−	0.995941i	$-0.528691\pi$
$971$	7.25552	−	1.54221i	0.232841	−	0.0494919i	0.322854	+	0.946449i	$0.395358\pi$
$972$	−0.104528	+	0.994522i	−0.00335275	+	0.0318993i
$973$	−28.1053	−	31.2141i	−0.901015	−	1.00068i
$974$	17.5336	−	19.4730i	0.561812	−	0.623956i
$975$	0.606798	+	5.77330i	0.0194331	+	0.184894i
$976$	−1.14122	−	3.51230i	−0.0365294	−	0.112426i
$977$	−16.7411	−	51.5239i	−0.535596	−	1.64840i	−0.742357	−	0.670004i	$-0.766292\pi$
$977$	−16.7411	−	51.5239i	−0.535596	−	1.64840i	0.206761	−	0.978391i	$-0.433708\pi$
$978$	1.25398	+	11.9308i	0.0400977	+	0.381504i
$979$	53.7961	−	59.7466i	1.71933	−	1.90951i
$980$	−1.13856	−	1.26450i	−0.0363701	−	0.0403931i
$981$	1.25151	−	11.9073i	0.0399576	−	0.380171i
$982$	11.3421	−	2.41084i	0.361942	−	0.0769331i
$983$	12.7125	+	5.65997i	0.405466	+	0.180525i	0.599328	−	0.800504i	$-0.295435\pi$
$983$	12.7125	+	5.65997i	0.405466	+	0.180525i	−0.193862	+	0.981029i	$0.562101\pi$
$984$	2.78826	−	2.02579i	0.0888864	−	0.0645797i
$985$	−11.3991	+	5.07521i	−0.363206	+	0.161710i
$986$	−9.65983	+	16.7313i	−0.307632	+	0.532834i
$987$	6.27754	+	10.8730i	0.199816	+	0.346092i
$988$	−20.0190	−	14.5447i	−0.636889	−	0.462727i
$989$	5.02953	+	1.06906i	0.159930	+	0.0339941i
$990$	−1.51200	+	4.65345i	−0.0480544	+	0.147896i
$991$	−43.4769			−1.38109			−0.690544	−	0.723290i	$-0.742629\pi$
$991$	−43.4769			−1.38109			−0.690544	+	0.723290i	$0.742629\pi$
$992$	−4.43934	+	3.36039i	−0.140949	+	0.106693i
$993$	15.4862			0.491441
$994$	−4.96467	+	15.2797i	−0.157470	+	0.484642i
$995$	1.82073	+	0.387008i	0.0577210	+	0.0122690i
$996$	10.4361	+	7.58226i	0.330680	+	0.240253i
$997$	−24.5905	−	42.5920i	−0.778789	−	1.34890i	−0.932640	−	0.360808i	$-0.882501\pi$
$997$	−24.5905	−	42.5920i	−0.778789	−	1.34890i	0.153851	−	0.988094i	$-0.450832\pi$
$998$	−8.27050	+	14.3249i	−0.261798	+	0.453448i
$999$	−2.24239	+	0.998375i	−0.0709460	+	0.0315872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.d.691.2	✓	16
31.7	even	15	inner	930.2.bg.d.751.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.d.691.2	✓	16	1.1	even	1	trivial
930.2.bg.d.751.2	yes	16	31.7	even	15	inner

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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.69481 - 1.19981i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.69481 - 1.19981i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.978148 - 0.207912i) q^{10} +(-0.511450 + 4.86612i) q^{11} +(0.669131 + 0.743145i) q^{12} +(-3.88437 + 4.31403i) q^{13} +(-0.308342 - 2.93368i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(0.454946 + 4.32852i) q^{17} +(0.669131 - 0.743145i) q^{18} +(-2.85224 - 3.16773i) q^{19} +(0.104528 - 0.994522i) q^{20} +(-2.88538 + 0.613306i) q^{21} +(4.46991 + 1.99013i) q^{22} +(0.665173 - 0.483276i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.90255 + 5.02736i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-2.88538 - 0.613306i) q^{28} +(-1.37169 + 4.22164i) q^{29} -1.00000 q^{30} +(-4.43934 + 3.36039i) q^{31} +1.00000 q^{32} +(1.51200 - 4.65345i) q^{33} +(4.25725 + 0.904907i) q^{34} +(2.38647 + 1.73387i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.22730 - 2.12574i) q^{37} +(-3.89408 + 1.73376i) q^{38} +(4.69642 - 3.41215i) q^{39} +(-0.913545 - 0.406737i) q^{40} +(3.37116 - 0.716562i) q^{41} +(-0.308342 + 2.93368i) q^{42} +(4.18463 + 4.64750i) q^{43} +(3.27400 - 3.63615i) q^{44} +(0.104528 + 0.994522i) q^{45} +(-0.254073 - 0.781958i) q^{46} +(-1.31524 - 4.04788i) q^{47} +(-0.104528 - 0.994522i) q^{48} +(1.13856 - 1.26450i) q^{49} +(0.669131 + 0.743145i) q^{50} +(0.454946 - 4.32852i) q^{51} +(5.67824 - 1.20695i) q^{52} +(10.5453 + 4.69509i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-4.46991 + 1.99013i) q^{55} +(-1.47492 + 2.55464i) q^{56} +(2.13130 + 3.69152i) q^{57} +(3.59114 + 2.60912i) q^{58} +(11.3426 + 2.41095i) q^{59} +(-0.309017 + 0.951057i) q^{60} -3.69305 q^{61} +(1.82409 + 5.26048i) q^{62} +2.94984 q^{63} +(0.309017 - 0.951057i) q^{64} +(-5.67824 - 1.20695i) q^{65} +(-3.95846 - 2.87599i) q^{66} +(7.38101 + 12.7843i) q^{67} +(2.17618 - 3.76926i) q^{68} +(-0.751116 + 0.334418i) q^{69} +(2.38647 - 1.73387i) q^{70} +(-4.97553 - 2.21525i) q^{71} +(-0.978148 + 0.207912i) q^{72} +(-0.565177 + 5.37730i) q^{73} +(-1.64245 - 1.82412i) q^{74} +(0.669131 - 0.743145i) q^{75} +(0.445564 + 4.23925i) q^{76} +(4.46015 + 13.7269i) q^{77} +(-1.79387 - 5.52098i) q^{78} +(-0.418690 - 3.98357i) q^{79} +(-0.669131 + 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(0.360255 - 3.42759i) q^{82} +(12.6178 - 2.68200i) q^{83} +(2.69481 + 1.19981i) q^{84} +(-3.52114 + 2.55825i) q^{85} +(5.71316 - 2.54366i) q^{86} +(2.21945 - 3.84419i) q^{87} +(-2.44646 - 4.23740i) q^{88} +(-13.2932 - 9.65806i) q^{89} +(0.978148 + 0.207912i) q^{90} +(-5.29164 + 16.2860i) q^{91} -0.822199 q^{92} +(5.04100 - 2.36397i) q^{93} -4.25619 q^{94} +(1.31722 - 4.05398i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-15.0500 - 10.9345i) q^{97} +(-0.850779 - 1.47359i) q^{98} +(-2.44646 + 4.23740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Introduction

L-functions

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