LMFDB - Embedded newform 418.2.v.b.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	418.13
Dual form			418.2.v.b.193.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.374607 - 0.927184i) q^{2} +(0.411485 + 1.43502i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-0.764836 + 0.406670i) q^{5} +(1.17638 - 0.919089i) q^{6} +(0.622864 + 1.39897i) q^{7} +(0.913545 + 0.406737i) q^{8} +(0.654189 - 0.408783i) q^{9} +O(q^{10})$	\(q+(-0.374607 - 0.927184i) q^{2} +(0.411485 + 1.43502i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-0.764836 + 0.406670i) q^{5} +(1.17638 - 0.919089i) q^{6} +(0.622864 + 1.39897i) q^{7} +(0.913545 + 0.406737i) q^{8} +(0.654189 - 0.408783i) q^{9} +(0.663571 + 0.556802i) q^{10} +(-3.22684 + 0.766497i) q^{11} +(-1.29284 - 0.746424i) q^{12} +(0.130745 + 3.74405i) q^{13} +(1.06378 - 1.10157i) q^{14} +(-0.898297 - 0.930214i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(-2.19537 + 3.51332i) q^{17} +(-0.624080 - 0.453421i) q^{18} +(1.34542 - 4.14606i) q^{19} +(0.267680 - 0.823834i) q^{20} +(-1.75125 + 1.46948i) q^{21} +(1.91948 + 2.70474i) q^{22} +(-1.33370 + 7.56380i) q^{23} +(-0.207764 + 1.47832i) q^{24} +(-2.37637 + 3.52312i) q^{25} +(3.42244 - 1.52377i) q^{26} +(4.18401 + 3.76730i) q^{27} +(-1.41986 - 0.573661i) q^{28} +(-0.135673 - 0.544155i) q^{29} +(-0.525971 + 1.18135i) q^{30} +(4.11917 - 3.70891i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-2.42773 - 4.31517i) q^{33} +(4.07990 + 0.719396i) q^{34} +(-1.04531 - 0.816686i) q^{35} +(-0.186620 + 0.748491i) q^{36} +(-5.53090 + 7.61264i) q^{37} +(-4.34817 + 0.305695i) q^{38} +(-5.31898 + 1.72824i) q^{39} +(-0.864120 + 0.0604252i) q^{40} +(-5.26355 + 1.50930i) q^{41} +(2.01851 + 1.07326i) q^{42} +(11.9919 - 2.11450i) q^{43} +(1.78874 - 2.79292i) q^{44} +(-0.334107 + 0.578691i) q^{45} +(7.51265 - 1.59686i) q^{46} +(-1.79204 - 0.125311i) q^{47} +(1.44850 - 0.361153i) q^{48} +(3.11474 - 3.45927i) q^{49} +(4.15678 + 0.883551i) q^{50} +(-5.94504 - 1.70471i) q^{51} +(-2.69489 - 2.60242i) q^{52} +(5.32263 - 10.0104i) q^{53} +(1.92562 - 5.29060i) q^{54} +(2.15629 - 1.89850i) q^{55} +1.53137i q^{56} +(6.50329 + 0.224654i) q^{57} +(-0.453708 + 0.329638i) q^{58} +(0.144927 + 2.07256i) q^{59} +(1.29236 + 0.0451303i) q^{60} +(-1.08799 - 7.74145i) q^{61} +(-4.98191 - 2.42984i) q^{62} +(0.979347 + 0.660578i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-1.62259 - 2.81041i) q^{65} +(-3.09151 + 3.86744i) q^{66} +(-1.58142 + 1.88467i) q^{67} +(-0.861344 - 4.05230i) q^{68} +(-11.4030 + 1.19850i) q^{69} +(-0.365638 + 1.27513i) q^{70} +(4.77504 + 8.98054i) q^{71} +(0.763898 - 0.107359i) q^{72} +(-0.408207 + 0.275339i) q^{73} +(9.13023 + 2.27642i) q^{74} +(-6.03357 - 1.96043i) q^{75} +(1.91229 + 3.91703i) q^{76} +(-3.08219 - 4.03684i) q^{77} +(3.59492 + 4.28426i) q^{78} +(10.1991 - 13.0543i) q^{79} +(0.379730 + 0.778563i) q^{80} +(-2.66999 + 5.47430i) q^{81} +(3.37116 + 4.31488i) q^{82} +(3.30508 - 15.5492i) q^{83} +(0.238963 - 2.27358i) q^{84} +(0.250332 - 3.57991i) q^{85} +(-6.45277 - 10.3266i) q^{86} +(0.725044 - 0.418605i) q^{87} +(-3.25963 - 0.612244i) q^{88} +(5.09038 + 13.9857i) q^{89} +(0.661712 + 0.0929975i) q^{90} +(-5.15639 + 2.51494i) q^{91} +(-4.29487 - 6.36741i) q^{92} +(7.01733 + 4.38491i) q^{93} +(0.555122 + 1.70849i) q^{94} +(0.657059 + 3.71820i) q^{95} +(-0.877474 - 1.20774i) q^{96} +(-8.65192 + 3.49560i) q^{97} +(-4.37418 - 1.59207i) q^{98} +(-1.79763 + 1.82051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.374607	−	0.927184i	−0.264887	−	0.655618i
$2$	−0.374607	−	0.927184i	−0.264887	−	0.655618i
$3$	0.411485	+	1.43502i	0.237571	+	0.828508i	0.986206	+	0.165525i	$0.0529319\pi$
$3$	0.411485	+	1.43502i	0.237571	+	0.828508i	−0.748635	+	0.662983i	$0.769290\pi$
$4$	−0.719340	+	0.694658i	−0.359670	+	0.347329i
$5$	−0.764836	+	0.406670i	−0.342045	+	0.181869i	−0.631603	−	0.775292i	$-0.717603\pi$
$5$	−0.764836	+	0.406670i	−0.342045	+	0.181869i	0.289558	+	0.957160i	$0.406492\pi$
$6$	1.17638	−	0.919089i	0.480255	−	0.375216i
$7$	0.622864	+	1.39897i	0.235420	+	0.528763i	0.992163	−	0.124950i	$-0.0398771\pi$
$7$	0.622864	+	1.39897i	0.235420	+	0.528763i	−0.756743	+	0.653713i	$0.773210\pi$
$8$	0.913545	+	0.406737i	0.322987	+	0.143803i
$9$	0.654189	−	0.408783i	0.218063	−	0.136261i
$10$	0.663571	+	0.556802i	0.209840	+	0.176076i
$11$	−3.22684	+	0.766497i	−0.972928	+	0.231107i
$11$	−3.22684	+	0.766497i	−0.972928	+	0.231107i
$12$	−1.29284	−	0.746424i	−0.373212	−	0.215474i
$13$	0.130745	+	3.74405i	0.0362622	+	1.03841i	0.872067	+	0.489386i	$0.162779\pi$
$13$	0.130745	+	3.74405i	0.0362622	+	1.03841i	−0.835805	+	0.549026i	$0.814999\pi$
$14$	1.06378	−	1.10157i	0.284307	−	0.294408i
$15$	−0.898297	−	0.930214i	−0.231939	−	0.240180i
$16$	0.0348995	−	0.999391i	0.00872487	−	0.249848i
$17$	−2.19537	+	3.51332i	−0.532455	+	0.852106i	−0.999484	−	0.0321361i	$-0.989769\pi$
$17$	−2.19537	+	3.51332i	−0.532455	+	0.852106i	0.467028	+	0.884242i	$0.345325\pi$
$18$	−0.624080	−	0.453421i	−0.147097	−	0.106872i
$19$	1.34542	−	4.14606i	0.308660	−	0.951173i
$19$	1.34542	−	4.14606i	0.308660	−	0.951173i
$20$	0.267680	−	0.823834i	0.0598550	−	0.184215i
$21$	−1.75125	+	1.46948i	−0.382155	+	0.320666i
$22$	1.91948	+	2.70474i	0.409234	+	0.576652i
$23$	−1.33370	+	7.56380i	−0.278096	+	1.57716i	0.450856	+	0.892597i	$0.351119\pi$
$23$	−1.33370	+	7.56380i	−0.278096	+	1.57716i	−0.728952	+	0.684565i	$0.759992\pi$
$24$	−0.207764	+	1.47832i	−0.0424097	+	0.301761i
$25$	−2.37637	+	3.52312i	−0.475274	+	0.704623i
$26$	3.42244	−	1.52377i	0.671197	−	0.298836i
$27$	4.18401	+	3.76730i	0.805212	+	0.725016i
$28$	−1.41986	−	0.573661i	−0.268328	−	0.108412i
$29$	−0.135673	−	0.544155i	−0.0251939	−	0.101047i	0.956383	−	0.292117i	$-0.0943597\pi$
$29$	−0.135673	−	0.544155i	−0.0251939	−	0.101047i	−0.981576	+	0.191070i	$0.938804\pi$
$30$	−0.525971	+	1.18135i	−0.0960288	+	0.215684i
$31$	4.11917	−	3.70891i	0.739824	−	0.666140i	−0.210433	−	0.977608i	$-0.567487\pi$
$31$	4.11917	−	3.70891i	0.739824	−	0.666140i	0.950257	+	0.311468i	$0.100821\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−2.42773	−	4.31517i	−0.422614	−	0.751174i
$34$	4.07990	+	0.719396i	0.699697	+	0.123375i
$35$	−1.04531	−	0.816686i	−0.176690	−	0.138045i
$36$	−0.186620	+	0.748491i	−0.0311033	+	0.124749i
$37$	−5.53090	+	7.61264i	−0.909275	+	1.25151i	0.0581385	+	0.998309i	$0.481484\pi$
$37$	−5.53090	+	7.61264i	−0.909275	+	1.25151i	−0.967414	+	0.253201i	$0.918516\pi$
$38$	−4.34817	+	0.305695i	−0.705366	+	0.0495902i
$39$	−5.31898	+	1.72824i	−0.851718	+	0.276740i
$40$	−0.864120	+	0.0604252i	−0.136629	+	0.00955406i
$41$	−5.26355	+	1.50930i	−0.822028	+	0.235713i	−0.660184	−	0.751104i	$-0.729522\pi$
$41$	−5.26355	+	1.50930i	−0.822028	+	0.235713i	−0.161844	+	0.986816i	$0.551744\pi$
$42$	2.01851	+	1.07326i	0.311462	+	0.165607i
$43$	11.9919	−	2.11450i	1.82875	−	0.322457i	0.849883	−	0.526971i	$-0.176672\pi$
$43$	11.9919	−	2.11450i	1.82875	−	0.322457i	0.978864	+	0.204513i	$0.0655611\pi$
$44$	1.78874	−	2.79292i	0.269663	−	0.421049i
$45$	−0.334107	+	0.578691i	−0.0498058	+	0.0862662i
$46$	7.51265	−	1.59686i	1.10768	−	0.235445i
$47$	−1.79204	−	0.125311i	−0.261395	−	0.0182785i	−0.0615424	−	0.998104i	$-0.519602\pi$
$47$	−1.79204	−	0.125311i	−0.261395	−	0.0182785i	−0.199853	+	0.979826i	$0.564046\pi$
$48$	1.44850	−	0.361153i	0.209074	−	0.0521279i
$49$	3.11474	−	3.45927i	0.444963	−	0.494182i
$50$	4.15678	+	0.883551i	0.587857	+	0.124953i
$51$	−5.94504	−	1.70471i	−0.832472	−	0.238708i
$52$	−2.69489	−	2.60242i	−0.373713	−	0.360891i
$53$	5.32263	−	10.0104i	0.731119	−	1.37504i	−0.188440	−	0.982085i	$-0.560343\pi$
$53$	5.32263	−	10.0104i	0.731119	−	1.37504i	0.919559	−	0.392951i	$-0.128546\pi$
$54$	1.92562	−	5.29060i	0.262044	−	0.719959i
$55$	2.15629	−	1.89850i	0.290754	−	0.255994i
$56$			1.53137i			0.204638i
$57$	6.50329	+	0.224654i	0.861382	+	0.0297562i
$58$	−0.453708	+	0.329638i	−0.0595747	+	0.0432836i
$59$	0.144927	+	2.07256i	0.0188679	+	0.269824i	0.997833	+	0.0657965i	$0.0209588\pi$
$59$	0.144927	+	2.07256i	0.0188679	+	0.269824i	−0.978965	+	0.204028i	$0.934597\pi$
$60$	1.29236	+	0.0451303i	0.166843	+	0.00582629i
$61$	−1.08799	−	7.74145i	−0.139303	−	0.991191i	−0.926982	−	0.375106i	$-0.877606\pi$
$61$	−1.08799	−	7.74145i	−0.139303	−	0.991191i	0.787679	−	0.616086i	$-0.211282\pi$
$62$	−4.98191	−	2.42984i	−0.632703	−	0.308590i
$63$	0.979347	+	0.660578i	0.123386	+	0.0832250i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	−1.62259	−	2.81041i	−0.201258	−	0.348589i
$66$	−3.09151	+	3.86744i	−0.380539	+	0.476049i
$67$	−1.58142	+	1.88467i	−0.193202	+	0.230249i	−0.853945	−	0.520363i	$-0.825797\pi$
$67$	−1.58142	+	1.88467i	−0.193202	+	0.230249i	0.660744	+	0.750612i	$0.270241\pi$
$68$	−0.861344	−	4.05230i	−0.104453	−	0.491414i
$69$	−11.4030	+	1.19850i	−1.37276	+	0.144283i
$70$	−0.365638	+	1.27513i	−0.0437021	+	0.152407i
$71$	4.77504	+	8.98054i	0.566693	+	1.06579i	0.987347	+	0.158574i	$0.0506895\pi$
$71$	4.77504	+	8.98054i	0.566693	+	1.06579i	−0.420654	+	0.907221i	$0.638199\pi$
$72$	0.763898	−	0.107359i	0.0900263	−	0.0126524i
$73$	−0.408207	+	0.275339i	−0.0477771	+	0.0322260i	−0.582849	−	0.812580i	$-0.698062\pi$
$73$	−0.408207	+	0.275339i	−0.0477771	+	0.0322260i	0.535072	+	0.844806i	$0.320284\pi$
$74$	9.13023	+	2.27642i	1.06137	+	0.264629i
$75$	−6.03357	−	1.96043i	−0.696697	−	0.226371i
$76$	1.91229	+	3.91703i	0.219354	+	0.449315i
$77$	−3.08219	−	4.03684i	−0.351248	−	0.460041i
$78$	3.59492	+	4.28426i	0.407045	+	0.485097i
$79$	10.1991	−	13.0543i	1.14749	−	1.46872i	0.287951	−	0.957645i	$-0.407026\pi$
$79$	10.1991	−	13.0543i	1.14749	−	1.46872i	0.859537	−	0.511073i	$-0.170752\pi$
$80$	0.379730	+	0.778563i	0.0424551	+	0.0870459i
$81$	−2.66999	+	5.47430i	−0.296666	+	0.608256i
$82$	3.37116	+	4.31488i	0.372282	+	0.476499i
$83$	3.30508	−	15.5492i	0.362779	−	1.70674i	−0.296659	−	0.954983i	$-0.595873\pi$
$83$	3.30508	−	15.5492i	0.362779	−	1.70674i	0.659439	−	0.751758i	$-0.270794\pi$
$84$	0.238963	−	2.27358i	0.0260730	−	0.248068i
$85$	0.250332	−	3.57991i	0.0271523	−	0.388296i
$86$	−6.45277	−	10.3266i	−0.695820	−	1.11354i
$87$	0.725044	−	0.418605i	0.0777329	−	0.0448791i
$88$	−3.25963	−	0.612244i	−0.347477	−	0.0652654i
$89$	5.09038	+	13.9857i	0.539580	+	1.48248i	0.847357	+	0.531024i	$0.178193\pi$
$89$	5.09038	+	13.9857i	0.539580	+	1.48248i	−0.307777	+	0.951459i	$0.599585\pi$
$90$	0.661712	+	0.0929975i	0.0697505	+	0.00980280i
$91$	−5.15639	+	2.51494i	−0.540537	+	0.263638i
$92$	−4.29487	−	6.36741i	−0.447772	−	0.663849i
$93$	7.01733	+	4.38491i	0.727663	+	0.454694i
$94$	0.555122	+	1.70849i	0.0572564	+	0.176217i
$95$	0.657059	+	3.71820i	0.0674128	+	0.381479i
$96$	−0.877474	−	1.20774i	−0.0895568	−	0.123264i
$97$	−8.65192	+	3.49560i	−0.878470	+	0.354925i	−0.769140	−	0.639081i	$-0.779315\pi$
$97$	−8.65192	+	3.49560i	−0.878470	+	0.354925i	−0.109330	+	0.994006i	$0.534871\pi$
$98$	−4.37418	−	1.59207i	−0.441859	−	0.160824i
$99$	−1.79763	+	1.82051i	−0.180669	+	0.182968i
$100$	−0.737943	−	4.18508i	−0.0737943	−	0.418508i
$101$	3.60299	−	0.125819i	0.358510	−	0.0125195i	0.144922	−	0.989443i	$-0.453707\pi$
$101$	3.60299	−	0.125819i	0.358510	−	0.0125195i	0.213589	+	0.976924i	$0.431485\pi$
$102$	0.646469	+	6.15074i	0.0640100	+	0.609014i
$103$	−0.347288	−	0.0365014i	−0.0342193	−	0.00359659i	0.0874034	−	0.996173i	$-0.472143\pi$
$103$	−0.347288	−	0.0365014i	−0.0342193	−	0.00359659i	−0.121623	+	0.992576i	$0.538810\pi$
$104$	−1.40340	+	3.47354i	−0.137615	+	0.340608i
$105$	0.741829	−	1.83609i	0.0723951	−	0.179184i
$106$	−11.2754	−	1.18509i	−1.09516	−	0.115106i
$107$	−1.96219	−	18.6689i	−0.189692	−	1.80480i	−0.512880	−	0.858460i	$-0.671421\pi$
$107$	−1.96219	−	18.6689i	−0.189692	−	1.80480i	0.323188	−	0.946335i	$-0.395245\pi$
$108$	−5.62670	+	0.196489i	−0.541430	+	0.0189071i
$109$	0.0618314	+	0.350663i	0.00592237	+	0.0335874i	0.987626	−	0.156829i	$-0.0501272\pi$
$109$	0.0618314	+	0.350663i	0.00592237	+	0.0335874i	−0.981703	+	0.190417i	$0.939016\pi$
$110$	−2.56802	−	1.28809i	−0.244851	−	0.122814i
$111$	−13.2001	−	4.80446i	−1.25290	−	0.456019i
$112$	1.41986	−	0.573661i	0.134164	−	0.0542058i
$113$	−2.29171	−	3.15427i	−0.215586	−	0.296729i	0.687503	−	0.726181i	$-0.258707\pi$
$113$	−2.29171	−	3.15427i	−0.215586	−	0.296729i	−0.903090	+	0.429452i	$0.858707\pi$
$114$	−2.22788	−	6.11391i	−0.208660	−	0.572620i
$115$	−2.05591	−	6.32745i	−0.191715	−	0.590037i
$116$	0.475597	+	0.297186i	0.0441581	+	0.0275930i
$117$	1.61603	+	2.39587i	0.149402	+	0.221498i
$118$	1.86735	−	0.910768i	0.171904	−	0.0838430i
$119$	−6.28247	−	0.882943i	−0.575913	−	0.0809393i
$120$	−0.442283	−	1.21516i	−0.0403748	−	0.110929i
$121$	9.82497	−	4.94672i	0.893179	−	0.449702i
$122$	−6.77018	+	3.90876i	−0.612943	+	0.353883i
$123$	−4.33174	−	6.93223i	−0.390580	−	0.625058i
$124$	−0.386652	+	5.52938i	−0.0347224	+	0.496553i
$125$	0.837516	−	7.96843i	0.0749097	−	0.712718i
$126$	0.245607	−	1.15549i	0.0218804	−	0.102939i
$127$	5.01806	+	6.42282i	0.445281	+	0.569933i	0.957321	−	0.289028i	$-0.0933322\pi$
$127$	5.01806	+	6.42282i	0.445281	+	0.569933i	−0.512040	+	0.858962i	$0.671110\pi$
$128$	0.438371	−	0.898794i	0.0387469	−	0.0794429i
$129$	7.96882	+	16.3385i	0.701615	+	1.43852i
$130$	−1.99794	+	2.55724i	−0.175231	+	0.224285i
$131$	−10.5438	−	12.5656i	−0.921215	−	1.09786i	−0.994929	−	0.100582i	$-0.967930\pi$
$131$	−10.5438	−	12.5656i	−0.921215	−	1.09786i	0.0737139	−	0.997279i	$-0.476515\pi$
$132$	4.74393	+	1.41763i	0.412906	+	0.123389i
$133$	6.63825	−	0.700229i	0.575609	−	0.0607176i
$134$	2.33984	+	0.760261i	0.202132	+	0.0656766i
$135$	−4.73213	−	1.17985i	−0.407276	−	0.101545i
$136$	−3.43457	+	2.31664i	−0.294512	+	0.198651i
$137$	−20.8267	+	2.92700i	−1.77934	+	0.250070i	−0.950789	−	0.309840i	$-0.899725\pi$
$137$	−20.8267	+	2.92700i	−1.77934	+	0.250070i	−0.828553	+	0.559910i	$0.810836\pi$
$138$	5.38287	+	10.1237i	0.458220	+	0.861786i
$139$	−1.68406	+	5.87303i	−0.142840	+	0.498144i	−0.999853	−	0.0171520i	$-0.994540\pi$
$139$	−1.68406	+	5.87303i	−0.142840	+	0.498144i	0.857013	+	0.515296i	$0.172318\pi$
$140$	1.31925	−	0.138659i	0.111497	−	0.0117188i
$141$	−0.557571	−	2.62317i	−0.0469560	−	0.220910i
$142$	6.53785	−	7.79151i	0.548645	−	0.653849i
$143$	−3.29169	−	11.9812i	−0.275265	−	1.00192i
$144$	−0.385703	−	0.668057i	−0.0321419	−	0.0556714i
$145$	0.325059	+	0.361015i	0.0269947	+	0.0299807i
$146$	0.408207	+	0.275339i	0.0337835	+	0.0227872i
$147$	6.24578	+	3.04627i	0.515144	+	0.251252i
$148$	−1.30958	−	9.31816i	−0.107647	−	0.765948i
$149$	−1.08746	−	0.0379750i	−0.0890884	−	0.00311104i	−0.00967940	−	0.999953i	$-0.503081\pi$
$149$	−1.08746	−	0.0379750i	−0.0890884	−	0.00311104i	−0.0794090	+	0.996842i	$0.525303\pi$
$150$	0.442540	+	6.32862i	0.0361333	+	0.516730i
$151$	−0.565526	+	0.410879i	−0.0460218	+	0.0334368i	−0.610558	−	0.791971i	$-0.709055\pi$
$151$	−0.565526	+	0.410879i	−0.0460218	+	0.0334368i	0.564537	+	0.825408i	$0.309055\pi$
$152$	2.91546	−	3.24039i	0.236475	−	0.262830i
$153$			3.19581i			0.258366i
$154$	−2.58829	+	4.36998i	−0.208570	+	0.352143i
$155$	−1.64218	+	4.51185i	−0.131903	+	0.362401i
$156$	2.62561	−	4.93806i	0.210217	−	0.395361i
$157$	12.2885	+	11.8669i	0.980731	+	0.947081i	0.998607	−	0.0527594i	$-0.0168016\pi$
$157$	12.2885	+	11.8669i	0.980731	+	0.947081i	−0.0178763	+	0.999840i	$0.505691\pi$
$158$	−15.9243	−	4.56623i	−1.26687	−	0.363270i
$159$	16.5553	+	3.51894i	1.31292	+	0.279070i
$160$	0.579621	−	0.643735i	0.0458231	−	0.0508917i
$161$	−11.4123	+	2.84540i	−0.899414	+	0.224249i
$162$	6.07588	+	0.424867i	0.477366	+	0.0333807i
$163$	19.0107	−	4.04085i	1.48903	−	0.316504i	0.609670	−	0.792655i	$-0.291302\pi$
$163$	19.0107	−	4.04085i	1.48903	−	0.316504i	0.879363	+	0.476152i	$0.157969\pi$
$164$	2.73783	−	4.74207i	0.213789	−	0.370293i
$165$	3.61167	+	2.31311i	0.281168	+	0.180075i
$166$	−15.6550	+	2.76040i	−1.21507	+	0.214249i
$167$	20.7986	+	11.0588i	1.60944	+	0.855757i	0.997916	+	0.0645341i	$0.0205561\pi$
$167$	20.7986	+	11.0588i	1.60944	+	0.855757i	0.611528	+	0.791222i	$0.290555\pi$
$168$	−2.19754	+	0.630135i	−0.169544	+	0.0486159i
$169$	−1.03248	+	0.0721979i	−0.0794214	+	0.00555369i
$170$	−3.41301	+	1.10895i	−0.261766	+	0.0850529i
$171$	−0.814683	−	3.26229i	−0.0623003	−	0.249474i
$172$	−7.15740	+	9.85131i	−0.545746	+	0.751156i
$173$	−5.52014	+	22.1401i	−0.419688	+	1.68328i	0.272979	+	0.962020i	$0.411991\pi$
$173$	−5.52014	+	22.1401i	−0.419688	+	1.68328i	−0.692667	+	0.721258i	$0.743564\pi$
$174$	−0.659730	−	0.515437i	−0.0500140	−	0.0390752i
$175$	−6.40891	−	1.13006i	−0.484468	−	0.0854247i
$176$	0.653415	+	3.25162i	0.0492530	+	0.245100i
$177$	−2.91452	+	1.06080i	−0.219069	+	0.0797346i
$178$	11.0604	−	9.95886i	0.829015	−	0.746448i
$179$	6.59147	−	14.8047i	0.492669	−	1.10655i	−0.480611	−	0.876934i	$-0.659585\pi$
$179$	6.59147	−	14.8047i	0.492669	−	1.10655i	0.973280	−	0.229620i	$-0.0737483\pi$
$180$	−0.161656	−	0.648366i	−0.0120491	−	0.0483263i
$181$	14.3989	+	5.81754i	1.07026	+	0.432414i	0.841047	−	0.540961i	$-0.181939\pi$
$181$	14.3989	+	5.81754i	1.07026	+	0.432414i	0.229216	+	0.973376i	$0.426384\pi$
$182$	4.26343	+	3.83881i	0.316027	+	0.284552i
$183$	10.6614	−	4.74677i	0.788115	−	0.350891i
$184$	−4.29487	+	6.36741i	−0.316622	+	0.469412i
$185$	1.13440	−	8.07167i	0.0834027	−	0.593441i
$186$	1.43688	−	8.14897i	0.105357	−	0.597512i
$187$	4.39115	−	13.0197i	0.321112	−	0.952093i
$188$	1.37613	−	1.15471i	0.100365	−	0.0842160i
$189$	−2.66429	+	8.19983i	−0.193798	+	0.596450i
$190$	3.20132	−	2.00208i	0.232248	−	0.145246i
$191$	−3.14067	−	2.28183i	−0.227251	−	0.165107i	0.468334	−	0.883552i	$-0.344854\pi$
$191$	−3.14067	−	2.28183i	−0.227251	−	0.165107i	−0.695584	+	0.718444i	$0.744854\pi$
$192$	−0.791089	+	1.26601i	−0.0570919	+	0.0913662i
$193$	−0.0486348	+	1.39272i	−0.00350081	+	0.100250i	0.996383	+	0.0849806i	$0.0270828\pi$
$193$	−0.0486348	+	1.39272i	−0.00350081	+	0.100250i	−0.999883	+	0.0152694i	$0.995139\pi$
$194$	6.48214	+	6.71245i	0.465390	+	0.481926i
$195$	3.36532	−	3.48489i	0.240996	−	0.249558i
$196$	0.162454	+	4.65207i	0.0116039	+	0.332291i
$197$	14.4085	+	8.31874i	1.02656	+	0.592686i	0.915998	−	0.401183i	$-0.131401\pi$
$197$	14.4085	+	8.31874i	1.02656	+	0.592686i	0.110564	+	0.993869i	$0.464734\pi$
$198$	2.36135	+	0.984760i	0.167814	+	0.0699838i
$199$	5.18610	+	4.35165i	0.367633	+	0.308481i	0.807824	−	0.589423i	$-0.200645\pi$
$199$	5.18610	+	4.35165i	0.367633	+	0.308481i	−0.440192	+	0.897904i	$0.645089\pi$
$200$	−3.60390	+	2.25197i	−0.254834	+	0.159238i
$201$	−3.35526	−	1.49386i	−0.236662	−	0.105369i
$202$	−1.46636	−	3.29350i	−0.103173	−	0.231730i
$203$	0.676753	−	0.528738i	0.0474988	−	0.0371101i
$204$	5.46070	−	2.90350i	0.382325	−	0.203286i
$205$	3.41196	−	3.29490i	0.238302	−	0.230125i
$206$	0.0962528	+	0.335673i	0.00670625	+	0.0233875i
$207$	2.21946	+	5.49335i	0.154263	+	0.381814i
$208$	3.74633			0.259761
$209$	−1.16350	+	14.4099i	−0.0804808	+	0.996756i
$210$	−1.98029			−0.136653
$211$	8.20669	+	20.3123i	0.564972	+	1.39835i	0.891437	+	0.453145i	$0.149698\pi$
$211$	8.20669	+	20.3123i	0.564972	+	1.39835i	−0.326465	+	0.945209i	$0.605858\pi$
$212$	3.12504	+	10.8983i	0.214628	+	0.748498i
$213$	−10.9224	+	10.5476i	−0.748389	+	0.722711i
$214$	−16.5745	+	8.81282i	−1.13301	+	0.602432i
$215$	−8.31193	+	6.49399i	−0.566869	+	0.442887i
$216$	2.28998	+	5.14338i	0.155814	+	0.349963i
$217$	7.75435	+	3.45246i	0.526400	+	0.234368i
$218$	0.301967	−	0.188690i	0.0204518	−	0.0127797i
$219$	−0.563088	−	0.472487i	−0.0380500	−	0.0319277i
$220$	−0.232294	+	2.86355i	−0.0156612	+	0.193061i
$221$	−13.4411	−	7.76022i	−0.904146	−	0.522009i
$222$	0.490244	+	14.0387i	0.0329030	+	0.942219i
$223$	−13.3379	+	13.8118i	−0.893172	+	0.924907i	−0.997573	−	0.0696287i	$-0.977819\pi$
$223$	−13.3379	+	13.8118i	−0.893172	+	0.924907i	0.104401	+	0.994535i	$0.466707\pi$
$224$	−1.06378	−	1.10157i	−0.0710767	−	0.0736020i
$225$	−0.114408	+	3.27620i	−0.00762717	+	0.218414i
$226$	−2.06610	+	3.30645i	−0.137435	+	0.219942i
$227$	8.16232	+	5.93028i	0.541752	+	0.393606i	0.824735	−	0.565519i	$-0.191324\pi$
$227$	8.16232	+	5.93028i	0.541752	+	0.393606i	−0.282983	+	0.959125i	$0.591324\pi$
$228$	−4.83414	+	4.35596i	−0.320148	+	0.288481i
$229$	4.09434	−	12.6011i	0.270562	−	0.832703i	−0.719798	−	0.694183i	$-0.755766\pi$
$229$	4.09434	−	12.6011i	0.270562	−	0.832703i	0.990360	−	0.138520i	$-0.0442344\pi$
$230$	−5.09655	+	4.27651i	−0.336056	+	0.281985i
$231$	4.52466	−	6.08409i	0.297701	−	0.400304i
$232$	0.0973842	−	0.552293i	0.00639359	−	0.0362598i
$233$	2.13158	−	15.1669i	0.139644	−	0.993620i	−0.786805	−	0.617201i	$-0.788266\pi$
$233$	2.13158	−	15.1669i	0.139644	−	0.993620i	0.926450	−	0.376419i	$-0.122845\pi$
$234$	1.61603	−	2.39587i	0.105643	−	0.156623i
$235$	1.42157	−	0.632925i	0.0927332	−	0.0412875i
$236$	−1.54397	−	1.39020i	−0.100504	−	0.0904942i
$237$	22.9299	+	9.26426i	1.48945	+	0.601779i
$238$	1.53480	+	6.15576i	0.0994865	+	0.399019i
$239$	4.25654	−	9.56036i	0.275333	−	0.618408i	−0.721960	−	0.691935i	$-0.756759\pi$
$239$	4.25654	−	9.56036i	0.275333	−	0.618408i	0.997293	+	0.0735265i	$0.0234253\pi$
$240$	−0.960998	+	0.865286i	−0.0620321	+	0.0558540i
$241$	−11.7764	+	4.28626i	−0.758585	+	0.276102i	−0.692214	−	0.721693i	$-0.743364\pi$
$241$	−11.7764	+	4.28626i	−0.758585	+	0.276102i	−0.0663712	+	0.997795i	$0.521142\pi$
$242$	−8.26702	−	7.25648i	−0.531424	−	0.466464i
$243$	7.67942	+	1.35409i	0.492635	+	0.0868649i
$244$	6.16030	+	4.81295i	0.394373	+	0.308118i
$245$	−0.975483	+	3.91245i	−0.0623213	+	0.249957i
$246$	−4.80475	+	6.61318i	−0.306340	+	0.421641i
$247$	15.6990	+	4.49523i	0.998902	+	0.286025i
$248$	5.27160	−	1.71285i	0.334747	−	0.108766i
$249$	23.6733	−	1.65540i	1.50023	−	0.104907i
$250$	−7.70194	+	2.20850i	−0.487113	+	0.139678i
$251$	−16.0805	−	8.55017i	−1.01499	−	0.539682i	−0.123323	−	0.992367i	$-0.539355\pi$
$251$	−16.0805	−	8.55017i	−1.01499	−	0.539682i	−0.891671	+	0.452685i	$0.850466\pi$
$252$	−1.16336	+	0.205132i	−0.0732848	+	0.0129221i
$253$	−1.49399	−	25.4294i	−0.0939262	−	1.59874i
$254$	4.07534	−	7.05870i	0.255710	−	0.442902i
$255$	5.24024	−	1.11385i	0.328156	−	0.0697518i
$256$	−0.997564	−	0.0697565i	−0.0623478	−	0.00435978i
$257$	−1.34928	+	0.336413i	−0.0841656	+	0.0209849i	−0.283777	−	0.958890i	$-0.591588\pi$
$257$	−1.34928	+	0.336413i	−0.0841656	+	0.0209849i	0.199611	+	0.979875i	$0.436032\pi$
$258$	12.1636	−	13.5091i	0.757274	−	0.841038i
$259$	−14.0949	−	2.99596i	−0.875814	−	0.186160i
$260$	3.11947	+	0.894494i	0.193461	+	0.0554742i
$261$	−0.311197	−	0.300519i	−0.0192626	−	0.0186017i
$262$	−7.70085	+	14.4832i	−0.475760	+	0.894774i
$263$	−0.543140	+	1.49226i	−0.0334914	+	0.0920169i	−0.955311	−	0.295601i	$-0.904480\pi$
$263$	−0.543140	+	1.49226i	−0.0334914	+	0.0920169i	0.921820	+	0.387618i	$0.126702\pi$
$264$	−0.462705	−	4.92955i	−0.0284775	−	0.303393i
$265$			9.82088i			0.603292i
$266$	−3.13597	−	5.89257i	−0.192279	−	0.361297i
$267$	−17.9751	+	13.0597i	−1.10006	+	0.799240i
$268$	−0.171619	−	2.45426i	−0.0104833	−	0.149918i
$269$	10.5852	+	0.369645i	0.645393	+	0.0225376i	0.355727	−	0.934590i	$-0.384233\pi$
$269$	10.5852	+	0.369645i	0.645393	+	0.0225376i	0.289667	+	0.957128i	$0.406456\pi$
$270$	0.678746	+	4.82953i	0.0413072	+	0.293916i
$271$	−2.17517	−	1.06090i	−0.132132	−	0.0644452i	0.371119	−	0.928585i	$-0.378974\pi$
$271$	−2.17517	−	1.06090i	−0.132132	−	0.0644452i	−0.503251	+	0.864140i	$0.667863\pi$
$272$	3.43457	+	2.31664i	0.208251	+	0.140467i
$273$	−5.73076	−	6.36466i	−0.346841	−	0.385206i
$274$	10.5157	+	18.2137i	0.635275	+	1.10033i
$275$	4.96771	−	13.1900i	0.299564	−	0.795387i
$276$	7.37007	−	8.78331i	0.443626	−	0.528693i
$277$	−3.49724	−	16.4532i	−0.210129	−	0.988578i	−0.949132	−	0.314877i	$-0.898037\pi$
$277$	−3.49724	−	16.4532i	−0.210129	−	0.988578i	0.739004	−	0.673701i	$-0.235297\pi$
$278$	6.07624	−	0.638638i	0.364428	−	0.0383030i
$279$	1.17857	−	4.11017i	0.0705593	−	0.246070i
$280$	−0.622762	−	1.17125i	−0.0372172	−	0.0699953i
$281$	−10.3095	+	1.44891i	−0.615016	+	0.0864348i	−0.439801	−	0.898095i	$-0.644951\pi$
$281$	−10.3095	+	1.44891i	−0.615016	+	0.0864348i	−0.175215	+	0.984530i	$0.556062\pi$
$282$	−2.22329	+	1.49963i	−0.132395	+	0.0893014i
$283$	−9.86402	−	2.45938i	−0.586355	−	0.146195i	−0.0625632	−	0.998041i	$-0.519928\pi$
$283$	−9.86402	−	2.45938i	−0.586355	−	0.146195i	−0.523792	+	0.851846i	$0.675483\pi$
$284$	−9.67329	−	3.14304i	−0.574004	−	0.186505i
$285$	−5.06531	+	2.47287i	−0.300043	+	0.146480i
$286$	−9.87571	+	7.54025i	−0.583963	+	0.445864i
$287$	−5.38994	−	6.42348i	−0.318158	−	0.379166i
$288$	−0.474925	+	0.607876i	−0.0279852	+	0.0358194i
$289$	−0.0714932	−	0.146583i	−0.00420548	−	0.00862252i
$290$	0.212958	−	0.436628i	0.0125053	−	0.0256397i
$291$	−8.57639	−	10.9773i	−0.502757	−	0.643499i
$292$	0.102373	−	0.481627i	0.00599093	−	0.0281851i
$293$	−0.858340	+	8.16656i	−0.0501447	+	0.477095i	0.940417	+	0.340025i	$0.110435\pi$
$293$	−0.858340	+	8.16656i	−0.0501447	+	0.477095i	−0.990561	+	0.137071i	$0.956231\pi$
$294$	0.484743	−	6.93214i	0.0282708	−	0.404291i
$295$	−0.953694	−	1.52623i	−0.0555262	−	0.0888605i
$296$	−8.14907	+	4.70487i	−0.473655	+	0.273465i
$297$	−16.3887	−	8.94943i	−0.950970	−	0.519298i
$298$	0.372161	+	1.02250i	0.0215587	+	0.0592320i
$299$	−28.4936	−	4.00452i	−1.64783	−	0.231587i
$300$	5.70202	−	2.78106i	0.329206	−	0.160565i
$301$	10.4274	+	15.4593i	0.601028	+	0.891060i
$302$	0.592810	+	0.370429i	0.0341124	+	0.0213158i
$303$	1.66313	+	5.11857i	0.0955441	+	0.294054i
$304$	−4.09658	−	1.48929i	−0.234955	−	0.0854168i
$305$	3.98035	+	5.47849i	0.227914	+	0.313697i
$306$	2.96310	−	1.19717i	0.169389	−	0.0684377i
$307$	−23.6844	−	8.62042i	−1.35174	−	0.491993i	−0.438250	−	0.898853i	$-0.644401\pi$
$307$	−23.6844	−	8.62042i	−1.35174	−	0.491993i	−0.913490	+	0.406860i	$0.866624\pi$
$308$	5.02137	+	0.762792i	0.286119	+	0.0434641i
$309$	−0.0905234	−	0.513384i	−0.00514970	−	0.0292054i
$310$	4.79849	−	0.167567i	0.272536	−	0.00951716i
$311$	0.368932	+	3.51015i	0.0209202	+	0.199043i	0.999990	−	0.00448248i	$-0.00142682\pi$
$311$	0.368932	+	3.51015i	0.0209202	+	0.199043i	−0.979070	+	0.203525i	$0.934760\pi$
$312$	−5.56207	−	0.584597i	−0.314890	−	0.0330963i
$313$	−2.73914	+	6.77961i	−0.154825	+	0.383206i	−0.984583	−	0.174918i	$-0.944034\pi$
$313$	−2.73914	+	6.77961i	−0.154825	+	0.383206i	0.829758	+	0.558124i	$0.188479\pi$
$314$	6.39943	−	15.8391i	0.361141	−	0.893854i
$315$	−1.01768	−	0.106962i	−0.0573396	−	0.00602664i
$316$	1.73163	+	16.4753i	0.0974117	+	0.926810i
$317$	7.66643	−	0.267718i	0.430590	−	0.0150365i	0.181215	−	0.983444i	$-0.441997\pi$
$317$	7.66643	−	0.267718i	0.430590	−	0.0150365i	0.249375	+	0.968407i	$0.419775\pi$
$318$	−2.93902	−	16.6680i	−0.164812	−	0.934696i
$319$	0.854888	+	1.65191i	0.0478645	+	0.0924890i
$320$	−0.813990	−	0.296268i	−0.0455034	−	0.0165619i
$321$	25.9829	−	10.4978i	1.45022	−	0.585928i
$322$	6.91333	+	9.51538i	0.385265	+	0.530271i
$323$	11.6128	+	13.8290i	0.646153	+	0.769468i
$324$	−1.88214	−	5.79262i	−0.104563	−	0.321812i
$325$	−13.5014	−	8.43662i	−0.748924	−	0.467980i
$326$	−10.8681	−	16.1127i	−0.601931	−	0.892399i
$327$	−0.477765	+	0.233022i	−0.0264205	+	0.0128861i
$328$	−5.42238	−	0.762065i	−0.299401	−	0.0420780i
$329$	−0.940886	−	2.58506i	−0.0518728	−	0.142519i
$330$	0.791723	−	4.21518i	0.0435829	−	0.232038i
$331$	−17.0732	+	9.85724i	−0.938430	+	0.541803i	−0.889468	−	0.456998i	$-0.848925\pi$
$331$	−17.0732	+	9.85724i	−0.938430	+	0.541803i	−0.0489621	+	0.998801i	$0.515591\pi$
$332$	8.42388	+	13.4810i	0.462320	+	0.739867i
$333$	−0.506343	+	7.24104i	−0.0277474	+	0.396807i
$334$	2.46226	−	23.4268i	0.134729	−	1.28186i
$335$	0.443091	−	2.08458i	0.0242086	−	0.113893i
$336$	1.40746	+	1.80147i	0.0767834	+	0.0982783i
$337$	−2.14651	+	4.40100i	−0.116928	+	0.239738i	−0.949229	−	0.314586i	$-0.898134\pi$
$337$	−2.14651	+	4.40100i	−0.116928	+	0.239738i	0.832301	+	0.554324i	$0.187023\pi$
$338$	0.453714	+	0.930252i	0.0246788	+	0.0505990i
$339$	3.58343	−	4.58658i	0.194625	−	0.249109i
$340$	2.30674	+	2.74907i	0.125101	+	0.149089i
$341$	−10.4490	+	15.1254i	−0.565846	+	0.819086i
$342$	−2.71956	+	1.97744i	−0.147057	+	0.106928i
$343$	16.9744	+	5.51532i	0.916533	+	0.297800i
$344$	11.8152	+	2.94586i	0.637032	+	0.158830i
$345$	8.23402	−	5.55392i	0.443305	−	0.299013i
$346$	22.5958	−	3.17563i	1.21476	−	0.170723i
$347$	−8.39236	−	15.7837i	−0.450526	−	0.847315i	−0.999931	−	0.0117594i	$-0.996257\pi$
$347$	−8.39236	−	15.7837i	−0.450526	−	0.847315i	0.549405	−	0.835556i	$-0.314854\pi$
$348$	−0.230766	+	0.804777i	−0.0123704	+	0.0431406i
$349$	−8.86583	+	0.931836i	−0.474577	+	0.0498800i	−0.338798	−	0.940859i	$-0.610020\pi$
$349$	−8.86583	+	0.931836i	−0.474577	+	0.0498800i	−0.135779	+	0.990739i	$0.543354\pi$
$350$	1.35304	+	6.36556i	0.0723231	+	0.340254i
$351$	−13.5579	+	16.1577i	−0.723667	+	0.862433i
$352$	2.77008	−	1.82391i	0.147646	−	0.0972150i
$353$	−11.6514	−	20.1808i	−0.620140	−	1.07411i	−0.989459	−	0.144812i	$-0.953742\pi$
$353$	−11.6514	−	20.1808i	−0.620140	−	1.07411i	0.369319	−	0.929303i	$-0.379591\pi$
$354$	2.07536	+	2.30492i	0.110304	+	0.122505i
$355$	−7.30424	−	4.92678i	−0.387669	−	0.261486i
$356$	−13.3770	−	6.52440i	−0.708980	−	0.345793i
$357$	−1.31810	−	9.37877i	−0.0697612	−	0.496377i
$358$	−16.1959	−	0.565572i	−0.855978	−	0.0298914i
$359$	0.181330	+	2.59315i	0.00957025	+	0.136861i	0.999999	−	0.00116166i	$-0.000369768\pi$
$359$	0.181330	+	2.59315i	0.00957025	+	0.136861i	−0.990429	+	0.138023i	$0.955925\pi$
$360$	−0.540597	+	0.392767i	−0.0284920	+	0.0207006i
$361$	−15.3797	−	11.1564i	−0.809458	−	0.587177i
$362$		−	15.5297i		−	0.816225i
$363$	11.1415	+	12.0635i	0.584775	+	0.633169i
$364$	1.96217	−	5.39103i	0.102846	−	0.282567i
$365$	0.200239	−	0.376595i	0.0104810	−	0.0197119i
$366$	−8.39497	−	8.10693i	−0.438812	−	0.423756i
$367$	−19.5213	−	5.59764i	−1.01900	−	0.292194i	−0.275767	−	0.961224i	$-0.588932\pi$
$367$	−19.5213	−	5.59764i	−1.01900	−	0.292194i	−0.743235	+	0.669030i	$0.766710\pi$
$368$	7.51265	+	1.59686i	0.391624	+	0.0832422i
$369$	−2.82638	+	3.13901i	−0.147135	+	0.163411i
$370$	−7.90888	+	1.97191i	−0.411163	+	0.102514i
$371$	17.3196	+	1.21110i	0.899188	+	0.0628774i
$372$	−8.09386	+	1.72040i	−0.419647	+	0.0891987i
$373$	7.95867	−	13.7848i	0.412084	−	0.713751i	−0.583033	−	0.812448i	$-0.698134\pi$
$373$	7.95867	−	13.7848i	0.412084	−	0.713751i	0.995118	+	0.0986973i	$0.0314676\pi$
$374$	−13.7166	+	0.805853i	−0.709267	+	0.0416697i
$375$	11.7795	−	2.07704i	0.608289	−	0.107258i
$376$	−1.58614	−	0.843364i	−0.0817988	−	0.0434932i
$377$	2.01960	−	0.579112i	0.104015	−	0.0298258i
$378$	8.60081	−	0.601427i	0.442378	−	0.0309341i
$379$	−15.2000	+	4.93877i	−0.780770	+	0.253687i	−0.672169	−	0.740398i	$-0.734637\pi$
$379$	−15.2000	+	4.93877i	−0.780770	+	0.253687i	−0.108601	+	0.994085i	$0.534637\pi$
$380$	−3.05553	−	2.21822i	−0.156745	−	0.113792i
$381$	−7.15201	+	9.84390i	−0.366408	+	0.504318i
$382$	−0.939159	+	3.76676i	−0.0480516	+	0.192724i
$383$	13.7981	+	10.7803i	0.705050	+	0.550845i	0.903144	−	0.429338i	$-0.141253\pi$
$383$	13.7981	+	10.7803i	0.705050	+	0.550845i	−0.198094	+	0.980183i	$0.563475\pi$
$384$	1.47017	+	0.259230i	0.0750242	+	0.0132288i
$385$	3.99903	+	1.83409i	0.203810	+	0.0934737i
$386$	1.30952	−	0.476628i	0.0666530	−	0.0242597i
$387$	6.98060	−	6.28536i	0.354844	−	0.319503i
$388$	3.79542	−	8.52466i	0.192683	−	0.432774i
$389$	3.65747	+	14.6693i	0.185441	+	0.743764i	0.988922	+	0.148434i	$0.0474232\pi$
$389$	3.65747	+	14.6693i	0.185441	+	0.743764i	−0.803481	+	0.595330i	$0.797021\pi$
$390$	−4.49181	−	1.81481i	−0.227451	−	0.0918963i
$391$	−23.6461	−	21.2911i	−1.19584	−	1.07674i
$392$	4.25247	−	1.89332i	0.214782	−	0.0956272i
$393$	13.6932	−	20.3011i	0.690733	−	1.02405i
$394$	2.31549	−	16.4756i	0.116653	−	0.830027i
$395$	−2.49186	+	14.1320i	−0.125379	+	0.711060i
$396$	0.0284759	−	2.55830i	0.00143097	−	0.128560i
$397$	2.00874	−	1.68553i	0.100816	−	0.0845944i	−0.590987	−	0.806681i	$-0.701261\pi$
$397$	2.00874	−	1.68553i	0.100816	−	0.0845944i	0.691802	+	0.722087i	$0.256817\pi$
$398$	2.09204	−	6.43862i	0.104864	−	0.322739i
$399$	3.73638	+	9.23787i	0.187053	+	0.462472i
$400$	3.43804	+	2.49788i	0.171902	+	0.124894i
$401$	−6.80312	+	10.8873i	−0.339731	+	0.543684i	−0.973164	−	0.230114i	$-0.926090\pi$
$401$	−6.80312	+	10.8873i	−0.339731	+	0.543684i	0.633432	+	0.773798i	$0.281646\pi$
$402$	−0.128178	+	3.67055i	−0.00639296	+	0.183070i
$403$	14.4249	+	14.9374i	0.718556	+	0.744087i
$404$	−2.50437	+	2.59335i	−0.124597	+	0.129024i
$405$	−0.184128	−	5.27275i	−0.00914942	−	0.262005i
$406$	−0.743753	−	0.429406i	−0.0369118	−	0.0213111i
$407$	12.0123	−	28.8042i	0.595426	−	1.42777i
$408$	−4.73770	−	3.97540i	−0.234551	−	0.196812i
$409$	3.18475	−	1.99005i	0.157476	−	0.0984018i	−0.448892	−	0.893586i	$-0.648181\pi$
$409$	3.18475	−	1.99005i	0.157476	−	0.0984018i	0.606368	+	0.795184i	$0.292626\pi$
$410$	−4.33312	−	1.92923i	−0.213997	−	0.0952778i
$411$	−12.7701	−	28.6822i	−0.629905	−	1.41479i
$412$	0.275174	−	0.214989i	0.0135568	−	0.0105918i
$413$	−2.80919	+	1.49367i	−0.138231	+	0.0734988i
$414$	4.26192	−	4.11569i	0.209462	−	0.202275i
$415$	3.79554	+	13.2366i	0.186316	+	0.649761i
$416$	−1.40340	−	3.47354i	−0.0688074	−	0.170304i
$417$	−9.12086			−0.446651
$418$	13.7965	−	4.31928i	0.674810	−	0.211263i
$419$	−3.84641			−0.187909			−0.0939547	−	0.995576i	$-0.529951\pi$
$419$	−3.84641			−0.187909			−0.0939547	+	0.995576i	$0.529951\pi$
$420$	0.741829	+	1.83609i	0.0361976	+	0.0895921i
$421$	1.30879	+	4.56431i	0.0637867	+	0.222451i	0.986699	−	0.162561i	$-0.0519753\pi$
$421$	1.30879	+	4.56431i	0.0637867	+	0.222451i	−0.922912	+	0.385011i	$0.874198\pi$
$422$	15.7589	−	15.2182i	0.767133	−	0.740811i
$423$	−1.22355	+	0.650576i	−0.0594913	+	0.0316321i
$424$	8.93406	−	6.98006i	0.433877	−	0.338981i
$425$	−7.16084	−	16.0835i	−0.347352	−	0.780164i
$426$	13.8712	+	6.17585i	0.672061	+	0.299221i
$427$	10.1524	−	6.34394i	0.491310	−	0.307005i
$428$	14.3800	+	12.0663i	0.695084	+	0.583245i
$429$	15.8388	−	9.65373i	0.764704	−	0.466086i
$430$	9.13483	+	5.27400i	0.440521	+	0.254335i
$431$	0.610389	+	17.4793i	0.0294014	+	0.841946i	0.921102	+	0.389321i	$0.127290\pi$
$431$	0.610389	+	17.4793i	0.0294014	+	0.841946i	−0.891701	+	0.452625i	$0.850488\pi$
$432$	3.91102	−	4.04998i	0.188169	−	0.194855i
$433$	15.3968	+	15.9438i	0.739921	+	0.766210i	0.978795	−	0.204840i	$-0.0656674\pi$
$433$	15.3968	+	15.9438i	0.739921	+	0.766210i	−0.238875	+	0.971050i	$0.576779\pi$
$434$	0.296234	−	8.48303i	0.0142197	−	0.407198i
$435$	−0.384306	+	0.615018i	−0.0184261	+	0.0294879i
$436$	−0.288069	−	0.209294i	−0.0137960	−	0.0100234i
$437$	29.5656	+	15.7061i	1.41432	+	0.751324i
$438$	−0.227146	+	0.699083i	−0.0108534	+	0.0334035i
$439$	4.88692	−	4.10062i	0.233240	−	0.195712i	−0.518675	−	0.854971i	$-0.673575\pi$
$439$	4.88692	−	4.10062i	0.233240	−	0.195712i	0.751915	+	0.659260i	$0.229130\pi$
$440$	2.74206	−	0.857327i	0.130723	−	0.0408715i
$441$	0.623540	−	3.53627i	0.0296924	−	0.168394i
$442$	−2.16003	+	15.3694i	−0.102742	+	0.731047i
$443$	−6.63206	+	9.83244i	−0.315099	+	0.467153i	−0.953002	−	0.302963i	$-0.902024\pi$
$443$	−6.63206	+	9.83244i	−0.315099	+	0.467153i	0.637904	+	0.770116i	$0.279802\pi$
$444$	12.8329	−	5.71355i	0.609020	−	0.271153i
$445$	−9.58089	−	8.62667i	−0.454178	−	0.408943i
$446$	17.8025	+	7.19270i	0.842975	+	0.340584i
$447$	−0.392979	−	1.57615i	−0.0185873	−	0.0745495i
$448$	−0.622864	+	1.39897i	−0.0294275	+	0.0660953i
$449$	0.595100	−	0.535830i	0.0280845	−	0.0252874i	−0.654969	−	0.755656i	$-0.727318\pi$
$449$	0.595100	−	0.535830i	0.0280845	−	0.0252874i	0.683053	+	0.730368i	$0.260652\pi$
$450$	3.08050	−	1.12121i	0.145216	−	0.0528544i
$451$	15.8277	−	8.90475i	0.745299	−	0.419308i
$452$	3.83966	+	0.677036i	0.180602	+	0.0318451i
$453$	−0.822323	−	0.642469i	−0.0386361	−	0.0301858i
$454$	2.44080	−	9.78949i	0.114552	−	0.459444i
$455$	2.92104	−	4.02047i	0.136941	−	0.188483i
$456$	5.84968	+	2.85036i	0.273936	+	0.133480i
$457$	1.58137	−	0.513818i	0.0739733	−	0.0240354i	−0.271797	−	0.962355i	$-0.587618\pi$
$457$	1.58137	−	0.513818i	0.0739733	−	0.0240354i	0.345770	+	0.938319i	$0.387618\pi$
$458$	−13.2173	+	0.924243i	−0.617603	+	0.0431870i
$459$	−22.4212	+	6.42916i	−1.04653	+	0.300088i
$460$	5.87431	+	3.12343i	0.273891	+	0.145631i
$461$	−8.27343	+	1.45883i	−0.385332	+	0.0679445i	−0.362959	−	0.931805i	$-0.618233\pi$
$461$	−8.27343	+	1.45883i	−0.385332	+	0.0679445i	−0.0223735	+	0.999750i	$0.507122\pi$
$462$	−7.33604	−	1.91605i	−0.341304	−	0.0891429i
$463$	18.0667	−	31.2924i	0.839630	−	1.45428i	−0.0505752	−	0.998720i	$-0.516105\pi$
$463$	18.0667	−	31.2924i	0.839630	−	1.45428i	0.890205	−	0.455561i	$-0.150561\pi$
$464$	−0.548558	+	0.116600i	−0.0254662	+	0.00541300i
$465$	−7.15032	−	0.499999i	−0.331588	−	0.0231869i
$466$	−14.8611	+	3.70528i	−0.688425	+	0.171644i
$467$	2.30581	−	2.56087i	0.106700	−	0.118503i	−0.687429	−	0.726252i	$-0.741261\pi$
$467$	2.30581	−	2.56087i	0.106700	−	0.118503i	0.794129	+	0.607749i	$0.207927\pi$
$468$	−2.82679	−	0.600852i	−0.130668	−	0.0277744i
$469$	−3.62161	−	1.03848i	−0.167230	−	0.0479526i
$470$	−1.11937	−	1.08096i	−0.0516326	−	0.0498611i
$471$	−11.9727	+	22.5173i	−0.551671	+	1.03754i
$472$	−0.710588	+	1.95232i	−0.0327074	+	0.0898630i
$473$	−37.0752	+	16.0149i	−1.70472	+	0.736365i
$474$		−	24.7306i		−	1.13592i
$475$	11.4099	+	14.5926i	0.523520	+	0.669557i
$476$	5.13257	−	3.72903i	0.235251	−	0.170920i
$477$	−0.610076	−	8.72450i	−0.0279335	−	0.399467i
$478$	−10.4587	−	0.365227i	−0.478372	−	0.0167051i
$479$	2.54623	+	18.1174i	0.116340	+	0.827805i	0.957790	+	0.287469i	$0.0928139\pi$
$479$	2.54623	+	18.1174i	0.116340	+	0.827805i	−0.841449	+	0.540336i	$0.818297\pi$
$480$	1.16228	+	0.566880i	0.0530504	+	0.0258744i
$481$	−29.2252	−	19.7127i	−1.33256	−	0.898820i
$482$	8.38567	+	9.31323i	0.381957	+	0.424206i
$483$	−8.77918	−	15.2060i	−0.399467	−	0.691896i
$484$	−3.63121	+	10.3834i	−0.165055	+	0.471971i
$485$	5.19574	−	6.19204i	0.235927	−	0.281166i
$486$	−1.62127	−	7.62749i	−0.0735424	−	0.345990i
$487$	16.5032	−	1.73455i	0.747829	−	0.0786000i	0.277055	−	0.960854i	$-0.410641\pi$
$487$	16.5032	−	1.73455i	0.747829	−	0.0786000i	0.470774	+	0.882254i	$0.343975\pi$
$488$	2.15480	−	7.51469i	0.0975434	−	0.340174i
$489$	13.6213	+	25.6179i	0.615976	+	1.15848i
$490$	3.99298	−	0.561177i	0.180385	−	0.0253514i
$491$	25.7820	−	17.3902i	1.16352	−	0.784807i	0.183370	−	0.983044i	$-0.441299\pi$
$491$	25.7820	−	17.3902i	1.16352	−	0.784807i	0.980154	+	0.198237i	$0.0635216\pi$
$492$	7.93152	+	1.97755i	0.357581	+	0.0891549i
$493$	2.20964	+	0.717957i	0.0995174	+	0.0323352i
$494$	−1.71304	−	16.2398i	−0.0770732	−	0.730662i
$495$	0.634546	−	2.12343i	0.0285207	−	0.0954413i
$496$	−3.56290	−	4.24610i	−0.159979	−	0.190655i
$497$	−9.58936	+	12.2738i	−0.430141	+	0.550556i
$498$	−10.4030	−	21.3294i	−0.466171	−	0.955792i
$499$	−6.98157	+	14.3143i	−0.312538	+	0.640798i	−0.996016	−	0.0891729i	$-0.971578\pi$
$499$	−6.98157	+	14.3143i	−0.312538	+	0.640798i	0.683478	+	0.729971i	$0.260467\pi$
$500$	4.93288	+	6.31380i	0.220605	+	0.282362i
$501$	−7.31128	+	34.3969i	−0.326644	+	1.53674i
$502$	−1.90371	+	18.1125i	−0.0849665	+	0.808403i
$503$	−0.549279	+	7.85505i	−0.0244911	+	0.350239i	0.969827	+	0.243793i	$0.0783917\pi$
$503$	−0.549279	+	7.85505i	−0.0244911	+	0.350239i	−0.994318	+	0.106447i	$0.966053\pi$
$504$	0.625997	+	1.00180i	0.0278841	+	0.0446239i
$505$	−2.70453	+	1.56146i	−0.120350	+	0.0694840i
$506$	−23.0181	+	10.9112i	−1.02328	+	0.485064i
$507$	−0.528454	−	1.45192i	−0.0234695	−	0.0644819i
$508$	−8.07136	−	1.13436i	−0.358109	−	0.0503289i
$509$	−21.7310	+	10.5989i	−0.963208	+	0.469788i	−0.851731	−	0.523979i	$-0.824447\pi$
$509$	−21.7310	+	10.5989i	−0.963208	+	0.469788i	−0.111477	+	0.993767i	$0.535558\pi$
$510$	−2.99577	−	4.44141i	−0.132655	−	0.196669i
$511$	−0.639450	−	0.399573i	−0.0282876	−	0.0176761i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	21.2487	−	12.2786i	0.938152	−	0.542112i
$514$	0.817365	+	1.12501i	0.0360524	+	0.0496219i
$515$	0.280462	−	0.113314i	0.0123586	−	0.00499321i
$516$	−17.0820	−	6.21733i	−0.751992	−	0.273703i
$517$	5.87866	−	0.969230i	0.258543	−	0.0426267i
$518$	2.50223	+	14.1909i	0.109942	+	0.623511i
$519$	−34.0428	+	1.18880i	−1.49431	+	0.0521826i
$520$	−0.339214	−	3.22741i	−0.0148755	−	0.141531i
$521$	17.2828	+	1.81650i	0.757174	+	0.0795822i	0.475246	−	0.879853i	$-0.342359\pi$
$521$	17.2828	+	1.81650i	0.757174	+	0.0795822i	0.281929	+	0.959435i	$0.409026\pi$
$522$	−0.162060	+	0.401113i	−0.00709319	+	0.0175562i
$523$	−0.990121	+	2.45064i	−0.0432950	+	0.107159i	−0.947282	−	0.320401i	$-0.896182\pi$
$523$	−0.990121	+	2.45064i	−0.0432950	+	0.107159i	0.903987	+	0.427560i	$0.140627\pi$
$524$	16.3134	+	1.71460i	0.712653	+	0.0749028i
$525$	−1.01551	−	9.66189i	−0.0443203	−	0.421680i
$526$	1.58707	−	0.0554216i	0.0691994	−	0.00241650i
$527$	3.98753	+	22.6144i	0.173699	+	0.985098i
$528$	−4.39726	+	2.27565i	−0.191366	+	0.0990351i
$529$	−33.8194	−	12.3093i	−1.47041	−	0.535185i
$530$	9.10576	−	3.67897i	0.395529	−	0.159804i
$531$	0.942036	+	1.29660i	0.0408809	+	0.0562677i
$532$	−4.28874	+	5.11502i	−0.185940	+	0.221764i
$533$	−6.33907	−	19.5097i	−0.274576	−	0.845057i
$534$	18.8423	+	11.7740i	0.815388	+	0.509511i
$535$	9.09286	+	13.4807i	0.393119	+	0.582822i
$536$	−2.21126	+	1.07851i	−0.0955121	+	0.0465843i
$537$	23.9573	+	3.36697i	1.03383	+	0.145296i
$538$	−3.62257	−	9.95293i	−0.156180	−	0.429101i
$539$	−7.39925	+	13.5500i	−0.318708	+	0.583638i
$540$	4.22360	−	2.43850i	0.181755	−	0.104936i
$541$	−16.5186	−	26.4352i	−0.710189	−	1.13654i	−0.984582	−	0.174922i	$-0.944033\pi$
$541$	−16.5186	−	26.4352i	−0.710189	−	1.13654i	0.274394	−	0.961617i	$-0.411523\pi$
$542$	−0.168818	+	2.41420i	−0.00725134	+	0.103699i
$543$	−2.42334	+	23.0565i	−0.103995	+	0.989450i
$544$	0.861344	−	4.05230i	0.0369298	−	0.173741i
$545$	−0.189895	−	0.243055i	−0.00813422	−	0.0104113i
$546$	−3.75442	+	7.69771i	−0.160675	+	0.329432i
$547$	−10.2717	−	21.0602i	−0.439187	−	0.900467i	−0.997488	−	0.0708290i	$-0.977436\pi$
$547$	−10.2717	−	21.0602i	−0.439187	−	0.900467i	0.558301	−	0.829638i	$-0.311453\pi$
$548$	12.9482	−	16.5729i	0.553119	−	0.707960i
$549$	−3.87632	−	4.61962i	−0.165437	−	0.197161i
$550$	−14.0905	+	0.335082i	−0.600821	+	0.0142880i
$551$	−2.43864	−	0.169606i	−0.103889	−	0.00722545i
$552$	−10.9046	−	3.54313i	−0.464132	−	0.150805i
$553$	24.6152	+	6.13726i	1.04675	+	0.260983i
$554$	−13.9451	+	9.40607i	−0.592469	+	0.399626i
$555$	12.0498	−	1.69349i	0.511485	−	0.0718845i
$556$	−2.86833	−	5.39455i	−0.121644	−	0.228780i
$557$	5.70023	−	19.8791i	0.241527	−	0.842303i	−0.743329	−	0.668926i	$-0.766754\pi$
$557$	5.70023	−	19.8791i	0.241527	−	0.842303i	0.984856	−	0.173377i	$-0.0554679\pi$
$558$	−4.25239	+	0.446944i	−0.180018	+	0.0189206i
$559$	9.48466	+	44.6218i	0.401158	+	1.88730i
$560$	−0.852669	+	1.01617i	−0.0360318	+	0.0429411i
$561$	20.4903	+	0.943979i	0.865103	+	0.0398548i
$562$	5.20543	+	9.01607i	0.219578	+	0.380320i
$563$	−9.91554	−	11.0123i	−0.417890	−	0.464114i	0.497039	−	0.867728i	$-0.334421\pi$
$563$	−9.91554	−	11.0123i	−0.417890	−	0.464114i	−0.914929	+	0.403614i	$0.867754\pi$
$564$	2.22329	+	1.49963i	0.0936173	+	0.0631456i
$565$	3.03553	+	1.48053i	0.127706	+	0.0622863i
$566$	1.41483	+	10.0671i	0.0594699	+	0.423150i
$567$	−9.32145	−	0.325512i	−0.391464	−	0.0136702i
$568$	0.709500	+	10.1463i	0.0297700	+	0.425730i
$569$	9.93506	−	7.21824i	0.416499	−	0.302605i	−0.359728	−	0.933057i	$-0.617131\pi$
$569$	9.93506	−	7.21824i	0.416499	−	0.302605i	0.776228	+	0.630453i	$0.217131\pi$
$570$	4.19031	+	3.77012i	0.175513	+	0.157913i
$571$		−	17.9962i		−	0.753116i	−0.926393	−	0.376558i	$-0.877108\pi$
$571$		−	17.9962i		−	0.753116i	0.926393	−	0.376558i	$-0.122892\pi$
$572$	10.6907	+	6.33197i	0.447001	+	0.264753i
$573$	1.98213	−	5.44585i	0.0828045	−	0.227503i
$574$	−3.93664	+	7.40375i	−0.164312	+	0.309026i
$575$	−23.4788	−	22.6732i	−0.979133	−	0.945538i
$576$	0.741523	+	0.212628i	0.0308968	+	0.00885951i
$577$	−43.6360	−	9.27512i	−1.81659	−	0.386128i	−0.831136	−	0.556069i	$-0.812309\pi$
$577$	−43.6360	−	9.27512i	−1.81659	−	0.386128i	−0.985454	+	0.169941i	$0.945642\pi$
$578$	−0.109127	+	0.121198i	−0.00453910	+	0.00504118i
$579$	−2.01859	+	0.503290i	−0.0838896	+	0.0209160i
$580$	−0.484610	−	0.0338872i	−0.0201223	−	0.00140709i
$581$	23.8115	−	5.06129i	0.987867	−	0.209978i
$582$	−6.96518	+	12.0640i	−0.288716	+	0.500071i
$583$	−9.50232	+	36.3817i	−0.393546	+	1.50678i
$584$	−0.484907	+	0.0855021i	−0.0200656	+	0.00353810i
$585$	−2.21033	−	1.17525i	−0.0913859	−	0.0485908i
$586$	7.89344	−	2.26341i	0.326075	−	0.0935005i
$587$	26.8657	−	1.87864i	1.10887	−	0.0775396i	0.496444	−	0.868069i	$-0.334639\pi$
$587$	26.8657	−	1.87864i	1.10887	−	0.0775396i	0.612424	+	0.790529i	$0.290194\pi$
$588$	−6.60896	+	2.14738i	−0.272549	+	0.0885565i
$589$	−9.83540	−	22.0684i	−0.405261	−	0.909311i
$590$	−1.05784	+	1.45599i	−0.0435504	+	0.0599420i
$591$	−6.00867	+	24.0995i	−0.247164	+	0.991319i
$592$	7.41497	+	5.79321i	0.304754	+	0.238100i
$593$	5.67045	+	0.999853i	0.232857	+	0.0410591i	0.288859	−	0.957372i	$-0.406724\pi$
$593$	5.67045	+	0.999853i	0.232857	+	0.0410591i	−0.0560016	+	0.998431i	$0.517835\pi$
$594$	−2.15844	+	18.5479i	−0.0885618	+	0.761029i
$595$	5.16412	−	1.87959i	0.211708	−	0.0770556i
$596$	0.808635	−	0.728098i	0.0331230	−	0.0298241i
$597$	−4.11070	+	9.23278i	−0.168240	+	0.377873i
$598$	6.96098	+	27.9190i	0.284655	+	1.14169i
$599$	1.34448	+	0.543204i	0.0549338	+	0.0221947i	0.401909	−	0.915680i	$-0.368347\pi$
$599$	1.34448	+	0.543204i	0.0549338	+	0.0221947i	−0.346975	+	0.937874i	$0.612791\pi$
$600$	−4.71457	−	4.24501i	−0.192471	−	0.173302i
$601$	−16.2019	+	7.21354i	−0.660888	+	0.294246i	−0.709640	−	0.704564i	$-0.751142\pi$
$601$	−16.2019	+	7.21354i	−0.660888	+	0.294246i	0.0487516	+	0.998811i	$0.484476\pi$
$602$	10.4274	−	15.4593i	0.424991	−	0.630075i
$603$	−0.264130	+	1.87939i	−0.0107562	+	0.0765345i
$604$	0.121385	−	0.688408i	0.00493909	−	0.0280109i
$605$	−5.50280	+	7.77895i	−0.223721	+	0.316259i
$606$	4.12284	−	3.45947i	0.167479	−	0.140532i
$607$	−8.67971	+	26.7134i	−0.352299	+	1.08426i	0.605261	+	0.796027i	$0.293069\pi$
$607$	−8.67971	+	26.7134i	−0.352299	+	1.08426i	−0.957559	+	0.288236i	$0.906931\pi$
$608$	0.153760	+	4.35619i	0.00623578	+	0.176667i
$609$	1.03722	+	0.753585i	0.0420303	+	0.0305368i
$610$	3.58850	−	5.74280i	0.145294	−	0.232519i
$611$	0.234872	−	6.72585i	0.00950190	−	0.272099i
$612$	−2.21999	−	2.29887i	−0.0897379	−	0.0929263i
$613$	25.7136	−	26.6272i	1.03856	−	1.07546i	0.0414779	−	0.999139i	$-0.486793\pi$
$613$	25.7136	−	26.6272i	1.03856	−	1.07546i	0.997083	−	0.0763221i	$-0.0243177\pi$
$614$	0.879621	+	25.1891i	0.0354986	+	1.01655i
$615$	6.13220	+	3.54043i	0.247274	+	0.142764i
$616$	−1.17379	−	4.94148i	−0.0472933	−	0.199098i
$617$	14.2571	+	11.9631i	0.573970	+	0.481618i	0.882961	−	0.469447i	$-0.155547\pi$
$617$	14.2571	+	11.9631i	0.573970	+	0.481618i	−0.308991	+	0.951065i	$0.599991\pi$
$618$	−0.442090	+	0.276249i	−0.0177835	+	0.0111124i
$619$	26.8824	+	11.9688i	1.08049	+	0.481067i	0.868239	−	0.496147i	$-0.165252\pi$
$619$	26.8824	+	11.9688i	1.08049	+	0.481067i	0.212256	+	0.977214i	$0.431919\pi$
$620$	−1.95291	−	4.38631i	−0.0784308	−	0.176158i
$621$	−34.0753	+	26.6225i	−1.36739	+	1.06833i
$622$	3.11635	−	1.65699i	0.124954	−	0.0664394i
$623$	−16.3950	+	15.8325i	−0.656854	+	0.634316i
$624$	1.54156	+	5.37605i	0.0617117	+	0.215214i
$625$	−5.35976	−	13.2659i	−0.214391	−	0.530635i
$626$	7.31204			0.292248
$627$	−21.1573	+	4.25983i	−0.844940	+	0.170121i
$628$	−17.0831			−0.681688
$629$	−14.6033	−	36.1444i	−0.582271	−	1.44117i
$630$	0.282055	+	0.983643i	0.0112373	+	0.0391893i
$631$	11.5178	−	11.1226i	0.458518	−	0.442785i	−0.429175	−	0.903221i	$-0.641196\pi$
$631$	11.5178	−	11.1226i	0.458518	−	0.442785i	0.887693	+	0.460436i	$0.152307\pi$
$632$	14.6270	−	7.77731i	0.581830	−	0.309365i
$633$	−25.7715	+	20.1349i	−1.02433	+	0.800292i
$634$	−3.12012	−	7.00790i	−0.123916	−	0.278319i
$635$	−6.44996	−	2.87171i	−0.255959	−	0.113960i
$636$	−14.3533	+	8.96896i	−0.569147	+	0.355642i
$637$	13.3589	+	11.2095i	0.529300	+	0.444135i
$638$	1.21137	−	1.41145i	0.0479588	−	0.0558800i
$639$	6.79487	+	3.92302i	0.268801	+	0.155192i
$640$	0.0302310	+	0.865703i	0.00119499	+	0.0342199i
$641$	−1.57838	+	1.63446i	−0.0623422	+	0.0645573i	−0.749786	−	0.661680i	$-0.769844\pi$
$641$	−1.57838	+	1.63446i	−0.0623422	+	0.0645573i	0.687444	+	0.726237i	$0.258733\pi$
$642$	−19.4667	−	20.1584i	−0.768289	−	0.795587i
$643$	−0.753183	+	21.5684i	−0.0297027	+	0.850573i	0.889534	+	0.456868i	$0.151029\pi$
$643$	−0.753183	+	21.5684i	−0.0297027	+	0.850573i	−0.919237	+	0.393705i	$0.871193\pi$
$644$	6.23273	−	9.97445i	0.245604	−	0.393048i
$645$	−12.7392	−	9.25559i	−0.501606	−	0.364438i
$646$	8.47182	−	15.9476i	0.333319	−	0.627451i
$647$	6.95332	−	21.4001i	0.273363	−	0.841325i	−0.716285	−	0.697808i	$-0.754159\pi$
$647$	6.95332	−	21.4001i	0.273363	−	0.841325i	0.989648	−	0.143517i	$-0.0458412\pi$
$648$	−4.66576	+	3.91504i	−0.183288	+	0.153797i
$649$	−2.05627	−	6.57672i	−0.0807155	−	0.258159i
$650$	−2.76458	+	15.6787i	−0.108436	+	0.614970i
$651$	−1.76354	+	12.5483i	−0.0691187	+	0.491805i
$652$	−10.8681	+	16.1127i	−0.425629	+	0.631021i
$653$	6.71507	−	2.98974i	0.262781	−	0.116998i	−0.271117	−	0.962546i	$-0.587393\pi$
$653$	6.71507	−	2.98974i	0.262781	−	0.116998i	0.533898	+	0.845549i	$0.320727\pi$
$654$	0.395028	+	0.355685i	0.0154468	+	0.0139084i
$655$	13.1743	+	5.32277i	0.514763	+	0.207978i
$656$	1.32468	+	5.31302i	0.0517202	+	0.207438i
$657$	−0.154491	+	0.346992i	−0.00602726	+	0.0135375i
$658$	−2.04437	+	1.84076i	−0.0796977	+	0.0717602i
$659$	31.2548	−	11.3758i	1.21751	−	0.443139i	0.348210	−	0.937417i	$-0.386790\pi$
$659$	31.2548	−	11.3758i	1.21751	−	0.443139i	0.869304	+	0.494278i	$0.164568\pi$
$660$	−4.20484	+	0.844963i	−0.163673	+	0.0328901i
$661$	30.0472	+	5.29812i	1.16870	+	0.206073i	0.724125	−	0.689669i	$-0.242244\pi$
$661$	30.0472	+	5.29812i	1.16870	+	0.206073i	0.444574	+	0.895742i	$0.353355\pi$
$662$	15.5352	+	12.1374i	0.603793	+	0.471735i
$663$	5.60525	−	22.4814i	0.217690	−	0.873106i
$664$	9.34375	−	12.8606i	0.362608	−	0.499087i
$665$	−4.79241	+	3.23514i	−0.185842	+	0.125453i
$666$	6.90346	−	2.24307i	0.267503	−	0.0869171i
$667$	4.29683	−	0.300463i	0.166374	−	0.0116340i
$668$	−22.6434	+	6.49288i	−0.876098	+	0.251217i
$669$	−25.3085	−	13.4568i	−0.978484	−	0.520269i
$670$	−2.09877	+	0.370070i	−0.0810826	+	0.0142971i
$671$	9.44456	+	24.1465i	0.364603	+	0.932164i
$672$	1.14305	−	1.97982i	0.0440941	−	0.0763732i
$673$	−32.2388	+	6.85256i	−1.24271	+	0.264147i	−0.781930	−	0.623366i	$-0.785765\pi$
$673$	−32.2388	+	6.85256i	−1.24271	+	0.264147i	−0.460783	+	0.887513i	$0.652431\pi$
$674$	4.88463	+	0.341567i	0.188149	+	0.0131567i
$675$	−23.2154	+	5.78824i	−0.893560	+	0.222789i
$676$	0.692550	−	0.769155i	0.0266365	−	0.0295829i
$677$	18.3727	+	3.90524i	0.706120	+	0.150091i	0.546956	−	0.837162i	$-0.315787\pi$
$677$	18.3727	+	3.90524i	0.706120	+	0.150091i	0.159165	+	0.987252i	$0.449120\pi$
$678$	−5.59498	−	1.60433i	−0.214874	−	0.0616141i
$679$	−10.2792	−	9.92654i	−0.394481	−	0.380946i
$680$	1.68477	−	3.16859i	0.0646079	−	0.121510i
$681$	−5.15138	+	14.1533i	−0.197401	+	0.542355i
$682$	17.9383	+	4.02208i	0.686892	+	0.154014i
$683$			14.0948i			0.539322i	0.962955	+	0.269661i	$0.0869117\pi$
$683$			14.0948i			0.539322i	−0.962955	+	0.269661i	$0.913088\pi$
$684$	2.85221	+	1.78077i	0.109057	+	0.0680895i
$685$	14.7387	−	10.7083i	0.563135	−	0.409142i
$686$	−1.24501	−	17.8045i	−0.0475347	−	0.679778i
$687$	19.7675	+	0.690297i	0.754178	+	0.0263365i
$688$	−1.69470	−	12.0584i	−0.0646097	−	0.459722i
$689$	38.1754	+	18.6194i	1.45437	+	0.709342i
$690$	−8.23402	−	5.55392i	−0.313464	−	0.211434i
$691$	−15.2808	−	16.9711i	−0.581310	−	0.645610i	0.378719	−	0.925512i	$-0.376365\pi$
$691$	−15.2808	−	16.9711i	−0.581310	−	0.645610i	−0.960029	+	0.279902i	$0.909698\pi$
$692$	−11.4089	−	19.7608i	−0.433702	−	0.751194i
$693$	−3.66653	−	1.38091i	−0.139280	−	0.0524565i
$694$	−11.4906	+	13.6940i	−0.436177	+	0.519815i
$695$	−1.10035	−	5.17676i	−0.0417388	−	0.196366i
$696$	0.832623	−	0.0875122i	0.0315605	−	0.00331714i
$697$	6.25277	−	21.8060i	0.236841	−	0.825962i
$698$	4.18518	+	7.87118i	0.158411	+	0.297929i
$699$	22.6419	−	3.18212i	0.856397	−	0.120359i
$700$	5.39519	−	3.63910i	0.203919	−	0.137545i
$701$	20.8895	+	5.20834i	0.788985	+	0.196716i	0.615517	−	0.788123i	$-0.288947\pi$
$701$	20.8895	+	5.20834i	0.788985	+	0.196716i	0.173468	+	0.984840i	$0.444503\pi$
$702$	20.0600	+	6.51789i	0.757117	+	0.246002i
$703$	24.1211	+	33.1737i	0.909745	+	1.25117i
$704$	−2.72879	−	1.88512i	−0.102845	−	0.0710482i
$705$	1.49321	+	1.77954i	0.0562377	+	0.0670215i
$706$	−14.3466	+	18.3628i	−0.539942	+	0.691094i
$707$	2.42019	+	4.96212i	0.0910205	+	0.186620i
$708$	1.35964	−	2.78767i	0.0510983	−	0.104767i
$709$	−30.8492	−	39.4852i	−1.15857	−	1.48290i	−0.846145	−	0.532953i	$-0.821082\pi$
$709$	−30.8492	−	39.4852i	−1.15857	−	1.48290i	−0.312421	−	0.949944i	$-0.601140\pi$
$710$	−1.83181	+	8.61798i	−0.0687465	+	0.323427i
$711$	1.33579	−	12.7092i	0.0500959	−	0.476631i
$712$	−1.03821	+	14.8470i	−0.0389084	+	0.556416i
$713$	22.5597	+	36.1031i	0.844869	+	1.35207i
$714$	−8.20207	+	4.73547i	−0.306955	+	0.177220i
$715$	7.39002	+	7.82504i	0.276371	+	0.292640i
$716$	5.54269	+	15.2284i	0.207140	+	0.569113i
$717$	15.4708	+	2.17428i	0.577767	+	0.0811998i
$718$	2.33640	−	1.13954i	0.0871935	−	0.0425271i
$719$	24.5750	+	36.4339i	0.916492	+	1.35876i	0.933377	+	0.358898i	$0.116848\pi$
$719$	24.5750	+	36.4339i	0.916492	+	1.35876i	−0.0168842	+	0.999857i	$0.505375\pi$
$720$	0.566678	+	0.354100i	0.0211189	+	0.0131965i
$721$	−0.165248	−	0.508582i	−0.00615417	−	0.0189406i
$722$	−4.58267	+	18.4391i	−0.170549	+	0.686231i
$723$	−10.9967	−	15.1356i	−0.408970	−	0.562899i
$724$	−14.3989	+	5.81754i	−0.535132	+	0.216207i
$725$	2.23953	+	0.815122i	0.0831741	+	0.0302729i
$726$	7.01142	−	14.8492i	0.260218	−	0.551107i
$727$	−4.26974	−	24.2149i	−0.158356	−	0.898080i	−0.955653	−	0.294494i	$-0.904849\pi$
$727$	−4.26974	−	24.2149i	−0.158356	−	0.898080i	0.797298	−	0.603586i	$-0.206262\pi$
$728$	−5.73352	+	0.200219i	−0.212498	+	0.00742061i
$729$	3.12678	+	29.7493i	0.115807	+	1.10183i
$730$	−0.424184	−	0.0445835i	−0.0156998	−	0.00165011i
$731$	−18.8977	+	46.7735i	−0.698958	+	1.72998i
$732$	−4.37180	+	10.8206i	−0.161586	+	0.399940i
$733$	−52.1537	−	5.48157i	−1.92634	−	0.202467i	−0.937132	−	0.348976i	$-0.886529\pi$
$733$	−52.1537	−	5.48157i	−1.92634	−	0.202467i	−0.989209	+	0.146510i	$0.953196\pi$
$734$	2.12276	+	20.1967i	0.0783525	+	0.745475i
$735$	−6.01583	+	0.210077i	−0.221897	+	0.00774882i
$736$	−1.33370	−	7.56380i	−0.0491609	−	0.278805i
$737$	3.65840	−	7.29367i	0.134759	−	0.268666i
$738$	3.96922	+	1.44468i	0.146109	+	0.0531794i
$739$	−14.8528	+	6.00093i	−0.546370	+	0.220748i	−0.631162	−	0.775651i	$-0.717422\pi$
$739$	−14.8528	+	6.00093i	−0.546370	+	0.220748i	0.0847924	+	0.996399i	$0.472977\pi$
$740$	4.79104	+	6.59430i	0.176122	+	0.242411i
$741$	0.00915660	+	24.3780i	0.000336376	+	0.895549i
$742$	−5.36511	−	16.5121i	−0.196960	−	0.606179i
$743$	11.0335	+	6.89453i	0.404782	+	0.252936i	0.716998	−	0.697075i	$-0.245516\pi$
$743$	11.0335	+	6.89453i	0.404782	+	0.252936i	−0.312216	+	0.950011i	$0.601071\pi$
$744$	4.62714	+	6.86002i	0.169639	+	0.251501i
$745$	0.847174	−	0.413194i	0.0310381	−	0.0151383i
$746$	−15.7624	−	2.21527i	−0.577104	−	0.0811067i
$747$	−4.19408	−	11.5231i	−0.153453	−	0.421610i
$748$	5.88550	+	12.4159i	0.215195	+	0.453971i
$749$	24.8952	−	14.3733i	0.909651	−	0.525187i
$750$	−6.33846	−	10.1437i	−0.231448	−	0.370394i
$751$	2.40684	−	34.4194i	0.0878268	−	1.25598i	−0.731175	−	0.682190i	$-0.761028\pi$
$751$	2.40684	−	34.4194i	0.0878268	−	1.25598i	0.819001	−	0.573791i	$-0.194528\pi$
$752$	−0.187776	+	1.78657i	−0.00684749	+	0.0651495i
$753$	5.65275	−	26.5941i	0.205998	−	0.969143i
$754$	−1.29350	−	1.65561i	−0.0471065	−	0.0602936i
$755$	0.265442	−	0.544237i	0.00966043	−	0.0198068i
$756$	−3.77955	−	7.74923i	−0.137461	−	0.281837i
$757$	16.2027	−	20.7384i	0.588895	−	0.753752i	−0.397597	−	0.917560i	$-0.630156\pi$
$757$	16.2027	−	20.7384i	0.588895	−	0.753752i	0.986492	+	0.163809i	$0.0523779\pi$
$758$	10.2732	+	12.2431i	0.373138	+	0.444688i
$759$	35.8769	−	12.6077i	1.30225	−	0.457631i
$760$	−0.912075	+	3.66400i	−0.0330844	+	0.132907i
$761$	−6.97164	−	2.26522i	−0.252722	−	0.0821142i	0.179917	−	0.983682i	$-0.442417\pi$
$761$	−6.97164	−	2.26522i	−0.252722	−	0.0821142i	−0.432638	+	0.901568i	$0.642417\pi$
$762$	11.8063	+	2.94364i	0.427697	+	0.106637i
$763$	−0.452056	+	0.304916i	−0.0163655	+	0.0110387i
$764$	3.84430	−	0.540280i	0.139082	−	0.0195467i
$765$	−1.29964	−	2.44427i	−0.0469886	−	0.0883727i
$766$	4.82642	−	16.8317i	0.174386	−	0.608155i
$767$	−7.74081	+	0.813592i	−0.279505	+	0.0293771i
$768$	−0.310381	−	1.46023i	−0.0111999	−	0.0526913i
$769$	27.0676	−	32.2579i	0.976081	−	1.16325i	−0.0104945	−	0.999945i	$-0.503341\pi$
$769$	27.0676	−	32.2579i	0.976081	−	1.16325i	0.986576	−	0.163304i	$-0.0522150\pi$
$770$	0.202471	−	4.39490i	0.00729654	−	0.158381i
$771$	−1.03797	−	1.79781i	−0.0373814	−	0.0647465i
$772$	−0.932478	−	1.03562i	−0.0335606	−	0.0372728i
$773$	−16.4501	−	11.0957i	−0.591668	−	0.399085i	0.226545	−	0.974001i	$-0.427257\pi$
$773$	−16.4501	−	11.0957i	−0.591668	−	0.399085i	−0.818213	+	0.574916i	$0.805035\pi$
$774$	−8.44266	−	4.11776i	−0.303465	−	0.148010i
$775$	3.27826	+	23.3261i	0.117759	+	0.837896i
$776$	−9.32572	−	0.325661i	−0.334774	−	0.0116906i
$777$	−1.50057	−	21.4592i	−0.0538328	−	0.769845i
$778$	12.2310	−	8.88638i	0.438504	−	0.318592i
$779$	−0.824017	+	23.8536i	−0.0295235	+	0.854646i
$780$			4.84457i			0.173463i
$781$	−22.2918	−	25.3187i	−0.797665	−	0.905975i
$782$	−10.8827	+	29.9001i	−0.389166	+	1.06922i
$783$	1.48234	−	2.78787i	0.0529743	−	0.0996302i
$784$	−3.34846	−	3.23357i	−0.119588	−	0.115485i
$785$	−14.2246	−	4.07884i	−0.507698	−	0.145580i
$786$	−23.9524	−	5.09124i	−0.854354	−	0.181599i
$787$	16.6943	−	18.5409i	0.595087	−	0.660911i	−0.368086	−	0.929792i	$-0.619987\pi$
$787$	16.6943	−	18.5409i	0.595087	−	0.660911i	0.963174	+	0.268880i	$0.0866536\pi$
$788$	−16.1433	+	4.02497i	−0.575081	+	0.143384i
$789$	−2.36492	−	0.165371i	−0.0841933	−	0.00588737i
$790$	14.0365	−	2.98354i	0.499395	−	0.106150i
$791$	2.98532	−	5.17073i	0.106146	−	0.183850i
$792$	−2.38269	+	0.931955i	−0.0846650	+	0.0331156i
$793$	28.8421	−	5.08564i	1.02421	−	0.180597i
$794$	−2.31528	−	1.23106i	−0.0821664	−	0.0436886i
$795$	−14.0931	+	4.04114i	−0.499832	+	0.143324i
$796$	−6.75348	+	0.472249i	−0.239371	+	0.0167384i
$797$	−21.1615	+	6.87577i	−0.749577	+	0.243552i	−0.658799	−	0.752319i	$-0.728935\pi$
$797$	−21.1615	+	6.87577i	−0.749577	+	0.243552i	−0.0907779	+	0.995871i	$0.528935\pi$
$798$	7.16553	−	6.92488i	0.253657	−	0.245138i
$799$	4.37444	−	6.02090i	0.154756	−	0.213004i
$800$	1.02808	−	4.12341i	0.0363482	−	0.145785i
$801$	9.04719	+	7.06844i	0.319667	+	0.249751i
$802$	12.6430	+	2.22930i	0.446439	+	0.0787193i
$803$	1.10617	−	1.20137i	0.0390360	−	0.0423953i
$804$	3.45129	−	1.25617i	0.121718	−	0.0443016i
$805$	7.57138	−	6.81731i	0.266856	−	0.240278i
$806$	8.44608	−	18.9702i	0.297501	−	0.668197i
$807$	3.82522	+	15.3421i	0.134654	+	0.540068i
$808$	3.34267	+	1.35052i	0.117595	+	0.0475113i
$809$	21.1207	+	19.0172i	0.742564	+	0.668608i	0.950917	−	0.309446i	$-0.100143\pi$
$809$	21.1207	+	19.0172i	0.742564	+	0.668608i	−0.208353	+	0.978054i	$0.566810\pi$
$810$	−4.81983	+	2.14593i	−0.169352	+	0.0754002i
$811$	16.2997	−	24.1654i	0.572361	−	0.848560i	−0.426062	−	0.904694i	$-0.640099\pi$
$811$	16.2997	−	24.1654i	0.572361	−	0.848560i	0.998423	+	0.0561335i	$0.0178773\pi$
$812$	−0.119524	+	0.850454i	−0.00419445	+	0.0298451i
$813$	0.627363	−	3.55795i	0.0220026	−	0.124783i
$814$	−31.2066	−	0.347354i	−1.09379	−	0.0121748i
$815$	−12.8968	+	10.8217i	−0.451754	+	0.379067i
$816$	−1.91115	+	5.88193i	−0.0669038	+	0.205909i
$817$	7.36727	−	52.5641i	0.257748	−	1.83898i
$818$	−3.03818	−	2.20736i	−0.106227	−	0.0771787i
$819$	−2.34519	+	3.75309i	−0.0819476	+	0.131144i
$820$	−0.165535	+	4.74030i	−0.00578073	+	0.165538i
$821$	0.497335	+	0.515005i	0.0173571	+	0.0179738i	0.727962	−	0.685617i	$-0.240468\pi$
$821$	0.497335	+	0.515005i	0.0173571	+	0.0179738i	−0.710605	+	0.703591i	$0.751579\pi$
$822$	−21.8099	+	22.5848i	−0.760708	+	0.787736i
$823$	1.05193	+	30.1232i	0.0366678	+	1.05003i	0.868711	+	0.495319i	$0.164949\pi$
$823$	1.05193	+	30.1232i	0.0366678	+	1.05003i	−0.832044	+	0.554710i	$0.812829\pi$
$824$	−0.302417	−	0.174600i	−0.0105352	−	0.00608249i
$825$	20.9720	+	1.70127i	0.730152	+	0.0592305i
$826$	2.43725	+	2.04509i	0.0848027	+	0.0711579i
$827$	0.630417	−	0.393928i	0.0219218	−	0.0136982i	−0.518914	−	0.854826i	$-0.673664\pi$
$827$	0.630417	−	0.393928i	0.0219218	−	0.0136982i	0.540836	+	0.841128i	$0.318108\pi$
$828$	−5.41255	−	2.40982i	−0.188099	−	0.0837471i
$829$	8.23896	+	18.5050i	0.286151	+	0.642705i	0.998235	−	0.0593890i	$-0.0189152\pi$
$829$	8.23896	+	18.5050i	0.286151	+	0.642705i	−0.712084	+	0.702094i	$0.752249\pi$
$830$	10.8510	−	8.47769i	0.376642	−	0.294265i
$831$	22.1716	−	11.7889i	0.769124	−	0.408951i
$832$	−2.69489	+	2.60242i	−0.0934283	+	0.0902227i
$833$	5.31554	+	18.5375i	0.184172	+	0.642286i
$834$	3.41674	+	8.45672i	0.118312	+	0.292832i
$835$	−20.4048			−0.706137
$836$	−9.17303	−	11.1739i	−0.317256	−	0.386457i
$837$	31.2072			1.07868
$838$	1.44089	+	3.56633i	0.0497747	+	0.123197i
$839$	−12.3698	−	43.1385i	−0.427052	−	1.48931i	−0.821404	−	0.570347i	$-0.806809\pi$
$839$	−12.3698	−	43.1385i	−0.427052	−	1.48931i	0.394352	−	0.918959i	$-0.370969\pi$
$840$	1.42450	−	1.37562i	0.0491499	−	0.0474636i
$841$	25.3278	−	13.4670i	0.873372	−	0.464380i
$842$	3.74167	−	2.92331i	0.128946	−	0.100744i
$843$	−6.32143	−	14.1982i	−0.217722	−	0.489011i
$844$	−20.0135	−	8.91058i	−0.688893	−	0.306715i
$845$	0.760316	−	0.475098i	0.0261557	−	0.0163439i
$846$	1.06155	+	0.890750i	0.0364970	+	0.0306246i
$847$	13.0400	+	10.6637i	0.448058	+	0.366411i
$848$	−9.81855	−	5.66875i	−0.337171	−	0.194666i
$849$	−0.529645	−	15.1670i	−0.0181774	−	0.520531i
$850$	−12.2299	+	12.6644i	−0.419481	+	0.434385i
$851$	−50.2039	−	51.9877i	−1.72097	−	1.78211i
$852$	0.529910	−	15.1746i	0.0181544	−	0.519875i
$853$	−16.1161	+	25.7912i	−0.551805	+	0.883073i	−0.999941	−	0.0108927i	$-0.996533\pi$
$853$	−16.1161	+	25.7912i	−0.551805	+	0.883073i	0.448135	+	0.893966i	$0.352088\pi$
$854$	−9.68516	−	7.03668i	−0.331419	−	0.240790i
$855$	1.94978	+	2.16381i	0.0666810	+	0.0740008i
$856$	5.80080	−	17.8530i	0.198267	−	0.610204i
$857$	29.0498	−	24.3756i	0.992321	−	0.832656i	0.00641878	−	0.999979i	$-0.497957\pi$
$857$	29.0498	−	24.3756i	0.992321	−	0.832656i	0.985902	+	0.167323i	$0.0535124\pi$
$858$	−14.8841	−	11.0691i	−0.508135	−	0.377893i
$859$	−6.05972	+	34.3664i	−0.206755	+	1.17257i	0.687899	+	0.725806i	$0.258533\pi$
$859$	−6.05972	+	34.3664i	−0.206755	+	1.17257i	−0.894654	+	0.446760i	$0.852578\pi$
$860$	1.46800	−	10.4453i	0.0500583	−	0.356183i
$861$	6.99993	−	10.3778i	0.238557	−	0.353675i
$862$	15.9778	−	7.11379i	0.544207	−	0.242297i
$863$	8.19832	+	7.38180i	0.279074	+	0.251279i	0.796766	−	0.604288i	$-0.206542\pi$
$863$	8.19832	+	7.38180i	0.279074	+	0.251279i	−0.517692	+	0.855567i	$0.673209\pi$
$864$	−5.22017	−	2.10909i	−0.177594	−	0.0717525i
$865$	−4.78171	−	19.1784i	−0.162583	−	0.652085i
$866$	9.01511	−	20.2483i	0.306346	−	0.688064i
$867$	0.180931	−	0.162911i	0.00614472	−	0.00553273i
$868$	−7.97630	+	2.90313i	−0.270733	+	0.0985388i
$869$	−22.9048	+	49.9415i	−0.776992	+	1.69415i
$870$	0.714198	+	0.125932i	0.0242136	+	0.00426951i
$871$	−7.26305	−	5.67451i	−0.246099	−	0.192274i
$872$	−0.0861418	+	0.345496i	−0.00291713	+	0.0117000i
$873$	−4.23105	+	5.82354i	−0.143199	+	0.197097i
$874$	3.48695	−	33.2964i	0.117948	−	1.12627i
$875$	11.6693	−	3.79158i	0.394494	−	0.128179i
$876$	0.733268	−	0.0512751i	0.0247748	−	0.00173243i
$877$	−29.0747	+	8.33704i	−0.981783	+	0.281522i	−0.727877	−	0.685707i	$-0.759493\pi$
$877$	−29.0747	+	8.33704i	−0.981783	+	0.281522i	−0.253906	+	0.967229i	$0.581715\pi$
$878$	−5.63270	−	2.99496i	−0.190094	−	0.101075i
$879$	−12.0723	+	2.12868i	−0.407190	+	0.0717986i
$880$	−1.82209	−	2.22123i	−0.0614228	−	0.0748778i
$881$	24.7734	−	42.9088i	0.834637	−	1.44563i	−0.0596882	−	0.998217i	$-0.519011\pi$
$881$	24.7734	−	42.9088i	0.834637	−	1.44563i	0.894325	−	0.447417i	$-0.147656\pi$
$882$	−3.51236	+	0.746574i	−0.118267	+	0.0251385i
$883$	22.5943	+	1.57995i	0.760358	+	0.0531694i	0.444671	−	0.895694i	$-0.353321\pi$
$883$	22.5943	+	1.57995i	0.760358	+	0.0531694i	0.315687	+	0.948863i	$0.397765\pi$
$884$	15.0594	−	3.75473i	0.506503	−	0.126285i
$885$	1.79774	−	1.99659i	0.0604302	−	0.0671145i
$886$	11.6009	+	2.46585i	0.389739	+	0.0828417i
$887$	22.0980	+	6.33650i	0.741978	+	0.212759i	0.625271	−	0.780407i	$-0.284988\pi$
$887$	22.0980	+	6.33650i	0.741978	+	0.212759i	0.116707	+	0.993166i	$0.462766\pi$
$888$	−10.1048	−	9.75808i	−0.339094	−	0.327460i
$889$	−5.85980	+	11.0207i	−0.196531	+	0.369622i
$890$	−4.40944	+	12.1148i	−0.147805	+	0.406091i
$891$	4.41961	−	19.7112i	0.148062	−	0.660351i
$892$		−	19.2007i		−	0.642886i
$893$	−2.93058	+	7.26130i	−0.0980682	+	0.242990i
$894$	−1.31417	+	0.954802i	−0.0439525	+	0.0319334i
$895$	0.979234	+	14.0037i	0.0327322	+	0.468092i
$896$	1.53044	+	0.0534440i	0.0511283	+	0.00178544i
$897$	−5.97814	−	42.5367i	−0.199604	−	1.42026i
$898$	−0.719741	−	0.351041i	−0.0240181	−	0.0117144i
$899$	−2.57708	−	1.73826i	−0.0859505	−	0.0579744i
$900$	−2.19354	−	2.43618i	−0.0731181	−	0.0812059i
$901$	23.4847	+	40.6767i	0.782388	+	1.35514i
$902$	−14.1855	−	11.3395i	−0.472326	−	0.377562i
$903$	−17.8937	+	21.3248i	−0.595464	+	0.709646i
$904$	−0.810625	−	3.81369i	−0.0269610	−	0.126842i
$905$	−13.3786	+	1.40615i	−0.444721	+	0.0467420i
$906$	−0.287639	+	1.00312i	−0.00955618	+	0.0333264i
$907$	−9.13604	−	17.1824i	−0.303357	−	0.570532i	0.683917	−	0.729560i	$-0.260275\pi$
$907$	−9.13604	−	17.1824i	−0.303357	−	0.570532i	−0.987274	+	0.159028i	$0.949164\pi$
$908$	−9.99100	+	1.40414i	−0.331563	+	0.0465981i
$909$	2.30560	−	1.55515i	0.0764719	−	0.0515810i
$910$	−4.82196	−	1.20225i	−0.159846	−	0.0398542i
$911$	−29.5340	−	9.59619i	−0.978506	−	0.317936i	−0.224261	−	0.974529i	$-0.571997\pi$
$911$	−29.5340	−	9.59619i	−0.978506	−	0.317936i	−0.754245	+	0.656593i	$0.771997\pi$
$912$	0.451479	−	6.49149i	0.0149500	−	0.214955i
$913$	1.25343	+	52.7079i	0.0414826	+	1.74438i
$914$	−1.06879	−	1.27374i	−0.0353526	−	0.0421316i
$915$	−6.22387	+	7.96619i	−0.205755	+	0.263354i
$916$	5.80823	+	11.9086i	0.191909	+	0.393472i
$917$	11.0116	−	22.5771i	0.363635	−	0.745563i
$918$	14.3601	+	18.3801i	0.473955	+	0.606635i
$919$	−5.76986	+	27.1451i	−0.190330	+	0.895433i	0.774503	+	0.632570i	$0.218000\pi$
$919$	−5.76986	+	27.1451i	−0.190330	+	0.895433i	−0.964833	+	0.262863i	$0.915333\pi$
$920$	0.695435	−	6.61662i	0.0229278	−	0.218144i
$921$	2.62468	−	37.5347i	0.0864862	−	1.23681i
$922$	4.45189	+	7.12451i	0.146615	+	0.234633i
$923$	−32.9993	+	19.0521i	−1.08618	+	0.627109i
$924$	0.971595	+	7.51963i	0.0319631	+	0.247378i
$925$	−13.6767	−	37.5765i	−0.449688	−	1.23551i
$926$	−35.7817	−	5.02879i	−1.17586	−	0.165256i
$927$	−0.242113	+	0.118086i	−0.00795203	+	0.00387847i
$928$	0.313603	+	0.464935i	0.0102945	+	0.0152623i
$929$	−8.10941	−	5.06732i	−0.266061	−	0.166253i	0.390328	−	0.920676i	$-0.372362\pi$
$929$	−8.10941	−	5.06732i	−0.266061	−	0.166253i	−0.656389	+	0.754422i	$0.727917\pi$
$930$	2.21497	+	6.81696i	0.0726316	+	0.223537i
$931$	−10.1517	−	17.5681i	−0.332710	−	0.575771i
$932$	9.00252	+	12.3909i	0.294887	+	0.405878i
$933$	−4.88532	+	1.97380i	−0.159938	+	0.0646193i
$934$	−3.23817	−	1.17860i	−0.105956	−	0.0385649i
$935$	1.93621	+	11.7437i	0.0633208	+	0.384059i
$936$	0.501833	+	2.84604i	0.0164029	+	0.0930256i
$937$	53.1037	−	1.85442i	1.73482	−	0.0605813i	0.850077	−	0.526658i	$-0.176555\pi$
$937$	53.1037	−	1.85442i	1.73482	−	0.0605813i	0.884744	+	0.466077i	$0.154333\pi$
$938$	0.393817	+	3.74692i	0.0128586	+	0.122341i
$939$	−10.8560	−	1.14101i	−0.354271	−	0.0372354i
$940$	−0.582928	+	1.44280i	−0.0190130	+	0.0470588i
$941$	−1.83456	+	4.54070i	−0.0598050	+	0.148023i	−0.954128	−	0.299400i	$-0.903214\pi$
$941$	−1.83456	+	4.54070i	−0.0598050	+	0.148023i	0.894323	+	0.447423i	$0.147658\pi$
$942$	25.3627	+	2.66573i	0.826361	+	0.0868541i
$943$	−4.39603	−	41.8254i	−0.143154	−	1.36202i
$944$	2.07635	−	0.0725079i	0.0675796	−	0.00235993i
$945$	−1.29689	−	7.35501i	−0.0421877	−	0.239259i
$946$	28.7373	+	28.3762i	0.934331	+	0.922590i
$947$	39.8866	+	14.5176i	1.29614	+	0.471757i	0.895738	−	0.444582i	$-0.146648\pi$
$947$	39.8866	+	14.5176i	1.29614	+	0.471757i	0.400403	+	0.916339i	$0.368870\pi$
$948$	−22.9299	+	9.26426i	−0.744727	+	0.300889i
$949$	−1.08426	−	1.49235i	−0.0351964	−	0.0484437i
$950$	9.25586	−	16.0455i	0.300300	−	0.520586i
$951$	3.53880	+	10.8913i	0.114753	+	0.353175i
$952$	−5.38019	−	3.36192i	−0.174373	−	0.108960i
$953$	3.14644	+	4.66479i	0.101923	+	0.151107i	0.876549	−	0.481312i	$-0.159840\pi$
$953$	3.14644	+	4.66479i	0.101923	+	0.151107i	−0.774626	+	0.632420i	$0.782062\pi$
$954$	−7.86068	+	3.83391i	−0.254499	+	0.124127i
$955$	3.33004	+	0.468007i	0.107758	+	0.0151444i
$956$	3.57928	+	9.83399i	0.115762	+	0.318054i
$957$	−2.01874	+	1.90651i	−0.0652566	+	0.0616288i
$958$	15.8443	−	9.14773i	0.511907	−	0.295550i
$959$	−17.0670	−	27.3129i	−0.551121	−	0.881978i
$960$	0.0902056	−	1.29000i	0.00291137	−	0.0416346i
$961$	−0.0288957	+	0.274925i	−0.000932121	+	0.00886854i
$962$	−7.32930	+	34.4817i	−0.236306	+	1.11173i
$963$	−8.91518	−	11.4109i	−0.287288	−	0.367711i
$964$	5.49375	−	11.2639i	0.176942	−	0.362784i
$965$	−0.529179	−	1.08498i	−0.0170349	−	0.0349267i
$966$	−10.8100	+	13.8362i	−0.347806	+	0.445172i
$967$	−7.94458	−	9.46798i	−0.255481	−	0.304470i	0.623025	−	0.782202i	$-0.285903\pi$
$967$	−7.94458	−	9.46798i	−0.255481	−	0.304470i	−0.878506	+	0.477732i	$0.841459\pi$
$968$	10.9876	−	0.522881i	0.353154	−	0.0168060i
$969$	−15.0664	+	22.3550i	−0.484003	+	0.718145i
$970$	−7.68752	−	2.49783i	−0.246832	−	0.0802004i
$971$	−23.5536	−	5.87256i	−0.755870	−	0.188459i	−0.155119	−	0.987896i	$-0.549576\pi$
$971$	−23.5536	−	5.87256i	−0.755870	−	0.188459i	−0.600751	+	0.799436i	$0.705132\pi$
$972$	−6.46474	+	4.36052i	−0.207357	+	0.139864i
$973$	−9.26516	+	1.30213i	−0.297027	+	0.0417445i
$974$	−7.79044	−	14.6517i	−0.249622	−	0.469470i
$975$	6.55107	−	22.8463i	0.209802	−	0.731667i
$976$	−7.77470	+	0.817154i	−0.248862	+	0.0261565i
$977$	−2.05564	−	9.67105i	−0.0657659	−	0.309404i	0.932953	−	0.359997i	$-0.117222\pi$
$977$	−2.05564	−	9.67105i	−0.0657659	−	0.309404i	−0.998719	+	0.0505928i	$0.983889\pi$
$978$	18.6499	−	22.2261i	0.596358	−	0.710712i
$979$	−27.1458	−	41.2279i	−0.867585	−	1.31765i
$980$	−2.01611	−	3.49201i	−0.0644023	−	0.111548i
$981$	0.183794	+	0.204124i	0.00586810	+	0.00651719i
$982$	−25.7820	−	17.3902i	−0.822736	−	0.554942i
$983$	50.6284	+	24.6931i	1.61480	+	0.787589i	0.999999	−	0.00109670i	$-0.000349089\pi$
$983$	50.6284	+	24.6931i	1.61480	+	0.787589i	0.614797	+	0.788685i	$0.289238\pi$
$984$	−1.13765	−	8.09478i	−0.0362669	−	0.258052i
$985$	−14.4031	−	0.502968i	−0.458921	−	0.0160259i
$986$	−0.162069	−	2.31770i	−0.00516134	−	0.0738106i
$987$	3.32245	−	2.41390i	0.105755	−	0.0768354i
$988$	−14.4155	+	7.67183i	−0.458620	+	0.244073i
$989$			93.5245i			2.97391i
$990$	−2.20652	+	0.207112i	−0.0701278	+	0.00658245i
$991$	−14.1246	+	38.8069i	−0.448682	+	1.23274i	0.484961	+	0.874536i	$0.338834\pi$
$991$	−14.1246	+	38.8069i	−0.448682	+	1.23274i	−0.933642	+	0.358207i	$0.883388\pi$
$992$	−2.60223	+	4.89408i	−0.0826208	+	0.155387i
$993$	−21.1707	−	20.4443i	−0.671831	−	0.648780i
$994$	14.9723	+	4.29324i	0.474893	+	0.136173i
$995$	−5.73620	−	1.21927i	−0.181850	−	0.0386534i
$996$	−15.8792	+	17.6356i	−0.503152	+	0.558807i
$997$	−34.5435	+	8.61267i	−1.09401	+	0.272766i	−0.746817	−	0.665029i	$-0.768419\pi$
$997$	−34.5435	+	8.61267i	−1.09401	+	0.272766i	−0.347188	+	0.937796i	$0.612863\pi$
$998$	15.8874	+	1.11095i	0.502906	+	0.0351666i
$999$	−51.8204	+	11.0148i	−1.63952	+	0.348492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.b.13.8	yes	240
11.6	odd	10		418.2.v.a.127.3	yes	240
19.3	odd	18		418.2.v.a.79.3	✓	240
209.193	even	90	inner	418.2.v.b.193.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.79.3	✓	240	19.3	odd	18
418.2.v.a.127.3	yes	240	11.6	odd	10
418.2.v.b.13.8	yes	240	1.1	even	1	trivial
418.2.v.b.193.8	yes	240	209.193	even	90	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.374607 - 0.927184i) q^{2} +(0.411485 + 1.43502i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-0.764836 + 0.406670i) q^{5} +(1.17638 - 0.919089i) q^{6} +(0.622864 + 1.39897i) q^{7} +(0.913545 + 0.406737i) q^{8} +(0.654189 - 0.408783i) q^{9} +O(q^{10})\)	\(q+(-0.374607 - 0.927184i) q^{2} +(0.411485 + 1.43502i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-0.764836 + 0.406670i) q^{5} +(1.17638 - 0.919089i) q^{6} +(0.622864 + 1.39897i) q^{7} +(0.913545 + 0.406737i) q^{8} +(0.654189 - 0.408783i) q^{9} +(0.663571 + 0.556802i) q^{10} +(-3.22684 + 0.766497i) q^{11} +(-1.29284 - 0.746424i) q^{12} +(0.130745 + 3.74405i) q^{13} +(1.06378 - 1.10157i) q^{14} +(-0.898297 - 0.930214i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(-2.19537 + 3.51332i) q^{17} +(-0.624080 - 0.453421i) q^{18} +(1.34542 - 4.14606i) q^{19} +(0.267680 - 0.823834i) q^{20} +(-1.75125 + 1.46948i) q^{21} +(1.91948 + 2.70474i) q^{22} +(-1.33370 + 7.56380i) q^{23} +(-0.207764 + 1.47832i) q^{24} +(-2.37637 + 3.52312i) q^{25} +(3.42244 - 1.52377i) q^{26} +(4.18401 + 3.76730i) q^{27} +(-1.41986 - 0.573661i) q^{28} +(-0.135673 - 0.544155i) q^{29} +(-0.525971 + 1.18135i) q^{30} +(4.11917 - 3.70891i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-2.42773 - 4.31517i) q^{33} +(4.07990 + 0.719396i) q^{34} +(-1.04531 - 0.816686i) q^{35} +(-0.186620 + 0.748491i) q^{36} +(-5.53090 + 7.61264i) q^{37} +(-4.34817 + 0.305695i) q^{38} +(-5.31898 + 1.72824i) q^{39} +(-0.864120 + 0.0604252i) q^{40} +(-5.26355 + 1.50930i) q^{41} +(2.01851 + 1.07326i) q^{42} +(11.9919 - 2.11450i) q^{43} +(1.78874 - 2.79292i) q^{44} +(-0.334107 + 0.578691i) q^{45} +(7.51265 - 1.59686i) q^{46} +(-1.79204 - 0.125311i) q^{47} +(1.44850 - 0.361153i) q^{48} +(3.11474 - 3.45927i) q^{49} +(4.15678 + 0.883551i) q^{50} +(-5.94504 - 1.70471i) q^{51} +(-2.69489 - 2.60242i) q^{52} +(5.32263 - 10.0104i) q^{53} +(1.92562 - 5.29060i) q^{54} +(2.15629 - 1.89850i) q^{55} +1.53137i q^{56} +(6.50329 + 0.224654i) q^{57} +(-0.453708 + 0.329638i) q^{58} +(0.144927 + 2.07256i) q^{59} +(1.29236 + 0.0451303i) q^{60} +(-1.08799 - 7.74145i) q^{61} +(-4.98191 - 2.42984i) q^{62} +(0.979347 + 0.660578i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-1.62259 - 2.81041i) q^{65} +(-3.09151 + 3.86744i) q^{66} +(-1.58142 + 1.88467i) q^{67} +(-0.861344 - 4.05230i) q^{68} +(-11.4030 + 1.19850i) q^{69} +(-0.365638 + 1.27513i) q^{70} +(4.77504 + 8.98054i) q^{71} +(0.763898 - 0.107359i) q^{72} +(-0.408207 + 0.275339i) q^{73} +(9.13023 + 2.27642i) q^{74} +(-6.03357 - 1.96043i) q^{75} +(1.91229 + 3.91703i) q^{76} +(-3.08219 - 4.03684i) q^{77} +(3.59492 + 4.28426i) q^{78} +(10.1991 - 13.0543i) q^{79} +(0.379730 + 0.778563i) q^{80} +(-2.66999 + 5.47430i) q^{81} +(3.37116 + 4.31488i) q^{82} +(3.30508 - 15.5492i) q^{83} +(0.238963 - 2.27358i) q^{84} +(0.250332 - 3.57991i) q^{85} +(-6.45277 - 10.3266i) q^{86} +(0.725044 - 0.418605i) q^{87} +(-3.25963 - 0.612244i) q^{88} +(5.09038 + 13.9857i) q^{89} +(0.661712 + 0.0929975i) q^{90} +(-5.15639 + 2.51494i) q^{91} +(-4.29487 - 6.36741i) q^{92} +(7.01733 + 4.38491i) q^{93} +(0.555122 + 1.70849i) q^{94} +(0.657059 + 3.71820i) q^{95} +(-0.877474 - 1.20774i) q^{96} +(-8.65192 + 3.49560i) q^{97} +(-4.37418 - 1.59207i) q^{98} +(-1.79763 + 1.82051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Introduction

L-functions

Modular forms

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Database

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