LMFDB - Embedded newform 429.2.bg.b.367.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(16,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 12, 10]))

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

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

chi := DirichletCharacter("429.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			367.4
Character	$\chi$	$=$	429.367
Dual form			429.2.bg.b.256.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.176325 + 1.67762i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(-0.827032 - 0.175791i) q^{4} +(0.993113 - 0.721539i) q^{5} +(-0.176325 - 1.67762i) q^{6} +(-1.11199 - 0.236360i) q^{7} +(-0.601801 + 1.85215i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.176325 + 1.67762i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(-0.827032 - 0.175791i) q^{4} +(0.993113 - 0.721539i) q^{5} +(-0.176325 - 1.67762i) q^{6} +(-1.11199 - 0.236360i) q^{7} +(-0.601801 + 1.85215i) q^{8} +(0.913545 - 0.406737i) q^{9} +(1.03536 + 1.79330i) q^{10} +(-2.96420 + 1.48779i) q^{11} +0.845508 q^{12} +(-2.43747 + 2.65683i) q^{13} +(0.592594 - 1.82382i) q^{14} +(-0.821395 + 0.912252i) q^{15} +(-4.54592 - 2.02398i) q^{16} +(0.565232 + 5.37782i) q^{17} +(0.521269 + 1.60430i) q^{18} +(0.236084 + 0.262198i) q^{19} +(-0.948177 + 0.422155i) q^{20} +1.13683 q^{21} +(-1.97328 - 5.23515i) q^{22} +(1.63636 + 2.83426i) q^{23} +(0.203566 - 1.93680i) q^{24} +(-1.07943 + 3.32214i) q^{25} +(-4.02737 - 4.55762i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.878098 + 0.390955i) q^{28} +(-3.33609 + 3.70510i) q^{29} +(-1.38558 - 1.53884i) q^{30} +(-6.97570 - 5.06814i) q^{31} +(2.24956 - 3.89635i) q^{32} +(2.59010 - 2.07157i) q^{33} -9.12162 q^{34} +(-1.27487 + 0.567609i) q^{35} +(-0.827032 + 0.175791i) q^{36} +(6.53612 - 7.25910i) q^{37} +(-0.481497 + 0.349828i) q^{38} +(1.83182 - 3.10555i) q^{39} +(0.738745 + 2.27362i) q^{40} +(7.50302 - 1.59482i) q^{41} +(-0.200452 + 1.90717i) q^{42} +(4.03087 - 6.98167i) q^{43} +(2.71303 - 0.709366i) q^{44} +(0.613778 - 1.06309i) q^{45} +(-5.04336 + 2.24545i) q^{46} +(-0.140144 + 0.431320i) q^{47} +(4.86739 + 1.03460i) q^{48} +(-5.21417 - 2.32150i) q^{49} +(-5.38297 - 2.39665i) q^{50} +(-1.67099 - 5.14278i) q^{51} +(2.48291 - 1.76880i) q^{52} +(4.50262 + 3.27134i) q^{53} +(-0.843432 - 1.46087i) q^{54} +(-1.87029 + 3.61633i) q^{55} +(1.10697 - 1.91733i) q^{56} +(-0.285439 - 0.207384i) q^{57} +(-5.62752 - 6.25000i) q^{58} +(5.70073 + 1.21173i) q^{59} +(0.839686 - 0.610067i) q^{60} +(1.43570 + 13.6598i) q^{61} +(9.73242 - 10.8089i) q^{62} +(-1.11199 + 0.236360i) q^{63} +(-1.91160 - 1.38886i) q^{64} +(-0.503675 + 4.39726i) q^{65} +(3.01861 + 4.71048i) q^{66} +(4.50295 + 7.79934i) q^{67} +(0.477908 - 4.54699i) q^{68} +(-2.18988 - 2.43211i) q^{69} +(-0.727442 - 2.23884i) q^{70} +(0.418352 + 3.98035i) q^{71} +(0.203566 + 1.93680i) q^{72} +(2.20851 + 6.79711i) q^{73} +(11.0255 + 12.2451i) q^{74} +(0.365129 - 3.47397i) q^{75} +(-0.149157 - 0.258348i) q^{76} +(3.64781 - 0.953779i) q^{77} +(4.88695 + 3.62069i) q^{78} +(-12.7430 - 9.25834i) q^{79} +(-5.97499 + 1.27002i) q^{80} +(0.669131 - 0.743145i) q^{81} +(1.35253 + 12.8684i) q^{82} +(6.54868 - 4.75790i) q^{83} +(-0.940194 - 0.199844i) q^{84} +(4.44165 + 4.93295i) q^{85} +(11.0019 + 7.99332i) q^{86} +(2.49285 - 4.31775i) q^{87} +(-0.971747 - 6.38551i) q^{88} +(-0.558088 - 0.966637i) q^{89} +(1.67525 + 1.21714i) q^{90} +(3.33840 - 2.37824i) q^{91} +(-0.855086 - 2.63168i) q^{92} +(7.87699 + 3.50706i) q^{93} +(-0.698881 - 0.311162i) q^{94} +(0.423645 + 0.0900485i) q^{95} +(-1.39030 + 4.27891i) q^{96} +(4.67961 - 2.08350i) q^{97} +(4.81399 - 8.33807i) q^{98} +(-2.10280 + 2.56481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 14 q^{3} + 8 q^{4} - 6 q^{5} - 24 q^{8} + 14 q^{9}+O(q^{10}) $ 112 * q + 14 * q^3 + 8 * q^4 - 6 * q^5 - 24 * q^8 + 14 * q^9	\( 112 q + 14 q^{3} + 8 q^{4} - 6 q^{5} - 24 q^{8} + 14 q^{9} - 24 q^{10} + q^{11} + 104 q^{12} - 15 q^{13} - 30 q^{14} - 2 q^{15} + 24 q^{16} + 4 q^{17} - 28 q^{20} + 7 q^{22} + 8 q^{23} - 18 q^{24} - 42 q^{25} + 7 q^{26} - 28 q^{27} - 6 q^{28} - 2 q^{29} + 6 q^{30} + 12 q^{31} - 6 q^{32} + 6 q^{33} + 64 q^{34} - 8 q^{35} + 8 q^{36} + 4 q^{37} - 6 q^{38} + 12 q^{39} - 36 q^{40} - 26 q^{41} - 20 q^{42} - 76 q^{43} + 12 q^{44} - 2 q^{45} + 18 q^{46} + 50 q^{47} - 6 q^{48} + 32 q^{49} + 17 q^{50} - 18 q^{51} - 39 q^{52} - 54 q^{53} - 36 q^{55} + 12 q^{56} + 48 q^{58} + 20 q^{59} + 56 q^{60} + 34 q^{61} + 33 q^{62} - 68 q^{64} - 44 q^{65} - 4 q^{66} - 36 q^{67} + 4 q^{68} + 3 q^{69} - 92 q^{70} + 22 q^{71} - 18 q^{72} - 34 q^{73} - 4 q^{74} - 4 q^{75} + 4 q^{76} + 32 q^{77} - 18 q^{78} - 20 q^{79} + 30 q^{80} + 14 q^{81} - 41 q^{82} + 56 q^{83} + 9 q^{84} + 6 q^{85} - 86 q^{86} - 52 q^{87} - 70 q^{88} - 96 q^{89} - 12 q^{90} - 7 q^{91} - 126 q^{92} - 6 q^{93} - 10 q^{94} + 52 q^{95} - 88 q^{96} - 5 q^{97} + 104 q^{98} - 2 q^{99}+O(q^{100}) \) 112 * q + 14 * q^3 + 8 * q^4 - 6 * q^5 - 24 * q^8 + 14 * q^9 - 24 * q^10 + q^11 + 104 * q^12 - 15 * q^13 - 30 * q^14 - 2 * q^15 + 24 * q^16 + 4 * q^17 - 28 * q^20 + 7 * q^22 + 8 * q^23 - 18 * q^24 - 42 * q^25 + 7 * q^26 - 28 * q^27 - 6 * q^28 - 2 * q^29 + 6 * q^30 + 12 * q^31 - 6 * q^32 + 6 * q^33 + 64 * q^34 - 8 * q^35 + 8 * q^36 + 4 * q^37 - 6 * q^38 + 12 * q^39 - 36 * q^40 - 26 * q^41 - 20 * q^42 - 76 * q^43 + 12 * q^44 - 2 * q^45 + 18 * q^46 + 50 * q^47 - 6 * q^48 + 32 * q^49 + 17 * q^50 - 18 * q^51 - 39 * q^52 - 54 * q^53 - 36 * q^55 + 12 * q^56 + 48 * q^58 + 20 * q^59 + 56 * q^60 + 34 * q^61 + 33 * q^62 - 68 * q^64 - 44 * q^65 - 4 * q^66 - 36 * q^67 + 4 * q^68 + 3 * q^69 - 92 * q^70 + 22 * q^71 - 18 * q^72 - 34 * q^73 - 4 * q^74 - 4 * q^75 + 4 * q^76 + 32 * q^77 - 18 * q^78 - 20 * q^79 + 30 * q^80 + 14 * q^81 - 41 * q^82 + 56 * q^83 + 9 * q^84 + 6 * q^85 - 86 * q^86 - 52 * q^87 - 70 * q^88 - 96 * q^89 - 12 * q^90 - 7 * q^91 - 126 * q^92 - 6 * q^93 - 10 * q^94 + 52 * q^95 - 88 * q^96 - 5 * q^97 + 104 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.176325	+	1.67762i	−0.124681	+	1.18626i	0.735953	+	0.677033i	$0.236735\pi$
$2$	−0.176325	+	1.67762i	−0.124681	+	1.18626i	−0.860633	+	0.509225i	$0.829932\pi$
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$4$	−0.827032	−	0.175791i	−0.413516	−	0.0878955i
$5$	0.993113	−	0.721539i	0.444134	−	0.322682i	−0.343142	−	0.939284i	$-0.611491\pi$
$5$	0.993113	−	0.721539i	0.444134	−	0.322682i	0.787275	+	0.616602i	$0.211491\pi$
$6$	−0.176325	−	1.67762i	−0.0719845	−	0.684887i
$7$	−1.11199	−	0.236360i	−0.420291	−	0.0893357i	−0.00708892	−	0.999975i	$-0.502256\pi$
$7$	−1.11199	−	0.236360i	−0.420291	−	0.0893357i	−0.413202	+	0.910639i	$0.635590\pi$
$8$	−0.601801	+	1.85215i	−0.212769	+	0.654835i
$9$	0.913545	−	0.406737i	0.304515	−	0.135579i
$10$	1.03536	+	1.79330i	0.327409	+	0.567090i
$11$	−2.96420	+	1.48779i	−0.893741	+	0.448584i
$11$	−2.96420	+	1.48779i	−0.893741	+	0.448584i
$12$	0.845508			0.244077
$13$	−2.43747	+	2.65683i	−0.676032	+	0.736872i
$13$	−2.43747	+	2.65683i	−0.676032	+	0.736872i
$14$	0.592594	−	1.82382i	0.158377	−	0.487436i
$15$	−0.821395	+	0.912252i	−0.212083	+	0.235542i
$16$	−4.54592	−	2.02398i	−1.13648	−	0.505994i
$17$	0.565232	+	5.37782i	0.137089	+	1.30431i	0.819388	+	0.573240i	$0.194314\pi$
$17$	0.565232	+	5.37782i	0.137089	+	1.30431i	−0.682299	+	0.731073i	$0.739020\pi$
$18$	0.521269	+	1.60430i	0.122864	+	0.378138i
$19$	0.236084	+	0.262198i	0.0541615	+	0.0601524i	0.769617	−	0.638506i	$-0.220447\pi$
$19$	0.236084	+	0.262198i	0.0541615	+	0.0601524i	−0.715455	+	0.698659i	$0.753781\pi$
$20$	−0.948177	+	0.422155i	−0.212019	+	0.0943968i
$21$	1.13683			0.248076
$22$	−1.97328	−	5.23515i	−0.420704	−	1.11614i
$23$	1.63636	+	2.83426i	0.341205	+	0.590985i	0.984657	−	0.174502i	$-0.0558315\pi$
$23$	1.63636	+	2.83426i	0.341205	+	0.590985i	−0.643452	+	0.765487i	$0.722498\pi$
$24$	0.203566	−	1.93680i	0.0415527	−	0.395348i
$25$	−1.07943	+	3.32214i	−0.215886	+	0.664428i
$26$	−4.02737	−	4.55762i	−0.789833	−	0.893822i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	0.878098	+	0.390955i	0.165945	+	0.0738835i
$29$	−3.33609	+	3.70510i	−0.619496	+	0.688020i	−0.968475	−	0.249111i	$-0.919862\pi$
$29$	−3.33609	+	3.70510i	−0.619496	+	0.688020i	0.348979	+	0.937130i	$0.386528\pi$
$30$	−1.38558	−	1.53884i	−0.252971	−	0.280953i
$31$	−6.97570	−	5.06814i	−1.25287	−	0.910265i	−0.254487	−	0.967076i	$-0.581907\pi$
$31$	−6.97570	−	5.06814i	−1.25287	−	0.910265i	−0.998385	+	0.0568114i	$0.981907\pi$
$32$	2.24956	−	3.89635i	0.397669	−	0.688784i
$33$	2.59010	−	2.07157i	0.450878	−	0.360613i
$34$	−9.12162			−1.56434
$35$	−1.27487	+	0.567609i	−0.215493	+	0.0959435i
$36$	−0.827032	+	0.175791i	−0.137839	+	0.0292985i
$37$	6.53612	−	7.25910i	1.07453	−	1.19339i	0.0942988	−	0.995544i	$-0.469939\pi$
$37$	6.53612	−	7.25910i	1.07453	−	1.19339i	0.980233	−	0.197845i	$-0.0633942\pi$
$38$	−0.481497	+	0.349828i	−0.0781092	+	0.0567496i
$39$	1.83182	−	3.10555i	0.293326	−	0.497286i
$40$	0.738745	+	2.27362i	0.116806	+	0.359491i
$41$	7.50302	−	1.59482i	1.17178	−	0.249068i	0.419399	−	0.907802i	$-0.362241\pi$
$41$	7.50302	−	1.59482i	1.17178	−	0.249068i	0.752376	+	0.658734i	$0.228908\pi$
$42$	−0.200452	+	1.90717i	−0.0309304	+	0.294283i
$43$	4.03087	−	6.98167i	0.614702	−	1.06470i	−0.375735	−	0.926727i	$-0.622610\pi$
$43$	4.03087	−	6.98167i	0.614702	−	1.06470i	0.990437	−	0.137968i	$-0.0440571\pi$
$44$	2.71303	−	0.709366i	0.409005	−	0.106941i
$45$	0.613778	−	1.06309i	0.0914966	−	0.158477i
$46$	−5.04336	+	2.24545i	−0.743603	+	0.331073i
$47$	−0.140144	+	0.431320i	−0.0204421	+	0.0629145i	−0.960757	−	0.277391i	$-0.910530\pi$
$47$	−0.140144	+	0.431320i	−0.0204421	+	0.0629145i	0.940315	+	0.340305i	$0.110530\pi$
$48$	4.86739	+	1.03460i	0.702548	+	0.149331i
$49$	−5.21417	−	2.32150i	−0.744881	−	0.331643i
$50$	−5.38297	−	2.39665i	−0.761267	−	0.338938i
$51$	−1.67099	−	5.14278i	−0.233986	−	0.720134i
$52$	2.48291	−	1.76880i	0.344318	−	0.245288i
$53$	4.50262	+	3.27134i	0.618482	+	0.449354i	0.852391	−	0.522905i	$-0.175152\pi$
$53$	4.50262	+	3.27134i	0.618482	+	0.449354i	−0.233909	+	0.972259i	$0.575152\pi$
$54$	−0.843432	−	1.46087i	−0.114777	−	0.198799i
$55$	−1.87029	+	3.61633i	−0.252190	+	0.487626i
$56$	1.10697	−	1.91733i	0.147925	−	0.256214i
$57$	−0.285439	−	0.207384i	−0.0378074	−	0.0274687i
$58$	−5.62752	−	6.25000i	−0.738930	−	0.820665i
$59$	5.70073	+	1.21173i	0.742172	+	0.157753i	0.563455	−	0.826147i	$-0.309472\pi$
$59$	5.70073	+	1.21173i	0.742172	+	0.157753i	0.178717	+	0.983901i	$0.442805\pi$
$60$	0.839686	−	0.610067i	0.108403	−	0.0787594i
$61$	1.43570	+	13.6598i	0.183823	+	1.74896i	0.565576	+	0.824696i	$0.308654\pi$
$61$	1.43570	+	13.6598i	0.183823	+	1.74896i	−0.381753	+	0.924264i	$0.624680\pi$
$62$	9.73242	−	10.8089i	1.23602	−	1.37274i
$63$	−1.11199	+	0.236360i	−0.140097	+	0.0297786i
$64$	−1.91160	−	1.38886i	−0.238950	−	0.173608i
$65$	−0.503675	+	4.39726i	−0.0624732	+	0.545413i
$66$	3.01861	+	4.71048i	0.371565	+	0.579820i
$67$	4.50295	+	7.79934i	0.550123	+	0.952841i	0.998265	+	0.0588789i	$0.0187526\pi$
$67$	4.50295	+	7.79934i	0.550123	+	0.952841i	−0.448142	+	0.893962i	$0.647914\pi$
$68$	0.477908	−	4.54699i	0.0579549	−	0.551404i
$69$	−2.18988	−	2.43211i	−0.263631	−	0.292792i
$70$	−0.727442	−	2.23884i	−0.0869460	−	0.267592i
$71$	0.418352	+	3.98035i	0.0496493	+	0.472381i	0.990893	+	0.134653i	$0.0429919\pi$
$71$	0.418352	+	3.98035i	0.0496493	+	0.472381i	−0.941244	+	0.337728i	$0.890341\pi$
$72$	0.203566	+	1.93680i	0.0239905	+	0.228254i
$73$	2.20851	+	6.79711i	0.258487	+	0.795541i	0.993123	+	0.117079i	$0.0373532\pi$
$73$	2.20851	+	6.79711i	0.258487	+	0.795541i	−0.734635	+	0.678462i	$0.762647\pi$
$74$	11.0255	+	12.2451i	1.28169	+	1.42347i
$75$	0.365129	−	3.47397i	0.0421615	−	0.401140i
$76$	−0.149157	−	0.258348i	−0.0171095	−	0.0296345i
$77$	3.64781	−	0.953779i	0.415706	−	0.108693i
$78$	4.88695	+	3.62069i	0.553338	+	0.409962i
$79$	−12.7430	−	9.25834i	−1.43370	−	1.04164i	−0.989313	−	0.145811i	$-0.953421\pi$
$79$	−12.7430	−	9.25834i	−1.43370	−	1.04164i	−0.444388	−	0.895834i	$-0.646579\pi$
$80$	−5.97499	+	1.27002i	−0.668025	+	0.141993i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	1.35253	+	12.8684i	0.149362	+	1.42108i
$83$	6.54868	−	4.75790i	0.718811	−	0.522247i	−0.167193	−	0.985924i	$-0.553470\pi$
$83$	6.54868	−	4.75790i	0.718811	−	0.522247i	0.886004	+	0.463677i	$0.153470\pi$
$84$	−0.940194	−	0.199844i	−0.102584	−	0.0218048i
$85$	4.44165	+	4.93295i	0.481764	+	0.535053i
$86$	11.0019	+	7.99332i	1.18636	+	0.861942i
$87$	2.49285	−	4.31775i	0.267262	−	0.462911i
$88$	−0.971747	−	6.38551i	−0.103589	−	0.680698i
$89$	−0.558088	−	0.966637i	−0.0591572	−	0.102463i	0.834930	−	0.550356i	$-0.185508\pi$
$89$	−0.558088	−	0.966637i	−0.0591572	−	0.102463i	−0.894087	+	0.447893i	$0.852175\pi$
$90$	1.67525	+	1.21714i	0.176587	+	0.128298i
$91$	3.33840	−	2.37824i	0.349959	−	0.249307i
$92$	−0.855086	−	2.63168i	−0.0891489	−	0.274372i
$93$	7.87699	+	3.50706i	0.816805	+	0.363665i
$94$	−0.698881	−	0.311162i	−0.0720840	−	0.0320939i
$95$	0.423645	+	0.0900485i	0.0434650	+	0.00923878i
$96$	−1.39030	+	4.27891i	−0.141897	+	0.436715i
$97$	4.67961	−	2.08350i	0.475142	−	0.211547i	−0.155171	−	0.987888i	$-0.549593\pi$
$97$	4.67961	−	2.08350i	0.475142	−	0.211547i	0.630314	+	0.776341i	$0.282926\pi$
$98$	4.81399	−	8.33807i	0.486286	−	0.842272i
$99$	−2.10280	+	2.56481i	−0.211339	+	0.257773i
$100$	1.47673	−	2.55776i	0.147673	−	0.255776i
$101$	−1.39756	+	13.2969i	−0.139062	+	1.32309i	0.673054	+	0.739593i	$0.264982\pi$
$101$	−1.39756	+	13.2969i	−0.139062	+	1.32309i	−0.812116	+	0.583496i	$0.801685\pi$
$102$	8.92229	−	1.89649i	0.883438	−	0.187781i
$103$	−1.87352	−	5.76610i	−0.184603	−	0.568151i	0.815338	−	0.578985i	$-0.196551\pi$
$103$	−1.87352	−	5.76610i	−0.184603	−	0.568151i	−0.999941	+	0.0108346i	$0.996551\pi$
$104$	−3.45399	−	6.11345i	−0.338691	−	0.599473i
$105$	1.12900	−	0.820267i	0.110179	−	0.0800498i
$106$	−6.28201	+	6.97687i	−0.610162	+	0.677654i
$107$	−16.8340	+	3.57818i	−1.62741	+	0.345916i	−0.929085	−	0.369867i	$-0.879403\pi$
$107$	−16.8340	+	3.57818i	−1.62741	+	0.345916i	−0.698323	+	0.715783i	$0.746070\pi$
$108$	0.772410	−	0.343899i	0.0743252	−	0.0330917i
$109$	9.41607			0.901896			0.450948	−	0.892550i	$-0.351086\pi$
$109$	9.41607			0.901896			0.450948	+	0.892550i	$0.351086\pi$
$110$	−5.73705	−	3.77530i	−0.547007	−	0.359960i
$111$	−4.88404	+	8.45941i	−0.463573	+	0.802932i
$112$	4.57662	+	3.32511i	0.432450	+	0.314193i
$113$	6.01587	+	6.68130i	0.565926	+	0.628524i	0.956390	−	0.292094i	$-0.0943520\pi$
$113$	6.01587	+	6.68130i	0.565926	+	0.628524i	−0.390464	+	0.920618i	$0.627685\pi$
$114$	0.398242	−	0.442293i	0.0372988	−	0.0414245i
$115$	3.67013	+	1.63405i	0.342241	+	0.152376i
$116$	3.41037	−	2.47778i	0.316645	−	0.230056i
$117$	−1.14611	+	3.41854i	−0.105958	+	0.316044i
$118$	−3.03800	+	9.35001i	−0.279671	+	0.860738i
$119$	0.642572	−	6.11366i	0.0589045	−	0.560438i
$120$	−1.19531	−	2.07034i	−0.109117	−	0.188996i
$121$	6.57299	−	8.82019i	0.597544	−	0.801836i
$122$	−23.1692			−2.09764
$123$	−7.00748	+	3.11993i	−0.631843	+	0.281315i
$124$	4.87819	+	5.41778i	0.438074	+	0.486531i
$125$	3.22174	+	9.91549i	0.288161	+	0.886868i
$126$	−0.200452	−	1.90717i	−0.0178577	−	0.169904i
$127$	11.2628	+	5.01452i	0.999412	+	0.444967i	0.840199	−	0.542277i	$-0.182438\pi$
$127$	11.2628	+	5.01452i	0.999412	+	0.444967i	0.159212	+	0.987244i	$0.449105\pi$
$128$	8.68804	−	9.64905i	0.767921	−	0.852863i
$129$	−2.49122	+	7.66717i	−0.219339	+	0.675057i
$130$	−7.28814	−	1.62032i	−0.639212	−	0.142112i
$131$	6.66271			0.582124			0.291062	−	0.956704i	$-0.405991\pi$
$131$	6.66271			0.582124			0.291062	+	0.956704i	$0.405991\pi$
$132$	−2.50626	+	1.25793i	−0.218142	+	0.109489i
$133$	−0.200549	−	0.347362i	−0.0173898	−	0.0301201i
$134$	−13.8783	+	6.17903i	−1.19891	+	0.533787i
$135$	−0.379336	+	1.16747i	−0.0326480	+	0.100480i
$136$	−10.3007	−	2.18948i	−0.883278	−	0.187747i
$137$	−1.82375	−	17.3518i	−0.155813	−	1.48246i	−0.740967	−	0.671542i	$-0.765632\pi$
$137$	−1.82375	−	17.3518i	−0.155813	−	1.48246i	0.585153	−	0.810923i	$-0.301034\pi$
$138$	4.46629	−	3.24495i	0.380196	−	0.276229i
$139$	13.9646	+	2.96827i	1.18446	+	0.251765i	0.757703	−	0.652599i	$-0.226321\pi$
$139$	13.9646	+	2.96827i	1.18446	+	0.251765i	0.426760	+	0.904365i	$0.359655\pi$
$140$	1.15414	−	0.245320i	0.0975427	−	0.0207333i
$141$	0.0474054	−	0.451032i	0.00399225	−	0.0379837i
$142$	−6.75130			−0.566556
$143$	3.27235	−	11.5018i	0.273648	−	0.961830i
$144$	−4.97613			−0.414678
$145$	−0.639738	+	6.08670i	−0.0531274	+	0.505473i
$146$	−11.7924	+	2.50655i	−0.975946	+	0.207444i
$147$	5.58289	+	1.18668i	0.460469	+	0.0978758i
$148$	−6.68167	+	4.85452i	−0.549230	+	0.399039i
$149$	−2.19238	−	20.8591i	−0.179607	−	1.70885i	−0.598757	−	0.800931i	$-0.704338\pi$
$149$	−2.19238	−	20.8591i	−0.179607	−	1.70885i	0.419150	−	0.907917i	$-0.362328\pi$
$150$	5.76363	+	1.22510i	0.470599	+	0.100029i
$151$	0.264042	−	0.812636i	0.0214874	−	0.0661314i	−0.939738	−	0.341896i	$-0.888931\pi$
$151$	0.264042	−	0.812636i	0.0214874	−	0.0661314i	0.961225	+	0.275764i	$0.0889310\pi$
$152$	−0.627707	+	0.279473i	−0.0509138	+	0.0226683i
$153$	2.70372	+	4.68298i	0.218583	+	0.378597i
$154$	0.956880	+	6.28782i	0.0771076	+	0.506687i
$155$	−10.5845			−0.850169
$156$	−2.06090	+	2.24637i	−0.165004	+	0.179854i
$157$	−5.00409	+	15.4010i	−0.399370	+	1.22913i	0.526135	+	0.850401i	$0.323641\pi$
$157$	−5.00409	+	15.4010i	−0.399370	+	1.22913i	−0.925506	+	0.378734i	$0.876359\pi$
$158$	17.7789	−	19.7455i	1.41441	−	1.57087i
$159$	−5.08438	−	2.26371i	−0.403217	−	0.179524i
$160$	−0.577302	−	5.49266i	−0.0456397	−	0.434233i
$161$	−1.14971	−	3.53843i	−0.0906096	−	0.278868i
$162$	1.12873	+	1.25358i	0.0886816	+	0.0984908i
$163$	4.40152	−	1.95968i	0.344753	−	0.153494i	−0.227054	−	0.973882i	$-0.572909\pi$
$163$	4.40152	−	1.95968i	0.344753	−	0.153494i	0.571807	+	0.820388i	$0.306243\pi$
$164$	−6.48559			−0.506440
$165$	1.07755	−	3.92616i	0.0838869	−	0.305651i
$166$	6.82726	+	11.8252i	0.529898	+	0.917810i
$167$	−1.99469	+	18.9782i	−0.154354	+	1.46858i	0.593563	+	0.804788i	$0.297721\pi$
$167$	−1.99469	+	18.9782i	−0.154354	+	1.46858i	−0.747917	+	0.663792i	$0.768946\pi$
$168$	−0.684145	+	2.10558i	−0.0527829	+	0.162449i
$169$	−1.11750	−	12.9519i	−0.0859615	−	0.996298i
$170$	−9.05880	+	6.58160i	−0.694778	+	0.504786i
$171$	0.322319	+	0.143506i	0.0246484	+	0.0109742i
$172$	−4.56097	+	5.06547i	−0.347771	+	0.386239i
$173$	−0.528663	−	0.587140i	−0.0401935	−	0.0446394i	0.722713	−	0.691148i	$-0.242895\pi$
$173$	−0.528663	−	0.587140i	−0.0401935	−	0.0446394i	−0.762906	+	0.646509i	$0.776228\pi$
$174$	6.80399	+	4.94339i	0.515810	+	0.374758i
$175$	1.98553	−	3.43904i	0.150092	−	0.259967i
$176$	16.4863	−	0.763887i	1.24270	−	0.0575801i
$177$	−5.82809			−0.438066
$178$	1.72006	−	0.765819i	0.128924	−	0.0574005i
$179$	3.05594	−	0.649559i	0.228411	−	0.0485503i	−0.0922840	−	0.995733i	$-0.529417\pi$
$179$	3.05594	−	0.649559i	0.228411	−	0.0485503i	0.320695	+	0.947182i	$0.396083\pi$
$180$	−0.694496	+	0.771316i	−0.0517647	+	0.0574905i
$181$	10.9715	−	7.97123i	0.815502	−	0.592497i	−0.0999184	−	0.994996i	$-0.531858\pi$
$181$	10.9715	−	7.97123i	0.815502	−	0.592497i	0.915421	+	0.402499i	$0.131858\pi$
$182$	3.40114	+	6.01992i	0.252110	+	0.446226i
$183$	−4.24437	−	13.0628i	−0.313753	−	0.965631i
$184$	−6.23426	+	1.32513i	−0.459596	+	0.0976901i
$185$	1.25339	−	11.9252i	0.0921508	−	0.876757i
$186$	−7.27243	+	12.5962i	−0.533241	+	0.923600i
$187$	−9.67650	−	15.1000i	−0.707616	−	1.10422i
$188$	0.191726	−	0.332079i	0.0139831	−	0.0242194i
$189$	1.03854	−	0.462390i	0.0755430	−	0.0336339i
$190$	−0.225767	+	0.694838i	−0.0163788	+	0.0504089i
$191$	−9.96778	−	2.11872i	−0.721243	−	0.153305i	−0.167356	−	0.985897i	$-0.553523\pi$
$191$	−9.96778	−	2.11872i	−0.721243	−	0.153305i	−0.553887	+	0.832592i	$0.686856\pi$
$192$	2.15859	+	0.961066i	0.155783	+	0.0693590i
$193$	9.97536	+	4.44132i	0.718042	+	0.319693i	0.733032	−	0.680195i	$-0.238105\pi$
$193$	9.97536	+	4.44132i	0.718042	+	0.319693i	−0.0149893	+	0.999888i	$0.504771\pi$
$194$	2.67019	+	8.21799i	0.191708	+	0.590017i
$195$	−0.421574	−	4.40589i	−0.0301895	−	0.315512i
$196$	3.90419	+	2.83656i	0.278870	+	0.202611i
$197$	0.199977	+	0.346371i	0.0142478	+	0.0246779i	0.873061	−	0.487610i	$-0.162131\pi$
$197$	0.199977	+	0.346371i	0.0142478	+	0.0246779i	−0.858814	+	0.512288i	$0.828798\pi$
$198$	−3.93201	−	3.97994i	−0.279436	−	0.282842i
$199$	4.88736	−	8.46516i	0.346456	−	0.600079i	−0.639161	−	0.769073i	$-0.720718\pi$
$199$	4.88736	−	8.46516i	0.346456	−	0.600079i	0.985617	+	0.168994i	$0.0540517\pi$
$200$	−5.50352	−	3.99854i	−0.389157	−	0.282739i
$201$	−6.02613	−	6.69269i	−0.425050	−	0.472066i
$202$	−22.0607	−	4.68915i	−1.55219	−	0.329927i
$203$	4.58542	−	3.33150i	0.321833	−	0.233826i
$204$	0.477908	+	4.54699i	0.0334603	+	0.318353i
$205$	6.30063	−	6.99756i	0.440055	−	0.488731i
$206$	10.0037	−	2.12635i	0.696990	−	0.148150i
$207$	2.64769	+	1.92366i	0.184027	+	0.133704i
$208$	16.4579	−	7.14437i	1.14115	−	0.495373i
$209$	−1.08990	−	0.425966i	−0.0753897	−	0.0294647i
$210$	1.17703	+	2.03867i	0.0812226	+	0.140682i
$211$	−1.71488	+	16.3160i	−0.118057	+	1.12324i	0.761737	+	0.647886i	$0.224347\pi$
$211$	−1.71488	+	16.3160i	−0.118057	+	1.12324i	−0.879794	+	0.475354i	$0.842320\pi$
$212$	−3.14874	−	3.49703i	−0.216256	−	0.240177i
$213$	−1.23677	−	3.80639i	−0.0847422	−	0.260810i
$214$	−3.03458	−	28.8721i	−0.207439	−	1.97365i
$215$	−1.03444	−	9.84202i	−0.0705481	−	0.671220i
$216$	−0.601801	−	1.85215i	−0.0409474	−	0.126023i
$217$	6.55897	+	7.28448i	0.445252	+	0.494503i
$218$	−1.66029	+	15.7966i	−0.112449	+	1.06988i
$219$	−3.57345	−	6.18940i	−0.241471	−	0.418241i
$220$	2.18251	−	2.66204i	0.147145	−	0.179475i
$221$	−15.6657	−	11.6065i	−1.05379	−	0.780740i
$222$	−13.3305	−	9.68519i	−0.894686	−	0.650027i
$223$	3.16206	−	0.672116i	0.211747	−	0.0450082i	−0.100817	−	0.994905i	$-0.532146\pi$
$223$	3.16206	−	0.672116i	0.211747	−	0.0450082i	0.312564	+	0.949897i	$0.398812\pi$
$224$	−3.42242	+	3.80098i	−0.228670	+	0.253964i
$225$	0.365129	+	3.47397i	0.0243419	+	0.231598i
$226$	−12.2695	+	8.91428i	−0.816152	+	0.592969i
$227$	−15.7359	−	3.34478i	−1.04443	−	0.222001i	−0.346414	−	0.938082i	$-0.612601\pi$
$227$	−15.7359	−	3.34478i	−1.04443	−	0.222001i	−0.698017	+	0.716081i	$0.745934\pi$
$228$	0.199611	+	0.221691i	0.0132196	+	0.0146818i
$229$	−15.8373	−	11.5065i	−1.04656	−	0.760370i	−0.0750042	−	0.997183i	$-0.523897\pi$
$229$	−15.8373	−	11.5065i	−1.04656	−	0.760370i	−0.971555	+	0.236813i	$0.923897\pi$
$230$	−3.38845	+	5.86896i	−0.223428	+	0.386988i
$231$	−3.36979	+	1.69136i	−0.221716	+	0.111283i
$232$	−4.85475	−	8.40868i	−0.318730	−	0.552057i
$233$	−4.69648	−	3.41219i	−0.307677	−	0.223540i	0.423222	−	0.906026i	$-0.360899\pi$
$233$	−4.69648	−	3.41219i	−0.307677	−	0.223540i	−0.730899	+	0.682486i	$0.760899\pi$
$234$	−5.53294	−	2.52551i	−0.361699	−	0.165098i
$235$	0.172035	+	0.529469i	0.0112223	+	0.0345388i
$236$	−4.50167	−	2.00427i	−0.293034	−	0.130467i
$237$	14.3895	+	6.40660i	0.934696	+	0.416154i
$238$	10.1431	+	2.15599i	0.657481	+	0.139752i
$239$	−2.06034	+	6.34106i	−0.133272	+	0.410169i	−0.995317	−	0.0966621i	$-0.969183\pi$
$239$	−2.06034	+	6.34106i	−0.133272	+	0.410169i	0.862045	+	0.506831i	$0.169183\pi$
$240$	5.58037	−	2.48454i	0.360212	−	0.160377i
$241$	4.11466	−	7.12680i	0.265048	−	0.459077i	−0.702528	−	0.711656i	$-0.747945\pi$
$241$	4.11466	−	7.12680i	0.265048	−	0.459077i	0.967576	+	0.252579i	$0.0812787\pi$
$242$	13.6380	+	12.5822i	0.876682	+	0.808816i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.21390	−	11.5495i	0.0777120	−	0.739380i
$245$	−6.85331	+	1.45672i	−0.437842	+	0.0930662i
$246$	−3.99847	−	12.3060i	−0.254933	−	0.784604i
$247$	−1.27206	−	0.0118636i	−0.0809395	−	0.000754866i
$248$	13.5850	−	9.87005i	0.862646	−	0.626749i
$249$	−5.41636	+	6.01547i	−0.343248	+	0.381215i
$250$	−17.2025	+	3.65651i	−1.08798	+	0.231258i
$251$	−12.0919	+	5.38366i	−0.763234	+	0.339814i	−0.751166	−	0.660113i	$-0.770508\pi$
$251$	−12.0919	+	5.38366i	−0.763234	+	0.339814i	−0.0120682	+	0.999927i	$0.503842\pi$
$252$	0.961198			0.0605498
$253$	−9.06729	−	5.96677i	−0.570056	−	0.375128i
$254$	−10.3984	+	18.0105i	−0.652453	+	1.13008i
$255$	−5.37020	−	3.90168i	−0.336295	−	0.244333i
$256$	11.4934	+	12.7647i	0.718337	+	0.797795i
$257$	−9.28709	+	10.3144i	−0.579313	+	0.643392i	−0.959564	−	0.281491i	$-0.909171\pi$
$257$	−9.28709	+	10.3144i	−0.579313	+	0.643392i	0.380251	+	0.924883i	$0.375838\pi$
$258$	−12.4234	−	5.53123i	−0.773444	−	0.344360i
$259$	−8.98384	+	6.52714i	−0.558229	+	0.405577i
$260$	1.18955	−	3.54814i	0.0737730	−	0.220046i
$261$	−1.54067	+	4.74169i	−0.0953649	+	0.293503i
$262$	−1.17480	+	11.1775i	−0.0725796	+	0.690549i
$263$	−1.51955	−	2.63193i	−0.0936992	−	0.162292i	0.815366	−	0.578946i	$-0.196536\pi$
$263$	−1.51955	−	2.63193i	−0.0936992	−	0.162292i	−0.909065	+	0.416654i	$0.863203\pi$
$264$	2.27813	+	6.04393i	0.140209	+	0.371978i
$265$	6.83201			0.419687
$266$	0.618104	−	0.275198i	0.0378984	−	0.0168734i
$267$	0.746868	+	0.829480i	0.0457075	+	0.0507634i
$268$	−2.35303	−	7.24188i	−0.143734	−	0.442368i
$269$	3.07499	+	29.2566i	0.187486	+	1.78381i	0.533724	+	0.845659i	$0.320792\pi$
$269$	3.07499	+	29.2566i	0.187486	+	1.78381i	−0.346238	+	0.938147i	$0.612541\pi$
$270$	−1.89170	−	0.842237i	−0.115125	−	0.0512569i
$271$	−13.8221	+	15.3510i	−0.839632	+	0.932506i	−0.998498	−	0.0547947i	$-0.982550\pi$
$271$	−13.8221	+	15.3510i	−0.839632	+	0.932506i	0.158866	+	0.987300i	$0.449216\pi$
$272$	8.31508	−	25.5912i	0.504176	−	1.55169i
$273$	−2.77098	+	3.02036i	−0.167708	+	0.182801i
$274$	29.4314			1.77801
$275$	−1.74299	−	11.4535i	−0.105106	−	0.690670i
$276$	1.38356	+	2.39639i	0.0832804	+	0.144246i
$277$	21.5360	−	9.58846i	1.29397	−	0.576114i	0.359833	−	0.933017i	$-0.382834\pi$
$277$	21.5360	−	9.58846i	1.29397	−	0.576114i	0.934142	+	0.356902i	$0.116167\pi$
$278$	−7.44195	+	22.9040i	−0.446339	+	1.37369i
$279$	−8.43401	−	1.79270i	−0.504931	−	0.107326i
$280$	−0.284081	−	2.70285i	−0.0169771	−	0.161526i
$281$	4.04447	−	2.93848i	0.241273	−	0.175295i	−0.460577	−	0.887620i	$-0.652358\pi$
$281$	4.04447	−	2.93848i	0.241273	−	0.175295i	0.701850	+	0.712325i	$0.252358\pi$
$282$	0.748303	+	0.159057i	0.0445608	+	0.00947169i
$283$	13.7659	−	2.92603i	0.818297	−	0.173934i	0.220299	−	0.975432i	$-0.429297\pi$
$283$	13.7659	−	2.92603i	0.818297	−	0.173934i	0.597998	+	0.801498i	$0.295963\pi$
$284$	0.353720	−	3.36542i	0.0209894	−	0.199701i
$285$	−0.433109			−0.0256552
$286$	18.7187	+	7.51783i	1.10686	+	0.444539i
$287$	−8.72021			−0.514738
$288$	0.470286	−	4.47447i	0.0277118	−	0.263661i
$289$	−11.9730	+	2.54493i	−0.704292	+	0.149702i
$290$	−10.0984	−	2.14648i	−0.592998	−	0.126046i
$291$	−4.14416	+	3.01091i	−0.242935	+	0.176503i
$292$	−0.631641	−	6.00966i	−0.0369640	−	0.351689i
$293$	1.61970	+	0.344278i	0.0946239	+	0.0201129i	0.254980	−	0.966946i	$-0.417931\pi$
$293$	1.61970	+	0.344278i	0.0946239	+	0.0201129i	−0.160356	+	0.987059i	$0.551264\pi$
$294$	−2.97521	+	9.15675i	−0.173518	+	0.534032i
$295$	6.53578	−	2.90992i	0.380528	−	0.169422i
$296$	9.51152	+	16.4744i	0.552846	+	0.957558i
$297$	1.52359	−	2.94596i	0.0884077	−	0.170942i
$298$	35.3803			2.04953
$299$	−11.5187	−	2.56089i	−0.666146	−	0.148100i
$300$	−0.912666	+	2.80890i	−0.0526928	+	0.162172i
$301$	−6.13246	+	6.81079i	−0.353469	+	0.392567i
$302$	1.31674	+	0.586250i	0.0757699	+	0.0337349i
$303$	−1.39756	−	13.2969i	−0.0802876	−	0.763886i
$304$	−0.542538	−	1.66976i	−0.0311167	−	0.0957674i
$305$	11.2819	+	12.5298i	0.646000	+	0.717456i
$306$	−8.33301	+	3.71010i	−0.476367	+	0.212092i
$307$	−3.56447			−0.203435			−0.101718	−	0.994813i	$-0.532434\pi$
$307$	−3.56447			−0.203435			−0.101718	+	0.994813i	$0.532434\pi$
$308$	−3.18452	+	0.147554i	−0.181455	+	0.00840765i
$309$	3.03142	+	5.25057i	0.172451	+	0.298695i
$310$	1.86632	−	17.7568i	0.106000	−	1.00852i
$311$	−4.09219	+	12.5945i	−0.232047	+	0.714167i	0.765452	+	0.643493i	$0.222515\pi$
$311$	−4.09219	+	12.5945i	−0.232047	+	0.714167i	−0.997499	+	0.0706748i	$0.977485\pi$
$312$	4.64957	+	5.26173i	0.263230	+	0.297887i
$313$	−20.9327	+	15.2085i	−1.18319	+	0.859636i	−0.992528	−	0.122020i	$-0.961063\pi$
$313$	−20.9327	+	15.2085i	−1.18319	+	0.859636i	−0.190660	+	0.981656i	$0.561063\pi$
$314$	−24.9547	−	11.1106i	−1.40828	−	0.627006i
$315$	−0.933786	+	1.03707i	−0.0526129	+	0.0584325i
$316$	8.91134	+	9.89705i	0.501302	+	0.556753i
$317$	14.7747	+	10.7345i	0.829830	+	0.602907i	0.919511	−	0.393064i	$-0.128585\pi$
$317$	14.7747	+	10.7345i	0.829830	+	0.602907i	−0.0896810	+	0.995971i	$0.528585\pi$
$318$	4.69416	−	8.13052i	0.263235	−	0.455937i
$319$	4.37644	−	15.9460i	0.245034	−	0.892807i
$320$	−2.90056			−0.162146
$321$	15.7222	−	6.99998i	0.877529	−	0.390701i
$322$	6.13888	−	1.30486i	0.342106	−	0.0727170i
$323$	−1.27661	+	1.41782i	−0.0710326	+	0.0788897i
$324$	−0.684031	+	0.496977i	−0.0380017	+	0.0276098i
$325$	−6.19529	−	10.9655i	−0.343653	−	0.608255i
$326$	2.51151	+	7.72962i	0.139099	+	0.428104i
$327$	−9.21030	+	1.95771i	−0.509331	+	0.108262i
$328$	−1.56148	+	14.8565i	−0.0862184	+	0.820314i
$329$	0.257785	−	0.446497i	0.0142122	−	0.0246162i
$330$	6.39661	+	2.50000i	0.352122	+	0.137620i
$331$	−2.32987	+	4.03546i	−0.128061	+	0.221809i	−0.922925	−	0.384979i	$-0.874209\pi$
$331$	−2.32987	+	4.03546i	−0.128061	+	0.221809i	0.794864	+	0.606788i	$0.207542\pi$
$332$	−6.25236	+	2.78373i	−0.343143	+	0.152777i
$333$	3.01850	−	9.29000i	0.165413	−	0.509089i
$334$	−31.4866	−	6.69268i	−1.72287	−	0.366207i
$335$	10.0995	+	4.49658i	0.551793	+	0.245674i
$336$	−5.16794	−	2.30091i	−0.281934	−	0.125525i
$337$	6.47616	+	19.9316i	0.352779	+	1.08574i	0.957286	+	0.289142i	$0.0933701\pi$
$337$	6.47616	+	19.9316i	0.352779	+	1.08574i	−0.604507	+	0.796600i	$0.706630\pi$
$338$	21.9254	+	0.409001i	1.19259	+	0.0222467i
$339$	−7.27353	−	5.28453i	−0.395044	−	0.287016i
$340$	−2.80622	−	4.86051i	−0.152188	−	0.263598i
$341$	28.2177	+	4.64465i	1.52807	+	0.251522i
$342$	−0.297582	+	0.515427i	−0.0160914	+	0.0278711i
$343$	11.6874	+	8.49138i	0.631059	+	0.458491i
$344$	10.5053	+	11.6674i	0.566410	+	0.629063i
$345$	−3.92966	−	0.835276i	−0.211566	−	0.0449697i
$346$	1.07822	−	0.783369i	0.0579652	−	0.0421142i
$347$	2.03642	+	19.3752i	0.109321	+	1.04012i	0.902371	+	0.430961i	$0.141825\pi$
$347$	2.03642	+	19.3752i	0.109321	+	1.04012i	−0.793050	+	0.609157i	$0.791508\pi$
$348$	−2.82069	+	3.13269i	−0.151205	+	0.167930i
$349$	−34.9284	+	7.42427i	−1.86968	+	0.397412i	−0.996020	−	0.0891323i	$-0.971591\pi$
$349$	−34.9284	+	7.42427i	−1.86968	+	0.397412i	−0.873656	+	0.486544i	$0.838257\pi$
$350$	5.41932	+	3.93736i	0.289675	+	0.210461i
$351$	0.410307	−	3.58213i	0.0219006	−	0.191200i
$352$	−0.871213	+	14.8964i	−0.0464358	+	0.793982i
$353$	−10.3475	−	17.9224i	−0.550742	−	0.953913i	−0.998221	−	0.0596190i	$-0.981011\pi$
$353$	−10.3475	−	17.9224i	−0.550742	−	0.953913i	0.447479	−	0.894294i	$-0.352322\pi$
$354$	1.02764	−	9.77733i	0.0546184	−	0.519659i
$355$	3.28745	+	3.65109i	0.174480	+	0.193779i
$356$	0.291630	+	0.897546i	0.0154564	+	0.0475699i
$357$	0.642572	+	6.11366i	0.0340085	+	0.323569i
$358$	0.550877	+	5.24124i	0.0291147	+	0.277008i
$359$	−7.82600	−	24.0859i	−0.413040	−	1.27121i	−0.913992	−	0.405732i	$-0.867017\pi$
$359$	−7.82600	−	24.0859i	−0.413040	−	1.27121i	0.500952	−	0.865475i	$-0.332983\pi$
$360$	1.59964	+	1.77658i	0.0843086	+	0.0936341i
$361$	1.97303	−	18.7721i	0.103844	−	0.988006i
$362$	11.4382	+	19.8115i	0.601177	+	1.04127i
$363$	−4.59553	+	9.99405i	−0.241203	+	0.524552i
$364$	−3.17904	+	1.38002i	−0.166627	+	0.0723327i
$365$	7.09769	+	5.15677i	0.371510	+	0.269918i
$366$	22.6629	−	4.81714i	1.18461	−	0.251796i
$367$	9.97208	−	11.0751i	0.520538	−	0.578116i	−0.424355	−	0.905496i	$-0.639499\pi$
$367$	9.97208	−	11.0751i	0.520538	−	0.578116i	0.944893	+	0.327380i	$0.106166\pi$
$368$	−1.70230	−	16.1963i	−0.0887385	−	0.844291i
$369$	6.20568	−	4.50869i	0.323055	−	0.234713i
$370$	19.7849	+	4.20542i	1.02857	+	0.218629i
$371$	−4.23364	−	4.70193i	−0.219799	−	0.244112i
$372$	−5.89801	−	4.28515i	−0.305797	−	0.222175i
$373$	9.42367	−	16.3223i	0.487939	−	0.845135i	−0.511965	−	0.859006i	$-0.671082\pi$
$373$	9.42367	−	16.3223i	0.487939	−	0.845135i	0.999904	+	0.0138713i	$0.00441550\pi$
$374$	27.0383	−	13.5710i	1.39812	−	0.701740i
$375$	−5.21288	−	9.02897i	−0.269192	−	0.466254i
$376$	−0.714532	−	0.519138i	−0.0368492	−	0.0267725i
$377$	−1.71222	−	17.8945i	−0.0881837	−	0.921613i
$378$	0.592594	+	1.82382i	0.0304798	+	0.0938070i
$379$	28.9489	+	12.8889i	1.48700	+	0.662056i	0.979838	−	0.199793i	$-0.0640269\pi$
$379$	28.9489	+	12.8889i	1.48700	+	0.662056i	0.507165	+	0.861849i	$0.330694\pi$
$380$	−0.334538	−	0.148946i	−0.0171614	−	0.00764076i
$381$	−12.0593	−	2.56327i	−0.617815	−	0.131321i
$382$	5.31198	−	16.3486i	0.271784	−	0.836467i
$383$	−17.1277	+	7.62575i	−0.875185	+	0.389657i	−0.794631	−	0.607093i	$-0.792336\pi$
$383$	−17.1277	+	7.62575i	−0.875185	+	0.389657i	−0.0805541	+	0.996750i	$0.525669\pi$
$384$	−6.49204	+	11.2445i	−0.331295	+	0.573820i
$385$	2.93450	−	3.57925i	0.149556	−	0.182415i
$386$	−9.20976	+	15.9518i	−0.468765	+	0.811924i
$387$	0.842681	−	8.01758i	0.0428359	−	0.407556i
$388$	−4.23644	+	0.900484i	−0.215073	+	0.0457151i
$389$	7.33628	+	22.5787i	0.371964	+	1.14479i	0.945504	+	0.325610i	$0.105570\pi$
$389$	7.33628	+	22.5787i	0.371964	+	1.14479i	−0.573540	+	0.819177i	$0.694430\pi$
$390$	7.46576	+	0.0696279i	0.378043	+	0.00352574i
$391$	−14.3172	+	10.4021i	−0.724054	+	0.526056i
$392$	7.43767	−	8.26037i	0.375659	−	0.417211i
$393$	−6.51711	+	1.38526i	−0.328745	+	0.0698769i
$394$	−0.616341	+	0.274413i	−0.0310508	+	0.0138247i
$395$	−19.3355			−0.972875
$396$	2.18995	−	1.75153i	0.110049	−	0.0880175i
$397$	−1.90570	+	3.30078i	−0.0956446	+	0.165661i	−0.909877	−	0.414877i	$-0.863825\pi$
$397$	−1.90570	+	3.30078i	−0.0956446	+	0.165661i	0.814233	+	0.580538i	$0.197158\pi$
$398$	13.3396	+	9.69177i	0.668652	+	0.485804i
$399$	0.268387	+	0.298075i	0.0134362	+	0.0149224i
$400$	11.6309	−	12.9175i	0.581547	−	0.645873i
$401$	10.6293	+	4.73245i	0.530800	+	0.236328i	0.654594	−	0.755980i	$-0.272840\pi$
$401$	10.6293	+	4.73245i	0.530800	+	0.236328i	−0.123794	+	0.992308i	$0.539506\pi$
$402$	12.2904	−	8.92948i	0.612988	−	0.445362i
$403$	30.4682	−	6.17981i	1.51773	−	0.307839i
$404$	3.49330	−	10.7513i	0.173798	−	0.534895i
$405$	0.128315	−	1.22083i	0.00637600	−	0.0606636i
$406$	4.78048	+	8.28003i	0.237251	+	0.410931i
$407$	−8.57441	+	31.2418i	−0.425018	+	1.54860i
$408$	10.5308			0.521354
$409$	1.63153	−	0.726403i	0.0806739	−	0.0359183i	−0.366003	−	0.930614i	$-0.619274\pi$
$409$	1.63153	−	0.726403i	0.0806739	−	0.0359183i	0.446677	+	0.894695i	$0.352607\pi$
$410$	10.6283	+	11.8039i	0.524894	+	0.582954i
$411$	5.39154	+	16.5934i	0.265945	+	0.818494i
$412$	0.535832	+	5.09810i	0.0263985	+	0.251165i
$413$	−6.05273	−	2.69485i	−0.297835	−	0.132605i
$414$	−3.69403	+	4.10264i	−0.181552	+	0.201634i
$415$	3.07058	−	9.45026i	0.150729	−	0.463895i
$416$	4.86871	+	15.4739i	0.238708	+	0.758671i
$417$	−14.2766			−0.699128
$418$	0.906786	−	1.75333i	0.0443523	−	0.0857580i
$419$	−16.4450	−	28.4835i	−0.803389	−	1.39151i	−0.917373	−	0.398029i	$-0.869694\pi$
$419$	−16.4450	−	28.4835i	−0.803389	−	1.39151i	0.113984	−	0.993483i	$-0.463639\pi$
$420$	−1.07791	+	0.479919i	−0.0525968	+	0.0234176i
$421$	−2.94761	+	9.07181i	−0.143658	+	0.442133i	−0.996836	−	0.0794866i	$-0.974672\pi$
$421$	−2.94761	+	9.07181i	−0.143658	+	0.442133i	0.853178	+	0.521619i	$0.174672\pi$
$422$	−27.0697	−	5.75385i	−1.31773	−	0.280093i
$423$	0.0474054	+	0.451032i	0.00230493	+	0.0219299i
$424$	−8.76872	+	6.37084i	−0.425846	+	0.309396i
$425$	−18.4760	−	3.92720i	−0.896218	−	0.190497i
$426$	6.60377	−	1.40367i	0.319953	−	0.0680082i
$427$	1.63215	−	15.5289i	0.0789853	−	0.751495i
$428$	14.5513			0.703363
$429$	−0.809483	+	11.9308i	−0.0390822	+	0.576026i
$430$	16.6936			0.805037
$431$	2.03448	−	19.3568i	0.0979975	−	0.932384i	−0.829488	−	0.558525i	$-0.811368\pi$
$431$	2.03448	−	19.3568i	0.0979975	−	0.932384i	0.927485	−	0.373859i	$-0.121966\pi$
$432$	4.86739	−	1.03460i	0.234183	−	0.0497770i
$433$	−3.26833	−	0.694705i	−0.157066	−	0.0333854i	0.128708	−	0.991683i	$-0.458917\pi$
$433$	−3.26833	−	0.694705i	−0.157066	−	0.0333854i	−0.285773	+	0.958297i	$0.592250\pi$
$434$	−13.3771	+	9.71905i	−0.642122	+	0.466529i
$435$	−0.639738	−	6.08670i	−0.0306731	−	0.291835i
$436$	−7.78739	−	1.65526i	−0.372948	−	0.0792726i
$437$	−0.356819	+	1.09818i	−0.0170690	+	0.0525329i
$438$	11.0136	−	4.90356i	0.526249	−	0.234301i
$439$	0.227135	+	0.393409i	0.0108405	+	0.0187764i	0.871395	−	0.490582i	$-0.163216\pi$
$439$	0.227135	+	0.393409i	0.0108405	+	0.0187764i	−0.860554	+	0.509359i	$0.829883\pi$
$440$	−5.57245	−	5.64038i	−0.265656	−	0.268895i
$441$	−5.70762			−0.271791
$442$	22.2337	−	24.2346i	1.05755	−	1.15272i
$443$	−2.27482	+	7.00117i	−0.108080	+	0.332636i	−0.990441	−	0.137937i	$-0.955953\pi$
$443$	−2.27482	+	7.00117i	−0.108080	+	0.332636i	0.882361	+	0.470573i	$0.155953\pi$
$444$	5.52635	−	6.13763i	0.262269	−	0.291279i
$445$	−1.25171	−	0.557298i	−0.0593368	−	0.0264184i
$446$	0.570007	+	5.42325i	0.0269906	+	0.256798i
$447$	6.48134	+	19.9475i	0.306557	+	0.943484i
$448$	1.79741	+	1.99622i	0.0849194	+	0.0943126i
$449$	28.0961	−	12.5092i	1.32594	−	0.590346i	0.383134	−	0.923693i	$-0.374845\pi$
$449$	28.0961	−	12.5092i	1.32594	−	0.590346i	0.942804	+	0.333347i	$0.108178\pi$
$450$	−5.89239			−0.277770
$451$	−19.8677	+	15.8902i	−0.935535	+	0.748242i
$452$	−3.80081	−	6.58319i	−0.178775	−	0.309647i
$453$	−0.0893150	+	0.849775i	−0.00419638	+	0.0399259i
$454$	8.38592	−	25.8092i	0.393571	−	1.21129i
$455$	1.59942	−	4.77065i	0.0749818	−	0.223651i
$456$	0.555885	−	0.403874i	0.0260317	−	0.0189131i
$457$	5.66825	+	2.52367i	0.265150	+	0.118052i	0.535006	−	0.844848i	$-0.320309\pi$
$457$	5.66825	+	2.52367i	0.265150	+	0.118052i	−0.269856	+	0.962901i	$0.586976\pi$
$458$	22.0961	−	24.5402i	1.03248	−	1.14669i
$459$	−3.61829	−	4.01851i	−0.168887	−	0.187568i
$460$	−2.74806	−	1.99658i	−0.128129	−	0.0930912i
$461$	−1.56681	+	2.71380i	−0.0729737	+	0.126394i	−0.900203	−	0.435470i	$-0.856582\pi$
$461$	−1.56681	+	2.71380i	−0.0729737	+	0.126394i	0.827230	+	0.561864i	$0.189916\pi$
$462$	−2.24328	−	5.95147i	−0.104367	−	0.276887i
$463$	−7.21614			−0.335362			−0.167681	−	0.985841i	$-0.553628\pi$
$463$	−7.21614			−0.335362			−0.167681	+	0.985841i	$0.553628\pi$
$464$	22.6646	−	10.0909i	1.05218	−	0.468460i
$465$	10.3532	−	2.20065i	0.480119	−	0.102052i
$466$	6.55248	−	7.27727i	0.303538	−	0.337113i
$467$	9.82249	−	7.13646i	0.454531	−	0.330236i	−0.336851	−	0.941558i	$-0.609362\pi$
$467$	9.82249	−	7.13646i	0.454531	−	0.330236i	0.791382	+	0.611322i	$0.209362\pi$
$468$	1.54882	−	2.62577i	0.0715941	−	0.121376i
$469$	−3.16377	−	9.73708i	−0.146089	−	0.449617i
$470$	−0.918583	+	0.195251i	−0.0423711	+	0.00900625i
$471$	1.69269	−	16.1049i	0.0779951	−	0.742074i
$472$	−5.67501	+	9.82941i	−0.261214	+	0.452435i
$473$	−1.56108	+	26.6922i	−0.0717787	+	1.22731i
$474$	−13.2851	+	23.0104i	−0.610204	+	1.05690i
$475$	−1.12590	+	0.501281i	−0.0516597	+	0.0230004i
$476$	−1.60615	+	4.94323i	−0.0736180	+	0.226573i
$477$	5.44392	+	1.15714i	0.249260	+	0.0529819i
$478$	−10.2746	−	4.57456i	−0.469950	−	0.209235i
$479$	−11.2539	−	5.01056i	−0.514204	−	0.228938i	0.133195	−	0.991090i	$-0.457476\pi$
$479$	−11.2539	−	5.01056i	−0.514204	−	0.228938i	−0.647399	+	0.762152i	$0.724143\pi$
$480$	1.70667	+	5.25260i	0.0778987	+	0.239748i
$481$	3.35461	+	35.0592i	0.152957	+	1.59856i
$482$	11.2306	+	8.15948i	0.511538	+	0.371654i
$483$	1.86027	+	3.22207i	0.0846450	+	0.146609i
$484$	−6.98658	+	6.13911i	−0.317572	+	0.279050i
$485$	3.14406	−	5.44567i	0.142764	−	0.247275i
$486$	−1.36470	−	0.991513i	−0.0619041	−	0.0449760i
$487$	10.7508	+	11.9399i	0.487164	+	0.541051i	0.935738	−	0.352695i	$-0.114735\pi$
$487$	10.7508	+	11.9399i	0.487164	+	0.541051i	−0.448574	+	0.893746i	$0.648068\pi$
$488$	−26.1641	−	5.56135i	−1.18439	−	0.251750i
$489$	−3.89789	+	2.83198i	−0.176269	+	0.128067i
$490$	−1.23541	−	11.7541i	−0.0558101	−	0.530998i
$491$	10.5145	−	11.6775i	0.474513	−	0.527000i	−0.457604	−	0.889156i	$-0.651292\pi$
$491$	10.5145	−	11.6775i	0.474513	−	0.527000i	0.932118	+	0.362156i	$0.117959\pi$
$492$	6.34387	−	1.34843i	0.286004	−	0.0607919i
$493$	−21.8110	−	15.8466i	−0.982319	−	0.713697i
$494$	0.244200	−	2.13195i	0.0109871	−	0.0959210i
$495$	−0.237705	+	4.06440i	−0.0106841	+	0.182681i
$496$	21.4532	+	37.1580i	0.963277	+	1.66844i
$497$	0.475595	−	4.52498i	0.0213333	−	0.202973i
$498$	−9.13665	−	10.1473i	−0.409423	−	0.454710i
$499$	−4.07936	−	12.5550i	−0.182617	−	0.562039i	0.817282	−	0.576238i	$-0.195480\pi$
$499$	−4.07936	−	12.5550i	−0.182617	−	0.562039i	−0.999899	+	0.0141996i	$0.995480\pi$
$500$	−0.921426	−	8.76678i	−0.0412074	−	0.392062i
$501$	−1.99469	−	18.9782i	−0.0891163	−	0.847885i
$502$	−6.89964	−	21.2349i	−0.307946	−	0.947761i
$503$	−7.42329	−	8.24440i	−0.330988	−	0.367600i	0.554563	−	0.832142i	$-0.312886\pi$
$503$	−7.42329	−	8.24440i	−0.330988	−	0.367600i	−0.885551	+	0.464542i	$0.846219\pi$
$504$	0.231420	−	2.20181i	0.0103083	−	0.0980765i
$505$	8.20628	+	14.2137i	0.365175	+	0.632501i
$506$	11.6088	−	14.1594i	0.516074	−	0.629462i
$507$	3.78593	+	12.4365i	0.168139	+	0.552325i
$508$	−8.43319	−	6.12707i	−0.374162	−	0.271845i
$509$	32.4083	−	6.88859i	1.43647	−	0.305331i	0.577095	−	0.816677i	$-0.304186\pi$
$509$	32.4083	−	6.88859i	1.43647	−	0.305331i	0.859375	+	0.511346i	$0.170853\pi$
$510$	7.49245	−	8.32121i	0.331771	−	0.368469i
$511$	−0.849274	−	8.08030i	−0.0375697	−	0.357451i
$512$	−2.43228	+	1.76715i	−0.107492	+	0.0780978i
$513$	−0.345112	−	0.0733559i	−0.0152371	−	0.00323874i
$514$	−15.6661	−	17.3989i	−0.691000	−	0.767433i
$515$	−6.02109	−	4.37457i	−0.265321	−	0.192767i
$516$	3.40813	−	5.90306i	0.150035	−	0.259868i
$517$	−0.226295	−	1.48702i	−0.00995246	−	0.0653992i
$518$	−9.36601	−	16.2224i	−0.411519	−	0.712771i
$519$	0.639183	+	0.464394i	0.0280570	+	0.0203846i
$520$	−7.84130	−	3.57916i	−0.343864	−	0.156957i
$521$	−5.44170	−	16.7478i	−0.238405	−	0.733736i	−0.996651	−	0.0817673i	$-0.973944\pi$
$521$	−5.44170	−	16.7478i	−0.238405	−	0.733736i	0.758246	−	0.651968i	$-0.226056\pi$
$522$	−7.68310	−	3.42074i	−0.336280	−	0.149722i
$523$	20.8928	+	9.30209i	0.913580	+	0.406752i	0.809030	−	0.587767i	$-0.199993\pi$
$523$	20.8928	+	9.30209i	0.913580	+	0.406752i	0.104550	+	0.994520i	$0.466660\pi$
$524$	−5.51027	−	1.17124i	−0.240717	−	0.0511661i
$525$	−1.22713	+	3.77671i	−0.0535562	+	0.164829i
$526$	4.68332	−	2.08515i	0.204202	−	0.0909168i
$527$	23.3127	−	40.3787i	1.01552	−	1.75892i
$528$	−15.9672	+	4.17488i	−0.694883	+	0.181688i
$529$	6.14463	−	10.6428i	0.267158	−	0.462731i
$530$	−1.20466	+	11.4615i	−0.0523269	+	0.497858i
$531$	5.70073	−	1.21173i	0.247391	−	0.0525845i
$532$	0.104798	+	0.322534i	0.00454355	+	0.0139836i
$533$	−14.0512	+	23.8216i	−0.608626	+	1.03183i
$534$	−1.52325	+	1.10670i	−0.0659173	+	0.0478917i
$535$	−14.1363	+	15.7000i	−0.611166	+	0.678768i
$536$	−17.1555	+	3.64651i	−0.741003	+	0.157505i
$537$	−2.85411	+	1.27073i	−0.123164	+	0.0548360i
$538$	−49.6237			−2.13943
$539$	18.9097	−	0.876177i	0.814500	−	0.0377396i
$540$	0.518954	−	0.898855i	0.0223322	−	0.0386806i
$541$	−20.6087	−	14.9731i	−0.886037	−	0.643743i	0.0488049	−	0.998808i	$-0.484459\pi$
$541$	−20.6087	−	14.9731i	−0.886037	−	0.643743i	−0.934842	+	0.355065i	$0.884459\pi$
$542$	−23.3160	−	25.8950i	−1.00151	−	1.11229i
$543$	−9.07439	+	10.0781i	−0.389420	+	0.432494i
$544$	22.2254	+	9.89538i	0.952905	+	0.424261i
$545$	9.35122	−	6.79406i	0.400562	−	0.291026i
$546$	−4.57843	−	5.18123i	−0.195939	−	0.221736i
$547$	−3.29887	+	10.1529i	−0.141050	+	0.434106i	−0.996482	−	0.0838086i	$-0.973292\pi$
$547$	−3.29887	+	10.1529i	−0.141050	+	0.434106i	0.855432	+	0.517915i	$0.173292\pi$
$548$	−1.54199	+	14.6711i	−0.0658707	+	0.626718i
$549$	6.86753	+	11.8949i	0.293099	+	0.507662i
$550$	19.5219	−	0.904542i	0.832417	−	0.0385698i
$551$	−1.75907			−0.0749388
$552$	5.82252	−	2.59235i	0.247823	−	0.110338i
$553$	11.9818	+	13.3071i	0.509516	+	0.565875i
$554$	12.2885	+	37.8200i	0.522087	+	1.60682i
$555$	1.25339	+	11.9252i	0.0532033	+	0.506196i
$556$	−11.0274	−	4.90971i	−0.467665	−	0.208218i
$557$	−27.2375	+	30.2503i	−1.15409	+	1.28175i	−0.200819	+	0.979628i	$0.564360\pi$
$557$	−27.2375	+	30.2503i	−1.15409	+	1.28175i	−0.953271	+	0.302118i	$0.902306\pi$
$558$	4.49461	−	13.8330i	0.190272	−	0.585597i
$559$	8.72400	+	27.7269i	0.368986	+	1.17272i
$560$	6.94430			0.293450
$561$	12.6045	+	12.7582i	0.532163	+	0.538651i
$562$	4.21652	+	7.30322i	0.177863	+	0.308068i
$563$	29.9885	−	13.3517i	1.26387	−	0.562709i	0.338208	−	0.941071i	$-0.390179\pi$
$563$	29.9885	−	13.3517i	1.26387	−	0.562709i	0.925658	+	0.378362i	$0.123513\pi$
$564$	−0.118493	+	0.364684i	−0.00498946	+	0.0153560i
$565$	10.7953	+	2.29460i	0.454160	+	0.0965347i
$566$	2.48150	+	23.6099i	0.104305	+	0.992398i
$567$	−0.919714	+	0.668211i	−0.0386244	+	0.0280622i
$568$	−7.62399	−	1.62053i	−0.319896	−	0.0679959i
$569$	2.95028	−	0.627102i	0.123682	−	0.0262895i	−0.145655	−	0.989336i	$-0.546529\pi$
$569$	2.95028	−	0.627102i	0.123682	−	0.0262895i	0.269337	+	0.963046i	$0.413195\pi$
$570$	0.0763681	−	0.726594i	0.00319871	−	0.0304337i
$571$	−4.24547			−0.177668			−0.0888338	−	0.996046i	$-0.528314\pi$
$571$	−4.24547			−0.177668			−0.0888338	+	0.996046i	$0.528314\pi$
$572$	−4.72826	+	8.93712i	−0.197698	+	0.373680i
$573$	10.1905			0.425713
$574$	1.53759	−	14.6292i	0.0641779	−	0.610612i
$575$	−11.1822	+	2.37684i	−0.466329	+	0.0991212i
$576$	−2.31124	−	0.491268i	−0.0963015	−	0.0204695i
$577$	9.22804	−	6.70457i	0.384168	−	0.279115i	−0.378893	−	0.925440i	$-0.623695\pi$
$577$	9.22804	−	6.70457i	0.384168	−	0.279115i	0.763062	+	0.646326i	$0.223695\pi$
$578$	−2.15830	−	20.5348i	−0.0897734	−	0.854137i
$579$	−10.6808	−	2.27027i	−0.443878	−	0.0943492i
$580$	1.59907	−	4.92144i	0.0663978	−	0.204351i
$581$	−8.40662	+	3.74287i	−0.348765	+	0.155280i
$582$	−4.32045	−	7.48324i	−0.179088	−	0.310190i
$583$	−18.2137	−	2.99799i	−0.754336	−	0.124164i
$584$	−13.9184			−0.575947
$585$	1.32840	+	4.22196i	0.0549225	+	0.174557i
$586$	−0.863162	+	2.65654i	−0.0356569	+	0.109741i
$587$	−15.2330	+	16.9179i	−0.628732	+	0.698278i	−0.970389	−	0.241547i	$-0.922345\pi$
$587$	−15.2330	+	16.9179i	−0.628732	+	0.698278i	0.341657	+	0.939825i	$0.389012\pi$
$588$	−4.40862	−	1.96285i	−0.181809	−	0.0809464i
$589$	−0.317995	−	3.02552i	−0.0131028	−	0.124665i
$590$	3.72932	+	11.4777i	0.153534	+	0.472528i
$591$	−0.267622	−	0.297224i	−0.0110085	−	0.0122262i
$592$	−44.4050	+	19.7704i	−1.82503	+	0.812557i
$593$	2.17360			0.0892590			0.0446295	−	0.999004i	$-0.485789\pi$
$593$	2.17360			0.0892590			0.0446295	+	0.999004i	$0.485789\pi$
$594$	4.67356	+	3.07546i	0.191758	+	0.126188i
$595$	−3.77310	−	6.53520i	−0.154682	−	0.267917i
$596$	−1.85368	+	17.6366i	−0.0759297	+	0.722423i
$597$	−3.02055	+	9.29631i	−0.123623	+	0.380473i
$598$	6.32725	−	18.8726i	0.258740	−	0.771756i
$599$	−20.6855	+	15.0289i	−0.845186	+	0.614064i	−0.923815	−	0.382840i	$-0.874946\pi$
$599$	−20.6855	+	15.0289i	−0.845186	+	0.614064i	0.0786282	+	0.996904i	$0.474946\pi$
$600$	6.21459	+	2.76692i	0.253710	+	0.112959i
$601$	−9.39011	+	10.4288i	−0.383030	+	0.425398i	−0.903571	−	0.428439i	$-0.859064\pi$
$601$	−9.39011	+	10.4288i	−0.383030	+	0.425398i	0.520540	+	0.853837i	$0.325730\pi$
$602$	−10.3446	−	11.4889i	−0.421615	−	0.468251i
$603$	7.28593	+	5.29354i	0.296706	+	0.215570i
$604$	−0.361225	+	0.625660i	−0.0146980	+	0.0254577i
$605$	0.163608	−	13.5021i	0.00665160	−	0.548939i
$606$	22.5536			0.916176
$607$	−29.4480	+	13.1111i	−1.19526	+	0.532163i	−0.905258	−	0.424863i	$-0.860322\pi$
$607$	−29.4480	+	13.1111i	−1.19526	+	0.532163i	−0.290001	+	0.957026i	$0.593656\pi$
$608$	1.55270	−	0.330037i	0.0629703	−	0.0133848i
$609$	−3.79256	+	4.21206i	−0.153682	+	0.170681i
$610$	−23.0096	+	16.7175i	−0.931632	+	0.676870i
$611$	−0.804346	−	1.42367i	−0.0325404	−	0.0575954i
$612$	−1.41284	−	4.34827i	−0.0571106	−	0.175768i
$613$	−15.4126	+	3.27605i	−0.622509	+	0.132318i	−0.508359	−	0.861145i	$-0.669748\pi$
$613$	−15.4126	+	3.27605i	−0.622509	+	0.132318i	−0.114150	+	0.993464i	$0.536414\pi$
$614$	0.628507	−	5.97984i	0.0253645	−	0.241327i
$615$	−4.70807	+	8.15462i	−0.189848	+	0.328826i
$616$	−0.428710	+	7.33028i	−0.0172732	+	0.295346i
$617$	6.02261	−	10.4315i	0.242461	−	0.419955i	−0.718954	−	0.695058i	$-0.755379\pi$
$617$	6.02261	−	10.4315i	0.242461	−	0.419955i	0.961415	+	0.275103i	$0.0887120\pi$
$618$	−9.34299	+	4.15977i	−0.375830	+	0.167330i
$619$	4.41787	−	13.5968i	0.177569	−	0.546502i	−0.822172	−	0.569239i	$-0.807238\pi$
$619$	4.41787	−	13.5968i	0.177569	−	0.546502i	0.999741	+	0.0227369i	$0.00723800\pi$
$620$	8.75373	+	1.86066i	0.351558	+	0.0747261i
$621$	−2.98978	−	1.33114i	−0.119976	−	0.0534167i
$622$	−20.4072	−	9.08588i	−0.818255	−	0.364311i
$623$	0.392112	+	1.20680i	0.0157096	+	0.0483493i
$624$	−14.6129	+	10.4100i	−0.584983	+	0.416735i
$625$	−3.77595	−	2.74339i	−0.151038	−	0.109736i
$626$	−21.8232	−	37.7989i	−0.872230	−	1.51075i
$627$	1.15464	+	0.190055i	0.0461120	+	0.00759007i
$628$	6.84591	−	11.8575i	0.273181	−	0.473164i
$629$	42.7326	+	31.0470i	1.70386	+	1.23793i
$630$	−1.57517	−	1.74940i	−0.0627562	−	0.0696979i
$631$	−43.3272	−	9.20947i	−1.72483	−	0.366623i	−0.764311	−	0.644848i	$-0.776921\pi$
$631$	−43.3272	−	9.20947i	−1.72483	−	0.366623i	−0.960516	+	0.278224i	$0.910254\pi$
$632$	24.8166	−	18.0303i	0.987153	−	0.717208i
$633$	−1.71488	−	16.3160i	−0.0681604	−	0.648503i
$634$	−20.6135	+	22.8936i	−0.818667	+	0.909222i
$635$	14.8034	−	3.14656i	0.587456	−	0.124868i
$636$	3.80700	+	2.76595i	0.150957	+	0.109677i
$637$	18.8772	−	8.19459i	0.747942	−	0.324681i
$638$	25.9798	+	10.1537i	1.02855	+	0.401989i
$639$	2.00114	+	3.46607i	0.0791638	+	0.137116i
$640$	1.66604	−	15.8514i	0.0658562	−	0.626580i
$641$	−25.9861	−	28.8605i	−1.02639	−	1.13992i	−0.990069	−	0.140581i	$-0.955103\pi$
$641$	−25.9861	−	28.8605i	−1.02639	−	1.13992i	−0.0363207	−	0.999340i	$-0.511564\pi$
$642$	8.97111	+	27.6102i	0.354061	+	1.08969i
$643$	1.93209	+	18.3826i	0.0761942	+	0.724939i	0.964212	+	0.265131i	$0.0854152\pi$
$643$	1.93209	+	18.3826i	0.0761942	+	0.724939i	−0.888018	+	0.459808i	$0.847918\pi$
$644$	0.328819	+	3.12851i	0.0129573	+	0.123280i
$645$	3.05811	+	9.41188i	0.120413	+	0.370592i
$646$	−2.15347	−	2.39167i	−0.0847272	−	0.0940991i
$647$	−0.797965	+	7.59213i	−0.0313713	+	0.298478i	0.967575	+	0.252584i	$0.0812803\pi$
$647$	−0.797965	+	7.59213i	−0.0313713	+	0.298478i	−0.998946	+	0.0458939i	$0.985386\pi$
$648$	0.973735	+	1.68656i	0.0382519	+	0.0662543i
$649$	−18.7009	+	4.88966i	−0.734075	+	0.191936i
$650$	19.4883	−	8.45988i	0.764395	−	0.331824i
$651$	−7.93017	−	5.76161i	−0.310808	−	0.225815i
$652$	−3.98469	+	0.846972i	−0.156052	+	0.0331700i
$653$	18.8887	−	20.9780i	0.739171	−	0.820932i	−0.249916	−	0.968268i	$-0.580403\pi$
$653$	18.8887	−	20.9780i	0.739171	−	0.820932i	0.989087	+	0.147335i	$0.0470697\pi$
$654$	−1.66029	−	15.7966i	−0.0649225	−	0.617696i
$655$	6.61683	−	4.80741i	0.258541	−	0.187841i
$656$	−37.3360	−	7.93602i	−1.45773	−	0.309849i
$657$	4.78221	+	5.31118i	0.186572	+	0.207209i
$658$	0.703600	+	0.511195i	0.0274292	+	0.0199285i
$659$	−19.5156	+	33.8020i	−0.760220	+	1.31674i	0.182516	+	0.983203i	$0.441576\pi$
$659$	−19.5156	+	33.8020i	−0.760220	+	1.31674i	−0.942737	+	0.333538i	$0.891758\pi$
$660$	−1.58135	+	3.05763i	−0.0615539	+	0.119018i
$661$	3.70774	+	6.42200i	0.144214	+	0.249787i	0.929080	−	0.369880i	$-0.120601\pi$
$661$	3.70774	+	6.42200i	0.144214	+	0.249787i	−0.784865	+	0.619667i	$0.787268\pi$
$662$	−6.35916	−	4.62020i	−0.247156	−	0.179569i
$663$	17.7365	+	8.09583i	0.688828	+	0.314416i
$664$	4.87135	+	14.9925i	0.189045	+	0.581821i
$665$	−0.449803	−	0.200265i	−0.0174426	−	0.00776596i
$666$	15.0529	+	6.70197i	0.583287	+	0.259696i
$667$	−15.9603	−	3.39246i	−0.617985	−	0.131357i
$668$	4.98588	−	15.3450i	0.192909	−	0.593714i
$669$	−2.95322	+	1.31486i	−0.114178	+	0.0508354i
$670$	−9.32435	+	16.1502i	−0.360231	+	0.623938i
$671$	−24.5786	−	38.3544i	−0.948846	−	1.48066i
$672$	2.55736	−	4.42948i	0.0986524	−	0.170871i
$673$	−1.72967	+	16.4567i	−0.0666739	+	0.634359i	0.909250	+	0.416250i	$0.136656\pi$
$673$	−1.72967	+	16.4567i	−0.0666739	+	0.634359i	−0.975924	+	0.218110i	$0.930011\pi$
$674$	−34.5796	+	7.35011i	−1.33196	+	0.283116i
$675$	−1.07943	−	3.32214i	−0.0415473	−	0.127869i
$676$	−1.35262	+	10.9081i	−0.0520237	+	0.419541i
$677$	−9.76910	+	7.09767i	−0.375457	+	0.272785i	−0.759470	−	0.650542i	$-0.774542\pi$
$677$	−9.76910	+	7.09767i	−0.375457	+	0.272785i	0.384013	+	0.923328i	$0.374542\pi$
$678$	10.1480	−	11.2704i	0.389730	−	0.432839i
$679$	−5.69612	+	1.21075i	−0.218597	+	0.0464642i
$680$	−11.8096	+	5.25796i	−0.452876	+	0.201634i
$681$	16.0875			0.616474
$682$	−12.7675	+	46.5196i	−0.488891	+	1.78133i
$683$	9.79246	−	16.9610i	0.374698	−	0.648996i	−0.615584	−	0.788072i	$-0.711080\pi$
$683$	9.79246	−	16.9610i	0.374698	−	0.648996i	0.990282	+	0.139075i	$0.0444130\pi$
$684$	−0.241341	−	0.175345i	−0.00922792	−	0.00670447i
$685$	−14.3312	−	15.9164i	−0.547567	−	0.608135i
$686$	−16.3061	+	18.1098i	−0.622570	+	0.691434i
$687$	17.8836	+	7.96228i	0.682301	+	0.303780i
$688$	−32.4548	+	23.5798i	−1.23733	+	0.898970i
$689$	−19.6664	+	3.98890i	−0.749230	+	0.151965i
$690$	2.09418	−	6.44521i	0.0797239	−	0.245365i
$691$	−3.74550	+	35.6360i	−0.142486	+	1.35566i	0.656508	+	0.754319i	$0.272033\pi$
$691$	−3.74550	+	35.6360i	−0.142486	+	1.35566i	−0.798993	+	0.601340i	$0.794634\pi$
$692$	0.334007	+	0.578517i	0.0126970	+	0.0219919i
$693$	2.94450	−	2.35502i	0.111852	−	0.0894597i
$694$	−32.8634			−1.24748
$695$	16.0102	−	7.12819i	0.607301	−	0.270388i
$696$	6.49693	+	7.21557i	0.246265	+	0.273505i
$697$	12.8176	+	39.4485i	0.485501	+	1.49422i
$698$	−6.29635	−	59.9058i	−0.238321	−	2.26747i
$699$	5.30329	+	2.36118i	0.200589	+	0.0893079i
$700$	−2.24665	+	2.49516i	−0.0849155	+	0.0943082i
$701$	9.50612	−	29.2568i	0.359041	−	1.10502i	−0.594588	−	0.804031i	$-0.702685\pi$
$701$	9.50612	−	29.2568i	0.359041	−	1.10502i	0.953629	−	0.300985i	$-0.0973153\pi$
$702$	5.93711	+	1.31996i	0.224082	+	0.0498187i
$703$	3.44640			0.129983
$704$	7.73270	+	1.27281i	0.291437	+	0.0479708i
$705$	−0.278358	−	0.482131i	−0.0104836	−	0.0181581i
$706$	31.8916	−	14.1990i	1.20025	−	0.534388i
$707$	4.69692	−	14.4556i	0.176646	−	0.543660i
$708$	4.82001	+	1.02453i	0.181147	+	0.0385040i
$709$	1.26346	+	12.0210i	0.0474502	+	0.451458i	0.992291	+	0.123929i	$0.0395494\pi$
$709$	1.26346	+	12.0210i	0.0474502	+	0.451458i	−0.944841	+	0.327530i	$0.893784\pi$
$710$	−6.70480	+	4.87133i	−0.251627	+	0.182818i
$711$	−15.4070	−	3.27486i	−0.577809	−	0.122817i
$712$	2.12622	−	0.451942i	0.0796834	−	0.0169372i
$713$	2.94968	−	28.0643i	0.110466	−	1.05102i
$714$	−10.3697			−0.388077
$715$	−5.04919	−	13.7837i	−0.188829	−	0.515483i
$716$	−2.64154			−0.0987191
$717$	0.696932	−	6.63086i	0.0260274	−	0.247634i
$718$	41.7870	−	8.88211i	1.55948	−	0.331477i
$719$	21.9425	+	4.66403i	0.818318	+	0.173939i	0.598007	−	0.801491i	$-0.295959\pi$
$719$	21.9425	+	4.66403i	0.818318	+	0.173939i	0.220311	+	0.975430i	$0.429293\pi$
$720$	−4.94186	+	3.59047i	−0.184172	+	0.133809i
$721$	0.720453	+	6.85465i	0.0268311	+	0.255281i
$722$	31.1446	+	6.62000i	1.15908	+	0.246371i
$723$	−2.54300	+	7.82654i	−0.0945751	+	0.291072i
$724$	−10.4750	+	4.66378i	−0.389301	+	0.173328i
$725$	−8.70780	−	15.0823i	−0.323399	−	0.560144i
$726$	−15.9559	−	9.47177i	−0.592181	−	0.351530i
$727$	27.3245			1.01341			0.506705	−	0.862120i	$-0.330863\pi$
$727$	27.3245			1.01341			0.506705	+	0.862120i	$0.330863\pi$
$728$	2.39581	+	7.61446i	0.0887947	+	0.282211i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−9.90262	+	10.9980i	−0.366512	+	0.407053i
$731$	39.8246	+	17.7310i	1.47296	+	0.655806i
$732$	1.21390	+	11.5495i	0.0448670	+	0.426881i
$733$	−3.05483	−	9.40179i	−0.112833	−	0.347263i	0.878656	−	0.477455i	$-0.158441\pi$
$733$	−3.05483	−	9.40179i	−0.112833	−	0.347263i	−0.991489	+	0.130192i	$0.958441\pi$
$734$	16.8215	+	18.6822i	0.620894	+	0.689573i
$735$	6.40068	−	2.84977i	0.236093	−	0.105115i
$736$	14.7244			0.542748
$737$	−24.9514	−	16.4194i	−0.919097	−	0.604816i
$738$	6.46966	+	11.2058i	0.238152	+	0.412491i
$739$	−1.99622	+	18.9928i	−0.0734321	+	0.698660i	0.894435	+	0.447198i	$0.147578\pi$
$739$	−1.99622	+	18.9928i	−0.0734321	+	0.698660i	−0.967867	+	0.251462i	$0.919089\pi$
$740$	−3.13293	+	9.64217i	−0.115169	+	0.354453i
$741$	1.24673	−	0.252873i	0.0457999	−	0.00928951i
$742$	8.63456	−	6.27338i	0.316985	−	0.230303i
$743$	−2.89955	−	1.29096i	−0.106374	−	0.0473608i	0.352860	−	0.935676i	$-0.385209\pi$
$743$	−2.89955	−	1.29096i	−0.106374	−	0.0473608i	−0.459234	+	0.888315i	$0.651876\pi$
$744$	−11.2360	+	12.4788i	−0.411932	+	0.457496i
$745$	−17.2280	−	19.1336i	−0.631184	−	0.701001i
$746$	25.7210	+	18.6874i	0.941712	+	0.684194i
$747$	4.04731	−	7.01014i	0.148083	−	0.256488i
$748$	5.34833	+	14.1892i	0.195554	+	0.518810i
$749$	19.5650			0.714888
$750$	16.0664	−	7.15321i	0.586661	−	0.261198i
$751$	20.2258	−	4.29913i	0.738051	−	0.156878i	0.176478	−	0.984305i	$-0.443530\pi$
$751$	20.2258	−	4.29913i	0.738051	−	0.156878i	0.561573	+	0.827427i	$0.310196\pi$
$752$	1.51007	−	1.67710i	0.0550664	−	0.0611575i
$753$	10.7083	−	7.78006i	0.390234	−	0.283521i
$754$	30.3221	+	0.282793i	1.10427	+	0.0102987i
$755$	−0.324126	−	0.997556i	−0.0117961	−	0.0363048i
$756$	−0.940194	+	0.199844i	−0.0341945	+	0.00726827i
$757$	3.35725	−	31.9421i	0.122021	−	1.16096i	−0.746528	−	0.665354i	$-0.768281\pi$
$757$	3.35725	−	31.9421i	0.122021	−	1.16096i	0.868549	−	0.495603i	$-0.165053\pi$
$758$	−26.7271	+	46.2926i	−0.970771	+	1.68142i
$759$	10.1097	+	3.95119i	0.366959	+	0.143419i
$760$	−0.421734	+	0.730464i	−0.0152979	+	0.0264967i
$761$	−28.6677	+	12.7637i	−1.03920	+	0.462683i	−0.854140	−	0.520043i	$-0.825916\pi$
$761$	−28.6677	+	12.7637i	−1.03920	+	0.462683i	−0.185064	+	0.982727i	$0.559249\pi$
$762$	6.42656	−	19.7789i	0.232810	−	0.716515i
$763$	−10.4705	−	2.22558i	−0.379059	−	0.0805715i
$764$	7.87122	+	3.50449i	0.284771	+	0.126788i
$765$	6.06406	+	2.69989i	0.219246	+	0.0976148i
$766$	−9.77308	−	30.0784i	−0.353116	−	1.08678i
$767$	−17.1147	+	12.1923i	−0.617976	+	0.440239i
$768$	−13.8962	−	10.0962i	−0.501435	−	0.364314i
$769$	−15.6500	−	27.1067i	−0.564355	−	0.977491i	−0.997109	−	0.0759792i	$-0.975792\pi$
$769$	−15.6500	−	27.1067i	−0.564355	−	0.977491i	0.432755	−	0.901512i	$-0.357542\pi$
$770$	5.48720	+	5.55409i	0.197745	+	0.200155i
$771$	6.93967	−	12.0199i	0.249926	−	0.432885i
$772$	−7.46920	−	5.42669i	−0.268822	−	0.195311i
$773$	−8.07698	−	8.97040i	−0.290509	−	0.322643i	0.580169	−	0.814496i	$-0.302986\pi$
$773$	−8.07698	−	8.97040i	−0.290509	−	0.322643i	−0.870678	+	0.491853i	$0.836320\pi$
$774$	13.3019	+	2.82740i	0.478126	+	0.101629i
$775$	24.3669	−	17.7036i	0.875283	−	0.635930i
$776$	1.04276	+	9.92120i	0.0374329	+	0.356150i
$777$	7.43045	−	8.25236i	0.266566	−	0.296052i
$778$	−39.1722	+	8.32630i	−1.40439	+	0.298512i
$779$	2.18950	+	1.59077i	0.0784471	+	0.0569952i
$780$	−0.425861	+	3.71792i	−0.0152483	+	0.133123i
$781$	−7.16199	−	11.1762i	−0.256276	−	0.399914i
$782$	−14.9263	−	25.8531i	−0.533763	−	0.924504i
$783$	0.521148	−	4.95839i	0.0186243	−	0.177198i
$784$	19.0046	+	21.1067i	0.678734	+	0.753811i
$785$	6.14280	+	18.9056i	0.219246	+	0.674770i
$786$	−1.17480	−	11.1775i	−0.0419039	−	0.398689i
$787$	−1.03246	−	9.82318i	−0.0368032	−	0.350159i	−0.997391	−	0.0721833i	$-0.977003\pi$
$787$	−1.03246	−	9.82318i	−0.0368032	−	0.350159i	0.960588	−	0.277975i	$-0.0896633\pi$
$788$	−0.104499	−	0.321614i	−0.00372261	−	0.0114570i
$789$	2.03355	+	2.25848i	0.0723962	+	0.0804042i
$790$	3.40934	−	32.4377i	0.121299	−	1.15408i
$791$	−5.11038	−	8.85143i	−0.181704	−	0.314721i
$792$	−3.48496	−	5.43821i	−0.123833	−	0.193238i
$793$	−39.7913	−	29.4809i	−1.41303	−	1.04690i
$794$	−5.20143	−	3.77906i	−0.184592	−	0.134114i
$795$	−6.68272	+	1.42046i	−0.237012	+	0.0503784i
$796$	−5.53010	+	6.14180i	−0.196009	+	0.217690i
$797$	4.13199	+	39.3132i	0.146362	+	1.39255i	0.783307	+	0.621636i	$0.213532\pi$
$797$	4.13199	+	39.3132i	0.146362	+	1.39255i	−0.636944	+	0.770910i	$0.719802\pi$
$798$	−0.547380	+	0.397695i	−0.0193770	+	0.0140782i
$799$	−2.39877	−	0.509875i	−0.0848625	−	0.0180381i
$800$	10.5160	+	11.6792i	0.371796	+	0.412922i
$801$	−0.903005	−	0.656072i	−0.0319061	−	0.0231812i
$802$	−9.81348	+	16.9974i	−0.346526	+	0.600201i
$803$	−16.6591	−	16.8622i	−0.587888	−	0.595054i
$804$	3.80728	+	6.59441i	0.134273	+	0.232567i
$805$	−3.69491	−	2.68451i	−0.130228	−	0.0946165i
$806$	4.99508	+	52.2038i	0.175944	+	1.83880i
$807$	−9.09058	−	27.9779i	−0.320004	−	0.984870i
$808$	−23.7868	−	10.5906i	−0.836817	−	0.372575i
$809$	33.8493	+	15.0707i	1.19008	+	0.529858i	0.903662	−	0.428247i	$-0.140869\pi$
$809$	33.8493	+	15.0707i	1.19008	+	0.529858i	0.286418	+	0.958105i	$0.407535\pi$
$810$	2.02547	+	0.430527i	0.0711677	+	0.0151272i
$811$	−4.08424	+	12.5700i	−0.143417	+	0.441392i	−0.996804	−	0.0798856i	$-0.974545\pi$
$811$	−4.08424	+	12.5700i	−0.143417	+	0.441392i	0.853387	+	0.521278i	$0.174545\pi$
$812$	−4.37794	+	1.94918i	−0.153635	+	0.0684029i
$813$	10.3284	−	17.8893i	0.362232	−	0.627405i
$814$	−50.9001	−	19.8933i	−1.78405	−	0.697261i
$815$	2.95722	−	5.12205i	0.103587	−	0.179418i
$816$	−2.81267	+	26.7607i	−0.0984631	+	0.936813i
$817$	2.78221	−	0.591376i	0.0973371	−	0.0206896i
$818$	0.930951	+	2.86517i	0.0325499	+	0.100178i
$819$	2.08246	−	3.53048i	0.0727671	−	0.123365i
$820$	−6.44093	+	4.67961i	−0.224927	+	0.163419i
$821$	11.8052	−	13.1110i	0.412005	−	0.457577i	−0.501048	−	0.865420i	$-0.667052\pi$
$821$	11.8052	−	13.1110i	0.412005	−	0.457577i	0.913052	+	0.407842i	$0.133719\pi$
$822$	−28.7882	+	6.11912i	−1.00410	+	0.213429i
$823$	41.3634	−	18.4162i	1.44184	−	0.641947i	0.471098	−	0.882081i	$-0.343858\pi$
$823$	41.3634	−	18.4162i	1.44184	−	0.641947i	0.970740	+	0.240134i	$0.0771913\pi$
$824$	11.8072			0.411323
$825$	4.08621	+	10.8408i	0.142263	+	0.377428i
$826$	5.58819	−	9.67903i	0.194438	−	0.336776i
$827$	6.28703	+	4.56780i	0.218622	+	0.158838i	0.691706	−	0.722179i	$-0.256859\pi$
$827$	6.28703	+	4.56780i	0.218622	+	0.158838i	−0.473084	+	0.881017i	$0.656859\pi$
$828$	−1.85156	−	2.05637i	−0.0643463	−	0.0714638i
$829$	24.4137	−	27.1142i	0.847925	−	0.941716i	−0.150979	−	0.988537i	$-0.548243\pi$
$829$	24.4137	−	27.1142i	0.847925	−	0.941716i	0.998903	+	0.0468214i	$0.0149092\pi$
$830$	15.3126	+	6.81759i	0.531506	+	0.236642i
$831$	−19.0719	+	13.8565i	−0.661595	+	0.480677i
$832$	8.34944	−	1.69350i	0.289465	−	0.0587116i
$833$	9.53739	−	29.3531i	0.330451	−	1.01702i
$834$	2.51732	−	23.9507i	0.0871678	−	0.829346i
$835$	11.7126	+	20.2868i	0.405331	+	0.702053i
$836$	0.826498	+	0.543881i	0.0285850	+	0.0188105i
$837$	8.62243			0.298035
$838$	50.6843	−	22.5661i	1.75086	−	0.779533i
$839$	−12.0739	−	13.4095i	−0.416838	−	0.462946i	0.497757	−	0.867317i	$-0.334157\pi$
$839$	−12.0739	−	13.4095i	−0.416838	−	0.462946i	−0.914595	+	0.404371i	$0.867491\pi$
$840$	0.839826	+	2.58472i	0.0289768	+	0.0891813i
$841$	0.433037	+	4.12007i	0.0149323	+	0.142071i
$842$	−14.6993	−	6.54456i	−0.506572	−	0.225541i
$843$	−3.34514	+	3.71516i	−0.115213	+	0.127957i
$844$	4.28647	−	13.1924i	0.147546	−	0.454101i
$845$	−10.4551	−	12.0564i	−0.359666	−	0.414752i
$846$	−0.765020			−0.0263019
$847$	−9.39382	+	8.25435i	−0.322775	+	0.283623i
$848$	−13.8474	−	23.9845i	−0.475523	−	0.823630i
$849$	−12.8567	+	5.72418i	−0.441241	+	0.196453i
$850$	9.84614	−	30.3033i	0.337720	−	1.03939i
$851$	31.2697	+	6.64658i	1.07191	+	0.227842i
$852$	0.353720	+	3.36542i	0.0121183	+	0.115297i
$853$	−8.18380	+	5.94588i	−0.280208	+	0.203583i	−0.719008	−	0.695002i	$-0.755404\pi$
$853$	−8.18380	+	5.94588i	−0.280208	+	0.203583i	0.438800	+	0.898585i	$0.355404\pi$
$854$	25.7638	+	5.47626i	0.881619	+	0.187394i
$855$	0.423645	−	0.0900485i	0.0144883	−	0.00307959i
$856$	3.50339	−	33.3326i	0.119744	−	1.13928i
$857$	−46.6515			−1.59358			−0.796792	−	0.604254i	$-0.793471\pi$
$857$	−46.6515			−1.59358			−0.796792	+	0.604254i	$0.793471\pi$
$858$	−19.8727	−	3.46171i	−0.678443	−	0.118181i
$859$	36.6983			1.25213			0.626065	−	0.779771i	$-0.284664\pi$
$859$	36.6983			1.25213			0.626065	+	0.779771i	$0.284664\pi$
$860$	−0.874626	+	8.32151i	−0.0298245	+	0.283761i
$861$	8.52965	−	1.81303i	0.290690	−	0.0617880i
$862$	32.1147	+	6.82618i	1.09383	+	0.232501i
$863$	19.5366	−	14.1942i	0.665035	−	0.483176i	−0.203325	−	0.979111i	$-0.565175\pi$
$863$	19.5366	−	14.1942i	0.665035	−	0.483176i	0.868359	+	0.495935i	$0.165175\pi$
$864$	0.470286	+	4.47447i	0.0159994	+	0.152225i
$865$	−0.948666	−	0.201645i	−0.0322556	−	0.00685614i
$866$	1.74174	−	5.36053i	0.0591868	−	0.182158i
$867$	11.1822	−	4.97864i	0.379767	−	0.169083i
$868$	−4.14393	−	7.17751i	−0.140654	−	0.243620i
$869$	51.5473	+	8.48472i	1.74862	+	0.287825i
$870$	10.3240			0.350016
$871$	−31.6973	−	7.04707i	−1.07402	−	0.238781i
$872$	−5.66660	+	17.4400i	−0.191895	+	0.590593i
$873$	3.42760	−	3.80674i	0.116007	−	0.128838i
$874$	−1.77941	−	0.792244i	−0.0601894	−	0.0267981i
$875$	−1.23890	−	11.7874i	−0.0418826	−	0.398486i
$876$	1.86732	+	5.74701i	0.0630908	+	0.194174i
$877$	11.2673	+	12.5136i	0.380471	+	0.422555i	0.902714	−	0.430241i	$-0.141571\pi$
$877$	11.2673	+	12.5136i	0.380471	+	0.422555i	−0.522243	+	0.852796i	$0.674905\pi$
$878$	−0.700041	+	0.311678i	−0.0236252	+	0.0105186i
$879$	−1.65588			−0.0558516
$880$	15.8216	−	12.6541i	0.533345	−	0.426570i
$881$	4.02435	+	6.97037i	0.135584	+	0.234838i	0.925820	−	0.377964i	$-0.123376\pi$
$881$	4.02435	+	6.97037i	0.135584	+	0.234838i	−0.790237	+	0.612802i	$0.790042\pi$
$882$	1.00640	−	9.57523i	0.0338872	−	0.322415i
$883$	7.08476	−	21.8047i	0.238421	−	0.733785i	−0.758228	−	0.651990i	$-0.773935\pi$
$883$	7.08476	−	21.8047i	0.238421	−	0.733785i	0.996649	−	0.0817956i	$-0.0260655\pi$
$884$	10.9157	+	12.3529i	0.367135	+	0.415472i
$885$	−5.78795	+	4.20519i	−0.194560	+	0.141356i
$886$	−11.3442	−	5.05077i	−0.381116	−	0.169684i
$887$	−1.22620	+	1.36183i	−0.0411717	+	0.0457258i	−0.763379	−	0.645951i	$-0.776461\pi$
$887$	−1.22620	+	1.36183i	−0.0411717	+	0.0457258i	0.722207	+	0.691677i	$0.243128\pi$
$888$	−12.7289	−	14.1369i	−0.427154	−	0.474403i
$889$	−11.3388	−	8.23816i	−0.380293	−	0.276299i
$890$	1.15564	−	2.00163i	0.0387373	−	0.0670949i
$891$	−0.877798	+	3.19835i	−0.0294073	+	0.107149i
$892$	−2.73328			−0.0915168
$893$	−0.146177	+	0.0650823i	−0.00489163	+	0.00217789i
$894$	−34.6072	+	7.35599i	−1.15744	+	0.246021i
$895$	2.56621	−	2.85006i	0.0857789	−	0.0952671i
$896$	−11.9416	+	8.67610i	−0.398942	+	0.289848i
$897$	11.7995	+	0.110045i	0.393973	+	0.00367431i
$898$	16.0317	+	49.3404i	0.534984	+	1.64651i
$899$	42.0495	−	8.93789i	1.40243	−	0.298095i
$900$	0.308720	−	2.93727i	0.0102907	−	0.0979090i
$901$	−15.0477	+	26.0633i	−0.501311	+	0.868296i
$902$	−23.1547	−	36.1324i	−0.770966	−	1.20308i
$903$	4.58241	−	7.93697i	0.152493	−	0.264126i
$904$	−15.9952	+	7.12151i	−0.531991	+	0.236858i
$905$	5.14435	−	15.8327i	0.171004	−	0.526296i
$906$	−1.40985	−	0.299674i	−0.0468393	−	0.00995599i
$907$	22.2276	+	9.89639i	0.738057	+	0.328604i	0.741103	−	0.671391i	$-0.234303\pi$
$907$	22.2276	+	9.89639i	0.738057	+	0.328604i	−0.00304615	+	0.999995i	$0.500970\pi$
$908$	12.4261	+	5.53247i	0.412376	+	0.183602i
$909$	4.13159	+	12.7157i	0.137036	+	0.421755i
$910$	7.72133	+	3.52440i	0.255960	+	0.116833i
$911$	8.96280	+	6.51186i	0.296951	+	0.215747i	0.726277	−	0.687402i	$-0.241249\pi$
$911$	8.96280	+	6.51186i	0.296951	+	0.215747i	−0.429326	+	0.903149i	$0.641249\pi$
$912$	0.877846	+	1.52047i	0.0290684	+	0.0503479i
$913$	−12.3329	+	23.8464i	−0.408159	+	0.789201i
$914$	−5.23322	+	9.06420i	−0.173100	+	0.299817i
$915$	−13.6405	−	9.91038i	−0.450940	−	0.327627i
$916$	11.0752	+	12.3003i	0.365936	+	0.406413i
$917$	−7.40884	−	1.57480i	−0.244662	−	0.0520044i
$918$	7.37954	−	5.36155i	0.243561	−	0.176958i
$919$	−5.22062	−	49.6708i	−0.172212	−	1.63849i	−0.649943	−	0.759983i	$-0.725207\pi$
$919$	−5.22062	−	49.6708i	−0.172212	−	1.63849i	0.477730	−	0.878507i	$-0.341460\pi$
$920$	−5.23519	+	5.81427i	−0.172599	+	0.191691i
$921$	3.48658	−	0.741096i	0.114887	−	0.0244199i
$922$	−4.27646	−	3.10703i	−0.140838	−	0.102325i
$923$	−11.5948	−	8.59049i	−0.381649	−	0.282760i
$924$	3.08425	−	0.806428i	0.101464	−	0.0265295i
$925$	17.0605	+	29.5496i	0.560945	+	0.971585i
$926$	1.27239	−	12.1060i	0.0418132	−	0.397826i
$927$	−4.05683	−	4.50557i	−0.133244	−	0.147982i
$928$	6.93164	+	21.3334i	0.227542	+	0.700303i
$929$	1.47424	+	14.0265i	0.0483684	+	0.460195i	0.991722	+	0.128405i	$0.0409858\pi$
$929$	1.47424	+	14.0265i	0.0483684	+	0.460195i	−0.943353	+	0.331790i	$0.892348\pi$
$930$	1.86632	+	17.7568i	0.0611990	+	0.582269i
$931$	−0.622291	−	1.91522i	−0.0203948	−	0.0627686i
$932$	3.28431	+	3.64759i	0.107581	+	0.119481i
$933$	1.38423	−	13.1701i	0.0453177	−	0.431169i
$934$	10.2403	+	17.7368i	0.335074	+	0.580365i
$935$	−20.5051	−	8.01404i	−0.670589	−	0.262087i
$936$	−5.64194	−	4.18005i	−0.184413	−	0.136629i
$937$	−5.54137	−	4.02604i	−0.181029	−	0.131525i	0.493581	−	0.869700i	$-0.335688\pi$
$937$	−5.54137	−	4.02604i	−0.181029	−	0.131525i	−0.674609	+	0.738175i	$0.735688\pi$
$938$	16.8930	−	3.59072i	0.551576	−	0.117241i
$939$	17.3133	−	19.2283i	0.564997	−	0.627493i
$940$	−0.0492024	−	0.468130i	−0.00160481	−	0.0152687i
$941$	−16.8570	+	12.2473i	−0.549523	+	0.399252i	−0.827610	−	0.561304i	$-0.810300\pi$
$941$	−16.8570	+	12.2473i	−0.549523	+	0.399252i	0.278087	+	0.960556i	$0.410300\pi$
$942$	26.7194	+	5.67939i	0.870566	+	0.185045i
$943$	16.7978	+	18.6558i	0.547012	+	0.607518i
$944$	−23.4626	−	17.0466i	−0.763642	−	0.554818i
$945$	0.697760	−	1.20856i	0.0226981	−	0.0393143i
$946$	−44.5041	−	7.32541i	−1.44695	−	0.238170i
$947$	4.49117	+	7.77893i	0.145943	+	0.252781i	0.929724	−	0.368256i	$-0.120045\pi$
$947$	4.49117	+	7.77893i	0.145943	+	0.252781i	−0.783781	+	0.621037i	$0.786712\pi$
$948$	−10.7743	−	7.82800i	−0.349934	−	0.254242i
$949$	−23.4420	−	10.7001i	−0.760958	−	0.347340i
$950$	−0.642437	−	1.97722i	−0.0208434	−	0.0641494i
$951$	−16.6837	−	7.42805i	−0.541005	−	0.240871i
$952$	10.9367	+	4.86935i	0.354462	+	0.157817i
$953$	39.2860	+	8.35050i	1.27260	+	0.270499i	0.794207	−	0.607648i	$-0.207887\pi$
$953$	39.2860	+	8.35050i	1.27260	+	0.270499i	0.478392	+	0.878147i	$0.341220\pi$
$954$	−2.90115	+	8.92881i	−0.0939281	+	0.289081i
$955$	−11.4279	+	5.08802i	−0.369797	+	0.164644i
$956$	2.81867	−	4.88207i	0.0911622	−	0.157898i
$957$	−0.965436	+	16.5075i	−0.0312081	+	0.533612i
$958$	10.3902	−	17.9963i	0.335691	−	0.581434i
$959$	−2.07329	+	19.7260i	−0.0669500	+	0.636987i
$960$	2.83717	−	0.603059i	0.0915693	−	0.0194637i
$961$	13.3948	+	41.2249i	0.432089	+	1.32983i
$962$	−59.4076	−	0.554053i	−1.91538	−	0.0178634i
$963$	−13.9233	+	10.1159i	−0.448671	+	0.325979i
$964$	−4.65578	+	5.17077i	−0.149953	+	0.166539i
$965$	13.1113	−	2.78688i	0.422066	−	0.0897129i
$966$	−5.73344	+	2.55269i	−0.184470	+	0.0821315i
$967$	−11.9745			−0.385073			−0.192537	−	0.981290i	$-0.561671\pi$
$967$	−11.9745			−0.385073			−0.192537	+	0.981290i	$0.561671\pi$
$968$	12.3807	+	17.4822i	0.397932	+	0.561899i
$969$	0.953934	−	1.65226i	0.0306448	−	0.0530783i
$970$	8.58140	+	6.23475i	0.275532	+	0.200186i
$971$	22.7669	+	25.2852i	0.730625	+	0.811441i	0.987932	−	0.154889i	$-0.0495018\pi$
$971$	22.7669	+	25.2852i	0.730625	+	0.811441i	−0.257307	+	0.966330i	$0.582835\pi$
$972$	0.565755	−	0.628335i	0.0181466	−	0.0201539i
$973$	−14.8269	−	6.60136i	−0.475328	−	0.211630i
$974$	−21.9264	+	15.9304i	−0.702566	+	0.510444i
$975$	8.33976	+	9.43778i	0.267086	+	0.302251i
$976$	21.1205	−	65.0023i	0.676052	−	2.08067i
$977$	−6.04804	+	57.5433i	−0.193494	+	1.84097i	0.279788	+	0.960062i	$0.409736\pi$
$977$	−6.04804	+	57.5433i	−0.193494	+	1.84097i	−0.473282	+	0.880911i	$0.656931\pi$
$978$	−4.06370	−	7.03854i	−0.129943	−	0.225068i
$979$	3.09243	+	2.03499i	0.0988346	+	0.0650386i
$980$	5.92399			0.189235
$981$	8.60201	−	3.82986i	0.274641	−	0.122278i
$982$	17.7365	+	19.6984i	0.565996	+	0.628602i
$983$	15.1757	+	46.7059i	0.484029	+	1.48969i	0.833382	+	0.552697i	$0.186401\pi$
$983$	15.1757	+	46.7059i	0.484029	+	1.48969i	−0.349354	+	0.936991i	$0.613599\pi$
$984$	−1.56148	−	14.8565i	−0.0497782	−	0.473608i
$985$	0.448520	+	0.199694i	0.0142910	+	0.00636279i
$986$	30.4305	−	33.7965i	0.969105	−	1.07630i
$987$	−0.159320	+	0.490337i	−0.00507121	+	0.0156076i
$988$	1.04995	+	0.233429i	0.0334034	+	0.00742637i
$989$	26.3839			0.838958
$990$	−6.77661	−	1.11544i	−0.215375	−	0.0354509i
$991$	−24.7515	−	42.8708i	−0.786256	−	1.36184i	−0.928246	−	0.371967i	$-0.878683\pi$
$991$	−24.7515	−	42.8708i	−0.786256	−	1.36184i	0.141990	−	0.989868i	$-0.454650\pi$
$992$	−35.4395	+	15.7787i	−1.12520	+	0.500973i
$993$	1.43994	−	4.43168i	0.0456951	−	0.140635i
$994$	7.50735	+	1.59574i	0.238119	+	0.0506137i
$995$	−1.25424	−	11.9333i	−0.0397620	−	0.378310i
$996$	5.53696	−	4.02284i	0.175445	−	0.127469i
$997$	−23.6673	−	5.03064i	−0.749551	−	0.159322i	−0.182730	−	0.983163i	$-0.558494\pi$
$997$	−23.6673	−	5.03064i	−0.749551	−	0.159322i	−0.566821	+	0.823841i	$0.691827\pi$
$998$	21.7818	−	4.62987i	0.689492	−	0.146556i
$999$	−1.02104	+	9.71457i	−0.0323044	+	0.307355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bg.b.367.4	yes	112
11.3	even	5	inner	429.2.bg.b.289.11	yes	112
13.9	even	3	inner	429.2.bg.b.334.11	yes	112
143.113	even	15	inner	429.2.bg.b.256.4	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bg.b.256.4	✓	112	143.113	even	15	inner
429.2.bg.b.289.11	yes	112	11.3	even	5	inner
429.2.bg.b.334.11	yes	112	13.9	even	3	inner
429.2.bg.b.367.4	yes	112	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.176325 + 1.67762i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(-0.827032 - 0.175791i) q^{4} +(0.993113 - 0.721539i) q^{5} +(-0.176325 - 1.67762i) q^{6} +(-1.11199 - 0.236360i) q^{7} +(-0.601801 + 1.85215i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.176325 + 1.67762i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(-0.827032 - 0.175791i) q^{4} +(0.993113 - 0.721539i) q^{5} +(-0.176325 - 1.67762i) q^{6} +(-1.11199 - 0.236360i) q^{7} +(-0.601801 + 1.85215i) q^{8} +(0.913545 - 0.406737i) q^{9} +(1.03536 + 1.79330i) q^{10} +(-2.96420 + 1.48779i) q^{11} +0.845508 q^{12} +(-2.43747 + 2.65683i) q^{13} +(0.592594 - 1.82382i) q^{14} +(-0.821395 + 0.912252i) q^{15} +(-4.54592 - 2.02398i) q^{16} +(0.565232 + 5.37782i) q^{17} +(0.521269 + 1.60430i) q^{18} +(0.236084 + 0.262198i) q^{19} +(-0.948177 + 0.422155i) q^{20} +1.13683 q^{21} +(-1.97328 - 5.23515i) q^{22} +(1.63636 + 2.83426i) q^{23} +(0.203566 - 1.93680i) q^{24} +(-1.07943 + 3.32214i) q^{25} +(-4.02737 - 4.55762i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.878098 + 0.390955i) q^{28} +(-3.33609 + 3.70510i) q^{29} +(-1.38558 - 1.53884i) q^{30} +(-6.97570 - 5.06814i) q^{31} +(2.24956 - 3.89635i) q^{32} +(2.59010 - 2.07157i) q^{33} -9.12162 q^{34} +(-1.27487 + 0.567609i) q^{35} +(-0.827032 + 0.175791i) q^{36} +(6.53612 - 7.25910i) q^{37} +(-0.481497 + 0.349828i) q^{38} +(1.83182 - 3.10555i) q^{39} +(0.738745 + 2.27362i) q^{40} +(7.50302 - 1.59482i) q^{41} +(-0.200452 + 1.90717i) q^{42} +(4.03087 - 6.98167i) q^{43} +(2.71303 - 0.709366i) q^{44} +(0.613778 - 1.06309i) q^{45} +(-5.04336 + 2.24545i) q^{46} +(-0.140144 + 0.431320i) q^{47} +(4.86739 + 1.03460i) q^{48} +(-5.21417 - 2.32150i) q^{49} +(-5.38297 - 2.39665i) q^{50} +(-1.67099 - 5.14278i) q^{51} +(2.48291 - 1.76880i) q^{52} +(4.50262 + 3.27134i) q^{53} +(-0.843432 - 1.46087i) q^{54} +(-1.87029 + 3.61633i) q^{55} +(1.10697 - 1.91733i) q^{56} +(-0.285439 - 0.207384i) q^{57} +(-5.62752 - 6.25000i) q^{58} +(5.70073 + 1.21173i) q^{59} +(0.839686 - 0.610067i) q^{60} +(1.43570 + 13.6598i) q^{61} +(9.73242 - 10.8089i) q^{62} +(-1.11199 + 0.236360i) q^{63} +(-1.91160 - 1.38886i) q^{64} +(-0.503675 + 4.39726i) q^{65} +(3.01861 + 4.71048i) q^{66} +(4.50295 + 7.79934i) q^{67} +(0.477908 - 4.54699i) q^{68} +(-2.18988 - 2.43211i) q^{69} +(-0.727442 - 2.23884i) q^{70} +(0.418352 + 3.98035i) q^{71} +(0.203566 + 1.93680i) q^{72} +(2.20851 + 6.79711i) q^{73} +(11.0255 + 12.2451i) q^{74} +(0.365129 - 3.47397i) q^{75} +(-0.149157 - 0.258348i) q^{76} +(3.64781 - 0.953779i) q^{77} +(4.88695 + 3.62069i) q^{78} +(-12.7430 - 9.25834i) q^{79} +(-5.97499 + 1.27002i) q^{80} +(0.669131 - 0.743145i) q^{81} +(1.35253 + 12.8684i) q^{82} +(6.54868 - 4.75790i) q^{83} +(-0.940194 - 0.199844i) q^{84} +(4.44165 + 4.93295i) q^{85} +(11.0019 + 7.99332i) q^{86} +(2.49285 - 4.31775i) q^{87} +(-0.971747 - 6.38551i) q^{88} +(-0.558088 - 0.966637i) q^{89} +(1.67525 + 1.21714i) q^{90} +(3.33840 - 2.37824i) q^{91} +(-0.855086 - 2.63168i) q^{92} +(7.87699 + 3.50706i) q^{93} +(-0.698881 - 0.311162i) q^{94} +(0.423645 + 0.0900485i) q^{95} +(-1.39030 + 4.27891i) q^{96} +(4.67961 - 2.08350i) q^{97} +(4.81399 - 8.33807i) q^{98} +(-2.10280 + 2.56481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 14 q^{3} + 8 q^{4} - 6 q^{5} - 24 q^{8} + 14 q^{9}+O(q^{10}) \) 112 * q + 14 * q^3 + 8 * q^4 - 6 * q^5 - 24 * q^8 + 14 * q^9	\( 112 q + 14 q^{3} + 8 q^{4} - 6 q^{5} - 24 q^{8} + 14 q^{9} - 24 q^{10} + q^{11} + 104 q^{12} - 15 q^{13} - 30 q^{14} - 2 q^{15} + 24 q^{16} + 4 q^{17} - 28 q^{20} + 7 q^{22} + 8 q^{23} - 18 q^{24} - 42 q^{25} + 7 q^{26} - 28 q^{27} - 6 q^{28} - 2 q^{29} + 6 q^{30} + 12 q^{31} - 6 q^{32} + 6 q^{33} + 64 q^{34} - 8 q^{35} + 8 q^{36} + 4 q^{37} - 6 q^{38} + 12 q^{39} - 36 q^{40} - 26 q^{41} - 20 q^{42} - 76 q^{43} + 12 q^{44} - 2 q^{45} + 18 q^{46} + 50 q^{47} - 6 q^{48} + 32 q^{49} + 17 q^{50} - 18 q^{51} - 39 q^{52} - 54 q^{53} - 36 q^{55} + 12 q^{56} + 48 q^{58} + 20 q^{59} + 56 q^{60} + 34 q^{61} + 33 q^{62} - 68 q^{64} - 44 q^{65} - 4 q^{66} - 36 q^{67} + 4 q^{68} + 3 q^{69} - 92 q^{70} + 22 q^{71} - 18 q^{72} - 34 q^{73} - 4 q^{74} - 4 q^{75} + 4 q^{76} + 32 q^{77} - 18 q^{78} - 20 q^{79} + 30 q^{80} + 14 q^{81} - 41 q^{82} + 56 q^{83} + 9 q^{84} + 6 q^{85} - 86 q^{86} - 52 q^{87} - 70 q^{88} - 96 q^{89} - 12 q^{90} - 7 q^{91} - 126 q^{92} - 6 q^{93} - 10 q^{94} + 52 q^{95} - 88 q^{96} - 5 q^{97} + 104 q^{98} - 2 q^{99}+O(q^{100}) \) 112 * q + 14 * q^3 + 8 * q^4 - 6 * q^5 - 24 * q^8 + 14 * q^9 - 24 * q^10 + q^11 + 104 * q^12 - 15 * q^13 - 30 * q^14 - 2 * q^15 + 24 * q^16 + 4 * q^17 - 28 * q^20 + 7 * q^22 + 8 * q^23 - 18 * q^24 - 42 * q^25 + 7 * q^26 - 28 * q^27 - 6 * q^28 - 2 * q^29 + 6 * q^30 + 12 * q^31 - 6 * q^32 + 6 * q^33 + 64 * q^34 - 8 * q^35 + 8 * q^36 + 4 * q^37 - 6 * q^38 + 12 * q^39 - 36 * q^40 - 26 * q^41 - 20 * q^42 - 76 * q^43 + 12 * q^44 - 2 * q^45 + 18 * q^46 + 50 * q^47 - 6 * q^48 + 32 * q^49 + 17 * q^50 - 18 * q^51 - 39 * q^52 - 54 * q^53 - 36 * q^55 + 12 * q^56 + 48 * q^58 + 20 * q^59 + 56 * q^60 + 34 * q^61 + 33 * q^62 - 68 * q^64 - 44 * q^65 - 4 * q^66 - 36 * q^67 + 4 * q^68 + 3 * q^69 - 92 * q^70 + 22 * q^71 - 18 * q^72 - 34 * q^73 - 4 * q^74 - 4 * q^75 + 4 * q^76 + 32 * q^77 - 18 * q^78 - 20 * q^79 + 30 * q^80 + 14 * q^81 - 41 * q^82 + 56 * q^83 + 9 * q^84 + 6 * q^85 - 86 * q^86 - 52 * q^87 - 70 * q^88 - 96 * q^89 - 12 * q^90 - 7 * q^91 - 126 * q^92 - 6 * q^93 - 10 * q^94 + 52 * q^95 - 88 * q^96 - 5 * q^97 + 104 * q^98 - 2 * q^99

Introduction

L-functions

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