LMFDB - Embedded newform 418.2.v.a.13.9

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			13.9
Character	$\chi$	$=$	418.13
Dual form			418.2.v.a.193.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.374607 + 0.927184i) q^{2} +(0.765882 + 2.67095i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-2.13408 + 1.13471i) q^{5} +(-2.18956 + 1.71067i) q^{6} +(-1.72666 - 3.87814i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-4.00325 + 2.50151i) q^{9} +O(q^{10})$	\(q+(0.374607 + 0.927184i) q^{2} +(0.765882 + 2.67095i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-2.13408 + 1.13471i) q^{5} +(-2.18956 + 1.71067i) q^{6} +(-1.72666 - 3.87814i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-4.00325 + 2.50151i) q^{9} +(-1.85152 - 1.55361i) q^{10} +(0.0333387 + 3.31646i) q^{11} +(-2.40633 - 1.38929i) q^{12} +(-0.0952431 - 2.72741i) q^{13} +(2.94893 - 3.05371i) q^{14} +(-4.66520 - 4.83096i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(-2.38215 + 3.81224i) q^{17} +(-3.81900 - 2.77467i) q^{18} +(2.52439 + 3.55351i) q^{19} +(0.746891 - 2.29869i) q^{20} +(9.03591 - 7.58203i) q^{21} +(-3.06248 + 1.27328i) q^{22} +(-1.23623 + 7.01100i) q^{23} +(0.386705 - 2.75155i) q^{24} +(0.470752 - 0.697919i) q^{25} +(2.49313 - 1.11001i) q^{26} +(-3.55274 - 3.19890i) q^{27} +(3.93604 + 1.59026i) q^{28} +(-0.0935878 - 0.375360i) q^{29} +(2.73157 - 6.13520i) q^{30} +(1.95954 - 1.76438i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-8.83256 + 2.62906i) q^{33} +(-4.42702 - 0.780604i) q^{34} +(8.08539 + 6.31700i) q^{35} +(1.14200 - 4.58033i) q^{36} +(1.52375 - 2.09726i) q^{37} +(-2.34911 + 3.67174i) q^{38} +(7.21182 - 2.34326i) q^{39} +(2.41110 - 0.168601i) q^{40} +(6.79052 - 1.94715i) q^{41} +(10.4148 + 5.53767i) q^{42} +(4.15049 - 0.731844i) q^{43} +(-2.32779 - 2.36250i) q^{44} +(5.70476 - 9.88093i) q^{45} +(-6.96359 + 1.48016i) q^{46} +(-7.33929 - 0.513213i) q^{47} +(2.69605 - 0.672201i) q^{48} +(-7.37473 + 8.19047i) q^{49} +(0.823446 + 0.175029i) q^{50} +(-12.0068 - 3.44288i) q^{51} +(1.96313 + 1.89577i) q^{52} +(-2.80744 + 5.28003i) q^{53} +(1.63509 - 4.49237i) q^{54} +(-3.83436 - 7.03974i) q^{55} +4.24516i q^{56} +(-7.55786 + 9.46409i) q^{57} +(0.312969 - 0.227385i) q^{58} +(0.487139 + 6.96641i) q^{59} +(6.71173 + 0.234379i) q^{60} +(1.03442 + 7.36028i) q^{61} +(2.36996 + 1.15590i) q^{62} +(16.6135 + 11.2059i) q^{63} +(0.669131 + 0.743145i) q^{64} +(3.29806 + 5.71242i) q^{65} +(-5.74636 - 7.20454i) q^{66} +(2.88184 - 3.43445i) q^{67} +(-0.934629 - 4.39708i) q^{68} +(-19.6728 + 2.06770i) q^{69} +(-2.82818 + 9.86303i) q^{70} +(-5.86433 - 11.0292i) q^{71} +(4.67461 - 0.656973i) q^{72} +(-8.71665 + 5.87946i) q^{73} +(2.51535 + 0.627147i) q^{74} +(2.22465 + 0.722832i) q^{75} +(-4.28437 - 0.802594i) q^{76} +(12.8041 - 5.85569i) q^{77} +(4.87423 + 5.80888i) q^{78} +(3.12206 - 3.99606i) q^{79} +(1.05954 + 2.17238i) q^{80} +(-0.384928 + 0.789219i) q^{81} +(4.34914 + 5.56665i) q^{82} +(3.17864 - 14.9543i) q^{83} +(-1.23297 + 11.7309i) q^{84} +(0.757914 - 10.8387i) q^{85} +(2.23336 + 3.57412i) q^{86} +(0.930890 - 0.537450i) q^{87} +(1.31847 - 3.04329i) q^{88} +(3.24292 + 8.90984i) q^{89} +(11.2985 + 1.58790i) q^{90} +(-10.4128 + 5.07867i) q^{91} +(-3.98098 - 5.90205i) q^{92} +(6.21333 + 3.88252i) q^{93} +(-2.27350 - 6.99712i) q^{94} +(-9.41944 - 4.71902i) q^{95} +(1.63321 + 2.24792i) q^{96} +(7.86908 - 3.17931i) q^{97} +(-10.3567 - 3.76953i) q^{98} +(-8.42961 - 13.1932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * 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
$3$	0.765882	+	2.67095i	0.442182	+	1.54207i	0.795135	+	0.606432i	$0.207400\pi$
$3$	0.765882	+	2.67095i	0.442182	+	1.54207i	−0.352953	+	0.935641i	$0.614822\pi$
$4$	−0.719340	+	0.694658i	−0.359670	+	0.347329i
$5$	−2.13408	+	1.13471i	−0.954388	+	0.507457i	−0.872194	−	0.489159i	$-0.837304\pi$
$5$	−2.13408	+	1.13471i	−0.954388	+	0.507457i	−0.0821933	+	0.996616i	$0.526192\pi$
$6$	−2.18956	+	1.71067i	−0.893883	+	0.698378i
$7$	−1.72666	−	3.87814i	−0.652616	−	1.46580i	−0.871673	−	0.490088i	$-0.836964\pi$
$7$	−1.72666	−	3.87814i	−0.652616	−	1.46580i	0.219056	−	0.975712i	$-0.429702\pi$
$8$	−0.913545	−	0.406737i	−0.322987	−	0.143803i
$9$	−4.00325	+	2.50151i	−1.33442	+	0.833836i
$10$	−1.85152	−	1.55361i	−0.585503	−	0.491295i
$11$	0.0333387	+	3.31646i	0.0100520	+	0.999949i
$11$	0.0333387	+	3.31646i	0.0100520	+	0.999949i
$12$	−2.40633	−	1.38929i	−0.694647	−	0.401054i
$13$	−0.0952431	−	2.72741i	−0.0264157	−	0.756446i	−0.938264	−	0.345919i	$-0.887567\pi$
$13$	−0.0952431	−	2.72741i	−0.0264157	−	0.756446i	0.911849	−	0.410527i	$-0.134655\pi$
$14$	2.94893	−	3.05371i	0.788136	−	0.816138i
$15$	−4.66520	−	4.83096i	−1.20455	−	1.24735i
$16$	0.0348995	−	0.999391i	0.00872487	−	0.249848i
$17$	−2.38215	+	3.81224i	−0.577757	+	0.924605i	0.422080	+	0.906559i	$0.361300\pi$
$17$	−2.38215	+	3.81224i	−0.577757	+	0.924605i	−0.999837	+	0.0180464i	$0.994255\pi$
$18$	−3.81900	−	2.77467i	−0.900147	−	0.653995i
$19$	2.52439	+	3.55351i	0.579135	+	0.815232i
$19$	2.52439	+	3.55351i	0.579135	+	0.815232i
$20$	0.746891	−	2.29869i	0.167010	−	0.514004i
$21$	9.03591	−	7.58203i	1.97180	−	1.65453i
$22$	−3.06248	+	1.27328i	−0.652922	+	0.271464i
$23$	−1.23623	+	7.01100i	−0.257772	+	1.46190i	0.531085	+	0.847318i	$0.321784\pi$
$23$	−1.23623	+	7.01100i	−0.257772	+	1.46190i	−0.788857	+	0.614577i	$0.789327\pi$
$24$	0.386705	−	2.75155i	0.0789357	−	0.561657i
$25$	0.470752	−	0.697919i	0.0941504	−	0.139584i
$26$	2.49313	−	1.11001i	0.488942	−	0.217691i
$27$	−3.55274	−	3.19890i	−0.683725	−	0.615629i
$28$	3.93604	+	1.59026i	0.743842	+	0.300532i
$29$	−0.0935878	−	0.375360i	−0.0173788	−	0.0697026i	0.960980	−	0.276617i	$-0.0892134\pi$
$29$	−0.0935878	−	0.375360i	−0.0173788	−	0.0697026i	−0.978359	+	0.206914i	$0.933658\pi$
$30$	2.73157	−	6.13520i	0.498714	−	1.12013i
$31$	1.95954	−	1.76438i	0.351943	−	0.316891i	−0.474129	−	0.880455i	$-0.657237\pi$
$31$	1.95954	−	1.76438i	0.351943	−	0.316891i	0.826072	+	0.563564i	$0.190570\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−8.83256	+	2.62906i	−1.53755	+	0.457661i
$34$	−4.42702	−	0.780604i	−0.759228	−	0.133872i
$35$	8.08539	+	6.31700i	1.36668	+	1.06777i
$36$	1.14200	−	4.58033i	0.190334	−	0.763388i
$37$	1.52375	−	2.09726i	0.250503	−	0.344787i	−0.665185	−	0.746679i	$-0.731647\pi$
$37$	1.52375	−	2.09726i	0.250503	−	0.344787i	0.915687	+	0.401892i	$0.131647\pi$
$38$	−2.34911	+	3.67174i	−0.381075	+	0.595635i
$39$	7.21182	−	2.34326i	1.15481	−	0.375222i
$40$	2.41110	−	0.168601i	0.381229	−	0.0266581i
$41$	6.79052	−	1.94715i	1.06050	−	0.304094i	0.300343	−	0.953831i	$-0.402899\pi$
$41$	6.79052	−	1.94715i	1.06050	−	0.304094i	0.760159	+	0.649737i	$0.225121\pi$
$42$	10.4148	+	5.53767i	1.60705	+	0.854481i
$43$	4.15049	−	0.731844i	0.632944	−	0.111605i	0.152034	−	0.988375i	$-0.451418\pi$
$43$	4.15049	−	0.731844i	0.632944	−	0.111605i	0.480910	+	0.876770i	$0.340306\pi$
$44$	−2.32779	−	2.36250i	−0.350927	−	0.356160i
$45$	5.70476	−	9.88093i	0.850415	−	1.47296i
$46$	−6.96359	+	1.48016i	−1.02673	+	0.218237i
$47$	−7.33929	−	0.513213i	−1.07054	−	0.0748598i	−0.476408	−	0.879224i	$-0.658062\pi$
$47$	−7.33929	−	0.513213i	−1.07054	−	0.0748598i	−0.594136	+	0.804364i	$0.702506\pi$
$48$	2.69605	−	0.672201i	0.389141	−	0.0970239i
$49$	−7.37473	+	8.19047i	−1.05353	+	1.17007i
$50$	0.823446	+	0.175029i	0.116453	+	0.0247528i
$51$	−12.0068	−	3.44288i	−1.68128	−	0.482100i
$52$	1.96313	+	1.89577i	0.272237	+	0.262896i
$53$	−2.80744	+	5.28003i	−0.385631	+	0.725267i	−0.997858	−	0.0654150i	$-0.979163\pi$
$53$	−2.80744	+	5.28003i	−0.385631	+	0.725267i	0.612227	+	0.790682i	$0.290274\pi$
$54$	1.63509	−	4.49237i	0.222508	−	0.611335i
$55$	−3.83436	−	7.03974i	−0.517025	−	0.949239i
$56$			4.24516i			0.567283i
$57$	−7.55786	+	9.46409i	−1.00106	+	1.25355i
$58$	0.312969	−	0.227385i	0.0410949	−	0.0298572i
$59$	0.487139	+	6.96641i	0.0634201	+	0.906949i	0.920245	+	0.391342i	$0.127989\pi$
$59$	0.487139	+	6.96641i	0.0634201	+	0.906949i	−0.856825	+	0.515607i	$0.827566\pi$
$60$	6.71173	+	0.234379i	0.866480	+	0.0302582i
$61$	1.03442	+	7.36028i	0.132444	+	0.942387i	0.937203	+	0.348785i	$0.113406\pi$
$61$	1.03442	+	7.36028i	0.132444	+	0.942387i	−0.804759	+	0.593602i	$0.797705\pi$
$62$	2.36996	+	1.15590i	0.300985	+	0.146800i
$63$	16.6135	+	11.2059i	2.09310	+	1.41181i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	3.29806	+	5.71242i	0.409075	+	0.708538i
$66$	−5.74636	−	7.20454i	−0.707328	−	0.886817i
$67$	2.88184	−	3.43445i	0.352073	−	0.419584i	−0.560721	−	0.828005i	$-0.689476\pi$
$67$	2.88184	−	3.43445i	0.352073	−	0.419584i	0.912794	+	0.408421i	$0.133920\pi$
$68$	−0.934629	−	4.39708i	−0.113340	−	0.533225i
$69$	−19.6728	+	2.06770i	−2.36833	+	0.248922i
$70$	−2.82818	+	9.86303i	−0.338032	+	1.17886i
$71$	−5.86433	−	11.0292i	−0.695968	−	1.30892i	−0.940669	−	0.339326i	$-0.889801\pi$
$71$	−5.86433	−	11.0292i	−0.695968	−	1.30892i	0.244701	−	0.969599i	$-0.421310\pi$
$72$	4.67461	−	0.656973i	0.550908	−	0.0774250i
$73$	−8.71665	+	5.87946i	−1.02021	+	0.688138i	−0.950913	−	0.309458i	$-0.899852\pi$
$73$	−8.71665	+	5.87946i	−1.02021	+	0.688138i	−0.0692938	+	0.997596i	$0.522075\pi$
$74$	2.51535	+	0.627147i	0.292404	+	0.0729044i
$75$	2.22465	+	0.722832i	0.256880	+	0.0834654i
$76$	−4.28437	−	0.802594i	−0.491451	−	0.0920638i
$77$	12.8041	−	5.85569i	1.45917	−	0.667318i
$78$	4.87423	+	5.80888i	0.551898	+	0.657726i
$79$	3.12206	−	3.99606i	0.351259	−	0.449591i	−0.579637	−	0.814875i	$-0.696806\pi$
$79$	3.12206	−	3.99606i	0.351259	−	0.449591i	0.930896	+	0.365283i	$0.119028\pi$
$80$	1.05954	+	2.17238i	0.118460	+	0.242879i
$81$	−0.384928	+	0.789219i	−0.0427697	+	0.0876910i
$82$	4.34914	+	5.56665i	0.480282	+	0.614733i
$83$	3.17864	−	14.9543i	0.348901	−	1.64145i	−0.357699	−	0.933837i	$-0.616438\pi$
$83$	3.17864	−	14.9543i	0.348901	−	1.64145i	0.706600	−	0.707614i	$-0.250228\pi$
$84$	−1.23297	+	11.7309i	−0.134528	+	1.27995i
$85$	0.757914	−	10.8387i	0.0822073	−	1.17562i
$86$	2.23336	+	3.57412i	0.240829	+	0.385407i
$87$	0.930890	−	0.537450i	0.0998019	−	0.0576207i
$88$	1.31847	−	3.04329i	0.140549	−	0.324416i
$89$	3.24292	+	8.90984i	0.343748	+	0.944441i	0.984297	+	0.176523i	$0.0564850\pi$
$89$	3.24292	+	8.90984i	0.343748	+	0.944441i	−0.640548	+	0.767918i	$0.721293\pi$
$90$	11.2985	+	1.58790i	1.19096	+	0.167379i
$91$	−10.4128	+	5.07867i	−1.09156	+	0.532389i
$92$	−3.98098	−	5.90205i	−0.415046	−	0.615331i
$93$	6.21333	+	3.88252i	0.644293	+	0.402599i
$94$	−2.27350	−	6.99712i	−0.234494	−	0.721698i
$95$	−9.41944	−	4.71902i	−0.966414	−	0.484161i
$96$	1.63321	+	2.24792i	0.166689	+	0.229428i
$97$	7.86908	−	3.17931i	0.798984	−	0.322810i	0.0614410	−	0.998111i	$-0.480430\pi$
$97$	7.86908	−	3.17931i	0.798984	−	0.322810i	0.737543	+	0.675300i	$0.235986\pi$
$98$	−10.3567	−	3.76953i	−1.04618	−	0.380780i
$99$	−8.42961	−	13.1932i	−0.847207	−	1.32597i
$100$	0.146184	+	0.829053i	0.0146184	+	0.0829053i
$101$	13.0547	−	0.455881i	1.29899	−	0.0453618i	0.622972	−	0.782244i	$-0.285925\pi$
$101$	13.0547	−	0.455881i	1.29899	−	0.0453618i	0.676021	+	0.736883i	$0.263703\pi$
$102$	−1.30563	−	12.4222i	−0.129276	−	1.22998i
$103$	6.16172	+	0.647623i	0.607132	+	0.0638121i	0.403106	−	0.915153i	$-0.367931\pi$
$103$	6.16172	+	0.647623i	0.607132	+	0.0638121i	0.204026	+	0.978965i	$0.434597\pi$
$104$	−1.02233	+	2.53035i	−0.100247	+	0.248121i
$105$	−10.6799	+	26.4337i	−1.04225	+	2.57967i
$106$	−5.94724	−	0.625080i	−0.577647	−	0.0607131i
$107$	−1.01407	−	9.64826i	−0.0980341	−	0.932733i	−0.927411	−	0.374043i	$-0.877971\pi$
$107$	−1.01407	−	9.64826i	−0.0980341	−	0.932733i	0.829377	−	0.558689i	$-0.188696\pi$
$108$	4.77777	−	0.166844i	0.459741	−	0.0160545i
$109$	2.65526	+	15.0587i	0.254328	+	1.44237i	0.797792	+	0.602933i	$0.206001\pi$
$109$	2.65526	+	15.0587i	0.254328	+	1.44237i	−0.543464	+	0.839433i	$0.682887\pi$
$110$	5.09076	−	6.19229i	0.485385	−	0.590412i
$111$	6.76868	+	2.46360i	0.642455	+	0.233835i
$112$	−3.93604	+	1.59026i	−0.371921	+	0.150266i
$113$	8.86519	+	12.2019i	0.833967	+	1.14786i	0.987172	+	0.159663i	$0.0510406\pi$
$113$	8.86519	+	12.2019i	0.833967	+	1.14786i	−0.153205	+	0.988194i	$0.548959\pi$
$114$	−11.6062	−	3.46222i	−1.08702	−	0.324266i
$115$	−5.31724	−	16.3648i	−0.495835	−	1.52602i
$116$	0.328068	+	0.205000i	0.0304604	+	0.0190338i
$117$	7.20391	+	10.6802i	0.666001	+	0.987388i
$118$	−6.27666	+	3.06133i	−0.577813	+	0.281818i
$119$	18.8976	+	2.65589i	1.73234	+	0.243465i
$120$	2.29694	+	6.31080i	0.209681	+	0.576095i
$121$	−10.9978	+	0.221133i	−0.999798	+	0.0201030i
$122$	−6.43683	+	3.71631i	−0.582763	+	0.336458i
$123$	10.4015	+	16.6459i	0.937870	+	1.50091i
$124$	−0.183935	+	2.63039i	−0.0165179	+	0.236216i
$125$	1.05053	−	9.99517i	0.0939627	−	0.893995i
$126$	−4.16644	+	19.6015i	−0.371176	+	1.74624i
$127$	12.3201	+	15.7690i	1.09323	+	1.39928i	0.909202	+	0.416355i	$0.136693\pi$
$127$	12.3201	+	15.7690i	1.09323	+	1.39928i	0.184032	+	0.982920i	$0.441085\pi$
$128$	−0.438371	+	0.898794i	−0.0387469	+	0.0794429i
$129$	5.13351	+	10.5253i	0.451980	+	0.926697i
$130$	−4.06098	+	5.19782i	−0.356172	+	0.455879i
$131$	−0.0352466	−	0.0420053i	−0.00307951	−	0.00367002i	0.764502	−	0.644621i	$-0.222985\pi$
$131$	−0.0352466	−	0.0420053i	−0.00307951	−	0.00367002i	−0.767582	+	0.640951i	$0.778540\pi$
$132$	4.52731	−	8.02680i	0.394052	−	0.698643i
$133$	9.42227	−	15.9257i	0.817014	−	1.38093i
$134$	4.26392	+	1.38543i	0.368347	+	0.119683i
$135$	11.2116	+	2.79538i	0.964944	+	0.240588i
$136$	3.72679	−	2.51375i	0.319569	−	0.215552i
$137$	4.72393	−	0.663905i	0.403593	−	0.0567213i	0.0655436	−	0.997850i	$-0.479122\pi$
$137$	4.72393	−	0.663905i	0.403593	−	0.0567213i	0.338049	+	0.941128i	$0.390233\pi$
$138$	−9.28671	−	17.4658i	−0.790537	−	1.48678i
$139$	−0.842099	+	2.93675i	−0.0714259	+	0.249092i	−0.988872	−	0.148768i	$-0.952469\pi$
$139$	−0.842099	+	2.93675i	−0.0714259	+	0.249092i	0.917446	+	0.397860i	$0.130247\pi$
$140$	−10.2043	+	1.07251i	−0.862420	+	0.0906440i
$141$	−4.25026	−	19.9959i	−0.357937	−	1.68396i
$142$	8.02928	−	9.56892i	0.673802	−	0.803006i
$143$	9.04215	−	0.406798i	0.756142	−	0.0340181i
$144$	2.36027	+	4.08811i	0.196689	+	0.340676i
$145$	0.625648	+	0.694852i	0.0519572	+	0.0577043i
$146$	−8.71665	−	5.87946i	−0.721395	−	0.486587i
$147$	−27.5245	−	13.4246i	−2.27018	−	1.10724i
$148$	0.360786	+	2.56713i	0.0296564	+	0.211016i
$149$	−10.4361	−	0.364436i	−0.854958	−	0.0298558i	−0.395933	−	0.918279i	$-0.629579\pi$
$149$	−10.4361	−	0.364436i	−0.854958	−	0.0298558i	−0.459024	+	0.888424i	$0.651801\pi$
$150$	0.163170	+	2.33343i	0.0133227	+	0.190524i
$151$	5.57616	−	4.05131i	0.453781	−	0.329691i	−0.337306	−	0.941395i	$-0.609516\pi$
$151$	5.57616	−	4.05131i	0.453781	−	0.329691i	0.791087	+	0.611704i	$0.209516\pi$
$152$	−0.860802	−	4.27306i	−0.0698203	−	0.346591i
$153$		−	21.2203i		−	1.71556i
$154$	10.2258	+	9.67821i	0.824020	+	0.779892i
$155$	−2.17975	+	5.98881i	−0.175082	+	0.481033i
$156$	−3.55998	+	6.69535i	−0.285027	+	0.536057i
$157$	−15.6726	−	15.1348i	−1.25081	−	1.20789i	−0.968624	−	0.248530i	$-0.920052\pi$
$157$	−15.6726	−	15.1348i	−1.25081	−	1.20789i	−0.282183	−	0.959360i	$-0.591059\pi$
$158$	4.87462	+	1.39778i	0.387804	+	0.111201i
$159$	−16.2528	−	3.45465i	−1.28893	−	0.273972i
$160$	−1.61728	+	1.79617i	−0.127857	+	0.142000i
$161$	29.3242	−	7.31135i	2.31107	−	0.576215i
$162$	−0.875947	−	0.0612522i	−0.0688209	−	0.00481243i
$163$	18.3463	−	3.89963i	1.43699	−	0.305443i	0.577418	−	0.816449i	$-0.304060\pi$
$163$	18.3463	−	3.89963i	1.43699	−	0.305443i	0.859577	+	0.511006i	$0.170727\pi$
$164$	−3.53209	+	6.11776i	−0.275810	+	0.477717i
$165$	15.8661	−	15.6330i	1.23518	−	1.21703i
$166$	15.0562	−	2.65481i	1.16858	−	0.206053i
$167$	−13.8714	−	7.37554i	−1.07340	−	0.570737i	−0.163915	−	0.986474i	$-0.552412\pi$
$167$	−13.8714	−	7.37554i	−1.07340	−	0.570737i	−0.909484	+	0.415738i	$0.863523\pi$
$168$	−11.3386	+	3.25129i	−0.874792	+	0.250843i
$169$	5.53867	−	0.387301i	0.426051	−	0.0297924i
$170$	10.3334	−	3.35751i	0.792532	−	0.257509i
$171$	−18.9949	−	7.91081i	−1.45258	−	0.604955i
$172$	−2.47723	+	3.40962i	−0.188887	+	0.259981i
$173$	−5.31298	+	21.3092i	−0.403938	+	1.62011i	0.332152	+	0.943226i	$0.392225\pi$
$173$	−5.31298	+	21.3092i	−0.403938	+	1.62011i	−0.736091	+	0.676883i	$0.763330\pi$
$174$	0.847032	+	0.661774i	0.0642134	+	0.0501690i
$175$	−3.51946	−	0.620576i	−0.266046	−	0.0469111i
$176$	3.31560	+	0.0824243i	0.249923	+	0.00621297i
$177$	−18.2338	+	6.63657i	−1.37054	+	0.498835i
$178$	−7.04624	+	6.34446i	−0.528138	+	0.475538i
$179$	6.48116	−	14.5569i	0.484425	−	1.08804i	−0.491688	−	0.870771i	$-0.663620\pi$
$179$	6.48116	−	14.5569i	0.484425	−	1.08804i	0.976113	−	0.217264i	$-0.0697134\pi$
$180$	2.76021	+	11.0706i	0.205734	+	0.825154i
$181$	0.565682	+	0.228550i	0.0420468	+	0.0169880i	0.395534	−	0.918451i	$-0.370560\pi$
$181$	0.565682	+	0.228550i	0.0420468	+	0.0169880i	−0.353487	+	0.935439i	$0.615004\pi$
$182$	−8.60957	−	7.75209i	−0.638184	−	0.574623i
$183$	−18.8667	+	8.39999i	−1.39467	+	0.620945i
$184$	3.98098	−	5.90205i	0.293482	−	0.435105i
$185$	−0.872016	+	6.20472i	−0.0641119	+	0.456180i
$186$	−1.27226	+	7.21532i	−0.0932863	+	0.529053i
$187$	−12.7226	−	7.77322i	−0.930366	−	0.568434i
$188$	5.63595	−	4.72912i	0.411044	−	0.344907i
$189$	−6.27143	+	19.3015i	−0.456179	+	1.40397i
$190$	0.846812	−	10.5013i	0.0614342	−	0.761846i
$191$	18.0819	+	13.1372i	1.30836	+	0.950578i	1.00000		0.000692323i	$-0.000220373\pi$
$191$	18.0819	+	13.1372i	1.30836	+	0.950578i	0.308358	+	0.951270i	$0.400220\pi$
$192$	−1.47243	+	2.35638i	−0.106263	+	0.170057i
$193$	0.594297	−	17.0184i	0.0427784	−	1.22501i	−0.768305	−	0.640084i	$-0.778900\pi$
$193$	0.594297	−	17.0184i	0.0427784	−	1.22501i	0.811084	−	0.584930i	$-0.198878\pi$
$194$	5.89562	+	6.10509i	0.423281	+	0.438320i
$195$	−12.7316	+	13.1840i	−0.911732	+	0.944126i
$196$	−0.384640	−	11.0146i	−0.0274743	−	0.786760i
$197$	5.07514	+	2.93014i	0.361589	+	0.208764i	0.669778	−	0.742562i	$-0.266389\pi$
$197$	5.07514	+	2.93014i	0.361589	+	0.208764i	−0.308189	+	0.951325i	$0.599723\pi$
$198$	9.07474	−	12.7581i	0.644914	−	0.906676i
$199$	−9.63970	−	8.08867i	−0.683340	−	0.573390i	0.233640	−	0.972323i	$-0.424936\pi$
$199$	−9.63970	−	8.08867i	−0.683340	−	0.573390i	−0.916980	+	0.398933i	$0.869381\pi$
$200$	−0.713923	+	0.446108i	−0.0504820	+	0.0315446i
$201$	11.3804	+	5.06687i	0.802711	+	0.357390i
$202$	5.31307	+	11.9333i	0.373826	+	0.839627i
$203$	−1.29411	+	1.01107i	−0.0908284	+	0.0709629i
$204$	11.0286	−	5.86399i	0.772154	−	0.410562i
$205$	−12.2820	+	11.8606i	−0.857815	+	0.828382i
$206$	1.70775	+	5.95565i	0.118985	+	0.414950i
$207$	−12.5891	−	31.1592i	−0.875006	−	2.16572i
$208$	−2.72907			−0.189227
$209$	−11.7009	+	8.49050i	−0.809369	+	0.587300i
$210$	−28.5097			−1.96736
$211$	−4.24092	−	10.4966i	−0.291957	−	0.722618i	−0.999867	−	0.0163156i	$-0.994806\pi$
$211$	−4.24092	−	10.4966i	−0.291957	−	0.722618i	0.707910	−	0.706302i	$-0.249638\pi$
$212$	−1.64831	−	5.74834i	−0.113206	−	0.394798i
$213$	24.9670	−	24.1104i	1.71071	−	1.65202i
$214$	8.56583	−	4.55453i	0.585548	−	0.311342i
$215$	−8.02704	+	6.27141i	−0.547440	+	0.427707i
$216$	1.94448	+	4.36737i	0.132305	+	0.297162i
$217$	−10.2260	−	4.55289i	−0.694183	−	0.309070i
$218$	−12.9675	+	8.10302i	−0.878273	+	0.548806i
$219$	−22.3797	−	18.7788i	−1.51228	−	1.26895i
$220$	7.64842	+	2.40040i	0.515657	+	0.161835i
$221$	10.6244	+	6.13401i	0.714676	+	0.412618i
$222$	0.251384	+	7.19870i	0.0168718	+	0.483145i
$223$	−15.3068	+	15.8507i	−1.02502	+	1.06144i	−0.0269319	+	0.999637i	$0.508574\pi$
$223$	−15.3068	+	15.8507i	−1.02502	+	1.06144i	−0.998088	+	0.0618023i	$0.980315\pi$
$224$	−2.94893	−	3.05371i	−0.197034	−	0.204035i
$225$	−0.138689	+	3.97153i	−0.00924593	+	0.264769i
$226$	−7.99243	+	12.7906i	−0.531649	+	0.850816i
$227$	−10.4033	−	7.55844i	−0.690492	−	0.501671i	0.186330	−	0.982487i	$-0.440341\pi$
$227$	−10.4033	−	7.55844i	−0.690492	−	0.501671i	−0.876822	+	0.480816i	$0.840341\pi$
$228$	−1.13764	−	12.0580i	−0.0753419	−	0.798563i
$229$	−4.37865	+	13.4761i	−0.289349	+	0.890526i	0.695712	+	0.718321i	$0.255089\pi$
$229$	−4.37865	+	13.4761i	−0.289349	+	0.890526i	−0.985061	+	0.172205i	$0.944911\pi$
$230$	13.1813	−	11.0604i	0.869148	−	0.729302i
$231$	25.4467	+	29.7144i	1.67427	+	1.95507i
$232$	−0.0671760	+	0.380974i	−0.00441032	+	0.0250122i
$233$	0.00194314	−	0.0138262i	0.000127299	−	0.000905783i	−0.990204	−	0.139626i	$-0.955410\pi$
$233$	0.00194314	−	0.0138262i	0.000127299	−	0.000905783i	0.990332	+	0.138720i	$0.0442989\pi$
$234$	−7.20391	+	10.6802i	−0.470934	+	0.698189i
$235$	16.2449	−	7.23271i	1.05970	−	0.471810i
$236$	−5.18969	−	4.67282i	−0.337820	−	0.304175i
$237$	13.0644	+	5.27836i	0.848624	+	0.342866i
$238$	4.61667	+	18.5165i	0.299255	+	1.20024i
$239$	−7.37436	+	16.5631i	−0.477008	+	1.07138i	0.501499	+	0.865158i	$0.332782\pi$
$239$	−7.37436	+	16.5631i	−0.477008	+	1.07138i	−0.978506	+	0.206218i	$0.933884\pi$
$240$	−4.99083	+	4.49376i	−0.322156	+	0.290071i
$241$	−8.10603	+	2.95035i	−0.522155	+	0.190049i	−0.589632	−	0.807672i	$-0.700727\pi$
$241$	−8.10603	+	2.95035i	−0.522155	+	0.190049i	0.0674769	+	0.997721i	$0.478505\pi$
$242$	−4.32487	−	10.1141i	−0.278013	−	0.650160i
$243$	−16.5269	−	2.91415i	−1.06020	−	0.186943i
$244$	−5.85698	−	4.57597i	−0.374955	−	0.292947i
$245$	6.44444	−	25.8472i	0.411720	−	1.65132i
$246$	−11.5373	+	15.8797i	−0.735591	+	1.01245i
$247$	9.45144	−	7.22348i	0.601381	−	0.459619i
$248$	−2.50776	+	0.814821i	−0.159243	+	0.0517412i
$249$	42.3767	−	2.96327i	2.68552	−	0.187790i
$250$	9.66090	−	2.77022i	0.611009	−	0.175204i
$251$	2.91595	+	1.55044i	0.184053	+	0.0978627i	0.558941	−	0.829207i	$-0.311208\pi$
$251$	2.91595	+	1.55044i	0.184053	+	0.0978627i	−0.374888	+	0.927070i	$0.622319\pi$
$252$	−19.7350	+	3.47982i	−1.24319	+	0.219208i
$253$	−23.2929	−	3.86616i	−1.46441	−	0.243064i
$254$	−10.0056	+	17.3302i	−0.627807	+	1.08739i
$255$	29.5300	−	6.27680i	1.84924	−	0.393068i
$256$	−0.997564	−	0.0697565i	−0.0623478	−	0.00435978i
$257$	−13.8545	+	3.45432i	−0.864221	+	0.215475i	−0.648718	−	0.761029i	$-0.724695\pi$
$257$	−13.8545	+	3.45432i	−0.864221	+	0.215475i	−0.215503	+	0.976503i	$0.569139\pi$
$258$	−7.83580	+	8.70253i	−0.487835	+	0.541796i
$259$	−10.7645	−	2.28806i	−0.668872	−	0.142173i
$260$	−6.34061	−	1.81814i	−0.393228	−	0.112756i
$261$	1.31362	+	1.26855i	0.0813111	+	0.0785212i
$262$	0.0257430	−	0.0484155i	0.00159041	−	0.00299112i
$263$	9.57769	−	26.3145i	0.590586	−	1.62262i	−0.178835	−	0.983879i	$-0.557233\pi$
$263$	9.57769	−	26.3145i	0.590586	−	1.62262i	0.769421	−	0.638742i	$-0.220545\pi$
$264$	9.13828	+	1.19076i	0.562422	+	0.0732860i
$265$		−	14.4536i		−	0.887878i
$266$	18.2957	+	2.77031i	1.12178	+	0.169859i
$267$	−21.3140	+	15.4856i	−1.30440	+	0.947700i
$268$	0.312743	+	4.47243i	0.0191038	+	0.273197i
$269$	−6.74099	−	0.235401i	−0.411006	−	0.0143526i	−0.171349	−	0.985210i	$-0.554813\pi$
$269$	−6.74099	−	0.235401i	−0.411006	−	0.0143526i	−0.239657	+	0.970858i	$0.577035\pi$
$270$	1.60813	+	11.4424i	0.0978675	+	0.696363i
$271$	−5.11354	−	2.49404i	−0.310625	−	0.151502i	0.276464	−	0.961024i	$-0.410837\pi$
$271$	−5.11354	−	2.49404i	−0.310625	−	0.151502i	−0.587089	+	0.809522i	$0.699726\pi$
$272$	3.72679	+	2.51375i	0.225970	+	0.152418i
$273$	−21.5399	−	23.9224i	−1.30365	−	1.44785i
$274$	2.38518	+	4.13125i	0.144094	+	0.249578i
$275$	2.33031	+	1.53796i	0.140523	+	0.0927426i
$276$	12.7151	−	15.1533i	0.765360	−	0.912120i
$277$	5.34290	+	25.1363i	0.321023	+	1.51030i	0.782222	+	0.623000i	$0.214086\pi$
$277$	5.34290	+	25.1363i	0.321023	+	1.51030i	−0.461198	+	0.887297i	$0.652580\pi$
$278$	−3.03836	+	0.319344i	−0.182229	+	0.0191530i
$279$	−3.43092	+	11.9650i	−0.205404	+	0.716328i
$280$	−4.81701	−	9.05949i	−0.287872	−	0.541408i
$281$	32.1145	−	4.51339i	1.91579	−	0.269246i	0.922599	−	0.385761i	$-0.126061\pi$
$281$	32.1145	−	4.51339i	1.91579	−	0.269246i	0.993189	+	0.116515i	$0.0371722\pi$
$282$	16.9477	−	11.4314i	1.00922	−	0.680729i
$283$	−24.6262	−	6.14000i	−1.46388	−	0.364985i	−0.573122	−	0.819470i	$-0.694268\pi$
$283$	−24.6262	−	6.14000i	−1.46388	−	0.364985i	−0.890754	+	0.454485i	$0.849823\pi$
$284$	11.8800	+	3.86004i	0.704946	+	0.229051i
$285$	5.39007	−	28.7731i	0.319280	−	1.70437i
$286$	3.76442	+	8.23134i	0.222595	+	0.486730i
$287$	−19.2763	−	22.9726i	−1.13784	−	1.35603i
$288$	−2.90626	+	3.71984i	−0.171253	+	0.219194i
$289$	−1.40624	−	2.88322i	−0.0827199	−	0.169601i
$290$	−0.409884	+	0.840386i	−0.0240692	+	0.0493492i
$291$	14.5186	+	18.5829i	0.851094	+	1.08935i
$292$	2.18602	−	10.2844i	0.127927	−	0.601850i
$293$	1.57195	−	14.9561i	0.0918344	−	0.873746i	−0.847512	−	0.530776i	$-0.821900\pi$
$293$	1.57195	−	14.9561i	0.0918344	−	0.873746i	0.939346	−	0.342970i	$-0.111433\pi$
$294$	2.13621	−	30.5492i	0.124586	−	1.78167i
$295$	−8.94443	−	14.3141i	−0.520765	−	0.833398i
$296$	−2.24505	+	1.29618i	−0.130491	+	0.0753388i
$297$	10.4906	−	11.8892i	0.608725	−	0.689879i
$298$	−3.57153	−	9.81269i	−0.206893	−	0.568434i
$299$	19.2396	+	2.70395i	1.11265	+	0.156373i
$300$	−2.10240	+	1.02541i	−0.121382	+	0.0592020i
$301$	−10.0047	−	14.8326i	−0.576661	−	0.854935i
$302$	5.84518	+	3.65247i	0.336352	+	0.210176i
$303$	11.2160	+	34.5193i	0.644343	+	1.98308i
$304$	3.63945	−	2.39884i	0.208737	−	0.137583i
$305$	−10.5593	−	14.5336i	−0.604624	−	0.832193i
$306$	19.6752	−	7.94928i	1.12475	−	0.454430i
$307$	6.47621	+	2.35715i	0.369617	+	0.134529i	0.520149	−	0.854076i	$-0.325876\pi$
$307$	6.47621	+	2.35715i	0.369617	+	0.134529i	−0.150532	+	0.988605i	$0.548099\pi$
$308$	−5.14282	+	13.1067i	−0.293039	+	0.746825i
$309$	2.98938	+	16.9536i	0.170060	+	0.964459i
$310$	−6.36928	+	0.222420i	−0.361751	+	0.0126326i
$311$	2.01802	+	19.2002i	0.114432	+	1.08874i	0.889522	+	0.456893i	$0.151038\pi$
$311$	2.01802	+	19.2002i	0.114432	+	1.08874i	−0.775090	+	0.631851i	$0.782296\pi$
$312$	−7.54141	−	0.792634i	−0.426948	−	0.0448741i
$313$	7.55218	−	18.6923i	0.426874	−	1.05655i	−0.548531	−	0.836130i	$-0.684813\pi$
$313$	7.55218	−	18.6923i	0.426874	−	1.05655i	0.975405	−	0.220421i	$-0.0707430\pi$
$314$	8.16172	−	20.2010i	0.460592	−	1.14001i
$315$	−48.1698	−	5.06285i	−2.71406	−	0.285260i
$316$	0.530071	+	5.04329i	0.0298188	+	0.283707i
$317$	16.2268	−	0.566654i	0.911390	−	0.0318264i	0.424635	−	0.905365i	$-0.360403\pi$
$317$	16.2268	−	0.566654i	0.911390	−	0.0318264i	0.486755	+	0.873538i	$0.338180\pi$
$318$	−2.88533	−	16.3635i	−0.161801	−	0.917620i
$319$	1.24175	−	0.322894i	0.0695244	−	0.0180786i
$320$	−2.27123	−	0.826659i	−0.126966	−	0.0462117i
$321$	24.9934	−	10.0980i	1.39499	−	0.563614i
$322$	17.7640	+	24.4501i	0.989950	+	1.36255i
$323$	−19.5603	+	1.15858i	−1.08837	+	0.0644651i
$324$	−0.271344	−	0.835110i	−0.0150746	−	0.0463950i
$325$	−1.94834	−	1.21746i	−0.108075	−	0.0675325i
$326$	10.4883	+	15.5496i	0.580895	+	0.861212i
$327$	−38.1875	+	18.6253i	−2.11177	+	1.02998i
$328$	−6.99543	−	0.983143i	−0.386258	−	0.0542850i
$329$	10.6821	+	29.3490i	0.588926	+	1.61806i
$330$	20.4382	+	8.85459i	1.12509	+	0.487429i
$331$	19.5222	−	11.2711i	1.07304	−	0.619517i	0.144026	−	0.989574i	$-0.453995\pi$
$331$	19.5222	−	11.2711i	1.07304	−	0.619517i	0.929009	+	0.370056i	$0.120662\pi$
$332$	8.10163	+	12.9653i	0.444635	+	0.711564i
$333$	−0.853633	+	12.2075i	−0.0467788	+	0.668968i
$334$	1.64217	−	15.6242i	0.0898558	−	0.854921i
$335$	−2.25298	+	10.5994i	−0.123093	+	0.579108i
$336$	−7.26206	−	9.29501i	−0.396178	−	0.507084i
$337$	−10.0430	+	20.5911i	−0.547075	+	1.12167i	0.428812	+	0.903394i	$0.358932\pi$
$337$	−10.0430	+	20.5911i	−0.547075	+	1.12167i	−0.975887	+	0.218276i	$0.929957\pi$
$338$	2.43392	+	4.99028i	0.132388	+	0.271435i
$339$	−25.8009	+	33.0237i	−1.40131	+	1.79360i
$340$	6.98398	+	8.32318i	0.378759	+	0.451388i
$341$	5.91680	+	6.43990i	0.320413	+	0.348740i
$342$	0.219161	−	20.5752i	0.0118508	−	1.11258i
$343$	16.2358	+	5.27532i	0.876649	+	0.284841i
$344$	−4.08933	−	1.01959i	−0.220482	−	0.0549723i
$345$	39.6371	−	26.7356i	2.13399	−	1.43939i
$346$	−21.7478	+	3.05646i	−1.16917	+	0.164316i
$347$	7.64237	+	14.3732i	0.410264	+	0.771594i	0.999334	−	0.0364878i	$-0.0116170\pi$
$347$	7.64237	+	14.3732i	0.410264	+	0.771594i	−0.589070	+	0.808082i	$0.700506\pi$
$348$	−0.296282	+	1.03326i	−0.0158824	+	0.0553885i
$349$	6.83268	−	0.718144i	0.365745	−	0.0384414i	0.0801264	−	0.996785i	$-0.474468\pi$
$349$	6.83268	−	0.718144i	0.365745	−	0.0384414i	0.285619	+	0.958343i	$0.407801\pi$
$350$	−0.743025	−	3.49566i	−0.0397164	−	0.186851i
$351$	−8.38633	+	9.99444i	−0.447629	+	0.533464i
$352$	1.16562	+	3.10505i	0.0621279	+	0.165500i
$353$	−3.35921	−	5.81832i	−0.178793	−	0.309678i	0.762675	−	0.646782i	$-0.223886\pi$
$353$	−3.35921	−	5.81832i	−0.178793	−	0.309678i	−0.941467	+	0.337104i	$0.890552\pi$
$354$	−12.9838	−	14.4200i	−0.690083	−	0.766415i
$355$	25.0298	+	16.8828i	1.32845	+	0.896048i
$356$	−8.52205	−	4.15648i	−0.451668	−	0.220293i
$357$	7.37961	+	52.5086i	0.390570	+	2.77905i
$358$	15.9248	+	0.556107i	0.841654	+	0.0293912i
$359$	−1.59884	−	22.8645i	−0.0843835	−	1.20674i	−0.836596	−	0.547820i	$-0.815458\pi$
$359$	−1.59884	−	22.8645i	−0.0843835	−	1.20674i	0.752213	−	0.658920i	$-0.228987\pi$
$360$	−9.23049	+	6.70634i	−0.486490	+	0.353455i
$361$	−6.25490	+	17.9409i	−0.329205	+	0.944258i
$362$			0.610108i			0.0320666i
$363$	−9.01364	−	29.2051i	−0.473093	−	1.53287i
$364$	3.96241	−	10.8866i	0.207687	−	0.570615i
$365$	11.9305	−	22.4381i	0.624472	−	1.17446i
$366$	−14.8559	−	14.3462i	−0.776531	−	0.749888i
$367$	8.18155	+	2.34602i	0.427073	+	0.122461i	0.482287	−	0.876013i	$-0.339806\pi$
$367$	8.18155	+	2.34602i	0.427073	+	0.122461i	−0.0552136	+	0.998475i	$0.517584\pi$
$368$	6.96359	+	1.48016i	0.363002	+	0.0771585i
$369$	−22.3133	+	24.7815i	−1.16159	+	1.29007i
$370$	−6.07958	+	1.51581i	−0.316062	+	0.0788032i
$371$	25.3242	+	1.77084i	1.31477	+	0.0919374i
$372$	−7.16652	+	1.52329i	−0.371567	+	0.0789790i
$373$	3.91334	−	6.77811i	0.202625	−	0.350957i	−0.746748	−	0.665107i	$-0.768386\pi$
$373$	3.91334	−	6.77811i	0.202625	−	0.350957i	0.949373	+	0.314150i	$0.101719\pi$
$374$	2.44125	−	14.7081i	0.126234	−	0.760535i
$375$	27.5012	−	4.84920i	1.42015	−	0.250412i
$376$	6.49603	+	3.45400i	0.335007	+	0.178126i
$377$	−1.01485	+	0.291002i	−0.0522672	+	0.0149874i
$378$	−20.2453	+	1.41569i	−1.04131	+	0.0728153i
$379$	16.2928	−	5.29387i	0.836907	−	0.271928i	0.140955	−	0.990016i	$-0.454983\pi$
$379$	16.2928	−	5.29387i	0.836907	−	0.271928i	0.695952	+	0.718088i	$0.254983\pi$
$380$	10.0539	−	3.14872i	0.515753	−	0.161526i
$381$	−32.6825	+	44.9836i	−1.67438	+	2.30458i
$382$	−5.40706	+	21.6865i	−0.276649	+	1.10958i
$383$	−10.9474	−	8.55302i	−0.559385	−	0.437039i	0.295884	−	0.955224i	$-0.404386\pi$
$383$	−10.9474	−	8.55302i	−0.559385	−	0.437039i	−0.855269	+	0.518185i	$0.826608\pi$
$384$	−2.73637	−	0.482497i	−0.139640	−	0.0246223i
$385$	−20.6805	+	27.0254i	−1.05398	+	1.37734i
$386$	16.0019	−	5.82420i	0.814473	−	0.296444i
$387$	−14.7847	+	13.3122i	−0.751551	+	0.676700i
$388$	−3.45200	+	7.75333i	−0.175249	+	0.393616i
$389$	−5.98782	−	24.0158i	−0.303595	−	1.21765i	−0.907314	−	0.420455i	$-0.861871\pi$
$389$	−5.98782	−	24.0158i	−0.303595	−	1.21765i	0.603719	−	0.797197i	$-0.293685\pi$
$390$	−16.9934	−	6.86576i	−0.860492	−	0.347661i
$391$	−23.7828	−	21.4141i	−1.20275	−	1.08296i
$392$	10.0685	−	4.48279i	0.508537	−	0.226415i
$393$	0.0851992	−	0.126313i	0.00429773	−	0.00637165i
$394$	−0.815592	+	5.80324i	−0.0410889	+	0.292363i
$395$	−2.12836	+	12.0705i	−0.107089	+	0.607334i
$396$	15.2285	+	3.63470i	0.765262	+	0.182651i
$397$	−14.7755	+	12.3981i	−0.741562	+	0.622244i	−0.933257	−	0.359210i	$-0.883046\pi$
$397$	−14.7755	+	12.3981i	−0.741562	+	0.622244i	0.191695	+	0.981455i	$0.438602\pi$
$398$	3.88859	−	11.9678i	0.194917	−	0.599894i
$399$	49.7530	+	12.9692i	2.49076	+	0.649272i
$400$	−0.681065	−	0.494822i	−0.0340532	−	0.0247411i
$401$	−9.62113	+	15.3970i	−0.480456	+	0.768891i	−0.996130	−	0.0878943i	$-0.971986\pi$
$401$	−9.62113	+	15.3970i	−0.480456	+	0.768891i	0.515673	+	0.856785i	$0.327542\pi$
$402$	−0.434756	+	12.4498i	−0.0216837	+	0.620939i
$403$	−4.99880	−	5.17641i	−0.249008	−	0.257855i
$404$	−9.07409	+	9.39650i	−0.451453	+	0.467493i
$405$	−0.0740681	−	2.12103i	−0.00368047	−	0.105395i
$406$	−1.42222	−	0.821122i	−0.0705838	−	0.0407516i
$407$	7.00627	+	4.98352i	0.347288	+	0.247024i
$408$	9.56838	+	8.02882i	0.473705	+	0.397486i
$409$	−5.08677	+	3.17857i	−0.251525	+	0.157170i	−0.649822	−	0.760086i	$-0.725157\pi$
$409$	−5.08677	+	3.17857i	−0.251525	+	0.157170i	0.398298	+	0.917256i	$0.369601\pi$
$410$	−15.5979	−	6.94464i	−0.770326	−	0.342971i
$411$	5.39123	+	12.1089i	0.265930	+	0.597289i
$412$	−4.88224	+	3.81443i	−0.240531	+	0.187923i
$413$	26.1756	−	13.9178i	1.28802	−	0.684851i
$414$	24.1744	−	23.3449i	1.18811	−	1.14734i
$415$	10.1853	+	35.5205i	0.499979	+	1.74363i
$416$	−1.02233	−	2.53035i	−0.0501237	−	0.124060i
$417$	−8.48885			−0.415701
$418$	−12.2555	−	7.66830i	−0.599436	−	0.375069i
$419$	−12.1250			−0.592346			−0.296173	−	0.955134i	$-0.595711\pi$
$419$	−12.1250			−0.592346			−0.296173	+	0.955134i	$0.595711\pi$
$420$	−10.6799	−	26.4337i	−0.521127	−	1.28983i
$421$	5.46485	+	19.0582i	0.266341	+	0.928840i	0.974799	+	0.223087i	$0.0716134\pi$
$421$	5.46485	+	19.0582i	0.266341	+	0.928840i	−0.708458	+	0.705753i	$0.750609\pi$
$422$	8.14363	−	7.86422i	0.396426	−	0.382824i
$423$	30.6648	−	16.3048i	1.49097	−	0.792765i
$424$	4.71230	−	3.68165i	0.228850	−	0.178797i
$425$	1.53923	+	3.45717i	0.0746638	+	0.167698i
$426$	31.7076	+	14.1171i	1.53624	+	0.683977i
$427$	26.7581	−	16.7203i	1.29492	−	0.809154i
$428$	7.43171	+	6.23594i	0.359225	+	0.301426i
$429$	8.01176	+	23.8396i	0.386811	+	1.15098i
$430$	−8.82173	−	5.09323i	−0.425422	−	0.245617i
$431$	0.0447544	+	1.28160i	0.00215574	+	0.0617324i	0.999992	−	0.00401665i	$-0.00127854\pi$
$431$	0.0447544	+	1.28160i	0.00215574	+	0.0617324i	−0.997836	+	0.0657490i	$0.979056\pi$
$432$	−3.32094	+	3.43894i	−0.159779	+	0.165456i
$433$	−12.3443	−	12.7829i	−0.593229	−	0.614307i	0.353852	−	0.935302i	$-0.384872\pi$
$433$	−12.3443	−	12.7829i	−0.593229	−	0.614307i	−0.947081	+	0.320995i	$0.895983\pi$
$434$	0.390655	−	11.1869i	0.0187520	−	0.536988i
$435$	−1.37674	+	2.20325i	−0.0660097	+	0.105638i
$436$	−12.3707	−	8.98785i	−0.592450	−	0.430440i
$437$	−28.0344	+	13.3056i	−1.34107	+	0.636491i
$438$	9.02780	−	27.7847i	0.431365	−	1.32760i
$439$	12.6553	−	10.6190i	0.604002	−	0.506818i	−0.288727	−	0.957411i	$-0.593232\pi$
$439$	12.6553	−	10.6190i	0.604002	−	0.506818i	0.892729	+	0.450593i	$0.148788\pi$
$440$	0.639540	+	7.99070i	0.0304889	+	0.380942i
$441$	9.03436	−	51.2364i	0.430208	−	2.43983i
$442$	−1.70738	+	12.1486i	−0.0812117	+	0.577851i
$443$	1.89617	−	2.81119i	0.0900900	−	0.133564i	−0.781298	−	0.624158i	$-0.785442\pi$
$443$	1.89617	−	2.81119i	0.0900900	−	0.133564i	0.871388	+	0.490594i	$0.163220\pi$
$444$	−6.58034	+	2.92976i	−0.312289	+	0.139040i
$445$	−17.0307	−	15.3345i	−0.807332	−	0.726925i
$446$	−20.4305	−	8.25447i	−0.967413	−	0.390860i
$447$	−7.01942	−	28.1534i	−0.332007	−	1.33161i
$448$	1.72666	−	3.87814i	0.0815771	−	0.183225i
$449$	−29.4639	+	26.5294i	−1.39049	+	1.25200i	−0.458895	+	0.888490i	$0.651755\pi$
$449$	−29.4639	+	26.5294i	−1.39049	+	1.25200i	−0.931591	+	0.363509i	$0.881579\pi$
$450$	−3.73430	+	1.35917i	−0.176036	+	0.0640720i
$451$	6.68403	+	22.4556i	0.314739	+	1.05739i
$452$	−14.8532	−	2.61902i	−0.698637	−	0.123189i
$453$	15.0915	+	11.7908i	0.709062	+	0.553980i
$454$	3.11092	−	12.4772i	0.146003	−	0.585585i
$455$	16.4589	−	22.6538i	0.771607	−	1.06203i
$456$	10.7538	−	5.57182i	0.503595	−	0.260924i
$457$	18.8172	−	6.11408i	0.880232	−	0.286005i	0.166179	−	0.986096i	$-0.446857\pi$
$457$	18.8172	−	6.11408i	0.880232	−	0.286005i	0.714054	+	0.700091i	$0.246857\pi$
$458$	−14.1351	+	0.988422i	−0.660489	+	0.0461859i
$459$	20.6582	−	5.92364i	0.964241	−	0.276492i
$460$	15.1928	+	8.07817i	0.708369	+	0.376647i
$461$	20.0485	−	3.53510i	0.933754	−	0.164646i	0.313983	−	0.949429i	$-0.398337\pi$
$461$	20.0485	−	3.53510i	0.933754	−	0.164646i	0.619771	+	0.784783i	$0.287225\pi$
$462$	−18.0182	+	34.7250i	−0.838284	+	1.61555i
$463$	1.47564	−	2.55588i	0.0685788	−	0.118782i	−0.829697	−	0.558214i	$-0.811487\pi$
$463$	1.47564	−	2.55588i	0.0685788	−	0.118782i	0.898276	+	0.439432i	$0.144820\pi$
$464$	−0.378398	+	0.0804309i	−0.0175667	+	0.00373391i
$465$	−17.6653	−	1.23527i	−0.819206	−	0.0572845i
$466$	0.0135473	−	0.00337773i	0.000627568	−	0.000156470i
$467$	23.9493	−	26.5984i	1.10824	−	1.23083i	0.137549	−	0.990495i	$-0.456077\pi$
$467$	23.9493	−	26.5984i	1.10824	−	1.23083i	0.970691	−	0.240331i	$-0.0772559\pi$
$468$	−12.6012	−	2.67846i	−0.582489	−	0.123812i
$469$	−18.2952	−	5.24608i	−0.844796	−	0.242241i
$470$	12.7915	+	12.3526i	0.590029	+	0.569784i
$471$	28.4210	−	53.4521i	1.30957	−	2.46294i
$472$	2.38847	−	6.56227i	0.109938	−	0.302053i
$473$	2.56550	+	13.7405i	0.117962	+	0.631791i
$474$			14.0904i			0.647194i
$475$	3.66843	−	0.0889962i	0.168319	−	0.00408343i
$476$	−15.4387	+	11.2169i	−0.707633	+	0.514126i
$477$	−1.96915	−	28.1601i	−0.0901610	−	1.28936i
$478$	−18.1195	−	0.632747i	−0.828767	−	0.0289412i
$479$	2.79065	+	19.8565i	0.127508	+	0.907268i	0.944008	+	0.329923i	$0.107023\pi$
$479$	2.79065	+	19.8565i	0.127508	+	0.907268i	−0.816500	+	0.577346i	$0.804088\pi$
$480$	−6.03614	−	2.94402i	−0.275511	−	0.134376i
$481$	−5.86520	−	3.95613i	−0.267430	−	0.180384i
$482$	−5.77209	−	6.41056i	−0.262912	−	0.291993i
$483$	41.9872	+	72.7239i	1.91048	+	3.30905i
$484$	7.75753	−	7.79877i	0.352615	−	0.354489i
$485$	−13.1856	+	15.7140i	−0.598728	+	0.713536i
$486$	−3.48915	−	16.4152i	−0.158271	−	0.744607i
$487$	18.8336	−	1.97949i	0.853433	−	0.0896994i	0.332299	−	0.943174i	$-0.392176\pi$
$487$	18.8336	−	1.97949i	0.853433	−	0.0896994i	0.521134	+	0.853475i	$0.325509\pi$
$488$	2.04871	−	7.14468i	0.0927405	−	0.323425i
$489$	24.4668	+	46.0154i	1.10643	+	2.08089i
$490$	26.3793	−	3.70736i	1.19169	−	0.167482i
$491$	7.89598	−	5.32590i	0.356340	−	0.240355i	−0.367956	−	0.929843i	$-0.619942\pi$
$491$	7.89598	−	5.32590i	0.356340	−	0.240355i	0.724297	+	0.689488i	$0.242165\pi$
$492$	−19.0454	−	4.74855i	−0.858632	−	0.214081i
$493$	1.65390	+	0.537386i	0.0744881	+	0.0242027i
$494$	10.2381	+	6.05725i	0.460632	+	0.272529i
$495$	32.9599	+	18.5902i	1.48144	+	0.835566i
$496$	−1.69491	−	2.01992i	−0.0761039	−	0.0906971i
$497$	−32.6471	+	41.7864i	−1.46442	+	1.87438i
$498$	18.6221	+	38.1809i	0.834476	+	1.71093i
$499$	−13.6060	+	27.8964i	−0.609087	+	1.24881i	0.341944	+	0.939720i	$0.388915\pi$
$499$	−13.6060	+	27.8964i	−0.609087	+	1.24881i	−0.951032	+	0.309094i	$0.899974\pi$
$500$	6.18754	+	7.91969i	0.276715	+	0.354179i
$501$	9.07585	−	42.6985i	0.405479	−	1.90763i
$502$	−0.345207	+	3.28442i	−0.0154073	+	0.146591i
$503$	0.523564	−	7.48732i	0.0233446	−	0.333843i	−0.971827	−	0.235695i	$-0.924264\pi$
$503$	0.523564	−	7.48732i	0.0233446	−	0.333843i	0.995172	−	0.0981486i	$-0.0312920\pi$
$504$	−10.6193	−	16.9944i	−0.473021	−	0.756992i
$505$	−27.3425	+	15.7862i	−1.21672	+	0.702476i
$506$	−5.14103	−	23.0451i	−0.228547	−	1.02448i
$507$	5.27643	+	14.4969i	0.234334	+	0.643828i
$508$	−19.8164	−	2.78502i	−0.879212	−	0.123565i
$509$	8.72302	−	4.25450i	0.386641	−	0.188577i	−0.234790	−	0.972046i	$-0.575440\pi$
$509$	8.72302	−	4.25450i	0.386641	−	0.188577i	0.621431	+	0.783469i	$0.286551\pi$
$510$	16.8819	+	25.0284i	0.747542	+	1.10828i
$511$	37.8521	+	23.6526i	1.67448	+	1.04633i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	2.39883	−	20.7000i	0.105911	−	0.913927i
$514$	−8.39279	−	11.5517i	−0.370190	−	0.509523i
$515$	−13.8844	+	5.60968i	−0.611821	+	0.247192i
$516$	−11.0042	−	4.00520i	−0.484432	−	0.176319i
$517$	1.45737	−	24.3575i	0.0640949	−	1.07124i
$518$	−1.91099	−	10.8378i	−0.0839641	−	0.476184i
$519$	−60.9849	+	2.12964i	−2.67694	+	0.0934808i
$520$	−0.689483	−	6.56000i	−0.0302358	−	0.287675i
$521$	−24.6912	−	2.59515i	−1.08174	−	0.113696i	−0.453153	−	0.891433i	$-0.649701\pi$
$521$	−24.6912	−	2.59515i	−1.08174	−	0.113696i	−0.628590	+	0.777737i	$0.716368\pi$
$522$	−0.684087	+	1.69318i	−0.0299417	+	0.0741083i
$523$	9.40509	−	23.2784i	0.411256	−	1.01789i	−0.569383	−	0.822072i	$-0.692818\pi$
$523$	9.40509	−	23.2784i	0.411256	−	1.01789i	0.980639	−	0.195822i	$-0.0627376\pi$
$524$	0.0545336	+	0.00573171i	0.00238231	+	0.000250391i
$525$	−1.03797	−	9.87558i	−0.0453005	−	0.431006i
$526$	27.9862	−	0.977301i	1.22026	−	0.0426123i
$527$	2.05831	+	11.6733i	0.0896614	+	0.508495i
$528$	2.31921	+	8.91893i	0.100931	+	0.388147i
$529$	−26.0130	−	9.46795i	−1.13100	−	0.411650i
$530$	13.4011	−	5.41441i	0.582109	−	0.235187i
$531$	−19.3767	−	26.6697i	−0.840876	−	1.15737i
$532$	4.28508	+	18.0012i	0.185782	+	0.780452i
$533$	−5.95742	−	18.3351i	−0.258044	−	0.794179i
$534$	−22.3423	−	13.9610i	−0.966847	−	0.604153i
$535$	13.1121	+	19.4394i	0.566884	+	0.840440i
$536$	−4.02961	+	1.96537i	−0.174053	+	0.0848912i
$537$	43.8446	+	6.16196i	1.89204	+	0.265908i
$538$	−2.30696	−	6.33832i	−0.0994601	−	0.273264i
$539$	−27.4092	−	24.1849i	−1.18060	−	1.04172i
$540$	−10.0068	+	5.77744i	−0.430625	+	0.248621i
$541$	9.88020	+	15.8116i	0.424783	+	0.679795i	0.989344	−	0.145596i	$-0.0465100\pi$
$541$	9.88020	+	15.8116i	0.424783	+	0.679795i	−0.564561	+	0.825391i	$0.690954\pi$
$542$	0.396868	−	5.67547i	0.0170469	−	0.243782i
$543$	−0.177201	+	1.68595i	−0.00760441	+	0.0723511i
$544$	−0.934629	+	4.39708i	−0.0400719	+	0.188523i
$545$	−22.7538	−	29.1236i	−0.974666	−	1.24752i
$546$	14.1115	−	28.9329i	0.603918	−	1.23821i
$547$	−5.44263	−	11.1591i	−0.232710	−	0.477127i	0.750200	−	0.661211i	$-0.229957\pi$
$547$	−5.44263	−	11.1591i	−0.232710	−	0.477127i	−0.982911	+	0.184084i	$0.941068\pi$
$548$	−2.93693	+	3.75909i	−0.125459	+	0.160581i
$549$	−22.5528	−	26.8774i	−0.962531	−	1.14710i
$550$	−0.553023	+	2.73676i	−0.0235810	+	0.116696i
$551$	1.09759	−	1.28012i	0.0467591	−	0.0545350i
$552$	18.8130	+	6.11273i	0.800736	+	0.260175i
$553$	−20.8880	−	5.20797i	−0.888249	−	0.221465i
$554$	−21.3045	+	14.3701i	−0.905143	+	0.610527i
$555$	−17.2404	+	2.42297i	−0.731812	+	0.102849i
$556$	−1.43428	−	2.69749i	−0.0608271	−	0.114399i
$557$	−3.02951	+	10.5652i	−0.128365	+	0.447660i	−0.999021	−	0.0442305i	$-0.985916\pi$
$557$	−3.02951	+	10.5652i	−0.128365	+	0.447660i	0.870657	+	0.491891i	$0.163694\pi$
$558$	−12.3790	+	1.30109i	−0.524046	+	0.0550795i
$559$	−2.39134	−	11.2504i	−0.101143	−	0.475840i
$560$	6.59532	−	7.86000i	0.278703	−	0.332146i
$561$	11.0179	−	39.9347i	0.465176	−	1.68604i
$562$	16.2150	+	28.0853i	0.683990	+	1.18471i
$563$	0.715448	+	0.794585i	0.0301525	+	0.0334878i	0.758032	−	0.652217i	$-0.226161\pi$
$563$	0.715448	+	0.794585i	0.0301525	+	0.0334878i	−0.727880	+	0.685705i	$0.759494\pi$
$564$	16.9477	+	11.4314i	0.713628	+	0.481348i
$565$	−32.7646	−	15.9803i	−1.37842	−	0.672298i
$566$	−3.53223	−	25.1331i	−0.148471	−	1.05642i
$567$	3.72534	+	0.130092i	0.156450	+	0.00546334i
$568$	0.871352	+	12.4609i	0.0365611	+	0.522848i
$569$	14.9945	−	10.8941i	0.628601	−	0.456706i	−0.227314	−	0.973822i	$-0.572994\pi$
$569$	14.9945	−	10.8941i	0.628601	−	0.456706i	0.855915	+	0.517116i	$0.172994\pi$
$570$	28.6971	−	5.78099i	1.20199	−	0.242139i
$571$			5.69086i			0.238155i	0.992885	+	0.119078i	$0.0379937\pi$
$571$			5.69086i			0.238155i	−0.992885	+	0.119078i	$0.962006\pi$
$572$	−6.22179	+	6.57383i	−0.260146	+	0.274866i
$573$	−21.2403	+	58.3573i	−0.887328	+	2.43791i
$574$	14.0788	−	26.4783i	0.587636	−	1.10518i
$575$	4.31115	+	4.16323i	0.179788	+	0.173619i
$576$	−4.53768	−	1.30116i	−0.189070	−	0.0542149i
$577$	−1.14049	−	0.242418i	−0.0474791	−	0.0100920i	0.184111	−	0.982905i	$-0.441059\pi$
$577$	−1.14049	−	0.242418i	−0.0474791	−	0.0100920i	−0.231590	+	0.972813i	$0.574393\pi$
$578$	2.14648	−	2.38391i	0.0892820	−	0.0991577i
$579$	45.9106	−	11.4468i	1.90798	−	0.475712i
$580$	−0.932738	−	0.0652234i	−0.0387298	−	0.00270825i
$581$	−63.4835	+	13.4938i	−2.63374	+	0.559818i
$582$	−11.7910	+	20.4227i	−0.488754	+	0.846547i
$583$	−17.6046	−	9.13472i	−0.729107	−	0.378322i
$584$	10.3544	−	1.82577i	0.428470	−	0.0755508i
$585$	−27.4926	−	14.6181i	−1.13668	−	0.604384i
$586$	14.4559	−	4.14517i	0.597169	−	0.171236i
$587$	−6.58893	+	0.460743i	−0.271954	+	0.0190169i	−0.205083	−	0.978745i	$-0.565746\pi$
$587$	−6.58893	+	0.460743i	−0.271954	+	0.0190169i	−0.0668718	+	0.997762i	$0.521302\pi$
$588$	29.1250	−	9.46328i	1.20109	−	0.390259i
$589$	11.2164	+	2.50927i	0.462162	+	0.103393i
$590$	9.92115	−	13.6553i	0.408447	−	0.562179i
$591$	−3.93928	+	15.7996i	−0.162040	+	0.649908i
$592$	−2.04280	−	1.59601i	−0.0839587	−	0.0655957i
$593$	−9.16445	−	1.61594i	−0.376339	−	0.0663587i	−0.0177206	−	0.999843i	$-0.505641\pi$
$593$	−9.16445	−	1.61594i	−0.376339	−	0.0663587i	−0.358618	+	0.933484i	$0.616752\pi$
$594$	14.9533	+	5.27294i	0.613541	+	0.216351i
$595$	−43.3426	+	15.7754i	−1.77687	+	0.646729i
$596$	7.76025	−	6.98736i	0.317872	−	0.286213i
$597$	14.2215	−	31.9421i	0.582049	−	1.30730i
$598$	4.70022	+	18.8516i	0.192206	+	0.770897i
$599$	−12.3301	−	4.98168i	−0.503794	−	0.203546i	0.108620	−	0.994083i	$-0.465357\pi$
$599$	−12.3301	−	4.98168i	−0.503794	−	0.203546i	−0.612414	+	0.790537i	$0.709801\pi$
$600$	−1.73831	−	1.56518i	−0.0709664	−	0.0638984i
$601$	30.8347	−	13.7285i	1.25778	−	0.559998i	0.333870	−	0.942619i	$-0.391645\pi$
$601$	30.8347	−	13.7285i	1.25778	−	0.559998i	0.923905	+	0.382622i	$0.124979\pi$
$602$	10.0047	−	14.8326i	0.407761	−	0.604530i
$603$	−2.94544	+	20.9579i	−0.119948	+	0.853472i
$604$	−1.19687	+	6.78779i	−0.0487000	+	0.276191i
$605$	23.2192	−	12.9512i	0.943993	−	0.526540i
$606$	−27.8042	+	23.3305i	−1.12947	+	0.947736i
$607$	−1.04829	+	3.22632i	−0.0425490	+	0.130952i	−0.970074	−	0.242808i	$-0.921932\pi$
$607$	−1.04829	+	3.22632i	−0.0425490	+	0.130952i	0.927525	+	0.373760i	$0.121932\pi$
$608$	3.58752	+	2.47582i	0.145493	+	0.100408i
$609$	−3.69164	−	2.68213i	−0.149593	−	0.108686i
$610$	9.51976	−	15.2348i	0.385444	−	0.616839i
$611$	−0.700723	+	20.0661i	−0.0283482	+	0.811787i
$612$	14.7409	+	15.2646i	0.595865	+	0.617036i
$613$	4.70367	−	4.87080i	0.189980	−	0.196730i	−0.617593	−	0.786498i	$-0.711892\pi$
$613$	4.70367	−	4.87080i	0.189980	−	0.196730i	0.807572	+	0.589768i	$0.200781\pi$
$614$	0.240522	+	6.88764i	0.00970666	+	0.277962i
$615$	−41.0857	−	23.7209i	−1.65674	−	0.956517i
$616$	−14.0789	+	0.141528i	−0.567254	+	0.00570233i
$617$	−6.34941	−	5.32778i	−0.255617	−	0.214489i	0.505969	−	0.862551i	$-0.331135\pi$
$617$	−6.34941	−	5.32778i	−0.255617	−	0.214489i	−0.761587	+	0.648063i	$0.775579\pi$
$618$	−14.5993	+	9.12265i	−0.587270	+	0.366967i
$619$	0.633775	+	0.282175i	0.0254736	+	0.0113416i	0.419434	−	0.907786i	$-0.362229\pi$
$619$	0.633775	+	0.282175i	0.0254736	+	0.0113416i	−0.393960	+	0.919127i	$0.628895\pi$
$620$	−2.59220	−	5.82217i	−0.104105	−	0.233824i
$621$	26.8195	−	20.9537i	1.07623	−	0.840843i
$622$	−17.0462	+	9.06360i	−0.683488	+	0.363417i
$623$	28.9542	−	27.9608i	1.16003	−	1.12022i
$624$	−2.09014	−	7.28920i	−0.0836728	−	0.291802i
$625$	10.6765	+	26.4252i	0.427059	+	1.05701i
$626$	20.1603			0.805767
$627$	−31.6392	−	24.7498i	−1.26355	−	0.988412i
$628$	21.7874			0.869414
$629$	4.36546	+	10.8049i	0.174062	+	0.430819i
$630$	−13.3505	−	46.5589i	−0.531898	−	1.85495i
$631$	−25.2104	+	24.3454i	−1.00361	+	0.969173i	−0.999525	−	0.0308185i	$-0.990189\pi$
$631$	−25.2104	+	24.3454i	−1.00361	+	0.969173i	−0.00408324	+	0.999992i	$0.501300\pi$
$632$	−4.47749	+	2.38072i	−0.178105	+	0.0947000i
$633$	24.7879	−	19.3665i	0.985232	−	0.769747i
$634$	6.60407	+	14.8330i	0.262281	+	0.589093i
$635$	−44.1853	−	19.6726i	−1.75344	−	0.780682i
$636$	14.0911	−	8.80511i	0.558749	−	0.349145i
$637$	23.0411	+	19.3338i	0.912922	+	0.766032i
$638$	0.764548	+	1.03037i	0.0302687	+	0.0407927i
$639$	51.0660	+	29.4830i	2.02014	+	1.16633i
$640$	−0.0843517	−	2.41552i	−0.00333430	−	0.0954817i
$641$	−7.20480	+	7.46079i	−0.284573	+	0.294683i	−0.846374	−	0.532588i	$-0.821219\pi$
$641$	−7.20480	+	7.46079i	−0.284573	+	0.294683i	0.561802	+	0.827272i	$0.310108\pi$
$642$	18.7254	+	19.3907i	0.739031	+	0.765289i
$643$	0.116154	−	3.32622i	0.00458067	−	0.131173i	−0.994946	−	0.100411i	$-0.967984\pi$
$643$	0.116154	−	3.32622i	0.00458067	−	0.131173i	0.999527	−	0.0307624i	$-0.00979352\pi$
$644$	−16.0152	+	25.6297i	−0.631087	+	1.00995i
$645$	−22.8984	−	16.6367i	−0.901623	−	0.655067i
$646$	−8.40165	−	17.7020i	−0.330559	−	0.696477i
$647$	−11.8057	+	36.3341i	−0.464129	+	1.42844i	0.395947	+	0.918273i	$0.370416\pi$
$647$	−11.8057	+	36.3341i	−0.464129	+	1.42844i	−0.860075	+	0.510167i	$0.829584\pi$
$648$	0.672653	−	0.564423i	0.0264243	−	0.0221726i
$649$	−23.0876	+	1.84783i	−0.906266	+	0.0725335i
$650$	0.398947	−	2.26254i	0.0156480	−	0.0887442i
$651$	4.32866	−	30.8000i	0.169653	−	1.20715i
$652$	−10.4883	+	15.5496i	−0.410755	+	0.608969i
$653$	11.0626	−	4.92538i	0.432913	−	0.192745i	−0.178698	−	0.983904i	$-0.557189\pi$
$653$	11.0626	−	4.92538i	0.432913	−	0.192745i	0.611611	+	0.791159i	$0.290522\pi$
$654$	−31.5744	−	28.4297i	−1.23466	−	1.11169i
$655$	0.122883	+	0.0496478i	0.00480142	+	0.00193990i
$656$	−1.70898	−	6.85434i	−0.0667244	−	0.267617i
$657$	20.1874	−	45.3417i	0.787587	−	1.76895i
$658$	−23.2103	+	20.8986i	−0.904831	+	0.814713i
$659$	−22.6186	+	8.23248i	−0.881094	+	0.320692i	−0.742651	−	0.669678i	$-0.766432\pi$
$659$	−22.6186	+	8.23248i	−0.881094	+	0.320692i	−0.138443	+	0.990370i	$0.544210\pi$
$660$	−0.553547	+	22.2670i	−0.0215468	+	0.866741i
$661$	29.7781	+	5.25068i	1.15823	+	0.204228i	0.719567	−	0.694423i	$-0.244340\pi$
$661$	29.7781	+	5.25068i	1.15823	+	0.204228i	0.438666	+	0.898650i	$0.355451\pi$
$662$	17.7635	+	13.8784i	0.690400	+	0.539399i
$663$	−8.24658	+	33.0752i	−0.320271	+	1.28453i
$664$	−8.98631	+	12.3686i	−0.348736	+	0.479994i
$665$	−2.03685	+	44.6781i	−0.0789856	+	1.73254i
$666$	−11.6384	+	3.78154i	−0.450979	+	0.146532i
$667$	2.74735	−	0.192113i	0.106378	−	0.00743865i
$668$	15.1017	−	4.33035i	0.584303	−	0.167546i
$669$	−54.0596	−	28.7440i	−2.09006	−	1.11131i
$670$	−10.6716	+	1.88169i	−0.412280	+	0.0726960i
$671$	−24.3756	+	3.67599i	−0.941008	+	0.141910i
$672$	5.89777	−	10.2152i	0.227511	−	0.394061i
$673$	−12.8138	+	2.72365i	−0.493934	+	0.104989i	−0.448143	−	0.893962i	$-0.647914\pi$
$673$	−12.8138	+	2.72365i	−0.493934	+	0.104989i	−0.0457914	+	0.998951i	$0.514581\pi$
$674$	−22.8539	−	1.59810i	−0.880300	−	0.0615566i
$675$	−3.90504	+	0.973635i	−0.150305	+	0.0374752i
$676$	−3.71514	+	4.12608i	−0.142890	+	0.158695i
$677$	−19.6074	−	4.16769i	−0.753575	−	0.160177i	−0.184920	−	0.982754i	$-0.559203\pi$
$677$	−19.6074	−	4.16769i	−0.753575	−	0.160177i	−0.568655	+	0.822576i	$0.692536\pi$
$678$	−40.2842	−	11.5513i	−1.54711	−	0.443626i
$679$	−25.9171	−	25.0278i	−0.994606	−	0.960480i
$680$	−5.10087	+	9.59335i	−0.195610	+	0.367888i
$681$	12.2205	−	33.5756i	0.468291	−	1.28662i
$682$	−3.75450	+	7.89839i	−0.143767	+	0.302445i
$683$			16.0686i			0.614850i	0.951572	+	0.307425i	$0.0994673\pi$
$683$			16.0686i			0.614850i	−0.951572	+	0.307425i	$0.900533\pi$
$684$	19.1591	−	7.50441i	0.732567	−	0.286938i
$685$	−9.32789	+	6.77711i	−0.356400	+	0.258940i
$686$	1.19083	+	17.0297i	0.0454662	+	0.650197i
$687$	−39.3475	−	1.37405i	−1.50120	−	0.0524231i
$688$	−0.586548	−	4.17351i	−0.0223619	−	0.159113i
$689$	14.6682	+	7.15414i	0.558812	+	0.272551i
$690$	39.6371	+	26.7356i	1.50896	+	1.01781i
$691$	33.3948	+	37.0887i	1.27040	+	1.41092i	0.868846	+	0.495083i	$0.164862\pi$
$691$	33.3948	+	37.0887i	1.27040	+	1.41092i	0.401552	+	0.915836i	$0.368471\pi$
$692$	−10.9808	−	19.0193i	−0.417426	−	0.723004i
$693$	−36.6101	+	55.4714i	−1.39070	+	2.10719i
$694$	−10.4637	+	12.4702i	−0.397197	+	0.473361i
$695$	−1.53525	−	7.22278i	−0.0582353	−	0.273976i
$696$	−1.06901	+	0.112358i	−0.0405208	+	0.00425890i
$697$	−8.75306	+	30.5255i	−0.331546	+	1.15624i
$698$	3.22542	+	6.06613i	0.122084	+	0.229606i
$699$	0.0384172	−	0.00539919i	0.00145307	−	0.000204216i
$700$	2.96278	−	1.99842i	0.111982	−	0.0755331i
$701$	−17.6950	−	4.41187i	−0.668332	−	0.166634i	−0.107044	−	0.994254i	$-0.534139\pi$
$701$	−17.6950	−	4.41187i	−0.668332	−	0.166634i	−0.561288	+	0.827620i	$0.689694\pi$
$702$	−12.4083	−	4.03169i	−0.468319	−	0.152166i
$703$	11.2992	+	0.120355i	0.426156	+	0.00453928i
$704$	−2.44230	+	2.24392i	−0.0920476	+	0.0845709i
$705$	31.7599	+	37.8500i	1.19615	+	1.42551i
$706$	4.13627	−	5.29419i	0.155671	−	0.199249i
$707$	−24.3090	−	49.8409i	−0.914235	−	1.87446i
$708$	8.50617	−	17.4402i	0.319682	−	0.655444i
$709$	−19.3639	−	24.7846i	−0.727226	−	0.930807i	0.272281	−	0.962218i	$-0.412222\pi$
$709$	−19.3639	−	24.7846i	−0.727226	−	0.930807i	−0.999507	+	0.0314111i	$0.990000\pi$
$710$	−6.27715	+	29.5317i	−0.235577	+	1.10830i
$711$	−2.50222	+	23.8071i	−0.0938407	+	0.892835i
$712$	0.661407	−	9.45856i	0.0247873	−	0.354474i
$713$	9.94760	+	15.9195i	0.372541	+	0.596190i
$714$	−45.9207	+	26.5123i	−1.71854	+	0.992199i
$715$	−18.8350	+	11.1283i	−0.704390	+	0.416176i
$716$	5.44993	+	14.9736i	0.203674	+	0.559589i
$717$	−49.8870	−	7.01116i	−1.86307	−	0.261837i
$718$	20.6006	−	10.0476i	0.768809	−	0.374973i
$719$	−6.75205	−	10.0103i	−0.251809	−	0.373322i	0.681846	−	0.731496i	$-0.261177\pi$
$719$	−6.75205	−	10.0103i	−0.251809	−	0.373322i	−0.933655	+	0.358173i	$0.883400\pi$
$720$	−9.67582	−	6.04612i	−0.360596	−	0.225326i
$721$	−8.12762	−	25.0142i	−0.302688	−	0.931579i
$722$	−18.9776	+	0.921340i	−0.706275	+	0.0342887i
$723$	−14.0885	−	19.3912i	−0.523957	−	0.721166i
$724$	−0.565682	+	0.228550i	−0.0210234	+	0.00849401i
$725$	−0.306027	−	0.111385i	−0.0113656	−	0.00413673i
$726$	23.7020	−	19.2977i	0.879663	−	0.716206i
$727$	−3.77482	−	21.4080i	−0.140000	−	0.793980i	−0.971247	−	0.238076i	$-0.923483\pi$
$727$	−3.77482	−	21.4080i	−0.140000	−	0.793980i	0.831246	−	0.555904i	$-0.187628\pi$
$728$	11.5783	−	0.404322i	0.429119	−	0.0149852i
$729$	−4.59880	−	43.7547i	−0.170326	−	1.62054i
$730$	25.2735	+	2.65635i	0.935413	+	0.0983158i
$731$	−7.09715	+	17.5661i	−0.262498	+	0.649704i
$732$	7.73643	−	19.1483i	0.285947	−	0.707743i
$733$	−20.0904	−	2.11159i	−0.742058	−	0.0779934i	−0.274047	−	0.961716i	$-0.588362\pi$
$733$	−20.0904	−	2.11159i	−0.742058	−	0.0779934i	−0.468011	+	0.883723i	$0.655029\pi$
$734$	0.889669	+	8.46464i	0.0328383	+	0.312435i
$735$	73.9723	−	2.58317i	2.72851	−	0.0952817i
$736$	1.23623	+	7.01100i	0.0455680	+	0.258429i
$737$	11.4863	+	9.44301i	0.423102	+	0.347838i
$738$	−31.3357	−	11.4053i	−1.15348	−	0.419834i
$739$	48.9263	−	19.7675i	1.79978	−	0.727160i	0.809673	−	0.586882i	$-0.199645\pi$
$739$	48.9263	−	19.7675i	1.79978	−	0.727160i	0.990112	−	0.140279i	$-0.0447998\pi$
$740$	−3.68288	−	5.06905i	−0.135386	−	0.186342i
$741$	26.5322	+	19.7120i	0.974686	+	0.724137i
$742$	7.84472	+	24.1436i	0.287989	+	0.886338i
$743$	22.0525	+	13.7799i	0.809028	+	0.505537i	0.870264	−	0.492586i	$-0.163948\pi$
$743$	22.0525	+	13.7799i	0.809028	+	0.505537i	−0.0612353	+	0.998123i	$0.519504\pi$
$744$	−4.09700	−	6.07405i	−0.150203	−	0.222685i
$745$	22.6849	−	11.0642i	0.831111	−	0.405360i
$746$	7.75052	+	1.08926i	0.283767	+	0.0398808i
$747$	24.6835	+	67.8173i	0.903121	+	2.48131i
$748$	14.5516	−	3.24625i	0.532058	−	0.118695i
$749$	−35.6664	+	20.5920i	−1.30322	+	0.752415i
$750$	14.7982	+	23.6821i	0.540355	+	0.864748i
$751$	0.772776	−	11.0512i	0.0281990	−	0.403265i	−0.962875	−	0.269949i	$-0.912993\pi$
$751$	0.772776	−	11.0512i	0.0281990	−	0.403265i	0.991074	−	0.133316i	$-0.0425624\pi$
$752$	−0.769038	+	7.31690i	−0.0280439	+	0.266820i
$753$	−1.90787	+	8.97580i	−0.0695265	+	0.327096i
$754$	−0.649980	−	0.831937i	−0.0236709	−	0.0302974i
$755$	−7.30288	+	14.9731i	−0.265779	+	0.544928i
$756$	−8.89664	−	18.2408i	−0.323568	−	0.663412i
$757$	−5.23832	+	6.70475i	−0.190390	+	0.243688i	−0.873729	−	0.486413i	$-0.838305\pi$
$757$	−5.23832	+	6.70475i	−0.190390	+	0.243688i	0.683339	+	0.730101i	$0.260527\pi$
$758$	11.0118	+	13.1233i	0.399966	+	0.476661i
$759$	−7.51330	−	65.1752i	−0.272716	−	2.36571i
$760$	6.68569	+	8.14227i	0.242515	+	0.295351i
$761$	−22.0643	−	7.16912i	−0.799830	−	0.259881i	−0.119546	−	0.992829i	$-0.538144\pi$
$761$	−22.0643	−	7.16912i	−0.799830	−	0.259881i	−0.680284	+	0.732948i	$0.738144\pi$
$762$	−53.9512	−	13.4515i	−1.95445	−	0.487298i
$763$	53.8152	−	36.2988i	1.94824	−	1.31411i
$764$	−22.1329	+	3.11058i	−0.800741	+	0.112537i
$765$	24.0789	+	45.2858i	0.870575	+	1.63731i
$766$	3.82927	−	13.3542i	0.138357	−	0.482508i
$767$	18.9538	−	1.99213i	0.684383	−	0.0719316i
$768$	−0.577701	−	2.71787i	−0.0208460	−	0.0980726i
$769$	13.3441	−	15.9028i	0.481199	−	0.573471i	−0.469757	−	0.882796i	$-0.655659\pi$
$769$	13.3441	−	15.9028i	0.481199	−	0.573471i	0.950956	+	0.309325i	$0.100103\pi$
$770$	−32.8046	−	9.05071i	−1.18220	−	0.326165i
$771$	−19.8373	−	34.3591i	−0.714421	−	1.23741i
$772$	11.3945	+	12.6549i	0.410097	+	0.455459i
$773$	17.2034	+	11.6039i	0.618764	+	0.417362i	0.828178	−	0.560465i	$-0.189378\pi$
$773$	17.2034	+	11.6039i	0.618764	+	0.417362i	−0.209414	+	0.977827i	$0.567156\pi$
$774$	−17.8814	−	8.72132i	−0.642732	−	0.313482i
$775$	−0.308934	−	2.19818i	−0.0110972	−	0.0789610i
$776$	−8.48190	−	0.296195i	−0.304483	−	0.0106328i
$777$	−2.13303	−	30.5037i	−0.0765220	−	1.09432i
$778$	20.0240	−	14.5483i	0.717896	−	0.521582i
$779$	24.0612	+	19.2148i	0.862080	+	0.688443i
$780$		−	18.3279i		−	0.656245i
$781$	36.3823	−	19.8165i	1.30186	−	0.709090i
$782$	10.9456	−	30.0729i	0.391415	−	1.07540i
$783$	−0.868247	+	1.63294i	−0.0310286	+	0.0583564i
$784$	7.92810	+	7.65608i	0.283146	+	0.273431i
$785$	50.6201	+	14.5151i	1.80671	+	0.518065i
$786$	0.149032	+	0.0316776i	0.00531578	+	0.00112990i
$787$	19.8146	−	22.0063i	0.706314	−	0.784441i	−0.278054	−	0.960565i	$-0.589689\pi$
$787$	19.8146	−	22.0063i	0.706314	−	0.784441i	0.984368	+	0.176124i	$0.0563561\pi$
$788$	−5.68620	+	1.41773i	−0.202562	+	0.0505045i
$789$	77.6201	+	5.42772i	2.76335	+	0.193232i
$790$	−11.9889	+	2.54832i	−0.426545	+	0.0906650i
$791$	32.0135	−	55.4490i	1.13827	−	1.97154i
$792$	2.33467	+	15.4812i	0.0829588	+	0.550101i
$793$	19.9759	−	3.52230i	0.709366	−	0.125080i
$794$	−17.0303	−	9.05520i	−0.604384	−	0.321357i
$795$	38.6048	−	11.0698i	1.36917	−	0.392604i
$796$	12.5531	−	0.877797i	0.444932	−	0.0311127i
$797$	−23.9118	+	7.76941i	−0.846999	+	0.275207i	−0.700188	−	0.713958i	$-0.746901\pi$
$797$	−23.9118	+	7.76941i	−0.846999	+	0.275207i	−0.146810	+	0.989165i	$0.546901\pi$
$798$	6.61296	+	50.9885i	0.234096	+	1.80497i
$799$	19.4398	−	26.7566i	0.687731	−	0.946580i
$800$	0.203660	−	0.816836i	0.00720047	−	0.0288795i
$801$	−35.2702	−	27.5561i	−1.24621	−	0.973648i
$802$	−17.8800	−	3.15273i	−0.631365	−	0.111327i
$803$	−19.7896	−	28.7124i	−0.698359	−	1.01324i
$804$	−11.7061	+	4.26068i	−0.412843	+	0.150262i
$805$	−54.2839	+	48.8774i	−1.91326	+	1.72270i
$806$	2.92690	−	6.57392i	0.103096	−	0.231557i
$807$	−4.53406	−	18.1851i	−0.159607	−	0.640147i
$808$	−12.1115	−	4.89336i	−0.426081	−	0.172148i
$809$	7.44405	+	6.70266i	0.261719	+	0.235653i	0.789534	−	0.613706i	$-0.210322\pi$
$809$	7.44405	+	6.70266i	0.261719	+	0.235653i	−0.527815	+	0.849359i	$0.676989\pi$
$810$	1.93884	−	0.863228i	0.0681239	−	0.0303307i
$811$	−22.8172	+	33.8278i	−0.801219	+	1.18786i	0.177796	+	0.984067i	$0.443103\pi$
$811$	−22.8172	+	33.8278i	−0.801219	+	1.18786i	−0.979015	+	0.203788i	$0.934675\pi$
$812$	0.228556	−	1.62626i	0.00802075	−	0.0570706i
$813$	2.74508	−	15.5681i	0.0962742	−	0.545998i
$814$	−1.99605	+	8.36296i	−0.0699615	+	0.293122i
$815$	−34.7275	+	29.1398i	−1.21645	+	1.02072i
$816$	−3.85982	+	11.8793i	−0.135121	+	0.415858i
$817$	13.0781	+	12.9014i	0.457544	+	0.451362i
$818$	−4.85266	−	3.52566i	−0.169669	−	0.123272i
$819$	28.9808	−	46.3789i	1.01267	−	1.62061i
$820$	0.595876	−	17.0636i	0.0208089	−	0.595888i
$821$	38.3783	+	39.7419i	1.33941	+	1.38700i	0.860771	+	0.508992i	$0.169982\pi$
$821$	38.3783	+	39.7419i	1.33941	+	1.38700i	0.478642	+	0.878010i	$0.341129\pi$
$822$	−9.20760	+	9.53474i	−0.321152	+	0.332562i
$823$	−1.26144	−	36.1228i	−0.0439710	−	1.25916i	−0.798136	−	0.602478i	$-0.794180\pi$
$823$	−1.26144	−	36.1228i	−0.0439710	−	1.25916i	0.754165	−	0.656685i	$-0.228042\pi$
$824$	−5.36560	−	3.09783i	−0.186919	−	0.107918i
$825$	−2.32307	+	7.40204i	−0.0808790	+	0.257706i
$826$	22.7099	+	19.0559i	0.790180	+	0.663040i
$827$	12.5662	−	7.85221i	0.436968	−	0.273048i	−0.293547	−	0.955945i	$-0.594836\pi$
$827$	12.5662	−	7.85221i	0.436968	−	0.273048i	0.730515	+	0.682897i	$0.239280\pi$
$828$	30.7009	+	13.6689i	1.06693	+	0.475028i
$829$	14.3499	+	32.2304i	0.498393	+	1.11941i	0.971205	+	0.238245i	$0.0765722\pi$
$829$	14.3499	+	32.2304i	0.498393	+	1.11941i	−0.472812	+	0.881163i	$0.656761\pi$
$830$	−29.1185	+	22.7499i	−1.01072	+	0.789660i
$831$	−63.0459	+	33.5221i	−2.18704	+	1.16287i
$832$	1.96313	−	1.89577i	0.0680592	−	0.0657240i
$833$	−13.6563	−	47.6252i	−0.473163	−	1.65012i
$834$	−3.17998	−	7.87072i	−0.110114	−	0.272541i
$835$	37.9717			1.31406
$836$	2.51893	−	14.2357i	0.0871191	−	0.492352i
$837$	−12.6058			−0.435720
$838$	−4.54212	−	11.2421i	−0.156905	−	0.388353i
$839$	11.3417	+	39.5532i	0.391559	+	1.36553i	0.872431	+	0.488737i	$0.162542\pi$
$839$	11.3417	+	39.5532i	0.391559	+	1.36553i	−0.480873	+	0.876790i	$0.659680\pi$
$840$	20.5082	−	19.8045i	0.707599	−	0.683320i
$841$	25.4733	−	13.5444i	0.878391	−	0.467049i
$842$	−15.6233	+	12.2063i	−0.538414	+	0.420655i
$843$	36.6509	+	82.3193i	1.26233	+	2.83523i
$844$	10.3422	+	4.60466i	0.355994	+	0.158499i
$845$	−11.3805	+	7.11130i	−0.391500	+	0.244636i
$846$	26.6047	+	22.3240i	0.914690	+	0.767516i
$847$	19.8470	+	42.2691i	0.681952	+	1.45238i
$848$	5.17883	+	2.99000i	0.177842	+	0.102677i
$849$	−2.46114	−	70.4779i	−0.0844662	−	2.41879i
$850$	−2.62883	+	2.72223i	−0.0901681	+	0.0933718i
$851$	12.8202	+	13.2757i	0.439470	+	0.455085i
$852$	−1.21130	+	34.6871i	−0.0414985	+	1.18836i
$853$	5.39732	−	8.63752i	0.184801	−	0.295743i	−0.742656	−	0.669673i	$-0.766434\pi$
$853$	5.39732	−	8.63752i	0.184801	−	0.295743i	0.927457	+	0.373930i	$0.121990\pi$
$854$	25.5266	+	18.5462i	0.873502	+	0.634636i
$855$	49.5130	−	4.67140i	1.69331	−	0.159759i
$856$	−2.99790	+	9.22659i	−0.102466	+	0.315358i
$857$	−27.1461	+	22.7783i	−0.927293	+	0.778091i	−0.975329	−	0.220755i	$-0.929148\pi$
$857$	−27.1461	+	22.7783i	−0.927293	+	0.778091i	0.0480366	+	0.998846i	$0.484704\pi$
$858$	−19.1024	+	16.3588i	−0.652145	+	0.558481i
$859$	−2.19999	+	12.4768i	−0.0750627	+	0.425702i	0.923999	+	0.382395i	$0.124901\pi$
$859$	−2.19999	+	12.4768i	−0.0750627	+	0.425702i	−0.999062	+	0.0433071i	$0.986211\pi$
$860$	1.41768	−	10.0873i	0.0483425	−	0.343975i
$861$	46.5952	−	69.0802i	1.58796	−	2.35425i
$862$	−1.17151	+	0.521591i	−0.0399018	+	0.0177654i
$863$	−33.6670	−	30.3139i	−1.14604	−	1.03190i	−0.999086	−	0.0427546i	$-0.986387\pi$
$863$	−33.6670	−	30.3139i	−1.14604	−	1.03190i	−0.146953	−	0.989143i	$-0.546947\pi$
$864$	−4.43257	−	1.79088i	−0.150799	−	0.0609268i
$865$	−12.8414	−	51.5041i	−0.436621	−	1.75119i
$866$	7.22784	−	16.2340i	0.245612	−	0.551654i
$867$	6.62391	−	5.96419i	0.224960	−	0.202555i
$868$	10.5186	−	3.82847i	0.357026	−	0.129947i
$869$	13.3568	+	10.2210i	0.453100	+	0.346722i
$870$	−2.55855	−	0.451142i	−0.0867430	−	0.0152951i
$871$	−9.64160	−	7.53285i	−0.326693	−	0.255241i
$872$	3.69924	−	14.8368i	0.125272	−	0.502439i
$873$	−23.5488	+	32.4122i	−0.797006	+	1.09699i
$874$	−22.8386	−	21.0087i	−0.772526	−	0.710630i
$875$	−40.5766	+	13.1841i	−1.37174	+	0.445705i
$876$	29.1434	−	2.03791i	0.984664	−	0.0688544i
$877$	28.3661	−	8.13385i	0.957855	−	0.274660i	0.239937	−	0.970788i	$-0.422873\pi$
$877$	28.3661	−	8.13385i	0.957855	−	0.274660i	0.717918	+	0.696128i	$0.245095\pi$
$878$	14.5865	+	7.75579i	0.492271	+	0.261745i
$879$	41.1510	−	7.25603i	1.38799	−	0.244740i
$880$	−7.16927	+	3.58634i	−0.241676	+	0.120895i
$881$	−10.6742	+	18.4883i	−0.359623	+	0.622886i	−0.987898	−	0.155106i	$-0.950428\pi$
$881$	−10.6742	+	18.4883i	−0.359623	+	0.622886i	0.628275	+	0.777992i	$0.283761\pi$
$882$	50.8899	−	10.8170i	1.71355	−	0.364227i
$883$	−38.4980	−	2.69204i	−1.29556	−	0.0905943i	−0.594731	−	0.803925i	$-0.702742\pi$
$883$	−38.4980	−	2.69204i	−1.29556	−	0.0905943i	−0.700828	+	0.713330i	$0.747186\pi$
$884$	−11.9036	+	2.96790i	−0.400362	+	0.0998214i
$885$	31.3818	−	34.8530i	1.05489	−	1.17157i
$886$	3.31681	+	0.705011i	0.111431	+	0.0236853i
$887$	−5.11951	−	1.46799i	−0.171896	−	0.0492904i	0.188585	−	0.982057i	$-0.439610\pi$
$887$	−5.11951	−	1.46799i	−0.171896	−	0.0492904i	−0.360481	+	0.932766i	$0.617388\pi$
$888$	−5.18146	−	5.00368i	−0.173879	−	0.167913i
$889$	39.8819	−	75.0070i	1.33760	−	2.51565i
$890$	7.83810	−	21.5350i	0.262734	−	0.721855i
$891$	−2.63024	−	1.25028i	−0.0881165	−	0.0418861i
$892$		−	22.0350i		−	0.737787i
$893$	−16.7035	−	27.3758i	−0.558962	−	0.916096i
$894$	23.4738	−	17.0547i	0.785082	−	0.570396i
$895$	2.68658	+	38.4198i	0.0898023	+	1.28423i
$896$	4.24257	+	0.148154i	0.141734	+	0.00494947i
$897$	7.51315	+	53.4589i	0.250857	+	1.78494i
$898$	−35.6350	−	17.3803i	−1.18915	−	0.579990i
$899$	−0.845665	−	0.570408i	−0.0282045	−	0.0190242i
$900$	−2.65909	−	2.95322i	−0.0886365	−	0.0984408i
$901$	−13.4410	−	23.2805i	−0.447784	−	0.775585i
$902$	−18.3166	+	14.6093i	−0.609874	+	0.486437i
$903$	31.9546	−	38.0820i	1.06338	−	1.26729i
$904$	−3.13580	−	14.7528i	−0.104295	−	0.490670i
$905$	−1.46655	+	0.154140i	−0.0487497	+	0.00512380i
$906$	−5.27885	+	18.4095i	−0.175378	+	0.611616i
$907$	7.62469	+	14.3400i	0.253174	+	0.476150i	0.976832	−	0.214008i	$-0.0686519\pi$
$907$	7.62469	+	14.3400i	0.253174	+	0.476150i	−0.723658	+	0.690159i	$0.757541\pi$
$908$	12.7340	−	1.78965i	0.422594	−	0.0593917i
$909$	−51.1209	+	34.4815i	−1.69557	+	1.14368i
$910$	27.1698	+	6.77420i	0.900671	+	0.224563i
$911$	15.2124	+	4.94281i	0.504010	+	0.163763i	0.549976	−	0.835180i	$-0.314637\pi$
$911$	15.2124	+	4.94281i	0.504010	+	0.163763i	−0.0459665	+	0.998943i	$0.514637\pi$
$912$	9.19456	+	7.88355i	0.304462	+	0.261051i
$913$	49.7014	+	10.0433i	1.64487	+	0.332384i
$914$	12.7179	+	15.1566i	0.420672	+	0.501337i
$915$	30.7314	−	39.3344i	1.01595	−	1.30035i
$916$	−6.21155	−	12.7356i	−0.205235	−	0.420795i
$917$	−0.102044	+	0.209220i	−0.00336977	+	0.00690906i
$918$	13.2310	+	16.9349i	0.436688	+	0.558935i
$919$	4.11877	−	19.3773i	0.135866	−	0.639198i	−0.856529	−	0.516099i	$-0.827383\pi$
$919$	4.11877	−	19.3773i	0.135866	−	0.639198i	0.992394	−	0.123099i	$-0.0392832\pi$
$920$	−1.79861	+	17.1127i	−0.0592986	+	0.564188i
$921$	−1.33581	+	19.1029i	−0.0440163	+	0.629462i
$922$	10.7880	+	17.2644i	0.355284	+	0.568573i
$923$	−29.5225	+	17.0449i	−0.971747	+	0.561038i
$924$	−38.9462	−	3.69800i	−1.28124	−	0.121655i
$925$	−0.746409	−	2.05074i	−0.0245418	−	0.0674280i
$926$	2.92256	+	0.410739i	0.0960412	+	0.0134977i
$927$	−26.2869	+	12.8210i	−0.863376	+	0.421097i
$928$	−0.216324	−	0.320714i	−0.00710120	−	0.0105280i
$929$	3.09225	+	1.93225i	0.101454	+	0.0633952i	0.579697	−	0.814832i	$-0.303171\pi$
$929$	3.09225	+	1.93225i	0.101454	+	0.0633952i	−0.478244	+	0.878227i	$0.658726\pi$
$930$	−5.47219	−	16.8417i	−0.179440	−	0.552260i
$931$	−47.7216	−	5.53025i	−1.56401	−	0.181247i
$932$	0.00820669	+	0.0112955i	0.000268819	+	0.000369998i
$933$	−49.7372	+	20.0951i	−1.62832	+	0.657885i
$934$	33.6331	+	12.2415i	1.10051	+	0.400553i
$935$	35.9713	+	2.15224i	1.17639	+	0.0703858i
$936$	−2.23706	−	12.6870i	−0.0731204	−	0.414687i
$937$	27.5658	−	0.962620i	0.900536	−	0.0314474i	0.419111	−	0.907935i	$-0.362342\pi$
$937$	27.5658	−	0.962620i	0.900536	−	0.0314474i	0.481425	+	0.876487i	$0.340119\pi$
$938$	−1.98944	−	18.9283i	−0.0649576	−	0.618030i
$939$	55.7103	+	5.85538i	1.81804	+	0.191083i
$940$	−6.66137	+	16.4875i	−0.217270	+	0.537762i
$941$	7.50092	−	18.5654i	0.244523	−	0.605215i	−0.754151	−	0.656701i	$-0.771951\pi$
$941$	7.50092	−	18.5654i	0.244523	−	0.605215i	0.998674	+	0.0514859i	$0.0163957\pi$
$942$	60.2067	+	6.32798i	1.96164	+	0.206177i
$943$	5.25684	+	50.0155i	0.171186	+	1.62873i
$944$	6.97917	−	0.243718i	0.227153	−	0.00793234i
$945$	−8.51783	−	48.3070i	−0.277085	−	1.57143i
$946$	−11.7789	+	7.52599i	−0.382967	+	0.244691i
$947$	9.45994	+	3.44314i	0.307407	+	0.111887i	0.491117	−	0.871093i	$-0.336589\pi$
$947$	9.45994	+	3.44314i	0.307407	+	0.111887i	−0.183710	+	0.982980i	$0.558811\pi$
$948$	−13.0644	+	5.27836i	−0.424312	+	0.171433i
$949$	16.8659	+	23.2139i	0.547489	+	0.753554i
$950$	1.45673	+	3.36797i	0.0472626	+	0.109271i
$951$	13.9414	+	42.9071i	0.452079	+	1.39136i
$952$	−16.1836	−	10.1126i	−0.524513	−	0.327752i
$953$	−14.2334	−	21.1019i	−0.461066	−	0.683558i	0.524775	−	0.851241i	$-0.324149\pi$
$953$	−14.2334	−	21.1019i	−0.461066	−	0.683558i	−0.985841	+	0.167683i	$0.946372\pi$
$954$	25.3719	−	12.3747i	0.821447	−	0.400646i
$955$	−53.4950	−	7.51824i	−1.73106	−	0.243284i
$956$	−6.20101	−	17.0371i	−0.200555	−	0.551020i
$957$	1.81346	+	3.06934i	0.0586210	+	0.0992177i
$958$	−17.3653	+	10.0258i	−0.561046	+	0.323920i
$959$	−10.7314	−	17.1738i	−0.346533	−	0.554569i
$960$	0.468472	−	6.69946i	0.0151199	−	0.216224i
$961$	−2.51362	+	23.9155i	−0.0810844	+	0.771466i
$962$	1.47092	−	6.92011i	0.0474242	−	0.223113i
$963$	28.1948	+	36.0877i	0.908564	+	1.16291i
$964$	3.78150	−	7.75323i	0.121794	−	0.249715i
$965$	18.0427	+	36.9930i	0.580815	+	1.19085i
$966$	−51.6998	+	66.1727i	−1.66341	+	2.12907i
$967$	7.72336	+	9.20434i	0.248367	+	0.295992i	0.875796	−	0.482682i	$-0.160337\pi$
$967$	7.72336	+	9.20434i	0.248367	+	0.295992i	−0.627429	+	0.778674i	$0.715893\pi$
$968$	10.1369	+	4.27118i	0.325813	+	0.137281i
$969$	−18.0754	−	51.3574i	−0.580667	−	1.64984i
$970$	−19.5092	−	6.33892i	−0.626402	−	0.203530i
$971$	17.3690	+	4.33059i	0.557399	+	0.138975i	0.510427	−	0.859921i	$-0.329487\pi$
$971$	17.3690	+	4.33059i	0.557399	+	0.138975i	0.0469721	+	0.998896i	$0.485043\pi$
$972$	13.9128	−	9.38432i	0.446254	−	0.301002i
$973$	12.8431	−	1.80499i	0.411732	−	0.0578652i
$974$	8.89055	+	16.7207i	0.284872	+	0.535766i
$975$	1.75957	−	6.13636i	0.0563514	−	0.196521i
$976$	7.39189	−	0.776919i	0.236609	−	0.0248686i
$977$	3.46375	+	16.2956i	0.110815	+	0.521344i	0.998182	+	0.0602791i	$0.0191991\pi$
$977$	3.46375	+	16.2956i	0.110815	+	0.521344i	−0.887367	+	0.461065i	$0.847468\pi$
$978$	−33.4993	+	39.9229i	−1.07119	+	1.27660i
$979$	−29.4410	+	11.0520i	−0.940938	+	0.353225i
$980$	13.3193	+	23.0696i	0.425468	+	0.736932i
$981$	−48.2992	−	53.6418i	−1.54208	−	1.71265i
$982$	7.89598	+	5.32590i	0.251971	+	0.169956i
$983$	1.79809	+	0.876989i	0.0573503	+	0.0279716i	0.466823	−	0.884351i	$-0.345398\pi$
$983$	1.79809	+	0.876989i	0.0573503	+	0.0279716i	−0.409473	+	0.912322i	$0.634287\pi$
$984$	−2.73175	−	19.4374i	−0.0870850	−	0.619642i
$985$	−14.1556	−	0.494324i	−0.451035	−	0.0157505i
$986$	0.121308	+	1.73478i	0.00386323	+	0.0552467i
$987$	−70.2083	+	51.0093i	−2.23475	+	1.62364i
$988$	−1.78094	+	11.7617i	−0.0566593	+	0.374188i
$989$			30.0039i			0.954067i
$990$	−4.88952	+	37.5239i	−0.155399	+	1.19259i
$991$	−7.16660	+	19.6901i	−0.227654	+	0.625475i	−0.999952	−	0.00978540i	$-0.996885\pi$
$991$	−7.16660	+	19.6901i	−0.227654	+	0.625475i	0.772298	+	0.635261i	$0.219107\pi$
$992$	1.23791	−	2.32817i	0.0393037	−	0.0739195i
$993$	45.0563	+	43.5104i	1.42982	+	1.38076i
$994$	−50.9735	−	14.6164i	−1.61678	−	0.463604i
$995$	29.7501	+	6.32358i	0.943142	+	0.200471i
$996$	−28.4248	+	31.5689i	−0.900674	+	1.00030i
$997$	5.21876	−	1.30118i	0.165280	−	0.0412089i	−0.158403	−	0.987375i	$-0.550634\pi$
$997$	5.21876	−	1.30118i	0.165280	−	0.0412089i	0.323683	+	0.946166i	$0.395079\pi$
$998$	−30.9620	−	2.16507i	−0.980084	−	0.0685342i
$999$	−12.1224	+	2.57670i	−0.383536	+	0.0815231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.a.13.9	✓	240
11.6	odd	10		418.2.v.b.127.2	yes	240
19.3	odd	18		418.2.v.b.79.2	yes	240
209.193	even	90	inner	418.2.v.a.193.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.13.9	✓	240	1.1	even	1	trivial
418.2.v.a.193.9	yes	240	209.193	even	90	inner
418.2.v.b.79.2	yes	240	19.3	odd	18
418.2.v.b.127.2	yes	240	11.6	odd	10

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)

\(f(q)\)	\(=\)	\(q+(0.374607 + 0.927184i) q^{2} +(0.765882 + 2.67095i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-2.13408 + 1.13471i) q^{5} +(-2.18956 + 1.71067i) q^{6} +(-1.72666 - 3.87814i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-4.00325 + 2.50151i) q^{9} +O(q^{10})\)	\(q+(0.374607 + 0.927184i) q^{2} +(0.765882 + 2.67095i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(-2.13408 + 1.13471i) q^{5} +(-2.18956 + 1.71067i) q^{6} +(-1.72666 - 3.87814i) q^{7} +(-0.913545 - 0.406737i) q^{8} +(-4.00325 + 2.50151i) q^{9} +(-1.85152 - 1.55361i) q^{10} +(0.0333387 + 3.31646i) q^{11} +(-2.40633 - 1.38929i) q^{12} +(-0.0952431 - 2.72741i) q^{13} +(2.94893 - 3.05371i) q^{14} +(-4.66520 - 4.83096i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(-2.38215 + 3.81224i) q^{17} +(-3.81900 - 2.77467i) q^{18} +(2.52439 + 3.55351i) q^{19} +(0.746891 - 2.29869i) q^{20} +(9.03591 - 7.58203i) q^{21} +(-3.06248 + 1.27328i) q^{22} +(-1.23623 + 7.01100i) q^{23} +(0.386705 - 2.75155i) q^{24} +(0.470752 - 0.697919i) q^{25} +(2.49313 - 1.11001i) q^{26} +(-3.55274 - 3.19890i) q^{27} +(3.93604 + 1.59026i) q^{28} +(-0.0935878 - 0.375360i) q^{29} +(2.73157 - 6.13520i) q^{30} +(1.95954 - 1.76438i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-8.83256 + 2.62906i) q^{33} +(-4.42702 - 0.780604i) q^{34} +(8.08539 + 6.31700i) q^{35} +(1.14200 - 4.58033i) q^{36} +(1.52375 - 2.09726i) q^{37} +(-2.34911 + 3.67174i) q^{38} +(7.21182 - 2.34326i) q^{39} +(2.41110 - 0.168601i) q^{40} +(6.79052 - 1.94715i) q^{41} +(10.4148 + 5.53767i) q^{42} +(4.15049 - 0.731844i) q^{43} +(-2.32779 - 2.36250i) q^{44} +(5.70476 - 9.88093i) q^{45} +(-6.96359 + 1.48016i) q^{46} +(-7.33929 - 0.513213i) q^{47} +(2.69605 - 0.672201i) q^{48} +(-7.37473 + 8.19047i) q^{49} +(0.823446 + 0.175029i) q^{50} +(-12.0068 - 3.44288i) q^{51} +(1.96313 + 1.89577i) q^{52} +(-2.80744 + 5.28003i) q^{53} +(1.63509 - 4.49237i) q^{54} +(-3.83436 - 7.03974i) q^{55} +4.24516i q^{56} +(-7.55786 + 9.46409i) q^{57} +(0.312969 - 0.227385i) q^{58} +(0.487139 + 6.96641i) q^{59} +(6.71173 + 0.234379i) q^{60} +(1.03442 + 7.36028i) q^{61} +(2.36996 + 1.15590i) q^{62} +(16.6135 + 11.2059i) q^{63} +(0.669131 + 0.743145i) q^{64} +(3.29806 + 5.71242i) q^{65} +(-5.74636 - 7.20454i) q^{66} +(2.88184 - 3.43445i) q^{67} +(-0.934629 - 4.39708i) q^{68} +(-19.6728 + 2.06770i) q^{69} +(-2.82818 + 9.86303i) q^{70} +(-5.86433 - 11.0292i) q^{71} +(4.67461 - 0.656973i) q^{72} +(-8.71665 + 5.87946i) q^{73} +(2.51535 + 0.627147i) q^{74} +(2.22465 + 0.722832i) q^{75} +(-4.28437 - 0.802594i) q^{76} +(12.8041 - 5.85569i) q^{77} +(4.87423 + 5.80888i) q^{78} +(3.12206 - 3.99606i) q^{79} +(1.05954 + 2.17238i) q^{80} +(-0.384928 + 0.789219i) q^{81} +(4.34914 + 5.56665i) q^{82} +(3.17864 - 14.9543i) q^{83} +(-1.23297 + 11.7309i) q^{84} +(0.757914 - 10.8387i) q^{85} +(2.23336 + 3.57412i) q^{86} +(0.930890 - 0.537450i) q^{87} +(1.31847 - 3.04329i) q^{88} +(3.24292 + 8.90984i) q^{89} +(11.2985 + 1.58790i) q^{90} +(-10.4128 + 5.07867i) q^{91} +(-3.98098 - 5.90205i) q^{92} +(6.21333 + 3.88252i) q^{93} +(-2.27350 - 6.99712i) q^{94} +(-9.41944 - 4.71902i) q^{95} +(1.63321 + 2.24792i) q^{96} +(7.86908 - 3.17931i) q^{97} +(-10.3567 - 3.76953i) q^{98} +(-8.42961 - 13.1932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 12 q^{6} + 33 q^{7} - 30 q^{8} + 3 q^{9} - 3 q^{11} - 6 q^{13} - 18 q^{14} + 21 q^{15} + 21 q^{17} - 60 q^{18} + 45 q^{19} + 12 q^{20} + 48 q^{21} - 12 q^{22} + 12 q^{24} - 18 q^{25} - 96 q^{26} - 9 q^{27} - 6 q^{28} + 18 q^{29} + 9 q^{31} + 87 q^{33} - 24 q^{34} - 36 q^{35} - 12 q^{36} - 36 q^{38} + 60 q^{41} - 6 q^{42} - 12 q^{43} + 18 q^{44} + 48 q^{45} + 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} - 21 q^{50} - 75 q^{51} + 3 q^{52} - 39 q^{53} + 27 q^{54} - 126 q^{55} - 90 q^{57} - 24 q^{58} + 69 q^{59} - 42 q^{60} + 66 q^{61} - 45 q^{62} - 9 q^{63} + 30 q^{64} - 12 q^{66} - 9 q^{67} + 12 q^{68} - 54 q^{69} + 9 q^{70} + 48 q^{71} + 6 q^{72} - 12 q^{74} + 72 q^{77} - 36 q^{79} - 27 q^{81} + 45 q^{82} + 36 q^{83} + 36 q^{84} - 210 q^{85} + 3 q^{86} + 216 q^{87} + 3 q^{88} + 18 q^{89} - 96 q^{90} - 108 q^{91} - 30 q^{92} + 147 q^{93} - 18 q^{94} + 66 q^{95} - 9 q^{97} - 12 q^{98} - 42 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 12 * q^6 + 33 * q^7 - 30 * q^8 + 3 * q^9 - 3 * q^11 - 6 * q^13 - 18 * q^14 + 21 * q^15 + 21 * q^17 - 60 * q^18 + 45 * q^19 + 12 * q^20 + 48 * q^21 - 12 * q^22 + 12 * q^24 - 18 * q^25 - 96 * q^26 - 9 * q^27 - 6 * q^28 + 18 * q^29 + 9 * q^31 + 87 * q^33 - 24 * q^34 - 36 * q^35 - 12 * q^36 - 36 * q^38 + 60 * q^41 - 6 * q^42 - 12 * q^43 + 18 * q^44 + 48 * q^45 + 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 - 21 * q^50 - 75 * q^51 + 3 * q^52 - 39 * q^53 + 27 * q^54 - 126 * q^55 - 90 * q^57 - 24 * q^58 + 69 * q^59 - 42 * q^60 + 66 * q^61 - 45 * q^62 - 9 * q^63 + 30 * q^64 - 12 * q^66 - 9 * q^67 + 12 * q^68 - 54 * q^69 + 9 * q^70 + 48 * q^71 + 6 * q^72 - 12 * q^74 + 72 * q^77 - 36 * q^79 - 27 * q^81 + 45 * q^82 + 36 * q^83 + 36 * q^84 - 210 * q^85 + 3 * q^86 + 216 * q^87 + 3 * q^88 + 18 * q^89 - 96 * q^90 - 108 * q^91 - 30 * q^92 + 147 * q^93 - 18 * q^94 + 66 * q^95 - 9 * q^97 - 12 * q^98 - 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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