LMFDB - Embedded newform 418.2.u.b.9.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(5,418)]

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([36, 80]))

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

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

chi := DirichletCharacter("418.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.u (of order $45$, 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:	$264$
Relative dimension:	$11$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			9.6
Character	$\chi$	$=$	418.9
Dual form			418.2.u.b.93.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.990268 + 0.139173i) q^{2} +(0.0134323 - 0.0538742i) q^{3} +(0.961262 + 0.275637i) q^{4} +(-0.0826337 + 2.36632i) q^{5} +(0.0207995 - 0.0514805i) q^{6} +(1.41811 - 0.631382i) q^{7} +(0.913545 + 0.406737i) q^{8} +(2.64612 + 1.40697i) q^{9} +O(q^{10})$	\(q+(0.990268 + 0.139173i) q^{2} +(0.0134323 - 0.0538742i) q^{3} +(0.961262 + 0.275637i) q^{4} +(-0.0826337 + 2.36632i) q^{5} +(0.0207995 - 0.0514805i) q^{6} +(1.41811 - 0.631382i) q^{7} +(0.913545 + 0.406737i) q^{8} +(2.64612 + 1.40697i) q^{9} +(-0.411158 + 2.33179i) q^{10} +(-3.19622 - 0.885541i) q^{11} +(0.0277617 - 0.0480847i) q^{12} +(-1.52875 + 0.955270i) q^{13} +(1.49218 - 0.427875i) q^{14} +(0.126374 + 0.0362371i) q^{15} +(0.848048 + 0.529919i) q^{16} +(2.91207 - 1.54837i) q^{17} +(2.42456 + 1.76154i) q^{18} +(-1.01932 + 4.23804i) q^{19} +(-0.731679 + 2.25188i) q^{20} +(-0.0149667 - 0.0848803i) q^{21} +(-3.04187 - 1.32175i) q^{22} +(-0.383630 + 0.139630i) q^{23} +(0.0341837 - 0.0437531i) q^{24} +(-0.604821 - 0.0422932i) q^{25} +(-1.64682 + 0.733212i) q^{26} +(0.222800 - 0.247445i) q^{27} +(1.53720 - 0.216040i) q^{28} +(3.50020 - 3.38010i) q^{29} +(0.120101 + 0.0534722i) q^{30} +(-1.44994 - 1.61032i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-0.0906406 + 0.160299i) q^{33} +(3.09922 - 1.12802i) q^{34} +(1.37687 + 3.40787i) q^{35} +(2.15580 + 2.08183i) q^{36} +(7.60559 + 5.52579i) q^{37} +(-1.59922 + 4.05493i) q^{38} +(0.0309297 + 0.0951918i) q^{39} +(-1.03796 + 2.12813i) q^{40} +(2.96761 - 11.9024i) q^{41} +(-0.00300798 - 0.0861372i) q^{42} +(-10.0205 - 3.64716i) q^{43} +(-2.82831 - 1.73223i) q^{44} +(-3.54799 + 6.14531i) q^{45} +(-0.399329 + 0.0848800i) q^{46} +(-5.81442 - 11.9213i) q^{47} +(0.0399403 - 0.0385699i) q^{48} +(-3.07153 + 3.41128i) q^{49} +(-0.593049 - 0.126057i) q^{50} +(-0.0443015 - 0.177684i) q^{51} +(-1.73284 + 0.496883i) q^{52} +(-0.0282477 - 0.808908i) q^{53} +(0.255070 - 0.214029i) q^{54} +(2.35959 - 7.49010i) q^{55} +1.55231 q^{56} +(0.214629 + 0.111842i) q^{57} +(3.93655 - 2.86007i) q^{58} +(1.69626 - 3.47786i) q^{59} +(0.111490 + 0.0696666i) q^{60} +(-7.38243 - 9.44908i) q^{61} +(-1.21172 - 1.79644i) q^{62} +(4.64081 + 0.324517i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-2.13415 - 3.69645i) q^{65} +(-0.112068 + 0.146124i) q^{66} +(-1.74957 + 9.92229i) q^{67} +(3.22605 - 0.685718i) q^{68} +(0.00236940 + 0.0225433i) q^{69} +(0.889185 + 3.56632i) q^{70} +(0.0454433 - 1.30132i) q^{71} +(1.84509 + 2.36160i) q^{72} +(-15.1317 + 1.05811i) q^{73} +(6.76253 + 6.53050i) q^{74} +(-0.0104027 + 0.0320162i) q^{75} +(-2.14800 + 3.79290i) q^{76} +(-5.09169 + 0.762242i) q^{77} +(0.0173805 + 0.0985700i) q^{78} +(-1.00169 - 2.47926i) q^{79} +(-1.32404 + 1.96296i) q^{80} +(5.01723 + 7.43834i) q^{81} +(4.59523 - 11.3736i) q^{82} +(11.4112 + 2.42552i) q^{83} +(0.00900928 - 0.0857175i) q^{84} +(3.42331 + 7.01883i) q^{85} +(-9.41538 - 5.00625i) q^{86} +(-0.135084 - 0.233973i) q^{87} +(-2.55971 - 2.10900i) q^{88} +(0.0997797 + 0.0837251i) q^{89} +(-4.36873 + 5.59171i) q^{90} +(-1.56479 + 2.31990i) q^{91} +(-0.407256 + 0.0284781i) q^{92} +(-0.106231 + 0.0564840i) q^{93} +(-4.09871 - 12.6145i) q^{94} +(-9.94433 - 2.76225i) q^{95} +(0.0449194 - 0.0326359i) q^{96} +(-6.45139 - 0.906683i) q^{97} +(-3.51640 + 2.95061i) q^{98} +(-7.21165 - 6.84023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.990268	+	0.139173i	0.700225	+	0.0984102i
$2$	0.990268	+	0.139173i	0.700225	+	0.0984102i
$3$	0.0134323	−	0.0538742i	0.00775517	−	0.0311043i	−0.966293	−	0.257443i	$-0.917120\pi$
$3$	0.0134323	−	0.0538742i	0.00775517	−	0.0311043i	0.974049	+	0.226339i	$0.0726756\pi$
$4$	0.961262	+	0.275637i	0.480631	+	0.137819i
$5$	−0.0826337	+	2.36632i	−0.0369549	+	1.05825i	0.829348	+	0.558732i	$0.188712\pi$
$5$	−0.0826337	+	2.36632i	−0.0369549	+	1.05825i	−0.866303	+	0.499518i	$0.833510\pi$
$6$	0.0207995	−	0.0514805i	0.00849135	−	0.0210168i
$7$	1.41811	−	0.631382i	0.535994	−	0.238640i	−0.120844	−	0.992671i	$-0.538560\pi$
$7$	1.41811	−	0.631382i	0.535994	−	0.238640i	0.656838	+	0.754032i	$0.271893\pi$
$8$	0.913545	+	0.406737i	0.322987	+	0.143803i
$9$	2.64612	+	1.40697i	0.882040	+	0.468989i
$10$	−0.411158	+	2.33179i	−0.130019	+	0.737377i
$11$	−3.19622	−	0.885541i	−0.963696	−	0.267001i
$11$	−3.19622	−	0.885541i	−0.963696	−	0.267001i
$12$	0.0277617	−	0.0480847i	0.00801412	−	0.0138809i
$13$	−1.52875	+	0.955270i	−0.423999	+	0.264944i	−0.725094	−	0.688650i	$-0.758204\pi$
$13$	−1.52875	+	0.955270i	−0.423999	+	0.264944i	0.301094	+	0.953594i	$0.402648\pi$
$14$	1.49218	−	0.427875i	0.398801	−	0.114354i
$15$	0.126374	+	0.0362371i	0.0326295	+	0.00935637i
$16$	0.848048	+	0.529919i	0.212012	+	0.132480i
$17$	2.91207	−	1.54837i	0.706280	−	0.375536i	−0.0771470	−	0.997020i	$-0.524581\pi$
$17$	2.91207	−	1.54837i	0.706280	−	0.375536i	0.783427	+	0.621484i	$0.213470\pi$
$18$	2.42456	+	1.76154i	0.571474	+	0.415200i
$19$	−1.01932	+	4.23804i	−0.233849	+	0.972273i
$19$	−1.01932	+	4.23804i	−0.233849	+	0.972273i
$20$	−0.731679	+	2.25188i	−0.163608	+	0.503535i
$21$	−0.0149667	−	0.0848803i	−0.00326600	−	0.0185224i
$22$	−3.04187	−	1.32175i	−0.648529	−	0.281798i
$23$	−0.383630	+	0.139630i	−0.0799923	+	0.0291148i	−0.381706	−	0.924284i	$-0.624663\pi$
$23$	−0.383630	+	0.139630i	−0.0799923	+	0.0291148i	0.301714	+	0.953398i	$0.402441\pi$
$24$	0.0341837	−	0.0437531i	0.00697771	−	0.00893106i
$25$	−0.604821	−	0.0422932i	−0.120964	−	0.00845865i
$26$	−1.64682	+	0.733212i	−0.322968	+	0.143795i
$27$	0.222800	−	0.247445i	0.0428779	−	0.0476208i
$28$	1.53720	−	0.216040i	0.290504	−	0.0408277i
$29$	3.50020	−	3.38010i	0.649970	−	0.627669i	−0.294739	−	0.955578i	$-0.595233\pi$
$29$	3.50020	−	3.38010i	0.649970	−	0.627669i	0.944709	+	0.327909i	$0.106344\pi$
$30$	0.120101	+	0.0534722i	0.0219273	+	0.00976264i
$31$	−1.44994	−	1.61032i	−0.260417	−	0.289222i	0.598730	−	0.800951i	$-0.295672\pi$
$31$	−1.44994	−	1.61032i	−0.260417	−	0.289222i	−0.859147	+	0.511728i	$0.829005\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−0.0906406	+	0.160299i	−0.0157785	+	0.0279044i
$34$	3.09922	−	1.12802i	0.531512	−	0.193454i
$35$	1.37687	+	3.40787i	0.232733	+	0.576035i
$36$	2.15580	+	2.08183i	0.359300	+	0.346972i
$37$	7.60559	+	5.52579i	1.25035	+	0.908433i	0.998242	−	0.0592653i	$-0.0188758\pi$
$37$	7.60559	+	5.52579i	1.25035	+	0.908433i	0.252109	+	0.967699i	$0.418876\pi$
$38$	−1.59922	+	4.05493i	−0.259428	+	0.657797i
$39$	0.0309297	+	0.0951918i	0.00495271	+	0.0152429i
$40$	−1.03796	+	2.12813i	−0.164116	+	0.336487i
$41$	2.96761	−	11.9024i	0.463463	−	1.85885i	−0.0469151	−	0.998899i	$-0.514939\pi$
$41$	2.96761	−	11.9024i	0.463463	−	1.85885i	0.510378	−	0.859950i	$-0.329505\pi$
$42$	−0.00300798	−	0.0861372i	−0.000464141	−	0.0132913i
$43$	−10.0205	−	3.64716i	−1.52811	−	0.556187i	−0.564952	−	0.825124i	$-0.691105\pi$
$43$	−10.0205	−	3.64716i	−1.52811	−	0.556187i	−0.963158	+	0.268937i	$0.913328\pi$
$44$	−2.82831	−	1.73223i	−0.426384	−	0.261144i
$45$	−3.54799	+	6.14531i	−0.528904	+	0.916088i
$46$	−0.399329	+	0.0848800i	−0.0588778	+	0.0125149i
$47$	−5.81442	−	11.9213i	−0.848121	−	1.73890i	−0.651839	−	0.758357i	$-0.726002\pi$
$47$	−5.81442	−	11.9213i	−0.848121	−	1.73890i	−0.196281	−	0.980548i	$-0.562887\pi$
$48$	0.0399403	−	0.0385699i	0.00576488	−	0.00556708i
$49$	−3.07153	+	3.41128i	−0.438790	+	0.487326i
$50$	−0.593049	−	0.126057i	−0.0838698	−	0.0178271i
$51$	−0.0443015	−	0.177684i	−0.00620345	−	0.0248807i
$52$	−1.73284	+	0.496883i	−0.240301	+	0.0689053i
$53$	−0.0282477	−	0.808908i	−0.00388012	−	0.111112i	−0.999786	−	0.0207105i	$-0.993407\pi$
$53$	−0.0282477	−	0.808908i	−0.00388012	−	0.111112i	0.995905	−	0.0904016i	$-0.0288150\pi$
$54$	0.255070	−	0.214029i	0.0347106	−	0.0291256i
$55$	2.35959	−	7.49010i	0.318167	−	1.00997i
$56$	1.55231			0.207436
$57$	0.214629	+	0.111842i	0.0284283	+	0.0148138i
$58$	3.93655	−	2.86007i	0.516894	−	0.375546i
$59$	1.69626	−	3.47786i	0.220835	−	0.452778i	−0.759398	−	0.650626i	$-0.774506\pi$
$59$	1.69626	−	3.47786i	0.220835	−	0.452778i	0.980233	+	0.197848i	$0.0633953\pi$
$60$	0.111490	+	0.0696666i	0.0143933	+	0.00899392i
$61$	−7.38243	−	9.44908i	−0.945223	−	1.20983i	−0.977625	−	0.210356i	$-0.932538\pi$
$61$	−7.38243	−	9.44908i	−0.945223	−	1.20983i	0.0324017	−	0.999475i	$-0.489684\pi$
$62$	−1.21172	−	1.79644i	−0.153888	−	0.228149i
$63$	4.64081	+	0.324517i	0.584688	+	0.0408853i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	−2.13415	−	3.69645i	−0.264708	−	0.458488i
$66$	−0.112068	+	0.146124i	−0.0137946	+	0.0179866i
$67$	−1.74957	+	9.92229i	−0.213744	+	1.21220i	0.669329	+	0.742966i	$0.266582\pi$
$67$	−1.74957	+	9.92229i	−0.213744	+	1.21220i	−0.883073	+	0.469235i	$0.844530\pi$
$68$	3.22605	−	0.685718i	0.391216	−	0.0831555i
$69$	0.00236940	+	0.0225433i	0.000285242	+	0.00271389i
$70$	0.889185	+	3.56632i	0.106278	+	0.426257i
$71$	0.0454433	−	1.30132i	0.00539312	−	0.154439i	−0.993707	−	0.112015i	$-0.964270\pi$
$71$	0.0454433	−	1.30132i	0.00539312	−	0.154439i	0.999100	−	0.0424243i	$-0.0135081\pi$
$72$	1.84509	+	2.36160i	0.217446	+	0.278318i
$73$	−15.1317	+	1.05811i	−1.77103	+	0.123842i	−0.917635	−	0.397423i	$-0.869904\pi$
$73$	−15.1317	+	1.05811i	−1.77103	+	0.123842i	−0.853394	+	0.521266i	$0.825460\pi$
$74$	6.76253	+	6.53050i	0.786128	+	0.759155i
$75$	−0.0104027	+	0.0320162i	−0.00120120	+	0.00369691i
$76$	−2.14800	+	3.79290i	−0.246392	+	0.435076i
$77$	−5.09169	+	0.762242i	−0.580252	+	0.0868656i
$78$	0.0173805	+	0.0985700i	0.00196796	+	0.0111608i
$79$	−1.00169	−	2.47926i	−0.112698	−	0.278938i	0.860285	−	0.509813i	$-0.170286\pi$
$79$	−1.00169	−	2.47926i	−0.112698	−	0.278938i	−0.972983	+	0.230875i	$0.925841\pi$
$80$	−1.32404	+	1.96296i	−0.148032	+	0.219466i
$81$	5.01723	+	7.43834i	0.557470	+	0.826483i
$82$	4.59523	−	11.3736i	0.507458	−	1.25600i
$83$	11.4112	+	2.42552i	1.25254	+	0.266235i	0.785978	−	0.618254i	$-0.212160\pi$
$83$	11.4112	+	2.42552i	1.25254	+	0.266235i	0.466560	+	0.884489i	$0.345493\pi$
$84$	0.00900928	−	0.0857175i	0.000982993	−	0.00935255i
$85$	3.42331	+	7.01883i	0.371310	+	0.761299i
$86$	−9.41538	−	5.00625i	−1.01529	−	0.539838i
$87$	−0.135084	−	0.233973i	−0.0144826	−	0.0250845i
$88$	−2.55971	−	2.10900i	−0.272866	−	0.224820i
$89$	0.0997797	+	0.0837251i	0.0105766	+	0.00887485i	0.648061	−	0.761589i	$-0.275580\pi$
$89$	0.0997797	+	0.0837251i	0.0105766	+	0.00887485i	−0.637484	+	0.770464i	$0.720025\pi$
$90$	−4.36873	+	5.59171i	−0.460504	+	0.589418i
$91$	−1.56479	+	2.31990i	−0.164035	+	0.243192i
$92$	−0.407256	+	0.0284781i	−0.0424593	+	0.00296905i
$93$	−0.106231	+	0.0564840i	−0.0110156	+	0.00585712i
$94$	−4.09871	−	12.6145i	−0.422749	−	1.30109i
$95$	−9.94433	−	2.76225i	−1.02027	−	0.283401i
$96$	0.0449194	−	0.0326359i	0.00458457	−	0.00333089i
$97$	−6.45139	−	0.906683i	−0.655039	−	0.0920598i	−0.196179	−	0.980568i	$-0.562853\pi$
$97$	−6.45139	−	0.906683i	−0.655039	−	0.0920598i	−0.458860	+	0.888508i	$0.651742\pi$
$98$	−3.51640	+	2.95061i	−0.355210	+	0.298056i
$99$	−7.21165	−	6.84023i	−0.724798	−	0.687469i
$100$	−0.569734	−	0.207366i	−0.0569734	−	0.0207366i
$101$	−5.46678	+	3.41602i	−0.543965	+	0.339907i	−0.773909	−	0.633297i	$-0.781701\pi$
$101$	−5.46678	+	3.41602i	−0.543965	+	0.339907i	0.229944	+	0.973204i	$0.426146\pi$
$102$	−0.0191416	−	0.182120i	−0.00189530	−	0.0180326i
$103$	0.454640	−	4.32561i	0.0447970	−	0.426215i	−0.949023	−	0.315208i	$-0.897926\pi$
$103$	0.454640	−	4.32561i	0.0447970	−	0.426215i	0.993820	−	0.111007i	$-0.0354076\pi$
$104$	−1.78513	+	0.250883i	−0.175046	+	0.0246011i
$105$	0.202091	−	0.0284020i	0.0197220	−	0.00277175i
$106$	0.0846054	−	0.804967i	0.00821761	−	0.0781853i
$107$	−0.430780	−	4.09860i	−0.0416451	−	0.396227i	−0.995412	−	0.0956798i	$-0.969498\pi$
$107$	−0.430780	−	4.09860i	−0.0416451	−	0.396227i	0.953767	−	0.300547i	$-0.0971691\pi$
$108$	0.282374	−	0.176447i	0.0271715	−	0.0169786i
$109$	14.6573	+	5.33482i	1.40391	+	0.510983i	0.929338	−	0.369231i	$-0.120379\pi$
$109$	14.6573	+	5.33482i	1.40391	+	0.510983i	0.474577	+	0.880214i	$0.342601\pi$
$110$	3.37905	−	7.08882i	0.322179	−	0.675892i
$111$	0.399858	−	0.335521i	0.0379529	−	0.0318462i
$112$	1.53720	+	0.216040i	0.145252	+	0.0204139i
$113$	3.37328	−	2.45083i	0.317331	−	0.230555i	−0.417705	−	0.908583i	$-0.637165\pi$
$113$	3.37328	−	2.45083i	0.317331	−	0.230555i	0.735036	+	0.678028i	$0.237165\pi$
$114$	0.196975	+	0.140624i	0.0184484	+	0.0131707i
$115$	−0.298708	−	0.919329i	−0.0278547	−	0.0857278i
$116$	4.29629	−	2.28438i	0.398900	−	0.212099i
$117$	−5.38929	+	0.376856i	−0.498240	+	0.0348404i
$118$	2.16378	−	3.20794i	0.199192	−	0.295315i
$119$	3.15201	−	4.03438i	0.288944	−	0.369831i
$120$	0.100709	+	0.0845050i	0.00919344	+	0.00771421i
$121$	9.43163	+	5.66077i	0.857421	+	0.514615i
$122$	−5.99553	−	10.3846i	−0.542809	−	0.940174i
$123$	−0.601372	−	0.319755i	−0.0542239	−	0.0288314i
$124$	−0.949907	−	1.94760i	−0.0853042	−	0.174900i
$125$	−1.08743	+	10.3463i	−0.0972631	+	0.925397i
$126$	4.55049	+	0.967236i	0.405390	+	0.0861682i
$127$	6.41859	−	15.8866i	0.569558	−	1.40971i	−0.317593	−	0.948227i	$-0.602875\pi$
$127$	6.41859	−	15.8866i	0.569558	−	1.40971i	0.887151	−	0.461479i	$-0.152681\pi$
$128$	0.559193	+	0.829038i	0.0494261	+	0.0732773i
$129$	−0.331086	+	0.490856i	−0.0291505	+	0.0432175i
$130$	−1.59893	−	3.95749i	−0.140236	−	0.347095i
$131$	1.09882	+	6.23171i	0.0960042	+	0.544467i	0.994435	+	0.105352i	$0.0335969\pi$
$131$	1.09882	+	6.23171i	0.0960042	+	0.544467i	−0.898431	+	0.439115i	$0.855292\pi$
$132$	−0.131314	+	0.129105i	−0.0114294	+	0.0112372i
$133$	1.23031	+	6.65357i	0.106682	+	0.576938i
$134$	−3.11346	+	9.58224i	−0.268962	+	0.827779i
$135$	0.567123	+	0.547664i	0.0488101	+	0.0471354i
$136$	3.29009	−	0.230065i	0.282122	−	0.0197279i
$137$	−5.27327	−	6.74948i	−0.450526	−	0.576647i	0.508107	−	0.861294i	$-0.330346\pi$
$137$	−5.27327	−	6.74948i	−0.450526	−	0.576647i	−0.958632	+	0.284648i	$0.908123\pi$
$138$	−0.000791083		0.0226537i	−6.73415e−5		0.00192841i
$139$	−0.0949191	−	0.380700i	−0.00805093	−	0.0322905i	0.966136	−	0.258034i	$-0.0830745\pi$
$139$	−0.0949191	−	0.380700i	−0.00805093	−	0.0322905i	−0.974187	+	0.225743i	$0.927519\pi$
$140$	0.384195	+	3.65537i	0.0324704	+	0.308935i
$141$	−0.720354	+	0.153116i	−0.0606647	+	0.0128947i
$142$	0.226110	−	1.28234i	0.0189748	−	0.107611i
$143$	5.73216	−	1.69948i	0.479347	−	0.142118i
$144$	1.49846	+	2.59541i	0.124872	+	0.216284i
$145$	7.70916	+	8.56189i	0.640211	+	0.711026i
$146$	−15.1317	−	1.05811i	−1.25231	−	0.0875698i
$147$	0.142522	+	0.211298i	0.0117550	+	0.0174275i
$148$	5.78785	+	7.40811i	0.475758	+	0.608943i
$149$	2.08951	+	1.30567i	0.171180	+	0.106965i	0.612803	−	0.790235i	$-0.290042\pi$
$149$	2.08951	+	1.30567i	0.171180	+	0.106965i	−0.441624	+	0.897200i	$0.645597\pi$
$150$	−0.0147572	+	0.0302568i	−0.00120492	+	0.00247046i
$151$	12.8929	−	9.36725i	1.04921	−	0.762296i	0.0771480	−	0.997020i	$-0.475419\pi$
$151$	12.8929	−	9.36725i	1.04921	−	0.762296i	0.972062	+	0.234724i	$0.0754186\pi$
$152$	−2.65496	+	3.45705i	−0.215346	+	0.280404i
$153$	9.88419			0.799089
$154$	−5.14823	+	0.0461974i	−0.414856	+	0.00372269i
$155$	3.93035	−	3.29796i	0.315693	−	0.264898i
$156$	0.00349311	+	0.100030i	0.000279673	+	0.00800878i
$157$	−5.33144	+	1.52877i	−0.425495	+	0.122009i	−0.481549	−	0.876419i	$-0.659926\pi$
$157$	−5.33144	+	1.52877i	−0.425495	+	0.122009i	0.0560543	+	0.998428i	$0.482148\pi$
$158$	−0.646891	−	2.59454i	−0.0514639	−	0.206410i
$159$	−0.0439587	−	0.00934371i	−0.00348615	−	0.000741004i
$160$	−1.58434	+	1.75959i	−0.125253	+	0.139108i
$161$	−0.455868	+	0.440227i	−0.0359274	+	0.0346947i
$162$	3.93318	+	8.06422i	0.309020	+	0.633585i
$163$	2.92673	−	0.622095i	0.229239	−	0.0487262i	−0.0918599	−	0.995772i	$-0.529281\pi$
$163$	2.92673	−	0.622095i	0.229239	−	0.0487262i	0.321099	+	0.947046i	$0.395948\pi$
$164$	6.13341	−	10.6234i	0.478939	−	0.829546i
$165$	−0.371828	−	0.227731i	−0.0289468	−	0.0177288i
$166$	10.9625	+	3.99004i	0.850859	+	0.309687i
$167$	0.0964885	+	2.76307i	0.00746650	+	0.213813i	0.997390	+	0.0722071i	$0.0230042\pi$
$167$	0.0964885	+	2.76307i	0.00746650	+	0.213813i	−0.989923	+	0.141606i	$0.954774\pi$
$168$	0.0208512	−	0.0836295i	0.00160870	−	0.00645216i
$169$	−4.27428	+	8.76358i	−0.328791	+	0.674122i
$170$	2.41316	+	7.42695i	0.185081	+	0.569621i
$171$	−8.66003	+	9.78021i	−0.662249	+	0.747912i
$172$	−8.62702	−	6.26790i	−0.657804	−	0.477923i
$173$	2.23324	+	2.15661i	0.169790	+	0.163964i	0.774699	−	0.632331i	$-0.217902\pi$
$173$	2.23324	+	2.15661i	0.169790	+	0.163964i	−0.604909	+	0.796295i	$0.706790\pi$
$174$	−0.101207	−	0.250496i	−0.00767248	−	0.0189901i
$175$	−0.884404	+	0.321897i	−0.0668547	+	0.0243331i
$176$	−2.24128	−	2.44472i	−0.168943	−	0.184278i
$177$	−0.164582	−	0.138101i	−0.0123707	−	0.0103803i
$178$	0.0871564	+	0.0967970i	0.00653265	+	0.00725524i
$179$	−17.5863	−	7.82994i	−1.31446	−	0.585237i	−0.374727	−	0.927135i	$-0.622263\pi$
$179$	−17.5863	−	7.82994i	−1.31446	−	0.585237i	−0.939737	+	0.341898i	$0.888930\pi$
$180$	−5.10443	+	4.92929i	−0.380461	+	0.367407i
$181$	4.07739	−	0.573040i	0.303070	−	0.0425937i	0.0140010	−	0.999902i	$-0.495543\pi$
$181$	4.07739	−	0.573040i	0.303070	−	0.0425937i	0.289069	+	0.957308i	$0.406654\pi$
$182$	−1.87243	+	2.07955i	−0.138794	+	0.154146i
$183$	−0.608225	+	0.270799i	−0.0449613	+	0.0200181i
$184$	−0.407256	−	0.0284781i	−0.0300233	−	0.00209943i
$185$	−13.7043	+	17.5406i	−1.00756	+	1.28961i
$186$	−0.113058	+	0.0411498i	−0.00828983	+	0.00301725i
$187$	−10.6788	+	2.37018i	−0.780908	+	0.173325i
$188$	−2.30322	−	13.0622i	−0.167979	−	0.952658i
$189$	0.159722	−	0.491575i	0.0116181	−	0.0357568i
$190$	−9.46312	−	4.11935i	−0.686527	−	0.298849i
$191$	15.0342	+	10.9230i	1.08784	+	0.790360i	0.979033	−	0.203703i	$-0.0652978\pi$
$191$	15.0342	+	10.9230i	1.08784	+	0.790360i	0.108804	+	0.994063i	$0.465298\pi$
$192$	0.0490243	−	0.0260667i	0.00353803	−	0.00188120i
$193$	16.1053	+	10.0637i	1.15928	+	0.724401i	0.966456	−	0.256832i	$-0.0826786\pi$
$193$	16.1053	+	10.0637i	1.15928	+	0.724401i	0.192828	+	0.981233i	$0.438234\pi$
$194$	−6.26242	−	1.79572i	−0.449615	−	0.128925i
$195$	−0.227810	+	0.0653235i	−0.0163138	+	0.00467791i
$196$	−3.89282	+	2.43251i	−0.278059	+	0.173750i
$197$	4.29852	−	7.44526i	0.306257	−	0.530453i	−0.671283	−	0.741201i	$-0.734257\pi$
$197$	4.29852	−	7.44526i	0.306257	−	0.530453i	0.977540	+	0.210748i	$0.0675900\pi$
$198$	−6.18950	−	7.77733i	−0.439868	−	0.552710i
$199$	−4.89211	+	27.7445i	−0.346792	+	1.96676i	−0.120355	+	0.992731i	$0.538403\pi$
$199$	−4.89211	+	27.7445i	−0.346792	+	1.96676i	−0.226437	+	0.974026i	$0.572708\pi$
$200$	−0.535330	−	0.284640i	−0.0378535	−	0.0201271i
$201$	0.511055	+	0.227536i	0.0360470	+	0.0160492i
$202$	−5.88899	+	2.62195i	−0.414348	+	0.184480i
$203$	2.82952	−	7.00330i	0.198593	−	0.491535i
$204$	0.00639090	−	0.183012i	0.000447453	−	0.0128134i
$205$	27.9198	+	8.00586i	1.95000	+	0.559154i
$206$	1.05222	−	4.22024i	0.0733119	−	0.294038i
$207$	−1.21158	−	0.170277i	−0.0842110	−	0.0118351i
$208$	−1.80267			−0.124993
$209$	7.01094	−	12.6431i	0.484957	−	0.874538i
$210$	0.204077			0.0140826
$211$	−16.3177	−	2.29330i	−1.12336	−	0.157878i	−0.447058	−	0.894505i	$-0.647528\pi$
$211$	−16.3177	−	2.29330i	−1.12336	−	0.157878i	−0.676299	+	0.736627i	$0.736417\pi$
$212$	0.195812	−	0.785358i	0.0134484	−	0.0539386i
$213$	−0.0694974	−	0.0199281i	−0.00476188	−	0.00136545i
$214$	0.143827	−	4.11866i	0.00983181	−	0.281546i
$215$	9.45838	−	23.4103i	0.645056	−	1.59657i
$216$	0.304183	−	0.135431i	0.0206970	−	0.00921491i
$217$	−3.07290	−	1.36814i	−0.208602	−	0.0928756i
$218$	13.7722	+	7.32281i	0.932771	+	0.495963i
$219$	−0.146249	+	0.829420i	−0.00988260	+	0.0560470i
$220$	4.33273	−	6.54956i	0.292113	−	0.441571i
$221$	−2.97271	+	5.14889i	−0.199966	+	0.346352i
$222$	0.442662	−	0.276606i	0.0297095	−	0.0185646i
$223$	−12.9949	+	3.72622i	−0.870201	+	0.249526i	−0.680885	−	0.732390i	$-0.738405\pi$
$223$	−12.9949	+	3.72622i	−0.870201	+	0.249526i	−0.189316	+	0.981916i	$0.560627\pi$
$224$	1.49218	+	0.427875i	0.0997003	+	0.0285886i
$225$	−1.54093	−	0.962877i	−0.102728	−	0.0641918i
$226$	3.68154	−	1.95751i	0.244892	−	0.130212i
$227$	8.85521	+	6.43369i	0.587741	+	0.427019i	0.841507	−	0.540247i	$-0.181669\pi$
$227$	8.85521	+	6.43369i	0.587741	+	0.427019i	−0.253766	+	0.967266i	$0.581669\pi$
$228$	0.175487	+	0.166669i	0.0116219	+	0.0110379i
$229$	−1.06156	+	3.26716i	−0.0701501	+	0.215900i	−0.979985	−	0.199070i	$-0.936208\pi$
$229$	−1.06156	+	3.26716i	−0.0701501	+	0.215900i	0.909835	+	0.414970i	$0.136208\pi$
$230$	−0.167855	−	0.951954i	−0.0110680	−	0.0627700i
$231$	−0.0273282	+	0.284550i	−0.00179806	+	0.0187220i
$232$	4.57240	−	1.66422i	0.300193	−	0.109261i
$233$	−10.8209	+	13.8501i	−0.708901	+	0.907352i	−0.998763	−	0.0497167i	$-0.984168\pi$
$233$	−10.8209	+	13.8501i	−0.708901	+	0.907352i	0.289863	+	0.957068i	$0.406390\pi$
$234$	−5.38929	−	0.376856i	−0.352309	−	0.0246359i
$235$	28.6902	−	12.7737i	1.87154	−	0.833263i
$236$	2.58918	−	2.87558i	0.168541	−	0.187184i
$237$	−0.147023	+	0.0206627i	−0.00955017	+	0.00134219i
$238$	3.68281	−	3.55645i	0.238721	−	0.230530i
$239$	4.38259	+	1.95126i	0.283486	+	0.126216i	0.543554	−	0.839374i	$-0.317078\pi$
$239$	4.38259	+	1.95126i	0.283486	+	0.126216i	−0.260068	+	0.965590i	$0.583745\pi$
$240$	0.0879682	+	0.0976986i	0.00567832	+	0.00630642i
$241$	18.2409	+	15.3059i	1.17500	+	0.985942i	0.999999	+	0.00137388i	$0.000437318\pi$
$241$	18.2409	+	15.3059i	1.17500	+	0.985942i	0.175001	+	0.984568i	$0.444007\pi$
$242$	8.55202	+	6.91831i	0.549745	+	0.444726i
$243$	1.40680	−	0.512032i	0.0902460	−	0.0328468i
$244$	−4.49193	−	11.1179i	−0.287566	−	0.711751i
$245$	−7.81837	−	7.55011i	−0.499497	−	0.482359i
$246$	−0.551019	−	0.400338i	−0.0351317	−	0.0255246i
$247$	−2.49018	−	7.45264i	−0.158446	−	0.474200i
$248$	−0.669610	−	2.06085i	−0.0425203	−	0.130864i
$249$	0.283952	−	0.582187i	0.0179947	−	0.0368946i
$250$	−2.51677	+	10.0942i	−0.159175	+	0.638415i
$251$	0.293747	+	8.41180i	0.0185411	+	0.530948i	0.972757	+	0.231828i	$0.0744708\pi$
$251$	0.293747	+	8.41180i	0.0185411	+	0.530948i	−0.954216	+	0.299120i	$0.903307\pi$
$252$	4.37159	+	1.59113i	0.275384	+	0.100232i
$253$	1.34981	−	0.106567i	0.0848620	−	0.00669984i
$254$	8.56711	−	14.8387i	0.537548	−	0.931061i
$255$	0.424117	−	0.0901488i	0.0265592	−	0.00564534i
$256$	0.438371	+	0.898794i	0.0273982	+	0.0561746i
$257$	−15.9268	+	15.3803i	−0.993484	+	0.959397i	−0.999176	−	0.0405870i	$-0.987077\pi$
$257$	−15.9268	+	15.3803i	−0.993484	+	0.959397i	0.00569155	+	0.999984i	$0.498188\pi$
$258$	−0.396178	+	0.440001i	−0.0246650	+	0.0273932i
$259$	14.2744	+	3.03412i	0.886969	+	0.188531i
$260$	−1.03259	−	4.14151i	−0.0640388	−	0.256845i
$261$	14.0176	−	4.01949i	0.867669	−	0.248800i
$262$	0.220839	+	6.32399i	0.0136435	+	0.390697i
$263$	−13.0830	+	10.9780i	−0.806735	+	0.676931i	−0.949826	−	0.312778i	$-0.898740\pi$
$263$	−13.0830	+	10.9780i	−0.806735	+	0.676931i	0.143091	+	0.989710i	$0.454296\pi$
$264$	−0.148004	+	0.109573i	−0.00910900	+	0.00674378i
$265$	1.91647			0.117728
$266$	0.292342	+	6.76005i	0.0179246	+	0.414485i
$267$	0.00585090	−	0.00425093i	0.000358069	−	0.000260153i
$268$	−4.41675	+	9.05568i	−0.269796	+	0.553163i
$269$	−16.0145	−	10.0070i	−0.976422	−	0.610136i	−0.0549123	−	0.998491i	$-0.517488\pi$
$269$	−16.0145	−	10.0070i	−0.976422	−	0.610136i	−0.921510	+	0.388355i	$0.873043\pi$
$270$	0.485383	+	0.621262i	0.0295395	+	0.0378088i
$271$	7.60587	+	11.2762i	0.462024	+	0.684978i	0.985998	−	0.166756i	$-0.0533291\pi$
$271$	7.60587	+	11.2762i	0.462024	+	0.684978i	−0.523975	+	0.851734i	$0.675551\pi$
$272$	3.29009	+	0.230065i	0.199491	+	0.0139497i
$273$	0.103964	+	0.115464i	0.00629218	+	0.00698818i
$274$	−4.28260	−	7.41769i	−0.258722	−	0.448119i
$275$	1.89569	+	0.670773i	0.114314	+	0.0404491i
$276$	−0.00393616	+	0.0223231i	−0.000236929	+	0.00134369i
$277$	−17.0700	+	3.62834i	−1.02564	+	0.218006i	−0.689865	−	0.723938i	$-0.742330\pi$
$277$	−17.0700	+	3.62834i	−1.02564	+	0.218006i	−0.335771	+	0.941944i	$0.608997\pi$
$278$	−0.0410122	−	0.390205i	−0.00245975	−	0.0234029i
$279$	−1.57105	−	6.30113i	−0.0940561	−	0.377239i
$280$	−0.128273	+	3.67326i	−0.00766579	+	0.219520i
$281$	6.81854	+	8.72733i	0.406760	+	0.520629i	0.947152	−	0.320784i	$-0.103946\pi$
$281$	6.81854	+	8.72733i	0.406760	+	0.520629i	−0.540392	+	0.841413i	$0.681724\pi$
$282$	−0.734653	+	0.0513719i	−0.0437479	+	0.00305915i
$283$	−4.61948	−	4.46098i	−0.274600	−	0.265178i	0.544588	−	0.838704i	$-0.316686\pi$
$283$	−4.61948	−	4.46098i	−0.274600	−	0.265178i	−0.819187	+	0.573526i	$0.805575\pi$
$284$	0.402377	−	1.23839i	0.0238767	−	0.0734848i
$285$	−0.282390	+	0.498639i	−0.0167273	+	0.0295368i
$286$	5.91289	−	0.885178i	0.349637	−	0.0523417i
$287$	−3.30659	−	18.7526i	−0.195182	−	1.10693i
$288$	1.12266	+	2.77869i	0.0661537	+	0.163736i
$289$	−3.42361	+	5.07571i	−0.201389	+	0.298571i
$290$	6.44255	+	9.55148i	0.378320	+	0.560882i
$291$	−0.135504	+	0.335384i	−0.00794339	+	0.0196606i
$292$	−14.8372	−	3.15374i	−0.868279	−	0.184558i
$293$	1.75895	−	16.7353i	0.102759	−	0.977689i	−0.814706	−	0.579874i	$-0.803102\pi$
$293$	1.75895	−	16.7353i	0.102759	−	0.977689i	0.917466	−	0.397815i	$-0.130231\pi$
$294$	0.111728	+	0.229077i	0.00651612	+	0.0133600i
$295$	8.08955	+	4.30129i	0.470992	+	0.250431i
$296$	4.70051	+	8.14153i	0.273212	+	0.473217i
$297$	−0.931241	+	0.593589i	−0.0540361	+	0.0344435i
$298$	1.88746	+	1.58377i	0.109338	+	0.0917454i
$299$	0.453090	−	0.579929i	0.0262029	−	0.0335382i
$300$	−0.0188246	+	0.0279086i	−0.00108684	+	0.00161130i
$301$	−16.5129	+	1.15469i	−0.951786	+	0.0665554i
$302$	14.0711	−	7.48174i	0.809701	−	0.430526i
$303$	0.110604	+	0.340403i	0.00635402	+	0.0195557i
$304$	−3.11025	+	3.05390i	−0.178385	+	0.175153i
$305$	22.9696	−	16.6884i	1.31523	−	0.955574i
$306$	9.78800	+	1.37561i	0.559543	+	0.0786386i
$307$	−11.1724	+	9.37472i	−0.637640	+	0.535043i	−0.903292	−	0.429026i	$-0.858857\pi$
$307$	−11.1724	+	9.37472i	−0.637640	+	0.535043i	0.265653	+	0.964069i	$0.414413\pi$
$308$	−5.10455	−	0.670747i	−0.290859	−	0.0382193i
$309$	−0.226932	−	0.0825965i	−0.0129097	−	0.00469875i
$310$	4.35109	−	2.71886i	0.247125	−	0.154421i
$311$	−0.0826622	−	0.786478i	−0.00468734	−	0.0445971i	0.991928	−	0.126801i	$-0.0404709\pi$
$311$	−0.0826622	−	0.786478i	−0.00468734	−	0.0445971i	−0.996616	+	0.0822036i	$0.973804\pi$
$312$	−0.0104623	+	0.0995422i	−0.000592312	+	0.00563547i
$313$	12.0463	−	1.69299i	0.680895	−	0.0956935i	0.209758	−	0.977753i	$-0.432733\pi$
$313$	12.0463	−	1.69299i	0.680895	−	0.0956935i	0.471137	+	0.882060i	$0.343844\pi$
$314$	−5.49232	+	0.771895i	−0.309949	+	0.0435605i
$315$	−1.15140	+	10.9548i	−0.0648740	+	0.617235i
$316$	−0.279506	−	2.65932i	−0.0157234	−	0.149598i
$317$	16.2844	−	10.1756i	0.914622	−	0.571519i	0.0110423	−	0.999939i	$-0.496485\pi$
$317$	16.2844	−	10.1756i	0.914622	−	0.571519i	0.903580	+	0.428420i	$0.140929\pi$
$318$	−0.0422305	−	0.0153706i	−0.00236817	−	0.000861943i
$319$	−14.1806	+	7.70397i	−0.793962	+	0.431340i
$320$	−1.81381	+	1.52197i	−0.101395	+	0.0850806i
$321$	−0.226595	−	0.0318459i	−0.0126473	−	0.00177746i
$322$	−0.512699	+	0.372498i	−0.0285716	+	0.0207585i
$323$	3.59373	+	13.9197i	0.199961	+	0.774515i
$324$	2.77258	+	8.53313i	0.154032	+	0.474063i
$325$	0.965023	−	0.513112i	0.0535298	−	0.0284623i
$326$	2.98482	−	0.208719i	0.165314	−	0.0115599i
$327$	0.484291	−	0.717991i	0.0267814	−	0.0397050i
$328$	7.55221	−	9.66638i	0.417001	−	0.533737i
$329$	−15.7724	−	13.2346i	−0.869559	−	0.729647i
$330$	−0.336516	−	0.277263i	−0.0185246	−	0.0152628i
$331$	9.06408	+	15.6994i	0.498207	+	0.862920i	0.999998	−	0.00206925i	$-0.000658665\pi$
$331$	9.06408	+	15.6994i	0.498207	+	0.862920i	−0.501791	+	0.864989i	$0.667325\pi$
$332$	10.3006	+	5.47690i	0.565316	+	0.300584i
$333$	12.3507	+	25.3227i	0.676815	+	1.38768i
$334$	−0.288995	+	2.74961i	−0.0158131	+	0.150452i
$335$	−23.3348	−	4.95995i	−1.27491	−	0.270991i
$336$	0.0322872	−	0.0799137i	0.00176141	−	0.00435965i
$337$	−9.76778	−	14.4813i	−0.532085	−	0.788848i	0.463158	−	0.886276i	$-0.346716\pi$
$337$	−9.76778	−	14.4813i	−0.532085	−	0.788848i	−0.995243	+	0.0974278i	$0.968939\pi$
$338$	−5.45234	+	8.08343i	−0.296568	+	0.439681i
$339$	−0.0867254	−	0.214653i	−0.00471028	−	0.0116583i
$340$	1.35605	+	7.69052i	0.0735420	+	0.417077i
$341$	3.20832	+	6.43092i	0.173740	+	0.348254i
$342$	−9.93690	+	8.47979i	−0.537326	+	0.458534i
$343$	−5.55977	+	17.1112i	−0.300199	+	0.923919i
$344$	−7.67074	−	7.40755i	−0.413578	−	0.399388i
$345$	−0.0535404	+	0.00374391i	−0.00288252	+	0.000201565i
$346$	1.91136	+	2.44643i	0.102755	+	0.131521i
$347$	0.564874	−	16.1759i	0.0303240	−	0.868367i	−0.884986	−	0.465617i	$-0.845832\pi$
$347$	0.564874	−	16.1759i	0.0303240	−	0.868367i	0.915310	−	0.402749i	$-0.131945\pi$
$348$	−0.0653597	−	0.262143i	−0.00350365	−	0.0140524i
$349$	−0.469439	−	4.46641i	−0.0251285	−	0.239081i	−0.999876	−	0.0157701i	$-0.994980\pi$
$349$	−0.469439	−	4.46641i	−0.0251285	−	0.239081i	0.974747	−	0.223311i	$-0.0716866\pi$
$350$	−0.920597	+	0.195679i	−0.0492080	+	0.0104595i
$351$	−0.104230	+	0.591116i	−0.00556337	+	0.0315514i
$352$	−1.87923	−	2.73285i	−0.100163	−	0.145662i
$353$	8.62165	+	14.9331i	0.458884	+	0.794811i	0.998902	−	0.0468426i	$-0.0149159\pi$
$353$	8.62165	+	14.9331i	0.458884	+	0.794811i	−0.540018	+	0.841653i	$0.681583\pi$
$354$	−0.143760	−	0.159662i	−0.00764078	−	0.00848594i
$355$	3.07560	+	0.215067i	0.163236	+	0.0114145i
$356$	0.0728367	+	0.107985i	0.00386034	+	0.00572318i
$357$	−0.175010	−	0.224003i	−0.00926253	−	0.0118555i
$358$	−16.3255	−	10.2013i	−0.862827	−	0.539154i
$359$	10.7390	−	22.0182i	0.566783	−	1.16208i	−0.402338	−	0.915491i	$-0.631802\pi$
$359$	10.7390	−	22.0182i	0.566783	−	1.16208i	0.969121	−	0.246586i	$-0.0793086\pi$
$360$	−5.74077	+	4.17092i	−0.302565	+	0.219827i
$361$	−16.9220	−	8.63985i	−0.890630	−	0.454729i
$362$	4.11746			0.216409
$363$	0.431658	−	0.432084i	0.0226562	−	0.0226785i
$364$	−2.14363	+	1.79872i	−0.112357	+	0.0942783i
$365$	−1.25344	−	35.8938i	−0.0656081	−	1.87877i
$366$	−0.639994	+	0.183515i	−0.0334530	+	0.00959250i
$367$	−7.62039	−	30.5637i	−0.397781	−	1.59541i	−0.751284	−	0.659979i	$-0.770565\pi$
$367$	−7.62039	−	30.5637i	−0.397781	−	1.59541i	0.353503	−	0.935433i	$-0.384990\pi$
$368$	−0.399329	−	0.0848800i	−0.0208165	−	0.00442467i
$369$	24.5990	−	27.3200i	1.28057	−	1.42222i
$370$	−16.0121	+	15.4627i	−0.832428	+	0.803866i
$371$	−0.550788	−	1.12928i	−0.0285955	−	0.0586294i
$372$	−0.117685	+	0.0250147i	−0.00610167	+	0.00129695i
$373$	−0.604831	+	1.04760i	−0.0313170	+	0.0542426i	−0.881259	−	0.472633i	$-0.843303\pi$
$373$	−0.604831	+	1.04760i	−0.0313170	+	0.0542426i	0.849942	+	0.526876i	$0.176637\pi$
$374$	−10.9047	+	0.860923i	−0.563868	+	0.0445173i
$375$	0.542789	+	0.197559i	0.0280295	+	0.0102019i
$376$	−0.462896	−	13.2556i	−0.0238721	−	0.683606i
$377$	−2.12202	+	8.51096i	−0.109290	+	0.438337i
$378$	0.226582	−	0.464562i	0.0116541	−	0.0238945i
$379$	11.0181	+	33.9102i	0.565961	+	1.74185i	0.665077	+	0.746774i	$0.268399\pi$
$379$	11.0181	+	33.9102i	0.565961	+	1.74185i	−0.0991160	+	0.995076i	$0.531601\pi$
$380$	−8.79772	−	5.39627i	−0.451314	−	0.276823i
$381$	−0.769660	−	0.559191i	−0.0394309	−	0.0286482i
$382$	13.3677	+	12.9090i	0.683952	+	0.660484i
$383$	−6.09177	−	15.0777i	−0.311275	−	0.770432i	−0.999011	−	0.0444713i	$-0.985840\pi$
$383$	−6.09177	−	15.0777i	−0.311275	−	0.770432i	0.687736	−	0.725961i	$-0.258605\pi$
$384$	0.0521750	−	0.0189902i	0.00266254	−	0.000969087i
$385$	−1.38296	−	12.1116i	−0.0704823	−	0.617262i
$386$	14.5480	+	12.2072i	0.740471	+	0.621329i
$387$	−21.3840	−	23.7493i	−1.08701	−	1.20725i
$388$	−5.95156	−	2.64980i	−0.302145	−	0.134523i
$389$	−4.70972	+	4.54813i	−0.238792	+	0.230599i	−0.804419	−	0.594062i	$-0.797523\pi$
$389$	−4.70972	+	4.54813i	−0.238792	+	0.230599i	0.565627	+	0.824661i	$0.308634\pi$
$390$	−0.234684	+	0.0329827i	−0.0118837	+	0.00167015i
$391$	−0.900956	+	1.00061i	−0.0455633	+	0.0506032i
$392$	−4.19348	+	1.86706i	−0.211803	+	0.0943006i
$393$	0.350488	+	0.0245085i	0.0176798	+	0.00123629i
$394$	5.29287	−	6.77456i	0.266651	−	0.341298i
$395$	5.94949	−	2.16544i	0.299351	−	0.108955i
$396$	−5.04687	−	8.56305i	−0.253615	−	0.430309i
$397$	−5.91075	−	33.5215i	−0.296652	−	1.68240i	−0.660410	−	0.750905i	$-0.729618\pi$
$397$	−5.91075	−	33.5215i	−0.296652	−	1.68240i	0.363758	−	0.931493i	$-0.381493\pi$
$398$	−8.70579	+	26.7937i	−0.436382	+	1.34304i
$399$	0.374982	+	0.0230909i	0.0187726	+	0.00115599i
$400$	−0.490506	−	0.356373i	−0.0245253	−	0.0178187i
$401$	−13.3940	+	7.12174i	−0.668867	+	0.355643i	−0.768925	−	0.639339i	$-0.779208\pi$
$401$	−13.3940	+	7.12174i	−0.668867	+	0.355643i	0.100058	+	0.994982i	$0.468097\pi$
$402$	0.474414	+	0.296447i	0.0236616	+	0.0147854i
$403$	3.75489	+	1.07670i	0.187044	+	0.0536341i
$404$	−6.19658	+	1.77684i	−0.308292	+	0.0884012i
$405$	−18.0161	+	11.2577i	−0.895227	+	0.559400i
$406$	3.77665	−	6.54135i	0.187432	−	0.324642i
$407$	−19.4158	−	24.3967i	−0.962407	−	1.20930i
$408$	0.0317990	−	0.180341i	0.00157428	−	0.00892821i
$409$	−17.7278	−	9.42602i	−0.876581	−	0.466087i	−0.0307438	−	0.999527i	$-0.509788\pi$
$409$	−17.7278	−	9.42602i	−0.876581	−	0.466087i	−0.845837	+	0.533441i	$0.820899\pi$
$410$	26.5338	+	11.8136i	1.31041	+	0.583434i
$411$	−0.434455	+	0.193432i	−0.0214301	+	0.00954129i
$412$	1.62933	−	4.03273i	0.0802712	−	0.198678i
$413$	0.209628	−	6.00296i	0.0103151	−	0.295386i
$414$	−1.17610	−	0.337240i	−0.0578020	−	0.0165744i
$415$	−6.68250	+	26.8020i	−0.328031	+	1.31566i
$416$	−1.78513	−	0.250883i	−0.0875231	−	0.0123006i
$417$	−0.0217849			−0.00106681
$418$	8.70228	−	11.5443i	0.425642	−	0.564649i
$419$	−12.4464			−0.608044			−0.304022	−	0.952665i	$-0.598330\pi$
$419$	−12.4464			−0.608044			−0.304022	+	0.952665i	$0.598330\pi$
$420$	0.202091	+	0.0284020i	0.00986101	+	0.00138588i
$421$	3.43807	−	13.7894i	0.167562	−	0.672053i	−0.826472	−	0.562978i	$-0.809656\pi$
$421$	3.43807	−	13.7894i	0.167562	−	0.672053i	0.994034	−	0.109075i	$-0.0347888\pi$
$422$	−15.8397	−	4.54197i	−0.771066	−	0.221100i
$423$	1.38726	−	39.7260i	0.0674510	−	1.93154i
$424$	0.303207	−	0.750464i	0.0147250	−	0.0364457i
$425$	−1.82677	+	0.813329i	−0.0886112	+	0.0394522i
$426$	−0.0660476	−	0.0294063i	−0.00320002	−	0.00142474i
$427$	−16.4350	−	8.73867i	−0.795348	−	0.422894i
$428$	0.715635	−	4.05857i	0.0345915	−	0.196178i
$429$	−0.0145618	−	0.331643i	−0.000703050	−	0.0160119i
$430$	12.6244	−	21.8661i	0.608803	−	1.05448i
$431$	24.4254	−	15.2627i	1.17653	−	0.735176i	0.206566	−	0.978433i	$-0.433771\pi$
$431$	24.4254	−	15.2627i	1.17653	−	0.735176i	0.969962	+	0.243256i	$0.0782156\pi$
$432$	0.320071	−	0.0917789i	0.0153994	−	0.00441571i
$433$	21.3773	+	6.12983i	1.02733	+	0.294581i	0.746647	−	0.665221i	$-0.231663\pi$
$433$	21.3773	+	6.12983i	1.02733	+	0.294581i	0.280679	+	0.959802i	$0.409440\pi$
$434$	−2.85258	−	1.78249i	−0.136928	−	0.0855624i
$435$	0.564817	−	0.300319i	0.0270809	−	0.0143992i
$436$	12.6190	+	9.16826i	0.604342	+	0.439080i
$437$	−0.200714	−	1.76817i	−0.00960147	−	0.0845828i
$438$	−0.260259	+	0.800994i	−0.0124357	+	0.0382730i
$439$	2.72631	+	15.4617i	0.130120	+	0.737945i	0.978135	+	0.207973i	$0.0666866\pi$
$439$	2.72631	+	15.4617i	0.130120	+	0.737945i	−0.848015	+	0.529972i	$0.822202\pi$
$440$	5.20209	−	5.88282i	0.248000	−	0.280452i
$441$	−12.9272	+	4.70512i	−0.615581	+	0.224053i
$442$	−3.66037	+	4.68506i	−0.174106	+	0.222845i
$443$	−10.5201	−	0.735640i	−0.499827	−	0.0349513i	−0.182382	−	0.983228i	$-0.558381\pi$
$443$	−10.5201	−	0.735640i	−0.499827	−	0.0349513i	−0.317446	+	0.948276i	$0.602825\pi$
$444$	0.476850	−	0.212307i	0.0226303	−	0.0100757i
$445$	−0.206366	+	0.229192i	−0.00978267	+	0.0108648i
$446$	−13.3870	+	1.88142i	−0.633893	+	0.0890878i
$447$	0.0984092	−	0.0950327i	0.00465460	−	0.00449489i
$448$	1.41811	+	0.631382i	0.0669992	+	0.0298300i
$449$	−6.94153	−	7.70935i	−0.327591	−	0.363827i	0.556740	−	0.830687i	$-0.312052\pi$
$449$	−6.94153	−	7.70935i	−0.327591	−	0.363827i	−0.884331	+	0.466860i	$0.845385\pi$
$450$	−1.39192	−	1.16796i	−0.0656159	−	0.0550582i
$451$	−20.0252	+	35.4149i	−0.942952	+	1.66762i
$452$	3.91814	−	1.42609i	0.184294	−	0.0670775i
$453$	−0.331471	−	0.820419i	−0.0155739	−	0.0385467i
$454$	7.87364	+	7.60348i	0.369528	+	0.356849i
$455$	−5.36032	−	3.89450i	−0.251296	−	0.182577i
$456$	0.150583	+	0.189470i	0.00705171	+	0.00887276i
$457$	−6.32876	−	19.4779i	−0.296047	−	0.911139i	−0.982868	−	0.184312i	$-0.940994\pi$
$457$	−6.32876	−	19.4779i	−0.296047	−	0.911139i	0.686821	−	0.726827i	$-0.259006\pi$
$458$	−1.50593	+	3.08762i	−0.0703676	+	0.144275i
$459$	0.265672	−	1.06555i	0.0124005	−	0.0497358i
$460$	−0.0337352	−	0.966050i	−0.00157291	−	0.0450423i
$461$	−22.8296	−	8.30930i	−1.06328	−	0.387003i	−0.249621	−	0.968344i	$-0.580306\pi$
$461$	−22.8296	−	8.30930i	−1.06328	−	0.387003i	−0.813660	+	0.581341i	$0.802528\pi$
$462$	−0.0666639	+	0.277977i	−0.00310149	+	0.0129327i
$463$	7.00645	−	12.1355i	0.325617	−	0.563986i	−0.656020	−	0.754744i	$-0.727761\pi$
$463$	7.00645	−	12.1355i	0.325617	−	0.563986i	0.981637	+	0.190758i	$0.0610946\pi$
$464$	4.75951	−	1.01167i	0.220955	−	0.0469654i
$465$	−0.124881	−	0.256044i	−0.00579121	−	0.0118737i
$466$	−12.6432	+	12.2094i	−0.585683	+	0.565587i
$467$	−16.3440	+	18.1518i	−0.756309	+	0.839966i	−0.991244	−	0.132045i	$-0.957846\pi$
$467$	−16.3440	+	18.1518i	−0.756309	+	0.839966i	0.234935	+	0.972011i	$0.424512\pi$
$468$	−5.28440	−	1.12323i	−0.244271	−	0.0519215i
$469$	3.78368	+	15.1755i	0.174714	+	0.700740i
$470$	30.1887	−	8.65647i	1.39250	−	0.399293i
$471$	0.0107473	+	0.307762i	0.000495209	+	0.0141809i
$472$	2.96419	−	2.48725i	0.136438	−	0.114485i
$473$	28.7980	+	20.5307i	1.32413	+	0.944002i
$474$	−0.148468			−0.00681936
$475$	0.795748	−	2.52015i	0.0365114	−	0.115632i
$476$	4.14193	−	3.00929i	0.189845	−	0.137930i
$477$	1.06336	−	2.18021i	0.0486879	−	0.0998250i
$478$	4.06838	+	2.54220i	0.186083	+	0.116278i
$479$	−0.909114	−	1.16361i	−0.0415385	−	0.0531668i	0.766793	−	0.641894i	$-0.221851\pi$
$479$	−0.909114	−	1.16361i	−0.0415385	−	0.0531668i	−0.808331	+	0.588728i	$0.799629\pi$
$480$	0.0735151	+	0.108991i	0.00335549	+	0.00497472i
$481$	−16.9057	−	1.18216i	−0.770832	−	0.0539018i
$482$	15.9332	+	17.6956i	0.725738	+	0.806014i
$483$	0.0175935	+	0.0304728i	0.000800531	+	0.00138656i
$484$	7.50595	+	8.04119i	0.341179	+	0.365509i
$485$	2.67861	−	15.1911i	0.121629	−	0.689793i
$486$	1.46437	−	0.311261i	0.0664250	−	0.0141191i
$487$	1.33243	+	12.6773i	0.0603784	+	0.574462i	0.982330	+	0.187157i	$0.0599272\pi$
$487$	1.33243	+	12.6773i	0.0603784	+	0.574462i	−0.921952	+	0.387305i	$0.873406\pi$
$488$	−2.90090	−	11.6349i	−0.131317	−	0.526686i
$489$	0.00579794	−	0.166031i	0.000262192	−	0.00750819i
$490$	−6.69151	−	8.56474i	−0.302292	−	0.386916i
$491$	−11.8026	+	0.825320i	−0.532645	+	0.0372462i	−0.333547	−	0.942733i	$-0.608246\pi$
$491$	−11.8026	+	0.825320i	−0.532645	+	0.0372462i	−0.199098	+	0.979980i	$0.563801\pi$
$492$	−0.489940	−	0.473129i	−0.0220882	−	0.0213303i
$493$	4.95915	−	15.2627i	0.223349	−	0.687397i
$494$	−1.42874	−	7.72667i	−0.0642821	−	0.347640i
$495$	16.7821	−	16.4998i	0.754299	−	0.741613i
$496$	−0.376279	−	2.13398i	−0.0168954	−	0.0958186i
$497$	−0.757189	−	1.87411i	−0.0339646	−	0.0840653i
$498$	0.362213	−	0.537003i	0.0162312	−	0.0240637i
$499$	10.0402	+	14.8852i	0.449462	+	0.666355i	0.983873	−	0.178870i	$-0.0572442\pi$
$499$	10.0402	+	14.8852i	0.449462	+	0.666355i	−0.534411	+	0.845225i	$0.679466\pi$
$500$	−3.89712	+	9.64572i	−0.174285	+	0.431370i
$501$	0.150154	+	0.0319163i	0.00670839	+	0.00142591i
$502$	−0.879809	+	8.37082i	−0.0392678	+	0.373608i
$503$	−12.8414	−	26.3288i	−0.572570	−	1.17394i	−0.966943	−	0.254992i	$-0.917927\pi$
$503$	−12.8414	−	26.3288i	−0.572570	−	1.17394i	0.394373	−	0.918950i	$-0.370962\pi$
$504$	4.10760	+	2.18405i	0.182967	+	0.0972853i
$505$	−7.63166	−	13.2184i	−0.339604	−	0.588212i
$506$	1.35151	+	0.0823272i	0.0600818	+	0.00365989i
$507$	0.414717	+	0.347989i	0.0184182	+	0.0154547i
$508$	10.5489	−	13.5020i	0.468031	−	0.599052i
$509$	−21.0204	+	31.1640i	−0.931714	+	1.38132i	−0.00728232	+	0.999973i	$0.502318\pi$
$509$	−21.0204	+	31.1640i	−0.931714	+	1.38132i	−0.924431	+	0.381349i	$0.875460\pi$
$510$	0.432536	−	0.0302458i	0.0191530	−	0.00133931i
$511$	−20.7903	+	11.0544i	−0.919707	+	0.489017i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	0.821576	+	1.19646i	0.0362734	+	0.0528251i
$514$	−17.9123	+	13.0140i	−0.790077	+	0.574025i
$515$	10.1982	+	1.43326i	0.449387	+	0.0631572i
$516$	−0.453559	+	0.380581i	−0.0199668	+	0.0167542i
$517$	8.02733	+	43.2521i	0.353042	+	1.90223i
$518$	13.7132	+	4.99121i	0.602525	+	0.219301i
$519$	0.146183	−	0.0913454i	0.00641673	−	0.00400962i
$520$	−0.446158	−	4.24491i	−0.0195653	−	0.186152i
$521$	2.35934	−	22.4476i	0.103365	−	0.983449i	−0.812772	−	0.582582i	$-0.802042\pi$
$521$	2.35934	−	22.4476i	0.103365	−	0.983449i	0.916136	−	0.400867i	$-0.131291\pi$
$522$	14.4406	−	2.02950i	0.632049	−	0.0888286i
$523$	−18.1151	+	2.54591i	−0.792117	+	0.111325i	−0.523616	−	0.851954i	$-0.675417\pi$
$523$	−18.1151	+	2.54591i	−0.792117	+	0.111325i	−0.268501	+	0.963279i	$0.586528\pi$
$524$	−0.661440	+	6.29318i	−0.0288951	+	0.274919i
$525$	0.00546231	+	0.0519704i	0.000238395	+	0.00226817i
$526$	−14.4836	+	9.05033i	−0.631513	+	0.394613i
$527$	−6.71570	−	2.44432i	−0.292541	−	0.106476i
$528$	−0.161813	+	0.0879090i	−0.00704201	+	0.00382575i
$529$	−17.4913	+	14.6770i	−0.760493	+	0.638130i
$530$	1.89782	+	0.266721i	0.0824360	+	0.0115856i
$531$	9.38175	−	6.81624i	0.407133	−	0.295800i
$532$	−0.651320	+	6.73495i	−0.0282383	+	0.291997i
$533$	6.83330	+	21.0307i	0.295983	+	0.910943i
$534$	0.00638558	−	0.00339527i	0.000276331	−	0.000146928i
$535$	9.73419	−	0.680681i	0.420846	−	0.0294284i
$536$	−5.63407	+	8.35285i	−0.243355	+	0.360788i
$537$	−0.658057	+	0.842275i	−0.0283973	+	0.0363468i
$538$	−14.4660	−	12.1384i	−0.623672	−	0.523323i
$539$	12.8381	−	8.18323i	0.552977	−	0.352477i
$540$	0.394197	+	0.682769i	0.0169635	+	0.0293817i
$541$	14.8446	+	7.89301i	0.638219	+	0.339347i	0.756847	−	0.653592i	$-0.226739\pi$
$541$	14.8446	+	7.89301i	0.638219	+	0.339347i	−0.118629	+	0.992939i	$0.537850\pi$
$542$	5.96251	+	12.2250i	0.256112	+	0.525107i
$543$	0.0238969	−	0.227363i	0.00102551	−	0.00975710i
$544$	3.22605	+	0.685718i	0.138316	+	0.0293999i
$545$	−13.8351	+	34.2430i	−0.592630	+	1.46681i
$546$	0.0868827	+	0.128809i	0.00371824	+	0.00551251i
$547$	6.18513	−	9.16983i	0.264457	−	0.392074i	−0.673298	−	0.739371i	$-0.735123\pi$
$547$	6.18513	−	9.16983i	0.264457	−	0.392074i	0.937755	+	0.347298i	$0.112901\pi$
$548$	−3.20858	−	7.94152i	−0.137064	−	0.339245i
$549$	−6.24025	−	35.3902i	−0.266328	−	1.51042i
$550$	1.78389	+	0.928074i	0.0760652	+	0.0395732i
$551$	10.7572	+	18.2794i	0.458271	+	0.778728i
$552$	−0.00700463	+	0.0215580i	−0.000298137	+	0.000917571i
$553$	−2.98585	−	2.88341i	−0.126971	−	0.122615i
$554$	−17.4088	+	1.21734i	−0.739630	+	0.0517200i
$555$	0.760908	+	0.973918i	0.0322987	+	0.0413405i
$556$	0.0136930	−	0.392115i	0.000580711	−	0.0166294i
$557$	−2.27584	−	9.12788i	−0.0964303	−	0.386761i	0.902615	−	0.430449i	$-0.141645\pi$
$557$	−2.27584	−	9.12788i	−0.0964303	−	0.386761i	−0.999045	+	0.0436882i	$0.986089\pi$
$558$	−0.678811	−	6.45845i	−0.0287363	−	0.273408i
$559$	18.8029	−	3.99667i	0.795276	−	0.169041i
$560$	−0.638244	+	3.61966i	−0.0269707	+	0.152959i
$561$	−0.0157489	+	0.607146i	−0.000664918	+	0.0256337i
$562$	5.53757	+	9.59135i	0.233588	+	0.404587i
$563$	11.0964	+	12.3238i	0.467656	+	0.519384i	0.930121	−	0.367253i	$-0.119702\pi$
$563$	11.0964	+	12.3238i	0.467656	+	0.519384i	−0.462465	+	0.886637i	$0.653035\pi$
$564$	−0.734653	−	0.0513719i	−0.0309345	−	0.00216315i
$565$	5.52070	+	8.18477i	0.232258	+	0.344336i
$566$	−3.95368	−	5.06048i	−0.166185	−	0.212708i
$567$	11.8114	+	7.38058i	0.496032	+	0.309955i
$568$	0.570811	−	1.17034i	0.0239507	−	0.0491062i
$569$	−1.59540	+	1.15913i	−0.0668827	+	0.0485931i	−0.620724	−	0.784029i	$-0.713161\pi$
$569$	−1.59540	+	1.15913i	−0.0668827	+	0.0485931i	0.553842	+	0.832622i	$0.313161\pi$
$570$	−0.349038	+	0.454486i	−0.0146196	+	0.0190363i
$571$	39.1812			1.63968			0.819841	−	0.572591i	$-0.194062\pi$
$571$	39.1812			1.63968			0.819841	+	0.572591i	$0.194062\pi$
$572$	5.97854	−	0.0536482i	0.249975	−	0.00224314i
$573$	0.790412	−	0.663235i	0.0330199	−	0.0277070i
$574$	−0.664553	−	19.0303i	−0.0277379	−	0.794310i
$575$	0.237933	−	0.0682261i	0.00992248	−	0.00284523i
$576$	0.725020	+	2.90790i	0.0302092	+	0.121162i
$577$	13.4611	+	2.86124i	0.560391	+	0.119115i	0.479394	−	0.877600i	$-0.340856\pi$
$577$	13.4611	+	2.86124i	0.560391	+	0.119115i	0.0809966	+	0.996714i	$0.474190\pi$
$578$	−4.09669	+	4.54984i	−0.170400	+	0.189248i
$579$	0.758505	−	0.732480i	0.0315224	−	0.0304408i
$580$	5.05055	+	10.3552i	0.209712	+	0.429974i
$581$	17.7137	−	3.76516i	0.734887	−	0.156205i
$582$	−0.180862	+	0.313262i	−0.00749697	+	0.0129851i
$583$	−0.626036	+	2.61046i	−0.0259277	+	0.108114i
$584$	−14.2539	−	5.18798i	−0.589829	−	0.214680i
$585$	−0.446425	−	12.7839i	−0.0184574	−	0.528551i
$586$	4.07094	−	16.3277i	0.168169	−	0.674490i
$587$	1.71484	−	3.51594i	0.0707790	−	0.145119i	−0.860471	−	0.509500i	$-0.829831\pi$
$587$	1.71484	−	3.51594i	0.0707790	−	0.145119i	0.931250	+	0.364381i	$0.118719\pi$
$588$	0.0787595	+	0.242397i	0.00324799	+	0.00999628i
$589$	8.30257	−	4.50347i	0.342101	−	0.185562i
$590$	7.41220	+	5.38528i	0.305156	+	0.221709i
$591$	−0.343368	−	0.331587i	−0.0141243	−	0.0136397i
$592$	3.52169	+	8.71648i	0.144740	+	0.358245i
$593$	−1.11066	+	0.404248i	−0.0456094	+	0.0166005i	−0.364724	−	0.931116i	$-0.618837\pi$
$593$	−1.11066	+	0.404248i	−0.0456094	+	0.0166005i	0.319115	+	0.947716i	$0.396614\pi$
$594$	−1.00479	+	0.458208i	−0.0412270	+	0.0188005i
$595$	9.28618	+	7.79203i	0.380696	+	0.319442i
$596$	1.64868	+	1.83104i	0.0675325	+	0.0750024i
$597$	1.42900	+	0.636232i	0.0584851	+	0.0260393i
$598$	0.529391	−	0.511227i	0.0216484	−	0.0209056i
$599$	−13.5615	+	1.90595i	−0.554110	+	0.0778751i	−0.410670	−	0.911784i	$-0.634705\pi$
$599$	−13.5615	+	1.90595i	−0.554110	+	0.0778751i	−0.143440	+	0.989659i	$0.545816\pi$
$600$	−0.0225255	+	0.0250171i	−0.000919599	+	0.00102132i
$601$	41.4375	−	18.4491i	1.69027	−	0.752556i	0.690702	−	0.723140i	$-0.257302\pi$
$601$	41.4375	−	18.4491i	1.69027	−	0.752556i	0.999567	−	0.0294168i	$-0.00936500\pi$
$602$	−16.5129	−	1.15469i	−0.673014	−	0.0470617i
$603$	−18.5899	+	23.7940i	−0.757040	+	0.968967i
$604$	14.9754	−	5.45061i	0.609341	−	0.221782i
$605$	−14.1746	+	21.8505i	−0.576278	+	0.888349i
$606$	0.0621524	+	0.352484i	0.00252477	+	0.0143187i
$607$	5.25487	−	16.1728i	0.213289	−	0.656435i	−0.785982	−	0.618249i	$-0.787842\pi$
$607$	5.25487	−	16.1728i	0.213289	−	0.656435i	0.999271	−	0.0381855i	$-0.0121578\pi$
$608$	−3.50501	+	2.59132i	−0.142147	+	0.105092i
$609$	−0.339290	−	0.246509i	−0.0137487	−	0.00998904i
$610$	25.0686	−	13.3292i	1.01500	−	0.539684i
$611$	20.2769	+	12.6704i	0.820315	+	0.512590i
$612$	9.50129	+	2.72445i	0.384067	+	0.110129i
$613$	0.307307	−	0.0881187i	0.0124120	−	0.00355908i	−0.269426	−	0.963021i	$-0.586834\pi$
$613$	0.307307	−	0.0881187i	0.0124120	−	0.00355908i	0.281838	+	0.959462i	$0.409056\pi$
$614$	−12.3683	+	7.72859i	−0.499145	+	0.311901i
$615$	0.806337	−	1.39662i	0.0325147	−	0.0563170i
$616$	−4.96153	−	1.37464i	−0.199906	−	0.0553856i
$617$	−3.80700	+	21.5906i	−0.153264	+	0.869205i	0.807091	+	0.590427i	$0.201040\pi$
$617$	−3.80700	+	21.5906i	−0.153264	+	0.869205i	−0.960356	+	0.278778i	$0.910071\pi$
$618$	−0.213228	−	0.113375i	−0.00857730	−	0.00456063i
$619$	18.1093	+	8.06277i	0.727874	+	0.324070i	0.737004	−	0.675888i	$-0.236240\pi$
$619$	18.1093	+	8.06277i	0.727874	+	0.324070i	−0.00913068	+	0.999958i	$0.502906\pi$
$620$	4.68714	−	2.08685i	0.188240	−	0.0838098i
$621$	−0.0509221	+	0.126037i	−0.00204343	+	0.00505768i
$622$	0.0275989	−	0.790328i	0.00110661	−	0.0316893i
$623$	0.194361	+	0.0557321i	0.00778690	+	0.00223286i
$624$	−0.0242141	+	0.0971174i	−0.000969340	+	0.00388781i
$625$	−27.3947	−	3.85007i	−1.09579	−	0.154003i
$626$	12.1646			0.486197
$627$	−0.586961	−	0.547534i	−0.0234410	−	0.0218664i
$628$	−5.54629			−0.221321
$629$	30.7040	+	4.31516i	1.22425	+	0.172057i
$630$	−2.66481	+	10.6880i	−0.106169	+	0.425819i
$631$	4.77313	+	1.36867i	0.190015	+	0.0544860i	0.369295	−	0.929312i	$-0.379599\pi$
$631$	4.77313	+	1.36867i	0.190015	+	0.0544860i	−0.179280	+	0.983798i	$0.557377\pi$
$632$	0.0933201	−	2.67234i	0.00371207	−	0.106300i
$633$	−0.342735	+	0.848299i	−0.0136225	+	0.0337168i
$634$	17.5421	−	7.81024i	0.696685	−	0.310184i
$635$	37.0623	+	16.5012i	1.47077	+	0.654831i
$636$	−0.0396803	−	0.0210984i	−0.00157343	−	0.000836606i
$637$	1.43691	−	8.14914i	0.0569326	−	0.322881i
$638$	−15.1148	+	5.65544i	−0.598400	+	0.223901i
$639$	1.95117	−	3.37953i	0.0771871	−	0.133692i
$640$	−2.00798	+	1.25472i	−0.0793722	+	0.0495973i
$641$	30.2726	−	8.68052i	1.19570	−	0.342860i	0.382006	−	0.924160i	$-0.375233\pi$
$641$	30.2726	−	8.68052i	1.19570	−	0.342860i	0.813689	+	0.581300i	$0.197456\pi$
$642$	−0.219958	−	0.0630719i	−0.00868104	−	0.00248925i
$643$	18.6048	+	11.6256i	0.733702	+	0.458468i	0.844623	−	0.535361i	$-0.179825\pi$
$643$	18.6048	+	11.6256i	0.733702	+	0.458468i	−0.110921	+	0.993829i	$0.535380\pi$
$644$	−0.559551	+	0.297519i	−0.0220494	+	0.0117239i
$645$	−1.13416	−	0.824018i	−0.0446576	−	0.0324457i
$646$	1.62151	+	14.2844i	0.0637973	+	0.562013i
$647$	0.928618	−	2.85799i	0.0365077	−	0.112359i	−0.931142	−	0.364657i	$-0.881186\pi$
$647$	0.928618	−	2.85799i	0.0365077	−	0.112359i	0.967650	+	0.252298i	$0.0811862\pi$
$648$	1.55802	+	8.83595i	0.0612047	+	0.347109i
$649$	−8.50142	+	9.61388i	−0.333710	+	0.377378i
$650$	1.02704	−	0.373813i	0.0402839	−	0.0146622i
$651$	−0.114984	+	0.147173i	−0.00450657	+	0.00576815i
$652$	2.98482	+	0.208719i	0.116895	+	0.00817407i
$653$	−39.1357	+	17.4244i	−1.53150	+	0.681868i	−0.987558	−	0.157255i	$-0.949736\pi$
$653$	−39.1357	+	17.4244i	−1.53150	+	0.681868i	−0.543942	+	0.839123i	$0.683069\pi$
$654$	0.579503	−	0.643603i	0.0226604	−	0.0251669i
$655$	−14.8370	+	2.08521i	−0.579730	+	0.0814758i
$656$	8.82401	−	8.52125i	0.344520	−	0.332699i
$657$	−41.5290	−	18.4899i	−1.62020	−	0.721360i
$658$	−13.7770	−	15.3009i	−0.537083	−	0.596491i
$659$	18.0267	+	15.1262i	0.702221	+	0.589234i	0.922405	−	0.386225i	$-0.126221\pi$
$659$	18.0267	+	15.1262i	0.702221	+	0.589234i	−0.220183	+	0.975458i	$0.570666\pi$
$660$	−0.294653	−	0.321399i	−0.0114694	−	0.0125104i
$661$	0.174136	−	0.0633805i	0.00677312	−	0.00246522i	−0.338631	−	0.940919i	$-0.609964\pi$
$661$	0.174136	−	0.0633805i	0.00677312	−	0.00246522i	0.345404	+	0.938454i	$0.387742\pi$
$662$	6.79093	+	16.8081i	0.263937	+	0.653267i
$663$	0.237462	+	0.229314i	0.00922225	+	0.00890582i
$664$	9.43807	+	6.85716i	0.366268	+	0.266110i
$665$	−15.8461	+	2.36151i	−0.614487	+	0.0915753i
$666$	8.70628	+	26.7952i	0.337361	+	1.03829i
$667$	−0.870816	+	1.78544i	−0.0337181	+	0.0691324i
$668$	−0.668854	+	2.68263i	−0.0258787	+	0.103794i
$669$	0.0261955	+	0.750140i	0.00101278	+	0.0290021i
$670$	−22.4174	−	8.15925i	−0.866058	−	0.315219i
$671$	15.2283	+	36.7388i	0.587882	+	1.41828i
$672$	0.0430949	−	0.0746425i	0.00166242	−	0.00287940i
$673$	7.85807	−	1.67029i	0.302907	−	0.0643848i	−0.0539510	−	0.998544i	$-0.517181\pi$
$673$	7.85807	−	1.67029i	0.302907	−	0.0643848i	0.356858	+	0.934159i	$0.383848\pi$
$674$	−7.65731	−	15.6998i	−0.294948	−	0.604734i
$675$	−0.145220	+	0.140237i	−0.00558950	+	0.00539772i
$676$	−6.52428	+	7.24594i	−0.250934	+	0.278690i
$677$	37.0815	+	7.88192i	1.42516	+	0.302927i	0.855008	−	0.518614i	$-0.173552\pi$
$677$	37.0815	+	7.88192i	1.42516	+	0.302927i	0.570149	+	0.821541i	$0.306885\pi$
$678$	−0.0560075	−	0.224634i	−0.00215096	−	0.00862701i
$679$	−9.72122	+	2.78751i	−0.373066	+	0.106975i
$680$	0.272536	+	7.80440i	0.0104513	+	0.299285i
$681$	0.465556	−	0.390648i	0.0178401	−	0.0149697i
$682$	2.28209	+	6.81485i	0.0873856	+	0.260954i
$683$	28.7739			1.10100			0.550502	−	0.834834i	$-0.314436\pi$
$683$	28.7739			1.10100			0.550502	+	0.834834i	$0.314436\pi$
$684$	−11.0204	+	7.01432i	−0.421374	+	0.268199i
$685$	16.4072	−	11.9205i	0.626886	−	0.455459i
$686$	−7.88708	+	16.1709i	−0.301130	+	0.617409i
$687$	0.161756	+	0.101077i	0.00617138	+	0.00385631i
$688$	−6.56516	−	8.40302i	−0.250294	−	0.320362i
$689$	0.815909	+	1.20963i	0.0310837	+	0.0460834i
$690$	−0.0535404	−	0.00374391i	−0.00203825	−	0.000142528i
$691$	12.7139	+	14.1202i	0.483660	+	0.537159i	0.934744	−	0.355323i	$-0.115629\pi$
$691$	12.7139	+	14.1202i	0.483660	+	0.537159i	−0.451084	+	0.892482i	$0.648962\pi$
$692$	1.55228	+	2.68863i	0.0590089	+	0.102206i
$693$	−14.5457	−	5.14686i	−0.552545	−	0.195513i
$694$	2.81062	−	15.9398i	0.106690	−	0.605068i
$695$	0.908700	−	0.193150i	0.0344690	−	0.00732661i
$696$	−0.0282403	−	0.268689i	−0.00107045	−	0.0101846i
$697$	−9.78754	−	39.2557i	−0.370729	−	1.48691i
$698$	0.156734	−	4.48828i	0.00593247	−	0.169884i
$699$	0.600814	+	0.769007i	0.0227249	+	0.0290865i
$700$	−0.938871	+	0.0656522i	−0.0354860	+	0.00248142i
$701$	−7.37199	−	7.11905i	−0.278436	−	0.268883i	0.542307	−	0.840181i	$-0.317551\pi$
$701$	−7.37199	−	7.11905i	−0.278436	−	0.268883i	−0.820743	+	0.571298i	$0.806440\pi$
$702$	−0.185483	+	0.570857i	−0.00700059	+	0.0215456i
$703$	−31.1710	+	26.6002i	−1.17564	+	1.00325i
$704$	−1.48060	−	2.96780i	−0.0558023	−	0.111853i
$705$	−0.302796	−	1.71724i	−0.0114039	−	0.0646750i
$706$	6.45946	+	15.9877i	0.243105	+	0.601705i
$707$	−5.59566	+	8.29590i	−0.210446	+	0.312000i
$708$	−0.120141	−	0.178116i	−0.00451516	−	0.00669400i
$709$	17.7252	−	43.8715i	0.665685	−	1.64763i	−0.0925999	−	0.995703i	$-0.529518\pi$
$709$	17.7252	−	43.8715i	0.665685	−	1.64763i	0.758284	−	0.651924i	$-0.226038\pi$
$710$	3.01573	+	0.641014i	0.113178	+	0.0240568i
$711$	0.837655	−	7.96976i	0.0314145	−	0.298889i
$712$	0.0570992	+	0.117071i	0.00213988	+	0.00438741i
$713$	0.781089	+	0.415312i	0.0292520	+	0.0155536i
$714$	−0.142132	−	0.246180i	−0.00531915	−	0.00921305i
$715$	3.54784	+	13.7045i	0.132682	+	0.512521i
$716$	−14.7468	−	12.3741i	−0.551115	−	0.462441i
$717$	0.163991	−	0.209899i	0.00612435	−	0.00783881i
$718$	13.6988	−	20.3093i	0.511236	−	0.757938i
$719$	13.4000	−	0.937020i	0.499736	−	0.0349449i	0.182335	−	0.983236i	$-0.441634\pi$
$719$	13.4000	−	0.937020i	0.499736	−	0.0349449i	0.317401	+	0.948292i	$0.397190\pi$
$720$	−6.26539	+	3.33136i	−0.233497	+	0.124153i
$721$	−2.08638	−	6.42123i	−0.0777010	−	0.239139i
$722$	−15.5548	−	10.9109i	−0.578891	−	0.406060i
$723$	1.06961	−	0.777120i	0.0397793	−	0.0289014i
$724$	4.07739	+	0.573040i	0.151535	+	0.0212969i
$725$	−2.25995	+	1.89632i	−0.0839324	+	0.0704276i
$726$	0.487592	−	0.367804i	0.0180962	−	0.0136505i
$727$	−47.5010	−	17.2890i	−1.76172	−	0.641212i	−0.761738	−	0.647886i	$-0.775653\pi$
$727$	−47.5010	−	17.2890i	−1.76172	−	0.641212i	−0.999978	+	0.00667372i	$0.997876\pi$
$728$	−2.37310	+	1.48288i	−0.0879528	+	0.0549590i
$729$	2.80488	+	26.6867i	0.103885	+	0.988395i
$730$	3.75422	−	35.7190i	0.138950	−	1.32202i
$731$	−34.8275	+	4.89468i	−1.28814	+	0.181036i
$732$	−0.659306	+	0.0926594i	−0.0243686	+	0.00342479i
$733$	1.79710	−	17.0982i	0.0663772	−	0.631537i	−0.909872	−	0.414888i	$-0.863821\pi$
$733$	1.79710	−	17.0982i	0.0663772	−	0.631537i	0.976250	−	0.216649i	$-0.0695127\pi$
$734$	−3.29258	−	31.3268i	−0.121531	−	1.15629i
$735$	−0.511775	+	0.319793i	−0.0188771	+	0.0117957i
$736$	−0.383630	−	0.139630i	−0.0141408	−	0.00514682i
$737$	14.3786	−	30.1645i	0.529643	−	1.11112i
$738$	28.1618	−	23.6306i	1.03665	−	0.869853i
$739$	−10.7007	−	1.50388i	−0.393631	−	0.0553212i	−0.0604188	−	0.998173i	$-0.519244\pi$
$739$	−10.7007	−	1.50388i	−0.393631	−	0.0553212i	−0.333212	+	0.942852i	$0.608133\pi$
$740$	−18.0082	+	13.0837i	−0.661996	+	0.480968i
$741$	−0.434954	+	0.0340502i	−0.0159784	+	0.00125086i
$742$	−0.388262	−	1.19495i	−0.0142535	−	0.0438679i
$743$	−35.8178	+	19.0447i	−1.31403	+	0.698681i	−0.970645	−	0.240515i	$-0.922684\pi$
$743$	−35.8178	+	19.0447i	−1.31403	+	0.698681i	−0.343382	+	0.939196i	$0.611573\pi$
$744$	−0.120021	+	0.00839268i	−0.00440018	+	0.000307690i
$745$	−3.26231	+	4.83657i	−0.119522	+	0.177198i
$746$	−0.744742	+	0.953226i	−0.0272669	+	0.0349001i
$747$	26.7827	+	22.4734i	0.979928	+	0.822257i
$748$	−10.9184	−	0.665095i	−0.399216	−	0.0243183i
$749$	−3.19867	−	5.54026i	−0.116877	−	0.202437i
$750$	0.510012	+	0.271178i	0.0186230	+	0.00990203i
$751$	15.1823	+	31.1284i	0.554011	+	1.13589i	0.973618	+	0.228186i	$0.0732793\pi$
$751$	15.1823	+	31.1284i	0.554011	+	1.13589i	−0.419606	+	0.907706i	$0.637832\pi$
$752$	1.38643	−	13.1910i	0.0505580	−	0.481028i
$753$	0.457125	+	0.0971649i	0.0166586	+	0.00354089i
$754$	−3.28587	+	8.13281i	−0.119664	+	0.296179i
$755$	21.1005	+	31.2828i	0.767926	+	1.13850i
$756$	0.289031	−	0.428507i	0.0105120	−	0.0155846i
$757$	−4.95494	−	12.2639i	−0.180090	−	0.445739i	0.809954	−	0.586493i	$-0.199492\pi$
$757$	−4.95494	−	12.2639i	−0.180090	−	0.445739i	−0.990045	+	0.140754i	$0.955047\pi$
$758$	6.19148	+	35.1136i	0.224885	+	1.27538i
$759$	0.0123899	−	0.0741515i	0.000449725	−	0.00269153i
$760$	−7.96109	−	6.56816i	−0.288779	−	0.238252i
$761$	−9.58664	+	29.5046i	−0.347515	+	1.06954i	0.612708	+	0.790309i	$0.290080\pi$
$761$	−9.58664	+	29.5046i	−0.347515	+	1.06954i	−0.960223	+	0.279233i	$0.909920\pi$
$762$	−0.684345	−	0.660865i	−0.0247912	−	0.0239406i
$763$	24.1539	−	1.68901i	0.874431	−	0.0611461i
$764$	11.4410	+	14.6438i	0.413922	+	0.529796i
$765$	−0.816767	+	23.3892i	−0.0295303	+	0.845637i
$766$	−3.93408	−	15.7787i	−0.142144	−	0.570109i
$767$	0.729126	+	6.93717i	0.0263272	+	0.250487i
$768$	0.0543102	−	0.0115440i	0.00195975	−	0.000416558i
$769$	3.65417	−	20.7238i	0.131773	−	0.747320i	−0.845280	−	0.534323i	$-0.820567\pi$
$769$	3.65417	−	20.7238i	0.131773	−	0.747320i	0.977053	−	0.212997i	$-0.0683224\pi$
$770$	0.316099	−	12.1862i	0.0113914	−	0.439159i
$771$	0.614668	+	1.06464i	0.0221367	+	0.0383419i
$772$	12.7075	+	14.1131i	0.457352	+	0.507940i
$773$	−27.3924	−	1.91546i	−0.985236	−	0.0688944i	−0.431960	−	0.901893i	$-0.642178\pi$
$773$	−27.3924	−	1.91546i	−0.985236	−	0.0688944i	−0.553276	+	0.832998i	$0.686622\pi$
$774$	−17.8706	−	26.4943i	−0.642346	−	0.952317i
$775$	0.808849	+	1.03528i	0.0290547	+	0.0371884i
$776$	−5.52486	−	3.45231i	−0.198331	−	0.123931i
$777$	0.355200	−	0.728267i	0.0127427	−	0.0261264i
$778$	−5.29686	+	3.84840i	−0.189902	+	0.137972i
$779$	47.4181	+	24.7093i	1.69893	+	0.885302i
$780$	−0.236991			−0.00848563
$781$	−1.29762	+	4.11908i	−0.0464326	+	0.147392i
$782$	−1.03145	+	0.865486i	−0.0368844	+	0.0309497i
$783$	−0.0565434	−	1.61919i	−0.00202070	−	0.0578652i
$784$	−4.41251	+	1.26527i	−0.157590	+	0.0451881i
$785$	−3.17699	−	12.7422i	−0.113392	−	0.454789i
$786$	0.343666	+	0.0730485i	0.0122582	+	0.00260555i
$787$	−23.1953	+	25.7610i	−0.826824	+	0.918281i	−0.997753	−	0.0670024i	$-0.978656\pi$
$787$	−23.1953	+	25.7610i	−0.826824	+	0.918281i	0.170929	+	0.985283i	$0.445323\pi$
$788$	6.18420	−	5.97201i	0.220303	−	0.212744i
$789$	0.415694	+	0.852299i	0.0147991	+	0.0303426i
$790$	6.19296	−	1.31635i	0.220336	−	0.0468338i
$791$	3.23626	−	5.60536i	0.115068	−	0.199304i
$792$	−3.80600	−	9.18210i	−0.135240	−	0.326272i
$793$	20.3123	+	7.39308i	0.721312	+	0.262536i
$794$	−1.18793	−	34.0179i	−0.0421581	−	1.20725i
$795$	0.0257427	−	0.103248i	0.000912999	−	0.00366184i
$796$	−12.3500	+	25.3213i	−0.437735	+	0.897489i
$797$	−6.44676	−	19.8411i	−0.228356	−	0.702808i	−0.997934	−	0.0642544i	$-0.979533\pi$
$797$	−6.44676	−	19.8411i	−0.228356	−	0.702808i	0.769577	−	0.638553i	$-0.220467\pi$
$798$	0.368119	+	0.0750536i	0.0130313	+	0.00265687i
$799$	−35.3907	−	25.7128i	−1.25203	−	0.909654i
$800$	−0.436135	−	0.421170i	−0.0154197	−	0.0148906i
$801$	0.146231	+	0.361934i	0.00516681	+	0.0127883i
$802$	−14.2549	+	5.18834i	−0.503356	+	0.183207i
$803$	49.3012	+	10.0178i	1.73980	+	0.353520i
$804$	0.428540	+	0.359588i	0.0151134	+	0.0126817i
$805$	−1.00405	−	1.11511i	−0.0353880	−	0.0393024i
$806$	3.56850	+	1.58880i	0.125695	+	0.0559631i
$807$	−0.754231	+	0.728352i	−0.0265502	+	0.0256392i
$808$	−6.38357	+	0.897152i	−0.224573	+	0.0315617i
$809$	−12.4879	+	13.8693i	−0.439053	+	0.487617i	−0.921539	−	0.388286i	$-0.873067\pi$
$809$	−12.4879	+	13.8693i	−0.439053	+	0.487617i	0.482486	+	0.875904i	$0.339734\pi$
$810$	−19.4075	+	8.64079i	−0.681911	+	0.303606i
$811$	−20.4697	−	1.43138i	−0.718790	−	0.0502627i	−0.294323	−	0.955706i	$-0.595094\pi$
$811$	−20.4697	−	1.43138i	−0.718790	−	0.0502627i	−0.424467	+	0.905443i	$0.639539\pi$
$812$	4.65028	−	5.95208i	0.163193	−	0.208877i
$813$	0.709659	−	0.258295i	0.0248888	−	0.00905879i
$814$	−15.8315	−	26.8614i	−0.554894	−	0.941492i
$815$	1.23023	+	6.97698i	0.0430931	+	0.244393i
$816$	0.0565881	−	0.174160i	0.00198098	−	0.00609683i
$817$	25.6709	−	38.7496i	0.898112	−	1.35568i
$818$	−16.2434	−	11.8015i	−0.567937	−	0.412630i
$819$	−7.40465	+	3.93712i	−0.258740	+	0.137574i
$820$	24.6315	+	15.3915i	0.860169	+	0.537493i
$821$	23.8276	+	6.83247i	0.831591	+	0.238455i	0.664312	−	0.747455i	$-0.268724\pi$
$821$	23.8276	+	6.83247i	0.831591	+	0.238455i	0.167278	+	0.985910i	$0.446502\pi$
$822$	−0.457147	+	0.131085i	−0.0159448	+	0.00457211i
$823$	28.7295	−	17.9522i	1.00145	−	0.625774i	0.0730373	−	0.997329i	$-0.476731\pi$
$823$	28.7295	−	17.9522i	1.00145	−	0.625774i	0.928411	+	0.371555i	$0.121175\pi$
$824$	2.17472	−	3.76672i	0.0757599	−	0.131220i
$825$	0.0616009	−	0.0931187i	0.00214467	−	0.00324198i
$826$	1.04304	−	5.91537i	0.0362920	−	0.205822i
$827$	−23.6711	−	12.5862i	−0.823126	−	0.437664i	0.00378749	−	0.999993i	$-0.498794\pi$
$827$	−23.6711	−	12.5862i	−0.823126	−	0.437664i	−0.826914	+	0.562329i	$0.809906\pi$
$828$	−1.11772	−	0.497639i	−0.0388433	−	0.0172941i
$829$	−40.8300	+	18.1787i	−1.41808	+	0.631371i	−0.965512	−	0.260357i	$-0.916160\pi$
$829$	−40.8300	+	18.1787i	−1.41808	+	0.631371i	−0.452571	+	0.891728i	$0.649493\pi$
$830$	−10.3476	+	25.6112i	−0.359170	+	0.888977i
$831$	−0.0338162	+	0.968369i	−0.00117307	+	0.0335923i
$832$	−1.73284	−	0.496883i	−0.0600754	−	0.0172263i
$833$	−3.66257	+	14.6898i	−0.126900	+	0.508970i
$834$	−0.0215729	−	0.00303187i	−0.000747007	−	0.000104985i
$835$	−6.54628			−0.226543
$836$	10.2242	−	10.2208i	0.353613	−	0.353494i
$837$	−0.721513			−0.0249391
$838$	−12.3252	−	1.73220i	−0.425768	−	0.0598378i
$839$	2.90405	−	11.6475i	0.100259	−	0.402116i	−0.899107	−	0.437729i	$-0.855783\pi$
$839$	2.90405	−	11.6475i	0.100259	−	0.402116i	0.999366	+	0.0356130i	$0.0113384\pi$
$840$	0.196171	+	0.0562512i	0.00676855	+	0.00194085i
$841$	−0.185790	+	5.32032i	−0.00640654	+	0.183459i
$842$	5.32372	−	13.1767i	0.183468	−	0.454098i
$843$	0.561767	−	0.250115i	0.0193483	−	0.00861441i
$844$	−15.0535	−	6.70223i	−0.518162	−	0.230700i
$845$	−20.3842	−	10.8385i	−0.701239	−	0.372855i
$846$	6.90255	−	39.1463i	0.237315	−	1.34588i
$847$	16.9492	+	2.07261i	0.582380	+	0.0712158i
$848$	0.404700	−	0.700962i	0.0138975	−	0.0240711i
$849$	−0.302382	+	0.188949i	−0.0103777	+	0.00648473i
$850$	−1.92218	+	0.551177i	−0.0659303	+	0.0189052i
$851$	−3.68929	−	1.05789i	−0.126467	−	0.0362639i
$852$	−0.0613123	−	0.0383122i	−0.00210052	−	0.00131255i
$853$	−38.5588	+	20.5021i	−1.32023	+	0.701977i	−0.971900	−	0.235396i	$-0.924361\pi$
$853$	−38.5588	+	20.5021i	−1.32023	+	0.701977i	−0.348327	+	0.937373i	$0.613250\pi$
$854$	−15.0589	−	10.9409i	−0.515305	−	0.374391i
$855$	−22.4275	−	21.3006i	−0.767004	−	0.728465i
$856$	1.27351	−	3.91947i	0.0435278	−	0.133965i
$857$	−1.79793	−	10.1966i	−0.0614162	−	0.348309i	−0.999995	−	0.00324298i	$-0.998968\pi$
$857$	−1.79793	−	10.1966i	−0.0614162	−	0.348309i	0.938579	−	0.345066i	$-0.112143\pi$
$858$	0.0317357	−	0.330442i	0.00108344	−	0.0112811i
$859$	−21.1599	+	7.70157i	−0.721966	+	0.262774i	−0.676760	−	0.736204i	$-0.736617\pi$
$859$	−21.1599	+	7.70157i	−0.721966	+	0.262774i	−0.0452057	+	0.998978i	$0.514394\pi$
$860$	15.5447	−	19.8963i	0.530071	−	0.678460i
$861$	−1.05470	−	0.0737517i	−0.0359440	−	0.00251345i
$862$	26.3118	−	11.7148i	0.896184	−	0.399007i
$863$	16.0422	−	17.8166i	0.546081	−	0.606485i	−0.405420	−	0.914131i	$-0.632875\pi$
$863$	16.0422	−	17.8166i	0.546081	−	0.606485i	0.951501	+	0.307646i	$0.0995412\pi$
$864$	0.329729	−	0.0463404i	0.0112176	−	0.00157653i
$865$	−5.28777	+	5.10634i	−0.179790	+	0.173621i
$866$	20.3161	+	9.04531i	0.690369	+	0.307372i
$867$	0.227463	+	0.252623i	0.00772504	+	0.00857952i
$868$	−2.57675	−	2.16215i	−0.0874605	−	0.0733881i
$869$	1.00612	+	8.81129i	0.0341303	+	0.298902i
$870$	0.601117	−	0.218789i	0.0203798	−	0.00741763i
$871$	−6.80381	−	16.8400i	−0.230538	−	0.570603i
$872$	11.2202	+	10.8353i	0.379965	+	0.366928i
$873$	−15.7955	−	11.4761i	−0.534596	−	0.388407i
$874$	0.0473200	−	1.77889i	0.00160062	−	0.0601719i
$875$	4.99033	+	15.3587i	0.168704	+	0.519218i
$876$	−0.369203	+	0.756978i	−0.0124742	+	0.0255759i
$877$	9.69898	−	38.9005i	0.327511	−	1.31358i	−0.550460	−	0.834862i	$-0.685548\pi$
$877$	9.69898	−	38.9005i	0.327511	−	1.31358i	0.877971	−	0.478714i	$-0.158897\pi$
$878$	0.547929	+	15.6906i	0.0184917	+	0.529533i
$879$	−0.877976	−	0.319557i	−0.0296134	−	0.0107784i
$880$	5.97019	−	5.10157i	0.201255	−	0.171974i
$881$	−9.09395	+	15.7512i	−0.306383	+	0.530671i	−0.977568	−	0.210619i	$-0.932452\pi$
$881$	−9.09395	+	15.7512i	−0.306383	+	0.530671i	0.671185	+	0.741290i	$0.265786\pi$
$882$	−13.4562	+	2.86021i	−0.453095	+	0.0963082i
$883$	−16.2302	−	33.2769i	−0.546191	−	1.11986i	−0.976168	−	0.217018i	$-0.930367\pi$
$883$	−16.2302	−	33.2769i	−0.546191	−	1.11986i	0.429976	−	0.902840i	$-0.358522\pi$
$884$	−4.27678	+	4.13004i	−0.143844	+	0.138908i
$885$	0.340390	−	0.378042i	0.0114421	−	0.0127077i
$886$	−10.3154	−	2.19260i	−0.346552	−	0.0736619i
$887$	9.44339	+	37.8754i	0.317078	+	1.27173i	0.891444	+	0.453131i	$0.149693\pi$
$887$	9.44339	+	37.8754i	0.317078	+	1.27173i	−0.574366	+	0.818599i	$0.694751\pi$
$888$	0.501757	−	0.143877i	0.0168379	−	0.00482818i
$889$	−0.928244	−	26.5814i	−0.0311323	−	0.891513i
$890$	−0.236255	+	0.198241i	−0.00791928	+	0.00664506i
$891$	−9.44919	−	28.2175i	−0.316560	−	0.945323i
$892$	−13.5186			−0.452635
$893$	56.4498	−	12.4901i	1.88902	−	0.417964i
$894$	0.110677	−	0.0804119i	0.00370161	−	0.00268938i
$895$	19.9814	−	40.9679i	0.667903	−	1.36940i
$896$	1.31643	+	0.822599i	0.0439790	+	0.0274811i
$897$	−0.0251571	−	0.0321997i	−0.000839973	−	0.00107512i
$898$	−5.80104	−	8.60039i	−0.193583	−	0.286999i
$899$	−10.5181	−	0.735499i	−0.350799	−	0.0245303i
$900$	−1.21583	−	1.35031i	−0.0405276	−	0.0450104i
$901$	−1.33475	−	2.31186i	−0.0444670	−	0.0770191i
$902$	−24.7592	+	32.2832i	−0.824390	+	1.07491i
$903$	−0.159598	+	0.905128i	−0.00531110	+	0.0301208i
$904$	4.07848	−	0.866908i	0.135648	−	0.0288329i
$905$	1.01907	+	9.69576i	0.0338749	+	0.322298i
$906$	−0.214065	−	0.858567i	−0.00711183	−	0.0285240i
$907$	0.931239	−	26.6672i	0.0309213	−	0.885470i	−0.880513	−	0.474023i	$-0.842801\pi$
$907$	0.931239	−	26.6672i	0.0309213	−	0.885470i	0.911434	−	0.411447i	$-0.134976\pi$
$908$	6.73881	+	8.62528i	0.223635	+	0.286240i
$909$	−19.2720	+	1.34763i	−0.639211	+	0.0446980i
$910$	−4.76614	−	4.60261i	−0.157996	−	0.152575i
$911$	−2.70645	+	8.32959i	−0.0896686	+	0.275972i	−0.985828	−	0.167761i	$-0.946346\pi$
$911$	−2.70645	+	8.32959i	−0.0896686	+	0.275972i	0.896159	+	0.443733i	$0.146346\pi$
$912$	0.122749	+	0.208583i	0.00406461	+	0.00690689i
$913$	−34.3247	−	17.8576i	−1.13598	−	0.590999i
$914$	−3.55637	−	20.1692i	−0.117634	−	0.667137i
$915$	−0.590538	−	1.46163i	−0.0195226	−	0.0483201i
$916$	−1.92099	+	2.84799i	−0.0634713	+	0.0941001i
$917$	5.49283	+	8.14345i	0.181389	+	0.268921i
$918$	0.411383	−	1.01821i	0.0135777	−	0.0336059i
$919$	−0.685013	−	0.145604i	−0.0225965	−	0.00480304i	0.196600	−	0.980484i	$-0.437010\pi$
$919$	−0.685013	−	0.145604i	−0.0225965	−	0.00480304i	−0.219196	+	0.975681i	$0.570343\pi$
$920$	0.101041	−	0.961344i	0.00333123	−	0.0316946i
$921$	0.354984	+	0.727826i	0.0116971	+	0.0239827i
$922$	−21.4510	−	11.4057i	−0.706451	−	0.375627i
$923$	1.17364	+	2.03281i	0.0386310	+	0.0669108i
$924$	−0.104702	+	0.265994i	−0.00344444	+	0.00875056i
$925$	−4.36632	−	3.66378i	−0.143564	−	0.120464i
$926$	8.62720	−	11.0423i	0.283507	−	0.362873i
$927$	7.28902	−	10.8064i	0.239403	−	0.354929i
$928$	4.85399	−	0.339424i	0.159340	−	0.0111421i
$929$	40.0971	−	21.3200i	1.31554	−	0.699486i	0.344588	−	0.938754i	$-0.388018\pi$
$929$	40.0971	−	21.3200i	1.31554	−	0.699486i	0.970954	+	0.239268i	$0.0769074\pi$
$930$	−0.0880312	−	0.270932i	−0.00288666	−	0.00888421i
$931$	−11.3263	−	16.4945i	−0.371203	−	0.540584i
$932$	−14.2193	+	10.3309i	−0.465770	+	0.338401i
$933$	−0.0434812	−	0.00611089i	−0.00142351	−	0.000200061i
$934$	−18.7112	+	15.7005i	−0.612248	+	0.513737i
$935$	−4.72619	−	25.4652i	−0.154563	−	0.832801i
$936$	−5.07665	−	1.84775i	−0.165935	−	0.0603955i
$937$	−8.98610	+	5.61514i	−0.293563	+	0.183439i	−0.668703	−	0.743530i	$-0.733150\pi$
$937$	−8.98610	+	5.61514i	−0.293563	+	0.183439i	0.375140	+	0.926968i	$0.377595\pi$
$938$	1.63483	+	15.5544i	0.0533793	+	0.507870i
$939$	0.0706010	−	0.671724i	0.00230398	−	0.0219209i
$940$	31.0996	−	4.37077i	1.01436	−	0.142559i
$941$	−22.5194	+	3.16490i	−0.734113	+	0.103173i	−0.496316	−	0.868142i	$-0.665314\pi$
$941$	−22.5194	+	3.16490i	−0.734113	+	0.103173i	−0.237797	+	0.971315i	$0.576425\pi$
$942$	−0.0321895	+	0.306262i	−0.00104879	+	0.00997857i
$943$	0.523471	+	4.98050i	0.0170466	+	0.162187i
$944$	3.28150	−	2.05051i	0.106804	−	0.0667383i
$945$	1.15003	+	0.418575i	0.0374103	+	0.0136162i
$946$	25.6604	+	24.3388i	0.834291	+	0.791322i
$947$	−17.6847	+	14.8393i	−0.574677	+	0.482211i	−0.883194	−	0.469008i	$-0.844612\pi$
$947$	−17.6847	+	14.8393i	−0.574677	+	0.482211i	0.308517	+	0.951219i	$0.400167\pi$
$948$	−0.147023	−	0.0206627i	−0.00477509	−	0.000671095i
$949$	22.1218	−	16.0724i	0.718104	−	0.521733i
$950$	1.13874	−	2.38487i	0.0369456	−	0.0773755i
$951$	−0.329466	−	1.01399i	−0.0106837	−	0.0328809i
$952$	4.52043	−	2.40356i	0.146508	−	0.0778997i
$953$	−53.5668	+	3.74576i	−1.73520	+	0.121337i	−0.902028	−	0.431678i	$-0.857922\pi$
$953$	−53.5668	+	3.74576i	−1.73520	+	0.121337i	−0.833171	+	0.553015i	$0.813477\pi$
$954$	1.35644	−	2.01100i	0.0439163	−	0.0651086i
$955$	−27.0896	+	34.6731i	−0.876600	+	1.12200i
$956$	3.67498	+	3.08367i	0.118857	+	0.0997331i
$957$	0.224566	+	0.867451i	0.00725920	+	0.0280407i
$958$	−0.738323	−	1.27881i	−0.0238541	−	0.0413166i
$959$	−11.7396	−	6.24203i	−0.379090	−	0.201566i
$960$	0.0576311	+	0.118161i	0.00186004	+	0.00381364i
$961$	2.74957	−	26.1604i	0.0886959	−	0.843885i
$962$	−16.5766	−	3.52347i	−0.534452	−	0.113601i
$963$	4.62670	−	11.4515i	0.149093	−	0.369019i
$964$	13.3154	+	19.7409i	0.428860	+	0.635811i
$965$	−25.1448	+	37.2787i	−0.809439	+	1.20004i
$966$	0.0131813	+	0.0326248i	0.000424100	+	0.00104969i
$967$	7.63338	+	43.2911i	0.245473	+	1.39215i	0.819392	+	0.573234i	$0.194311\pi$
$967$	7.63338	+	43.2911i	0.245473	+	1.39215i	−0.573919	+	0.818912i	$0.694577\pi$
$968$	6.31378	+	9.00756i	0.202933	+	0.289514i
$969$	0.798187	−	0.00663471i	0.0256415	−	0.000213138i
$970$	4.76673	−	14.6705i	0.153051	−	0.471041i
$971$	36.0068	+	34.7714i	1.15551	+	1.11587i	0.991593	+	0.129393i	$0.0413030\pi$
$971$	36.0068	+	34.7714i	1.15551	+	1.11587i	0.163921	+	0.986474i	$0.447586\pi$
$972$	1.49343	−	0.104431i	0.0479019	−	0.00334963i
$973$	−0.374972	−	0.479942i	−0.0120211	−	0.0153862i
$974$	−0.444867	+	12.7393i	−0.0142545	+	0.408194i
$975$	−0.0146810	−	0.0588821i	−0.000470167	−	0.00188574i
$976$	−1.25341	−	11.9254i	−0.0401206	−	0.381722i
$977$	55.7201	−	11.8437i	1.78264	−	0.378913i	0.805686	−	0.592343i	$-0.201797\pi$
$977$	55.7201	−	11.8437i	1.78264	−	0.378913i	0.976958	+	0.213430i	$0.0684636\pi$
$978$	0.0288486	−	0.163609i	0.000922476	−	0.00523162i
$979$	−0.244776	−	0.355963i	−0.00782307	−	0.0113766i
$980$	−5.43441	−	9.41267i	−0.173596	−	0.300677i
$981$	31.2791	+	34.7389i	0.998664	+	1.10913i
$982$	−11.8026	−	0.825320i	−0.376637	−	0.0263370i
$983$	−28.0445	−	41.5777i	−0.894482	−	1.32612i	−0.944888	−	0.327395i	$-0.893829\pi$
$983$	−28.0445	−	41.5777i	−0.894482	−	1.32612i	0.0504059	−	0.998729i	$-0.483949\pi$
$984$	−0.419325	−	0.536711i	−0.0133676	−	0.0171097i
$985$	17.2627	+	10.7869i	0.550034	+	0.343700i
$986$	7.03504	−	14.4240i	0.224041	−	0.459353i
$987$	−0.924863	+	0.671953i	−0.0294387	+	0.0213885i
$988$	−0.339491	−	7.85032i	−0.0108007	−	0.249752i
$989$	4.35341			0.138430
$990$	18.9151	−	14.0037i	0.601161	−	0.445065i
$991$	−5.87817	+	4.93237i	−0.186726	+	0.156682i	−0.731359	−	0.681993i	$-0.761114\pi$
$991$	−5.87817	+	4.93237i	−0.186726	+	0.156682i	0.544633	+	0.838675i	$0.316669\pi$
$992$	−0.0756238	−	2.16558i	−0.00240106	−	0.0687573i
$993$	0.967547	−	0.277440i	0.0307042	−	0.00880428i
$994$	−0.488995	−	1.96125i	−0.0155100	−	0.0622071i
$995$	−65.2482	−	13.8689i	−2.06851	−	0.439674i
$996$	0.433424	−	0.481367i	0.0137336	−	0.0152527i
$997$	−11.0092	+	10.6314i	−0.348664	+	0.336701i	−0.848282	−	0.529545i	$-0.822363\pi$
$997$	−11.0092	+	10.6314i	−0.348664	+	0.336701i	0.499618	+	0.866246i	$0.333474\pi$
$998$	7.87089	+	16.1377i	0.249149	+	0.510830i
$999$	3.06185	−	0.650817i	0.0968728	−	0.0205909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.u.b.9.6	✓	264
11.5	even	5	inner	418.2.u.b.313.6	yes	264
19.17	even	9	inner	418.2.u.b.207.6	yes	264
209.93	even	45	inner	418.2.u.b.93.6	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.9.6	✓	264	1.1	even	1	trivial
418.2.u.b.93.6	yes	264	209.93	even	45	inner
418.2.u.b.207.6	yes	264	19.17	even	9	inner
418.2.u.b.313.6	yes	264	11.5	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.u (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.990268 + 0.139173i) q^{2} +(0.0134323 - 0.0538742i) q^{3} +(0.961262 + 0.275637i) q^{4} +(-0.0826337 + 2.36632i) q^{5} +(0.0207995 - 0.0514805i) q^{6} +(1.41811 - 0.631382i) q^{7} +(0.913545 + 0.406737i) q^{8} +(2.64612 + 1.40697i) q^{9} +O(q^{10})\)	\(q+(0.990268 + 0.139173i) q^{2} +(0.0134323 - 0.0538742i) q^{3} +(0.961262 + 0.275637i) q^{4} +(-0.0826337 + 2.36632i) q^{5} +(0.0207995 - 0.0514805i) q^{6} +(1.41811 - 0.631382i) q^{7} +(0.913545 + 0.406737i) q^{8} +(2.64612 + 1.40697i) q^{9} +(-0.411158 + 2.33179i) q^{10} +(-3.19622 - 0.885541i) q^{11} +(0.0277617 - 0.0480847i) q^{12} +(-1.52875 + 0.955270i) q^{13} +(1.49218 - 0.427875i) q^{14} +(0.126374 + 0.0362371i) q^{15} +(0.848048 + 0.529919i) q^{16} +(2.91207 - 1.54837i) q^{17} +(2.42456 + 1.76154i) q^{18} +(-1.01932 + 4.23804i) q^{19} +(-0.731679 + 2.25188i) q^{20} +(-0.0149667 - 0.0848803i) q^{21} +(-3.04187 - 1.32175i) q^{22} +(-0.383630 + 0.139630i) q^{23} +(0.0341837 - 0.0437531i) q^{24} +(-0.604821 - 0.0422932i) q^{25} +(-1.64682 + 0.733212i) q^{26} +(0.222800 - 0.247445i) q^{27} +(1.53720 - 0.216040i) q^{28} +(3.50020 - 3.38010i) q^{29} +(0.120101 + 0.0534722i) q^{30} +(-1.44994 - 1.61032i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-0.0906406 + 0.160299i) q^{33} +(3.09922 - 1.12802i) q^{34} +(1.37687 + 3.40787i) q^{35} +(2.15580 + 2.08183i) q^{36} +(7.60559 + 5.52579i) q^{37} +(-1.59922 + 4.05493i) q^{38} +(0.0309297 + 0.0951918i) q^{39} +(-1.03796 + 2.12813i) q^{40} +(2.96761 - 11.9024i) q^{41} +(-0.00300798 - 0.0861372i) q^{42} +(-10.0205 - 3.64716i) q^{43} +(-2.82831 - 1.73223i) q^{44} +(-3.54799 + 6.14531i) q^{45} +(-0.399329 + 0.0848800i) q^{46} +(-5.81442 - 11.9213i) q^{47} +(0.0399403 - 0.0385699i) q^{48} +(-3.07153 + 3.41128i) q^{49} +(-0.593049 - 0.126057i) q^{50} +(-0.0443015 - 0.177684i) q^{51} +(-1.73284 + 0.496883i) q^{52} +(-0.0282477 - 0.808908i) q^{53} +(0.255070 - 0.214029i) q^{54} +(2.35959 - 7.49010i) q^{55} +1.55231 q^{56} +(0.214629 + 0.111842i) q^{57} +(3.93655 - 2.86007i) q^{58} +(1.69626 - 3.47786i) q^{59} +(0.111490 + 0.0696666i) q^{60} +(-7.38243 - 9.44908i) q^{61} +(-1.21172 - 1.79644i) q^{62} +(4.64081 + 0.324517i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-2.13415 - 3.69645i) q^{65} +(-0.112068 + 0.146124i) q^{66} +(-1.74957 + 9.92229i) q^{67} +(3.22605 - 0.685718i) q^{68} +(0.00236940 + 0.0225433i) q^{69} +(0.889185 + 3.56632i) q^{70} +(0.0454433 - 1.30132i) q^{71} +(1.84509 + 2.36160i) q^{72} +(-15.1317 + 1.05811i) q^{73} +(6.76253 + 6.53050i) q^{74} +(-0.0104027 + 0.0320162i) q^{75} +(-2.14800 + 3.79290i) q^{76} +(-5.09169 + 0.762242i) q^{77} +(0.0173805 + 0.0985700i) q^{78} +(-1.00169 - 2.47926i) q^{79} +(-1.32404 + 1.96296i) q^{80} +(5.01723 + 7.43834i) q^{81} +(4.59523 - 11.3736i) q^{82} +(11.4112 + 2.42552i) q^{83} +(0.00900928 - 0.0857175i) q^{84} +(3.42331 + 7.01883i) q^{85} +(-9.41538 - 5.00625i) q^{86} +(-0.135084 - 0.233973i) q^{87} +(-2.55971 - 2.10900i) q^{88} +(0.0997797 + 0.0837251i) q^{89} +(-4.36873 + 5.59171i) q^{90} +(-1.56479 + 2.31990i) q^{91} +(-0.407256 + 0.0284781i) q^{92} +(-0.106231 + 0.0564840i) q^{93} +(-4.09871 - 12.6145i) q^{94} +(-9.94433 - 2.76225i) q^{95} +(0.0449194 - 0.0326359i) q^{96} +(-6.45139 - 0.906683i) q^{97} +(-3.51640 + 2.95061i) q^{98} +(-7.21165 - 6.84023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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