LMFDB - Embedded newform 418.2.u.b.9.7

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			9.7
Character	$\chi$	$=$	418.9
Dual form			418.2.u.b.93.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.990268 + 0.139173i) q^{2} +(0.161628 - 0.648256i) q^{3} +(0.961262 + 0.275637i) q^{4} +(0.0866869 - 2.48239i) q^{5} +(0.250275 - 0.619453i) q^{6} +(-0.941853 + 0.419340i) q^{7} +(0.913545 + 0.406737i) q^{8} +(2.25473 + 1.19886i) q^{9} +O(q^{10})$	\(q+(0.990268 + 0.139173i) q^{2} +(0.161628 - 0.648256i) q^{3} +(0.961262 + 0.275637i) q^{4} +(0.0866869 - 2.48239i) q^{5} +(0.250275 - 0.619453i) q^{6} +(-0.941853 + 0.419340i) q^{7} +(0.913545 + 0.406737i) q^{8} +(2.25473 + 1.19886i) q^{9} +(0.431325 - 2.44617i) q^{10} +(-3.31068 - 0.198423i) q^{11} +(0.334051 - 0.578593i) q^{12} +(5.56316 - 3.47625i) q^{13} +(-0.991048 + 0.284178i) q^{14} +(-1.59521 - 0.457420i) q^{15} +(0.848048 + 0.529919i) q^{16} +(4.37522 - 2.32634i) q^{17} +(2.06594 + 1.50099i) q^{18} +(-3.79622 - 2.14213i) q^{19} +(0.767568 - 2.36233i) q^{20} +(0.119610 + 0.678340i) q^{21} +(-3.25085 - 0.657250i) q^{22} +(-4.50639 + 1.64019i) q^{23} +(0.411325 - 0.526471i) q^{24} +(-1.16692 - 0.0815988i) q^{25} +(5.99282 - 2.66817i) q^{26} +(2.48274 - 2.75736i) q^{27} +(-1.02095 + 0.143486i) q^{28} +(-6.20440 + 5.99152i) q^{29} +(-1.51603 - 0.674979i) q^{30} +(0.188993 + 0.209898i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-0.663729 + 2.11410i) q^{33} +(4.65640 - 1.69479i) q^{34} +(0.959319 + 2.37440i) q^{35} +(1.83693 + 1.77391i) q^{36} +(-1.81699 - 1.32012i) q^{37} +(-3.46115 - 2.64962i) q^{38} +(-1.35433 - 4.16821i) q^{39} +(1.08887 - 2.23252i) q^{40} +(-1.22842 + 4.92692i) q^{41} +(0.0240389 + 0.688385i) q^{42} +(8.37808 + 3.04937i) q^{43} +(-3.12774 - 1.10328i) q^{44} +(3.17150 - 5.49319i) q^{45} +(-4.69081 + 0.997062i) q^{46} +(4.97140 + 10.1929i) q^{47} +(0.480592 - 0.464103i) q^{48} +(-3.97267 + 4.41210i) q^{49} +(-1.14420 - 0.243208i) q^{50} +(-0.800908 - 3.21227i) q^{51} +(6.30583 - 1.80817i) q^{52} +(0.380022 + 10.8824i) q^{53} +(2.84233 - 2.38500i) q^{54} +(-0.779555 + 8.20120i) q^{55} -1.03099 q^{56} +(-2.00223 + 2.11469i) q^{57} +(-6.97788 + 5.06972i) q^{58} +(2.41639 - 4.95433i) q^{59} +(-1.40734 - 0.879401i) q^{60} +(-2.07907 - 2.66108i) q^{61} +(0.157942 + 0.234158i) q^{62} +(-2.62636 - 0.183653i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-8.14714 - 14.1113i) q^{65} +(-0.951496 + 2.00115i) q^{66} +(0.179305 - 1.01689i) q^{67} +(4.84696 - 1.03025i) q^{68} +(0.334904 + 3.18640i) q^{69} +(0.619530 + 2.48480i) q^{70} +(-0.349823 + 10.0176i) q^{71} +(1.57218 + 2.01230i) q^{72} +(-1.91177 + 0.133684i) q^{73} +(-1.61558 - 1.56015i) q^{74} +(-0.241504 + 0.743273i) q^{75} +(-3.05871 - 3.10553i) q^{76} +(3.20139 - 1.20142i) q^{77} +(-0.761051 - 4.31613i) q^{78} +(-5.12677 - 12.6892i) q^{79} +(1.38898 - 2.05925i) q^{80} +(2.89774 + 4.29607i) q^{81} +(-1.90216 + 4.70801i) q^{82} +(-12.4536 - 2.64709i) q^{83} +(-0.0719996 + 0.685031i) q^{84} +(-5.39561 - 11.0626i) q^{85} +(7.87215 + 4.18570i) q^{86} +(2.88123 + 4.99044i) q^{87} +(-2.94375 - 1.52784i) q^{88} +(9.28812 + 7.79365i) q^{89} +(3.90513 - 4.99834i) q^{90} +(-3.78195 + 5.60697i) q^{91} +(-4.78392 + 0.334524i) q^{92} +(0.166615 - 0.0885905i) q^{93} +(3.50445 + 10.7856i) q^{94} +(-5.64668 + 9.23799i) q^{95} +(0.540506 - 0.392700i) q^{96} +(-10.4805 - 1.47294i) q^{97} +(-4.54806 + 3.81627i) q^{98} +(-7.22682 - 4.41644i) 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
$3$	0.161628	−	0.648256i	0.0933162	−	0.374271i	−0.905421	−	0.424515i	$-0.860444\pi$
$3$	0.161628	−	0.648256i	0.0933162	−	0.374271i	0.998737	+	0.0502444i	$0.0160000\pi$
$4$	0.961262	+	0.275637i	0.480631	+	0.137819i
$5$	0.0866869	−	2.48239i	0.0387676	−	1.11016i	−0.811681	−	0.584100i	$-0.801447\pi$
$5$	0.0866869	−	2.48239i	0.0387676	−	1.11016i	0.850449	−	0.526057i	$-0.176330\pi$
$6$	0.250275	−	0.619453i	0.102174	−	0.252891i
$7$	−0.941853	+	0.419340i	−0.355987	+	0.158496i	−0.576935	−	0.816790i	$-0.695752\pi$
$7$	−0.941853	+	0.419340i	−0.355987	+	0.158496i	0.220948	+	0.975286i	$0.429085\pi$
$8$	0.913545	+	0.406737i	0.322987	+	0.143803i
$9$	2.25473	+	1.19886i	0.751577	+	0.399620i
$10$	0.431325	−	2.44617i	0.136397	−	0.773545i
$11$	−3.31068	−	0.198423i	−0.998209	−	0.0598266i
$11$	−3.31068	−	0.198423i	−0.998209	−	0.0598266i
$12$	0.334051	−	0.578593i	0.0964322	−	0.167025i
$13$	5.56316	−	3.47625i	1.54294	−	0.964137i	0.551415	−	0.834231i	$-0.314088\pi$
$13$	5.56316	−	3.47625i	1.54294	−	0.964137i	0.991526	−	0.129906i	$-0.0414676\pi$
$14$	−0.991048	+	0.284178i	−0.264869	+	0.0759499i
$15$	−1.59521	−	0.457420i	−0.411882	−	0.118105i
$16$	0.848048	+	0.529919i	0.212012	+	0.132480i
$17$	4.37522	−	2.32634i	1.06115	−	0.564221i	0.155317	−	0.987865i	$-0.450360\pi$
$17$	4.37522	−	2.32634i	1.06115	−	0.564221i	0.905829	+	0.423643i	$0.139249\pi$
$18$	2.06594	+	1.50099i	0.486946	+	0.353787i
$19$	−3.79622	−	2.14213i	−0.870912	−	0.491439i
$19$	−3.79622	−	2.14213i	−0.870912	−	0.491439i
$20$	0.767568	−	2.36233i	0.171633	−	0.528233i
$21$	0.119610	+	0.678340i	0.0261010	+	0.148026i
$22$	−3.25085	−	0.657250i	−0.693083	−	0.140126i
$23$	−4.50639	+	1.64019i	−0.939648	+	0.342004i	−0.766027	−	0.642809i	$-0.777769\pi$
$23$	−4.50639	+	1.64019i	−0.939648	+	0.342004i	−0.173621	+	0.984813i	$0.555547\pi$
$24$	0.411325	−	0.526471i	0.0839613	−	0.107466i
$25$	−1.16692	−	0.0815988i	−0.233383	−	0.0163198i
$26$	5.99282	−	2.66817i	1.17529	−	0.523272i
$27$	2.48274	−	2.75736i	0.477804	−	0.530655i
$28$	−1.02095	+	0.143486i	−0.192942	+	0.0271162i
$29$	−6.20440	+	5.99152i	−1.15213	+	1.11260i	−0.160032	+	0.987112i	$0.551160\pi$
$29$	−6.20440	+	5.99152i	−1.15213	+	1.11260i	−0.992095	+	0.125485i	$0.959951\pi$
$30$	−1.51603	−	0.674979i	−0.276788	−	0.123234i
$31$	0.188993	+	0.209898i	0.0339442	+	0.0376988i	0.759878	−	0.650066i	$-0.225259\pi$
$31$	0.188993	+	0.209898i	0.0339442	+	0.0376988i	−0.725934	+	0.687765i	$0.758592\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−0.663729	+	2.11410i	−0.115540	+	0.368018i
$34$	4.65640	−	1.69479i	0.798566	−	0.290654i
$35$	0.959319	+	2.37440i	0.162154	+	0.401346i
$36$	1.83693	+	1.77391i	0.306156	+	0.295651i
$37$	−1.81699	−	1.32012i	−0.298711	−	0.217026i	0.428326	−	0.903624i	$-0.359103\pi$
$37$	−1.81699	−	1.32012i	−0.298711	−	0.217026i	−0.727037	+	0.686598i	$0.759103\pi$
$38$	−3.46115	−	2.64962i	−0.561472	−	0.429824i
$39$	−1.35433	−	4.16821i	−0.216867	−	0.667448i
$40$	1.08887	−	2.23252i	0.172166	−	0.352992i
$41$	−1.22842	+	4.92692i	−0.191847	+	0.769456i	0.794839	+	0.606820i	$0.207555\pi$
$41$	−1.22842	+	4.92692i	−0.191847	+	0.769456i	−0.986686	+	0.162636i	$0.948000\pi$
$42$	0.0240389	+	0.688385i	0.00370929	+	0.106220i
$43$	8.37808	+	3.04937i	1.27765	+	0.465025i	0.889653	−	0.456638i	$-0.150946\pi$
$43$	8.37808	+	3.04937i	1.27765	+	0.465025i	0.387993	+	0.921663i	$0.373169\pi$
$44$	−3.12774	−	1.10328i	−0.471525	−	0.166326i
$45$	3.17150	−	5.49319i	0.472779	−	0.818877i
$46$	−4.69081	+	0.997062i	−0.691622	+	0.147009i
$47$	4.97140	+	10.1929i	0.725154	+	1.48679i	0.867748	+	0.497004i	$0.165567\pi$
$47$	4.97140	+	10.1929i	0.725154	+	1.48679i	−0.142594	+	0.989781i	$0.545544\pi$
$48$	0.480592	−	0.464103i	0.0693675	−	0.0669874i
$49$	−3.97267	+	4.41210i	−0.567525	+	0.630300i
$50$	−1.14420	−	0.243208i	−0.161815	−	0.0343948i
$51$	−0.800908	−	3.21227i	−0.112150	−	0.449807i
$52$	6.30583	−	1.80817i	0.874461	−	0.250748i
$53$	0.380022	+	10.8824i	0.0522001	+	1.49481i	0.689549	+	0.724239i	$0.257809\pi$
$53$	0.380022	+	10.8824i	0.0522001	+	1.49481i	−0.637349	+	0.770576i	$0.719969\pi$
$54$	2.84233	−	2.38500i	0.386792	−	0.324557i
$55$	−0.779555	+	8.20120i	−0.105115	+	1.10585i
$56$	−1.03099			−0.137771
$57$	−2.00223	+	2.11469i	−0.265201	+	0.280098i
$58$	−6.97788	+	5.06972i	−0.916240	+	0.665687i
$59$	2.41639	−	4.95433i	0.314587	−	0.644999i	−0.681649	−	0.731679i	$-0.738737\pi$
$59$	2.41639	−	4.95433i	0.314587	−	0.644999i	0.996236	+	0.0866801i	$0.0276258\pi$
$60$	−1.40734	−	0.879401i	−0.181686	−	0.113530i
$61$	−2.07907	−	2.66108i	−0.266197	−	0.340717i	0.636277	−	0.771461i	$-0.280473\pi$
$61$	−2.07907	−	2.66108i	−0.266197	−	0.340717i	−0.902474	+	0.430744i	$0.858251\pi$
$62$	0.157942	+	0.234158i	0.0200586	+	0.0297381i
$63$	−2.62636	−	0.183653i	−0.330890	−	0.0231381i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	−8.14714	−	14.1113i	−1.01053	−	1.75029i
$66$	−0.951496	+	2.00115i	−0.117121	+	0.246325i
$67$	0.179305	−	1.01689i	0.0219055	−	0.124233i	−0.971894	−	0.235419i	$-0.924354\pi$
$67$	0.179305	−	1.01689i	0.0219055	−	0.124233i	0.993800	+	0.111186i	$0.0354650\pi$
$68$	4.84696	−	1.03025i	0.587780	−	0.124936i
$69$	0.334904	+	3.18640i	0.0403177	+	0.383597i
$70$	0.619530	+	2.48480i	0.0740481	+	0.296991i
$71$	−0.349823	+	10.0176i	−0.0415164	+	1.18887i	0.782627	+	0.622491i	$0.213879\pi$
$71$	−0.349823	+	10.0176i	−0.0415164	+	1.18887i	−0.824143	+	0.566382i	$0.808343\pi$
$72$	1.57218	+	2.01230i	0.185283	+	0.237151i
$73$	−1.91177	+	0.133684i	−0.223755	+	0.0156465i	−0.181194	−	0.983447i	$-0.557996\pi$
$73$	−1.91177	+	0.133684i	−0.223755	+	0.0156465i	−0.0425613	+	0.999094i	$0.513552\pi$
$74$	−1.61558	−	1.56015i	−0.187807	−	0.181364i
$75$	−0.241504	+	0.743273i	−0.0278865	+	0.0858257i
$76$	−3.05871	−	3.10553i	−0.350858	−	0.356229i
$77$	3.20139	−	1.20142i	0.364832	−	0.136914i
$78$	−0.761051	−	4.31613i	−0.0861720	−	0.488706i
$79$	−5.12677	−	12.6892i	−0.576807	−	1.42765i	−0.880118	−	0.474756i	$-0.842536\pi$
$79$	−5.12677	−	12.6892i	−0.576807	−	1.42765i	0.303311	−	0.952892i	$-0.401908\pi$
$80$	1.38898	−	2.05925i	0.155293	−	0.230231i
$81$	2.89774	+	4.29607i	0.321971	+	0.477341i
$82$	−1.90216	+	4.70801i	−0.210058	+	0.519913i
$83$	−12.4536	−	2.64709i	−1.36696	−	0.290556i	−0.534745	−	0.845014i	$-0.679592\pi$
$83$	−12.4536	−	2.64709i	−1.36696	−	0.290556i	−0.832212	+	0.554458i	$0.812926\pi$
$84$	−0.0719996	+	0.685031i	−0.00785580	+	0.0747430i
$85$	−5.39561	−	11.0626i	−0.585237	−	1.19991i
$86$	7.87215	+	4.18570i	0.848876	+	0.451356i
$87$	2.88123	+	4.99044i	0.308901	+	0.535031i
$88$	−2.94375	−	1.52784i	−0.313805	−	0.162869i
$89$	9.28812	+	7.79365i	0.984538	+	0.826126i	0.984768	−	0.173874i	$-0.0556286\pi$
$89$	9.28812	+	7.79365i	0.984538	+	0.826126i	−0.000229552		1.00000i	$0.500073\pi$
$90$	3.90513	−	4.99834i	0.411637	−	0.526872i
$91$	−3.78195	+	5.60697i	−0.396456	+	0.587770i
$92$	−4.78392	+	0.334524i	−0.498758	+	0.0348766i
$93$	0.166615	−	0.0885905i	0.0172771	−	0.00918641i
$94$	3.50445	+	10.7856i	0.361456	+	1.11245i
$95$	−5.64668	+	9.23799i	−0.579338	+	0.947798i
$96$	0.540506	−	0.392700i	0.0551651	−	0.0400798i
$97$	−10.4805	−	1.47294i	−1.06413	−	0.149554i	−0.414690	−	0.909963i	$-0.636110\pi$
$97$	−10.4805	−	1.47294i	−1.06413	−	0.149554i	−0.649445	+	0.760409i	$0.724999\pi$
$98$	−4.54806	+	3.81627i	−0.459423	+	0.385502i
$99$	−7.22682	−	4.41644i	−0.726323	−	0.443869i
$100$	−1.09922	−	0.400084i	−0.109922	−	0.0400084i
$101$	1.27066	−	0.793995i	0.126435	−	0.0790055i	−0.465227	−	0.885191i	$-0.654027\pi$
$101$	1.27066	−	0.793995i	0.126435	−	0.0790055i	0.591662	+	0.806186i	$0.298472\pi$
$102$	−0.346052	−	3.29247i	−0.0342643	−	0.326003i
$103$	0.187344	−	1.78246i	0.0184595	−	0.175631i	−0.981408	−	0.191935i	$-0.938524\pi$
$103$	0.187344	−	1.78246i	0.0184595	−	0.175631i	0.999867	+	0.0163049i	$0.00519023\pi$
$104$	6.49611	−	0.912969i	0.636996	−	0.0895240i
$105$	1.69427	−	0.238114i	0.165344	−	0.0232376i
$106$	−1.13822	+	10.8294i	−0.110553	+	1.05184i
$107$	−0.416508	−	3.96281i	−0.0402653	−	0.383099i	−0.996034	−	0.0889781i	$-0.971640\pi$
$107$	−0.416508	−	3.96281i	−0.0402653	−	0.383099i	0.955768	−	0.294121i	$-0.0950268\pi$
$108$	3.14660	−	1.96621i	0.302781	−	0.189199i
$109$	6.88518	+	2.50600i	0.659480	+	0.240031i	0.650012	−	0.759924i	$-0.274764\pi$
$109$	6.88518	+	2.50600i	0.659480	+	0.240031i	0.00946826	+	0.999955i	$0.496986\pi$
$110$	−1.91335	+	8.01290i	−0.182431	+	0.764000i
$111$	−1.14945	+	0.964505i	−0.109101	+	0.0915468i
$112$	−1.02095	−	0.143486i	−0.0964710	−	0.0135581i
$113$	0.998084	−	0.725150i	0.0938918	−	0.0682164i	−0.539849	−	0.841762i	$-0.681519\pi$
$113$	0.998084	−	0.725150i	0.0938918	−	0.0682164i	0.633741	+	0.773546i	$0.281519\pi$
$114$	−2.27705	+	1.81546i	−0.213265	+	0.170033i
$115$	3.68095	+	11.3288i	0.343250	+	1.05642i
$116$	−7.61554	+	4.04925i	−0.707085	+	0.375964i
$117$	16.7110	−	1.16854i	1.54493	−	0.108032i
$118$	3.08238	−	4.56982i	0.283756	−	0.420686i
$119$	−3.14528	+	4.02578i	−0.288328	+	0.369043i
$120$	−1.27125	−	1.06671i	−0.116049	−	0.0973764i
$121$	10.9213	+	1.31383i	0.992842	+	0.119439i
$122$	−1.68848	−	2.92454i	−0.152868	−	0.264775i
$123$	2.99536	+	1.59266i	0.270082	+	0.143605i
$124$	0.123816	+	0.253861i	0.0111190	+	0.0227974i
$125$	0.994476	−	9.46180i	0.0889486	−	0.846289i
$126$	−2.57524	−	0.547383i	−0.229420	−	0.0487648i
$127$	−3.31896	+	8.21471i	−0.294510	+	0.728938i	0.705290	+	0.708919i	$0.250817\pi$
$127$	−3.31896	+	8.21471i	−0.294510	+	0.728938i	−0.999800	+	0.0200185i	$0.993628\pi$
$128$	0.559193	+	0.829038i	0.0494261	+	0.0732773i
$129$	3.33091	−	4.93828i	0.293270	−	0.434791i
$130$	−6.10394	−	15.1078i	−0.535351	−	1.32504i
$131$	−1.72609	−	9.78917i	−0.150810	−	0.855283i	−0.962517	−	0.271220i	$-0.912573\pi$
$131$	−1.72609	−	9.78917i	−0.150810	−	0.855283i	0.811708	−	0.584064i	$-0.198538\pi$
$132$	−1.22074	+	1.84926i	−0.106252	+	0.160957i
$133$	4.47376	+	0.425667i	0.387924	+	0.0369100i
$134$	0.319083	−	0.982036i	0.0275646	−	0.0848350i
$135$	−6.62962	−	6.40215i	−0.570587	−	0.551010i
$136$	4.94317	−	0.345660i	0.423873	−	0.0296401i
$137$	−5.99950	−	7.67901i	−0.512572	−	0.656062i	0.460203	−	0.887814i	$-0.347777\pi$
$137$	−5.99950	−	7.67901i	−0.512572	−	0.656062i	−0.972775	+	0.231752i	$0.925554\pi$
$138$	−0.111816	+	3.20200i	−0.00951843	+	0.272572i
$139$	−1.48988	−	5.97559i	−0.126370	−	0.506843i	−0.999802	−	0.0198967i	$-0.993666\pi$
$139$	−1.48988	−	5.97559i	−0.126370	−	0.506843i	0.873432	−	0.486946i	$-0.161889\pi$
$140$	0.267684	+	2.54684i	0.0226234	+	0.215247i
$141$	7.41112	−	1.57528i	0.624129	−	0.132663i
$142$	−1.74060	+	9.87145i	−0.146068	+	0.828394i
$143$	−19.1076	+	10.4049i	−1.59786	+	0.870101i
$144$	1.27682	+	2.21152i	0.106402	+	0.184293i
$145$	14.3354	+	15.9211i	1.19049	+	1.32218i
$146$	−1.91177	−	0.133684i	−0.158219	−	0.0110637i
$147$	2.21807	+	3.28843i	0.182944	+	0.271225i
$148$	−1.38273	−	1.76981i	−0.113659	−	0.145477i
$149$	−20.0980	−	12.5586i	−1.64649	−	1.02884i	−0.950470	−	0.310816i	$-0.899398\pi$
$149$	−20.0980	−	12.5586i	−1.64649	−	1.02884i	−0.696019	−	0.718024i	$-0.745047\pi$
$150$	−0.342597	+	0.702428i	−0.0279729	+	0.0573530i
$151$	15.9949	−	11.6210i	1.30165	−	0.945702i	0.301677	−	0.953410i	$-0.402453\pi$
$151$	15.9949	−	11.6210i	1.30165	−	0.945702i	0.999970	+	0.00770766i	$0.00245345\pi$
$152$	−2.59673	−	3.50100i	−0.210623	−	0.283968i
$153$	12.6539			1.02301
$154$	3.33743	−	0.744179i	0.268938	−	0.0599676i
$155$	0.537432	−	0.450959i	0.0431676	−	0.0362219i
$156$	−0.152955	−	4.38005i	−0.0122462	−	0.350684i
$157$	−19.4513	+	5.57757i	−1.55238	+	0.445138i	−0.938791	−	0.344487i	$-0.888053\pi$
$157$	−19.4513	+	5.57757i	−1.55238	+	0.445138i	−0.613590	+	0.789625i	$0.710275\pi$
$158$	−3.31088	−	13.2792i	−0.263400	−	1.05644i
$159$	7.11602	+	1.51256i	0.564337	+	0.119954i
$160$	1.66205	−	1.84590i	0.131397	−	0.145931i
$161$	3.55656	−	3.43453i	0.280296	−	0.270679i
$162$	2.27164	+	4.65755i	0.178477	+	0.365932i
$163$	17.5128	−	3.72246i	1.37171	−	0.291566i	0.537616	−	0.843190i	$-0.319325\pi$
$163$	17.5128	−	3.72246i	1.37171	−	0.291566i	0.834093	+	0.551624i	$0.185992\pi$
$164$	−2.53888	+	4.39746i	−0.198253	+	0.343384i
$165$	5.19048	+	1.83090i	0.404079	+	0.142535i
$166$	−11.9640	−	4.35453i	−0.928584	−	0.337977i
$167$	0.589278	+	16.8747i	0.0455997	+	1.30580i	0.779438	+	0.626479i	$0.215505\pi$
$167$	0.589278	+	16.8747i	0.0455997	+	1.30580i	−0.733838	+	0.679324i	$0.762273\pi$
$168$	−0.166637	+	0.668344i	−0.0128563	+	0.0515638i
$169$	13.1656	−	26.9935i	1.01274	−	2.07642i
$170$	−3.80348	−	11.7059i	−0.291714	−	0.897803i
$171$	−5.99133	−	9.38107i	−0.458168	−	0.717388i
$172$	7.21301	+	5.24056i	0.549987	+	0.399589i
$173$	−9.47337	−	9.14832i	−0.720247	−	0.695534i	0.241215	−	0.970472i	$-0.422454\pi$
$173$	−9.47337	−	9.14832i	−0.720247	−	0.695534i	−0.961462	+	0.274937i	$0.911343\pi$
$174$	2.15866	+	5.34286i	0.163647	+	0.405041i
$175$	1.13328	−	0.412481i	0.0856681	−	0.0311806i
$176$	−2.70247	−	1.92267i	−0.203706	−	0.144926i
$177$	−2.82112	−	2.36720i	−0.212048	−	0.177930i
$178$	8.11306	+	9.01046i	0.608099	+	0.675363i
$179$	1.94310	+	0.865125i	0.145234	+	0.0646625i	0.478067	−	0.878323i	$-0.341338\pi$
$179$	1.94310	+	0.865125i	0.145234	+	0.0646625i	−0.332832	+	0.942986i	$0.608004\pi$
$180$	4.56277	−	4.40621i	0.340088	−	0.328420i
$181$	20.5537	−	2.88863i	1.52774	−	0.214710i	0.675306	−	0.737538i	$-0.264012\pi$
$181$	20.5537	−	2.88863i	1.52774	−	0.214710i	0.852439	+	0.522827i	$0.175123\pi$
$182$	−4.52548	+	5.02606i	−0.335451	+	0.372556i
$183$	−2.06110	+	0.917661i	−0.152361	+	0.0678354i
$184$	−4.78392	−	0.334524i	−0.352675	−	0.0246615i
$185$	−3.43456	+	4.39603i	−0.252514	+	0.323203i
$186$	0.177323	−	0.0645401i	0.0130019	−	0.00473231i
$187$	−14.9466	+	6.83365i	−1.09300	+	0.499726i
$188$	1.96928	+	11.1683i	0.143624	+	0.814535i
$189$	−1.18210	+	3.63814i	−0.0859854	+	0.264636i
$190$	−6.87741	+	8.36222i	−0.498940	+	0.606659i
$191$	−0.0169063	−	0.0122832i	−0.00122330	−	0.000888778i	0.587173	−	0.809461i	$-0.300241\pi$
$191$	−0.0169063	−	0.0122832i	−0.00122330	−	0.000888778i	−0.588397	+	0.808572i	$0.700241\pi$
$192$	0.589899	−	0.313655i	0.0425723	−	0.0226361i
$193$	−14.4785	−	9.04720i	−1.04219	−	0.651231i	−0.103017	−	0.994680i	$-0.532849\pi$
$193$	−14.4785	−	9.04720i	−1.04219	−	0.651231i	−0.939172	+	0.343448i	$0.888405\pi$
$194$	−10.1735	−	2.91721i	−0.730416	−	0.209443i
$195$	−10.4645	+	3.00065i	−0.749380	+	0.214881i
$196$	−5.03492	+	3.14617i	−0.359637	+	0.224726i
$197$	−6.22823	+	10.7876i	−0.443743	+	0.768585i	−0.997964	−	0.0637845i	$-0.979683\pi$
$197$	−6.22823	+	10.7876i	−0.443743	+	0.768585i	0.554221	+	0.832370i	$0.313016\pi$
$198$	−6.54184	−	5.37924i	−0.464908	−	0.382286i
$199$	−3.18271	+	18.0500i	−0.225616	+	1.27953i	0.635888	+	0.771782i	$0.280634\pi$
$199$	−3.18271	+	18.0500i	−0.225616	+	1.27953i	−0.861504	+	0.507751i	$0.830477\pi$
$200$	−1.03284	−	0.549172i	−0.0730330	−	0.0388323i
$201$	−0.630223	−	0.280593i	−0.0444525	−	0.0197915i
$202$	1.36879	−	0.609427i	0.0963081	−	0.0428791i
$203$	3.33115	−	8.24488i	0.233801	−	0.578677i
$204$	0.115538	−	3.30859i	0.00808931	−	0.231647i
$205$	12.1240	+	3.47651i	0.846780	+	0.242810i
$206$	0.433590	−	1.73904i	0.0302097	−	0.121164i
$207$	−12.1271	−	1.70435i	−0.842889	−	0.118460i
$208$	6.55995			0.454851
$209$	12.1430	+	7.84517i	0.839951	+	0.542662i
$210$	1.71092			0.118065
$211$	27.2008	+	3.82283i	1.87258	+	0.263174i	0.981612	−	0.190887i	$-0.0611363\pi$
$211$	27.2008	+	3.82283i	1.87258	+	0.263174i	0.890971	+	0.454061i	$0.150025\pi$
$212$	−2.63430	+	10.5656i	−0.180924	+	0.725648i
$213$	6.43745	+	1.84591i	0.441087	+	0.126480i
$214$	0.139062	−	3.98221i	0.00950606	−	0.272218i
$215$	8.29600	−	20.5333i	0.565782	−	1.40036i
$216$	3.38962	−	1.50915i	0.230634	−	0.102685i
$217$	−0.266023	−	0.118441i	−0.0180588	−	0.00804030i
$218$	6.46940	+	3.43984i	0.438163	+	0.232975i
$219$	−0.222335	+	1.26092i	−0.0150240	+	0.0852052i
$220$	−3.00991	+	7.66863i	−0.202928	+	0.517019i
$221$	16.2531	−	28.1511i	1.09330	−	1.89365i
$222$	−1.27250	+	0.795146i	−0.0854046	+	0.0533667i
$223$	6.27591	−	1.79959i	0.420266	−	0.120509i	−0.0588378	−	0.998268i	$-0.518739\pi$
$223$	6.27591	−	1.79959i	0.420266	−	0.120509i	0.479104	+	0.877758i	$0.340962\pi$
$224$	−0.991048	−	0.284178i	−0.0662172	−	0.0189875i
$225$	−2.53326	−	1.58296i	−0.168884	−	0.105530i
$226$	1.08929	−	0.579187i	0.0724586	−	0.0385269i
$227$	1.50588	+	1.09409i	0.0999489	+	0.0726171i	0.636637	−	0.771163i	$-0.280325\pi$
$227$	1.50588	+	1.09409i	0.0999489	+	0.0726171i	−0.536688	+	0.843781i	$0.680325\pi$
$228$	−2.50755	+	1.48089i	−0.166067	+	0.0980740i
$229$	−2.06650	+	6.36002i	−0.136558	+	0.420282i	−0.995829	−	0.0912382i	$-0.970918\pi$
$229$	−2.06650	+	6.36002i	−0.136558	+	0.420282i	0.859271	+	0.511520i	$0.170918\pi$
$230$	2.06846	+	11.7308i	0.136390	+	0.773508i
$231$	−0.261392	−	2.26950i	−0.0171983	−	0.149322i
$232$	−8.10497	+	2.94997i	−0.532117	+	0.193675i
$233$	14.6571	−	18.7602i	0.960217	−	1.22902i	−0.0131842	−	0.999913i	$-0.504197\pi$
$233$	14.6571	−	18.7602i	0.960217	−	1.22902i	0.973401	−	0.229108i	$-0.0735810\pi$
$234$	16.7110	+	1.16854i	1.09243	+	0.0763901i
$235$	25.7337	−	11.4574i	1.67868	−	0.747396i
$236$	3.68838	−	4.09636i	0.240093	−	0.266651i
$237$	−9.05449	+	1.27253i	−0.588152	+	0.0826594i
$238$	−3.67495	+	3.54886i	−0.238212	+	0.230039i
$239$	−10.5077	−	4.67831i	−0.679684	−	0.302615i	0.0377038	−	0.999289i	$-0.487996\pi$
$239$	−10.5077	−	4.67831i	−0.679684	−	0.302615i	−0.717388	+	0.696674i	$0.754662\pi$
$240$	−1.11042	−	1.23325i	−0.0716774	−	0.0796058i
$241$	1.31142	+	1.10041i	0.0844760	+	0.0708837i	0.684048	−	0.729437i	$-0.260218\pi$
$241$	1.31142	+	1.10041i	0.0844760	+	0.0708837i	−0.599572	+	0.800321i	$0.704662\pi$
$242$	10.6321	+	2.82099i	0.683459	+	0.181340i
$243$	13.7132	−	4.99120i	0.879703	−	0.320186i
$244$	−1.26503	−	3.13107i	−0.0809854	−	0.200446i
$245$	10.6082	+	10.2442i	0.677731	+	0.654477i
$246$	2.74455	+	1.99403i	0.174986	+	0.127135i
$247$	−28.5655	+	1.27958i	−1.81758	+	0.0814176i
$248$	0.0872806	+	0.268622i	0.00554232	+	0.0170575i
$249$	−3.72884	+	7.64526i	−0.236306	+	0.484499i
$250$	2.30163	−	9.23132i	0.145568	−	0.583840i
$251$	−0.0531120	−	1.52093i	−0.00335240	−	0.0960002i	−0.999914	−	0.0131409i	$-0.995817\pi$
$251$	−0.0531120	−	1.52093i	−0.00335240	−	0.0960002i	0.996561	−	0.0828593i	$-0.0264052\pi$
$252$	−2.47399	−	0.900460i	−0.155847	−	0.0567237i
$253$	15.2447	−	4.53599i	0.958425	−	0.285175i
$254$	−4.42993	+	7.67286i	−0.277958	+	0.481438i
$255$	−8.04352	+	1.70970i	−0.503705	+	0.107066i
$256$	0.438371	+	0.898794i	0.0273982	+	0.0561746i
$257$	−1.50462	+	1.45299i	−0.0938555	+	0.0906352i	−0.740106	−	0.672490i	$-0.765225\pi$
$257$	−1.50462	+	1.45299i	−0.0938555	+	0.0906352i	0.646251	+	0.763125i	$0.276336\pi$
$258$	3.98577	−	4.42665i	0.248143	−	0.275591i
$259$	2.26492	+	0.481423i	0.140735	+	0.0299142i
$260$	−3.94194	−	15.8103i	−0.244469	−	0.980511i
$261$	−21.1722	+	6.07104i	−1.31053	+	0.375788i
$262$	−0.346907	−	9.93412i	−0.0214320	−	0.613732i
$263$	−6.44538	+	5.40832i	−0.397439	+	0.333491i	−0.819503	−	0.573075i	$-0.805750\pi$
$263$	−6.44538	+	5.40832i	−0.397439	+	0.333491i	0.422063	+	0.906566i	$0.361306\pi$
$264$	−1.46623	+	1.66136i	−0.0902402	+	0.102250i
$265$	27.0473			1.66150
$266$	4.37098	+	1.04415i	0.268002	+	0.0640210i
$267$	6.55351	−	4.76140i	0.401068	−	0.291393i
$268$	0.452651	−	0.928071i	0.0276500	−	0.0566910i
$269$	0.325508	+	0.203400i	0.0198466	+	0.0124015i	0.539806	−	0.841789i	$-0.318497\pi$
$269$	0.325508	+	0.203400i	0.0198466	+	0.0124015i	−0.519960	+	0.854191i	$0.674053\pi$
$270$	−5.67410	−	7.26251i	−0.345315	−	0.441982i
$271$	−15.7613	−	23.3671i	−0.957431	−	1.41945i	−0.907194	−	0.420712i	$-0.861780\pi$
$271$	−15.7613	−	23.3671i	−0.957431	−	1.41945i	−0.0502364	−	0.998737i	$-0.515997\pi$
$272$	4.94317	+	0.345660i	0.299724	+	0.0209587i
$273$	3.02348	+	3.35792i	0.182989	+	0.203230i
$274$	−4.87240	−	8.43925i	−0.294352	−	0.509833i
$275$	3.84710	+	0.501690i	0.231989	+	0.0302531i
$276$	−0.556360	+	3.15528i	−0.0334889	+	0.189925i
$277$	−23.0970	+	4.90943i	−1.38777	+	0.294979i	−0.840424	−	0.541930i	$-0.817694\pi$
$277$	−23.0970	+	4.90943i	−1.38777	+	0.294979i	−0.547343	+	0.836908i	$0.684361\pi$
$278$	−0.643741	−	6.12479i	−0.0386090	−	0.367340i
$279$	0.174490	+	0.699841i	0.0104464	+	0.0418984i
$280$	−0.0893731	+	2.55931i	−0.00534106	+	0.152948i
$281$	8.46156	+	10.8303i	0.504774	+	0.646082i	0.971140	−	0.238510i	$-0.0766591\pi$
$281$	8.46156	+	10.8303i	0.504774	+	0.646082i	−0.466366	+	0.884592i	$0.654437\pi$
$282$	7.55824	−	0.528523i	0.450086	−	0.0314731i
$283$	11.7500	+	11.3468i	0.698464	+	0.674498i	0.956532	−	0.291628i	$-0.0941970\pi$
$283$	11.7500	+	11.3468i	0.698464	+	0.674498i	−0.258068	+	0.966127i	$0.583086\pi$
$284$	−3.09750	+	9.53313i	−0.183803	+	0.565687i
$285$	5.07592	+	5.15362i	0.300672	+	0.305274i
$286$	−20.3697	+	7.64437i	−1.20449	+	0.452021i
$287$	−0.909064	−	5.15556i	−0.0536604	−	0.304323i
$288$	0.956610	+	2.36769i	0.0563688	+	0.139518i
$289$	4.22436	−	6.26288i	0.248492	−	0.368405i
$290$	11.9801	+	17.7613i	0.703498	+	1.04298i
$291$	−2.64879	+	6.55599i	−0.155275	+	0.384319i
$292$	−1.87456	−	0.398449i	−0.109700	−	0.0233175i
$293$	2.17793	−	20.7216i	0.127236	−	1.21057i	−0.725497	−	0.688225i	$-0.758390\pi$
$293$	2.17793	−	20.7216i	0.127236	−	1.21057i	0.852734	−	0.522346i	$-0.174943\pi$
$294$	1.73883	+	3.56512i	0.101410	+	0.207922i
$295$	−12.0891	−	6.42789i	−0.703855	−	0.374246i
$296$	−1.12296	−	1.94502i	−0.0652708	−	0.113052i
$297$	−8.76669	+	8.63612i	−0.508695	+	0.501119i
$298$	−18.1545	−	15.2335i	−1.05166	−	0.882451i
$299$	−19.3680	+	24.7900i	−1.12008	+	1.43364i
$300$	−0.437022	+	0.647912i	−0.0252315	+	0.0374072i
$301$	−9.16965	+	0.641204i	−0.528530	+	0.0369584i
$302$	17.4566	−	9.28183i	1.00451	−	0.534109i
$303$	−0.309338	−	0.952044i	−0.0177710	−	0.0546935i
$304$	−2.08422	−	3.82832i	−0.119538	−	0.219569i
$305$	−6.78607	+	4.93037i	−0.388569	+	0.282312i
$306$	12.5307	+	1.76108i	0.716335	+	0.100674i
$307$	−0.201529	+	0.169103i	−0.0115019	+	0.00965123i	−0.648520	−	0.761197i	$-0.724612\pi$
$307$	−0.201529	+	0.169103i	−0.0115019	+	0.00965123i	0.637019	+	0.770848i	$0.280167\pi$
$308$	3.40852	−	0.272455i	0.194219	−	0.0155246i
$309$	−1.12521	−	0.409542i	−0.0640109	−	0.0232980i
$310$	0.594963	−	0.371774i	0.0337917	−	0.0211154i
$311$	0.409794	+	3.89893i	0.0232373	+	0.221088i	0.999978	+	0.00666331i	$0.00212101\pi$
$311$	0.409794	+	3.89893i	0.0232373	+	0.221088i	−0.976741	+	0.214425i	$0.931212\pi$
$312$	0.458119	−	4.35871i	0.0259359	−	0.246763i
$313$	−8.36318	+	1.17537i	−0.472715	+	0.0664357i	−0.371508	−	0.928430i	$-0.621159\pi$
$313$	−8.36318	+	1.17537i	−0.472715	+	0.0664357i	−0.101207	+	0.994865i	$0.532270\pi$
$314$	−20.0382	+	2.81619i	−1.13082	+	0.158927i
$315$	−0.683568	+	6.50372i	−0.0385147	+	0.366443i
$316$	−1.43055	−	13.6108i	−0.0804748	−	0.765666i
$317$	11.6933	−	7.30676i	0.656759	−	0.410389i	−0.160200	−	0.987085i	$-0.551214\pi$
$317$	11.6933	−	7.30676i	0.656759	−	0.410389i	0.816959	+	0.576696i	$0.195658\pi$
$318$	6.83626	+	2.48819i	0.383358	+	0.139531i
$319$	21.7297	−	18.6049i	1.21663	−	1.04168i
$320$	1.90278	−	1.59662i	0.106369	−	0.0892538i
$321$	−2.63623	−	0.370498i	−0.147140	−	0.0206792i
$322$	3.99994	−	2.90613i	0.222908	−	0.161952i
$323$	−21.5926	−	0.540978i	−1.20145	−	0.0301008i
$324$	1.60133	+	4.92837i	0.0889625	+	0.273798i
$325$	−6.77540	+	3.60254i	−0.375832	+	0.199833i
$326$	17.8604	−	1.24892i	0.989198	−	0.0691715i
$327$	2.73737	−	4.05832i	0.151377	−	0.224425i
$328$	−3.12618	+	4.00132i	−0.172614	+	0.220936i
$329$	−8.95662	−	7.51550i	−0.493794	−	0.414343i
$330$	4.88516	+	2.53546i	0.268919	+	0.139572i
$331$	−5.22215	−	9.04503i	−0.287035	−	0.497160i	0.686065	−	0.727540i	$-0.259336\pi$
$331$	−5.22215	−	9.04503i	−0.287035	−	0.497160i	−0.973101	+	0.230380i	$0.926003\pi$
$332$	−11.2415	−	5.97721i	−0.616957	−	0.328042i
$333$	−2.51418	−	5.15483i	−0.137776	−	0.282483i
$334$	−1.76496	+	16.7925i	−0.0965744	+	0.918844i
$335$	−2.50876	−	0.533254i	−0.137068	−	0.0291348i
$336$	−0.258031	+	0.638648i	−0.0140767	+	0.0348411i
$337$	2.80849	+	4.16376i	0.152988	+	0.226814i	0.897738	−	0.440529i	$-0.145209\pi$
$337$	2.80849	+	4.16376i	0.152988	+	0.226814i	−0.744750	+	0.667343i	$0.767431\pi$
$338$	16.7942	−	24.8985i	0.913486	−	1.35430i
$339$	−0.308765	−	0.764219i	−0.0167698	−	0.0415067i
$340$	−2.13732	−	12.1213i	−0.115912	−	0.657372i
$341$	−0.584048	−	0.732407i	−0.0316280	−	0.0396621i
$342$	−4.62743	−	10.1236i	−0.250223	−	0.547422i
$343$	4.12165	−	12.6851i	0.222548	−	0.684933i
$344$	6.41347	+	6.19341i	0.345791	+	0.333926i
$345$	7.93891	−	0.555143i	0.427417	−	0.0298879i
$346$	−8.10797	−	10.3777i	−0.435887	−	0.557910i
$347$	−0.318294	+	9.11475i	−0.0170869	+	0.489306i	0.960439	+	0.278490i	$0.0898340\pi$
$347$	−0.318294	+	9.11475i	−0.0170869	+	0.489306i	−0.977526	+	0.210815i	$0.932388\pi$
$348$	1.39407	+	5.59129i	0.0747298	+	0.299725i
$349$	−0.352079	−	3.34981i	−0.0188464	−	0.179311i	0.981049	−	0.193758i	$-0.0620678\pi$
$349$	−0.352079	−	3.34981i	−0.0188464	−	0.179311i	−0.999896	+	0.0144472i	$0.995401\pi$
$350$	1.17966	−	0.250744i	0.0630555	−	0.0134029i
$351$	4.22660	−	23.9702i	0.225599	−	1.27944i
$352$	−2.40859	−	2.28007i	−0.128378	−	0.121528i
$353$	6.11187	+	10.5861i	0.325302	+	0.563440i	0.981573	−	0.191085i	$-0.0612007\pi$
$353$	6.11187	+	10.5861i	0.325302	+	0.563440i	−0.656271	+	0.754525i	$0.727867\pi$
$354$	−2.46421	−	2.73679i	−0.130972	−	0.145459i
$355$	24.8373	+	1.73679i	1.31823	+	0.0921795i
$356$	6.78009	+	10.0519i	0.359344	+	0.532749i
$357$	2.10137	+	2.68963i	0.111216	+	0.142350i
$358$	1.80379	+	1.12713i	0.0953333	+	0.0595709i
$359$	−1.03142	+	2.11473i	−0.0544365	+	0.111611i	−0.924278	−	0.381720i	$-0.875332\pi$
$359$	−1.03142	+	2.11473i	−0.0544365	+	0.111611i	0.869842	+	0.493331i	$0.164221\pi$
$360$	5.13159	−	3.72832i	0.270458	−	0.196500i
$361$	9.82255	+	16.2640i	0.516976	+	0.856000i
$362$	20.7557			1.09090
$363$	2.61688	−	6.86742i	0.137351	−	0.360446i
$364$	−5.18093	+	4.34732i	−0.271555	+	0.227861i
$365$	0.166130	+	4.75734i	0.00869563	+	0.249010i
$366$	−2.16876	+	0.621881i	−0.113363	+	0.0325062i
$367$	−0.724503	−	2.90582i	−0.0378188	−	0.151683i	0.948418	−	0.317023i	$-0.102683\pi$
$367$	−0.724503	−	2.90582i	−0.0378188	−	0.151683i	−0.986237	+	0.165340i	$0.947128\pi$
$368$	−4.69081	−	0.997062i	−0.244525	−	0.0519754i
$369$	−8.67645	+	9.63617i	−0.451678	+	0.501639i
$370$	−4.01294	+	3.87525i	−0.208623	+	0.201465i
$371$	−4.92136	−	10.0903i	−0.255504	−	0.523861i
$372$	0.184579	−	0.0392335i	0.00956998	−	0.00203416i
$373$	−1.99062	+	3.44785i	−0.103070	+	0.178523i	−0.912948	−	0.408076i	$-0.866200\pi$
$373$	−1.99062	+	3.44785i	−0.103070	+	0.178523i	0.809878	+	0.586598i	$0.199533\pi$
$374$	−15.7522	+	4.68698i	−0.814525	+	0.242358i
$375$	−5.97294	−	2.17397i	−0.308441	−	0.112263i
$376$	0.395782	+	11.3337i	0.0204109	+	0.584492i
$377$	−13.6880	+	54.8998i	−0.704970	+	2.82748i
$378$	−1.67693	+	3.43822i	−0.0862521	+	0.176843i
$379$	2.99251	+	9.21000i	0.153715	+	0.473086i	0.998028	−	0.0627638i	$-0.0199915\pi$
$379$	2.99251	+	9.21000i	0.153715	+	0.473086i	−0.844314	+	0.535849i	$0.819991\pi$
$380$	−7.97428	+	7.32369i	−0.409072	+	0.375697i
$381$	4.78880	+	3.47927i	0.245338	+	0.178248i
$382$	−0.0150323	−	0.0145165i	−0.000769120	−	0.000742730i
$383$	−10.9398	−	27.0770i	−0.558999	−	1.38357i	−0.896834	−	0.442367i	$-0.854139\pi$
$383$	−10.9398	−	27.0770i	−0.558999	−	1.38357i	0.337835	−	0.941205i	$-0.390305\pi$
$384$	0.627810	−	0.228504i	0.0320378	−	0.0116608i
$385$	−2.70487	−	8.05123i	−0.137853	−	0.410329i
$386$	−13.0785	−	10.9742i	−0.665679	−	0.558571i
$387$	15.2345	+	16.9197i	0.774415	+	0.860075i
$388$	−9.66852	−	4.30470i	−0.490845	−	0.218538i
$389$	−26.0747	+	25.1800i	−1.32204	+	1.27668i	−0.387024	+	0.922069i	$0.626497\pi$
$389$	−26.0747	+	25.1800i	−1.32204	+	1.27668i	−0.935015	+	0.354609i	$0.884614\pi$
$390$	−10.7803	+	1.51507i	−0.545881	+	0.0767186i
$391$	−15.9008	+	17.6596i	−0.804137	+	0.893085i
$392$	−5.42378	+	2.41482i	−0.273942	+	0.121967i
$393$	−6.62487	−	0.463256i	−0.334181	−	0.0233682i
$394$	−7.66896	+	9.81582i	−0.386357	+	0.494514i
$395$	−31.9440	+	11.6267i	−1.60728	+	0.585000i
$396$	−5.72953	−	6.23734i	−0.287920	−	0.313438i
$397$	0.593928	+	3.36833i	0.0298084	+	0.169052i	0.996078	−	0.0884815i	$-0.0282014\pi$
$397$	0.593928	+	3.36833i	0.0298084	+	0.169052i	−0.966269	+	0.257533i	$0.917090\pi$
$398$	−5.66381	+	17.4314i	−0.283901	+	0.873758i
$399$	0.999028	−	2.83135i	0.0500140	−	0.141745i
$400$	−0.946361	−	0.687572i	−0.0473181	−	0.0343786i
$401$	−15.4491	+	8.21444i	−0.771492	+	0.410209i	−0.808044	−	0.589122i	$-0.799474\pi$
$401$	−15.4491	+	8.21444i	−0.771492	+	0.410209i	0.0365521	+	0.999332i	$0.488363\pi$
$402$	−0.585038	−	0.365573i	−0.0291791	−	0.0182331i
$403$	1.78106	+	0.510710i	0.0887208	+	0.0254403i
$404$	1.44029	−	0.412996i	0.0716571	−	0.0205473i
$405$	10.9157	−	6.82089i	0.542406	−	0.338933i
$406$	4.44620	−	7.70104i	0.220661	−	0.382196i
$407$	5.75353	+	4.73103i	0.285192	+	0.234508i
$408$	0.574880	−	3.26031i	0.0284608	−	0.161409i
$409$	8.95863	+	4.76339i	0.442976	+	0.235534i	0.675948	−	0.736949i	$-0.263734\pi$
$409$	8.95863	+	4.76339i	0.442976	+	0.235534i	−0.232973	+	0.972483i	$0.574845\pi$
$410$	11.5222	+	5.13002i	0.569042	+	0.253354i
$411$	−5.94766	+	2.64807i	−0.293376	+	0.130619i
$412$	0.671398	−	1.66177i	0.0330774	−	0.0818694i
$413$	−0.198334	+	5.67954i	−0.00975938	+	0.279472i
$414$	−11.7718	−	3.37552i	−0.578554	−	0.165898i
$415$	−7.65066	+	30.6851i	−0.375556	+	1.50627i
$416$	6.49611	+	0.912969i	0.318498	+	0.0447620i
$417$	−4.11452			−0.201489
$418$	10.9330	+	9.45881i	0.534751	+	0.462645i
$419$	10.4393			0.509995			0.254998	−	0.966942i	$-0.417925\pi$
$419$	10.4393			0.509995			0.254998	+	0.966942i	$0.417925\pi$
$420$	1.69427	+	0.238114i	0.0826720	+	0.0116188i
$421$	0.121547	−	0.487497i	0.00592383	−	0.0237592i	−0.967261	−	0.253783i	$-0.918325\pi$
$421$	0.121547	−	0.487497i	0.00592383	−	0.0237592i	0.973185	+	0.230024i	$0.0738805\pi$
$422$	26.4041	+	7.57125i	1.28533	+	0.368563i
$423$	−1.01069	+	28.9422i	−0.0491412	+	1.40722i
$424$	−4.07911	+	10.0962i	−0.198099	+	0.490312i
$425$	−5.29534	+	2.35764i	−0.256862	+	0.114362i
$426$	6.11790	+	2.72386i	0.296413	+	0.131972i
$427$	3.07407	+	1.63451i	0.148765	+	0.0790997i
$428$	0.691924	−	3.92410i	0.0334454	−	0.189678i
$429$	3.65670	+	14.0684i	0.176547	+	0.679227i
$430$	11.0729	−	19.1789i	0.533985	−	0.924889i
$431$	−28.0865	+	17.5504i	−1.35288	+	0.845373i	−0.996050	−	0.0887960i	$-0.971698\pi$
$431$	−28.0865	+	17.5504i	−1.35288	+	0.845373i	−0.356830	+	0.934169i	$0.616143\pi$
$432$	3.56666	−	1.02272i	0.171601	−	0.0492058i
$433$	15.9018	+	4.55977i	0.764192	+	0.219128i	0.635022	−	0.772494i	$-0.280991\pi$
$433$	15.9018	+	4.55977i	0.764192	+	0.219128i	0.129170	+	0.991623i	$0.458769\pi$
$434$	−0.246950	−	0.154311i	−0.0118540	−	0.00740719i
$435$	12.6380	−	6.71973i	0.605945	−	0.322186i
$436$	5.92771	+	4.30673i	0.283886	+	0.206255i
$437$	20.6208	+	3.42675i	0.986424	+	0.163924i
$438$	−0.395657	+	1.21771i	−0.0189052	+	0.0581843i
$439$	0.801995	+	4.54834i	0.0382771	+	0.217080i	0.997947	−	0.0640501i	$-0.0204017\pi$
$439$	0.801995	+	4.54834i	0.0382771	+	0.217080i	−0.959670	+	0.281130i	$0.909291\pi$
$440$	−4.04789	+	7.17510i	−0.192976	+	0.342059i
$441$	−14.2468	+	5.18541i	−0.678419	+	0.246924i
$442$	20.0128	−	25.6152i	0.951911	−	1.21839i
$443$	−2.95399	−	0.206563i	−0.140348	−	0.00981411i	−0.000590465	−	1.00000i	$-0.500188\pi$
$443$	−2.95399	−	0.206563i	−0.140348	−	0.00981411i	−0.139758	+	0.990186i	$0.544632\pi$
$444$	−1.37078	+	0.610310i	−0.0650543	+	0.0289640i
$445$	20.1520	−	22.3811i	0.955298	−	1.06097i
$446$	6.46529	−	0.908637i	0.306140	−	0.0430252i
$447$	−11.3896	+	10.9988i	−0.538709	+	0.520225i
$448$	−0.941853	−	0.419340i	−0.0444984	−	0.0198120i
$449$	−12.0364	−	13.3678i	−0.568034	−	0.630866i	0.388862	−	0.921296i	$-0.372868\pi$
$449$	−12.0364	−	13.3678i	−0.568034	−	0.630866i	−0.956896	+	0.290430i	$0.906202\pi$
$450$	−2.28830	−	1.92011i	−0.107871	−	0.0905149i
$451$	5.04452	−	16.0677i	0.237537	−	0.756600i
$452$	1.15930	−	0.421950i	0.0545288	−	0.0198469i
$453$	−4.94814	−	12.2471i	−0.232484	−	0.575418i
$454$	1.33896	+	1.29302i	0.0628405	+	0.0606843i
$455$	13.5908	+	9.87431i	0.637148	+	0.462915i
$456$	−2.68925	+	1.11749i	−0.125936	+	0.0523312i
$457$	−6.73441	−	20.7264i	−0.315023	−	0.969540i	−0.975745	−	0.218910i	$-0.929750\pi$
$457$	−6.73441	−	20.7264i	−0.315023	−	0.969540i	0.660723	−	0.750630i	$-0.270250\pi$
$458$	−2.93153	+	6.01053i	−0.136981	+	0.280854i
$459$	4.44795	−	17.8398i	0.207613	−	0.832689i
$460$	0.415716	+	11.9045i	0.0193829	+	0.555052i
$461$	−28.1845	−	10.2583i	−1.31268	−	0.477777i	−0.411576	−	0.911376i	$-0.635021\pi$
$461$	−28.1845	−	10.2583i	−1.31268	−	0.477777i	−0.901106	+	0.433598i	$0.857244\pi$
$462$	0.0570057	−	2.28379i	0.00265215	−	0.106252i
$463$	1.51929	−	2.63149i	0.0706074	−	0.122296i	−0.828560	−	0.559900i	$-0.810840\pi$
$463$	1.51929	−	2.63149i	0.0706074	−	0.122296i	0.899168	+	0.437604i	$0.144173\pi$
$464$	−8.43665	+	1.79327i	−0.391662	+	0.0832502i
$465$	−0.205473	−	0.421282i	−0.00952857	−	0.0195365i
$466$	17.1253	−	16.5378i	0.793316	−	0.766097i
$467$	−16.5291	+	18.3574i	−0.764874	+	0.849479i	−0.992241	−	0.124331i	$-0.960322\pi$
$467$	−16.5291	+	18.3574i	−0.764874	+	0.849479i	0.227367	+	0.973809i	$0.426988\pi$
$468$	16.3857	+	3.48289i	0.757429	+	0.160996i
$469$	0.257543	+	1.03295i	0.0118922	+	0.0476971i
$470$	27.0778	−	7.76443i	1.24900	−	0.358146i
$471$	0.471811	+	13.5109i	0.0217399	+	0.622550i
$472$	4.22259	−	3.54317i	0.194360	−	0.163088i
$473$	−27.1321	−	11.7579i	−1.24754	−	0.540629i
$474$	−9.14347			−0.419974
$475$	4.25508	+	2.80946i	0.195236	+	0.128907i
$476$	−4.13309	+	3.00287i	−0.189440	+	0.137636i
$477$	−12.1897	+	24.9925i	−0.558126	+	1.14433i
$478$	−9.75430	−	6.09516i	−0.446151	−	0.278786i
$479$	−5.77448	−	7.39099i	−0.263843	−	0.337703i	0.637787	−	0.770213i	$-0.279850\pi$
$479$	−5.77448	−	7.39099i	−0.263843	−	0.337703i	−0.901629	+	0.432510i	$0.857628\pi$
$480$	−0.927980	−	1.37579i	−0.0423563	−	0.0627958i
$481$	−14.6972	−	1.02773i	−0.670137	−	0.0468605i
$482$	1.14551	+	1.27222i	0.0521765	+	0.0579479i
$483$	−1.65162	−	2.86068i	−0.0751511	−	0.130166i
$484$	10.1360	+	4.27324i	0.460729	+	0.194238i
$485$	−4.56493	+	25.8890i	−0.207283	+	1.17556i
$486$	14.2744	−	3.03412i	0.647500	−	0.137630i
$487$	0.402445	+	3.82901i	0.0182365	+	0.173509i	0.999849	−	0.0173755i	$-0.00553109\pi$
$487$	0.402445	+	3.82901i	0.0182365	+	0.173509i	−0.981613	+	0.190884i	$0.938864\pi$
$488$	−0.816961	−	3.27665i	−0.0369821	−	0.148327i
$489$	0.417458	−	11.9544i	0.0188781	−	0.540599i
$490$	9.07921	+	11.6209i	0.410157	+	0.524977i
$491$	−7.02143	+	0.490986i	−0.316873	+	0.0221579i	−0.227307	−	0.973823i	$-0.572992\pi$
$491$	−7.02143	+	0.490986i	−0.316873	+	0.0221579i	−0.0895654	+	0.995981i	$0.528548\pi$
$492$	2.44033	+	2.35660i	0.110018	+	0.106244i
$493$	−13.2073	+	40.6478i	−0.594825	+	1.83068i
$494$	−28.4656	−	2.70843i	−1.28073	−	0.121858i
$495$	−11.5898	+	17.5569i	−0.520922	+	0.789125i
$496$	0.0490462	+	0.278155i	0.00220224	+	0.0124895i
$497$	−3.87131	−	9.58183i	−0.173652	−	0.429804i
$498$	−4.75657	+	7.05190i	−0.213147	+	0.316003i
$499$	−12.7099	−	18.8432i	−0.568975	−	0.843540i	0.429245	−	0.903188i	$-0.358780\pi$
$499$	−12.7099	−	18.8432i	−0.568975	−	0.843540i	−0.998219	+	0.0596486i	$0.981002\pi$
$500$	3.56398	−	8.82116i	0.159386	−	0.394494i
$501$	11.0344	+	2.34543i	0.492980	+	0.104786i
$502$	0.159077	−	1.51352i	0.00709996	−	0.0675517i
$503$	−7.76113	−	15.9127i	−0.346052	−	0.709511i	0.652794	−	0.757535i	$-0.273597\pi$
$503$	−7.76113	−	15.9127i	−0.346052	−	0.709511i	−0.998846	+	0.0480239i	$0.984708\pi$
$504$	−2.32460	−	1.23601i	−0.103546	−	0.0550563i
$505$	−1.86085	−	3.22310i	−0.0828070	−	0.143426i
$506$	15.7276	−	2.37019i	0.699178	−	0.105368i
$507$	−15.3708	−	12.8976i	−0.682639	−	0.572802i
$508$	−5.45467	+	6.98166i	−0.242012	+	0.309761i
$509$	9.87295	−	14.6372i	0.437611	−	0.648785i	−0.544132	−	0.839000i	$-0.683141\pi$
$509$	9.87295	−	14.6372i	0.437611	−	0.648785i	0.981742	+	0.190215i	$0.0609186\pi$
$510$	−8.20318	+	0.573622i	−0.363243	+	0.0254004i
$511$	1.74454	−	0.927591i	0.0771741	−	0.0410342i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−15.3317	+	5.14919i	−0.676909	+	0.227342i
$514$	−1.69219	+	1.22945i	−0.0746394	+	0.0542287i
$515$	−4.40851	−	0.619575i	−0.194262	−	0.0273018i
$516$	4.56305	−	3.82885i	0.200877	−	0.168556i
$517$	−14.4362	−	34.7319i	−0.634905	−	1.52751i
$518$	2.17587	+	0.791953i	0.0956024	+	0.0347964i
$519$	−7.46163	+	4.66254i	−0.327529	+	0.204663i
$520$	−1.70322	−	16.2050i	−0.0746909	−	0.710637i
$521$	3.26773	−	31.0904i	0.143162	−	1.36209i	−0.653160	−	0.757220i	$-0.726557\pi$
$521$	3.26773	−	31.0904i	0.143162	−	1.36209i	0.796321	−	0.604874i	$-0.206776\pi$
$522$	−21.8111	+	3.06535i	−0.954647	+	0.134167i
$523$	28.4612	−	3.99996i	1.24452	−	0.174906i	0.513996	−	0.857792i	$-0.328165\pi$
$523$	28.4612	−	3.99996i	1.24452	−	0.174906i	0.730525	+	0.682886i	$0.239276\pi$
$524$	1.03903	−	9.88573i	0.0453903	−	0.431860i
$525$	−0.0842228	−	0.801326i	−0.00367578	−	0.0349727i
$526$	−7.13535	+	4.45866i	−0.311116	+	0.194407i
$527$	1.31518	+	0.478687i	0.0572902	+	0.0208519i
$528$	−1.68318	+	1.44114i	−0.0732509	+	0.0627174i
$529$	−0.00168731	+	0.00141582i	−7.33614e−5	+	6.15575e-5i
$530$	26.7841	+	3.76426i	1.16343	+	0.163509i
$531$	11.3879	−	8.27377i	0.494191	−	0.359051i
$532$	4.18313	+	1.64231i	0.181362	+	0.0712033i
$533$	10.2933	+	31.6795i	0.445852	+	1.37219i
$534$	7.15239	−	3.80299i	0.309514	−	0.164572i
$535$	−9.87333	+	0.690410i	−0.426861	+	0.0298490i
$536$	0.577408	−	0.856043i	0.0249402	−	0.0369754i
$537$	0.874884	−	1.11980i	0.0377540	−	0.0483229i
$538$	0.294033	+	0.246723i	0.0126767	+	0.0106370i
$539$	14.0277	−	13.8188i	0.604217	−	0.595218i
$540$	−4.60813	−	7.98152i	−0.198302	−	0.343470i
$541$	−12.8129	−	6.81272i	−0.550868	−	0.292902i	0.170610	−	0.985339i	$-0.445426\pi$
$541$	−12.8129	−	6.81272i	−0.550868	−	0.292902i	−0.721479	+	0.692437i	$0.756537\pi$
$542$	−12.3558	−	25.3332i	−0.530729	−	1.08816i
$543$	1.44949	−	13.7910i	0.0622035	−	0.591826i
$544$	4.84696	+	1.03025i	0.207811	+	0.0441717i
$545$	6.81772	−	16.8744i	0.292039	−	0.722822i
$546$	2.52673	+	3.74603i	0.108134	+	0.160315i
$547$	−14.0823	+	20.8778i	−0.602114	+	0.892670i	−0.999690	−	0.0248987i	$-0.992074\pi$
$547$	−14.0823	+	20.8778i	−0.602114	+	0.892670i	0.397576	+	0.917569i	$0.369851\pi$
$548$	−3.65047	−	9.03522i	−0.155940	−	0.385966i
$549$	−1.49746	−	8.49254i	−0.0639102	−	0.362453i
$550$	3.73984	+	1.03222i	0.159467	+	0.0440141i
$551$	36.3879	−	9.45448i	1.55018	−	0.402774i
$552$	−0.990075	+	3.04714i	−0.0421404	+	0.129695i
$553$	10.1498	+	9.80151i	0.431612	+	0.416803i
$554$	−23.5555	+	1.64716i	−1.00078	+	0.0699812i
$555$	2.29463	+	2.93700i	0.0974018	+	0.124669i
$556$	0.214929	−	6.15477i	0.00911504	−	0.261021i
$557$	−5.20460	−	20.8745i	−0.220526	−	0.884481i	−0.973916	−	0.226908i	$-0.927138\pi$
$557$	−5.20460	−	20.8745i	−0.220526	−	0.884481i	0.753390	−	0.657574i	$-0.228417\pi$
$558$	0.0753928	+	0.717314i	0.00319163	+	0.0303663i
$559$	57.2089	−	12.1601i	2.41968	−	0.514319i
$560$	−0.444690	+	2.52196i	−0.0187916	+	0.106572i
$561$	2.01417	+	10.7937i	0.0850382	+	0.455711i
$562$	6.87193	+	11.9025i	0.289875	+	0.502078i
$563$	22.2563	+	24.7181i	0.937992	+	1.04175i	0.999049	+	0.0436112i	$0.0138863\pi$
$563$	22.2563	+	24.7181i	0.937992	+	1.04175i	−0.0610567	+	0.998134i	$0.519447\pi$
$564$	7.55824	+	0.528523i	0.318259	+	0.0222548i
$565$	−1.71358	−	2.54049i	−0.0720910	−	0.106879i
$566$	10.0565	+	12.8717i	0.422704	+	0.541037i
$567$	−4.53076	−	2.83113i	−0.190274	−	0.118896i
$568$	−4.39411	+	9.00927i	−0.184373	+	0.378021i
$569$	−1.59851	+	1.16138i	−0.0670130	+	0.0486878i	−0.620787	−	0.783979i	$-0.713187\pi$
$569$	−1.59851	+	1.16138i	−0.0670130	+	0.0486878i	0.553774	+	0.832667i	$0.313187\pi$
$570$	4.30928	+	5.80990i	0.180496	+	0.243350i
$571$	44.1325			1.84689			0.923444	−	0.383733i	$-0.125362\pi$
$571$	44.1325			1.84689			0.923444	+	0.383733i	$0.125362\pi$
$572$	−21.2354	+	4.73505i	−0.887897	+	0.197983i
$573$	−0.0106952	+	0.00897432i	−0.000446798	+	0.000374908i
$574$	−0.182702	−	5.23190i	−0.00762584	−	0.218375i
$575$	5.39242	−	1.54625i	0.224880	−	0.0644832i
$576$	0.617781	+	2.47779i	0.0257409	+	0.103241i
$577$	−28.4164	−	6.04008i	−1.18299	−	0.251452i	−0.425904	−	0.904769i	$-0.640044\pi$
$577$	−28.4164	−	6.04008i	−1.18299	−	0.251452i	−0.757085	+	0.653317i	$0.773377\pi$
$578$	5.05488	−	5.61401i	0.210255	−	0.233512i
$579$	−8.20505	+	7.92352i	−0.340990	+	0.329290i
$580$	9.39165	+	19.2557i	0.389967	+	0.799551i
$581$	12.8395	−	2.72911i	0.532671	−	0.113223i
$582$	−3.53543	+	6.12355i	−0.146548	+	0.253829i
$583$	0.901182	−	36.1036i	0.0373232	−	1.49526i
$584$	−1.80086	−	0.655459i	−0.0745201	−	0.0271231i
$585$	−1.45216	−	41.5844i	−0.0600394	−	1.71930i
$586$	5.04063	−	20.2169i	0.208227	−	0.835151i
$587$	−0.893073	+	1.83107i	−0.0368611	+	0.0755764i	−0.916430	−	0.400195i	$-0.868942\pi$
$587$	−0.893073	+	1.83107i	−0.0368611	+	0.0755764i	0.879569	+	0.475772i	$0.157831\pi$
$588$	1.22574	+	3.77243i	0.0505485	+	0.155572i
$589$	−0.267830	−	1.20167i	−0.0110357	−	0.0495139i
$590$	−11.0769	−	8.04782i	−0.456027	−	0.331323i
$591$	5.98648	+	5.78107i	0.246251	+	0.237802i
$592$	−0.841337	−	2.08238i	−0.0345787	−	0.0855854i
$593$	23.2548	−	8.46407i	0.954961	−	0.347578i	0.182904	−	0.983131i	$-0.441450\pi$
$593$	23.2548	−	8.46407i	0.954961	−	0.347578i	0.772057	+	0.635553i	$0.219228\pi$
$594$	−9.88329	+	7.33199i	−0.405516	+	0.300835i
$595$	9.72089	+	8.15680i	0.398518	+	0.334396i
$596$	−15.8578	−	17.6118i	−0.649560	−	0.721409i
$597$	11.1866	+	4.98061i	0.457838	+	0.203843i
$598$	−22.6297	+	21.8532i	−0.925395	+	0.893644i
$599$	35.9597	−	5.05380i	1.46927	−	0.206493i	0.641312	−	0.767280i	$-0.278390\pi$
$599$	35.9597	−	5.05380i	1.46927	−	0.206493i	0.827960	+	0.560787i	$0.189502\pi$
$600$	−0.522941	+	0.580785i	−0.0213490	+	0.0237104i
$601$	−1.49290	+	0.664682i	−0.0608967	+	0.0271129i	−0.436959	−	0.899481i	$-0.643945\pi$
$601$	−1.49290	+	0.664682i	−0.0608967	+	0.0271129i	0.376062	+	0.926594i	$0.377278\pi$
$602$	−9.16965	−	0.641204i	−0.373727	−	0.0261335i
$603$	1.62339	−	2.07784i	0.0661095	−	0.0846164i
$604$	18.5785	−	6.76201i	0.755947	−	0.275142i
$605$	4.20816	−	26.9969i	0.171086	−	1.09758i
$606$	−0.173829	−	0.985831i	−0.00706130	−	0.0400466i
$607$	−4.19657	+	12.9157i	−0.170334	+	0.524233i	−0.999390	−	0.0349324i	$-0.988878\pi$
$607$	−4.19657	+	12.9157i	−0.170334	+	0.524233i	0.829056	+	0.559166i	$0.188878\pi$
$608$	−1.53114	−	4.08113i	−0.0620958	−	0.165512i
$609$	−4.80639	−	3.49205i	−0.194765	−	0.141505i
$610$	−7.40620	+	3.93795i	−0.299868	+	0.159443i
$611$	63.0897	+	39.4228i	2.55233	+	1.59488i
$612$	12.1637	+	3.48789i	0.491689	+	0.140989i
$613$	9.64959	−	2.76697i	0.389743	−	0.111757i	−0.0750424	−	0.997180i	$-0.523909\pi$
$613$	9.64959	−	2.76697i	0.389743	−	0.111757i	0.464786	+	0.885423i	$0.346131\pi$
$614$	−0.223103	+	0.139410i	−0.00900369	+	0.00562613i
$615$	4.21326	−	7.29758i	0.169895	−	0.294267i
$616$	3.41327	+	0.204571i	0.137525	+	0.00824240i
$617$	1.03677	−	5.87983i	0.0417389	−	0.236713i	−0.956800	−	0.290746i	$-0.906097\pi$
$617$	1.03677	−	5.87983i	0.0417389	−	0.236713i	0.998539	+	0.0540330i	$0.0172076\pi$
$618$	−1.05726	−	0.562155i	−0.0425293	−	0.0226132i
$619$	−11.8853	−	5.29169i	−0.477712	−	0.212691i	0.153732	−	0.988113i	$-0.450871\pi$
$619$	−11.8853	−	5.29169i	−0.477712	−	0.212691i	−0.631444	+	0.775421i	$0.717537\pi$
$620$	0.640914	−	0.285353i	0.0257397	−	0.0114601i
$621$	−6.66559	+	16.4979i	−0.267481	+	0.662039i
$622$	−0.136820	+	3.91802i	−0.00548599	+	0.157098i
$623$	−12.0162	−	3.44560i	−0.481420	−	0.138045i
$624$	1.06028	−	4.25253i	0.0424450	−	0.170237i
$625$	−29.1936	−	4.10289i	−1.16774	−	0.164116i
$626$	−8.44537			−0.337545
$627$	7.04834	−	6.60379i	0.281484	−	0.263730i
$628$	−20.2352			−0.807471
$629$	−11.0208	−	1.54887i	−0.439427	−	0.0617574i
$630$	−1.58206	+	6.34529i	−0.0630307	+	0.252802i
$631$	−10.7730	−	3.08910i	−0.428865	−	0.122975i	0.0542591	−	0.998527i	$-0.482720\pi$
$631$	−10.7730	−	3.08910i	−0.428865	−	0.122975i	−0.483124	+	0.875552i	$0.660498\pi$
$632$	0.477626	−	13.6774i	0.0189989	−	0.544058i
$633$	6.87460	−	17.0152i	0.273241	−	0.676295i
$634$	12.5964	−	5.60827i	0.500266	−	0.222733i
$635$	20.1044	+	8.95105i	0.797818	+	0.355212i
$636$	6.42344	+	3.41540i	0.254706	+	0.135430i
$637$	−6.76305	+	38.3552i	−0.267962	+	1.51969i
$638$	24.1075	−	15.3997i	0.954425	−	0.609679i
$639$	−12.7985	+	22.1677i	−0.506301	+	0.876939i
$640$	2.10647	−	1.31627i	0.0832655	−	0.0520300i
$641$	31.0358	−	8.89937i	1.22584	−	0.351504i	0.400583	−	0.916261i	$-0.368808\pi$
$641$	31.0358	−	8.89937i	1.22584	−	0.351504i	0.825258	+	0.564756i	$0.191030\pi$
$642$	−2.55901	−	0.733785i	−0.100996	−	0.0289602i
$643$	−5.98622	−	3.74061i	−0.236074	−	0.147515i	0.406724	−	0.913551i	$-0.366671\pi$
$643$	−5.98622	−	3.74061i	−0.236074	−	0.147515i	−0.642798	+	0.766036i	$0.722227\pi$
$644$	4.36547	−	2.32116i	0.172024	−	0.0914666i
$645$	−11.9700	−	8.69670i	−0.471317	−	0.342432i
$646$	−21.3072	−	3.54082i	−0.838320	−	0.139312i
$647$	3.98331	−	12.2594i	0.156600	−	0.481965i	−0.841719	−	0.539915i	$-0.818456\pi$
$647$	3.98331	−	12.2594i	0.156600	−	0.481965i	0.998319	+	0.0579498i	$0.0184563\pi$
$648$	0.899844	+	5.10327i	0.0353492	+	0.200475i
$649$	−8.98295	+	15.9228i	−0.352612	+	0.625023i
$650$	−7.21084	+	2.62453i	−0.282832	+	0.102943i
$651$	−0.119777	+	0.153307i	−0.00469443	+	0.00600859i
$652$	17.8604	+	1.24892i	0.699469	+	0.0489116i
$653$	34.8624	−	15.5217i	1.36427	−	0.607412i	0.411585	−	0.911371i	$-0.364975\pi$
$653$	34.8624	−	15.5217i	1.36427	−	0.607412i	0.952685	+	0.303959i	$0.0983087\pi$
$654$	3.27554	−	3.63785i	0.128084	−	0.142251i
$655$	−24.4501	+	3.43624i	−0.955346	+	0.134265i
$656$	−3.65263	+	3.52730i	−0.142611	+	0.137718i
$657$	−4.47079	−	1.99052i	−0.174422	−	0.0776577i
$658$	−7.82350	−	8.68888i	−0.304992	−	0.338728i
$659$	5.62878	+	4.72311i	0.219266	+	0.183986i	0.745804	−	0.666166i	$-0.232066\pi$
$659$	5.62878	+	4.72311i	0.219266	+	0.183986i	−0.526538	+	0.850152i	$0.676510\pi$
$660$	4.48475	+	3.19066i	0.174569	+	0.124196i
$661$	−0.0782404	+	0.0284772i	−0.00304320	+	0.00110763i	−0.343541	−	0.939138i	$-0.611627\pi$
$661$	−0.0782404	+	0.0284772i	−0.00304320	+	0.00110763i	0.340498	+	0.940245i	$0.389404\pi$
$662$	−3.91251	−	9.68379i	−0.152064	−	0.376371i
$663$	−15.6222	−	15.0862i	−0.606716	−	0.585899i
$664$	−10.3002	−	7.48356i	−0.399726	−	0.290418i
$665$	1.44449	−	11.0687i	0.0560148	−	0.429226i
$666$	−1.77230	−	5.45457i	−0.0686751	−	0.211360i
$667$	18.1322	−	37.1765i	0.702082	−	1.43948i
$668$	−4.08485	+	16.3834i	−0.158048	+	0.633894i
$669$	−0.152229	−	4.35926i	−0.00588551	−	0.168539i
$670$	−2.41014	−	0.877217i	−0.0931116	−	0.0338899i
$671$	6.35511	+	9.22254i	0.245336	+	0.356032i
$672$	−0.344402	+	0.596522i	−0.0132856	+	0.0230113i
$673$	−35.9661	+	7.64482i	−1.38639	+	0.294686i	−0.839883	−	0.542768i	$-0.817376\pi$
$673$	−35.9661	+	7.64482i	−1.38639	+	0.294686i	−0.546507	+	0.837454i	$0.684043\pi$
$674$	2.20168	+	4.51411i	0.0848054	+	0.173877i
$675$	−3.12215	+	3.01502i	−0.120172	+	0.116048i
$676$	20.0960	−	22.3189i	0.772923	−	0.858418i
$677$	−5.80999	−	1.23495i	−0.223296	−	0.0474630i	0.0949049	−	0.995486i	$-0.469745\pi$
$677$	−5.80999	−	1.23495i	−0.223296	−	0.0474630i	−0.318201	+	0.948023i	$0.603079\pi$
$678$	−0.199401	−	0.799753i	−0.00765795	−	0.0307143i
$679$	10.4888	−	3.00761i	0.402522	−	0.115421i
$680$	−0.429554	−	12.3008i	−0.0164727	−	0.471715i
$681$	0.952642	−	0.799362i	0.0365053	−	0.0306316i
$682$	−0.476433	−	0.806564i	−0.0182436	−	0.0308849i
$683$	26.7153			1.02223			0.511115	−	0.859512i	$-0.329232\pi$
$683$	26.7153			1.02223			0.511115	+	0.859512i	$0.329232\pi$
$684$	−3.17346	−	10.6691i	−0.121340	−	0.407943i
$685$	−19.5824	+	14.2274i	−0.748203	+	0.543602i
$686$	5.84697	−	11.9881i	0.223238	−	0.457706i
$687$	3.78892	+	2.36758i	0.144556	+	0.0903288i
$688$	5.48909	+	7.02572i	0.209270	+	0.267853i
$689$	39.9441	+	59.2195i	1.52175	+	2.25608i
$690$	7.93891	+	0.555143i	0.302229	+	0.0211339i
$691$	−2.12865	−	2.36411i	−0.0809778	−	0.0899349i	0.701294	−	0.712872i	$-0.252606\pi$
$691$	−2.12865	−	2.36411i	−0.0809778	−	0.0899349i	−0.782272	+	0.622937i	$0.785939\pi$
$692$	−6.58477	−	11.4051i	−0.250315	−	0.433559i
$693$	8.65859	+	1.12914i	0.328913	+	0.0428926i
$694$	−1.58372	+	8.98175i	−0.0601174	+	0.340943i
$695$	−14.9629	+	3.18046i	−0.567575	+	0.120642i
$696$	0.602342	+	5.73090i	0.0228317	+	0.217229i
$697$	6.08711	+	24.4141i	0.230566	+	0.924749i
$698$	0.117551	−	3.36621i	0.00444936	−	0.127413i
$699$	−9.79242	−	12.5337i	−0.370383	−	0.474069i
$700$	1.20308	−	0.0841273i	0.0454720	−	0.00317971i
$701$	−17.9981	−	17.3805i	−0.679778	−	0.656454i	0.272335	−	0.962203i	$-0.412204\pi$
$701$	−17.9981	−	17.3805i	−0.679778	−	0.656454i	−0.952112	+	0.305749i	$0.901093\pi$
$702$	7.52148	−	23.1487i	0.283880	−	0.873693i
$703$	4.06982	+	8.90369i	0.153496	+	0.335809i
$704$	−2.06782	−	2.59309i	−0.0779340	−	0.0977307i
$705$	−3.26802	−	18.5338i	−0.123081	−	0.698025i
$706$	4.57909	+	11.3337i	0.172336	+	0.426548i
$707$	−0.863819	+	1.28066i	−0.0324873	+	0.0481644i
$708$	−2.05935	−	3.05311i	−0.0773950	−	0.114743i
$709$	10.5039	−	25.9980i	0.394481	−	0.976374i	−0.591013	−	0.806662i	$-0.701272\pi$
$709$	10.5039	−	25.9980i	0.394481	−	0.976374i	0.985494	−	0.169712i	$-0.0542837\pi$
$710$	24.3539	+	5.17658i	0.913985	+	0.194273i
$711$	3.65311	−	34.7570i	0.137002	−	1.30349i
$712$	5.31515	+	10.8977i	0.199194	+	0.408408i
$713$	−1.19595	−	0.635899i	−0.0447887	−	0.0238146i
$714$	1.70659	+	2.95591i	0.0638677	+	0.110622i
$715$	24.1726	+	48.3345i	0.904004	+	1.80761i
$716$	1.62937	+	1.36720i	0.0608924	+	0.0510948i
$717$	−4.73108	+	6.05551i	−0.176685	+	0.226147i
$718$	−1.31570	+	1.95061i	−0.0491015	+	0.0727960i
$719$	−23.7256	+	1.65905i	−0.884814	+	0.0618722i	−0.504928	−	0.863161i	$-0.668481\pi$
$719$	−23.7256	+	1.65905i	−0.884814	+	0.0618722i	−0.379886	+	0.925033i	$0.624037\pi$
$720$	5.60053	−	2.97785i	0.208719	−	0.110978i
$721$	0.571005	+	1.75737i	0.0212653	+	0.0654480i
$722$	7.46345	+	17.4727i	0.277761	+	0.650268i
$723$	0.925312	−	0.672278i	0.0344127	−	0.0250023i
$724$	20.5537	+	2.88863i	0.763872	+	0.107355i
$725$	7.72892	−	6.48533i	0.287045	−	0.240859i
$726$	3.54718	−	6.43639i	0.131648	−	0.238877i
$727$	12.2512	+	4.45909i	0.454373	+	0.165378i	0.559061	−	0.829127i	$-0.311162\pi$
$727$	12.2512	+	4.45909i	0.454373	+	0.165378i	−0.104687	+	0.994505i	$0.533384\pi$
$728$	−5.73554	+	3.58396i	−0.212573	+	0.132831i
$729$	0.605866	+	5.76443i	0.0224395	+	0.213498i
$730$	−0.497580	+	4.73416i	−0.0184163	+	0.175219i
$731$	43.7498	−	6.14863i	1.61814	−	0.227415i
$732$	−2.23420	+	0.313996i	−0.0825783	+	0.0116056i
$733$	2.99274	−	28.4740i	0.110539	−	1.05171i	−0.788857	−	0.614577i	$-0.789327\pi$
$733$	2.99274	−	28.4740i	0.110539	−	1.05171i	0.899396	−	0.437135i	$-0.144007\pi$
$734$	−0.313040	−	2.97838i	−0.0115545	−	0.109934i
$735$	8.35544	−	5.22106i	0.308195	−	0.192582i
$736$	−4.50639	−	1.64019i	−0.166108	−	0.0604583i
$737$	−0.795394	+	3.33101i	−0.0292987	+	0.122699i
$738$	−9.93310	+	8.33486i	−0.365643	+	0.306811i
$739$	−5.91843	−	0.831781i	−0.217713	−	0.0305975i	0.0294733	−	0.999566i	$-0.490617\pi$
$739$	−5.91843	−	0.831781i	−0.217713	−	0.0305975i	−0.247186	+	0.968968i	$0.579506\pi$
$740$	−4.51322	+	3.27905i	−0.165909	+	0.120540i
$741$	−3.78751	+	18.7246i	−0.139138	+	0.687865i
$742$	−3.46917	−	10.6770i	−0.127357	−	0.391965i
$743$	0.559989	−	0.297752i	0.0205440	−	0.0109234i	−0.459168	−	0.888350i	$-0.651852\pi$
$743$	0.559989	−	0.297752i	0.0205440	−	0.0109234i	0.479712	+	0.877426i	$0.340741\pi$
$744$	0.188243	−	0.0131632i	0.00690132	−	0.000482588i
$745$	−32.9175	+	48.8023i	−1.20601	+	1.78798i
$746$	−2.45109	+	3.13725i	−0.0897408	+	0.114863i
$747$	−24.9059	−	20.8986i	−0.911261	−	0.764638i
$748$	−16.2512	+	2.44909i	−0.594201	+	0.0895478i
$749$	2.05405	+	3.55772i	0.0750534	+	0.129996i
$750$	−5.61225	−	2.98409i	−0.204930	−	0.108963i
$751$	−17.7610	−	36.4154i	−0.648108	−	1.32882i	−0.929356	−	0.369184i	$-0.879637\pi$
$751$	−17.7610	−	36.4154i	−0.648108	−	1.32882i	0.281248	−	0.959635i	$-0.409252\pi$
$752$	−1.18542	+	11.2785i	−0.0432278	+	0.411285i
$753$	−0.994536	−	0.211395i	−0.0362429	−	0.00770367i
$754$	−21.1954	+	52.4605i	−0.771891	+	1.91050i
$755$	−27.4612	−	40.7130i	−0.999417	−	1.48170i
$756$	−2.13912	+	3.17138i	−0.0777990	+	0.115342i
$757$	12.9933	+	32.1594i	0.472248	+	1.16885i	0.955926	+	0.293608i	$0.0948562\pi$
$757$	12.9933	+	32.1594i	0.472248	+	1.16885i	−0.483678	+	0.875246i	$0.660699\pi$
$758$	1.68160	+	9.53684i	0.0610785	+	0.346394i
$759$	−0.476508	−	10.6156i	−0.0172961	−	0.385322i
$760$	−8.91593	+	6.14261i	−0.323415	+	0.222816i
$761$	12.6247	−	38.8550i	0.457647	−	1.40849i	−0.410353	−	0.911927i	$-0.634595\pi$
$761$	12.6247	−	38.8550i	0.457647	−	1.40849i	0.868000	−	0.496565i	$-0.165405\pi$
$762$	4.25798	+	4.11188i	0.154250	+	0.148958i
$763$	−7.53569	+	0.526947i	−0.272810	+	0.0190768i
$764$	−0.0128657	−	0.0164673i	−0.000465465	−	0.000595768i
$765$	1.09693	−	31.4119i	0.0396595	−	1.13570i
$766$	−7.06497	−	28.3361i	−0.255268	−	1.02382i
$767$	−3.77973	−	35.9617i	−0.136478	−	1.29850i
$768$	0.653502	−	0.138906i	0.0235812	−	0.00501234i
$769$	2.88727	−	16.3745i	0.104118	−	0.590481i	−0.887451	−	0.460901i	$-0.847526\pi$
$769$	2.88727	−	16.3745i	0.104118	−	0.590481i	0.991569	−	0.129579i	$-0.0413627\pi$
$770$	−1.55803	−	8.34932i	−0.0561475	−	0.300889i
$771$	0.698723	+	1.21022i	0.0251639	+	0.0435851i
$772$	−11.4239	−	12.6875i	−0.411156	−	0.456635i
$773$	40.8758	+	2.85831i	1.47020	+	0.102806i	0.782255	−	0.622958i	$-0.214069\pi$
$773$	40.8758	+	2.85831i	1.47020	+	0.102806i	0.687944	+	0.725764i	$0.258514\pi$
$774$	12.7315	+	18.8752i	0.457625	+	0.678457i
$775$	−0.203412	−	0.260356i	−0.00730678	−	0.00935225i
$776$	−8.97532	−	5.60840i	−0.322195	−	0.201330i
$777$	0.678160	−	1.39043i	0.0243289	−	0.0498816i
$778$	−29.3253	+	21.3061i	−1.05136	+	0.763860i
$779$	15.2175	−	16.0722i	0.545222	−	0.575847i
$780$	−10.8862			−0.389790
$781$	3.14588	−	33.0958i	0.112568	−	1.18426i
$782$	−18.2038	+	15.2748i	−0.650966	+	0.546225i
$783$	1.11688	+	31.9832i	0.0399139	+	1.14298i
$784$	−5.70707	+	1.63648i	−0.203824	+	0.0584456i
$785$	12.1595	+	48.7691i	0.433992	+	1.74065i
$786$	−6.49593	−	1.38075i	−0.231702	−	0.0492498i
$787$	−7.76969	+	8.62912i	−0.276960	+	0.307595i	−0.865536	−	0.500847i	$-0.833022\pi$
$787$	−7.76969	+	8.62912i	−0.276960	+	0.307595i	0.588576	+	0.808442i	$0.299689\pi$
$788$	−8.96042	+	8.65298i	−0.319202	+	0.308250i
$789$	2.46422	+	5.05240i	0.0877286	+	0.179870i
$790$	−33.2512	+	7.06776i	−1.18302	+	0.251460i
$791$	−0.635964	+	1.10152i	−0.0226123	+	0.0391656i
$792$	−4.80570	−	6.97403i	−0.170763	−	0.247811i
$793$	−20.8167	−	7.57667i	−0.739224	−	0.269056i
$794$	0.119367	+	3.41821i	0.00423616	+	0.121308i
$795$	4.37162	−	17.5336i	0.155045	−	0.621853i
$796$	−8.03468	+	16.4735i	−0.284782	+	0.583889i
$797$	12.1334	+	37.3427i	0.429786	+	1.32275i	0.898336	+	0.439309i	$0.144777\pi$
$797$	12.1334	+	37.3427i	0.429786	+	1.32275i	−0.468550	+	0.883437i	$0.655223\pi$
$798$	1.38335	−	2.66475i	0.0489702	−	0.0943312i
$799$	45.4631	+	33.0309i	1.60837	+	1.16855i
$800$	−0.841460	−	0.812588i	−0.0297501	−	0.0287293i
$801$	11.5987	+	28.7078i	0.409819	+	1.01434i
$802$	−16.4420	+	5.98440i	−0.580587	+	0.211316i
$803$	6.35578	−	0.0632471i	0.224291	−	0.00223194i
$804$	−0.528467	−	0.443436i	−0.0186376	−	0.0156388i
$805$	−8.21753	−	9.12650i	−0.289630	−	0.321667i
$806$	1.69265	+	0.753615i	0.0596209	+	0.0265450i
$807$	0.184467	−	0.178138i	0.00649354	−	0.00627074i
$808$	1.48375	−	0.208528i	0.0521982	−	0.00733597i
$809$	15.2888	−	16.9800i	0.537527	−	0.596984i	−0.411800	−	0.911274i	$-0.635100\pi$
$809$	15.2888	−	16.9800i	0.537527	−	0.596984i	0.949327	+	0.314290i	$0.101767\pi$
$810$	11.7588	−	5.23534i	0.413161	−	0.183951i
$811$	44.6909	+	3.12509i	1.56931	+	0.109737i	0.827730	−	0.561127i	$-0.189632\pi$
$811$	44.6909	+	3.12509i	1.56931	+	0.109737i	0.741581	+	0.670864i	$0.234076\pi$
$812$	5.47470	−	7.00730i	0.192124	−	0.245908i
$813$	−17.6953	+	6.44058i	−0.620603	+	0.225881i
$814$	5.03911	+	5.48572i	0.176621	+	0.192275i
$815$	−7.72247	−	43.7963i	−0.270506	−	1.53412i
$816$	1.02303	−	3.14857i	0.0358133	−	0.110222i
$817$	−25.2729	−	29.5230i	−0.884186	−	1.03288i
$818$	8.20851	+	5.96383i	0.287004	+	0.208520i
$819$	−15.2492	+	8.10817i	−0.532852	+	0.283322i
$820$	10.6961	+	6.68368i	0.373525	+	0.233404i
$821$	−29.2818	−	8.39641i	−1.02194	−	0.293037i	−0.277500	−	0.960726i	$-0.589506\pi$
$821$	−29.2818	−	8.39641i	−1.02194	−	0.293037i	−0.744441	+	0.667689i	$0.767284\pi$
$822$	−6.25831	+	1.79454i	−0.218284	+	0.0625918i
$823$	−43.3056	+	27.0603i	−1.50954	+	0.943263i	−0.513153	+	0.858297i	$0.671523\pi$
$823$	−43.3056	+	27.0603i	−1.50954	+	0.943263i	−0.996384	+	0.0849659i	$0.972922\pi$
$824$	0.896137	−	1.55216i	0.0312184	−	0.0540719i
$825$	0.947025	−	2.41282i	0.0329712	−	0.0840037i
$826$	−0.986844	+	5.59667i	−0.0343367	+	0.194733i
$827$	−27.1755	−	14.4495i	−0.944985	−	0.502457i	−0.0758973	−	0.997116i	$-0.524182\pi$
$827$	−27.1755	−	14.4495i	−0.944985	−	0.502457i	−0.869088	+	0.494658i	$0.835293\pi$
$828$	−11.1875	−	4.98099i	−0.388792	−	0.173102i
$829$	−24.6654	+	10.9817i	−0.856665	+	0.381412i	−0.787590	−	0.616200i	$-0.788671\pi$
$829$	−24.6654	+	10.9817i	−0.856665	+	0.381412i	−0.0690750	+	0.997611i	$0.522005\pi$
$830$	−11.8467	+	29.3217i	−0.411207	+	1.01777i
$831$	−0.550572	+	15.7663i	−0.0190991	+	0.546927i
$832$	6.30583	+	1.80817i	0.218615	+	0.0626869i
$833$	−7.11724	+	28.5457i	−0.246598	+	0.989050i
$834$	−4.07448	−	0.572631i	−0.141088	−	0.0198286i
$835$	41.9406			1.45142
$836$	9.51021	+	10.8883i	0.328917	+	0.376581i
$837$	1.04799			0.0362237
$838$	10.3377	+	1.45288i	0.357112	+	0.0501888i
$839$	1.59225	−	6.38618i	0.0549707	−	0.220476i	−0.936528	−	0.350593i	$-0.885980\pi$
$839$	1.59225	−	6.38618i	0.0549707	−	0.220476i	0.991499	+	0.130118i	$0.0415355\pi$
$840$	1.64464	+	0.471594i	0.0567456	+	0.0162715i
$841$	1.58419	−	45.3652i	0.0546272	−	1.56432i
$842$	0.188210	−	0.465837i	0.00648616	−	0.0160538i
$843$	8.38844	−	3.73478i	0.288913	−	0.128633i
$844$	25.0934	+	11.1723i	0.863751	+	0.384567i
$845$	−65.8670	−	35.0221i	−2.26589	−	1.20480i
$846$	−5.02883	+	28.5199i	−0.172895	+	0.980535i
$847$	−10.8372	+	3.34229i	−0.372369	+	0.114842i
$848$	−5.44452	+	9.43019i	−0.186966	+	0.323834i
$849$	9.25478	−	5.78303i	0.317623	−	0.198473i
$850$	−5.57193	+	1.59772i	−0.191116	+	0.0548015i
$851$	10.3533	+	2.96876i	0.354907	+	0.101768i
$852$	5.67927	+	3.54880i	0.194569	+	0.121580i
$853$	−9.62879	+	5.11972i	−0.329684	+	0.175296i	−0.626059	−	0.779776i	$-0.715333\pi$
$853$	−9.62879	+	5.11972i	−0.329684	+	0.175296i	0.296375	+	0.955071i	$0.404222\pi$
$854$	2.81668	+	2.04644i	0.0963847	+	0.0700276i
$855$	−23.8068	+	14.0596i	−0.814176	+	0.480828i
$856$	1.23132	−	3.78961i	0.0420856	−	0.129526i
$857$	1.07937	+	6.12139i	0.0368705	+	0.209103i	0.997677	−	0.0681154i	$-0.0216986\pi$
$857$	1.07937	+	6.12139i	0.0368705	+	0.209103i	−0.960807	+	0.277218i	$0.910588\pi$
$858$	1.66318	+	14.4404i	0.0567800	+	0.492986i
$859$	−11.1118	+	4.04437i	−0.379130	+	0.137992i	−0.524554	−	0.851377i	$-0.675768\pi$
$859$	−11.1118	+	4.04437i	−0.379130	+	0.137992i	0.145423	+	0.989370i	$0.453546\pi$
$860$	13.6344	−	17.4512i	0.464928	−	0.595081i
$861$	−3.48906	−	0.243979i	−0.118907	−	0.00831477i
$862$	−30.2557	+	13.4707i	−1.03051	+	0.458814i
$863$	−35.2406	+	39.1387i	−1.19961	+	1.33230i	−0.270393	+	0.962750i	$0.587154\pi$
$863$	−35.2406	+	39.1387i	−1.19961	+	1.33230i	−0.929212	+	0.369547i	$0.879513\pi$
$864$	3.67429	−	0.516387i	0.125002	−	0.0175679i
$865$	−23.5309	+	22.7235i	−0.800075	+	0.772623i
$866$	15.1124	+	6.72850i	0.513542	+	0.228644i
$867$	−3.37717	−	3.75073i	−0.114695	−	0.127381i
$868$	−0.223071	−	0.187179i	−0.00757151	−	0.00635325i
$869$	14.4553	+	43.0272i	0.490362	+	1.45960i
$870$	13.4502	−	4.89547i	0.456004	−	0.165972i
$871$	−2.53745	−	6.28041i	−0.0859782	−	0.212803i
$872$	5.27064	+	5.08980i	0.178486	+	0.172362i
$873$	−21.8649	−	15.8858i	−0.740014	−	0.537652i
$874$	19.9432	+	6.26326i	0.674588	+	0.211858i
$875$	3.03106	+	9.32866i	0.102469	+	0.315366i
$876$	−0.561279	+	1.15079i	−0.0189639	+	0.0388817i
$877$	−7.42404	+	29.7762i	−0.250692	+	1.00547i	0.704552	+	0.709652i	$0.251148\pi$
$877$	−7.42404	+	29.7762i	−0.250692	+	1.00547i	−0.955244	+	0.295819i	$0.904408\pi$
$878$	0.161184	+	4.61569i	0.00543968	+	0.155772i
$879$	−13.0809	−	4.76107i	−0.441208	−	0.160587i
$880$	−5.00708	+	6.54191i	−0.168788	+	0.220528i
$881$	−27.5241	+	47.6731i	−0.927309	+	1.60615i	−0.139505	+	0.990221i	$0.544551\pi$
$881$	−27.5241	+	47.6731i	−0.927309	+	1.60615i	−0.787804	+	0.615926i	$0.788782\pi$
$882$	−14.8298	+	3.15218i	−0.499346	+	0.106139i
$883$	1.41397	+	2.89907i	0.0475839	+	0.0975615i	0.921261	−	0.388944i	$-0.127160\pi$
$883$	1.41397	+	2.89907i	0.0475839	+	0.0975615i	−0.873677	+	0.486506i	$0.838271\pi$
$884$	23.3830	−	22.5807i	0.786454	−	0.759470i
$885$	−6.12087	+	6.79791i	−0.205751	+	0.228509i
$886$	−2.89649	−	0.615669i	−0.0973096	−	0.0206838i
$887$	2.05298	+	8.23406i	0.0689324	+	0.276473i	0.994864	−	0.101218i	$-0.0322739\pi$
$887$	2.05298	+	8.23406i	0.0689324	+	0.276473i	−0.925932	+	0.377691i	$0.876718\pi$
$888$	−1.44238	+	0.413595i	−0.0484030	+	0.0138793i
$889$	−0.318786	−	9.12883i	−0.0106917	−	0.306171i
$890$	23.0708	−	19.3587i	0.773334	−	0.648904i
$891$	−8.74105	−	14.7979i	−0.292836	−	0.495749i
$892$	6.52883			0.218601
$893$	2.96197	−	49.3438i	0.0991185	−	1.65123i
$894$	−12.8095	+	9.30664i	−0.428413	+	0.311260i
$895$	2.31602	−	4.74854i	0.0774159	−	0.158726i
$896$	−0.874326	−	0.546340i	−0.0292092	−	0.0182519i
$897$	12.9398	+	16.5622i	0.432048	+	0.552997i
$898$	−10.0588	−	14.9129i	−0.335668	−	0.497648i
$899$	−2.43020	−	0.169936i	−0.0810517	−	0.00566769i
$900$	−1.99880	−	2.21989i	−0.0666267	−	0.0739965i
$901$	26.9789	+	46.7289i	0.898798	+	1.55676i
$902$	7.23162	−	15.2093i	0.240787	−	0.506414i
$903$	−1.06641	+	6.04792i	−0.0354879	+	0.201262i
$904$	1.20674	−	0.256501i	0.0401356	−	0.00853108i
$905$	−5.38898	−	51.2727i	−0.179136	−	1.70436i
$906$	−3.19552	−	12.8165i	−0.106164	−	0.425801i
$907$	−0.496845	+	14.2278i	−0.0164975	+	0.472426i	0.962826	+	0.270124i	$0.0870645\pi$
$907$	−0.496845	+	14.2278i	−0.0164975	+	0.472426i	−0.979323	+	0.202302i	$0.935158\pi$
$908$	1.14598	+	1.46678i	0.0380305	+	0.0486768i
$909$	3.81688	−	0.266902i	0.126598	−	0.00885259i
$910$	12.0843	+	11.6697i	0.400591	+	0.386847i
$911$	6.63032	−	20.4060i	0.219672	−	0.676082i	−0.779116	−	0.626879i	$-0.784332\pi$
$911$	6.63032	−	20.4060i	0.219672	−	0.676082i	0.998789	−	0.0492030i	$-0.0156681\pi$
$912$	−2.81860	+	0.732343i	−0.0933332	+	0.0242503i
$913$	40.7046	+	11.2347i	1.34712	+	0.371815i
$914$	−3.78432	−	21.4619i	−0.125174	−	0.709898i
$915$	2.09932	+	5.19600i	0.0694014	+	0.171774i
$916$	−3.73950	+	5.54404i	−0.123557	+	0.183180i
$917$	5.73072	+	8.49614i	0.189245	+	0.280567i
$918$	6.88748	−	17.0471i	0.227321	−	0.562639i
$919$	−4.15282	−	0.882709i	−0.136989	−	0.0291179i	0.138907	−	0.990305i	$-0.455641\pi$
$919$	−4.15282	−	0.882709i	−0.136989	−	0.0291179i	−0.275896	+	0.961188i	$0.588974\pi$
$920$	−1.24512	+	11.8465i	−0.0410505	+	0.390569i
$921$	0.0770493	+	0.157975i	0.00253886	+	0.00520544i
$922$	−26.4825	−	14.0810i	−0.872155	−	0.463733i
$923$	32.8776	+	56.9457i	1.08218	+	1.87439i
$924$	0.374294	−	2.25363i	0.0123134	−	0.0741391i
$925$	2.01255	+	1.68873i	0.0661724	+	0.0555252i
$926$	1.87074	−	2.39443i	0.0614762	−	0.0786860i
$927$	2.55933	−	3.79436i	0.0840593	−	0.124623i
$928$	−8.60412	+	0.601659i	−0.282444	+	0.0197504i
$929$	−11.1778	+	5.94334i	−0.366732	+	0.194995i	−0.642602	−	0.766200i	$-0.722145\pi$
$929$	−11.1778	+	5.94334i	−0.366732	+	0.194995i	0.275870	+	0.961195i	$0.411034\pi$
$930$	−0.144842	−	0.445778i	−0.00474956	−	0.0146176i
$931$	24.5324	−	8.23931i	0.804018	−	0.270032i
$932$	19.2603	−	13.9934i	0.630892	−	0.458370i
$933$	2.59374	+	0.364527i	0.0849153	+	0.0119341i
$934$	−18.9231	+	15.8783i	−0.619181	+	0.519555i
$935$	15.6681	+	37.6955i	0.512402	+	1.23278i
$936$	15.7415	+	5.72944i	0.514527	+	0.187273i
$937$	−17.4244	+	10.8880i	−0.569230	+	0.355694i	−0.783799	−	0.621015i	$-0.786721\pi$
$937$	−17.4244	+	10.8880i	−0.569230	+	0.355694i	0.214569	+	0.976709i	$0.431165\pi$
$938$	0.111278	+	1.05874i	0.00363335	+	0.0345690i
$939$	−0.589788	+	5.61145i	−0.0192470	+	0.183123i
$940$	27.8949	−	3.92037i	0.909830	−	0.127868i
$941$	6.63710	−	0.932784i	0.216363	−	0.0304079i	−0.0301584	−	0.999545i	$-0.509601\pi$
$941$	6.63710	−	0.932784i	0.216363	−	0.0304079i	0.246522	+	0.969137i	$0.420712\pi$
$942$	−1.41314	+	13.4451i	−0.0460424	+	0.438065i
$943$	−2.54536	−	24.2175i	−0.0828883	−	0.788629i
$944$	4.67461	−	2.92102i	0.152146	−	0.0950711i
$945$	8.92881	+	3.24982i	0.290454	+	0.105717i
$946$	−25.2317	−	15.4195i	−0.820353	−	0.501332i
$947$	−7.08289	+	5.94325i	−0.230163	+	0.193130i	−0.750574	−	0.660786i	$-0.770223\pi$
$947$	−7.08289	+	5.94325i	−0.230163	+	0.193130i	0.520411	+	0.853916i	$0.325779\pi$
$948$	−9.05449	−	1.27253i	−0.294076	−	0.0413297i
$949$	−10.1707	+	7.38947i	−0.330156	+	0.239872i
$950$	3.82267	+	3.37431i	0.124024	+	0.109477i
$951$	−2.84669	−	8.76121i	−0.0923103	−	0.284102i
$952$	−4.51079	+	2.39843i	−0.146196	+	0.0777336i
$953$	35.6736	−	2.49454i	1.15558	−	0.0808061i	0.520926	−	0.853602i	$-0.325587\pi$
$953$	35.6736	−	2.49454i	1.15558	−	0.0808061i	0.634655	+	0.772796i	$0.281142\pi$
$954$	−15.5493	+	23.0528i	−0.503428	+	0.746362i
$955$	−0.0319571	+	0.0409033i	−0.00103411	+	0.00132360i
$956$	−8.81109	−	7.39338i	−0.284971	−	0.239119i
$957$	−8.54863	−	17.0935i	−0.276338	−	0.552553i
$958$	−4.68965	−	8.12271i	−0.151516	−	0.262433i
$959$	8.87076	+	4.71667i	0.286452	+	0.152309i
$960$	−0.727477	−	1.49155i	−0.0234792	−	0.0481395i
$961$	3.23204	−	30.7508i	0.104259	−	0.991963i
$962$	−14.4112	−	3.06319i	−0.464635	−	0.0987613i
$963$	3.81174	−	9.43439i	0.122832	−	0.304019i
$964$	0.957303	+	1.41926i	0.0308326	+	0.0457113i
$965$	−23.7138	+	35.1571i	−0.763373	+	1.13175i
$966$	−1.23741	−	3.06270i	−0.0398131	−	0.0985408i
$967$	5.85580	+	33.2099i	0.188310	+	1.06796i	0.921628	+	0.388073i	$0.126859\pi$
$967$	5.85580	+	33.2099i	0.188310	+	1.06796i	−0.733319	+	0.679885i	$0.762030\pi$
$968$	9.44268	+	5.64232i	0.303499	+	0.181351i
$969$	−3.84067	+	13.9101i	−0.123380	+	0.446857i
$970$	−8.12356	+	25.0017i	−0.260832	+	0.802758i
$971$	−36.3945	−	35.1457i	−1.16795	−	1.12788i	−0.989590	−	0.143916i	$-0.954030\pi$
$971$	−36.3945	−	35.1457i	−1.16795	−	1.12788i	−0.178365	−	0.983964i	$-0.557081\pi$
$972$	14.5577	−	1.01798i	0.466940	−	0.0326516i
$973$	3.90906	+	5.00336i	0.125319	+	0.160400i
$974$	−0.134367	+	3.84775i	−0.00430538	+	0.123290i
$975$	1.24027	+	4.97447i	0.0397206	+	0.159310i
$976$	−0.352989	−	3.35846i	−0.0112989	−	0.107502i
$977$	−32.6767	+	6.94564i	−1.04542	+	0.222211i	−0.698445	−	0.715664i	$-0.746124\pi$
$977$	−32.6767	+	6.94564i	−1.04542	+	0.222211i	−0.346975	+	0.937875i	$0.612791\pi$
$978$	2.07713	−	11.7800i	0.0664194	−	0.376683i
$979$	−29.2036	−	27.6453i	−0.933350	−	0.883548i
$980$	7.37354	+	12.7714i	0.235539	+	0.407966i
$981$	12.5199	+	13.9047i	0.399729	+	0.443944i
$982$	−7.02143	−	0.490986i	−0.224063	−	0.0156680i
$983$	−18.2882	−	27.1134i	−0.583305	−	0.864785i	0.415695	−	0.909504i	$-0.363538\pi$
$983$	−18.2882	−	27.1134i	−0.583305	−	0.864785i	−0.999000	+	0.0447195i	$0.985761\pi$
$984$	2.08860	+	2.67329i	0.0665822	+	0.0852214i
$985$	26.2391	+	16.3960i	0.836048	+	0.522421i
$986$	−18.7358	+	38.4141i	−0.596669	+	1.22335i
$987$	−6.31961	+	4.59147i	−0.201155	+	0.146148i
$988$	−27.8116	−	6.64372i	−0.884806	−	0.211365i
$989$	−42.7565			−1.35958
$990$	−13.9205	+	15.7731i	−0.442421	+	0.501301i
$991$	9.53725	−	8.00270i	0.302961	−	0.254214i	−0.478615	−	0.878025i	$-0.658861\pi$
$991$	9.53725	−	8.00270i	0.302961	−	0.254214i	0.781575	+	0.623811i	$0.214416\pi$
$992$	0.00985722	+	0.282274i	0.000312967	+	0.00896221i
$993$	−6.70755	+	1.92336i	−0.212858	+	0.0610359i
$994$	−2.50010	−	10.0274i	−0.0792984	−	0.318049i
$995$	44.5313	+	9.46542i	1.41174	+	0.300074i
$996$	−5.69171	+	6.32129i	−0.180349	+	0.200298i
$997$	4.58644	−	4.42907i	0.145254	−	0.140270i	−0.618482	−	0.785799i	$-0.712252\pi$
$997$	4.58644	−	4.42907i	0.145254	−	0.140270i	0.763736	+	0.645529i	$0.223363\pi$
$998$	−9.96377	−	20.4287i	−0.315397	−	0.646661i
$999$	−8.15116	+	1.73258i	−0.257891	+	0.0548165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.u.b.9.7	✓	264
11.5	even	5	inner	418.2.u.b.313.7	yes	264
19.17	even	9	inner	418.2.u.b.207.7	yes	264
209.93	even	45	inner	418.2.u.b.93.7	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.9.7	✓	264	1.1	even	1	trivial
418.2.u.b.93.7	yes	264	209.93	even	45	inner
418.2.u.b.207.7	yes	264	19.17	even	9	inner
418.2.u.b.313.7	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)

\(f(q)\)	\(=\)	\(q+(0.990268 + 0.139173i) q^{2} +(0.161628 - 0.648256i) q^{3} +(0.961262 + 0.275637i) q^{4} +(0.0866869 - 2.48239i) q^{5} +(0.250275 - 0.619453i) q^{6} +(-0.941853 + 0.419340i) q^{7} +(0.913545 + 0.406737i) q^{8} +(2.25473 + 1.19886i) q^{9} +O(q^{10})\)	\(q+(0.990268 + 0.139173i) q^{2} +(0.161628 - 0.648256i) q^{3} +(0.961262 + 0.275637i) q^{4} +(0.0866869 - 2.48239i) q^{5} +(0.250275 - 0.619453i) q^{6} +(-0.941853 + 0.419340i) q^{7} +(0.913545 + 0.406737i) q^{8} +(2.25473 + 1.19886i) q^{9} +(0.431325 - 2.44617i) q^{10} +(-3.31068 - 0.198423i) q^{11} +(0.334051 - 0.578593i) q^{12} +(5.56316 - 3.47625i) q^{13} +(-0.991048 + 0.284178i) q^{14} +(-1.59521 - 0.457420i) q^{15} +(0.848048 + 0.529919i) q^{16} +(4.37522 - 2.32634i) q^{17} +(2.06594 + 1.50099i) q^{18} +(-3.79622 - 2.14213i) q^{19} +(0.767568 - 2.36233i) q^{20} +(0.119610 + 0.678340i) q^{21} +(-3.25085 - 0.657250i) q^{22} +(-4.50639 + 1.64019i) q^{23} +(0.411325 - 0.526471i) q^{24} +(-1.16692 - 0.0815988i) q^{25} +(5.99282 - 2.66817i) q^{26} +(2.48274 - 2.75736i) q^{27} +(-1.02095 + 0.143486i) q^{28} +(-6.20440 + 5.99152i) q^{29} +(-1.51603 - 0.674979i) q^{30} +(0.188993 + 0.209898i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-0.663729 + 2.11410i) q^{33} +(4.65640 - 1.69479i) q^{34} +(0.959319 + 2.37440i) q^{35} +(1.83693 + 1.77391i) q^{36} +(-1.81699 - 1.32012i) q^{37} +(-3.46115 - 2.64962i) q^{38} +(-1.35433 - 4.16821i) q^{39} +(1.08887 - 2.23252i) q^{40} +(-1.22842 + 4.92692i) q^{41} +(0.0240389 + 0.688385i) q^{42} +(8.37808 + 3.04937i) q^{43} +(-3.12774 - 1.10328i) q^{44} +(3.17150 - 5.49319i) q^{45} +(-4.69081 + 0.997062i) q^{46} +(4.97140 + 10.1929i) q^{47} +(0.480592 - 0.464103i) q^{48} +(-3.97267 + 4.41210i) q^{49} +(-1.14420 - 0.243208i) q^{50} +(-0.800908 - 3.21227i) q^{51} +(6.30583 - 1.80817i) q^{52} +(0.380022 + 10.8824i) q^{53} +(2.84233 - 2.38500i) q^{54} +(-0.779555 + 8.20120i) q^{55} -1.03099 q^{56} +(-2.00223 + 2.11469i) q^{57} +(-6.97788 + 5.06972i) q^{58} +(2.41639 - 4.95433i) q^{59} +(-1.40734 - 0.879401i) q^{60} +(-2.07907 - 2.66108i) q^{61} +(0.157942 + 0.234158i) q^{62} +(-2.62636 - 0.183653i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-8.14714 - 14.1113i) q^{65} +(-0.951496 + 2.00115i) q^{66} +(0.179305 - 1.01689i) q^{67} +(4.84696 - 1.03025i) q^{68} +(0.334904 + 3.18640i) q^{69} +(0.619530 + 2.48480i) q^{70} +(-0.349823 + 10.0176i) q^{71} +(1.57218 + 2.01230i) q^{72} +(-1.91177 + 0.133684i) q^{73} +(-1.61558 - 1.56015i) q^{74} +(-0.241504 + 0.743273i) q^{75} +(-3.05871 - 3.10553i) q^{76} +(3.20139 - 1.20142i) q^{77} +(-0.761051 - 4.31613i) q^{78} +(-5.12677 - 12.6892i) q^{79} +(1.38898 - 2.05925i) q^{80} +(2.89774 + 4.29607i) q^{81} +(-1.90216 + 4.70801i) q^{82} +(-12.4536 - 2.64709i) q^{83} +(-0.0719996 + 0.685031i) q^{84} +(-5.39561 - 11.0626i) q^{85} +(7.87215 + 4.18570i) q^{86} +(2.88123 + 4.99044i) q^{87} +(-2.94375 - 1.52784i) q^{88} +(9.28812 + 7.79365i) q^{89} +(3.90513 - 4.99834i) q^{90} +(-3.78195 + 5.60697i) q^{91} +(-4.78392 + 0.334524i) q^{92} +(0.166615 - 0.0885905i) q^{93} +(3.50445 + 10.7856i) q^{94} +(-5.64668 + 9.23799i) q^{95} +(0.540506 - 0.392700i) q^{96} +(-10.4805 - 1.47294i) q^{97} +(-4.54806 + 3.81627i) q^{98} +(-7.22682 - 4.41644i) 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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