LMFDB - Embedded newform 294.2.p.a.101.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(5,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 29]))

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

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

chi := DirichletCharacter("294.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.p (of order $42$, degree $12$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			101.10
Character	$\chi$	$=$	294.101
Dual form			294.2.p.a.131.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.930874 + 0.365341i) q^{2} +(-1.67895 - 0.425595i) q^{3} +(0.733052 + 0.680173i) q^{4} +(0.562333 + 0.383392i) q^{5} +(-1.40740 - 1.00956i) q^{6} +(-1.02876 + 2.43755i) q^{7} +(0.433884 + 0.900969i) q^{8} +(2.63774 + 1.42910i) q^{9} +O(q^{10})$	\(q+(0.930874 + 0.365341i) q^{2} +(-1.67895 - 0.425595i) q^{3} +(0.733052 + 0.680173i) q^{4} +(0.562333 + 0.383392i) q^{5} +(-1.40740 - 1.00956i) q^{6} +(-1.02876 + 2.43755i) q^{7} +(0.433884 + 0.900969i) q^{8} +(2.63774 + 1.42910i) q^{9} +(0.383392 + 0.562333i) q^{10} +(0.601718 + 3.99214i) q^{11} +(-0.941279 - 1.45396i) q^{12} +(1.92643 - 1.53628i) q^{13} +(-1.84818 + 1.89320i) q^{14} +(-0.780959 - 0.883022i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(1.73034 + 0.533738i) q^{17} +(1.93329 + 2.29399i) q^{18} +(1.85545 - 1.07124i) q^{19} +(0.151446 + 0.663530i) q^{20} +(2.76464 - 3.65469i) q^{21} +(-0.898369 + 3.93601i) q^{22} +(2.52571 + 8.18816i) q^{23} +(-0.345021 - 1.69734i) q^{24} +(-1.65748 - 4.22318i) q^{25} +(2.35453 - 0.726277i) q^{26} +(-3.82041 - 3.52200i) q^{27} +(-2.41209 + 1.08712i) q^{28} +(-5.96180 + 1.36074i) q^{29} +(-0.404370 - 1.10730i) q^{30} +(-4.37167 - 2.52398i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(0.688780 - 6.95869i) q^{33} +(1.41573 + 1.12901i) q^{34} +(-1.51304 + 0.976297i) q^{35} +(0.961562 + 2.84172i) q^{36} +(6.91047 - 6.41197i) q^{37} +(2.11855 - 0.319321i) q^{38} +(-3.88821 + 1.75945i) q^{39} +(-0.101437 + 0.672993i) q^{40} +(-6.53147 + 3.14539i) q^{41} +(3.90874 - 2.39202i) q^{42} +(1.51981 + 0.731902i) q^{43} +(-2.27425 + 3.33572i) q^{44} +(0.935381 + 1.81492i) q^{45} +(-0.640351 + 8.54489i) q^{46} +(4.27236 - 10.8858i) q^{47} +(0.298937 - 1.70606i) q^{48} +(-4.88331 - 5.01531i) q^{49} -4.53679i q^{50} +(-2.67799 - 1.63254i) q^{51} +(2.45711 + 0.184135i) q^{52} +(7.86348 - 8.47481i) q^{53} +(-2.26959 - 4.67429i) q^{54} +(-1.19219 + 2.47561i) q^{55} +(-2.64252 + 0.130733i) q^{56} +(-3.57111 + 1.00889i) q^{57} +(-6.04681 - 0.911410i) q^{58} +(-0.00789152 + 0.00538035i) q^{59} +(0.0281241 - 1.17849i) q^{60} +(2.82091 + 3.04022i) q^{61} +(-3.14736 - 3.94666i) q^{62} +(-6.19711 + 4.95942i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(1.67229 - 0.125321i) q^{65} +(3.18346 - 6.22602i) q^{66} +(3.82751 - 6.62945i) q^{67} +(0.905393 + 1.56819i) q^{68} +(-0.755705 - 14.8224i) q^{69} +(-1.76513 + 0.356033i) q^{70} +(-5.04771 - 1.15211i) q^{71} +(-0.143106 + 2.99658i) q^{72} +(-4.71005 + 1.84856i) q^{73} +(8.77533 - 3.44406i) q^{74} +(0.985454 + 7.79592i) q^{75} +(2.08877 + 0.476748i) q^{76} +(-10.3501 - 2.64023i) q^{77} +(-4.26224 + 0.217305i) q^{78} +(1.53473 + 2.65823i) q^{79} +(-0.340297 + 0.589412i) q^{80} +(4.91533 + 7.53920i) q^{81} +(-7.22911 + 0.541747i) q^{82} +(-0.403303 + 0.505726i) q^{83} +(4.51245 - 0.798641i) q^{84} +(0.768395 + 0.963537i) q^{85} +(1.14736 + 1.23656i) q^{86} +(10.5887 + 0.252694i) q^{87} +(-3.33572 + 2.27425i) q^{88} +(10.5964 + 1.59715i) q^{89} +(0.207656 + 2.03120i) q^{90} +(1.76292 + 6.27624i) q^{91} +(-3.71788 + 7.72026i) q^{92} +(6.26561 + 6.09820i) q^{93} +(7.95405 - 8.57243i) q^{94} +(1.45408 + 0.108969i) q^{95} +(0.901566 - 1.47891i) q^{96} -9.68391i q^{97} +(-2.71344 - 6.45269i) q^{98} +(-4.11801 + 11.3901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9	$ 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9} + 6 q^{10} - 12 q^{15} + 18 q^{16} - 4 q^{18} - 12 q^{19} + 10 q^{22} - 6 q^{24} + 16 q^{25} - 42 q^{27} + 2 q^{28} + 4 q^{30} + 6 q^{31} + 18 q^{33} - 10 q^{36} - 36 q^{37} + 4 q^{39} - 22 q^{40} + 20 q^{42} + 40 q^{43} - 14 q^{45} - 156 q^{46} - 134 q^{49} - 12 q^{51} + 16 q^{52} - 18 q^{54} - 322 q^{55} - 34 q^{57} - 164 q^{58} - 6 q^{60} + 56 q^{61} - 24 q^{63} + 36 q^{64} - 28 q^{69} - 4 q^{70} + 4 q^{72} - 24 q^{73} + 84 q^{75} + 16 q^{78} + 22 q^{79} - 52 q^{81} + 24 q^{82} + 42 q^{84} + 32 q^{85} - 94 q^{87} - 2 q^{88} + 42 q^{90} - 100 q^{91} - 266 q^{93} - 88 q^{94} - 6 q^{96} + 224 q^{99}+O(q^{100}) $ 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9 + 6 * q^10 - 12 * q^15 + 18 * q^16 - 4 * q^18 - 12 * q^19 + 10 * q^22 - 6 * q^24 + 16 * q^25 - 42 * q^27 + 2 * q^28 + 4 * q^30 + 6 * q^31 + 18 * q^33 - 10 * q^36 - 36 * q^37 + 4 * q^39 - 22 * q^40 + 20 * q^42 + 40 * q^43 - 14 * q^45 - 156 * q^46 - 134 * q^49 - 12 * q^51 + 16 * q^52 - 18 * q^54 - 322 * q^55 - 34 * q^57 - 164 * q^58 - 6 * q^60 + 56 * q^61 - 24 * q^63 + 36 * q^64 - 28 * q^69 - 4 * q^70 + 4 * q^72 - 24 * q^73 + 84 * q^75 + 16 * q^78 + 22 * q^79 - 52 * q^81 + 24 * q^82 + 42 * q^84 + 32 * q^85 - 94 * q^87 - 2 * q^88 + 42 * q^90 - 100 * q^91 - 266 * q^93 - 88 * q^94 - 6 * q^96 + 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{1}{42}\right)$

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 $

$2$	0.930874	+	0.365341i	0.658227	+	0.258335i
$2$	0.930874	+	0.365341i	0.658227	+	0.258335i
$3$	−1.67895	−	0.425595i	−0.969342	−	0.245717i
$3$	−1.67895	−	0.425595i	−0.969342	−	0.245717i
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	0.562333	+	0.383392i	0.251483	+	0.171458i	0.682500	−	0.730886i	$-0.260893\pi$
$5$	0.562333	+	0.383392i	0.251483	+	0.171458i	−0.431017	+	0.902344i	$0.641845\pi$
$6$	−1.40740	−	1.00956i	−0.574570	−	0.412153i
$7$	−1.02876	+	2.43755i	−0.388835	+	0.921308i
$7$	−1.02876	+	2.43755i	−0.388835	+	0.921308i
$8$	0.433884	+	0.900969i	0.153401	+	0.318541i
$9$	2.63774	+	1.42910i	0.879246	+	0.476368i
$10$	0.383392	+	0.562333i	0.121239	+	0.177825i
$11$	0.601718	+	3.99214i	0.181425	+	1.20368i	0.875300	+	0.483580i	$0.160664\pi$
$11$	0.601718	+	3.99214i	0.181425	+	1.20368i	−0.693875	+	0.720095i	$0.744098\pi$
$12$	−0.941279	−	1.45396i	−0.271724	−	0.419722i
$13$	1.92643	−	1.53628i	0.534296	−	0.426087i	−0.318814	−	0.947817i	$-0.603285\pi$
$13$	1.92643	−	1.53628i	0.534296	−	0.426087i	0.853111	+	0.521730i	$0.174713\pi$
$14$	−1.84818	+	1.89320i	−0.493948	+	0.505980i
$15$	−0.780959	−	0.883022i	−0.201643	−	0.227995i
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	1.73034	+	0.533738i	0.419668	+	0.129451i	0.497395	−	0.867524i	$-0.334290\pi$
$17$	1.73034	+	0.533738i	0.419668	+	0.129451i	−0.0777267	+	0.996975i	$0.524766\pi$
$18$	1.93329	+	2.29399i	0.455681	+	0.540698i
$19$	1.85545	−	1.07124i	0.425668	−	0.245760i	−0.271831	−	0.962345i	$-0.587629\pi$
$19$	1.85545	−	1.07124i	0.425668	−	0.245760i	0.697500	+	0.716585i	$0.254296\pi$
$20$	0.151446	+	0.663530i	0.0338645	+	0.148370i
$21$	2.76464	−	3.65469i	0.603295	−	0.797518i
$22$	−0.898369	+	3.93601i	−0.191533	+	0.839160i
$23$	2.52571	+	8.18816i	0.526647	+	1.70735i	0.692695	+	0.721231i	$0.256423\pi$
$23$	2.52571	+	8.18816i	0.526647	+	1.70735i	−0.166047	+	0.986118i	$0.553100\pi$
$24$	−0.345021	−	1.69734i	−0.0704271	−	0.346468i
$25$	−1.65748	−	4.22318i	−0.331495	−	0.844636i
$26$	2.35453	−	0.726277i	0.461762	−	0.142435i
$27$	−3.82041	−	3.52200i	−0.735238	−	0.677809i
$28$	−2.41209	+	1.08712i	−0.455842	+	0.205446i
$29$	−5.96180	+	1.36074i	−1.10708	+	0.252683i	−0.736715	−	0.676204i	$-0.763624\pi$
$29$	−5.96180	+	1.36074i	−1.10708	+	0.252683i	−0.370363	+	0.928887i	$0.620767\pi$
$30$	−0.404370	−	1.10730i	−0.0738275	−	0.202164i
$31$	−4.37167	−	2.52398i	−0.785175	−	0.453321i	0.0530864	−	0.998590i	$-0.483094\pi$
$31$	−4.37167	−	2.52398i	−0.785175	−	0.453321i	−0.838261	+	0.545269i	$0.816427\pi$
$32$	−0.294755	+	0.955573i	−0.0521058	+	0.168923i
$33$	0.688780	−	6.95869i	0.119901	−	1.21135i
$34$	1.41573	+	1.12901i	0.242795	+	0.193623i
$35$	−1.51304	+	0.976297i	−0.255751	+	0.165024i
$36$	0.961562	+	2.84172i	0.160260	+	0.473621i
$37$	6.91047	−	6.41197i	1.13607	−	1.05412i	0.138105	−	0.990418i	$-0.455899\pi$
$37$	6.91047	−	6.41197i	1.13607	−	1.05412i	0.997969	−	0.0637045i	$-0.0202915\pi$
$38$	2.11855	−	0.319321i	0.343675	−	0.0518006i
$39$	−3.88821	+	1.75945i	−0.622612	+	0.281738i
$40$	−0.101437	+	0.672993i	−0.0160386	+	0.106409i
$41$	−6.53147	+	3.14539i	−1.02004	+	0.491227i	−0.867694	−	0.497099i	$-0.834398\pi$
$41$	−6.53147	+	3.14539i	−1.02004	+	0.491227i	−0.152350	+	0.988327i	$0.548684\pi$
$42$	3.90874	−	2.39202i	0.603132	−	0.369096i
$43$	1.51981	+	0.731902i	0.231769	+	0.111614i	0.546164	−	0.837678i	$-0.316087\pi$
$43$	1.51981	+	0.731902i	0.231769	+	0.111614i	−0.314395	+	0.949292i	$0.601802\pi$
$44$	−2.27425	+	3.33572i	−0.342857	+	0.502879i
$45$	0.935381	+	1.81492i	0.139438	+	0.270552i
$46$	−0.640351	+	8.54489i	−0.0944146	+	1.25987i
$47$	4.27236	−	10.8858i	0.623187	−	1.58786i	−0.174415	−	0.984672i	$-0.555804\pi$
$47$	4.27236	−	10.8858i	0.623187	−	1.58786i	0.797603	−	0.603183i	$-0.206101\pi$
$48$	0.298937	−	1.70606i	0.0431478	−	0.246248i
$49$	−4.88331	−	5.01531i	−0.697615	−	0.716473i
$50$		−	4.53679i		−	0.641599i
$51$	−2.67799	−	1.63254i	−0.374994	−	0.228602i
$52$	2.45711	+	0.184135i	0.340740	+	0.0255349i
$53$	7.86348	−	8.47481i	1.08013	−	1.16410i	0.0944424	−	0.995530i	$-0.469893\pi$
$53$	7.86348	−	8.47481i	1.08013	−	1.16410i	0.985689	−	0.168574i	$-0.0539164\pi$
$54$	−2.26959	−	4.67429i	−0.308852	−	0.636090i
$55$	−1.19219	+	2.47561i	−0.160755	+	0.333811i
$56$	−2.64252	+	0.130733i	−0.353122	+	0.0174700i
$57$	−3.57111	+	1.00889i	−0.473005	+	0.133631i
$58$	−6.04681	−	0.911410i	−0.793986	−	0.119674i
$59$	−0.00789152	+	0.00538035i	−0.00102739	+	0.000700462i	−0.563834	−	0.825888i	$-0.690674\pi$
$59$	−0.00789152	+	0.00538035i	−0.00102739	+	0.000700462i	0.562806	+	0.826589i	$0.309722\pi$
$60$	0.0281241	−	1.17849i	0.00363081	−	0.152142i
$61$	2.82091	+	3.04022i	0.361181	+	0.389260i	0.887332	−	0.461131i	$-0.152556\pi$
$61$	2.82091	+	3.04022i	0.361181	+	0.389260i	−0.526152	+	0.850391i	$0.676366\pi$
$62$	−3.14736	−	3.94666i	−0.399715	−	0.501226i
$63$	−6.19711	+	4.95942i	−0.780763	+	0.624828i
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	1.67229	−	0.125321i	0.207423	−	0.0155442i
$66$	3.18346	−	6.22602i	0.391857	−	0.766370i
$67$	3.82751	−	6.62945i	0.467605	−	0.809916i	−0.531710	−	0.846927i	$-0.678450\pi$
$67$	3.82751	−	6.62945i	0.467605	−	0.809916i	0.999315	+	0.0370108i	$0.0117836\pi$
$68$	0.905393	+	1.56819i	0.109795	+	0.190170i
$69$	−0.755705	−	14.8224i	−0.0909762	−	1.78441i
$70$	−1.76513	+	0.356033i	−0.210974	+	0.0425540i
$71$	−5.04771	−	1.15211i	−0.599053	−	0.136730i	−0.0877679	−	0.996141i	$-0.527973\pi$
$71$	−5.04771	−	1.15211i	−0.599053	−	0.136730i	−0.511285	+	0.859411i	$0.670831\pi$
$72$	−0.143106	+	2.99658i	−0.0168652	+	0.353151i
$73$	−4.71005	+	1.84856i	−0.551270	+	0.216358i	−0.624593	−	0.780951i	$-0.714735\pi$
$73$	−4.71005	+	1.84856i	−0.551270	+	0.216358i	0.0733225	+	0.997308i	$0.476640\pi$
$74$	8.77533	−	3.44406i	1.02011	−	0.400364i
$75$	0.985454	+	7.79592i	0.113790	+	0.900195i
$76$	2.08877	+	0.476748i	0.239598	+	0.0546867i
$77$	−10.3501	−	2.64023i	−1.17950	−	0.300883i
$78$	−4.26224	+	0.217305i	−0.482603	+	0.0246050i
$79$	1.53473	+	2.65823i	0.172670	+	0.299074i	0.939353	−	0.342953i	$-0.111427\pi$
$79$	1.53473	+	2.65823i	0.172670	+	0.299074i	−0.766682	+	0.642027i	$0.778094\pi$
$80$	−0.340297	+	0.589412i	−0.0380464	+	0.0658983i
$81$	4.91533	+	7.53920i	0.546147	+	0.837689i
$82$	−7.22911	+	0.541747i	−0.798322	+	0.0598259i
$83$	−0.403303	+	0.505726i	−0.0442683	+	0.0555107i	−0.803473	−	0.595341i	$-0.797017\pi$
$83$	−0.403303	+	0.505726i	−0.0442683	+	0.0555107i	0.759205	+	0.650852i	$0.225588\pi$
$84$	4.51245	−	0.798641i	0.492348	−	0.0871389i
$85$	0.768395	+	0.963537i	0.0833441	+	0.104510i
$86$	1.14736	+	1.23656i	0.123723	+	0.133341i
$87$	10.5887	+	0.252694i	1.13522	+	0.0270917i
$88$	−3.33572	+	2.27425i	−0.355589	+	0.242436i
$89$	10.5964	+	1.59715i	1.12322	+	0.169297i	0.684279	−	0.729221i	$-0.260117\pi$
$89$	10.5964	+	1.59715i	1.12322	+	0.169297i	0.438937	+	0.898518i	$0.355355\pi$
$90$	0.207656	+	2.03120i	0.0218889	+	0.214107i
$91$	1.76292	+	6.27624i	0.184804	+	0.657929i
$92$	−3.71788	+	7.72026i	−0.387616	+	0.804893i
$93$	6.26561	+	6.09820i	0.649714	+	0.632354i
$94$	7.95405	−	8.57243i	0.820398	−	0.884178i
$95$	1.45408	+	0.108969i	0.149186	+	0.0111799i
$96$	0.901566	−	1.47891i	0.0920157	−	0.150941i
$97$		−	9.68391i		−	0.983252i	−0.870807	−	0.491626i	$-0.836403\pi$
$97$		−	9.68391i		−	0.983252i	0.870807	−	0.491626i	$-0.163597\pi$
$98$	−2.71344	−	6.45269i	−0.274099	−	0.651820i
$99$	−4.11801	+	11.3901i	−0.413875	+	1.14475i
$100$	1.65748	−	4.22318i	0.165748	−	0.422318i
$101$	−1.26652	+	16.9005i	−0.126023	+	1.68166i	0.473103	+	0.881007i	$0.343134\pi$
$101$	−1.26652	+	16.9005i	−0.126023	+	1.68166i	−0.599126	+	0.800655i	$0.704485\pi$
$102$	−1.89644	−	2.49807i	−0.187775	−	0.247346i
$103$	−3.75711	+	5.51066i	−0.370199	+	0.542982i	−0.965460	−	0.260550i	$-0.916096\pi$
$103$	−3.75711	+	5.51066i	−0.370199	+	0.542982i	0.595262	+	0.803532i	$0.297048\pi$
$104$	2.21999	+	1.06909i	0.217688	+	0.104833i
$105$	2.95583	−	0.995210i	0.288460	−	0.0971225i
$106$	10.4161	−	5.01613i	1.01170	−	0.487209i
$107$	0.306075	−	2.03067i	0.0295893	−	0.196312i	−0.969152	−	0.246462i	$-0.920732\pi$
$107$	0.306075	−	2.03067i	0.0295893	−	0.196312i	0.998742	+	0.0501499i	$0.0159699\pi$
$108$	−0.404990	−	5.18035i	−0.0389702	−	0.498479i
$109$	4.21772	−	0.635719i	0.403984	−	0.0608908i	0.0560927	−	0.998426i	$-0.482136\pi$
$109$	4.21772	−	0.635719i	0.403984	−	0.0608908i	0.347892	+	0.937535i	$0.386898\pi$
$110$	−2.01422	+	1.86892i	−0.192048	+	0.178195i
$111$	−14.3312	+	7.82432i	−1.36026	+	0.742652i
$112$	−2.50761	−	0.843725i	−0.236947	−	0.0797245i
$113$	8.02433	+	6.39919i	0.754866	+	0.601985i	0.923458	−	0.383701i	$-0.125350\pi$
$113$	8.02433	+	6.39919i	0.754866	+	0.601985i	−0.168592	+	0.985686i	$0.553922\pi$
$114$	−3.69285	−	0.365522i	−0.345867	−	0.0342343i
$115$	−1.71898	+	5.57281i	−0.160296	+	0.519667i
$116$	−5.29584	−	3.05756i	−0.491707	−	0.283887i
$117$	7.27693	−	1.29923i	0.672752	−	0.120114i
$118$	−0.00931167	+	0.00212533i	−0.000857209	+	0.000195652i
$119$	−3.08112	+	3.66870i	−0.282445	+	0.336309i
$120$	0.456730	−	1.08675i	0.0416936	−	0.0992061i
$121$	−5.06382	+	1.56198i	−0.460347	+	0.141998i
$122$	1.51520	+	3.86066i	0.137179	+	0.349527i
$123$	12.3047	−	2.50119i	1.10947	−	0.225525i
$124$	−1.48791	−	4.82370i	−0.133619	−	0.433181i
$125$	1.44431	−	6.32795i	0.129183	−	0.565989i
$126$	−7.58061	+	2.35253i	−0.675334	+	0.209580i
$127$	0.0462898	+	0.202809i	0.00410755	+	0.0179964i	0.976940	−	0.213513i	$-0.0684907\pi$
$127$	0.0462898	+	0.202809i	0.00410755	+	0.0179964i	−0.972833	+	0.231510i	$0.925634\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−2.24019	−	1.87565i	−0.197238	−	0.165142i
$130$	1.60248	+	0.494300i	0.140547	+	0.0433529i
$131$	−0.520135	−	6.94072i	−0.0454444	−	0.606413i	−0.972712	−	0.232015i	$-0.925468\pi$
$131$	−0.520135	−	6.94072i	−0.0454444	−	0.606413i	0.927268	−	0.374399i	$-0.122151\pi$
$132$	5.23802	−	4.63259i	0.455911	−	0.403215i
$133$	0.702399	+	5.62479i	0.0609057	+	0.487731i
$134$	5.98494	−	4.77283i	0.517020	−	0.412310i
$135$	−0.798036	−	3.44525i	−0.0686840	−	0.296520i
$136$	0.269884	+	1.79056i	0.0231423	+	0.153539i
$137$	−5.82904	−	8.54963i	−0.498008	−	0.730444i	0.492132	−	0.870520i	$-0.336218\pi$
$137$	−5.82904	−	8.54963i	−0.498008	−	0.730444i	−0.990141	+	0.140076i	$0.955265\pi$
$138$	4.71177	−	14.0739i	0.401093	−	1.19805i
$139$	−7.45755	−	15.4858i	−0.632541	−	1.31348i	−0.933064	−	0.359710i	$-0.882875\pi$
$139$	−7.45755	−	15.4858i	−0.632541	−	1.31348i	0.300523	−	0.953775i	$-0.402839\pi$
$140$	−1.77319	−	0.313455i	−0.149862	−	0.0264918i
$141$	−11.8060	+	16.4584i	−0.994245	+	1.38605i
$142$	−4.27787	−	2.91660i	−0.358991	−	0.244756i
$143$	7.29221	+	6.76618i	0.609805	+	0.565817i
$144$	−1.22799	+	2.73716i	−0.102332	+	0.228097i
$145$	−3.87421	−	1.52052i	−0.321736	−	0.126272i
$146$	−5.05982			−0.418754
$147$	6.06433	+	10.4988i	0.500178	+	0.865923i
$148$	9.42698			0.774893
$149$	9.01210	+	3.53699i	0.738300	+	0.289761i	0.704536	−	0.709668i	$-0.251155\pi$
$149$	9.01210	+	3.53699i	0.738300	+	0.289761i	0.0337642	+	0.999430i	$0.489250\pi$
$150$	−1.93083	+	7.61704i	−0.157652	+	0.621929i
$151$	−16.4517	−	15.2649i	−1.33882	−	1.24224i	−0.946616	−	0.322364i	$-0.895523\pi$
$151$	−16.4517	−	15.2649i	−1.33882	−	1.24224i	−0.392203	−	0.919879i	$-0.628287\pi$
$152$	1.77020	+	1.20690i	0.143582	+	0.0978929i
$153$	3.80141	+	3.88069i	0.307326	+	0.313735i
$154$	−8.67002	−	6.23903i	−0.698650	−	0.502755i
$155$	−1.49066	−	3.09538i	−0.119733	−	0.248627i
$156$	−4.04699	−	1.35489i	−0.324019	−	0.108478i
$157$	6.08911	+	8.93109i	0.485964	+	0.712778i	0.988406	−	0.151833i	$-0.0485174\pi$
$157$	6.08911	+	8.93109i	0.485964	+	0.712778i	−0.502442	+	0.864611i	$0.667565\pi$
$158$	0.457478	+	3.03517i	0.0363950	+	0.241465i
$159$	−16.8092	+	10.8821i	−1.33306	+	0.863008i
$160$	−0.532110	+	0.424344i	−0.0420670	+	0.0335473i
$161$	−22.5574	−	2.26709i	−1.77777	−	0.178672i
$162$	1.82117	+	8.81382i	0.143085	+	0.692479i
$163$	0.425484	+	5.67769i	0.0333265	+	0.444711i	0.988761	+	0.149507i	$0.0477686\pi$
$163$	0.425484	+	5.67769i	0.0333265	+	0.444711i	−0.955434	+	0.295204i	$0.904612\pi$
$164$	−6.92731	−	2.13679i	−0.540932	−	0.166855i
$165$	3.05523	−	3.64903i	0.237849	−	0.284077i
$166$	−0.560187	+	0.323424i	−0.0434789	+	0.0251026i
$167$	1.65409	+	7.24703i	0.127997	+	0.560792i	0.997734	+	0.0672767i	$0.0214310\pi$
$167$	1.65409	+	7.24703i	0.127997	+	0.560792i	−0.869737	+	0.493515i	$0.835712\pi$
$168$	4.49229	+	0.905148i	0.346588	+	0.0698337i
$169$	−1.54178	+	6.75499i	−0.118599	+	0.519615i
$170$	0.363259	+	1.17766i	0.0278607	+	0.0903222i
$171$	6.42510	−	0.174032i	0.491339	−	0.0133086i
$172$	0.616280	+	1.57026i	0.0469909	+	0.119731i
$173$	5.61612	−	1.73234i	0.426986	−	0.131708i	−0.0738116	−	0.997272i	$-0.523516\pi$
$173$	5.61612	−	1.73234i	0.426986	−	0.131708i	0.500797	+	0.865565i	$0.333040\pi$
$174$	9.76440	+	4.10370i	0.740237	+	0.311101i
$175$	11.9994	+	0.304455i	0.907066	+	0.0230147i
$176$	−3.93601	+	0.898369i	−0.296688	+	0.0677171i
$177$	0.0155393	−	0.00567474i	0.00116801	−	0.000426540i
$178$	9.28040	+	5.35804i	0.695595	+	0.401602i
$179$	4.40928	−	14.2945i	0.329565	−	1.06842i	−0.627516	−	0.778604i	$-0.715928\pi$
$179$	4.40928	−	14.2945i	0.329565	−	1.06842i	0.957081	−	0.289820i	$-0.0935954\pi$
$180$	−0.548777	+	1.96665i	−0.0409034	+	0.146586i
$181$	11.6926	+	9.32453i	0.869103	+	0.693087i	0.952864	−	0.303399i	$-0.0981216\pi$
$181$	11.6926	+	9.32453i	0.869103	+	0.693087i	−0.0837602	+	0.996486i	$0.526693\pi$
$182$	−0.651910	+	6.48645i	−0.0483228	+	0.480808i
$183$	−3.44227	−	6.30494i	−0.254460	−	0.466074i
$184$	−6.28141	+	5.82830i	−0.463072	+	0.429668i
$185$	6.34429	−	0.956247i	0.466441	−	0.0703047i
$186$	3.60457	+	7.96574i	0.264300	+	0.584076i
$187$	−1.08958	+	7.22891i	−0.0796782	+	0.528630i
$188$	10.5361	−	5.07391i	0.768422	−	0.370053i
$189$	12.5153	−	5.68915i	0.910357	−	0.413825i
$190$	1.31376	+	0.632673i	0.0953101	+	0.0458989i
$191$	−9.11282	+	13.3660i	−0.659380	+	0.967133i	0.340260	+	0.940331i	$0.389485\pi$
$191$	−9.11282	+	13.3660i	−0.659380	+	0.967133i	−0.999641	+	0.0268021i	$0.991468\pi$
$192$	1.37955	−	1.04730i	0.0995605	−	0.0755824i
$193$	0.597374	−	7.97140i	0.0429999	−	0.573794i	−0.933542	−	0.358468i	$-0.883299\pi$
$193$	0.597374	−	7.97140i	0.0429999	−	0.573794i	0.976542	−	0.215327i	$-0.0690816\pi$
$194$	3.53793	−	9.01450i	0.254008	−	0.647203i
$195$	−2.86103	−	0.501312i	−0.204883	−	0.0358997i
$196$	−0.168442	−	6.99797i	−0.0120316	−	0.499855i
$197$		−	15.3131i		−	1.09101i	−0.838108	−	0.545505i	$-0.816338\pi$
$197$		−	15.3131i		−	1.09101i	0.838108	−	0.545505i	$-0.183662\pi$
$198$	−7.99463	+	9.09831i	−0.568154	+	0.646588i
$199$	10.7755	+	0.807512i	0.763854	+	0.0572430i	0.450959	−	0.892545i	$-0.351082\pi$
$199$	10.7755	+	0.807512i	0.763854	+	0.0572430i	0.312895	+	0.949788i	$0.398701\pi$
$200$	3.08580	−	3.32570i	0.218199	−	0.235163i
$201$	−9.24766	+	9.50153i	−0.652279	+	0.670186i
$202$	−7.35341	+	15.2695i	−0.517384	+	1.07436i
$203$	2.81638	−	15.9321i	0.197671	−	1.11821i
$204$	−0.852696	−	3.01823i	−0.0597007	−	0.211319i
$205$	−4.87878	−	0.735358i	−0.340749	−	0.0513596i
$206$	−5.51066	+	3.75711i	−0.383946	+	0.261770i
$207$	−5.03956	+	25.2077i	−0.350273	+	1.75206i
$208$	1.67595	+	1.80624i	0.116206	+	0.125240i
$209$	5.39300	+	6.76261i	0.373042	+	0.467780i
$210$	3.11510	+	0.153472i	0.214962	+	0.0105905i
$211$	8.83533	−	11.0792i	0.608249	−	0.762720i	−0.378389	−	0.925647i	$-0.623522\pi$
$211$	8.83533	−	11.0792i	0.608249	−	0.762720i	0.986638	+	0.162926i	$0.0520933\pi$
$212$	11.5287	−	0.863954i	0.791792	−	0.0593366i
$213$	7.98452	+	4.08261i	0.547090	+	0.279736i
$214$	1.02680	−	1.77848i	0.0701909	−	0.121574i
$215$	0.574034	+	0.994256i	0.0391488	+	0.0678077i
$216$	1.51560	−	4.97021i	0.103123	−	0.338180i
$217$	10.6497	−	8.05959i	0.722951	−	0.547121i
$218$	4.15842	+	0.949132i	0.281644	+	0.0642833i
$219$	8.69468	−	1.09906i	0.587532	−	0.0742678i
$220$	−2.55778	+	1.00385i	−0.172445	+	0.0676798i
$221$	4.15335	−	1.63007i	0.279384	−	0.109650i
$222$	−16.1991	+	2.04767i	−1.08721	+	0.137431i
$223$	3.27991	+	0.748619i	0.219639	+	0.0501312i	0.330924	−	0.943657i	$-0.392640\pi$
$223$	3.27991	+	0.748619i	0.219639	+	0.0501312i	−0.111285	+	0.993789i	$0.535497\pi$
$224$	−2.02602	−	1.70154i	−0.135369	−	0.113689i
$225$	1.66337	−	13.5083i	0.110892	−	0.900557i
$226$	5.13175	+	8.88846i	0.341359	+	0.591252i
$227$	−4.35030	+	7.53495i	−0.288740	+	0.500112i	−0.973509	−	0.228648i	$-0.926570\pi$
$227$	−4.35030	+	7.53495i	−0.288740	+	0.500112i	0.684769	+	0.728760i	$0.259903\pi$
$228$	−3.30403	−	1.68940i	−0.218815	−	0.111883i
$229$	2.67974	−	0.200819i	0.177082	−	0.0132705i	0.0141061	−	0.999901i	$-0.495510\pi$
$229$	2.67974	−	0.200819i	0.177082	−	0.0132705i	0.162976	+	0.986630i	$0.447891\pi$
$230$	−3.63613	+	4.55957i	−0.239760	+	0.300649i
$231$	16.2536	+	8.83775i	1.06941	+	0.581481i
$232$	−3.81271	−	4.78099i	−0.250317	−	0.313887i
$233$	−9.19313	−	9.90784i	−0.602262	−	0.649084i	0.356165	−	0.934423i	$-0.384084\pi$
$233$	−9.19313	−	9.90784i	−0.602262	−	0.649084i	−0.958427	+	0.285339i	$0.907894\pi$
$234$	7.24856	+	1.44914i	0.473853	+	0.0947333i
$235$	6.57602	−	4.48345i	0.428972	−	0.292468i
$236$	−0.00944446	−	0.00142352i	−0.000614782	−	9.26635e-5i
$237$	−1.44540	−	5.11620i	−0.0938889	−	0.332333i
$238$	−4.20845	+	2.28943i	−0.272794	+	0.148402i
$239$	0.826044	−	1.71530i	0.0534323	−	0.110953i	−0.872543	−	0.488537i	$-0.837531\pi$
$239$	0.826044	−	1.71530i	0.0534323	−	0.110953i	0.925975	+	0.377584i	$0.123245\pi$
$240$	0.822192	−	0.844764i	0.0530723	−	0.0545293i
$241$	−20.7130	+	22.3233i	−1.33424	+	1.43797i	−0.524210	+	0.851589i	$0.675639\pi$
$241$	−20.7130	+	22.3233i	−1.33424	+	1.43797i	−0.810033	+	0.586384i	$0.800551\pi$
$242$	−5.28443	−	0.396014i	−0.339696	−	0.0254567i
$243$	−5.04394	−	14.7499i	−0.323569	−	0.946205i
$244$			4.14735i			0.265507i
$245$	−0.823216	−	4.69250i	−0.0525933	−	0.299793i
$246$	12.3679	+	2.16711i	0.788547	+	0.138170i
$247$	1.92866	−	4.91416i	0.122718	−	0.312680i
$248$	0.377235	−	5.03385i	0.0239544	−	0.319650i
$249$	0.892360	−	0.677445i	0.0565510	−	0.0429313i
$250$	3.65633	−	5.36286i	0.231247	−	0.339177i
$251$	−5.09927	−	2.45568i	−0.321863	−	0.155001i	0.265974	−	0.963980i	$-0.414306\pi$
$251$	−5.09927	−	2.45568i	−0.321863	−	0.155001i	−0.587838	+	0.808979i	$0.700021\pi$
$252$	−7.91606	−	0.579596i	−0.498665	−	0.0365111i
$253$	−31.1685	+	15.0100i	−1.95955	+	0.943668i
$254$	−0.0310044	+	0.205701i	−0.00194539	+	0.0129068i
$255$	−0.880020	−	1.94475i	−0.0551090	−	0.121785i
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	−17.6960	+	16.4195i	−1.10385	+	1.02422i	−0.104288	+	0.994547i	$0.533256\pi$
$257$	−17.6960	+	16.4195i	−1.10385	+	1.02422i	−0.999560	+	0.0296733i	$0.990553\pi$
$258$	−1.40008	−	2.56443i	−0.0871653	−	0.159654i
$259$	8.52031	+	23.4410i	0.529426	+	1.45655i
$260$	1.31112	+	1.04558i	0.0813121	+	0.0648443i
$261$	−17.6703	−	4.93074i	−1.09376	−	0.305205i
$262$	2.05155	−	6.65096i	0.126745	−	0.410898i
$263$	−20.1804	−	11.6512i	−1.24438	−	0.718441i	−0.274395	−	0.961617i	$-0.588477\pi$
$263$	−20.1804	−	11.6512i	−1.24438	−	0.718441i	−0.969982	+	0.243176i	$0.921811\pi$
$264$	6.56841	−	2.39869i	0.404258	−	0.147629i
$265$	7.67107	−	1.75087i	0.471230	−	0.107555i
$266$	−1.40112	+	5.49259i	−0.0859083	+	0.336772i
$267$	−17.1111	−	7.19130i	−1.04718	−	0.440100i
$268$	7.31493	−	2.25636i	0.446831	−	0.137829i
$269$	−10.7151	−	27.3016i	−0.653310	−	1.66461i	−0.743545	−	0.668686i	$-0.766857\pi$
$269$	−10.7151	−	27.3016i	−0.653310	−	1.66461i	0.0902356	−	0.995920i	$-0.471238\pi$
$270$	0.515822	−	3.49865i	0.0313919	−	0.212921i
$271$	0.501432	+	1.62560i	0.0304598	+	0.0987484i	0.969526	−	0.244987i	$-0.0787838\pi$
$271$	0.501432	+	1.62560i	0.0304598	+	0.0987484i	−0.939066	+	0.343736i	$0.888308\pi$
$272$	−0.402938	+	1.76538i	−0.0244317	+	0.107042i
$273$	−0.288721	−	11.2878i	−0.0174742	−	0.683167i
$274$	−2.30257	−	10.0882i	−0.139103	−	0.609451i
$275$	15.8622	−	9.15804i	0.956526	−	0.552251i
$276$	9.52784	−	11.3796i	0.573509	−	0.684972i
$277$	29.1066	+	8.97819i	1.74885	+	0.539447i	0.993291	−	0.115639i	$-0.0368915\pi$
$277$	29.1066	+	8.97819i	1.74885	+	0.539447i	0.755554	+	0.655086i	$0.227368\pi$
$278$	−1.28445	−	17.1398i	−0.0770364	−	1.02798i
$279$	−7.92428	−	12.9052i	−0.474414	−	0.772612i
$280$	−1.53610	−	0.939606i	−0.0917995	−	0.0561522i
$281$	18.5604	−	14.8014i	1.10722	−	0.882980i	0.113354	−	0.993555i	$-0.463841\pi$
$281$	18.5604	−	14.8014i	1.10722	−	0.882980i	0.993868	+	0.110575i	$0.0352693\pi$
$282$	−17.0028	+	11.0075i	−1.01250	+	0.655485i
$283$	−3.09682	−	20.5461i	−0.184087	−	1.22134i	−0.869778	−	0.493444i	$-0.835738\pi$
$283$	−3.09682	−	20.5461i	−0.184087	−	1.22134i	0.685691	−	0.727893i	$-0.259500\pi$
$284$	−2.91660	−	4.27787i	−0.173069	−	0.253845i
$285$	−2.39496	−	0.801803i	−0.141865	−	0.0474947i
$286$	4.31616	+	8.96260i	0.255220	+	0.529970i
$287$	−0.947735	−	19.1566i	−0.0559430	−	1.13078i
$288$	−2.14310	+	2.09932i	−0.126283	+	0.123703i
$289$	−11.3369	−	7.72935i	−0.666875	−	0.454667i
$290$	−3.05090	−	2.83082i	−0.179155	−	0.166231i
$291$	−4.12142	+	16.2588i	−0.241602	+	0.953107i
$292$	−4.71005	−	1.84856i	−0.275635	−	0.108179i
$293$	−2.26947			−0.132584			−0.0662920	−	0.997800i	$-0.521117\pi$
$293$	−2.26947			−0.132584			−0.0662920	+	0.997800i	$0.521117\pi$
$294$	1.80950	+	11.9886i	0.105532	+	0.699187i
$295$	−0.00650045			−0.000378471
$296$	8.77533	+	3.44406i	0.510056	+	0.200182i
$297$	11.7615	−	17.3709i	0.682472	−	1.00796i
$298$	7.09692	+	6.58498i	0.411114	+	0.381458i
$299$	17.4449	+	11.8937i	1.00886	+	0.687832i
$300$	−4.58018	+	6.38509i	−0.264437	+	0.368643i
$301$	−3.34757	+	2.95166i	−0.192951	+	0.170131i
$302$	−9.73753	−	20.2202i	−0.560332	−	1.16354i
$303$	9.31918	−	27.8360i	0.535373	−	1.59914i
$304$	1.20690	+	1.77020i	0.0692207	+	0.101528i
$305$	0.420696	+	2.79113i	0.0240890	+	0.159820i
$306$	2.12086	+	5.00125i	0.121241	+	0.285902i
$307$	−2.45690	+	1.95931i	−0.140222	+	0.111824i	−0.691089	−	0.722770i	$-0.742869\pi$
$307$	−2.45690	+	1.95931i	−0.140222	+	0.111824i	0.550867	+	0.834593i	$0.314297\pi$
$308$	−5.79132	−	8.97526i	−0.329991	−	0.511413i
$309$	8.65330	−	7.65312i	0.492269	−	0.435371i
$310$	−0.256744	−	3.42601i	−0.0145821	−	0.194584i
$311$	−29.4534	−	9.08517i	−1.67015	−	0.515173i	−0.691793	−	0.722096i	$-0.743179\pi$
$311$	−29.4534	−	9.08517i	−1.67015	−	0.515173i	−0.978357	+	0.206923i	$0.933655\pi$
$312$	−3.27225	−	2.73976i	−0.185254	−	0.155108i
$313$	−13.2273	+	7.63676i	−0.747649	+	0.431655i	−0.824844	−	0.565361i	$-0.808737\pi$
$313$	−13.2273	+	7.63676i	−0.747649	+	0.431655i	0.0771948	+	0.997016i	$0.475404\pi$
$314$	2.40530	+	10.5383i	0.135739	+	0.594712i
$315$	−5.38624	+	0.412920i	−0.303480	+	0.0232654i
$316$	−0.683018	+	2.99250i	−0.0384228	+	0.168341i
$317$	7.49810	+	24.3083i	0.421135	+	1.36529i	0.879236	+	0.476387i	$0.158054\pi$
$317$	7.49810	+	24.3083i	0.421135	+	1.36529i	−0.458100	+	0.888900i	$0.651470\pi$
$318$	−19.6229	+	3.98879i	−1.10040	+	0.223680i
$319$	−9.01959	−	22.9815i	−0.505000	−	1.28672i
$320$	−0.650357	+	0.200609i	−0.0363561	+	0.0112144i
$321$	−1.37813	+	3.27913i	−0.0769195	+	0.183023i
$322$	−20.1698	−	10.3515i	−1.12402	−	0.576868i
$323$	3.78231	−	0.863287i	0.210453	−	0.0480346i
$324$	−1.52477	+	8.86990i	−0.0847095	+	0.492772i
$325$	−9.68100	−	5.58933i	−0.537005	−	0.310040i
$326$	−1.67822	+	5.44066i	−0.0929480	+	0.301330i
$327$	−7.35190	−	0.727700i	−0.406561	−	0.0402419i
$328$	−5.66779	−	4.51992i	−0.312952	−	0.249571i
$329$	22.1394	+	21.6129i	1.22059	+	1.19156i
$330$	4.17717	−	2.28058i	0.229946	−	0.125542i
$331$	−1.67318	+	1.55249i	−0.0919663	+	0.0853323i	−0.724816	−	0.688942i	$-0.758075\pi$
$331$	−1.67318	+	1.55249i	−0.0919663	+	0.0853323i	0.632850	+	0.774274i	$0.281885\pi$
$332$	−0.639623	+	0.0964077i	−0.0351039	+	0.00529106i
$333$	27.3914	−	7.03734i	1.50104	−	0.385644i
$334$	−1.10789	+	7.35037i	−0.0606211	+	0.402194i
$335$	4.69402	−	2.26052i	0.256462	−	0.123505i
$336$	3.85107	+	2.48380i	0.210093	+	0.135502i
$337$	−17.6398	−	8.49488i	−0.960902	−	0.462746i	−0.113406	−	0.993549i	$-0.536176\pi$
$337$	−17.6398	−	8.49488i	−0.960902	−	0.462746i	−0.847495	+	0.530803i	$0.821890\pi$
$338$	−3.90308	+	5.72477i	−0.212300	+	0.311386i
$339$	−10.7490	−	14.1590i	−0.583805	−	0.769013i
$340$	−0.0920981	+	1.22896i	−0.00499472	+	0.0666499i
$341$	7.44558	−	18.9710i	0.403201	−	1.02734i
$342$	6.04453	+	2.18535i	0.326851	+	0.118170i
$343$	17.2488	−	6.74376i	0.931349	−	0.364129i
$344$			1.68686i			0.0909495i
$345$	5.25785	−	8.62488i	0.283073	−	0.464348i
$346$	5.86080	+	0.439206i	0.315078	+	0.0236119i
$347$	−18.2146	+	19.6306i	−0.977809	+	1.05383i	0.0207295	+	0.999785i	$0.493401\pi$
$347$	−18.2146	+	19.6306i	−0.977809	+	1.05383i	−0.998539	+	0.0540425i	$0.982789\pi$
$348$	7.59017	+	7.38737i	0.406876	+	0.396004i
$349$	2.56184	−	5.31971i	0.137132	−	0.284758i	−0.821082	−	0.570811i	$-0.806629\pi$
$349$	2.56184	−	5.31971i	0.137132	−	0.284758i	0.958214	+	0.286053i	$0.0923433\pi$
$350$	11.0587	+	4.66727i	0.591110	+	0.249476i
$351$	−12.7705	−	0.915681i	−0.681640	−	0.0488754i
$352$	−3.99214	−	0.601718i	−0.212782	−	0.0320717i
$353$	−10.5609	+	7.20030i	−0.562100	+	0.383234i	−0.810779	−	0.585353i	$-0.800956\pi$
$353$	−10.5609	+	7.20030i	−0.562100	+	0.383234i	0.248679	+	0.968586i	$0.420004\pi$
$354$	0.0165384		0.000394681i	0.000879004		2.09771e-5i
$355$	−2.39679	−	2.58312i	−0.127208	−	0.137098i
$356$	6.68137	+	8.37817i	0.354112	+	0.444042i
$357$	6.73441	−	4.84825i	0.356423	−	0.256596i
$358$	9.32686	−	11.6955i	0.492940	−	0.618127i
$359$	4.43056	−	0.332025i	0.233836	−	0.0175236i	0.0427034	−	0.999088i	$-0.486403\pi$
$359$	4.43056	−	0.332025i	0.233836	−	0.0175236i	0.191133	+	0.981564i	$0.438784\pi$
$360$	−1.22934	+	1.63021i	−0.0647920	+	0.0859198i
$361$	−7.20488	+	12.4792i	−0.379204	+	0.656801i
$362$	7.47769	+	12.9517i	0.393019	+	0.680728i
$363$	9.16667	−	0.467352i	0.481125	−	0.0245296i
$364$	−2.97661	+	5.79990i	−0.156017	+	0.303997i
$365$	−3.35734	−	0.766292i	−0.175731	−	0.0401096i
$366$	−0.900861	−	7.12670i	−0.0470888	−	0.372519i
$367$	23.0497	−	9.04635i	1.20319	−	0.472216i	0.322797	−	0.946468i	$-0.395377\pi$
$367$	23.0497	−	9.04635i	1.20319	−	0.472216i	0.880389	+	0.474253i	$0.157282\pi$
$368$	−7.97651	+	3.13055i	−0.415805	+	0.163191i
$369$	−21.7234	−	1.03743i	−1.13087	−	0.0540064i
$370$	6.25509	+	1.42768i	0.325186	+	0.0742217i
$371$	12.5682	+	27.8862i	0.652506	+	1.44778i
$372$	0.445191	+	8.73199i	0.0230821	+	0.452733i
$373$	−8.32930	−	14.4268i	−0.431275	−	0.746990i	0.565709	−	0.824605i	$-0.308603\pi$
$373$	−8.32930	−	14.4268i	−0.431275	−	0.746990i	−0.996983	+	0.0776156i	$0.975269\pi$
$374$	−3.65528	+	6.33113i	−0.189010	+	0.327375i
$375$	−5.11807	+	10.0096i	−0.264296	+	0.516894i
$376$	11.6615	−	0.873906i	0.601394	−	0.0450682i
$377$	−9.39452	+	11.7804i	−0.483842	+	0.606719i
$378$	13.7287	−	0.723515i	0.706127	−	0.0372136i
$379$	15.9055	+	19.9448i	0.817010	+	1.02450i	0.999150	+	0.0412253i	$0.0131261\pi$
$379$	15.9055	+	19.9448i	0.817010	+	1.02450i	−0.182140	+	0.983273i	$0.558302\pi$
$380$	0.991802	+	1.06891i	0.0508784	+	0.0548338i
$381$	0.00859617	−	0.360206i	0.000440395	−	0.0184539i
$382$	−13.3660	+	9.11282i	−0.683867	+	0.466252i
$383$	27.0885	+	4.08293i	1.38416	+	0.208628i	0.798531	−	0.601954i	$-0.205611\pi$
$383$	27.0885	+	4.08293i	1.38416	+	0.208628i	0.585625	+	0.810582i	$0.300849\pi$
$384$	1.66681	−	0.470899i	0.0850590	−	0.0240304i
$385$	−4.80794	−	5.45283i	−0.245035	−	0.277902i
$386$	3.46836	−	7.20212i	0.176535	−	0.366578i
$387$	2.96290	+	4.10253i	0.150613	+	0.208543i
$388$	6.58673	−	7.09881i	0.334391	−	0.360387i
$389$	−17.9745	−	1.34700i	−0.911344	−	0.0682958i	−0.389200	−	0.921153i	$-0.627248\pi$
$389$	−17.9745	−	1.34700i	−0.911344	−	0.0682958i	−0.522144	+	0.852858i	$0.674868\pi$
$390$	−2.48011	−	1.51191i	−0.125585	−	0.0765586i
$391$			15.5163i			0.784695i
$392$	2.39985	−	6.57577i	0.121211	−	0.332126i
$393$	−2.08065	+	11.8745i	−0.104955	+	0.598988i
$394$	5.59449	−	14.2545i	0.281846	−	0.718132i
$395$	−0.156115	+	2.08321i	−0.00785500	+	0.104818i
$396$	−10.7660	+	5.54861i	−0.541011	+	0.278828i
$397$	15.8431	−	23.2375i	0.795142	−	1.16626i	−0.187776	−	0.982212i	$-0.560128\pi$
$397$	15.8431	−	23.2375i	0.795142	−	1.16626i	0.982917	−	0.184047i	$-0.0589198\pi$
$398$	9.73561	+	4.68842i	0.488002	+	0.235009i
$399$	1.21459	−	9.74268i	0.0608055	−	0.487744i
$400$	4.08751	−	1.96844i	0.204375	−	0.0984220i
$401$	1.20081	−	7.96684i	0.0599655	−	0.397845i	−0.938633	−	0.344918i	$-0.887907\pi$
$401$	1.20081	−	7.96684i	0.0599655	−	0.397845i	0.998598	−	0.0529273i	$-0.0168551\pi$
$402$	−12.0797	+	5.46618i	−0.602481	+	0.272628i
$403$	−12.2993	+	1.85382i	−0.612670	+	0.0923451i
$404$	−12.4237	+	11.5275i	−0.618101	+	0.573514i
$405$	−0.126421	+	6.12404i	−0.00628189	+	0.304306i
$406$	8.44233	−	13.8018i	0.418986	−	0.684971i
$407$	29.7557	+	23.7293i	1.47493	+	1.17622i
$408$	0.308932	−	3.12112i	0.0152944	−	0.154518i
$409$	−11.7984	+	38.2495i	−0.583394	+	1.89132i	−0.154401	+	0.988008i	$0.549345\pi$
$409$	−11.7984	+	38.2495i	−0.583394	+	1.89132i	−0.428993	+	0.903308i	$0.641132\pi$
$410$	−4.27287	−	2.46694i	−0.211022	−	0.121834i
$411$	6.14798	+	16.8352i	0.303257	+	0.830419i
$412$	−6.50236	+	1.48412i	−0.320348	+	0.0731174i
$413$	−0.00499639	−	0.0247711i	−0.000245856	−	0.00121890i
$414$	−13.9006	+	21.6240i	−0.683177	+	1.06276i
$415$	−0.420682	+	0.129763i	−0.0206505	+	0.00636983i
$416$	0.900200	+	2.29367i	0.0441359	+	0.112457i
$417$	5.93019	+	29.1737i	0.290402	+	1.42864i
$418$	2.54955	+	8.26542i	0.124702	+	0.404275i
$419$	−5.32079	+	23.3119i	−0.259938	+	1.13886i	0.661380	+	0.750051i	$0.269971\pi$
$419$	−5.32079	+	23.3119i	−0.259938	+	1.13886i	−0.921318	+	0.388811i	$0.872886\pi$
$420$	2.84369	+	1.28094i	0.138758	+	0.0625032i
$421$	1.92599	+	8.43830i	0.0938669	+	0.411258i	0.999929	−	0.0118863i	$-0.00378362\pi$
$421$	1.92599	+	8.43830i	0.0938669	+	0.411258i	−0.906063	+	0.423144i	$0.860926\pi$
$422$	12.2722	−	7.08539i	0.597404	−	0.344911i
$423$	26.8263	−	22.6082i	1.30434	−	1.09925i
$424$	11.0474	+	3.40766i	0.536508	+	0.165491i
$425$	−0.613919	−	8.19218i	−0.0297795	−	0.397379i
$426$	5.94104	+	6.71747i	0.287844	+	0.325462i
$427$	−10.3127	+	3.74846i	−0.499068	+	0.181401i
$428$	1.60558	−	1.28040i	0.0776085	−	0.0618907i
$429$	−9.36360	−	14.4636i	−0.452079	−	0.698309i
$430$	0.171111	+	1.13525i	0.00825169	+	0.0547464i
$431$	2.95229	+	4.33022i	0.142207	+	0.208579i	0.890734	−	0.454525i	$-0.150191\pi$
$431$	2.95229	+	4.33022i	0.142207	+	0.208579i	−0.748527	+	0.663104i	$0.769239\pi$
$432$	3.22665	−	4.07293i	0.155242	−	0.195959i
$433$	−16.0932	−	33.4179i	−0.773389	−	1.60596i	−0.795312	−	0.606200i	$-0.792693\pi$
$433$	−16.0932	−	33.4179i	−0.773389	−	1.60596i	0.0219228	−	0.999760i	$-0.493021\pi$
$434$	12.8581	−	3.61168i	0.617206	−	0.173366i
$435$	5.85748	+	4.20172i	0.280845	+	0.201457i
$436$	3.52421	+	2.40276i	0.168779	+	0.115072i
$437$	13.4578	+	12.4870i	0.643775	+	0.597336i
$438$	8.49518	+	2.15343i	0.405915	+	0.102895i
$439$	22.5988	+	8.86936i	1.07858	+	0.423312i	0.837075	−	0.547088i	$-0.184264\pi$
$439$	22.5988	+	8.86936i	1.07858	+	0.423312i	0.241505	+	0.970400i	$0.422359\pi$
$440$	−2.74772			−0.130992
$441$	−5.71349	−	20.2078i	−0.272071	−	0.962277i
$442$	4.46177			0.212225
$443$	6.91940	+	2.71566i	0.328751	+	0.129025i	0.523975	−	0.851733i	$-0.324448\pi$
$443$	6.91940	+	2.71566i	0.328751	+	0.129025i	−0.195225	+	0.980759i	$0.562544\pi$
$444$	−15.8274	−	4.01207i	−0.751136	−	0.190405i
$445$	5.34637	+	4.96071i	0.253442	+	0.235160i
$446$	2.77969	+	1.89516i	0.131622	+	0.0897383i
$447$	−13.6255	−	9.77393i	−0.644466	−	0.462291i
$448$	−1.26433	−	2.32410i	−0.0597341	−	0.109804i
$449$	−9.34456	−	19.4042i	−0.440997	−	0.915740i	−0.996450	−	0.0841917i	$-0.973169\pi$
$449$	−9.34456	−	19.4042i	−0.440997	−	0.915740i	0.555452	−	0.831548i	$-0.312545\pi$
$450$	6.48354	−	11.9669i	0.305637	−	0.564124i
$451$	−16.4869	−	24.1819i	−0.776340	−	1.13868i
$452$	1.52970	+	10.1489i	0.0719509	+	0.477363i
$453$	21.1249	+	32.6308i	0.992533	+	1.53313i
$454$	−6.80241	+	5.42474i	−0.319253	+	0.254596i
$455$	−1.41491	+	4.20523i	−0.0663321	+	0.197144i
$456$	−2.45843	−	2.77972i	−0.115126	−	0.130172i
$457$	1.76211	+	23.5137i	0.0824280	+	1.09993i	0.873053	+	0.487625i	$0.162137\pi$
$457$	1.76211	+	23.5137i	0.0824280	+	1.09993i	−0.790625	+	0.612301i	$0.790244\pi$
$458$	2.56787	+	0.792082i	0.119989	+	0.0370116i
$459$	−4.73077	−	8.13334i	−0.220813	−	0.379632i
$460$	−5.05058	+	2.91595i	−0.235484	+	0.135957i
$461$	7.65132	+	33.5226i	0.356358	+	1.56130i	0.762188	+	0.647356i	$0.224125\pi$
$461$	7.65132	+	33.5226i	0.356358	+	1.56130i	−0.405830	+	0.913949i	$0.633017\pi$
$462$	11.9012	+	14.1649i	0.553695	+	0.659012i
$463$	−0.587861	+	2.57559i	−0.0273202	+	0.119698i	−0.986749	−	0.162252i	$-0.948124\pi$
$463$	−0.587861	+	2.57559i	−0.0273202	+	0.119698i	0.959429	+	0.281950i	$0.0909813\pi$
$464$	−1.80246	−	5.84344i	−0.0836772	−	0.271275i
$465$	1.18536	+	5.83141i	0.0549698	+	0.270425i
$466$	−4.93790	−	12.5816i	−0.228744	−	0.582830i
$467$	−39.9536	+	12.3240i	−1.84883	+	0.570289i	−0.849760	+	0.527170i	$0.823253\pi$
$467$	−39.9536	+	12.3240i	−1.84883	+	0.570289i	−0.999070	+	0.0431188i	$0.986271\pi$
$468$	6.21806	+	3.99716i	0.287430	+	0.184769i
$469$	12.2220	+	16.1499i	0.564361	+	0.745731i
$470$	7.75943	−	1.77104i	0.357916	−	0.0816920i
$471$	−6.42228	−	17.5863i	−0.295923	−	0.810335i
$472$	−0.00827153	−	0.00477557i	−0.000380728	−	0.000219813i
$473$	−2.00736	+	6.50769i	−0.0922984	+	0.299224i
$474$	0.523670	−	5.29060i	0.0240530	−	0.243005i
$475$	−7.59940	−	6.06032i	−0.348685	−	0.278067i
$476$	−4.75396	+	0.593654i	−0.217898	+	0.0272101i
$477$	32.8532	−	11.1166i	1.50424	−	0.508995i
$478$	1.39561	−	1.29494i	0.0638338	−	0.0592291i
$479$	−28.3635	+	4.27511i	−1.29596	+	0.195335i	−0.760563	−	0.649265i	$-0.775077\pi$
$479$	−28.3635	+	4.27511i	−1.29596	+	0.195335i	−0.535399	+	0.844599i	$0.679839\pi$
$480$	1.07398	−	0.485988i	0.0490204	−	0.0221822i
$481$	3.46196	−	22.9686i	0.157852	−	1.04728i
$482$	−27.4368	+	13.2129i	−1.24971	+	0.601831i
$483$	36.9079	+	13.4066i	1.67937	+	0.610023i
$484$	−4.77446	−	2.29926i	−0.217021	−	0.104512i
$485$	3.71274	−	5.44558i	0.168587	−	0.247271i
$486$	0.693464	−	15.5730i	0.0314562	−	0.706407i
$487$	−0.635157	+	8.47559i	−0.0287817	+	0.384066i	0.964148	+	0.265364i	$0.0854922\pi$
$487$	−0.635157	+	8.47559i	−0.0287817	+	0.384066i	−0.992930	+	0.118701i	$0.962127\pi$
$488$	−1.51520	+	3.86066i	−0.0685897	+	0.174764i
$489$	1.70203	−	9.71363i	0.0769684	−	0.439265i
$490$	0.948052	−	4.66888i	0.0428286	−	0.210918i
$491$		−	22.9535i		−	1.03588i	−0.855418	−	0.517938i	$-0.826700\pi$
$491$		−	22.9535i		−	1.03588i	0.855418	−	0.517938i	$-0.173300\pi$
$492$	10.7212	+	6.53579i	0.483349	+	0.294656i
$493$	−11.0422	−	0.827498i	−0.497315	−	0.0372686i
$494$	3.59069	−	3.86984i	0.161553	−	0.174112i
$495$	−6.68259	+	4.82624i	−0.300360	+	0.216923i
$496$	2.19023	−	4.54806i	0.0983443	−	0.204214i
$497$	8.00120	−	11.1188i	0.358903	−	0.498747i
$498$	1.07817	−	0.304600i	0.0483141	−	0.0136494i
$499$	24.6799	+	3.71989i	1.10482	+	0.166525i	0.676027	−	0.736876i	$-0.263700\pi$
$499$	24.6799	+	3.71989i	1.10482	+	0.166525i	0.428795	+	0.903402i	$0.358938\pi$
$500$	5.36286	−	3.65633i	0.239834	−	0.163516i
$501$	0.307169	−	12.8714i	0.0137233	−	0.575050i
$502$	−3.84962	−	4.14890i	−0.171817	−	0.185175i
$503$	5.05658	+	6.34075i	0.225462	+	0.282720i	0.881677	−	0.471854i	$-0.156415\pi$
$503$	5.05658	+	6.34075i	0.225462	+	0.282720i	−0.656215	+	0.754574i	$0.727844\pi$
$504$	−7.15711	−	3.43159i	−0.318803	−	0.152855i
$505$	−7.19172	+	9.01814i	−0.320028	+	0.401302i
$506$	−34.4977	+	2.58525i	−1.53361	+	0.114928i
$507$	5.46346	−	10.6851i	0.242641	−	0.474542i
$508$	−0.104012	+	0.180154i	−0.00461479	+	0.00799306i
$509$	5.09815	+	8.83025i	0.225971	+	0.391394i	0.956610	−	0.291370i	$-0.0941111\pi$
$509$	5.09815	+	8.83025i	0.225971	+	0.391394i	−0.730639	+	0.682764i	$0.760778\pi$
$510$	−0.108689	−	2.13183i	−0.00481282	−	0.0943989i
$511$	0.339555	−	13.3827i	0.0150210	−	0.592017i
$512$	−0.974928	−	0.222521i	−0.0430861	−	0.00983413i
$513$	−10.8615	−	2.44230i	−0.479546	−	0.107830i
$514$	−22.4715	+	8.81940i	−0.991174	+	0.389007i
$515$	−4.22549	+	1.65838i	−0.186197	+	0.0730771i
$516$	−0.366410	−	2.89866i	−0.0161303	−	0.127607i
$517$	46.0284	+	10.5057i	2.02432	+	0.462039i
$518$	−0.632626	+	24.9334i	−0.0277960	+	1.09551i
$519$	−10.1665	+	0.518326i	−0.446258	+	0.0227520i
$520$	0.838492	+	1.45231i	0.0367703	+	0.0636880i
$521$	−10.6900	+	18.5156i	−0.468338	+	0.811185i	−0.999345	−	0.0361825i	$-0.988480\pi$
$521$	−10.6900	+	18.5156i	−0.468338	+	0.811185i	0.531008	+	0.847367i	$0.321814\pi$
$522$	−14.6474	−	11.0456i	−0.641100	−	0.483452i
$523$	−25.3176	+	1.89729i	−1.10706	+	0.0829629i	−0.615691	−	0.787987i	$-0.711123\pi$
$523$	−25.3176	+	1.89729i	−1.10706	+	0.0829629i	−0.491371	+	0.870950i	$0.663504\pi$
$524$	4.33960	−	5.44169i	0.189576	−	0.237721i
$525$	−20.0167	−	5.61803i	−0.873602	−	0.245191i
$526$	−14.5288	−	18.2185i	−0.633484	−	0.794364i
$527$	−6.21731	−	6.70067i	−0.270830	−	0.291886i
$528$	6.99070	+	0.166830i	0.304231	+	0.00726035i
$529$	−41.6632	+	28.4055i	−1.81144	+	1.23502i
$530$	7.78046	+	1.17272i	0.337962	+	0.0509395i
$531$	−0.0285049	+	0.00291415i	−0.00123701	+	0.000126463i
$532$	−3.31094	+	4.60102i	−0.143547	+	0.199479i
$533$	−7.75024	+	16.0935i	−0.335700	+	0.697088i
$534$	−13.3010	−	12.9456i	−0.575589	−	0.560209i
$535$	0.950660	−	1.02457i	0.0411006	−	0.0442959i
$536$	7.63362	+	0.572061i	0.329722	+	0.0247093i
$537$	−13.4866	+	22.1232i	−0.581991	+	0.954687i
$538$		−	29.3290i		−	1.26446i
$539$	17.0834	−	22.5127i	0.735836	−	0.969689i
$540$	1.75837	−	3.06835i	0.0756680	−	0.132041i
$541$	−10.8578	+	27.6652i	−0.466812	+	1.18942i	0.482727	+	0.875771i	$0.339646\pi$
$541$	−10.8578	+	27.6652i	−0.466812	+	1.18942i	−0.949540	+	0.313647i	$0.898449\pi$
$542$	−0.127129	+	1.69643i	−0.00546068	+	0.0728677i
$543$	−15.6628	−	20.6317i	−0.672155	−	0.885391i
$544$	−1.02005	+	1.49614i	−0.0437344	+	0.0641465i
$545$	2.61549	+	1.25956i	0.112035	+	0.0539534i
$546$	3.85512	−	10.6130i	0.164984	−	0.454193i
$547$	15.2556	−	7.34669i	0.652281	−	0.314122i	−0.0783184	−	0.996928i	$-0.524955\pi$
$547$	15.2556	−	7.34669i	0.652281	−	0.314122i	0.730599	+	0.682806i	$0.239241\pi$
$548$	1.54224	−	10.2321i	0.0658811	−	0.437092i
$549$	3.09604	+	12.0507i	0.132136	+	0.514310i
$550$	18.1115	−	2.72987i	0.772277	−	0.116402i
$551$	−9.60410	+	8.91131i	−0.409149	+	0.379634i
$552$	13.0267	−	7.11208i	0.554451	−	0.302710i
$553$	−8.05843	+	1.00630i	−0.342679	+	0.0427922i
$554$	23.8145	+	18.9914i	1.01178	+	0.806867i
$555$	−11.0587	−	1.09460i	−0.469416	−	0.0464634i
$556$	5.06622	−	16.4243i	0.214856	−	0.696545i
$557$	−8.99285	−	5.19202i	−0.381039	−	0.219993i	0.297231	−	0.954806i	$-0.403937\pi$
$557$	−8.99285	−	5.19202i	−0.381039	−	0.219993i	−0.678270	+	0.734812i	$0.737270\pi$
$558$	−2.66172	−	14.9082i	−0.112679	−	0.631112i
$559$	4.05222	−	0.924892i	0.171390	−	0.0391188i
$560$	−1.08664	−	1.43585i	−0.0459188	−	0.0606759i
$561$	4.90594	−	11.6732i	0.207129	−	0.492845i
$562$	22.6850	−	6.99739i	0.956908	−	0.295167i
$563$	−1.72588	−	4.39746i	−0.0727371	−	0.185331i	0.889881	−	0.456192i	$-0.150787\pi$
$563$	−1.72588	−	4.39746i	−0.0727371	−	0.185331i	−0.962619	+	0.270861i	$0.912692\pi$
$564$	−19.8490	+	4.03473i	−0.835792	+	0.169893i
$565$	2.05895	+	6.67495i	0.0866206	+	0.280817i
$566$	4.62357	−	20.2572i	0.194343	−	0.851473i
$567$	−23.4339	+	4.22533i	−0.984130	+	0.177447i
$568$	−1.15211	−	5.04771i	−0.0483414	−	0.211797i
$569$	14.8988	−	8.60182i	0.624590	−	0.360607i	−0.154064	−	0.988061i	$-0.549236\pi$
$569$	14.8988	−	8.60182i	0.624590	−	0.360607i	0.778654	+	0.627454i	$0.215903\pi$
$570$	−1.93647	−	1.62135i	−0.0811099	−	0.0679110i
$571$	4.38679	+	1.35314i	0.183581	+	0.0566273i	0.385183	−	0.922840i	$-0.374138\pi$
$571$	4.38679	+	1.35314i	0.183581	+	0.0566273i	−0.201601	+	0.979468i	$0.564615\pi$
$572$	0.743396	+	9.91992i	0.0310829	+	0.414773i
$573$	20.9885	−	18.5625i	0.876806	−	0.775461i
$574$	6.11648	−	18.1787i	0.255297	−	0.758762i
$575$	30.3938	−	24.2382i	1.26751	−	1.01080i
$576$	−2.76192	+	1.17124i	−0.115080	+	0.0488015i
$577$	−0.772526	−	5.12537i	−0.0321607	−	0.213372i	0.966978	−	0.254858i	$-0.0820288\pi$
$577$	−0.772526	−	5.12537i	−0.0321607	−	0.213372i	−0.999139	+	0.0414862i	$0.986791\pi$
$578$	−7.72935	−	11.3369i	−0.321498	−	0.471552i
$579$	−4.39555	+	13.1293i	−0.182673	+	0.545637i
$580$	−1.80579	−	3.74975i	−0.0749812	−	0.155700i
$581$	−0.817831	−	1.50334i	−0.0339294	−	0.0623692i
$582$	−9.77652	+	13.6292i	−0.405250	+	0.564947i
$583$	38.5642	+	26.2926i	1.59717	+	1.08893i
$584$	−3.70911	−	3.44155i	−0.153484	−	0.142412i
$585$	4.59017	+	2.05932i	0.189780	+	0.0851423i
$586$	−2.11259	−	0.829131i	−0.0872704	−	0.0342511i
$587$	23.7502			0.980275			0.490138	−	0.871645i	$-0.336947\pi$
$587$	23.7502			0.980275			0.490138	+	0.871645i	$0.336947\pi$
$588$	−2.69549	+	11.8209i	−0.111160	+	0.487487i
$589$	−10.8152			−0.445632
$590$	−0.00605110	−	0.00237488i	−0.000249120	−	9.77723e-5i
$591$	−6.51716	+	25.7098i	−0.268080	+	1.05756i
$592$	6.91047	+	6.41197i	0.284018	+	0.263531i
$593$	33.2405	+	22.6630i	1.36502	+	0.930658i	1.00000		0.000340625i	$-0.000108424\pi$
$593$	33.2405	+	22.6630i	1.36502	+	0.930658i	0.365024	+	0.930998i	$0.381061\pi$
$594$	17.2948	−	11.8731i	0.709613	−	0.487160i
$595$	−3.13916	+	0.881754i	−0.128693	+	0.0361484i
$596$	4.20057	+	8.72258i	0.172062	+	0.357291i
$597$	−17.7478	−	5.94176i	−0.726370	−	0.243180i
$598$	11.8937	+	17.4449i	0.486371	+	0.713375i
$599$	−3.22340	−	21.3858i	−0.131704	−	0.873801i	−0.952928	−	0.303195i	$-0.901947\pi$
$599$	−3.22340	−	21.3858i	−0.131704	−	0.873801i	0.821224	−	0.570606i	$-0.193292\pi$
$600$	−6.59631	+	4.27039i	−0.269293	+	0.174338i
$601$	−14.8291	+	11.8258i	−0.604890	+	0.482384i	−0.877394	−	0.479771i	$-0.840720\pi$
$601$	−14.8291	+	11.8258i	−0.604890	+	0.482384i	0.272503	+	0.962155i	$0.412148\pi$
$602$	−4.19453	+	1.52462i	−0.170956	+	0.0621389i
$603$	19.5701	−	12.0168i	0.796958	−	0.489363i
$604$	−1.67715	−	22.3800i	−0.0682421	−	0.910628i
$605$	−3.44641	−	1.06308i	−0.140116	−	0.0432202i
$606$	18.8446	−	22.5072i	0.765510	−	0.914291i
$607$	20.6543	−	11.9247i	0.838330	−	0.484010i	−0.0183661	−	0.999831i	$-0.505846\pi$
$607$	20.6543	−	11.9247i	0.838330	−	0.484010i	0.856696	+	0.515821i	$0.172513\pi$
$608$	0.476748	+	2.08877i	0.0193347	+	0.0847107i
$609$	−11.5092	+	25.5505i	−0.466375	+	1.03536i
$610$	−0.628101	+	2.75189i	−0.0254311	+	0.111421i
$611$	−8.49320	−	27.5343i	−0.343598	−	1.11392i
$612$	0.147089	+	5.43036i	0.00594571	+	0.219509i
$613$	7.47544	+	19.0471i	0.301930	+	0.769306i	0.998649	+	0.0519613i	$0.0165473\pi$
$613$	7.47544	+	19.0471i	0.301930	+	0.769306i	−0.696719	+	0.717344i	$0.745358\pi$
$614$	−3.00288	+	0.926265i	−0.121186	+	0.0373810i
$615$	7.87826	+	3.31101i	0.317682	+	0.133513i
$616$	−2.11196	−	10.4706i	−0.0850932	−	0.421874i
$617$	−23.0892	+	5.26996i	−0.929537	+	0.212161i	−0.660377	−	0.750935i	$-0.729603\pi$
$617$	−23.0892	+	5.26996i	−0.929537	+	0.212161i	−0.269160	+	0.963095i	$0.586746\pi$
$618$	10.8511	−	3.96268i	0.436496	−	0.159402i
$619$	−28.1492	−	16.2520i	−1.13141	−	0.653221i	−0.187122	−	0.982337i	$-0.559916\pi$
$619$	−28.1492	−	16.2520i	−1.13141	−	0.653221i	−0.944290	+	0.329115i	$0.893249\pi$
$620$	1.01267	−	3.28298i	0.0406696	−	0.131848i
$621$	19.1894	−	40.1777i	0.770045	−	1.61227i
$622$	−24.0982	−	19.2177i	−0.966251	−	0.770559i
$623$	−14.7943	+	24.1862i	−0.592720	+	0.968998i
$624$	−2.04510	−	3.74586i	−0.0818695	−	0.149954i
$625$	−13.3902	+	12.4243i	−0.535610	+	0.496973i
$626$	−15.1029	+	2.27640i	−0.603635	+	0.0909833i
$627$	−6.17645	−	13.6493i	−0.246663	−	0.545101i
$628$	−1.61105	+	10.6886i	−0.0642878	+	0.426521i
$629$	15.3798	−	7.40650i	0.613231	−	0.295316i
$630$	−5.16477	−	1.58344i	−0.205769	−	0.0630857i
$631$	35.2092	+	16.9559i	1.40166	+	0.675002i	0.973497	−	0.228702i	$-0.0734480\pi$
$631$	35.2092	+	16.9559i	1.40166	+	0.675002i	0.428159	+	0.903703i	$0.359162\pi$
$632$	−1.72909	+	2.53610i	−0.0687793	+	0.100881i
$633$	−19.5493	+	14.8411i	−0.777015	+	0.589879i
$634$	−1.90101	+	25.3673i	−0.0754989	+	1.00746i
$635$	−0.0517250	+	0.131793i	−0.00205265	+	0.00523006i
$636$	−19.7237	−	3.45601i	−0.782097	−	0.137040i
$637$	−17.1123	−	2.15953i	−0.678013	−	0.0855637i
$638$		−	24.6881i		−	0.977413i
$639$	−11.6681	−	10.2527i	−0.461582	−	0.405589i
$640$	−0.678691	−	0.0508609i	−0.0268276	−	0.00201045i
$641$	5.96631	−	6.43016i	0.235655	−	0.253976i	−0.604141	−	0.796877i	$-0.706484\pi$
$641$	5.96631	−	6.43016i	0.235655	−	0.253976i	0.839797	+	0.542901i	$0.182674\pi$
$642$	−2.48086	+	2.54897i	−0.0979118	+	0.100600i
$643$	−7.12801	+	14.8015i	−0.281101	+	0.583713i	−0.992938	−	0.118632i	$-0.962149\pi$
$643$	−7.12801	+	14.8015i	−0.281101	+	0.583713i	0.711837	+	0.702345i	$0.247863\pi$
$644$	−14.9937	−	17.0048i	−0.590836	−	0.670084i
$645$	−0.540624	−	1.91361i	−0.0212870	−	0.0753484i
$646$	3.83625	+	0.578221i	0.150935	+	0.0227498i
$647$	27.5563	−	18.7876i	1.08335	−	0.738616i	0.116303	−	0.993214i	$-0.462895\pi$
$647$	27.5563	−	18.7876i	1.08335	−	0.738616i	0.967047	+	0.254598i	$0.0819431\pi$
$648$	−4.65991	+	7.69969i	−0.183058	+	0.302473i
$649$	−0.0262276	−	0.0282666i	−0.00102952	−	0.00110956i
$650$	−6.96978	−	8.73982i	−0.273377	−	0.342804i
$651$	−21.3105	+	8.99917i	−0.835223	+	0.352705i
$652$	−3.54991	+	4.45144i	−0.139025	+	0.174332i
$653$	−18.6549	+	1.39799i	−0.730024	+	0.0547077i	−0.434556	−	0.900645i	$-0.643095\pi$
$653$	−18.6549	+	1.39799i	−0.730024	+	0.0547077i	−0.295468	+	0.955353i	$0.595476\pi$
$654$	−6.57783	−	3.36335i	−0.257213	−	0.131517i
$655$	2.36853	−	4.10241i	0.0925461	−	0.160295i
$656$	−3.62469	−	6.27815i	−0.141520	−	0.245121i
$657$	−15.0657	−	1.85514i	−0.587768	−	0.0723758i
$658$	12.7129	+	28.2074i	0.495601	+	1.09964i
$659$	−5.78843	−	1.32117i	−0.225485	−	0.0514655i	0.108285	−	0.994120i	$-0.465464\pi$
$659$	−5.78843	−	1.32117i	−0.225485	−	0.0514655i	−0.333771	+	0.942654i	$0.608321\pi$
$660$	4.72161	−	0.596843i	0.183789	−	0.0232321i
$661$	5.65608	−	2.21985i	0.219996	−	0.0863420i	−0.252783	−	0.967523i	$-0.581346\pi$
$661$	5.65608	−	2.21985i	0.219996	−	0.0863420i	0.472779	+	0.881181i	$0.343251\pi$
$662$	−2.12471	+	0.833886i	−0.0825791	+	0.0324099i
$663$	−7.66701	+	0.969159i	−0.297762	+	0.0376390i
$664$	−0.630630	−	0.143937i	−0.0244732	−	0.00558585i
$665$	−1.76152	+	3.43230i	−0.0683088	+	0.133099i
$666$	28.0689	+	3.45632i	1.08765	+	0.133930i
$667$	−26.1997	−	45.3793i	−1.01446	−	1.75709i
$668$	−3.71670	+	6.43751i	−0.143803	+	0.249075i
$669$	−5.18820	−	2.65281i	−0.200587	−	0.102563i
$670$	5.19540	−	0.389341i	0.200716	−	0.0150416i
$671$	−10.4396	+	13.0908i	−0.403016	+	0.505366i
$672$	2.67743	+	3.71906i	0.103284	+	0.143466i
$673$	−3.93259	−	4.93131i	−0.151590	−	0.190088i	0.700238	−	0.713910i	$-0.253077\pi$
$673$	−3.93259	−	4.93131i	−0.151590	−	0.190088i	−0.851828	+	0.523822i	$0.824506\pi$
$674$	−13.3169	−	14.3522i	−0.512948	−	0.552827i
$675$	−8.54180	+	21.9719i	−0.328774	+	0.845699i
$676$	−5.72477	+	3.90308i	−0.220183	+	0.150118i
$677$	−22.3849	−	3.37399i	−0.860323	−	0.129673i	−0.295961	−	0.955200i	$-0.595640\pi$
$677$	−22.3849	−	3.37399i	−0.860323	−	0.129673i	−0.564362	+	0.825527i	$0.690878\pi$
$678$	−4.83307	−	17.1073i	−0.185613	−	0.657003i
$679$	23.6050	+	9.96241i	0.905877	+	0.382322i
$680$	−0.534723	+	1.11036i	−0.0205057	+	0.0425805i
$681$	10.5108	−	10.7993i	0.402774	−	0.413831i
$682$	13.8618	−	14.9395i	0.530796	−	0.572062i
$683$	0.396902	+	0.0297437i	0.0151870	+	0.00113811i	0.0823214	−	0.996606i	$-0.473767\pi$
$683$	0.396902	+	0.0297437i	0.0151870	+	0.00113811i	−0.0671344	+	0.997744i	$0.521386\pi$
$684$	4.82830	+	4.24260i	0.184615	+	0.162220i
$685$		−	7.04255i		−	0.269082i
$686$	18.5202	+	0.0241082i	0.707106	+	0.000920454i
$687$	−4.58461	−	0.803319i	−0.174914	−	0.0306485i
$688$	−0.616280	+	1.57026i	−0.0234954	+	0.0598654i
$689$	2.12878	−	28.4066i	0.0811002	−	1.08221i
$690$	8.04541	−	6.10776i	0.306284	−	0.232519i
$691$	23.6184	−	34.6418i	0.898485	−	1.31784i	−0.0492533	−	0.998786i	$-0.515684\pi$
$691$	23.6184	−	34.6418i	0.898485	−	1.31784i	0.947738	−	0.319049i	$-0.103363\pi$
$692$	5.29520	+	2.55004i	0.201293	+	0.0969378i
$693$	−23.5276	−	21.7556i	−0.893740	−	0.826426i
$694$	−24.1273	+	11.6191i	−0.915861	+	0.441055i
$695$	1.74349	−	11.5673i	0.0661345	−	0.438774i
$696$	4.36658	+	9.64971i	0.165515	+	0.365771i
$697$	−12.9805	+	1.95649i	−0.491670	+	0.0741073i
$698$	4.32826	−	4.01604i	0.163827	−	0.152009i
$699$	11.2181	+	20.5473i	0.424306	+	0.777170i
$700$	8.58907	+	8.38482i	0.324636	+	0.316916i
$701$	29.7860	+	23.7535i	1.12500	+	0.897158i	0.995532	−	0.0944257i	$-0.0301015\pi$
$701$	29.7860	+	23.7535i	1.12500	+	0.897158i	0.129468	+	0.991584i	$0.458673\pi$
$702$	−11.5532	−	5.51798i	−0.436048	−	0.208263i
$703$	5.95322	−	19.2998i	0.224530	−	0.727908i
$704$	−3.49635	−	2.01862i	−0.131774	−	0.0760795i
$705$	−12.9489	+	4.72877i	−0.487685	+	0.178096i
$706$	−12.4614	+	2.84424i	−0.468992	+	0.107044i
$707$	−39.8929	−	20.4737i	−1.50033	−	0.769994i
$708$	0.0152509	+	0.00640954i	0.000573165	+	0.000240885i
$709$	−34.6499	+	10.6881i	−1.30130	+	0.401399i	−0.866523	−	0.499137i	$-0.833651\pi$
$709$	−34.6499	+	10.6881i	−1.30130	+	0.401399i	−0.434782	+	0.900536i	$0.643174\pi$
$710$	−1.28739	−	3.28021i	−0.0483147	−	0.123104i
$711$	0.249329	+	9.20499i	0.00935059	+	0.345214i
$712$	3.15862	+	10.2400i	0.118374	+	0.383760i
$713$	9.62520	−	42.1708i	0.360467	−	1.57931i
$714$	8.04015	−	2.05275i	0.300895	−	0.0768222i
$715$	1.50655	+	6.60063i	0.0563418	+	0.246849i
$716$	12.9550	−	7.47956i	0.484150	−	0.279524i
$717$	−2.11691	+	2.52834i	−0.0790573	+	0.0944225i
$718$	4.24559	+	1.30959i	0.158444	+	0.0488736i
$719$	−1.75615	−	23.4341i	−0.0654932	−	0.873946i	−0.929112	−	0.369800i	$-0.879426\pi$
$719$	−1.75615	−	23.4341i	−0.0654932	−	0.873946i	0.863618	−	0.504146i	$-0.168193\pi$
$720$	−1.73995	+	1.06839i	−0.0648439	+	0.0398167i
$721$	−9.56736	−	14.8273i	−0.356307	−	0.552197i
$722$	−11.2660	+	8.98434i	−0.419277	+	0.334363i
$723$	44.2768	−	28.6644i	1.64667	−	1.06604i
$724$	2.22898	+	14.7883i	0.0828395	+	0.549604i
$725$	15.6282	+	22.9223i	0.580416	+	0.851314i
$726$	8.70375	+	2.91391i	0.323027	+	0.108145i
$727$	21.9812	+	45.6444i	0.815236	+	1.69286i	0.716333	+	0.697759i	$0.245819\pi$
$727$	21.9812	+	45.6444i	0.815236	+	1.69286i	0.0989036	+	0.995097i	$0.468466\pi$
$728$	−4.88979	+	4.31149i	−0.181228	+	0.159795i
$729$	2.19105	+	26.9110i	0.0811498	+	0.996702i
$730$	−2.84531	−	1.93990i	−0.105310	−	0.0717988i
$731$	2.23914	+	2.07762i	0.0828176	+	0.0768435i
$732$	1.76509	−	6.96318i	0.0652396	−	0.257367i
$733$	11.5043	+	4.51509i	0.424920	+	0.166769i	0.568158	−	0.822920i	$-0.307656\pi$
$733$	11.5043	+	4.51509i	0.424920	+	0.166769i	−0.143238	+	0.989688i	$0.545752\pi$
$734$	24.7614			0.913959
$735$	−0.614965	+	8.22882i	−0.0226833	+	0.303525i
$736$	−8.56885			−0.315852
$737$	28.7688	+	11.2909i	1.05971	+	0.415906i
$738$	−19.8427	−	8.90216i	−0.730420	−	0.327693i
$739$	−13.7172	−	12.7277i	−0.504594	−	0.468195i	0.386321	−	0.922364i	$-0.373746\pi$
$739$	−13.7172	−	12.7277i	−0.504594	−	0.468195i	−0.890915	+	0.454170i	$0.849936\pi$
$740$	5.30111	+	3.61423i	0.194872	+	0.132862i
$741$	−5.32957	+	7.42979i	−0.195787	+	0.272940i
$742$	1.51141	+	30.5502i	0.0554855	+	1.12153i
$743$	−14.6695	−	30.4616i	−0.538173	−	1.11753i	−0.975859	−	0.218399i	$-0.929916\pi$
$743$	−14.6695	−	30.4616i	−0.538173	−	1.11753i	0.437687	−	0.899127i	$-0.355798\pi$
$744$	−2.77574	+	8.29103i	−0.101764	+	0.303964i
$745$	3.71175	+	5.44414i	0.135988	+	0.199458i
$746$	−2.48283	−	16.4725i	−0.0909030	−	0.603102i
$747$	−1.78654	+	0.757611i	−0.0653662	+	0.0277195i
$748$	−5.71563	+	4.55806i	−0.208984	+	0.166659i
$749$	4.63499	+	2.83515i	0.169359	+	0.103594i
$750$	−8.42120	+	7.44784i	−0.307499	+	0.271957i
$751$	0.817204	+	10.9048i	0.0298202	+	0.397923i	0.992064	+	0.125734i	$0.0401285\pi$
$751$	0.817204	+	10.9048i	0.0298202	+	0.397923i	−0.962244	+	0.272189i	$0.912252\pi$
$752$	11.1746	+	3.44691i	0.407497	+	0.125696i
$753$	7.51629	+	6.29318i	0.273909	+	0.229336i
$754$	−13.0490	+	7.53382i	−0.475215	+	0.274366i
$755$	−3.39887	−	14.8914i	−0.123698	−	0.541955i
$756$	13.0440	+	4.34215i	0.474405	+	0.157922i
$757$	5.40129	−	23.6646i	0.196313	−	0.860105i	−0.776794	−	0.629754i	$-0.783156\pi$
$757$	5.40129	−	23.6646i	0.196313	−	0.860105i	0.973108	−	0.230351i	$-0.0739873\pi$
$758$	7.51933	+	24.3771i	0.273114	+	0.885415i
$759$	58.7185	−	11.9358i	2.13135	−	0.433242i
$760$	0.532726	+	1.35736i	0.0193240	+	0.0492368i
$761$	−21.4784	+	6.62522i	−0.778592	+	0.240164i	−0.658482	−	0.752597i	$-0.728801\pi$
$761$	−21.4784	+	6.62522i	−0.778592	+	0.240164i	−0.120110	+	0.992761i	$0.538325\pi$
$762$	0.139600	−	0.332166i	0.00505718	−	0.0120331i
$763$	−2.78942	+	10.9349i	−0.100984	+	0.395870i
$764$	−15.7714	+	3.59972i	−0.570589	+	0.130233i
$765$	0.649831	+	3.63967i	0.0234947	+	0.131593i
$766$	23.7243	+	13.6972i	0.857193	+	0.494901i
$767$	−0.00693677	+	0.0224885i	−0.000250472	+	0.000812011i
$768$	1.72363	+	0.170607i	0.0621961	+	0.00615624i
$769$	12.2175	+	9.74310i	0.440573	+	0.351345i	0.818516	−	0.574484i	$-0.194797\pi$
$769$	12.2175	+	9.74310i	0.440573	+	0.351345i	−0.377943	+	0.925829i	$0.623368\pi$
$770$	−2.48345	−	6.83243i	−0.0894972	−	0.246224i
$771$	36.6988	−	20.0362i	1.32167	−	0.721585i
$772$	5.85984	−	5.43713i	0.210900	−	0.195687i
$773$	−11.7031	+	1.76396i	−0.420932	+	0.0634453i	−0.356093	−	0.934450i	$-0.615891\pi$
$773$	−11.7031	+	1.76396i	−0.420932	+	0.0634453i	−0.0648389	+	0.997896i	$0.520653\pi$
$774$	1.25926	+	4.90141i	0.0452632	+	0.176177i
$775$	−3.41330	+	22.6458i	−0.122609	+	0.813460i
$776$	8.72490	−	4.20169i	0.313206	−	0.150832i
$777$	−4.32880	−	42.9824i	−0.155295	−	1.54199i
$778$	−16.2399	−	7.82071i	−0.582228	−	0.280386i
$779$	−8.74931	+	12.8329i	−0.313477	+	0.459786i
$780$	−1.75631	−	2.31348i	−0.0628859	−	0.0828360i
$781$	1.56207	−	20.8444i	0.0558954	−	0.745872i
$782$	−5.66876	+	14.4438i	−0.202714	+	0.516508i
$783$	27.5690	+	15.7989i	0.985237	+	0.564605i
$784$	4.63635	−	5.24445i	0.165584	−	0.187302i
$785$			7.35677i			0.262574i
$786$	−6.27506	+	10.2935i	−0.223824	+	0.367157i
$787$	−7.51394	−	0.563092i	−0.267843	−	0.0200721i	−0.0598684	−	0.998206i	$-0.519068\pi$
$787$	−7.51394	−	0.563092i	−0.267843	−	0.0200721i	−0.207975	+	0.978134i	$0.566687\pi$
$788$	10.4155	−	11.2253i	0.371038	−	0.399883i
$789$	28.9232	+	28.1504i	1.02969	+	1.00218i
$790$	−0.906406	+	1.88217i	−0.0322485	+	0.0669647i
$791$	−23.8535	+	12.9765i	−0.848132	+	0.461391i
$792$	−12.0489	+	1.23180i	−0.428139	+	0.0437701i
$793$	10.1049	+	1.52307i	0.358836	+	0.0540859i
$794$	23.2375	−	15.8431i	0.824670	−	0.562250i
$795$	−13.6245	−	0.325143i	−0.483211	−	0.0115316i
$796$	7.34975	+	7.92114i	0.260505	+	0.280758i
$797$	−22.7355	−	28.5095i	−0.805334	−	1.00986i	−0.999582	−	0.0289049i	$-0.990798\pi$
$797$	−22.7355	−	28.5095i	−0.805334	−	1.00986i	0.194248	−	0.980952i	$-0.437773\pi$
$798$	4.69003	−	8.62546i	0.166025	−	0.305338i
$799$	13.2028	−	16.5558i	0.467081	−	0.585701i
$800$	4.52411	−	0.339035i	0.159951	−	0.0119867i
$801$	25.6680	+	19.3562i	0.906935	+	0.683918i
$802$	4.02842	−	6.97742i	0.142248	−	0.246381i
$803$	−10.2138	−	17.6909i	−0.360439	−	0.624298i
$804$	−13.2417	+	0.675113i	−0.466999	+	0.0238094i
$805$	−11.8156	−	9.92320i	−0.416445	−	0.349747i
$806$	−12.1263	−	2.76776i	−0.427132	−	0.0974901i
$807$	6.37066	+	50.3982i	0.224258	+	1.77410i
$808$	−15.7763	+	6.19176i	−0.555010	+	0.217825i
$809$	−0.113012	+	0.0443541i	−0.00397330	+	0.00155941i	−0.367327	−	0.930092i	$-0.619727\pi$
$809$	−0.113012	+	0.0443541i	−0.00397330	+	0.00155941i	0.363354	+	0.931651i	$0.381632\pi$
$810$	−2.35505	+	5.65452i	−0.0827479	+	0.198680i
$811$	−44.7444	−	10.2126i	−1.57119	−	0.358614i	−0.653820	−	0.756650i	$-0.726835\pi$
$811$	−44.7444	−	10.2126i	−1.57119	−	0.358614i	−0.917370	+	0.398036i	$0.869692\pi$
$812$	12.9011	−	9.76340i	0.452740	−	0.342628i
$813$	−0.150031	−	2.94271i	−0.00526181	−	0.103205i
$814$	19.0295	+	32.9600i	0.666982	+	1.15525i
$815$	−1.93752	+	3.35588i	−0.0678683	+	0.117551i
$816$	1.42785	−	2.79250i	0.0499848	−	0.0977572i
$817$	3.60397	−	0.270080i	0.126087	−	0.00944891i
$818$	−24.9569	+	31.2950i	−0.872599	+	1.09420i
$819$	−4.31927	+	19.0745i	−0.150927	+	0.666516i
$820$	−3.07623	−	3.85747i	−0.107427	−	0.134709i
$821$	−16.9347	−	18.2513i	−0.591025	−	0.636974i	0.364738	−	0.931110i	$-0.381158\pi$
$821$	−16.9347	−	18.2513i	−0.591025	−	0.636974i	−0.955763	+	0.294136i	$0.904968\pi$
$822$	−0.427595	+	17.9175i	−0.0149141	+	0.624946i
$823$	40.7118	−	27.7569i	1.41913	−	0.967543i	0.420955	−	0.907082i	$-0.361695\pi$
$823$	40.7118	−	27.7569i	1.41913	−	0.967543i	0.998171	−	0.0604615i	$-0.0192572\pi$
$824$	−6.59508	−	0.994049i	−0.229751	−	0.0346293i
$825$	−30.5294	+	8.62502i	−1.06290	+	0.300285i
$826$	0.00439888	−	0.0248841i	0.000153057	−	0.000865830i
$827$	−12.5799	+	26.1224i	−0.437446	+	0.908366i	0.559392	+	0.828903i	$0.311035\pi$
$827$	−12.5799	+	26.1224i	−0.437446	+	0.908366i	−0.996838	+	0.0794628i	$0.974680\pi$
$828$	−20.8399	+	15.0508i	−0.724235	+	0.523051i
$829$	35.4328	−	38.1875i	1.23063	−	1.32631i	0.302917	−	0.953017i	$-0.402039\pi$
$829$	35.4328	−	38.1875i	1.23063	−	1.32631i	0.927715	−	0.373289i	$-0.121770\pi$
$830$	−0.439010	−	0.0328993i	−0.0152383	−	0.00114195i
$831$	−45.0474	−	27.4615i	−1.56268	−	0.952630i
$832$			2.46400i			0.0854238i
$833$	−5.77291	−	11.2846i	−0.200019	−	0.390988i
$834$	−5.13809	+	29.3236i	−0.177918	+	1.01539i
$835$	−1.84831	+	4.70941i	−0.0639633	+	0.162976i
$836$	−0.646393	+	8.62552i	−0.0223560	+	0.298320i
$837$	7.81209	+	25.0397i	0.270025	+	0.865497i
$838$	−13.4698	+	19.7565i	−0.465306	+	0.682479i
$839$	29.1203	+	14.0236i	1.00534	+	0.484148i	0.862748	−	0.505633i	$-0.168741\pi$
$839$	29.1203	+	14.0236i	1.00534	+	0.484148i	0.142595	+	0.989781i	$0.454455\pi$
$840$	2.17914	+	2.23131i	0.0751875	+	0.0769874i
$841$	7.56329	−	3.64229i	0.260803	−	0.125596i
$842$	−1.29001	+	8.55863i	−0.0444566	+	0.294950i
$843$	−37.4614	+	16.9516i	−1.29024	+	0.583845i
$844$	14.0125	−	2.11204i	0.482330	−	0.0726995i
$845$	−3.45681	+	3.20745i	−0.118918	+	0.110340i
$846$	33.2316	−	11.2447i	1.14253	−	0.386599i
$847$	1.40204	−	13.9502i	0.0481748	−	0.479335i
$848$	9.03875	+	7.20816i	0.310392	+	0.247529i
$849$	−3.54489	+	35.8138i	−0.121660	+	1.22913i
$850$	2.42146	−	7.85018i	0.0830554	−	0.269259i
$851$	69.9561	+	40.3892i	2.39806	+	1.38452i
$852$	3.07619	+	8.42362i	0.105388	+	0.288588i
$853$	13.7805	−	3.14532i	0.471836	−	0.107694i	0.0200105	−	0.999800i	$-0.493630\pi$
$853$	13.7805	−	3.14532i	0.471836	−	0.107694i	0.451826	+	0.892106i	$0.350773\pi$
$854$	−10.9693	−	0.278320i	−0.375362	−	0.00952393i
$855$	3.67977	+	2.36547i	0.125845	+	0.0808973i
$856$	1.96237	−	0.605312i	0.0670725	−	0.0206891i
$857$	2.35624	+	6.00360i	0.0804876	+	0.205079i	0.965453	−	0.260578i	$-0.0839132\pi$
$857$	2.35624	+	6.00360i	0.0804876	+	0.205079i	−0.884965	+	0.465657i	$0.845818\pi$
$858$	−3.43218	−	16.8847i	−0.117173	−	0.576434i
$859$	−9.60240	−	31.1302i	−0.327630	−	1.06215i	−0.958220	−	0.286033i	$-0.907663\pi$
$859$	−9.60240	−	31.1302i	−0.327630	−	1.06215i	0.630590	−	0.776116i	$-0.282813\pi$
$860$	−0.255469	+	1.11928i	−0.00871143	+	0.0381673i
$861$	−6.56176	+	32.5664i	−0.223624	+	1.10986i
$862$	1.16620	+	5.10948i	0.0397211	+	0.174029i
$863$	−17.7306	+	10.2368i	−0.603556	+	0.348463i	−0.770439	−	0.637514i	$-0.779963\pi$
$863$	−17.7306	+	10.2368i	−0.603556	+	0.348463i	0.166883	+	0.985977i	$0.446630\pi$
$864$	4.49161	−	2.61255i	0.152808	−	0.0888808i
$865$	3.82230	+	1.17902i	0.129962	+	0.0400880i
$866$	−2.77182	−	36.9873i	−0.0941901	−	1.25688i
$867$	15.7445	+	17.8021i	0.534710	+	0.604591i
$868$	13.2887	+	1.33556i	0.451049	+	0.0453319i
$869$	−9.68854	+	7.72635i	−0.328661	+	0.262099i
$870$	3.91752	+	6.05125i	0.132816	+	0.205156i
$871$	−2.81123	−	18.6513i	−0.0952550	−	0.631975i
$872$	2.40276	+	3.52421i	0.0813678	+	0.119345i
$873$	13.8393	−	25.5436i	0.468390	−	0.864520i
$874$	7.96550	+	16.5405i	0.269437	+	0.559492i
$875$	13.9388	+	10.0305i	0.471219	+	0.339094i
$876$	7.12120	+	5.10821i	0.240603	+	0.172591i
$877$	−9.47374	−	6.45909i	−0.319905	−	0.218108i	0.392711	−	0.919662i	$-0.371537\pi$
$877$	−9.47374	−	6.45909i	−0.319905	−	0.218108i	−0.712616	+	0.701554i	$0.752490\pi$
$878$	17.7963	+	16.5125i	0.600595	+	0.557270i
$879$	3.81033	+	0.965875i	0.128519	+	0.0325782i
$880$	−2.55778	−	1.00385i	−0.0862227	−	0.0338399i
$881$	−33.0838			−1.11462			−0.557312	−	0.830303i	$-0.688167\pi$
$881$	−33.0838			−1.11462			−0.557312	+	0.830303i	$0.688167\pi$
$882$	2.06421	−	20.8983i	0.0695054	−	0.703682i
$883$	−2.48650			−0.0836774			−0.0418387	−	0.999124i	$-0.513322\pi$
$883$	−2.48650			−0.0836774			−0.0418387	+	0.999124i	$0.513322\pi$
$884$	4.15335	+	1.63007i	0.139692	+	0.0548252i
$885$	0.0109139	+	0.00276656i	0.000366868	+	9.29968e-5i
$886$	5.44894	+	5.05588i	0.183061	+	0.169856i
$887$	28.0916	+	19.1525i	0.943223	+	0.643079i	0.934150	−	0.356880i	$-0.116159\pi$
$887$	28.0916	+	19.1525i	0.943223	+	0.643079i	0.00907321	+	0.999959i	$0.497112\pi$
$888$	−13.2676	−	9.51714i	−0.445230	−	0.319374i
$889$	−0.541978	−	0.0958078i	−0.0181773	−	0.00321329i
$890$	3.16445	+	6.57104i	0.106072	+	0.220262i
$891$	−27.1399	+	24.1592i	−0.909221	+	0.809362i
$892$	1.89516	+	2.77969i	0.0634546	+	0.0930707i
$893$	−3.73419	−	24.7747i	−0.124960	−	0.829054i
$894$	−9.11283	−	14.0763i	−0.304779	−	0.470780i
$895$	7.95990	−	6.34781i	0.266070	−	0.212184i
$896$	−0.327843	−	2.62536i	−0.0109525	−	0.0877071i
$897$	−24.2272	−	27.3934i	−0.808922	−	0.914640i
$898$	−1.60946	−	21.4768i	−0.0537085	−	0.716690i
$899$	29.4975	+	9.09877i	0.983796	+	0.303461i
$900$	10.4073	−	8.77094i	0.346912	−	0.292365i
$901$	18.1298	−	10.4672i	0.603991	−	0.348714i
$902$	−6.51262	−	28.5336i	−0.216846	−	0.950067i
$903$	6.87661	−	3.53098i	0.228839	−	0.117504i
$904$	−2.28385	+	10.0062i	−0.0759596	+	0.332801i
$905$	3.00018	+	9.72634i	0.0997293	+	0.323315i
$906$	7.74321	+	38.0929i	0.257251	+	1.26555i
$907$	−3.10636	−	7.91488i	−0.103145	−	0.262809i	0.869980	−	0.493087i	$-0.164132\pi$
$907$	−3.10636	−	7.91488i	−0.103145	−	0.262809i	−0.973125	+	0.230278i	$0.926036\pi$
$908$	−8.31407	+	2.56455i	−0.275912	+	0.0851076i
$909$	−27.4933	+	42.7691i	−0.911895	+	1.41856i
$910$	−2.85345	+	3.39761i	−0.0945909	+	0.112630i
$911$	−43.3160	+	9.88659i	−1.43512	+	0.327557i	−0.868200	−	0.496214i	$-0.834723\pi$
$911$	−43.3160	+	9.88659i	−1.43512	+	0.327557i	−0.566922	+	0.823771i	$0.691866\pi$
$912$	−1.27294	−	3.48573i	−0.0421513	−	0.115424i
$913$	−2.26161	−	1.30574i	−0.0748482	−	0.0432136i
$914$	−6.95023	+	22.5321i	−0.229893	+	0.745295i
$915$	0.481565	−	4.86522i	0.0159200	−	0.160839i
$916$	2.10098	+	1.67548i	0.0694183	+	0.0553593i
$917$	17.4534	+	5.87248i	0.576364	+	0.193926i
$918$	−1.43230	−	9.29946i	−0.0472731	−	0.306928i
$919$	−22.7505	+	21.1094i	−0.750470	+	0.696335i	−0.959542	−	0.281566i	$-0.909146\pi$
$919$	−22.7505	+	21.1094i	−0.750470	+	0.696335i	0.209072	+	0.977900i	$0.432956\pi$
$920$	−5.76677	+	0.869201i	−0.190125	+	0.0286567i
$921$	4.95887	−	2.24394i	0.163400	−	0.0739403i
$922$	−5.12478	+	34.0007i	−0.168776	+	1.11975i
$923$	−11.4940	+	5.53524i	−0.378331	+	0.182195i
$924$	5.90351	+	17.5338i	0.194211	+	0.576818i
$925$	−38.5329	−	18.5564i	−1.26695	−	0.610132i
$926$	−1.48819	+	2.18278i	−0.0489050	+	0.0717305i
$927$	−17.7856	+	9.16639i	−0.584155	+	0.301064i
$928$	0.456983	−	6.09802i	0.0150012	−	0.200177i
$929$	15.4365	−	39.3315i	0.506455	−	1.29043i	−0.417761	−	0.908557i	$-0.637185\pi$
$929$	15.4365	−	39.3315i	0.506455	−	1.29043i	0.924216	−	0.381869i	$-0.124720\pi$
$930$	−1.02703	+	5.86136i	−0.0336777	+	0.192202i
$931$	−14.4333	−	4.07443i	−0.473033	−	0.133534i
$932$		−	13.5159i		−	0.442727i
$933$	45.5842	+	27.7888i	1.49236	+	0.909763i
$934$	−41.6942	−	3.12455i	−1.36428	−	0.102238i
$935$	−3.38422	+	3.64732i	−0.110676	+	0.119280i
$936$	4.32791	+	5.99257i	0.141462	+	0.195873i
$937$	20.2680	−	42.0869i	0.662127	−	1.37492i	−0.251297	−	0.967910i	$-0.580857\pi$
$937$	20.2680	−	42.0869i	0.662127	−	1.37492i	0.913424	−	0.407010i	$-0.133429\pi$
$938$	5.47695	+	19.4987i	0.178829	+	0.636655i
$939$	25.4581	−	7.19228i	0.830792	−	0.234711i
$940$	7.87008	+	1.18622i	0.256694	+	0.0386904i
$941$	23.9532	−	16.3310i	0.780852	−	0.532376i	−0.106035	−	0.994362i	$-0.533816\pi$
$941$	23.9532	−	16.3310i	0.780852	−	0.532376i	0.886887	+	0.461986i	$0.152863\pi$
$942$	0.446673	−	18.7170i	0.0145534	−	0.609832i
$943$	−42.2515	−	45.5363i	−1.37590	−	1.48287i
$944$	−0.00595504	−	0.00746738i	−0.000193820	−	0.000243043i
$945$	9.21897	+	1.59908i	0.299893	+	0.0520182i
$946$	−4.24612	+	5.32447i	−0.138053	+	0.173113i
$947$	−13.1659	+	0.986651i	−0.427836	+	0.0320618i	−0.286908	−	0.957958i	$-0.592627\pi$
$947$	−13.1659	+	0.986651i	−0.427836	+	0.0320618i	−0.140927	+	0.990020i	$0.545008\pi$
$948$	2.42034	−	4.73356i	0.0786091	−	0.153739i
$949$	−6.23370	+	10.7971i	−0.202354	+	0.350488i
$950$	−4.86000	−	8.41777i	−0.157679	−	0.273108i
$951$	−2.24347	−	44.0035i	−0.0727494	−	1.42691i
$952$	−4.64223	−	1.18420i	−0.150455	−	0.0383802i
$953$	−29.1722	−	6.65836i	−0.944979	−	0.215685i	−0.277847	−	0.960625i	$-0.589621\pi$
$953$	−29.1722	−	6.65836i	−0.944979	−	0.215685i	−0.667132	+	0.744940i	$0.732478\pi$
$954$	34.6435	+	1.65445i	1.12163	+	0.0535647i
$955$	−10.2489	+	4.02239i	−0.331646	+	0.130161i
$956$	1.77223	−	0.695550i	0.0573181	−	0.0224957i
$957$	5.36261	+	42.4235i	0.173349	+	1.37136i
$958$	−27.9647	−	6.38276i	−0.903499	−	0.206218i
$959$	26.8368	−	5.41306i	0.866606	−	0.174797i
$960$	1.17729	−	0.0600230i	0.0379970	−	0.00193724i
$961$	−2.75902	−	4.77875i	−0.0890005	−	0.154153i
$962$	11.6140	−	20.1161i	0.374452	−	0.648569i
$963$	3.70938	−	4.91897i	0.119533	−	0.158512i
$964$	−30.3675	+	2.27573i	−0.978070	+	0.0732962i
$965$	3.39210	−	4.25356i	0.109196	−	0.136927i
$966$	29.4586	+	25.9638i	0.947813	+	0.835373i
$967$	11.4884	+	14.4061i	0.369444	+	0.463267i	0.931452	−	0.363864i	$-0.118543\pi$
$967$	11.4884	+	14.4061i	0.369444	+	0.463267i	−0.562009	+	0.827131i	$0.689971\pi$
$968$	−3.60441	−	3.88463i	−0.115850	−	0.124857i
$969$	−6.71771	−	0.160315i	−0.215804	−	0.00515007i
$970$	5.44558	−	3.71274i	0.174847	−	0.119209i
$971$	−11.3400	−	1.70923i	−0.363918	−	0.0548519i	−0.0354620	−	0.999371i	$-0.511290\pi$
$971$	−11.3400	−	1.70923i	−0.363918	−	0.0548519i	−0.328456	+	0.944519i	$0.606528\pi$
$972$	6.33499	−	14.2432i	0.203195	−	0.456850i
$973$	45.4194	−	2.24703i	1.45608	−	0.0720364i
$974$	−3.68773	+	7.65765i	−0.118163	+	0.245367i
$975$	13.8751	+	13.5044i	0.444359	+	0.432486i
$976$	−2.82091	+	3.04022i	−0.0902952	+	0.0973151i
$977$	29.0349	+	2.17586i	0.928908	+	0.0696121i	0.530584	−	0.847633i	$-0.321973\pi$
$977$	29.0349	+	2.17586i	0.928908	+	0.0696121i	0.398325	+	0.917245i	$0.369592\pi$
$978$	5.13316	−	8.42034i	0.164140	−	0.269253i
$979$			43.2633i			1.38270i
$980$	2.58825	−	3.99977i	0.0826786	−	0.127768i
$981$	12.0338	+	4.35070i	0.384208	+	0.138907i
$982$	8.38585	−	21.3668i	0.267603	−	0.681842i
$983$	3.03230	−	40.4632i	0.0967152	−	1.29057i	−0.711918	−	0.702262i	$-0.752173\pi$
$983$	3.03230	−	40.4632i	0.0967152	−	1.29057i	0.808634	−	0.588313i	$-0.200208\pi$
$984$	7.59229	+	10.0009i	0.242033	+	0.318817i
$985$	5.87091	−	8.61104i	0.187063	−	0.274371i
$986$	−9.97657	−	4.80446i	−0.317719	−	0.153005i
$987$	−27.9726	−	45.7095i	−0.890378	−	1.45495i
$988$	4.75629	−	2.29051i	0.151318	−	0.0728707i
$989$	−2.15433	+	14.2930i	−0.0685036	+	0.454491i
$990$	−7.98387	+	2.05120i	−0.253744	+	0.0651914i
$991$	−11.9874	+	1.80681i	−0.380791	+	0.0573951i	−0.336649	−	0.941630i	$-0.609294\pi$
$991$	−11.9874	+	1.80681i	−0.380791	+	0.0573951i	−0.0441423	+	0.999025i	$0.514056\pi$
$992$	3.70042	−	3.43349i	0.117489	−	0.109013i
$993$	3.46991	−	1.89445i	0.110114	−	0.0601184i
$994$	11.5103	−	7.42705i	0.365084	−	0.235572i
$995$	5.74983	+	4.58533i	0.182282	+	0.145365i
$996$	1.11493	+	0.110357i	0.0353278	+	0.00349679i
$997$	−7.72539	+	25.0451i	−0.244666	+	0.793187i	0.747054	+	0.664764i	$0.231468\pi$
$997$	−7.72539	+	25.0451i	−0.244666	+	0.793187i	−0.991719	+	0.128423i	$0.959008\pi$
$998$	21.6148	+	12.4793i	0.684205	+	0.395026i
$999$	−48.9838	+	0.157712i	−1.54978	+	0.00498979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.p.a.101.10	yes	216
3.2	odd	2	inner	294.2.p.a.101.1	✓	216
49.33	odd	42	inner	294.2.p.a.131.1	yes	216
147.131	even	42	inner	294.2.p.a.131.10	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.p.a.101.1	✓	216	3.2	odd	2	inner
294.2.p.a.101.10	yes	216	1.1	even	1	trivial
294.2.p.a.131.1	yes	216	49.33	odd	42	inner
294.2.p.a.131.10	yes	216	147.131	even	42	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.p (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.930874 + 0.365341i) q^{2} +(-1.67895 - 0.425595i) q^{3} +(0.733052 + 0.680173i) q^{4} +(0.562333 + 0.383392i) q^{5} +(-1.40740 - 1.00956i) q^{6} +(-1.02876 + 2.43755i) q^{7} +(0.433884 + 0.900969i) q^{8} +(2.63774 + 1.42910i) q^{9} +O(q^{10})\)	\(q+(0.930874 + 0.365341i) q^{2} +(-1.67895 - 0.425595i) q^{3} +(0.733052 + 0.680173i) q^{4} +(0.562333 + 0.383392i) q^{5} +(-1.40740 - 1.00956i) q^{6} +(-1.02876 + 2.43755i) q^{7} +(0.433884 + 0.900969i) q^{8} +(2.63774 + 1.42910i) q^{9} +(0.383392 + 0.562333i) q^{10} +(0.601718 + 3.99214i) q^{11} +(-0.941279 - 1.45396i) q^{12} +(1.92643 - 1.53628i) q^{13} +(-1.84818 + 1.89320i) q^{14} +(-0.780959 - 0.883022i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(1.73034 + 0.533738i) q^{17} +(1.93329 + 2.29399i) q^{18} +(1.85545 - 1.07124i) q^{19} +(0.151446 + 0.663530i) q^{20} +(2.76464 - 3.65469i) q^{21} +(-0.898369 + 3.93601i) q^{22} +(2.52571 + 8.18816i) q^{23} +(-0.345021 - 1.69734i) q^{24} +(-1.65748 - 4.22318i) q^{25} +(2.35453 - 0.726277i) q^{26} +(-3.82041 - 3.52200i) q^{27} +(-2.41209 + 1.08712i) q^{28} +(-5.96180 + 1.36074i) q^{29} +(-0.404370 - 1.10730i) q^{30} +(-4.37167 - 2.52398i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(0.688780 - 6.95869i) q^{33} +(1.41573 + 1.12901i) q^{34} +(-1.51304 + 0.976297i) q^{35} +(0.961562 + 2.84172i) q^{36} +(6.91047 - 6.41197i) q^{37} +(2.11855 - 0.319321i) q^{38} +(-3.88821 + 1.75945i) q^{39} +(-0.101437 + 0.672993i) q^{40} +(-6.53147 + 3.14539i) q^{41} +(3.90874 - 2.39202i) q^{42} +(1.51981 + 0.731902i) q^{43} +(-2.27425 + 3.33572i) q^{44} +(0.935381 + 1.81492i) q^{45} +(-0.640351 + 8.54489i) q^{46} +(4.27236 - 10.8858i) q^{47} +(0.298937 - 1.70606i) q^{48} +(-4.88331 - 5.01531i) q^{49} -4.53679i q^{50} +(-2.67799 - 1.63254i) q^{51} +(2.45711 + 0.184135i) q^{52} +(7.86348 - 8.47481i) q^{53} +(-2.26959 - 4.67429i) q^{54} +(-1.19219 + 2.47561i) q^{55} +(-2.64252 + 0.130733i) q^{56} +(-3.57111 + 1.00889i) q^{57} +(-6.04681 - 0.911410i) q^{58} +(-0.00789152 + 0.00538035i) q^{59} +(0.0281241 - 1.17849i) q^{60} +(2.82091 + 3.04022i) q^{61} +(-3.14736 - 3.94666i) q^{62} +(-6.19711 + 4.95942i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(1.67229 - 0.125321i) q^{65} +(3.18346 - 6.22602i) q^{66} +(3.82751 - 6.62945i) q^{67} +(0.905393 + 1.56819i) q^{68} +(-0.755705 - 14.8224i) q^{69} +(-1.76513 + 0.356033i) q^{70} +(-5.04771 - 1.15211i) q^{71} +(-0.143106 + 2.99658i) q^{72} +(-4.71005 + 1.84856i) q^{73} +(8.77533 - 3.44406i) q^{74} +(0.985454 + 7.79592i) q^{75} +(2.08877 + 0.476748i) q^{76} +(-10.3501 - 2.64023i) q^{77} +(-4.26224 + 0.217305i) q^{78} +(1.53473 + 2.65823i) q^{79} +(-0.340297 + 0.589412i) q^{80} +(4.91533 + 7.53920i) q^{81} +(-7.22911 + 0.541747i) q^{82} +(-0.403303 + 0.505726i) q^{83} +(4.51245 - 0.798641i) q^{84} +(0.768395 + 0.963537i) q^{85} +(1.14736 + 1.23656i) q^{86} +(10.5887 + 0.252694i) q^{87} +(-3.33572 + 2.27425i) q^{88} +(10.5964 + 1.59715i) q^{89} +(0.207656 + 2.03120i) q^{90} +(1.76292 + 6.27624i) q^{91} +(-3.71788 + 7.72026i) q^{92} +(6.26561 + 6.09820i) q^{93} +(7.95405 - 8.57243i) q^{94} +(1.45408 + 0.108969i) q^{95} +(0.901566 - 1.47891i) q^{96} -9.68391i q^{97} +(-2.71344 - 6.45269i) q^{98} +(-4.11801 + 11.3901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9	\( 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9} + 6 q^{10} - 12 q^{15} + 18 q^{16} - 4 q^{18} - 12 q^{19} + 10 q^{22} - 6 q^{24} + 16 q^{25} - 42 q^{27} + 2 q^{28} + 4 q^{30} + 6 q^{31} + 18 q^{33} - 10 q^{36} - 36 q^{37} + 4 q^{39} - 22 q^{40} + 20 q^{42} + 40 q^{43} - 14 q^{45} - 156 q^{46} - 134 q^{49} - 12 q^{51} + 16 q^{52} - 18 q^{54} - 322 q^{55} - 34 q^{57} - 164 q^{58} - 6 q^{60} + 56 q^{61} - 24 q^{63} + 36 q^{64} - 28 q^{69} - 4 q^{70} + 4 q^{72} - 24 q^{73} + 84 q^{75} + 16 q^{78} + 22 q^{79} - 52 q^{81} + 24 q^{82} + 42 q^{84} + 32 q^{85} - 94 q^{87} - 2 q^{88} + 42 q^{90} - 100 q^{91} - 266 q^{93} - 88 q^{94} - 6 q^{96} + 224 q^{99}+O(q^{100}) \) 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9 + 6 * q^10 - 12 * q^15 + 18 * q^16 - 4 * q^18 - 12 * q^19 + 10 * q^22 - 6 * q^24 + 16 * q^25 - 42 * q^27 + 2 * q^28 + 4 * q^30 + 6 * q^31 + 18 * q^33 - 10 * q^36 - 36 * q^37 + 4 * q^39 - 22 * q^40 + 20 * q^42 + 40 * q^43 - 14 * q^45 - 156 * q^46 - 134 * q^49 - 12 * q^51 + 16 * q^52 - 18 * q^54 - 322 * q^55 - 34 * q^57 - 164 * q^58 - 6 * q^60 + 56 * q^61 - 24 * q^63 + 36 * q^64 - 28 * q^69 - 4 * q^70 + 4 * q^72 - 24 * q^73 + 84 * q^75 + 16 * q^78 + 22 * q^79 - 52 * q^81 + 24 * q^82 + 42 * q^84 + 32 * q^85 - 94 * q^87 - 2 * q^88 + 42 * q^90 - 100 * q^91 - 266 * q^93 - 88 * q^94 - 6 * q^96 + 224 * q^99

Introduction

L-functions

Modular forms

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