LMFDB - Embedded newform 294.2.p.a.101.1

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			101.1
Character	$\chi$	$=$	294.101
Dual form			294.2.p.a.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.930874 - 0.365341i) q^{2} +(-1.72363 + 0.170607i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.562333 - 0.383392i) q^{5} +(1.66681 + 0.470899i) q^{6} +(-1.02876 + 2.43755i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(2.94179 - 0.588125i) q^{9} +O(q^{10})$	\(q+(-0.930874 - 0.365341i) q^{2} +(-1.72363 + 0.170607i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.562333 - 0.383392i) q^{5} +(1.66681 + 0.470899i) q^{6} +(-1.02876 + 2.43755i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(2.94179 - 0.588125i) q^{9} +(0.383392 + 0.562333i) q^{10} +(-0.601718 - 3.99214i) q^{11} +(-1.37955 - 1.04730i) q^{12} +(1.92643 - 1.53628i) q^{13} +(1.84818 - 1.89320i) q^{14} +(1.03466 + 0.564888i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(-1.73034 - 0.533738i) q^{17} +(-2.95330 - 0.527285i) q^{18} +(1.85545 - 1.07124i) q^{19} +(-0.151446 - 0.663530i) q^{20} +(1.35734 - 4.37694i) q^{21} +(-0.898369 + 3.93601i) q^{22} +(-2.52571 - 8.18816i) q^{23} +(0.901566 + 1.47891i) q^{24} +(-1.65748 - 4.22318i) q^{25} +(-2.35453 + 0.726277i) q^{26} +(-4.97021 + 1.51560i) q^{27} +(-2.41209 + 1.08712i) q^{28} +(5.96180 - 1.36074i) q^{29} +(-0.756764 - 0.903844i) q^{30} +(-4.37167 - 2.52398i) q^{31} +(0.294755 - 0.955573i) q^{32} +(1.71823 + 6.77831i) q^{33} +(1.41573 + 1.12901i) q^{34} +(1.51304 - 0.976297i) q^{35} +(2.55651 + 1.56980i) q^{36} +(6.91047 - 6.41197i) q^{37} +(-2.11855 + 0.319321i) q^{38} +(-3.05835 + 2.97664i) q^{39} +(-0.101437 + 0.672993i) q^{40} +(6.53147 - 3.14539i) q^{41} +(-2.86259 + 3.57849i) q^{42} +(1.51981 + 0.731902i) q^{43} +(2.27425 - 3.33572i) q^{44} +(-1.87975 - 0.797136i) 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} +(3.07352 + 0.624759i) q^{51} +(2.45711 + 0.184135i) q^{52} +(-7.86348 + 8.47481i) q^{53} +(5.18035 + 0.404990i) q^{54} +(-1.19219 + 2.47561i) q^{55} +(2.64252 - 0.130733i) q^{56} +(-3.01534 + 2.16297i) q^{57} +(-6.04681 - 0.911410i) q^{58} +(0.00789152 - 0.00538035i) q^{59} +(0.374240 + 1.11784i) q^{60} +(2.82091 + 3.04022i) q^{61} +(3.14736 + 3.94666i) q^{62} +(-1.59281 + 7.77579i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(-1.67229 + 0.125321i) q^{65} +(0.876943 - 6.93749i) q^{66} +(3.82751 - 6.62945i) q^{67} +(-0.905393 - 1.56819i) q^{68} +(5.75034 + 13.6824i) q^{69} +(-1.76513 + 0.356033i) q^{70} +(5.04771 + 1.15211i) q^{71} +(-1.80628 - 2.39528i) q^{72} +(-4.71005 + 1.84856i) q^{73} +(-8.77533 + 3.44406i) q^{74} +(3.57738 + 6.99641i) q^{75} +(2.08877 + 0.476748i) q^{76} +(10.3501 + 2.64023i) q^{77} +(3.93443 - 1.65353i) q^{78} +(1.53473 + 2.65823i) q^{79} +(0.340297 - 0.589412i) q^{80} +(8.30822 - 3.46028i) q^{81} +(-7.22911 + 0.541747i) q^{82} +(0.403303 - 0.505726i) q^{83} +(3.97208 - 2.28530i) q^{84} +(0.768395 + 0.963537i) q^{85} +(-1.14736 - 1.23656i) q^{86} +(-10.0438 + 3.36253i) q^{87} +(-3.33572 + 2.27425i) q^{88} +(-10.5964 - 1.59715i) q^{89} +(1.45858 + 1.42878i) q^{90} +(1.76292 + 6.27624i) q^{91} +(3.71788 - 7.72026i) q^{92} +(7.96574 + 3.60457i) q^{93} +(7.95405 - 8.57243i) q^{94} +(-1.45408 - 0.108969i) q^{95} +(-0.345021 + 1.69734i) 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
$3$	−1.72363	+	0.170607i	−0.995137	+	0.0984999i
$3$	−1.72363	+	0.170607i	−0.995137	+	0.0984999i
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	−0.562333	−	0.383392i	−0.251483	−	0.171458i	0.431017	−	0.902344i	$-0.358155\pi$
$5$	−0.562333	−	0.383392i	−0.251483	−	0.171458i	−0.682500	+	0.730886i	$0.739107\pi$
$6$	1.66681	+	0.470899i	0.680472	+	0.192244i
$7$	−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
$9$	2.94179	−	0.588125i	0.980596	−	0.196042i
$10$	0.383392	+	0.562333i	0.121239	+	0.177825i
$11$	−0.601718	−	3.99214i	−0.181425	−	1.20368i	−0.875300	−	0.483580i	$-0.839336\pi$
$11$	−0.601718	−	3.99214i	−0.181425	−	1.20368i	0.693875	−	0.720095i	$-0.255902\pi$
$12$	−1.37955	−	1.04730i	−0.398242	−	0.302330i
$13$	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
$15$	1.03466	+	0.564888i	0.267149	+	0.145853i
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−1.73034	−	0.533738i	−0.419668	−	0.129451i	0.0777267	−	0.996975i	$-0.475234\pi$
$17$	−1.73034	−	0.533738i	−0.419668	−	0.129451i	−0.497395	+	0.867524i	$0.665710\pi$
$18$	−2.95330	−	0.527285i	−0.696099	−	0.124282i
$19$	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
$21$	1.35734	−	4.37694i	0.296195	−	0.955127i
$22$	−0.898369	+	3.93601i	−0.191533	+	0.839160i
$23$	−2.52571	−	8.18816i	−0.526647	−	1.70735i	−0.692695	−	0.721231i	$-0.743577\pi$
$23$	−2.52571	−	8.18816i	−0.526647	−	1.70735i	0.166047	−	0.986118i	$-0.446900\pi$
$24$	0.901566	+	1.47891i	0.184031	+	0.301882i
$25$	−1.65748	−	4.22318i	−0.331495	−	0.844636i
$26$	−2.35453	+	0.726277i	−0.461762	+	0.142435i
$27$	−4.97021	+	1.51560i	−0.956517	+	0.291677i
$28$	−2.41209	+	1.08712i	−0.455842	+	0.205446i
$29$	5.96180	−	1.36074i	1.10708	−	0.252683i	0.370363	−	0.928887i	$-0.379233\pi$
$29$	5.96180	−	1.36074i	1.10708	−	0.252683i	0.736715	+	0.676204i	$0.236376\pi$
$30$	−0.756764	−	0.903844i	−0.138166	−	0.165019i
$31$	−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
$33$	1.71823	+	6.77831i	0.299105	+	1.17995i
$34$	1.41573	+	1.12901i	0.242795	+	0.193623i
$35$	1.51304	−	0.976297i	0.255751	−	0.165024i
$36$	2.55651	+	1.56980i	0.426085	+	0.261633i
$37$	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
$39$	−3.05835	+	2.97664i	−0.489728	+	0.476643i
$40$	−0.101437	+	0.672993i	−0.0160386	+	0.106409i
$41$	6.53147	−	3.14539i	1.02004	−	0.491227i	0.152350	−	0.988327i	$-0.451316\pi$
$41$	6.53147	−	3.14539i	1.02004	−	0.491227i	0.867694	+	0.497099i	$0.165602\pi$
$42$	−2.86259	+	3.57849i	−0.441707	+	0.552173i
$43$	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
$45$	−1.87975	−	0.797136i	−0.280216	−	0.118830i
$46$	−0.640351	+	8.54489i	−0.0944146	+	1.25987i
$47$	−4.27236	+	10.8858i	−0.623187	+	1.58786i	0.174415	+	0.984672i	$0.444196\pi$
$47$	−4.27236	+	10.8858i	−0.623187	+	1.58786i	−0.797603	+	0.603183i	$0.793899\pi$
$48$	−0.298937	−	1.70606i	−0.0431478	−	0.246248i
$49$	−4.88331	−	5.01531i	−0.697615	−	0.716473i
$50$			4.53679i			0.641599i
$51$	3.07352	+	0.624759i	0.430378	+	0.0874837i
$52$	2.45711	+	0.184135i	0.340740	+	0.0255349i
$53$	−7.86348	+	8.47481i	−1.08013	+	1.16410i	−0.0944424	+	0.995530i	$0.530107\pi$
$53$	−7.86348	+	8.47481i	−1.08013	+	1.16410i	−0.985689	+	0.168574i	$0.946084\pi$
$54$	5.18035	+	0.404990i	0.704956	+	0.0551122i
$55$	−1.19219	+	2.47561i	−0.160755	+	0.333811i
$56$	2.64252	−	0.130733i	0.353122	−	0.0174700i
$57$	−3.01534	+	2.16297i	−0.399391	+	0.286493i
$58$	−6.04681	−	0.911410i	−0.793986	−	0.119674i
$59$	0.00789152	−	0.00538035i	0.00102739	−	0.000700462i	−0.562806	−	0.826589i	$-0.690278\pi$
$59$	0.00789152	−	0.00538035i	0.00102739	−	0.000700462i	0.563834	+	0.825888i	$0.309326\pi$
$60$	0.374240	+	1.11784i	0.0483142	+	0.144313i
$61$	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
$63$	−1.59281	+	7.77579i	−0.200675	+	0.979658i
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	−1.67229	+	0.125321i	−0.207423	+	0.0155442i
$66$	0.876943	−	6.93749i	0.107944	−	0.853946i
$67$	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
$69$	5.75034	+	13.6824i	0.692260	+	1.64717i
$70$	−1.76513	+	0.356033i	−0.210974	+	0.0425540i
$71$	5.04771	+	1.15211i	0.599053	+	0.136730i	0.511285	−	0.859411i	$-0.329169\pi$
$71$	5.04771	+	1.15211i	0.599053	+	0.136730i	0.0877679	+	0.996141i	$0.472027\pi$
$72$	−1.80628	−	2.39528i	−0.212872	−	0.282286i
$73$	−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
$75$	3.57738	+	6.99641i	0.413080	+	0.807876i
$76$	2.08877	+	0.476748i	0.239598	+	0.0546867i
$77$	10.3501	+	2.64023i	1.17950	+	0.300883i
$78$	3.93443	−	1.65353i	0.445486	−	0.187225i
$79$	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
$81$	8.30822	−	3.46028i	0.923135	−	0.384475i
$82$	−7.22911	+	0.541747i	−0.798322	+	0.0598259i
$83$	0.403303	−	0.505726i	0.0442683	−	0.0555107i	−0.759205	−	0.650852i	$-0.774412\pi$
$83$	0.403303	−	0.505726i	0.0442683	−	0.0555107i	0.803473	+	0.595341i	$0.202983\pi$
$84$	3.97208	−	2.28530i	0.433389	−	0.249347i
$85$	0.768395	+	0.963537i	0.0833441	+	0.104510i
$86$	−1.14736	−	1.23656i	−0.123723	−	0.133341i
$87$	−10.0438	+	3.36253i	−1.07680	+	0.360501i
$88$	−3.33572	+	2.27425i	−0.355589	+	0.242436i
$89$	−10.5964	−	1.59715i	−1.12322	−	0.169297i	−0.438937	−	0.898518i	$-0.644645\pi$
$89$	−10.5964	−	1.59715i	−1.12322	−	0.169297i	−0.684279	+	0.729221i	$0.739883\pi$
$90$	1.45858	+	1.42878i	0.153748	+	0.150607i
$91$	1.76292	+	6.27624i	0.184804	+	0.657929i
$92$	3.71788	−	7.72026i	0.387616	−	0.804893i
$93$	7.96574	+	3.60457i	0.826008	+	0.373777i
$94$	7.95405	−	8.57243i	0.820398	−	0.884178i
$95$	−1.45408	−	0.108969i	−0.149186	−	0.0111799i
$96$	−0.345021	+	1.69734i	−0.0352136	+	0.173234i
$97$		−	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	$-0.656866\pi$
$101$	1.26652	−	16.9005i	0.126023	−	1.68166i	0.599126	−	0.800655i	$-0.295515\pi$
$102$	−2.63281	−	1.70445i	−0.260687	−	0.168766i
$103$	−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
$105$	−2.44136	+	1.94091i	−0.238253	+	0.189413i
$106$	10.4161	−	5.01613i	1.01170	−	0.487209i
$107$	−0.306075	+	2.03067i	−0.0295893	+	0.196312i	−0.998742	−	0.0501499i	$-0.984030\pi$
$107$	−0.306075	+	2.03067i	−0.0295893	+	0.196312i	0.969152	+	0.246462i	$0.0792682\pi$
$108$	−4.67429	−	2.26959i	−0.449784	−	0.218391i
$109$	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
$111$	−10.8171	+	12.2308i	−1.02672	+	1.16090i
$112$	−2.50761	−	0.843725i	−0.236947	−	0.0797245i
$113$	−8.02433	−	6.39919i	−0.754866	−	0.601985i	0.168592	−	0.985686i	$-0.446078\pi$
$113$	−8.02433	−	6.39919i	−0.754866	−	0.601985i	−0.923458	+	0.383701i	$0.874650\pi$
$114$	3.59712	−	0.911830i	0.336901	−	0.0854007i
$115$	−1.71898	+	5.57281i	−0.160296	+	0.519667i
$116$	5.29584	+	3.05756i	0.491707	+	0.283887i
$117$	4.76363	−	5.65239i	0.440398	−	0.522563i
$118$	−0.00931167	+	0.00212533i	−0.000857209	+	0.000195652i
$119$	3.08112	−	3.66870i	0.282445	−	0.336309i
$120$	0.0600230	−	1.17729i	0.00547933	−	0.107472i
$121$	−5.06382	+	1.56198i	−0.460347	+	0.141998i
$122$	−1.51520	−	3.86066i	−0.137179	−	0.349527i
$123$	−10.7212	+	6.53579i	−0.966698	+	0.589313i
$124$	−1.48791	−	4.82370i	−0.133619	−	0.433181i
$125$	−1.44431	+	6.32795i	−0.129183	+	0.565989i
$126$	4.32352	−	6.65637i	0.385170	−	0.592996i
$127$	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
$129$	−2.74445	−	1.00224i	−0.241636	−	0.0882420i
$130$	1.60248	+	0.494300i	0.140547	+	0.0433529i
$131$	0.520135	+	6.94072i	0.0454444	+	0.606413i	0.972712	+	0.232015i	$0.0745318\pi$
$131$	0.520135	+	6.94072i	0.0454444	+	0.606413i	−0.927268	+	0.374399i	$0.877849\pi$
$132$	−3.35087	+	6.13754i	−0.291656	+	0.534204i
$133$	0.702399	+	5.62479i	0.0609057	+	0.487731i
$134$	−5.98494	+	4.77283i	−0.517020	+	0.412310i
$135$	3.37598	+	1.05327i	0.290558	+	0.0906509i
$136$	0.269884	+	1.79056i	0.0231423	+	0.153539i
$137$	5.82904	+	8.54963i	0.498008	+	0.730444i	0.990141	−	0.140076i	$-0.0447348\pi$
$137$	5.82904	+	8.54963i	0.498008	+	0.730444i	−0.492132	+	0.870520i	$0.663782\pi$
$138$	−0.354090	−	14.8375i	−0.0301421	−	1.26305i
$139$	−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
$141$	5.50676	−	19.4919i	0.463753	−	1.64152i
$142$	−4.27787	−	2.91660i	−0.358991	−	0.244756i
$143$	−7.29221	−	6.76618i	−0.609805	−	0.565817i
$144$	0.806321	+	2.88961i	0.0671934	+	0.240801i
$145$	−3.87421	−	1.52052i	−0.321736	−	0.126272i
$146$	5.05982			0.418754
$147$	9.27265	+	7.81140i	0.764795	+	0.644273i
$148$	9.42698			0.774893
$149$	−9.01210	−	3.53699i	−0.738300	−	0.289761i	−0.0337642	−	0.999430i	$-0.510750\pi$
$149$	−9.01210	−	3.53699i	−0.738300	−	0.289761i	−0.704536	+	0.709668i	$0.748845\pi$
$150$	−0.774008	−	7.81974i	−0.0631975	−	0.638479i
$151$	−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
$153$	−5.40419	−	0.552489i	−0.436903	−	0.0446661i
$154$	−8.67002	−	6.23903i	−0.698650	−	0.502755i
$155$	1.49066	+	3.09538i	0.119733	+	0.248627i
$156$	−4.26656	+	0.101820i	−0.341598	+	0.00815209i
$157$	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
$159$	12.1078	−	15.9490i	0.960215	−	1.26484i
$160$	−0.532110	+	0.424344i	−0.0420670	+	0.0335473i
$161$	22.5574	+	2.26709i	1.77777	+	0.178672i
$162$	−8.99808	+	0.185750i	−0.706956	+	0.0145939i
$163$	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
$165$	1.63254	−	4.47042i	0.127093	−	0.348022i
$166$	−0.560187	+	0.323424i	−0.0434789	+	0.0251026i
$167$	−1.65409	−	7.24703i	−0.127997	−	0.560792i	−0.997734	−	0.0672767i	$-0.978569\pi$
$167$	−1.65409	−	7.24703i	−0.127997	−	0.560792i	0.869737	−	0.493515i	$-0.164288\pi$
$168$	−4.53242	+	0.676167i	−0.349684	+	0.0521674i
$169$	−1.54178	+	6.75499i	−0.118599	+	0.519615i
$170$	−0.363259	−	1.17766i	−0.0278607	−	0.0903222i
$171$	4.82830	−	4.24260i	0.369229	−	0.324440i
$172$	0.616280	+	1.57026i	0.0469909	+	0.119731i
$173$	−5.61612	+	1.73234i	−0.426986	+	0.131708i	−0.500797	−	0.865565i	$-0.666960\pi$
$173$	−5.61612	+	1.73234i	−0.426986	+	0.131708i	0.0738116	+	0.997272i	$0.476484\pi$
$174$	10.5779	+	0.539305i	0.801912	+	0.0408846i
$175$	11.9994	+	0.304455i	0.907066	+	0.0230147i
$176$	3.93601	−	0.898369i	0.296688	−	0.0677171i
$177$	−0.0126841	+	0.0106201i	−0.000953397	+	0.000798253i
$178$	9.28040	+	5.35804i	0.695595	+	0.401602i
$179$	−4.40928	+	14.2945i	−0.329565	+	1.06842i	0.627516	+	0.778604i	$0.284072\pi$
$179$	−4.40928	+	14.2945i	−0.329565	+	1.06842i	−0.957081	+	0.289820i	$0.906405\pi$
$180$	−0.835762	−	1.86289i	−0.0622940	−	0.138852i
$181$	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
$183$	−5.38088	−	4.75894i	−0.397766	−	0.351791i
$184$	−6.28141	+	5.82830i	−0.463072	+	0.429668i
$185$	−6.34429	+	0.956247i	−0.466441	+	0.0703047i
$186$	−6.09820	−	6.26561i	−0.447142	−	0.459417i
$187$	−1.08958	+	7.22891i	−0.0796782	+	0.528630i
$188$	−10.5361	+	5.07391i	−0.768422	+	0.370053i
$189$	1.41880	−	13.6743i	0.103203	−	0.994660i
$190$	1.31376	+	0.632673i	0.0953101	+	0.0458989i
$191$	9.11282	−	13.3660i	0.659380	−	0.967133i	−0.340260	−	0.940331i	$-0.610515\pi$
$191$	9.11282	−	13.3660i	0.659380	−	0.967133i	0.999641	−	0.0268021i	$-0.00853239\pi$
$192$	0.941279	−	1.45396i	0.0679309	−	0.104930i
$193$	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	$0.183662\pi$
$197$			15.3131i			1.09101i	−0.838108	+	0.545505i	$0.816338\pi$
$198$	−0.327941	+	12.1073i	−0.0233058	+	0.860425i
$199$	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
$201$	−5.46618	+	12.0797i	−0.385555	+	0.852036i
$202$	−7.35341	+	15.2695i	−0.517384	+	1.07436i
$203$	−2.81638	+	15.9321i	−0.197671	+	1.11821i
$204$	1.82810	+	2.54850i	0.127993	+	0.178431i
$205$	−4.87878	−	0.735358i	−0.340749	−	0.0513596i
$206$	5.51066	−	3.75711i	0.383946	−	0.261770i
$207$	−12.2458	−	22.6024i	−0.851140	−	1.57097i
$208$	1.67595	+	1.80624i	0.116206	+	0.125240i
$209$	−5.39300	−	6.76261i	−0.373042	−	0.467780i
$210$	2.98169	−	0.914812i	0.205756	−	0.0631280i
$211$	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
$213$	−8.89694	−	1.12463i	−0.609608	−	0.0770584i
$214$	1.02680	−	1.77848i	0.0701909	−	0.121574i
$215$	−0.574034	−	0.994256i	−0.0391488	−	0.0678077i
$216$	3.52200	+	3.82041i	0.239642	+	0.259946i
$217$	10.6497	−	8.05959i	0.722951	−	0.547121i
$218$	−4.15842	−	0.949132i	−0.281644	−	0.0642833i
$219$	7.80300	−	3.98980i	0.527278	−	0.269606i
$220$	−2.55778	+	1.00385i	−0.172445	+	0.0676798i
$221$	−4.15335	+	1.63007i	−0.279384	+	0.109650i
$222$	14.5378	−	7.43341i	0.975715	−	0.498898i
$223$	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
$225$	−7.35970	−	11.4489i	−0.490647	−	0.763259i
$226$	5.13175	+	8.88846i	0.341359	+	0.591252i
$227$	4.35030	−	7.53495i	0.288740	−	0.500112i	−0.684769	−	0.728760i	$-0.740097\pi$
$227$	4.35030	−	7.53495i	0.288740	−	0.500112i	0.973509	+	0.228648i	$0.0734304\pi$
$228$	−3.68159	−	0.465377i	−0.243820	−	0.0308204i
$229$	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
$231$	−18.2901	−	2.78499i	−1.20340	−	0.183239i
$232$	−3.81271	−	4.78099i	−0.250317	−	0.313887i
$233$	9.19313	+	9.90784i	0.602262	+	0.649084i	0.958427	−	0.285339i	$-0.0921062\pi$
$233$	9.19313	+	9.90784i	0.602262	+	0.649084i	−0.356165	+	0.934423i	$0.615916\pi$
$234$	−6.49939	+	3.52131i	−0.424878	+	0.230195i
$235$	6.57602	−	4.48345i	0.428972	−	0.292468i
$236$	0.00944446	+	0.00142352i	0.000614782	+	9.26635e-5i
$237$	−3.09881	−	4.31996i	−0.201289	−	0.280611i
$238$	−4.20845	+	2.28943i	−0.272794	+	0.148402i
$239$	−0.826044	+	1.71530i	−0.0534323	+	0.110953i	−0.925975	−	0.377584i	$-0.876755\pi$
$239$	−0.826044	+	1.71530i	−0.0534323	+	0.110953i	0.872543	+	0.488537i	$0.162469\pi$
$240$	−0.485988	+	1.07398i	−0.0313704	+	0.0693254i
$241$	−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
$243$	−13.7299	+	7.38167i	−0.880775	+	0.473534i
$244$			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
$249$	−0.608864	+	0.940490i	−0.0385852	+	0.0596011i
$250$	3.65633	−	5.36286i	0.231247	−	0.339177i
$251$	5.09927	+	2.45568i	0.321863	+	0.155001i	0.587838	−	0.808979i	$-0.299979\pi$
$251$	5.09927	+	2.45568i	0.321863	+	0.155001i	−0.265974	+	0.963980i	$0.585694\pi$
$252$	−6.45649	+	4.61668i	−0.406721	+	0.290823i
$253$	−31.1685	+	15.0100i	−1.95955	+	0.943668i
$254$	0.0310044	−	0.205701i	0.00194539	−	0.0129068i
$255$	−1.48881	−	1.52969i	−0.0932331	−	0.0957926i
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	17.6960	−	16.4195i	1.10385	−	1.02422i	0.104288	−	0.994547i	$-0.466744\pi$
$257$	17.6960	−	16.4195i	1.10385	−	1.02422i	0.999560	−	0.0296733i	$-0.00944670\pi$
$258$	2.18858	+	1.93562i	0.136255	+	0.120506i
$259$	8.52031	+	23.4410i	0.529426	+	1.45655i
$260$	−1.31112	−	1.04558i	−0.0813121	−	0.0648443i
$261$	16.7380	−	7.50929i	1.03606	−	0.464814i
$262$	2.05155	−	6.65096i	0.126745	−	0.410898i
$263$	20.1804	+	11.6512i	1.24438	+	0.718441i	0.969982	−	0.243176i	$-0.0781892\pi$
$263$	20.1804	+	11.6512i	1.24438	+	0.718441i	0.274395	+	0.961617i	$0.411523\pi$
$264$	5.36153	−	4.48906i	0.329980	−	0.276283i
$265$	7.67107	−	1.75087i	0.471230	−	0.107555i
$266$	1.40112	−	5.49259i	0.0859083	−	0.336772i
$267$	18.5367	+	0.945074i	1.13443	+	0.0578376i
$268$	7.31493	−	2.25636i	0.446831	−	0.137829i
$269$	10.7151	+	27.3016i	0.653310	+	1.66461i	0.743545	+	0.668686i	$0.233143\pi$
$269$	10.7151	+	27.3016i	0.653310	+	1.66461i	−0.0902356	+	0.995920i	$0.528762\pi$
$270$	−2.75781	−	2.21384i	−0.167835	−	0.134730i
$271$	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
$273$	−4.10939	−	10.5171i	−0.248712	−	0.636526i
$274$	−2.30257	−	10.0882i	−0.139103	−	0.609451i
$275$	−15.8622	+	9.15804i	−0.956526	+	0.552251i
$276$	−5.09112	+	13.9412i	−0.306449	+	0.839159i
$277$	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
$279$	−14.3449	−	4.85393i	−0.858809	−	0.290597i
$280$	−1.53610	−	0.939606i	−0.0917995	−	0.0561522i
$281$	−18.5604	+	14.8014i	−1.10722	+	0.882980i	−0.993868	−	0.110575i	$-0.964731\pi$
$281$	−18.5604	+	14.8014i	−1.10722	+	0.882980i	−0.113354	+	0.993555i	$0.536159\pi$
$282$	−12.2473	+	16.1327i	−0.729317	+	0.960688i
$283$	−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
$285$	2.52489	−	0.0602555i	0.149562	−	0.00356923i
$286$	4.31616	+	8.96260i	0.255220	+	0.529970i
$287$	0.947735	+	19.1566i	0.0559430	+	1.13078i
$288$	0.305110	−	2.98444i	0.0179788	−	0.175860i
$289$	−11.3369	−	7.72935i	−0.666875	−	0.454667i
$290$	3.05090	+	2.83082i	0.179155	+	0.166231i
$291$	1.65214	+	16.6915i	0.0968502	+	0.978470i
$292$	−4.71005	−	1.84856i	−0.275635	−	0.108179i
$293$	2.26947			0.132584			0.0662920	−	0.997800i	$-0.478883\pi$
$293$	2.26947			0.132584			0.0662920	+	0.997800i	$0.478883\pi$
$294$	−5.77784	−	10.6591i	−0.336971	−	0.621652i
$295$	−0.00650045			−0.000378471
$296$	−8.77533	−	3.44406i	−0.510056	−	0.200182i
$297$	9.04115	+	18.9298i	0.524621	+	1.09842i
$298$	7.09692	+	6.58498i	0.411114	+	0.381458i
$299$	−17.4449	−	11.8937i	−1.00886	−	0.687832i
$300$	−2.13637	+	7.56197i	−0.123343	+	0.436590i
$301$	−3.34757	+	2.95166i	−0.192951	+	0.170131i
$302$	9.73753	+	20.2202i	0.560332	+	1.16354i
$303$	0.700336	+	29.3462i	0.0402332	+	1.68590i
$304$	1.20690	+	1.77020i	0.0692207	+	0.101528i
$305$	−0.420696	−	2.79113i	−0.0240890	−	0.159820i
$306$	4.82877	+	2.48867i	0.276042	+	0.142268i
$307$	−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
$309$	5.53570	−	10.1393i	0.314915	−	0.576806i
$310$	−0.256744	−	3.42601i	−0.0145821	−	0.194584i
$311$	29.4534	+	9.08517i	1.67015	+	0.515173i	0.978357	−	0.206923i	$-0.0663451\pi$
$311$	29.4534	+	9.08517i	1.67015	+	0.515173i	0.691793	+	0.722096i	$0.256821\pi$
$312$	4.00883	+	1.46397i	0.226955	+	0.0828808i
$313$	−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
$315$	3.87687	−	3.76192i	0.218437	−	0.211960i
$316$	−0.683018	+	2.99250i	−0.0384228	+	0.168341i
$317$	−7.49810	−	24.3083i	−0.421135	−	1.36529i	−0.879236	−	0.476387i	$-0.841946\pi$
$317$	−7.49810	−	24.3083i	−0.421135	−	1.36529i	0.458100	−	0.888900i	$-0.348530\pi$
$318$	−17.0977	+	10.4230i	−0.958791	+	0.584493i
$319$	−9.01959	−	22.9815i	−0.505000	−	1.28672i
$320$	0.650357	−	0.200609i	0.0363561	−	0.0112144i
$321$	0.181112	−	3.55234i	0.0101087	−	0.198272i
$322$	−20.1698	−	10.3515i	−1.12402	−	0.576868i
$323$	−3.78231	+	0.863287i	−0.210453	+	0.0480346i
$324$	8.44394	+	3.11446i	0.469108	+	0.173025i
$325$	−9.68100	−	5.58933i	−0.537005	−	0.310040i
$326$	1.67822	−	5.44066i	0.0929480	−	0.301330i
$327$	−7.16132	+	1.81532i	−0.396022	+	0.100387i
$328$	−5.66779	−	4.51992i	−0.312952	−	0.249571i
$329$	−22.1394	−	21.6129i	−1.22059	−	1.19156i
$330$	−3.15291	+	3.56497i	−0.173562	+	0.196245i
$331$	−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
$333$	16.5581	−	22.9269i	0.907377	−	1.25639i
$334$	−1.10789	+	7.35037i	−0.0606211	+	0.402194i
$335$	−4.69402	+	2.26052i	−0.256462	+	0.123505i
$336$	4.46614	+	1.02645i	0.243648	+	0.0559975i
$337$	−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
$339$	14.9227	+	9.66082i	0.810491	+	0.524704i
$340$	−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
$345$	2.01213	−	9.89872i	0.108329	−	0.532929i
$346$	5.86080	+	0.439206i	0.315078	+	0.0236119i
$347$	18.2146	−	19.6306i	0.977809	−	1.05383i	−0.0207295	−	0.999785i	$-0.506599\pi$
$347$	18.2146	−	19.6306i	0.977809	−	1.05383i	0.998539	−	0.0540425i	$-0.0172106\pi$
$348$	−9.64971	−	4.36658i	−0.517279	−	0.234073i
$349$	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
$351$	−7.24639	+	10.5553i	−0.386784	+	0.563401i
$352$	−3.99214	−	0.601718i	−0.212782	−	0.0320717i
$353$	10.5609	−	7.20030i	0.562100	−	0.383234i	−0.248679	−	0.968586i	$-0.579996\pi$
$353$	10.5609	−	7.20030i	0.562100	−	0.383234i	0.810779	+	0.585353i	$0.199044\pi$
$354$	0.0156873	−	0.00525191i	0.000833769	−	0.000279136i
$355$	−2.39679	−	2.58312i	−0.127208	−	0.137098i
$356$	−6.68137	−	8.37817i	−0.354112	−	0.444042i
$357$	−4.68479	+	6.84913i	−0.247945	+	0.362494i
$358$	9.32686	−	11.6955i	0.492940	−	0.618127i
$359$	−4.43056	+	0.332025i	−0.233836	+	0.0175236i	−0.191133	−	0.981564i	$-0.561216\pi$
$359$	−4.43056	+	0.332025i	−0.233836	+	0.0175236i	−0.0427034	+	0.999088i	$0.513597\pi$
$360$	0.0973971	+	2.03946i	0.00513328	+	0.107489i
$361$	−7.20488	+	12.4792i	−0.379204	+	0.656801i
$362$	−7.47769	−	12.9517i	−0.393019	−	0.680728i
$363$	8.46166	−	3.55620i	0.444122	−	0.186652i
$364$	−2.97661	+	5.79990i	−0.156017	+	0.303997i
$365$	3.35734	+	0.766292i	0.175731	+	0.0401096i
$366$	3.27029	+	6.39583i	0.170941	+	0.334315i
$367$	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
$369$	17.3643	−	13.0944i	0.903949	−	0.681666i
$370$	6.25509	+	1.42768i	0.325186	+	0.0742217i
$371$	−12.5682	−	27.8862i	−0.652506	−	1.44778i
$372$	3.38757	+	8.06042i	0.175637	+	0.417913i
$373$	−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
$375$	1.40987	−	11.1534i	0.0728052	−	0.575961i
$376$	11.6615	−	0.873906i	0.601394	−	0.0450682i
$377$	9.39452	−	11.7804i	0.483842	−	0.606719i
$378$	−6.31651	+	12.2107i	−0.324886	+	0.628052i
$379$	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
$381$	−0.114387	−	0.341669i	−0.00586022	−	0.0175043i
$382$	−13.3660	+	9.11282i	−0.683867	+	0.466252i
$383$	−27.0885	−	4.08293i	−1.38416	−	0.208628i	−0.585625	−	0.810582i	$-0.699151\pi$
$383$	−27.0885	−	4.08293i	−1.38416	−	0.208628i	−0.798531	+	0.601954i	$0.794389\pi$
$384$	−1.40740	+	1.00956i	−0.0718212	+	0.0515191i
$385$	−4.80794	−	5.45283i	−0.245035	−	0.277902i
$386$	−3.46836	+	7.20212i	−0.176535	+	0.366578i
$387$	4.90141	+	1.25926i	0.249152	+	0.0640118i
$388$	6.58673	−	7.09881i	0.334391	−	0.360387i
$389$	17.9745	+	1.34700i	0.911344	+	0.0682958i	0.522144	−	0.852858i	$-0.325132\pi$
$389$	17.9745	+	1.34700i	0.911344	+	0.0682958i	0.389200	+	0.921153i	$0.372752\pi$
$390$	−2.84641	−	0.578595i	−0.144134	−	0.0292983i
$391$			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
$396$	4.72855	−	11.1505i	0.237619	−	0.560335i
$397$	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
$399$	−2.17030	−	9.57522i	−0.108651	−	0.479360i
$400$	4.08751	−	1.96844i	0.204375	−	0.0984220i
$401$	−1.20081	+	7.96684i	−0.0599655	+	0.397845i	0.938633	+	0.344918i	$0.112093\pi$
$401$	−1.20081	+	7.96684i	−0.0599655	+	0.397845i	−0.998598	+	0.0529273i	$0.983145\pi$
$402$	9.50153	−	9.24766i	0.473893	−	0.461231i
$403$	−12.2993	+	1.85382i	−0.612670	+	0.0923451i
$404$	12.4237	−	11.5275i	0.618101	−	0.573514i
$405$	−5.99863	−	1.23948i	−0.298074	−	0.0615901i
$406$	8.44233	−	13.8018i	0.418986	−	0.684971i
$407$	−29.7557	−	23.7293i	−1.47493	−	1.17622i
$408$	−0.770661	−	3.04022i	−0.0381534	−	0.150513i
$409$	−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
$411$	−11.5057	−	13.7419i	−0.567535	−	0.677838i
$412$	−6.50236	+	1.48412i	−0.320348	+	0.0731174i
$413$	0.00499639	+	0.0247711i	0.000245856	+	0.00121890i
$414$	3.14169	+	25.5138i	0.154406	+	1.25394i
$415$	−0.420682	+	0.129763i	−0.0206505	+	0.00636983i
$416$	−0.900200	−	2.29367i	−0.0441359	−	0.112457i
$417$	15.4960	+	25.4194i	0.758843	+	1.24479i
$418$	2.54955	+	8.26542i	0.124702	+	0.404275i
$419$	5.32079	−	23.3119i	0.259938	−	1.13886i	−0.661380	−	0.750051i	$-0.730029\pi$
$419$	5.32079	−	23.3119i	0.259938	−	1.13886i	0.921318	−	0.388811i	$-0.127114\pi$
$420$	−3.10980	−	0.237761i	−0.151743	−	0.0116015i
$421$	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
$423$	−6.16615	+	34.5363i	−0.299809	+	1.67921i
$424$	11.0474	+	3.40766i	0.536508	+	0.165491i
$425$	0.613919	+	8.19218i	0.0297795	+	0.397379i
$426$	7.87105	+	4.29731i	0.381354	+	0.208205i
$427$	−10.3127	+	3.74846i	−0.499068	+	0.181401i
$428$	−1.60558	+	1.28040i	−0.0776085	+	0.0618907i
$429$	13.7234	+	10.4183i	0.662573	+	0.502999i
$430$	0.171111	+	1.13525i	0.00825169	+	0.0547464i
$431$	−2.95229	−	4.33022i	−0.142207	−	0.208579i	0.748527	−	0.663104i	$-0.230761\pi$
$431$	−2.95229	−	4.33022i	−0.142207	−	0.208579i	−0.890734	+	0.454525i	$0.849809\pi$
$432$	−1.88278	−	4.84305i	−0.0905855	−	0.233011i
$433$	−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
$435$	6.93711	+	1.95984i	0.332609	+	0.0939670i
$436$	3.52421	+	2.40276i	0.168779	+	0.115072i
$437$	−13.4578	−	12.4870i	−0.643775	−	0.597336i
$438$	−8.72125	+	0.863240i	−0.416717	+	0.0412472i
$439$	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
$441$	−17.3153	−	11.8820i	−0.824537	−	0.565808i
$442$	4.46177			0.212225
$443$	−6.91940	−	2.71566i	−0.328751	−	0.129025i	0.195225	−	0.980759i	$-0.437456\pi$
$443$	−6.91940	−	2.71566i	−0.328751	−	0.129025i	−0.523975	+	0.851733i	$0.675552\pi$
$444$	−16.2486	+	1.60831i	−0.771125	+	0.0763269i
$445$	5.34637	+	4.96071i	0.253442	+	0.235160i
$446$	−2.77969	−	1.89516i	−0.131622	−	0.0897383i
$447$	16.1369	+	4.55893i	0.763251	+	0.215630i
$448$	−1.26433	−	2.32410i	−0.0597341	−	0.109804i
$449$	9.34456	+	19.4042i	0.440997	+	0.915740i	0.996450	+	0.0841917i	$0.0268308\pi$
$449$	9.34456	+	19.4042i	0.440997	+	0.915740i	−0.555452	+	0.831548i	$0.687455\pi$
$450$	2.66820	+	13.3463i	0.125780	+	0.629149i
$451$	−16.4869	−	24.1819i	−0.776340	−	1.13868i
$452$	−1.52970	−	10.1489i	−0.0719509	−	0.477363i
$453$	30.9609	+	23.5043i	1.45467	+	1.10433i
$454$	−6.80241	+	5.42474i	−0.319253	+	0.254596i
$455$	1.41491	−	4.20523i	0.0663321	−	0.197144i
$456$	3.25708	+	1.77824i	0.152527	+	0.0832739i
$457$	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
$459$	9.40907	+	0.0302942i	0.439178	+	0.00141401i
$460$	−5.05058	+	2.91595i	−0.235484	+	0.135957i
$461$	−7.65132	−	33.5226i	−0.356358	−	1.56130i	−0.762188	−	0.647356i	$-0.775875\pi$
$461$	−7.65132	−	33.5226i	−0.356358	−	1.56130i	0.405830	−	0.913949i	$-0.366983\pi$
$462$	16.0083	+	9.27460i	0.744774	+	0.431493i
$463$	−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
$465$	−3.09743	−	5.08097i	−0.143640	−	0.235625i
$466$	−4.93790	−	12.5816i	−0.228744	−	0.582830i
$467$	39.9536	−	12.3240i	1.84883	−	0.570289i	0.849760	−	0.527170i	$-0.176747\pi$
$467$	39.9536	−	12.3240i	1.84883	−	0.570289i	0.999070	−	0.0431188i	$-0.0137294\pi$
$468$	7.33659	−	0.903403i	0.339134	−	0.0417598i
$469$	12.2220	+	16.1499i	0.564361	+	0.745731i
$470$	−7.75943	+	1.77104i	−0.357916	+	0.0816920i
$471$	−12.0191	−	14.3550i	−0.553809	−	0.661445i
$472$	−0.00827153	−	0.00477557i	−0.000380728	−	0.000219813i
$473$	2.00736	−	6.50769i	0.0922984	−	0.299224i
$474$	1.30634	+	5.15346i	0.0600024	+	0.236706i
$475$	−7.59940	−	6.06032i	−0.348685	−	0.278067i
$476$	4.75396	−	0.593654i	0.217898	−	0.0272101i
$477$	−18.1484	+	29.5558i	−0.830959	+	1.35327i
$478$	1.39561	−	1.29494i	0.0638338	−	0.0592291i
$479$	28.3635	−	4.27511i	1.29596	−	0.195335i	0.535399	−	0.844599i	$-0.320161\pi$
$479$	28.3635	−	4.27511i	1.29596	−	0.195335i	0.760563	+	0.649265i	$0.224923\pi$
$480$	0.844764	−	0.822192i	0.0385580	−	0.0375278i
$481$	3.46196	−	22.9686i	0.157852	−	1.04728i
$482$	27.4368	−	13.2129i	1.24971	−	0.601831i
$483$	−39.2673	−	0.0591810i	−1.78673	−	0.00269283i
$484$	−4.77446	−	2.29926i	−0.217021	−	0.104512i
$485$	−3.71274	+	5.44558i	−0.168587	+	0.247271i
$486$	15.4777	−	1.85530i	0.702081	−	0.0841581i
$487$	−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	$0.173300\pi$
$491$			22.9535i			1.03588i	−0.855418	+	0.517938i	$0.826700\pi$
$492$	−12.3047	−	2.50119i	−0.554737	−	0.112762i
$493$	−11.0422	−	0.827498i	−0.497315	−	0.0372686i
$494$	−3.59069	+	3.86984i	−0.161553	+	0.174112i
$495$	−2.05120	+	7.98387i	−0.0921946	+	0.358848i
$496$	2.19023	−	4.54806i	0.0983443	−	0.204214i
$497$	−8.00120	+	11.1188i	−0.358903	+	0.498747i
$498$	0.910375	−	0.653034i	0.0407949	−	0.0292632i
$499$	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
$501$	4.08742	+	12.2090i	0.182613	+	0.545457i
$502$	−3.84962	−	4.14890i	−0.171817	−	0.185175i
$503$	−5.05658	−	6.34075i	−0.225462	−	0.282720i	0.656215	−	0.754574i	$-0.272156\pi$
$503$	−5.05658	−	6.34075i	−0.225462	−	0.282720i	−0.881677	+	0.471854i	$0.843585\pi$
$504$	7.69684	−	1.93872i	0.342845	−	0.0863575i
$505$	−7.19172	+	9.01814i	−0.320028	+	0.401302i
$506$	34.4977	−	2.58525i	1.53361	−	0.114928i
$507$	1.50501	−	11.9061i	0.0668399	−	0.528770i
$508$	−0.104012	+	0.180154i	−0.00461479	+	0.00799306i
$509$	−5.09815	−	8.83025i	−0.225971	−	0.391394i	0.730639	−	0.682764i	$-0.239222\pi$
$509$	−5.09815	−	8.83025i	−0.225971	−	0.391394i	−0.956610	+	0.291370i	$0.905889\pi$
$510$	0.827040	+	1.96787i	0.0366219	+	0.0871387i
$511$	0.339555	−	13.3827i	0.0150210	−	0.592017i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$	−7.59838	+	8.13640i	−0.335477	+	0.359231i
$514$	−22.4715	+	8.81940i	−0.991174	+	0.389007i
$515$	4.22549	−	1.65838i	0.186197	−	0.0730771i
$516$	−1.33013	−	2.60139i	−0.0585559	−	0.114520i
$517$	46.0284	+	10.5057i	2.02432	+	0.462039i
$518$	0.632626	−	24.9334i	0.0277960	−	1.09551i
$519$	9.38456	−	3.94407i	0.411936	−	0.173125i
$520$	0.838492	+	1.45231i	0.0367703	+	0.0636880i
$521$	10.6900	−	18.5156i	0.468338	−	0.811185i	−0.531008	−	0.847367i	$-0.678186\pi$
$521$	10.6900	−	18.5156i	0.468338	−	0.811185i	0.999345	+	0.0361825i	$0.0115197\pi$
$522$	−18.3245	+	0.875109i	−0.802040	+	0.0383025i
$523$	−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
$525$	−20.7344	+	1.52241i	−0.904922	+	0.0664432i
$526$	−14.5288	−	18.2185i	−0.633484	−	0.794364i
$527$	6.21731	+	6.70067i	0.270830	+	0.291886i
$528$	−6.63095	+	2.21996i	−0.288575	+	0.0966115i
$529$	−41.6632	+	28.4055i	−1.81144	+	1.23502i
$530$	−7.78046	−	1.17272i	−0.337962	−	0.0509395i
$531$	0.0200509	−	0.0204690i	0.000870133	−	0.000888281i
$532$	−3.31094	+	4.60102i	−0.143547	+	0.199479i
$533$	7.75024	−	16.0935i	0.335700	−	0.697088i
$534$	−16.9101	−	7.65197i	−0.731770	−	0.331133i
$535$	0.950660	−	1.02457i	0.0411006	−	0.0442959i
$536$	−7.63362	−	0.572061i	−0.329722	−	0.0247093i
$537$	5.16121	−	25.3907i	0.222723	−	1.09569i
$538$		−	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
$543$	−21.7445	−	14.0772i	−0.933146	−	0.604110i
$544$	−1.02005	+	1.49614i	−0.0437344	+	0.0641465i
$545$	−2.61549	−	1.25956i	−0.112035	−	0.0539534i
$546$	−0.0170177	+	11.2915i	−0.000728290	+	0.483230i
$547$	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
$549$	10.0866	+	7.28463i	0.430484	+	0.310900i
$550$	18.1115	−	2.72987i	0.772277	−	0.116402i
$551$	9.60410	−	8.91131i	0.409149	−	0.379634i
$552$	9.83246	−	11.1175i	0.418497	−	0.473191i
$553$	−8.05843	+	1.00630i	−0.342679	+	0.0427922i
$554$	−23.8145	−	18.9914i	−1.01178	−	0.806867i
$555$	10.7720	−	2.73059i	0.457248	−	0.115907i
$556$	5.06622	−	16.4243i	0.214856	−	0.696545i
$557$	8.99285	+	5.19202i	0.381039	+	0.219993i	0.678270	−	0.734812i	$-0.262730\pi$
$557$	8.99285	+	5.19202i	0.381039	+	0.219993i	−0.297231	+	0.954806i	$0.596063\pi$
$558$	11.5800	+	9.75919i	0.490220	+	0.413139i
$559$	4.05222	−	0.924892i	0.171390	−	0.0391188i
$560$	1.08664	+	1.43585i	0.0459188	+	0.0606759i
$561$	0.644734	−	12.6458i	0.0272207	−	0.533908i
$562$	22.6850	−	6.99739i	0.956908	−	0.295167i
$563$	1.72588	+	4.39746i	0.0727371	+	0.185331i	0.962619	−	0.270861i	$-0.0873083\pi$
$563$	1.72588	+	4.39746i	0.0727371	+	0.185331i	−0.889881	+	0.456192i	$0.849213\pi$
$564$	17.2946	−	10.5431i	0.728235	−	0.443943i
$565$	2.05895	+	6.67495i	0.0866206	+	0.280817i
$566$	−4.62357	+	20.2572i	−0.194343	+	0.851473i
$567$	−0.112553	+	23.8115i	−0.00472678	+	0.999989i
$568$	−1.15211	−	5.04771i	−0.0483414	−	0.211797i
$569$	−14.8988	+	8.60182i	−0.624590	+	0.360607i	−0.778654	−	0.627454i	$-0.784097\pi$
$569$	−14.8988	+	8.60182i	−0.624590	+	0.360607i	0.154064	+	0.988061i	$0.450764\pi$
$570$	−2.37237	−	0.866356i	−0.0993676	−	0.0362877i
$571$	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
$573$	−13.4268	+	24.5928i	−0.560911	+	1.02738i
$574$	6.11648	−	18.1787i	0.255297	−	0.758762i
$575$	−30.3938	+	24.2382i	−1.26751	+	1.01080i
$576$	−1.37436	+	2.66667i	−0.0572650	+	0.111111i
$577$	−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
$579$	0.330325	+	13.8416i	0.0137278	+	0.575239i
$580$	−1.80579	−	3.74975i	−0.0749812	−	0.155700i
$581$	0.817831	+	1.50334i	0.0339294	+	0.0623692i
$582$	4.56014	−	16.1412i	0.189024	−	0.669076i
$583$	38.5642	+	26.2926i	1.59717	+	1.08893i
$584$	3.70911	+	3.44155i	0.153484	+	0.142412i
$585$	−4.84583	+	1.35219i	−0.200350	+	0.0559061i
$586$	−2.11259	−	0.829131i	−0.0872704	−	0.0342511i
$587$	−23.7502			−0.980275			−0.490138	−	0.871645i	$-0.663053\pi$
$587$	−23.7502			−0.980275			−0.490138	+	0.871645i	$0.663053\pi$
$588$	1.48423	+	12.0332i	0.0612087	+	0.496239i
$589$	−10.8152			−0.445632
$590$	0.00605110	+	0.00237488i	0.000249120	+	9.77723e-5i
$591$	−2.61251	−	26.3940i	−0.107464	−	1.08570i
$592$	6.91047	+	6.41197i	0.284018	+	0.263531i
$593$	−33.2405	−	22.6630i	−1.36502	−	0.930658i	−0.365024	−	0.930998i	$-0.618939\pi$
$593$	−33.2405	−	22.6630i	−1.36502	−	0.930658i	−1.00000		0.000340625i	$0.999892\pi$
$594$	−1.50033	−	20.9244i	−0.0615594	−	0.858537i
$595$	−3.13916	+	0.881754i	−0.128693	+	0.0361484i
$596$	−4.20057	−	8.72258i	−0.172062	−	0.357291i
$597$	−18.7107	+	0.446523i	−0.765778	+	0.0182750i
$598$	11.8937	+	17.4449i	0.486371	+	0.713375i
$599$	3.22340	+	21.3858i	0.131704	+	0.873801i	0.952928	+	0.303195i	$0.0980535\pi$
$599$	3.22340	+	21.3858i	0.131704	+	0.873801i	−0.821224	+	0.570606i	$0.806708\pi$
$600$	4.75139	−	6.25873i	0.193975	−	0.255512i
$601$	−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
$603$	7.36078	−	21.7535i	0.299754	−	0.885870i
$604$	−1.67715	−	22.3800i	−0.0682421	−	0.910628i
$605$	3.44641	+	1.06308i	0.140116	+	0.0432202i
$606$	10.0695	−	27.5735i	0.409044	−	1.12010i
$607$	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
$609$	2.13627	−	27.9414i	0.0865662	−	1.13224i
$610$	−0.628101	+	2.75189i	−0.0254311	+	0.111421i
$611$	8.49320	+	27.5343i	0.343598	+	1.11392i
$612$	−3.58576	−	4.08078i	−0.144946	−	0.164956i
$613$	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
$615$	8.53466	+	0.435130i	0.344151	+	0.0175461i
$616$	−2.11196	−	10.4706i	−0.0850932	−	0.421874i
$617$	23.0892	−	5.26996i	0.929537	−	0.212161i	0.269160	−	0.963095i	$-0.413254\pi$
$617$	23.0892	−	5.26996i	0.929537	−	0.212161i	0.660377	+	0.750935i	$0.270397\pi$
$618$	−8.85735	+	7.41601i	−0.356295	+	0.298316i
$619$	−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
$621$	24.9633	+	36.8689i	1.00174	+	1.47950i
$622$	−24.0982	−	19.2177i	−0.966251	−	0.770559i
$623$	14.7943	−	24.1862i	0.592720	−	0.968998i
$624$	−3.19686	−	2.82736i	−0.127977	−	0.113185i
$625$	−13.3902	+	12.4243i	−0.535610	+	0.496973i
$626$	15.1029	−	2.27640i	0.603635	−	0.0909833i
$627$	10.4493	+	10.7361i	0.417304	+	0.428760i
$628$	−1.61105	+	10.6886i	−0.0642878	+	0.426521i
$629$	−15.3798	+	7.40650i	−0.613231	+	0.295316i
$630$	−4.98326	+	2.08549i	−0.198538	+	0.0830880i
$631$	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
$633$	−13.3386	+	20.6037i	−0.530163	+	0.818924i
$634$	−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
$639$	15.5269	+	0.420566i	0.614234	+	0.0166373i
$640$	−0.678691	−	0.0508609i	−0.0268276	−	0.00201045i
$641$	−5.96631	+	6.43016i	−0.235655	+	0.253976i	−0.839797	−	0.542901i	$-0.817326\pi$
$641$	−5.96631	+	6.43016i	−0.235655	+	0.253976i	0.604141	+	0.796877i	$0.293516\pi$
$642$	−1.46641	+	3.24061i	−0.0578745	+	0.127897i
$643$	−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
$645$	1.15905	+	1.61579i	0.0456375	+	0.0636218i
$646$	3.83625	+	0.578221i	0.150935	+	0.0227498i
$647$	−27.5563	+	18.7876i	−1.08335	+	0.738616i	−0.967047	−	0.254598i	$-0.918057\pi$
$647$	−27.5563	+	18.7876i	−1.08335	+	0.738616i	−0.116303	+	0.993214i	$0.537105\pi$
$648$	−6.72240	−	5.98409i	−0.264081	−	0.235077i
$649$	−0.0262276	−	0.0282666i	−0.00102952	−	0.00110956i
$650$	6.96978	+	8.73982i	0.273377	+	0.342804i
$651$	−16.9812	+	15.7087i	−0.665544	+	0.615671i
$652$	−3.54991	+	4.45144i	−0.139025	+	0.174332i
$653$	18.6549	−	1.39799i	0.730024	−	0.0547077i	0.295468	−	0.955353i	$-0.404524\pi$
$653$	18.6549	−	1.39799i	0.730024	−	0.0547077i	0.434556	+	0.900645i	$0.356905\pi$
$654$	7.32950	+	0.926496i	0.286606	+	0.0362289i
$655$	2.36853	−	4.10241i	0.0925461	−	0.160295i
$656$	3.62469	+	6.27815i	0.141520	+	0.245121i
$657$	−12.7688	+	8.20817i	−0.498158	+	0.320231i
$658$	12.7129	+	28.2074i	0.495601	+	1.09964i
$659$	5.78843	+	1.32117i	0.225485	+	0.0514655i	0.333771	−	0.942654i	$-0.391679\pi$
$659$	5.78843	+	1.32117i	0.225485	+	0.0514655i	−0.108285	+	0.994120i	$0.534536\pi$
$660$	4.23739	−	2.16665i	0.164940	−	0.0843365i
$661$	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
$663$	6.88073	−	3.51822i	0.267225	−	0.136636i
$664$	−0.630630	−	0.143937i	−0.0244732	−	0.00558585i
$665$	1.76152	−	3.43230i	0.0683088	−	0.133099i
$666$	−23.7896	+	15.2927i	−0.921828	+	0.592580i
$667$	−26.1997	−	45.3793i	−1.01446	−	1.75709i
$668$	3.71670	−	6.43751i	0.143803	−	0.249075i
$669$	−5.78107	−	0.730765i	−0.223509	−	0.0282530i
$670$	5.19540	−	0.389341i	0.200716	−	0.0150416i
$671$	10.4396	−	13.0908i	0.403016	−	0.505366i
$672$	−3.78241	−	2.58716i	−0.145910	−	0.0998019i
$673$	−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
$675$	14.6386	+	18.4780i	0.563442	+	0.711219i
$676$	−5.72477	+	3.90308i	−0.220183	+	0.150118i
$677$	22.3849	+	3.37399i	0.860323	+	0.129673i	0.564362	−	0.825527i	$-0.309122\pi$
$677$	22.3849	+	3.37399i	0.860323	+	0.129673i	0.295961	+	0.955200i	$0.404360\pi$
$678$	−10.3617	−	14.4449i	−0.397937	−	0.554752i
$679$	23.6050	+	9.96241i	0.905877	+	0.382322i
$680$	0.534723	−	1.11036i	0.0205057	−	0.0425805i
$681$	−6.21279	+	13.7296i	−0.238075	+	0.526121i
$682$	13.8618	−	14.9395i	0.530796	−	0.572062i
$683$	−0.396902	−	0.0297437i	−0.0151870	−	0.00113811i	0.0671344	−	0.997744i	$-0.478614\pi$
$683$	−0.396902	−	0.0297437i	−0.0151870	−	0.00113811i	−0.0823214	+	0.996606i	$0.526233\pi$
$684$	6.42510	+	0.174032i	0.245670	+	0.00665429i
$685$		−	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
$690$	−5.48945	+	8.47935i	−0.208980	+	0.322803i
$691$	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
$693$	32.0005	+	1.67987i	1.21560	+	0.0638129i
$694$	−24.1273	+	11.6191i	−0.915861	+	0.441055i
$695$	−1.74349	+	11.5673i	−0.0661345	+	0.438774i
$696$	7.38737	+	7.59017i	0.280017	+	0.287705i
$697$	−12.9805	+	1.95649i	−0.491670	+	0.0741073i
$698$	−4.32826	+	4.01604i	−0.163827	+	0.152009i
$699$	−17.5359	−	15.5090i	−0.663268	−	0.586605i
$700$	8.58907	+	8.38482i	0.324636	+	0.316916i
$701$	−29.7860	−	23.7535i	−1.12500	−	0.897158i	−0.129468	−	0.991584i	$-0.541327\pi$
$701$	−29.7860	−	23.7535i	−1.12500	−	0.897158i	−0.995532	+	0.0944257i	$0.969899\pi$
$702$	10.6018	−	7.17827i	0.400138	−	0.270926i
$703$	5.95322	−	19.2998i	0.224530	−	0.727908i
$704$	3.49635	+	2.01862i	0.131774	+	0.0760795i
$705$	−10.5697	+	8.84972i	−0.398078	+	0.333300i
$706$	−12.4614	+	2.84424i	−0.468992	+	0.107044i
$707$	39.8929	+	20.4737i	1.50033	+	0.769994i
$708$	−0.0165216		0.000842335i	−0.000620920		3.16569e-5i
$709$	−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
$711$	6.07821	+	6.91732i	0.227951	+	0.259420i
$712$	3.15862	+	10.2400i	0.118374	+	0.383760i
$713$	−9.62520	+	42.1708i	−0.360467	+	1.57931i
$714$	6.86322	−	4.66413i	0.256849	−	0.174550i
$715$	1.50655	+	6.60063i	0.0563418	+	0.246849i
$716$	−12.9550	+	7.47956i	−0.484150	+	0.279524i
$717$	1.13115	−	3.09746i	0.0422436	−	0.115677i
$718$	4.24559	+	1.30959i	0.158444	+	0.0488736i
$719$	1.75615	+	23.4341i	0.0654932	+	0.873946i	0.929112	+	0.369800i	$0.120574\pi$
$719$	1.75615	+	23.4341i	0.0654932	+	0.873946i	−0.863618	+	0.504146i	$0.831807\pi$
$720$	0.654433	−	1.93406i	0.0243893	−	0.0720782i
$721$	−9.56736	−	14.8273i	−0.356307	−	0.552197i
$722$	11.2660	−	8.98434i	0.419277	−	0.334363i
$723$	31.8930	−	42.0109i	1.18612	−	1.56240i
$724$	2.22898	+	14.7883i	0.0828395	+	0.549604i
$725$	−15.6282	−	22.9223i	−0.580416	−	0.851314i
$726$	−9.17596	+	0.218980i	−0.340552	+	0.00812713i
$727$	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
$729$	22.4059	−	15.0657i	0.829849	−	0.557988i
$730$	−2.84531	−	1.93990i	−0.105310	−	0.0717988i
$731$	−2.23914	−	2.07762i	−0.0828176	−	0.0768435i
$732$	−0.707566	−	7.14848i	−0.0261524	−	0.264215i
$733$	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
$735$	−2.21949	−	7.94767i	−0.0818671	−	0.293154i
$736$	−8.56885			−0.315852
$737$	−28.7688	−	11.2909i	−1.05971	−	0.415906i
$738$	−20.9479	+	5.84533i	−0.771102	+	0.215169i
$739$	−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
$741$	−2.48591	+	8.79922i	−0.0913222	+	0.323247i
$742$	1.51141	+	30.5502i	0.0554855	+	1.12153i
$743$	14.6695	+	30.4616i	0.538173	+	1.11753i	0.975859	+	0.218399i	$0.0700836\pi$
$743$	14.6695	+	30.4616i	0.538173	+	1.11753i	−0.437687	+	0.899127i	$0.644202\pi$
$744$	−0.208597	−	8.74085i	−0.00764752	−	0.320455i
$745$	3.71175	+	5.44414i	0.135988	+	0.199458i
$746$	2.48283	+	16.4725i	0.0909030	+	0.603102i
$747$	0.889001	−	1.72493i	0.0325269	−	0.0631119i
$748$	−5.71563	+	4.55806i	−0.208984	+	0.166659i
$749$	−4.63499	−	2.83515i	−0.169359	−	0.103594i
$750$	−5.38722	+	9.86736i	−0.196713	+	0.360305i
$751$	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
$753$	−9.20820	−	3.36271i	−0.335566	−	0.122544i
$754$	−13.0490	+	7.53382i	−0.475215	+	0.274366i
$755$	3.39887	+	14.8914i	0.123698	+	0.541955i
$756$	10.3410	−	9.05896i	0.376097	−	0.329471i
$757$	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
$759$	51.1621	−	31.1891i	1.85707	−	1.13209i
$760$	0.532726	+	1.35736i	0.0193240	+	0.0492368i
$761$	21.4784	−	6.62522i	0.778592	−	0.240164i	0.120110	−	0.992761i	$-0.461675\pi$
$761$	21.4784	−	6.62522i	0.778592	−	0.240164i	0.658482	+	0.752597i	$0.271199\pi$
$762$	−0.0183461	+	0.359841i	−0.000664609	+	0.0130357i
$763$	−2.78942	+	10.9349i	−0.100984	+	0.395870i
$764$	15.7714	−	3.59972i	0.570589	−	0.130233i
$765$	2.82713	+	2.38261i	0.102215	+	0.0861433i
$766$	23.7243	+	13.6972i	0.857193	+	0.494901i
$767$	0.00693677	−	0.0224885i	0.000250472	−	0.000812011i
$768$	1.67895	−	0.425595i	0.0605838	−	0.0153573i
$769$	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
$771$	−27.7001	+	31.3202i	−0.997594	+	1.12797i
$772$	5.85984	−	5.43713i	0.210900	−	0.195687i
$773$	11.7031	−	1.76396i	0.420932	−	0.0634453i	0.0648389	−	0.997896i	$-0.479347\pi$
$773$	11.7031	−	1.76396i	0.420932	−	0.0634453i	0.356093	+	0.934450i	$0.384109\pi$
$774$	−4.10253	−	2.96290i	−0.147462	−	0.106499i
$775$	−3.41330	+	22.6458i	−0.122609	+	0.813460i
$776$	−8.72490	+	4.20169i	−0.313206	+	0.150832i
$777$	−18.6850	−	38.9499i	−0.670322	−	1.39732i
$778$	−16.2399	−	7.82071i	−0.582228	−	0.280386i
$779$	8.74931	−	12.8329i	0.313477	−	0.459786i
$780$	2.43826	+	1.57851i	0.0873039	+	0.0565197i
$781$	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
$786$	−2.40141	+	11.8138i	−0.0856554	+	0.421384i
$787$	−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
$789$	−36.7713	−	16.6393i	−1.30909	−	0.592377i
$790$	−0.906406	+	1.88217i	−0.0322485	+	0.0669647i
$791$	23.8535	−	12.9765i	0.848132	−	0.461391i
$792$	−8.47543	+	8.65219i	−0.301161	+	0.307442i
$793$	10.1049	+	1.52307i	0.358836	+	0.0540859i
$794$	−23.2375	+	15.8431i	−0.824670	+	0.562250i
$795$	−12.9234	+	4.32659i	−0.458344	+	0.153448i
$796$	7.34975	+	7.92114i	0.260505	+	0.280758i
$797$	22.7355	+	28.5095i	0.805334	+	1.00986i	0.999582	+	0.0289049i	$0.00920199\pi$
$797$	22.7355	+	28.5095i	0.805334	+	1.00986i	−0.194248	+	0.980952i	$0.562227\pi$
$798$	−1.47794	+	9.70622i	−0.0523186	+	0.343596i
$799$	13.2028	−	16.5558i	0.467081	−	0.585701i
$800$	−4.52411	+	0.339035i	−0.159951	+	0.0119867i
$801$	−32.1116	+	1.53354i	−1.13461	+	0.0541848i
$802$	4.02842	−	6.97742i	0.142248	−	0.246381i
$803$	10.2138	+	17.6909i	0.360439	+	0.624298i
$804$	−12.2233	+	5.13710i	−0.431082	+	0.181172i
$805$	−11.8156	−	9.92320i	−0.416445	−	0.349747i
$806$	12.1263	+	2.76776i	0.427132	+	0.0974901i
$807$	−23.1266	−	45.2297i	−0.814096	−	1.59216i
$808$	−15.7763	+	6.19176i	−0.555010	+	0.217825i
$809$	0.113012	−	0.0443541i	0.00397330	−	0.00155941i	−0.363354	−	0.931651i	$-0.618368\pi$
$809$	0.113012	−	0.0443541i	0.00397330	−	0.00155941i	0.367327	+	0.930092i	$0.380273\pi$
$810$	5.13114	+	3.34534i	0.180290	+	0.117543i
$811$	−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
$813$	−1.14162	−	2.71639i	−0.0400384	−	0.0952679i
$814$	19.0295	+	32.9600i	0.666982	+	1.15525i
$815$	1.93752	−	3.35588i	0.0678683	−	0.117551i
$816$	−0.393328	+	3.11161i	−0.0137692	+	0.108928i
$817$	3.60397	−	0.270080i	0.126087	−	0.00944891i
$818$	24.9569	−	31.2950i	0.872599	−	1.09420i
$819$	8.87735	+	17.4265i	0.310200	+	0.608932i
$820$	−3.07623	−	3.85747i	−0.107427	−	0.134709i
$821$	16.9347	+	18.2513i	0.591025	+	0.636974i	0.955763	−	0.294136i	$-0.0950320\pi$
$821$	16.9347	+	18.2513i	0.591025	+	0.636974i	−0.364738	+	0.931110i	$0.618842\pi$
$822$	5.68989	+	16.9955i	0.198458	+	0.592786i
$823$	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
$825$	25.7781	−	18.4913i	0.897478	−	0.643783i
$826$	0.00439888	−	0.0248841i	0.000153057	−	0.000865830i
$827$	12.5799	−	26.1224i	0.437446	−	0.908366i	−0.559392	−	0.828903i	$-0.688965\pi$
$827$	12.5799	−	26.1224i	0.437446	−	0.908366i	0.996838	−	0.0794628i	$-0.0253205\pi$
$828$	6.39674	−	24.8980i	0.222302	−	0.865264i
$829$	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
$831$	−51.7007	−	10.5093i	−1.79348	−	0.364563i
$832$			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
$837$	25.5534	+	5.91903i	0.883256	+	0.204592i
$838$	−13.4698	+	19.7565i	−0.465306	+	0.682479i
$839$	−29.1203	−	14.0236i	−1.00534	−	0.484148i	−0.142595	−	0.989781i	$-0.545545\pi$
$839$	−29.1203	−	14.0236i	−1.00534	−	0.484148i	−0.862748	+	0.505633i	$0.831259\pi$
$840$	2.80797	+	1.35746i	0.0968840	+	0.0468369i
$841$	7.56329	−	3.64229i	0.260803	−	0.125596i
$842$	1.29001	−	8.55863i	0.0444566	−	0.294950i
$843$	29.4660	−	28.6787i	1.01486	−	0.987747i
$844$	14.0125	−	2.11204i	0.482330	−	0.0726995i
$845$	3.45681	−	3.20745i	0.118918	−	0.110340i
$846$	18.3575	−	29.8962i	0.631142	−	1.02785i
$847$	1.40204	−	13.9502i	0.0481748	−	0.479335i
$848$	−9.03875	−	7.20816i	−0.310392	−	0.247529i
$849$	8.84307	+	34.8854i	0.303493	+	1.19727i
$850$	2.42146	−	7.85018i	0.0830554	−	0.269259i
$851$	−69.9561	−	40.3892i	−2.39806	−	1.38452i
$852$	−5.75697	−	6.87587i	−0.197231	−	0.235563i
$853$	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
$855$	−4.34169	+	0.534622i	−0.148483	+	0.0182837i
$856$	1.96237	−	0.605312i	0.0670725	−	0.0206891i
$857$	−2.35624	−	6.00360i	−0.0804876	−	0.205079i	0.884965	−	0.465657i	$-0.154182\pi$
$857$	−2.35624	−	6.00360i	−0.0804876	−	0.205079i	−0.965453	+	0.260578i	$0.916087\pi$
$858$	−8.96854	−	14.7118i	−0.306181	−	0.502254i
$859$	−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
$861$	−4.90179	−	32.8572i	−0.167053	−	1.11977i
$862$	1.16620	+	5.10948i	0.0397211	+	0.174029i
$863$	17.7306	−	10.2368i	0.603556	−	0.348463i	−0.166883	−	0.985977i	$-0.553370\pi$
$863$	17.7306	−	10.2368i	0.603556	−	0.348463i	0.770439	+	0.637514i	$0.220037\pi$
$864$	−0.0167299	+	5.19613i	−0.000569162	+	0.176776i
$865$	3.82230	+	1.17902i	0.129962	+	0.0400880i
$866$	2.77182	+	36.9873i	0.0941901	+	1.25688i
$867$	20.8592	+	11.3884i	0.708416	+	0.386769i
$868$	13.2887	+	1.33556i	0.451049	+	0.0453319i
$869$	9.68854	−	7.72635i	0.328661	−	0.262099i
$870$	−5.74157	−	4.35877i	−0.194657	−	0.147776i
$871$	−2.81123	−	18.6513i	−0.0952550	−	0.631975i
$872$	−2.40276	−	3.52421i	−0.0813678	−	0.119345i
$873$	−5.69535	−	28.4880i	−0.192758	−	0.964172i
$874$	7.96550	+	16.5405i	0.269437	+	0.559492i
$875$	−13.9388	−	10.0305i	−0.471219	−	0.339094i
$876$	8.43376	+	2.38266i	0.284950	+	0.0805027i
$877$	−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
$879$	−3.91173	+	0.387187i	−0.131939	+	0.0130595i
$880$	−2.55778	−	1.00385i	−0.0862227	−	0.0338399i
$881$	33.0838			1.11462			0.557312	−	0.830303i	$-0.311833\pi$
$881$	33.0838			1.11462			0.557312	+	0.830303i	$0.311833\pi$
$882$	11.7774	+	17.3866i	0.396565	+	0.585437i
$883$	−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
$885$	0.0112044	−	0.00110902i	0.000376630	−	3.72793e-5i
$886$	5.44894	+	5.05588i	0.183061	+	0.169856i
$887$	−28.0916	−	19.1525i	−0.943223	−	0.643079i	−0.00907321	−	0.999959i	$-0.502888\pi$
$887$	−28.0916	−	19.1525i	−0.943223	−	0.643079i	−0.934150	+	0.356880i	$0.883841\pi$
$888$	15.7130	+	4.43915i	0.527293	+	0.148968i
$889$	−0.541978	−	0.0958078i	−0.0181773	−	0.00321329i
$890$	−3.16445	−	6.57104i	−0.106072	−	0.220262i
$891$	−18.8131	−	31.0855i	−0.630263	−	1.04140i
$892$	1.89516	+	2.77969i	0.0634546	+	0.0930707i
$893$	3.73419	+	24.7747i	0.124960	+	0.829054i
$894$	−13.3559	−	10.1393i	−0.446688	−	0.339108i
$895$	7.95990	−	6.34781i	0.266070	−	0.212184i
$896$	0.327843	+	2.62536i	0.0109525	+	0.0877071i
$897$	32.0977	+	17.5242i	1.07171	+	0.585114i
$898$	−1.60946	−	21.4768i	−0.0537085	−	0.716690i
$899$	−29.4975	−	9.09877i	−0.983796	−	0.303461i
$900$	2.39218	−	13.3985i	0.0797394	−	0.446617i
$901$	18.1298	−	10.4672i	0.603991	−	0.348714i
$902$	6.51262	+	28.5336i	0.216846	+	0.950067i
$903$	5.26639	−	5.65869i	0.175254	−	0.188309i
$904$	−2.28385	+	10.0062i	−0.0759596	+	0.332801i
$905$	−3.00018	−	9.72634i	−0.0997293	−	0.323315i
$906$	−20.2336	−	33.1908i	−0.672216	−	1.10269i
$907$	−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
$909$	−6.21379	−	50.4625i	−0.206098	−	1.67374i
$910$	−2.85345	+	3.39761i	−0.0945909	+	0.112630i
$911$	43.3160	−	9.88659i	1.43512	−	0.327557i	0.566922	−	0.823771i	$-0.308134\pi$
$911$	43.3160	−	9.88659i	1.43512	−	0.327557i	0.868200	+	0.496214i	$0.165277\pi$
$912$	−2.38226	−	2.84527i	−0.0788846	−	0.0942162i
$913$	−2.26161	−	1.30574i	−0.0748482	−	0.0432136i
$914$	6.95023	−	22.5321i	0.229893	−	0.745295i
$915$	1.20131	+	4.73910i	0.0397141	+	0.156670i
$916$	2.10098	+	1.67548i	0.0694183	+	0.0553593i
$917$	−17.4534	−	5.87248i	−0.576364	−	0.193926i
$918$	−8.74759	−	3.46572i	−0.288713	−	0.114386i
$919$	−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
$921$	3.90050	−	3.79628i	0.128526	−	0.125092i
$922$	−5.12478	+	34.0007i	−0.168776	+	1.11975i
$923$	11.4940	−	5.53524i	0.378331	−	0.182195i
$924$	−11.5133	−	14.4820i	−0.378761	−	0.476422i
$925$	−38.5329	−	18.5564i	−1.26695	−	0.610132i
$926$	1.48819	−	2.18278i	0.0489050	−	0.0717305i
$927$	−7.81165	+	18.4208i	−0.256568	+	0.605020i
$928$	0.456983	−	6.09802i	0.0150012	−	0.200177i
$929$	−15.4365	+	39.3315i	−0.506455	+	1.29043i	0.417761	+	0.908557i	$0.362815\pi$
$929$	−15.4365	+	39.3315i	−0.506455	+	1.29043i	−0.924216	+	0.381869i	$0.875280\pi$
$930$	1.02703	+	5.86136i	0.0336777	+	0.192202i
$931$	−14.4333	−	4.07443i	−0.473033	−	0.133534i
$932$			13.5159i			0.442727i
$933$	−52.3167	−	10.6345i	−1.71277	−	0.348158i
$934$	−41.6942	−	3.12455i	−1.36428	−	0.102238i
$935$	3.38422	−	3.64732i	0.110676	−	0.119280i
$936$	−7.15949	−	1.83940i	−0.234015	−	0.0601227i
$937$	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
$939$	21.4960	−	15.4196i	0.701495	−	0.503200i
$940$	7.87008	+	1.18622i	0.256694	+	0.0386904i
$941$	−23.9532	+	16.3310i	−0.780852	+	0.532376i	−0.886887	−	0.461986i	$-0.847137\pi$
$941$	−23.9532	+	16.3310i	−0.780852	+	0.532376i	0.106035	+	0.994362i	$0.466184\pi$
$942$	5.94375	+	17.7538i	0.193658	+	0.578449i
$943$	−42.2515	−	45.5363i	−1.37590	−	1.48287i
$944$	0.00595504	+	0.00746738i	0.000193820	+	0.000243043i
$945$	−6.04047	+	7.14557i	−0.196496	+	0.232445i
$946$	−4.24612	+	5.32447i	−0.138053	+	0.173113i
$947$	13.1659	−	0.986651i	0.427836	−	0.0320618i	0.140927	−	0.990020i	$-0.454992\pi$
$947$	13.1659	−	0.986651i	0.427836	−	0.0320618i	0.286908	+	0.957958i	$0.407373\pi$
$948$	0.666728	−	5.27448i	0.0216543	−	0.171307i
$949$	−6.23370	+	10.7971i	−0.202354	+	0.350488i
$950$	4.86000	+	8.41777i	0.157679	+	0.273108i
$951$	17.0711	+	40.6192i	0.553568	+	1.31717i
$952$	−4.64223	−	1.18420i	−0.150455	−	0.0383802i
$953$	29.1722	+	6.65836i	0.944979	+	0.215685i	0.667132	−	0.744940i	$-0.267522\pi$
$953$	29.1722	+	6.65836i	0.944979	+	0.215685i	0.277847	+	0.960625i	$0.410379\pi$
$954$	27.6918	−	20.8824i	0.896556	−	0.676091i
$955$	−10.2489	+	4.02239i	−0.331646	+	0.130161i
$956$	−1.77223	+	0.695550i	−0.0573181	+	0.0224957i
$957$	19.4672	+	38.0728i	0.629286	+	1.23072i
$958$	−27.9647	−	6.38276i	−0.903499	−	0.206218i
$959$	−26.8368	+	5.41306i	−0.866606	+	0.174797i
$960$	−1.08675	+	0.456730i	−0.0350747	+	0.0147409i
$961$	−2.75902	−	4.77875i	−0.0890005	−	0.154153i
$962$	−11.6140	+	20.1161i	−0.374452	+	0.648569i
$963$	0.293884	+	6.15381i	0.00947027	+	0.198304i
$964$	−30.3675	+	2.27573i	−0.978070	+	0.0732962i
$965$	−3.39210	+	4.25356i	−0.109196	+	0.136927i
$966$	36.5313	+	14.4011i	1.17538	+	0.463347i
$967$	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
$969$	6.37201	−	2.13327i	0.204698	−	0.0685306i
$970$	5.44558	−	3.71274i	0.174847	−	0.119209i
$971$	11.3400	+	1.70923i	0.363918	+	0.0548519i	0.328456	−	0.944519i	$-0.393472\pi$
$971$	11.3400	+	1.70923i	0.363918	+	0.0548519i	0.0354620	+	0.999371i	$0.488710\pi$
$972$	−15.0856	−	3.92757i	−0.483870	−	0.125977i
$973$	45.4194	−	2.24703i	1.45608	−	0.0720364i
$974$	3.68773	−	7.65765i	0.118163	−	0.245367i
$975$	17.6400	+	7.98227i	0.564933	+	0.255637i
$976$	−2.82091	+	3.04022i	−0.0902952	+	0.0973151i
$977$	−29.0349	−	2.17586i	−0.928908	−	0.0696121i	−0.398325	−	0.917245i	$-0.630408\pi$
$977$	−29.0349	−	2.17586i	−0.928908	−	0.0696121i	−0.530584	+	0.847633i	$0.678027\pi$
$978$	−1.96441	+	9.66398i	−0.0628150	+	0.309020i
$979$			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	$0.247827\pi$
$983$	−3.03230	+	40.4632i	−0.0967152	+	1.29057i	−0.808634	+	0.588313i	$0.799792\pi$
$984$	10.5403	+	6.82369i	0.336012	+	0.217531i
$985$	5.87091	−	8.61104i	0.187063	−	0.274371i
$986$	9.97657	+	4.80446i	0.317719	+	0.153005i
$987$	41.8475	+	33.4755i	1.33202	+	1.06554i
$988$	4.75629	−	2.29051i	0.151318	−	0.0728707i
$989$	2.15433	−	14.2930i	0.0685036	−	0.454491i
$990$	4.82624	−	6.68259i	0.153388	−	0.212386i
$991$	−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
$993$	2.61908	−	2.96136i	0.0831139	−	0.0939760i
$994$	11.5103	−	7.42705i	0.365084	−	0.235572i
$995$	−5.74983	−	4.58533i	−0.182282	−	0.145365i
$996$	−1.08602	+	0.275295i	−0.0344120	+	0.00872306i
$997$	−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
$999$	−24.6285	+	42.3423i	−0.779210	+	1.33965i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.930874 - 0.365341i) q^{2} +(-1.72363 + 0.170607i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.562333 - 0.383392i) q^{5} +(1.66681 + 0.470899i) q^{6} +(-1.02876 + 2.43755i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(2.94179 - 0.588125i) q^{9} +O(q^{10})\)	\(q+(-0.930874 - 0.365341i) q^{2} +(-1.72363 + 0.170607i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.562333 - 0.383392i) q^{5} +(1.66681 + 0.470899i) q^{6} +(-1.02876 + 2.43755i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(2.94179 - 0.588125i) q^{9} +(0.383392 + 0.562333i) q^{10} +(-0.601718 - 3.99214i) q^{11} +(-1.37955 - 1.04730i) q^{12} +(1.92643 - 1.53628i) q^{13} +(1.84818 - 1.89320i) q^{14} +(1.03466 + 0.564888i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(-1.73034 - 0.533738i) q^{17} +(-2.95330 - 0.527285i) q^{18} +(1.85545 - 1.07124i) q^{19} +(-0.151446 - 0.663530i) q^{20} +(1.35734 - 4.37694i) q^{21} +(-0.898369 + 3.93601i) q^{22} +(-2.52571 - 8.18816i) q^{23} +(0.901566 + 1.47891i) q^{24} +(-1.65748 - 4.22318i) q^{25} +(-2.35453 + 0.726277i) q^{26} +(-4.97021 + 1.51560i) q^{27} +(-2.41209 + 1.08712i) q^{28} +(5.96180 - 1.36074i) q^{29} +(-0.756764 - 0.903844i) q^{30} +(-4.37167 - 2.52398i) q^{31} +(0.294755 - 0.955573i) q^{32} +(1.71823 + 6.77831i) q^{33} +(1.41573 + 1.12901i) q^{34} +(1.51304 - 0.976297i) q^{35} +(2.55651 + 1.56980i) q^{36} +(6.91047 - 6.41197i) q^{37} +(-2.11855 + 0.319321i) q^{38} +(-3.05835 + 2.97664i) q^{39} +(-0.101437 + 0.672993i) q^{40} +(6.53147 - 3.14539i) q^{41} +(-2.86259 + 3.57849i) q^{42} +(1.51981 + 0.731902i) q^{43} +(2.27425 - 3.33572i) q^{44} +(-1.87975 - 0.797136i) 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} +(3.07352 + 0.624759i) q^{51} +(2.45711 + 0.184135i) q^{52} +(-7.86348 + 8.47481i) q^{53} +(5.18035 + 0.404990i) q^{54} +(-1.19219 + 2.47561i) q^{55} +(2.64252 - 0.130733i) q^{56} +(-3.01534 + 2.16297i) q^{57} +(-6.04681 - 0.911410i) q^{58} +(0.00789152 - 0.00538035i) q^{59} +(0.374240 + 1.11784i) q^{60} +(2.82091 + 3.04022i) q^{61} +(3.14736 + 3.94666i) q^{62} +(-1.59281 + 7.77579i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(-1.67229 + 0.125321i) q^{65} +(0.876943 - 6.93749i) q^{66} +(3.82751 - 6.62945i) q^{67} +(-0.905393 - 1.56819i) q^{68} +(5.75034 + 13.6824i) q^{69} +(-1.76513 + 0.356033i) q^{70} +(5.04771 + 1.15211i) q^{71} +(-1.80628 - 2.39528i) q^{72} +(-4.71005 + 1.84856i) q^{73} +(-8.77533 + 3.44406i) q^{74} +(3.57738 + 6.99641i) q^{75} +(2.08877 + 0.476748i) q^{76} +(10.3501 + 2.64023i) q^{77} +(3.93443 - 1.65353i) q^{78} +(1.53473 + 2.65823i) q^{79} +(0.340297 - 0.589412i) q^{80} +(8.30822 - 3.46028i) q^{81} +(-7.22911 + 0.541747i) q^{82} +(0.403303 - 0.505726i) q^{83} +(3.97208 - 2.28530i) q^{84} +(0.768395 + 0.963537i) q^{85} +(-1.14736 - 1.23656i) q^{86} +(-10.0438 + 3.36253i) q^{87} +(-3.33572 + 2.27425i) q^{88} +(-10.5964 - 1.59715i) q^{89} +(1.45858 + 1.42878i) q^{90} +(1.76292 + 6.27624i) q^{91} +(3.71788 - 7.72026i) q^{92} +(7.96574 + 3.60457i) q^{93} +(7.95405 - 8.57243i) q^{94} +(-1.45408 - 0.108969i) q^{95} +(-0.345021 + 1.69734i) 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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