LMFDB - Embedded newform 294.2.p.a.101.3

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			101.3
Character	$\chi$	$=$	294.101
Dual form			294.2.p.a.131.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.930874 - 0.365341i) q^{2} +(-1.11291 - 1.32719i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-1.59223 - 1.08556i) q^{5} +(0.551106 + 1.64204i) q^{6} +(1.91180 - 1.82894i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.522848 + 2.95409i) q^{9} +O(q^{10})$	\(q+(-0.930874 - 0.365341i) q^{2} +(-1.11291 - 1.32719i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-1.59223 - 1.08556i) q^{5} +(0.551106 + 1.64204i) q^{6} +(1.91180 - 1.82894i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.522848 + 2.95409i) q^{9} +(1.08556 + 1.59223i) q^{10} +(-0.652132 - 4.32662i) q^{11} +(0.0868930 - 1.72987i) q^{12} +(-2.72177 + 2.17054i) q^{13} +(-2.44783 + 1.00405i) q^{14} +(0.331267 + 3.32132i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(-2.73850 - 0.844714i) q^{17} +(1.56596 - 2.55886i) q^{18} +(-4.83029 + 2.78877i) q^{19} +(-0.428815 - 1.87876i) q^{20} +(-4.55501 - 0.501871i) q^{21} +(-0.973637 + 4.26578i) q^{22} +(1.92503 + 6.24079i) q^{23} +(-0.712879 + 1.57854i) q^{24} +(-0.469963 - 1.19745i) q^{25} +(3.32661 - 1.02612i) q^{26} +(4.50251 - 2.59372i) q^{27} +(2.64544 - 0.0403496i) q^{28} +(-6.29435 + 1.43664i) q^{29} +(0.905046 - 3.21275i) q^{30} +(-2.87900 - 1.66219i) q^{31} +(0.294755 - 0.955573i) q^{32} +(-5.01646 + 5.68065i) q^{33} +(2.24059 + 1.78681i) q^{34} +(-5.02945 + 0.836703i) q^{35} +(-2.39256 + 1.80987i) q^{36} +(7.08497 - 6.57390i) q^{37} +(5.51524 - 0.831289i) q^{38} +(5.90980 + 1.19667i) q^{39} +(-0.287216 + 1.90555i) q^{40} +(-5.79984 + 2.79305i) q^{41} +(4.05679 + 2.13131i) q^{42} +(-0.565103 - 0.272139i) q^{43} +(2.46480 - 3.61520i) q^{44} +(4.03934 - 4.13599i) q^{45} +(0.488057 - 6.51267i) q^{46} +(0.490473 - 1.24971i) q^{47} +(1.24031 - 1.20898i) q^{48} +(0.309979 - 6.99313i) q^{49} +1.28637i q^{50} +(1.92662 + 4.57459i) q^{51} +(-3.47154 - 0.260156i) q^{52} +(3.51633 - 3.78970i) q^{53} +(-5.13886 + 0.769479i) q^{54} +(-3.65847 + 7.59688i) q^{55} +(-2.47732 - 0.928929i) q^{56} +(9.07691 + 3.30704i) q^{57} +(6.38411 + 0.962250i) q^{58} +(1.59180 - 1.08527i) q^{59} +(-2.01623 + 2.66002i) q^{60} +(-9.97775 - 10.7535i) q^{61} +(2.07272 + 2.59910i) q^{62} +(4.40326 + 6.60389i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(6.68992 - 0.501340i) q^{65} +(6.74506 - 3.45525i) q^{66} +(2.49630 - 4.32372i) q^{67} +(-1.43291 - 2.48187i) q^{68} +(6.14030 - 9.50032i) q^{69} +(4.98746 + 1.05860i) q^{70} +(8.32433 + 1.89997i) q^{71} +(2.88840 - 0.810660i) q^{72} +(10.7216 - 4.20791i) q^{73} +(-8.99693 + 3.53103i) q^{74} +(-1.06621 + 1.95638i) q^{75} +(-5.43770 - 1.24112i) q^{76} +(-9.15985 - 7.07893i) q^{77} +(-5.06408 - 3.27304i) q^{78} +(0.441270 + 0.764303i) q^{79} +(0.963539 - 1.66890i) q^{80} +(-8.45326 - 3.08908i) q^{81} +(6.41933 - 0.481063i) q^{82} +(6.56486 - 8.23208i) q^{83} +(-2.99770 - 3.46609i) q^{84} +(3.44332 + 4.31778i) q^{85} +(0.426616 + 0.459783i) q^{86} +(8.91176 + 6.75491i) q^{87} +(-3.61520 + 2.46480i) q^{88} +(1.87383 + 0.282434i) q^{89} +(-5.27116 + 2.37435i) q^{90} +(-1.23371 + 9.12758i) q^{91} +(-2.83367 + 5.88417i) q^{92} +(0.998038 + 5.67084i) q^{93} +(-0.913137 + 0.984128i) q^{94} +(10.7183 + 0.803225i) q^{95} +(-1.59626 + 0.672274i) q^{96} +13.3614i q^{97} +(-2.84343 + 6.39648i) q^{98} +(13.1222 + 0.335709i) 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
$3$	−1.11291	−	1.32719i	−0.642541	−	0.766252i
$3$	−1.11291	−	1.32719i	−0.642541	−	0.766252i
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	−1.59223	−	1.08556i	−0.712066	−	0.485478i	0.152305	−	0.988334i	$-0.451330\pi$
$5$	−1.59223	−	1.08556i	−0.712066	−	0.485478i	−0.864371	+	0.502855i	$0.832283\pi$
$6$	0.551106	+	1.64204i	0.224988	+	0.670358i
$7$	1.91180	−	1.82894i	0.722593	−	0.691273i
$7$	1.91180	−	1.82894i	0.722593	−	0.691273i
$8$	−0.433884	−	0.900969i	−0.153401	−	0.318541i
$9$	−0.522848	+	2.95409i	−0.174283	+	0.984696i
$10$	1.08556	+	1.59223i	0.343285	+	0.503506i
$11$	−0.652132	−	4.32662i	−0.196625	−	1.30452i	−0.841509	−	0.540243i	$-0.818332\pi$
$11$	−0.652132	−	4.32662i	−0.196625	−	1.30452i	0.644884	−	0.764281i	$-0.276906\pi$
$12$	0.0868930	−	1.72987i	0.0250839	−	0.499370i
$13$	−2.72177	+	2.17054i	−0.754882	+	0.601999i	−0.923462	−	0.383689i	$-0.874653\pi$
$13$	−2.72177	+	2.17054i	−0.754882	+	0.601999i	0.168580	+	0.985688i	$0.446082\pi$
$14$	−2.44783	+	1.00405i	−0.654211	+	0.268344i
$15$	0.331267	+	3.32132i	0.0855328	+	0.857561i
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−2.73850	−	0.844714i	−0.664183	−	0.204873i	−0.0557089	−	0.998447i	$-0.517742\pi$
$17$	−2.73850	−	0.844714i	−0.664183	−	0.204873i	−0.608474	+	0.793574i	$0.708218\pi$
$18$	1.56596	−	2.55886i	0.369099	−	0.603130i
$19$	−4.83029	+	2.78877i	−1.10814	+	0.639787i	−0.938348	−	0.345692i	$-0.887644\pi$
$19$	−4.83029	+	2.78877i	−1.10814	+	0.639787i	−0.169796	+	0.985479i	$0.554311\pi$
$20$	−0.428815	−	1.87876i	−0.0958860	−	0.420104i
$21$	−4.55501	−	0.501871i	−0.993985	−	0.109517i
$22$	−0.973637	+	4.26578i	−0.207580	+	0.909468i
$23$	1.92503	+	6.24079i	0.401396	+	1.30129i	0.900539	+	0.434774i	$0.143172\pi$
$23$	1.92503	+	6.24079i	0.401396	+	1.30129i	−0.499144	+	0.866519i	$0.666352\pi$
$24$	−0.712879	+	1.57854i	−0.145516	+	0.322219i
$25$	−0.469963	−	1.19745i	−0.0939926	−	0.239489i
$26$	3.32661	−	1.02612i	0.652401	−	0.201239i
$27$	4.50251	−	2.59372i	0.866508	−	0.499163i
$28$	2.64544	−	0.0403496i	0.499942	−	0.00762536i
$29$	−6.29435	+	1.43664i	−1.16883	+	0.266778i	−0.762525	−	0.646959i	$-0.776041\pi$
$29$	−6.29435	+	1.43664i	−1.16883	+	0.266778i	−0.406306	+	0.913737i	$0.633183\pi$
$30$	0.905046	−	3.21275i	0.165238	−	0.586566i
$31$	−2.87900	−	1.66219i	−0.517083	−	0.298538i	0.218657	−	0.975802i	$-0.429832\pi$
$31$	−2.87900	−	1.66219i	−0.517083	−	0.298538i	−0.735740	+	0.677264i	$0.763166\pi$
$32$	0.294755	−	0.955573i	0.0521058	−	0.168923i
$33$	−5.01646	+	5.68065i	−0.873253	+	0.988874i
$34$	2.24059	+	1.78681i	0.384257	+	0.306435i
$35$	−5.02945	+	0.836703i	−0.850132	+	0.141429i
$36$	−2.39256	+	1.80987i	−0.398761	+	0.301645i
$37$	7.08497	−	6.57390i	1.16476	−	1.08074i	0.169302	−	0.985564i	$-0.445849\pi$
$37$	7.08497	−	6.57390i	1.16476	−	1.08074i	0.995460	−	0.0951775i	$-0.0303419\pi$
$38$	5.51524	−	0.831289i	0.894690	−	0.134853i
$39$	5.90980	+	1.19667i	0.946325	+	0.191621i
$40$	−0.287216	+	1.90555i	−0.0454129	+	0.301295i
$41$	−5.79984	+	2.79305i	−0.905782	+	0.436202i	−0.827974	−	0.560766i	$-0.810507\pi$
$41$	−5.79984	+	2.79305i	−0.905782	+	0.436202i	−0.0778085	+	0.996968i	$0.524792\pi$
$42$	4.05679	+	2.13131i	0.625976	+	0.328868i
$43$	−0.565103	−	0.272139i	−0.0861775	−	0.0415009i	0.390299	−	0.920688i	$-0.372372\pi$
$43$	−0.565103	−	0.272139i	−0.0861775	−	0.0415009i	−0.476476	+	0.879187i	$0.658086\pi$
$44$	2.46480	−	3.61520i	0.371582	−	0.545011i
$45$	4.03934	−	4.13599i	0.602149	−	0.616557i
$46$	0.488057	−	6.51267i	0.0719602	−	0.960241i
$47$	0.490473	−	1.24971i	0.0715429	−	0.182288i	−0.890629	−	0.454730i	$-0.849736\pi$
$47$	0.490473	−	1.24971i	0.0715429	−	0.182288i	0.962172	+	0.272441i	$0.0878311\pi$
$48$	1.24031	−	1.20898i	0.179023	−	0.174502i
$49$	0.309979	−	6.99313i	0.0442827	−	0.999019i
$50$			1.28637i			0.181920i
$51$	1.92662	+	4.57459i	0.269780	+	0.640571i
$52$	−3.47154	−	0.260156i	−0.481416	−	0.0360771i
$53$	3.51633	−	3.78970i	0.483005	−	0.520555i	−0.443786	−	0.896133i	$-0.646365\pi$
$53$	3.51633	−	3.78970i	0.483005	−	0.520555i	0.926791	+	0.375577i	$0.122556\pi$
$54$	−5.13886	+	0.769479i	−0.699311	+	0.104713i
$55$	−3.65847	+	7.59688i	−0.493307	+	1.02436i
$56$	−2.47732	−	0.928929i	−0.331045	−	0.124133i
$57$	9.07691	+	3.30704i	1.20227	+	0.438028i
$58$	6.38411	+	0.962250i	0.838275	+	0.126350i
$59$	1.59180	−	1.08527i	0.207235	−	0.141290i	−0.455255	−	0.890361i	$-0.650452\pi$
$59$	1.59180	−	1.08527i	0.207235	−	0.141290i	0.662490	+	0.749071i	$0.269500\pi$
$60$	−2.01623	+	2.66002i	−0.260295	+	0.343407i
$61$	−9.97775	−	10.7535i	−1.27752	−	1.37684i	−0.890640	−	0.454709i	$-0.849743\pi$
$61$	−9.97775	−	10.7535i	−1.27752	−	1.37684i	−0.386880	−	0.922130i	$-0.626447\pi$
$62$	2.07272	+	2.59910i	0.263235	+	0.330087i
$63$	4.40326	+	6.60389i	0.554758	+	0.832012i
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	6.68992	−	0.501340i	0.829783	−	0.0621836i
$66$	6.74506	−	3.45525i	0.830260	−	0.425312i
$67$	2.49630	−	4.32372i	0.304972	−	0.528227i	−0.672283	−	0.740294i	$-0.734686\pi$
$67$	2.49630	−	4.32372i	0.304972	−	0.528227i	0.977255	+	0.212067i	$0.0680196\pi$
$68$	−1.43291	−	2.48187i	−0.173766	−	0.300971i
$69$	6.14030	−	9.50032i	0.739205	−	1.14370i
$70$	4.98746	+	1.05860i	0.596116	+	0.126527i
$71$	8.32433	+	1.89997i	0.987916	+	0.225485i	0.685804	−	0.727787i	$-0.259451\pi$
$71$	8.32433	+	1.89997i	0.987916	+	0.225485i	0.302113	+	0.953272i	$0.402308\pi$
$72$	2.88840	−	0.810660i	0.340401	−	0.0955372i
$73$	10.7216	−	4.20791i	1.25486	−	0.492498i	0.357552	−	0.933893i	$-0.383612\pi$
$73$	10.7216	−	4.20791i	1.25486	−	0.492498i	0.897313	+	0.441395i	$0.145516\pi$
$74$	−8.99693	+	3.53103i	−1.04587	+	0.410474i
$75$	−1.06621	+	1.95638i	−0.123115	+	0.225904i
$76$	−5.43770	−	1.24112i	−0.623747	−	0.142366i
$77$	−9.15985	−	7.07893i	−1.04386	−	0.806718i
$78$	−5.06408	−	3.27304i	−0.573394	−	0.370599i
$79$	0.441270	+	0.764303i	0.0496468	+	0.0859908i	0.889781	−	0.456388i	$-0.150857\pi$
$79$	0.441270	+	0.764303i	0.0496468	+	0.0859908i	−0.840134	+	0.542379i	$0.817524\pi$
$80$	0.963539	−	1.66890i	0.107727	−	0.186589i
$81$	−8.45326	−	3.08908i	−0.939251	−	0.343231i
$82$	6.41933	−	0.481063i	0.708897	−	0.0531245i
$83$	6.56486	−	8.23208i	0.720587	−	0.903588i	−0.277784	−	0.960644i	$-0.589600\pi$
$83$	6.56486	−	8.23208i	0.720587	−	0.903588i	0.998371	+	0.0570559i	$0.0181713\pi$
$84$	−2.99770	−	3.46609i	−0.327076	−	0.378182i
$85$	3.44332	+	4.31778i	0.373480	+	0.468329i
$86$	0.426616	+	0.459783i	0.0460032	+	0.0495797i
$87$	8.91176	+	6.75491i	0.955441	+	0.724203i
$88$	−3.61520	+	2.46480i	−0.385381	+	0.262748i
$89$	1.87383	+	0.282434i	0.198625	+	0.0299379i	0.247601	−	0.968862i	$-0.420358\pi$
$89$	1.87383	+	0.282434i	0.198625	+	0.0299379i	−0.0489761	+	0.998800i	$0.515596\pi$
$90$	−5.27116	+	2.37435i	−0.555629	+	0.250279i
$91$	−1.23371	+	9.12758i	−0.129328	+	0.956830i
$92$	−2.83367	+	5.88417i	−0.295430	+	0.613467i
$93$	0.998038	+	5.67084i	0.103492	+	0.588039i
$94$	−0.913137	+	0.984128i	−0.0941829	+	0.101505i
$95$	10.7183	+	0.803225i	1.09967	+	0.0824092i
$96$	−1.59626	+	0.672274i	−0.162918	+	0.0686137i
$97$			13.3614i			1.35664i	0.734765	+	0.678322i	$0.237293\pi$
$97$			13.3614i			1.35664i	−0.734765	+	0.678322i	$0.762707\pi$
$98$	−2.84343	+	6.39648i	−0.287230	+	0.646142i
$99$	13.1222	+	0.335709i	1.31883	+	0.0337400i
$100$	0.469963	−	1.19745i	0.0469963	−	0.119745i
$101$	0.135976	−	1.81447i	0.0135301	−	0.180546i	−0.986344	−	0.164696i	$-0.947336\pi$
$101$	0.135976	−	1.81447i	0.0135301	−	0.180546i	0.999874	−	0.0158499i	$-0.00504538\pi$
$102$	−0.122150	−	4.96224i	−0.0120947	−	0.491335i
$103$	4.50901	−	6.61350i	0.444286	−	0.651648i	−0.537139	−	0.843494i	$-0.680495\pi$
$103$	4.50901	−	6.61350i	0.444286	−	0.651648i	0.981425	+	0.191846i	$0.0614474\pi$
$104$	3.13652	+	1.51047i	0.307561	+	0.148113i
$105$	6.70780	+	5.74384i	0.654614	+	0.560541i
$106$	−4.65779	+	2.24307i	−0.452405	+	0.217867i
$107$	−1.64012	+	10.8815i	−0.158556	+	1.05195i	0.758060	+	0.652184i	$0.226147\pi$
$107$	−1.64012	+	10.8815i	−0.158556	+	1.05195i	−0.916617	+	0.399767i	$0.869091\pi$
$108$	5.06475	+	1.16115i	0.487356	+	0.111732i
$109$	−15.7605	+	2.37552i	−1.50959	+	0.227533i	−0.851078	−	0.525040i	$-0.824050\pi$
$109$	−15.7605	+	2.37552i	−1.50959	+	0.227533i	−0.658508	+	0.752573i	$0.728812\pi$
$110$	6.18102	−	5.73515i	0.589337	−	0.546825i
$111$	−16.6097	−	2.08691i	−1.57653	−	0.198081i
$112$	1.96669	+	1.76978i	0.185835	+	0.167229i
$113$	−15.2416	−	12.1547i	−1.43381	−	1.14342i	−0.965672	−	0.259764i	$-0.916355\pi$
$113$	−15.2416	−	12.1547i	−1.43381	−	1.14342i	−0.468133	−	0.883658i	$-0.655073\pi$
$114$	−7.24126	−	6.39460i	−0.678206	−	0.598909i
$115$	3.70968	−	12.0265i	0.345929	−	1.12148i
$116$	−5.59125	−	3.22811i	−0.519135	−	0.299722i
$117$	−4.98888	−	9.17520i	−0.461222	−	0.848247i
$118$	−1.87826	+	0.428700i	−0.172908	+	0.0394650i
$119$	−6.78039	+	3.39361i	−0.621558	+	0.311092i
$120$	2.84867	−	1.73953i	0.260047	−	0.158796i
$121$	−7.78302	+	2.40074i	−0.707547	+	0.218249i
$122$	5.35935	+	13.6554i	0.485212	+	1.23630i
$123$	10.1616	+	4.58904i	0.916242	+	0.413780i
$124$	−0.979878	−	3.17669i	−0.0879957	−	0.285275i
$125$	−2.69569	+	11.8106i	−0.241110	+	1.05637i
$126$	−1.68620	−	7.75608i	−0.150219	−	0.690966i
$127$	−2.43999	−	10.6903i	−0.216515	−	0.948612i	−0.960031	−	0.279894i	$-0.909701\pi$
$127$	−2.43999	−	10.6903i	−0.216515	−	0.948612i	0.743516	−	0.668718i	$-0.233157\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	0.267731	+	1.05287i	0.0235724	+	0.0926996i
$130$	−6.41063	−	1.97742i	−0.562250	−	0.173431i
$131$	−0.338698	−	4.51961i	−0.0295922	−	0.394880i	−0.992259	−	0.124190i	$-0.960367\pi$
$131$	−0.338698	−	4.51961i	−0.0295922	−	0.394880i	0.962666	−	0.270691i	$-0.0872521\pi$
$132$	−7.54115	+	0.752151i	−0.656373	+	0.0654664i
$133$	−4.13408	+	14.1659i	−0.358470	+	1.22834i
$134$	−3.90337	+	3.11284i	−0.337200	+	0.268908i
$135$	−9.98467	−	0.757954i	−0.859343	−	0.0652343i
$136$	0.427128	+	2.83381i	0.0366259	+	0.242997i
$137$	−3.81896	−	5.60138i	−0.326276	−	0.478559i	0.627695	−	0.778460i	$-0.283999\pi$
$137$	−3.81896	−	5.60138i	−0.326276	−	0.478559i	−0.953970	+	0.299901i	$0.903046\pi$
$138$	−9.18670	+	6.60030i	−0.782024	+	0.561855i
$139$	−5.52085	−	11.4642i	−0.468272	−	0.972377i	−0.992665	−	0.120901i	$-0.961422\pi$
$139$	−5.52085	−	11.4642i	−0.468272	−	0.972377i	0.524392	−	0.851477i	$-0.324293\pi$
$140$	−4.25595	−	2.80755i	−0.359693	−	0.237281i
$141$	−2.20445	+	0.739864i	−0.185648	+	0.0623078i
$142$	−7.05476	−	4.80986i	−0.592023	−	0.403634i
$143$	11.1660	+	10.3606i	0.933750	+	0.866394i
$144$	−2.98490	−	0.300627i	−0.248742	−	0.0250523i
$145$	11.5816	+	4.54544i	0.961799	+	0.377478i
$146$	−11.5177			−0.953216
$147$	−9.62617	+	7.37135i	−0.793953	+	0.607979i
$148$	9.66504			0.794461
$149$	5.61292	+	2.20291i	0.459829	+	0.180469i	0.583937	−	0.811799i	$-0.301512\pi$
$149$	5.61292	+	2.20291i	0.459829	+	0.180469i	−0.124108	+	0.992269i	$0.539607\pi$
$150$	1.70725	−	1.43162i	0.139396	−	0.116891i
$151$	8.00589	+	7.42838i	0.651510	+	0.604513i	0.935079	−	0.354439i	$-0.115328\pi$
$151$	8.00589	+	7.42838i	0.651510	+	0.604513i	−0.283569	+	0.958952i	$0.591519\pi$
$152$	4.60838	+	3.14194i	0.373789	+	0.254845i
$153$	3.92718	−	7.64810i	0.317494	−	0.618312i
$154$	5.94045	+	9.93606i	0.478695	+	0.800670i
$155$	2.77961	+	5.77191i	0.223263	+	0.463611i
$156$	3.51824	+	4.89691i	0.281685	+	0.392066i
$157$	−13.0248	−	19.1038i	−1.03949	−	1.52465i	−0.838384	−	0.545081i	$-0.816499\pi$
$157$	−13.0248	−	19.1038i	−1.03949	−	1.52465i	−0.201105	−	0.979570i	$-0.564453\pi$
$158$	−0.131536	−	0.872684i	−0.0104644	−	0.0694270i
$159$	−8.94301	−	0.449216i	−0.709227	−	0.0356251i
$160$	−1.50665	+	1.20151i	−0.119111	+	0.0949880i
$161$	15.0943	+	8.41040i	1.18960	+	0.662832i
$162$	6.74035	+	5.96387i	0.529572	+	0.468566i
$163$	0.985326	+	13.1483i	0.0771767	+	1.02985i	0.892560	+	0.450929i	$0.148907\pi$
$163$	0.985326	+	13.1483i	0.0771767	+	1.02985i	−0.815383	+	0.578922i	$0.803474\pi$
$164$	−6.15134	−	1.89744i	−0.480339	−	0.148165i
$165$	14.1540	−	3.59920i	1.10189	−	0.280198i
$166$	−9.11857	+	5.26461i	−0.707738	+	0.408613i
$167$	−2.18483	−	9.57234i	−0.169067	−	0.740730i	−0.986373	−	0.164526i	$-0.947391\pi$
$167$	−2.18483	−	9.57234i	−0.169067	−	0.740730i	0.817306	−	0.576204i	$-0.195467\pi$
$168$	1.52418	+	4.32168i	0.117593	+	0.333425i
$169$	−0.195986	+	0.858670i	−0.0150758	+	0.0660515i
$170$	−1.62783	−	5.27730i	−0.124849	−	0.404750i
$171$	−5.71276	−	15.7272i	−0.436865	−	1.20269i
$172$	−0.229148	−	0.583860i	−0.0174724	−	0.0445189i
$173$	9.42829	−	2.90824i	0.716820	−	0.221110i	0.0851732	−	0.996366i	$-0.472856\pi$
$173$	9.42829	−	2.90824i	0.716820	−	0.221110i	0.631646	+	0.775257i	$0.282379\pi$
$174$	−5.82787	−	9.54380i	−0.441810	−	0.723514i
$175$	−3.08853	−	1.42975i	−0.233471	−	0.108079i
$176$	4.26578	−	0.973637i	0.321546	−	0.0733907i
$177$	−3.21189	−	0.904803i	−0.241420	−	0.0680092i
$178$	−1.64111	−	0.947495i	−0.123006	−	0.0710178i
$179$	3.25575	−	10.5549i	0.243346	−	0.788909i	−0.748686	−	0.662925i	$-0.769315\pi$
$179$	3.25575	−	10.5549i	0.243346	−	0.788909i	0.992032	−	0.125984i	$-0.0402088\pi$
$180$	5.77423	−	0.284450i	0.430386	−	0.0212016i
$181$	1.06069	+	0.845872i	0.0788405	+	0.0628732i	0.662117	−	0.749400i	$-0.269658\pi$
$181$	1.06069	+	0.845872i	0.0788405	+	0.0628732i	−0.583277	+	0.812274i	$0.698230\pi$
$182$	4.48310	−	8.04590i	0.332310	−	0.596402i
$183$	−3.16747	+	25.2100i	−0.234146	+	1.86358i
$184$	4.78752	−	4.44216i	0.352940	−	0.327481i
$185$	−18.4173	+	2.77595i	−1.35406	+	0.204092i
$186$	1.14274	−	5.64346i	0.0837900	−	0.413799i
$187$	−1.86889	+	12.3993i	−0.136667	+	0.906726i
$188$	1.20956	−	0.582492i	0.0882161	−	0.0424826i
$189$	3.86415	−	13.1935i	0.281076	−	0.959686i
$190$	−9.68393	−	4.66353i	−0.702546	−	0.338328i
$191$	4.20572	−	6.16866i	0.304315	−	0.446349i	−0.643370	−	0.765556i	$-0.722464\pi$
$191$	4.20572	−	6.16866i	0.304315	−	0.446349i	0.947685	+	0.319207i	$0.103417\pi$
$192$	1.73153	−	0.0426233i	0.124962	−	0.00307607i
$193$	−1.05602	+	14.0916i	−0.0760141	+	1.01434i	0.820594	+	0.571512i	$0.193643\pi$
$193$	−1.05602	+	14.0916i	−0.0760141	+	1.01434i	−0.896608	+	0.442826i	$0.853976\pi$
$194$	4.88147	−	12.4378i	0.350469	−	0.892980i
$195$	−8.11068	−	8.32083i	−0.580818	−	0.595867i
$196$	4.98377	−	4.91549i	0.355984	−	0.351106i
$197$		−	15.5486i		−	1.10779i	−0.832586	−	0.553896i	$-0.813141\pi$
$197$		−	15.5486i		−	1.10779i	0.832586	−	0.553896i	$-0.186859\pi$
$198$	−12.0924	−	5.10657i	−0.859372	−	0.362908i
$199$	10.7443	+	0.805177i	0.761646	+	0.0570775i	0.449889	−	0.893084i	$-0.351464\pi$
$199$	10.7443	+	0.805177i	0.761646	+	0.0570775i	0.311757	+	0.950162i	$0.399083\pi$
$200$	−0.874953	+	0.942975i	−0.0618685	+	0.0666784i
$201$	−8.51655	+	1.49887i	−0.600711	+	0.105722i
$202$	−0.789475	+	1.63936i	−0.0555473	+	0.115345i
$203$	−9.40602	+	14.2585i	−0.660173	+	1.00075i
$204$	−1.69920	+	4.66384i	−0.118968	+	0.326534i
$205$	12.2667	+	1.84891i	0.856743	+	0.129133i
$206$	−6.61350	+	4.50901i	−0.460784	+	0.314157i
$207$	−19.4423	+	2.42371i	−1.35133	+	0.168460i
$208$	−2.36787	−	2.55195i	−0.164182	−	0.176946i
$209$	15.2159	+	19.0802i	1.05251	+	1.31980i
$210$	−4.14565	−	7.79742i	−0.286077	−	0.538073i
$211$	−6.01190	+	7.53869i	−0.413876	+	0.518985i	−0.944450	−	0.328654i	$-0.893405\pi$
$211$	−6.01190	+	7.53869i	−0.413876	+	0.518985i	0.530574	+	0.847639i	$0.321976\pi$
$212$	5.15530	−	0.386336i	0.354068	−	0.0265337i
$213$	−6.74264	−	13.1624i	−0.461998	−	0.901876i
$214$	5.50219	−	9.53007i	0.376122	−	0.651462i
$215$	0.604349	+	1.04676i	0.0412162	+	0.0713886i
$216$	−4.29043	−	2.93125i	−0.291927	−	0.199446i
$217$	−8.54411	+	2.08773i	−0.580012	+	0.141724i
$218$	15.5389	+	3.54666i	1.05243	+	0.240210i
$219$	−17.5169	−	9.54649i	−1.18368	−	0.645092i
$220$	−7.84904	+	3.08052i	−0.529182	+	0.207689i
$221$	9.28703	−	3.64489i	0.624714	−	0.245182i
$222$	14.6991	+	8.01087i	0.986542	+	0.537654i
$223$	13.9753	+	3.18977i	0.935855	+	0.213603i	0.663143	−	0.748493i	$-0.269222\pi$
$223$	13.9753	+	3.18977i	0.935855	+	0.213603i	0.272712	+	0.962096i	$0.412079\pi$
$224$	−1.18417	−	2.36596i	−0.0791206	−	0.158082i
$225$	3.78308	−	0.762229i	0.252205	−	0.0508153i
$226$	9.74735	+	16.8829i	0.648384	+	1.12303i
$227$	−5.18143	+	8.97450i	−0.343903	+	0.595658i	−0.985154	−	0.171673i	$-0.945083\pi$
$227$	−5.18143	+	8.97450i	−0.343903	+	0.595658i	0.641251	+	0.767332i	$0.278416\pi$
$228$	4.40449	+	8.59809i	0.291694	+	0.569423i
$229$	4.50798	−	0.337827i	0.297896	−	0.0223242i	0.0750562	−	0.997179i	$-0.476086\pi$
$229$	4.50798	−	0.337827i	0.297896	−	0.0223242i	0.222840	+	0.974855i	$0.428467\pi$
$230$	−7.84701	+	9.83984i	−0.517417	+	0.648820i
$231$	0.799068	+	20.0351i	0.0525748	+	1.31821i
$232$	4.02539	+	5.04768i	0.264280	+	0.331396i
$233$	17.0290	+	18.3529i	1.11561	+	1.20234i	0.977281	+	0.211950i	$0.0679813\pi$
$233$	17.0290	+	18.3529i	1.11561	+	1.20234i	0.138325	+	0.990387i	$0.455828\pi$
$234$	1.29194	+	10.3636i	0.0844570	+	0.677489i
$235$	−2.13758	+	1.45738i	−0.139440	+	0.0950687i
$236$	1.90504	+	0.287139i	0.124008	+	0.0186912i
$237$	0.523277	−	1.43625i	0.0339905	−	0.0932945i
$238$	7.55152	−	0.681867i	0.489492	−	0.0441989i
$239$	8.31301	−	17.2621i	0.537724	−	1.11660i	−0.438279	−	0.898839i	$-0.644412\pi$
$239$	8.31301	−	17.2621i	0.537724	−	1.11660i	0.976003	−	0.217756i	$-0.0698738\pi$
$240$	−3.28728	+	0.578543i	−0.212193	+	0.0373448i
$241$	−8.23876	+	8.87928i	−0.530705	+	0.571964i	−0.940319	−	0.340295i	$-0.889473\pi$
$241$	−8.23876	+	8.87928i	−0.530705	+	0.571964i	0.409613	+	0.912259i	$0.365664\pi$
$242$	8.12210	+	0.608667i	0.522108	+	0.0391266i
$243$	5.30796	+	14.6569i	0.340506	+	0.940242i
$244$		−	14.6694i		−	0.939114i
$245$	−8.08504	+	10.7982i	−0.516534	+	0.689869i
$246$	−7.78262	−	7.98427i	−0.496202	−	0.509059i
$247$	7.09380	−	18.0747i	0.451367	−	1.15007i
$248$	−0.248431	+	3.31508i	−0.0157754	+	0.210508i
$249$	−18.2316	+	0.448790i	−1.15538	+	0.0284409i
$250$	6.82424	−	10.0093i	0.431603	−	0.633045i
$251$	7.02560	+	3.38335i	0.443452	+	0.213555i	0.642266	−	0.766482i	$-0.277995\pi$
$251$	7.02560	+	3.38335i	0.443452	+	0.213555i	−0.198814	+	0.980037i	$0.563709\pi$
$252$	−1.26397	+	7.83597i	−0.0796226	+	0.493620i
$253$	25.7461	−	12.3987i	1.61864	−	0.779498i
$254$	−1.63428	+	10.8428i	−0.102544	+	0.680335i
$255$	1.89839	−	9.37525i	0.118882	−	0.587101i
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	8.29617	−	7.69772i	0.517501	−	0.480171i	−0.377641	−	0.925952i	$-0.623265\pi$
$257$	8.29617	−	7.69772i	0.517501	−	0.480171i	0.895142	+	0.445781i	$0.147074\pi$
$258$	0.135431	−	1.07790i	0.00843156	−	0.0671070i
$259$	1.52183	−	25.5260i	0.0945621	−	1.58611i
$260$	5.24506	+	4.18280i	0.325285	+	0.259406i
$261$	−0.952981	−	19.3452i	−0.0589880	−	1.19744i
$262$	−1.33591	+	4.33093i	−0.0825331	+	0.267566i
$263$	−21.3092	−	12.3029i	−1.31398	−	0.758627i	−0.331228	−	0.943551i	$-0.607463\pi$
$263$	−21.3092	−	12.3029i	−1.31398	−	0.758627i	−0.982753	+	0.184924i	$0.940796\pi$
$264$	7.29465	+	2.05493i	0.448955	+	0.126472i
$265$	−9.71275	+	2.21687i	−0.596649	+	0.136181i
$266$	9.02368	−	11.6763i	0.553277	−	0.715919i
$267$	−1.71056	−	2.80124i	−0.104685	−	0.171433i
$268$	4.77080	−	1.47160i	0.291423	−	0.0898920i
$269$	3.51543	+	8.95717i	0.214340	+	0.546128i	0.997092	−	0.0762047i	$-0.0242803\pi$
$269$	3.51543	+	8.95717i	0.214340	+	0.546128i	−0.782753	+	0.622333i	$0.786185\pi$
$270$	9.01755	+	4.35337i	0.548791	+	0.264938i
$271$	−6.15735	−	19.9616i	−0.374032	−	1.21258i	−0.925616	−	0.378463i	$-0.876453\pi$
$271$	−6.15735	−	19.9616i	−0.374032	−	1.21258i	0.551584	−	0.834119i	$-0.314024\pi$
$272$	0.637704	−	2.79396i	0.0386665	−	0.169409i
$273$	13.4870	−	8.52084i	0.816271	−	0.515705i
$274$	1.50855	+	6.60940i	0.0911350	+	0.399289i
$275$	−4.87441	+	2.81424i	−0.293938	+	0.169705i
$276$	10.9630	−	2.78777i	0.659896	−	0.167804i
$277$	30.8897	+	9.52820i	1.85598	+	0.572494i	0.998298	+	0.0583143i	$0.0185725\pi$
$277$	30.8897	+	9.52820i	1.85598	+	0.572494i	0.857682	+	0.514180i	$0.171904\pi$
$278$	0.950885	+	12.6887i	0.0570303	+	0.761016i
$279$	6.41553	−	7.63573i	0.384088	−	0.457139i
$280$	2.93604	+	4.16834i	0.175462	+	0.249106i
$281$	14.9147	−	11.8941i	0.889738	−	0.709542i	−0.0678463	−	0.997696i	$-0.521613\pi$
$281$	14.9147	−	11.8941i	0.889738	−	0.709542i	0.957584	+	0.288153i	$0.0930413\pi$
$282$	2.32236	+	0.116655i	0.138295	+	0.00694668i
$283$	−0.0602975	−	0.400048i	−0.00358432	−	0.0237804i	0.986967	−	0.160922i	$-0.0514467\pi$
$283$	−0.0602975	−	0.400048i	−0.00358432	−	0.0237804i	−0.990551	+	0.137141i	$0.956209\pi$
$284$	4.80986	+	7.05476i	0.285412	+	0.418623i
$285$	−10.8625	−	15.1191i	−0.643439	−	0.895578i
$286$	−6.60903	−	13.7238i	−0.390800	−	0.811504i
$287$	−5.97982	+	15.9473i	−0.352978	+	0.941340i
$288$	2.66873	+	1.37035i	0.157257	+	0.0807488i
$289$	−7.26024	−	4.94995i	−0.427073	−	0.291173i
$290$	−9.12037	−	8.46247i	−0.535566	−	0.496933i
$291$	17.7331	−	14.8701i	1.03953	−	0.871699i
$292$	10.7216	+	4.20791i	0.627432	+	0.246249i
$293$	1.58808			0.0927765			0.0463882	−	0.998923i	$-0.485229\pi$
$293$	1.58808			0.0927765			0.0463882	+	0.998923i	$0.485229\pi$
$294$	11.6538	−	3.34496i	0.679664	−	0.195082i
$295$	−3.71263			−0.216158
$296$	−8.99693	−	3.53103i	−0.522936	−	0.205237i
$297$	−14.1583	−	17.7892i	−0.821547	−	1.03223i
$298$	−4.42011	−	4.10126i	−0.256050	−	0.237580i
$299$	−18.7853	−	12.8076i	−1.08638	−	0.740684i
$300$	−2.11226	+	0.708925i	−0.121952	+	0.0409298i
$301$	−1.57809	+	0.513262i	−0.0909597	+	0.0295839i
$302$	−4.73858	−	9.83976i	−0.272675	−	0.566215i
$303$	−2.55947	+	1.83888i	−0.147037	+	0.105641i
$304$	−3.14194	−	4.60838i	−0.180203	−	0.264309i
$305$	4.21330	+	27.9534i	0.241253	+	1.60061i
$306$	−6.44987	+	5.68466i	−0.368715	+	0.324970i
$307$	6.07033	−	4.84092i	0.346452	−	0.276286i	−0.434767	−	0.900543i	$-0.643169\pi$
$307$	6.07033	−	4.84092i	0.346452	−	0.276286i	0.781219	+	0.624257i	$0.214598\pi$
$308$	−1.89976	−	11.4195i	−0.108249	−	0.650687i
$309$	−13.7955	+	1.37596i	−0.784798	+	0.0782754i
$310$	−0.478746	−	6.38843i	−0.0271910	−	0.362838i
$311$	19.0510	+	5.87646i	1.08028	+	0.333223i	0.783290	−	0.621656i	$-0.213540\pi$
$311$	19.0510	+	5.87646i	1.08028	+	0.333223i	0.296993	+	0.954880i	$0.404016\pi$
$312$	−1.48600	−	5.84376i	−0.0841282	−	0.330838i
$313$	−11.2879	+	6.51706i	−0.638029	+	0.368366i	−0.783855	−	0.620944i	$-0.786749\pi$
$313$	−11.2879	+	6.51706i	−0.638029	+	0.368366i	0.145826	+	0.989310i	$0.453416\pi$
$314$	5.14500	+	22.5417i	0.290349	+	1.27210i
$315$	0.157947	−	15.2949i	0.00889933	−	0.861770i
$316$	−0.196384	+	0.860414i	−0.0110475	+	0.0484021i
$317$	−4.56335	−	14.7940i	−0.256303	−	0.830915i	−0.988683	−	0.150019i	$-0.952067\pi$
$317$	−4.56335	−	14.7940i	−0.256303	−	0.830915i	0.732380	−	0.680896i	$-0.238410\pi$
$318$	8.16069	+	3.68541i	0.457629	+	0.206668i
$319$	10.3206	+	26.2963i	0.577840	+	1.47231i
$320$	1.84146	−	0.568016i	0.102941	−	0.0317531i
$321$	16.2671	−	9.93339i	0.907938	−	0.554428i
$322$	−10.9782	−	13.3436i	−0.611791	−	0.743608i
$323$	15.5834	−	3.55682i	0.867086	−	0.197907i
$324$	−4.09557	−	8.01413i	−0.227532	−	0.445230i
$325$	3.87823	+	2.23910i	0.215126	+	0.124203i
$326$	3.88639	−	12.5994i	0.215247	−	0.697814i
$327$	20.6929	+	18.2734i	1.14432	+	1.01052i
$328$	5.03291	+	4.01361i	0.277896	+	0.221615i
$329$	−1.34794	−	3.28624i	−0.0743146	−	0.181176i
$330$	−14.4906	−	1.82065i	−0.797679	−	0.100223i
$331$	−4.20048	+	3.89747i	−0.230879	+	0.214224i	−0.787125	−	0.616793i	$-0.788432\pi$
$331$	−4.20048	+	3.89747i	−0.230879	+	0.214224i	0.556246	+	0.831017i	$0.312241\pi$
$332$	10.4116	−	1.56930i	0.571412	−	0.0861265i
$333$	15.7155	+	24.3668i	0.861204	+	1.33529i
$334$	−1.46337	+	9.70885i	−0.0800722	+	0.531245i
$335$	−8.66835	+	4.17446i	−0.473602	+	0.228075i
$336$	0.160071	−	4.57978i	0.00873259	−	0.249847i
$337$	−22.0235	−	10.6060i	−1.19970	−	0.577743i	−0.276107	−	0.961127i	$-0.589044\pi$
$337$	−22.0235	−	10.6060i	−1.19970	−	0.577743i	−0.923589	+	0.383383i	$0.874759\pi$
$338$	0.496145	−	0.727712i	0.0269868	−	0.0395823i
$339$	0.830927	+	33.7556i	0.0451298	+	1.83335i
$340$	−0.412708	+	5.50721i	−0.0223823	+	0.298670i
$341$	−5.31417	+	13.5403i	−0.287778	+	0.733247i
$342$	−0.427936	+	16.7271i	−0.0231401	+	0.904500i
$343$	−12.1974	−	13.9364i	−0.658597	−	0.752496i
$344$			0.627217i			0.0338173i
$345$	−20.0899	+	8.46100i	−1.08161	+	0.455525i
$346$	−9.83905	−	0.737335i	−0.528951	−	0.0396394i
$347$	−14.0500	+	15.1423i	−0.754246	+	0.812883i	−0.987180	−	0.159609i	$-0.948977\pi$
$347$	−14.0500	+	15.1423i	−0.754246	+	0.812883i	0.232935	+	0.972492i	$0.425167\pi$
$348$	1.93827	+	11.0132i	0.103902	+	0.590372i
$349$	−3.45435	+	7.17303i	−0.184907	+	0.383964i	−0.972731	−	0.231937i	$-0.925494\pi$
$349$	−3.45435	+	7.17303i	−0.184907	+	0.383964i	0.787824	+	0.615901i	$0.211208\pi$
$350$	2.35269	+	2.45928i	0.125756	+	0.131454i
$351$	−6.62501	+	16.8324i	−0.353617	+	0.898446i
$352$	−4.32662	−	0.652132i	−0.230609	−	0.0347588i
$353$	−28.1100	+	19.1651i	−1.49615	+	1.02006i	−0.508906	+	0.860822i	$0.669950\pi$
$353$	−28.1100	+	19.1651i	−1.49615	+	1.02006i	−0.987241	+	0.159233i	$0.949098\pi$
$354$	2.65930	+	2.01569i	0.141340	+	0.107133i
$355$	−11.1917	−	12.0618i	−0.593993	−	0.640172i
$356$	1.18151	+	1.48156i	0.0626198	+	0.0785227i
$357$	12.0499	+	5.22205i	0.637751	+	0.276380i
$358$	−6.88682	+	8.63580i	−0.363980	+	0.456416i
$359$	10.1473	−	0.760433i	0.535552	−	0.0401341i	0.195791	−	0.980646i	$-0.437273\pi$
$359$	10.1473	−	0.760433i	0.535552	−	0.0401341i	0.339762	+	0.940512i	$0.389654\pi$
$360$	−5.47900	−	1.84478i	−0.288769	−	0.0972283i
$361$	6.05446	−	10.4866i	0.318656	−	0.551928i
$362$	−0.678337	−	1.17491i	−0.0356526	−	0.0617521i
$363$	11.8481	+	7.65770i	0.621862	+	0.401925i
$364$	−7.11270	+	5.85186i	−0.372807	+	0.306721i
$365$	−21.6391	−	4.93899i	−1.13264	−	0.258518i
$366$	12.1588	−	22.3101i	0.635549	−	1.16617i
$367$	1.79502	−	0.704495i	0.0936994	−	0.0367743i	−0.318028	−	0.948081i	$-0.603021\pi$
$367$	1.79502	−	0.704495i	0.0936994	−	0.0367743i	0.411728	+	0.911307i	$0.364925\pi$
$368$	−6.07948	+	2.38602i	−0.316915	+	0.124380i
$369$	−5.21849	−	18.5936i	−0.271664	−	0.967943i
$370$	18.1583	+	4.14452i	0.944006	+	0.215463i
$371$	−0.208598	−	13.6763i	−0.0108299	−	0.710038i
$372$	−3.12554	+	4.83586i	−0.162052	+	0.250728i
$373$	3.13256	+	5.42575i	0.162198	+	0.280935i	0.935657	−	0.352912i	$-0.114808\pi$
$373$	3.13256	+	5.42575i	0.162198	+	0.280935i	−0.773459	+	0.633847i	$0.781475\pi$
$374$	6.26967	−	10.8594i	0.324197	−	0.561526i
$375$	18.6749	−	9.56648i	0.964369	−	0.494011i
$376$	−1.33875	+	0.100326i	−0.0690410	+	0.00517391i
$377$	14.0135	−	17.5723i	0.721730	−	0.905021i
$378$	−8.41716	+	10.8697i	−0.432932	+	0.559079i
$379$	−3.65672	−	4.58538i	−0.187833	−	0.235535i	0.678994	−	0.734143i	$-0.262416\pi$
$379$	−3.65672	−	4.58538i	−0.187833	−	0.235535i	−0.866827	+	0.498608i	$0.833845\pi$
$380$	7.31074	+	7.87910i	0.375033	+	0.404189i
$381$	−11.4725	+	15.1357i	−0.587756	+	0.775426i
$382$	−6.16866	+	4.20572i	−0.315616	+	0.215183i
$383$	−5.61543	−	0.846390i	−0.286935	−	0.0432485i	0.00399759	−	0.999992i	$-0.498728\pi$
$383$	−5.61543	−	0.846390i	−0.286935	−	0.0432485i	−0.290933	+	0.956743i	$0.593966\pi$
$384$	−1.62740	−	0.592921i	−0.0830481	−	0.0302574i
$385$	6.89996	+	21.2148i	0.351654	+	1.08121i
$386$	6.13128	−	12.7317i	0.312074	−	0.648028i
$387$	1.09939	−	1.52708i	0.0558850	−	0.0776257i
$388$	−9.08806	+	9.79460i	−0.461376	+	0.497245i
$389$	−32.8598	−	2.46250i	−1.66606	−	0.124854i	−0.791949	−	0.610587i	$-0.790933\pi$
$389$	−32.8598	−	2.46250i	−1.66606	−	0.124854i	−0.874107	+	0.485734i	$0.838553\pi$
$390$	4.51008	+	10.7088i	0.228377	+	0.542261i
$391$		−	18.7165i		−	0.946532i
$392$	−6.43509	+	2.75493i	−0.325021	+	0.139145i
$393$	−5.62143	+	5.47945i	−0.283564	+	0.276402i
$394$	−5.68054	+	14.4738i	−0.286181	+	0.729178i
$395$	0.127095	−	1.69597i	0.00639486	−	0.0853335i
$396$	9.39089	+	9.17143i	0.471910	+	0.460882i
$397$	−7.80113	+	11.4422i	−0.391527	+	0.574265i	−0.970506	−	0.241078i	$-0.922499\pi$
$397$	−7.80113	+	11.4422i	−0.391527	+	0.574265i	0.578978	+	0.815343i	$0.303452\pi$
$398$	−9.70746	−	4.67486i	−0.486591	−	0.234330i
$399$	23.4016	−	10.2787i	1.17155	−	0.514578i
$400$	1.15898	−	0.558134i	0.0579489	−	0.0279067i
$401$	3.78241	−	25.0947i	0.188885	−	1.25317i	−0.670528	−	0.741884i	$-0.733932\pi$
$401$	3.78241	−	25.0947i	0.188885	−	1.25317i	0.859412	−	0.511283i	$-0.170830\pi$
$402$	8.47543	+	1.71619i	0.422716	+	0.0855957i
$403$	11.4438	−	1.72488i	0.570057	−	0.0859222i
$404$	1.33383	−	1.23761i	0.0663604	−	0.0615735i
$405$	10.1061	+	14.0951i	0.502177	+	0.700389i
$406$	13.9651	−	9.83650i	0.693074	−	0.488177i
$407$	−33.0631	−	26.3669i	−1.63887	−	1.30696i
$408$	3.28564	−	3.72066i	0.162663	−	0.184200i
$409$	−10.5676	+	34.2594i	−0.522536	+	1.69402i	0.181105	+	0.983464i	$0.442033\pi$
$409$	−10.5676	+	34.2594i	−0.522536	+	1.69402i	−0.703641	+	0.710556i	$0.748444\pi$
$410$	−10.7433	−	6.20262i	−0.530572	−	0.306326i
$411$	−3.18391	+	11.3023i	−0.157051	+	0.557503i
$412$	7.80366	−	1.78113i	0.384459	−	0.0877502i
$413$	1.05831	−	4.98612i	0.0520763	−	0.245351i
$414$	18.9838	+	4.84691i	0.933004	+	0.238212i
$415$	−19.3892	+	5.98077i	−0.951777	+	0.293584i
$416$	1.27185	+	3.24062i	0.0623576	+	0.158885i
$417$	−9.07086	+	20.0858i	−0.444202	+	0.983606i
$418$	−7.19333	−	23.3202i	−0.351837	−	1.14063i
$419$	−1.10027	+	4.82058i	−0.0537515	+	0.235501i	−0.994667	−	0.103142i	$-0.967110\pi$
$419$	−1.10027	+	4.82058i	−0.0537515	+	0.235501i	0.940915	+	0.338642i	$0.109968\pi$
$420$	1.01036	+	8.77299i	0.0493006	+	0.428078i
$421$	−0.589336	−	2.58205i	−0.0287225	−	0.125841i	0.958534	−	0.284978i	$-0.0919862\pi$
$421$	−0.589336	−	2.58205i	−0.0287225	−	0.125841i	−0.987257	+	0.159136i	$0.949129\pi$
$422$	8.35051	−	4.82117i	0.406497	−	0.234691i
$423$	3.43530	+	2.10231i	0.167030	+	0.102218i
$424$	−4.94008	−	1.52381i	−0.239911	−	0.0740029i
$425$	0.275492	+	3.67619i	0.0133633	+	0.178321i
$426$	1.46776	+	14.7159i	0.0711133	+	0.712990i
$427$	−38.7429	−	2.30981i	−1.87490	−	0.111780i
$428$	−8.60357	+	6.86112i	−0.415869	+	0.331645i
$429$	1.32358	−	26.3498i	0.0639029	−	1.27218i
$430$	−0.180147	−	1.19520i	−0.00868746	−	0.0576375i
$431$	−11.3493	−	16.6463i	−0.546676	−	0.801826i	0.449116	−	0.893474i	$-0.351739\pi$
$431$	−11.3493	−	16.6463i	−0.546676	−	0.801826i	−0.995792	+	0.0916474i	$0.970787\pi$
$432$	2.92295	+	4.29609i	0.140630	+	0.206696i
$433$	10.6630	+	22.1419i	0.512430	+	1.06407i	0.983321	+	0.181881i	$0.0582184\pi$
$433$	10.6630	+	22.1419i	0.512430	+	1.06407i	−0.470890	+	0.882192i	$0.656067\pi$
$434$	8.71622	+	1.17811i	0.418392	+	0.0565509i
$435$	−6.85666	−	20.4296i	−0.328752	−	0.979525i
$436$	−13.1691	−	8.97851i	−0.630683	−	0.429993i
$437$	−26.7025	−	24.7763i	−1.27736	−	1.18521i
$438$	12.8183	+	15.2862i	0.612480	+	0.730403i
$439$	29.0552	+	11.4033i	1.38673	+	0.544251i	0.937130	−	0.348980i	$-0.113472\pi$
$439$	29.0552	+	11.4033i	1.38673	+	0.544251i	0.449598	+	0.893231i	$0.351567\pi$
$440$	8.43190			0.401975
$441$	20.4963	+	4.57205i	0.976012	+	0.217717i
$442$	−9.97668			−0.474543
$443$	1.95411	+	0.766931i	0.0928425	+	0.0364380i	0.411308	−	0.911497i	$-0.365072\pi$
$443$	1.95411	+	0.766931i	0.0928425	+	0.0364380i	−0.318465	+	0.947935i	$0.603167\pi$
$444$	−10.7563	−	12.8273i	−0.510474	−	0.608757i
$445$	−2.67696	−	2.48385i	−0.126900	−	0.117746i
$446$	−11.8439	−	8.07502i	−0.560824	−	0.382363i
$447$	−3.32302	−	9.90104i	−0.157174	−	0.468303i
$448$	0.237931	+	2.63503i	0.0112412	+	0.124494i
$449$	11.1540	+	23.1615i	0.526389	+	1.09306i	0.979470	+	0.201589i	$0.0646107\pi$
$449$	11.1540	+	23.1615i	0.526389	+	1.09306i	−0.453081	+	0.891470i	$0.649675\pi$
$450$	−3.80004	−	0.672576i	−0.179136	−	0.0317055i
$451$	15.8667	+	23.2722i	0.747135	+	1.09585i
$452$	−2.90553	−	19.2770i	−0.136665	−	0.906711i
$453$	0.948986	−	18.8924i	0.0445872	−	0.887644i
$454$	8.10201	−	6.46113i	0.380246	−	0.303236i
$455$	11.8729	−	13.1939i	0.556610	−	0.618540i
$456$	−0.958785	−	9.61288i	−0.0448992	−	0.450164i
$457$	−0.594664	−	7.93524i	−0.0278172	−	0.371195i	−0.993689	−	0.112173i	$-0.964219\pi$
$457$	−0.594664	−	7.93524i	−0.0278172	−	0.371195i	0.965871	−	0.259022i	$-0.0834001\pi$
$458$	−4.31978	−	1.33248i	−0.201850	−	0.0622626i
$459$	−14.5211	+	3.29957i	−0.677785	+	0.154011i
$460$	10.8995	−	6.29281i	0.508191	−	0.293404i
$461$	−2.60314	−	11.4051i	−0.121240	−	0.531188i	−0.998674	−	0.0514895i	$-0.983603\pi$
$461$	−2.60314	−	11.4051i	−0.121240	−	0.531188i	0.877433	−	0.479699i	$-0.159254\pi$
$462$	6.57580	−	18.9420i	0.305934	−	0.881264i
$463$	2.35165	−	10.3032i	0.109290	−	0.478832i	−0.890429	−	0.455123i	$-0.849595\pi$
$463$	2.35165	−	10.3032i	0.109290	−	0.478832i	0.999719	−	0.0237091i	$-0.00754753\pi$
$464$	−1.90300	−	6.16939i	−0.0883447	−	0.286407i
$465$	4.56694	−	10.1127i	0.211787	−	0.468965i
$466$	−9.14677	−	23.3056i	−0.423716	−	1.07961i
$467$	13.0995	−	4.04066i	0.606173	−	0.186980i	0.0235506	−	0.999723i	$-0.492503\pi$
$467$	13.0995	−	4.04066i	0.606173	−	0.186980i	0.582622	+	0.812743i	$0.302027\pi$
$468$	2.58361	−	10.1192i	0.119427	−	0.467760i
$469$	−3.13538	−	12.8317i	−0.144778	−	0.592512i
$470$	2.52225	−	0.575688i	0.116343	−	0.0265545i
$471$	−10.8589	+	38.5472i	−0.500352	+	1.77616i
$472$	−1.66845	−	0.963280i	−0.0767967	−	0.0443386i
$473$	−0.808921	+	2.62246i	−0.0371942	+	0.120581i
$474$	−1.01183	+	1.14579i	−0.0464747	+	0.0526281i
$475$	5.60946	+	4.47339i	0.257380	+	0.205253i
$476$	−7.27862	−	2.12415i	−0.333615	−	0.0973601i
$477$	9.35660	+	12.3690i	0.428409	+	0.566337i
$478$	−14.0449	+	13.0318i	−0.642400	+	0.596060i
$479$	−15.9780	+	2.40829i	−0.730053	+	0.110038i	−0.503542	−	0.863971i	$-0.667970\pi$
$479$	−15.9780	+	2.40829i	−0.730053	+	0.110038i	−0.226511	+	0.974009i	$0.572732\pi$
$480$	3.27140	+	0.662426i	0.149318	+	0.0302355i
$481$	−5.01477	+	33.2708i	−0.228654	+	1.51702i
$482$	10.9132	−	5.25553i	0.497083	−	0.239383i
$483$	−5.63645	−	29.3930i	−0.256467	−	1.33743i
$484$	−7.33828	−	3.53393i	−0.333558	−	0.160633i
$485$	14.5046	−	21.2744i	0.658621	−	0.966020i
$486$	0.413739	−	15.5830i	0.0187676	−	0.706858i
$487$	0.158707	−	2.11779i	0.00719168	−	0.0959663i	−0.992453	−	0.122627i	$-0.960868\pi$
$487$	0.158707	−	2.11779i	0.00719168	−	0.0959663i	0.999645	+	0.0266604i	$0.00848727\pi$
$488$	−5.35935	+	13.6554i	−0.242606	+	0.618151i
$489$	16.3536	−	15.9406i	0.739536	−	0.720858i
$490$	11.4712	−	7.09792i	0.518214	−	0.320651i
$491$			37.8718i			1.70913i	0.519344	+	0.854565i	$0.326176\pi$
$491$			37.8718i			1.70913i	−0.519344	+	0.854565i	$0.673824\pi$
$492$	4.32766	+	10.2757i	0.195106	+	0.463263i
$493$	18.4506	+	1.38268i	0.830973	+	0.0622729i
$494$	−13.2069	+	14.2336i	−0.594205	+	0.640400i
$495$	−20.5290	−	14.7794i	−0.922711	−	0.664287i
$496$	1.44239	−	2.99516i	0.0647654	−	0.134487i
$497$	19.3894	−	11.5923i	0.869734	−	0.519986i
$498$	17.1353	+	6.24299i	0.767851	+	0.279755i
$499$	8.70183	+	1.31159i	0.389548	+	0.0587148i	0.340896	−	0.940101i	$-0.389270\pi$
$499$	8.70183	+	1.31159i	0.389548	+	0.0587148i	0.0486514	+	0.998816i	$0.484508\pi$
$500$	−10.0093	+	6.82424i	−0.447631	+	0.305189i
$501$	−10.2728	+	13.5529i	−0.458953	+	0.605497i
$502$	−5.30387	−	5.71621i	−0.236723	−	0.255127i
$503$	5.29402	+	6.63849i	0.236048	+	0.295995i	0.885720	−	0.464219i	$-0.153665\pi$
$503$	5.29402	+	6.63849i	0.236048	+	0.295995i	−0.649672	+	0.760215i	$0.725094\pi$
$504$	4.03940	−	6.83252i	0.179929	−	0.304344i
$505$	−2.18622	+	2.74143i	−0.0972855	+	0.121992i
$506$	−28.4961	+	2.13549i	−1.26681	+	0.0949340i
$507$	1.35773	−	0.695515i	0.0602989	−	0.0308889i
$508$	5.48262	−	9.49617i	0.243252	−	0.421325i
$509$	20.7355	+	35.9149i	0.919085	+	1.59190i	0.800808	+	0.598921i	$0.204404\pi$
$509$	20.7355	+	35.9149i	0.919085	+	1.59190i	0.118277	+	0.992981i	$0.462263\pi$
$510$	−5.19232	+	8.03361i	−0.229920	+	0.355734i
$511$	12.8015	−	27.6538i	0.566306	−	1.22333i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$	−14.5151	+	25.0849i	−0.640858	+	1.10753i
$514$	−10.5350	+	4.13467i	−0.464678	+	0.182373i
$515$	−14.3587	+	5.63539i	−0.632721	+	0.248325i
$516$	−0.519869	+	0.953908i	−0.0228860	+	0.0419935i
$517$	−5.72685	−	1.30712i	−0.251867	−	0.0574869i
$518$	−10.7423	+	23.2055i	−0.471990	+	1.01959i
$519$	−14.3526	−	9.27648i	−0.630011	−	0.407192i
$520$	−3.35434	−	5.80989i	−0.147098	−	0.254781i
$521$	−1.87234	+	3.24299i	−0.0820287	+	0.142078i	−0.904121	−	0.427276i	$-0.859473\pi$
$521$	−1.87234	+	3.24299i	−0.0820287	+	0.142078i	0.822092	+	0.569354i	$0.192807\pi$
$522$	−6.18049	+	18.3561i	−0.270513	+	0.803425i
$523$	19.5290	−	1.46349i	0.853942	−	0.0639941i	0.359438	−	0.933169i	$-0.382969\pi$
$523$	19.5290	−	1.46349i	0.853942	−	0.0639941i	0.494505	+	0.869175i	$0.335349\pi$
$524$	2.82583	−	3.54348i	0.123447	−	0.154798i
$525$	1.53972	+	5.69024i	0.0671991	+	0.248343i
$526$	15.3414	+	19.2375i	0.668918	+	0.838796i
$527$	6.48005	+	6.98383i	0.282275	+	0.304220i
$528$	−6.03964	−	4.57792i	−0.262842	−	0.199228i
$529$	−16.2382	+	11.0710i	−0.706008	+	0.481348i
$530$	9.85126	+	1.48484i	0.427911	+	0.0644972i
$531$	2.37371	+	5.26975i	0.103010	+	0.228687i
$532$	−12.6657	+	7.57243i	−0.549129	+	0.328306i
$533$	9.72338	−	20.1908i	0.421166	−	0.874561i
$534$	0.568910	+	3.23254i	0.0246191	+	0.139886i
$535$	14.4240	−	15.5453i	0.623602	−	0.672083i
$536$	−4.97864	−	0.373098i	−0.215045	−	0.0161154i
$537$	−17.6317	+	7.42568i	−0.760862	+	0.320442i
$538$		−	9.62232i		−	0.414848i
$539$	−30.4587	+	3.21929i	−1.31195	+	0.138665i
$540$	−6.80374	−	7.34692i	−0.292786	−	0.316161i
$541$	−8.99479	+	22.9183i	−0.386716	+	0.985336i	0.596455	+	0.802647i	$0.296576\pi$
$541$	−8.99479	+	22.9183i	−0.386716	+	0.985336i	−0.983171	+	0.182690i	$0.941520\pi$
$542$	−1.56109	+	20.8313i	−0.0670545	+	0.894781i
$543$	−0.0578259	−	2.34912i	−0.00248155	−	0.100810i
$544$	−1.61437	+	2.36785i	−0.0692156	+	0.101521i
$545$	27.6731	+	13.3267i	1.18539	+	0.570852i
$546$	−15.6677	+	3.00447i	−0.670516	+	0.128580i
$547$	−24.9951	+	12.0370i	−1.06871	+	0.514665i	−0.883692	−	0.468070i	$-0.844950\pi$
$547$	−24.9951	+	12.0370i	−1.06871	+	0.514665i	−0.185021	+	0.982735i	$0.559235\pi$
$548$	1.01041	−	6.70366i	0.0431627	−	0.286366i
$549$	36.9835	−	23.8527i	1.57842	−	1.01801i
$550$	5.56562	−	0.838883i	0.237319	−	0.0357701i
$551$	26.3971	−	24.4929i	1.12455	−	1.04343i
$552$	−11.2237	−	1.41018i	−0.477711	−	0.0600213i
$553$	2.24148	+	0.654140i	0.0953176	+	0.0278169i
$554$	−25.2733	−	20.1548i	−1.07376	−	0.856296i
$555$	24.1810	+	21.3537i	1.02643	+	0.906416i
$556$	3.75054	−	12.1590i	0.159058	−	0.515655i
$557$	8.48153	+	4.89681i	0.359374	+	0.207485i	0.668806	−	0.743437i	$-0.266806\pi$
$557$	8.48153	+	4.89681i	0.359374	+	0.207485i	−0.309432	+	0.950922i	$0.600139\pi$
$558$	−8.76170	+	4.76405i	−0.370912	+	0.201678i
$559$	2.12877	−	0.485878i	0.0900373	−	0.0205504i
$560$	−1.21021	−	4.95286i	−0.0511409	−	0.209296i
$561$	18.5361	−	11.3190i	0.782594	−	0.477887i
$562$	−18.2291	+	5.62294i	−0.768949	+	0.237189i
$563$	−15.1276	−	38.5446i	−0.637554	−	1.62446i	−0.773538	−	0.633750i	$-0.781515\pi$
$563$	−15.1276	−	38.5446i	−0.637554	−	1.62446i	0.135984	−	0.990711i	$-0.456580\pi$
$564$	−2.11921	−	0.957046i	−0.0892348	−	0.0402989i
$565$	11.0733	+	35.8988i	0.465857	+	1.51027i
$566$	−0.0900246	+	0.394423i	−0.00378401	+	0.0165789i
$567$	−21.8107	+	9.55477i	−0.915963	+	0.401263i
$568$	−1.89997	−	8.32433i	−0.0797211	−	0.349281i
$569$	−30.5614	+	17.6446i	−1.28120	+	0.739701i	−0.977068	−	0.212929i	$-0.931700\pi$
$569$	−30.5614	+	17.6446i	−1.28120	+	0.739701i	−0.304132	+	0.952630i	$0.598366\pi$
$570$	4.58799	+	18.0425i	0.192170	+	0.755717i
$571$	3.70952	+	1.14423i	0.155238	+	0.0478847i	0.371400	−	0.928473i	$-0.378878\pi$
$571$	3.70952	+	1.14423i	0.155238	+	0.0478847i	−0.216162	+	0.976358i	$0.569354\pi$
$572$	1.13831	+	15.1897i	0.0475950	+	0.635112i
$573$	−12.8676	+	1.28341i	−0.537550	+	0.0536151i
$574$	11.3927	−	12.6603i	0.475521	−	0.528429i
$575$	6.56832	−	5.23806i	0.273918	−	0.218442i
$576$	−1.98361	−	2.25062i	−0.0826503	−	0.0937759i
$577$	−4.90365	−	32.5336i	−0.204142	−	1.35439i	−0.822621	−	0.568590i	$-0.807489\pi$
$577$	−4.90365	−	32.5336i	−0.204142	−	1.35439i	0.618480	−	0.785801i	$-0.287749\pi$
$578$	4.94995	+	7.26024i	0.205891	+	0.301986i
$579$	19.8775	−	14.2812i	0.826080	−	0.593508i
$580$	5.39823	+	11.2095i	0.224149	+	0.465450i
$581$	−2.50523	−	27.7448i	−0.103934	−	1.15105i
$582$	−21.9399	+	7.36354i	−0.909438	+	0.305229i
$583$	−18.6897	−	12.7424i	−0.774048	−	0.527737i
$584$	−8.44311	−	7.83406i	−0.349378	−	0.324176i
$585$	−2.01681	+	20.0247i	−0.0833850	+	0.827921i
$586$	−1.47830	−	0.580190i	−0.0610680	−	0.0239674i
$587$	23.7054			0.978427			0.489214	−	0.872164i	$-0.337284\pi$
$587$	23.7054			0.978427			0.489214	+	0.872164i	$0.337284\pi$
$588$	−12.0703	−	1.14388i	−0.497770	−	0.0471727i
$589$	18.5418			0.764004
$590$	3.45599	+	1.35638i	0.142281	+	0.0558412i
$591$	−20.6359	+	17.3042i	−0.848847	+	0.711801i
$592$	7.08497	+	6.57390i	0.291191	+	0.270185i
$593$	1.49423	+	1.01875i	0.0613605	+	0.0418349i	0.593612	−	0.804752i	$-0.297701\pi$
$593$	1.49423	+	1.01875i	0.0613605	+	0.0418349i	−0.532251	+	0.846586i	$0.678654\pi$
$594$	6.68046	+	21.7321i	0.274102	+	0.891678i
$595$	14.4799	+	1.95714i	0.593618	+	0.0802349i
$596$	2.61620	+	5.43260i	0.107164	+	0.222528i
$597$	−10.8889	−	15.1558i	−0.445653	−	0.620287i
$598$	12.8076	+	18.7853i	0.523743	+	0.768189i
$599$	−1.74111	−	11.5515i	−0.0711397	−	0.471981i	−0.995828	−	0.0912549i	$-0.970912\pi$
$599$	−1.74111	−	11.5515i	−0.0711397	−	0.471981i	0.924688	−	0.380726i	$-0.124326\pi$
$600$	2.22525	+	0.111776i	0.0908455	+	0.00456326i
$601$	−14.0068	+	11.1700i	−0.571349	+	0.455636i	−0.866052	−	0.499953i	$-0.833351\pi$
$601$	−14.0068	+	11.1700i	−0.571349	+	0.455636i	0.294703	+	0.955589i	$0.404779\pi$
$602$	1.65652	+	0.0987601i	0.0675147	+	0.00402516i
$603$	11.4675	+	9.63494i	0.466991	+	0.392365i
$604$	0.816150	+	10.8908i	0.0332087	+	0.443139i
$605$	14.9985	+	4.62642i	0.609775	+	0.188091i
$606$	3.05436	−	0.776687i	0.124075	−	0.0315508i
$607$	35.9405	−	20.7502i	1.45878	−	0.842226i	0.459828	−	0.888008i	$-0.347911\pi$
$607$	35.9405	−	20.7502i	1.45878	−	0.842226i	0.998951	+	0.0457817i	$0.0145779\pi$
$608$	1.24112	+	5.43770i	0.0503340	+	0.220528i
$609$	29.3918	−	3.38498i	1.19102	−	0.137166i
$610$	6.29048	−	27.5604i	0.254694	−	1.11589i
$611$	1.37758	+	4.46600i	0.0557308	+	0.180675i
$612$	8.08085	−	2.93529i	0.326649	−	0.118652i
$613$	−13.7356	−	34.9977i	−0.554775	−	1.41354i	−0.883192	−	0.469011i	$-0.844610\pi$
$613$	−13.7356	−	34.9977i	−0.554775	−	1.41354i	0.328417	−	0.944533i	$-0.393485\pi$
$614$	−7.41930	+	2.28855i	−0.299418	+	0.0923584i
$615$	−11.1979	−	18.3379i	−0.451544	−	0.739454i
$616$	−2.40358	+	11.3242i	−0.0968430	+	0.456264i
$617$	21.6825	−	4.94889i	0.872905	−	0.199235i	0.237475	−	0.971394i	$-0.423680\pi$
$617$	21.6825	−	4.94889i	0.872905	−	0.199235i	0.635430	+	0.772159i	$0.280823\pi$
$618$	13.3445	+	3.75921i	0.536796	+	0.151218i
$619$	18.5553	+	10.7129i	0.745799	+	0.430587i	0.824174	−	0.566337i	$-0.191640\pi$
$619$	18.5553	+	10.7129i	0.745799	+	0.430587i	−0.0783752	+	0.996924i	$0.524973\pi$
$620$	−1.88830	+	6.12172i	−0.0758360	+	0.245854i
$621$	24.8543	+	23.1062i	0.997370	+	0.927220i
$622$	−15.5872	−	12.4304i	−0.624988	−	0.498412i
$623$	4.09894	−	2.88715i	0.164220	−	0.115671i
$624$	−0.751688	+	5.98270i	−0.0300916	+	0.239500i
$625$	12.3984	−	11.5040i	0.495936	−	0.460162i
$626$	12.8885	−	1.94263i	0.515130	−	0.0776433i
$627$	8.38893	−	41.4289i	0.335022	−	1.65451i
$628$	3.44607	−	22.8632i	0.137513	−	0.912340i
$629$	−24.9552	+	12.0178i	−0.995031	+	0.479181i
$630$	−5.73488	+	14.1799i	−0.228483	+	0.564941i
$631$	−28.0413	−	13.5040i	−1.11631	−	0.537585i	−0.217558	−	0.976047i	$-0.569809\pi$
$631$	−28.0413	−	13.5040i	−1.11631	−	0.537585i	−0.898750	+	0.438462i	$0.855523\pi$
$632$	0.497153	−	0.729190i	0.0197757	−	0.0290056i
$633$	16.6960	−	0.410988i	0.663605	−	0.0163353i
$634$	−1.15696	+	15.4385i	−0.0459487	+	0.613143i
$635$	−7.71997	+	19.6702i	−0.306358	+	0.780587i
$636$	−6.25014	−	6.41209i	−0.247834	−	0.254256i
$637$	14.3352	+	19.7065i	0.567980	+	0.780800i
$638$		−	28.2491i		−	1.11839i
$639$	−9.96505	+	23.5974i	−0.394211	+	0.933499i
$640$	−1.92169	−	0.144011i	−0.0759615	−	0.00569252i
$641$	3.52614	−	3.80027i	0.139274	−	0.150102i	−0.659563	−	0.751649i	$-0.729259\pi$
$641$	3.52614	−	3.80027i	0.139274	−	0.150102i	0.798837	+	0.601548i	$0.205449\pi$
$642$	−18.7716	+	3.30371i	−0.740858	+	0.130387i
$643$	11.4570	−	23.7908i	0.451822	−	0.938217i	−0.543298	−	0.839540i	$-0.682825\pi$
$643$	11.4570	−	23.7908i	0.451822	−	0.938217i	0.995119	−	0.0986773i	$-0.0314612\pi$
$644$	5.34436	+	16.4320i	0.210597	+	0.647510i
$645$	0.716662	−	1.96704i	0.0282185	−	0.0774521i
$646$	−15.8057	−	2.38232i	−0.621866	−	0.0937312i
$647$	3.35424	−	2.28689i	0.131869	−	0.0899067i	−0.495589	−	0.868557i	$-0.665048\pi$
$647$	3.35424	−	2.28689i	0.131869	−	0.0899067i	0.627458	+	0.778650i	$0.284095\pi$
$648$	0.884567	+	8.95642i	0.0347491	+	0.351842i
$649$	−5.73361	−	6.17936i	−0.225064	−	0.242561i
$650$	−2.79211	−	3.50120i	−0.109516	−	0.137328i
$651$	12.2797	+	9.01618i	0.481278	+	0.353372i
$652$	−8.22080	+	10.3086i	−0.321951	+	0.403714i
$653$	7.91203	−	0.592925i	0.309622	−	0.0232029i	0.0809867	−	0.996715i	$-0.474193\pi$
$653$	7.91203	−	0.592925i	0.309622	−	0.0232029i	0.228635	+	0.973512i	$0.426574\pi$
$654$	−12.5864	−	24.5702i	−0.492168	−	0.960771i
$655$	−4.36704	+	7.56393i	−0.170634	+	0.295547i
$656$	−3.21867	−	5.57489i	−0.125668	−	0.217663i
$657$	6.82476	+	33.8725i	0.266259	+	1.32149i
$658$	0.0541697	+	3.55153i	0.00211175	+	0.138453i
$659$	29.0612	+	6.63302i	1.13206	+	0.258386i	0.747207	−	0.664591i	$-0.231394\pi$
$659$	29.0612	+	6.63302i	1.13206	+	0.258386i	0.384855	+	0.922977i	$0.374251\pi$
$660$	12.8237	+	6.98879i	0.499163	+	0.272038i
$661$	17.2684	−	6.77733i	0.671661	−	0.263608i	−0.00490650	−	0.999988i	$-0.501562\pi$
$661$	17.2684	−	6.77733i	0.671661	−	0.263608i	0.676568	+	0.736380i	$0.263467\pi$
$662$	5.33402	−	2.09345i	0.207313	−	0.0813642i
$663$	−15.1731	−	8.26918i	−0.589275	−	0.321148i
$664$	−10.2652	−	2.34297i	−0.398368	−	0.0909249i
$665$	21.9603	−	18.0675i	0.851585	−	0.700627i
$666$	−5.72695	−	28.4239i	−0.221915	−	1.10140i
$667$	−21.0826	−	36.5161i	−0.816321	−	1.41391i
$668$	4.90926	−	8.50308i	0.189945	−	0.328994i
$669$	−11.3199	−	22.0978i	−0.437652	−	0.854349i
$670$	9.59424	−	0.718989i	0.370658	−	0.0277770i
$671$	−40.0193	+	50.1826i	−1.54493	+	1.93728i
$672$	−1.82219	+	4.20472i	−0.0702924	+	0.162200i
$673$	24.6297	+	30.8847i	0.949406	+	1.19052i	0.981583	+	0.191035i	$0.0611845\pi$
$673$	24.6297	+	30.8847i	0.949406	+	1.19052i	−0.0321773	+	0.999482i	$0.510244\pi$
$674$	16.6263	+	17.9189i	0.640421	+	0.690210i
$675$	−5.22186	−	4.17256i	−0.200990	−	0.160602i
$676$	−0.727712	+	0.496145i	−0.0279889	+	0.0190825i
$677$	−11.7201	−	1.76652i	−0.450441	−	0.0678931i	−0.0800957	−	0.996787i	$-0.525523\pi$
$677$	−11.7201	−	1.76652i	−0.450441	−	0.0678931i	−0.370345	+	0.928894i	$0.620761\pi$
$678$	11.5588	−	31.7257i	0.443913	−	1.21842i
$679$	24.4372	+	25.5444i	0.937812	+	0.980302i
$680$	2.39619	−	4.97574i	0.0918897	−	0.190811i
$681$	17.6773	−	3.11111i	0.677396	−	0.119218i
$682$	9.89364	−	10.6628i	0.378847	−	0.408300i
$683$	20.1215	+	1.50790i	0.769928	+	0.0576981i	0.453901	−	0.891052i	$-0.350032\pi$
$683$	20.1215	+	1.50790i	0.769928	+	0.0576981i	0.316027	+	0.948750i	$0.397651\pi$
$684$	6.50946	−	15.4145i	0.248896	−	0.589389i
$685$			13.0644i			0.499165i
$686$	6.26268	+	17.4293i	0.239110	+	0.665452i
$687$	−5.46535	−	5.60696i	−0.208516	−	0.213919i
$688$	0.229148	−	0.583860i	0.00873620	−	0.0222595i
$689$	−1.34494	+	17.9470i	−0.0512382	+	0.683726i
$690$	21.7923	−	0.536441i	0.829620	−	0.0204219i
$691$	−26.6365	+	39.0685i	−1.01330	+	1.48624i	−0.145478	+	0.989362i	$0.546472\pi$
$691$	−26.6365	+	39.0685i	−1.01330	+	1.48624i	−0.867822	+	0.496876i	$0.834480\pi$
$692$	8.88953	+	4.28097i	0.337929	+	0.162738i
$693$	25.7010	−	23.3578i	0.976299	−	0.887290i
$694$	18.6109	−	8.96255i	0.706461	−	0.340214i
$695$	−3.65461	+	24.2468i	−0.138627	+	0.919732i
$696$	2.21930	−	10.9601i	0.0841224	−	0.415440i
$697$	18.2422	−	2.74956i	0.690971	−	0.104147i
$698$	5.83617	−	5.41517i	0.220902	−	0.204967i
$699$	5.40591	−	43.0258i	0.204470	−	1.62738i
$700$	−1.29158	−	3.14881i	−0.0488170	−	0.119014i
$701$	−28.1255	−	22.4294i	−1.06229	−	0.847146i	−0.0736226	−	0.997286i	$-0.523456\pi$
$701$	−28.1255	−	22.4294i	−1.06229	−	0.847146i	−0.988665	+	0.150140i	$0.952027\pi$
$702$	12.3166	−	13.2484i	0.464860	−	0.500030i
$703$	−15.8894	+	51.5122i	−0.599280	+	1.94282i
$704$	3.78928	+	2.18774i	0.142814	+	0.0824537i
$705$	4.31315	+	1.21503i	0.162443	+	0.0457607i
$706$	33.1687	−	7.57054i	1.24832	−	0.284921i
$707$	−3.05859	−	3.71759i	−0.115030	−	0.139815i
$708$	−1.73906	−	2.84791i	−0.0653579	−	0.107031i
$709$	−6.23401	+	1.92294i	−0.234123	+	0.0722175i	−0.409597	−	0.912267i	$-0.634331\pi$
$709$	−6.23401	+	1.92294i	−0.234123	+	0.0722175i	0.175473	+	0.984484i	$0.443854\pi$
$710$	6.01139	+	15.3168i	0.225603	+	0.574828i
$711$	−2.48853	+	0.903937i	−0.0933273	+	0.0339003i
$712$	−0.558558	−	1.81080i	−0.0209329	−	0.0678627i
$713$	4.83122	−	21.1670i	0.180931	−	0.792709i
$714$	−9.30915	−	9.26341i	−0.348386	−	0.346674i
$715$	−6.53182	−	28.6178i	−0.244276	−	1.07024i
$716$	9.56577	−	5.52280i	0.357490	−	0.206397i
$717$	−32.1617	+	8.17835i	−1.20110	+	0.305426i
$718$	−9.72364	−	2.99935i	−0.362883	−	0.111935i
$719$	2.03516	+	27.1573i	0.0758987	+	1.01280i	0.897004	+	0.442021i	$0.145739\pi$
$719$	2.03516	+	27.1573i	0.0758987	+	1.01280i	−0.821106	+	0.570776i	$0.806642\pi$
$720$	4.42629	+	3.71896i	0.164958	+	0.138597i
$721$	−3.47534	−	20.8904i	−0.129428	−	0.777999i
$722$	−9.46713	+	7.54978i	−0.352330	+	0.280974i
$723$	20.9535	+	1.05251i	0.779268	+	0.0391434i
$724$	0.202202	+	1.34152i	0.00751477	+	0.0498572i
$725$	4.67842	+	6.86198i	0.173752	+	0.254847i
$726$	−8.23138	−	11.4569i	−0.305495	−	0.425207i
$727$	−22.2518	−	46.2062i	−0.825272	−	1.71369i	−0.691127	−	0.722733i	$-0.742886\pi$
$727$	−22.2518	−	46.2062i	−0.825272	−	1.71369i	−0.134144	−	0.990962i	$-0.542829\pi$
$728$	8.75895	−	2.84878i	0.324628	−	0.105583i
$729$	13.5452	−	23.3565i	0.501673	−	0.865057i
$730$	18.3389	+	12.5032i	0.678752	+	0.462765i
$731$	1.31765	+	1.22260i	0.0487352	+	0.0452196i
$732$	−19.4691	+	16.3258i	−0.719598	+	0.603419i
$733$	12.9345	+	5.07640i	0.477745	+	0.187501i	0.591980	−	0.805953i	$-0.298346\pi$
$733$	12.9345	+	5.07640i	0.477745	+	0.187501i	−0.114235	+	0.993454i	$0.536442\pi$
$734$	−1.92832			−0.0711756
$735$	23.3291	−	1.28706i	0.860507	−	0.0474738i
$736$	6.53094			0.240734
$737$	−20.3350	−	7.98090i	−0.749049	−	0.293980i
$738$	−1.93524	+	19.2148i	−0.0712371	+	0.707306i
$739$	−6.24702	−	5.79639i	−0.229801	−	0.213224i	0.556865	−	0.830603i	$-0.312004\pi$
$739$	−6.24702	−	5.79639i	−0.229801	−	0.213224i	−0.786666	+	0.617379i	$0.788194\pi$
$740$	−15.3889	−	10.4920i	−0.565708	−	0.385693i
$741$	−31.8833	+	10.7008i	−1.17126	+	0.393103i
$742$	−4.80234	+	12.8071i	−0.176299	+	0.470164i
$743$	1.71093	+	3.55278i	0.0627679	+	0.130339i	0.929993	−	0.367578i	$-0.119813\pi$
$743$	1.71093	+	3.55278i	0.0627679	+	0.130339i	−0.867225	+	0.497917i	$0.834099\pi$
$744$	4.67622	−	3.35969i	0.171438	−	0.123172i
$745$	−6.54565	−	9.60071i	−0.239814	−	0.351743i
$746$	−0.933768	−	6.19514i	−0.0341877	−	0.226820i
$747$	20.8858	+	23.6973i	0.764173	+	0.867039i
$748$	−9.80365	+	7.81815i	−0.358457	+	0.285860i
$749$	16.7659	+	23.8029i	0.612614	+	0.869739i
$750$	−20.8790	+	2.08247i	−0.762394	+	0.0760409i
$751$	−1.63326	−	21.7944i	−0.0595986	−	0.795288i	−0.944291	−	0.329113i	$-0.893250\pi$
$751$	−1.63326	−	21.7944i	−0.0595986	−	0.795288i	0.884692	−	0.466176i	$-0.154369\pi$
$752$	1.28286	+	0.395711i	0.0467812	+	0.0144301i
$753$	−3.32854	−	13.0897i	−0.121299	−	0.477013i
$754$	−19.4647	+	11.2379i	−0.708861	+	0.409261i
$755$	−4.68322	−	20.5185i	−0.170440	−	0.746746i
$756$	11.8065	−	7.04323i	0.429397	−	0.256160i
$757$	6.43709	−	28.2027i	0.233960	−	1.02505i	−0.712360	−	0.701814i	$-0.752374\pi$
$757$	6.43709	−	28.2027i	0.233960	−	1.02505i	0.946320	−	0.323231i	$-0.104769\pi$
$758$	1.72872	+	5.60436i	0.0627898	+	0.203560i
$759$	−45.1085	−	20.3712i	−1.63734	−	0.739429i
$760$	−3.92681	−	10.0054i	−0.142440	−	0.362932i
$761$	30.8662	−	9.52096i	1.11890	−	0.345134i	0.320491	−	0.947252i	$-0.396152\pi$
$761$	30.8662	−	9.52096i	1.11890	−	0.345134i	0.798408	+	0.602117i	$0.205676\pi$
$762$	16.2092	−	9.89806i	0.587197	−	0.358569i
$763$	−25.7864	+	33.3666i	−0.933529	+	1.20795i
$764$	7.27877	−	1.66133i	0.263337	−	0.0601048i
$765$	−14.5554	+	7.91431i	−0.526253	+	0.286143i
$766$	4.91804	+	2.83943i	0.177696	+	0.102593i
$767$	−1.97689	+	6.40891i	−0.0713813	+	0.231412i
$768$	1.29829	+	1.14649i	0.0468480	+	0.0413705i
$769$	−25.5985	−	20.4141i	−0.923106	−	0.736153i	0.0416958	−	0.999130i	$-0.486724\pi$
$769$	−25.5985	−	20.4141i	−0.923106	−	0.736153i	−0.964802	+	0.262978i	$0.915295\pi$
$770$	1.32767	−	22.2692i	0.0478458	−	0.802526i
$771$	−19.4492	−	2.44367i	−0.700447	−	0.0880066i
$772$	−10.3589	+	9.61162i	−0.372824	+	0.345930i
$773$	35.0834	−	5.28798i	1.26186	−	0.190195i	0.516171	−	0.856486i	$-0.327357\pi$
$773$	35.0834	−	5.28798i	1.26186	−	0.190195i	0.745692	+	0.666290i	$0.232119\pi$
$774$	−1.58129	+	1.01986i	−0.0568385	+	0.0366583i
$775$	−0.637361	+	4.22861i	−0.0228947	+	0.151896i
$776$	12.0382	−	5.79729i	0.432146	−	0.208111i
$777$	−35.5714	+	26.3884i	−1.27612	+	0.946679i
$778$	29.6886	+	14.2973i	1.06439	+	0.512583i
$779$	20.2257	−	29.6657i	0.724661	−	1.06288i
$780$	−0.285946	−	11.6163i	−0.0102385	−	0.415929i
$781$	2.79189	−	37.2552i	0.0999018	−	1.33310i
$782$	−6.83789	+	17.4227i	−0.244523	+	0.623033i
$783$	−24.6141	+	22.7943i	−0.879636	+	0.814602i
$784$	6.99674	−	0.213485i	0.249884	−	0.00762447i
$785$			44.5568i			1.59030i
$786$	7.23471	−	3.04694i	0.258054	−	0.108681i
$787$	37.5911	+	2.81706i	1.33998	+	0.100417i	0.725339	−	0.688392i	$-0.241683\pi$
$787$	37.5911	+	2.81706i	1.33998	+	0.100417i	0.614638	+	0.788810i	$0.289302\pi$
$788$	10.5757	−	11.3979i	0.376745	−	0.406034i
$789$	7.38708	+	41.9733i	0.262987	+	1.49429i
$790$	−0.737917	+	1.53230i	−0.0262539	+	0.0545168i
$791$	−51.3691	+	4.63839i	−1.82648	+	0.164922i
$792$	−5.39103	−	11.9683i	−0.191562	−	0.425276i
$793$	50.4979	+	7.61133i	1.79323	+	0.270286i
$794$	11.4422	−	7.80113i	0.406067	−	0.276852i
$795$	13.7516	+	10.4234i	0.487721	+	0.369681i
$796$	7.32850	+	7.89824i	0.259752	+	0.279946i
$797$	12.0240	+	15.0777i	0.425913	+	0.534078i	0.947770	−	0.318955i	$-0.103332\pi$
$797$	12.0240	+	15.0777i	0.425913	+	0.534078i	−0.521857	+	0.853033i	$0.674760\pi$
$798$	−25.5392	+	1.01859i	−0.904077	+	0.0360577i
$799$	−2.39880	+	3.00800i	−0.0848636	+	0.106416i
$800$	−1.28277	+	0.0961304i	−0.0453528	+	0.00339872i
$801$	−1.81406	+	5.38777i	−0.0640967	+	0.190368i
$802$	−12.6891	+	21.9781i	−0.448066	+	0.776073i
$803$	−25.1979	−	43.6440i	−0.889214	−	1.54016i
$804$	−7.26256	−	4.69398i	−0.256131	−	0.165544i
$805$	−14.9035	−	29.7770i	−0.525280	−	1.04950i
$806$	−11.2829	−	2.57525i	−0.397423	−	0.0907093i
$807$	7.97547	−	14.6342i	0.280750	−	0.515148i
$808$	−1.69378	+	0.664758i	−0.0595868	+	0.0233861i
$809$	12.3665	−	4.85349i	0.434783	−	0.170640i	−0.137847	−	0.990453i	$-0.544018\pi$
$809$	12.3665	−	4.85349i	0.434783	−	0.170640i	0.572630	+	0.819814i	$0.305923\pi$
$810$	−4.25802	−	16.8129i	−0.149612	−	0.590745i
$811$	7.11354	+	1.62362i	0.249790	+	0.0570130i	0.345583	−	0.938388i	$-0.387681\pi$
$811$	7.11354	+	1.62362i	0.249790	+	0.0570130i	−0.0957923	+	0.995401i	$0.530538\pi$
$812$	−16.5934	+	4.05454i	−0.582313	+	0.142286i
$813$	−19.6402	+	30.3875i	−0.688812	+	1.06574i
$814$	21.1446	+	36.6236i	0.741118	+	1.28365i
$815$	12.7044	−	22.0047i	0.445015	−	0.770789i
$816$	−4.41782	+	2.26309i	−0.154655	+	0.0792239i
$817$	3.48855	−	0.261430i	0.122049	−	0.00914629i
$818$	22.3535	−	28.0304i	0.781572	−	0.980060i
$819$	−26.3186	−	8.41682i	−0.919647	−	0.294107i
$820$	7.73455	+	9.69881i	0.270102	+	0.338697i
$821$	−24.8438	−	26.7753i	−0.867056	−	0.934464i	0.131325	−	0.991339i	$-0.458077\pi$
$821$	−24.8438	−	26.7753i	−0.867056	−	0.934464i	−0.998381	+	0.0568749i	$0.981886\pi$
$822$	7.09302	−	9.35783i	0.247398	−	0.326392i
$823$	−12.0266	+	8.19959i	−0.419221	+	0.285820i	−0.754501	−	0.656298i	$-0.772121\pi$
$823$	−12.0266	+	8.19959i	−0.419221	+	0.285820i	0.335281	+	0.942118i	$0.391169\pi$
$824$	−7.91494	−	1.19299i	−0.275730	−	0.0415596i
$825$	9.15982	+	3.33725i	0.318904	+	0.116188i
$826$	−2.80679	+	4.25481i	−0.0976608	+	0.148044i
$827$	−24.2131	+	50.2790i	−0.841972	+	1.74837i	−0.202943	+	0.979191i	$0.565050\pi$
$827$	−24.2131	+	50.2790i	−0.841972	+	1.74837i	−0.639029	+	0.769182i	$0.720664\pi$
$828$	−15.9008	−	11.4474i	−0.552590	−	0.397826i
$829$	−13.4501	+	14.4958i	−0.467142	+	0.503460i	−0.922046	−	0.387081i	$-0.873483\pi$
$829$	−13.4501	+	14.4958i	−0.467142	+	0.503460i	0.454903	+	0.890541i	$0.349674\pi$
$830$	20.2339	+	1.51632i	0.702329	+	0.0526323i
$831$	−21.7318	−	51.6004i	−0.753869	−	1.79000i
$832$		−	3.48127i		−	0.120691i
$833$	−6.75608	+	18.8888i	−0.234084	+	0.654459i
$834$	15.7820	−	15.3834i	0.546486	−	0.532684i
$835$	−6.91264	+	17.6131i	−0.239222	+	0.609527i
$836$	−1.82375	+	24.3362i	−0.0630756	+	0.841685i
$837$	−17.2740	−	0.0166990i	−0.597076	−	0.000577201i
$838$	2.78536	−	4.08538i	0.0962188	−	0.141127i
$839$	−20.9854	−	10.1060i	−0.724496	−	0.348899i	0.0350208	−	0.999387i	$-0.488850\pi$
$839$	−20.9854	−	10.1060i	−0.724496	−	0.348899i	−0.759517	+	0.650488i	$0.774565\pi$
$840$	2.26461	−	8.53568i	0.0781366	−	0.294509i
$841$	11.4268	−	5.50285i	0.394027	−	0.189753i
$842$	−0.394731	+	2.61887i	−0.0136033	+	0.0902522i
$843$	−32.3845	−	6.55753i	−1.11538	−	0.225853i
$844$	−9.53465	+	1.43712i	−0.328196	+	0.0494676i
$845$	1.24419	−	1.15444i	0.0428015	−	0.0397140i
$846$	−2.42977	−	3.21204i	−0.0835371	−	0.110432i
$847$	−10.4888	+	18.8244i	−0.360399	+	0.646814i
$848$	4.04188	+	3.22329i	0.138799	+	0.110688i
$849$	−0.463832	+	0.525245i	−0.0159187	+	0.0180264i
$850$	1.08661	−	3.52272i	0.0372706	−	0.120828i
$851$	54.6650	+	31.5609i	1.87389	+	1.08189i
$852$	4.01003	−	14.2349i	0.137382	−	0.487680i
$853$	−7.59657	+	1.73387i	−0.260102	+	0.0593665i	−0.350583	−	0.936532i	$-0.614017\pi$
$853$	−7.59657	+	1.73387i	−0.260102	+	0.0593665i	0.0904815	+	0.995898i	$0.471159\pi$
$854$	35.2209	+	16.3045i	1.20523	+	0.557929i
$855$	−7.97684	+	31.2428i	−0.272802	+	1.06848i
$856$	10.5155	−	3.24360i	0.359412	−	0.110864i
$857$	5.72719	+	14.5926i	0.195637	+	0.498475i	0.994706	−	0.102765i	$-0.0327688\pi$
$857$	5.72719	+	14.5926i	0.195637	+	0.498475i	−0.799069	+	0.601240i	$0.794674\pi$
$858$	−10.8588	+	24.0448i	−0.370712	+	0.820876i
$859$	−4.67335	−	15.1506i	−0.159453	−	0.516933i	0.840227	−	0.542234i	$-0.182422\pi$
$859$	−4.67335	−	15.1506i	−0.159453	−	0.516933i	−0.999680	+	0.0253017i	$0.991945\pi$
$860$	−0.268960	+	1.17839i	−0.00917148	+	0.0401829i
$861$	27.8201	−	9.81163i	0.948106	−	0.334379i
$862$	4.48316	+	19.6420i	0.152697	+	0.669009i
$863$	−30.8196	+	17.7937i	−1.04911	+	0.605704i	−0.922400	−	0.386236i	$-0.873775\pi$
$863$	−30.8196	+	17.7937i	−1.04911	+	0.605704i	−0.126710	+	0.991940i	$0.540442\pi$
$864$	−1.15135	−	5.06699i	−0.0391699	−	0.172382i
$865$	−18.1691	−	5.60441i	−0.617766	−	0.190556i
$866$	−1.83654	−	24.5069i	−0.0624082	−	0.832780i
$867$	1.51051	+	15.1446i	0.0512997	+	0.514336i
$868$	−7.68329	−	4.28106i	−0.260788	−	0.145309i
$869$	3.01908	−	2.40763i	0.102415	−	0.0816734i
$870$	−1.08109	+	21.5224i	−0.0366525	+	0.729678i
$871$	2.59044	+	17.1865i	0.0877739	+	0.582342i
$872$	8.97851	+	13.1691i	0.304051	+	0.445961i
$873$	−39.4707	−	6.98599i	−1.33588	−	0.236440i
$874$	15.8049	+	32.8192i	0.534608	+	1.11013i
$875$	16.4472	+	27.5098i	0.556017	+	0.930000i
$876$	−6.34750	−	18.9126i	−0.214462	−	0.638996i
$877$	3.08771	+	2.10516i	0.104265	+	0.0710864i	0.614330	−	0.789049i	$-0.289426\pi$
$877$	3.08771	+	2.10516i	0.104265	+	0.0710864i	−0.510065	+	0.860136i	$0.670379\pi$
$878$	−22.8806	−	21.2301i	−0.772183	−	0.716481i
$879$	−1.76739	−	2.10767i	−0.0596127	−	0.0710901i
$880$	−7.84904	−	3.08052i	−0.264591	−	0.103844i
$881$	−21.4542			−0.722809			−0.361405	−	0.932409i	$-0.617703\pi$
$881$	−21.4542			−0.722809			−0.361405	+	0.932409i	$0.617703\pi$
$882$	−17.4091	−	11.7441i	−0.586194	−	0.395445i
$883$	−37.6383			−1.26663			−0.633314	−	0.773895i	$-0.718306\pi$
$883$	−37.6383			−1.26663			−0.633314	+	0.773895i	$0.718306\pi$
$884$	9.28703	+	3.64489i	0.312357	+	0.122591i
$885$	4.13184	+	4.92736i	0.138890	+	0.165631i
$886$	−1.53884	−	1.42783i	−0.0516982	−	0.0479689i
$887$	−23.1343	−	15.7727i	−0.776775	−	0.529596i	0.108816	−	0.994062i	$-0.465294\pi$
$887$	−23.1343	−	15.7727i	−0.776775	−	0.529596i	−0.885591	+	0.464466i	$0.846246\pi$
$888$	5.32646	+	15.8703i	0.178744	+	0.532574i
$889$	−24.2167	−	15.9752i	−0.812202	−	0.535790i
$890$	1.58445	+	3.29015i	0.0531110	+	0.110286i
$891$	−7.85262	+	38.5885i	−0.263073	+	1.29276i
$892$	8.07502	+	11.8439i	0.270372	+	0.396563i
$893$	1.11601	+	7.40426i	0.0373459	+	0.247774i
$894$	−0.523942	+	10.4307i	−0.0175232	+	0.348853i
$895$	−16.6419	+	13.2714i	−0.556276	+	0.443616i
$896$	0.741201	−	2.53981i	0.0247618	−	0.0848490i
$897$	3.90834	+	39.1854i	0.130496	+	1.30836i
$898$	−1.92111	−	25.6354i	−0.0641083	−	0.855466i
$899$	20.5094	+	6.32631i	0.684026	+	0.210994i
$900$	3.29164	+	2.01440i	0.109721	+	0.0671465i
$901$	−12.8307	+	7.40779i	−0.427452	+	0.246789i
$902$	−6.26763	−	27.4603i	−0.208689	−	0.914327i
$903$	2.43747	+	1.52321i	0.0811140	+	0.0506892i
$904$	−4.33798	+	19.0059i	−0.144279	+	0.632127i
$905$	−0.770613	−	2.49827i	−0.0256160	−	0.0830452i
$906$	−7.78557	+	17.2398i	−0.258658	+	0.572753i
$907$	−10.0690	−	25.6553i	−0.334334	−	0.851870i	−0.994878	−	0.101082i	$-0.967769\pi$
$907$	−10.0690	−	25.6553i	−0.334334	−	0.851870i	0.660544	−	0.750787i	$-0.270326\pi$
$908$	−9.90246	+	3.05450i	−0.328625	+	0.101367i
$909$	5.28900	+	1.35037i	0.175425	+	0.0447891i
$910$	−15.8724	+	7.94421i	−0.526166	+	0.263348i
$911$	32.5895	−	7.43834i	1.07974	−	0.246443i	0.354580	−	0.935026i	$-0.384624\pi$
$911$	32.5895	−	7.43834i	1.07974	−	0.246443i	0.725158	+	0.688582i	$0.241767\pi$
$912$	−2.61947	+	9.29866i	−0.0867394	+	0.307909i
$913$	−39.8982	−	23.0352i	−1.32044	−	0.762355i
$914$	−2.34551	+	7.60396i	−0.0775826	+	0.251517i
$915$	32.4104	−	36.7016i	1.07145	−	1.21332i
$916$	3.53437	+	2.81856i	0.116779	+	0.0931279i
$917$	−8.91361	−	8.02115i	−0.294353	−	0.264882i
$918$	14.7227	+	2.23365i	0.485923	+	0.0737216i
$919$	42.7041	−	39.6236i	1.40868	−	1.30706i	0.515842	−	0.856684i	$-0.327479\pi$
$919$	42.7041	−	39.6236i	1.40868	−	1.30706i	0.892837	−	0.450379i	$-0.148711\pi$
$920$	−12.4451	+	1.87579i	−0.410301	+	0.0618430i
$921$	−13.1806	−	2.66893i	−0.434314	−	0.0879442i
$922$	−1.74356	+	11.5677i	−0.0574209	+	0.380963i
$923$	−26.7809	+	12.8970i	−0.881503	+	0.424509i
$924$	−13.0415	+	15.2302i	−0.429035	+	0.501038i
$925$	−11.2016	−	5.39439i	−0.368305	−	0.177366i
$926$	−5.95328	+	8.73186i	−0.195637	+	0.286947i
$927$	17.1793	+	16.7779i	0.564243	+	0.551057i
$928$	−0.482474	+	6.43817i	−0.0158380	+	0.211343i
$929$	−2.36490	+	6.02567i	−0.0775899	+	0.197696i	−0.964406	−	0.264427i	$-0.914817\pi$
$929$	−2.36490	+	6.02567i	−0.0775899	+	0.197696i	0.886816	+	0.462123i	$0.152912\pi$
$930$	−7.94583	+	7.74515i	−0.260554	+	0.253973i
$931$	18.0049	+	34.6433i	0.590088	+	1.13539i
$932$			25.0363i			0.820090i
$933$	−13.4030	−	31.8242i	−0.438793	−	1.04188i
$934$	−13.6702	−	1.02444i	−0.447303	−	0.0335207i
$935$	16.4359	−	17.7137i	0.537511	−	0.579299i
$936$	−6.10197	+	8.47580i	−0.199449	+	0.277040i
$937$	−15.8479	+	32.9086i	−0.517730	+	1.07508i	0.464182	+	0.885740i	$0.346348\pi$
$937$	−15.8479	+	32.9086i	−0.517730	+	1.07508i	−0.981912	+	0.189338i	$0.939366\pi$
$938$	−1.76930	+	13.0902i	−0.0577696	+	0.427409i
$939$	21.2118	+	7.72820i	0.692220	+	0.252200i
$940$	−2.55822	−	0.385590i	−0.0834400	−	0.0125766i
$941$	−3.01734	+	2.05719i	−0.0983625	+	0.0670624i	−0.611502	−	0.791243i	$-0.709435\pi$
$941$	−3.01734	+	2.05719i	−0.0983625	+	0.0670624i	0.513140	+	0.858305i	$0.328482\pi$
$942$	24.1911	−	31.9153i	0.788189	−	1.03986i
$943$	−28.5957	−	30.8188i	−0.931204	−	1.00360i
$944$	1.20119	+	1.50625i	0.0390954	+	0.0490241i
$945$	−20.4750	+	16.8123i	−0.666051	+	0.546903i
$946$	1.71109	−	2.14564i	0.0556325	−	0.0697609i
$947$	38.2528	−	2.86665i	1.24305	−	0.0931535i	0.563084	−	0.826400i	$-0.309615\pi$
$947$	38.2528	−	2.86665i	1.24305	−	0.0931535i	0.679963	+	0.733246i	$0.261996\pi$
$948$	1.36049	−	0.696928i	0.0441866	−	0.0226352i
$949$	−20.0482	+	34.7245i	−0.650792	+	1.12720i
$950$	−3.58738	−	6.21353i	−0.116390	−	0.201594i
$951$	−14.5558	+	22.5209i	−0.472005	+	0.730290i
$952$	5.99944	+	4.63649i	0.194443	+	0.150270i
$953$	−29.4182	−	6.71452i	−0.952950	−	0.217505i	−0.282340	−	0.959314i	$-0.591111\pi$
$953$	−29.4182	−	6.71452i	−0.952950	−	0.217505i	−0.670610	+	0.741810i	$0.733968\pi$
$954$	−4.19092	−	14.9323i	−0.135686	−	0.483451i
$955$	−13.3929	+	5.25634i	−0.433385	+	0.170091i
$956$	17.8351	−	6.99976i	0.576829	−	0.226389i
$957$	23.4143	−	42.9628i	0.756876	−	1.38879i
$958$	15.7533	+	3.59560i	0.508967	+	0.116168i
$959$	−17.5457	−	3.72411i	−0.566579	−	0.120258i
$960$	−2.80325	−	1.81181i	−0.0904746	−	0.0584760i
$961$	−9.97425	−	17.2759i	−0.321750	−	0.557287i
$962$	16.8233	−	29.1388i	0.542405	−	0.939473i
$963$	−31.2873	−	10.5344i	−1.00822	−	0.339467i
$964$	−12.0789	+	0.905187i	−0.389035	+	0.0291541i
$965$	16.9788	−	21.2907i	0.546566	−	0.685372i
$966$	−5.49163	+	29.4204i	−0.176690	+	0.946585i
$967$	27.4319	+	34.3985i	0.882149	+	1.10618i	0.993661	+	0.112417i	$0.0358592\pi$
$967$	27.4319	+	34.3985i	0.882149	+	1.10618i	−0.111512	+	0.993763i	$0.535569\pi$
$968$	5.53992	+	5.97062i	0.178060	+	0.191903i
$969$	−22.0636	−	16.7237i	−0.708784	−	0.537243i
$970$	−21.2744	+	14.5046i	−0.683079	+	0.465715i
$971$	31.5644	+	4.75756i	1.01295	+	0.152677i	0.634482	−	0.772938i	$-0.281213\pi$
$971$	31.5644	+	4.75756i	1.01295	+	0.152677i	0.378466	+	0.925615i	$0.376452\pi$
$972$	−6.07824	+	14.3546i	−0.194959	+	0.460425i
$973$	−31.5220	−	11.8199i	−1.01055	−	0.378930i
$974$	−0.921452	+	1.91341i	−0.0295252	+	0.0613098i
$975$	−1.34443	−	7.63906i	−0.0430564	−	0.244646i
$976$	9.97775	−	10.7535i	0.319380	−	0.344210i
$977$	−54.4560	−	4.08092i	−1.74220	−	0.130560i	−0.834727	−	0.550664i	$-0.814375\pi$
$977$	−54.4560	−	4.08092i	−1.74220	−	0.130560i	−0.907476	+	0.420104i	$0.861994\pi$
$978$	−21.0469	+	8.86403i	−0.673006	+	0.283440i
$979$		−	8.29151i		−	0.264998i
$980$	−13.2714	+	2.41639i	−0.423938	+	0.0771886i
$981$	1.22288	−	47.8000i	0.0390437	−	1.52614i
$982$	13.8361	−	35.2539i	0.441528	−	1.12500i
$983$	1.57046	−	20.9563i	0.0500897	−	0.668401i	−0.914490	−	0.404609i	$-0.867408\pi$
$983$	1.57046	−	20.9563i	0.0500897	−	0.668401i	0.964580	−	0.263792i	$-0.0849733\pi$
$984$	−0.274380	−	11.1464i	−0.00874692	−	0.355335i
$985$	−16.8790	+	24.7569i	−0.537808	+	0.788820i
$986$	−16.6700	−	8.02787i	−0.530882	−	0.255659i
$987$	−2.86130	+	5.44627i	−0.0910763	+	0.173357i
$988$	17.4940	−	8.42468i	0.556559	−	0.268025i
$989$	0.610524	−	4.05056i	0.0194135	−	0.128800i
$990$	13.7104	+	21.2579i	0.435745	+	0.675620i
$991$	34.6953	−	5.22948i	1.10213	−	0.166120i	0.427314	−	0.904103i	$-0.359460\pi$
$991$	34.6953	−	5.22948i	1.10213	−	0.166120i	0.674819	+	0.737984i	$0.264222\pi$
$992$	−2.43694	+	2.26115i	−0.0773730	+	0.0717917i
$993$	9.84744	+	1.23727i	0.312499	+	0.0392635i
$994$	−22.2842	+	3.70722i	−0.706813	+	0.117586i
$995$	−16.2334	−	12.9457i	−0.514632	−	0.410405i
$996$	−13.6700	−	12.0717i	−0.433150	−	0.382505i
$997$	4.64949	−	15.0733i	0.147251	−	0.477375i	−0.851657	−	0.524099i	$-0.824402\pi$
$997$	4.64949	−	15.0733i	0.147251	−	0.477375i	0.998908	+	0.0467244i	$0.0148782\pi$
$998$	−7.62113	−	4.40006i	−0.241243	−	0.139282i
$999$	14.8493	−	47.9755i	0.469811	−	1.51788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.p.a.101.3	✓	216
3.2	odd	2	inner	294.2.p.a.101.12	yes	216
49.33	odd	42	inner	294.2.p.a.131.12	yes	216
147.131	even	42	inner	294.2.p.a.131.3	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.p.a.101.3	✓	216	1.1	even	1	trivial
294.2.p.a.101.12	yes	216	3.2	odd	2	inner
294.2.p.a.131.3	yes	216	147.131	even	42	inner
294.2.p.a.131.12	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)

\(f(q)\)	\(=\)	\(q+(-0.930874 - 0.365341i) q^{2} +(-1.11291 - 1.32719i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-1.59223 - 1.08556i) q^{5} +(0.551106 + 1.64204i) q^{6} +(1.91180 - 1.82894i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.522848 + 2.95409i) q^{9} +O(q^{10})\)	\(q+(-0.930874 - 0.365341i) q^{2} +(-1.11291 - 1.32719i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-1.59223 - 1.08556i) q^{5} +(0.551106 + 1.64204i) q^{6} +(1.91180 - 1.82894i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-0.522848 + 2.95409i) q^{9} +(1.08556 + 1.59223i) q^{10} +(-0.652132 - 4.32662i) q^{11} +(0.0868930 - 1.72987i) q^{12} +(-2.72177 + 2.17054i) q^{13} +(-2.44783 + 1.00405i) q^{14} +(0.331267 + 3.32132i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(-2.73850 - 0.844714i) q^{17} +(1.56596 - 2.55886i) q^{18} +(-4.83029 + 2.78877i) q^{19} +(-0.428815 - 1.87876i) q^{20} +(-4.55501 - 0.501871i) q^{21} +(-0.973637 + 4.26578i) q^{22} +(1.92503 + 6.24079i) q^{23} +(-0.712879 + 1.57854i) q^{24} +(-0.469963 - 1.19745i) q^{25} +(3.32661 - 1.02612i) q^{26} +(4.50251 - 2.59372i) q^{27} +(2.64544 - 0.0403496i) q^{28} +(-6.29435 + 1.43664i) q^{29} +(0.905046 - 3.21275i) q^{30} +(-2.87900 - 1.66219i) q^{31} +(0.294755 - 0.955573i) q^{32} +(-5.01646 + 5.68065i) q^{33} +(2.24059 + 1.78681i) q^{34} +(-5.02945 + 0.836703i) q^{35} +(-2.39256 + 1.80987i) q^{36} +(7.08497 - 6.57390i) q^{37} +(5.51524 - 0.831289i) q^{38} +(5.90980 + 1.19667i) q^{39} +(-0.287216 + 1.90555i) q^{40} +(-5.79984 + 2.79305i) q^{41} +(4.05679 + 2.13131i) q^{42} +(-0.565103 - 0.272139i) q^{43} +(2.46480 - 3.61520i) q^{44} +(4.03934 - 4.13599i) q^{45} +(0.488057 - 6.51267i) q^{46} +(0.490473 - 1.24971i) q^{47} +(1.24031 - 1.20898i) q^{48} +(0.309979 - 6.99313i) q^{49} +1.28637i q^{50} +(1.92662 + 4.57459i) q^{51} +(-3.47154 - 0.260156i) q^{52} +(3.51633 - 3.78970i) q^{53} +(-5.13886 + 0.769479i) q^{54} +(-3.65847 + 7.59688i) q^{55} +(-2.47732 - 0.928929i) q^{56} +(9.07691 + 3.30704i) q^{57} +(6.38411 + 0.962250i) q^{58} +(1.59180 - 1.08527i) q^{59} +(-2.01623 + 2.66002i) q^{60} +(-9.97775 - 10.7535i) q^{61} +(2.07272 + 2.59910i) q^{62} +(4.40326 + 6.60389i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(6.68992 - 0.501340i) q^{65} +(6.74506 - 3.45525i) q^{66} +(2.49630 - 4.32372i) q^{67} +(-1.43291 - 2.48187i) q^{68} +(6.14030 - 9.50032i) q^{69} +(4.98746 + 1.05860i) q^{70} +(8.32433 + 1.89997i) q^{71} +(2.88840 - 0.810660i) q^{72} +(10.7216 - 4.20791i) q^{73} +(-8.99693 + 3.53103i) q^{74} +(-1.06621 + 1.95638i) q^{75} +(-5.43770 - 1.24112i) q^{76} +(-9.15985 - 7.07893i) q^{77} +(-5.06408 - 3.27304i) q^{78} +(0.441270 + 0.764303i) q^{79} +(0.963539 - 1.66890i) q^{80} +(-8.45326 - 3.08908i) q^{81} +(6.41933 - 0.481063i) q^{82} +(6.56486 - 8.23208i) q^{83} +(-2.99770 - 3.46609i) q^{84} +(3.44332 + 4.31778i) q^{85} +(0.426616 + 0.459783i) q^{86} +(8.91176 + 6.75491i) q^{87} +(-3.61520 + 2.46480i) q^{88} +(1.87383 + 0.282434i) q^{89} +(-5.27116 + 2.37435i) q^{90} +(-1.23371 + 9.12758i) q^{91} +(-2.83367 + 5.88417i) q^{92} +(0.998038 + 5.67084i) q^{93} +(-0.913137 + 0.984128i) q^{94} +(10.7183 + 0.803225i) q^{95} +(-1.59626 + 0.672274i) q^{96} +13.3614i q^{97} +(-2.84343 + 6.39648i) q^{98} +(13.1222 + 0.335709i) 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

Varieties

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Database

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