LMFDB - Embedded newform 380.2.bb.a.279.54

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			279.54
Character	$\chi$	$=$	380.279
Dual form			380.2.bb.a.79.54

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39852 - 0.210104i) q^{2} +(0.305059 - 0.838142i) q^{3} +(1.91171 - 0.587670i) q^{4} +(1.86109 - 1.23949i) q^{5} +(0.250533 - 1.23625i) q^{6} +(-0.893843 + 1.54818i) q^{7} +(2.55009 - 1.22353i) q^{8} +(1.68871 + 1.41700i) q^{9} +O(q^{10})$	\(q+(1.39852 - 0.210104i) q^{2} +(0.305059 - 0.838142i) q^{3} +(1.91171 - 0.587670i) q^{4} +(1.86109 - 1.23949i) q^{5} +(0.250533 - 1.23625i) q^{6} +(-0.893843 + 1.54818i) q^{7} +(2.55009 - 1.22353i) q^{8} +(1.68871 + 1.41700i) q^{9} +(2.34235 - 2.12448i) q^{10} +(-2.85412 + 1.64782i) q^{11} +(0.0906334 - 1.78156i) q^{12} +(-2.39281 + 0.870912i) q^{13} +(-0.924777 + 2.35296i) q^{14} +(-0.471127 - 1.93798i) q^{15} +(3.30929 - 2.24691i) q^{16} +(-4.04286 - 4.81810i) q^{17} +(2.65941 + 1.62689i) q^{18} +(-2.78516 + 3.35304i) q^{19} +(2.82946 - 3.46326i) q^{20} +(1.02492 + 1.22145i) q^{21} +(-3.64532 + 2.90418i) q^{22} +(0.254094 - 1.44104i) q^{23} +(-0.247561 - 2.51059i) q^{24} +(1.92733 - 4.61361i) q^{25} +(-3.16341 + 1.72073i) q^{26} +(4.02011 - 2.32101i) q^{27} +(-0.798950 + 3.48496i) q^{28} +(0.615783 - 0.733862i) q^{29} +(-1.06606 - 2.61131i) q^{30} +(-2.40205 + 4.16048i) q^{31} +(4.15602 - 3.83765i) q^{32} +(0.510438 + 2.89484i) q^{33} +(-6.66633 - 5.88878i) q^{34} +(0.255433 + 3.98922i) q^{35} +(4.06106 + 1.71649i) q^{36} +1.29518 q^{37} +(-3.19061 + 5.27447i) q^{38} +2.27120i q^{39} +(3.22941 - 5.43792i) q^{40} +(-3.38958 + 9.31281i) q^{41} +(1.69001 + 1.49289i) q^{42} +(-0.140245 - 0.795371i) q^{43} +(-4.48787 + 4.82744i) q^{44} +(4.89920 + 0.544020i) q^{45} +(0.0525867 - 2.06871i) q^{46} +(-6.25117 - 5.24536i) q^{47} +(-0.873706 - 3.45909i) q^{48} +(1.90209 + 3.29451i) q^{49} +(1.72606 - 6.85717i) q^{50} +(-5.27156 + 1.91869i) q^{51} +(-4.06256 + 3.07112i) q^{52} +(-0.195369 + 1.10799i) q^{53} +(5.13455 - 4.09062i) q^{54} +(-3.26931 + 6.60440i) q^{55} +(-0.385141 + 5.04165i) q^{56} +(1.96069 + 3.35723i) q^{57} +(0.706997 - 1.15570i) q^{58} +(8.95499 - 7.51412i) q^{59} +(-2.03955 - 3.42799i) q^{60} +(-0.772146 + 4.37906i) q^{61} +(-2.48518 + 6.32319i) q^{62} +(-3.70321 + 1.34786i) q^{63} +(5.00596 - 6.24022i) q^{64} +(-3.37375 + 4.58671i) q^{65} +(1.32208 + 3.94124i) q^{66} +(8.67340 - 10.3366i) q^{67} +(-10.5602 - 6.83495i) q^{68} +(-1.13028 - 0.652570i) q^{69} +(1.19538 + 5.52533i) q^{70} +(-0.784140 - 4.44708i) q^{71} +(6.04011 + 1.54729i) q^{72} +(-4.08525 + 11.2241i) q^{73} +(1.81134 - 0.272124i) q^{74} +(-3.27892 - 3.02280i) q^{75} +(-3.35394 + 8.04681i) q^{76} -5.89159i q^{77} +(0.477188 + 3.17631i) q^{78} +(-4.94158 - 1.79859i) q^{79} +(3.37386 - 8.28354i) q^{80} +(0.429431 + 2.43543i) q^{81} +(-2.78374 + 13.7363i) q^{82} +(-6.85928 + 11.8806i) q^{83} +(2.67717 + 1.73275i) q^{84} +(-13.4961 - 3.95583i) q^{85} +(-0.363247 - 1.08288i) q^{86} +(-0.427231 - 0.739985i) q^{87} +(-5.26210 + 7.69420i) q^{88} +(-3.77737 - 10.3782i) q^{89} +(6.96593 - 0.268522i) q^{90} +(0.790467 - 4.48296i) q^{91} +(-0.361102 - 2.90418i) q^{92} +(2.75431 + 3.28246i) q^{93} +(-9.84446 - 6.02233i) q^{94} +(-1.02737 + 9.69250i) q^{95} +(-1.94867 - 4.65404i) q^{96} +(-2.48501 + 2.08517i) q^{97} +(3.35230 + 4.20780i) q^{98} +(-7.15474 - 1.26157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$	$-1$

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 $

$2$	1.39852	−	0.210104i	0.988902	−	0.148566i
$2$	1.39852	−	0.210104i	0.988902	−	0.148566i
$3$	0.305059	−	0.838142i	0.176126	−	0.483902i	−0.819947	−	0.572439i	$-0.805997\pi$
$3$	0.305059	−	0.838142i	0.176126	−	0.483902i	0.996073	+	0.0885377i	$0.0282194\pi$
$4$	1.91171	−	0.587670i	0.955856	−	0.293835i
$5$	1.86109	−	1.23949i	0.832306	−	0.554317i
$5$	1.86109	−	1.23949i	0.832306	−	0.554317i
$6$	0.250533	−	1.23625i	0.102280	−	0.504698i
$7$	−0.893843	+	1.54818i	−0.337841	+	0.585158i	−0.984026	−	0.178023i	$-0.943030\pi$
$7$	−0.893843	+	1.54818i	−0.337841	+	0.585158i	0.646185	+	0.763180i	$0.276363\pi$
$8$	2.55009	−	1.22353i	0.901594	−	0.432582i
$9$	1.68871	+	1.41700i	0.562904	+	0.472332i
$10$	2.34235	−	2.12448i	0.740716	−	0.671818i
$11$	−2.85412	+	1.64782i	−0.860548	+	0.496838i	−0.864196	−	0.503156i	$-0.832172\pi$
$11$	−2.85412	+	1.64782i	−0.860548	+	0.496838i	0.00364771	+	0.999993i	$0.498839\pi$
$12$	0.0906334	−	1.78156i	0.0261636	−	0.514292i
$13$	−2.39281	+	0.870912i	−0.663646	+	0.241547i	−0.651810	−	0.758382i	$-0.725990\pi$
$13$	−2.39281	+	0.870912i	−0.663646	+	0.241547i	−0.0118364	+	0.999930i	$0.503768\pi$
$14$	−0.924777	+	2.35296i	−0.247157	+	0.628856i
$15$	−0.471127	−	1.93798i	−0.121645	−	0.500384i
$16$	3.30929	−	2.24691i	0.827322	−	0.561728i
$17$	−4.04286	−	4.81810i	−0.980539	−	1.16856i	−0.985689	−	0.168574i	$-0.946084\pi$
$17$	−4.04286	−	4.81810i	−0.980539	−	1.16856i	0.00515039	−	0.999987i	$-0.498361\pi$
$18$	2.65941	+	1.62689i	0.626830	+	0.383462i
$19$	−2.78516	+	3.35304i	−0.638959	+	0.769241i
$19$	−2.78516	+	3.35304i	−0.638959	+	0.769241i
$20$	2.82946	−	3.46326i	0.632686	−	0.774408i
$21$	1.02492	+	1.22145i	0.223656	+	0.266543i
$22$	−3.64532	+	2.90418i	−0.777185	+	0.619172i
$23$	0.254094	−	1.44104i	0.0529823	−	0.300478i	−0.946789	−	0.321854i	$-0.895694\pi$
$23$	0.254094	−	1.44104i	0.0529823	−	0.300478i	0.999771	+	0.0213767i	$0.00680493\pi$
$24$	−0.247561	−	2.51059i	−0.0505333	−	0.512472i
$25$	1.92733	−	4.61361i	0.385465	−	0.922722i
$26$	−3.16341	+	1.72073i	−0.620396	+	0.337462i
$27$	4.02011	−	2.32101i	0.773671	−	0.446679i
$28$	−0.798950	+	3.48496i	−0.150987	+	0.658596i
$29$	0.615783	−	0.733862i	0.114348	−	0.136275i	−0.705834	−	0.708377i	$-0.749428\pi$
$29$	0.615783	−	0.733862i	0.114348	−	0.136275i	0.820182	+	0.572102i	$0.193872\pi$
$30$	−1.06606	−	2.61131i	−0.194635	−	0.476758i
$31$	−2.40205	+	4.16048i	−0.431422	+	0.747244i	−0.996996	−	0.0774530i	$-0.975321\pi$
$31$	−2.40205	+	4.16048i	−0.431422	+	0.747244i	0.565574	+	0.824697i	$0.308655\pi$
$32$	4.15602	−	3.83765i	0.734687	−	0.678407i
$33$	0.510438	+	2.89484i	0.0888559	+	0.503927i
$34$	−6.66633	−	5.88878i	−1.14327	−	1.00992i
$35$	0.255433	+	3.98922i	0.0431760	+	0.674301i
$36$	4.06106	+	1.71649i	0.676843	+	0.286081i
$37$	1.29518			0.212927			0.106464	−	0.994317i	$-0.466047\pi$
$37$	1.29518			0.212927			0.106464	+	0.994317i	$0.466047\pi$
$38$	−3.19061	+	5.27447i	−0.517585	+	0.855632i
$39$			2.27120i			0.363682i
$40$	3.22941	−	5.43792i	0.510614	−	0.859810i
$41$	−3.38958	+	9.31281i	−0.529364	+	1.45442i	0.330457	+	0.943821i	$0.392797\pi$
$41$	−3.38958	+	9.31281i	−0.529364	+	1.45442i	−0.859821	+	0.510595i	$0.829425\pi$
$42$	1.69001	+	1.49289i	0.260774	+	0.230357i
$43$	−0.140245	−	0.795371i	−0.0213872	−	0.121293i	0.972245	−	0.233965i	$-0.0751701\pi$
$43$	−0.140245	−	0.795371i	−0.0213872	−	0.121293i	−0.993632	+	0.112672i	$0.964059\pi$
$44$	−4.48787	+	4.82744i	−0.676572	+	0.727765i
$45$	4.89920	+	0.544020i	0.730330	+	0.0810977i
$46$	0.0525867	−	2.06871i	0.00775349	−	0.305015i
$47$	−6.25117	−	5.24536i	−0.911827	−	0.765114i	0.0606385	−	0.998160i	$-0.480686\pi$
$47$	−6.25117	−	5.24536i	−0.911827	−	0.765114i	−0.972466	+	0.233046i	$0.925131\pi$
$48$	−0.873706	−	3.45909i	−0.126109	−	0.499277i
$49$	1.90209	+	3.29451i	0.271727	+	0.470645i
$50$	1.72606	−	6.85717i	0.244102	−	0.969750i
$51$	−5.27156	+	1.91869i	−0.738167	+	0.268671i
$52$	−4.06256	+	3.07112i	−0.563375	+	0.425887i
$53$	−0.195369	+	1.10799i	−0.0268360	+	0.152194i	−0.995281	−	0.0970319i	$-0.969065\pi$
$53$	−0.195369	+	1.10799i	−0.0268360	+	0.152194i	0.968445	+	0.249226i	$0.0801762\pi$
$54$	5.13455	−	4.09062i	0.698723	−	0.556663i
$55$	−3.26931	+	6.60440i	−0.440833	+	0.890537i
$56$	−0.385141	+	5.04165i	−0.0514667	+	0.673719i
$57$	1.96069	+	3.35723i	0.259700	+	0.444677i
$58$	0.706997	−	1.15570i	0.0928333	−	0.151751i
$59$	8.95499	−	7.51412i	1.16584	−	0.978256i	0.165871	−	0.986147i	$-0.446957\pi$
$59$	8.95499	−	7.51412i	1.16584	−	0.978256i	0.999969	+	0.00789177i	$0.00251206\pi$
$60$	−2.03955	−	3.42799i	−0.263305	−	0.442551i
$61$	−0.772146	+	4.37906i	−0.0988632	+	0.560681i	0.894632	+	0.446804i	$0.147438\pi$
$61$	−0.772146	+	4.37906i	−0.0988632	+	0.560681i	−0.993495	+	0.113877i	$0.963673\pi$
$62$	−2.48518	+	6.32319i	−0.315619	+	0.803046i
$63$	−3.70321	+	1.34786i	−0.466561	+	0.169814i
$64$	5.00596	−	6.24022i	0.625745	−	0.780028i
$65$	−3.37375	+	4.58671i	−0.418463	+	0.568912i
$66$	1.32208	+	3.94124i	0.162736	+	0.485133i
$67$	8.67340	−	10.3366i	1.05962	−	1.26281i	0.0960483	−	0.995377i	$-0.469380\pi$
$67$	8.67340	−	10.3366i	1.05962	−	1.26281i	0.963576	−	0.267434i	$-0.0861759\pi$
$68$	−10.5602	−	6.83495i	−1.28062	−	0.828859i
$69$	−1.13028	−	0.652570i	−0.136070	−	0.0785601i
$70$	1.19538	+	5.52533i	0.142875	+	0.660403i
$71$	−0.784140	−	4.44708i	−0.0930603	−	0.527771i	−0.995324	−	0.0965875i	$-0.969207\pi$
$71$	−0.784140	−	4.44708i	−0.0930603	−	0.527771i	0.902264	−	0.431184i	$-0.141904\pi$
$72$	6.04011	+	1.54729i	0.711834	+	0.182350i
$73$	−4.08525	+	11.2241i	−0.478142	+	1.31368i	0.432927	+	0.901429i	$0.357481\pi$
$73$	−4.08525	+	11.2241i	−0.478142	+	1.31368i	−0.911069	+	0.412255i	$0.864741\pi$
$74$	1.81134	−	0.272124i	0.210564	−	0.0316338i
$75$	−3.27892	−	3.02280i	−0.378617	−	0.349042i
$76$	−3.35394	+	8.04681i	−0.384723	+	0.923032i
$77$		−	5.89159i		−	0.671408i
$78$	0.477188	+	3.17631i	0.0540309	+	0.359646i
$79$	−4.94158	−	1.79859i	−0.555971	−	0.202357i	0.0487265	−	0.998812i	$-0.484484\pi$
$79$	−4.94158	−	1.79859i	−0.555971	−	0.202357i	−0.604697	+	0.796455i	$0.706706\pi$
$80$	3.37386	−	8.28354i	0.377209	−	0.926128i
$81$	0.429431	+	2.43543i	0.0477146	+	0.270603i
$82$	−2.78374	+	13.7363i	−0.307412	+	1.51692i
$83$	−6.85928	+	11.8806i	−0.752903	+	1.30407i	0.193507	+	0.981099i	$0.438014\pi$
$83$	−6.85928	+	11.8806i	−0.752903	+	1.30407i	−0.946410	+	0.322968i	$0.895319\pi$
$84$	2.67717	+	1.73275i	0.292103	+	0.189059i
$85$	−13.4961	−	3.95583i	−1.46386	−	0.429070i
$86$	−0.363247	−	1.08288i	−0.0391699	−	0.116769i
$87$	−0.427231	−	0.739985i	−0.0458039	−	0.0793347i
$88$	−5.26210	+	7.69420i	−0.560942	+	0.820204i
$89$	−3.77737	−	10.3782i	−0.400400	−	1.10009i	−0.962088	−	0.272741i	$-0.912070\pi$
$89$	−3.77737	−	10.3782i	−0.400400	−	1.10009i	0.561687	−	0.827350i	$-0.310152\pi$
$90$	6.96593	−	0.268522i	0.734273	−	0.0283048i
$91$	0.790467	−	4.48296i	0.0828635	−	0.469942i
$92$	−0.361102	−	2.90418i	−0.0376474	−	0.302782i
$93$	2.75431	+	3.28246i	0.285608	+	0.340375i
$94$	−9.84446	−	6.02233i	−1.01538	−	0.621156i
$95$	−1.02737	+	9.69250i	−0.105406	+	0.994429i
$96$	−1.94867	−	4.65404i	−0.198885	−	0.475001i
$97$	−2.48501	+	2.08517i	−0.252314	+	0.211717i	−0.760168	−	0.649726i	$-0.774883\pi$
$97$	−2.48501	+	2.08517i	−0.252314	+	0.211717i	0.507854	+	0.861443i	$0.330439\pi$
$98$	3.35230	+	4.20780i	0.338633	+	0.425052i
$99$	−7.15474	−	1.26157i	−0.719078	−	0.126793i
$100$	0.973208	−	9.95253i	0.0973208	−	0.995253i
$101$	9.11270	−	3.31675i	0.906748	−	0.330029i	0.153794	−	0.988103i	$-0.450851\pi$
$101$	9.11270	−	3.31675i	0.906748	−	0.330029i	0.752954	+	0.658074i	$0.228628\pi$
$102$	−6.96926	+	3.79091i	−0.690059	+	0.375356i
$103$	−3.53954	+	2.04355i	−0.348761	+	0.201357i	−0.664139	−	0.747609i	$-0.731202\pi$
$103$	−3.53954	+	2.04355i	−0.348761	+	0.201357i	0.315379	+	0.948966i	$0.397869\pi$
$104$	−5.03631	+	5.14858i	−0.493851	+	0.504859i
$105$	3.42146	+	1.00286i	0.333900	+	0.0978689i
$106$	−0.0404330	+	1.59059i	−0.00392720	+	0.154492i
$107$	10.1335	+	5.85059i	0.979645	+	0.565598i	0.902163	−	0.431395i	$-0.141979\pi$
$107$	10.1335	+	5.85059i	0.979645	+	0.565598i	0.0774821	+	0.996994i	$0.475312\pi$
$108$	6.32130	−	6.79961i	0.608268	−	0.654292i
$109$	15.6324	−	2.75642i	1.49732	−	0.264017i	0.635842	−	0.771819i	$-0.280653\pi$
$109$	15.6324	−	2.75642i	1.49732	−	0.264017i	0.861474	+	0.507802i	$0.169542\pi$
$110$	−3.18458	+	9.92328i	−0.303637	+	0.946147i
$111$	0.395108	−	1.08555i	0.0375020	−	0.103036i
$112$	0.520646	+	7.13177i	0.0491964	+	0.673889i
$113$	8.57360			0.806536			0.403268	−	0.915082i	$-0.367874\pi$
$113$	8.57360			0.806536			0.403268	+	0.915082i	$0.367874\pi$
$114$	3.44743	+	4.28321i	0.322882	+	0.401159i
$115$	−1.31326	−	2.99686i	−0.122462	−	0.279458i
$116$	0.745931	−	1.76481i	0.0692580	−	0.163859i
$117$	−5.27485	−	1.91989i	−0.487660	−	0.177494i
$118$	10.9450	−	12.3901i	1.00757	−	1.14060i
$119$	11.0730	−	1.95246i	1.01506	−	0.178982i
$120$	−3.57259	−	4.36559i	−0.326131	−	0.398522i
$121$	−0.0693514	+	0.120120i	−0.00630467	+	0.0109200i
$122$	−0.159802	+	6.28643i	−0.0144677	+	0.569147i
$123$	6.77143	+	5.68191i	0.610560	+	0.512320i
$124$	−2.14705	+	9.36526i	−0.192810	+	0.841025i
$125$	−2.13160	−	10.9753i	−0.190656	−	0.981657i
$126$	−4.89582	+	2.66307i	−0.436155	+	0.237245i
$127$	−5.48910	−	15.0812i	−0.487079	−	1.33824i	−0.903313	−	0.428981i	$-0.858873\pi$
$127$	−5.48910	−	15.0812i	−0.487079	−	1.33824i	0.416235	−	0.909257i	$-0.363350\pi$
$128$	5.68983	−	9.77884i	0.502915	−	0.864336i
$129$	−0.709417	−	0.125089i	−0.0624607	−	0.0110135i
$130$	−3.75457	+	7.12345i	−0.329297	+	0.624768i
$131$	8.64226	+	10.2994i	0.755078	+	0.899866i	0.997526	−	0.0702979i	$-0.0223950\pi$
$131$	8.64226	+	10.2994i	0.755078	+	0.899866i	−0.242449	+	0.970164i	$0.577951\pi$
$132$	2.67702	+	5.23413i	0.233005	+	0.455572i
$133$	−2.70163	−	7.30902i	−0.234261	−	0.633773i
$134$	9.95816	−	16.2782i	0.860254	−	1.40622i
$135$	4.60492	−	9.30251i	0.396329	−	0.800632i
$136$	−16.2048	−	7.34005i	−1.38955	−	0.629404i
$137$	−2.92830	−	0.516339i	−0.250182	−	0.0441138i	0.0471508	−	0.998888i	$-0.484986\pi$
$137$	−2.92830	−	0.516339i	−0.250182	−	0.0441138i	−0.297332	+	0.954774i	$0.596097\pi$
$138$	−1.71783	−	0.675153i	−0.146232	−	0.0574729i
$139$	−2.17764	−	5.98302i	−0.184705	−	0.507473i	0.812435	−	0.583052i	$-0.198142\pi$
$139$	−2.17764	−	5.98302i	−0.184705	−	0.507473i	−0.997140	+	0.0755791i	$0.975919\pi$
$140$	2.83266	+	7.47613i	0.239403	+	0.631848i
$141$	−6.30333	+	3.63923i	−0.530836	+	0.306478i
$142$	−2.03099	−	6.05457i	−0.170437	−	0.508089i
$143$	5.39425	−	6.42861i	0.451090	−	0.537588i
$144$	8.77230	+	0.894863i	0.731025	+	0.0745719i
$145$	0.236414	−	2.12904i	0.0196331	−	0.176807i
$146$	−3.35506	+	16.5555i	−0.277666	+	1.37014i
$147$	3.34152	−	0.589200i	0.275604	−	0.0485964i
$148$	2.47602	−	0.761142i	0.203528	−	0.0625655i
$149$	−12.0063	−	4.36994i	−0.983594	−	0.357999i	−0.200358	−	0.979723i	$-0.564210\pi$
$149$	−12.0063	−	4.36994i	−0.983594	−	0.357999i	−0.783237	+	0.621724i	$0.786433\pi$
$150$	−5.22073	−	3.53852i	−0.426271	−	0.288919i
$151$	2.20757			0.179650			0.0898249	−	0.995958i	$-0.471369\pi$
$151$	2.20757			0.179650			0.0898249	+	0.995958i	$0.471369\pi$
$152$	−2.99987	+	11.9583i	−0.243322	+	0.969946i
$153$		−	13.8651i		−	1.12093i
$154$	−1.23785	−	8.23950i	−0.0997487	−	0.663957i
$155$	0.686433	+	10.7204i	0.0551356	+	0.861080i
$156$	1.33471	+	4.34187i	0.106863	+	0.347628i
$157$	−6.21632	+	1.09610i	−0.496116	+	0.0874786i	−0.416107	−	0.909316i	$-0.636606\pi$
$157$	−6.21632	+	1.09610i	−0.496116	+	0.0874786i	−0.0800087	+	0.996794i	$0.525495\pi$
$158$	−7.28878	−	1.47711i	−0.579864	−	0.117513i
$159$	0.869055	+	0.501749i	0.0689206	+	0.0397913i
$160$	2.97800	−	12.2936i	0.235431	−	0.971891i
$161$	2.00387	+	1.68145i	0.157927	+	0.132517i
$162$	1.11226	+	3.31577i	0.0873876	+	0.260511i
$163$	−2.12976	−	3.68885i	−0.166816	−	0.288933i	0.770483	−	0.637461i	$-0.220015\pi$
$163$	−2.12976	−	3.68885i	−0.166816	−	0.288933i	−0.937299	+	0.348528i	$0.886682\pi$
$164$	−1.00705	+	19.7954i	−0.0786374	+	1.54576i
$165$	4.53810	+	4.75488i	0.353290	+	0.370167i
$166$	−7.09666	+	18.0564i	−0.550808	+	1.40145i
$167$	15.0401	+	2.65198i	1.16384	+	0.205216i	0.722010	−	0.691882i	$-0.243218\pi$
$167$	15.0401	+	2.65198i	1.16384	+	0.205216i	0.441830	+	0.897099i	$0.354329\pi$
$168$	4.10813	+	1.86080i	0.316949	+	0.143564i
$169$	−4.99152	+	4.18839i	−0.383963	+	0.322184i
$170$	−19.7057	−	2.69671i	−1.51136	−	0.206828i
$171$	−9.45458	+	1.71576i	−0.723010	+	0.131208i
$172$	−0.735525	−	1.43810i	−0.0560832	−	0.109654i
$173$	15.7790	−	13.2401i	1.19965	−	1.00663i	0.200015	−	0.979793i	$-0.435901\pi$
$173$	15.7790	−	13.2401i	1.19965	−	1.00663i	0.999640	−	0.0268368i	$-0.00854344\pi$
$174$	−0.752964	−	0.945120i	−0.0570821	−	0.0716494i
$175$	5.41998	+	7.10770i	0.409712	+	0.537291i
$176$	−5.74257	+	11.8661i	−0.432862	+	0.894439i
$177$	−3.56611	−	9.79780i	−0.268045	−	0.736448i
$178$	−7.46323	−	13.7205i	−0.559393	−	1.02840i
$179$	6.59509	+	11.4230i	0.492940	+	0.853797i	0.999967	−	0.00813287i	$-0.00258880\pi$
$179$	6.59509	+	11.4230i	0.492940	+	0.853797i	−0.507027	+	0.861930i	$0.669255\pi$
$180$	9.68557	−	1.83911i	0.721920	−	0.137079i
$181$	−3.85090	+	4.58933i	−0.286236	+	0.341122i	−0.889933	−	0.456091i	$-0.849249\pi$
$181$	−3.85090	+	4.58933i	−0.286236	+	0.341122i	0.603697	+	0.797213i	$0.293693\pi$
$182$	0.163593	−	6.43559i	0.0121263	−	0.477038i
$183$	3.43473	+	1.98304i	0.253902	+	0.146591i
$184$	−1.11519	−	3.98568i	−0.0822128	−	0.293828i
$185$	2.41046	−	1.60537i	0.177220	−	0.118029i
$186$	4.54161	+	4.01188i	0.333007	+	0.294166i
$187$	19.4782	+	7.08948i	1.42439	+	0.518434i
$188$	−15.0330	−	6.35398i	−1.09639	−	0.463412i
$189$			8.29848i			0.603626i
$190$	0.599643	+	13.7710i	0.0435027	+	0.999053i
$191$		−	25.7389i		−	1.86240i	−0.364507	−	0.931201i	$-0.618762\pi$
$191$		−	25.7389i		−	1.86240i	0.364507	−	0.931201i	$-0.381238\pi$
$192$	−3.70308	−	6.09934i	−0.267247	−	0.440182i
$193$	0.498074	+	0.181284i	0.0358522	+	0.0130491i	0.359884	−	0.932997i	$-0.382816\pi$
$193$	0.498074	+	0.181284i	0.0358522	+	0.0130491i	−0.324032	+	0.946046i	$0.605038\pi$
$194$	−3.03723	+	3.43826i	−0.218060	+	0.246853i
$195$	2.81513	+	4.22690i	0.201595	+	0.302695i
$196$	5.57234	+	5.18036i	0.398024	+	0.370026i
$197$	−7.79349	−	4.49957i	−0.555263	−	0.320581i	0.195979	−	0.980608i	$-0.437212\pi$
$197$	−7.79349	−	4.49957i	−0.555263	−	0.320581i	−0.751242	+	0.660027i	$0.770545\pi$
$198$	−10.2711	−	0.261092i	−0.729936	−	0.0185550i
$199$	10.6747	−	12.7217i	0.756712	−	0.901815i	−0.240923	−	0.970544i	$-0.577450\pi$
$199$	10.6747	−	12.7217i	0.756712	−	0.901815i	0.997635	+	0.0687296i	$0.0218946\pi$
$200$	−0.730021	−	14.1233i	−0.0516202	−	0.998667i
$201$	−6.01761	−	10.4228i	−0.424449	−	0.735168i
$202$	12.0474	−	6.55316i	0.847654	−	0.461079i
$203$	0.585738	+	1.60930i	0.0411107	+	0.112951i
$204$	−8.95015	+	6.76593i	−0.626636	+	0.473710i
$205$	5.23481	+	21.5333i	0.365615	+	1.50395i
$206$	−4.52075	+	3.60162i	−0.314976	+	0.250937i
$207$	2.47104	−	2.07345i	0.171749	−	0.144115i
$208$	−5.96163	+	8.25853i	−0.413365	+	0.572626i
$209$	2.42393	−	14.1594i	0.167667	−	0.979428i
$210$	4.99568	+	0.683652i	0.344734	+	0.0471765i
$211$	4.74414	−	3.98080i	0.326600	−	0.274050i	−0.464713	−	0.885461i	$-0.653842\pi$
$211$	4.74414	−	3.98080i	0.326600	−	0.274050i	0.791313	+	0.611412i	$0.209398\pi$
$212$	0.277645	+	2.23297i	0.0190687	+	0.153361i
$213$	−3.96649	−	0.699400i	−0.271780	−	0.0479221i
$214$	15.4012	+	6.05307i	1.05280	+	0.413779i
$215$	−1.24686	−	1.30643i	−0.0850354	−	0.0890975i
$216$	7.41184	−	10.8375i	0.504312	−	0.737399i
$217$	−4.29412	−	7.43763i	−0.291504	−	0.504899i
$218$	21.2831	−	7.13935i	1.44148	−	0.483538i
$219$	8.16117	+	6.84804i	0.551481	+	0.462747i
$220$	−2.36876	+	14.5470i	−0.159702	+	0.980758i
$221$	13.8699	+	8.00782i	0.932994	+	0.538664i
$222$	0.324487	−	1.60118i	0.0217781	−	0.107464i
$223$	−22.2404	+	3.92158i	−1.48933	+	0.262608i	−0.858298	−	0.513152i	$-0.828478\pi$
$223$	−22.2404	+	3.92158i	−1.48933	+	0.262608i	−0.631028	+	0.775760i	$0.717367\pi$
$224$	2.22655	+	9.86452i	0.148768	+	0.659101i
$225$	9.79217	−	5.06005i	0.652811	−	0.337336i
$226$	11.9903	−	1.80135i	0.797586	−	0.119824i
$227$		−	8.05762i		−	0.534803i	−0.963585	−	0.267402i	$-0.913835\pi$
$227$		−	8.05762i		−	0.534803i	0.963585	−	0.267402i	$-0.0861650\pi$
$228$	5.72122	+	5.26583i	0.378897	+	0.348738i
$229$	−28.3035			−1.87035			−0.935174	−	0.354187i	$-0.884757\pi$
$229$	−28.3035			−1.87035			−0.935174	+	0.354187i	$0.884757\pi$
$230$	−2.46628	−	3.91524i	−0.162622	−	0.258163i
$231$	−4.93799	−	1.79728i	−0.324896	−	0.118252i
$232$	0.672405	−	2.62484i	0.0441456	−	0.172329i
$233$	10.2573	−	1.80863i	0.671977	−	0.118488i	0.172759	−	0.984964i	$-0.444732\pi$
$233$	10.2573	−	1.80863i	0.671977	−	0.118488i	0.499218	+	0.866477i	$0.333621\pi$
$234$	−7.78035	−	1.57673i	−0.508617	−	0.103074i
$235$	−18.1356	−	2.01382i	−1.18303	−	0.131367i
$236$	12.7035	−	19.6274i	0.826929	−	1.27764i
$237$	−3.01494	+	3.59307i	−0.195842	+	0.233395i
$238$	15.0756	−	5.05704i	0.977203	−	0.327799i
$239$	−14.7145	+	8.49543i	−0.951803	+	0.549524i	−0.893640	−	0.448784i	$-0.851857\pi$
$239$	−14.7145	+	8.49543i	−0.951803	+	0.549524i	−0.0581622	+	0.998307i	$0.518524\pi$
$240$	−5.91356	−	5.35474i	−0.381719	−	0.345647i
$241$	−6.05899	−	16.6469i	−0.390294	−	1.07232i	−0.966868	−	0.255278i	$-0.917833\pi$
$241$	−6.05899	−	16.6469i	−0.390294	−	1.07232i	0.576574	−	0.817045i	$-0.304389\pi$
$242$	−0.0717515	+	0.182561i	−0.00461236	+	0.0117355i
$243$	15.8867	+	2.80126i	1.01913	+	0.179701i
$244$	1.09732	+	8.82527i	0.0702488	+	0.564980i
$245$	7.62348	+	3.77377i	0.487046	+	0.241097i
$246$	10.6638	+	6.52355i	0.679898	+	0.415926i
$247$	3.74415	−	10.4488i	0.238235	−	0.664843i
$248$	−1.03500	+	13.5486i	−0.0657227	+	0.860337i
$249$	7.86516	+	9.37334i	0.498434	+	0.594011i
$250$	−5.28703	−	14.9013i	−0.334381	−	0.942438i
$251$	26.1900	+	4.61800i	1.65310	+	0.291486i	0.920956	−	0.389667i	$-0.127410\pi$
$251$	26.1900	+	4.61800i	1.65310	+	0.291486i	0.732142	+	0.681152i	$0.238521\pi$
$252$	−6.28738	+	4.75299i	−0.396068	+	0.299410i
$253$	1.64937	+	4.53160i	0.103695	+	0.284899i
$254$	−10.8452	−	19.9380i	−0.680491	−	1.25102i
$255$	−7.43266	+	10.1049i	−0.465451	+	0.632794i
$256$	5.90276	−	14.8714i	0.368923	−	0.929460i
$257$	9.93001	+	8.33227i	0.619417	+	0.519753i	0.897620	−	0.440770i	$-0.145294\pi$
$257$	9.93001	+	8.33227i	0.619417	+	0.519753i	−0.278203	+	0.960522i	$0.589739\pi$
$258$	−1.01842	−	0.0258882i	−0.0634038	−	0.00161173i
$259$	−1.15769	+	2.00518i	−0.0719355	+	0.124596i
$260$	−3.75417	+	10.7511i	−0.232824	+	0.666757i
$261$	2.07976	−	0.366718i	0.128734	−	0.0226993i
$262$	14.2503	+	12.5882i	0.880388	+	0.777701i
$263$	−8.38174	−	3.05070i	−0.516840	−	0.188114i	0.0704128	−	0.997518i	$-0.477568\pi$
$263$	−8.38174	−	3.05070i	−0.516840	−	0.188114i	−0.587253	+	0.809404i	$0.699791\pi$
$264$	4.84358	+	6.75757i	0.298102	+	0.415900i
$265$	1.00975	+	2.30423i	0.0620282	+	0.141548i
$266$	−5.31393	−	9.65419i	−0.325818	−	0.591936i
$267$	−9.85075			−0.602856
$268$	10.5066	−	24.8576i	0.641790	−	1.51842i
$269$	7.20640	−	19.7994i	0.439382	−	1.20719i	−0.500513	−	0.865729i	$-0.666855\pi$
$269$	7.20640	−	19.7994i	0.439382	−	1.20719i	0.939895	−	0.341463i	$-0.110922\pi$
$270$	4.48557	−	13.9772i	0.272983	−	0.850628i
$271$	−16.4732	+	2.90467i	−1.00068	+	0.176446i	−0.649905	−	0.760015i	$-0.725191\pi$
$271$	−16.4732	+	2.90467i	−1.00068	+	0.176446i	−0.350770	+	0.936461i	$0.614080\pi$
$272$	−24.2048	−	6.86051i	−1.46763	−	0.415979i
$273$	−3.51622	−	2.03009i	−0.212811	−	0.122867i
$274$	−4.20377	−	0.106860i	−0.253959	−	0.00645566i
$275$	2.10161	+	16.3437i	0.126732	+	0.985561i
$276$	−2.54427	−	0.583291i	−0.153147	−	0.0351100i
$277$	24.5849	−	14.1941i	1.47716	−	0.852839i	0.477494	−	0.878635i	$-0.341545\pi$
$277$	24.5849	−	14.1941i	1.47716	−	0.852839i	0.999667	+	0.0257959i	$0.00821200\pi$
$278$	−4.30253	−	7.90984i	−0.258049	−	0.474400i
$279$	−9.95177	+	3.62215i	−0.595797	+	0.216852i
$280$	5.53230	+	9.86035i	0.330618	+	0.589269i
$281$	−6.43302	−	1.13432i	−0.383762	−	0.0676676i	−0.0215608	−	0.999768i	$-0.506864\pi$
$281$	−6.43302	−	1.13432i	−0.383762	−	0.0676676i	−0.362201	+	0.932100i	$0.617975\pi$
$282$	−8.05071	+	6.41389i	−0.479413	+	0.381942i
$283$	−8.13980	+	6.83010i	−0.483861	+	0.406007i	−0.851820	−	0.523835i	$-0.824501\pi$
$283$	−8.13980	+	6.83010i	−0.483861	+	0.406007i	0.367959	+	0.929842i	$0.380057\pi$
$284$	−4.11247	−	8.04072i	−0.244030	−	0.477129i
$285$	7.81029	+	3.81786i	0.462641	+	0.226151i
$286$	6.19328	−	10.1239i	0.366216	−	0.598638i
$287$	−11.3882	−	13.5719i	−0.672222	−	0.801123i
$288$	12.4562	−	0.591617i	0.733991	−	0.0348614i
$289$	−3.91730	+	22.2161i	−0.230429	+	1.30683i
$290$	−0.116692	−	3.02718i	−0.00685237	−	0.177762i
$291$	0.989595	+	2.71889i	0.0580111	+	0.159384i
$292$	−1.21373	+	23.8581i	−0.0710283	+	1.39619i
$293$	−2.15923	−	3.73989i	−0.126143	−	0.218487i	0.796036	−	0.605249i	$-0.206927\pi$
$293$	−2.15923	−	3.73989i	−0.126143	−	0.218487i	−0.922179	+	0.386763i	$0.873593\pi$
$294$	4.54939	−	1.52608i	0.265326	−	0.0890026i
$295$	7.35236	−	25.0841i	0.428071	−	1.46045i
$296$	3.30284	−	1.58469i	0.191974	−	0.0921085i
$297$	−7.64924	+	13.2489i	−0.443854	+	0.768777i
$298$	−17.7092	−	3.58886i	−1.02587	−	0.207897i
$299$	0.647020	+	3.66943i	0.0374181	+	0.212209i
$300$	−8.04475	−	3.85180i	−0.464464	−	0.222383i
$301$	1.35674	+	0.493811i	0.0782010	+	0.0284628i
$302$	3.08733	−	0.463821i	0.177656	−	0.0266899i
$303$		−	8.64955i		−	0.496904i
$304$	−1.68289	+	17.3542i	−0.0965204	+	0.995331i
$305$	3.99077	+	9.10690i	0.228511	+	0.521460i
$306$	−2.91312	−	19.3906i	−0.166532	−	1.10849i
$307$	4.53486	−	12.4594i	0.258818	−	0.711098i	−0.740423	−	0.672142i	$-0.765375\pi$
$307$	4.53486	−	12.4594i	0.258818	−	0.711098i	0.999241	−	0.0389560i	$-0.0124032\pi$
$308$	−3.46231	−	11.2630i	−0.197283	−	0.641770i
$309$	0.633021	+	3.59004i	0.0360113	+	0.204230i
$310$	3.21239	+	14.8484i	0.182451	+	0.843333i
$311$	3.17743	+	1.83449i	0.180176	+	0.104024i	0.587375	−	0.809315i	$-0.300161\pi$
$311$	3.17743	+	1.83449i	0.180176	+	0.104024i	−0.407200	+	0.913339i	$0.633495\pi$
$312$	2.77887	+	5.79176i	0.157323	+	0.327894i
$313$	−5.61195	+	6.68806i	−0.317206	+	0.378032i	−0.900962	−	0.433897i	$-0.857138\pi$
$313$	−5.61195	+	6.68806i	−0.317206	+	0.378032i	0.583756	+	0.811929i	$0.301582\pi$
$314$	−8.46334	+	2.83900i	−0.477614	+	0.160214i
$315$	−5.22136	+	7.09859i	−0.294190	+	0.399960i
$316$	−10.5039	−	0.534363i	−0.590888	−	0.0300602i
$317$	−18.5391	+	6.74768i	−1.04126	+	0.378988i	−0.805358	−	0.592789i	$-0.798027\pi$
$317$	−18.5391	+	6.74768i	−1.04126	+	0.378988i	−0.235902	+	0.971777i	$0.575804\pi$
$318$	1.32081	+	0.519114i	0.0740674	+	0.0291104i
$319$	−0.548241	+	3.10923i	−0.0306956	+	0.174083i
$320$	1.58186	−	17.8185i	0.0884284	−	0.996083i
$321$	7.99495	−	6.70856i	0.446235	−	0.374435i
$322$	3.15573	+	1.93052i	0.175862	+	0.107583i
$323$	27.4153	−	0.136736i	1.52543	−	0.00760818i
$324$	2.25218	+	4.40347i	0.125121	+	0.244637i
$325$	−0.593675	+	12.7180i	−0.0329312	+	0.705469i
$326$	−3.75355	−	4.71146i	−0.207890	−	0.260943i
$327$	2.45854	−	13.9431i	0.135958	−	0.771054i
$328$	2.75072	+	27.8958i	0.151883	+	1.54029i
$329$	13.7083	−	4.98942i	0.755765	−	0.275076i
$330$	7.34564	+	5.69631i	0.404364	+	0.313572i
$331$	13.1913	+	22.8480i	0.725059	+	1.25584i	0.958950	+	0.283577i	$0.0915211\pi$
$331$	13.1913	+	22.8480i	0.725059	+	1.25584i	−0.233890	+	0.972263i	$0.575146\pi$
$332$	−6.13108	+	26.7433i	−0.336487	+	1.46773i
$333$	2.18719	+	1.83527i	0.119857	+	0.100572i
$334$	21.5911	+	0.548847i	1.18141	+	0.0300316i
$335$	3.32993	−	29.9879i	0.181933	−	1.63841i
$336$	6.13626	+	1.73923i	0.334761	+	0.0948829i
$337$	1.41000	+	7.99650i	0.0768075	+	0.435597i	0.998826	+	0.0484502i	$0.0154282\pi$
$337$	1.41000	+	7.99650i	0.0768075	+	0.435597i	−0.922018	+	0.387147i	$0.873461\pi$
$338$	−6.10074	+	6.90628i	−0.331837	+	0.375652i
$339$	2.61545	−	7.18590i	0.142052	−	0.390284i
$340$	−28.1254	+	0.368867i	−1.52532	+	0.0200046i
$341$		−	15.8327i		−	0.857386i
$342$	−12.8619	+	4.38598i	−0.695493	+	0.237166i
$343$	−19.3145			−1.04288
$344$	−1.33080	−	1.85668i	−0.0717518	−	0.100105i
$345$	−2.91242	+	0.186484i	−0.156799	+	0.0100400i
$346$	19.2854	−	21.8318i	1.03679	−	1.17369i
$347$	6.32575	+	35.8751i	0.339584	+	1.92588i	0.376182	+	0.926546i	$0.377237\pi$
$347$	6.32575	+	35.8751i	0.339584	+	1.92588i	−0.0365977	+	0.999330i	$0.511652\pi$
$348$	−1.25161	−	1.16357i	−0.0670933	−	0.0623738i
$349$	−2.66537	+	4.61655i	−0.142674	+	0.247118i	−0.928503	−	0.371326i	$-0.878903\pi$
$349$	−2.66537	+	4.61655i	−0.142674	+	0.247118i	0.785829	+	0.618444i	$0.212237\pi$
$350$	9.07331	+	8.80149i	0.484989	+	0.470459i
$351$	−7.59797	+	9.05490i	−0.405549	+	0.483315i
$352$	−5.53798	+	17.8015i	−0.295175	+	0.948821i
$353$	−7.66870	+	4.42752i	−0.408163	+	0.235653i	−0.690000	−	0.723809i	$-0.742390\pi$
$353$	−7.66870	+	4.42752i	−0.408163	+	0.235653i	0.281837	+	0.959462i	$0.409056\pi$
$354$	−7.04583	−	12.9532i	−0.374482	−	0.688453i
$355$	−6.97147	−	7.30449i	−0.370007	−	0.387682i
$356$	−13.3202	−	17.6203i	−0.705970	−	0.933876i
$357$	1.74147	−	9.87635i	0.0921682	−	0.522712i
$358$	11.6234	+	14.5897i	0.614315	+	0.771088i
$359$	−4.62892	−	5.51654i	−0.244305	−	0.291152i	0.629932	−	0.776650i	$-0.283083\pi$
$359$	−4.62892	−	5.51654i	−0.244305	−	0.291152i	−0.874238	+	0.485498i	$0.838638\pi$
$360$	13.1591	−	4.60701i	0.693543	−	0.242811i
$361$	−3.48579	−	18.6775i	−0.183463	−	0.983027i
$362$	−4.42133	+	7.22736i	−0.232380	+	0.379862i
$363$	0.0795215	+	0.0947701i	0.00417380	+	0.00497414i
$364$	−1.12336	−	9.03467i	−0.0588800	−	0.473545i
$365$	6.30918	+	25.9527i	0.330237	+	1.35843i
$366$	5.22017	+	2.05167i	0.272863	+	0.107242i
$367$	−28.9341	+	10.5311i	−1.51035	+	0.549722i	−0.958716	−	0.284366i	$-0.908217\pi$
$367$	−28.9341	+	10.5311i	−1.51035	+	0.549722i	−0.551632	+	0.834088i	$0.685995\pi$
$368$	−2.39702	−	5.33975i	−0.124953	−	0.278353i
$369$	−18.9203	+	10.9236i	−0.984949	+	0.568661i
$370$	3.03378	−	2.75159i	0.157719	−	0.143048i
$371$	−1.54074	−	1.29284i	−0.0799914	−	0.0671207i
$372$	7.19444	+	4.65649i	0.373015	+	0.241428i
$373$	−15.3722	+	26.6254i	−0.795941	+	1.37861i	0.126300	+	0.991992i	$0.459690\pi$
$373$	−15.3722	+	26.6254i	−0.795941	+	1.37861i	−0.922240	+	0.386617i	$0.873643\pi$
$374$	28.7301	+	5.82232i	1.48560	+	0.301065i
$375$	−9.84909	−	1.56152i	−0.508605	−	0.0806363i
$376$	−22.3589	−	5.72767i	−1.15307	−	0.295382i
$377$	−0.834324	+	2.29229i	−0.0429698	+	0.118059i
$378$	1.74355	+	11.6056i	0.0896784	+	0.596927i
$379$	−25.8758			−1.32915			−0.664576	−	0.747221i	$-0.731388\pi$
$379$	−25.8758			−1.32915			−0.664576	+	0.747221i	$0.731388\pi$
$380$	3.73196	+	19.1330i	0.191446	+	0.981503i
$381$	−14.3147			−0.733363
$382$	−5.40786	−	35.9963i	−0.276690	−	1.84173i
$383$	−8.13760	+	22.3579i	−0.415812	+	1.14243i	0.538240	+	0.842792i	$0.319090\pi$
$383$	−8.13760	+	22.3579i	−0.415812	+	1.14243i	−0.954052	+	0.299642i	$0.903133\pi$
$384$	−6.46033	−	7.75201i	−0.329677	−	0.395593i
$385$	−7.30257	−	10.9648i	−0.372173	−	0.558817i
$386$	0.734655	+	0.148882i	0.0373930	+	0.00757788i
$387$	0.890204	−	1.54188i	0.0452516	−	0.0783781i
$388$	−3.52523	+	5.44661i	−0.178966	+	0.276510i
$389$	14.4649	+	12.1375i	0.733399	+	0.615395i	0.931056	−	0.364876i	$-0.118889\pi$
$389$	14.4649	+	12.1375i	0.733399	+	0.615395i	−0.197657	+	0.980271i	$0.563333\pi$
$390$	4.82510	+	5.31993i	0.244328	+	0.269385i
$391$	−7.97035	+	4.60168i	−0.403078	+	0.232717i
$392$	8.88144	+	6.07406i	0.448580	+	0.306787i
$393$	11.2688	−	4.10151i	0.568436	−	0.206894i
$394$	−11.8447	−	4.65529i	−0.596729	−	0.234530i
$395$	−11.4261	+	2.77770i	−0.574908	+	0.139761i
$396$	−14.4192	+	1.79286i	−0.724592	+	0.0900947i
$397$	−16.5462	−	19.7190i	−0.830432	−	0.989670i	−0.999991	−	0.00414989i	$-0.998679\pi$
$397$	−16.5462	−	19.7190i	−0.830432	−	0.989670i	0.169560	−	0.985520i	$-0.445765\pi$
$398$	12.2560	−	20.0343i	0.614335	−	1.00423i
$399$	−6.95016	+	0.0346644i	−0.347943	+	0.00173539i
$400$	−3.98831	−	19.5983i	−0.199416	−	0.979915i
$401$	16.9222	+	20.1671i	0.845054	+	1.00710i	0.999817	+	0.0191450i	$0.00609441\pi$
$401$	16.9222	+	20.1671i	0.845054	+	1.00710i	−0.154762	+	0.987952i	$0.549461\pi$
$402$	−10.6056	−	13.3122i	−0.528960	−	0.663950i
$403$	2.12425	−	12.0472i	0.105816	−	0.600115i
$404$	15.4717	−	11.6959i	0.769746	−	0.581895i
$405$	3.81790	+	4.00028i	0.189713	+	0.198775i
$406$	1.15729	+	2.12757i	0.0574352	+	0.105590i
$407$	−3.69661	+	2.13424i	−0.183234	+	0.105790i
$408$	−11.0954	+	11.3428i	−0.549305	+	0.561550i
$409$	4.69140	−	5.59100i	0.231975	−	0.276457i	−0.637483	−	0.770465i	$-0.720024\pi$
$409$	4.69140	−	5.59100i	0.231975	−	0.276457i	0.869457	+	0.494008i	$0.164469\pi$
$410$	11.8452	+	29.0149i	0.584994	+	1.43295i
$411$	−1.32607	+	2.29682i	−0.0654102	+	0.113294i
$412$	−5.56564	+	5.98676i	−0.274199	+	0.294947i
$413$	3.62888	+	20.5804i	0.178565	+	1.01269i
$414$	3.02016	−	3.41894i	0.148433	−	0.168032i
$415$	1.96017	+	30.6129i	0.0962209	+	1.50273i
$416$	−6.60230	+	12.8023i	−0.323705	+	0.627684i
$417$	−5.67893			−0.278098
$418$	0.414962	−	20.3115i	0.0202965	−	0.993468i
$419$			31.1957i			1.52401i	0.647570	+	0.762006i	$0.275785\pi$
$419$			31.1957i			1.52401i	−0.647570	+	0.762006i	$0.724215\pi$
$420$	7.13019	−	0.0935128i	0.347918	−	0.00456296i
$421$	−5.19107	+	14.2623i	−0.252997	+	0.695104i	0.746559	+	0.665319i	$0.231704\pi$
$421$	−5.19107	+	14.2623i	−0.252997	+	0.695104i	−0.999556	+	0.0297849i	$0.990518\pi$
$422$	5.79838	−	6.56400i	0.282261	−	0.319530i
$423$	−3.12377	−	17.7158i	−0.151883	−	0.861371i
$424$	0.857449	+	3.06452i	0.0416414	+	0.148826i
$425$	−30.0208	+	9.36617i	−1.45622	+	0.454326i
$426$	−5.69417	−	0.144746i	−0.275883	−	0.00701297i
$427$	−6.08940	−	5.10962i	−0.294687	−	0.247272i
$428$	22.8106	+	5.22948i	1.10259	+	0.252776i
$429$	−3.74253	−	6.48225i	−0.180691	−	0.312966i
$430$	−2.01825	−	1.56509i	−0.0973286	−	0.0754753i
$431$	3.86348	−	1.40619i	0.186097	−	0.0677338i	−0.247291	−	0.968941i	$-0.579540\pi$
$431$	3.86348	−	1.40619i	0.186097	−	0.0677338i	0.433388	+	0.901208i	$0.357318\pi$
$432$	8.08859	−	16.7137i	0.389162	−	0.804140i
$433$	0.182834	−	1.03690i	0.00878643	−	0.0498303i	−0.980099	−	0.198508i	$-0.936391\pi$
$433$	0.182834	−	1.03690i	0.00878643	−	0.0498303i	0.988886	+	0.148677i	$0.0475016\pi$
$434$	−7.56809	−	9.49946i	−0.363280	−	0.455989i
$435$	−1.71232	−	0.847632i	−0.0820995	−	0.0406408i
$436$	28.2649	−	14.4562i	1.35364	−	0.692327i
$437$	4.12418	+	4.86552i	0.197286	+	0.232749i
$438$	12.8524	+	7.86241i	0.614109	+	0.375681i
$439$	7.95540	−	6.67537i	0.379690	−	0.318598i	−0.432890	−	0.901447i	$-0.642506\pi$
$439$	7.95540	−	6.67537i	0.379690	−	0.318598i	0.812581	+	0.582848i	$0.198062\pi$
$440$	−0.256375	+	20.8419i	−0.0122222	+	0.993600i
$441$	−1.45624	+	8.25874i	−0.0693447	+	0.393273i
$442$	21.0799	+	8.28495i	1.00267	+	0.394075i
$443$	7.69787	−	2.80180i	0.365737	−	0.133117i	−0.152613	−	0.988286i	$-0.548769\pi$
$443$	7.69787	−	2.80180i	0.365737	−	0.133117i	0.518350	+	0.855169i	$0.326547\pi$
$444$	0.117387	−	2.30745i	0.00557094	−	0.109507i
$445$	−19.8937	−	14.6328i	−0.943054	−	0.693663i
$446$	−30.2796	+	10.1572i	−1.43378	+	0.480958i
$447$	−7.32526	+	8.72990i	−0.346473	+	0.412910i
$448$	5.18645	+	13.3279i	0.245037	+	0.629685i
$449$	−0.594207	−	0.343065i	−0.0280423	−	0.0161903i	0.485913	−	0.874007i	$-0.338487\pi$
$449$	−0.594207	−	0.343065i	−0.0280423	−	0.0161903i	−0.513956	+	0.857817i	$0.671820\pi$
$450$	12.6314	−	9.13395i	0.595450	−	0.430579i
$451$	−5.67160	−	32.1653i	−0.267065	−	1.51460i
$452$	16.3903	−	5.03845i	0.770933	−	0.236989i
$453$	0.673440	−	1.85026i	0.0316410	−	0.0869328i
$454$	−1.69294	−	11.2687i	−0.0794537	−	0.528868i
$455$	−4.08546	−	9.32298i	−0.191529	−	0.437068i
$456$	9.10761	+	6.16230i	0.426503	+	0.288576i
$457$			2.46398i			0.115260i	0.998338	+	0.0576300i	$0.0183544\pi$
$457$			2.46398i			0.115260i	−0.998338	+	0.0576300i	$0.981646\pi$
$458$	−39.5830	+	5.94670i	−1.84959	+	0.277871i
$459$	−27.4356	−	9.98575i	−1.28059	−	0.466095i
$460$	−4.27175	−	4.95736i	−0.199171	−	0.231138i
$461$	−5.81183	−	32.9605i	−0.270684	−	1.53512i	−0.752347	−	0.658767i	$-0.771078\pi$
$461$	−5.81183	−	32.9605i	−0.270684	−	1.53512i	0.481663	−	0.876357i	$-0.340033\pi$
$462$	−7.28349	−	1.47604i	−0.338858	−	0.0686715i
$463$	−3.44837	+	5.97275i	−0.160259	+	0.277577i	−0.934962	−	0.354749i	$-0.884566\pi$
$463$	−3.44837	+	5.97275i	−0.160259	+	0.277577i	0.774702	+	0.632326i	$0.217900\pi$
$464$	0.388880	−	3.81217i	0.0180533	−	0.176976i
$465$	9.19459	+	2.69501i	0.426389	+	0.124978i
$466$	13.9650	−	4.68451i	0.646916	−	0.217006i
$467$	−14.9505	−	25.8951i	−0.691828	−	1.19828i	−0.971238	−	0.238109i	$-0.923472\pi$
$467$	−14.9505	−	25.8951i	−0.691828	−	1.19828i	0.279411	−	0.960172i	$-0.409861\pi$
$468$	−11.2122	−	0.570401i	−0.518286	−	0.0263668i
$469$	8.25021	+	22.6673i	0.380959	+	1.04668i
$470$	−25.7861	+	0.994001i	−1.18942	+	0.0458498i
$471$	−0.977651	+	5.54453i	−0.0450478	+	0.255479i
$472$	13.6423	−	30.1184i	0.627939	−	1.38631i
$473$	1.71091	+	2.03898i	0.0786676	+	0.0937524i
$474$	−3.46154	+	5.65843i	−0.158994	+	0.259900i
$475$	10.1017	+	19.3120i	0.463499	+	0.886097i
$476$	20.0209	−	10.2398i	0.917658	−	0.469341i
$477$	−1.89994	+	1.59424i	−0.0869923	+	0.0729952i
$478$	−18.7936	+	14.9726i	−0.859599	+	0.684831i
$479$	32.8277	+	5.78841i	1.49994	+	0.264479i	0.862513	−	0.506034i	$-0.168889\pi$
$479$	32.8277	+	5.78841i	1.49994	+	0.264479i	0.637423	+	0.770514i	$0.280000\pi$
$480$	−9.39529	−	6.24624i	−0.428834	−	0.285101i
$481$	−3.09913	+	1.12799i	−0.141308	+	0.0514320i
$482$	−11.9712	−	22.0080i	−0.545273	−	1.00244i
$483$	2.02059	−	1.16659i	0.0919401	−	0.0530817i
$484$	−0.0619889	+	0.270391i	−0.00281768	+	0.0122905i
$485$	−2.04028	+	6.96083i	−0.0926443	+	0.316075i
$486$	22.8065	+	0.579742i	1.03452	+	0.0262976i
$487$	12.1002	+	6.98605i	0.548312	+	0.316568i	0.748441	−	0.663202i	$-0.230803\pi$
$487$	12.1002	+	6.98605i	0.548312	+	0.316568i	−0.200129	+	0.979770i	$0.564136\pi$
$488$	3.38885	+	12.1118i	0.153406	+	0.548273i
$489$	−3.74148	+	0.659724i	−0.169196	+	0.0298338i
$490$	11.4545	+	3.67597i	0.517460	+	0.166063i
$491$	4.20166	−	11.5440i	0.189618	−	0.520972i	−0.808058	−	0.589103i	$-0.799481\pi$
$491$	4.20166	−	11.5440i	0.189618	−	0.520972i	0.997676	+	0.0681306i	$0.0217035\pi$
$492$	16.2841	+	6.88280i	0.734145	+	0.310301i
$493$	−6.02535			−0.271368
$494$	3.04092	−	15.3995i	0.136817	−	0.692858i
$495$	−14.8793	+	6.52033i	−0.668776	+	0.293067i
$496$	1.39915	+	19.1654i	0.0628237	+	0.860553i
$497$	7.58578	+	2.76100i	0.340269	+	0.123848i
$498$	12.9690	+	11.4563i	0.581153	+	0.513368i
$499$	−13.9432	+	2.45856i	−0.624183	+	0.110060i	−0.476790	−	0.879017i	$-0.658200\pi$
$499$	−13.9432	+	2.45856i	−0.624183	+	0.110060i	−0.147394	+	0.989078i	$0.547089\pi$
$500$	−10.5248	−	19.7289i	−0.470685	−	0.882301i
$501$	6.81086	−	11.7968i	0.304287	−	0.527040i
$502$	37.5975	+	0.955730i	1.67806	+	0.0426563i
$503$	−2.43324	−	2.04173i	−0.108493	−	0.0910363i	0.586927	−	0.809640i	$-0.300337\pi$
$503$	−2.43324	−	2.04173i	−0.108493	−	0.0910363i	−0.695420	+	0.718603i	$0.744782\pi$
$504$	−7.79440	+	7.96815i	−0.347190	+	0.354930i
$505$	12.8485	−	17.4679i	0.571751	−	0.777311i
$506$	3.25878	+	5.99099i	0.144870	+	0.266332i
$507$	1.98776	+	5.46131i	0.0882793	+	0.242545i
$508$	−19.3563	−	25.6051i	−0.858799	−	1.13604i
$509$	29.8953	+	5.27135i	1.32509	+	0.233649i	0.791018	−	0.611793i	$-0.209551\pi$
$509$	29.8953	+	5.27135i	1.32509	+	0.233649i	0.534069	+	0.845441i	$0.320662\pi$
$510$	−8.27163	+	15.6936i	−0.366274	+	0.694922i
$511$	−13.7254	−	16.3573i	−0.607176	−	0.723605i
$512$	5.13059	−	22.0381i	0.226742	−	0.973955i
$513$	−3.41419	+	19.9440i	−0.150740	+	0.880549i
$514$	15.6380	+	9.56650i	0.689761	+	0.421960i
$515$	−4.05444	+	8.19046i	−0.178660	+	0.360915i
$516$	−1.42971	+	0.177768i	−0.0629396	+	0.00782582i
$517$	26.4850	+	4.67002i	1.16481	+	0.205387i
$518$	−1.19776	+	3.04752i	−0.0526264	+	0.133900i
$519$	−6.28361	−	17.2641i	−0.275820	−	0.757808i
$520$	−2.99142	+	15.8244i	−0.131182	+	0.693947i
$521$	−7.30862	+	4.21963i	−0.320196	+	0.184865i	−0.651480	−	0.758666i	$-0.725852\pi$
$521$	−7.30862	+	4.21963i	−0.320196	+	0.184865i	0.331284	+	0.943531i	$0.392518\pi$
$522$	2.83154	−	0.949829i	0.123933	−	0.0415729i
$523$	1.24128	−	1.47930i	0.0542773	−	0.0646852i	−0.738223	−	0.674557i	$-0.764335\pi$
$523$	1.24128	−	1.47930i	0.0542773	−	0.0646852i	0.792500	+	0.609872i	$0.208779\pi$
$524$	22.5742	+	14.6108i	0.986158	+	0.638274i
$525$	7.61067	−	2.37445i	0.332157	−	0.103630i
$526$	−12.3630	−	2.50543i	−0.539052	−	0.109242i
$527$	29.7568	−	5.24692i	1.29623	−	0.228560i
$528$	8.19364	+	8.43294i	0.356582	+	0.366997i
$529$	19.6009	+	7.13414i	0.852213	+	0.310180i
$530$	1.89628	+	3.01036i	0.0823690	+	0.130762i
$531$	25.7699			1.11832
$532$	−9.46003	−	12.3851i	−0.410144	−	0.536962i
$533$		−	25.2358i		−	1.09308i
$534$	−13.7765	+	2.06969i	−0.596166	+	0.0895641i
$535$	26.1112	−	1.67192i	1.12888	−	0.0722834i
$536$	9.47092	−	36.9713i	0.409082	−	1.59692i
$537$	11.5860	−	2.04293i	0.499974	−	0.0881588i
$538$	5.91834	−	29.2040i	0.255158	−	1.25907i
$539$	−10.8576	−	6.26862i	−0.467668	−	0.270008i
$540$	3.33648	−	20.4899i	0.143579	−	0.881744i
$541$	4.11653	+	3.45418i	0.176983	+	0.148507i	0.726976	−	0.686663i	$-0.240925\pi$
$541$	4.11653	+	3.45418i	0.176983	+	0.148507i	−0.549993	+	0.835169i	$0.685369\pi$
$542$	−22.4278	+	7.52333i	−0.963357	+	0.323155i
$543$	2.67176	+	4.62762i	0.114656	+	0.198590i
$544$	−35.2924	−	4.50900i	−1.51315	−	0.193322i
$545$	25.6768	−	24.5062i	1.09988	−	1.04973i
$546$	−5.34404	−	2.10035i	−0.228704	−	0.0898866i
$547$	17.8856	+	3.15372i	0.764734	+	0.134843i	0.542392	−	0.840126i	$-0.317519\pi$
$547$	17.8856	+	3.15372i	0.764734	+	0.134843i	0.222342	+	0.974969i	$0.428630\pi$
$548$	−5.90151	+	0.733785i	−0.252100	+	0.0313458i
$549$	−7.50905	+	6.30084i	−0.320478	+	0.268913i
$550$	6.37303	+	22.4154i	0.271747	+	0.955795i
$551$	0.745617	+	4.10867i	0.0317644	+	0.175035i
$552$	−3.68077	−	0.281181i	−0.156664	−	0.0119678i
$553$	7.20154	−	6.04281i	0.306240	−	0.256966i
$554$	31.4002	−	25.0161i	1.33406	−	1.06283i
$555$	−0.610197	−	2.51004i	−0.0259014	−	0.106545i
$556$	−7.67907	−	10.1581i	−0.325665	−	0.430798i
$557$	6.81227	+	18.7166i	0.288645	+	0.793046i	0.996257	+	0.0864442i	$0.0275504\pi$
$557$	6.81227	+	18.7166i	0.288645	+	0.793046i	−0.707612	+	0.706602i	$0.750227\pi$
$558$	−13.1567	+	7.15655i	−0.556968	+	0.302961i
$559$	1.02828	+	1.78103i	0.0434915	+	0.0753295i
$560$	9.80873	+	12.6275i	0.414494	+	0.533611i
$561$	11.8840	−	14.1628i	0.501742	−	0.597953i
$562$	−9.23503	−	0.234755i	−0.389556	−	0.00990255i
$563$	−5.69788	−	3.28967i	−0.240137	−	0.138643i	0.375103	−	0.926983i	$-0.377607\pi$
$563$	−5.69788	−	3.28967i	−0.240137	−	0.138643i	−0.615240	+	0.788340i	$0.710941\pi$
$564$	−9.91149	+	10.6614i	−0.417349	+	0.448928i
$565$	15.9563	−	10.6269i	0.671285	−	0.447077i
$566$	−9.94863	+	11.2622i	−0.418172	+	0.473387i
$567$	−4.15433	−	1.51205i	−0.174465	−	0.0635002i
$568$	−7.44075	−	10.3811i	−0.312207	−	0.435579i
$569$		−	42.1512i		−	1.76707i	−0.468365	−	0.883535i	$-0.655157\pi$
$569$		−	42.1512i		−	1.76707i	0.468365	−	0.883535i	$-0.344843\pi$
$570$	11.7250	+	3.69838i	0.491106	+	0.154908i
$571$			24.7975i			1.03774i	0.854852	+	0.518872i	$0.173648\pi$
$571$			24.7975i			1.03774i	−0.854852	+	0.518872i	$0.826352\pi$
$572$	6.53434	−	15.4597i	0.273215	−	0.646402i
$573$	−21.5729	−	7.85188i	−0.901219	−	0.328017i
$574$	−18.7781	−	16.5878i	−0.783782	−	0.692363i
$575$	−6.15868	−	3.94965i	−0.256835	−	0.164712i
$576$	17.2960	−	3.44450i	0.720667	−	0.143521i
$577$	3.50533	+	2.02380i	0.145929	+	0.0842520i	0.571187	−	0.820820i	$-0.306483\pi$
$577$	3.50533	+	2.02380i	0.145929	+	0.0842520i	−0.425258	+	0.905072i	$0.639817\pi$
$578$	−0.810714	+	31.8927i	−0.0337213	+	1.32656i
$579$	0.303884	−	0.362155i	0.0126290	−	0.0150506i
$580$	−0.799219	−	4.20905i	−0.0331858	−	0.174771i
$581$	−12.2622	−	21.2388i	−0.508723	−	0.881134i
$582$	1.95522	+	3.59450i	0.0810464	+	0.148997i
$583$	−1.26817	−	3.48427i	−0.0525222	−	0.144304i
$584$	3.31526	+	33.6210i	0.137186	+	1.39125i
$585$	−12.1967	+	2.96504i	−0.504270	+	0.122589i
$586$	−3.80549	−	4.77665i	−0.157203	−	0.197321i
$587$	−10.1779	+	8.54025i	−0.420086	+	0.352494i	−0.828196	−	0.560439i	$-0.810632\pi$
$587$	−10.1779	+	8.54025i	−0.420086	+	0.352494i	0.408110	+	0.912933i	$0.366188\pi$
$588$	6.04177	−	3.09009i	0.249158	−	0.127433i
$589$	−7.26017	−	19.6418i	−0.299150	−	0.809326i
$590$	5.01214	−	36.6254i	0.206346	−	1.50784i
$591$	−6.14876	+	5.15942i	−0.252926	+	0.212230i
$592$	4.28614	−	2.91017i	0.176159	−	0.119607i
$593$	−34.3076	−	6.04935i	−1.40884	−	0.248417i	−0.583071	−	0.812421i	$-0.698149\pi$
$593$	−34.3076	−	6.04935i	−1.40884	−	0.248417i	−0.825772	+	0.564004i	$0.809260\pi$
$594$	−7.91396	+	20.1359i	−0.324714	+	0.826188i
$595$	18.1878	−	17.3586i	0.745626	−	0.711632i
$596$	−25.5207	−	1.29831i	−1.04537	−	0.0531810i
$597$	−7.40614	−	12.8278i	−0.303113	−	0.525007i
$598$	1.67583	+	4.99583i	0.0685299	+	0.204295i
$599$	33.5173	+	28.1243i	1.36948	+	1.14913i	0.972926	+	0.231118i	$0.0742384\pi$
$599$	33.5173	+	28.1243i	1.36948	+	1.14913i	0.396554	+	0.918012i	$0.370206\pi$
$600$	−12.0600	−	3.69657i	−0.492348	−	0.150912i
$601$	33.3310	+	19.2437i	1.35960	+	0.784965i	0.989570	−	0.144054i	$-0.0460140\pi$
$601$	33.3310	+	19.2437i	1.35960	+	0.784965i	0.370030	+	0.929020i	$0.379347\pi$
$602$	2.00117	+	0.405549i	0.0815617	+	0.0165289i
$603$	29.2937	−	5.16528i	1.19293	−	0.210346i
$604$	4.22024	−	1.29733i	0.171719	−	0.0527874i
$605$	0.0198185	+	0.309515i	0.000805736	+	0.0125836i
$606$	−1.81731	−	12.0966i	−0.0738231	−	0.491389i
$607$			41.1783i			1.67138i	0.549203	+	0.835689i	$0.314931\pi$
$607$			41.1783i			1.67138i	−0.549203	+	0.835689i	$0.685069\pi$
$608$	1.29264	+	24.6238i	0.0524234	+	0.998625i
$609$	1.52751			0.0618978
$610$	7.49457	+	11.8977i	0.303446	+	0.481724i
$611$	19.5261	+	7.10692i	0.789942	+	0.287515i
$612$	−8.14811	−	26.5061i	−0.329368	−	1.07145i
$613$	13.3449	−	2.35306i	0.538995	−	0.0950393i	0.102478	−	0.994735i	$-0.467323\pi$
$613$	13.3449	−	2.35306i	0.538995	−	0.0950393i	0.436517	+	0.899696i	$0.356212\pi$
$614$	3.72431	−	18.3776i	0.150301	−	0.741658i
$615$	19.6449	+	2.18142i	0.792160	+	0.0879634i
$616$	−7.20852	−	15.0241i	−0.290439	−	0.605338i
$617$	9.84259	−	11.7299i	0.396248	−	0.472230i	−0.530624	−	0.847607i	$-0.678042\pi$
$617$	9.84259	−	11.7299i	0.396248	−	0.472230i	0.926872	+	0.375377i	$0.122487\pi$
$618$	1.63957	+	4.88774i	0.0659534	+	0.196614i
$619$	16.2788	−	9.39859i	0.654301	−	0.377761i	−0.135801	−	0.990736i	$-0.543361\pi$
$619$	16.2788	−	9.39859i	0.654301	−	0.377761i	0.790102	+	0.612975i	$0.210027\pi$
$620$	7.61230	+	20.0908i	0.305717	+	0.806868i
$621$	−2.32319	−	6.38290i	−0.0932262	−	0.256137i
$622$	4.82914	+	1.89798i	0.193631	+	0.0761020i
$623$	19.4438	+	3.42846i	0.778998	+	0.137358i
$624$	5.10318	+	7.51604i	0.204291	+	0.300882i
$625$	−17.5708	−	17.7839i	−0.702833	−	0.711355i
$626$	−6.44323	+	10.5325i	−0.257523	+	0.420963i
$627$	−11.1282	−	6.35106i	−0.444416	−	0.253637i
$628$	−11.2397	+	5.74858i	−0.448511	+	0.229393i
$629$	−5.23626	−	6.24033i	−0.208783	−	0.248818i
$630$	−5.81073	+	11.0245i	−0.231505	+	0.439228i
$631$	12.0895	+	2.13171i	0.481277	+	0.0848621i	0.409023	−	0.912524i	$-0.365870\pi$
$631$	12.0895	+	2.13171i	0.481277	+	0.0848621i	0.0722540	+	0.997386i	$0.476981\pi$
$632$	−14.8021	+	1.45959i	−0.588796	+	0.0580594i
$633$	−1.88924	−	5.19064i	−0.0750905	−	0.206310i
$634$	−24.5096	+	13.3319i	−0.973399	+	0.529478i
$635$	−28.9087	−	21.2638i	−1.14721	−	0.843827i
$636$	1.95625	+	0.448482i	0.0775702	+	0.0177835i
$637$	−7.42057	−	6.22660i	−0.294014	−	0.246707i
$638$	−0.113463	+	4.46350i	−0.00449203	+	0.176712i
$639$	4.97731	−	8.62096i	0.196899	−	0.341040i
$640$	−1.53148	−	25.2518i	−0.0605372	−	0.998166i
$641$	5.59019	−	0.985702i	0.220799	−	0.0389329i	−0.0621540	−	0.998067i	$-0.519797\pi$
$641$	5.59019	−	0.985702i	0.220799	−	0.0389329i	0.282953	+	0.959134i	$0.408686\pi$
$642$	9.77160	−	11.0618i	0.385654	−	0.436576i
$643$	−5.87814	−	2.13947i	−0.231811	−	0.0843724i	0.223503	−	0.974703i	$-0.428251\pi$
$643$	−5.87814	−	2.13947i	−0.231811	−	0.0843724i	−0.455314	+	0.890331i	$0.650473\pi$
$644$	4.81897	+	2.03683i	0.189894	+	0.0802623i
$645$	−1.47534	+	0.646513i	−0.0580914	+	0.0254564i
$646$	38.3121	−	5.95131i	1.50737	−	0.234151i
$647$	−8.20388			−0.322528			−0.161264	−	0.986911i	$-0.551557\pi$
$647$	−8.20388			−0.322528			−0.161264	+	0.986911i	$0.551557\pi$
$648$	4.07490	+	5.68515i	0.160077	+	0.223334i
$649$	−13.1766	+	36.2024i	−0.517227	+	1.42107i
$650$	1.84185	+	17.9111i	0.0722433	+	0.702533i
$651$	−7.54376	+	1.33017i	−0.295663	+	0.0521334i
$652$	−6.23931	−	5.80042i	−0.244350	−	0.227162i
$653$	−5.73574	−	3.31153i	−0.224457	−	0.129590i	0.383555	−	0.923518i	$-0.374699\pi$
$653$	−5.73574	−	3.31153i	−0.224457	−	0.129590i	−0.608012	+	0.793928i	$0.708033\pi$
$654$	0.508814	−	20.0162i	0.0198962	−	0.782696i
$655$	28.8501	+	8.45621i	1.12727	+	0.330411i
$656$	9.70796	+	38.4349i	0.379032	+	1.50063i
$657$	−22.8033	+	13.1655i	−0.889643	+	0.513636i
$658$	18.1231	−	9.85799i	0.706511	−	0.384304i
$659$	6.86844	−	2.49991i	0.267557	−	0.0973826i	−0.204758	−	0.978813i	$-0.565641\pi$
$659$	6.86844	−	2.49991i	0.267557	−	0.0973826i	0.472315	+	0.881430i	$0.343419\pi$
$660$	11.4698	+	6.42305i	0.446463	+	0.250017i
$661$	−4.37386	−	0.771229i	−0.170123	−	0.0299973i	0.0879376	−	0.996126i	$-0.471972\pi$
$661$	−4.37386	−	0.771229i	−0.170123	−	0.0299973i	−0.258061	+	0.966129i	$0.583084\pi$
$662$	23.2488	+	29.1818i	0.903589	+	1.13418i
$663$	10.9428	−	9.18213i	0.424985	−	0.356605i
$664$	−2.95554	+	38.6892i	−0.114697	+	1.50143i
$665$	−14.0874	−	10.2541i	−0.546288	−	0.397638i
$666$	3.44443	+	2.10713i	0.133469	+	0.0816495i
$667$	−0.901058	−	1.07384i	−0.0348891	−	0.0415792i
$668$	30.3109	−	3.76881i	1.17276	−	0.145820i
$669$	−3.49778	+	19.8369i	−0.135232	+	0.766939i
$670$	−1.64362	−	42.6383i	−0.0634985	−	1.64726i
$671$	−5.01213	−	13.7707i	−0.193491	−	0.531612i
$672$	8.94710	+	1.14309i	0.345142	+	0.0440958i
$673$	7.09412	+	12.2874i	0.273458	+	0.473643i	0.969745	−	0.244120i	$-0.0784992\pi$
$673$	7.09412	+	12.2874i	0.273458	+	0.473643i	−0.696287	+	0.717764i	$0.745166\pi$
$674$	3.65201	+	10.8870i	0.140670	+	0.419352i
$675$	−2.96019	−	23.0206i	−0.113938	−	0.886062i
$676$	−7.08097	+	10.9404i	−0.272345	+	0.420783i
$677$	3.33372	−	5.77417i	0.128125	−	0.221919i	−0.794825	−	0.606839i	$-0.792437\pi$
$677$	3.33372	−	5.77417i	0.128125	−	0.221919i	0.922950	+	0.384919i	$0.125771\pi$
$678$	2.14797	−	10.5991i	0.0824924	−	0.407057i
$679$	−1.00701	−	5.71106i	−0.0386456	−	0.219170i
$680$	−39.2565	+	6.42515i	−1.50542	+	0.246393i
$681$	−6.75343	−	2.45805i	−0.258792	−	0.0941926i
$682$	−3.32651	−	22.1423i	−0.127379	−	0.847871i
$683$			1.59724i			0.0611167i	0.999533	+	0.0305584i	$0.00972855\pi$
$683$			1.59724i			0.0611167i	−0.999533	+	0.0305584i	$0.990271\pi$
$684$	−17.0661	+	8.83622i	−0.652540	+	0.337861i
$685$	−6.08984	+	2.66865i	−0.232681	+	0.101964i
$686$	−27.0117	+	4.05806i	−1.03131	+	0.154937i
$687$	−8.63424	+	23.7224i	−0.329417	+	0.905065i
$688$	−2.25124	−	2.31699i	−0.0858278	−	0.0883345i
$689$	−0.497482	−	2.82136i	−0.0189526	−	0.107485i
$690$	−4.03389	+	0.872713i	−0.153567	+	0.0332236i
$691$	28.7722	+	16.6116i	1.09455	+	0.631937i	0.934783	−	0.355219i	$-0.115594\pi$
$691$	28.7722	+	16.6116i	1.09455	+	0.631937i	0.159763	+	0.987155i	$0.448927\pi$
$692$	22.3841	−	34.5842i	0.850914	−	1.31469i
$693$	8.34836	−	9.94919i	0.317128	−	0.377938i
$694$	16.3842	+	48.8429i	0.621936	+	1.85405i
$695$	−11.4687	−	8.43578i	−0.435032	−	0.319987i
$696$	−1.99487	−	1.36430i	−0.0756154	−	0.0517138i
$697$	58.5736	−	21.3191i	2.21863	−	0.807517i
$698$	−2.75761	+	7.01634i	−0.104377	+	0.265572i
$699$	1.61318	−	9.14880i	0.0610161	−	0.346039i
$700$	14.5384	+	10.4027i	0.549501	+	0.393185i
$701$	−17.0027	+	14.2670i	−0.642183	+	0.538856i	−0.904688	−	0.426075i	$-0.859896\pi$
$701$	−17.0027	+	14.2670i	−0.642183	+	0.538856i	0.262504	+	0.964931i	$0.415452\pi$
$702$	−8.72343	+	14.2598i	−0.329244	+	0.538202i
$703$	−3.60729	+	4.34281i	−0.136052	+	0.163792i
$704$	−4.00480	+	26.0593i	−0.150937	+	0.982145i
$705$	−7.22029	+	14.5859i	−0.271932	+	0.549335i
$706$	−9.79458	+	7.80320i	−0.368624	+	0.293677i
$707$	−3.01039	+	17.0728i	−0.113217	+	0.642088i
$708$	−12.5753	−	16.6349i	−0.472607	−	0.625177i
$709$	14.6520	−	5.33290i	0.550268	−	0.200281i	−0.0518977	−	0.998652i	$-0.516527\pi$
$709$	14.6520	−	5.33290i	0.550268	−	0.200281i	0.602165	+	0.798371i	$0.294305\pi$
$710$	−11.2844	−	8.75073i	−0.423498	−	0.328409i
$711$	−5.79631	−	10.0395i	−0.217378	−	0.376511i
$712$	−22.3307	−	21.8438i	−0.836878	−	0.818629i
$713$	5.38507	+	4.51861i	0.201673	+	0.169223i
$714$	0.360410	−	14.1782i	0.0134880	−	0.530604i
$715$	2.07098	−	18.6504i	0.0774503	−	0.697484i
$716$	19.3209	+	17.9618i	0.722056	+	0.671264i
$717$	2.63159	+	14.9245i	0.0982784	+	0.557364i
$718$	−7.63269	−	6.74243i	−0.284849	−	0.251625i
$719$	16.0856	−	44.1949i	0.599892	−	1.64819i	−0.151595	−	0.988443i	$-0.548441\pi$
$719$	16.0856	−	44.1949i	0.599892	−	1.64819i	0.751487	−	0.659748i	$-0.229337\pi$
$720$	17.4352	−	9.20776i	0.649773	−	0.343153i
$721$		−	7.30646i		−	0.272107i
$722$	−8.79918	−	25.3885i	−0.327472	−	0.944861i
$723$	−15.8008			−0.587640
$724$	−4.66481	+	11.0365i	−0.173366	+	0.410170i
$725$	−2.19894	−	4.25538i	−0.0816666	−	0.158041i
$726$	0.131124	+	0.115830i	0.00486647	+	0.00429885i
$727$	0.413595	+	2.34561i	0.0153394	+	0.0869940i	0.991516	−	0.129982i	$-0.0414919\pi$
$727$	0.413595	+	2.34561i	0.0153394	+	0.0869940i	−0.976177	+	0.216976i	$0.930381\pi$
$728$	−3.46926	−	12.3991i	−0.128579	−	0.459543i
$729$	3.48475	−	6.03576i	0.129065	−	0.223547i
$730$	14.2763	+	34.9698i	0.528389	+	1.29429i
$731$	−3.26518	+	3.89129i	−0.120767	+	0.143925i
$732$	7.73158	+	1.77251i	0.285767	+	0.0655140i
$733$	16.6999	−	9.64168i	0.616824	−	0.356124i	−0.158807	−	0.987310i	$-0.550765\pi$
$733$	16.6999	−	9.64168i	0.616824	−	0.356124i	0.775631	+	0.631186i	$0.217432\pi$
$734$	−38.2522	+	20.8072i	−1.41192	+	0.768008i
$735$	5.48857	−	5.23834i	0.202449	−	0.193219i
$736$	−4.47419	−	6.96411i	−0.164921	−	0.256701i
$737$	−7.72206	+	43.7940i	−0.284446	+	1.61317i
$738$	−24.1652	+	19.2521i	−0.889535	+	0.708680i
$739$	6.74845	+	8.04249i	0.248246	+	0.295848i	0.875750	−	0.482766i	$-0.160368\pi$
$739$	6.74845	+	8.04249i	0.248246	+	0.295848i	−0.627504	+	0.778614i	$0.715923\pi$
$740$	3.66467	−	4.48556i	0.134716	−	0.164892i
$741$	−7.61541	−	6.32564i	−0.279759	−	0.232378i
$742$	−2.42639	−	1.48434i	−0.0890755	−	0.0544918i
$743$	−6.17731	−	7.36183i	−0.226624	−	0.270079i	0.640736	−	0.767761i	$-0.278629\pi$
$743$	−6.17731	−	7.36183i	−0.226624	−	0.270079i	−0.867360	+	0.497682i	$0.834185\pi$
$744$	11.0399	+	5.00060i	0.404743	+	0.183331i
$745$	−27.7613	+	6.74885i	−1.01710	+	0.247259i
$746$	−15.9042	+	40.4659i	−0.582293	+	1.48156i
$747$	−28.4181	+	10.3434i	−1.03977	+	0.378444i
$748$	41.4029	+	2.10629i	1.51384	+	0.0770137i
$749$	−18.1156	+	10.4590i	−0.661928	+	0.382165i
$750$	−14.1022	−	0.114471i	−0.514941	−	0.00417988i
$751$	−36.6620	−	30.7631i	−1.33782	−	1.12256i	−0.982181	−	0.187936i	$-0.939820\pi$
$751$	−36.6620	−	30.7631i	−1.33782	−	1.12256i	−0.355634	−	0.934625i	$-0.615735\pi$
$752$	−32.4728	−	3.31255i	−1.18416	−	0.120796i
$753$	11.8600	−	20.5422i	0.432204	−	0.748599i
$754$	−0.685198	+	3.38110i	−0.0249534	+	0.123132i
$755$	4.10850	−	2.73627i	0.149523	−	0.0995829i
$756$	4.87677	+	15.8643i	0.177366	+	0.576979i
$757$	3.00240	−	8.24902i	0.109124	−	0.299816i	−0.873096	−	0.487548i	$-0.837891\pi$
$757$	3.00240	−	8.24902i	0.109124	−	0.299816i	0.982220	+	0.187732i	$0.0601137\pi$
$758$	−36.1878	+	5.43662i	−1.31440	+	0.197467i
$759$	4.30128			0.156127
$760$	9.23915	+	25.9738i	0.335139	+	0.942169i
$761$	−44.1631			−1.60091			−0.800455	−	0.599393i	$-0.795409\pi$
$761$	−44.1631			−1.60091			−0.800455	+	0.599393i	$0.795409\pi$
$762$	−20.0193	+	3.00758i	−0.725224	+	0.108953i
$763$	−9.70551	+	26.6657i	−0.351363	+	0.965362i
$764$	−15.1260	−	49.2054i	−0.547239	−	1.78019i
$765$	−17.1857	−	25.8042i	−0.621349	−	0.932954i
$766$	−6.68310	+	32.9777i	−0.241470	+	1.19153i
$767$	−14.8834	+	25.7789i	−0.537410	+	0.930821i
$768$	−10.6636	−	9.48400i	−0.384791	−	0.342224i
$769$	−36.7324	−	30.8221i	−1.32460	−	1.11147i	−0.985307	−	0.170795i	$-0.945367\pi$
$769$	−36.7324	−	30.8221i	−1.32460	−	1.11147i	−0.339297	−	0.940679i	$-0.610189\pi$
$770$	−12.5165	−	13.8002i	−0.451064	−	0.497323i
$771$	10.0129	−	5.78093i	0.360604	−	0.208195i
$772$	1.05871	+	0.0538598i	0.0381038	+	0.00193846i
$773$	−43.2842	+	15.7542i	−1.55683	+	0.566638i	−0.970006	−	0.243079i	$-0.921843\pi$
$773$	−43.2842	+	15.7542i	−1.55683	+	0.566638i	−0.586820	+	0.809718i	$0.699620\pi$
$774$	0.921012	−	2.34338i	0.0331051	−	0.0842312i
$775$	14.5653	+	19.1007i	0.523201	+	0.686119i
$776$	−3.78574	+	8.35785i	−0.135900	+	0.300029i
$777$	1.32746	+	1.58201i	0.0476225	+	0.0567543i
$778$	22.7796	+	13.9354i	0.816688	+	0.499607i
$779$	−21.7857	−	37.3031i	−0.780554	−	1.33652i
$780$	7.86573	+	6.42626i	0.281638	+	0.230097i
$781$	9.56603	+	11.4004i	0.342299	+	0.407937i
$782$	−10.1798	+	8.11014i	−0.364031	+	0.290018i
$783$	0.772214	−	4.37945i	0.0275967	−	0.156509i
$784$	13.6970	+	6.62867i	0.489180	+	0.236738i
$785$	−10.2105	+	9.74502i	−0.364429	+	0.347815i
$786$	14.8979	−	8.10366i	0.531390	−	0.289048i
$787$	18.4631	−	10.6597i	0.658139	−	0.379977i	−0.133429	−	0.991058i	$-0.542599\pi$
$787$	18.4631	−	10.6597i	0.658139	−	0.379977i	0.791568	+	0.611082i	$0.209265\pi$
$788$	−17.5432	−	4.02189i	−0.624950	−	0.143274i
$789$	−5.11385	+	6.09445i	−0.182058	+	0.216968i
$790$	−15.3960	+	6.28534i	−0.547764	+	0.223622i
$791$	−7.66345	+	13.2735i	−0.272481	+	0.471951i
$792$	−19.7888	+	5.53689i	−0.703165	+	0.196745i
$793$	−1.96617	−	11.1507i	−0.0698209	−	0.395974i
$794$	−27.2833	−	24.1010i	−0.968247	−	0.855313i
$795$	2.23930	−	0.143384i	0.0794200	−	0.00508532i
$796$	12.9309	−	30.5934i	0.458323	−	1.08435i
$797$	27.4438			0.972111			0.486055	−	0.873928i	$-0.338435\pi$
$797$	27.4438			0.972111			0.486055	+	0.873928i	$0.338435\pi$
$798$	−9.71265	+	1.50874i	−0.343824	+	0.0534088i
$799$			51.3250i			1.81575i
$800$	−9.69542	−	26.5706i	−0.342785	−	0.939414i
$801$	8.32704	−	22.8784i	0.294222	−	0.808367i
$802$	27.9032	+	24.6486i	0.985297	+	0.870374i
$803$	−6.83561	−	38.7667i	−0.241224	−	1.36805i
$804$	−17.6291	−	16.3890i	−0.621731	−	0.577996i
$805$	5.81353	+	0.645549i	0.204900	+	0.0227526i
$806$	0.439629	−	17.2946i	0.0154853	−	0.609176i
$807$	−14.3964	−	12.0800i	−0.506776	−	0.425235i
$808$	19.1801	−	19.6077i	0.674754	−	0.689796i
$809$	−10.3311	−	17.8939i	−0.363221	−	0.629117i	0.625268	−	0.780410i	$-0.284990\pi$
$809$	−10.3311	−	17.8939i	−0.363221	−	0.629117i	−0.988489	+	0.151293i	$0.951656\pi$
$810$	6.17988	+	4.79231i	0.217139	+	0.168384i
$811$	40.6653	−	14.8010i	1.42795	−	0.519732i	0.491608	−	0.870817i	$-0.336409\pi$
$811$	40.6653	−	14.8010i	1.42795	−	0.519732i	0.936344	+	0.351085i	$0.114187\pi$
$812$	2.06550	+	2.73230i	0.0724849	+	0.0958850i
$813$	−2.59077	+	14.6930i	−0.0908622	+	0.515305i
$814$	−4.72136	+	3.76145i	−0.165484	+	0.131839i
$815$	−8.53597	−	4.22547i	−0.299002	−	0.148012i
$816$	−13.1340	+	18.1943i	−0.459781	+	0.636926i
$817$	3.05752	+	1.74498i	0.106969	+	0.0610493i
$818$	5.38632	−	8.80480i	0.188328	−	0.307853i
$819$	7.68722	−	6.45034i	0.268613	−	0.225393i
$820$	22.6620	+	38.0892i	0.791390	+	1.33013i
$821$	−5.42087	+	30.7433i	−0.189190	+	1.07295i	0.731263	+	0.682095i	$0.238931\pi$
$821$	−5.42087	+	30.7433i	−0.189190	+	1.07295i	−0.920453	+	0.390853i	$0.872180\pi$
$822$	−1.37196	+	3.49076i	−0.0478527	+	0.121754i
$823$	45.3559	−	16.5082i	1.58101	−	0.575440i	0.605584	−	0.795781i	$-0.292939\pi$
$823$	45.3559	−	16.5082i	1.58101	−	0.575440i	0.975423	+	0.220342i	$0.0707172\pi$
$824$	−6.52581	+	9.54197i	−0.227337	+	0.332410i
$825$	14.3394	+	3.22433i	0.499235	+	0.112257i
$826$	9.39909	+	28.0196i	0.327036	+	0.974928i
$827$	−32.7690	+	39.0525i	−1.13949	+	1.35799i	−0.215075	+	0.976597i	$0.569000\pi$
$827$	−32.7690	+	39.0525i	−1.13949	+	1.35799i	−0.924413	+	0.381392i	$0.875445\pi$
$828$	3.50542	−	5.41600i	0.121822	−	0.188219i
$829$	−9.58302	−	5.53276i	−0.332832	−	0.192161i	0.324266	−	0.945966i	$-0.394883\pi$
$829$	−9.58302	−	5.53276i	−0.332832	−	0.192161i	−0.657098	+	0.753805i	$0.728216\pi$
$830$	9.17325	+	42.4009i	0.318408	+	1.47176i
$831$	−4.39683	−	24.9356i	−0.152524	−	0.865008i
$832$	−6.54363	+	19.2914i	−0.226860	+	0.668809i
$833$	8.18341	−	22.4837i	0.283538	−	0.779015i
$834$	−7.94209	+	1.19317i	−0.275012	+	0.0413161i
$835$	31.2782	−	13.7065i	1.08243	−	0.474334i
$836$	−3.68720	−	28.4932i	−0.127525	−	0.985458i
$837$			22.3008i			0.770828i
$838$	6.55437	+	43.6279i	0.226417	+	1.50710i
$839$	33.3764	+	12.1480i	1.15228	+	0.419396i	0.846334	−	0.532652i	$-0.178805\pi$
$839$	33.3764	+	12.1480i	1.15228	+	0.419396i	0.305947	+	0.952048i	$0.401027\pi$
$840$	9.95206	−	1.62886i	0.343379	−	0.0562011i
$841$	4.87643	+	27.6556i	0.168153	+	0.953642i
$842$	−4.26323	+	21.0368i	−0.146920	+	0.724977i
$843$	−2.91317	+	5.04576i	−0.100335	+	0.173785i
$844$	6.73003	−	10.3981i	0.231657	−	0.357919i
$845$	−4.09822	+	13.9819i	−0.140983	+	0.480993i
$846$	−8.09082	−	24.1196i	−0.278168	−	0.829247i
$847$	−0.123979	−	0.214737i	−0.00425995	−	0.00737846i
$848$	1.84303	+	4.10564i	0.0632898	+	0.140988i
$849$	3.24148	+	8.90589i	0.111247	+	0.305649i
$850$	−40.0167	+	19.4063i	−1.37256	+	0.665629i
$851$	0.329099	−	1.86641i	0.0112814	−	0.0639799i
$852$	−7.99381	+	0.993940i	−0.273863	+	0.0340518i
$853$	31.5094	+	37.5514i	1.07886	+	1.28574i	0.956018	+	0.293309i	$0.0947566\pi$
$853$	31.5094	+	37.5514i	1.07886	+	1.28574i	0.122842	+	0.992426i	$0.460799\pi$
$854$	−9.58970	−	5.86648i	−0.328153	−	0.200747i
$855$	−15.4692	+	14.9121i	−0.529034	+	0.509982i
$856$	32.9998	+	2.52092i	1.12791	+	0.0861632i
$857$	−26.1562	+	21.9477i	−0.893480	+	0.749718i	−0.968905	−	0.247433i	$-0.920413\pi$
$857$	−26.1562	+	21.9477i	−0.893480	+	0.749718i	0.0754254	+	0.997151i	$0.475969\pi$
$858$	−6.59595	−	8.27923i	−0.225182	−	0.282648i
$859$	−31.2853	−	5.51644i	−1.06744	−	0.188219i	−0.387785	−	0.921750i	$-0.626760\pi$
$859$	−31.2853	−	5.51644i	−1.06744	−	0.188219i	−0.679656	+	0.733531i	$0.737871\pi$
$860$	−3.15139	−	1.76476i	−0.107462	−	0.0601780i
$861$	−14.8492	+	5.40468i	−0.506060	+	0.184191i
$862$	5.10770	−	2.77832i	0.173969	−	0.0946299i
$863$	−9.03848	+	5.21837i	−0.307673	+	0.177635i	−0.645885	−	0.763435i	$-0.723511\pi$
$863$	−9.03848	+	5.21837i	−0.307673	+	0.177635i	0.338212	+	0.941070i	$0.390178\pi$
$864$	7.80042	−	25.0739i	0.265376	−	0.853032i
$865$	12.9551	−	44.1990i	0.440487	−	1.50281i
$866$	0.0378388	−	1.48854i	0.00128581	−	0.0505827i
$867$	17.4253	+	10.0605i	0.591793	+	0.341672i
$868$	−12.5800	−	11.6951i	−0.426993	−	0.396957i
$869$	17.0676	−	3.00948i	0.578978	−	0.102089i
$870$	−2.57280	−	0.825663i	−0.0872262	−	0.0279926i
$871$	−11.7516	+	32.2872i	−0.398187	+	1.09401i
$872$	36.4916	−	26.1558i	1.23576	−	0.885749i
$873$	−7.15114			−0.242029
$874$	6.79001	+	5.93801i	0.229676	+	0.200856i
$875$	18.8970	+	6.51005i	0.638836	+	0.220080i
$876$	19.6262	+	8.29539i	0.663108	+	0.280275i
$877$	3.11496	+	1.13375i	0.105185	+	0.0382841i	0.394076	−	0.919078i	$-0.371065\pi$
$877$	3.11496	+	1.13375i	0.105185	+	0.0382841i	−0.288892	+	0.957362i	$0.593287\pi$
$878$	9.72325	−	11.0071i	0.328144	−	0.371472i
$879$	−3.79325	+	0.668853i	−0.127943	+	0.0225599i
$880$	4.02044	+	29.2017i	0.135529	+	0.984389i
$881$	−12.5195	+	21.6844i	−0.421792	+	0.730564i	−0.996115	−	0.0880642i	$-0.971932\pi$
$881$	−12.5195	+	21.6844i	−0.421792	+	0.730564i	0.574323	+	0.818629i	$0.305265\pi$
$882$	−0.301380	+	11.8560i	−0.0101480	+	0.399211i
$883$	4.23946	+	3.55733i	0.142669	+	0.119714i	0.711329	−	0.702859i	$-0.248094\pi$
$883$	4.23946	+	3.55733i	0.142669	+	0.119714i	−0.568660	+	0.822573i	$0.692538\pi$
$884$	31.2213	+	7.15769i	1.05009	+	0.240739i
$885$	−18.7811	−	13.8145i	−0.631321	−	0.464368i
$886$	10.1770	−	5.53572i	0.341901	−	0.185976i
$887$	−2.26002	−	6.20937i	−0.0758842	−	0.208490i	0.895950	−	0.444154i	$-0.146496\pi$
$887$	−2.26002	−	6.20937i	−0.0758842	−	0.208490i	−0.971835	+	0.235664i	$0.924274\pi$
$888$	−0.320638	−	3.25168i	−0.0107599	−	0.109119i
$889$	28.2548	+	4.98208i	0.947636	+	0.167094i
$890$	−30.8962	−	16.2845i	−1.03564	−	0.545859i
$891$	−5.23880	−	6.24336i	−0.175506	−	0.209160i
$892$	−40.2126	+	20.5669i	−1.34642	+	0.688632i
$893$	34.9984	−	6.35131i	1.17118	−	0.212538i
$894$	−8.41032	+	13.7480i	−0.281283	+	0.459802i
$895$	26.4328	+	13.0848i	0.883551	+	0.437375i
$896$	10.0536	+	17.5496i	0.335867	+	0.586293i
$897$	3.27288	+	0.577098i	0.109278	+	0.0192687i
$898$	−0.903089	−	0.354938i	−0.0301365	−	0.0118444i
$899$	1.57407	+	4.32473i	0.0524983	+	0.144238i
$900$	15.7462	−	15.4279i	0.524873	−	0.514264i
$901$	6.12826	−	3.53815i	0.204162	−	0.117873i
$902$	−14.6899	−	43.7921i	−0.489121	−	1.45812i
$903$	0.827769	−	0.986496i	0.0275464	−	0.0328285i
$904$	21.8635	−	10.4900i	0.727169	−	0.348893i
$905$	−1.47846	+	13.3143i	−0.0491455	+	0.442583i
$906$	0.553070	−	2.72912i	0.0183745	−	0.0906689i
$907$	−28.0686	+	4.94924i	−0.932001	+	0.164337i	−0.618978	−	0.785408i	$-0.712453\pi$
$907$	−28.0686	+	4.94924i	−0.932001	+	0.164337i	−0.313023	+	0.949745i	$0.601342\pi$
$908$	−4.73523	−	15.4039i	−0.157144	−	0.511195i
$909$	20.0886	+	7.31164i	0.666296	+	0.242512i
$910$	−7.67239	−	12.1800i	−0.254337	−	0.403763i
$911$	−35.6953			−1.18264			−0.591318	−	0.806438i	$-0.701392\pi$
$911$	−35.6953			−1.18264			−0.591318	+	0.806438i	$0.701392\pi$
$912$	14.0319	+	6.70455i	0.464643	+	0.222010i
$913$		−	45.2115i		−	1.49628i
$914$	0.517693	+	3.44592i	0.0171238	+	0.113981i
$915$	8.85030	−	0.566692i	0.292582	−	0.0187342i
$916$	−54.1082	+	16.6331i	−1.78778	+	0.549574i
$917$	−23.6702	+	4.17370i	−0.781660	+	0.137828i
$918$	−40.4673	−	8.20092i	−1.33562	−	0.270671i
$919$	−22.2068	−	12.8211i	−0.732534	−	0.422928i	0.0868147	−	0.996224i	$-0.472331\pi$
$919$	−22.2068	−	12.8211i	−0.732534	−	0.422928i	−0.819348	+	0.573296i	$0.805665\pi$
$920$	−7.01568	−	6.03545i	−0.231300	−	0.198983i
$921$	−9.05938	−	7.60172i	−0.298517	−	0.250485i
$922$	−15.0531	−	44.8748i	−0.495747	−	1.47787i
$923$	5.74931	+	9.95810i	0.189241	+	0.327775i
$924$	−10.4962	−	0.533974i	−0.345300	−	0.0175665i
$925$	2.49624	−	5.97548i	0.0820760	−	0.196473i
$926$	−3.56771	+	9.07753i	−0.117242	+	0.298306i
$927$	−8.87296	−	1.56454i	−0.291426	−	0.0513863i
$928$	−0.257098	−	5.41310i	−0.00843967	−	0.177694i
$929$	8.82990	−	7.40916i	0.289700	−	0.243087i	−0.486342	−	0.873769i	$-0.661669\pi$
$929$	8.82990	−	7.40916i	0.289700	−	0.243087i	0.776042	+	0.630682i	$0.217225\pi$
$930$	13.4250	+	1.83720i	0.440225	+	0.0602442i
$931$	−16.3443	−	2.79796i	−0.535662	−	0.0916993i
$932$	18.5461	−	9.48549i	0.607497	−	0.310707i
$933$	2.50687	−	2.10351i	0.0820712	−	0.0688659i
$934$	−26.3493	−	33.0736i	−0.862174	−	1.08220i
$935$	45.0380	−	10.9489i	1.47290	−	0.358066i
$936$	−15.8004	+	1.55803i	−0.516452	+	0.0509257i
$937$	7.41609	+	20.3755i	0.242273	+	0.665640i	0.999916	+	0.0129704i	$0.00412871\pi$
$937$	7.41609	+	20.3755i	0.242273	+	0.665640i	−0.757643	+	0.652669i	$0.773649\pi$
$938$	16.3006	+	29.9672i	0.532232	+	0.978463i
$939$	3.89357	+	6.74387i	0.127062	+	0.220078i
$940$	−35.8535	+	6.80790i	−1.16941	+	0.222049i
$941$	−3.43244	+	4.09062i	−0.111894	+	0.133350i	−0.819084	−	0.573673i	$-0.805518\pi$
$941$	−3.43244	+	4.09062i	−0.111894	+	0.133350i	0.707190	+	0.707023i	$0.249962\pi$
$942$	−0.202332	+	7.95955i	−0.00659234	+	0.259336i
$943$	12.5589	+	7.25086i	0.408973	+	0.236121i
$944$	12.7510	−	44.9875i	0.415011	−	1.46422i
$945$	10.2859	+	15.4442i	0.334600	+	0.502401i
$946$	2.82114	+	2.49208i	0.0917230	+	0.0810246i
$947$	−23.8938	−	8.69664i	−0.776445	−	0.282603i	−0.0767556	−	0.997050i	$-0.524456\pi$
$947$	−23.8938	−	8.69664i	−0.776445	−	0.282603i	−0.699690	+	0.714447i	$0.746678\pi$
$948$	−3.65216	+	8.64071i	−0.118617	+	0.280637i
$949$		−	30.4151i		−	0.987315i
$950$	18.1850	+	24.8858i	0.590000	+	0.807403i
$951$			17.5968i			0.570617i
$952$	25.8482	−	18.5271i	0.837746	−	0.600466i
$953$	−35.6169	−	12.9635i	−1.15375	−	0.419929i	−0.306886	−	0.951746i	$-0.599287\pi$
$953$	−35.6169	−	12.9635i	−1.15375	−	0.419929i	−0.846859	+	0.531817i	$0.821509\pi$
$954$	−2.32215	+	2.62876i	−0.0751823	+	0.0851093i
$955$	−31.9031	−	47.9025i	−1.03236	−	1.55009i
$956$	−23.1374	+	24.8881i	−0.748317	+	0.804939i
$957$	2.43873	+	1.40800i	0.0788330	+	0.0455142i
$958$	47.1264	+	1.19796i	1.52258	+	0.0387042i
$959$	3.41683	−	4.07202i	0.110335	−	0.131492i
$960$	−14.4519	−	6.76150i	−0.466432	−	0.218227i
$961$	3.96027	+	6.85939i	0.127751	+	0.221271i
$962$	−4.09720	+	2.22866i	−0.132099	+	0.0718549i
$963$	8.82233	+	24.2391i	0.284296	+	0.781096i
$964$	−21.3659	−	28.2634i	−0.688151	−	0.910304i
$965$	1.15166	−	0.279972i	0.0370733	−	0.00901261i
$966$	2.58073	−	2.05603i	0.0830337	−	0.0661518i
$967$	12.2124	−	10.2474i	0.392723	−	0.329534i	−0.424950	−	0.905217i	$-0.639708\pi$
$967$	12.2124	−	10.2474i	0.392723	−	0.329534i	0.817673	+	0.575683i	$0.195264\pi$
$968$	−0.0298823	+	0.391171i	−0.000960453	+	0.0125727i
$969$	8.24868	−	23.0196i	0.264986	−	0.739497i
$970$	−1.39087	+	10.1635i	−0.0446581	+	0.326331i
$971$	−0.877458	+	0.736275i	−0.0281590	+	0.0236282i	−0.656759	−	0.754101i	$-0.728073\pi$
$971$	−0.877458	+	0.736275i	−0.0281590	+	0.0236282i	0.628600	+	0.777729i	$0.283628\pi$
$972$	32.0171	−	3.98096i	1.02695	−	0.127689i
$973$	11.2093	+	1.97650i	0.359353	+	0.0633636i
$974$	18.3901	+	7.22782i	0.589258	+	0.231594i
$975$	10.4784	+	4.37733i	0.335578	+	0.140187i
$976$	7.28411	+	16.2265i	0.233159	+	0.519398i
$977$	−2.90463	−	5.03097i	−0.0929274	−	0.160955i	0.815814	−	0.578314i	$-0.196289\pi$
$977$	−2.90463	−	5.03097i	−0.0929274	−	0.160955i	−0.908742	+	0.417359i	$0.862956\pi$
$978$	−5.09392	+	1.70874i	−0.162886	+	0.0546395i
$979$	27.8825	+	23.3962i	0.891130	+	0.747747i
$980$	16.7916	+	2.73427i	0.536389	+	0.0873431i
$981$	30.3045	+	17.4963i	0.967549	+	0.558615i
$982$	3.45067	−	17.0273i	0.110115	−	0.543362i
$983$	45.6329	−	8.04631i	1.45546	−	0.256637i	0.610736	−	0.791834i	$-0.290874\pi$
$983$	45.6329	−	8.04631i	1.45546	−	0.256637i	0.844727	+	0.535197i	$0.179763\pi$
$984$	24.2198	+	6.20436i	0.772098	+	0.197788i
$985$	−20.0816	+	1.28584i	−0.639852	+	0.0409703i
$986$	−8.42656	+	1.26595i	−0.268356	+	0.0403161i
$987$		−	13.0116i		−	0.414164i
$988$	1.01727	−	22.1755i	0.0323638	−	0.705496i
$989$	−1.18180			−0.0375790
$990$	−19.4391	+	12.2450i	−0.617815	+	0.389172i
$991$	−3.71404	−	1.35180i	−0.117980	−	0.0429413i	0.282355	−	0.959310i	$-0.408884\pi$
$991$	−3.71404	−	1.35180i	−0.117980	−	0.0429413i	−0.400336	+	0.916369i	$0.631106\pi$
$992$	5.98348	+	26.5093i	0.189976	+	0.841670i
$993$	23.1740	−	4.08620i	0.735405	−	0.129672i
$994$	11.1890	+	2.26750i	0.354892	+	0.0719209i
$995$	4.09829	−	36.9074i	0.129925	−	1.17004i
$996$	20.5444	+	13.2970i	0.650973	+	0.421332i
$997$	−8.92660	+	10.6383i	−0.282708	+	0.336919i	−0.888646	−	0.458593i	$-0.848353\pi$
$997$	−8.92660	+	10.6383i	−0.282708	+	0.336919i	0.605938	+	0.795512i	$0.292798\pi$
$998$	−18.9833	+	6.36788i	−0.600905	+	0.201572i
$999$	5.20679	−	3.00614i	0.164735	−	0.0951101i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.279.54	yes	336
4.3	odd	2	inner	380.2.bb.a.279.35	yes	336
5.4	even	2	inner	380.2.bb.a.279.3	yes	336
19.3	odd	18	inner	380.2.bb.a.79.22	yes	336
20.19	odd	2	inner	380.2.bb.a.279.22	yes	336
76.3	even	18	inner	380.2.bb.a.79.3	✓	336
95.79	odd	18	inner	380.2.bb.a.79.35	yes	336
380.79	even	18	inner	380.2.bb.a.79.54	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.79.3	✓	336	76.3	even	18	inner
380.2.bb.a.79.22	yes	336	19.3	odd	18	inner
380.2.bb.a.79.35	yes	336	95.79	odd	18	inner
380.2.bb.a.79.54	yes	336	380.79	even	18	inner
380.2.bb.a.279.3	yes	336	5.4	even	2	inner
380.2.bb.a.279.22	yes	336	20.19	odd	2	inner
380.2.bb.a.279.35	yes	336	4.3	odd	2	inner
380.2.bb.a.279.54	yes	336	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39852 - 0.210104i) q^{2} +(0.305059 - 0.838142i) q^{3} +(1.91171 - 0.587670i) q^{4} +(1.86109 - 1.23949i) q^{5} +(0.250533 - 1.23625i) q^{6} +(-0.893843 + 1.54818i) q^{7} +(2.55009 - 1.22353i) q^{8} +(1.68871 + 1.41700i) q^{9} +O(q^{10})\)	\(q+(1.39852 - 0.210104i) q^{2} +(0.305059 - 0.838142i) q^{3} +(1.91171 - 0.587670i) q^{4} +(1.86109 - 1.23949i) q^{5} +(0.250533 - 1.23625i) q^{6} +(-0.893843 + 1.54818i) q^{7} +(2.55009 - 1.22353i) q^{8} +(1.68871 + 1.41700i) q^{9} +(2.34235 - 2.12448i) q^{10} +(-2.85412 + 1.64782i) q^{11} +(0.0906334 - 1.78156i) q^{12} +(-2.39281 + 0.870912i) q^{13} +(-0.924777 + 2.35296i) q^{14} +(-0.471127 - 1.93798i) q^{15} +(3.30929 - 2.24691i) q^{16} +(-4.04286 - 4.81810i) q^{17} +(2.65941 + 1.62689i) q^{18} +(-2.78516 + 3.35304i) q^{19} +(2.82946 - 3.46326i) q^{20} +(1.02492 + 1.22145i) q^{21} +(-3.64532 + 2.90418i) q^{22} +(0.254094 - 1.44104i) q^{23} +(-0.247561 - 2.51059i) q^{24} +(1.92733 - 4.61361i) q^{25} +(-3.16341 + 1.72073i) q^{26} +(4.02011 - 2.32101i) q^{27} +(-0.798950 + 3.48496i) q^{28} +(0.615783 - 0.733862i) q^{29} +(-1.06606 - 2.61131i) q^{30} +(-2.40205 + 4.16048i) q^{31} +(4.15602 - 3.83765i) q^{32} +(0.510438 + 2.89484i) q^{33} +(-6.66633 - 5.88878i) q^{34} +(0.255433 + 3.98922i) q^{35} +(4.06106 + 1.71649i) q^{36} +1.29518 q^{37} +(-3.19061 + 5.27447i) q^{38} +2.27120i q^{39} +(3.22941 - 5.43792i) q^{40} +(-3.38958 + 9.31281i) q^{41} +(1.69001 + 1.49289i) q^{42} +(-0.140245 - 0.795371i) q^{43} +(-4.48787 + 4.82744i) q^{44} +(4.89920 + 0.544020i) q^{45} +(0.0525867 - 2.06871i) q^{46} +(-6.25117 - 5.24536i) q^{47} +(-0.873706 - 3.45909i) q^{48} +(1.90209 + 3.29451i) q^{49} +(1.72606 - 6.85717i) q^{50} +(-5.27156 + 1.91869i) q^{51} +(-4.06256 + 3.07112i) q^{52} +(-0.195369 + 1.10799i) q^{53} +(5.13455 - 4.09062i) q^{54} +(-3.26931 + 6.60440i) q^{55} +(-0.385141 + 5.04165i) q^{56} +(1.96069 + 3.35723i) q^{57} +(0.706997 - 1.15570i) q^{58} +(8.95499 - 7.51412i) q^{59} +(-2.03955 - 3.42799i) q^{60} +(-0.772146 + 4.37906i) q^{61} +(-2.48518 + 6.32319i) q^{62} +(-3.70321 + 1.34786i) q^{63} +(5.00596 - 6.24022i) q^{64} +(-3.37375 + 4.58671i) q^{65} +(1.32208 + 3.94124i) q^{66} +(8.67340 - 10.3366i) q^{67} +(-10.5602 - 6.83495i) q^{68} +(-1.13028 - 0.652570i) q^{69} +(1.19538 + 5.52533i) q^{70} +(-0.784140 - 4.44708i) q^{71} +(6.04011 + 1.54729i) q^{72} +(-4.08525 + 11.2241i) q^{73} +(1.81134 - 0.272124i) q^{74} +(-3.27892 - 3.02280i) q^{75} +(-3.35394 + 8.04681i) q^{76} -5.89159i q^{77} +(0.477188 + 3.17631i) q^{78} +(-4.94158 - 1.79859i) q^{79} +(3.37386 - 8.28354i) q^{80} +(0.429431 + 2.43543i) q^{81} +(-2.78374 + 13.7363i) q^{82} +(-6.85928 + 11.8806i) q^{83} +(2.67717 + 1.73275i) q^{84} +(-13.4961 - 3.95583i) q^{85} +(-0.363247 - 1.08288i) q^{86} +(-0.427231 - 0.739985i) q^{87} +(-5.26210 + 7.69420i) q^{88} +(-3.77737 - 10.3782i) q^{89} +(6.96593 - 0.268522i) q^{90} +(0.790467 - 4.48296i) q^{91} +(-0.361102 - 2.90418i) q^{92} +(2.75431 + 3.28246i) q^{93} +(-9.84446 - 6.02233i) q^{94} +(-1.02737 + 9.69250i) q^{95} +(-1.94867 - 4.65404i) q^{96} +(-2.48501 + 2.08517i) q^{97} +(3.35230 + 4.20780i) q^{98} +(-7.15474 - 1.26157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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