LMFDB - Embedded newform 370.2.v.b.169.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(99,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.v (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.3
Character	$\chi$	$=$	370.169
Dual form			370.2.v.b.289.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.434686 - 1.19429i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.33445 + 1.79422i) q^{5} -1.27094i q^{6} +(2.39627 + 0.422528i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.06076 - 0.890080i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.434686 - 1.19429i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.33445 + 1.79422i) q^{5} -1.27094i q^{6} +(2.39627 + 0.422528i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.06076 - 0.890080i) q^{9} +(-1.86764 + 1.22961i) q^{10} +(-0.539279 - 0.934058i) q^{11} +(0.434686 - 1.19429i) q^{12} +(4.50286 + 3.77835i) q^{13} +(2.10725 + 1.21662i) q^{14} +(2.72289 + 0.813802i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.03001 - 2.54248i) q^{17} +(1.30121 - 0.473602i) q^{18} +(-0.238962 - 0.656543i) q^{19} +(-2.17555 + 0.516683i) q^{20} +(-0.537006 - 3.04551i) q^{21} +(-0.187290 - 1.06217i) q^{22} +(-4.52323 + 7.83447i) q^{23} +(0.816943 - 0.973594i) q^{24} +(-1.43847 - 4.78861i) q^{25} +(2.93904 + 5.09056i) q^{26} +(-4.82610 - 2.78635i) q^{27} +(1.56406 + 1.86397i) q^{28} +(3.50388 - 2.02297i) q^{29} +(2.28034 + 1.69601i) q^{30} -3.83883i q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.881119 + 1.05008i) q^{33} +(3.71685 - 1.35282i) q^{34} +(-3.95583 + 3.73560i) q^{35} +1.38472 q^{36} +(5.80362 + 1.82155i) q^{37} -0.698678i q^{38} +(2.55512 - 7.02012i) q^{39} +(-2.22107 - 0.258560i) q^{40} +(-4.58982 - 3.85131i) q^{41} +(0.537006 - 3.04551i) q^{42} -2.24316 q^{43} +(0.187290 - 1.06217i) q^{44} +(0.181471 + 3.09100i) q^{45} +(-6.92999 + 5.81496i) q^{46} +(-6.62640 - 3.82576i) q^{47} +(1.10066 - 0.635469i) q^{48} +(-1.01425 - 0.369155i) q^{49} +(0.286087 - 4.99181i) q^{50} +(-4.35356 - 2.51353i) q^{51} +(1.02072 + 5.78877i) q^{52} +(-7.71511 + 1.36038i) q^{53} +(-3.58206 - 4.26894i) q^{54} +(2.39555 + 0.278872i) q^{55} +(0.832217 + 2.28650i) q^{56} +(-0.680229 + 0.570780i) q^{57} +(3.98447 - 0.702569i) q^{58} +(-8.83478 + 1.55781i) q^{59} +(1.56275 + 2.37365i) q^{60} +(-7.74469 + 9.22977i) q^{61} +(1.31296 - 3.60732i) q^{62} +(2.91795 - 1.68468i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-12.7881 + 3.03710i) q^{65} +(-1.18713 + 0.685389i) q^{66} +(4.03216 + 0.710979i) q^{67} +3.95539 q^{68} +(11.3228 + 1.99652i) q^{69} +(-4.99491 + 2.15735i) q^{70} +(10.0976 - 3.67522i) q^{71} +(1.30121 + 0.473602i) q^{72} -0.0962140i q^{73} +(4.83061 + 3.69665i) q^{74} +(-5.09371 + 3.79949i) q^{75} +(0.238962 - 0.656543i) q^{76} +(-0.897594 - 2.46612i) q^{77} +(4.80205 - 5.72286i) q^{78} +(-0.293157 - 0.0516914i) q^{79} +(-1.99869 - 1.00262i) q^{80} +(-0.508511 + 2.88391i) q^{81} +(-2.99579 - 5.18886i) q^{82} +(-9.17763 - 10.9375i) q^{83} +(1.54625 - 2.67818i) q^{84} +(0.518365 + 8.82932i) q^{85} +(-2.10788 - 0.767204i) q^{86} +(-3.93910 - 3.30529i) q^{87} +(0.539279 - 0.934058i) q^{88} +(12.0788 - 2.12982i) q^{89} +(-0.886658 + 2.96666i) q^{90} +(9.19364 + 10.9566i) q^{91} +(-8.50090 + 3.09407i) q^{92} +(-4.58468 + 1.66869i) q^{93} +(-4.91830 - 5.86140i) q^{94} +(1.49687 + 0.447375i) q^{95} +(1.25163 - 0.220696i) q^{96} +(-2.60024 + 4.50374i) q^{97} +(-0.826821 - 0.693785i) q^{98} +(-1.40343 - 0.510807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9	$ 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} - 6 q^{15} - 3 q^{17} - 12 q^{18} + 3 q^{19} + 3 q^{20} + 12 q^{21} + 3 q^{22} + 18 q^{23} - 18 q^{25} - 27 q^{26} + 18 q^{30} + 66 q^{33} + 21 q^{34} + 9 q^{35} - 72 q^{36} - 6 q^{37} + 12 q^{39} + 12 q^{40} - 57 q^{41} - 12 q^{42} - 60 q^{43} - 3 q^{44} + 9 q^{45} - 21 q^{46} + 18 q^{47} - 6 q^{49} + 6 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{55} - 30 q^{57} - 15 q^{58} - 12 q^{59} - 9 q^{60} + 42 q^{61} + 12 q^{62} + 9 q^{63} - 30 q^{64} - 15 q^{65} + 18 q^{67} + 24 q^{68} + 36 q^{69} - 12 q^{70} + 18 q^{71} - 12 q^{72} + 3 q^{74} - 78 q^{75} - 3 q^{76} - 21 q^{77} - 6 q^{78} - 24 q^{79} - 36 q^{81} - 27 q^{82} - 30 q^{83} + 12 q^{84} - 30 q^{85} - 18 q^{86} + 30 q^{87} - 6 q^{88} + 3 q^{89} + 57 q^{91} - 15 q^{92} - 60 q^{93} + 3 q^{94} + 6 q^{95} - 84 q^{97} + 6 q^{98} - 45 q^{99}+O(q^{100}) $ 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 - 6 * q^15 - 3 * q^17 - 12 * q^18 + 3 * q^19 + 3 * q^20 + 12 * q^21 + 3 * q^22 + 18 * q^23 - 18 * q^25 - 27 * q^26 + 18 * q^30 + 66 * q^33 + 21 * q^34 + 9 * q^35 - 72 * q^36 - 6 * q^37 + 12 * q^39 + 12 * q^40 - 57 * q^41 - 12 * q^42 - 60 * q^43 - 3 * q^44 + 9 * q^45 - 21 * q^46 + 18 * q^47 - 6 * q^49 + 6 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^55 - 30 * q^57 - 15 * q^58 - 12 * q^59 - 9 * q^60 + 42 * q^61 + 12 * q^62 + 9 * q^63 - 30 * q^64 - 15 * q^65 + 18 * q^67 + 24 * q^68 + 36 * q^69 - 12 * q^70 + 18 * q^71 - 12 * q^72 + 3 * q^74 - 78 * q^75 - 3 * q^76 - 21 * q^77 - 6 * q^78 - 24 * q^79 - 36 * q^81 - 27 * q^82 - 30 * q^83 + 12 * q^84 - 30 * q^85 - 18 * q^86 + 30 * q^87 - 6 * q^88 + 3 * q^89 + 57 * q^91 - 15 * q^92 - 60 * q^93 + 3 * q^94 + 6 * q^95 - 84 * q^97 + 6 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−0.434686	−	1.19429i	−0.250966	−	0.689524i	−0.999646	−	0.0265924i	$-0.991534\pi$
$3$	−0.434686	−	1.19429i	−0.250966	−	0.689524i	0.748680	−	0.662931i	$-0.230688\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−1.33445	+	1.79422i	−0.596786	+	0.802400i
$5$	−1.33445	+	1.79422i	−0.596786	+	0.802400i
$6$		−	1.27094i		−	0.518858i
$7$	2.39627	+	0.422528i	0.905707	+	0.159701i	0.607053	−	0.794661i	$-0.292351\pi$
$7$	2.39627	+	0.422528i	0.905707	+	0.159701i	0.298653	+	0.954362i	$0.403463\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	1.06076	−	0.890080i	0.353585	−	0.296693i
$10$	−1.86764	+	1.22961i	−0.590599	+	0.388836i
$11$	−0.539279	−	0.934058i	−0.162599	−	0.281629i	0.773201	−	0.634161i	$-0.218654\pi$
$11$	−0.539279	−	0.934058i	−0.162599	−	0.281629i	−0.935800	+	0.352532i	$0.885321\pi$
$12$	0.434686	−	1.19429i	0.125483	−	0.344762i
$13$	4.50286	+	3.77835i	1.24887	+	1.04793i	0.996777	+	0.0802232i	$0.0255633\pi$
$13$	4.50286	+	3.77835i	1.24887	+	1.04793i	0.252093	+	0.967703i	$0.418881\pi$
$14$	2.10725	+	1.21662i	0.563186	+	0.325156i
$15$	2.72289	+	0.813802i	0.703047	+	0.210123i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	3.03001	−	2.54248i	0.734884	−	0.616641i	−0.196574	−	0.980489i	$-0.562982\pi$
$17$	3.03001	−	2.54248i	0.734884	−	0.616641i	0.931458	+	0.363848i	$0.118537\pi$
$18$	1.30121	−	0.473602i	0.306698	−	0.111629i
$19$	−0.238962	−	0.656543i	−0.0548216	−	0.150621i	0.909259	−	0.416231i	$-0.136649\pi$
$19$	−0.238962	−	0.656543i	−0.0548216	−	0.150621i	−0.964081	+	0.265609i	$0.914427\pi$
$20$	−2.17555	+	0.516683i	−0.486469	+	0.115534i
$21$	−0.537006	−	3.04551i	−0.117184	−	0.664586i
$22$	−0.187290	−	1.06217i	−0.0399303	−	0.226456i
$23$	−4.52323	+	7.83447i	−0.943159	+	1.63360i	−0.183764	+	0.982970i	$0.558828\pi$
$23$	−4.52323	+	7.83447i	−0.943159	+	1.63360i	−0.759396	+	0.650629i	$0.774505\pi$
$24$	0.816943	−	0.973594i	0.166758	−	0.198734i
$25$	−1.43847	−	4.78861i	−0.287693	−	0.957723i
$26$	2.93904	+	5.09056i	0.576392	+	0.998341i
$27$	−4.82610	−	2.78635i	−0.928784	−	0.536233i
$28$	1.56406	+	1.86397i	0.295579	+	0.352257i
$29$	3.50388	−	2.02297i	0.650654	−	0.375655i	−0.138053	−	0.990425i	$-0.544084\pi$
$29$	3.50388	−	2.02297i	0.650654	−	0.375655i	0.788707	+	0.614770i	$0.210751\pi$
$30$	2.28034	+	1.69601i	0.416332	+	0.309647i
$31$		−	3.83883i		−	0.689475i	−0.938699	−	0.344738i	$-0.887968\pi$
$31$		−	3.83883i		−	0.689475i	0.938699	−	0.344738i	$-0.112032\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−0.881119	+	1.05008i	−0.153383	+	0.182795i
$34$	3.71685	−	1.35282i	0.637435	−	0.232007i
$35$	−3.95583	+	3.73560i	−0.668657	+	0.631432i
$36$	1.38472			0.230787
$37$	5.80362	+	1.82155i	0.954109	+	0.299460i
$37$	5.80362	+	1.82155i	0.954109	+	0.299460i
$38$		−	0.698678i		−	0.113341i
$39$	2.55512	−	7.02012i	0.409146	−	1.12412i
$40$	−2.22107	−	0.258560i	−0.351182	−	0.0408819i
$41$	−4.58982	−	3.85131i	−0.716809	−	0.601474i	0.209691	−	0.977768i	$-0.432754\pi$
$41$	−4.58982	−	3.85131i	−0.716809	−	0.601474i	−0.926501	+	0.376293i	$0.877199\pi$
$42$	0.537006	−	3.04551i	0.0828619	−	0.469933i
$43$	−2.24316			−0.342078			−0.171039	−	0.985264i	$-0.554712\pi$
$43$	−2.24316			−0.342078			−0.171039	+	0.985264i	$0.554712\pi$
$44$	0.187290	−	1.06217i	0.0282350	−	0.160128i
$45$	0.181471	+	3.09100i	0.0270521	+	0.460780i
$46$	−6.92999	+	5.81496i	−1.02177	+	0.857368i
$47$	−6.62640	−	3.82576i	−0.966560	−	0.558044i	−0.0683744	−	0.997660i	$-0.521781\pi$
$47$	−6.62640	−	3.82576i	−0.966560	−	0.558044i	−0.898186	+	0.439616i	$0.855115\pi$
$48$	1.10066	−	0.635469i	0.158867	−	0.0917220i
$49$	−1.01425	−	0.369155i	−0.144892	−	0.0527365i
$50$	0.286087	−	4.99181i	0.0404588	−	0.705948i
$51$	−4.35356	−	2.51353i	−0.609620	−	0.351964i
$52$	1.02072	+	5.78877i	0.141548	+	0.802758i
$53$	−7.71511	+	1.36038i	−1.05975	+	0.186863i	−0.676246	−	0.736676i	$-0.736394\pi$
$53$	−7.71511	+	1.36038i	−1.05975	+	0.186863i	−0.383506	+	0.923539i	$0.625283\pi$
$54$	−3.58206	−	4.26894i	−0.487457	−	0.580929i
$55$	2.39555	+	0.278872i	0.323016	+	0.0376031i
$56$	0.832217	+	2.28650i	0.111210	+	0.305546i
$57$	−0.680229	+	0.570780i	−0.0900985	+	0.0756016i
$58$	3.98447	−	0.702569i	0.523186	−	0.0922518i
$59$	−8.83478	+	1.55781i	−1.15019	+	0.202810i	−0.716059	−	0.698040i	$-0.754056\pi$
$59$	−8.83478	+	1.55781i	−1.15019	+	0.202810i	−0.434132	+	0.900850i	$0.642945\pi$
$60$	1.56275	+	2.37365i	0.201751	+	0.306437i
$61$	−7.74469	+	9.22977i	−0.991606	+	1.18175i	−0.00826793	+	0.999966i	$0.502632\pi$
$61$	−7.74469	+	9.22977i	−0.991606	+	1.18175i	−0.983338	+	0.181785i	$0.941813\pi$
$62$	1.31296	−	3.60732i	0.166746	−	0.458131i
$63$	2.91795	−	1.68468i	0.367627	−	0.212249i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−12.7881	+	3.03710i	−1.58616	+	0.376706i
$66$	−1.18713	+	0.685389i	−0.146125	+	0.0843656i
$67$	4.03216	+	0.710979i	0.492607	+	0.0868599i	0.414433	−	0.910080i	$-0.363980\pi$
$67$	4.03216	+	0.710979i	0.492607	+	0.0868599i	0.0781740	+	0.996940i	$0.475091\pi$
$68$	3.95539			0.479662
$69$	11.3228	+	1.99652i	1.36311	+	0.240352i
$70$	−4.99491	+	2.15735i	−0.597006	+	0.257852i
$71$	10.0976	−	3.67522i	1.19836	−	0.436169i	0.335711	−	0.941965i	$-0.391023\pi$
$71$	10.0976	−	3.67522i	1.19836	−	0.436169i	0.862653	+	0.505796i	$0.168801\pi$
$72$	1.30121	+	0.473602i	0.153349	+	0.0558145i
$73$		−	0.0962140i		−	0.0112610i	−0.999984	−	0.00563050i	$-0.998208\pi$
$73$		−	0.0962140i		−	0.0112610i	0.999984	−	0.00563050i	$-0.00179225\pi$
$74$	4.83061	+	3.69665i	0.561547	+	0.429726i
$75$	−5.09371	+	3.79949i	−0.588171	+	0.438727i
$76$	0.238962	−	0.656543i	0.0274108	−	0.0753106i
$77$	−0.897594	−	2.46612i	−0.102290	−	0.281040i
$78$	4.80205	−	5.72286i	0.543725	−	0.647986i
$79$	−0.293157	−	0.0516914i	−0.0329827	−	0.00581574i	0.157132	−	0.987578i	$-0.449775\pi$
$79$	−0.293157	−	0.0516914i	−0.0329827	−	0.00581574i	−0.190115	+	0.981762i	$0.560886\pi$
$80$	−1.99869	−	1.00262i	−0.223460	−	0.112096i
$81$	−0.508511	+	2.88391i	−0.0565012	+	0.320434i
$82$	−2.99579	−	5.18886i	−0.330830	−	0.573014i
$83$	−9.17763	−	10.9375i	−1.00738	−	1.20054i	−0.979606	−	0.200929i	$-0.935604\pi$
$83$	−9.17763	−	10.9375i	−1.00738	−	1.20054i	−0.0277696	−	0.999614i	$-0.508840\pi$
$84$	1.54625	−	2.67818i	0.168709	−	0.292213i
$85$	0.518365	+	8.82932i	0.0562245	+	0.957674i
$86$	−2.10788	−	0.767204i	−0.227298	−	0.0827298i
$87$	−3.93910	−	3.30529i	−0.422315	−	0.354365i
$88$	0.539279	−	0.934058i	0.0574873	−	0.0995709i
$89$	12.0788	−	2.12982i	1.28035	−	0.225761i	0.508223	−	0.861226i	$-0.330303\pi$
$89$	12.0788	−	2.12982i	1.28035	−	0.225761i	0.772130	+	0.635465i	$0.219192\pi$
$90$	−0.886658	+	2.96666i	−0.0934620	+	0.312713i
$91$	9.19364	+	10.9566i	0.963755	+	1.14856i
$92$	−8.50090	+	3.09407i	−0.886280	+	0.322579i
$93$	−4.58468	+	1.66869i	−0.475409	+	0.173035i
$94$	−4.91830	−	5.86140i	−0.507284	−	0.604557i
$95$	1.49687	+	0.447375i	0.153575	+	0.0458997i
$96$	1.25163	−	0.220696i	0.127744	−	0.0225247i
$97$	−2.60024	+	4.50374i	−0.264014	+	0.457286i	−0.967305	−	0.253616i	$-0.918380\pi$
$97$	−2.60024	+	4.50374i	−0.264014	+	0.457286i	0.703291	+	0.710902i	$0.251713\pi$
$98$	−0.826821	−	0.693785i	−0.0835215	−	0.0700829i
$99$	−1.40343	−	0.510807i	−0.141050	−	0.0513380i
$100$	1.97613	−	4.59292i	0.197613	−	0.459292i
$101$	−8.57976	+	14.8606i	−0.853718	+	1.47868i	0.0241116	+	0.999709i	$0.492324\pi$
$101$	−8.57976	+	14.8606i	−0.853718	+	1.47868i	−0.877829	+	0.478973i	$0.841009\pi$
$102$	−3.23133	−	3.85095i	−0.319949	−	0.381300i
$103$	−6.45081	−	11.1731i	−0.635618	−	1.10092i	−0.986384	−	0.164459i	$-0.947412\pi$
$103$	−6.45081	−	11.1731i	−0.635618	−	1.10092i	0.350766	−	0.936463i	$-0.385921\pi$
$104$	−1.02072	+	5.78877i	−0.100089	+	0.567636i
$105$	6.18094	+	3.10059i	0.603198	+	0.302587i
$106$	−7.71511	−	1.36038i	−0.749358	−	0.132132i
$107$	0.771918	−	0.919936i	0.0746241	−	0.0889336i	−0.727441	−	0.686171i	$-0.759290\pi$
$107$	0.771918	−	0.919936i	0.0746241	−	0.0889336i	0.802065	+	0.597237i	$0.203735\pi$
$108$	−1.90598	−	5.23663i	−0.183403	−	0.503895i
$109$	4.13045	−	11.3483i	0.395625	−	1.08697i	−0.568768	−	0.822498i	$-0.692580\pi$
$109$	4.13045	−	11.3483i	0.395625	−	1.08697i	0.964393	−	0.264473i	$-0.0851979\pi$
$110$	2.15570	+	1.08138i	0.205538	+	0.103106i
$111$	−0.347298	−	7.72300i	−0.0329641	−	0.733035i
$112$			2.43324i			0.229920i
$113$	1.55367	+	0.565491i	0.146157	+	0.0531970i	0.414063	−	0.910248i	$-0.364109\pi$
$113$	1.55367	+	0.565491i	0.146157	+	0.0531970i	−0.267906	+	0.963445i	$0.586332\pi$
$114$	−0.834424	+	0.303706i	−0.0781510	+	0.0284446i
$115$	−8.02073	−	18.5704i	−0.747937	−	1.73170i
$116$	3.98447	+	0.702569i	0.369948	+	0.0652319i
$117$	8.13948			0.752495
$118$	−8.83478	−	1.55781i	−0.813307	−	0.143408i
$119$	8.33499	−	4.81221i	0.764067	−	0.441135i
$120$	0.656672	+	2.76499i	0.0599457	+	0.252408i
$121$	4.91836	−	8.51884i	0.447123	−	0.774440i
$122$	−10.4344	+	6.02430i	−0.944686	+	0.545415i
$123$	−2.60446	+	7.15569i	−0.234836	+	0.645207i
$124$	2.46756	−	2.94072i	0.221593	−	0.264084i
$125$	10.5114	+	3.80926i	0.940168	+	0.340710i
$126$	3.31817	−	0.585082i	0.295606	−	0.0521233i
$127$	4.26508	−	0.752049i	0.378465	−	0.0667336i	0.0188202	−	0.999823i	$-0.494009\pi$
$127$	4.26508	−	0.752049i	0.378465	−	0.0667336i	0.359645	+	0.933089i	$0.382898\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	0.975068	+	2.67898i	0.0858500	+	0.235871i
$130$	−13.0556	−	1.51983i	−1.14505	−	0.133298i
$131$	−3.04658	−	3.63077i	−0.266181	−	0.317222i	0.616354	−	0.787469i	$-0.288609\pi$
$131$	−3.04658	−	3.63077i	−0.266181	−	0.317222i	−0.882535	+	0.470247i	$0.844165\pi$
$132$	−1.34995	+	0.238033i	−0.117498	+	0.0207181i
$133$	−0.295211	−	1.67422i	−0.0255980	−	0.145174i
$134$	3.54582	+	2.04718i	0.306312	+	0.176850i
$135$	11.4395	−	4.94084i	0.984559	−	0.425240i
$136$	3.71685	+	1.35282i	0.318717	+	0.116004i
$137$	18.1348	−	10.4701i	1.54936	−	0.894522i	0.551166	−	0.834395i	$-0.314183\pi$
$137$	18.1348	−	10.4701i	1.54936	−	0.894522i	0.998191	−	0.0601265i	$-0.0191504\pi$
$138$	9.95712	+	5.74874i	0.847606	+	0.489366i
$139$	5.79033	−	4.85866i	0.491129	−	0.412107i	−0.363301	−	0.931672i	$-0.618350\pi$
$139$	5.79033	−	4.85866i	0.491129	−	0.412107i	0.854431	+	0.519565i	$0.173906\pi$
$140$	−5.43154	+	0.318883i	−0.459049	+	0.0269505i
$141$	−1.68866	+	9.57685i	−0.142211	+	0.806516i
$142$	10.7456			0.901754
$143$	1.10090	−	6.24352i	0.0920620	−	0.522110i
$144$	1.06076	+	0.890080i	0.0883964	+	0.0741734i
$145$	−1.04612	+	8.98629i	−0.0868752	+	0.746271i
$146$	0.0329071	−	0.0904115i	0.00272341	−	0.00748251i
$147$			1.37177i			0.113142i
$148$	3.27496	+	5.12588i	0.269200	+	0.421345i
$149$	−6.24076			−0.511263			−0.255632	−	0.966774i	$-0.582283\pi$
$149$	−6.24076			−0.511263			−0.255632	+	0.966774i	$0.582283\pi$
$150$	−6.08603	+	1.82820i	−0.496922	+	0.149272i
$151$	−4.73108	+	1.72197i	−0.385010	+	0.140132i	−0.527271	−	0.849697i	$-0.676785\pi$
$151$	−4.73108	+	1.72197i	−0.385010	+	0.140132i	0.142262	+	0.989829i	$0.454563\pi$
$152$	0.449102	−	0.535218i	0.0364270	−	0.0434120i
$153$	0.951089	−	5.39390i	0.0768910	−	0.436071i
$154$		−	2.62439i		−	0.211479i
$155$	6.88772	+	5.12275i	0.553235	+	0.411469i
$156$	6.46978	−	3.73533i	0.517997	−	0.299066i
$157$	2.62863	+	3.13268i	0.209787	+	0.250015i	0.860670	−	0.509164i	$-0.170045\pi$
$157$	2.62863	+	3.13268i	0.209787	+	0.250015i	−0.650882	+	0.759179i	$0.725601\pi$
$158$	−0.257798	−	0.148840i	−0.0205093	−	0.0118410i
$159$	4.97834	+	8.62274i	0.394808	+	0.683828i
$160$	−1.53524	−	1.62574i	−0.121371	−	0.128526i
$161$	−14.1492	+	16.8623i	−1.11511	+	1.32894i
$162$	−1.46420	+	2.53607i	−0.115038	+	0.199252i
$163$	3.46859	+	19.6714i	0.271681	+	1.54078i	0.749310	+	0.662219i	$0.230385\pi$
$163$	3.46859	+	19.6714i	0.271681	+	1.54078i	−0.477629	+	0.878562i	$0.658504\pi$
$164$	−1.04043	−	5.90056i	−0.0812437	−	0.460756i
$165$	−0.708258	−	2.98220i	−0.0551378	−	0.232164i
$166$	−4.88331	−	13.4168i	−0.379019	−	1.04135i
$167$	−8.48472	+	3.08819i	−0.656568	+	0.238971i	−0.648754	−	0.760998i	$-0.724709\pi$
$167$	−8.48472	+	3.08819i	−0.656568	+	0.238971i	−0.00781383	+	0.999969i	$0.502487\pi$
$168$	2.36899	−	1.98782i	0.182772	−	0.153364i
$169$	3.74242	+	21.2243i	0.287878	+	1.63264i
$170$	−2.53270	+	8.47414i	−0.194249	+	0.649937i
$171$	−0.837856	−	0.483736i	−0.0640725	−	0.0369923i
$172$	−1.71836	−	1.44187i	−0.131023	−	0.109942i
$173$	−3.12335	+	8.58134i	−0.237464	+	0.652427i	0.762521	+	0.646964i	$0.223961\pi$
$173$	−3.12335	+	8.58134i	−0.237464	+	0.652427i	−0.999985	+	0.00546385i	$0.998261\pi$
$174$	−2.57106	−	4.45321i	−0.194912	−	0.337597i
$175$	−1.42364	−	12.0826i	−0.107617	−	0.913361i
$176$	0.826223	−	0.693283i	0.0622789	−	0.0522582i
$177$	5.70083	+	9.87413i	0.428501	+	0.742185i
$178$	12.0788	+	2.12982i	0.905346	+	0.159637i
$179$		−	12.3400i		−	0.922337i	−0.887313	−	0.461168i	$-0.847430\pi$
$179$		−	12.3400i		−	0.922337i	0.887313	−	0.461168i	$-0.152570\pi$
$180$	−1.84784	+	2.48449i	−0.137730	+	0.185183i
$181$	−2.90277	−	2.43572i	−0.215761	−	0.181045i	0.528501	−	0.848933i	$-0.322754\pi$
$181$	−2.90277	−	2.43572i	−0.215761	−	0.181045i	−0.744262	+	0.667887i	$0.767199\pi$
$182$	4.89183	+	13.4402i	0.362607	+	0.996254i
$183$	14.3895	+	5.23736i	1.06370	+	0.387157i
$184$	−9.04647			−0.666914
$185$	−11.0129	+	7.98221i	−0.809686	+	0.586864i
$186$	−4.87892			−0.357740
$187$	−4.00884	−	1.45910i	−0.293155	−	0.106700i
$188$	−2.61697	−	7.19007i	−0.190862	−	0.524390i
$189$	−10.3874	−	8.71602i	−0.755569	−	0.633997i
$190$	1.25358	+	0.932354i	0.0909445	+	0.0676401i
$191$		−	23.6507i		−	1.71131i	−0.517550	−	0.855653i	$-0.673156\pi$
$191$		−	23.6507i		−	1.71131i	0.517550	−	0.855653i	$-0.326844\pi$
$192$	1.25163	+	0.220696i	0.0903285	+	0.0159274i
$193$	−6.57365	−	11.3859i	−0.473182	−	0.819575i	0.526347	−	0.850270i	$-0.323561\pi$
$193$	−6.57365	−	11.3859i	−0.473182	−	0.819575i	−0.999529	+	0.0306947i	$0.990228\pi$
$194$	−3.98379	+	3.34280i	−0.286020	+	0.239999i
$195$	9.18598	+	13.9525i	0.657821	+	0.999158i
$196$	−0.539669	−	0.934734i	−0.0385478	−	0.0667667i
$197$	−9.19070	+	25.2513i	−0.654811	+	1.79908i	−0.0556470	+	0.998451i	$0.517722\pi$
$197$	−9.19070	+	25.2513i	−0.654811	+	1.79908i	−0.599164	+	0.800627i	$0.704500\pi$
$198$	−1.14409	−	0.960003i	−0.0813067	−	0.0682244i
$199$	8.84155	+	5.10467i	0.626761	+	0.361860i	0.779496	−	0.626407i	$-0.215475\pi$
$199$	8.84155	+	5.10467i	0.626761	+	0.361860i	−0.152736	+	0.988267i	$0.548808\pi$
$200$	3.42783	−	3.64005i	0.242384	−	0.257391i
$201$	−0.903609	−	5.12462i	−0.0637357	−	0.361463i
$202$	−13.1450	+	11.0299i	−0.924876	+	0.776063i
$203$	9.25102	−	3.36710i	0.649294	−	0.236324i
$204$	−1.71935	−	4.72388i	−0.120379	−	0.330738i
$205$	13.0350	−	3.09575i	0.910405	−	0.216217i
$206$	−2.24034	−	12.7056i	−0.156092	−	0.885243i
$207$	2.17526	+	12.3365i	0.151191	+	0.857446i
$208$	−2.93904	+	5.09056i	−0.203785	+	0.352967i
$209$	−0.484382	+	0.577264i	−0.0335054	+	0.0399302i
$210$	4.74772	+	5.02761i	0.327624	+	0.346938i
$211$	13.0360	+	22.5790i	0.897435	+	1.55440i	0.830762	+	0.556629i	$0.187905\pi$
$211$	13.0360	+	22.5790i	0.897435	+	1.55440i	0.0666737	+	0.997775i	$0.478761\pi$
$212$	−6.78455	−	3.91706i	−0.465965	−	0.269025i
$213$	−8.77857	−	10.4619i	−0.601497	−	0.716837i
$214$	1.04000	−	0.600446i	0.0710931	−	0.0410456i
$215$	2.99339	−	4.02472i	0.204147	−	0.274484i
$216$		−	5.57270i		−	0.379174i
$217$	1.62201	−	9.19890i	0.110110	−	0.624462i
$218$	7.76270	−	9.25122i	0.525756	−	0.626572i
$219$	−0.114907	+	0.0418229i	−0.00776472	+	0.00282613i
$220$	1.65584	+	1.75346i	0.111637	+	0.118218i
$221$	23.2501			1.56397
$222$	2.31507	−	7.37603i	0.155377	−	0.495047i
$223$		−	1.64685i		−	0.110282i	−0.998479	−	0.0551408i	$-0.982439\pi$
$223$		−	1.64685i		−	0.110282i	0.998479	−	0.0551408i	$-0.0175608\pi$
$224$	−0.832217	+	2.28650i	−0.0556049	+	0.152773i
$225$	−5.78811	−	3.79920i	−0.385874	−	0.253280i
$226$	1.26657	+	1.06278i	0.0842508	+	0.0706948i
$227$	−3.25682	+	18.4704i	−0.216163	+	1.22592i	0.662714	+	0.748873i	$0.269404\pi$
$227$	−3.25682	+	18.4704i	−0.216163	+	1.22592i	−0.878877	+	0.477048i	$0.841707\pi$
$228$	−0.887976			−0.0588076
$229$	1.58566	−	8.99274i	0.104784	−	0.594257i	−0.886523	−	0.462684i	$-0.846886\pi$
$229$	1.58566	−	8.99274i	0.104784	−	0.594257i	0.991307	−	0.131572i	$-0.0420026\pi$
$230$	−1.18556	−	20.1937i	−0.0781737	−	1.33154i
$231$	−2.55509	+	2.14398i	−0.168113	+	0.141063i
$232$	3.50388	+	2.02297i	0.230041	+	0.132814i
$233$	−6.71498	+	3.87690i	−0.439913	+	0.253984i	−0.703561	−	0.710635i	$-0.748408\pi$
$233$	−6.71498	+	3.87690i	−0.439913	+	0.253984i	0.263648	+	0.964619i	$0.415074\pi$
$234$	7.64861	+	2.78387i	0.500005	+	0.181987i
$235$	15.7069	−	6.78394i	1.02460	−	0.442536i
$236$	−7.76917	−	4.48554i	−0.505730	−	0.291983i
$237$	0.0656965	+	0.372584i	0.00426745	+	0.0242019i
$238$	9.47820	−	1.67126i	0.614381	−	0.108332i
$239$	−1.16301	−	1.38602i	−0.0752288	−	0.0896542i	0.727117	−	0.686513i	$-0.240860\pi$
$239$	−1.16301	−	1.38602i	−0.0752288	−	0.0896542i	−0.802346	+	0.596859i	$0.796415\pi$
$240$	−0.328613	+	2.82284i	−0.0212119	+	0.182213i
$241$	−1.67662	−	4.60646i	−0.108000	−	0.296728i	0.873906	−	0.486094i	$-0.161579\pi$
$241$	−1.67662	−	4.60646i	−0.108000	−	0.296728i	−0.981907	+	0.189366i	$0.939357\pi$
$242$	7.53536	−	6.32292i	0.484391	−	0.406453i
$243$	−12.7989	+	2.25678i	−0.821047	+	0.144773i
$244$	−11.8656	+	2.09222i	−0.759615	+	0.133941i
$245$	2.01581	−	1.32716i	0.128785	−	0.0847892i
$246$	−4.89478	+	5.83337i	−0.312080	+	0.371922i
$247$	1.40464	−	3.85920i	0.0893748	−	0.245555i
$248$	3.32453	−	1.91942i	0.211108	−	0.121883i
$249$	−9.07313	+	15.7151i	−0.574986	+	0.995905i
$250$	8.57464	+	7.17464i	0.542308	+	0.453764i
$251$	9.87930	−	5.70382i	0.623576	−	0.360022i	−0.154684	−	0.987964i	$-0.549436\pi$
$251$	9.87930	−	5.70382i	0.623576	−	0.360022i	0.778260	+	0.627942i	$0.216103\pi$
$252$	3.31817	+	0.585082i	0.209025	+	0.0368567i
$253$	9.75713			0.613426
$254$	4.26508	+	0.752049i	0.267615	+	0.0471878i
$255$	10.3194	−	4.45706i	0.646229	−	0.279112i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−17.5936	−	6.40353i	−1.09746	−	0.399441i	−0.271078	−	0.962557i	$-0.587380\pi$
$257$	−17.5936	−	6.40353i	−1.09746	−	0.399441i	−0.826378	+	0.563116i	$0.809602\pi$
$258$			2.85091i			0.177490i
$259$	13.1374	+	6.81711i	0.816319	+	0.423595i
$260$	−11.7484	−	5.89346i	−0.728607	−	0.365497i
$261$	1.91616	−	5.26461i	0.118607	−	0.325871i
$262$	−1.62105	−	4.45380i	−0.100149	−	0.275157i
$263$	−14.0217	+	16.7104i	−0.864616	+	1.03041i	0.134603	+	0.990900i	$0.457024\pi$
$263$	−14.0217	+	16.7104i	−0.864616	+	1.03041i	−0.999219	+	0.0395099i	$0.987420\pi$
$264$	−1.34995	−	0.238033i	−0.0830839	−	0.0146499i
$265$	7.85463	−	15.6580i	0.482506	−	0.961862i
$266$	0.295211	−	1.67422i	0.0181005	−	0.102653i
$267$	−7.79412	−	13.4998i	−0.476992	−	0.826175i
$268$	2.63181	+	3.13646i	0.160763	+	0.191590i
$269$	−6.13693	+	10.6295i	−0.374175	+	0.648090i	−0.990203	−	0.139634i	$-0.955407\pi$
$269$	−6.13693	+	10.6295i	−0.374175	+	0.648090i	0.616028	+	0.787724i	$0.288741\pi$
$270$	12.4395	−	0.730317i	0.757045	−	0.0444457i
$271$	−4.11051	−	1.49610i	−0.249695	−	0.0908817i	0.214140	−	0.976803i	$-0.431305\pi$
$271$	−4.11051	−	1.49610i	−0.249695	−	0.0908817i	−0.463836	+	0.885921i	$0.653527\pi$
$272$	3.03001	+	2.54248i	0.183721	+	0.154160i
$273$	9.08896	−	15.7425i	0.550089	−	0.952782i
$274$	20.6221	−	3.63623i	1.24583	−	0.219673i
$275$	−3.69711	+	3.92601i	−0.222944	+	0.236747i
$276$	7.39044	+	8.80759i	0.444852	+	0.530154i
$277$	20.3075	−	7.39133i	1.22016	−	0.444102i	0.349943	−	0.936771i	$-0.386201\pi$
$277$	20.3075	−	7.39133i	1.22016	−	0.444102i	0.870217	+	0.492669i	$0.163979\pi$
$278$	7.10289	−	2.58524i	0.426003	−	0.155052i
$279$	−3.41687	−	4.07207i	−0.204563	−	0.243788i
$280$	−5.21304	−	1.55804i	−0.311539	−	0.0931110i
$281$	19.2899	−	3.40133i	1.15074	−	0.202906i	0.434440	−	0.900701i	$-0.356946\pi$
$281$	19.2899	−	3.40133i	1.15074	−	0.202906i	0.716298	+	0.697794i	$0.245835\pi$
$282$	−4.86229	+	8.42174i	−0.289545	+	0.501507i
$283$	−2.71956	−	2.28199i	−0.161661	−	0.135650i	0.558369	−	0.829593i	$-0.311428\pi$
$283$	−2.71956	−	2.28199i	−0.161661	−	0.135650i	−0.720030	+	0.693943i	$0.755872\pi$
$284$	10.0976	+	3.67522i	0.599182	+	0.218084i
$285$	−0.116372	−	1.98216i	−0.00689326	−	0.117413i
$286$	3.16992	−	5.49046i	0.187441	−	0.324658i
$287$	−9.37118	−	11.1681i	−0.553163	−	0.659234i
$288$	0.692360	+	1.19920i	0.0407977	+	0.0706637i
$289$	−0.235273	+	1.33430i	−0.0138396	+	0.0784882i
$290$	−4.05652	+	8.08656i	−0.238207	+	0.474859i
$291$	6.50906	+	1.14772i	0.381568	+	0.0672807i
$292$	0.0618451	−	0.0737042i	0.00361921	−	0.00431321i
$293$	6.51994	+	17.9134i	0.380899	+	1.04651i	0.970979	+	0.239166i	$0.0768741\pi$
$293$	6.51994	+	17.9134i	0.380899	+	1.04651i	−0.590080	+	0.807345i	$0.700904\pi$
$294$	−0.469173	+	1.28904i	−0.0273627	+	0.0751785i
$295$	8.99455	−	17.9304i	0.523683	−	1.04395i
$296$	1.32430	+	5.93685i	0.0769736	+	0.345073i
$297$			6.01048i			0.348763i
$298$	−5.86440	−	2.13447i	−0.339715	−	0.123646i
$299$	−49.9689	+	18.1872i	−2.88977	+	1.05179i
$300$	−6.34427	−	0.363598i	−0.366287	−	0.0209924i
$301$	−5.37522	−	0.947796i	−0.309822	−	0.0546300i
$302$	−5.03471			−0.289715
$303$	21.4773	+	3.78703i	1.23384	+	0.217559i
$304$	0.605073	−	0.349339i	0.0347033	−	0.0200360i
$305$	−6.22531	−	26.2124i	−0.356460	−	1.50092i
$306$	2.73855	−	4.74331i	0.156553	−	0.271157i
$307$	−1.85530	+	1.07116i	−0.105888	+	0.0611342i	−0.552009	−	0.833838i	$-0.686138\pi$
$307$	−1.85530	+	1.07116i	−0.105888	+	0.0611342i	0.446121	+	0.894973i	$0.352805\pi$
$308$	0.897594	−	2.46612i	0.0511452	−	0.140520i
$309$	−10.5399	+	12.5610i	−0.599593	+	0.714568i
$310$	4.72026	+	7.16955i	0.268093	+	0.407203i
$311$	0.577196	−	0.101775i	0.0327298	−	0.00577114i	−0.157259	−	0.987557i	$-0.550266\pi$
$311$	0.577196	−	0.101775i	0.0327298	−	0.00577114i	0.189989	+	0.981786i	$0.439155\pi$
$312$	7.35716	−	1.29727i	0.416517	−	0.0734432i
$313$	−16.0499	+	13.4675i	−0.907193	+	0.761226i	−0.971583	−	0.236699i	$-0.923934\pi$
$313$	−16.0499	+	13.4675i	−0.907193	+	0.761226i	0.0643896	+	0.997925i	$0.479490\pi$
$314$	1.39866	+	3.84280i	0.0789312	+	0.216862i
$315$	−0.871180	+	7.48357i	−0.0490855	+	0.421651i
$316$	−0.191344	−	0.228035i	−0.0107640	−	0.0128280i
$317$	10.6354	−	1.87531i	0.597345	−	0.105328i	0.133203	−	0.991089i	$-0.457474\pi$
$317$	10.6354	−	1.87531i	0.597345	−	0.105328i	0.464142	+	0.885761i	$0.346363\pi$
$318$	1.72896	+	9.80542i	0.0969552	+	0.549860i
$319$	−3.77914	−	2.18189i	−0.211591	−	0.122162i
$320$	−0.886615	−	2.05278i	−0.0495633	−	0.114754i
$321$	−1.43421	−	0.522011i	−0.0800499	−	0.0291358i
$322$	−19.0632	+	11.0061i	−1.06235	+	0.613347i
$323$	−2.39330	−	1.38177i	−0.133167	−	0.0768839i
$324$	−2.24328	+	1.88234i	−0.124627	+	0.104574i
$325$	11.6159	−	26.9975i	0.644331	−	1.49755i
$326$	−3.46859	+	19.6714i	−0.192108	+	1.08950i
$327$	−15.3486			−0.848781
$328$	1.04043	−	5.90056i	0.0574480	−	0.325804i
$329$	−14.2622	−	11.9674i	−0.786300	−	0.659784i
$330$	0.354428	−	3.04459i	0.0195106	−	0.167599i
$331$	−7.94257	+	21.8220i	−0.436563	+	1.19945i	0.505150	+	0.863031i	$0.331437\pi$
$331$	−7.94257	+	21.8220i	−0.436563	+	1.19945i	−0.941713	+	0.336416i	$0.890785\pi$
$332$		−	14.2779i		−	0.783599i
$333$	7.77755	−	3.23347i	0.426207	−	0.177193i
$334$	−9.02925			−0.494059
$335$	−6.65639	+	6.28582i	−0.363677	+	0.343431i
$336$	2.90600	−	1.05770i	0.158535	−	0.0577020i
$337$	−4.16895	+	4.96836i	−0.227097	+	0.270644i	−0.867546	−	0.497357i	$-0.834304\pi$
$337$	−4.16895	+	4.96836i	−0.227097	+	0.270644i	0.640449	+	0.768001i	$0.278748\pi$
$338$	−3.74242	+	21.2243i	−0.203561	+	1.15445i
$339$		−	2.10135i		−	0.114130i
$340$	−5.27829	+	7.09685i	−0.286255	+	0.384881i
$341$	−3.58569	+	2.07020i	−0.194176	+	0.112108i
$342$	−0.621880	−	0.741127i	−0.0336274	−	0.0400756i
$343$	−17.0252	−	9.82949i	−0.919273	−	0.530742i
$344$	−1.12158	−	1.94263i	−0.0604714	−	0.104740i
$345$	−18.6920	+	17.6514i	−1.00634	+	0.950319i
$346$	−5.86998	+	6.99557i	−0.315572	+	0.376084i
$347$	12.4617	−	21.5843i	0.668979	−	1.15871i	−0.309210	−	0.950994i	$-0.600065\pi$
$347$	12.4617	−	21.5843i	0.668979	−	1.15871i	0.978190	−	0.207713i	$-0.0666019\pi$
$348$	−0.892921	−	5.06400i	−0.0478656	−	0.271459i
$349$	−5.21759	−	29.5904i	−0.279291	−	1.58394i	−0.724992	−	0.688758i	$-0.758156\pi$
$349$	−5.21759	−	29.5904i	−0.279291	−	1.58394i	0.445700	−	0.895182i	$-0.352955\pi$
$350$	2.79472	−	11.8409i	0.149384	−	0.632921i
$351$	−11.2035	−	30.7813i	−0.597997	−	1.64298i
$352$	1.01351	−	0.368888i	0.0540204	−	0.0196618i
$353$	−19.6999	+	16.5302i	−1.04852	+	0.879812i	−0.992937	−	0.118642i	$-0.962146\pi$
$353$	−19.6999	+	16.5302i	−1.04852	+	0.879812i	−0.0555825	+	0.998454i	$0.517702\pi$
$354$	1.97988	+	11.2284i	0.105229	+	0.596785i
$355$	−6.88061	+	23.0217i	−0.365185	+	1.22187i
$356$	10.6219	+	6.13258i	0.562962	+	0.325026i
$357$	−9.37028	−	7.86260i	−0.495928	−	0.416133i
$358$	4.22054	−	11.5958i	0.223062	−	0.612859i
$359$	−4.65048	−	8.05487i	−0.245443	−	0.425120i	0.716813	−	0.697265i	$-0.245600\pi$
$359$	−4.65048	−	8.05487i	−0.245443	−	0.425120i	−0.962256	+	0.272146i	$0.912267\pi$
$360$	−2.58615	+	1.70266i	−0.136302	+	0.0897381i
$361$	14.1809	−	11.8992i	0.746363	−	0.626273i
$362$	−1.89465	−	3.28163i	−0.0995806	−	0.172479i
$363$	−12.3119	−	2.17092i	−0.646208	−	0.113944i
$364$			14.3028i			0.749669i
$365$	0.172629	+	0.128393i	0.00903583	+	0.00672040i
$366$	11.7305	+	9.84302i	0.613160	+	0.514503i
$367$	−8.25956	−	22.6929i	−0.431145	−	1.18456i	−0.945110	−	0.326751i	$-0.894046\pi$
$367$	−8.25956	−	22.6929i	−0.431145	−	1.18456i	0.513965	−	0.857811i	$-0.328176\pi$
$368$	−8.50090	−	3.09407i	−0.443140	−	0.161290i
$369$	−8.29666			−0.431907
$370$	−13.0788	+	3.73418i	−0.679936	+	0.194131i
$371$	−19.0623			−0.989666
$372$	−4.58468	−	1.66869i	−0.237705	−	0.0865174i
$373$	−4.80248	−	13.1947i	−0.248663	−	0.683196i	−0.999736	−	0.0229766i	$-0.992686\pi$
$373$	−4.80248	−	13.1947i	−0.248663	−	0.683196i	0.751073	−	0.660219i	$-0.229537\pi$
$374$	−3.26803	−	2.74221i	−0.168986	−	0.141796i
$375$	−0.0198010	−	14.2095i	−0.00102252	−	0.733775i
$376$		−	7.65151i		−	0.394597i
$377$	23.4210	+	4.12975i	1.20624	+	0.212693i
$378$	−6.77986	−	11.7431i	−0.348719	−	0.603998i
$379$	−7.22523	+	6.06268i	−0.371135	+	0.311419i	−0.809210	−	0.587519i	$-0.800105\pi$
$379$	−7.22523	+	6.06268i	−0.371135	+	0.311419i	0.438075	+	0.898938i	$0.355660\pi$
$380$	0.859100	+	1.30488i	0.0440709	+	0.0669388i
$381$	−2.75214	−	4.76684i	−0.140996	−	0.244213i
$382$	8.08902	−	22.2244i	0.413870	−	1.13710i
$383$	7.32984	+	6.15047i	0.374538	+	0.314274i	0.810553	−	0.585665i	$-0.199166\pi$
$383$	7.32984	+	6.15047i	0.374538	+	0.314274i	−0.436016	+	0.899939i	$0.643611\pi$
$384$	1.10066	+	0.635469i	0.0561680	+	0.0324286i
$385$	5.62257	+	1.68044i	0.286552	+	0.0856432i
$386$	−2.28301	−	12.9476i	−0.116202	−	0.659014i
$387$	−2.37944	+	1.99659i	−0.120954	+	0.101492i
$388$	−4.88685	+	1.77867i	−0.248092	+	0.0902981i
$389$	3.01354	+	8.27964i	0.152793	+	0.419794i	0.992347	−	0.123481i	$-0.0394060\pi$
$389$	3.01354	+	8.27964i	0.152793	+	0.419794i	−0.839554	+	0.543276i	$0.817184\pi$
$390$	3.85997	+	16.2528i	0.195457	+	0.822994i
$391$	6.21353	+	35.2387i	0.314232	+	1.78210i
$392$	−0.187425	−	1.06294i	−0.00946640	−	0.0536866i
$393$	−3.01189	+	5.21675i	−0.151930	+	0.263150i
$394$	−17.2729	+	20.5850i	−0.870195	+	1.03706i
$395$	0.483950	−	0.457008i	0.0243502	−	0.0229946i
$396$	−0.746750	−	1.29341i	−0.0375256	−	0.0649962i
$397$	12.8990	+	7.44724i	0.647382	+	0.373766i	0.787453	−	0.616375i	$-0.211400\pi$
$397$	12.8990	+	7.44724i	0.647382	+	0.373766i	−0.140070	+	0.990142i	$0.544733\pi$
$398$	6.56244	+	7.82081i	0.328945	+	0.392022i
$399$	−1.87119	+	1.08033i	−0.0936765	+	0.0540841i
$400$	4.46608	−	2.24815i	0.223304	−	0.112407i
$401$			7.58921i			0.378987i	0.981882	+	0.189494i	$0.0606846\pi$
$401$			7.58921i			0.378987i	−0.981882	+	0.189494i	$0.939315\pi$
$402$	0.903609	−	5.12462i	0.0450679	−	0.255593i
$403$	14.5045	−	17.2858i	0.722519	−	0.861065i
$404$	−16.1247	+	5.86890i	−0.802232	+	0.291989i
$405$	−4.49579	−	4.76082i	−0.223397	−	0.236567i
$406$	9.84473			0.488586
$407$	−1.42834	−	6.40324i	−0.0708001	−	0.317397i
$408$		−	5.02705i		−	0.248876i
$409$	−4.25236	+	11.6833i	−0.210266	+	0.577701i	−0.999330	−	0.0366107i	$-0.988344\pi$
$409$	−4.25236	+	11.6833i	−0.210266	+	0.577701i	0.789064	+	0.614311i	$0.210566\pi$
$410$	13.3077	+	1.54918i	0.657221	+	0.0765087i
$411$	−20.3873	−	17.1070i	−1.00563	−	0.843824i
$412$	2.24034	−	12.7056i	0.110374	−	0.625961i
$413$	−21.8288			−1.07412
$414$	−2.17526	+	12.3365i	−0.106908	+	0.606306i
$415$	31.8714	−	1.87115i	1.56450	−	0.0918512i
$416$	−4.50286	+	3.77835i	−0.220771	+	0.185249i
$417$	−8.31963	−	4.80334i	−0.407414	−	0.235221i
$418$	−0.652606	+	0.376782i	−0.0319200	+	0.0184290i
$419$	−0.492147	−	0.179127i	−0.0240430	−	0.00875092i	0.329971	−	0.943991i	$-0.392961\pi$
$419$	−0.492147	−	0.179127i	−0.0240430	−	0.00875092i	−0.354014	+	0.935240i	$0.615183\pi$
$420$	2.74185	+	6.34822i	0.133789	+	0.309761i
$421$	−13.6218	−	7.86458i	−0.663888	−	0.383296i	0.129869	−	0.991531i	$-0.458544\pi$
$421$	−13.6218	−	7.86458i	−0.663888	−	0.383296i	−0.793757	+	0.608235i	$0.791878\pi$
$422$	4.52736	+	25.6759i	0.220388	+	1.24988i
$423$	−10.4342	+	1.83984i	−0.507330	+	0.0894559i
$424$	−5.03568	−	6.00129i	−0.244554	−	0.291448i
$425$	−16.5335	−	10.8523i	−0.801992	−	0.526412i
$426$	−4.67098	−	12.8334i	−0.226310	−	0.621781i
$427$	−22.4582	+	18.8447i	−1.08683	+	0.911959i
$428$	1.18265	−	0.208533i	0.0571654	−	0.0100798i
$429$	−7.93512	+	1.39918i	−0.383111	+	0.0675529i
$430$	4.18940	−	2.75820i	0.202031	−	0.133012i
$431$	1.75090	−	2.08664i	0.0843380	−	0.100510i	−0.722225	−	0.691658i	$-0.756881\pi$
$431$	1.75090	−	2.08664i	0.0843380	−	0.100510i	0.806563	+	0.591148i	$0.201325\pi$
$432$	1.90598	−	5.23663i	0.0917013	−	0.251947i
$433$	17.1961	−	9.92816i	0.826391	−	0.477117i	−0.0262243	−	0.999656i	$-0.508348\pi$
$433$	17.1961	−	9.92816i	0.826391	−	0.477117i	0.852615	+	0.522539i	$0.175015\pi$
$434$	4.67041	−	8.08938i	0.224187	−	0.388303i
$435$	11.1870	−	2.65685i	0.536374	−	0.127386i
$436$	10.4587	−	6.03831i	0.500879	−	0.289183i
$437$	6.22454	+	1.09755i	0.297760	+	0.0525032i
$438$	−0.122282			−0.00584285
$439$	27.5270	+	4.85376i	1.31379	+	0.231657i	0.786270	−	0.617883i	$-0.212010\pi$
$439$	27.5270	+	4.85376i	1.31379	+	0.231657i	0.527524	+	0.849540i	$0.323121\pi$
$440$	0.956265	+	2.21404i	0.0455882	+	0.105550i
$441$	−1.40445	+	0.511176i	−0.0668784	+	0.0243417i
$442$	21.8479	+	7.95199i	1.03920	+	0.378238i
$443$			22.8450i			1.08540i	0.839927	+	0.542699i	$0.182598\pi$
$443$			22.8450i			1.08540i	−0.839927	+	0.542699i	$0.817402\pi$
$444$	4.69821	−	6.13940i	0.222967	−	0.291363i
$445$	−12.2973	+	24.5142i	−0.582946	+	1.16209i
$446$	0.563257	−	1.54754i	0.0266710	−	0.0732780i
$447$	2.71277	+	7.45328i	0.128310	+	0.352528i
$448$	−1.56406	+	1.86397i	−0.0738948	+	0.0880643i
$449$	12.4686	+	2.19856i	0.588431	+	0.103756i	0.459933	−	0.887953i	$-0.347873\pi$
$449$	12.4686	+	2.19856i	0.588431	+	0.103756i	0.128498	+	0.991710i	$0.458984\pi$
$450$	−4.13964	−	5.54973i	−0.195145	−	0.261617i
$451$	−1.12216	+	6.36409i	−0.0528405	+	0.299673i
$452$	0.826693	+	1.43187i	0.0388844	+	0.0673497i
$453$	4.11307	+	4.90176i	0.193249	+	0.230305i
$454$	−9.37765	+	16.2426i	−0.440115	+	0.762301i
$455$	−31.9270	+	1.87442i	−1.49676	+	0.0878740i
$456$	−0.834424	−	0.303706i	−0.0390755	−	0.0142223i
$457$	15.2111	+	12.7636i	0.711546	+	0.597058i	0.925033	−	0.379888i	$-0.124037\pi$
$457$	15.2111	+	12.7636i	0.711546	+	0.597058i	−0.213486	+	0.976946i	$0.568482\pi$
$458$	4.56573	−	7.90808i	0.213343	−	0.369520i
$459$	−21.7073	+	3.82759i	−1.01321	+	0.178657i
$460$	5.79260	−	19.3814i	0.270081	−	0.903662i
$461$	−6.98381	−	8.32299i	−0.325269	−	0.387640i	0.578485	−	0.815693i	$-0.303644\pi$
$461$	−6.98381	−	8.32299i	−0.325269	−	0.387640i	−0.903754	+	0.428053i	$0.859200\pi$
$462$	−3.13428	+	1.14079i	−0.145820	+	0.0530742i
$463$	5.62872	−	2.04869i	0.261589	−	0.0952105i	−0.207897	−	0.978151i	$-0.566662\pi$
$463$	5.62872	−	2.04869i	0.261589	−	0.0952105i	0.469485	+	0.882940i	$0.344440\pi$
$464$	2.60068	+	3.09936i	0.120733	+	0.143884i
$465$	3.12405	−	10.4527i	0.144874	−	0.484734i
$466$	−7.63600	+	1.34643i	−0.353731	+	0.0623723i
$467$	18.0030	−	31.1820i	0.833078	−	1.44293i	−0.0625080	−	0.998044i	$-0.519910\pi$
$467$	18.0030	−	31.1820i	0.833078	−	1.44293i	0.895586	−	0.444889i	$-0.146757\pi$
$468$	6.23520	+	5.23196i	0.288222	+	0.241847i
$469$	9.36176	+	3.40740i	0.432286	+	0.157339i
$470$	17.0799	−	1.00275i	0.787837	−	0.0462535i
$471$	2.59870	−	4.50108i	0.119742	−	0.207399i
$472$	−5.76649	−	6.87224i	−0.265424	−	0.316320i
$473$	1.20969	+	2.09524i	0.0556214	+	0.0963391i
$474$	−0.0656965	+	0.372584i	−0.00301754	+	0.0171133i
$475$	−2.80019	+	2.08871i	−0.128482	+	0.0958366i
$476$	9.47820	+	1.67126i	0.434433	+	0.0766022i
$477$	−6.97300	+	8.31010i	−0.319272	+	0.380493i
$478$	−0.618825	−	1.70021i	−0.0283044	−	0.0777656i
$479$	−13.3126	+	36.5762i	−0.608270	+	1.67121i	0.125734	+	0.992064i	$0.459871\pi$
$479$	−13.3126	+	36.5762i	−0.608270	+	1.67121i	−0.734004	+	0.679145i	$0.762351\pi$
$480$	−1.27426	+	2.54021i	−0.0581619	+	0.115944i
$481$	19.2505	+	30.1303i	0.877745	+	1.37382i
$482$		−	4.90209i		−	0.223284i
$483$	26.2890	+	9.56841i	1.19619	+	0.435378i
$484$	9.24349	−	3.36435i	0.420159	−	0.152925i
$485$	−4.61082	−	10.6754i	−0.209366	−	0.484747i
$486$	−12.7989	−	2.25678i	−0.580568	−	0.102370i
$487$	−26.1658			−1.18569			−0.592843	−	0.805318i	$-0.701995\pi$
$487$	−26.1658			−1.18569			−0.592843	+	0.805318i	$0.701995\pi$
$488$	−11.8656	−	2.09222i	−0.537129	−	0.0947103i
$489$	21.9856	−	12.6934i	0.994222	−	0.574014i
$490$	2.34816	−	0.557676i	0.106079	−	0.0251932i
$491$	16.7368	−	28.9889i	0.755320	−	1.30825i	−0.189896	−	0.981804i	$-0.560815\pi$
$491$	16.7368	−	28.9889i	0.755320	−	1.30825i	0.945215	−	0.326448i	$-0.105852\pi$
$492$	−6.59472	+	3.80746i	−0.297313	+	0.171654i
$493$	5.47343	−	15.0381i	0.246511	−	0.677283i
$494$	2.63985	−	3.14605i	0.118773	−	0.141548i
$495$	2.78931	−	1.83642i	0.125370	−	0.0825408i
$496$	3.78051	−	0.666607i	0.169750	−	0.0299315i
$497$	25.7495	−	4.54033i	1.15502	−	0.203662i
$498$	−13.9008	+	11.6642i	−0.622911	+	0.522685i
$499$	1.88387	+	5.17590i	0.0843337	+	0.231705i	0.974691	−	0.223558i	$-0.0717673\pi$
$499$	1.88387	+	5.17590i	0.0843337	+	0.231705i	−0.890357	+	0.455263i	$0.849545\pi$
$500$	5.60366	+	9.67466i	0.250603	+	0.432664i
$501$	7.37638	+	8.79083i	0.329552	+	0.392745i
$502$	11.2343	−	1.98091i	0.501413	−	0.0884126i
$503$	4.59324	+	26.0496i	0.204803	+	1.16149i	0.897750	+	0.440505i	$0.145201\pi$
$503$	4.59324	+	26.0496i	0.204803	+	1.16149i	−0.692948	+	0.720988i	$0.743688\pi$
$504$	2.91795	+	1.68468i	0.129976	+	0.0750415i
$505$	−15.2139	−	35.2247i	−0.677009	−	1.56748i
$506$	9.16871	+	3.33714i	0.407599	+	0.148354i
$507$	23.7212	−	13.6954i	1.05350	−	0.608236i
$508$	3.75065	+	2.16544i	0.166408	+	0.0960759i
$509$	6.42650	−	5.39247i	0.284849	−	0.239017i	−0.489156	−	0.872197i	$-0.662695\pi$
$509$	6.42650	−	5.39247i	0.284849	−	0.239017i	0.774005	+	0.633179i	$0.218251\pi$
$510$	11.2215	−	0.658809i	0.496897	−	0.0291725i
$511$	0.0406531	−	0.230555i	0.00179839	−	0.0101992i
$512$	−1.00000			−0.0441942
$513$	−0.676103	+	3.83437i	−0.0298507	+	0.169292i
$514$	−14.3424	−	12.0347i	−0.632616	−	0.530828i
$515$	28.6554	+	3.33584i	1.26271	+	0.146995i
$516$	−0.975068	+	2.67898i	−0.0429250	+	0.117935i
$517$			8.25260i			0.362949i
$518$	10.0135	+	10.8992i	0.439969	+	0.478885i
$519$	11.6063			0.509460
$520$	−9.02424	−	9.55624i	−0.395739	−	0.419069i
$521$	31.0040	−	11.2845i	1.35831	−	0.494384i	0.442778	−	0.896631i	$-0.353993\pi$
$521$	31.0040	−	11.2845i	1.35831	−	0.494384i	0.915531	+	0.402247i	$0.131771\pi$
$522$	3.60120	−	4.29175i	0.157620	−	0.187845i
$523$	6.17373	−	35.0130i	0.269958	−	1.53101i	−0.484576	−	0.874749i	$-0.661026\pi$
$523$	6.17373	−	35.0130i	0.269958	−	1.53101i	0.754534	−	0.656260i	$-0.227863\pi$
$524$		−	4.73964i		−	0.207052i
$525$	−13.8113	+	6.95238i	−0.602776	+	0.303427i
$526$	−18.8914	+	10.9070i	−0.823705	+	0.475566i
$527$	−9.76015	−	11.6317i	−0.425159	−	0.506684i
$528$	−1.18713	−	0.685389i	−0.0516632	−	0.0298277i
$529$	−29.4193	−	50.9557i	−1.27910	−	2.21546i
$530$	12.7363	−	12.0273i	0.553229	−	0.522430i
$531$	−7.98497	+	9.51612i	−0.346518	+	0.412964i
$532$	0.850026	−	1.47229i	0.0368533	−	0.0638318i
$533$	−6.11571	−	34.6839i	−0.264901	−	1.50233i
$534$	−2.70687	−	15.3514i	−0.117138	−	0.664321i
$535$	0.620481	+	2.61260i	0.0268257	+	0.112953i
$536$	1.40035	+	3.84744i	0.0604861	+	0.166184i
$537$	−14.7376	+	5.36404i	−0.635973	+	0.231475i
$538$	−9.40232	+	7.88948i	−0.405363	+	0.340140i
$539$	0.202149	+	1.14644i	0.00870716	+	0.0493808i
$540$	11.9391	+	3.56829i	0.513777	+	0.153555i
$541$	−1.77881	−	1.02700i	−0.0764771	−	0.0441541i	0.461274	−	0.887258i	$-0.347393\pi$
$541$	−1.77881	−	1.02700i	−0.0764771	−	0.0441541i	−0.537751	+	0.843104i	$0.680726\pi$
$542$	−3.35091	−	2.81175i	−0.143934	−	0.120775i
$543$	−1.64716	+	4.52553i	−0.0706863	+	0.194209i
$544$	1.97770	+	3.42547i	0.0847930	+	0.146866i
$545$	14.8495	+	22.5547i	0.636082	+	0.966139i
$546$	13.9251	−	11.6845i	0.595939	−	0.500052i
$547$	3.63042	+	6.28808i	0.155226	+	0.268859i	0.933141	−	0.359510i	$-0.117056\pi$
$547$	3.63042	+	6.28808i	0.155226	+	0.268859i	−0.777915	+	0.628369i	$0.783723\pi$
$548$	20.6221	+	3.63623i	0.880932	+	0.155332i
$549$			16.6839i			0.712053i
$550$	−4.81692	+	2.42475i	−0.205394	+	0.103392i
$551$	−2.16546	−	1.81703i	−0.0922516	−	0.0774083i
$552$	3.93237	+	10.8041i	0.167373	+	0.459853i
$553$	−0.680643	−	0.247734i	−0.0289439	−	0.0105347i
$554$	21.6108			0.918155
$555$	14.3202	+	9.68286i	0.607860	+	0.411015i
$556$	7.55874			0.320562
$557$	1.82309	+	0.663551i	0.0772469	+	0.0281156i	0.380355	−	0.924841i	$-0.375802\pi$
$557$	1.82309	+	0.663551i	0.0772469	+	0.0281156i	−0.303108	+	0.952956i	$0.598024\pi$
$558$	−1.81808	−	4.99513i	−0.0769654	−	0.211461i
$559$	−10.1006	−	8.47543i	−0.427211	−	0.358473i
$560$	−4.36577	−	3.24705i	−0.184488	−	0.137213i
$561$			5.42197i			0.228916i
$562$	19.2899	+	3.40133i	0.813695	+	0.143476i
$563$	14.2773	+	24.7290i	0.601717	+	1.04220i	0.992561	+	0.121747i	$0.0388496\pi$
$563$	14.2773	+	24.7290i	0.601717	+	1.04220i	−0.390845	+	0.920457i	$0.627817\pi$
$564$	−7.44947	+	6.25085i	−0.313679	+	0.263208i
$565$	−3.08792	+	2.03302i	−0.129910	+	0.0855296i
$566$	−1.77507	−	3.07451i	−0.0746118	−	0.129231i
$567$	−2.43706	+	6.69577i	−0.102347	+	0.281196i
$568$	8.23163	+	6.90716i	0.345392	+	0.289818i
$569$	33.9187	+	19.5830i	1.42195	+	0.820962i	0.996465	−	0.0840054i	$-0.0267713\pi$
$569$	33.9187	+	19.5830i	1.42195	+	0.820962i	0.425482	+	0.904967i	$0.360105\pi$
$570$	0.568586	−	1.90242i	0.0238154	−	0.0796838i
$571$	3.28921	+	18.6540i	0.137649	+	0.780648i	0.972978	+	0.230897i	$0.0741661\pi$
$571$	3.28921	+	18.6540i	0.137649	+	0.780648i	−0.835329	+	0.549750i	$0.814723\pi$
$572$	4.85660	−	4.07517i	0.203065	−	0.170391i
$573$	−28.2458	+	10.2806i	−1.17999	+	0.429480i
$574$	−4.98630	−	13.6997i	−0.208124	−	0.571816i
$575$	44.0228	+	10.3904i	1.83588	+	0.433310i
$576$	0.240454	+	1.36368i	0.0100189	+	0.0568201i
$577$	5.10497	+	28.9517i	0.212523	+	1.20528i	0.885154	+	0.465298i	$0.154053\pi$
$577$	5.10497	+	28.9517i	0.212523	+	1.20528i	−0.672631	+	0.739978i	$0.734836\pi$
$578$	−0.677441	+	1.17336i	−0.0281778	+	0.0488055i
$579$	−10.7406	+	12.8001i	−0.446364	+	0.531956i
$580$	−6.57765	+	6.21147i	−0.273122	+	0.257917i
$581$	−17.3707	−	30.0870i	−0.720659	−	1.24822i
$582$	5.72397	+	3.30474i	0.237266	+	0.136986i
$583$	5.43127	+	6.47273i	0.224940	+	0.268073i
$584$	0.0833237	−	0.0481070i	0.00344796	−	0.00199068i
$585$	−10.8618	+	14.6040i	−0.449078	+	0.603802i
$586$			19.0630i			0.787487i
$587$	−3.29520	+	18.6880i	−0.136008	+	0.771337i	0.838145	+	0.545447i	$0.183640\pi$
$587$	−3.29520	+	18.6880i	−0.136008	+	0.771337i	−0.974153	+	0.225890i	$0.927471\pi$
$588$	−0.881757	+	1.05084i	−0.0363631	+	0.0433358i
$589$	−2.52036	+	0.917336i	−0.103850	+	0.0377982i
$590$	14.5847	−	13.7727i	0.600441	−	0.567014i
$591$	34.1524			1.40484
$592$	−0.786084	+	6.03176i	−0.0323079	+	0.247904i
$593$		−	11.8449i		−	0.486413i	−0.969975	−	0.243206i	$-0.921801\pi$
$593$		−	11.8449i		−	0.486413i	0.969975	−	0.243206i	$-0.0781992\pi$
$594$	−2.05570	+	5.64800i	−0.0843466	+	0.231740i
$595$	−2.48849	+	21.3765i	−0.102018	+	0.876351i
$596$	−4.78070	−	4.01148i	−0.195825	−	0.164317i
$597$	2.25316	−	12.7783i	0.0922157	−	0.522981i
$598$	−53.1758			−2.17452
$599$	−1.74991	+	9.92421i	−0.0714992	+	0.405492i	0.927962	+	0.372674i	$0.121559\pi$
$599$	−1.74991	+	9.92421i	−0.0714992	+	0.405492i	−0.999461	+	0.0328177i	$0.989552\pi$
$600$	−5.83731	−	2.51154i	−0.238307	−	0.102533i
$601$	−8.15176	+	6.84014i	−0.332517	+	0.279015i	−0.793725	−	0.608277i	$-0.791861\pi$
$601$	−8.15176	+	6.84014i	−0.332517	+	0.279015i	0.461207	+	0.887292i	$0.347416\pi$
$602$	−4.72689	−	2.72907i	−0.192654	−	0.111229i
$603$	4.90997	−	2.83477i	0.199949	−	0.115441i
$604$	−4.73108	−	1.72197i	−0.192505	−	0.0700660i
$605$	8.72138	+	20.1926i	0.354574	+	0.820947i
$606$	18.8869	+	10.9043i	0.767226	+	0.442958i
$607$	−2.82902	−	16.0442i	−0.114826	−	0.651213i	−0.986836	−	0.161724i	$-0.948295\pi$
$607$	−2.82902	−	16.0442i	−0.114826	−	0.651213i	0.872010	−	0.489489i	$-0.162817\pi$
$608$	0.688064	−	0.121324i	0.0279047	−	0.00492035i
$609$	−8.04258	−	9.58477i	−0.325902	−	0.388395i
$610$	3.11529	−	26.7608i	0.126134	−	1.08351i
$611$	−15.3827	−	42.2637i	−0.622319	−	1.70981i
$612$	4.19571	−	3.52062i	0.169601	−	0.142312i
$613$	−24.0338	+	4.23782i	−0.970718	+	0.171164i	−0.636453	−	0.771315i	$-0.719599\pi$
$613$	−24.0338	+	4.23782i	−0.970718	+	0.171164i	−0.334265	+	0.942479i	$0.608488\pi$
$614$	−2.10977	+	0.372009i	−0.0851433	+	0.0150131i
$615$	−9.36336	−	14.2219i	−0.377567	−	0.573483i
$616$	1.68693	−	2.01040i	0.0679682	−	0.0810013i
$617$	1.12580	−	3.09312i	0.0453232	−	0.124524i	−0.914966	−	0.403531i	$-0.867783\pi$
$617$	1.12580	−	3.09312i	0.0453232	−	0.124524i	0.960289	+	0.279006i	$0.0900051\pi$
$618$	−14.2004	+	8.19858i	−0.571222	+	0.329795i
$619$	−11.1508	+	19.3137i	−0.448188	+	0.776285i	−0.998268	−	0.0588271i	$-0.981264\pi$
$619$	−11.1508	+	19.3137i	−0.448188	+	0.776285i	0.550080	+	0.835112i	$0.314597\pi$
$620$	1.98346	+	8.35160i	0.0796578	+	0.335408i
$621$	43.6592	−	25.2066i	1.75198	−	1.01151i
$622$	0.577196	+	0.101775i	0.0231434	+	0.00408081i
$623$	29.8441			1.19568
$624$	7.35716	+	1.29727i	0.294522	+	0.0519322i
$625$	−20.8616	+	13.7765i	−0.834465	+	0.551060i
$626$	−19.6881	+	7.16588i	−0.786895	+	0.286406i
$627$	0.899975	+	0.327564i	0.0359415	+	0.0130816i
$628$			4.08942i			0.163186i
$629$	22.2162	−	9.23627i	0.885819	−	0.368274i
$630$	−3.37817	+	6.73429i	−0.134590	+	0.268301i
$631$	−3.80487	+	10.4538i	−0.151470	+	0.416159i	−0.992100	−	0.125450i	$-0.959963\pi$
$631$	−3.80487	+	10.4538i	−0.151470	+	0.416159i	0.840630	+	0.541609i	$0.182185\pi$
$632$	−0.101812	−	0.279727i	−0.00404987	−	0.0111269i
$633$	21.2993	−	25.3835i	0.846572	−	1.00891i
$634$	10.6354	+	1.87531i	0.422387	+	0.0744782i
$635$	−4.34221	+	8.65608i	−0.172316	+	0.343506i
$636$	−1.72896	+	9.80542i	−0.0685577	+	0.388810i
$637$	−3.17221	−	5.49443i	−0.125688	−	0.217697i
$638$	−2.80498	−	3.34284i	−0.111050	−	0.132344i
$639$	7.43984	−	12.8862i	0.294316	−	0.509770i
$640$	−0.131053	−	2.23222i	−0.00518031	−	0.0882364i
$641$	−40.8165	−	14.8560i	−1.61215	−	0.586776i	−0.630290	−	0.776360i	$-0.717064\pi$
$641$	−40.8165	−	14.8560i	−1.61215	−	0.586776i	−0.981865	+	0.189583i	$0.939286\pi$
$642$	−1.16918	−	0.981059i	−0.0461439	−	0.0387193i
$643$	1.59851	−	2.76871i	0.0630393	−	0.109187i	−0.832783	−	0.553599i	$-0.813254\pi$
$643$	1.59851	−	2.76871i	0.0630393	−	0.109187i	0.895823	+	0.444412i	$0.146587\pi$
$644$	−21.6778	+	3.82238i	−0.854226	+	0.150623i
$645$	−6.10787	−	1.82548i	−0.240497	−	0.0718784i
$646$	−1.77637	−	2.11700i	−0.0698904	−	0.0832922i
$647$	3.93506	−	1.43225i	0.154703	−	0.0563074i	−0.263508	−	0.964657i	$-0.584879\pi$
$647$	3.93506	−	1.43225i	0.154703	−	0.0563074i	0.418211	+	0.908350i	$0.362657\pi$
$648$	−2.75179	+	1.00157i	−0.108101	+	0.0393454i
$649$	6.21949	+	7.41210i	0.244136	+	0.290951i
$650$	20.1490	−	21.3965i	0.790310	−	0.839240i
$651$	−11.6912	+	2.06148i	−0.458215	+	0.0807957i
$652$	−9.98742	+	17.2987i	−0.391137	+	0.677470i
$653$	28.4766	+	23.8947i	1.11438	+	0.935073i	0.998307	−	0.0581681i	$-0.0185259\pi$
$653$	28.4766	+	23.8947i	1.11438	+	0.935073i	0.116070	+	0.993241i	$0.462970\pi$
$654$	−14.4230	−	5.24954i	−0.563983	−	0.205273i
$655$	10.5799	−	0.621142i	0.413392	−	0.0242700i
$656$	2.99579	−	5.18886i	0.116966	−	0.202591i
$657$	−0.0856381	−	0.102060i	−0.00334106	−	0.00398172i
$658$	−9.30899	−	16.1236i	−0.362902	−	0.628565i
$659$	−6.47563	+	36.7251i	−0.252255	+	1.43061i	0.550767	+	0.834659i	$0.314335\pi$
$659$	−6.47563	+	36.7251i	−0.252255	+	1.43061i	−0.803022	+	0.595949i	$0.796776\pi$
$660$	1.37437	−	2.73976i	0.0534971	−	0.106645i
$661$	8.09644	+	1.42762i	0.314915	+	0.0555280i	0.328872	−	0.944375i	$-0.393332\pi$
$661$	8.09644	+	1.42762i	0.314915	+	0.0555280i	−0.0139567	+	0.999903i	$0.504443\pi$
$662$	−14.9272	+	17.7895i	−0.580160	+	0.691408i
$663$	−10.1065	−	27.7673i	−0.392503	−	1.07839i
$664$	4.88331	−	13.4168i	0.189509	−	0.520673i
$665$	3.39788	+	1.70450i	0.131764	+	0.0660977i
$666$	8.41441	−	0.378390i	0.326052	−	0.0146623i
$667$			36.6014i			1.41721i
$668$	−8.48472	−	3.08819i	−0.328284	−	0.119486i
$669$	−1.96682	+	0.715865i	−0.0760417	+	0.0276769i
$670$	−8.40484	+	3.63012i	−0.324707	+	0.140244i
$671$	12.7977	+	2.25658i	0.494049	+	0.0871142i
$672$	3.09250			0.119296
$673$	29.8649	+	5.26598i	1.15121	+	0.202989i	0.716502	−	0.697585i	$-0.245742\pi$
$673$	29.8649	+	5.26598i	1.15121	+	0.202989i	0.434704	+	0.900573i	$0.356853\pi$
$674$	−5.61681	+	3.24287i	−0.216351	+	0.124911i
$675$	−6.40058	+	27.1184i	−0.246358	+	1.04379i
$676$	−10.7759	+	18.6643i	−0.414456	+	0.717859i
$677$	24.9696	−	14.4162i	0.959659	−	0.554059i	0.0635907	−	0.997976i	$-0.479745\pi$
$677$	24.9696	−	14.4162i	0.959659	−	0.554059i	0.896068	+	0.443917i	$0.146411\pi$
$678$	0.718704	−	1.97462i	0.0276017	−	0.0758349i
$679$	−8.13384	+	9.69353i	−0.312148	+	0.372004i
$680$	−7.38723	+	4.86358i	−0.283287	+	0.186510i
$681$	23.4747	−	4.13922i	0.899551	−	0.158615i
$682$	−4.07750	+	0.718974i	−0.156136	+	0.0275309i
$683$	28.1200	−	23.5955i	1.07598	−	0.902857i	0.0804015	−	0.996763i	$-0.474380\pi$
$683$	28.1200	−	23.5955i	1.07598	−	0.902857i	0.995581	+	0.0939060i	$0.0299353\pi$
$684$	−0.330895	−	0.909127i	−0.0126521	−	0.0347613i
$685$	−5.41430	+	46.5097i	−0.206870	+	1.77704i
$686$	−12.6365	−	15.0596i	−0.482466	−	0.574980i
$687$	−11.4292	+	2.01528i	−0.436051	+	0.0768876i
$688$	−0.389520	−	2.20908i	−0.0148503	−	0.0842203i
$689$	−39.8801	−	23.0248i	−1.51931	−	0.877174i
$690$	−23.6018	+	10.1938i	−0.898507	+	0.388073i
$691$	4.44315	+	1.61717i	0.169025	+	0.0615202i	0.425147	−	0.905124i	$-0.360222\pi$
$691$	4.44315	+	1.61717i	0.169025	+	0.0615202i	−0.256121	+	0.966645i	$0.582445\pi$
$692$	−7.90861	+	4.56604i	−0.300640	+	0.173575i
$693$	−3.14717	−	1.81702i	−0.119551	−	0.0690229i
$694$	19.0924	−	16.0205i	0.724739	−	0.608128i
$695$	0.990593	+	16.8728i	0.0375753	+	0.640022i
$696$	0.892921	−	5.06400i	0.0338461	−	0.191951i
$697$	−23.6991			−0.897666
$698$	5.21759	−	29.5904i	0.197489	−	1.12001i
$699$	7.54905	+	6.33440i	0.285531	+	0.239589i
$700$	6.67599	−	10.1709i	0.252329	−	0.384425i
$701$	−7.86506	+	21.6091i	−0.297059	+	0.816163i	0.697929	+	0.716167i	$0.254105\pi$
$701$	−7.86506	+	21.6091i	−0.297059	+	0.816163i	−0.994988	+	0.0999960i	$0.968117\pi$
$702$		−	32.7567i		−	1.23632i
$703$	−0.190922	−	4.24560i	−0.00720075	−	0.160126i
$704$	1.07856			0.0406497
$705$	−14.9296	−	15.8097i	−0.562280	−	0.595427i
$706$	−24.1655	+	8.79552i	−0.909481	+	0.331024i
$707$	−26.8385	+	31.9848i	−1.00936	+	1.20291i
$708$	−1.97988	+	11.2284i	−0.0744084	+	0.421991i
$709$		−	31.7787i		−	1.19347i	−0.802437	−	0.596737i	$-0.796464\pi$
$709$		−	31.7787i		−	1.19347i	0.802437	−	0.596737i	$-0.203536\pi$
$710$	−14.3396	+	19.2801i	−0.538154	+	0.723568i
$711$	−0.356977	+	0.206101i	−0.0133877	+	0.00772939i
$712$	7.88389	+	9.39566i	0.295461	+	0.352117i
$713$	30.0752	+	17.3639i	1.12633	+	0.650285i
$714$	−6.11602	−	10.5932i	−0.228886	−	0.396442i
$715$	9.73316	+	10.3070i	0.364000	+	0.385458i
$716$	7.93202	−	9.45301i	0.296433	−	0.353276i
$717$	−1.14977	+	1.99146i	−0.0429388	+	0.0743723i
$718$	−1.61509	−	9.15966i	−0.0602748	−	0.341835i
$719$	−5.05214	−	28.6521i	−0.188413	−	1.06854i	−0.921491	−	0.388399i	$-0.873028\pi$
$719$	−5.05214	−	28.6521i	−0.188413	−	1.06854i	0.733078	−	0.680144i	$-0.238083\pi$
$720$	−3.01253	+	0.715461i	−0.112270	+	0.0266637i
$721$	−10.7370	−	29.4996i	−0.399865	−	1.09862i
$722$	17.3954	−	6.33143i	0.647392	−	0.235631i
$723$	−4.77265	+	4.00473i	−0.177497	+	0.148938i
$724$	−0.658005	−	3.73173i	−0.0244546	−	0.138689i
$725$	−14.7274	−	13.8688i	−0.546962	−	0.515073i
$726$	−10.8269	−	6.25092i	−0.401824	−	0.231993i
$727$	13.2103	+	11.0847i	0.489942	+	0.411110i	0.854006	−	0.520264i	$-0.174166\pi$
$727$	13.2103	+	11.0847i	0.489942	+	0.411110i	−0.364063	+	0.931374i	$0.618611\pi$
$728$	−4.89183	+	13.4402i	−0.181303	+	0.498127i
$729$	12.6513	+	21.9128i	0.468568	+	0.811583i
$730$	0.118305	+	0.179693i	0.00437868	+	0.00665073i
$731$	−6.79677	+	5.70317i	−0.251388	+	0.210939i
$732$	7.65651	+	13.2615i	0.282993	+	0.490158i
$733$	−13.3168	−	2.34812i	−0.491869	−	0.0867298i	−0.0777881	−	0.996970i	$-0.524786\pi$
$733$	−13.3168	−	2.34812i	−0.491869	−	0.0867298i	−0.414081	+	0.910240i	$0.635897\pi$
$734$		−	24.1493i		−	0.891368i
$735$	−2.46126	−	1.83056i	−0.0907850	−	0.0675214i
$736$	−6.92999	−	5.81496i	−0.255443	−	0.214342i
$737$	−1.51036	−	4.14969i	−0.0556349	−	0.152856i
$738$	−7.79631	−	2.83762i	−0.286986	−	0.104454i
$739$	35.1115			1.29160			0.645798	−	0.763508i	$-0.276525\pi$
$739$	35.1115			1.29160			0.645798	+	0.763508i	$0.276525\pi$
$740$	−13.5672	−	0.964239i	−0.498742	−	0.0354461i
$741$	−5.21959			−0.191746
$742$	−17.9127	−	6.51970i	−0.657597	−	0.239346i
$743$	−8.07319	−	22.1809i	−0.296177	−	0.813739i	−0.995130	−	0.0985716i	$-0.968573\pi$
$743$	−8.07319	−	22.1809i	−0.296177	−	0.813739i	0.698953	−	0.715167i	$-0.253650\pi$
$744$	−3.73747	−	3.13611i	−0.137022	−	0.114975i
$745$	8.32801	−	11.1973i	0.305115	−	0.410238i
$746$		−	14.0415i		−	0.514096i
$747$	−19.4705	−	3.43317i	−0.712387	−	0.125613i
$748$	−2.13306	−	3.69457i	−0.0779923	−	0.135087i
$749$	2.23843	−	1.87826i	0.0817903	−	0.0686302i
$750$	4.84133	−	13.3593i	0.176780	−	0.487814i
$751$	22.7321	+	39.3732i	0.829506	+	1.43675i	0.898426	+	0.439125i	$0.144711\pi$
$751$	22.7321	+	39.3732i	0.829506	+	1.43675i	−0.0689201	+	0.997622i	$0.521955\pi$
$752$	2.61697	−	7.19007i	0.0954311	−	0.262195i
$753$	−11.1064	−	9.31938i	−0.404740	−	0.339617i
$754$	20.5961	+	11.8911i	0.750064	+	0.433050i
$755$	3.22381	−	10.7865i	0.117326	−	0.392561i
$756$	−2.35462	−	13.3537i	−0.0856368	−	0.485670i
$757$	26.5103	−	22.2448i	0.963533	−	0.808500i	−0.0179911	−	0.999838i	$-0.505727\pi$
$757$	26.5103	−	22.2448i	0.963533	−	0.808500i	0.981524	+	0.191338i	$0.0612826\pi$
$758$	−8.86305	+	3.22589i	−0.321921	+	0.117169i
$759$	−4.24129	−	11.6528i	−0.153949	−	0.422972i
$760$	0.360995	+	1.52001i	0.0130947	+	0.0551366i
$761$	2.82580	+	16.0259i	0.102435	+	0.580938i	0.992214	+	0.124546i	$0.0397474\pi$
$761$	2.82580	+	16.0259i	0.102435	+	0.580938i	−0.889779	+	0.456392i	$0.849141\pi$
$762$	−0.955807	−	5.42065i	−0.0346252	−	0.196370i
$763$	14.6927	−	25.4484i	0.531910	−	0.921295i
$764$	15.2024	−	18.1175i	0.550003	−	0.655468i
$765$	8.40866	+	8.90437i	0.304016	+	0.321938i
$766$	4.78422	+	8.28650i	0.172861	+	0.299404i
$767$	−45.6678	−	26.3663i	−1.64897	−	0.952032i
$768$	0.816943	+	0.973594i	0.0294789	+	0.0351316i
$769$	0.136772	−	0.0789652i	0.00493212	−	0.00284756i	−0.497532	−	0.867446i	$-0.665760\pi$
$769$	0.136772	−	0.0789652i	0.00493212	−	0.00284756i	0.502464	+	0.864598i	$0.332427\pi$
$770$	4.70874	+	3.50213i	0.169691	+	0.126208i
$771$			23.7953i			0.856968i
$772$	2.28301	−	12.9476i	0.0821672	−	0.465993i
$773$	21.2518	−	25.3269i	0.764373	−	0.910944i	−0.233743	−	0.972298i	$-0.575098\pi$
$773$	21.2518	−	25.3269i	0.764373	−	0.910944i	0.998116	+	0.0613543i	$0.0195419\pi$
$774$	−2.91882	+	1.06236i	−0.104915	+	0.0381858i
$775$	−18.3827	+	5.52203i	−0.660326	+	0.198357i
$776$	−5.20047			−0.186686
$777$	2.43096	−	18.6532i	0.0872103	−	0.669179i
$778$			8.81101i			0.315890i
$779$	−1.43176	+	3.93373i	−0.0512981	+	0.140940i
$780$	−1.93161	+	16.5928i	−0.0691629	+	0.594119i
$781$	−8.87829	−	7.44977i	−0.317690	−	0.266574i
$782$	−6.21353	+	35.2387i	−0.222195	+	1.26013i
$783$	−22.5468			−0.805756
$784$	0.187425	−	1.06294i	0.00669375	−	0.0379622i
$785$	−9.12850	+	0.535929i	−0.325810	+	0.0191281i
$786$	−4.61448	+	3.87201i	−0.164593	+	0.138110i
$787$	−24.3543	−	14.0609i	−0.868135	−	0.501218i	−0.00140721	−	0.999999i	$-0.500448\pi$
$787$	−24.3543	−	14.0609i	−0.868135	−	0.501218i	−0.866728	+	0.498781i	$0.833781\pi$
$788$	−23.2717	+	13.4359i	−0.829019	+	0.478634i
$789$	26.0522	+	9.48221i	0.927481	+	0.337576i
$790$	0.611070	−	0.263927i	0.0217409	−	0.00939009i
$791$	3.48410	+	2.01154i	0.123880	+	0.0715223i
$792$	−0.259343	−	1.47081i	−0.00921537	−	0.0522629i
$793$	−69.7466	+	12.2982i	−2.47677	+	0.436722i
$794$	9.57399	+	11.4098i	0.339768	+	0.404920i
$795$	−22.1145	−	2.57440i	−0.784320	−	0.0913045i
$796$	3.49180	+	9.59364i	0.123764	+	0.340038i
$797$	25.8553	−	21.6952i	0.915843	−	0.768484i	−0.0573784	−	0.998353i	$-0.518274\pi$
$797$	25.8553	−	21.6952i	0.915843	−	0.768484i	0.973222	+	0.229869i	$0.0738297\pi$
$798$	−2.12783	+	0.375195i	−0.0753245	+	0.0132817i
$799$	−29.8049	+	5.25541i	−1.05442	+	0.185923i
$800$	4.96565	−	0.585078i	0.175562	−	0.0206856i
$801$	10.9170	−	13.0103i	0.385732	−	0.459698i
$802$	−2.59566	+	7.13153i	−0.0916561	+	0.251823i
$803$	−0.0898694	+	0.0518861i	−0.00317142	+	0.00183102i
$804$	2.60184	−	4.50652i	0.0917598	−	0.158933i
$805$	−11.3734	−	47.8888i	−0.400858	−	1.68786i
$806$	19.5418	−	11.2825i	0.688331	−	0.397408i
$807$	15.3623	+	2.70879i	0.540779	+	0.0953539i
$808$	−17.1595			−0.603670
$809$	11.4101	+	2.01191i	0.401158	+	0.0707350i	0.370587	−	0.928798i	$-0.379156\pi$
$809$	11.4101	+	2.01191i	0.401158	+	0.0707350i	0.0305707	+	0.999533i	$0.490268\pi$
$810$	−2.59636	−	6.01136i	−0.0912268	−	0.211218i
$811$	−41.4889	+	15.1007i	−1.45687	+	0.530259i	−0.944502	−	0.328505i	$-0.893455\pi$
$811$	−41.4889	+	15.1007i	−1.45687	+	0.530259i	−0.512371	+	0.858764i	$0.671233\pi$
$812$	9.25102	+	3.36710i	0.324647	+	0.118162i
$813$			5.55947i			0.194979i
$814$	0.847837	−	6.50559i	0.0297167	−	0.228021i
$815$	−39.9235	−	20.0271i	−1.39846	−	0.701519i
$816$	1.71935	−	4.72388i	0.0601894	−	0.165369i
$817$	0.536029	+	1.47273i	0.0187533	+	0.0515242i
$818$	−7.99183	+	9.52429i	−0.279428	+	0.333009i
$819$	19.5044	+	3.43916i	0.681540	+	0.120174i
$820$	11.9753	+	6.00726i	0.418196	+	0.209783i
$821$	2.50778	−	14.2223i	0.0875221	−	0.496363i	−0.909262	−	0.416225i	$-0.863353\pi$
$821$	2.50778	−	14.2223i	0.0875221	−	0.496363i	0.996784	−	0.0801377i	$-0.0255360\pi$
$822$	−13.3068	−	23.0481i	−0.464130	−	0.803896i
$823$	22.5648	+	26.8917i	0.786560	+	0.937385i	0.999210	−	0.0397429i	$-0.0126539\pi$
$823$	22.5648	+	26.8917i	0.786560	+	0.937385i	−0.212650	+	0.977128i	$0.568209\pi$
$824$	6.45081	−	11.1731i	0.224725	−	0.389235i
$825$	6.29587	+	2.70884i	0.219194	+	0.0943097i
$826$	−20.5123	−	7.46588i	−0.713716	−	0.259771i
$827$	16.1147	+	13.5218i	0.560363	+	0.470200i	0.878432	−	0.477867i	$-0.158590\pi$
$827$	16.1147	+	13.5218i	0.560363	+	0.470200i	−0.318069	+	0.948067i	$0.603034\pi$
$828$	−6.26341	+	10.8485i	−0.217668	+	0.377013i
$829$	−29.8827	+	5.26912i	−1.03787	+	0.183004i	−0.666518	−	0.745489i	$-0.732216\pi$
$829$	−29.8827	+	5.26912i	−1.03787	+	0.183004i	−0.371350	+	0.928493i	$0.621105\pi$
$830$	30.5893	+	9.14234i	1.06177	+	0.317335i
$831$	−17.6548	−	21.0401i	−0.612438	−	0.729875i
$832$	−5.52358	+	2.01042i	−0.191496	+	0.0696987i
$833$	−4.01174	+	1.46015i	−0.138999	+	0.0505913i
$834$	−6.17506	−	7.35915i	−0.213825	−	0.254826i
$835$	5.78158	−	19.3445i	0.200080	−	0.669445i
$836$	−0.742116	+	0.130855i	−0.0256666	+	0.00452572i
$837$	−10.6963	+	18.5266i	−0.369720	+	0.640373i
$838$	−0.401202	−	0.336648i	−0.0138593	−	0.0116293i
$839$	33.6716	+	12.2554i	1.16247	+	0.423105i	0.849980	−	0.526815i	$-0.176614\pi$
$839$	33.6716	+	12.2554i	1.16247	+	0.423105i	0.312492	+	0.949920i	$0.398836\pi$
$840$	0.405280	+	6.90314i	0.0139835	+	0.238181i
$841$	−6.31522	+	10.9383i	−0.217766	+	0.377182i
$842$	−10.1105	−	12.0492i	−0.348431	−	0.415244i
$843$	−12.4472	−	21.5592i	−0.428705	−	0.742539i
$844$	−4.52736	+	25.6759i	−0.155838	+	0.883801i
$845$	−43.0752	−	21.6081i	−1.48183	−	0.743342i
$846$	−10.4342	−	1.83984i	−0.358736	−	0.0632549i
$847$	15.3852	−	18.3353i	0.528641	−	0.630010i
$848$	−2.67943	−	7.36167i	−0.0920120	−	0.252801i
$849$	−1.54320	+	4.23990i	−0.0529624	+	0.145513i
$850$	−11.8247	−	15.8526i	−0.405584	−	0.543739i
$851$	−40.5220	+	37.2290i	−1.38907	+	1.27619i
$852$		−	13.6570i		−	0.467882i
$853$	23.0861	+	8.40265i	0.790453	+	0.287701i	0.705524	−	0.708686i	$-0.250712\pi$
$853$	23.0861	+	8.40265i	0.790453	+	0.287701i	0.0849286	+	0.996387i	$0.472934\pi$
$854$	−27.5491	+	10.0271i	−0.942711	+	0.343119i
$855$	1.98601	−	0.857776i	0.0679201	−	0.0293353i
$856$	1.18265	+	0.208533i	0.0404220	+	0.00712750i
$857$	3.10084			0.105923			0.0529613	−	0.998597i	$-0.483134\pi$
$857$	3.10084			0.105923			0.0529613	+	0.998597i	$0.483134\pi$
$858$	−7.93512	−	1.39918i	−0.270901	−	0.0477671i
$859$	14.4811	−	8.36065i	0.494088	−	0.285262i	−0.232181	−	0.972673i	$-0.574586\pi$
$859$	14.4811	−	8.36065i	0.494088	−	0.285262i	0.726269	+	0.687411i	$0.241253\pi$
$860$	4.88011	−	1.15900i	0.166410	−	0.0395216i
$861$	−9.26447	+	16.0465i	−0.315732	+	0.546865i
$862$	2.35898	−	1.36196i	0.0803473	−	0.0463885i
$863$	−6.31398	+	17.3475i	−0.214930	+	0.590516i	−0.999567	−	0.0294402i	$-0.990628\pi$
$863$	−6.31398	+	17.3475i	−0.214930	+	0.590516i	0.784636	+	0.619956i	$0.212850\pi$
$864$	3.58206	−	4.26894i	0.121864	−	0.145232i
$865$	−11.2289	−	17.0554i	−0.381793	−	0.579901i
$866$	19.5547	−	3.44802i	0.664495	−	0.117168i
$867$	1.69581	−	0.299017i	0.0575927	−	0.0101552i
$868$	7.15548	−	6.00416i	0.242873	−	0.203794i
$869$	0.109810	+	0.301701i	0.00372506	+	0.0102345i
$870$	11.4210	+	1.32955i	0.387209	+	0.0450759i
$871$	15.4699	+	18.4364i	0.524179	+	0.624692i
$872$	11.8931	−	2.09708i	0.402753	−	0.0710162i
$873$	1.25047	+	7.09179i	0.0423222	+	0.240021i
$874$	5.47377	+	3.16028i	0.185153	+	0.106898i
$875$	23.5787	+	13.5694i	0.797105	+	0.458729i
$876$	−0.114907	−	0.0418229i	−0.00388236	−	0.00141306i
$877$	−50.3114	+	29.0473i	−1.69890	+	0.980858i	−0.752086	+	0.659065i	$0.770952\pi$
$877$	−50.3114	+	29.0473i	−1.69890	+	0.980858i	−0.946810	+	0.321794i	$0.895714\pi$
$878$	24.2069	+	13.9758i	0.816942	+	0.471662i
$879$	18.5597	−	15.5734i	0.626002	−	0.525278i
$880$	0.141348	+	2.40758i	0.00476483	+	0.0811596i
$881$	1.10109	−	6.24462i	0.0370968	−	0.210386i	−0.960625	−	0.277848i	$-0.910379\pi$
$881$	1.10109	−	6.24462i	0.0370968	−	0.210386i	0.997722	+	0.0674615i	$0.0214900\pi$
$882$	−1.49458			−0.0503251
$883$	−2.03111	+	11.5190i	−0.0683524	+	0.387646i	0.931370	+	0.364075i	$0.118615\pi$
$883$	−2.03111	+	11.5190i	−0.0683524	+	0.387646i	−0.999722	+	0.0235710i	$0.992496\pi$
$884$	17.8106	+	14.9449i	0.599035	+	0.502650i
$885$	−25.3239	−	2.94801i	−0.851253	−	0.0990964i
$886$	−7.81344	+	21.4673i	−0.262498	+	0.721207i
$887$		−	27.9053i		−	0.936968i	−0.883472	−	0.468484i	$-0.844800\pi$
$887$		−	27.9053i		−	0.936968i	0.883472	−	0.468484i	$-0.155200\pi$
$888$	6.51467	−	4.16227i	0.218618	−	0.139677i
$889$	10.5381			0.353436
$890$	−19.9400	+	18.8299i	−0.668390	+	0.631181i
$891$	2.96797	−	1.08025i	0.0994306	−	0.0361898i
$892$	1.05858	−	1.26156i	0.0354438	−	0.0422403i
$893$	−0.928313	+	5.26473i	−0.0310648	+	0.176177i
$894$			7.93161i			0.265273i
$895$	22.1407	+	16.4672i	0.740084	+	0.550438i
$896$	−2.10725	+	1.21662i	−0.0703982	+	0.0406444i
$897$	43.4416	+	51.7716i	1.45047	+	1.72860i
$898$	10.9647	+	6.33049i	0.365898	+	0.211251i
$899$	−7.76583	−	13.4508i	−0.259005	−	0.448610i
$900$	−1.99187	−	6.63088i	−0.0663957	−	0.221029i
$901$	−19.9181	+	23.7374i	−0.663567	+	0.790809i
$902$	−3.23113	+	5.59649i	−0.107585	+	0.186343i
$903$	1.20459	+	6.83156i	0.0400862	+	0.227340i
$904$	0.287108	+	1.62827i	0.00954905	+	0.0541554i
$905$	8.24383	−	1.95787i	0.274034	−	0.0650818i
$906$	2.18852	+	6.01290i	0.0727086	+	0.199765i
$907$	−22.7578	+	8.28317i	−0.755661	+	0.275038i	−0.690986	−	0.722868i	$-0.742823\pi$
$907$	−22.7578	+	8.28317i	−0.755661	+	0.275038i	−0.0646752	+	0.997906i	$0.520601\pi$
$908$	−14.3674	+	12.0557i	−0.476799	+	0.400082i
$909$	4.12607	+	23.4001i	0.136853	+	0.776133i
$910$	−30.6426	−	9.15830i	−1.01579	−	0.303595i
$911$	25.9838	+	15.0017i	0.860881	+	0.497030i	0.864307	−	0.502964i	$-0.167757\pi$
$911$	25.9838	+	15.0017i	0.860881	+	0.497030i	−0.00342628	+	0.999994i	$0.501091\pi$
$912$	−0.680229	−	0.570780i	−0.0225246	−	0.0189004i
$913$	−5.26693	+	14.4708i	−0.174310	+	0.478913i
$914$	9.92836	+	17.1964i	0.328401	+	0.568807i
$915$	−28.5991	+	18.8290i	−0.945459	+	0.622467i
$916$	6.99511	−	5.86959i	0.231125	−	0.193937i
$917$	−5.76634	−	9.98759i	−0.190421	−	0.329819i
$918$	−21.7073	−	3.82759i	−0.716449	−	0.126329i
$919$		−	50.6212i		−	1.66984i	−0.550372	−	0.834920i	$-0.685514\pi$
$919$		−	50.6212i		−	1.66984i	0.550372	−	0.834920i	$-0.314486\pi$
$920$	12.0721	−	16.2314i	0.398005	−	0.535132i
$921$	2.08575	+	1.75015i	0.0687277	+	0.0576694i
$922$	−3.71601	−	10.2097i	−0.122380	−	0.336237i
$923$	59.3544	+	21.6032i	1.95367	+	0.711079i
$924$	−3.33543			−0.109728
$925$	0.374374	−	30.4115i	0.0123093	−	0.999924i
$926$	5.98996			0.196842
$927$	−16.7877	−	6.11023i	−0.551381	−	0.200686i
$928$	1.38379	+	3.80193i	0.0454251	+	0.124805i
$929$	15.2989	+	12.8373i	0.501941	+	0.421178i	0.858283	−	0.513177i	$-0.171532\pi$
$929$	15.2989	+	12.8373i	0.501941	+	0.421178i	−0.356342	+	0.934356i	$0.615976\pi$
$930$	6.51069	−	8.75386i	0.213494	−	0.287050i
$931$			0.754110i			0.0247150i
$932$	−7.63600	−	1.34643i	−0.250125	−	0.0441039i
$933$	−0.372448	−	0.645099i	−0.0121934	−	0.0211196i
$934$	27.5821	−	23.1442i	0.902515	−	0.757300i
$935$	7.96755	−	5.24565i	0.260567	−	0.171551i
$936$	4.06974	+	7.04900i	0.133024	+	0.230404i
$937$	−7.22742	+	19.8572i	−0.236109	+	0.648705i	0.763885	+	0.645352i	$0.223289\pi$
$937$	−7.22742	+	19.8572i	−0.236109	+	0.648705i	−0.999994	+	0.00335278i	$0.998933\pi$
$938$	7.63177	+	6.40382i	0.249186	+	0.209092i
$939$	23.0607	+	13.3141i	0.752558	+	0.434490i
$940$	16.3928	+	4.89939i	0.534674	+	0.159800i
$941$	−5.59678	−	31.7409i	−0.182450	−	1.03472i	−0.929188	−	0.369606i	$-0.879493\pi$
$941$	−5.59678	−	31.7409i	−0.182450	−	1.03472i	0.746739	−	0.665117i	$-0.231619\pi$
$942$	3.98144	−	3.34082i	0.129722	−	0.108850i
$943$	50.9338	−	18.5384i	1.65863	−	0.603693i
$944$	−3.06829	−	8.43005i	−0.0998642	−	0.274375i
$945$	29.4999	−	7.00609i	0.959633	−	0.227908i
$946$	0.420120	+	2.38262i	0.0136593	+	0.0774655i
$947$	−5.20536	−	29.5210i	−0.169151	−	0.959305i	−0.944680	−	0.327993i	$-0.893628\pi$
$947$	−5.20536	−	29.5210i	−0.169151	−	0.959305i	0.775529	−	0.631312i	$-0.217483\pi$
$948$	−0.189166	+	0.327645i	−0.00614381	+	0.0106414i
$949$	0.363530	−	0.433238i	0.0118007	−	0.0140635i
$950$	−3.34570	+	1.00502i	−0.108549	+	0.0326073i
$951$	−6.86274	−	11.8866i	−0.222540	−	0.385450i
$952$	8.33499	+	4.81221i	0.270139	+	0.155965i
$953$	−24.5483	−	29.2556i	−0.795199	−	0.947681i	0.204314	−	0.978905i	$-0.434504\pi$
$953$	−24.5483	−	29.2556i	−0.795199	−	0.947681i	−0.999512	+	0.0312245i	$0.990059\pi$
$954$	−9.39470	+	5.42403i	−0.304165	+	0.175610i
$955$	42.4346	+	31.5608i	1.37315	+	1.02128i
$956$		−	1.80932i		−	0.0585177i
$957$	−0.963066	+	5.46182i	−0.0311315	+	0.176556i
$958$	−25.0196	+	29.8172i	−0.808346	+	0.963350i
$959$	47.8798	−	17.4268i	1.54612	−	0.562741i
$960$	−2.06622	+	1.95119i	−0.0666869	+	0.0629744i
$961$	16.2633			0.524624
$962$	7.78435	+	34.8972i	0.250978	+	1.12513i
$963$		−	1.66290i		−	0.0535861i
$964$	1.67662	−	4.60646i	0.0540001	−	0.148364i
$965$	29.2011	+	3.39937i	0.940016	+	0.109430i
$966$	21.4310	+	17.9827i	0.689530	+	0.578585i
$967$	−4.72277	+	26.7841i	−0.151874	+	0.861320i	0.809714	+	0.586824i	$0.199622\pi$
$967$	−4.72277	+	26.7841i	−0.151874	+	0.861320i	−0.961588	+	0.274496i	$0.911489\pi$
$968$	9.83671			0.316164
$969$	−0.609903	+	3.45893i	−0.0195929	+	0.111117i
$970$	−0.681536	−	11.6086i	−0.0218828	−	0.372731i
$971$	18.7695	−	15.7495i	0.602341	−	0.505424i	−0.289856	−	0.957070i	$-0.593607\pi$
$971$	18.7695	−	15.7495i	0.602341	−	0.505424i	0.892197	+	0.451646i	$0.149163\pi$
$972$	−11.2551	−	6.49815i	−0.361008	−	0.208428i
$973$	15.9281	−	9.19612i	0.510633	−	0.294814i
$974$	−24.5878	−	8.94924i	−0.787845	−	0.286752i
$975$	−37.2921	−	2.13726i	−1.19430	−	0.0684470i
$976$	−10.4344	−	6.02430i	−0.333997	−	0.192833i
$977$	−4.96750	−	28.1721i	−0.158925	−	0.901306i	−0.955110	−	0.296253i	$-0.904263\pi$
$977$	−4.96750	−	28.1721i	−0.158925	−	0.901306i	0.796185	−	0.605053i	$-0.206848\pi$
$978$	25.0011	−	4.40836i	0.799446	−	0.140964i
$979$	−8.50323	−	10.1338i	−0.271764	−	0.323876i
$980$	2.39728	+	0.279074i	0.0765784	+	0.00891468i
$981$	−5.71951	−	15.7142i	−0.182610	−	0.501716i
$982$	25.6422	−	21.5164i	0.818276	−	0.686615i
$983$	26.1393	−	4.60906i	0.833714	−	0.147006i	0.259533	−	0.965734i	$-0.416431\pi$
$983$	26.1393	−	4.60906i	0.833714	−	0.147006i	0.574182	+	0.818728i	$0.305320\pi$
$984$	−7.49924	+	1.32232i	−0.239067	+	0.0421539i
$985$	−33.0418	−	50.1868i	−1.05280	−	1.59908i
$986$	10.2867	−	12.2592i	0.327595	−	0.390412i
$987$	−8.09297	+	22.2353i	−0.257602	+	0.707756i
$988$	3.55666	−	2.05344i	0.113153	−	0.0653286i
$989$	10.1463	−	17.5739i	0.322634	−	0.558819i
$990$	3.24919	−	0.771666i	0.103266	−	0.0245252i
$991$	−42.9167	+	24.7780i	−1.36330	+	0.787099i	−0.990061	−	0.140638i	$-0.955085\pi$
$991$	−42.9167	+	24.7780i	−1.36330	+	0.787099i	−0.373234	+	0.927737i	$0.621751\pi$
$992$	3.78051	+	0.666607i	0.120031	+	0.0211648i
$993$	29.5144			0.936610
$994$	25.7495	+	4.54033i	0.816724	+	0.144011i
$995$	−20.9575	+	9.05175i	−0.664399	+	0.286960i
$996$	−17.0519	+	6.20638i	−0.540310	+	0.196657i
$997$	−52.1491	−	18.9807i	−1.65158	−	0.601125i	−0.662572	−	0.748998i	$-0.730535\pi$
$997$	−52.1491	−	18.9807i	−1.65158	−	0.601125i	−0.989006	+	0.147873i	$0.952757\pi$
$998$			5.50807i			0.174355i
$999$	−22.9334	−	24.9619i	−0.725580	−	0.789759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.v.b.169.3	yes	60
5.4	even	2		370.2.v.a.169.8	✓	60
37.30	even	18		370.2.v.a.289.8	yes	60
185.104	even	18	inner	370.2.v.b.289.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.v.a.169.8	✓	60	5.4	even	2
370.2.v.a.289.8	yes	60	37.30	even	18
370.2.v.b.169.3	yes	60	1.1	even	1	trivial
370.2.v.b.289.3	yes	60	185.104	even	18	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.434686 - 1.19429i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.33445 + 1.79422i) q^{5} -1.27094i q^{6} +(2.39627 + 0.422528i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.06076 - 0.890080i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.434686 - 1.19429i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.33445 + 1.79422i) q^{5} -1.27094i q^{6} +(2.39627 + 0.422528i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.06076 - 0.890080i) q^{9} +(-1.86764 + 1.22961i) q^{10} +(-0.539279 - 0.934058i) q^{11} +(0.434686 - 1.19429i) q^{12} +(4.50286 + 3.77835i) q^{13} +(2.10725 + 1.21662i) q^{14} +(2.72289 + 0.813802i) q^{15} +(0.173648 + 0.984808i) q^{16} +(3.03001 - 2.54248i) q^{17} +(1.30121 - 0.473602i) q^{18} +(-0.238962 - 0.656543i) q^{19} +(-2.17555 + 0.516683i) q^{20} +(-0.537006 - 3.04551i) q^{21} +(-0.187290 - 1.06217i) q^{22} +(-4.52323 + 7.83447i) q^{23} +(0.816943 - 0.973594i) q^{24} +(-1.43847 - 4.78861i) q^{25} +(2.93904 + 5.09056i) q^{26} +(-4.82610 - 2.78635i) q^{27} +(1.56406 + 1.86397i) q^{28} +(3.50388 - 2.02297i) q^{29} +(2.28034 + 1.69601i) q^{30} -3.83883i q^{31} +(-0.173648 + 0.984808i) q^{32} +(-0.881119 + 1.05008i) q^{33} +(3.71685 - 1.35282i) q^{34} +(-3.95583 + 3.73560i) q^{35} +1.38472 q^{36} +(5.80362 + 1.82155i) q^{37} -0.698678i q^{38} +(2.55512 - 7.02012i) q^{39} +(-2.22107 - 0.258560i) q^{40} +(-4.58982 - 3.85131i) q^{41} +(0.537006 - 3.04551i) q^{42} -2.24316 q^{43} +(0.187290 - 1.06217i) q^{44} +(0.181471 + 3.09100i) q^{45} +(-6.92999 + 5.81496i) q^{46} +(-6.62640 - 3.82576i) q^{47} +(1.10066 - 0.635469i) q^{48} +(-1.01425 - 0.369155i) q^{49} +(0.286087 - 4.99181i) q^{50} +(-4.35356 - 2.51353i) q^{51} +(1.02072 + 5.78877i) q^{52} +(-7.71511 + 1.36038i) q^{53} +(-3.58206 - 4.26894i) q^{54} +(2.39555 + 0.278872i) q^{55} +(0.832217 + 2.28650i) q^{56} +(-0.680229 + 0.570780i) q^{57} +(3.98447 - 0.702569i) q^{58} +(-8.83478 + 1.55781i) q^{59} +(1.56275 + 2.37365i) q^{60} +(-7.74469 + 9.22977i) q^{61} +(1.31296 - 3.60732i) q^{62} +(2.91795 - 1.68468i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-12.7881 + 3.03710i) q^{65} +(-1.18713 + 0.685389i) q^{66} +(4.03216 + 0.710979i) q^{67} +3.95539 q^{68} +(11.3228 + 1.99652i) q^{69} +(-4.99491 + 2.15735i) q^{70} +(10.0976 - 3.67522i) q^{71} +(1.30121 + 0.473602i) q^{72} -0.0962140i q^{73} +(4.83061 + 3.69665i) q^{74} +(-5.09371 + 3.79949i) q^{75} +(0.238962 - 0.656543i) q^{76} +(-0.897594 - 2.46612i) q^{77} +(4.80205 - 5.72286i) q^{78} +(-0.293157 - 0.0516914i) q^{79} +(-1.99869 - 1.00262i) q^{80} +(-0.508511 + 2.88391i) q^{81} +(-2.99579 - 5.18886i) q^{82} +(-9.17763 - 10.9375i) q^{83} +(1.54625 - 2.67818i) q^{84} +(0.518365 + 8.82932i) q^{85} +(-2.10788 - 0.767204i) q^{86} +(-3.93910 - 3.30529i) q^{87} +(0.539279 - 0.934058i) q^{88} +(12.0788 - 2.12982i) q^{89} +(-0.886658 + 2.96666i) q^{90} +(9.19364 + 10.9566i) q^{91} +(-8.50090 + 3.09407i) q^{92} +(-4.58468 + 1.66869i) q^{93} +(-4.91830 - 5.86140i) q^{94} +(1.49687 + 0.447375i) q^{95} +(1.25163 - 0.220696i) q^{96} +(-2.60024 + 4.50374i) q^{97} +(-0.826821 - 0.693785i) q^{98} +(-1.40343 - 0.510807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9	\( 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} - 6 q^{15} - 3 q^{17} - 12 q^{18} + 3 q^{19} + 3 q^{20} + 12 q^{21} + 3 q^{22} + 18 q^{23} - 18 q^{25} - 27 q^{26} + 18 q^{30} + 66 q^{33} + 21 q^{34} + 9 q^{35} - 72 q^{36} - 6 q^{37} + 12 q^{39} + 12 q^{40} - 57 q^{41} - 12 q^{42} - 60 q^{43} - 3 q^{44} + 9 q^{45} - 21 q^{46} + 18 q^{47} - 6 q^{49} + 6 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{55} - 30 q^{57} - 15 q^{58} - 12 q^{59} - 9 q^{60} + 42 q^{61} + 12 q^{62} + 9 q^{63} - 30 q^{64} - 15 q^{65} + 18 q^{67} + 24 q^{68} + 36 q^{69} - 12 q^{70} + 18 q^{71} - 12 q^{72} + 3 q^{74} - 78 q^{75} - 3 q^{76} - 21 q^{77} - 6 q^{78} - 24 q^{79} - 36 q^{81} - 27 q^{82} - 30 q^{83} + 12 q^{84} - 30 q^{85} - 18 q^{86} + 30 q^{87} - 6 q^{88} + 3 q^{89} + 57 q^{91} - 15 q^{92} - 60 q^{93} + 3 q^{94} + 6 q^{95} - 84 q^{97} + 6 q^{98} - 45 q^{99}+O(q^{100}) \) 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 - 6 * q^15 - 3 * q^17 - 12 * q^18 + 3 * q^19 + 3 * q^20 + 12 * q^21 + 3 * q^22 + 18 * q^23 - 18 * q^25 - 27 * q^26 + 18 * q^30 + 66 * q^33 + 21 * q^34 + 9 * q^35 - 72 * q^36 - 6 * q^37 + 12 * q^39 + 12 * q^40 - 57 * q^41 - 12 * q^42 - 60 * q^43 - 3 * q^44 + 9 * q^45 - 21 * q^46 + 18 * q^47 - 6 * q^49 + 6 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^55 - 30 * q^57 - 15 * q^58 - 12 * q^59 - 9 * q^60 + 42 * q^61 + 12 * q^62 + 9 * q^63 - 30 * q^64 - 15 * q^65 + 18 * q^67 + 24 * q^68 + 36 * q^69 - 12 * q^70 + 18 * q^71 - 12 * q^72 + 3 * q^74 - 78 * q^75 - 3 * q^76 - 21 * q^77 - 6 * q^78 - 24 * q^79 - 36 * q^81 - 27 * q^82 - 30 * q^83 + 12 * q^84 - 30 * q^85 - 18 * q^86 + 30 * q^87 - 6 * q^88 + 3 * q^89 + 57 * q^91 - 15 * q^92 - 60 * q^93 + 3 * q^94 + 6 * q^95 - 84 * q^97 + 6 * q^98 - 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more