LMFDB - Embedded newform 230.2.l.a.7.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.12
Character	$\chi$	$=$	230.7
Dual form			230.2.l.a.33.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.997452 - 0.0713392i) q^{2} +(0.544276 - 2.50200i) q^{3} +(0.989821 - 0.142315i) q^{4} +(2.18999 + 0.451614i) q^{5} +(0.364399 - 2.53445i) q^{6} +(-0.470705 + 0.862032i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-3.23486 - 1.47731i) q^{9} +(2.21663 + 0.294232i) q^{10} +(-4.13264 + 3.58095i) q^{11} +(0.182665 - 2.55399i) q^{12} +(-3.04895 + 1.66485i) q^{13} +(-0.408009 + 0.893415i) q^{14} +(2.32190 - 5.23354i) q^{15} +(0.959493 - 0.281733i) q^{16} +(0.102855 + 0.137398i) q^{17} +(-3.33201 - 1.24278i) q^{18} +(-0.241301 - 1.67828i) q^{19} +(2.23197 + 0.135350i) q^{20} +(1.90061 + 1.64689i) q^{21} +(-3.86665 + 3.86665i) q^{22} +(4.29439 - 2.13500i) q^{23} -2.56051i q^{24} +(4.59209 + 1.97806i) q^{25} +(-2.92241 + 1.87812i) q^{26} +(-0.853517 + 1.14017i) q^{27} +(-0.343234 + 0.920246i) q^{28} +(-5.01202 - 0.720619i) q^{29} +(1.94262 - 5.38585i) q^{30} +(-8.53830 - 5.48723i) q^{31} +(0.936950 - 0.349464i) q^{32} +(6.71024 + 12.2889i) q^{33} +(0.112394 + 0.129710i) q^{34} +(-1.42014 + 1.67526i) q^{35} +(-3.41218 - 1.00191i) q^{36} +(1.77232 + 4.75179i) q^{37} +(-0.360413 - 1.65679i) q^{38} +(2.50598 + 8.53460i) q^{39} +(2.23594 - 0.0242217i) q^{40} +(1.70890 + 3.74198i) q^{41} +(2.01325 + 1.50710i) q^{42} +(5.15679 + 1.12179i) q^{43} +(-3.58095 + 4.13264i) q^{44} +(-6.41713 - 4.69621i) q^{45} +(4.13114 - 2.43592i) q^{46} +(-5.74203 - 5.74203i) q^{47} +(-0.182665 - 2.55399i) q^{48} +(3.26295 + 5.07725i) q^{49} +(4.72150 + 1.64542i) q^{50} +(0.399750 - 0.182560i) q^{51} +(-2.78098 + 2.08182i) q^{52} +(9.18578 + 5.01582i) q^{53} +(-0.770004 + 1.19815i) q^{54} +(-10.6676 + 5.97588i) q^{55} +(-0.276710 + 0.942387i) q^{56} +(-4.33039 - 0.309716i) q^{57} +(-5.05066 - 0.361230i) q^{58} +(0.184613 - 0.628733i) q^{59} +(1.55345 - 5.51071i) q^{60} +(2.53267 - 3.94090i) q^{61} +(-8.90800 - 4.86414i) q^{62} +(2.79616 - 2.09318i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-7.42902 + 2.26905i) q^{65} +(7.56982 + 11.7789i) q^{66} +(0.0211304 + 0.295442i) q^{67} +(0.121361 + 0.121361i) q^{68} +(-3.00444 - 11.9066i) q^{69} +(-1.29701 + 1.77231i) q^{70} +(6.31730 - 7.29055i) q^{71} +(-3.47496 - 0.755932i) q^{72} +(-1.54732 - 1.15831i) q^{73} +(2.10680 + 4.61324i) q^{74} +(7.44847 - 10.4128i) q^{75} +(-0.477689 - 1.62686i) q^{76} +(-1.14164 - 5.24804i) q^{77} +(3.10845 + 8.33408i) q^{78} +(-16.2406 - 4.76868i) q^{79} +(2.22851 - 0.183670i) q^{80} +(-4.59837 - 5.30680i) q^{81} +(1.97150 + 3.61053i) q^{82} +(4.28996 - 1.60007i) q^{83} +(2.11564 + 1.35964i) q^{84} +(0.163199 + 0.347350i) q^{85} +(5.22368 + 0.751051i) q^{86} +(-4.53091 + 12.1478i) q^{87} +(-3.27701 + 4.37757i) q^{88} +(8.23324 - 5.29118i) q^{89} +(-6.73581 - 4.22645i) q^{90} -3.41194i q^{91} +(3.94683 - 2.72443i) q^{92} +(-18.3762 + 18.3762i) q^{93} +(-6.13703 - 5.31777i) q^{94} +(0.229491 - 3.78439i) q^{95} +(-0.364399 - 2.53445i) q^{96} +(-9.77637 - 3.64640i) q^{97} +(3.61684 + 4.83154i) q^{98} +(18.6587 - 5.47869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$3$	0.544276	−	2.50200i	0.314238	−	1.44453i	−0.501022	−	0.865435i	$-0.667042\pi$
$3$	0.544276	−	2.50200i	0.314238	−	1.44453i	0.815260	−	0.579095i	$-0.196594\pi$
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	2.18999	+	0.451614i	0.979392	+	0.201968i
$5$	2.18999	+	0.451614i	0.979392	+	0.201968i
$6$	0.364399	−	2.53445i	0.148765	−	1.03469i
$7$	−0.470705	+	0.862032i	−0.177910	+	0.325817i	−0.951382	−	0.308012i	$-0.900336\pi$
$7$	−0.470705	+	0.862032i	−0.177910	+	0.325817i	0.773473	+	0.633830i	$0.218518\pi$
$8$	0.977147	−	0.212565i	0.345474	−	0.0751532i
$9$	−3.23486	−	1.47731i	−1.07829	−	0.492438i
$10$	2.21663	+	0.294232i	0.700958	+	0.0930443i
$11$	−4.13264	+	3.58095i	−1.24604	+	1.07970i	−0.252336	+	0.967640i	$0.581199\pi$
$11$	−4.13264	+	3.58095i	−1.24604	+	1.07970i	−0.993702	+	0.112058i	$0.964256\pi$
$12$	0.182665	−	2.55399i	0.0527308	−	0.737274i
$13$	−3.04895	+	1.66485i	−0.845625	+	0.461746i	−0.842786	−	0.538250i	$-0.819086\pi$
$13$	−3.04895	+	1.66485i	−0.845625	+	0.461746i	−0.00283996	+	0.999996i	$0.500904\pi$
$14$	−0.408009	+	0.893415i	−0.109045	+	0.238775i
$15$	2.32190	−	5.23354i	0.599511	−	1.35129i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	0.102855	+	0.137398i	0.0249459	+	0.0333238i	0.812841	−	0.582486i	$-0.197920\pi$
$17$	0.102855	+	0.137398i	0.0249459	+	0.0333238i	−0.787895	+	0.615810i	$0.788829\pi$
$18$	−3.33201	−	1.24278i	−0.785363	−	0.292925i
$19$	−0.241301	−	1.67828i	−0.0553581	−	0.385024i	−0.998599	−	0.0529149i	$-0.983149\pi$
$19$	−0.241301	−	1.67828i	−0.0553581	−	0.385024i	0.943241	−	0.332109i	$-0.107760\pi$
$20$	2.23197	+	0.135350i	0.499083	+	0.0302652i
$21$	1.90061	+	1.64689i	0.414747	+	0.359380i
$22$	−3.86665	+	3.86665i	−0.824372	+	0.824372i
$23$	4.29439	−	2.13500i	0.895442	−	0.445179i
$23$	4.29439	−	2.13500i	0.895442	−	0.445179i
$24$		−	2.56051i		−	0.522663i
$25$	4.59209	+	1.97806i	0.918418	+	0.395612i
$26$	−2.92241	+	1.87812i	−0.573131	+	0.368329i
$27$	−0.853517	+	1.14017i	−0.164259	+	0.219425i
$28$	−0.343234	+	0.920246i	−0.0648651	+	0.173910i
$29$	−5.01202	−	0.720619i	−0.930708	−	0.133816i	−0.339748	−	0.940516i	$-0.610342\pi$
$29$	−5.01202	−	0.720619i	−0.930708	−	0.133816i	−0.590960	+	0.806701i	$0.701251\pi$
$30$	1.94262	−	5.38585i	0.354673	−	0.983317i
$31$	−8.53830	−	5.48723i	−1.53352	−	0.985536i	−0.989185	−	0.146670i	$-0.953144\pi$
$31$	−8.53830	−	5.48723i	−1.53352	−	0.985536i	−0.544339	−	0.838866i	$-0.683219\pi$
$32$	0.936950	−	0.349464i	0.165631	−	0.0617771i
$33$	6.71024	+	12.2889i	1.16810	+	2.13922i
$34$	0.112394	+	0.129710i	0.0192755	+	0.0222451i
$35$	−1.42014	+	1.67526i	−0.240048	+	0.283171i
$36$	−3.41218	−	1.00191i	−0.568697	−	0.166984i
$37$	1.77232	+	4.75179i	0.291368	+	0.781189i	0.997336	+	0.0729448i	$0.0232397\pi$
$37$	1.77232	+	4.75179i	0.291368	+	0.781189i	−0.705968	+	0.708244i	$0.749488\pi$
$38$	−0.360413	−	1.65679i	−0.0584667	−	0.268767i
$39$	2.50598	+	8.53460i	0.401279	+	1.36663i
$40$	2.23594	−	0.0242217i	0.353533	−	0.00382979i
$41$	1.70890	+	3.74198i	0.266886	+	0.584399i	0.994866	−	0.101199i	$-0.0322680\pi$
$41$	1.70890	+	3.74198i	0.266886	+	0.584399i	−0.727980	+	0.685598i	$0.759541\pi$
$42$	2.01325	+	1.50710i	0.310652	+	0.232551i
$43$	5.15679	+	1.12179i	0.786403	+	0.171071i	0.587797	−	0.809008i	$-0.299995\pi$
$43$	5.15679	+	1.12179i	0.786403	+	0.171071i	0.198605	+	0.980080i	$0.436359\pi$
$44$	−3.58095	+	4.13264i	−0.539849	+	0.623019i
$45$	−6.41713	−	4.69621i	−0.956610	−	0.700069i
$46$	4.13114	−	2.43592i	0.609103	−	0.359157i
$47$	−5.74203	−	5.74203i	−0.837561	−	0.837561i	0.150976	−	0.988537i	$-0.451758\pi$
$47$	−5.74203	−	5.74203i	−0.837561	−	0.837561i	−0.988537	+	0.150976i	$0.951758\pi$
$48$	−0.182665	−	2.55399i	−0.0263654	−	0.368637i
$49$	3.26295	+	5.07725i	0.466136	+	0.725321i
$50$	4.72150	+	1.64542i	0.667721	+	0.232698i
$51$	0.399750	−	0.182560i	0.0559762	−	0.0255635i
$52$	−2.78098	+	2.08182i	−0.385652	+	0.288696i
$53$	9.18578	+	5.01582i	1.26176	+	0.688975i	0.964060	−	0.265683i	$-0.0855974\pi$
$53$	9.18578	+	5.01582i	1.26176	+	0.688975i	0.297704	+	0.954658i	$0.403779\pi$
$54$	−0.770004	+	1.19815i	−0.104784	+	0.163047i
$55$	−10.6676	+	5.97588i	−1.43842	+	0.805788i
$56$	−0.276710	+	0.942387i	−0.0369769	+	0.125932i
$57$	−4.33039	−	0.309716i	−0.573575	−	0.0410229i
$58$	−5.05066	−	0.361230i	−0.663184	−	0.0474318i
$59$	0.184613	−	0.628733i	0.0240345	−	0.0818541i	−0.946602	−	0.322403i	$-0.895509\pi$
$59$	0.184613	−	0.628733i	0.0240345	−	0.0818541i	0.970637	+	0.240549i	$0.0773275\pi$
$60$	1.55345	−	5.51071i	0.200550	−	0.711430i
$61$	2.53267	−	3.94090i	0.324275	−	0.504581i	−0.640394	−	0.768046i	$-0.721229\pi$
$61$	2.53267	−	3.94090i	0.324275	−	0.504581i	0.964669	+	0.263465i	$0.0848654\pi$
$62$	−8.90800	−	4.86414i	−1.13132	−	0.617746i
$63$	2.79616	−	2.09318i	0.352283	−	0.263716i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	−7.42902	+	2.26905i	−0.921457	+	0.281441i
$66$	7.56982	+	11.7789i	0.931781	+	1.44988i
$67$	0.0211304	+	0.295442i	0.00258149	+	0.0360940i	0.998580	−	0.0532805i	$-0.0169678\pi$
$67$	0.0211304	+	0.295442i	0.00258149	+	0.0360940i	−0.995998	+	0.0893745i	$0.971513\pi$
$68$	0.121361	+	0.121361i	0.0147172	+	0.0147172i
$69$	−3.00444	−	11.9066i	−0.361692	−	1.43338i
$70$	−1.29701	+	1.77231i	−0.155023	+	0.211831i
$71$	6.31730	−	7.29055i	0.749726	−	0.865230i	−0.244816	−	0.969570i	$-0.578728\pi$
$71$	6.31730	−	7.29055i	0.749726	−	0.865230i	0.994542	+	0.104340i	$0.0332730\pi$
$72$	−3.47496	−	0.755932i	−0.409528	−	0.0890874i
$73$	−1.54732	−	1.15831i	−0.181100	−	0.135570i	0.504882	−	0.863189i	$-0.331536\pi$
$73$	−1.54732	−	1.15831i	−0.181100	−	0.135570i	−0.685982	+	0.727619i	$0.740627\pi$
$74$	2.10680	+	4.61324i	0.244910	+	0.536279i
$75$	7.44847	−	10.4128i	0.860075	−	1.20237i
$76$	−0.477689	−	1.62686i	−0.0547947	−	0.186614i
$77$	−1.14164	−	5.24804i	−0.130102	−	0.598070i
$78$	3.10845	+	8.33408i	0.351963	+	0.943648i
$79$	−16.2406	−	4.76868i	−1.82722	−	0.536519i	−0.827525	−	0.561428i	$-0.810252\pi$
$79$	−16.2406	−	4.76868i	−1.82722	−	0.536519i	−0.999690	+	0.0249096i	$0.992070\pi$
$80$	2.22851	−	0.183670i	0.249155	−	0.0205349i
$81$	−4.59837	−	5.30680i	−0.510930	−	0.589645i
$82$	1.97150	+	3.61053i	0.217716	+	0.398717i
$83$	4.28996	−	1.60007i	0.470885	−	0.175631i	−0.102809	−	0.994701i	$-0.532783\pi$
$83$	4.28996	−	1.60007i	0.470885	−	0.175631i	0.573693	+	0.819070i	$0.305510\pi$
$84$	2.11564	+	1.35964i	0.230835	+	0.148349i
$85$	0.163199	+	0.347350i	0.0177015	+	0.0376754i
$86$	5.22368	+	0.751051i	0.563283	+	0.0809879i
$87$	−4.53091	+	12.1478i	−0.485765	+	1.30239i
$88$	−3.27701	+	4.37757i	−0.349330	+	0.466651i
$89$	8.23324	−	5.29118i	0.872722	−	0.560864i	−0.0258624	−	0.999666i	$-0.508233\pi$
$89$	8.23324	−	5.29118i	0.872722	−	0.560864i	0.898584	+	0.438801i	$0.144597\pi$
$90$	−6.73581	−	4.22645i	−0.710016	−	0.445507i
$91$		−	3.41194i		−	0.357669i
$92$	3.94683	−	2.72443i	0.411486	−	0.284041i
$93$	−18.3762	+	18.3762i	−1.90553	+	1.90553i
$94$	−6.13703	−	5.31777i	−0.632986	−	0.548486i
$95$	0.229491	−	3.78439i	0.0235453	−	0.388270i
$96$	−0.364399	−	2.53445i	−0.0371913	−	0.258671i
$97$	−9.77637	−	3.64640i	−0.992640	−	0.370235i	−0.199914	−	0.979814i	$-0.564066\pi$
$97$	−9.77637	−	3.64640i	−0.992640	−	0.370235i	−0.792726	+	0.609578i	$0.791339\pi$
$98$	3.61684	+	4.83154i	0.365356	+	0.488059i
$99$	18.6587	−	5.47869i	1.87527	−	0.550629i
$100$	4.82686	+	1.30440i	0.482686	+	0.130440i
$101$	4.80496	−	10.5214i	0.478111	−	1.04692i	−0.504867	−	0.863197i	$-0.668459\pi$
$101$	4.80496	−	10.5214i	0.478111	−	1.04692i	0.982978	−	0.183721i	$-0.0588142\pi$
$102$	0.385708	−	0.210612i	0.0381908	−	0.0208537i
$103$	−0.0952323	+	1.33152i	−0.00938352	+	0.131199i	−0.999984	−	0.00558538i	$-0.998222\pi$
$103$	−0.0952323	+	1.33152i	−0.00938352	+	0.131199i	0.990601	+	0.136784i	$0.0436767\pi$
$104$	−2.62538	+	2.27490i	−0.257440	+	0.223073i
$105$	3.41855	+	4.46500i	0.333617	+	0.435740i
$106$	9.52020	+	4.34773i	0.924684	+	0.422289i
$107$	15.2929	−	3.32677i	1.47842	−	0.321611i	0.600193	−	0.799855i	$-0.295090\pi$
$107$	15.2929	−	3.32677i	1.47842	−	0.321611i	0.878227	+	0.478244i	$0.158727\pi$
$108$	−0.682567	+	1.25003i	−0.0656800	+	0.120284i
$109$	−2.02885	+	14.1109i	−0.194328	+	1.35158i	0.626059	+	0.779775i	$0.284667\pi$
$109$	−2.02885	+	14.1109i	−0.194328	+	1.35158i	−0.820388	+	0.571808i	$0.806242\pi$
$110$	−10.2141	+	6.72168i	−0.973880	+	0.640887i
$111$	12.8536	−	1.84807i	1.22001	−	0.175411i
$112$	−0.208776	+	0.959727i	−0.0197275	+	0.0906856i
$113$	−12.7108	+	0.909094i	−1.19573	+	0.0855203i	−0.654969	−	0.755656i	$-0.727318\pi$
$113$	−12.7108	+	0.909094i	−1.19573	+	0.0855203i	−0.540761	+	0.841176i	$0.681864\pi$
$114$	−4.34145			−0.406614
$115$	10.3689	−	2.73622i	0.966900	−	0.255154i
$116$	−5.06356			−0.470140
$117$	12.3224	−	0.881318i	1.13921	−	0.0814778i
$118$	0.139289	−	0.640301i	0.0128226	−	0.0589445i
$119$	−0.166855	+	0.0239902i	−0.0152956	+	0.00219918i
$120$	1.15636	−	5.60749i	0.105561	−	0.511892i
$121$	2.69002	−	18.7095i	0.244548	−	1.70087i
$122$	2.24507	−	4.11154i	0.203259	−	0.372241i
$123$	10.2925	−	2.23901i	0.928047	−	0.201884i
$124$	−9.23231	−	4.21625i	−0.829086	−	0.378631i
$125$	9.16330	+	6.40578i	0.819590	+	0.572950i
$126$	2.63971	−	2.28732i	0.235164	−	0.203771i
$127$	−1.39277	+	19.4735i	−0.123589	+	1.72799i	0.436623	+	0.899645i	$0.356174\pi$
$127$	−1.39277	+	19.4735i	−0.123589	+	1.72799i	−0.560211	+	0.828350i	$0.689280\pi$
$128$	0.877679	−	0.479249i	0.0775766	−	0.0423600i
$129$	5.61344	−	12.2917i	0.494235	−	1.08222i
$130$	−7.24822	+	2.79325i	−0.635711	+	0.244984i
$131$	1.20305	−	0.353248i	0.105111	−	0.0308634i	−0.228754	−	0.973484i	$-0.573465\pi$
$131$	1.20305	−	0.353248i	0.105111	−	0.0308634i	0.333865	+	0.942621i	$0.391647\pi$
$132$	8.39083	+	11.2088i	0.730328	+	0.975604i
$133$	1.56031	+	0.581967i	0.135296	+	0.0504629i
$134$	0.0421532	+	0.293182i	0.00364148	+	0.0253270i
$135$	−2.38411	+	2.11149i	−0.205191	+	0.181728i
$136$	0.129710	+	0.112394i	0.0111225	+	0.00963774i
$137$	3.52577	−	3.52577i	0.301227	−	0.301227i	−0.540267	−	0.841494i	$-0.681677\pi$
$137$	3.52577	−	3.52577i	0.301227	−	0.301227i	0.841494	+	0.540267i	$0.181677\pi$
$138$	−3.84619	−	11.6619i	−0.327409	−	0.992728i
$139$			18.3939i			1.56015i	0.625685	+	0.780076i	$0.284819\pi$
$139$			18.3939i			1.56015i	−0.625685	+	0.780076i	$0.715181\pi$
$140$	−1.16727	+	1.86032i	−0.0986527	+	0.157226i
$141$	−17.4918	+	11.2413i	−1.47308	+	0.946688i
$142$	5.78110	−	7.72265i	0.485139	−	0.648070i
$143$	6.63844	−	17.7984i	0.555135	−	1.48837i
$144$	−3.52004	−	0.506105i	−0.293336	−	0.0421754i
$145$	−10.6508	−	3.84165i	−0.884502	−	0.319031i
$146$	−1.62601	−	1.04497i	−0.134570	−	0.0864827i
$147$	14.4792	−	5.40047i	1.19423	−	0.445423i
$148$	2.43053	+	4.45119i	0.199789	+	0.365886i
$149$	−7.16272	−	8.26622i	−0.586793	−	0.677195i	0.382258	−	0.924056i	$-0.375147\pi$
$149$	−7.16272	−	8.26622i	−0.586793	−	0.677195i	−0.969051	+	0.246860i	$0.920601\pi$
$150$	6.68665	−	10.9176i	0.545963	−	0.891420i
$151$	−17.9797	−	5.27931i	−1.46316	−	0.429624i	−0.549294	−	0.835629i	$-0.685103\pi$
$151$	−17.9797	−	5.27931i	−1.46316	−	0.429624i	−0.913871	+	0.406005i	$0.866922\pi$
$152$	−0.592531	−	1.58864i	−0.0480606	−	0.128855i
$153$	−0.129741	−	0.596411i	−0.0104890	−	0.0482170i
$154$	−1.51312	−	5.15322i	−0.121931	−	0.415259i
$155$	−16.2207	−	15.8730i	−1.30287	−	1.27495i
$156$	3.69508	+	8.09109i	0.295843	+	0.647806i
$157$	−5.08986	−	3.81022i	−0.406215	−	0.304089i	0.376562	−	0.926392i	$-0.377106\pi$
$157$	−5.08986	−	3.81022i	−0.406215	−	0.304089i	−0.782777	+	0.622303i	$0.786197\pi$
$158$	−16.5395	−	3.59794i	−1.31581	−	0.286237i
$159$	17.5492	−	20.2528i	1.39174	−	1.60615i
$160$	2.20973	−	0.342182i	0.174695	−	0.0270519i
$161$	−0.180950	+	4.70686i	−0.0142609	+	0.370952i
$162$	−4.96524	−	4.96524i	−0.390106	−	0.390106i
$163$	−1.18962	−	16.6331i	−0.0931783	−	1.30280i	−0.801961	−	0.597376i	$-0.796210\pi$
$163$	−1.18962	−	16.6331i	−0.0931783	−	1.30280i	0.708783	−	0.705427i	$-0.249245\pi$
$164$	2.22405	+	3.46069i	0.173669	+	0.270234i
$165$	9.14550	+	29.9429i	0.711976	+	2.33105i
$166$	4.16489	−	1.90204i	0.323258	−	0.147627i
$167$	−10.5487	+	7.89664i	−0.816281	+	0.611060i	−0.923684	−	0.383155i	$-0.874837\pi$
$167$	−10.5487	+	7.89664i	−0.816281	+	0.611060i	0.107403	+	0.994216i	$0.465746\pi$
$168$	2.20725	+	1.20525i	0.170293	+	0.0929868i
$169$	−0.503986	+	0.784217i	−0.0387681	+	0.0603244i
$170$	0.187563	+	0.334822i	0.0143854	+	0.0256797i
$171$	−1.69877	+	5.78549i	−0.129908	+	0.442427i
$172$	5.26395	+	0.376485i	0.401372	+	0.0287067i
$173$	12.0394	+	0.861075i	0.915338	+	0.0654663i	0.521055	−	0.853523i	$-0.325538\pi$
$173$	12.0394	+	0.861075i	0.915338	+	0.0654663i	0.394283	+	0.918989i	$0.370993\pi$
$174$	−3.65275	+	12.4401i	−0.276914	+	0.943084i
$175$	−3.86667	+	3.02745i	−0.292293	+	0.228853i
$176$	−2.95637	+	4.60020i	−0.222845	+	0.346753i
$177$	−1.47261	−	0.804105i	−0.110688	−	0.0604402i
$178$	7.83479	−	5.86505i	0.587243	−	0.439604i
$179$	−5.27780	+	2.41029i	−0.394482	+	0.180154i	−0.602772	−	0.797913i	$-0.705937\pi$
$179$	−5.27780	+	2.41029i	−0.394482	+	0.180154i	0.208291	+	0.978067i	$0.433210\pi$
$180$	−7.02016	−	3.73515i	−0.523252	−	0.278402i
$181$	−1.79055	−	2.78615i	−0.133091	−	0.207093i	0.768311	−	0.640076i	$-0.221097\pi$
$181$	−1.79055	−	2.78615i	−0.133091	−	0.207093i	−0.901402	+	0.432983i	$0.857461\pi$
$182$	−0.243405	−	3.40325i	−0.0180424	−	0.252266i
$183$	−8.48167	−	8.48167i	−0.626983	−	0.626983i
$184$	3.74242	−	2.99905i	0.275895	−	0.221093i
$185$	1.73539	+	11.2068i	0.127589	+	0.823937i
$186$	−17.0185	+	19.6404i	−1.24786	+	1.44010i
$187$	−0.917075	−	0.199498i	−0.0670632	−	0.0145887i
$188$	−6.50076	−	4.86641i	−0.474117	−	0.354919i
$189$	−0.581104	−	1.27244i	−0.0422691	−	0.0925564i
$190$	−0.0410689	−	3.79112i	−0.00297945	−	0.275037i
$191$	2.03282	+	6.92315i	0.147090	+	0.500942i	0.999769	−	0.0214931i	$-0.00684198\pi$
$191$	2.03282	+	6.92315i	0.147090	+	0.500942i	−0.852679	+	0.522435i	$0.825024\pi$
$192$	−0.544276	−	2.50200i	−0.0392798	−	0.180566i
$193$	1.86925	+	5.01166i	0.134552	+	0.360747i	0.986700	−	0.162554i	$-0.0519730\pi$
$193$	1.86925	+	5.01166i	0.134552	+	0.360747i	−0.852148	+	0.523301i	$0.824700\pi$
$194$	−10.0116	−	2.93967i	−0.718790	−	0.211056i
$195$	1.63373	+	19.8224i	0.116994	+	1.41951i
$196$	3.95231	+	4.56120i	0.282308	+	0.325800i
$197$	4.56233	+	8.35528i	0.325052	+	0.595289i	0.988195	−	0.153204i	$-0.0489593\pi$
$197$	4.56233	+	8.35528i	0.325052	+	0.595289i	−0.663142	+	0.748494i	$0.730777\pi$
$198$	18.2203	−	6.79583i	1.29486	−	0.482959i
$199$	9.68462	+	6.22393i	0.686525	+	0.441203i	0.836849	−	0.547434i	$-0.184395\pi$
$199$	9.68462	+	6.22393i	0.686525	+	0.441203i	−0.150324	+	0.988637i	$0.548032\pi$
$200$	4.90761	+	0.956736i	0.347021	+	0.0676514i
$201$	0.750696	+	0.107934i	0.0529500	+	0.00761306i
$202$	4.04213	−	10.8374i	0.284403	−	0.762515i
$203$	2.98038	−	3.98132i	0.209182	−	0.279434i
$204$	0.369700	−	0.237592i	0.0258842	−	0.0166348i
$205$	2.05255	+	8.96665i	0.143356	+	0.626258i
$206$			1.33492i			0.0930085i
$207$	−17.0458	+	0.562287i	−1.18477	+	0.0390816i
$208$	−2.45640	+	2.45640i	−0.170321	+	0.170321i
$209$	7.00706	+	6.07165i	0.484688	+	0.419985i
$210$	3.72837	+	4.20975i	0.257282	+	0.290500i
$211$	2.53957	+	17.6631i	0.174831	+	1.21598i	0.868503	+	0.495684i	$0.165083\pi$
$211$	2.53957	+	17.6631i	0.174831	+	1.21598i	−0.693672	+	0.720291i	$0.744008\pi$
$212$	9.80611	+	3.65749i	0.673486	+	0.251197i
$213$	−14.8026	−	19.7740i	−1.01426	−	1.35489i
$214$	15.0166	−	4.40927i	1.02651	−	0.301412i
$215$	10.7867	+	4.78559i	0.735646	+	0.326374i
$216$	−0.591652	+	1.29554i	−0.0402568	+	0.0881501i
$217$	8.74919	−	4.77742i	0.593934	−	0.324312i
$218$	−1.01701	+	14.2197i	−0.0688809	+	0.963081i
$219$	−3.74026	+	3.24095i	−0.252743	+	0.219003i
$220$	−9.70860	+	7.43322i	−0.654554	+	0.501147i
$221$	−0.542345	−	0.247680i	−0.0364820	−	0.0166608i
$222$	12.6890	−	2.76032i	0.851631	−	0.185261i
$223$	−3.18929	+	5.84075i	−0.213571	+	0.391126i	−0.962400	−	0.271638i	$-0.912435\pi$
$223$	−3.18929	+	5.84075i	−0.213571	+	0.391126i	0.748829	+	0.662764i	$0.230617\pi$
$224$	−0.139778	+	0.972175i	−0.00933929	+	0.0649562i
$225$	−11.9326	−	13.1827i	−0.795505	−	0.878847i
$226$	−12.6135	+	1.81355i	−0.839041	+	0.120636i
$227$	0.645476	−	2.96721i	0.0428418	−	0.196940i	−0.950752	−	0.309953i	$-0.899687\pi$
$227$	0.645476	−	2.96721i	0.0428418	−	0.196940i	0.993594	+	0.113013i	$0.0360502\pi$
$228$	−4.33039	+	0.309716i	−0.286787	+	0.0205114i
$229$	−20.0994			−1.32821			−0.664104	−	0.747641i	$-0.731187\pi$
$229$	−20.0994			−1.32821			−0.664104	+	0.747641i	$0.731187\pi$
$230$	10.1472	−	3.46895i	0.669089	−	0.228736i
$231$	−13.7520			−0.904812
$232$	−5.05066	+	0.361230i	−0.331592	+	0.0237159i
$233$	3.36250	−	15.4572i	0.220285	−	1.01263i	−0.725596	−	0.688121i	$-0.758436\pi$
$233$	3.36250	−	15.4572i	0.220285	−	1.01263i	0.945881	−	0.324513i	$-0.105200\pi$
$234$	12.2282	−	1.75814i	0.799380	−	0.114933i
$235$	−9.98179	−	15.1682i	−0.651140	−	0.989461i
$236$	0.0932555	−	0.648607i	0.00607042	−	0.0422207i
$237$	−20.7706	+	38.0386i	−1.34920	+	2.47087i
$238$	−0.164719	+	0.0358324i	−0.0106771	+	0.00232267i
$239$	1.08709	+	0.496459i	0.0703183	+	0.0321133i	0.450264	−	0.892896i	$-0.351330\pi$
$239$	1.08709	+	0.496459i	0.0703183	+	0.0321133i	−0.379945	+	0.925009i	$0.624057\pi$
$240$	0.753385	−	5.67570i	0.0486308	−	0.366365i
$241$	−10.9334	+	9.47388i	−0.704285	+	0.610266i	−0.931570	−	0.363562i	$-0.881560\pi$
$241$	−10.9334	+	9.47388i	−0.704285	+	0.610266i	0.227285	+	0.973828i	$0.427015\pi$
$242$	1.34845	−	18.8538i	0.0866815	−	1.21197i
$243$	−19.5305	+	10.6644i	−1.25288	+	0.684125i
$244$	1.94604	−	4.26123i	0.124582	−	0.272797i
$245$	4.85286	+	12.5927i	0.310038	+	0.804518i
$246$	10.1066	−	2.96756i	0.644372	−	0.189205i
$247$	3.52980	+	4.71526i	0.224596	+	0.300025i
$248$	−9.50957	−	3.54689i	−0.603858	−	0.225227i
$249$	−1.66846	−	11.6044i	−0.105734	−	0.735397i
$250$	9.59693	+	5.73576i	0.606963	+	0.362761i
$251$	16.7278	+	14.4947i	1.05585	+	0.914900i	0.996521	−	0.0833381i	$-0.0265582\pi$
$251$	16.7278	+	14.4947i	1.05585	+	0.914900i	0.0593299	+	0.998238i	$0.481104\pi$
$252$	2.46981	−	2.46981i	0.155583	−	0.155583i
$253$	−10.1018	+	24.2012i	−0.635096	+	1.52152i
$254$			19.5232i			1.22500i
$255$	0.957894	−	0.219271i	0.0599856	−	0.0137313i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	18.1276	−	24.2156i	1.13077	−	1.51053i	0.299971	−	0.953948i	$-0.403023\pi$
$257$	18.1276	−	24.2156i	1.13077	−	1.51053i	0.830795	−	0.556578i	$-0.187886\pi$
$258$	4.72225	−	12.6608i	0.293995	−	0.788230i
$259$	−4.93043	−	0.708890i	−0.306362	−	0.0440483i
$260$	−7.03049	+	3.30322i	−0.436012	+	0.204857i
$261$	15.1486	+	9.73542i	0.937676	+	0.602608i
$262$	1.17479	−	0.438173i	0.0725786	−	0.0270704i
$263$	0.188836	+	0.345827i	0.0116441	+	0.0213246i	0.883436	−	0.468551i	$-0.155224\pi$
$263$	0.188836	+	0.345827i	0.0116441	+	0.0213246i	−0.871792	+	0.489876i	$0.837042\pi$
$264$	9.16908	+	10.5817i	0.564318	+	0.651257i
$265$	17.8515	+	15.1330i	1.09661	+	0.929613i
$266$	1.59786	+	0.469173i	0.0979708	+	0.0287668i
$267$	−8.75737	−	23.4794i	−0.535942	−	1.43692i
$268$	0.0629611	+	0.289427i	0.00384596	+	0.0176796i
$269$	−0.661200	−	2.25184i	−0.0403141	−	0.137297i	0.936877	−	0.349659i	$-0.113703\pi$
$269$	−0.661200	−	2.25184i	−0.0403141	−	0.137297i	−0.977191	+	0.212362i	$0.931884\pi$
$270$	−2.22740	+	2.27619i	−0.135555	+	0.138524i
$271$	−7.20738	−	15.7820i	−0.437817	−	0.958685i	−0.991994	−	0.126286i	$-0.959694\pi$
$271$	−7.20738	−	15.7820i	−0.437817	−	0.958685i	0.554177	−	0.832399i	$-0.313033\pi$
$272$	0.137398	+	0.102855i	0.00833096	+	0.00623647i
$273$	−8.53668	−	1.85704i	−0.516663	−	0.112393i
$274$	3.26526	−	3.76832i	0.197262	−	0.227652i
$275$	−26.0608	+	8.26945i	−1.57152	+	0.498666i
$276$	−4.66834	−	11.3578i	−0.281001	−	0.683660i
$277$	11.0319	+	11.0319i	0.662840	+	0.662840i	0.956049	−	0.293208i	$-0.0947229\pi$
$277$	11.0319	+	11.0319i	0.662840	+	0.662840i	−0.293208	+	0.956049i	$0.594723\pi$
$278$	1.31221	+	18.3470i	0.0787009	+	1.10038i
$279$	19.5139	+	30.3642i	1.16827	+	1.81786i
$280$	−1.03159	+	1.93885i	−0.0616491	+	0.115868i
$281$	−15.5856	+	7.11770i	−0.929758	+	0.424606i	−0.821946	−	0.569565i	$-0.807112\pi$
$281$	−15.5856	+	7.11770i	−0.929758	+	0.424606i	−0.107812	+	0.994171i	$0.534384\pi$
$282$	−16.6453	+	12.4605i	−0.991213	+	0.742012i
$283$	13.8718	+	7.57458i	0.824593	+	0.450262i	0.835375	−	0.549680i	$-0.185250\pi$
$283$	13.8718	+	7.57458i	0.824593	+	0.450262i	−0.0107821	+	0.999942i	$0.503432\pi$
$284$	5.21545	−	8.11539i	0.309480	−	0.481560i
$285$	−9.34363	−	2.63394i	−0.553469	−	0.156021i
$286$	5.35181	−	18.2266i	0.316459	−	1.07776i
$287$	−4.03010	−	0.288238i	−0.237889	−	0.0170142i
$288$	−3.54717	−	0.253699i	−0.209019	−	0.0149493i
$289$	4.78115	−	16.2831i	0.281244	−	0.957830i
$290$	−10.8977	−	3.07204i	−0.639937	−	0.180396i
$291$	−14.4443	+	22.4758i	−0.846741	+	1.31756i
$292$	−1.69642	−	0.926313i	−0.0992752	−	0.0542084i
$293$	19.9142	−	14.9076i	1.16340	−	0.870912i	0.169983	−	0.985447i	$-0.445629\pi$
$293$	19.9142	−	14.9076i	1.16340	−	0.870912i	0.993419	+	0.114535i	$0.0365377\pi$
$294$	14.0571	−	6.41964i	0.819824	−	0.374401i
$295$	0.688244	−	1.29354i	0.0400711	−	0.0753130i
$296$	2.74189	+	4.26646i	0.159369	+	0.247983i
$297$	−0.555599	−	7.76829i	−0.0322391	−	0.450762i
$298$	−7.73418	−	7.73418i	−0.448029	−	0.448029i
$299$	−9.53890	+	13.6590i	−0.551649	+	0.789922i
$300$	5.89076	−	11.3668i	0.340103	−	0.656264i
$301$	−3.39434	+	3.91728i	−0.195647	+	0.225788i
$302$	−18.3105	−	3.98320i	−1.05365	−	0.229208i
$303$	−23.7093	−	17.7485i	−1.36206	−	1.01963i
$304$	−0.704353	−	1.54232i	−0.0403974	−	0.0884580i
$305$	7.32627	−	7.48674i	0.419501	−	0.428690i
$306$	−0.171958	−	0.585636i	−0.00983019	−	0.0334786i
$307$	−4.66256	−	21.4335i	−0.266107	−	1.22327i	−0.895101	−	0.445863i	$-0.852897\pi$
$307$	−4.66256	−	21.4335i	−0.266107	−	1.22327i	0.628995	−	0.777410i	$-0.283467\pi$
$308$	−1.87689	−	5.03215i	−0.106946	−	0.286733i
$309$	3.27963	+	0.962987i	0.186572	+	0.0547824i
$310$	−17.3117	−	14.6754i	−0.983238	−	0.833505i
$311$	4.62138	+	5.33335i	0.262054	+	0.302427i	0.871495	−	0.490405i	$-0.163151\pi$
$311$	4.62138	+	5.33335i	0.262054	+	0.302427i	−0.609440	+	0.792832i	$0.708606\pi$
$312$	4.26287	+	7.80687i	0.241338	+	0.441977i
$313$	19.4735	−	7.26325i	1.10071	−	0.410543i	0.267532	−	0.963549i	$-0.413792\pi$
$313$	19.4735	−	7.26325i	1.10071	−	0.410543i	0.833177	+	0.553006i	$0.186519\pi$
$314$	−5.34871	−	3.43741i	−0.301845	−	0.193984i
$315$	7.06886	−	3.32125i	0.398285	−	0.187131i
$316$	−16.7540	−	2.40886i	−0.942486	−	0.135509i
$317$	7.54065	−	20.2173i	0.423525	−	1.13552i	−0.533574	−	0.845754i	$-0.679151\pi$
$317$	7.54065	−	20.2173i	0.423525	−	1.13552i	0.957099	−	0.289761i	$-0.0935760\pi$
$318$	16.0596	−	21.4532i	0.900580	−	1.20303i
$319$	23.2934	−	14.9697i	1.30418	−	0.838145i
$320$	2.17969	−	0.498951i	0.121848	−	0.0278922i
$321$		−	40.0735i		−	2.23668i
$322$	0.155294	+	4.70777i	0.00865421	+	0.262354i
$323$	0.205773	−	0.205773i	0.0114495	−	0.0114495i
$324$	−5.30680	−	4.59837i	−0.294822	−	0.255465i
$325$	−17.2942	+	1.61415i	−0.959310	+	0.0895367i
$326$	−2.37318	−	16.5058i	−0.131438	−	0.914174i
$327$	34.2013	+	12.7564i	1.89134	+	0.705432i
$328$	2.46527	+	3.29321i	0.136121	+	0.181837i
$329$	7.65262	−	2.24701i	0.421902	−	0.123882i
$330$	11.2583	+	29.2142i	0.619749	+	1.60819i
$331$	−3.44212	+	7.53718i	−0.189196	+	0.414281i	−0.980331	−	0.197360i	$-0.936763\pi$
$331$	−3.44212	+	7.53718i	−0.189196	+	0.414281i	0.791135	+	0.611641i	$0.209490\pi$
$332$	4.01858	−	2.19431i	0.220548	−	0.120429i
$333$	1.28665	−	17.9897i	0.0705078	−	0.985827i
$334$	−9.95846	+	8.62905i	−0.544903	+	0.472161i
$335$	−0.0871504	+	0.656557i	−0.00476154	+	0.0358715i
$336$	2.28760	+	1.04471i	0.124799	+	0.0569938i
$337$	−15.6732	+	3.40949i	−0.853773	+	0.185727i	−0.618094	−	0.786104i	$-0.712095\pi$
$337$	−15.6732	+	3.40949i	−0.853773	+	0.185727i	−0.235679	+	0.971831i	$0.575731\pi$
$338$	−0.446756	+	0.818173i	−0.0243003	+	0.0445027i
$339$	−4.64363	+	32.2972i	−0.252207	+	1.75414i
$340$	0.210971	+	0.320588i	0.0114415	+	0.0173864i
$341$	54.9352	−	7.89849i	2.97491	−	0.427727i
$342$	−1.28171	+	5.89194i	−0.0693071	+	0.318600i
$343$	−12.7703	+	0.913352i	−0.689533	+	0.0493164i
$344$	5.27739			0.284538
$345$	−1.20250	−	27.4321i	−0.0647402	−	1.47690i
$346$	12.0701			0.648895
$347$	−10.6935	+	0.764815i	−0.574057	+	0.0410574i	−0.355350	−	0.934733i	$-0.615638\pi$
$347$	−10.6935	+	0.764815i	−0.574057	+	0.0410574i	−0.218707	+	0.975791i	$0.570184\pi$
$348$	−2.75598	+	12.6690i	−0.147736	+	0.679130i
$349$	4.34521	−	0.624747i	0.232594	−	0.0334420i	−0.0250322	−	0.999687i	$-0.507969\pi$
$349$	4.34521	−	0.624747i	0.232594	−	0.0334420i	0.257626	+	0.966245i	$0.417060\pi$
$350$	−3.64084	+	3.29558i	−0.194611	+	0.176156i
$351$	0.704123	−	4.89728i	0.0375833	−	0.261397i
$352$	−2.62066	+	4.79938i	−0.139682	+	0.255808i
$353$	13.7510	−	2.99134i	0.731890	−	0.159213i	0.168849	−	0.985642i	$-0.445995\pi$
$353$	13.7510	−	2.99134i	0.731890	−	0.159213i	0.563041	+	0.826429i	$0.309631\pi$
$354$	−1.52622	−	0.697002i	−0.0811177	−	0.0370452i
$355$	17.1273	−	13.1132i	0.909024	−	0.695978i
$356$	7.39642	−	6.40904i	0.392010	−	0.339678i
$357$	−0.0307920	+	0.430529i	−0.00162969	+	0.0227860i
$358$	−5.09241	+	2.78067i	−0.269142	+	0.146963i
$359$	−10.3530	+	22.6699i	−0.546410	+	1.19647i	0.412028	+	0.911171i	$0.364821\pi$
$359$	−10.3530	+	22.6699i	−0.546410	+	1.19647i	−0.958438	+	0.285301i	$0.907907\pi$
$360$	−7.26873	−	3.22482i	−0.383096	−	0.169963i
$361$	15.4720	−	4.54298i	0.814314	−	0.239104i
$362$	−1.98475	−	2.65132i	−0.104316	−	0.139350i
$363$	−45.3471	−	16.9136i	−2.38011	−	0.887734i
$364$	−0.485570	−	3.37721i	−0.0254508	−	0.177014i
$365$	−2.86550	−	3.23548i	−0.149987	−	0.169353i
$366$	−9.06513	−	7.85498i	−0.473842	−	0.410586i
$367$	17.9948	−	17.9948i	0.939321	−	0.939321i	−0.0589403	−	0.998262i	$-0.518772\pi$
$367$	17.9948	−	17.9948i	0.939321	−	0.939321i	0.998262	+	0.0589403i	$0.0187722\pi$
$368$	3.51894	−	3.25839i	0.183437	−	0.169855i
$369$		−	14.6294i		−	0.761575i
$370$	2.53045	+	11.0544i	0.131552	+	0.574691i
$371$	−8.64759	+	5.55747i	−0.448960	+	0.288529i
$372$	−15.5740	+	20.8044i	−0.807474	+	1.07866i
$373$	1.22636	−	3.28799i	0.0634983	−	0.170246i	−0.901326	−	0.433142i	$-0.857405\pi$
$373$	1.22636	−	3.28799i	0.0634983	−	0.170246i	0.964824	+	0.262896i	$0.0846777\pi$
$374$	−0.928971	−	0.133566i	−0.0480359	−	0.00690652i
$375$	21.0146	−	19.4400i	1.08519	−	1.00388i
$376$	−6.83136	−	4.39025i	−0.352301	−	0.226410i
$377$	16.4811	−	6.14713i	0.848820	−	0.316593i
$378$	−0.670398	−	1.22774i	−0.0344816	−	0.0631483i
$379$	22.4911	+	25.9561i	1.15529	+	1.33328i	0.933667	+	0.358143i	$0.116590\pi$
$379$	22.4911	+	25.9561i	1.15529	+	1.33328i	0.221623	+	0.975132i	$0.428865\pi$
$380$	−0.311420	−	3.77853i	−0.0159755	−	0.193835i
$381$	47.9646	+	14.0837i	2.45730	+	0.721529i
$382$	2.52153	+	6.76049i	0.129013	+	0.345897i
$383$	7.97374	+	36.6547i	0.407439	+	1.87297i	0.482671	+	0.875802i	$0.339667\pi$
$383$	7.97374	+	36.6547i	0.407439	+	1.87297i	−0.0752314	+	0.997166i	$0.523970\pi$
$384$	−0.721380	−	2.45680i	−0.0368128	−	0.125373i
$385$	−0.130090	−	12.0087i	−0.00662998	−	0.612021i
$386$	2.22202	+	4.86554i	0.113098	+	0.247650i
$387$	−15.0243	−	11.2470i	−0.763726	−	0.571718i
$388$	−10.1958	−	2.21796i	−0.517613	−	0.112600i
$389$	−17.2453	+	19.9021i	−0.874370	+	1.00908i	0.125485	+	0.992095i	$0.459951\pi$
$389$	−17.2453	+	19.9021i	−0.874370	+	1.00908i	−0.999856	+	0.0169818i	$0.994594\pi$
$390$	3.04368	+	19.6553i	0.154123	+	0.995287i
$391$	0.735042	+	0.370444i	0.0371727	+	0.0187342i
$392$	4.26763	+	4.26763i	0.215548	+	0.215548i
$393$	−0.229033	−	3.20230i	−0.0115532	−	0.161535i
$394$	5.14676	+	8.00852i	0.259290	+	0.403463i
$395$	−33.4132	−	17.7779i	−1.68120	−	0.894501i
$396$	17.6891	−	8.07834i	0.888910	−	0.405952i
$397$	−10.2094	+	7.64263i	−0.512393	+	0.383573i	−0.823957	−	0.566652i	$-0.808238\pi$
$397$	−10.2094	+	7.64263i	−0.512393	+	0.383573i	0.311564	+	0.950225i	$0.399147\pi$
$398$	10.1040	+	5.51718i	0.506466	+	0.276551i
$399$	2.30532	−	3.58715i	0.115411	−	0.179582i
$400$	4.96336	+	0.604193i	0.248168	+	0.0302097i
$401$	−0.760440	+	2.58982i	−0.0379745	+	0.129329i	−0.976299	−	0.216427i	$-0.930560\pi$
$401$	−0.760440	+	2.58982i	−0.0379745	+	0.129329i	0.938324	+	0.345757i	$0.112378\pi$
$402$	0.756483	+	0.0541047i	0.0377299	+	0.00269850i
$403$	35.1682	+	2.51528i	1.75185	+	0.125295i
$404$	3.25870	−	11.0981i	0.162126	−	0.552152i
$405$	−7.67374	−	13.6985i	−0.381311	−	0.680685i
$406$	2.68876	−	4.18380i	0.133441	−	0.207638i
$407$	−24.3403	−	13.2908i	−1.20650	−	0.658801i
$408$	0.351809	−	0.263361i	0.0174171	−	0.0130383i
$409$	22.5455	−	10.2962i	1.11480	−	0.509114i	0.229118	−	0.973399i	$-0.426416\pi$
$409$	22.5455	−	10.2962i	1.11480	−	0.509114i	0.885686	+	0.464285i	$0.153689\pi$
$410$	2.68699	+	8.79738i	0.132701	+	0.434472i
$411$	−6.90248	−	10.7405i	−0.340474	−	0.529788i
$412$	0.0952323	+	1.33152i	0.00469176	+	0.0655994i
$413$	0.455090	+	0.455090i	0.0223935	+	0.0223935i
$414$	−16.9623	+	1.77689i	−0.833651	+	0.0873293i
$415$	10.1176	−	1.56673i	0.496653	−	0.0769078i
$416$	−2.27490	+	2.62538i	−0.111536	+	0.128720i
$417$	46.0215	+	10.0114i	2.25368	+	0.490259i
$418$	7.42235	+	5.55630i	0.363039	+	0.271768i
$419$	−6.88135	−	15.0681i	−0.336176	−	0.736122i	0.663754	−	0.747951i	$-0.268962\pi$
$419$	−6.88135	−	15.0681i	−0.336176	−	0.736122i	−0.999930	+	0.0118283i	$0.996235\pi$
$420$	4.01919	+	3.93305i	0.196117	+	0.191913i
$421$	3.98170	+	13.5604i	0.194056	+	0.660895i	0.997823	+	0.0659503i	$0.0210079\pi$
$421$	3.98170	+	13.5604i	0.194056	+	0.660895i	−0.803767	+	0.594945i	$0.797174\pi$
$422$	3.79316	+	17.4369i	0.184648	+	0.848815i
$423$	10.0919	+	27.0575i	0.490685	+	1.31558i
$424$	10.0420	+	2.94861i	0.487685	+	0.143197i
$425$	0.200537	+	0.834395i	0.00972746	+	0.0404741i
$426$	−16.1755	−	18.6676i	−0.783707	−	0.904447i
$427$	2.20505	+	4.03824i	0.106710	+	0.195424i
$428$	14.6638	−	5.46931i	0.708801	−	0.264369i
$429$	−40.9183	−	26.2966i	−1.97555	−	1.26961i
$430$	11.1006	+	4.00388i	0.535318	+	0.193084i
$431$	−34.3181	−	4.93420i	−1.65305	−	0.237672i	−0.748219	−	0.663452i	$-0.769091\pi$
$431$	−34.3181	−	4.93420i	−1.65305	−	0.237672i	−0.904827	+	0.425780i	$0.860000\pi$
$432$	−0.497722	+	1.33444i	−0.0239467	+	0.0642035i
$433$	−7.46814	+	9.97627i	−0.358896	+	0.479429i	−0.943256	−	0.332065i	$-0.892255\pi$
$433$	−7.46814	+	9.97627i	−0.358896	+	0.479429i	0.584360	+	0.811494i	$0.301346\pi$
$434$	8.38608	−	5.38941i	0.402545	−	0.258700i
$435$	−15.4088	+	24.5574i	−0.738795	+	1.17744i
$436$			14.2561i			0.682741i
$437$	−4.61937	−	6.69202i	−0.220975	−	0.320123i
$438$	−3.49952	+	3.49952i	−0.167214	+	0.167214i
$439$	11.6089	+	10.0592i	0.554064	+	0.480099i	0.886309	−	0.463094i	$-0.153261\pi$
$439$	11.6089	+	10.0592i	0.554064	+	0.480099i	−0.332245	+	0.943193i	$0.607806\pi$
$440$	−9.15358	+	8.10688i	−0.436380	+	0.386480i
$441$	−3.05451	−	21.2446i	−0.145453	−	1.01165i
$442$	−0.558632	−	0.208359i	−0.0265714	−	0.00991063i
$443$	6.48999	+	8.66962i	0.308349	+	0.411906i	0.927770	−	0.373153i	$-0.121723\pi$
$443$	6.48999	+	8.66962i	0.308349	+	0.411906i	−0.619421	+	0.785059i	$0.712633\pi$
$444$	12.4598	−	3.65852i	0.591314	−	0.173625i
$445$	20.4203	−	7.86937i	0.968013	−	0.373044i
$446$	−2.76449	+	6.05339i	−0.130903	+	0.286636i
$447$	−24.5806	+	13.4220i	−1.16262	+	0.634839i
$448$	−0.0700674	+	0.979670i	−0.00331037	+	0.0462851i
$449$	−8.63127	+	7.47904i	−0.407335	+	0.352958i	−0.834300	−	0.551310i	$-0.814128\pi$
$449$	−8.63127	+	7.47904i	−0.407335	+	0.352958i	0.426965	+	0.904268i	$0.359583\pi$
$450$	−12.8426	−	12.2979i	−0.605406	−	0.579726i
$451$	−20.4621	−	9.34474i	−0.963524	−	0.440027i
$452$	−12.4520	+	2.70877i	−0.585694	+	0.127410i
$453$	−22.9947	+	42.1117i	−1.08039	+	1.97858i
$454$	0.432154	−	3.00569i	0.0202820	−	0.141064i
$455$	1.54088	−	7.47211i	0.0722377	−	0.350298i
$456$	−4.29726	+	0.617853i	−0.201238	+	0.0289336i
$457$	−1.08255	+	4.97639i	−0.0506394	+	0.232786i	−0.995510	−	0.0946590i	$-0.969824\pi$
$457$	−1.08255	+	4.97639i	−0.0506394	+	0.232786i	0.944870	+	0.327445i	$0.106188\pi$
$458$	−20.0482	+	1.43388i	−0.936791	+	0.0670006i
$459$	−0.244444			−0.0114097
$460$	9.87391	−	4.18401i	0.460373	−	0.195081i
$461$	−20.4621			−0.953013			−0.476506	−	0.879171i	$-0.658097\pi$
$461$	−20.4621			−0.953013			−0.476506	+	0.879171i	$0.658097\pi$
$462$	−13.7169	+	0.981053i	−0.638169	+	0.0456427i
$463$	6.11046	−	28.0893i	0.283977	−	1.30542i	−0.585187	−	0.810898i	$-0.698979\pi$
$463$	6.11046	−	28.0893i	0.283977	−	1.30542i	0.869164	−	0.494523i	$-0.164657\pi$
$464$	−5.01202	+	0.720619i	−0.232677	+	0.0334539i
$465$	−48.5427	+	31.9448i	−2.25111	+	1.48140i
$466$	2.25123	−	15.6577i	0.104286	−	0.725328i
$467$	−0.646211	+	1.18345i	−0.0299031	+	0.0547634i	−0.892203	−	0.451634i	$-0.850841\pi$
$467$	−0.646211	+	1.18345i	−0.0299031	+	0.0547634i	0.862300	+	0.506397i	$0.169023\pi$
$468$	12.0716	−	2.62601i	0.558009	−	0.121387i
$469$	−0.264626	−	0.120851i	−0.0122193	−	0.00558037i
$470$	−11.0384	−	14.4174i	−0.509165	−	0.665026i
$471$	−12.3035	+	10.6610i	−0.566913	+	0.491233i
$472$	0.0467469	−	0.653607i	0.00215170	−	0.0300847i
$473$	−25.3282	+	13.8303i	−1.16459	+	0.635916i
$474$	−18.0041	+	39.4234i	−0.826955	+	1.81078i
$475$	2.21167	−	8.18413i	0.101478	−	0.375514i
$476$	−0.161743	+	0.0474920i	−0.00741347	+	0.00217679i
$477$	−22.3048	−	29.7958i	−1.02127	−	1.36425i
$478$	1.11974	+	0.417642i	0.0512158	+	0.0191025i
$479$	1.22456	+	8.51702i	0.0559517	+	0.389153i	0.998484	+	0.0550383i	$0.0175281\pi$
$479$	1.22456	+	8.51702i	0.0559517	+	0.389153i	−0.942533	+	0.334114i	$0.891563\pi$
$480$	0.346565	−	5.71499i	0.0158185	−	0.260852i
$481$	−13.3147	−	11.5373i	−0.607100	−	0.526055i
$482$	−10.2297	+	10.2297i	−0.465951	+	0.465951i
$483$	11.6781	+	3.01457i	0.531370	+	0.137168i
$484$		−	18.9019i		−	0.859179i
$485$	−19.7634	−	12.4007i	−0.897408	−	0.563087i
$486$	−18.7199	+	12.0306i	−0.849153	+	0.545718i
$487$	−3.60777	+	4.81942i	−0.163484	+	0.218389i	−0.874801	−	0.484482i	$-0.839008\pi$
$487$	−3.60777	+	4.81942i	−0.163484	+	0.218389i	0.711317	+	0.702871i	$0.248099\pi$
$488$	1.63709	−	4.38920i	0.0741074	−	0.198690i
$489$	−42.2634	−	6.07656i	−1.91122	−	0.274792i
$490$	5.73885	+	12.2144i	0.259255	+	0.551791i
$491$	35.9776	+	23.1214i	1.62365	+	1.04346i	0.953573	+	0.301163i	$0.0973747\pi$
$491$	35.9776	+	23.1214i	1.62365	+	1.04346i	0.670076	+	0.742293i	$0.266262\pi$
$492$	9.86913	−	3.68100i	0.444935	−	0.165952i
$493$	−0.416498	−	0.762759i	−0.0187581	−	0.0343529i
$494$	3.85719	+	4.45143i	0.173543	+	0.200280i
$495$	43.3366	−	3.57172i	1.94784	−	0.160537i
$496$	−9.73837	−	2.85944i	−0.437266	−	0.128393i
$497$	3.31111	+	8.87742i	0.148523	+	0.398207i
$498$	−2.49205	−	11.4558i	−0.111671	−	0.513345i
$499$	−5.51281	−	18.7749i	−0.246787	−	0.840480i	−0.985963	−	0.166967i	$-0.946603\pi$
$499$	−5.51281	−	18.7749i	−0.246787	−	0.840480i	0.739175	−	0.673513i	$-0.235215\pi$
$500$	9.98166	+	5.03650i	0.446394	+	0.225239i
$501$	14.0160	+	30.6907i	0.626188	+	1.37116i
$502$	17.7193	+	13.2645i	0.790849	+	0.592022i
$503$	11.1598	+	2.42767i	0.497591	+	0.108244i	0.454355	−	0.890821i	$-0.349870\pi$
$503$	11.1598	+	2.42767i	0.497591	+	0.108244i	0.0432360	+	0.999065i	$0.486233\pi$
$504$	2.28732	−	2.63971i	0.101885	−	0.117582i
$505$	15.2744	−	20.8717i	0.679702	−	0.928780i
$506$	−8.34958	+	24.8602i	−0.371184	+	1.10517i
$507$	1.68780	+	1.68780i	0.0749579	+	0.0749579i
$508$	1.39277	+	19.4735i	0.0617943	+	0.863997i
$509$	−5.84113	−	9.08898i	−0.258904	−	0.402862i	0.687330	−	0.726345i	$-0.258783\pi$
$509$	−5.84113	−	9.08898i	−0.258904	−	0.402862i	−0.946234	+	0.323483i	$0.895146\pi$
$510$	0.939811	−	0.287047i	0.0416155	−	0.0127107i
$511$	1.72683	−	0.788618i	0.0763906	−	0.0348864i
$512$	0.800541	−	0.599278i	0.0353793	−	0.0264846i
$513$	2.11947	+	1.15732i	0.0935770	+	0.0510969i
$514$	16.3539	−	25.4471i	0.721337	−	1.12242i
$515$	−0.809892	+	2.87301i	−0.0356881	+	0.126600i
$516$	3.80701	−	12.9655i	0.167594	−	0.570773i
$517$	44.2917	+	3.16780i	1.94795	+	0.139320i
$518$	−4.96844	−	0.355350i	−0.218301	−	0.0156132i
$519$	8.70717	−	29.6539i	0.382202	−	1.30166i
$520$	−6.77693	+	3.79635i	−0.297188	+	0.166481i
$521$	−7.00871	+	10.9058i	−0.307057	+	0.477790i	−0.960149	−	0.279489i	$-0.909835\pi$
$521$	−7.00871	+	10.9058i	−0.307057	+	0.477790i	0.653092	+	0.757279i	$0.273471\pi$
$522$	15.8045	+	8.62993i	0.691746	+	0.377722i
$523$	2.54293	−	1.90361i	0.111195	−	0.0832392i	−0.542233	−	0.840228i	$-0.682421\pi$
$523$	2.54293	−	1.90361i	0.111195	−	0.0832392i	0.653428	+	0.756989i	$0.273330\pi$
$524$	1.14053	−	0.520865i	0.0498245	−	0.0227541i
$525$	5.47013	+	11.3222i	0.238736	+	0.494140i
$526$	0.213026	+	0.331475i	0.00928837	+	0.0144530i
$527$	−0.124271	−	1.73753i	−0.00541331	−	0.0756880i
$528$	9.90061	+	9.90061i	0.430869	+	0.430869i
$529$	13.8835	−	18.3371i	0.603632	−	0.797263i
$530$	18.8856	+	13.8209i	0.820339	+	0.600343i
$531$	−1.52603	+	1.76113i	−0.0662241	+	0.0764267i
$532$	1.62726	+	0.353988i	0.0705505	+	0.0153473i
$533$	−11.4402	−	8.56402i	−0.495530	−	0.370949i
$534$	−10.4101	−	22.7949i	−0.450487	−	0.986430i
$535$	34.9937	−	0.379084i	1.51291	−	0.0163892i
$536$	0.0834482	+	0.284198i	0.00360441	+	0.0122755i
$537$	3.15796	+	14.5169i	0.136276	+	0.626451i
$538$	−0.820159	−	2.19893i	−0.0353596	−	0.0948027i
$539$	−31.6660	−	9.29797i	−1.36395	−	0.400492i
$540$	−2.05934	+	2.42929i	−0.0886200	+	0.104540i
$541$	−5.26412	−	6.07512i	−0.226322	−	0.261190i	0.631219	−	0.775604i	$-0.282555\pi$
$541$	−5.26412	−	6.07512i	−0.226322	−	0.261190i	−0.857542	+	0.514414i	$0.828009\pi$
$542$	−8.31488	−	15.2276i	−0.357155	−	0.654080i
$543$	−7.94551	+	2.96352i	−0.340974	+	0.127177i
$544$	0.144385	+	0.0927907i	0.00619046	+	0.00397837i
$545$	−10.8159	+	29.9865i	−0.463300	+	1.28448i
$546$	−8.64740	−	1.24331i	−0.370075	−	0.0532087i
$547$	−6.94426	+	18.6183i	−0.296915	+	0.796060i	0.699745	+	0.714393i	$0.253297\pi$
$547$	−6.94426	+	18.6183i	−0.296915	+	0.796060i	−0.996660	+	0.0816671i	$0.973976\pi$
$548$	2.98812	−	3.99166i	0.127646	−	0.170515i
$549$	−14.0148	+	9.00675i	−0.598136	+	0.384399i
$550$	−25.4044	+	10.1075i	−1.08325	+	0.430987i
$551$			8.58547i			0.365753i
$552$	−5.46670	−	10.9958i	−0.232678	−	0.468014i
$553$	11.7553	−	11.7553i	0.499887	−	0.499887i
$554$	11.7908	+	10.2168i	0.500941	+	0.434068i
$555$	28.9838	+	1.75762i	1.23030	+	0.0746069i
$556$	2.61773	+	18.2067i	0.111016	+	0.772136i
$557$	16.2807	+	6.07240i	0.689837	+	0.257296i	0.669841	−	0.742504i	$-0.266362\pi$
$557$	16.2807	+	6.07240i	0.689837	+	0.257296i	0.0199955	+	0.999800i	$0.493635\pi$
$558$	21.6303	+	28.8947i	0.915684	+	1.22321i
$559$	−17.5904	+	5.16500i	−0.743994	+	0.218456i
$560$	−0.890643	+	2.00750i	−0.0376365	+	0.0848325i
$561$	−0.998285	+	2.18594i	−0.0421476	+	0.0922904i
$562$	−15.0381	+	8.21142i	−0.634344	+	0.346378i
$563$	−1.50016	+	20.9749i	−0.0632241	+	0.883988i	0.862565	+	0.505947i	$0.168857\pi$
$563$	−1.50016	+	20.9749i	−0.0632241	+	0.883988i	−0.925789	+	0.378041i	$0.876598\pi$
$564$	−15.7140	+	13.6162i	−0.661677	+	0.573346i
$565$	−28.2470	−	3.74947i	−1.18836	−	0.157741i
$566$	14.3768	+	6.56568i	0.604303	+	0.275976i
$567$	6.73911	−	1.46600i	0.283016	−	0.0615664i
$568$	4.62321	−	8.46678i	0.193986	−	0.355258i
$569$	−1.73171	+	12.0443i	−0.0725969	+	0.504922i	0.920786	+	0.390069i	$0.127549\pi$
$569$	−1.73171	+	12.0443i	−0.0725969	+	0.504922i	−0.993382	+	0.114853i	$0.963360\pi$
$570$	−9.50773	−	1.96066i	−0.398235	−	0.0821231i
$571$	21.1486	−	3.04072i	0.885043	−	0.127250i	0.315221	−	0.949018i	$-0.397921\pi$
$571$	21.1486	−	3.04072i	0.885043	−	0.127250i	0.569822	+	0.821768i	$0.307012\pi$
$572$	4.03790	−	18.5619i	0.168833	−	0.776114i
$573$	18.4281	−	1.31801i	0.769846	−	0.0550605i
$574$	−4.04039			−0.168643
$575$	23.9434	−	1.30956i	0.998508	−	0.0546126i
$576$	−3.55623			−0.148176
$577$	−23.3127	+	1.66736i	−0.970520	+	0.0694130i	−0.547588	−	0.836748i	$-0.684454\pi$
$577$	−23.3127	+	1.66736i	−0.970520	+	0.0694130i	−0.422933	+	0.906161i	$0.638999\pi$
$578$	3.60735	−	16.5827i	0.150046	−	0.689750i
$579$	13.5566	−	1.94914i	0.563392	−	0.0810035i
$580$	−11.0891	−	2.28678i	−0.460451	−	0.0949532i
$581$	−0.639993	+	4.45125i	−0.0265514	+	0.184669i
$582$	−12.8041	+	23.4490i	−0.530748	+	0.971992i
$583$	−55.9229	+	12.1653i	−2.31609	+	0.503835i
$584$	−1.75818	−	0.802932i	−0.0727539	−	0.0332256i
$585$	27.3840	+	3.63491i	1.13219	+	0.150285i
$586$	18.8000	−	16.2903i	0.776621	−	0.672946i
$587$	0.483374	−	6.75845i	0.0199510	−	0.278951i	−0.977677	−	0.210114i	$-0.932617\pi$
$587$	0.483374	−	6.75845i	0.0199510	−	0.278951i	0.997628	−	0.0688373i	$-0.0219289\pi$
$588$	13.5633	−	7.40611i	0.559340	−	0.305423i
$589$	−7.14883	+	15.6537i	−0.294562	+	0.645001i
$590$	0.594210	−	1.33935i	0.0244633	−	0.0551400i
$591$	23.3881	−	6.86736i	0.962056	−	0.282485i
$592$	3.03927	+	4.05998i	0.124913	+	0.166864i
$593$	19.1942	+	7.15907i	0.788212	+	0.293988i	0.711152	−	0.703039i	$-0.248174\pi$
$593$	19.1942	+	7.15907i	0.788212	+	0.293988i	0.0770602	+	0.997026i	$0.475447\pi$
$594$	−1.10837	−	7.70887i	−0.0454769	−	0.316299i
$595$	−0.376245	−	0.0228161i	−0.0154246	−	0.000935368i
$596$	−8.26622	−	7.16272i	−0.338598	−	0.293397i
$597$	20.8434	−	20.8434i	0.853062	−	0.853062i
$598$	−8.54017	+	14.3047i	−0.349234	+	0.584963i
$599$		−	22.1792i		−	0.906216i	−0.891456	−	0.453108i	$-0.850315\pi$
$599$		−	22.1792i		−	0.906216i	0.891456	−	0.453108i	$-0.149685\pi$
$600$	5.06485	−	11.7581i	0.206772	−	0.480023i
$601$	8.66226	−	5.56690i	0.353341	−	0.227079i	−0.351914	−	0.936032i	$-0.614469\pi$
$601$	8.66226	−	5.56690i	0.353341	−	0.227079i	0.705255	+	0.708954i	$0.250833\pi$
$602$	−3.10624	+	4.14945i	−0.126601	+	0.169119i
$603$	0.368106	−	0.986930i	0.0149904	−	0.0401909i
$604$	−18.5480	−	2.66680i	−0.754707	−	0.108510i
$605$	14.3406	−	39.7588i	0.583029	−	1.61642i
$606$	−24.9150	−	16.0119i	−1.01210	−	0.650440i
$607$	−6.67162	+	2.48839i	−0.270793	+	0.101000i	−0.481192	−	0.876615i	$-0.659796\pi$
$607$	−6.67162	+	2.48839i	−0.270793	+	0.101000i	0.210400	+	0.977615i	$0.432523\pi$
$608$	−0.812586	−	1.48814i	−0.0329547	−	0.0603520i
$609$	−8.33911	−	9.62385i	−0.337918	−	0.389978i
$610$	6.77351	−	7.99032i	0.274251	−	0.323518i
$611$	27.0668	+	7.94752i	1.09500	+	0.321522i
$612$	−0.213299	−	0.571876i	−0.00862209	−	0.0231167i
$613$	−2.54791	−	11.7125i	−0.102909	−	0.473065i	−0.999541	−	0.0302890i	$-0.990357\pi$
$613$	−2.54791	−	11.7125i	−0.102909	−	0.473065i	0.896632	−	0.442776i	$-0.146006\pi$
$614$	−6.17973	−	21.0462i	−0.249394	−	0.849357i
$615$	23.5517	−	0.255134i	0.949696	−	0.0102880i
$616$	−2.23110	−	4.88543i	−0.0898937	−	0.196840i
$617$	−6.32090	−	4.73177i	−0.254470	−	0.190494i	0.464425	−	0.885612i	$-0.346261\pi$
$617$	−6.32090	−	4.73177i	−0.254470	−	0.190494i	−0.718895	+	0.695119i	$0.755352\pi$
$618$	3.33997	+	0.726567i	0.134353	+	0.0292268i
$619$	13.8197	−	15.9488i	0.555461	−	0.641036i	−0.406686	−	0.913568i	$-0.633316\pi$
$619$	13.8197	−	15.9488i	0.555461	−	0.641036i	0.962147	+	0.272532i	$0.0878610\pi$
$620$	−18.3145	−	13.4030i	−0.735529	−	0.538277i
$621$	−1.23108	+	6.71857i	−0.0494015	+	0.269607i
$622$	4.99008	+	4.99008i	0.200084	+	0.200084i
$623$	0.685740	+	9.58790i	0.0274736	+	0.384131i
$624$	4.80895	+	7.48287i	0.192512	+	0.299554i
$625$	17.1746	+	18.1668i	0.686982	+	0.726674i
$626$	18.9058	−	8.63397i	0.755626	−	0.345083i
$627$	19.0050	−	14.2270i	0.758988	−	0.568171i
$628$	−5.58030	−	3.04707i	−0.222678	−	0.121592i
$629$	−0.470593	+	0.732256i	−0.0187638	+	0.0291970i
$630$	6.81391	−	3.81707i	0.271473	−	0.152076i
$631$	2.05380	−	6.99460i	0.0817605	−	0.278451i	−0.908458	−	0.417976i	$-0.862740\pi$
$631$	2.05380	−	6.99460i	0.0817605	−	0.278451i	0.990218	+	0.139526i	$0.0445577\pi$
$632$	−16.8831	−	1.20751i	−0.671576	−	0.0480320i
$633$	45.5752	+	3.25960i	1.81145	+	0.129558i
$634$	6.07916	−	20.7037i	0.241434	−	0.822249i
$635$	−11.8447	+	42.0177i	−0.470041	+	1.66742i
$636$	14.4883	−	22.5442i	0.574497	−	0.893935i
$637$	−18.4014	−	10.0479i	−0.729091	−	0.398114i
$638$	22.1661	−	16.5933i	0.877564	−	0.656936i
$639$	−31.2060	+	14.2513i	−1.23449	+	0.563773i
$640$	2.13854	−	0.653177i	0.0845333	−	0.0258191i
$641$	−10.9663	−	17.0639i	−0.433142	−	0.673982i	0.554237	−	0.832359i	$-0.313010\pi$
$641$	−10.9663	−	17.0639i	−0.433142	−	0.673982i	−0.987379	+	0.158377i	$0.949374\pi$
$642$	−2.85881	−	39.9714i	−0.112828	−	1.57754i
$643$	−0.374000	−	0.374000i	−0.0147491	−	0.0147491i	0.699694	−	0.714443i	$-0.253320\pi$
$643$	−0.374000	−	0.374000i	−0.0147491	−	0.0147491i	−0.714443	+	0.699694i	$0.753320\pi$
$644$	0.490747	+	4.68470i	0.0193381	+	0.184603i
$645$	17.8445	−	24.3836i	0.702625	−	0.960102i
$646$	0.190569	−	0.219929i	0.00749784	−	0.00865297i
$647$	−24.5069	−	5.33115i	−0.963465	−	0.209589i	−0.296795	−	0.954941i	$-0.595918\pi$
$647$	−24.5069	−	5.33115i	−0.963465	−	0.209589i	−0.666671	+	0.745352i	$0.732281\pi$
$648$	−5.62132	−	4.20807i	−0.220826	−	0.165309i
$649$	1.48853	+	3.25942i	0.0584297	+	0.127943i
$650$	−17.1350	+	2.84379i	−0.672090	+	0.111542i
$651$	−7.19112	−	24.4907i	−0.281842	−	0.959866i
$652$	−3.54465	−	16.2945i	−0.138819	−	0.638141i
$653$	−3.14663	−	8.43644i	−0.123137	−	0.330143i	0.860725	−	0.509070i	$-0.170010\pi$
$653$	−3.14663	−	8.43644i	−0.123137	−	0.330143i	−0.983862	+	0.178926i	$0.942738\pi$
$654$	35.0242	+	10.2840i	1.36955	+	0.402137i
$655$	2.79420	−	0.230293i	0.109179	−	0.00899829i
$656$	2.69392	+	3.10895i	0.105180	+	0.121384i
$657$	3.29419	+	6.03285i	0.128518	+	0.235364i
$658$	7.47282	−	2.78722i	0.291321	−	0.108657i
$659$	−25.2459	−	16.2245i	−0.983439	−	0.632018i	−0.0530503	−	0.998592i	$-0.516894\pi$
$659$	−25.2459	−	16.2245i	−0.983439	−	0.632018i	−0.930389	+	0.366574i	$0.880531\pi$
$660$	13.3137	+	28.3366i	0.518237	+	1.10300i
$661$	−21.9067	−	3.14972i	−0.852074	−	0.122510i	−0.297579	−	0.954697i	$-0.596179\pi$
$661$	−21.9067	−	3.14972i	−0.852074	−	0.122510i	−0.554495	+	0.832187i	$0.687088\pi$
$662$	−2.89565	+	7.76354i	−0.112543	+	0.301738i
$663$	−0.914882	+	1.22214i	−0.0355311	+	0.0474639i
$664$	3.85180	−	2.47540i	0.149479	−	0.0960643i
$665$	3.15424	+	1.97916i	0.122316	+	0.0767486i
$666$		−	18.0356i		−	0.698866i
$667$	−23.0621	+	7.60605i	−0.892967	+	0.294507i
$668$	−9.31749	+	9.31749i	−0.360505	+	0.360505i
$669$	12.8777	+	11.1586i	0.497881	+	0.431416i
$670$	−0.0400902	+	0.661101i	−0.00154882	+	0.0255406i
$671$	3.64560	+	25.3557i	0.140737	+	0.978846i
$672$	2.35630	+	0.878856i	0.0908964	+	0.0339026i
$673$	−15.4604	−	20.6527i	−0.595955	−	0.796102i	0.396588	−	0.917997i	$-0.370194\pi$
$673$	−15.4604	−	20.6527i	−0.595955	−	0.796102i	−0.992543	+	0.121894i	$0.961103\pi$
$674$	−15.3900	+	4.51892i	−0.592801	+	0.174062i
$675$	−6.17474	+	3.54743i	−0.237666	+	0.136541i
$676$	−0.387250	+	0.847959i	−0.0148942	+	0.0326138i
$677$	−32.8988	+	17.9641i	−1.26440	+	0.690416i	−0.964633	−	0.263595i	$-0.915092\pi$
$677$	−32.8988	+	17.9641i	−1.26440	+	0.690416i	−0.299770	+	0.954012i	$0.596910\pi$
$678$	−2.32775	+	32.5462i	−0.0893966	+	1.24993i
$679$	7.74510	−	6.71116i	0.297230	−	0.257551i
$680$	0.233304	+	0.304721i	0.00894681	+	0.0116855i
$681$	−7.07263	−	3.22996i	−0.271024	−	0.123772i
$682$	54.2318	−	11.7974i	2.07664	−	0.451746i
$683$	15.2203	−	27.8738i	0.582387	−	1.06656i	−0.405894	−	0.913920i	$-0.633040\pi$
$683$	15.2203	−	27.8738i	0.582387	−	1.06656i	0.988281	−	0.152643i	$-0.0487783\pi$
$684$	−0.858121	+	5.96836i	−0.0328111	+	0.228206i
$685$	9.31369	−	6.12911i	0.355858	−	0.234181i
$686$	−12.6726	+	1.82205i	−0.483843	+	0.0695662i
$687$	−10.9396	+	50.2887i	−0.417373	+	1.91863i
$688$	5.26395	−	0.376485i	0.200686	−	0.0143533i
$689$	−36.3575			−1.38511
$690$	−3.15642	−	27.2764i	−0.120163	−	1.03840i
$691$	−34.1617			−1.29957			−0.649786	−	0.760117i	$-0.725142\pi$
$691$	−34.1617			−1.29957			−0.649786	+	0.760117i	$0.725142\pi$
$692$	12.0394	−	0.861075i	0.457669	−	0.0327331i
$693$	−4.05994	+	18.6633i	−0.154224	+	0.708958i
$694$	−10.6117	+	1.52573i	−0.402815	+	0.0579160i
$695$	−8.30696	+	40.2824i	−0.315101	+	1.52800i
$696$	−1.84516	+	12.8333i	−0.0699405	+	0.486447i
$697$	−0.338370	+	0.619679i	−0.0128167	+	0.0234720i
$698$	4.28957	−	0.933139i	0.162363	−	0.0353198i
$699$	−36.8437	−	16.8260i	−1.39356	−	0.636416i
$700$	−3.39646	+	3.54691i	−0.128374	+	0.134061i
$701$	15.9847	−	13.8508i	0.603734	−	0.523138i	−0.298486	−	0.954414i	$-0.596482\pi$
$701$	15.9847	−	13.8508i	0.603734	−	0.523138i	0.902220	+	0.431275i	$0.141936\pi$
$702$	0.352961	−	4.93503i	0.0133216	−	0.186261i
$703$	7.54718	−	4.12107i	0.284647	−	0.155429i
$704$	−2.27160	+	4.97411i	−0.0856141	+	0.187469i
$705$	−43.3836	+	16.7188i	−1.63392	+	0.629665i
$706$	13.5025	−	3.96470i	0.508175	−	0.149214i
$707$	6.80806	+	9.09450i	0.256043	+	0.342034i
$708$	−1.57206	−	0.586346i	−0.0590815	−	0.0220362i
$709$	4.76319	+	33.1287i	0.178885	+	1.24417i	0.859348	+	0.511392i	$0.170870\pi$
$709$	4.76319	+	33.1287i	0.178885	+	1.24417i	−0.680462	+	0.732783i	$0.738221\pi$
$710$	16.1482	−	14.3017i	0.606031	−	0.536732i
$711$	45.4914	+	39.4185i	1.70606	+	1.47831i
$712$	6.92036	−	6.92036i	0.259352	−	0.259352i
$713$	−48.3820	−	5.33502i	−1.81192	−	0.199798i
$714$			0.431629i			0.0161533i
$715$	22.5761	−	35.9802i	0.844298	−	1.34558i
$716$	−4.88106	+	3.13687i	−0.182414	+	0.117230i
$717$	1.83382	−	2.44970i	0.0684853	−	0.0914856i
$718$	−8.70937	+	23.3507i	−0.325031	+	0.871441i
$719$	14.6856	+	2.11147i	0.547679	+	0.0787444i	0.410600	−	0.911816i	$-0.365319\pi$
$719$	14.6856	+	2.11147i	0.547679	+	0.0787444i	0.137079	+	0.990560i	$0.456228\pi$
$720$	−7.48027	−	2.69806i	−0.278773	−	0.100551i
$721$	−1.10299	−	0.708847i	−0.0410774	−	0.0263988i
$722$	15.1084	−	5.63516i	0.562278	−	0.209719i
$723$	17.7528	+	32.5119i	0.660234	+	1.20913i
$724$	−2.16884	−	2.50297i	−0.0806042	−	0.0930222i
$725$	−21.5902	−	13.2232i	−0.801840	−	0.491098i
$726$	−46.4382	−	13.6355i	−1.72348	−	0.506060i
$727$	−10.5679	−	28.3336i	−0.391941	−	1.05084i	−0.971735	−	0.236072i	$-0.924140\pi$
$727$	−10.5679	−	28.3336i	−0.391941	−	1.05084i	0.579794	−	0.814763i	$-0.303133\pi$
$728$	−0.725261	−	3.33397i	−0.0268799	−	0.123565i
$729$	10.1176	+	34.4572i	0.374724	+	1.27619i
$730$	−3.08902	−	3.02281i	−0.114330	−	0.111879i
$731$	0.376268	+	0.823912i	0.0139168	+	0.0304735i
$732$	−9.60240	−	7.18827i	−0.354915	−	0.265686i
$733$	14.7002	+	3.19783i	0.542964	+	0.118115i	0.475679	−	0.879619i	$-0.342203\pi$
$733$	14.7002	+	3.19783i	0.542964	+	0.118115i	0.0672855	+	0.997734i	$0.478566\pi$
$734$	16.6652	−	19.2327i	0.615125	−	0.709892i
$735$	34.1482	−	5.28794i	1.25958	−	0.195048i
$736$	3.27752	−	3.50112i	0.120811	−	0.129053i
$737$	−1.14529	−	1.14529i	−0.0421872	−	0.0421872i
$738$	−1.04365	−	14.5921i	−0.0384172	−	0.537143i
$739$	6.31805	+	9.83108i	0.232413	+	0.361642i	0.937797	−	0.347183i	$-0.112862\pi$
$739$	6.31805	+	9.83108i	0.232413	+	0.361642i	−0.705384	+	0.708825i	$0.749225\pi$
$740$	3.31262	+	10.8457i	0.121774	+	0.398697i
$741$	13.7188	−	6.26515i	0.503971	−	0.230156i
$742$	−8.22909	+	6.16022i	−0.302099	+	0.226149i
$743$	−38.1323	−	20.8218i	−1.39894	−	0.763877i	−0.409982	−	0.912094i	$-0.634465\pi$
$743$	−38.1323	−	20.8218i	−1.39894	−	0.763877i	−0.988955	+	0.148216i	$0.952647\pi$
$744$	−14.0501	+	21.8624i	−0.515103	+	0.801516i
$745$	−11.9531	−	21.3377i	−0.437929	−	0.781753i
$746$	0.988669	−	3.36710i	0.0361977	−	0.123278i
$747$	−16.2413	−	1.16160i	−0.594236	−	0.0425006i
$748$	−0.936132	−	0.0669535i	−0.0342284	−	0.00244806i
$749$	−4.33067	+	14.7489i	−0.158239	+	0.538913i
$750$	19.5742	−	20.8897i	0.714750	−	0.762783i
$751$	14.5006	−	22.5634i	0.529136	−	0.823351i	−0.469074	−	0.883159i	$-0.655412\pi$
$751$	14.5006	−	22.5634i	0.529136	−	0.823351i	0.998210	+	0.0598077i	$0.0190488\pi$
$752$	−7.12715	−	3.89172i	−0.259901	−	0.141916i
$753$	45.3704	−	33.9639i	1.65339	−	1.23771i
$754$	16.0006	−	7.30722i	0.582707	−	0.266113i
$755$	−36.9910	−	19.6815i	−1.34624	−	0.716283i
$756$	−0.756276	−	1.17679i	−0.0275055	−	0.0427994i
$757$	3.25941	+	45.5724i	0.118465	+	1.65636i	0.615137	+	0.788420i	$0.289101\pi$
$757$	3.25941	+	45.5724i	0.118465	+	1.65636i	−0.496672	+	0.867938i	$0.665445\pi$
$758$	24.2855	+	24.2855i	0.882088	+	0.882088i
$759$	55.0532	+	38.4469i	1.99830	+	1.39553i
$760$	−0.580184	−	3.74669i	−0.0210455	−	0.135907i
$761$	29.7315	−	34.3120i	1.07777	−	1.24381i	0.109473	−	0.993990i	$-0.465084\pi$
$761$	29.7315	−	34.3120i	1.07777	−	1.24381i	0.968293	−	0.249818i	$-0.0803707\pi$
$762$	48.8471	+	10.6260i	1.76955	+	0.384941i
$763$	−11.2091	−	8.39102i	−0.405797	−	0.303775i
$764$	2.99740	+	6.56338i	0.108442	+	0.237455i
$765$	−0.0147840	−	1.36473i	−0.000534515	−	0.0493418i
$766$	10.5683	+	35.9925i	0.381850	+	1.30046i
$767$	0.483872	+	2.22433i	0.0174716	+	0.0803157i
$768$	−0.894808	−	2.39907i	−0.0322886	−	0.0865691i
$769$	−13.3546	−	3.92127i	−0.481580	−	0.141405i	0.0319265	−	0.999490i	$-0.489836\pi$
$769$	−13.3546	−	3.92127i	−0.481580	−	0.141405i	−0.513507	+	0.858085i	$0.671654\pi$
$770$	−0.986451	−	11.9688i	−0.0355492	−	0.431327i
$771$	−50.7209	−	58.5351i	−1.82667	−	2.10809i
$772$	2.56346	+	4.69463i	0.0922610	+	0.168963i
$773$	10.6708	−	3.98001i	0.383803	−	0.143151i	−0.150154	−	0.988663i	$-0.547977\pi$
$773$	10.6708	−	3.98001i	0.383803	−	0.143151i	0.533957	+	0.845512i	$0.320704\pi$
$774$	−15.7883	−	10.1465i	−0.567500	−	0.364710i
$775$	−28.3546	−	42.0871i	−1.01853	−	1.51181i
$776$	−10.3280	−	1.48495i	−0.370755	−	0.0533065i
$777$	−4.45716	+	11.9501i	−0.159900	+	0.428708i
$778$	−15.7815	+	21.0817i	−0.565796	+	0.755815i
$779$	5.86774	−	3.77096i	0.210233	−	0.135109i
$780$	4.43812	+	19.3881i	0.158910	+	0.694206i
$781$			52.7512i			1.88759i
$782$	0.759596	+	0.317063i	0.0271631	+	0.0113381i
$783$	5.09947	−	5.09947i	0.182240	−	0.182240i
$784$	4.56120	+	3.95231i	0.162900	+	0.141154i
$785$	−9.42597	−	10.6430i	−0.336427	−	0.379864i
$786$	−0.456899	−	3.17780i	−0.0162970	−	0.113348i
$787$	25.4186	+	9.48065i	0.906075	+	0.337949i	0.758934	−	0.651167i	$-0.225720\pi$
$787$	25.4186	+	9.48065i	0.906075	+	0.337949i	0.147141	+	0.989116i	$0.452993\pi$
$788$	5.70497	+	7.62095i	0.203231	+	0.271485i
$789$	0.968038	−	0.284242i	0.0344631	−	0.0101193i
$790$	−34.5963	−	15.3489i	−1.23088	−	0.546089i
$791$	5.19937	−	11.3850i	0.184868	−	0.404805i
$792$	17.0677	−	9.31968i	0.606475	−	0.331160i
$793$	−1.16094	+	16.2321i	−0.0412263	+	0.576419i
$794$	−9.63813	+	8.35149i	−0.342045	+	0.296383i
$795$	47.5789	−	36.4280i	1.68745	−	1.29197i
$796$	10.4718	+	4.78231i	0.371163	+	0.169505i
$797$	27.9223	−	6.07411i	0.989057	−	0.215156i	0.311196	−	0.950346i	$-0.399271\pi$
$797$	27.9223	−	6.07411i	0.989057	−	0.215156i	0.677861	+	0.735190i	$0.262907\pi$
$798$	2.04354	−	3.74247i	0.0723407	−	0.132482i
$799$	0.198347	−	1.37954i	0.00701702	−	0.0488045i
$800$	4.99382	+	0.248572i	0.176558	+	0.00878834i
$801$	−34.4501	+	4.95318i	−1.21724	+	0.175012i
$802$	−0.573746	+	2.63747i	−0.0202597	+	0.0931323i
$803$	10.5424	−	0.754005i	0.372032	−	0.0266083i
$804$	0.758415			0.0267472
$805$	−2.52196	+	10.2262i	−0.0888875	+	0.360427i
$806$	35.2581			1.24191
$807$	−5.99397	+	0.428697i	−0.210998	+	0.0150909i
$808$	2.45867	−	11.3023i	0.0864956	−	0.397614i
$809$	40.9101	−	5.88198i	1.43832	−	0.206799i	0.621375	−	0.783513i	$-0.286574\pi$
$809$	40.9101	−	5.88198i	1.43832	−	0.206799i	0.816946	+	0.576714i	$0.195665\pi$
$810$	−8.63143	−	13.1162i	−0.303278	−	0.460856i
$811$	−1.16548	+	8.10609i	−0.0409255	+	0.284643i	0.959073	+	0.283158i	$0.0913820\pi$
$811$	−1.16548	+	8.10609i	−0.0409255	+	0.284643i	−0.999999	+	0.00148562i	$0.999527\pi$
$812$	2.38344	−	4.36495i	0.0836424	−	0.153180i
$813$	−43.4092	+	9.44310i	−1.52243	+	0.331184i
$814$	−25.2264	−	11.5205i	−0.884186	−	0.403794i
$815$	4.90648	−	36.9635i	0.171867	−	1.29477i
$816$	0.332124	−	0.287787i	0.0116267	−	0.0100746i
$817$	0.638345	−	8.92523i	0.0223329	−	0.312254i
$818$	21.7535	−	11.8783i	0.760595	−	0.415316i
$819$	−5.04051	+	11.0372i	−0.176130	+	0.385670i
$820$	3.30774	+	8.58327i	0.115511	+	0.299741i
$821$	−38.9805	+	11.4457i	−1.36043	+	0.399458i	−0.878914	−	0.476981i	$-0.841731\pi$
$821$	−38.9805	+	11.4457i	−1.36043	+	0.399458i	−0.481514	+	0.876438i	$0.659913\pi$
$822$	−7.65111	−	10.2207i	−0.266863	−	0.356487i
$823$	0.204990	+	0.0764573i	0.00714550	+	0.00266513i	0.353034	−	0.935610i	$-0.385150\pi$
$823$	0.204990	+	0.0764573i	0.00714550	+	0.00266513i	−0.345889	+	0.938275i	$0.612423\pi$
$824$	0.189979	+	1.32134i	0.00661824	+	0.0460309i
$825$	6.50587	+	69.7049i	0.226505	+	2.42681i
$826$	0.486396	+	0.421465i	0.0169239	+	0.0146646i
$827$	−26.5057	+	26.5057i	−0.921693	+	0.921693i	−0.997149	−	0.0754559i	$-0.975959\pi$
$827$	−26.5057	+	26.5057i	−0.921693	+	0.921693i	0.0754559	+	0.997149i	$0.475959\pi$
$828$	−16.7923	+	2.98244i	−0.583573	+	0.103647i
$829$			47.4529i			1.64811i	0.566512	+	0.824054i	$0.308293\pi$
$829$			47.4529i			1.64811i	−0.566512	+	0.824054i	$0.691707\pi$
$830$	9.98003	−	2.28452i	0.346412	−	0.0792969i
$831$	33.6061	−	21.5973i	1.16578	−	0.749203i
$832$	−2.08182	+	2.78098i	−0.0721739	+	0.0964131i
$833$	−0.361993	+	0.970540i	−0.0125423	+	0.0336272i
$834$	46.6185	+	6.70273i	1.61427	+	0.232096i
$835$	−26.6677	+	12.5296i	−0.922874	+	0.433605i
$836$	7.79982	+	5.01264i	0.269762	+	0.173366i
$837$	13.5439	−	5.05163i	0.468147	−	0.174610i
$838$	−7.93876	−	14.5387i	−0.274240	−	0.502233i
$839$	−1.47534	−	1.70264i	−0.0509345	−	0.0587815i	0.729711	−	0.683756i	$-0.239655\pi$
$839$	−1.47534	−	1.70264i	−0.0509345	−	0.0587815i	−0.780645	+	0.624975i	$0.785109\pi$
$840$	4.28953	+	3.63630i	0.148003	+	0.125464i
$841$	−3.22426	−	0.946728i	−0.111181	−	0.0326458i
$842$	4.93895	+	13.2418i	0.170207	+	0.456344i
$843$	9.32560	+	42.8691i	0.321191	+	1.47649i
$844$	5.02743	+	17.1219i	0.173051	+	0.589359i
$845$	−1.45789	+	1.48982i	−0.0501528	+	0.0512513i
$846$	11.9965	+	26.2686i	0.412447	+	0.903132i
$847$	14.8620	+	11.1256i	0.510665	+	0.382279i
$848$	10.2268	+	2.22471i	0.351190	+	0.0763967i
$849$	26.5017	−	30.5846i	0.909535	−	1.04966i
$850$	0.259551	+	0.817963i	0.00890252	+	0.0280559i
$851$	17.7561	+	16.6221i	0.608672	+	0.569798i
$852$	−17.4661	−	17.4661i	−0.598377	−	0.598377i
$853$	−3.78022	−	52.8544i	−0.129432	−	1.80970i	−0.484425	−	0.874833i	$-0.660971\pi$
$853$	−3.78022	−	52.8544i	−0.129432	−	1.80970i	0.354993	−	0.934869i	$-0.384483\pi$
$854$	2.48751	+	3.87065i	0.0851210	+	0.132451i
$855$	−6.33310	+	11.9030i	−0.216587	+	0.407073i
$856$	14.2363	−	6.50148i	0.486585	−	0.222216i
$857$	−16.9334	+	12.6762i	−0.578435	+	0.433011i	−0.848019	−	0.529966i	$-0.822205\pi$
$857$	−16.9334	+	12.6762i	−0.578435	+	0.433011i	0.269584	+	0.962977i	$0.413114\pi$
$858$	−42.6900	−	23.3105i	−1.45741	−	0.795808i
$859$	3.07912	−	4.79121i	0.105058	−	0.163474i	−0.784744	−	0.619820i	$-0.787206\pi$
$859$	3.07912	−	4.79121i	0.105058	−	0.163474i	0.889802	+	0.456346i	$0.150842\pi$
$860$	11.3579	+	3.20177i	0.387303	+	0.109179i
$861$	−2.91466	+	9.92641i	−0.0993312	+	0.338291i
$862$	−34.5827	−	2.47340i	−1.17789	−	0.0842444i
$863$	−5.84461	−	0.418015i	−0.198953	−	0.0142294i	−0.0284929	−	0.999594i	$-0.509071\pi$
$863$	−5.84461	−	0.418015i	−0.198953	−	0.0142294i	−0.170460	+	0.985365i	$0.554525\pi$
$864$	−0.401256	+	1.36655i	−0.0136510	+	0.0464910i
$865$	25.9773	+	7.32291i	0.883253	+	0.248986i
$866$	−6.73742	+	10.4836i	−0.228947	+	0.356248i
$867$	−38.1381	−	20.8250i	−1.29524	−	0.707253i
$868$	7.98024	−	5.97393i	0.270867	−	0.202768i
$869$	84.1931	−	38.4497i	2.85606	−	1.30432i
$870$	−13.6176	+	25.5941i	−0.461680	+	0.867721i
$871$	−0.556292	−	0.865607i	−0.0188492	−	0.0293300i
$872$	1.01701	+	14.2197i	0.0344405	+	0.481541i
$873$	26.2383	+	26.2383i	0.888033	+	0.888033i
$874$	−5.08501	−	6.34542i	−0.172003	−	0.214637i
$875$	−9.83520	+	4.88382i	−0.332490	+	0.165103i
$876$	−3.24095	+	3.74026i	−0.109502	+	0.126372i
$877$	−40.1860	−	8.74194i	−1.35699	−	0.295194i	−0.525525	−	0.850778i	$-0.676131\pi$
$877$	−40.1860	−	8.74194i	−1.35699	−	0.295194i	−0.831461	+	0.555584i	$0.812495\pi$
$878$	12.2970	+	9.20539i	0.415002	+	0.310667i
$879$	−26.4600	−	57.9393i	−0.892473	−	1.95424i
$880$	−8.55192	+	8.73924i	−0.288285	+	0.294600i
$881$	−14.4785	−	49.3093i	−0.487794	−	1.66127i	−0.724177	−	0.689614i	$-0.757780\pi$
$881$	−14.4785	−	49.3093i	−0.487794	−	1.66127i	0.236383	−	0.971660i	$-0.424038\pi$
$882$	−4.56230	−	20.9726i	−0.153621	−	0.706183i
$883$	1.96958	+	5.28066i	0.0662818	+	0.177708i	0.965868	−	0.259035i	$-0.0834045\pi$
$883$	1.96958	+	5.28066i	0.0662818	+	0.177708i	−0.899586	+	0.436743i	$0.856132\pi$
$884$	−0.572073	−	0.167976i	−0.0192409	−	0.00564964i
$885$	−2.86185	−	2.42603i	−0.0962000	−	0.0815502i
$886$	7.09194	+	8.18454i	0.238258	+	0.274965i
$887$	−6.02923	−	11.0417i	−0.202442	−	0.370745i	0.756659	−	0.653810i	$-0.226830\pi$
$887$	−6.02923	−	11.0417i	−0.202442	−	0.370745i	−0.959101	+	0.283065i	$0.908649\pi$
$888$	12.1670	−	4.53806i	0.408298	−	0.152287i
$889$	−16.1312	−	10.3669i	−0.541023	−	0.347694i
$890$	19.8068	−	9.30609i	0.663927	−	0.311941i
$891$	38.0068	+	5.46455i	1.27328	+	0.183069i
$892$	−2.32560	+	6.23519i	−0.0778670	+	0.208769i
$893$	−8.25119	+	11.0223i	−0.276116	+	0.368847i
$894$	−23.5604	+	15.1414i	−0.787979	+	0.506403i
$895$	−12.6468	+	2.89498i	−0.422737	+	0.0967684i
$896$			0.982172i			0.0328121i
$897$	28.9830	+	31.3006i	0.967716	+	1.04510i
$898$	−8.07573	+	8.07573i	−0.269491	+	0.269491i
$899$	38.8399	+	33.6550i	1.29538	+	1.12246i
$900$	−13.6872	−	11.3503i	−0.456240	−	0.378345i
$901$	0.255638	+	1.77800i	0.00851655	+	0.0592339i
$902$	−21.0766	−	7.86118i	−0.701775	−	0.261749i
$903$	7.95357	+	10.6247i	0.264678	+	0.353569i
$904$	−12.2271	+	3.59019i	−0.406666	+	0.119408i
$905$	−2.66302	−	6.91028i	−0.0885218	−	0.229705i
$906$	−19.9319	+	43.6448i	−0.662194	+	1.45000i
$907$	−35.6870	+	19.4866i	−1.18497	+	0.647042i	−0.946057	−	0.324000i	$-0.894972\pi$
$907$	−35.6870	+	19.4866i	−1.18497	+	0.647042i	−0.238911	+	0.971041i	$0.576790\pi$
$908$	0.216629	−	3.02887i	0.00718908	−	0.100516i
$909$	−31.0868	+	26.9368i	−1.03108	+	0.893439i
$910$	1.00390	−	7.56300i	0.0332790	−	0.250711i
$911$	−31.3361	−	14.3107i	−1.03821	−	0.474135i	−0.177977	−	0.984035i	$-0.556955\pi$
$911$	−31.3361	−	14.3107i	−1.03821	−	0.474135i	−0.860234	+	0.509900i	$0.829683\pi$
$912$	−4.24224	+	0.922843i	−0.140475	+	0.0305584i
$913$	−11.9991	+	21.9747i	−0.397112	+	0.727256i
$914$	−0.724778	+	5.04094i	−0.0239735	+	0.166739i
$915$	−14.7443	−	22.4052i	−0.487432	−	0.740693i
$916$	−19.8948	+	2.86045i	−0.657344	+	0.0945118i
$917$	−0.261772	+	1.20335i	−0.00864447	+	0.0397380i
$918$	−0.243821	+	0.0174384i	−0.00804730	+	0.000575554i
$919$	25.7553			0.849588			0.424794	−	0.905290i	$-0.360347\pi$
$919$	25.7553			0.849588			0.424794	+	0.905290i	$0.360347\pi$
$920$	9.55027	−	4.87775i	0.314863	−	0.160815i
$921$	−56.1642			−1.85067
$922$	−20.4099	+	1.45975i	−0.672165	+	0.0480742i
$923$	−7.12343	+	32.7459i	−0.234470	+	1.07784i
$924$	−13.6120	+	1.95711i	−0.447801	+	0.0643841i
$925$	−1.26064	+	25.3264i	−0.0414497	+	0.832727i
$926$	4.09102	−	28.4537i	0.134439	−	0.935046i
$927$	2.27514	−	4.16660i	0.0747253	−	0.136849i
$928$	−4.94784	+	1.07634i	−0.162421	+	0.0353325i
$929$	24.0797	+	10.9968i	0.790031	+	0.360795i	0.769216	−	0.638988i	$-0.220647\pi$
$929$	24.0797	+	10.9968i	0.790031	+	0.360795i	0.0208143	+	0.999783i	$0.493374\pi$
$930$	−46.1401	+	35.3264i	−1.51299	+	1.15840i
$931$	7.73370	−	6.70129i	0.253462	−	0.219626i
$932$	1.12849	−	15.7784i	0.0369650	−	0.516838i
$933$	15.8594	−	8.65986i	0.519212	−	0.283511i
$934$	−0.560138	+	1.22653i	−0.0183283	+	0.0401333i
$935$	−1.91829	−	0.851061i	−0.0627347	−	0.0278327i
$936$	11.8535	−	3.48050i	0.387443	−	0.113764i
$937$	−7.88648	−	10.5351i	−0.257640	−	0.344167i	0.653007	−	0.757352i	$-0.273507\pi$
$937$	−7.88648	−	10.5351i	−0.257640	−	0.344167i	−0.910647	+	0.413185i	$0.864416\pi$
$938$	−0.272574	−	0.101665i	−0.00889984	−	0.00331947i
$939$	−7.57366	−	52.6760i	−0.247157	−	1.71902i
$940$	−12.0388	−	13.5932i	−0.392664	−	0.443362i
$941$	7.93208	+	6.87319i	0.258578	+	0.224059i	0.774496	−	0.632579i	$-0.218004\pi$
$941$	7.93208	+	6.87319i	0.258578	+	0.224059i	−0.515918	+	0.856638i	$0.672549\pi$
$942$	−11.5116	+	11.5116i	−0.375067	+	0.375067i
$943$	15.3278	+	12.4210i	0.499143	+	0.404483i
$944$		−	0.655276i		−	0.0213274i
$945$	−0.697958	−	3.04906i	−0.0227046	−	0.0991860i
$946$	−24.2770	+	15.6019i	−0.789315	+	0.507262i
$947$	23.0470	−	30.7872i	0.748928	−	1.00045i	−0.250549	−	0.968104i	$-0.580611\pi$
$947$	23.0470	−	30.7872i	0.748928	−	1.00045i	0.999477	−	0.0323465i	$-0.0102980\pi$
$948$	−15.1458	+	40.6074i	−0.491912	+	1.31887i
$949$	6.64611	+	0.955567i	0.215742	+	0.0310190i
$950$	1.62218	−	8.32105i	0.0526306	−	0.269971i
$951$	−46.4794	−	29.8705i	−1.50720	−	0.968617i
$952$	−0.157943	+	0.0589096i	−0.00511895	+	0.00190927i
$953$	16.2556	+	29.7699i	0.526570	+	0.964341i	0.996655	+	0.0817201i	$0.0260414\pi$
$953$	16.2556	+	29.7699i	0.526570	+	0.964341i	−0.470085	+	0.882621i	$0.655777\pi$
$954$	−24.3736	−	28.1286i	−0.789124	−	0.910698i
$955$	1.32526	+	16.0797i	0.0428843	+	0.520326i
$956$	1.14668	+	0.336696i	0.0370864	+	0.0108895i
$957$	−24.7762	−	66.4277i	−0.800902	−	2.14730i
$958$	1.82904	+	8.40796i	0.0590936	+	0.271649i
$959$	1.37973	+	4.69893i	0.0445538	+	0.151736i
$960$	−0.0620201	−	5.72515i	−0.00200169	−	0.184778i
$961$	29.9150	+	65.5047i	0.965000	+	2.11305i
$962$	−14.1039	−	10.5580i	−0.454727	−	0.340404i
$963$	−54.3851	−	11.8308i	−1.75254	−	0.381241i
$964$	−9.47388	+	10.9334i	−0.305133	+	0.352142i
$965$	1.83030	+	11.8197i	0.0589195	+	0.380488i
$966$	11.8634	+	2.17378i	0.381697	+	0.0699403i
$967$	−15.9732	−	15.9732i	−0.513663	−	0.513663i	0.401984	−	0.915647i	$-0.368321\pi$
$967$	−15.9732	−	15.9732i	−0.513663	−	0.513663i	−0.915647	+	0.401984i	$0.868321\pi$
$968$	−1.34845	−	18.8538i	−0.0433408	−	0.605983i
$969$	−0.402847	−	0.626841i	−0.0129413	−	0.0201370i
$970$	−20.5977	−	10.9592i	−0.661351	−	0.351879i
$971$	14.2140	−	6.49133i	0.456150	−	0.208317i	−0.174070	−	0.984733i	$-0.555692\pi$
$971$	14.2140	−	6.49133i	0.456150	−	0.208317i	0.630220	+	0.776417i	$0.282965\pi$
$972$	−17.8140	+	13.3354i	−0.571384	+	0.427732i
$973$	−15.8561	−	8.65811i	−0.508325	−	0.277566i
$974$	−3.25477	+	5.06452i	−0.104289	+	0.162278i
$975$	−5.37424	+	44.1486i	−0.172113	+	1.41389i
$976$	1.31979	−	4.49480i	0.0422456	−	0.143875i
$977$	19.9125	+	1.42417i	0.637059	+	0.0455633i	0.386133	−	0.922443i	$-0.373811\pi$
$977$	19.9125	+	1.42417i	0.637059	+	0.0455633i	0.250926	+	0.968006i	$0.419265\pi$
$978$	−42.5892	−	3.04604i	−1.36185	−	0.0974017i
$979$	−15.0775	+	51.3494i	−0.481880	+	1.64113i
$980$	6.59559	+	11.7739i	0.210689	+	0.376103i
$981$	27.4093	−	42.6497i	0.875112	−	1.36170i
$982$	37.5354	+	20.4959i	1.19780	+	0.654051i
$983$	−41.9893	+	31.4328i	−1.33925	+	1.00255i	−0.341209	+	0.939988i	$0.610836\pi$
$983$	−41.9893	+	31.4328i	−1.33925	+	1.00255i	−0.998041	+	0.0625624i	$0.980073\pi$
$984$	9.58139	−	4.37567i	0.305444	−	0.139491i
$985$	6.21808	+	20.3584i	0.198124	+	0.648672i
$986$	−0.469851	−	0.731102i	−0.0149631	−	0.0232830i
$987$	−1.45688	−	20.3698i	−0.0463730	−	0.648379i
$988$	4.16492	+	4.16492i	0.132504	+	0.132504i
$989$	24.5403	−	6.19235i	0.780335	−	0.196905i
$990$	42.9714	−	6.65422i	1.36572	−	0.211485i
$991$	−8.64352	+	9.97515i	−0.274570	+	0.316871i	−0.876241	−	0.481873i	$-0.839957\pi$
$991$	−8.64352	+	9.97515i	−0.274570	+	0.316871i	0.601671	+	0.798744i	$0.294502\pi$
$992$	−9.91755	−	2.15743i	−0.314883	−	0.0684985i
$993$	16.9846	+	12.7145i	0.538989	+	0.403482i
$994$	3.93598	+	8.61859i	0.124842	+	0.273365i
$995$	18.3984	+	18.0040i	0.583268	+	0.570766i
$996$	−3.30295	−	11.2488i	−0.104658	−	0.356432i
$997$	−5.08969	−	23.3969i	−0.161192	−	0.740988i	−0.984781	−	0.173801i	$-0.944395\pi$
$997$	−5.08969	−	23.3969i	−0.161192	−	0.740988i	0.823589	−	0.567187i	$-0.191968\pi$
$998$	−6.83815	−	18.3338i	−0.216458	−	0.580346i
$999$	−6.93053	−	2.03499i	−0.219272	−	0.0643842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.7.12	✓	240
5.3	odd	4	inner	230.2.l.a.53.6	yes	240
23.10	odd	22	inner	230.2.l.a.217.6	yes	240
115.33	even	44	inner	230.2.l.a.33.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.12	✓	240	1.1	even	1	trivial
230.2.l.a.33.12	yes	240	115.33	even	44	inner
230.2.l.a.53.6	yes	240	5.3	odd	4	inner
230.2.l.a.217.6	yes	240	23.10	odd	22	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997452 - 0.0713392i) q^{2} +(0.544276 - 2.50200i) q^{3} +(0.989821 - 0.142315i) q^{4} +(2.18999 + 0.451614i) q^{5} +(0.364399 - 2.53445i) q^{6} +(-0.470705 + 0.862032i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-3.23486 - 1.47731i) q^{9} +(2.21663 + 0.294232i) q^{10} +(-4.13264 + 3.58095i) q^{11} +(0.182665 - 2.55399i) q^{12} +(-3.04895 + 1.66485i) q^{13} +(-0.408009 + 0.893415i) q^{14} +(2.32190 - 5.23354i) q^{15} +(0.959493 - 0.281733i) q^{16} +(0.102855 + 0.137398i) q^{17} +(-3.33201 - 1.24278i) q^{18} +(-0.241301 - 1.67828i) q^{19} +(2.23197 + 0.135350i) q^{20} +(1.90061 + 1.64689i) q^{21} +(-3.86665 + 3.86665i) q^{22} +(4.29439 - 2.13500i) q^{23} -2.56051i q^{24} +(4.59209 + 1.97806i) q^{25} +(-2.92241 + 1.87812i) q^{26} +(-0.853517 + 1.14017i) q^{27} +(-0.343234 + 0.920246i) q^{28} +(-5.01202 - 0.720619i) q^{29} +(1.94262 - 5.38585i) q^{30} +(-8.53830 - 5.48723i) q^{31} +(0.936950 - 0.349464i) q^{32} +(6.71024 + 12.2889i) q^{33} +(0.112394 + 0.129710i) q^{34} +(-1.42014 + 1.67526i) q^{35} +(-3.41218 - 1.00191i) q^{36} +(1.77232 + 4.75179i) q^{37} +(-0.360413 - 1.65679i) q^{38} +(2.50598 + 8.53460i) q^{39} +(2.23594 - 0.0242217i) q^{40} +(1.70890 + 3.74198i) q^{41} +(2.01325 + 1.50710i) q^{42} +(5.15679 + 1.12179i) q^{43} +(-3.58095 + 4.13264i) q^{44} +(-6.41713 - 4.69621i) q^{45} +(4.13114 - 2.43592i) q^{46} +(-5.74203 - 5.74203i) q^{47} +(-0.182665 - 2.55399i) q^{48} +(3.26295 + 5.07725i) q^{49} +(4.72150 + 1.64542i) q^{50} +(0.399750 - 0.182560i) q^{51} +(-2.78098 + 2.08182i) q^{52} +(9.18578 + 5.01582i) q^{53} +(-0.770004 + 1.19815i) q^{54} +(-10.6676 + 5.97588i) q^{55} +(-0.276710 + 0.942387i) q^{56} +(-4.33039 - 0.309716i) q^{57} +(-5.05066 - 0.361230i) q^{58} +(0.184613 - 0.628733i) q^{59} +(1.55345 - 5.51071i) q^{60} +(2.53267 - 3.94090i) q^{61} +(-8.90800 - 4.86414i) q^{62} +(2.79616 - 2.09318i) q^{63} +(0.909632 - 0.415415i) q^{64} +(-7.42902 + 2.26905i) q^{65} +(7.56982 + 11.7789i) q^{66} +(0.0211304 + 0.295442i) q^{67} +(0.121361 + 0.121361i) q^{68} +(-3.00444 - 11.9066i) q^{69} +(-1.29701 + 1.77231i) q^{70} +(6.31730 - 7.29055i) q^{71} +(-3.47496 - 0.755932i) q^{72} +(-1.54732 - 1.15831i) q^{73} +(2.10680 + 4.61324i) q^{74} +(7.44847 - 10.4128i) q^{75} +(-0.477689 - 1.62686i) q^{76} +(-1.14164 - 5.24804i) q^{77} +(3.10845 + 8.33408i) q^{78} +(-16.2406 - 4.76868i) q^{79} +(2.22851 - 0.183670i) q^{80} +(-4.59837 - 5.30680i) q^{81} +(1.97150 + 3.61053i) q^{82} +(4.28996 - 1.60007i) q^{83} +(2.11564 + 1.35964i) q^{84} +(0.163199 + 0.347350i) q^{85} +(5.22368 + 0.751051i) q^{86} +(-4.53091 + 12.1478i) q^{87} +(-3.27701 + 4.37757i) q^{88} +(8.23324 - 5.29118i) q^{89} +(-6.73581 - 4.22645i) q^{90} -3.41194i q^{91} +(3.94683 - 2.72443i) q^{92} +(-18.3762 + 18.3762i) q^{93} +(-6.13703 - 5.31777i) q^{94} +(0.229491 - 3.78439i) q^{95} +(-0.364399 - 2.53445i) q^{96} +(-9.77637 - 3.64640i) q^{97} +(3.61684 + 4.83154i) q^{98} +(18.6587 - 5.47869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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