LMFDB - Embedded newform 185.2.u.a.23.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(8,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.u (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.8
Character	$\chi$	$=$	185.23
Dual form			185.2.u.a.177.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.305683 - 0.176486i) q^{2} +(2.52485 + 0.676530i) q^{3} +(-0.937705 - 1.62415i) q^{4} +(2.22668 - 0.204678i) q^{5} +(-0.652403 - 0.652403i) q^{6} +(-1.50833 - 0.404156i) q^{7} +1.36791i q^{8} +(3.31908 + 1.91627i) q^{9} +(-0.716780 - 0.330411i) q^{10} -2.57054i q^{11} +(-1.26877 - 4.73512i) q^{12} +(-4.41433 + 2.54861i) q^{13} +(0.389743 + 0.389743i) q^{14} +(5.76050 + 0.989636i) q^{15} +(-1.63399 + 2.83016i) q^{16} +(-0.342624 + 0.593443i) q^{17} +(-0.676389 - 1.17154i) q^{18} +(4.59908 + 1.23232i) q^{19} +(-2.42040 - 3.42454i) q^{20} +(-3.53488 - 2.04087i) q^{21} +(-0.453664 + 0.785768i) q^{22} +5.83340i q^{23} +(-0.925433 + 3.45376i) q^{24} +(4.91621 - 0.911506i) q^{25} +1.79918 q^{26} +(1.53879 + 1.53879i) q^{27} +(0.757959 + 2.82874i) q^{28} +(-4.71673 - 4.71673i) q^{29} +(-1.58623 - 1.31916i) q^{30} +(-1.40786 + 1.40786i) q^{31} +(3.36826 - 1.94466i) q^{32} +(1.73905 - 6.49021i) q^{33} +(0.209469 - 0.120937i) q^{34} +(-3.44130 - 0.591204i) q^{35} -7.18758i q^{36} +(4.74646 - 3.80409i) q^{37} +(-1.18837 - 1.18837i) q^{38} +(-12.8697 + 3.44843i) q^{39} +(0.279982 + 3.04590i) q^{40} +(-6.82923 + 3.94286i) q^{41} +(0.720368 + 1.24771i) q^{42} +2.28668i q^{43} +(-4.17495 + 2.41041i) q^{44} +(7.78274 + 3.58758i) q^{45} +(1.02951 - 1.78317i) q^{46} +(-7.99119 + 7.99119i) q^{47} +(-6.04027 + 6.04027i) q^{48} +(-3.95045 - 2.28080i) q^{49} +(-1.66367 - 0.589011i) q^{50} +(-1.26656 + 1.26656i) q^{51} +(8.27868 + 4.77970i) q^{52} +(4.37275 - 1.17167i) q^{53} +(-0.198807 - 0.741957i) q^{54} +(-0.526133 - 5.72377i) q^{55} +(0.552850 - 2.06326i) q^{56} +(10.7783 + 6.22283i) q^{57} +(0.609385 + 2.27426i) q^{58} +(-2.43277 - 9.07924i) q^{59} +(-3.79433 - 10.2839i) q^{60} +(-2.49030 - 0.667274i) q^{61} +(0.678826 - 0.181891i) q^{62} +(-4.23180 - 4.23180i) q^{63} +5.16315 q^{64} +(-9.30766 + 6.57847i) q^{65} +(-1.67703 + 1.67703i) q^{66} +(0.100851 - 0.376380i) q^{67} +1.28512 q^{68} +(-3.94647 + 14.7284i) q^{69} +(0.947605 + 0.788061i) q^{70} +(0.0695659 + 0.120492i) q^{71} +(-2.62128 + 4.54020i) q^{72} +(6.70047 - 6.70047i) q^{73} +(-2.12228 + 0.325159i) q^{74} +(13.0293 + 1.02455i) q^{75} +(-2.31111 - 8.62517i) q^{76} +(-1.03890 + 3.87723i) q^{77} +(4.54265 + 1.21720i) q^{78} +(0.455083 + 0.121939i) q^{79} +(-3.05911 + 6.63631i) q^{80} +(-2.90463 - 5.03097i) q^{81} +2.78343 q^{82} +(-3.06472 + 0.821188i) q^{83} +7.65492i q^{84} +(-0.641450 + 1.39154i) q^{85} +(0.403567 - 0.698999i) q^{86} +(-8.71800 - 15.1000i) q^{87} +3.51627 q^{88} +(15.2422 - 4.08413i) q^{89} +(-1.74589 - 2.47020i) q^{90} +(7.68831 - 2.06008i) q^{91} +(9.47433 - 5.47001i) q^{92} +(-4.50709 + 2.60217i) q^{93} +(3.85310 - 1.03243i) q^{94} +(10.4929 + 1.80265i) q^{95} +(9.81995 - 2.63125i) q^{96} +13.7731 q^{97} +(0.805056 + 1.39440i) q^{98} +(4.92584 - 8.53181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.305683	−	0.176486i	−0.216150	−	0.124794i	0.388016	−	0.921653i	$-0.373160\pi$
$2$	−0.305683	−	0.176486i	−0.216150	−	0.124794i	−0.604166	+	0.796858i	$0.706494\pi$
$3$	2.52485	+	0.676530i	1.45772	+	0.390595i	0.898702	−	0.438560i	$-0.144511\pi$
$3$	2.52485	+	0.676530i	1.45772	+	0.390595i	0.559018	+	0.829155i	$0.311178\pi$
$4$	−0.937705	−	1.62415i	−0.468853	−	0.812077i
$5$	2.22668	−	0.204678i	0.995802	−	0.0915349i
$5$	2.22668	−	0.204678i	0.995802	−	0.0915349i
$6$	−0.652403	−	0.652403i	−0.266342	−	0.266342i
$7$	−1.50833	−	0.404156i	−0.570096	−	0.152757i	−0.0377554	−	0.999287i	$-0.512021\pi$
$7$	−1.50833	−	0.404156i	−0.570096	−	0.152757i	−0.532341	+	0.846530i	$0.678687\pi$
$8$			1.36791i			0.483629i
$9$	3.31908	+	1.91627i	1.10636	+	0.638756i
$10$	−0.716780	−	0.330411i	−0.226666	−	0.104485i
$11$		−	2.57054i		−	0.775046i	−0.921860	−	0.387523i	$-0.873331\pi$
$11$		−	2.57054i		−	0.775046i	0.921860	−	0.387523i	$-0.126669\pi$
$12$	−1.26877	−	4.73512i	−0.366263	−	1.36691i
$13$	−4.41433	+	2.54861i	−1.22431	+	0.706858i	−0.965835	−	0.259158i	$-0.916555\pi$
$13$	−4.41433	+	2.54861i	−1.22431	+	0.706858i	−0.258480	+	0.966017i	$0.583222\pi$
$14$	0.389743	+	0.389743i	0.104163	+	0.104163i
$15$	5.76050	+	0.989636i	1.48735	+	0.255523i
$16$	−1.63399	+	2.83016i	−0.408499	+	0.707540i
$17$	−0.342624	+	0.593443i	−0.0830986	+	0.143931i	−0.904579	−	0.426305i	$-0.859815\pi$
$17$	−0.342624	+	0.593443i	−0.0830986	+	0.143931i	0.821481	+	0.570236i	$0.193148\pi$
$18$	−0.676389	−	1.17154i	−0.159426	−	0.276135i
$19$	4.59908	+	1.23232i	1.05510	+	0.282714i	0.744358	−	0.667780i	$-0.232755\pi$
$19$	4.59908	+	1.23232i	1.05510	+	0.282714i	0.310743	+	0.950494i	$0.399422\pi$
$20$	−2.42040	−	3.42454i	−0.541218	−	0.765751i
$21$	−3.53488	−	2.04087i	−0.771374	−	0.445353i
$22$	−0.453664	+	0.785768i	−0.0967214	+	0.167526i
$23$			5.83340i			1.21635i	0.793804	+	0.608174i	$0.208098\pi$
$23$			5.83340i			1.21635i	−0.793804	+	0.608174i	$0.791902\pi$
$24$	−0.925433	+	3.45376i	−0.188903	+	0.704996i
$25$	4.91621	−	0.911506i	0.983243	−	0.182301i
$26$	1.79918			0.352848
$27$	1.53879	+	1.53879i	0.296141	+	0.296141i
$28$	0.757959	+	2.82874i	0.143241	+	0.534582i
$29$	−4.71673	−	4.71673i	−0.875874	−	0.875874i	0.117231	−	0.993105i	$-0.462598\pi$
$29$	−4.71673	−	4.71673i	−0.875874	−	0.875874i	−0.993105	+	0.117231i	$0.962598\pi$
$30$	−1.58623	−	1.31916i	−0.289604	−	0.240845i
$31$	−1.40786	+	1.40786i	−0.252859	+	0.252859i	−0.822142	−	0.569283i	$-0.807221\pi$
$31$	−1.40786	+	1.40786i	−0.252859	+	0.252859i	0.569283	+	0.822142i	$0.307221\pi$
$32$	3.36826	−	1.94466i	0.595429	−	0.343771i
$33$	1.73905	−	6.49021i	0.302729	−	1.12980i
$34$	0.209469	−	0.120937i	0.0359236	−	0.0207405i
$35$	−3.44130	−	0.591204i	−0.581685	−	0.0999318i
$36$		−	7.18758i		−	1.19793i
$37$	4.74646	−	3.80409i	0.780314	−	0.625388i
$37$	4.74646	−	3.80409i	0.780314	−	0.625388i
$38$	−1.18837	−	1.18837i	−0.192779	−	0.192779i
$39$	−12.8697	+	3.44843i	−2.06080	+	0.552191i
$40$	0.279982	+	3.04590i	0.0442690	+	0.481599i
$41$	−6.82923	+	3.94286i	−1.06655	+	0.615771i	−0.927236	−	0.374478i	$-0.877822\pi$
$41$	−6.82923	+	3.94286i	−1.06655	+	0.615771i	−0.139311	+	0.990249i	$0.544489\pi$
$42$	0.720368	+	1.24771i	0.111155	+	0.192526i
$43$			2.28668i			0.348716i	0.984682	+	0.174358i	$0.0557850\pi$
$43$			2.28668i			0.348716i	−0.984682	+	0.174358i	$0.944215\pi$
$44$	−4.17495	+	2.41041i	−0.629397	+	0.363383i
$45$	7.78274	+	3.58758i	1.16018	+	0.534804i
$46$	1.02951	−	1.78317i	0.151793	−	0.262914i
$47$	−7.99119	+	7.99119i	−1.16563	+	1.16563i	−0.182412	+	0.983222i	$0.558390\pi$
$47$	−7.99119	+	7.99119i	−1.16563	+	1.16563i	−0.983222	+	0.182412i	$0.941610\pi$
$48$	−6.04027	+	6.04027i	−0.871838	+	0.871838i
$49$	−3.95045	−	2.28080i	−0.564351	−	0.325828i
$50$	−1.66367	−	0.589011i	−0.235278	−	0.0832987i
$51$	−1.26656	+	1.26656i	−0.177353	+	0.177353i
$52$	8.27868	+	4.77970i	1.14805	+	0.662825i
$53$	4.37275	−	1.17167i	0.600643	−	0.160942i	0.0543303	−	0.998523i	$-0.482698\pi$
$53$	4.37275	−	1.17167i	0.600643	−	0.160942i	0.546313	+	0.837581i	$0.316031\pi$
$54$	−0.198807	−	0.741957i	−0.0270542	−	0.100968i
$55$	−0.526133	−	5.72377i	−0.0709438	−	0.771793i
$56$	0.552850	−	2.06326i	0.0738777	−	0.275715i
$57$	10.7783	+	6.22283i	1.42762	+	0.824235i
$58$	0.609385	+	2.27426i	0.0800162	+	0.298624i
$59$	−2.43277	−	9.07924i	−0.316720	−	1.18202i	−0.922377	−	0.386290i	$-0.873756\pi$
$59$	−2.43277	−	9.07924i	−0.316720	−	1.18202i	0.605657	−	0.795726i	$-0.292910\pi$
$60$	−3.79433	−	10.2839i	−0.489846	−	1.32765i
$61$	−2.49030	−	0.667274i	−0.318850	−	0.0854357i	0.0958442	−	0.995396i	$-0.469445\pi$
$61$	−2.49030	−	0.667274i	−0.318850	−	0.0854357i	−0.414695	+	0.909961i	$0.636112\pi$
$62$	0.678826	−	0.181891i	0.0862110	−	0.0231002i
$63$	−4.23180	−	4.23180i	−0.533156	−	0.533156i
$64$	5.16315			0.645394
$65$	−9.30766	+	6.57847i	−1.15447	+	0.815958i
$66$	−1.67703	+	1.67703i	−0.206428	+	0.206428i
$67$	0.100851	−	0.376380i	0.0123209	−	0.0459822i	−0.959492	−	0.281737i	$-0.909089\pi$
$67$	0.100851	−	0.376380i	0.0123209	−	0.0459822i	0.971813	+	0.235755i	$0.0757562\pi$
$68$	1.28512			0.155844
$69$	−3.94647	+	14.7284i	−0.475099	+	1.77309i
$70$	0.947605	+	0.788061i	0.113260	+	0.0941913i
$71$	0.0695659	+	0.120492i	0.00825595	+	0.0142997i	0.870124	−	0.492833i	$-0.164039\pi$
$71$	0.0695659	+	0.120492i	0.00825595	+	0.0142997i	−0.861868	+	0.507133i	$0.830705\pi$
$72$	−2.62128	+	4.54020i	−0.308921	+	0.535067i
$73$	6.70047	−	6.70047i	0.784231	−	0.784231i	−0.196311	−	0.980542i	$-0.562896\pi$
$73$	6.70047	−	6.70047i	0.784231	−	0.784231i	0.980542	+	0.196311i	$0.0628962\pi$
$74$	−2.12228	+	0.325159i	−0.246710	+	0.0377989i
$75$	13.0293	+	1.02455i	1.50450	+	0.118305i
$76$	−2.31111	−	8.62517i	−0.265102	−	0.989374i
$77$	−1.03890	+	3.87723i	−0.118394	+	0.441851i
$78$	4.54265	+	1.21720i	0.514353	+	0.137821i
$79$	0.455083	+	0.121939i	0.0512008	+	0.0137192i	0.284329	−	0.958727i	$-0.408229\pi$
$79$	0.455083	+	0.121939i	0.0512008	+	0.0137192i	−0.233128	+	0.972446i	$0.574896\pi$
$80$	−3.05911	+	6.63631i	−0.342019	+	0.741962i
$81$	−2.90463	−	5.03097i	−0.322737	−	0.558997i
$82$	2.78343			0.307379
$83$	−3.06472	+	0.821188i	−0.336396	+	0.0901371i	−0.423063	−	0.906100i	$-0.639045\pi$
$83$	−3.06472	+	0.821188i	−0.336396	+	0.0901371i	0.0866667	+	0.996237i	$0.472378\pi$
$84$			7.65492i			0.835220i
$85$	−0.641450	+	1.39154i	−0.0695750	+	0.150933i
$86$	0.403567	−	0.698999i	0.0435178	−	0.0753750i
$87$	−8.71800	−	15.1000i	−0.934667	−	1.61889i
$88$	3.51627			0.374835
$89$	15.2422	−	4.08413i	1.61567	−	0.432917i	0.665944	−	0.746002i	$-0.268029\pi$
$89$	15.2422	−	4.08413i	1.61567	−	0.432917i	0.949725	+	0.313084i	$0.101362\pi$
$90$	−1.74589	−	2.47020i	−0.184033	−	0.260382i
$91$	7.68831	−	2.06008i	0.805954	−	0.215955i
$92$	9.47433	−	5.47001i	0.987768	−	0.570288i
$93$	−4.50709	+	2.60217i	−0.467364	+	0.269832i
$94$	3.85310	−	1.03243i	0.397417	−	0.106487i
$95$	10.4929	+	1.80265i	1.07655	+	0.184948i
$96$	9.81995	−	2.63125i	1.00224	−	0.268551i
$97$	13.7731			1.39845			0.699224	−	0.714902i	$-0.253529\pi$
$97$	13.7731			1.39845			0.699224	+	0.714902i	$0.253529\pi$
$98$	0.805056	+	1.39440i	0.0813230	+	0.140856i
$99$	4.92584	−	8.53181i	0.495066	−	0.857479i
$100$	−6.09039	−	7.12996i	−0.609039	−	0.712996i
$101$		−	12.9947i		−	1.29302i	−0.762904	−	0.646512i	$-0.776227\pi$
$101$		−	12.9947i		−	1.29302i	0.762904	−	0.646512i	$-0.223773\pi$
$102$	0.610693	−	0.163635i	0.0604676	−	0.0162023i
$103$	15.5723			1.53439			0.767194	−	0.641415i	$-0.221652\pi$
$103$	15.5723			1.53439			0.767194	+	0.641415i	$0.221652\pi$
$104$	−3.48628	−	6.03841i	−0.341858	−	0.592115i
$105$	−8.28877	−	3.82084i	−0.808902	−	0.372876i
$106$	−1.54346	−	0.413568i	−0.149914	−	0.0401693i
$107$	−15.0746	−	4.03924i	−1.45732	−	0.390488i	−0.558758	−	0.829331i	$-0.688722\pi$
$107$	−15.0746	−	4.03924i	−1.45732	−	0.390488i	−0.898564	+	0.438843i	$0.855388\pi$
$108$	1.05630	−	3.94217i	0.101643	−	0.379335i
$109$	4.41374	+	16.4723i	0.422760	+	1.57776i	0.768767	+	0.639530i	$0.220871\pi$
$109$	4.41374	+	16.4723i	0.422760	+	1.57776i	−0.346007	+	0.938232i	$0.612463\pi$
$110$	−0.849334	+	1.84251i	−0.0809808	+	0.175676i
$111$	14.5577	−	6.39360i	1.38175	−	0.606854i
$112$	3.60843	−	3.60843i	0.340965	−	0.340965i
$113$	4.95674	−	8.58533i	0.466291	−	0.807640i	−0.532968	−	0.846136i	$-0.678923\pi$
$113$	4.95674	−	8.58533i	0.466291	−	0.807640i	0.999259	+	0.0384957i	$0.0122566\pi$
$114$	−2.19649	−	3.80442i	−0.205720	−	0.356317i
$115$	1.19397	+	12.9891i	0.111338	+	1.21124i
$116$	−3.23779	+	12.0836i	−0.300621	+	1.12193i
$117$	−19.5353			−1.80604
$118$	−0.858701	+	3.20471i	−0.0790498	+	0.295018i
$119$	0.756635	−	0.756635i	0.0693606	−	0.0693606i
$120$	−1.35373	+	7.87984i	−0.123578	+	0.719328i
$121$	4.39234			0.399303
$122$	0.643477	+	0.643477i	0.0582577	+	0.0582577i
$123$	−19.9102	+	5.33493i	−1.79524	+	0.481034i
$124$	3.60674	+	0.966423i	0.323895	+	0.0867874i
$125$	10.7603	−	3.03588i	0.962428	−	0.271537i
$126$	0.546734	+	2.04044i	0.0487069	+	0.181777i
$127$	3.49690	+	13.0506i	0.310299	+	1.15805i	0.928287	+	0.371865i	$0.121282\pi$
$127$	3.49690	+	13.0506i	0.310299	+	1.15805i	−0.617987	+	0.786188i	$0.712052\pi$
$128$	−8.31480	−	4.80055i	−0.734931	−	0.424313i
$129$	−1.54701	+	5.77352i	−0.136207	+	0.508330i
$130$	4.00619	−	0.368253i	0.351366	−	0.0322979i
$131$	2.35244	+	8.77941i	0.205533	+	0.767061i	0.989286	+	0.145988i	$0.0466362\pi$
$131$	2.35244	+	8.77941i	0.205533	+	0.767061i	−0.783753	+	0.621073i	$0.786697\pi$
$132$	−12.1718	+	3.26143i	−1.05942	+	0.283871i
$133$	−6.43889	−	3.71750i	−0.558323	−	0.322348i
$134$	−0.0972542	+	0.0972542i	−0.00840148	+	0.00840148i
$135$	3.74136	+	3.11144i	0.322005	+	0.267790i
$136$	−0.811777	−	0.468680i	−0.0696093	−	0.0401889i
$137$	−3.39738	+	3.39738i	−0.290258	+	0.290258i	−0.837182	−	0.546924i	$-0.815799\pi$
$137$	−3.39738	+	3.39738i	−0.290258	+	0.290258i	0.546924	+	0.837182i	$0.315799\pi$
$138$	3.80573	−	3.80573i	0.323965	−	0.323965i
$139$	5.14118	−	8.90478i	0.436069	−	0.755293i	−0.561313	−	0.827603i	$-0.689704\pi$
$139$	5.14118	−	8.90478i	0.436069	−	0.755293i	0.997382	+	0.0723099i	$0.0230371\pi$
$140$	2.26672	+	6.14357i	0.191572	+	0.519226i
$141$	−25.5828	+	14.7702i	−2.15446	+	1.24388i
$142$		−	0.0491096i		−	0.00412119i
$143$	6.55131	+	11.3472i	0.547848	+	0.948901i
$144$	−10.8467	+	6.26234i	−0.903891	+	0.521862i
$145$	−11.4681	−	9.53723i	−0.952370	−	0.792024i
$146$	−3.23075	+	0.865678i	−0.267379	+	0.0716440i
$147$	−8.43126	−	8.43126i	−0.695398	−	0.695398i
$148$	−10.6292	−	4.14187i	−0.873715	−	0.340460i
$149$		−	13.8216i		−	1.13231i	−0.824298	−	0.566156i	$-0.808430\pi$
$149$		−	13.8216i		−	1.13231i	0.824298	−	0.566156i	$-0.191570\pi$
$150$	−3.80202	−	2.61268i	−0.310434	−	0.213325i
$151$	−18.7800	+	10.8426i	−1.52829	+	0.882359i	−0.528857	+	0.848711i	$0.677379\pi$
$151$	−18.7800	+	10.8426i	−1.52829	+	0.882359i	−0.999434	+	0.0336485i	$0.989287\pi$
$152$	−1.68570	+	6.29113i	−0.136729	+	0.510278i
$153$	−2.27439	+	1.31312i	−0.183874	+	0.106160i
$154$	1.00185	−	1.00185i	0.0807313	−	0.0807313i
$155$	−2.84670	+	3.42301i	−0.228652	+	0.274943i
$156$	17.6688	+	17.6688i	1.41463	+	1.41463i
$157$	−2.49678	−	9.31810i	−0.199265	−	0.743665i	−0.991122	−	0.132959i	$-0.957552\pi$
$157$	−2.49678	−	9.31810i	−0.199265	−	0.743665i	0.791857	−	0.610706i	$-0.209114\pi$
$158$	−0.117590	−	0.117590i	−0.00935498	−	0.00935498i
$159$	11.8332			0.938433
$160$	7.10200	−	5.01956i	0.561463	−	0.396831i
$161$	2.35761	−	8.79870i	0.185805	−	0.693435i
$162$			2.05051i			0.161103i
$163$	−9.72549	+	16.8451i	−0.761760	+	1.31941i	0.180183	+	0.983633i	$0.442331\pi$
$163$	−9.72549	+	16.8451i	−0.761760	+	1.31941i	−0.941943	+	0.335773i	$0.891002\pi$
$164$	12.8076	+	7.39448i	1.00011	+	0.577412i
$165$	2.54390	−	14.8076i	0.198042	−	1.15277i
$166$	1.08176	+	0.289856i	0.0839607	+	0.0224972i
$167$	−2.03581	−	3.52613i	−0.157536	−	0.272860i	0.776444	−	0.630187i	$-0.217022\pi$
$167$	−2.03581	−	3.52613i	−0.157536	−	0.272860i	−0.933980	+	0.357326i	$0.883688\pi$
$168$	2.79172	−	4.83540i	0.215386	−	0.373059i
$169$	6.49087	−	11.2425i	0.499297	−	0.864809i
$170$	0.441667	−	0.312161i	0.0338743	−	0.0239417i
$171$	12.9032	+	12.9032i	0.986735	+	0.986735i
$172$	3.71392	−	2.14423i	0.283184	−	0.163496i
$173$	−0.919404	−	3.43126i	−0.0699010	−	0.260874i	0.922128	−	0.386885i	$-0.126449\pi$
$173$	−0.919404	−	3.43126i	−0.0699010	−	0.260874i	−0.992029	+	0.126011i	$0.959782\pi$
$174$			6.15441i			0.466565i
$175$	−7.78368	−	0.612065i	−0.588391	−	0.0462677i
$176$	7.27504	+	4.20024i	0.548376	+	0.316605i
$177$		−	24.5695i		−	1.84676i
$178$	−5.38006	−	1.44158i	−0.403253	−	0.108051i
$179$	−5.13938	−	5.13938i	−0.384135	−	0.384135i	0.488454	−	0.872590i	$-0.337561\pi$
$179$	−5.13938	−	5.13938i	−0.384135	−	0.384135i	−0.872590	+	0.488454i	$0.837561\pi$
$180$	−1.47114	−	16.0045i	−0.109652	−	1.19290i
$181$	4.66518	+	8.08032i	0.346760	+	0.600606i	0.985672	−	0.168674i	$-0.0539485\pi$
$181$	4.66518	+	8.08032i	0.346760	+	0.600606i	−0.638912	+	0.769280i	$0.720615\pi$
$182$	−2.71376	−	0.727149i	−0.201157	−	0.0538999i
$183$	−5.83620	−	3.36953i	−0.431424	−	0.249083i
$184$	−7.97957			−0.588261
$185$	9.79025	−	9.44198i	0.719793	−	0.694188i
$186$	1.83699			0.134694
$187$	1.52547	+	0.880729i	0.111553	+	0.0644053i
$188$	20.4723	+	5.48553i	1.49310	+	0.400074i
$189$	−1.69910	−	2.94292i	−0.123591	−	0.214066i
$190$	−2.88936	−	2.40289i	−0.209616	−	0.174324i
$191$	1.71277	+	1.71277i	0.123932	+	0.123932i	0.766352	−	0.642420i	$-0.222070\pi$
$191$	1.71277	+	1.71277i	0.123932	+	0.123932i	−0.642420	+	0.766352i	$0.722070\pi$
$192$	13.0362	+	3.49303i	0.940804	+	0.252088i
$193$		−	9.20371i		−	0.662498i	−0.943543	−	0.331249i	$-0.892530\pi$
$193$		−	9.20371i		−	0.662498i	0.943543	−	0.331249i	$-0.107470\pi$
$194$	−4.21020	−	2.43076i	−0.302275	−	0.174518i
$195$	−27.9509	+	10.3127i	−2.00161	+	0.738508i
$196$			8.55486i			0.611061i
$197$	−0.594910	−	2.22023i	−0.0423856	−	0.158185i	0.941489	−	0.337043i	$-0.109427\pi$
$197$	−0.594910	−	2.22023i	−0.0423856	−	0.158185i	−0.983875	+	0.178857i	$0.942760\pi$
$198$	−3.01149	+	1.73868i	−0.214017	+	0.123563i
$199$	−13.0048	−	13.0048i	−0.921884	−	0.921884i	0.0752787	−	0.997163i	$-0.476015\pi$
$199$	−13.0048	−	13.0048i	−0.921884	−	0.921884i	−0.997163	+	0.0752787i	$0.976015\pi$
$200$	1.24686	+	6.72494i	0.0881663	+	0.475525i
$201$	0.509266	−	0.882074i	0.0359208	−	0.0622167i
$202$	−2.29339	+	3.97226i	−0.161362	+	0.279487i
$203$	5.20810	+	9.02069i	0.365537	+	0.633128i
$204$	3.24474	+	0.869425i	0.227177	+	0.0608719i
$205$	−14.3995	+	10.1773i	−1.00570	+	0.710812i
$206$	−4.76019	−	2.74830i	−0.331658	−	0.191483i
$207$	−11.1784	+	19.3615i	−0.776950	+	1.34572i
$208$		−	16.6577i		−	1.15500i
$209$	3.16773	−	11.8221i	0.219116	−	0.817753i
$210$	1.85941	+	2.63082i	0.128311	+	0.181544i
$211$	18.9546			1.30489			0.652445	−	0.757836i	$-0.273744\pi$
$211$	18.9546			1.30489			0.652445	+	0.757836i	$0.273744\pi$
$212$	−6.00333	−	6.00333i	−0.412310	−	0.412310i
$213$	0.0941269	+	0.351286i	0.00644947	+	0.0240697i
$214$	3.89519	+	3.89519i	0.266270	+	0.266270i
$215$	0.468034	+	5.09171i	0.0319197	+	0.347252i
$216$	−2.10493	+	2.10493i	−0.143222	+	0.143222i
$217$	2.69252	−	1.55453i	0.182780	−	0.105528i
$218$	1.55793	−	5.81426i	0.105516	−	0.393792i
$219$	21.4507	−	12.3846i	1.44951	−	0.836872i
$220$	−8.80292	+	6.22173i	−0.593493	+	0.419469i
$221$		−	3.49287i		−	0.234956i
$222$	−5.57841	−	0.614811i	−0.374398	−	0.0412634i
$223$	12.6125	+	12.6125i	0.844597	+	0.844597i	0.989453	−	0.144856i	$-0.0462718\pi$
$223$	12.6125	+	12.6125i	0.844597	+	0.844597i	−0.144856	+	0.989453i	$0.546272\pi$
$224$	−5.86640	+	1.57190i	−0.391965	+	0.105027i
$225$	18.0640	+	6.39543i	1.20426	+	0.426362i
$226$	−3.03038	+	1.74959i	−0.201578	+	0.116381i
$227$	7.55203	+	13.0805i	0.501246	+	0.868183i	0.999999	+	0.00143883i	$0.000457994\pi$
$227$	7.55203	+	13.0805i	0.501246	+	0.868183i	−0.498753	+	0.866744i	$0.666209\pi$
$228$		−	23.3407i		−	1.54578i
$229$	−17.9565	+	10.3672i	−1.18660	+	0.685083i	−0.957532	−	0.288328i	$-0.906901\pi$
$229$	−17.9565	+	10.3672i	−1.18660	+	0.685083i	−0.229067	+	0.973411i	$0.573567\pi$
$230$	1.92742	−	4.18126i	0.127090	−	0.275704i
$231$	−5.24612	+	9.08655i	−0.345169	+	0.597851i
$232$	6.45206	−	6.45206i	0.423598	−	0.423598i
$233$	−0.0618698	+	0.0618698i	−0.00405322	+	0.00405322i	−0.709130	−	0.705077i	$-0.750912\pi$
$233$	−0.0618698	+	0.0618698i	−0.00405322	+	0.00405322i	0.705077	+	0.709130i	$0.250912\pi$
$234$	5.97161	+	3.44771i	0.390376	+	0.225384i
$235$	−16.1582	+	19.4294i	−1.05404	+	1.26744i
$236$	−12.4648	+	12.4648i	−0.811393	+	0.811393i
$237$	1.06652	+	0.615754i	0.0692778	+	0.0399975i
$238$	−0.364826	+	0.0977547i	−0.0236481	+	0.00633650i
$239$	3.92002	+	14.6297i	0.253565	+	0.946318i	0.968883	+	0.247519i	$0.0796152\pi$
$239$	3.92002	+	14.6297i	0.253565	+	0.946318i	−0.715318	+	0.698799i	$0.753718\pi$
$240$	−12.2134	+	14.6861i	−0.788374	+	0.947982i
$241$	3.24330	−	12.1042i	0.208919	−	0.779697i	−0.779300	−	0.626651i	$-0.784425\pi$
$241$	3.24330	−	12.1042i	0.208919	−	0.779697i	0.988219	−	0.153046i	$-0.0489083\pi$
$242$	−1.34266	−	0.775185i	−0.0863095	−	0.0498308i
$243$	−5.61986	−	20.9736i	−0.360514	−	1.34546i
$244$	1.25141	+	4.67034i	0.0801135	+	0.298988i
$245$	−9.26323	−	4.27003i	−0.591806	−	0.272802i
$246$	7.02774	+	1.88308i	0.448072	+	0.120061i
$247$	−23.4426	+	6.28142i	−1.49161	+	0.399677i
$248$	−1.92583	−	1.92583i	−0.122290	−	0.122290i
$249$	−8.29350			−0.525579
$250$	−3.82502	−	0.971022i	−0.241915	−	0.0614128i
$251$	0.772329	−	0.772329i	0.0487490	−	0.0487490i	−0.682312	−	0.731061i	$-0.739025\pi$
$251$	0.772329	−	0.772329i	0.0487490	−	0.0487490i	0.731061	+	0.682312i	$0.239025\pi$
$252$	−2.90491	+	10.8413i	−0.182992	+	0.682935i
$253$	14.9950			0.942726
$254$	1.23431	−	4.60649i	0.0774472	−	0.289037i
$255$	−2.56098	+	3.07945i	−0.160375	+	0.192843i
$256$	−3.46869	−	6.00795i	−0.216793	−	0.375497i
$257$	0.226136	−	0.391679i	0.0141060	−	0.0244322i	−0.858886	−	0.512166i	$-0.828843\pi$
$257$	0.226136	−	0.391679i	0.0141060	−	0.0244322i	0.872992	+	0.487734i	$0.162176\pi$
$258$	1.49184	−	1.49184i	0.0928778	−	0.0928778i
$259$	−8.69669	+	3.81951i	−0.540386	+	0.237333i
$260$	19.4123	+	8.94840i	1.20390	+	0.554956i
$261$	−6.61665	−	24.6937i	−0.409561	−	1.52850i
$262$	0.830344	−	3.09889i	0.0512988	−	0.191450i
$263$	−14.5598	−	3.90128i	−0.897794	−	0.240563i	−0.219725	−	0.975562i	$-0.570516\pi$
$263$	−14.5598	−	3.90128i	−0.897794	−	0.240563i	−0.678069	+	0.734999i	$0.737183\pi$
$264$	8.87803	+	2.37886i	0.546405	+	0.146409i
$265$	9.49690	−	3.50395i	0.583390	−	0.215246i
$266$	1.31217	+	2.27275i	0.0804544	+	0.139351i
$267$	41.2472			2.52429
$268$	−0.705868	+	0.189137i	−0.0431177	+	0.0115534i
$269$		−	17.7593i		−	1.08280i	−0.840764	−	0.541402i	$-0.817894\pi$
$269$		−	17.7593i		−	1.08280i	0.840764	−	0.541402i	$-0.182106\pi$
$270$	−0.594542	−	1.61141i	−0.0361827	−	0.0980673i
$271$	5.45528	−	9.44882i	0.331385	−	0.573975i	−0.651399	−	0.758735i	$-0.725818\pi$
$271$	5.45528	−	9.44882i	0.331385	−	0.573975i	0.982784	+	0.184760i	$0.0591509\pi$
$272$	−1.11969	−	1.93936i	−0.0678913	−	0.117591i
$273$	20.8055			1.25921
$274$	1.63811	−	0.438930i	0.0989618	−	0.0265167i
$275$	−2.34306	−	12.6373i	−0.141292	−	0.762059i
$276$	27.6219	−	7.40125i	1.66264	−	0.445503i
$277$	11.1460	−	6.43516i	0.669700	−	0.386652i	−0.126263	−	0.991997i	$-0.540298\pi$
$277$	11.1460	−	6.43516i	0.669700	−	0.386652i	0.795963	+	0.605345i	$0.206965\pi$
$278$	−3.14314	+	1.81469i	−0.188513	+	0.108838i
$279$	−7.37063	+	1.97496i	−0.441268	+	0.118238i
$280$	0.808715	−	4.70739i	0.0483300	−	0.281320i
$281$	−25.0501	+	6.71215i	−1.49436	+	0.400413i	−0.911208	−	0.411947i	$-0.864849\pi$
$281$	−25.0501	+	6.71215i	−1.49436	+	0.400413i	−0.583155	+	0.812361i	$0.698182\pi$
$282$	10.4269			0.620916
$283$	2.54545	+	4.40886i	0.151312	+	0.262079i	0.931710	−	0.363203i	$-0.118317\pi$
$283$	2.54545	+	4.40886i	0.151312	+	0.262079i	−0.780398	+	0.625283i	$0.784984\pi$
$284$	0.130465	−	0.225971i	0.00774165	−	0.0134089i
$285$	25.2734	+	11.6502i	1.49707	+	0.690098i
$286$		−	4.62485i		−	0.273473i
$287$	11.8943	−	3.18706i	0.702097	−	0.188126i
$288$	14.9060			0.878344
$289$	8.26522	+	14.3158i	0.486189	+	0.842104i
$290$	1.82240	+	4.93931i	0.107015	+	0.290047i
$291$	34.7750	+	9.31793i	2.03855	+	0.546227i
$292$	−17.1657	−	4.59952i	−1.00454	−	0.269167i
$293$	−6.05444	+	22.5955i	−0.353704	+	1.32004i	0.528403	+	0.848993i	$0.322791\pi$
$293$	−6.05444	+	22.5955i	−0.353704	+	1.32004i	−0.882108	+	0.471048i	$0.843876\pi$
$294$	1.08929	+	4.06529i	0.0635287	+	0.237092i
$295$	−7.27533	−	19.7186i	−0.423586	−	1.14806i
$296$	5.20365	+	6.49274i	0.302456	+	0.377383i
$297$	3.95552	−	3.95552i	0.229523	−	0.229523i
$298$	−2.43932	+	4.22503i	−0.141306	+	0.244749i
$299$	−14.8671	−	25.7505i	−0.859785	−	1.48919i
$300$	−10.5537	−	22.1224i	−0.609315	−	1.27724i
$301$	0.924177	−	3.44908i	0.0532687	−	0.198801i
$302$	7.65427			0.440454
$303$	8.79133	−	32.8097i	0.505049	−	1.88487i
$304$	−11.0025	+	11.0025i	−0.631039	+	0.631039i
$305$	−5.68168	−	0.976096i	−0.325332	−	0.0558911i
$306$	0.926989			0.0529925
$307$	−2.66991	−	2.66991i	−0.152380	−	0.152380i	0.626800	−	0.779180i	$-0.284364\pi$
$307$	−2.66991	−	2.66991i	−0.152380	−	0.152380i	−0.779180	+	0.626800i	$0.784364\pi$
$308$	7.27139	−	1.94836i	0.414326	−	0.111018i
$309$	39.3177	+	10.5352i	2.23671	+	0.599324i
$310$	1.47430	−	0.543954i	0.0837346	−	0.0308945i
$311$	−2.32734	−	8.68575i	−0.131971	−	0.492524i	0.868021	−	0.496528i	$-0.165392\pi$
$311$	−2.32734	−	8.68575i	−0.131971	−	0.492524i	−0.999992	+	0.00400430i	$0.998725\pi$
$312$	−4.71714	−	17.6046i	−0.267056	−	0.996665i
$313$	1.29441	+	0.747326i	0.0731642	+	0.0422414i	0.536136	−	0.844132i	$-0.319883\pi$
$313$	1.29441	+	0.747326i	0.0731642	+	0.0422414i	−0.462972	+	0.886373i	$0.653217\pi$
$314$	−0.881292	+	3.28903i	−0.0497342	+	0.185610i
$315$	−10.2890	−	8.55670i	−0.579720	−	0.482115i
$316$	−0.228686	−	0.853467i	−0.0128646	−	0.0480113i
$317$	−18.1650	+	4.86730i	−1.02025	+	0.273375i	−0.729906	−	0.683548i	$-0.760436\pi$
$317$	−18.1650	+	4.86730i	−1.02025	+	0.273375i	−0.290343	+	0.956923i	$0.593770\pi$
$318$	−3.61720	−	2.08839i	−0.202842	−	0.117111i
$319$	−12.1245	+	12.1245i	−0.678843	+	0.678843i
$320$	11.4967	−	1.05679i	0.642685	−	0.0590761i
$321$	−35.3285	−	20.3969i	−1.97184	−	1.13844i
$322$	−2.27353	+	2.27353i	−0.126699	+	0.126699i
$323$	−2.30707	+	2.30707i	−0.128369	+	0.128369i
$324$	−5.44738	+	9.43514i	−0.302632	+	0.524175i
$325$	−19.3787	+	16.5532i	−1.07494	+	0.918207i
$326$	5.94583	−	3.43282i	0.329309	−	0.190127i
$327$			44.5761i			2.46506i
$328$	−5.39348	−	9.34178i	−0.297805	−	0.515813i
$329$	15.2831	−	8.82367i	0.842582	−	0.486465i
$330$	−3.39095	+	4.07745i	−0.186666	+	0.224456i
$331$	−3.69837	+	0.990975i	−0.203281	+	0.0544689i	−0.359023	−	0.933329i	$-0.616890\pi$
$331$	−3.69837	+	0.990975i	−0.203281	+	0.0544689i	0.155742	+	0.987798i	$0.450223\pi$
$332$	4.20754	+	4.20754i	0.230919	+	0.230919i
$333$	23.0435	−	3.53055i	1.26278	−	0.193473i
$334$			1.43717i			0.0786384i
$335$	0.147526	−	0.858721i	0.00806019	−	0.0469169i
$336$	11.5520	−	6.66952i	0.630211	−	0.363852i
$337$	−1.37651	+	5.13720i	−0.0749832	+	0.279841i	−0.993230	−	0.116169i	$-0.962939\pi$
$337$	−1.37651	+	5.13720i	−0.0749832	+	0.279841i	0.918246	+	0.396010i	$0.129605\pi$
$338$	−3.96829	+	2.29109i	−0.215846	+	0.124619i
$339$	18.3232	−	18.3232i	0.995182	−	0.995182i
$340$	2.86156	−	0.263037i	0.155190	−	0.0142652i
$341$	3.61896	+	3.61896i	0.195978	+	0.195978i
$342$	−1.66705	−	6.22153i	−0.0901440	−	0.336422i
$343$	12.7660	+	12.7660i	0.689301	+	0.689301i
$344$	−3.12798			−0.168649
$345$	−5.77294	+	33.6033i	−0.310805	+	1.80914i
$346$	−0.324524	+	1.21114i	−0.0174465	+	0.0651112i
$347$			17.6817i			0.949201i	0.880201	+	0.474600i	$0.157407\pi$
$347$			17.6817i			0.949201i	−0.880201	+	0.474600i	$0.842593\pi$
$348$	−16.3498	+	28.3187i	−0.876443	+	1.51804i
$349$	−12.9795	−	7.49374i	−0.694779	−	0.401131i	0.110621	−	0.993863i	$-0.464716\pi$
$349$	−12.9795	−	7.49374i	−0.694779	−	0.401131i	−0.805400	+	0.592732i	$0.798049\pi$
$350$	2.27131	+	1.56081i	0.121407	+	0.0834286i
$351$	−10.7145	−	2.87095i	−0.571899	−	0.153240i
$352$	−4.99883	−	8.65823i	−0.266439	−	0.461485i
$353$	−5.89156	+	10.2045i	−0.313576	+	0.543130i	−0.979134	−	0.203216i	$-0.934860\pi$
$353$	−5.89156	+	10.2045i	−0.313576	+	0.543130i	0.665558	+	0.746347i	$0.268194\pi$
$354$	−4.33617	+	7.51047i	−0.230465	+	0.399177i
$355$	0.179563	+	0.254058i	0.00953022	+	0.0134840i
$356$	−20.9260	−	20.9260i	−1.10907	−	1.10907i
$357$	2.42227	−	1.39850i	0.128200	−	0.0740165i
$358$	0.663991	+	2.47805i	0.0350930	+	0.130969i
$359$			3.55034i			0.187380i	0.995601	+	0.0936900i	$0.0298663\pi$
$359$			3.55034i			0.187380i	−0.995601	+	0.0936900i	$0.970134\pi$
$360$	−4.90748	+	10.6461i	−0.258647	+	0.561098i
$361$	3.17845	+	1.83508i	0.167287	+	0.0965831i
$362$		−	3.29335i		−	0.173095i
$363$	11.0900	+	2.97155i	0.582072	+	0.155966i
$364$	−10.5553	−	10.5553i	−0.553246	−	0.553246i
$365$	13.5484	−	16.2912i	0.709154	−	0.852723i
$366$	1.18935	+	2.06001i	0.0621683	+	0.107679i
$367$	−5.68539	−	1.52339i	−0.296775	−	0.0795206i	0.107359	−	0.994220i	$-0.465760\pi$
$367$	−5.68539	−	1.52339i	−0.296775	−	0.0795206i	−0.404134	+	0.914700i	$0.632427\pi$
$368$	−16.5095	−	9.53174i	−0.860615	−	0.496876i
$369$	−30.2223			−1.57331
$370$	−4.65908	+	1.15841i	−0.242214	+	0.0602228i
$371$	−7.06910			−0.367009
$372$	8.45265	+	4.88014i	0.438249	+	0.253023i
$373$	−25.7256	−	6.89317i	−1.33202	−	0.356915i	−0.478554	−	0.878058i	$-0.658839\pi$
$373$	−25.7256	−	6.89317i	−1.33202	−	0.356915i	−0.853469	+	0.521143i	$0.825506\pi$
$374$	−0.310872	−	0.538447i	−0.0160748	−	0.0278424i
$375$	29.2219	−	0.385468i	1.50901	−	0.0199055i
$376$	−10.9312	−	10.9312i	−0.563735	−	0.563735i
$377$	32.8423	+	8.80007i	1.69146	+	0.453226i
$378$			1.19947i			0.0616939i
$379$	21.5060	+	12.4165i	1.10469	+	0.637793i	0.937449	−	0.348123i	$-0.113181\pi$
$379$	21.5060	+	12.4165i	1.10469	+	0.637793i	0.167241	+	0.985916i	$0.446514\pi$
$380$	−6.91148	−	18.7325i	−0.354551	−	0.960955i
$381$			35.3165i			1.80932i
$382$	−0.221284	−	0.825845i	−0.0113219	−	0.0422539i
$383$	−0.836267	+	0.482819i	−0.0427312	+	0.0246709i	−0.521213	−	0.853426i	$-0.674520\pi$
$383$	−0.836267	+	0.482819i	−0.0427312	+	0.0246709i	0.478482	+	0.878097i	$0.341187\pi$
$384$	−17.7459	−	17.7459i	−0.905590	−	0.905590i
$385$	−1.51971	+	8.84598i	−0.0774518	+	0.450833i
$386$	−1.62433	+	2.81341i	−0.0826760	+	0.143199i
$387$	−4.38190	+	7.58967i	−0.222744	+	0.385805i
$388$	−12.9151	−	22.3697i	−0.655666	−	1.13565i
$389$	17.1704	+	4.60080i	0.870574	+	0.233270i	0.666336	−	0.745651i	$-0.267862\pi$
$389$	17.1704	+	4.60080i	0.870574	+	0.233270i	0.204238	+	0.978921i	$0.434528\pi$
$390$	10.3642	+	1.78053i	0.524809	+	0.0901607i
$391$	−3.46179	−	1.99866i	−0.175070	−	0.101077i
$392$	3.11992	−	5.40387i	0.157580	−	0.272937i
$393$			23.7582i			1.19844i
$394$	−0.209986	+	0.783680i	−0.0105790	+	0.0394812i
$395$	1.03828	+	0.178374i	0.0522416	+	0.00897495i
$396$	−18.4760			−0.928452
$397$	−24.5436	−	24.5436i	−1.23181	−	1.23181i	−0.963268	−	0.268541i	$-0.913459\pi$
$397$	−24.5436	−	24.5436i	−1.23181	−	1.23181i	−0.268541	−	0.963268i	$-0.586541\pi$
$398$	1.68017	+	6.27049i	0.0842194	+	0.314311i
$399$	−13.7422	−	13.7422i	−0.687971	−	0.687971i
$400$	−5.45335	+	15.4031i	−0.272668	+	0.770154i
$401$	−12.2360	+	12.2360i	−0.611036	+	0.611036i	−0.943216	−	0.332180i	$-0.892216\pi$
$401$	−12.2360	+	12.2360i	−0.611036	+	0.611036i	0.332180	+	0.943216i	$0.392216\pi$
$402$	−0.311347	+	0.179756i	−0.0155286	+	0.00896543i
$403$	2.62667	−	9.80285i	0.130844	−	0.488315i
$404$	−21.1054	+	12.1852i	−1.05003	+	0.606238i
$405$	−7.49742	−	10.6079i	−0.372550	−	0.527109i
$406$		−	3.67662i		−	0.182468i
$407$	−9.77855	−	12.2010i	−0.484705	−	0.604780i
$408$	−1.73254	−	1.73254i	−0.0857733	−	0.0857733i
$409$	32.7833	−	8.78426i	1.62103	−	0.434354i	0.669727	−	0.742608i	$-0.266411\pi$
$409$	32.7833	−	8.78426i	1.62103	−	0.434354i	0.951304	+	0.308254i	$0.0997446\pi$
$410$	6.19782	−	0.569709i	0.306089	−	0.0281359i
$411$	−10.8763	+	6.27943i	−0.536488	+	0.309742i
$412$	−14.6023	−	25.2919i	−0.719402	−	1.24604i
$413$			14.6777i			0.722244i
$414$	6.83406	−	3.94565i	0.335876	−	0.193918i
$415$	−6.65607	+	2.45581i	−0.326733	+	0.120551i
$416$	−9.91240	+	17.1688i	−0.485995	+	0.841769i
$417$	19.0050	−	19.0050i	0.930680	−	0.930680i
$418$	−3.05475	+	3.05475i	−0.149413	+	0.149413i
$419$	18.2797	+	10.5538i	0.893023	+	0.515587i	0.874930	−	0.484249i	$-0.160907\pi$
$419$	18.2797	+	10.5538i	0.893023	+	0.515587i	0.0180930	+	0.999836i	$0.494241\pi$
$420$	1.56680	+	17.0451i	0.0764518	+	0.831714i
$421$	21.7979	−	21.7979i	1.06237	−	1.06237i	0.0644457	−	0.997921i	$-0.479472\pi$
$421$	21.7979	−	21.7979i	1.06237	−	1.06237i	0.997921	−	0.0644457i	$-0.0205279\pi$
$422$	−5.79409	−	3.34522i	−0.282052	−	0.162843i
$423$	−41.8366	+	11.2101i	−2.03417	+	0.545053i
$424$	1.60275	+	5.98153i	0.0778362	+	0.290489i
$425$	−1.14349	+	3.22980i	−0.0554673	+	0.156668i
$426$	0.0332241	−	0.123994i	0.00160971	−	0.00600754i
$427$	3.48652	+	2.01294i	0.168725	+	0.0974131i
$428$	7.57523	+	28.2712i	0.366163	+	1.36654i
$429$	8.86432	+	33.0821i	0.427973	+	1.59722i
$430$	0.755545	−	1.63905i	0.0364356	−	0.0790419i
$431$	30.9974	+	8.30574i	1.49309	+	0.400073i	0.910781	−	0.412891i	$-0.135481\pi$
$431$	30.9974	+	8.30574i	1.49309	+	0.400073i	0.582314	+	0.812964i	$0.302147\pi$
$432$	−6.86941	+	1.84065i	−0.330504	+	0.0885584i
$433$	6.59714	+	6.59714i	0.317038	+	0.317038i	0.847628	−	0.530590i	$-0.178030\pi$
$433$	6.59714	+	6.59714i	0.317038	+	0.317038i	−0.530590	+	0.847628i	$0.678030\pi$
$434$	−1.09741			−0.0526772
$435$	−22.5028	−	31.8385i	−1.07893	−	1.52654i
$436$	22.6148	−	22.6148i	1.08305	−	1.08305i
$437$	−7.18861	+	26.8283i	−0.343878	+	1.28337i
$438$	−8.74281			−0.417748
$439$	−1.83248	+	6.83892i	−0.0874597	+	0.326404i	−0.995769	−	0.0918961i	$-0.970707\pi$
$439$	−1.83248	+	6.83892i	−0.0874597	+	0.326404i	0.908309	+	0.418300i	$0.137374\pi$
$440$	7.82960	−	0.719703i	0.373262	−	0.0343105i
$441$	−8.74124	−	15.1403i	−0.416249	−	0.720965i
$442$	−0.616442	+	1.06771i	−0.0293212	+	0.0507857i
$443$	18.7004	−	18.7004i	0.888481	−	0.888481i	−0.105896	−	0.994377i	$-0.533771\pi$
$443$	18.7004	−	18.7004i	0.888481	−	0.888481i	0.994377	+	0.105896i	$0.0337712\pi$
$444$	−24.0350	−	17.6486i	−1.14065	−	0.837564i
$445$	33.1036	−	12.2138i	1.56926	−	0.578990i
$446$	−1.62950	−	6.08136i	−0.0771588	−	0.287961i
$447$	9.35075	−	34.8975i	0.442275	−	1.65059i
$448$	−7.78775	−	2.08672i	−0.367937	−	0.0985883i
$449$	−14.0578	−	3.76677i	−0.663427	−	0.177765i	−0.0886349	−	0.996064i	$-0.528250\pi$
$449$	−14.0578	−	3.76677i	−0.663427	−	0.177765i	−0.574792	+	0.818299i	$0.694917\pi$
$450$	−4.39314	−	5.14301i	−0.207095	−	0.242444i
$451$	10.1353	+	17.5548i	0.477251	+	0.826623i
$452$	−18.5919			−0.874488
$453$	−54.7518	+	14.6707i	−2.57247	+	0.689290i
$454$		−	5.33130i		−	0.250210i
$455$	16.6978	−	6.16077i	0.782803	−	0.288821i
$456$	−8.51228	+	14.7437i	−0.398624	+	0.690437i
$457$	8.63291	+	14.9526i	0.403831	+	0.699455i	0.994185	−	0.107689i	$-0.0343451\pi$
$457$	8.63291	+	14.9526i	0.403831	+	0.699455i	−0.590354	+	0.807145i	$0.701012\pi$
$458$	7.31865			0.341978
$459$	−1.44041	+	0.385958i	−0.0672327	+	0.0180150i
$460$	19.9767	−	14.1192i	0.931420	−	0.658309i
$461$	−12.8182	+	3.43463i	−0.597004	+	0.159967i	−0.544652	−	0.838662i	$-0.683338\pi$
$461$	−12.8182	+	3.43463i	−0.597004	+	0.159967i	−0.0523519	+	0.998629i	$0.516672\pi$
$462$	3.20729	−	1.85173i	0.149217	−	0.0861504i
$463$	−20.6820	+	11.9408i	−0.961176	+	0.554935i	−0.896535	−	0.442973i	$-0.853924\pi$
$463$	−20.6820	+	11.9408i	−0.961176	+	0.554935i	−0.0646411	+	0.997909i	$0.520590\pi$
$464$	21.0562	−	5.64199i	0.977509	−	0.261923i
$465$	−9.50324	+	6.71671i	−0.440702	+	0.311480i
$466$	0.0298317	−	0.00799337i	0.00138192	−	0.000370286i
$467$	−20.4259			−0.945199			−0.472600	−	0.881277i	$-0.656684\pi$
$467$	−20.4259			−0.945199			−0.472600	+	0.881277i	$0.656684\pi$
$468$	18.3184	+	31.7284i	0.846767	+	1.46664i
$469$	−0.304233	+	0.526947i	−0.0140482	+	0.0243322i
$470$	8.36830	−	3.08755i	0.386001	−	0.142418i
$471$		−	25.2159i		−	1.16189i
$472$	12.4196	−	3.32782i	0.571658	−	0.153175i
$473$	5.87800			0.270271
$474$	−0.217344	−	0.376451i	−0.00998293	−	0.0172910i
$475$	23.7333	+	1.86626i	1.08896	+	0.0856297i
$476$	−1.93839	−	0.519391i	−0.0888461	−	0.0238062i
$477$	16.7587	+	4.49049i	0.767329	+	0.205605i
$478$	1.38366	−	5.16388i	0.0632870	−	0.236190i
$479$	−3.51612	−	13.1223i	−0.160655	−	0.599574i	−0.998554	−	0.0537489i	$-0.982883\pi$
$479$	−3.51612	−	13.1223i	−0.160655	−	0.599574i	0.837899	−	0.545825i	$-0.183784\pi$
$480$	21.3273	−	7.86888i	0.973456	−	0.359164i
$481$	−11.2573	+	28.8894i	−0.513289	+	1.31724i
$482$	−3.12763	+	3.12763i	−0.142460	+	0.142460i
$483$	11.9052	−	20.6204i	0.541704	−	0.938259i
$484$	−4.11872	−	7.13383i	−0.187214	−	0.324265i
$485$	30.6683	−	2.81906i	1.39258	−	0.128007i
$486$	−1.98365	+	7.40309i	−0.0899802	+	0.335811i
$487$	−30.9463			−1.40231			−0.701154	−	0.713009i	$-0.747332\pi$
$487$	−30.9463			−1.40231			−0.701154	+	0.713009i	$0.747332\pi$
$488$	0.912772	−	3.40651i	0.0413192	−	0.154205i
$489$	−35.9516	+	35.9516i	−1.62579	+	1.62579i
$490$	2.07801	+	2.94010i	0.0938748	+	0.132820i
$491$	9.00052			0.406188			0.203094	−	0.979159i	$-0.434900\pi$
$491$	9.00052			0.406188			0.203094	+	0.979159i	$0.434900\pi$
$492$	27.3347	+	27.3347i	1.23234	+	1.23234i
$493$	4.41517	−	1.18304i	0.198849	−	0.0532815i
$494$	8.27456	+	2.21716i	0.372290	+	0.0997549i
$495$	9.22200	−	20.0058i	0.414498	−	0.899195i
$496$	−1.68404	−	6.28491i	−0.0756154	−	0.282201i
$497$	−0.0562310	−	0.209857i	−0.00252231	−	0.00941337i
$498$	2.53518	+	1.46368i	0.113604	+	0.0655893i
$499$	−11.3719	+	42.4404i	−0.509075	+	1.89989i	−0.0795648	+	0.996830i	$0.525353\pi$
$499$	−11.3719	+	42.4404i	−0.509075	+	1.89989i	−0.429510	+	0.903062i	$0.641314\pi$
$500$	−15.0207	−	14.6296i	−0.671746	−	0.654255i
$501$	−2.75458	−	10.2802i	−0.123066	−	0.459287i
$502$	−0.372393	+	0.0997823i	−0.0166207	+	0.00445350i
$503$	−0.523159	−	0.302046i	−0.0233265	−	0.0134676i	0.488291	−	0.872681i	$-0.337620\pi$
$503$	−0.523159	−	0.302046i	−0.0233265	−	0.0134676i	−0.511618	+	0.859213i	$0.670954\pi$
$504$	5.78872	−	5.78872i	0.257850	−	0.257850i
$505$	−2.65974	−	28.9351i	−0.118357	−	1.28760i
$506$	−4.58370	−	2.64640i	−0.203770	−	0.117647i
$507$	23.9943	−	23.9943i	1.06563	−	1.06563i
$508$	17.9171	−	17.9171i	0.794943	−	0.794943i
$509$	−8.77913	+	15.2059i	−0.389128	+	0.673990i	−0.992333	−	0.123597i	$-0.960557\pi$
$509$	−8.77913	+	15.2059i	−0.389128	+	0.673990i	0.603204	+	0.797587i	$0.293890\pi$
$510$	1.32633	−	0.489358i	0.0587307	−	0.0216691i
$511$	−12.8146	+	7.39850i	−0.566883	+	0.327290i
$512$			21.6509i			0.956844i
$513$	5.18075	+	8.97331i	0.228735	+	0.396181i
$514$	−0.138252	+	0.0798196i	−0.00609801	+	0.00352069i
$515$	34.6746	−	3.18732i	1.52795	−	0.140450i
$516$	10.8277	−	2.90128i	0.476664	−	0.127722i
$517$	20.5416	+	20.5416i	0.903421	+	0.903421i
$518$	3.33252	+	0.367285i	0.146422	+	0.0161376i
$519$		−	9.28541i		−	0.407584i
$520$	−8.99876	−	12.7320i	−0.394622	−	0.558337i
$521$	−19.5517	+	11.2882i	−0.856576	+	0.494545i	−0.862864	−	0.505436i	$-0.831332\pi$
$521$	−19.5517	+	11.2882i	−0.856576	+	0.494545i	0.00628804	+	0.999980i	$0.497998\pi$
$522$	−2.33549	+	8.71617i	−0.102222	+	0.381497i
$523$	−11.0610	+	6.38608i	−0.483665	+	0.279244i	−0.721942	−	0.691953i	$-0.756750\pi$
$523$	−11.0610	+	6.38608i	−0.483665	+	0.279244i	0.238278	+	0.971197i	$0.423417\pi$
$524$	12.0532	−	12.0532i	0.526547	−	0.526547i
$525$	−19.2385	−	6.81126i	−0.839637	−	0.297268i
$526$	3.76215	+	3.76215i	0.164037	+	0.164037i
$527$	−0.353117	−	1.31785i	−0.0153820	−	0.0574065i
$528$	15.5267	+	15.5267i	0.675715	+	0.675715i
$529$	−11.0285			−0.479501
$530$	−3.52143	−	0.604972i	−0.152961	−	0.0262783i
$531$	9.32370	−	34.7965i	0.404614	−	1.51004i
$532$			13.9437i			0.604535i
$533$	20.0976	−	34.8101i	0.870526	−	1.50779i
$534$	−12.6086	−	7.27955i	−0.545626	−	0.315017i
$535$	−34.3932	−	5.90864i	−1.48695	−	0.255453i
$536$	0.514855	+	0.137955i	0.0222383	+	0.00595874i
$537$	−9.49919	−	16.4531i	−0.409920	−	0.710003i
$538$	−3.13427	+	5.42871i	−0.135128	+	0.234048i
$539$	−5.86287	+	10.1548i	−0.252532	+	0.437398i
$540$	1.54517	−	8.99415i	0.0664935	−	0.387047i
$541$	20.2821	+	20.2821i	0.871996	+	0.871996i	0.992690	−	0.120694i	$-0.0385120\pi$
$541$	20.2821	+	20.2821i	0.871996	+	0.871996i	−0.120694	+	0.992690i	$0.538512\pi$
$542$	−3.33517	+	1.92556i	−0.143258	+	0.0827099i
$543$	6.31227	+	23.5577i	0.270885	+	1.01096i
$544$			2.66516i			0.114268i
$545$	13.1995	+	35.7752i	0.565405	+	1.53244i
$546$	−6.35988	−	3.67188i	−0.272178	−	0.157142i
$547$		−	1.42392i		−	0.0608826i	−0.999537	−	0.0304413i	$-0.990309\pi$
$547$		−	1.42392i		−	0.0608826i	0.999537	−	0.0304413i	$-0.00969126\pi$
$548$	8.70361	+	2.33213i	0.371800	+	0.0996235i
$549$	−6.98682	−	6.98682i	−0.298190	−	0.298190i
$550$	−1.51407	+	4.27652i	−0.0645603	+	0.182352i
$551$	−15.8801	−	27.5051i	−0.676514	−	1.17176i
$552$	−20.1472	−	5.39842i	−0.857521	−	0.229772i
$553$	−0.637133	−	0.367849i	−0.0270937	−	0.0156425i
$554$	−4.54286			−0.193008
$555$	31.1066	−	17.2162i	1.32040	−	0.730785i
$556$	−19.2836			−0.817808
$557$	20.2319	+	11.6809i	0.857251	+	0.494934i	0.863091	−	0.505049i	$-0.168525\pi$
$557$	20.2319	+	11.6809i	0.857251	+	0.494934i	−0.00583957	+	0.999983i	$0.501859\pi$
$558$	2.60163	+	0.697104i	0.110136	+	0.0295107i
$559$	−5.82787	−	10.0942i	−0.246493	−	0.426938i
$560$	7.29626	−	8.77340i	0.308323	−	0.370744i
$561$	3.25573	+	3.25573i	0.137457	+	0.137457i
$562$	8.84197	+	2.36920i	0.372976	+	0.0999387i
$563$		−	33.5056i		−	1.41209i	−0.708166	−	0.706045i	$-0.750477\pi$
$563$		−	33.5056i		−	1.41209i	0.708166	−	0.706045i	$-0.249523\pi$
$564$	47.9782	+	27.7003i	2.02025	+	1.16639i
$565$	9.27985	−	20.1313i	0.390406	−	0.846931i
$566$		−	1.79695i		−	0.0755313i
$567$	2.34785	+	8.76231i	0.0986005	+	0.367982i
$568$	−0.164822	+	0.0951599i	−0.00691577	+	0.00399282i
$569$	−28.8255	−	28.8255i	−1.20843	−	1.20843i	−0.971536	−	0.236893i	$-0.923871\pi$
$569$	−28.8255	−	28.8255i	−1.20843	−	1.20843i	−0.236893	−	0.971536i	$-0.576129\pi$
$570$	−5.66955	−	8.02166i	−0.237471	−	0.335991i
$571$	15.6780	−	27.1551i	0.656105	−	1.13641i	−0.325510	−	0.945538i	$-0.605536\pi$
$571$	15.6780	−	27.1551i	0.656105	−	1.13641i	0.981616	−	0.190869i	$-0.0611306\pi$
$572$	12.2864	−	21.2807i	0.513720	−	0.889789i
$573$	3.16574	+	5.48323i	0.132251	+	0.229065i
$574$	−4.19834	−	1.12494i	−0.175236	−	0.0469542i
$575$	5.31718	+	28.6782i	0.221742	+	1.19596i
$576$	17.1369	+	9.89399i	0.714037	+	0.412250i
$577$	−2.25843	+	3.91171i	−0.0940195	+	0.162847i	−0.909199	−	0.416362i	$-0.863305\pi$
$577$	−2.25843	+	3.91171i	−0.0940195	+	0.162847i	0.815179	+	0.579208i	$0.196638\pi$
$578$		−	5.83478i		−	0.242695i
$579$	6.22659	−	23.2379i	0.258768	−	0.965736i
$580$	−4.73627	+	27.5690i	−0.196663	+	1.14474i
$581$	4.95450			0.205547
$582$	−8.98562	−	8.98562i	−0.372466	−	0.372466i
$583$	−3.01183	−	11.2403i	−0.124737	−	0.465526i
$584$	9.16564	+	9.16564i	0.379277	+	0.379277i
$585$	−43.4989	+	3.99846i	−1.79846	+	0.165316i
$586$	5.83852	−	5.83852i	0.241187	−	0.241187i
$587$	−8.52007	+	4.91907i	−0.351661	+	0.203032i	−0.665417	−	0.746472i	$-0.731746\pi$
$587$	−8.52007	+	4.91907i	−0.351661	+	0.203032i	0.313756	+	0.949504i	$0.398413\pi$
$588$	−5.78762	+	21.5997i	−0.238677	+	0.890756i
$589$	−8.20980	+	4.73993i	−0.338279	+	0.195305i
$590$	−1.25612	+	7.31163i	−0.0517135	+	0.301015i
$591$		−	6.00822i		−	0.247145i
$592$	3.01048	+	19.6491i	0.123730	+	0.807574i
$593$	30.7170	+	30.7170i	1.26139	+	1.26139i	0.950417	+	0.310977i	$0.100656\pi$
$593$	30.7170	+	30.7170i	1.26139	+	1.26139i	0.310977	+	0.950417i	$0.399344\pi$
$594$	−1.90723	+	0.511040i	−0.0782545	+	0.0209682i
$595$	1.52992	−	1.83965i	0.0627205	−	0.0754184i
$596$	−22.4484	+	12.9606i	−0.919524	+	0.530887i
$597$	−24.0369	−	41.6332i	−0.983765	−	1.70393i
$598$			10.4953i			0.429186i
$599$	−19.3744	+	11.1858i	−0.791617	+	0.457040i	−0.840532	−	0.541763i	$-0.817757\pi$
$599$	−19.3744	+	11.1858i	−0.791617	+	0.457040i	0.0489144	+	0.998803i	$0.484424\pi$
$600$	−1.40150	+	17.8230i	−0.0572160	+	0.727620i
$601$	−1.50390	+	2.60484i	−0.0613456	+	0.106254i	−0.895067	−	0.445931i	$-0.852872\pi$
$601$	−1.50390	+	2.60484i	−0.0613456	+	0.106254i	0.833722	+	0.552185i	$0.186206\pi$
$602$	−0.891218	+	0.891218i	−0.0363233	+	0.0363233i
$603$	1.05598	−	1.05598i	0.0430027	−	0.0430027i
$604$	35.2201	+	20.3344i	1.43309	+	0.827393i
$605$	9.78033	−	0.899016i	0.397627	−	0.0365502i
$606$	−8.47780	+	8.47780i	−0.344387	+	0.344387i
$607$	−14.0611	−	8.11816i	−0.570721	−	0.329506i	0.186716	−	0.982414i	$-0.440216\pi$
$607$	−14.0611	−	8.11816i	−0.570721	−	0.329506i	−0.757437	+	0.652908i	$0.773549\pi$
$608$	17.8873	−	4.79290i	0.725427	−	0.194378i
$609$	7.04687	+	26.2993i	0.285554	+	1.06570i
$610$	1.56452	+	1.30111i	0.0633457	+	0.0526805i
$611$	14.9093	−	55.6422i	0.603165	−	2.25104i
$612$	4.26542	+	2.46264i	0.172419	+	0.0995464i
$613$	−7.57761	−	28.2800i	−0.306057	−	1.14222i	−0.932032	−	0.362377i	$-0.881965\pi$
$613$	−7.57761	−	28.2800i	−0.306057	−	1.14222i	0.625975	−	0.779843i	$-0.284701\pi$
$614$	0.344943	+	1.28735i	0.0139208	+	0.0519531i
$615$	−43.2417	+	15.9544i	−1.74368	+	0.643342i
$616$	−5.30370	−	1.42112i	−0.213692	−	0.0572586i
$617$	−22.8600	+	6.12531i	−0.920307	+	0.246596i	−0.687717	−	0.725979i	$-0.741387\pi$
$617$	−22.8600	+	6.12531i	−0.920307	+	0.246596i	−0.232591	+	0.972575i	$0.574720\pi$
$618$	−10.1594	−	10.1594i	−0.408673	−	0.408673i
$619$	29.6822			1.19303			0.596514	−	0.802603i	$-0.296552\pi$
$619$	29.6822			1.19303			0.596514	+	0.802603i	$0.296552\pi$
$620$	8.22887	+	1.41369i	0.330479	+	0.0567753i
$621$	−8.97639	+	8.97639i	−0.360210	+	0.360210i
$622$	−0.821485	+	3.06583i	−0.0329386	+	0.122928i
$623$	−24.6409			−0.987218
$624$	11.2694	−	42.0581i	0.451138	−	1.68367i
$625$	23.3383	−	8.96232i	0.933532	−	0.358493i
$626$	−0.263785	−	0.456889i	−0.0105430	−	0.0182610i
$627$	15.9960	−	27.7059i	0.638820	−	1.10647i
$628$	−12.7928	+	12.7928i	−0.510488	+	0.510488i
$629$	0.631253	+	4.12013i	0.0251697	+	0.164280i
$630$	1.63504	+	4.43150i	0.0651414	+	0.176555i
$631$	2.72026	+	10.1521i	0.108292	+	0.404151i	0.998698	−	0.0510167i	$-0.0162462\pi$
$631$	2.72026	+	10.1521i	0.108292	+	0.404151i	−0.890406	+	0.455167i	$0.849579\pi$
$632$	−0.166802	+	0.622512i	−0.00663501	+	0.0247622i
$633$	47.8575	+	12.8234i	1.90216	+	0.509683i
$634$	6.41174	+	1.71802i	0.254643	+	0.0682313i
$635$	10.4576	+	28.3438i	0.414999	+	1.12479i
$636$	−11.0960	−	19.2189i	−0.439987	−	0.762080i
$637$	23.2515			0.921257
$638$	5.84606	−	1.56645i	0.231448	−	0.0620163i
$639$			0.533228i			0.0210942i
$640$	−19.4970	−	8.98744i	−0.770686	−	0.355260i
$641$	2.73142	−	4.73096i	0.107885	−	0.186862i	−0.807028	−	0.590513i	$-0.798926\pi$
$641$	2.73142	−	4.73096i	0.107885	−	0.186862i	0.914913	+	0.403651i	$0.132259\pi$
$642$	7.19953	+	12.4700i	0.284143	+	0.492150i
$643$	−11.2760			−0.444683			−0.222341	−	0.974969i	$-0.571370\pi$
$643$	−11.2760			−0.444683			−0.222341	+	0.974969i	$0.571370\pi$
$644$	−16.5012	+	4.42148i	−0.650238	+	0.174231i
$645$	−2.26298	+	13.1724i	−0.0891049	+	0.518664i
$646$	1.11240	−	0.298066i	0.0437666	−	0.0117272i
$647$	13.5603	−	7.82906i	0.533112	−	0.307792i	−0.209171	−	0.977879i	$-0.567077\pi$
$647$	13.5603	−	7.82906i	0.533112	−	0.307792i	0.742283	+	0.670087i	$0.233743\pi$
$648$	6.88192	−	3.97328i	0.270347	−	0.156085i
$649$	−23.3385	+	6.25354i	−0.916117	+	0.245473i
$650$	8.84514	−	1.63996i	0.346935	−	0.0643246i
$651$	7.84987	−	2.10337i	0.307661	−	0.0824375i
$652$	36.4786			1.42861
$653$	−13.0781	−	22.6519i	−0.511784	−	0.886436i	−0.999907	−	0.0136613i	$-0.995651\pi$
$653$	−13.0781	−	22.6519i	−0.511784	−	0.886436i	0.488122	−	0.872775i	$-0.337682\pi$
$654$	7.86705	−	13.6261i	0.307626	−	0.532824i
$655$	7.03508	+	19.0675i	0.274883	+	0.745027i
$656$		−	25.7704i		−	1.00617i
$657$	35.0793	−	9.39946i	1.36857	−	0.366708i
$658$	−6.22902			−0.242832
$659$	−12.9748	−	22.4730i	−0.505425	−	0.875422i	−0.999980	−	0.00627593i	$-0.998002\pi$
$659$	−12.9748	−	22.4730i	−0.505425	−	0.875422i	0.494555	−	0.869146i	$-0.335331\pi$
$660$	−26.4352	+	9.75346i	−1.02899	+	0.379653i
$661$	20.5645	+	5.51024i	0.799866	+	0.214324i	0.635525	−	0.772080i	$-0.280784\pi$
$661$	20.5645	+	5.51024i	0.799866	+	0.214324i	0.164341	+	0.986404i	$0.447450\pi$
$662$	1.30542	+	0.349786i	0.0507366	+	0.0135948i
$663$	2.36303	−	8.81896i	0.0917726	−	0.342500i
$664$	−1.12331	−	4.19226i	−0.0435930	−	0.162691i
$665$	−15.0982	−	6.95978i	−0.585485	−	0.269889i
$666$	−7.66709	−	2.98763i	−0.297094	−	0.115768i
$667$	27.5145	−	27.5145i	1.06537	−	1.06537i
$668$	−3.81799	+	6.61295i	−0.147722	+	0.255863i
$669$	23.3119	+	40.3774i	0.901291	+	1.56108i
$670$	−0.196648	+	0.236460i	−0.00759718	+	0.00913524i
$671$	−1.71525	+	6.40142i	−0.0662166	+	0.247124i
$672$	−15.8752			−0.612399
$673$	−5.01583	+	18.7193i	−0.193346	+	0.721577i	0.799343	+	0.600875i	$0.205181\pi$
$673$	−5.01583	+	18.7193i	−0.193346	+	0.721577i	−0.992689	+	0.120702i	$0.961485\pi$
$674$	1.32742	−	1.32742i	0.0511303	−	0.0511303i
$675$	8.96765	+	6.16241i	0.345165	+	0.237191i
$676$	−24.3461			−0.936388
$677$	16.3844	+	16.3844i	0.629705	+	0.629705i	0.947994	−	0.318289i	$-0.103108\pi$
$677$	16.3844	+	16.3844i	0.629705	+	0.629705i	−0.318289	+	0.947994i	$0.603108\pi$
$678$	−8.83489	+	2.36730i	−0.339302	+	0.0909157i
$679$	−20.7744	−	5.56649i	−0.797250	−	0.213622i
$680$	−1.90350	−	0.877447i	−0.0729958	−	0.0336485i
$681$	10.2183	+	38.1354i	0.391568	+	1.46135i
$682$	−0.467557	−	1.74495i	−0.0179037	−	0.0668175i
$683$	−6.50589	−	3.75618i	−0.248941	−	0.143726i	0.370338	−	0.928897i	$-0.379242\pi$
$683$	−6.50589	−	3.75618i	−0.248941	−	0.143726i	−0.619279	+	0.785171i	$0.712575\pi$
$684$	8.85740	−	33.0563i	0.338671	−	1.26394i
$685$	−6.86951	+	8.26025i	−0.262471	+	0.315608i
$686$	−1.64933	−	6.15538i	−0.0629716	−	0.235013i
$687$	−52.3511	+	14.0274i	−1.99732	+	0.535180i
$688$	−6.47168	−	3.73643i	−0.246730	−	0.142450i
$689$	−16.3166	+	16.3166i	−0.621613	+	0.621613i
$690$	7.69519	−	9.25309i	0.292951	−	0.352259i
$691$	−2.18961	−	1.26417i	−0.0832966	−	0.0480913i	0.457773	−	0.889069i	$-0.348647\pi$
$691$	−2.18961	−	1.26417i	−0.0832966	−	0.0480913i	−0.541070	+	0.840978i	$0.681981\pi$
$692$	−4.71077	+	4.71077i	−0.179077	+	0.179077i
$693$	−10.8780	+	10.8780i	−0.413221	+	0.413221i
$694$	3.12056	−	5.40497i	0.118455	−	0.205170i
$695$	9.62514	−	20.8804i	0.365102	−	0.792038i
$696$	20.6555	−	11.9254i	0.782943	−	0.452033i
$697$		−	5.40368i		−	0.204679i
$698$	2.64508	+	4.58141i	0.100118	+	0.173409i
$699$	−0.198068	+	0.114355i	−0.00749164	+	0.00432530i
$700$	6.30471	+	13.2158i	0.238296	+	0.499511i
$701$	2.22557	−	0.596340i	0.0840587	−	0.0225235i	−0.216545	−	0.976273i	$-0.569479\pi$
$701$	2.22557	−	0.596340i	0.0840587	−	0.0225235i	0.300603	+	0.953749i	$0.402812\pi$
$702$	2.76856	+	2.76856i	0.104493	+	0.104493i
$703$	26.5172	−	11.6461i	1.00012	−	0.439242i
$704$		−	13.2721i		−	0.500210i
$705$	−53.9416	+	38.1248i	−2.03156	+	1.43586i
$706$	3.60190	−	2.07956i	0.135559	−	0.0782651i
$707$	−5.25190	+	19.6004i	−0.197518	+	0.737148i
$708$	−39.9047	+	23.0390i	−1.49971	+	0.865857i
$709$	−19.7666	+	19.7666i	−0.742350	+	0.742350i	−0.973030	−	0.230680i	$-0.925905\pi$
$709$	−19.7666	+	19.7666i	−0.742350	+	0.742350i	0.230680	+	0.973030i	$0.425905\pi$
$710$	−0.0100517	−	0.109351i	−0.000377232	−	0.00410388i
$711$	1.27679	+	1.27679i	0.0478832	+	0.0478832i
$712$	5.58673	+	20.8500i	0.209372	+	0.781385i
$713$	−8.21261	−	8.21261i	−0.307565	−	0.307565i
$714$	−0.987262			−0.0369474
$715$	16.9102	+	23.9257i	0.632406	+	0.894770i
$716$	−3.52792	+	13.1664i	−0.131844	+	0.492050i
$717$			39.5898i			1.47851i
$718$	0.626586	−	1.08528i	0.0233840	−	0.0405022i
$719$	−19.1043	−	11.0299i	−0.712469	−	0.411344i	0.0995054	−	0.995037i	$-0.468274\pi$
$719$	−19.1043	−	11.0299i	−0.712469	−	0.411344i	−0.811975	+	0.583693i	$0.801607\pi$
$720$	−22.8704	+	16.1643i	−0.852328	+	0.602409i
$721$	−23.4883	−	6.29366i	−0.874748	−	0.234388i
$722$	−0.647731	−	1.12190i	−0.0241060	−	0.0417529i
$723$	16.3777	−	28.3669i	0.609092	−	1.05498i
$724$	8.74913	−	15.1539i	0.325159	−	0.563191i
$725$	−27.4878	−	18.8891i	−1.02087	−	0.701524i
$726$	−2.86557	−	2.86557i	−0.106351	−	0.106351i
$727$	−30.8570	+	17.8153i	−1.14442	+	0.660734i	−0.947522	−	0.319689i	$-0.896421\pi$
$727$	−30.8570	+	17.8153i	−1.14442	+	0.660734i	−0.196902	+	0.980423i	$0.563088\pi$
$728$	2.81800	+	10.5169i	0.104442	+	0.389783i
$729$		−	39.3293i		−	1.45664i
$730$	−7.01667	+	2.58885i	−0.259699	+	0.0958178i
$731$	−1.35702	−	0.783473i	−0.0501910	−	0.0289778i
$732$			12.6385i			0.467133i
$733$	−14.3167	−	3.83616i	−0.528801	−	0.141692i	−0.0154665	−	0.999880i	$-0.504923\pi$
$733$	−14.3167	−	3.83616i	−0.528801	−	0.141692i	−0.513335	+	0.858189i	$0.671590\pi$
$734$	1.46907	+	1.46907i	0.0542242	+	0.0542242i
$735$	−20.4994	−	17.0480i	−0.756132	−	0.628826i
$736$	11.3440	+	19.6484i	0.418145	+	0.724249i
$737$	−0.967500	−	0.259241i	−0.0356383	−	0.00954926i
$738$	9.23843	+	5.33381i	0.340071	+	0.196340i
$739$	2.13171			0.0784161			0.0392080	−	0.999231i	$-0.487516\pi$
$739$	2.13171			0.0784161			0.0392080	+	0.999231i	$0.487516\pi$
$740$	−24.5156	−	7.04706i	−0.901211	−	0.259055i
$741$	−63.4384			−2.33047
$742$	2.16090	+	1.24760i	0.0793291	+	0.0458007i
$743$	−3.71803	−	0.996243i	−0.136401	−	0.0365486i	0.189972	−	0.981789i	$-0.439160\pi$
$743$	−3.71803	−	0.996243i	−0.136401	−	0.0365486i	−0.326374	+	0.945241i	$0.605827\pi$
$744$	−3.55954	−	6.16530i	−0.130499	−	0.226031i
$745$	−2.82899	−	30.7763i	−0.103646	−	1.12756i
$746$	6.64733	+	6.64733i	0.243376	+	0.243376i
$747$	−11.7456	−	3.14724i	−0.429751	−	0.115151i
$748$		−	3.30346i		−	0.120786i
$749$	21.1051	+	12.1850i	0.771163	+	0.445231i
$750$	−9.00065	−	5.03942i	−0.328657	−	0.184014i
$751$			1.28407i			0.0468564i	0.999726	+	0.0234282i	$0.00745811\pi$
$751$			1.28407i			0.0468564i	−0.999726	+	0.0234282i	$0.992542\pi$
$752$	−9.55879	−	35.6739i	−0.348573	−	1.30089i
$753$	2.47252	−	1.42751i	0.0901035	−	0.0520213i
$754$	−8.48623	−	8.48623i	−0.309050	−	0.309050i
$755$	−39.5977	+	27.9869i	−1.44111	+	1.01855i
$756$	−3.18651	+	5.51919i	−0.115892	+	0.200731i
$757$	6.93453	−	12.0110i	0.252040	−	0.436546i	−0.712047	−	0.702131i	$-0.752232\pi$
$757$	6.93453	−	12.0110i	0.252040	−	0.436546i	0.964087	+	0.265586i	$0.0855653\pi$
$758$	−4.38267	−	7.59101i	−0.159186	−	0.275718i
$759$	37.8600	+	10.1446i	1.37423	+	0.368224i
$760$	−2.46587	+	14.3534i	−0.0894463	+	0.520651i
$761$	9.48381	+	5.47548i	0.343788	+	0.198486i	0.661946	−	0.749552i	$-0.269731\pi$
$761$	9.48381	+	5.47548i	0.343788	+	0.198486i	−0.318158	+	0.948038i	$0.603064\pi$
$762$	6.23286	−	10.7956i	0.225793	−	0.391085i
$763$		−	26.6296i		−	0.964055i
$764$	1.17573	−	4.38788i	0.0425364	−	0.158748i
$765$	−4.79558	+	3.38942i	−0.173384	+	0.122545i
$766$	0.340843			0.0123152
$767$	33.8785	+	33.8785i	1.22328	+	1.22328i
$768$	−4.69335	−	17.5158i	−0.169357	−	0.632048i
$769$	9.51657	+	9.51657i	0.343176	+	0.343176i	0.857560	−	0.514384i	$-0.171979\pi$
$769$	9.51657	+	9.51657i	0.343176	+	0.343176i	−0.514384	+	0.857560i	$0.671979\pi$
$770$	2.02574	−	2.43585i	0.0730026	−	0.0877821i
$771$	0.835940	−	0.835940i	0.0301057	−	0.0301057i
$772$	−14.9482	+	8.63037i	−0.537999	+	0.310614i
$773$	−0.370532	+	1.38284i	−0.0133271	+	0.0497374i	−0.972269	−	0.233865i	$-0.924863\pi$
$773$	−0.370532	+	1.38284i	−0.0133271	+	0.0497374i	0.958942	+	0.283602i	$0.0915294\pi$
$774$	2.67894	−	1.54669i	0.0962925	−	0.0555945i
$775$	−5.63807	+	8.20462i	−0.202525	+	0.294719i
$776$			18.8404i			0.676331i
$777$	−24.5418	+	3.76010i	−0.880433	+	0.134893i
$778$	−4.43672	−	4.43672i	−0.159064	−	0.159064i
$779$	−36.2670	+	9.71772i	−1.29940	+	0.348174i
$780$	42.9591	+	35.7263i	1.53818	+	1.27921i
$781$	0.309728	−	0.178822i	0.0110830	−	0.00639875i
$782$	0.705472	+	1.22191i	0.0252276	+	0.0436955i
$783$		−	14.5161i		−	0.518764i
$784$	12.9100	−	7.45361i	0.461073	−	0.266200i
$785$	−7.46674	−	20.2374i	−0.266499	−	0.722304i
$786$	4.19298	−	7.26245i	0.149559	−	0.259043i
$787$	2.47029	−	2.47029i	0.0880563	−	0.0880563i	−0.661707	−	0.749763i	$-0.730168\pi$
$787$	2.47029	−	2.47029i	0.0880563	−	0.0880563i	0.749763	+	0.661707i	$0.230168\pi$
$788$	−3.04815	+	3.04815i	−0.108586	+	0.108586i
$789$	−34.1218	−	19.7003i	−1.21477	−	0.701348i
$790$	−0.285904	−	0.237768i	−0.0101720	−	0.00845940i
$791$	−10.9462	+	10.9462i	−0.389203	+	0.389203i
$792$	11.6708	+	6.73811i	0.414702	+	0.239428i
$793$	12.6936	−	3.40125i	0.450764	−	0.120782i
$794$	3.17095	+	11.8342i	0.112533	+	0.419979i
$795$	26.3487	−	2.42200i	0.934493	−	0.0858994i
$796$	−8.92710	+	33.3164i	−0.316413	+	1.18087i
$797$	−20.6121	−	11.9004i	−0.730119	−	0.421534i	0.0883467	−	0.996090i	$-0.471842\pi$
$797$	−20.6121	−	11.9004i	−0.730119	−	0.421534i	−0.818466	+	0.574555i	$0.805175\pi$
$798$	1.77545	+	6.62606i	0.0628501	+	0.234560i
$799$	−2.00434	−	7.48029i	−0.0709083	−	0.264634i
$800$	14.7865	−	12.6306i	0.522782	−	0.446558i
$801$	58.4163	+	15.6526i	2.06404	+	0.553057i
$802$	5.89980	−	1.58085i	0.208329	−	0.0558217i
$803$	−17.2238	−	17.2238i	−0.607815	−	0.607815i
$804$	−1.91016			−0.0673663
$805$	3.44873	−	20.0745i	0.121552	−	0.707531i
$806$	−2.53299	+	2.53299i	−0.0892208	+	0.0892208i
$807$	12.0147	−	44.8395i	0.422938	−	1.57842i
$808$	17.7756			0.625344
$809$	−1.72550	+	6.43967i	−0.0606655	+	0.226407i	−0.989602	−	0.143832i	$-0.954057\pi$
$809$	−1.72550	+	6.43967i	−0.0606655	+	0.226407i	0.928937	+	0.370239i	$0.120724\pi$
$810$	0.419694	+	4.56583i	0.0147466	+	0.160427i
$811$	22.7108	+	39.3363i	0.797486	+	1.38129i	0.921249	+	0.388974i	$0.127170\pi$
$811$	22.7108	+	39.3363i	0.797486	+	1.38129i	−0.123763	+	0.992312i	$0.539496\pi$
$812$	9.76732	−	16.9175i	0.342766	−	0.593688i
$813$	20.1662	−	20.1662i	0.707258	−	0.707258i
$814$	0.835833	+	5.45540i	0.0292959	+	0.191212i
$815$	−18.2078	+	39.4991i	−0.637790	+	1.38359i
$816$	−1.51501	−	5.65410i	−0.0530360	−	0.197933i
$817$	−2.81792	+	10.5166i	−0.0985867	+	0.367931i
$818$	−11.5716	−	3.10060i	−0.404591	−	0.108410i
$819$	29.4658	+	7.89532i	1.02962	+	0.275885i
$820$	30.0319	+	13.8437i	1.04876	+	0.483443i
$821$	9.75300	+	16.8927i	0.340382	+	0.589559i	0.984504	−	0.175364i	$-0.0561103\pi$
$821$	9.75300	+	16.8927i	0.340382	+	0.589559i	−0.644122	+	0.764923i	$0.722777\pi$
$822$	4.43292			0.154616
$823$	22.7385	−	6.09277i	0.792616	−	0.212381i	0.160276	−	0.987072i	$-0.448761\pi$
$823$	22.7385	−	6.09277i	0.792616	−	0.212381i	0.632339	+	0.774691i	$0.282095\pi$
$824$			21.3016i			0.742075i
$825$	2.63366	−	33.4924i	0.0916921	−	1.16606i
$826$	2.59041	−	4.48672i	0.0901319	−	0.156113i
$827$	−13.6805	−	23.6954i	−0.475719	−	0.823970i	0.523894	−	0.851783i	$-0.324479\pi$
$827$	−13.6805	−	23.6954i	−0.475719	−	0.823970i	−0.999613	+	0.0278138i	$0.991145\pi$
$828$	41.9280			1.45710
$829$	29.7958	−	7.98376i	1.03485	−	0.277287i	0.298873	−	0.954293i	$-0.403389\pi$
$829$	29.7958	−	7.98376i	1.03485	−	0.277287i	0.735978	+	0.677006i	$0.236723\pi$
$830$	2.46806	+	0.424005i	0.0856676	+	0.0147174i
$831$	32.4956	−	8.70717i	1.12726	−	0.302048i
$832$	−22.7919	+	13.1589i	−0.790165	+	0.456202i
$833$	2.70704	−	1.56291i	0.0937935	−	0.0541517i
$834$	−9.16362	+	2.45539i	−0.317310	+	0.0850231i
$835$	−5.25483	−	7.43489i	−0.181851	−	0.257295i
$836$	−22.1713	+	5.94079i	−0.766811	+	0.205466i
$837$	−4.33281			−0.149764
$838$	−3.72520	−	6.45223i	−0.128685	−	0.222889i
$839$	20.9908	−	36.3572i	0.724684	−	1.25519i	−0.234420	−	0.972135i	$-0.575319\pi$
$839$	20.9908	−	36.3572i	0.724684	−	1.25519i	0.959104	−	0.283054i	$-0.0913476\pi$
$840$	5.22657	−	11.3383i	0.180334	−	0.391209i
$841$			15.4950i			0.534311i
$842$	−10.5103	+	2.81622i	−0.362208	+	0.0970534i
$843$	−67.7886			−2.33476
$844$	−17.7738	−	30.7852i	−0.611801	−	1.05967i
$845$	12.1520	−	26.3620i	0.418041	−	0.906881i
$846$	14.7671	+	3.95684i	0.507705	+	0.136039i
$847$	−6.62510	−	1.77519i	−0.227641	−	0.0609963i
$848$	−3.82902	+	14.2901i	−0.131489	+	0.490724i
$849$	3.44415	+	12.8538i	0.118203	+	0.441140i
$850$	0.919558	−	0.785483i	0.0315406	−	0.0269418i
$851$	22.1907	+	27.6880i	0.760689	+	0.949133i
$852$	0.482280	−	0.482280i	0.0165226	−	0.0165226i
$853$	7.35019	−	12.7309i	0.251666	−	0.435898i	−0.712319	−	0.701856i	$-0.752355\pi$
$853$	7.35019	−	12.7309i	0.251666	−	0.435898i	0.963985	+	0.265958i	$0.0856883\pi$
$854$	−0.710512	−	1.23064i	−0.0243132	−	0.0421117i
$855$	31.3724	+	26.0904i	1.07291	+	0.892272i
$856$	5.52532	−	20.6208i	0.188852	−	0.704804i
$857$	−39.5459			−1.35086			−0.675431	−	0.737424i	$-0.736042\pi$
$857$	−39.5459			−1.35086			−0.675431	+	0.737424i	$0.736042\pi$
$858$	3.12885	−	11.6770i	0.106817	−	0.398648i
$859$	12.0746	−	12.0746i	0.411980	−	0.411980i	−0.470448	−	0.882428i	$-0.655908\pi$
$859$	12.0746	−	12.0746i	0.411980	−	0.411980i	0.882428	+	0.470448i	$0.155908\pi$
$860$	7.83084	−	5.53468i	0.267030	−	0.188731i
$861$	32.1874			1.09694
$862$	−8.00953	−	8.00953i	−0.272806	−	0.272806i
$863$	−2.69662	+	0.722557i	−0.0917940	+	0.0245961i	−0.304424	−	0.952537i	$-0.598464\pi$
$863$	−2.69662	+	0.722557i	−0.0917940	+	0.0245961i	0.212630	+	0.977133i	$0.431797\pi$
$864$	8.17548	+	2.19061i	0.278136	+	0.0745262i
$865$	−2.74952	−	7.45214i	−0.0934866	−	0.253381i
$866$	−0.852328	−	3.18093i	−0.0289633	−	0.108092i
$867$	11.1833	+	41.7368i	0.379806	+	1.41746i
$868$	−5.04958	−	2.91537i	−0.171394	−	0.0989543i
$869$	0.313449	−	1.16981i	0.0106330	−	0.0396830i
$870$	1.25967	+	13.7039i	0.0427070	+	0.464606i
$871$	0.514060	+	1.91850i	0.0174182	+	0.0650058i
$872$	−22.5327	+	6.03761i	−0.763052	+	0.204459i
$873$	45.7140	+	26.3930i	1.54719	+	0.893268i
$874$	6.93224	−	6.93224i	0.234487	−	0.234487i
$875$	−17.4570	+	0.230277i	−0.590156	+	0.00778478i
$876$	−40.2289	−	23.2262i	−1.35921	−	0.784740i
$877$	19.2511	−	19.2511i	0.650064	−	0.650064i	−0.302944	−	0.953008i	$-0.597970\pi$
$877$	19.2511	−	19.2511i	0.650064	−	0.650064i	0.953008	+	0.302944i	$0.0979695\pi$
$878$	1.76713	−	1.76713i	0.0596378	−	0.0596378i
$879$	−30.5730	+	52.9541i	−1.03120	+	1.78610i
$880$	17.0589	+	7.86356i	0.575055	+	0.265081i
$881$	43.1969	−	24.9397i	1.45534	−	0.840241i	0.456564	−	0.889691i	$-0.349080\pi$
$881$	43.1969	−	24.9397i	1.45534	−	0.840241i	0.998777	+	0.0494498i	$0.0157468\pi$
$882$			6.17082i			0.207782i
$883$	22.8298	+	39.5424i	0.768285	+	1.33071i	0.938492	+	0.345300i	$0.112223\pi$
$883$	22.8298	+	39.5424i	0.768285	+	1.33071i	−0.170207	+	0.985408i	$0.554444\pi$
$884$	−5.67296	+	3.27528i	−0.190802	+	0.110160i
$885$	−5.02885	−	54.7085i	−0.169043	−	1.83900i
$886$	−9.01672	+	2.41602i	−0.302923	+	0.0811679i
$887$	4.12526	+	4.12526i	0.138513	+	0.138513i	0.772963	−	0.634451i	$-0.218774\pi$
$887$	4.12526	+	4.12526i	0.138513	+	0.138513i	−0.634451	+	0.772963i	$0.718774\pi$
$888$	8.74588	+	19.9136i	0.293492	+	0.668256i
$889$		−	21.0979i		−	0.707602i
$890$	−12.2747	−	2.10876i	−0.411450	−	0.0706860i
$891$	−12.9323	+	7.46647i	−0.433249	+	0.250136i
$892$	8.65784	−	32.3115i	0.289886	−	1.08187i
$893$	−46.5998	+	26.9044i	−1.55940	+	0.900322i
$894$	−9.01727	+	9.01727i	−0.301583	+	0.301583i
$895$	−12.4957	−	10.3918i	−0.417684	−	0.347361i
$896$	10.6013	+	10.6013i	0.354165	+	0.354165i
$897$	−20.1161	−	75.0742i	−0.671656	−	2.50665i
$898$	3.63243	+	3.63243i	0.121216	+	0.121216i
$899$	13.2810			0.442946
$900$	−6.55153	−	35.3357i	−0.218384	−	1.17786i
$901$	−0.802889	+	2.99642i	−0.0267481	+	0.0998253i
$902$		−	7.15492i		−	0.238233i
$903$	4.66681	−	8.08315i	0.155302	−	0.268990i
$904$	11.7440	+	6.78038i	0.390598	+	0.225512i
$905$	12.0417	+	17.0374i	0.400281	+	0.566344i
$906$	19.3259	+	5.17835i	0.642058	+	0.172039i
$907$	−2.05682	−	3.56252i	−0.0682957	−	0.118292i	0.829855	−	0.557978i	$-0.188423\pi$
$907$	−2.05682	−	3.56252i	−0.0682957	−	0.118292i	−0.898151	+	0.439687i	$0.855089\pi$
$908$	14.1632	−	24.5313i	0.470021	−	0.814100i
$909$	24.9014	−	43.1305i	0.825927	−	1.43055i
$910$	−6.19150	−	1.06368i	−0.205246	−	0.0352607i
$911$	23.6772	+	23.6772i	0.784460	+	0.784460i	0.980580	−	0.196120i	$-0.0628341\pi$
$911$	23.6772	+	23.6772i	0.784460	+	0.784460i	−0.196120	+	0.980580i	$0.562834\pi$
$912$	−35.2232	+	20.3361i	−1.16636	+	0.673397i
$913$	2.11090	+	7.87797i	0.0698605	+	0.260723i
$914$		−	6.09435i		−	0.201583i
$915$	−13.6850	−	6.30832i	−0.452413	−	0.208547i
$916$	33.6758	+	19.4427i	1.11268	+	0.642406i
$917$		−	14.1930i		−	0.468695i
$918$	0.508425	+	0.136232i	0.0167805	+	0.00449633i
$919$	37.5747	+	37.5747i	1.23947	+	1.23947i	0.960216	+	0.279258i	$0.0900884\pi$
$919$	37.5747	+	37.5747i	1.23947	+	1.23947i	0.279258	+	0.960216i	$0.409912\pi$
$920$	−17.7679	+	1.63324i	−0.585792	+	0.0538465i
$921$	−4.93484	−	8.54739i	−0.162608	−	0.281646i
$922$	4.52447	+	1.21233i	0.149006	+	0.0399259i
$923$	−0.614173	−	0.354593i	−0.0202158	−	0.0116716i
$924$	19.6773			0.647334
$925$	19.8672	−	23.0281i	0.653229	−	0.757160i
$926$	8.42952			0.277011
$927$	51.6857	+	29.8408i	1.69758	+	0.980100i
$928$	−25.0596	−	6.71470i	−0.822622	−	0.220421i
$929$	1.68883	+	2.92515i	0.0554088	+	0.0959709i	0.892399	−	0.451246i	$-0.149020\pi$
$929$	1.68883	+	2.92515i	0.0554088	+	0.0959709i	−0.836991	+	0.547217i	$0.815687\pi$
$930$	4.09038	−	0.375991i	0.134129	−	0.0123292i
$931$	−15.3578	−	15.3578i	−0.503331	−	0.503331i
$932$	0.158502	+	0.0424704i	0.00519189	+	0.00139116i
$933$		−	23.5047i		−	0.769509i
$934$	6.24385	+	3.60489i	0.204305	+	0.117956i
$935$	3.57699	+	1.64887i	0.116980	+	0.0539239i
$936$		−	26.7226i		−	0.873455i
$937$	−13.6061	−	50.7787i	−0.444492	−	1.65887i	−0.717275	−	0.696791i	$-0.754611\pi$
$937$	−13.6061	−	50.7787i	−0.444492	−	1.65887i	0.272783	−	0.962076i	$-0.412056\pi$
$938$	0.185997	−	0.107386i	0.00607303	−	0.00350627i
$939$	2.76259	+	2.76259i	0.0901537	+	0.0901537i
$940$	46.7080	+	8.02430i	1.52345	+	0.261724i
$941$	15.5502	−	26.9338i	0.506924	−	0.878017i	−0.493044	−	0.870004i	$-0.664116\pi$
$941$	15.5502	−	26.9338i	0.506924	−	0.878017i	0.999968	−	0.00801323i	$-0.00255072\pi$
$942$	−4.45025	+	7.70806i	−0.144997	+	0.251142i
$943$	−23.0003	−	39.8376i	−0.748991	−	1.29729i
$944$	29.6708	+	7.95028i	0.965703	+	0.258759i
$945$	−4.38570	−	6.20518i	−0.142667	−	0.201855i
$946$	−1.79680	−	1.03738i	−0.0584191	−	0.0337283i
$947$	−11.3518	+	19.6619i	−0.368884	+	0.638926i	−0.989391	−	0.145275i	$-0.953593\pi$
$947$	−11.3518	+	19.6619i	−0.368884	+	0.638926i	0.620507	+	0.784201i	$0.286927\pi$
$948$		−	2.30958i		−	0.0750118i
$949$	−12.5012	+	46.6550i	−0.405805	+	1.51448i
$950$	−6.92550	−	4.75908i	−0.224693	−	0.154405i
$951$	−49.1568			−1.59402
$952$	1.03501	+	1.03501i	0.0335448	+	0.0335448i
$953$	4.34551	+	16.2177i	0.140765	+	0.525342i	0.999907	+	0.0136055i	$0.00433090\pi$
$953$	4.34551	+	16.2177i	0.140765	+	0.525342i	−0.859142	+	0.511736i	$0.829002\pi$
$954$	−4.33034	−	4.33034i	−0.140200	−	0.140200i
$955$	4.16436	+	3.46323i	0.134756	+	0.112067i
$956$	20.0851	−	20.0851i	0.649598	−	0.649598i
$957$	−38.8152	+	22.4099i	−1.25472	+	0.724410i
$958$	−1.24109	+	4.63181i	−0.0400978	+	0.149647i
$959$	6.49745	−	3.75131i	0.209814	−	0.121136i
$960$	29.7423	+	5.10964i	0.959929	+	0.164913i
$961$			27.0359i			0.872124i
$962$	8.53973	−	6.84423i	0.275332	−	0.220667i
$963$	−42.2936	−	42.2936i	−1.36289	−	1.36289i
$964$	−22.7003	+	6.08252i	−0.731126	+	0.195905i
$965$	−1.88380	−	20.4937i	−0.0606417	−	0.659716i
$966$	−7.27841	+	4.20219i	−0.234179	+	0.135203i
$967$	18.4488	+	31.9542i	0.593272	+	1.02758i	0.993788	+	0.111288i	$0.0354976\pi$
$967$	18.4488	+	31.9542i	0.593272	+	1.02758i	−0.400516	+	0.916290i	$0.631169\pi$
$968$			6.00832i			0.193115i
$969$	−7.38579	+	4.26419i	−0.237266	+	0.136986i
$970$	−9.87230	−	4.55079i	−0.316980	−	0.146117i
$971$	−11.0965	+	19.2197i	−0.356103	+	0.616788i	−0.987306	−	0.158829i	$-0.949228\pi$
$971$	−11.0965	+	19.2197i	−0.356103	+	0.616788i	0.631203	+	0.775618i	$0.282561\pi$
$972$	−28.7946	+	28.7946i	−0.923586	+	0.923586i
$973$	−11.3535	+	11.3535i	−0.363977	+	0.363977i
$974$	9.45973	+	5.46158i	0.303109	+	0.175000i
$975$	−60.1270	+	28.6840i	−1.92560	+	0.918625i
$976$	5.95763	−	5.95763i	0.190699	−	0.190699i
$977$	−25.8120	−	14.9026i	−0.825798	−	0.476775i	0.0266135	−	0.999646i	$-0.491528\pi$
$977$	−25.8120	−	14.9026i	−0.825798	−	0.476775i	−0.852412	+	0.522871i	$0.824861\pi$
$978$	17.3347	−	4.64482i	0.554303	−	0.148525i
$979$	−10.4984	−	39.1806i	−0.335531	−	1.25222i
$980$	1.75099	+	19.0489i	0.0559334	+	0.608496i
$981$	−16.9158	+	63.1308i	−0.540081	+	2.01561i
$982$	−2.75130	−	1.58846i	−0.0877975	−	0.0506899i
$983$	1.36230	+	5.08418i	0.0434507	+	0.162160i	0.984242	−	0.176825i	$-0.0565828\pi$
$983$	1.36230	+	5.08418i	0.0434507	+	0.162160i	−0.940792	+	0.338986i	$0.889916\pi$
$984$	−7.29770	−	27.2354i	−0.232642	−	0.868233i
$985$	−1.77911	−	4.82199i	−0.0566871	−	0.153641i
$986$	−1.55843	−	0.417580i	−0.0496306	−	0.0132985i
$987$	44.5568	−	11.9390i	1.41826	−	0.380021i
$988$	32.1842	+	32.1842i	1.02392	+	1.02392i
$989$	−13.3391			−0.424160
$990$	−6.34975	+	4.48788i	−0.201808	+	0.142634i
$991$	−12.3261	+	12.3261i	−0.391550	+	0.391550i	−0.875240	−	0.483690i	$-0.839296\pi$
$991$	−12.3261	+	12.3261i	−0.391550	+	0.391550i	0.483690	+	0.875240i	$0.339296\pi$
$992$	−2.00422	+	7.47985i	−0.0636341	+	0.237486i
$993$	−10.0082			−0.317602
$994$	−0.0198480	+	0.0740736i	−0.000629539	+	0.00234947i
$995$	−31.6193	−	26.2957i	−1.00240	−	0.833629i
$996$	7.77686	+	13.4699i	0.246419	+	0.426810i
$997$	−25.5597	+	44.2707i	−0.809484	+	1.40207i	0.103738	+	0.994605i	$0.466920\pi$
$997$	−25.5597	+	44.2707i	−0.809484	+	1.40207i	−0.913222	+	0.407462i	$0.866414\pi$
$998$	10.9663	−	10.9663i	0.347132	−	0.347132i
$999$	13.1575	+	1.45012i	0.416286	+	0.0458799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.u.a.23.8	yes	68
5.2	odd	4		185.2.p.a.97.10	✓	68
5.3	odd	4		925.2.t.b.282.8		68
5.4	even	2		925.2.y.b.393.10		68
37.29	odd	12		185.2.p.a.103.10	yes	68
185.29	odd	12		925.2.t.b.843.8		68
185.103	even	12		925.2.y.b.732.10		68
185.177	even	12	inner	185.2.u.a.177.8	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.10	✓	68	5.2	odd	4
185.2.p.a.103.10	yes	68	37.29	odd	12
185.2.u.a.23.8	yes	68	1.1	even	1	trivial
185.2.u.a.177.8	yes	68	185.177	even	12	inner
925.2.t.b.282.8		68	5.3	odd	4
925.2.t.b.843.8		68	185.29	odd	12
925.2.y.b.393.10		68	5.4	even	2
925.2.y.b.732.10		68	185.103	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.305683 - 0.176486i) q^{2} +(2.52485 + 0.676530i) q^{3} +(-0.937705 - 1.62415i) q^{4} +(2.22668 - 0.204678i) q^{5} +(-0.652403 - 0.652403i) q^{6} +(-1.50833 - 0.404156i) q^{7} +1.36791i q^{8} +(3.31908 + 1.91627i) q^{9} +(-0.716780 - 0.330411i) q^{10} -2.57054i q^{11} +(-1.26877 - 4.73512i) q^{12} +(-4.41433 + 2.54861i) q^{13} +(0.389743 + 0.389743i) q^{14} +(5.76050 + 0.989636i) q^{15} +(-1.63399 + 2.83016i) q^{16} +(-0.342624 + 0.593443i) q^{17} +(-0.676389 - 1.17154i) q^{18} +(4.59908 + 1.23232i) q^{19} +(-2.42040 - 3.42454i) q^{20} +(-3.53488 - 2.04087i) q^{21} +(-0.453664 + 0.785768i) q^{22} +5.83340i q^{23} +(-0.925433 + 3.45376i) q^{24} +(4.91621 - 0.911506i) q^{25} +1.79918 q^{26} +(1.53879 + 1.53879i) q^{27} +(0.757959 + 2.82874i) q^{28} +(-4.71673 - 4.71673i) q^{29} +(-1.58623 - 1.31916i) q^{30} +(-1.40786 + 1.40786i) q^{31} +(3.36826 - 1.94466i) q^{32} +(1.73905 - 6.49021i) q^{33} +(0.209469 - 0.120937i) q^{34} +(-3.44130 - 0.591204i) q^{35} -7.18758i q^{36} +(4.74646 - 3.80409i) q^{37} +(-1.18837 - 1.18837i) q^{38} +(-12.8697 + 3.44843i) q^{39} +(0.279982 + 3.04590i) q^{40} +(-6.82923 + 3.94286i) q^{41} +(0.720368 + 1.24771i) q^{42} +2.28668i q^{43} +(-4.17495 + 2.41041i) q^{44} +(7.78274 + 3.58758i) q^{45} +(1.02951 - 1.78317i) q^{46} +(-7.99119 + 7.99119i) q^{47} +(-6.04027 + 6.04027i) q^{48} +(-3.95045 - 2.28080i) q^{49} +(-1.66367 - 0.589011i) q^{50} +(-1.26656 + 1.26656i) q^{51} +(8.27868 + 4.77970i) q^{52} +(4.37275 - 1.17167i) q^{53} +(-0.198807 - 0.741957i) q^{54} +(-0.526133 - 5.72377i) q^{55} +(0.552850 - 2.06326i) q^{56} +(10.7783 + 6.22283i) q^{57} +(0.609385 + 2.27426i) q^{58} +(-2.43277 - 9.07924i) q^{59} +(-3.79433 - 10.2839i) q^{60} +(-2.49030 - 0.667274i) q^{61} +(0.678826 - 0.181891i) q^{62} +(-4.23180 - 4.23180i) q^{63} +5.16315 q^{64} +(-9.30766 + 6.57847i) q^{65} +(-1.67703 + 1.67703i) q^{66} +(0.100851 - 0.376380i) q^{67} +1.28512 q^{68} +(-3.94647 + 14.7284i) q^{69} +(0.947605 + 0.788061i) q^{70} +(0.0695659 + 0.120492i) q^{71} +(-2.62128 + 4.54020i) q^{72} +(6.70047 - 6.70047i) q^{73} +(-2.12228 + 0.325159i) q^{74} +(13.0293 + 1.02455i) q^{75} +(-2.31111 - 8.62517i) q^{76} +(-1.03890 + 3.87723i) q^{77} +(4.54265 + 1.21720i) q^{78} +(0.455083 + 0.121939i) q^{79} +(-3.05911 + 6.63631i) q^{80} +(-2.90463 - 5.03097i) q^{81} +2.78343 q^{82} +(-3.06472 + 0.821188i) q^{83} +7.65492i q^{84} +(-0.641450 + 1.39154i) q^{85} +(0.403567 - 0.698999i) q^{86} +(-8.71800 - 15.1000i) q^{87} +3.51627 q^{88} +(15.2422 - 4.08413i) q^{89} +(-1.74589 - 2.47020i) q^{90} +(7.68831 - 2.06008i) q^{91} +(9.47433 - 5.47001i) q^{92} +(-4.50709 + 2.60217i) q^{93} +(3.85310 - 1.03243i) q^{94} +(10.4929 + 1.80265i) q^{95} +(9.81995 - 2.63125i) q^{96} +13.7731 q^{97} +(0.805056 + 1.39440i) q^{98} +(4.92584 - 8.53181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

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