LMFDB - Embedded newform 273.2.bh.a.248.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(131,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("273.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			248.18
Character	$\chi$	$=$	273.248
Dual form			273.2.bh.a.131.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.326193 - 0.188328i) q^{2} +(1.30806 - 1.13534i) q^{3} +(-0.929065 + 1.60919i) q^{4} +(-2.06368 - 3.57439i) q^{5} +(0.212864 - 0.616683i) q^{6} +(2.50486 - 0.851866i) q^{7} +1.45319i q^{8} +(0.422020 - 2.97017i) q^{9} +O(q^{10})$	\(q+(0.326193 - 0.188328i) q^{2} +(1.30806 - 1.13534i) q^{3} +(-0.929065 + 1.60919i) q^{4} +(-2.06368 - 3.57439i) q^{5} +(0.212864 - 0.616683i) q^{6} +(2.50486 - 0.851866i) q^{7} +1.45319i q^{8} +(0.422020 - 2.97017i) q^{9} +(-1.34632 - 0.777295i) q^{10} +(-0.580523 - 0.335165i) q^{11} +(0.611702 + 3.15971i) q^{12} -1.00000i q^{13} +(0.656639 - 0.749608i) q^{14} +(-6.75754 - 2.33254i) q^{15} +(-1.58445 - 2.74436i) q^{16} +(-0.299470 + 0.518697i) q^{17} +(-0.421705 - 1.04833i) q^{18} +(3.14918 - 1.81818i) q^{19} +7.66916 q^{20} +(2.30934 - 3.95815i) q^{21} -0.252484 q^{22} +(2.29950 - 1.32762i) q^{23} +(1.64986 + 1.90085i) q^{24} +(-6.01752 + 10.4226i) q^{25} +(-0.188328 - 0.326193i) q^{26} +(-2.82012 - 4.36428i) q^{27} +(-0.956366 + 4.82223i) q^{28} +10.5070i q^{29} +(-2.64355 + 0.511776i) q^{30} +(5.49237 + 3.17102i) q^{31} +(-3.55067 - 2.04998i) q^{32} +(-1.13988 + 0.220674i) q^{33} +0.225594i q^{34} +(-8.21412 - 7.19538i) q^{35} +(4.38748 + 3.43859i) q^{36} +(1.51009 + 2.61556i) q^{37} +(0.684827 - 1.18616i) q^{38} +(-1.13534 - 1.30806i) q^{39} +(5.19426 - 2.99891i) q^{40} +5.54647 q^{41} +(0.00786267 - 1.72604i) q^{42} -2.77503 q^{43} +(1.07869 - 0.622780i) q^{44} +(-11.4875 + 4.62100i) q^{45} +(0.500055 - 0.866121i) q^{46} +(2.81801 + 4.88093i) q^{47} +(-5.18832 - 1.79088i) q^{48} +(5.54865 - 4.26761i) q^{49} +4.53306i q^{50} +(0.197173 + 1.01848i) q^{51} +(1.60919 + 0.929065i) q^{52} +(-3.07789 - 1.77702i) q^{53} +(-1.74182 - 0.892493i) q^{54} +2.76669i q^{55} +(1.23792 + 3.64003i) q^{56} +(2.05505 - 5.95366i) q^{57} +(1.97876 + 3.42732i) q^{58} +(-2.22679 + 3.85691i) q^{59} +(10.0317 - 8.70708i) q^{60} +(-8.52262 + 4.92054i) q^{61} +2.38877 q^{62} +(-1.47308 - 7.79936i) q^{63} +4.79355 q^{64} +(-3.57439 + 2.06368i) q^{65} +(-0.330263 + 0.286654i) q^{66} +(2.10315 - 3.64276i) q^{67} +(-0.556455 - 0.963807i) q^{68} +(1.50058 - 4.34731i) q^{69} +(-4.03448 - 0.800137i) q^{70} -9.82614i q^{71} +(4.31621 + 0.613274i) q^{72} +(0.629525 + 0.363456i) q^{73} +(0.985165 + 0.568785i) q^{74} +(3.96197 + 20.4653i) q^{75} +6.75683i q^{76} +(-1.73964 - 0.345014i) q^{77} +(-0.616683 - 0.212864i) q^{78} +(7.67474 + 13.2930i) q^{79} +(-6.53960 + 11.3269i) q^{80} +(-8.64380 - 2.50694i) q^{81} +(1.80922 - 1.04456i) q^{82} -5.42091 q^{83} +(4.22388 + 7.39354i) q^{84} +2.47204 q^{85} +(-0.905198 + 0.522616i) q^{86} +(11.9290 + 13.7437i) q^{87} +(0.487057 - 0.843608i) q^{88} +(3.67079 + 6.35799i) q^{89} +(-2.87687 + 3.67075i) q^{90} +(-0.851866 - 2.50486i) q^{91} +4.93378i q^{92} +(10.7845 - 2.08782i) q^{93} +(1.83843 + 1.06142i) q^{94} +(-12.9978 - 7.50426i) q^{95} +(-6.97189 + 1.34972i) q^{96} -15.4274i q^{97} +(1.00622 - 2.43703i) q^{98} +(-1.24049 + 1.58280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.326193	−	0.188328i	0.230654	−	0.133168i	−0.380220	−	0.924896i	$-0.624152\pi$
$2$	0.326193	−	0.188328i	0.230654	−	0.133168i	0.610874	+	0.791728i	$0.290818\pi$
$3$	1.30806	−	1.13534i	0.755206	−	0.655487i
$3$	1.30806	−	1.13534i	0.755206	−	0.655487i
$4$	−0.929065	+	1.60919i	−0.464533	+	0.804594i
$5$	−2.06368	−	3.57439i	−0.922904	−	1.59852i	−0.794898	−	0.606743i	$-0.792476\pi$
$5$	−2.06368	−	3.57439i	−0.922904	−	1.59852i	−0.128006	−	0.991773i	$-0.540858\pi$
$6$	0.212864	−	0.616683i	0.0869012	−	0.251760i
$7$	2.50486	−	0.851866i	0.946748	−	0.321975i
$7$	2.50486	−	0.851866i	0.946748	−	0.321975i
$8$			1.45319i			0.513779i
$9$	0.422020	−	2.97017i	0.140673	−	0.990056i
$10$	−1.34632	−	0.777295i	−0.425742	−	0.245802i
$11$	−0.580523	−	0.335165i	−0.175034	−	0.101056i	0.409923	−	0.912120i	$-0.365555\pi$
$11$	−0.580523	−	0.335165i	−0.175034	−	0.101056i	−0.584957	+	0.811064i	$0.698889\pi$
$12$	0.611702	+	3.15971i	0.176583	+	0.912130i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	0.656639	−	0.749608i	0.175494	−	0.200341i
$15$	−6.75754	−	2.33254i	−1.74479	−	0.602258i
$16$	−1.58445	−	2.74436i	−0.396114	−	0.686089i
$17$	−0.299470	+	0.518697i	−0.0726322	+	0.125803i	−0.900054	−	0.435778i	$-0.856473\pi$
$17$	−0.299470	+	0.518697i	−0.0726322	+	0.125803i	0.827422	+	0.561581i	$0.189807\pi$
$18$	−0.421705	−	1.04833i	−0.0993969	−	0.247093i
$19$	3.14918	−	1.81818i	0.722471	−	0.417119i	−0.0931906	−	0.995648i	$-0.529707\pi$
$19$	3.14918	−	1.81818i	0.722471	−	0.417119i	0.815661	+	0.578530i	$0.196373\pi$
$20$	7.66916			1.71488
$21$	2.30934	−	3.95815i	0.503940	−	0.863739i
$22$	−0.252484			−0.0538297
$23$	2.29950	−	1.32762i	0.479480	−	0.276828i	−0.240720	−	0.970595i	$-0.577384\pi$
$23$	2.29950	−	1.32762i	0.479480	−	0.276828i	0.720200	+	0.693767i	$0.244050\pi$
$24$	1.64986	+	1.90085i	0.336776	+	0.388009i
$25$	−6.01752	+	10.4226i	−1.20350	+	2.08453i
$26$	−0.188328	−	0.326193i	−0.0369341	−	0.0639718i
$27$	−2.82012	−	4.36428i	−0.542732	−	0.839906i
$28$	−0.956366	+	4.82223i	−0.180736	+	0.911316i
$29$			10.5070i			1.95110i	0.219774	+	0.975551i	$0.429468\pi$
$29$			10.5070i			1.95110i	−0.219774	+	0.975551i	$0.570532\pi$
$30$	−2.64355	+	0.511776i	−0.482644	+	0.0934370i
$31$	5.49237	+	3.17102i	0.986460	+	0.569533i	0.904214	−	0.427079i	$-0.140458\pi$
$31$	5.49237	+	3.17102i	0.986460	+	0.569533i	0.0822455	+	0.996612i	$0.473791\pi$
$32$	−3.55067	−	2.04998i	−0.627676	−	0.362389i
$33$	−1.13988	+	0.220674i	−0.198428	+	0.0384145i
$34$			0.225594i			0.0386891i
$35$	−8.21412	−	7.19538i	−1.38844	−	1.21624i
$36$	4.38748	+	3.43859i	0.731246	+	0.573098i
$37$	1.51009	+	2.61556i	0.248258	+	0.429995i	0.963043	−	0.269349i	$-0.0868086\pi$
$37$	1.51009	+	2.61556i	0.248258	+	0.429995i	−0.714785	+	0.699345i	$0.753475\pi$
$38$	0.684827	−	1.18616i	0.111094	−	0.192420i
$39$	−1.13534	−	1.30806i	−0.181799	−	0.209457i
$40$	5.19426	−	2.99891i	0.821285	−	0.474169i
$41$	5.54647			0.866214			0.433107	−	0.901343i	$-0.357417\pi$
$41$	5.54647			0.866214			0.433107	+	0.901343i	$0.357417\pi$
$42$	0.00786267	−	1.72604i	0.00121324	−	0.266333i
$43$	−2.77503			−0.423189			−0.211594	−	0.977358i	$-0.567866\pi$
$43$	−2.77503			−0.423189			−0.211594	+	0.977358i	$0.567866\pi$
$44$	1.07869	−	0.622780i	0.162618	−	0.0938877i
$45$	−11.4875	+	4.62100i	−1.71245	+	0.688858i
$46$	0.500055	−	0.866121i	0.0737291	−	0.127703i
$47$	2.81801	+	4.88093i	0.411049	+	0.711957i	0.995005	−	0.0998279i	$-0.0318292\pi$
$47$	2.81801	+	4.88093i	0.411049	+	0.711957i	−0.583956	+	0.811785i	$0.698496\pi$
$48$	−5.18832	−	1.79088i	−0.748870	−	0.258491i
$49$	5.54865	−	4.26761i	0.792664	−	0.609658i
$50$			4.53306i			0.641072i
$51$	0.197173	+	1.01848i	0.0276097	+	0.142616i
$52$	1.60919	+	0.929065i	0.223154	+	0.128838i
$53$	−3.07789	−	1.77702i	−0.422781	−	0.244093i	0.273485	−	0.961876i	$-0.411823\pi$
$53$	−3.07789	−	1.77702i	−0.422781	−	0.244093i	−0.696266	+	0.717783i	$0.745157\pi$
$54$	−1.74182	−	0.892493i	−0.237032	−	0.121453i
$55$			2.76669i			0.373060i
$56$	1.23792	+	3.64003i	0.165424	+	0.486419i
$57$	2.05505	−	5.95366i	0.272199	−	0.788581i
$58$	1.97876	+	3.42732i	0.259824	+	0.450029i
$59$	−2.22679	+	3.85691i	−0.289903	+	0.502126i	−0.973786	−	0.227465i	$-0.926956\pi$
$59$	−2.22679	+	3.85691i	−0.289903	+	0.502126i	0.683884	+	0.729591i	$0.260290\pi$
$60$	10.0317	−	8.70708i	1.29509	−	1.12408i
$61$	−8.52262	+	4.92054i	−1.09121	+	0.630011i	−0.933898	−	0.357538i	$-0.883616\pi$
$61$	−8.52262	+	4.92054i	−1.09121	+	0.630011i	−0.157312	+	0.987549i	$0.550283\pi$
$62$	2.38877			0.303374
$63$	−1.47308	−	7.79936i	−0.185591	−	0.982627i
$64$	4.79355			0.599193
$65$	−3.57439	+	2.06368i	−0.443349	+	0.255968i
$66$	−0.330263	+	0.286654i	−0.0406525	+	0.0352847i
$67$	2.10315	−	3.64276i	0.256941	−	0.445035i	−0.708480	−	0.705731i	$-0.750619\pi$
$67$	2.10315	−	3.64276i	0.256941	−	0.445035i	0.965421	+	0.260696i	$0.0839521\pi$
$68$	−0.556455	−	0.963807i	−0.0674800	−	0.116879i
$69$	1.50058	−	4.34731i	0.180649	−	0.523355i
$70$	−4.03448	−	0.800137i	−0.482213	−	0.0956346i
$71$		−	9.82614i		−	1.16615i	−0.812419	−	0.583074i	$-0.801850\pi$
$71$		−	9.82614i		−	1.16615i	0.812419	−	0.583074i	$-0.198150\pi$
$72$	4.31621	+	0.613274i	0.508670	+	0.0722750i
$73$	0.629525	+	0.363456i	0.0736803	+	0.0425393i	0.536388	−	0.843972i	$-0.319789\pi$
$73$	0.629525	+	0.363456i	0.0736803	+	0.0425393i	−0.462707	+	0.886511i	$0.653122\pi$
$74$	0.985165	+	0.568785i	0.114523	+	0.0661200i
$75$	3.96197	+	20.4653i	0.457489	+	2.36313i
$76$			6.75683i			0.775061i
$77$	−1.73964	−	0.345014i	−0.198251	−	0.0393180i
$78$	−0.616683	−	0.212864i	−0.0698256	−	0.0241021i
$79$	7.67474	+	13.2930i	0.863476	+	1.49558i	0.868552	+	0.495597i	$0.165051\pi$
$79$	7.67474	+	13.2930i	0.863476	+	1.49558i	−0.00507650	+	0.999987i	$0.501616\pi$
$80$	−6.53960	+	11.3269i	−0.731150	+	1.26639i
$81$	−8.64380	−	2.50694i	−0.960422	−	0.278549i
$82$	1.80922	−	1.04456i	0.199795	−	0.115352i
$83$	−5.42091			−0.595022			−0.297511	−	0.954718i	$-0.596157\pi$
$83$	−5.42091			−0.595022			−0.297511	+	0.954718i	$0.596157\pi$
$84$	4.22388	+	7.39354i	0.460863	+	0.806702i
$85$	2.47204			0.268130
$86$	−0.905198	+	0.522616i	−0.0976100	+	0.0563551i
$87$	11.9290	+	13.7437i	1.27892	+	1.47348i
$88$	0.487057	−	0.843608i	0.0519205	−	0.0899289i
$89$	3.67079	+	6.35799i	0.389103	+	0.673946i	0.992329	−	0.123624i	$-0.0394518\pi$
$89$	3.67079	+	6.35799i	0.389103	+	0.673946i	−0.603226	+	0.797570i	$0.706118\pi$
$90$	−2.87687	+	3.67075i	−0.303249	+	0.386931i
$91$	−0.851866	−	2.50486i	−0.0892998	−	0.262581i
$92$			4.93378i			0.514382i
$93$	10.7845	−	2.08782i	1.11830	−	0.216497i
$94$	1.83843	+	1.06142i	0.189620	+	0.109477i
$95$	−12.9978	−	7.50426i	−1.33354	−	0.769921i
$96$	−6.97189	+	1.34972i	−0.711566	+	0.137755i
$97$		−	15.4274i		−	1.56642i	−0.621760	−	0.783208i	$-0.713582\pi$
$97$		−	15.4274i		−	1.56642i	0.621760	−	0.783208i	$-0.286418\pi$
$98$	1.00622	−	2.43703i	0.101644	−	0.246177i
$99$	−1.24049	+	1.58280i	−0.124674	+	0.159078i
$100$	−11.1813	−	19.3666i	−1.11813	−	1.93666i
$101$	1.61957	−	2.80517i	0.161153	−	0.279125i	−0.774130	−	0.633027i	$-0.781812\pi$
$101$	1.61957	−	2.80517i	0.161153	−	0.279125i	0.935282	+	0.353902i	$0.115145\pi$
$102$	0.256125	+	0.295090i	0.0253602	+	0.0292183i
$103$	3.59454	−	2.07531i	0.354180	−	0.204486i	−0.312345	−	0.949969i	$-0.601114\pi$
$103$	3.59454	−	2.07531i	0.354180	−	0.204486i	0.666525	+	0.745483i	$0.267781\pi$
$104$	1.45319			0.142497
$105$	−18.9137	−	0.0861583i	−1.84579	−	0.00840819i
$106$	−1.33865			−0.130021
$107$	−2.88667	+	1.66662i	−0.279065	+	0.161118i	−0.633000	−	0.774152i	$-0.718177\pi$
$107$	−2.88667	+	1.66662i	−0.279065	+	0.161118i	0.353935	+	0.935270i	$0.384843\pi$
$108$	9.64302	−	0.483397i	0.927900	−	0.0465149i
$109$	−4.13336	+	7.15919i	−0.395904	+	0.685726i	−0.993216	−	0.116283i	$-0.962902\pi$
$109$	−4.13336	+	7.15919i	−0.395904	+	0.685726i	0.597312	+	0.802009i	$0.296235\pi$
$110$	0.521044	+	0.902475i	0.0496796	+	0.0860477i
$111$	4.94483	+	1.70683i	0.469342	+	0.162005i
$112$	−6.30666	−	5.52449i	−0.595923	−	0.522015i
$113$		−	8.93818i		−	0.840833i	−0.907331	−	0.420417i	$-0.861884\pi$
$113$		−	8.93818i		−	0.840833i	0.907331	−	0.420417i	$-0.138116\pi$
$114$	−0.450894	−	2.32907i	−0.0422301	−	0.218137i
$115$	−9.49086	−	5.47955i	−0.885027	−	0.510971i
$116$	−16.9077	−	9.76169i	−1.56984	−	0.906350i
$117$	−2.97017	−	0.422020i	−0.274592	−	0.0390158i
$118$			1.67746i			0.154423i
$119$	−0.308270	+	1.55437i	−0.0282591	+	0.142489i
$120$	3.38961	−	9.81997i	0.309428	−	0.896437i
$121$	−5.27533	−	9.13714i	−0.479575	−	0.830649i
$122$	−1.85335	+	3.21010i	−0.167794	+	0.290628i
$123$	7.25510	−	6.29712i	0.654170	−	0.567792i
$124$	−10.2055	+	5.89218i	−0.916485	+	0.529133i
$125$	29.0361			2.59706
$126$	−1.94935	−	2.26668i	−0.173662	−	0.201932i
$127$	7.61621			0.675829			0.337915	−	0.941177i	$-0.390278\pi$
$127$	7.61621			0.675829			0.337915	+	0.941177i	$0.390278\pi$
$128$	8.66497	−	5.00272i	0.765882	−	0.442182i
$129$	−3.62990	+	3.15060i	−0.319595	+	0.277395i
$130$	−0.777295	+	1.34632i	−0.0681733	+	0.118080i
$131$	−7.07877	−	12.2608i	−0.618475	−	1.07123i	−0.989764	−	0.142712i	$-0.954418\pi$
$131$	−7.07877	−	12.2608i	−0.618475	−	1.07123i	0.371289	−	0.928517i	$-0.378916\pi$
$132$	0.703917	−	2.03930i	0.0612681	−	0.177499i
$133$	6.33941	−	7.23696i	0.549696	−	0.627524i
$134$		−	1.58433i		−	0.136865i
$135$	−9.77984	+	19.0867i	−0.841715	+	1.64272i
$136$	−0.753764	−	0.435186i	−0.0646348	−	0.0373169i
$137$	12.4012	+	7.15984i	1.05951	+	0.611706i	0.925296	−	0.379247i	$-0.123817\pi$
$137$	12.4012	+	7.15984i	1.05951	+	0.611706i	0.134210	+	0.990953i	$0.457150\pi$
$138$	−0.329239	−	1.70067i	−0.0280267	−	0.144770i
$139$			10.3190i			0.875244i	0.899159	+	0.437622i	$0.144179\pi$
$139$			10.3190i			0.875244i	−0.899159	+	0.437622i	$0.855821\pi$
$140$	19.2102	−	6.53309i	1.62356	−	0.552147i
$141$	9.22762	+	3.18514i	0.777106	+	0.268238i
$142$	−1.85054	−	3.20522i	−0.155294	−	0.268976i
$143$	−0.335165	+	0.580523i	−0.0280279	+	0.0485458i
$144$	−8.81987	+	3.54792i	−0.734989	+	0.295660i
$145$	37.5561	−	21.6830i	3.11887	−	1.80068i
$146$	0.273796			0.0226595
$147$	2.41277	−	11.8819i	0.199002	−	0.979999i
$148$	−5.61190			−0.461295
$149$	9.97877	−	5.76125i	0.817493	−	0.471980i	−0.0320582	−	0.999486i	$-0.510206\pi$
$149$	9.97877	−	5.76125i	0.817493	−	0.471980i	0.849551	+	0.527506i	$0.176873\pi$
$150$	5.14656	+	5.92950i	0.420215	+	0.484142i
$151$	−8.09664	+	14.0238i	−0.658895	+	1.14124i	0.322007	+	0.946737i	$0.395643\pi$
$151$	−8.09664	+	14.0238i	−0.658895	+	1.14124i	−0.980902	+	0.194503i	$0.937691\pi$
$152$	2.64215	+	4.57634i	0.214307	+	0.371190i
$153$	1.41424	+	1.10838i	0.114334	+	0.0896070i
$154$	−0.632436	+	0.215082i	−0.0509632	+	0.0173318i
$155$		−	26.1759i		−	2.10250i
$156$	3.15971	−	0.611702i	0.252979	−	0.0489753i
$157$	−16.5538	−	9.55735i	−1.32114	−	0.762760i	−0.337228	−	0.941423i	$-0.609489\pi$
$157$	−16.5538	−	9.55735i	−1.32114	−	0.762760i	−0.983910	+	0.178663i	$0.942823\pi$
$158$	5.00690	+	2.89074i	0.398328	+	0.229975i
$159$	−6.04357	+	1.17000i	−0.479287	+	0.0927871i
$160$			16.9220i			1.33780i
$161$	4.62898	−	5.28437i	0.364815	−	0.416466i
$162$	−3.29168	+	0.810121i	−0.258619	+	0.0636491i
$163$	−10.2890	−	17.8210i	−0.805894	−	1.39585i	−0.915686	−	0.401894i	$-0.868352\pi$
$163$	−10.2890	−	17.8210i	−0.805894	−	1.39585i	0.109792	−	0.993955i	$-0.464981\pi$
$164$	−5.15304	+	8.92532i	−0.402385	+	0.696951i
$165$	3.14112	+	3.61898i	0.244536	+	0.281737i
$166$	−1.76827	+	1.02091i	−0.137244	+	0.0792379i
$167$	−13.2663			−1.02658			−0.513290	−	0.858215i	$-0.671573\pi$
$167$	−13.2663			−1.02658			−0.513290	+	0.858215i	$0.671573\pi$
$168$	5.75193	+	3.35591i	0.443771	+	0.258914i
$169$	−1.00000			−0.0769231
$170$	0.806362	−	0.465553i	0.0618452	−	0.0357063i
$171$	−4.07128	−	10.1209i	−0.311339	−	0.773964i
$172$	2.57819	−	4.46555i	0.196585	−	0.340495i
$173$	5.25361	+	9.09952i	0.399424	+	0.691824i	0.993655	−	0.112471i	$-0.0358766\pi$
$173$	5.25361	+	9.09952i	0.399424	+	0.691824i	−0.594230	+	0.804295i	$0.702543\pi$
$174$	6.47949	+	2.23656i	0.491209	+	0.169553i
$175$	−6.19435	+	31.2334i	−0.468249	+	2.36102i
$176$			2.12422i			0.160119i
$177$	1.46613	+	7.57320i	0.110201	+	0.569237i
$178$	2.39477	+	1.38262i	0.179496	+	0.103632i
$179$	7.96336	+	4.59765i	0.595209	+	0.343644i	0.767155	−	0.641462i	$-0.221672\pi$
$179$	7.96336	+	4.59765i	0.595209	+	0.343644i	−0.171945	+	0.985106i	$0.555005\pi$
$180$	3.23654	−	22.7787i	0.241237	−	1.69782i
$181$		−	14.6613i		−	1.08977i	−0.838512	−	0.544883i	$-0.816574\pi$
$181$		−	14.6613i		−	1.08977i	0.838512	−	0.544883i	$-0.183426\pi$
$182$	−0.749608	−	0.656639i	−0.0555646	−	0.0486733i
$183$	−5.56160	+	16.1124i	−0.411125	+	1.19106i
$184$	1.92928	+	3.34161i	0.142228	+	0.246347i
$185$	6.23269	−	10.7953i	0.458236	−	0.793689i
$186$	3.12464	−	2.71206i	0.229110	−	0.198858i
$187$	0.347698	−	0.200744i	0.0254262	−	0.0146798i
$188$	−10.4725			−0.763782
$189$	−10.7818	−	8.52955i	−0.784259	−	0.620434i
$190$	−5.65305			−0.410115
$191$	−13.1078	+	7.56781i	−0.948449	+	0.547587i	−0.892599	−	0.450852i	$-0.851120\pi$
$191$	−13.1078	+	7.56781i	−0.948449	+	0.547587i	−0.0558501	+	0.998439i	$0.517787\pi$
$192$	6.27022	−	5.44229i	0.452515	−	0.392763i
$193$	−1.20773	+	2.09186i	−0.0869346	+	0.150575i	−0.906214	−	0.422819i	$-0.861040\pi$
$193$	−1.20773	+	2.09186i	−0.0869346	+	0.150575i	0.819279	+	0.573395i	$0.194374\pi$
$194$	−2.90541	−	5.03232i	−0.208596	−	0.361299i
$195$	−2.33254	+	6.75754i	−0.167036	+	0.483918i
$196$	1.71233	+	12.8937i	0.122309	+	0.920979i
$197$			13.9719i			0.995457i	0.867333	+	0.497729i	$0.165832\pi$
$197$			13.9719i			0.995457i	−0.867333	+	0.497729i	$0.834168\pi$
$198$	−0.106553	+	0.749919i	−0.00757240	+	0.0532944i
$199$	−1.69123	−	0.976431i	−0.119888	−	0.0692174i	0.438857	−	0.898557i	$-0.355384\pi$
$199$	−1.69123	−	0.976431i	−0.119888	−	0.0692174i	−0.558745	+	0.829340i	$0.688717\pi$
$200$	−15.1461	−	8.74458i	−1.07099	−	0.618335i
$201$	−1.38473	−	7.15273i	−0.0976711	−	0.504514i
$202$		−	1.22004i		−	0.0858415i
$203$	8.95056	+	26.3186i	0.628206	+	1.84720i
$204$	−1.82212	−	0.628951i	−0.127574	−	0.0440353i
$205$	−11.4461	−	19.8253i	−0.799432	−	1.38466i
$206$	0.781676	−	1.35390i	0.0544620	−	0.0943309i
$207$	−2.97281	−	7.39019i	−0.206625	−	0.513654i
$208$	−2.74436	+	1.58445i	−0.190287	+	0.109862i
$209$	−2.43756			−0.168609
$210$	−6.18575	+	3.53387i	−0.426857	+	0.243860i
$211$	−16.1760			−1.11360			−0.556800	−	0.830646i	$-0.687971\pi$
$211$	−16.1760			−1.11360			−0.556800	+	0.830646i	$0.687971\pi$
$212$	5.71913	−	3.30194i	0.392791	−	0.226778i
$213$	−11.1560	−	12.8531i	−0.764395	−	0.880683i
$214$	−0.627742	+	1.08728i	−0.0429116	+	0.0743250i
$215$	5.72677	+	9.91906i	0.390562	+	0.676474i
$216$	6.34212	−	4.09816i	0.431526	−	0.278844i
$217$	16.4589	+	3.26421i	1.11730	+	0.221589i
$218$			3.11371i			0.210887i
$219$	1.23610	−	0.239302i	0.0835278	−	0.0161705i
$220$	−4.45212	−	2.57043i	−0.300162	−	0.173299i
$221$	0.518697	+	0.299470i	0.0348914	+	0.0201445i
$222$	1.93441	−	0.374491i	0.129829	−	0.0251342i
$223$			1.01169i			0.0677477i	0.999426	+	0.0338739i	$0.0107844\pi$
$223$			1.01169i			0.0677477i	−0.999426	+	0.0338739i	$0.989216\pi$
$224$	−10.6402	−	2.11022i	−0.710931	−	0.140995i
$225$	28.4175	+	22.2716i	1.89450	+	1.48477i
$226$	−1.68331	−	2.91558i	−0.111972	−	0.193941i
$227$	−2.38431	+	4.12975i	−0.158252	+	0.274101i	−0.934239	−	0.356649i	$-0.883919\pi$
$227$	−2.38431	+	4.12975i	−0.158252	+	0.274101i	0.775986	+	0.630750i	$0.217253\pi$
$228$	7.67127	+	8.83830i	0.508043	+	0.585331i
$229$	13.6165	−	7.86147i	0.899801	−	0.519500i	0.0226655	−	0.999743i	$-0.492785\pi$
$229$	13.6165	−	7.86147i	0.899801	−	0.519500i	0.877136	+	0.480243i	$0.159451\pi$
$230$	−4.12781			−0.272180
$231$	−2.66726	+	1.52378i	−0.175493	+	0.100258i
$232$	−15.2686			−1.00244
$233$	−24.7417	+	14.2846i	−1.62088	+	0.935818i	−0.634199	+	0.773170i	$0.718670\pi$
$233$	−24.7417	+	14.2846i	−1.62088	+	0.935818i	−0.986684	+	0.162648i	$0.947997\pi$
$234$	−1.04833	+	0.421705i	−0.0685313	+	0.0275677i
$235$	11.6309	−	20.1453i	0.758717	−	1.31414i
$236$	−4.13766	−	7.16663i	−0.269339	−	0.466508i
$237$	25.1311	+	8.67462i	1.63244	+	0.563477i
$238$	0.192176	+	0.565082i	0.0124569	+	0.0366288i
$239$			14.5590i			0.941746i	0.882201	+	0.470873i	$0.156061\pi$
$239$			14.5590i			0.941746i	−0.882201	+	0.470873i	$0.843939\pi$
$240$	4.30571	+	22.2409i	0.277932	+	1.43564i
$241$	6.70820	+	3.87298i	0.432113	+	0.249481i	0.700247	−	0.713901i	$-0.253073\pi$
$241$	6.70820	+	3.87298i	0.432113	+	0.249481i	−0.268133	+	0.963382i	$0.586407\pi$
$242$	−3.44156	−	1.98698i	−0.221232	−	0.127728i
$243$	−14.1528	+	6.53441i	−0.907902	+	0.419182i
$244$		−	18.2860i		−	1.17064i
$245$	−26.7047	−	11.0261i	−1.70610	−	0.704431i
$246$	1.18064	−	3.42042i	0.0752750	−	0.218078i
$247$	−1.81818	−	3.14918i	−0.115688	−	0.200377i
$248$	−4.60809	+	7.98145i	−0.292614	+	0.506822i
$249$	−7.09086	+	6.15456i	−0.449365	+	0.390030i
$250$	9.47137	−	5.46830i	0.599022	−	0.345846i
$251$	−6.72085			−0.424216			−0.212108	−	0.977246i	$-0.568033\pi$
$251$	−6.72085			−0.424216			−0.212108	+	0.977246i	$0.568033\pi$
$252$	13.9192	+	4.87565i	0.876829	+	0.307137i
$253$	−1.77989			−0.111900
$254$	2.48436	−	1.43434i	0.155882	−	0.0899988i
$255$	3.23356	−	2.80660i	0.202494	−	0.175756i
$256$	−2.90924	+	5.03896i	−0.181828	+	0.314935i
$257$	7.92158	+	13.7206i	0.494135	+	0.855867i	0.999977	−	0.00675933i	$-0.00215158\pi$
$257$	7.92158	+	13.7206i	0.494135	+	0.855867i	−0.505842	+	0.862626i	$0.668818\pi$
$258$	−0.590704	+	1.71132i	−0.0367756	+	0.106542i
$259$	6.01068	+	5.26521i	0.373485	+	0.327164i
$260$		−	7.66916i		−	0.475621i
$261$	31.2076	+	4.43416i	1.93170	+	0.274468i
$262$	−4.61809	−	2.66626i	−0.285307	−	0.164722i
$263$	5.85189	+	3.37859i	0.360843	+	0.208333i	0.669451	−	0.742857i	$-0.266530\pi$
$263$	5.85189	+	3.37859i	0.360843	+	0.208333i	−0.308607	+	0.951190i	$0.599863\pi$
$264$	−0.320681	−	1.65646i	−0.0197366	−	0.101948i
$265$			14.6688i			0.901097i
$266$	0.704951	−	3.55454i	0.0432233	−	0.217943i
$267$	12.0201	+	4.14903i	0.735615	+	0.253916i
$268$	3.90793	+	6.76873i	0.238715	+	0.413466i
$269$	−1.74611	+	3.02435i	−0.106462	+	0.184398i	−0.914335	−	0.404959i	$-0.867286\pi$
$269$	−1.74611	+	3.02435i	−0.106462	+	0.184398i	0.807872	+	0.589357i	$0.200619\pi$
$270$	0.404430	+	8.06776i	0.0246128	+	0.490988i
$271$	−8.03997	+	4.64188i	−0.488393	+	0.281974i	−0.723908	−	0.689897i	$-0.757656\pi$
$271$	−8.03997	+	4.64188i	−0.488393	+	0.281974i	0.235514	+	0.971871i	$0.424323\pi$
$272$	1.89799			0.115082
$273$	−3.95815	−	2.30934i	−0.239558	−	0.139768i
$274$	5.39359			0.325838
$275$	6.98661	−	4.03372i	0.421309	−	0.243243i
$276$	5.60150	+	6.45366i	0.337171	+	0.388464i
$277$	−8.96306	+	15.5245i	−0.538538	+	0.932775i	0.460445	+	0.887688i	$0.347690\pi$
$277$	−8.96306	+	15.5245i	−0.538538	+	0.932775i	−0.998983	+	0.0450872i	$0.985643\pi$
$278$	1.94335	+	3.36598i	0.116554	+	0.201878i
$279$	11.7364	−	14.9750i	0.702638	−	0.896532i
$280$	10.4562	−	11.9367i	0.624879	−	0.713352i
$281$		−	19.7386i		−	1.17751i	−0.808313	−	0.588753i	$-0.799619\pi$
$281$		−	19.7386i		−	1.17751i	0.808313	−	0.588753i	$-0.200381\pi$
$282$	3.60984	−	0.698844i	0.214963	−	0.0416156i
$283$	21.1104	+	12.1881i	1.25488	+	0.724506i	0.972075	−	0.234671i	$-0.0754014\pi$
$283$	21.1104	+	12.1881i	1.25488	+	0.724506i	0.282806	+	0.959177i	$0.408735\pi$
$284$	15.8121	+	9.12913i	0.938276	+	0.541714i
$285$	−25.5217	+	4.94085i	−1.51177	+	0.292671i
$286$			0.252484i			0.0149297i
$287$	13.8931	−	4.72485i	0.820086	−	0.278899i
$288$	−7.58724	+	9.68096i	−0.447083	+	0.570456i
$289$	8.32064	+	14.4118i	0.489449	+	0.847751i
$290$	8.16704	−	14.1457i	0.479585	−	0.830666i
$291$	−17.5153	−	20.1799i	−1.02677	−	1.18297i
$292$	−1.16974	+	0.675349i	−0.0684538	+	0.0395218i
$293$	−6.46901			−0.377923			−0.188962	−	0.981984i	$-0.560512\pi$
$293$	−6.46901			−0.377923			−0.188962	+	0.981984i	$0.560512\pi$
$294$	−1.45066	−	4.33018i	−0.0846039	−	0.252541i
$295$	18.3815			1.07021
$296$	−3.80090	+	2.19445i	−0.220923	+	0.127550i
$297$	0.174388	+	3.47877i	0.0101190	+	0.201859i
$298$	2.17001	−	3.75856i	0.125705	−	0.217728i
$299$	−1.32762	−	2.29950i	−0.0767782	−	0.132984i
$300$	−36.6135	−	12.6381i	−2.11388	−	0.729659i
$301$	−6.95107	+	2.36396i	−0.400653	+	0.136256i
$302$			6.09929i			0.350975i
$303$	−1.06633	−	5.50807i	−0.0612591	−	0.316431i
$304$	−9.97946	−	5.76164i	−0.572361	−	0.330453i
$305$	35.1759	+	20.3088i	2.01416	+	1.16288i
$306$	0.670053	+	0.0952053i	0.0383044	+	0.00544252i
$307$		−	15.0804i		−	0.860685i	−0.902666	−	0.430342i	$-0.858393\pi$
$307$		−	15.0804i		−	0.860685i	0.902666	−	0.430342i	$-0.141607\pi$
$308$	2.17144	−	2.47887i	0.123729	−	0.141247i
$309$	2.34568	−	6.79563i	0.133441	−	0.386590i
$310$	−4.92964	−	8.53840i	−0.279985	−	0.484948i
$311$	−11.7458	+	20.3442i	−0.666040	+	1.15362i	0.312962	+	0.949766i	$0.398679\pi$
$311$	−11.7458	+	20.3442i	−0.666040	+	1.15362i	−0.979002	+	0.203850i	$0.934654\pi$
$312$	1.90085	−	1.64986i	0.107614	−	0.0934048i
$313$	18.5033	−	10.6829i	1.04587	−	0.603833i	0.124380	−	0.992235i	$-0.460306\pi$
$313$	18.5033	−	10.6829i	1.04587	−	0.603833i	0.921490	+	0.388401i	$0.126973\pi$
$314$	−7.19966			−0.406300
$315$	−24.8380	+	21.3607i	−1.39946	+	1.20354i
$316$	−28.5213			−1.60445
$317$	−15.9985	+	9.23676i	−0.898568	+	0.518788i	−0.876735	−	0.480973i	$-0.840283\pi$
$317$	−15.9985	+	9.23676i	−0.898568	+	0.518788i	−0.0218326	+	0.999762i	$0.506950\pi$
$318$	−1.75103	+	1.51982i	−0.0981929	+	0.0852273i
$319$	3.52158	−	6.09955i	0.197171	−	0.341509i
$320$	−9.89232	−	17.1340i	−0.552998	−	0.957820i
$321$	−1.88375	+	5.45738i	−0.105141	+	0.304601i
$322$	0.514750	−	2.59549i	0.0286859	−	0.144641i
$323$			2.17796i			0.121185i
$324$	12.0648	−	11.5804i	0.670266	−	0.643355i
$325$	10.4226	+	6.01752i	0.578144	+	0.333792i
$326$	−6.71238	−	3.87540i	−0.371765	−	0.214638i
$327$	2.72143	+	14.0574i	0.150495	+	0.777375i
$328$			8.06006i			0.445043i
$329$	11.2166	+	9.82549i	0.618392	+	0.541697i
$330$	1.70617	+	0.588927i	0.0939215	+	0.0324194i
$331$	6.12611	+	10.6107i	0.336721	+	0.583218i	0.983814	−	0.179193i	$-0.0573487\pi$
$331$	6.12611	+	10.6107i	0.336721	+	0.583218i	−0.647093	+	0.762411i	$0.724015\pi$
$332$	5.03638	−	8.72327i	0.276407	−	0.478752i
$333$	8.40594	−	3.38141i	0.460643	−	0.185300i
$334$	−4.32739	+	2.49842i	−0.236784	+	0.136707i
$335$	−17.3609			−0.948527
$336$	−14.5216	−	0.0661508i	−0.792219	−	0.00360882i
$337$	−7.76601			−0.423042			−0.211521	−	0.977373i	$-0.567842\pi$
$337$	−7.76601			−0.423042			−0.211521	+	0.977373i	$0.567842\pi$
$338$	−0.326193	+	0.188328i	−0.0177426	+	0.0102437i
$339$	−10.1478	−	11.6916i	−0.551155	−	0.635003i
$340$	−2.29668	+	3.97797i	−0.124555	+	0.215736i
$341$	−2.12563	−	3.68170i	−0.115109	−	0.199375i
$342$	−3.23407	−	2.53463i	−0.174879	−	0.137057i
$343$	10.2632	−	15.4165i	0.554159	−	0.832411i
$344$		−	4.03264i		−	0.217425i
$345$	−18.6357	+	3.60777i	−1.00331	+	0.194236i
$346$	3.42739	+	1.97880i	0.184257	+	0.106381i
$347$	10.0494	+	5.80201i	0.539479	+	0.311468i	0.744868	−	0.667212i	$-0.232513\pi$
$347$	10.0494	+	5.80201i	0.539479	+	0.311468i	−0.205389	+	0.978680i	$0.565846\pi$
$348$	−33.1991	+	6.42715i	−1.77966	+	0.344531i
$349$			0.846216i			0.0452969i	0.999743	+	0.0226485i	$0.00720984\pi$
$349$			0.846216i			0.0452969i	−0.999743	+	0.0226485i	$0.992790\pi$
$350$	3.86156	+	11.3547i	0.206409	+	0.606934i
$351$	−4.36428	+	2.82012i	−0.232948	+	0.150527i
$352$	1.37416	+	2.38012i	0.0732432	+	0.126861i
$353$	12.5877	−	21.8025i	0.669976	−	1.16043i	−0.307935	−	0.951408i	$-0.599638\pi$
$353$	12.5877	−	21.8025i	0.669976	−	1.16043i	0.977910	−	0.209025i	$-0.0670289\pi$
$354$	1.90449	+	2.19422i	0.101222	+	0.116621i
$355$	−35.1225	+	20.2780i	−1.86411	+	1.07624i
$356$	−13.6416			−0.723004
$357$	1.36150	+	2.38320i	0.0720583	+	0.126132i
$358$	3.46346			0.183050
$359$	6.10737	−	3.52609i	0.322335	−	0.186100i	−0.330098	−	0.943947i	$-0.607082\pi$
$359$	6.10737	−	3.52609i	0.322335	−	0.186100i	0.652433	+	0.757847i	$0.273749\pi$
$360$	−6.71518	−	16.6934i	−0.353921	−	0.879821i
$361$	−2.88845	+	5.00295i	−0.152024	+	0.263313i
$362$	−2.76113	−	4.78242i	−0.145122	−	0.251358i
$363$	−17.2742	−	5.96261i	−0.906658	−	0.312956i
$364$	4.82223	+	0.956366i	0.252754	+	0.0501272i
$365$		−	3.00022i		−	0.157039i
$366$	1.22026	+	6.30316i	0.0637838	+	0.329471i
$367$	1.25896	+	0.726863i	0.0657174	+	0.0379419i	0.532499	−	0.846431i	$-0.321253\pi$
$367$	1.25896	+	0.726863i	0.0657174	+	0.0379419i	−0.466781	+	0.884373i	$0.654586\pi$
$368$	−7.28692	−	4.20710i	−0.379857	−	0.219310i
$369$	2.34072	−	16.4740i	0.121853	−	0.857600i
$370$		−	4.69515i		−	0.244089i
$371$	−9.22347	−	1.82924i	−0.478859	−	0.0949694i
$372$	−6.65982	+	19.2940i	−0.345296	+	1.00035i
$373$	−0.575580	−	0.996933i	−0.0298024	−	0.0516192i	0.850740	−	0.525588i	$-0.176154\pi$
$373$	−0.575580	−	0.996933i	−0.0298024	−	0.0516192i	−0.880542	+	0.473968i	$0.842821\pi$
$374$	0.0756113	−	0.130963i	0.00390977	−	0.00677192i
$375$	37.9808	−	32.9657i	1.96132	−	1.70234i
$376$	−7.09291	+	4.09509i	−0.365789	+	0.211188i
$377$	10.5070			0.541138
$378$	−5.12330	−	0.751775i	−0.263514	−	0.0386671i
$379$	−25.9474			−1.33283			−0.666415	−	0.745581i	$-0.732172\pi$
$379$	−25.9474			−1.33283			−0.666415	+	0.745581i	$0.732172\pi$
$380$	24.1515	−	13.9439i	1.23895	−	0.715307i
$381$	9.96243	−	8.64696i	0.510391	−	0.442997i
$382$	−2.85046	+	4.93714i	−0.145842	+	0.252606i
$383$	1.13541	+	1.96659i	0.0580167	+	0.100488i	0.893575	−	0.448914i	$-0.148189\pi$
$383$	1.13541	+	1.96659i	0.0580167	+	0.100488i	−0.835558	+	0.549402i	$0.814856\pi$
$384$	5.65448	−	16.3815i	0.288554	−	0.835965i
$385$	2.35685	+	6.93017i	0.120116	+	0.353194i
$386$			0.909800i			0.0463076i
$387$	−1.17112	+	8.24232i	−0.0595313	+	0.418980i
$388$	24.8256	+	14.3331i	1.26033	+	0.727651i
$389$	19.5369	+	11.2796i	0.990561	+	0.571901i	0.905442	−	0.424470i	$-0.139540\pi$
$389$	19.5369	+	11.2796i	0.990561	+	0.571901i	0.0851189	+	0.996371i	$0.472873\pi$
$390$	0.511776	+	2.64355i	0.0259148	+	0.133861i
$391$			1.59033i			0.0804264i
$392$	6.20163	+	8.06323i	0.313230	+	0.407254i
$393$	−23.1795	−	8.00100i	−1.16925	−	0.403597i
$394$	2.63130	+	4.55755i	0.132563	+	0.229606i
$395$	31.6764	−	54.8651i	1.59381	−	2.76056i
$396$	−1.39453	−	3.46671i	−0.0700780	−	0.174209i
$397$	−4.37371	+	2.52516i	−0.219510	+	0.126734i	−0.605724	−	0.795675i	$-0.707116\pi$
$397$	−4.37371	+	2.52516i	−0.219510	+	0.126734i	0.386213	+	0.922410i	$0.373783\pi$
$398$	−0.735557			−0.0368701
$399$	0.0759088	−	16.6637i	0.00380019	−	0.834229i
$400$	38.1379			1.90690
$401$	28.3341	−	16.3587i	1.41494	−	0.816915i	0.419090	−	0.907945i	$-0.362349\pi$
$401$	28.3341	−	16.3587i	1.41494	−	0.816915i	0.995848	+	0.0910299i	$0.0290159\pi$
$402$	−1.79875	−	2.07239i	−0.0897133	−	0.103361i
$403$	3.17102	−	5.49237i	0.157960	−	0.273595i
$404$	3.00936	+	5.21237i	0.149722	+	0.259325i
$405$	8.87721	+	36.0698i	0.441112	+	1.79232i
$406$	7.87613	+	6.89931i	0.390886	+	0.342407i
$407$		−	2.02452i		−	0.100352i
$408$	−1.48005	+	0.286529i	−0.0732733	+	0.0141853i
$409$	−20.4013	−	11.7787i	−1.00878	−	0.582419i	−0.0979449	−	0.995192i	$-0.531227\pi$
$409$	−20.4013	−	11.7787i	−1.00878	−	0.582419i	−0.910834	+	0.412773i	$0.864560\pi$
$410$	−7.46730	−	4.31125i	−0.368784	−	0.212917i
$411$	24.3503	−	4.71408i	1.20111	−	0.232528i
$412$			7.71238i			0.379962i
$413$	−2.29222	+	11.5579i	−0.112793	+	0.568729i
$414$	−2.36149	−	1.85077i	−0.116061	−	0.0909603i
$415$	11.1870	+	19.3765i	0.549149	+	0.951153i
$416$	−2.04998	+	3.55067i	−0.100509	+	0.174086i
$417$	11.7155	+	13.4978i	0.573711	+	0.660990i
$418$	−0.795116	+	0.459060i	−0.0388904	+	0.0224534i
$419$	−28.9733			−1.41544			−0.707718	−	0.706495i	$-0.750275\pi$
$419$	−28.9733			−1.41544			−0.707718	+	0.706495i	$0.750275\pi$
$420$	17.7107	−	30.3557i	0.864194	−	1.48120i
$421$	8.30751			0.404883			0.202442	−	0.979294i	$-0.435112\pi$
$421$	8.30751			0.404883			0.202442	+	0.979294i	$0.435112\pi$
$422$	−5.27650	+	3.04639i	−0.256856	+	0.148296i
$423$	15.6865	−	6.31011i	0.762701	−	0.306808i
$424$	2.58234	−	4.47275i	0.125410	−	0.217216i
$425$	−3.60413	−	6.24254i	−0.174826	−	0.302808i
$426$	−6.05961	−	2.09163i	−0.293589	−	0.101340i
$427$	−17.1563	+	19.5854i	−0.830254	+	0.947804i
$428$		−	6.19360i		−	0.299379i
$429$	0.220674	+	1.13988i	0.0106543	+	0.0550340i
$430$	3.73607	+	2.15702i	0.180169	+	0.104021i
$431$	−11.9518	−	6.90038i	−0.575698	−	0.332380i	0.183724	−	0.982978i	$-0.441185\pi$
$431$	−11.9518	−	6.90038i	−0.575698	−	0.332380i	−0.759422	+	0.650598i	$0.774518\pi$
$432$	−7.50879	+	14.6544i	−0.361267	+	0.705061i
$433$			4.27688i			0.205534i	0.994705	+	0.102767i	$0.0327695\pi$
$433$			4.27688i			0.205534i	−0.994705	+	0.102767i	$0.967230\pi$
$434$	5.98353	−	2.03491i	0.287219	−	0.0976788i
$435$	24.5080	−	71.0015i	1.17507	−	3.40426i
$436$	−7.68033	−	13.3027i	−0.367821	−	0.637085i
$437$	4.82770	−	8.36181i	0.230940	−	0.400000i
$438$	0.358140	−	0.310850i	0.0171126	−	0.0148530i
$439$	8.47220	−	4.89143i	0.404356	−	0.233455i	−0.284006	−	0.958823i	$-0.591663\pi$
$439$	8.47220	−	4.89143i	0.404356	−	0.233455i	0.688362	+	0.725367i	$0.258330\pi$
$440$	−4.02051			−0.191671
$441$	−10.3339	−	18.2814i	−0.492089	−	0.870545i
$442$	0.225594			0.0107304
$443$	−10.6399	+	6.14297i	−0.505519	+	0.291861i	−0.730990	−	0.682389i	$-0.760941\pi$
$443$	−10.6399	+	6.14297i	−0.505519	+	0.291861i	0.225471	+	0.974250i	$0.427608\pi$
$444$	−7.34068	+	6.37140i	−0.348373	+	0.302373i
$445$	15.1506	−	26.2417i	0.718209	−	1.24397i
$446$	0.190529	+	0.330006i	0.00902182	+	0.0156262i
$447$	6.51184	−	18.8653i	0.307999	−	0.892298i
$448$	12.0072	−	4.08346i	0.567285	−	0.192925i
$449$		−	26.4987i		−	1.25055i	−0.780404	−	0.625276i	$-0.784986\pi$
$449$		−	26.4987i		−	1.25055i	0.780404	−	0.625276i	$-0.215014\pi$
$450$	13.4640	+	1.91304i	0.634697	+	0.0901817i
$451$	−3.21985	−	1.85898i	−0.151617	−	0.0875361i
$452$	14.3832	+	8.30415i	0.676530	+	0.390595i
$453$	5.33087	+	27.5363i	0.250466	+	1.29377i
$454$			1.79613i			0.0842965i
$455$	−7.19538	+	8.21412i	−0.337324	+	0.385084i
$456$	8.65178	+	2.98638i	0.405156	+	0.139850i
$457$	4.97542	+	8.61768i	0.232740	+	0.403118i	0.958614	−	0.284710i	$-0.0918974\pi$
$457$	4.97542	+	8.61768i	0.232740	+	0.403118i	−0.725873	+	0.687828i	$0.758564\pi$
$458$	2.96107	−	5.12872i	0.138362	−	0.239649i
$459$	3.10828	−	0.155816i	0.145082	−	0.00727285i
$460$	17.6353	−	10.1817i	0.822248	−	0.474725i
$461$	−15.6920			−0.730849			−0.365424	−	0.930841i	$-0.619076\pi$
$461$	−15.6920			−0.730849			−0.365424	+	0.930841i	$0.619076\pi$
$462$	−0.583071	+	0.999368i	−0.0271269	+	0.0464948i
$463$	−28.3707			−1.31850			−0.659250	−	0.751924i	$-0.729126\pi$
$463$	−28.3707			−1.31850			−0.659250	+	0.751924i	$0.729126\pi$
$464$	28.8350	−	16.6479i	1.33863	−	0.772858i
$465$	−29.7184	−	34.2395i	−1.37816	−	1.58782i
$466$	−5.38039	+	9.31911i	−0.249242	+	0.431699i
$467$	7.08321	+	12.2685i	0.327772	+	0.567718i	0.982069	−	0.188520i	$-0.0603689\pi$
$467$	7.08321	+	12.2685i	0.327772	+	0.567718i	−0.654297	+	0.756237i	$0.727036\pi$
$468$	3.43859	−	4.38748i	0.158949	−	0.202811i
$469$	2.16495	−	10.9162i	0.0999683	−	0.504064i
$470$		−	8.76170i		−	0.404147i
$471$	−32.5041	+	6.29261i	−1.49771	+	0.289948i
$472$	−5.60480	−	3.23594i	−0.257982	−	0.148946i
$473$	1.61097	+	0.930094i	0.0740725	+	0.0427658i
$474$	9.83126	−	1.90328i	0.451565	−	0.0874204i
$475$			43.7637i			2.00802i
$476$	−2.21488	−	1.94018i	−0.101519	−	0.0889279i
$477$	−6.57699	+	8.39192i	−0.301139	+	0.384240i
$478$	2.74187	+	4.74907i	0.125410	+	0.217217i
$479$	−7.03930	+	12.1924i	−0.321634	+	0.557087i	−0.980825	−	0.194889i	$-0.937565\pi$
$479$	−7.03930	+	12.1924i	−0.321634	+	0.557087i	0.659191	+	0.751975i	$0.270899\pi$
$480$	19.2122	+	22.1349i	0.876911	+	1.01032i
$481$	2.61556	−	1.51009i	0.119259	−	0.0688543i
$482$	2.91756			0.132891
$483$	0.0554280	−	12.1677i	0.00252206	−	0.553650i
$484$	19.6045			0.891114
$485$	−55.1436	+	31.8372i	−2.50394	+	1.44565i
$486$	−3.38594	+	4.79685i	−0.153589	+	0.217589i
$487$	−6.61172	+	11.4518i	−0.299606	+	0.518933i	−0.976046	−	0.217565i	$-0.930189\pi$
$487$	−6.61172	+	11.4518i	−0.299606	+	0.518933i	0.676440	+	0.736498i	$0.263522\pi$
$488$	−7.15046	−	12.3850i	−0.323686	−	0.560641i
$489$	−33.6914	−	11.6294i	−1.52358	−	0.525901i
$490$	−10.7874	+	1.43261i	−0.487326	+	0.0647186i
$491$			22.1935i			1.00158i	0.865569	+	0.500790i	$0.166957\pi$
$491$			22.1935i			1.00158i	−0.865569	+	0.500790i	$0.833043\pi$
$492$	3.39279	+	17.5253i	0.152959	+	0.790099i
$493$	−5.44996	−	3.14653i	−0.245454	−	0.141713i
$494$	−1.18616	−	0.684827i	−0.0533677	−	0.0308118i
$495$	8.21753	+	1.16760i	0.369350	+	0.0524796i
$496$		−	20.0974i		−	0.902399i
$497$	−8.37055	−	24.6131i	−0.375471	−	1.10405i
$498$	−1.15391	+	3.34298i	−0.0517082	+	0.149803i
$499$	−11.2460	−	19.4787i	−0.503442	−	0.871988i	−0.999992	−	0.00397934i	$-0.998733\pi$
$499$	−11.2460	−	19.4787i	−0.503442	−	0.871988i	0.496550	−	0.868008i	$-0.334600\pi$
$500$	−26.9764	+	46.7245i	−1.20642	+	2.08958i
$501$	−17.3531	+	15.0618i	−0.775279	+	0.672910i
$502$	−2.19230	+	1.26572i	−0.0978469	+	0.0564920i
$503$	−20.0211			−0.892697			−0.446349	−	0.894859i	$-0.647276\pi$
$503$	−20.0211			−0.892697			−0.446349	+	0.894859i	$0.647276\pi$
$504$	11.3339	−	2.14067i	0.504853	−	0.0953528i
$505$	−13.3690			−0.594914
$506$	−0.580587	+	0.335202i	−0.0258102	+	0.0149015i
$507$	−1.30806	+	1.13534i	−0.0580928	+	0.0504221i
$508$	−7.07596	+	12.2559i	−0.313945	+	0.543768i
$509$	−19.5355	−	33.8365i	−0.865896	−	1.49978i	−0.866155	−	0.499776i	$-0.833416\pi$
$509$	−19.5355	−	33.8365i	−0.865896	−	1.49978i	0.000258738	−	1.00000i	$-0.499918\pi$
$510$	0.526207	−	1.52446i	0.0233008	−	0.0675043i
$511$	1.88649	+	0.374137i	0.0834533	+	0.0165508i
$512$			22.2024i			0.981219i
$513$	−16.8161	−	8.61642i	−0.742448	−	0.380424i
$514$	5.16794	+	2.98371i	0.227948	+	0.131606i
$515$	−14.8359	−	8.56552i	−0.653749	−	0.377442i
$516$	−1.69749	−	8.76830i	−0.0747279	−	0.386003i
$517$		−	3.77799i		−	0.166156i
$518$	2.95223	+	0.585499i	0.129714	+	0.0257254i
$519$	17.2030	+	5.93806i	0.755129	+	0.260652i
$520$	−2.99891	−	5.19426i	−0.131511	−	0.227783i
$521$	18.1493	−	31.4355i	0.795136	−	1.37722i	−0.127617	−	0.991823i	$-0.540733\pi$
$521$	18.1493	−	31.4355i	0.795136	−	1.37722i	0.922753	−	0.385392i	$-0.125934\pi$
$522$	11.0148	−	4.43086i	0.482104	−	0.193933i
$523$	12.7402	−	7.35555i	0.557090	−	0.321636i	−0.194887	−	0.980826i	$-0.562434\pi$
$523$	12.7402	−	7.35555i	0.557090	−	0.321636i	0.751977	+	0.659190i	$0.229101\pi$
$524$	26.3065			1.14921
$525$	27.3579	+	47.8877i	1.19400	+	2.08999i
$526$	2.54513			0.110973
$527$	−3.28960	+	1.89925i	−0.143297	+	0.0827328i
$528$	2.41170	+	2.77859i	0.104956	+	0.120923i
$529$	−7.97486	+	13.8129i	−0.346733	+	0.600559i
$530$	2.76254	+	4.78486i	0.119997	+	0.207841i
$531$	10.5159	+	8.24162i	0.456352	+	0.357656i
$532$	5.75591	+	16.9249i	0.249550	+	0.733788i
$533$		−	5.54647i		−	0.240244i
$534$	4.70224	−	0.910327i	0.203486	−	0.0393937i
$535$	11.9143	+	6.87873i	0.515101	+	0.297394i
$536$	5.29362	+	3.05627i	0.228649	+	0.132011i
$537$	15.6364	−	3.02712i	0.674760	−	0.130630i
$538$			1.31536i			0.0567094i
$539$	−4.65147	+	0.617731i	−0.200353	+	0.0266076i
$540$	−21.6279	−	33.4704i	−0.930717	−	1.44033i
$541$	−4.97360	−	8.61453i	−0.213832	−	0.370368i	0.739079	−	0.673619i	$-0.235261\pi$
$541$	−4.97360	−	8.61453i	−0.213832	−	0.370368i	−0.952911	+	0.303251i	$0.901928\pi$
$542$	−1.74839	+	3.02830i	−0.0750998	+	0.130077i
$543$	−16.6455	−	19.1778i	−0.714328	−	0.822998i
$544$	2.12664	−	1.22782i	0.0911789	−	0.0526422i
$545$	34.1197			1.46153
$546$	−1.72604	−	0.00786267i	−0.0738675	−	0.000336491i
$547$	−11.2450			−0.480803			−0.240401	−	0.970674i	$-0.577279\pi$
$547$	−11.2450			−0.480803			−0.240401	+	0.970674i	$0.577279\pi$
$548$	−23.0430	+	13.3039i	−0.984350	+	0.568315i
$549$	11.0181	+	27.3902i	0.470242	+	1.16899i
$550$	1.51932	−	2.63155i	0.0647842	−	0.112210i
$551$	19.1036	+	33.0884i	0.813841	+	1.40961i
$552$	6.31745	+	2.18063i	0.268889	+	0.0928137i
$553$	30.5480	+	26.7594i	1.29904	+	1.13792i
$554$			6.75198i			0.286864i
$555$	−4.10364	−	21.1971i	−0.174190	−	0.899767i
$556$	−16.6052	−	9.58700i	−0.704216	−	0.406579i
$557$	4.04380	+	2.33469i	0.171341	+	0.0989239i	0.583218	−	0.812316i	$-0.301793\pi$
$557$	4.04380	+	2.33469i	0.171341	+	0.0989239i	−0.411877	+	0.911240i	$0.635127\pi$
$558$	1.00811	−	7.09504i	0.0426766	−	0.300357i
$559$			2.77503i			0.117371i
$560$	−6.73177	+	33.9432i	−0.284469	+	1.43436i
$561$	0.226897	−	0.657339i	0.00957960	−	0.0277529i
$562$	−3.71733	−	6.43860i	−0.156806	−	0.271596i
$563$	14.8560	−	25.7314i	0.626106	−	1.08445i	−0.362220	−	0.932093i	$-0.617981\pi$
$563$	14.8560	−	25.7314i	0.626106	−	1.08445i	0.988326	−	0.152355i	$-0.0486856\pi$
$564$	−13.6986	+	11.8898i	−0.576813	+	0.500650i
$565$	−31.9486	+	18.4455i	−1.34409	+	0.776009i
$566$	9.18142			0.385924
$567$	−23.7871	+	1.08382i	−0.998964	+	0.0455162i
$568$	14.2792			0.599143
$569$	−12.5662	+	7.25512i	−0.526804	+	0.304151i	−0.739714	−	0.672921i	$-0.765039\pi$
$569$	−12.5662	+	7.25512i	−0.526804	+	0.304151i	0.212910	+	0.977072i	$0.431706\pi$
$570$	−7.39450	+	6.41811i	−0.309722	+	0.268825i
$571$	13.3797	−	23.1744i	0.559925	−	0.969818i	−0.437577	−	0.899181i	$-0.644163\pi$
$571$	13.3797	−	23.1744i	0.559925	−	0.969818i	0.997502	−	0.0706372i	$-0.0225033\pi$
$572$	−0.622780	−	1.07869i	−0.0260398	−	0.0451022i
$573$	−8.55376	+	24.7809i	−0.357338	+	1.03524i
$574$	3.64203	−	4.15768i	0.152015	−	0.173538i
$575$			31.9559i			1.33265i
$576$	2.02297	−	14.2376i	0.0842905	−	0.593235i
$577$	6.98695	+	4.03392i	0.290870	+	0.167934i	0.638334	−	0.769759i	$-0.279624\pi$
$577$	6.98695	+	4.03392i	0.290870	+	0.167934i	−0.347464	+	0.937693i	$0.612957\pi$
$578$	5.42827	+	3.13401i	0.225786	+	0.130358i
$579$	0.795179	+	4.10745i	0.0330465	+	0.170700i
$580$			80.5799i			3.34590i
$581$	−13.5786	+	4.61789i	−0.563336	+	0.191582i
$582$	−9.51381	−	3.28393i	−0.394360	−	0.136123i
$583$	1.19119	+	2.06320i	0.0493341	+	0.0854492i
$584$	−0.528170	+	0.914817i	−0.0218558	+	0.0378554i
$585$	4.62100	+	11.4875i	0.191055	+	0.474948i
$586$	−2.11015	+	1.21829i	−0.0871694	+	0.0503273i
$587$	36.9526			1.52520			0.762598	−	0.646873i	$-0.223924\pi$
$587$	36.9526			1.52520			0.762598	+	0.646873i	$0.223924\pi$
$588$	16.8785	+	14.9216i	0.696059	+	0.615357i
$589$	23.0620			0.950251
$590$	5.99591	−	3.46174i	0.246848	−	0.142518i
$591$	15.8628	+	18.2760i	0.652509	+	0.751776i
$592$	4.78535	−	8.28847i	0.196677	−	0.340654i
$593$	−14.1813	−	24.5627i	−0.582355	−	1.00867i	−0.995199	−	0.0978671i	$-0.968798\pi$
$593$	−14.1813	−	24.5627i	−0.582355	−	1.00867i	0.412844	−	0.910802i	$-0.364535\pi$
$594$	0.712033	+	1.10191i	0.0292151	+	0.0452119i
$595$	6.19211	−	2.10584i	0.253852	−	0.0863312i
$596$			21.4103i			0.877000i
$597$	−3.32080	+	0.642888i	−0.135911	+	0.0263116i
$598$	−0.866121	−	0.500055i	−0.0354183	−	0.0204488i
$599$	−1.90744	−	1.10126i	−0.0779357	−	0.0449962i	0.460526	−	0.887646i	$-0.347661\pi$
$599$	−1.90744	−	1.10126i	−0.0779357	−	0.0449962i	−0.538461	+	0.842650i	$0.680994\pi$
$600$	−29.7399	+	5.75748i	−1.21413	+	0.235048i
$601$			13.5961i			0.554595i	0.960784	+	0.277298i	$0.0894388\pi$
$601$			13.5961i			0.554595i	−0.960784	+	0.277298i	$0.910561\pi$
$602$	−1.82219	+	2.08019i	−0.0742671	+	0.0847821i
$603$	−9.93205	−	7.78403i	−0.404464	−	0.316990i
$604$	−15.0446	−	26.0580i	−0.612157	−	1.06029i
$605$	−21.7731	+	37.7122i	−0.885204	+	1.53322i
$606$	−1.38515	−	1.59588i	−0.0562680	−	0.0648281i
$607$	32.7403	−	18.9026i	1.32889	−	0.767234i	0.343760	−	0.939057i	$-0.388299\pi$
$607$	32.7403	−	18.9026i	1.32889	−	0.767234i	0.985128	+	0.171823i	$0.0549658\pi$
$608$	−14.9089			−0.604637
$609$	41.5883	+	24.2643i	1.68524	+	0.983238i
$610$	15.2989			0.619432
$611$	4.88093	−	2.81801i	0.197461	−	0.114004i
$612$	−3.09751	+	1.24602i	−0.125209	+	0.0503673i
$613$	15.7885	−	27.3464i	0.637691	−	1.10451i	−0.348248	−	0.937403i	$-0.613223\pi$
$613$	15.7885	−	27.3464i	0.637691	−	1.10451i	0.985938	−	0.167110i	$-0.0534435\pi$
$614$	−2.84006	−	4.91913i	−0.114616	−	0.198520i
$615$	−37.4805	−	12.9374i	−1.51136	−	0.521684i
$616$	0.501370	−	2.52803i	0.0202008	−	0.101857i
$617$			13.4929i			0.543202i	0.962410	+	0.271601i	$0.0875532\pi$
$617$			13.4929i			0.543202i	−0.962410	+	0.271601i	$0.912447\pi$
$618$	−0.514660	−	2.65845i	−0.0207027	−	0.106938i
$619$	−29.4320	−	16.9926i	−1.18297	−	0.682990i	−0.226272	−	0.974064i	$-0.572654\pi$
$619$	−29.4320	−	16.9926i	−1.18297	−	0.682990i	−0.956700	+	0.291075i	$0.905987\pi$
$620$	42.1219	+	24.3191i	1.69166	+	0.976678i
$621$	−12.2790	−	6.29164i	−0.492738	−	0.252475i
$622$			8.84821i			0.354781i
$623$	14.6110	+	12.7989i	0.585376	+	0.512775i
$624$	−1.79088	+	5.18832i	−0.0716926	+	0.207699i
$625$	−29.8334	−	51.6730i	−1.19334	−	2.06692i
$626$	4.02378	−	6.96939i	0.160822	−	0.278553i
$627$	−3.18846	+	2.76745i	−0.127335	+	0.110521i
$628$	30.7592	−	17.7588i	1.22742	−	0.708653i
$629$	−1.80891			−0.0721260
$630$	−4.07917	+	11.6454i	−0.162518	+	0.463965i
$631$	−36.4238			−1.45001			−0.725005	−	0.688744i	$-0.758162\pi$
$631$	−36.4238			−1.45001			−0.725005	+	0.688744i	$0.758162\pi$
$632$	−19.3173	+	11.1528i	−0.768400	+	0.443636i
$633$	−21.1591	+	18.3652i	−0.840998	+	0.729951i
$634$	−3.47908	+	6.02594i	−0.138172	+	0.239321i
$635$	−15.7174	−	27.2233i	−0.623726	−	1.08032i
$636$	3.73212	−	10.8123i	0.147988	−	0.428734i
$637$	−4.26761	−	5.54865i	−0.169089	−	0.219846i
$638$		−	2.65285i		−	0.105027i
$639$	−29.1853	−	4.14683i	−1.15455	−	0.164046i
$640$	−35.7634	−	20.6480i	−1.41367	−	0.816183i
$641$	−11.4454	−	6.60802i	−0.452067	−	0.261001i	0.256636	−	0.966508i	$-0.417386\pi$
$641$	−11.4454	−	6.60802i	−0.452067	−	0.261001i	−0.708703	+	0.705507i	$0.750719\pi$
$642$	0.413309	+	2.13492i	0.0163120	+	0.0842587i
$643$		−	12.5686i		−	0.495658i	−0.968804	−	0.247829i	$-0.920283\pi$
$643$		−	12.5686i		−	0.495658i	0.968804	−	0.247829i	$-0.0797172\pi$
$644$	4.20292	+	12.3584i	0.165618	+	0.486990i
$645$	18.7524	+	6.47287i	0.738375	+	0.254869i
$646$	0.410171	+	0.710436i	0.0161379	+	0.0279517i
$647$	8.60547	−	14.9051i	0.338316	−	0.585981i	−0.645800	−	0.763507i	$-0.723476\pi$
$647$	8.60547	−	14.9051i	0.338316	−	0.585981i	0.984116	+	0.177526i	$0.0568094\pi$
$648$	3.64305	−	12.5611i	0.143113	−	0.493445i
$649$	2.58540	−	1.49268i	0.101486	−	0.0585929i
$650$	4.53306			0.177801
$651$	25.2352	−	14.4167i	0.989044	−	0.565033i
$652$	38.2365			1.49746
$653$	21.4516	−	12.3851i	0.839465	−	0.484666i	−0.0176171	−	0.999845i	$-0.505608\pi$
$653$	21.4516	−	12.3851i	0.839465	−	0.484666i	0.857082	+	0.515179i	$0.172275\pi$
$654$	3.53511	+	4.07290i	0.138234	+	0.159263i
$655$	−29.2166	+	50.6046i	−1.14159	+	1.97728i
$656$	−8.78814	−	15.2215i	−0.343119	−	0.594300i
$657$	1.34520	−	1.71641i	0.0524812	−	0.0669635i
$658$	5.50920	+	1.09261i	0.214771	+	0.0425944i
$659$		−	15.4940i		−	0.603562i	−0.953377	−	0.301781i	$-0.902419\pi$
$659$		−	15.4940i		−	0.603562i	0.953377	−	0.301781i	$-0.0975812\pi$
$660$	−8.74193	+	1.69239i	−0.340279	+	0.0658761i
$661$	16.3468	+	9.43785i	0.635818	+	0.367090i	0.783002	−	0.622019i	$-0.213687\pi$
$661$	16.3468	+	9.43785i	0.635818	+	0.367090i	−0.147183	+	0.989109i	$0.547021\pi$
$662$	3.99659	+	2.30743i	0.155332	+	0.0896809i
$663$	1.01848	−	0.197173i	0.0395547	−	0.00765756i
$664$		−	7.87760i		−	0.305710i
$665$	−38.9502	−	7.72478i	−1.51042	−	0.299554i
$666$	2.10515	−	2.68607i	0.0815728	−	0.104083i
$667$	13.9493	+	24.1609i	0.540119	+	0.935513i
$668$	12.3253	−	21.3480i	0.476880	−	0.825980i
$669$	1.14861	+	1.32335i	0.0444077	+	0.0511635i
$670$	−5.66301	+	3.26954i	−0.218781	+	0.126313i
$671$	6.59677			0.254666
$672$	−16.3138	+	9.31998i	−0.629320	+	0.359526i
$673$	9.90685			0.381881			0.190940	−	0.981602i	$-0.438846\pi$
$673$	9.90685			0.381881			0.190940	+	0.981602i	$0.438846\pi$
$674$	−2.53322	+	1.46256i	−0.0975761	+	0.0563356i
$675$	62.4574	−	3.13094i	2.40399	−	0.120510i
$676$	0.929065	−	1.60919i	0.0357333	−	0.0618919i
$677$	16.9448	+	29.3492i	0.651240	+	1.12798i	0.982822	+	0.184555i	$0.0590843\pi$
$677$	16.9448	+	29.3492i	0.651240	+	1.12798i	−0.331582	+	0.943426i	$0.607582\pi$
$678$	−5.51202	−	1.90261i	−0.211688	−	0.0730694i
$679$	−13.1421	−	38.6435i	−0.504347	−	1.48300i
$680$			3.59233i			0.137760i
$681$	1.56984	+	8.10894i	0.0601565	+	0.310735i
$682$	−1.38673	−	0.800632i	−0.0531008	−	0.0306578i
$683$	23.4427	+	13.5347i	0.897011	+	0.517889i	0.876229	−	0.481895i	$-0.160051\pi$
$683$	23.4427	+	13.5347i	0.897011	+	0.517889i	0.0207815	+	0.999784i	$0.493385\pi$
$684$	20.0689	+	2.85151i	0.767354	+	0.109030i
$685$		−	59.1023i		−	2.25818i
$686$	0.444426	−	6.96159i	0.0169682	−	0.265795i
$687$	8.88568	−	25.7425i	0.339010	−	0.982138i
$688$	4.39692	+	7.61568i	0.167631	+	0.290345i
$689$	−1.77702	+	3.07789i	−0.0676991	+	0.117258i
$690$	−5.39940	+	4.68645i	−0.205552	+	0.178410i
$691$	21.8850	−	12.6353i	0.832545	−	0.480670i	−0.0221783	−	0.999754i	$-0.507060\pi$
$691$	21.8850	−	12.6353i	0.832545	−	0.480670i	0.854723	+	0.519084i	$0.173727\pi$
$692$	−19.5238			−0.742183
$693$	−1.75891	+	5.02143i	−0.0668156	+	0.190748i
$694$	4.37072			0.165910
$695$	36.8840	−	21.2950i	1.39909	−	0.807766i
$696$	−19.9722	+	17.3351i	−0.757045	+	0.657083i
$697$	−1.66100	+	2.87694i	−0.0629150	+	0.108972i
$698$	0.159366	+	0.276030i	0.00603210	+	0.0104479i
$699$	−16.1457	+	46.7753i	−0.610685	+	1.76920i
$700$	−44.5054	−	38.9857i	−1.68215	−	1.47352i
$701$			2.83213i			0.106968i	0.998569	+	0.0534840i	$0.0170326\pi$
$701$			2.83213i			0.106968i	−0.998569	+	0.0534840i	$0.982967\pi$
$702$	−0.892493	+	1.74182i	−0.0336850	+	0.0657407i
$703$	9.51110	+	5.49124i	0.358718	+	0.207106i
$704$	−2.78276	−	1.60663i	−0.104879	−	0.0605521i
$705$	−7.65786	−	39.5562i	−0.288412	−	1.48977i
$706$		−	9.48246i		−	0.356877i
$707$	1.66716	−	8.40621i	0.0626999	−	0.316148i
$708$	−13.5488	−	4.67672i	−0.509196	−	0.175762i
$709$	16.5476	+	28.6613i	0.621458	+	1.07640i	0.989214	+	0.146475i	$0.0467928\pi$
$709$	16.5476	+	28.6613i	0.621458	+	1.07640i	−0.367756	+	0.929922i	$0.619874\pi$
$710$	−7.63781	+	13.2291i	−0.286642	+	0.496479i
$711$	42.7215	−	17.1853i	1.60218	−	0.644501i
$712$	−9.23935	+	5.33434i	−0.346259	+	0.199913i
$713$	16.8396			0.630650
$714$	0.892935	+	0.520974i	0.0334173	+	0.0194970i
$715$	2.76669			0.103468
$716$	−14.7970	+	8.54303i	−0.552988	+	0.319268i
$717$	16.5294	+	19.0440i	0.617303	+	0.711213i
$718$	1.32812	−	2.30038i	0.0495651	−	0.0858492i
$719$	2.28833	+	3.96350i	0.0853401	+	0.147813i	0.905536	−	0.424269i	$-0.139469\pi$
$719$	2.28833	+	3.96350i	0.0853401	+	0.147813i	−0.820196	+	0.572083i	$0.806136\pi$
$720$	30.8830	+	24.2039i	1.15094	+	0.902026i
$721$	7.23593	−	8.26042i	0.269480	−	0.307634i
$722$			2.17591i			0.0809788i
$723$	13.1718	−	2.54999i	0.489866	−	0.0948353i
$724$	23.5928	+	13.6213i	0.876819	+	0.506232i
$725$	−109.511	−	63.2261i	−4.06713	−	2.34816i
$726$	−6.75764	+	1.30824i	−0.250800	+	0.0485534i
$727$		−	28.8022i		−	1.06821i	−0.845417	−	0.534107i	$-0.820648\pi$
$727$		−	28.8022i		−	1.06821i	0.845417	−	0.534107i	$-0.179352\pi$
$728$	3.64003	−	1.23792i	0.134908	−	0.0458804i
$729$	−11.0939	+	24.6156i	−0.410885	+	0.911687i
$730$	−0.565026	−	0.978653i	−0.0209125	−	0.0362216i
$731$	0.831039	−	1.43940i	0.0307371	−	0.0532382i
$732$	−20.7608	−	23.9191i	−0.767341	−	0.884076i
$733$	−15.5664	+	8.98728i	−0.574959	+	0.331953i	−0.759128	−	0.650942i	$-0.774374\pi$
$733$	−15.5664	+	8.98728i	−0.574959	+	0.331953i	0.184168	+	0.982895i	$0.441041\pi$
$734$	0.547554			0.0202106
$735$	−47.4496	+	15.8961i	−1.75020	+	0.586337i
$736$	−10.8864			−0.401277
$737$	−2.44185	+	1.40981i	−0.0899469	+	0.0519308i
$738$	−2.33898	−	5.81452i	−0.0860990	−	0.214035i
$739$	−19.5409	+	33.8458i	−0.718822	+	1.24504i	0.242645	+	0.970115i	$0.421985\pi$
$739$	−19.5409	+	33.8458i	−0.718822	+	1.24504i	−0.961467	+	0.274921i	$0.911348\pi$
$740$	11.5811	+	20.0591i	0.425731	+	0.737388i
$741$	−5.95366	−	2.05505i	−0.218713	−	0.0754943i
$742$	−3.35313	+	1.14035i	−0.123097	+	0.0418636i
$743$		−	1.51895i		−	0.0557250i	−0.999612	−	0.0278625i	$-0.991130\pi$
$743$		−	1.51895i		−	0.0557250i	0.999612	−	0.0278625i	$-0.00887005\pi$
$744$	3.03399	+	15.6719i	0.111232	+	0.574560i
$745$	−41.1859	−	23.7787i	−1.50894	−	0.871184i
$746$	−0.375501	−	0.216795i	−0.0137481	−	0.00793744i
$747$	−2.28773	+	16.1010i	−0.0837038	+	0.589106i
$748$			0.746016i			0.0272771i
$749$	−5.81097	+	6.63371i	−0.212328	+	0.242390i
$750$	6.18072	−	17.9060i	0.225688	−	0.653836i
$751$	16.5737	+	28.7065i	0.604783	+	1.04751i	0.992086	+	0.125562i	$0.0400735\pi$
$751$	16.5737	+	28.7065i	0.604783	+	1.04751i	−0.387303	+	0.921953i	$0.626593\pi$
$752$	8.93002	−	15.4672i	0.325644	−	0.564032i
$753$	−8.79124	+	7.63042i	−0.320371	+	0.278068i
$754$	3.42732	−	1.97876i	0.124815	−	0.0720622i
$755$	66.8354			2.43239
$756$	23.7426	−	9.42540i	0.863511	−	0.342798i
$757$	8.31863			0.302346			0.151173	−	0.988507i	$-0.451695\pi$
$757$	8.31863			0.302346			0.151173	+	0.988507i	$0.451695\pi$
$758$	−8.46389	+	4.88663i	−0.307422	+	0.177490i
$759$	−2.32819	+	2.02077i	−0.0845079	+	0.0733493i
$760$	10.9051	−	18.8882i	0.395569	−	0.685146i
$761$	−10.2309	−	17.7204i	−0.370868	−	0.642363i	0.618831	−	0.785524i	$-0.287607\pi$
$761$	−10.2309	−	17.7204i	−0.370868	−	0.642363i	−0.989699	+	0.143161i	$0.954273\pi$
$762$	1.62121	−	4.69679i	0.0587304	−	0.170147i
$763$	−4.25482	+	21.4538i	−0.154035	+	0.776681i
$764$		−	28.1239i		−	1.01749i
$765$	1.04325	−	7.34237i	0.0377187	−	0.265464i
$766$	0.740727	+	0.427659i	0.0267635	+	0.0154519i
$767$	3.85691	+	2.22679i	0.139265	+	0.0804046i
$768$	1.91546	+	9.89421i	0.0691183	+	0.357026i
$769$			8.60167i			0.310184i	0.987900	+	0.155092i	$0.0495674\pi$
$769$			8.60167i			0.310184i	−0.987900	+	0.155092i	$0.950433\pi$
$770$	2.07393	+	1.81671i	0.0747393	+	0.0654699i
$771$	25.9394	+	8.95362i	0.934183	+	0.322457i
$772$	−2.24413	−	3.88694i	−0.0807679	−	0.139894i
$773$	10.0218	−	17.3582i	0.360458	−	0.624332i	−0.627578	−	0.778554i	$-0.715954\pi$
$773$	10.0218	−	17.3582i	0.360458	−	0.624332i	0.988036	+	0.154222i	$0.0492871\pi$
$774$	1.17025	+	2.90914i	0.0420636	+	0.104567i
$775$	−66.1009	+	38.1634i	−2.37442	+	1.37087i
$776$	22.4189			0.804792
$777$	13.8401	+	0.0630463i	0.496511	+	0.00226177i
$778$	8.49708			0.304635
$779$	17.4668	−	10.0845i	0.625814	−	0.361314i
$780$	−8.70708	−	10.0317i	−0.311763	−	0.359192i
$781$	−3.29338	+	5.70430i	−0.117846	+	0.204116i
$782$	0.299503	+	0.518755i	0.0107102	+	0.0185506i
$783$	45.8555	−	29.6310i	1.63874	−	1.05892i
$784$	−20.5034	−	8.46564i	−0.732265	−	0.302344i
$785$			78.8931i			2.81582i
$786$	−9.06783	+	1.75548i	−0.323439	+	0.0626159i
$787$	−5.60081	−	3.23363i	−0.199647	−	0.115267i	0.396844	−	0.917886i	$-0.370106\pi$
$787$	−5.60081	−	3.23363i	−0.199647	−	0.115267i	−0.596491	+	0.802620i	$0.703439\pi$
$788$	−22.4834	−	12.9808i	−0.800939	−	0.462422i
$789$	11.4904	−	2.22448i	0.409071	−	0.0791937i
$790$		−	23.8622i		−	0.848978i
$791$	−7.61413	−	22.3889i	−0.270727	−	0.796058i
$792$	−2.30011	−	1.80266i	−0.0817309	−	0.0640548i
$793$	4.92054	+	8.52262i	0.174733	+	0.302647i
$794$	−0.951117	+	1.64738i	−0.0337539	+	0.0584635i
$795$	16.6540	+	19.1876i	0.590657	+	0.680514i
$796$	3.14252	−	1.81434i	0.111384	−	0.0643075i
$797$	2.04250			0.0723491			0.0361745	−	0.999345i	$-0.488483\pi$
$797$	2.04250			0.0723491			0.0361745	+	0.999345i	$0.488483\pi$
$798$	−3.11348	−	5.44989i	−0.110216	−	0.192924i
$799$	−3.37564			−0.119421
$800$	42.7325	−	24.6716i	1.51082	−	0.872272i
$801$	20.4334	−	8.21966i	0.721980	−	0.290427i
$802$	6.16160	−	10.6722i	0.217574	−	0.376849i
$803$	−0.243636	−	0.421989i	−0.00859772	−	0.0148917i
$804$	12.7966	+	4.41706i	0.451301	+	0.155778i
$805$	−28.4411	−	5.64057i	−1.00242	−	0.198804i
$806$		−	2.38877i		−	0.0841408i
$807$	1.14965	+	5.93844i	0.0404695	+	0.209043i
$808$	4.07644	+	2.35353i	0.143409	+	0.0827970i
$809$	−12.9105	−	7.45386i	−0.453907	−	0.262064i	0.255572	−	0.966790i	$-0.417736\pi$
$809$	−12.9105	−	7.45386i	−0.453907	−	0.262064i	−0.709479	+	0.704727i	$0.751070\pi$
$810$	9.68864	+	10.0939i	0.340424	+	0.354664i
$811$		−	22.1938i		−	0.779330i	−0.920957	−	0.389665i	$-0.872591\pi$
$811$		−	22.1938i		−	0.779330i	0.920957	−	0.389665i	$-0.127409\pi$
$812$	−50.6672	−	10.0485i	−1.77807	−	0.352635i
$813$	−5.24663	+	15.1999i	−0.184007	+	0.533084i
$814$	−0.381274	−	0.660386i	−0.0133636	−	0.0231465i
$815$	−42.4662	+	73.5536i	−1.48753	+	2.57647i
$816$	2.48267	−	2.15486i	0.0869110	−	0.0754350i
$817$	−8.73907	+	5.04551i	−0.305741	+	0.176520i
$818$	−8.87302			−0.310238
$819$	−7.79936	+	1.47308i	−0.272532	+	0.0514737i
$820$	42.5368			1.48545
$821$	35.1981	−	20.3216i	1.22842	−	0.709230i	0.261723	−	0.965143i	$-0.415709\pi$
$821$	35.1981	−	20.3216i	1.22842	−	0.709230i	0.966700	+	0.255913i	$0.0823761\pi$
$822$	7.05511	−	6.12354i	0.246075	−	0.213583i
$823$	−2.71653	+	4.70517i	−0.0946923	+	0.164012i	−0.909480	−	0.415747i	$-0.863520\pi$
$823$	−2.71653	+	4.70517i	−0.0946923	+	0.164012i	0.814788	+	0.579759i	$0.196853\pi$
$824$	3.01581	+	5.22354i	0.105061	+	0.181970i
$825$	4.55924	−	13.2085i	0.158733	−	0.459861i
$826$	1.42897	+	4.20181i	0.0497203	+	0.146200i
$827$		−	53.9947i		−	1.87758i	−0.344490	−	0.938790i	$-0.611948\pi$
$827$		−	53.9947i		−	1.87758i	0.344490	−	0.938790i	$-0.388052\pi$
$828$	14.6541	+	2.08215i	0.509267	+	0.0723598i
$829$	−0.944032	−	0.545037i	−0.0327876	−	0.0189299i	0.483517	−	0.875335i	$-0.339359\pi$
$829$	−0.944032	−	0.545037i	−0.0327876	−	0.0189299i	−0.516304	+	0.856405i	$0.672693\pi$
$830$	7.29826	+	4.21365i	0.253326	+	0.146258i
$831$	5.90133	+	30.4830i	0.204715	+	1.05744i
$832$		−	4.79355i		−	0.166186i
$833$	0.551943	+	4.15609i	0.0191237	+	0.144000i
$834$	6.36353	+	2.19653i	0.220351	+	0.0760597i
$835$	27.3774	+	47.4191i	0.947434	+	1.64100i
$836$	2.26465	−	3.92249i	0.0783246	−	0.135662i
$837$	−1.64990	−	32.9129i	−0.0570288	−	1.13764i
$838$	−9.45089	+	5.45647i	−0.326475	+	0.188491i
$839$	−49.5517			−1.71072			−0.855358	−	0.518038i	$-0.826663\pi$
$839$	−49.5517			−1.71072			−0.855358	+	0.518038i	$0.826663\pi$
$840$	0.125204	−	27.4852i	0.00431995	−	0.948328i
$841$	−81.3971			−2.80680
$842$	2.70986	−	1.56454i	0.0933878	−	0.0539175i
$843$	−22.4100	−	25.8192i	−0.771840	−	0.889260i
$844$	15.0285	−	26.0302i	0.517304	−	0.895997i
$845$	2.06368	+	3.57439i	0.0709926	+	0.122963i
$846$	3.92845	−	5.01251i	0.135063	−	0.172334i
$847$	−20.9976	−	18.3934i	−0.721485	−	0.632004i
$848$			11.2624i			0.386754i
$849$	41.4511	−	8.02470i	1.42260	−	0.275407i
$850$	−2.35129	−	1.35752i	−0.0806485	−	0.0465625i
$851$	6.94493	+	4.00966i	0.238069	+	0.137449i
$852$	31.0478	−	6.01067i	1.06368	−	0.205922i
$853$		−	40.8406i		−	1.39835i	−0.714949	−	0.699177i	$-0.753550\pi$
$853$		−	40.8406i		−	1.39835i	0.714949	−	0.699177i	$-0.246450\pi$
$854$	−1.90781	+	9.61965i	−0.0652840	+	0.329177i
$855$	−27.7742	+	35.4386i	−0.949859	+	1.21197i
$856$	−2.42191	−	4.19487i	−0.0827792	−	0.143378i
$857$	18.8011	−	32.5645i	0.642235	−	1.11238i	−0.342698	−	0.939446i	$-0.611341\pi$
$857$	18.8011	−	32.5645i	0.642235	−	1.11238i	0.984933	−	0.172938i	$-0.0553259\pi$
$858$	0.286654	+	0.330263i	0.00978621	+	0.0112750i
$859$	−42.3619	+	24.4577i	−1.44537	+	0.834485i	−0.998201	−	0.0599646i	$-0.980901\pi$
$859$	−42.3619	+	24.4577i	−1.44537	+	0.834485i	−0.447169	+	0.894449i	$0.647568\pi$
$860$	−21.2822			−0.725716
$861$	12.8087	−	21.9538i	0.436520	−	0.748182i
$862$	−5.19813			−0.177049
$863$	36.9536	−	21.3352i	1.25791	−	0.726257i	0.285246	−	0.958454i	$-0.407925\pi$
$863$	36.9536	−	21.3352i	1.25791	−	0.726257i	0.972669	+	0.232197i	$0.0745914\pi$
$864$	1.06661	+	21.2773i	0.0362869	+	0.723869i
$865$	21.6835	−	37.5569i	0.737261	−	1.27697i
$866$	0.805455	+	1.39509i	0.0273705	+	0.0474071i
$867$	27.2461	+	9.40467i	0.925325	+	0.319399i
$868$	−20.5441	+	23.4528i	−0.697313	+	0.796041i
$869$		−	10.2892i		−	0.349038i
$870$	−5.37723	−	27.7758i	−0.182305	−	0.941686i
$871$	−3.64276	−	2.10315i	−0.123430	−	0.0712626i
$872$	−10.4036	−	6.00655i	−0.352312	−	0.203407i
$873$	−45.8220	−	6.51067i	−1.55084	−	0.220353i
$874$		−	3.63676i		−	0.123015i
$875$	72.7313	−	24.7348i	2.45877	−	0.836190i
$876$	−0.763335	+	2.21144i	−0.0257907	+	0.0747177i
$877$	−14.0547	−	24.3435i	−0.474595	−	0.822022i	0.524982	−	0.851113i	$-0.324072\pi$
$877$	−14.0547	−	24.3435i	−0.474595	−	0.822022i	−0.999577	+	0.0290914i	$0.990739\pi$
$878$	1.84238	−	3.19110i	0.0621775	−	0.107695i
$879$	−8.46182	+	7.34450i	−0.285410	+	0.247724i
$880$	7.59278	−	4.38369i	0.255952	−	0.147774i
$881$	−27.6273			−0.930786			−0.465393	−	0.885104i	$-0.654087\pi$
$881$	−27.6273			−0.930786			−0.465393	+	0.885104i	$0.654087\pi$
$882$	−6.81375	−	4.01713i	−0.229431	−	0.135264i
$883$	6.77548			0.228013			0.114007	−	0.993480i	$-0.463632\pi$
$883$	6.77548			0.228013			0.114007	+	0.993480i	$0.463632\pi$
$884$	−0.963807	+	0.556455i	−0.0324164	+	0.0187156i
$885$	24.0440	−	20.8691i	0.808229	−	0.701509i
$886$	−2.31378	+	4.00759i	−0.0777331	+	0.134638i
$887$	14.1684	+	24.5403i	0.475727	+	0.823984i	0.999613	−	0.0278043i	$-0.00885152\pi$
$887$	14.1684	+	24.5403i	0.475727	+	0.823984i	−0.523886	+	0.851788i	$0.675518\pi$
$888$	−2.48035	+	7.18576i	−0.0832349	+	0.241138i
$889$	19.0775	−	6.48799i	0.639840	−	0.217600i
$890$		−	11.4131i		−	0.382569i
$891$	4.17768	+	4.35243i	0.139958	+	0.145812i
$892$	−1.62800	−	0.939925i	−0.0545094	−	0.0314710i
$893$	17.7488	+	10.2473i	0.593942	+	0.342912i
$894$	−1.42874	−	7.38010i	−0.0477844	−	0.246827i
$895$		−	37.9522i		−	1.26860i
$896$	17.4429	−	19.9125i	0.582726	−	0.665230i
$897$	−4.34731	−	1.50058i	−0.145152	−	0.0501030i
$898$	−4.99045	−	8.64371i	−0.166533	−	0.288444i
$899$	−33.3180	+	57.7084i	−1.11122	+	1.92468i
$900$	−62.2409	+	25.0373i	−2.07470	+	0.834578i
$901$	1.84347	−	1.06433i	0.0614150	−	0.0354580i
$902$	−1.40039			−0.0466280
$903$	−6.40850	+	10.9840i	−0.213262	+	0.365524i
$904$	12.9888			0.432003
$905$	−52.4052	+	30.2562i	−1.74201	+	1.00575i
$906$	6.92475	+	7.97822i	0.230059	+	0.265058i
$907$	−10.5246	+	18.2292i	−0.349465	+	0.605291i	−0.986154	−	0.165829i	$-0.946970\pi$
$907$	−10.5246	+	18.2292i	−0.349465	+	0.605291i	0.636690	+	0.771120i	$0.280303\pi$
$908$	−4.43036	−	7.67361i	−0.147027	−	0.254658i
$909$	−7.64834	−	5.99422i	−0.253679	−	0.198816i
$910$	−0.800137	+	4.03448i	−0.0265243	+	0.133742i
$911$		−	25.5666i		−	0.847061i	−0.905882	−	0.423530i	$-0.860791\pi$
$911$		−	25.5666i		−	0.847061i	0.905882	−	0.423530i	$-0.139209\pi$
$912$	−19.5951	+	3.79350i	−0.648858	+	0.125615i
$913$	3.14696	+	1.81690i	0.104149	+	0.0601306i
$914$	3.24590	+	1.87402i	0.107365	+	0.0619871i
$915$	69.0693	−	13.3714i	2.28336	−	0.442046i
$916$			29.2153i			0.965300i
$917$	−28.1759	−	24.6814i	−0.930449	−	0.815051i
$918$	0.984557	−	0.636202i	0.0324952	−	0.0209978i
$919$	13.4051	+	23.2183i	0.442194	+	0.765903i	0.997852	−	0.0655084i	$-0.0208669\pi$
$919$	13.4051	+	23.2183i	0.442194	+	0.765903i	−0.555658	+	0.831411i	$0.687534\pi$
$920$	7.96281	−	13.7920i	0.262526	−	0.454708i
$921$	−17.1214	−	19.7260i	−0.564168	−	0.649995i
$922$	−5.11862	+	2.95524i	−0.168573	+	0.0973256i
$923$	−9.82614			−0.323431
$924$	0.0260010	−	5.70782i	0.000855371	−	0.187773i
$925$	−36.3481			−1.19512
$926$	−9.25435	+	5.34300i	−0.304117	+	0.175582i
$927$	−4.64705	−	11.5522i	−0.152629	−	0.379424i
$928$	21.5392	−	37.3069i	0.707057	−	1.22466i
$929$	5.32379	+	9.22107i	0.174668	+	0.302534i	0.940046	−	0.341047i	$-0.110782\pi$
$929$	5.32379	+	9.22107i	0.174668	+	0.302534i	−0.765378	+	0.643580i	$0.777448\pi$
$930$	−16.1422	−	5.57189i	−0.529324	−	0.182709i
$931$	9.71441	−	23.5279i	0.318377	−	0.771096i
$932$		−	53.0854i		−	1.73887i
$933$	7.73347	+	39.9468i	0.253182	+	1.30780i
$934$	4.62099	+	2.66793i	0.151204	+	0.0872974i
$935$	−1.43507	−	0.828540i	−0.0469319	−	0.0270962i
$936$	0.613274	−	4.31621i	0.0200455	−	0.141080i
$937$			18.5079i			0.604627i	0.953209	+	0.302313i	$0.0977589\pi$
$937$			18.5079i			0.604627i	−0.953209	+	0.302313i	$0.902241\pi$
$938$	−1.34963	−	3.96852i	−0.0440671	−	0.129577i
$939$	12.0747	−	34.9813i	0.394043	−	1.14157i
$940$	21.6118	+	37.4327i	0.704898	+	1.22092i
$941$	−7.69614	+	13.3301i	−0.250887	+	0.434549i	−0.963770	−	0.266734i	$-0.914056\pi$
$941$	−7.69614	+	13.3301i	−0.250887	+	0.434549i	0.712883	+	0.701283i	$0.247389\pi$
$942$	−9.41756	+	8.17404i	−0.306841	+	0.266325i
$943$	12.7541	−	7.36360i	0.415332	−	0.239792i
$944$	14.1130			0.459338
$945$	−8.23786	+	56.1405i	−0.267978	+	1.82625i
$946$	0.700650			0.0227801
$947$	−5.12650	+	2.95979i	−0.166589	+	0.0961801i	−0.580976	−	0.813920i	$-0.697329\pi$
$947$	−5.12650	+	2.95979i	−0.166589	+	0.0961801i	0.414388	+	0.910101i	$0.363996\pi$
$948$	−37.3075	+	32.3813i	−1.21169	+	1.05170i
$949$	0.363456	−	0.629525i	0.0117983	−	0.0204352i
$950$	8.24192	+	14.2754i	0.267403	+	0.463156i
$951$	−10.4401	+	30.2459i	−0.338545	+	0.980792i
$952$	−2.25879	−	0.447974i	−0.0732079	−	0.0145189i
$953$			55.2301i			1.78908i	0.446989	+	0.894539i	$0.352496\pi$
$953$			55.2301i			1.78908i	−0.446989	+	0.894539i	$0.647504\pi$
$954$	−0.564937	+	3.97602i	−0.0182905	+	0.128728i
$955$	54.1006	+	31.2350i	1.75065	+	1.01074i
$956$	−23.4282	−	13.5263i	−0.757724	−	0.437472i
$957$	−2.31863	−	11.9767i	−0.0749506	−	0.387153i
$958$			5.30279i			0.171325i
$959$	37.1625	+	7.37023i	1.20004	+	0.237997i
$960$	−32.3926	−	11.1811i	−1.04547	−	0.360869i
$961$	4.61079	+	7.98612i	0.148735	+	0.257617i
$962$	0.568785	−	0.985165i	0.0183384	−	0.0317630i
$963$	3.73191	+	9.27725i	0.120259	+	0.298955i
$964$	−12.4647	+	7.19651i	−0.401461	+	0.231784i
$965$	9.96949			0.320929
$966$	−2.27344	−	3.97946i	−0.0731466	−	0.128037i
$967$	15.0451			0.483819			0.241909	−	0.970299i	$-0.422226\pi$
$967$	15.0451			0.483819			0.241909	+	0.970299i	$0.422226\pi$
$968$	13.2780	−	7.66604i	0.426770	−	0.246396i
$969$	2.47272	+	2.84889i	0.0794352	+	0.0915196i
$970$	−11.9916	+	20.7701i	−0.385029	+	0.666889i
$971$	3.83896	+	6.64927i	0.123198	+	0.213385i	0.921027	−	0.389498i	$-0.127352\pi$
$971$	3.83896	+	6.64927i	0.123198	+	0.213385i	−0.797829	+	0.602884i	$0.794018\pi$
$972$	2.63378	−	28.8454i	0.0844784	−	0.925217i
$973$	8.79038	+	25.8476i	0.281807	+	0.828635i
$974$			4.98069i			0.159592i
$975$	20.4653	−	3.96197i	0.655415	−	0.126884i
$976$	27.0074	+	15.5927i	0.864487	+	0.499112i
$977$	30.4153	+	17.5603i	0.973072	+	0.561803i	0.900171	−	0.435536i	$-0.143441\pi$
$977$	30.4153	+	17.5603i	0.973072	+	0.561803i	0.0729003	+	0.997339i	$0.476775\pi$
$978$	−13.1801	+	2.55158i	−0.421452	+	0.0815906i
$979$		−	4.92128i		−	0.157285i
$980$	42.5535	−	32.7290i	1.35932	−	1.04549i
$981$	19.5196	+	15.2981i	0.623214	+	0.488431i
$982$	4.17966	+	7.23938i	0.133378	+	0.231018i
$983$	−10.7605	+	18.6377i	−0.343205	+	0.594449i	−0.985026	−	0.172406i	$-0.944846\pi$
$983$	−10.7605	+	18.6377i	−0.343205	+	0.594449i	0.641821	+	0.766855i	$0.278179\pi$
$984$	9.15089	+	10.5430i	0.291720	+	0.336099i
$985$	49.9411	−	28.8335i	1.59126	−	0.918712i
$986$	−2.37032			−0.0754863
$987$	25.8272	+	0.117652i	0.822089	+	0.00374489i
$988$	6.75683			0.214963
$989$	−6.38120	+	3.68419i	−0.202910	+	0.117150i
$990$	2.90039	−	1.16673i	0.0921806	−	0.0370810i
$991$	−9.20760	+	15.9480i	−0.292489	+	0.506606i	−0.974398	−	0.224831i	$-0.927817\pi$
$991$	−9.20760	+	15.9480i	−0.292489	+	0.506606i	0.681909	+	0.731437i	$0.261150\pi$
$992$	−13.0011	−	22.5185i	−0.412785	−	0.714964i
$993$	20.0600	+	6.92423i	0.636586	+	0.219734i
$994$	−7.36575	−	6.45223i	−0.233627	−	0.204652i
$995$			8.06015i			0.255524i
$996$	−3.31598	−	17.1285i	−0.105071	−	0.542738i
$997$	−6.67542	−	3.85405i	−0.211413	−	0.122059i	0.390555	−	0.920580i	$-0.372283\pi$
$997$	−6.67542	−	3.85405i	−0.211413	−	0.122059i	−0.601968	+	0.798520i	$0.705616\pi$
$998$	−7.33677	−	4.23589i	−0.232242	−	0.134085i
$999$	7.15639	−	13.9667i	0.226418	−	0.441885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bh.a.248.18	yes	64
3.2	odd	2	inner	273.2.bh.a.248.15	yes	64
7.5	odd	6	inner	273.2.bh.a.131.15	✓	64
21.5	even	6	inner	273.2.bh.a.131.18	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.15	✓	64	7.5	odd	6	inner
273.2.bh.a.131.18	yes	64	21.5	even	6	inner
273.2.bh.a.248.15	yes	64	3.2	odd	2	inner
273.2.bh.a.248.18	yes	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.326193 - 0.188328i) q^{2} +(1.30806 - 1.13534i) q^{3} +(-0.929065 + 1.60919i) q^{4} +(-2.06368 - 3.57439i) q^{5} +(0.212864 - 0.616683i) q^{6} +(2.50486 - 0.851866i) q^{7} +1.45319i q^{8} +(0.422020 - 2.97017i) q^{9} +O(q^{10})\)	\(q+(0.326193 - 0.188328i) q^{2} +(1.30806 - 1.13534i) q^{3} +(-0.929065 + 1.60919i) q^{4} +(-2.06368 - 3.57439i) q^{5} +(0.212864 - 0.616683i) q^{6} +(2.50486 - 0.851866i) q^{7} +1.45319i q^{8} +(0.422020 - 2.97017i) q^{9} +(-1.34632 - 0.777295i) q^{10} +(-0.580523 - 0.335165i) q^{11} +(0.611702 + 3.15971i) q^{12} -1.00000i q^{13} +(0.656639 - 0.749608i) q^{14} +(-6.75754 - 2.33254i) q^{15} +(-1.58445 - 2.74436i) q^{16} +(-0.299470 + 0.518697i) q^{17} +(-0.421705 - 1.04833i) q^{18} +(3.14918 - 1.81818i) q^{19} +7.66916 q^{20} +(2.30934 - 3.95815i) q^{21} -0.252484 q^{22} +(2.29950 - 1.32762i) q^{23} +(1.64986 + 1.90085i) q^{24} +(-6.01752 + 10.4226i) q^{25} +(-0.188328 - 0.326193i) q^{26} +(-2.82012 - 4.36428i) q^{27} +(-0.956366 + 4.82223i) q^{28} +10.5070i q^{29} +(-2.64355 + 0.511776i) q^{30} +(5.49237 + 3.17102i) q^{31} +(-3.55067 - 2.04998i) q^{32} +(-1.13988 + 0.220674i) q^{33} +0.225594i q^{34} +(-8.21412 - 7.19538i) q^{35} +(4.38748 + 3.43859i) q^{36} +(1.51009 + 2.61556i) q^{37} +(0.684827 - 1.18616i) q^{38} +(-1.13534 - 1.30806i) q^{39} +(5.19426 - 2.99891i) q^{40} +5.54647 q^{41} +(0.00786267 - 1.72604i) q^{42} -2.77503 q^{43} +(1.07869 - 0.622780i) q^{44} +(-11.4875 + 4.62100i) q^{45} +(0.500055 - 0.866121i) q^{46} +(2.81801 + 4.88093i) q^{47} +(-5.18832 - 1.79088i) q^{48} +(5.54865 - 4.26761i) q^{49} +4.53306i q^{50} +(0.197173 + 1.01848i) q^{51} +(1.60919 + 0.929065i) q^{52} +(-3.07789 - 1.77702i) q^{53} +(-1.74182 - 0.892493i) q^{54} +2.76669i q^{55} +(1.23792 + 3.64003i) q^{56} +(2.05505 - 5.95366i) q^{57} +(1.97876 + 3.42732i) q^{58} +(-2.22679 + 3.85691i) q^{59} +(10.0317 - 8.70708i) q^{60} +(-8.52262 + 4.92054i) q^{61} +2.38877 q^{62} +(-1.47308 - 7.79936i) q^{63} +4.79355 q^{64} +(-3.57439 + 2.06368i) q^{65} +(-0.330263 + 0.286654i) q^{66} +(2.10315 - 3.64276i) q^{67} +(-0.556455 - 0.963807i) q^{68} +(1.50058 - 4.34731i) q^{69} +(-4.03448 - 0.800137i) q^{70} -9.82614i q^{71} +(4.31621 + 0.613274i) q^{72} +(0.629525 + 0.363456i) q^{73} +(0.985165 + 0.568785i) q^{74} +(3.96197 + 20.4653i) q^{75} +6.75683i q^{76} +(-1.73964 - 0.345014i) q^{77} +(-0.616683 - 0.212864i) q^{78} +(7.67474 + 13.2930i) q^{79} +(-6.53960 + 11.3269i) q^{80} +(-8.64380 - 2.50694i) q^{81} +(1.80922 - 1.04456i) q^{82} -5.42091 q^{83} +(4.22388 + 7.39354i) q^{84} +2.47204 q^{85} +(-0.905198 + 0.522616i) q^{86} +(11.9290 + 13.7437i) q^{87} +(0.487057 - 0.843608i) q^{88} +(3.67079 + 6.35799i) q^{89} +(-2.87687 + 3.67075i) q^{90} +(-0.851866 - 2.50486i) q^{91} +4.93378i q^{92} +(10.7845 - 2.08782i) q^{93} +(1.83843 + 1.06142i) q^{94} +(-12.9978 - 7.50426i) q^{95} +(-6.97189 + 1.34972i) q^{96} -15.4274i q^{97} +(1.00622 - 2.43703i) q^{98} +(-1.24049 + 1.58280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

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