LMFDB - Embedded newform 273.2.bh.a.131.15

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			131.15
Character	$\chi$	$=$	273.131
Dual form			273.2.bh.a.248.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.326193 - 0.188328i) q^{2} +(-0.329203 - 1.70048i) q^{3} +(-0.929065 - 1.60919i) q^{4} +(2.06368 - 3.57439i) q^{5} +(-0.212864 + 0.616683i) q^{6} +(2.50486 + 0.851866i) q^{7} +1.45319i q^{8} +(-2.78325 + 1.11960i) q^{9} +O(q^{10})$	\(q+(-0.326193 - 0.188328i) q^{2} +(-0.329203 - 1.70048i) 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} +(-2.78325 + 1.11960i) q^{9} +(-1.34632 + 0.777295i) q^{10} +(0.580523 - 0.335165i) q^{11} +(-2.43054 + 2.10960i) 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} +(1.11873 + 0.158956i) q^{18} +(3.14918 + 1.81818i) q^{19} -7.66916 q^{20} +(0.623972 - 4.53990i) q^{21} -0.252484 q^{22} +(-2.29950 - 1.32762i) q^{23} +(2.47111 - 0.478393i) 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} +(1.76498 + 2.03349i) q^{30} +(5.49237 - 3.17102i) q^{31} +(3.55067 - 2.04998i) q^{32} +(-0.761050 - 0.876829i) 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} +(1.70048 - 0.329203i) q^{39} +(5.19426 + 2.99891i) q^{40} -5.54647 q^{41} +(-1.05852 + 1.36337i) q^{42} -2.77503 q^{43} +(-1.07869 - 0.622780i) q^{44} +(-1.74182 + 12.2589i) 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} +(0.783447 - 0.679999i) q^{51} +(1.60919 - 0.929065i) q^{52} +(3.07789 - 1.77702i) q^{53} +(-0.0979878 - 1.95471i) 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} +(2.52471 + 13.0412i) q^{60} +(-8.52262 - 4.92054i) q^{61} -2.38877 q^{62} +(-7.92541 + 0.433496i) q^{63} +4.79355 q^{64} +(3.57439 + 2.06368i) q^{65} +(0.0831183 + 0.429343i) 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} +(-1.62699 - 4.04458i) q^{72} +(0.629525 - 0.363456i) q^{73} +(-0.985165 + 0.568785i) q^{74} +(-15.7425 + 13.6638i) 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} +(6.49297 - 6.23228i) q^{81} +(1.80922 + 1.04456i) q^{82} +5.42091 q^{83} +(-7.88526 + 3.21377i) q^{84} +2.47204 q^{85} +(0.905198 + 0.522616i) q^{86} +(17.8669 - 3.45893i) 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} +(-7.20036 - 8.29575i) q^{93} +(1.83843 - 1.06142i) q^{94} +(12.9978 - 7.50426i) q^{95} +(-4.65484 - 5.36298i) 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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	$-0.375848\pi$
$2$	−0.326193	−	0.188328i	−0.230654	−	0.133168i	−0.610874	+	0.791728i	$0.709182\pi$
$3$	−0.329203	−	1.70048i	−0.190065	−	0.981771i
$3$	−0.329203	−	1.70048i	−0.190065	−	0.981771i
$4$	−0.929065	−	1.60919i	−0.464533	−	0.804594i
$5$	2.06368	−	3.57439i	0.922904	−	1.59852i	0.128006	−	0.991773i	$-0.459142\pi$
$5$	2.06368	−	3.57439i	0.922904	−	1.59852i	0.794898	−	0.606743i	$-0.207524\pi$
$6$	−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
$9$	−2.78325	+	1.11960i	−0.927750	+	0.373201i
$10$	−1.34632	+	0.777295i	−0.425742	+	0.245802i
$11$	0.580523	−	0.335165i	0.175034	−	0.101056i	−0.409923	−	0.912120i	$-0.634445\pi$
$11$	0.580523	−	0.335165i	0.175034	−	0.101056i	0.584957	+	0.811064i	$0.301111\pi$
$12$	−2.43054	+	2.10960i	−0.701636	+	0.608990i
$13$			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	$-0.143527\pi$
$17$	0.299470	+	0.518697i	0.0726322	+	0.125803i	−0.827422	+	0.561581i	$0.810193\pi$
$18$	1.11873	+	0.158956i	0.263687	+	0.0374663i
$19$	3.14918	+	1.81818i	0.722471	+	0.417119i	0.815661	−	0.578530i	$-0.196373\pi$
$19$	3.14918	+	1.81818i	0.722471	+	0.417119i	−0.0931906	+	0.995648i	$0.529707\pi$
$20$	−7.66916			−1.71488
$21$	0.623972	−	4.53990i	0.136162	−	0.990687i
$22$	−0.252484			−0.0538297
$23$	−2.29950	−	1.32762i	−0.479480	−	0.276828i	0.240720	−	0.970595i	$-0.422616\pi$
$23$	−2.29950	−	1.32762i	−0.479480	−	0.276828i	−0.720200	+	0.693767i	$0.755950\pi$
$24$	2.47111	−	0.478393i	0.504414	−	0.0976516i
$25$	−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	$0.570532\pi$
$30$	1.76498	+	2.03349i	0.322241	+	0.371263i
$31$	5.49237	−	3.17102i	0.986460	−	0.569533i	0.0822455	−	0.996612i	$-0.473791\pi$
$31$	5.49237	−	3.17102i	0.986460	−	0.569533i	0.904214	+	0.427079i	$0.140458\pi$
$32$	3.55067	−	2.04998i	0.627676	−	0.362389i
$33$	−0.761050	−	0.876829i	−0.132482	−	0.152636i
$34$		−	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	−0.714785	−	0.699345i	$-0.753475\pi$
$37$	1.51009	−	2.61556i	0.248258	−	0.429995i	0.963043	+	0.269349i	$0.0868086\pi$
$38$	−0.684827	−	1.18616i	−0.111094	−	0.192420i
$39$	1.70048	−	0.329203i	0.272294	−	0.0527146i
$40$	5.19426	+	2.99891i	0.821285	+	0.474169i
$41$	−5.54647			−0.866214			−0.433107	−	0.901343i	$-0.642583\pi$
$41$	−5.54647			−0.866214			−0.433107	+	0.901343i	$0.642583\pi$
$42$	−1.05852	+	1.36337i	−0.163334	+	0.210373i
$43$	−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
$45$	−1.74182	+	12.2589i	−0.259656	+	1.82745i
$46$	0.500055	+	0.866121i	0.0737291	+	0.127703i
$47$	−2.81801	+	4.88093i	−0.411049	+	0.711957i	−0.995005	−	0.0998279i	$-0.968171\pi$
$47$	−2.81801	+	4.88093i	−0.411049	+	0.711957i	0.583956	+	0.811785i	$0.301504\pi$
$48$	5.18832	+	1.79088i	0.748870	+	0.258491i
$49$	5.54865	+	4.26761i	0.792664	+	0.609658i
$50$			4.53306i			0.641072i
$51$	0.783447	−	0.679999i	0.109705	−	0.0952189i
$52$	1.60919	−	0.929065i	0.223154	−	0.128838i
$53$	3.07789	−	1.77702i	0.422781	−	0.244093i	−0.273485	−	0.961876i	$-0.588177\pi$
$53$	3.07789	−	1.77702i	0.422781	−	0.244093i	0.696266	+	0.717783i	$0.254843\pi$
$54$	−0.0979878	−	1.95471i	−0.0133344	−	0.266002i
$55$		−	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	$-0.0730437\pi$
$59$	2.22679	+	3.85691i	0.289903	+	0.502126i	−0.683884	+	0.729591i	$0.739710\pi$
$60$	2.52471	+	13.0412i	0.325938	+	1.68362i
$61$	−8.52262	−	4.92054i	−1.09121	−	0.630011i	−0.157312	−	0.987549i	$-0.550283\pi$
$61$	−8.52262	−	4.92054i	−1.09121	−	0.630011i	−0.933898	+	0.357538i	$0.883616\pi$
$62$	−2.38877			−0.303374
$63$	−7.92541	+	0.433496i	−0.998507	+	0.0546154i
$64$	4.79355			0.599193
$65$	3.57439	+	2.06368i	0.443349	+	0.255968i
$66$	0.0831183	+	0.429343i	0.0102312	+	0.0528485i
$67$	2.10315	+	3.64276i	0.256941	+	0.445035i	0.965421	−	0.260696i	$-0.0839521\pi$
$67$	2.10315	+	3.64276i	0.256941	+	0.445035i	−0.708480	+	0.705731i	$0.750619\pi$
$68$	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	$-0.198150\pi$
$72$	−1.62699	−	4.04458i	−0.191743	−	0.476659i
$73$	0.629525	−	0.363456i	0.0736803	−	0.0425393i	−0.462707	−	0.886511i	$-0.653122\pi$
$73$	0.629525	−	0.363456i	0.0736803	−	0.0425393i	0.536388	+	0.843972i	$0.319789\pi$
$74$	−0.985165	+	0.568785i	−0.114523	+	0.0661200i
$75$	−15.7425	+	13.6638i	−1.81779	+	1.57776i
$76$		−	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	−0.00507650	−	0.999987i	$-0.501616\pi$
$79$	7.67474	−	13.2930i	0.863476	−	1.49558i	0.868552	−	0.495597i	$-0.165051\pi$
$80$	6.53960	+	11.3269i	0.731150	+	1.26639i
$81$	6.49297	−	6.23228i	0.721441	−	0.692475i
$82$	1.80922	+	1.04456i	0.199795	+	0.115352i
$83$	5.42091			0.595022			0.297511	−	0.954718i	$-0.403843\pi$
$83$	5.42091			0.595022			0.297511	+	0.954718i	$0.403843\pi$
$84$	−7.88526	+	3.21377i	−0.860352	+	0.350651i
$85$	2.47204			0.268130
$86$	0.905198	+	0.522616i	0.0976100	+	0.0563551i
$87$	17.8669	−	3.45893i	1.91554	−	0.370837i
$88$	0.487057	+	0.843608i	0.0519205	+	0.0899289i
$89$	−3.67079	+	6.35799i	−0.389103	+	0.673946i	−0.992329	−	0.123624i	$-0.960548\pi$
$89$	−3.67079	+	6.35799i	−0.389103	+	0.673946i	0.603226	+	0.797570i	$0.293882\pi$
$90$	2.87687	−	3.67075i	0.303249	−	0.386931i
$91$	−0.851866	+	2.50486i	−0.0892998	+	0.262581i
$92$			4.93378i			0.514382i
$93$	−7.20036	−	8.29575i	−0.746643	−	0.860230i
$94$	1.83843	−	1.06142i	0.189620	−	0.109477i
$95$	12.9978	−	7.50426i	1.33354	−	0.769921i
$96$	−4.65484	−	5.36298i	−0.475082	−	0.547357i
$97$			15.4274i			1.56642i	0.621760	+	0.783208i	$0.286418\pi$
$97$			15.4274i			1.56642i	−0.621760	+	0.783208i	$0.713582\pi$
$98$	−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	$-0.218188\pi$
$101$	−1.61957	−	2.80517i	−0.161153	−	0.279125i	−0.935282	+	0.353902i	$0.884855\pi$
$102$	−0.383618	+	0.0742663i	−0.0379838	+	0.00735345i
$103$	3.59454	+	2.07531i	0.354180	+	0.204486i	0.666525	−	0.745483i	$-0.267781\pi$
$103$	3.59454	+	2.07531i	0.354180	+	0.204486i	−0.312345	+	0.949969i	$0.601114\pi$
$104$	−1.45319			−0.142497
$105$	−14.9397	−	11.5992i	−1.45796	−	1.13197i
$106$	−1.33865			−0.130021
$107$	2.88667	+	1.66662i	0.279065	+	0.161118i	0.633000	−	0.774152i	$-0.281823\pi$
$107$	2.88667	+	1.66662i	0.279065	+	0.161118i	−0.353935	+	0.935270i	$0.615157\pi$
$108$	4.40288	−	8.59280i	0.423667	−	0.826842i
$109$	−4.13336	−	7.15919i	−0.395904	−	0.685726i	0.597312	−	0.802009i	$-0.296235\pi$
$109$	−4.13336	−	7.15919i	−0.395904	−	0.685726i	−0.993216	+	0.116283i	$0.962902\pi$
$110$	−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	$-0.138116\pi$
$114$	−1.79158	+	1.55502i	−0.167797	+	0.145641i
$115$	−9.49086	+	5.47955i	−0.885027	+	0.510971i
$116$	16.9077	−	9.76169i	1.56984	−	0.906350i
$117$	−1.11960	−	2.78325i	−0.103507	−	0.257312i
$118$		−	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
$123$	1.82591	+	9.43166i	0.164637	+	0.850424i
$124$	−10.2055	−	5.89218i	−0.916485	−	0.529133i
$125$	−29.0361			−2.59706
$126$	2.66686	+	1.35117i	0.237582	+	0.120372i
$127$	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
$129$	0.913549	+	4.71888i	0.0804335	+	0.415474i
$130$	−0.777295	−	1.34632i	−0.0681733	−	0.118080i
$131$	7.07877	−	12.2608i	0.618475	−	1.07123i	−0.371289	−	0.928517i	$-0.621084\pi$
$131$	7.07877	−	12.2608i	0.618475	−	1.07123i	0.989764	−	0.142712i	$-0.0455824\pi$
$132$	−0.703917	+	2.03930i	−0.0612681	+	0.177499i
$133$	6.33941	+	7.23696i	0.549696	+	0.627524i
$134$		−	1.58433i		−	0.136865i
$135$	21.4195	−	1.07374i	1.84349	−	0.0924128i
$136$	−0.753764	+	0.435186i	−0.0646348	+	0.0373169i
$137$	−12.4012	+	7.15984i	−1.05951	+	0.611706i	−0.925296	−	0.379247i	$-0.876183\pi$
$137$	−12.4012	+	7.15984i	−1.05951	+	0.611706i	−0.134210	+	0.990953i	$0.542850\pi$
$138$	1.30820	−	1.13546i	0.111361	−	0.0966570i
$139$		−	10.3190i		−	0.875244i	−0.899159	−	0.437622i	$-0.855821\pi$
$139$		−	10.3190i		−	0.875244i	0.899159	−	0.437622i	$-0.144179\pi$
$140$	−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
$144$	1.33734	−	9.41220i	0.111445	−	0.784350i
$145$	37.5561	+	21.6830i	3.11887	+	1.80068i
$146$	−0.273796			−0.0226595
$147$	5.43034	−	10.8403i	0.447887	−	0.894090i
$148$	−5.61190			−0.461295
$149$	−9.97877	−	5.76125i	−0.817493	−	0.471980i	0.0320582	−	0.999486i	$-0.489794\pi$
$149$	−9.97877	−	5.76125i	−0.817493	−	0.471980i	−0.849551	+	0.527506i	$0.823127\pi$
$150$	7.70838	−	1.49230i	0.629386	−	0.121846i
$151$	−8.09664	−	14.0238i	−0.658895	−	1.14124i	−0.980902	−	0.194503i	$-0.937691\pi$
$151$	−8.09664	−	14.0238i	−0.658895	−	1.14124i	0.322007	−	0.946737i	$-0.395643\pi$
$152$	−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
$156$	−2.10960	−	2.43054i	−0.168904	−	0.194599i
$157$	−16.5538	+	9.55735i	−1.32114	+	0.762760i	−0.983910	−	0.178663i	$-0.942823\pi$
$157$	−16.5538	+	9.55735i	−1.32114	+	0.762760i	−0.337228	+	0.941423i	$0.609489\pi$
$158$	−5.00690	+	2.89074i	−0.398328	+	0.229975i
$159$	−4.03504	−	4.64889i	−0.319999	−	0.368681i
$160$		−	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	0.109792	+	0.993955i	$0.464981\pi$
$163$	−10.2890	+	17.8210i	−0.805894	+	1.39585i	−0.915686	+	0.401894i	$0.868352\pi$
$164$	5.15304	+	8.92532i	0.402385	+	0.696951i
$165$	−4.70469	+	0.910801i	−0.366260	+	0.0709058i
$166$	−1.76827	−	1.02091i	−0.137244	−	0.0792379i
$167$	13.2663			1.02658			0.513290	−	0.858215i	$-0.328427\pi$
$167$	13.2663			1.02658			0.513290	+	0.858215i	$0.328427\pi$
$168$	6.59732	+	0.906748i	0.508994	+	0.0699571i
$169$	−1.00000			−0.0769231
$170$	−0.806362	−	0.465553i	−0.0618452	−	0.0357063i
$171$	−10.8006	−	1.53461i	−0.825942	−	0.117355i
$172$	2.57819	+	4.46555i	0.196585	+	0.340495i
$173$	−5.25361	+	9.09952i	−0.399424	+	0.691824i	−0.993655	−	0.112471i	$-0.964123\pi$
$173$	−5.25361	+	9.09952i	−0.399424	+	0.691824i	0.594230	+	0.804295i	$0.297457\pi$
$174$	−6.47949	−	2.23656i	−0.491209	−	0.169553i
$175$	−6.19435	−	31.2334i	−0.468249	−	2.36102i
$176$			2.12422i			0.160119i
$177$	5.82552	−	5.05630i	0.437873	−	0.380055i
$178$	2.39477	−	1.38262i	0.179496	−	0.103632i
$179$	−7.96336	+	4.59765i	−0.595209	+	0.343644i	−0.767155	−	0.641462i	$-0.778328\pi$
$179$	−7.96336	+	4.59765i	−0.595209	+	0.343644i	0.171945	+	0.985106i	$0.444995\pi$
$180$	21.3452	−	8.58642i	1.59098	−	0.639994i
$181$			14.6613i			1.08977i	0.838512	+	0.544883i	$0.183426\pi$
$181$			14.6613i			1.08977i	−0.838512	+	0.544883i	$0.816574\pi$
$182$	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
$186$	0.786389	+	4.06205i	0.0576609	+	0.297844i
$187$	0.347698	+	0.200744i	0.0254262	+	0.0146798i
$188$	10.4725			0.763782
$189$	3.34622	+	13.3343i	0.243401	+	0.969926i
$190$	−5.65305			−0.410115
$191$	13.1078	+	7.56781i	0.948449	+	0.547587i	0.892599	−	0.450852i	$-0.148880\pi$
$191$	13.1078	+	7.56781i	0.948449	+	0.547587i	0.0558501	+	0.998439i	$0.482213\pi$
$192$	−1.57805	−	8.15132i	−0.113886	−	0.588271i
$193$	−1.20773	−	2.09186i	−0.0869346	−	0.150575i	0.819279	−	0.573395i	$-0.194374\pi$
$193$	−1.20773	−	2.09186i	−0.0869346	−	0.150575i	−0.906214	+	0.422819i	$0.861040\pi$
$194$	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	$0.834168\pi$
$198$	0.702725	−	0.282682i	0.0499405	−	0.0200893i
$199$	−1.69123	+	0.976431i	−0.119888	+	0.0692174i	−0.558745	−	0.829340i	$-0.688717\pi$
$199$	−1.69123	+	0.976431i	−0.119888	+	0.0692174i	0.438857	+	0.898557i	$0.355384\pi$
$200$	15.1461	−	8.74458i	1.07099	−	0.618335i
$201$	5.50208	−	4.77557i	0.388087	−	0.336843i
$202$			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
$207$	7.88650	+	1.12056i	0.548150	+	0.0778845i
$208$	−2.74436	−	1.58445i	−0.190287	−	0.109862i
$209$	2.43756			0.168609
$210$	2.68878	+	6.59714i	0.185543	+	0.455246i
$211$	−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
$213$	−16.7091	+	3.23479i	−1.14489	+	0.221644i
$214$	−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
$219$	−0.825291	−	0.950842i	−0.0557680	−	0.0642520i
$220$	−4.45212	+	2.57043i	−0.300162	+	0.173299i
$221$	−0.518697	+	0.299470i	−0.0348914	+	0.0201445i
$222$	1.29153	+	1.48801i	0.0866816	+	0.0998684i
$223$		−	1.01169i		−	0.0677477i	−0.999426	−	0.0338739i	$-0.989216\pi$
$223$		−	1.01169i		−	0.0677477i	0.999426	−	0.0338739i	$-0.0107844\pi$
$224$	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	$-0.116081\pi$
$227$	2.38431	+	4.12975i	0.158252	+	0.274101i	−0.775986	+	0.630750i	$0.782747\pi$
$228$	−11.4898	+	2.22437i	−0.760933	+	0.147312i
$229$	13.6165	+	7.86147i	0.899801	+	0.519500i	0.877136	−	0.480243i	$-0.159451\pi$
$229$	13.6165	+	7.86147i	0.899801	+	0.519500i	0.0226655	+	0.999743i	$0.492785\pi$
$230$	4.12781			0.272180
$231$	−1.15938	−	2.84465i	−0.0762819	−	0.187164i
$232$	−15.2686			−1.00244
$233$	24.7417	+	14.2846i	1.62088	+	0.935818i	0.986684	+	0.162648i	$0.0520035\pi$
$233$	24.7417	+	14.2846i	1.62088	+	0.935818i	0.634199	+	0.773170i	$0.281330\pi$
$234$	−0.158956	+	1.11873i	−0.0103913	+	0.0731337i
$235$	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	$0.843939\pi$
$240$	17.1083	−	14.8493i	1.10434	−	0.958519i
$241$	6.70820	−	3.87298i	0.432113	−	0.249481i	−0.268133	−	0.963382i	$-0.586407\pi$
$241$	6.70820	−	3.87298i	0.432113	−	0.249481i	0.700247	+	0.713901i	$0.253073\pi$
$242$	3.44156	−	1.98698i	0.221232	−	0.127728i
$243$	−12.7354	−	8.98947i	−0.816974	−	0.576675i
$244$			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
$249$	−1.78458	−	9.21814i	−0.113093	−	0.584176i
$250$	9.47137	+	5.46830i	0.599022	+	0.345846i
$251$	6.72085			0.424216			0.212108	−	0.977246i	$-0.431967\pi$
$251$	6.72085			0.424216			0.212108	+	0.977246i	$0.431967\pi$
$252$	8.06080	+	12.3507i	0.507782	+	0.778023i
$253$	−1.77989			−0.111900
$254$	−2.48436	−	1.43434i	−0.155882	−	0.0899988i
$255$	−0.813801	−	4.20364i	−0.0509622	−	0.263242i
$256$	−2.90924	−	5.03896i	−0.181828	−	0.314935i
$257$	−7.92158	+	13.7206i	−0.494135	+	0.855867i	−0.999977	−	0.00675933i	$-0.997848\pi$
$257$	−7.92158	+	13.7206i	−0.494135	+	0.855867i	0.505842	+	0.862626i	$0.331182\pi$
$258$	0.590704	−	1.71132i	0.0367756	−	0.106542i
$259$	6.01068	−	5.26521i	0.373485	−	0.327164i
$260$		−	7.66916i		−	0.475621i
$261$	−11.7637	−	29.2436i	−0.728154	−	1.81014i
$262$	−4.61809	+	2.66626i	−0.285307	+	0.164722i
$263$	−5.85189	+	3.37859i	−0.360843	+	0.208333i	−0.669451	−	0.742857i	$-0.733470\pi$
$263$	−5.85189	+	3.37859i	−0.360843	+	0.208333i	0.308607	+	0.951190i	$0.400137\pi$
$264$	1.27420	−	1.10595i	0.0784214	−	0.0680664i
$265$		−	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	$-0.132714\pi$
$269$	1.74611	+	3.02435i	0.106462	+	0.184398i	−0.807872	+	0.589357i	$0.799381\pi$
$270$	−7.18910	−	3.68363i	−0.437515	−	0.224179i
$271$	−8.03997	−	4.64188i	−0.488393	−	0.281974i	0.235514	−	0.971871i	$-0.424323\pi$
$271$	−8.03997	−	4.64188i	−0.488393	−	0.281974i	−0.723908	+	0.689897i	$0.757656\pi$
$272$	−1.89799			−0.115082
$273$	4.53990	+	0.623972i	0.274767	+	0.0377645i
$274$	5.39359			0.325838
$275$	−6.98661	−	4.03372i	−0.421309	−	0.243243i
$276$	8.38978	−	1.62421i	0.505005	−	0.0977661i
$277$	−8.96306	−	15.5245i	−0.538538	−	0.932775i	−0.998983	−	0.0450872i	$-0.985643\pi$
$277$	−8.96306	−	15.5245i	−0.538538	−	0.932775i	0.460445	−	0.887688i	$-0.347690\pi$
$278$	−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	$-0.200381\pi$
$282$	−2.41014	−	2.77679i	−0.143522	−	0.165355i
$283$	21.1104	−	12.1881i	1.25488	−	0.724506i	0.282806	−	0.959177i	$-0.408735\pi$
$283$	21.1104	−	12.1881i	1.25488	−	0.724506i	0.972075	+	0.234671i	$0.0754014\pi$
$284$	−15.8121	+	9.12913i	−0.938276	+	0.541714i
$285$	−17.0397	−	19.6320i	−1.00935	−	1.16290i
$286$		−	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
$291$	26.2340	−	5.07874i	1.53786	−	0.297721i
$292$	−1.16974	−	0.675349i	−0.0684538	−	0.0395218i
$293$	6.46901			0.377923			0.188962	−	0.981984i	$-0.439488\pi$
$293$	6.46901			0.377923			0.188962	+	0.981984i	$0.439488\pi$
$294$	−3.81287	+	2.51334i	−0.222371	+	0.146581i
$295$	18.3815			1.07021
$296$	3.80090	+	2.19445i	0.220923	+	0.127550i
$297$	3.09990	+	1.58836i	0.179874	+	0.0921660i
$298$	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
$303$	−4.23697	+	3.67751i	−0.243407	+	0.211267i
$304$	−9.97946	+	5.76164i	−0.572361	+	0.330453i
$305$	−35.1759	+	20.3088i	−2.01416	+	1.16288i
$306$	0.252576	+	0.627885i	0.0144388	+	0.0358938i
$307$			15.0804i			0.860685i	0.902666	+	0.430342i	$0.141607\pi$
$307$			15.0804i			0.860685i	−0.902666	+	0.430342i	$0.858393\pi$
$308$	−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	0.979002	+	0.203850i	$0.0653455\pi$
$311$	11.7458	+	20.3442i	0.666040	+	1.15362i	−0.312962	+	0.949766i	$0.601321\pi$
$312$	0.478393	+	2.47111i	0.0270837	+	0.139899i
$313$	18.5033	+	10.6829i	1.04587	+	0.603833i	0.921490	−	0.388401i	$-0.126973\pi$
$313$	18.5033	+	10.6829i	1.04587	+	0.603833i	0.124380	+	0.992235i	$0.460306\pi$
$314$	7.19966			0.406300
$315$	−14.8060	+	29.2231i	−0.834223	+	1.64654i
$316$	−28.5213			−1.60445
$317$	15.9985	+	9.23676i	0.898568	+	0.518788i	0.876735	−	0.480973i	$-0.159717\pi$
$317$	15.9985	+	9.23676i	0.898568	+	0.518788i	0.0218326	+	0.999762i	$0.493050\pi$
$318$	0.440688	+	2.27635i	0.0247125	+	0.127651i
$319$	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
$324$	−16.0613	−	4.65822i	−0.892295	−	0.258790i
$325$	10.4226	−	6.01752i	0.578144	−	0.333792i
$326$	6.71238	−	3.87540i	0.371765	−	0.214638i
$327$	−10.8133	+	9.38552i	−0.597979	+	0.519020i
$328$		−	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	−0.647093	−	0.762411i	$-0.724015\pi$
$331$	6.12611	−	10.6107i	0.336721	−	0.583218i	0.983814	+	0.179193i	$0.0573487\pi$
$332$	−5.03638	−	8.72327i	−0.276407	−	0.478752i
$333$	−1.27458	+	8.97046i	−0.0698465	+	0.491578i
$334$	−4.32739	−	2.49842i	−0.236784	−	0.136707i
$335$	17.3609			0.948527
$336$	11.4704	+	8.90566i	0.625764	+	0.485844i
$337$	−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
$339$	−15.1992	+	2.94247i	−0.825506	+	0.159813i
$340$	−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
$345$	12.4423	+	14.3351i	0.669869	+	0.771777i
$346$	3.42739	−	1.97880i	0.184257	−	0.106381i
$347$	−10.0494	+	5.80201i	−0.539479	+	0.311468i	−0.744868	−	0.667212i	$-0.767487\pi$
$347$	−10.0494	+	5.80201i	−0.539479	+	0.311468i	0.205389	+	0.978680i	$0.434154\pi$
$348$	−22.1656	−	25.5377i	−1.18820	−	1.36896i
$349$		−	0.846216i		−	0.0452969i	−0.999743	−	0.0226485i	$-0.992790\pi$
$349$		−	0.846216i		−	0.0452969i	0.999743	−	0.0226485i	$-0.00720984\pi$
$350$	−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	−0.977910	−	0.209025i	$-0.932971\pi$
$353$	−12.5877	−	21.8025i	−0.669976	−	1.16043i	0.307935	−	0.951408i	$-0.400362\pi$
$354$	−2.85249	+	0.552225i	−0.151608	+	0.0293505i
$355$	−35.1225	−	20.2780i	−1.86411	−	1.07624i
$356$	13.6416			0.723004
$357$	2.54169	−	1.03591i	0.134521	−	0.0548262i
$358$	3.46346			0.183050
$359$	−6.10737	−	3.52609i	−0.322335	−	0.186100i	0.330098	−	0.943947i	$-0.392918\pi$
$359$	−6.10737	−	3.52609i	−0.322335	−	0.186100i	−0.652433	+	0.757847i	$0.726251\pi$
$360$	−17.8145	−	2.53120i	−0.938907	−	0.133406i
$361$	−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
$366$	4.84857	−	4.20835i	0.253439	−	0.219974i
$367$	1.25896	−	0.726863i	0.0657174	−	0.0379419i	−0.466781	−	0.884373i	$-0.654586\pi$
$367$	1.25896	−	0.726863i	0.0657174	−	0.0379419i	0.532499	+	0.846431i	$0.321253\pi$
$368$	7.28692	−	4.20710i	0.379857	−	0.219310i
$369$	15.4372	−	6.20986i	0.803630	−	0.323272i
$370$			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	−0.880542	−	0.473968i	$-0.842821\pi$
$373$	−0.575580	+	0.996933i	−0.0298024	+	0.0516192i	0.850740	+	0.525588i	$0.176154\pi$
$374$	−0.0756113	−	0.130963i	−0.00390977	−	0.00677192i
$375$	9.55875	+	49.3752i	0.493612	+	2.54972i
$376$	−7.09291	−	4.09509i	−0.365789	−	0.211188i
$377$	−10.5070			−0.541138
$378$	1.41970	−	4.97974i	0.0730216	−	0.256130i
$379$	−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
$381$	−2.50728	−	12.9512i	−0.128452	−	0.663510i
$382$	−2.85046	−	4.93714i	−0.145842	−	0.252606i
$383$	−1.13541	+	1.96659i	−0.0580167	+	0.100488i	−0.893575	−	0.448914i	$-0.851811\pi$
$383$	−1.13541	+	1.96659i	−0.0580167	+	0.100488i	0.835558	+	0.549402i	$0.185144\pi$
$384$	−5.65448	+	16.3815i	−0.288554	+	0.835965i
$385$	2.35685	−	6.93017i	0.120116	−	0.353194i
$386$			0.909800i			0.0463076i
$387$	7.72361	−	3.10694i	0.392613	−	0.157935i
$388$	24.8256	−	14.3331i	1.26033	−	0.727651i
$389$	−19.5369	+	11.2796i	−0.990561	+	0.571901i	−0.905442	−	0.424470i	$-0.860460\pi$
$389$	−19.5369	+	11.2796i	−0.990561	+	0.571901i	−0.0851189	+	0.996371i	$0.527127\pi$
$390$	−2.03349	+	1.76498i	−0.102970	+	0.0893735i
$391$		−	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
$396$	3.69952	+	0.525651i	0.185908	+	0.0264150i
$397$	−4.37371	−	2.52516i	−0.219510	−	0.126734i	0.386213	−	0.922410i	$-0.373783\pi$
$397$	−4.37371	−	2.52516i	−0.219510	−	0.126734i	−0.605724	+	0.795675i	$0.707116\pi$
$398$	0.735557			0.0368701
$399$	10.2193	−	13.1624i	0.511607	−	0.658947i
$400$	38.1379			1.90690
$401$	−28.3341	−	16.3587i	−1.41494	−	0.816915i	−0.419090	−	0.907945i	$-0.637651\pi$
$401$	−28.3341	−	16.3587i	−1.41494	−	0.816915i	−0.995848	+	0.0910299i	$0.970984\pi$
$402$	−2.69411	+	0.521565i	−0.134370	+	0.0260133i
$403$	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
$408$	0.988166	+	1.13850i	0.0489215	+	0.0563639i
$409$	−20.4013	+	11.7787i	−1.00878	+	0.582419i	−0.910834	−	0.412773i	$-0.864560\pi$
$409$	−20.4013	+	11.7787i	−1.00878	+	0.582419i	−0.0979449	+	0.995192i	$0.531227\pi$
$410$	7.46730	−	4.31125i	0.368784	−	0.212917i
$411$	16.2577	+	18.7309i	0.801931	+	0.923929i
$412$		−	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
$417$	−17.5472	+	3.39703i	−0.859289	+	0.166353i
$418$	−0.795116	−	0.459060i	−0.0388904	−	0.0224534i
$419$	28.9733			1.41544			0.707718	−	0.706495i	$-0.249725\pi$
$419$	28.9733			1.41544			0.707718	+	0.706495i	$0.249725\pi$
$420$	−4.78534	+	34.8172i	−0.233501	+	1.69890i
$421$	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
$423$	2.37851	−	16.7399i	0.115647	−	0.813923i
$424$	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
$429$	0.876829	−	0.761050i	0.0423337	−	0.0367439i
$430$	3.73607	−	2.15702i	0.180169	−	0.104021i
$431$	11.9518	−	6.90038i	0.575698	−	0.332380i	−0.183724	−	0.982978i	$-0.558815\pi$
$431$	11.9518	−	6.90038i	0.575698	−	0.332380i	0.759422	+	0.650598i	$0.225482\pi$
$432$	−16.4455	+	0.824399i	−0.791234	+	0.0396639i
$433$		−	4.27688i		−	0.205534i	−0.994705	−	0.102767i	$-0.967230\pi$
$433$		−	4.27688i		−	0.205534i	0.994705	−	0.102767i	$-0.0327695\pi$
$434$	−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
$438$	0.0901343	+	0.465584i	0.00430679	+	0.0222465i
$439$	8.47220	+	4.89143i	0.404356	+	0.233455i	0.688362	−	0.725367i	$-0.258330\pi$
$439$	8.47220	+	4.89143i	0.404356	+	0.233455i	−0.284006	+	0.958823i	$0.591663\pi$
$440$	4.02051			0.191671
$441$	−20.2213	−	5.66554i	−0.962920	−	0.269787i
$442$	0.225594			0.0107304
$443$	10.6399	+	6.14297i	0.505519	+	0.291861i	0.730990	−	0.682389i	$-0.239059\pi$
$443$	10.6399	+	6.14297i	0.505519	+	0.291861i	−0.225471	+	0.974250i	$0.572392\pi$
$444$	1.84745	+	9.54292i	0.0876763	+	0.452887i
$445$	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	$-0.215014\pi$
$450$	−5.07524	−	12.6167i	−0.239249	−	0.594755i
$451$	−3.21985	+	1.85898i	−0.151617	+	0.0875361i
$452$	−14.3832	+	8.30415i	−0.676530	+	0.390595i
$453$	−21.1817	+	18.3848i	−0.995204	+	0.863795i
$454$		−	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	−0.725873	−	0.687828i	$-0.758564\pi$
$457$	4.97542	−	8.61768i	0.232740	−	0.403118i	0.958614	+	0.284710i	$0.0918974\pi$
$458$	−2.96107	−	5.12872i	−0.138362	−	0.239649i
$459$	−1.41920	+	2.76976i	−0.0662426	+	0.129281i
$460$	17.6353	+	10.1817i	0.822248	+	0.474725i
$461$	15.6920			0.730849			0.365424	−	0.930841i	$-0.380924\pi$
$461$	15.6920			0.730849			0.365424	+	0.930841i	$0.380924\pi$
$462$	−0.157543	+	1.14625i	−0.00732955	+	0.0533284i
$463$	−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
$465$	−44.5115	+	8.61717i	−2.06417	+	0.399612i
$466$	−5.38039	−	9.31911i	−0.249242	−	0.431699i
$467$	−7.08321	+	12.2685i	−0.327772	+	0.567718i	−0.982069	−	0.188520i	$-0.939631\pi$
$467$	−7.08321	+	12.2685i	−0.327772	+	0.567718i	0.654297	+	0.756237i	$0.272964\pi$
$468$	−3.43859	+	4.38748i	−0.158949	+	0.202811i
$469$	2.16495	+	10.9162i	0.0999683	+	0.504064i
$470$		−	8.76170i		−	0.404147i
$471$	21.7016	+	25.0031i	0.999958	+	1.15208i
$472$	−5.60480	+	3.23594i	−0.257982	+	0.148946i
$473$	−1.61097	+	0.930094i	−0.0740725	+	0.0427658i
$474$	6.56392	+	7.56249i	0.301491	+	0.347357i
$475$		−	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	$-0.0624346\pi$
$479$	7.03930	+	12.1924i	0.321634	+	0.557087i	−0.659191	+	0.751975i	$0.729101\pi$
$480$	−28.7755	+	5.57076i	−1.31341	+	0.254269i
$481$	2.61556	+	1.51009i	0.119259	+	0.0688543i
$482$	−2.91756			−0.132891
$483$	−7.46208	+	9.61111i	−0.339536	+	0.437321i
$484$	19.6045			0.891114
$485$	55.1436	+	31.8372i	2.50394	+	1.44565i
$486$	2.46122	+	5.33073i	0.111643	+	0.241807i
$487$	−6.61172	−	11.4518i	−0.299606	−	0.518933i	0.676440	−	0.736498i	$-0.263522\pi$
$487$	−6.61172	−	11.4518i	−0.299606	−	0.518933i	−0.976046	+	0.217565i	$0.930189\pi$
$488$	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	$0.833043\pi$
$492$	13.4809	−	11.7009i	0.607767	−	0.527516i
$493$	−5.44996	+	3.14653i	−0.245454	+	0.141713i
$494$	1.18616	−	0.684827i	0.0533677	−	0.0308118i
$495$	3.09760	+	7.70039i	0.139227	+	0.346107i
$496$			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	0.496550	+	0.868008i	$0.334600\pi$
$499$	−11.2460	+	19.4787i	−0.503442	+	0.871988i	−0.999992	+	0.00397934i	$0.998733\pi$
$500$	26.9764	+	46.7245i	1.20642	+	2.08958i
$501$	−4.36731	−	22.5591i	−0.195117	−	1.00787i
$502$	−2.19230	−	1.26572i	−0.0978469	−	0.0564920i
$503$	20.0211			0.892697			0.446349	−	0.894859i	$-0.352724\pi$
$503$	20.0211			0.892697			0.446349	+	0.894859i	$0.352724\pi$
$504$	−0.629951	−	11.5171i	−0.0280602	−	0.513012i
$505$	−13.3690			−0.594914
$506$	0.580587	+	0.335202i	0.0258102	+	0.0149015i
$507$	0.329203	+	1.70048i	0.0146204	+	0.0755209i
$508$	−7.07596	−	12.2559i	−0.313945	−	0.543768i
$509$	19.5355	−	33.8365i	0.865896	−	1.49978i	−0.000258738	−	1.00000i	$-0.500082\pi$
$509$	19.5355	−	33.8365i	0.865896	−	1.49978i	0.866155	−	0.499776i	$-0.166584\pi$
$510$	−0.526207	+	1.52446i	−0.0233008	+	0.0675043i
$511$	1.88649	−	0.374137i	0.0834533	−	0.0165508i
$512$			22.2024i			0.981219i
$513$	0.946006	+	18.8714i	0.0417672	+	0.833191i
$514$	5.16794	−	2.98371i	0.227948	−	0.131606i
$515$	14.8359	−	8.56552i	0.653749	−	0.377442i
$516$	6.74482	−	5.85422i	0.296924	−	0.257718i
$517$			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	−0.922753	−	0.385392i	$-0.874066\pi$
$521$	−18.1493	−	31.4355i	−0.795136	−	1.37722i	0.127617	−	0.991823i	$-0.459267\pi$
$522$	−1.67015	+	11.7545i	−0.0731006	+	0.514481i
$523$	12.7402	+	7.35555i	0.557090	+	0.321636i	0.751977	−	0.659190i	$-0.229101\pi$
$523$	12.7402	+	7.35555i	0.557090	+	0.321636i	−0.194887	+	0.980826i	$0.562434\pi$
$524$	−26.3065			−1.14921
$525$	−51.0725	+	20.8155i	−2.22899	+	0.908461i
$526$	2.54513			0.110973
$527$	3.28960	+	1.89925i	0.143297	+	0.0827328i
$528$	3.61218	−	0.699298i	0.157200	−	0.0304330i
$529$	−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
$534$	−3.13949	−	3.61710i	−0.135859	−	0.156527i
$535$	11.9143	−	6.87873i	0.515101	−	0.297394i
$536$	−5.29362	+	3.05627i	−0.228649	+	0.132011i
$537$	10.4398	+	12.0280i	0.450509	+	0.519045i
$538$		−	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	−0.952911	−	0.303251i	$-0.901928\pi$
$541$	−4.97360	+	8.61453i	−0.213832	+	0.370368i	0.739079	+	0.673619i	$0.235261\pi$
$542$	1.74839	+	3.02830i	0.0750998	+	0.130077i
$543$	24.9312	−	4.82654i	1.06990	−	0.207127i
$544$	2.12664	+	1.22782i	0.0911789	+	0.0526422i
$545$	−34.1197			−1.46153
$546$	−1.36337	−	1.05852i	−0.0583470	−	0.0453007i
$547$	−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
$549$	29.2297	+	4.15313i	1.24749	+	0.177251i
$550$	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
$555$	−16.3054	+	14.1524i	−0.692126	+	0.600736i
$556$	−16.6052	+	9.58700i	−0.704216	+	0.406579i
$557$	−4.04380	+	2.33469i	−0.171341	+	0.0989239i	−0.583218	−	0.812316i	$-0.698207\pi$
$557$	−4.04380	+	2.33469i	−0.171341	+	0.0989239i	0.411877	+	0.911240i	$0.364873\pi$
$558$	6.64854	−	2.67448i	0.281455	−	0.113220i
$559$		−	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	−0.988326	−	0.152355i	$-0.951314\pi$
$563$	−14.8560	−	25.7314i	−0.626106	−	1.08445i	0.362220	−	0.932093i	$-0.382019\pi$
$564$	−3.44756	−	17.8082i	−0.145169	−	0.749860i
$565$	−31.9486	−	18.4455i	−1.34409	−	0.776009i
$566$	−9.18142			−0.385924
$567$	21.5731	−	10.0798i	0.905983	−	0.423314i
$568$	14.2792			0.599143
$569$	12.5662	+	7.25512i	0.526804	+	0.304151i	0.739714	−	0.672921i	$-0.234961\pi$
$569$	12.5662	+	7.25512i	0.526804	+	0.304151i	−0.212910	+	0.977072i	$0.568294\pi$
$570$	1.86100	+	9.61288i	0.0779487	+	0.402639i
$571$	13.3797	+	23.1744i	0.559925	+	0.969818i	0.997502	+	0.0706372i	$0.0225033\pi$
$571$	13.3797	+	23.1744i	0.559925	+	0.969818i	−0.437577	+	0.899181i	$0.644163\pi$
$572$	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
$576$	−13.3416	+	5.36687i	−0.555902	+	0.223620i
$577$	6.98695	−	4.03392i	0.290870	−	0.167934i	−0.347464	−	0.937693i	$-0.612957\pi$
$577$	6.98695	−	4.03392i	0.290870	−	0.167934i	0.638334	+	0.769759i	$0.279624\pi$
$578$	−5.42827	+	3.13401i	−0.225786	+	0.130358i
$579$	−3.15957	+	2.74237i	−0.131307	+	0.113969i
$580$		−	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
$585$	−12.2589	−	1.74182i	−0.506844	−	0.0720156i
$586$	−2.11015	−	1.21829i	−0.0871694	−	0.0503273i
$587$	−36.9526			−1.52520			−0.762598	−	0.646873i	$-0.776076\pi$
$587$	−36.9526			−1.52520			−0.762598	+	0.646873i	$0.776076\pi$
$588$	−22.4892	+	1.33287i	−0.927438	+	0.0549665i
$589$	23.0620			0.950251
$590$	−5.99591	−	3.46174i	−0.246848	−	0.142518i
$591$	23.7589	−	4.59959i	0.977312	−	0.189202i
$592$	4.78535	+	8.28847i	0.196677	+	0.340654i
$593$	14.1813	−	24.5627i	0.582355	−	1.00867i	−0.412844	−	0.910802i	$-0.635465\pi$
$593$	14.1813	−	24.5627i	0.582355	−	1.00867i	0.995199	−	0.0978671i	$-0.0312020\pi$
$594$	−0.712033	−	1.10191i	−0.0292151	−	0.0452119i
$595$	6.19211	+	2.10584i	0.253852	+	0.0863312i
$596$			21.4103i			0.877000i
$597$	2.21716	+	2.55445i	0.0907422	+	0.104547i
$598$	−0.866121	+	0.500055i	−0.0354183	+	0.0204488i
$599$	1.90744	−	1.10126i	0.0779357	−	0.0449962i	−0.460526	−	0.887646i	$-0.652339\pi$
$599$	1.90744	−	1.10126i	0.0779357	−	0.0449962i	0.538461	+	0.842650i	$0.319006\pi$
$600$	−19.8561	−	22.8768i	−0.810621	−	0.933941i
$601$		−	13.5961i		−	0.554595i	−0.960784	−	0.277298i	$-0.910561\pi$
$601$		−	13.5961i		−	0.554595i	0.960784	−	0.277298i	$-0.0894388\pi$
$602$	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
$606$	2.07465	−	0.401640i	0.0842768	−	0.0163155i
$607$	32.7403	+	18.9026i	1.32889	+	0.767234i	0.985128	−	0.171823i	$-0.0549658\pi$
$607$	32.7403	+	18.9026i	1.32889	+	0.767234i	0.343760	+	0.939057i	$0.388299\pi$
$608$	14.9089			0.604637
$609$	47.7007	+	6.55607i	1.93293	+	0.265666i
$610$	15.2989			0.619432
$611$	−4.88093	−	2.81801i	−0.197461	−	0.114004i
$612$	−0.469670	+	3.30553i	−0.0189853	+	0.133618i
$613$	15.7885	+	27.3464i	0.637691	+	1.10451i	0.985938	+	0.167110i	$0.0534435\pi$
$613$	15.7885	+	27.3464i	0.637691	+	1.10451i	−0.348248	+	0.937403i	$0.613223\pi$
$614$	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	$0.912447\pi$
$618$	−2.04495	+	1.77493i	−0.0822601	+	0.0713982i
$619$	−29.4320	+	16.9926i	−1.18297	+	0.682990i	−0.956700	−	0.291075i	$-0.905987\pi$
$619$	−29.4320	+	16.9926i	−1.18297	+	0.682990i	−0.226272	+	0.974064i	$0.572654\pi$
$620$	−42.1219	+	24.3191i	−1.69166	+	0.976678i
$621$	−0.690766	−	13.7797i	−0.0277195	−	0.552961i
$622$		−	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
$627$	−0.802451	−	4.14502i	−0.0320468	−	0.165536i
$628$	30.7592	+	17.7588i	1.22742	+	0.708653i
$629$	1.80891			0.0721260
$630$	10.3331	−	6.74400i	0.411682	−	0.268688i
$631$	−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
$633$	5.32518	+	27.5069i	0.211657	+	1.09330i
$634$	−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
$639$	11.0014	+	27.3486i	0.435208	+	1.08189i
$640$	−35.7634	+	20.6480i	−1.41367	+	0.816183i
$641$	11.4454	−	6.60802i	0.452067	−	0.261001i	−0.256636	−	0.966508i	$-0.582614\pi$
$641$	11.4454	−	6.60802i	0.452067	−	0.261001i	0.708703	+	0.705507i	$0.249281\pi$
$642$	−1.64224	+	1.42540i	−0.0648142	+	0.0562560i
$643$			12.5686i			0.495658i	0.968804	+	0.247829i	$0.0797172\pi$
$643$			12.5686i			0.495658i	−0.968804	+	0.247829i	$0.920283\pi$
$644$	−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	$-0.276524\pi$
$647$	−8.60547	−	14.9051i	−0.338316	−	0.585981i	−0.984116	+	0.177526i	$0.943191\pi$
$648$	9.05667	+	9.43550i	0.355779	+	0.370662i
$649$	2.58540	+	1.49268i	0.101486	+	0.0585929i
$650$	−4.53306			−0.177801
$651$	−10.9690	−	26.9134i	−0.429910	−	1.05482i
$652$	38.2365			1.49746
$653$	−21.4516	−	12.3851i	−0.839465	−	0.484666i	0.0176171	−	0.999845i	$-0.494392\pi$
$653$	−21.4516	−	12.3851i	−0.839465	−	0.484666i	−0.857082	+	0.515179i	$0.827725\pi$
$654$	5.29479	−	1.02504i	0.207043	−	0.0400823i
$655$	−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	$-0.0975812\pi$
$660$	5.83662	+	6.72454i	0.227190	+	0.261752i
$661$	16.3468	−	9.43785i	0.635818	−	0.367090i	−0.147183	−	0.989109i	$-0.547021\pi$
$661$	16.3468	−	9.43785i	0.635818	−	0.367090i	0.783002	+	0.622019i	$0.213687\pi$
$662$	−3.99659	+	2.30743i	−0.155332	+	0.0896809i
$663$	0.679999	+	0.783447i	0.0264090	+	0.0304266i
$664$			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
$669$	−1.72035	+	0.333051i	−0.0665128	+	0.0128765i
$670$	−5.66301	−	3.26954i	−0.218781	−	0.126313i
$671$	−6.59677			−0.254666
$672$	−7.09118	−	17.3988i	−0.273548	−	0.671174i
$673$	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
$675$	28.5173	−	55.6552i	1.09763	−	2.14217i
$676$	0.929065	+	1.60919i	0.0357333	+	0.0618919i
$677$	−16.9448	+	29.3492i	−0.651240	+	1.12798i	0.331582	+	0.943426i	$0.392418\pi$
$677$	−16.9448	+	29.3492i	−0.651240	+	1.12798i	−0.982822	+	0.184555i	$0.940916\pi$
$678$	5.51202	+	1.90261i	0.211688	+	0.0730694i
$679$	−13.1421	+	38.6435i	−0.504347	+	1.48300i
$680$			3.59233i			0.137760i
$681$	6.23762	−	5.41399i	0.239026	−	0.207465i
$682$	−1.38673	+	0.800632i	−0.0531008	+	0.0306578i
$683$	−23.4427	+	13.5347i	−0.897011	+	0.517889i	−0.876229	−	0.481895i	$-0.839949\pi$
$683$	−23.4427	+	13.5347i	−0.897011	+	0.517889i	−0.0207815	+	0.999784i	$0.506615\pi$
$684$	7.56497	+	18.8059i	0.289254	+	0.719063i
$685$			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
$690$	−1.35889	−	7.01925i	−0.0517319	−	0.267218i
$691$	21.8850	+	12.6353i	0.832545	+	0.480670i	0.854723	−	0.519084i	$-0.173727\pi$
$691$	21.8850	+	12.6353i	0.832545	+	0.480670i	−0.0221783	+	0.999754i	$0.507060\pi$
$692$	19.5238			0.742183
$693$	−4.45559	+	2.90797i	−0.169254	+	0.110465i
$694$	4.37072			0.165910
$695$	−36.8840	−	21.2950i	−1.39909	−	0.807766i
$696$	5.02648	+	25.9640i	0.190528	+	0.984162i
$697$	−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	$0.982967\pi$
$702$	1.95471	−	0.0979878i	0.0737756	−	0.00369831i
$703$	9.51110	−	5.49124i	0.358718	−	0.207106i
$704$	2.78276	−	1.60663i	0.104879	−	0.0605521i
$705$	30.4278	−	26.4100i	1.14598	−	0.994659i
$706$			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	−0.367756	−	0.929922i	$-0.619874\pi$
$709$	16.5476	−	28.6613i	0.621458	−	1.07640i	0.989214	−	0.146475i	$-0.0467928\pi$
$710$	7.63781	+	13.2291i	0.286642	+	0.496479i
$711$	−6.47779	+	45.5906i	−0.242936	+	1.70978i
$712$	−9.23935	−	5.33434i	−0.346259	−	0.199913i
$713$	−16.8396			−0.630650
$714$	−1.02417	−	0.140764i	−0.0383288	−	0.00526798i
$715$	2.76669			0.103468
$716$	14.7970	+	8.54303i	0.552988	+	0.319268i
$717$	24.7573	−	4.79288i	0.924580	−	0.178993i
$718$	1.32812	+	2.30038i	0.0495651	+	0.0858492i
$719$	−2.28833	+	3.96350i	−0.0853401	+	0.147813i	−0.905536	−	0.424269i	$-0.860531\pi$
$719$	−2.28833	+	3.96350i	−0.0853401	+	0.147813i	0.820196	+	0.572083i	$0.193864\pi$
$720$	−30.8830	−	24.2039i	−1.15094	−	0.902026i
$721$	7.23593	+	8.26042i	0.269480	+	0.307634i
$722$			2.17591i			0.0809788i
$723$	−8.79428	−	10.1322i	−0.327063	−	0.376819i
$724$	23.5928	−	13.6213i	0.876819	−	0.506232i
$725$	109.511	−	63.2261i	4.06713	−	2.34816i
$726$	−4.51179	−	5.19817i	−0.167448	−	0.192922i
$727$			28.8022i			1.06821i	0.845417	+	0.534107i	$0.179352\pi$
$727$			28.8022i			1.06821i	−0.845417	+	0.534107i	$0.820648\pi$
$728$	−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
$732$	31.0950	−	6.01981i	1.14930	−	0.222498i
$733$	−15.5664	−	8.98728i	−0.574959	−	0.331953i	0.184168	−	0.982895i	$-0.441041\pi$
$733$	−15.5664	−	8.98728i	−0.574959	−	0.331953i	−0.759128	+	0.650942i	$0.774374\pi$
$734$	−0.547554			−0.0202106
$735$	−27.5409	−	41.7810i	−1.01586	−	1.54111i
$736$	−10.8864			−0.401277
$737$	2.44185	+	1.40981i	0.0899469	+	0.0519308i
$738$	−6.20501	−	0.881647i	−0.228410	−	0.0324539i
$739$	−19.5409	−	33.8458i	−0.718822	−	1.24504i	−0.961467	−	0.274921i	$-0.911348\pi$
$739$	−19.5409	−	33.8458i	−0.718822	−	1.24504i	0.242645	−	0.970115i	$-0.421985\pi$
$740$	−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	$-0.00887005\pi$
$744$	12.0553	−	10.4635i	0.441968	−	0.383609i
$745$	−41.1859	+	23.7787i	−1.50894	+	0.871184i
$746$	0.375501	−	0.216795i	0.0137481	−	0.00793744i
$747$	−15.0878	+	6.06928i	−0.552032	+	0.222063i
$748$		−	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	−0.387303	−	0.921953i	$-0.626593\pi$
$751$	16.5737	−	28.7065i	0.604783	−	1.04751i	0.992086	−	0.125562i	$-0.0400735\pi$
$752$	−8.93002	−	15.4672i	−0.325644	−	0.564032i
$753$	−2.21252	−	11.4287i	−0.0806287	−	0.416483i
$754$	3.42732	+	1.97876i	0.124815	+	0.0720622i
$755$	−66.8354			−2.43239
$756$	18.3485	−	17.7731i	0.667329	−	0.646401i
$757$	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
$759$	0.585943	+	3.02666i	0.0212684	+	0.109861i
$760$	10.9051	+	18.8882i	0.395569	+	0.685146i
$761$	10.2309	−	17.7204i	0.370868	−	0.642363i	−0.618831	−	0.785524i	$-0.712393\pi$
$761$	10.2309	−	17.7204i	0.370868	−	0.642363i	0.989699	+	0.143161i	$0.0457267\pi$
$762$	−1.62121	+	4.69679i	−0.0587304	+	0.170147i
$763$	−4.25482	−	21.4538i	−0.154035	−	0.776681i
$764$		−	28.1239i		−	1.01749i
$765$	−6.88030	+	2.76770i	−0.248758	+	0.100067i
$766$	0.740727	−	0.427659i	0.0267635	−	0.0154519i
$767$	−3.85691	+	2.22679i	−0.139265	+	0.0804046i
$768$	−7.61090	+	6.60594i	−0.274635	+	0.238371i
$769$		−	8.60167i		−	0.310184i	−0.987900	−	0.155092i	$-0.950433\pi$
$769$		−	8.60167i		−	0.310184i	0.987900	−	0.155092i	$-0.0495674\pi$
$770$	−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	$-0.284046\pi$
$773$	−10.0218	−	17.3582i	−0.360458	−	0.624332i	−0.988036	+	0.154222i	$0.950713\pi$
$774$	−3.10452	−	0.441109i	−0.111589	−	0.0158553i
$775$	−66.1009	−	38.1634i	−2.37442	−	1.37087i
$776$	−22.4189			−0.804792
$777$	−10.9321	−	8.48770i	−0.392187	−	0.304495i
$778$	8.49708			0.304635
$779$	−17.4668	−	10.0845i	−0.625814	−	0.361314i
$780$	−13.0412	+	2.52471i	−0.466951	+	0.0903991i
$781$	−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
$786$	6.05420	+	6.97523i	0.215946	+	0.248798i
$787$	−5.60081	+	3.23363i	−0.199647	+	0.115267i	−0.596491	−	0.802620i	$-0.703439\pi$
$787$	−5.60081	+	3.23363i	−0.199647	+	0.115267i	0.396844	+	0.917886i	$0.370106\pi$
$788$	22.4834	−	12.9808i	0.800939	−	0.462422i
$789$	7.67168	+	8.83878i	0.273119	+	0.314669i
$790$			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
$795$	−24.9440	+	4.82901i	−0.884671	+	0.171267i
$796$	3.14252	+	1.81434i	0.111384	+	0.0643075i
$797$	−2.04250			−0.0723491			−0.0361745	−	0.999345i	$-0.511517\pi$
$797$	−2.04250			−0.0723491			−0.0361745	+	0.999345i	$0.511517\pi$
$798$	−5.81234	+	2.36892i	−0.205754	+	0.0838588i
$799$	−3.37564			−0.119421
$800$	−42.7325	−	24.6716i	−1.51082	−	0.872272i
$801$	3.09829	−	21.8057i	0.109473	−	0.770467i
$802$	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
$807$	4.56802	−	3.96485i	0.160802	−	0.139569i
$808$	4.07644	−	2.35353i	0.143409	−	0.0827970i
$809$	12.9105	−	7.45386i	0.453907	−	0.262064i	−0.255572	−	0.966790i	$-0.582264\pi$
$809$	12.9105	−	7.45386i	0.453907	−	0.262064i	0.709479	+	0.704727i	$0.248930\pi$
$810$	−3.89727	+	13.4376i	−0.136936	+	0.472148i
$811$			22.1938i			0.779330i	0.920957	+	0.389665i	$0.127409\pi$
$811$			22.1938i			0.779330i	−0.920957	+	0.389665i	$0.872591\pi$
$812$	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
$816$	0.624823	+	3.22749i	0.0218732	+	0.112985i
$817$	−8.73907	−	5.04551i	−0.305741	−	0.176520i
$818$	8.87302			0.310238
$819$	−0.433496	−	7.92541i	−0.0151476	−	0.276936i
$820$	42.5368			1.48545
$821$	−35.1981	−	20.3216i	−1.22842	−	0.709230i	−0.261723	−	0.965143i	$-0.584291\pi$
$821$	−35.1981	−	20.3216i	−1.22842	−	0.709230i	−0.966700	+	0.255913i	$0.917624\pi$
$822$	−1.77558	−	9.17168i	−0.0619306	−	0.319899i
$823$	−2.71653	−	4.70517i	−0.0946923	−	0.164012i	0.814788	−	0.579759i	$-0.196853\pi$
$823$	−2.71653	−	4.70517i	−0.0946923	−	0.164012i	−0.909480	+	0.415747i	$0.863520\pi$
$824$	−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	$-0.388052\pi$
$828$	−5.52388	−	13.7319i	−0.191968	−	0.477218i
$829$	−0.944032	+	0.545037i	−0.0327876	+	0.0189299i	−0.516304	−	0.856405i	$-0.672693\pi$
$829$	−0.944032	+	0.545037i	−0.0327876	+	0.0189299i	0.483517	+	0.875335i	$0.339359\pi$
$830$	−7.29826	+	4.21365i	−0.253326	+	0.146258i
$831$	−23.4484	+	20.3522i	−0.813415	+	0.706010i
$832$			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
$837$	29.3284	+	15.0276i	1.01374	+	0.519430i
$838$	−9.45089	−	5.45647i	−0.326475	−	0.188491i
$839$	49.5517			1.71072			0.855358	−	0.518038i	$-0.173337\pi$
$839$	49.5517			1.71072			0.855358	+	0.518038i	$0.173337\pi$
$840$	16.8558	−	21.7102i	0.581580	−	0.749072i
$841$	−81.3971			−2.80680
$842$	−2.70986	−	1.56454i	−0.0933878	−	0.0539175i
$843$	−33.5651	+	6.49800i	−1.15604	+	0.223803i
$844$	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
$849$	−27.6751	−	31.8854i	−0.949808	−	1.09430i
$850$	−2.35129	+	1.35752i	−0.0806485	+	0.0465625i
$851$	−6.94493	+	4.00966i	−0.238069	+	0.137449i
$852$	20.7293	+	23.8828i	0.710173	+	0.818212i
$853$			40.8406i			1.39835i	0.714949	+	0.699177i	$0.246450\pi$
$853$			40.8406i			1.39835i	−0.714949	+	0.699177i	$0.753550\pi$
$854$	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	−0.984933	−	0.172938i	$-0.944674\pi$
$857$	−18.8011	−	32.5645i	−0.642235	−	1.11238i	0.342698	−	0.939446i	$-0.388659\pi$
$858$	−0.429343	+	0.0831183i	−0.0146575	+	0.00283761i
$859$	−42.3619	−	24.4577i	−1.44537	−	0.834485i	−0.447169	−	0.894449i	$-0.647568\pi$
$859$	−42.3619	−	24.4577i	−1.44537	−	0.834485i	−0.998201	+	0.0599646i	$0.980901\pi$
$860$	21.2822			0.725716
$861$	−3.46084	+	25.1804i	−0.117945	+	0.858146i
$862$	−5.19813			−0.177049
$863$	−36.9536	−	21.3352i	−1.25791	−	0.726257i	−0.285246	−	0.958454i	$-0.592075\pi$
$863$	−36.9536	−	21.3352i	−1.25791	−	0.726257i	−0.972669	+	0.232197i	$0.925409\pi$
$864$	18.9600	+	9.71494i	0.645032	+	0.330509i
$865$	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
$870$	−21.3659	+	18.5447i	−0.724372	+	0.628724i
$871$	−3.64276	+	2.10315i	−0.123430	+	0.0712626i
$872$	10.4036	−	6.00655i	0.352312	−	0.203407i
$873$	−17.2726	−	42.9383i	−0.584588	−	1.45324i
$874$			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	−0.999577	−	0.0290914i	$-0.990739\pi$
$877$	−14.0547	+	24.3435i	−0.474595	+	0.822022i	0.524982	+	0.851113i	$0.324072\pi$
$878$	−1.84238	−	3.19110i	−0.0621775	−	0.107695i
$879$	−2.12961	−	11.0004i	−0.0718301	−	0.371034i
$880$	7.59278	+	4.38369i	0.255952	+	0.147774i
$881$	27.6273			0.930786			0.465393	−	0.885104i	$-0.345913\pi$
$881$	27.6273			0.930786			0.465393	+	0.885104i	$0.345913\pi$
$882$	5.52908	+	5.65630i	0.186174	+	0.190457i
$883$	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
$885$	−6.05123	−	31.2573i	−0.203410	−	1.05070i
$886$	−2.31378	−	4.00759i	−0.0777331	−	0.134638i
$887$	−14.1684	+	24.5403i	−0.475727	+	0.823984i	−0.999613	−	0.0278043i	$-0.991148\pi$
$887$	−14.1684	+	24.5403i	−0.475727	+	0.823984i	0.523886	+	0.851788i	$0.324482\pi$
$888$	2.48035	−	7.18576i	0.0832349	−	0.241138i
$889$	19.0775	+	6.48799i	0.639840	+	0.217600i
$890$		−	11.4131i		−	0.382569i
$891$	1.68048	−	5.79420i	0.0562981	−	0.194113i
$892$	−1.62800	+	0.939925i	−0.0545094	+	0.0314710i
$893$	−17.7488	+	10.2473i	−0.593942	+	0.342912i
$894$	5.67698	−	4.92738i	0.189867	−	0.164796i
$895$			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
$900$	9.43749	−	66.4209i	0.314583	−	2.21403i
$901$	1.84347	+	1.06433i	0.0614150	+	0.0354580i
$902$	1.40039			0.0466280
$903$	−1.73154	+	12.5984i	−0.0576221	+	0.419247i
$904$	12.9888			0.432003
$905$	52.4052	+	30.2562i	1.74201	+	1.00575i
$906$	10.3717	−	2.00790i	0.344577	−	0.0667081i
$907$	−10.5246	−	18.2292i	−0.349465	−	0.605291i	0.636690	−	0.771120i	$-0.280303\pi$
$907$	−10.5246	−	18.2292i	−0.349465	−	0.605291i	−0.986154	+	0.165829i	$0.946970\pi$
$908$	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	$-0.139209\pi$
$912$	13.0828	+	15.0731i	0.433215	+	0.499120i
$913$	3.14696	−	1.81690i	0.104149	−	0.0601306i
$914$	−3.24590	+	1.87402i	−0.107365	+	0.0619871i
$915$	46.1147	+	53.1301i	1.52450	+	1.75643i
$916$		−	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	−0.555658	−	0.831411i	$-0.687534\pi$
$919$	13.4051	−	23.2183i	0.442194	−	0.765903i	0.997852	+	0.0655084i	$0.0208669\pi$
$920$	−7.96281	−	13.7920i	−0.262526	−	0.454708i
$921$	25.6439	−	4.96452i	0.844996	−	0.163586i
$922$	−5.11862	−	2.95524i	−0.168573	−	0.0973256i
$923$	9.82614			0.323431
$924$	−3.50043	+	4.50853i	−0.115156	+	0.148320i
$925$	−36.3481			−1.19512
$926$	9.25435	+	5.34300i	0.304117	+	0.175582i
$927$	−12.3280	−	1.75164i	−0.404905	−	0.0575315i
$928$	21.5392	+	37.3069i	0.707057	+	1.22466i
$929$	−5.32379	+	9.22107i	−0.174668	+	0.302534i	−0.940046	−	0.341047i	$-0.889218\pi$
$929$	−5.32379	+	9.22107i	−0.174668	+	0.302534i	0.765378	+	0.643580i	$0.222552\pi$
$930$	16.1422	+	5.57189i	0.529324	+	0.182709i
$931$	9.71441	+	23.5279i	0.318377	+	0.771096i
$932$		−	53.0854i		−	1.73887i
$933$	30.7282	−	26.6708i	1.00600	−	0.873162i
$934$	4.62099	−	2.66793i	0.151204	−	0.0872974i
$935$	1.43507	−	0.828540i	0.0469319	−	0.0270962i
$936$	4.04458	−	1.62699i	0.132201	−	0.0531800i
$937$		−	18.5079i		−	0.604627i	−0.953209	−	0.302313i	$-0.902241\pi$
$937$		−	18.5079i		−	0.604627i	0.953209	−	0.302313i	$-0.0977589\pi$
$938$	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	$-0.0859444\pi$
$941$	7.69614	+	13.3301i	0.250887	+	0.434549i	−0.712883	+	0.701283i	$0.752611\pi$
$942$	−2.37015	−	12.2429i	−0.0772236	−	0.398894i
$943$	12.7541	+	7.36360i	0.415332	+	0.239792i
$944$	−14.1130			−0.459338
$945$	54.5674	+	15.5569i	1.77508	+	0.506067i
$946$	0.700650			0.0227801
$947$	5.12650	+	2.95979i	0.166589	+	0.0961801i	0.580976	−	0.813920i	$-0.302671\pi$
$947$	5.12650	+	2.95979i	0.166589	+	0.0961801i	−0.414388	+	0.910101i	$0.636004\pi$
$948$	9.38931	+	48.4999i	0.304950	+	1.57520i
$949$	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	$0.647504\pi$
$954$	3.72580	−	1.49876i	0.120627	−	0.0485241i
$955$	54.1006	−	31.2350i	1.75065	−	1.01074i
$956$	23.4282	−	13.5263i	0.757724	−	0.437472i
$957$	9.21284	−	7.99636i	0.297809	−	0.258486i
$958$		−	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
$963$	−9.90029	−	1.40669i	−0.319032	−	0.0453301i
$964$	−12.4647	−	7.19651i	−0.401461	−	0.231784i
$965$	−9.96949			−0.320929
$966$	4.24412	−	1.72976i	0.136552	−	0.0556542i
$967$	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
$969$	3.70357	−	0.716991i	0.118976	−	0.0230331i
$970$	−11.9916	−	20.7701i	−0.385029	−	0.666889i
$971$	−3.83896	+	6.64927i	−0.123198	+	0.213385i	−0.921027	−	0.389498i	$-0.872648\pi$
$971$	−3.83896	+	6.64927i	−0.123198	+	0.213385i	0.797829	+	0.602884i	$0.205982\pi$
$972$	−2.63378	+	28.8454i	−0.0844784	+	0.925217i
$973$	8.79038	−	25.8476i	0.281807	−	0.828635i
$974$			4.98069i			0.159592i
$975$	−13.6638	−	15.7425i	−0.437592	−	0.504163i
$976$	27.0074	−	15.5927i	0.864487	−	0.499112i
$977$	−30.4153	+	17.5603i	−0.973072	+	0.561803i	−0.900171	−	0.435536i	$-0.856559\pi$
$977$	−30.4153	+	17.5603i	−0.973072	+	0.561803i	−0.0729003	+	0.997339i	$0.523225\pi$
$978$	−8.79976	−	10.1385i	−0.281385	−	0.324193i
$979$			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	$-0.0551540\pi$
$983$	10.7605	+	18.6377i	0.343205	+	0.594449i	−0.641821	+	0.766855i	$0.721821\pi$
$984$	−13.7060	+	2.65340i	−0.436930	+	0.0845872i
$985$	49.9411	+	28.8335i	1.59126	+	0.918712i
$986$	2.37032			0.0754863
$987$	20.4006	+	15.8390i	0.649358	+	0.504162i
$988$	6.75683			0.214963
$989$	6.38120	+	3.68419i	0.202910	+	0.117150i
$990$	0.439782	−	3.09518i	0.0139772	−	0.0983712i
$991$	−9.20760	−	15.9480i	−0.292489	−	0.506606i	0.681909	−	0.731437i	$-0.261150\pi$
$991$	−9.20760	−	15.9480i	−0.292489	−	0.506606i	−0.974398	+	0.224831i	$0.927817\pi$
$992$	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
$996$	−13.1757	+	11.4360i	−0.417489	+	0.362363i
$997$	−6.67542	+	3.85405i	−0.211413	+	0.122059i	−0.601968	−	0.798520i	$-0.705616\pi$
$997$	−6.67542	+	3.85405i	−0.211413	+	0.122059i	0.390555	+	0.920580i	$0.372283\pi$
$998$	7.33677	−	4.23589i	0.232242	−	0.134085i
$999$	15.6737	−	0.785708i	0.495893	−	0.0248587i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.15	✓	64	1.1	even	1	trivial
273.2.bh.a.131.18	yes	64	3.2	odd	2	inner
273.2.bh.a.248.15	yes	64	21.17	even	6	inner
273.2.bh.a.248.18	yes	64	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.326193 - 0.188328i) q^{2} +(-0.329203 - 1.70048i) q^{3} +(-0.929065 - 1.60919i) q^{4} +(2.06368 - 3.57439i) q^{5} +(-0.212864 + 0.616683i) q^{6} +(2.50486 + 0.851866i) q^{7} +1.45319i q^{8} +(-2.78325 + 1.11960i) q^{9} +O(q^{10})\)	\(q+(-0.326193 - 0.188328i) q^{2} +(-0.329203 - 1.70048i) 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} +(-2.78325 + 1.11960i) q^{9} +(-1.34632 + 0.777295i) q^{10} +(0.580523 - 0.335165i) q^{11} +(-2.43054 + 2.10960i) 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} +(1.11873 + 0.158956i) q^{18} +(3.14918 + 1.81818i) q^{19} -7.66916 q^{20} +(0.623972 - 4.53990i) q^{21} -0.252484 q^{22} +(-2.29950 - 1.32762i) q^{23} +(2.47111 - 0.478393i) 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} +(1.76498 + 2.03349i) q^{30} +(5.49237 - 3.17102i) q^{31} +(3.55067 - 2.04998i) q^{32} +(-0.761050 - 0.876829i) 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} +(1.70048 - 0.329203i) q^{39} +(5.19426 + 2.99891i) q^{40} -5.54647 q^{41} +(-1.05852 + 1.36337i) q^{42} -2.77503 q^{43} +(-1.07869 - 0.622780i) q^{44} +(-1.74182 + 12.2589i) 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} +(0.783447 - 0.679999i) q^{51} +(1.60919 - 0.929065i) q^{52} +(3.07789 - 1.77702i) q^{53} +(-0.0979878 - 1.95471i) 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} +(2.52471 + 13.0412i) q^{60} +(-8.52262 - 4.92054i) q^{61} -2.38877 q^{62} +(-7.92541 + 0.433496i) q^{63} +4.79355 q^{64} +(3.57439 + 2.06368i) q^{65} +(0.0831183 + 0.429343i) 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} +(-1.62699 - 4.04458i) q^{72} +(0.629525 - 0.363456i) q^{73} +(-0.985165 + 0.568785i) q^{74} +(-15.7425 + 13.6638i) 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} +(6.49297 - 6.23228i) q^{81} +(1.80922 + 1.04456i) q^{82} +5.42091 q^{83} +(-7.88526 + 3.21377i) q^{84} +2.47204 q^{85} +(0.905198 + 0.522616i) q^{86} +(17.8669 - 3.45893i) 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} +(-7.20036 - 8.29575i) q^{93} +(1.83843 - 1.06142i) q^{94} +(12.9978 - 7.50426i) q^{95} +(-4.65484 - 5.36298i) 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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