LMFDB - Embedded newform 168.2.v.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(11,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))

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

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

chi := DirichletCharacter("168.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.v (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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	168.11
Dual form			168.2.v.a.107.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866151 + 1.11794i) q^{2} +(1.66017 - 0.493786i) q^{3} +(-0.499565 - 1.93660i) q^{4} +(-1.09212 - 1.89161i) q^{5} +(-0.885940 + 2.28366i) q^{6} +(0.451847 - 2.60688i) q^{7} +(2.59770 + 1.11891i) q^{8} +(2.51235 - 1.63954i) q^{9} +(3.06064 + 0.417497i) q^{10} +(-1.45052 - 0.837460i) q^{11} +(-1.78563 - 2.96842i) q^{12} +1.56085i q^{13} +(2.52296 + 2.76309i) q^{14} +(-2.74716 - 2.60112i) q^{15} +(-3.50087 + 1.93492i) q^{16} +(-0.278795 - 0.160963i) q^{17} +(-0.343174 + 4.22874i) q^{18} +(2.87437 + 4.97856i) q^{19} +(-3.11771 + 3.05999i) q^{20} +(-0.537096 - 4.55099i) q^{21} +(2.19260 - 0.896227i) q^{22} +(3.26717 + 5.65891i) q^{23} +(4.86513 + 0.574878i) q^{24} +(0.114544 - 0.198397i) q^{25} +(-1.74494 - 1.35194i) q^{26} +(3.36136 - 3.96248i) q^{27} +(-5.27423 + 0.427257i) q^{28} -7.04205 q^{29} +(5.28735 - 0.818183i) q^{30} +(7.76983 + 4.48591i) q^{31} +(0.869166 - 5.58968i) q^{32} +(-2.82165 - 0.674082i) q^{33} +(0.421425 - 0.172258i) q^{34} +(-5.42467 + 1.99231i) q^{35} +(-4.43022 - 4.04637i) q^{36} +(-0.946173 + 0.546273i) q^{37} +(-8.05536 - 1.09882i) q^{38} +(0.770727 + 2.59129i) q^{39} +(-0.720462 - 6.13582i) q^{40} -3.44933i q^{41} +(5.55293 + 3.34141i) q^{42} -11.6570 q^{43} +(-0.897199 + 3.22746i) q^{44} +(-5.84516 - 2.96181i) q^{45} +(-9.15616 - 1.24898i) q^{46} +(2.25371 + 3.90354i) q^{47} +(-4.85662 + 4.94098i) q^{48} +(-6.59167 - 2.35583i) q^{49} +(0.122582 + 0.299895i) q^{50} +(-0.542330 - 0.129561i) q^{51} +(3.02276 - 0.779748i) q^{52} +(4.42876 - 7.67084i) q^{53} +(1.51836 + 7.18989i) q^{54} +3.65843i q^{55} +(4.09063 - 6.26632i) q^{56} +(7.23030 + 6.84595i) q^{57} +(6.09948 - 7.87257i) q^{58} +(5.37016 + 3.10046i) q^{59} +(-3.66496 + 6.61959i) q^{60} +(-3.80578 + 2.19727i) q^{61} +(-11.7448 + 4.80070i) q^{62} +(-3.13889 - 7.29023i) q^{63} +(5.49608 + 5.81318i) q^{64} +(2.95253 - 1.70464i) q^{65} +(3.19755 - 2.57057i) q^{66} +(0.716072 - 1.24027i) q^{67} +(-0.172444 + 0.620328i) q^{68} +(8.21836 + 7.78149i) q^{69} +(2.47131 - 7.79008i) q^{70} +6.37080 q^{71} +(8.36083 - 1.44794i) q^{72} +(-4.49012 + 7.77711i) q^{73} +(0.208830 - 1.53092i) q^{74} +(0.0921980 - 0.385933i) q^{75} +(8.20557 - 8.05364i) q^{76} +(-2.83858 + 3.40294i) q^{77} +(-3.56446 - 1.38282i) q^{78} +(3.58799 - 2.07153i) q^{79} +(7.48348 + 4.50911i) q^{80} +(3.62382 - 8.23820i) q^{81} +(3.85613 + 2.98764i) q^{82} +9.06459i q^{83} +(-8.54515 + 3.31366i) q^{84} +0.703162i q^{85} +(10.0968 - 13.0318i) q^{86} +(-11.6910 + 3.47726i) q^{87} +(-2.83098 - 3.79848i) q^{88} +(4.57586 - 2.64187i) q^{89} +(8.37391 - 3.96914i) q^{90} +(4.06896 + 0.705268i) q^{91} +(9.32690 - 9.15421i) q^{92} +(15.1143 + 3.61076i) q^{93} +(-6.31596 - 0.861550i) q^{94} +(6.27833 - 10.8744i) q^{95} +(-1.31714 - 9.70902i) q^{96} +4.23153 q^{97} +(8.34304 - 5.32857i) q^{98} +(-5.01728 + 0.274197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) $ 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.866151	+	1.11794i	−0.612461	+	0.790501i
$2$	−0.866151	+	1.11794i	−0.612461	+	0.790501i
$3$	1.66017	−	0.493786i	0.958502	−	0.285087i
$3$	1.66017	−	0.493786i	0.958502	−	0.285087i
$4$	−0.499565	−	1.93660i	−0.249782	−	0.968302i
$5$	−1.09212	−	1.89161i	−0.488411	−	0.845953i	0.511500	−	0.859283i	$-0.329090\pi$
$5$	−1.09212	−	1.89161i	−0.488411	−	0.845953i	−0.999911	+	0.0133302i	$0.995757\pi$
$6$	−0.885940	+	2.28366i	−0.361683	+	0.932301i
$7$	0.451847	−	2.60688i	0.170782	−	0.985309i
$7$	0.451847	−	2.60688i	0.170782	−	0.985309i
$8$	2.59770	+	1.11891i	0.918425	+	0.395594i
$9$	2.51235	−	1.63954i	0.837450	−	0.546513i
$10$	3.06064	+	0.417497i	0.967859	+	0.132024i
$11$	−1.45052	−	0.837460i	−0.437349	−	0.252504i	0.265123	−	0.964215i	$-0.414587\pi$
$11$	−1.45052	−	0.837460i	−0.437349	−	0.252504i	−0.702473	+	0.711711i	$0.747921\pi$
$12$	−1.78563	−	2.96842i	−0.515467	−	0.856909i
$13$			1.56085i			0.432903i	0.976293	+	0.216452i	$0.0694483\pi$
$13$			1.56085i			0.432903i	−0.976293	+	0.216452i	$0.930552\pi$
$14$	2.52296	+	2.76309i	0.674290	+	0.738467i
$15$	−2.74716	−	2.60112i	−0.709313	−	0.671608i
$16$	−3.50087	+	1.93492i	−0.875218	+	0.483730i
$17$	−0.278795	−	0.160963i	−0.0676178	−	0.0390392i	0.465810	−	0.884885i	$-0.345763\pi$
$17$	−0.278795	−	0.160963i	−0.0676178	−	0.0390392i	−0.533428	+	0.845846i	$0.679096\pi$
$18$	−0.343174	+	4.22874i	−0.0808870	+	0.996723i
$19$	2.87437	+	4.97856i	0.659427	+	1.14216i	0.980764	+	0.195196i	$0.0625343\pi$
$19$	2.87437	+	4.97856i	0.659427	+	1.14216i	−0.321337	+	0.946965i	$0.604132\pi$
$20$	−3.11771	+	3.05999i	−0.697142	+	0.684234i
$21$	−0.537096	−	4.55099i	−0.117204	−	0.993108i
$22$	2.19260	−	0.896227i	0.467464	−	0.191076i
$23$	3.26717	+	5.65891i	0.681252	+	1.17996i	0.974599	+	0.223958i	$0.0718977\pi$
$23$	3.26717	+	5.65891i	0.681252	+	1.17996i	−0.293346	+	0.956006i	$0.594769\pi$
$24$	4.86513	+	0.574878i	0.993091	+	0.117346i
$25$	0.114544	−	0.198397i	0.0229089	−	0.0396793i
$26$	−1.74494	−	1.35194i	−0.342210	−	0.265136i
$27$	3.36136	−	3.96248i	0.646894	−	0.762580i
$28$	−5.27423	+	0.427257i	−0.996735	+	0.0807440i
$29$	−7.04205			−1.30768			−0.653838	−	0.756635i	$-0.726842\pi$
$29$	−7.04205			−1.30768			−0.653838	+	0.756635i	$0.726842\pi$
$30$	5.28735	−	0.818183i	0.965333	−	0.149379i
$31$	7.76983	+	4.48591i	1.39550	+	0.805694i	0.993917	−	0.110128i	$-0.0351259\pi$
$31$	7.76983	+	4.48591i	1.39550	+	0.805694i	0.401585	+	0.915822i	$0.368459\pi$
$32$	0.869166	−	5.58968i	0.153648	−	0.988126i
$33$	−2.82165	−	0.674082i	−0.491186	−	0.117343i
$34$	0.421425	−	0.172258i	0.0722738	−	0.0295419i
$35$	−5.42467	+	1.99231i	−0.916937	+	0.336762i
$36$	−4.43022	−	4.04637i	−0.738370	−	0.674396i
$37$	−0.946173	+	0.546273i	−0.155550	+	0.0898068i	−0.575755	−	0.817623i	$-0.695292\pi$
$37$	−0.946173	+	0.546273i	−0.155550	+	0.0898068i	0.420205	+	0.907429i	$0.361958\pi$
$38$	−8.05536	−	1.09882i	−1.30675	−	0.178252i
$39$	0.770727	+	2.59129i	0.123415	+	0.414938i
$40$	−0.720462	−	6.13582i	−0.113915	−	0.970158i
$41$		−	3.44933i		−	0.538694i	−0.963043	−	0.269347i	$-0.913192\pi$
$41$		−	3.44933i		−	0.538694i	0.963043	−	0.269347i	$-0.0868079\pi$
$42$	5.55293	+	3.34141i	0.856835	+	0.515590i
$43$	−11.6570			−1.77768			−0.888841	−	0.458215i	$-0.848489\pi$
$43$	−11.6570			−1.77768			−0.888841	+	0.458215i	$0.848489\pi$
$44$	−0.897199	+	3.22746i	−0.135258	+	0.486557i
$45$	−5.84516	−	2.96181i	−0.871345	−	0.441521i
$46$	−9.15616	−	1.24898i	−1.35000	−	0.184152i
$47$	2.25371	+	3.90354i	0.328737	+	0.569390i	0.982262	−	0.187516i	$-0.0600436\pi$
$47$	2.25371	+	3.90354i	0.328737	+	0.569390i	−0.653524	+	0.756906i	$0.726710\pi$
$48$	−4.85662	+	4.94098i	−0.700992	+	0.713169i
$49$	−6.59167	−	2.35583i	−0.941667	−	0.336546i
$50$	0.122582	+	0.299895i	0.0173357	+	0.0424115i
$51$	−0.542330	−	0.129561i	−0.0759413	−	0.0181421i
$52$	3.02276	−	0.779748i	0.419181	−	0.108132i
$53$	4.42876	−	7.67084i	0.608337	−	1.05367i	−0.383177	−	0.923675i	$-0.625170\pi$
$53$	4.42876	−	7.67084i	0.608337	−	1.05367i	0.991515	−	0.129996i	$-0.0414964\pi$
$54$	1.51836	+	7.18989i	0.206623	+	0.978421i
$55$			3.65843i			0.493303i
$56$	4.09063	−	6.26632i	0.546633	−	0.837372i
$57$	7.23030	+	6.84595i	0.957677	+	0.906769i
$58$	6.09948	−	7.87257i	0.800901	−	1.03372i
$59$	5.37016	+	3.10046i	0.699135	+	0.403646i	0.807025	−	0.590517i	$-0.201076\pi$
$59$	5.37016	+	3.10046i	0.699135	+	0.403646i	−0.107890	+	0.994163i	$0.534409\pi$
$60$	−3.66496	+	6.61959i	−0.473145	+	0.854585i
$61$	−3.80578	+	2.19727i	−0.487280	+	0.281331i	−0.723445	−	0.690382i	$-0.757443\pi$
$61$	−3.80578	+	2.19727i	−0.487280	+	0.281331i	0.236165	+	0.971713i	$0.424109\pi$
$62$	−11.7448	+	4.80070i	−1.49159	+	0.609690i
$63$	−3.13889	−	7.29023i	−0.395463	−	0.918482i
$64$	5.49608	+	5.81318i	0.687010	+	0.726648i
$65$	2.95253	−	1.70464i	0.366216	−	0.211435i
$66$	3.19755	−	2.57057i	0.393592	−	0.316415i
$67$	0.716072	−	1.24027i	0.0874821	−	0.151523i	−0.818964	−	0.573845i	$-0.805451\pi$
$67$	0.716072	−	1.24027i	0.0874821	−	0.151523i	0.906446	+	0.422321i	$0.138785\pi$
$68$	−0.172444	+	0.620328i	−0.0209120	+	0.0752258i
$69$	8.21836	+	7.78149i	0.989374	+	0.936781i
$70$	2.47131	−	7.79008i	0.295378	−	0.931093i
$71$	6.37080			0.756074			0.378037	−	0.925790i	$-0.376599\pi$
$71$	6.37080			0.756074			0.378037	+	0.925790i	$0.376599\pi$
$72$	8.36083	−	1.44794i	0.985333	−	0.170641i
$73$	−4.49012	+	7.77711i	−0.525528	+	0.910242i	0.474030	+	0.880509i	$0.342799\pi$
$73$	−4.49012	+	7.77711i	−0.525528	+	0.910242i	−0.999558	+	0.0297328i	$0.990534\pi$
$74$	0.208830	−	1.53092i	0.0242760	−	0.177965i
$75$	0.0921980	−	0.385933i	0.0106461	−	0.0445637i
$76$	8.20557	−	8.05364i	0.941243	−	0.923816i
$77$	−2.83858	+	3.40294i	−0.323486	+	0.387801i
$78$	−3.56446	−	1.38282i	−0.403596	−	0.156574i
$79$	3.58799	−	2.07153i	0.403681	−	0.233065i	−0.284390	−	0.958709i	$-0.591791\pi$
$79$	3.58799	−	2.07153i	0.403681	−	0.233065i	0.688071	+	0.725643i	$0.258458\pi$
$80$	7.48348	+	4.50911i	0.836679	+	0.504134i
$81$	3.62382	−	8.23820i	0.402647	−	0.915356i
$82$	3.85613	+	2.98764i	0.425838	+	0.329929i
$83$			9.06459i			0.994968i	0.867473	+	0.497484i	$0.165743\pi$
$83$			9.06459i			0.994968i	−0.867473	+	0.497484i	$0.834257\pi$
$84$	−8.54515	+	3.31366i	−0.932353	+	0.361550i
$85$			0.703162i			0.0762687i
$86$	10.0968	−	13.0318i	1.08876	−	1.40526i
$87$	−11.6910	+	3.47726i	−1.25341	+	0.372802i
$88$	−2.83098	−	3.79848i	−0.301784	−	0.404919i
$89$	4.57586	−	2.64187i	0.485040	−	0.280038i	−0.237474	−	0.971394i	$-0.576320\pi$
$89$	4.57586	−	2.64187i	0.485040	−	0.280038i	0.722515	+	0.691356i	$0.242986\pi$
$90$	8.37391	−	3.96914i	0.882687	−	0.418384i
$91$	4.06896	+	0.705268i	0.426543	+	0.0739322i
$92$	9.32690	−	9.15421i	0.972397	−	0.954392i
$93$	15.1143	+	3.61076i	1.56728	+	0.374419i
$94$	−6.31596	−	0.861550i	−0.651442	−	0.0888621i
$95$	6.27833	−	10.8744i	0.644143	−	1.11569i
$96$	−1.31714	−	9.70902i	−0.134430	−	0.990923i
$97$	4.23153			0.429647			0.214823	−	0.976653i	$-0.431082\pi$
$97$	4.23153			0.429647			0.214823	+	0.976653i	$0.431082\pi$
$98$	8.34304	−	5.32857i	0.842775	−	0.538267i
$99$	−5.01728	+	0.274197i	−0.504255	+	0.0275578i
$100$	−0.441438	−	0.122715i	−0.0441438	−	0.0122715i
$101$	−2.47136	+	4.28052i	−0.245909	+	0.425927i	−0.962387	−	0.271683i	$-0.912420\pi$
$101$	−2.47136	+	4.28052i	−0.245909	+	0.425927i	0.716478	+	0.697610i	$0.245753\pi$
$102$	0.614580	−	0.494071i	0.0608525	−	0.0489203i
$103$	−15.8817	+	9.16928i	−1.56487	+	0.903476i	−0.568114	+	0.822950i	$0.692327\pi$
$103$	−15.8817	+	9.16928i	−1.56487	+	0.903476i	−0.996752	+	0.0805264i	$0.974340\pi$
$104$	−1.74646	+	4.05463i	−0.171254	+	0.397589i
$105$	−8.02212	+	5.98621i	−0.782879	+	0.584194i
$106$	4.73954	+	11.5952i	0.460344	+	1.12622i
$107$	−3.83045	+	2.21151i	−0.370303	+	0.213795i	−0.673591	−	0.739104i	$-0.735249\pi$
$107$	−3.83045	+	2.21151i	−0.370303	+	0.213795i	0.303288	+	0.952899i	$0.401916\pi$
$108$	−9.35298	−	4.53010i	−0.899991	−	0.435909i
$109$	7.04986	+	4.07024i	0.675255	+	0.389858i	0.798065	−	0.602572i	$-0.205857\pi$
$109$	7.04986	+	4.07024i	0.675255	+	0.389858i	−0.122810	+	0.992430i	$0.539191\pi$
$110$	−4.08990	−	3.16875i	−0.389956	−	0.302129i
$111$	−1.30107	+	1.37411i	−0.123492	+	0.130425i
$112$	3.46224	+	10.0006i	0.327151	+	0.944972i
$113$			13.4000i			1.26056i	0.776367	+	0.630281i	$0.217060\pi$
$113$			13.4000i			1.26056i	−0.776367	+	0.630281i	$0.782940\pi$
$114$	−13.9159	+	2.15339i	−1.30334	+	0.201684i
$115$	7.13629	−	12.3604i	0.665463	−	1.15262i
$116$	3.51796	+	13.6377i	0.326634	+	1.26623i
$117$	2.55908	+	3.92141i	0.236587	+	0.362535i
$118$	−8.11749	+	3.31803i	−0.747275	+	0.305449i
$119$	−0.545583	+	0.654056i	−0.0500136	+	0.0599572i
$120$	−4.22587	−	9.83076i	−0.385767	−	0.897422i
$121$	−4.09732	−	7.09677i	−0.372484	−	0.645161i
$122$	0.839974	−	6.15779i	0.0760476	−	0.557500i
$123$	−1.70323	−	5.72648i	−0.153575	−	0.516339i
$124$	4.80591	−	17.2881i	0.431583	−	1.55252i
$125$	−11.4216			−1.02158
$126$	10.8688	+	2.80536i	0.968266	+	0.249921i
$127$		−	12.5356i		−	1.11236i	−0.831063	−	0.556178i	$-0.812267\pi$
$127$		−	12.5356i		−	1.11236i	0.831063	−	0.556178i	$-0.187733\pi$
$128$	−11.2592	+	1.10918i	−0.995183	+	0.0980383i
$129$	−19.3527	+	5.75608i	−1.70391	+	0.506795i
$130$	−0.651652	+	4.77721i	−0.0571537	+	0.418989i
$131$	14.8145	−	8.55318i	1.29435	−	0.747295i	0.314930	−	0.949115i	$-0.398019\pi$
$131$	14.8145	−	8.55318i	1.29435	−	0.747295i	0.979423	+	0.201820i	$0.0646855\pi$
$132$	0.104166	+	5.80116i	0.00906653	+	0.504926i
$133$	14.2773	−	5.24361i	1.23800	−	0.454678i
$134$	0.766320	+	1.87479i	0.0662000	+	0.161957i
$135$	−11.1665	−	2.03086i	−0.961057	−	0.174789i
$136$	−0.544124	−	0.730079i	−0.0466582	−	0.0626038i
$137$	−17.9399	−	10.3576i	−1.53271	−	0.884909i	−0.999236	−	0.0390917i	$-0.987554\pi$
$137$	−17.9399	−	10.3576i	−1.53271	−	0.884909i	−0.533472	−	0.845818i	$-0.679113\pi$
$138$	−15.8175	+	2.44766i	−1.34648	+	0.208359i
$139$	1.27255			0.107936			0.0539682	−	0.998543i	$-0.482813\pi$
$139$	1.27255			0.107936			0.0539682	+	0.998543i	$0.482813\pi$
$140$	6.56829	+	9.51015i	0.555122	+	0.803755i
$141$	5.66906	+	5.36770i	0.477421	+	0.452042i
$142$	−5.51807	+	7.12215i	−0.463066	+	0.597677i
$143$	1.30715	−	2.26406i	0.109310	−	0.189330i
$144$	−5.62304	+	10.6010i	−0.468587	+	0.883417i
$145$	7.69077	+	13.3208i	0.638684	+	1.10623i
$146$	−4.80520	−	11.7558i	−0.397681	−	0.972918i
$147$	−12.1066	−	0.656207i	−0.998534	−	0.0541230i
$148$	1.53059	+	1.55946i	0.125814	+	0.128187i
$149$	−2.47136	−	4.28052i	−0.202461	−	0.350674i	0.746859	−	0.664982i	$-0.231561\pi$
$149$	−2.47136	−	4.28052i	−0.202461	−	0.350674i	−0.949321	+	0.314308i	$0.898227\pi$
$150$	0.351591	+	0.437348i	0.0287073	+	0.0357093i
$151$	−5.48605	−	3.16737i	−0.446448	−	0.257757i	0.259881	−	0.965641i	$-0.416317\pi$
$151$	−5.48605	−	3.16737i	−0.446448	−	0.257757i	−0.706329	+	0.707884i	$0.749650\pi$
$152$	1.89620	+	16.1490i	0.153802	+	1.30985i
$153$	−0.964337	+	0.0527015i	−0.0779620	+	0.00426066i
$154$	−1.34564	−	6.12081i	−0.108435	−	0.493229i
$155$		−	19.5966i		−	1.57404i
$156$	4.63327	−	2.78711i	0.370959	−	0.223147i
$157$	−2.09256	−	1.20814i	−0.167004	−	0.0964199i	0.414168	−	0.910200i	$-0.364072\pi$
$157$	−2.09256	−	1.20814i	−0.167004	−	0.0964199i	−0.581172	+	0.813780i	$0.697406\pi$
$158$	−0.791906	+	5.80541i	−0.0630007	+	0.461853i
$159$	3.56476	−	14.9218i	0.282704	−	1.18337i
$160$	−11.5227	+	4.46049i	−0.910952	+	0.352632i
$161$	16.2284	−	5.96017i	1.27897	−	0.469727i
$162$	6.07101	+	11.1867i	0.476984	+	0.878912i
$163$	4.46077	+	7.72628i	0.349395	+	0.605169i	0.986142	−	0.165903i	$-0.0530539\pi$
$163$	4.46077	+	7.72628i	0.349395	+	0.605169i	−0.636747	+	0.771072i	$0.719721\pi$
$164$	−6.67998	+	1.72316i	−0.521619	+	0.134556i
$165$	1.80648	+	6.07363i	0.140634	+	0.472832i
$166$	−10.1336	−	7.85130i	−0.786523	−	0.609379i
$167$	−7.01131			−0.542551			−0.271276	−	0.962502i	$-0.587445\pi$
$167$	−7.01131			−0.542551			−0.271276	+	0.962502i	$0.587445\pi$
$168$	3.69694	−	12.4231i	0.285225	−	0.958461i
$169$	10.5637			0.812595
$170$	−0.786091	−	0.609045i	−0.0602904	−	0.0467116i
$171$	15.3840	+	7.79525i	1.17644	+	0.596118i
$172$	5.82345	+	22.5751i	0.444034	+	1.72133i
$173$	7.11660	+	12.3263i	0.541065	+	0.937152i	0.998843	+	0.0480854i	$0.0153120\pi$
$173$	7.11660	+	12.3263i	0.541065	+	0.937152i	−0.457778	+	0.889066i	$0.651355\pi$
$174$	6.23883	−	16.0817i	0.472965	−	1.21915i
$175$	−0.465440	−	0.388249i	−0.0351840	−	0.0293488i
$176$	6.69851	+	0.125195i	0.504919	+	0.00943693i
$177$	10.4464	+	2.49560i	0.785196	+	0.187581i
$178$	−1.00994	+	7.40378i	−0.0756981	+	0.554937i
$179$	1.07613	+	0.621304i	0.0804338	+	0.0464384i	0.539677	−	0.841872i	$-0.318546\pi$
$179$	1.07613	+	0.621304i	0.0804338	+	0.0464384i	−0.459244	+	0.888310i	$0.651880\pi$
$180$	−2.81582	+	12.7994i	−0.209879	+	0.954009i
$181$		−	20.9487i		−	1.55710i	−0.627580	−	0.778552i	$-0.715954\pi$
$181$		−	20.9487i		−	1.55710i	0.627580	−	0.778552i	$-0.284046\pi$
$182$	−4.31278	+	3.93797i	−0.319685	+	0.291902i
$183$	−5.23327	+	5.52709i	−0.386855	+	0.408574i
$184$	2.15532	+	18.3558i	0.158892	+	1.35321i
$185$	2.06667	+	1.19319i	0.151945	+	0.0877253i
$186$	−17.1279	+	13.7694i	−1.25588	+	1.00962i
$187$	0.269600	+	0.466960i	0.0197151	+	0.0341475i
$188$	6.43374	−	6.31461i	0.469228	−	0.460541i
$189$	−8.81091	−	10.5531i	−0.640899	−	0.767625i
$190$	6.71889	+	16.4376i	0.487440	+	1.19251i
$191$	−12.2119	−	21.1516i	−0.883621	−	1.53048i	−0.847287	−	0.531136i	$-0.821765\pi$
$191$	−12.2119	−	21.1516i	−0.883621	−	1.53048i	−0.0363339	−	0.999340i	$-0.511568\pi$
$192$	11.9949	+	6.93700i	0.865658	+	0.500635i
$193$	0.00662606	−	0.0114767i	0.000476954	−	0.000826109i	−0.865787	−	0.500413i	$-0.833182\pi$
$193$	0.00662606	−	0.0114767i	0.000476954	−	0.000826109i	0.866264	+	0.499587i	$0.166515\pi$
$194$	−3.66515	+	4.73058i	−0.263142	+	0.339636i
$195$	4.05998	−	4.28792i	0.290741	−	0.307064i
$196$	−1.26934	+	13.9423i	−0.0906668	+	0.995881i
$197$	−6.48422			−0.461981			−0.230991	−	0.972956i	$-0.574197\pi$
$197$	−6.48422			−0.461981			−0.230991	+	0.972956i	$0.574197\pi$
$198$	4.03918	−	5.84649i	0.287052	−	0.415492i
$199$	−4.47013	−	2.58083i	−0.316879	−	0.182950i	0.333121	−	0.942884i	$-0.391898\pi$
$199$	−4.47013	−	2.58083i	−0.316879	−	0.182950i	−0.650001	+	0.759934i	$0.725231\pi$
$200$	0.519540	−	0.387210i	0.0367370	−	0.0273799i
$201$	0.576375	−	2.41265i	0.0406543	−	0.170175i
$202$	−2.64478	−	6.47039i	−0.186086	−	0.455255i
$203$	−3.18193	+	18.3578i	−0.223328	+	1.28846i
$204$	0.0200211	+	1.11500i	0.00140176	+	0.0780657i
$205$	−6.52478	+	3.76708i	−0.455710	+	0.263104i
$206$	3.50524	−	25.6967i	0.244222	−	1.79037i
$207$	17.4863	+	8.86051i	1.21538	+	0.615848i
$208$	−3.02013	−	5.46435i	−0.209408	−	0.378884i
$209$		−	9.62870i		−	0.666031i
$210$	0.256167	−	14.1532i	0.0176772	−	0.976663i
$211$	−16.8357			−1.15902			−0.579509	−	0.814966i	$-0.696756\pi$
$211$	−16.8357			−1.15902			−0.579509	+	0.814966i	$0.696756\pi$
$212$	−17.0678	−	4.74468i	−1.17222	−	0.325866i
$213$	10.5766	−	3.14581i	0.724698	−	0.215547i
$214$	0.845418	−	6.19770i	0.0577916	−	0.423666i
$215$	12.7309	+	22.0506i	0.868240	+	1.50384i
$216$	13.1655	−	6.53228i	0.895796	−	0.444466i
$217$	15.2050	−	18.2281i	1.03218	−	1.23740i
$218$	−10.6565	+	4.35586i	−0.721751	+	0.295016i
$219$	−3.61415	+	15.1285i	−0.244221	+	1.02229i
$220$	7.08493	−	1.82762i	0.477666	−	0.123218i
$221$	0.251239	−	0.435159i	0.0169002	−	0.0292720i
$222$	−0.409251	−	2.64470i	−0.0274671	−	0.177501i
$223$			1.80170i			0.120651i	0.998179	+	0.0603254i	$0.0192138\pi$
$223$			1.80170i			0.120651i	−0.998179	+	0.0603254i	$0.980786\pi$
$224$	−14.1789	−	4.79150i	−0.947368	−	0.320145i
$225$	−0.0375035	−	0.686242i	−0.00250023	−	0.0457495i
$226$	−14.9803	−	11.6064i	−0.996475	−	0.772045i
$227$	−10.0476	−	5.80096i	−0.666879	−	0.385023i	0.128014	−	0.991772i	$-0.459140\pi$
$227$	−10.0476	−	5.80096i	−0.666879	−	0.385023i	−0.794893	+	0.606749i	$0.792473\pi$
$228$	9.64589	−	17.4222i	0.638815	−	1.15382i
$229$	−8.50697	+	4.91150i	−0.562156	+	0.324561i	−0.754010	−	0.656862i	$-0.771883\pi$
$229$	−8.50697	+	4.91150i	−0.562156	+	0.324561i	0.191854	+	0.981423i	$0.438550\pi$
$230$	7.63706	+	18.6839i	0.503573	+	1.23198i
$231$	−3.03220	+	7.05112i	−0.199504	+	0.463930i
$232$	−18.2931	−	7.87942i	−1.20100	−	0.517309i
$233$	−6.94161	+	4.00774i	−0.454760	+	0.262556i	−0.709838	−	0.704365i	$-0.751232\pi$
$233$	−6.94161	+	4.00774i	−0.454760	+	0.262556i	0.255079	+	0.966920i	$0.417899\pi$
$234$	−6.60044	−	0.535645i	−0.431485	−	0.0350162i
$235$	4.92265	−	8.52627i	0.321118	−	0.556193i
$236$	3.32163	−	11.9488i	0.216219	−	0.777797i
$237$	4.93380	−	5.21080i	0.320485	−	0.338478i
$238$	−0.258636	−	1.17644i	−0.0167649	−	0.0762572i
$239$	6.02441			0.389686			0.194843	−	0.980834i	$-0.437580\pi$
$239$	6.02441			0.389686			0.194843	+	0.980834i	$0.437580\pi$
$240$	14.6504	+	3.79067i	0.945680	+	0.244687i
$241$	5.11917	−	8.86666i	0.329755	−	0.571152i	−0.652708	−	0.757609i	$-0.726367\pi$
$241$	5.11917	−	8.86666i	0.329755	−	0.571152i	0.982463	+	0.186457i	$0.0597006\pi$
$242$	11.4826	+	1.56633i	0.738132	+	0.100687i
$243$	1.94826	−	15.4662i	0.124981	−	0.992159i
$244$	6.15647	+	6.27261i	0.394128	+	0.401563i
$245$	2.74260	+	15.0417i	0.175218	+	0.960979i
$246$	7.87710	+	3.05590i	0.502225	+	0.194837i
$247$	−7.77081	+	4.48648i	−0.494445	+	0.285468i
$248$	15.1644	+	20.3468i	0.962937	+	1.29202i
$249$	4.47597	+	15.0488i	0.283653	+	0.953678i
$250$	9.89282	−	12.7686i	0.625677	−	0.807558i
$251$			9.97684i			0.629733i	0.949136	+	0.314866i	$0.101960\pi$
$251$			9.97684i			0.629733i	−0.949136	+	0.314866i	$0.898040\pi$
$252$	−12.5502	+	9.72072i	−0.790588	+	0.612348i
$253$		−	10.9445i		−	0.688075i
$254$	14.0140	+	10.8577i	0.879319	+	0.681275i
$255$	0.347212	+	1.16737i	0.0217432	+	0.0731036i
$256$	8.51218	−	13.5478i	0.532011	−	0.846737i
$257$	−17.1555	+	9.90475i	−1.07013	+	0.617841i	−0.928218	−	0.372038i	$-0.878659\pi$
$257$	−17.1555	+	9.90475i	−1.07013	+	0.617841i	−0.141915	+	0.989879i	$0.545326\pi$
$258$	10.3274	−	26.6207i	0.642958	−	1.65733i
$259$	0.996544	+	2.71339i	0.0619222	+	0.168602i
$260$	−4.77619	−	4.86629i	−0.296207	−	0.301795i
$261$	−17.6921	+	11.5457i	−1.09511	+	0.714662i
$262$	−3.26972	+	23.9701i	−0.202004	+	1.48088i
$263$	−3.41780	+	5.91981i	−0.210751	+	0.365031i	−0.951950	−	0.306254i	$-0.900924\pi$
$263$	−3.41780	+	5.91981i	−0.210751	+	0.365031i	0.741199	+	0.671285i	$0.234258\pi$
$264$	−6.57555	−	4.90823i	−0.404697	−	0.302081i
$265$	−19.3470			−1.18847
$266$	−6.50428	+	20.5029i	−0.398803	+	1.25711i
$267$	6.29220	−	6.64546i	0.385077	−	0.406696i
$268$	−2.75964	−	0.767151i	−0.168572	−	0.0468612i
$269$	12.0822	−	20.9270i	0.736665	−	1.27594i	−0.217324	−	0.976099i	$-0.569733\pi$
$269$	12.0822	−	20.9270i	0.736665	−	1.27594i	0.953989	−	0.299842i	$-0.0969338\pi$
$270$	11.9422	−	10.7244i	0.726781	−	0.652665i
$271$	15.2835	−	8.82392i	0.928405	−	0.536015i	0.0420983	−	0.999113i	$-0.486596\pi$
$271$	15.2835	−	8.82392i	0.928405	−	0.536015i	0.886307	+	0.463099i	$0.153262\pi$
$272$	1.28748	+	0.0240629i	0.0780647	+	0.00145903i
$273$	7.10344	−	0.838329i	0.429919	−	0.0507380i
$274$	27.1178	−	11.0844i	1.63825	−	0.669634i
$275$	−0.332299	+	0.191853i	−0.0200384	+	0.0115692i
$276$	10.9641	−	19.8031i	0.659958	−	1.19200i
$277$	−12.9250	−	7.46224i	−0.776587	−	0.448363i	0.0586324	−	0.998280i	$-0.481326\pi$
$277$	−12.9250	−	7.46224i	−0.776587	−	0.448363i	−0.835219	+	0.549917i	$0.814659\pi$
$278$	−1.10222	+	1.42263i	−0.0661068	+	0.0853237i
$279$	26.8754	−	1.46875i	1.60899	−	0.0879320i
$280$	−16.3209	−	0.894293i	−0.975359	−	0.0534442i
$281$			13.8890i			0.828547i	0.910152	+	0.414273i	$0.135964\pi$
$281$			13.8890i			0.828547i	−0.910152	+	0.414273i	$0.864036\pi$
$282$	−10.9110	+	1.68841i	−0.649741	+	0.100543i
$283$	2.88865	−	5.00329i	0.171712	−	0.297415i	−0.767306	−	0.641281i	$-0.778403\pi$
$283$	2.88865	−	5.00329i	0.171712	−	0.297415i	0.939019	+	0.343866i	$0.111737\pi$
$284$	−3.18263	−	12.3377i	−0.188854	−	0.732108i
$285$	5.05350	−	21.1535i	0.299343	−	1.25303i
$286$	1.39888	+	3.42233i	0.0827175	+	0.202367i
$287$	−8.99199	−	1.55857i	−0.530780	−	0.0919994i
$288$	−6.98085	−	15.4683i	−0.411351	−	0.911477i
$289$	−8.44818	−	14.6327i	−0.496952	−	0.860746i
$290$	−21.5532	−	2.94003i	−1.26565	−	0.172645i
$291$	7.02508	−	2.08947i	0.411817	−	0.122487i
$292$	17.3043	+	4.81041i	1.01266	+	0.281508i
$293$	15.6381			0.913587			0.456794	−	0.889573i	$-0.348998\pi$
$293$	15.6381			0.913587			0.456794	+	0.889573i	$0.348998\pi$
$294$	11.2197	−	12.9660i	0.654348	−	0.756194i
$295$		−	13.5443i		−	0.788581i
$296$	−3.06910	+	0.360371i	−0.178388	+	0.0209461i
$297$	−8.19415	+	2.93267i	−0.475473	+	0.170171i
$298$	6.92591	+	0.944753i	0.401207	+	0.0547281i
$299$	−8.83273	+	5.09958i	−0.510810	+	0.294916i
$300$	−0.793458	+	0.0142475i	−0.0458103	+	0.000822577i
$301$	−5.26720	+	30.3885i	−0.303597	+	1.75157i
$302$	8.29267	−	3.38963i	0.477190	−	0.195052i
$303$	−1.98922	+	8.32672i	−0.114278	+	0.478358i
$304$	−19.6959	−	11.8676i	−1.12964	−	0.680655i
$305$	8.31274	+	4.79936i	0.475986	+	0.274811i
$306$	0.776344	−	1.12371i	0.0443806	−	0.0642385i
$307$	7.19887			0.410861			0.205430	−	0.978672i	$-0.434141\pi$
$307$	7.19887			0.410861			0.205430	+	0.978672i	$0.434141\pi$
$308$	8.00820	+	3.79721i	0.456310	+	0.216366i
$309$	−21.8387	+	23.0647i	−1.24236	+	1.31211i
$310$	21.9078	+	16.9737i	1.24428	+	0.964039i
$311$	−4.35089	+	7.53597i	−0.246717	+	0.427326i	−0.962613	−	0.270881i	$-0.912685\pi$
$311$	−4.35089	+	7.53597i	−0.246717	+	0.427326i	0.715896	+	0.698207i	$0.246018\pi$
$312$	−0.897300	+	7.59376i	−0.0507996	+	0.429912i
$313$	9.57541	+	16.5851i	0.541234	+	0.937445i	0.998834	+	0.0482863i	$0.0153760\pi$
$313$	9.57541	+	16.5851i	0.541234	+	0.937445i	−0.457600	+	0.889158i	$0.651291\pi$
$314$	3.16309	−	1.29292i	0.178504	−	0.0729634i
$315$	−10.3622	+	13.8994i	−0.583844	+	0.783140i
$316$	−5.80417	−	5.91366i	−0.326510	−	0.332669i
$317$	−1.83178	−	3.17274i	−0.102883	−	0.178199i	0.809988	−	0.586446i	$-0.199473\pi$
$317$	−1.83178	−	3.17274i	−0.102883	−	0.178199i	−0.912871	+	0.408247i	$0.866140\pi$
$318$	13.5940	+	16.9097i	0.762313	+	0.948249i
$319$	10.2147	+	5.89744i	0.571911	+	0.330193i
$320$	4.99388	−	16.7451i	0.279166	−	0.936081i
$321$	−5.26720	+	5.56291i	−0.293986	+	0.310491i
$322$	−7.39313	+	23.3047i	−0.412003	+	1.29872i
$323$		−	1.85067i		−	0.102974i
$324$	−17.7645	−	2.90239i	−0.986915	−	0.161244i
$325$	0.309668	+	0.178787i	0.0171773	+	0.00991732i
$326$	−12.5012	−	1.70527i	−0.692377	−	0.0944461i
$327$	13.7138	+	3.27618i	0.758376	+	0.181173i
$328$	3.85949	−	8.96031i	0.213104	−	0.494751i
$329$	11.1944	−	4.11135i	0.617167	−	0.226666i
$330$	−8.35462	−	3.24115i	−0.459907	−	0.178419i
$331$	5.41365	+	9.37672i	0.297561	+	0.515391i	0.975577	−	0.219656i	$-0.0704934\pi$
$331$	5.41365	+	9.37672i	0.297561	+	0.515391i	−0.678016	+	0.735047i	$0.737160\pi$
$332$	17.5545	−	4.52835i	0.963430	−	0.248525i
$333$	−1.48148	+	2.92372i	−0.0811847	+	0.160219i
$334$	6.07285	−	7.83820i	0.332292	−	0.428887i
$335$	−3.12815			−0.170909
$336$	10.6861	+	14.8932i	0.582975	+	0.812490i
$337$	−20.0426			−1.09179			−0.545894	−	0.837854i	$-0.683810\pi$
$337$	−20.0426			−1.09179			−0.545894	+	0.837854i	$0.683810\pi$
$338$	−9.14979	+	11.8096i	−0.497683	+	0.642357i
$339$	6.61670	+	22.2462i	0.359370	+	1.20825i
$340$	1.36175	−	0.351275i	0.0738511	−	0.0190506i
$341$	−7.51355	−	13.0139i	−0.406882	−	0.704740i
$342$	−22.0395	+	10.4465i	−1.19176	+	0.564880i
$343$	−9.11979	+	16.1192i	−0.492422	+	0.870357i
$344$	−30.2815	−	13.0432i	−1.63267	−	0.703241i
$345$	5.74408	−	24.0442i	0.309251	−	1.29450i
$346$	−19.9441	−	2.72054i	−1.07220	−	0.146257i
$347$	5.06136	+	2.92218i	0.271708	+	0.156871i	0.629664	−	0.776868i	$-0.283193\pi$
$347$	5.06136	+	2.92218i	0.271708	+	0.156871i	−0.357955	+	0.933739i	$0.616526\pi$
$348$	12.5745	+	20.9038i	0.674064	+	1.12056i
$349$			18.6166i			0.996526i	0.867026	+	0.498263i	$0.166029\pi$
$349$			18.6166i			0.996526i	−0.867026	+	0.498263i	$0.833971\pi$
$350$	0.837179	−	0.184051i	0.0447491	−	0.00983792i
$351$	6.18486	+	5.24659i	0.330123	+	0.280042i
$352$	−5.94188	+	7.38008i	−0.316704	+	0.393359i
$353$	−5.78219	−	3.33835i	−0.307755	−	0.177682i	0.338167	−	0.941086i	$-0.390193\pi$
$353$	−5.78219	−	3.33835i	−0.307755	−	0.177682i	−0.645921	+	0.763404i	$0.723527\pi$
$354$	−11.8380	+	9.51680i	−0.629185	+	0.505812i
$355$	−6.95768	−	12.0511i	−0.369275	−	0.639603i
$356$	−7.40220	−	7.54184i	−0.392316	−	0.399717i
$357$	−0.582800	+	1.35525i	−0.0308450	+	0.0717273i
$358$	−1.62667	+	0.664902i	−0.0859722	+	0.0351412i
$359$	12.1282	+	21.0067i	0.640102	+	1.10869i	0.985410	+	0.170200i	$0.0544414\pi$
$359$	12.1282	+	21.0067i	0.640102	+	1.10869i	−0.345307	+	0.938490i	$0.612225\pi$
$360$	−11.8700	−	14.2341i	−0.625602	−	0.750203i
$361$	−7.02406	+	12.1660i	−0.369687	+	0.640317i
$362$	23.4193	+	18.1447i	1.23089	+	0.953666i
$363$	−10.3065	−	9.75866i	−0.540953	−	0.512197i
$364$	−0.666886	−	8.23230i	−0.0349543	−	0.431490i
$365$	19.6150			1.02670
$366$	−1.64612	−	10.6378i	−0.0860443	−	0.556045i
$367$	6.54864	+	3.78086i	0.341836	+	0.197359i	0.661084	−	0.750312i	$-0.270097\pi$
$367$	6.54864	+	3.78086i	0.341836	+	0.197359i	−0.319248	+	0.947671i	$0.603430\pi$
$368$	−22.3875	−	13.4894i	−1.16703	−	0.703183i
$369$	−5.65531	−	8.66592i	−0.294404	−	0.451130i
$370$	−3.12396	+	1.27692i	−0.162407	+	0.0663840i
$371$	−17.9958	−	15.0113i	−0.934298	−	0.779348i
$372$	−0.557975	−	31.0743i	−0.0289296	−	1.61113i
$373$	16.9620	−	9.79302i	0.878260	−	0.507063i	0.00817543	−	0.999967i	$-0.497398\pi$
$373$	16.9620	−	9.79302i	0.878260	−	0.507063i	0.870084	+	0.492903i	$0.164064\pi$
$374$	−0.755546	−	0.103063i	−0.0390684	−	0.00532925i
$375$	−18.9618	+	5.63982i	−0.979184	+	0.291239i
$376$	1.48675	+	12.6619i	0.0766733	+	0.652989i
$377$		−	10.9916i		−	0.566097i
$378$	19.4293	−	0.709456i	0.999334	−	0.0364905i
$379$	4.99759			0.256709			0.128354	−	0.991728i	$-0.459031\pi$
$379$	4.99759			0.256709			0.128354	+	0.991728i	$0.459031\pi$
$380$	−24.1958	−	6.72618i	−1.24122	−	0.345046i
$381$	−6.18991	−	20.8113i	−0.317119	−	1.06620i
$382$	34.2235	+	4.66837i	1.75103	+	0.238855i
$383$	−15.1532	−	26.2461i	−0.774292	−	1.34111i	−0.935192	−	0.354142i	$-0.884773\pi$
$383$	−15.1532	−	26.2461i	−0.774292	−	1.34111i	0.160900	−	0.986971i	$-0.448560\pi$
$384$	−18.1445	+	7.40106i	−0.925935	+	0.377684i
$385$	9.53710	+	1.65305i	0.486056	+	0.0842474i
$386$	0.00709102	+	0.0173480i	0.000360924	+	0.000882992i
$387$	−29.2866	+	19.1122i	−1.48872	+	0.971527i
$388$	−2.11392	−	8.19480i	−0.107318	−	0.416028i
$389$	−2.13059	+	3.69030i	−0.108025	+	0.187106i	−0.914970	−	0.403521i	$-0.867786\pi$
$389$	−2.13059	+	3.69030i	−0.108025	+	0.187106i	0.806945	+	0.590627i	$0.201119\pi$
$390$	1.27706	+	8.25278i	0.0646667	+	0.417896i
$391$		−	2.10357i		−	0.106382i
$392$	−14.4872	−	13.4952i	−0.731715	−	0.681611i
$393$	20.3713	−	21.5150i	1.02760	−	1.08529i
$394$	5.61631	−	7.24894i	0.282946	−	0.365196i
$395$	−7.83704	−	4.52472i	−0.394324	−	0.227663i
$396$	3.03746	+	9.57950i	0.152638	+	0.481388i
$397$	−17.1398	+	9.89568i	−0.860223	+	0.496650i	−0.864087	−	0.503343i	$-0.832103\pi$
$397$	−17.1398	+	9.89568i	−0.860223	+	0.496650i	0.00386406	+	0.999993i	$0.498770\pi$
$398$	6.75702	−	2.76194i	0.338699	−	0.138443i
$399$	21.1136	−	15.7552i	1.05700	−	0.788748i
$400$	−0.0171236	+	0.916195i	−0.000856182	+	0.0458097i
$401$	−1.98773	+	1.14762i	−0.0992627	+	0.0573094i	−0.548810	−	0.835947i	$-0.684919\pi$
$401$	−1.98773	+	1.14762i	−0.0992627	+	0.0573094i	0.449547	+	0.893257i	$0.351585\pi$
$402$	2.19797	+	2.73407i	0.109625	+	0.136363i
$403$	−7.00186	+	12.1276i	−0.348787	+	0.604118i
$404$	9.52427	+	2.64765i	0.473850	+	0.131725i
$405$	−19.5411	+	2.14226i	−0.971005	+	0.106450i
$406$	−17.7668	−	19.4578i	−0.881752	−	0.965675i
$407$	1.82993			0.0907062
$408$	−1.26384	−	0.943378i	−0.0625695	−	0.0467042i
$409$	−0.750621	+	1.30011i	−0.0371158	+	0.0642865i	−0.883987	−	0.467512i	$-0.845150\pi$
$409$	−0.750621	+	1.30011i	−0.0371158	+	0.0642865i	0.846871	+	0.531799i	$0.178484\pi$
$410$	1.44008	−	10.5571i	0.0711207	−	0.521380i
$411$	−34.8978	−	8.33695i	−1.72138	−	0.411231i
$412$	25.6912	+	26.1758i	1.26571	+	1.28959i
$413$	10.5090	−	12.5984i	0.517116	−	0.619928i
$414$	−25.0513	+	11.8740i	−1.23120	+	0.583576i
$415$	17.1467	−	9.89963i	0.841696	−	0.485954i
$416$	8.72468	+	1.35664i	0.427763	+	0.0665149i
$417$	2.11265	−	0.628367i	0.103457	−	0.0307713i
$418$	10.7643	+	8.33991i	0.526498	+	0.407918i
$419$			8.44514i			0.412572i	0.978492	+	0.206286i	$0.0661378\pi$
$419$			8.44514i			0.412572i	−0.978492	+	0.206286i	$0.933862\pi$
$420$	15.6005	+	12.5452i	0.761226	+	0.612142i
$421$		−	13.9326i		−	0.679032i	−0.940600	−	0.339516i	$-0.889737\pi$
$421$		−	13.9326i		−	0.679032i	0.940600	−	0.339516i	$-0.110263\pi$
$422$	14.5823	−	18.8213i	0.709854	−	0.916204i
$423$	12.0621	+	6.11202i	0.586480	+	0.297176i
$424$	20.0876	−	14.9711i	0.975538	−	0.727063i
$425$	−0.0638689	+	0.0368747i	−0.00309809	+	0.00178869i
$426$	−5.64414	+	14.5487i	−0.273460	+	0.704889i
$427$	4.00839	+	10.9140i	0.193979	+	0.528168i
$428$	6.19638	+	6.31327i	0.299513	+	0.305163i
$429$	1.05214	−	4.40418i	0.0507979	−	0.212636i
$430$	−35.6780	−	4.86678i	−1.72055	−	0.234697i
$431$	−16.9743	+	29.4004i	−0.817624	+	1.41617i	0.0898039	+	0.995959i	$0.471376\pi$
$431$	−16.9743	+	29.4004i	−0.817624	+	1.41617i	−0.907428	+	0.420207i	$0.861957\pi$
$432$	−4.10060	+	20.3761i	−0.197290	+	0.980345i
$433$	4.44336			0.213534			0.106767	−	0.994284i	$-0.465950\pi$
$433$	4.44336			0.213534			0.106767	+	0.994284i	$0.465950\pi$
$434$	7.20800	+	32.7865i	0.345995	+	1.57380i
$435$	19.3456	+	18.3173i	0.927552	+	0.878245i
$436$	4.36058	−	15.6861i	0.208834	−	0.751230i
$437$	−18.7822	+	32.5316i	−0.898472	+	1.55620i
$438$	−13.7823	−	17.1440i	−0.658544	−	0.819170i
$439$	7.55680	−	4.36292i	0.360667	−	0.208231i	−0.308707	−	0.951157i	$-0.599896\pi$
$439$	7.55680	−	4.36292i	0.360667	−	0.208231i	0.669373	+	0.742926i	$0.266563\pi$
$440$	−4.09346	+	9.50351i	−0.195148	+	0.453062i
$441$	−20.4231	+	4.88864i	−0.972526	+	0.232792i
$442$	0.268869	+	0.657783i	0.0127888	+	0.0312875i
$443$	32.0121	−	18.4822i	1.52094	−	0.878115i	0.521244	−	0.853407i	$-0.325468\pi$
$443$	32.0121	−	18.4822i	1.52094	−	0.878115i	0.999695	−	0.0247072i	$-0.00786534\pi$
$444$	3.31108	+	1.83320i	0.157137	+	0.0869997i
$445$	−9.99478	−	5.77049i	−0.473798	−	0.273548i
$446$	−2.01419	−	1.56055i	−0.0953745	−	0.0738940i
$447$	−6.21654	−	5.88608i	−0.294032	−	0.278402i
$448$	17.6377	−	11.7010i	0.833302	−	0.552819i
$449$			23.4269i			1.10559i	0.833319	+	0.552793i	$0.186438\pi$
$449$			23.4269i			1.10559i	−0.833319	+	0.552793i	$0.813562\pi$
$450$	0.799659	+	0.552463i	0.0376963	+	0.0260433i
$451$	−2.88868	+	5.00333i	−0.136022	+	0.235598i
$452$	25.9504	−	6.69414i	1.22060	−	0.314866i
$453$	−10.6718	−	2.54945i	−0.501405	−	0.119784i
$454$	15.1878	−	6.20802i	0.712799	−	0.291357i
$455$	−3.10971	−	8.46712i	−0.145785	−	0.396945i
$456$	11.1221	+	25.8738i	0.520842	+	1.21165i
$457$	0.661376	+	1.14554i	0.0309378	+	0.0535859i	0.881080	−	0.472968i	$-0.156817\pi$
$457$	0.661376	+	1.14554i	0.0309378	+	0.0535859i	−0.850142	+	0.526554i	$0.823484\pi$
$458$	1.87757	−	13.7644i	0.0877332	−	0.643166i
$459$	−1.57494	+	0.563669i	−0.0735120	+	0.0263098i
$460$	−27.5023	−	7.64534i	−1.28230	−	0.356466i
$461$	23.5461			1.09665			0.548325	−	0.836266i	$-0.315266\pi$
$461$	23.5461			1.09665			0.548325	+	0.836266i	$0.315266\pi$
$462$	−5.25636	−	9.49715i	−0.244548	−	0.441847i
$463$			14.4502i			0.671557i	0.941941	+	0.335778i	$0.108999\pi$
$463$			14.4502i			0.671557i	−0.941941	+	0.335778i	$0.891001\pi$
$464$	24.6533	−	13.6258i	1.14450	−	0.632562i
$465$	−9.67654	−	32.5338i	−0.448739	−	1.50872i
$466$	1.53208	−	11.2316i	0.0709723	−	0.520293i
$467$	13.0084	−	7.51039i	0.601956	−	0.347540i	−0.167855	−	0.985812i	$-0.553684\pi$
$467$	13.0084	−	7.51039i	0.601956	−	0.347540i	0.769811	+	0.638272i	$0.220351\pi$
$468$	6.31580	−	6.91493i	0.291948	−	0.319643i
$469$	−2.90969	−	2.42713i	−0.134357	−	0.112074i
$470$	5.26808	+	12.8882i	0.242998	+	0.594491i
$471$	−4.07057	−	0.972444i	−0.187562	−	0.0448079i
$472$	10.4809	+	14.0628i	0.482423	+	0.647292i
$473$	16.9088	+	9.76231i	0.777468	+	0.448872i
$474$	1.55192	+	10.0290i	0.0712823	+	0.460648i
$475$	1.31697			0.0604269
$476$	1.53920	+	0.729836i	0.0705492	+	0.0334520i
$477$	−1.45004	−	26.5330i	−0.0663928	−	1.21486i
$478$	−5.21805	+	6.73491i	−0.238668	+	0.308047i
$479$	10.9550	−	18.9745i	0.500545	−	0.866969i	−0.499455	−	0.866340i	$-0.666466\pi$
$479$	10.9550	−	18.9745i	0.500545	−	0.866969i	1.00000		0.000629369i	$-0.000200335\pi$
$480$	−16.9272	+	13.0949i	−0.772617	+	0.597699i
$481$	−0.852653	−	1.47684i	−0.0388776	−	0.0673380i
$482$	5.47839	+	13.4028i	0.249534	+	0.610480i
$483$	23.9989	−	17.9083i	1.09199	−	0.814854i
$484$	−11.6967	+	11.4802i	−0.531670	+	0.521826i
$485$	−4.62134	−	8.00440i	−0.209844	−	0.363461i
$486$	15.6028	+	15.5741i	0.707756	+	0.706457i
$487$	−9.51388	−	5.49284i	−0.431115	−	0.248904i	0.268707	−	0.963222i	$-0.413404\pi$
$487$	−9.51388	−	5.49284i	−0.431115	−	0.248904i	−0.699821	+	0.714318i	$0.746737\pi$
$488$	−12.3448	+	1.44952i	−0.558824	+	0.0656165i
$489$	11.2208	+	10.6243i	0.507421	+	0.480448i
$490$	−19.1912	−	9.96233i	−0.866969	−	0.450052i
$491$		−	32.3525i		−	1.46005i	−0.683422	−	0.730024i	$-0.739509\pi$
$491$		−	32.3525i		−	1.46005i	0.683422	−	0.730024i	$-0.260491\pi$
$492$	−10.2391	+	6.15923i	−0.461612	+	0.277679i
$493$	1.96329	+	1.13351i	0.0884222	+	0.0510506i
$494$	1.71510	−	12.5732i	0.0771658	−	0.565697i
$495$	5.99814	+	9.19127i	0.269597	+	0.413117i
$496$	−35.8810	−	0.670615i	−1.61111	−	0.0301115i
$497$	2.87863	−	16.6079i	0.129124	−	0.744967i
$498$	−20.7005	−	8.03068i	−0.927610	−	0.359863i
$499$	−7.10372	−	12.3040i	−0.318006	−	0.550803i	0.662066	−	0.749446i	$-0.269680\pi$
$499$	−7.10372	−	12.3040i	−0.318006	−	0.550803i	−0.980072	+	0.198643i	$0.936347\pi$
$500$	5.70583	+	22.1191i	0.255172	+	0.989196i
$501$	−11.6400	+	3.46208i	−0.520036	+	0.154674i
$502$	−11.1535	−	8.64145i	−0.497804	−	0.385687i
$503$	−33.4106			−1.48970			−0.744852	−	0.667229i	$-0.767480\pi$
$503$	−33.4106			−1.48970			−0.744852	+	0.667229i	$0.767480\pi$
$504$	0.00322006	−	22.4499i	0.000143433	−	1.00000i
$505$	10.7961			0.480419
$506$	12.2353	+	9.47960i	0.543924	+	0.421420i
$507$	17.5376	−	5.21622i	0.778873	−	0.231660i
$508$	−24.2765	+	6.26235i	−1.07710	+	0.277847i
$509$	−8.44815	−	14.6326i	−0.374458	−	0.648580i	0.615788	−	0.787912i	$-0.288838\pi$
$509$	−8.44815	−	14.6326i	−0.374458	−	0.648580i	−0.990246	+	0.139332i	$0.955504\pi$
$510$	−1.60578	−	0.622960i	−0.0711054	−	0.0275851i
$511$	18.2452	+	15.2193i	0.807118	+	0.673261i
$512$	7.77274	+	21.2505i	0.343510	+	0.939149i
$513$	29.3893	+	5.34507i	1.29757	+	0.235991i
$514$	3.78640	−	27.7578i	0.167011	−	1.22434i
$515$	34.6894	+	20.0279i	1.52860	+	0.882536i
$516$	20.8152	+	34.6030i	0.916337	+	1.52331i
$517$		−	7.54957i		−	0.332030i
$518$	−3.89656	−	1.23614i	−0.171205	−	0.0543127i
$519$	17.9013	+	16.9497i	0.785781	+	0.744011i
$520$	9.57711	−	1.12454i	0.419984	−	0.0493142i
$521$	31.0684	+	17.9374i	1.36113	+	0.785850i	0.989775	−	0.142639i	$-0.0455589\pi$
$521$	31.0684	+	17.9374i	1.36113	+	0.785850i	0.371358	+	0.928490i	$0.378892\pi$
$522$	2.41665	−	29.7790i	0.105774	−	1.30339i
$523$	−1.10840	−	1.91980i	−0.0484669	−	0.0839471i	0.840774	−	0.541386i	$-0.182100\pi$
$523$	−1.10840	−	1.91980i	−0.0484669	−	0.0839471i	−0.889241	+	0.457439i	$0.848767\pi$
$524$	−23.9650	−	24.4170i	−1.04691	−	1.06666i
$525$	−0.964423	−	0.414732i	−0.0420909	−	0.0181004i
$526$	−3.65764	−	8.94834i	−0.159481	−	0.390166i
$527$	−1.44413	−	2.50130i	−0.0629072	−	0.108959i
$528$	11.1825	−	3.09978i	0.486656	−	0.134901i
$529$	−9.84883	+	17.0587i	−0.428210	+	0.741681i
$530$	16.7574	−	21.6287i	0.727895	−	0.939490i
$531$	18.5751	−	1.01514i	0.806089	−	0.0440532i
$532$	−17.2872	−	25.0300i	−0.749496	−	1.08519i
$533$	5.38390			0.233202
$534$	1.97921	+	12.7903i	0.0856488	+	0.553489i
$535$	8.36662	+	4.83047i	0.361721	+	0.208840i
$536$	3.24789	−	2.42064i	0.140288	−	0.104556i
$537$	2.09335	+	0.500095i	0.0903349	+	0.0215807i
$538$	12.9300	+	31.6331i	0.557453	+	1.36380i
$539$	7.58846	+	8.93744i	0.326858	+	0.384963i
$540$	1.64540	+	22.6396i	0.0708067	+	0.974253i
$541$	32.2404	−	18.6140i	1.38612	−	0.800279i	0.393248	−	0.919432i	$-0.371351\pi$
$541$	32.2404	−	18.6140i	1.38612	−	0.800279i	0.992876	+	0.119153i	$0.0380180\pi$
$542$	−3.37322	+	24.7288i	−0.144892	+	1.06219i
$543$	−10.3442	−	34.7785i	−0.443911	−	1.49249i
$544$	−1.14205	+	1.41847i	−0.0489650	+	0.0608166i
$545$		−	17.7808i		−	0.761645i
$546$	−5.21545	+	8.66731i	−0.223201	+	0.370927i
$547$	12.2271			0.522792			0.261396	−	0.965232i	$-0.415817\pi$
$547$	12.2271			0.522792			0.261396	+	0.965232i	$0.415817\pi$
$548$	−11.0964	+	39.9167i	−0.474016	+	1.70516i
$549$	−5.95895	+	11.7600i	−0.254322	+	0.501906i
$550$	0.0733416	−	0.537662i	0.00312730	−	0.0229260i
$551$	−20.2415	−	35.0593i	−0.862317	−	1.49358i
$552$	12.6420	+	29.4096i	0.538081	+	1.25175i
$553$	−3.77901	−	10.2895i	−0.160700	−	0.437554i
$554$	19.5373	−	7.98588i	0.830060	−	0.339288i
$555$	4.02021	+	0.960414i	0.170649	+	0.0407673i
$556$	−0.635721	−	2.46443i	−0.0269606	−	0.104515i
$557$	−0.649106	+	1.12428i	−0.0275035	+	0.0476375i	−0.879450	−	0.475992i	$-0.842089\pi$
$557$	−0.649106	+	1.12428i	−0.0275035	+	0.0476375i	0.851946	+	0.523630i	$0.175422\pi$
$558$	−21.6362	+	31.3171i	−0.915932	+	1.32576i
$559$		−	18.1949i		−	0.769564i
$560$	15.1361	−	17.4711i	0.639618	−	0.738290i
$561$	0.678160	+	0.642111i	0.0286320	+	0.0271099i
$562$	−15.5270	−	12.0300i	−0.654967	−	0.507453i
$563$	−24.2080	−	13.9765i	−1.02024	−	0.589038i	−0.106070	−	0.994359i	$-0.533827\pi$
$563$	−24.2080	−	13.9765i	−1.02024	−	0.589038i	−0.914175	+	0.405320i	$0.867160\pi$
$564$	7.56305	−	13.6602i	0.318462	−	0.575200i
$565$	25.3475	−	14.6344i	1.06638	−	0.615672i
$566$	3.09135	+	7.56293i	0.129939	+	0.317894i
$567$	−19.8386	−	13.1693i	−0.833143	−	0.553058i
$568$	16.5494	+	7.12835i	0.694398	+	0.299099i
$569$	−26.1457	+	15.0952i	−1.09608	+	0.632825i	−0.935190	−	0.354147i	$-0.884771\pi$
$569$	−26.1457	+	15.0952i	−1.09608	+	0.632825i	−0.160895	+	0.986972i	$0.551438\pi$
$570$	19.2712	+	23.9716i	0.807181	+	1.00406i
$571$	−16.0016	+	27.7156i	−0.669646	+	1.15986i	0.308357	+	0.951271i	$0.400221\pi$
$571$	−16.0016	+	27.7156i	−0.669646	+	1.15986i	−0.978003	+	0.208591i	$0.933112\pi$
$572$	−5.03759	−	1.40040i	−0.210632	−	0.0585535i
$573$	−30.7182	−	29.0853i	−1.28327	−	1.21505i
$574$	9.53080	−	8.70252i	0.397808	−	0.363236i
$575$	1.49694			0.0624269
$576$	23.3390	+	5.59371i	0.972460	+	0.233071i
$577$	7.72204	−	13.3750i	0.321473	−	0.556807i	−0.659319	−	0.751863i	$-0.729155\pi$
$577$	7.72204	−	13.3750i	0.321473	−	0.556807i	0.980792	+	0.195056i	$0.0624888\pi$
$578$	23.6758	+	3.22958i	0.984784	+	0.134333i
$579$	0.00533339	−	0.0223251i	0.000221648	−	0.000927800i
$580$	21.9551	−	21.5486i	0.911635	−	0.894756i
$581$	23.6303	+	4.09581i	0.980351	+	0.169923i
$582$	−3.74888	+	9.66339i	−0.155396	+	0.400560i
$583$	−12.8480	+	7.41782i	−0.532112	+	0.307215i
$584$	−20.3659	+	15.1786i	−0.842745	+	0.628093i
$585$	4.62295	−	9.12344i	0.191136	−	0.377208i
$586$	−13.5450	+	17.4824i	−0.559537	+	0.722191i
$587$		−	1.97510i		−	0.0815212i	−0.999169	−	0.0407606i	$-0.987022\pi$
$587$		−	1.97510i		−	0.0815212i	0.999169	−	0.0407606i	$-0.0129781\pi$
$588$	4.77721	+	23.7735i	0.197009	+	0.980402i
$589$			51.5768i			2.12518i
$590$	15.1417	+	11.7314i	0.623373	+	0.482975i
$591$	−10.7649	+	3.20181i	−0.442810	+	0.131705i
$592$	2.25543	−	3.74320i	0.0926978	−	0.153845i
$593$	−14.0265	+	8.09823i	−0.576001	+	0.332554i	−0.759543	−	0.650458i	$-0.774577\pi$
$593$	−14.0265	+	8.09823i	−0.576001	+	0.332554i	0.183542	+	0.983012i	$0.441244\pi$
$594$	3.81883	−	11.7007i	0.156689	−	0.480085i
$595$	1.83306	+	0.317722i	0.0751482	+	0.0130253i
$596$	−7.05506	+	6.92443i	−0.288987	+	0.283636i
$597$	−8.69558	−	2.07734i	−0.355886	−	0.0850200i
$598$	1.94947	−	14.2914i	0.0797198	−	0.584420i
$599$	7.00327	−	12.1300i	0.286146	−	0.495619i	−0.686741	−	0.726903i	$-0.740959\pi$
$599$	7.00327	−	12.1300i	0.286146	−	0.495619i	0.972886	+	0.231283i	$0.0742925\pi$
$600$	0.671327	−	0.899377i	0.0274068	−	0.0367169i
$601$	−15.5923			−0.636024			−0.318012	−	0.948087i	$-0.603015\pi$
$601$	−15.5923			−0.636024			−0.318012	+	0.948087i	$0.603015\pi$
$602$	−29.4103	−	32.2095i	−1.19867	−	1.31276i
$603$	−0.234452	−	4.29003i	−0.00954764	−	0.174704i
$604$	−3.39331	+	12.2066i	−0.138072	+	0.496680i
$605$	−8.94954	+	15.5011i	−0.363850	+	0.630207i
$606$	−7.58578	−	9.43602i	−0.308151	−	0.383312i
$607$	−28.3416	+	16.3630i	−1.15035	+	0.664155i	−0.948973	−	0.315359i	$-0.897875\pi$
$607$	−28.3416	+	16.3630i	−1.15035	+	0.664155i	−0.201378	+	0.979514i	$0.564542\pi$
$608$	30.3269	−	11.7396i	1.22992	−	0.476105i
$609$	3.78226	+	32.0483i	0.153265	+	1.29866i
$610$	−12.5655	+	5.13615i	−0.508761	+	0.207956i
$611$	−6.09286	+	3.51771i	−0.246491	+	0.142311i
$612$	0.583810	+	1.84121i	0.0235991	+	0.0744265i
$613$	0.287887	+	0.166212i	0.0116277	+	0.00671323i	0.505803	−	0.862649i	$-0.331196\pi$
$613$	0.287887	+	0.166212i	0.0116277	+	0.00671323i	−0.494175	+	0.869363i	$0.664530\pi$
$614$	−6.23530	+	8.04788i	−0.251636	+	0.324786i
$615$	−8.97213	+	9.47585i	−0.361791	+	0.382103i
$616$	−11.1814	+	5.66371i	−0.450509	+	0.228197i
$617$		−	39.1386i		−	1.57566i	−0.615893	−	0.787830i	$-0.711205\pi$
$617$		−	39.1386i		−	1.57566i	0.615893	−	0.787830i	$-0.288795\pi$
$618$	−6.86934	−	44.3918i	−0.276325	−	1.78570i
$619$	1.61116	−	2.79062i	0.0647581	−	0.112164i	−0.831829	−	0.555033i	$-0.812706\pi$
$619$	1.61116	−	2.79062i	0.0647581	−	0.112164i	0.896587	+	0.442868i	$0.146039\pi$
$620$	−37.9509	+	9.78979i	−1.52415	+	0.393167i
$621$	33.4055	+	6.07550i	1.34052	+	0.243801i
$622$	−4.65621	−	11.3913i	−0.186697	−	0.456750i
$623$	−4.81946	−	13.1225i	−0.193088	−	0.525740i
$624$	−7.71215	−	7.58047i	−0.308733	−	0.303462i
$625$	11.9010	+	20.6132i	0.476042	+	0.824528i
$626$	−26.8348	−	3.66050i	−1.07254	−	0.146303i
$627$	−4.75451	−	15.9853i	−0.189877	−	0.638392i
$628$	−1.29432	+	4.65599i	−0.0516489	+	0.185794i
$629$	0.351718			0.0140239
$630$	−6.56336	−	23.6232i	−0.261490	−	0.941172i
$631$			10.2850i			0.409441i	0.978820	+	0.204721i	$0.0656286\pi$
$631$			10.2850i			0.409441i	−0.978820	+	0.204721i	$0.934371\pi$
$632$	11.6384	−	1.36657i	0.462950	−	0.0543591i
$633$	−27.9502	+	8.31323i	−1.11092	+	0.330421i
$634$	5.13352	+	0.700255i	0.203878	+	0.0278107i
$635$	−23.7125	+	13.6904i	−0.941002	+	0.543287i
$636$	−30.6784	+	0.550866i	−1.21648	+	0.0218433i
$637$	3.67710	−	10.2886i	0.145692	−	0.407650i
$638$	−15.4404	+	6.31127i	−0.611292	+	0.249866i
$639$	16.0057	−	10.4452i	0.633175	−	0.413205i
$640$	14.3945	+	20.0867i	0.568994	+	0.793995i
$641$	−26.2428	−	15.1513i	−1.03653	−	0.598439i	−0.117680	−	0.993052i	$-0.537546\pi$
$641$	−26.2428	−	15.1513i	−1.03653	−	0.598439i	−0.918848	+	0.394612i	$0.870879\pi$
$642$	−1.65679	−	10.7067i	−0.0653885	−	0.422560i
$643$	−37.4668			−1.47755			−0.738773	−	0.673955i	$-0.764594\pi$
$643$	−37.4668			−1.47755			−0.738773	+	0.673955i	$0.764594\pi$
$644$	−19.6496	−	28.4504i	−0.774303	−	1.12110i
$645$	32.0238	+	30.3214i	1.26093	+	1.19390i
$646$	2.06893	+	1.60296i	0.0814009	+	0.0630675i
$647$	−0.130900	+	0.226726i	−0.00514622	+	0.00891351i	−0.868587	−	0.495537i	$-0.834971\pi$
$647$	−0.130900	+	0.226726i	−0.00514622	+	0.00891351i	0.863441	+	0.504450i	$0.168305\pi$
$648$	18.6314	−	17.3456i	0.731910	−	0.681401i
$649$	−5.19303	−	8.99459i	−0.203844	−	0.353069i
$650$	−0.468092	+	0.191333i	−0.0183601	+	0.00750469i
$651$	16.2422	−	37.7698i	0.636583	−	1.48032i
$652$	12.7343	−	12.4985i	0.498714	−	0.489480i
$653$	22.1548	+	38.3732i	0.866984	+	1.50166i	0.865064	+	0.501662i	$0.167278\pi$
$653$	22.1548	+	38.3732i	0.866984	+	1.50166i	0.00192051	+	0.999998i	$0.499389\pi$
$654$	−15.5408	+	12.4935i	−0.607694	+	0.488535i
$655$	−32.3586	−	18.6822i	−1.26435	−	0.729975i
$656$	6.67417	+	12.0756i	0.260582	+	0.471475i
$657$	1.47013	+	26.9006i	0.0573552	+	1.04949i
$658$	−5.09981	+	16.0757i	−0.198811	+	0.626695i
$659$			23.4513i			0.913534i	0.889586	+	0.456767i	$0.150993\pi$
$659$			23.4513i			0.913534i	−0.889586	+	0.456767i	$0.849007\pi$
$660$	10.8598	−	6.53261i	0.422716	−	0.254282i
$661$	29.3695	+	16.9565i	1.14234	+	0.659531i	0.947009	−	0.321206i	$-0.104088\pi$
$661$	29.3695	+	16.9565i	1.14234	+	0.659531i	0.195332	+	0.980737i	$0.437422\pi$
$662$	−15.1716	−	2.06954i	−0.589662	−	0.0804348i
$663$	0.202225	−	0.846498i	0.00785378	−	0.0328752i
$664$	−10.1425	+	23.5471i	−0.393604	+	0.913804i
$665$	−25.5114	−	21.2804i	−0.989289	−	0.825219i
$666$	−1.98534	−	4.18858i	−0.0769305	−	0.162304i
$667$	−23.0076	−	39.8503i	−0.890857	−	1.54301i
$668$	3.50260	+	13.5781i	0.135520	+	0.525353i
$669$	0.889654	+	2.99114i	0.0343960	+	0.115644i
$670$	2.70945	−	3.49707i	0.104675	−	0.135104i
$671$	7.36050			0.284149
$672$	−25.9054	−	0.953372i	−0.999323	−	0.0367771i
$673$	−13.3855			−0.515973			−0.257986	−	0.966149i	$-0.583059\pi$
$673$	−13.3855			−0.515973			−0.257986	+	0.966149i	$0.583059\pi$
$674$	17.3599	−	22.4063i	0.668678	−	0.863059i
$675$	−0.401119	−	1.12076i	−0.0154391	−	0.0431381i
$676$	−5.27727	−	20.4578i	−0.202972	−	0.786837i
$677$	13.0777	+	22.6513i	0.502618	+	0.870559i	0.999995	+	0.00302522i	$0.000962959\pi$
$677$	13.0777	+	22.6513i	0.502618	+	0.870559i	−0.497378	+	0.867534i	$0.665704\pi$
$678$	−30.6010	−	11.8716i	−1.17522	−	0.455924i
$679$	1.91201	−	11.0311i	0.0733761	−	0.423335i
$680$	−0.786775	+	1.82660i	−0.0301715	+	0.0700471i
$681$	−19.5451	−	4.66926i	−0.748970	−	0.178926i
$682$	21.0565	+	2.87229i	0.806296	+	0.109986i
$683$	−19.0543	−	11.0010i	−0.729092	−	0.420942i	0.0889978	−	0.996032i	$-0.471634\pi$
$683$	−19.0543	−	11.0010i	−0.729092	−	0.420942i	−0.818090	+	0.575090i	$0.804967\pi$
$684$	7.41101	−	33.6869i	0.283367	−	1.28805i
$685$			45.2470i			1.72880i
$686$	−10.1212	−	24.1570i	−0.386428	−	0.922320i
$687$	−11.6978	+	12.3546i	−0.446299	+	0.471356i
$688$	40.8098	−	22.5554i	1.55586	−	0.859917i
$689$	11.9731	+	6.91265i	0.456137	+	0.263351i
$690$	21.9047	+	27.2475i	0.833898	+	1.03729i
$691$	17.0852	+	29.5924i	0.649952	+	1.12575i	0.983134	+	0.182887i	$0.0585442\pi$
$691$	17.0852	+	29.5924i	0.649952	+	1.12575i	−0.333182	+	0.942862i	$0.608122\pi$
$692$	20.3160	−	19.9398i	0.772297	−	0.757998i
$693$	−1.55224	+	13.2033i	−0.0589649	+	0.501553i
$694$	−7.65072	+	3.12724i	−0.290417	+	0.118708i
$695$	−1.38978	−	2.40717i	−0.0527173	−	0.0913091i
$696$	−34.2605	−	4.04832i	−1.29864	−	0.153451i
$697$	−0.555213	+	0.961656i	−0.0210302	+	0.0364253i
$698$	−20.8122	−	16.1248i	−0.787755	−	0.610334i
$699$	−9.54531	+	10.0812i	−0.361037	+	0.381306i
$700$	−0.519366	+	1.09533i	−0.0196302	+	0.0413995i
$701$	−25.6168			−0.967533			−0.483767	−	0.875197i	$-0.660732\pi$
$701$	−25.6168			−0.967533			−0.483767	+	0.875197i	$0.660732\pi$
$702$	−11.2224	+	2.36994i	−0.423561	+	0.0894477i
$703$	−5.43931	−	3.14039i	−0.205147	−	0.118442i
$704$	−3.10389	−	13.0349i	−0.116982	−	0.491272i
$705$	3.96229	−	16.5858i	0.149229	−	0.624658i
$706$	8.74031	−	3.57261i	0.328946	−	0.134457i
$707$	10.0421	+	8.37668i	0.377673	+	0.315037i
$708$	−0.385647	−	21.4772i	−0.0144935	−	0.807162i
$709$	0.228674	−	0.132025i	0.00858802	−	0.00495830i	−0.495700	−	0.868494i	$-0.665088\pi$
$709$	0.228674	−	0.132025i	0.00858802	−	0.00495830i	0.504288	+	0.863536i	$0.331755\pi$
$710$	19.4987	+	2.65979i	0.731774	+	0.0998201i
$711$	5.61795	−	11.0871i	0.210689	−	0.415797i
$712$	14.8427	−	1.74282i	0.556255	−	0.0653149i
$713$			58.6250i			2.19552i
$714$	−1.01029	−	1.82538i	−0.0378091	−	0.0683132i
$715$	−5.71028			−0.213552
$716$	0.665623	−	2.39442i	0.0248755	−	0.0894837i
$717$	10.0016	−	2.97477i	0.373515	−	0.111095i
$718$	−33.9890	−	4.63638i	−1.26846	−	0.173028i
$719$	19.9630	+	34.5770i	0.744496	+	1.28950i	0.950430	+	0.310939i	$0.100643\pi$
$719$	19.9630	+	34.5770i	0.744496	+	1.28950i	−0.205934	+	0.978566i	$0.566023\pi$
$720$	26.1940	−	0.940990i	0.976193	−	0.0350686i
$721$	16.7271	+	45.5447i	0.622952	+	1.69617i
$722$	−7.51695	−	18.3901i	−0.279752	−	0.684408i
$723$	4.12048	−	17.2480i	0.153242	−	0.641459i
$724$	−40.5693	+	10.4652i	−1.50775	+	0.388937i
$725$	−0.806627	+	1.39712i	−0.0299574	+	0.0518877i
$726$	19.8366	−	3.06958i	0.736205	−	0.113923i
$727$			4.46181i			0.165479i	0.996571	+	0.0827397i	$0.0263670\pi$
$727$			4.46181i			0.165479i	−0.996571	+	0.0827397i	$0.973633\pi$
$728$	9.78081	+	6.38488i	0.362501	+	0.236639i
$729$	−4.40255	−	26.6386i	−0.163057	−	0.986617i
$730$	−16.9895	+	21.9283i	−0.628811	+	0.811604i
$731$	3.24993	+	1.87635i	0.120203	+	0.0693992i
$732$	13.3181	+	7.37364i	0.492252	+	0.272538i
$733$	3.91514	−	2.26041i	0.144609	−	0.0834900i	−0.425950	−	0.904747i	$-0.640060\pi$
$733$	3.91514	−	2.26041i	0.144609	−	0.0834900i	0.570559	+	0.821257i	$0.306727\pi$
$734$	−9.89887	+	4.04617i	−0.365374	+	0.149347i
$735$	11.9806	+	23.6176i	0.441910	+	0.871148i
$736$	34.4712	−	13.3439i	1.27063	−	0.491863i
$737$	−2.07736	+	1.19936i	−0.0765205	+	0.0441791i
$738$	14.5863	+	1.18372i	0.536929	+	0.0435734i
$739$	−0.571921	+	0.990596i	−0.0210384	+	0.0364397i	−0.876353	−	0.481670i	$-0.840031\pi$
$739$	−0.571921	+	0.990596i	−0.0210384	+	0.0364397i	0.855315	+	0.518109i	$0.173364\pi$
$740$	1.27831	−	4.59840i	0.0469915	−	0.169040i
$741$	−10.6855	+	11.2854i	−0.392543	+	0.414581i
$742$	32.3688	−	7.11616i	1.18830	−	0.261243i
$743$	−13.5335			−0.496495			−0.248248	−	0.968697i	$-0.579855\pi$
$743$	−13.5335			−0.496495			−0.248248	+	0.968697i	$0.579855\pi$
$744$	35.2224	+	26.2913i	1.29132	+	0.963885i
$745$	−5.39804	+	9.34968i	−0.197769	+	0.342546i
$746$	−3.74369	+	27.4447i	−0.137066	+	1.00482i
$747$	14.8618	+	22.7734i	0.543763	+	0.833237i
$748$	0.769635	−	0.755385i	0.0281406	−	0.0276196i
$749$	4.03437	+	10.9848i	0.147413	+	0.401375i
$750$	10.1188	−	26.0831i	0.369488	−	0.952418i
$751$	−13.7335	+	7.92906i	−0.501144	+	0.289336i	−0.729186	−	0.684316i	$-0.760101\pi$
$751$	−13.7335	+	7.92906i	−0.501144	+	0.289336i	0.228042	+	0.973651i	$0.426768\pi$
$752$	−15.4430	−	9.30504i	−0.563147	−	0.339320i
$753$	4.92642	+	16.5633i	0.179529	+	0.603600i
$754$	12.2879	+	9.52040i	0.447500	+	0.346712i
$755$			13.8366i			0.503566i
$756$	−16.0356	+	22.3352i	−0.583208	+	0.812323i
$757$		−	41.0141i		−	1.49068i	−0.666683	−	0.745341i	$-0.732287\pi$
$757$		−	41.0141i		−	1.49068i	0.666683	−	0.745341i	$-0.267713\pi$
$758$	−4.32866	+	5.58698i	−0.157224	+	0.202928i
$759$	−5.40424	−	18.1698i	−0.196162	−	0.659521i
$760$	28.4767	−	21.2235i	1.03296	−	0.769857i
$761$	−8.79472	+	5.07763i	−0.318808	+	0.184064i	−0.650861	−	0.759197i	$-0.725592\pi$
$761$	−8.79472	+	5.07763i	−0.318808	+	0.184064i	0.332053	+	0.943261i	$0.392259\pi$
$762$	28.6271	+	11.1058i	1.03705	+	0.402321i
$763$	13.7961	−	16.5390i	0.499452	−	0.598753i
$764$	−34.8616	+	34.2162i	−1.26125	+	1.23790i
$765$	1.15286	+	1.76659i	0.0416818	+	0.0638712i
$766$	42.4664	+	5.79277i	1.53437	+	0.209301i
$767$	−4.83937	+	8.38203i	−0.174740	+	0.302658i
$768$	7.44199	−	26.6949i	0.268540	−	0.963269i
$769$	15.2996			0.551719			0.275859	−	0.961198i	$-0.411038\pi$
$769$	15.2996			0.551719			0.275859	+	0.961198i	$0.411038\pi$
$770$	−10.1086	+	9.23008i	−0.364288	+	0.332629i
$771$	−23.5903	+	24.9148i	−0.849585	+	0.897283i
$772$	−0.0255359	−	0.00709871i	−0.000919057	−	0.000255488i
$773$	18.3453	−	31.7750i	0.659835	−	1.14287i	−0.320823	−	0.947139i	$-0.603960\pi$
$773$	18.3453	−	31.7750i	0.659835	−	1.14287i	0.980658	−	0.195728i	$-0.0627071\pi$
$774$	4.00040	−	49.2946i	0.143791	−	1.77186i
$775$	1.77998	−	1.02767i	0.0639388	−	0.0369151i
$776$	10.9922	+	4.73470i	0.394599	+	0.169966i
$777$	2.99427	+	4.01262i	0.107419	+	0.143952i
$778$	−2.28010	−	5.57823i	−0.0817457	−	0.199989i
$779$	17.1727	−	9.91466i	0.615276	−	0.355230i
$780$	−10.3322	−	5.72048i	−0.369953	−	0.204826i
$781$	−9.24099	−	5.33529i	−0.330669	−	0.190912i
$782$	2.35166	+	1.82201i	0.0840951	+	0.0651549i
$783$	−23.6709	+	27.9040i	−0.845927	+	0.997208i
$784$	27.6349	−	4.50690i	0.986961	−	0.160961i
$785$			5.27773i			0.188370i
$786$	6.40778	+	41.4090i	0.228558	+	1.47701i
$787$	14.6430	−	25.3624i	0.521965	−	0.904071i	−0.477708	−	0.878519i	$-0.658532\pi$
$787$	14.6430	−	25.3624i	0.521965	−	0.904071i	0.999673	−	0.0255520i	$-0.00813435\pi$
$788$	3.23929	+	12.5574i	0.115395	+	0.447337i
$789$	−2.75103	+	11.5156i	−0.0979393	+	0.409965i
$790$	11.8464	−	4.84223i	0.421476	−	0.172279i
$791$	34.9321	+	6.05473i	1.24204	+	0.215281i
$792$	−13.3402	−	4.90160i	−0.474022	−	0.174171i
$793$	−3.42962	−	5.94027i	−0.121789	−	0.210945i
$794$	3.78293	−	27.7324i	0.134251	−	0.984185i
$795$	−32.1193	+	9.55326i	−1.13915	+	0.338819i
$796$	−2.76493	+	9.94617i	−0.0980004	+	0.352533i
$797$	−18.4577			−0.653805			−0.326903	−	0.945058i	$-0.606005\pi$
$797$	−18.4577			−0.653805			−0.326903	+	0.945058i	$0.606005\pi$
$798$	−0.674212	+	37.2501i	−0.0238668	+	1.31864i
$799$		−	1.45105i		−	0.0513345i
$800$	−1.00942	−	0.812706i	−0.0356882	−	0.0287335i
$801$	7.16471	−	14.1396i	0.253153	−	0.499599i
$802$	0.438713	−	3.21617i	0.0154915	−	0.113567i
$803$	13.0260	−	7.52059i	0.459679	−	0.265396i
$804$	−4.96029	+	0.0890677i	−0.174936	+	0.00314118i
$805$	−28.9976	−	24.1885i	−1.02203	−	0.852533i
$806$	−7.49319	−	18.3319i	−0.263936	−	0.645715i
$807$	9.72510	−	40.7084i	0.342340	−	1.43301i
$808$	−11.2094	+	8.35427i	−0.394344	+	0.293902i
$809$	12.9060	+	7.45126i	0.453750	+	0.261972i	0.709412	−	0.704794i	$-0.248960\pi$
$809$	12.9060	+	7.45126i	0.453750	+	0.261972i	−0.255663	+	0.966766i	$0.582294\pi$
$810$	14.5306	−	23.7012i	0.510554	−	0.832776i
$811$	29.7496			1.04465			0.522325	−	0.852747i	$-0.325065\pi$
$811$	29.7496			1.04465			0.522325	+	0.852747i	$0.325065\pi$
$812$	37.1414	−	3.00877i	1.30341	−	0.105587i
$813$	21.0161	−	22.1960i	0.737067	−	0.778448i
$814$	−1.58499	+	2.04574i	−0.0555540	+	0.0717033i
$815$	9.74341	−	16.8761i	0.341297	−	0.591143i
$816$	2.14932	−	0.595789i	0.0752411	−	0.0208568i
$817$	−33.5067	−	58.0353i	−1.17225	−	2.03040i
$818$	−0.803294	−	1.96524i	−0.0280865	−	0.0687131i
$819$	11.3790	−	4.89935i	0.397614	−	0.171197i
$820$	10.5549	+	10.7540i	0.368593	+	0.375546i
$821$	−7.25813	−	12.5715i	−0.253311	−	0.438747i	0.711125	−	0.703066i	$-0.248186\pi$
$821$	−7.25813	−	12.5715i	−0.253311	−	0.438747i	−0.964435	+	0.264319i	$0.914853\pi$
$822$	39.5469	−	31.7924i	1.37936	−	1.10889i
$823$	42.5817	+	24.5846i	1.48431	+	0.856965i	0.999841	−	0.0178459i	$-0.00568083\pi$
$823$	42.5817	+	24.5846i	1.48431	+	0.856965i	0.484465	+	0.874810i	$0.339014\pi$
$824$	−51.5154	+	6.04889i	−1.79462	+	0.210723i
$825$	−0.456939	+	0.482593i	−0.0159086	+	0.0168017i
$826$	4.98184	+	22.6606i	0.173340	+	0.788462i
$827$		−	0.00653186i		−	0.000227135i	−1.00000		0.000113567i	$-0.999964\pi$
$827$		−	0.00653186i		−	0.000227135i	1.00000		0.000113567i	$-3.61496e-5\pi$
$828$	8.42376	−	38.2904i	0.292746	−	1.33068i
$829$	−7.61159	−	4.39455i	−0.264361	−	0.152629i	0.361961	−	0.932193i	$-0.382107\pi$
$829$	−7.61159	−	4.39455i	−0.264361	−	0.152629i	−0.626322	+	0.779564i	$0.715441\pi$
$830$	−3.78444	+	27.7435i	−0.131360	+	0.962989i
$831$	−25.1425	−	6.00645i	−0.872182	−	0.208361i
$832$	−9.07353	+	8.57858i	−0.314568	+	0.297409i
$833$	1.45853	+	1.71781i	0.0505350	+	0.0595184i
$834$	−1.12740	+	2.90607i	−0.0390388	+	0.100629i
$835$	7.65719	+	13.2626i	0.264988	+	0.458973i
$836$	−18.6470	+	4.81016i	−0.644919	+	0.166363i
$837$	43.8925	−	15.7091i	1.51715	−	0.542985i
$838$	−9.44114	−	7.31477i	−0.326139	−	0.252685i
$839$	35.4452			1.22371			0.611853	−	0.790972i	$-0.290425\pi$
$839$	35.4452			1.22371			0.611853	+	0.790972i	$0.290425\pi$
$840$	−27.5371	+	6.57434i	−0.950120	+	0.226836i
$841$	20.5905			0.710017
$842$	15.5757	+	12.0677i	0.536775	+	0.415881i
$843$	6.85818	+	23.0581i	0.236208	+	0.794164i
$844$	8.41053	+	32.6041i	0.289502	+	1.12228i
$845$	−11.5369	−	19.9825i	−0.396881	−	0.687417i
$846$	−17.2805	+	8.19075i	−0.594115	+	0.281604i
$847$	−20.3518	+	7.47458i	−0.699296	+	0.256829i
$848$	−0.662071	+	35.4239i	−0.0227356	+	1.21646i
$849$	2.32511	−	9.73270i	0.0797975	−	0.334025i
$850$	0.0140965	−	0.103340i	0.000483506	−	0.00354455i
$851$	−6.18262	−	3.56954i	−0.211937	−	0.122362i
$852$	−11.3759	−	18.9112i	−0.389732	−	0.647887i
$853$		−	23.8784i		−	0.817581i	−0.912628	−	0.408791i	$-0.865951\pi$
$853$		−	23.8784i		−	0.817581i	0.912628	−	0.408791i	$-0.134049\pi$
$854$	−15.6731	−	4.97209i	−0.536322	−	0.170141i
$855$	−2.05562	−	37.6138i	−0.0703006	−	1.28637i
$856$	−12.4248	+	1.45891i	−0.424672	+	0.0498646i
$857$	46.6784	+	26.9498i	1.59451	+	0.920588i	0.992520	+	0.122081i	$0.0389567\pi$
$857$	46.6784	+	26.9498i	1.59451	+	0.920588i	0.601985	+	0.798507i	$0.294377\pi$
$858$	4.01228	+	4.99091i	0.136977	+	0.170387i
$859$	9.18799	+	15.9141i	0.313490	+	0.542981i	0.979115	−	0.203305i	$-0.0651684\pi$
$859$	9.18799	+	15.9141i	0.313490	+	0.542981i	−0.665625	+	0.746286i	$0.731835\pi$
$860$	36.3433	−	35.6704i	1.23930	−	1.21635i
$861$	−15.6979	+	1.85262i	−0.534982	+	0.0631371i
$862$	−18.1654	−	44.4414i	−0.618717	−	1.51368i
$863$	24.6737	+	42.7360i	0.839901	+	1.45475i	0.889977	+	0.456006i	$0.150721\pi$
$863$	24.6737	+	42.7360i	0.839901	+	1.45475i	−0.0500753	+	0.998745i	$0.515946\pi$
$864$	−19.2274	−	22.2330i	−0.654131	−	0.756381i
$865$	15.5444	−	26.9236i	0.528524	−	0.915431i
$866$	−3.84862	+	4.96739i	−0.130781	+	0.168799i
$867$	−21.2509	−	20.1212i	−0.721717	−	0.683352i
$868$	−42.8965	−	20.3400i	−1.45600	−	0.690385i
$869$	−6.93929			−0.235399
$870$	−37.2338	+	5.76169i	−1.26234	+	0.195339i
$871$	1.93589	+	1.11768i	0.0655950	+	0.0378713i
$872$	13.7592	+	18.4614i	0.465945	+	0.625183i
$873$	10.6311	−	6.93776i	0.359808	−	0.234808i
$874$	−20.1001	−	49.1746i	−0.679897	−	1.66335i
$875$	−5.16082	+	29.7747i	−0.174467	+	1.00657i
$876$	31.1034	−	0.558497i	1.05089	−	0.0188699i
$877$	−51.2316	+	29.5786i	−1.72997	+	0.998797i	−0.840467	+	0.541863i	$0.817719\pi$
$877$	−51.2316	+	29.5786i	−1.72997	+	0.998797i	−0.889500	+	0.456935i	$0.848947\pi$
$878$	−1.66786	+	12.2270i	−0.0562876	+	0.412640i
$879$	25.9620	−	7.72187i	0.875675	−	0.260452i
$880$	−7.07877	−	12.8077i	−0.238625	−	0.431747i
$881$		−	51.0955i		−	1.72145i	−0.509068	−	0.860726i	$-0.670010\pi$
$881$		−	51.0955i		−	1.72145i	0.509068	−	0.860726i	$-0.329990\pi$
$882$	12.2243	−	27.0660i	0.411612	−	0.911359i
$883$	10.4148			0.350486			0.175243	−	0.984525i	$-0.443929\pi$
$883$	10.4148			0.350486			0.175243	+	0.984525i	$0.443929\pi$
$884$	−0.968241	−	0.269161i	−0.0325655	−	0.00905285i
$885$	−6.68799	−	22.4859i	−0.224814	−	0.755856i
$886$	−7.06538	+	51.7958i	−0.237366	+	1.74011i
$887$	−12.2631	−	21.2404i	−0.411756	−	0.713183i	0.583326	−	0.812238i	$-0.301751\pi$
$887$	−12.2631	−	21.2404i	−0.411756	−	0.713183i	−0.995082	+	0.0990557i	$0.968418\pi$
$888$	−4.91730	+	2.11376i	−0.165014	+	0.0709331i
$889$	−32.6789	−	5.66419i	−1.09601	−	0.189971i
$890$	15.1080	−	6.17542i	0.506423	−	0.207001i
$891$	−12.1556	+	8.91490i	−0.407228	+	0.298660i
$892$	3.48918	−	0.900066i	0.116826	−	0.0301364i
$893$	−12.9560	+	22.4405i	−0.433556	+	0.750942i
$894$	11.9647	−	1.85146i	0.400160	−	0.0619222i
$895$		−	2.71416i		−	0.0907242i
$896$	−2.19595	+	29.8526i	−0.0733615	+	0.997305i
$897$	−12.1458	+	12.8277i	−0.405535	+	0.428303i
$898$	−26.1898	−	20.2913i	−0.873966	−	0.677128i
$899$	−54.7155	−	31.5900i	−1.82487	−	1.05359i
$900$	−1.31024	+	0.415452i	−0.0436748	+	0.0138484i
$901$	−2.46944	+	1.42573i	−0.0822688	+	0.0474979i
$902$	−3.09138	−	7.56300i	−0.102932	−	0.251820i
$903$	6.26095	+	53.0511i	0.208351	+	1.76543i
$904$	−14.9933	+	34.8090i	−0.498671	+	1.15773i
$905$	−39.6267	+	22.8785i	−1.31724	+	0.760507i
$906$	12.0935	−	9.72218i	0.401780	−	0.322998i
$907$	14.6718	−	25.4124i	0.487170	−	0.843803i	−0.512721	−	0.858555i	$-0.671362\pi$
$907$	14.6718	−	25.4124i	0.487170	−	0.843803i	0.999891	+	0.0147518i	$0.00469582\pi$
$908$	−6.21475	+	22.3561i	−0.206244	+	0.741913i
$909$	0.809158	+	14.8060i	0.0268381	+	0.491086i
$910$	12.1592	+	3.85735i	0.403073	+	0.127870i
$911$	−21.9953			−0.728738			−0.364369	−	0.931255i	$-0.618715\pi$
$911$	−21.9953			−0.728738			−0.364369	+	0.931255i	$0.618715\pi$
$912$	−38.5587	−	9.97675i	−1.27681	−	0.330363i
$913$	7.59124	−	13.1484i	0.251233	−	0.435149i
$914$	−1.85349	−	0.252831i	−0.0613079	−	0.00836292i
$915$	16.1705	+	3.86306i	0.534579	+	0.127709i
$916$	13.7614	+	14.0210i	0.454690	+	0.463267i
$917$	−15.6032	−	42.4845i	−0.515264	−	1.40296i
$918$	0.733992	−	2.24891i	0.0242253	−	0.0742250i
$919$	32.9464	−	19.0216i	1.08680	−	0.627464i	0.154077	−	0.988059i	$-0.450759\pi$
$919$	32.9464	−	19.0216i	1.08680	−	0.627464i	0.932723	+	0.360594i	$0.117426\pi$
$920$	32.3681	−	24.1238i	1.06715	−	0.795338i
$921$	11.9514	−	3.55470i	0.393811	−	0.117131i
$922$	−20.3944	+	26.3230i	−0.671655	+	0.866902i
$923$			9.94388i			0.327307i
$924$	15.1700	+	2.34969i	0.499057	+	0.0772991i
$925$			0.250290i			0.00822948i
$926$	−16.1544	−	12.5160i	−0.530866	−	0.411302i
$927$	−24.8669	+	49.0751i	−0.816737	+	1.61184i
$928$	−6.12071	+	39.3628i	−0.200922	+	1.29215i
$929$	26.6079	−	15.3621i	0.872978	−	0.504014i	0.00464125	−	0.999989i	$-0.498523\pi$
$929$	26.6079	−	15.3621i	0.872978	−	0.504014i	0.868337	+	0.495975i	$0.165189\pi$
$930$	44.7521	+	17.3614i	1.46748	+	0.569304i
$931$	−7.21830	−	39.5886i	−0.236570	−	1.29746i
$932$	11.2292	+	11.4410i	0.367824	+	0.374763i
$933$	−3.50209	+	14.6594i	−0.114653	+	0.479928i
$934$	−2.87108	+	21.0477i	−0.0939446	+	0.688701i
$935$	0.588871	−	1.01995i	0.0192581	−	0.0333561i
$936$	2.26002	+	13.0500i	0.0738710	+	0.426554i
$937$	37.2804			1.21790			0.608949	−	0.793210i	$-0.291592\pi$
$937$	37.2804			1.21790			0.608949	+	0.793210i	$0.291592\pi$
$938$	5.23361	−	1.15059i	0.170883	−	0.0375681i
$939$	24.0863	+	22.8059i	0.786027	+	0.744243i
$940$	−18.9712	−	5.27379i	−0.618772	−	0.172012i
$941$	−16.0848	+	27.8596i	−0.524348	+	0.908198i	0.475250	+	0.879851i	$0.342358\pi$
$941$	−16.0848	+	27.8596i	−0.524348	+	0.908198i	−0.999598	+	0.0283471i	$0.990976\pi$
$942$	4.61286	−	3.70835i	0.150295	−	0.120825i
$943$	19.5194	−	11.2695i	0.635640	−	0.366987i
$944$	−24.7994	−	0.463499i	−0.807151	−	0.0150856i
$945$	−10.3398	+	28.1920i	−0.336353	+	0.917087i
$946$	−25.5592	+	10.4474i	−0.831003	+	0.339673i
$947$	33.3248	−	19.2401i	1.08291	−	0.625219i	0.151231	−	0.988498i	$-0.451676\pi$
$947$	33.3248	−	19.2401i	1.08291	−	0.625219i	0.931680	+	0.363279i	$0.118343\pi$
$948$	−12.5560	−	6.95169i	−0.407800	−	0.225780i
$949$	−12.1389	−	7.00842i	−0.394046	−	0.227503i
$950$	−1.14070	+	1.47229i	−0.0370091	+	0.0477675i
$951$	−4.60773	−	4.36279i	−0.149416	−	0.141473i
$952$	−2.14909	+	1.08858i	−0.0696525	+	0.0352812i
$953$		−	37.1213i		−	1.20248i	−0.799070	−	0.601238i	$-0.794674\pi$
$953$		−	37.1213i		−	1.20248i	0.799070	−	0.601238i	$-0.205326\pi$
$954$	30.9181	+	21.3605i	1.00101	+	0.691572i
$955$	−26.6737	+	46.2002i	−0.863140	+	1.49500i
$956$	−3.00958	−	11.6669i	−0.0973368	−	0.377334i
$957$	19.8702	+	4.74692i	0.642312	+	0.153446i
$958$	11.7237	+	28.6818i	0.378775	+	0.926666i
$959$	−35.1071	+	42.0871i	−1.13367	+	1.35906i
$960$	0.0222022	−	30.2657i	0.000716572	−	0.976822i
$961$	24.7469	+	42.8628i	0.798286	+	1.38267i
$962$	2.38954	+	0.325953i	0.0770418	+	0.0105091i
$963$	−5.99757	+	11.8363i	−0.193269	+	0.381418i
$964$	−19.7286	−	5.48433i	−0.635415	−	0.176638i
$965$	−0.0289458			−0.000931799
$966$	−0.766346	+	42.3405i	−0.0246568	+	1.36228i
$967$		−	28.7342i		−	0.924030i	−0.886872	−	0.462015i	$-0.847127\pi$
$967$		−	28.7342i		−	0.924030i	0.886872	−	0.462015i	$-0.152873\pi$
$968$	−2.70296	−	23.0198i	−0.0868765	−	0.739884i
$969$	−0.913833	−	3.07243i	−0.0293565	−	0.0987006i
$970$	12.9512	+	1.76665i	0.415838	+	0.0567238i
$971$	−17.2557	+	9.96261i	−0.553763	+	0.319715i	−0.750638	−	0.660713i	$-0.770254\pi$
$971$	−17.2557	+	9.96261i	−0.553763	+	0.319715i	0.196875	+	0.980429i	$0.436921\pi$
$972$	−30.9252	+	3.95337i	−0.991928	+	0.126804i
$973$	0.574998	−	3.31739i	0.0184336	−	0.106351i
$974$	14.3811	−	5.87828i	0.460800	−	0.188352i
$975$	0.602385	+	0.143908i	0.0192918	+	0.00460874i
$976$	9.07201	−	15.0562i	0.290388	−	0.481938i
$977$	−11.6105	−	6.70332i	−0.371453	−	0.214458i	0.302640	−	0.953105i	$-0.402132\pi$
$977$	−11.6105	−	6.70332i	−0.371453	−	0.214458i	−0.674093	+	0.738647i	$0.735465\pi$
$978$	−21.5962	+	3.34187i	−0.690570	+	0.106861i
$979$	−8.84986			−0.282843
$980$	27.7597	−	12.8256i	0.886752	−	0.409700i
$981$	24.3851	−	1.33266i	0.778555	−	0.0425484i
$982$	36.1680	+	28.0221i	1.15417	+	0.894222i
$983$	10.2774	−	17.8010i	0.327799	−	0.567765i	−0.654276	−	0.756256i	$-0.727026\pi$
$983$	10.2774	−	17.8010i	0.327799	−	0.567765i	0.982075	+	0.188491i	$0.0603597\pi$
$984$	1.98294	−	16.7814i	0.0632139	−	0.534973i
$985$	7.08155	+	12.2656i	0.225637	+	0.390814i
$986$	−2.96770	+	1.21305i	−0.0945107	+	0.0386313i
$987$	16.5545	−	12.3532i	0.526936	−	0.393206i
$988$	12.5706	+	12.8077i	0.399923	+	0.407467i
$989$	−38.0856	−	65.9661i	−1.21105	−	2.09760i
$990$	−15.4706	−	1.25548i	−0.491686	−	0.0399018i
$991$	4.87181	+	2.81274i	0.154758	+	0.0893497i	0.575379	−	0.817887i	$-0.304854\pi$
$991$	4.87181	+	2.81274i	0.154758	+	0.0893497i	−0.420621	+	0.907236i	$0.638188\pi$
$992$	31.8281	−	39.5319i	1.01054	−	1.25514i
$993$	13.6177	+	12.8938i	0.432144	+	0.409172i
$994$	16.0733	+	17.6031i	0.509813	+	0.558336i
$995$			11.2743i			0.357420i
$996$	26.9075	−	16.1860i	0.852597	−	0.512874i
$997$	2.03245	+	1.17343i	0.0643683	+	0.0371631i	0.531839	−	0.846846i	$-0.321501\pi$
$997$	2.03245	+	1.17343i	0.0643683	+	0.0371631i	−0.467470	+	0.884009i	$0.654835\pi$
$998$	19.9080	+	2.71562i	0.630176	+	0.0859613i
$999$	−1.01583	+	5.58541i	−0.0321394	+	0.176715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.v.a.11.9	yes	56
3.2	odd	2	inner	168.2.v.a.11.20	yes	56
4.3	odd	2		672.2.bd.a.431.3		56
7.2	even	3	inner	168.2.v.a.107.27	yes	56
8.3	odd	2	inner	168.2.v.a.11.2	✓	56
8.5	even	2		672.2.bd.a.431.4		56
12.11	even	2		672.2.bd.a.431.18		56
21.2	odd	6	inner	168.2.v.a.107.2	yes	56
24.5	odd	2		672.2.bd.a.431.17		56
24.11	even	2	inner	168.2.v.a.11.27	yes	56
28.23	odd	6		672.2.bd.a.527.17		56
56.37	even	6		672.2.bd.a.527.18		56
56.51	odd	6	inner	168.2.v.a.107.20	yes	56
84.23	even	6		672.2.bd.a.527.4		56
168.107	even	6	inner	168.2.v.a.107.9	yes	56
168.149	odd	6		672.2.bd.a.527.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.2	✓	56	8.3	odd	2	inner
168.2.v.a.11.9	yes	56	1.1	even	1	trivial
168.2.v.a.11.20	yes	56	3.2	odd	2	inner
168.2.v.a.11.27	yes	56	24.11	even	2	inner
168.2.v.a.107.2	yes	56	21.2	odd	6	inner
168.2.v.a.107.9	yes	56	168.107	even	6	inner
168.2.v.a.107.20	yes	56	56.51	odd	6	inner
168.2.v.a.107.27	yes	56	7.2	even	3	inner
672.2.bd.a.431.3		56	4.3	odd	2
672.2.bd.a.431.4		56	8.5	even	2
672.2.bd.a.431.17		56	24.5	odd	2
672.2.bd.a.431.18		56	12.11	even	2
672.2.bd.a.527.3		56	168.149	odd	6
672.2.bd.a.527.4		56	84.23	even	6
672.2.bd.a.527.17		56	28.23	odd	6
672.2.bd.a.527.18		56	56.37	even	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866151 + 1.11794i) q^{2} +(1.66017 - 0.493786i) q^{3} +(-0.499565 - 1.93660i) q^{4} +(-1.09212 - 1.89161i) q^{5} +(-0.885940 + 2.28366i) q^{6} +(0.451847 - 2.60688i) q^{7} +(2.59770 + 1.11891i) q^{8} +(2.51235 - 1.63954i) q^{9} +(3.06064 + 0.417497i) q^{10} +(-1.45052 - 0.837460i) q^{11} +(-1.78563 - 2.96842i) q^{12} +1.56085i q^{13} +(2.52296 + 2.76309i) q^{14} +(-2.74716 - 2.60112i) q^{15} +(-3.50087 + 1.93492i) q^{16} +(-0.278795 - 0.160963i) q^{17} +(-0.343174 + 4.22874i) q^{18} +(2.87437 + 4.97856i) q^{19} +(-3.11771 + 3.05999i) q^{20} +(-0.537096 - 4.55099i) q^{21} +(2.19260 - 0.896227i) q^{22} +(3.26717 + 5.65891i) q^{23} +(4.86513 + 0.574878i) q^{24} +(0.114544 - 0.198397i) q^{25} +(-1.74494 - 1.35194i) q^{26} +(3.36136 - 3.96248i) q^{27} +(-5.27423 + 0.427257i) q^{28} -7.04205 q^{29} +(5.28735 - 0.818183i) q^{30} +(7.76983 + 4.48591i) q^{31} +(0.869166 - 5.58968i) q^{32} +(-2.82165 - 0.674082i) q^{33} +(0.421425 - 0.172258i) q^{34} +(-5.42467 + 1.99231i) q^{35} +(-4.43022 - 4.04637i) q^{36} +(-0.946173 + 0.546273i) q^{37} +(-8.05536 - 1.09882i) q^{38} +(0.770727 + 2.59129i) q^{39} +(-0.720462 - 6.13582i) q^{40} -3.44933i q^{41} +(5.55293 + 3.34141i) q^{42} -11.6570 q^{43} +(-0.897199 + 3.22746i) q^{44} +(-5.84516 - 2.96181i) q^{45} +(-9.15616 - 1.24898i) q^{46} +(2.25371 + 3.90354i) q^{47} +(-4.85662 + 4.94098i) q^{48} +(-6.59167 - 2.35583i) q^{49} +(0.122582 + 0.299895i) q^{50} +(-0.542330 - 0.129561i) q^{51} +(3.02276 - 0.779748i) q^{52} +(4.42876 - 7.67084i) q^{53} +(1.51836 + 7.18989i) q^{54} +3.65843i q^{55} +(4.09063 - 6.26632i) q^{56} +(7.23030 + 6.84595i) q^{57} +(6.09948 - 7.87257i) q^{58} +(5.37016 + 3.10046i) q^{59} +(-3.66496 + 6.61959i) q^{60} +(-3.80578 + 2.19727i) q^{61} +(-11.7448 + 4.80070i) q^{62} +(-3.13889 - 7.29023i) q^{63} +(5.49608 + 5.81318i) q^{64} +(2.95253 - 1.70464i) q^{65} +(3.19755 - 2.57057i) q^{66} +(0.716072 - 1.24027i) q^{67} +(-0.172444 + 0.620328i) q^{68} +(8.21836 + 7.78149i) q^{69} +(2.47131 - 7.79008i) q^{70} +6.37080 q^{71} +(8.36083 - 1.44794i) q^{72} +(-4.49012 + 7.77711i) q^{73} +(0.208830 - 1.53092i) q^{74} +(0.0921980 - 0.385933i) q^{75} +(8.20557 - 8.05364i) q^{76} +(-2.83858 + 3.40294i) q^{77} +(-3.56446 - 1.38282i) q^{78} +(3.58799 - 2.07153i) q^{79} +(7.48348 + 4.50911i) q^{80} +(3.62382 - 8.23820i) q^{81} +(3.85613 + 2.98764i) q^{82} +9.06459i q^{83} +(-8.54515 + 3.31366i) q^{84} +0.703162i q^{85} +(10.0968 - 13.0318i) q^{86} +(-11.6910 + 3.47726i) q^{87} +(-2.83098 - 3.79848i) q^{88} +(4.57586 - 2.64187i) q^{89} +(8.37391 - 3.96914i) q^{90} +(4.06896 + 0.705268i) q^{91} +(9.32690 - 9.15421i) q^{92} +(15.1143 + 3.61076i) q^{93} +(-6.31596 - 0.861550i) q^{94} +(6.27833 - 10.8744i) q^{95} +(-1.31714 - 9.70902i) q^{96} +4.23153 q^{97} +(8.34304 - 5.32857i) q^{98} +(-5.01728 + 0.274197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{3} - 2 q^{4} - 8 q^{6} - 2 q^{9} + 6 q^{10} + 10 q^{12} - 10 q^{16} - 10 q^{18} - 4 q^{19} - 20 q^{22} - 8 q^{24} - 16 q^{25} - 8 q^{27} - 22 q^{28} - 12 q^{30} - 14 q^{33} - 56 q^{34} + 4 q^{36}+ \cdots - 44 q^{99}+O(q^{100}) \) 56 * q - 2 * q^3 - 2 * q^4 - 8 * q^6 - 2 * q^9 + 6 * q^10 + 10 * q^12 - 10 * q^16 - 10 * q^18 - 4 * q^19 - 20 * q^22 - 8 * q^24 - 16 * q^25 - 8 * q^27 - 22 * q^28 - 12 * q^30 - 14 * q^33 - 56 * q^34 + 4 * q^36 + 14 * q^40 - 8 * q^42 - 16 * q^43 - 12 * q^46 + 64 * q^48 - 16 * q^49 - 34 * q^51 - 8 * q^52 + 32 * q^54 + 4 * q^57 - 18 * q^58 + 40 * q^60 + 4 * q^64 - 20 * q^66 - 36 * q^67 - 42 * q^70 + 22 * q^72 + 4 * q^73 + 104 * q^76 + 28 * q^78 - 10 * q^81 + 52 * q^82 + 4 * q^84 + 46 * q^88 + 140 * q^90 + 72 * q^91 - 46 * q^96 - 32 * q^97 - 44 * q^99

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