LMFDB - Embedded newform 168.2.v.a.107.27

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			107.27
Character	$\chi$	$=$	168.107
Dual form			168.2.v.a.11.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40124 + 0.191140i) q^{2} +(-0.402456 + 1.68465i) q^{3} +(1.92693 + 0.535666i) 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} +(-2.67606 - 1.35599i) q^{9} +(-1.89188 + 2.44184i) q^{10} +(1.45052 - 0.837460i) q^{11} +(-1.67791 + 3.03061i) q^{12} +1.56085i q^{13} +(-0.134864 - 3.73923i) q^{14} +(-2.74716 - 2.60112i) q^{15} +(3.42612 + 2.06438i) q^{16} +(0.278795 - 0.160963i) q^{17} +(-3.49061 - 2.41157i) q^{18} +(2.87437 - 4.97856i) q^{19} +(-3.11771 + 3.05999i) q^{20} +(4.57352 + 0.287952i) q^{21} +(2.19260 - 0.896227i) q^{22} +(3.26717 - 5.65891i) q^{23} +(-2.93043 + 3.92589i) q^{24} +(0.114544 + 0.198397i) q^{25} +(-0.298342 + 2.18713i) q^{26} +(3.36136 - 3.96248i) q^{27} +(0.525740 - 5.26532i) q^{28} -7.04205 q^{29} +(-3.35224 - 4.16989i) q^{30} +(-7.76983 + 4.48591i) q^{31} +(4.40622 + 3.54756i) q^{32} +(0.827052 + 2.78066i) 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} +(4.97929 - 6.42674i) q^{38} +(-2.62949 - 0.628175i) q^{39} +(-4.95354 + 3.69185i) q^{40} -3.44933i q^{41} +(6.35355 + 1.27767i) q^{42} -11.6570 q^{43} +(3.24366 - 0.836731i) q^{44} +(5.48758 - 3.58115i) q^{45} +(5.65973 - 7.30498i) 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} +(0.158962 + 0.534452i) q^{51} +(-0.836097 + 3.00766i) q^{52} +(4.42876 + 7.67084i) q^{53} +(5.46745 - 4.90989i) q^{54} +3.65843i q^{55} +(1.74310 - 7.27747i) q^{56} +(7.23030 + 6.84595i) q^{57} +(-9.86758 - 1.34602i) q^{58} +(-5.37016 + 3.10046i) q^{59} +(-3.90025 - 6.48375i) q^{60} +(3.80578 + 2.19727i) q^{61} +(-11.7448 + 4.80070i) q^{62} +(-2.32574 + 7.58887i) q^{63} +(5.49608 + 5.81318i) q^{64} +(-2.95253 - 1.70464i) q^{65} +(0.627399 + 4.05445i) q^{66} +(0.716072 + 1.24027i) q^{67} +(0.623442 - 0.160822i) q^{68} +(8.21836 + 7.78149i) q^{69} +(7.22044 + 3.82858i) q^{70} +6.37080 q^{71} +(-5.43436 - 6.51672i) q^{72} +(-4.49012 - 7.77711i) q^{73} +(1.22140 + 0.946310i) q^{74} +(-0.380327 + 0.113121i) 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} +(-7.64675 + 4.22633i) q^{80} +(5.32258 + 7.25742i) q^{81} +(0.659306 - 4.83333i) q^{82} +9.06459i q^{83} +(8.65861 + 3.00474i) q^{84} +0.703162i q^{85} +(-16.3343 - 2.22813i) q^{86} +(2.83411 - 11.8634i) q^{87} +(4.70507 - 0.552465i) 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} +(-4.43016 - 14.8948i) q^{93} +(3.90411 - 5.03901i) q^{94} +(6.27833 + 10.8744i) q^{95} +(-7.74969 + 5.99519i) q^{96} +4.23153 q^{97} +(-9.68678 + 2.04113i) 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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.40124	+	0.191140i	0.990824	+	0.135157i
$2$	1.40124	+	0.191140i	0.990824	+	0.135157i
$3$	−0.402456	+	1.68465i	−0.232358	+	0.972630i
$3$	−0.402456	+	1.68465i	−0.232358	+	0.972630i
$4$	1.92693	+	0.535666i	0.963465	+	0.267833i
$5$	−1.09212	+	1.89161i	−0.488411	+	0.845953i	−0.999911	−	0.0133302i	$-0.995757\pi$
$5$	−1.09212	+	1.89161i	−0.488411	+	0.845953i	0.511500	+	0.859283i	$0.329090\pi$
$6$	−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
$9$	−2.67606	−	1.35599i	−0.892020	−	0.451997i
$10$	−1.89188	+	2.44184i	−0.598266	+	0.772179i
$11$	1.45052	−	0.837460i	0.437349	−	0.252504i	−0.265123	−	0.964215i	$-0.585413\pi$
$11$	1.45052	−	0.837460i	0.437349	−	0.252504i	0.702473	+	0.711711i	$0.252079\pi$
$12$	−1.67791	+	3.03061i	−0.484371	+	0.874862i
$13$			1.56085i			0.432903i	0.976293	+	0.216452i	$0.0694483\pi$
$13$			1.56085i			0.432903i	−0.976293	+	0.216452i	$0.930552\pi$
$14$	−0.134864	−	3.73923i	−0.0360440	−	0.999350i
$15$	−2.74716	−	2.60112i	−0.709313	−	0.671608i
$16$	3.42612	+	2.06438i	0.856531	+	0.516096i
$17$	0.278795	−	0.160963i	0.0676178	−	0.0390392i	−0.465810	−	0.884885i	$-0.654237\pi$
$17$	0.278795	−	0.160963i	0.0676178	−	0.0390392i	0.533428	+	0.845846i	$0.320904\pi$
$18$	−3.49061	−	2.41157i	−0.822744	−	0.568412i
$19$	2.87437	−	4.97856i	0.659427	−	1.14216i	−0.321337	−	0.946965i	$-0.604132\pi$
$19$	2.87437	−	4.97856i	0.659427	−	1.14216i	0.980764	−	0.195196i	$-0.0625343\pi$
$20$	−3.11771	+	3.05999i	−0.697142	+	0.684234i
$21$	4.57352	+	0.287952i	0.998024	+	0.0628364i
$22$	2.19260	−	0.896227i	0.467464	−	0.191076i
$23$	3.26717	−	5.65891i	0.681252	−	1.17996i	−0.293346	−	0.956006i	$-0.594769\pi$
$23$	3.26717	−	5.65891i	0.681252	−	1.17996i	0.974599	−	0.223958i	$-0.0718977\pi$
$24$	−2.93043	+	3.92589i	−0.598171	+	0.801369i
$25$	0.114544	+	0.198397i	0.0229089	+	0.0396793i
$26$	−0.298342	+	2.18713i	−0.0585098	+	0.428931i
$27$	3.36136	−	3.96248i	0.646894	−	0.762580i
$28$	0.525740	−	5.26532i	0.0993556	−	0.995052i
$29$	−7.04205			−1.30768			−0.653838	−	0.756635i	$-0.726842\pi$
$29$	−7.04205			−1.30768			−0.653838	+	0.756635i	$0.726842\pi$
$30$	−3.35224	−	4.16989i	−0.612033	−	0.761314i
$31$	−7.76983	+	4.48591i	−1.39550	+	0.805694i	−0.993917	−	0.110128i	$-0.964874\pi$
$31$	−7.76983	+	4.48591i	−1.39550	+	0.805694i	−0.401585	+	0.915822i	$0.631541\pi$
$32$	4.40622	+	3.54756i	0.778918	+	0.627126i
$33$	0.827052	+	2.78066i	0.143971	+	0.484051i
$34$	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	$-0.304708\pi$
$37$	0.946173	+	0.546273i	0.155550	+	0.0898068i	−0.420205	+	0.907429i	$0.638042\pi$
$38$	4.97929	−	6.42674i	0.807747	−	1.04255i
$39$	−2.62949	−	0.628175i	−0.421055	−	0.100588i
$40$	−4.95354	+	3.69185i	−0.783224	+	0.583732i
$41$		−	3.44933i		−	0.538694i	−0.963043	−	0.269347i	$-0.913192\pi$
$41$		−	3.44933i		−	0.538694i	0.963043	−	0.269347i	$-0.0868079\pi$
$42$	6.35355	+	1.27767i	0.980373	+	0.197149i
$43$	−11.6570			−1.77768			−0.888841	−	0.458215i	$-0.848489\pi$
$43$	−11.6570			−1.77768			−0.888841	+	0.458215i	$0.848489\pi$
$44$	3.24366	−	0.836731i	0.489000	−	0.126142i
$45$	5.48758	−	3.58115i	0.818041	−	0.533846i
$46$	5.65973	−	7.30498i	0.834481	−	1.07706i
$47$	2.25371	−	3.90354i	0.328737	−	0.569390i	−0.653524	−	0.756906i	$-0.726710\pi$
$47$	2.25371	−	3.90354i	0.328737	−	0.569390i	0.982262	+	0.187516i	$0.0600436\pi$
$48$	−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
$51$	0.158962	+	0.534452i	0.0222591	+	0.0748382i
$52$	−0.836097	+	3.00766i	−0.115946	+	0.417087i
$53$	4.42876	+	7.67084i	0.608337	+	1.05367i	0.991515	+	0.129996i	$0.0414964\pi$
$53$	4.42876	+	7.67084i	0.608337	+	1.05367i	−0.383177	+	0.923675i	$0.625170\pi$
$54$	5.46745	−	4.90989i	0.744026	−	0.668151i
$55$			3.65843i			0.493303i
$56$	1.74310	−	7.27747i	0.232932	−	0.972493i
$57$	7.23030	+	6.84595i	0.957677	+	0.906769i
$58$	−9.86758	−	1.34602i	−1.29568	−	0.176741i
$59$	−5.37016	+	3.10046i	−0.699135	+	0.403646i	−0.807025	−	0.590517i	$-0.798924\pi$
$59$	−5.37016	+	3.10046i	−0.699135	+	0.403646i	0.107890	+	0.994163i	$0.465591\pi$
$60$	−3.90025	−	6.48375i	−0.503520	−	0.837048i
$61$	3.80578	+	2.19727i	0.487280	+	0.281331i	0.723445	−	0.690382i	$-0.242557\pi$
$61$	3.80578	+	2.19727i	0.487280	+	0.281331i	−0.236165	+	0.971713i	$0.575891\pi$
$62$	−11.7448	+	4.80070i	−1.49159	+	0.609690i
$63$	−2.32574	+	7.58887i	−0.293015	+	0.956108i
$64$	5.49608	+	5.81318i	0.687010	+	0.726648i
$65$	−2.95253	−	1.70464i	−0.366216	−	0.211435i
$66$	0.627399	+	4.05445i	0.0772275	+	0.499068i
$67$	0.716072	+	1.24027i	0.0874821	+	0.151523i	0.906446	−	0.422321i	$-0.138785\pi$
$67$	0.716072	+	1.24027i	0.0874821	+	0.151523i	−0.818964	+	0.573845i	$0.805451\pi$
$68$	0.623442	−	0.160822i	0.0756034	−	0.0195026i
$69$	8.21836	+	7.78149i	0.989374	+	0.936781i
$70$	7.22044	+	3.82858i	0.863008	+	0.457602i
$71$	6.37080			0.756074			0.378037	−	0.925790i	$-0.376599\pi$
$71$	6.37080			0.756074			0.378037	+	0.925790i	$0.376599\pi$
$72$	−5.43436	−	6.51672i	−0.640446	−	0.768003i
$73$	−4.49012	−	7.77711i	−0.525528	−	0.910242i	−0.999558	−	0.0297328i	$-0.990534\pi$
$73$	−4.49012	−	7.77711i	−0.525528	−	0.910242i	0.474030	−	0.880509i	$-0.342799\pi$
$74$	1.22140	+	0.946310i	0.141985	+	0.110006i
$75$	−0.380327	+	0.113121i	−0.0439164	+	0.0130621i
$76$	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	$-0.408209\pi$
$79$	−3.58799	−	2.07153i	−0.403681	−	0.233065i	−0.688071	+	0.725643i	$0.741542\pi$
$80$	−7.64675	+	4.22633i	−0.854932	+	0.472518i
$81$	5.32258	+	7.25742i	0.591398	+	0.806380i
$82$	0.659306	−	4.83333i	0.0728082	−	0.533751i
$83$			9.06459i			0.994968i	0.867473	+	0.497484i	$0.165743\pi$
$83$			9.06459i			0.994968i	−0.867473	+	0.497484i	$0.834257\pi$
$84$	8.65861	+	3.00474i	0.944732	+	0.327844i
$85$			0.703162i			0.0762687i
$86$	−16.3343	−	2.22813i	−1.76137	−	0.240266i
$87$	2.83411	−	11.8634i	0.303849	−	1.27189i
$88$	4.70507	−	0.552465i	0.501562	−	0.0588929i
$89$	−4.57586	−	2.64187i	−0.485040	−	0.280038i	0.237474	−	0.971394i	$-0.423680\pi$
$89$	−4.57586	−	2.64187i	−0.485040	−	0.280038i	−0.722515	+	0.691356i	$0.757014\pi$
$90$	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
$93$	−4.43016	−	14.8948i	−0.459386	−	1.54452i
$94$	3.90411	−	5.03901i	0.402678	−	0.519734i
$95$	6.27833	+	10.8744i	0.644143	+	1.11569i
$96$	−7.74969	+	5.99519i	−0.790950	+	0.611881i
$97$	4.23153			0.429647			0.214823	−	0.976653i	$-0.431082\pi$
$97$	4.23153			0.429647			0.214823	+	0.976653i	$0.431082\pi$
$98$	−9.68678	+	2.04113i	−0.978513	+	0.206186i
$99$	−5.01728	+	0.274197i	−0.504255	+	0.0275578i
$100$	0.114445	+	0.443654i	0.0114445	+	0.0443654i
$101$	−2.47136	−	4.28052i	−0.245909	−	0.425927i	0.716478	−	0.697610i	$-0.245753\pi$
$101$	−2.47136	−	4.28052i	−0.245909	−	0.425927i	−0.962387	+	0.271683i	$0.912420\pi$
$102$	0.120588	+	0.779278i	0.0119400	+	0.0771600i
$103$	15.8817	+	9.16928i	1.56487	+	0.903476i	0.996752	+	0.0805264i	$0.0256601\pi$
$103$	15.8817	+	9.16928i	1.56487	+	0.903476i	0.568114	+	0.822950i	$0.307673\pi$
$104$	−1.74646	+	4.05463i	−0.171254	+	0.397589i
$105$	−5.53953	+	8.33683i	−0.540603	+	0.813591i
$106$	4.73954	+	11.5952i	0.460344	+	1.12622i
$107$	3.83045	+	2.21151i	0.370303	+	0.213795i	0.673591	−	0.739104i	$-0.264751\pi$
$107$	3.83045	+	2.21151i	0.370303	+	0.213795i	−0.303288	+	0.952899i	$0.598084\pi$
$108$	8.59967	−	5.83486i	0.827504	−	0.561460i
$109$	−7.04986	+	4.07024i	−0.675255	+	0.389858i	−0.798065	−	0.602572i	$-0.794143\pi$
$109$	−7.04986	+	4.07024i	−0.675255	+	0.389858i	0.122810	+	0.992430i	$0.460809\pi$
$110$	−0.699274	+	5.12633i	−0.0666732	+	0.488776i
$111$	−1.30107	+	1.37411i	−0.123492	+	0.130425i
$112$	3.83352	−	9.86429i	0.362234	−	0.932087i
$113$			13.4000i			1.26056i	0.776367	+	0.630281i	$0.217060\pi$
$113$			13.4000i			1.26056i	−0.776367	+	0.630281i	$0.782940\pi$
$114$	8.82283	+	10.9748i	0.826334	+	1.02788i
$115$	7.13629	+	12.3604i	0.665463	+	1.15262i
$116$	−13.5695	−	3.77219i	−1.25990	−	0.350239i
$117$	2.11650	−	4.17694i	0.195671	−	0.386158i
$118$	−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
$122$	4.91281	+	3.80633i	0.444785	+	0.344609i
$123$	5.81089	+	1.38820i	0.523951	+	0.125170i
$124$	−17.3749	+	4.48201i	−1.56031	+	0.402496i
$125$	−11.4216			−1.02158
$126$	−4.70945	+	10.1893i	−0.419551	+	0.907732i
$127$		−	12.5356i		−	1.11236i	−0.831063	−	0.556178i	$-0.812267\pi$
$127$		−	12.5356i		−	1.11236i	0.831063	−	0.556178i	$-0.187733\pi$
$128$	6.59018	+	9.19617i	0.582495	+	0.812834i
$129$	4.69144	−	19.6380i	0.413059	−	1.72903i
$130$	−3.81136	−	2.95295i	−0.334279	−	0.258991i
$131$	−14.8145	−	8.55318i	−1.29435	−	0.747295i	−0.314930	−	0.949115i	$-0.601981\pi$
$131$	−14.8145	−	8.55318i	−1.29435	−	0.747295i	−0.979423	+	0.201820i	$0.935315\pi$
$132$	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
$135$	3.82446	+	10.6859i	0.329157	+	0.919694i
$136$	0.904329	−	0.106185i	0.0775456	−	0.00910533i
$137$	17.9399	−	10.3576i	1.53271	−	0.884909i	0.533472	−	0.845818i	$-0.320887\pi$
$137$	17.9399	−	10.3576i	1.53271	−	0.884909i	0.999236	−	0.0390917i	$-0.0124464\pi$
$138$	10.0285	+	12.4746i	0.853684	+	1.06191i
$139$	1.27255			0.107936			0.0539682	−	0.998543i	$-0.482813\pi$
$139$	1.27255			0.107936			0.0539682	+	0.998543i	$0.482813\pi$
$140$	9.38575	+	6.74486i	0.793241	+	0.570045i
$141$	5.66906	+	5.36770i	0.477421	+	0.452042i
$142$	8.92700	+	1.21772i	0.749137	+	0.102189i
$143$	1.30715	+	2.26406i	0.109310	+	0.189330i
$144$	−6.36922	−	10.1702i	−0.530769	−	0.847517i
$145$	7.69077	−	13.3208i	0.638684	−	1.10623i
$146$	−4.80520	−	11.7558i	−0.397681	−	0.972918i
$147$	−1.31587	−	12.0527i	−0.108532	−	0.994093i
$148$	1.53059	+	1.55946i	0.125814	+	0.128187i
$149$	−2.47136	+	4.28052i	−0.202461	+	0.350674i	−0.949321	−	0.314308i	$-0.898227\pi$
$149$	−2.47136	+	4.28052i	−0.202461	+	0.350674i	0.746859	+	0.664982i	$0.231561\pi$
$150$	−0.554550	+	0.0858130i	−0.0452788	+	0.00700661i
$151$	5.48605	−	3.16737i	0.446448	−	0.257757i	−0.259881	−	0.965641i	$-0.583683\pi$
$151$	5.48605	−	3.16737i	0.446448	−	0.257757i	0.706329	+	0.707884i	$0.250350\pi$
$152$	13.0373	−	9.71664i	1.05747	−	0.788124i
$153$	−0.964337	+	0.0527015i	−0.0779620	+	0.00426066i
$154$	−3.32708	−	5.31089i	−0.268104	−	0.427964i
$155$		−	19.5966i		−	1.57404i
$156$	−4.73034	−	2.61898i	−0.378731	−	0.209686i
$157$	2.09256	−	1.20814i	0.167004	−	0.0964199i	−0.414168	−	0.910200i	$-0.635928\pi$
$157$	2.09256	−	1.20814i	0.167004	−	0.0964199i	0.581172	+	0.813780i	$0.302594\pi$
$158$	−4.63168	−	3.58851i	−0.368476	−	0.285487i
$159$	−14.7050	+	4.37372i	−1.16618	+	0.346858i
$160$	−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	−0.636747	−	0.771072i	$-0.719721\pi$
$163$	4.46077	−	7.72628i	0.349395	−	0.605169i	0.986142	+	0.165903i	$0.0530539\pi$
$164$	1.84769	−	6.64661i	0.144280	−	0.519013i
$165$	−6.16316	−	1.47236i	−0.479801	−	0.114623i
$166$	−1.73261	+	12.7016i	−0.134477	+	0.985839i
$167$	−7.01131			−0.542551			−0.271276	−	0.962502i	$-0.587445\pi$
$167$	−7.01131			−0.542551			−0.271276	+	0.962502i	$0.587445\pi$
$168$	11.5584	+	5.86537i	0.891753	+	0.452523i
$169$	10.5637			0.812595
$170$	−0.134403	+	0.985297i	−0.0103082	+	0.0755688i
$171$	−14.4429	+	9.42530i	−1.10447	+	0.720771i
$172$	−22.4623	−	6.24428i	−1.71274	−	0.476122i
$173$	7.11660	−	12.3263i	0.541065	−	0.937152i	−0.457778	−	0.889066i	$-0.651355\pi$
$173$	7.11660	−	12.3263i	0.541065	−	0.937152i	0.998843	−	0.0480854i	$-0.0153120\pi$
$174$	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
$177$	−3.06193	−	10.2946i	−0.230149	−	0.773790i
$178$	−5.90690	−	4.57652i	−0.442741	−	0.343025i
$179$	−1.07613	+	0.621304i	−0.0804338	+	0.0464384i	−0.539677	−	0.841872i	$-0.681454\pi$
$179$	−1.07613	+	0.621304i	−0.0804338	+	0.0464384i	0.459244	+	0.888310i	$0.348120\pi$
$180$	12.4925	−	3.96112i	0.931135	−	0.295244i
$181$		−	20.9487i		−	1.55710i	−0.627580	−	0.778552i	$-0.715954\pi$
$181$		−	20.9487i		−	1.55710i	0.627580	−	0.778552i	$-0.284046\pi$
$182$	5.83639	−	0.210504i	0.432622	−	0.0156036i
$183$	−5.23327	+	5.52709i	−0.386855	+	0.408574i
$184$	14.8189	−	11.0445i	1.09247	−	0.814209i
$185$	−2.06667	+	1.19319i	−0.151945	+	0.0877253i
$186$	−3.36071	−	21.7179i	−0.246419	−	1.59243i
$187$	0.269600	−	0.466960i	0.0197151	−	0.0341475i
$188$	6.43374	−	6.31461i	0.469228	−	0.460541i
$189$	−11.8485	−	6.97223i	−0.861855	−	0.507155i
$190$	6.71889	+	16.4376i	0.487440	+	1.19251i
$191$	−12.2119	+	21.1516i	−0.883621	+	1.53048i	−0.0363339	+	0.999340i	$0.511568\pi$
$191$	−12.2119	+	21.1516i	−0.883621	+	1.53048i	−0.847287	+	0.531136i	$0.821765\pi$
$192$	−12.0051	+	6.91940i	−0.866392	+	0.499365i
$193$	0.00662606	+	0.0114767i	0.000476954	+	0.000826109i	0.866264	−	0.499587i	$-0.166515\pi$
$193$	0.00662606	+	0.0114767i	0.000476954	+	0.000826109i	−0.865787	+	0.500413i	$0.833182\pi$
$194$	5.92938	+	0.808817i	0.425705	+	0.0580697i
$195$	4.05998	−	4.28792i	0.290741	−	0.307064i
$196$	−13.9636	+	1.00858i	−0.997402	+	0.0720413i
$197$	−6.48422			−0.461981			−0.230991	−	0.972956i	$-0.574197\pi$
$197$	−6.48422			−0.461981			−0.230991	+	0.972956i	$0.574197\pi$
$198$	−7.08280	−	0.574790i	−0.503353	−	0.0408485i
$199$	4.47013	−	2.58083i	0.316879	−	0.182950i	−0.333121	−	0.942884i	$-0.608102\pi$
$199$	4.47013	−	2.58083i	0.316879	−	0.182950i	0.650001	+	0.759934i	$0.274769\pi$
$200$	0.0755638	+	0.643539i	0.00534317	+	0.0455051i
$201$	−2.37761	+	0.707172i	−0.167703	+	0.0498801i
$202$	−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
$206$	20.5014	+	15.8840i	1.42840	+	1.10669i
$207$	−16.4166	+	10.7133i	−1.14103	+	0.744627i
$208$	−3.22220	+	5.34768i	−0.223419	+	0.370795i
$209$		−	9.62870i		−	0.666031i
$210$	−9.35570	+	10.6230i	−0.645605	+	0.733060i
$211$	−16.8357			−1.15902			−0.579509	−	0.814966i	$-0.696756\pi$
$211$	−16.8357			−1.15902			−0.579509	+	0.814966i	$0.696756\pi$
$212$	4.42491	+	17.1535i	0.303904	+	1.17811i
$213$	−2.56396	+	10.7325i	−0.175680	+	0.735381i
$214$	4.94466	+	3.83100i	0.338010	+	0.261882i
$215$	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
$219$	14.9087	−	4.43431i	1.00744	−	0.299643i
$220$	−1.95970	+	7.04954i	−0.132123	+	0.475280i
$221$	0.251239	+	0.435159i	0.0169002	+	0.0292720i
$222$	−2.08576	+	1.67677i	−0.139987	+	0.112538i
$223$			1.80170i			0.120651i	0.998179	+	0.0603254i	$0.0192138\pi$
$223$			1.80170i			0.120651i	−0.998179	+	0.0603254i	$0.980786\pi$
$224$	7.25713	−	13.0895i	0.484888	−	0.874576i
$225$	−0.0375035	−	0.686242i	−0.00250023	−	0.0457495i
$226$	−2.56127	+	18.7765i	−0.170373	+	1.24899i
$227$	10.0476	−	5.80096i	0.666879	−	0.385023i	−0.128014	−	0.991772i	$-0.540860\pi$
$227$	10.0476	−	5.80096i	0.666879	−	0.385023i	0.794893	+	0.606749i	$0.207527\pi$
$228$	10.2651	+	17.0647i	0.679826	+	1.13014i
$229$	8.50697	+	4.91150i	0.562156	+	0.324561i	0.754010	−	0.656862i	$-0.228117\pi$
$229$	8.50697	+	4.91150i	0.562156	+	0.324561i	−0.191854	+	0.981423i	$0.561450\pi$
$230$	7.63706	+	18.6839i	0.503573	+	1.23198i
$231$	6.87515	−	3.41246i	0.452352	−	0.224523i
$232$	−18.2931	−	7.87942i	−1.20100	−	0.517309i
$233$	6.94161	+	4.00774i	0.454760	+	0.262556i	0.709838	−	0.704365i	$-0.248768\pi$
$233$	6.94161	+	4.00774i	0.454760	+	0.262556i	−0.255079	+	0.966920i	$0.582101\pi$
$234$	3.76410	−	5.44833i	0.246067	−	0.356169i
$235$	4.92265	+	8.52627i	0.321118	+	0.556193i
$236$	−12.0087	+	3.09776i	−0.781702	+	0.201647i
$237$	4.93380	−	5.21080i	0.320485	−	0.338478i
$238$	−0.639475	−	1.02077i	−0.0414510	−	0.0661667i
$239$	6.02441			0.389686			0.194843	−	0.980834i	$-0.437580\pi$
$239$	6.02441			0.389686			0.194843	+	0.980834i	$0.437580\pi$
$240$	−4.04239	−	14.5830i	−0.260935	−	0.941326i
$241$	5.11917	+	8.86666i	0.329755	+	0.571152i	0.982463	−	0.186457i	$-0.0597006\pi$
$241$	5.11917	+	8.86666i	0.329755	+	0.571152i	−0.652708	+	0.757609i	$0.726367\pi$
$242$	−7.09780	+	9.16109i	−0.456264	+	0.588897i
$243$	−14.3683	+	6.04587i	−0.921726	+	0.387843i
$244$	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
$248$	−25.2030	+	2.95931i	−1.60039	+	0.187917i
$249$	−15.2706	−	3.64810i	−0.967736	−	0.231189i
$250$	−16.0044	−	2.18313i	−1.01220	−	0.138073i
$251$			9.97684i			0.629733i	0.949136	+	0.314866i	$0.101960\pi$
$251$			9.97684i			0.629733i	−0.949136	+	0.314866i	$0.898040\pi$
$252$	−8.54664	+	13.3774i	−0.538387	+	0.842697i
$253$		−	10.9445i		−	0.688075i
$254$	2.39606	−	17.5654i	0.150342	−	1.10215i
$255$	−1.18458	−	0.282992i	−0.0741812	−	0.0177216i
$256$	7.47664	+	14.1457i	0.467290	+	0.884104i
$257$	17.1555	+	9.90475i	1.07013	+	0.617841i	0.928218	−	0.372038i	$-0.121341\pi$
$257$	17.1555	+	9.90475i	1.07013	+	0.617841i	0.141915	+	0.989879i	$0.454674\pi$
$258$	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
$261$	18.8449	+	9.54895i	1.16647	+	0.591065i
$262$	−19.1238	−	14.8167i	−1.18147	−	0.915379i
$263$	−3.41780	−	5.91981i	−0.210751	−	0.365031i	0.741199	−	0.671285i	$-0.234258\pi$
$263$	−3.41780	−	5.91981i	−0.210751	−	0.365031i	−0.951950	+	0.306254i	$0.900924\pi$
$264$	−0.962875	+	8.14871i	−0.0592608	+	0.501519i
$265$	−19.3470			−1.18847
$266$	−19.0036	−	10.0765i	−1.16519	−	0.617830i
$267$	6.29220	−	6.64546i	0.385077	−	0.406696i
$268$	0.715449	+	2.77350i	0.0437030	+	0.169418i
$269$	12.0822	+	20.9270i	0.736665	+	1.27594i	0.953989	+	0.299842i	$0.0969338\pi$
$269$	12.0822	+	20.9270i	0.736665	+	1.27594i	−0.217324	+	0.976099i	$0.569733\pi$
$270$	3.31647	+	15.7045i	0.201834	+	0.955743i
$271$	−15.2835	−	8.82392i	−0.928405	−	0.536015i	−0.0420983	−	0.999113i	$-0.513404\pi$
$271$	−15.2835	−	8.82392i	−0.928405	−	0.536015i	−0.886307	+	0.463099i	$0.846738\pi$
$272$	1.28748	+	0.0240629i	0.0780647	+	0.00145903i
$273$	−0.449452	+	7.13860i	−0.0272021	+	0.432048i
$274$	27.1178	−	11.0844i	1.63825	−	0.669634i
$275$	0.332299	+	0.191853i	0.0200384	+	0.0115692i
$276$	11.6679	+	19.3967i	0.702327	+	1.16754i
$277$	12.9250	−	7.46224i	0.776587	−	0.448363i	−0.0586324	−	0.998280i	$-0.518674\pi$
$277$	12.9250	−	7.46224i	0.776587	−	0.448363i	0.835219	+	0.549917i	$0.185341\pi$
$278$	1.78314	+	0.243236i	0.106946	+	0.0145883i
$279$	26.8754	−	1.46875i	1.60899	−	0.0879320i
$280$	11.8624	+	11.2451i	0.708917	+	0.672026i
$281$			13.8890i			0.828547i	0.910152	+	0.414273i	$0.135964\pi$
$281$			13.8890i			0.828547i	−0.910152	+	0.414273i	$0.864036\pi$
$282$	6.91771	+	8.60501i	0.411944	+	0.512421i
$283$	2.88865	+	5.00329i	0.171712	+	0.297415i	0.939019	−	0.343866i	$-0.111737\pi$
$283$	2.88865	+	5.00329i	0.171712	+	0.297415i	−0.767306	+	0.641281i	$0.778403\pi$
$284$	12.2761	+	3.41262i	0.728451	+	0.202502i
$285$	−20.8462	+	6.20030i	−1.23482	+	0.367274i
$286$	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
$290$	13.3227	−	17.1956i	0.782338	−	1.00976i
$291$	−1.70300	+	7.12863i	−0.0998319	+	0.417888i
$292$	−4.48621	−	17.3912i	−0.262535	−	1.01774i
$293$	15.6381			0.913587			0.456794	−	0.889573i	$-0.348998\pi$
$293$	15.6381			0.913587			0.456794	+	0.889573i	$0.348998\pi$
$294$	0.459914	−	17.1403i	0.0268227	−	0.999640i
$295$		−	13.5443i		−	0.788581i
$296$	1.84664	+	2.47774i	0.107334	+	0.144015i
$297$	1.55731	−	8.56268i	0.0903641	−	0.496857i
$298$	−4.28114	+	5.52564i	−0.248000	+	0.320092i
$299$	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
$303$	8.20576	−	2.44064i	0.471409	−	0.140211i
$304$	20.1256	−	11.1234i	1.15428	−	0.637968i
$305$	−8.31274	+	4.79936i	−0.475986	+	0.274811i
$306$	−1.36134	−	0.110476i	−0.0778225	−	0.00631552i
$307$	7.19887			0.410861			0.205430	−	0.978672i	$-0.434141\pi$
$307$	7.19887			0.410861			0.205430	+	0.978672i	$0.434141\pi$
$308$	−3.64690	−	8.07776i	−0.207801	−	0.460273i
$309$	−21.8387	+	23.0647i	−1.24236	+	1.31211i
$310$	3.74571	−	27.4595i	0.212742	−	1.55960i
$311$	−4.35089	−	7.53597i	−0.246717	−	0.427326i	0.715896	−	0.698207i	$-0.246018\pi$
$311$	−4.35089	−	7.53597i	−0.246717	−	0.427326i	−0.962613	+	0.270881i	$0.912685\pi$
$312$	−6.12774	−	4.57397i	−0.346915	−	0.258950i
$313$	9.57541	−	16.5851i	0.541234	−	0.937445i	−0.457600	−	0.889158i	$-0.651291\pi$
$313$	9.57541	−	16.5851i	0.541234	−	0.937445i	0.998834	−	0.0482863i	$-0.0153760\pi$
$314$	3.16309	−	1.29292i	0.178504	−	0.0729634i
$315$	−11.8152	−	12.6873i	−0.665710	−	0.714851i
$316$	−5.80417	−	5.91366i	−0.326510	−	0.332669i
$317$	−1.83178	+	3.17274i	−0.102883	+	0.178199i	−0.912871	−	0.408247i	$-0.866140\pi$
$317$	−1.83178	+	3.17274i	−0.102883	+	0.178199i	0.809988	+	0.586446i	$0.199473\pi$
$318$	−21.4412	+	3.31789i	−1.20236	+	0.186058i
$319$	−10.2147	+	5.89744i	−0.571911	+	0.330193i
$320$	−16.9987	+	4.04774i	−0.950253	+	0.226275i
$321$	−5.26720	+	5.56291i	−0.293986	+	0.310491i
$322$	−21.6006	−	11.4535i	−1.20375	−	0.638279i
$323$		−	1.85067i		−	0.102974i
$324$	6.36869	+	16.8357i	0.353816	+	0.935315i
$325$	−0.309668	+	0.178787i	−0.0171773	+	0.00991732i
$326$	7.72741	−	9.97372i	0.427981	−	0.552393i
$327$	−4.01965	−	13.5146i	−0.222287	−	0.747360i
$328$	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	−0.678016	−	0.735047i	$-0.737160\pi$
$331$	5.41365	−	9.37672i	0.297561	−	0.515391i	0.975577	+	0.219656i	$0.0704934\pi$
$332$	−4.85560	+	17.4668i	−0.266485	+	0.958617i
$333$	−1.79127	−	2.74486i	−0.0981612	−	0.150417i
$334$	−9.82450	−	1.34014i	−0.537573	−	0.0733294i
$335$	−3.12815			−0.170909
$336$	15.0750	+	10.4281i	0.822409	+	0.568897i
$337$	−20.0426			−1.09179			−0.545894	−	0.837854i	$-0.683810\pi$
$337$	−20.0426			−1.09179			−0.545894	+	0.837854i	$0.683810\pi$
$338$	14.8023	+	2.01916i	0.805139	+	0.109828i
$339$	−22.5742	−	5.39289i	−1.22606	−	0.292901i
$340$	−0.376660	+	1.35495i	−0.0204273	+	0.0734822i
$341$	−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
$345$	−23.6950	+	7.04760i	−1.27569	+	0.379430i
$346$	12.3281	−	15.9118i	0.662762	−	0.855424i
$347$	−5.06136	+	2.92218i	−0.271708	+	0.156871i	−0.629664	−	0.776868i	$-0.716807\pi$
$347$	−5.06136	+	2.92218i	−0.271708	+	0.156871i	0.357955	+	0.933739i	$0.383474\pi$
$348$	11.8159	−	21.3417i	0.633401	−	1.14404i
$349$			18.6166i			0.996526i	0.867026	+	0.498263i	$0.166029\pi$
$349$			18.6166i			0.996526i	−0.867026	+	0.498263i	$0.833971\pi$
$350$	0.726402	−	0.455064i	0.0388278	−	0.0243242i
$351$	6.18486	+	5.24659i	0.330123	+	0.280042i
$352$	9.36228	+	1.45578i	0.499011	+	0.0775936i
$353$	5.78219	−	3.33835i	0.307755	−	0.177682i	−0.338167	−	0.941086i	$-0.609807\pi$
$353$	5.78219	−	3.33835i	0.307755	−	0.177682i	0.645921	+	0.763404i	$0.276473\pi$
$354$	−2.32277	−	15.0104i	−0.123454	−	0.797796i
$355$	−6.95768	+	12.0511i	−0.369275	+	0.639603i
$356$	−7.40220	−	7.54184i	−0.392316	−	0.399717i
$357$	1.32143	−	0.655886i	0.0699373	−	0.0347132i
$358$	−1.62667	+	0.664902i	−0.0859722	+	0.0351412i
$359$	12.1282	−	21.0067i	0.640102	−	1.10869i	−0.345307	−	0.938490i	$-0.612225\pi$
$359$	12.1282	−	21.0067i	0.640102	−	1.10869i	0.985410	−	0.170200i	$-0.0544414\pi$
$360$	18.2621	−	3.16264i	0.962496	−	0.166686i
$361$	−7.02406	−	12.1660i	−0.369687	−	0.640317i
$362$	4.00414	−	29.3541i	0.210453	−	1.54282i
$363$	−10.3065	−	9.75866i	−0.540953	−	0.512197i
$364$	8.21840	+	0.820604i	0.430761	+	0.0430113i
$365$	19.6150			1.02670
$366$	−8.38951	+	6.74447i	−0.438527	+	0.352539i
$367$	−6.54864	+	3.78086i	−0.341836	+	0.197359i	−0.661084	−	0.750312i	$-0.729903\pi$
$367$	−6.54864	+	3.78086i	−0.341836	+	0.197359i	0.319248	+	0.947671i	$0.396570\pi$
$368$	22.8759	−	12.6434i	1.19249	−	0.659084i
$369$	−4.67725	+	9.23060i	−0.243488	+	0.480526i
$370$	−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	$-0.502602\pi$
$373$	−16.9620	−	9.79302i	−0.878260	−	0.507063i	−0.870084	+	0.492903i	$0.835936\pi$
$374$	0.467028	−	0.602791i	0.0241494	−	0.0311696i
$375$	4.59669	−	19.2413i	0.237372	−	0.993618i
$376$	10.2222	−	7.61852i	0.527168	−	0.392895i
$377$		−	10.9916i		−	0.566097i
$378$	−15.2699	−	12.0345i	−0.785401	−	0.618987i
$379$	4.99759			0.256709			0.128354	−	0.991728i	$-0.459031\pi$
$379$	4.99759			0.256709			0.128354	+	0.991728i	$0.459031\pi$
$380$	6.27286	+	24.3173i	0.321791	+	1.24745i
$381$	21.1181	+	5.04503i	1.08191	+	0.258465i
$382$	−21.1547	+	27.3042i	−1.08237	+	1.39701i
$383$	−15.1532	+	26.2461i	−0.774292	+	1.34111i	0.160900	+	0.986971i	$0.448560\pi$
$383$	−15.1532	+	26.2461i	−0.774292	+	1.34111i	−0.935192	+	0.354142i	$0.884773\pi$
$384$	−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
$387$	31.1949	+	15.8068i	1.58573	+	0.803507i
$388$	8.15387	+	2.26669i	0.413950	+	0.115074i
$389$	−2.13059	−	3.69030i	−0.108025	−	0.187106i	0.806945	−	0.590627i	$-0.201119\pi$
$389$	−2.13059	−	3.69030i	−0.108025	−	0.187106i	−0.914970	+	0.403521i	$0.867786\pi$
$390$	6.50858	−	5.23236i	0.329575	−	0.264951i
$391$		−	2.10357i		−	0.106382i
$392$	−19.7591	−	1.25576i	−0.997987	−	0.0634253i
$393$	20.3713	−	21.5150i	1.02760	−	1.08529i
$394$	−9.08592	−	1.23940i	−0.457742	−	0.0624399i
$395$	7.83704	−	4.52472i	0.394324	−	0.227663i
$396$	−9.81482	−	2.15923i	−0.493213	−	0.108505i
$397$	17.1398	+	9.89568i	0.860223	+	0.496650i	0.864087	−	0.503343i	$-0.167897\pi$
$397$	17.1398	+	9.89568i	0.860223	+	0.496650i	−0.00386406	+	0.999993i	$0.501230\pi$
$398$	6.75702	−	2.76194i	0.338699	−	0.138443i
$399$	14.5796	−	21.9419i	0.729893	−	1.09847i
$400$	−0.0171236	+	0.916195i	−0.000856182	+	0.0458097i
$401$	1.98773	+	1.14762i	0.0992627	+	0.0573094i	0.548810	−	0.835947i	$-0.315081\pi$
$401$	1.98773	+	1.14762i	0.0992627	+	0.0573094i	−0.449547	+	0.893257i	$0.648415\pi$
$402$	−3.46676	+	0.536459i	−0.172906	+	0.0267561i
$403$	−7.00186	−	12.1276i	−0.348787	−	0.604118i
$404$	−2.46921	−	9.57208i	−0.122848	−	0.476229i
$405$	−19.5411	+	2.14226i	−0.971005	+	0.106450i
$406$	0.949723	+	26.3318i	0.0471339	+	1.30683i
$407$	1.82993			0.0907062
$408$	−0.185068	+	1.56621i	−0.00916221	+	0.0775389i
$409$	−0.750621	−	1.30011i	−0.0371158	−	0.0642865i	0.846871	−	0.531799i	$-0.178484\pi$
$409$	−0.750621	−	1.30011i	−0.0371158	−	0.0642865i	−0.883987	+	0.467512i	$0.845150\pi$
$410$	8.42272	+	6.52572i	0.415968	+	0.322283i
$411$	10.2289	+	34.3908i	0.504553	+	1.69637i
$412$	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
$416$	−5.53723	+	6.87747i	−0.271485	+	0.337196i
$417$	−0.512145	+	2.14380i	−0.0250799	+	0.104982i
$418$	1.84043	−	13.4921i	0.0900186	−	0.659920i
$419$			8.44514i			0.412572i	0.978492	+	0.206286i	$0.0661378\pi$
$419$			8.44514i			0.412572i	−0.978492	+	0.206286i	$0.933862\pi$
$420$	−15.1400	+	13.0972i	−0.738759	+	0.639076i
$421$		−	13.9326i		−	0.679032i	−0.940600	−	0.339516i	$-0.889737\pi$
$421$		−	13.9326i		−	0.679032i	0.940600	−	0.339516i	$-0.110263\pi$
$422$	−23.5908	−	3.21799i	−1.14838	−	0.156649i
$423$	−11.3242	+	7.39009i	−0.550602	+	0.359319i
$424$	2.92161	+	24.8819i	0.141886	+	1.20837i
$425$	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
$429$	−4.34020	+	1.29091i	−0.209547	+	0.0623256i
$430$	22.0538	−	28.4647i	1.06353	−	1.37269i
$431$	−16.9743	−	29.4004i	−0.817624	−	1.41617i	−0.907428	−	0.420207i	$-0.861957\pi$
$431$	−16.9743	−	29.4004i	−0.817624	−	1.41617i	0.0898039	−	0.995959i	$-0.471376\pi$
$432$	19.6965	−	6.63683i	0.947649	−	0.319314i
$433$	4.44336			0.213534			0.106767	−	0.994284i	$-0.465950\pi$
$433$	4.44336			0.213534			0.106767	+	0.994284i	$0.465950\pi$
$434$	17.8217	+	28.4482i	0.855470	+	1.36556i
$435$	19.3456	+	18.3173i	0.927552	+	0.878245i
$436$	−15.7649	+	4.06670i	−0.755001	+	0.194760i
$437$	−18.7822	−	32.5316i	−0.898472	−	1.55620i
$438$	21.7383	−	3.36386i	1.03869	−	0.160731i
$439$	−7.55680	−	4.36292i	−0.360667	−	0.208231i	0.308707	−	0.951157i	$-0.400104\pi$
$439$	−7.55680	−	4.36292i	−0.360667	−	0.208231i	−0.669373	+	0.742926i	$0.733437\pi$
$440$	−4.09346	+	9.50351i	−0.195148	+	0.453062i
$441$	20.8342	+	2.63391i	0.992103	+	0.125424i
$442$	0.268869	+	0.657783i	0.0127888	+	0.0312875i
$443$	−32.0121	−	18.4822i	−1.52094	−	0.878115i	−0.999695	−	0.0247072i	$-0.992135\pi$
$443$	−32.0121	−	18.4822i	−1.52094	−	0.878115i	−0.521244	−	0.853407i	$-0.674532\pi$
$444$	−3.24314	+	1.95089i	−0.153912	+	0.0925849i
$445$	9.99478	−	5.77049i	0.473798	−	0.273548i
$446$	−0.344378	+	2.52461i	−0.0163068	+	0.119544i
$447$	−6.21654	−	5.88608i	−0.294032	−	0.278402i
$448$	12.6709	−	16.9543i	0.598643	−	0.801016i
$449$			23.4269i			1.10559i	0.833319	+	0.552793i	$0.186438\pi$
$449$			23.4269i			1.10559i	−0.833319	+	0.552793i	$0.813562\pi$
$450$	0.0786173	−	0.968756i	0.00370606	−	0.0456676i
$451$	−2.88868	−	5.00333i	−0.136022	−	0.235598i
$452$	−7.17790	+	25.8208i	−0.337620	+	1.21451i
$453$	3.12801	+	10.5168i	0.146967	+	0.494121i
$454$	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	−0.850142	−	0.526554i	$-0.823484\pi$
$457$	0.661376	−	1.14554i	0.0309378	−	0.0535859i	0.881080	+	0.472968i	$0.156817\pi$
$458$	10.9815	+	8.50820i	0.513131	+	0.397562i
$459$	0.299319	−	1.64577i	0.0139710	−	0.0768182i
$460$	7.13008	+	27.6403i	0.332442	+	1.28874i
$461$	23.5461			1.09665			0.548325	−	0.836266i	$-0.315266\pi$
$461$	23.5461			1.09665			0.548325	+	0.836266i	$0.315266\pi$
$462$	10.2860	−	3.46755i	0.478547	−	0.161325i
$463$			14.4502i			0.671557i	0.941941	+	0.335778i	$0.108999\pi$
$463$			14.4502i			0.671557i	−0.941941	+	0.335778i	$0.891001\pi$
$464$	−24.1269	−	14.5375i	−1.12006	−	0.674886i
$465$	33.0134	+	7.88678i	1.53096	+	0.365741i
$466$	8.96079	+	6.94261i	0.415101	+	0.321610i
$467$	−13.0084	−	7.51039i	−0.601956	−	0.347540i	0.167855	−	0.985812i	$-0.446316\pi$
$467$	−13.0084	−	7.51039i	−0.601956	−	0.347540i	−0.769811	+	0.638272i	$0.779649\pi$
$468$	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
$471$	1.19312	+	4.01144i	0.0549762	+	0.184837i
$472$	−17.4192	+	2.04535i	−0.801783	+	0.0941447i
$473$	−16.9088	+	9.76231i	−0.777468	+	0.448872i
$474$	7.90942	−	6.35851i	0.363292	−	0.292056i
$475$	1.31697			0.0604269
$476$	−0.700946	−	1.55257i	−0.0321278	−	0.0711620i
$477$	−1.45004	−	26.5330i	−0.0663928	−	1.21486i
$478$	8.44162	+	1.15151i	0.386111	+	0.0526687i
$479$	10.9550	+	18.9745i	0.500545	+	0.866969i	1.00000		0.000629369i	$0.000200335\pi$
$479$	10.9550	+	18.9745i	0.500545	+	0.866969i	−0.499455	+	0.866340i	$0.666466\pi$
$480$	−2.87695	−	21.2069i	−0.131314	−	0.967956i
$481$	−0.852653	+	1.47684i	−0.0388776	+	0.0673380i
$482$	5.47839	+	13.4028i	0.249534	+	0.610480i
$483$	16.5720	−	24.9403i	0.754051	−	1.13482i
$484$	−11.6967	+	11.4802i	−0.531670	+	0.521826i
$485$	−4.62134	+	8.00440i	−0.209844	+	0.363461i
$486$	−21.2890	+	5.72534i	−0.965688	+	0.259707i
$487$	9.51388	−	5.49284i	0.431115	−	0.248904i	−0.268707	−	0.963222i	$-0.586596\pi$
$487$	9.51388	−	5.49284i	0.431115	−	0.248904i	0.699821	+	0.714318i	$0.253263\pi$
$488$	7.42773	+	9.96617i	0.336237	+	0.451147i
$489$	11.2208	+	10.6243i	0.507421	+	0.480448i
$490$	6.71811	−	20.5528i	0.303493	−	0.928479i
$491$		−	32.3525i		−	1.46005i	−0.683422	−	0.730024i	$-0.739509\pi$
$491$		−	32.3525i		−	1.46005i	0.683422	−	0.730024i	$-0.260491\pi$
$492$	10.4536	+	5.78767i	0.471283	+	0.260928i
$493$	−1.96329	+	1.13351i	−0.0884222	+	0.0510506i
$494$	10.0312	+	7.77194i	0.451325	+	0.349676i
$495$	4.96080	−	9.79018i	0.222971	−	0.440036i
$496$	−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	−0.980072	−	0.198643i	$-0.936347\pi$
$499$	−7.10372	+	12.3040i	−0.318006	+	0.550803i	0.662066	+	0.749446i	$0.269680\pi$
$500$	−22.0086	−	6.11816i	−0.984255	−	0.273613i
$501$	2.82174	−	11.8116i	0.126066	−	0.527702i
$502$	−1.90698	+	13.9799i	−0.0851126	+	0.623954i
$503$	−33.4106			−1.48970			−0.744852	−	0.667229i	$-0.767480\pi$
$503$	−33.4106			−1.48970			−0.744852	+	0.667229i	$0.767480\pi$
$504$	−14.5328	+	17.1113i	−0.647344	+	0.762198i
$505$	10.7961			0.480419
$506$	2.09194	−	15.3359i	0.0929980	−	0.681762i
$507$	−4.25144	+	17.7961i	−0.188813	+	0.790354i
$508$	6.71491	−	24.1553i	0.297926	−	1.07172i
$509$	−8.44815	+	14.6326i	−0.374458	+	0.648580i	−0.990246	−	0.139332i	$-0.955504\pi$
$509$	−8.44815	+	14.6326i	−0.374458	+	0.648580i	0.615788	+	0.787912i	$0.288838\pi$
$510$	−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
$513$	−10.0657	−	28.1244i	−0.444410	−	1.24172i
$514$	22.1458	+	17.1580i	0.976808	+	0.756808i
$515$	−34.6894	+	20.0279i	−1.52860	+	0.882536i
$516$	19.5595	−	35.3280i	0.861059	−	1.55523i
$517$		−	7.54957i		−	0.332030i
$518$	1.91503	−	3.61163i	0.0841418	−	0.158686i
$519$	17.9013	+	16.9497i	0.785781	+	0.744011i
$520$	−5.76243	−	7.73176i	−0.252699	−	0.339060i
$521$	−31.0684	+	17.9374i	−1.36113	+	0.785850i	−0.989775	−	0.142639i	$-0.954441\pi$
$521$	−31.0684	+	17.9374i	−1.36113	+	0.785850i	−0.371358	+	0.928490i	$0.621108\pi$
$522$	24.5810	+	16.9824i	1.07588	+	0.743298i
$523$	−1.10840	+	1.91980i	−0.0484669	+	0.0839471i	−0.889241	−	0.457439i	$-0.848767\pi$
$523$	−1.10840	+	1.91980i	−0.0484669	+	0.0839471i	0.840774	+	0.541386i	$0.182100\pi$
$524$	−23.9650	−	24.4170i	−1.04691	−	1.06666i
$525$	0.466742	+	0.940354i	0.0203703	+	0.0410404i
$526$	−3.65764	−	8.94834i	−0.159481	−	0.390166i
$527$	−1.44413	+	2.50130i	−0.0629072	+	0.108959i
$528$	−2.90676	+	11.2342i	−0.126501	+	0.488907i
$529$	−9.84883	−	17.0587i	−0.428210	−	0.741681i
$530$	−27.1097	−	3.69799i	−1.17757	−	0.160630i
$531$	18.5751	−	1.01514i	0.806089	−	0.0440532i
$532$	−24.7026	−	17.7519i	−1.07099	−	0.769644i
$533$	5.38390			0.233202
$534$	10.0871	−	8.10918i	0.436511	−	0.350918i
$535$	−8.36662	+	4.83047i	−0.361721	+	0.208840i
$536$	0.472386	+	4.02308i	0.0204040	+	0.173770i
$537$	−0.613582	−	2.06295i	−0.0264780	−	0.0890227i
$538$	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	$-0.628649\pi$
$541$	−32.2404	−	18.6140i	−1.38612	−	0.800279i	−0.992876	+	0.119153i	$0.961982\pi$
$542$	−19.7292	−	15.2857i	−0.847440	−	0.656577i
$543$	35.2911	+	8.43092i	1.51449	+	0.361806i
$544$	1.79946	+	0.279807i	0.0771512	+	0.0119966i
$545$		−	17.7808i		−	0.761645i
$546$	−1.99426	+	9.91696i	−0.0853466	+	0.424407i
$547$	12.2271			0.522792			0.261396	−	0.965232i	$-0.415817\pi$
$547$	12.2271			0.522792			0.261396	+	0.965232i	$0.415817\pi$
$548$	40.1171	−	10.3486i	1.71372	−	0.442069i
$549$	−7.20502	−	11.0406i	−0.307503	−	0.471202i
$550$	0.428958	+	0.332347i	0.0182908	+	0.0141713i
$551$	−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
$555$	−1.17836	−	3.96181i	−0.0500187	−	0.168170i
$556$	2.45212	+	0.681662i	0.103993	+	0.0289089i
$557$	−0.649106	−	1.12428i	−0.0275035	−	0.0476375i	0.851946	−	0.523630i	$-0.175422\pi$
$557$	−0.649106	−	1.12428i	−0.0275035	−	0.0476375i	−0.879450	+	0.475992i	$0.842089\pi$
$558$	37.9395	+	3.07890i	1.60611	+	0.130340i
$559$		−	18.1949i		−	0.769564i
$560$	14.4727	+	18.0245i	0.611583	+	0.761675i
$561$	0.678160	+	0.642111i	0.0286320	+	0.0271099i
$562$	−2.65475	+	19.4618i	−0.111984	+	0.820944i
$563$	24.2080	−	13.9765i	1.02024	−	0.589038i	0.106070	−	0.994359i	$-0.466173\pi$
$563$	24.2080	−	13.9765i	1.02024	−	0.589038i	0.914175	+	0.405320i	$0.132840\pi$
$564$	8.04859	+	13.3799i	0.338907	+	0.563396i
$565$	−25.3475	−	14.6344i	−1.06638	−	0.615672i
$566$	3.09135	+	7.56293i	0.129939	+	0.317894i
$567$	16.5142	−	17.1546i	0.693533	−	0.720425i
$568$	16.5494	+	7.12835i	0.694398	+	0.299099i
$569$	26.1457	+	15.0952i	1.09608	+	0.632825i	0.935190	−	0.354147i	$-0.115229\pi$
$569$	26.1457	+	15.0952i	1.09608	+	0.632825i	0.160895	+	0.986972i	$0.448562\pi$
$570$	−30.3956	+	4.70353i	−1.27313	+	0.197009i
$571$	−16.0016	−	27.7156i	−0.669646	−	1.15986i	−0.978003	−	0.208591i	$-0.933112\pi$
$571$	−16.0016	−	27.7156i	−0.669646	−	1.15986i	0.308357	−	0.951271i	$-0.400221\pi$
$572$	1.30602	+	5.06288i	0.0546073	+	0.211690i
$573$	−30.7182	−	29.0853i	−1.28327	−	1.21505i
$574$	−12.8978	+	0.465192i	−0.538344	+	0.0194167i
$575$	1.49694			0.0624269
$576$	−6.82522	−	23.0091i	−0.284384	−	0.958710i
$577$	7.72204	+	13.3750i	0.321473	+	0.556807i	0.980792	−	0.195056i	$-0.0624888\pi$
$577$	7.72204	+	13.3750i	0.321473	+	0.556807i	−0.659319	+	0.751863i	$0.729155\pi$
$578$	−14.6348	+	18.8891i	−0.608728	+	0.785682i
$579$	−0.0220008	+	0.00654370i	−0.000914322	+	0.000271947i
$580$	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
$584$	−2.96209	−	25.2266i	−0.122572	−	1.04389i
$585$	5.58965	+	8.56532i	0.231104	+	0.354132i
$586$	21.9127	+	2.98907i	0.905204	+	0.123477i
$587$		−	1.97510i		−	0.0815212i	−0.999169	−	0.0407606i	$-0.987022\pi$
$587$		−	1.97510i		−	0.0815212i	0.999169	−	0.0407606i	$-0.0129781\pi$
$588$	3.92065	−	23.9297i	0.161685	−	0.986842i
$589$			51.5768i			2.12518i
$590$	2.58887	−	18.9788i	0.106582	−	0.781345i
$591$	2.60961	−	10.9236i	0.107345	−	0.449337i
$592$	2.11399	+	3.82486i	0.0868844	+	0.157201i
$593$	14.0265	+	8.09823i	0.576001	+	0.332554i	0.759543	−	0.650458i	$-0.225423\pi$
$593$	14.0265	+	8.09823i	0.576001	+	0.332554i	−0.183542	+	0.983012i	$0.558756\pi$
$594$	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
$597$	2.54876	+	8.56926i	0.104314	+	0.350717i
$598$	11.4020	+	8.83401i	0.466263	+	0.361250i
$599$	7.00327	+	12.1300i	0.286146	+	0.495619i	0.972886	−	0.231283i	$-0.0742925\pi$
$599$	7.00327	+	12.1300i	0.286146	+	0.495619i	−0.686741	+	0.726903i	$0.740959\pi$
$600$	−1.11455	−	0.131698i	−0.0455012	−	0.00537655i
$601$	−15.5923			−0.636024			−0.318012	−	0.948087i	$-0.603015\pi$
$601$	−15.5923			−0.636024			−0.318012	+	0.948087i	$0.603015\pi$
$602$	1.57212	+	43.5883i	0.0640749	+	1.77653i
$603$	−0.234452	−	4.29003i	−0.00954764	−	0.174704i
$604$	12.2679	−	3.16462i	0.499174	−	0.128766i
$605$	−8.94954	−	15.5011i	−0.363850	−	0.630207i
$606$	11.9647	−	1.85146i	0.486034	−	0.0752106i
$607$	28.3416	+	16.3630i	1.15035	+	0.664155i	0.948973	−	0.315359i	$-0.102125\pi$
$607$	28.3416	+	16.3630i	1.15035	+	0.664155i	0.201378	+	0.979514i	$0.435458\pi$
$608$	30.3269	−	11.7396i	1.22992	−	0.476105i
$609$	−32.2070	−	2.02778i	−1.30509	−	0.0821696i
$610$	−12.5655	+	5.13615i	−0.508761	+	0.207956i
$611$	6.09286	+	3.51771i	0.246491	+	0.142311i
$612$	−1.88644	−	0.415010i	−0.0762548	−	0.0167758i
$613$	−0.287887	+	0.166212i	−0.0116277	+	0.00671323i	−0.505803	−	0.862649i	$-0.668804\pi$
$613$	−0.287887	+	0.166212i	−0.0116277	+	0.00671323i	0.494175	+	0.869363i	$0.335470\pi$
$614$	10.0873	+	1.37599i	0.407091	+	0.0555306i
$615$	−8.97213	+	9.47585i	−0.361791	+	0.382103i
$616$	−3.56618	−	12.0159i	−0.143686	−	0.484136i
$617$		−	39.1386i		−	1.57566i	−0.615893	−	0.787830i	$-0.711205\pi$
$617$		−	39.1386i		−	1.57566i	0.615893	−	0.787830i	$-0.288795\pi$
$618$	−35.0097	+	28.1449i	−1.40830	+	1.13215i
$619$	1.61116	+	2.79062i	0.0647581	+	0.112164i	0.896587	−	0.442868i	$-0.146039\pi$
$619$	1.61116	+	2.79062i	0.0647581	+	0.112164i	−0.831829	+	0.555033i	$0.812706\pi$
$620$	10.4973	−	37.7614i	0.421580	−	1.51653i
$621$	−11.4412	−	31.9677i	−0.459119	−	1.28282i
$622$	−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
$626$	16.5875	−	21.4094i	0.662970	−	0.855691i
$627$	16.2209	+	3.87513i	0.647802	+	0.154758i
$628$	4.67937	−	1.20709i	0.186727	−	0.0481680i
$629$	0.351718			0.0140239
$630$	−14.1308	−	20.0363i	−0.562985	−	0.798267i
$631$			10.2850i			0.409441i	0.978820	+	0.204721i	$0.0656286\pi$
$631$			10.2850i			0.409441i	−0.978820	+	0.204721i	$0.934371\pi$
$632$	−7.00267	−	9.39585i	−0.278551	−	0.373747i
$633$	6.77563	−	28.3622i	0.269307	−	1.12730i
$634$	−3.17320	+	4.09563i	−0.126024	+	0.162658i
$635$	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
$639$	−17.0486	−	8.63874i	−0.674433	−	0.341743i
$640$	−24.5928	+	2.42271i	−0.972117	+	0.0957661i
$641$	26.2428	−	15.1513i	1.03653	−	0.598439i	0.117680	−	0.993052i	$-0.462454\pi$
$641$	26.2428	−	15.1513i	1.03653	−	0.598439i	0.918848	+	0.394612i	$0.129121\pi$
$642$	−8.44389	+	6.78818i	−0.333254	+	0.267908i
$643$	−37.4668			−1.47755			−0.738773	−	0.673955i	$-0.764594\pi$
$643$	−37.4668			−1.47755			−0.738773	+	0.673955i	$0.764594\pi$
$644$	−28.0783	−	20.1778i	−1.10644	−	0.795118i
$645$	32.0238	+	30.3214i	1.26093	+	1.19390i
$646$	0.353737	−	2.59322i	0.0139176	−	0.102029i
$647$	−0.130900	−	0.226726i	−0.00514622	−	0.00891351i	0.863441	−	0.504450i	$-0.168305\pi$
$647$	−0.130900	−	0.226726i	−0.00514622	−	0.00891351i	−0.868587	+	0.495537i	$0.834971\pi$
$648$	5.70606	+	24.8081i	0.224155	+	0.974553i
$649$	−5.19303	+	8.99459i	−0.203844	+	0.353069i
$650$	−0.468092	+	0.191333i	−0.0183601	+	0.00750469i
$651$	−36.8272	+	18.2791i	−1.44337	+	0.716413i
$652$	12.7343	−	12.4985i	0.498714	−	0.489480i
$653$	22.1548	−	38.3732i	0.866984	−	1.50166i	0.00192051	−	0.999998i	$-0.499389\pi$
$653$	22.1548	−	38.3732i	0.866984	−	1.50166i	0.865064	−	0.501662i	$-0.167278\pi$
$654$	−3.04930	−	19.7055i	−0.119237	−	0.770546i
$655$	32.3586	−	18.6822i	1.26435	−	0.729975i
$656$	7.12073	−	11.8178i	0.278018	−	0.461408i
$657$	1.47013	+	26.9006i	0.0573552	+	1.04949i
$658$	−14.9002	−	7.90068i	−0.580869	−	0.308001i
$659$			23.4513i			0.913534i	0.889586	+	0.456767i	$0.150993\pi$
$659$			23.4513i			0.913534i	−0.889586	+	0.456767i	$0.849007\pi$
$660$	−11.0873	−	6.13853i	−0.431572	−	0.238942i
$661$	−29.3695	+	16.9565i	−1.14234	+	0.659531i	−0.947009	−	0.321206i	$-0.895912\pi$
$661$	−29.3695	+	16.9565i	−1.14234	+	0.659531i	−0.195332	+	0.980737i	$0.562578\pi$
$662$	9.37808	−	12.1042i	0.364490	−	0.470445i
$663$	−0.834201	+	0.248117i	−0.0323977	+	0.00963605i
$664$	−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
$668$	−13.5103	−	3.75572i	−0.522729	−	0.145313i
$669$	−3.03523	−	0.725105i	−0.117349	−	0.0280342i
$670$	−4.38328	−	0.597916i	−0.169341	−	0.0230995i
$671$	7.36050			0.284149
$672$	19.1304	+	17.4936i	0.737972	+	0.674831i
$673$	−13.3855			−0.515973			−0.257986	−	0.966149i	$-0.583059\pi$
$673$	−13.3855			−0.515973			−0.257986	+	0.966149i	$0.583059\pi$
$674$	−28.0844	−	3.83095i	−1.08177	−	0.147563i
$675$	1.17117	+	0.213002i	0.0450783	+	0.00819845i
$676$	20.3556	+	5.65864i	0.782907	+	0.217640i
$677$	13.0777	−	22.6513i	0.502618	−	0.870559i	−0.497378	−	0.867534i	$-0.665704\pi$
$677$	13.0777	−	22.6513i	0.502618	−	0.870559i	0.999995	−	0.00302522i	$-0.000962959\pi$
$678$	−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
$681$	5.72886	+	19.2612i	0.219530	+	0.738090i
$682$	−13.0157	+	16.7993i	−0.498398	+	0.643280i
$683$	19.0543	−	11.0010i	0.729092	−	0.420942i	−0.0889978	−	0.996032i	$-0.528366\pi$
$683$	19.0543	−	11.0010i	0.729092	−	0.420942i	0.818090	+	0.575090i	$0.195033\pi$
$684$	−32.8792	+	10.4253i	−1.25717	+	0.398623i
$685$			45.2470i			1.72880i
$686$	9.69794	+	24.3300i	0.370269	+	0.928924i
$687$	−11.6978	+	12.3546i	−0.446299	+	0.471356i
$688$	−39.9385	−	24.0646i	−1.52264	−	0.917454i
$689$	−11.9731	+	6.91265i	−0.456137	+	0.263351i
$690$	−34.5493	+	5.34629i	−1.31527	+	0.203530i
$691$	17.0852	−	29.5924i	0.649952	−	1.12575i	−0.333182	−	0.942862i	$-0.608122\pi$
$691$	17.0852	−	29.5924i	0.649952	−	1.12575i	0.983134	−	0.182887i	$-0.0585442\pi$
$692$	20.3160	−	19.9398i	0.772297	−	0.757998i
$693$	2.98184	+	12.9556i	0.113271	+	0.492141i
$694$	−7.65072	+	3.12724i	−0.290417	+	0.118708i
$695$	−1.38978	+	2.40717i	−0.0527173	+	0.0913091i
$696$	20.6362	−	27.6463i	0.782213	−	1.04793i
$697$	−0.555213	−	0.961656i	−0.0210302	−	0.0364253i
$698$	−3.55840	+	26.0863i	−0.134687	+	0.987383i
$699$	−9.54531	+	10.0812i	−0.361037	+	0.381306i
$700$	1.10484	−	0.498807i	0.0417591	−	0.0188531i
$701$	−25.6168			−0.967533			−0.483767	−	0.875197i	$-0.660732\pi$
$701$	−25.6168			−0.967533			−0.483767	+	0.875197i	$0.660732\pi$
$702$	7.66362	+	8.53389i	0.289245	+	0.322091i
$703$	5.43931	−	3.14039i	0.205147	−	0.118442i
$704$	12.8405	+	3.82941i	0.483945	+	0.144326i
$705$	−16.3449	+	4.86146i	−0.615584	+	0.183093i
$706$	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	$-0.334912\pi$
$709$	−0.228674	−	0.132025i	−0.00858802	−	0.00495830i	−0.504288	+	0.863536i	$0.668245\pi$
$710$	−12.0528	+	15.5565i	−0.452334	+	0.583825i
$711$	6.79271	+	10.4088i	0.254746	+	0.390361i
$712$	−8.93069	−	11.9828i	−0.334692	−	0.449073i
$713$			58.6250i			2.19552i
$714$	1.97700	−	0.666474i	0.0739873	−	0.0249421i
$715$	−5.71028			−0.213552
$716$	−2.40644	+	0.620763i	−0.0899329	+	0.0231990i
$717$	−2.42456	+	10.1490i	−0.0905467	+	0.379021i
$718$	21.0097	−	27.1171i	0.784076	−	1.01200i
$719$	19.9630	−	34.5770i	0.744496	−	1.28950i	−0.205934	−	0.978566i	$-0.566023\pi$
$719$	19.9630	−	34.5770i	0.744496	−	1.28950i	0.950430	−	0.310939i	$-0.100643\pi$
$720$	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
$723$	−16.9974	+	5.05555i	−0.632141	+	0.188018i
$724$	11.2215	−	40.3667i	0.417044	−	1.50022i
$725$	−0.806627	−	1.39712i	−0.0299574	−	0.0518877i
$726$	−12.5766	−	15.6442i	−0.466763	−	0.580611i
$727$			4.46181i			0.165479i	0.996571	+	0.0827397i	$0.0263670\pi$
$727$			4.46181i			0.165479i	−0.996571	+	0.0827397i	$0.973633\pi$
$728$	11.3591	+	2.72073i	0.420995	+	0.100837i
$729$	−4.40255	−	26.6386i	−0.163057	−	0.986617i
$730$	27.4853	+	3.74922i	1.01728	+	0.138765i
$731$	−3.24993	+	1.87635i	−0.120203	+	0.0693992i
$732$	−13.0448	+	7.84702i	−0.482151	+	0.290034i
$733$	−3.91514	−	2.26041i	−0.144609	−	0.0834900i	0.425950	−	0.904747i	$-0.359940\pi$
$733$	−3.91514	−	2.26041i	−0.144609	−	0.0834900i	−0.570559	+	0.821257i	$0.693273\pi$
$734$	−9.89887	+	4.04617i	−0.365374	+	0.149347i
$735$	24.2362	+	10.6739i	0.893964	+	0.393714i
$736$	34.4712	−	13.3439i	1.27063	−	0.491863i
$737$	2.07736	+	1.19936i	0.0765205	+	0.0441791i
$738$	−8.31828	+	12.0402i	−0.306200	+	0.443208i
$739$	−0.571921	−	0.990596i	−0.0210384	−	0.0364397i	0.855315	−	0.518109i	$-0.173364\pi$
$739$	−0.571921	−	0.990596i	−0.0210384	−	0.0364397i	−0.876353	+	0.481670i	$0.840031\pi$
$740$	−4.62148	+	1.19215i	−0.169889	+	0.0438244i
$741$	−10.6855	+	11.2854i	−0.392543	+	0.414581i
$742$	28.0857	−	17.5947i	1.03106	−	0.645920i
$743$	−13.5335			−0.496495			−0.248248	−	0.968697i	$-0.579855\pi$
$743$	−13.5335			−0.496495			−0.248248	+	0.968697i	$0.579855\pi$
$744$	5.15770	−	43.6491i	0.189091	−	1.60025i
$745$	−5.39804	−	9.34968i	−0.197769	−	0.342546i
$746$	−21.8960	−	16.9645i	−0.801668	−	0.621113i
$747$	12.2915	−	24.2574i	0.449722	−	0.887531i
$748$	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	$-0.239899\pi$
$751$	13.7335	+	7.92906i	0.501144	+	0.289336i	−0.228042	+	0.973651i	$0.573232\pi$
$752$	15.7799	−	8.72149i	0.575433	−	0.318040i
$753$	−16.8074	−	4.01524i	−0.612497	−	0.146323i
$754$	2.10094	−	15.4019i	0.0765118	−	0.560903i
$755$			13.8366i			0.503566i
$756$	−19.0965	−	19.7819i	−0.694535	−	0.719459i
$757$		−	41.0141i		−	1.49068i	−0.666683	−	0.745341i	$-0.732287\pi$
$757$		−	41.0141i		−	1.49068i	0.666683	−	0.745341i	$-0.267713\pi$
$758$	7.00280	+	0.955241i	0.254353	+	0.0346959i
$759$	18.4376	+	4.40468i	0.669243	+	0.159880i
$760$	4.14175	+	35.2733i	0.150237	+	1.27950i
$761$	8.79472	+	5.07763i	0.318808	+	0.184064i	0.650861	−	0.759197i	$-0.274408\pi$
$761$	8.79472	+	5.07763i	0.318808	+	0.184064i	−0.332053	+	0.943261i	$0.607741\pi$
$762$	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
$765$	0.953481	−	1.88170i	0.0344732	−	0.0680331i
$766$	−26.2499	+	33.8806i	−0.948447	+	1.22416i
$767$	−4.83937	−	8.38203i	−0.174740	−	0.302658i
$768$	−26.8394	+	6.90249i	−0.968485	+	0.249072i
$769$	15.2996			0.551719			0.275859	−	0.961198i	$-0.411038\pi$
$769$	15.2996			0.551719			0.275859	+	0.961198i	$0.411038\pi$
$770$	13.6797	−	0.493393i	0.492982	−	0.0177806i
$771$	−23.5903	+	24.9148i	−0.849585	+	0.897283i
$772$	0.00662029	+	0.0256641i	0.000238269	+	0.000923671i
$773$	18.3453	+	31.7750i	0.659835	+	1.14287i	0.980658	+	0.195728i	$0.0627071\pi$
$773$	18.3453	+	31.7750i	0.659835	+	1.14287i	−0.320823	+	0.947139i	$0.603960\pi$
$774$	40.6902	+	28.1117i	1.46258	+	1.01046i
$775$	−1.77998	−	1.02767i	−0.0639388	−	0.0369151i
$776$	10.9922	+	4.73470i	0.394599	+	0.169966i
$777$	4.17004	+	2.77084i	0.149599	+	0.0994035i
$778$	−2.28010	−	5.57823i	−0.0817457	−	0.199989i
$779$	−17.1727	−	9.91466i	−0.615276	−	0.355230i
$780$	10.1202	−	6.08772i	0.362361	−	0.217975i
$781$	9.24099	−	5.33529i	0.330669	−	0.190912i
$782$	0.402077	−	2.94760i	0.0143783	−	0.105406i
$783$	−23.6709	+	27.9040i	−0.845927	+	0.997208i
$784$	−27.4472	−	5.53638i	−0.980257	−	0.197728i
$785$			5.27773i			0.188370i
$786$	32.6574	−	26.2538i	1.16485	−	0.936442i
$787$	14.6430	+	25.3624i	0.521965	+	0.904071i	0.999673	+	0.0255520i	$0.00813435\pi$
$787$	14.6430	+	25.3624i	0.521965	+	0.904071i	−0.477708	+	0.878519i	$0.658532\pi$
$788$	−12.4946	−	3.47338i	−0.445103	−	0.123734i
$789$	11.3483	−	3.37533i	0.404010	−	0.120165i
$790$	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
$794$	22.1255	+	17.1423i	0.785204	+	0.608358i
$795$	7.78630	−	32.5928i	0.276152	−	1.15595i
$796$	9.99610	−	2.57859i	0.354303	−	0.0913956i
$797$	−18.4577			−0.653805			−0.326903	−	0.945058i	$-0.606005\pi$
$797$	−18.4577			−0.653805			−0.326903	+	0.945058i	$0.606005\pi$
$798$	24.6235	−	27.9590i	0.871661	−	0.989738i
$799$		−	1.45105i		−	0.0513345i
$800$	−0.199116	+	1.28053i	−0.00703982	+	0.0452737i
$801$	8.66291	+	13.2746i	0.306089	+	0.469036i
$802$	2.56593	+	1.98802i	0.0906062	+	0.0701995i
$803$	−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
$807$	−40.1171	+	11.9320i	−1.41219	+	0.420028i
$808$	−1.63033	−	13.8847i	−0.0573548	−	0.488463i
$809$	−12.9060	+	7.45126i	−0.453750	+	0.261972i	−0.709412	−	0.704794i	$-0.751040\pi$
$809$	−12.9060	+	7.45126i	−0.453750	+	0.261972i	0.255663	+	0.966766i	$0.417706\pi$
$810$	−27.7912	−	0.733280i	−0.976483	−	0.0257648i
$811$	29.7496			1.04465			0.522325	−	0.852747i	$-0.325065\pi$
$811$	29.7496			1.04465			0.522325	+	0.852747i	$0.325065\pi$
$812$	−3.70229	+	37.0787i	−0.129925	+	1.30121i
$813$	21.0161	−	22.1960i	0.737067	−	0.778448i
$814$	2.56416	+	0.349773i	0.0898739	+	0.0122596i
$815$	9.74341	+	16.8761i	0.341297	+	0.591143i
$816$	−0.558690	+	2.15926i	−0.0195580	+	0.0755891i
$817$	−33.5067	+	58.0353i	−1.17225	+	2.03040i
$818$	−0.803294	−	1.96524i	−0.0280865	−	0.0687131i
$819$	−11.8451	−	3.63014i	−0.413902	−	0.126847i
$820$	10.5549	+	10.7540i	0.368593	+	0.375546i
$821$	−7.25813	+	12.5715i	−0.253311	+	0.438747i	−0.964435	−	0.264319i	$-0.914853\pi$
$821$	−7.25813	+	12.5715i	−0.253311	+	0.438747i	0.711125	+	0.703066i	$0.248186\pi$
$822$	7.75959	+	50.1448i	0.270647	+	1.74900i
$823$	−42.5817	+	24.5846i	−1.48431	+	0.856965i	−0.999841	−	0.0178459i	$-0.994319\pi$
$823$	−42.5817	+	24.5846i	−1.48431	+	0.856965i	−0.484465	+	0.874810i	$0.660986\pi$
$824$	30.9962	+	41.5892i	1.07980	+	1.44883i
$825$	−0.456939	+	0.482593i	−0.0159086	+	0.0168017i
$826$	12.3176	+	19.6621i	0.428583	+	0.684132i
$827$		−	0.00653186i		−	0.000227135i	−1.00000		0.000113567i	$-0.999964\pi$
$827$		−	0.00653186i		−	0.000227135i	1.00000		0.000113567i	$-3.61496e-5\pi$
$828$	−37.3724	+	11.8500i	−1.29878	+	0.411816i
$829$	7.61159	−	4.39455i	0.264361	−	0.152629i	−0.361961	−	0.932193i	$-0.617893\pi$
$829$	7.61159	−	4.39455i	0.264361	−	0.152629i	0.626322	+	0.779564i	$0.284559\pi$
$830$	−22.1343	−	17.1491i	−0.768293	−	0.595256i
$831$	7.36950	+	24.7772i	0.255645	+	0.859513i
$832$	−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
$836$	5.15777	−	18.5538i	0.178385	−	0.641698i
$837$	−8.34182	+	45.8666i	−0.288336	+	1.58538i
$838$	−1.61421	+	11.8336i	−0.0557619	+	0.408787i
$839$	35.4452			1.22371			0.611853	−	0.790972i	$-0.290425\pi$
$839$	35.4452			1.22371			0.611853	+	0.790972i	$0.290425\pi$
$840$	−23.7182	+	15.4583i	−0.818355	+	0.533364i
$841$	20.5905			0.710017
$842$	2.66308	−	19.5228i	0.0917757	−	0.672801i
$843$	−23.3980	−	5.58970i	−0.805870	−	0.192519i
$844$	−32.4412	−	9.01832i	−1.11667	−	0.310423i
$845$	−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
$849$	−9.59132	+	2.85275i	−0.329173	+	0.0979061i
$850$	0.0824472	+	0.0638781i	0.00282791	+	0.00219100i
$851$	6.18262	−	3.56954i	0.211937	−	0.122362i
$852$	−10.6896	+	19.3074i	−0.366221	+	0.661461i
$853$		−	23.8784i		−	0.817581i	−0.912628	−	0.408791i	$-0.865951\pi$
$853$		−	23.8784i		−	0.817581i	0.912628	−	0.408791i	$-0.134049\pi$
$854$	7.70282	−	14.5270i	0.263585	−	0.497104i
$855$	−2.05562	−	37.6138i	−0.0703006	−	1.28637i
$856$	7.47587	+	10.0308i	0.255520	+	0.342844i
$857$	−46.6784	+	26.9498i	−1.59451	+	0.920588i	−0.601985	+	0.798507i	$0.705623\pi$
$857$	−46.6784	+	26.9498i	−1.59451	+	0.920588i	−0.992520	+	0.122081i	$0.961043\pi$
$858$	−6.32840	+	0.979279i	−0.216048	+	0.0334320i
$859$	9.18799	−	15.9141i	0.313490	−	0.542981i	−0.665625	−	0.746286i	$-0.731835\pi$
$859$	9.18799	−	15.9141i	0.313490	−	0.542981i	0.979115	+	0.203305i	$0.0651684\pi$
$860$	36.3433	−	35.6704i	1.23930	−	1.21635i
$861$	0.993242	−	15.7756i	0.0338496	−	0.537630i
$862$	−18.1654	−	44.4414i	−0.618717	−	1.51368i
$863$	24.6737	−	42.7360i	0.839901	−	1.45475i	−0.0500753	−	0.998745i	$-0.515946\pi$
$863$	24.6737	−	42.7360i	0.839901	−	1.45475i	0.889977	−	0.456006i	$-0.150721\pi$
$864$	28.8680	−	5.53496i	0.982111	−	0.188303i
$865$	15.5444	+	26.9236i	0.528524	+	0.915431i
$866$	6.22620	+	0.849306i	0.211575	+	0.0288606i
$867$	−21.2509	−	20.1212i	−0.721717	−	0.683352i
$868$	19.5349	+	43.2691i	0.663056	+	1.46865i
$869$	−6.93929			−0.235399
$870$	23.6067	+	29.3645i	0.800340	+	0.995551i
$871$	−1.93589	+	1.11768i	−0.0655950	+	0.0378713i
$872$	−22.8677	+	2.68510i	−0.774397	+	0.0909289i
$873$	−11.3238	−	5.73792i	−0.383253	−	0.194199i
$874$	−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	0.889500	+	0.456935i	$0.151053\pi$
$877$	51.2316	+	29.5786i	1.72997	+	0.998797i	0.840467	+	0.541863i	$0.182281\pi$
$878$	−9.75494	−	7.55790i	−0.329213	−	0.255067i
$879$	−6.29364	+	26.3446i	−0.212279	+	0.888583i
$880$	−7.55241	+	12.5342i	−0.254592	+	0.422529i
$881$		−	51.0955i		−	1.72145i	−0.509068	−	0.860726i	$-0.670010\pi$
$881$		−	51.0955i		−	1.72145i	0.509068	−	0.860726i	$-0.329990\pi$
$882$	28.6902	+	7.67299i	0.966048	+	0.258363i
$883$	10.4148			0.350486			0.175243	−	0.984525i	$-0.443929\pi$
$883$	10.4148			0.350486			0.175243	+	0.984525i	$0.443929\pi$
$884$	0.251020	+	0.973101i	0.00844273	+	0.0327289i
$885$	22.8174	+	5.45099i	0.766997	+	0.183233i
$886$	−41.3238	−	32.0167i	−1.38830	−	1.07562i
$887$	−12.2631	+	21.2404i	−0.411756	+	0.713183i	−0.995082	−	0.0990557i	$-0.968418\pi$
$887$	−12.2631	+	21.2404i	−0.411756	+	0.713183i	0.583326	+	0.812238i	$0.301751\pi$
$888$	−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
$891$	13.7983	+	6.06961i	0.462262	+	0.203340i
$892$	−0.965110	+	3.47175i	−0.0323143	+	0.116243i
$893$	−12.9560	−	22.4405i	−0.433556	−	0.750942i
$894$	−7.58578	−	9.43602i	−0.253706	−	0.315588i
$895$		−	2.71416i		−	0.0907242i
$896$	20.9956	−	21.3351i	0.701413	−	0.712755i
$897$	−12.1458	+	12.8277i	−0.405535	+	0.428303i
$898$	−4.47783	+	32.8267i	−0.149427	+	1.09544i
$899$	54.7155	−	31.5900i	1.82487	−	1.05359i
$900$	0.295330	−	1.34243i	0.00984433	−	0.0447477i
$901$	2.46944	+	1.42573i	0.0822688	+	0.0474979i
$902$	−3.09138	−	7.56300i	−0.102932	−	0.251820i
$903$	−53.3137	−	3.35667i	−1.77417	−	0.111703i
$904$	−14.9933	+	34.8090i	−0.498671	+	1.15773i
$905$	39.6267	+	22.8785i	1.31724	+	0.760507i
$906$	2.37290	+	15.3344i	0.0788342	+	0.509451i
$907$	14.6718	+	25.4124i	0.487170	+	0.843803i	0.999891	−	0.0147518i	$-0.00469582\pi$
$907$	14.6718	+	25.4124i	0.487170	+	0.843803i	−0.512721	+	0.858555i	$0.671362\pi$
$908$	22.4683	−	5.79591i	0.745637	−	0.192344i
$909$	0.809158	+	14.8060i	0.0268381	+	0.491086i
$910$	−5.97585	+	11.2701i	−0.198097	+	0.373599i
$911$	−21.9953			−0.728738			−0.364369	−	0.931255i	$-0.618715\pi$
$911$	−21.9953			−0.728738			−0.364369	+	0.931255i	$0.618715\pi$
$912$	10.6392	+	38.3812i	0.352300	+	1.27093i
$913$	7.59124	+	13.1484i	0.251233	+	0.435149i
$914$	1.14570	−	1.47875i	0.0378965	−	0.0489128i
$915$	−4.73971	−	15.9356i	−0.156690	−	0.526813i
$916$	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	$-0.549241\pi$
$919$	−32.9464	−	19.0216i	−1.08680	−	0.627464i	−0.932723	+	0.360594i	$0.882574\pi$
$920$	4.70774	+	40.0935i	0.155210	+	1.32184i
$921$	−2.89722	+	12.1275i	−0.0954668	+	0.399616i
$922$	32.9936	+	4.50060i	1.08659	+	0.148220i
$923$			9.94388i			0.327307i
$924$	15.0759	−	2.89279i	0.495960	−	0.0951658i
$925$			0.250290i			0.00822948i
$926$	−2.76201	+	20.2481i	−0.0907654	+	0.665395i
$927$	−30.0668	−	46.0729i	−0.987523	−	1.51323i
$928$	−31.0289	−	24.9821i	−1.01857	−	0.820078i
$929$	−26.6079	−	15.3621i	−0.872978	−	0.504014i	−0.00464125	−	0.999989i	$-0.501477\pi$
$929$	−26.6079	−	15.3621i	−0.872978	−	0.504014i	−0.868337	+	0.495975i	$0.834811\pi$
$930$	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
$933$	14.4465	−	4.29682i	0.472957	−	0.140672i
$934$	−16.7923	−	13.0103i	−0.549460	−	0.425709i
$935$	0.588871	+	1.01995i	0.0192581	+	0.0333561i
$936$	10.1717	−	8.48225i	0.332471	−	0.277251i
$937$	37.2804			1.21790			0.608949	−	0.793210i	$-0.291592\pi$
$937$	37.2804			1.21790			0.608949	+	0.793210i	$0.291592\pi$
$938$	4.54109	−	2.84482i	0.148272	−	0.0928868i
$939$	24.0863	+	22.8059i	0.786027	+	0.744243i
$940$	4.91836	+	19.0664i	0.160419	+	0.621878i
$941$	−16.0848	−	27.8596i	−0.524348	−	0.908198i	−0.999598	−	0.0283471i	$-0.990976\pi$
$941$	−16.0848	−	27.8596i	−0.524348	−	0.908198i	0.475250	−	0.879851i	$-0.342358\pi$
$942$	0.905099	+	5.84903i	0.0294897	+	0.190572i
$943$	−19.5194	−	11.2695i	−0.635640	−	0.366987i
$944$	−24.7994	−	0.463499i	−0.807151	−	0.0150856i
$945$	26.1288	−	14.7983i	0.849969	−	0.481389i
$946$	−25.5592	+	10.4474i	−0.831003	+	0.339673i
$947$	−33.3248	−	19.2401i	−1.08291	−	0.625219i	−0.151231	−	0.988498i	$-0.548324\pi$
$947$	−33.3248	−	19.2401i	−1.08291	−	0.625219i	−0.931680	+	0.363279i	$0.881657\pi$
$948$	12.2983	−	7.39797i	0.399431	−	0.240275i
$949$	12.1389	−	7.00842i	0.394046	−	0.227503i
$950$	1.84539	+	0.251727i	0.0598724	+	0.00816710i
$951$	−4.60773	−	4.36279i	−0.149416	−	0.141473i
$952$	−0.685432	−	2.30950i	−0.0222150	−	0.0748513i
$953$		−	37.1213i		−	1.20248i	−0.799070	−	0.601238i	$-0.794674\pi$
$953$		−	37.1213i		−	1.20248i	0.799070	−	0.601238i	$-0.205326\pi$
$954$	3.03967	−	37.4561i	0.0984131	−	1.21269i
$955$	−26.6737	−	46.2002i	−0.863140	−	1.49500i
$956$	11.6086	+	3.22707i	0.375449	+	0.104371i
$957$	−5.82414	−	19.5815i	−0.188268	−	0.632981i
$958$	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
$962$	−1.47705	+	1.90642i	−0.0476221	+	0.0614656i
$963$	−7.25172	−	11.1122i	−0.233683	−	0.358085i
$964$	5.11471	+	19.8276i	0.164734	+	0.638604i
$965$	−0.0289458			−0.000931799
$966$	27.9884	−	31.7798i	0.900511	−	1.02250i
$967$		−	28.7342i		−	0.924030i	−0.886872	−	0.462015i	$-0.847127\pi$
$967$		−	28.7342i		−	0.924030i	0.886872	−	0.462015i	$-0.152873\pi$
$968$	−18.5842	+	13.8507i	−0.597320	+	0.445179i
$969$	3.11772	+	0.744812i	0.100156	+	0.0239268i
$970$	−8.00556	+	10.3327i	−0.257043	+	0.331764i
$971$	17.2557	+	9.96261i	0.553763	+	0.319715i	0.750638	−	0.660713i	$-0.229746\pi$
$971$	17.2557	+	9.96261i	0.553763	+	0.319715i	−0.196875	+	0.980429i	$0.563079\pi$
$972$	−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
$975$	−0.176565	−	0.593635i	−0.00565460	−	0.0190115i
$976$	8.50307	+	15.3847i	0.272177	+	0.492452i
$977$	11.6105	−	6.70332i	0.371453	−	0.214458i	−0.302640	−	0.953105i	$-0.597868\pi$
$977$	11.6105	−	6.70332i	0.371453	−	0.214458i	0.674093	+	0.738647i	$0.264535\pi$
$978$	13.6922	+	17.0319i	0.437830	+	0.544621i
$979$	−8.84986			−0.282843
$980$	13.3421	−	27.5152i	0.426199	−	0.878941i
$981$	24.3851	−	1.33266i	0.778555	−	0.0425484i
$982$	6.18387	−	45.3335i	0.197335	−	1.44665i
$983$	10.2774	+	17.8010i	0.327799	+	0.567765i	0.982075	−	0.188491i	$-0.0603597\pi$
$983$	10.2774	+	17.8010i	0.327799	+	0.567765i	−0.654276	+	0.756256i	$0.727026\pi$
$984$	13.5417	+	10.1080i	0.431693	+	0.322231i
$985$	7.08155	−	12.2656i	0.225637	−	0.390814i
$986$	−2.96770	+	1.21305i	−0.0945107	+	0.0386313i
$987$	11.4314	−	17.2040i	0.363866	−	0.547608i
$988$	12.5706	+	12.8077i	0.399923	+	0.407467i
$989$	−38.0856	+	65.9661i	−1.21105	+	2.09760i
$990$	8.82255	−	12.7702i	0.280399	−	0.405862i
$991$	−4.87181	+	2.81274i	−0.154758	+	0.0893497i	−0.575379	−	0.817887i	$-0.695146\pi$
$991$	−4.87181	+	2.81274i	−0.154758	+	0.0893497i	0.420621	+	0.907236i	$0.361812\pi$
$992$	−50.1497	−	7.79801i	−1.59225	−	0.247587i
$993$	13.6177	+	12.8938i	0.432144	+	0.409172i
$994$	−0.859194	−	23.8218i	−0.0272520	−	0.755583i
$995$			11.2743i			0.357420i
$996$	−27.4713	−	15.2096i	−0.870460	−	0.481934i
$997$	−2.03245	+	1.17343i	−0.0643683	+	0.0371631i	−0.531839	−	0.846846i	$-0.678499\pi$
$997$	−2.03245	+	1.17343i	−0.0643683	+	0.0371631i	0.467470	+	0.884009i	$0.345165\pi$
$998$	−12.3058	+	15.8830i	−0.389533	+	0.502768i
$999$	5.34502	−	1.91297i	0.169109	−	0.0605238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.v.a.107.27	yes	56
3.2	odd	2	inner	168.2.v.a.107.2	yes	56
4.3	odd	2		672.2.bd.a.527.17		56
7.4	even	3	inner	168.2.v.a.11.9	yes	56
8.3	odd	2	inner	168.2.v.a.107.20	yes	56
8.5	even	2		672.2.bd.a.527.18		56
12.11	even	2		672.2.bd.a.527.4		56
21.11	odd	6	inner	168.2.v.a.11.20	yes	56
24.5	odd	2		672.2.bd.a.527.3		56
24.11	even	2	inner	168.2.v.a.107.9	yes	56
28.11	odd	6		672.2.bd.a.431.3		56
56.11	odd	6	inner	168.2.v.a.11.2	✓	56
56.53	even	6		672.2.bd.a.431.4		56
84.11	even	6		672.2.bd.a.431.18		56
168.11	even	6	inner	168.2.v.a.11.27	yes	56
168.53	odd	6		672.2.bd.a.431.17		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.2	✓	56	56.11	odd	6	inner
168.2.v.a.11.9	yes	56	7.4	even	3	inner
168.2.v.a.11.20	yes	56	21.11	odd	6	inner
168.2.v.a.11.27	yes	56	168.11	even	6	inner
168.2.v.a.107.2	yes	56	3.2	odd	2	inner
168.2.v.a.107.9	yes	56	24.11	even	2	inner
168.2.v.a.107.20	yes	56	8.3	odd	2	inner
168.2.v.a.107.27	yes	56	1.1	even	1	trivial
672.2.bd.a.431.3		56	28.11	odd	6
672.2.bd.a.431.4		56	56.53	even	6
672.2.bd.a.431.17		56	168.53	odd	6
672.2.bd.a.431.18		56	84.11	even	6
672.2.bd.a.527.3		56	24.5	odd	2
672.2.bd.a.527.4		56	12.11	even	2
672.2.bd.a.527.17		56	4.3	odd	2
672.2.bd.a.527.18		56	8.5	even	2

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+(1.40124 + 0.191140i) q^{2} +(-0.402456 + 1.68465i) q^{3} +(1.92693 + 0.535666i) 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} +(-2.67606 - 1.35599i) q^{9} +(-1.89188 + 2.44184i) q^{10} +(1.45052 - 0.837460i) q^{11} +(-1.67791 + 3.03061i) q^{12} +1.56085i q^{13} +(-0.134864 - 3.73923i) q^{14} +(-2.74716 - 2.60112i) q^{15} +(3.42612 + 2.06438i) q^{16} +(0.278795 - 0.160963i) q^{17} +(-3.49061 - 2.41157i) q^{18} +(2.87437 - 4.97856i) q^{19} +(-3.11771 + 3.05999i) q^{20} +(4.57352 + 0.287952i) q^{21} +(2.19260 - 0.896227i) q^{22} +(3.26717 - 5.65891i) q^{23} +(-2.93043 + 3.92589i) q^{24} +(0.114544 + 0.198397i) q^{25} +(-0.298342 + 2.18713i) q^{26} +(3.36136 - 3.96248i) q^{27} +(0.525740 - 5.26532i) q^{28} -7.04205 q^{29} +(-3.35224 - 4.16989i) q^{30} +(-7.76983 + 4.48591i) q^{31} +(4.40622 + 3.54756i) q^{32} +(0.827052 + 2.78066i) 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} +(4.97929 - 6.42674i) q^{38} +(-2.62949 - 0.628175i) q^{39} +(-4.95354 + 3.69185i) q^{40} -3.44933i q^{41} +(6.35355 + 1.27767i) q^{42} -11.6570 q^{43} +(3.24366 - 0.836731i) q^{44} +(5.48758 - 3.58115i) q^{45} +(5.65973 - 7.30498i) 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} +(0.158962 + 0.534452i) q^{51} +(-0.836097 + 3.00766i) q^{52} +(4.42876 + 7.67084i) q^{53} +(5.46745 - 4.90989i) q^{54} +3.65843i q^{55} +(1.74310 - 7.27747i) q^{56} +(7.23030 + 6.84595i) q^{57} +(-9.86758 - 1.34602i) q^{58} +(-5.37016 + 3.10046i) q^{59} +(-3.90025 - 6.48375i) q^{60} +(3.80578 + 2.19727i) q^{61} +(-11.7448 + 4.80070i) q^{62} +(-2.32574 + 7.58887i) q^{63} +(5.49608 + 5.81318i) q^{64} +(-2.95253 - 1.70464i) q^{65} +(0.627399 + 4.05445i) q^{66} +(0.716072 + 1.24027i) q^{67} +(0.623442 - 0.160822i) q^{68} +(8.21836 + 7.78149i) q^{69} +(7.22044 + 3.82858i) q^{70} +6.37080 q^{71} +(-5.43436 - 6.51672i) q^{72} +(-4.49012 - 7.77711i) q^{73} +(1.22140 + 0.946310i) q^{74} +(-0.380327 + 0.113121i) 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} +(-7.64675 + 4.22633i) q^{80} +(5.32258 + 7.25742i) q^{81} +(0.659306 - 4.83333i) q^{82} +9.06459i q^{83} +(8.65861 + 3.00474i) q^{84} +0.703162i q^{85} +(-16.3343 - 2.22813i) q^{86} +(2.83411 - 11.8634i) q^{87} +(4.70507 - 0.552465i) 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} +(-4.43016 - 14.8948i) q^{93} +(3.90411 - 5.03901i) q^{94} +(6.27833 + 10.8744i) q^{95} +(-7.74969 + 5.99519i) q^{96} +4.23153 q^{97} +(-9.68678 + 2.04113i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more