LMFDB - Embedded newform 616.2.bp.c.251.66

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(27,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 5, 4]))

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

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

chi := DirichletCharacter("616.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bp (of order $10$, degree $4$, 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:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$88$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			251.66
Character	$\chi$	$=$	616.251
Dual form			616.2.bp.c.27.66

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.929869 + 1.06552i) q^{2} +(0.891388 + 1.22689i) q^{3} +(-0.270686 + 1.98160i) q^{4} +(-0.0834388 - 0.256798i) q^{5} +(-0.478407 + 2.09064i) q^{6} +(2.48735 + 0.901708i) q^{7} +(-2.36314 + 1.55420i) q^{8} +(0.216364 - 0.665900i) q^{9} +(0.196038 - 0.327695i) q^{10} +(-3.27175 - 0.543723i) q^{11} +(-2.67249 + 1.43427i) q^{12} +(-2.13341 + 6.56597i) q^{13} +(1.35212 + 3.48881i) q^{14} +(0.240687 - 0.331277i) q^{15} +(-3.85346 - 1.07278i) q^{16} +(3.21212 - 1.04368i) q^{17} +(0.910724 - 0.388659i) q^{18} +(0.0370236 + 0.0509587i) q^{19} +(0.531457 - 0.0958306i) q^{20} +(1.11090 + 3.85548i) q^{21} +(-2.46295 - 3.99172i) q^{22} +3.24436i q^{23} +(-4.01332 - 1.51392i) q^{24} +(3.98610 - 2.89607i) q^{25} +(-8.98000 + 3.83229i) q^{26} +(5.33674 - 1.73401i) q^{27} +(-2.46011 + 4.68485i) q^{28} +(2.31211 - 3.18235i) q^{29} +(0.576791 - 0.0515866i) q^{30} +(-0.974373 + 2.99881i) q^{31} +(-2.44014 - 5.10350i) q^{32} +(-2.24931 - 4.49875i) q^{33} +(4.09892 + 2.45211i) q^{34} +(0.0240153 - 0.713985i) q^{35} +(1.26098 + 0.608996i) q^{36} +(4.81529 - 6.62767i) q^{37} +(-0.0198706 + 0.0868345i) q^{38} +(-9.95742 + 3.23536i) q^{39} +(0.596295 + 0.477170i) q^{40} +(-2.44596 - 3.36658i) q^{41} +(-3.07512 + 4.76878i) q^{42} -7.11479 q^{43} +(1.96306 - 6.33612i) q^{44} -0.189055 q^{45} +(-3.45694 + 3.01683i) q^{46} +(0.494132 - 0.359008i) q^{47} +(-2.11874 - 5.68403i) q^{48} +(5.37385 + 4.48573i) q^{49} +(6.79239 + 1.55432i) q^{50} +(4.14373 + 3.01060i) q^{51} +(-12.4336 - 6.00488i) q^{52} +(-11.7326 - 3.81214i) q^{53} +(6.81010 + 4.07402i) q^{54} +(0.133364 + 0.885548i) q^{55} +(-7.27941 + 1.73499i) q^{56} +(-0.0295182 + 0.0908478i) q^{57} +(5.54083 - 0.495556i) q^{58} +(0.709701 - 0.976819i) q^{59} +(0.591307 + 0.566617i) q^{60} +(2.29148 + 7.05244i) q^{61} +(-4.10135 + 1.75029i) q^{62} +(1.13862 - 1.46123i) q^{63} +(3.16889 - 7.34562i) q^{64} +1.86414 q^{65} +(2.70196 - 6.57995i) q^{66} +7.60314 q^{67} +(1.19868 + 6.64765i) q^{68} +(-3.98047 + 2.89198i) q^{69} +(0.783100 - 0.638324i) q^{70} +(7.10243 - 2.30772i) q^{71} +(0.523646 + 1.90989i) q^{72} +(7.13145 - 9.81560i) q^{73} +(11.5395 - 1.03206i) q^{74} +(7.10632 + 2.30898i) q^{75} +(-0.111001 + 0.0595722i) q^{76} +(-7.64772 - 4.30260i) q^{77} +(-12.7065 - 7.60141i) q^{78} +(9.50920 + 3.08973i) q^{79} +(0.0460400 + 1.07907i) q^{80} +(5.18520 + 3.76727i) q^{81} +(1.31275 - 5.73672i) q^{82} +(7.87395 - 2.55840i) q^{83} +(-7.94071 + 1.15773i) q^{84} +(-0.536032 - 0.737784i) q^{85} +(-6.61582 - 7.58098i) q^{86} +5.96537 q^{87} +(8.57668 - 3.80008i) q^{88} -6.36308i q^{89} +(-0.175797 - 0.201443i) q^{90} +(-11.2271 + 14.4082i) q^{91} +(-6.42901 - 0.878201i) q^{92} +(-4.54776 + 1.47766i) q^{93} +(0.842010 + 0.192679i) q^{94} +(0.00999689 - 0.0137595i) q^{95} +(4.08632 - 7.54298i) q^{96} +(-13.5188 - 4.39251i) q^{97} +(0.217319 + 9.89711i) q^{98} +(-1.06996 + 2.06102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 2 q^{2} - 10 q^{4} - 14 q^{8} + 84 q^{9} - 28 q^{11} - 32 q^{14} + 14 q^{16} - 4 q^{18} - 62 q^{22} - 108 q^{25} - 44 q^{28} + 24 q^{30} - 112 q^{32} + 14 q^{35} + 20 q^{36} - 2 q^{42} + 8 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) $ 352 * q - 2 * q^2 - 10 * q^4 - 14 * q^8 + 84 * q^9 - 28 * q^11 - 32 * q^14 + 14 * q^16 - 4 * q^18 - 62 * q^22 - 108 * q^25 - 44 * q^28 + 24 * q^30 - 112 * q^32 + 14 * q^35 + 20 * q^36 - 2 * q^42 + 8 * q^43 + 22 * q^44 - 38 * q^46 - 34 * q^49 - 24 * q^50 - 36 * q^51 - 120 * q^56 - 36 * q^57 + 30 * q^58 - 136 * q^60 + 86 * q^64 + 8 * q^65 + 24 * q^67 + 52 * q^70 + 30 * q^72 + 94 * q^74 - 68 * q^78 - 60 * q^81 - 128 * q^84 + 34 * q^86 - 38 * q^88 + 78 * q^91 - 8 * q^92 - 100 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$-1$	$-1$

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 $

$2$	0.929869	+	1.06552i	0.657517	+	0.753440i
$2$	0.929869	+	1.06552i	0.657517	+	0.753440i
$3$	0.891388	+	1.22689i	0.514643	+	0.708345i	0.984694	−	0.174294i	$-0.0557644\pi$
$3$	0.891388	+	1.22689i	0.514643	+	0.708345i	−0.470051	+	0.882639i	$0.655764\pi$
$4$	−0.270686	+	1.98160i	−0.135343	+	0.990799i
$5$	−0.0834388	−	0.256798i	−0.0373150	−	0.114844i	0.930664	−	0.365875i	$-0.119230\pi$
$5$	−0.0834388	−	0.256798i	−0.0373150	−	0.114844i	−0.967979	+	0.251031i	$0.919230\pi$
$6$	−0.478407	+	2.09064i	−0.195309	+	0.853501i
$7$	2.48735	+	0.901708i	0.940131	+	0.340814i
$7$	2.48735	+	0.901708i	0.940131	+	0.340814i
$8$	−2.36314	+	1.55420i	−0.835497	+	0.549494i
$9$	0.216364	−	0.665900i	0.0721214	−	0.221967i
$10$	0.196038	−	0.327695i	0.0619926	−	0.103626i
$11$	−3.27175	−	0.543723i	−0.986471	−	0.163939i
$11$	−3.27175	−	0.543723i	−0.986471	−	0.163939i
$12$	−2.67249	+	1.43427i	−0.771481	+	0.414038i
$13$	−2.13341	+	6.56597i	−0.591702	+	1.82107i	−0.0212008	+	0.999775i	$0.506749\pi$
$13$	−2.13341	+	6.56597i	−0.591702	+	1.82107i	−0.570501	+	0.821297i	$0.693251\pi$
$14$	1.35212	+	3.48881i	0.361370	+	0.932423i
$15$	0.240687	−	0.331277i	0.0621451	−	0.0855354i
$16$	−3.85346	−	1.07278i	−0.963365	−	0.268195i
$17$	3.21212	−	1.04368i	0.779054	−	0.253130i	0.107618	−	0.994192i	$-0.465678\pi$
$17$	3.21212	−	1.04368i	0.779054	−	0.253130i	0.671436	+	0.741062i	$0.265678\pi$
$18$	0.910724	−	0.388659i	0.214660	−	0.0916078i
$19$	0.0370236	+	0.0509587i	0.00849380	+	0.0116907i	0.813243	−	0.581925i	$-0.197700\pi$
$19$	0.0370236	+	0.0509587i	0.00849380	+	0.0116907i	−0.804749	+	0.593615i	$0.797700\pi$
$20$	0.531457	−	0.0958306i	0.118837	−	0.0214284i
$21$	1.11090	+	3.85548i	0.242418	+	0.841335i
$22$	−2.46295	−	3.99172i	−0.525103	−	0.851039i
$23$			3.24436i			0.676496i	0.941057	+	0.338248i	$0.109834\pi$
$23$			3.24436i			0.676496i	−0.941057	+	0.338248i	$0.890166\pi$
$24$	−4.01332	−	1.51392i	−0.819215	−	0.309027i
$25$	3.98610	−	2.89607i	0.797220	−	0.579214i
$26$	−8.98000	+	3.83229i	−1.76112	+	0.751574i
$27$	5.33674	−	1.73401i	1.02706	−	0.333711i
$28$	−2.46011	+	4.68485i	−0.464918	+	0.885354i
$29$	2.31211	−	3.18235i	0.429348	−	0.590947i	−0.538455	−	0.842654i	$-0.680992\pi$
$29$	2.31211	−	3.18235i	0.429348	−	0.590947i	0.967803	+	0.251707i	$0.0809920\pi$
$30$	0.576791	−	0.0515866i	0.105307	−	0.00941839i
$31$	−0.974373	+	2.99881i	−0.175003	+	0.538603i	−0.999634	−	0.0270684i	$-0.991383\pi$
$31$	−0.974373	+	2.99881i	−0.175003	+	0.538603i	0.824631	+	0.565671i	$0.191383\pi$
$32$	−2.44014	−	5.10350i	−0.431360	−	0.902180i
$33$	−2.24931	−	4.49875i	−0.391555	−	0.783132i
$34$	4.09892	+	2.45211i	0.702960	+	0.420533i
$35$	0.0240153	−	0.713985i	0.00405932	−	0.120686i
$36$	1.26098	+	0.608996i	0.210163	+	0.101499i
$37$	4.81529	−	6.62767i	0.791628	−	1.08958i	−0.202275	−	0.979329i	$-0.564834\pi$
$37$	4.81529	−	6.62767i	0.791628	−	1.08958i	0.993903	−	0.110254i	$-0.0351664\pi$
$38$	−0.0198706	+	0.0868345i	−0.00322343	+	0.0140864i
$39$	−9.95742	+	3.23536i	−1.59446	+	0.518072i
$40$	0.596295	+	0.477170i	0.0942825	+	0.0754472i
$41$	−2.44596	−	3.36658i	−0.381995	−	0.525772i	0.574116	−	0.818774i	$-0.305346\pi$
$41$	−2.44596	−	3.36658i	−0.381995	−	0.525772i	−0.956112	+	0.293002i	$0.905346\pi$
$42$	−3.07512	+	4.76878i	−0.474501	+	0.735839i
$43$	−7.11479			−1.08500			−0.542498	−	0.840057i	$-0.682521\pi$
$43$	−7.11479			−1.08500			−0.542498	+	0.840057i	$0.682521\pi$
$44$	1.96306	−	6.33612i	0.295942	−	0.955206i
$45$	−0.189055			−0.0281827
$46$	−3.45694	+	3.01683i	−0.509699	+	0.444807i
$47$	0.494132	−	0.359008i	0.0720766	−	0.0523667i	−0.551163	−	0.834397i	$-0.685816\pi$
$47$	0.494132	−	0.359008i	0.0720766	−	0.0523667i	0.623240	+	0.782031i	$0.285816\pi$
$48$	−2.11874	−	5.68403i	−0.305814	−	0.820419i
$49$	5.37385	+	4.48573i	0.767692	+	0.640819i
$50$	6.79239	+	1.55432i	0.960589	+	0.219814i
$51$	4.14373	+	3.01060i	0.580238	+	0.421568i
$52$	−12.4336	−	6.00488i	−1.72423	−	0.832727i
$53$	−11.7326	−	3.81214i	−1.61159	−	0.523638i	−0.641654	−	0.766994i	$-0.721752\pi$
$53$	−11.7326	−	3.81214i	−1.61159	−	0.523638i	−0.969937	+	0.243356i	$0.921752\pi$
$54$	6.81010	+	4.07402i	0.926737	+	0.554404i
$55$	0.133364	+	0.885548i	0.0179828	+	0.119407i
$56$	−7.27941	+	1.73499i	−0.972752	+	0.231848i
$57$	−0.0295182	+	0.0908478i	−0.00390979	+	0.0120331i
$58$	5.54083	−	0.495556i	0.727546	−	0.0650698i
$59$	0.709701	−	0.976819i	0.0923951	−	0.127171i	−0.760317	−	0.649552i	$-0.774956\pi$
$59$	0.709701	−	0.976819i	0.0923951	−	0.127171i	0.852712	+	0.522381i	$0.174956\pi$
$60$	0.591307	+	0.566617i	0.0763375	+	0.0731499i
$61$	2.29148	+	7.05244i	0.293394	+	0.902973i	0.983756	+	0.179509i	$0.0574510\pi$
$61$	2.29148	+	7.05244i	0.293394	+	0.902973i	−0.690363	+	0.723464i	$0.742549\pi$
$62$	−4.10135	+	1.75029i	−0.520872	+	0.222286i
$63$	1.13862	−	1.46123i	0.143453	−	0.184098i
$64$	3.16889	−	7.34562i	0.396112	−	0.918202i
$65$	1.86414			0.231218
$66$	2.70196	−	6.57995i	0.332588	−	0.809935i
$67$	7.60314			0.928872			0.464436	−	0.885607i	$-0.346257\pi$
$67$	7.60314			0.928872			0.464436	+	0.885607i	$0.346257\pi$
$68$	1.19868	+	6.64765i	0.145362	+	0.806145i
$69$	−3.98047	+	2.89198i	−0.479192	+	0.348154i
$70$	0.783100	−	0.638324i	0.0935984	−	0.0762943i
$71$	7.10243	−	2.30772i	0.842903	−	0.273876i	0.144433	−	0.989515i	$-0.453864\pi$
$71$	7.10243	−	2.30772i	0.842903	−	0.273876i	0.698471	+	0.715639i	$0.253864\pi$
$72$	0.523646	+	1.90989i	0.0617123	+	0.225083i
$73$	7.13145	−	9.81560i	0.834673	−	1.14883i	−0.152362	−	0.988325i	$-0.548688\pi$
$73$	7.13145	−	9.81560i	0.834673	−	1.14883i	0.987035	−	0.160504i	$-0.0513119\pi$
$74$	11.5395	−	1.03206i	1.34144	−	0.119975i
$75$	7.10632	+	2.30898i	0.820568	+	0.266619i
$76$	−0.111001	+	0.0595722i	−0.0127327	+	0.00683340i
$77$	−7.64772	−	4.30260i	−0.871539	−	0.490326i
$78$	−12.7065	−	7.60141i	−1.43872	−	0.860690i
$79$	9.50920	+	3.08973i	1.06987	+	0.347621i	0.790436	−	0.612544i	$-0.209854\pi$
$79$	9.50920	+	3.08973i	1.06987	+	0.347621i	0.279432	+	0.960165i	$0.409854\pi$
$80$	0.0460400	+	1.07907i	0.00514743	+	0.120644i
$81$	5.18520	+	3.76727i	0.576133	+	0.418585i
$82$	1.31275	−	5.73672i	0.144969	−	0.633514i
$83$	7.87395	−	2.55840i	0.864278	−	0.280821i	0.156864	−	0.987620i	$-0.449862\pi$
$83$	7.87395	−	2.55840i	0.864278	−	0.280821i	0.707414	+	0.706799i	$0.249862\pi$
$84$	−7.94071	+	1.15773i	−0.866403	+	0.126319i
$85$	−0.536032	−	0.737784i	−0.0581408	−	0.0800239i
$86$	−6.61582	−	7.58098i	−0.713403	−	0.817478i
$87$	5.96537			0.639555
$88$	8.57668	−	3.80008i	0.914277	−	0.405090i
$89$		−	6.36308i		−	0.674485i	−0.941418	−	0.337243i	$-0.890506\pi$
$89$		−	6.36308i		−	0.674485i	0.941418	−	0.337243i	$-0.109494\pi$
$90$	−0.175797	−	0.201443i	−0.0185306	−	0.0212340i
$91$	−11.2271	+	14.4082i	−1.17692	+	1.51039i
$92$	−6.42901	−	0.878201i	−0.670271	−	0.0915588i
$93$	−4.54776	+	1.47766i	−0.471580	+	0.153226i
$94$	0.842010	+	0.192679i	0.0868467	+	0.0198734i
$95$	0.00999689	−	0.0137595i	0.00102566	−	0.00141170i
$96$	4.08632	−	7.54298i	0.417059	−	0.769852i
$97$	−13.5188	−	4.39251i	−1.37262	−	0.445992i	−0.472385	−	0.881392i	$-0.656607\pi$
$97$	−13.5188	−	4.39251i	−1.37262	−	0.445992i	−0.900237	+	0.435400i	$0.856607\pi$
$98$	0.217319	+	9.89711i	0.0219525	+	0.999759i
$99$	−1.06996	+	2.06102i	−0.107535	+	0.207140i
$100$	4.65987	+	8.68277i	0.465987	+	0.868277i
$101$	2.70662	−	8.33012i	0.269319	−	0.828878i	−0.721348	−	0.692573i	$-0.756477\pi$
$101$	2.70662	−	8.33012i	0.269319	−	0.828878i	0.990667	−	0.136305i	$-0.0435228\pi$
$102$	0.645264	+	7.21471i	0.0638906	+	0.714363i
$103$	0.506106	+	0.367708i	0.0498681	+	0.0362313i	0.612440	−	0.790517i	$-0.290188\pi$
$103$	0.506106	+	0.367708i	0.0498681	+	0.0362313i	−0.562572	+	0.826748i	$0.690188\pi$
$104$	−5.16330	−	18.8321i	−0.506303	−	1.84664i
$105$	0.897388	−	0.606974i	0.0875761	−	0.0592346i
$106$	−6.84782	−	16.0461i	−0.665119	−	1.55854i
$107$	6.95435	−	5.05263i	0.672302	−	0.488456i	−0.198493	−	0.980102i	$-0.563605\pi$
$107$	6.95435	−	5.05263i	0.672302	−	0.488456i	0.870795	+	0.491646i	$0.163605\pi$
$108$	1.99153	+	11.0446i	0.191635	+	1.06277i
$109$			11.4190i			1.09375i	0.837215	+	0.546873i	$0.184182\pi$
$109$			11.4190i			1.09375i	−0.837215	+	0.546873i	$0.815818\pi$
$110$	−0.819562	+	0.965547i	−0.0781422	+	0.0920613i
$111$	12.4237			1.17921
$112$	−8.61758	−	6.14308i	−0.814284	−	0.580466i
$113$	−6.33099	+	4.59973i	−0.595569	+	0.432706i	−0.844303	−	0.535865i	$-0.819985\pi$
$113$	−6.33099	+	4.59973i	−0.595569	+	0.432706i	0.248734	+	0.968572i	$0.419985\pi$
$114$	−0.124249	+	0.0530242i	−0.0116370	+	0.00496617i
$115$	0.833146	−	0.270705i	0.0776913	−	0.0252434i
$116$	5.68028	+	5.44309i	0.527400	+	0.505378i
$117$	3.91069	+	2.84128i	0.361543	+	0.262676i
$118$	1.70075	−	0.152111i	0.156567	−	0.0140029i
$119$	8.93078	+	0.300391i	0.818683	+	0.0275368i
$120$	−0.0539051	+	1.15693i	−0.00492084	+	0.105613i
$121$	10.4087	+	3.55786i	0.946248	+	0.323441i
$122$	−5.38378	+	8.99948i	−0.487424	+	0.814774i
$123$	1.95012	−	6.00186i	0.175837	−	0.541169i
$124$	−5.67869	−	2.74255i	−0.509962	−	0.246288i
$125$	−2.16853	−	1.57553i	−0.193959	−	0.140920i
$126$	2.61575	−	0.145526i	0.233029	−	0.0129644i
$127$	−10.0620	+	3.26935i	−0.892859	+	0.290108i	−0.719287	−	0.694713i	$-0.755531\pi$
$127$	−10.0620	+	3.26935i	−0.892859	+	0.290108i	−0.173573	+	0.984821i	$0.555531\pi$
$128$	10.7736	−	3.45393i	0.952260	−	0.305287i
$129$	−6.34203	−	8.72906i	−0.558385	−	0.768551i
$130$	1.73341	+	1.98629i	0.152030	+	0.174209i
$131$			18.9540i			1.65602i	0.560714	+	0.828009i	$0.310527\pi$
$131$			18.9540i			1.65602i	−0.560714	+	0.828009i	$0.689473\pi$
$132$	9.52357	−	3.23948i	0.828920	−	0.281961i
$133$	0.0461410	+	0.160137i	0.00400093	+	0.0138856i
$134$	7.06993	+	8.10133i	0.610749	+	0.699849i
$135$	−0.890582	−	1.22578i	−0.0766491	−	0.105498i
$136$	−5.96861	+	7.45867i	−0.511804	+	0.639576i
$137$	−1.45708	−	4.48444i	−0.124487	−	0.383132i	0.869320	−	0.494249i	$-0.164557\pi$
$137$	−1.45708	−	4.48444i	−0.124487	−	0.383132i	−0.993807	+	0.111117i	$0.964557\pi$
$138$	−6.78280	−	1.55212i	−0.577390	−	0.132126i
$139$	−6.72472	+	9.25579i	−0.570384	+	0.785066i	−0.992600	−	0.121429i	$-0.961252\pi$
$139$	−6.72472	+	9.25579i	−0.570384	+	0.785066i	0.422216	+	0.906495i	$0.361252\pi$
$140$	1.40833	+	0.240854i	0.119026	+	0.0203559i
$141$	0.880927	+	0.286230i	0.0741874	+	0.0241049i
$142$	9.06326	+	5.42193i	0.760572	+	0.454999i
$143$	10.5501	−	20.3222i	0.882241	−	1.69943i
$144$	−1.54811	+	2.33391i	−0.129010	+	0.194492i
$145$	−1.01014	−	0.328215i	−0.0838876	−	0.0272567i
$146$	17.0901	−	1.52849i	1.41438	−	0.126499i
$147$	−0.713317	+	10.5916i	−0.0588334	+	0.873584i
$148$	11.8300	+	11.3360i	0.972416	+	0.931811i
$149$	11.0892	−	3.60311i	0.908466	−	0.295178i	0.182739	−	0.983161i	$-0.441504\pi$
$149$	11.0892	−	3.60311i	0.908466	−	0.295178i	0.725727	+	0.687983i	$0.241504\pi$
$150$	4.14767	+	9.71902i	0.338656	+	0.793554i
$151$	−4.45382	−	6.13015i	−0.362446	−	0.498865i	0.588382	−	0.808583i	$-0.299765\pi$
$151$	−4.45382	−	6.13015i	−0.362446	−	0.498865i	−0.950828	+	0.309719i	$0.899765\pi$
$152$	−0.166692	−	0.0628803i	−0.0135205	−	0.00510027i
$153$		−	2.36477i		−	0.191180i
$154$	−2.52686	−	12.1497i	−0.203620	−	0.979050i
$155$	0.851391			0.0683853
$156$	−3.71585	−	20.6074i	−0.297506	−	1.64991i
$157$	−6.43336	+	4.67411i	−0.513438	+	0.373034i	−0.814126	−	0.580688i	$-0.802784\pi$
$157$	−6.43336	+	4.67411i	−0.513438	+	0.373034i	0.300688	+	0.953722i	$0.402784\pi$
$158$	5.55013	+	13.0053i	0.441545	+	1.03465i
$159$	−5.78119	−	17.7927i	−0.458478	−	1.41105i
$160$	−1.10697	+	1.05245i	−0.0875135	+	0.0832038i
$161$	−2.92546	+	8.06986i	−0.230559	+	0.635994i
$162$	0.807441	+	9.02802i	0.0634386	+	0.709308i
$163$	0.953361	−	2.93414i	0.0746730	−	0.229820i	−0.906753	−	0.421663i	$-0.861446\pi$
$163$	0.953361	−	2.93414i	0.0746730	−	0.229820i	0.981426	+	0.191843i	$0.0614465\pi$
$164$	7.33330	−	3.93563i	0.572634	−	0.307321i
$165$	−0.967591	+	0.952990i	−0.0753269	+	0.0741901i
$166$	10.0478	+	6.01091i	0.779859	+	0.466537i
$167$	−4.35966	+	13.4177i	−0.337361	+	1.03829i	0.628187	+	0.778063i	$0.283797\pi$
$167$	−4.35966	+	13.4177i	−0.337361	+	1.03829i	−0.965547	+	0.260227i	$0.916203\pi$
$168$	−8.61742	−	7.38448i	−0.664848	−	0.569725i
$169$	−28.0433	−	20.3746i	−2.15717	−	1.56728i
$170$	0.287688	−	1.25720i	0.0220646	−	0.0964227i
$171$	0.0419440	−	0.0136284i	0.00320754	−	0.00104219i
$172$	1.92587	−	14.0986i	0.146846	−	1.07501i
$173$	−5.07769	+	3.68916i	−0.386050	+	0.280482i	−0.763835	−	0.645412i	$-0.776686\pi$
$173$	−5.07769	+	3.68916i	−0.386050	+	0.280482i	0.377785	+	0.925893i	$0.376686\pi$
$174$	5.54702	+	6.35625i	0.420518	+	0.481866i
$175$	12.5263	−	3.60925i	0.946896	−	0.272834i
$176$	12.0243	+	5.60509i	0.906363	+	0.422499i
$177$	1.83107			0.137631
$178$	6.78002	−	5.91684i	0.508184	−	0.443486i
$179$	−10.3540	+	7.52262i	−0.773894	+	0.562267i	−0.903140	−	0.429345i	$-0.858744\pi$
$179$	−10.3540	+	7.52262i	−0.773894	+	0.562267i	0.129246	+	0.991613i	$0.458744\pi$
$180$	0.0511745	−	0.374631i	0.00381432	−	0.0279234i
$181$	−6.20519	−	19.0976i	−0.461228	−	1.41951i	−0.863665	−	0.504067i	$-0.831837\pi$
$181$	−6.20519	−	19.0976i	−0.461228	−	1.41951i	0.402436	−	0.915448i	$-0.368163\pi$
$182$	−25.7920	+	1.43492i	−1.91183	+	0.106364i
$183$	−6.60998	+	9.09785i	−0.488624	+	0.672533i
$184$	−5.04240	−	7.66689i	−0.371731	−	0.565210i
$185$	−2.10376	−	0.683552i	−0.154671	−	0.0502557i
$186$	−5.80330	−	3.47172i	−0.425519	−	0.254559i
$187$	−11.0767	+	1.66816i	−0.810012	+	0.121988i
$188$	0.577655	+	1.07635i	0.0421298	+	0.0785008i
$189$	14.8379	+	0.499081i	1.07930	+	0.0363028i
$190$	0.0239569	−	0.00214264i	0.00173802	−	0.000155444i
$191$	4.03868	−	5.55877i	0.292229	−	0.402218i	−0.637508	−	0.770444i	$-0.720035\pi$
$191$	4.03868	−	5.55877i	0.292229	−	0.402218i	0.929736	+	0.368226i	$0.120035\pi$
$192$	11.8370	−	2.65991i	0.854260	−	0.191962i
$193$	−4.06283	−	12.5041i	−0.292449	−	0.900066i	−0.984066	−	0.177802i	$-0.943101\pi$
$193$	−4.06283	−	12.5041i	−0.292449	−	0.900066i	0.691617	−	0.722264i	$-0.256899\pi$
$194$	−7.89035	−	18.4890i	−0.566494	−	1.32744i
$195$	1.66167	+	2.28709i	0.118995	+	0.163782i
$196$	−10.3435	+	9.43458i	−0.738824	+	0.673898i
$197$		−	17.0577i		−	1.21531i	−0.794200	−	0.607657i	$-0.792110\pi$
$197$		−	17.0577i		−	1.21531i	0.794200	−	0.607657i	$-0.207890\pi$
$198$	−3.19099	+	0.776415i	−0.226773	+	0.0551774i
$199$	−4.45836			−0.316044			−0.158022	−	0.987436i	$-0.550512\pi$
$199$	−4.45836			−0.316044			−0.158022	+	0.987436i	$0.550512\pi$
$200$	−4.91864	+	13.0391i	−0.347800	+	0.922000i
$201$	6.77735	+	9.32822i	0.478037	+	0.657962i
$202$	11.3927	−	4.86195i	0.801591	−	0.342086i
$203$	8.62058	−	5.83077i	0.605046	−	0.409240i
$204$	−7.08744	+	7.39628i	−0.496220	+	0.517843i
$205$	−0.660444	+	0.909023i	−0.0461274	+	0.0634889i
$206$	0.0788111	+	0.881189i	0.00549103	+	0.0613954i
$207$	2.16042	+	0.701963i	0.150160	+	0.0487898i
$208$	15.2649	−	23.0130i	1.05843	−	1.59566i
$209$	−0.0934247	−	0.186855i	−0.00646232	−	0.0129250i
$210$	1.48120	+	0.391783i	0.102212	+	0.0270356i
$211$	−0.0411581	+	0.126672i	−0.00283344	+	0.00872044i	−0.952463	−	0.304654i	$-0.901459\pi$
$211$	−0.0411581	+	0.126672i	−0.00283344	+	0.00872044i	0.949630	+	0.313374i	$0.101459\pi$
$212$	10.7300	−	22.2173i	0.736937	−	1.52589i
$213$	9.16233	+	6.65682i	0.627793	+	0.456118i
$214$	11.8503	+	2.71174i	0.810072	+	0.185371i
$215$	0.593650	+	1.82707i	0.0404866	+	0.124605i
$216$	−9.91647	+	12.3921i	−0.674730	+	0.843176i
$217$	−5.12766	+	6.58050i	−0.348088	+	0.446714i
$218$	−12.1673	+	10.6182i	−0.824072	+	0.719157i
$219$	18.3995			1.24333
$220$	−1.79090	+	0.0245687i	−0.120742	+	0.00165642i
$221$			23.3173i			1.56849i
$222$	11.5524	+	13.2378i	0.775348	+	0.888461i
$223$	−7.67963	+	5.57958i	−0.514266	+	0.373636i	−0.814439	−	0.580249i	$-0.802955\pi$
$223$	−7.67963	+	5.57958i	−0.514266	+	0.373636i	0.300174	+	0.953885i	$0.402955\pi$
$224$	−1.46762	−	14.8945i	−0.0980597	−	0.995181i
$225$	−1.06605	−	3.28095i	−0.0710698	−	0.218730i
$226$	−10.7881	−	2.46867i	−0.717615	−	0.164214i
$227$	−6.66401	+	9.17223i	−0.442306	+	0.608782i	−0.970723	−	0.240203i	$-0.922786\pi$
$227$	−6.66401	+	9.17223i	−0.442306	+	0.608782i	0.528417	+	0.848985i	$0.322786\pi$
$228$	−0.172034	−	0.0830845i	−0.0113932	−	0.00550240i
$229$	−4.37810	+	13.4744i	−0.289313	+	0.890414i	0.695760	+	0.718275i	$0.255068\pi$
$229$	−4.37810	+	13.4744i	−0.289313	+	0.890414i	−0.985073	+	0.172139i	$0.944932\pi$
$230$	1.06316	+	0.636017i	0.0701027	+	0.0419377i
$231$	−1.53827	−	13.2182i	−0.101211	−	0.869693i
$232$	−0.517829	+	11.1138i	−0.0339971	+	0.729659i
$233$	6.00356	−	18.4771i	0.393307	−	1.21047i	−0.536966	−	0.843604i	$-0.680430\pi$
$233$	6.00356	−	18.4771i	0.393307	−	1.21047i	0.930272	−	0.366869i	$-0.119570\pi$
$234$	0.608974	+	6.80895i	0.0398099	+	0.445115i
$235$	−0.133422	−	0.0969371i	−0.00870352	−	0.00632348i
$236$	1.74356	+	1.67075i	0.113496	+	0.108757i
$237$	4.68563	+	14.4209i	0.304364	+	0.936737i
$238$	7.98438	+	9.79529i	0.517551	+	0.634934i
$239$	4.72648	+	6.50545i	0.305731	+	0.420802i	0.934044	−	0.357158i	$-0.116254\pi$
$239$	4.72648	+	6.50545i	0.305731	+	0.420802i	−0.628313	+	0.777961i	$0.716254\pi$
$240$	−1.28286	+	1.01836i	−0.0828085	+	0.0657348i
$241$			25.4494i			1.63934i	0.572836	+	0.819670i	$0.305843\pi$
$241$			25.4494i			1.63934i	−0.572836	+	0.819670i	$0.694157\pi$
$242$	5.88778	+	14.3991i	0.378481	+	0.925609i
$243$		−	7.11437i		−	0.456387i
$244$	−14.5954	+	2.63179i	−0.934373	+	0.168483i
$245$	0.703541	−	1.75428i	0.0449476	−	0.112077i
$246$	8.20849	−	3.50304i	0.523354	−	0.223346i
$247$	−0.413580	+	0.134380i	−0.0263154	+	0.00855040i
$248$	−2.35819	−	8.60100i	−0.149745	−	0.546164i
$249$	10.1576	+	7.37994i	0.643713	+	0.467685i
$250$	−0.337685	−	3.77566i	−0.0213570	−	0.238794i
$251$	−23.7962	−	7.73187i	−1.50201	−	0.488031i	−0.561403	−	0.827542i	$-0.689738\pi$
$251$	−23.7962	−	7.73187i	−1.50201	−	0.488031i	−0.940602	+	0.339511i	$0.889738\pi$
$252$	2.58737	+	2.65182i	0.162989	+	0.167049i
$253$	1.76403	−	10.6147i	0.110904	−	0.667343i
$254$	−12.8399	−	7.68126i	−0.805649	−	0.481965i
$255$	0.427368	−	1.31530i	0.0267628	−	0.0823675i
$256$	13.6983	+	8.26783i	0.856143	+	0.516739i
$257$	17.9782	−	24.7448i	1.12145	−	1.54354i	0.318072	−	0.948067i	$-0.396965\pi$
$257$	17.9782	−	24.7448i	1.12145	−	1.54354i	0.803375	−	0.595473i	$-0.203035\pi$
$258$	3.40377	−	14.8745i	0.211909	−	0.926045i
$259$	17.9535	−	12.1434i	1.11558	−	0.754553i
$260$	−0.504596	+	3.69397i	−0.0312937	+	0.229090i
$261$	−1.61887	−	2.22818i	−0.100205	−	0.137921i
$262$	−20.1960	+	17.6247i	−1.24771	+	1.08886i
$263$		−	17.4129i		−	1.07373i	−0.843669	−	0.536864i	$-0.819609\pi$
$263$		−	17.4129i		−	1.07373i	0.843669	−	0.536864i	$-0.180391\pi$
$264$	12.3074	+	7.13530i	0.757470	+	0.439147i
$265$			3.33098i			0.204621i
$266$	−0.127724	+	0.198071i	−0.00783129	+	0.0121445i
$267$	7.80680	−	5.67197i	0.477768	−	0.347119i
$268$	−2.05806	+	15.0664i	−0.125716	+	0.920325i
$269$	−4.70769	−	14.4888i	−0.287033	−	0.883397i	−0.985782	−	0.168030i	$-0.946259\pi$
$269$	−4.70769	−	14.4888i	−0.287033	−	0.883397i	0.698749	−	0.715367i	$-0.253741\pi$
$270$	0.477975	−	2.08875i	0.0290886	−	0.127118i
$271$	−3.05407	−	2.21892i	−0.185522	−	0.134790i	0.491148	−	0.871076i	$-0.336577\pi$
$271$	−3.05407	−	2.21892i	−0.185522	−	0.134790i	−0.676670	+	0.736287i	$0.736577\pi$
$272$	−13.4974	+	0.575885i	−0.818402	+	0.0349181i
$273$	−27.6850	−	0.931197i	−1.67557	−	0.0563586i
$274$	3.42339	−	5.72251i	0.206814	−	0.345709i
$275$	−14.6162	+	7.30790i	−0.881390	+	0.440683i
$276$	−4.65329	−	8.67051i	−0.280095	−	0.521903i
$277$	−21.4668	−	6.97498i	−1.28981	−	0.419086i	−0.417788	−	0.908545i	$-0.637194\pi$
$277$	−21.4668	−	6.97498i	−1.28981	−	0.419086i	−0.872027	+	0.489459i	$0.837194\pi$
$278$	−16.1154	+	1.44132i	−0.966537	+	0.0864444i
$279$	1.78609	+	1.29767i	0.106930	+	0.0776895i
$280$	1.05293	+	1.72457i	0.0629245	+	0.103063i
$281$	6.60588	+	20.3308i	0.394074	+	1.21283i	0.929680	+	0.368367i	$0.120083\pi$
$281$	6.60588	+	20.3308i	0.394074	+	1.21283i	−0.535607	+	0.844468i	$0.679917\pi$
$282$	0.514161	+	1.20481i	0.0306179	+	0.0717451i
$283$	16.6529	+	22.9207i	0.989911	+	1.36250i	0.931316	+	0.364213i	$0.118662\pi$
$283$	16.6529	+	22.9207i	0.989911	+	1.36250i	0.0585952	+	0.998282i	$0.481338\pi$
$284$	2.65045	+	14.6988i	0.157275	+	0.872215i
$285$	0.0257925			0.00152782
$286$	31.4640	−	7.65567i	1.86051	−	0.452689i
$287$	−3.04830	−	10.5794i	−0.179936	−	0.624483i
$288$	−3.92638	+	0.520676i	−0.231364	+	0.0306811i
$289$	−4.52483	+	3.28748i	−0.266166	+	0.193381i
$290$	−0.589578	−	1.38153i	−0.0346212	−	0.0811260i
$291$	−6.66133	−	20.5015i	−0.390494	−	1.20182i
$292$	17.5202	+	16.7886i	1.02529	+	0.982479i
$293$	−25.5031	−	18.5291i	−1.48991	−	1.08248i	−0.974192	−	0.225723i	$-0.927526\pi$
$293$	−25.5031	−	18.5291i	−1.48991	−	1.08248i	−0.515717	−	0.856759i	$-0.672474\pi$
$294$	−11.9489	+	9.08879i	−0.696877	+	0.530069i
$295$	−0.310062	−	0.100745i	−0.0180525	−	0.00586562i
$296$	−1.07845	+	23.1461i	−0.0626836	+	1.34534i
$297$	−18.4033	+	2.77155i	−1.06787	+	0.160821i
$298$	14.1507	+	8.46543i	0.819731	+	0.490389i
$299$	−21.3024	−	6.92156i	−1.23195	−	0.400284i
$300$	−6.49906	+	13.4569i	−0.375223	+	0.776933i
$301$	−17.6970	−	6.41546i	−1.02004	−	0.369781i
$302$	2.39036	−	10.4459i	0.137550	−	0.601093i
$303$	12.6328	−	4.10464i	0.725735	−	0.235805i
$304$	−0.0880016	−	0.236085i	−0.00504724	−	0.0135404i
$305$	1.61986	−	1.17690i	0.0927527	−	0.0673888i
$306$	2.51972	−	2.19893i	0.144043	−	0.125704i
$307$			4.09109i			0.233491i	0.993162	+	0.116746i	$0.0372462\pi$
$307$			4.09109i			0.233491i	−0.993162	+	0.116746i	$0.962754\pi$
$308$	10.5961	−	13.9901i	0.603771	−	0.797158i
$309$			0.948707i			0.0539701i
$310$	0.791682	+	0.907178i	0.0449645	+	0.0515242i
$311$	−19.7077	+	14.3185i	−1.11752	+	0.811928i	−0.983832	−	0.179095i	$-0.942683\pi$
$311$	−19.7077	+	14.3185i	−1.11752	+	0.811928i	−0.133691	+	0.991023i	$0.542683\pi$
$312$	18.5024	−	23.1215i	1.04749	−	1.30900i
$313$	−25.0321	+	8.13341i	−1.41490	+	0.459728i	−0.913977	−	0.405766i	$-0.867005\pi$
$313$	−25.0321	+	8.13341i	−1.41490	+	0.459728i	−0.500919	+	0.865494i	$0.667005\pi$
$314$	−10.9626	−	2.50859i	−0.618653	−	0.141568i
$315$	−0.470247	−	0.170473i	−0.0264954	−	0.00960504i
$316$	−8.69660	+	18.0071i	−0.489222	+	1.01298i
$317$	8.51045	+	2.76521i	0.477994	+	0.155310i	0.538098	−	0.842882i	$-0.319143\pi$
$317$	8.51045	+	2.76521i	0.477994	+	0.155310i	−0.0601035	+	0.998192i	$0.519143\pi$
$318$	13.5828	−	22.7048i	0.761684	−	1.27322i
$319$	−9.29497	+	9.15470i	−0.520418	+	0.512565i
$320$	−2.15075	−	0.200857i	−0.120231	−	0.0112282i
$321$	12.3980	+	4.02837i	0.691991	+	0.224842i
$322$	−11.3189	+	4.38677i	−0.630780	+	0.244465i
$323$	0.172109	+	0.125045i	0.00957641	+	0.00695767i
$324$	−8.86876	+	9.25523i	−0.492709	+	0.514179i
$325$	10.5115	+	32.3511i	0.583074	+	1.79452i
$326$	4.01291	−	1.71254i	0.222254	−	0.0948489i
$327$	−14.0099	+	10.1788i	−0.774750	+	0.562889i
$328$	11.0125	+	4.15418i	0.608065	+	0.229376i
$329$	1.55280	−	0.447417i	0.0856087	−	0.0246669i
$330$	−1.91517	−	0.144836i	−0.105426	−	0.00797297i
$331$	6.16504			0.338861			0.169431	−	0.985542i	$-0.445807\pi$
$331$	6.16504			0.338861			0.169431	+	0.985542i	$0.445807\pi$
$332$	2.93836	+	16.2955i	0.161263	+	0.894333i
$333$	−3.37151	−	4.64049i	−0.184758	−	0.254297i
$334$	−18.3508	+	7.83135i	−1.00411	+	0.428512i
$335$	−0.634397	−	1.95247i	−0.0346608	−	0.106675i
$336$	−0.144724	−	16.0487i	−0.00789535	−	0.875527i
$337$	5.63501	+	4.09407i	0.306958	+	0.223018i	0.730590	−	0.682816i	$-0.239245\pi$
$337$	5.63501	+	4.09407i	0.306958	+	0.223018i	−0.423632	+	0.905834i	$0.639245\pi$
$338$	−4.36691	−	48.8265i	−0.237529	−	2.65581i
$339$	−11.2867	−	3.66728i	−0.613011	−	0.199179i
$340$	1.60709	−	0.862491i	0.0871565	−	0.0467752i
$341$	4.81843	−	9.28158i	0.260933	−	0.502626i
$342$	0.0535238	+	0.0320197i	0.00289424	+	0.00173143i
$343$	9.32183	+	16.0032i	0.503332	+	0.864093i
$344$	16.8133	−	11.0578i	0.906511	−	0.596199i
$345$	1.07478	+	0.780875i	0.0578643	+	0.0420409i
$346$	−8.65248	−	1.97997i	−0.465160	−	0.106444i
$347$	−2.83827	−	8.73529i	−0.152366	−	0.468935i	0.845518	−	0.533947i	$-0.179292\pi$
$347$	−2.83827	−	8.73529i	−0.152366	−	0.468935i	−0.997885	+	0.0650113i	$0.979292\pi$
$348$	−1.61474	+	11.8210i	−0.0865592	+	0.633671i
$349$	0.718241	−	0.521833i	0.0384466	−	0.0279331i	−0.568396	−	0.822755i	$-0.692436\pi$
$349$	0.718241	−	0.521833i	0.0384466	−	0.0279331i	0.606843	+	0.794822i	$0.292436\pi$
$350$	15.4935	+	9.99089i	0.828164	+	0.534036i
$351$			38.7402i			2.06780i
$352$	5.20864	+	18.0242i	0.277622	+	0.960691i
$353$			11.6057i			0.617708i	0.951110	+	0.308854i	$0.0999454\pi$
$353$			11.6057i			0.617708i	−0.951110	+	0.308854i	$0.900055\pi$
$354$	1.70265	+	1.95105i	0.0904950	+	0.103697i
$355$	−1.18524	−	1.63134i	−0.0629058	−	0.0865824i
$356$	12.6091	+	1.72239i	0.668279	+	0.0912867i
$357$	7.59224	+	11.2248i	0.401824	+	0.594082i
$358$	−17.6434	−	4.03739i	−0.932483	−	0.213383i
$359$	−1.49820	+	2.06209i	−0.0790718	+	0.108833i	−0.846721	−	0.532038i	$-0.821426\pi$
$359$	−1.49820	+	2.06209i	−0.0790718	+	0.108833i	0.767649	+	0.640871i	$0.221426\pi$
$360$	0.446765	−	0.293831i	0.0235466	−	0.0154862i
$361$	5.87010	−	18.0663i	0.308952	−	0.950858i
$362$	14.5790	−	24.3701i	0.766253	−	1.28086i
$363$	4.91312	+	15.9418i	0.257872	+	0.836727i
$364$	−25.5122	−	26.1477i	−1.33720	−	1.37051i
$365$	−3.11567	−	1.01234i	−0.163082	−	0.0529884i
$366$	−15.8404	+	1.41672i	−0.827991	+	0.0740532i
$367$	−15.8256	−	11.4980i	−0.826089	−	0.600189i	0.0923609	−	0.995726i	$-0.470559\pi$
$367$	−15.8256	−	11.4980i	−0.826089	−	0.600189i	−0.918450	+	0.395537i	$0.870559\pi$
$368$	3.48048	−	12.5020i	0.181433	−	0.651712i
$369$	−2.77103	+	0.900361i	−0.144254	+	0.0468709i
$370$	−1.22788	−	2.87722i	−0.0638343	−	0.149579i
$371$	−25.7456	−	20.0615i	−1.33664	−	1.04154i
$372$	−1.69711	−	9.41181i	−0.0879909	−	0.487979i
$373$		−	0.194032i		−	0.0100466i	−0.999987	−	0.00502331i	$-0.998401\pi$
$373$		−	0.194032i		−	0.0100466i	0.999987	−	0.00502331i	$-0.00159898\pi$
$374$	−12.0774	−	10.2514i	−0.624507	−	0.530086i
$375$		−	4.06496i		−	0.209913i
$376$	−0.609733	+	1.61637i	−0.0314446	+	0.0833579i
$377$	15.9625	+	21.9705i	0.822111	+	1.13154i
$378$	13.2655	+	16.2742i	0.682306	+	0.837057i
$379$	8.52362	+	26.2330i	0.437829	+	1.34750i	0.890160	+	0.455649i	$0.150593\pi$
$379$	8.52362	+	26.2330i	0.437829	+	1.34750i	−0.452331	+	0.891850i	$0.649407\pi$
$380$	0.0245598	+	0.0235343i	0.00125989	+	0.00120728i
$381$	−12.9803	−	9.43073i	−0.665000	−	0.483151i
$382$	9.67845	−	0.865614i	0.495192	−	0.0442886i
$383$	6.14397	−	18.9092i	0.313942	−	0.966215i	−0.662245	−	0.749287i	$-0.730396\pi$
$383$	6.14397	−	18.9092i	0.313942	−	0.966215i	0.976188	−	0.216928i	$-0.0696036\pi$
$384$	13.8410	+	10.1392i	0.706323	+	0.517415i
$385$	−0.466782	+	2.32293i	−0.0237894	+	0.118387i
$386$	9.54554	−	15.9562i	0.485855	−	0.812152i
$387$	−1.53939	+	4.73774i	−0.0782514	+	0.240833i
$388$	12.3635	−	25.5998i	0.627663	−	1.29963i
$389$	−6.60110	+	9.08564i	−0.334689	+	0.460660i	−0.942881	−	0.333130i	$-0.891895\pi$
$389$	−6.60110	+	9.08564i	−0.334689	+	0.460660i	0.608192	+	0.793790i	$0.291895\pi$
$390$	−0.891818	+	3.89725i	−0.0451589	+	0.197345i
$391$	3.38608	+	10.4213i	0.171241	+	0.527027i
$392$	−19.6709	−	2.24837i	−0.993531	−	0.113560i
$393$	−23.2545	+	16.8954i	−1.17303	+	0.852258i
$394$	18.1754	−	15.8615i	0.915665	−	0.799089i
$395$		−	2.69975i		−	0.135839i
$396$	−3.79449	−	2.67811i	−0.190680	−	0.134580i
$397$	23.4894			1.17890			0.589450	−	0.807805i	$-0.299345\pi$
$397$	23.4894			1.17890			0.589450	+	0.807805i	$0.299345\pi$
$398$	−4.14569	−	4.75049i	−0.207805	−	0.238120i
$399$	−0.155340	+	0.199354i	−0.00777675	+	0.00998017i
$400$	−18.4671	+	6.88369i	−0.923356	+	0.344184i
$401$	2.40972	+	7.41635i	0.120336	+	0.370355i	0.993022	−	0.117925i	$-0.0376243\pi$
$401$	2.40972	+	7.41635i	0.120336	+	0.370355i	−0.872687	+	0.488280i	$0.837624\pi$
$402$	−3.63740	+	15.8955i	−0.181417	+	0.792793i
$403$	−17.6114	−	12.7954i	−0.877285	−	0.637385i
$404$	15.7743	+	7.61827i	0.784801	+	0.379023i
$405$	0.534781	−	1.64589i	0.0265735	−	0.0817847i
$406$	14.2288	+	3.76358i	0.706166	+	0.186784i
$407$	−19.3580	+	19.0659i	−0.959543	+	0.945063i
$408$	−14.4713	−	0.674265i	−0.716437	−	0.0333811i
$409$	11.8275	+	3.84300i	0.584834	+	0.190024i	0.586465	−	0.809974i	$-0.300519\pi$
$409$	11.8275	+	3.84300i	0.584834	+	0.190024i	−0.00163074	+	0.999999i	$0.500519\pi$
$410$	−1.58271	+	0.141553i	−0.0781646	+	0.00699083i
$411$	4.20309	−	5.78506i	0.207323	−	0.285356i
$412$	−0.865645	+	0.903366i	−0.0426473	+	0.0445057i
$413$	2.64608	−	1.78975i	0.130205	−	0.0880679i
$414$	1.26095	+	2.95471i	0.0619723	+	0.145216i
$415$	−1.31399	−	1.80855i	−0.0645011	−	0.0887781i
$416$	38.7152	−	5.13401i	1.89817	−	0.251716i
$417$	−17.3502			−0.849642
$418$	0.112225	−	0.273297i	0.00548913	−	0.0133674i
$419$		−	34.5803i		−	1.68936i	−0.535272	−	0.844680i	$-0.679791\pi$
$419$		−	34.5803i		−	1.68936i	0.535272	−	0.844680i	$-0.320209\pi$
$420$	0.959868	+	1.94256i	0.0468367	+	0.0947873i
$421$	−21.8061	−	30.0135i	−1.06276	−	1.46277i	−0.877192	−	0.480140i	$-0.840586\pi$
$421$	−21.8061	−	30.0135i	−1.06276	−	1.46277i	−0.185573	−	0.982631i	$-0.559414\pi$
$422$	−0.173244	+	0.0739332i	−0.00843336	+	0.00359901i
$423$	−0.132151	−	0.406719i	−0.00642541	−	0.0197754i
$424$	33.6506	−	9.22617i	1.63422	−	0.448063i
$425$	9.78127	−	13.4628i	0.474461	−	0.653040i
$426$	1.42676	+	15.9527i	0.0691269	+	0.772909i
$427$	−0.659530	+	19.6082i	−0.0319169	+	0.948905i
$428$	8.12984	+	15.1484i	0.392970	+	0.732225i
$429$	34.3373	−	5.17122i	1.65782	−	0.249669i
$430$	−1.39477	+	2.33148i	−0.0672616	+	0.112434i
$431$	−25.2643	−	8.20888i	−1.21694	−	0.395408i	−0.370973	−	0.928643i	$-0.620976\pi$
$431$	−25.2643	−	8.20888i	−1.21694	−	0.395408i	−0.845967	+	0.533236i	$0.820976\pi$
$432$	−22.4251	+	0.956796i	−1.07893	+	0.0460339i
$433$	−10.9566	+	15.0804i	−0.526539	+	0.724719i	−0.986598	−	0.163169i	$-0.947828\pi$
$433$	−10.9566	+	15.0804i	−0.526539	+	0.724719i	0.460059	+	0.887888i	$0.347828\pi$
$434$	−11.7797	+	0.655359i	−0.565446	+	0.0314582i
$435$	−0.497744	−	1.53190i	−0.0238650	−	0.0734489i
$436$	−22.6280	−	3.09097i	−1.08368	−	0.148031i
$437$	−0.165328	+	0.120118i	−0.00790872	+	0.00574602i
$438$	17.1092	+	19.6052i	0.817508	+	0.936771i
$439$	−16.2986			−0.777889			−0.388945	−	0.921261i	$-0.627160\pi$
$439$	−16.2986			−0.777889			−0.388945	+	0.921261i	$0.627160\pi$
$440$	−1.69148	−	1.88540i	−0.0806382	−	0.0898830i
$441$	4.14976	−	2.60790i	0.197608	−	0.124185i
$442$	−24.8452	+	21.6820i	−1.18176	+	1.03131i
$443$	0.100487	−	0.0730078i	0.00477426	−	0.00346870i	−0.585396	−	0.810748i	$-0.699061\pi$
$443$	0.100487	−	0.0730078i	0.00477426	−	0.00346870i	0.590170	+	0.807279i	$0.299061\pi$
$444$	−3.36292	+	24.6188i	−0.159597	+	1.16836i
$445$	−1.63403	+	0.530928i	−0.0774604	+	0.0251684i
$446$	−13.0862	−	2.99456i	−0.619651	−	0.141796i
$447$	14.3054	+	10.3935i	0.676624	+	0.491596i
$448$	14.5058	−	15.4137i	0.685333	−	0.728230i
$449$	7.89960	−	24.3125i	0.372805	−	1.14738i	−0.572142	−	0.820155i	$-0.693887\pi$
$449$	7.89960	−	24.3125i	0.372805	−	1.14738i	0.944947	−	0.327222i	$-0.106113\pi$
$450$	2.50465	−	4.18676i	0.118070	−	0.197366i
$451$	6.17210	+	12.3445i	0.290633	+	0.581282i
$452$	−7.40111	−	13.7905i	−0.348119	−	0.648653i
$453$	3.55094	−	10.9287i	0.166838	−	0.513474i
$454$	−15.9699	+	1.42830i	−0.749504	+	0.0670336i
$455$	4.63677	+	1.68091i	0.217375	+	0.0788022i
$456$	−0.0714403	−	0.260564i	−0.00334550	−	0.0122020i
$457$	10.2107	+	31.4254i	0.477638	+	1.47002i	0.842367	+	0.538905i	$0.181162\pi$
$457$	10.2107	+	31.4254i	0.477638	+	1.47002i	−0.364729	+	0.931114i	$0.618838\pi$
$458$	−18.4284	+	7.86447i	−0.861102	+	0.367482i
$459$	15.3325	−	11.1397i	0.715660	−	0.519957i
$460$	0.310909	+	1.72424i	0.0144962	+	0.0803929i
$461$	37.4098			1.74235			0.871174	−	0.490974i	$-0.163359\pi$
$461$	37.4098			1.74235			0.871174	+	0.490974i	$0.163359\pi$
$462$	12.6539	−	13.9303i	0.588714	−	0.648095i
$463$		−	7.02019i		−	0.326256i	−0.986605	−	0.163128i	$-0.947842\pi$
$463$		−	7.02019i		−	0.326256i	0.986605	−	0.163128i	$-0.0521583\pi$
$464$	−12.3236	+	9.78265i	−0.572108	+	0.454148i
$465$	0.758919	+	1.04456i	0.0351940	+	0.0484404i
$466$	25.2703	−	10.7843i	1.17062	−	0.499574i
$467$	−26.0139	+	8.45242i	−1.20378	+	0.391131i	−0.841150	−	0.540803i	$-0.818121\pi$
$467$	−26.0139	+	8.45242i	−1.20378	+	0.391131i	−0.362628	+	0.931934i	$0.618121\pi$
$468$	−6.68884	+	6.98031i	−0.309192	+	0.322665i
$469$	18.9117	+	6.85581i	0.873261	+	0.316572i
$470$	−0.0207766	−	0.232304i	−0.000958353	−	0.0107154i
$471$	−11.4692	−	3.72658i	−0.528474	−	0.171712i
$472$	−0.158947	+	3.41138i	−0.00731614	+	0.157022i
$473$	23.2778	+	3.86848i	1.07032	+	0.177873i
$474$	−11.0088	+	18.4022i	−0.505650	+	0.845241i
$475$	0.295160	+	0.0959033i	0.0135429	+	0.00440034i
$476$	−3.01269	+	17.6159i	−0.138086	+	0.807423i
$477$	−5.07701	+	6.98791i	−0.232460	+	0.319954i
$478$	−2.53670	+	11.0854i	−0.116026	+	0.507034i
$479$	5.93557	+	18.2678i	0.271203	+	0.834678i	0.990199	+	0.139663i	$0.0446020\pi$
$479$	5.93557	+	18.2678i	0.271203	+	0.834678i	−0.718996	+	0.695014i	$0.755398\pi$
$480$	−2.27798	−	0.419983i	−0.103975	−	0.0191695i
$481$	33.2441	+	45.7566i	1.51580	+	2.08632i
$482$	−27.1170	+	23.6646i	−1.23514	+	1.07789i
$483$	−12.5086	+	3.60416i	−0.569159	+	0.163995i
$484$	−9.86773	+	19.6629i	−0.448533	+	0.893766i
$485$			3.83810i			0.174279i
$486$	7.58054	−	6.61544i	0.343860	−	0.300082i
$487$	−15.3832	−	21.1731i	−0.697078	−	0.959445i	−0.999979	−	0.00642354i	$-0.997955\pi$
$487$	−15.3832	−	21.1731i	−0.697078	−	0.959445i	0.302901	−	0.953022i	$-0.402045\pi$
$488$	−16.3760	−	13.1045i	−0.741308	−	0.593213i
$489$	4.44969	−	1.44579i	0.201222	−	0.0653809i
$490$	2.52343	−	0.881610i	0.113997	−	0.0398271i
$491$	2.89984	+	2.10685i	0.130868	+	0.0950810i	0.651293	−	0.758826i	$-0.274227\pi$
$491$	2.89984	+	2.10685i	0.130868	+	0.0950810i	−0.520426	+	0.853907i	$0.674227\pi$
$492$	11.3654	+	5.48897i	0.512392	+	0.247462i
$493$	4.10542	−	12.6352i	0.184899	−	0.569061i
$494$	−0.527760	−	0.315723i	−0.0237451	−	0.0142051i
$495$	0.618542	+	0.102794i	0.0278014	+	0.00462023i
$496$	6.97177	−	10.5105i	0.313042	−	0.471936i
$497$	19.7471	+	0.664205i	0.885780	+	0.0297936i
$498$	1.58175	+	17.6856i	0.0708799	+	0.792510i
$499$	13.7916	+	10.0202i	0.617398	+	0.448566i	0.852012	−	0.523523i	$-0.175383\pi$
$499$	13.7916	+	10.0202i	0.617398	+	0.448566i	−0.234614	+	0.972089i	$0.575383\pi$
$500$	3.70906	−	3.87068i	0.165874	−	0.173102i
$501$	−20.3481	+	6.61151i	−0.909088	+	0.295381i
$502$	−13.8889	−	32.5451i	−0.619892	−	1.45256i
$503$	−8.76124	+	6.36542i	−0.390645	+	0.283820i	−0.765720	−	0.643175i	$-0.777617\pi$
$503$	−8.76124	+	6.36542i	−0.390645	+	0.283820i	0.375075	+	0.926994i	$0.377617\pi$
$504$	−0.419672	+	5.22275i	−0.0186937	+	0.232640i
$505$	−2.36500			−0.105241
$506$	12.9506	−	7.99070i	0.575724	−	0.355230i
$507$		−	52.5677i		−	2.33461i
$508$	−3.75489	−	20.8238i	−0.166596	−	0.923908i
$509$	5.47446	−	3.97743i	0.242651	−	0.176296i	−0.459812	−	0.888016i	$-0.652083\pi$
$509$	5.47446	−	3.97743i	0.242651	−	0.176296i	0.702464	+	0.711720i	$0.252083\pi$
$510$	1.79888	−	0.767689i	0.0796559	−	0.0339939i
$511$	26.5892	−	17.9844i	1.17624	−	0.795582i
$512$	3.92805	+	22.2839i	0.173597	+	0.984817i
$513$	0.285948	+	0.207754i	0.0126249	+	0.00917254i
$514$	43.0836	−	3.85328i	1.90033	−	0.169961i
$515$	0.0521978	−	0.160648i	0.00230011	−	0.00707901i
$516$	19.0142	−	10.2045i	0.837053	−	0.449229i
$517$	−1.81188	+	0.905914i	−0.0796863	+	0.0398421i
$518$	29.6335	+	7.83818i	1.30202	+	0.344390i
$519$	−9.05239	−	2.94130i	−0.397356	−	0.129109i
$520$	−4.40523	+	2.89725i	−0.193182	+	0.127053i
$521$	−2.06910	+	2.84787i	−0.0906488	+	0.124767i	−0.851933	−	0.523651i	$-0.824569\pi$
$521$	−2.06910	+	2.84787i	−0.0906488	+	0.124767i	0.761284	+	0.648419i	$0.224569\pi$
$522$	0.868846	−	3.79686i	0.0380283	−	0.166184i
$523$	29.9080	−	9.71771i	1.30779	−	0.424926i	0.429503	−	0.903065i	$-0.358689\pi$
$523$	29.9080	−	9.71771i	1.30779	−	0.424926i	0.878284	+	0.478140i	$0.158689\pi$
$524$	−37.5592	−	5.13058i	−1.64078	−	0.224130i
$525$	15.5939	+	12.1511i	0.680574	+	0.530317i
$526$	18.5539	−	16.1918i	0.808989	−	0.705994i
$527$			10.6495i			0.463899i
$528$	3.84146	+	19.7488i	0.167178	+	0.859454i
$529$	12.4741			0.542354
$530$	−3.54924	+	3.09738i	−0.154169	+	0.134542i
$531$	−0.496910	−	0.683939i	−0.0215641	−	0.0296804i
$532$	−0.329816	+	0.0480862i	−0.0142993	+	0.00208480i
$533$	27.3231	−	8.87782i	1.18350	−	0.384541i
$534$	13.3029	+	3.04414i	0.575674	+	0.131733i
$535$	−1.87777	−	1.36428i	−0.0811830	−	0.0589829i
$536$	−17.9673	+	11.8168i	−0.776070	+	0.510410i
$537$	−18.4589	−	5.99765i	−0.796558	−	0.258818i
$538$	11.0606	−	18.4888i	0.476857	−	0.797111i
$539$	−15.1429	−	17.5981i	−0.652251	−	0.758003i
$540$	2.67007	−	1.43297i	0.114902	−	0.0616654i
$541$	2.63155	+	0.855043i	0.113139	+	0.0367612i	0.365039	−	0.930992i	$-0.381055\pi$
$541$	2.63155	+	0.855043i	0.113139	+	0.0367612i	−0.251900	+	0.967753i	$0.581055\pi$
$542$	−0.475582	−	5.31749i	−0.0204280	−	0.228406i
$543$	17.8994	−	24.6365i	0.768139	−	1.05725i
$544$	−13.1645	−	13.8463i	−0.564422	−	0.593657i
$545$	2.93239	−	0.952792i	0.125610	−	0.0408131i
$546$	−24.7512	−	30.3649i	−1.05925	−	1.29950i
$547$	26.0211	−	18.9055i	1.11258	−	0.808339i	0.129515	−	0.991578i	$-0.458658\pi$
$547$	26.0211	−	18.9055i	1.11258	−	0.808339i	0.983068	+	0.183239i	$0.0586581\pi$
$548$	9.28077	−	1.67348i	0.396455	−	0.0714875i
$549$	5.19202			0.221590
$550$	−21.3779	−	8.77853i	−0.911557	−	0.374318i
$551$	0.247771			0.0105554
$552$	4.91169	−	13.0206i	0.209056	−	0.554195i
$553$	20.8667	+	16.2598i	0.887342	+	0.691435i
$554$	−12.5293	−	29.3592i	−0.532319	−	1.24735i
$555$	−1.03662	−	3.19039i	−0.0440021	−	0.135424i
$556$	−16.5210	−	15.8311i	−0.700645	−	0.671389i
$557$	−12.7594	+	17.5618i	−0.540634	+	0.744119i	−0.988704	−	0.149879i	$-0.952112\pi$
$557$	−12.7594	+	17.5618i	−0.540634	+	0.744119i	0.448070	+	0.893999i	$0.352112\pi$
$558$	0.278131	+	3.10979i	0.0117742	+	0.131648i
$559$	15.1788	−	46.7155i	0.641994	−	1.97585i
$560$	−0.858491	+	2.72555i	−0.0362779	+	0.115176i
$561$	−11.9203	−	12.1030i	−0.503277	−	0.510988i
$562$	−15.5204	+	25.9437i	−0.654688	+	1.09437i
$563$	−27.7125	−	9.00434i	−1.16794	−	0.379488i	−0.340068	−	0.940401i	$-0.610450\pi$
$563$	−27.7125	−	9.00434i	−1.16794	−	0.379488i	−0.827875	+	0.560913i	$0.810450\pi$
$564$	−0.805648	+	1.66816i	−0.0339239	+	0.0702424i
$565$	1.70945	+	1.24199i	0.0719172	+	0.0522509i
$566$	−8.93759	+	39.0573i	−0.375675	+	1.64170i
$567$	9.50044	+	14.0461i	0.398981	+	0.589879i
$568$	−13.1974	+	16.4921i	−0.553750	+	0.691993i
$569$	−14.1324	+	10.2678i	−0.592460	+	0.430448i	−0.843195	−	0.537608i	$-0.819328\pi$
$569$	−14.1324	+	10.2678i	−0.592460	+	0.430448i	0.250734	+	0.968056i	$0.419328\pi$
$570$	0.0239837	+	0.0274826i	0.00100457	+	0.00115112i
$571$	−40.3181			−1.68726			−0.843630	−	0.536924i	$-0.819586\pi$
$571$	−40.3181			−1.68726			−0.843630	+	0.536924i	$0.819586\pi$
$572$	37.4147	+	26.4069i	1.56439	+	1.10413i
$573$	10.4200			0.435303
$574$	8.43811	−	13.0855i	0.352200	−	0.546179i
$575$	9.39590	+	12.9323i	0.391836	+	0.539316i
$576$	−4.20582	−	3.69950i	−0.175242	−	0.154146i
$577$	4.80211	−	1.56030i	0.199914	−	0.0649561i	−0.207348	−	0.978267i	$-0.566483\pi$
$577$	4.80211	−	1.56030i	0.199914	−	0.0649561i	0.407263	+	0.913311i	$0.366483\pi$
$578$	−7.71039	−	1.76439i	−0.320710	−	0.0733889i
$579$	11.7196	−	16.1307i	0.487051	−	0.670368i
$580$	0.923820	−	1.91285i	0.0383595	−	0.0794268i
$581$	21.8922	+	0.736356i	0.908242	+	0.0305492i
$582$	15.6506	−	26.1615i	0.648740	−	1.08443i
$583$	36.3133	+	18.8516i	1.50394	+	0.780756i
$584$	−1.59719	+	34.2794i	−0.0660920	+	1.41849i
$585$	0.403333	−	1.24133i	0.0166758	−	0.0513227i
$586$	−3.97136	−	44.4039i	−0.164055	−	1.83431i
$587$	10.0471	−	13.8287i	0.414690	−	0.570772i	−0.549664	−	0.835386i	$-0.685244\pi$
$587$	10.0471	−	13.8287i	0.414690	−	0.570772i	0.964355	+	0.264614i	$0.0852444\pi$
$588$	−20.7953	−	4.28051i	−0.857583	−	0.176525i
$589$	−0.188890	+	0.0613742i	−0.00778309	+	0.00252888i
$590$	−0.180971	−	0.424059i	−0.00745044	−	0.0174582i
$591$	20.9280	−	15.2051i	0.860861	−	0.625452i
$592$	−25.6655	+	20.3737i	−1.05485	+	0.837355i
$593$		−	5.20740i		−	0.213842i	−0.994268	−	0.106921i	$-0.965901\pi$
$593$		−	5.20740i		−	0.213842i	0.994268	−	0.106921i	$-0.0340992\pi$
$594$	−20.0658	−	17.0320i	−0.823311	−	0.698831i
$595$	−0.668034	−	2.31847i	−0.0273867	−	0.0950481i
$596$	4.13822	+	22.9497i	0.169508	+	0.940057i
$597$	−3.97412	−	5.46991i	−0.162650	−	0.223869i
$598$	−12.4333	−	29.1343i	−0.508436	−	1.19139i
$599$	−5.50064	+	1.78727i	−0.224750	+	0.0730257i	−0.419227	−	0.907881i	$-0.637699\pi$
$599$	−5.50064	+	1.78727i	−0.224750	+	0.0730257i	0.194477	+	0.980907i	$0.437699\pi$
$600$	−20.3819	+	5.58822i	−0.832088	+	0.228138i
$601$	5.92855	−	8.15995i	0.241831	−	0.332851i	−0.670799	−	0.741640i	$-0.734048\pi$
$601$	5.92855	−	8.15995i	0.241831	−	0.332851i	0.912629	+	0.408788i	$0.134048\pi$
$602$	−9.62006	−	24.8221i	−0.392084	−	1.01167i
$603$	1.64505	−	5.06293i	0.0669915	−	0.206179i
$604$	13.3531	−	7.16633i	0.543329	−	0.291594i
$605$	0.0451590	−	2.96981i	0.00183598	−	0.120740i
$606$	16.1204	+	9.64376i	0.654848	+	0.391751i
$607$	1.58571	−	4.88032i	0.0643621	−	0.198086i	−0.913704	−	0.406380i	$-0.866791\pi$
$607$	1.58571	−	4.88032i	0.0643621	−	0.198086i	0.978066	+	0.208294i	$0.0667910\pi$
$608$	0.169725	−	0.313296i	0.00688324	−	0.0127058i
$609$	14.8380	+	5.37903i	0.601266	+	0.217969i
$610$	2.76027	+	0.631639i	0.111760	+	0.0255743i
$611$	1.30305	+	4.01037i	0.0527157	+	0.162242i
$612$	4.68602	+	0.640109i	0.189421	+	0.0258749i
$613$	16.3107	+	22.4497i	0.658783	+	0.906737i	0.999440	−	0.0334508i	$-0.0106497\pi$
$613$	16.3107	+	22.4497i	0.658783	+	0.906737i	−0.340658	+	0.940187i	$0.610650\pi$
$614$	−4.35916	+	3.80418i	−0.175921	+	0.153524i
$615$	−1.70398			−0.0687112
$616$	24.7598	−	1.71848i	0.997600	−	0.0692394i
$617$	−20.0028			−0.805282			−0.402641	−	0.915358i	$-0.631908\pi$
$617$	−20.0028			−0.805282			−0.402641	+	0.915358i	$0.631908\pi$
$618$	−1.01087	+	0.882174i	−0.0406632	+	0.0354862i
$619$	−12.5351	−	17.2531i	−0.503827	−	0.693459i	0.479036	−	0.877795i	$-0.340986\pi$
$619$	−12.5351	−	17.2531i	−0.503827	−	0.693459i	−0.982863	+	0.184337i	$0.940986\pi$
$620$	−0.230459	+	1.68711i	−0.00925546	+	0.0677561i
$621$	5.62575	+	17.3143i	0.225754	+	0.694799i
$622$	−33.5823	−	7.68473i	−1.34653	−	0.308130i
$623$	5.73764	−	15.8272i	0.229874	−	0.634104i
$624$	41.8413	−	1.78521i	1.67499	−	0.0714657i
$625$	7.38912	−	22.7414i	0.295565	−	0.909655i
$626$	−31.9429	−	19.1093i	−1.27670	−	0.763760i
$627$	0.145972	−	0.281182i	0.00582958	−	0.0112293i
$628$	−7.52078	−	14.0135i	−0.300112	−	0.559201i
$629$	8.55011	−	26.3145i	0.340915	−	1.04923i
$630$	−0.255626	−	0.659577i	−0.0101844	−	0.0262782i
$631$	−25.6043	+	35.2413i	−1.01929	+	1.40293i	−0.106593	+	0.994303i	$0.533994\pi$
$631$	−25.6043	+	35.2413i	−1.01929	+	1.40293i	−0.912699	+	0.408632i	$0.866006\pi$
$632$	−27.2737	+	7.47778i	−1.08489	+	0.297450i
$633$	−0.192100	+	0.0624171i	−0.00763529	+	0.00248086i
$634$	4.96720	+	11.6394i	0.197273	+	0.462259i
$635$	1.67913	+	2.31112i	0.0666340	+	0.0917139i
$636$	36.8228	−	6.63977i	1.46012	−	0.263284i
$637$	−40.9178	+	25.7146i	−1.62122	+	1.01885i
$638$	−18.3977	−	1.39134i	−0.728371	−	0.0550836i
$639$		−	5.22882i		−	0.206849i
$640$	−1.78590	−	2.47845i	−0.0705939	−	0.0979693i
$641$	−2.53543	+	1.84210i	−0.100144	+	0.0727586i	−0.636730	−	0.771087i	$-0.719713\pi$
$641$	−2.53543	+	1.84210i	−0.100144	+	0.0727586i	0.536587	+	0.843845i	$0.319713\pi$
$642$	7.23623	+	16.9563i	0.285591	+	0.669211i
$643$	26.0731	−	8.47166i	1.02822	−	0.334090i	0.254135	−	0.967169i	$-0.418209\pi$
$643$	26.0731	−	8.47166i	1.02822	−	0.334090i	0.774087	+	0.633079i	$0.218209\pi$
$644$	−15.1993	−	7.98149i	−0.598938	−	0.314515i
$645$	−1.71244	+	2.35697i	−0.0674271	+	0.0928055i
$646$	0.0268009	+	0.299662i	0.00105447	+	0.0117900i
$647$	−12.6139	+	38.8215i	−0.495903	+	1.52623i	0.319642	+	0.947538i	$0.396437\pi$
$647$	−12.6139	+	38.8215i	−0.495903	+	1.52623i	−0.815545	+	0.578694i	$0.803563\pi$
$648$	−18.1085	−	0.843731i	−0.711368	−	0.0331449i
$649$	−2.85308	+	2.81003i	−0.111993	+	0.110303i
$650$	−24.6966	+	41.2826i	−0.968680	+	1.61924i
$651$	−12.6443	−	0.425297i	−0.495569	−	0.0166687i
$652$	5.55623	+	2.68341i	0.217599	+	0.105090i
$653$	3.15151	−	4.33769i	0.123328	−	0.169747i	−0.742889	−	0.669415i	$-0.766545\pi$
$653$	3.15151	−	4.33769i	0.123328	−	0.169747i	0.866217	+	0.499668i	$0.166545\pi$
$654$	−23.8732	−	5.46296i	−0.933514	−	0.213618i
$655$	4.86736	−	1.58150i	0.190183	−	0.0617943i
$656$	5.81382	+	15.5970i	0.226992	+	0.608959i
$657$	−4.99322	−	6.87258i	−0.194804	−	0.268125i
$658$	1.92064	+	1.23851i	0.0748742	+	0.0482821i
$659$	48.0909			1.87336			0.936678	−	0.350193i	$-0.113884\pi$
$659$	48.0909			1.87336			0.936678	+	0.350193i	$0.113884\pi$
$660$	−1.62653	−	2.17534i	−0.0633126	−	0.0846749i
$661$	32.0893			1.24813			0.624064	−	0.781374i	$-0.285481\pi$
$661$	32.0893			1.24813			0.624064	+	0.781374i	$0.285481\pi$
$662$	5.73268	+	6.56900i	0.222807	+	0.255311i
$663$	−28.6078	+	20.7848i	−1.11103	+	0.807213i
$664$	−14.6310	+	18.2836i	−0.567793	+	0.709541i
$665$	0.0372729	−	0.0252105i	0.00144538	−	0.000977623i
$666$	1.80949	−	7.90748i	0.0701163	−	0.306409i
$667$	10.3247	+	7.50131i	0.399773	+	0.290452i
$668$	−25.4083	−	12.2711i	−0.983077	−	0.474782i
$669$	−13.6911	−	4.44849i	−0.529327	−	0.171989i
$670$	1.49050	−	2.49151i	0.0575831	−	0.0962555i
$671$	−3.66257	−	24.3198i	−0.141392	−	0.938855i
$672$	16.9657	−	15.0774i	0.654466	−	0.581623i
$673$	−7.55370	+	23.2479i	−0.291174	+	0.896140i	0.693306	+	0.720643i	$0.256153\pi$
$673$	−7.55370	+	23.2479i	−0.291174	+	0.896140i	−0.984480	+	0.175497i	$0.943847\pi$
$674$	0.877486	+	9.81119i	0.0337995	+	0.377913i
$675$	16.2510	−	22.3675i	0.625500	−	0.860926i
$676$	47.9652	−	50.0554i	1.84482	−	1.92521i
$677$	−0.877490	−	2.70064i	−0.0337247	−	0.103794i	0.932777	−	0.360454i	$-0.117378\pi$
$677$	−0.877490	−	2.70064i	−0.0337247	−	0.103794i	−0.966502	+	0.256660i	$0.917378\pi$
$678$	−6.58761	−	15.4364i	−0.252995	−	0.592831i
$679$	−29.6652	−	23.1157i	−1.13844	−	0.887099i
$680$	2.41339	+	0.910387i	0.0925492	+	0.0349117i
$681$	−17.1935			−0.658858
$682$	14.3703	−	3.49650i	0.550266	−	0.133888i
$683$	15.7082			0.601058			0.300529	−	0.953773i	$-0.402837\pi$
$683$	15.7082			0.601058			0.300529	+	0.953773i	$0.402837\pi$
$684$	0.0156524	+	0.0868051i	0.000598485	+	0.00331908i
$685$	−1.03002	+	0.748353i	−0.0393550	+	0.0285931i
$686$	−8.38375	+	24.8136i	−0.320093	+	0.947386i
$687$	−20.4342	+	6.63948i	−0.779614	+	0.253312i
$688$	27.4165	+	7.63260i	1.04525	+	0.290990i
$689$	50.0608	−	68.9028i	1.90716	−	2.62499i
$690$	0.167366	+	1.87132i	0.00637150	+	0.0712399i
$691$	34.7853	+	11.3024i	1.32330	+	0.429965i	0.883626	−	0.468194i	$-0.155095\pi$
$691$	34.7853	+	11.3024i	1.32330	+	0.429965i	0.439671	+	0.898159i	$0.355095\pi$
$692$	−5.93597	−	11.0605i	−0.225652	−	0.420459i
$693$	−4.51979	+	4.16169i	−0.171693	+	0.158090i
$694$	6.66845	−	11.1469i	0.253131	−	0.423132i
$695$	2.93797	+	0.954606i	0.111444	+	0.0362103i
$696$	−14.0970	+	9.27142i	−0.534347	+	0.351432i
$697$	−11.3704	−	8.26106i	−0.430684	−	0.312910i
$698$	1.22390	+	0.280067i	0.0463251	+	0.0106007i
$699$	28.0208	−	9.10452i	1.05985	−	0.344365i
$700$	3.76141	+	25.7990i	0.142168	+	0.975109i
$701$	−12.0117	−	16.5326i	−0.453674	−	0.624429i	0.519508	−	0.854466i	$-0.326115\pi$
$701$	−12.0117	−	16.5326i	−0.453674	−	0.624429i	−0.973182	+	0.230037i	$0.926115\pi$
$702$	−41.2786	+	36.0233i	−1.55796	+	1.35961i
$703$	0.516017			0.0194619
$704$	−14.3618	+	22.3100i	−0.541281	+	0.840841i
$705$		−	0.250103i		−	0.00941943i
$706$	−12.3661	+	10.7918i	−0.465405	+	0.406153i
$707$	14.2437	−	18.2794i	0.535688	−	0.687466i
$708$	−0.495644	+	3.62844i	−0.0186274	+	0.136365i
$709$	−12.8086	+	4.16176i	−0.481036	+	0.156298i	−0.539490	−	0.841992i	$-0.681383\pi$
$709$	−12.8086	+	4.16176i	−0.481036	+	0.156298i	0.0584538	+	0.998290i	$0.481383\pi$
$710$	0.636116	−	2.77983i	0.0238730	−	0.104325i
$711$	4.11490	−	5.66367i	0.154321	−	0.212404i
$712$	9.88953	+	15.0369i	0.370626	+	0.563531i
$713$	−9.72923	−	3.16122i	−0.364362	−	0.118389i
$714$	−4.90056	+	18.5274i	−0.183399	+	0.693369i
$715$	−6.09900	−	1.01358i	−0.228090	−	0.0379056i
$716$	−12.1041	−	22.5537i	−0.452353	−	0.842872i
$717$	−3.76834	+	11.5978i	−0.140731	+	0.433126i
$718$	−3.59034	+	0.321110i	−0.133990	+	0.0119837i
$719$	36.2494	+	26.3367i	1.35187	+	0.982194i	0.998916	+	0.0465550i	$0.0148243\pi$
$719$	36.2494	+	26.3367i	1.35187	+	0.982194i	0.352958	+	0.935639i	$0.385176\pi$
$720$	0.728517	+	0.202815i	0.0271502	+	0.00755846i
$721$	0.927300	+	1.37098i	0.0345345	+	0.0510579i
$722$	24.7085	−	10.5446i	0.919556	−	0.392428i
$723$	−31.2236	+	22.6853i	−1.16122	+	0.843675i
$724$	39.5235	−	7.12674i	1.46888	−	0.264863i
$725$		−	19.3812i		−	0.719799i
$726$	−12.4178	+	20.0588i	−0.460868	+	0.744453i
$727$	−19.8703			−0.736950			−0.368475	−	0.929638i	$-0.620120\pi$
$727$	−19.8703			−0.736950			−0.368475	+	0.929638i	$0.620120\pi$
$728$	4.13809	−	51.4978i	0.153368	−	1.90864i
$729$	24.2841	−	17.6435i	0.899413	−	0.653462i
$730$	−1.81849	−	4.26117i	−0.0673053	−	0.157713i
$731$	−22.8536	+	7.42558i	−0.845270	+	0.274645i
$732$	−16.2391	−	15.5610i	−0.600213	−	0.575150i
$733$	−7.51197	−	5.45776i	−0.277461	−	0.201587i	0.440348	−	0.897827i	$-0.354855\pi$
$733$	−7.51197	−	5.45776i	−0.277461	−	0.201587i	−0.717809	+	0.696240i	$0.754855\pi$
$734$	−2.46437	−	27.5542i	−0.0909615	−	1.01704i
$735$	2.77943	−	0.700575i	0.102521	−	0.0258411i
$736$	16.5576	−	7.91669i	0.610321	−	0.291813i
$737$	−24.8756	−	4.13400i	−0.916304	−	0.152278i
$738$	−3.53605	−	2.11538i	−0.130164	−	0.0778682i
$739$	−1.02995	+	3.16987i	−0.0378874	+	0.116605i	−0.968211	−	0.250133i	$-0.919526\pi$
$739$	−1.02995	+	3.16987i	−0.0378874	+	0.116605i	0.930324	+	0.366738i	$0.119526\pi$
$740$	1.92398	−	3.98377i	0.0707270	−	0.146446i
$741$	−0.533529	−	0.387632i	−0.0195997	−	0.0142400i
$742$	−2.56403	−	46.0871i	−0.0941284	−	1.69191i
$743$	−6.64140	+	2.15792i	−0.243649	+	0.0791665i	−0.428296	−	0.903638i	$-0.640886\pi$
$743$	−6.64140	+	2.15792i	−0.243649	+	0.0791665i	0.184647	+	0.982805i	$0.440886\pi$
$744$	8.45042	−	10.5601i	0.309808	−	0.387151i
$745$	−1.85055	−	2.54706i	−0.0677987	−	0.0933170i
$746$	0.206746	−	0.180425i	0.00756952	−	0.00660582i
$747$		−	5.79681i		−	0.212094i
$748$	−0.307314	−	22.4012i	−0.0112365	−	0.819069i
$749$	21.8539	−	6.29688i	0.798524	−	0.230083i
$750$	4.33131	−	3.77988i	0.158157	−	0.138022i
$751$	11.8999	+	16.3788i	0.434234	+	0.597672i	0.968919	−	0.247380i	$-0.0795695\pi$
$751$	11.8999	+	16.3788i	0.434234	+	0.597672i	−0.534684	+	0.845052i	$0.679570\pi$
$752$	−2.28925	+	0.853327i	−0.0834805	+	0.0311177i
$753$	−11.7255	−	36.0875i	−0.427302	−	1.31510i
$754$	−8.56706	+	37.4381i	−0.311994	+	1.36342i
$755$	−1.20259	+	1.65522i	−0.0437668	+	0.0602398i
$756$	−5.00539	+	29.2677i	−0.182044	+	1.06446i
$757$	16.0415	+	5.21221i	0.583040	+	0.189441i	0.585662	−	0.810555i	$-0.300835\pi$
$757$	16.0415	+	5.21221i	0.583040	+	0.189441i	−0.00262211	+	0.999997i	$0.500835\pi$
$758$	−20.0261	+	33.4754i	−0.727379	+	1.21588i
$759$	14.5956	−	7.29757i	0.529785	−	0.264885i
$760$	−0.00223894	+	0.0480530i	−8.12149e−5	+	0.00174306i
$761$	33.2165	+	10.7927i	1.20410	+	0.391235i	0.841267	−	0.540620i	$-0.181810\pi$
$761$	33.2165	+	10.7927i	1.20410	+	0.391235i	0.362831	+	0.931855i	$0.381810\pi$
$762$	−2.02130	−	22.6002i	−0.0732238	−	0.818717i
$763$	−10.2966	+	28.4032i	−0.372764	+	1.02826i
$764$	9.92202	+	9.50772i	0.358966	+	0.343977i
$765$	−0.607269	+	0.197314i	−0.0219558	+	0.00713389i
$766$	25.8613	−	11.0365i	0.934407	−	0.398766i
$767$	4.89968	+	6.74383i	0.176917	+	0.243506i
$768$	2.06677	+	24.1761i	0.0745782	+	0.872381i
$769$			3.66026i			0.131992i	0.997820	+	0.0659961i	$0.0210225\pi$
$769$			3.66026i			0.131992i	−0.997820	+	0.0659961i	$0.978978\pi$
$770$	−2.90918	+	1.66265i	−0.104840	+	0.0599177i
$771$	46.3847			1.67050
$772$	25.8779	−	4.66622i	0.931365	−	0.167941i
$773$	−17.0099	+	12.3584i	−0.611802	+	0.444500i	−0.850049	−	0.526704i	$-0.823427\pi$
$773$	−17.0099	+	12.3584i	−0.611802	+	0.444500i	0.238246	+	0.971205i	$0.423427\pi$
$774$	−6.47961	+	2.76523i	−0.232905	+	0.0993940i
$775$	4.80083	+	14.7754i	0.172451	+	0.530749i
$776$	38.7736	−	10.6308i	1.39189	−	0.381623i
$777$	30.9021	+	11.2026i	1.10861	+	0.401889i
$778$	−15.8191	+	1.41482i	−0.567144	+	0.0507238i
$779$	0.0809979	−	0.249286i	0.00290205	−	0.00893160i
$780$	−4.98189	+	2.67368i	−0.178380	+	0.0957331i
$781$	−24.4921	+	3.68853i	−0.876398	+	0.131986i
$782$	−7.95552	+	13.2984i	−0.284489	+	0.475549i
$783$	6.82090	−	20.9926i	0.243759	−	0.750213i
$784$	−15.8957	−	23.0505i	−0.567703	−	0.823233i
$785$	1.73709	+	1.26207i	0.0619996	+	0.0450453i
$786$	−39.6261	−	9.06773i	−1.41341	−	0.323435i
$787$	25.5846	−	8.31295i	0.911993	−	0.296325i	0.184815	−	0.982773i	$-0.440831\pi$
$787$	25.5846	−	8.31295i	0.911993	−	0.296325i	0.727178	+	0.686449i	$0.240831\pi$
$788$	33.8016	+	4.61728i	1.20413	+	0.164484i
$789$	21.3638	−	15.5217i	0.760570	−	0.552586i
$790$	2.87665	−	2.51041i	0.102347	−	0.0893165i
$791$	−19.8950	+	5.73245i	−0.707385	+	0.203823i
$792$	−0.674788	−	6.53341i	−0.0239775	−	0.232155i
$793$	−51.1948			−1.81798
$794$	21.8421	+	25.0285i	0.775147	+	0.888230i
$795$	−4.08675	+	2.96920i	−0.144942	+	0.105307i
$796$	1.20681	−	8.83467i	0.0427743	−	0.313137i
$797$	8.57659	+	26.3960i	0.303798	+	0.934995i	0.980123	+	0.198391i	$0.0635717\pi$
$797$	8.57659	+	26.3960i	0.303798	+	0.934995i	−0.676325	+	0.736604i	$0.736428\pi$
$798$	−0.356863	+	0.0198538i	−0.0126328	+	0.000702818i
$799$	1.21252	−	1.66889i	0.0428960	−	0.0590412i
$800$	−24.5068	−	13.2762i	−0.866445	−	0.469386i
$801$	−4.23718	−	1.37674i	−0.149713	−	0.0486448i
$802$	−5.66158	+	9.46386i	−0.199917	+	0.334180i
$803$	−28.6693	+	28.2367i	−1.01172	+	0.996450i
$804$	−20.3193	+	10.9050i	−0.716607	+	0.384588i
$805$	2.31642	+	0.0779141i	0.0816432	+	0.00274611i
$806$	−2.74245	−	30.6634i	−0.0965987	−	1.08007i
$807$	13.5798	−	18.6909i	0.478030	−	0.657953i
$808$	6.55058	+	23.8919i	0.230449	+	0.840514i
$809$	11.4219	+	35.1530i	0.401572	+	1.23591i	0.923724	+	0.383060i	$0.125130\pi$
$809$	11.4219	+	35.1530i	0.401572	+	1.23591i	−0.522151	+	0.852853i	$0.674870\pi$
$810$	2.25101	−	0.960637i	0.0790924	−	0.0337533i
$811$	−1.24680	−	1.71607i	−0.0437810	−	0.0602593i	0.786565	−	0.617507i	$-0.211857\pi$
$811$	−1.24680	−	1.71607i	−0.0437810	−	0.0602593i	−0.830346	+	0.557248i	$0.811857\pi$
$812$	9.22077	+	18.6608i	0.323586	+	0.654867i
$813$		−	5.72493i		−	0.200782i
$814$	−38.3157	−	2.89765i	−1.34296	−	0.101563i
$815$	−0.833031			−0.0291798
$816$	−12.7380	−	16.0465i	−0.445919	−	0.561740i
$817$	−0.263415	−	0.362560i	−0.00921573	−	0.0126844i
$818$	6.90326	+	16.1760i	0.241367	+	0.565582i
$819$	7.16525	+	10.5936i	0.250374	+	0.370169i
$820$	−1.62255	−	1.55479i	−0.0566617	−	0.0542957i
$821$	16.5368	−	22.7610i	0.577140	−	0.794365i	−0.416238	−	0.909256i	$-0.636652\pi$
$821$	16.5368	−	22.7610i	0.577140	−	0.794365i	0.993378	+	0.114891i	$0.0366518\pi$
$822$	10.0725	−	0.900852i	0.351317	−	0.0314208i
$823$	−7.30480	−	2.37347i	−0.254629	−	0.0827340i	0.178921	−	0.983863i	$-0.442739\pi$
$823$	−7.30480	−	2.37347i	−0.254629	−	0.0827340i	−0.433550	+	0.901129i	$0.642739\pi$
$824$	−1.76750	−	0.0823532i	−0.0615736	−	0.00286891i
$825$	−21.9947	−	11.4183i	−0.765757	−	0.397534i
$826$	4.36753	+	1.15523i	0.151966	+	0.0401956i
$827$	−3.34248	+	10.2871i	−0.116229	+	0.357718i	−0.992201	−	0.124644i	$-0.960221\pi$
$827$	−3.34248	+	10.2871i	−0.116229	+	0.357718i	0.875972	+	0.482362i	$0.160221\pi$
$828$	−1.97580	+	4.09107i	−0.0686639	+	0.142175i
$829$	−8.10175	−	5.88626i	−0.281385	−	0.204438i	0.438136	−	0.898909i	$-0.355639\pi$
$829$	−8.10175	−	5.88626i	−0.281385	−	0.204438i	−0.719521	+	0.694470i	$0.755639\pi$
$830$	0.705216	−	3.08180i	0.0244784	−	0.106971i
$831$	−10.5777	−	32.5548i	−0.366936	−	1.12931i
$832$	41.4705	+	36.4781i	1.43773	+	1.26465i
$833$	21.9431	+	8.80013i	0.760284	+	0.304907i
$834$	−16.1334	−	18.4870i	−0.558654	−	0.640154i
$835$	3.80940			0.131830
$836$	0.395560	−	0.134551i	0.0136807	−	0.00465356i
$837$			17.6935i			0.611575i
$838$	36.8462	−	32.1552i	1.27283	−	1.11078i
$839$	−15.0576	+	10.9400i	−0.519848	+	0.377691i	−0.816546	−	0.577280i	$-0.804114\pi$
$839$	−15.0576	+	10.9400i	−0.519848	+	0.377691i	0.296699	+	0.954971i	$0.404114\pi$
$840$	−1.17730	+	2.82909i	−0.0406206	+	0.0976129i
$841$	4.18002	+	12.8648i	0.144139	+	0.443613i
$842$	11.7033	−	51.1436i	0.403323	−	1.76253i
$843$	−19.0553	+	26.2273i	−0.656298	+	0.903317i
$844$	−0.239872	−	0.115847i	−0.00825672	−	0.00398762i
$845$	−2.89227	+	8.90150i	−0.0994972	+	0.306221i
$846$	0.310486	−	0.519006i	0.0106747	−	0.0178438i
$847$	22.6820	+	18.2353i	0.779364	+	0.626571i
$848$	41.1214	+	27.2764i	1.41211	+	0.936675i
$849$	−13.2770	+	40.8625i	−0.455666	+	1.40240i
$850$	23.4402	−	2.09643i	0.803993	−	0.0719069i
$851$	21.5025	+	15.6225i	0.737098	+	0.535533i
$852$	−15.6713	+	16.3542i	−0.536889	+	0.560284i
$853$	1.69449	+	5.21512i	0.0580184	+	0.178562i	0.975866	−	0.218371i	$-0.0700744\pi$
$853$	1.69449	+	5.21512i	0.0580184	+	0.178562i	−0.917847	+	0.396933i	$0.870074\pi$
$854$	−21.5063	+	17.5303i	−0.735929	+	0.599874i
$855$	−0.00699951	−	0.00963400i	−0.000239378	−	0.000329476i
$856$	−8.58130	+	22.7486i	−0.293303	+	0.777530i
$857$			36.0251i			1.23059i	0.788296	+	0.615297i	$0.210964\pi$
$857$			36.0251i			1.23059i	−0.788296	+	0.615297i	$0.789036\pi$
$858$	37.4393	+	31.7787i	1.27816	+	1.08491i
$859$		−	46.4331i		−	1.58428i	−0.610341	−	0.792139i	$-0.708967\pi$
$859$		−	46.4331i		−	1.58428i	0.610341	−	0.792139i	$-0.291033\pi$
$860$	−3.78120	+	0.681814i	−0.128938	+	0.0232497i
$861$	10.2626	−	13.1703i	0.349747	−	0.448842i
$862$	−14.7458	−	34.5530i	−0.502243	−	1.17688i
$863$	−37.1283	+	12.0637i	−1.26386	+	0.410654i	−0.862869	−	0.505427i	$-0.831335\pi$
$863$	−37.1283	+	12.0637i	−1.26386	+	0.410654i	−0.400993	+	0.916081i	$0.631335\pi$
$864$	−21.8719	−	23.0048i	−0.744098	−	0.782640i
$865$	1.37105	+	0.996124i	0.0466170	+	0.0338692i
$866$	−26.2567	+	2.34833i	−0.892241	+	0.0797995i
$867$	−8.06675	−	2.62105i	−0.273961	−	0.0890154i
$868$	−11.6519	−	11.9422i	−0.395492	−	0.405345i
$869$	−29.4318	−	15.2792i	−0.998405	−	0.518311i
$870$	1.16944	−	1.95482i	0.0396477	−	0.0662747i
$871$	−16.2206	+	49.9220i	−0.549615	+	1.69154i
$872$	−17.7475	−	26.9848i	−0.601008	−	0.913822i
$873$	−5.84995	+	8.05176i	−0.197991	+	0.272511i
$874$	−0.281722	−	0.0644672i	−0.00952940	−	0.00218064i
$875$	−3.97323	−	5.87428i	−0.134320	−	0.198587i
$876$	−4.98049	+	36.4605i	−0.168275	+	1.23189i
$877$	7.99167	+	10.9996i	0.269860	+	0.371430i	0.922342	−	0.386374i	$-0.126273\pi$
$877$	7.99167	+	10.9996i	0.269860	+	0.371430i	−0.652483	+	0.757804i	$0.726273\pi$
$878$	−15.1556	−	17.3665i	−0.511475	−	0.586093i
$879$		−	47.8061i		−	1.61246i
$880$	0.436086	−	3.55549i	0.0147004	−	0.119856i
$881$			15.0890i			0.508361i	0.967157	+	0.254180i	$0.0818057\pi$
$881$			15.0890i			0.508361i	−0.967157	+	0.254180i	$0.918194\pi$
$882$	6.63751	+	1.99667i	0.223497	+	0.0672313i
$883$	−7.81538	+	5.67821i	−0.263009	+	0.191087i	−0.711472	−	0.702714i	$-0.751971\pi$
$883$	−7.81538	+	5.67821i	−0.263009	+	0.191087i	0.448464	+	0.893801i	$0.351971\pi$
$884$	−46.2055	−	6.31166i	−1.55406	−	0.212284i
$885$	−0.152782	−	0.470215i	−0.00513572	−	0.0158061i
$886$	0.171231	+	0.0391832i	0.00575262	+	0.00131639i
$887$	34.5974	+	25.1365i	1.16167	+	0.843999i	0.989988	−	0.141154i	$-0.0450812\pi$
$887$	34.5974	+	25.1365i	1.16167	+	0.843999i	0.171678	+	0.985153i	$0.445081\pi$
$888$	−29.3590	+	19.3090i	−0.985224	+	0.647967i
$889$	−27.9758	−	0.940979i	−0.938277	−	0.0315594i
$890$	−2.08515	−	1.24740i	−0.0698944	−	0.0418131i
$891$	−14.9163	−	15.1449i	−0.499716	−	0.507372i
$892$	−8.97771	−	16.7282i	−0.300596	−	0.560103i
$893$	0.0365891	+	0.0118885i	0.00122441	+	0.000397834i
$894$	2.22765	+	24.9074i	0.0745037	+	0.833028i
$895$	2.79572	+	2.03121i	0.0934507	+	0.0678959i
$896$	29.9122	+	1.12349i	0.999295	+	0.0375331i
$897$	−10.4967	−	32.3054i	−0.350474	−	1.07865i
$898$	33.2511	−	14.1902i	1.10961	−	0.473533i
$899$	7.29040	+	10.0344i	0.243149	+	0.334665i
$900$	6.79009	−	1.22437i	0.226336	−	0.0408123i
$901$	−41.6651			−1.38807
$902$	−7.41417	+	18.0553i	−0.246865	+	0.601177i
$903$	−7.90381	−	27.4309i	−0.263022	−	0.912844i
$904$	7.81210	−	20.7095i	0.259827	−	0.688787i
$905$	−4.38648	+	3.18697i	−0.145812	+	0.105938i
$906$	14.9467	−	6.37863i	0.496571	−	0.211916i
$907$	−2.32434	−	7.15357i	−0.0771783	−	0.237530i	0.905023	−	0.425363i	$-0.139854\pi$
$907$	−2.32434	−	7.15357i	−0.0771783	−	0.237530i	−0.982201	+	0.187833i	$0.939854\pi$
$908$	−16.3718	−	15.6882i	−0.543318	−	0.520631i
$909$	−4.96141	−	3.60468i	−0.164560	−	0.119560i
$910$	2.52054	+	6.50362i	0.0835551	+	0.215593i
$911$	36.1543	+	11.7472i	1.19784	+	0.389203i	0.838968	−	0.544181i	$-0.183160\pi$
$911$	36.1543	+	11.7472i	1.19784	+	0.389203i	0.358877	+	0.933385i	$0.383160\pi$
$912$	0.211207	−	0.318412i	0.00699376	−	0.0105437i
$913$	−27.1527	+	4.08921i	−0.898623	+	0.135333i
$914$	−23.9899	+	40.1013i	−0.793515	+	1.32643i
$915$	2.88784	+	0.938317i	0.0954691	+	0.0310198i
$916$	−25.5158	−	12.3230i	−0.843065	−	0.407162i
$917$	−17.0910	+	47.1453i	−0.564394	+	1.55687i
$918$	26.1269	+	5.97868i	0.862315	+	0.197326i
$919$	−11.5734	+	3.76044i	−0.381773	+	0.124045i	−0.493615	−	0.869680i	$-0.664325\pi$
$919$	−11.5734	+	3.76044i	−0.381773	+	0.124045i	0.111842	+	0.993726i	$0.464325\pi$
$920$	−1.54811	+	1.93460i	−0.0510397	+	0.0637817i
$921$	−5.01932	+	3.64675i	−0.165392	+	0.120165i
$922$	34.7862	+	39.8611i	1.14562	+	1.31275i
$923$			51.5576i			1.69704i
$924$	26.6095	+	0.529734i	0.875389	+	0.0174270i
$925$		−	40.3640i		−	1.32716i
$926$	7.48018	−	6.52786i	0.245814	−	0.214519i
$927$	0.354360	−	0.257458i	0.0116387	−	0.00845602i
$928$	−21.8830	−	4.03448i	−0.718344	−	0.132438i
$929$	−39.1710	+	12.7274i	−1.28516	+	0.417573i	−0.870394	−	0.492356i	$-0.836136\pi$
$929$	−39.1710	+	12.7274i	−1.28516	+	0.417573i	−0.414764	+	0.909929i	$0.636136\pi$
$930$	−0.407311	+	1.77995i	−0.0133563	+	0.0583670i
$931$	−0.0296275	+	0.439922i	−0.000971002	+	0.0144179i
$932$	34.9890	+	16.8981i	1.14610	+	0.553517i
$933$	−35.1345	−	11.4159i	−1.15025	−	0.373739i
$934$	−33.1958	−	19.8588i	−1.08620	−	0.649799i
$935$	1.35261	+	2.70530i	0.0442351	+	0.0884728i
$936$	−13.6574	−	0.636344i	−0.446408	−	0.0207996i
$937$	17.5046	+	5.68758i	0.571850	+	0.185805i	0.580646	−	0.814156i	$-0.302800\pi$
$937$	17.5046	+	5.68758i	0.571850	+	0.185805i	−0.00879636	+	0.999961i	$0.502800\pi$
$938$	10.2804	+	26.5259i	0.335666	+	0.866101i
$939$	−32.2921	−	23.4616i	−1.05381	−	0.765639i
$940$	0.228206	−	0.238150i	0.00744325	−	0.00776760i
$941$	2.19790	+	6.76444i	0.0716495	+	0.220515i	0.980469	−	0.196676i	$-0.0630147\pi$
$941$	2.19790	+	6.76444i	0.0716495	+	0.220515i	−0.908819	+	0.417191i	$0.863015\pi$
$942$	−6.69413	−	15.6860i	−0.218106	−	0.511077i
$943$	10.9224	−	7.93559i	0.355682	−	0.258418i
$944$	−3.78271	+	3.00278i	−0.123117	+	0.0977321i
$945$	−1.10990	−	3.85200i	−0.0361049	−	0.125305i
$946$	17.5234	+	28.4003i	0.569734	+	0.923373i
$947$	−1.57810			−0.0512814			−0.0256407	−	0.999671i	$-0.508163\pi$
$947$	−1.57810			−0.0512814			−0.0256407	+	0.999671i	$0.508163\pi$
$948$	−29.8447	+	5.38151i	−0.969311	+	0.174783i
$949$	49.2346	+	67.7656i	1.59822	+	2.19976i
$950$	0.172273	+	0.403678i	0.00558927	+	0.0130970i
$951$	4.19350	+	12.9063i	0.135983	+	0.418514i
$952$	−21.5716	+	13.1704i	−0.699139	+	0.426855i
$953$	−19.1279	−	13.8972i	−0.619612	−	0.450175i	0.233174	−	0.972435i	$-0.425089\pi$
$953$	−19.1279	−	13.8972i	−0.619612	−	0.450175i	−0.852786	+	0.522260i	$0.825089\pi$
$954$	−12.1667	+	1.08816i	−0.393913	+	0.0352305i
$955$	−1.76446	−	0.573309i	−0.0570967	−	0.0185518i
$956$	−14.1706	+	7.60506i	−0.458309	+	0.245965i
$957$	−19.5172	−	3.24351i	−0.630902	−	0.104848i
$958$	−13.9455	+	23.3112i	−0.450559	+	0.753150i
$959$	0.419376	−	12.4683i	0.0135424	−	0.402621i
$960$	−1.67072	−	2.81778i	−0.0539224	−	0.0909433i
$961$	17.0361	+	12.3774i	0.549550	+	0.399271i
$962$	−17.8421	+	77.9700i	−0.575252	+	2.51385i
$963$	−1.85988	−	5.72411i	−0.0599337	−	0.184457i
$964$	−50.4305	−	6.88878i	−1.62426	−	0.221873i
$965$	−2.87204	+	2.08666i	−0.0924542	+	0.0671719i
$966$	−15.4716	−	9.97678i	−0.497792	−	0.320998i
$967$		−	57.3670i		−	1.84480i	−0.386238	−	0.922399i	$-0.626226\pi$
$967$		−	57.3670i		−	1.84480i	0.386238	−	0.922399i	$-0.373774\pi$
$968$	−30.1270	+	7.76958i	−0.968317	+	0.249724i
$969$			0.322622i			0.0103641i
$970$	−4.08959	+	3.56893i	−0.131309	+	0.114591i
$971$	−15.2697	−	21.0169i	−0.490027	−	0.674464i	0.490366	−	0.871516i	$-0.336863\pi$
$971$	−15.2697	−	21.0169i	−0.490027	−	0.674464i	−0.980393	+	0.197053i	$0.936863\pi$
$972$	14.0978	+	1.92576i	0.452188	+	0.0617687i
$973$	−25.0728	+	16.9587i	−0.803796	+	0.543670i
$974$	8.25614	−	36.0794i	0.264544	−	1.15606i
$975$	−30.3214	+	41.7339i	−0.971063	+	1.33655i
$976$	−1.26440	−	29.6345i	−0.0404723	−	0.948579i
$977$	−16.2790	+	50.1015i	−0.520810	+	1.60289i	0.251645	+	0.967819i	$0.419028\pi$
$977$	−16.2790	+	50.1015i	−0.520810	+	1.60289i	−0.772455	+	0.635069i	$0.780972\pi$
$978$	5.67815	+	3.39685i	0.181567	+	0.108619i
$979$	−3.45976	+	20.8184i	−0.110574	+	0.665360i
$980$	3.28584	+	1.86899i	0.104962	+	0.0597028i
$981$	7.60395	+	2.47067i	0.242775	+	0.0788825i
$982$	0.451564	+	5.04895i	0.0144100	+	0.161118i
$983$	−20.0304	−	14.5529i	−0.638869	−	0.464166i	0.220592	−	0.975366i	$-0.429201\pi$
$983$	−20.0304	−	14.5529i	−0.638869	−	0.464166i	−0.859462	+	0.511200i	$0.829201\pi$
$984$	4.71970	+	17.2141i	0.150459	+	0.548767i
$985$	−4.38040	+	1.42328i	−0.139571	+	0.0453494i
$986$	17.2806	−	7.37465i	0.550327	−	0.234857i
$987$	1.93308	+	1.50629i	0.0615306	+	0.0479459i
$988$	−0.154337	−	0.855923i	−0.00491013	−	0.0272305i
$989$		−	23.0829i		−	0.733994i
$990$	0.465634	+	0.754657i	0.0147988	+	0.0239846i
$991$			38.2433i			1.21484i	0.794382	+	0.607419i	$0.207795\pi$
$991$			38.2433i			1.21484i	−0.794382	+	0.607419i	$0.792205\pi$
$992$	17.6820	−	2.34481i	0.561406	−	0.0744477i
$993$	5.49544	+	7.56382i	0.174392	+	0.240031i
$994$	17.6545	+	21.6587i	0.559968	+	0.686972i
$995$	0.372000	+	1.14490i	0.0117932	+	0.0362957i
$996$	−17.3736	+	18.1307i	−0.550504	+	0.574492i
$997$	−22.8031	−	16.5674i	−0.722181	−	0.524696i	0.164899	−	0.986310i	$-0.447270\pi$
$997$	−22.8031	−	16.5674i	−0.722181	−	0.524696i	−0.887080	+	0.461615i	$0.847270\pi$
$998$	2.14764	+	24.0128i	0.0679823	+	0.760112i
$999$	14.2055	−	43.7199i	0.449441	−	1.38324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bp.c.251.66	yes	352
7.6	odd	2	inner	616.2.bp.c.251.65	yes	352
8.3	odd	2	inner	616.2.bp.c.251.6	yes	352
11.5	even	5	inner	616.2.bp.c.27.5	✓	352
56.27	even	2	inner	616.2.bp.c.251.5	yes	352
77.27	odd	10	inner	616.2.bp.c.27.6	yes	352
88.27	odd	10	inner	616.2.bp.c.27.65	yes	352
616.27	even	10	inner	616.2.bp.c.27.66	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bp.c.27.5	✓	352	11.5	even	5	inner
616.2.bp.c.27.6	yes	352	77.27	odd	10	inner
616.2.bp.c.27.65	yes	352	88.27	odd	10	inner
616.2.bp.c.27.66	yes	352	616.27	even	10	inner
616.2.bp.c.251.5	yes	352	56.27	even	2	inner
616.2.bp.c.251.6	yes	352	8.3	odd	2	inner
616.2.bp.c.251.65	yes	352	7.6	odd	2	inner
616.2.bp.c.251.66	yes	352	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bp (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.929869 + 1.06552i) q^{2} +(0.891388 + 1.22689i) q^{3} +(-0.270686 + 1.98160i) q^{4} +(-0.0834388 - 0.256798i) q^{5} +(-0.478407 + 2.09064i) q^{6} +(2.48735 + 0.901708i) q^{7} +(-2.36314 + 1.55420i) q^{8} +(0.216364 - 0.665900i) q^{9} +(0.196038 - 0.327695i) q^{10} +(-3.27175 - 0.543723i) q^{11} +(-2.67249 + 1.43427i) q^{12} +(-2.13341 + 6.56597i) q^{13} +(1.35212 + 3.48881i) q^{14} +(0.240687 - 0.331277i) q^{15} +(-3.85346 - 1.07278i) q^{16} +(3.21212 - 1.04368i) q^{17} +(0.910724 - 0.388659i) q^{18} +(0.0370236 + 0.0509587i) q^{19} +(0.531457 - 0.0958306i) q^{20} +(1.11090 + 3.85548i) q^{21} +(-2.46295 - 3.99172i) q^{22} +3.24436i q^{23} +(-4.01332 - 1.51392i) q^{24} +(3.98610 - 2.89607i) q^{25} +(-8.98000 + 3.83229i) q^{26} +(5.33674 - 1.73401i) q^{27} +(-2.46011 + 4.68485i) q^{28} +(2.31211 - 3.18235i) q^{29} +(0.576791 - 0.0515866i) q^{30} +(-0.974373 + 2.99881i) q^{31} +(-2.44014 - 5.10350i) q^{32} +(-2.24931 - 4.49875i) q^{33} +(4.09892 + 2.45211i) q^{34} +(0.0240153 - 0.713985i) q^{35} +(1.26098 + 0.608996i) q^{36} +(4.81529 - 6.62767i) q^{37} +(-0.0198706 + 0.0868345i) q^{38} +(-9.95742 + 3.23536i) q^{39} +(0.596295 + 0.477170i) q^{40} +(-2.44596 - 3.36658i) q^{41} +(-3.07512 + 4.76878i) q^{42} -7.11479 q^{43} +(1.96306 - 6.33612i) q^{44} -0.189055 q^{45} +(-3.45694 + 3.01683i) q^{46} +(0.494132 - 0.359008i) q^{47} +(-2.11874 - 5.68403i) q^{48} +(5.37385 + 4.48573i) q^{49} +(6.79239 + 1.55432i) q^{50} +(4.14373 + 3.01060i) q^{51} +(-12.4336 - 6.00488i) q^{52} +(-11.7326 - 3.81214i) q^{53} +(6.81010 + 4.07402i) q^{54} +(0.133364 + 0.885548i) q^{55} +(-7.27941 + 1.73499i) q^{56} +(-0.0295182 + 0.0908478i) q^{57} +(5.54083 - 0.495556i) q^{58} +(0.709701 - 0.976819i) q^{59} +(0.591307 + 0.566617i) q^{60} +(2.29148 + 7.05244i) q^{61} +(-4.10135 + 1.75029i) q^{62} +(1.13862 - 1.46123i) q^{63} +(3.16889 - 7.34562i) q^{64} +1.86414 q^{65} +(2.70196 - 6.57995i) q^{66} +7.60314 q^{67} +(1.19868 + 6.64765i) q^{68} +(-3.98047 + 2.89198i) q^{69} +(0.783100 - 0.638324i) q^{70} +(7.10243 - 2.30772i) q^{71} +(0.523646 + 1.90989i) q^{72} +(7.13145 - 9.81560i) q^{73} +(11.5395 - 1.03206i) q^{74} +(7.10632 + 2.30898i) q^{75} +(-0.111001 + 0.0595722i) q^{76} +(-7.64772 - 4.30260i) q^{77} +(-12.7065 - 7.60141i) q^{78} +(9.50920 + 3.08973i) q^{79} +(0.0460400 + 1.07907i) q^{80} +(5.18520 + 3.76727i) q^{81} +(1.31275 - 5.73672i) q^{82} +(7.87395 - 2.55840i) q^{83} +(-7.94071 + 1.15773i) q^{84} +(-0.536032 - 0.737784i) q^{85} +(-6.61582 - 7.58098i) q^{86} +5.96537 q^{87} +(8.57668 - 3.80008i) q^{88} -6.36308i q^{89} +(-0.175797 - 0.201443i) q^{90} +(-11.2271 + 14.4082i) q^{91} +(-6.42901 - 0.878201i) q^{92} +(-4.54776 + 1.47766i) q^{93} +(0.842010 + 0.192679i) q^{94} +(0.00999689 - 0.0137595i) q^{95} +(4.08632 - 7.54298i) q^{96} +(-13.5188 - 4.39251i) q^{97} +(0.217319 + 9.89711i) q^{98} +(-1.06996 + 2.06102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 2 q^{2} - 10 q^{4} - 14 q^{8} + 84 q^{9} - 28 q^{11} - 32 q^{14} + 14 q^{16} - 4 q^{18} - 62 q^{22} - 108 q^{25} - 44 q^{28} + 24 q^{30} - 112 q^{32} + 14 q^{35} + 20 q^{36} - 2 q^{42} + 8 q^{43}+ \cdots + 24 q^{99}+O(q^{100}) \) 352 * q - 2 * q^2 - 10 * q^4 - 14 * q^8 + 84 * q^9 - 28 * q^11 - 32 * q^14 + 14 * q^16 - 4 * q^18 - 62 * q^22 - 108 * q^25 - 44 * q^28 + 24 * q^30 - 112 * q^32 + 14 * q^35 + 20 * q^36 - 2 * q^42 + 8 * q^43 + 22 * q^44 - 38 * q^46 - 34 * q^49 - 24 * q^50 - 36 * q^51 - 120 * q^56 - 36 * q^57 + 30 * q^58 - 136 * q^60 + 86 * q^64 + 8 * q^65 + 24 * q^67 + 52 * q^70 + 30 * q^72 + 94 * q^74 - 68 * q^78 - 60 * q^81 - 128 * q^84 + 34 * q^86 - 38 * q^88 + 78 * q^91 - 8 * q^92 - 100 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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