LMFDB - Embedded newform 220.2.r.b.51.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(51,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,5,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.1
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	220.51
Dual form			220.2.r.b.151.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.478148 - 1.33093i) q^{2} +(2.28716 + 0.743145i) q^{3} +(-1.54275 + 1.27276i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.104528 - 3.39939i) q^{6} +(1.53158 + 4.71372i) q^{7} +(2.43162 + 1.44472i) q^{8} +(2.25181 + 1.63603i) q^{9} +(-1.16913 - 0.795697i) q^{10} +(-2.66078 - 1.97996i) q^{11} +(-4.47437 + 1.76453i) q^{12} +(0.446568 - 0.614648i) q^{13} +(5.54131 - 4.29228i) q^{14} +(2.28716 - 0.743145i) q^{15} +(0.760154 - 3.92711i) q^{16} +(-1.55800 - 2.14440i) q^{17} +(1.10075 - 3.77926i) q^{18} +(-0.730909 + 2.24951i) q^{19} +(-0.500000 + 1.93649i) q^{20} +11.9192i q^{21} +(-1.36294 + 4.48803i) q^{22} -8.25186i q^{23} +(4.48787 + 5.11137i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-1.03158 - 0.300458i) q^{26} +(-0.306194 - 0.421439i) q^{27} +(-8.36228 - 5.32275i) q^{28} +(-2.81641 + 0.915107i) q^{29} +(-2.08268 - 2.68872i) q^{30} +(4.03003 - 5.54687i) q^{31} +(-5.59017 + 0.866025i) q^{32} +(-4.61426 - 6.50584i) q^{33} +(-2.10910 + 3.09893i) q^{34} +(4.00973 + 2.91324i) q^{35} +(-5.55626 + 0.342024i) q^{36} +(0.119477 + 0.367713i) q^{37} +(3.34342 - 0.102807i) q^{38} +(1.47815 - 1.07394i) q^{39} +(2.81641 - 0.260464i) q^{40} +(2.54226 + 0.826031i) q^{41} +(15.8637 - 5.69915i) q^{42} -4.07985 q^{43} +(6.62494 - 0.331966i) q^{44} +2.78339 q^{45} +(-10.9827 + 3.94561i) q^{46} +(1.30290 + 0.423339i) q^{47} +(4.65701 - 8.41704i) q^{48} +(-14.2103 + 10.3244i) q^{49} +(-1.41355 + 0.0434654i) q^{50} +(-1.96980 - 6.06242i) q^{51} +(0.0933582 + 1.51662i) q^{52} +(4.51101 + 3.27744i) q^{53} +(-0.414501 + 0.609032i) q^{54} +(-3.31641 - 0.0378495i) q^{55} +(-3.08580 + 13.6747i) q^{56} +(-3.34342 + 4.60182i) q^{57} +(2.56460 + 3.31089i) q^{58} +(-12.1345 + 3.94274i) q^{59} +(-2.58268 + 4.05750i) q^{60} +(4.02149 + 5.53510i) q^{61} +(-9.30944 - 2.71147i) q^{62} +(-4.26298 + 13.1201i) q^{63} +(3.82555 + 7.02604i) q^{64} -0.759747i q^{65} +(-6.45252 + 9.25200i) q^{66} -0.0695515i q^{67} +(5.13292 + 1.32531i) q^{68} +(6.13233 - 18.8734i) q^{69} +(1.96007 - 6.72962i) q^{70} +(9.22857 + 12.7020i) q^{71} +(3.11192 + 7.23145i) q^{72} +(-3.13942 + 1.02006i) q^{73} +(0.432273 - 0.334837i) q^{74} +(1.41355 - 1.94558i) q^{75} +(-1.73548 - 4.40070i) q^{76} +(5.25776 - 15.5746i) q^{77} +(-2.13611 - 1.45381i) q^{78} +(-0.948113 - 0.688845i) q^{79} +(-1.69332 - 3.62390i) q^{80} +(-2.96747 - 9.13292i) q^{81} +(-0.116187 - 3.77854i) q^{82} +(-1.79301 + 1.30270i) q^{83} +(-15.1703 - 18.3884i) q^{84} +(-2.52090 - 0.819089i) q^{85} +(1.95077 + 5.43000i) q^{86} -7.12165 q^{87} +(-3.60952 - 8.65860i) q^{88} +9.02957 q^{89} +(-1.33087 - 3.70449i) q^{90} +(3.58123 + 1.16361i) q^{91} +(10.5027 + 12.7306i) q^{92} +(13.3395 - 9.69170i) q^{93} +(-0.0595456 - 1.93649i) q^{94} +(0.730909 + 2.24951i) q^{95} +(-13.4292 - 2.17356i) q^{96} +(-11.6194 - 8.44200i) q^{97} +(20.5356 + 13.9763i) q^{98} +(-2.75229 - 8.81161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} + 5 q^{3} - q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 5 q^{8} + 3 q^{9} - 5 q^{10} - q^{11} - 10 q^{12} + 10 q^{13} + 5 q^{14} + 5 q^{15} + 7 q^{16} - 5 q^{17} - 10 q^{18} - 11 q^{19} - 4 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 8 * q + 5 * q^2 + 5 * q^3 - q^4 + 2 * q^5 + q^6 - 3 * q^7 + 5 * q^8 + 3 * q^9 - 5 * q^10 - q^11 - 10 * q^12 + 10 * q^13 + 5 * q^14 + 5 * q^15 + 7 * q^16 - 5 * q^17 - 10 * q^18 - 11 * q^19 - 4 * q^20 + q^22 + 3 * q^24 - 2 * q^25 + 7 * q^26 - 10 * q^27 - 9 * q^28 - 5 * q^29 - 6 * q^30 + 10 * q^31 - 11 * q^33 - 14 * q^34 + 8 * q^35 - 26 * q^36 + 20 * q^37 - 5 * q^38 + 3 * q^39 + 5 * q^40 + 10 * q^41 + 29 * q^42 - 34 * q^43 + 32 * q^44 - 8 * q^45 - 10 * q^46 - 23 * q^49 - 5 * q^50 + 9 * q^51 - 5 * q^52 - 7 * q^53 - 26 * q^54 - 9 * q^55 + 15 * q^56 + 5 * q^57 + 18 * q^58 - 5 * q^59 - 10 * q^60 - 10 * q^61 - q^62 - 23 * q^63 + 11 * q^64 - 17 * q^66 - 15 * q^68 + 15 * q^69 + 15 * q^70 + 90 * q^71 + 10 * q^72 + 5 * q^73 + 35 * q^74 + 5 * q^75 - 18 * q^76 - 14 * q^77 - 21 * q^79 - 7 * q^80 - 10 * q^81 - 2 * q^82 + 19 * q^83 - 30 * q^84 - 30 * q^86 - 18 * q^87 + 43 * q^88 + 20 * q^89 - 15 * q^90 - 10 * q^91 + 25 * q^92 + 11 * q^93 + 11 * q^95 - 36 * q^96 - 44 * q^97 + 50 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

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 $

$2$	−0.478148	−	1.33093i	−0.338101	−	0.941110i
$2$	−0.478148	−	1.33093i	−0.338101	−	0.941110i
$3$	2.28716	+	0.743145i	1.32050	+	0.429055i	0.882665	−	0.470003i	$-0.155747\pi$
$3$	2.28716	+	0.743145i	1.32050	+	0.429055i	0.437830	+	0.899058i	$0.355747\pi$
$4$	−1.54275	+	1.27276i	−0.771375	+	0.636381i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	−0.104528	−	3.39939i	−0.0426736	−	1.38779i
$7$	1.53158	+	4.71372i	0.578883	+	1.78162i	0.622560	+	0.782572i	$0.286093\pi$
$7$	1.53158	+	4.71372i	0.578883	+	1.78162i	−0.0436777	+	0.999046i	$0.513907\pi$
$8$	2.43162	+	1.44472i	0.859707	+	0.510787i
$9$	2.25181	+	1.63603i	0.750602	+	0.545344i
$10$	−1.16913	−	0.795697i	−0.369712	−	0.251621i
$11$	−2.66078	−	1.97996i	−0.802256	−	0.596980i
$11$	−2.66078	−	1.97996i	−0.802256	−	0.596980i
$12$	−4.47437	+	1.76453i	−1.29164	+	0.509376i
$13$	0.446568	−	0.614648i	0.123856	−	0.170473i	−0.742586	−	0.669750i	$-0.766401\pi$
$13$	0.446568	−	0.614648i	0.123856	−	0.170473i	0.866442	+	0.499277i	$0.166401\pi$
$14$	5.54131	−	4.29228i	1.48098	−	1.14716i
$15$	2.28716	−	0.743145i	0.590543	−	0.191879i
$16$	0.760154	−	3.92711i	0.190038	−	0.981777i
$17$	−1.55800	−	2.14440i	−0.377871	−	0.520094i	0.577148	−	0.816639i	$-0.304165\pi$
$17$	−1.55800	−	2.14440i	−0.377871	−	0.520094i	−0.955019	+	0.296545i	$0.904165\pi$
$18$	1.10075	−	3.77926i	0.259449	−	0.890781i
$19$	−0.730909	+	2.24951i	−0.167682	+	0.516072i	−0.999224	−	0.0393897i	$-0.987459\pi$
$19$	−0.730909	+	2.24951i	−0.167682	+	0.516072i	0.831542	+	0.555462i	$0.187459\pi$
$20$	−0.500000	+	1.93649i	−0.111803	+	0.433013i
$21$			11.9192i			2.60099i
$22$	−1.36294	+	4.48803i	−0.290579	+	0.956851i
$23$		−	8.25186i		−	1.72063i	−0.509761	−	0.860316i	$-0.670266\pi$
$23$		−	8.25186i		−	1.72063i	0.509761	−	0.860316i	$-0.329734\pi$
$24$	4.48787	+	5.11137i	0.916084	+	1.04335i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−1.03158	−	0.300458i	−0.202309	−	0.0589247i
$27$	−0.306194	−	0.421439i	−0.0589270	−	0.0811060i
$28$	−8.36228	−	5.32275i	−1.58032	−	1.00591i
$29$	−2.81641	+	0.915107i	−0.522994	+	0.169931i	−0.558604	−	0.829435i	$-0.688663\pi$
$29$	−2.81641	+	0.915107i	−0.522994	+	0.169931i	0.0356097	+	0.999366i	$0.488663\pi$
$30$	−2.08268	−	2.68872i	−0.380243	−	0.490891i
$31$	4.03003	−	5.54687i	0.723815	−	0.996247i	−0.275573	−	0.961280i	$-0.588868\pi$
$31$	4.03003	−	5.54687i	0.723815	−	0.996247i	0.999388	−	0.0349664i	$-0.0111324\pi$
$32$	−5.59017	+	0.866025i	−0.988212	+	0.153093i
$33$	−4.61426	−	6.50584i	−0.803239	−	1.13252i
$34$	−2.10910	+	3.09893i	−0.361707	+	0.531462i
$35$	4.00973	+	2.91324i	0.677768	+	0.492427i
$36$	−5.55626	+	0.342024i	−0.926043	+	0.0570040i
$37$	0.119477	+	0.367713i	0.0196419	+	0.0604517i	0.960397	−	0.278635i	$-0.0898820\pi$
$37$	0.119477	+	0.367713i	0.0196419	+	0.0604517i	−0.940755	+	0.339087i	$0.889882\pi$
$38$	3.34342	−	0.102807i	0.542374	−	0.0166776i
$39$	1.47815	−	1.07394i	0.236693	−	0.171968i
$40$	2.81641	−	0.260464i	0.445313	−	0.0411829i
$41$	2.54226	+	0.826031i	0.397035	+	0.129004i	0.500727	−	0.865605i	$-0.333066\pi$
$41$	2.54226	+	0.826031i	0.397035	+	0.129004i	−0.103693	+	0.994609i	$0.533066\pi$
$42$	15.8637	−	5.69915i	2.44782	−	0.879398i
$43$	−4.07985			−0.622172			−0.311086	−	0.950382i	$-0.600693\pi$
$43$	−4.07985			−0.622172			−0.311086	+	0.950382i	$0.600693\pi$
$44$	6.62494	−	0.331966i	0.998747	−	0.0500458i
$45$	2.78339			0.414923
$46$	−10.9827	+	3.94561i	−1.61930	+	0.581748i
$47$	1.30290	+	0.423339i	0.190048	+	0.0617503i	0.402495	−	0.915422i	$-0.368143\pi$
$47$	1.30290	+	0.423339i	0.190048	+	0.0617503i	−0.212447	+	0.977173i	$0.568143\pi$
$48$	4.65701	−	8.41704i	0.672181	−	1.21489i
$49$	−14.2103	+	10.3244i	−2.03004	+	1.47491i
$50$	−1.41355	+	0.0434654i	−0.199906	+	0.00614693i
$51$	−1.96980	−	6.06242i	−0.275827	−	0.848909i
$52$	0.0933582	+	1.51662i	0.0129464	+	0.210318i
$53$	4.51101	+	3.27744i	0.619634	+	0.450191i	0.852794	−	0.522248i	$-0.174906\pi$
$53$	4.51101	+	3.27744i	0.619634	+	0.450191i	−0.233160	+	0.972439i	$0.574906\pi$
$54$	−0.414501	+	0.609032i	−0.0564064	+	0.0828788i
$55$	−3.31641	−	0.0378495i	−0.447184	−	0.00510362i
$56$	−3.08580	+	13.6747i	−0.412358	+	1.82736i
$57$	−3.34342	+	4.60182i	−0.442847	+	0.609526i
$58$	2.56460	+	3.31089i	0.336749	+	0.434741i
$59$	−12.1345	+	3.94274i	−1.57978	+	0.513301i	−0.961999	−	0.273052i	$-0.911967\pi$
$59$	−12.1345	+	3.94274i	−1.57978	+	0.513301i	−0.617778	+	0.786353i	$0.711967\pi$
$60$	−2.58268	+	4.05750i	−0.333422	+	0.523821i
$61$	4.02149	+	5.53510i	0.514899	+	0.708697i	0.984736	−	0.174056i	$-0.0556873\pi$
$61$	4.02149	+	5.53510i	0.514899	+	0.708697i	−0.469837	+	0.882753i	$0.655687\pi$
$62$	−9.30944	−	2.71147i	−1.18230	−	0.344357i
$63$	−4.26298	+	13.1201i	−0.537085	+	1.65298i
$64$	3.82555	+	7.02604i	0.478193	+	0.878255i
$65$		−	0.759747i		−	0.0942350i
$66$	−6.45252	+	9.25200i	−0.794250	+	1.13884i
$67$		−	0.0695515i		−	0.00849707i	−0.999991	−	0.00424854i	$-0.998648\pi$
$67$		−	0.0695515i		−	0.00849707i	0.999991	−	0.00424854i	$-0.00135236\pi$
$68$	5.13292	+	1.32531i	0.622458	+	0.160718i
$69$	6.13233	−	18.8734i	0.738246	−	2.27209i
$70$	1.96007	−	6.72962i	0.234274	−	0.804344i
$71$	9.22857	+	12.7020i	1.09523	+	1.50746i	0.841559	+	0.540164i	$0.181638\pi$
$71$	9.22857	+	12.7020i	1.09523	+	1.50746i	0.253671	+	0.967291i	$0.418362\pi$
$72$	3.11192	+	7.23145i	0.366743	+	0.852234i
$73$	−3.13942	+	1.02006i	−0.367441	+	0.119389i	−0.486917	−	0.873448i	$-0.661879\pi$
$73$	−3.13942	+	1.02006i	−0.367441	+	0.119389i	0.119476	+	0.992837i	$0.461879\pi$
$74$	0.432273	−	0.334837i	0.0502507	−	0.0389240i
$75$	1.41355	−	1.94558i	0.163222	−	0.224656i
$76$	−1.73548	−	4.40070i	−0.199073	−	0.504795i
$77$	5.25776	−	15.5746i	0.599177	−	1.77490i
$78$	−2.13611	−	1.45381i	−0.241867	−	0.164612i
$79$	−0.948113	−	0.688845i	−0.106671	−	0.0775011i	0.533171	−	0.846008i	$-0.321000\pi$
$79$	−0.948113	−	0.688845i	−0.106671	−	0.0775011i	−0.639842	+	0.768506i	$0.721000\pi$
$80$	−1.69332	−	3.62390i	−0.189319	−	0.405165i
$81$	−2.96747	−	9.13292i	−0.329718	−	1.01477i
$82$	−0.116187	−	3.77854i	−0.0128307	−	0.417270i
$83$	−1.79301	+	1.30270i	−0.196809	+	0.142990i	−0.681825	−	0.731515i	$-0.738814\pi$
$83$	−1.79301	+	1.30270i	−0.196809	+	0.142990i	0.485017	+	0.874505i	$0.338814\pi$
$84$	−15.1703	−	18.3884i	−1.65522	−	2.00634i
$85$	−2.52090	−	0.819089i	−0.273430	−	0.0888427i
$86$	1.95077	+	5.43000i	0.210357	+	0.585532i
$87$	−7.12165			−0.763521
$88$	−3.60952	−	8.65860i	−0.384776	−	0.923010i
$89$	9.02957			0.957132			0.478566	−	0.878052i	$-0.341157\pi$
$89$	9.02957			0.957132			0.478566	+	0.878052i	$0.341157\pi$
$90$	−1.33087	−	3.70449i	−0.140286	−	0.390488i
$91$	3.58123	+	1.16361i	0.375415	+	0.121980i
$92$	10.5027	+	12.7306i	1.09498	+	1.32725i
$93$	13.3395	−	9.69170i	1.38324	−	1.00498i
$94$	−0.0595456	−	1.93649i	−0.00614165	−	0.199734i
$95$	0.730909	+	2.24951i	0.0749897	+	0.230795i
$96$	−13.4292	−	2.17356i	−1.37061	−	0.221838i
$97$	−11.6194	−	8.44200i	−1.17977	−	0.857155i	−0.187627	−	0.982240i	$-0.560080\pi$
$97$	−11.6194	−	8.44200i	−1.17977	−	0.857155i	−0.992146	+	0.125085i	$0.960080\pi$
$98$	20.5356	+	13.9763i	2.07441	+	1.41182i
$99$	−2.75229	−	8.81161i	−0.276616	−	0.885600i
$100$	0.733733	+	1.86055i	0.0733733	+	0.186055i
$101$	−4.21743	+	5.80479i	−0.419649	+	0.577598i	−0.965539	−	0.260259i	$-0.916192\pi$
$101$	−4.21743	+	5.80479i	−0.419649	+	0.577598i	0.545889	+	0.837857i	$0.316192\pi$
$102$	−7.12681	+	5.52040i	−0.705659	+	0.546601i
$103$	8.74658	−	2.84194i	0.861827	−	0.280024i	0.155435	−	0.987846i	$-0.450322\pi$
$103$	8.74658	−	2.84194i	0.861827	−	0.280024i	0.706391	+	0.707822i	$0.250322\pi$
$104$	1.97388	−	0.849423i	0.193555	−	0.0832928i
$105$	7.00595	+	9.64286i	0.683711	+	0.941047i
$106$	2.20511	−	7.57093i	0.214180	−	0.735354i
$107$	3.17807	−	9.78109i	0.307235	−	0.945573i	−0.671598	−	0.740916i	$-0.734392\pi$
$107$	3.17807	−	9.78109i	0.307235	−	0.945573i	0.978834	−	0.204658i	$-0.0656081\pi$
$108$	1.00877	+	0.260464i	0.0970691	+	0.0250631i
$109$		−	10.4527i		−	1.00118i	−0.865683	−	0.500592i	$-0.833116\pi$
$109$		−	10.4527i		−	1.00118i	0.865683	−	0.500592i	$-0.166884\pi$
$110$	1.53536	+	4.43201i	0.146391	+	0.422575i
$111$			0.929809i			0.0882536i
$112$	19.6755	−	2.43153i	1.85916	−	0.229758i
$113$	1.12553	−	3.46402i	0.105881	−	0.325867i	−0.884055	−	0.467382i	$-0.845197\pi$
$113$	1.12553	−	3.46402i	0.105881	−	0.325867i	0.989936	+	0.141515i	$0.0451972\pi$
$114$	7.72335	+	2.24951i	0.723358	+	0.210686i
$115$	−4.85032	−	6.67590i	−0.452295	−	0.622531i
$116$	3.18030	−	4.99640i	0.295284	−	0.463904i
$117$	2.01117	−	0.653469i	0.185933	−	0.0604132i
$118$	11.0496	+	14.2650i	1.01720	+	1.31320i
$119$	7.72191	−	10.6283i	0.707866	−	0.974294i
$120$	6.63515	+	1.49728i	0.605704	+	0.136682i
$121$	3.15954	+	10.5365i	0.287231	+	0.957861i
$122$	5.44397	−	7.99891i	0.492874	−	0.724188i
$123$	5.20071	+	3.77854i	0.468932	+	0.340699i
$124$	0.842507	+	13.6867i	0.0756593	+	1.22910i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	19.5003	−	0.599617i	1.73722	−	0.0534181i
$127$	−5.41355	+	3.93317i	−0.480374	+	0.349012i	−0.801471	−	0.598034i	$-0.795949\pi$
$127$	−5.41355	+	3.93317i	−0.480374	+	0.349012i	0.321096	+	0.947047i	$0.395949\pi$
$128$	7.52199	−	8.45102i	0.664856	−	0.746971i
$129$	−9.33129	−	3.03192i	−0.821575	−	0.266946i
$130$	−1.01117	+	0.363271i	−0.0886855	+	0.0318610i
$131$	−11.2581			−0.983623			−0.491811	−	0.870702i	$-0.663665\pi$
$131$	−11.2581			−0.983623			−0.491811	+	0.870702i	$0.663665\pi$
$132$	15.3990	+	4.16403i	1.34031	+	0.362432i
$133$	−11.7230			−1.01651
$134$	−0.0925682	+	0.0332559i	−0.00799668	+	0.00287287i
$135$	−0.495432	−	0.160975i	−0.0426400	−	0.0138546i
$136$	−0.690393	−	7.46525i	−0.0592007	−	0.640140i
$137$	−1.47155	+	1.06914i	−0.125723	+	0.0913428i	−0.648870	−	0.760900i	$-0.724758\pi$
$137$	−1.47155	+	1.06914i	−0.125723	+	0.0913428i	0.523147	+	0.852243i	$0.324758\pi$
$138$	−28.0513	+	0.862555i	−2.38788	+	0.0734255i
$139$	2.39044	+	7.35701i	0.202754	+	0.624013i	0.999798	+	0.0200919i	$0.00639587\pi$
$139$	2.39044	+	7.35701i	0.202754	+	0.624013i	−0.797044	+	0.603921i	$0.793604\pi$
$140$	−9.89386	+	0.609032i	−0.836184	+	0.0514726i
$141$	2.66535	+	1.93649i	0.224463	+	0.163082i
$142$	12.4929	−	18.3560i	1.04838	−	1.54040i
$143$	−2.40520	+	0.751261i	−0.201133	+	0.0628236i
$144$	8.13660	−	7.59945i	0.678050	−	0.633287i
$145$	−1.74064	+	2.39578i	−0.144552	+	0.198959i
$146$	2.85873	+	3.69061i	0.236590	+	0.305437i
$147$	−40.1737	+	13.0532i	−3.31347	+	1.07661i
$148$	−0.652335	−	0.415223i	−0.0536216	−	0.0341311i
$149$	3.56509	+	4.90693i	0.292064	+	0.401991i	0.929683	−	0.368360i	$-0.120081\pi$
$149$	3.56509	+	4.90693i	0.292064	+	0.401991i	−0.637619	+	0.770351i	$0.720081\pi$
$150$	−3.26531	−	0.951057i	−0.266612	−	0.0776534i
$151$	6.28651	−	19.3479i	0.511589	−	1.57451i	−0.277815	−	0.960635i	$-0.589610\pi$
$151$	6.28651	−	19.3479i	0.511589	−	1.57451i	0.789404	−	0.613874i	$-0.210390\pi$
$152$	−5.02721	+	4.41398i	−0.407761	+	0.358021i
$153$		−	7.37772i		−	0.596453i
$154$	−23.2427	+	0.449273i	−1.87295	+	0.0362035i
$155$		−	6.85630i		−	0.550712i
$156$	−0.913545	+	3.53815i	−0.0731422	+	0.283278i
$157$	−4.00043	+	12.3120i	−0.319269	+	0.982608i	0.654693	+	0.755895i	$0.272798\pi$
$157$	−4.00043	+	12.3120i	−0.319269	+	0.982608i	−0.973962	+	0.226713i	$0.927202\pi$
$158$	−0.463466	+	1.59124i	−0.0368714	+	0.126592i
$159$	7.88180	+	10.8484i	0.625067	+	0.860332i
$160$	−4.01351	+	3.98645i	−0.317295	+	0.315156i
$161$	38.8969	−	12.6384i	3.06551	−	0.996044i
$162$	−10.7364	+	8.31637i	−0.843531	+	0.653396i
$163$	4.11115	−	5.65851i	0.322010	−	0.443209i	−0.617069	−	0.786909i	$-0.711680\pi$
$163$	4.11115	−	5.65851i	0.322010	−	0.443209i	0.939080	+	0.343700i	$0.111680\pi$
$164$	−4.97341	+	1.96134i	−0.388358	+	0.153155i
$165$	−7.55705	−	2.55114i	−0.588315	−	0.198606i
$166$	2.59112	+	1.76349i	0.201110	+	0.136873i
$167$	11.1765	+	8.12017i	0.864860	+	0.628358i	0.929203	−	0.369570i	$-0.120495\pi$
$167$	11.1765	+	8.12017i	0.864860	+	0.628358i	−0.0643425	+	0.997928i	$0.520495\pi$
$168$	−17.2200	+	28.9830i	−1.32855	+	2.23609i
$169$	3.83885	+	11.8148i	0.295296	+	0.908828i
$170$	0.115211	+	3.74678i	0.00883625	+	0.287365i
$171$	−5.32614	+	3.86966i	−0.407300	+	0.295921i
$172$	6.29419	−	5.19268i	0.479928	−	0.395938i
$173$	−14.0625	−	4.56919i	−1.06915	−	0.347389i	−0.278996	−	0.960292i	$-0.590002\pi$
$173$	−14.0625	−	4.56919i	−1.06915	−	0.347389i	−0.790158	+	0.612903i	$0.790002\pi$
$174$	3.40520	+	9.47841i	0.258147	+	0.718557i
$175$	4.95630			0.374661
$176$	−9.79811	+	8.94411i	−0.738560	+	0.674188i
$177$	−30.6836			−2.30632
$178$	−4.31747	−	12.0177i	−0.323608	−	0.900766i
$179$	8.58123	+	2.78821i	0.641391	+	0.208401i	0.611615	−	0.791156i	$-0.290520\pi$
$179$	8.58123	+	2.78821i	0.641391	+	0.208401i	0.0297769	+	0.999557i	$0.490520\pi$
$180$	−4.29407	+	3.54259i	−0.320061	+	0.264049i
$181$	−13.1639	+	9.56414i	−0.978466	+	0.710897i	−0.957365	−	0.288880i	$-0.906717\pi$
$181$	−13.1639	+	9.56414i	−0.978466	+	0.710897i	−0.0211005	+	0.999777i	$0.506717\pi$
$182$	−0.163670	−	5.32275i	−0.0121320	−	0.394548i
$183$	5.08442	+	15.6482i	0.375851	+	1.15675i
$184$	11.9217	−	20.0654i	0.878877	−	1.47924i
$185$	0.312795	+	0.227259i	0.0229972	+	0.0167084i
$186$	−19.2772	−	13.1198i	−1.41347	−	0.961994i
$187$	−0.100325	+	8.79057i	−0.00733648	+	0.642830i
$188$	−2.54886	+	1.00518i	−0.185895	+	0.0733103i
$189$	1.51759	−	2.08878i	0.110388	−	0.151936i
$190$	2.64445	−	2.04839i	0.191849	−	0.148606i
$191$	2.23308	−	0.725571i	0.161580	−	0.0525005i	−0.227110	−	0.973869i	$-0.572928\pi$
$191$	2.23308	−	0.725571i	0.161580	−	0.0525005i	0.388690	+	0.921369i	$0.372928\pi$
$192$	3.52829	+	18.9126i	0.254632	+	1.36490i
$193$	4.16893	+	5.73804i	0.300086	+	0.413033i	0.932258	−	0.361795i	$-0.117836\pi$
$193$	4.16893	+	5.73804i	0.300086	+	0.413033i	−0.632171	+	0.774829i	$0.717836\pi$
$194$	−5.67991	+	19.5011i	−0.407794	+	1.40010i
$195$	0.564602	−	1.73767i	0.0404320	−	0.124437i
$196$	8.78243	−	34.0142i	0.627317	−	2.42959i
$197$			0.673611i			0.0479928i	0.999712	+	0.0239964i	$0.00763902\pi$
$197$			0.673611i			0.0479928i	−0.999712	+	0.0239964i	$0.992361\pi$
$198$	−10.4116	+	7.87636i	−0.739923	+	0.559749i
$199$			0.733078i			0.0519665i	0.999662	+	0.0259833i	$0.00827166\pi$
$199$			0.733078i			0.0519665i	−0.999662	+	0.0259833i	$0.991728\pi$
$200$	2.12543	−	1.86616i	0.150290	−	0.131958i
$201$	0.0516869	−	0.159076i	0.00364571	−	0.0112203i
$202$	9.74232	+	2.83755i	0.685467	+	0.199650i
$203$	−8.62711	−	11.8742i	−0.605504	−	0.833405i
$204$	10.7549	+	6.84571i	0.752996	+	0.479296i
$205$	2.54226	−	0.826031i	0.177559	−	0.0576925i
$206$	−7.96458	−	10.2822i	−0.554919	−	0.716397i
$207$	13.5003	−	18.5816i	0.938337	−	1.29151i
$208$	−2.07433	−	2.22095i	−0.143829	−	0.153995i
$209$	6.39872	−	4.53828i	0.442609	−	0.313920i
$210$	9.48410	−	13.9351i	0.654465	−	0.961616i
$211$	15.3093	+	11.1228i	1.05393	+	0.765728i	0.972957	−	0.230988i	$-0.0741958\pi$
$211$	15.3093	+	11.1228i	1.05393	+	0.765728i	0.0809775	+	0.996716i	$0.474196\pi$
$212$	−11.1307	+	0.685171i	−0.764463	+	0.0470577i
$213$	11.6678	+	35.9098i	0.799465	+	2.46050i
$214$	−14.5375	+	0.447017i	−0.993765	+	0.0305575i
$215$	−3.30067	+	2.39808i	−0.225104	+	0.163548i
$216$	−0.135683	−	1.46715i	−0.00923204	−	0.0998266i
$217$	32.3187	+	10.5010i	2.19393	+	0.712853i
$218$	−13.9118	+	4.99792i	−0.942224	+	0.338502i
$219$	−7.93842			−0.536429
$220$	5.16456	−	4.16261i	0.348195	−	0.280643i
$221$	−2.01381			−0.135463
$222$	1.23751	−	0.444586i	0.0830563	−	0.0298387i
$223$	17.7048	+	5.75263i	1.18560	+	0.385225i	0.834444	−	0.551092i	$-0.185789\pi$
$223$	17.7048	+	5.75263i	1.18560	+	0.385225i	0.351156	+	0.936317i	$0.385789\pi$
$224$	−12.6440	−	25.0241i	−0.844812	−	1.67199i
$225$	2.25181	−	1.63603i	0.150120	−	0.109069i
$226$	−5.14853	+	0.158313i	−0.342475	+	0.0105308i
$227$	−5.40658	−	16.6397i	−0.358847	−	1.10442i	−0.953745	−	0.300617i	$-0.902807\pi$
$227$	−5.40658	−	16.6397i	−0.358847	−	1.10442i	0.594898	−	0.803801i	$-0.297193\pi$
$228$	−0.698965	−	11.3548i	−0.0462901	−	0.751993i
$229$	−11.5358	−	8.38124i	−0.762306	−	0.553848i	0.137311	−	0.990528i	$-0.456154\pi$
$229$	−11.5358	−	8.38124i	−0.762306	−	0.553848i	−0.899617	+	0.436680i	$0.856154\pi$
$230$	−6.56598	+	9.64751i	−0.432948	+	0.636138i
$231$	23.5996	−	31.7145i	1.55274	−	2.08666i
$232$	−8.17051	−	1.84374i	−0.536420	−	0.121048i
$233$	−0.364886	+	0.502223i	−0.0239045	+	0.0329017i	−0.820802	−	0.571213i	$-0.806473\pi$
$233$	−0.364886	+	0.502223i	−0.0239045	+	0.0329017i	0.796897	+	0.604115i	$0.206473\pi$
$234$	−1.83136	−	2.36427i	−0.119720	−	0.154557i
$235$	1.30290	−	0.423339i	0.0849920	−	0.0276156i
$236$	13.7023	−	21.5270i	0.891946	−	1.40129i
$237$	−1.65658	−	2.28009i	−0.107606	−	0.148108i
$238$	−17.8377	−	5.19543i	−1.15625	−	0.336770i
$239$	−7.02906	+	21.6332i	−0.454672	+	1.39934i	0.416848	+	0.908976i	$0.363135\pi$
$239$	−7.02906	+	21.6332i	−0.454672	+	1.39934i	−0.871520	+	0.490360i	$0.836865\pi$
$240$	−1.17981	−	9.54684i	−0.0761566	−	0.616246i
$241$		−	0.216356i		−	0.0139367i	−0.999976	−	0.00696835i	$-0.997782\pi$
$241$		−	0.216356i		−	0.0139367i	0.999976	−	0.00696835i	$-0.00221811\pi$
$242$	12.5126	−	9.24312i	0.804339	−	0.594170i
$243$		−	21.5310i		−	1.38121i
$244$	−13.2490	−	3.42088i	−0.848181	−	0.219000i
$245$	−5.42784	+	16.7052i	−0.346772	+	1.06725i
$246$	2.54226	−	8.72848i	0.162089	−	0.556508i
$247$	1.05626	+	1.45381i	0.0672079	+	0.0925038i
$248$	17.8132	−	7.66558i	1.13114	−	0.486765i
$249$	−5.06901	+	1.64702i	−0.321235	+	0.104376i
$250$	−1.11803	+	0.866025i	−0.0707107	+	0.0547723i
$251$	−10.1492	+	13.9691i	−0.640609	+	0.881723i	−0.998648	−	0.0519837i	$-0.983446\pi$
$251$	−10.1492	+	13.9691i	−0.640609	+	0.881723i	0.358039	+	0.933707i	$0.383446\pi$
$252$	−10.1221	−	25.6668i	−0.637629	−	1.61685i
$253$	−16.3383	+	21.9564i	−1.02718	+	1.38039i
$254$	7.82325	+	5.32441i	0.490874	+	0.334083i
$255$	−5.15701	−	3.74678i	−0.322944	−	0.234633i
$256$	−14.8443	−	5.97041i	−0.927771	−	0.373151i
$257$	2.58735	+	7.96303i	0.161394	+	0.496720i	0.998753	−	0.0499341i	$-0.0159011\pi$
$257$	2.58735	+	7.96303i	0.161394	+	0.496720i	−0.837358	+	0.546654i	$0.815901\pi$
$258$	0.426461	+	13.8690i	0.0265503	+	0.863447i
$259$	−1.55031	+	1.12636i	−0.0963314	+	0.0699888i
$260$	0.966977	+	1.17210i	0.0599694	+	0.0726905i
$261$	−7.83915	−	2.54710i	−0.485231	−	0.157661i
$262$	5.38302	+	14.9837i	0.332564	+	0.925697i
$263$	−26.1341			−1.61150			−0.805749	−	0.592257i	$-0.798237\pi$
$263$	−26.1341			−1.61150			−0.805749	+	0.592257i	$0.798237\pi$
$264$	−1.82098	−	22.4860i	−0.112073	−	1.38392i
$265$	5.57591			0.342525
$266$	5.60532	+	15.6025i	0.343684	+	0.956649i
$267$	20.6521	+	6.71028i	1.26389	+	0.410662i
$268$	0.0885226	+	0.107301i	0.00540738	+	0.00655443i
$269$	−13.4462	+	9.76926i	−0.819832	+	0.595643i	−0.916664	−	0.399658i	$-0.869129\pi$
$269$	−13.4462	+	9.76926i	−0.819832	+	0.595643i	0.0968327	+	0.995301i	$0.469129\pi$
$270$	0.0226423	+	0.736355i	0.00137797	+	0.0448131i
$271$	8.40677	+	25.8734i	0.510675	+	1.57169i	0.791017	+	0.611795i	$0.209552\pi$
$271$	8.40677	+	25.8734i	0.510675	+	1.57169i	−0.280342	+	0.959900i	$0.590448\pi$
$272$	−9.60562	+	4.48836i	−0.582426	+	0.272147i
$273$	7.32614	+	5.32275i	0.443398	+	0.322147i
$274$	2.12657	+	1.44732i	0.128471	+	0.0874356i
$275$	−2.70528	+	1.91872i	−0.163134	+	0.115703i
$276$	14.5607	+	36.9219i	0.876449	+	2.22244i
$277$	9.54061	−	13.1315i	0.573240	−	0.788997i	−0.419694	−	0.907666i	$-0.637863\pi$
$277$	9.54061	−	13.1315i	0.573240	−	0.788997i	0.992934	+	0.118669i	$0.0378626\pi$
$278$	8.64868	−	6.69924i	0.518713	−	0.401794i
$279$	18.1497	−	5.89720i	1.08660	−	0.353056i
$280$	5.54131	+	12.8768i	0.331156	+	0.769538i
$281$	−15.2651	−	21.0106i	−0.910639	−	1.25339i	−0.966948	−	0.254973i	$-0.917933\pi$
$281$	−15.2651	−	21.0106i	−0.910639	−	1.25339i	0.0563096	−	0.998413i	$-0.482067\pi$
$282$	1.30290	−	4.47333i	0.0775868	−	0.266383i
$283$	−0.400142	+	1.23151i	−0.0237860	+	0.0732057i	−0.962245	−	0.272185i	$-0.912254\pi$
$283$	−0.400142	+	1.23151i	−0.0237860	+	0.0732057i	0.938459	+	0.345391i	$0.112254\pi$
$284$	−30.4041	−	7.85029i	−1.80415	−	0.465829i
$285$			5.68817i			0.336938i
$286$	2.14992	+	2.84194i	0.127127	+	0.168047i
$287$			13.2486i			0.782042i
$288$	−14.0048	−	7.19558i	−0.825242	−	0.424004i
$289$	3.08219	−	9.48600i	0.181305	−	0.558000i
$290$	4.02090	+	1.17113i	0.236115	+	0.0687710i
$291$	−20.3019	−	27.9431i	−1.19012	−	1.63806i
$292$	3.54505	−	5.56943i	0.207458	−	0.325926i
$293$	11.8883	−	3.86275i	0.694523	−	0.225664i	0.0595804	−	0.998224i	$-0.481024\pi$
$293$	11.8883	−	3.86275i	0.694523	−	0.225664i	0.634943	+	0.772559i	$0.281024\pi$
$294$	36.5819	+	47.2271i	2.13350	+	2.75434i
$295$	−7.49953	+	10.3222i	−0.436640	+	0.600983i
$296$	−0.240721	+	1.06675i	−0.0139916	+	0.0620036i
$297$	−0.0197168	+	1.72761i	−0.00114409	+	0.100246i
$298$	4.82614	−	7.09112i	0.279571	−	0.410778i
$299$	−5.07199	−	3.68502i	−0.293321	−	0.213110i
$300$	0.295511	+	4.80065i	0.0170614	+	0.277166i
$301$	−6.24862	−	19.2313i	−0.360164	−	1.10847i
$302$	−28.7566	+	0.884241i	−1.65475	+	0.0508824i
$303$	−13.9597	+	10.1423i	−0.801966	+	0.582663i
$304$	8.27845	+	4.58033i	0.474802	+	0.262700i
$305$	6.50690	+	2.11422i	0.372584	+	0.121060i
$306$	−9.81923	+	3.52764i	−0.561328	+	0.201662i
$307$	19.5223			1.11420			0.557098	−	0.830447i	$-0.311915\pi$
$307$	19.5223			1.11420			0.557098	+	0.830447i	$0.311915\pi$
$308$	11.7114	+	30.7196i	0.667320	+	1.75041i
$309$	22.1169			1.25818
$310$	−9.12526	+	3.27833i	−0.518280	+	0.186196i
$311$	−5.77951	−	1.87788i	−0.327726	−	0.106485i	0.140533	−	0.990076i	$-0.455118\pi$
$311$	−5.77951	−	1.87788i	−0.327726	−	0.106485i	−0.468259	+	0.883591i	$0.655118\pi$
$312$	5.14583	−	0.475891i	0.291326	−	0.0269420i
$313$	−7.34624	+	5.33736i	−0.415234	+	0.301685i	−0.775717	−	0.631080i	$-0.782612\pi$
$313$	−7.34624	+	5.33736i	−0.415234	+	0.301685i	0.360483	+	0.932766i	$0.382612\pi$
$314$	18.2993	−	0.562687i	1.03269	−	0.0317543i
$315$	4.26298	+	13.1201i	0.240192	+	0.739234i
$316$	2.33944	−	0.144008i	0.131604	−	0.00810107i
$317$	−20.4878	−	14.8853i	−1.15071	−	0.836040i	−0.162135	−	0.986769i	$-0.551838\pi$
$317$	−20.4878	−	14.8853i	−1.15071	−	0.836040i	−0.988575	+	0.150729i	$0.951838\pi$
$318$	10.6698	−	15.6772i	0.598330	−	0.879136i
$319$	9.30573	+	3.14147i	0.521021	+	0.175888i
$320$	7.22473	+	3.43558i	0.403875	+	0.192055i
$321$	14.5375	−	20.0092i	0.811406	−	1.11680i
$322$	−35.4193	−	45.7261i	−1.97384	−	2.54822i
$323$	5.96261	−	1.93737i	0.331768	−	0.107798i
$324$	16.2021	+	10.3129i	0.900116	+	0.572941i
$325$	−0.446568	−	0.614648i	−0.0247711	−	0.0340946i
$326$	−9.49682	−	2.76605i	−0.525980	−	0.153197i
$327$	7.76785	−	23.9070i	0.429563	−	1.32206i
$328$	4.98843	+	5.68146i	0.275440	+	0.313706i
$329$			6.78989i			0.374339i
$330$	0.217994	+	11.2777i	0.0120002	+	0.620818i
$331$			10.8522i			0.596490i	0.954489	+	0.298245i	$0.0964012\pi$
$331$			10.8522i			0.596490i	−0.954489	+	0.298245i	$0.903599\pi$
$332$	1.10814	−	4.29181i	0.0608172	−	0.235544i
$333$	−0.332551	+	1.02349i	−0.0182237	+	0.0560868i
$334$	5.46339	−	18.7577i	0.298943	−	1.02638i
$335$	−0.0408814	−	0.0562684i	−0.00223359	−	0.00307427i
$336$	46.8081	+	9.06045i	2.55359	+	0.494288i
$337$	11.5810	−	3.76291i	0.630859	−	0.204979i	0.0239035	−	0.999714i	$-0.492391\pi$
$337$	11.5810	−	3.76291i	0.630859	−	0.204979i	0.606956	+	0.794736i	$0.292391\pi$
$338$	13.8891	−	10.7584i	0.755467	−	0.585182i
$339$	5.14853	−	7.08635i	0.279630	−	0.384878i
$340$	4.93162	−	1.94485i	0.267455	−	0.105474i
$341$	−21.7056	+	6.77972i	−1.17542	+	0.367142i
$342$	7.69693	+	5.23844i	0.416202	+	0.283263i
$343$	−42.3622	−	30.7779i	−2.28734	−	1.66185i
$344$	−9.92065	−	5.89426i	−0.534886	−	0.317797i
$345$	−6.13233	−	18.8734i	−0.330154	−	1.01611i
$346$	0.642688	+	20.9010i	0.0345511	+	1.12364i
$347$	4.44591	−	3.23015i	0.238669	−	0.173403i	−0.462021	−	0.886869i	$-0.652876\pi$
$347$	4.44591	−	3.23015i	0.238669	−	0.173403i	0.700690	+	0.713466i	$0.252876\pi$
$348$	10.9869	−	9.06416i	0.588961	−	0.485890i
$349$	6.78828	+	2.20565i	0.363368	+	0.118065i	0.485010	−	0.874509i	$-0.338816\pi$
$349$	6.78828	+	2.20565i	0.363368	+	0.118065i	−0.121642	+	0.992574i	$0.538816\pi$
$350$	−2.36984	−	6.59648i	−0.126673	−	0.352597i
$351$	−0.395773			−0.0211248
$352$	16.5889	+	8.76399i	0.884193	+	0.467122i
$353$	18.1264			0.964770			0.482385	−	0.875959i	$-0.339771\pi$
$353$	18.1264			0.964770			0.482385	+	0.875959i	$0.339771\pi$
$354$	14.6713	+	40.8378i	0.779771	+	2.17050i
$355$	14.9321	+	4.85175i	0.792516	+	0.257504i
$356$	−13.9304	+	11.4925i	−0.738308	+	0.609101i
$357$	25.5596	−	18.5702i	1.35276	−	0.982837i
$358$	−0.392181	−	12.7542i	−0.0207274	−	0.674080i
$359$	−1.75703	−	5.40758i	−0.0927324	−	0.285401i	0.893924	−	0.448219i	$-0.147942\pi$
$359$	−1.75703	−	5.40758i	−0.0927324	−	0.285401i	−0.986656	+	0.162818i	$0.947942\pi$
$360$	6.76814	+	4.02122i	0.356712	+	0.211937i
$361$	10.8453	+	7.87955i	0.570804	+	0.414713i
$362$	19.0235	+	12.9472i	0.999853	+	0.680488i
$363$	−0.603739	+	26.4466i	−0.0316881	+	1.38809i
$364$	−7.00595	+	2.76289i	−0.367211	+	0.144815i
$365$	−1.94027	+	2.67055i	−0.101558	+	0.139783i
$366$	18.3956	−	14.2492i	0.961554	−	0.744816i
$367$	15.7671	−	5.12303i	0.823034	−	0.267420i	0.132925	−	0.991126i	$-0.457563\pi$
$367$	15.7671	−	5.12303i	0.823034	−	0.267420i	0.690108	+	0.723706i	$0.257563\pi$
$368$	−32.4059	−	6.27268i	−1.68928	−	0.326986i
$369$	4.37327	+	6.01929i	0.227663	+	0.313352i
$370$	0.152904	−	0.524972i	0.00794909	−	0.0272920i
$371$	−8.53995	+	26.2833i	−0.443372	+	1.36456i
$372$	−8.24425	+	31.9298i	−0.427444	+	1.65549i
$373$			10.8750i			0.563088i	0.959548	+	0.281544i	$0.0908465\pi$
$373$			10.8750i			0.563088i	−0.959548	+	0.281544i	$0.909154\pi$
$374$	11.7476	−	4.06966i	0.607454	−	0.210437i
$375$		−	2.40487i		−	0.124187i
$376$	2.55656	+	2.91173i	0.131844	+	0.150161i
$377$	−0.695250	+	2.13976i	−0.0358072	+	0.110203i
$378$	−3.50565	−	1.02106i	−0.180311	−	0.0525175i
$379$	−4.96011	−	6.82701i	−0.254784	−	0.350680i	0.662396	−	0.749154i	$-0.269540\pi$
$379$	−4.96011	−	6.82701i	−0.254784	−	0.350680i	−0.917180	+	0.398474i	$0.869540\pi$
$380$	−3.99070	−	2.54015i	−0.204718	−	0.130307i
$381$	−15.3046	+	4.97276i	−0.784078	+	0.254762i
$382$	−2.03343	−	2.62514i	−0.104039	−	0.134314i
$383$	10.4119	−	14.3308i	0.532023	−	0.732267i	−0.455414	−	0.890280i	$-0.650509\pi$
$383$	10.4119	−	14.3308i	0.532023	−	0.732267i	0.987437	+	0.158013i	$0.0505087\pi$
$384$	23.4844	−	13.7389i	1.19843	−	0.701112i
$385$	−4.90093	−	15.6906i	−0.249775	−	0.799666i
$386$	5.64357	−	8.29219i	0.287250	−	0.422061i
$387$	−9.18704	−	6.67477i	−0.467003	−	0.339298i
$388$	28.6705	−	1.76486i	1.45552	−	0.0895971i
$389$	5.80134	+	17.8547i	0.294139	+	0.905268i	0.983509	+	0.180858i	$0.0578876\pi$
$389$	5.80134	+	17.8547i	0.294139	+	0.905268i	−0.689370	+	0.724410i	$0.742112\pi$
$390$	−2.58268	+	0.0794152i	−0.130779	+	0.00402134i
$391$	−17.6953	+	12.8564i	−0.894891	+	0.650176i
$392$	−49.4698	+	4.57501i	−2.49860	+	0.231073i
$393$	−25.7491	−	8.36638i	−1.29887	−	0.422028i
$394$	0.896529	−	0.322085i	0.0451665	−	0.0162264i
$395$	−1.17193			−0.0589663
$396$	15.4612	+	10.0911i	0.776954	+	0.507097i
$397$	24.1271			1.21091			0.605453	−	0.795881i	$-0.292992\pi$
$397$	24.1271			1.21091			0.605453	+	0.795881i	$0.292992\pi$
$398$	0.975676	−	0.350520i	0.0489062	−	0.0175700i
$399$	−26.8124	−	8.71188i	−1.34230	−	0.436139i
$400$	−3.50000	−	1.93649i	−0.175000	−	0.0968246i
$401$	10.2112	−	7.41891i	0.509925	−	0.370482i	−0.302870	−	0.953032i	$-0.597945\pi$
$401$	10.2112	−	7.41891i	0.509925	−	0.370482i	0.812795	+	0.582549i	$0.197945\pi$
$402$	−0.236433	+	0.00727012i	−0.0117922	+	0.000362600i
$403$	−1.60969	−	4.95411i	−0.0801842	−	0.246782i
$404$	−0.881682	−	14.3231i	−0.0438653	−	0.712602i
$405$	−7.76893	−	5.64445i	−0.386041	−	0.280475i
$406$	−11.6787	+	17.1597i	−0.579604	+	0.851621i
$407$	0.410153	−	1.21496i	0.0203305	−	0.0602236i
$408$	3.96872	−	17.5873i	0.196481	−	0.870702i
$409$	−3.26373	+	4.49214i	−0.161381	+	0.222122i	−0.882048	−	0.471159i	$-0.843836\pi$
$409$	−3.26373	+	4.49214i	−0.161381	+	0.222122i	0.720667	+	0.693281i	$0.243836\pi$
$410$	−2.31497	−	2.98861i	−0.114328	−	0.147597i
$411$	−4.16019	+	1.35173i	−0.205207	+	0.0666759i
$412$	−9.87668	+	15.5167i	−0.486589	+	0.764454i
$413$	−37.1699	−	51.1600i	−1.82901	−	2.51742i
$414$	−31.1860	−	9.08324i	−1.53271	−	0.446417i
$415$	−0.684869	+	2.10781i	−0.0336189	+	0.103468i
$416$	−1.96409	+	3.82273i	−0.0962975	+	0.187425i
$417$			18.6031i			0.910999i
$418$	−9.09967	−	6.34628i	−0.445079	−	0.310407i
$419$		−	24.9743i		−	1.22007i	−0.792373	−	0.610037i	$-0.791155\pi$
$419$		−	24.9743i		−	1.22007i	0.792373	−	0.610037i	$-0.208845\pi$
$420$	−23.0815	−	5.95962i	−1.12626	−	0.290799i
$421$	3.86570	−	11.8974i	0.188403	−	0.579843i	−0.811588	−	0.584230i	$-0.801396\pi$
$421$	3.86570	−	11.8974i	0.188403	−	0.579843i	0.999990	+	0.00438699i	$0.00139643\pi$
$422$	7.48363	−	25.6939i	0.364297	−	1.25076i
$423$	2.24129	+	3.08487i	0.108975	+	0.149992i
$424$	6.23406	+	14.4866i	0.302753	+	0.703533i
$425$	−2.52090	+	0.819089i	−0.122281	+	0.0397317i
$426$	42.2145	−	32.6992i	2.04530	−	1.58428i
$427$	−19.9317	+	27.4336i	−0.964562	+	1.32761i
$428$	7.54603	+	19.1347i	0.364751	+	0.924910i
$429$	−6.05938	−	0.0691544i	−0.292550	−	0.00333881i
$430$	4.76988	+	3.24633i	0.230024	+	0.156552i
$431$	20.1602	+	14.6472i	0.971082	+	0.705532i	0.955698	−	0.294349i	$-0.0951029\pi$
$431$	20.1602	+	14.6472i	0.971082	+	0.705532i	0.0153841	+	0.999882i	$0.495103\pi$
$432$	−1.88779	+	0.882096i	−0.0908264	+	0.0424399i
$433$	4.81653	+	14.8238i	0.231468	+	0.712385i	0.997570	+	0.0696662i	$0.0221934\pi$
$433$	4.81653	+	14.8238i	0.231468	+	0.712385i	−0.766103	+	0.642718i	$0.777807\pi$
$434$	−1.47703	−	48.0349i	−0.0708999	−	2.30575i
$435$	−5.76153	+	4.18600i	−0.276244	+	0.200703i
$436$	13.3038	+	16.1259i	0.637135	+	0.772288i
$437$	18.5626	+	6.03136i	0.887971	+	0.288519i
$438$	3.79574	+	10.5655i	0.181367	+	0.504838i
$439$	−23.9599			−1.14354			−0.571772	−	0.820413i	$-0.693744\pi$
$439$	−23.9599			−1.14354			−0.571772	+	0.820413i	$0.693744\pi$
$440$	−8.00956	−	4.88333i	−0.381841	−	0.232804i
$441$	−48.8898			−2.32809
$442$	0.962897	+	2.68024i	0.0458003	+	0.127486i
$443$	11.4486	+	3.71986i	0.543937	+	0.176736i	0.568081	−	0.822972i	$-0.307686\pi$
$443$	11.4486	+	3.71986i	0.543937	+	0.176736i	−0.0241437	+	0.999708i	$0.507686\pi$
$444$	−1.18343	−	1.43446i	−0.0561629	−	0.0680766i
$445$	7.30507	−	5.30745i	0.346294	−	0.251597i
$446$	−0.809148	−	26.3144i	−0.0383142	−	1.24602i
$447$	4.50739	+	13.8723i	0.213192	+	0.656138i
$448$	−27.2596	+	28.7935i	−1.28790	+	1.36036i
$449$	2.22256	+	1.61479i	0.104889	+	0.0762065i	0.638994	−	0.769212i	$-0.279351\pi$
$449$	2.22256	+	1.61479i	0.104889	+	0.0762065i	−0.534104	+	0.845419i	$0.679351\pi$
$450$	−3.25414	−	2.21473i	−0.153402	−	0.104403i
$451$	−5.12890	−	7.23146i	−0.241511	−	0.340516i
$452$	2.67246	+	6.77664i	0.125702	+	0.318746i
$453$	28.7566	−	39.5800i	1.35110	−	1.85963i
$454$	−19.5612	+	15.1520i	−0.918052	+	0.711120i
$455$	3.58123	−	1.16361i	0.167891	−	0.0545510i
$456$	−14.7783	+	6.35956i	−0.692057	+	0.297814i
$457$	−14.7874	−	20.3531i	−0.691726	−	0.952079i	−1.00000		0.000780976i	$-0.999751\pi$
$457$	−14.7874	−	20.3531i	−0.691726	−	0.952079i	0.308274	−	0.951298i	$-0.400249\pi$
$458$	−5.63903	+	19.3608i	−0.263495	+	0.904670i
$459$	−0.426686	+	1.31321i	−0.0199160	+	0.0612952i
$460$	15.9797	+	4.12593i	0.745056	+	0.192373i
$461$		−	15.7819i		−	0.735038i	−0.930016	−	0.367519i	$-0.880207\pi$
$461$		−	15.7819i		−	0.735038i	0.930016	−	0.367519i	$-0.119793\pi$
$462$	−53.4939	−	16.2452i	−2.48876	−	0.755793i
$463$			10.9329i			0.508093i	0.967192	+	0.254046i	$0.0817616\pi$
$463$			10.9329i			0.508093i	−0.967192	+	0.254046i	$0.918238\pi$
$464$	1.45282	+	11.7560i	0.0674454	+	0.545757i
$465$	5.09523	−	15.6815i	0.236285	−	0.727212i
$466$	0.842893	+	0.245501i	0.0390462	+	0.0113726i
$467$	−8.38774	−	11.5447i	−0.388138	−	0.534226i	0.569579	−	0.821936i	$-0.307106\pi$
$467$	−8.38774	−	11.5447i	−0.388138	−	0.534226i	−0.957718	+	0.287710i	$0.907106\pi$
$468$	−2.27102	+	3.56788i	−0.104978	+	0.164925i
$469$	0.327846	−	0.106524i	0.0151385	−	0.00491881i
$470$	−1.18641	−	1.53165i	−0.0547252	−	0.0706500i
$471$	−18.2993	+	25.1868i	−0.843185	+	1.16055i
$472$	−35.2027	−	7.94376i	−1.62033	−	0.365641i
$473$	10.8556	+	8.07793i	0.499141	+	0.371424i
$474$	−2.24255	+	3.29501i	−0.103004	+	0.151345i
$475$	1.91355	+	1.39027i	0.0877995	+	0.0637901i
$476$	1.61432	+	26.2250i	0.0739922	+	1.20202i
$477$	4.79592	+	14.7603i	0.219590	+	0.675828i
$478$	32.1532	−	0.988686i	1.47065	−	0.0452214i
$479$	22.4482	−	16.3096i	1.02569	−	0.745205i	0.0582456	−	0.998302i	$-0.481449\pi$
$479$	22.4482	−	16.3096i	1.02569	−	0.745205i	0.967441	+	0.253097i	$0.0814493\pi$
$480$	−12.1421	+	6.13505i	−0.554207	+	0.280025i
$481$	0.279369	+	0.0907725i	0.0127381	+	0.00413887i
$482$	−0.287955	+	0.103450i	−0.0131160	+	0.00471202i
$483$	98.3559			4.47535
$484$	−18.2848	−	12.2338i	−0.831128	−	0.556082i
$485$	−14.3624			−0.652162
$486$	−28.6562	+	10.2950i	−1.29987	+	0.466990i
$487$	18.0972	+	5.88015i	0.820064	+	0.266455i	0.688854	−	0.724900i	$-0.258114\pi$
$487$	18.0972	+	5.88015i	0.820064	+	0.266455i	0.131210	+	0.991355i	$0.458114\pi$
$488$	1.78203	+	19.2692i	0.0806688	+	0.872276i
$489$	13.6080	−	9.88677i	0.615374	−	0.447095i
$490$	24.8287	−	0.763463i	1.12165	−	0.0344898i
$491$	−6.65250	−	20.4743i	−0.300223	−	0.923992i	−0.981417	−	0.191888i	$-0.938539\pi$
$491$	−6.65250	−	20.4743i	−0.300223	−	0.923992i	0.681194	−	0.732103i	$-0.261461\pi$
$492$	−12.8326	+	0.789929i	−0.578537	+	0.0356128i
$493$	6.35032	+	4.61378i	0.286004	+	0.207794i
$494$	1.42987	−	2.10094i	0.0643331	−	0.0945257i
$495$	−7.40599	−	5.51098i	−0.332874	−	0.247700i
$496$	−18.7197	−	20.0428i	−0.840539	−	0.899950i
$497$	−45.7395	+	62.9551i	−2.05170	+	2.82392i
$498$	4.61580	+	5.95897i	0.206839	+	0.267028i
$499$	−36.8951	+	11.9879i	−1.65165	+	0.536654i	−0.979097	−	0.203395i	$-0.934803\pi$
$499$	−36.8951	+	11.9879i	−1.65165	+	0.536654i	−0.672554	+	0.740048i	$0.734803\pi$
$500$	1.68720	+	1.07394i	0.0754541	+	0.0480279i
$501$	19.5279	+	26.8779i	0.872444	+	1.20082i
$502$	23.4447	+	6.82852i	1.04639	+	0.304772i
$503$	−4.42967	+	13.6331i	−0.197509	+	0.607871i	0.802429	+	0.596748i	$0.203541\pi$
$503$	−4.42967	+	13.6331i	−0.197509	+	0.607871i	−0.999938	+	0.0111232i	$0.996459\pi$
$504$	−29.3209	+	25.7443i	−1.30605	+	1.14674i
$505$			7.17511i			0.319288i
$506$	37.0346	+	11.2468i	1.64639	+	0.499980i
$507$			29.8751i			1.32680i
$508$	3.34576	−	12.9581i	0.148444	−	0.574921i
$509$	−0.564518	+	1.73741i	−0.0250218	+	0.0770092i	−0.962788	−	0.270259i	$-0.912891\pi$
$509$	−0.564518	+	1.73741i	−0.0250218	+	0.0770092i	0.937766	+	0.347268i	$0.112891\pi$
$510$	−2.52090	+	8.65513i	−0.111627	+	0.383256i
$511$	−9.61654	−	13.2360i	−0.425411	−	0.585528i
$512$	−0.848413	+	22.6115i	−0.0374949	+	0.999297i
$513$	1.17183	−	0.380751i	0.0517376	−	0.0168106i
$514$	9.36111	−	7.25108i	0.412901	−	0.319832i
$515$	5.40569	−	7.44029i	0.238203	−	0.327858i
$516$	18.2548	−	7.19902i	0.803621	−	0.316919i
$517$	−2.62855	−	3.70611i	−0.115604	−	0.162994i
$518$	2.24039	+	1.52478i	0.0984369	+	0.0669951i
$519$	−28.7677	−	20.9010i	−1.26276	−	0.917452i
$520$	1.09762	−	1.84742i	0.0481340	−	0.0810145i
$521$	3.14213	+	9.67049i	0.137659	+	0.423672i	0.995994	−	0.0894181i	$-0.0285007\pi$
$521$	3.14213	+	9.67049i	0.137659	+	0.423672i	−0.858335	+	0.513090i	$0.828501\pi$
$522$	0.358267	+	11.6513i	0.0156809	+	0.509961i
$523$	10.1341	−	7.36285i	0.443133	−	0.321955i	−0.343746	−	0.939063i	$-0.611696\pi$
$523$	10.1341	−	7.36285i	0.443133	−	0.321955i	0.786879	+	0.617108i	$0.211696\pi$
$524$	17.3684	−	14.3289i	0.758742	−	0.625959i
$525$	11.3359	+	3.68325i	0.494738	+	0.160750i
$526$	12.4960	+	34.7827i	0.544850	+	1.51660i
$527$	−18.1735			−0.791651
$528$	−29.0567	+	13.1752i	−1.26453	+	0.573379i
$529$	−45.0932			−1.96058
$530$	−2.66611	−	7.42115i	−0.115808	−	0.322354i
$531$	−33.7750	−	10.9742i	−1.46571	−	0.476238i
$532$	18.0856	−	14.9206i	0.784112	−	0.646889i
$533$	1.64301	−	1.19372i	0.0711667	−	0.0517057i
$534$	−0.943847	−	30.6950i	−0.0408442	−	1.32830i
$535$	−3.17807	−	9.78109i	−0.137400	−	0.422873i
$536$	0.100483	−	0.169123i	0.00434020	−	0.00730500i
$537$	17.5546	+	12.7542i	0.757539	+	0.550384i
$538$	19.4315	+	13.2249i	0.837751	+	0.570164i
$539$	58.2523	+	0.664821i	2.50910	+	0.0286359i
$540$	0.969210	−	0.382222i	0.0417082	−	0.0164482i
$541$	11.2680	−	15.5091i	0.484449	−	0.666787i	−0.494903	−	0.868948i	$-0.664796\pi$
$541$	11.2680	−	15.5091i	0.484449	−	0.666787i	0.979352	+	0.202161i	$0.0647965\pi$
$542$	30.4160	−	23.5601i	1.30648	−	1.01199i
$543$	−37.2156	+	12.0921i	−1.59707	+	0.518920i
$544$	10.5666	+	10.6383i	0.453039	+	0.456114i
$545$	−6.14392	−	8.45639i	−0.263177	−	0.362232i
$546$	3.58123	−	12.2956i	0.153263	−	0.526205i
$547$	7.75142	−	23.8564i	0.331427	−	1.02003i	−0.637029	−	0.770840i	$-0.719837\pi$
$547$	7.75142	−	23.8564i	0.331427	−	1.02003i	0.968456	−	0.249186i	$-0.0801632\pi$
$548$	0.909465	−	3.52234i	0.0388504	−	0.150467i
$549$			19.0433i			0.812747i
$550$	3.84720	+	2.68311i	0.164045	+	0.114408i
$551$		−	7.00439i		−	0.298397i
$552$	42.1783	−	37.0333i	1.79523	−	1.57624i
$553$	1.79491	−	5.52416i	0.0763273	−	0.234911i
$554$	−22.0390	−	6.41908i	−0.936346	−	0.272721i
$555$	0.546528	+	0.752232i	0.0231988	+	0.0319305i
$556$	−13.0516	−	8.30756i	−0.553510	−	0.352319i
$557$	−4.53001	+	1.47189i	−0.191943	+	0.0623660i	−0.403411	−	0.915019i	$-0.632176\pi$
$557$	−4.53001	+	1.47189i	−0.191943	+	0.0623660i	0.211468	+	0.977385i	$0.432176\pi$
$558$	−16.5270	−	21.3363i	−0.699644	−	0.903236i
$559$	−1.82193	+	2.50767i	−0.0770595	+	0.106063i
$560$	14.4886	−	13.5321i	0.612255	−	0.571836i
$561$	−6.76212	+	20.0309i	−0.285497	+	0.845706i
$562$	−20.6647	+	30.3629i	−0.871686	+	1.28078i
$563$	−27.4781	−	19.9640i	−1.15806	−	0.841382i	−0.168531	−	0.985696i	$-0.553902\pi$
$563$	−27.4781	−	19.9640i	−1.15806	−	0.841382i	−0.989532	+	0.144314i	$0.953902\pi$
$564$	−6.57666	+	0.404837i	−0.276928	+	0.0170467i
$565$	−1.12553	−	3.46402i	−0.0473513	−	0.145732i
$566$	1.83038	−	0.0562827i	0.0769367	−	0.00236574i
$567$	38.5051	−	27.9756i	1.61706	−	1.17486i
$568$	4.08943	+	44.2193i	0.171589	+	1.85540i
$569$	−16.7584	−	5.44514i	−0.702549	−	0.228272i	−0.0641084	−	0.997943i	$-0.520420\pi$
$569$	−16.7584	−	5.44514i	−0.702549	−	0.228272i	−0.638441	+	0.769671i	$0.720420\pi$
$570$	7.57055	−	2.71978i	0.317095	−	0.113919i
$571$	−43.7338			−1.83020			−0.915101	−	0.403225i	$-0.867889\pi$
$571$	−43.7338			−1.83020			−0.915101	+	0.403225i	$0.867889\pi$
$572$	2.75444	−	4.22025i	0.115169	−	0.176458i
$573$	5.64662			0.235891
$574$	17.6330	−	6.33480i	0.735987	−	0.264410i
$575$	−7.84799	−	2.54997i	−0.327284	−	0.106341i
$576$	−2.88044	+	22.0800i	−0.120018	+	0.920000i
$577$	26.4309	−	19.2032i	1.10033	−	0.799439i	0.119219	−	0.992868i	$-0.461961\pi$
$577$	26.4309	−	19.2032i	1.10033	−	0.799439i	0.981114	+	0.193429i	$0.0619610\pi$
$578$	−14.0989	+	0.433531i	−0.586439	+	0.0180325i
$579$	5.27084	+	16.2220i	0.219048	+	0.674162i
$580$	−0.363892	−	5.91151i	−0.0151098	−	0.245462i
$581$	−8.88669	−	6.45656i	−0.368682	−	0.267863i
$582$	−27.4831	+	40.3813i	−1.13921	+	1.67386i
$583$	−5.51362	−	17.6521i	−0.228351	−	0.731077i
$584$	−9.10758	−	2.05520i	−0.376874	−	0.0850447i
$585$	1.24297	−	1.71080i	0.0513906	−	0.0707330i
$586$	−10.8254	−	13.9756i	−0.447194	−	0.577325i
$587$	−9.83489	+	3.19555i	−0.405929	+	0.131894i	−0.504863	−	0.863200i	$-0.668457\pi$
$587$	−9.83489	+	3.19555i	−0.405929	+	0.131894i	0.0989335	+	0.995094i	$0.468457\pi$
$588$	45.3643	−	71.2695i	1.87079	−	2.93910i
$589$	9.53213	+	13.1198i	0.392764	+	0.540594i
$590$	17.3240	+	5.04581i	0.713219	+	0.207733i
$591$	−0.500590	+	1.54066i	−0.0205915	+	0.0633742i
$592$	1.53487	−	0.189681i	0.0630828	−	0.00779586i
$593$		−	2.43272i		−	0.0998998i	−0.998752	−	0.0499499i	$-0.984094\pi$
$593$		−	2.43272i		−	0.0998998i	0.998752	−	0.0499499i	$-0.0159062\pi$
$594$	2.30875	−	0.799810i	0.0947293	−	0.0328166i
$595$		−	13.1373i		−	0.538577i
$596$	−11.7454	−	3.03265i	−0.481110	−	0.124222i
$597$	−0.544783	+	1.67667i	−0.0222965	+	0.0686216i
$598$	−2.47934	+	8.51245i	−0.101388	+	0.348100i
$599$	23.0637	+	31.7445i	0.942358	+	1.29704i	0.954839	+	0.297123i	$0.0960271\pi$
$599$	23.0637	+	31.7445i	0.942358	+	1.29704i	−0.0124810	+	0.999922i	$0.503973\pi$
$600$	6.24803	−	2.68872i	0.255075	−	0.109767i
$601$	−35.3596	+	11.4890i	−1.44235	+	0.468647i	−0.922629	−	0.385690i	$-0.873964\pi$
$601$	−35.3596	+	11.4890i	−1.44235	+	0.468647i	−0.519719	+	0.854337i	$0.673964\pi$
$602$	−22.6077	+	17.5119i	−0.921422	+	0.713730i
$603$	0.113789	−	0.156617i	0.00463383	−	0.00637792i
$604$	14.9267	+	37.8502i	0.607361	+	1.54010i
$605$	8.74931	+	6.66706i	0.355710	+	0.271054i
$606$	20.1736	+	13.7299i	0.819495	+	0.557739i
$607$	−21.5413	−	15.6507i	−0.874334	−	0.635241i	0.0574121	−	0.998351i	$-0.481715\pi$
$607$	−21.5413	−	15.6507i	−0.874334	−	0.635241i	−0.931746	+	0.363109i	$0.881715\pi$
$608$	2.13778	−	13.2081i	0.0866983	−	0.535660i
$609$	−10.9074	−	33.5694i	−0.441989	−	1.36030i
$610$	−0.297380	−	9.67114i	−0.0120406	−	0.391573i
$611$	0.842040	−	0.611778i	0.0340653	−	0.0247499i
$612$	9.39008	+	11.3820i	0.379572	+	0.460089i
$613$	8.99599	+	2.92298i	0.363345	+	0.118058i	0.484999	−	0.874515i	$-0.338820\pi$
$613$	8.99599	+	2.92298i	0.363345	+	0.118058i	−0.121654	+	0.992573i	$0.538820\pi$
$614$	−9.33454	−	25.9828i	−0.376711	−	1.04858i
$615$	6.42843			0.259219
$616$	35.2859	−	30.2756i	1.42171	−	1.21984i
$617$	3.91621			0.157661			0.0788303	−	0.996888i	$-0.474881\pi$
$617$	3.91621			0.157661			0.0788303	+	0.996888i	$0.474881\pi$
$618$	−10.5751	−	29.4360i	−0.425394	−	1.18409i
$619$	0.867870	+	0.281988i	0.0348826	+	0.0113341i	0.326406	−	0.945230i	$-0.394162\pi$
$619$	0.867870	+	0.281988i	0.0348826	+	0.0113341i	−0.291524	+	0.956564i	$0.594162\pi$
$620$	8.72644	+	10.5776i	0.350462	+	0.424805i
$621$	−3.47766	+	2.52667i	−0.139554	+	0.101392i
$622$	0.264136	+	8.59002i	0.0105909	+	0.344428i
$623$	13.8295	+	42.5628i	0.554067	+	1.70524i
$624$	−3.09385	−	6.62120i	−0.123853	−	0.265060i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	10.6162	+	7.22529i	0.424310	+	0.288781i
$627$	18.0075	−	5.62463i	0.719151	−	0.224626i
$628$	−9.49865	−	24.0860i	−0.379037	−	0.961136i
$629$	0.602380	−	0.829105i	0.0240185	−	0.0330586i
$630$	15.4236	−	11.9471i	0.614491	−	0.475982i
$631$	44.5679	−	14.4810i	1.77422	−	0.576480i	0.775714	−	0.631085i	$-0.217390\pi$
$631$	44.5679	−	14.4810i	1.77422	−	0.576480i	0.998508	+	0.0546051i	$0.0173900\pi$
$632$	−1.31026	−	3.04477i	−0.0521194	−	0.121114i
$633$	26.7490	+	36.8168i	1.06318	+	1.46334i
$634$	−10.0151	+	34.3852i	−0.397748	+	1.36561i
$635$	−2.06779	+	6.36400i	−0.0820578	+	0.252548i
$636$	−25.9670	−	6.70466i	−1.02966	−	0.265857i
$637$			13.3449i			0.528742i
$638$	−0.268437	−	13.8874i	−0.0106275	−	0.549806i
$639$			43.7008i			1.72878i
$640$	1.11803	−	11.2583i	0.0441942	−	0.445025i
$641$	−0.536678	+	1.65172i	−0.0211975	+	0.0652392i	−0.961096	−	0.276216i	$-0.910920\pi$
$641$	−0.536678	+	1.65172i	−0.0211975	+	0.0652392i	0.939898	+	0.341455i	$0.110920\pi$
$642$	−33.5819	−	9.78109i	−1.32537	−	0.386029i
$643$	21.6395	+	29.7842i	0.853378	+	1.17457i	0.983108	+	0.183025i	$0.0585890\pi$
$643$	21.6395	+	29.7842i	0.853378	+	1.17457i	−0.129730	+	0.991549i	$0.541411\pi$
$644$	−43.9226	+	69.0044i	−1.73079	+	2.71916i
$645$	−9.33129	+	3.03192i	−0.367419	+	0.119382i
$646$	−5.42951	−	7.00947i	−0.213621	−	0.275784i
$647$	9.08992	−	12.5112i	0.357361	−	0.491866i	−0.592050	−	0.805901i	$-0.701681\pi$
$647$	9.08992	−	12.5112i	0.357361	−	0.491866i	0.949411	+	0.314036i	$0.101681\pi$
$648$	5.97880	−	26.4950i	0.234869	−	1.04082i
$649$	40.0937	+	13.5350i	1.57382	+	0.531296i
$650$	−0.604528	+	0.888244i	−0.0237116	+	0.0348398i
$651$	66.1144	+	48.0349i	2.59123	+	1.88264i
$652$	0.859465	+	13.9622i	0.0336592	+	0.546802i
$653$	−13.1151	−	40.3641i	−0.513233	−	1.57957i	−0.786474	−	0.617623i	$-0.788096\pi$
$653$	−13.1151	−	40.3641i	−0.513233	−	1.57957i	0.273241	−	0.961945i	$-0.411904\pi$
$654$	−35.5327	+	1.09260i	−1.38944	+	0.0427241i
$655$	−9.10798	+	6.61733i	−0.355878	+	0.258561i
$656$	5.17642	−	9.35582i	0.202105	−	0.365283i
$657$	−8.73822	−	2.83922i	−0.340910	−	0.110768i
$658$	9.03687	−	3.24657i	0.352294	−	0.126565i
$659$	17.9220			0.698142			0.349071	−	0.937096i	$-0.386497\pi$
$659$	17.9220			0.698142			0.349071	+	0.937096i	$0.386497\pi$
$660$	14.9056	−	5.68255i	0.580201	−	0.221193i
$661$	−1.60621			−0.0624742			−0.0312371	−	0.999512i	$-0.509945\pi$
$661$	−1.60621			−0.0624742			−0.0312371	+	0.999512i	$0.509945\pi$
$662$	14.4435	−	5.18894i	0.561362	−	0.201674i
$663$	−4.60591	−	1.49655i	−0.178879	−	0.0581212i
$664$	−6.24196	+	0.577262i	−0.242235	+	0.0224021i
$665$	−9.48410	+	6.89060i	−0.367777	+	0.267206i
$666$	1.52120	−	0.0467756i	0.0589453	−	0.00181252i
$667$	7.55134	+	23.2406i	0.292389	+	0.899880i
$668$	−27.5775	+	1.69758i	−1.06701	+	0.0656813i
$669$	36.2187	+	26.3144i	1.40030	+	1.01737i
$670$	−0.0553420	+	0.0813148i	−0.00213805	+	0.00314147i
$671$	0.258957	−	22.6901i	0.00999693	−	0.875941i
$672$	−10.3224	−	66.6305i	−0.398194	−	2.57033i
$673$	−3.76456	+	5.18148i	−0.145113	+	0.199731i	−0.875386	−	0.483424i	$-0.839393\pi$
$673$	−3.76456	+	5.18148i	−0.145113	+	0.199731i	0.730273	+	0.683155i	$0.239393\pi$
$674$	−10.5456	−	13.6143i	−0.406202	−	0.524404i
$675$	−0.495432	+	0.160975i	−0.0190692	+	0.00619595i
$676$	−20.9598	−	13.3413i	−0.806145	−	0.513126i
$677$	28.7388	+	39.5556i	1.10452	+	1.52024i	0.829249	+	0.558879i	$0.188768\pi$
$677$	28.7388	+	39.5556i	1.10452	+	1.52024i	0.275273	+	0.961366i	$0.411232\pi$
$678$	−11.8932	−	3.46402i	−0.456755	−	0.133035i
$679$	21.9971	−	67.7002i	0.844173	−	2.59810i
$680$	−4.94651	−	5.63371i	−0.189690	−	0.216043i
$681$		−	42.0757i		−	1.61234i
$682$	19.4018	+	25.6469i	0.742934	+	0.982072i
$683$		−	22.2573i		−	0.851653i	−0.904805	−	0.425826i	$-0.859983\pi$
$683$		−	22.2573i		−	0.851653i	0.904805	−	0.425826i	$-0.140017\pi$
$684$	3.29173	−	12.7488i	0.125863	−	0.487464i
$685$	−0.562080	+	1.72991i	−0.0214760	+	0.0660963i
$686$	−20.7079	+	71.0975i	−0.790632	+	2.71452i
$687$	−20.1558	−	27.7420i	−0.768990	−	1.05842i
$688$	−3.10131	+	16.0220i	−0.118237	+	0.610834i
$689$	4.02894	−	1.30908i	0.153490	−	0.0498721i
$690$	−22.1870	+	17.1860i	−0.844644	+	0.654258i
$691$	1.44985	−	1.99555i	0.0551549	−	0.0759142i	−0.780549	−	0.625095i	$-0.785060\pi$
$691$	1.44985	−	1.99555i	0.0551549	−	0.0759142i	0.835704	+	0.549181i	$0.185060\pi$
$692$	27.5105	−	10.8491i	1.04579	−	0.412422i
$693$	37.3201	−	26.4692i	1.41767	−	1.00548i
$694$	−6.42490	−	4.37272i	−0.243886	−	0.165986i
$695$	6.25824	+	4.54688i	0.237389	+	0.172473i
$696$	−17.3171	−	10.2888i	−0.656404	−	0.389996i
$697$	−2.18950	−	6.73859i	−0.0829333	−	0.255242i
$698$	−0.310239	−	10.0893i	−0.0117427	−	0.381887i
$699$	−1.20778	+	0.877503i	−0.0456824	+	0.0331902i
$700$	−7.64632	+	6.30818i	−0.289004	+	0.238427i
$701$	8.35087	+	2.71336i	0.315408	+	0.102482i	0.462443	−	0.886649i	$-0.346973\pi$
$701$	8.35087	+	2.71336i	0.315408	+	0.102482i	−0.147035	+	0.989131i	$0.546973\pi$
$702$	0.189238	+	0.526747i	0.00714233	+	0.0198808i
$703$	−0.914501			−0.0344910
$704$	3.73230	−	26.2692i	0.140666	−	0.990057i
$705$	3.29456			0.124080
$706$	−8.66709	−	24.1250i	−0.326190	−	0.907955i
$707$	−33.8214	−	10.9893i	−1.27199	−	0.413293i
$708$	47.3372	−	39.0530i	1.77904	−	1.46770i
$709$	−12.4275	+	9.02909i	−0.466724	+	0.339095i	−0.796163	−	0.605082i	$-0.793140\pi$
$709$	−12.4275	+	9.02909i	−0.466724	+	0.339095i	0.329439	+	0.944177i	$0.393140\pi$
$710$	−0.682432	−	22.1935i	−0.0256112	−	0.832907i
$711$	−1.00800	−	3.10229i	−0.0378028	−	0.116345i
$712$	21.9565	+	13.0452i	0.822854	+	0.488891i
$713$	−45.7720	−	33.2553i	−1.71417	−	1.24542i
$714$	−36.9369	−	25.1388i	−1.38233	−	0.940796i
$715$	−1.50427	+	2.02152i	−0.0562564	+	0.0756007i
$716$	−16.7874	+	6.62035i	−0.627376	+	0.247414i
$717$	−32.1532	+	44.2551i	−1.20078	+	1.65274i
$718$	−6.35699	+	4.92410i	−0.237241	+	0.183766i
$719$	44.4263	−	14.4350i	1.65682	−	0.538333i	0.676618	−	0.736334i	$-0.263445\pi$
$719$	44.4263	−	14.4350i	1.65682	−	0.538333i	0.980202	+	0.198001i	$0.0634450\pi$
$720$	2.11580	−	10.9307i	0.0788512	−	0.407361i
$721$	26.7922	+	36.8763i	0.997793	+	1.37334i
$722$	5.30149	−	18.2019i	0.197301	−	0.677404i
$723$	0.160784	−	0.494841i	0.00597961	−	0.0184034i
$724$	8.13574	−	31.5096i	0.302363	−	1.17104i
$725$			2.96135i			0.109982i
$726$	35.4873	−	11.8419i	1.31706	−	0.439493i
$727$			9.15647i			0.339595i	0.985479	+	0.169797i	$0.0543113\pi$
$727$			9.15647i			0.339595i	−0.985479	+	0.169797i	$0.945689\pi$
$728$	7.02710	+	8.00336i	0.260441	+	0.296624i
$729$	7.09823	−	21.8461i	0.262897	−	0.809115i
$730$	4.48205	+	1.30544i	0.165888	+	0.0483167i
$731$	6.35641	+	8.74885i	0.235100	+	0.323588i
$732$	−27.7605	−	17.6701i	−1.02606	−	0.653104i
$733$	10.4343	−	3.39030i	0.385399	−	0.125224i	−0.109908	−	0.993942i	$-0.535056\pi$
$733$	10.4343	−	3.39030i	0.385399	−	0.125224i	0.495307	+	0.868718i	$0.335056\pi$
$734$	−14.3574	−	18.5353i	−0.529940	−	0.684150i
$735$	−24.8287	+	34.1738i	−0.915822	+	1.26052i
$736$	7.14632	+	46.1293i	0.263417	+	1.70035i
$737$	−0.137709	+	0.185062i	−0.00507258	+	0.00681683i
$738$	5.92018	−	8.69862i	0.217925	−	0.320201i
$739$	17.2487	+	12.5319i	0.634504	+	0.460994i	0.857958	−	0.513720i	$-0.171733\pi$
$739$	17.2487	+	12.5319i	0.634504	+	0.460994i	−0.223453	+	0.974715i	$0.571733\pi$
$740$	−0.771812	+	0.0475101i	−0.0283724	+	0.00174651i
$741$	1.33544	+	4.11005i	0.0490585	+	0.150987i
$742$	39.0645	−	1.20120i	1.43410	−	0.0440975i
$743$	−35.2681	+	25.6237i	−1.29386	+	0.940044i	−0.999876	−	0.0157661i	$-0.994981\pi$
$743$	−35.2681	+	25.6237i	−1.29386	+	0.940044i	−0.293984	+	0.955810i	$0.594981\pi$
$744$	46.4384	−	4.29466i	1.70251	−	0.157450i
$745$	5.76844	+	1.87428i	0.211339	+	0.0686683i
$746$	14.4739	−	5.19987i	0.529927	−	0.190381i
$747$	−6.16877			−0.225704
$748$	−11.0335	−	13.6893i	−0.403426	−	0.500532i
$749$	50.9727			1.86250
$750$	−3.20071	+	1.14988i	−0.116873	+	0.0419877i
$751$	−30.9957	−	10.0711i	−1.13105	−	0.367500i	−0.317075	−	0.948400i	$-0.602701\pi$
$751$	−30.9957	−	10.0711i	−1.13105	−	0.367500i	−0.813975	+	0.580900i	$0.802701\pi$
$752$	2.65290	−	4.79484i	0.0967414	−	0.174850i
$753$	−33.5939	+	24.4074i	−1.22423	+	0.889454i
$754$	3.18030	−	0.0977917i	0.115820	−	0.00356136i
$755$	−6.28651	−	19.3479i	−0.228790	−	0.704142i
$756$	0.317262	+	5.15399i	0.0115387	+	0.187449i
$757$	−6.76669	−	4.91629i	−0.245940	−	0.178686i	0.457986	−	0.888960i	$-0.348571\pi$
$757$	−6.76669	−	4.91629i	−0.245940	−	0.178686i	−0.703925	+	0.710274i	$0.748571\pi$
$758$	−6.71461	+	9.86588i	−0.243885	+	0.358345i
$759$	−53.6853	+	38.0762i	−1.94865	+	1.38208i
$760$	−1.47262	+	6.52591i	−0.0534177	+	0.236720i
$761$	0.872669	−	1.20113i	0.0316342	−	0.0435408i	−0.792907	−	0.609343i	$-0.791433\pi$
$761$	0.872669	−	1.20113i	0.0316342	−	0.0435408i	0.824541	+	0.565802i	$0.191433\pi$
$762$	13.9362	+	17.9916i	0.504857	+	0.651768i
$763$	49.2709	−	16.0091i	1.78373	−	0.579568i
$764$	−2.52160	+	3.96155i	−0.0912284	+	0.143324i
$765$	−4.33652	−	5.96870i	−0.156787	−	0.215799i
$766$	−24.0517	−	7.00530i	−0.869022	−	0.253112i
$767$	−2.99548	+	9.21915i	−0.108161	+	0.332884i
$768$	−29.5146	−	24.6868i	−1.06501	−	0.890808i
$769$		−	46.3151i		−	1.67016i	−0.550126	−	0.835082i	$-0.685420\pi$
$769$		−	46.3151i		−	1.67016i	0.550126	−	0.835082i	$-0.314580\pi$
$770$	−18.5397	+	14.0252i	−0.668124	+	0.505434i
$771$			20.1355i			0.725164i
$772$	−13.7348	−	3.54630i	−0.494325	−	0.127634i
$773$	−8.23288	+	25.3382i	−0.296116	+	0.911352i	0.686728	+	0.726914i	$0.259046\pi$
$773$	−8.23288	+	25.3382i	−0.296116	+	0.911352i	−0.982844	+	0.184437i	$0.940954\pi$
$774$	−4.49090	+	15.4188i	−0.161422	+	0.554219i
$775$	−4.03003	−	5.54687i	−0.144763	−	0.199249i
$776$	−16.0576	−	37.3146i	−0.576436	−	1.33952i
$777$	−4.38286	+	1.42408i	−0.157234	+	0.0510885i
$778$	20.9894	−	16.2583i	0.752508	−	0.582890i
$779$	−3.71633	+	5.11508i	−0.133151	+	0.183267i
$780$	1.34060	+	3.39939i	0.0480011	+	0.121718i
$781$	0.594259	−	52.0696i	0.0212643	−	1.86320i
$782$	25.5720	+	17.4040i	0.914451	+	0.622365i
$783$	1.24803	+	0.906746i	0.0446009	+	0.0324044i
$784$	29.7429	+	63.6534i	1.06225	+	2.27333i
$785$	4.00043	+	12.3120i	0.142781	+	0.439436i
$786$	1.17679	+	38.2706i	0.0419747	+	1.36507i
$787$	40.5870	−	29.4881i	1.44677	−	1.05114i	0.460196	−	0.887817i	$-0.347779\pi$
$787$	40.5870	−	29.4881i	1.44677	−	1.05114i	0.986573	−	0.163321i	$-0.0522208\pi$
$788$	−0.857346	−	1.03921i	−0.0305417	−	0.0370204i
$789$	−59.7730	−	19.4214i	−2.12798	−	0.691421i
$790$	0.560357	+	1.55976i	0.0199366	+	0.0554938i
$791$	18.0522			0.641864
$792$	6.03781	−	25.4028i	0.214544	−	0.902649i
$793$	5.19801			0.184587
$794$	−11.5363	−	32.1115i	−0.409409	−	1.13960i
$795$	12.7530	+	4.14371i	0.452303	+	0.146962i
$796$	−0.933034	−	1.13096i	−0.0330705	−	0.0400857i
$797$	8.29499	−	6.02666i	0.293824	−	0.213475i	−0.431101	−	0.902304i	$-0.641875\pi$
$797$	8.29499	−	6.02666i	0.293824	−	0.213475i	0.724924	+	0.688828i	$0.241875\pi$
$798$	1.22539	+	39.8510i	0.0433782	+	1.41071i
$799$	−1.12211	−	3.45351i	−0.0396975	−	0.122176i
$800$	−0.903818	+	5.58418i	−0.0319548	+	0.197431i
$801$	20.3328	+	14.7727i	0.718426	+	0.521967i
$802$	−14.7565	−	10.0431i	−0.521071	−	0.354635i
$803$	10.3730	+	3.50176i	0.366055	+	0.123574i
$804$	0.122726	+	0.311199i	0.00432820	+	0.0109752i
$805$	24.0396	−	33.0877i	0.847286	−	1.16619i
$806$	−5.82390	+	4.51118i	−0.205138	+	0.158899i
$807$	−38.0137	+	12.3514i	−1.33815	+	0.434790i
$808$	−18.6415	+	8.02202i	−0.655805	+	0.282214i
$809$	20.7304	+	28.5330i	0.728843	+	1.00317i	0.999184	+	0.0404011i	$0.0128636\pi$
$809$	20.7304	+	28.5330i	0.728843	+	1.00317i	−0.270341	+	0.962765i	$0.587136\pi$
$810$	−3.79768	+	13.0388i	−0.133437	+	0.458136i
$811$	−10.1337	+	31.1884i	−0.355844	+	1.09517i	0.599675	+	0.800243i	$0.295296\pi$
$811$	−10.1337	+	31.1884i	−0.355844	+	1.09517i	−0.955519	+	0.294930i	$0.904704\pi$
$812$	28.4225	+	7.33866i	0.997434	+	0.257536i
$813$			65.4241i			2.29452i
$814$	−1.81315	+	0.0350474i	−0.0635508	+	0.00122841i
$815$		−	6.99431i		−	0.245000i
$816$	−25.3051	+	3.12724i	−0.885857	+	0.109475i
$817$	2.98200	−	9.17766i	0.104327	−	0.321086i
$818$	7.53927	+	2.19589i	0.263604	+	0.0767776i
$819$	6.16053	+	8.47925i	0.215266	+	0.296289i
$820$	−2.87073	+	4.51005i	−0.100250	+	0.157498i
$821$	−31.6384	+	10.2800i	−1.10419	+	0.358773i	−0.803713	−	0.595017i	$-0.797145\pi$
$821$	−31.6384	+	10.2800i	−1.10419	+	0.358773i	−0.300476	+	0.953789i	$0.597145\pi$
$822$	3.78824	+	4.89060i	0.132130	+	0.170579i
$823$	−17.5150	+	24.1074i	−0.610536	+	0.840330i	−0.996621	−	0.0821327i	$-0.973827\pi$
$823$	−17.5150	+	24.1074i	−0.610536	+	0.840330i	0.386086	+	0.922463i	$0.373827\pi$
$824$	25.3742	+	5.72589i	0.883951	+	0.199471i
$825$	−7.61330	+	2.37800i	−0.265061	+	0.0827915i
$826$	−50.3177	+	73.9326i	−1.75078	+	2.57244i
$827$	−19.6989	−	14.3121i	−0.684998	−	0.497680i	0.190014	−	0.981781i	$-0.439147\pi$
$827$	−19.6989	−	14.3121i	−0.684998	−	0.497680i	−0.875012	+	0.484101i	$0.839147\pi$
$828$	2.82234	+	45.8495i	0.0980830	+	1.59338i
$829$	3.25611	+	10.0213i	0.113089	+	0.348054i	0.991544	−	0.129773i	$-0.0414248\pi$
$829$	3.25611	+	10.0213i	0.113089	+	0.348054i	−0.878454	+	0.477826i	$0.841425\pi$
$830$	3.13282	−	0.0963316i	0.108742	−	0.00334372i
$831$	31.5796	−	22.9439i	1.09548	−	0.795915i
$832$	6.02691	+	0.786239i	0.208945	+	0.0272579i
$833$	44.2792	+	14.3872i	1.53418	+	0.498487i
$834$	24.7595	−	8.89504i	0.857350	−	0.308010i
$835$	13.8149			0.478083
$836$	−4.09547	+	15.1455i	−0.141645	+	0.523818i
$837$	−3.57164			−0.123454
$838$	−33.2390	+	11.9414i	−1.14822	+	0.412509i
$839$	−21.1828	−	6.88271i	−0.731312	−	0.237618i	−0.0803912	−	0.996763i	$-0.525617\pi$
$839$	−21.1828	−	6.88271i	−0.731312	−	0.237618i	−0.650921	+	0.759146i	$0.725617\pi$
$840$	3.10453	+	33.5694i	0.107116	+	1.15826i
$841$	−16.3668	+	11.8911i	−0.564371	+	0.410039i
$842$	−17.6830	+	0.543737i	−0.609395	+	0.0187384i
$843$	−19.2999	−	59.3988i	−0.664722	−	2.04580i
$844$	−37.7751	+	2.32531i	−1.30027	+	0.0800404i
$845$	10.0502	+	7.30193i	0.345739	+	0.251194i
$846$	3.03408	−	4.45802i	0.104314	−	0.153270i
$847$	−44.8269	+	31.0306i	−1.54027	+	1.06622i
$848$	16.2999	−	15.2238i	0.559741	−	0.522789i
$849$	−1.83038	+	2.51930i	−0.0628185	+	0.0864623i
$850$	2.29551	+	2.96349i	0.0787354	+	0.101647i
$851$	3.03432	−	0.985910i	0.104015	−	0.0337966i
$852$	−63.7052	−	40.5495i	−2.18250	−	1.38920i
$853$	−17.6216	−	24.2541i	−0.603353	−	0.830444i	0.392657	−	0.919685i	$-0.371556\pi$
$853$	−17.6216	−	24.2541i	−0.603353	−	0.830444i	−0.996010	+	0.0892409i	$0.971556\pi$
$854$	46.0425	+	13.4104i	1.57554	+	0.458893i
$855$	−2.03440	+	6.26125i	−0.0695751	+	0.214130i
$856$	21.8588	−	19.1924i	0.747119	−	0.655984i
$857$		−	23.4642i		−	0.801521i	−0.916183	−	0.400760i	$-0.868746\pi$
$857$		−	23.4642i		−	0.801521i	0.916183	−	0.400760i	$-0.131254\pi$
$858$	2.80524	+	8.09768i	0.0957693	+	0.276450i
$859$		−	16.9811i		−	0.579388i	−0.957119	−	0.289694i	$-0.906447\pi$
$859$		−	16.9811i		−	0.579388i	0.957119	−	0.289694i	$-0.0935535\pi$
$860$	2.03993	−	7.90060i	0.0695609	−	0.269408i
$861$	−9.84565	+	30.3018i	−0.335539	+	1.03268i
$862$	9.85490	−	33.8353i	0.335659	−	1.15244i
$863$	−2.95439	−	4.06637i	−0.100569	−	0.138421i	0.755767	−	0.654841i	$-0.227264\pi$
$863$	−2.95439	−	4.06637i	−0.100569	−	0.138421i	−0.856335	+	0.516420i	$0.827264\pi$
$864$	2.07665	+	2.09075i	0.0706491	+	0.0711286i
$865$	−14.0625	+	4.56919i	−0.478140	+	0.155357i
$866$	17.4264	−	13.4984i	0.592172	−	0.458695i
$867$	14.0989	−	19.4055i	0.478825	−	0.659046i
$868$	−63.2249	+	24.9336i	−2.14599	+	0.846302i
$869$	1.15884	+	3.71009i	0.0393110	+	0.125856i
$870$	8.32614	+	5.66667i	0.282282	+	0.192118i
$871$	−0.0427497	−	0.0310595i	−0.00144852	−	0.00105241i
$872$	15.1012	−	25.4169i	0.511392	−	0.860725i
$873$	−12.3533	−	38.0195i	−0.418095	−	1.28677i
$874$	−0.848353	−	27.5894i	−0.0286960	−	0.933227i
$875$	4.00973	−	2.91324i	0.135554	−	0.0984854i
$876$	12.2470	−	10.1037i	0.413788	−	0.341373i
$877$	−52.6518	−	17.1076i	−1.77793	−	0.577683i	−0.779135	−	0.626856i	$-0.784342\pi$
$877$	−52.6518	−	17.1076i	−1.77793	−	0.577683i	−0.998790	+	0.0491726i	$0.984342\pi$
$878$	11.4564	+	31.8890i	0.386634	+	1.07620i
$879$	30.0611			1.01394
$880$	−2.66962	+	12.9951i	−0.0899928	+	0.438065i
$881$	−19.2345			−0.648026			−0.324013	−	0.946053i	$-0.605032\pi$
$881$	−19.2345			−0.648026			−0.324013	+	0.946053i	$0.605032\pi$
$882$	23.3765	+	65.0689i	0.787129	+	2.19098i
$883$	−34.8363	−	11.3190i	−1.17234	−	0.380915i	−0.342822	−	0.939401i	$-0.611383\pi$
$883$	−34.8363	−	11.3190i	−1.17234	−	0.380915i	−0.829514	+	0.558486i	$0.811383\pi$
$884$	3.10680	−	2.56310i	0.104493	−	0.0862063i
$885$	−24.8236	+	18.0354i	−0.834435	+	0.606253i
$886$	−0.523224	−	17.0159i	−0.0175781	−	0.571660i
$887$	−11.0239	−	33.9280i	−0.370146	−	1.13919i	−0.946696	−	0.322129i	$-0.895601\pi$
$887$	−11.0239	−	33.9280i	−0.370146	−	1.13919i	0.576550	−	0.817062i	$-0.304399\pi$
$888$	−1.34332	+	2.26094i	−0.0450788	+	0.0758723i
$889$	−26.8311	−	19.4940i	−0.899887	−	0.653806i
$890$	−10.5567	−	7.18480i	−0.353863	−	0.240835i
$891$	−10.1870	+	30.1762i	−0.341278	+	1.01094i
$892$	−34.6358	+	13.6591i	−1.15969	+	0.457341i
$893$	−1.90461	+	2.62147i	−0.0637353	+	0.0877241i
$894$	16.3079	−	12.6320i	0.545418	−	0.422479i
$895$	8.58123	−	2.78821i	0.286839	−	0.0931996i
$896$	51.3562	+	22.5131i	1.71569	+	0.752111i
$897$	−8.86198	−	12.1975i	−0.295893	−	0.407262i
$898$	1.08645	−	3.73018i	0.0362555	−	0.124478i
$899$	−6.27425	+	19.3102i	−0.209258	+	0.644030i
$900$	−1.39169	+	5.39000i	−0.0463898	+	0.179667i
$901$		−	14.7797i		−	0.492382i
$902$	−7.17219	+	10.2839i	−0.238808	+	0.342417i
$903$		−	48.6287i		−	1.61826i
$904$	7.74141	−	6.79710i	0.257475	−	0.226068i
$905$	−5.02817	+	15.4751i	−0.167142	+	0.514410i
$906$	−66.4281	−	19.3479i	−2.20693	−	0.642791i
$907$	19.7683	+	27.2087i	0.656395	+	0.903450i	0.999355	−	0.0358996i	$-0.0114297\pi$
$907$	19.7683	+	27.2087i	0.656395	+	0.903450i	−0.342960	+	0.939350i	$0.611430\pi$
$908$	29.5194	+	18.7897i	0.979637	+	0.623557i
$909$	−18.9937	+	6.17141i	−0.629980	+	0.204693i
$910$	−3.26105	−	4.20999i	−0.108103	−	0.139560i
$911$	−17.1652	+	23.6259i	−0.568709	+	0.782761i	−0.992401	−	0.123045i	$-0.960734\pi$
$911$	−17.1652	+	23.6259i	−0.568709	+	0.782761i	0.423692	+	0.905806i	$0.360734\pi$
$912$	15.5303	+	16.6281i	0.514261	+	0.550610i
$913$	7.35010	+	0.0838852i	0.243253	+	0.00277619i
$914$	−20.0180	+	29.4128i	−0.662137	+	0.972889i
$915$	13.3112	+	9.67114i	0.440054	+	0.319718i
$916$	28.4641	−	1.75216i	0.940482	−	0.0578929i
$917$	−17.2426	−	53.0674i	−0.569402	−	1.75244i
$918$	1.95180	−	0.0600164i	0.0644191	−	0.00198084i
$919$	−19.1153	+	13.8881i	−0.630557	+	0.458126i	−0.856593	−	0.515993i	$-0.827423\pi$
$919$	−19.1153	+	13.8881i	−0.630557	+	0.458126i	0.226036	+	0.974119i	$0.427423\pi$
$920$	−2.14931	−	23.2406i	−0.0708607	−	0.766221i
$921$	44.6507	+	14.5079i	1.47129	+	0.478051i
$922$	−21.0047	+	7.54610i	−0.691752	+	0.248518i
$923$	11.9285			0.392631
$924$	3.95678	+	78.9642i	0.130169	+	2.59773i
$925$	0.386636			0.0127125
$926$	14.5509	−	5.22752i	0.478171	−	0.171787i
$927$	24.3451	+	7.91021i	0.799599	+	0.259805i
$928$	14.9517	−	7.55468i	0.490814	−	0.247995i
$929$	8.58219	−	6.23532i	0.281572	−	0.204574i	−0.438031	−	0.898960i	$-0.644324\pi$
$929$	8.58219	−	6.23532i	0.281572	−	0.204574i	0.719603	+	0.694386i	$0.244324\pi$
$930$	−23.3072	+	0.716679i	−0.764275	+	0.0235008i
$931$	−12.8383	−	39.5123i	−0.420759	−	1.29496i
$932$	−0.0762820	−	1.23922i	−0.00249870	−	0.0405919i
$933$	−11.8231	−	8.59002i	−0.387072	−	0.281225i
$934$	−11.3547	+	16.6836i	−0.371536	+	0.545903i
$935$	5.08580	+	7.17069i	0.166323	+	0.234507i
$936$	5.83448	+	1.31660i	0.190706	+	0.0430344i
$937$	28.4401	−	39.1444i	0.929097	−	1.27879i	−0.0311137	−	0.999516i	$-0.509905\pi$
$937$	28.4401	−	39.1444i	0.929097	−	1.27879i	0.960211	−	0.279276i	$-0.0900946\pi$
$938$	−0.298535	−	0.385406i	−0.00974750	−	0.0125840i
$939$	−20.7685	+	6.74809i	−0.677754	+	0.220216i
$940$	−1.47124	+	2.31139i	−0.0479867	+	0.0753893i
$941$	6.50846	+	8.95813i	0.212170	+	0.292027i	0.901816	−	0.432119i	$-0.142234\pi$
$941$	6.50846	+	8.95813i	0.212170	+	0.292027i	−0.689647	+	0.724146i	$0.742234\pi$
$942$	42.2716	+	12.3120i	1.37728	+	0.401148i
$943$	6.81629	−	20.9784i	0.221969	−	0.683151i
$944$	6.25947	+	50.6506i	0.203728	+	1.64854i
$945$		−	2.58187i		−	0.0839883i
$946$	5.56058	−	18.3105i	0.180790	−	0.595326i
$947$			28.2608i			0.918354i	0.888345	+	0.459177i	$0.151856\pi$
$947$			28.2608i			0.918354i	−0.888345	+	0.459177i	$0.848144\pi$
$948$	5.45770	+	1.40917i	0.177258	+	0.0457678i
$949$	−0.774987	+	2.38516i	−0.0251571	+	0.0774257i
$950$	0.935398	−	3.21155i	0.0303483	−	0.104196i
$951$	−35.7971	−	49.2705i	−1.16080	−	1.59770i
$952$	34.1317	−	14.6879i	1.10621	−	0.476039i
$953$	−10.2856	+	3.34199i	−0.333183	+	0.108258i	−0.470831	−	0.882224i	$-0.656046\pi$
$953$	−10.2856	+	3.34199i	−0.333183	+	0.108258i	0.137648	+	0.990481i	$0.456046\pi$
$954$	17.3518	−	13.4406i	0.561785	−	0.435157i
$955$	1.38012	−	1.89957i	0.0446596	−	0.0614687i
$956$	−16.6899	−	42.3210i	−0.539789	−	1.36876i
$957$	18.9492	+	14.1006i	0.612539	+	0.455806i
$958$	−32.4405	−	22.0786i	−1.04811	−	0.713329i
$959$	−7.29341	−	5.29898i	−0.235517	−	0.171113i
$960$	13.9710	+	13.2268i	0.450913	+	0.426892i
$961$	−4.94702	−	15.2254i	−0.159581	−	0.491141i
$962$	−0.0127678	−	0.415223i	−0.000411650	−	0.0133873i
$963$	23.1586	−	16.8257i	0.746275	−	0.542200i
$964$	0.275370	+	0.333783i	0.00886905	+	0.0107504i
$965$	6.74547	+	2.19174i	0.217144	+	0.0705545i
$966$	−47.0286	−	130.905i	−1.51312	−	4.21179i
$967$	−22.0712			−0.709761			−0.354880	−	0.934912i	$-0.615478\pi$
$967$	−22.0712			−0.709761			−0.354880	+	0.934912i	$0.615478\pi$
$968$	−7.53950	+	30.1854i	−0.242329	+	0.970194i
$969$	15.0772			0.484350
$970$	6.86734	+	19.1153i	0.220497	+	0.613756i
$971$	−41.7333	−	13.5600i	−1.33929	−	0.435160i	−0.450211	−	0.892922i	$-0.648651\pi$
$971$	−41.7333	−	13.5600i	−1.33929	−	0.435160i	−0.889075	+	0.457762i	$0.848651\pi$
$972$	27.4038	+	33.2169i	0.878977	+	1.06543i
$973$	−31.0177	+	22.5357i	−0.994382	+	0.722461i
$974$	−0.827084	−	26.8977i	−0.0265015	−	0.861859i
$975$	−0.564602	−	1.73767i	−0.0180817	−	0.0556499i
$976$	24.7939	−	11.5853i	0.793633	−	0.370836i
$977$	−15.6621	−	11.3792i	−0.501075	−	0.364052i	0.308352	−	0.951272i	$-0.400222\pi$
$977$	−15.6621	−	11.3792i	−0.501075	−	0.364052i	−0.809428	+	0.587220i	$0.800222\pi$
$978$	−19.6652	−	13.3839i	−0.628825	−	0.427971i
$979$	−24.0257	−	17.8782i	−0.767866	−	0.571388i
$980$	−12.8879	−	32.6803i	−0.411689	−	1.04393i
$981$	17.1009	−	23.5374i	0.545990	−	0.751491i
$982$	−24.0690	+	18.6437i	−0.768072	+	0.594946i
$983$	−15.2135	+	4.94317i	−0.485236	+	0.157663i	−0.541411	−	0.840758i	$-0.682110\pi$
$983$	−15.2135	+	4.94317i	−0.485236	+	0.157663i	0.0561748	+	0.998421i	$0.482110\pi$
$984$	7.18720	+	16.7016i	0.229120	+	0.532426i
$985$	0.395938	+	0.544962i	0.0126156	+	0.0173639i
$986$	3.10423	−	10.6579i	0.0988587	−	0.339417i
$987$	−5.04587	+	15.5296i	−0.160612	+	0.494313i
$988$	−3.47989	−	0.898504i	−0.110710	−	0.0285852i
$989$			33.6664i			1.07053i
$990$	−3.79358	+	12.4919i	−0.120568	+	0.397019i
$991$			6.70465i			0.212980i	0.994314	+	0.106490i	$0.0339613\pi$
$991$			6.70465i			0.212980i	−0.994314	+	0.106490i	$0.966039\pi$
$992$	−17.7248	+	34.4980i	−0.562765	+	1.09531i
$993$	−8.06474	+	24.8207i	−0.255927	+	0.787662i
$994$	105.659	+	30.7743i	3.35130	+	0.976102i
$995$	0.430893	+	0.593073i	0.0136602	+	0.0188017i
$996$	5.72394	−	8.99258i	0.181370	−	0.284941i
$997$	−25.1647	+	8.17652i	−0.796975	+	0.258953i	−0.679071	−	0.734072i	$-0.737617\pi$
$997$	−25.1647	+	8.17652i	−0.796975	+	0.258953i	−0.117903	+	0.993025i	$0.537617\pi$
$998$	33.5964	+	43.3728i	1.06348	+	1.37294i
$999$	0.118386	−	0.162944i	0.00374555	−	0.00515531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.r.b.51.1	yes	8
4.3	odd	2		220.2.r.a.51.2	✓	8
11.8	odd	10		220.2.r.a.151.2	yes	8
44.19	even	10	inner	220.2.r.b.151.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.r.a.51.2	✓	8	4.3	odd	2
220.2.r.a.151.2	yes	8	11.8	odd	10
220.2.r.b.51.1	yes	8	1.1	even	1	trivial
220.2.r.b.151.1	yes	8	44.19	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.478148 - 1.33093i) q^{2} +(2.28716 + 0.743145i) q^{3} +(-1.54275 + 1.27276i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.104528 - 3.39939i) q^{6} +(1.53158 + 4.71372i) q^{7} +(2.43162 + 1.44472i) q^{8} +(2.25181 + 1.63603i) q^{9} +(-1.16913 - 0.795697i) q^{10} +(-2.66078 - 1.97996i) q^{11} +(-4.47437 + 1.76453i) q^{12} +(0.446568 - 0.614648i) q^{13} +(5.54131 - 4.29228i) q^{14} +(2.28716 - 0.743145i) q^{15} +(0.760154 - 3.92711i) q^{16} +(-1.55800 - 2.14440i) q^{17} +(1.10075 - 3.77926i) q^{18} +(-0.730909 + 2.24951i) q^{19} +(-0.500000 + 1.93649i) q^{20} +11.9192i q^{21} +(-1.36294 + 4.48803i) q^{22} -8.25186i q^{23} +(4.48787 + 5.11137i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-1.03158 - 0.300458i) q^{26} +(-0.306194 - 0.421439i) q^{27} +(-8.36228 - 5.32275i) q^{28} +(-2.81641 + 0.915107i) q^{29} +(-2.08268 - 2.68872i) q^{30} +(4.03003 - 5.54687i) q^{31} +(-5.59017 + 0.866025i) q^{32} +(-4.61426 - 6.50584i) q^{33} +(-2.10910 + 3.09893i) q^{34} +(4.00973 + 2.91324i) q^{35} +(-5.55626 + 0.342024i) q^{36} +(0.119477 + 0.367713i) q^{37} +(3.34342 - 0.102807i) q^{38} +(1.47815 - 1.07394i) q^{39} +(2.81641 - 0.260464i) q^{40} +(2.54226 + 0.826031i) q^{41} +(15.8637 - 5.69915i) q^{42} -4.07985 q^{43} +(6.62494 - 0.331966i) q^{44} +2.78339 q^{45} +(-10.9827 + 3.94561i) q^{46} +(1.30290 + 0.423339i) q^{47} +(4.65701 - 8.41704i) q^{48} +(-14.2103 + 10.3244i) q^{49} +(-1.41355 + 0.0434654i) q^{50} +(-1.96980 - 6.06242i) q^{51} +(0.0933582 + 1.51662i) q^{52} +(4.51101 + 3.27744i) q^{53} +(-0.414501 + 0.609032i) q^{54} +(-3.31641 - 0.0378495i) q^{55} +(-3.08580 + 13.6747i) q^{56} +(-3.34342 + 4.60182i) q^{57} +(2.56460 + 3.31089i) q^{58} +(-12.1345 + 3.94274i) q^{59} +(-2.58268 + 4.05750i) q^{60} +(4.02149 + 5.53510i) q^{61} +(-9.30944 - 2.71147i) q^{62} +(-4.26298 + 13.1201i) q^{63} +(3.82555 + 7.02604i) q^{64} -0.759747i q^{65} +(-6.45252 + 9.25200i) q^{66} -0.0695515i q^{67} +(5.13292 + 1.32531i) q^{68} +(6.13233 - 18.8734i) q^{69} +(1.96007 - 6.72962i) q^{70} +(9.22857 + 12.7020i) q^{71} +(3.11192 + 7.23145i) q^{72} +(-3.13942 + 1.02006i) q^{73} +(0.432273 - 0.334837i) q^{74} +(1.41355 - 1.94558i) q^{75} +(-1.73548 - 4.40070i) q^{76} +(5.25776 - 15.5746i) q^{77} +(-2.13611 - 1.45381i) q^{78} +(-0.948113 - 0.688845i) q^{79} +(-1.69332 - 3.62390i) q^{80} +(-2.96747 - 9.13292i) q^{81} +(-0.116187 - 3.77854i) q^{82} +(-1.79301 + 1.30270i) q^{83} +(-15.1703 - 18.3884i) q^{84} +(-2.52090 - 0.819089i) q^{85} +(1.95077 + 5.43000i) q^{86} -7.12165 q^{87} +(-3.60952 - 8.65860i) q^{88} +9.02957 q^{89} +(-1.33087 - 3.70449i) q^{90} +(3.58123 + 1.16361i) q^{91} +(10.5027 + 12.7306i) q^{92} +(13.3395 - 9.69170i) q^{93} +(-0.0595456 - 1.93649i) q^{94} +(0.730909 + 2.24951i) q^{95} +(-13.4292 - 2.17356i) q^{96} +(-11.6194 - 8.44200i) q^{97} +(20.5356 + 13.9763i) q^{98} +(-2.75229 - 8.81161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} + 5 q^{3} - q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 5 q^{8} + 3 q^{9} - 5 q^{10} - q^{11} - 10 q^{12} + 10 q^{13} + 5 q^{14} + 5 q^{15} + 7 q^{16} - 5 q^{17} - 10 q^{18} - 11 q^{19} - 4 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 8 * q + 5 * q^2 + 5 * q^3 - q^4 + 2 * q^5 + q^6 - 3 * q^7 + 5 * q^8 + 3 * q^9 - 5 * q^10 - q^11 - 10 * q^12 + 10 * q^13 + 5 * q^14 + 5 * q^15 + 7 * q^16 - 5 * q^17 - 10 * q^18 - 11 * q^19 - 4 * q^20 + q^22 + 3 * q^24 - 2 * q^25 + 7 * q^26 - 10 * q^27 - 9 * q^28 - 5 * q^29 - 6 * q^30 + 10 * q^31 - 11 * q^33 - 14 * q^34 + 8 * q^35 - 26 * q^36 + 20 * q^37 - 5 * q^38 + 3 * q^39 + 5 * q^40 + 10 * q^41 + 29 * q^42 - 34 * q^43 + 32 * q^44 - 8 * q^45 - 10 * q^46 - 23 * q^49 - 5 * q^50 + 9 * q^51 - 5 * q^52 - 7 * q^53 - 26 * q^54 - 9 * q^55 + 15 * q^56 + 5 * q^57 + 18 * q^58 - 5 * q^59 - 10 * q^60 - 10 * q^61 - q^62 - 23 * q^63 + 11 * q^64 - 17 * q^66 - 15 * q^68 + 15 * q^69 + 15 * q^70 + 90 * q^71 + 10 * q^72 + 5 * q^73 + 35 * q^74 + 5 * q^75 - 18 * q^76 - 14 * q^77 - 21 * q^79 - 7 * q^80 - 10 * q^81 - 2 * q^82 + 19 * q^83 - 30 * q^84 - 30 * q^86 - 18 * q^87 + 43 * q^88 + 20 * q^89 - 15 * q^90 - 10 * q^91 + 25 * q^92 + 11 * q^93 + 11 * q^95 - 36 * q^96 - 44 * q^97 + 50 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

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