LMFDB - Embedded newform 525.2.bb.a.41.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(41,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 2, 5]))

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

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

chi := DirichletCharacter("525.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bb (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			41.13
Character	$\chi$	$=$	525.41
Dual form			525.2.bb.a.461.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17599 + 1.61862i) q^{2} +(-0.838989 + 1.51529i) q^{3} +(-0.618923 - 1.90485i) q^{4} +(0.0163558 - 2.23601i) q^{5} +(-1.46602 - 3.13997i) q^{6} +(1.60206 + 2.10557i) q^{7} +(0.00547699 + 0.00177958i) q^{8} +(-1.59219 - 2.54262i) q^{9} +O(q^{10})$	\(q+(-1.17599 + 1.61862i) q^{2} +(-0.838989 + 1.51529i) q^{3} +(-0.618923 - 1.90485i) q^{4} +(0.0163558 - 2.23601i) q^{5} +(-1.46602 - 3.13997i) q^{6} +(1.60206 + 2.10557i) q^{7} +(0.00547699 + 0.00177958i) q^{8} +(-1.59219 - 2.54262i) q^{9} +(3.60000 + 2.65600i) q^{10} +(3.19077 - 4.39171i) q^{11} +(3.40567 + 0.660302i) q^{12} +(-0.335181 - 0.461337i) q^{13} +(-5.29211 + 0.116979i) q^{14} +(3.37447 + 1.90077i) q^{15} +(3.23140 - 2.34775i) q^{16} +(-0.101358 + 0.311948i) q^{17} +(5.98794 + 0.412953i) q^{18} +(6.40959 + 2.08260i) q^{19} +(-4.26938 + 1.35276i) q^{20} +(-4.53465 + 0.661027i) q^{21} +(3.35618 + 10.3292i) q^{22} +(1.00148 - 1.37842i) q^{23} +(-0.00729172 + 0.00680617i) q^{24} +(-4.99946 - 0.0731433i) q^{25} +1.14090 q^{26} +(5.18864 - 0.279402i) q^{27} +(3.01924 - 4.35486i) q^{28} +(5.33761 - 1.73429i) q^{29} +(-7.04498 + 3.22668i) q^{30} +(-6.23429 - 2.02564i) q^{31} +8.00286i q^{32} +(3.97769 + 8.51953i) q^{33} +(-0.385728 - 0.530909i) q^{34} +(4.73427 - 3.54777i) q^{35} +(-3.85786 + 4.60658i) q^{36} +(4.11051 - 2.98646i) q^{37} +(-10.9086 + 7.92554i) q^{38} +(0.980271 - 0.120839i) q^{39} +(0.00406874 - 0.0122175i) q^{40} +(-2.46982 + 1.79443i) q^{41} +(4.26277 - 8.11722i) q^{42} +7.24920 q^{43} +(-10.3404 - 3.35980i) q^{44} +(-5.71136 + 3.51857i) q^{45} +(1.05340 + 3.24202i) q^{46} +(-0.892483 - 2.74678i) q^{47} +(0.846408 + 6.86625i) q^{48} +(-1.86683 + 6.74648i) q^{49} +(5.99773 - 8.00620i) q^{50} +(-0.387653 - 0.415308i) q^{51} +(-0.671327 + 0.924002i) q^{52} +(-8.89796 + 2.89112i) q^{53} +(-5.64956 + 8.72698i) q^{54} +(-9.76772 - 7.20641i) q^{55} +(0.00502741 + 0.0143832i) q^{56} +(-8.53332 + 7.96510i) q^{57} +(-3.46984 + 10.6791i) q^{58} +(-8.43418 + 6.12779i) q^{59} +(1.53214 - 7.60430i) q^{60} +(0.801601 - 1.10331i) q^{61} +(10.6102 - 7.70878i) q^{62} +(2.80287 - 7.42589i) q^{63} +(-6.49075 - 4.71581i) q^{64} +(-1.03704 + 0.741922i) q^{65} +(-18.4676 - 3.58055i) q^{66} +(-1.97262 + 6.07111i) q^{67} +0.656948 q^{68} +(1.24847 + 2.67401i) q^{69} +(0.175010 + 11.8351i) q^{70} +(12.0359 - 3.91071i) q^{71} +(-0.00419563 - 0.0167593i) q^{72} +(7.16680 - 9.86425i) q^{73} +10.1654i q^{74} +(4.30533 - 7.51426i) q^{75} -13.4983i q^{76} +(14.3588 - 0.317394i) q^{77} +(-0.957201 + 1.72879i) q^{78} +(1.42961 + 4.39990i) q^{79} +(-5.19674 - 7.26384i) q^{80} +(-3.92983 + 8.09669i) q^{81} -6.10792i q^{82} +(3.14459 - 9.67804i) q^{83} +(4.06576 + 8.22870i) q^{84} +(0.695862 + 0.231740i) q^{85} +(-8.52501 + 11.7337i) q^{86} +(-1.85024 + 9.54307i) q^{87} +(0.0252912 - 0.0183751i) q^{88} +(11.1450 + 8.09732i) q^{89} +(1.02130 - 13.3823i) q^{90} +(0.434398 - 1.44483i) q^{91} +(-3.24552 - 1.05453i) q^{92} +(8.29993 - 7.74725i) q^{93} +(5.49553 + 1.78561i) q^{94} +(4.76155 - 14.2978i) q^{95} +(-12.1266 - 6.71431i) q^{96} +(2.27022 - 0.737640i) q^{97} +(-8.72457 - 10.9555i) q^{98} +(-16.2468 - 1.12044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	$ 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) $ 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$

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 $

$2$	−1.17599	+	1.61862i	−0.831553	+	1.14453i	0.156079	+	0.987745i	$0.450115\pi$
$2$	−1.17599	+	1.61862i	−0.831553	+	1.14453i	−0.987632	+	0.156790i	$0.949885\pi$
$3$	−0.838989	+	1.51529i	−0.484391	+	0.874852i
$3$	−0.838989	+	1.51529i	−0.484391	+	0.874852i
$4$	−0.618923	−	1.90485i	−0.309462	−	0.952425i
$5$	0.0163558	−	2.23601i	0.00731452	−	0.999973i
$5$	0.0163558	−	2.23601i	0.00731452	−	0.999973i
$6$	−1.46602	−	3.13997i	−0.598502	−	1.28189i
$7$	1.60206	+	2.10557i	0.605520	+	0.795830i
$7$	1.60206	+	2.10557i	0.605520	+	0.795830i
$8$	0.00547699	+	0.00177958i	0.00193641	+	0.000629177i
$9$	−1.59219	−	2.54262i	−0.530732	−	0.847540i
$10$	3.60000	+	2.65600i	1.13842	+	0.839902i
$11$	3.19077	−	4.39171i	0.962052	−	1.32415i	0.0160912	−	0.999871i	$-0.494878\pi$
$11$	3.19077	−	4.39171i	0.962052	−	1.32415i	0.945961	−	0.324281i	$-0.105122\pi$
$12$	3.40567	+	0.660302i	0.983131	+	0.190613i
$13$	−0.335181	−	0.461337i	−0.0929625	−	0.127952i	0.760002	−	0.649920i	$-0.225198\pi$
$13$	−0.335181	−	0.461337i	−0.0929625	−	0.127952i	−0.852965	+	0.521969i	$0.825198\pi$
$14$	−5.29211	+	0.116979i	−1.41438	+	0.0312640i
$15$	3.37447	+	1.90077i	0.871285	+	0.490777i
$16$	3.23140	−	2.34775i	0.807851	−	0.586938i
$17$	−0.101358	+	0.311948i	−0.0245830	+	0.0756586i	−0.962595	−	0.270943i	$-0.912664\pi$
$17$	−0.101358	+	0.311948i	−0.0245830	+	0.0756586i	0.938012	+	0.346602i	$0.112664\pi$
$18$	5.98794	+	0.412953i	1.41137	+	0.0973339i
$19$	6.40959	+	2.08260i	1.47046	+	0.477782i	0.931248	−	0.364387i	$-0.118721\pi$
$19$	6.40959	+	2.08260i	1.47046	+	0.477782i	0.539214	+	0.842169i	$0.318721\pi$
$20$	−4.26938	+	1.35276i	−0.954663	+	0.302487i
$21$	−4.53465	+	0.661027i	−0.989542	+	0.144248i
$22$	3.35618	+	10.3292i	0.715539	+	2.20220i
$23$	1.00148	−	1.37842i	0.208823	−	0.287420i	−0.691739	−	0.722147i	$-0.743155\pi$
$23$	1.00148	−	1.37842i	0.208823	−	0.287420i	0.900562	+	0.434727i	$0.143155\pi$
$24$	−0.00729172	+	0.00680617i	−0.00148842	+	0.00138930i
$25$	−4.99946	−	0.0731433i	−0.999893	−	0.0146287i
$26$	1.14090			0.223749
$27$	5.18864	−	0.279402i	0.998553	−	0.0537710i
$28$	3.01924	−	4.35486i	0.570583	−	0.822992i
$29$	5.33761	−	1.73429i	0.991169	−	0.322050i	0.231838	−	0.972754i	$-0.425526\pi$
$29$	5.33761	−	1.73429i	0.991169	−	0.322050i	0.759331	+	0.650704i	$0.225526\pi$
$30$	−7.04498	+	3.22668i	−1.28623	+	0.589109i
$31$	−6.23429	−	2.02564i	−1.11971	−	0.363816i	−0.310054	−	0.950719i	$-0.600347\pi$
$31$	−6.23429	−	2.02564i	−1.11971	−	0.363816i	−0.809657	+	0.586903i	$0.800347\pi$
$32$			8.00286i			1.41472i
$33$	3.97769	+	8.51953i	0.692427	+	1.48306i
$34$	−0.385728	−	0.530909i	−0.0661518	−	0.0910502i
$35$	4.73427	−	3.54777i	0.800238	−	0.599683i
$36$	−3.85786	+	4.60658i	−0.642977	+	0.767763i
$37$	4.11051	−	2.98646i	0.675763	−	0.490971i	−0.196186	−	0.980567i	$-0.562856\pi$
$37$	4.11051	−	2.98646i	0.675763	−	0.490971i	0.871949	+	0.489596i	$0.162856\pi$
$38$	−10.9086	+	7.92554i	−1.76960	+	1.28569i
$39$	0.980271	−	0.120839i	0.156969	−	0.0193497i
$40$	0.00406874	−	0.0122175i	0.000643324	−	0.00193175i
$41$	−2.46982	+	1.79443i	−0.385721	+	0.280243i	−0.763700	−	0.645572i	$-0.776619\pi$
$41$	−2.46982	+	1.79443i	−0.385721	+	0.280243i	0.377979	+	0.925814i	$0.376619\pi$
$42$	4.26277	−	8.11722i	0.657759	−	1.25251i
$43$	7.24920			1.10549			0.552747	−	0.833349i	$-0.313580\pi$
$43$	7.24920			1.10549			0.552747	+	0.833349i	$0.313580\pi$
$44$	−10.3404	−	3.35980i	−1.55887	−	0.506509i
$45$	−5.71136	+	3.51857i	−0.851399	+	0.524518i
$46$	1.05340	+	3.24202i	0.155315	+	0.478010i
$47$	−0.892483	−	2.74678i	−0.130182	−	0.400659i	0.864628	−	0.502413i	$-0.167554\pi$
$47$	−0.892483	−	2.74678i	−0.130182	−	0.400659i	−0.994810	+	0.101754i	$0.967554\pi$
$48$	0.846408	+	6.86625i	0.122168	+	0.991057i
$49$	−1.86683	+	6.74648i	−0.266691	+	0.963782i
$50$	5.99773	−	8.00620i	0.848207	−	1.13225i
$51$	−0.387653	−	0.415308i	−0.0542823	−	0.0581548i
$52$	−0.671327	+	0.924002i	−0.0930963	+	0.128136i
$53$	−8.89796	+	2.89112i	−1.22223	+	0.397126i	−0.847893	−	0.530167i	$-0.822129\pi$
$53$	−8.89796	+	2.89112i	−1.22223	+	0.397126i	−0.374336	+	0.927293i	$0.622129\pi$
$54$	−5.64956	+	8.72698i	−0.768807	+	1.18759i
$55$	−9.76772	−	7.20641i	−1.31708	−	0.971712i
$56$	0.00502741	+	0.0143832i	0.000671817	+	0.00192203i
$57$	−8.53332	+	7.96510i	−1.13027	+	1.05500i
$58$	−3.46984	+	10.6791i	−0.455612	+	1.40223i
$59$	−8.43418	+	6.12779i	−1.09804	+	0.797770i	−0.980738	−	0.195327i	$-0.937423\pi$
$59$	−8.43418	+	6.12779i	−1.09804	+	0.797770i	−0.117298	+	0.993097i	$0.537423\pi$
$60$	1.53214	−	7.60430i	0.197799	−	0.981711i
$61$	0.801601	−	1.10331i	0.102635	−	0.141264i	−0.754611	−	0.656173i	$-0.772174\pi$
$61$	0.801601	−	1.10331i	0.102635	−	0.141264i	0.857245	+	0.514909i	$0.172174\pi$
$62$	10.6102	−	7.70878i	1.34750	−	0.979016i
$63$	2.80287	−	7.42589i	0.353129	−	0.935575i
$64$	−6.49075	−	4.71581i	−0.811344	−	0.589476i
$65$	−1.03704	+	0.741922i	−0.128628	+	0.0920241i
$66$	−18.4676	−	3.58055i	−2.27320	−	0.440736i
$67$	−1.97262	+	6.07111i	−0.240994	+	0.741704i	0.755275	+	0.655408i	$0.227503\pi$
$67$	−1.97262	+	6.07111i	−0.240994	+	0.741704i	−0.996270	+	0.0862964i	$0.972497\pi$
$68$	0.656948			0.0796667
$69$	1.24847	+	2.67401i	0.150298	+	0.321913i
$70$	0.175010	+	11.8351i	0.0209177	+	1.41457i
$71$	12.0359	−	3.91071i	1.42840	−	0.464116i	0.510140	−	0.860091i	$-0.329594\pi$
$71$	12.0359	−	3.91071i	1.42840	−	0.464116i	0.918261	+	0.395976i	$0.129594\pi$
$72$	−0.00419563	−	0.0167593i	−0.000494460	−	0.00197511i
$73$	7.16680	−	9.86425i	0.838810	−	1.15452i	−0.147408	−	0.989076i	$-0.547093\pi$
$73$	7.16680	−	9.86425i	0.838810	−	1.15452i	0.986219	−	0.165448i	$-0.0529069\pi$
$74$			10.1654i			1.18170i
$75$	4.30533	−	7.51426i	0.497137	−	0.867672i
$76$		−	13.4983i		−	1.54836i
$77$	14.3588	−	0.317394i	1.63634	−	0.0361704i
$78$	−0.957201	+	1.72879i	−0.108382	+	0.195747i
$79$	1.42961	+	4.39990i	0.160844	+	0.495027i	0.998706	−	0.0508549i	$-0.0161946\pi$
$79$	1.42961	+	4.39990i	0.160844	+	0.495027i	−0.837862	+	0.545882i	$0.816195\pi$
$80$	−5.19674	−	7.26384i	−0.581013	−	0.812123i
$81$	−3.92983	+	8.09669i	−0.436648	+	0.899632i
$82$		−	6.10792i		−	0.674507i
$83$	3.14459	−	9.67804i	0.345163	−	1.06230i	−0.616333	−	0.787485i	$-0.711383\pi$
$83$	3.14459	−	9.67804i	0.345163	−	1.06230i	0.961496	−	0.274817i	$-0.0886174\pi$
$84$	4.06576	+	8.22870i	0.443611	+	0.897825i
$85$	0.695862	+	0.231740i	0.0754768	+	0.0251357i
$86$	−8.52501	+	11.7337i	−0.919276	+	1.26527i
$87$	−1.85024	+	9.54307i	−0.198367	+	1.02312i
$88$	0.0252912	−	0.0183751i	0.00269605	−	0.00195880i
$89$	11.1450	+	8.09732i	1.18137	+	0.858314i	0.992325	−	0.123655i	$-0.0394616\pi$
$89$	11.1450	+	8.09732i	1.18137	+	0.858314i	0.189043	+	0.981969i	$0.439462\pi$
$90$	1.02130	−	13.3823i	0.107655	−	1.41062i
$91$	0.434398	−	1.44483i	0.0455373	−	0.151460i
$92$	−3.24552	−	1.05453i	−0.338369	−	0.109943i
$93$	8.29993	−	7.74725i	0.860663	−	0.803352i
$94$	5.49553	+	1.78561i	0.566821	+	0.184171i
$95$	4.76155	−	14.2978i	0.488525	−	1.46693i
$96$	−12.1266	−	6.71431i	−1.23767	−	0.685277i
$97$	2.27022	−	0.737640i	0.230506	−	0.0748960i	−0.191487	−	0.981495i	$-0.561331\pi$
$97$	2.27022	−	0.737640i	0.230506	−	0.0748960i	0.421993	+	0.906599i	$0.361331\pi$
$98$	−8.72457	−	10.9555i	−0.881315	−	1.10667i
$99$	−16.2468	−	1.12044i	−1.63286	−	0.112609i
$100$	2.95496	+	9.56850i	0.295496	+	0.956850i
$101$	4.77425			0.475056			0.237528	−	0.971381i	$-0.423663\pi$
$101$	4.77425			0.475056			0.237528	+	0.971381i	$0.423663\pi$
$102$	1.12810	−	0.139062i	0.111699	−	0.0137692i
$103$	9.40619	−	3.05626i	0.926819	−	0.301142i	0.193558	−	0.981089i	$-0.437997\pi$
$103$	9.40619	−	3.05626i	0.926819	−	0.301142i	0.733261	+	0.679947i	$0.237997\pi$
$104$	−0.00101480	−	0.00312322i	−9.95089e−5	−	0.000306257i
$105$	1.40389	+	10.1503i	0.137006	+	0.990570i
$106$	5.78432	−	17.8023i	0.561823	−	1.72911i
$107$		−	3.28840i		−	0.317901i	−0.987287	−	0.158951i	$-0.949189\pi$
$107$		−	3.28840i		−	0.317901i	0.987287	−	0.158951i	$-0.0508111\pi$
$108$	−3.74359	−	9.71065i	−0.360227	−	0.934407i
$109$	13.0300	−	9.46687i	1.24805	−	0.906762i	0.249944	−	0.968260i	$-0.419588\pi$
$109$	13.0300	−	9.46687i	1.24805	−	0.906762i	0.998107	+	0.0614982i	$0.0195879\pi$
$110$	23.1512	−	7.33550i	2.20738	−	0.699412i
$111$	1.07667	+	8.73421i	0.102193	+	0.829014i
$112$	10.1202	+	3.04271i	0.956273	+	0.287509i
$113$	0.0510876	+	0.0703161i	0.00480592	+	0.00661478i	0.811413	−	0.584473i	$-0.198699\pi$
$113$	0.0510876	+	0.0703161i	0.00480592	+	0.00661478i	−0.806607	+	0.591088i	$0.798699\pi$
$114$	−2.85730	−	23.1791i	−0.267611	−	2.17092i
$115$	−3.06577	−	2.26186i	−0.285885	−	0.210920i
$116$	−6.60714	−	9.09395i	−0.613458	−	0.844352i
$117$	−0.639331	+	1.58678i	−0.0591062	+	0.146697i
$118$		−	20.8579i		−	1.92013i
$119$	−0.819210	+	0.286342i	−0.0750969	+	0.0262490i
$120$	0.0150994	+	0.0164157i	0.00137838	+	0.00149854i
$121$	−5.70696	−	17.5642i	−0.518815	−	1.59675i
$122$	0.843157	+	2.59497i	0.0763358	+	0.234937i
$123$	−0.646924	−	5.24799i	−0.0583312	−	0.473195i
$124$			13.1291i			1.17903i
$125$	−0.245319	+	11.1776i	−0.0219420	+	0.999759i
$126$	8.72351	+	13.2696i	0.777152	+	1.18215i
$127$	−3.72799	−	2.70855i	−0.330806	−	0.240345i	0.409967	−	0.912101i	$-0.365540\pi$
$127$	−3.72799	−	2.70855i	−0.330806	−	0.240345i	−0.740773	+	0.671756i	$0.765540\pi$
$128$	0.0438159	−	0.0142366i	0.00387281	−	0.00125835i
$129$	−6.08200	+	10.9846i	−0.535490	+	0.967143i
$130$	0.0186603	−	2.55106i	0.00163661	−	0.223743i
$131$	4.87400	−	15.0006i	0.425844	−	1.31061i	−0.476340	−	0.879261i	$-0.658037\pi$
$131$	4.87400	−	15.0006i	0.425844	−	1.31061i	0.902184	−	0.431351i	$-0.141963\pi$
$132$	13.7665	−	12.8498i	1.19822	−	1.11844i
$133$	5.88347	+	16.8323i	0.510161	+	1.45954i
$134$	−7.50700	−	10.3325i	−0.648506	−	0.892592i
$135$	−0.539882	−	11.6064i	−0.0464657	−	0.998920i
$136$	−0.00111028	+	0.00152816i	−9.52054e−5	+	0.000131039i
$137$	6.75119	+	9.29222i	0.576793	+	0.793888i	0.993339	−	0.115227i	$-0.0367595\pi$
$137$	6.75119	+	9.29222i	0.576793	+	0.793888i	−0.416546	+	0.909115i	$0.636759\pi$
$138$	−5.79638	−	1.12382i	−0.493421	−	0.0956660i
$139$	−1.53076	+	2.10691i	−0.129838	+	0.178706i	−0.868986	−	0.494836i	$-0.835228\pi$
$139$	−1.53076	+	2.10691i	−0.129838	+	0.178706i	0.739149	+	0.673542i	$0.235228\pi$
$140$	−9.68813	−	6.82228i	−0.818796	−	0.576588i
$141$	4.91094	+	0.952150i	0.413576	+	0.0801855i
$142$	−7.82423	+	24.0805i	−0.656595	+	2.02079i
$143$	−3.09554			−0.258862
$144$	−11.1145	−	4.47815i	−0.926205	−	0.373179i
$145$	−3.79060	−	11.9633i	−0.314792	−	0.993498i
$146$	7.53833	+	23.2006i	0.623876	+	1.92009i
$147$	−8.65660	−	8.48901i	−0.713984	−	0.700162i
$148$	−8.23284	−	5.98151i	−0.676736	−	0.491677i
$149$			20.5510i			1.68361i	0.539786	+	0.841803i	$0.318505\pi$
$149$			20.5510i			1.68361i	−0.539786	+	0.841803i	$0.681495\pi$
$150$	7.09967	+	15.8054i	0.579685	+	1.29051i
$151$	−17.6368			−1.43526			−0.717632	−	0.696422i	$-0.754774\pi$
$151$	−17.6368			−1.43526			−0.717632	+	0.696422i	$0.754774\pi$
$152$	0.0313991	+	0.0228128i	0.00254681	+	0.00185036i
$153$	0.954548	−	0.238967i	0.0771707	−	0.0193194i
$154$	−16.3722	+	23.6147i	−1.31931	+	1.90293i
$155$	−4.63132	+	13.9068i	−0.371997	+	1.11702i
$156$	−0.836893	−	1.79248i	−0.0670051	−	0.143513i
$157$			7.11496i			0.567835i	0.958849	+	0.283918i	$0.0916342\pi$
$157$			7.11496i			0.567835i	−0.958849	+	0.283918i	$0.908366\pi$
$158$	−8.80296	−	2.86026i	−0.700326	−	0.227550i
$159$	3.08441	−	15.9086i	0.244610	−	1.26163i
$160$	17.8945	+	0.130893i	1.41468	+	0.0103480i
$161$	4.50678	−	0.0996198i	0.355184	−	0.00785114i
$162$	−8.48398	−	15.8825i	−0.666564	−	1.24785i
$163$	10.1323	−	7.36155i	0.793623	−	0.576601i	−0.115413	−	0.993318i	$-0.536819\pi$
$163$	10.1323	−	7.36155i	0.793623	−	0.576601i	0.909037	+	0.416716i	$0.136819\pi$
$164$	4.94675	+	3.59402i	0.386276	+	0.280646i
$165$	19.1148	−	8.75481i	1.48808	−	0.681561i
$166$	11.9670	+	16.4712i	0.928821	+	1.27841i
$167$	−2.44782	+	7.53361i	−0.189418	+	0.582968i	−0.999996	−	0.00266169i	$-0.999153\pi$
$167$	−2.44782	+	7.53361i	−0.189418	+	0.582968i	0.810579	+	0.585630i	$0.199153\pi$
$168$	−0.0260126	−	0.00444934i	−0.00200691	−	0.000343274i
$169$	3.91674	−	12.0545i	0.301287	−	0.927267i
$170$	−1.19343	+	0.853808i	−0.0915316	+	0.0654841i
$171$	−4.91005	−	19.6131i	−0.375481	−	1.49985i
$172$	−4.48670	−	13.8086i	−0.342108	−	1.05290i
$173$	−2.71844	−	1.97506i	−0.206679	−	0.150161i	0.479631	−	0.877470i	$-0.340771\pi$
$173$	−2.71844	−	1.97506i	−0.206679	−	0.150161i	−0.686310	+	0.727309i	$0.740771\pi$
$174$	−13.2707	−	14.2174i	−1.00605	−	1.07782i
$175$	−7.85541	−	10.6439i	−0.593814	−	0.804603i
$176$		−	21.6825i		−	1.63438i
$177$	−2.20918	−	17.9214i	−0.166052	−	1.34705i
$178$	−26.2129	+	8.51709i	−1.96474	+	0.638383i
$179$	−13.6608	+	4.43866i	−1.02106	+	0.331761i	−0.771249	−	0.636534i	$-0.780367\pi$
$179$	−13.6608	+	4.43866i	−1.02106	+	0.331761i	−0.249808	+	0.968295i	$0.580367\pi$
$180$	10.2373	+	8.70156i	0.763040	+	0.648576i
$181$	−2.70841	−	0.880015i	−0.201314	−	0.0654110i	0.206624	−	0.978420i	$-0.433752\pi$
$181$	−2.70841	−	0.880015i	−0.201314	−	0.0654110i	−0.407939	+	0.913009i	$0.633752\pi$
$182$	1.82778	+	2.40224i	0.135484	+	0.178066i
$183$	0.999297	+	2.14032i	0.0738701	+	0.158217i
$184$	0.00793810	−	0.00576737i	0.000585205	−	0.000425176i
$185$	−6.61051	−	9.23997i	−0.486015	−	0.679336i
$186$	2.77916	+	22.5451i	0.203778	+	1.65309i
$187$	1.04658	+	1.44049i	0.0765333	+	0.105339i
$188$	−4.67983	+	3.40009i	−0.341311	+	0.247977i
$189$	8.90078	+	10.4774i	0.647437	+	0.762119i
$190$	17.5432	+	24.5213i	1.27271	+	1.77896i
$191$	1.90829	+	2.62654i	0.138079	+	0.190050i	0.872457	−	0.488692i	$-0.162526\pi$
$191$	1.90829	+	2.62654i	0.138079	+	0.190050i	−0.734377	+	0.678742i	$0.762526\pi$
$192$	12.5915	−	5.87885i	0.908711	−	0.424269i
$193$	−16.2868			−1.17235			−0.586175	−	0.810184i	$-0.699367\pi$
$193$	−16.2868			−1.17235			−0.586175	+	0.810184i	$0.699367\pi$
$194$	−1.47581	+	4.54208i	−0.105957	+	0.326102i
$195$	−0.254164	−	2.19387i	−0.0182010	−	0.157106i
$196$	14.0065	−	0.619513i	1.00046	−	0.0442509i
$197$	−25.2117	+	8.19177i	−1.79626	+	0.583639i	−0.999779	−	0.0210278i	$-0.993306\pi$
$197$	−25.2117	+	8.19177i	−1.79626	+	0.583639i	−0.796478	+	0.604667i	$0.793306\pi$
$198$	20.9197	−	24.9797i	1.48670	−	1.77523i
$199$		−	12.3318i		−	0.874181i	−0.899418	−	0.437091i	$-0.856009\pi$
$199$		−	12.3318i		−	0.874181i	0.899418	−	0.437091i	$-0.143991\pi$
$200$	−0.0272519	−	0.00929757i	−0.00192700	−	0.000657437i
$201$	−7.54447	−	8.08269i	−0.532146	−	0.570109i
$202$	−5.61449	+	7.72768i	−0.395034	+	0.543718i
$203$	12.2028	+	8.46026i	0.856470	+	0.593794i
$204$	−0.551172	+	0.995466i	−0.0385898	+	0.0696965i
$205$	3.97196	+	5.55188i	0.277414	+	0.387760i
$206$	−6.11471	+	18.8191i	−0.426032	+	1.31119i
$207$	−5.09934	−	0.351672i	−0.354429	−	0.0244429i
$208$	−2.16621	−	0.703844i	−0.150200	−	0.0488028i
$209$	29.5977	−	21.5040i	2.04732	−	1.48746i
$210$	−18.0804	−	9.66435i	−1.24767	−	0.666903i
$211$	3.35130	+	2.43486i	0.230713	+	0.167623i	0.697136	−	0.716939i	$-0.254457\pi$
$211$	3.35130	+	2.43486i	0.230713	+	0.167623i	−0.466423	+	0.884562i	$0.654457\pi$
$212$	11.0143	+	15.1599i	0.756466	+	1.04119i
$213$	−4.17216	+	21.5189i	−0.285872	+	1.47445i
$214$	5.32265	+	3.86713i	0.363849	+	0.264352i
$215$	0.118566	−	16.2093i	0.00808615	−	1.10546i
$216$	0.0289153	+	0.00770332i	0.00196744	+	0.000524144i
$217$	−5.72255	−	16.3719i	−0.388472	−	1.11140i
$218$			32.2236i			2.18246i
$219$	8.93431	+	19.1358i	0.603725	+	1.29307i
$220$	−7.68166	+	23.0663i	−0.517898	+	1.55513i
$221$	0.177887	−	0.0577989i	0.0119660	−	0.00388797i
$222$	−15.4035	−	8.52865i	−1.03381	−	0.572405i
$223$	3.56359	−	4.90486i	0.238636	−	0.328454i	−0.672855	−	0.739774i	$-0.734932\pi$
$223$	3.56359	−	4.90486i	0.238636	−	0.328454i	0.911491	+	0.411320i	$0.134932\pi$
$224$	−16.8506	+	12.8210i	−1.12588	+	0.856641i
$225$	7.77415	+	12.8282i	0.518276	+	0.855213i
$226$	−0.173893			−0.0115672
$227$	0.338526	+	0.245954i	0.0224688	+	0.0163245i	0.598963	−	0.800777i	$-0.295580\pi$
$227$	0.338526	+	0.245954i	0.0224688	+	0.0163245i	−0.576494	+	0.817101i	$0.695580\pi$
$228$	20.4538	+	11.3249i	1.35459	+	0.750011i
$229$	−14.6929	+	4.77400i	−0.970932	+	0.315475i	−0.751192	−	0.660083i	$-0.770521\pi$
$229$	−14.6929	+	4.77400i	−0.970932	+	0.315475i	−0.219740	+	0.975558i	$0.570521\pi$
$230$	7.26641	−	2.30238i	0.479133	−	0.151814i
$231$	−11.5660	+	22.0241i	−0.760984	+	1.44908i
$232$	0.0323204			0.00212194
$233$	9.30166	+	3.02229i	0.609372	+	0.197997i	0.597416	−	0.801932i	$-0.296194\pi$
$233$	9.30166	+	3.02229i	0.609372	+	0.197997i	0.0119560	+	0.999929i	$0.496194\pi$
$234$	−1.81653	−	2.90087i	−0.118750	−	0.189636i
$235$	−6.15642	+	1.95067i	−0.401600	+	0.127248i
$236$	16.8926	+	12.2732i	1.09962	+	0.798918i
$237$	−7.86654	−	1.52519i	−0.510987	−	0.0990718i
$238$	0.499908	−	1.66272i	0.0324042	−	0.107778i
$239$	1.11995	−	1.54148i	0.0724438	−	0.0997103i	−0.771258	−	0.636523i	$-0.780372\pi$
$239$	1.11995	−	1.54148i	0.0724438	−	0.0997103i	0.843701	+	0.536813i	$0.180372\pi$
$240$	15.3668	−	1.78027i	0.991924	−	0.114916i
$241$	3.36720	+	4.63456i	0.216901	+	0.298538i	0.903577	−	0.428425i	$-0.140931\pi$
$241$	3.36720	+	4.63456i	0.216901	+	0.298538i	−0.686677	+	0.726963i	$0.740931\pi$
$242$	35.1411	+	11.4180i	2.25896	+	0.733979i
$243$	−8.97173	−	12.7479i	−0.575537	−	0.817776i
$244$	−2.59777	−	0.844066i	−0.166305	−	0.0540358i
$245$	15.0546	+	4.28460i	0.961806	+	0.273733i
$246$	9.25526	+	5.12448i	0.590094	+	0.326725i
$247$	−1.18759	−	3.65503i	−0.0755647	−	0.232564i
$248$	−0.0305404	−	0.0221889i	−0.00193931	−	0.00140899i
$249$	12.0267	+	12.8847i	0.762164	+	0.816536i
$250$	−17.8038	−	13.5419i	−1.12601	−	0.856466i
$251$	0.864772			0.0545840			0.0272920	−	0.999628i	$-0.491312\pi$
$251$	0.864772			0.0545840			0.0272920	+	0.999628i	$0.491312\pi$
$252$	−15.8800	−	0.742998i	−1.00034	−	0.0468045i
$253$	−2.85813	−	8.79642i	−0.179689	−	0.553026i
$254$	8.76819	−	2.84896i	0.550165	−	0.178760i
$255$	−0.934973	+	0.860003i	−0.0585503	+	0.0538555i
$256$	4.93001	−	15.1730i	0.308126	−	0.948313i
$257$	−31.2974			−1.95228			−0.976141	−	0.217140i	$-0.930327\pi$
$257$	−31.2974			−1.95228			−0.976141	+	0.217140i	$0.930327\pi$
$258$	−10.6275	−	22.7623i	−0.661639	−	1.41712i
$259$	12.8735	+	3.87048i	0.799917	+	0.240500i
$260$	2.05510	+	1.51620i	0.127452	+	0.0940310i
$261$	−12.9082	−	10.8102i	−0.798995	−	0.669133i
$262$	18.5485	+	25.5298i	1.14593	+	1.57724i
$263$	4.84924	+	6.67440i	0.299017	+	0.411561i	0.931917	−	0.362672i	$-0.118136\pi$
$263$	4.84924	+	6.67440i	0.299017	+	0.411561i	−0.632900	+	0.774234i	$0.718136\pi$
$264$	0.00662458	+	0.0537400i	0.000407714	+	0.00330747i
$265$	6.31904	+	19.9432i	0.388176	+	1.22510i
$266$	−34.1639	−	10.2716i	−2.09472	−	0.629791i
$267$	−21.6203	+	10.0943i	−1.32314	+	0.617763i
$268$	12.7855			0.780996
$269$	5.96754	−	18.3662i	0.363847	−	1.11981i	−0.586852	−	0.809694i	$-0.699633\pi$
$269$	5.96754	−	18.3662i	0.363847	−	1.11981i	0.950700	−	0.310113i	$-0.100367\pi$
$270$	19.4212	+	12.7752i	1.18194	+	0.777473i
$271$	4.39420	−	1.42776i	0.266929	−	0.0867304i	−0.172495	−	0.985010i	$-0.555183\pi$
$271$	4.39420	−	1.42776i	0.266929	−	0.0867304i	0.439423	+	0.898280i	$0.355183\pi$
$272$	0.404848	+	1.24600i	0.0245475	+	0.0755496i
$273$	1.82488	+	1.87044i	0.110447	+	0.113204i
$274$	−22.9799			−1.38827
$275$	−16.2733	+	21.7228i	−0.981320	+	1.30994i
$276$	4.32088	−	4.03315i	0.260086	−	0.242767i
$277$	−5.38954	−	3.91573i	−0.323826	−	0.235273i	0.413980	−	0.910286i	$-0.364138\pi$
$277$	−5.38954	−	3.91573i	−0.323826	−	0.235273i	−0.737806	+	0.675013i	$0.764138\pi$
$278$	−1.61012	−	4.95544i	−0.0965685	−	0.297207i
$279$	4.77576	+	19.0766i	0.285917	+	1.14209i
$280$	0.0322431	−	0.0110061i	0.00192689	−	0.000657740i
$281$	11.4468	+	3.71928i	0.682857	+	0.221874i	0.629846	−	0.776720i	$-0.283118\pi$
$281$	11.4468	+	3.71928i	0.682857	+	0.221874i	0.0530112	+	0.998594i	$0.483118\pi$
$282$	−7.31640	+	6.82921i	−0.435685	+	0.406674i
$283$	−22.2772	−	7.23829i	−1.32424	−	0.430272i	−0.440291	−	0.897855i	$-0.645125\pi$
$283$	−22.2772	−	7.23829i	−1.32424	−	0.430272i	−0.883949	+	0.467583i	$0.845125\pi$
$284$	−14.8986	−	20.5062i	−0.884071	−	1.21682i
$285$	17.6705	+	19.2109i	1.04671	+	1.13795i
$286$	3.64034	−	5.01050i	0.215258	−	0.296277i
$287$	−7.73508	−	2.32560i	−0.456587	−	0.137276i
$288$	20.3482	−	12.7421i	1.19903	−	0.750836i
$289$	13.6663	+	9.92911i	0.803897	+	0.584065i
$290$	23.8217	+	7.93325i	1.39886	+	0.465856i
$291$	−0.786955	+	4.05891i	−0.0461321	+	0.237938i
$292$	−23.2256	−	7.54646i	−1.35918	−	0.441623i
$293$	−18.9155			−1.10506			−0.552529	−	0.833494i	$-0.686337\pi$
$293$	−18.9155			−1.10506			−0.552529	+	0.833494i	$0.686337\pi$
$294$	23.9206	−	4.02869i	1.39507	−	0.234958i
$295$	13.5638	+	18.9591i	0.789717	+	1.10384i
$296$	0.0278279	−	0.00904182i	0.00161746	−	0.000525545i
$297$	15.3287	−	23.6785i	0.889459	−	1.37397i
$298$	−33.2642	−	24.1679i	−1.92694	−	1.40001i
$299$	−0.971592			−0.0561886
$300$	−16.9782	−	3.55026i	−0.980238	−	0.204974i
$301$	11.6136	+	15.2637i	0.669398	+	0.879784i
$302$	20.7408	−	28.5472i	1.19350	−	1.64271i
$303$	−4.00554	+	7.23436i	−0.230113	+	0.415603i
$304$	25.6014	−	8.31841i	1.46834	−	0.477093i
$305$	−2.45390	−	1.81043i	−0.140510	−	0.103665i
$306$	−0.735746	+	1.82607i	−0.0420598	+	0.104390i
$307$			24.5503i			1.40116i	0.713573	+	0.700581i	$0.247076\pi$
$307$			24.5503i			1.40116i	−0.713573	+	0.700581i	$0.752924\pi$
$308$	−9.49161	−	27.1550i	−0.540835	−	1.54730i
$309$	−3.26058	+	16.8172i	−0.185488	+	0.956700i
$310$	−17.0634	−	23.8506i	−0.969133	−	1.35462i
$311$	−7.53562	−	5.47495i	−0.427306	−	0.310456i	0.353265	−	0.935523i	$-0.385071\pi$
$311$	−7.53562	−	5.47495i	−0.427306	−	0.310456i	−0.780571	+	0.625068i	$0.785071\pi$
$312$	0.00558398	+	0.00108264i	0.000316131	+	6.12924e-5i
$313$	−7.65297	−	10.5334i	−0.432571	−	0.595383i	0.535970	−	0.844237i	$-0.319946\pi$
$313$	−7.65297	−	10.5334i	−0.432571	−	0.595383i	−0.968541	+	0.248854i	$0.919946\pi$
$314$	−11.5164	−	8.36714i	−0.649907	−	0.472185i
$315$	−16.5585	−	6.38871i	−0.932967	−	0.359963i
$316$	7.49633	−	5.44640i	0.421701	−	0.306384i
$317$	6.97023	+	2.26477i	0.391487	+	0.127202i	0.498145	−	0.867094i	$-0.334015\pi$
$317$	6.97023	+	2.26477i	0.391487	+	0.127202i	−0.106657	+	0.994296i	$0.534015\pi$
$318$	22.1227	+	23.7009i	1.24058	+	1.32908i
$319$	9.41454	−	28.9750i	0.527113	−	1.62229i
$320$	−10.6507	+	14.4362i	−0.595395	+	0.807011i
$321$	4.98287	+	2.75893i	0.278117	+	0.153988i
$322$	−5.13870	+	7.41190i	−0.286368	+	0.413049i
$323$	−1.29933	+	1.78837i	−0.0722967	+	0.0995078i
$324$	17.8553	+	2.47451i	0.991958	+	0.137473i
$325$	1.64198	+	2.33095i	0.0910808	+	0.129298i
$326$			25.0574i			1.38780i
$327$	3.41298	+	27.6869i	0.188738	+	1.53109i
$328$	−0.0167205	+	0.00543282i	−0.000923236	+	0.000299977i
$329$	4.35372	−	6.27968i	0.240029	−	0.346210i
$330$	−8.30820	+	41.2351i	−0.457351	+	2.26992i
$331$	−8.35491	+	25.7138i	−0.459227	+	1.41336i	0.406872	+	0.913485i	$0.366619\pi$
$331$	−8.35491	+	25.7138i	−0.459227	+	1.41336i	−0.866100	+	0.499871i	$0.833381\pi$
$332$	−20.3815			−1.11858
$333$	−14.1382	−	5.69643i	−0.774766	−	0.312163i
$334$	−9.31540	−	12.8216i	−0.509716	−	0.701564i
$335$	13.5428	+	4.51010i	0.739922	+	0.246413i
$336$	−13.1014	+	12.7823i	−0.714738	+	0.697330i
$337$	−10.6552	+	7.74143i	−0.580424	+	0.421703i	−0.838877	−	0.544321i	$-0.816787\pi$
$337$	−10.6552	+	7.74143i	−0.580424	+	0.421703i	0.258453	+	0.966024i	$0.416787\pi$
$338$	14.9055	+	20.5157i	0.810753	+	1.11591i
$339$	−0.149411	+	0.0184180i	−0.00811490	+	0.00100033i
$340$	0.0107449	−	1.46894i	0.000582724	−	0.0796645i
$341$	−28.7882	+	20.9159i	−1.55897	+	1.13266i
$342$	37.5202	+	15.1174i	2.02886	+	0.817453i
$343$	−17.1959	+	6.87749i	−0.928493	+	0.371349i
$344$	0.0397038	+	0.0129006i	0.00214069	+	0.000695551i
$345$	5.99952	−	2.74785i	0.323003	−	0.147939i
$346$	6.39374	−	2.07745i	0.343730	−	0.111685i
$347$	7.76669	−	2.52355i	0.416938	−	0.135471i	−0.0930330	−	0.995663i	$-0.529656\pi$
$347$	7.76669	−	2.52355i	0.416938	−	0.135471i	0.509971	+	0.860192i	$0.329656\pi$
$348$	19.3233	−	2.38200i	1.03584	−	0.127688i
$349$		−	15.0638i		−	0.806345i	−0.915124	−	0.403173i	$-0.867907\pi$
$349$		−	15.0638i		−	0.806345i	0.915124	−	0.403173i	$-0.132093\pi$
$350$	26.4663	−	0.197751i	1.41468	−	0.0105702i
$351$	−1.86803	−	2.30006i	−0.0997081	−	0.122768i
$352$	35.1463	+	25.5353i	1.87330	+	1.36103i
$353$	−3.68811	−	11.3508i	−0.196298	−	0.604144i	−0.999959	−	0.00905607i	$-0.997117\pi$
$353$	−3.68811	−	11.3508i	−0.196298	−	0.604144i	0.803661	−	0.595088i	$-0.202883\pi$
$354$	31.6058	+	17.4996i	1.67983	+	0.930092i
$355$	−8.54752	−	26.9764i	−0.453655	−	1.43176i
$356$	8.52628	−	26.2412i	0.451892	−	1.39078i
$357$	0.253417	−	1.48158i	0.0134123	−	0.0784134i
$358$	8.88052	−	27.3314i	0.469350	−	1.44451i
$359$	−21.0743	−	29.0063i	−1.11226	−	1.53089i	−0.818045	−	0.575154i	$-0.804942\pi$
$359$	−21.0743	−	29.0063i	−1.11226	−	1.53089i	−0.294214	−	0.955740i	$-0.595058\pi$
$360$	−0.0375427	+	0.00910736i	−0.00197867	+	0.000480000i
$361$	21.3743	+	15.5294i	1.12497	+	0.817335i
$362$	4.60948	−	3.34898i	0.242269	−	0.176019i
$363$	31.4029	+	6.08850i	1.64823	+	0.319564i
$364$	−3.02105	+	0.0667787i	−0.158346	+	0.00350015i
$365$	−21.9393	−	16.1864i	−1.14836	−	0.847233i
$366$	−4.63952	−	0.899526i	−0.242512	−	0.0470190i
$367$	−23.7961	−	7.73181i	−1.24214	−	0.403597i	−0.387045	−	0.922061i	$-0.626504\pi$
$367$	−23.7961	−	7.73181i	−1.24214	−	0.403597i	−0.855100	+	0.518464i	$0.826504\pi$
$368$		−	6.80545i		−	0.354759i
$369$	8.49498	+	3.42273i	0.442231	+	0.178180i
$370$	22.7299	+	0.166263i	1.18167	+	0.00864359i
$371$	−20.3425	−	14.1035i	−1.05613	−	0.732218i
$372$	−19.8944	−	11.0152i	−1.03148	−	0.571110i
$373$	22.8723	+	16.6177i	1.18428	+	0.860432i	0.992648	−	0.121034i	$-0.0386211\pi$
$373$	22.8723	+	16.6177i	1.18428	+	0.860432i	0.191635	+	0.981466i	$0.438621\pi$
$374$	−3.56237			−0.184206
$375$	−16.7315	−	9.74965i	−0.864013	−	0.503470i
$376$		−	0.0166323i		−	0.000857747i
$377$	−2.58916	−	1.88113i	−0.133348	−	0.0968833i
$378$	−27.4262	+	2.08559i	−1.41065	+	0.107271i
$379$	5.94150	+	18.2861i	0.305194	+	0.939292i	0.979605	+	0.200935i	$0.0643980\pi$
$379$	5.94150	+	18.2861i	0.305194	+	0.939292i	−0.674410	+	0.738357i	$0.735602\pi$
$380$	−30.1823	−	0.220775i	−1.54832	−	0.0113255i
$381$	7.23197	−	3.37654i	0.370505	−	0.172986i
$382$	−6.49551			−0.332339
$383$	−2.66423	+	8.19966i	−0.136136	+	0.418983i	−0.995765	−	0.0919355i	$-0.970695\pi$
$383$	−2.66423	+	8.19966i	−0.136136	+	0.418983i	0.859629	+	0.510919i	$0.170695\pi$
$384$	−0.0151884	+	0.0783381i	−0.000775082	+	0.00399767i
$385$	−0.474846	−	32.1117i	−0.0242004	−	1.63656i
$386$	19.1532	−	26.3621i	0.974871	−	1.34180i
$387$	−11.5421	−	18.4320i	−0.586720	−	0.936950i
$388$	−2.81019	−	3.86789i	−0.142666	−	0.196362i
$389$	−5.93025	+	8.16229i	−0.300676	+	0.413845i	−0.932445	−	0.361312i	$-0.882329\pi$
$389$	−5.93025	+	8.16229i	−0.300676	+	0.413845i	0.631769	+	0.775156i	$0.282329\pi$
$390$	3.84993	+	2.16858i	0.194949	+	0.109811i
$391$	0.328487	+	0.452124i	0.0166123	+	0.0228649i
$392$	−0.0222305	+	0.0336282i	−0.00112281	+	0.00169848i
$393$	18.6411	+	19.9709i	0.940317	+	1.00740i
$394$	16.3894	−	50.4415i	0.825688	−	2.54121i
$395$	9.86159	−	3.12466i	0.496191	−	0.157219i
$396$	7.92123	+	31.6412i	0.398057	+	1.59003i
$397$	28.6716	−	9.31596i	1.43898	−	0.467554i	0.517404	−	0.855741i	$-0.326899\pi$
$397$	28.6716	−	9.31596i	1.43898	−	0.467554i	0.921581	+	0.388187i	$0.126899\pi$
$398$	19.9605	+	14.5022i	1.00053	+	0.726928i
$399$	−30.4419	−	5.20696i	−1.52400	−	0.260674i
$400$	−16.3270	+	11.5012i	−0.816351	+	0.575058i
$401$			9.51293i			0.475053i	0.971381	+	0.237527i	$0.0763367\pi$
$401$			9.51293i			0.475053i	−0.971381	+	0.237527i	$0.923663\pi$
$402$	21.9550	−	2.70641i	1.09502	−	0.134984i
$403$	1.15511	+	3.55507i	0.0575402	+	0.177090i
$404$	−2.95490	−	9.09423i	−0.147012	−	0.452455i
$405$	18.0400	+	8.91957i	0.896414	+	0.443217i
$406$	−28.0444	+	9.80247i	−1.39182	+	0.486489i
$407$		−	27.5812i		−	1.36715i
$408$	−0.00138410	−	0.00296450i	−6.85231e−5	−	0.000146765i
$409$	16.8780	+	23.2306i	0.834564	+	1.14868i	0.987056	+	0.160374i	$0.0512700\pi$
$409$	16.8780	+	23.2306i	0.834564	+	1.14868i	−0.152492	+	0.988305i	$0.548730\pi$
$410$	−13.6574	−	0.0998998i	−0.674489	−	0.00493370i
$411$	−19.7446	+	2.43393i	−0.973927	+	0.120057i
$412$	−11.6434	−	16.0258i	−0.573630	−	0.789534i
$413$	−26.4145	−	7.94168i	−1.29977	−	0.390784i
$414$	6.56601	−	7.84031i	0.322702	−	0.385330i
$415$	−21.5887	−	7.18961i	−1.05975	−	0.352924i
$416$	3.69202	−	2.68241i	0.181016	−	0.131516i
$417$	−1.90829	−	4.08723i	−0.0934493	−	0.200152i
$418$			73.1959i			3.58013i
$419$	4.28360	−	13.1836i	0.209268	−	0.644059i	−0.790243	−	0.612793i	$-0.790046\pi$
$419$	4.28360	−	13.1836i	0.209268	−	0.644059i	0.999511	−	0.0312664i	$-0.00995404\pi$
$420$	18.4659	−	8.95648i	0.901046	−	0.437032i
$421$	−10.0592	−	30.9591i	−0.490257	−	1.50886i	−0.824220	−	0.566270i	$-0.808386\pi$
$421$	−10.0592	−	30.9591i	−0.490257	−	1.50886i	0.333963	−	0.942586i	$-0.391614\pi$
$422$	−7.88222	+	2.56109i	−0.383700	+	0.124672i
$423$	−5.56301	+	6.64265i	−0.270483	+	0.322977i
$424$	−0.0538790			−0.00261660
$425$	0.529554	−	1.55216i	0.0256871	−	0.0752909i
$426$	−29.9244	−	32.0592i	−1.44984	−	1.55327i
$427$	3.60730	−	0.0797374i	0.174570	−	0.00385877i
$428$	−6.26390	+	2.03527i	−0.302777	+	0.0983783i
$429$	2.59713	−	4.69064i	0.125390	−	0.226466i
$430$	26.0972	+	19.2539i	1.25852	+	0.928506i
$431$	8.85538	+	2.87729i	0.426548	+	0.138594i	0.514421	−	0.857538i	$-0.328007\pi$
$431$	8.85538	+	2.87729i	0.426548	+	0.138594i	−0.0878726	+	0.996132i	$0.528007\pi$
$432$	16.1106	−	13.0845i	0.775122	−	0.629528i
$433$	−19.0699	−	6.19620i	−0.916443	−	0.297770i	−0.187436	−	0.982277i	$-0.560018\pi$
$433$	−19.0699	−	6.19620i	−0.916443	−	0.297770i	−0.729007	+	0.684507i	$0.760018\pi$
$434$	33.2295	+	9.99065i	1.59507	+	0.479567i
$435$	21.3081	+	4.29324i	1.02165	+	0.205845i
$436$	−26.0976	−	18.9610i	−1.24985	−	0.908067i
$437$	9.28977	−	6.74941i	0.444390	−	0.322868i
$438$	−41.4801	−	8.04230i	−1.98200	−	0.384276i
$439$	0.631110	−	0.868648i	0.0301212	−	0.0414583i	−0.793691	−	0.608321i	$-0.791843\pi$
$439$	0.631110	−	0.868648i	0.0301212	−	0.0414583i	0.823812	+	0.566863i	$0.191843\pi$
$440$	−0.0406733	−	0.0568519i	−0.00193902	−	0.00271031i
$441$	20.1261	−	5.99505i	0.958385	−	0.285479i
$442$	−0.115639	+	0.355901i	−0.00550040	+	0.0169285i
$443$			11.5440i			0.548473i	0.961662	+	0.274236i	$0.0884251\pi$
$443$			11.5440i			0.548473i	−0.961662	+	0.274236i	$0.911575\pi$
$444$	15.9710	−	7.45671i	0.757949	−	0.353880i
$445$	18.2880	−	24.7879i	0.866932	−	1.17506i
$446$	3.74833	+	11.5362i	0.177488	+	0.546253i
$447$	−31.1407	−	17.2421i	−1.47291	−	0.815523i
$448$	−0.469094	−	21.2217i	−0.0221626	−	1.00263i
$449$		−	1.43083i		−	0.0675252i	−0.999430	−	0.0337626i	$-0.989251\pi$
$449$		−	1.43083i		−	0.0675252i	0.999430	−	0.0337626i	$-0.0107490\pi$
$450$	−29.9063	−	2.50252i	−1.40980	−	0.117970i
$451$			16.5723i			0.780361i
$452$	0.102322	−	0.140835i	0.00481284	−	0.00662430i
$453$	14.7971	−	26.7249i	0.695229	−	1.25564i
$454$	−0.796210	+	0.258704i	−0.0373680	+	0.0121416i
$455$	−3.22356	−	0.994948i	−0.151123	−	0.0466439i
$456$	−0.0609115	+	0.0284390i	−0.00285244	+	0.00133178i
$457$	−29.4126			−1.37586			−0.687931	−	0.725776i	$-0.741481\pi$
$457$	−29.4126			−1.37586			−0.687931	+	0.725776i	$0.741481\pi$
$458$	9.55144	−	29.3963i	0.446310	−	1.37360i
$459$	−0.438752	+	1.64691i	−0.0204792	+	0.0768710i
$460$	−2.41103	+	7.23976i	−0.112415	+	0.337556i
$461$	−7.29919	−	5.30317i	−0.339957	−	0.246993i	0.404687	−	0.914455i	$-0.367381\pi$
$461$	−7.29919	−	5.30317i	−0.339957	−	0.246993i	−0.744644	+	0.667462i	$0.767381\pi$
$462$	−22.0470	−	44.6210i	−1.02572	−	2.07596i
$463$	8.88179	−	6.45299i	0.412772	−	0.299896i	−0.361951	−	0.932197i	$-0.617889\pi$
$463$	8.88179	−	6.45299i	0.412772	−	0.299896i	0.774723	+	0.632301i	$0.217889\pi$
$464$	13.1763	−	18.1356i	0.611693	−	0.841924i
$465$	−17.1872	−	18.6854i	−0.797036	−	0.866516i
$466$	−15.8306	+	11.5016i	−0.733339	+	0.532802i
$467$	−10.8087	+	33.2658i	−0.500167	+	1.53936i	0.308579	+	0.951199i	$0.400147\pi$
$467$	−10.8087	+	33.2658i	−0.500167	+	1.53936i	−0.808746	+	0.588158i	$0.799853\pi$
$468$	3.41827	+	0.235738i	0.158010	+	0.0108970i
$469$	−15.9434	+	5.57277i	−0.736197	+	0.257326i
$470$	4.08252	−	12.2589i	0.188312	−	0.565459i
$471$	−10.7812	−	5.96937i	−0.496772	−	0.275054i
$472$	−0.0570988	+	0.0185525i	−0.00262819	+	0.000853950i
$473$	23.1305	−	31.8364i	1.06354	−	1.46384i
$474$	11.7197	−	10.9393i	0.538304	−	0.502459i
$475$	−31.8922	−	10.8807i	−1.46332	−	0.499242i
$476$	1.05247	+	1.38325i	0.0482398	+	0.0634011i
$477$	21.5183	+	18.0209i	0.985256	+	0.825120i
$478$	1.17801	+	3.62555i	0.0538810	+	0.165829i
$479$	−1.99721	−	6.14678i	−0.0912549	−	0.280854i	0.895005	−	0.446057i	$-0.147172\pi$
$479$	−1.99721	−	6.14678i	−0.0912549	−	0.280854i	−0.986260	+	0.165203i	$0.947172\pi$
$480$	−15.2116	+	27.0054i	−0.694311	+	1.23262i
$481$	−2.75553	−	0.895325i	−0.125641	−	0.0408233i
$482$	−11.4614			−0.522051
$483$	−3.63019	+	6.91265i	−0.165179	+	0.314536i
$484$	−29.9251	+	21.7418i	−1.36023	+	0.988265i
$485$	−1.61224	−	5.08830i	−0.0732079	−	0.231048i
$486$	31.1846	+	0.469617i	1.41456	+	0.0213023i
$487$	24.8540	−	18.0575i	1.12624	−	0.818262i	0.141098	−	0.989996i	$-0.454937\pi$
$487$	24.8540	−	18.0575i	1.12624	−	0.818262i	0.985143	+	0.171733i	$0.0549367\pi$
$488$	0.00635379	−	0.00461630i	0.000287623	−	0.000208970i
$489$	2.65397	+	21.5296i	0.120017	+	0.973603i
$490$	−24.6393	+	19.3290i	−1.11309	+	0.873196i
$491$	5.72031	+	7.87333i	0.258154	+	0.355318i	0.918346	−	0.395778i	$-0.129525\pi$
$491$	5.72031	+	7.87333i	0.258154	+	0.355318i	−0.660192	+	0.751097i	$0.729525\pi$
$492$	−9.59624	+	4.48040i	−0.432632	+	0.201992i
$493$			1.84084i			0.0829074i
$494$	7.31269	+	2.37604i	0.329014	+	0.106903i
$495$	−2.77105	+	36.3096i	−0.124550	+	1.63200i
$496$	−24.9012	+	8.09090i	−1.11810	+	0.363292i
$497$	27.5165	+	19.0773i	1.23428	+	0.855733i
$498$	−34.9988	+	4.31433i	−1.56833	+	0.193330i
$499$	0.100586			0.00450286			0.00225143	−	0.999997i	$-0.499283\pi$
$499$	0.100586			0.00450286			0.00225143	+	0.999997i	$0.499283\pi$
$500$	21.4436	−	6.45081i	0.958986	−	0.288489i
$501$	−9.36189	−	10.0298i	−0.418259	−	0.448097i
$502$	−1.01697	+	1.39973i	−0.0453894	+	0.0624732i
$503$	4.08494	+	12.5722i	0.182138	+	0.560565i	0.999887	−	0.0150106i	$-0.00477820\pi$
$503$	4.08494	+	12.5722i	0.182138	+	0.560565i	−0.817749	+	0.575575i	$0.804778\pi$
$504$	0.0285663	−	0.0356836i	0.00127244	−	0.00158947i
$505$	0.0780865	−	10.6753i	0.00347481	−	0.475043i
$506$	17.5992	+	5.71831i	0.782378	+	0.254210i
$507$	14.9799	+	16.0486i	0.665281	+	0.712741i
$508$	−2.85203	+	8.77765i	−0.126538	+	0.389445i
$509$	−28.2423	+	20.5192i	−1.25182	+	0.909498i	−0.998326	−	0.0578404i	$-0.981579\pi$
$509$	−28.2423	+	20.5192i	−1.25182	+	0.909498i	−0.253490	+	0.967338i	$0.581579\pi$
$510$	−0.292493	−	2.52472i	−0.0129518	−	0.111796i
$511$	32.2515	−	0.712901i	1.42672	−	0.0315369i
$512$	18.8158	+	25.8977i	0.831548	+	1.14453i
$513$	33.8389	+	9.01501i	1.49403	+	0.398023i
$514$	36.8056	−	50.6586i	1.62343	−	2.23445i
$515$	−6.67997	−	21.0823i	−0.294355	−	0.928997i
$516$	24.6884	+	4.78666i	1.08684	+	0.210721i
$517$	−14.9108	−	4.84480i	−0.655775	−	0.213074i
$518$	−21.4039	+	16.2855i	−0.940434	+	0.715544i
$519$	5.27353	−	2.46217i	0.231482	−	0.108077i
$520$	−0.00700014	+	0.00221801i	−0.000306977	+	9.72661e-5i
$521$	−1.74005	−	5.35533i	−0.0762331	−	0.234621i	0.905677	−	0.423968i	$-0.139363\pi$
$521$	−1.74005	−	5.35533i	−0.0762331	−	0.234621i	−0.981910	+	0.189347i	$0.939363\pi$
$522$	32.6774	−	8.18066i	1.43025	−	0.358058i
$523$	15.5813	−	21.4459i	0.681324	−	0.937762i	−0.318625	−	0.947881i	$-0.603221\pi$
$523$	15.5813	−	21.4459i	0.681324	−	0.937762i	0.999949	+	0.0101191i	$0.00322106\pi$
$524$	−31.5906			−1.38004
$525$	22.7192	−	2.97310i	0.991546	−	0.129757i
$526$	−16.5060			−0.719694
$527$	1.26379	−	1.73946i	0.0550517	−	0.0757721i
$528$	32.8553	+	18.1914i	1.42984	+	0.791679i
$529$	6.21032	+	19.1134i	0.270014	+	0.831017i
$530$	−39.7115	−	13.2250i	−1.72496	−	0.574456i
$531$	29.0095	+	11.6883i	1.25890	+	0.507228i
$532$	28.4216	−	21.6250i	1.23223	−	0.937563i
$533$	1.65567	+	0.537960i	0.0717151	+	0.0233017i
$534$	9.08650	−	46.8658i	0.393211	−	2.02808i
$535$	−7.35288	−	0.0537842i	−0.317893	−	0.00232530i
$536$	−0.0216081	+	0.0297410i	−0.000933327	+	0.00128461i
$537$	4.73541	−	24.4240i	0.204348	−	1.05398i
$538$	22.7100	+	31.2577i	0.979099	+	1.34761i
$539$	23.6720	+	29.7250i	1.01962	+	1.28035i
$540$	−21.7743	+	8.21187i	−0.937017	+	0.353383i
$541$	−21.8830	+	15.8990i	−0.940826	+	0.683550i	−0.948619	−	0.316420i	$-0.897519\pi$
$541$	−21.8830	+	15.8990i	−0.940826	+	0.683550i	0.00779355	+	0.999970i	$0.497519\pi$
$542$	−2.85655	+	8.79157i	−0.122699	+	0.377630i
$543$	3.60580	−	3.36570i	0.154740	−	0.144436i
$544$	−2.49648	−	0.811156i	−0.107036	−	0.0347780i
$545$	−20.9549	−	29.2901i	−0.897609	−	1.25465i
$546$	−5.17357	+	0.754165i	−0.221408	+	0.0322753i
$547$	−3.94381	−	12.1378i	−0.168625	−	0.518975i	0.830660	−	0.556780i	$-0.187963\pi$
$547$	−3.94381	−	12.1378i	−0.168625	−	0.518975i	−0.999285	+	0.0378049i	$0.987963\pi$
$548$	13.5218	−	18.6112i	0.577623	−	0.795030i
$549$	−4.08160	−	0.281484i	−0.174199	−	0.0120134i
$550$	−16.0236	−	51.8862i	−0.683247	−	2.21244i
$551$	37.8238			1.61135
$552$	0.00207924	+	0.0168673i	8.84984e−5	+	0.000717919i
$553$	−6.97397	+	10.0590i	−0.296563	+	0.427754i
$554$	12.6761	−	4.11872i	0.538557	−	0.174988i
$555$	19.5474	−	2.26459i	0.829739	−	0.0961267i
$556$	4.96078	+	1.61186i	0.210384	+	0.0683579i
$557$			28.6293i			1.21306i	0.795060	+	0.606531i	$0.207439\pi$
$557$			28.6293i			1.21306i	−0.795060	+	0.606531i	$0.792561\pi$
$558$	−36.4940	−	14.7039i	−1.54492	−	0.622465i
$559$	−2.42979	−	3.34433i	−0.102769	−	0.141450i
$560$	6.96905	−	22.5792i	0.294496	−	0.954144i
$561$	−3.06083	+	0.377311i	−0.129228	+	0.0159301i
$562$	−19.4814	+	14.1541i	−0.821774	+	0.597054i
$563$	12.7495	−	9.26303i	0.537326	−	0.390390i	−0.285765	−	0.958300i	$-0.592248\pi$
$563$	12.7495	−	9.26303i	0.537326	−	0.390390i	0.823091	+	0.567910i	$0.192248\pi$
$564$	−1.22580	−	9.94392i	−0.0516153	−	0.418715i
$565$	0.158063	−	0.113082i	0.00664976	−	0.00475741i
$566$	37.9138	−	27.5460i	1.59364	−	1.15785i
$567$	−23.3439	+	4.69682i	−0.980354	+	0.197248i
$568$	0.0728801			0.00305798
$569$	−23.5932	−	7.66590i	−0.989079	−	0.321371i	−0.230586	−	0.973052i	$-0.574064\pi$
$569$	−23.5932	−	7.66590i	−0.989079	−	0.321371i	−0.758494	+	0.651681i	$0.774064\pi$
$570$	−51.8753	+	6.00984i	−2.17282	+	0.251725i
$571$	11.2543	+	34.6370i	0.470976	+	1.44952i	0.851308	+	0.524666i	$0.175810\pi$
$571$	11.2543	+	34.6370i	0.470976	+	1.44952i	−0.380332	+	0.924850i	$0.624190\pi$
$572$	1.91590	+	5.89655i	0.0801080	+	0.246547i
$573$	−5.58101	+	0.687975i	−0.233150	+	0.0287406i
$574$	12.8606	−	9.78523i	0.536793	−	0.408428i
$575$	−5.10768	+	6.81810i	−0.213005	+	0.284334i
$576$	−1.65597	+	24.0120i	−0.0689986	+	1.00050i
$577$	−15.2676	+	21.0140i	−0.635598	+	0.874826i	−0.998371	−	0.0570515i	$-0.981830\pi$
$577$	−15.2676	+	21.0140i	−0.635598	+	0.874826i	0.362773	+	0.931878i	$0.381830\pi$
$578$	−32.1428	+	10.4438i	−1.33697	+	0.434407i
$579$	13.6645	−	24.6792i	0.567876	−	1.02563i
$580$	−20.4422	+	14.6249i	−0.848817	+	0.607265i
$581$	25.4156	−	8.88362i	1.05442	−	0.368555i
$582$	−5.64436	−	6.04703i	−0.233966	−	0.250657i
$583$	−15.6943	+	48.3022i	−0.649993	+	2.00047i
$584$	0.0568067	−	0.0412725i	0.00235068	−	0.00170787i
$585$	3.53759	+	1.45550i	0.146261	+	0.0601776i
$586$	22.2446	−	30.6170i	0.918914	−	1.26478i
$587$	4.04193	−	2.93663i	0.166828	−	0.121208i	−0.501238	−	0.865309i	$-0.667122\pi$
$587$	4.04193	−	2.93663i	0.166828	−	0.121208i	0.668067	+	0.744101i	$0.267122\pi$
$588$	−10.8125	+	21.7436i	−0.445901	+	0.896690i
$589$	−35.7407	−	25.9671i	−1.47267	−	1.06996i
$590$	−46.6385	−	0.341148i	−1.92008	−	0.0140448i
$591$	8.73943	−	45.0757i	0.359492	−	1.85417i
$592$	6.27124	−	19.3009i	0.257746	−	0.793262i
$593$	38.7697			1.59208			0.796041	−	0.605243i	$-0.206924\pi$
$593$	38.7697			1.59208			0.796041	+	0.605243i	$0.206924\pi$
$594$	20.3000	+	52.6570i	0.832919	+	2.16054i
$595$	0.626865	+	1.83644i	0.0256990	+	0.0752869i
$596$	39.1466	−	12.7195i	1.60351	−	0.521011i
$597$	18.6863	+	10.3463i	0.764779	+	0.423445i
$598$	1.14259	−	1.57263i	0.0467238	−	0.0643098i
$599$			11.5335i			0.471247i	0.971844	+	0.235623i	$0.0757132\pi$
$599$			11.5335i			0.471247i	−0.971844	+	0.235623i	$0.924287\pi$
$600$	0.0369525	−	0.0334939i	0.00150858	−	0.00136738i
$601$			24.4445i			0.997114i	0.866857	+	0.498557i	$0.166136\pi$
$601$			24.4445i			0.997114i	−0.866857	+	0.498557i	$0.833864\pi$
$602$	−38.3636	+	0.848006i	−1.56358	+	0.0345622i
$603$	18.5773	−	4.65076i	0.756527	−	0.189393i
$604$	10.9158	+	33.5955i	0.444159	+	1.36698i
$605$	−39.3671	+	12.4735i	−1.60050	+	0.507122i
$606$	−6.99916	−	14.9910i	−0.284322	−	0.608968i
$607$		−	17.3660i		−	0.704863i	−0.935838	−	0.352431i	$-0.885355\pi$
$607$		−	17.3660i		−	0.704863i	0.935838	−	0.352431i	$-0.114645\pi$
$608$	−16.6668	+	51.2951i	−0.675927	+	2.08029i
$609$	−23.0578	+	11.3927i	−0.934348	+	0.461656i
$610$	5.81616	−	1.84286i	0.235490	−	0.0746153i
$611$	−0.968048	+	1.33240i	−0.0391630	+	0.0539033i
$612$	−1.04599	−	1.67037i	−0.0422816	−	0.0675207i
$613$	−18.3125	+	13.3048i	−0.739635	+	0.537376i	−0.892597	−	0.450856i	$-0.851119\pi$
$613$	−18.3125	+	13.3048i	−0.739635	+	0.537376i	0.152962	+	0.988232i	$0.451119\pi$
$614$	−39.7376	−	28.8710i	−1.60368	−	1.16514i
$615$	−11.7451	+	1.36069i	−0.473609	+	0.0548684i
$616$	0.0792080	+	0.0238144i	0.00319138	+	0.000959508i
$617$	−44.1653	−	14.3502i	−1.77803	−	0.577716i	−0.779229	−	0.626740i	$-0.784389\pi$
$617$	−44.1653	−	14.3502i	−1.77803	−	0.577716i	−0.998798	+	0.0490238i	$0.984389\pi$
$618$	−23.3862	−	25.0546i	−0.940733	−	1.00784i
$619$	−14.7368	−	4.78827i	−0.592321	−	0.192457i	−0.00250833	−	0.999997i	$-0.500798\pi$
$619$	−14.7368	−	4.78827i	−0.592321	−	0.192457i	−0.589813	+	0.807540i	$0.700798\pi$
$620$	29.3568	+	0.214737i	1.17900	+	0.00862403i
$621$	4.81118	−	7.43192i	0.193066	−	0.298233i
$622$	17.7237	−	5.75877i	0.710654	−	0.230906i
$623$	0.805462	+	36.4389i	0.0322702	+	1.45989i
$624$	2.88395	−	2.69191i	0.115451	−	0.107763i
$625$	24.9893	+	0.731354i	0.999572	+	0.0292542i
$626$	26.0494			1.04114
$627$	7.75259	+	62.8907i	0.309608	+	2.51161i
$628$	13.5529	−	4.40361i	0.540821	−	0.175723i
$629$	0.514987	+	1.58497i	0.0205339	+	0.0631968i
$630$	29.8136	−	19.2888i	1.18780	−	0.768484i
$631$	0.834763	−	2.56914i	0.0332314	−	0.102276i	−0.933065	−	0.359708i	$-0.882876\pi$
$631$	0.834763	−	2.56914i	0.0332314	−	0.102276i	0.966296	+	0.257432i	$0.0828764\pi$
$632$			0.0266423i			0.00105977i
$633$	−6.50122	+	3.03536i	−0.258400	+	0.120645i
$634$	−11.8627	+	8.61878i	−0.471129	+	0.342295i
$635$	−6.11730	+	8.29152i	−0.242758	+	0.329039i
$636$	−32.2125	+	3.97086i	−1.27731	+	0.157455i
$637$	3.73813	−	1.40005i	0.148110	−	0.0554720i
$638$	35.8279	+	49.3129i	1.41844	+	1.95232i
$639$	−29.1070	−	24.3762i	−1.15145	−	0.964306i
$640$	−0.0311166	−	0.0982055i	−0.00122999	−	0.00388191i
$641$	9.42622	+	12.9741i	0.372313	+	0.512445i	0.953528	−	0.301305i	$-0.0974223\pi$
$641$	9.42622	+	12.9741i	0.372313	+	0.512445i	−0.581215	+	0.813750i	$0.697422\pi$
$642$	−10.3255	+	4.82087i	−0.407514	+	0.190264i
$643$			19.5504i			0.770992i	0.922709	+	0.385496i	$0.125970\pi$
$643$			19.5504i			0.770992i	−0.922709	+	0.385496i	$0.874030\pi$
$644$	−2.97911	−	8.52308i	−0.117393	−	0.335856i
$645$	24.4622	+	13.7791i	0.963200	+	0.542550i
$646$	−1.36669	−	4.20623i	−0.0537716	−	0.165492i
$647$	13.4867	+	41.5079i	0.530218	+	1.63184i	0.753761	+	0.657148i	$0.228237\pi$
$647$	13.4867	+	41.5079i	0.530218	+	1.63184i	−0.223544	+	0.974694i	$0.571763\pi$
$648$	−0.0359324	+	0.0373520i	−0.00141156	+	0.00146733i
$649$			56.5928i			2.22146i
$650$	−5.70388	−	0.0834490i	−0.223725	−	0.00327314i
$651$	29.6093	+	5.06455i	1.16048	+	0.198495i
$652$	−20.2938	−	14.7443i	−0.794766	−	0.577431i
$653$	11.9748	−	3.89086i	0.468611	−	0.152261i	−0.0651868	−	0.997873i	$-0.520764\pi$
$653$	11.9748	−	3.89086i	0.468611	−	0.152261i	0.533798	+	0.845612i	$0.320764\pi$
$654$	−48.8280	−	27.0353i	−1.90933	−	1.05716i
$655$	−33.4618	−	11.1437i	−1.30746	−	0.435419i
$656$	−3.76811	+	11.5970i	−0.147120	+	0.452789i
$657$	−36.4920	−	2.51664i	−1.42369	−	0.0981834i
$658$	5.04444	+	14.4319i	0.196653	+	0.562613i
$659$	−13.2404	−	18.2238i	−0.515771	−	0.709898i	0.469108	−	0.883141i	$-0.344576\pi$
$659$	−13.2404	−	18.2238i	−0.515771	−	0.709898i	−0.984879	+	0.173243i	$0.944576\pi$
$660$	−28.5072	−	30.9923i	−1.10964	−	1.20637i
$661$	−24.2411	+	33.3651i	−0.942871	+	1.29775i	0.0117507	+	0.999931i	$0.496260\pi$
$661$	−24.2411	+	33.3651i	−0.942871	+	1.29775i	−0.954622	+	0.297820i	$0.903740\pi$
$662$	−31.7954	−	43.7626i	−1.23576	−	1.70088i
$663$	−0.0616630	+	0.318042i	−0.00239479	+	0.0123517i
$664$	0.0344457	−	0.0474105i	0.00133675	−	0.00183988i
$665$	37.7334	−	12.8802i	1.46324	−	0.499472i
$666$	25.8467	−	16.1853i	1.00154	−	0.627167i
$667$	2.95492	−	9.09432i	0.114415	−	0.352133i
$668$	15.8654			0.613851
$669$	4.44246	+	9.51499i	0.171756	+	0.367871i
$670$	−23.2263	+	16.6167i	−0.897312	+	0.641960i
$671$	−2.28770	−	7.04080i	−0.0883155	−	0.271807i
$672$	−5.29011	−	36.2902i	−0.204070	−	1.39992i
$673$	11.9407	+	8.67544i	0.460281	+	0.334413i	0.793641	−	0.608386i	$-0.208183\pi$
$673$	11.9407	+	8.67544i	0.460281	+	0.334413i	−0.333361	+	0.942799i	$0.608183\pi$
$674$		−	26.3505i		−	1.01498i
$675$	−25.9608	+	1.01735i	−0.999233	+	0.0391578i
$676$	−25.3861			−0.976389
$677$	−9.63366	−	6.99926i	−0.370252	−	0.269004i	0.387064	−	0.922053i	$-0.373489\pi$
$677$	−9.63366	−	6.99926i	−0.370252	−	0.269004i	−0.757315	+	0.653049i	$0.773489\pi$
$678$	0.145895	−	0.263499i	0.00560305	−	0.0101196i
$679$	5.19017	+	3.59837i	0.199181	+	0.138093i
$680$	0.00339883	+	0.00250758i	0.000130339	+	9.61613e-5i
$681$	−0.656711	+	0.306612i	−0.0251652	+	0.0117494i
$682$		−	71.1939i		−	2.72616i
$683$	−7.93476	−	2.57816i	−0.303615	−	0.0986506i	0.153247	−	0.988188i	$-0.451027\pi$
$683$	−7.93476	−	2.57816i	−0.303615	−	0.0986506i	−0.456863	+	0.889537i	$0.651027\pi$
$684$	−34.3210	+	21.4919i	−1.31230	+	0.821764i
$685$	20.8879	−	14.9437i	0.798086	−	0.570971i
$686$	9.09030	−	35.9215i	0.347069	−	1.37149i
$687$	5.09317	−	26.2693i	0.194317	−	1.00223i
$688$	23.4251	−	17.0193i	0.893074	−	0.648856i
$689$	4.31621	+	3.13591i	0.164434	+	0.119469i
$690$	−2.60768	+	12.9424i	−0.0992726	+	0.492708i
$691$	−10.3553	−	14.2528i	−0.393933	−	0.542202i	0.565276	−	0.824902i	$-0.308770\pi$
$691$	−10.3553	−	14.2528i	−0.393933	−	0.542202i	−0.959208	+	0.282700i	$0.908770\pi$
$692$	−2.07969	+	6.40064i	−0.0790581	+	0.243316i
$693$	−23.6691	−	36.0037i	−0.899114	−	1.36767i
$694$	−5.04892	+	15.5390i	−0.191654	+	0.589851i
$695$	4.68604	+	3.45726i	0.177752	+	0.131141i
$696$	−0.0271164	+	0.0489746i	−0.00102785	+	0.00185638i
$697$	−0.309433	−	0.952336i	−0.0117206	−	0.0360723i
$698$	24.3825	+	17.7149i	0.922890	+	0.670519i
$699$	−12.3836	+	11.5590i	−0.468392	+	0.437202i
$700$	−15.4131	+	21.5511i	−0.582561	+	0.814557i
$701$			6.68060i			0.252323i	0.992010	+	0.126161i	$0.0402657\pi$
$701$			6.68060i			0.252323i	−0.992010	+	0.126161i	$0.959734\pi$
$702$	5.91970	−	0.318770i	0.223425	−	0.0120312i
$703$	32.5663	−	10.5814i	1.22826	−	0.399086i
$704$	−41.4209	+	13.4585i	−1.56111	+	0.507236i
$705$	2.20934	−	10.9653i	0.0832084	−	0.412979i
$706$	22.7098	+	7.37887i	0.854696	+	0.277707i
$707$	7.64862	+	10.0525i	0.287656	+	0.378064i
$708$	−32.7702	+	15.3001i	−1.23158	+	0.575013i
$709$	−29.6077	+	21.5113i	−1.11194	+	0.807873i	−0.982968	−	0.183775i	$-0.941168\pi$
$709$	−29.6077	+	21.5113i	−1.11194	+	0.807873i	−0.128973	+	0.991648i	$0.541168\pi$
$710$	53.7162	+	17.8889i	2.01593	+	0.671358i
$711$	8.91105	−	10.6405i	0.334190	−	0.399048i
$712$	0.0466312	+	0.0641824i	0.00174758	+	0.00240534i
$713$	−9.03569	+	6.56482i	−0.338389	+	0.245854i
$714$	2.10009	+	2.15251i	0.0785938	+	0.0805557i
$715$	−0.0506300	+	6.92166i	−0.00189345	+	0.258855i
$716$	16.9100	+	23.2746i	0.631956	+	0.869812i
$717$	1.39616	+	2.99034i	0.0521407	+	0.111676i
$718$	71.7333			2.67706
$719$	8.95489	−	27.5603i	0.333961	−	1.02783i	−0.633270	−	0.773931i	$-0.718288\pi$
$719$	8.95489	−	27.5603i	0.333961	−	1.02783i	0.967232	−	0.253896i	$-0.0817121\pi$
$720$	−10.1950	+	24.7788i	−0.379944	+	0.923451i
$721$	21.5044	+	14.9091i	0.800865	+	0.555243i
$722$	−50.2722	+	16.3344i	−1.87094	+	0.607904i
$723$	−9.84774	+	1.21394i	−0.366241	+	0.0451469i
$724$			5.70378i			0.211979i
$725$	−26.8120	+	8.28013i	−0.995774	+	0.307516i
$726$	−46.7846	+	43.6693i	−1.73634	+	1.62072i
$727$	19.9692	−	27.4852i	0.740616	−	1.01937i	−0.257967	−	0.966154i	$-0.583053\pi$
$727$	19.9692	−	27.4852i	0.740616	−	1.01937i	0.998583	−	0.0532167i	$-0.0169474\pi$
$728$	0.00495039	−	0.00714030i	0.000183474	−	0.000264637i
$729$	26.8439	−	2.89943i	0.994217	−	0.107386i
$730$	52.0000	−	16.4763i	1.92461	−	0.609815i
$731$	−0.734766	+	2.26138i	−0.0271763	+	0.0836401i
$732$	3.45850	−	3.22821i	0.127830	−	0.119318i
$733$	−8.12608	−	2.64032i	−0.300144	−	0.0975226i	0.155074	−	0.987903i	$-0.450438\pi$
$733$	−8.12608	−	2.64032i	−0.300144	−	0.0975226i	−0.455217	+	0.890380i	$0.650438\pi$
$734$	40.4988	−	29.4241i	1.49484	−	1.08606i
$735$	−19.1231	+	19.2174i	−0.705365	+	0.708844i
$736$	11.0313	+	8.01470i	0.406619	+	0.295426i
$737$	20.3684	+	28.0347i	0.750279	+	1.03267i
$738$	−15.5301	+	9.72500i	−0.571672	+	0.357982i
$739$	3.61140	+	2.62384i	0.132848	+	0.0965194i	0.652225	−	0.758026i	$-0.273836\pi$
$739$	3.61140	+	2.62384i	0.132848	+	0.0965194i	−0.519377	+	0.854545i	$0.673836\pi$
$740$	−13.5094	+	18.3109i	−0.496614	+	0.673121i
$741$	6.53480	+	1.26699i	0.240062	+	0.0465440i
$742$	46.7508	−	16.3410i	1.71628	−	0.599898i
$743$			2.31212i			0.0848236i	0.999100	+	0.0424118i	$0.0135041\pi$
$743$			2.31212i			0.0848236i	−0.999100	+	0.0424118i	$0.986496\pi$
$744$	0.0592455	−	0.0276612i	0.00217205	−	0.00101411i
$745$	45.9522	+	0.336128i	1.68356	+	0.0123148i
$746$	−53.7954	+	17.4792i	−1.96959	+	0.639958i
$747$	−29.6144	+	7.41383i	−1.08353	+	0.271258i
$748$	2.09617	−	2.88513i	0.0766435	−	0.105491i
$749$	6.92394	−	5.26819i	0.252995	−	0.192496i
$750$	35.4571	−	15.6164i	1.29471	−	0.570230i
$751$	26.4783			0.966208			0.483104	−	0.875563i	$-0.339509\pi$
$751$	26.4783			0.966208			0.483104	+	0.875563i	$0.339509\pi$
$752$	−9.33273	−	6.78062i	−0.340330	−	0.247264i
$753$	−0.725535	+	1.31038i	−0.0264400	+	0.0477529i
$754$	6.08967	−	1.97865i	0.221773	−	0.0720583i
$755$	−0.288464	+	39.4361i	−0.0104983	+	1.43523i
$756$	14.4490	−	23.4394i	0.525505	−	0.852482i
$757$	43.3354			1.57505			0.787527	−	0.616281i	$-0.211361\pi$
$757$	43.3354			1.57505			0.787527	+	0.616281i	$0.211361\pi$
$758$	−36.5853	−	11.8873i	−1.32884	−	0.431765i
$759$	15.7270	+	3.04921i	0.570856	+	0.110679i
$760$	0.0515232	−	0.0698356i	0.00186894	−	0.00253320i
$761$	23.8012	+	17.2926i	0.862793	+	0.626856i	0.928643	−	0.370974i	$-0.120976\pi$
$761$	23.8012	+	17.2926i	0.862793	+	0.626856i	−0.0658503	+	0.997830i	$0.520976\pi$
$762$	−3.03943	+	15.6766i	−0.110107	+	0.567903i
$763$	40.8080	+	12.2692i	1.47735	+	0.444174i
$764$	3.82208	−	5.26064i	0.138278	−	0.190323i
$765$	−0.518720	−	2.13829i	−0.0187544	−	0.0773099i
$766$	−10.1390	−	13.9551i	−0.366336	−	0.504219i
$767$	5.65395	+	1.83708i	0.204152	+	0.0663331i
$768$	18.8553	+	20.2004i	0.680380	+	0.728918i
$769$	27.4584	+	8.92178i	0.990176	+	0.321728i	0.758933	−	0.651168i	$-0.225721\pi$
$769$	27.4584	+	8.92178i	0.990176	+	0.321728i	0.231243	+	0.972896i	$0.425721\pi$
$770$	52.5349	+	36.9945i	1.89323	+	1.33319i
$771$	26.2582	−	47.4246i	0.945667	−	1.70796i
$772$	10.0803	+	31.0239i	0.362798	+	1.11658i
$773$	11.4415	+	8.31275i	0.411523	+	0.298989i	0.774218	−	0.632919i	$-0.218143\pi$
$773$	11.4415	+	8.31275i	0.411523	+	0.298989i	−0.362695	+	0.931908i	$0.618143\pi$
$774$	43.4078	+	2.99358i	1.56026	+	0.107602i
$775$	31.0199	+	10.5831i	1.11427	+	0.380157i
$776$	0.0137467			0.000493477
$777$	−16.6656	+	16.2597i	−0.597874	+	0.583313i
$778$	−6.23768	−	19.1976i	−0.223632	−	0.688267i
$779$	−19.5676	+	6.35790i	−0.701083	+	0.227796i
$780$	−4.02169	+	1.84198i	−0.144000	+	0.0659535i
$781$	21.2291	−	65.3364i	0.759637	−	2.33792i
$782$	−1.11811			−0.0399837
$783$	27.2103	−	10.4900i	0.972418	−	0.374881i
$784$	9.80656	+	26.1835i	0.350234	+	0.935123i
$785$	15.9091	+	0.116371i	0.567820	+	0.00415344i
$786$	−54.2470	+	6.68707i	−1.93493	+	0.238520i
$787$	−18.7052	−	25.7454i	−0.666767	−	0.917726i	0.332915	−	0.942957i	$-0.391968\pi$
$787$	−18.7052	−	25.7454i	−0.666767	−	0.917726i	−0.999682	+	0.0252312i	$0.991968\pi$
$788$	31.2082	+	42.9544i	1.11175	+	1.53019i
$789$	−14.1821	+	1.74824i	−0.504896	+	0.0622390i
$790$	−6.53954	+	19.6367i	−0.232666	+	0.698643i
$791$	−0.0662101	+	0.220219i	−0.00235416	+	0.00783008i
$792$	−0.0869895	−	0.0350491i	−0.00309104	−	0.00124542i
$793$	−0.777679			−0.0276162
$794$	−18.6386	+	57.3638i	−0.661460	+	2.03576i
$795$	−35.5213	−	7.15696i	−1.25981	−	0.253831i
$796$	−23.4903	+	7.63247i	−0.832592	+	0.270526i
$797$	7.91669	+	24.3651i	0.280424	+	0.863055i	0.987733	+	0.156151i	$0.0499087\pi$
$797$	7.91669	+	24.3651i	0.280424	+	0.863055i	−0.707310	+	0.706904i	$0.750091\pi$
$798$	44.2276	−	43.1504i	1.56564	−	1.52751i
$799$	0.947314			0.0335136
$800$	0.585355	−	40.0100i	0.0206954	−	1.41457i
$801$	2.84339	−	41.2300i	0.100466	−	1.45679i
$802$	−15.3978	−	11.1871i	−0.543715	−	0.395032i
$803$	−20.4534	−	62.9490i	−0.721784	−	2.22142i
$804$	−10.7269	+	19.3737i	−0.378307	+	0.683256i
$805$	−0.149039	−	10.0788i	−0.00525293	−	0.355232i
$806$	−7.11269	−	2.31105i	−0.250534	−	0.0814034i
$807$	22.8234	+	24.4516i	0.803421	+	0.860737i
$808$	0.0261485	+	0.00849617i	0.000919902	+	0.000298894i
$809$	16.8290	+	23.1631i	0.591675	+	0.814371i	0.994914	−	0.100723i	$-0.0321157\pi$
$809$	16.8290	+	23.1631i	0.591675	+	0.814371i	−0.403239	+	0.915095i	$0.632116\pi$
$810$	−35.6523	+	18.7105i	−1.25269	+	0.657419i
$811$	−0.517060	+	0.711672i	−0.0181564	+	0.0249902i	−0.817999	−	0.575220i	$-0.804916\pi$
$811$	−0.517060	+	0.711672i	−0.0181564	+	0.0249902i	0.799842	+	0.600210i	$0.204916\pi$
$812$	8.56292	−	28.4808i	0.300500	−	0.999480i
$813$	−1.52322	+	7.85636i	−0.0534215	+	0.275535i
$814$	44.6435	+	32.4354i	1.56475	+	1.13686i
$815$	−16.2948	−	22.7763i	−0.570781	−	0.797820i
$816$	−2.22771	−	0.431915i	−0.0779853	−	0.0151200i
$817$	46.4644	+	15.0972i	1.62559	+	0.528185i
$818$	−57.4498			−2.00869
$819$	−4.36531	+	1.19595i	−0.152536	+	0.0417898i
$820$	8.11717	−	11.0022i	0.283464	−	0.384213i
$821$	−4.00855	+	1.30246i	−0.139899	+	0.0454560i	−0.378130	−	0.925753i	$-0.623433\pi$
$821$	−4.00855	+	1.30246i	−0.139899	+	0.0454560i	0.238230	+	0.971209i	$0.423433\pi$
$822$	19.2799	−	34.8212i	0.672463	−	1.21453i
$823$	−14.9101	−	10.8328i	−0.519734	−	0.377609i	0.296770	−	0.954949i	$-0.404091\pi$
$823$	−14.9101	−	10.8328i	−0.519734	−	0.377609i	−0.816504	+	0.577340i	$0.804091\pi$
$824$	0.0569565			0.00198417
$825$	−19.2632	−	42.8840i	−0.670658	−	1.49303i
$826$	43.9178	−	33.4156i	1.52810	−	1.16268i
$827$	2.43567	−	3.35242i	0.0846966	−	0.116575i	−0.764566	−	0.644545i	$-0.777047\pi$
$827$	2.43567	−	3.35242i	0.0846966	−	0.116575i	0.849263	+	0.527970i	$0.177047\pi$
$828$	2.48622	+	9.93114i	0.0864021	+	0.345131i
$829$	−35.5915	+	11.5644i	−1.23614	+	0.401648i	−0.852937	−	0.522015i	$-0.825181\pi$
$829$	−35.5915	+	11.5644i	−1.23614	+	0.401648i	−0.383208	+	0.923662i	$0.625181\pi$
$830$	37.0254	−	26.4889i	1.28517	−	0.919445i
$831$	10.4552	−	4.88145i	0.362688	−	0.169336i
$832$			4.57507i			0.158612i
$833$	−1.91533	−	1.26617i	−0.0663624	−	0.0438701i
$834$	8.85978	+	1.71776i	0.306789	+	0.0594813i
$835$	16.8052	+	5.59656i	0.581567	+	0.193677i
$836$	−59.2806	−	43.0699i	−2.05026	−	1.48960i
$837$	−32.9134	−	8.76845i	−1.13765	−	0.303082i
$838$	16.3016	+	22.4373i	0.563131	+	0.775083i
$839$	−16.4779	−	11.9719i	−0.568879	−	0.413315i	0.265819	−	0.964023i	$-0.414358\pi$
$839$	−16.4779	−	11.9719i	−0.568879	−	0.413315i	−0.834698	+	0.550708i	$0.814358\pi$
$840$	−0.0103742	+	0.0580916i	−0.000357945	+	0.00200435i
$841$	2.02080	−	1.46820i	0.0696828	−	0.0506275i
$842$	61.9405	+	20.1257i	2.13461	+	0.693577i
$843$	−15.2395	+	14.2247i	−0.524876	+	0.489925i
$844$	2.56385	−	7.89072i	0.0882514	−	0.271610i
$845$	−26.8898	−	8.95501i	−0.925038	−	0.308062i
$846$	−4.20984	−	16.8161i	−0.144737	−	0.578149i
$847$	27.8398	−	40.1553i	0.956587	−	1.37975i
$848$	−21.9653	+	30.2326i	−0.754290	+	1.03819i
$849$	29.6584	−	27.6835i	1.01787	−	0.950095i
$850$	1.88960	+	2.68248i	0.0648128	+	0.0920082i
$851$		−	8.65687i		−	0.296754i
$852$	43.5726	−	5.37123i	1.49277	−	0.184015i
$853$	−39.2414	+	12.7503i	−1.34360	+	0.436562i	−0.890535	−	0.454915i	$-0.849670\pi$
$853$	−39.2414	+	12.7503i	−1.34360	+	0.436562i	−0.453065	+	0.891477i	$0.649670\pi$
$854$	−4.11310	+	5.93261i	−0.140747	+	0.203010i
$855$	−43.9353	+	10.6581i	−1.50256	+	0.364500i
$856$	0.00585197	−	0.0180105i	0.000200016	−	0.000615587i
$857$	29.7430			1.01600			0.508001	−	0.861357i	$-0.330385\pi$
$857$	29.7430			1.01600			0.508001	+	0.861357i	$0.330385\pi$
$858$	4.53814	+	9.71991i	0.154930	+	0.331832i
$859$	−29.7053	−	40.8858i	−1.01353	−	1.39501i	−0.916642	−	0.399710i	$-0.869111\pi$
$859$	−29.7053	−	40.8858i	−1.01353	−	1.39501i	−0.0968893	−	0.995295i	$-0.530889\pi$
$860$	−30.9496	+	9.80645i	−1.05537	+	0.334397i
$861$	10.0136	−	9.76972i	0.341262	−	0.332951i
$862$	−15.0711	+	10.9498i	−0.513323	+	0.372951i
$863$	−27.1880	−	37.4211i	−0.925491	−	1.27383i	−0.961593	−	0.274480i	$-0.911494\pi$
$863$	−27.1880	−	37.4211i	−0.925491	−	1.27383i	0.0361021	−	0.999348i	$-0.488506\pi$
$864$	2.23602	+	41.5239i	0.0760709	+	1.41267i
$865$	−4.46072	+	6.04616i	−0.151669	+	0.205575i
$866$	32.4554	−	23.5802i	1.10288	−	0.801288i
$867$	−26.5113	+	12.3779i	−0.900371	+	0.420375i
$868$	−27.6442	+	21.0336i	−0.938306	+	0.713926i
$869$	23.8847	+	7.76060i	0.810232	+	0.263260i
$870$	−32.0073	+	29.4408i	−1.08515	+	0.998138i
$871$	3.46201	−	1.12488i	0.117306	−	0.0381150i
$872$	0.0882125	−	0.0286620i	0.00298725	−	0.000970617i
$873$	−5.49017	−	4.59784i	−0.185814	−	0.155613i
$874$			22.9738i			0.777102i
$875$	−23.9283	+	17.3907i	−0.808925	+	0.587912i
$876$	30.9211	−	28.8621i	1.04473	−	0.975160i
$877$	−26.2084	−	19.0415i	−0.884995	−	0.642986i	0.0495734	−	0.998770i	$-0.484214\pi$
$877$	−26.2084	−	19.0415i	−0.884995	−	0.642986i	−0.934568	+	0.355784i	$0.884214\pi$
$878$	0.663827	+	2.04305i	0.0224031	+	0.0689495i
$879$	15.8699	−	28.6625i	0.535280	−	0.966762i
$880$	−48.4823	−	0.354634i	−1.63434	−	0.0119547i
$881$	−1.26974	+	3.90786i	−0.0427787	+	0.131659i	−0.970165	−	0.242446i	$-0.922050\pi$
$881$	−1.26974	+	3.90786i	−0.0427787	+	0.131659i	0.927386	+	0.374105i	$0.122050\pi$
$882$	−13.9645	+	39.6265i	−0.470208	+	1.33430i
$883$	−5.46621	+	16.8233i	−0.183953	+	0.566148i	−0.999929	−	0.0119375i	$-0.996200\pi$
$883$	−5.46621	+	16.8233i	−0.183953	+	0.566148i	0.815976	+	0.578086i	$0.196200\pi$
$884$	−0.220197	−	0.303074i	−0.00740601	−	0.0101935i
$885$	−40.1084	+	4.64663i	−1.34823	+	0.156195i
$886$	−18.6853	−	13.5757i	−0.627746	−	0.456084i
$887$	32.8565	−	23.8716i	1.10321	−	0.801531i	0.121632	−	0.992575i	$-0.461187\pi$
$887$	32.8565	−	23.8716i	1.10321	−	0.801531i	0.981581	+	0.191044i	$0.0611873\pi$
$888$	−0.00964631	+	0.0497532i	−0.000323709	+	0.00166961i
$889$	−0.269426	−	12.1888i	−0.00903627	−	0.408799i
$890$	18.6155	+	58.7516i	0.623994	+	1.96936i
$891$	23.0192	+	43.0933i	0.771171	+	1.44368i
$892$	−11.5486	−	3.75237i	−0.386676	−	0.125639i
$893$		−	19.4644i		−	0.651352i
$894$	64.5296	−	30.1283i	2.15819	−	1.00764i
$895$	9.70146	+	30.6183i	0.324284	+	1.02346i
$896$	0.100172	+	0.0694494i	0.00334650	+	0.00232014i
$897$	0.815155	−	1.47224i	0.0272172	−	0.0491567i
$898$	2.31597	+	1.68265i	0.0772849	+	0.0561508i
$899$	−36.7893			−1.22699
$900$	19.6242	−	22.7483i	0.654140	−	0.758275i
$901$		−	3.06874i		−	0.102235i
$902$	−26.8242	−	19.4890i	−0.893150	−	0.648911i
$903$	−32.8726	+	4.79192i	−1.09393	+	0.159465i
$904$	0.000154673	0	0.000476035i	5.14435e−6	0	1.58327e-5i
$905$	−2.01202	+	6.04163i	−0.0668818	+	0.200831i
$906$	25.8560	+	55.3791i	0.859008	+	1.83985i
$907$	30.5786			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$907$	30.5786			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$908$	0.258983	−	0.797069i	0.00859467	−	0.0264517i
$909$	−7.60154	−	12.1391i	−0.252127	−	0.402629i
$910$	5.40132	−	4.04765i	0.179052	−	0.134178i
$911$	2.56095	−	3.52485i	0.0848481	−	0.116783i	−0.764483	−	0.644644i	$-0.777006\pi$
$911$	2.56095	−	3.52485i	0.0848481	−	0.116783i	0.849331	+	0.527861i	$0.177006\pi$
$912$	−8.87454	+	45.7726i	−0.293865	+	1.51568i
$913$	−32.4695	−	44.6905i	−1.07458	−	1.47904i
$914$	34.5890	−	47.6077i	1.14410	−	1.57472i
$915$	4.80212	−	2.19943i	0.158753	−	0.0727109i
$916$	18.1875	+	25.0330i	0.600933	+	0.827113i
$917$	39.3933	−	13.7693i	1.30088	−	0.454703i
$918$	−2.14974	−	2.64692i	−0.0709520	−	0.0873614i
$919$	0.492931	−	1.51709i	0.0162603	−	0.0500440i	−0.942597	−	0.333932i	$-0.891624\pi$
$919$	0.492931	−	1.51709i	0.0162603	−	0.0500440i	0.958857	+	0.283888i	$0.0916244\pi$
$920$	−0.0127660	−	0.0178440i	−0.000420884	−	0.000588299i
$921$	−37.2008	−	20.5975i	−1.22581	−	0.678709i
$922$	17.1676	−	5.57809i	0.565385	−	0.183705i
$923$	−5.83836	−	4.24182i	−0.192172	−	0.139621i
$924$	49.1110	+	8.40022i	1.61563	+	0.276347i
$925$	−20.7688	+	14.6300i	−0.682873	+	0.481033i
$926$			21.9649i			0.721811i
$927$	−22.7474	−	19.0502i	−0.747122	−	0.625691i
$928$	13.8793	+	42.7161i	0.455611	+	1.40223i
$929$	9.92218	+	30.5373i	0.325536	+	1.00190i	0.971198	+	0.238274i	$0.0765817\pi$
$929$	9.92218	+	30.5373i	0.325536	+	1.00190i	−0.645662	+	0.763624i	$0.723418\pi$
$930$	50.4565	−	5.84547i	1.65453	−	0.191681i
$931$	−26.0159	+	39.3543i	−0.852636	+	1.28978i
$932$		−	19.5888i		−	0.641654i
$933$	14.6184	−	6.82521i	0.478585	−	0.223447i
$934$	−41.1336	−	56.6155i	−1.34593	−	1.85252i
$935$	3.23807	−	2.31660i	0.105896	−	0.0757608i
$936$	−0.00632541	+	0.00755302i	−0.000206753	+	0.000246878i
$937$	−1.55846	−	2.14504i	−0.0509127	−	0.0700754i	0.782802	−	0.622271i	$-0.213790\pi$
$937$	−1.55846	−	2.14504i	−0.0509127	−	0.0700754i	−0.833714	+	0.552196i	$0.813790\pi$
$938$	9.72915	−	32.3598i	0.317668	−	1.05658i
$939$	22.3819	−	2.75904i	0.730406	−	0.0900377i
$940$	7.52609	+	10.5197i	0.245474	+	0.343116i
$941$	−15.8191	+	11.4933i	−0.515689	+	0.374670i	−0.814977	−	0.579493i	$-0.803251\pi$
$941$	−15.8191	+	11.4933i	−0.515689	+	0.374670i	0.299289	+	0.954163i	$0.403251\pi$
$942$	22.3407	−	10.4307i	0.727901	−	0.339850i
$943$			5.20152i			0.169385i
$944$	−12.8677	+	39.6027i	−0.418808	+	1.28896i
$945$	23.5731	−	19.7309i	0.766834	−	0.641845i
$946$	24.3296	+	74.8788i	0.791024	+	2.43452i
$947$	14.7341	−	4.78740i	0.478794	−	0.155570i	−0.0596699	−	0.998218i	$-0.519005\pi$
$947$	14.7341	−	4.78740i	0.478794	−	0.155570i	0.538464	+	0.842649i	$0.319005\pi$
$948$	1.96353	+	15.9286i	0.0637724	+	0.517336i
$949$	−6.95292			−0.225701
$950$	55.1167	−	38.8256i	1.78822	−	1.25967i
$951$	−9.27972	+	8.66179i	−0.300916	+	0.280878i
$952$	−0.00499638		0.000110442i	−0.000161934		3.57945e-6i
$953$	−30.3812	+	9.87146i	−0.984145	+	0.319768i	−0.756513	−	0.653979i	$-0.773098\pi$
$953$	−30.3812	+	9.87146i	−0.984145	+	0.319768i	−0.227632	+	0.973747i	$0.573098\pi$
$954$	−54.4743	+	13.6374i	−1.76367	+	0.441528i
$955$	5.90418	−	4.22400i	0.191055	−	0.136686i
$956$	−3.62946	−	1.17928i	−0.117385	−	0.0381408i
$957$	36.0067	+	38.5754i	1.16393	+	1.24697i
$958$	12.2980	+	3.99586i	0.397330	+	0.129100i
$959$	−8.74961	+	29.1017i	−0.282540	+	0.939744i
$960$	−12.9392	−	28.2508i	−0.417611	−	0.911790i
$961$	9.68361	+	7.03555i	0.312374	+	0.226953i
$962$	4.68967	−	3.40724i	0.151201	−	0.109854i
$963$	−8.36114	+	5.23577i	−0.269434	+	0.168720i
$964$	6.74410	−	9.28245i	0.217213	−	0.298968i
$965$	−0.266383	+	36.4174i	−0.00857518	+	1.17232i
$966$	−6.91985	−	14.0051i	−0.222642	−	0.450607i
$967$	5.79123	−	17.8236i	0.186233	−	0.573167i	−0.813734	−	0.581237i	$-0.802569\pi$
$967$	5.79123	−	17.8236i	0.186233	−	0.573167i	0.999967	+	0.00806996i	$0.00256878\pi$
$968$		−	0.106355i		−	0.00341838i
$969$	−1.61978	−	3.46929i	−0.0520348	−	0.111450i
$970$	10.1320	+	3.37421i	0.325318	+	0.108339i
$971$	13.1731	+	40.5425i	0.422744	+	1.30107i	0.905138	+	0.425117i	$0.139767\pi$
$971$	13.1731	+	40.5425i	0.422744	+	1.30107i	−0.482395	+	0.875954i	$0.660233\pi$
$972$	−18.7300	+	24.9798i	−0.600764	+	0.801226i
$973$	−6.88862	+	0.152269i	−0.220839	+	0.00488153i
$974$			61.4645i			1.96945i
$975$	−4.90967	+	0.532430i	−0.157235	+	0.0170514i
$976$		−	5.44720i		−	0.174361i
$977$	7.06847	−	9.72891i	0.226140	−	0.311255i	−0.680837	−	0.732435i	$-0.738384\pi$
$977$	7.06847	−	9.72891i	0.226140	−	0.311255i	0.906977	+	0.421180i	$0.138384\pi$
$978$	−37.9692	−	21.0229i	−1.21412	−	0.672239i
$979$	71.1222	−	23.1090i	2.27307	−	0.738567i
$980$	−1.15615	−	31.3287i	−0.0369318	−	1.00076i
$981$	−44.8170	−	18.0573i	−1.43090	−	0.576526i
$982$	−19.4709			−0.621343
$983$	3.43151	−	10.5611i	0.109448	−	0.336847i	−0.881301	−	0.472556i	$-0.843331\pi$
$983$	3.43151	−	10.5611i	0.109448	−	0.336847i	0.990749	+	0.135710i	$0.0433314\pi$
$984$	0.00579603	−	0.0298945i	0.000184771	−	0.000953001i
$985$	17.9045	+	56.5075i	0.570485	+	1.80048i
$986$	−2.97962	−	2.16482i	−0.0948904	−	0.0689419i
$987$	5.86279	+	11.8657i	0.186615	+	0.377690i
$988$	−6.22726	+	4.52437i	−0.198116	+	0.143939i
$989$	7.25993	−	9.99243i	0.230852	−	0.317741i
$990$	−55.5126	−	47.1851i	−1.76430	−	1.49964i
$991$	−23.7227	+	17.2355i	−0.753576	+	0.547505i	−0.896933	−	0.442166i	$-0.854210\pi$
$991$	−23.7227	+	17.2355i	−0.753576	+	0.547505i	0.143357	+	0.989671i	$0.454210\pi$
$992$	16.2109	−	49.8922i	0.514698	−	1.58408i
$993$	−31.9541	−	34.2337i	−1.01403	−	1.08637i
$994$	−63.2380	+	22.1039i	−2.00579	+	0.701092i
$995$	−27.5741	−	0.201697i	−0.874158	−	0.00639422i
$996$	17.0998	−	30.8838i	0.541829	−	0.978591i
$997$	−27.5075	+	8.93772i	−0.871171	+	0.283061i	−0.710286	−	0.703913i	$-0.751435\pi$
$997$	−27.5075	+	8.93772i	−0.871171	+	0.283061i	−0.160884	+	0.986973i	$0.551435\pi$
$998$	−0.118289	+	0.162810i	−0.00374436	+	0.00515368i
$999$	20.4935	−	16.6441i	0.648385	−	0.526597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bb.a.41.13	✓	304
3.2	odd	2	inner	525.2.bb.a.41.63	yes	304
7.6	odd	2	inner	525.2.bb.a.41.14	yes	304
21.20	even	2	inner	525.2.bb.a.41.64	yes	304
25.11	even	5	inner	525.2.bb.a.461.64	yes	304
75.11	odd	10	inner	525.2.bb.a.461.14	yes	304
175.111	odd	10	inner	525.2.bb.a.461.63	yes	304
525.461	even	10	inner	525.2.bb.a.461.13	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bb.a.41.13	✓	304	1.1	even	1	trivial
525.2.bb.a.41.14	yes	304	7.6	odd	2	inner
525.2.bb.a.41.63	yes	304	3.2	odd	2	inner
525.2.bb.a.41.64	yes	304	21.20	even	2	inner
525.2.bb.a.461.13	yes	304	525.461	even	10	inner
525.2.bb.a.461.14	yes	304	75.11	odd	10	inner
525.2.bb.a.461.63	yes	304	175.111	odd	10	inner
525.2.bb.a.461.64	yes	304	25.11	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17599 + 1.61862i) q^{2} +(-0.838989 + 1.51529i) q^{3} +(-0.618923 - 1.90485i) q^{4} +(0.0163558 - 2.23601i) q^{5} +(-1.46602 - 3.13997i) q^{6} +(1.60206 + 2.10557i) q^{7} +(0.00547699 + 0.00177958i) q^{8} +(-1.59219 - 2.54262i) q^{9} +O(q^{10})\)	\(q+(-1.17599 + 1.61862i) q^{2} +(-0.838989 + 1.51529i) q^{3} +(-0.618923 - 1.90485i) q^{4} +(0.0163558 - 2.23601i) q^{5} +(-1.46602 - 3.13997i) q^{6} +(1.60206 + 2.10557i) q^{7} +(0.00547699 + 0.00177958i) q^{8} +(-1.59219 - 2.54262i) q^{9} +(3.60000 + 2.65600i) q^{10} +(3.19077 - 4.39171i) q^{11} +(3.40567 + 0.660302i) q^{12} +(-0.335181 - 0.461337i) q^{13} +(-5.29211 + 0.116979i) q^{14} +(3.37447 + 1.90077i) q^{15} +(3.23140 - 2.34775i) q^{16} +(-0.101358 + 0.311948i) q^{17} +(5.98794 + 0.412953i) q^{18} +(6.40959 + 2.08260i) q^{19} +(-4.26938 + 1.35276i) q^{20} +(-4.53465 + 0.661027i) q^{21} +(3.35618 + 10.3292i) q^{22} +(1.00148 - 1.37842i) q^{23} +(-0.00729172 + 0.00680617i) q^{24} +(-4.99946 - 0.0731433i) q^{25} +1.14090 q^{26} +(5.18864 - 0.279402i) q^{27} +(3.01924 - 4.35486i) q^{28} +(5.33761 - 1.73429i) q^{29} +(-7.04498 + 3.22668i) q^{30} +(-6.23429 - 2.02564i) q^{31} +8.00286i q^{32} +(3.97769 + 8.51953i) q^{33} +(-0.385728 - 0.530909i) q^{34} +(4.73427 - 3.54777i) q^{35} +(-3.85786 + 4.60658i) q^{36} +(4.11051 - 2.98646i) q^{37} +(-10.9086 + 7.92554i) q^{38} +(0.980271 - 0.120839i) q^{39} +(0.00406874 - 0.0122175i) q^{40} +(-2.46982 + 1.79443i) q^{41} +(4.26277 - 8.11722i) q^{42} +7.24920 q^{43} +(-10.3404 - 3.35980i) q^{44} +(-5.71136 + 3.51857i) q^{45} +(1.05340 + 3.24202i) q^{46} +(-0.892483 - 2.74678i) q^{47} +(0.846408 + 6.86625i) q^{48} +(-1.86683 + 6.74648i) q^{49} +(5.99773 - 8.00620i) q^{50} +(-0.387653 - 0.415308i) q^{51} +(-0.671327 + 0.924002i) q^{52} +(-8.89796 + 2.89112i) q^{53} +(-5.64956 + 8.72698i) q^{54} +(-9.76772 - 7.20641i) q^{55} +(0.00502741 + 0.0143832i) q^{56} +(-8.53332 + 7.96510i) q^{57} +(-3.46984 + 10.6791i) q^{58} +(-8.43418 + 6.12779i) q^{59} +(1.53214 - 7.60430i) q^{60} +(0.801601 - 1.10331i) q^{61} +(10.6102 - 7.70878i) q^{62} +(2.80287 - 7.42589i) q^{63} +(-6.49075 - 4.71581i) q^{64} +(-1.03704 + 0.741922i) q^{65} +(-18.4676 - 3.58055i) q^{66} +(-1.97262 + 6.07111i) q^{67} +0.656948 q^{68} +(1.24847 + 2.67401i) q^{69} +(0.175010 + 11.8351i) q^{70} +(12.0359 - 3.91071i) q^{71} +(-0.00419563 - 0.0167593i) q^{72} +(7.16680 - 9.86425i) q^{73} +10.1654i q^{74} +(4.30533 - 7.51426i) q^{75} -13.4983i q^{76} +(14.3588 - 0.317394i) q^{77} +(-0.957201 + 1.72879i) q^{78} +(1.42961 + 4.39990i) q^{79} +(-5.19674 - 7.26384i) q^{80} +(-3.92983 + 8.09669i) q^{81} -6.10792i q^{82} +(3.14459 - 9.67804i) q^{83} +(4.06576 + 8.22870i) q^{84} +(0.695862 + 0.231740i) q^{85} +(-8.52501 + 11.7337i) q^{86} +(-1.85024 + 9.54307i) q^{87} +(0.0252912 - 0.0183751i) q^{88} +(11.1450 + 8.09732i) q^{89} +(1.02130 - 13.3823i) q^{90} +(0.434398 - 1.44483i) q^{91} +(-3.24552 - 1.05453i) q^{92} +(8.29993 - 7.74725i) q^{93} +(5.49553 + 1.78561i) q^{94} +(4.76155 - 14.2978i) q^{95} +(-12.1266 - 6.71431i) q^{96} +(2.27022 - 0.737640i) q^{97} +(-8.72457 - 10.9555i) q^{98} +(-16.2468 - 1.12044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9	\( 304 q + 60 q^{4} - 12 q^{7} - 6 q^{9} + 8 q^{15} - 92 q^{16} - 16 q^{18} + 12 q^{21} - 48 q^{22} - 32 q^{25} - 36 q^{28} - 14 q^{30} - 8 q^{36} - 4 q^{37} - 26 q^{39} - 11 q^{42} - 20 q^{49} + 20 q^{51} - 168 q^{57} + 32 q^{58} + 76 q^{60} + 29 q^{63} + 68 q^{64} - 44 q^{67} + 30 q^{70} - 114 q^{72} - 124 q^{78} - 68 q^{79} - 2 q^{81} + 102 q^{84} + 72 q^{85} - 156 q^{88} + 70 q^{91} - 32 q^{93} - 36 q^{99}+O(q^{100}) \) 304 * q + 60 * q^4 - 12 * q^7 - 6 * q^9 + 8 * q^15 - 92 * q^16 - 16 * q^18 + 12 * q^21 - 48 * q^22 - 32 * q^25 - 36 * q^28 - 14 * q^30 - 8 * q^36 - 4 * q^37 - 26 * q^39 - 11 * q^42 - 20 * q^49 + 20 * q^51 - 168 * q^57 + 32 * q^58 + 76 * q^60 + 29 * q^63 + 68 * q^64 - 44 * q^67 + 30 * q^70 - 114 * q^72 - 124 * q^78 - 68 * q^79 - 2 * q^81 + 102 * q^84 + 72 * q^85 - 156 * q^88 + 70 * q^91 - 32 * q^93 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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