LMFDB - Embedded newform 350.2.h.c.281.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(71,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([6, 0]))

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

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

chi := DirichletCharacter("350.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.h (of order $5$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 241x^{12} + 1145x^{10} + 2841x^{8} + 3600x^{6} + 2156x^{4} + 480x^{2} + 16 $ x^16 + 25x^14 + 241x^12 + 1145x^10 + 2841x^8 + 3600x^6 + 2156x^4 + 480*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			281.1
Root			$-2.46620i$ of defining polynomial
Character	$\chi$	$=$	350.281
Dual form			350.2.h.c.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-1.78422 + 1.29631i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.298278 + 2.21608i) q^{5} +(-1.78422 - 1.29631i) q^{6} -1.00000 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.575968 - 1.77265i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-1.78422 + 1.29631i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.298278 + 2.21608i) q^{5} +(-1.78422 - 1.29631i) q^{6} -1.00000 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.575968 - 1.77265i) q^{9} +(-2.19979 + 0.401128i) q^{10} +(1.24562 + 3.83361i) q^{11} +(0.681512 - 2.09748i) q^{12} +(1.20223 - 3.70007i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-2.34054 - 4.34065i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-5.86426 - 4.26063i) q^{17} +1.86387 q^{18} +(-3.26168 - 2.36975i) q^{19} +(-1.06127 - 1.96817i) q^{20} +(1.78422 - 1.29631i) q^{21} +(-3.26106 + 2.36930i) q^{22} +(2.38359 + 7.33594i) q^{23} +2.20542 q^{24} +(-4.82206 - 1.32202i) q^{25} +3.89049 q^{26} +(-0.774284 - 2.38300i) q^{27} +(0.809017 - 0.587785i) q^{28} +(3.78201 - 2.74779i) q^{29} +(3.40493 - 3.56732i) q^{30} +(7.06220 + 5.13099i) q^{31} +1.00000 q^{32} +(-7.19201 - 5.22530i) q^{33} +(2.23995 - 6.89385i) q^{34} +(0.298278 - 2.21608i) q^{35} +(0.575968 + 1.77265i) q^{36} +(-0.432558 + 1.33128i) q^{37} +(1.24585 - 3.83433i) q^{38} +(2.65141 + 8.16021i) q^{39} +(1.54389 - 1.61753i) q^{40} +(-3.32221 + 10.2247i) q^{41} +(1.78422 + 1.29631i) q^{42} -9.39984 q^{43} +(-3.26106 - 2.36930i) q^{44} +(3.75654 + 1.80514i) q^{45} +(-6.24033 + 4.53386i) q^{46} +(-5.95545 + 4.32689i) q^{47} +(0.681512 + 2.09748i) q^{48} +1.00000 q^{49} +(-0.232784 - 4.99458i) q^{50} +15.9863 q^{51} +(1.20223 + 3.70007i) q^{52} +(-1.61865 + 1.17602i) q^{53} +(2.02710 - 1.47278i) q^{54} +(-8.86715 + 1.61691i) q^{55} +(0.809017 + 0.587785i) q^{56} +8.89149 q^{57} +(3.78201 + 2.74779i) q^{58} +(-0.566673 + 1.74404i) q^{59} +(4.44491 + 2.13592i) q^{60} +(-0.939817 - 2.89246i) q^{61} +(-2.69752 + 8.30212i) q^{62} +(-0.575968 + 1.77265i) q^{63} +(0.309017 + 0.951057i) q^{64} +(7.84107 + 3.76788i) q^{65} +(2.74710 - 8.45472i) q^{66} +(9.85111 + 7.15725i) q^{67} +7.24862 q^{68} +(-13.7625 - 9.99907i) q^{69} +(2.19979 - 0.401128i) q^{70} +(0.580895 - 0.422045i) q^{71} +(-1.50790 + 1.09556i) q^{72} +(1.11710 + 3.43807i) q^{73} -1.39979 q^{74} +(10.3174 - 3.89212i) q^{75} +4.03166 q^{76} +(-1.24562 - 3.83361i) q^{77} +(-6.94149 + 5.04329i) q^{78} +(-10.8709 + 7.89820i) q^{79} +(2.01545 + 0.968487i) q^{80} +(8.99432 + 6.53476i) q^{81} -10.7509 q^{82} +(5.92741 + 4.30651i) q^{83} +(-0.681512 + 2.09748i) q^{84} +(11.1911 - 11.7248i) q^{85} +(-2.90471 - 8.93978i) q^{86} +(-3.18595 + 9.80534i) q^{87} +(1.24562 - 3.83361i) q^{88} +(0.584454 + 1.79876i) q^{89} +(-0.555952 + 4.13050i) q^{90} +(-1.20223 + 3.70007i) q^{91} +(-6.24033 - 4.53386i) q^{92} -19.2519 q^{93} +(-5.95545 - 4.32689i) q^{94} +(6.22445 - 6.52131i) q^{95} +(-1.78422 + 1.29631i) q^{96} +(-0.578244 + 0.420119i) q^{97} +(0.309017 + 0.951057i) q^{98} +7.51308 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9} + q^{10} + 7 q^{11} - 4 q^{12} + 9 q^{13} + 4 q^{14} - 4 q^{16} - 2 q^{17} + 14 q^{18} - 24 q^{19} - 9 q^{20} - q^{21} - 8 q^{22} - 5 q^{23} + 6 q^{24} - 6 q^{25} - 6 q^{26} - 32 q^{27} + 4 q^{28} + 20 q^{29} + 15 q^{30} + 7 q^{31} + 16 q^{32} + 15 q^{33} + 3 q^{34} + 4 q^{35} - q^{36} - 6 q^{37} + 6 q^{38} + 34 q^{39} + 11 q^{40} + 9 q^{41} - q^{42} - 22 q^{43} - 8 q^{44} - 8 q^{45} - 40 q^{47} - 4 q^{48} + 16 q^{49} - q^{50} + 14 q^{51} + 9 q^{52} - 24 q^{53} + 23 q^{54} - 26 q^{55} + 4 q^{56} + 52 q^{57} + 20 q^{58} - 17 q^{59} - 5 q^{60} + 2 q^{61} - 23 q^{62} + q^{63} - 4 q^{64} - 16 q^{65} - 10 q^{66} - 14 q^{67} - 2 q^{68} - 35 q^{69} - q^{70} + 7 q^{71} - 6 q^{72} + 5 q^{73} - 36 q^{74} + 35 q^{75} + 36 q^{76} - 7 q^{77} - 46 q^{78} + 20 q^{79} + q^{80} + 49 q^{81} + 44 q^{82} + 17 q^{83} + 4 q^{84} - 13 q^{85} + 8 q^{86} - 66 q^{87} + 7 q^{88} + 27 q^{89} + 37 q^{90} - 9 q^{91} - 34 q^{93} - 40 q^{94} - 20 q^{95} + q^{96} + 6 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9 + q^10 + 7 * q^11 - 4 * q^12 + 9 * q^13 + 4 * q^14 - 4 * q^16 - 2 * q^17 + 14 * q^18 - 24 * q^19 - 9 * q^20 - q^21 - 8 * q^22 - 5 * q^23 + 6 * q^24 - 6 * q^25 - 6 * q^26 - 32 * q^27 + 4 * q^28 + 20 * q^29 + 15 * q^30 + 7 * q^31 + 16 * q^32 + 15 * q^33 + 3 * q^34 + 4 * q^35 - q^36 - 6 * q^37 + 6 * q^38 + 34 * q^39 + 11 * q^40 + 9 * q^41 - q^42 - 22 * q^43 - 8 * q^44 - 8 * q^45 - 40 * q^47 - 4 * q^48 + 16 * q^49 - q^50 + 14 * q^51 + 9 * q^52 - 24 * q^53 + 23 * q^54 - 26 * q^55 + 4 * q^56 + 52 * q^57 + 20 * q^58 - 17 * q^59 - 5 * q^60 + 2 * q^61 - 23 * q^62 + q^63 - 4 * q^64 - 16 * q^65 - 10 * q^66 - 14 * q^67 - 2 * q^68 - 35 * q^69 - q^70 + 7 * q^71 - 6 * q^72 + 5 * q^73 - 36 * q^74 + 35 * q^75 + 36 * q^76 - 7 * q^77 - 46 * q^78 + 20 * q^79 + q^80 + 49 * q^81 + 44 * q^82 + 17 * q^83 + 4 * q^84 - 13 * q^85 + 8 * q^86 - 66 * q^87 + 7 * q^88 + 27 * q^89 + 37 * q^90 - 9 * q^91 - 34 * q^93 - 40 * q^94 - 20 * q^95 + q^96 + 6 * q^97 - 4 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−1.78422	+	1.29631i	−1.03012	+	0.748427i	−0.968333	−	0.249663i	$-0.919680\pi$
$3$	−1.78422	+	1.29631i	−1.03012	+	0.748427i	−0.0617879	+	0.998089i	$0.519680\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.298278	+	2.21608i	−0.133394	+	0.991063i
$5$	−0.298278	+	2.21608i	−0.133394	+	0.991063i
$6$	−1.78422	−	1.29631i	−0.728405	−	0.529217i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	0.575968	−	1.77265i	0.191989	−	0.590883i
$10$	−2.19979	+	0.401128i	−0.695636	+	0.126848i
$11$	1.24562	+	3.83361i	0.375567	+	1.15588i	0.943095	+	0.332523i	$0.107900\pi$
$11$	1.24562	+	3.83361i	0.375567	+	1.15588i	−0.567528	+	0.823354i	$0.692100\pi$
$12$	0.681512	−	2.09748i	0.196736	−	0.605490i
$13$	1.20223	−	3.70007i	0.333438	−	1.02622i	−0.634049	−	0.773293i	$-0.718608\pi$
$13$	1.20223	−	3.70007i	0.333438	−	1.02622i	0.967487	−	0.252922i	$-0.0813917\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	−2.34054	−	4.34065i	−0.604326	−	1.12075i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−5.86426	−	4.26063i	−1.42229	−	1.03336i	−0.991388	−	0.130958i	$-0.958195\pi$
$17$	−5.86426	−	4.26063i	−1.42229	−	1.03336i	−0.430904	−	0.902398i	$-0.641805\pi$
$18$	1.86387			0.439319
$19$	−3.26168	−	2.36975i	−0.748281	−	0.543658i	0.147013	−	0.989135i	$-0.453034\pi$
$19$	−3.26168	−	2.36975i	−0.748281	−	0.543658i	−0.895293	+	0.445477i	$0.853034\pi$
$20$	−1.06127	−	1.96817i	−0.237307	−	0.440097i
$21$	1.78422	−	1.29631i	0.389349	−	0.282879i
$22$	−3.26106	+	2.36930i	−0.695261	+	0.505137i
$23$	2.38359	+	7.33594i	0.497013	+	1.52965i	0.813795	+	0.581152i	$0.197398\pi$
$23$	2.38359	+	7.33594i	0.497013	+	1.52965i	−0.316782	+	0.948498i	$0.602602\pi$
$24$	2.20542			0.450179
$25$	−4.82206	−	1.32202i	−0.964412	−	0.264404i
$26$	3.89049			0.762987
$27$	−0.774284	−	2.38300i	−0.149011	−	0.458609i
$28$	0.809017	−	0.587785i	0.152890	−	0.111081i
$29$	3.78201	−	2.74779i	0.702302	−	0.510252i	−0.178379	−	0.983962i	$-0.557085\pi$
$29$	3.78201	−	2.74779i	0.702302	−	0.510252i	0.880681	+	0.473709i	$0.157085\pi$
$30$	3.40493	−	3.56732i	0.621653	−	0.651301i
$31$	7.06220	+	5.13099i	1.26841	+	0.921553i	0.999138	−	0.0415116i	$-0.0132173\pi$
$31$	7.06220	+	5.13099i	1.26841	+	0.921553i	0.269271	+	0.963065i	$0.413217\pi$
$32$	1.00000			0.176777
$33$	−7.19201	−	5.22530i	−1.25197	−	0.909609i
$34$	2.23995	−	6.89385i	0.384148	−	1.18229i
$35$	0.298278	−	2.21608i	0.0504182	−	0.374587i
$36$	0.575968	+	1.77265i	0.0959947	+	0.295441i
$37$	−0.432558	+	1.33128i	−0.0711121	+	0.218861i	−0.980296	−	0.197534i	$-0.936707\pi$
$37$	−0.432558	+	1.33128i	−0.0711121	+	0.218861i	0.909184	+	0.416395i	$0.136707\pi$
$38$	1.24585	−	3.83433i	0.202104	−	0.622011i
$39$	2.65141	+	8.16021i	0.424566	+	1.30668i
$40$	1.54389	−	1.61753i	0.244111	−	0.255753i
$41$	−3.32221	+	10.2247i	−0.518842	+	1.59683i	0.257338	+	0.966322i	$0.417155\pi$
$41$	−3.32221	+	10.2247i	−0.518842	+	1.59683i	−0.776180	+	0.630511i	$0.782845\pi$
$42$	1.78422	+	1.29631i	0.275311	+	0.200025i
$43$	−9.39984			−1.43346			−0.716731	−	0.697350i	$-0.754362\pi$
$43$	−9.39984			−1.43346			−0.716731	+	0.697350i	$0.754362\pi$
$44$	−3.26106	−	2.36930i	−0.491624	−	0.357186i
$45$	3.75654	+	1.80514i	0.559992	+	0.269094i
$46$	−6.24033	+	4.53386i	−0.920086	+	0.668482i
$47$	−5.95545	+	4.32689i	−0.868691	+	0.631141i	−0.930235	−	0.366963i	$-0.880397\pi$
$47$	−5.95545	+	4.32689i	−0.868691	+	0.631141i	0.0615443	+	0.998104i	$0.480397\pi$
$48$	0.681512	+	2.09748i	0.0983678	+	0.302745i
$49$	1.00000			0.142857
$50$	−0.232784	−	4.99458i	−0.0329206	−	0.706340i
$51$	15.9863			2.23852
$52$	1.20223	+	3.70007i	0.166719	+	0.513108i
$53$	−1.61865	+	1.17602i	−0.222339	+	0.161538i	−0.693379	−	0.720573i	$-0.743879\pi$
$53$	−1.61865	+	1.17602i	−0.222339	+	0.161538i	0.471040	+	0.882112i	$0.343879\pi$
$54$	2.02710	−	1.47278i	0.275854	−	0.200419i
$55$	−8.86715	+	1.61691i	−1.19565	+	0.218024i
$56$	0.809017	+	0.587785i	0.108109	+	0.0785461i
$57$	8.89149			1.17771
$58$	3.78201	+	2.74779i	0.496603	+	0.360803i
$59$	−0.566673	+	1.74404i	−0.0737746	+	0.227055i	−0.981144	−	0.193280i	$-0.938087\pi$
$59$	−0.566673	+	1.74404i	−0.0737746	+	0.227055i	0.907369	+	0.420335i	$0.138087\pi$
$60$	4.44491	+	2.13592i	0.573835	+	0.275746i
$61$	−0.939817	−	2.89246i	−0.120331	−	0.370341i	0.872690	−	0.488274i	$-0.162373\pi$
$61$	−0.939817	−	2.89246i	−0.120331	−	0.370341i	−0.993022	+	0.117933i	$0.962373\pi$
$62$	−2.69752	+	8.30212i	−0.342585	+	1.05437i
$63$	−0.575968	+	1.77265i	−0.0725652	+	0.223333i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	7.84107	+	3.76788i	0.972565	+	0.467349i
$66$	2.74710	−	8.45472i	0.338145	−	1.04070i
$67$	9.85111	+	7.15725i	1.20350	+	0.874397i	0.994625	−	0.103544i	$-0.0330184\pi$
$67$	9.85111	+	7.15725i	1.20350	+	0.874397i	0.208879	+	0.977941i	$0.433018\pi$
$68$	7.24862			0.879025
$69$	−13.7625	−	9.99907i	−1.65681	−	1.20375i
$70$	2.19979	−	0.401128i	0.262926	−	0.0479440i
$71$	0.580895	−	0.422045i	0.0689396	−	0.0500875i	−0.552782	−	0.833326i	$-0.686434\pi$
$71$	0.580895	−	0.422045i	0.0689396	−	0.0500875i	0.621721	+	0.783239i	$0.286434\pi$
$72$	−1.50790	+	1.09556i	−0.177708	+	0.129113i
$73$	1.11710	+	3.43807i	0.130746	+	0.402395i	0.994904	−	0.100825i	$-0.0321483\pi$
$73$	1.11710	+	3.43807i	0.130746	+	0.402395i	−0.864158	+	0.503221i	$0.832148\pi$
$74$	−1.39979			−0.162722
$75$	10.3174	−	3.89212i	1.19135	−	0.449424i
$76$	4.03166			0.462463
$77$	−1.24562	−	3.83361i	−0.141951	−	0.436881i
$78$	−6.94149	+	5.04329i	−0.785969	+	0.571040i
$79$	−10.8709	+	7.89820i	−1.22308	+	0.888617i	−0.996352	−	0.0853413i	$-0.972802\pi$
$79$	−10.8709	+	7.89820i	−1.22308	+	0.888617i	−0.226725	+	0.973959i	$0.572802\pi$
$80$	2.01545	+	0.968487i	0.225334	+	0.108280i
$81$	8.99432	+	6.53476i	0.999369	+	0.726084i
$82$	−10.7509			−1.18724
$83$	5.92741	+	4.30651i	0.650617	+	0.472701i	0.863481	−	0.504381i	$-0.168279\pi$
$83$	5.92741	+	4.30651i	0.650617	+	0.472701i	−0.212864	+	0.977082i	$0.568279\pi$
$84$	−0.681512	+	2.09748i	−0.0743590	+	0.228854i
$85$	11.1911	−	11.7248i	1.21385	−	1.27174i
$86$	−2.90471	−	8.93978i	−0.313223	−	0.964001i
$87$	−3.18595	+	9.80534i	−0.341570	+	1.05124i
$88$	1.24562	−	3.83361i	0.132783	−	0.408664i
$89$	0.584454	+	1.79876i	0.0619520	+	0.190669i	0.977242	−	0.212126i	$-0.0680388\pi$
$89$	0.584454	+	1.79876i	0.0619520	+	0.190669i	−0.915290	+	0.402795i	$0.868039\pi$
$90$	−0.555952	+	4.13050i	−0.0586025	+	0.435393i
$91$	−1.20223	+	3.70007i	−0.126028	+	0.387873i
$92$	−6.24033	−	4.53386i	−0.650599	−	0.472688i
$93$	−19.2519			−1.99633
$94$	−5.95545	−	4.32689i	−0.614257	−	0.446284i
$95$	6.22445	−	6.52131i	0.638615	−	0.669073i
$96$	−1.78422	+	1.29631i	−0.182101	+	0.132304i
$97$	−0.578244	+	0.420119i	−0.0587118	+	0.0426566i	−0.616754	−	0.787156i	$-0.711553\pi$
$97$	−0.578244	+	0.420119i	−0.0587118	+	0.0426566i	0.558042	+	0.829813i	$0.311553\pi$
$98$	0.309017	+	0.951057i	0.0312154	+	0.0960712i
$99$	7.51308			0.755093
$100$	4.67819	−	1.76480i	0.467819	−	0.176480i
$101$	5.21519			0.518931			0.259465	−	0.965752i	$-0.416454\pi$
$101$	5.21519			0.518931			0.259465	+	0.965752i	$0.416454\pi$
$102$	4.94002	+	15.2038i	0.489135	+	1.50540i
$103$	−10.9068	+	7.92423i	−1.07468	+	0.780798i	−0.976747	−	0.214396i	$-0.931222\pi$
$103$	−10.9068	+	7.92423i	−1.07468	+	0.780798i	−0.0979291	+	0.995193i	$0.531222\pi$
$104$	−3.14747	+	2.28677i	−0.308635	+	0.224236i
$105$	2.34054	+	4.34065i	0.228414	+	0.423604i
$106$	−1.61865	−	1.17602i	−0.157217	−	0.114225i
$107$	9.43850			0.912455			0.456227	−	0.889863i	$-0.349200\pi$
$107$	9.43850			0.912455			0.456227	+	0.889863i	$0.349200\pi$
$108$	2.02710	+	1.47278i	0.195058	+	0.141718i
$109$	1.74710	−	5.37701i	0.167341	−	0.515024i	−0.831860	−	0.554986i	$-0.812724\pi$
$109$	1.74710	−	5.37701i	0.167341	−	0.515024i	0.999201	+	0.0399618i	$0.0127236\pi$
$110$	−4.27787	−	7.93350i	−0.407879	−	0.756430i
$111$	−0.953972	−	2.93602i	−0.0905470	−	0.278675i
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	2.92527	−	9.00306i	0.275186	−	0.846937i	−0.713984	−	0.700162i	$-0.753111\pi$
$113$	2.92527	−	9.00306i	0.275186	−	0.846937i	0.989170	−	0.146774i	$-0.0468891\pi$
$114$	2.74762	+	8.45631i	0.257338	+	0.792006i
$115$	−16.9680	+	3.09409i	−1.58228	+	0.288526i
$116$	−1.44460	+	4.44602i	−0.134128	+	0.412803i
$117$	−5.86648	−	4.26225i	−0.542356	−	0.394045i
$118$	−1.83379			−0.168814
$119$	5.86426	+	4.26063i	0.537576	+	0.390572i
$120$	−0.657828	+	4.88739i	−0.0600512	+	0.446156i
$121$	−4.24583	+	3.08477i	−0.385984	+	0.280434i
$122$	2.46047	−	1.78764i	0.222761	−	0.161845i
$123$	−7.32687	−	22.5498i	−0.660642	−	2.03325i
$124$	−8.72936			−0.783920
$125$	4.36802	−	10.2918i	0.390688	−	0.920523i
$126$	−1.86387			−0.166047
$127$	−3.66373	−	11.2758i	−0.325104	−	1.00057i	−0.971394	−	0.237474i	$-0.923680\pi$
$127$	−3.66373	−	11.2758i	−0.325104	−	1.00057i	0.646290	−	0.763092i	$-0.276320\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	16.7714	−	12.1851i	1.47664	−	1.07284i
$130$	−1.16045	+	8.62164i	−0.101778	+	0.756168i
$131$	−11.6750	−	8.48239i	−1.02005	−	0.741110i	−0.0537568	−	0.998554i	$-0.517120\pi$
$131$	−11.6750	−	8.48239i	−1.02005	−	0.741110i	−0.966293	+	0.257444i	$0.917120\pi$
$132$	8.88982			0.773759
$133$	3.26168	+	2.36975i	0.282823	+	0.205483i
$134$	−3.76279	+	11.5807i	−0.325055	+	1.00042i
$135$	5.51188	−	1.00508i	0.474388	−	0.0865037i
$136$	2.23995	+	6.89385i	0.192074	+	0.591143i
$137$	−0.996400	+	3.06660i	−0.0851282	+	0.261998i	−0.984556	−	0.175073i	$-0.943984\pi$
$137$	−0.996400	+	3.06660i	−0.0851282	+	0.261998i	0.899427	+	0.437070i	$0.143984\pi$
$138$	5.25682	−	16.1788i	0.447490	−	1.37723i
$139$	−2.04486	−	6.29344i	−0.173443	−	0.533802i	0.826116	−	0.563500i	$-0.190546\pi$
$139$	−2.04486	−	6.29344i	−0.173443	−	0.533802i	−0.999559	+	0.0296977i	$0.990546\pi$
$140$	1.06127	+	1.96817i	0.0896937	+	0.166341i
$141$	5.01684	−	15.4402i	0.422494	−	1.30030i
$142$	0.580895	+	0.422045i	0.0487476	+	0.0354172i
$143$	15.6821			1.31141
$144$	−1.50790	−	1.09556i	−0.125659	−	0.0912964i
$145$	4.96125	+	9.20087i	0.412009	+	0.764090i
$146$	−2.92459	+	2.12484i	−0.242041	+	0.175853i
$147$	−1.78422	+	1.29631i	−0.147160	+	0.106918i
$148$	−0.432558	−	1.33128i	−0.0355561	−	0.109430i
$149$	5.43370			0.445146			0.222573	−	0.974916i	$-0.428554\pi$
$149$	5.43370			0.445146			0.222573	+	0.974916i	$0.428554\pi$
$150$	6.88987	+	8.60967i	0.562556	+	0.702977i
$151$	−9.39608			−0.764642			−0.382321	−	0.924030i	$-0.624875\pi$
$151$	−9.39608			−0.764642			−0.382321	+	0.924030i	$0.624875\pi$
$152$	1.24585	+	3.83433i	0.101052	+	0.311006i
$153$	−10.9302	+	7.94128i	−0.883657	+	0.642014i
$154$	3.26106	−	2.36930i	0.262784	−	0.190924i
$155$	−13.4772	+	14.1200i	−1.08252	+	1.13414i
$156$	−6.94149	−	5.04329i	−0.555764	−	0.403786i
$157$	−12.0524			−0.961889			−0.480944	−	0.876751i	$-0.659706\pi$
$157$	−12.0524			−0.961889			−0.480944	+	0.876751i	$0.659706\pi$
$158$	−10.8709	−	7.89820i	−0.864846	−	0.628347i
$159$	1.36354	−	4.19655i	0.108136	−	0.332808i
$160$	−0.298278	+	2.21608i	−0.0235810	+	0.175197i
$161$	−2.38359	−	7.33594i	−0.187853	−	0.578153i
$162$	−3.43553	+	10.5735i	−0.269920	+	0.830730i
$163$	−1.05620	+	3.25064i	−0.0827278	+	0.254610i	−0.983862	−	0.178931i	$-0.942736\pi$
$163$	−1.05620	+	3.25064i	−0.0827278	+	0.254610i	0.901134	+	0.433541i	$0.142736\pi$
$164$	−3.32221	−	10.2247i	−0.259421	−	0.798416i
$165$	13.7249	−	14.3795i	1.06848	−	1.11944i
$166$	−2.26407	+	6.96808i	−0.175726	+	0.540828i
$167$	20.2661	+	14.7242i	1.56823	+	1.13939i	0.928823	+	0.370524i	$0.120822\pi$
$167$	20.2661	+	14.7242i	1.56823	+	1.13939i	0.639412	+	0.768865i	$0.279178\pi$
$168$	−2.20542			−0.170152
$169$	−1.72796	−	1.25544i	−0.132920	−	0.0965720i
$170$	14.6092	+	7.02020i	1.12048	+	0.538425i
$171$	−6.07936	+	4.41691i	−0.464900	+	0.337770i
$172$	7.60463	−	5.52509i	0.579847	−	0.421284i
$173$	−1.23897	−	3.81316i	−0.0941972	−	0.289909i	0.892846	−	0.450361i	$-0.148705\pi$
$173$	−1.23897	−	3.81316i	−0.0941972	−	0.289909i	−0.987044	+	0.160452i	$0.948705\pi$
$174$	−10.3099			−0.781595
$175$	4.82206	+	1.32202i	0.364514	+	0.0999352i
$176$	4.03090			0.303840
$177$	−1.24975	−	3.84634i	−0.0939371	−	0.289109i
$178$	−1.53012	+	1.11170i	−0.114687	+	0.0833252i
$179$	1.18270	−	0.859283i	0.0883993	−	0.0642258i	−0.542708	−	0.839922i	$-0.682601\pi$
$179$	1.18270	−	0.859283i	0.0883993	−	0.0642258i	0.631107	+	0.775696i	$0.282601\pi$
$180$	−4.10014	+	0.747652i	−0.305606	+	0.0557267i
$181$	15.6550	+	11.3740i	1.16363	+	0.845425i	0.990232	−	0.139427i	$-0.0445262\pi$
$181$	15.6550	+	11.3740i	1.16363	+	0.845425i	0.173395	+	0.984852i	$0.444526\pi$
$182$	−3.89049			−0.288382
$183$	5.42637	+	3.94249i	0.401129	+	0.291437i
$184$	2.38359	−	7.33594i	0.175721	−	0.540813i
$185$	−2.82120	−	1.35568i	−0.207419	−	0.0996713i
$186$	−5.94916	−	18.3096i	−0.436214	−	1.34253i
$187$	9.02900	−	27.7884i	0.660266	−	2.03209i
$188$	2.27478	−	7.00105i	0.165905	−	0.510604i
$189$	0.774284	+	2.38300i	0.0563209	+	0.173338i
$190$	8.12560	+	3.90461i	0.589493	+	0.283270i
$191$	1.63099	−	5.01969i	0.118015	−	0.363212i	−0.874549	−	0.484937i	$-0.838843\pi$
$191$	1.63099	−	5.01969i	0.118015	−	0.363212i	0.992564	+	0.121725i	$0.0388426\pi$
$192$	−1.78422	−	1.29631i	−0.128765	−	0.0935533i
$193$	15.1918			1.09353			0.546766	−	0.837286i	$-0.315859\pi$
$193$	15.1918			1.09353			0.546766	+	0.837286i	$0.315859\pi$
$194$	−0.578244	−	0.420119i	−0.0415155	−	0.0301628i
$195$	−18.8746	+	3.44174i	−1.35164	+	0.246468i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−11.8799	+	8.63123i	−0.846405	+	0.614949i	−0.924153	−	0.382024i	$-0.875227\pi$
$197$	−11.8799	+	8.63123i	−0.846405	+	0.614949i	0.0777473	+	0.996973i	$0.475227\pi$
$198$	2.32167	+	7.14536i	0.164994	+	0.507799i
$199$	5.61713			0.398188			0.199094	−	0.979980i	$-0.436200\pi$
$199$	5.61713			0.398188			0.199094	+	0.979980i	$0.436200\pi$
$200$	3.12407	+	3.90387i	0.220905	+	0.276045i
$201$	−26.8546			−1.89418
$202$	1.61158	+	4.95994i	0.113391	+	0.348980i
$203$	−3.78201	+	2.74779i	−0.265445	+	0.192857i
$204$	−12.9331	+	9.39648i	−0.905501	+	0.657885i
$205$	−21.6679	−	10.4121i	−1.51335	−	0.727213i
$206$	−10.9068	−	7.92423i	−0.759911	−	0.552107i
$207$	14.3769			0.999265
$208$	−3.14747	−	2.28677i	−0.218238	−	0.158559i
$209$	5.02190	−	15.4558i	0.347372	−	1.06910i
$210$	−3.40493	+	3.56732i	−0.234963	+	0.246169i
$211$	−0.109560	−	0.337192i	−0.00754243	−	0.0232132i	0.947214	−	0.320601i	$-0.103885\pi$
$211$	−0.109560	−	0.337192i	−0.00754243	−	0.0232132i	−0.954757	+	0.297387i	$0.903885\pi$
$212$	0.618269	−	1.90284i	0.0424629	−	0.130687i
$213$	−0.489343	+	1.50604i	−0.0335293	+	0.103192i
$214$	2.91666	+	8.97655i	0.199379	+	0.613624i
$215$	2.80377	−	20.8308i	0.191215	−	1.42065i
$216$	−0.774284	+	2.38300i	−0.0526834	+	0.162143i
$217$	−7.06220	−	5.13099i	−0.479413	−	0.348314i
$218$	5.65372			0.382918
$219$	−6.44995	−	4.68617i	−0.435847	−	0.316662i
$220$	6.22328	−	6.52008i	0.419573	−	0.439584i
$221$	−22.8148	+	16.5759i	−1.53469	+	1.11502i
$222$	2.49753	−	1.81456i	0.167623	−	0.121785i
$223$	0.430808	+	1.32589i	0.0288491	+	0.0887883i	0.964444	−	0.264286i	$-0.0851363\pi$
$223$	0.430808	+	1.32589i	0.0288491	+	0.0887883i	−0.935595	+	0.353074i	$0.885136\pi$
$224$	−1.00000			−0.0668153
$225$	−5.12083	+	7.78638i	−0.341389	+	0.519092i
$226$	9.46638			0.629694
$227$	5.66088	+	17.4224i	0.375726	+	1.15636i	0.942988	+	0.332827i	$0.108003\pi$
$227$	5.66088	+	17.4224i	0.375726	+	1.15636i	−0.567262	+	0.823537i	$0.691997\pi$
$228$	−7.19337	+	5.22629i	−0.476393	+	0.346119i
$229$	−8.61834	+	6.26159i	−0.569516	+	0.413777i	−0.834929	−	0.550357i	$-0.814492\pi$
$229$	−8.61834	+	6.26159i	−0.569516	+	0.413777i	0.265414	+	0.964135i	$0.414492\pi$
$230$	−8.18607	−	15.1814i	−0.539773	−	1.00103i
$231$	7.19201	+	5.22530i	0.473200	+	0.343800i
$232$	−4.67483			−0.306917
$233$	19.1845	+	13.9384i	1.25682	+	0.913132i	0.998597	−	0.0529539i	$-0.0168636\pi$
$233$	19.1845	+	13.9384i	1.25682	+	0.913132i	0.258221	+	0.966086i	$0.416864\pi$
$234$	2.24080	−	6.89646i	0.146485	−	0.450836i
$235$	−7.81236	−	14.4884i	−0.509622	−	0.945118i
$236$	−0.566673	−	1.74404i	−0.0368873	−	0.113527i
$237$	9.15763	−	28.1843i	0.594852	−	1.83077i
$238$	−2.23995	+	6.89385i	−0.145194	+	0.446862i
$239$	−0.202490	−	0.623199i	−0.0130980	−	0.0403114i	0.944294	−	0.329103i	$-0.106746\pi$
$239$	−0.202490	−	0.623199i	−0.0130980	−	0.0403114i	−0.957392	+	0.288792i	$0.906746\pi$
$240$	−4.85147	+	0.884656i	−0.313161	+	0.0571043i
$241$	−6.97076	+	21.4538i	−0.449026	+	1.38196i	0.428981	+	0.903313i	$0.358873\pi$
$241$	−6.97076	+	21.4538i	−0.449026	+	1.38196i	−0.878007	+	0.478647i	$0.841127\pi$
$242$	−4.24583	−	3.08477i	−0.272932	−	0.198297i
$243$	−17.0020			−1.09068
$244$	2.46047	+	1.78764i	0.157516	+	0.114442i
$245$	−0.298278	+	2.21608i	−0.0190563	+	0.141580i
$246$	19.1820	−	13.9365i	1.22300	−	0.888561i
$247$	−12.6895	+	9.21947i	−0.807414	+	0.586621i
$248$	−2.69752	−	8.30212i	−0.171293	−	0.527185i
$249$	−16.1584			−1.02400
$250$	11.1378	+	0.973904i	0.704419	+	0.0615951i
$251$	18.5908			1.17344			0.586720	−	0.809790i	$-0.300419\pi$
$251$	18.5908			1.17344			0.586720	+	0.809790i	$0.300419\pi$
$252$	−0.575968	−	1.77265i	−0.0362826	−	0.111666i
$253$	−25.1541	+	18.2755i	−1.58143	+	1.14897i
$254$	9.59177	−	6.96883i	0.601841	−	0.437263i
$255$	−4.76835	+	35.4269i	−0.298606	+	2.21852i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	12.4131			0.774307			0.387154	−	0.922015i	$-0.373458\pi$
$257$	12.4131			0.774307			0.387154	+	0.922015i	$0.373458\pi$
$258$	16.7714	+	12.1851i	1.04414	+	0.758613i
$259$	0.432558	−	1.33128i	0.0268779	−	0.0827215i
$260$	−8.55827	+	1.56058i	−0.530761	+	0.0967833i
$261$	−2.69255	−	8.28682i	−0.166665	−	0.512941i
$262$	4.45945	−	13.7248i	0.275506	−	0.847920i
$263$	5.16797	−	15.9054i	0.318671	−	0.980768i	−0.655546	−	0.755155i	$-0.727562\pi$
$263$	5.16797	−	15.9054i	0.318671	−	0.980768i	0.974217	−	0.225613i	$-0.0724384\pi$
$264$	2.74710	+	8.45472i	0.169073	+	0.520352i
$265$	−2.12335	−	3.93784i	−0.130436	−	0.241900i
$266$	−1.24585	+	3.83433i	−0.0763880	+	0.235098i
$267$	−3.37456	−	2.45176i	−0.206519	−	0.150045i
$268$	−12.1766			−0.743807
$269$	−11.9931	−	8.71353i	−0.731235	−	0.531273i	0.158719	−	0.987324i	$-0.449264\pi$
$269$	−11.9931	−	8.71353i	−0.731235	−	0.531273i	−0.889954	+	0.456051i	$0.849264\pi$
$270$	2.65916	+	4.93153i	0.161831	+	0.300123i
$271$	17.4609	−	12.6861i	1.06067	−	0.770623i	0.0864593	−	0.996255i	$-0.472445\pi$
$271$	17.4609	−	12.6861i	1.06067	−	0.770623i	0.974213	+	0.225632i	$0.0724448\pi$
$272$	−5.86426	+	4.26063i	−0.355573	+	0.258339i
$273$	−2.65141	−	8.16021i	−0.160471	−	0.493878i
$274$	−3.22442			−0.194794
$275$	−0.938328	−	20.1326i	−0.0565833	−	1.21404i
$276$	17.0114			1.02397
$277$	−1.33551	−	4.11026i	−0.0802427	−	0.246962i	0.902885	−	0.429882i	$-0.141445\pi$
$277$	−1.33551	−	4.11026i	−0.0802427	−	0.246962i	−0.983128	+	0.182920i	$0.941445\pi$
$278$	5.35352	−	3.88956i	0.321083	−	0.233280i
$279$	13.1630	−	9.56351i	0.788051	−	0.572553i
$280$	−1.54389	+	1.61753i	−0.0922653	+	0.0966657i
$281$	−4.50036	−	3.26970i	−0.268469	−	0.195054i	0.445403	−	0.895330i	$-0.353060\pi$
$281$	−4.50036	−	3.26970i	−0.268469	−	0.195054i	−0.713872	+	0.700276i	$0.753060\pi$
$282$	16.2348			0.966770
$283$	6.50307	+	4.72476i	0.386567	+	0.280858i	0.764047	−	0.645160i	$-0.223209\pi$
$283$	6.50307	+	4.72476i	0.386567	+	0.280858i	−0.377480	+	0.926018i	$0.623209\pi$
$284$	−0.221882	+	0.682883i	−0.0131663	+	0.0405217i
$285$	−2.65214	+	19.7043i	−0.157099	+	1.16718i
$286$	4.84605	+	14.9146i	0.286553	+	0.881919i
$287$	3.32221	−	10.2247i	0.196104	−	0.603546i
$288$	0.575968	−	1.77265i	0.0339393	−	0.104454i
$289$	10.9832	+	33.8030i	0.646073	+	1.98841i
$290$	−7.21743	+	7.56165i	−0.423822	+	0.444036i
$291$	0.487110	−	1.49917i	0.0285549	−	0.0878830i
$292$	−2.92459	−	2.12484i	−0.171149	−	0.124347i
$293$	20.1181			1.17531			0.587657	−	0.809110i	$-0.300051\pi$
$293$	20.1181			1.17531			0.587657	+	0.809110i	$0.300051\pi$
$294$	−1.78422	−	1.29631i	−0.104058	−	0.0756025i
$295$	−3.69592	−	1.77600i	−0.215185	−	0.103403i
$296$	1.13245	−	0.822774i	0.0658224	−	0.0478228i
$297$	8.17104	−	5.93661i	0.474132	−	0.344477i
$298$	1.67911	+	5.16776i	0.0972680	+	0.299360i
$299$	30.0091			1.73547
$300$	−6.05920	+	9.21319i	−0.349828	+	0.531924i
$301$	9.39984			0.541798
$302$	−2.90355	−	8.93620i	−0.167080	−	0.514221i
$303$	−9.30505	+	6.76052i	−0.534561	+	0.388382i
$304$	−3.26168	+	2.36975i	−0.187070	+	0.135914i
$305$	6.69026	−	1.21996i	0.383083	−	0.0698545i
$306$	−10.9302	−	7.94128i	−0.624840	−	0.453973i
$307$	−2.98143			−0.170159			−0.0850797	−	0.996374i	$-0.527114\pi$
$307$	−2.98143			−0.170159			−0.0850797	+	0.996374i	$0.527114\pi$
$308$	3.26106	+	2.36930i	0.185816	+	0.135004i
$309$	9.18781	−	28.2772i	0.522676	−	1.60863i
$310$	−17.5936	−	8.45427i	−0.999248	−	0.480170i
$311$	−2.27324	−	6.99630i	−0.128903	−	0.396724i	0.865689	−	0.500583i	$-0.166881\pi$
$311$	−2.27324	−	6.99630i	−0.128903	−	0.396724i	−0.994592	+	0.103859i	$0.966881\pi$
$312$	2.65141	−	8.16021i	0.150107	−	0.461981i
$313$	−8.00858	+	24.6479i	−0.452672	+	1.39318i	0.421175	+	0.906979i	$0.361618\pi$
$313$	−8.00858	+	24.6479i	−0.452672	+	1.39318i	−0.873847	+	0.486201i	$0.838382\pi$
$314$	−3.72441	−	11.4625i	−0.210180	−	0.646869i
$315$	−3.75654	−	1.80514i	−0.211657	−	0.101708i
$316$	4.15233	−	12.7796i	0.233587	−	0.718907i
$317$	−0.741598	−	0.538802i	−0.0416523	−	0.0302621i	0.566764	−	0.823880i	$-0.308195\pi$
$317$	−0.741598	−	0.538802i	−0.0416523	−	0.0302621i	−0.608417	+	0.793618i	$0.708195\pi$
$318$	4.41251			0.247442
$319$	15.2449	+	11.0761i	0.853551	+	0.620141i
$320$	−2.19979	+	0.401128i	−0.122972	+	0.0224238i
$321$	−16.8404	+	12.2353i	−0.939938	+	0.682905i
$322$	6.24033	−	4.53386i	0.347760	−	0.252662i
$323$	9.03070	+	27.7936i	0.502482	+	1.54648i
$324$	−11.1176			−0.617644
$325$	−10.6888	+	16.2526i	−0.592906	+	0.901532i
$326$	−3.41793			−0.189301
$327$	3.85308	+	11.8586i	0.213076	+	0.655780i
$328$	8.69766	−	6.31922i	0.480248	−	0.348921i
$329$	5.95545	−	4.32689i	0.328334	−	0.238549i
$330$	17.9170	+	8.60967i	0.986297	+	0.473947i
$331$	5.24236	+	3.80879i	0.288146	+	0.209350i	0.722463	−	0.691410i	$-0.243010\pi$
$331$	5.24236	+	3.80879i	0.288146	+	0.209350i	−0.434317	+	0.900760i	$0.643010\pi$
$332$	−7.32668			−0.402104
$333$	2.11075	+	1.53355i	0.115668	+	0.0840379i
$334$	−7.74094	+	23.8242i	−0.423566	+	1.30360i
$335$	−18.7994	+	19.6960i	−1.02712	+	1.07611i
$336$	−0.681512	−	2.09748i	−0.0371795	−	0.114427i
$337$	−2.72812	+	8.39630i	−0.148610	+	0.457375i	−0.997458	−	0.0712627i	$-0.977297\pi$
$337$	−2.72812	+	8.39630i	−0.148610	+	0.457375i	0.848847	+	0.528638i	$0.177297\pi$
$338$	0.660021	−	2.03134i	0.0359004	−	0.110490i
$339$	6.45145	+	19.8555i	0.350395	+	1.07840i
$340$	−2.16211	+	16.0636i	−0.117257	+	0.871169i
$341$	−10.8734	+	33.4650i	−0.588829	+	1.81223i
$342$	−6.07936	−	4.41691i	−0.328734	−	0.238839i
$343$	−1.00000			−0.0539949
$344$	7.60463	+	5.52509i	0.410014	+	0.297893i
$345$	26.2638	−	27.5164i	1.41400	−	1.48144i
$346$	3.24367	−	2.35666i	0.174381	−	0.126695i
$347$	−1.95644	+	1.42143i	−0.105027	+	0.0763066i	−0.639059	−	0.769158i	$-0.720676\pi$
$347$	−1.95644	+	1.42143i	−0.105027	+	0.0763066i	0.534032	+	0.845464i	$0.320676\pi$
$348$	−3.18595	−	9.80534i	−0.170785	−	0.525622i
$349$	18.9646			1.01515			0.507576	−	0.861607i	$-0.330542\pi$
$349$	18.9646			1.01515			0.507576	+	0.861607i	$0.330542\pi$
$350$	0.232784	+	4.99458i	0.0124428	+	0.266971i
$351$	−9.74814			−0.520317
$352$	1.24562	+	3.83361i	0.0663915	+	0.204332i
$353$	10.1388	−	7.36630i	0.539636	−	0.392069i	−0.284314	−	0.958731i	$-0.591766\pi$
$353$	10.1388	−	7.36630i	0.539636	−	0.392069i	0.823950	+	0.566663i	$0.191766\pi$
$354$	3.27189	−	2.37717i	0.173899	−	0.126345i
$355$	0.762019	+	1.41320i	0.0404438	+	0.0750049i
$356$	−1.53012	−	1.11170i	−0.0810962	−	0.0589198i
$357$	−15.9863			−0.846082
$358$	1.18270	+	0.859283i	0.0625077	+	0.0454145i
$359$	−10.3807	+	31.9485i	−0.547873	+	1.68618i	0.166186	+	0.986094i	$0.446855\pi$
$359$	−10.3807	+	31.9485i	−0.547873	+	1.68618i	−0.714059	+	0.700085i	$0.753145\pi$
$360$	−1.97807	−	3.66843i	−0.104254	−	0.193343i
$361$	−0.848480	−	2.61135i	−0.0446569	−	0.137440i
$362$	−5.97968	+	18.4036i	−0.314285	+	0.967270i
$363$	3.57666	−	11.0078i	0.187726	−	0.577762i
$364$	−1.20223	−	3.70007i	−0.0630138	−	0.193936i
$365$	−7.95225	+	1.45008i	−0.416240	+	0.0759005i
$366$	−2.07269	+	6.37908i	−0.108341	+	0.333440i
$367$	−29.2597	−	21.2584i	−1.52734	−	1.10968i	−0.957692	−	0.287796i	$-0.907078\pi$
$367$	−29.2597	−	21.2584i	−1.52734	−	1.10968i	−0.569653	−	0.821885i	$-0.692922\pi$
$368$	7.71347			0.402092
$369$	16.2113	+	11.7782i	0.843929	+	0.613150i
$370$	0.417526	−	3.10205i	0.0217061	−	0.161268i
$371$	1.61865	−	1.17602i	0.0840361	−	0.0610558i
$372$	15.5751	−	11.3160i	0.807532	−	0.586706i
$373$	−6.16034	−	18.9596i	−0.318970	−	0.981689i	−0.974089	−	0.226164i	$-0.927382\pi$
$373$	−6.16034	−	18.9596i	−0.318970	−	0.981689i	0.655119	−	0.755526i	$-0.272618\pi$
$374$	29.2185			1.51085
$375$	5.54783	+	24.0251i	0.286489	+	1.24065i
$376$	7.36134			0.379632
$377$	−5.62020	−	17.2972i	−0.289455	−	0.890850i
$378$	−2.02710	+	1.47278i	−0.104263	+	0.0757514i
$379$	8.00249	−	5.81415i	0.411060	−	0.298653i	−0.362971	−	0.931801i	$-0.618237\pi$
$379$	8.00249	−	5.81415i	0.411060	−	0.298653i	0.774031	+	0.633148i	$0.218237\pi$
$380$	−1.20255	+	8.93449i	−0.0616898	+	0.458330i
$381$	21.1539	+	15.3692i	1.08375	+	0.787388i
$382$	5.27801			0.270046
$383$	10.7159	+	7.78554i	0.547556	+	0.397823i	0.826884	−	0.562373i	$-0.190112\pi$
$383$	10.7159	+	7.78554i	0.547556	+	0.397823i	−0.279328	+	0.960196i	$0.590112\pi$
$384$	0.681512	−	2.09748i	0.0347783	−	0.107036i
$385$	8.86715	−	1.61691i	0.451912	−	0.0824052i
$386$	4.69453	+	14.4483i	0.238945	+	0.735398i
$387$	−5.41401	+	16.6626i	−0.275210	+	0.847008i
$388$	0.220870	−	0.679767i	0.0112130	−	0.0345099i
$389$	8.26155	+	25.4265i	0.418877	+	1.28917i	0.908736	+	0.417371i	$0.137048\pi$
$389$	8.26155	+	25.4265i	0.418877	+	1.28917i	−0.489859	+	0.871802i	$0.662952\pi$
$390$	−9.10585	−	16.8872i	−0.461093	−	0.855118i
$391$	17.2778	−	53.1755i	0.873774	−	2.68920i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$	31.8266			1.60544
$394$	−11.8799	−	8.63123i	−0.598499	−	0.434835i
$395$	−14.2605	−	26.4468i	−0.717525	−	1.33068i
$396$	−6.07821	+	4.41608i	−0.305442	+	0.221916i
$397$	15.2466	−	11.0773i	0.765207	−	0.555955i	−0.135296	−	0.990805i	$-0.543199\pi$
$397$	15.2466	−	11.0773i	0.765207	−	0.555955i	0.900503	+	0.434850i	$0.143199\pi$
$398$	1.73579	+	5.34220i	0.0870072	+	0.267781i
$399$	−8.89149			−0.445131
$400$	−2.74741	+	4.17753i	−0.137371	+	0.208876i
$401$	−16.2595			−0.811960			−0.405980	−	0.913882i	$-0.633070\pi$
$401$	−16.2595			−0.811960			−0.405980	+	0.913882i	$0.633070\pi$
$402$	−8.29852	−	25.5402i	−0.413893	−	1.27383i
$403$	27.4754	−	19.9620i	1.36865	−	0.994380i
$404$	−4.21918	+	3.06541i	−0.209912	+	0.152510i
$405$	−17.1644	+	17.9830i	−0.852905	+	0.893583i
$406$	−3.78201	−	2.74779i	−0.187698	−	0.136371i
$407$	−5.64240			−0.279683
$408$	−12.9331	−	9.39648i	−0.640286	−	0.465195i
$409$	2.76737	−	8.51708i	0.136837	−	0.421142i	−0.859034	−	0.511919i	$-0.828935\pi$
$409$	2.76737	−	8.51708i	0.136837	−	0.421142i	0.995871	+	0.0907764i	$0.0289348\pi$
$410$	3.20676	−	23.8249i	0.158371	−	1.17663i
$411$	−2.19748	−	6.76315i	−0.108394	−	0.333601i
$412$	4.16602	−	12.8217i	0.205245	−	0.631679i
$413$	0.566673	−	1.74404i	0.0278842	−	0.0858186i
$414$	4.44271	+	13.6733i	0.218347	+	0.672004i
$415$	−11.3116	+	11.8511i	−0.555265	+	0.581747i
$416$	1.20223	−	3.70007i	0.0589440	−	0.181411i
$417$	11.8067	+	8.57810i	0.578179	+	0.420072i
$418$	16.2512			0.794872
$419$	−10.7728	−	7.82692i	−0.526287	−	0.382370i	0.292680	−	0.956210i	$-0.405453\pi$
$419$	−10.7728	−	7.82692i	−0.526287	−	0.382370i	−0.818967	+	0.573841i	$0.805453\pi$
$420$	−4.44491	−	2.13592i	−0.216889	−	0.104222i
$421$	11.7902	−	8.56608i	0.574619	−	0.417485i	−0.262161	−	0.965024i	$-0.584435\pi$
$421$	11.7902	−	8.56608i	0.574619	−	0.417485i	0.836780	+	0.547539i	$0.184435\pi$
$422$	0.286832	−	0.208396i	0.0139628	−	0.0101446i
$423$	4.23990	+	13.0491i	0.206151	+	0.634467i
$424$	2.00076			0.0971655
$425$	22.6452	+	28.2977i	1.09845	+	1.37264i
$426$	−1.58355			−0.0767232
$427$	0.939817	+	2.89246i	0.0454809	+	0.139976i
$428$	−7.63591	+	5.54781i	−0.369096	+	0.268164i
$429$	−27.9804	+	20.3290i	−1.35091	+	0.981492i
$430$	20.6777	−	3.77054i	0.997168	−	0.181832i
$431$	−14.7271	−	10.6999i	−0.709381	−	0.515395i	0.173593	−	0.984817i	$-0.444462\pi$
$431$	−14.7271	−	10.6999i	−0.709381	−	0.515395i	−0.882974	+	0.469422i	$0.844462\pi$
$432$	−2.50564			−0.120552
$433$	16.5432	+	12.0194i	0.795016	+	0.577613i	0.909448	−	0.415818i	$-0.136505\pi$
$433$	16.5432	+	12.0194i	0.795016	+	0.577613i	−0.114431	+	0.993431i	$0.536505\pi$
$434$	2.69752	−	8.30212i	0.129485	−	0.398514i
$435$	−20.7792	−	9.98505i	−0.996285	−	0.478747i
$436$	1.74710	+	5.37701i	0.0836707	+	0.257512i
$437$	9.60983	−	29.5760i	0.459700	−	1.41481i
$438$	2.46366	−	7.58238i	0.117718	−	0.362300i
$439$	1.08213	+	3.33046i	0.0516473	+	0.158954i	0.973554	−	0.228459i	$-0.0733687\pi$
$439$	1.08213	+	3.33046i	0.0516473	+	0.158954i	−0.921906	+	0.387413i	$0.873369\pi$
$440$	8.12407	+	3.90387i	0.387300	+	0.186110i
$441$	0.575968	−	1.77265i	0.0274271	−	0.0844118i
$442$	−22.8148	−	16.5759i	−1.08519	−	0.788437i
$443$	−6.13951			−0.291697			−0.145848	−	0.989307i	$-0.546591\pi$
$443$	−6.13951			−0.291697			−0.145848	+	0.989307i	$0.546591\pi$
$444$	2.49753	+	1.81456i	0.118528	+	0.0861153i
$445$	−4.16054	+	0.758667i	−0.197229	+	0.0359643i
$446$	−1.12787	+	0.819446i	−0.0534062	+	0.0388019i
$447$	−9.69492	+	7.04377i	−0.458554	+	0.333159i
$448$	−0.309017	−	0.951057i	−0.0145997	−	0.0449332i
$449$	−24.8876			−1.17452			−0.587259	−	0.809399i	$-0.699793\pi$
$449$	−24.8876			−1.17452			−0.587259	+	0.809399i	$0.699793\pi$
$450$	−8.98771	−	2.46408i	−0.423685	−	0.116158i
$451$	−43.3358			−2.04060
$452$	2.92527	+	9.00306i	0.137593	+	0.423468i
$453$	16.7647	−	12.1803i	0.787674	−	0.572279i
$454$	−14.8204	+	10.7676i	−0.695555	+	0.505350i
$455$	−7.84107	−	3.76788i	−0.367595	−	0.176641i
$456$	−7.19337	−	5.22629i	−0.336860	−	0.244743i
$457$	24.0936			1.12705			0.563525	−	0.826099i	$-0.309445\pi$
$457$	24.0936			1.12705			0.563525	+	0.826099i	$0.309445\pi$
$458$	−8.61834	−	6.26159i	−0.402708	−	0.292585i
$459$	−5.61249	+	17.2735i	−0.261969	+	0.806257i
$460$	11.9088	−	12.4767i	0.555250	−	0.581731i
$461$	−1.77577	−	5.46525i	−0.0827057	−	0.254542i	0.901149	−	0.433509i	$-0.142725\pi$
$461$	−1.77577	−	5.46525i	−0.0827057	−	0.254542i	−0.983855	+	0.178967i	$0.942725\pi$
$462$	−2.74710	+	8.45472i	−0.127807	+	0.393349i
$463$	5.48904	−	16.8935i	0.255097	−	0.785109i	−0.738713	−	0.674020i	$-0.764566\pi$
$463$	5.48904	−	16.8935i	0.255097	−	0.785109i	0.993810	−	0.111089i	$-0.0354339\pi$
$464$	−1.44460	−	4.44602i	−0.0670639	−	0.206401i
$465$	5.74242	−	42.6638i	0.266298	−	1.97849i
$466$	−7.32783	+	22.5527i	−0.339455	+	1.04474i
$467$	14.5218	+	10.5507i	0.671989	+	0.488229i	0.870690	−	0.491831i	$-0.163672\pi$
$467$	14.5218	+	10.5507i	0.671989	+	0.488229i	−0.198701	+	0.980060i	$0.563672\pi$
$468$	7.25137			0.335195
$469$	−9.85111	−	7.15725i	−0.454882	−	0.330491i
$470$	11.3651	−	11.9072i	0.524234	−	0.549236i
$471$	21.5042	−	15.6237i	0.990862	−	0.719903i
$472$	1.48357	−	1.07788i	0.0682868	−	0.0496133i
$473$	−11.7086	−	36.0353i	−0.538361	−	1.65691i
$474$	29.6347			1.36117
$475$	12.5952	+	15.7391i	0.577906	+	0.722158i
$476$	−7.24862			−0.332240
$477$	1.15237	+	3.54664i	0.0527636	+	0.162390i
$478$	0.530125	−	0.385158i	0.0242474	−	0.0176167i
$479$	−9.87975	+	7.17806i	−0.451417	+	0.327974i	−0.790155	−	0.612907i	$-0.790000\pi$
$479$	−9.87975	+	7.17806i	−0.451417	+	0.327974i	0.338738	+	0.940881i	$0.390000\pi$
$480$	−2.34054	−	4.34065i	−0.106831	−	0.198123i
$481$	4.40579	+	3.20099i	0.200887	+	0.145953i
$482$	−22.5579			−1.02748
$483$	13.7625	+	9.99907i	0.626217	+	0.454973i
$484$	1.62176	−	4.99127i	0.0737164	−	0.226876i
$485$	−0.758542	−	1.40675i	−0.0344436	−	0.0638773i
$486$	−5.25392	−	16.1699i	−0.238323	−	0.733482i
$487$	−6.97128	+	21.4554i	−0.315899	+	0.972236i	0.659484	+	0.751718i	$0.270775\pi$
$487$	−6.97128	+	21.4554i	−0.315899	+	0.972236i	−0.975383	+	0.220518i	$0.929225\pi$
$488$	−0.939817	+	2.89246i	−0.0425435	+	0.130935i
$489$	−2.32936	−	7.16903i	−0.105337	−	0.324195i
$490$	−2.19979	+	0.401128i	−0.0993766	+	0.0181211i
$491$	0.316982	−	0.975570i	0.0143052	−	0.0440268i	−0.943649	−	0.330948i	$-0.892632\pi$
$491$	0.316982	−	0.975570i	0.0143052	−	0.0440268i	0.957954	+	0.286921i	$0.0926317\pi$
$492$	19.1820	+	13.9365i	0.864791	+	0.628308i
$493$	−33.8860			−1.52615
$494$	−12.6895	−	9.21947i	−0.570928	−	0.414804i
$495$	−2.24099	+	16.6496i	−0.100725	+	0.748345i
$496$	7.06220	−	5.13099i	0.317102	−	0.230388i
$497$	−0.580895	+	0.422045i	−0.0260567	+	0.0189313i
$498$	−4.99322	−	15.3675i	−0.223751	−	0.688636i
$499$	12.5238			0.560642			0.280321	−	0.959906i	$-0.409559\pi$
$499$	12.5238			0.560642			0.280321	+	0.959906i	$0.409559\pi$
$500$	2.51554	+	10.8937i	0.112499	+	0.487180i
$501$	−55.2462			−2.46822
$502$	5.74487	+	17.6809i	0.256406	+	0.789137i
$503$	−23.6336	+	17.1708i	−1.05377	+	0.765610i	−0.972926	−	0.231117i	$-0.925762\pi$
$503$	−23.6336	+	17.1708i	−1.05377	+	0.765610i	−0.0808458	+	0.996727i	$0.525762\pi$
$504$	1.50790	−	1.09556i	0.0671674	−	0.0488000i
$505$	−1.55558	+	11.5573i	−0.0692223	+	0.514293i
$506$	−25.1541	−	18.2755i	−1.11824	−	0.812447i
$507$	4.71050			0.209201
$508$	9.59177	+	6.96883i	0.425566	+	0.309192i
$509$	−3.31549	+	10.2040i	−0.146957	+	0.452286i	−0.997257	−	0.0740112i	$-0.976420\pi$
$509$	−3.31549	+	10.2040i	−0.146957	+	0.452286i	0.850301	+	0.526297i	$0.176420\pi$
$510$	−35.1665	+	6.41254i	−1.55720	+	0.283952i
$511$	−1.11710	−	3.43807i	−0.0494174	−	0.152091i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−3.12165	+	9.60745i	−0.137824	+	0.424179i
$514$	3.83586	+	11.8056i	0.169192	+	0.520721i
$515$	−14.3075	−	26.5339i	−0.630465	−	1.16923i
$516$	−6.40610	+	19.7160i	−0.282013	+	0.867946i
$517$	−24.0058	−	17.4412i	−1.05577	−	0.767064i
$518$	1.39979			0.0615031
$519$	7.15364	+	5.19743i	0.314010	+	0.228142i
$520$	−4.12885	−	7.65715i	−0.181062	−	0.335788i
$521$	0.565992	−	0.411218i	0.0247966	−	0.0180158i	−0.575318	−	0.817930i	$-0.695122\pi$
$521$	0.565992	−	0.411218i	0.0247966	−	0.0180158i	0.600115	+	0.799914i	$0.295122\pi$
$522$	7.04919	−	5.12154i	0.308535	−	0.224164i
$523$	−12.7042	−	39.0996i	−0.555518	−	1.70971i	−0.694573	−	0.719423i	$-0.744406\pi$
$523$	−12.7042	−	39.0996i	−0.555518	−	1.70971i	0.139055	−	0.990285i	$-0.455594\pi$
$524$	14.4311			0.630426
$525$	−10.3174	+	3.89212i	−0.450287	+	0.169866i
$526$	16.7239			0.729197
$527$	−19.5533	−	60.1789i	−0.851756	−	2.62143i
$528$	−7.19201	+	5.22530i	−0.312992	+	0.227402i
$529$	−29.5272	+	21.4527i	−1.28379	+	0.932728i
$530$	3.08896	−	3.23628i	0.134176	−	0.140575i
$531$	2.76519	+	2.00902i	0.119999	+	0.0871843i
$532$	−4.03166			−0.174795
$533$	33.8381	+	24.5848i	1.46569	+	1.06489i
$534$	1.28897	−	3.96703i	0.0557790	−	0.171670i
$535$	−2.81530	+	20.9165i	−0.121716	+	0.904300i
$536$	−3.76279	−	11.5807i	−0.162528	−	0.500209i
$537$	−0.996302	+	3.06630i	−0.0429936	+	0.132321i
$538$	4.58097	−	14.0988i	0.197500	−	0.607842i
$539$	1.24562	+	3.83361i	0.0536525	+	0.165125i
$540$	−3.86844	+	4.05293i	−0.166471	+	0.174410i
$541$	9.90250	−	30.4768i	0.425742	−	1.31030i	−0.476541	−	0.879152i	$-0.658110\pi$
$541$	9.90250	−	30.4768i	0.425742	−	1.31030i	0.902282	−	0.431146i	$-0.141890\pi$
$542$	17.4609	+	12.6861i	0.750008	+	0.544913i
$543$	−42.6763			−1.83142
$544$	−5.86426	−	4.26063i	−0.251428	−	0.182673i
$545$	11.3948	+	5.47556i	0.488099	+	0.234547i
$546$	6.94149	−	5.04329i	0.297068	−	0.215833i
$547$	13.8969	−	10.0967i	0.594187	−	0.431702i	−0.249624	−	0.968343i	$-0.580307\pi$
$547$	13.8969	−	10.0967i	0.594187	−	0.431702i	0.843811	+	0.536641i	$0.180307\pi$
$548$	−0.996400	−	3.06660i	−0.0425641	−	0.130999i
$549$	−5.66862			−0.241931
$550$	18.8573	−	7.11373i	0.804078	−	0.303330i
$551$	−18.8473			−0.802922
$552$	5.25682	+	16.1788i	0.223745	+	0.688617i
$553$	10.8709	−	7.89820i	0.462280	−	0.335866i
$554$	3.49640	−	2.54028i	0.148548	−	0.107926i
$555$	6.79102	−	1.23833i	0.288263	−	0.0525642i
$556$	5.35352	+	3.88956i	0.227040	+	0.164954i
$557$	−28.6499			−1.21394			−0.606969	−	0.794726i	$-0.707615\pi$
$557$	−28.6499			−1.21394			−0.606969	+	0.794726i	$0.707615\pi$
$558$	13.1630	+	9.56351i	0.557236	+	0.404856i
$559$	−11.3007	+	34.7801i	−0.477970	+	1.47104i
$560$	−2.01545	−	0.968487i	−0.0851682	−	0.0409260i
$561$	19.9127	+	61.2851i	0.840716	+	2.58746i
$562$	1.71898	−	5.29049i	0.0725109	−	0.223166i
$563$	10.4984	−	32.3106i	0.442453	−	1.36173i	−0.442799	−	0.896621i	$-0.646015\pi$
$563$	10.4984	−	32.3106i	0.442453	−	1.36173i	0.885253	−	0.465110i	$-0.153985\pi$
$564$	5.01684	+	15.4402i	0.211247	+	0.650152i
$565$	19.0790	+	9.16806i	0.802659	+	0.385703i
$566$	−2.48395	+	7.64481i	−0.104408	+	0.321336i
$567$	−8.99432	−	6.53476i	−0.377726	−	0.274434i
$568$	−0.718026			−0.0301277
$569$	−19.6853	−	14.3022i	−0.825252	−	0.599581i	0.0929598	−	0.995670i	$-0.470367\pi$
$569$	−19.6853	−	14.3022i	−0.825252	−	0.599581i	−0.918212	+	0.396089i	$0.870367\pi$
$570$	−19.5595	+	3.56663i	−0.819256	+	0.149390i
$571$	−1.66741	+	1.21145i	−0.0697791	+	0.0506975i	−0.622128	−	0.782916i	$-0.713732\pi$
$571$	−1.66741	+	1.21145i	−0.0697791	+	0.0506975i	0.552349	+	0.833613i	$0.313732\pi$
$572$	−12.6871	+	9.21773i	−0.530475	+	0.385413i
$573$	3.59703	+	11.0705i	0.150268	+	0.462477i
$574$	10.7509			0.448734
$575$	−1.79557	−	38.5255i	−0.0748805	−	1.60663i
$576$	1.86387			0.0776614
$577$	2.13911	+	6.58349i	0.0890521	+	0.274074i	0.985658	−	0.168755i	$-0.0539747\pi$
$577$	2.13911	+	6.58349i	0.0890521	+	0.274074i	−0.896606	+	0.442829i	$0.853975\pi$
$578$	−28.7545	+	20.8914i	−1.19603	+	0.868967i
$579$	−27.1056	+	19.6934i	−1.12647	+	0.818428i
$580$	−9.42187	−	4.52751i	−0.391222	−	0.187995i
$581$	−5.92741	−	4.30651i	−0.245910	−	0.178664i
$582$	1.57632			0.0653406
$583$	−6.52461	−	4.74040i	−0.270222	−	0.196327i
$584$	1.11710	−	3.43807i	0.0462257	−	0.142268i
$585$	11.1953	−	11.7293i	0.462871	−	0.484946i
$586$	6.21684	+	19.1335i	0.256815	+	0.790397i
$587$	−11.0363	+	33.9662i	−0.455516	+	1.40194i	0.415011	+	0.909816i	$0.363778\pi$
$587$	−11.0363	+	33.9662i	−0.455516	+	1.40194i	−0.870528	+	0.492119i	$0.836222\pi$
$588$	0.681512	−	2.09748i	0.0281051	−	0.0864985i
$589$	−10.8755	−	33.4713i	−0.448116	−	1.37916i
$590$	0.546980	−	4.06384i	0.0225188	−	0.167306i
$591$	10.0075	−	30.8000i	0.411655	−	1.26694i
$592$	1.13245	+	0.822774i	0.0465435	+	0.0338158i
$593$	−15.8326			−0.650166			−0.325083	−	0.945685i	$-0.605392\pi$
$593$	−15.8326			−0.650166			−0.325083	+	0.945685i	$0.605392\pi$
$594$	8.17104	+	5.93661i	0.335262	+	0.243582i
$595$	−11.1911	+	11.7248i	−0.458791	+	0.480672i
$596$	−4.39596	+	3.19385i	−0.180065	+	0.130825i
$597$	−10.0222	+	7.28155i	−0.410181	+	0.298014i
$598$	9.27333	+	28.5404i	0.379215	+	1.16710i
$599$	11.9483			0.488195			0.244097	−	0.969751i	$-0.421508\pi$
$599$	11.9483			0.488195			0.244097	+	0.969751i	$0.421508\pi$
$600$	−10.6347	−	2.91561i	−0.434158	−	0.119029i
$601$	32.8363			1.33942			0.669711	−	0.742622i	$-0.266418\pi$
$601$	32.8363			1.33942			0.669711	+	0.742622i	$0.266418\pi$
$602$	2.90471	+	8.93978i	0.118387	+	0.364358i
$603$	18.3612	−	13.3402i	0.747726	−	0.543255i
$604$	7.60159	−	5.52288i	0.309304	−	0.224723i
$605$	−5.56968	−	10.3292i	−0.226440	−	0.419943i
$606$	−9.30505	−	6.76052i	−0.377992	−	0.274627i
$607$	−12.8699			−0.522372			−0.261186	−	0.965288i	$-0.584114\pi$
$607$	−12.8699			−0.522372			−0.261186	+	0.965288i	$0.584114\pi$
$608$	−3.26168	−	2.36975i	−0.132279	−	0.0961060i
$609$	3.18595	−	9.80534i	0.129101	−	0.397333i
$610$	3.22765	+	5.98583i	0.130684	+	0.242359i
$611$	8.84999	+	27.2375i	0.358032	+	1.10191i
$612$	4.17498	−	12.8493i	0.168763	−	0.519401i
$613$	6.72794	−	20.7065i	0.271739	−	0.836326i	−0.718325	−	0.695708i	$-0.755091\pi$
$613$	6.72794	−	20.7065i	0.271739	−	0.836326i	0.990064	−	0.140619i	$-0.0449091\pi$
$614$	−0.921314	−	2.83551i	−0.0371812	−	0.114432i
$615$	52.1577	−	9.51086i	2.10320	−	0.383515i
$616$	−1.24562	+	3.83361i	−0.0501873	+	0.154461i
$617$	27.1418	+	19.7196i	1.09269	+	0.793883i	0.979851	−	0.199731i	$-0.0640068\pi$
$617$	27.1418	+	19.7196i	1.09269	+	0.793883i	0.112835	+	0.993614i	$0.464007\pi$
$618$	29.7324			1.19601
$619$	−15.0653	−	10.9456i	−0.605526	−	0.439940i	0.242310	−	0.970199i	$-0.422095\pi$
$619$	−15.0653	−	10.9456i	−0.605526	−	0.439940i	−0.847836	+	0.530258i	$0.822095\pi$
$620$	2.60378	−	19.3450i	0.104570	−	0.776914i
$621$	15.6360	−	11.3602i	0.627451	−	0.455870i
$622$	5.95141	−	4.32395i	0.238630	−	0.173375i
$623$	−0.584454	−	1.79876i	−0.0234157	−	0.0720660i
$624$	8.58015			0.343481
$625$	21.5045	+	12.7497i	0.860181	+	0.509988i
$626$	−25.9163			−1.03582
$627$	11.0754	+	34.0865i	0.442308	+	1.36128i
$628$	9.75062	−	7.08424i	0.389092	−	0.282692i
$629$	8.20872	−	5.96398i	0.327303	−	0.237800i
$630$	0.555952	−	4.13050i	0.0221497	−	0.164563i
$631$	0.334943	+	0.243350i	0.0133339	+	0.00968761i	0.594432	−	0.804146i	$-0.297377\pi$
$631$	0.334943	+	0.243350i	0.0133339	+	0.00968761i	−0.581098	+	0.813833i	$0.697377\pi$
$632$	13.4372			0.534504
$633$	0.632585	+	0.459600i	0.0251430	+	0.0182675i
$634$	0.283265	−	0.871800i	0.0112499	−	0.0346236i
$635$	26.0809	−	4.75581i	1.03499	−	0.188729i
$636$	1.36354	+	4.19655i	0.0540680	+	0.166404i
$637$	1.20223	−	3.70007i	0.0476339	−	0.146602i
$638$	−5.82304	+	17.9215i	−0.230536	+	0.709517i
$639$	−0.413560	−	1.27281i	−0.0163602	−	0.0503515i
$640$	−1.06127	−	1.96817i	−0.0419504	−	0.0777989i
$641$	9.15267	−	28.1690i	0.361509	−	1.11261i	−0.590630	−	0.806943i	$-0.701121\pi$
$641$	9.15267	−	28.1690i	0.361509	−	1.11261i	0.952138	−	0.305667i	$-0.0988794\pi$
$642$	−16.8404	−	12.2353i	−0.664637	−	0.482887i
$643$	−16.1608			−0.637321			−0.318661	−	0.947869i	$-0.603233\pi$
$643$	−16.1608			−0.637321			−0.318661	+	0.947869i	$0.603233\pi$
$644$	6.24033	+	4.53386i	0.245903	+	0.178659i
$645$	22.0007	+	40.8014i	0.866278	+	1.60655i
$646$	−23.6427	+	17.1774i	−0.930209	+	0.675836i
$647$	−20.3111	+	14.7569i	−0.798512	+	0.580153i	−0.910477	−	0.413559i	$-0.864286\pi$
$647$	−20.3111	+	14.7569i	−0.798512	+	0.580153i	0.111965	+	0.993712i	$0.464286\pi$
$648$	−3.43553	−	10.5735i	−0.134960	−	0.415365i
$649$	−7.39183			−0.290155
$650$	−18.7602	−	5.14329i	−0.735834	−	0.201737i
$651$	19.2519			0.754541
$652$	−1.05620	−	3.25064i	−0.0413639	−	0.127305i
$653$	36.7320	−	26.6874i	1.43743	−	1.04436i	0.448864	−	0.893600i	$-0.351829\pi$
$653$	36.7320	−	26.6874i	1.43743	−	1.04436i	0.988571	−	0.150757i	$-0.0481713\pi$
$654$	−10.0875	+	7.32899i	−0.394452	+	0.286586i
$655$	22.2801	−	23.3427i	0.870555	−	0.912074i
$656$	8.69766	+	6.31922i	0.339587	+	0.246724i
$657$	6.73789			0.262870
$658$	5.95545	+	4.32689i	0.232167	+	0.168680i
$659$	2.30562	−	7.09597i	0.0898142	−	0.276420i	−0.896053	−	0.443946i	$-0.853578\pi$
$659$	2.30562	−	7.09597i	0.0898142	−	0.276420i	0.985868	+	0.167527i	$0.0535781\pi$
$660$	−2.65164	+	19.7006i	−0.103215	+	0.766844i
$661$	1.50727	+	4.63891i	0.0586261	+	0.180433i	0.976081	−	0.217407i	$-0.0697600\pi$
$661$	1.50727	+	4.63891i	0.0586261	+	0.180433i	−0.917455	+	0.397840i	$0.869760\pi$
$662$	−2.00240	+	6.16276i	−0.0778256	+	0.239522i
$663$	19.2191	−	59.1503i	0.746407	−	2.29721i
$664$	−2.26407	−	6.96808i	−0.0878629	−	0.270414i
$665$	−6.22445	+	6.52131i	−0.241374	+	0.252886i
$666$	−0.806233	+	2.48133i	−0.0312409	+	0.0961496i
$667$	29.1724	+	21.1950i	1.12956	+	0.820674i
$668$	−25.0502			−0.969222
$669$	−2.48743	−	1.80722i	−0.0961695	−	0.0698713i
$670$	−24.5414	−	11.7929i	−0.948116	−	0.455600i
$671$	9.91791	−	7.20578i	0.382877	−	0.278176i
$672$	1.78422	−	1.29631i	0.0688278	−	0.0500064i
$673$	−4.07169	−	12.5314i	−0.156952	−	0.483049i	0.841401	−	0.540411i	$-0.181731\pi$
$673$	−4.07169	−	12.5314i	−0.156952	−	0.483049i	−0.998353	+	0.0573617i	$0.981731\pi$
$674$	−8.82839			−0.340057
$675$	0.583272	+	12.5146i	0.0224502	+	0.481687i
$676$	2.13587			0.0821490
$677$	10.3028	+	31.7087i	0.395967	+	1.21866i	0.928206	+	0.372068i	$0.121351\pi$
$677$	10.3028	+	31.7087i	0.395967	+	1.21866i	−0.532238	+	0.846595i	$0.678649\pi$
$678$	−16.8901	+	12.2714i	−0.648661	+	0.471280i
$679$	0.578244	−	0.420119i	0.0221910	−	0.0161227i
$680$	−15.9455	+	2.90763i	−0.611481	+	0.111502i
$681$	−32.6851	−	23.7471i	−1.25250	−	0.909992i
$682$	−35.1872			−1.34739
$683$	15.7778	+	11.4633i	0.603722	+	0.438630i	0.847198	−	0.531277i	$-0.178288\pi$
$683$	15.7778	+	11.4633i	0.603722	+	0.438630i	−0.243476	+	0.969907i	$0.578288\pi$
$684$	2.32211	−	7.14671i	0.0887880	−	0.273261i
$685$	−6.49865	−	3.12281i	−0.248301	−	0.119316i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	7.26004	−	22.3441i	0.276988	−	0.852481i
$688$	−2.90471	+	8.93978i	−0.110741	+	0.340826i
$689$	2.40537	+	7.40295i	0.0916371	+	0.282030i
$690$	34.2857	+	16.4753i	1.30523	+	0.627206i
$691$	1.28664	−	3.95987i	0.0489461	−	0.150641i	−0.923596	−	0.383367i	$-0.874765\pi$
$691$	1.28664	−	3.95987i	0.0489461	−	0.150641i	0.972542	+	0.232726i	$0.0747645\pi$
$692$	3.24367	+	2.35666i	0.123306	+	0.0895868i
$693$	−7.51308			−0.285398
$694$	−1.95644	−	1.42143i	−0.0742653	−	0.0539569i
$695$	14.5567	−	2.65439i	0.552168	−	0.100687i
$696$	8.34092	−	6.06004i	0.316162	−	0.229705i
$697$	63.0461	−	45.8057i	2.38804	−	1.73501i
$698$	5.86038	+	18.0364i	0.221819	+	0.682688i
$699$	−52.2979			−1.97809
$700$	−4.67819	+	1.76480i	−0.176819	+	0.0667032i
$701$	−48.9596			−1.84918			−0.924590	−	0.380964i	$-0.875592\pi$
$701$	−48.9596			−1.84918			−0.924590	+	0.380964i	$0.875592\pi$
$702$	−3.01234	−	9.27103i	−0.113693	−	0.349913i
$703$	4.56566	−	3.31714i	0.172197	−	0.125108i
$704$	−3.26106	+	2.36930i	−0.122906	+	0.0892964i
$705$	32.7205	+	15.7232i	1.23232	+	0.592171i
$706$	10.1388	+	7.36630i	0.381580	+	0.277234i
$707$	−5.21519			−0.196137
$708$	3.27189	+	2.37717i	0.122965	+	0.0893395i
$709$	11.8299	−	36.4087i	0.444281	−	1.36736i	−0.438989	−	0.898492i	$-0.644663\pi$
$709$	11.8299	−	36.4087i	0.444281	−	1.36736i	0.883270	−	0.468864i	$-0.155337\pi$
$710$	−1.10856	+	1.16143i	−0.0416034	+	0.0435875i
$711$	7.73942	+	23.8195i	0.290251	+	0.893300i
$712$	0.584454	−	1.79876i	0.0219033	−	0.0674115i
$713$	−20.8072	+	64.0381i	−0.779237	+	2.39825i
$714$	−4.94002	−	15.2038i	−0.184876	−	0.568989i
$715$	−4.67764	+	34.7530i	−0.174934	+	1.29969i
$716$	−0.451752	+	1.39035i	−0.0168828	+	0.0519598i
$717$	1.16915	+	0.849436i	0.0436626	+	0.0317228i
$718$	−33.5927			−1.25367
$719$	−3.67115	−	2.66725i	−0.136911	−	0.0994716i	0.517222	−	0.855851i	$-0.326966\pi$
$719$	−3.67115	−	2.66725i	−0.136911	−	0.0994716i	−0.654133	+	0.756380i	$0.726966\pi$
$720$	2.87762	−	3.01486i	0.107243	−	0.112357i
$721$	10.9068	−	7.92423i	0.406189	−	0.295114i
$722$	2.22135	−	1.61391i	0.0826701	−	0.0600634i
$723$	−15.3734	−	47.3146i	−0.571745	−	1.75965i
$724$	−19.3507			−0.719161
$725$	−21.8697	+	8.25013i	−0.812221	+	0.306402i
$726$	11.5743			0.429564
$727$	−3.35289	−	10.3191i	−0.124352	−	0.382716i	0.869431	−	0.494055i	$-0.164486\pi$
$727$	−3.35289	−	10.3191i	−0.124352	−	0.382716i	−0.993782	+	0.111339i	$0.964486\pi$
$728$	3.14747	−	2.28677i	0.116653	−	0.0847533i
$729$	3.35245	−	2.43570i	0.124165	−	0.0902110i
$730$	−3.83649	−	7.11494i	−0.141995	−	0.263336i
$731$	55.1231	+	40.0493i	2.03880	+	1.48128i
$732$	−6.70736			−0.247911
$733$	16.2519	+	11.8077i	0.600279	+	0.436128i	0.845978	−	0.533218i	$-0.179017\pi$
$733$	16.2519	+	11.8077i	0.600279	+	0.436128i	−0.245699	+	0.969346i	$0.579017\pi$
$734$	11.1762	−	34.3969i	0.412522	−	1.26961i
$735$	−2.34054	−	4.34065i	−0.0863323	−	0.160107i
$736$	2.38359	+	7.33594i	0.0878604	+	0.270406i
$737$	−15.1674	+	46.6805i	−0.558699	+	1.71950i
$738$	−6.19218	+	19.0576i	−0.227937	+	0.701519i
$739$	−15.2812	−	47.0307i	−0.562128	−	1.73005i	−0.676333	−	0.736596i	$-0.736432\pi$
$739$	−15.2812	−	47.0307i	−0.562128	−	1.73005i	0.114205	−	0.993457i	$-0.463568\pi$
$740$	3.07924	−	0.561495i	0.113195	−	0.0206410i
$741$	10.6896	−	32.8992i	0.392692	−	1.20858i
$742$	1.61865	+	1.17602i	0.0594225	+	0.0431730i
$743$	−8.98945			−0.329791			−0.164896	−	0.986311i	$-0.552729\pi$
$743$	−8.98945			−0.329791			−0.164896	+	0.986311i	$0.552729\pi$
$744$	15.5751	+	11.3160i	0.571011	+	0.414864i
$745$	−1.62075	+	12.0415i	−0.0593798	+	0.441168i
$746$	16.1280	−	11.7177i	0.590487	−	0.429014i
$747$	11.0479	−	8.02679i	0.404223	−	0.293685i
$748$	9.02900	+	27.7884i	0.330133	+	1.01604i
$749$	−9.43850			−0.344875
$750$	−21.1349	+	12.7005i	−0.771736	+	0.463755i
$751$	7.56188			0.275937			0.137968	−	0.990437i	$-0.455943\pi$
$751$	7.56188			0.275937			0.137968	+	0.990437i	$0.455943\pi$
$752$	2.27478	+	7.00105i	0.0829526	+	0.255302i
$753$	−33.1701	+	24.0995i	−1.20878	+	0.878234i
$754$	14.7139	−	10.6902i	0.535847	−	0.389316i
$755$	2.80265	−	20.8225i	0.101999	−	0.757809i
$756$	−2.02710	−	1.47278i	−0.0737250	−	0.0535643i
$757$	25.3319			0.920703			0.460352	−	0.887737i	$-0.347723\pi$
$757$	25.3319			0.920703			0.460352	+	0.887737i	$0.347723\pi$
$758$	8.00249	+	5.81415i	0.290664	+	0.211180i
$759$	21.1897	−	65.2152i	0.769138	−	2.36716i
$760$	−8.86882	+	1.61721i	−0.321706	+	0.0586625i
$761$	−13.5457	−	41.6893i	−0.491030	−	1.51123i	−0.823054	−	0.567963i	$-0.807732\pi$
$761$	−13.5457	−	41.6893i	−0.491030	−	1.51123i	0.332024	−	0.943271i	$-0.392268\pi$
$762$	−8.08006	+	24.8679i	−0.292710	+	0.900868i
$763$	−1.74710	+	5.37701i	−0.0632491	+	0.194661i
$764$	1.63099	+	5.01969i	0.0590073	+	0.181606i
$765$	−14.3383	−	26.5910i	−0.518402	−	0.961401i
$766$	−4.09310	+	12.5973i	−0.147890	+	0.455158i
$767$	5.77181	+	4.19346i	0.208408	+	0.151417i
$768$	2.20542			0.0795812
$769$	35.7140	+	25.9477i	1.28788	+	0.935699i	0.999760	−	0.0218950i	$-0.00696994\pi$
$769$	35.7140	+	25.9477i	1.28788	+	0.935699i	0.288120	+	0.957594i	$0.406970\pi$
$770$	4.27787	+	7.93350i	0.154164	+	0.285904i
$771$	−22.1477	+	16.0912i	−0.797630	+	0.579512i
$772$	−12.2904	+	8.92953i	−0.442343	+	0.321381i
$773$	11.7773	+	36.2467i	0.423599	+	1.30370i	0.904329	+	0.426835i	$0.140372\pi$
$773$	11.7773	+	36.2467i	0.423599	+	1.30370i	−0.480731	+	0.876868i	$0.659628\pi$
$774$	−17.5201			−0.629747
$775$	−27.2711	−	34.0783i	−0.979607	−	1.22413i
$776$	0.714749			0.0256580
$777$	0.953972	+	2.93602i	0.0342236	+	0.105329i
$778$	−21.6290	+	15.7144i	−0.775438	+	0.563389i
$779$	35.0660	−	25.4769i	1.25637	−	0.912806i
$780$	13.2468	−	13.8786i	0.474313	−	0.496934i
$781$	2.34153	+	1.70122i	0.0837865	+	0.0608745i
$782$	55.9120			1.99941
$783$	−9.47635	−	6.88497i	−0.338657	−	0.246049i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	3.59498	−	26.7092i	0.128310	−	0.953293i
$786$	9.83497	+	30.2689i	0.350802	+	1.07966i
$787$	−4.10958	+	12.6480i	−0.146491	+	0.450852i	−0.997200	−	0.0747847i	$-0.976173\pi$
$787$	−4.10958	+	12.6480i	−0.146491	+	0.450852i	0.850709	+	0.525637i	$0.176173\pi$
$788$	4.53770	−	13.9656i	0.161649	−	0.497505i
$789$	11.3975	+	35.0780i	0.405763	+	1.24881i
$790$	20.7457	−	21.7351i	0.738097	−	0.773299i
$791$	−2.92527	+	9.00306i	−0.104011	+	0.320112i
$792$	−6.07821	−	4.41608i	−0.215980	−	0.156918i
$793$	−11.8322			−0.420173
$794$	15.2466	+	11.0773i	0.541083	+	0.393120i
$795$	8.89320	+	4.27346i	0.315409	+	0.151564i
$796$	−4.54435	+	3.30166i	−0.161070	+	0.117024i
$797$	−32.6150	+	23.6962i	−1.15528	+	0.839362i	−0.989174	−	0.146745i	$-0.953120\pi$
$797$	−32.6150	+	23.6962i	−1.15528	+	0.839362i	−0.166109	+	0.986107i	$0.553120\pi$
$798$	−2.74762	−	8.45631i	−0.0972648	−	0.299350i
$799$	53.3596			1.88773
$800$	−4.82206	−	1.32202i	−0.170486	−	0.0467404i
$801$	3.52520			0.124557
$802$	−5.02446	−	15.4637i	−0.177420	−	0.546042i
$803$	−11.7887	+	8.56502i	−0.416015	+	0.302253i
$804$	21.7258	−	15.7847i	0.766211	−	0.556685i
$805$	16.9680	−	3.09409i	0.598045	−	0.109052i
$806$	27.4754	+	19.9620i	0.967779	+	0.703133i
$807$	32.6939			1.15088
$808$	−4.21918	−	3.06541i	−0.148430	−	0.107841i
$809$	−11.1598	+	34.3463i	−0.392357	+	1.20755i	0.538644	+	0.842534i	$0.318937\pi$
$809$	−11.1598	+	34.3463i	−0.392357	+	1.20755i	−0.931001	+	0.365017i	$0.881063\pi$
$810$	−22.4069	−	10.7672i	−0.787300	−	0.378323i
$811$	−7.73154	−	23.7952i	−0.271491	−	0.835563i	−0.990127	−	0.140176i	$-0.955233\pi$
$811$	−7.73154	−	23.7952i	−0.271491	−	0.835563i	0.718636	−	0.695387i	$-0.244767\pi$
$812$	1.44460	−	4.44602i	0.0506955	−	0.156025i
$813$	−14.7089	+	45.2695i	−0.515865	+	1.58767i
$814$	−1.74360	−	5.36624i	−0.0611131	−	0.188087i
$815$	−6.88866	−	3.31022i	−0.241299	−	0.115952i
$816$	4.94002	−	15.2038i	0.172935	−	0.532240i
$817$	30.6593	+	22.2753i	1.07263	+	0.779312i
$818$	8.95539			0.313118
$819$	5.86648	+	4.26225i	0.204991	+	0.148935i
$820$	23.6498	−	4.31249i	0.825886	−	0.150599i
$821$	−24.4926	+	17.7949i	−0.854798	+	0.621047i	−0.926465	−	0.376382i	$-0.877168\pi$
$821$	−24.4926	+	17.7949i	−0.854798	+	0.621047i	0.0716668	+	0.997429i	$0.477168\pi$
$822$	5.75308	−	4.17985i	0.200662	−	0.145789i
$823$	−8.15100	−	25.0862i	−0.284126	−	0.874450i	−0.986659	−	0.162799i	$-0.947948\pi$
$823$	−8.15100	−	25.0862i	−0.284126	−	0.874450i	0.702533	−	0.711651i	$-0.252052\pi$
$824$	13.4815			0.469651
$825$	27.7724	+	34.7047i	0.966910	+	1.20826i
$826$	1.83379			0.0638058
$827$	8.56799	+	26.3696i	0.297938	+	0.916960i	0.982219	+	0.187741i	$0.0601165\pi$
$827$	8.56799	+	26.3696i	0.297938	+	0.916960i	−0.684280	+	0.729219i	$0.739883\pi$
$828$	−11.6312	+	8.45054i	−0.404211	+	0.293677i
$829$	5.77840	−	4.19825i	0.200692	−	0.145811i	−0.482900	−	0.875675i	$-0.660417\pi$
$829$	5.77840	−	4.19825i	0.200692	−	0.145811i	0.683592	+	0.729864i	$0.260417\pi$
$830$	−14.7665	−	7.09579i	−0.512554	−	0.246299i
$831$	7.71102	+	5.60239i	0.267492	+	0.194345i
$832$	3.89049			0.134878
$833$	−5.86426	−	4.26063i	−0.203185	−	0.147622i
$834$	−4.50978	+	13.8797i	−0.156161	+	0.480613i
$835$	−38.6749	+	40.5194i	−1.33840	+	1.40223i
$836$	5.02190	+	15.4558i	0.173686	+	0.534550i
$837$	6.75901	−	20.8021i	0.233625	−	0.719025i
$838$	4.11485	−	12.6642i	0.142145	−	0.437478i
$839$	3.46404	+	10.6612i	0.119592	+	0.368066i	0.992877	−	0.119144i	$-0.0380149\pi$
$839$	3.46404	+	10.6612i	0.119592	+	0.368066i	−0.873285	+	0.487209i	$0.838015\pi$
$840$	0.657828	−	4.88739i	0.0226972	−	0.168631i
$841$	−2.20824	+	6.79626i	−0.0761461	+	0.234354i
$842$	11.7902	+	8.56608i	0.406317	+	0.295207i
$843$	12.2682			0.422539
$844$	0.286832	+	0.208396i	0.00987317	+	0.00717328i
$845$	3.29756	−	3.45483i	0.113440	−	0.118850i
$846$	−11.1002	+	8.06476i	−0.381633	+	0.277272i
$847$	4.24583	−	3.08477i	0.145888	−	0.105994i
$848$	0.618269	+	1.90284i	0.0212314	+	0.0653437i
$849$	−17.7277			−0.608412
$850$	−19.9150	+	30.2813i	−0.683078	+	1.03864i
$851$	−10.7972			−0.370124
$852$	−0.489343	−	1.50604i	−0.0167646	−	0.0515962i
$853$	−35.8581	+	26.0524i	−1.22776	+	0.892018i	−0.996720	−	0.0809265i	$-0.974212\pi$
$853$	−35.8581	+	26.0524i	−1.22776	+	0.892018i	−0.231038	+	0.972945i	$0.574212\pi$
$854$	−2.46047	+	1.78764i	−0.0841956	+	0.0611717i
$855$	−7.97491	−	14.7898i	−0.272736	−	0.505802i
$856$	−7.63591	−	5.54781i	−0.260990	−	0.189620i
$857$	−34.7385			−1.18664			−0.593322	−	0.804965i	$-0.702184\pi$
$857$	−34.7385			−1.18664			−0.593322	+	0.804965i	$0.702184\pi$
$858$	−27.9804	−	20.3290i	−0.955236	−	0.694019i
$859$	11.2136	−	34.5121i	0.382605	−	1.17754i	−0.555598	−	0.831451i	$-0.687511\pi$
$859$	11.2136	−	34.5121i	0.382605	−	1.17754i	0.938203	−	0.346085i	$-0.112489\pi$
$860$	9.97576	+	18.5005i	0.340171	+	0.630862i
$861$	7.32687	+	22.5498i	0.249699	+	0.768495i
$862$	5.62526	−	17.3128i	0.191597	−	0.589675i
$863$	−4.79484	+	14.7570i	−0.163218	+	0.502335i	−0.998901	−	0.0468788i	$-0.985073\pi$
$863$	−4.79484	+	14.7570i	−0.163218	+	0.502335i	0.835682	+	0.549213i	$0.185073\pi$
$864$	−0.774284	−	2.38300i	−0.0263417	−	0.0810714i
$865$	8.81984	−	1.60828i	0.299883	−	0.0546832i
$866$	−6.31895	+	19.4477i	−0.214727	+	0.660860i
$867$	−63.4157	−	46.0742i	−2.15371	−	1.56476i
$868$	8.72936			0.296294
$869$	−43.8197	−	31.8369i	−1.48648	−	1.07999i
$870$	3.07523	−	22.8477i	0.104260	−	0.774610i
$871$	38.3256	−	27.8452i	1.29861	−	0.943497i
$872$	−4.57396	+	3.32317i	−0.154894	+	0.112537i
$873$	0.411673	+	1.26700i	0.0139330	+	0.0428814i
$874$	31.0981			1.05191
$875$	−4.36802	+	10.2918i	−0.147666	+	0.347925i
$876$	7.97258			0.269369
$877$	−12.1410	−	37.3660i	−0.409971	−	1.26176i	−0.916673	−	0.399639i	$-0.869135\pi$
$877$	−12.1410	−	37.3660i	−0.409971	−	1.26176i	0.506702	−	0.862121i	$-0.330865\pi$
$878$	−2.83306	+	2.05834i	−0.0956111	+	0.0694655i
$879$	−35.8952	+	26.0794i	−1.21071	+	0.879636i
$880$	−1.20233	+	8.93281i	−0.0405305	+	0.301125i
$881$	27.1198	+	19.7037i	0.913688	+	0.663833i	0.941945	−	0.335767i	$-0.108996\pi$
$881$	27.1198	+	19.7037i	0.913688	+	0.663833i	−0.0282567	+	0.999601i	$0.508996\pi$
$882$	1.86387			0.0627599
$883$	32.0140	+	23.2596i	1.07736	+	0.782747i	0.977220	−	0.212227i	$-0.0680716\pi$
$883$	32.0140	+	23.2596i	1.07736	+	0.782747i	0.100138	+	0.994974i	$0.468072\pi$
$884$	8.71448	−	26.8204i	0.293100	−	0.902068i
$885$	8.89659	−	1.62228i	0.299056	−	0.0545322i
$886$	−1.89721	−	5.83902i	−0.0637381	−	0.196166i
$887$	2.87661	−	8.85330i	0.0965872	−	0.297265i	−0.891077	−	0.453852i	$-0.850049\pi$
$887$	2.87661	−	8.85330i	0.0965872	−	0.297265i	0.987664	+	0.156588i	$0.0500493\pi$
$888$	−0.953972	+	2.93602i	−0.0320132	+	0.0985265i
$889$	3.66373	+	11.2758i	0.122878	+	0.378178i
$890$	−2.00721	−	3.72247i	−0.0672820	−	0.124777i
$891$	−13.8483	+	42.6205i	−0.463934	+	1.42784i
$892$	−1.12787	−	0.819446i	−0.0377639	−	0.0274371i
$893$	29.6784			0.993149
$894$	−9.69492	−	7.04377i	−0.324247	−	0.235579i
$895$	1.55147	+	2.87727i	0.0518599	+	0.0961766i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−53.5429	+	38.9012i	−1.78775	+	1.29887i
$898$	−7.69068	−	23.6695i	−0.256641	−	0.789861i
$899$	40.8082			1.36103
$900$	−0.433880	−	9.30926i	−0.0144627	−	0.310309i
$901$	14.5028			0.483157
$902$	−13.3915	−	41.2148i	−0.445888	−	1.37230i
$903$	−16.7714	+	12.1851i	−0.558117	+	0.405496i
$904$	−7.65846	+	5.56420i	−0.254717	+	0.185062i
$905$	−29.8754	+	31.3002i	−0.993090	+	1.04045i
$906$	16.7647	+	12.1803i	0.556970	+	0.404662i
$907$	−55.1755			−1.83207			−0.916036	−	0.401097i	$-0.868629\pi$
$907$	−55.1755			−1.83207			−0.916036	+	0.401097i	$0.868629\pi$
$908$	−14.8204	−	10.7676i	−0.491831	−	0.357336i
$909$	3.00378	−	9.24470i	0.0996292	−	0.306627i
$910$	1.16045	−	8.62164i	0.0384684	−	0.285805i
$911$	−4.56288	−	14.0431i	−0.151175	−	0.465269i	0.846578	−	0.532264i	$-0.178659\pi$
$911$	−4.56288	−	14.0431i	−0.151175	−	0.465269i	−0.997753	+	0.0669955i	$0.978659\pi$
$912$	2.74762	−	8.45631i	0.0909829	−	0.280016i
$913$	−9.12622	+	28.0876i	−0.302034	+	0.929565i
$914$	7.44532	+	22.9143i	0.246269	+	0.757939i
$915$	−10.3555	+	10.8493i	−0.342341	+	0.358668i
$916$	3.29191	−	10.1315i	0.108768	−	0.334753i
$917$	11.6750	+	8.48239i	0.385543	+	0.280113i
$918$	−18.1624			−0.599449
$919$	12.1618	+	8.83605i	0.401180	+	0.291474i	0.770021	−	0.638018i	$-0.220245\pi$
$919$	12.1618	+	8.83605i	0.401180	+	0.291474i	−0.368841	+	0.929492i	$0.620245\pi$
$920$	15.5461	+	7.47039i	0.512540	+	0.246292i
$921$	5.31954	−	3.86487i	0.175285	−	0.127352i
$922$	4.64902	−	3.37771i	0.153107	−	0.111239i
$923$	−0.863230	−	2.65675i	−0.0284135	−	0.0874479i
$924$	−8.88982			−0.292454
$925$	3.84579	−	5.84765i	0.126449	−	0.192269i
$926$	17.7629			0.583725
$927$	7.76492	+	23.8980i	0.255034	+	0.784913i
$928$	3.78201	−	2.74779i	0.124151	−	0.0902007i
$929$	−31.2790	+	22.7255i	−1.02623	+	0.745600i	−0.967551	−	0.252676i	$-0.918689\pi$
$929$	−31.2790	+	22.7255i	−1.02623	+	0.745600i	−0.0586801	+	0.998277i	$0.518689\pi$
$930$	42.3502	−	7.72248i	1.38872	−	0.253230i
$931$	−3.26168	−	2.36975i	−0.106897	−	0.0776654i
$932$	−23.7133			−0.776756
$933$	13.1253	+	9.53612i	0.429705	+	0.312199i
$934$	−5.54684	+	17.0714i	−0.181498	+	0.558594i
$935$	58.8883	+	28.2977i	1.92585	+	0.925434i
$936$	2.24080	+	6.89646i	0.0732427	+	0.225418i
$937$	0.508913	−	1.56627i	0.0166255	−	0.0511679i	−0.942400	−	0.334489i	$-0.891436\pi$
$937$	0.508913	−	1.56627i	0.0166255	−	0.0511679i	0.959025	+	0.283321i	$0.0914363\pi$
$938$	3.76279	−	11.5807i	0.122859	−	0.378122i
$939$	−17.6623	−	54.3589i	−0.576387	−	1.77394i
$940$	14.8364	+	7.12936i	0.483910	+	0.232534i
$941$	0.346817	−	1.06739i	0.0113059	−	0.0347960i	−0.945244	−	0.326363i	$-0.894177\pi$
$941$	0.346817	−	1.06739i	0.0113059	−	0.0347960i	0.956550	+	0.291567i	$0.0941767\pi$
$942$	21.5042	+	15.6237i	0.700645	+	0.509048i
$943$	−82.9268			−2.70047
$944$	1.48357	+	1.07788i	0.0482861	+	0.0350819i
$945$	−5.51188	+	1.00508i	−0.179302	+	0.0326953i
$946$	30.6535	−	22.2711i	0.996630	−	0.724094i
$947$	3.92308	−	2.85028i	0.127483	−	0.0926217i	−0.522217	−	0.852813i	$-0.674895\pi$
$947$	3.92308	−	2.85028i	0.127483	−	0.0926217i	0.649699	+	0.760191i	$0.274895\pi$
$948$	9.15763	+	28.1843i	0.297426	+	0.915383i
$949$	14.0641			0.456540
$950$	−11.0766	+	16.8424i	−0.359373	+	0.546438i
$951$	2.02163			0.0655559
$952$	−2.23995	−	6.89385i	−0.0725971	−	0.223431i
$953$	21.7779	−	15.8226i	0.705456	−	0.512544i	−0.176249	−	0.984346i	$-0.556396\pi$
$953$	21.7779	−	15.8226i	0.705456	−	0.512544i	0.881704	+	0.471802i	$0.156396\pi$
$954$	−3.01696	+	2.19195i	−0.0976776	+	0.0709669i
$955$	10.6376	+	5.11168i	0.344223	+	0.165410i
$956$	0.530125	+	0.385158i	0.0171455	+	0.0124569i
$957$	−41.5583			−1.34339
$958$	−9.87975	−	7.17806i	−0.319200	−	0.231913i
$959$	0.996400	−	3.06660i	0.0321754	−	0.0990258i
$960$	3.40493	−	3.56732i	0.109894	−	0.115135i
$961$	13.9681	+	42.9894i	0.450584	+	1.38676i
$962$	−1.68286	+	5.17931i	−0.0542576	+	0.166988i
$963$	5.43628	−	16.7312i	0.175182	−	0.539154i
$964$	−6.97076	−	21.4538i	−0.224513	−	0.690980i
$965$	−4.53139	+	33.6664i	−0.145871	+	1.08376i
$966$	−5.25682	+	16.1788i	−0.169135	+	0.520545i
$967$	17.9196	+	13.0194i	0.576257	+	0.418675i	0.837373	−	0.546632i	$-0.184090\pi$
$967$	17.9196	+	13.0194i	0.576257	+	0.418675i	−0.261116	+	0.965307i	$0.584090\pi$
$968$	5.24813			0.168681
$969$	−52.1420	−	37.8834i	−1.67504	−	1.21699i
$970$	1.10350	−	1.15613i	0.0354312	−	0.0371210i
$971$	−0.309203	+	0.224649i	−0.00992279	+	0.00720933i	−0.592736	−	0.805397i	$-0.701952\pi$
$971$	−0.309203	+	0.224649i	−0.00992279	+	0.00720933i	0.582813	+	0.812606i	$0.301952\pi$
$972$	13.7549	−	9.99355i	0.441190	−	0.320543i
$973$	2.04486	+	6.29344i	0.0655552	+	0.201758i
$974$	−22.5595			−0.722854
$975$	−1.99732	−	42.8542i	−0.0639655	−	1.37243i
$976$	−3.04131			−0.0973500
$977$	−0.617375	−	1.90008i	−0.0197516	−	0.0607891i	0.940695	−	0.339254i	$-0.110175\pi$
$977$	−0.617375	−	1.90008i	−0.0197516	−	0.0607891i	−0.960446	+	0.278465i	$0.910175\pi$
$978$	6.09834	−	4.43070i	0.195003	−	0.141678i
$979$	−6.16776	+	4.48114i	−0.197122	+	0.143218i
$980$	−1.06127	−	1.96817i	−0.0339010	−	0.0628710i
$981$	−8.52528	−	6.19398i	−0.272191	−	0.197758i
$982$	1.02577			0.0327338
$983$	22.6405	+	16.4493i	0.722120	+	0.524651i	0.887061	−	0.461653i	$-0.152743\pi$
$983$	22.6405	+	16.4493i	0.722120	+	0.524651i	−0.164941	+	0.986303i	$0.552743\pi$
$984$	−7.32687	+	22.5498i	−0.233572	+	0.718861i
$985$	−15.5840	−	28.9013i	−0.496548	−	0.920872i
$986$	−10.4714	−	32.2275i	−0.333476	−	1.02633i
$987$	−5.01684	+	15.4402i	−0.159688	+	0.491468i
$988$	4.84696	−	14.9174i	0.154202	−	0.474586i
$989$	−22.4054	−	68.9567i	−0.712450	−	2.19269i
$990$	−16.5272	+	3.01371i	−0.525270	+	0.0957820i
$991$	−2.90661	+	8.94564i	−0.0923316	+	0.284167i	−0.986549	−	0.163465i	$-0.947733\pi$
$991$	−2.90661	+	8.94564i	−0.0923316	+	0.284167i	0.894217	+	0.447633i	$0.147733\pi$
$992$	7.06220	+	5.13099i	0.224225	+	0.162909i
$993$	−14.2909			−0.453508
$994$	−0.580895	−	0.422045i	−0.0184249	−	0.0133865i
$995$	−1.67547	+	12.4480i	−0.0531158	+	0.394629i
$996$	13.0724	−	9.49766i	0.414215	−	0.300945i
$997$	21.4236	−	15.5652i	0.678493	−	0.492954i	−0.194365	−	0.980929i	$-0.562264\pi$
$997$	21.4236	−	15.5652i	0.678493	−	0.492954i	0.872857	+	0.487975i	$0.162264\pi$
$998$	3.87007	+	11.9108i	0.122505	+	0.377031i
$999$	3.50736			0.110968

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.h.c.281.1	yes	16
25.11	even	5		8750.2.a.u.1.7		8
25.14	even	10		8750.2.a.s.1.2		8
25.21	even	5	inner	350.2.h.c.71.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.h.c.71.1	✓	16	25.21	even	5	inner
350.2.h.c.281.1	yes	16	1.1	even	1	trivial
8750.2.a.s.1.2		8	25.14	even	10
8750.2.a.u.1.7		8	25.11	even	5

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-1.78422 + 1.29631i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.298278 + 2.21608i) q^{5} +(-1.78422 - 1.29631i) q^{6} -1.00000 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.575968 - 1.77265i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-1.78422 + 1.29631i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.298278 + 2.21608i) q^{5} +(-1.78422 - 1.29631i) q^{6} -1.00000 q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.575968 - 1.77265i) q^{9} +(-2.19979 + 0.401128i) q^{10} +(1.24562 + 3.83361i) q^{11} +(0.681512 - 2.09748i) q^{12} +(1.20223 - 3.70007i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-2.34054 - 4.34065i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-5.86426 - 4.26063i) q^{17} +1.86387 q^{18} +(-3.26168 - 2.36975i) q^{19} +(-1.06127 - 1.96817i) q^{20} +(1.78422 - 1.29631i) q^{21} +(-3.26106 + 2.36930i) q^{22} +(2.38359 + 7.33594i) q^{23} +2.20542 q^{24} +(-4.82206 - 1.32202i) q^{25} +3.89049 q^{26} +(-0.774284 - 2.38300i) q^{27} +(0.809017 - 0.587785i) q^{28} +(3.78201 - 2.74779i) q^{29} +(3.40493 - 3.56732i) q^{30} +(7.06220 + 5.13099i) q^{31} +1.00000 q^{32} +(-7.19201 - 5.22530i) q^{33} +(2.23995 - 6.89385i) q^{34} +(0.298278 - 2.21608i) q^{35} +(0.575968 + 1.77265i) q^{36} +(-0.432558 + 1.33128i) q^{37} +(1.24585 - 3.83433i) q^{38} +(2.65141 + 8.16021i) q^{39} +(1.54389 - 1.61753i) q^{40} +(-3.32221 + 10.2247i) q^{41} +(1.78422 + 1.29631i) q^{42} -9.39984 q^{43} +(-3.26106 - 2.36930i) q^{44} +(3.75654 + 1.80514i) q^{45} +(-6.24033 + 4.53386i) q^{46} +(-5.95545 + 4.32689i) q^{47} +(0.681512 + 2.09748i) q^{48} +1.00000 q^{49} +(-0.232784 - 4.99458i) q^{50} +15.9863 q^{51} +(1.20223 + 3.70007i) q^{52} +(-1.61865 + 1.17602i) q^{53} +(2.02710 - 1.47278i) q^{54} +(-8.86715 + 1.61691i) q^{55} +(0.809017 + 0.587785i) q^{56} +8.89149 q^{57} +(3.78201 + 2.74779i) q^{58} +(-0.566673 + 1.74404i) q^{59} +(4.44491 + 2.13592i) q^{60} +(-0.939817 - 2.89246i) q^{61} +(-2.69752 + 8.30212i) q^{62} +(-0.575968 + 1.77265i) q^{63} +(0.309017 + 0.951057i) q^{64} +(7.84107 + 3.76788i) q^{65} +(2.74710 - 8.45472i) q^{66} +(9.85111 + 7.15725i) q^{67} +7.24862 q^{68} +(-13.7625 - 9.99907i) q^{69} +(2.19979 - 0.401128i) q^{70} +(0.580895 - 0.422045i) q^{71} +(-1.50790 + 1.09556i) q^{72} +(1.11710 + 3.43807i) q^{73} -1.39979 q^{74} +(10.3174 - 3.89212i) q^{75} +4.03166 q^{76} +(-1.24562 - 3.83361i) q^{77} +(-6.94149 + 5.04329i) q^{78} +(-10.8709 + 7.89820i) q^{79} +(2.01545 + 0.968487i) q^{80} +(8.99432 + 6.53476i) q^{81} -10.7509 q^{82} +(5.92741 + 4.30651i) q^{83} +(-0.681512 + 2.09748i) q^{84} +(11.1911 - 11.7248i) q^{85} +(-2.90471 - 8.93978i) q^{86} +(-3.18595 + 9.80534i) q^{87} +(1.24562 - 3.83361i) q^{88} +(0.584454 + 1.79876i) q^{89} +(-0.555952 + 4.13050i) q^{90} +(-1.20223 + 3.70007i) q^{91} +(-6.24033 - 4.53386i) q^{92} -19.2519 q^{93} +(-5.95545 - 4.32689i) q^{94} +(6.22445 - 6.52131i) q^{95} +(-1.78422 + 1.29631i) q^{96} +(-0.578244 + 0.420119i) q^{97} +(0.309017 + 0.951057i) q^{98} +7.51308 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9	\( 16 q - 4 q^{2} + q^{3} - 4 q^{4} - 4 q^{5} + q^{6} - 16 q^{7} - 4 q^{8} - q^{9} + q^{10} + 7 q^{11} - 4 q^{12} + 9 q^{13} + 4 q^{14} - 4 q^{16} - 2 q^{17} + 14 q^{18} - 24 q^{19} - 9 q^{20} - q^{21} - 8 q^{22} - 5 q^{23} + 6 q^{24} - 6 q^{25} - 6 q^{26} - 32 q^{27} + 4 q^{28} + 20 q^{29} + 15 q^{30} + 7 q^{31} + 16 q^{32} + 15 q^{33} + 3 q^{34} + 4 q^{35} - q^{36} - 6 q^{37} + 6 q^{38} + 34 q^{39} + 11 q^{40} + 9 q^{41} - q^{42} - 22 q^{43} - 8 q^{44} - 8 q^{45} - 40 q^{47} - 4 q^{48} + 16 q^{49} - q^{50} + 14 q^{51} + 9 q^{52} - 24 q^{53} + 23 q^{54} - 26 q^{55} + 4 q^{56} + 52 q^{57} + 20 q^{58} - 17 q^{59} - 5 q^{60} + 2 q^{61} - 23 q^{62} + q^{63} - 4 q^{64} - 16 q^{65} - 10 q^{66} - 14 q^{67} - 2 q^{68} - 35 q^{69} - q^{70} + 7 q^{71} - 6 q^{72} + 5 q^{73} - 36 q^{74} + 35 q^{75} + 36 q^{76} - 7 q^{77} - 46 q^{78} + 20 q^{79} + q^{80} + 49 q^{81} + 44 q^{82} + 17 q^{83} + 4 q^{84} - 13 q^{85} + 8 q^{86} - 66 q^{87} + 7 q^{88} + 27 q^{89} + 37 q^{90} - 9 q^{91} - 34 q^{93} - 40 q^{94} - 20 q^{95} + q^{96} + 6 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + q^3 - 4 * q^4 - 4 * q^5 + q^6 - 16 * q^7 - 4 * q^8 - q^9 + q^10 + 7 * q^11 - 4 * q^12 + 9 * q^13 + 4 * q^14 - 4 * q^16 - 2 * q^17 + 14 * q^18 - 24 * q^19 - 9 * q^20 - q^21 - 8 * q^22 - 5 * q^23 + 6 * q^24 - 6 * q^25 - 6 * q^26 - 32 * q^27 + 4 * q^28 + 20 * q^29 + 15 * q^30 + 7 * q^31 + 16 * q^32 + 15 * q^33 + 3 * q^34 + 4 * q^35 - q^36 - 6 * q^37 + 6 * q^38 + 34 * q^39 + 11 * q^40 + 9 * q^41 - q^42 - 22 * q^43 - 8 * q^44 - 8 * q^45 - 40 * q^47 - 4 * q^48 + 16 * q^49 - q^50 + 14 * q^51 + 9 * q^52 - 24 * q^53 + 23 * q^54 - 26 * q^55 + 4 * q^56 + 52 * q^57 + 20 * q^58 - 17 * q^59 - 5 * q^60 + 2 * q^61 - 23 * q^62 + q^63 - 4 * q^64 - 16 * q^65 - 10 * q^66 - 14 * q^67 - 2 * q^68 - 35 * q^69 - q^70 + 7 * q^71 - 6 * q^72 + 5 * q^73 - 36 * q^74 + 35 * q^75 + 36 * q^76 - 7 * q^77 - 46 * q^78 + 20 * q^79 + q^80 + 49 * q^81 + 44 * q^82 + 17 * q^83 + 4 * q^84 - 13 * q^85 + 8 * q^86 - 66 * q^87 + 7 * q^88 + 27 * q^89 + 37 * q^90 - 9 * q^91 - 34 * q^93 - 40 * q^94 - 20 * q^95 + q^96 + 6 * q^97 - 4 * q^98 - 16 * q^99

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