LMFDB - Embedded newform 126.2.f.d.43.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(43,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("126.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			43.1
Root			$1.68614 - 0.396143i$ of defining polynomial
Character	$\chi$	$=$	126.43
Dual form			126.2.f.d.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.18614 - 3.78651i) q^{5} +(-0.500000 + 1.65831i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.18614 - 3.78651i) q^{5} +(-0.500000 + 1.65831i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} -4.37228 q^{10} +(0.686141 - 1.18843i) q^{11} +(1.18614 + 1.26217i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +(5.18614 + 5.51856i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.37228 q^{17} +(0.186141 - 2.99422i) q^{18} +5.00000 q^{19} +(-2.18614 + 3.78651i) q^{20} +(0.500000 - 1.65831i) q^{21} +(-0.686141 - 1.18843i) q^{22} +(0.813859 + 1.40965i) q^{23} +(1.68614 - 0.396143i) q^{24} +(-7.05842 + 12.2255i) q^{25} -2.00000 q^{26} +(-4.00000 + 3.31662i) q^{27} +1.00000 q^{28} +(4.37228 - 7.57301i) q^{29} +(7.37228 - 1.73205i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.686141 + 2.27567i) q^{33} +(0.686141 - 1.18843i) q^{34} +4.37228 q^{35} +(-2.50000 - 1.65831i) q^{36} +2.00000 q^{37} +(2.50000 - 4.33013i) q^{38} +(2.37228 + 2.52434i) q^{39} +(2.18614 + 3.78651i) q^{40} +(-2.31386 - 4.00772i) q^{41} +(-1.18614 - 1.26217i) q^{42} +(4.05842 - 7.02939i) q^{43} -1.37228 q^{44} +(-10.9307 - 7.25061i) q^{45} +1.62772 q^{46} +(0.500000 - 1.65831i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(7.05842 + 12.2255i) q^{50} +(-2.31386 + 0.543620i) q^{51} +(-1.00000 + 1.73205i) q^{52} -8.74456 q^{53} +(0.872281 + 5.12241i) q^{54} -6.00000 q^{55} +(0.500000 - 0.866025i) q^{56} +(-8.43070 + 1.98072i) q^{57} +(-4.37228 - 7.57301i) q^{58} +(5.05842 + 8.76144i) q^{59} +(2.18614 - 7.25061i) q^{60} +(-1.55842 + 2.69927i) q^{61} -2.00000 q^{62} +(-0.186141 + 2.99422i) q^{63} +1.00000 q^{64} +(-4.37228 + 7.57301i) q^{65} +(1.62772 + 1.73205i) q^{66} +(1.05842 + 1.83324i) q^{67} +(-0.686141 - 1.18843i) q^{68} +(-1.93070 - 2.05446i) q^{69} +(2.18614 - 3.78651i) q^{70} -7.11684 q^{71} +(-2.68614 + 1.33591i) q^{72} +12.1168 q^{73} +(1.00000 - 1.73205i) q^{74} +(7.05842 - 23.4101i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(0.686141 + 1.18843i) q^{77} +(3.37228 - 0.792287i) q^{78} +(2.55842 - 4.43132i) q^{79} +4.37228 q^{80} +(5.43070 - 7.17687i) q^{81} -4.62772 q^{82} +(-8.74456 + 15.1460i) q^{83} +(-1.68614 + 0.396143i) q^{84} +(-3.00000 - 5.19615i) q^{85} +(-4.05842 - 7.02939i) q^{86} +(-4.37228 + 14.5012i) q^{87} +(-0.686141 + 1.18843i) q^{88} +14.7446 q^{89} +(-11.7446 + 5.84096i) q^{90} +2.00000 q^{91} +(0.813859 - 1.40965i) q^{92} +(2.37228 + 2.52434i) q^{93} +(-10.9307 - 18.9325i) q^{95} +(-1.18614 - 1.26217i) q^{96} +(4.05842 - 7.02939i) q^{97} -1.00000 q^{98} +(0.255437 - 4.10891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 5 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - q^3 - 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 5 * q^9	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 5 q^{9} - 6 q^{10} - 3 q^{11} - q^{12} - 4 q^{13} + 2 q^{14} + 15 q^{15} - 2 q^{16} - 6 q^{17} - 5 q^{18} + 20 q^{19} - 3 q^{20} + 2 q^{21} + 3 q^{22} + 9 q^{23} + q^{24} - 11 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} + 6 q^{29} + 18 q^{30} - 4 q^{31} + 2 q^{32} + 3 q^{33} - 3 q^{34} + 6 q^{35} - 10 q^{36} + 8 q^{37} + 10 q^{38} - 2 q^{39} + 3 q^{40} - 15 q^{41} + q^{42} - q^{43} + 6 q^{44} - 15 q^{45} + 18 q^{46} + 2 q^{48} - 2 q^{49} + 11 q^{50} - 15 q^{51} - 4 q^{52} - 12 q^{53} - 8 q^{54} - 24 q^{55} + 2 q^{56} - 5 q^{57} - 6 q^{58} + 3 q^{59} + 3 q^{60} + 11 q^{61} - 8 q^{62} + 5 q^{63} + 4 q^{64} - 6 q^{65} + 18 q^{66} - 13 q^{67} + 3 q^{68} + 21 q^{69} + 3 q^{70} + 6 q^{71} - 5 q^{72} + 14 q^{73} + 4 q^{74} + 11 q^{75} - 10 q^{76} - 3 q^{77} + 2 q^{78} - 7 q^{79} + 6 q^{80} - 7 q^{81} - 30 q^{82} - 12 q^{83} - q^{84} - 12 q^{85} + q^{86} - 6 q^{87} + 3 q^{88} + 36 q^{89} - 24 q^{90} + 8 q^{91} + 9 q^{92} - 2 q^{93} - 15 q^{95} + q^{96} - q^{97} - 4 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 5 * q^9 - 6 * q^10 - 3 * q^11 - q^12 - 4 * q^13 + 2 * q^14 + 15 * q^15 - 2 * q^16 - 6 * q^17 - 5 * q^18 + 20 * q^19 - 3 * q^20 + 2 * q^21 + 3 * q^22 + 9 * q^23 + q^24 - 11 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 + 6 * q^29 + 18 * q^30 - 4 * q^31 + 2 * q^32 + 3 * q^33 - 3 * q^34 + 6 * q^35 - 10 * q^36 + 8 * q^37 + 10 * q^38 - 2 * q^39 + 3 * q^40 - 15 * q^41 + q^42 - q^43 + 6 * q^44 - 15 * q^45 + 18 * q^46 + 2 * q^48 - 2 * q^49 + 11 * q^50 - 15 * q^51 - 4 * q^52 - 12 * q^53 - 8 * q^54 - 24 * q^55 + 2 * q^56 - 5 * q^57 - 6 * q^58 + 3 * q^59 + 3 * q^60 + 11 * q^61 - 8 * q^62 + 5 * q^63 + 4 * q^64 - 6 * q^65 + 18 * q^66 - 13 * q^67 + 3 * q^68 + 21 * q^69 + 3 * q^70 + 6 * q^71 - 5 * q^72 + 14 * q^73 + 4 * q^74 + 11 * q^75 - 10 * q^76 - 3 * q^77 + 2 * q^78 - 7 * q^79 + 6 * q^80 - 7 * q^81 - 30 * q^82 - 12 * q^83 - q^84 - 12 * q^85 + q^86 - 6 * q^87 + 3 * q^88 + 36 * q^89 - 24 * q^90 + 8 * q^91 + 9 * q^92 - 2 * q^93 - 15 * q^95 + q^96 - q^97 - 4 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.68614	+	0.396143i	−0.973494	+	0.228714i
$3$	−1.68614	+	0.396143i	−0.973494	+	0.228714i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.18614	−	3.78651i	−0.977672	−	1.69338i	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−2.18614	−	3.78651i	−0.977672	−	1.69338i	−0.306851	−	0.951757i	$-0.599275\pi$
$6$	−0.500000	+	1.65831i	−0.204124	+	0.677003i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−1.00000			−0.353553
$9$	2.68614	−	1.33591i	0.895380	−	0.445302i
$10$	−4.37228			−1.38264
$11$	0.686141	−	1.18843i	0.206879	−	0.358325i	−0.743851	−	0.668346i	$-0.767003\pi$
$11$	0.686141	−	1.18843i	0.206879	−	0.358325i	0.950730	+	0.310021i	$0.100336\pi$
$12$	1.18614	+	1.26217i	0.342409	+	0.364357i
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$	5.18614	+	5.51856i	1.33906	+	1.42489i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.37228			0.332827			0.166414	−	0.986056i	$-0.446781\pi$
$17$	1.37228			0.332827			0.166414	+	0.986056i	$0.446781\pi$
$18$	0.186141	−	2.99422i	0.0438738	−	0.705744i
$19$	5.00000			1.14708			0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000			1.14708			0.573539	+	0.819178i	$0.305570\pi$
$20$	−2.18614	+	3.78651i	−0.488836	+	0.846689i
$21$	0.500000	−	1.65831i	0.109109	−	0.361873i
$22$	−0.686141	−	1.18843i	−0.146286	−	0.253374i
$23$	0.813859	+	1.40965i	0.169701	+	0.293931i	0.938315	−	0.345782i	$-0.112386\pi$
$23$	0.813859	+	1.40965i	0.169701	+	0.293931i	−0.768613	+	0.639713i	$0.779053\pi$
$24$	1.68614	−	0.396143i	0.344182	−	0.0808625i
$25$	−7.05842	+	12.2255i	−1.41168	+	2.44511i
$26$	−2.00000			−0.392232
$27$	−4.00000	+	3.31662i	−0.769800	+	0.638285i
$28$	1.00000			0.188982
$29$	4.37228	−	7.57301i	0.811912	−	1.40627i	−0.0996117	−	0.995026i	$-0.531760\pi$
$29$	4.37228	−	7.57301i	0.811912	−	1.40627i	0.911524	−	0.411247i	$-0.134907\pi$
$30$	7.37228	−	1.73205i	1.34599	−	0.316228i
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.686141	+	2.27567i	−0.119442	+	0.396143i
$34$	0.686141	−	1.18843i	0.117672	−	0.203814i
$35$	4.37228			0.739050
$36$	−2.50000	−	1.65831i	−0.416667	−	0.276385i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	2.50000	−	4.33013i	0.405554	−	0.702439i
$39$	2.37228	+	2.52434i	0.379869	+	0.404218i
$40$	2.18614	+	3.78651i	0.345659	+	0.598699i
$41$	−2.31386	−	4.00772i	−0.361364	−	0.625901i	0.626821	−	0.779163i	$-0.284356\pi$
$41$	−2.31386	−	4.00772i	−0.361364	−	0.625901i	−0.988186	+	0.153262i	$0.951022\pi$
$42$	−1.18614	−	1.26217i	−0.183025	−	0.194757i
$43$	4.05842	−	7.02939i	0.618904	−	1.07197i	−0.370783	−	0.928720i	$-0.620910\pi$
$43$	4.05842	−	7.02939i	0.618904	−	1.07197i	0.989686	−	0.143253i	$-0.0457562\pi$
$44$	−1.37228			−0.206879
$45$	−10.9307	−	7.25061i	−1.62945	−	1.08086i
$46$	1.62772			0.239994
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	0.500000	−	1.65831i	0.0721688	−	0.239357i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	7.05842	+	12.2255i	0.998212	+	1.72895i
$51$	−2.31386	+	0.543620i	−0.324005	+	0.0761221i
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−8.74456			−1.20116			−0.600579	−	0.799565i	$-0.705063\pi$
$53$	−8.74456			−1.20116			−0.600579	+	0.799565i	$0.705063\pi$
$54$	0.872281	+	5.12241i	0.118702	+	0.697072i
$55$	−6.00000			−0.809040
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	−8.43070	+	1.98072i	−1.11667	+	0.262352i
$58$	−4.37228	−	7.57301i	−0.574109	−	0.994385i
$59$	5.05842	+	8.76144i	0.658550	+	1.14064i	0.980991	+	0.194053i	$0.0621634\pi$
$59$	5.05842	+	8.76144i	0.658550	+	1.14064i	−0.322441	+	0.946590i	$0.604503\pi$
$60$	2.18614	−	7.25061i	0.282230	−	0.936050i
$61$	−1.55842	+	2.69927i	−0.199535	+	0.345606i	−0.948378	−	0.317142i	$-0.897277\pi$
$61$	−1.55842	+	2.69927i	−0.199535	+	0.345606i	0.748842	+	0.662748i	$0.230610\pi$
$62$	−2.00000			−0.254000
$63$	−0.186141	+	2.99422i	−0.0234515	+	0.377236i
$64$	1.00000			0.125000
$65$	−4.37228	+	7.57301i	−0.542315	+	0.939317i
$66$	1.62772	+	1.73205i	0.200358	+	0.213201i
$67$	1.05842	+	1.83324i	0.129307	+	0.223966i	0.923408	−	0.383819i	$-0.125391\pi$
$67$	1.05842	+	1.83324i	0.129307	+	0.223966i	−0.794101	+	0.607785i	$0.792058\pi$
$68$	−0.686141	−	1.18843i	−0.0832068	−	0.144118i
$69$	−1.93070	−	2.05446i	−0.232429	−	0.247327i
$70$	2.18614	−	3.78651i	0.261294	−	0.452574i
$71$	−7.11684			−0.844614			−0.422307	−	0.906453i	$-0.638780\pi$
$71$	−7.11684			−0.844614			−0.422307	+	0.906453i	$0.638780\pi$
$72$	−2.68614	+	1.33591i	−0.316565	+	0.157438i
$73$	12.1168			1.41817			0.709085	−	0.705123i	$-0.249108\pi$
$73$	12.1168			1.41817			0.709085	+	0.705123i	$0.249108\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	7.05842	−	23.4101i	0.815036	−	2.70317i
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	0.686141	+	1.18843i	0.0781930	+	0.135434i
$78$	3.37228	−	0.792287i	0.381836	−	0.0897088i
$79$	2.55842	−	4.43132i	0.287845	−	0.498562i	−0.685450	−	0.728120i	$-0.740395\pi$
$79$	2.55842	−	4.43132i	0.287845	−	0.498562i	0.973295	+	0.229557i	$0.0737279\pi$
$80$	4.37228			0.488836
$81$	5.43070	−	7.17687i	0.603411	−	0.797430i
$82$	−4.62772			−0.511046
$83$	−8.74456	+	15.1460i	−0.959840	+	1.66249i	−0.236960	+	0.971519i	$0.576151\pi$
$83$	−8.74456	+	15.1460i	−0.959840	+	1.66249i	−0.722881	+	0.690973i	$0.757182\pi$
$84$	−1.68614	+	0.396143i	−0.183973	+	0.0432228i
$85$	−3.00000	−	5.19615i	−0.325396	−	0.563602i
$86$	−4.05842	−	7.02939i	−0.437631	−	0.757999i
$87$	−4.37228	+	14.5012i	−0.468758	+	1.55469i
$88$	−0.686141	+	1.18843i	−0.0731428	+	0.126687i
$89$	14.7446			1.56292			0.781460	−	0.623955i	$-0.214475\pi$
$89$	14.7446			1.56292			0.781460	+	0.623955i	$0.214475\pi$
$90$	−11.7446	+	5.84096i	−1.23799	+	0.615692i
$91$	2.00000			0.209657
$92$	0.813859	−	1.40965i	0.0848507	−	0.146966i
$93$	2.37228	+	2.52434i	0.245994	+	0.261762i
$94$		0			0
$95$	−10.9307	−	18.9325i	−1.12147	−	1.94244i
$96$	−1.18614	−	1.26217i	−0.121060	−	0.128820i
$97$	4.05842	−	7.02939i	0.412070	−	0.713727i	−0.583046	−	0.812439i	$-0.698139\pi$
$97$	4.05842	−	7.02939i	0.412070	−	0.713727i	0.995116	+	0.0987127i	$0.0314725\pi$
$98$	−1.00000			−0.101015
$99$	0.255437	−	4.10891i	0.0256724	−	0.412961i
$100$	14.1168			1.41168
$101$	−0.813859	+	1.40965i	−0.0809820	+	0.140265i	−0.903672	−	0.428225i	$-0.859139\pi$
$101$	−0.813859	+	1.40965i	−0.0809820	+	0.140265i	0.822690	+	0.568490i	$0.192472\pi$
$102$	−0.686141	+	2.27567i	−0.0679380	+	0.225325i
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	0.999964	−	0.00844953i	$-0.00268960\pi$
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	−0.507300	+	0.861770i	$0.669356\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$	−7.37228	+	1.73205i	−0.719461	+	0.169031i
$106$	−4.37228	+	7.57301i	−0.424674	+	0.735556i
$107$	−7.37228			−0.712705			−0.356353	−	0.934352i	$-0.615980\pi$
$107$	−7.37228			−0.712705			−0.356353	+	0.934352i	$0.615980\pi$
$108$	4.87228	+	1.80579i	0.468835	+	0.173762i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	−3.00000	+	5.19615i	−0.286039	+	0.495434i
$111$	−3.37228	+	0.792287i	−0.320083	+	0.0752006i
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	2.18614	+	3.78651i	0.205655	+	0.356205i	0.950341	−	0.311210i	$-0.100734\pi$
$113$	2.18614	+	3.78651i	0.205655	+	0.356205i	−0.744686	+	0.667415i	$0.767401\pi$
$114$	−2.50000	+	8.29156i	−0.234146	+	0.776576i
$115$	3.55842	−	6.16337i	0.331825	−	0.574737i
$116$	−8.74456			−0.811912
$117$	−5.00000	−	3.31662i	−0.462250	−	0.306622i
$118$	10.1168			0.931331
$119$	−0.686141	+	1.18843i	−0.0628984	+	0.108943i
$120$	−5.18614	−	5.51856i	−0.473428	−	0.503773i
$121$	4.55842	+	7.89542i	0.414402	+	0.717765i
$122$	1.55842	+	2.69927i	0.141093	+	0.244380i
$123$	5.48913	+	5.84096i	0.494938	+	0.526662i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	39.8614			3.56531
$126$	2.50000	+	1.65831i	0.222718	+	0.147734i
$127$	3.11684			0.276575			0.138288	−	0.990392i	$-0.455840\pi$
$127$	3.11684			0.276575			0.138288	+	0.990392i	$0.455840\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.05842	+	13.4603i	−0.357324	+	1.18511i
$130$	4.37228	+	7.57301i	0.383474	+	0.664197i
$131$	0.813859	+	1.40965i	0.0711072	+	0.123161i	0.899387	−	0.437154i	$-0.144013\pi$
$131$	0.813859	+	1.40965i	0.0711072	+	0.123161i	−0.828280	+	0.560315i	$0.810680\pi$
$132$	2.31386	−	0.543620i	0.201396	−	0.0473161i
$133$	−2.50000	+	4.33013i	−0.216777	+	0.375470i
$134$	2.11684			0.182867
$135$	21.3030	+	7.89542i	1.83347	+	0.679529i
$136$	−1.37228			−0.117672
$137$	−5.31386	+	9.20387i	−0.453994	+	0.786340i	−0.998630	−	0.0523324i	$-0.983334\pi$
$137$	−5.31386	+	9.20387i	−0.453994	+	0.786340i	0.544636	+	0.838672i	$0.316668\pi$
$138$	−2.74456	+	0.644810i	−0.233633	+	0.0548899i
$139$	−6.61684	−	11.4607i	−0.561233	−	0.972085i	−0.997389	−	0.0722136i	$-0.976994\pi$
$139$	−6.61684	−	11.4607i	−0.561233	−	0.972085i	0.436156	−	0.899871i	$-0.356340\pi$
$140$	−2.18614	−	3.78651i	−0.184763	−	0.320018i
$141$		0			0
$142$	−3.55842	+	6.16337i	−0.298616	+	0.517218i
$143$	−2.74456			−0.229512
$144$	−0.186141	+	2.99422i	−0.0155117	+	0.249518i
$145$	−38.2337			−3.17513
$146$	6.05842	−	10.4935i	0.501399	−	0.868448i
$147$	1.18614	+	1.26217i	0.0978312	+	0.104102i
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	−1.62772	−	2.81929i	−0.133348	−	0.230965i	0.791617	−	0.611017i	$-0.209239\pi$
$149$	−1.62772	−	2.81929i	−0.133348	−	0.230965i	−0.924965	+	0.380052i	$0.875906\pi$
$150$	−16.7446	−	17.8178i	−1.36719	−	1.45482i
$151$	−4.55842	+	7.89542i	−0.370959	+	0.642520i	−0.989713	−	0.143065i	$-0.954304\pi$
$151$	−4.55842	+	7.89542i	−0.370959	+	0.642520i	0.618754	+	0.785585i	$0.287638\pi$
$152$	−5.00000			−0.405554
$153$	3.68614	−	1.83324i	0.298007	−	0.148209i
$154$	1.37228			0.110582
$155$	−4.37228	+	7.57301i	−0.351190	+	0.608279i
$156$	1.00000	−	3.31662i	0.0800641	−	0.265543i
$157$	−4.55842	−	7.89542i	−0.363802	−	0.630123i	0.624781	−	0.780800i	$-0.285188\pi$
$157$	−4.55842	−	7.89542i	−0.363802	−	0.630123i	−0.988583	+	0.150677i	$0.951855\pi$
$158$	−2.55842	−	4.43132i	−0.203537	−	0.352537i
$159$	14.7446	−	3.46410i	1.16932	−	0.274721i
$160$	2.18614	−	3.78651i	0.172830	−	0.299350i
$161$	−1.62772			−0.128282
$162$	−3.50000	−	8.29156i	−0.274986	−	0.651447i
$163$	−18.2337			−1.42817			−0.714086	−	0.700058i	$-0.753158\pi$
$163$	−18.2337			−1.42817			−0.714086	+	0.700058i	$0.753158\pi$
$164$	−2.31386	+	4.00772i	−0.180682	+	0.312951i
$165$	10.1168	−	2.37686i	0.787595	−	0.185038i
$166$	8.74456	+	15.1460i	0.678710	+	1.17556i
$167$	2.74456	+	4.75372i	0.212381	+	0.367854i	0.952459	−	0.304666i	$-0.0985450\pi$
$167$	2.74456	+	4.75372i	0.212381	+	0.367854i	−0.740078	+	0.672521i	$0.765212\pi$
$168$	−0.500000	+	1.65831i	−0.0385758	+	0.127942i
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	−6.00000			−0.460179
$171$	13.4307	−	6.67954i	1.02707	−	0.510797i
$172$	−8.11684			−0.618904
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$	10.3723	+	11.0371i	0.786321	+	0.836722i
$175$	−7.05842	−	12.2255i	−0.533567	−	0.924164i
$176$	0.686141	+	1.18843i	0.0517198	+	0.0895813i
$177$	−12.0000	−	12.7692i	−0.901975	−	0.959789i
$178$	7.37228	−	12.7692i	0.552576	−	0.957089i
$179$	3.25544			0.243323			0.121661	−	0.992572i	$-0.461178\pi$
$179$	3.25544			0.243323			0.121661	+	0.992572i	$0.461178\pi$
$180$	−0.813859	+	13.0916i	−0.0606615	+	0.975788i
$181$	0.883156			0.0656445			0.0328222	−	0.999461i	$-0.489550\pi$
$181$	0.883156			0.0656445			0.0328222	+	0.999461i	$0.489550\pi$
$182$	1.00000	−	1.73205i	0.0741249	−	0.128388i
$183$	1.55842	−	5.16870i	0.115202	−	0.382081i
$184$	−0.813859	−	1.40965i	−0.0599985	−	0.103920i
$185$	−4.37228	−	7.57301i	−0.321457	−	0.556779i
$186$	3.37228	−	0.792287i	0.247268	−	0.0580933i
$187$	0.941578	−	1.63086i	0.0688550	−	0.119260i
$188$		0			0
$189$	−0.872281	−	5.12241i	−0.0634491	−	0.372601i
$190$	−21.8614			−1.58599
$191$	9.55842	−	16.5557i	0.691623	−	1.19793i	−0.279683	−	0.960092i	$-0.590229\pi$
$191$	9.55842	−	16.5557i	0.691623	−	1.19793i	0.971306	−	0.237834i	$-0.0764374\pi$
$192$	−1.68614	+	0.396143i	−0.121687	+	0.0285892i
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	0.964059	−	0.265689i	$-0.0855996\pi$
$193$	3.50000	+	6.06218i	0.251936	+	0.436365i	−0.712123	+	0.702055i	$0.752266\pi$
$194$	−4.05842	−	7.02939i	−0.291378	−	0.504681i
$195$	4.37228	−	14.5012i	0.313106	−	1.03845i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	−3.43070	−	2.27567i	−0.243809	−	0.161725i
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$	7.05842	−	12.2255i	0.499106	−	0.864477i
$201$	−2.51087	−	2.67181i	−0.177103	−	0.188455i
$202$	0.813859	+	1.40965i	0.0572629	+	0.0991823i
$203$	4.37228	+	7.57301i	0.306874	+	0.531521i
$204$	1.62772	+	1.73205i	0.113963	+	0.121268i
$205$	−10.1168	+	17.5229i	−0.706591	+	1.22385i
$206$	10.0000			0.696733
$207$	4.06930	+	2.69927i	0.282836	+	0.187612i
$208$	2.00000			0.138675
$209$	3.43070	−	5.94215i	0.237307	−	0.411027i
$210$	−2.18614	+	7.25061i	−0.150858	+	0.500340i
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$	4.37228	+	7.57301i	0.300290	+	0.520117i
$213$	12.0000	−	2.81929i	0.822226	−	0.193175i
$214$	−3.68614	+	6.38458i	−0.251979	+	0.436441i
$215$	−35.4891			−2.42034
$216$	4.00000	−	3.31662i	0.272166	−	0.225668i
$217$	2.00000			0.135769
$218$	7.00000	−	12.1244i	0.474100	−	0.821165i
$219$	−20.4307	+	4.80001i	−1.38058	+	0.324355i
$220$	3.00000	+	5.19615i	0.202260	+	0.350325i
$221$	−1.37228	−	2.37686i	−0.0923096	−	0.159885i
$222$	−1.00000	+	3.31662i	−0.0671156	+	0.222597i
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	−0.791258	−	0.611482i	$-0.790574\pi$
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	0.925188	+	0.379509i	$0.123907\pi$
$224$	−1.00000			−0.0668153
$225$	−2.62772	+	42.2689i	−0.175181	+	2.81793i
$226$	4.37228			0.290840
$227$	6.12772	−	10.6135i	0.406711	−	0.704444i	−0.587808	−	0.809000i	$-0.700009\pi$
$227$	6.12772	−	10.6135i	0.406711	−	0.704444i	0.994519	+	0.104556i	$0.0333423\pi$
$228$	5.93070	+	6.31084i	0.392770	+	0.417946i
$229$	1.44158	+	2.49689i	0.0952622	+	0.164999i	0.909718	−	0.415227i	$-0.136298\pi$
$229$	1.44158	+	2.49689i	0.0952622	+	0.164999i	−0.814456	+	0.580226i	$0.802964\pi$
$230$	−3.55842	−	6.16337i	−0.234635	−	0.406400i
$231$	−1.62772	−	1.73205i	−0.107096	−	0.113961i
$232$	−4.37228	+	7.57301i	−0.287054	+	0.497193i
$233$	−0.255437			−0.0167343			−0.00836713	−	0.999965i	$-0.502663\pi$
$233$	−0.255437			−0.0167343			−0.00836713	+	0.999965i	$0.502663\pi$
$234$	−5.37228	+	2.67181i	−0.351197	+	0.174662i
$235$		0			0
$236$	5.05842	−	8.76144i	0.329275	−	0.570321i
$237$	−2.55842	+	8.48533i	−0.166187	+	0.551181i
$238$	0.686141	+	1.18843i	0.0444759	+	0.0770345i
$239$	−4.93070	−	8.54023i	−0.318941	−	0.552421i	0.661327	−	0.750098i	$-0.269994\pi$
$239$	−4.93070	−	8.54023i	−0.318941	−	0.552421i	−0.980267	+	0.197677i	$0.936660\pi$
$240$	−7.37228	+	1.73205i	−0.475879	+	0.111803i
$241$	−9.05842	+	15.6896i	−0.583504	+	1.01066i	0.411556	+	0.911385i	$0.364986\pi$
$241$	−9.05842	+	15.6896i	−0.583504	+	1.01066i	−0.995060	+	0.0992745i	$0.968348\pi$
$242$	9.11684			0.586053
$243$	−6.31386	+	14.2525i	−0.405034	+	0.914302i
$244$	3.11684			0.199535
$245$	−2.18614	+	3.78651i	−0.139667	+	0.241911i
$246$	7.80298	−	1.83324i	0.497500	−	0.116883i
$247$	−5.00000	−	8.66025i	−0.318142	−	0.551039i
$248$	1.00000	+	1.73205i	0.0635001	+	0.109985i
$249$	8.74456	−	29.0024i	0.554164	−	1.83795i
$250$	19.9307	−	34.5210i	1.26053	−	2.18330i
$251$	−9.00000			−0.568075			−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000			−0.568075			−0.284037	+	0.958813i	$0.591674\pi$
$252$	2.68614	−	1.33591i	0.169211	−	0.0841543i
$253$	2.23369			0.140431
$254$	1.55842	−	2.69927i	0.0977841	−	0.169367i
$255$	7.11684	+	7.57301i	0.445674	+	0.474240i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.43070	+	5.94215i	0.214001	+	0.370661i	0.952963	−	0.303086i	$-0.0980170\pi$
$257$	3.43070	+	5.94215i	0.214001	+	0.370661i	−0.738962	+	0.673747i	$0.764684\pi$
$258$	9.62772	+	10.2448i	0.599396	+	0.637815i
$259$	−1.00000	+	1.73205i	−0.0621370	+	0.107624i
$260$	8.74456			0.542315
$261$	1.62772	−	26.1831i	0.100753	−	1.62070i
$262$	1.62772			0.100561
$263$	−3.81386	+	6.60580i	−0.235173	+	0.407331i	−0.959323	−	0.282311i	$-0.908899\pi$
$263$	−3.81386	+	6.60580i	−0.235173	+	0.407331i	0.724150	+	0.689642i	$0.242232\pi$
$264$	0.686141	−	2.27567i	0.0422290	−	0.140058i
$265$	19.1168	+	33.1113i	1.17434	+	2.03401i
$266$	2.50000	+	4.33013i	0.153285	+	0.265497i
$267$	−24.8614	+	5.84096i	−1.52149	+	0.357461i
$268$	1.05842	−	1.83324i	0.0646534	−	0.111983i
$269$	−1.62772			−0.0992438			−0.0496219	−	0.998768i	$-0.515802\pi$
$269$	−1.62772			−0.0992438			−0.0496219	+	0.998768i	$0.515802\pi$
$270$	17.4891	−	14.5012i	1.06435	−	0.882516i
$271$	16.2337			0.986126			0.493063	−	0.869994i	$-0.335877\pi$
$271$	16.2337			0.986126			0.493063	+	0.869994i	$0.335877\pi$
$272$	−0.686141	+	1.18843i	−0.0416034	+	0.0720592i
$273$	−3.37228	+	0.792287i	−0.204100	+	0.0479514i
$274$	5.31386	+	9.20387i	0.321022	+	0.556026i
$275$	9.68614	+	16.7769i	0.584096	+	1.01168i
$276$	−0.813859	+	2.69927i	−0.0489886	+	0.162477i
$277$	6.11684	−	10.5947i	0.367526	−	0.636573i	−0.621652	−	0.783293i	$-0.713538\pi$
$277$	6.11684	−	10.5947i	0.367526	−	0.636573i	0.989178	+	0.146720i	$0.0468717\pi$
$278$	−13.2337			−0.793704
$279$	−5.00000	−	3.31662i	−0.299342	−	0.198561i
$280$	−4.37228			−0.261294
$281$	−8.18614	+	14.1788i	−0.488344	+	0.845837i	−0.999910	−	0.0134071i	$-0.995732\pi$
$281$	−8.18614	+	14.1788i	−0.488344	+	0.845837i	0.511566	+	0.859244i	$0.329066\pi$
$282$		0			0
$283$	−13.5584	−	23.4839i	−0.805965	−	1.39597i	−0.915638	−	0.402004i	$-0.868314\pi$
$283$	−13.5584	−	23.4839i	−0.805965	−	1.39597i	0.109673	−	0.993968i	$-0.465019\pi$
$284$	3.55842	+	6.16337i	0.211153	+	0.365729i
$285$	25.9307	+	27.5928i	1.53600	+	1.63446i
$286$	−1.37228	+	2.37686i	−0.0811447	+	0.140547i
$287$	4.62772			0.273166
$288$	2.50000	+	1.65831i	0.147314	+	0.0977170i
$289$	−15.1168			−0.889226
$290$	−19.1168	+	33.1113i	−1.12258	+	1.94437i
$291$	−4.05842	+	13.4603i	−0.237909	+	0.789055i
$292$	−6.05842	−	10.4935i	−0.354542	−	0.614085i
$293$	5.18614	+	8.98266i	0.302978	+	0.524773i	0.976809	−	0.214113i	$-0.0686859\pi$
$293$	5.18614	+	8.98266i	0.302978	+	0.524773i	−0.673831	+	0.738885i	$0.735353\pi$
$294$	1.68614	−	0.396143i	0.0983377	−	0.0231036i
$295$	22.1168	−	38.3075i	1.28769	−	2.23035i
$296$	−2.00000			−0.116248
$297$	1.19702	+	7.02939i	0.0694579	+	0.407887i
$298$	−3.25544			−0.188582
$299$	1.62772	−	2.81929i	0.0941334	−	0.163044i
$300$	−23.8030	+	5.59230i	−1.37427	+	0.322871i
$301$	4.05842	+	7.02939i	0.233924	+	0.405167i
$302$	4.55842	+	7.89542i	0.262308	+	0.454330i
$303$	0.813859	−	2.69927i	0.0467550	−	0.155069i
$304$	−2.50000	+	4.33013i	−0.143385	+	0.248350i
$305$	13.6277			0.780321
$306$	0.255437	−	4.10891i	0.0146024	−	0.234891i
$307$	−13.0000			−0.741949			−0.370975	−	0.928643i	$-0.620976\pi$
$307$	−13.0000			−0.741949			−0.370975	+	0.928643i	$0.620976\pi$
$308$	0.686141	−	1.18843i	0.0390965	−	0.0677171i
$309$	−11.8614	−	12.6217i	−0.674772	−	0.718023i
$310$	4.37228	+	7.57301i	0.248329	+	0.430118i
$311$	−4.11684	−	7.13058i	−0.233445	−	0.404338i	0.725375	−	0.688354i	$-0.241666\pi$
$311$	−4.11684	−	7.13058i	−0.233445	−	0.404338i	−0.958820	+	0.284016i	$0.908333\pi$
$312$	−2.37228	−	2.52434i	−0.134304	−	0.142912i
$313$	10.0584	−	17.4217i	0.568536	−	0.984733i	−0.428175	−	0.903696i	$-0.640843\pi$
$313$	10.0584	−	17.4217i	0.568536	−	0.984733i	0.996711	−	0.0810370i	$-0.0258232\pi$
$314$	−9.11684			−0.514493
$315$	11.7446	−	5.84096i	0.661731	−	0.329101i
$316$	−5.11684			−0.287845
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$	4.37228	−	14.5012i	0.245185	−	0.813188i
$319$	−6.00000	−	10.3923i	−0.335936	−	0.581857i
$320$	−2.18614	−	3.78651i	−0.122209	−	0.211672i
$321$	12.4307	−	2.92048i	0.693814	−	0.163005i
$322$	−0.813859	+	1.40965i	−0.0453546	+	0.0785565i
$323$	6.86141			0.381779
$324$	−8.93070	−	1.11469i	−0.496150	−	0.0619273i
$325$	28.2337			1.56612
$326$	−9.11684	+	15.7908i	−0.504935	+	0.874574i
$327$	−23.6060	+	5.54601i	−1.30541	+	0.306695i
$328$	2.31386	+	4.00772i	0.127762	+	0.221289i
$329$		0			0
$330$	3.00000	−	9.94987i	0.165145	−	0.547723i
$331$	−11.1168	+	19.2549i	−0.611037	+	1.05835i	0.380029	+	0.924975i	$0.375914\pi$
$331$	−11.1168	+	19.2549i	−0.611037	+	1.05835i	−0.991066	+	0.133373i	$0.957419\pi$
$332$	17.4891			0.959840
$333$	5.37228	−	2.67181i	0.294399	−	0.146415i
$334$	5.48913			0.300352
$335$	4.62772	−	8.01544i	0.252839	−	0.437930i
$336$	1.18614	+	1.26217i	0.0647093	+	0.0688570i
$337$	4.05842	+	7.02939i	0.221076	+	0.382915i	0.955135	−	0.296171i	$-0.0957097\pi$
$337$	4.05842	+	7.02939i	0.221076	+	0.382915i	−0.734059	+	0.679086i	$0.762376\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$	−5.18614	−	5.51856i	−0.281672	−	0.299727i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−2.74456			−0.148626
$342$	0.930703	−	14.9711i	0.0503267	−	0.809544i
$343$	1.00000			0.0539949
$344$	−4.05842	+	7.02939i	−0.218815	+	0.378999i
$345$	−3.55842	+	11.8020i	−0.191579	+	0.635396i
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	5.05842	+	8.76144i	0.271550	+	0.470339i	0.969259	−	0.246043i	$-0.0791303\pi$
$347$	5.05842	+	8.76144i	0.271550	+	0.470339i	−0.697709	+	0.716382i	$0.745797\pi$
$348$	14.7446	−	3.46410i	0.790392	−	0.185695i
$349$	11.0000	−	19.0526i	0.588817	−	1.01986i	−0.405571	−	0.914063i	$-0.632927\pi$
$349$	11.0000	−	19.0526i	0.588817	−	1.01986i	0.994388	−	0.105797i	$-0.0337393\pi$
$350$	−14.1168			−0.754577
$351$	9.74456	+	3.61158i	0.520126	+	0.192772i
$352$	1.37228			0.0731428
$353$	6.68614	−	11.5807i	0.355867	−	0.616380i	−0.631399	−	0.775458i	$-0.717519\pi$
$353$	6.68614	−	11.5807i	0.355867	−	0.616380i	0.987266	+	0.159078i	$0.0508522\pi$
$354$	−17.0584	+	4.00772i	−0.906645	+	0.213008i
$355$	15.5584	+	26.9480i	0.825755	+	1.43025i
$356$	−7.37228	−	12.7692i	−0.390730	−	0.676764i
$357$	0.686141	−	2.27567i	0.0363144	−	0.120441i
$358$	1.62772	−	2.81929i	0.0860276	−	0.149004i
$359$	21.8614			1.15380			0.576900	−	0.816814i	$-0.304262\pi$
$359$	21.8614			1.15380			0.576900	+	0.816814i	$0.304262\pi$
$360$	10.9307	+	7.25061i	0.576099	+	0.382141i
$361$	6.00000			0.315789
$362$	0.441578	−	0.764836i	0.0232088	−	0.0401989i
$363$	−10.8139	−	11.5070i	−0.567580	−	0.603961i
$364$	−1.00000	−	1.73205i	−0.0524142	−	0.0907841i
$365$	−26.4891	−	45.8805i	−1.38650	−	2.40150i
$366$	−3.69702	−	3.93398i	−0.193246	−	0.205633i
$367$	6.11684	−	10.5947i	0.319297	−	0.553038i	−0.661045	−	0.750346i	$-0.729887\pi$
$367$	6.11684	−	10.5947i	0.319297	−	0.553038i	0.980341	+	0.197308i	$0.0632200\pi$
$368$	−1.62772			−0.0848507
$369$	−11.5693	−	7.67420i	−0.602274	−	0.399503i
$370$	−8.74456			−0.454608
$371$	4.37228	−	7.57301i	0.226998	−	0.393171i
$372$	1.00000	−	3.31662i	0.0518476	−	0.171959i
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	−0.941578	−	1.63086i	−0.0486878	−	0.0843298i
$375$	−67.2119	+	15.7908i	−3.47081	+	0.815435i
$376$		0			0
$377$	−17.4891			−0.900736
$378$	−4.87228	−	1.80579i	−0.250603	−	0.0928798i
$379$	−8.11684			−0.416934			−0.208467	−	0.978029i	$-0.566847\pi$
$379$	−8.11684			−0.416934			−0.208467	+	0.978029i	$0.566847\pi$
$380$	−10.9307	+	18.9325i	−0.560733	+	0.971218i
$381$	−5.25544	+	1.23472i	−0.269244	+	0.0632565i
$382$	−9.55842	−	16.5557i	−0.489051	−	0.847062i
$383$	16.3723	+	28.3576i	0.836584	+	1.44901i	0.892734	+	0.450584i	$0.148784\pi$
$383$	16.3723	+	28.3576i	0.836584	+	1.44901i	−0.0561493	+	0.998422i	$0.517882\pi$
$384$	−0.500000	+	1.65831i	−0.0255155	+	0.0846254i
$385$	3.00000	−	5.19615i	0.152894	−	0.264820i
$386$	7.00000			0.356291
$387$	1.51087	−	24.3036i	0.0768021	−	1.23542i
$388$	−8.11684			−0.412070
$389$	−5.48913	+	9.50744i	−0.278310	+	0.482047i	−0.970965	−	0.239222i	$-0.923107\pi$
$389$	−5.48913	+	9.50744i	−0.278310	+	0.482047i	0.692655	+	0.721269i	$0.256441\pi$
$390$	−10.3723	−	11.0371i	−0.525221	−	0.558886i
$391$	1.11684	+	1.93443i	0.0564812	+	0.0978284i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$	−1.93070	−	2.05446i	−0.0973911	−	0.103634i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	−22.3723			−1.12567
$396$	−3.68614	+	1.83324i	−0.185236	+	0.0921238i
$397$	−22.0000			−1.10415			−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000			−1.10415			−0.552074	+	0.833795i	$0.686163\pi$
$398$	−5.00000	+	8.66025i	−0.250627	+	0.434099i
$399$	2.50000	−	8.29156i	0.125157	−	0.415097i
$400$	−7.05842	−	12.2255i	−0.352921	−	0.611277i
$401$	5.87228	+	10.1711i	0.293248	+	0.507920i	0.974576	−	0.224058i	$-0.0719306\pi$
$401$	5.87228	+	10.1711i	0.293248	+	0.507920i	−0.681328	+	0.731978i	$0.738597\pi$
$402$	−3.56930	+	0.838574i	−0.178020	+	0.0418243i
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	1.62772			0.0809820
$405$	−39.0475	−	4.87375i	−1.94029	−	0.242178i
$406$	8.74456			0.433985
$407$	1.37228	−	2.37686i	0.0680215	−	0.117817i
$408$	2.31386	−	0.543620i	0.114553	−	0.0269132i
$409$	11.1753	+	19.3561i	0.552581	+	0.957099i	0.998087	+	0.0618200i	$0.0196905\pi$
$409$	11.1753	+	19.3561i	0.552581	+	0.957099i	−0.445506	+	0.895279i	$0.646976\pi$
$410$	10.1168	+	17.5229i	0.499635	+	0.865394i
$411$	5.31386	−	17.6241i	0.262113	−	0.869332i
$412$	5.00000	−	8.66025i	0.246332	−	0.426660i
$413$	−10.1168			−0.497817
$414$	4.37228	−	2.17448i	0.214886	−	0.106870i
$415$	76.4674			3.75364
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	15.6970	+	16.7031i	0.768686	+	0.817957i
$418$	−3.43070	−	5.94215i	−0.167801	−	0.290640i
$419$	6.30298	+	10.9171i	0.307921	+	0.533335i	0.977907	−	0.209039i	$-0.0670334\pi$
$419$	6.30298	+	10.9171i	0.307921	+	0.533335i	−0.669986	+	0.742373i	$0.733700\pi$
$420$	5.18614	+	5.51856i	0.253058	+	0.269278i
$421$	−17.1168	+	29.6472i	−0.834224	+	1.44492i	0.0604368	+	0.998172i	$0.480751\pi$
$421$	−17.1168	+	29.6472i	−0.834224	+	1.44492i	−0.894661	+	0.446746i	$0.852583\pi$
$422$	16.0000			0.778868
$423$		0			0
$424$	8.74456			0.424674
$425$	−9.68614	+	16.7769i	−0.469847	+	0.813799i
$426$	3.55842	−	11.8020i	0.172406	−	0.571806i
$427$	−1.55842	−	2.69927i	−0.0754173	−	0.130627i
$428$	3.68614	+	6.38458i	0.178176	+	0.308610i
$429$	4.62772	−	1.08724i	0.223428	−	0.0524925i
$430$	−17.7446	+	30.7345i	−0.855719	+	1.48215i
$431$	−6.51087			−0.313618			−0.156809	−	0.987629i	$-0.550121\pi$
$431$	−6.51087			−0.313618			−0.156809	+	0.987629i	$0.550121\pi$
$432$	−0.872281	−	5.12241i	−0.0419677	−	0.246452i
$433$	−20.1168			−0.966754			−0.483377	−	0.875412i	$-0.660590\pi$
$433$	−20.1168			−0.966754			−0.483377	+	0.875412i	$0.660590\pi$
$434$	1.00000	−	1.73205i	0.0480015	−	0.0831411i
$435$	64.4674	−	15.1460i	3.09097	−	0.726196i
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	4.06930	+	7.04823i	0.194661	+	0.337162i
$438$	−6.05842	+	20.0935i	−0.289483	+	0.960105i
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	6.00000			0.286039
$441$	−2.50000	−	1.65831i	−0.119048	−	0.0789673i
$442$	−2.74456			−0.130546
$443$	20.0584	−	34.7422i	0.953004	−	1.65065i	0.214134	−	0.976804i	$-0.431307\pi$
$443$	20.0584	−	34.7422i	0.953004	−	1.65065i	0.738870	−	0.673848i	$-0.235360\pi$
$444$	2.37228	+	2.52434i	0.112583	+	0.119800i
$445$	−32.2337	−	55.8304i	−1.52802	−	2.64661i
$446$	−2.00000	−	3.46410i	−0.0947027	−	0.164030i
$447$	3.86141	+	4.10891i	0.182638	+	0.194345i
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	33.0000			1.55737			0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000			1.55737			0.778683	+	0.627417i	$0.215888\pi$
$450$	35.2921	+	23.4101i	1.66369	+	1.10356i
$451$	−6.35053			−0.299035
$452$	2.18614	−	3.78651i	0.102827	−	0.178102i
$453$	4.55842	−	15.1186i	0.214173	−	0.710333i
$454$	−6.12772	−	10.6135i	−0.287588	−	0.498117i
$455$	−4.37228	−	7.57301i	−0.204976	−	0.355028i
$456$	8.43070	−	1.98072i	0.394804	−	0.0927556i
$457$	17.7337	−	30.7156i	0.829547	−	1.43682i	−0.0688472	−	0.997627i	$-0.521932\pi$
$457$	17.7337	−	30.7156i	0.829547	−	1.43682i	0.898394	−	0.439190i	$-0.144735\pi$
$458$	2.88316			0.134721
$459$	−5.48913	+	4.55134i	−0.256210	+	0.212438i
$460$	−7.11684			−0.331825
$461$	−1.06930	+	1.85208i	−0.0498021	+	0.0862598i	−0.889852	−	0.456250i	$-0.849192\pi$
$461$	−1.06930	+	1.85208i	−0.0498021	+	0.0862598i	0.840050	+	0.542509i	$0.182526\pi$
$462$	−2.31386	+	0.543620i	−0.107650	+	0.0252915i
$463$	11.5584	+	20.0198i	0.537165	+	0.930398i	0.999055	+	0.0434604i	$0.0138382\pi$
$463$	11.5584	+	20.0198i	0.537165	+	0.930398i	−0.461890	+	0.886937i	$0.652828\pi$
$464$	4.37228	+	7.57301i	0.202978	+	0.351568i
$465$	4.37228	−	14.5012i	0.202760	−	0.672478i
$466$	−0.127719	+	0.221215i	−0.00591645	+	0.0102476i
$467$	33.0951			1.53146			0.765729	−	0.643163i	$-0.222378\pi$
$467$	33.0951			1.53146			0.765729	+	0.643163i	$0.222378\pi$
$468$	−0.372281	+	5.98844i	−0.0172087	+	0.276816i
$469$	−2.11684			−0.0977468
$470$		0			0
$471$	10.8139	+	11.5070i	0.498276	+	0.530214i
$472$	−5.05842	−	8.76144i	−0.232833	−	0.403278i
$473$	−5.56930	−	9.64630i	−0.256077	−	0.443538i
$474$	6.06930	+	6.45832i	0.278772	+	0.296641i
$475$	−35.2921	+	61.1277i	−1.61931	+	2.80473i
$476$	1.37228			0.0628984
$477$	−23.4891	+	11.6819i	−1.07549	+	0.534879i
$478$	−9.86141			−0.451050
$479$	−16.3723	+	28.3576i	−0.748069	+	1.29569i	0.200679	+	0.979657i	$0.435685\pi$
$479$	−16.3723	+	28.3576i	−0.748069	+	1.29569i	−0.948747	+	0.316036i	$0.897648\pi$
$480$	−2.18614	+	7.25061i	−0.0997832	+	0.330943i
$481$	−2.00000	−	3.46410i	−0.0911922	−	0.157949i
$482$	9.05842	+	15.6896i	0.412600	+	0.714644i
$483$	2.74456	−	0.644810i	0.124882	−	0.0293399i
$484$	4.55842	−	7.89542i	0.207201	−	0.358883i
$485$	−35.4891			−1.61148
$486$	9.18614	+	12.5942i	0.416692	+	0.571286i
$487$	35.3505			1.60189			0.800943	−	0.598741i	$-0.204332\pi$
$487$	35.3505			1.60189			0.800943	+	0.598741i	$0.204332\pi$
$488$	1.55842	−	2.69927i	0.0705464	−	0.122190i
$489$	30.7446	−	7.22316i	1.39032	−	0.326642i
$490$	2.18614	+	3.78651i	0.0987598	+	0.171057i
$491$	12.6861	+	21.9730i	0.572518	+	0.991629i	0.996306	+	0.0858685i	$0.0273665\pi$
$491$	12.6861	+	21.9730i	0.572518	+	0.991629i	−0.423789	+	0.905761i	$0.639300\pi$
$492$	2.31386	−	7.67420i	0.104317	−	0.345980i
$493$	6.00000	−	10.3923i	0.270226	−	0.468046i
$494$	−10.0000			−0.449921
$495$	−16.1168	+	8.01544i	−0.724398	+	0.360267i
$496$	2.00000			0.0898027
$497$	3.55842	−	6.16337i	0.159617	−	0.276465i
$498$	−20.7446	−	22.0742i	−0.929586	−	0.989170i
$499$	−9.05842	−	15.6896i	−0.405511	−	0.702365i	0.588870	−	0.808228i	$-0.299573\pi$
$499$	−9.05842	−	15.6896i	−0.405511	−	0.702365i	−0.994381	+	0.105863i	$0.966240\pi$
$500$	−19.9307	−	34.5210i	−0.891328	−	1.54383i
$501$	−6.51087	−	6.92820i	−0.290884	−	0.309529i
$502$	−4.50000	+	7.79423i	−0.200845	+	0.347873i
$503$	−32.2337			−1.43723			−0.718615	−	0.695409i	$-0.755223\pi$
$503$	−32.2337			−1.43723			−0.718615	+	0.695409i	$0.755223\pi$
$504$	0.186141	−	2.99422i	0.00829136	−	0.133373i
$505$	7.11684			0.316695
$506$	1.11684	−	1.93443i	0.0496498	−	0.0859959i
$507$	−4.50000	+	14.9248i	−0.199852	+	0.662834i
$508$	−1.55842	−	2.69927i	−0.0691438	−	0.119761i
$509$	14.4891	+	25.0959i	0.642219	+	1.11236i	0.984936	+	0.172918i	$0.0553194\pi$
$509$	14.4891	+	25.0959i	0.642219	+	1.11236i	−0.342717	+	0.939439i	$0.611347\pi$
$510$	10.1168	−	2.37686i	0.447981	−	0.105249i
$511$	−6.05842	+	10.4935i	−0.268009	+	0.464205i
$512$	−1.00000			−0.0441942
$513$	−20.0000	+	16.5831i	−0.883022	+	0.732163i
$514$	6.86141			0.302644
$515$	21.8614	−	37.8651i	0.963329	−	1.66853i
$516$	13.6861	−	3.21543i	0.602499	−	0.141552i
$517$		0			0
$518$	1.00000	+	1.73205i	0.0439375	+	0.0761019i
$519$	−3.00000	+	9.94987i	−0.131685	+	0.436751i
$520$	4.37228	−	7.57301i	0.191737	−	0.332099i
$521$	−24.8614			−1.08920			−0.544599	−	0.838697i	$-0.683318\pi$
$521$	−24.8614			−1.08920			−0.544599	+	0.838697i	$0.683318\pi$
$522$	−21.8614	−	14.5012i	−0.956848	−	0.634701i
$523$	−35.1168			−1.53555			−0.767776	−	0.640718i	$-0.778637\pi$
$523$	−35.1168			−1.53555			−0.767776	+	0.640718i	$0.778637\pi$
$524$	0.813859	−	1.40965i	0.0355536	−	0.0615807i
$525$	16.7446	+	17.8178i	0.730793	+	0.777634i
$526$	3.81386	+	6.60580i	0.166292	+	0.288026i
$527$	−1.37228	−	2.37686i	−0.0597775	−	0.103538i
$528$	−1.62772	−	1.73205i	−0.0708374	−	0.0753778i
$529$	10.1753	−	17.6241i	0.442403	−	0.766264i
$530$	38.2337			1.66077
$531$	25.2921	+	16.7769i	1.09758	+	0.728055i
$532$	5.00000			0.216777
$533$	−4.62772	+	8.01544i	−0.200449	+	0.347187i
$534$	−7.37228	+	24.4511i	−0.319030	+	1.05810i
$535$	16.1168	+	27.9152i	0.696792	+	1.20688i
$536$	−1.05842	−	1.83324i	−0.0457169	−	0.0791839i
$537$	−5.48913	+	1.28962i	−0.236873	+	0.0556512i
$538$	−0.813859	+	1.40965i	−0.0350880	+	0.0607741i
$539$	−1.37228			−0.0591083
$540$	−3.81386	−	22.3966i	−0.164122	−	0.963798i
$541$	−6.23369			−0.268007			−0.134004	−	0.990981i	$-0.542783\pi$
$541$	−6.23369			−0.268007			−0.134004	+	0.990981i	$0.542783\pi$
$542$	8.11684	−	14.0588i	0.348648	−	0.603877i
$543$	−1.48913	+	0.349857i	−0.0639045	+	0.0150138i
$544$	0.686141	+	1.18843i	0.0294180	+	0.0509535i
$545$	−30.6060	−	53.0111i	−1.31102	−	2.27075i
$546$	−1.00000	+	3.31662i	−0.0427960	+	0.141938i
$547$	−9.05842	+	15.6896i	−0.387310	+	0.670841i	−0.992087	−	0.125554i	$-0.959929\pi$
$547$	−9.05842	+	15.6896i	−0.387310	+	0.670841i	0.604777	+	0.796395i	$0.293262\pi$
$548$	10.6277			0.453994
$549$	−0.580171	+	9.33252i	−0.0247611	+	0.398302i
$550$	19.3723			0.826037
$551$	21.8614	−	37.8651i	0.931327	−	1.61311i
$552$	1.93070	+	2.05446i	0.0821762	+	0.0874434i
$553$	2.55842	+	4.43132i	0.108795	+	0.188439i
$554$	−6.11684	−	10.5947i	−0.259880	−	0.450125i
$555$	10.3723	+	11.0371i	0.440279	+	0.468499i
$556$	−6.61684	+	11.4607i	−0.280617	+	0.486042i
$557$	29.4891			1.24949			0.624747	−	0.780827i	$-0.285202\pi$
$557$	29.4891			1.24949			0.624747	+	0.780827i	$0.285202\pi$
$558$	−5.37228	+	2.67181i	−0.227427	+	0.113107i
$559$	−16.2337			−0.686612
$560$	−2.18614	+	3.78651i	−0.0923813	+	0.160009i
$561$	−0.941578	+	3.12286i	−0.0397535	+	0.131847i
$562$	8.18614	+	14.1788i	0.345312	+	0.598097i
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	0.832684	−	0.553748i	$-0.186803\pi$
$563$	−1.50000	−	2.59808i	−0.0632175	−	0.109496i	−0.895902	+	0.444252i	$0.853470\pi$
$564$		0			0
$565$	9.55842	−	16.5557i	0.402126	−	0.696502i
$566$	−27.1168			−1.13981
$567$	3.50000	+	8.29156i	0.146986	+	0.348213i
$568$	7.11684			0.298616
$569$	−8.05842	+	13.9576i	−0.337827	+	0.585133i	−0.984024	−	0.178038i	$-0.943025\pi$
$569$	−8.05842	+	13.9576i	−0.337827	+	0.585133i	0.646197	+	0.763171i	$0.276358\pi$
$570$	36.8614	−	8.66025i	1.54395	−	0.362738i
$571$	11.1753	+	19.3561i	0.467670	+	0.810029i	0.999318	−	0.0369371i	$-0.0117601\pi$
$571$	11.1753	+	19.3561i	0.467670	+	0.810029i	−0.531647	+	0.846966i	$0.678427\pi$
$572$	1.37228	+	2.37686i	0.0573780	+	0.0993815i
$573$	−9.55842	+	31.7017i	−0.399309	+	1.32436i
$574$	2.31386	−	4.00772i	0.0965786	−	0.167279i
$575$	−22.9783			−0.958259
$576$	2.68614	−	1.33591i	0.111923	−	0.0556628i
$577$	9.88316			0.411441			0.205721	−	0.978611i	$-0.434046\pi$
$577$	9.88316			0.411441			0.205721	+	0.978611i	$0.434046\pi$
$578$	−7.55842	+	13.0916i	−0.314389	+	0.544538i
$579$	−8.30298	−	8.83518i	−0.345060	−	0.367178i
$580$	19.1168	+	33.1113i	0.793784	+	1.37487i
$581$	−8.74456	−	15.1460i	−0.362786	−	0.628363i
$582$	9.62772	+	10.2448i	0.399082	+	0.424662i
$583$	−6.00000	+	10.3923i	−0.248495	+	0.430405i
$584$	−12.1168			−0.501399
$585$	−1.62772	+	26.1831i	−0.0672979	+	1.08254i
$586$	10.3723			0.428475
$587$	−7.24456	+	12.5480i	−0.299015	+	0.517909i	−0.975911	−	0.218170i	$-0.929991\pi$
$587$	−7.24456	+	12.5480i	−0.299015	+	0.517909i	0.676896	+	0.736079i	$0.263325\pi$
$588$	0.500000	−	1.65831i	0.0206197	−	0.0683877i
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$	−22.1168	−	38.3075i	−0.910536	−	1.57709i
$591$	10.1168	−	2.37686i	0.416151	−	0.0977710i
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	14.7446			0.605487			0.302743	−	0.953072i	$-0.402098\pi$
$593$	14.7446			0.605487			0.302743	+	0.953072i	$0.402098\pi$
$594$	6.68614	+	2.47805i	0.274336	+	0.101676i
$595$	6.00000			0.245976
$596$	−1.62772	+	2.81929i	−0.0666740	+	0.115483i
$597$	16.8614	−	3.96143i	0.690091	−	0.162131i
$598$	−1.62772	−	2.81929i	−0.0665624	−	0.115289i
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$	−7.05842	+	23.4101i	−0.288159	+	0.955715i
$601$	−12.0584	+	20.8858i	−0.491873	+	0.851950i	−0.999956	−	0.00935863i	$-0.997021\pi$
$601$	−12.0584	+	20.8858i	−0.491873	+	0.851950i	0.508083	+	0.861308i	$0.330354\pi$
$602$	8.11684			0.330818
$603$	5.29211	+	3.51039i	0.215511	+	0.142954i
$604$	9.11684			0.370959
$605$	19.9307	−	34.5210i	0.810298	−	1.40348i
$606$	−1.93070	−	2.05446i	−0.0784295	−	0.0834566i
$607$	−11.1168	−	19.2549i	−0.451219	−	0.781534i	0.547243	−	0.836974i	$-0.315677\pi$
$607$	−11.1168	−	19.2549i	−0.451219	−	0.781534i	−0.998462	+	0.0554398i	$0.982344\pi$
$608$	2.50000	+	4.33013i	0.101388	+	0.175610i
$609$	−10.3723	−	11.0371i	−0.420306	−	0.447246i
$610$	6.81386	−	11.8020i	0.275885	−	0.477847i
$611$		0			0
$612$	−3.43070	−	2.27567i	−0.138678	−	0.0919886i
$613$	−36.2337			−1.46346			−0.731732	−	0.681592i	$-0.761288\pi$
$613$	−36.2337			−1.46346			−0.731732	+	0.681592i	$0.761288\pi$
$614$	−6.50000	+	11.2583i	−0.262319	+	0.454349i
$615$	10.1168	−	33.5538i	0.407951	−	1.35302i
$616$	−0.686141	−	1.18843i	−0.0276454	−	0.0478832i
$617$	−9.43070	−	16.3345i	−0.379666	−	0.657600i	0.611348	−	0.791362i	$-0.290628\pi$
$617$	−9.43070	−	16.3345i	−0.379666	−	0.657600i	−0.991014	+	0.133762i	$0.957294\pi$
$618$	−16.8614	+	3.96143i	−0.678265	+	0.159352i
$619$	−22.7337	+	39.3759i	−0.913744	+	1.58265i	−0.105014	+	0.994471i	$0.533489\pi$
$619$	−22.7337	+	39.3759i	−0.913744	+	1.58265i	−0.808730	+	0.588180i	$0.799844\pi$
$620$	8.74456			0.351190
$621$	−7.93070	−	2.93932i	−0.318248	−	0.117951i
$622$	−8.23369			−0.330141
$623$	−7.37228	+	12.7692i	−0.295364	+	0.511586i
$624$	−3.37228	+	0.792287i	−0.134999	+	0.0317169i
$625$	−51.8505	−	89.8078i	−2.07402	−	3.59231i
$626$	−10.0584	−	17.4217i	−0.402015	−	0.696311i
$627$	−3.43070	+	11.3784i	−0.137009	+	0.454408i
$628$	−4.55842	+	7.89542i	−0.181901	+	0.315061i
$629$	2.74456			0.109433
$630$	0.813859	−	13.0916i	0.0324249	−	0.521581i
$631$	−37.3505			−1.48690			−0.743451	−	0.668791i	$-0.766812\pi$
$631$	−37.3505			−1.48690			−0.743451	+	0.668791i	$0.766812\pi$
$632$	−2.55842	+	4.43132i	−0.101769	+	0.176268i
$633$	−18.9783	−	20.1947i	−0.754318	−	0.802667i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$	−6.81386	−	11.8020i	−0.270400	−	0.468346i
$636$	−10.3723	−	11.0371i	−0.411288	−	0.437650i
$637$	−1.00000	+	1.73205i	−0.0396214	+	0.0686264i
$638$	−12.0000			−0.475085
$639$	−19.1168	+	9.50744i	−0.756251	+	0.376109i
$640$	−4.37228			−0.172830
$641$	−17.1060	+	29.6284i	−0.675645	+	1.17025i	0.300635	+	0.953739i	$0.402802\pi$
$641$	−17.1060	+	29.6284i	−0.675645	+	1.17025i	−0.976280	+	0.216512i	$0.930532\pi$
$642$	3.68614	−	12.2255i	0.145480	−	0.482504i
$643$	−13.1753	−	22.8202i	−0.519582	−	0.899942i	−0.999741	−	0.0227606i	$-0.992754\pi$
$643$	−13.1753	−	22.8202i	−0.519582	−	0.899942i	0.480159	−	0.877181i	$-0.340579\pi$
$644$	0.813859	+	1.40965i	0.0320706	+	0.0555478i
$645$	59.8397	−	14.0588i	2.35618	−	0.553564i
$646$	3.43070	−	5.94215i	0.134979	−	0.233791i
$647$	5.48913			0.215800			0.107900	−	0.994162i	$-0.465587\pi$
$647$	5.48913			0.215800			0.107900	+	0.994162i	$0.465587\pi$
$648$	−5.43070	+	7.17687i	−0.213338	+	0.281934i
$649$	13.8832			0.544962
$650$	14.1168	−	24.4511i	0.553708	−	0.959051i
$651$	−3.37228	+	0.792287i	−0.132170	+	0.0310522i
$652$	9.11684	+	15.7908i	0.357043	+	0.618417i
$653$	13.3723	+	23.1615i	0.523298	+	0.906378i	0.999632	+	0.0271143i	$0.00863179\pi$
$653$	13.3723	+	23.1615i	0.523298	+	0.906378i	−0.476335	+	0.879264i	$0.658035\pi$
$654$	−7.00000	+	23.2164i	−0.273722	+	0.907832i
$655$	3.55842	−	6.16337i	0.139039	−	0.240823i
$656$	4.62772			0.180682
$657$	32.5475	−	16.1870i	1.26980	−	0.631514i
$658$		0			0
$659$	10.3723	−	17.9653i	0.404047	−	0.699829i	−0.590163	−	0.807284i	$-0.700937\pi$
$659$	10.3723	−	17.9653i	0.404047	−	0.699829i	0.994210	+	0.107454i	$0.0342700\pi$
$660$	−7.11684	−	7.57301i	−0.277023	−	0.294779i
$661$	−13.5584	−	23.4839i	−0.527361	−	0.913417i	−0.999491	−	0.0318879i	$-0.989848\pi$
$661$	−13.5584	−	23.4839i	−0.527361	−	0.913417i	0.472130	−	0.881529i	$-0.343485\pi$
$662$	11.1168	+	19.2549i	0.432068	+	0.748364i
$663$	3.25544	+	3.46410i	0.126431	+	0.134535i
$664$	8.74456	−	15.1460i	0.339355	−	0.587780i
$665$	21.8614			0.847749
$666$	0.372281	−	5.98844i	0.0144256	−	0.232047i
$667$	14.2337			0.551131
$668$	2.74456	−	4.75372i	0.106190	−	0.183927i
$669$	−2.00000	+	6.63325i	−0.0773245	+	0.256456i
$670$	−4.62772	−	8.01544i	−0.178784	−	0.309664i
$671$	2.13859	+	3.70415i	0.0825595	+	0.142997i
$672$	1.68614	−	0.396143i	0.0650443	−	0.0152816i
$673$	1.44158	−	2.49689i	0.0555687	−	0.0962479i	−0.836903	−	0.547351i	$-0.815636\pi$
$673$	1.44158	−	2.49689i	0.0555687	−	0.0962479i	0.892472	+	0.451103i	$0.148969\pi$
$674$	8.11684			0.312649
$675$	−12.3139	−	72.3123i	−0.473961	−	2.78330i
$676$	−9.00000			−0.346154
$677$	−17.2337	+	29.8496i	−0.662344	+	1.14721i	0.317654	+	0.948207i	$0.397105\pi$
$677$	−17.2337	+	29.8496i	−0.662344	+	1.14721i	−0.979998	+	0.199007i	$0.936228\pi$
$678$	−7.37228	+	1.73205i	−0.283131	+	0.0665190i
$679$	4.05842	+	7.02939i	0.155748	+	0.269763i
$680$	3.00000	+	5.19615i	0.115045	+	0.199263i
$681$	−6.12772	+	20.3233i	−0.234815	+	0.778792i
$682$	−1.37228	+	2.37686i	−0.0525474	+	0.0910147i
$683$	29.8397			1.14178			0.570891	−	0.821026i	$-0.306598\pi$
$683$	29.8397			1.14178			0.570891	+	0.821026i	$0.306598\pi$
$684$	−12.5000	−	8.29156i	−0.477949	−	0.317036i
$685$	46.4674			1.77543
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−3.41983	−	3.63903i	−0.130475	−	0.138838i
$688$	4.05842	+	7.02939i	0.154726	+	0.267993i
$689$	8.74456	+	15.1460i	0.333141	+	0.577018i
$690$	8.44158	+	8.98266i	0.321365	+	0.341964i
$691$	11.5584	−	20.0198i	0.439703	−	0.761588i	−0.557963	−	0.829866i	$-0.688417\pi$
$691$	11.5584	−	20.0198i	0.439703	−	0.761588i	0.997666	+	0.0682775i	$0.0217503\pi$
$692$	−6.00000			−0.228086
$693$	3.43070	+	2.27567i	0.130322	+	0.0864456i
$694$	10.1168			0.384030
$695$	−28.9307	+	50.1094i	−1.09740	+	1.90076i
$696$	4.37228	−	14.5012i	0.165731	−	0.549667i
$697$	−3.17527	−	5.49972i	−0.120272	−	0.208317i
$698$	−11.0000	−	19.0526i	−0.416356	−	0.721150i
$699$	0.430703	−	0.101190i	0.0162907	−	0.00382735i
$700$	−7.05842	+	12.2255i	−0.266783	+	0.462082i
$701$	−38.2337			−1.44407			−0.722033	−	0.691858i	$-0.756792\pi$
$701$	−38.2337			−1.44407			−0.722033	+	0.691858i	$0.756792\pi$
$702$	8.00000	−	6.63325i	0.301941	−	0.250356i
$703$	10.0000			0.377157
$704$	0.686141	−	1.18843i	0.0258599	−	0.0447907i
$705$		0			0
$706$	−6.68614	−	11.5807i	−0.251636	−	0.435847i
$707$	−0.813859	−	1.40965i	−0.0306083	−	0.0530152i
$708$	−5.05842	+	16.7769i	−0.190107	+	0.630514i
$709$	−22.0000	+	38.1051i	−0.826227	+	1.43107i	0.0747503	+	0.997202i	$0.476184\pi$
$709$	−22.0000	+	38.1051i	−0.826227	+	1.43107i	−0.900978	+	0.433865i	$0.857149\pi$
$710$	31.1168			1.16779
$711$	0.952453	−	15.3210i	0.0357198	−	0.574581i
$712$	−14.7446			−0.552576
$713$	1.62772	−	2.81929i	0.0609585	−	0.105583i
$714$	−1.62772	−	1.73205i	−0.0609158	−	0.0648204i
$715$	6.00000	+	10.3923i	0.224387	+	0.388650i
$716$	−1.62772	−	2.81929i	−0.0608307	−	0.105362i
$717$	11.6970	+	12.4468i	0.436833	+	0.464833i
$718$	10.9307	−	18.9325i	0.407930	−	0.706556i
$719$	2.74456			0.102355			0.0511775	−	0.998690i	$-0.483703\pi$
$719$	2.74456			0.102355			0.0511775	+	0.998690i	$0.483703\pi$
$720$	11.7446	−	5.84096i	0.437694	−	0.217680i
$721$	−10.0000			−0.372419
$722$	3.00000	−	5.19615i	0.111648	−	0.193381i
$723$	9.05842	−	30.0434i	0.336886	−	1.11733i
$724$	−0.441578	−	0.764836i	−0.0164111	−	0.0284249i
$725$	61.7228	+	106.907i	2.29233	+	3.97043i
$726$	−15.3723	+	3.61158i	−0.570519	+	0.134038i
$727$	18.1168	−	31.3793i	0.671917	−	1.16379i	−0.305443	−	0.952210i	$-0.598805\pi$
$727$	18.1168	−	31.3793i	0.671917	−	1.16379i	0.977360	−	0.211583i	$-0.0678620\pi$
$728$	−2.00000			−0.0741249
$729$	5.00000	−	26.5330i	0.185185	−	0.982704i
$730$	−52.9783			−1.96081
$731$	5.56930	−	9.64630i	0.205988	−	0.356781i
$732$	−5.25544	+	1.23472i	−0.194247	+	0.0456365i
$733$	20.5584	+	35.6082i	0.759343	+	1.31522i	0.943186	+	0.332265i	$0.107813\pi$
$733$	20.5584	+	35.6082i	0.759343	+	1.31522i	−0.183844	+	0.982956i	$0.558854\pi$
$734$	−6.11684	−	10.5947i	−0.225777	−	0.391057i
$735$	2.18614	−	7.25061i	0.0806370	−	0.267443i
$736$	−0.813859	+	1.40965i	−0.0299993	+	0.0519602i
$737$	2.90491			0.107004
$738$	−12.4307	+	6.18220i	−0.457581	+	0.227570i
$739$	−8.11684			−0.298583			−0.149291	−	0.988793i	$-0.547699\pi$
$739$	−8.11684			−0.298583			−0.149291	+	0.988793i	$0.547699\pi$
$740$	−4.37228	+	7.57301i	−0.160728	+	0.278390i
$741$	11.8614	+	12.6217i	0.435740	+	0.463669i
$742$	−4.37228	−	7.57301i	−0.160511	−	0.278014i
$743$	6.86141	+	11.8843i	0.251721	+	0.435993i	0.964000	−	0.265904i	$-0.0856703\pi$
$743$	6.86141	+	11.8843i	0.251721	+	0.435993i	−0.712279	+	0.701896i	$0.752337\pi$
$744$	−2.37228	−	2.52434i	−0.0869721	−	0.0925467i
$745$	−7.11684	+	12.3267i	−0.260741	+	0.451617i
$746$	10.0000			0.366126
$747$	−3.25544	+	52.3663i	−0.119110	+	1.91598i
$748$	−1.88316			−0.0688550
$749$	3.68614	−	6.38458i	0.134689	−	0.233288i
$750$	−19.9307	+	66.1027i	−0.727766	+	2.41373i
$751$	8.55842	+	14.8236i	0.312301	+	0.540922i	0.978860	−	0.204531i	$-0.0655668\pi$
$751$	8.55842	+	14.8236i	0.312301	+	0.540922i	−0.666559	+	0.745452i	$0.732234\pi$
$752$		0			0
$753$	15.1753	−	3.56529i	0.553017	−	0.129926i
$754$	−8.74456	+	15.1460i	−0.318458	+	0.551586i
$755$	39.8614			1.45071
$756$	−4.00000	+	3.31662i	−0.145479	+	0.120624i
$757$	46.2337			1.68039			0.840196	−	0.542283i	$-0.182440\pi$
$757$	46.2337			1.68039			0.840196	+	0.542283i	$0.182440\pi$
$758$	−4.05842	+	7.02939i	−0.147409	+	0.255319i
$759$	−3.76631	+	0.884861i	−0.136708	+	0.0321184i
$760$	10.9307	+	18.9325i	0.396498	+	0.686755i
$761$	−17.7446	−	30.7345i	−0.643240	−	1.11412i	−0.984705	−	0.174230i	$-0.944256\pi$
$761$	−17.7446	−	30.7345i	−0.643240	−	1.11412i	0.341465	−	0.939894i	$-0.389077\pi$
$762$	−1.55842	+	5.16870i	−0.0564557	+	0.187242i
$763$	−7.00000	+	12.1244i	−0.253417	+	0.438931i
$764$	−19.1168			−0.691623
$765$	−15.0000	−	9.94987i	−0.542326	−	0.359738i
$766$	32.7446			1.18311
$767$	10.1168	−	17.5229i	0.365298	−	0.632715i
$768$	1.18614	+	1.26217i	0.0428012	+	0.0455446i
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	0.941984	−	0.335657i	$-0.108958\pi$
$769$	5.00000	+	8.66025i	0.180305	+	0.312297i	−0.761680	+	0.647954i	$0.775625\pi$
$770$	−3.00000	−	5.19615i	−0.108112	−	0.187256i
$771$	−8.13859	−	8.66025i	−0.293104	−	0.311891i
$772$	3.50000	−	6.06218i	0.125968	−	0.218183i
$773$	−39.8614			−1.43372			−0.716858	−	0.697220i	$-0.754420\pi$
$773$	−39.8614			−1.43372			−0.716858	+	0.697220i	$0.754420\pi$
$774$	−20.2921	−	13.4603i	−0.729385	−	0.483819i
$775$	28.2337			1.01418
$776$	−4.05842	+	7.02939i	−0.145689	+	0.252341i
$777$	1.00000	−	3.31662i	0.0358748	−	0.118983i
$778$	5.48913	+	9.50744i	0.196795	+	0.340858i
$779$	−11.5693	−	20.0386i	−0.414513	−	0.717958i
$780$	−14.7446	+	3.46410i	−0.527940	+	0.124035i
$781$	−4.88316	+	8.45787i	−0.174733	+	0.302647i
$782$	2.23369			0.0798765
$783$	7.62772	+	44.7933i	0.272592	+	1.60078i
$784$	1.00000			0.0357143
$785$	−19.9307	+	34.5210i	−0.711357	+	1.23211i
$786$	−2.74456	+	0.644810i	−0.0978953	+	0.0229996i
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	0.899468	−	0.436987i	$-0.143954\pi$
$787$	2.00000	+	3.46410i	0.0712923	+	0.123482i	−0.828176	+	0.560469i	$0.810621\pi$
$788$	3.00000	+	5.19615i	0.106871	+	0.185105i
$789$	3.81386	−	12.6491i	0.135777	−	0.450321i
$790$	−11.1861	+	19.3750i	−0.397985	+	0.689330i
$791$	−4.37228			−0.155460
$792$	−0.255437	+	4.10891i	−0.00907657	+	0.146004i
$793$	6.23369			0.221365
$794$	−11.0000	+	19.0526i	−0.390375	+	0.676150i
$795$	−45.3505	−	48.2574i	−1.60842	−	1.71151i
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	4.06930	+	7.04823i	0.144142	+	0.249661i	0.929052	−	0.369948i	$-0.120624\pi$
$797$	4.06930	+	7.04823i	0.144142	+	0.249661i	−0.784911	+	0.619609i	$0.787291\pi$
$798$	−5.93070	−	6.31084i	−0.209945	−	0.223401i
$799$		0			0
$800$	−14.1168			−0.499106
$801$	39.6060	−	19.6974i	1.39941	−	0.695972i
$802$	11.7446			0.414715
$803$	8.31386	−	14.4000i	0.293390	−	0.508166i
$804$	−1.05842	+	3.51039i	−0.0373277	+	0.123802i
$805$	3.55842	+	6.16337i	0.125418	+	0.217230i
$806$	2.00000	+	3.46410i	0.0704470	+	0.122018i
$807$	2.74456	−	0.644810i	0.0966132	−	0.0226984i
$808$	0.813859	−	1.40965i	0.0286315	−	0.0495912i
$809$	−6.86141			−0.241234			−0.120617	−	0.992699i	$-0.538487\pi$
$809$	−6.86141			−0.241234			−0.120617	+	0.992699i	$0.538487\pi$
$810$	−23.7446	+	31.3793i	−0.834299	+	1.10256i
$811$	42.1168			1.47892			0.739461	−	0.673199i	$-0.235080\pi$
$811$	42.1168			1.47892			0.739461	+	0.673199i	$0.235080\pi$
$812$	4.37228	−	7.57301i	0.153437	−	0.265761i
$813$	−27.3723	+	6.43087i	−0.959988	+	0.225540i
$814$	−1.37228	−	2.37686i	−0.0480984	−	0.0833089i
$815$	39.8614	+	69.0420i	1.39628	+	2.41844i
$816$	0.686141	−	2.27567i	0.0240197	−	0.0796644i
$817$	20.2921	−	35.1470i	0.709931	−	1.22964i
$818$	22.3505			0.781468
$819$	5.37228	−	2.67181i	0.187723	−	0.0933608i
$820$	20.2337			0.706591
$821$	1.88316	−	3.26172i	0.0657226	−	0.113835i	−0.831292	−	0.555836i	$-0.812398\pi$
$821$	1.88316	−	3.26172i	0.0657226	−	0.113835i	0.897014	+	0.442002i	$0.145731\pi$
$822$	−12.6060	−	13.4140i	−0.439684	−	0.467866i
$823$	6.11684	+	10.5947i	0.213220	+	0.369307i	0.952720	−	0.303848i	$-0.0982716\pi$
$823$	6.11684	+	10.5947i	0.213220	+	0.369307i	−0.739501	+	0.673156i	$0.764938\pi$
$824$	−5.00000	−	8.66025i	−0.174183	−	0.301694i
$825$	−22.9783	−	24.4511i	−0.800000	−	0.851278i
$826$	−5.05842	+	8.76144i	−0.176005	+	0.304850i
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$	0.302985	−	4.87375i	0.0105294	−	0.169374i
$829$	−13.7663			−0.478124			−0.239062	−	0.971004i	$-0.576840\pi$
$829$	−13.7663			−0.478124			−0.239062	+	0.971004i	$0.576840\pi$
$830$	38.2337	−	66.2227i	1.32711	−	2.29862i
$831$	−6.11684	+	20.2873i	−0.212191	+	0.703758i
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$	−0.686141	−	1.18843i	−0.0237734	−	0.0411767i
$834$	22.3139	−	5.24244i	0.772666	−	0.181531i
$835$	12.0000	−	20.7846i	0.415277	−	0.719281i
$836$	−6.86141			−0.237307
$837$	9.74456	+	3.61158i	0.336821	+	0.124834i
$838$	12.6060			0.435466
$839$	−2.74456	+	4.75372i	−0.0947528	+	0.164117i	−0.909505	−	0.415692i	$-0.863539\pi$
$839$	−2.74456	+	4.75372i	−0.0947528	+	0.164117i	0.814753	+	0.579809i	$0.196873\pi$
$840$	7.37228	−	1.73205i	0.254368	−	0.0597614i
$841$	−23.7337	−	41.1080i	−0.818403	−	1.41752i
$842$	17.1168	+	29.6472i	0.589885	+	1.02171i
$843$	8.18614	−	27.1504i	0.281946	−	0.935108i
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$	−39.3505			−1.35370
$846$		0			0
$847$	−9.11684			−0.313258
$848$	4.37228	−	7.57301i	0.150145	−	0.260058i
$849$	32.1644	+	34.2260i	1.10388	+	1.17463i
$850$	9.68614	+	16.7769i	0.332232	+	0.575443i
$851$	1.62772	+	2.81929i	0.0557975	+	0.0966441i
$852$	−8.44158	−	8.98266i	−0.289204	−	0.307741i
$853$	17.5584	−	30.4121i	0.601189	−	1.04129i	−0.391452	−	0.920198i	$-0.628027\pi$
$853$	17.5584	−	30.4121i	0.601189	−	1.04129i	0.992641	−	0.121091i	$-0.0386394\pi$
$854$	−3.11684			−0.106656
$855$	−54.6535	−	36.2530i	−1.86911	−	1.23983i
$856$	7.37228			0.251979
$857$	19.9783	−	34.6033i	0.682444	−	1.18203i	−0.291789	−	0.956483i	$-0.594250\pi$
$857$	19.9783	−	34.6033i	0.682444	−	1.18203i	0.974233	−	0.225545i	$-0.0724163\pi$
$858$	1.37228	−	4.55134i	0.0468489	−	0.155380i
$859$	−16.9416	−	29.3437i	−0.578039	−	1.00119i	−0.995704	−	0.0925921i	$-0.970485\pi$
$859$	−16.9416	−	29.3437i	−0.578039	−	1.00119i	0.417665	−	0.908601i	$-0.362849\pi$
$860$	17.7446	+	30.7345i	0.605085	+	1.04804i
$861$	−7.80298	+	1.83324i	−0.265925	+	0.0624767i
$862$	−3.25544	+	5.63858i	−0.110881	+	0.192051i
$863$	9.86141			0.335686			0.167843	−	0.985814i	$-0.446320\pi$
$863$	9.86141			0.335686			0.167843	+	0.985814i	$0.446320\pi$
$864$	−4.87228	−	1.80579i	−0.165758	−	0.0614342i
$865$	−26.2337			−0.891972
$866$	−10.0584	+	17.4217i	−0.341799	+	0.592013i
$867$	25.4891	−	5.98844i	0.865656	−	0.203378i
$868$	−1.00000	−	1.73205i	−0.0339422	−	0.0587896i
$869$	−3.51087	−	6.08101i	−0.119098	−	0.206284i
$870$	19.1168	−	63.4034i	0.648122	−	2.14958i
$871$	2.11684	−	3.66648i	0.0717265	−	0.124234i
$872$	−14.0000			−0.474100
$873$	1.51087	−	24.3036i	0.0511354	−	0.822553i
$874$	8.13859			0.275292
$875$	−19.9307	+	34.5210i	−0.673781	+	1.16702i
$876$	14.3723	+	15.2935i	0.485594	+	0.516720i
$877$	29.3505	+	50.8366i	0.991097	+	1.71663i	0.610852	+	0.791744i	$0.290827\pi$
$877$	29.3505	+	50.8366i	0.991097	+	1.71663i	0.380245	+	0.924886i	$0.375840\pi$
$878$	4.00000	+	6.92820i	0.134993	+	0.233816i
$879$	−12.3030	−	13.0916i	−0.414969	−	0.441568i
$880$	3.00000	−	5.19615i	0.101130	−	0.175162i
$881$	−20.2337			−0.681690			−0.340845	−	0.940119i	$-0.610713\pi$
$881$	−20.2337			−0.681690			−0.340845	+	0.940119i	$0.610713\pi$
$882$	−2.68614	+	1.33591i	−0.0904471	+	0.0449823i
$883$	−40.3505			−1.35790			−0.678952	−	0.734183i	$-0.737565\pi$
$883$	−40.3505			−1.35790			−0.678952	+	0.734183i	$0.737565\pi$
$884$	−1.37228	+	2.37686i	−0.0461548	+	0.0799425i
$885$	−22.1168	+	73.3533i	−0.743450	+	2.46574i
$886$	−20.0584	−	34.7422i	−0.673876	−	1.16719i
$887$	−12.8614	−	22.2766i	−0.431844	−	0.747975i	0.565188	−	0.824962i	$-0.308803\pi$
$887$	−12.8614	−	22.2766i	−0.431844	−	0.747975i	−0.997032	+	0.0769865i	$0.975470\pi$
$888$	3.37228	−	0.792287i	0.113166	−	0.0265874i
$889$	−1.55842	+	2.69927i	−0.0522678	+	0.0905305i
$890$	−64.4674			−2.16095
$891$	−4.80298	−	11.3784i	−0.160906	−	0.381189i
$892$	−4.00000			−0.133930
$893$		0			0
$894$	5.48913	−	1.28962i	0.183584	−	0.0431314i
$895$	−7.11684	−	12.3267i	−0.237890	−	0.412037i
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$	−1.62772	+	5.39853i	−0.0543479	+	0.180252i
$898$	16.5000	−	28.5788i	0.550612	−	0.953688i
$899$	−17.4891			−0.583295
$900$	37.9198	−	18.8588i	1.26399	−	0.628627i
$901$	−12.0000			−0.399778
$902$	−3.17527	+	5.49972i	−0.105725	+	0.183121i
$903$	−9.62772	−	10.2448i	−0.320390	−	0.340927i
$904$	−2.18614	−	3.78651i	−0.0727100	−	0.125937i
$905$	−1.93070	−	3.34408i	−0.0641787	−	0.111161i
$906$	−10.8139	−	11.5070i	−0.359266	−	0.382294i
$907$	13.0584	−	22.6179i	0.433598	−	0.751013i	−0.563582	−	0.826060i	$-0.690577\pi$
$907$	13.0584	−	22.6179i	0.433598	−	0.751013i	0.997180	+	0.0750466i	$0.0239105\pi$
$908$	−12.2554			−0.406711
$909$	−0.302985	+	4.87375i	−0.0100494	+	0.161652i
$910$	−8.74456			−0.289879
$911$	18.8139	−	32.5866i	0.623331	−	1.07964i	−0.365530	−	0.930800i	$-0.619112\pi$
$911$	18.8139	−	32.5866i	0.623331	−	1.07964i	0.988861	−	0.148841i	$-0.0475544\pi$
$912$	2.50000	−	8.29156i	0.0827833	−	0.274561i
$913$	12.0000	+	20.7846i	0.397142	+	0.687870i
$914$	−17.7337	−	30.7156i	−0.586578	−	1.01598i
$915$	−22.9783	+	5.39853i	−0.759638	+	0.178470i
$916$	1.44158	−	2.49689i	0.0476311	−	0.0824994i
$917$	−1.62772			−0.0537520
$918$	1.19702	+	7.02939i	0.0395074	+	0.232005i
$919$	−47.1168			−1.55424			−0.777121	−	0.629352i	$-0.783321\pi$
$919$	−47.1168			−1.55424			−0.777121	+	0.629352i	$0.783321\pi$
$920$	−3.55842	+	6.16337i	−0.117318	+	0.203200i
$921$	21.9198	−	5.14987i	0.722283	−	0.169694i
$922$	1.06930	+	1.85208i	0.0352154	+	0.0609949i
$923$	7.11684	+	12.3267i	0.234254	+	0.405739i
$924$	−0.686141	+	2.27567i	−0.0225724	+	0.0748641i
$925$	−14.1168	+	24.4511i	−0.464159	+	0.803947i
$926$	23.1168			0.759667
$927$	25.0000	+	16.5831i	0.821108	+	0.544661i
$928$	8.74456			0.287054
$929$	−22.1168	+	38.3075i	−0.725630	+	1.25683i	0.233084	+	0.972457i	$0.425118\pi$
$929$	−22.1168	+	38.3075i	−0.725630	+	1.25683i	−0.958714	+	0.284372i	$0.908215\pi$
$930$	−10.3723	−	11.0371i	−0.340121	−	0.361921i
$931$	−2.50000	−	4.33013i	−0.0819342	−	0.141914i
$932$	0.127719	+	0.221215i	0.00418356	+	0.00724615i
$933$	9.76631	+	10.3923i	0.319735	+	0.340229i
$934$	16.5475	−	28.6612i	0.541452	−	0.937823i
$935$	−8.23369			−0.269270
$936$	5.00000	+	3.31662i	0.163430	+	0.108407i
$937$	30.4674			0.995326			0.497663	−	0.867371i	$-0.334192\pi$
$937$	30.4674			0.995326			0.497663	+	0.867371i	$0.334192\pi$
$938$	−1.05842	+	1.83324i	−0.0345587	+	0.0598574i
$939$	−10.0584	+	33.3600i	−0.328244	+	1.08866i
$940$		0			0
$941$	−9.55842	−	16.5557i	−0.311596	−	0.539699i	0.667112	−	0.744957i	$-0.267530\pi$
$941$	−9.55842	−	16.5557i	−0.311596	−	0.539699i	−0.978708	+	0.205258i	$0.934197\pi$
$942$	15.3723	−	3.61158i	0.500856	−	0.117672i
$943$	3.76631	−	6.52344i	0.122648	−	0.212433i
$944$	−10.1168			−0.329275
$945$	−17.4891	+	14.5012i	−0.568921	+	0.471725i
$946$	−11.1386			−0.362147
$947$	−17.0584	+	29.5461i	−0.554324	+	0.960118i	0.443632	+	0.896209i	$0.353690\pi$
$947$	−17.0584	+	29.5461i	−0.554324	+	0.960118i	−0.997956	+	0.0639085i	$0.979643\pi$
$948$	8.62772	−	2.02700i	0.280215	−	0.0658340i
$949$	−12.1168	−	20.9870i	−0.393329	−	0.681267i
$950$	35.2921	+	61.1277i	1.14503	+	1.98325i
$951$	−3.00000	+	9.94987i	−0.0972817	+	0.322647i
$952$	0.686141	−	1.18843i	0.0222379	−	0.0385173i
$953$	28.1168			0.910794			0.455397	−	0.890288i	$-0.349497\pi$
$953$	28.1168			0.910794			0.455397	+	0.890288i	$0.349497\pi$
$954$	−1.62772	+	26.1831i	−0.0526993	+	0.847711i
$955$	−83.5842			−2.70472
$956$	−4.93070	+	8.54023i	−0.159470	+	0.276211i
$957$	14.2337	+	15.1460i	0.460110	+	0.489602i
$958$	16.3723	+	28.3576i	0.528964	+	0.916193i
$959$	−5.31386	−	9.20387i	−0.171593	−	0.297209i
$960$	5.18614	+	5.51856i	0.167382	+	0.178111i
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−4.00000			−0.128965
$963$	−19.8030	+	9.84868i	−0.638142	+	0.317369i
$964$	18.1168			0.583504
$965$	15.3030	−	26.5055i	0.492621	−	0.853244i
$966$	0.813859	−	2.69927i	0.0261855	−	0.0868475i
$967$	−15.4416	−	26.7456i	−0.496568	−	0.860080i	0.503424	−	0.864039i	$-0.332073\pi$
$967$	−15.4416	−	26.7456i	−0.496568	−	0.860080i	−0.999992	+	0.00395879i	$0.998740\pi$
$968$	−4.55842	−	7.89542i	−0.146513	−	0.253768i
$969$	−11.5693	+	2.71810i	−0.371659	+	0.0873180i
$970$	−17.7446	+	30.7345i	−0.569744	+	0.986825i
$971$	1.62772			0.0522360			0.0261180	−	0.999659i	$-0.491685\pi$
$971$	1.62772			0.0522360			0.0261180	+	0.999659i	$0.491685\pi$
$972$	15.5000	−	1.65831i	0.497163	−	0.0531904i
$973$	13.2337			0.424253
$974$	17.6753	−	30.6145i	0.566352	−	0.980951i
$975$	−47.6060	+	11.1846i	−1.52461	+	0.358194i
$976$	−1.55842	−	2.69927i	−0.0498839	−	0.0864014i
$977$	−20.0584	−	34.7422i	−0.641726	−	1.11150i	−0.985047	−	0.172284i	$-0.944885\pi$
$977$	−20.0584	−	34.7422i	−0.641726	−	1.11150i	0.343322	−	0.939218i	$-0.388448\pi$
$978$	9.11684	−	30.2372i	0.291525	−	0.966877i
$979$	10.1168	−	17.5229i	0.323336	−	0.560034i
$980$	4.37228			0.139667
$981$	37.6060	−	18.7027i	1.20067	−	0.597131i
$982$	25.3723			0.809662
$983$	19.6277	−	33.9962i	0.626027	−	1.08431i	−0.362314	−	0.932056i	$-0.618013\pi$
$983$	19.6277	−	33.9962i	0.626027	−	1.08431i	0.988341	−	0.152255i	$-0.0486534\pi$
$984$	−5.48913	−	5.84096i	−0.174987	−	0.186203i
$985$	13.1168	+	22.7190i	0.417937	+	0.723889i
$986$	−6.00000	−	10.3923i	−0.191079	−	0.330958i
$987$		0			0
$988$	−5.00000	+	8.66025i	−0.159071	+	0.275519i
$989$	13.2119			0.420115
$990$	−1.11684	+	17.9653i	−0.0354956	+	0.570975i
$991$	48.4674			1.53962			0.769808	−	0.638275i	$-0.220352\pi$
$991$	48.4674			1.53962			0.769808	+	0.638275i	$0.220352\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	11.1168	−	36.8704i	0.352782	−	1.17005i
$994$	−3.55842	−	6.16337i	−0.112866	−	0.195490i
$995$	21.8614	+	37.8651i	0.693053	+	1.20040i
$996$	−29.4891	+	6.92820i	−0.934399	+	0.219529i
$997$	2.55842	−	4.43132i	0.0810260	−	0.140341i	−0.822665	−	0.568527i	$-0.807514\pi$
$997$	2.55842	−	4.43132i	0.0810260	−	0.140341i	0.903691	+	0.428185i	$0.140847\pi$
$998$	−18.1168			−0.573479
$999$	−8.00000	+	6.63325i	−0.253109	+	0.209867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.f.d.43.1	✓	4
3.2	odd	2		378.2.f.c.127.2		4
4.3	odd	2		1008.2.r.f.673.2		4
7.2	even	3		882.2.e.l.655.1		4
7.3	odd	6		882.2.h.n.79.1		4
7.4	even	3		882.2.h.m.79.2		4
7.5	odd	6		882.2.e.k.655.2		4
7.6	odd	2		882.2.f.k.295.2		4
9.2	odd	6		1134.2.a.n.1.1		2
9.4	even	3	inner	126.2.f.d.85.1	yes	4
9.5	odd	6		378.2.f.c.253.2		4
9.7	even	3		1134.2.a.k.1.2		2
12.11	even	2		3024.2.r.f.2017.2		4
21.2	odd	6		2646.2.e.n.2125.2		4
21.5	even	6		2646.2.e.m.2125.1		4
21.11	odd	6		2646.2.h.k.667.1		4
21.17	even	6		2646.2.h.l.667.2		4
21.20	even	2		2646.2.f.j.883.1		4
36.7	odd	6		9072.2.a.bm.1.2		2
36.11	even	6		9072.2.a.bb.1.1		2
36.23	even	6		3024.2.r.f.1009.2		4
36.31	odd	6		1008.2.r.f.337.2		4
63.4	even	3		882.2.e.l.373.2		4
63.5	even	6		2646.2.h.l.361.2		4
63.13	odd	6		882.2.f.k.589.2		4
63.20	even	6		7938.2.a.bs.1.2		2
63.23	odd	6		2646.2.h.k.361.1		4
63.31	odd	6		882.2.e.k.373.1		4
63.32	odd	6		2646.2.e.n.1549.2		4
63.34	odd	6		7938.2.a.bh.1.1		2
63.40	odd	6		882.2.h.n.67.1		4
63.41	even	6		2646.2.f.j.1765.1		4
63.58	even	3		882.2.h.m.67.2		4
63.59	even	6		2646.2.e.m.1549.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.d.43.1	✓	4	1.1	even	1	trivial
126.2.f.d.85.1	yes	4	9.4	even	3	inner
378.2.f.c.127.2		4	3.2	odd	2
378.2.f.c.253.2		4	9.5	odd	6
882.2.e.k.373.1		4	63.31	odd	6
882.2.e.k.655.2		4	7.5	odd	6
882.2.e.l.373.2		4	63.4	even	3
882.2.e.l.655.1		4	7.2	even	3
882.2.f.k.295.2		4	7.6	odd	2
882.2.f.k.589.2		4	63.13	odd	6
882.2.h.m.67.2		4	63.58	even	3
882.2.h.m.79.2		4	7.4	even	3
882.2.h.n.67.1		4	63.40	odd	6
882.2.h.n.79.1		4	7.3	odd	6
1008.2.r.f.337.2		4	36.31	odd	6
1008.2.r.f.673.2		4	4.3	odd	2
1134.2.a.k.1.2		2	9.7	even	3
1134.2.a.n.1.1		2	9.2	odd	6
2646.2.e.m.1549.1		4	63.59	even	6
2646.2.e.m.2125.1		4	21.5	even	6
2646.2.e.n.1549.2		4	63.32	odd	6
2646.2.e.n.2125.2		4	21.2	odd	6
2646.2.f.j.883.1		4	21.20	even	2
2646.2.f.j.1765.1		4	63.41	even	6
2646.2.h.k.361.1		4	63.23	odd	6
2646.2.h.k.667.1		4	21.11	odd	6
2646.2.h.l.361.2		4	63.5	even	6
2646.2.h.l.667.2		4	21.17	even	6
3024.2.r.f.1009.2		4	36.23	even	6
3024.2.r.f.2017.2		4	12.11	even	2
7938.2.a.bh.1.1		2	63.34	odd	6
7938.2.a.bs.1.2		2	63.20	even	6
9072.2.a.bb.1.1		2	36.11	even	6
9072.2.a.bm.1.2		2	36.7	odd	6

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.18614 - 3.78651i) q^{5} +(-0.500000 + 1.65831i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.68614 + 0.396143i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.18614 - 3.78651i) q^{5} +(-0.500000 + 1.65831i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(2.68614 - 1.33591i) q^{9} -4.37228 q^{10} +(0.686141 - 1.18843i) q^{11} +(1.18614 + 1.26217i) q^{12} +(-1.00000 - 1.73205i) q^{13} +(0.500000 + 0.866025i) q^{14} +(5.18614 + 5.51856i) q^{15} +(-0.500000 + 0.866025i) q^{16} +1.37228 q^{17} +(0.186141 - 2.99422i) q^{18} +5.00000 q^{19} +(-2.18614 + 3.78651i) q^{20} +(0.500000 - 1.65831i) q^{21} +(-0.686141 - 1.18843i) q^{22} +(0.813859 + 1.40965i) q^{23} +(1.68614 - 0.396143i) q^{24} +(-7.05842 + 12.2255i) q^{25} -2.00000 q^{26} +(-4.00000 + 3.31662i) q^{27} +1.00000 q^{28} +(4.37228 - 7.57301i) q^{29} +(7.37228 - 1.73205i) q^{30} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.686141 + 2.27567i) q^{33} +(0.686141 - 1.18843i) q^{34} +4.37228 q^{35} +(-2.50000 - 1.65831i) q^{36} +2.00000 q^{37} +(2.50000 - 4.33013i) q^{38} +(2.37228 + 2.52434i) q^{39} +(2.18614 + 3.78651i) q^{40} +(-2.31386 - 4.00772i) q^{41} +(-1.18614 - 1.26217i) q^{42} +(4.05842 - 7.02939i) q^{43} -1.37228 q^{44} +(-10.9307 - 7.25061i) q^{45} +1.62772 q^{46} +(0.500000 - 1.65831i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(7.05842 + 12.2255i) q^{50} +(-2.31386 + 0.543620i) q^{51} +(-1.00000 + 1.73205i) q^{52} -8.74456 q^{53} +(0.872281 + 5.12241i) q^{54} -6.00000 q^{55} +(0.500000 - 0.866025i) q^{56} +(-8.43070 + 1.98072i) q^{57} +(-4.37228 - 7.57301i) q^{58} +(5.05842 + 8.76144i) q^{59} +(2.18614 - 7.25061i) q^{60} +(-1.55842 + 2.69927i) q^{61} -2.00000 q^{62} +(-0.186141 + 2.99422i) q^{63} +1.00000 q^{64} +(-4.37228 + 7.57301i) q^{65} +(1.62772 + 1.73205i) q^{66} +(1.05842 + 1.83324i) q^{67} +(-0.686141 - 1.18843i) q^{68} +(-1.93070 - 2.05446i) q^{69} +(2.18614 - 3.78651i) q^{70} -7.11684 q^{71} +(-2.68614 + 1.33591i) q^{72} +12.1168 q^{73} +(1.00000 - 1.73205i) q^{74} +(7.05842 - 23.4101i) q^{75} +(-2.50000 - 4.33013i) q^{76} +(0.686141 + 1.18843i) q^{77} +(3.37228 - 0.792287i) q^{78} +(2.55842 - 4.43132i) q^{79} +4.37228 q^{80} +(5.43070 - 7.17687i) q^{81} -4.62772 q^{82} +(-8.74456 + 15.1460i) q^{83} +(-1.68614 + 0.396143i) q^{84} +(-3.00000 - 5.19615i) q^{85} +(-4.05842 - 7.02939i) q^{86} +(-4.37228 + 14.5012i) q^{87} +(-0.686141 + 1.18843i) q^{88} +14.7446 q^{89} +(-11.7446 + 5.84096i) q^{90} +2.00000 q^{91} +(0.813859 - 1.40965i) q^{92} +(2.37228 + 2.52434i) q^{93} +(-10.9307 - 18.9325i) q^{95} +(-1.18614 - 1.26217i) q^{96} +(4.05842 - 7.02939i) q^{97} -1.00000 q^{98} +(0.255437 - 4.10891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 5 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 5 * q^9	\( 4 q + 2 q^{2} - q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 5 q^{9} - 6 q^{10} - 3 q^{11} - q^{12} - 4 q^{13} + 2 q^{14} + 15 q^{15} - 2 q^{16} - 6 q^{17} - 5 q^{18} + 20 q^{19} - 3 q^{20} + 2 q^{21} + 3 q^{22} + 9 q^{23} + q^{24} - 11 q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{28} + 6 q^{29} + 18 q^{30} - 4 q^{31} + 2 q^{32} + 3 q^{33} - 3 q^{34} + 6 q^{35} - 10 q^{36} + 8 q^{37} + 10 q^{38} - 2 q^{39} + 3 q^{40} - 15 q^{41} + q^{42} - q^{43} + 6 q^{44} - 15 q^{45} + 18 q^{46} + 2 q^{48} - 2 q^{49} + 11 q^{50} - 15 q^{51} - 4 q^{52} - 12 q^{53} - 8 q^{54} - 24 q^{55} + 2 q^{56} - 5 q^{57} - 6 q^{58} + 3 q^{59} + 3 q^{60} + 11 q^{61} - 8 q^{62} + 5 q^{63} + 4 q^{64} - 6 q^{65} + 18 q^{66} - 13 q^{67} + 3 q^{68} + 21 q^{69} + 3 q^{70} + 6 q^{71} - 5 q^{72} + 14 q^{73} + 4 q^{74} + 11 q^{75} - 10 q^{76} - 3 q^{77} + 2 q^{78} - 7 q^{79} + 6 q^{80} - 7 q^{81} - 30 q^{82} - 12 q^{83} - q^{84} - 12 q^{85} + q^{86} - 6 q^{87} + 3 q^{88} + 36 q^{89} - 24 q^{90} + 8 q^{91} + 9 q^{92} - 2 q^{93} - 15 q^{95} + q^{96} - q^{97} - 4 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - q^3 - 2 * q^4 - 3 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 5 * q^9 - 6 * q^10 - 3 * q^11 - q^12 - 4 * q^13 + 2 * q^14 + 15 * q^15 - 2 * q^16 - 6 * q^17 - 5 * q^18 + 20 * q^19 - 3 * q^20 + 2 * q^21 + 3 * q^22 + 9 * q^23 + q^24 - 11 * q^25 - 8 * q^26 - 16 * q^27 + 4 * q^28 + 6 * q^29 + 18 * q^30 - 4 * q^31 + 2 * q^32 + 3 * q^33 - 3 * q^34 + 6 * q^35 - 10 * q^36 + 8 * q^37 + 10 * q^38 - 2 * q^39 + 3 * q^40 - 15 * q^41 + q^42 - q^43 + 6 * q^44 - 15 * q^45 + 18 * q^46 + 2 * q^48 - 2 * q^49 + 11 * q^50 - 15 * q^51 - 4 * q^52 - 12 * q^53 - 8 * q^54 - 24 * q^55 + 2 * q^56 - 5 * q^57 - 6 * q^58 + 3 * q^59 + 3 * q^60 + 11 * q^61 - 8 * q^62 + 5 * q^63 + 4 * q^64 - 6 * q^65 + 18 * q^66 - 13 * q^67 + 3 * q^68 + 21 * q^69 + 3 * q^70 + 6 * q^71 - 5 * q^72 + 14 * q^73 + 4 * q^74 + 11 * q^75 - 10 * q^76 - 3 * q^77 + 2 * q^78 - 7 * q^79 + 6 * q^80 - 7 * q^81 - 30 * q^82 - 12 * q^83 - q^84 - 12 * q^85 + q^86 - 6 * q^87 + 3 * q^88 + 36 * q^89 - 24 * q^90 + 8 * q^91 + 9 * q^92 - 2 * q^93 - 15 * q^95 + q^96 - q^97 - 4 * q^98 + 24 * q^99

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