LMFDB - Embedded newform 630.2.i.f.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

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

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

chi := DirichletCharacter("630.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.i (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	12.0.91830304992969.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + x^{10} + 4x^{9} - 7x^{8} + x^{7} + 7x^{6} + 2x^{5} - 28x^{4} + 32x^{3} + 16x^{2} - 64x + 64 $ x^12 - 2x^11 + x^10 + 4x^9 - 7x^8 + x^7 + 7x^6 + 2x^5 - 28x^4 + 32x^3 + 16x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$-0.989378 - 1.01051i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.f.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.56899 + 0.733675i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.56899 - 0.733675i) q^{6} +(-2.56238 + 0.658939i) q^{7} -1.00000 q^{8} +(1.92344 - 2.30225i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.56899 + 0.733675i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.56899 - 0.733675i) q^{6} +(-2.56238 + 0.658939i) q^{7} -1.00000 q^{8} +(1.92344 - 2.30225i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.23607 - 3.87298i) q^{11} +(-1.56899 + 0.733675i) q^{12} +(0.827555 + 1.43337i) q^{13} +(2.56238 - 0.658939i) q^{14} +(0.149112 - 1.72562i) q^{15} +1.00000 q^{16} +(1.35309 - 2.34362i) q^{17} +(-1.92344 + 2.30225i) q^{18} +(0.827555 + 1.43337i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(3.53690 - 2.91382i) q^{21} +(2.23607 + 3.87298i) q^{22} +(-0.474466 + 0.821799i) q^{23} +(1.56899 - 0.733675i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.827555 - 1.43337i) q^{26} +(-1.32875 + 5.02339i) q^{27} +(-2.56238 + 0.658939i) q^{28} +(2.07678 - 3.59710i) q^{29} +(-0.149112 + 1.72562i) q^{30} +3.00713 q^{31} -1.00000 q^{32} +(6.34987 + 4.43611i) q^{33} +(-1.35309 + 2.34362i) q^{34} +(0.710533 - 2.54856i) q^{35} +(1.92344 - 2.30225i) q^{36} +(4.87541 + 8.44445i) q^{37} +(-0.827555 - 1.43337i) q^{38} +(-2.35005 - 1.64178i) q^{39} +(0.500000 - 0.866025i) q^{40} +(0.970293 + 1.68060i) q^{41} +(-3.53690 + 2.91382i) q^{42} +(2.50757 - 4.34323i) q^{43} +(-2.23607 - 3.87298i) q^{44} +(1.03209 + 2.81688i) q^{45} +(0.474466 - 0.821799i) q^{46} +1.01513 q^{47} +(-1.56899 + 0.733675i) q^{48} +(6.13160 - 3.37690i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.403524 + 4.66984i) q^{51} +(0.827555 + 1.43337i) q^{52} +(6.65730 - 11.5308i) q^{53} +(1.32875 - 5.02339i) q^{54} +4.47213 q^{55} +(2.56238 - 0.658939i) q^{56} +(-2.35005 - 1.64178i) q^{57} +(-2.07678 + 3.59710i) q^{58} +8.84247 q^{59} +(0.149112 - 1.72562i) q^{60} +12.0183 q^{61} -3.00713 q^{62} +(-3.41155 + 7.16668i) q^{63} +1.00000 q^{64} -1.65511 q^{65} +(-6.34987 - 4.43611i) q^{66} +0.773956 q^{67} +(1.35309 - 2.34362i) q^{68} +(0.141497 - 1.63750i) q^{69} +(-0.710533 + 2.54856i) q^{70} -13.8907 q^{71} +(-1.92344 + 2.30225i) q^{72} +(0.166120 - 0.287728i) q^{73} +(-4.87541 - 8.44445i) q^{74} +(1.41988 + 0.991945i) q^{75} +(0.827555 + 1.43337i) q^{76} +(8.28172 + 8.45063i) q^{77} +(2.35005 + 1.64178i) q^{78} +9.92508 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-1.60075 - 8.85650i) q^{81} +(-0.970293 - 1.68060i) q^{82} +(1.60804 - 2.78521i) q^{83} +(3.53690 - 2.91382i) q^{84} +(1.35309 + 2.34362i) q^{85} +(-2.50757 + 4.34323i) q^{86} +(-0.619347 + 7.16748i) q^{87} +(2.23607 + 3.87298i) q^{88} +(-2.86642 - 4.96478i) q^{89} +(-1.03209 - 2.81688i) q^{90} +(-3.06501 - 3.12753i) q^{91} +(-0.474466 + 0.821799i) q^{92} +(-4.71815 + 2.20626i) q^{93} -1.01513 q^{94} -1.65511 q^{95} +(1.56899 - 0.733675i) q^{96} +(-2.85868 + 4.95139i) q^{97} +(-6.13160 + 3.37690i) q^{98} +(-13.2175 - 2.30146i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 2 q^{19} - 6 q^{20} + 29 q^{21} + 7 q^{22} - 9 q^{23} - 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 4 q^{28} + 3 q^{29} + q^{30} + 18 q^{31} - 12 q^{32} + 27 q^{33} - q^{34} - 8 q^{35} - 4 q^{36} + 6 q^{37} + 2 q^{38} + 10 q^{39} + 6 q^{40} - 11 q^{41} - 29 q^{42} + 23 q^{43} - 7 q^{44} + 5 q^{45} + 9 q^{46} - 2 q^{47} + 2 q^{48} + 24 q^{49} + 6 q^{50} - 15 q^{51} - 2 q^{52} - 4 q^{53} - 11 q^{54} + 14 q^{55} - 4 q^{56} + 10 q^{57} - 3 q^{58} - 22 q^{59} - q^{60} + 50 q^{61} - 18 q^{62} - q^{63} + 12 q^{64} + 4 q^{65} - 27 q^{66} + 4 q^{67} + q^{68} - 12 q^{69} + 8 q^{70} + 22 q^{71} + 4 q^{72} + 24 q^{73} - 6 q^{74} - q^{75} - 2 q^{76} - 11 q^{77} - 10 q^{78} + 2 q^{79} - 6 q^{80} + 20 q^{81} + 11 q^{82} + 4 q^{83} + 29 q^{84} + q^{85} - 23 q^{86} + 7 q^{88} + 2 q^{89} - 5 q^{90} - 8 q^{91} - 9 q^{92} + 40 q^{93} + 2 q^{94} + 4 q^{95} - 2 q^{96} - 36 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^15 + 12 * q^16 + q^17 + 4 * q^18 - 2 * q^19 - 6 * q^20 + 29 * q^21 + 7 * q^22 - 9 * q^23 - 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 4 * q^28 + 3 * q^29 + q^30 + 18 * q^31 - 12 * q^32 + 27 * q^33 - q^34 - 8 * q^35 - 4 * q^36 + 6 * q^37 + 2 * q^38 + 10 * q^39 + 6 * q^40 - 11 * q^41 - 29 * q^42 + 23 * q^43 - 7 * q^44 + 5 * q^45 + 9 * q^46 - 2 * q^47 + 2 * q^48 + 24 * q^49 + 6 * q^50 - 15 * q^51 - 2 * q^52 - 4 * q^53 - 11 * q^54 + 14 * q^55 - 4 * q^56 + 10 * q^57 - 3 * q^58 - 22 * q^59 - q^60 + 50 * q^61 - 18 * q^62 - q^63 + 12 * q^64 + 4 * q^65 - 27 * q^66 + 4 * q^67 + q^68 - 12 * q^69 + 8 * q^70 + 22 * q^71 + 4 * q^72 + 24 * q^73 - 6 * q^74 - q^75 - 2 * q^76 - 11 * q^77 - 10 * q^78 + 2 * q^79 - 6 * q^80 + 20 * q^81 + 11 * q^82 + 4 * q^83 + 29 * q^84 + q^85 - 23 * q^86 + 7 * q^88 + 2 * q^89 - 5 * q^90 - 8 * q^91 - 9 * q^92 + 40 * q^93 + 2 * q^94 + 4 * q^95 - 2 * q^96 - 36 * q^97 - 24 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.56899	+	0.733675i	−0.905855	+	0.423588i
$3$	−1.56899	+	0.733675i	−0.905855	+	0.423588i
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.56899	−	0.733675i	0.640536	−	0.299522i
$7$	−2.56238	+	0.658939i	−0.968489	+	0.249055i
$7$	−2.56238	+	0.658939i	−0.968489	+	0.249055i
$8$	−1.00000			−0.353553
$9$	1.92344	−	2.30225i	0.641147	−	0.767418i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.23607	−	3.87298i	−0.674200	−	1.16775i	−0.976702	−	0.214599i	$-0.931155\pi$
$11$	−2.23607	−	3.87298i	−0.674200	−	1.16775i	0.302502	−	0.953149i	$-0.402178\pi$
$12$	−1.56899	+	0.733675i	−0.452928	+	0.211794i
$13$	0.827555	+	1.43337i	0.229522	+	0.397545i	0.957667	−	0.287879i	$-0.0929502\pi$
$13$	0.827555	+	1.43337i	0.229522	+	0.397545i	−0.728144	+	0.685424i	$0.759617\pi$
$14$	2.56238	−	0.658939i	0.684825	−	0.176109i
$15$	0.149112	−	1.72562i	0.0385006	−	0.445553i
$16$	1.00000			0.250000
$17$	1.35309	−	2.34362i	0.328172	−	0.568411i	−0.653977	−	0.756514i	$-0.726901\pi$
$17$	1.35309	−	2.34362i	0.328172	−	0.568411i	0.982149	+	0.188103i	$0.0602340\pi$
$18$	−1.92344	+	2.30225i	−0.453359	+	0.542647i
$19$	0.827555	+	1.43337i	0.189854	+	0.328837i	0.945201	−	0.326488i	$-0.105865\pi$
$19$	0.827555	+	1.43337i	0.189854	+	0.328837i	−0.755347	+	0.655325i	$0.772532\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	3.53690	−	2.91382i	0.771814	−	0.635848i
$22$	2.23607	+	3.87298i	0.476731	+	0.825723i
$23$	−0.474466	+	0.821799i	−0.0989330	+	0.171357i	−0.911243	−	0.411869i	$-0.864876\pi$
$23$	−0.474466	+	0.821799i	−0.0989330	+	0.171357i	0.812310	+	0.583226i	$0.198210\pi$
$24$	1.56899	−	0.733675i	0.320268	−	0.149761i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.827555	−	1.43337i	−0.162297	−	0.281106i
$27$	−1.32875	+	5.02339i	−0.255717	+	0.966752i
$28$	−2.56238	+	0.658939i	−0.484245	+	0.124528i
$29$	2.07678	−	3.59710i	0.385649	−	0.667964i	−0.606210	−	0.795305i	$-0.707311\pi$
$29$	2.07678	−	3.59710i	0.385649	−	0.667964i	0.991859	+	0.127341i	$0.0406442\pi$
$30$	−0.149112	+	1.72562i	−0.0272240	+	0.315054i
$31$	3.00713			0.540097			0.270048	−	0.962847i	$-0.412960\pi$
$31$	3.00713			0.540097			0.270048	+	0.962847i	$0.412960\pi$
$32$	−1.00000			−0.176777
$33$	6.34987	+	4.43611i	1.10537	+	0.772228i
$34$	−1.35309	+	2.34362i	−0.232053	+	0.401927i
$35$	0.710533	−	2.54856i	0.120102	−	0.430785i
$36$	1.92344	−	2.30225i	0.320573	−	0.383709i
$37$	4.87541	+	8.44445i	0.801512	+	1.38826i	0.918621	+	0.395140i	$0.129304\pi$
$37$	4.87541	+	8.44445i	0.801512	+	1.38826i	−0.117109	+	0.993119i	$0.537363\pi$
$38$	−0.827555	−	1.43337i	−0.134247	−	0.232523i
$39$	−2.35005	−	1.64178i	−0.376309	−	0.262895i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	0.970293	+	1.68060i	0.151534	+	0.262465i	0.931792	−	0.362993i	$-0.118245\pi$
$41$	0.970293	+	1.68060i	0.151534	+	0.262465i	−0.780257	+	0.625459i	$0.784912\pi$
$42$	−3.53690	+	2.91382i	−0.545755	+	0.449613i
$43$	2.50757	−	4.34323i	0.382400	−	0.662337i	−0.609005	−	0.793167i	$-0.708431\pi$
$43$	2.50757	−	4.34323i	0.382400	−	0.662337i	0.991405	+	0.130830i	$0.0417642\pi$
$44$	−2.23607	−	3.87298i	−0.337100	−	0.583874i
$45$	1.03209	+	2.81688i	0.153855	+	0.419915i
$46$	0.474466	−	0.821799i	0.0699562	−	0.121168i
$47$	1.01513			0.148072			0.0740361	−	0.997256i	$-0.476412\pi$
$47$	1.01513			0.148072			0.0740361	+	0.997256i	$0.476412\pi$
$48$	−1.56899	+	0.733675i	−0.226464	+	0.105897i
$49$	6.13160	−	3.37690i	0.875943	−	0.482415i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−0.403524	+	4.66984i	−0.0565046	+	0.653908i
$52$	0.827555	+	1.43337i	0.114761	+	0.198772i
$53$	6.65730	−	11.5308i	0.914451	−	1.58387i	0.106747	−	0.994286i	$-0.465957\pi$
$53$	6.65730	−	11.5308i	0.914451	−	1.58387i	0.807704	−	0.589589i	$-0.200710\pi$
$54$	1.32875	−	5.02339i	0.180820	−	0.683597i
$55$	4.47213			0.603023
$56$	2.56238	−	0.658939i	0.342413	−	0.0880544i
$57$	−2.35005	−	1.64178i	−0.311272	−	0.217459i
$58$	−2.07678	+	3.59710i	−0.272695	+	0.472322i
$59$	8.84247			1.15119			0.575596	−	0.817735i	$-0.304770\pi$
$59$	8.84247			1.15119			0.575596	+	0.817735i	$0.304770\pi$
$60$	0.149112	−	1.72562i	0.0192503	−	0.222777i
$61$	12.0183			1.53879			0.769394	−	0.638775i	$-0.220559\pi$
$61$	12.0183			1.53879			0.769394	+	0.638775i	$0.220559\pi$
$62$	−3.00713			−0.381906
$63$	−3.41155	+	7.16668i	−0.429814	+	0.902917i
$64$	1.00000			0.125000
$65$	−1.65511			−0.205291
$66$	−6.34987	−	4.43611i	−0.781615	−	0.546048i
$67$	0.773956			0.0945538			0.0472769	−	0.998882i	$-0.484946\pi$
$67$	0.773956			0.0945538			0.0472769	+	0.998882i	$0.484946\pi$
$68$	1.35309	−	2.34362i	0.164086	−	0.284206i
$69$	0.141497	−	1.63750i	0.0170343	−	0.197131i
$70$	−0.710533	+	2.54856i	−0.0849250	+	0.304611i
$71$	−13.8907			−1.64852			−0.824262	−	0.566209i	$-0.808410\pi$
$71$	−13.8907			−1.64852			−0.824262	+	0.566209i	$0.808410\pi$
$72$	−1.92344	+	2.30225i	−0.226680	+	0.271323i
$73$	0.166120	−	0.287728i	0.0194429	−	0.0336760i	−0.856140	−	0.516743i	$-0.827144\pi$
$73$	0.166120	−	0.287728i	0.0194429	−	0.0336760i	0.875583	+	0.483067i	$0.160477\pi$
$74$	−4.87541	−	8.44445i	−0.566754	−	0.981648i
$75$	1.41988	+	0.991945i	0.163953	+	0.114540i
$76$	0.827555	+	1.43337i	0.0949271	+	0.164419i
$77$	8.28172	+	8.45063i	0.943789	+	0.963038i
$78$	2.35005	+	1.64178i	0.266091	+	0.185895i
$79$	9.92508			1.11666			0.558329	−	0.829619i	$-0.311443\pi$
$79$	9.92508			1.11666			0.558329	+	0.829619i	$0.311443\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−1.60075	−	8.85650i	−0.177861	−	0.984056i
$82$	−0.970293	−	1.68060i	−0.107151	−	0.185591i
$83$	1.60804	−	2.78521i	0.176506	−	0.305717i	−0.764176	−	0.645008i	$-0.776854\pi$
$83$	1.60804	−	2.78521i	0.176506	−	0.305717i	0.940681	+	0.339292i	$0.110187\pi$
$84$	3.53690	−	2.91382i	0.385907	−	0.317924i
$85$	1.35309	+	2.34362i	0.146763	+	0.254201i
$86$	−2.50757	+	4.34323i	−0.270398	+	0.468343i
$87$	−0.619347	+	7.16748i	−0.0664010	+	0.768435i
$88$	2.23607	+	3.87298i	0.238366	+	0.412861i
$89$	−2.86642	−	4.96478i	−0.303840	−	0.526266i	0.673163	−	0.739494i	$-0.264935\pi$
$89$	−2.86642	−	4.96478i	−0.303840	−	0.526266i	−0.977002	+	0.213229i	$0.931602\pi$
$90$	−1.03209	−	2.81688i	−0.108792	−	0.296925i
$91$	−3.06501	−	3.12753i	−0.321301	−	0.327854i
$92$	−0.474466	+	0.821799i	−0.0494665	+	0.0856785i
$93$	−4.71815	+	2.20626i	−0.489249	+	0.228778i
$94$	−1.01513			−0.104703
$95$	−1.65511			−0.169811
$96$	1.56899	−	0.733675i	0.160134	−	0.0748804i
$97$	−2.85868	+	4.95139i	−0.290255	+	0.502737i	−0.973870	−	0.227106i	$-0.927074\pi$
$97$	−2.85868	+	4.95139i	−0.290255	+	0.502737i	0.683615	+	0.729843i	$0.260407\pi$
$98$	−6.13160	+	3.37690i	−0.619385	+	0.341119i
$99$	−13.2175	−	2.30146i	−1.32841	−	0.231305i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	4.63374	+	8.02588i	0.461075	+	0.798605i	0.999015	−	0.0443783i	$-0.0141307\pi$
$101$	4.63374	+	8.02588i	0.461075	+	0.798605i	−0.537940	+	0.842983i	$0.680797\pi$
$102$	0.403524	−	4.66984i	0.0399548	−	0.462383i
$103$	9.52418	−	16.4964i	0.938446	−	1.62544i	0.170075	−	0.985431i	$-0.445599\pi$
$103$	9.52418	−	16.4964i	0.938446	−	1.62544i	0.768371	−	0.640005i	$-0.221068\pi$
$104$	−0.827555	−	1.43337i	−0.0811484	−	0.140553i
$105$	0.754996	+	4.51995i	0.0736801	+	0.441102i
$106$	−6.65730	+	11.5308i	−0.646614	+	1.11997i
$107$	1.37308	+	2.37825i	0.132741	+	0.229914i	0.924732	−	0.380619i	$-0.124289\pi$
$107$	1.37308	+	2.37825i	0.132741	+	0.229914i	−0.791991	+	0.610532i	$0.790956\pi$
$108$	−1.32875	+	5.02339i	−0.127859	+	0.483376i
$109$	−4.00622	+	6.93898i	−0.383727	+	0.664634i	−0.991592	−	0.129406i	$-0.958693\pi$
$109$	−4.00622	+	6.93898i	−0.383727	+	0.664634i	0.607865	+	0.794040i	$0.292026\pi$
$110$	−4.47213			−0.426401
$111$	−13.8449	−	9.67227i	−1.31410	−	0.918051i
$112$	−2.56238	+	0.658939i	−0.242122	+	0.0622638i
$113$	−2.47971	−	4.29498i	−0.233271	−	0.404038i	0.725498	−	0.688225i	$-0.241610\pi$
$113$	−2.47971	−	4.29498i	−0.233271	−	0.404038i	−0.958769	+	0.284187i	$0.908276\pi$
$114$	2.35005	+	1.64178i	0.220102	+	0.153767i
$115$	−0.474466	−	0.821799i	−0.0442442	−	0.0766332i
$116$	2.07678	−	3.59710i	0.192825	−	0.333982i
$117$	4.89173	+	0.851755i	0.452241	+	0.0787448i
$118$	−8.84247			−0.814015
$119$	−1.92283	+	6.89685i	−0.176266	+	0.632233i
$120$	−0.149112	+	1.72562i	−0.0136120	+	0.157527i
$121$	−4.49999	+	7.79422i	−0.409090	+	0.708565i
$122$	−12.0183			−1.08809
$123$	−2.75539	−	1.92495i	−0.248445	−	0.173567i
$124$	3.00713			0.270048
$125$	1.00000			0.0894427
$126$	3.41155	−	7.16668i	0.303925	−	0.638459i
$127$	−19.3979			−1.72129			−0.860644	−	0.509208i	$-0.829938\pi$
$127$	−19.3979			−1.72129			−0.860644	+	0.509208i	$0.829938\pi$
$128$	−1.00000			−0.0883883
$129$	−0.747816	+	8.65421i	−0.0658416	+	0.761961i
$130$	1.65511			0.145163
$131$	1.77033	−	3.06630i	0.154674	−	0.267904i	−0.778266	−	0.627935i	$-0.783900\pi$
$131$	1.77033	−	3.06630i	0.154674	−	0.267904i	0.932940	+	0.360031i	$0.117234\pi$
$132$	6.34987	+	4.43611i	0.552685	+	0.386114i
$133$	−3.06501	−	3.12753i	−0.265770	−	0.271191i
$134$	−0.773956			−0.0668597
$135$	−3.68601	−	3.66242i	−0.317241	−	0.315211i
$136$	−1.35309	+	2.34362i	−0.116026	+	0.200964i
$137$	−8.90949	−	15.4317i	−0.761189	−	1.31842i	−0.942238	−	0.334945i	$-0.891282\pi$
$137$	−8.90949	−	15.4317i	−0.761189	−	1.31842i	0.181048	−	0.983474i	$-0.442051\pi$
$138$	−0.141497	+	1.63750i	−0.0120450	+	0.139393i
$139$	−6.41271	−	11.1071i	−0.543919	−	0.942095i	−0.998674	−	0.0514789i	$-0.983607\pi$
$139$	−6.41271	−	11.1071i	−0.543919	−	0.942095i	0.454755	−	0.890617i	$-0.349727\pi$
$140$	0.710533	−	2.54856i	0.0600510	−	0.215392i
$141$	−1.59273	+	0.744777i	−0.134132	+	0.0627215i
$142$	13.8907			1.16568
$143$	3.70094	−	6.41021i	0.309488	−	0.536049i
$144$	1.92344	−	2.30225i	0.160287	−	0.191855i
$145$	2.07678	+	3.59710i	0.172468	+	0.298723i
$146$	−0.166120	+	0.287728i	−0.0137482	+	0.0238125i
$147$	−7.14285	+	9.79692i	−0.589132	+	0.808037i
$148$	4.87541	+	8.44445i	0.400756	+	0.694130i
$149$	−4.96565	+	8.60076i	−0.406802	+	0.704602i	−0.994529	−	0.104457i	$-0.966690\pi$
$149$	−4.96565	+	8.60076i	−0.406802	+	0.704602i	0.587727	+	0.809059i	$0.300023\pi$
$150$	−1.41988	−	0.991945i	−0.115932	−	0.0809920i
$151$	−4.03641	−	6.99127i	−0.328479	−	0.568942i	0.653732	−	0.756727i	$-0.273203\pi$
$151$	−4.03641	−	6.99127i	−0.328479	−	0.568942i	−0.982210	+	0.187785i	$0.939869\pi$
$152$	−0.827555	−	1.43337i	−0.0671236	−	0.116261i
$153$	−2.79302	−	7.62297i	−0.225802	−	0.616280i
$154$	−8.28172	−	8.45063i	−0.667360	−	0.680971i
$155$	−1.50357	+	2.60425i	−0.120769	+	0.209179i
$156$	−2.35005	−	1.64178i	−0.188155	−	0.131447i
$157$	−19.8019			−1.58036			−0.790181	−	0.612874i	$-0.790013\pi$
$157$	−19.8019			−1.58036			−0.790181	+	0.612874i	$0.790013\pi$
$158$	−9.92508			−0.789597
$159$	−1.98537	+	22.9759i	−0.157450	+	1.82211i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	0.674248	−	2.41841i	0.0531382	−	0.190597i
$162$	1.60075	+	8.85650i	0.125767	+	0.695832i
$163$	−8.46813	−	14.6672i	−0.663275	−	1.14883i	−0.979750	−	0.200226i	$-0.935832\pi$
$163$	−8.46813	−	14.6672i	−0.663275	−	1.14883i	0.316474	−	0.948601i	$-0.397501\pi$
$164$	0.970293	+	1.68060i	0.0757671	+	0.131233i
$165$	−7.01672	+	3.28109i	−0.546251	+	0.255433i
$166$	−1.60804	+	2.78521i	−0.124808	+	0.216174i
$167$	9.80368	+	16.9805i	0.758631	+	1.31399i	0.943549	+	0.331234i	$0.107465\pi$
$167$	9.80368	+	16.9805i	0.758631	+	1.31399i	−0.184917	+	0.982754i	$0.559202\pi$
$168$	−3.53690	+	2.91382i	−0.272878	+	0.224806i
$169$	5.13031	−	8.88595i	0.394639	−	0.683535i
$170$	−1.35309	−	2.34362i	−0.103777	−	0.179747i
$171$	4.89173	+	0.851755i	0.374080	+	0.0651353i
$172$	2.50757	−	4.34323i	0.191200	−	0.331168i
$173$	7.46596			0.567626			0.283813	−	0.958880i	$-0.408400\pi$
$173$	7.46596			0.567626			0.283813	+	0.958880i	$0.408400\pi$
$174$	0.619347	−	7.16748i	0.0469526	−	0.543365i
$175$	1.85185	+	1.88962i	0.139987	+	0.142842i
$176$	−2.23607	−	3.87298i	−0.168550	−	0.291937i
$177$	−13.8737	+	6.48750i	−1.04281	+	0.487630i
$178$	2.86642	+	4.96478i	0.214847	+	0.372126i
$179$	−2.74363	+	4.75211i	−0.205069	+	0.355190i	−0.950155	−	0.311779i	$-0.899075\pi$
$179$	−2.74363	+	4.75211i	−0.205069	+	0.355190i	0.745086	+	0.666969i	$0.232408\pi$
$180$	1.03209	+	2.81688i	0.0769275	+	0.209958i
$181$	13.6477			1.01443			0.507213	−	0.861821i	$-0.330676\pi$
$181$	13.6477			1.01443			0.507213	+	0.861821i	$0.330676\pi$
$182$	3.06501	+	3.12753i	0.227194	+	0.231828i
$183$	−18.8566	+	8.81754i	−1.39392	+	0.651811i
$184$	0.474466	−	0.821799i	0.0349781	−	0.0605838i
$185$	−9.75081			−0.716894
$186$	4.71815	−	2.20626i	0.345952	−	0.161771i
$187$	−12.1024			−0.885015
$188$	1.01513			0.0740361
$189$	0.0946515	−	13.7474i	0.00688488	−	0.999976i
$190$	1.65511			0.120074
$191$	24.7176			1.78850			0.894251	−	0.447565i	$-0.147709\pi$
$191$	24.7176			1.78850			0.894251	+	0.447565i	$0.147709\pi$
$192$	−1.56899	+	0.733675i	−0.113232	+	0.0529485i
$193$	15.0374			1.08242			0.541208	−	0.840889i	$-0.317967\pi$
$193$	15.0374			1.08242			0.541208	+	0.840889i	$0.317967\pi$
$194$	2.85868	−	4.95139i	0.205242	−	0.355489i
$195$	2.59685	−	1.21431i	0.185964	−	0.0869588i
$196$	6.13160	−	3.37690i	0.437971	−	0.241207i
$197$	21.9097			1.56100			0.780500	−	0.625156i	$-0.214965\pi$
$197$	21.9097			1.56100			0.780500	+	0.625156i	$0.214965\pi$
$198$	13.2175	+	2.30146i	0.939329	+	0.163557i
$199$	−12.1642	+	21.0691i	−0.862300	+	1.49355i	0.00740280	+	0.999973i	$0.497644\pi$
$199$	−12.1642	+	21.0691i	−0.862300	+	1.49355i	−0.869703	+	0.493575i	$0.835690\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−1.21433	+	0.567833i	−0.0856521	+	0.0400518i
$202$	−4.63374	−	8.02588i	−0.326029	−	0.564699i
$203$	−2.95125	+	10.5856i	−0.207137	+	0.742964i
$204$	−0.403524	+	4.66984i	−0.0282523	+	0.326954i
$205$	−1.94059			−0.135536
$206$	−9.52418	+	16.4964i	−0.663581	+	1.14936i
$207$	0.979384	+	2.67302i	0.0680719	+	0.185788i
$208$	0.827555	+	1.43337i	0.0573806	+	0.0993861i
$209$	3.70094	−	6.41021i	0.255999	−	0.443404i
$210$	−0.754996	−	4.51995i	−0.0520997	−	0.311906i
$211$	9.43146	+	16.3358i	0.649288	+	1.12460i	0.983293	+	0.182029i	$0.0582664\pi$
$211$	9.43146	+	16.3358i	0.649288	+	1.12460i	−0.334005	+	0.942571i	$0.608400\pi$
$212$	6.65730	−	11.5308i	0.457225	−	0.791937i
$213$	21.7943	−	10.1913i	1.49332	−	0.698294i
$214$	−1.37308	−	2.37825i	−0.0938619	−	0.162574i
$215$	2.50757	+	4.34323i	0.171015	+	0.296206i
$216$	1.32875	−	5.02339i	0.0904098	−	0.341798i
$217$	−7.70542	+	1.98152i	−0.523078	+	0.134514i
$218$	4.00622	−	6.93898i	0.271336	−	0.469967i
$219$	−0.0495409	+	0.573319i	−0.00334766	+	0.0387413i
$220$	4.47213			0.301511
$221$	4.47902			0.301292
$222$	13.8449	+	9.67227i	0.929211	+	0.649160i
$223$	9.42519	−	16.3249i	0.631157	−	1.09320i	−0.356158	−	0.934426i	$-0.615914\pi$
$223$	9.42519	−	16.3249i	0.631157	−	1.09320i	0.987315	−	0.158771i	$-0.0507531\pi$
$224$	2.56238	−	0.658939i	0.171206	−	0.0440272i
$225$	−2.95553	−	0.514622i	−0.197035	−	0.0343081i
$226$	2.47971	+	4.29498i	0.164948	+	0.285698i
$227$	2.10153	+	3.63995i	0.139483	+	0.241592i	0.927301	−	0.374316i	$-0.122122\pi$
$227$	2.10153	+	3.63995i	0.139483	+	0.241592i	−0.787818	+	0.615908i	$0.788789\pi$
$228$	−2.35005	−	1.64178i	−0.155636	−	0.108729i
$229$	11.4403	−	19.8152i	0.755997	−	1.30943i	−0.188880	−	0.982000i	$-0.560486\pi$
$229$	11.4403	−	19.8152i	0.755997	−	1.30943i	0.944877	−	0.327426i	$-0.106181\pi$
$230$	0.474466	+	0.821799i	0.0312854	+	0.0541878i
$231$	−19.1939	−	7.18283i	−1.26287	−	0.472596i
$232$	−2.07678	+	3.59710i	−0.136348	+	0.236161i
$233$	−11.9917	−	20.7703i	−0.785605	−	1.36071i	−0.928637	−	0.370990i	$-0.879018\pi$
$233$	−11.9917	−	20.7703i	−0.785605	−	1.36071i	0.143032	−	0.989718i	$-0.454315\pi$
$234$	−4.89173	−	0.851755i	−0.319782	−	0.0556810i
$235$	−0.507566	+	0.879130i	−0.0331099	+	0.0573481i
$236$	8.84247			0.575596
$237$	−15.5723	+	7.28178i	−1.01153	+	0.473003i
$238$	1.92283	−	6.89685i	0.124639	−	0.447056i
$239$	−6.66407	−	11.5425i	−0.431063	−	0.746622i	0.565902	−	0.824472i	$-0.308528\pi$
$239$	−6.66407	−	11.5425i	−0.431063	−	0.746622i	−0.996965	+	0.0778498i	$0.975195\pi$
$240$	0.149112	−	1.72562i	0.00962514	−	0.111388i
$241$	−0.245101	−	0.424527i	−0.0157883	−	0.0273462i	0.858023	−	0.513611i	$-0.171692\pi$
$241$	−0.245101	−	0.424527i	−0.0157883	−	0.0273462i	−0.873812	+	0.486265i	$0.838359\pi$
$242$	4.49999	−	7.79422i	0.289271	−	0.501031i
$243$	9.00935	+	12.7213i	0.577950	+	0.816072i
$244$	12.0183			0.769394
$245$	−0.141315	+	6.99857i	−0.00902829	+	0.447122i
$246$	2.75539	+	1.92495i	0.175677	+	0.122731i
$247$	−1.36969	+	2.37238i	−0.0871516	+	0.150951i
$248$	−3.00713			−0.190953
$249$	−0.479557	+	5.54974i	−0.0303907	+	0.351700i
$250$	−1.00000			−0.0632456
$251$	−21.2007			−1.33818			−0.669089	−	0.743182i	$-0.733315\pi$
$251$	−21.2007			−1.33818			−0.669089	+	0.743182i	$0.733315\pi$
$252$	−3.41155	+	7.16668i	−0.214907	+	0.451459i
$253$	4.24375			0.266802
$254$	19.3979			1.21713
$255$	−3.84243	−	2.68438i	−0.240623	−	0.168102i
$256$	1.00000			0.0625000
$257$	−10.3554	+	17.9361i	−0.645953	+	1.11882i	0.338128	+	0.941100i	$0.390206\pi$
$257$	−10.3554	+	17.9361i	−0.645953	+	1.11882i	−0.984081	+	0.177723i	$0.943127\pi$
$258$	0.747816	−	8.65421i	0.0465570	−	0.538788i
$259$	−18.0570	−	18.4253i	−1.12201	−	1.14489i
$260$	−1.65511			−0.102646
$261$	−4.28686	−	11.7001i	−0.265350	−	0.724217i
$262$	−1.77033	+	3.06630i	−0.109371	+	0.189437i
$263$	−5.79295	−	10.0337i	−0.357208	−	0.618703i	0.630285	−	0.776364i	$-0.282938\pi$
$263$	−5.79295	−	10.0337i	−0.357208	−	0.618703i	−0.987493	+	0.157661i	$0.949605\pi$
$264$	−6.34987	−	4.43611i	−0.390808	−	0.273024i
$265$	6.65730	+	11.5308i	0.408955	+	0.708330i
$266$	3.06501	+	3.12753i	0.187928	+	0.191761i
$267$	8.13991	+	5.68666i	0.498154	+	0.348018i
$268$	0.773956			0.0472769
$269$	4.15928	−	7.20408i	0.253596	−	0.439240i	−0.710918	−	0.703275i	$-0.751720\pi$
$269$	4.15928	−	7.20408i	0.253596	−	0.439240i	0.964513	+	0.264035i	$0.0850534\pi$
$270$	3.68601	+	3.66242i	0.224323	+	0.222888i
$271$	−6.60231	−	11.4355i	−0.401062	−	0.694660i	0.592792	−	0.805355i	$-0.298025\pi$
$271$	−6.60231	−	11.4355i	−0.401062	−	0.694660i	−0.993854	+	0.110696i	$0.964692\pi$
$272$	1.35309	−	2.34362i	0.0820431	−	0.142103i
$273$	7.10355	+	2.65832i	0.429927	+	0.160889i
$274$	8.90949	+	15.4317i	0.538242	+	0.932263i
$275$	−2.23607	+	3.87298i	−0.134840	+	0.233550i
$276$	0.141497	−	1.63750i	0.00851713	−	0.0985657i
$277$	−3.17767	−	5.50389i	−0.190928	−	0.330697i	0.754630	−	0.656150i	$-0.227816\pi$
$277$	−3.17767	−	5.50389i	−0.190928	−	0.330697i	−0.945558	+	0.325454i	$0.894483\pi$
$278$	6.41271	+	11.1071i	0.384609	+	0.666162i
$279$	5.78404	−	6.92318i	0.346281	−	0.414480i
$280$	−0.710533	+	2.54856i	−0.0424625	+	0.152305i
$281$	−2.01375	+	3.48791i	−0.120130	+	0.208071i	−0.919819	−	0.392343i	$-0.871665\pi$
$281$	−2.01375	+	3.48791i	−0.120130	+	0.208071i	0.799689	+	0.600415i	$0.204998\pi$
$282$	1.59273	−	0.744777i	0.0948456	−	0.0443508i
$283$	16.6101			0.987370			0.493685	−	0.869641i	$-0.335650\pi$
$283$	16.6101			0.987370			0.493685	+	0.869641i	$0.335650\pi$
$284$	−13.8907			−0.824262
$285$	2.59685	−	1.21431i	0.153824	−	0.0719297i
$286$	−3.70094	+	6.41021i	−0.218841	+	0.379044i
$287$	−3.59367	−	3.66697i	−0.212128	−	0.216454i
$288$	−1.92344	+	2.30225i	−0.113340	+	0.135662i
$289$	4.83830	+	8.38018i	0.284606	+	0.492952i
$290$	−2.07678	−	3.59710i	−0.121953	−	0.211229i
$291$	0.852529	−	9.86601i	0.0499761	−	0.578356i
$292$	0.166120	−	0.287728i	0.00972143	−	0.0168380i
$293$	2.98560	+	5.17121i	0.174420	+	0.302105i	0.939961	−	0.341283i	$-0.110861\pi$
$293$	2.98560	+	5.17121i	0.174420	+	0.302105i	−0.765540	+	0.643388i	$0.777528\pi$
$294$	7.14285	−	9.79692i	0.416579	−	0.571368i
$295$	−4.42123	+	7.65780i	−0.257414	+	0.445854i
$296$	−4.87541	−	8.44445i	−0.283377	−	0.490824i
$297$	22.4267	−	6.08642i	1.30133	−	0.353170i
$298$	4.96565	−	8.60076i	0.287653	−	0.498229i
$299$	−1.57059			−0.0908294
$300$	1.41988	+	0.991945i	0.0819765	+	0.0572700i
$301$	−3.56342	+	12.7813i	−0.205392	+	0.736705i
$302$	4.03641	+	6.99127i	0.232270	+	0.402303i
$303$	−13.1587	−	9.19284i	−0.755946	−	0.528115i
$304$	0.827555	+	1.43337i	0.0474635	+	0.0822093i
$305$	−6.00916	+	10.4082i	−0.344083	+	0.595970i
$306$	2.79302	+	7.62297i	0.159666	+	0.435776i
$307$	19.3496			1.10434			0.552171	−	0.833731i	$-0.313800\pi$
$307$	19.3496			1.10434			0.552171	+	0.833731i	$0.313800\pi$
$308$	8.28172	+	8.45063i	0.471895	+	0.481519i
$309$	−2.84034	+	32.8703i	−0.161581	+	1.86992i
$310$	1.50357	−	2.60425i	0.0853968	−	0.147912i
$311$	20.5760			1.16676			0.583379	−	0.812200i	$-0.301730\pi$
$311$	20.5760			1.16676			0.583379	+	0.812200i	$0.301730\pi$
$312$	2.35005	+	1.64178i	0.133045	+	0.0929474i
$313$	−8.26984			−0.467439			−0.233720	−	0.972304i	$-0.575090\pi$
$313$	−8.26984			−0.467439			−0.233720	+	0.972304i	$0.575090\pi$
$314$	19.8019			1.11748
$315$	−4.50076	−	6.53783i	−0.253589	−	0.368365i
$316$	9.92508			0.558329
$317$	29.4641			1.65487			0.827435	−	0.561561i	$-0.189799\pi$
$317$	29.4641			1.65487			0.827435	+	0.561561i	$0.189799\pi$
$318$	1.98537	−	22.9759i	0.111334	−	1.28843i
$319$	−18.5753			−1.04002
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−3.89921	−	2.72404i	−0.217633	−	0.152041i
$322$	−0.674248	+	2.41841i	−0.0375744	+	0.134773i
$323$	4.47902			0.249219
$324$	−1.60075	−	8.85650i	−0.0889306	−	0.492028i
$325$	0.827555	−	1.43337i	0.0459045	−	0.0795089i
$326$	8.46813	+	14.6672i	0.469007	+	0.812343i
$327$	1.19475	−	13.8264i	0.0660699	−	0.764604i
$328$	−0.970293	−	1.68060i	−0.0535755	−	0.0927954i
$329$	−2.60115	+	0.668909i	−0.143406	+	0.0368782i
$330$	7.01672	−	3.28109i	0.386258	−	0.180618i
$331$	2.90680			0.159772			0.0798860	−	0.996804i	$-0.474544\pi$
$331$	2.90680			0.159772			0.0798860	+	0.996804i	$0.474544\pi$
$332$	1.60804	−	2.78521i	0.0882528	−	0.152858i
$333$	28.8188	+	5.01798i	1.57926	+	0.274983i
$334$	−9.80368	−	16.9805i	−0.536433	−	0.929130i
$335$	−0.386978	+	0.670266i	−0.0211429	+	0.0366205i
$336$	3.53690	−	2.91382i	0.192954	−	0.158962i
$337$	−7.13923	−	12.3655i	−0.388899	−	0.673592i	0.603403	−	0.797436i	$-0.293811\pi$
$337$	−7.13923	−	12.3655i	−0.388899	−	0.673592i	−0.992302	+	0.123844i	$0.960478\pi$
$338$	−5.13031	+	8.88595i	−0.279052	+	0.483332i
$339$	7.04175	+	4.91947i	0.382455	+	0.267189i
$340$	1.35309	+	2.34362i	0.0733816	+	0.127101i
$341$	−6.72415	−	11.6466i	−0.364133	−	0.630697i
$342$	−4.89173	−	0.851755i	−0.264514	−	0.0460576i
$343$	−13.4863	+	12.6933i	−0.728193	+	0.685372i
$344$	−2.50757	+	4.34323i	−0.135199	+	0.234171i
$345$	1.34736	+	0.941288i	0.0725397	+	0.0506773i
$346$	−7.46596			−0.401372
$347$	18.2254			0.978388			0.489194	−	0.872175i	$-0.337291\pi$
$347$	18.2254			0.978388			0.489194	+	0.872175i	$0.337291\pi$
$348$	−0.619347	+	7.16748i	−0.0332005	+	0.384217i
$349$	3.76675	−	6.52420i	0.201630	−	0.349233i	−0.747424	−	0.664347i	$-0.768710\pi$
$349$	3.76675	−	6.52420i	0.201630	−	0.349233i	0.949054	+	0.315115i	$0.102043\pi$
$350$	−1.85185	−	1.88962i	−0.0989855	−	0.101004i
$351$	−8.29997	+	2.25255i	−0.443020	+	0.120232i
$352$	2.23607	+	3.87298i	0.119183	+	0.206431i
$353$	−2.78377	−	4.82163i	−0.148165	−	0.256629i	0.782384	−	0.622796i	$-0.214003\pi$
$353$	−2.78377	−	4.82163i	−0.148165	−	0.256629i	−0.930549	+	0.366167i	$0.880670\pi$
$354$	13.8737	−	6.48750i	0.737380	−	0.344807i
$355$	6.94535	−	12.0297i	0.368621	−	0.638470i
$356$	−2.86642	−	4.96478i	−0.151920	−	0.263133i
$357$	−2.04315	−	12.2318i	−0.108135	−	0.647375i
$358$	2.74363	−	4.75211i	0.145006	−	0.251157i
$359$	10.7999	+	18.7059i	0.569994	+	0.987259i	0.996566	+	0.0828052i	$0.0263879\pi$
$359$	10.7999	+	18.7059i	0.569994	+	0.987259i	−0.426571	+	0.904454i	$0.640279\pi$
$360$	−1.03209	−	2.81688i	−0.0543959	−	0.148462i
$361$	8.13031	−	14.0821i	0.427911	−	0.741163i
$362$	−13.6477			−0.717308
$363$	1.34201	−	15.5306i	0.0704371	−	0.815143i
$364$	−3.06501	−	3.12753i	−0.160650	−	0.163927i
$365$	0.166120	+	0.287728i	0.00869511	+	0.0150604i
$366$	18.8566	−	8.81754i	0.985649	−	0.460900i
$367$	−10.2270	−	17.7136i	−0.533844	−	0.924644i	−0.999218	−	0.0395304i	$-0.987414\pi$
$367$	−10.2270	−	17.7136i	−0.533844	−	0.924644i	0.465375	−	0.885114i	$-0.345920\pi$
$368$	−0.474466	+	0.821799i	−0.0247333	+	0.0428392i
$369$	5.73546	+	0.998667i	0.298576	+	0.0519885i
$370$	9.75081			0.506921
$371$	−9.46047	+	33.9330i	−0.491163	+	1.76171i
$372$	−4.71815	+	2.20626i	−0.244625	+	0.114389i
$373$	1.10865	−	1.92024i	0.0574037	−	0.0994261i	−0.835896	−	0.548889i	$-0.815051\pi$
$373$	1.10865	−	1.92024i	0.0574037	−	0.0994261i	0.893299	+	0.449462i	$0.148384\pi$
$374$	12.1024			0.625800
$375$	−1.56899	+	0.733675i	−0.0810221	+	0.0378868i
$376$	−1.01513			−0.0523514
$377$	6.87461			0.354061
$378$	−0.0946515	+	13.7474i	−0.00486835	+	0.707090i
$379$	5.04110			0.258944			0.129472	−	0.991583i	$-0.458672\pi$
$379$	5.04110			0.258944			0.129472	+	0.991583i	$0.458672\pi$
$380$	−1.65511			−0.0849054
$381$	30.4351	−	14.2318i	1.55924	−	0.729116i
$382$	−24.7176			−1.26466
$383$	−13.1820	+	22.8319i	−0.673570	+	1.16666i	0.303314	+	0.952891i	$0.401907\pi$
$383$	−13.1820	+	22.8319i	−0.673570	+	1.16666i	−0.976885	+	0.213767i	$0.931427\pi$
$384$	1.56899	−	0.733675i	0.0800670	−	0.0374402i
$385$	−11.4593	+	2.94686i	−0.584021	+	0.150186i
$386$	−15.0374			−0.765384
$387$	−5.17607	−	14.1270i	−0.263114	−	0.718116i
$388$	−2.85868	+	4.95139i	−0.145128	+	0.251369i
$389$	−8.36238	−	14.4841i	−0.423989	−	0.734371i	0.572336	−	0.820019i	$-0.306037\pi$
$389$	−8.36238	−	14.4841i	−0.423989	−	0.734371i	−0.996325	+	0.0856480i	$0.972704\pi$
$390$	−2.59685	+	1.21431i	−0.131496	+	0.0614892i
$391$	1.28399	+	2.22394i	0.0649341	+	0.112469i
$392$	−6.13160	+	3.37690i	−0.309693	+	0.170559i
$393$	−0.527955	+	6.10983i	−0.0266318	+	0.308200i
$394$	−21.9097			−1.10379
$395$	−4.96254	+	8.59537i	−0.249692	+	0.432480i
$396$	−13.2175	−	2.30146i	−0.664206	−	0.115653i
$397$	−6.52922	−	11.3089i	−0.327692	−	0.567579i	0.654361	−	0.756182i	$-0.272938\pi$
$397$	−6.52922	−	11.3089i	−0.327692	−	0.567579i	−0.982054	+	0.188603i	$0.939604\pi$
$398$	12.1642	−	21.0691i	0.609738	−	1.05610i
$399$	7.10355	+	2.65832i	0.355623	+	0.133083i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−19.1172	+	33.1120i	−0.954668	+	1.65353i	−0.219542	+	0.975603i	$0.570456\pi$
$401$	−19.1172	+	33.1120i	−0.954668	+	1.65353i	−0.735126	+	0.677931i	$0.762877\pi$
$402$	1.21433	−	0.567833i	0.0605652	−	0.0283209i
$403$	2.48857	+	4.31032i	0.123964	+	0.214713i
$404$	4.63374	+	8.02588i	0.230537	+	0.399302i
$405$	8.47033	+	3.04196i	0.420894	+	0.151156i
$406$	2.95125	−	10.5856i	0.146468	−	0.525355i
$407$	21.8035	−	37.7647i	1.08076	−	1.87193i
$408$	0.403524	−	4.66984i	0.0199774	−	0.231191i
$409$	−13.6741			−0.676140			−0.338070	−	0.941121i	$-0.609774\pi$
$409$	−13.6741			−0.676140			−0.338070	+	0.941121i	$0.609774\pi$
$410$	1.94059			0.0958387
$411$	25.3007	+	17.6755i	1.24799	+	0.871866i
$412$	9.52418	−	16.4964i	0.469223	−	0.812718i
$413$	−22.6578	+	5.82664i	−1.11492	+	0.286710i
$414$	−0.979384	−	2.67302i	−0.0481341	−	0.131372i
$415$	1.60804	+	2.78521i	0.0789357	+	0.136721i
$416$	−0.827555	−	1.43337i	−0.0405742	−	0.0702766i
$417$	18.2105	+	12.7221i	0.891772	+	0.623005i
$418$	−3.70094	+	6.41021i	−0.181019	+	0.313534i
$419$	4.16825	+	7.21962i	0.203632	+	0.352701i	0.949696	−	0.313173i	$-0.101392\pi$
$419$	4.16825	+	7.21962i	0.203632	+	0.352701i	−0.746064	+	0.665874i	$0.768059\pi$
$420$	0.754996	+	4.51995i	0.0368400	+	0.220551i
$421$	−1.03373	+	1.79048i	−0.0503811	+	0.0872626i	−0.890116	−	0.455734i	$-0.849377\pi$
$421$	−1.03373	+	1.79048i	−0.0503811	+	0.0872626i	0.839735	+	0.542996i	$0.182710\pi$
$422$	−9.43146	−	16.3358i	−0.459116	−	0.795212i
$423$	1.95255	−	2.33709i	0.0949360	−	0.113633i
$424$	−6.65730	+	11.5308i	−0.323307	+	0.559984i
$425$	−2.70618			−0.131269
$426$	−21.7943	+	10.1913i	−1.05594	+	0.493769i
$427$	−30.7955	+	7.91933i	−1.49030	+	0.383243i
$428$	1.37308	+	2.37825i	0.0663704	+	0.114957i
$429$	−1.10371	+	12.7728i	−0.0532876	+	0.616678i
$430$	−2.50757	−	4.34323i	−0.120926	−	0.209449i
$431$	−1.71653	+	2.97311i	−0.0826822	+	0.143210i	−0.904401	−	0.426683i	$-0.859682\pi$
$431$	−1.71653	+	2.97311i	−0.0826822	+	0.143210i	0.821719	+	0.569893i	$0.193015\pi$
$432$	−1.32875	+	5.02339i	−0.0639294	+	0.241688i
$433$	7.62844			0.366599			0.183300	−	0.983057i	$-0.441322\pi$
$433$	7.62844			0.366599			0.183300	+	0.983057i	$0.441322\pi$
$434$	7.70542	−	1.98152i	0.369872	−	0.0951158i
$435$	−5.89755	−	4.12011i	−0.282766	−	0.197544i
$436$	−4.00622	+	6.93898i	−0.191863	+	0.332317i
$437$	−1.57059			−0.0751314
$438$	0.0495409	−	0.573319i	0.00236716	−	0.0273943i
$439$	−15.3407			−0.732174			−0.366087	−	0.930581i	$-0.619303\pi$
$439$	−15.3407			−0.732174			−0.366087	+	0.930581i	$0.619303\pi$
$440$	−4.47213			−0.213201
$441$	4.01928	−	20.6118i	0.191394	−	0.981513i
$442$	−4.47902			−0.213045
$443$	10.9405			0.519800			0.259900	−	0.965636i	$-0.416310\pi$
$443$	10.9405			0.519800			0.259900	+	0.965636i	$0.416310\pi$
$444$	−13.8449	−	9.67227i	−0.657052	−	0.459026i
$445$	5.73284			0.271762
$446$	−9.42519	+	16.3249i	−0.446296	+	0.773007i
$447$	1.48088	−	17.1377i	0.0700431	−	0.810584i
$448$	−2.56238	+	0.658939i	−0.121061	+	0.0311319i
$449$	11.4979			0.542617			0.271309	−	0.962492i	$-0.412544\pi$
$449$	11.4979			0.542617			0.271309	+	0.962492i	$0.412544\pi$
$450$	2.95553	+	0.514622i	0.139325	+	0.0242595i
$451$	4.33928	−	7.51585i	0.204329	−	0.353908i
$452$	−2.47971	−	4.29498i	−0.116636	−	0.202019i
$453$	11.4624	+	8.00780i	0.538551	+	0.376239i
$454$	−2.10153	−	3.63995i	−0.0986296	−	0.170832i
$455$	4.24102	−	1.09062i	0.198822	−	0.0511289i
$456$	2.35005	+	1.64178i	0.110051	+	0.0768833i
$457$	6.93375			0.324347			0.162174	−	0.986762i	$-0.448150\pi$
$457$	6.93375			0.324347			0.162174	+	0.986762i	$0.448150\pi$
$458$	−11.4403	+	19.8152i	−0.534571	+	0.925904i
$459$	9.97500	+	9.91117i	0.465593	+	0.462614i
$460$	−0.474466	−	0.821799i	−0.0221221	−	0.0383166i
$461$	−19.9618	+	34.5748i	−0.929711	+	1.61031i	−0.145908	+	0.989298i	$0.546610\pi$
$461$	−19.9618	+	34.5748i	−0.929711	+	1.61031i	−0.783803	+	0.621009i	$0.786723\pi$
$462$	19.1939	+	7.18283i	0.892982	+	0.334176i
$463$	0.419823	+	0.727155i	0.0195108	+	0.0337938i	0.875616	−	0.483008i	$-0.160456\pi$
$463$	0.419823	+	0.727155i	0.0195108	+	0.0337938i	−0.856105	+	0.516802i	$0.827122\pi$
$464$	2.07678	−	3.59710i	0.0964123	−	0.166991i
$465$	0.448400	−	5.18917i	0.0207940	−	0.240642i
$466$	11.9917	+	20.7703i	0.555507	+	0.962166i
$467$	6.54621	+	11.3384i	0.302922	+	0.524677i	0.976797	−	0.214169i	$-0.0687043\pi$
$467$	6.54621	+	11.3384i	0.302922	+	0.524677i	−0.673874	+	0.738846i	$0.735371\pi$
$468$	4.89173	+	0.851755i	0.226120	+	0.0393724i
$469$	−1.98317	+	0.509990i	−0.0915744	+	0.0235491i
$470$	0.507566	−	0.879130i	0.0234123	−	0.0405512i
$471$	31.0689	−	14.5281i	1.43158	−	0.669421i
$472$	−8.84247			−0.407008
$473$	−22.4283			−1.03126
$474$	15.5723	−	7.28178i	0.715260	−	0.334463i
$475$	0.827555	−	1.43337i	0.0379708	−	0.0657674i
$476$	−1.92283	+	6.89685i	−0.0881328	+	0.316117i
$477$	−13.7419	−	37.5056i	−0.629197	−	1.71726i
$478$	6.66407	+	11.5425i	0.304807	+	0.527942i
$479$	14.7920	+	25.6205i	0.675865	+	1.17063i	0.976215	+	0.216804i	$0.0695632\pi$
$479$	14.7920	+	25.6205i	0.675865	+	1.17063i	−0.300350	+	0.953829i	$0.597104\pi$
$480$	−0.149112	+	1.72562i	−0.00680600	+	0.0787634i
$481$	−8.06933	+	13.9765i	−0.367930	+	0.637273i
$482$	0.245101	+	0.424527i	0.0111640	+	0.0193367i
$483$	0.716440	+	4.28913i	0.0325991	+	0.195162i
$484$	−4.49999	+	7.79422i	−0.204545	+	0.354283i
$485$	−2.85868	−	4.95139i	−0.129806	−	0.224831i
$486$	−9.00935	−	12.7213i	−0.408673	−	0.577050i
$487$	19.1240	−	33.1238i	0.866592	−	1.50098i	0.00113426	−	0.999999i	$-0.499639\pi$
$487$	19.1240	−	33.1238i	0.866592	−	1.50098i	0.865458	−	0.500982i	$-0.167028\pi$
$488$	−12.0183			−0.544043
$489$	24.0474	+	16.7998i	1.08746	+	0.759715i
$490$	0.141315	−	6.99857i	0.00638396	−	0.316163i
$491$	−15.8531	−	27.4583i	−0.715439	−	1.23918i	−0.962790	−	0.270250i	$-0.912894\pi$
$491$	−15.8531	−	27.4583i	−0.715439	−	1.23918i	0.247351	−	0.968926i	$-0.420440\pi$
$492$	−2.75539	−	1.92495i	−0.124223	−	0.0867836i
$493$	−5.62015	−	9.73438i	−0.253119	−	0.438414i
$494$	1.36969	−	2.37238i	0.0616255	−	0.106738i
$495$	8.60189	−	10.2960i	0.386626	−	0.462770i
$496$	3.00713			0.135024
$497$	35.5933	−	9.15312i	1.59658	−	0.410574i
$498$	0.479557	−	5.54974i	0.0214895	−	0.248690i
$499$	−11.9392	+	20.6793i	−0.534472	+	0.925733i	0.464717	+	0.885459i	$0.346156\pi$
$499$	−11.9392	+	20.6793i	−0.534472	+	0.925733i	−0.999189	+	0.0402733i	$0.987177\pi$
$500$	1.00000			0.0447214
$501$	−27.8400	−	19.4494i	−1.24380	−	0.868936i
$502$	21.2007			0.946235
$503$	−26.8666			−1.19792			−0.598962	−	0.800777i	$-0.704420\pi$
$503$	−26.8666			−1.19792			−0.598962	+	0.800777i	$0.704420\pi$
$504$	3.41155	−	7.16668i	0.151962	−	0.319229i
$505$	−9.26749			−0.412398
$506$	−4.24375			−0.188658
$507$	−1.52998	+	17.7059i	−0.0679488	+	0.786347i
$508$	−19.3979			−0.860644
$509$	14.3070	−	24.7804i	0.634145	−	1.09837i	−0.352550	−	0.935793i	$-0.614685\pi$
$509$	14.3070	−	24.7804i	0.634145	−	1.09837i	0.986695	−	0.162579i	$-0.0519813\pi$
$510$	3.84243	+	2.68438i	0.170146	+	0.118866i
$511$	−0.236067	+	0.846731i	−0.0104430	+	0.0374572i
$512$	−1.00000			−0.0441942
$513$	−8.29997	+	2.25255i	−0.366453	+	0.0994524i
$514$	10.3554	−	17.9361i	0.456758	−	0.791127i
$515$	9.52418	+	16.4964i	0.419686	+	0.726917i
$516$	−0.747816	+	8.65421i	−0.0329208	+	0.380980i
$517$	−2.26990	−	3.93159i	−0.0998302	−	0.172911i
$518$	18.0570	+	18.4253i	0.793380	+	0.809562i
$519$	−11.7140	+	5.47759i	−0.514187	+	0.240439i
$520$	1.65511			0.0725814
$521$	−15.1514	+	26.2430i	−0.663795	+	1.14973i	0.315815	+	0.948821i	$0.397722\pi$
$521$	−15.1514	+	26.2430i	−0.663795	+	1.14973i	−0.979610	+	0.200906i	$0.935611\pi$
$522$	4.28686	+	11.7001i	0.187631	+	0.512099i
$523$	17.0208	+	29.4809i	0.744268	+	1.28911i	0.950536	+	0.310615i	$0.100535\pi$
$523$	17.0208	+	29.4809i	0.744268	+	1.28911i	−0.206267	+	0.978496i	$0.566132\pi$
$524$	1.77033	−	3.06630i	0.0773372	−	0.133952i
$525$	−4.29189	−	1.60613i	−0.187314	−	0.0700973i
$526$	5.79295	+	10.0337i	0.252584	+	0.437489i
$527$	4.06892	−	7.04757i	0.177245	−	0.306997i
$528$	6.34987	+	4.43611i	0.276343	+	0.193057i
$529$	11.0498	+	19.1388i	0.480425	+	0.832120i
$530$	−6.65730	−	11.5308i	−0.289175	−	0.500865i
$531$	17.0080	−	20.3576i	0.738083	−	0.883445i
$532$	−3.06501	−	3.12753i	−0.132885	−	0.135595i
$533$	−1.60594	+	2.78157i	−0.0695610	+	0.120483i
$534$	−8.13991	−	5.68666i	−0.352248	−	0.246086i
$535$	−2.74616			−0.118727
$536$	−0.773956			−0.0334298
$537$	0.818217	−	9.46894i	0.0353087	−	0.408615i
$538$	−4.15928	+	7.20408i	−0.179319	+	0.310590i
$539$	−26.7894	−	16.1966i	−1.15390	−	0.697637i
$540$	−3.68601	−	3.66242i	−0.158621	−	0.157606i
$541$	−3.17697	−	5.50267i	−0.136589	−	0.236578i	0.789615	−	0.613603i	$-0.210281\pi$
$541$	−3.17697	−	5.50267i	−0.136589	−	0.236578i	−0.926203	+	0.377025i	$0.876947\pi$
$542$	6.60231	+	11.4355i	0.283594	+	0.491198i
$543$	−21.4131	+	10.0130i	−0.918923	+	0.429698i
$544$	−1.35309	+	2.34362i	−0.0580132	+	0.100482i
$545$	−4.00622	−	6.93898i	−0.171608	−	0.297233i
$546$	−7.10355	−	2.65832i	−0.304004	−	0.113766i
$547$	−8.53992	+	14.7916i	−0.365141	+	0.632442i	−0.988799	−	0.149255i	$-0.952312\pi$
$547$	−8.53992	+	14.7916i	−0.365141	+	0.632442i	0.623658	+	0.781697i	$0.285646\pi$
$548$	−8.90949	−	15.4317i	−0.380595	−	0.659209i
$549$	23.1165	−	27.6692i	0.986589	−	1.18089i
$550$	2.23607	−	3.87298i	0.0953462	−	0.165145i
$551$	6.87461			0.292868
$552$	−0.141497	+	1.63750i	−0.00602252	+	0.0696965i
$553$	−25.4318	+	6.54002i	−1.08147	+	0.278110i
$554$	3.17767	+	5.50389i	0.135006	+	0.233838i
$555$	15.2989	−	7.15393i	0.649402	−	0.303667i
$556$	−6.41271	−	11.1071i	−0.271960	−	0.471048i
$557$	−8.97738	+	15.5493i	−0.380384	+	0.658844i	−0.991117	−	0.132992i	$-0.957541\pi$
$557$	−8.97738	+	15.5493i	−0.380384	+	0.658844i	0.610733	+	0.791837i	$0.290875\pi$
$558$	−5.78404	+	6.92318i	−0.244858	+	0.293082i
$559$	8.30059			0.351078
$560$	0.710533	−	2.54856i	0.0300255	−	0.107696i
$561$	18.9885	−	8.87923i	0.801695	−	0.374881i
$562$	2.01375	−	3.48791i	0.0849448	−	0.147129i
$563$	32.7771			1.38139			0.690695	−	0.723146i	$-0.257305\pi$
$563$	32.7771			1.38139			0.690695	+	0.723146i	$0.257305\pi$
$564$	−1.59273	+	0.744777i	−0.0670660	+	0.0313608i
$565$	4.95941			0.208644
$566$	−16.6101			−0.698176
$567$	9.93762	+	21.6389i	0.417341	+	0.908750i
$568$	13.8907			0.582841
$569$	−39.2617			−1.64593			−0.822967	−	0.568089i	$-0.807683\pi$
$569$	−39.2617			−1.64593			−0.822967	+	0.568089i	$0.807683\pi$
$570$	−2.59685	+	1.21431i	−0.108770	+	0.0508620i
$571$	12.6940			0.531229			0.265615	−	0.964079i	$-0.414425\pi$
$571$	12.6940			0.531229			0.265615	+	0.964079i	$0.414425\pi$
$572$	3.70094	−	6.41021i	0.154744	−	0.268024i
$573$	−38.7816	+	18.1347i	−1.62012	+	0.757588i
$574$	3.59367	+	3.66697i	0.149997	+	0.153056i
$575$	0.948932			0.0395732
$576$	1.92344	−	2.30225i	0.0801434	−	0.0959273i
$577$	−20.9847	+	36.3465i	−0.873603	+	1.51312i	−0.0153586	+	0.999882i	$0.504889\pi$
$577$	−20.9847	+	36.3465i	−0.873603	+	1.51312i	−0.858244	+	0.513242i	$0.828444\pi$
$578$	−4.83830	−	8.38018i	−0.201247	−	0.348570i
$579$	−23.5935	+	11.0326i	−0.980512	+	0.458498i
$580$	2.07678	+	3.59710i	0.0862338	+	0.149361i
$581$	−2.28513	+	8.19637i	−0.0948034	+	0.340043i
$582$	−0.852529	+	9.86601i	−0.0353384	+	0.408959i
$583$	−59.5447			−2.46609
$584$	−0.166120	+	0.287728i	−0.00687409	+	0.0119063i
$585$	−3.18351	+	3.81048i	−0.131622	+	0.157544i
$586$	−2.98560	−	5.17121i	−0.123334	−	0.213621i
$587$	−0.372630	+	0.645414i	−0.0153801	+	0.0266391i	−0.873613	−	0.486621i	$-0.838229\pi$
$587$	−0.372630	+	0.645414i	−0.0153801	+	0.0266391i	0.858233	+	0.513260i	$0.171562\pi$
$588$	−7.14285	+	9.79692i	−0.294566	+	0.404018i
$589$	2.48857	+	4.31032i	0.102540	+	0.177604i
$590$	4.42123	−	7.65780i	0.182019	−	0.315267i
$591$	−34.3760	+	16.0746i	−1.41404	+	0.661220i
$592$	4.87541	+	8.44445i	0.200378	+	0.347065i
$593$	0.925847	+	1.60361i	0.0380200	+	0.0658525i	0.884409	−	0.466712i	$-0.154562\pi$
$593$	0.925847	+	1.60361i	0.0380200	+	0.0658525i	−0.846389	+	0.532565i	$0.821228\pi$
$594$	−22.4267	+	6.08642i	−0.920177	+	0.249729i
$595$	−5.01143	−	5.11364i	−0.205449	−	0.209639i
$596$	−4.96565	+	8.60076i	−0.203401	+	0.352301i
$597$	3.62767	−	41.9817i	0.148471	−	1.71820i
$598$	1.57059			0.0642261
$599$	−25.0670			−1.02421			−0.512105	−	0.858923i	$-0.671134\pi$
$599$	−25.0670			−1.02421			−0.512105	+	0.858923i	$0.671134\pi$
$600$	−1.41988	−	0.991945i	−0.0579662	−	0.0404960i
$601$	−12.2717	+	21.2553i	−0.500574	+	0.867020i	0.499425	+	0.866357i	$0.333544\pi$
$601$	−12.2717	+	21.2553i	−0.500574	+	0.867020i	−1.00000		0.000663296i	$0.999789\pi$
$602$	3.56342	−	12.7813i	0.145234	−	0.520929i
$603$	1.48866	−	1.78184i	0.0606229	−	0.0725623i
$604$	−4.03641	−	6.99127i	−0.164239	−	0.284471i
$605$	−4.49999	−	7.79422i	−0.182951	−	0.316880i
$606$	13.1587	+	9.19284i	0.534535	+	0.373433i
$607$	17.4884	−	30.2908i	0.709832	−	1.22946i	−0.255087	−	0.966918i	$-0.582104\pi$
$607$	17.4884	−	30.2908i	0.709832	−	1.22946i	0.964919	−	0.262547i	$-0.0845625\pi$
$608$	−0.827555	−	1.43337i	−0.0335618	−	0.0581307i
$609$	−3.13593	−	18.7739i	−0.127074	−	0.760758i
$610$	6.00916	−	10.4082i	0.243304	−	0.421414i
$611$	0.840077	+	1.45506i	0.0339859	+	0.0588653i
$612$	−2.79302	−	7.62297i	−0.112901	−	0.308140i
$613$	−15.5565	+	26.9447i	−0.628322	+	1.08829i	0.359566	+	0.933120i	$0.382925\pi$
$613$	−15.5565	+	26.9447i	−0.628322	+	1.08829i	−0.987888	+	0.155167i	$0.950409\pi$
$614$	−19.3496			−0.780887
$615$	3.04475	−	1.42376i	0.122776	−	0.0574115i
$616$	−8.28172	−	8.45063i	−0.333680	−	0.340485i
$617$	−23.1494	−	40.0959i	−0.931959	−	1.61420i	−0.779969	−	0.625818i	$-0.784765\pi$
$617$	−23.1494	−	40.0959i	−0.931959	−	1.61420i	−0.151990	−	0.988382i	$-0.548568\pi$
$618$	2.84034	−	32.8703i	0.114255	−	1.32224i
$619$	4.25026	+	7.36167i	0.170832	+	0.295891i	0.938711	−	0.344705i	$-0.112021\pi$
$619$	4.25026	+	7.36167i	0.170832	+	0.295891i	−0.767879	+	0.640595i	$0.778688\pi$
$620$	−1.50357	+	2.60425i	−0.0603847	+	0.104589i
$621$	−3.49777	−	3.47539i	−0.140361	−	0.139463i
$622$	−20.5760			−0.825023
$623$	10.6163	+	10.8329i	0.425335	+	0.434010i
$624$	−2.35005	−	1.64178i	−0.0940773	−	0.0657237i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	8.26984			0.330529
$627$	−1.10371	+	12.7728i	−0.0440779	+	0.510098i
$628$	−19.8019			−0.790181
$629$	26.3874			1.05214
$630$	4.50076	+	6.53783i	0.179314	+	0.260473i
$631$	35.8244			1.42615			0.713074	−	0.701089i	$-0.247303\pi$
$631$	35.8244			1.42615			0.713074	+	0.701089i	$0.247303\pi$
$632$	−9.92508			−0.394798
$633$	−26.7830	−	18.7110i	−1.06453	−	0.743694i
$634$	−29.4641			−1.17017
$635$	9.69896	−	16.7991i	0.384892	−	0.666652i
$636$	−1.98537	+	22.9759i	−0.0787249	+	0.911056i
$637$	9.91458	+	5.99426i	0.392830	+	0.237501i
$638$	18.5753			0.735404
$639$	−26.7180	+	31.9799i	−1.05695	+	1.26511i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−16.4884	−	28.5587i	−0.651251	−	1.12800i	−0.982820	−	0.184569i	$-0.940911\pi$
$641$	−16.4884	−	28.5587i	−0.651251	−	1.12800i	0.331569	−	0.943431i	$-0.392422\pi$
$642$	3.89921	+	2.72404i	0.153889	+	0.107509i
$643$	2.96963	+	5.14355i	0.117111	+	0.202842i	0.918622	−	0.395139i	$-0.129303\pi$
$643$	2.96963	+	5.14355i	0.117111	+	0.202842i	−0.801511	+	0.597980i	$0.795970\pi$
$644$	0.674248	−	2.41841i	0.0265691	−	0.0952986i
$645$	−7.12086	−	4.97473i	−0.280384	−	0.195880i
$646$	−4.47902			−0.176225
$647$	5.04853	−	8.74431i	0.198478	−	0.343774i	−0.749557	−	0.661940i	$-0.769733\pi$
$647$	5.04853	−	8.74431i	0.198478	−	0.343774i	0.948035	+	0.318165i	$0.103067\pi$
$648$	1.60075	+	8.85650i	0.0628834	+	0.347916i
$649$	−19.7724	−	34.2467i	−0.776133	−	1.34430i
$650$	−0.827555	+	1.43337i	−0.0324594	+	0.0562213i
$651$	10.6359	−	8.76225i	0.416854	−	0.343420i
$652$	−8.46813	−	14.6672i	−0.331638	−	0.574413i
$653$	−0.0509954	+	0.0883267i	−0.00199561	+	0.00345649i	−0.867021	−	0.498271i	$-0.833969\pi$
$653$	−0.0509954	+	0.0883267i	−0.00199561	+	0.00345649i	0.865026	+	0.501727i	$0.167302\pi$
$654$	−1.19475	+	13.8264i	−0.0467185	+	0.540657i
$655$	1.77033	+	3.06630i	0.0691725	+	0.119810i
$656$	0.970293	+	1.68060i	0.0378836	+	0.0656163i
$657$	−0.342901	−	0.935878i	−0.0133779	−	0.0365121i
$658$	2.60115	−	0.668909i	0.101404	−	0.0260768i
$659$	−1.37572	+	2.38282i	−0.0535904	+	0.0928214i	−0.891576	−	0.452871i	$-0.850400\pi$
$659$	−1.37572	+	2.38282i	−0.0535904	+	0.0928214i	0.837986	+	0.545692i	$0.183733\pi$
$660$	−7.01672	+	3.28109i	−0.273126	+	0.127716i
$661$	4.22458			0.164317			0.0821587	−	0.996619i	$-0.473819\pi$
$661$	4.22458			0.164317			0.0821587	+	0.996619i	$0.473819\pi$
$662$	−2.90680			−0.112976
$663$	−7.02753	+	3.28615i	−0.272927	+	0.127623i
$664$	−1.60804	+	2.78521i	−0.0624041	+	0.108087i
$665$	4.24102	−	1.09062i	0.164460	−	0.0422923i
$666$	−28.8188	−	5.01798i	−1.11671	−	0.194443i
$667$	1.97073	+	3.41340i	0.0763069	+	0.132167i
$668$	9.80368	+	16.9805i	0.379316	+	0.656994i
$669$	−2.81082	+	32.5286i	−0.108673	+	1.25763i
$670$	0.386978	−	0.670266i	0.0149503	−	0.0258946i
$671$	−26.8738	−	46.5467i	−1.03745	−	1.79692i
$672$	−3.53690	+	2.91382i	−0.136439	+	0.112403i
$673$	16.8678	−	29.2159i	0.650207	−	1.12619i	−0.332865	−	0.942974i	$-0.608016\pi$
$673$	16.8678	−	29.2159i	0.650207	−	1.12619i	0.983072	−	0.183217i	$-0.0586512\pi$
$674$	7.13923	+	12.3655i	0.274993	+	0.476302i
$675$	5.01476	−	1.36097i	0.193018	−	0.0523836i
$676$	5.13031	−	8.88595i	0.197319	−	0.341767i
$677$	−34.6497			−1.33170			−0.665848	−	0.746087i	$-0.731930\pi$
$677$	−34.6497			−1.33170			−0.665848	+	0.746087i	$0.731930\pi$
$678$	−7.04175	−	4.91947i	−0.270437	−	0.188931i
$679$	4.06238	−	14.5710i	0.155900	−	0.559185i
$680$	−1.35309	−	2.34362i	−0.0518886	−	0.0898737i
$681$	−5.96782	−	4.16920i	−0.228687	−	0.159764i
$682$	6.72415	+	11.6466i	0.257481	+	0.445970i
$683$	4.89745	−	8.48264i	0.187396	−	0.324579i	−0.756985	−	0.653432i	$-0.773329\pi$
$683$	4.89745	−	8.48264i	0.187396	−	0.324579i	0.944381	+	0.328853i	$0.106662\pi$
$684$	4.89173	+	0.851755i	0.187040	+	0.0325677i
$685$	17.8190			0.680829
$686$	13.4863	−	12.6933i	0.514910	−	0.484631i
$687$	−3.41178	+	39.4833i	−0.130167	+	1.50638i
$688$	2.50757	−	4.34323i	0.0956000	−	0.165584i
$689$	22.0371			0.839548
$690$	−1.34736	−	0.941288i	−0.0512933	−	0.0358342i
$691$	5.52600			0.210219			0.105109	−	0.994461i	$-0.466481\pi$
$691$	5.52600			0.210219			0.105109	+	0.994461i	$0.466481\pi$
$692$	7.46596			0.283813
$693$	35.3849	−	2.81233i	1.34416	−	0.106832i
$694$	−18.2254			−0.691825
$695$	12.8254			0.486496
$696$	0.619347	−	7.16748i	0.0234763	−	0.271683i
$697$	5.25157			0.198917
$698$	−3.76675	+	6.52420i	−0.142574	+	0.246945i
$699$	34.0536	+	23.7903i	1.28802	+	0.899832i
$700$	1.85185	+	1.88962i	0.0699933	+	0.0714209i
$701$	25.3205			0.956342			0.478171	−	0.878267i	$-0.341300\pi$
$701$	25.3205			0.956342			0.478171	+	0.878267i	$0.341300\pi$
$702$	8.29997	−	2.25255i	0.313262	−	0.0850170i
$703$	−8.06933	+	13.9765i	−0.304341	+	0.527134i
$704$	−2.23607	−	3.87298i	−0.0842750	−	0.145969i
$705$	0.151368	−	1.75173i	0.00570086	−	0.0659740i
$706$	2.78377	+	4.82163i	0.104769	+	0.181464i
$707$	−17.1620	−	17.5120i	−0.645443	−	0.658607i
$708$	−13.8737	+	6.48750i	−0.521406	+	0.243815i
$709$	32.1097			1.20591			0.602953	−	0.797776i	$-0.293990\pi$
$709$	32.1097			1.20591			0.602953	+	0.797776i	$0.293990\pi$
$710$	−6.94535	+	12.0297i	−0.260654	+	0.451467i
$711$	19.0903	−	22.8501i	0.715942	−	0.856944i
$712$	2.86642	+	4.96478i	0.107424	+	0.186063i
$713$	−1.42678	+	2.47126i	−0.0534334	+	0.0925494i
$714$	2.04315	+	12.2318i	0.0764631	+	0.457764i
$715$	3.70094	+	6.41021i	0.138407	+	0.239728i
$716$	−2.74363	+	4.75211i	−0.102534	+	0.177595i
$717$	18.9243	+	13.2208i	0.706740	+	0.493739i
$718$	−10.7999	−	18.7059i	−0.403047	−	0.698098i
$719$	−2.59986	−	4.50309i	−0.0969584	−	0.167937i	0.813466	−	0.581613i	$-0.197578\pi$
$719$	−2.59986	−	4.50309i	−0.0969584	−	0.167937i	−0.910424	+	0.413676i	$0.864245\pi$
$720$	1.03209	+	2.81688i	0.0384637	+	0.104979i
$721$	−13.5345	+	48.5459i	−0.504051	+	1.80794i
$722$	−8.13031	+	14.0821i	−0.302579	+	0.524082i
$723$	0.696025	+	0.486253i	0.0258855	+	0.0180840i
$724$	13.6477			0.507213
$725$	−4.15357			−0.154260
$726$	−1.34201	+	15.5306i	−0.0498065	+	0.576393i
$727$	−16.5059	+	28.5891i	−0.612171	+	1.06031i	0.378703	+	0.925518i	$0.376370\pi$
$727$	−16.5059	+	28.5891i	−0.612171	+	1.06031i	−0.990874	+	0.134793i	$0.956963\pi$
$728$	3.06501	+	3.12753i	0.113597	+	0.115914i
$729$	−23.4689	−	13.3496i	−0.869217	−	0.494430i
$730$	−0.166120	−	0.287728i	−0.00614837	−	0.0106493i
$731$	−6.78592	−	11.7536i	−0.250986	−	0.434721i
$732$	−18.8566	+	8.81754i	−0.696959	+	0.325906i
$733$	25.1301	−	43.5267i	0.928202	−	1.60769i	0.141874	−	0.989885i	$-0.454687\pi$
$733$	25.1301	−	43.5267i	0.928202	−	1.60769i	0.786328	−	0.617809i	$-0.211979\pi$
$734$	10.2270	+	17.7136i	0.377484	+	0.653822i
$735$	−4.91296	−	11.0844i	−0.181217	−	0.408852i
$736$	0.474466	−	0.821799i	0.0174890	−	0.0302919i
$737$	−1.73062	−	2.99752i	−0.0637482	−	0.110415i
$738$	−5.73546	−	0.998667i	−0.211125	−	0.0367614i
$739$	1.09204	−	1.89147i	0.0401713	−	0.0695787i	−0.845241	−	0.534386i	$-0.820543\pi$
$739$	1.09204	−	1.89147i	0.0401713	−	0.0695787i	0.885412	+	0.464807i	$0.153876\pi$
$740$	−9.75081			−0.358447
$741$	0.408476	−	4.72715i	0.0150057	−	0.173656i
$742$	9.46047	−	33.9330i	0.347305	−	1.24572i
$743$	16.1375	+	27.9509i	0.592026	+	1.02542i	0.993959	+	0.109750i	$0.0350050\pi$
$743$	16.1375	+	27.9509i	0.592026	+	1.02542i	−0.401933	+	0.915669i	$0.631662\pi$
$744$	4.71815	−	2.20626i	0.172976	−	0.0808854i
$745$	−4.96565	−	8.60076i	−0.181927	−	0.315108i
$746$	−1.10865	+	1.92024i	−0.0405905	+	0.0703049i
$747$	−3.31929	−	9.05931i	−0.121446	−	0.331463i
$748$	−12.1024			−0.442507
$749$	−5.08548	−	5.18920i	−0.185819	−	0.189609i
$750$	1.56899	−	0.733675i	0.0572913	−	0.0267900i
$751$	19.6397	−	34.0169i	0.716663	−	1.24130i	−0.245652	−	0.969358i	$-0.579002\pi$
$751$	19.6397	−	34.0169i	0.716663	−	1.24130i	0.962315	−	0.271938i	$-0.0876646\pi$
$752$	1.01513			0.0370180
$753$	33.2637	−	15.5544i	1.21220	−	0.566836i
$754$	−6.87461			−0.250359
$755$	8.07283			0.293800
$756$	0.0946515	−	13.7474i	0.00344244	−	0.499988i
$757$	−11.5097			−0.418328			−0.209164	−	0.977881i	$-0.567074\pi$
$757$	−11.5097			−0.418328			−0.209164	+	0.977881i	$0.567074\pi$
$758$	−5.04110			−0.183101
$759$	−6.65839	+	3.11354i	−0.241684	+	0.113014i
$760$	1.65511			0.0600372
$761$	−5.05470	+	8.75501i	−0.183233	+	0.317369i	−0.942980	−	0.332850i	$-0.891990\pi$
$761$	−5.05470	+	8.75501i	−0.183233	+	0.317369i	0.759747	+	0.650219i	$0.225323\pi$
$762$	−30.4351	+	14.2318i	−1.10255	+	0.515563i
$763$	5.69311	−	20.4202i	0.206104	−	0.739260i
$764$	24.7176			0.894251
$765$	7.99819	+	1.39266i	0.289175	+	0.0503516i
$766$	13.1820	−	22.8319i	0.476286	−	0.824952i
$767$	7.31763	+	12.6745i	0.264224	+	0.457650i
$768$	−1.56899	+	0.733675i	−0.0566159	+	0.0264742i
$769$	18.6256	+	32.2605i	0.671657	+	1.16334i	0.977434	+	0.211241i	$0.0677504\pi$
$769$	18.6256	+	32.2605i	0.671657	+	1.16334i	−0.305777	+	0.952103i	$0.598916\pi$
$770$	11.4593	−	2.94686i	0.412965	−	0.106198i
$771$	3.08823	−	35.7390i	0.111220	−	1.28711i
$772$	15.0374			0.541208
$773$	4.89352	−	8.47582i	0.176008	−	0.304854i	−0.764502	−	0.644621i	$-0.777015\pi$
$773$	4.89352	−	8.47582i	0.176008	−	0.304854i	0.940510	+	0.339767i	$0.110348\pi$
$774$	5.17607	+	14.1270i	0.186050	+	0.507785i
$775$	−1.50357	−	2.60425i	−0.0540097	−	0.0935475i
$776$	2.85868	−	4.95139i	0.102621	−	0.177744i
$777$	41.8494	+	15.6611i	1.50134	+	0.561838i
$778$	8.36238	+	14.4841i	0.299806	+	0.519279i
$779$	−1.60594	+	2.78157i	−0.0575388	+	0.0996602i
$780$	2.59685	−	1.21431i	0.0929820	−	0.0434794i
$781$	31.0606	+	53.7985i	1.11143	+	1.92506i
$782$	−1.28399	−	2.22394i	−0.0459154	−	0.0795278i
$783$	15.3101	+	15.2121i	0.547138	+	0.543637i
$784$	6.13160	−	3.37690i	0.218986	−	0.120604i
$785$	9.90093	−	17.1489i	0.353379	−	0.612071i
$786$	0.527955	−	6.10983i	0.0188315	−	0.217930i
$787$	−23.9030			−0.852050			−0.426025	−	0.904711i	$-0.640086\pi$
$787$	−23.9030			−0.852050			−0.426025	+	0.904711i	$0.640086\pi$
$788$	21.9097			0.780500
$789$	16.4505	+	11.4926i	0.585654	+	0.409146i
$790$	4.96254	−	8.59537i	0.176559	−	0.305810i
$791$	9.18408	+	9.37140i	0.326548	+	0.333209i
$792$	13.2175	+	2.30146i	0.469665	+	0.0817787i
$793$	9.94581	+	17.2267i	0.353186	+	0.611736i
$794$	6.52922	+	11.3089i	0.231713	+	0.401339i
$795$	−18.9051	−	13.2074i	−0.670494	−	0.468417i
$796$	−12.1642	+	21.0691i	−0.431150	+	0.746774i
$797$	8.54896	+	14.8072i	0.302820	+	0.524499i	0.976773	−	0.214275i	$-0.0687387\pi$
$797$	8.54896	+	14.8072i	0.302820	+	0.524499i	−0.673954	+	0.738773i	$0.735405\pi$
$798$	−7.10355	−	2.65832i	−0.251463	−	0.0941036i
$799$	1.37356	−	2.37908i	0.0485932	−	0.0841659i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−16.9436	−	2.95024i	−0.598672	−	0.104242i
$802$	19.1172	−	33.1120i	0.675052	−	1.16922i
$803$	−1.48582			−0.0524335
$804$	−1.21433	+	0.567833i	−0.0428260	+	0.0200259i
$805$	1.75728	+	1.79312i	0.0619359	+	0.0631992i
$806$	−2.48857	−	4.31032i	−0.0876560	−	0.151825i
$807$	−1.24040	+	14.3547i	−0.0436640	+	0.505308i
$808$	−4.63374	−	8.02588i	−0.163015	−	0.282349i
$809$	−24.9280	+	43.1766i	−0.876422	+	1.51801i	−0.0211819	+	0.999776i	$0.506743\pi$
$809$	−24.9280	+	43.1766i	−0.876422	+	1.51801i	−0.855240	+	0.518232i	$0.826590\pi$
$810$	−8.47033	−	3.04196i	−0.297617	−	0.106884i
$811$	47.0854			1.65339			0.826697	−	0.562648i	$-0.190217\pi$
$811$	47.0854			1.65339			0.826697	+	0.562648i	$0.190217\pi$
$812$	−2.95125	+	10.5856i	−0.103569	+	0.371482i
$813$	18.7489	+	13.0983i	0.657553	+	0.459376i
$814$	−21.8035	+	37.7647i	−0.764211	+	1.32365i
$815$	16.9363			0.593252
$816$	−0.403524	+	4.66984i	−0.0141262	+	0.163477i
$817$	8.30059			0.290401
$818$	13.6741			0.478103
$819$	−13.0957	+	1.04083i	−0.457602	+	0.0363694i
$820$	−1.94059			−0.0677682
$821$	5.97295			0.208457			0.104229	−	0.994553i	$-0.466763\pi$
$821$	5.97295			0.208457			0.104229	+	0.994553i	$0.466763\pi$
$822$	−25.3007	−	17.6755i	−0.882465	−	0.616502i
$823$	55.2765			1.92682			0.963409	−	0.268034i	$-0.0863741\pi$
$823$	55.2765			1.92682			0.963409	+	0.268034i	$0.0863741\pi$
$824$	−9.52418	+	16.4964i	−0.331791	+	0.574678i
$825$	0.666849	−	7.71721i	0.0232167	−	0.268679i
$826$	22.6578	−	5.82664i	0.788365	−	0.202735i
$827$	29.0399			1.00981			0.504907	−	0.863174i	$-0.331527\pi$
$827$	29.0399			1.00981			0.504907	+	0.863174i	$0.331527\pi$
$828$	0.979384	+	2.67302i	0.0340359	+	0.0928940i
$829$	−10.9987	+	19.0504i	−0.382002	+	0.661647i	−0.991348	−	0.131257i	$-0.958099\pi$
$829$	−10.9987	+	19.0504i	−0.382002	+	0.661647i	0.609346	+	0.792904i	$0.291432\pi$
$830$	−1.60804	−	2.78521i	−0.0558160	−	0.0966761i
$831$	9.02380	+	6.30415i	0.313032	+	0.218689i
$832$	0.827555	+	1.43337i	0.0286903	+	0.0496931i
$833$	0.382424	−	18.9394i	0.0132502	−	0.656211i
$834$	−18.2105	−	12.7221i	−0.630578	−	0.440531i
$835$	−19.6074			−0.678540
$836$	3.70094	−	6.41021i	0.128000	−	0.221702i
$837$	−3.99572	+	15.1060i	−0.138112	+	0.522139i
$838$	−4.16825	−	7.21962i	−0.143990	−	0.249398i
$839$	3.93272	−	6.81166i	0.135772	−	0.235165i	−0.790120	−	0.612952i	$-0.789982\pi$
$839$	3.93272	−	6.81166i	0.135772	−	0.235165i	0.925892	+	0.377788i	$0.123315\pi$
$840$	−0.754996	−	4.51995i	−0.0260498	−	0.155953i
$841$	5.87394	+	10.1740i	0.202550	+	0.350826i
$842$	1.03373	−	1.79048i	0.0356248	−	0.0617040i
$843$	0.600548	−	6.94993i	0.0206840	−	0.239368i
$844$	9.43146	+	16.3358i	0.324644	+	0.562300i
$845$	5.13031	+	8.88595i	0.176488	+	0.305686i
$846$	−1.95255	+	2.33709i	−0.0671299	+	0.0803508i
$847$	6.39479	−	22.9370i	0.219728	−	0.788124i
$848$	6.65730	−	11.5308i	0.228613	−	0.395969i
$849$	−26.0611	+	12.1864i	−0.894414	+	0.418238i
$850$	2.70618			0.0928211
$851$	−9.25286			−0.317184
$852$	21.7943	−	10.1913i	0.746662	−	0.349147i
$853$	−20.3124	+	35.1821i	−0.695483	+	1.20461i	0.274535	+	0.961577i	$0.411476\pi$
$853$	−20.3124	+	35.1821i	−0.695483	+	1.20461i	−0.970018	+	0.243034i	$0.921857\pi$
$854$	30.7955	−	7.91933i	1.05380	−	0.270994i
$855$	−3.18351	+	3.81048i	−0.108874	+	0.130316i
$856$	−1.37308	−	2.37825i	−0.0469309	−	0.0812868i
$857$	−20.7885	−	36.0067i	−0.710122	−	1.22997i	−0.964811	−	0.262944i	$-0.915307\pi$
$857$	−20.7885	−	36.0067i	−0.710122	−	1.22997i	0.254689	−	0.967023i	$-0.418027\pi$
$858$	1.10371	−	12.7728i	0.0376800	−	0.436057i
$859$	19.7525	−	34.2123i	0.673946	−	1.16731i	−0.302830	−	0.953045i	$-0.597932\pi$
$859$	19.7525	−	34.2123i	0.673946	−	1.16731i	0.976776	−	0.214264i	$-0.0687352\pi$
$860$	2.50757	+	4.34323i	0.0855073	+	0.148103i
$861$	8.32879	+	3.11684i	0.283844	+	0.106221i
$862$	1.71653	−	2.97311i	0.0584651	−	0.101265i
$863$	−1.64838	−	2.85508i	−0.0561116	−	0.0971881i	0.836605	−	0.547806i	$-0.184537\pi$
$863$	−1.64838	−	2.85508i	−0.0561116	−	0.0971881i	−0.892717	+	0.450618i	$0.851204\pi$
$864$	1.32875	−	5.02339i	0.0452049	−	0.170899i
$865$	−3.73298	+	6.46571i	−0.126925	+	0.219841i
$866$	−7.62844			−0.259225
$867$	−13.7396	−	9.59866i	−0.466620	−	0.325987i
$868$	−7.70542	+	1.98152i	−0.261539	+	0.0672570i
$869$	−22.1931	−	38.4396i	−0.752851	−	1.30398i
$870$	5.89755	+	4.12011i	0.199946	+	0.139685i
$871$	0.640492	+	1.10936i	0.0217022	+	0.0375894i
$872$	4.00622	−	6.93898i	0.135668	−	0.234984i
$873$	5.90084	+	16.1051i	0.199713	+	0.545076i
$874$	1.57059			0.0531259
$875$	−2.56238	+	0.658939i	−0.0866243	+	0.0222762i
$876$	−0.0495409	+	0.573319i	−0.00167383	+	0.0193707i
$877$	8.64815	−	14.9790i	0.292027	−	0.505806i	−0.682262	−	0.731108i	$-0.739004\pi$
$877$	8.64815	−	14.9790i	0.292027	−	0.505806i	0.974289	+	0.225302i	$0.0723369\pi$
$878$	15.3407			0.517725
$879$	−8.47835	−	5.92310i	−0.285968	−	0.199781i
$880$	4.47213			0.150756
$881$	−4.70828			−0.158626			−0.0793130	−	0.996850i	$-0.525273\pi$
$881$	−4.70828			−0.158626			−0.0793130	+	0.996850i	$0.525273\pi$
$882$	−4.01928	+	20.6118i	−0.135336	+	0.694035i
$883$	4.72801			0.159110			0.0795551	−	0.996830i	$-0.474650\pi$
$883$	4.72801			0.159110			0.0795551	+	0.996830i	$0.474650\pi$
$884$	4.47902			0.150646
$885$	1.31852	−	15.2587i	0.0443215	−	0.512917i
$886$	−10.9405			−0.367554
$887$	−13.4429	+	23.2838i	−0.451368	+	0.781792i	−0.998471	−	0.0552730i	$-0.982397\pi$
$887$	−13.4429	+	23.2838i	−0.451368	+	0.781792i	0.547103	+	0.837065i	$0.315730\pi$
$888$	13.8449	+	9.67227i	0.464606	+	0.324580i
$889$	49.7049	−	12.7820i	1.66705	−	0.428696i
$890$	−5.73284			−0.192165
$891$	−30.7217	+	26.0034i	−1.02922	+	0.871147i
$892$	9.42519	−	16.3249i	0.315579	−	0.546598i
$893$	0.840077	+	1.45506i	0.0281121	+	0.0486916i
$894$	−1.48088	+	17.1377i	−0.0495279	+	0.573169i
$895$	−2.74363	−	4.75211i	−0.0917095	−	0.158846i
$896$	2.56238	−	0.658939i	0.0856032	−	0.0220136i
$897$	2.46423	−	1.15230i	0.0822783	−	0.0384742i
$898$	−11.4979			−0.383688
$899$	6.24516	−	10.8169i	0.208288	−	0.360765i
$900$	−2.95553	−	0.514622i	−0.0985177	−	0.0171541i
$901$	−18.0158	−	31.2044i	−0.600195	−	1.03957i
$902$	−4.33928	+	7.51585i	−0.144482	+	0.250251i
$903$	−3.78640	−	22.6682i	−0.126004	−	0.754349i
$904$	2.47971	+	4.29498i	0.0824738	+	0.142849i
$905$	−6.82385	+	11.8193i	−0.226833	+	0.392886i
$906$	−11.4624	−	8.00780i	−0.380813	−	0.266041i
$907$	−2.12513	−	3.68083i	−0.0705637	−	0.122220i	0.828585	−	0.559864i	$-0.189146\pi$
$907$	−2.12513	−	3.68083i	−0.0705637	−	0.122220i	−0.899148	+	0.437644i	$0.855813\pi$
$908$	2.10153	+	3.63995i	0.0697417	+	0.120796i
$909$	27.3903	+	4.76925i	0.908480	+	0.158186i
$910$	−4.24102	+	1.09062i	−0.140589	+	0.0361536i
$911$	4.94873	−	8.57146i	0.163959	−	0.283985i	−0.772326	−	0.635226i	$-0.780907\pi$
$911$	4.94873	−	8.57146i	0.163959	−	0.283985i	0.936285	+	0.351241i	$0.114240\pi$
$912$	−2.35005	−	1.64178i	−0.0778179	−	0.0543647i
$913$	−14.3828			−0.476000
$914$	−6.93375			−0.229348
$915$	1.79207	−	20.7390i	0.0592442	−	0.685612i
$916$	11.4403	−	19.8152i	0.377999	−	0.654713i
$917$	−2.51576	+	9.02357i	−0.0830776	+	0.297984i
$918$	−9.97500	−	9.91117i	−0.329224	−	0.327117i
$919$	2.32368	+	4.02474i	0.0766513	+	0.132764i	0.901803	−	0.432147i	$-0.142244\pi$
$919$	2.32368	+	4.02474i	0.0766513	+	0.132764i	−0.825152	+	0.564911i	$0.808911\pi$
$920$	0.474466	+	0.821799i	0.0156427	+	0.0270939i
$921$	−30.3593	+	14.1963i	−1.00037	+	0.467785i
$922$	19.9618	−	34.5748i	0.657405	−	1.13866i
$923$	−11.4953	−	19.9105i	−0.378373	−	0.655362i
$924$	−19.1939	−	7.18283i	−0.631434	−	0.236298i
$925$	4.87541	−	8.44445i	0.160302	−	0.277652i
$926$	−0.419823	−	0.727155i	−0.0137963	−	0.0238958i
$927$	−19.6596	−	53.6569i	−0.645707	−	1.76232i
$928$	−2.07678	+	3.59710i	−0.0681738	+	0.118080i
$929$	−51.3878			−1.68598			−0.842990	−	0.537930i	$-0.819206\pi$
$929$	−51.3878			−1.68598			−0.842990	+	0.537930i	$0.819206\pi$
$930$	−0.448400	+	5.18917i	−0.0147036	+	0.170160i
$931$	9.91458	+	5.99426i	0.324937	+	0.196454i
$932$	−11.9917	−	20.7703i	−0.392803	−	0.680354i
$933$	−32.2835	+	15.0961i	−1.05691	+	0.494224i
$934$	−6.54621	−	11.3384i	−0.214199	−	0.371003i
$935$	6.05120	−	10.4810i	0.197895	−	0.342765i
$936$	−4.89173	−	0.851755i	−0.159891	−	0.0278405i
$937$	−50.1135			−1.63714			−0.818568	−	0.574410i	$-0.805231\pi$
$937$	−50.1135			−1.63714			−0.818568	+	0.574410i	$0.805231\pi$
$938$	1.98317	−	0.509990i	0.0647529	−	0.0166518i
$939$	12.9753	−	6.06738i	0.423432	−	0.198001i
$940$	−0.507566	+	0.879130i	−0.0165550	+	0.0286741i
$941$	14.2726			0.465274			0.232637	−	0.972564i	$-0.425265\pi$
$941$	14.2726			0.465274			0.232637	+	0.972564i	$0.425265\pi$
$942$	−31.0689	+	14.5281i	−1.01228	+	0.473352i
$943$	−1.84148			−0.0599670
$944$	8.84247			0.287798
$945$	11.8583	+	6.95567i	0.385750	+	0.226268i
$946$	22.4283			0.729208
$947$	1.65912			0.0539142			0.0269571	−	0.999637i	$-0.491418\pi$
$947$	1.65912			0.0539142			0.0269571	+	0.999637i	$0.491418\pi$
$948$	−15.5723	+	7.28178i	−0.505765	+	0.236501i
$949$	0.549893			0.0178503
$950$	−0.827555	+	1.43337i	−0.0268494	+	0.0465046i
$951$	−46.2289	+	21.6171i	−1.49907	+	0.700983i
$952$	1.92283	−	6.89685i	0.0623193	−	0.223528i
$953$	37.7383			1.22246			0.611231	−	0.791452i	$-0.290675\pi$
$953$	37.7383			1.22246			0.611231	+	0.791452i	$0.290675\pi$
$954$	13.7419	+	37.5056i	0.444910	+	1.21429i
$955$	−12.3588	+	21.4061i	−0.399921	+	0.692684i
$956$	−6.66407	−	11.5425i	−0.215531	−	0.373311i
$957$	29.1444	−	13.6283i	0.942106	−	0.440539i
$958$	−14.7920	−	25.6205i	−0.477909	−	0.827762i
$959$	32.9981	+	33.6711i	1.06556	+	1.08730i
$960$	0.149112	−	1.72562i	0.00481257	−	0.0556942i
$961$	−21.9572			−0.708295
$962$	8.06933	−	13.9765i	0.260166	−	0.450620i
$963$	8.11637	+	1.41323i	0.261546	+	0.0455408i
$964$	−0.245101	−	0.424527i	−0.00789417	−	0.0136731i
$965$	−7.51870	+	13.0228i	−0.242036	+	0.419218i
$966$	−0.716440	−	4.28913i	−0.0230511	−	0.138000i
$967$	11.0171	+	19.0821i	0.354285	+	0.613639i	0.986995	−	0.160749i	$-0.0513910\pi$
$967$	11.0171	+	19.0821i	0.354285	+	0.613639i	−0.632710	+	0.774388i	$0.718058\pi$
$968$	4.49999	−	7.79422i	0.144635	−	0.250516i
$969$	−7.02753	+	3.28615i	−0.225757	+	0.105566i
$970$	2.85868	+	4.95139i	0.0917868	+	0.158979i
$971$	−14.2946	−	24.7590i	−0.458736	−	0.794554i	0.540158	−	0.841563i	$-0.318364\pi$
$971$	−14.2946	−	24.7590i	−0.458736	−	0.794554i	−0.998894	+	0.0470093i	$0.985031\pi$
$972$	9.00935	+	12.7213i	0.288975	+	0.408036i
$973$	23.7507	+	24.2352i	0.761414	+	0.776943i
$974$	−19.1240	+	33.1238i	−0.612773	+	1.06135i
$975$	−0.246797	+	2.85609i	−0.00790382	+	0.0914681i
$976$	12.0183			0.384697
$977$	46.9663			1.50259			0.751293	−	0.659969i	$-0.229430\pi$
$977$	46.9663			1.50259			0.751293	+	0.659969i	$0.229430\pi$
$978$	−24.0474	−	16.7998i	−0.768951	−	0.537200i
$979$	−12.8190	+	22.2032i	−0.409697	+	0.709616i
$980$	−0.141315	+	6.99857i	−0.00451414	+	0.223561i
$981$	8.26957	+	22.5701i	0.264027	+	0.720607i
$982$	15.8531	+	27.4583i	0.505892	+	0.876230i
$983$	−6.07768	−	10.5268i	−0.193848	−	0.335754i	0.752674	−	0.658393i	$-0.228763\pi$
$983$	−6.07768	−	10.5268i	−0.193848	−	0.335754i	−0.946522	+	0.322639i	$0.895430\pi$
$984$	2.75539	+	1.92495i	0.0878386	+	0.0613653i
$985$	−10.9548	+	18.9743i	−0.349050	+	0.604573i
$986$	5.62015	+	9.73438i	0.178982	+	0.310006i
$987$	3.59042	−	2.95791i	0.114284	−	0.0941514i
$988$	−1.36969	+	2.37238i	−0.0435758	+	0.0754755i
$989$	2.37951	+	4.12143i	0.0756640	+	0.131054i
$990$	−8.60189	+	10.2960i	−0.273386	+	0.327228i
$991$	21.8008	−	37.7601i	0.692525	−	1.19949i	−0.278482	−	0.960441i	$-0.589831\pi$
$991$	21.8008	−	37.7601i	0.692525	−	1.19949i	0.971008	−	0.239048i	$-0.0768353\pi$
$992$	−3.00713			−0.0954765
$993$	−4.56073	+	2.13264i	−0.144730	+	0.0676774i
$994$	−35.5933	+	9.15312i	−1.12895	+	0.290319i
$995$	−12.1642	−	21.0691i	−0.385632	−	0.667935i
$996$	−0.479557	+	5.54974i	−0.0151953	+	0.175850i
$997$	15.8374	+	27.4311i	0.501575	+	0.868753i	0.999998	+	0.00181943i	$0.000579143\pi$
$997$	15.8374	+	27.4311i	0.501575	+	0.868753i	−0.498423	+	0.866934i	$0.666088\pi$
$998$	11.9392	−	20.6793i	0.377929	−	0.654592i
$999$	−48.8979	+	13.2705i	−1.54706	+	0.419861i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.f.151.1	yes	12
3.2	odd	2		1890.2.i.h.991.2		12
7.2	even	3		630.2.l.h.331.4	yes	12
9.4	even	3		630.2.l.h.571.4	yes	12
9.5	odd	6		1890.2.l.f.361.5		12
21.2	odd	6		1890.2.l.f.1801.5		12
63.23	odd	6		1890.2.i.h.1171.2		12
63.58	even	3	inner	630.2.i.f.121.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.f.121.1	✓	12	63.58	even	3	inner
630.2.i.f.151.1	yes	12	1.1	even	1	trivial
630.2.l.h.331.4	yes	12	7.2	even	3
630.2.l.h.571.4	yes	12	9.4	even	3
1890.2.i.h.991.2		12	3.2	odd	2
1890.2.i.h.1171.2		12	63.23	odd	6
1890.2.l.f.361.5		12	9.5	odd	6
1890.2.l.f.1801.5		12	21.2	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.56899 + 0.733675i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.56899 - 0.733675i) q^{6} +(-2.56238 + 0.658939i) q^{7} -1.00000 q^{8} +(1.92344 - 2.30225i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.56899 + 0.733675i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.56899 - 0.733675i) q^{6} +(-2.56238 + 0.658939i) q^{7} -1.00000 q^{8} +(1.92344 - 2.30225i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.23607 - 3.87298i) q^{11} +(-1.56899 + 0.733675i) q^{12} +(0.827555 + 1.43337i) q^{13} +(2.56238 - 0.658939i) q^{14} +(0.149112 - 1.72562i) q^{15} +1.00000 q^{16} +(1.35309 - 2.34362i) q^{17} +(-1.92344 + 2.30225i) q^{18} +(0.827555 + 1.43337i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(3.53690 - 2.91382i) q^{21} +(2.23607 + 3.87298i) q^{22} +(-0.474466 + 0.821799i) q^{23} +(1.56899 - 0.733675i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.827555 - 1.43337i) q^{26} +(-1.32875 + 5.02339i) q^{27} +(-2.56238 + 0.658939i) q^{28} +(2.07678 - 3.59710i) q^{29} +(-0.149112 + 1.72562i) q^{30} +3.00713 q^{31} -1.00000 q^{32} +(6.34987 + 4.43611i) q^{33} +(-1.35309 + 2.34362i) q^{34} +(0.710533 - 2.54856i) q^{35} +(1.92344 - 2.30225i) q^{36} +(4.87541 + 8.44445i) q^{37} +(-0.827555 - 1.43337i) q^{38} +(-2.35005 - 1.64178i) q^{39} +(0.500000 - 0.866025i) q^{40} +(0.970293 + 1.68060i) q^{41} +(-3.53690 + 2.91382i) q^{42} +(2.50757 - 4.34323i) q^{43} +(-2.23607 - 3.87298i) q^{44} +(1.03209 + 2.81688i) q^{45} +(0.474466 - 0.821799i) q^{46} +1.01513 q^{47} +(-1.56899 + 0.733675i) q^{48} +(6.13160 - 3.37690i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.403524 + 4.66984i) q^{51} +(0.827555 + 1.43337i) q^{52} +(6.65730 - 11.5308i) q^{53} +(1.32875 - 5.02339i) q^{54} +4.47213 q^{55} +(2.56238 - 0.658939i) q^{56} +(-2.35005 - 1.64178i) q^{57} +(-2.07678 + 3.59710i) q^{58} +8.84247 q^{59} +(0.149112 - 1.72562i) q^{60} +12.0183 q^{61} -3.00713 q^{62} +(-3.41155 + 7.16668i) q^{63} +1.00000 q^{64} -1.65511 q^{65} +(-6.34987 - 4.43611i) q^{66} +0.773956 q^{67} +(1.35309 - 2.34362i) q^{68} +(0.141497 - 1.63750i) q^{69} +(-0.710533 + 2.54856i) q^{70} -13.8907 q^{71} +(-1.92344 + 2.30225i) q^{72} +(0.166120 - 0.287728i) q^{73} +(-4.87541 - 8.44445i) q^{74} +(1.41988 + 0.991945i) q^{75} +(0.827555 + 1.43337i) q^{76} +(8.28172 + 8.45063i) q^{77} +(2.35005 + 1.64178i) q^{78} +9.92508 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-1.60075 - 8.85650i) q^{81} +(-0.970293 - 1.68060i) q^{82} +(1.60804 - 2.78521i) q^{83} +(3.53690 - 2.91382i) q^{84} +(1.35309 + 2.34362i) q^{85} +(-2.50757 + 4.34323i) q^{86} +(-0.619347 + 7.16748i) q^{87} +(2.23607 + 3.87298i) q^{88} +(-2.86642 - 4.96478i) q^{89} +(-1.03209 - 2.81688i) q^{90} +(-3.06501 - 3.12753i) q^{91} +(-0.474466 + 0.821799i) q^{92} +(-4.71815 + 2.20626i) q^{93} -1.01513 q^{94} -1.65511 q^{95} +(1.56899 - 0.733675i) q^{96} +(-2.85868 + 4.95139i) q^{97} +(-6.13160 + 3.37690i) q^{98} +(-13.2175 - 2.30146i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9	\( 12 q - 12 q^{2} + 2 q^{3} + 12 q^{4} - 6 q^{5} - 2 q^{6} + 4 q^{7} - 12 q^{8} - 4 q^{9} + 6 q^{10} - 7 q^{11} + 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{15} + 12 q^{16} + q^{17} + 4 q^{18} - 2 q^{19} - 6 q^{20} + 29 q^{21} + 7 q^{22} - 9 q^{23} - 2 q^{24} - 6 q^{25} + 2 q^{26} + 11 q^{27} + 4 q^{28} + 3 q^{29} + q^{30} + 18 q^{31} - 12 q^{32} + 27 q^{33} - q^{34} - 8 q^{35} - 4 q^{36} + 6 q^{37} + 2 q^{38} + 10 q^{39} + 6 q^{40} - 11 q^{41} - 29 q^{42} + 23 q^{43} - 7 q^{44} + 5 q^{45} + 9 q^{46} - 2 q^{47} + 2 q^{48} + 24 q^{49} + 6 q^{50} - 15 q^{51} - 2 q^{52} - 4 q^{53} - 11 q^{54} + 14 q^{55} - 4 q^{56} + 10 q^{57} - 3 q^{58} - 22 q^{59} - q^{60} + 50 q^{61} - 18 q^{62} - q^{63} + 12 q^{64} + 4 q^{65} - 27 q^{66} + 4 q^{67} + q^{68} - 12 q^{69} + 8 q^{70} + 22 q^{71} + 4 q^{72} + 24 q^{73} - 6 q^{74} - q^{75} - 2 q^{76} - 11 q^{77} - 10 q^{78} + 2 q^{79} - 6 q^{80} + 20 q^{81} + 11 q^{82} + 4 q^{83} + 29 q^{84} + q^{85} - 23 q^{86} + 7 q^{88} + 2 q^{89} - 5 q^{90} - 8 q^{91} - 9 q^{92} + 40 q^{93} + 2 q^{94} + 4 q^{95} - 2 q^{96} - 36 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 2 * q^3 + 12 * q^4 - 6 * q^5 - 2 * q^6 + 4 * q^7 - 12 * q^8 - 4 * q^9 + 6 * q^10 - 7 * q^11 + 2 * q^12 - 2 * q^13 - 4 * q^14 - q^15 + 12 * q^16 + q^17 + 4 * q^18 - 2 * q^19 - 6 * q^20 + 29 * q^21 + 7 * q^22 - 9 * q^23 - 2 * q^24 - 6 * q^25 + 2 * q^26 + 11 * q^27 + 4 * q^28 + 3 * q^29 + q^30 + 18 * q^31 - 12 * q^32 + 27 * q^33 - q^34 - 8 * q^35 - 4 * q^36 + 6 * q^37 + 2 * q^38 + 10 * q^39 + 6 * q^40 - 11 * q^41 - 29 * q^42 + 23 * q^43 - 7 * q^44 + 5 * q^45 + 9 * q^46 - 2 * q^47 + 2 * q^48 + 24 * q^49 + 6 * q^50 - 15 * q^51 - 2 * q^52 - 4 * q^53 - 11 * q^54 + 14 * q^55 - 4 * q^56 + 10 * q^57 - 3 * q^58 - 22 * q^59 - q^60 + 50 * q^61 - 18 * q^62 - q^63 + 12 * q^64 + 4 * q^65 - 27 * q^66 + 4 * q^67 + q^68 - 12 * q^69 + 8 * q^70 + 22 * q^71 + 4 * q^72 + 24 * q^73 - 6 * q^74 - q^75 - 2 * q^76 - 11 * q^77 - 10 * q^78 + 2 * q^79 - 6 * q^80 + 20 * q^81 + 11 * q^82 + 4 * q^83 + 29 * q^84 + q^85 - 23 * q^86 + 7 * q^88 + 2 * q^89 - 5 * q^90 - 8 * q^91 - 9 * q^92 + 40 * q^93 + 2 * q^94 + 4 * q^95 - 2 * q^96 - 36 * q^97 - 24 * q^98 + 15 * q^99

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