LMFDB - Embedded newform 462.2.n.d.263.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(65,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("462.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.n (of order $6$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.1
Root			$-1.63746 - 1.52274i$ of defining polynomial
Character	$\chi$	$=$	462.263
Dual form			462.2.n.d.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.63746 + 1.52274i) q^{5} +1.73205i q^{6} +(2.63746 + 0.209313i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.63746 + 1.52274i) q^{5} +1.73205i q^{6} +(2.63746 + 0.209313i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.63746 - 1.52274i) q^{10} +(-2.50000 - 2.17945i) q^{11} +(-1.50000 + 0.866025i) q^{12} +6.09095i q^{13} +(1.13746 + 2.38876i) q^{14} -5.27492 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.13746 - 3.70219i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(1.86254 - 1.07534i) q^{19} -3.04547i q^{20} +(3.77492 + 2.59808i) q^{21} +(0.637459 - 3.25479i) q^{22} +(-6.41238 + 3.70219i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(2.13746 - 3.70219i) q^{25} +(-5.27492 + 3.04547i) q^{26} +5.19615i q^{27} +(-1.50000 + 2.17945i) q^{28} +1.00000 q^{29} +(-2.63746 - 4.56821i) q^{30} +(1.36254 - 2.35999i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.86254 - 5.43424i) q^{33} +4.27492 q^{34} +(-7.27492 + 3.46410i) q^{35} -3.00000 q^{36} +(-0.137459 - 0.238085i) q^{37} +(1.86254 + 1.07534i) q^{38} +(-5.27492 + 9.13642i) q^{39} +(2.63746 - 1.52274i) q^{40} +8.54983 q^{41} +(-0.362541 + 4.56821i) q^{42} -5.61478i q^{43} +(3.13746 - 1.07534i) q^{44} +(-7.91238 - 4.56821i) q^{45} +(-6.41238 - 3.70219i) q^{46} +(9.41238 - 5.43424i) q^{47} -1.73205i q^{48} +(6.91238 + 1.10411i) q^{49} +4.27492 q^{50} +(6.41238 - 3.70219i) q^{51} +(-5.27492 - 3.04547i) q^{52} +(7.18729 + 4.14959i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(9.91238 + 1.94136i) q^{55} +(-2.63746 - 0.209313i) q^{56} +3.72508 q^{57} +(0.500000 + 0.866025i) q^{58} +(-1.50000 - 0.866025i) q^{59} +(2.63746 - 4.56821i) q^{60} +(6.00000 - 3.46410i) q^{61} +2.72508 q^{62} +(3.41238 + 7.16629i) q^{63} +1.00000 q^{64} +(-9.27492 - 16.0646i) q^{65} +(3.77492 - 4.33013i) q^{66} +(-3.27492 + 5.67232i) q^{67} +(2.13746 + 3.70219i) q^{68} -12.8248 q^{69} +(-6.63746 - 4.56821i) q^{70} +5.61478i q^{71} +(-1.50000 - 2.59808i) q^{72} +(-10.5498 - 6.09095i) q^{73} +(0.137459 - 0.238085i) q^{74} +(6.41238 - 3.70219i) q^{75} +2.15068i q^{76} +(-6.13746 - 6.27149i) q^{77} -10.5498 q^{78} +(5.63746 - 3.25479i) q^{79} +(2.63746 + 1.52274i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(4.27492 + 7.40437i) q^{82} +2.72508 q^{83} +(-4.13746 + 1.97014i) q^{84} +13.0192i q^{85} +(4.86254 - 2.80739i) q^{86} +(1.50000 + 0.866025i) q^{87} +(2.50000 + 2.17945i) q^{88} +(5.27492 - 3.04547i) q^{89} -9.13642i q^{90} +(-1.27492 + 16.0646i) q^{91} -7.40437i q^{92} +(4.08762 - 2.35999i) q^{93} +(9.41238 + 5.43424i) q^{94} +(-3.27492 + 5.67232i) q^{95} +(1.50000 - 0.866025i) q^{96} +1.54983 q^{97} +(2.50000 + 6.53835i) q^{98} +(1.91238 - 9.76436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{7} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 6 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^7 - 4 * q^8 + 6 * q^9	$ 4 q + 2 q^{2} + 6 q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{7} - 4 q^{8} + 6 q^{9} - 3 q^{10} - 10 q^{11} - 6 q^{12} - 3 q^{14} - 6 q^{15} - 2 q^{16} + q^{17} - 6 q^{18} + 15 q^{19} - 5 q^{22} - 3 q^{23} - 6 q^{24} + q^{25} - 6 q^{26} - 6 q^{28} + 4 q^{29} - 3 q^{30} + 13 q^{31} + 2 q^{32} - 15 q^{33} + 2 q^{34} - 14 q^{35} - 12 q^{36} + 7 q^{37} + 15 q^{38} - 6 q^{39} + 3 q^{40} + 4 q^{41} - 9 q^{42} + 5 q^{44} - 9 q^{45} - 3 q^{46} + 15 q^{47} + 5 q^{49} + 2 q^{50} + 3 q^{51} - 6 q^{52} - 9 q^{53} - 18 q^{54} + 17 q^{55} - 3 q^{56} + 30 q^{57} + 2 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} + 26 q^{62} - 9 q^{63} + 4 q^{64} - 22 q^{65} + 2 q^{67} + q^{68} - 6 q^{69} - 19 q^{70} - 6 q^{72} - 12 q^{73} - 7 q^{74} + 3 q^{75} - 17 q^{77} - 12 q^{78} + 15 q^{79} + 3 q^{80} - 18 q^{81} + 2 q^{82} + 26 q^{83} - 9 q^{84} + 27 q^{86} + 6 q^{87} + 10 q^{88} + 6 q^{89} + 10 q^{91} + 39 q^{93} + 15 q^{94} + 2 q^{95} + 6 q^{96} - 24 q^{97} + 10 q^{98} - 15 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^7 - 4 * q^8 + 6 * q^9 - 3 * q^10 - 10 * q^11 - 6 * q^12 - 3 * q^14 - 6 * q^15 - 2 * q^16 + q^17 - 6 * q^18 + 15 * q^19 - 5 * q^22 - 3 * q^23 - 6 * q^24 + q^25 - 6 * q^26 - 6 * q^28 + 4 * q^29 - 3 * q^30 + 13 * q^31 + 2 * q^32 - 15 * q^33 + 2 * q^34 - 14 * q^35 - 12 * q^36 + 7 * q^37 + 15 * q^38 - 6 * q^39 + 3 * q^40 + 4 * q^41 - 9 * q^42 + 5 * q^44 - 9 * q^45 - 3 * q^46 + 15 * q^47 + 5 * q^49 + 2 * q^50 + 3 * q^51 - 6 * q^52 - 9 * q^53 - 18 * q^54 + 17 * q^55 - 3 * q^56 + 30 * q^57 + 2 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 + 26 * q^62 - 9 * q^63 + 4 * q^64 - 22 * q^65 + 2 * q^67 + q^68 - 6 * q^69 - 19 * q^70 - 6 * q^72 - 12 * q^73 - 7 * q^74 + 3 * q^75 - 17 * q^77 - 12 * q^78 + 15 * q^79 + 3 * q^80 - 18 * q^81 + 2 * q^82 + 26 * q^83 - 9 * q^84 + 27 * q^86 + 6 * q^87 + 10 * q^88 + 6 * q^89 + 10 * q^91 + 39 * q^93 + 15 * q^94 + 2 * q^95 + 6 * q^96 - 24 * q^97 + 10 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.63746	+	1.52274i	−1.17951	+	0.680989i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−2.63746	+	1.52274i	−1.17951	+	0.680989i	−0.223607	+	0.974679i	$0.571783\pi$
$6$			1.73205i			0.707107i
$7$	2.63746	+	0.209313i	0.996866	+	0.0791130i
$7$	2.63746	+	0.209313i	0.996866	+	0.0791130i
$8$	−1.00000			−0.353553
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	−2.63746	−	1.52274i	−0.834038	−	0.481532i
$11$	−2.50000	−	2.17945i	−0.753778	−	0.657129i
$11$	−2.50000	−	2.17945i	−0.753778	−	0.657129i
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$			6.09095i			1.68933i	0.535299	+	0.844663i	$0.320199\pi$
$13$			6.09095i			1.68933i	−0.535299	+	0.844663i	$0.679801\pi$
$14$	1.13746	+	2.38876i	0.303999	+	0.638424i
$15$	−5.27492			−1.36198
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.13746	−	3.70219i	0.518410	−	0.897912i	−0.481361	−	0.876522i	$-0.659858\pi$
$17$	2.13746	−	3.70219i	0.518410	−	0.897912i	0.999771	−	0.0213900i	$-0.00680916\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	1.86254	−	1.07534i	0.427296	−	0.246700i	−0.270898	−	0.962608i	$-0.587321\pi$
$19$	1.86254	−	1.07534i	0.427296	−	0.246700i	0.698194	+	0.715908i	$0.253987\pi$
$20$		−	3.04547i		−	0.680989i
$21$	3.77492	+	2.59808i	0.823754	+	0.566947i
$22$	0.637459	−	3.25479i	0.135907	−	0.693923i
$23$	−6.41238	+	3.70219i	−1.33707	+	0.771959i	−0.986372	−	0.164528i	$-0.947390\pi$
$23$	−6.41238	+	3.70219i	−1.33707	+	0.771959i	−0.350700	+	0.936488i	$0.614056\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	2.13746	−	3.70219i	0.427492	−	0.740437i
$26$	−5.27492	+	3.04547i	−1.03450	+	0.597267i
$27$			5.19615i			1.00000i
$28$	−1.50000	+	2.17945i	−0.283473	+	0.411877i
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$	−2.63746	−	4.56821i	−0.481532	−	0.834038i
$31$	1.36254	−	2.35999i	0.244720	−	0.423867i	−0.717333	−	0.696730i	$-0.754637\pi$
$31$	1.36254	−	2.35999i	0.244720	−	0.423867i	0.962053	+	0.272863i	$0.0879707\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.86254	−	5.43424i	−0.324227	−	0.945979i
$34$	4.27492			0.733142
$35$	−7.27492	+	3.46410i	−1.22969	+	0.585540i
$36$	−3.00000			−0.500000
$37$	−0.137459	−	0.238085i	−0.0225981	−	0.0391410i	0.854505	−	0.519443i	$-0.173860\pi$
$37$	−0.137459	−	0.238085i	−0.0225981	−	0.0391410i	−0.877103	+	0.480302i	$0.840527\pi$
$38$	1.86254	+	1.07534i	0.302144	+	0.174443i
$39$	−5.27492	+	9.13642i	−0.844663	+	1.46300i
$40$	2.63746	−	1.52274i	0.417019	−	0.240766i
$41$	8.54983			1.33526			0.667630	−	0.744493i	$-0.267309\pi$
$41$	8.54983			1.33526			0.667630	+	0.744493i	$0.267309\pi$
$42$	−0.362541	+	4.56821i	−0.0559414	+	0.704890i
$43$		−	5.61478i		−	0.856246i	−0.903721	−	0.428123i	$-0.859175\pi$
$43$		−	5.61478i		−	0.856246i	0.903721	−	0.428123i	$-0.140825\pi$
$44$	3.13746	−	1.07534i	0.472990	−	0.162113i
$45$	−7.91238	−	4.56821i	−1.17951	−	0.680989i
$46$	−6.41238	−	3.70219i	−0.945453	−	0.545858i
$47$	9.41238	−	5.43424i	1.37294	−	0.792665i	0.381639	−	0.924311i	$-0.375360\pi$
$47$	9.41238	−	5.43424i	1.37294	−	0.792665i	0.991297	+	0.131646i	$0.0420263\pi$
$48$		−	1.73205i		−	0.250000i
$49$	6.91238	+	1.10411i	0.987482	+	0.157730i
$50$	4.27492			0.604565
$51$	6.41238	−	3.70219i	0.897912	−	0.518410i
$52$	−5.27492	−	3.04547i	−0.731499	−	0.422331i
$53$	7.18729	+	4.14959i	0.987251	+	0.569989i	0.904451	−	0.426577i	$-0.140281\pi$
$53$	7.18729	+	4.14959i	0.987251	+	0.569989i	0.0827993	+	0.996566i	$0.473614\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$	9.91238	+	1.94136i	1.33658	+	0.261773i
$56$	−2.63746	−	0.209313i	−0.352445	−	0.0279707i
$57$	3.72508			0.493399
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$	−1.50000	−	0.866025i	−0.195283	−	0.112747i	0.399170	−	0.916877i	$-0.369298\pi$
$59$	−1.50000	−	0.866025i	−0.195283	−	0.112747i	−0.594454	+	0.804130i	$0.702632\pi$
$60$	2.63746	−	4.56821i	0.340494	−	0.589754i
$61$	6.00000	−	3.46410i	0.768221	−	0.443533i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.00000	−	3.46410i	0.768221	−	0.443533i	0.832240	+	0.554416i	$0.187058\pi$
$62$	2.72508			0.346086
$63$	3.41238	+	7.16629i	0.429919	+	0.902867i
$64$	1.00000			0.125000
$65$	−9.27492	−	16.0646i	−1.15041	−	1.99257i
$66$	3.77492	−	4.33013i	0.464660	−	0.533002i
$67$	−3.27492	+	5.67232i	−0.400095	+	0.692985i	−0.993737	−	0.111745i	$-0.964356\pi$
$67$	−3.27492	+	5.67232i	−0.400095	+	0.692985i	0.593642	+	0.804729i	$0.297689\pi$
$68$	2.13746	+	3.70219i	0.259205	+	0.448956i
$69$	−12.8248			−1.54392
$70$	−6.63746	−	4.56821i	−0.793328	−	0.546006i
$71$			5.61478i			0.666352i	0.942865	+	0.333176i	$0.108120\pi$
$71$			5.61478i			0.666352i	−0.942865	+	0.333176i	$0.891880\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	−10.5498	−	6.09095i	−1.23476	−	0.712892i	−0.266745	−	0.963767i	$-0.585948\pi$
$73$	−10.5498	−	6.09095i	−1.23476	−	0.712892i	−0.968019	+	0.250875i	$0.919282\pi$
$74$	0.137459	−	0.238085i	0.0159792	−	0.0276769i
$75$	6.41238	−	3.70219i	0.740437	−	0.427492i
$76$			2.15068i			0.246700i
$77$	−6.13746	−	6.27149i	−0.699428	−	0.714703i
$78$	−10.5498			−1.19453
$79$	5.63746	−	3.25479i	0.634264	−	0.366192i	−0.148138	−	0.988967i	$-0.547328\pi$
$79$	5.63746	−	3.25479i	0.634264	−	0.366192i	0.782401	+	0.622774i	$0.213995\pi$
$80$	2.63746	+	1.52274i	0.294877	+	0.170247i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	4.27492	+	7.40437i	0.472086	+	0.817676i
$83$	2.72508			0.299117			0.149558	−	0.988753i	$-0.452215\pi$
$83$	2.72508			0.299117			0.149558	+	0.988753i	$0.452215\pi$
$84$	−4.13746	+	1.97014i	−0.451434	+	0.214959i
$85$			13.0192i			1.41213i
$86$	4.86254	−	2.80739i	0.524341	−	0.302729i
$87$	1.50000	+	0.866025i	0.160817	+	0.0928477i
$88$	2.50000	+	2.17945i	0.266501	+	0.232330i
$89$	5.27492	−	3.04547i	0.559140	−	0.322820i	−0.193660	−	0.981069i	$-0.562036\pi$
$89$	5.27492	−	3.04547i	0.559140	−	0.322820i	0.752800	+	0.658249i	$0.228703\pi$
$90$		−	9.13642i		−	0.963064i
$91$	−1.27492	+	16.0646i	−0.133648	+	1.68403i
$92$		−	7.40437i		−	0.771959i
$93$	4.08762	−	2.35999i	0.423867	−	0.244720i
$94$	9.41238	+	5.43424i	0.970812	+	0.560499i
$95$	−3.27492	+	5.67232i	−0.335999	+	0.581968i
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	1.54983			0.157362			0.0786809	−	0.996900i	$-0.474929\pi$
$97$	1.54983			0.157362			0.0786809	+	0.996900i	$0.474929\pi$
$98$	2.50000	+	6.53835i	0.252538	+	0.660473i
$99$	1.91238	−	9.76436i	0.192201	−	0.981356i
$100$	2.13746	+	3.70219i	0.213746	+	0.370219i
$101$	−6.41238	+	11.1066i	−0.638055	+	1.10514i	0.347804	+	0.937567i	$0.386928\pi$
$101$	−6.41238	+	11.1066i	−0.638055	+	1.10514i	−0.985859	+	0.167577i	$0.946406\pi$
$102$	6.41238	+	3.70219i	0.634920	+	0.366571i
$103$	−8.54983	−	14.8087i	−0.842440	−	1.45915i	−0.887826	−	0.460180i	$-0.847785\pi$
$103$	−8.54983	−	14.8087i	−0.842440	−	1.45915i	0.0453856	−	0.998970i	$-0.485548\pi$
$104$		−	6.09095i		−	0.597267i
$105$	−13.9124	−	1.10411i	−1.35771	−	0.107750i
$106$			8.29917i			0.806087i
$107$	−3.36254	−	5.82409i	−0.325069	−	0.563036i	0.656457	−	0.754363i	$-0.272054\pi$
$107$	−3.36254	−	5.82409i	−0.325069	−	0.563036i	−0.981526	+	0.191327i	$0.938721\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	11.2749	+	6.50958i	1.07994	+	0.623504i	0.930881	−	0.365324i	$-0.119042\pi$
$109$	11.2749	+	6.50958i	1.07994	+	0.623504i	0.149061	+	0.988828i	$0.452375\pi$
$110$	3.27492	+	9.55505i	0.312251	+	0.911038i
$111$		−	0.476171i		−	0.0451961i
$112$	−1.13746	−	2.38876i	−0.107480	−	0.225717i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$	1.86254	+	3.22602i	0.174443	+	0.302144i
$115$	11.2749	−	19.5287i	1.05139	−	1.82106i
$116$	−0.500000	+	0.866025i	−0.0464238	+	0.0804084i
$117$	−15.8248	+	9.13642i	−1.46300	+	0.844663i
$118$		−	1.73205i		−	0.159448i
$119$	6.41238	−	9.31697i	0.587822	−	0.854085i
$120$	5.27492			0.481532
$121$	1.50000	+	10.8972i	0.136364	+	0.990659i
$122$	6.00000	+	3.46410i	0.543214	+	0.313625i
$123$	12.8248	+	7.40437i	1.15637	+	0.667630i
$124$	1.36254	+	2.35999i	0.122360	+	0.211933i
$125$		−	2.20822i		−	0.197509i
$126$	−4.50000	+	6.53835i	−0.400892	+	0.582482i
$127$		−	13.9140i		−	1.23466i	−0.786703	−	0.617332i	$-0.788214\pi$
$127$		−	13.9140i		−	1.23466i	0.786703	−	0.617332i	$-0.211786\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	4.86254	−	8.42217i	0.428123	−	0.741531i
$130$	9.27492	−	16.0646i	0.813464	−	1.40896i
$131$	1.36254	+	2.35999i	0.119046	+	0.206193i	0.919390	−	0.393348i	$-0.128683\pi$
$131$	1.36254	+	2.35999i	0.119046	+	0.206193i	−0.800344	+	0.599541i	$0.795350\pi$
$132$	5.63746	+	1.10411i	0.490678	+	0.0961005i
$133$	5.13746	−	2.44631i	0.445474	−	0.212122i
$134$	−6.54983			−0.565820
$135$	−7.91238	−	13.7046i	−0.680989	−	1.17951i
$136$	−2.13746	+	3.70219i	−0.183286	+	0.317460i
$137$	−11.2749	−	6.50958i	−0.963281	−	0.556151i	−0.0660998	−	0.997813i	$-0.521056\pi$
$137$	−11.2749	−	6.50958i	−0.963281	−	0.556151i	−0.897181	+	0.441662i	$0.854389\pi$
$138$	−6.41238	−	11.1066i	−0.545858	−	0.945453i
$139$		−	4.77753i		−	0.405224i	−0.979259	−	0.202612i	$-0.935057\pi$
$139$		−	4.77753i		−	0.405224i	0.979259	−	0.202612i	$-0.0649431\pi$
$140$	0.637459	−	8.03231i	0.0538751	−	0.678854i
$141$	18.8248			1.58533
$142$	−4.86254	+	2.80739i	−0.408055	+	0.235591i
$143$	13.2749	−	15.2274i	1.11010	−	1.27338i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	−2.63746	+	1.52274i	−0.219029	+	0.126456i
$146$		−	12.1819i		−	1.00818i
$147$	9.41238	+	7.64246i	0.776320	+	0.630339i
$148$	0.274917			0.0225981
$149$	0.137459	+	0.238085i	0.0112610	+	0.0195047i	0.871601	−	0.490216i	$-0.163082\pi$
$149$	0.137459	+	0.238085i	0.0112610	+	0.0195047i	−0.860340	+	0.509721i	$0.829749\pi$
$150$	6.41238	+	3.70219i	0.523568	+	0.302282i
$151$	−10.5000	−	6.06218i	−0.854478	−	0.493333i	0.00768132	−	0.999970i	$-0.497555\pi$
$151$	−10.5000	−	6.06218i	−0.854478	−	0.493333i	−0.862159	+	0.506637i	$0.830888\pi$
$152$	−1.86254	+	1.07534i	−0.151072	+	0.0872215i
$153$	12.8248			1.03682
$154$	2.36254	−	8.45094i	0.190379	−	0.680996i
$155$			8.29917i			0.666605i
$156$	−5.27492	−	9.13642i	−0.422331	−	0.731499i
$157$	−4.86254	+	8.42217i	−0.388073	+	0.672162i	−0.992190	−	0.124733i	$-0.960193\pi$
$157$	−4.86254	+	8.42217i	−0.388073	+	0.672162i	0.604117	+	0.796895i	$0.293526\pi$
$158$	5.63746	+	3.25479i	0.448492	+	0.258937i
$159$	7.18729	+	12.4488i	0.569989	+	0.987251i
$160$			3.04547i			0.240766i
$161$	−17.6873	+	8.42217i	−1.39395	+	0.663760i
$162$	−9.00000			−0.707107
$163$	−0.725083	−	1.25588i	−0.0567929	−	0.0983681i	0.836231	−	0.548377i	$-0.184754\pi$
$163$	−0.725083	−	1.25588i	−0.0567929	−	0.0983681i	−0.893024	+	0.450009i	$0.851421\pi$
$164$	−4.27492	+	7.40437i	−0.333815	+	0.578184i
$165$	13.1873	+	11.4964i	1.02663	+	0.894995i
$166$	1.36254	+	2.35999i	0.105754	+	0.183171i
$167$	22.5498			1.74496			0.872479	−	0.488651i	$-0.162511\pi$
$167$	22.5498			1.74496			0.872479	+	0.488651i	$0.162511\pi$
$168$	−3.77492	−	2.59808i	−0.291241	−	0.200446i
$169$	−24.0997			−1.85382
$170$	−11.2749	+	6.50958i	−0.864747	+	0.499262i
$171$	5.58762	+	3.22602i	0.427296	+	0.246700i
$172$	4.86254	+	2.80739i	0.370765	+	0.214061i
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	0.999293	+	0.0375896i	$0.0119679\pi$
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	−0.467093	+	0.884208i	$0.654699\pi$
$174$			1.73205i			0.131306i
$175$	6.41238	−	9.31697i	0.484730	−	0.704296i
$176$	−0.637459	+	3.25479i	−0.0480503	+	0.245339i
$177$	−1.50000	−	2.59808i	−0.112747	−	0.195283i
$178$	5.27492	+	3.04547i	0.395372	+	0.228268i
$179$	−16.1375	−	9.31697i	−1.20617	−	0.696383i	−0.244250	−	0.969712i	$-0.578542\pi$
$179$	−16.1375	−	9.31697i	−1.20617	−	0.696383i	−0.961920	+	0.273330i	$0.911875\pi$
$180$	7.91238	−	4.56821i	0.589754	−	0.340494i
$181$	8.54983			0.635504			0.317752	−	0.948174i	$-0.397072\pi$
$181$	8.54983			0.635504			0.317752	+	0.948174i	$0.397072\pi$
$182$	−14.5498	+	6.92820i	−1.07851	+	0.513553i
$183$	12.0000			0.887066
$184$	6.41238	−	3.70219i	0.472727	−	0.272929i
$185$	0.725083	+	0.418627i	0.0533091	+	0.0307781i
$186$	4.08762	+	2.35999i	0.299719	+	0.173043i
$187$	−13.4124	+	4.59698i	−0.980810	+	0.336165i
$188$			10.8685i			0.792665i
$189$	−1.08762	+	13.7046i	−0.0791130	+	0.996866i
$190$	−6.54983			−0.475175
$191$	−12.8248	+	7.40437i	−0.927966	+	0.535762i	−0.886168	−	0.463364i	$-0.846642\pi$
$191$	−12.8248	+	7.40437i	−0.927966	+	0.535762i	−0.0417986	+	0.999126i	$0.513309\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	−15.3625	−	8.86957i	−1.10582	−	0.638445i	−0.168076	−	0.985774i	$-0.553756\pi$
$193$	−15.3625	−	8.86957i	−1.10582	−	0.638445i	−0.937744	+	0.347329i	$0.887089\pi$
$194$	0.774917	+	1.34220i	0.0556358	+	0.0963641i
$195$		−	32.1293i		−	2.30082i
$196$	−4.41238	+	5.43424i	−0.315170	+	0.388160i
$197$	−20.2749			−1.44453			−0.722264	−	0.691617i	$-0.756898\pi$
$197$	−20.2749			−1.44453			−0.722264	+	0.691617i	$0.756898\pi$
$198$	9.41238	−	3.22602i	0.668908	−	0.229263i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	−2.13746	+	3.70219i	−0.151141	+	0.261784i
$201$	−9.82475	+	5.67232i	−0.692985	+	0.400095i
$202$	−12.8248			−0.902346
$203$	2.63746	+	0.209313i	0.185113	+	0.0146909i
$204$			7.40437i			0.518410i
$205$	−22.5498	+	13.0192i	−1.57495	+	0.909297i
$206$	8.54983	−	14.8087i	0.595695	−	1.03177i
$207$	−19.2371	−	11.1066i	−1.33707	−	0.771959i
$208$	5.27492	−	3.04547i	0.365750	−	0.211166i
$209$	−7.00000	−	1.37097i	−0.484200	−	0.0948318i
$210$	−6.00000	−	12.6005i	−0.414039	−	0.869519i
$211$			11.2296i			0.773075i	0.922274	+	0.386537i	$0.126329\pi$
$211$			11.2296i			0.773075i	−0.922274	+	0.386537i	$0.873671\pi$
$212$	−7.18729	+	4.14959i	−0.493625	+	0.284995i
$213$	−4.86254	+	8.42217i	−0.333176	+	0.577077i
$214$	3.36254	−	5.82409i	0.229859	−	0.398127i
$215$	8.54983	+	14.8087i	0.583094	+	1.00995i
$216$		−	5.19615i		−	0.353553i
$217$	4.08762	−	5.93918i	0.277486	−	0.403178i
$218$			13.0192i			0.881768i
$219$	−10.5498	−	18.2728i	−0.712892	−	1.23476i
$220$	−6.63746	+	7.61369i	−0.447497	+	0.513315i
$221$	22.5498	+	13.0192i	1.51687	+	0.875763i
$222$	0.412376	−	0.238085i	0.0276769	−	0.0159792i
$223$	−19.8248			−1.32756			−0.663782	−	0.747926i	$-0.731050\pi$
$223$	−19.8248			−1.32756			−0.663782	+	0.747926i	$0.731050\pi$
$224$	1.50000	−	2.17945i	0.100223	−	0.145621i
$225$	12.8248			0.854983
$226$		0			0
$227$	7.18729	−	12.4488i	0.477037	−	0.826253i	−0.522616	−	0.852568i	$-0.675044\pi$
$227$	7.18729	−	12.4488i	0.477037	−	0.826253i	0.999654	+	0.0263150i	$0.00837729\pi$
$228$	−1.86254	+	3.22602i	−0.123350	+	0.213648i
$229$	−4.27492	−	7.40437i	−0.282494	−	0.489295i	0.689504	−	0.724282i	$-0.257829\pi$
$229$	−4.27492	−	7.40437i	−0.282494	−	0.489295i	−0.971998	+	0.234987i	$0.924495\pi$
$230$	22.5498			1.48689
$231$	−3.77492	−	14.7224i	−0.248371	−	0.968665i
$232$	−1.00000			−0.0656532
$233$	−2.41238	−	4.17836i	−0.158040	−	0.273733i	0.776122	−	0.630583i	$-0.217184\pi$
$233$	−2.41238	−	4.17836i	−0.158040	−	0.273733i	−0.934162	+	0.356850i	$0.883851\pi$
$234$	−15.8248	−	9.13642i	−1.03450	−	0.597267i
$235$	−16.5498	+	28.6652i	−1.07959	+	1.86991i
$236$	1.50000	−	0.866025i	0.0976417	−	0.0563735i
$237$	11.2749			0.732385
$238$	11.2749	+	0.894797i	0.730844	+	0.0580011i
$239$	2.54983			0.164935			0.0824675	−	0.996594i	$-0.473720\pi$
$239$	2.54983			0.164935			0.0824675	+	0.996594i	$0.473720\pi$
$240$	2.63746	+	4.56821i	0.170247	+	0.294877i
$241$	7.91238	+	4.56821i	0.509681	+	0.294264i	0.732702	−	0.680549i	$-0.238259\pi$
$241$	7.91238	+	4.56821i	0.509681	+	0.294264i	−0.223022	+	0.974814i	$0.571592\pi$
$242$	−8.68729	+	6.74766i	−0.558440	+	0.433756i
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$			6.92820i			0.443533i
$245$	−19.9124	+	7.61369i	−1.27216	+	0.486421i
$246$			14.8087i			0.944171i
$247$	6.54983	+	11.3446i	0.416756	+	0.721843i
$248$	−1.36254	+	2.35999i	−0.0865215	+	0.149860i
$249$	4.08762	+	2.35999i	0.259043	+	0.149558i
$250$	1.91238	−	1.10411i	0.120949	−	0.0698301i
$251$			7.82300i			0.493783i	0.969043	+	0.246892i	$0.0794092\pi$
$251$			7.82300i			0.493783i	−0.969043	+	0.246892i	$0.920591\pi$
$252$	−7.91238	−	0.627940i	−0.498433	−	0.0395565i
$253$	24.0997	+	4.71998i	1.51513	+	0.296743i
$254$	12.0498	−	6.95698i	0.756074	−	0.436519i
$255$	−11.2749	+	19.5287i	−0.706063	+	1.22294i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.72508	+	3.88273i	−0.419499	+	0.242198i	−0.694863	−	0.719142i	$-0.744535\pi$
$257$	−6.72508	+	3.88273i	−0.419499	+	0.242198i	0.275364	+	0.961340i	$0.411202\pi$
$258$	9.72508			0.605457
$259$	−0.312707	−	0.656712i	−0.0194307	−	0.0408061i
$260$	18.5498			1.15041
$261$	1.50000	+	2.59808i	0.0928477	+	0.160817i
$262$	−1.36254	+	2.35999i	−0.0841781	+	0.145801i
$263$	0.549834	−	0.952341i	0.0339042	−	0.0587239i	−0.848575	−	0.529074i	$-0.822539\pi$
$263$	0.549834	−	0.952341i	0.0339042	−	0.0587239i	0.882480	+	0.470351i	$0.155873\pi$
$264$	1.86254	+	5.43424i	0.114631	+	0.334454i
$265$	−25.2749			−1.55263
$266$	4.68729	+	3.22602i	0.287396	+	0.197800i
$267$	10.5498			0.645639
$268$	−3.27492	−	5.67232i	−0.200047	−	0.346492i
$269$	−13.9124	−	8.03231i	−0.848253	−	0.489739i	0.0118083	−	0.999930i	$-0.496241\pi$
$269$	−13.9124	−	8.03231i	−0.848253	−	0.489739i	−0.860061	+	0.510191i	$0.829575\pi$
$270$	7.91238	−	13.7046i	0.481532	−	0.834038i
$271$	26.7371	−	15.4367i	1.62416	−	0.937712i	0.638376	−	0.769725i	$-0.279607\pi$
$271$	26.7371	−	15.4367i	1.62416	−	0.937712i	0.985789	−	0.167987i	$-0.0537267\pi$
$272$	−4.27492			−0.259205
$273$	−15.8248	+	22.9928i	−0.957758	+	1.39159i
$274$		−	13.0192i		−	0.786516i
$275$	−13.4124	+	4.59698i	−0.808797	+	0.277209i
$276$	6.41238	−	11.1066i	0.385980	−	0.668536i
$277$	−22.5498	−	13.0192i	−1.35489	−	0.782245i	−0.365959	−	0.930631i	$-0.619259\pi$
$277$	−22.5498	−	13.0192i	−1.35489	−	0.782245i	−0.988930	+	0.148386i	$0.952592\pi$
$278$	4.13746	−	2.38876i	0.248148	−	0.143268i
$279$	8.17525			0.489439
$280$	7.27492	−	3.46410i	0.434759	−	0.207020i
$281$	3.72508			0.222220			0.111110	−	0.993808i	$-0.464559\pi$
$281$	3.72508			0.222220			0.111110	+	0.993808i	$0.464559\pi$
$282$	9.41238	+	16.3027i	0.560499	+	0.970812i
$283$	2.27492	+	1.31342i	0.135230	+	0.0780750i	0.566089	−	0.824344i	$-0.308456\pi$
$283$	2.27492	+	1.31342i	0.135230	+	0.0780750i	−0.430859	+	0.902419i	$0.641789\pi$
$284$	−4.86254	−	2.80739i	−0.288539	−	0.166588i
$285$	−9.82475	+	5.67232i	−0.581968	+	0.335999i
$286$	19.8248	+	3.88273i	1.17226	+	0.229591i
$287$	22.5498	+	1.78959i	1.33107	+	0.105636i
$288$	3.00000			0.176777
$289$	−0.637459	−	1.10411i	−0.0374976	−	0.0649477i
$290$	−2.63746	−	1.52274i	−0.154877	−	0.0894182i
$291$	2.32475	+	1.34220i	0.136279	+	0.0786809i
$292$	10.5498	−	6.09095i	0.617382	−	0.356446i
$293$	−24.0997			−1.40792			−0.703959	−	0.710241i	$-0.748586\pi$
$293$	−24.0997			−1.40792			−0.703959	+	0.710241i	$0.748586\pi$
$294$	−1.91238	+	11.9726i	−0.111532	+	0.698255i
$295$	5.27492			0.307118
$296$	0.137459	+	0.238085i	0.00798962	+	0.0138384i
$297$	11.3248	−	12.9904i	0.657129	−	0.753778i
$298$	−0.137459	+	0.238085i	−0.00796276	+	0.0137919i
$299$	−22.5498	−	39.0575i	−1.30409	−	2.25875i
$300$			7.40437i			0.427492i
$301$	1.17525	−	14.8087i	0.0677402	−	0.853562i
$302$		−	12.1244i		−	0.697678i
$303$	−19.2371	+	11.1066i	−1.10514	+	0.638055i
$304$	−1.86254	−	1.07534i	−0.106824	−	0.0616749i
$305$	−10.5498	+	18.2728i	−0.604082	+	1.04630i
$306$	6.41238	+	11.1066i	0.366571	+	0.634920i
$307$			15.6460i			0.892964i	0.894793	+	0.446482i	$0.147323\pi$
$307$			15.6460i			0.892964i	−0.894793	+	0.446482i	$0.852677\pi$
$308$	8.50000	−	2.17945i	0.484332	−	0.124186i
$309$		−	29.6175i		−	1.68488i
$310$	−7.18729	+	4.14959i	−0.408211	+	0.235681i
$311$	19.1375	+	11.0490i	1.08519	+	0.626532i	0.932291	−	0.361710i	$-0.117807\pi$
$311$	19.1375	+	11.0490i	1.08519	+	0.626532i	0.152895	+	0.988242i	$0.451140\pi$
$312$	5.27492	−	9.13642i	0.298633	−	0.517248i
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	0.749993	−	0.661445i	$-0.230057\pi$
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	−0.947825	+	0.318791i	$0.896723\pi$
$314$	−9.72508			−0.548818
$315$	−19.9124	−	13.7046i	−1.12194	−	0.772169i
$316$			6.50958i			0.366192i
$317$	−7.18729	+	4.14959i	−0.403679	+	0.233064i	−0.688070	−	0.725644i	$-0.741542\pi$
$317$	−7.18729	+	4.14959i	−0.403679	+	0.233064i	0.284391	+	0.958708i	$0.408208\pi$
$318$	−7.18729	+	12.4488i	−0.403043	+	0.698092i
$319$	−2.50000	−	2.17945i	−0.139973	−	0.122026i
$320$	−2.63746	+	1.52274i	−0.147438	+	0.0851236i
$321$		−	11.6482i		−	0.650138i
$322$	−16.1375	−	11.1066i	−0.899305	−	0.618944i
$323$		−	9.19397i		−	0.511566i
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	22.5498	+	13.0192i	1.25084	+	0.722173i
$326$	0.725083	−	1.25588i	0.0401586	−	0.0695568i
$327$	11.2749	+	19.5287i	0.623504	+	1.07994i
$328$	−8.54983			−0.472086
$329$	25.9622	−	12.3624i	1.43134	−	0.681563i
$330$	−3.36254	+	17.1687i	−0.185102	+	0.945108i
$331$	−12.5498	−	21.7370i	−0.689801	−	1.19477i	−0.971902	−	0.235386i	$-0.924365\pi$
$331$	−12.5498	−	21.7370i	−0.689801	−	1.19477i	0.282101	−	0.959385i	$-0.408969\pi$
$332$	−1.36254	+	2.35999i	−0.0747792	+	0.129521i
$333$	0.412376	−	0.714256i	0.0225981	−	0.0391410i
$334$	11.2749	+	19.5287i	0.616936	+	1.06856i
$335$		−	19.9474i		−	1.08984i
$336$	0.362541	−	4.56821i	0.0197783	−	0.249216i
$337$		−	21.3183i		−	1.16128i	−0.814159	−	0.580642i	$-0.802802\pi$
$337$		−	21.3183i		−	1.16128i	0.814159	−	0.580642i	$-0.197198\pi$
$338$	−12.0498	−	20.8709i	−0.655425	−	1.13523i
$339$		0			0
$340$	−11.2749	−	6.50958i	−0.611468	−	0.353031i
$341$	−8.54983	+	2.93039i	−0.462999	+	0.158689i
$342$			6.45203i			0.348886i
$343$	18.0000	+	4.35890i	0.971909	+	0.235358i
$344$			5.61478i			0.302729i
$345$	33.8248	−	19.5287i	1.82106	−	1.05139i
$346$	−7.00000	+	12.1244i	−0.376322	+	0.651809i
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	−0.807337	−	0.590091i	$-0.799092\pi$
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	0.914702	+	0.404128i	$0.132425\pi$
$348$	−1.50000	+	0.866025i	−0.0804084	+	0.0464238i
$349$			35.7084i			1.91143i	0.294295	+	0.955715i	$0.404915\pi$
$349$			35.7084i			1.91143i	−0.294295	+	0.955715i	$0.595085\pi$
$350$	11.2749	+	0.894797i	0.602670	+	0.0478289i
$351$	−31.6495			−1.68933
$352$	−3.13746	+	1.07534i	−0.167227	+	0.0573157i
$353$	13.6495	+	7.88054i	0.726490	+	0.419439i	0.817137	−	0.576444i	$-0.195560\pi$
$353$	13.6495	+	7.88054i	0.726490	+	0.419439i	−0.0906469	+	0.995883i	$0.528893\pi$
$354$	1.50000	−	2.59808i	0.0797241	−	0.138086i
$355$	−8.54983	−	14.8087i	−0.453778	−	0.785967i
$356$			6.09095i			0.322820i
$357$	17.6873	−	8.42217i	0.936111	−	0.445748i
$358$		−	18.6339i		−	0.984834i
$359$	9.82475	+	17.0170i	0.518531	+	0.898121i	0.999768	+	0.0215311i	$0.00685409\pi$
$359$	9.82475	+	17.0170i	0.518531	+	0.898121i	−0.481238	+	0.876590i	$0.659813\pi$
$360$	7.91238	+	4.56821i	0.417019	+	0.240766i
$361$	−7.18729	+	12.4488i	−0.378279	+	0.655198i
$362$	4.27492	+	7.40437i	0.224685	+	0.389165i
$363$	−7.18729	+	17.6449i	−0.377235	+	0.926118i
$364$	−13.2749	−	9.13642i	−0.695795	−	0.478879i
$365$	37.0997			1.94189
$366$	6.00000	+	10.3923i	0.313625	+	0.543214i
$367$	−12.6375	+	21.8887i	−0.659670	+	1.14258i	0.321031	+	0.947069i	$0.395971\pi$
$367$	−12.6375	+	21.8887i	−0.659670	+	1.14258i	−0.980701	+	0.195513i	$0.937363\pi$
$368$	6.41238	+	3.70219i	0.334268	+	0.192990i
$369$	12.8248	+	22.2131i	0.667630	+	1.15637i
$370$			0.837253i			0.0435267i
$371$	18.0876	+	12.4488i	0.939063	+	0.646307i
$372$			4.71998i			0.244720i
$373$	−22.5498	+	13.0192i	−1.16759	+	0.674106i	−0.953110	−	0.302623i	$-0.902138\pi$
$373$	−22.5498	+	13.0192i	−1.16759	+	0.674106i	−0.214476	+	0.976729i	$0.568804\pi$
$374$	−10.6873	−	9.31697i	−0.552627	−	0.481769i
$375$	1.91238	−	3.31233i	0.0987547	−	0.171048i
$376$	−9.41238	+	5.43424i	−0.485406	+	0.280249i
$377$			6.09095i			0.313700i
$378$	−12.4124	+	5.91041i	−0.638424	+	0.303999i
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	−3.27492	−	5.67232i	−0.168000	−	0.290984i
$381$	12.0498	−	20.8709i	0.617332	−	1.06925i
$382$	−12.8248	−	7.40437i	−0.656171	−	0.378841i
$383$	−15.5120	+	8.95588i	−0.792628	+	0.457624i	−0.840887	−	0.541211i	$-0.817966\pi$
$383$	−15.5120	+	8.95588i	−0.792628	+	0.457624i	0.0482586	+	0.998835i	$0.484633\pi$
$384$			1.73205i			0.0883883i
$385$	25.7371	+	7.19506i	1.31169	+	0.366694i
$386$		−	17.7391i		−	0.902898i
$387$	14.5876	−	8.42217i	0.741531	−	0.428123i
$388$	−0.774917	+	1.34220i	−0.0393405	+	0.0681397i
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$	27.8248	−	16.0646i	1.40896	−	0.813464i
$391$			31.6531i			1.60077i
$392$	−6.91238	−	1.10411i	−0.349128	−	0.0557660i
$393$			4.71998i			0.238092i
$394$	−10.1375	−	17.5586i	−0.510718	−	0.884589i
$395$	−9.91238	+	17.1687i	−0.498746	+	0.863853i
$396$	7.50000	+	6.53835i	0.376889	+	0.328564i
$397$	9.13746	+	15.8265i	0.458596	+	0.794311i	0.998887	−	0.0471668i	$-0.0150192\pi$
$397$	9.13746	+	15.8265i	0.458596	+	0.794311i	−0.540291	+	0.841478i	$0.681686\pi$
$398$		0			0
$399$	9.82475	+	0.779710i	0.491853	+	0.0390343i
$400$	−4.27492			−0.213746
$401$	25.6495	−	14.8087i	1.28088	−	0.739514i	0.303867	−	0.952715i	$-0.401722\pi$
$401$	25.6495	−	14.8087i	1.28088	−	0.739514i	0.977008	+	0.213201i	$0.0683889\pi$
$402$	−9.82475	−	5.67232i	−0.490014	−	0.282910i
$403$	14.3746	+	8.29917i	0.716049	+	0.413411i
$404$	−6.41238	−	11.1066i	−0.319028	−	0.552572i
$405$		−	27.4093i		−	1.36198i
$406$	1.13746	+	2.38876i	0.0564511	+	0.118552i
$407$	−0.175248	+	0.894797i	−0.00868674	+	0.0443535i
$408$	−6.41238	+	3.70219i	−0.317460	+	0.183286i
$409$	−31.1873	−	18.0060i	−1.54211	−	0.890339i	−0.998705	−	0.0508697i	$-0.983801\pi$
$409$	−31.1873	−	18.0060i	−1.54211	−	0.890339i	−0.543407	−	0.839469i	$-0.682866\pi$
$410$	−22.5498	−	13.0192i	−1.11366	−	0.642970i
$411$	−11.2749	−	19.5287i	−0.556151	−	0.963281i
$412$	17.0997			0.842440
$413$	−3.77492	−	2.59808i	−0.185752	−	0.127843i
$414$		−	22.2131i		−	1.09172i
$415$	−7.18729	+	4.14959i	−0.352810	+	0.203695i
$416$	5.27492	+	3.04547i	0.258624	+	0.149317i
$417$	4.13746	−	7.16629i	0.202612	−	0.350935i
$418$	−2.31271	−	6.74766i	−0.113118	−	0.330039i
$419$		−	22.9353i		−	1.12046i	−0.828336	−	0.560231i	$-0.810712\pi$
$419$		−	22.9353i		−	1.12046i	0.828336	−	0.560231i	$-0.189288\pi$
$420$	7.91238	−	11.4964i	0.386084	−	0.560968i
$421$	−15.3746			−0.749311			−0.374656	−	0.927164i	$-0.622239\pi$
$421$	−15.3746			−0.749311			−0.374656	+	0.927164i	$0.622239\pi$
$422$	−9.72508	+	5.61478i	−0.473410	+	0.273323i
$423$	28.2371	+	16.3027i	1.37294	+	0.792665i
$424$	−7.18729	−	4.14959i	−0.349046	−	0.201522i
$425$	−9.13746	−	15.8265i	−0.443232	−	0.767700i
$426$	−9.72508			−0.471182
$427$	16.5498	−	7.88054i	0.800903	−	0.381366i
$428$	6.72508			0.325069
$429$	33.0997	−	11.3446i	1.59807	−	0.547725i
$430$	−8.54983	+	14.8087i	−0.412310	+	0.714141i
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	4.27492			0.205439			0.102720	−	0.994710i	$-0.467246\pi$
$433$	4.27492			0.205439			0.102720	+	0.994710i	$0.467246\pi$
$434$	7.18729	+	0.570396i	0.345001	+	0.0273799i
$435$	−5.27492			−0.252913
$436$	−11.2749	+	6.50958i	−0.539971	+	0.311752i
$437$	−7.96221	+	13.7910i	−0.380884	+	0.659711i
$438$	10.5498	−	18.2728i	0.504091	−	0.873111i
$439$	20.3248	−	11.7345i	0.970047	−	0.560057i	0.0707968	−	0.997491i	$-0.477446\pi$
$439$	20.3248	−	11.7345i	0.970047	−	0.560057i	0.899251	+	0.437434i	$0.144112\pi$
$440$	−9.91238	−	1.94136i	−0.472554	−	0.0925509i
$441$	7.50000	+	19.6150i	0.357143	+	0.934050i
$442$			26.0383i			1.23852i
$443$	12.0498	−	6.95698i	0.572505	−	0.330536i	−0.185644	−	0.982617i	$-0.559437\pi$
$443$	12.0498	−	6.95698i	0.572505	−	0.330536i	0.758149	+	0.652081i	$0.226104\pi$
$444$	0.412376	+	0.238085i	0.0195705	+	0.0112990i
$445$	−9.27492	+	16.0646i	−0.439673	+	0.761536i
$446$	−9.91238	−	17.1687i	−0.469365	−	0.812963i
$447$			0.476171i			0.0225221i
$448$	2.63746	+	0.209313i	0.124608	+	0.00988913i
$449$		−	13.0192i		−	0.614412i	−0.951643	−	0.307206i	$-0.900606\pi$
$449$		−	13.0192i		−	0.614412i	0.951643	−	0.307206i	$-0.0993940\pi$
$450$	6.41238	+	11.1066i	0.302282	+	0.523568i
$451$	−21.3746	−	18.6339i	−1.00649	−	0.877438i
$452$		0			0
$453$	−10.5000	−	18.1865i	−0.493333	−	0.854478i
$454$	14.3746			0.674633
$455$	−21.0997	−	44.3112i	−0.989168	−	2.07734i
$456$	−3.72508			−0.174443
$457$	32.8368	−	18.9583i	1.53604	−	0.886833i	0.536976	−	0.843598i	$-0.319567\pi$
$457$	32.8368	−	18.9583i	1.53604	−	0.886833i	0.999065	−	0.0432357i	$-0.0137666\pi$
$458$	4.27492	−	7.40437i	0.199754	−	0.345984i
$459$	19.2371	+	11.1066i	0.897912	+	0.518410i
$460$	11.2749	+	19.5287i	0.525696	+	0.910532i
$461$	12.8248			0.597308			0.298654	−	0.954361i	$-0.403462\pi$
$461$	12.8248			0.597308			0.298654	+	0.954361i	$0.403462\pi$
$462$	10.8625	−	10.6304i	0.505371	−	0.494571i
$463$	20.0000			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$464$	−0.500000	−	0.866025i	−0.0232119	−	0.0402042i
$465$	−7.18729	+	12.4488i	−0.333303	+	0.577297i
$466$	2.41238	−	4.17836i	0.111751	−	0.193559i
$467$	20.6873	−	11.9438i	0.957294	−	0.552694i	0.0619547	−	0.998079i	$-0.480267\pi$
$467$	20.6873	−	11.9438i	0.957294	−	0.552694i	0.895339	+	0.445385i	$0.146933\pi$
$468$		−	18.2728i		−	0.844663i
$469$	−9.82475	+	14.2750i	−0.453665	+	0.659160i
$470$	−33.0997			−1.52677
$471$	−14.5876	+	8.42217i	−0.672162	+	0.388073i
$472$	1.50000	+	0.866025i	0.0690431	+	0.0398621i
$473$	−12.2371	+	14.0369i	−0.562664	+	0.645420i
$474$	5.63746	+	9.76436i	0.258937	+	0.448492i
$475$		−	9.19397i		−	0.421848i
$476$	4.86254	+	10.2118i	0.222874	+	0.468055i
$477$			24.8975i			1.13998i
$478$	1.27492	+	2.20822i	0.0583134	+	0.101002i
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	−0.345827	−	0.938298i	$-0.612402\pi$
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	0.985504	−	0.169654i	$-0.0542649\pi$
$480$	−2.63746	+	4.56821i	−0.120383	+	0.208509i
$481$	1.45017	−	0.837253i	0.0661219	−	0.0381755i
$482$			9.13642i			0.416153i
$483$	−33.8248	−	2.68439i	−1.53908	−	0.122144i
$484$	−10.1873	−	4.14959i	−0.463059	−	0.188618i
$485$	−4.08762	+	2.35999i	−0.185609	+	0.107162i
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	−9.18729	+	15.9129i	−0.416316	+	0.721080i	−0.995566	−	0.0940698i	$-0.970012\pi$
$487$	−9.18729	+	15.9129i	−0.416316	+	0.721080i	0.579250	+	0.815150i	$0.303346\pi$
$488$	−6.00000	+	3.46410i	−0.271607	+	0.156813i
$489$		−	2.51176i		−	0.113586i
$490$	−16.5498	−	13.4378i	−0.747645	−	0.607057i
$491$	22.3746			1.00975			0.504875	−	0.863192i	$-0.331538\pi$
$491$	22.3746			1.00975			0.504875	+	0.863192i	$0.331538\pi$
$492$	−12.8248	+	7.40437i	−0.578184	+	0.333815i
$493$	2.13746	−	3.70219i	0.0962663	−	0.166738i
$494$	−6.54983	+	11.3446i	−0.294691	+	0.510420i
$495$	9.82475	+	28.6652i	0.441590	+	1.28840i
$496$	−2.72508			−0.122360
$497$	−1.17525	+	14.8087i	−0.0527171	+	0.664263i
$498$			4.71998i			0.211507i
$499$	−9.27492	−	16.0646i	−0.415202	−	0.719152i	0.580247	−	0.814440i	$-0.302956\pi$
$499$	−9.27492	−	16.0646i	−0.415202	−	0.719152i	−0.995450	+	0.0952888i	$0.969623\pi$
$500$	1.91238	+	1.10411i	0.0855240	+	0.0493773i
$501$	33.8248	+	19.5287i	1.51118	+	0.872479i
$502$	−6.77492	+	3.91150i	−0.302379	+	0.174579i
$503$	−11.6495			−0.519426			−0.259713	−	0.965686i	$-0.583628\pi$
$503$	−11.6495			−0.519426			−0.259713	+	0.965686i	$0.583628\pi$
$504$	−3.41238	−	7.16629i	−0.151999	−	0.319212i
$505$		−	39.0575i		−	1.73803i
$506$	7.96221	+	23.2309i	0.353963	+	1.03274i
$507$	−36.1495	−	20.8709i	−1.60546	−	0.926910i
$508$	12.0498	+	6.95698i	0.534625	+	0.308666i
$509$	31.9124	−	18.4246i	1.41449	−	0.816657i	0.418684	−	0.908132i	$-0.362492\pi$
$509$	31.9124	−	18.4246i	1.41449	−	0.816657i	0.995807	+	0.0914752i	$0.0291582\pi$
$510$	−22.5498			−0.998523
$511$	−26.5498	−	18.2728i	−1.17450	−	0.808343i
$512$	−1.00000			−0.0441942
$513$	5.58762	+	9.67805i	0.246700	+	0.427296i
$514$	−6.72508	−	3.88273i	−0.296631	−	0.171260i
$515$	45.0997	+	26.0383i	1.98733	+	1.14738i
$516$	4.86254	+	8.42217i	0.214061	+	0.370765i
$517$	−35.3746	−	6.92820i	−1.55577	−	0.304702i
$518$	0.412376	−	0.599168i	0.0181188	−	0.0263259i
$519$			24.2487i			1.06440i
$520$	9.27492	+	16.0646i	0.406732	+	0.704481i
$521$	−15.0997	−	8.71780i	−0.661529	−	0.381934i	0.131331	−	0.991339i	$-0.458075\pi$
$521$	−15.0997	−	8.71780i	−0.661529	−	0.381934i	−0.792859	+	0.609405i	$0.791408\pi$
$522$	−1.50000	+	2.59808i	−0.0656532	+	0.113715i
$523$	−6.09967	+	3.52165i	−0.266720	+	0.153991i	−0.627396	−	0.778700i	$-0.715879\pi$
$523$	−6.09967	+	3.52165i	−0.266720	+	0.153991i	0.360676	+	0.932691i	$0.382546\pi$
$524$	−2.72508			−0.119046
$525$	17.6873	−	8.42217i	0.771937	−	0.367574i
$526$	1.09967			0.0479478
$527$	−5.82475	−	10.0888i	−0.253730	−	0.439474i
$528$	−3.77492	+	4.33013i	−0.164282	+	0.188445i
$529$	15.9124	−	27.5610i	0.691842	−	1.19831i
$530$	−12.6375	−	21.8887i	−0.548936	−	0.950785i
$531$		−	5.19615i		−	0.225494i
$532$	−0.450166	+	5.67232i	−0.0195172	+	0.245926i
$533$			52.0766i			2.25569i
$534$	5.27492	+	9.13642i	0.228268	+	0.395372i
$535$	17.7371	+	10.2405i	0.766843	+	0.442737i
$536$	3.27492	−	5.67232i	0.141455	−	0.245007i
$537$	−16.1375	−	27.9509i	−0.696383	−	1.20617i
$538$		−	16.0646i		−	0.692595i
$539$	−14.8746	−	17.8255i	−0.640694	−	0.767797i
$540$	15.8248			0.680989
$541$	22.5498	−	13.0192i	0.969493	−	0.559737i	0.0704114	−	0.997518i	$-0.477569\pi$
$541$	22.5498	−	13.0192i	0.969493	−	0.559737i	0.899082	+	0.437781i	$0.144235\pi$
$542$	26.7371	+	15.4367i	1.14846	+	0.663063i
$543$	12.8248	+	7.40437i	0.550363	+	0.317752i
$544$	−2.13746	−	3.70219i	−0.0916428	−	0.158730i
$545$	−39.6495			−1.69840
$546$	−27.8248	−	2.20822i	−1.19079	−	0.0945032i
$547$		−	22.2131i		−	0.949764i	−0.880049	−	0.474882i	$-0.842491\pi$
$547$		−	22.2131i		−	0.949764i	0.880049	−	0.474882i	$-0.157509\pi$
$548$	11.2749	−	6.50958i	0.481641	−	0.278075i
$549$	18.0000	+	10.3923i	0.768221	+	0.443533i
$550$	−10.6873	−	9.31697i	−0.455708	−	0.397277i
$551$	1.86254	−	1.07534i	0.0793469	−	0.0458110i
$552$	12.8248			0.545858
$553$	15.5498	−	7.40437i	0.661246	−	0.314866i
$554$		−	26.0383i		−	1.10626i
$555$	0.725083	+	1.25588i	0.0307781	+	0.0533091i
$556$	4.13746	+	2.38876i	0.175467	+	0.101306i
$557$	15.3248	−	26.5432i	0.649331	−	1.12467i	−0.333952	−	0.942590i	$-0.608383\pi$
$557$	15.3248	−	26.5432i	0.649331	−	1.12467i	0.983283	−	0.182084i	$-0.0582842\pi$
$558$	4.08762	+	7.07997i	0.173043	+	0.299719i
$559$	34.1993			1.44648
$560$	6.63746	+	4.56821i	0.280484	+	0.193042i
$561$	−24.0997	−	4.71998i	−1.01749	−	0.199278i
$562$	1.86254	+	3.22602i	0.0785666	+	0.136081i
$563$	−15.3625	+	26.6087i	−0.647454	+	1.12142i	0.336275	+	0.941764i	$0.390833\pi$
$563$	−15.3625	+	26.6087i	−0.647454	+	1.12142i	−0.983729	+	0.179659i	$0.942500\pi$
$564$	−9.41238	+	16.3027i	−0.396333	+	0.686468i
$565$		0			0
$566$			2.62685i			0.110415i
$567$	−13.5000	+	19.6150i	−0.566947	+	0.823754i
$568$		−	5.61478i		−	0.235591i
$569$	14.6873	+	25.4391i	0.615723	+	1.06646i	0.990257	+	0.139251i	$0.0444694\pi$
$569$	14.6873	+	25.4391i	0.615723	+	1.06646i	−0.374534	+	0.927213i	$0.622197\pi$
$570$	−9.82475	−	5.67232i	−0.411514	−	0.237587i
$571$	7.96221	+	4.59698i	0.333208	+	0.192378i	0.657265	−	0.753660i	$-0.271713\pi$
$571$	7.96221	+	4.59698i	0.333208	+	0.192378i	−0.324056	+	0.946038i	$0.605047\pi$
$572$	6.54983	+	19.1101i	0.273862	+	0.799034i
$573$	−25.6495			−1.07152
$574$	9.72508	+	20.4235i	0.405917	+	0.852462i
$575$			31.6531i			1.32002i
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	−0.187293	+	0.324401i	−0.00779711	+	0.0135050i	−0.869898	−	0.493232i	$-0.835815\pi$
$577$	−0.187293	+	0.324401i	−0.00779711	+	0.0135050i	0.862101	+	0.506737i	$0.169149\pi$
$578$	0.637459	−	1.10411i	0.0265148	−	0.0459250i
$579$	−15.3625	−	26.6087i	−0.638445	−	1.10582i
$580$		−	3.04547i		−	0.126456i
$581$	7.18729	+	0.570396i	0.298179	+	0.0236640i
$582$			2.68439i			0.111272i
$583$	−8.92442	−	26.0383i	−0.369612	−	1.07840i
$584$	10.5498	+	6.09095i	0.436555	+	0.252045i
$585$	27.8248	−	48.1939i	1.15041	−	1.99257i
$586$	−12.0498	−	20.8709i	−0.497774	−	0.862170i
$587$			26.4569i			1.09199i	0.837787	+	0.545997i	$0.183849\pi$
$587$			26.4569i			1.09199i	−0.837787	+	0.545997i	$0.816151\pi$
$588$	−11.3248	+	4.33013i	−0.467025	+	0.178571i
$589$		−	5.86077i		−	0.241489i
$590$	2.63746	+	4.56821i	0.108582	+	0.188070i
$591$	−30.4124	−	17.5586i	−1.25100	−	0.722264i
$592$	−0.137459	+	0.238085i	−0.00564951	+	0.00978525i
$593$	−6.41238	−	11.1066i	−0.263325	−	0.456092i	0.703799	−	0.710400i	$-0.251486\pi$
$593$	−6.41238	−	11.1066i	−0.263325	−	0.456092i	−0.967123	+	0.254308i	$0.918152\pi$
$594$	16.9124	+	3.31233i	0.693923	+	0.135907i
$595$	−2.72508	+	34.3375i	−0.111718	+	1.40770i
$596$	−0.274917			−0.0112610
$597$		0			0
$598$	22.5498	−	39.0575i	0.922131	−	1.59718i
$599$	−24.0997	−	13.9140i	−0.984686	−	0.568509i	−0.0810042	−	0.996714i	$-0.525813\pi$
$599$	−24.0997	−	13.9140i	−0.984686	−	0.568509i	−0.903682	+	0.428205i	$0.859146\pi$
$600$	−6.41238	+	3.70219i	−0.261784	+	0.151141i
$601$			1.37097i			0.0559229i	0.999609	+	0.0279615i	$0.00890157\pi$
$601$			1.37097i			0.0559229i	−0.999609	+	0.0279615i	$0.991098\pi$
$602$	13.4124	−	6.38658i	0.546648	−	0.260298i
$603$	−19.6495			−0.800190
$604$	10.5000	−	6.06218i	0.427239	−	0.246667i
$605$	−20.5498	−	26.4569i	−0.835470	−	1.07563i
$606$	−19.2371	−	11.1066i	−0.781455	−	0.451173i
$607$	−18.3625	+	10.6016i	−0.745313	+	0.430306i	−0.823998	−	0.566593i	$-0.808261\pi$
$607$	−18.3625	+	10.6016i	−0.745313	+	0.430306i	0.0786852	+	0.996900i	$0.474928\pi$
$608$		−	2.15068i		−	0.0872215i
$609$	3.77492	+	2.59808i	0.152967	+	0.105279i
$610$	−21.0997			−0.854301
$611$	33.0997	+	57.3303i	1.33907	+	2.31934i
$612$	−6.41238	+	11.1066i	−0.259205	+	0.448956i
$613$	8.17525	+	4.71998i	0.330195	+	0.190638i	0.655928	−	0.754824i	$-0.272278\pi$
$613$	8.17525	+	4.71998i	0.330195	+	0.190638i	−0.325733	+	0.945462i	$0.605611\pi$
$614$	−13.5498	+	7.82300i	−0.546827	+	0.315711i
$615$	−45.0997			−1.81859
$616$	6.13746	+	6.27149i	0.247285	+	0.252686i
$617$			3.57919i			0.144093i	0.997401	+	0.0720464i	$0.0229530\pi$
$617$			3.57919i			0.144093i	−0.997401	+	0.0720464i	$0.977047\pi$
$618$	25.6495	−	14.8087i	1.03177	−	0.595695i
$619$	8.54983	−	14.8087i	0.343647	−	0.595214i	−0.641460	−	0.767156i	$-0.721671\pi$
$619$	8.54983	−	14.8087i	0.343647	−	0.595214i	0.985107	+	0.171943i	$0.0550044\pi$
$620$	−7.18729	−	4.14959i	−0.288649	−	0.166651i
$621$	−19.2371	−	33.3197i	−0.771959	−	1.33707i
$622$			22.0980i			0.886050i
$623$	14.5498	−	6.92820i	0.582927	−	0.277573i
$624$	10.5498			0.422331
$625$	14.0498	+	24.3350i	0.561993	+	0.973401i
$626$	3.50000	−	6.06218i	0.139888	−	0.242293i
$627$	−9.31271	−	8.11863i	−0.371914	−	0.324227i
$628$	−4.86254	−	8.42217i	−0.194037	−	0.336081i
$629$	−1.17525			−0.0468602
$630$	1.91238	−	24.0969i	0.0761909	−	0.960045i
$631$	24.9244			0.992226			0.496113	−	0.868258i	$-0.334760\pi$
$631$	24.9244			0.992226			0.496113	+	0.868258i	$0.334760\pi$
$632$	−5.63746	+	3.25479i	−0.224246	+	0.129469i
$633$	−9.72508	+	16.8443i	−0.386537	+	0.669502i
$634$	−7.18729	−	4.14959i	−0.285444	−	0.164801i
$635$	21.1873	+	36.6975i	0.840792	+	1.45629i
$636$	−14.3746			−0.569989
$637$	−6.72508	+	42.1029i	−0.266457	+	1.66818i
$638$	0.637459	−	3.25479i	0.0252372	−	0.128858i
$639$	−14.5876	+	8.42217i	−0.577077	+	0.333176i
$640$	−2.63746	−	1.52274i	−0.104255	−	0.0601915i
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$	10.0876	−	5.82409i	0.398127	−	0.229859i
$643$	11.6495			0.459412			0.229706	−	0.973260i	$-0.426224\pi$
$643$	11.6495			0.459412			0.229706	+	0.973260i	$0.426224\pi$
$644$	1.54983	−	19.5287i	0.0610720	−	0.769540i
$645$			29.6175i			1.16619i
$646$	7.96221	−	4.59698i	0.313269	−	0.180866i
$647$	0.824752	+	0.476171i	0.0324243	+	0.0187202i	0.516125	−	0.856514i	$-0.327374\pi$
$647$	0.824752	+	0.476171i	0.0324243	+	0.0187202i	−0.483700	+	0.875234i	$0.660707\pi$
$648$	4.50000	−	7.79423i	0.176777	−	0.306186i
$649$	1.86254	+	5.43424i	0.0731111	+	0.213312i
$650$			26.0383i			1.02131i
$651$	11.2749	−	5.36878i	0.441899	−	0.210419i
$652$	1.45017			0.0567929
$653$	−15.3625	+	8.86957i	−0.601183	+	0.347093i	−0.769507	−	0.638639i	$-0.779498\pi$
$653$	−15.3625	+	8.86957i	−0.601183	+	0.347093i	0.168324	+	0.985732i	$0.446165\pi$
$654$	−11.2749	+	19.5287i	−0.440884	+	0.763634i
$655$	−7.18729	−	4.14959i	−0.280831	−	0.162138i
$656$	−4.27492	−	7.40437i	−0.166907	−	0.289092i
$657$		−	36.5457i		−	1.42578i
$658$	23.6873	+	16.3027i	0.923427	+	0.635546i
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$	−16.5498	+	5.67232i	−0.644201	+	0.220795i
$661$	9.13746	−	15.8265i	0.355406	−	0.615581i	−0.631781	−	0.775147i	$-0.717676\pi$
$661$	9.13746	−	15.8265i	0.355406	−	0.615581i	0.987187	+	0.159565i	$0.0510093\pi$
$662$	12.5498	−	21.7370i	0.487763	−	0.844831i
$663$	22.5498	+	39.0575i	0.875763	+	1.51687i
$664$	−2.72508			−0.105754
$665$	−9.82475	+	14.2750i	−0.380988	+	0.553562i
$666$	0.824752			0.0319585
$667$	−6.41238	+	3.70219i	−0.248288	+	0.143349i
$668$	−11.2749	+	19.5287i	−0.436240	+	0.755589i
$669$	−29.7371	−	17.1687i	−1.14970	−	0.663782i
$670$	17.2749	−	9.97368i	0.667388	−	0.385317i
$671$	−22.5498	−	4.41644i	−0.870527	−	0.170495i
$672$	4.13746	−	1.97014i	0.159606	−	0.0759997i
$673$			17.7391i			0.683793i	0.939738	+	0.341897i	$0.111069\pi$
$673$			17.7391i			0.683793i	−0.939738	+	0.341897i	$0.888931\pi$
$674$	18.4622	−	10.6592i	0.711138	−	0.410576i
$675$	19.2371	+	11.1066i	0.740437	+	0.427492i
$676$	12.0498	−	20.8709i	0.463455	−	0.802728i
$677$	−13.5997	−	23.5553i	−0.522678	−	0.905304i	−0.999652	−	0.0263870i	$-0.991600\pi$
$677$	−13.5997	−	23.5553i	−0.522678	−	0.905304i	0.476974	−	0.878917i	$-0.341734\pi$
$678$		0			0
$679$	4.08762	+	0.324401i	0.156869	+	0.0124494i
$680$		−	13.0192i		−	0.499262i
$681$	21.5619	−	12.4488i	0.826253	−	0.477037i
$682$	−6.81271	−	5.93918i	−0.260872	−	0.227423i
$683$	18.6752	+	10.7822i	0.714589	+	0.412568i	0.812758	−	0.582602i	$-0.197965\pi$
$683$	18.6752	+	10.7822i	0.714589	+	0.412568i	−0.0981692	+	0.995170i	$0.531299\pi$
$684$	−5.58762	+	3.22602i	−0.213648	+	0.123350i
$685$	39.6495			1.51493
$686$	5.22508	+	17.7679i	0.199495	+	0.678382i
$687$		−	14.8087i		−	0.564989i
$688$	−4.86254	+	2.80739i	−0.185383	+	0.107031i
$689$	−25.2749	+	43.7774i	−0.962898	+	1.66779i
$690$	33.8248	+	19.5287i	1.28769	+	0.743446i
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	0.999276	+	0.0380440i	$0.0121127\pi$
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	−0.466691	+	0.884420i	$0.654554\pi$
$692$	−14.0000			−0.532200
$693$	7.08762	−	25.3528i	0.269237	−	0.963074i
$694$	4.00000			0.151838
$695$	7.27492	+	12.6005i	0.275953	+	0.477965i
$696$	−1.50000	−	0.866025i	−0.0568574	−	0.0328266i
$697$	18.2749	−	31.6531i	0.692212	−	1.19895i
$698$	−30.9244	+	17.8542i	−1.17051	+	0.675792i
$699$		−	8.35671i		−	0.316080i
$700$	4.86254	+	10.2118i	0.183787	+	0.385968i
$701$	−40.0997			−1.51454			−0.757272	−	0.653100i	$-0.773468\pi$
$701$	−40.0997			−1.51454			−0.757272	+	0.653100i	$0.773468\pi$
$702$	−15.8248	−	27.4093i	−0.597267	−	1.03450i
$703$	−0.512045	−	0.295629i	−0.0193121	−	0.0111499i
$704$	−2.50000	−	2.17945i	−0.0942223	−	0.0821411i
$705$	−49.6495	+	28.6652i	−1.86991	+	1.07959i
$706$			15.7611i			0.593176i
$707$	−19.2371	+	27.9509i	−0.723487	+	1.05120i
$708$	3.00000			0.112747
$709$	13.8625	+	24.0106i	0.520619	+	0.901738i	0.999713	+	0.0239743i	$0.00763200\pi$
$709$	13.8625	+	24.0106i	0.520619	+	0.901738i	−0.479094	+	0.877764i	$0.659035\pi$
$710$	8.54983	−	14.8087i	0.320870	−	0.555762i
$711$	16.9124	+	9.76436i	0.634264	+	0.366192i
$712$	−5.27492	+	3.04547i	−0.197686	+	0.114134i
$713$			20.1775i			0.755654i
$714$	16.1375	+	11.1066i	0.603929	+	0.415653i
$715$	−11.8248	+	60.3758i	−0.442221	+	2.25793i
$716$	16.1375	−	9.31697i	0.603085	−	0.348191i
$717$	3.82475	+	2.20822i	0.142838	+	0.0824675i
$718$	−9.82475	+	17.0170i	−0.366656	+	0.635068i
$719$	−24.4124	+	14.0945i	−0.910428	+	0.525636i	−0.880569	−	0.473918i	$-0.842839\pi$
$719$	−24.4124	+	14.0945i	−0.910428	+	0.525636i	−0.0298592	+	0.999554i	$0.509506\pi$
$720$			9.13642i			0.340494i
$721$	−19.4502	−	40.8471i	−0.724362	−	1.52122i
$722$	−14.3746			−0.534967
$723$	7.91238	+	13.7046i	0.294264	+	0.509681i
$724$	−4.27492	+	7.40437i	−0.158876	+	0.275181i
$725$	2.13746	−	3.70219i	0.0793832	−	0.137496i
$726$	−18.8746	+	2.59808i	−0.700502	+	0.0964237i
$727$	2.72508			0.101068			0.0505339	−	0.998722i	$-0.483908\pi$
$727$	2.72508			0.101068			0.0505339	+	0.998722i	$0.483908\pi$
$728$	1.27492	−	16.0646i	0.0472516	−	0.595395i
$729$	−27.0000			−1.00000
$730$	18.5498	+	32.1293i	0.686560	+	1.18916i
$731$	−20.7870	−	12.0014i	−0.768834	−	0.443886i
$732$	−6.00000	+	10.3923i	−0.221766	+	0.384111i
$733$	2.90033	−	1.67451i	0.107126	−	0.0618493i	−0.445480	−	0.895292i	$-0.646967\pi$
$733$	2.90033	−	1.67451i	0.107126	−	0.0618493i	0.552606	+	0.833443i	$0.313634\pi$
$734$	−25.2749			−0.932914
$735$	−36.4622	−	5.82409i	−1.34493	−	0.214825i
$736$			7.40437i			0.272929i
$737$	20.5498	−	7.04329i	0.756963	−	0.259443i
$738$	−12.8248	+	22.2131i	−0.472086	+	0.817676i
$739$	−24.0997	−	13.9140i	−0.886521	−	0.511833i	−0.0137178	−	0.999906i	$-0.504367\pi$
$739$	−24.0997	−	13.9140i	−0.886521	−	0.511833i	−0.872803	+	0.488073i	$0.837700\pi$
$740$	−0.725083	+	0.418627i	−0.0266546	+	0.0153890i
$741$			22.6893i			0.833512i
$742$	−1.73713	+	21.8887i	−0.0637720	+	0.803560i
$743$	47.6495			1.74809			0.874045	−	0.485844i	$-0.161488\pi$
$743$	47.6495			1.74809			0.874045	+	0.485844i	$0.161488\pi$
$744$	−4.08762	+	2.35999i	−0.149860	+	0.0865215i
$745$	−0.725083	−	0.418627i	−0.0265650	−	0.0153373i
$746$	−22.5498	−	13.0192i	−0.825608	−	0.476665i
$747$	4.08762	+	7.07997i	0.149558	+	0.259043i
$748$	2.72508	−	13.9140i	0.0996389	−	0.508744i
$749$	−7.64950	−	16.0646i	−0.279507	−	0.586989i
$750$	3.82475			0.139660
$751$	−13.3625	−	23.1446i	−0.487606	−	0.844558i	0.512292	−	0.858811i	$-0.328796\pi$
$751$	−13.3625	−	23.1446i	−0.487606	−	0.844558i	−0.999898	+	0.0142526i	$0.995463\pi$
$752$	−9.41238	−	5.43424i	−0.343234	−	0.198166i
$753$	−6.77492	+	11.7345i	−0.246892	+	0.427629i
$754$	−5.27492	+	3.04547i	−0.192101	+	0.110910i
$755$	36.9244			1.34382
$756$	−11.3248	−	7.79423i	−0.411877	−	0.283473i
$757$	−32.4743			−1.18030			−0.590148	−	0.807295i	$-0.700931\pi$
$757$	−32.4743			−1.18030			−0.590148	+	0.807295i	$0.700931\pi$
$758$	10.0000	+	17.3205i	0.363216	+	0.629109i
$759$	32.0619	+	27.9509i	1.16377	+	1.01455i
$760$	3.27492	−	5.67232i	0.118794	−	0.205757i
$761$	10.0997	+	17.4931i	0.366113	+	0.634126i	0.988954	−	0.148222i	$-0.0473551\pi$
$761$	10.0997	+	17.4931i	0.366113	+	0.634126i	−0.622841	+	0.782348i	$0.714022\pi$
$762$	24.0997			0.873039
$763$	28.3746	+	19.5287i	1.02723	+	0.706987i
$764$		−	14.8087i		−	0.535762i
$765$	−33.8248	+	19.5287i	−1.22294	+	0.706063i
$766$	−15.5120	−	8.95588i	−0.560473	−	0.323589i
$767$	5.27492	−	9.13642i	0.190466	−	0.329897i
$768$	−1.50000	+	0.866025i	−0.0541266	+	0.0312500i
$769$		−	18.8066i		−	0.678182i	−0.940754	−	0.339091i	$-0.889881\pi$
$769$		−	18.8066i		−	0.678182i	0.940754	−	0.339091i	$-0.110119\pi$
$770$	6.63746	+	25.8865i	0.239197	+	0.932886i
$771$	−13.4502			−0.484396
$772$	15.3625	−	8.86957i	0.552910	−	0.319223i
$773$	−12.0000	−	6.92820i	−0.431610	−	0.249190i	0.268422	−	0.963301i	$-0.413498\pi$
$773$	−12.0000	−	6.92820i	−0.431610	−	0.249190i	−0.700032	+	0.714111i	$0.746831\pi$
$774$	14.5876	+	8.42217i	0.524341	+	0.302729i
$775$	−5.82475	−	10.0888i	−0.209231	−	0.362399i
$776$	−1.54983			−0.0556358
$777$	0.0996689	−	1.25588i	0.00357560	−	0.0450545i
$778$		0			0
$779$	15.9244	−	9.19397i	0.570552	−	0.329408i
$780$	27.8248	+	16.0646i	0.996286	+	0.575206i
$781$	12.2371	−	14.0369i	0.437879	−	0.502281i
$782$	−27.4124	+	15.8265i	−0.980265	+	0.565956i
$783$			5.19615i			0.185695i
$784$	−2.50000	−	6.53835i	−0.0892857	−	0.233512i
$785$		−	29.6175i		−	1.05709i
$786$	−4.08762	+	2.35999i	−0.145801	+	0.0841781i
$787$	13.7629	+	7.94600i	0.490593	+	0.283244i	0.724821	−	0.688938i	$-0.241923\pi$
$787$	13.7629	+	7.94600i	0.490593	+	0.283244i	−0.234227	+	0.972182i	$0.575256\pi$
$788$	10.1375	−	17.5586i	0.361132	−	0.625499i
$789$	1.64950	−	0.952341i	0.0587239	−	0.0339042i
$790$	−19.8248			−0.705333
$791$		0			0
$792$	−1.91238	+	9.76436i	−0.0679533	+	0.346962i
$793$	21.0997	+	36.5457i	0.749271	+	1.29778i
$794$	−9.13746	+	15.8265i	−0.324276	+	0.561663i
$795$	−37.9124	−	21.8887i	−1.34461	−	0.776313i
$796$		0			0
$797$			11.6482i			0.412600i	0.978489	+	0.206300i	$0.0661423\pi$
$797$			11.6482i			0.412600i	−0.978489	+	0.206300i	$0.933858\pi$
$798$	4.23713	+	8.89834i	0.149993	+	0.314998i
$799$		−	46.4618i		−	1.64370i
$800$	−2.13746	−	3.70219i	−0.0755706	−	0.130892i
$801$	15.8248	+	9.13642i	0.559140	+	0.322820i
$802$	25.6495	+	14.8087i	0.905715	+	0.522915i
$803$	13.0997	+	38.2202i	0.462277	+	1.34876i
$804$		−	11.3446i		−	0.400095i
$805$	33.8248	−	49.1462i	1.19217	−	1.73218i
$806$			16.5983i			0.584652i
$807$	−13.9124	−	24.0969i	−0.489739	−	0.848253i
$808$	6.41238	−	11.1066i	0.225587	−	0.390727i
$809$	−6.82475	+	11.8208i	−0.239945	+	0.415598i	−0.960698	−	0.277594i	$-0.910463\pi$
$809$	−6.82475	+	11.8208i	−0.239945	+	0.415598i	0.720753	+	0.693192i	$0.243796\pi$
$810$	23.7371	−	13.7046i	0.834038	−	0.481532i
$811$			17.3205i			0.608205i	0.952639	+	0.304103i	$0.0983566\pi$
$811$			17.3205i			0.608205i	−0.952639	+	0.304103i	$0.901643\pi$
$812$	−1.50000	+	2.17945i	−0.0526397	+	0.0764837i
$813$	53.4743			1.87542
$814$	−0.862541	+	0.295629i	−0.0302321	+	0.0103618i
$815$	3.82475	+	2.20822i	0.133975	+	0.0773506i
$816$	−6.41238	−	3.70219i	−0.224478	−	0.129602i
$817$	−6.03779	−	10.4578i	−0.211236	−	0.365871i
$818$		−	36.0120i		−	1.25913i
$819$	−43.6495	+	20.7846i	−1.52524	+	0.726273i
$820$		−	26.0383i		−	0.909297i
$821$	−13.4622	−	23.3172i	−0.469834	−	0.813777i	0.529571	−	0.848266i	$-0.322353\pi$
$821$	−13.4622	−	23.3172i	−0.469834	−	0.813777i	−0.999405	+	0.0344888i	$0.989020\pi$
$822$	11.2749	−	19.5287i	0.393258	−	0.681143i
$823$	−28.5498	+	49.4498i	−0.995185	+	1.72371i	−0.412706	+	0.910864i	$0.635416\pi$
$823$	−28.5498	+	49.4498i	−0.995185	+	1.72371i	−0.582478	+	0.812846i	$0.697917\pi$
$824$	8.54983	+	14.8087i	0.297848	+	0.515887i
$825$	−24.0997	−	4.71998i	−0.839043	−	0.164329i
$826$	0.362541	−	4.56821i	0.0126144	−	0.158948i
$827$	−23.4743			−0.816280			−0.408140	−	0.912919i	$-0.633822\pi$
$827$	−23.4743			−0.816280			−0.408140	+	0.912919i	$0.633822\pi$
$828$	19.2371	−	11.1066i	0.668536	−	0.385980i
$829$	−10.6873	+	18.5109i	−0.371185	+	0.642911i	−0.989748	−	0.142824i	$-0.954382\pi$
$829$	−10.6873	+	18.5109i	−0.371185	+	0.642911i	0.618563	+	0.785735i	$0.287715\pi$
$830$	−7.18729	−	4.14959i	−0.249475	−	0.144034i
$831$	−22.5498	−	39.0575i	−0.782245	−	1.35489i
$832$			6.09095i			0.211166i
$833$	18.8625	−	23.2309i	0.653548	−	0.804904i
$834$	8.27492			0.286537
$835$	−59.4743	+	34.3375i	−2.05819	+	1.18830i
$836$	4.68729	−	5.37669i	0.162113	−	0.185957i
$837$	12.2629	+	7.07997i	0.423867	+	0.244720i
$838$	19.8625	−	11.4676i	0.686140	−	0.396143i
$839$		−	39.7796i		−	1.37335i	−0.726967	−	0.686673i	$-0.759071\pi$
$839$		−	39.7796i		−	1.37335i	0.726967	−	0.686673i	$-0.240929\pi$
$840$	13.9124	+	1.10411i	0.480023	+	0.0380954i
$841$	−28.0000			−0.965517
$842$	−7.68729	−	13.3148i	−0.264922	−	0.458858i
$843$	5.58762	+	3.22602i	0.192448	+	0.111110i
$844$	−9.72508	−	5.61478i	−0.334751	−	0.193269i
$845$	63.5619	−	36.6975i	2.18660	−	1.26243i
$846$			32.6054i			1.12100i
$847$	1.67525	+	29.0550i	0.0575622	+	0.998342i
$848$		−	8.29917i		−	0.284995i
$849$	2.27492	+	3.94027i	0.0780750	+	0.135230i
$850$	9.13746	−	15.8265i	0.313412	−	0.542846i
$851$	1.76287	+	1.01779i	0.0604305	+	0.0348896i
$852$	−4.86254	−	8.42217i	−0.166588	−	0.288539i
$853$			30.4547i			1.04275i	0.853327	+	0.521375i	$0.174581\pi$
$853$			30.4547i			1.04275i	−0.853327	+	0.521375i	$0.825419\pi$
$854$	15.0997	+	10.3923i	0.516700	+	0.355617i
$855$	−19.6495			−0.671999
$856$	3.36254	+	5.82409i	0.114929	+	0.199063i
$857$	4.86254	−	8.42217i	0.166101	−	0.287696i	−0.770945	−	0.636902i	$-0.780215\pi$
$857$	4.86254	−	8.42217i	0.166101	−	0.287696i	0.937046	+	0.349206i	$0.113549\pi$
$858$	26.3746	+	22.9928i	0.900414	+	0.784962i
$859$	−14.0000	−	24.2487i	−0.477674	−	0.827355i	0.521999	−	0.852946i	$-0.325187\pi$
$859$	−14.0000	−	24.2487i	−0.477674	−	0.827355i	−0.999672	+	0.0255910i	$0.991853\pi$
$860$	−17.0997			−0.583094
$861$	32.2749	+	22.2131i	1.09993	+	0.757021i
$862$	12.0000			0.408722
$863$	−27.1993	+	15.7035i	−0.925876	+	0.534555i	−0.885505	−	0.464630i	$-0.846187\pi$
$863$	−27.1993	+	15.7035i	−0.925876	+	0.534555i	−0.0403712	+	0.999185i	$0.512854\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$	−36.9244	−	21.3183i	−1.25547	−	0.724845i
$866$	2.13746	+	3.70219i	0.0726338	+	0.125805i
$867$		−	2.20822i		−	0.0749951i
$868$	3.09967	+	6.50958i	0.105210	+	0.220949i
$869$	−21.1873	−	4.14959i	−0.718730	−	0.140765i
$870$	−2.63746	−	4.56821i	−0.0894182	−	0.154877i
$871$	−34.5498	−	19.9474i	−1.17068	−	0.675890i
$872$	−11.2749	−	6.50958i	−0.381817	−	0.220442i
$873$	2.32475	+	4.02659i	0.0786809	+	0.136279i
$874$	−15.9244			−0.538652
$875$	0.462210	−	5.82409i	0.0156256	−	0.196890i
$876$	21.0997			0.712892
$877$	25.6495	−	14.8087i	0.866122	−	0.500056i	6.45221e−5	−	1.00000i	$-0.499979\pi$
$877$	25.6495	−	14.8087i	0.866122	−	0.500056i	0.866058	+	0.499944i	$0.166646\pi$
$878$	20.3248	+	11.7345i	0.685927	+	0.396020i
$879$	−36.1495	−	20.8709i	−1.21929	−	0.703959i
$880$	−3.27492	−	9.55505i	−0.110397	−	0.322101i
$881$			49.5649i			1.66988i	0.550339	+	0.834941i	$0.314498\pi$
$881$			49.5649i			1.66988i	−0.550339	+	0.834941i	$0.685502\pi$
$882$	−13.2371	+	16.3027i	−0.445717	+	0.548941i
$883$	26.1993			0.881678			0.440839	−	0.897586i	$-0.354681\pi$
$883$	26.1993			0.881678			0.440839	+	0.897586i	$0.354681\pi$
$884$	−22.5498	+	13.0192i	−0.758433	+	0.437882i
$885$	7.91238	+	4.56821i	0.265972	+	0.153559i
$886$	12.0498	+	6.95698i	0.404822	+	0.233724i
$887$	−11.2749	−	19.5287i	−0.378575	−	0.655711i	0.612280	−	0.790641i	$-0.290252\pi$
$887$	−11.2749	−	19.5287i	−0.378575	−	0.655711i	−0.990855	+	0.134930i	$0.956919\pi$
$888$			0.476171i			0.0159792i
$889$	2.91238	−	36.6975i	0.0976780	−	1.23079i
$890$	−18.5498			−0.621792
$891$	28.2371	−	9.67805i	0.945979	−	0.324227i
$892$	9.91238	−	17.1687i	0.331891	−	0.574852i
$893$	11.6873	−	20.2430i	0.391100	−	0.677406i
$894$	−0.412376	+	0.238085i	−0.0137919	+	0.00796276i
$895$	56.7492			1.89692
$896$	1.13746	+	2.38876i	0.0379998	+	0.0798030i
$897$		−	78.1149i		−	2.60818i
$898$	11.2749	−	6.50958i	0.376249	−	0.217227i
$899$	1.36254	−	2.35999i	0.0454433	−	0.0787101i
$900$	−6.41238	+	11.1066i	−0.213746	+	0.370219i
$901$	30.7251	−	17.7391i	1.02360	−	0.590976i
$902$	5.45017	−	27.8279i	0.181471	−	0.926568i
$903$	14.5876	−	21.1953i	0.485446	−	0.705336i
$904$		0			0
$905$	−22.5498	+	13.0192i	−0.749582	+	0.432771i
$906$	10.5000	−	18.1865i	0.348839	−	0.604207i
$907$	−13.2749	+	22.9928i	−0.440786	+	0.763464i	−0.997748	−	0.0670738i	$-0.978634\pi$
$907$	−13.2749	+	22.9928i	−0.440786	+	0.763464i	0.556962	+	0.830538i	$0.311967\pi$
$908$	7.18729	+	12.4488i	0.238519	+	0.413127i
$909$	−38.4743			−1.27611
$910$	27.8248	−	40.4284i	0.922382	−	1.34019i
$911$			12.7732i			0.423194i	0.977357	+	0.211597i	$0.0678664\pi$
$911$			12.7732i			0.423194i	−0.977357	+	0.211597i	$0.932134\pi$
$912$	−1.86254	−	3.22602i	−0.0616749	−	0.106824i
$913$	−6.81271	−	5.93918i	−0.225468	−	0.196558i
$914$	32.8368	+	18.9583i	1.08614	+	0.627086i
$915$	−31.6495	+	18.2728i	−1.04630	+	0.604082i
$916$	8.54983			0.282494
$917$	3.09967	+	6.50958i	0.102360	+	0.214965i
$918$			22.2131i			0.733142i
$919$	−38.6873	+	22.3361i	−1.27618	+	0.736801i	−0.976143	−	0.217128i	$-0.930331\pi$
$919$	−38.6873	+	22.3361i	−1.27618	+	0.736801i	−0.300033	+	0.953929i	$0.596998\pi$
$920$	−11.2749	+	19.5287i	−0.371723	+	0.643843i
$921$	−13.5498	+	23.4690i	−0.446482	+	0.773330i
$922$	6.41238	+	11.1066i	0.211180	+	0.365775i
$923$	−34.1993			−1.12568
$924$	14.6375	+	4.09204i	0.481537	+	0.134618i
$925$	−1.17525			−0.0386419
$926$	10.0000	+	17.3205i	0.328620	+	0.569187i
$927$	25.6495	−	44.4262i	0.842440	−	1.45915i
$928$	0.500000	−	0.866025i	0.0164133	−	0.0284287i
$929$	1.45017	−	0.837253i	0.0475784	−	0.0274694i	−0.476022	−	0.879433i	$-0.657922\pi$
$929$	1.45017	−	0.837253i	0.0475784	−	0.0274694i	0.523601	+	0.851964i	$0.324588\pi$
$930$	−14.3746			−0.471361
$931$	14.0619	−	5.37669i	0.460859	−	0.176214i
$932$	4.82475			0.158040
$933$	19.1375	+	33.1471i	0.626532	+	1.08519i
$934$	20.6873	+	11.9438i	0.676909	+	0.390814i
$935$	28.3746	−	32.5479i	0.927948	−	1.06443i
$936$	15.8248	−	9.13642i	0.517248	−	0.298633i
$937$		−	16.9019i		−	0.552160i	−0.961135	−	0.276080i	$-0.910964\pi$
$937$		−	16.9019i		−	0.552160i	0.961135	−	0.276080i	$-0.0890355\pi$
$938$	−17.2749	−	1.37097i	−0.564046	−	0.0447637i
$939$		−	12.1244i		−	0.395663i
$940$	−16.5498	−	28.6652i	−0.539796	−	0.934954i
$941$	−13.5997	+	23.5553i	−0.443337	+	0.767881i	−0.997935	−	0.0642369i	$-0.979539\pi$
$941$	−13.5997	+	23.5553i	−0.443337	+	0.767881i	0.554598	+	0.832118i	$0.312872\pi$
$942$	−14.5876	−	8.42217i	−0.475290	−	0.274409i
$943$	−54.8248	+	31.6531i	−1.78534	+	1.03077i
$944$			1.73205i			0.0563735i
$945$	−18.0000	−	37.8016i	−0.585540	−	1.22969i
$946$	−18.2749	−	3.57919i	−0.594169	−	0.116369i
$947$	19.2371	−	11.1066i	0.625123	−	0.360915i	−0.153738	−	0.988112i	$-0.549131\pi$
$947$	19.2371	−	11.1066i	0.625123	−	0.360915i	0.778861	+	0.627197i	$0.215798\pi$
$948$	−5.63746	+	9.76436i	−0.183096	+	0.317132i
$949$	37.0997	−	64.2585i	1.20431	−	2.08592i
$950$	7.96221	−	4.59698i	0.258328	−	0.149146i
$951$	−14.3746			−0.466128
$952$	−6.41238	+	9.31697i	−0.207826	+	0.301965i
$953$	−17.6495			−0.571723			−0.285862	−	0.958271i	$-0.592280\pi$
$953$	−17.6495			−0.571723			−0.285862	+	0.958271i	$0.592280\pi$
$954$	−21.5619	+	12.4488i	−0.698092	+	0.403043i
$955$	22.5498	−	39.0575i	0.729696	−	1.26387i
$956$	−1.27492	+	2.20822i	−0.0412338	+	0.0714190i
$957$	−1.86254	−	5.43424i	−0.0602074	−	0.175664i
$958$	28.0000			0.904639
$959$	−28.3746	−	19.5287i	−0.916263	−	0.630616i
$960$	−5.27492			−0.170247
$961$	11.7870	+	20.4156i	0.380225	+	0.658568i
$962$	1.45017	+	0.837253i	0.0467552	+	0.0269941i
$963$	10.0876	−	17.4723i	0.325069	−	0.563036i
$964$	−7.91238	+	4.56821i	−0.254840	+	0.147132i
$965$	54.0241			1.73910
$966$	−14.5876	−	30.6353i	−0.469349	−	0.985674i
$967$		−	10.3348i		−	0.332344i	−0.986097	−	0.166172i	$-0.946859\pi$
$967$		−	10.3348i		−	0.332344i	0.986097	−	0.166172i	$-0.0531406\pi$
$968$	−1.50000	−	10.8972i	−0.0482118	−	0.350251i
$969$	7.96221	−	13.7910i	0.255783	−	0.443029i
$970$	−4.08762	−	2.35999i	−0.131246	−	0.0757747i
$971$	15.2629	−	8.81202i	0.489809	−	0.282791i	−0.234686	−	0.972071i	$-0.575406\pi$
$971$	15.2629	−	8.81202i	0.489809	−	0.282791i	0.724495	+	0.689280i	$0.242073\pi$
$972$		−	15.5885i		−	0.500000i
$973$	1.00000	−	12.6005i	0.0320585	−	0.403954i
$974$	−18.3746			−0.588760
$975$	22.5498	+	39.0575i	0.722173	+	1.25084i
$976$	−6.00000	−	3.46410i	−0.192055	−	0.110883i
$977$	3.09967	+	1.78959i	0.0991672	+	0.0572542i	0.548763	−	0.835978i	$-0.315099\pi$
$977$	3.09967	+	1.78959i	0.0991672	+	0.0572542i	−0.449596	+	0.893232i	$0.648432\pi$
$978$	2.17525	−	1.25588i	0.0695568	−	0.0401586i
$979$	−19.8248	−	3.88273i	−0.633602	−	0.124093i
$980$	3.36254	−	21.0515i	0.107412	−	0.672464i
$981$			39.0575i			1.24701i
$982$	11.1873	+	19.3770i	0.357001	+	0.618344i
$983$	−0.312707	−	0.180541i	−0.00997380	−	0.00575838i	0.495005	−	0.868890i	$-0.335166\pi$
$983$	−0.312707	−	0.180541i	−0.00997380	−	0.00575838i	−0.504979	+	0.863132i	$0.668500\pi$
$984$	−12.8248	−	7.40437i	−0.408838	−	0.236043i
$985$	53.4743	−	30.8734i	1.70383	−	0.983708i
$986$	4.27492			0.136141
$987$	49.6495	+	3.94027i	1.58036	+	0.125420i
$988$	−13.0997			−0.416756
$989$	20.7870	+	36.0041i	0.660987	+	1.14486i
$990$	−19.9124	+	22.8411i	−0.632857	+	0.725937i
$991$	3.91238	−	6.77643i	0.124281	−	0.215261i	−0.797171	−	0.603754i	$-0.793671\pi$
$991$	3.91238	−	6.77643i	0.124281	−	0.215261i	0.921452	+	0.388493i	$0.127004\pi$
$992$	−1.36254	−	2.35999i	−0.0432607	−	0.0749298i
$993$		−	43.4739i		−	1.37960i
$994$	−13.4124	+	6.38658i	−0.425415	+	0.202570i
$995$		0			0
$996$	−4.08762	+	2.35999i	−0.129521	+	0.0747792i
$997$	32.3746	+	18.6915i	1.02531	+	0.591965i	0.915639	−	0.402003i	$-0.131686\pi$
$997$	32.3746	+	18.6915i	1.02531	+	0.591965i	0.109675	+	0.993968i	$0.465019\pi$
$998$	9.27492	−	16.0646i	0.293592	−	0.508517i
$999$	1.23713	−	0.714256i	0.0391410	−	0.0225981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.n.d.263.1	yes	4
3.2	odd	2		462.2.n.a.263.2	yes	4
7.2	even	3		462.2.n.c.65.2	yes	4
11.10	odd	2		462.2.n.b.263.1	yes	4
21.2	odd	6		462.2.n.b.65.1	yes	4
33.32	even	2		462.2.n.c.263.2	yes	4
77.65	odd	6		462.2.n.a.65.2	✓	4
231.65	even	6	inner	462.2.n.d.65.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.a.65.2	✓	4	77.65	odd	6
462.2.n.a.263.2	yes	4	3.2	odd	2
462.2.n.b.65.1	yes	4	21.2	odd	6
462.2.n.b.263.1	yes	4	11.10	odd	2
462.2.n.c.65.2	yes	4	7.2	even	3
462.2.n.c.263.2	yes	4	33.32	even	2
462.2.n.d.65.1	yes	4	231.65	even	6	inner
462.2.n.d.263.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.63746 + 1.52274i) q^{5} +1.73205i q^{6} +(2.63746 + 0.209313i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.63746 + 1.52274i) q^{5} +1.73205i q^{6} +(2.63746 + 0.209313i) q^{7} -1.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.63746 - 1.52274i) q^{10} +(-2.50000 - 2.17945i) q^{11} +(-1.50000 + 0.866025i) q^{12} +6.09095i q^{13} +(1.13746 + 2.38876i) q^{14} -5.27492 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.13746 - 3.70219i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(1.86254 - 1.07534i) q^{19} -3.04547i q^{20} +(3.77492 + 2.59808i) q^{21} +(0.637459 - 3.25479i) q^{22} +(-6.41238 + 3.70219i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(2.13746 - 3.70219i) q^{25} +(-5.27492 + 3.04547i) q^{26} +5.19615i q^{27} +(-1.50000 + 2.17945i) q^{28} +1.00000 q^{29} +(-2.63746 - 4.56821i) q^{30} +(1.36254 - 2.35999i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.86254 - 5.43424i) q^{33} +4.27492 q^{34} +(-7.27492 + 3.46410i) q^{35} -3.00000 q^{36} +(-0.137459 - 0.238085i) q^{37} +(1.86254 + 1.07534i) q^{38} +(-5.27492 + 9.13642i) q^{39} +(2.63746 - 1.52274i) q^{40} +8.54983 q^{41} +(-0.362541 + 4.56821i) q^{42} -5.61478i q^{43} +(3.13746 - 1.07534i) q^{44} +(-7.91238 - 4.56821i) q^{45} +(-6.41238 - 3.70219i) q^{46} +(9.41238 - 5.43424i) q^{47} -1.73205i q^{48} +(6.91238 + 1.10411i) q^{49} +4.27492 q^{50} +(6.41238 - 3.70219i) q^{51} +(-5.27492 - 3.04547i) q^{52} +(7.18729 + 4.14959i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(9.91238 + 1.94136i) q^{55} +(-2.63746 - 0.209313i) q^{56} +3.72508 q^{57} +(0.500000 + 0.866025i) q^{58} +(-1.50000 - 0.866025i) q^{59} +(2.63746 - 4.56821i) q^{60} +(6.00000 - 3.46410i) q^{61} +2.72508 q^{62} +(3.41238 + 7.16629i) q^{63} +1.00000 q^{64} +(-9.27492 - 16.0646i) q^{65} +(3.77492 - 4.33013i) q^{66} +(-3.27492 + 5.67232i) q^{67} +(2.13746 + 3.70219i) q^{68} -12.8248 q^{69} +(-6.63746 - 4.56821i) q^{70} +5.61478i q^{71} +(-1.50000 - 2.59808i) q^{72} +(-10.5498 - 6.09095i) q^{73} +(0.137459 - 0.238085i) q^{74} +(6.41238 - 3.70219i) q^{75} +2.15068i q^{76} +(-6.13746 - 6.27149i) q^{77} -10.5498 q^{78} +(5.63746 - 3.25479i) q^{79} +(2.63746 + 1.52274i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(4.27492 + 7.40437i) q^{82} +2.72508 q^{83} +(-4.13746 + 1.97014i) q^{84} +13.0192i q^{85} +(4.86254 - 2.80739i) q^{86} +(1.50000 + 0.866025i) q^{87} +(2.50000 + 2.17945i) q^{88} +(5.27492 - 3.04547i) q^{89} -9.13642i q^{90} +(-1.27492 + 16.0646i) q^{91} -7.40437i q^{92} +(4.08762 - 2.35999i) q^{93} +(9.41238 + 5.43424i) q^{94} +(-3.27492 + 5.67232i) q^{95} +(1.50000 - 0.866025i) q^{96} +1.54983 q^{97} +(2.50000 + 6.53835i) q^{98} +(1.91238 - 9.76436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{7} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 6 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^7 - 4 * q^8 + 6 * q^9	\( 4 q + 2 q^{2} + 6 q^{3} - 2 q^{4} - 3 q^{5} + 3 q^{7} - 4 q^{8} + 6 q^{9} - 3 q^{10} - 10 q^{11} - 6 q^{12} - 3 q^{14} - 6 q^{15} - 2 q^{16} + q^{17} - 6 q^{18} + 15 q^{19} - 5 q^{22} - 3 q^{23} - 6 q^{24} + q^{25} - 6 q^{26} - 6 q^{28} + 4 q^{29} - 3 q^{30} + 13 q^{31} + 2 q^{32} - 15 q^{33} + 2 q^{34} - 14 q^{35} - 12 q^{36} + 7 q^{37} + 15 q^{38} - 6 q^{39} + 3 q^{40} + 4 q^{41} - 9 q^{42} + 5 q^{44} - 9 q^{45} - 3 q^{46} + 15 q^{47} + 5 q^{49} + 2 q^{50} + 3 q^{51} - 6 q^{52} - 9 q^{53} - 18 q^{54} + 17 q^{55} - 3 q^{56} + 30 q^{57} + 2 q^{58} - 6 q^{59} + 3 q^{60} + 24 q^{61} + 26 q^{62} - 9 q^{63} + 4 q^{64} - 22 q^{65} + 2 q^{67} + q^{68} - 6 q^{69} - 19 q^{70} - 6 q^{72} - 12 q^{73} - 7 q^{74} + 3 q^{75} - 17 q^{77} - 12 q^{78} + 15 q^{79} + 3 q^{80} - 18 q^{81} + 2 q^{82} + 26 q^{83} - 9 q^{84} + 27 q^{86} + 6 q^{87} + 10 q^{88} + 6 q^{89} + 10 q^{91} + 39 q^{93} + 15 q^{94} + 2 q^{95} + 6 q^{96} - 24 q^{97} + 10 q^{98} - 15 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^3 - 2 * q^4 - 3 * q^5 + 3 * q^7 - 4 * q^8 + 6 * q^9 - 3 * q^10 - 10 * q^11 - 6 * q^12 - 3 * q^14 - 6 * q^15 - 2 * q^16 + q^17 - 6 * q^18 + 15 * q^19 - 5 * q^22 - 3 * q^23 - 6 * q^24 + q^25 - 6 * q^26 - 6 * q^28 + 4 * q^29 - 3 * q^30 + 13 * q^31 + 2 * q^32 - 15 * q^33 + 2 * q^34 - 14 * q^35 - 12 * q^36 + 7 * q^37 + 15 * q^38 - 6 * q^39 + 3 * q^40 + 4 * q^41 - 9 * q^42 + 5 * q^44 - 9 * q^45 - 3 * q^46 + 15 * q^47 + 5 * q^49 + 2 * q^50 + 3 * q^51 - 6 * q^52 - 9 * q^53 - 18 * q^54 + 17 * q^55 - 3 * q^56 + 30 * q^57 + 2 * q^58 - 6 * q^59 + 3 * q^60 + 24 * q^61 + 26 * q^62 - 9 * q^63 + 4 * q^64 - 22 * q^65 + 2 * q^67 + q^68 - 6 * q^69 - 19 * q^70 - 6 * q^72 - 12 * q^73 - 7 * q^74 + 3 * q^75 - 17 * q^77 - 12 * q^78 + 15 * q^79 + 3 * q^80 - 18 * q^81 + 2 * q^82 + 26 * q^83 - 9 * q^84 + 27 * q^86 + 6 * q^87 + 10 * q^88 + 6 * q^89 + 10 * q^91 + 39 * q^93 + 15 * q^94 + 2 * q^95 + 6 * q^96 - 24 * q^97 + 10 * q^98 - 15 * q^99

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