LMFDB - Embedded newform 770.2.i.l.331.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(221,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("770.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 8x^{6} + 3x^{5} + 50x^{4} - 12x^{3} + 11x^{2} + 2x + 1 $ x^8 - x^7 + 8x^6 + 3x^5 + 50x^4 - 12x^3 + 11x^2 + 2x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.3
Root			$0.267083 + 0.462601i$ of defining polynomial
Character	$\chi$	$=$	770.331
Dual form			770.2.i.l.221.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.267083 + 0.462601i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.534166 q^{6} +(1.70312 + 2.02469i) q^{7} +1.00000 q^{8} +(1.35733 - 2.35097i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.267083 + 0.462601i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.534166 q^{6} +(1.70312 + 2.02469i) q^{7} +1.00000 q^{8} +(1.35733 - 2.35097i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.267083 - 0.462601i) q^{12} -1.91092 q^{13} +(-2.60500 + 0.462601i) q^{14} +0.534166 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.43604 + 2.48729i) q^{17} +(1.35733 + 2.35097i) q^{18} +(2.99649 - 5.19008i) q^{19} -1.00000 q^{20} +(-0.481750 + 1.32863i) q^{21} -1.00000 q^{22} +(1.33791 - 2.31733i) q^{23} +(0.267083 + 0.462601i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.955460 - 1.65491i) q^{26} +3.05258 q^{27} +(0.901873 - 2.48729i) q^{28} +4.33791 q^{29} +(-0.267083 + 0.462601i) q^{30} +(-0.590251 - 1.02234i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.267083 + 0.462601i) q^{33} -2.87208 q^{34} +(2.60500 - 0.462601i) q^{35} -2.71467 q^{36} +(-4.68487 + 8.11444i) q^{37} +(2.99649 + 5.19008i) q^{38} +(-0.510374 - 0.883994i) q^{39} +(0.500000 - 0.866025i) q^{40} +5.74416 q^{41} +(-0.909749 - 1.08152i) q^{42} +10.6758 q^{43} +(0.500000 - 0.866025i) q^{44} +(-1.35733 - 2.35097i) q^{45} +(1.33791 + 2.31733i) q^{46} +(-1.40624 + 2.43569i) q^{47} -0.534166 q^{48} +(-1.19875 + 6.89659i) q^{49} +1.00000 q^{50} +(-0.767083 + 1.32863i) q^{51} +(0.955460 + 1.65491i) q^{52} +(3.96670 + 6.87052i) q^{53} +(-1.52629 + 2.64361i) q^{54} +1.00000 q^{55} +(1.70312 + 2.02469i) q^{56} +3.20125 q^{57} +(-2.16896 + 3.75674i) q^{58} +(-3.36170 - 5.82264i) q^{59} +(-0.267083 - 0.462601i) q^{60} +(-1.32317 + 2.29179i) q^{61} +1.18050 q^{62} +(7.07169 - 1.25581i) q^{63} +1.00000 q^{64} +(-0.955460 + 1.65491i) q^{65} +(-0.267083 - 0.462601i) q^{66} +(-4.03417 - 6.98738i) q^{67} +(1.43604 - 2.48729i) q^{68} +1.42933 q^{69} +(-0.901873 + 2.48729i) q^{70} +2.36801 q^{71} +(1.35733 - 2.35097i) q^{72} +(0.793373 + 1.37416i) q^{73} +(-4.68487 - 8.11444i) q^{74} +(0.267083 - 0.462601i) q^{75} -5.99299 q^{76} +(-0.901873 + 2.48729i) q^{77} +1.02075 q^{78} +(-5.50336 + 9.53210i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.25671 - 5.64079i) q^{81} +(-2.87208 + 4.97459i) q^{82} -1.68518 q^{83} +(1.39150 - 0.247106i) q^{84} +2.87208 q^{85} +(-5.33791 + 9.24554i) q^{86} +(1.15858 + 2.00672i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-3.40304 + 5.89425i) q^{89} +2.71467 q^{90} +(-3.25453 - 3.86902i) q^{91} -2.67582 q^{92} +(0.315292 - 0.546101i) q^{93} +(-1.40624 - 2.43569i) q^{94} +(-2.99649 - 5.19008i) q^{95} +(0.267083 - 0.462601i) q^{96} -5.96990 q^{97} +(-5.37325 - 4.48645i) q^{98} +2.71467 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} + 8 q^{8} - 3 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 + 8 * q^8 - 3 * q^9	\( 8 q - 4 q^{2} + q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} + 8 q^{8} - 3 q^{9} + 4 q^{10} + 4 q^{11} + q^{12} - 2 q^{13} - 3 q^{14} + 2 q^{15} - 4 q^{16} + 2 q^{17} - 3 q^{18} - 10 q^{19} - 8 q^{20} + 25 q^{21} - 8 q^{22} - 6 q^{23} + q^{24} - 4 q^{25} + q^{26} - 20 q^{27} + 18 q^{29} - q^{30} + 8 q^{31} - 4 q^{32} - q^{33} - 4 q^{34} + 3 q^{35} + 6 q^{36} + 2 q^{37} - 10 q^{38} - 13 q^{39} + 4 q^{40} + 8 q^{41} - 20 q^{42} + 52 q^{43} + 4 q^{44} + 3 q^{45} - 6 q^{46} + 10 q^{47} - 2 q^{48} - 13 q^{49} + 8 q^{50} - 5 q^{51} + q^{52} - 14 q^{53} + 10 q^{54} + 8 q^{55} + 3 q^{56} + 18 q^{57} - 9 q^{58} + q^{59} - q^{60} + q^{61} - 16 q^{62} - 7 q^{63} + 8 q^{64} - q^{65} - q^{66} - 30 q^{67} + 2 q^{68} - 44 q^{69} + 36 q^{71} - 3 q^{72} - 17 q^{73} + 2 q^{74} + q^{75} + 20 q^{76} + 26 q^{78} + 15 q^{79} + 4 q^{80} - 16 q^{81} - 4 q^{82} + 4 q^{83} - 5 q^{84} + 4 q^{85} - 26 q^{86} - 8 q^{87} + 4 q^{88} + 6 q^{89} - 6 q^{90} + 3 q^{91} + 12 q^{92} - 29 q^{93} + 10 q^{94} + 10 q^{95} + q^{96} - 14 q^{97} + 2 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 + 8 * q^8 - 3 * q^9 + 4 * q^10 + 4 * q^11 + q^12 - 2 * q^13 - 3 * q^14 + 2 * q^15 - 4 * q^16 + 2 * q^17 - 3 * q^18 - 10 * q^19 - 8 * q^20 + 25 * q^21 - 8 * q^22 - 6 * q^23 + q^24 - 4 * q^25 + q^26 - 20 * q^27 + 18 * q^29 - q^30 + 8 * q^31 - 4 * q^32 - q^33 - 4 * q^34 + 3 * q^35 + 6 * q^36 + 2 * q^37 - 10 * q^38 - 13 * q^39 + 4 * q^40 + 8 * q^41 - 20 * q^42 + 52 * q^43 + 4 * q^44 + 3 * q^45 - 6 * q^46 + 10 * q^47 - 2 * q^48 - 13 * q^49 + 8 * q^50 - 5 * q^51 + q^52 - 14 * q^53 + 10 * q^54 + 8 * q^55 + 3 * q^56 + 18 * q^57 - 9 * q^58 + q^59 - q^60 + q^61 - 16 * q^62 - 7 * q^63 + 8 * q^64 - q^65 - q^66 - 30 * q^67 + 2 * q^68 - 44 * q^69 + 36 * q^71 - 3 * q^72 - 17 * q^73 + 2 * q^74 + q^75 + 20 * q^76 + 26 * q^78 + 15 * q^79 + 4 * q^80 - 16 * q^81 - 4 * q^82 + 4 * q^83 - 5 * q^84 + 4 * q^85 - 26 * q^86 - 8 * q^87 + 4 * q^88 + 6 * q^89 - 6 * q^90 + 3 * q^91 + 12 * q^92 - 29 * q^93 + 10 * q^94 + 10 * q^95 + q^96 - 14 * q^97 + 2 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.267083	+	0.462601i	0.154200	+	0.267083i	0.932768	−	0.360478i	$-0.117387\pi$
$3$	0.267083	+	0.462601i	0.154200	+	0.267083i	−0.778567	+	0.627561i	$0.784053\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.534166			−0.218072
$7$	1.70312	+	2.02469i	0.643720	+	0.765261i
$7$	1.70312	+	2.02469i	0.643720	+	0.765261i
$8$	1.00000			0.353553
$9$	1.35733	−	2.35097i	0.452444	−	0.783657i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	0.267083	−	0.462601i	0.0771002	−	0.133541i
$13$	−1.91092			−0.529994			−0.264997	−	0.964249i	$-0.585371\pi$
$13$	−1.91092			−0.529994			−0.264997	+	0.964249i	$0.585371\pi$
$14$	−2.60500	+	0.462601i	−0.696214	+	0.123635i
$15$	0.534166			0.137921
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.43604	+	2.48729i	0.348291	+	0.603257i	0.985946	−	0.167065i	$-0.0534289\pi$
$17$	1.43604	+	2.48729i	0.348291	+	0.603257i	−0.637655	+	0.770322i	$0.720096\pi$
$18$	1.35733	+	2.35097i	0.319927	+	0.554129i
$19$	2.99649	−	5.19008i	0.687443	−	1.19069i	−0.285219	−	0.958462i	$-0.592066\pi$
$19$	2.99649	−	5.19008i	0.687443	−	1.19069i	0.972662	−	0.232224i	$-0.0746002\pi$
$20$	−1.00000			−0.223607
$21$	−0.481750	+	1.32863i	−0.105126	+	0.289930i
$22$	−1.00000			−0.213201
$23$	1.33791	−	2.31733i	0.278974	−	0.483197i	−0.692156	−	0.721748i	$-0.743339\pi$
$23$	1.33791	−	2.31733i	0.278974	−	0.483197i	0.971130	+	0.238551i	$0.0766723\pi$
$24$	0.267083	+	0.462601i	0.0545181	+	0.0944281i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.955460	−	1.65491i	0.187381	−	0.324554i
$27$	3.05258			0.587469
$28$	0.901873	−	2.48729i	0.170438	−	0.470054i
$29$	4.33791			0.805530			0.402765	−	0.915303i	$-0.368049\pi$
$29$	4.33791			0.805530			0.402765	+	0.915303i	$0.368049\pi$
$30$	−0.267083	+	0.462601i	−0.0487624	+	0.0844590i
$31$	−0.590251	−	1.02234i	−0.106012	−	0.183618i	0.808139	−	0.588992i	$-0.200475\pi$
$31$	−0.590251	−	1.02234i	−0.106012	−	0.183618i	−0.914151	+	0.405373i	$0.867142\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.267083	+	0.462601i	−0.0464932	+	0.0805285i
$34$	−2.87208			−0.492557
$35$	2.60500	−	0.462601i	0.440325	−	0.0781939i
$36$	−2.71467			−0.452444
$37$	−4.68487	+	8.11444i	−0.770188	+	1.33401i	0.167271	+	0.985911i	$0.446504\pi$
$37$	−4.68487	+	8.11444i	−0.770188	+	1.33401i	−0.937460	+	0.348094i	$0.886829\pi$
$38$	2.99649	+	5.19008i	0.486096	+	0.841942i
$39$	−0.510374	−	0.883994i	−0.0817253	−	0.141552i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	5.74416			0.897086			0.448543	−	0.893761i	$-0.351943\pi$
$41$	5.74416			0.897086			0.448543	+	0.893761i	$0.351943\pi$
$42$	−0.909749	−	1.08152i	−0.140377	−	0.166882i
$43$	10.6758			1.62805			0.814024	−	0.580831i	$-0.197272\pi$
$43$	10.6758			1.62805			0.814024	+	0.580831i	$0.197272\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	−1.35733	−	2.35097i	−0.202339	−	0.350462i
$46$	1.33791	+	2.31733i	0.197264	+	0.341672i
$47$	−1.40624	+	2.43569i	−0.205122	+	0.355281i	−0.950172	−	0.311728i	$-0.899092\pi$
$47$	−1.40624	+	2.43569i	−0.205122	+	0.355281i	0.745050	+	0.667009i	$0.232426\pi$
$48$	−0.534166			−0.0771002
$49$	−1.19875	+	6.89659i	−0.171250	+	0.985228i
$50$	1.00000			0.141421
$51$	−0.767083	+	1.32863i	−0.107413	+	0.186045i
$52$	0.955460	+	1.65491i	0.132498	+	0.229494i
$53$	3.96670	+	6.87052i	0.544868	+	0.943739i	0.998615	+	0.0526087i	$0.0167536\pi$
$53$	3.96670	+	6.87052i	0.544868	+	0.943739i	−0.453747	+	0.891130i	$0.649913\pi$
$54$	−1.52629	+	2.64361i	−0.207702	+	0.359750i
$55$	1.00000			0.134840
$56$	1.70312	+	2.02469i	0.227589	+	0.270561i
$57$	3.20125			0.424016
$58$	−2.16896	+	3.75674i	−0.284798	+	0.493284i
$59$	−3.36170	−	5.82264i	−0.437657	−	0.758043i	0.559852	−	0.828593i	$-0.310858\pi$
$59$	−3.36170	−	5.82264i	−0.437657	−	0.758043i	−0.997508	+	0.0705494i	$0.977525\pi$
$60$	−0.267083	−	0.462601i	−0.0344803	−	0.0597215i
$61$	−1.32317	+	2.29179i	−0.169414	+	0.293434i	−0.938214	−	0.346055i	$-0.887521\pi$
$61$	−1.32317	+	2.29179i	−0.169414	+	0.293434i	0.768800	+	0.639490i	$0.220854\pi$
$62$	1.18050			0.149924
$63$	7.07169	−	1.25581i	0.890950	−	0.158217i
$64$	1.00000			0.125000
$65$	−0.955460	+	1.65491i	−0.118510	+	0.205266i
$66$	−0.267083	−	0.462601i	−0.0328756	−	0.0569423i
$67$	−4.03417	−	6.98738i	−0.492852	−	0.853644i	0.507114	−	0.861879i	$-0.330712\pi$
$67$	−4.03417	−	6.98738i	−0.492852	−	0.853644i	−0.999966	+	0.00823447i	$0.997379\pi$
$68$	1.43604	−	2.48729i	0.174145	−	0.301629i
$69$	1.42933			0.172072
$70$	−0.901873	+	2.48729i	−0.107794	+	0.297288i
$71$	2.36801			0.281031			0.140516	−	0.990078i	$-0.455124\pi$
$71$	2.36801			0.281031			0.140516	+	0.990078i	$0.455124\pi$
$72$	1.35733	−	2.35097i	0.159963	−	0.277065i
$73$	0.793373	+	1.37416i	0.0928572	+	0.160833i	0.908712	−	0.417423i	$-0.137067\pi$
$73$	0.793373	+	1.37416i	0.0928572	+	0.160833i	−0.815855	+	0.578256i	$0.803733\pi$
$74$	−4.68487	−	8.11444i	−0.544605	−	0.943284i
$75$	0.267083	−	0.462601i	0.0308401	−	0.0534166i
$76$	−5.99299			−0.687443
$77$	−0.901873	+	2.48729i	−0.102778	+	0.283453i
$78$	1.02075			0.115577
$79$	−5.50336	+	9.53210i	−0.619177	+	1.07245i	0.370460	+	0.928849i	$0.379200\pi$
$79$	−5.50336	+	9.53210i	−0.619177	+	1.07245i	−0.989636	+	0.143597i	$0.954133\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−3.25671	−	5.64079i	−0.361857	−	0.626754i
$82$	−2.87208	+	4.97459i	−0.317168	+	0.549351i
$83$	−1.68518			−0.184972			−0.0924861	−	0.995714i	$-0.529481\pi$
$83$	−1.68518			−0.184972			−0.0924861	+	0.995714i	$0.529481\pi$
$84$	1.39150	−	0.247106i	0.151825	−	0.0269614i
$85$	2.87208			0.311521
$86$	−5.33791	+	9.24554i	−0.575602	+	0.996972i
$87$	1.15858	+	2.00672i	0.124213	+	0.215143i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−3.40304	+	5.89425i	−0.360722	+	0.624789i	−0.988080	−	0.153942i	$-0.950803\pi$
$89$	−3.40304	+	5.89425i	−0.360722	+	0.624789i	0.627358	+	0.778731i	$0.284136\pi$
$90$	2.71467			0.286151
$91$	−3.25453	−	3.86902i	−0.341167	−	0.405584i
$92$	−2.67582			−0.278974
$93$	0.315292	−	0.546101i	0.0326942	−	0.0566281i
$94$	−1.40624	−	2.43569i	−0.145043	−	0.251222i
$95$	−2.99649	−	5.19008i	−0.307434	−	0.532491i
$96$	0.267083	−	0.462601i	0.0272590	−	0.0472140i
$97$	−5.96990			−0.606151			−0.303076	−	0.952966i	$-0.598014\pi$
$97$	−5.96990			−0.606151			−0.303076	+	0.952966i	$0.598014\pi$
$98$	−5.37325	−	4.48645i	−0.542780	−	0.453199i
$99$	2.71467			0.272834
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	2.70999	+	4.69384i	0.269654	+	0.467055i	0.968772	−	0.247951i	$-0.0797573\pi$
$101$	2.70999	+	4.69384i	0.269654	+	0.467055i	−0.699118	+	0.715006i	$0.746424\pi$
$102$	−0.767083	−	1.32863i	−0.0759525	−	0.131554i
$103$	2.78300	−	4.82029i	0.274217	−	0.474958i	−0.695720	−	0.718313i	$-0.744915\pi$
$103$	2.78300	−	4.82029i	0.274217	−	0.474958i	0.969937	+	0.243355i	$0.0782480\pi$
$104$	−1.91092			−0.187381
$105$	0.909749	+	1.08152i	0.0887824	+	0.105546i
$106$	−7.93340			−0.770560
$107$	−0.127922	+	0.221567i	−0.0123667	+	0.0214197i	−0.872143	−	0.489252i	$-0.837270\pi$
$107$	−0.127922	+	0.221567i	−0.0123667	+	0.0214197i	0.859776	+	0.510672i	$0.170603\pi$
$108$	−1.52629	−	2.64361i	−0.146867	−	0.254382i
$109$	−5.17013	−	8.95492i	−0.495208	−	0.857726i	0.504776	−	0.863250i	$-0.331575\pi$
$109$	−5.17013	−	8.95492i	−0.495208	−	0.857726i	−0.999985	+	0.00552409i	$0.998242\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	−5.00500			−0.475053
$112$	−2.60500	+	0.462601i	−0.246149	+	0.0437117i
$113$	12.3309			1.15999			0.579997	−	0.814619i	$-0.303054\pi$
$113$	12.3309			1.15999			0.579997	+	0.814619i	$0.303054\pi$
$114$	−1.60062	+	2.77236i	−0.149912	+	0.259656i
$115$	−1.33791	−	2.31733i	−0.124761	−	0.216092i
$116$	−2.16896	−	3.75674i	−0.201383	−	0.348805i
$117$	−2.59376	+	4.49252i	−0.239793	+	0.415333i
$118$	6.72341			0.618940
$119$	−2.59025	+	7.14370i	−0.237448	+	0.654862i
$120$	0.534166			0.0487624
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−1.32317	−	2.29179i	−0.119794	−	0.207489i
$123$	1.53417	+	2.65725i	0.138331	+	0.239596i
$124$	−0.590251	+	1.02234i	−0.0530061	+	0.0918092i
$125$	−1.00000			−0.0894427
$126$	−2.44829	+	6.75217i	−0.218111	+	0.601531i
$127$	−0.351649			−0.0312038			−0.0156019	−	0.999878i	$-0.504966\pi$
$127$	−0.351649			−0.0312038			−0.0156019	+	0.999878i	$0.504966\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.85133	+	4.93865i	0.251046	+	0.434824i
$130$	−0.955460	−	1.65491i	−0.0837994	−	0.145145i
$131$	1.56396	−	2.70886i	0.136644	−	0.236674i	−0.789580	−	0.613647i	$-0.789702\pi$
$131$	1.56396	−	2.70886i	0.136644	−	0.236674i	0.926224	+	0.376973i	$0.123035\pi$
$132$	0.534166			0.0464932
$133$	15.6117	−	2.77236i	1.35371	−	0.240394i
$134$	8.06833			0.696998
$135$	1.52629	−	2.64361i	0.131362	−	0.227526i
$136$	1.43604	+	2.48729i	0.123139	+	0.213284i
$137$	3.72036	+	6.44386i	0.317852	+	0.550536i	0.980040	−	0.198802i	$-0.0637051\pi$
$137$	3.72036	+	6.44386i	0.317852	+	0.550536i	−0.662187	+	0.749338i	$0.730372\pi$
$138$	−0.714667	+	1.23784i	−0.0608365	+	0.105372i
$139$	−15.8701			−1.34608			−0.673041	−	0.739606i	$-0.735012\pi$
$139$	−15.8701			−1.34608			−0.673041	+	0.739606i	$0.735012\pi$
$140$	−1.70312	−	2.02469i	−0.143940	−	0.171118i
$141$	−1.50233			−0.126519
$142$	−1.18401	+	2.05076i	−0.0993596	+	0.172096i
$143$	−0.955460	−	1.65491i	−0.0798996	−	0.138390i
$144$	1.35733	+	2.35097i	0.113111	+	0.195914i
$145$	2.16896	−	3.75674i	0.180122	−	0.311980i
$146$	−1.58675			−0.131320
$147$	−3.51054	+	1.28742i	−0.289544	+	0.106184i
$148$	9.36974			0.770188
$149$	11.3960	−	19.7385i	0.933599	−	1.61704i	0.156487	−	0.987680i	$-0.449983\pi$
$149$	11.3960	−	19.7385i	0.933599	−	1.61704i	0.777113	−	0.629362i	$-0.216684\pi$
$150$	0.267083	+	0.462601i	0.0218072	+	0.0377712i
$151$	−6.38245	−	11.0547i	−0.519397	−	0.899621i	−0.999746	−	0.0225440i	$-0.992823\pi$
$151$	−6.38245	−	11.0547i	−0.519397	−	0.899621i	0.480349	−	0.877077i	$-0.340510\pi$
$152$	2.99649	−	5.19008i	0.243048	−	0.420971i
$153$	7.79674			0.630329
$154$	−1.70312	−	2.02469i	−0.137241	−	0.163154i
$155$	−1.18050			−0.0948201
$156$	−0.510374	+	0.883994i	−0.0408626	+	0.0707762i
$157$	−10.9369	−	18.9433i	−0.872860	−	1.51184i	−0.859025	−	0.511934i	$-0.828929\pi$
$157$	−10.9369	−	18.9433i	−0.872860	−	1.51184i	−0.0138349	−	0.999904i	$-0.504404\pi$
$158$	−5.50336	−	9.53210i	−0.437824	−	0.758334i
$159$	−2.11887	+	3.67000i	−0.168038	+	0.291050i
$160$	−1.00000			−0.0790569
$161$	6.97051	−	1.23784i	0.549353	−	0.0975554i
$162$	6.51342			0.511742
$163$	4.01124	−	6.94767i	0.314184	−	0.544184i	−0.665079	−	0.746773i	$-0.731602\pi$
$163$	4.01124	−	6.94767i	0.314184	−	0.544184i	0.979264	+	0.202589i	$0.0649356\pi$
$164$	−2.87208	−	4.97459i	−0.224272	−	0.388450i
$165$	0.267083	+	0.462601i	0.0207924	+	0.0360134i
$166$	0.842589	−	1.45941i	0.0653976	−	0.113272i
$167$	−9.03183			−0.698904			−0.349452	−	0.936954i	$-0.613632\pi$
$167$	−9.03183			−0.698904			−0.349452	+	0.936954i	$0.613632\pi$
$168$	−0.481750	+	1.32863i	−0.0371678	+	0.102506i
$169$	−9.34838			−0.719106
$170$	−1.43604	+	2.48729i	−0.110139	+	0.190767i
$171$	−8.13448	−	14.0893i	−0.622060	−	1.07744i
$172$	−5.33791	−	9.24554i	−0.407012	−	0.704965i
$173$	5.90087	−	10.2206i	0.448635	−	0.777058i	−0.549663	−	0.835387i	$-0.685244\pi$
$173$	5.90087	−	10.2206i	0.448635	−	0.777058i	0.998297	+	0.0583288i	$0.0185772\pi$
$174$	−2.31716			−0.175664
$175$	0.901873	−	2.48729i	0.0681752	−	0.188022i
$176$	−1.00000			−0.0753778
$177$	1.79571	−	3.11026i	0.134974	−	0.233781i
$178$	−3.40304	−	5.89425i	−0.255069	−	0.441792i
$179$	1.52847	+	2.64738i	0.114243	+	0.197875i	0.917477	−	0.397789i	$-0.130222\pi$
$179$	1.52847	+	2.64738i	0.114243	+	0.197875i	−0.803234	+	0.595664i	$0.796889\pi$
$180$	−1.35733	+	2.35097i	−0.101170	+	0.175231i
$181$	−21.2786			−1.58163			−0.790815	−	0.612056i	$-0.790343\pi$
$181$	−21.2786			−1.58163			−0.790815	+	0.612056i	$0.790343\pi$
$182$	4.97794	−	0.883994i	0.368989	−	0.0655260i
$183$	−1.41358			−0.104495
$184$	1.33791	−	2.31733i	0.0986322	−	0.170836i
$185$	4.68487	+	8.11444i	0.344439	+	0.596585i
$186$	0.315292	+	0.546101i	0.0231183	+	0.0400421i
$187$	−1.43604	+	2.48729i	−0.105014	+	0.181889i
$188$	2.81249			0.205122
$189$	5.19891	+	6.18053i	0.378165	+	0.449568i
$190$	5.99299			0.434777
$191$	−11.5168	+	19.9476i	−0.833325	+	1.44336i	0.0620619	+	0.998072i	$0.480232\pi$
$191$	−11.5168	+	19.9476i	−0.833325	+	1.44336i	−0.895387	+	0.445289i	$0.853101\pi$
$192$	0.267083	+	0.462601i	0.0192750	+	0.0333854i
$193$	−6.30461	−	10.9199i	−0.453816	−	0.786032i	0.544803	−	0.838564i	$-0.316604\pi$
$193$	−6.30461	−	10.9199i	−0.453816	−	0.786032i	−0.998619	+	0.0525317i	$0.983271\pi$
$194$	2.98495	−	5.17008i	0.214307	−	0.371190i
$195$	−1.02075			−0.0730973
$196$	6.57200	−	2.41015i	0.469429	−	0.172153i
$197$	15.2626			1.08741			0.543707	−	0.839275i	$-0.317020\pi$
$197$	15.2626			1.08741			0.543707	+	0.839275i	$0.317020\pi$
$198$	−1.35733	+	2.35097i	−0.0964615	+	0.167076i
$199$	−3.82504	−	6.62516i	−0.271150	−	0.469645i	0.698007	−	0.716091i	$-0.254071\pi$
$199$	−3.82504	−	6.62516i	−0.271150	−	0.469645i	−0.969157	+	0.246446i	$0.920737\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	2.15491	−	3.73242i	0.151996	−	0.263265i
$202$	−5.41998			−0.381349
$203$	7.38799	+	8.78293i	0.518536	+	0.616441i
$204$	1.53417			0.107413
$205$	2.87208	−	4.97459i	0.200595	−	0.347440i
$206$	2.78300	+	4.82029i	0.193901	+	0.335846i
$207$	−3.63199	−	6.29079i	−0.252441	−	0.437240i
$208$	0.955460	−	1.65491i	0.0662492	−	0.114747i
$209$	5.99299			0.414544
$210$	−1.39150	+	0.247106i	−0.0960226	+	0.0170519i
$211$	−11.8563			−0.816223			−0.408112	−	0.912932i	$-0.633813\pi$
$211$	−11.8563			−0.816223			−0.408112	+	0.912932i	$0.633813\pi$
$212$	3.96670	−	6.87052i	0.272434	−	0.471870i
$213$	0.632456	+	1.09545i	0.0433352	+	0.0750587i
$214$	−0.127922	−	0.221567i	−0.00874456	−	0.0151460i
$215$	5.33791	−	9.24554i	0.364043	−	0.630540i
$216$	3.05258			0.207702
$217$	1.06466	−	2.93625i	0.0722740	−	0.199326i
$218$	10.3403			0.700330
$219$	−0.423792	+	0.734030i	−0.0286372	+	0.0496012i
$220$	−0.500000	−	0.866025i	−0.0337100	−	0.0583874i
$221$	−2.74416	−	4.75302i	−0.184592	−	0.319723i
$222$	2.50250	−	4.33445i	0.167957	−	0.290909i
$223$	−11.6852			−0.782497			−0.391249	−	0.920285i	$-0.627957\pi$
$223$	−11.6852			−0.782497			−0.391249	+	0.920285i	$0.627957\pi$
$224$	0.901873	−	2.48729i	0.0602589	−	0.166189i
$225$	−2.71467			−0.180978
$226$	−6.16545	+	10.6789i	−0.410120	+	0.710348i
$227$	−9.91092	−	17.1662i	−0.657811	−	1.13936i	−0.981181	−	0.193089i	$-0.938149\pi$
$227$	−9.91092	−	17.1662i	−0.657811	−	1.13936i	0.323370	−	0.946273i	$-0.395184\pi$
$228$	−1.60062	−	2.77236i	−0.106004	−	0.183604i
$229$	−10.8858	+	18.8548i	−0.719355	+	1.24596i	0.241901	+	0.970301i	$0.422229\pi$
$229$	−10.8858	+	18.8548i	−0.719355	+	1.24596i	−0.961256	+	0.275658i	$0.911104\pi$
$230$	2.67582			0.176439
$231$	−1.39150	+	0.247106i	−0.0915539	+	0.0162584i
$232$	4.33791			0.284798
$233$	−9.98979	+	17.3028i	−0.654453	+	1.13355i	0.327578	+	0.944824i	$0.393768\pi$
$233$	−9.98979	+	17.3028i	−0.654453	+	1.13355i	−0.982031	+	0.188721i	$0.939566\pi$
$234$	−2.59376	−	4.49252i	−0.169559	−	0.293685i
$235$	1.40624	+	2.43569i	0.0917332	+	0.158887i
$236$	−3.36170	+	5.82264i	−0.218828	+	0.379022i
$237$	−5.87942			−0.381909
$238$	−4.89150	−	5.81507i	−0.317069	−	0.376935i
$239$	6.65975			0.430783			0.215392	−	0.976528i	$-0.430897\pi$
$239$	6.65975			0.430783			0.215392	+	0.976528i	$0.430897\pi$
$240$	−0.267083	+	0.462601i	−0.0172401	+	0.0298608i
$241$	−0.157411	−	0.272644i	−0.0101397	−	0.0175626i	0.860911	−	0.508756i	$-0.169894\pi$
$241$	−0.157411	−	0.272644i	−0.0101397	−	0.0175626i	−0.871051	+	0.491193i	$0.836561\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	6.31849	−	10.9439i	0.405331	−	0.702055i
$244$	2.64634			0.169414
$245$	5.37325	+	4.48645i	0.343284	+	0.286628i
$246$	−3.06833			−0.195630
$247$	−5.72606	+	9.91783i	−0.364341	+	0.631056i
$248$	−0.590251	−	1.02234i	−0.0374810	−	0.0649189i
$249$	−0.450082	−	0.779565i	−0.0285228	−	0.0494029i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	8.99533			0.567780			0.283890	−	0.958857i	$-0.408375\pi$
$251$	8.99533			0.567780			0.283890	+	0.958857i	$0.408375\pi$
$252$	−4.62341	−	5.49636i	−0.291247	−	0.346238i
$253$	2.67582			0.168228
$254$	0.175825	−	0.304537i	0.0110322	−	0.0191084i
$255$	0.767083	+	1.32863i	0.0480366	+	0.0832018i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.4438	+	18.0891i	−0.651465	+	1.12837i	0.331303	+	0.943524i	$0.392512\pi$
$257$	−10.4438	+	18.0891i	−0.651465	+	1.12837i	−0.982768	+	0.184845i	$0.940822\pi$
$258$	−5.70266			−0.355032
$259$	−24.4081	+	4.33445i	−1.51665	+	0.269330i
$260$	1.91092			0.118510
$261$	5.88799	−	10.1983i	0.364458	−	0.631259i
$262$	1.56396	+	2.70886i	0.0966218	+	0.167354i
$263$	10.8833	+	18.8505i	0.671094	+	1.16237i	0.977594	+	0.210498i	$0.0675087\pi$
$263$	10.8833	+	18.8505i	0.671094	+	1.16237i	−0.306500	+	0.951871i	$0.599158\pi$
$264$	−0.267083	+	0.462601i	−0.0164378	+	0.0284711i
$265$	7.93340			0.487345
$266$	−5.40492	+	14.9063i	−0.331397	+	0.913965i
$267$	−3.63558			−0.222494
$268$	−4.03417	+	6.98738i	−0.246426	+	0.426822i
$269$	−8.34025	−	14.4457i	−0.508514	−	0.880773i	−0.999951	−	0.00985950i	$-0.996862\pi$
$269$	−8.34025	−	14.4457i	−0.508514	−	0.880773i	0.491437	−	0.870913i	$-0.336472\pi$
$270$	1.52629	+	2.64361i	0.0928870	+	0.160885i
$271$	0.0763710	−	0.132278i	0.00463921	−	0.00803534i	−0.863696	−	0.504012i	$-0.831857\pi$
$271$	0.0763710	−	0.132278i	0.00463921	−	0.00803534i	0.868336	+	0.495977i	$0.165190\pi$
$272$	−2.87208			−0.174145
$273$	0.920586	−	2.53890i	0.0557164	−	0.153661i
$274$	−7.44073			−0.449511
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	−0.714667	−	1.23784i	−0.0430179	−	0.0745092i
$277$	6.49462	+	11.2490i	0.390224	+	0.675888i	0.992479	−	0.122416i	$-0.0390642\pi$
$277$	6.49462	+	11.2490i	0.390224	+	0.675888i	−0.602255	+	0.798304i	$0.705731\pi$
$278$	7.93503	−	13.7439i	0.475912	−	0.824303i
$279$	−3.20467			−0.191858
$280$	2.60500	−	0.462601i	0.155678	−	0.0276457i
$281$	−3.18751			−0.190151			−0.0950755	−	0.995470i	$-0.530309\pi$
$281$	−3.18751			−0.190151			−0.0950755	+	0.995470i	$0.530309\pi$
$282$	0.751167	−	1.30106i	0.0447314	−	0.0774770i
$283$	−12.3604	−	21.4088i	−0.734749	−	1.27262i	−0.954833	−	0.297142i	$-0.903967\pi$
$283$	−12.3604	−	21.4088i	−0.734749	−	1.27262i	0.220084	−	0.975481i	$-0.429367\pi$
$284$	−1.18401	−	2.05076i	−0.0702579	−	0.121690i
$285$	1.60062	−	2.77236i	0.0948128	−	0.164221i
$286$	1.91092			0.112995
$287$	9.78300	+	11.6301i	0.577472	+	0.686506i
$288$	−2.71467			−0.159963
$289$	4.37558	−	7.57873i	0.257387	−	0.445808i
$290$	2.16896	+	3.75674i	0.127365	+	0.220604i
$291$	−1.59446	−	2.76168i	−0.0934688	−	0.161893i
$292$	0.793373	−	1.37416i	0.0464286	−	0.0804167i
$293$	−12.9906			−0.758922			−0.379461	−	0.925208i	$-0.623891\pi$
$293$	−12.9906			−0.758922			−0.379461	+	0.925208i	$0.623891\pi$
$294$	0.640332	−	3.68392i	0.0373449	−	0.214851i
$295$	−6.72341			−0.391452
$296$	−4.68487	+	8.11444i	−0.272303	+	0.471642i
$297$	1.52629	+	2.64361i	0.0885643	+	0.153398i
$298$	11.3960	+	19.7385i	0.660154	+	1.14342i
$299$	−2.55664	+	4.42824i	−0.147855	+	0.256092i
$300$	−0.534166			−0.0308401
$301$	18.1822	+	21.6153i	1.04801	+	1.24588i
$302$	12.7649			0.734538
$303$	−1.44758	+	2.50729i	−0.0831615	+	0.144040i
$304$	2.99649	+	5.19008i	0.171861	+	0.297672i
$305$	1.32317	+	2.29179i	0.0757644	+	0.131228i
$306$	−3.89837	+	6.75217i	−0.222855	+	0.385996i
$307$	−5.38315			−0.307233			−0.153616	−	0.988131i	$-0.549092\pi$
$307$	−5.38315			−0.307233			−0.153616	+	0.988131i	$0.549092\pi$
$308$	2.60500	−	0.462601i	0.148433	−	0.0263591i
$309$	2.97316			0.169137
$310$	0.590251	−	1.02234i	0.0335240	−	0.0580652i
$311$	−15.4290	−	26.7239i	−0.874900	−	1.51537i	−0.856869	−	0.515534i	$-0.827594\pi$
$311$	−15.4290	−	26.7239i	−0.874900	−	1.51537i	−0.0180306	−	0.999837i	$-0.505740\pi$
$312$	−0.510374	−	0.883994i	−0.0288942	−	0.0500463i
$313$	−6.12661	+	10.6116i	−0.346296	+	0.599803i	−0.985588	−	0.169161i	$-0.945894\pi$
$313$	−6.12661	+	10.6116i	−0.346296	+	0.599803i	0.639292	+	0.768964i	$0.279228\pi$
$314$	21.8738			1.23441
$315$	2.44829	−	6.75217i	0.137945	−	0.380442i
$316$	11.0067			0.619177
$317$	−10.4322	+	18.0691i	−0.585932	+	1.01486i	0.408826	+	0.912612i	$0.365938\pi$
$317$	−10.4322	+	18.0691i	−0.585932	+	1.01486i	−0.994759	+	0.102252i	$0.967395\pi$
$318$	−2.11887	−	3.67000i	−0.118821	−	0.205803i
$319$	2.16896	+	3.75674i	0.121438	+	0.210337i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−0.136663			−0.00762778
$322$	−2.41325	+	6.65556i	−0.134485	+	0.370900i
$323$	17.2123			0.957720
$324$	−3.25671	+	5.64079i	−0.180928	+	0.313377i
$325$	0.955460	+	1.65491i	0.0529994	+	0.0917976i
$326$	4.01124	+	6.94767i	0.222162	+	0.384796i
$327$	2.76170	−	4.78341i	0.152723	−	0.264523i
$328$	5.74416			0.317168
$329$	−7.32652	+	1.30106i	−0.403924	+	0.0717298i
$330$	−0.534166			−0.0294049
$331$	11.0010	−	19.0543i	0.604671	−	1.04732i	−0.387432	−	0.921898i	$-0.626638\pi$
$331$	11.0010	−	19.0543i	0.604671	−	1.04732i	0.992103	−	0.125423i	$-0.0400288\pi$
$332$	0.842589	+	1.45941i	0.0462431	+	0.0800953i
$333$	12.7179	+	22.0280i	0.696935	+	1.20713i
$334$	4.51592	−	7.82180i	0.247100	−	0.427990i
$335$	−8.06833			−0.440820
$336$	−0.909749	−	1.08152i	−0.0496309	−	0.0590018i
$337$	6.69392			0.364641			0.182320	−	0.983239i	$-0.441639\pi$
$337$	6.69392			0.364641			0.182320	+	0.983239i	$0.441639\pi$
$338$	4.67419	−	8.09594i	0.254243	−	0.440361i
$339$	3.29337	+	5.70429i	0.178871	+	0.309814i
$340$	−1.43604	−	2.48729i	−0.0778802	−	0.134892i
$341$	0.590251	−	1.02234i	0.0319639	−	0.0553630i
$342$	16.2690			0.879725
$343$	−16.0051	+	9.31864i	−0.864194	+	0.503159i
$344$	10.6758			0.575602
$345$	0.714667	−	1.23784i	0.0384764	−	0.0666430i
$346$	5.90087	+	10.2206i	0.317233	+	0.549463i
$347$	6.69158	+	11.5902i	0.359223	+	0.622192i	0.987831	−	0.155530i	$-0.0497085\pi$
$347$	6.69158	+	11.5902i	0.359223	+	0.622192i	−0.628609	+	0.777722i	$0.716375\pi$
$348$	1.15858	−	2.00672i	0.0621065	−	0.107572i
$349$	33.5902			1.79804			0.899021	−	0.437905i	$-0.144279\pi$
$349$	33.5902			1.79804			0.899021	+	0.437905i	$0.144279\pi$
$350$	1.70312	+	2.02469i	0.0910357	+	0.108224i
$351$	−5.83324			−0.311355
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−6.78300	−	11.7485i	−0.361023	−	0.625309i	0.627107	−	0.778933i	$-0.284239\pi$
$353$	−6.78300	−	11.7485i	−0.361023	−	0.625309i	−0.988129	+	0.153624i	$0.950906\pi$
$354$	1.79571	+	3.11026i	0.0954408	+	0.165308i
$355$	1.18401	−	2.05076i	0.0628406	−	0.108843i
$356$	6.80609			0.360722
$357$	−3.99649	+	0.709707i	−0.211517	+	0.0375617i
$358$	−3.05694			−0.161564
$359$	8.45078	−	14.6372i	0.446015	−	0.772521i	−0.552107	−	0.833773i	$-0.686176\pi$
$359$	8.45078	−	14.6372i	0.446015	−	0.772521i	0.998122	+	0.0612521i	$0.0195094\pi$
$360$	−1.35733	−	2.35097i	−0.0715378	−	0.123907i
$361$	−8.45796	−	14.6496i	−0.445156	−	0.771032i
$362$	10.6393	−	18.4279i	0.559190	−	0.968546i
$363$	−0.534166			−0.0280364
$364$	−1.72341	+	4.75302i	−0.0903311	+	0.249126i
$365$	1.58675			0.0830540
$366$	0.706791	−	1.22420i	0.0369446	−	0.0639898i
$367$	2.88582	+	4.99838i	0.150638	+	0.260913i	0.931462	−	0.363838i	$-0.118534\pi$
$367$	2.88582	+	4.99838i	0.150638	+	0.260913i	−0.780824	+	0.624751i	$0.785200\pi$
$368$	1.33791	+	2.31733i	0.0697435	+	0.120799i
$369$	7.79674	−	13.5043i	0.405882	−	0.703008i
$370$	−9.36974			−0.487110
$371$	−7.15492	+	19.7327i	−0.371465	+	1.02447i
$372$	−0.630583			−0.0326942
$373$	−14.4438	+	25.0173i	−0.747870	+	1.29535i	0.200972	+	0.979597i	$0.435590\pi$
$373$	−14.4438	+	25.0173i	−0.747870	+	1.29535i	−0.948842	+	0.315752i	$0.897743\pi$
$374$	−1.43604	−	2.48729i	−0.0742558	−	0.128615i
$375$	−0.267083	−	0.462601i	−0.0137921	−	0.0238886i
$376$	−1.40624	+	2.43569i	−0.0725215	+	0.125611i
$377$	−8.28940			−0.426926
$378$	−7.95195	+	1.41213i	−0.409004	+	0.0726320i
$379$	13.2766			0.681973			0.340986	−	0.940068i	$-0.389239\pi$
$379$	13.2766			0.681973			0.340986	+	0.940068i	$0.389239\pi$
$380$	−2.99649	+	5.19008i	−0.153717	+	0.266246i
$381$	−0.0939196	−	0.162673i	−0.00481164	−	0.00833401i
$382$	−11.5168	−	19.9476i	−0.589250	−	1.02061i
$383$	9.36740	−	16.2248i	0.478652	−	0.829049i	−0.521049	−	0.853527i	$-0.674459\pi$
$383$	9.36740	−	16.2248i	0.478652	−	0.829049i	0.999700	+	0.0244777i	$0.00779228\pi$
$384$	−0.534166			−0.0272590
$385$	1.70312	+	2.02469i	0.0867991	+	0.103188i
$386$	12.6092			0.641793
$387$	14.4907	−	25.0985i	0.736601	−	1.27583i
$388$	2.98495	+	5.17008i	0.151538	+	0.262471i
$389$	19.5496	+	33.8610i	0.991206	+	1.71682i	0.610204	+	0.792244i	$0.291088\pi$
$389$	19.5496	+	33.8610i	0.991206	+	1.71682i	0.381002	+	0.924574i	$0.375579\pi$
$390$	0.510374	−	0.883994i	0.0258438	−	0.0447628i
$391$	7.68518			0.388656
$392$	−1.19875	+	6.89659i	−0.0605461	+	0.348331i
$393$	1.67083			0.0842822
$394$	−7.63128	+	13.2178i	−0.384459	+	0.665902i
$395$	5.50336	+	9.53210i	0.276904	+	0.479612i
$396$	−1.35733	−	2.35097i	−0.0682086	−	0.118141i
$397$	−14.3751	+	24.8984i	−0.721467	+	1.24962i	0.238945	+	0.971033i	$0.423198\pi$
$397$	−14.3751	+	24.8984i	−0.721467	+	1.24962i	−0.960412	+	0.278584i	$0.910135\pi$
$398$	7.65008			0.383464
$399$	5.45212	+	6.48154i	0.272947	+	0.324483i
$400$	1.00000			0.0500000
$401$	−9.22123	+	15.9716i	−0.460486	+	0.797586i	−0.998985	−	0.0450406i	$-0.985658\pi$
$401$	−9.22123	+	15.9716i	−0.460486	+	0.797586i	0.538499	+	0.842626i	$0.318992\pi$
$402$	2.15491	+	3.73242i	0.107477	+	0.186156i
$403$	1.12792	+	1.95362i	0.0561858	+	0.0973166i
$404$	2.70999	−	4.69384i	0.134827	−	0.233527i
$405$	−6.51342			−0.323654
$406$	−11.3002	+	2.00672i	−0.560822	+	0.0995920i
$407$	−9.36974			−0.464441
$408$	−0.767083	+	1.32863i	−0.0379763	+	0.0657768i
$409$	17.5251	+	30.3544i	0.866562	+	1.50093i	0.865487	+	0.500931i	$0.167009\pi$
$409$	17.5251	+	30.3544i	0.866562	+	1.50093i	0.00107496	+	0.999999i	$0.499658\pi$
$410$	2.87208	+	4.97459i	0.141842	+	0.245677i
$411$	−1.98729	+	3.44209i	−0.0980259	+	0.169786i
$412$	−5.56600			−0.274217
$413$	6.06366	−	16.7231i	0.298373	−	0.822889i
$414$	7.26397			0.357005
$415$	−0.842589	+	1.45941i	−0.0413611	+	0.0716395i
$416$	0.955460	+	1.65491i	0.0468453	+	0.0811384i
$417$	−4.23862	−	7.34151i	−0.207566	−	0.359515i
$418$	−2.99649	+	5.19008i	−0.146563	+	0.253855i
$419$	−35.0053			−1.71012			−0.855061	−	0.518527i	$-0.826480\pi$
$419$	−35.0053			−1.71012			−0.855061	+	0.518527i	$0.826480\pi$
$420$	0.481750	−	1.32863i	0.0235070	−	0.0648303i
$421$	−27.7401			−1.35197			−0.675986	−	0.736915i	$-0.736282\pi$
$421$	−27.7401			−1.35197			−0.675986	+	0.736915i	$0.736282\pi$
$422$	5.92816	−	10.2679i	0.288578	−	0.499833i
$423$	3.81748	+	6.61208i	0.185612	+	0.321490i
$424$	3.96670	+	6.87052i	0.192640	+	0.333662i
$425$	1.43604	−	2.48729i	0.0696581	−	0.120651i
$426$	−1.26491			−0.0612852
$427$	−6.89369	+	1.22420i	−0.333609	+	0.0592431i
$428$	0.255844			0.0123667
$429$	0.510374	−	0.883994i	0.0246411	−	0.0426796i
$430$	5.33791	+	9.24554i	0.257417	+	0.445859i
$431$	6.29337	+	10.9004i	0.303141	+	0.525056i	0.976846	−	0.213945i	$-0.0686313\pi$
$431$	6.29337	+	10.9004i	0.303141	+	0.525056i	−0.673705	+	0.739001i	$0.735298\pi$
$432$	−1.52629	+	2.64361i	−0.0734336	+	0.127191i
$433$	−17.5660			−0.844168			−0.422084	−	0.906557i	$-0.638701\pi$
$433$	−17.5660			−0.844168			−0.422084	+	0.906557i	$0.638701\pi$
$434$	2.01054	+	2.39015i	0.0965089	+	0.114731i
$435$	2.31716			0.111100
$436$	−5.17013	+	8.95492i	−0.247604	+	0.428863i
$437$	−8.01809	−	13.8877i	−0.383557	−	0.664341i
$438$	−0.423792	−	0.734030i	−0.0202496	−	0.0350733i
$439$	−13.8801	+	24.0411i	−0.662462	+	1.14742i	0.317505	+	0.948257i	$0.397155\pi$
$439$	−13.8801	+	24.0411i	−0.662462	+	1.14742i	−0.979967	+	0.199161i	$0.936178\pi$
$440$	1.00000			0.0476731
$441$	14.5866	+	12.1792i	0.694599	+	0.579962i
$442$	5.48831			0.261052
$443$	10.1052	−	17.5026i	0.480111	−	0.831576i	−0.519629	−	0.854392i	$-0.673930\pi$
$443$	10.1052	−	17.5026i	0.480111	−	0.831576i	0.999740	+	0.0228160i	$0.00726320\pi$
$444$	2.50250	+	4.33445i	0.118763	+	0.205704i
$445$	3.40304	+	5.89425i	0.161320	+	0.279414i
$446$	5.84259	−	10.1197i	0.276655	−	0.479180i
$447$	12.1747			0.575845
$448$	1.70312	+	2.02469i	0.0804649	+	0.0956577i
$449$	7.11655			0.335851			0.167925	−	0.985800i	$-0.446293\pi$
$449$	7.11655			0.335851			0.167925	+	0.985800i	$0.446293\pi$
$450$	1.35733	−	2.35097i	0.0639853	−	0.110826i
$451$	2.87208	+	4.97459i	0.135241	+	0.234244i
$452$	−6.16545	−	10.6789i	−0.289998	−	0.502292i
$453$	3.40929	−	5.90506i	0.160182	−	0.277444i
$454$	19.8218			0.930285
$455$	−4.97794	+	0.883994i	−0.233369	+	0.0414423i
$456$	3.20125			0.149912
$457$	−0.626751	+	1.08556i	−0.0293182	+	0.0507806i	−0.880312	−	0.474395i	$-0.842667\pi$
$457$	−0.626751	+	1.08556i	−0.0293182	+	0.0507806i	0.850994	+	0.525175i	$0.176000\pi$
$458$	−10.8858	−	18.8548i	−0.508661	−	0.881026i
$459$	4.38362	+	7.59266i	0.204610	+	0.354395i
$460$	−1.33791	+	2.31733i	−0.0623805	+	0.108046i
$461$	7.81983			0.364206			0.182103	−	0.983279i	$-0.441710\pi$
$461$	7.81983			0.364206			0.182103	+	0.983279i	$0.441710\pi$
$462$	0.481750	−	1.32863i	0.0224130	−	0.0618133i
$463$	2.39251			0.111189			0.0555946	−	0.998453i	$-0.482295\pi$
$463$	2.39251			0.111189			0.0555946	+	0.998453i	$0.482295\pi$
$464$	−2.16896	+	3.75674i	−0.100691	+	0.174402i
$465$	−0.315292	−	0.546101i	−0.0146213	−	0.0253248i
$466$	−9.98979	−	17.3028i	−0.462768	−	0.801538i
$467$	−20.8741	+	36.1550i	−0.965939	+	1.67306i	−0.258867	+	0.965913i	$0.583349\pi$
$467$	−20.8741	+	36.1550i	−0.965939	+	1.67306i	−0.707071	+	0.707142i	$0.749984\pi$
$468$	5.18751			0.239793
$469$	7.27661	−	20.0683i	0.336003	−	0.926668i
$470$	−2.81249			−0.129730
$471$	5.84212	−	10.1188i	0.269191	−	0.466252i
$472$	−3.36170	−	5.82264i	−0.154735	−	0.268009i
$473$	5.33791	+	9.24554i	0.245437	+	0.425110i
$474$	2.93971	−	5.09172i	0.135025	−	0.233871i
$475$	−5.99299			−0.274977
$476$	7.48175	−	1.32863i	0.342925	−	0.0608975i
$477$	21.5365			0.986090
$478$	−3.32987	+	5.76751i	−0.152305	+	0.263800i
$479$	7.85063	+	13.5977i	0.358704	+	0.621294i	0.987745	−	0.156079i	$-0.0498853\pi$
$479$	7.85063	+	13.5977i	0.358704	+	0.621294i	−0.629040	+	0.777373i	$0.716552\pi$
$480$	−0.267083	−	0.462601i	−0.0121906	−	0.0211148i
$481$	8.95242	−	15.5060i	0.408195	−	0.707015i
$482$	0.314822			0.0143398
$483$	2.43433	+	2.89396i	0.110766	+	0.131680i
$484$	1.00000			0.0454545
$485$	−2.98495	+	5.17008i	−0.135540	+	0.234761i
$486$	6.31849	+	10.9439i	0.286613	+	0.496428i
$487$	5.35601	+	9.27688i	0.242704	+	0.420375i	0.961484	−	0.274863i	$-0.0886324\pi$
$487$	5.35601	+	9.27688i	0.242704	+	0.420375i	−0.718780	+	0.695238i	$0.755299\pi$
$488$	−1.32317	+	2.29179i	−0.0598970	+	0.103745i
$489$	4.28533			0.193789
$490$	−6.57200	+	2.41015i	−0.296893	+	0.108879i
$491$	18.0560			0.814858			0.407429	−	0.913237i	$-0.366425\pi$
$491$	18.0560			0.814858			0.407429	+	0.913237i	$0.366425\pi$
$492$	1.53417	−	2.65725i	0.0691655	−	0.119798i
$493$	6.22941	+	10.7897i	0.280559	+	0.485942i
$494$	−5.72606	−	9.91783i	−0.257628	−	0.446224i
$495$	1.35733	−	2.35097i	0.0610076	−	0.105668i
$496$	1.18050			0.0530061
$497$	4.03302	+	4.79450i	0.180905	+	0.215063i
$498$	0.900164			0.0403373
$499$	−15.1527	+	26.2453i	−0.678330	+	1.17490i	0.297154	+	0.954830i	$0.403963\pi$
$499$	−15.1527	+	26.2453i	−0.678330	+	1.17490i	−0.975484	+	0.220072i	$0.929371\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−2.41225	−	4.17814i	−0.107771	−	0.186665i
$502$	−4.49767	+	7.79018i	−0.200741	+	0.347693i
$503$	−14.0783			−0.627721			−0.313861	−	0.949469i	$-0.601622\pi$
$503$	−14.0783			−0.627721			−0.313861	+	0.949469i	$0.601622\pi$
$504$	7.07169	−	1.25581i	0.314998	−	0.0559381i
$505$	5.41998			0.241186
$506$	−1.33791	+	2.31733i	−0.0594775	+	0.103018i
$507$	−2.49679	−	4.32457i	−0.110886	−	0.192061i
$508$	0.175825	+	0.304537i	0.00780096	+	0.0135117i
$509$	13.7736	−	23.8567i	0.610506	−	1.05743i	−0.380649	−	0.924720i	$-0.624299\pi$
$509$	13.7736	−	23.8567i	0.610506	−	1.05743i	0.991155	−	0.132708i	$-0.0423673\pi$
$510$	−1.53417			−0.0679340
$511$	−1.43104	+	3.94670i	−0.0633056	+	0.174592i
$512$	1.00000			0.0441942
$513$	9.14704	−	15.8431i	0.403852	−	0.699491i
$514$	−10.4438	−	18.0891i	−0.460655	−	0.797878i
$515$	−2.78300	−	4.82029i	−0.122634	−	0.212408i
$516$	2.85133	−	4.93865i	0.125523	−	0.217412i
$517$	−2.81249			−0.123693
$518$	8.45032	−	23.3053i	0.371286	−	1.02398i
$519$	6.30408			0.276718
$520$	−0.955460	+	1.65491i	−0.0418997	+	0.0725724i
$521$	−1.93004	−	3.34292i	−0.0845564	−	0.146456i	0.820646	−	0.571437i	$-0.193614\pi$
$521$	−1.93004	−	3.34292i	−0.0845564	−	0.146456i	−0.905202	+	0.424981i	$0.860281\pi$
$522$	5.88799	+	10.1983i	0.257710	+	0.446368i
$523$	3.72168	−	6.44614i	0.162738	−	0.281870i	−0.773112	−	0.634270i	$-0.781301\pi$
$523$	3.72168	−	6.44614i	0.162738	−	0.281870i	0.935850	+	0.352400i	$0.114634\pi$
$524$	−3.12792			−0.136644
$525$	1.39150	−	0.247106i	0.0607300	−	0.0107846i
$526$	−21.7666			−0.949070
$527$	1.69525	−	2.93625i	0.0738461	−	0.127905i
$528$	−0.267083	−	0.462601i	−0.0116233	−	0.0201321i
$529$	7.91998	+	13.7178i	0.344347	+	0.596426i
$530$	−3.96670	+	6.87052i	−0.172302	+	0.298437i
$531$	−18.2518			−0.792061
$532$	−10.2068	−	12.1340i	−0.442521	−	0.526074i
$533$	−10.9766			−0.475450
$534$	1.81779	−	3.14850i	0.0786635	−	0.136249i
$535$	0.127922	+	0.221567i	0.00553055	+	0.00957919i
$536$	−4.03417	−	6.98738i	−0.174249	−	0.301809i
$537$	−0.816455	+	1.41414i	−0.0352326	+	0.0610247i
$538$	16.6805			0.719148
$539$	−6.57200	+	2.41015i	−0.283076	+	0.103812i
$540$	−3.05258			−0.131362
$541$	7.58924	−	13.1450i	0.326287	−	0.565146i	−0.655485	−	0.755208i	$-0.727536\pi$
$541$	7.58924	−	13.1450i	0.326287	−	0.565146i	0.981772	+	0.190062i	$0.0608691\pi$
$542$	0.0763710	+	0.132278i	0.00328041	+	0.00568184i
$543$	−5.68316	−	9.84353i	−0.243888	−	0.422426i
$544$	1.43604	−	2.48729i	0.0615697	−	0.106642i
$545$	−10.3403			−0.442928
$546$	1.73846	+	2.06670i	0.0743992	+	0.0884466i
$547$	32.7757			1.40139			0.700693	−	0.713463i	$-0.252874\pi$
$547$	32.7757			1.40139			0.700693	+	0.713463i	$0.252874\pi$
$548$	3.72036	−	6.44386i	0.158926	−	0.275268i
$549$	3.59196	+	6.22146i	0.153301	+	0.265525i
$550$	0.500000	+	0.866025i	0.0213201	+	0.0369274i
$551$	12.9985	−	22.5141i	0.553756	−	0.959134i
$552$	1.42933			0.0608365
$553$	−28.6725	+	5.09172i	−1.21928	+	0.216522i
$554$	−12.9892			−0.551860
$555$	−2.50250	+	4.33445i	−0.106225	+	0.183987i
$556$	7.93503	+	13.7439i	0.336520	+	0.582870i
$557$	16.4612	+	28.5116i	0.697482	+	1.20807i	0.969337	+	0.245736i	$0.0790296\pi$
$557$	16.4612	+	28.5116i	0.697482	+	1.20807i	−0.271855	+	0.962338i	$0.587637\pi$
$558$	1.60233	−	2.77532i	0.0678322	−	0.117489i
$559$	−20.4007			−0.862856
$560$	−0.901873	+	2.48729i	−0.0381111	+	0.105107i
$561$	−1.53417			−0.0647725
$562$	1.59376	−	2.76047i	0.0672285	−	0.116443i
$563$	−20.8788	−	36.1631i	−0.879937	−	1.52410i	−0.851409	−	0.524502i	$-0.824252\pi$
$563$	−20.8788	−	36.1631i	−0.879937	−	1.52410i	−0.0285275	−	0.999593i	$-0.509082\pi$
$564$	0.751167	+	1.30106i	0.0316298	+	0.0547845i
$565$	6.16545	−	10.6789i	0.259382	−	0.449264i
$566$	24.7208			1.03909
$567$	5.87428	−	16.2008i	0.246696	−	0.680369i
$568$	2.36801			0.0993596
$569$	0.104832	−	0.181574i	0.00439478	−	0.00761198i	−0.863820	−	0.503801i	$-0.831934\pi$
$569$	0.104832	−	0.181574i	0.00439478	−	0.00761198i	0.868214	+	0.496189i	$0.165268\pi$
$570$	1.60062	+	2.77236i	0.0670428	+	0.116122i
$571$	−18.1507	−	31.4379i	−0.759583	−	1.31564i	−0.943063	−	0.332614i	$-0.892070\pi$
$571$	−18.1507	−	31.4379i	−0.759583	−	1.31564i	0.183480	−	0.983023i	$-0.441264\pi$
$572$	−0.955460	+	1.65491i	−0.0399498	+	0.0691951i
$573$	−12.3037			−0.513996
$574$	−14.9635	+	2.65725i	−0.624564	+	0.110912i
$575$	−2.67582			−0.111590
$576$	1.35733	−	2.35097i	0.0565556	−	0.0979571i
$577$	−5.21569	−	9.03384i	−0.217132	−	0.376084i	0.736798	−	0.676113i	$-0.236337\pi$
$577$	−5.21569	−	9.03384i	−0.217132	−	0.376084i	−0.953930	+	0.300029i	$0.903004\pi$
$578$	4.37558	+	7.57873i	0.182000	+	0.315234i
$579$	3.36771	−	5.83304i	0.139957	−	0.242413i
$580$	−4.33791			−0.180122
$581$	−2.87006	−	3.41196i	−0.119070	−	0.141552i
$582$	3.18892			0.132185
$583$	−3.96670	+	6.87052i	−0.164284	+	0.284548i
$584$	0.793373	+	1.37416i	0.0328300	+	0.0568632i
$585$	2.59376	+	4.49252i	0.107239	+	0.185743i
$586$	6.49532	−	11.2502i	0.268319	−	0.464743i
$587$	29.6691			1.22458			0.612288	−	0.790635i	$-0.290249\pi$
$587$	29.6691			1.22458			0.612288	+	0.790635i	$0.290249\pi$
$588$	2.87021	+	2.39651i	0.118365	+	0.0988302i
$589$	−7.07473			−0.291509
$590$	3.36170	−	5.82264i	0.138399	−	0.239714i
$591$	4.07637	+	7.06048i	0.167679	+	0.290429i
$592$	−4.68487	−	8.11444i	−0.192547	−	0.333501i
$593$	0.0683315	−	0.118354i	0.00280604	−	0.00486020i	−0.864619	−	0.502428i	$-0.832440\pi$
$593$	0.0683315	−	0.118354i	0.00280604	−	0.00486020i	0.867425	+	0.497568i	$0.165773\pi$
$594$	−3.05258			−0.125249
$595$	4.89150	+	5.81507i	0.200532	+	0.238395i
$596$	−22.7921			−0.933599
$597$	2.04321	−	3.53894i	0.0836228	−	0.144839i
$598$	−2.55664	−	4.42824i	−0.104549	−	0.181084i
$599$	−5.77395	−	10.0008i	−0.235917	−	0.408621i	0.723622	−	0.690197i	$-0.242476\pi$
$599$	−5.77395	−	10.0008i	−0.235917	−	0.408621i	−0.959539	+	0.281576i	$0.909143\pi$
$600$	0.267083	−	0.462601i	0.0109036	−	0.0188856i
$601$	33.1233			1.35113			0.675563	−	0.737302i	$-0.263900\pi$
$601$	33.1233			1.35113			0.675563	+	0.737302i	$0.263900\pi$
$602$	−27.8105	+	4.93865i	−1.13347	+	0.201284i
$603$	−21.9028			−0.891952
$604$	−6.38245	+	11.0547i	−0.259698	+	0.449811i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	−1.44758	−	2.50729i	−0.0588041	−	0.101852i
$607$	−15.9828	+	27.6830i	−0.648721	+	1.12362i	0.334708	+	0.942322i	$0.391362\pi$
$607$	−15.9828	+	27.6830i	−0.648721	+	1.12362i	−0.983429	+	0.181296i	$0.941971\pi$
$608$	−5.99299			−0.243048
$609$	−2.08979	+	5.76347i	−0.0846825	+	0.233547i
$610$	−2.64634			−0.107147
$611$	2.68722	−	4.65440i	0.108713	−	0.188297i
$612$	−3.89837	−	6.75217i	−0.157582	−	0.272940i
$613$	−9.41998	−	16.3159i	−0.380469	−	0.658992i	0.610660	−	0.791893i	$-0.290904\pi$
$613$	−9.41998	−	16.3159i	−0.380469	−	0.658992i	−0.991129	+	0.132901i	$0.957571\pi$
$614$	2.69158	−	4.66195i	0.108623	−	0.188141i
$615$	3.06833			0.123727
$616$	−0.901873	+	2.48729i	−0.0363375	+	0.100216i
$617$	−4.71872			−0.189969			−0.0949843	−	0.995479i	$-0.530280\pi$
$617$	−4.71872			−0.189969			−0.0949843	+	0.995479i	$0.530280\pi$
$618$	−1.48658	+	2.57484i	−0.0597991	+	0.103575i
$619$	−15.4431	−	26.7482i	−0.620709	−	1.07510i	−0.989354	−	0.145530i	$-0.953511\pi$
$619$	−15.4431	−	26.7482i	−0.620709	−	1.07510i	0.368644	−	0.929570i	$-0.379822\pi$
$620$	0.590251	+	1.02234i	0.0237050	+	0.0410583i
$621$	4.08408	−	7.07384i	0.163889	−	0.283863i
$622$	30.8581			1.23730
$623$	−17.7298	+	3.14850i	−0.710331	+	0.126142i
$624$	1.02075			0.0408626
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−6.12661	−	10.6116i	−0.244869	−	0.424125i
$627$	1.60062	+	2.77236i	0.0639228	+	0.110718i
$628$	−10.9369	+	18.9433i	−0.436430	+	0.755919i
$629$	−26.9106			−1.07300
$630$	4.62341	+	5.49636i	0.184201	+	0.218980i
$631$	32.3639			1.28838			0.644192	−	0.764864i	$-0.277194\pi$
$631$	32.3639			1.28838			0.644192	+	0.764864i	$0.277194\pi$
$632$	−5.50336	+	9.53210i	−0.218912	+	0.379167i
$633$	−3.16662	−	5.48475i	−0.125862	−	0.217999i
$634$	−10.4322	−	18.0691i	−0.414317	−	0.717618i
$635$	−0.175825	+	0.304537i	−0.00697739	+	0.0120852i
$636$	4.23775			0.168038
$637$	2.29072	−	13.1788i	0.0907616	−	0.522165i
$638$	−4.33791			−0.171740
$639$	3.21418	−	5.56713i	0.127151	−	0.220232i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−6.73964	−	11.6734i	−0.266200	−	0.461072i	0.701677	−	0.712495i	$-0.252435\pi$
$641$	−6.73964	−	11.6734i	−0.266200	−	0.461072i	−0.967877	+	0.251423i	$0.919101\pi$
$642$	0.0683315	−	0.118354i	0.00269683	−	0.00467104i
$643$	−6.26023			−0.246879			−0.123440	−	0.992352i	$-0.539393\pi$
$643$	−6.26023			−0.246879			−0.123440	+	0.992352i	$0.539393\pi$
$644$	−4.55726	−	5.41772i	−0.179581	−	0.213488i
$645$	5.70266			0.224542
$646$	−8.60617	+	14.9063i	−0.338605	+	0.586481i
$647$	−6.84259	−	11.8517i	−0.269010	−	0.465939i	0.699596	−	0.714538i	$-0.253363\pi$
$647$	−6.84259	−	11.8517i	−0.269010	−	0.465939i	−0.968606	+	0.248599i	$0.920030\pi$
$648$	−3.25671	−	5.64079i	−0.127936	−	0.221591i
$649$	3.36170	−	5.82264i	0.131958	−	0.228559i
$650$	−1.91092			−0.0749525
$651$	1.64267	−	0.291709i	0.0643812	−	0.0114330i
$652$	−8.02248			−0.314184
$653$	5.43838	−	9.41955i	0.212820	−	0.368616i	−0.739776	−	0.672853i	$-0.765068\pi$
$653$	5.43838	−	9.41955i	0.212820	−	0.368616i	0.952596	+	0.304238i	$0.0984018\pi$
$654$	2.76170	+	4.78341i	0.107991	+	0.187046i
$655$	−1.56396	−	2.70886i	−0.0611090	−	0.105844i
$656$	−2.87208	+	4.97459i	−0.112136	+	0.194225i
$657$	4.30748			0.168051
$658$	2.53651	−	6.99548i	0.0988834	−	0.272712i
$659$	24.1233			0.939709			0.469854	−	0.882744i	$-0.344306\pi$
$659$	24.1233			0.939709			0.469854	+	0.882744i	$0.344306\pi$
$660$	0.267083	−	0.462601i	0.0103962	−	0.0180067i
$661$	0.758178	+	1.31320i	0.0294897	+	0.0510777i	0.880394	−	0.474244i	$-0.157278\pi$
$661$	0.758178	+	1.31320i	0.0294897	+	0.0510777i	−0.850904	+	0.525321i	$0.823945\pi$
$662$	11.0010	+	19.0543i	0.427567	+	0.740568i
$663$	1.46583	−	2.53890i	0.0569283	−	0.0986027i
$664$	−1.68518			−0.0653976
$665$	5.40492	−	14.9063i	0.209594	−	0.578042i
$666$	−25.4357			−0.985615
$667$	5.80375	−	10.0524i	0.224722	−	0.389230i
$668$	4.51592	+	7.82180i	0.174726	+	0.302634i
$669$	−3.12091	−	5.40558i	−0.120661	−	0.208992i
$670$	4.03417	−	6.98738i	0.155853	−	0.269946i
$671$	−2.64634			−0.102161
$672$	1.39150	−	0.247106i	0.0536782	−	0.00953231i
$673$	−47.9854			−1.84970			−0.924850	−	0.380332i	$-0.875810\pi$
$673$	−47.9854			−1.84970			−0.924850	+	0.380332i	$0.875810\pi$
$674$	−3.34696	+	5.79710i	−0.128920	+	0.223296i
$675$	−1.52629	−	2.64361i	−0.0587469	−	0.101753i
$676$	4.67419	+	8.09594i	0.179777	+	0.311382i
$677$	−2.96817	+	5.14102i	−0.114076	+	0.197585i	−0.917410	−	0.397943i	$-0.869724\pi$
$677$	−2.96817	+	5.14102i	−0.114076	+	0.197585i	0.803334	+	0.595529i	$0.203057\pi$
$678$	−6.58675			−0.252962
$679$	−10.1675	−	12.0872i	−0.390192	−	0.463864i
$680$	2.87208			0.110139
$681$	5.29407	−	9.16961i	0.202869	−	0.351380i
$682$	0.590251	+	1.02234i	0.0226019	+	0.0391476i
$683$	−24.3705	−	42.2109i	−0.932510	−	1.61515i	−0.779015	−	0.627005i	$-0.784280\pi$
$683$	−24.3705	−	42.2109i	−0.932510	−	1.61515i	−0.153495	−	0.988149i	$-0.549053\pi$
$684$	−8.13448	+	14.0893i	−0.311030	+	0.538719i
$685$	7.44073			0.284296
$686$	−0.0676299	−	18.5201i	−0.00258212	−	0.707102i
$687$	−11.6297			−0.443699
$688$	−5.33791	+	9.24554i	−0.203506	+	0.352483i
$689$	−7.58005	−	13.1290i	−0.288777	−	0.500176i
$690$	0.714667	+	1.23784i	0.0272069	+	0.0471237i
$691$	23.5992	−	40.8750i	0.897755	−	1.55496i	0.0673968	−	0.997726i	$-0.478531\pi$
$691$	23.5992	−	40.8750i	0.897755	−	1.55496i	0.830358	−	0.557230i	$-0.188136\pi$
$692$	−11.8017			−0.448635
$693$	4.62341	+	5.49636i	0.175629	+	0.208790i
$694$	−13.3832			−0.508018
$695$	−7.93503	+	13.7439i	−0.300993	+	0.521335i
$696$	1.15858	+	2.00672i	0.0439159	+	0.0760646i
$697$	8.24883	+	14.2874i	0.312447	+	0.541174i
$698$	−16.7951	+	29.0900i	−0.635704	+	1.10107i
$699$	−10.6724			−0.403667
$700$	−2.60500	+	0.462601i	−0.0984596	+	0.0174847i
$701$	−36.1293			−1.36459			−0.682293	−	0.731079i	$-0.739017\pi$
$701$	−36.1293			−1.36459			−0.682293	+	0.731079i	$0.739017\pi$
$702$	2.91662	−	5.05173i	0.110081	−	0.190665i
$703$	28.0764	+	48.6297i	1.05892	+	1.83410i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−0.751167	+	1.30106i	−0.0282906	+	0.0490008i
$706$	13.5660			0.510563
$707$	−4.88814	+	13.4811i	−0.183837	+	0.507008i
$708$	−3.59141			−0.134974
$709$	10.7874	−	18.6843i	0.405129	−	0.701703i	−0.589208	−	0.807982i	$-0.700560\pi$
$709$	10.7874	−	18.6843i	0.405129	−	0.701703i	0.994336	+	0.106278i	$0.0338934\pi$
$710$	1.18401	+	2.05076i	0.0444350	+	0.0769636i
$711$	14.9398	+	25.8765i	0.560286	+	0.970444i
$712$	−3.40304	+	5.89425i	−0.127534	+	0.220896i
$713$	−3.15881			−0.118299
$714$	1.38362	−	3.81592i	0.0517808	−	0.142807i
$715$	−1.91092			−0.0714644
$716$	1.52847	−	2.64738i	0.0571215	−	0.0989374i
$717$	1.77870	+	3.08081i	0.0664269	+	0.115055i
$718$	8.45078	+	14.6372i	0.315380	+	0.546255i
$719$	16.3160	−	28.2601i	0.608484	−	1.05393i	−0.383006	−	0.923746i	$-0.625111\pi$
$719$	16.3160	−	28.2601i	0.608484	−	1.05393i	0.991490	−	0.130180i	$-0.0415554\pi$
$720$	2.71467			0.101170
$721$	14.4994	−	2.57484i	0.539986	−	0.0958919i
$722$	16.9159			0.629545
$723$	0.0840836	−	0.145637i	0.00312710	−	0.00541630i
$724$	10.6393	+	18.4279i	0.395407	+	0.684866i
$725$	−2.16896	−	3.75674i	−0.0805530	−	0.139522i
$726$	0.267083	−	0.462601i	0.00991238	−	0.0171687i
$727$	−7.05085			−0.261502			−0.130751	−	0.991415i	$-0.541739\pi$
$727$	−7.05085			−0.261502			−0.130751	+	0.991415i	$0.541739\pi$
$728$	−3.25453	−	3.86902i	−0.120621	−	0.143396i
$729$	−12.7900			−0.473704
$730$	−0.793373	+	1.37416i	−0.0293640	+	0.0508600i
$731$	15.3309	+	26.5539i	0.567034	+	0.982131i
$732$	0.706791	+	1.22420i	0.0261237	+	0.0452476i
$733$	−13.6751	+	23.6860i	−0.505102	+	0.874863i	0.494880	+	0.868961i	$0.335212\pi$
$733$	−13.6751	+	23.6860i	−0.505102	+	0.874863i	−0.999983	+	0.00590157i	$0.998121\pi$
$734$	−5.77163			−0.213035
$735$	−0.640332	+	3.68392i	−0.0236190	+	0.135884i
$736$	−2.67582			−0.0986322
$737$	4.03417	−	6.98738i	0.148600	−	0.257383i
$738$	7.79674	+	13.5043i	0.287002	+	0.497102i
$739$	1.60413	+	2.77844i	0.0590089	+	0.102206i	0.894021	−	0.448026i	$-0.147873\pi$
$739$	1.60413	+	2.77844i	0.0590089	+	0.102206i	−0.835012	+	0.550232i	$0.814539\pi$
$740$	4.68487	−	8.11444i	0.172219	−	0.298293i
$741$	−6.11733			−0.224726
$742$	−13.5115	−	16.0627i	−0.496024	−	0.589680i
$743$	11.1384			0.408628			0.204314	−	0.978905i	$-0.434504\pi$
$743$	11.1384			0.408628			0.204314	+	0.978905i	$0.434504\pi$
$744$	0.315292	−	0.546101i	0.0115592	−	0.0200210i
$745$	−11.3960	−	19.7385i	−0.417518	−	0.723163i
$746$	−14.4438	−	25.0173i	−0.528824	−	0.915950i
$747$	−2.28735	+	3.96180i	−0.0836897	+	0.144955i
$748$	2.87208			0.105014
$749$	−0.666472	+	0.118354i	−0.0243523	+	0.00432455i
$750$	0.534166			0.0195050
$751$	9.28036	−	16.0741i	0.338645	−	0.586550i	−0.645533	−	0.763732i	$-0.723365\pi$
$751$	9.28036	−	16.0741i	0.338645	−	0.586550i	0.984178	+	0.177182i	$0.0566981\pi$
$752$	−1.40624	−	2.43569i	−0.0512804	−	0.0888203i
$753$	2.40250	+	4.16125i	0.0875519	+	0.151644i
$754$	4.14470	−	7.17884i	0.150941	−	0.261438i
$755$	−12.7649			−0.464562
$756$	2.75304	−	7.59266i	0.100127	−	0.276142i
$757$	−16.2451			−0.590438			−0.295219	−	0.955430i	$-0.595393\pi$
$757$	−16.2451			−0.590438			−0.295219	+	0.955430i	$0.595393\pi$
$758$	−6.63830	+	11.4979i	−0.241114	+	0.417621i
$759$	0.714667	+	1.23784i	0.0259408	+	0.0449307i
$760$	−2.99649	−	5.19008i	−0.108694	−	0.188264i
$761$	16.8218	−	29.1363i	0.609791	−	1.05619i	−0.381483	−	0.924376i	$-0.624587\pi$
$761$	16.8218	−	29.1363i	0.609791	−	1.05619i	0.991275	−	0.131814i	$-0.0420801\pi$
$762$	0.187839			0.00680469
$763$	9.32560	−	25.7192i	0.337609	−	0.931099i
$764$	23.0336			0.833325
$765$	3.89837	−	6.75217i	0.140946	−	0.244125i
$766$	9.36740	+	16.2248i	0.338458	+	0.586226i
$767$	6.42395	+	11.1266i	0.231955	+	0.401758i
$768$	0.267083	−	0.462601i	0.00963752	−	0.0166927i
$769$	24.6343			0.888337			0.444168	−	0.895943i	$-0.353499\pi$
$769$	24.6343			0.888337			0.444168	+	0.895943i	$0.353499\pi$
$770$	−2.60500	+	0.462601i	−0.0938775	+	0.0166710i
$771$	−11.1574			−0.401824
$772$	−6.30461	+	10.9199i	−0.226908	+	0.393016i
$773$	20.9723	+	36.3250i	0.754320	+	1.30652i	0.945712	+	0.325007i	$0.105367\pi$
$773$	20.9723	+	36.3250i	0.754320	+	1.30652i	−0.191392	+	0.981514i	$0.561300\pi$
$774$	14.4907	+	25.0985i	0.520856	+	0.902149i
$775$	−0.590251	+	1.02234i	−0.0212024	+	0.0367237i
$776$	−5.96990			−0.214307
$777$	−8.52412	−	10.1336i	−0.305801	−	0.363540i
$778$	−39.0993			−1.40178
$779$	17.2123	−	29.8126i	0.616696	−	1.06815i
$780$	0.510374	+	0.883994i	0.0182743	+	0.0316521i
$781$	1.18401	+	2.05076i	0.0423671	+	0.0733820i
$782$	−3.84259	+	6.65556i	−0.137411	+	0.238002i
$783$	13.2418			0.473224
$784$	−5.37325	−	4.48645i	−0.191902	−	0.160230i
$785$	−21.8738			−0.780710
$786$	−0.835414	+	1.44698i	−0.0297982	+	0.0516121i
$787$	−25.2579	−	43.7480i	−0.900347	−	1.55945i	−0.827044	−	0.562137i	$-0.809979\pi$
$787$	−25.2579	−	43.7480i	−0.900347	−	1.55945i	−0.0733027	−	0.997310i	$-0.523354\pi$
$788$	−7.63128	−	13.2178i	−0.271853	−	0.470864i
$789$	−5.81350	+	10.0693i	−0.206966	+	0.358475i
$790$	−11.0067			−0.391602
$791$	21.0010	+	24.9663i	0.746711	+	0.887698i
$792$	2.71467			0.0964615
$793$	2.52847	−	4.37944i	0.0897885	−	0.155518i
$794$	−14.3751	−	24.8984i	−0.510154	−	0.883613i
$795$	2.11887	+	3.67000i	0.0751487	+	0.130161i
$796$	−3.82504	+	6.62516i	−0.135575	+	0.234823i
$797$	35.0623			1.24197			0.620984	−	0.783823i	$-0.286733\pi$
$797$	35.0623			1.24197			0.620984	+	0.783823i	$0.286733\pi$
$798$	−8.33924	+	1.48090i	−0.295206	+	0.0524233i
$799$	−8.07768			−0.285768
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	9.23813	+	16.0009i	0.326413	+	0.565364i
$802$	−9.22123	−	15.9716i	−0.325613	−	0.563978i
$803$	−0.793373	+	1.37416i	−0.0279975	+	0.0484931i
$804$	−4.30983			−0.151996
$805$	2.41325	−	6.65556i	0.0850561	−	0.234578i
$806$	−2.25584			−0.0794587
$807$	4.45508	−	7.71642i	0.156826	−	0.271631i
$808$	2.70999	+	4.69384i	0.0953371	+	0.165129i
$809$	3.26458	+	5.65443i	0.114777	+	0.198799i	0.917690	−	0.397296i	$-0.130051\pi$
$809$	3.26458	+	5.65443i	0.114777	+	0.198799i	−0.802914	+	0.596095i	$0.796718\pi$
$810$	3.25671	−	5.64079i	0.114429	−	0.198197i
$811$	50.0216			1.75649			0.878247	−	0.478207i	$-0.158713\pi$
$811$	50.0216			1.75649			0.878247	+	0.478207i	$0.158713\pi$
$812$	3.91225	−	10.7897i	0.137293	−	0.378643i
$813$	0.0815895			0.00286147
$814$	4.68487	−	8.11444i	0.164205	−	0.284411i
$815$	−4.01124	−	6.94767i	−0.140508	−	0.243366i
$816$	−0.767083	−	1.32863i	−0.0268533	−	0.0465112i
$817$	31.9900	−	55.4084i	1.11919	−	1.93849i
$818$	−35.0503			−1.22550
$819$	−13.5134	+	2.39975i	−0.472198	+	0.0838540i
$820$	−5.74416			−0.200595
$821$	14.3744	−	24.8972i	0.501671	−	0.868919i	−0.498327	−	0.866989i	$-0.666052\pi$
$821$	14.3744	−	24.8972i	0.501671	−	0.868919i	0.999998	−	0.00193025i	$-0.000614419\pi$
$822$	−1.98729	−	3.44209i	−0.0693147	−	0.120057i
$823$	22.2191	+	38.4845i	0.774508	+	1.34149i	0.935071	+	0.354461i	$0.115336\pi$
$823$	22.2191	+	38.4845i	0.774508	+	1.34149i	−0.160563	+	0.987026i	$0.551331\pi$
$824$	2.78300	−	4.82029i	0.0969503	−	0.167923i
$825$	0.534166			0.0185973
$826$	11.4508	+	13.6128i	0.398424	+	0.473651i
$827$	−12.3657			−0.429997			−0.214999	−	0.976614i	$-0.568975\pi$
$827$	−12.3657			−0.429997			−0.214999	+	0.976614i	$0.568975\pi$
$828$	−3.63199	+	6.29079i	−0.126220	+	0.218620i
$829$	9.25523	+	16.0305i	0.321447	+	0.556763i	0.980787	−	0.195082i	$-0.0624973\pi$
$829$	9.25523	+	16.0305i	0.321447	+	0.556763i	−0.659339	+	0.751845i	$0.729164\pi$
$830$	−0.842589	−	1.45941i	−0.0292467	−	0.0506567i
$831$	−3.46920	+	6.00884i	−0.120345	+	0.208444i
$832$	−1.91092			−0.0662492
$833$	−18.8753	+	6.92213i	−0.653990	+	0.239838i
$834$	8.47724			0.293543
$835$	−4.51592	+	7.82180i	−0.156280	+	0.270684i
$836$	−2.99649	−	5.19008i	−0.103636	−	0.179503i
$837$	−1.80179	−	3.12079i	−0.0622789	−	0.107870i
$838$	17.5027	−	30.3155i	0.604619	−	1.04723i
$839$	−2.54992			−0.0880329			−0.0440165	−	0.999031i	$-0.514015\pi$
$839$	−2.54992			−0.0880329			−0.0440165	+	0.999031i	$0.514015\pi$
$840$	0.909749	+	1.08152i	0.0313893	+	0.0373160i
$841$	−10.1825			−0.351121
$842$	13.8701	−	24.0237i	0.477994	−	0.827910i
$843$	−0.851330	−	1.47455i	−0.0293214	−	0.0507861i
$844$	5.92816	+	10.2679i	0.204056	+	0.353435i
$845$	−4.67419	+	8.09594i	−0.160797	+	0.278509i
$846$	−7.63497			−0.262496
$847$	−2.60500	+	0.462601i	−0.0895087	+	0.0158952i
$848$	−7.93340			−0.272434
$849$	6.60250	−	11.4359i	0.226597	−	0.392478i
$850$	1.43604	+	2.48729i	0.0492557	+	0.0853134i
$851$	12.5359	+	21.7128i	0.429725	+	0.744305i
$852$	0.632456	−	1.09545i	0.0216676	−	0.0375293i
$853$	−1.22778			−0.0420386			−0.0210193	−	0.999779i	$-0.506691\pi$
$853$	−1.22778			−0.0420386			−0.0210193	+	0.999779i	$0.506691\pi$
$854$	2.38666	−	6.58221i	0.0816698	−	0.225239i
$855$	−16.2690			−0.556387
$856$	−0.127922	+	0.221567i	−0.00437228	+	0.00757301i
$857$	13.1995	+	22.8622i	0.450885	+	0.780956i	0.998441	−	0.0558127i	$-0.0177750\pi$
$857$	13.1995	+	22.8622i	0.450885	+	0.780956i	−0.547556	+	0.836769i	$0.684442\pi$
$858$	0.510374	+	0.883994i	0.0174239	+	0.0301791i
$859$	−20.8275	+	36.0744i	−0.710626	+	1.23084i	0.253996	+	0.967205i	$0.418255\pi$
$859$	−20.8275	+	36.0744i	−0.710626	+	1.23084i	−0.964622	+	0.263636i	$0.915078\pi$
$860$	−10.6758			−0.364043
$861$	−2.76725	+	7.63184i	−0.0943075	+	0.260092i
$862$	−12.5867			−0.428706
$863$	−23.7164	+	41.0780i	−0.807316	+	1.39831i	0.107401	+	0.994216i	$0.465747\pi$
$863$	−23.7164	+	41.0780i	−0.807316	+	1.39831i	−0.914717	+	0.404096i	$0.867586\pi$
$864$	−1.52629	−	2.64361i	−0.0519254	−	0.0899375i
$865$	−5.90087	−	10.2206i	−0.200635	−	0.347511i
$866$	8.78300	−	15.2126i	0.298458	−	0.516945i
$867$	4.67457			0.158757
$868$	−3.07520	+	0.546101i	−0.104379	+	0.0185359i
$869$	−11.0067			−0.373378
$870$	−1.15858	+	2.00672i	−0.0392796	+	0.0680343i
$871$	7.70897	+	13.3523i	0.261208	+	0.452426i
$872$	−5.17013	−	8.95492i	−0.175083	−	0.303252i
$873$	−8.10314	+	14.0351i	−0.274250	+	0.475015i
$874$	16.0362			0.542432
$875$	−1.70312	−	2.02469i	−0.0575760	−	0.0684471i
$876$	0.847585			0.0286372
$877$	−5.85264	+	10.1371i	−0.197630	+	0.342305i	−0.947759	−	0.318986i	$-0.896658\pi$
$877$	−5.85264	+	10.1371i	−0.197630	+	0.342305i	0.750130	+	0.661291i	$0.229991\pi$
$878$	−13.8801	−	24.0411i	−0.468431	−	0.811347i
$879$	−3.46958	−	6.00949i	−0.117026	−	0.202695i
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	−48.3269			−1.62817			−0.814087	−	0.580743i	$-0.802762\pi$
$881$	−48.3269			−1.62817			−0.814087	+	0.580743i	$0.802762\pi$
$882$	−17.8408	+	6.54275i	−0.600731	+	0.220306i
$883$	43.6440			1.46874			0.734369	−	0.678750i	$-0.237478\pi$
$883$	43.6440			1.46874			0.734369	+	0.678750i	$0.237478\pi$
$884$	−2.74416	+	4.75302i	−0.0922960	+	0.159861i
$885$	−1.79571	−	3.11026i	−0.0603620	−	0.104550i
$886$	10.1052	+	17.5026i	0.339489	+	0.588013i
$887$	−25.3477	+	43.9035i	−0.851092	+	1.47413i	0.0291320	+	0.999576i	$0.490726\pi$
$887$	−25.3477	+	43.9035i	−0.851092	+	1.47413i	−0.880224	+	0.474559i	$0.842608\pi$
$888$	−5.00500			−0.167957
$889$	−0.598902	−	0.711982i	−0.0200865	−	0.0238791i
$890$	−6.80609			−0.228141
$891$	3.25671	−	5.64079i	0.109104	−	0.188973i
$892$	5.84259	+	10.1197i	0.195624	+	0.338831i
$893$	8.42760	+	14.5970i	0.282019	+	0.488471i
$894$	−6.08737	+	10.5436i	−0.203592	+	0.352632i
$895$	3.05694			0.102182
$896$	−2.60500	+	0.462601i	−0.0870268	+	0.0154544i
$897$	−2.73134			−0.0911969
$898$	−3.55828	+	6.16312i	−0.118741	+	0.205666i
$899$	−2.56046	−	4.43484i	−0.0853960	−	0.147910i
$900$	1.35733	+	2.35097i	0.0452444	+	0.0783657i
$901$	−11.3927	+	19.7327i	−0.379545	+	0.657391i
$902$	−5.74416			−0.191259
$903$	−5.14308	+	14.1842i	−0.171151	+	0.472020i
$904$	12.3309			0.410120
$905$	−10.6393	+	18.4279i	−0.353663	+	0.612562i
$906$	3.40929	+	5.90506i	0.113266	+	0.196182i
$907$	−23.7775	−	41.1838i	−0.789518	−	1.36749i	−0.926262	−	0.376879i	$-0.876997\pi$
$907$	−23.7775	−	41.1838i	−0.789518	−	1.36749i	0.136744	−	0.990606i	$-0.456336\pi$
$908$	−9.91092	+	17.1662i	−0.328905	+	0.569681i
$909$	14.7134			0.488014
$910$	1.72341	−	4.75302i	0.0571304	−	0.157561i
$911$	−11.0134			−0.364891			−0.182446	−	0.983216i	$-0.558401\pi$
$911$	−11.0134			−0.364891			−0.182446	+	0.983216i	$0.558401\pi$
$912$	−1.60062	+	2.77236i	−0.0530020	+	0.0918021i
$913$	−0.842589	−	1.45941i	−0.0278856	−	0.0482993i
$914$	−0.626751	−	1.08556i	−0.0207311	−	0.0359073i
$915$	−0.706791	+	1.22420i	−0.0233658	+	0.0404707i
$916$	21.7716			0.719355
$917$	8.14822	−	1.44698i	0.269078	−	0.0477835i
$918$	−8.76725			−0.289362
$919$	−12.1323	+	21.0138i	−0.400208	+	0.693180i	−0.993751	−	0.111622i	$-0.964395\pi$
$919$	−12.1323	+	21.0138i	−0.400208	+	0.693180i	0.593543	+	0.804802i	$0.297729\pi$
$920$	−1.33791	−	2.31733i	−0.0441097	−	0.0764002i
$921$	−1.43775	−	2.49025i	−0.0473754	−	0.0820566i
$922$	−3.90991	+	6.77217i	−0.128766	+	0.223029i
$923$	−4.52509			−0.148945
$924$	0.909749	+	1.08152i	0.0299286	+	0.0355794i
$925$	9.36974			0.308075
$926$	−1.19625	+	2.07197i	−0.0393113	+	0.0680892i
$927$	−7.55491	−	13.0855i	−0.248136	−	0.429784i
$928$	−2.16896	−	3.75674i	−0.0711995	−	0.123321i
$929$	6.29627	−	10.9055i	0.206574	−	0.357796i	−0.744059	−	0.668114i	$-0.767102\pi$
$929$	6.29627	−	10.9055i	0.206574	−	0.357796i	0.950633	+	0.310317i	$0.100435\pi$
$930$	0.630583			0.0206776
$931$	32.2018	+	26.8872i	1.05537	+	0.881193i
$932$	19.9796			0.654453
$933$	8.24166	−	14.2750i	0.269820	−	0.467342i
$934$	−20.8741	−	36.1550i	−0.683022	−	1.18303i
$935$	1.43604	+	2.48729i	0.0469635	+	0.0813432i
$936$	−2.59376	+	4.49252i	−0.0847796	+	0.146843i
$937$	53.4053			1.74468			0.872338	−	0.488904i	$-0.162603\pi$
$937$	53.4053			1.74468			0.872338	+	0.488904i	$0.162603\pi$
$938$	13.7414	+	16.3359i	0.448671	+	0.533385i
$939$	−6.54525			−0.213596
$940$	1.40624	−	2.43569i	0.0458666	−	0.0794433i
$941$	6.97240	+	12.0765i	0.227294	+	0.393684i	0.957005	−	0.290071i	$-0.0936789\pi$
$941$	6.97240	+	12.0765i	0.227294	+	0.393684i	−0.729711	+	0.683755i	$0.760346\pi$
$942$	5.84212	+	10.1188i	0.190347	+	0.329690i
$943$	7.68518	−	13.3111i	0.250264	−	0.433470i
$944$	6.72341			0.218828
$945$	7.95195	−	1.41213i	0.258677	−	0.0459365i
$946$	−10.6758			−0.347101
$947$	3.57621	−	6.19417i	0.116211	−	0.201284i	−0.802052	−	0.597254i	$-0.796258\pi$
$947$	3.57621	−	6.19417i	0.116211	−	0.201284i	0.918263	+	0.395970i	$0.129592\pi$
$948$	2.93971	+	5.09172i	0.0954773	+	0.165371i
$949$	−1.51607	−	2.62591i	−0.0492138	−	0.0852408i
$950$	2.99649	−	5.19008i	0.0972191	−	0.168388i
$951$	−11.1451			−0.361404
$952$	−2.59025	+	7.14370i	−0.0839505	+	0.231529i
$953$	−58.2898			−1.88819			−0.944095	−	0.329673i	$-0.893062\pi$
$953$	−58.2898			−1.88819			−0.944095	+	0.329673i	$0.893062\pi$
$954$	−10.7683	+	18.6512i	−0.348636	+	0.603854i
$955$	11.5168	+	19.9476i	0.372674	+	0.645491i
$956$	−3.32987	−	5.76751i	−0.107696	−	0.186535i
$957$	−1.15858	+	2.00672i	−0.0374516	+	0.0648681i
$958$	−15.7013			−0.507285
$959$	−6.71060	+	18.5073i	−0.216696	+	0.597631i
$960$	0.534166			0.0172401
$961$	14.8032	−	25.6399i	0.477523	−	0.827094i
$962$	8.95242	+	15.5060i	0.288637	+	0.499935i
$963$	0.347265	+	0.601481i	0.0111905	+	0.0193825i
$964$	−0.157411	+	0.272644i	−0.00506987	+	0.00878128i
$965$	−12.6092			−0.405905
$966$	−3.72341	+	0.661211i	−0.119799	+	0.0212741i
$967$	9.53682			0.306683			0.153342	−	0.988173i	$-0.450996\pi$
$967$	9.53682			0.306683			0.153342	+	0.988173i	$0.450996\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$	4.59712	+	7.96244i	0.147681	+	0.255791i
$970$	−2.98495	−	5.17008i	−0.0958410	−	0.166001i
$971$	26.5144	−	45.9244i	0.850889	−	1.47378i	−0.0295179	−	0.999564i	$-0.509397\pi$
$971$	26.5144	−	45.9244i	0.850889	−	1.47378i	0.880407	−	0.474219i	$-0.157269\pi$
$972$	−12.6370			−0.405331
$973$	−27.0287	−	32.1320i	−0.866499	−	1.03010i
$974$	−10.7120			−0.343235
$975$	−0.510374	+	0.883994i	−0.0163451	+	0.0283105i
$976$	−1.32317	−	2.29179i	−0.0423536	−	0.0733585i
$977$	4.99299	+	8.64811i	0.159740	+	0.276678i	0.934775	−	0.355241i	$-0.115601\pi$
$977$	4.99299	+	8.64811i	0.159740	+	0.276678i	−0.775035	+	0.631918i	$0.782268\pi$
$978$	−2.14267	+	3.71121i	−0.0685149	+	0.118671i
$979$	−6.80609			−0.217524
$980$	1.19875	−	6.89659i	0.0382927	−	0.220304i
$981$	−28.0703			−0.896217
$982$	−9.02802	+	15.6370i	−0.288096	+	0.498996i
$983$	−8.14867	−	14.1139i	−0.259902	−	0.450164i	0.706313	−	0.707899i	$-0.250357\pi$
$983$	−8.14867	−	14.1139i	−0.259902	−	0.450164i	−0.966215	+	0.257736i	$0.917024\pi$
$984$	1.53417	+	2.65725i	0.0489074	+	0.0847101i
$985$	7.63128	−	13.2178i	0.243153	−	0.421153i
$986$	−12.4588			−0.396770
$987$	−2.55866	−	3.04176i	−0.0814430	−	0.0968204i
$988$	11.4521			0.364341
$989$	14.2833	−	24.7394i	0.454183	−	0.786668i
$990$	1.35733	+	2.35097i	0.0431389	+	0.0747187i
$991$	−13.9970	−	24.2435i	−0.444628	−	0.770119i	0.553398	−	0.832917i	$-0.313331\pi$
$991$	−13.9970	−	24.2435i	−0.444628	−	0.770119i	−0.998026	+	0.0627983i	$0.979998\pi$
$992$	−0.590251	+	1.02234i	−0.0187405	+	0.0324595i
$993$	11.7527			0.372962
$994$	−6.16866	+	1.09545i	−0.195658	+	0.0347454i
$995$	−7.65008			−0.242524
$996$	−0.450082	+	0.779565i	−0.0142614	+	0.0247015i
$997$	0.901567	+	1.56156i	0.0285529	+	0.0494551i	0.879949	−	0.475069i	$-0.157577\pi$
$997$	0.901567	+	1.56156i	0.0285529	+	0.0494551i	−0.851396	+	0.524524i	$0.824243\pi$
$998$	−15.1527	−	26.2453i	−0.479652	−	0.830781i
$999$	−14.3009	+	24.7700i	−0.452462	+	0.783687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.l.331.3	yes	8
7.2	even	3		5390.2.a.ce.1.2		4
7.4	even	3	inner	770.2.i.l.221.3	✓	8
7.5	odd	6		5390.2.a.cf.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.l.221.3	✓	8	7.4	even	3	inner
770.2.i.l.331.3	yes	8	1.1	even	1	trivial
5390.2.a.ce.1.2		4	7.2	even	3
5390.2.a.cf.1.3		4	7.5	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.267083 + 0.462601i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.534166 q^{6} +(1.70312 + 2.02469i) q^{7} +1.00000 q^{8} +(1.35733 - 2.35097i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.267083 + 0.462601i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.534166 q^{6} +(1.70312 + 2.02469i) q^{7} +1.00000 q^{8} +(1.35733 - 2.35097i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.267083 - 0.462601i) q^{12} -1.91092 q^{13} +(-2.60500 + 0.462601i) q^{14} +0.534166 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.43604 + 2.48729i) q^{17} +(1.35733 + 2.35097i) q^{18} +(2.99649 - 5.19008i) q^{19} -1.00000 q^{20} +(-0.481750 + 1.32863i) q^{21} -1.00000 q^{22} +(1.33791 - 2.31733i) q^{23} +(0.267083 + 0.462601i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.955460 - 1.65491i) q^{26} +3.05258 q^{27} +(0.901873 - 2.48729i) q^{28} +4.33791 q^{29} +(-0.267083 + 0.462601i) q^{30} +(-0.590251 - 1.02234i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.267083 + 0.462601i) q^{33} -2.87208 q^{34} +(2.60500 - 0.462601i) q^{35} -2.71467 q^{36} +(-4.68487 + 8.11444i) q^{37} +(2.99649 + 5.19008i) q^{38} +(-0.510374 - 0.883994i) q^{39} +(0.500000 - 0.866025i) q^{40} +5.74416 q^{41} +(-0.909749 - 1.08152i) q^{42} +10.6758 q^{43} +(0.500000 - 0.866025i) q^{44} +(-1.35733 - 2.35097i) q^{45} +(1.33791 + 2.31733i) q^{46} +(-1.40624 + 2.43569i) q^{47} -0.534166 q^{48} +(-1.19875 + 6.89659i) q^{49} +1.00000 q^{50} +(-0.767083 + 1.32863i) q^{51} +(0.955460 + 1.65491i) q^{52} +(3.96670 + 6.87052i) q^{53} +(-1.52629 + 2.64361i) q^{54} +1.00000 q^{55} +(1.70312 + 2.02469i) q^{56} +3.20125 q^{57} +(-2.16896 + 3.75674i) q^{58} +(-3.36170 - 5.82264i) q^{59} +(-0.267083 - 0.462601i) q^{60} +(-1.32317 + 2.29179i) q^{61} +1.18050 q^{62} +(7.07169 - 1.25581i) q^{63} +1.00000 q^{64} +(-0.955460 + 1.65491i) q^{65} +(-0.267083 - 0.462601i) q^{66} +(-4.03417 - 6.98738i) q^{67} +(1.43604 - 2.48729i) q^{68} +1.42933 q^{69} +(-0.901873 + 2.48729i) q^{70} +2.36801 q^{71} +(1.35733 - 2.35097i) q^{72} +(0.793373 + 1.37416i) q^{73} +(-4.68487 - 8.11444i) q^{74} +(0.267083 - 0.462601i) q^{75} -5.99299 q^{76} +(-0.901873 + 2.48729i) q^{77} +1.02075 q^{78} +(-5.50336 + 9.53210i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-3.25671 - 5.64079i) q^{81} +(-2.87208 + 4.97459i) q^{82} -1.68518 q^{83} +(1.39150 - 0.247106i) q^{84} +2.87208 q^{85} +(-5.33791 + 9.24554i) q^{86} +(1.15858 + 2.00672i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-3.40304 + 5.89425i) q^{89} +2.71467 q^{90} +(-3.25453 - 3.86902i) q^{91} -2.67582 q^{92} +(0.315292 - 0.546101i) q^{93} +(-1.40624 - 2.43569i) q^{94} +(-2.99649 - 5.19008i) q^{95} +(0.267083 - 0.462601i) q^{96} -5.96990 q^{97} +(-5.37325 - 4.48645i) q^{98} +2.71467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} + 8 q^{8} - 3 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 + 8 * q^8 - 3 * q^9	\( 8 q - 4 q^{2} + q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} + 8 q^{8} - 3 q^{9} + 4 q^{10} + 4 q^{11} + q^{12} - 2 q^{13} - 3 q^{14} + 2 q^{15} - 4 q^{16} + 2 q^{17} - 3 q^{18} - 10 q^{19} - 8 q^{20} + 25 q^{21} - 8 q^{22} - 6 q^{23} + q^{24} - 4 q^{25} + q^{26} - 20 q^{27} + 18 q^{29} - q^{30} + 8 q^{31} - 4 q^{32} - q^{33} - 4 q^{34} + 3 q^{35} + 6 q^{36} + 2 q^{37} - 10 q^{38} - 13 q^{39} + 4 q^{40} + 8 q^{41} - 20 q^{42} + 52 q^{43} + 4 q^{44} + 3 q^{45} - 6 q^{46} + 10 q^{47} - 2 q^{48} - 13 q^{49} + 8 q^{50} - 5 q^{51} + q^{52} - 14 q^{53} + 10 q^{54} + 8 q^{55} + 3 q^{56} + 18 q^{57} - 9 q^{58} + q^{59} - q^{60} + q^{61} - 16 q^{62} - 7 q^{63} + 8 q^{64} - q^{65} - q^{66} - 30 q^{67} + 2 q^{68} - 44 q^{69} + 36 q^{71} - 3 q^{72} - 17 q^{73} + 2 q^{74} + q^{75} + 20 q^{76} + 26 q^{78} + 15 q^{79} + 4 q^{80} - 16 q^{81} - 4 q^{82} + 4 q^{83} - 5 q^{84} + 4 q^{85} - 26 q^{86} - 8 q^{87} + 4 q^{88} + 6 q^{89} - 6 q^{90} + 3 q^{91} + 12 q^{92} - 29 q^{93} + 10 q^{94} + 10 q^{95} + q^{96} - 14 q^{97} + 2 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 + 8 * q^8 - 3 * q^9 + 4 * q^10 + 4 * q^11 + q^12 - 2 * q^13 - 3 * q^14 + 2 * q^15 - 4 * q^16 + 2 * q^17 - 3 * q^18 - 10 * q^19 - 8 * q^20 + 25 * q^21 - 8 * q^22 - 6 * q^23 + q^24 - 4 * q^25 + q^26 - 20 * q^27 + 18 * q^29 - q^30 + 8 * q^31 - 4 * q^32 - q^33 - 4 * q^34 + 3 * q^35 + 6 * q^36 + 2 * q^37 - 10 * q^38 - 13 * q^39 + 4 * q^40 + 8 * q^41 - 20 * q^42 + 52 * q^43 + 4 * q^44 + 3 * q^45 - 6 * q^46 + 10 * q^47 - 2 * q^48 - 13 * q^49 + 8 * q^50 - 5 * q^51 + q^52 - 14 * q^53 + 10 * q^54 + 8 * q^55 + 3 * q^56 + 18 * q^57 - 9 * q^58 + q^59 - q^60 + q^61 - 16 * q^62 - 7 * q^63 + 8 * q^64 - q^65 - q^66 - 30 * q^67 + 2 * q^68 - 44 * q^69 + 36 * q^71 - 3 * q^72 - 17 * q^73 + 2 * q^74 + q^75 + 20 * q^76 + 26 * q^78 + 15 * q^79 + 4 * q^80 - 16 * q^81 - 4 * q^82 + 4 * q^83 - 5 * q^84 + 4 * q^85 - 26 * q^86 - 8 * q^87 + 4 * q^88 + 6 * q^89 - 6 * q^90 + 3 * q^91 + 12 * q^92 - 29 * q^93 + 10 * q^94 + 10 * q^95 + q^96 - 14 * q^97 + 2 * q^98 - 6 * q^99

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