LMFDB - Embedded newform 770.2.i.l.331.1

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			331.1
Root			$-1.15777 - 2.00531i$ of defining polynomial
Character	$\chi$	$=$	770.331
Dual form			770.2.i.l.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.15777 - 2.00531i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.31553 q^{6} +(-0.873699 + 2.49733i) q^{7} +1.00000 q^{8} +(-1.18085 + 2.04528i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.15777 - 2.00531i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.31553 q^{6} +(-0.873699 + 2.49733i) q^{7} +1.00000 q^{8} +(-1.18085 + 2.04528i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.15777 + 2.00531i) q^{12} +6.56089 q^{13} +(-1.72590 - 2.00531i) q^{14} -2.31553 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.284067 + 0.492018i) q^{17} +(-1.18085 - 2.04528i) q^{18} +(-3.27048 + 5.66463i) q^{19} -1.00000 q^{20} +(6.01946 - 1.13928i) q^{21} -1.00000 q^{22} +(1.88367 - 3.26261i) q^{23} +(-1.15777 - 2.00531i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.28045 + 5.68190i) q^{26} -1.47802 q^{27} +(2.59960 - 0.492018i) q^{28} +4.88367 q^{29} +(1.15777 - 2.00531i) q^{30} +(0.523079 + 0.906000i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.15777 - 2.00531i) q^{33} -0.568134 q^{34} +(1.72590 + 2.00531i) q^{35} +2.36169 q^{36} +(4.39316 - 7.60917i) q^{37} +(-3.27048 - 5.66463i) q^{38} +(-7.59598 - 13.1566i) q^{39} +(0.500000 - 0.866025i) q^{40} +1.13627 q^{41} +(-2.02308 + 5.78265i) q^{42} +11.7673 q^{43} +(0.500000 - 0.866025i) q^{44} +(1.18085 + 2.04528i) q^{45} +(1.88367 + 3.26261i) q^{46} +(3.74740 - 6.49068i) q^{47} +2.31553 q^{48} +(-5.47330 - 4.36383i) q^{49} +1.00000 q^{50} +(0.657766 - 1.13928i) q^{51} +(-3.28045 - 5.68190i) q^{52} +(-6.30194 - 10.9153i) q^{53} +(0.739012 - 1.28001i) q^{54} +1.00000 q^{55} +(-0.873699 + 2.49733i) q^{56} +15.1458 q^{57} +(-2.44183 + 4.22938i) q^{58} +(6.02784 + 10.4405i) q^{59} +(1.15777 + 2.00531i) q^{60} +(-1.63469 + 2.83136i) q^{61} -1.04616 q^{62} +(-4.07604 - 4.73592i) q^{63} +1.00000 q^{64} +(3.28045 - 5.68190i) q^{65} +(1.15777 + 2.00531i) q^{66} +(-1.18447 - 2.05156i) q^{67} +(0.284067 - 0.492018i) q^{68} -8.72338 q^{69} +(-2.59960 + 0.492018i) q^{70} +10.4486 q^{71} +(-1.18085 + 2.04528i) q^{72} +(-2.89678 - 5.01737i) q^{73} +(4.39316 + 7.60917i) q^{74} +(-1.15777 + 2.00531i) q^{75} +6.54096 q^{76} +(-2.59960 + 0.492018i) q^{77} +15.1920 q^{78} +(-0.0550218 + 0.0953005i) q^{79} +(0.500000 + 0.866025i) q^{80} +(5.25374 + 9.09975i) q^{81} +(-0.568134 + 0.984037i) q^{82} +3.85965 q^{83} +(-3.99638 - 4.64336i) q^{84} +0.568134 q^{85} +(-5.88367 + 10.1908i) q^{86} +(-5.65414 - 9.79327i) q^{87} +(0.500000 + 0.866025i) q^{88} +(4.48437 - 7.76716i) q^{89} -2.36169 q^{90} +(-5.73225 + 16.3847i) q^{91} -3.76733 q^{92} +(1.21121 - 2.09787i) q^{93} +(3.74740 + 6.49068i) q^{94} +(3.27048 + 5.66463i) q^{95} +(-1.15777 + 2.00531i) q^{96} +1.56497 q^{97} +(6.51584 - 2.55810i) q^{98} -2.36169 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
$3$	−1.15777	−	2.00531i	−0.668437	−	1.15777i	−0.978341	−	0.206999i	$-0.933630\pi$
$3$	−1.15777	−	2.00531i	−0.668437	−	1.15777i	0.309905	−	0.950768i	$-0.399703\pi$
$4$	−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
$6$	2.31553			0.945312
$7$	−0.873699	+	2.49733i	−0.330227	+	0.943901i
$7$	−0.873699	+	2.49733i	−0.330227	+	0.943901i
$8$	1.00000			0.353553
$9$	−1.18085	+	2.04528i	−0.393615	+	0.681762i
$10$	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
$12$	−1.15777	+	2.00531i	−0.334218	+	0.578883i
$13$	6.56089			1.81966			0.909832	−	0.414977i	$-0.136210\pi$
$13$	6.56089			1.81966			0.909832	+	0.414977i	$0.136210\pi$
$14$	−1.72590	−	2.00531i	−0.461266	−	0.535942i
$15$	−2.31553			−0.597868
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.284067	+	0.492018i	0.0688964	+	0.119332i	0.898416	−	0.439146i	$-0.144719\pi$
$17$	0.284067	+	0.492018i	0.0688964	+	0.119332i	−0.829519	+	0.558478i	$0.811386\pi$
$18$	−1.18085	−	2.04528i	−0.278328	−	0.482078i
$19$	−3.27048	+	5.66463i	−0.750299	+	1.29956i	0.197379	+	0.980327i	$0.436757\pi$
$19$	−3.27048	+	5.66463i	−0.750299	+	1.29956i	−0.947678	+	0.319229i	$0.896576\pi$
$20$	−1.00000			−0.223607
$21$	6.01946	−	1.13928i	1.31355	−	0.248612i
$22$	−1.00000			−0.213201
$23$	1.88367	−	3.26261i	0.392772	−	0.680300i	−0.600042	−	0.799968i	$-0.704850\pi$
$23$	1.88367	−	3.26261i	0.392772	−	0.680300i	0.992814	+	0.119668i	$0.0381830\pi$
$24$	−1.15777	−	2.00531i	−0.236328	−	0.409332i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.28045	+	5.68190i	−0.643348	+	1.11431i
$27$	−1.47802			−0.284446
$28$	2.59960	−	0.492018i	0.491278	−	0.0929827i
$29$	4.88367			0.906874			0.453437	−	0.891288i	$-0.350198\pi$
$29$	4.88367			0.906874			0.453437	+	0.891288i	$0.350198\pi$
$30$	1.15777	−	2.00531i	0.211378	−	0.366118i
$31$	0.523079	+	0.906000i	0.0939478	+	0.162722i	0.909169	−	0.416427i	$-0.136718\pi$
$31$	0.523079	+	0.906000i	0.0939478	+	0.162722i	−0.815221	+	0.579150i	$0.803385\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.15777	−	2.00531i	0.201541	−	0.349080i
$34$	−0.568134			−0.0974342
$35$	1.72590	+	2.00531i	0.291730	+	0.338959i
$36$	2.36169			0.393615
$37$	4.39316	−	7.60917i	0.722231	−	1.25094i	−0.237873	−	0.971296i	$-0.576450\pi$
$37$	4.39316	−	7.60917i	0.722231	−	1.25094i	0.960104	−	0.279644i	$-0.0902164\pi$
$38$	−3.27048	−	5.66463i	−0.530542	−	0.918925i
$39$	−7.59598	−	13.1566i	−1.21633	−	2.10675i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	1.13627			0.177455			0.0887276	−	0.996056i	$-0.471720\pi$
$41$	1.13627			0.177455			0.0887276	+	0.996056i	$0.471720\pi$
$42$	−2.02308	+	5.78265i	−0.312168	+	0.892282i
$43$	11.7673			1.79450			0.897251	−	0.441521i	$-0.145561\pi$
$43$	11.7673			1.79450			0.897251	+	0.441521i	$0.145561\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	1.18085	+	2.04528i	0.176030	+	0.304893i
$46$	1.88367	+	3.26261i	0.277731	+	0.481045i
$47$	3.74740	−	6.49068i	0.546614	−	0.946764i	−0.451889	−	0.892074i	$-0.649250\pi$
$47$	3.74740	−	6.49068i	0.546614	−	0.946764i	0.998503	−	0.0546896i	$-0.0174169\pi$
$48$	2.31553			0.334218
$49$	−5.47330	−	4.36383i	−0.781900	−	0.623404i
$50$	1.00000			0.141421
$51$	0.657766	−	1.13928i	0.0921057	−	0.159532i
$52$	−3.28045	−	5.68190i	−0.454916	−	0.787937i
$53$	−6.30194	−	10.9153i	−0.865639	−	1.49933i	−0.866412	−	0.499330i	$-0.833579\pi$
$53$	−6.30194	−	10.9153i	−0.865639	−	1.49933i	0.000773220	−	1.00000i	$-0.499754\pi$
$54$	0.739012	−	1.28001i	0.100567	−	0.174187i
$55$	1.00000			0.134840
$56$	−0.873699	+	2.49733i	−0.116753	+	0.333720i
$57$	15.1458			2.00611
$58$	−2.44183	+	4.22938i	−0.320628	+	0.555345i
$59$	6.02784	+	10.4405i	0.784758	+	1.35924i	0.929143	+	0.369720i	$0.120546\pi$
$59$	6.02784	+	10.4405i	0.784758	+	1.35924i	−0.144385	+	0.989522i	$0.546120\pi$
$60$	1.15777	+	2.00531i	0.149467	+	0.258884i
$61$	−1.63469	+	2.83136i	−0.209300	+	0.362519i	−0.951494	−	0.307666i	$-0.900452\pi$
$61$	−1.63469	+	2.83136i	−0.209300	+	0.362519i	0.742194	+	0.670185i	$0.233785\pi$
$62$	−1.04616			−0.132862
$63$	−4.07604	−	4.73592i	−0.513533	−	0.596670i
$64$	1.00000			0.125000
$65$	3.28045	−	5.68190i	0.406889	−	0.704753i
$66$	1.15777	+	2.00531i	0.142511	+	0.246837i
$67$	−1.18447	−	2.05156i	−0.144706	−	0.250638i	0.784557	−	0.620056i	$-0.212890\pi$
$67$	−1.18447	−	2.05156i	−0.144706	−	0.250638i	−0.929263	+	0.369419i	$0.879557\pi$
$68$	0.284067	−	0.492018i	0.0344482	−	0.0596660i
$69$	−8.72338			−1.05017
$70$	−2.59960	+	0.492018i	−0.310712	+	0.0588074i
$71$	10.4486			1.24003			0.620013	−	0.784592i	$-0.287127\pi$
$71$	10.4486			1.24003			0.620013	+	0.784592i	$0.287127\pi$
$72$	−1.18085	+	2.04528i	−0.139164	+	0.241039i
$73$	−2.89678	−	5.01737i	−0.339042	−	0.587238i	0.645211	−	0.764005i	$-0.276770\pi$
$73$	−2.89678	−	5.01737i	−0.339042	−	0.587238i	−0.984253	+	0.176766i	$0.943436\pi$
$74$	4.39316	+	7.60917i	0.510694	+	0.884548i
$75$	−1.15777	+	2.00531i	−0.133687	+	0.231553i
$76$	6.54096			0.750299
$77$	−2.59960	+	0.492018i	−0.296252	+	0.0560707i
$78$	15.1920			1.72015
$79$	−0.0550218	+	0.0953005i	−0.00619043	+	0.0107221i	−0.869104	−	0.494629i	$-0.835304\pi$
$79$	−0.0550218	+	0.0953005i	−0.00619043	+	0.0107221i	0.862914	+	0.505351i	$0.168637\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	5.25374	+	9.09975i	0.583749	+	1.01108i
$82$	−0.568134	+	0.984037i	−0.0627399	+	0.108669i
$83$	3.85965			0.423652			0.211826	−	0.977307i	$-0.432059\pi$
$83$	3.85965			0.423652			0.211826	+	0.977307i	$0.432059\pi$
$84$	−3.99638	−	4.64336i	−0.436041	−	0.506632i
$85$	0.568134			0.0616228
$86$	−5.88367	+	10.1908i	−0.634452	+	1.09890i
$87$	−5.65414	−	9.79327i	−0.606188	−	1.04995i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	4.48437	−	7.76716i	0.475342	−	0.823317i	−0.524259	−	0.851559i	$-0.675658\pi$
$89$	4.48437	−	7.76716i	0.475342	−	0.823317i	0.999601	+	0.0282420i	$0.00899090\pi$
$90$	−2.36169			−0.248944
$91$	−5.73225	+	16.3847i	−0.600903	+	1.71758i
$92$	−3.76733			−0.392772
$93$	1.21121	−	2.09787i	0.125596	−	0.217539i
$94$	3.74740	+	6.49068i	0.386515	+	0.669463i
$95$	3.27048	+	5.66463i	0.335544	+	0.581179i
$96$	−1.15777	+	2.00531i	−0.118164	+	0.204666i
$97$	1.56497			0.158899			0.0794494	−	0.996839i	$-0.474684\pi$
$97$	1.56497			0.158899			0.0794494	+	0.996839i	$0.474684\pi$
$98$	6.51584	−	2.55810i	0.658199	−	0.258407i
$99$	−2.36169			−0.237359
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	0.951800	+	1.64857i	0.0947077	+	0.164039i	0.909487	−	0.415733i	$-0.136475\pi$
$101$	0.951800	+	1.64857i	0.0947077	+	0.164039i	−0.814779	+	0.579772i	$0.803142\pi$
$102$	0.657766	+	1.13928i	0.0651286	+	0.112806i
$103$	−7.99276	+	13.8439i	−0.787550	+	1.36408i	0.139914	+	0.990164i	$0.455317\pi$
$103$	−7.99276	+	13.8439i	−0.787550	+	1.36408i	−0.927464	+	0.373912i	$0.878016\pi$
$104$	6.56089			0.643348
$105$	2.02308	−	5.78265i	0.197432	−	0.564328i
$106$	12.6039			1.22420
$107$	−2.43187	+	4.21212i	−0.235097	+	0.407201i	−0.959301	−	0.282386i	$-0.908874\pi$
$107$	−2.43187	+	4.21212i	−0.235097	+	0.407201i	0.724204	+	0.689586i	$0.242208\pi$
$108$	0.739012	+	1.28001i	0.0711115	+	0.123169i
$109$	4.14214	+	7.17439i	0.396745	+	0.687182i	0.993322	−	0.115373i	$-0.0368065\pi$
$109$	4.14214	+	7.17439i	0.396745	+	0.687182i	−0.596577	+	0.802555i	$0.703473\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	−20.3450			−1.93106
$112$	−1.72590	−	2.00531i	−0.163082	−	0.189484i
$113$	0.342710			0.0322395			0.0161197	−	0.999870i	$-0.494869\pi$
$113$	0.342710			0.0322395			0.0161197	+	0.999870i	$0.494869\pi$
$114$	−7.57290	+	13.1166i	−0.709267	+	1.22849i
$115$	−1.88367	−	3.26261i	−0.175653	−	0.304240i
$116$	−2.44183	−	4.22938i	−0.226719	−	0.392688i
$117$	−7.74740	+	13.4189i	−0.716247	+	1.24058i
$118$	−12.0557			−1.10982
$119$	−1.47692	+	0.279532i	−0.135389	+	0.0256247i
$120$	−2.31553			−0.211378
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−1.63469	−	2.83136i	−0.147998	−	0.256339i
$123$	−1.31553	−	2.27857i	−0.118618	−	0.205452i
$124$	0.523079	−	0.906000i	0.0469739	−	0.0813612i
$125$	−1.00000			−0.0894427
$126$	6.13945	−	1.16200i	0.546946	−	0.103519i
$127$	−2.53467			−0.224915			−0.112458	−	0.993657i	$-0.535872\pi$
$127$	−2.53467			−0.224915			−0.112458	+	0.993657i	$0.535872\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−13.6238	−	23.5972i	−1.19951	−	2.07761i
$130$	3.28045	+	5.68190i	0.287714	+	0.498335i
$131$	2.71593	−	4.70413i	0.237292	−	0.411002i	−0.722644	−	0.691220i	$-0.757073\pi$
$131$	2.71593	−	4.70413i	0.237292	−	0.411002i	0.959936	+	0.280218i	$0.0904068\pi$
$132$	−2.31553			−0.201541
$133$	−11.2890	−	13.1166i	−0.978884	−	1.13736i
$134$	2.36893			0.204645
$135$	−0.739012	+	1.28001i	−0.0636041	+	0.110165i
$136$	0.284067	+	0.492018i	0.0243585	+	0.0421902i
$137$	9.04778	+	15.6712i	0.773004	+	1.33888i	0.935910	+	0.352240i	$0.114580\pi$
$137$	9.04778	+	15.6712i	0.773004	+	1.33888i	−0.162906	+	0.986642i	$0.552087\pi$
$138$	4.36169	−	7.55467i	0.371292	−	0.643096i
$139$	−16.3722			−1.38867			−0.694335	−	0.719652i	$-0.744301\pi$
$139$	−16.3722			−1.38867			−0.694335	+	0.719652i	$0.744301\pi$
$140$	0.873699	−	2.49733i	0.0738411	−	0.211063i
$141$	−17.3544			−1.46151
$142$	−5.22432	+	9.04879i	−0.438415	+	0.759357i
$143$	3.28045	+	5.68190i	0.274325	+	0.475144i
$144$	−1.18085	−	2.04528i	−0.0984038	−	0.170440i
$145$	2.44183	−	4.22938i	0.202783	−	0.351231i
$146$	5.79356			0.479478
$147$	−2.41403	+	16.0280i	−0.199106	+	1.32196i
$148$	−8.78631			−0.722231
$149$	−9.02533	+	15.6323i	−0.739384	+	1.28065i	0.213390	+	0.976967i	$0.431550\pi$
$149$	−9.02533	+	15.6323i	−0.739384	+	1.28065i	−0.952773	+	0.303683i	$0.901784\pi$
$150$	−1.15777	−	2.00531i	−0.0945312	−	0.163733i
$151$	−11.1641	−	19.3368i	−0.908523	−	1.57361i	−0.816118	−	0.577886i	$-0.803878\pi$
$151$	−11.1641	−	19.3368i	−0.908523	−	1.57361i	−0.0924048	−	0.995722i	$-0.529455\pi$
$152$	−3.27048	+	5.66463i	−0.265271	+	0.459462i
$153$	−1.34176			−0.108475
$154$	0.873699	−	2.49733i	0.0704047	−	0.201240i
$155$	1.04616			0.0840295
$156$	−7.59598	+	13.1566i	−0.608165	+	1.05337i
$157$	3.33341	+	5.77363i	0.266035	+	0.460786i	0.967834	−	0.251589i	$-0.0809530\pi$
$157$	3.33341	+	5.77363i	0.266035	+	0.460786i	−0.701799	+	0.712375i	$0.747620\pi$
$158$	−0.0550218	−	0.0953005i	−0.00437730	−	0.00758170i
$159$	−14.5924	+	25.2747i	−1.15725	+	2.00441i
$160$	−1.00000			−0.0790569
$161$	6.50204	+	7.55467i	0.512433	+	0.595391i
$162$	−10.5075			−0.825546
$163$	−2.02150	+	3.50134i	−0.158336	+	0.274246i	−0.934269	−	0.356570i	$-0.883946\pi$
$163$	−2.02150	+	3.50134i	−0.158336	+	0.274246i	0.775933	+	0.630816i	$0.217280\pi$
$164$	−0.568134	−	0.984037i	−0.0443638	−	0.0768404i
$165$	−1.15777	−	2.00531i	−0.0901320	−	0.156113i
$166$	−1.92983	+	3.34256i	−0.149783	+	0.259433i
$167$	9.66998			0.748286			0.374143	−	0.927371i	$-0.377937\pi$
$167$	9.66998			0.748286			0.374143	+	0.927371i	$0.377937\pi$
$168$	6.01946	−	1.13928i	0.464411	−	0.0878977i
$169$	30.0453			2.31118
$170$	−0.284067	+	0.492018i	−0.0217869	+	0.0377361i
$171$	−7.72386	−	13.3781i	−0.590658	−	1.02305i
$172$	−5.88367	−	10.1908i	−0.448625	−	0.777042i
$173$	9.00162	−	15.5913i	0.684380	−	1.18538i	−0.289251	−	0.957253i	$-0.593406\pi$
$173$	9.00162	−	15.5913i	0.684380	−	1.18538i	0.973631	−	0.228128i	$-0.0732606\pi$
$174$	11.3083			0.857279
$175$	2.59960	−	0.492018i	0.196511	−	0.0371931i
$176$	−1.00000			−0.0753778
$177$	13.9577	−	24.1754i	1.04912	−	1.81713i
$178$	4.48437	+	7.76716i	0.336118	+	0.582173i
$179$	−11.7250	−	20.3083i	−0.876368	−	1.51791i	−0.855299	−	0.518136i	$-0.826626\pi$
$179$	−11.7250	−	20.3083i	−0.876368	−	1.51791i	−0.0210693	−	0.999778i	$-0.506707\pi$
$180$	1.18085	−	2.04528i	0.0880150	−	0.152447i
$181$	2.54316			0.189032			0.0945160	−	0.995523i	$-0.469870\pi$
$181$	2.54316			0.189032			0.0945160	+	0.995523i	$0.469870\pi$
$182$	−11.3234	−	13.1566i	−0.839349	−	0.975234i
$183$	7.57034			0.559616
$184$	1.88367	−	3.26261i	0.138866	−	0.240523i
$185$	−4.39316	−	7.60917i	−0.322991	−	0.559437i
$186$	1.21121	+	2.09787i	0.0888100	+	0.153823i
$187$	−0.284067	+	0.492018i	−0.0207730	+	0.0359799i
$188$	−7.49480			−0.546614
$189$	1.29135	−	3.69111i	0.0939318	−	0.268489i
$190$	−6.54096			−0.474531
$191$	10.9525	−	18.9702i	0.792493	−	1.37264i	−0.131927	−	0.991260i	$-0.542116\pi$
$191$	10.9525	−	18.9702i	0.792493	−	1.37264i	0.924419	−	0.381378i	$-0.124550\pi$
$192$	−1.15777	−	2.00531i	−0.0835546	−	0.144721i
$193$	3.41828	+	5.92063i	0.246053	+	0.426176i	0.962427	−	0.271540i	$-0.0875329\pi$
$193$	3.41828	+	5.92063i	0.246053	+	0.426176i	−0.716374	+	0.697716i	$0.754200\pi$
$194$	−0.782486	+	1.35531i	−0.0561792	+	0.0973053i
$195$	−15.1920			−1.08792
$196$	−1.04254	+	6.92193i	−0.0744669	+	0.494424i
$197$	8.97378			0.639355			0.319678	−	0.947526i	$-0.396425\pi$
$197$	8.97378			0.639355			0.319678	+	0.947526i	$0.396425\pi$
$198$	1.18085	−	2.04528i	0.0839190	−	0.145352i
$199$	10.3848	+	17.9870i	0.736160	+	1.27507i	0.954213	+	0.299129i	$0.0966961\pi$
$199$	10.3848	+	17.9870i	0.736160	+	1.27507i	−0.218053	+	0.975937i	$0.569971\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−2.74267	+	4.75045i	−0.193453	+	0.335071i
$202$	−1.90360			−0.133937
$203$	−4.26686	+	12.1961i	−0.299475	+	0.856000i
$204$	−1.31553			−0.0921057
$205$	0.568134	−	0.984037i	0.0396802	−	0.0687281i
$206$	−7.99276	−	13.8439i	−0.556882	−	0.964547i
$207$	4.44864	+	7.70527i	0.309202	+	0.535553i
$208$	−3.28045	+	5.68190i	−0.227458	+	0.393969i
$209$	−6.54096			−0.452447
$210$	3.99638	+	4.64336i	0.275776	+	0.320422i
$211$	−10.7212			−0.738076			−0.369038	−	0.929414i	$-0.620313\pi$
$211$	−10.7212			−0.738076			−0.369038	+	0.929414i	$0.620313\pi$
$212$	−6.30194	+	10.9153i	−0.432819	+	0.749665i
$213$	−12.0971	−	20.9528i	−0.828878	−	1.43566i
$214$	−2.43187	−	4.21212i	−0.166239	−	0.287934i
$215$	5.88367	−	10.1908i	0.401263	−	0.695007i
$216$	−1.47802			−0.100567
$217$	−2.71959	+	0.514729i	−0.184618	+	0.0349421i
$218$	−8.28427			−0.561082
$219$	−6.70759	+	11.6179i	−0.453257	+	0.785063i
$220$	−0.500000	−	0.866025i	−0.0337100	−	0.0583874i
$221$	1.86373	+	3.22808i	0.125368	+	0.217144i
$222$	10.1725	−	17.6193i	0.682733	−	1.18253i
$223$	−6.14035			−0.411188			−0.205594	−	0.978637i	$-0.565913\pi$
$223$	−6.14035			−0.411188			−0.205594	+	0.978637i	$0.565913\pi$
$224$	2.59960	−	0.492018i	0.173693	−	0.0328744i
$225$	2.36169			0.157446
$226$	−0.171355	+	0.296796i	−0.0113984	+	0.0197426i
$227$	−1.43911	−	2.49261i	−0.0955171	−	0.165440i	0.814307	−	0.580434i	$-0.197117\pi$
$227$	−1.43911	−	2.49261i	−0.0955171	−	0.165440i	−0.909824	+	0.414994i	$0.863784\pi$
$228$	−7.57290	−	13.1166i	−0.501527	−	0.868671i
$229$	−10.2191	+	17.7001i	−0.675299	+	1.16965i	0.301082	+	0.953598i	$0.402652\pi$
$229$	−10.2191	+	17.7001i	−0.675299	+	1.16965i	−0.976381	+	0.216055i	$0.930681\pi$
$230$	3.76733			0.248411
$231$	3.99638	+	4.64336i	0.262942	+	0.305511i
$232$	4.88367			0.320628
$233$	5.27793	−	9.14164i	0.345769	−	0.598889i	−0.639725	−	0.768604i	$-0.720952\pi$
$233$	5.27793	−	9.14164i	0.345769	−	0.598889i	0.985493	+	0.169716i	$0.0542849\pi$
$234$	−7.74740	−	13.4189i	−0.506463	−	0.877220i
$235$	−3.74740	−	6.49068i	−0.244453	−	0.423406i
$236$	6.02784	−	10.4405i	0.392379	−	0.679621i
$237$	0.254809			0.0165516
$238$	0.496378	−	1.41882i	0.0321754	−	0.0919682i
$239$	25.2843			1.63550			0.817752	−	0.575571i	$-0.195220\pi$
$239$	25.2843			1.63550			0.817752	+	0.575571i	$0.195220\pi$
$240$	1.15777	−	2.00531i	0.0747335	−	0.129442i
$241$	−2.92983	−	5.07461i	−0.188727	−	0.326884i	0.756099	−	0.654457i	$-0.227103\pi$
$241$	−2.92983	−	5.07461i	−0.188727	−	0.326884i	−0.944826	+	0.327573i	$0.893769\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	9.94818	−	17.2308i	0.638176	−	1.10535i
$244$	3.26937			0.209300
$245$	−6.51584	+	2.55810i	−0.416281	+	0.163431i
$246$	2.63107			0.167751
$247$	−21.4572	+	37.1650i	−1.36529	+	2.36476i
$248$	0.523079	+	0.906000i	0.0332156	+	0.0575311i
$249$	−4.46857	−	7.73980i	−0.283184	−	0.490490i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−22.7089			−1.43337			−0.716686	−	0.697396i	$-0.754342\pi$
$251$	−22.7089			−1.43337			−0.716686	+	0.697396i	$0.754342\pi$
$252$	−2.06341	+	5.89792i	−0.129982	+	0.371534i
$253$	3.76733			0.236850
$254$	1.26733	−	2.19509i	0.0795195	−	0.137732i
$255$	−0.657766	−	1.13928i	−0.0411909	−	0.0713448i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.00791	−	5.20985i	0.187628	−	0.324982i	−0.756831	−	0.653611i	$-0.773253\pi$
$257$	3.00791	−	5.20985i	0.187628	−	0.324982i	0.944459	+	0.328629i	$0.106587\pi$
$258$	27.2476			1.69636
$259$	15.1643	+	17.6193i	0.942264	+	1.09481i
$260$	−6.56089			−0.406889
$261$	−5.76686	+	9.98849i	−0.356959	+	0.618272i
$262$	2.71593	+	4.70413i	0.167791	+	0.290622i
$263$	2.54664	+	4.41090i	0.157032	+	0.271988i	0.933797	−	0.357803i	$-0.116474\pi$
$263$	2.54664	+	4.41090i	0.157032	+	0.271988i	−0.776765	+	0.629791i	$0.783141\pi$
$264$	1.15777	−	2.00531i	0.0712556	−	0.123418i
$265$	−12.6039			−0.774251
$266$	17.0039	−	3.21827i	1.04257	−	0.197325i
$267$	−20.7674			−1.27094
$268$	−1.18447	+	2.05156i	−0.0723529	+	0.125319i
$269$	10.2843	+	17.8129i	0.627043	+	1.08607i	0.988142	+	0.153543i	$0.0490684\pi$
$269$	10.2843	+	17.8129i	0.627043	+	1.08607i	−0.361099	+	0.932528i	$0.617598\pi$
$270$	−0.739012	−	1.28001i	−0.0449749	−	0.0778987i
$271$	−14.3895	+	24.9234i	−0.874102	+	1.51399i	−0.0163857	+	0.999866i	$0.505216\pi$
$271$	−14.3895	+	24.9234i	−0.874102	+	1.51399i	−0.857716	+	0.514123i	$0.828117\pi$
$272$	−0.568134			−0.0344482
$273$	39.4930	−	7.47472i	2.39023	−	0.452391i
$274$	−18.0956			−1.09319
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	4.36169	+	7.55467i	0.262543	+	0.454738i
$277$	14.7490	+	25.5460i	0.886183	+	1.53491i	0.844352	+	0.535789i	$0.179986\pi$
$277$	14.7490	+	25.5460i	0.886183	+	1.53491i	0.0418305	+	0.999125i	$0.486681\pi$
$278$	8.18609	−	14.1787i	0.490969	−	0.850383i
$279$	−2.47070			−0.147917
$280$	1.72590	+	2.00531i	0.103142	+	0.119840i
$281$	−13.4948			−0.805032			−0.402516	−	0.915413i	$-0.631864\pi$
$281$	−13.4948			−0.805032			−0.402516	+	0.915413i	$0.631864\pi$
$282$	8.67722	−	15.0294i	0.516721	−	0.894987i
$283$	−0.840670	−	1.45608i	−0.0499726	−	0.0865551i	0.839957	−	0.542653i	$-0.182580\pi$
$283$	−0.840670	−	1.45608i	−0.0499726	−	0.0865551i	−0.889930	+	0.456098i	$0.849247\pi$
$284$	−5.22432	−	9.04879i	−0.310006	−	0.536947i
$285$	7.57290	−	13.1166i	0.448580	−	0.776963i
$286$	−6.56089			−0.387954
$287$	−0.992756	+	2.83763i	−0.0586006	+	0.167500i
$288$	2.36169			0.139164
$289$	8.33861	−	14.4429i	0.490507	−	0.849582i
$290$	2.44183	+	4.22938i	0.143389	+	0.248358i
$291$	−1.81187	−	3.13825i	−0.106214	−	0.183968i
$292$	−2.89678	+	5.01737i	−0.169521	+	0.293619i
$293$	−19.6270			−1.14662			−0.573310	−	0.819338i	$-0.694341\pi$
$293$	−19.6270			−1.14662			−0.573310	+	0.819338i	$0.694341\pi$
$294$	−12.6736	−	10.1046i	−0.739139	−	0.589311i
$295$	12.0557			0.701909
$296$	4.39316	−	7.60917i	0.255347	−	0.442274i
$297$	−0.739012	−	1.28001i	−0.0428818	−	0.0742735i
$298$	−9.02533	−	15.6323i	−0.522823	−	0.905556i
$299$	12.3585	−	21.4056i	0.714712	−	1.23792i
$300$	2.31553			0.133687
$301$	−10.2811	+	29.3869i	−0.592593	+	1.69383i
$302$	22.3282			1.28484
$303$	2.20392	−	3.81731i	0.126612	−	0.219299i
$304$	−3.27048	−	5.66463i	−0.187575	−	0.324889i
$305$	1.63469	+	2.83136i	0.0936019	+	0.162123i
$306$	0.670878	−	1.16200i	0.0383516	−	0.0664269i
$307$	−5.22859			−0.298411			−0.149206	−	0.988806i	$-0.547672\pi$
$307$	−5.22859			−0.298411			−0.149206	+	0.988806i	$0.547672\pi$
$308$	1.72590	+	2.00531i	0.0983423	+	0.114263i
$309$	37.0150			2.10571
$310$	−0.523079	+	0.906000i	−0.0297089	+	0.0514573i
$311$	−1.74311	−	3.01916i	−0.0988428	−	0.171201i	0.812363	−	0.583152i	$-0.198181\pi$
$311$	−1.74311	−	3.01916i	−0.0988428	−	0.171201i	−0.911206	+	0.411951i	$0.864847\pi$
$312$	−7.59598	−	13.1566i	−0.430038	−	0.744847i
$313$	−6.30038	+	10.9126i	−0.356119	+	0.616815i	−0.987309	−	0.158813i	$-0.949233\pi$
$313$	−6.30038	+	10.9126i	−0.356119	+	0.616815i	0.631190	+	0.775628i	$0.282567\pi$
$314$	−6.66682			−0.376230
$315$	−6.13945	+	1.16200i	−0.345919	+	0.0654710i
$316$	0.110044			0.00619043
$317$	0.519918	−	0.900524i	0.0292015	−	0.0505785i	−0.851055	−	0.525076i	$-0.824037\pi$
$317$	0.519918	−	0.900524i	0.0292015	−	0.0505785i	0.880257	+	0.474498i	$0.157370\pi$
$318$	−14.5924	−	25.2747i	−0.818299	−	1.41733i
$319$	2.44183	+	4.22938i	0.136716	+	0.236800i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	11.2621			0.628591
$322$	−9.79356	+	1.85360i	−0.545774	+	0.103297i
$323$	−3.71614			−0.206772
$324$	5.25374	−	9.09975i	0.291875	−	0.505542i
$325$	−3.28045	−	5.68190i	−0.181966	−	0.315175i
$326$	−2.02150	−	3.50134i	−0.111960	−	0.193921i
$327$	9.59125	−	16.6125i	0.530397	−	0.918675i
$328$	1.13627			0.0627399
$329$	12.9353	+	15.0294i	0.713145	+	0.828597i
$330$	2.31553			0.127466
$331$	−10.2994	+	17.8391i	−0.566108	+	0.980527i	0.430838	+	0.902429i	$0.358218\pi$
$331$	−10.2994	+	17.8391i	−0.566108	+	0.980527i	−0.996946	+	0.0780979i	$0.975115\pi$
$332$	−1.92983	−	3.34256i	−0.105913	−	0.183447i
$333$	10.3753	+	17.9705i	0.568562	+	0.984778i
$334$	−4.83499	+	8.37445i	−0.264559	+	0.458229i
$335$	−2.36893			−0.129429
$336$	−2.02308	+	5.78265i	−0.110368	+	0.315469i
$337$	−12.5536			−0.683841			−0.341920	−	0.939729i	$-0.611077\pi$
$337$	−12.5536			−0.683841			−0.341920	+	0.939729i	$0.611077\pi$
$338$	−15.0226	+	26.0200i	−0.817124	+	1.41530i
$339$	−0.396779	−	0.687241i	−0.0215501	−	0.0373258i
$340$	−0.284067	−	0.492018i	−0.0154057	−	0.0266834i
$341$	−0.523079	+	0.906000i	−0.0283263	+	0.0490626i
$342$	15.4477			0.835317
$343$	15.6799	−	9.85595i	0.846637	−	0.532171i
$344$	11.7673			0.634452
$345$	−4.36169	+	7.55467i	−0.234826	+	0.406730i
$346$	9.00162	+	15.5913i	0.483930	+	0.838191i
$347$	6.61429	+	11.4563i	0.355074	+	0.615006i	0.987131	−	0.159916i	$-0.0511224\pi$
$347$	6.61429	+	11.4563i	0.355074	+	0.615006i	−0.632057	+	0.774922i	$0.717789\pi$
$348$	−5.65414	+	9.79327i	−0.303094	+	0.524974i
$349$	−26.2635			−1.40585			−0.702925	−	0.711264i	$-0.748123\pi$
$349$	−26.2635			−1.40585			−0.702925	+	0.711264i	$0.748123\pi$
$350$	−0.873699	+	2.49733i	−0.0467012	+	0.133488i
$351$	−9.69716			−0.517596
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	3.99276	+	6.91566i	0.212513	+	0.368083i	0.952500	−	0.304537i	$-0.0985019\pi$
$353$	3.99276	+	6.91566i	0.212513	+	0.368083i	−0.739987	+	0.672621i	$0.765169\pi$
$354$	13.9577	+	24.1754i	0.741842	+	1.28491i
$355$	5.22432	−	9.04879i	0.277278	−	0.480260i
$356$	−8.96874			−0.475342
$357$	2.27048	+	2.63805i	0.120166	+	0.139620i
$358$	23.4500			1.23937
$359$	7.53305	−	13.0476i	0.397579	−	0.688627i	−0.595848	−	0.803097i	$-0.703184\pi$
$359$	7.53305	−	13.0476i	0.397579	−	0.688627i	0.993427	+	0.114470i	$0.0365171\pi$
$360$	1.18085	+	2.04528i	0.0622360	+	0.107796i
$361$	−11.8921	−	20.5976i	−0.625898	−	1.08409i
$362$	−1.27158	+	2.20244i	−0.0668329	+	0.115758i
$363$	2.31553			0.121534
$364$	17.0557	−	3.22808i	0.893961	−	0.169197i
$365$	−5.79356			−0.303249
$366$	−3.78517	+	6.55611i	−0.197854	+	0.342693i
$367$	2.21913	+	3.84365i	0.115838	+	0.200637i	0.918114	−	0.396316i	$-0.129711\pi$
$367$	2.21913	+	3.84365i	0.115838	+	0.200637i	−0.802277	+	0.596953i	$0.796378\pi$
$368$	1.88367	+	3.26261i	0.0981929	+	0.170075i
$369$	−1.34176	+	2.32399i	−0.0698491	+	0.120982i
$370$	8.78631			0.456779
$371$	32.7651	−	6.20134i	1.70108	−	0.321958i
$372$	−2.42241			−0.125596
$373$	−0.992090	+	1.71835i	−0.0513685	+	0.0889728i	−0.890566	−	0.454853i	$-0.849692\pi$
$373$	−0.992090	+	1.71835i	−0.0513685	+	0.0889728i	0.839198	+	0.543826i	$0.183025\pi$
$374$	−0.284067	−	0.492018i	−0.0146888	−	0.0254417i
$375$	1.15777	+	2.00531i	0.0597868	+	0.103554i
$376$	3.74740	−	6.49068i	0.193257	−	0.334732i
$377$	32.0412			1.65021
$378$	2.55092	+	2.96390i	0.131205	+	0.152446i
$379$	32.0557			1.64659			0.823295	−	0.567614i	$-0.192133\pi$
$379$	32.0557			1.64659			0.823295	+	0.567614i	$0.192133\pi$
$380$	3.27048	−	5.66463i	0.167772	−	0.290590i
$381$	2.93455	+	5.08279i	0.150342	+	0.260399i
$382$	10.9525	+	18.9702i	0.560377	+	0.970601i
$383$	10.3816	−	17.9815i	0.530476	−	0.918812i	−0.468891	−	0.883256i	$-0.655346\pi$
$383$	10.3816	−	17.9815i	0.530476	−	0.918812i	0.999368	−	0.0355561i	$-0.0113202\pi$
$384$	2.31553			0.118164
$385$	−0.873699	+	2.49733i	−0.0445278	+	0.127276i
$386$	−6.83655			−0.347971
$387$	−13.8954	+	24.0675i	−0.706343	+	1.22342i
$388$	−0.782486	−	1.35531i	−0.0397247	−	0.0688052i
$389$	−7.89949	−	13.6823i	−0.400520	−	0.693721i	0.593269	−	0.805004i	$-0.297837\pi$
$389$	−7.89949	−	13.6823i	−0.400520	−	0.693721i	−0.993789	+	0.111284i	$0.964504\pi$
$390$	7.59598	−	13.1566i	0.384637	−	0.666211i
$391$	2.14035			0.108242
$392$	−5.47330	−	4.36383i	−0.276443	−	0.220407i
$393$	−12.5777			−0.634459
$394$	−4.48689	+	7.77152i	−0.226046	+	0.391523i
$395$	0.0550218	+	0.0953005i	0.00276845	+	0.00479509i
$396$	1.18085	+	2.04528i	0.0593397	+	0.102779i
$397$	12.0353	−	20.8458i	0.604036	−	1.04622i	−0.388167	−	0.921589i	$-0.626892\pi$
$397$	12.0353	−	20.8458i	0.604036	−	1.04622i	0.992203	−	0.124632i	$-0.0397750\pi$
$398$	−20.7696			−1.04109
$399$	−13.2329	+	37.8240i	−0.662472	+	1.89357i
$400$	1.00000			0.0500000
$401$	−1.43030	+	2.47736i	−0.0714259	+	0.123713i	−0.899526	−	0.436866i	$-0.856088\pi$
$401$	−1.43030	+	2.47736i	−0.0714259	+	0.123713i	0.828101	+	0.560580i	$0.189422\pi$
$402$	−2.74267	−	4.75045i	−0.136792	−	0.236931i
$403$	3.43187	+	5.94417i	0.170953	+	0.296100i
$404$	0.951800	−	1.64857i	0.0473538	−	0.0820193i
$405$	10.5075			0.522121
$406$	−8.42872	−	9.79327i	−0.418310	−	0.486032i
$407$	8.78631			0.435521
$408$	0.657766	−	1.13928i	0.0325643	−	0.0564030i
$409$	4.94755	+	8.56941i	0.244641	+	0.423730i	0.962031	−	0.272942i	$-0.0879967\pi$
$409$	4.94755	+	8.56941i	0.244641	+	0.423730i	−0.717390	+	0.696672i	$0.754663\pi$
$410$	0.568134	+	0.984037i	0.0280581	+	0.0485981i
$411$	20.9504	−	36.2872i	1.03341	−	1.78992i
$412$	15.9855			0.787550
$413$	−31.3400	+	5.93162i	−1.54214	+	0.291876i
$414$	−8.89728			−0.437277
$415$	1.92983	−	3.34256i	0.0947314	−	0.164080i
$416$	−3.28045	−	5.68190i	−0.160837	−	0.278578i
$417$	18.9552	+	32.8313i	0.928238	+	1.60775i
$418$	3.27048	−	5.66463i	0.159964	−	0.277066i
$419$	−33.9811			−1.66009			−0.830043	−	0.557700i	$-0.811684\pi$
$419$	−33.9811			−1.66009			−0.830043	+	0.557700i	$0.811684\pi$
$420$	−6.01946	+	1.13928i	−0.293719	+	0.0555914i
$421$	−28.7443			−1.40091			−0.700457	−	0.713695i	$-0.747020\pi$
$421$	−28.7443			−1.40091			−0.700457	+	0.713695i	$0.747020\pi$
$422$	5.36059	−	9.28481i	0.260949	−	0.451977i
$423$	8.85020	+	15.3290i	0.430311	+	0.745321i
$424$	−6.30194	−	10.9153i	−0.306049	−	0.530093i
$425$	0.284067	−	0.492018i	0.0137793	−	0.0238664i
$426$	24.1942			1.17221
$427$	−5.64261	−	6.55611i	−0.273065	−	0.317272i
$428$	4.86373			0.235097
$429$	7.59598	−	13.1566i	0.366737	−	0.635208i
$430$	5.88367	+	10.1908i	0.283736	+	0.491444i
$431$	2.60322	+	4.50891i	0.125393	+	0.217187i	0.921886	−	0.387460i	$-0.126648\pi$
$431$	2.60322	+	4.50891i	0.125393	+	0.217187i	−0.796494	+	0.604647i	$0.793314\pi$
$432$	0.739012	−	1.28001i	0.0355557	−	0.0615844i
$433$	3.98551			0.191532			0.0957658	−	0.995404i	$-0.469470\pi$
$433$	3.98551			0.191532			0.0957658	+	0.995404i	$0.469470\pi$
$434$	0.914028	−	2.61260i	0.0438748	−	0.125409i
$435$	−11.3083			−0.542191
$436$	4.14214	−	7.17439i	0.198372	−	0.343591i
$437$	12.3210	+	21.3406i	0.589392	+	1.02086i
$438$	−6.70759	−	11.6179i	−0.320501	−	0.555124i
$439$	−2.80966	+	4.86648i	−0.134098	+	0.232264i	−0.925253	−	0.379352i	$-0.876147\pi$
$439$	−2.80966	+	4.86648i	−0.134098	+	0.232264i	0.791155	+	0.611616i	$0.209480\pi$
$440$	1.00000			0.0476731
$441$	15.3884	−	6.04145i	0.732781	−	0.287688i
$442$	−3.72746			−0.177297
$443$	1.04395	−	1.80818i	0.0495996	−	0.0859090i	−0.840160	−	0.542339i	$-0.817539\pi$
$443$	1.04395	−	1.80818i	0.0495996	−	0.0859090i	0.889759	+	0.456430i	$0.150872\pi$
$444$	10.1725	+	17.6193i	0.482765	+	0.836174i
$445$	−4.48437	−	7.76716i	−0.212580	−	0.368199i
$446$	3.07017	−	5.31770i	0.145377	−	0.251800i
$447$	41.7969			1.97692
$448$	−0.873699	+	2.49733i	−0.0412784	+	0.117988i
$449$	18.8629			0.890195			0.445097	−	0.895482i	$-0.353169\pi$
$449$	18.8629			0.890195			0.445097	+	0.895482i	$0.353169\pi$
$450$	−1.18085	+	2.04528i	−0.0556656	+	0.0964156i
$451$	0.568134	+	0.984037i	0.0267524	+	0.0463365i
$452$	−0.171355	−	0.296796i	−0.00805987	−	0.0139601i
$453$	−25.8509	+	44.7750i	−1.21458	+	2.10371i
$454$	2.87822			0.135082
$455$	11.3234	+	13.1566i	0.530851	+	0.616792i
$456$	15.1458			0.709267
$457$	−12.5158	+	21.6781i	−0.585466	+	1.01406i	0.409351	+	0.912377i	$0.365755\pi$
$457$	−12.5158	+	21.6781i	−0.585466	+	1.01406i	−0.994817	+	0.101680i	$0.967578\pi$
$458$	−10.2191	−	17.7001i	−0.477509	−	0.827069i
$459$	−0.419858	−	0.727215i	−0.0195973	−	0.0339435i
$460$	−1.88367	+	3.26261i	−0.0878264	+	0.152120i
$461$	−6.31774			−0.294247			−0.147123	−	0.989118i	$-0.547001\pi$
$461$	−6.31774			−0.294247			−0.147123	+	0.989118i	$0.547001\pi$
$462$	−6.01946	+	1.13928i	−0.280051	+	0.0530043i
$463$	−4.39840			−0.204411			−0.102205	−	0.994763i	$-0.532590\pi$
$463$	−4.39840			−0.204411			−0.102205	+	0.994763i	$0.532590\pi$
$464$	−2.44183	+	4.22938i	−0.113359	+	0.196344i
$465$	−1.21121	−	2.09787i	−0.0561684	−	0.0972865i
$466$	5.27793	+	9.14164i	0.244495	+	0.423478i
$467$	4.13331	−	7.15911i	0.191267	−	0.331284i	−0.754403	−	0.656411i	$-0.772074\pi$
$467$	4.13331	−	7.15911i	0.191267	−	0.331284i	0.945670	+	0.325127i	$0.105407\pi$
$468$	15.4948			0.716247
$469$	6.15828	−	1.16556i	0.284363	−	0.0538205i
$470$	7.49480			0.345709
$471$	7.71862	−	13.3690i	0.355655	−	0.616013i
$472$	6.02784	+	10.4405i	0.277454	+	0.480564i
$473$	5.88367	+	10.1908i	0.270531	+	0.468574i
$474$	−0.127405	+	0.220671i	−0.00585189	+	0.0101358i
$475$	6.54096			0.300120
$476$	0.980542	+	1.13928i	0.0449431	+	0.0522190i
$477$	29.7665			1.36291
$478$	−12.6421	+	21.8968i	−0.578238	+	1.00154i
$479$	−3.68830	−	6.38831i	−0.168523	−	0.291890i	0.769378	−	0.638794i	$-0.220566\pi$
$479$	−3.68830	−	6.38831i	−0.168523	−	0.291890i	−0.937901	+	0.346904i	$0.887233\pi$
$480$	1.15777	+	2.00531i	0.0528446	+	0.0915295i
$481$	28.8230	−	49.9229i	1.31422	−	2.27629i
$482$	5.85965			0.266900
$483$	7.62161	−	21.7852i	0.346795	−	0.991259i
$484$	1.00000			0.0454545
$485$	0.782486	−	1.35531i	0.0355309	−	0.0615413i
$486$	9.94818	+	17.2308i	0.451259	+	0.781603i
$487$	−14.4373	−	25.0062i	−0.654217	−	1.13314i	−0.982089	−	0.188415i	$-0.939665\pi$
$487$	−14.4373	−	25.0062i	−0.654217	−	1.13314i	0.327872	−	0.944722i	$-0.393668\pi$
$488$	−1.63469	+	2.83136i	−0.0739988	+	0.128170i
$489$	9.36169			0.423350
$490$	1.04254	−	6.92193i	0.0470970	−	0.312701i
$491$	−38.9479			−1.75770			−0.878848	−	0.477102i	$-0.841687\pi$
$491$	−38.9479			−1.75770			−0.878848	+	0.477102i	$0.841687\pi$
$492$	−1.31553	+	2.27857i	−0.0593088	+	0.102726i
$493$	1.38729	+	2.40285i	0.0624803	+	0.108219i
$494$	−21.4572	−	37.1650i	−0.965407	−	1.67213i
$495$	−1.18085	+	2.04528i	−0.0530751	+	0.0919287i
$496$	−1.04616			−0.0469739
$497$	−9.12897	+	26.0937i	−0.409490	+	1.17046i
$498$	8.93715			0.400483
$499$	13.7791	−	23.8660i	0.616836	−	1.06839i	−0.373224	−	0.927741i	$-0.621748\pi$
$499$	13.7791	−	23.8660i	0.616836	−	1.06839i	0.990059	−	0.140650i	$-0.0449191\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−11.1956	−	19.3913i	−0.500182	−	0.866340i
$502$	11.3544	−	19.6665i	0.506774	−	0.877758i
$503$	−39.0589			−1.74155			−0.870776	−	0.491680i	$-0.836383\pi$
$503$	−39.0589			−1.74155			−0.870776	+	0.491680i	$0.836383\pi$
$504$	−4.07604	−	4.73592i	−0.181561	−	0.210955i
$505$	1.90360			0.0847091
$506$	−1.88367	+	3.26261i	−0.0837392	+	0.145041i
$507$	−34.7854	−	60.2501i	−1.54487	−	2.67580i
$508$	1.26733	+	2.19509i	0.0562288	+	0.0973912i
$509$	9.63423	−	16.6870i	0.427030	−	0.739637i	−0.569578	−	0.821937i	$-0.692893\pi$
$509$	9.63423	−	16.6870i	0.427030	−	0.739637i	0.996608	+	0.0823003i	$0.0262267\pi$
$510$	1.31553			0.0582528
$511$	15.0609	−	2.85054i	0.666256	−	0.126100i
$512$	1.00000			0.0441942
$513$	4.83385	−	8.37247i	0.213420	−	0.369654i
$514$	3.00791	+	5.20985i	0.132673	+	0.229797i
$515$	7.99276	+	13.8439i	0.352203	+	0.610033i
$516$	−13.6238	+	23.5972i	−0.599755	+	1.03881i
$517$	7.49480			0.329621
$518$	−22.8409	+	4.32303i	−1.00357	+	0.189943i
$519$	−41.6871			−1.82986
$520$	3.28045	−	5.68190i	0.143857	−	0.249168i
$521$	13.1589	+	22.7919i	0.576502	+	0.998531i	0.995877	+	0.0907178i	$0.0289161\pi$
$521$	13.1589	+	22.7919i	0.576502	+	0.998531i	−0.419374	+	0.907813i	$0.637751\pi$
$522$	−5.76686	−	9.98849i	−0.252408	−	0.437184i
$523$	11.1793	−	19.3631i	0.488835	−	0.846687i	−0.511082	−	0.859532i	$-0.670755\pi$
$523$	11.1793	−	19.3631i	0.488835	−	0.846687i	0.999918	+	0.0128445i	$0.00408863\pi$
$524$	−5.43187			−0.237292
$525$	−3.99638	−	4.64336i	−0.174416	−	0.202653i
$526$	−5.09327			−0.222077
$527$	−0.297179	+	0.514729i	−0.0129453	+	0.0224220i
$528$	1.15777	+	2.00531i	0.0503853	+	0.0872699i
$529$	4.40360	+	7.62726i	0.191461	+	0.331620i
$530$	6.30194	−	10.9153i	0.273739	−	0.474130i
$531$	−28.4718			−1.23557
$532$	−5.71483	+	16.3349i	−0.247769	+	0.708208i
$533$	7.45493			0.322909
$534$	10.3837	−	17.9851i	0.449347	−	0.778292i
$535$	2.43187	+	4.21212i	0.105139	+	0.182106i
$536$	−1.18447	−	2.05156i	−0.0511612	−	0.0886138i
$537$	−27.1496	+	47.0245i	−1.17159	+	2.02926i
$538$	−20.5685			−0.886773
$539$	1.04254	−	6.92193i	0.0449052	−	0.298149i
$540$	1.47802			0.0636041
$541$	7.87894	−	13.6467i	0.338742	−	0.586719i	−0.645454	−	0.763799i	$-0.723332\pi$
$541$	7.87894	−	13.6467i	0.338742	−	0.586719i	0.984196	+	0.177080i	$0.0566652\pi$
$542$	−14.3895	−	24.9234i	−0.618083	−	1.07055i
$543$	−2.94439	−	5.09983i	−0.126356	−	0.218855i
$544$	0.284067	−	0.492018i	0.0121793	−	0.0210951i
$545$	8.28427			0.354859
$546$	−13.2732	+	37.9393i	−0.568041	+	1.62365i
$547$	−44.2146			−1.89048			−0.945240	−	0.326377i	$-0.894172\pi$
$547$	−44.2146			−1.89048			−0.945240	+	0.326377i	$0.894172\pi$
$548$	9.04778	−	15.6712i	0.386502	−	0.669441i
$549$	−3.86063	−	6.68680i	−0.164767	−	0.285386i
$550$	0.500000	+	0.866025i	0.0213201	+	0.0369274i
$551$	−15.9719	+	27.6642i	−0.680427	+	1.17853i
$552$	−8.72338			−0.371292
$553$	−0.189924	−	0.220671i	−0.00807640	−	0.00938390i
$554$	−29.4980			−1.25325
$555$	−10.1725	+	17.6193i	−0.431798	+	0.747897i
$556$	8.18609	+	14.1787i	0.347167	+	0.601312i
$557$	−12.3934	−	21.4659i	−0.525124	−	0.909541i	−0.999572	−	0.0292574i	$-0.990686\pi$
$557$	−12.3934	−	21.4659i	−0.525124	−	0.909541i	0.474448	−	0.880283i	$-0.342648\pi$
$558$	1.23535	−	2.13969i	0.0522966	−	0.0905804i
$559$	77.2042			3.26539
$560$	−2.59960	+	0.492018i	−0.109853	+	0.0207916i
$561$	1.31553			0.0555418
$562$	6.74740	−	11.6868i	0.284622	−	0.492979i
$563$	−7.67818	−	13.2990i	−0.323597	−	0.560486i	0.657631	−	0.753340i	$-0.271559\pi$
$563$	−7.67818	−	13.2990i	−0.323597	−	0.560486i	−0.981227	+	0.192855i	$0.938225\pi$
$564$	8.67722	+	15.0294i	0.365377	+	0.632852i
$565$	0.171355	−	0.296796i	0.00720897	−	0.0124863i
$566$	1.68134			0.0706720
$567$	−27.3153	+	5.16988i	−1.14713	+	0.217114i
$568$	10.4486			0.438415
$569$	7.40785	−	12.8308i	0.310553	−	0.537894i	−0.667929	−	0.744225i	$-0.732819\pi$
$569$	7.40785	−	12.8308i	0.310553	−	0.537894i	0.978482	+	0.206331i	$0.0661524\pi$
$570$	7.57290	+	13.1166i	0.317194	+	0.549396i
$571$	−11.9224	−	20.6502i	−0.498936	−	0.864182i	0.501063	−	0.865411i	$-0.332942\pi$
$571$	−11.9224	−	20.6502i	−0.498936	−	0.864182i	−0.999999	+	0.00122829i	$0.999609\pi$
$572$	3.28045	−	5.68190i	0.137162	−	0.237572i
$573$	−50.7216			−2.11892
$574$	−1.96108	−	2.27857i	−0.0818541	−	0.0951056i
$575$	−3.76733			−0.157109
$576$	−1.18085	+	2.04528i	−0.0492019	+	0.0852202i
$577$	−13.8613	−	24.0084i	−0.577052	−	0.999484i	−0.995815	−	0.0913883i	$-0.970870\pi$
$577$	−13.8613	−	24.0084i	−0.577052	−	0.999484i	0.418763	−	0.908096i	$-0.362464\pi$
$578$	8.33861	+	14.4429i	0.346841	+	0.600745i
$579$	7.91513	−	13.7094i	0.328942	−	0.569744i
$580$	−4.88367			−0.202783
$581$	−3.37217	+	9.63881i	−0.139901	+	0.399885i
$582$	3.62374			0.150209
$583$	6.30194	−	10.9153i	0.261000	−	0.452065i
$584$	−2.89678	−	5.01737i	−0.119870	−	0.207620i
$585$	7.74740	+	13.4189i	0.320316	+	0.554803i
$586$	9.81349	−	16.9975i	0.405392	−	0.702159i
$587$	1.86248			0.0768727			0.0384363	−	0.999261i	$-0.487762\pi$
$587$	1.86248			0.0768727			0.0384363	+	0.999261i	$0.487762\pi$
$588$	15.0876	−	5.92337i	0.622203	−	0.244276i
$589$	−6.84288			−0.281956
$590$	−6.02784	+	10.4405i	−0.248162	+	0.429830i
$591$	−10.3895	−	17.9952i	−0.427368	−	0.740224i
$592$	4.39316	+	7.60917i	0.180558	+	0.312735i
$593$	−5.63107	+	9.75329i	−0.231240	+	0.400520i	−0.958173	−	0.286189i	$-0.907612\pi$
$593$	−5.63107	+	9.75329i	−0.231240	+	0.400520i	0.726933	+	0.686708i	$0.240945\pi$
$594$	1.47802			0.0606441
$595$	−0.496378	+	1.41882i	−0.0203495	+	0.0581658i
$596$	18.0507			0.739384
$597$	24.0464	−	41.6495i	0.984152	−	1.70460i
$598$	12.3585	+	21.4056i	0.505378	+	0.875340i
$599$	−5.16773	−	8.95078i	−0.211148	−	0.365719i	0.740926	−	0.671586i	$-0.234387\pi$
$599$	−5.16773	−	8.95078i	−0.211148	−	0.365719i	−0.952074	+	0.305868i	$0.901053\pi$
$600$	−1.15777	+	2.00531i	−0.0472656	+	0.0818664i
$601$	33.9729			1.38578			0.692892	−	0.721041i	$-0.256336\pi$
$601$	33.9729			1.38578			0.692892	+	0.721041i	$0.256336\pi$
$602$	−20.3092	−	23.5972i	−0.827743	−	0.961748i
$603$	5.59469			0.227833
$604$	−11.1641	+	19.3368i	−0.454261	+	0.786804i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	2.20392	+	3.81731i	0.0895283	+	0.155068i
$607$	11.8189	−	20.4709i	0.479714	−	0.830888i	−0.520016	−	0.854157i	$-0.674074\pi$
$607$	11.8189	−	20.4709i	0.479714	−	0.830888i	0.999729	+	0.0232683i	$0.00740720\pi$
$608$	6.54096			0.265271
$609$	29.3970	−	5.56389i	1.19123	−	0.225460i
$610$	−3.26937			−0.132373
$611$	24.5863	−	42.5847i	0.994654	−	1.72279i
$612$	0.670878	+	1.16200i	0.0271187	+	0.0469709i
$613$	−5.90360	−	10.2253i	−0.238444	−	0.412997i	0.721824	−	0.692077i	$-0.243304\pi$
$613$	−5.90360	−	10.2253i	−0.238444	−	0.412997i	−0.960268	+	0.279079i	$0.909971\pi$
$614$	2.61429	−	4.52809i	0.105504	−	0.182739i
$615$	−2.63107			−0.106095
$616$	−2.59960	+	0.492018i	−0.104741	+	0.0198240i
$617$	−24.2802			−0.977484			−0.488742	−	0.872428i	$-0.662544\pi$
$617$	−24.2802			−0.977484			−0.488742	+	0.872428i	$0.662544\pi$
$618$	−18.5075	+	32.0559i	−0.744480	+	1.28948i
$619$	−6.92762	−	11.9990i	−0.278444	−	0.482280i	0.692554	−	0.721366i	$-0.256485\pi$
$619$	−6.92762	−	11.9990i	−0.278444	−	0.482280i	−0.970998	+	0.239086i	$0.923152\pi$
$620$	−0.523079	−	0.906000i	−0.0210074	−	0.0363858i
$621$	−2.78411	+	4.82221i	−0.111722	+	0.193509i
$622$	3.48622			0.139785
$623$	15.4792	+	17.9851i	0.620159	+	0.720558i
$624$	15.1920			0.608165
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−6.30038	−	10.9126i	−0.251814	−	0.436154i
$627$	7.57290	+	13.1166i	0.302432	+	0.523828i
$628$	3.33341	−	5.77363i	0.133018	−	0.230393i
$629$	4.99180			0.199036
$630$	2.06341	−	5.89792i	0.0822081	−	0.234979i
$631$	−31.6292			−1.25914			−0.629570	−	0.776944i	$-0.716769\pi$
$631$	−31.6292			−1.25914			−0.629570	+	0.776944i	$0.716769\pi$
$632$	−0.0550218	+	0.0953005i	−0.00218865	+	0.00379085i
$633$	12.4126	+	21.4993i	0.493357	+	0.854520i
$634$	0.519918	+	0.900524i	0.0206486	+	0.0357644i
$635$	−1.26733	+	2.19509i	−0.0502926	+	0.0871093i
$636$	29.1847			1.15725
$637$	−35.9097	−	28.6306i	−1.42279	−	1.13439i
$638$	−4.88367			−0.193346
$639$	−12.3382	+	21.3704i	−0.488093	+	0.845402i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	2.73219	+	4.73229i	0.107915	+	0.186914i	0.914925	−	0.403623i	$-0.132249\pi$
$641$	2.73219	+	4.73229i	0.107915	+	0.186914i	−0.807010	+	0.590537i	$0.798916\pi$
$642$	−5.63107	+	9.75329i	−0.222240	+	0.384932i
$643$	−19.1417			−0.754876			−0.377438	−	0.926035i	$-0.623195\pi$
$643$	−19.1417			−0.754876			−0.377438	+	0.926035i	$0.623195\pi$
$644$	3.29152	−	9.40827i	0.129704	−	0.370738i
$645$	−27.2476			−1.07287
$646$	1.85807	−	3.21827i	0.0731048	−	0.126621i
$647$	−4.07017	−	7.04975i	−0.160015	−	0.277154i	0.774859	−	0.632134i	$-0.217821\pi$
$647$	−4.07017	−	7.04975i	−0.160015	−	0.277154i	−0.934874	+	0.354980i	$0.884488\pi$
$648$	5.25374	+	9.09975i	0.206387	+	0.357472i
$649$	−6.02784	+	10.4405i	−0.236614	+	0.409827i
$650$	6.56089			0.257339
$651$	4.18085	+	4.85769i	0.163860	+	0.190388i
$652$	4.04300			0.158336
$653$	−14.8839	+	25.7796i	−0.582451	+	1.00883i	0.412737	+	0.910850i	$0.364573\pi$
$653$	−14.8839	+	25.7796i	−0.582451	+	1.00883i	−0.995188	+	0.0979844i	$0.968760\pi$
$654$	9.59125	+	16.6125i	0.375048	+	0.649602i
$655$	−2.71593	−	4.70413i	−0.106120	−	0.183806i
$656$	−0.568134	+	0.984037i	−0.0221819	+	0.0384202i
$657$	13.6826			0.533809
$658$	−19.4835	+	3.68758i	−0.759545	+	0.143757i
$659$	−5.27703			−0.205564			−0.102782	−	0.994704i	$-0.532774\pi$
$659$	−5.27703			−0.205564			−0.102782	+	0.994704i	$0.532774\pi$
$660$	−1.15777	+	2.00531i	−0.0450660	+	0.0780566i
$661$	21.2182	+	36.7510i	0.825292	+	1.42945i	0.901696	+	0.432370i	$0.142323\pi$
$661$	21.2182	+	36.7510i	0.825292	+	1.42945i	−0.0764047	+	0.997077i	$0.524344\pi$
$662$	−10.2994	−	17.8391i	−0.400299	−	0.693337i
$663$	4.31553	−	7.47472i	0.167601	−	0.290294i
$664$	3.85965			0.149783
$665$	−17.0039	+	3.21827i	−0.659382	+	0.124799i
$666$	−20.7506			−0.804068
$667$	9.19920	−	15.9335i	0.356194	−	0.616947i
$668$	−4.83499	−	8.37445i	−0.187071	−	0.324017i
$669$	7.10909	+	12.3133i	0.274853	+	0.476060i
$670$	1.18447	−	2.05156i	0.0457600	−	0.0792586i
$671$	−3.26937			−0.126213
$672$	−3.99638	−	4.64336i	−0.154164	−	0.179122i
$673$	−15.8511			−0.611014			−0.305507	−	0.952190i	$-0.598826\pi$
$673$	−15.8511			−0.611014			−0.305507	+	0.952190i	$0.598826\pi$
$674$	6.27682	−	10.8718i	0.241774	−	0.418765i
$675$	0.739012	+	1.28001i	0.0284446	+	0.0492675i
$676$	−15.0226	−	26.0200i	−0.577794	−	1.00077i
$677$	−21.6700	+	37.5335i	−0.832845	+	1.44253i	0.0629280	+	0.998018i	$0.479956\pi$
$677$	−21.6700	+	37.5335i	−0.832845	+	1.44253i	−0.895773	+	0.444512i	$0.853377\pi$
$678$	0.793557			0.0304764
$679$	−1.36732	+	3.90825i	−0.0524727	+	0.149985i
$680$	0.568134			0.0217869
$681$	−3.33231	+	5.77172i	−0.127694	+	0.221173i
$682$	−0.523079	−	0.906000i	−0.0200297	−	0.0346925i
$683$	18.6192	+	32.2495i	0.712446	+	1.23399i	0.963936	+	0.266132i	$0.0857458\pi$
$683$	18.6192	+	32.2495i	0.712446	+	1.23399i	−0.251491	+	0.967860i	$0.580921\pi$
$684$	−7.72386	+	13.3781i	−0.295329	+	0.511525i
$685$	18.0956			0.691396
$686$	0.695539	+	18.5072i	0.0265558	+	0.706608i
$687$	47.3255			1.80558
$688$	−5.88367	+	10.1908i	−0.224313	+	0.388521i
$689$	−41.3464	−	71.6140i	−1.57517	−	2.72828i
$690$	−4.36169	−	7.55467i	−0.166047	−	0.287601i
$691$	15.7260	−	27.2382i	0.598244	−	1.03619i	−0.394837	−	0.918751i	$-0.629199\pi$
$691$	15.7260	−	27.2382i	0.598244	−	1.03619i	0.993080	−	0.117437i	$-0.0374678\pi$
$692$	−18.0032			−0.684380
$693$	2.06341	−	5.89792i	0.0783824	−	0.224043i
$694$	−13.2286			−0.502150
$695$	−8.18609	+	14.1787i	−0.310516	+	0.537829i
$696$	−5.65414	−	9.79327i	−0.214320	−	0.371213i
$697$	0.322776	+	0.559065i	0.0122260	+	0.0211761i
$698$	13.1317	−	22.7448i	0.497043	−	0.860904i
$699$	−24.4424			−0.924497
$700$	−1.72590	−	2.00531i	−0.0652329	−	0.0757936i
$701$	41.4840			1.56683			0.783414	−	0.621500i	$-0.213477\pi$
$701$	41.4840			1.56683			0.783414	+	0.621500i	$0.213477\pi$
$702$	4.84858	−	8.39799i	0.182998	−	0.316962i
$703$	28.7354	+	49.7713i	1.08378	+	1.87716i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−8.67722	+	15.0294i	−0.326803	+	0.566040i
$706$	−7.98551			−0.300539
$707$	−4.94860	+	0.936607i	−0.186111	+	0.0352247i
$708$	−27.9153			−1.04912
$709$	8.28523	−	14.3504i	0.311158	−	0.538942i	−0.667455	−	0.744650i	$-0.732616\pi$
$709$	8.28523	−	14.3504i	0.311158	−	0.538942i	0.978613	+	0.205708i	$0.0659498\pi$
$710$	5.22432	+	9.04879i	0.196065	+	0.339595i
$711$	−0.129944	−	0.225070i	−0.00487330	−	0.00844080i
$712$	4.48437	−	7.76716i	0.168059	−	0.291087i
$713$	3.94123			0.147600
$714$	−3.41986	+	0.647266i	−0.127985	+	0.0242233i
$715$	6.56089			0.245363
$716$	−11.7250	+	20.3083i	−0.438184	+	0.758957i
$717$	−29.2733	−	50.7028i	−1.09323	−	1.89353i
$718$	7.53305	+	13.0476i	0.281131	+	0.486933i
$719$	−22.7467	+	39.3985i	−0.848309	+	1.46931i	0.0344072	+	0.999408i	$0.489046\pi$
$719$	−22.7467	+	39.3985i	−0.848309	+	1.46931i	−0.882716	+	0.469906i	$0.844288\pi$
$720$	−2.36169			−0.0880150
$721$	−27.5894	−	32.0559i	−1.02748	−	1.19382i
$722$	23.7841			0.885153
$723$	−6.78411	+	11.7504i	−0.252304	+	0.437003i
$724$	−1.27158	−	2.20244i	−0.0472580	−	0.0818532i
$725$	−2.44183	−	4.22938i	−0.0906874	−	0.157075i
$726$	−1.15777	+	2.00531i	−0.0429687	+	0.0744240i
$727$	−28.7569			−1.06654			−0.533268	−	0.845947i	$-0.679036\pi$
$727$	−28.7569			−1.06654			−0.533268	+	0.845947i	$0.679036\pi$
$728$	−5.73225	+	16.3847i	−0.212451	+	0.607257i
$729$	−14.5482			−0.538822
$730$	2.89678	−	5.01737i	0.107215	−	0.185701i
$731$	3.34271	+	5.78974i	0.123635	+	0.214141i
$732$	−3.78517	−	6.55611i	−0.139904	−	0.242321i
$733$	−19.7029	+	34.1264i	−0.727742	+	1.26049i	0.230094	+	0.973168i	$0.426097\pi$
$733$	−19.7029	+	34.1264i	−0.727742	+	1.26049i	−0.957835	+	0.287317i	$0.907237\pi$
$734$	−4.43827			−0.163819
$735$	12.6736	+	10.1046i	0.467473	+	0.372713i
$736$	−3.76733			−0.138866
$737$	1.18447	−	2.05156i	0.0436304	−	0.0755701i
$738$	−1.34176	−	2.32399i	−0.0493908	−	0.0855473i
$739$	13.8434	+	23.9774i	0.509237	+	0.882024i	0.999943	+	0.0106988i	$0.00340561\pi$
$739$	13.8434	+	23.9774i	0.509237	+	0.882024i	−0.490706	+	0.871325i	$0.663261\pi$
$740$	−4.39316	+	7.60917i	−0.161496	+	0.279719i
$741$	99.3699			3.65044
$742$	−11.0120	+	31.4760i	−0.404264	+	1.15552i
$743$	−26.4971			−0.972084			−0.486042	−	0.873936i	$-0.661560\pi$
$743$	−26.4971			−0.972084			−0.486042	+	0.873936i	$0.661560\pi$
$744$	1.21121	−	2.09787i	0.0444050	−	0.0769117i
$745$	9.02533	+	15.6323i	0.330662	+	0.572724i
$746$	−0.992090	−	1.71835i	−0.0363230	−	0.0629133i
$747$	−4.55765	+	7.89408i	−0.166756	+	0.288829i
$748$	0.568134			0.0207730
$749$	−8.39432	−	9.75329i	−0.306722	−	0.356377i
$750$	−2.31553			−0.0845513
$751$	−20.8807	+	36.1665i	−0.761948	+	1.31973i	0.179897	+	0.983685i	$0.442423\pi$
$751$	−20.8807	+	36.1665i	−0.761948	+	1.31973i	−0.941845	+	0.336047i	$0.890910\pi$
$752$	3.74740	+	6.49068i	0.136654	+	0.236691i
$753$	26.2916	+	45.5384i	0.958119	+	1.65951i
$754$	−16.0206	+	27.7485i	−0.583436	+	1.01054i
$755$	−22.3282			−0.812607
$756$	−3.84227	+	0.727215i	−0.139742	+	0.0264486i
$757$	−37.3618			−1.35794			−0.678968	−	0.734168i	$-0.737573\pi$
$757$	−37.3618			−1.35794			−0.678968	+	0.734168i	$0.737573\pi$
$758$	−16.0278	+	27.7610i	−0.582158	+	1.00833i
$759$	−4.36169	−	7.55467i	−0.158319	−	0.274217i
$760$	3.27048	+	5.66463i	0.118633	+	0.205478i
$761$	−0.121781	+	0.210930i	−0.00441455	+	0.00764622i	−0.868224	−	0.496172i	$-0.834739\pi$
$761$	−0.121781	+	0.210930i	−0.00441455	+	0.00764622i	0.863810	+	0.503818i	$0.168072\pi$
$762$	−5.86910			−0.212615
$763$	−21.5358	+	4.07601i	−0.779648	+	0.147562i
$764$	−21.9049			−0.792493
$765$	−0.670878	+	1.16200i	−0.0242557	+	0.0420120i
$766$	10.3816	+	17.9815i	0.375103	+	0.649698i
$767$	39.5480	+	68.4992i	1.42800	+	2.47336i
$768$	−1.15777	+	2.00531i	−0.0417773	+	0.0723604i
$769$	−2.61658			−0.0943562			−0.0471781	−	0.998886i	$-0.515023\pi$
$769$	−2.61658			−0.0943562			−0.0471781	+	0.998886i	$0.515023\pi$
$770$	−1.72590	−	2.00531i	−0.0621971	−	0.0722664i
$771$	−13.9298			−0.501670
$772$	3.41828	−	5.92063i	0.123026	−	0.213088i
$773$	−25.6303	−	44.3930i	−0.921858	−	1.59671i	−0.796537	−	0.604589i	$-0.793337\pi$
$773$	−25.6303	−	44.3930i	−0.921858	−	1.59671i	−0.125321	−	0.992116i	$-0.539996\pi$
$774$	−13.8954	−	24.0675i	−0.499460	−	0.865090i
$775$	0.523079	−	0.906000i	0.0187896	−	0.0325445i
$776$	1.56497			0.0561792
$777$	17.7754	−	50.8081i	0.637689	−	1.82273i
$778$	15.7990			0.566421
$779$	−3.71614	+	6.43654i	−0.133144	+	0.230613i
$780$	7.59598	+	13.1566i	0.271980	+	0.471083i
$781$	5.22432	+	9.04879i	0.186941	+	0.323791i
$782$	−1.07017	+	1.85360i	−0.0382694	+	0.0662845i
$783$	−7.21818			−0.257957
$784$	6.51584	−	2.55810i	0.232708	−	0.0913608i
$785$	6.66682			0.237949
$786$	6.28883	−	10.8926i	0.224315	−	0.388525i
$787$	12.7351	+	22.0579i	0.453958	+	0.786278i	0.998628	−	0.0523724i	$-0.0166783\pi$
$787$	12.7351	+	22.0579i	0.453958	+	0.786278i	−0.544670	+	0.838651i	$0.683345\pi$
$788$	−4.48689	−	7.77152i	−0.159839	−	0.276849i
$789$	5.89682	−	10.2136i	0.209932	−	0.363613i
$790$	−0.110044			−0.00391517
$791$	−0.299426	+	0.855861i	−0.0106464	+	0.0304309i
$792$	−2.36169			−0.0839190
$793$	−10.7250	+	18.5762i	−0.380856	+	0.659662i
$794$	12.0353	+	20.8458i	0.427118	+	0.739790i
$795$	14.5924	+	25.2747i	0.517538	+	0.896401i
$796$	10.3848	−	17.9870i	0.368080	−	0.637533i
$797$	7.53109			0.266765			0.133382	−	0.991065i	$-0.457416\pi$
$797$	7.53109			0.266765			0.133382	+	0.991065i	$0.457416\pi$
$798$	−26.1401	−	30.3720i	−0.925351	−	1.07516i
$799$	4.25805			0.150639
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	10.5907	+	18.3436i	0.374204	+	0.648140i
$802$	−1.43030	−	2.47736i	−0.0505057	−	0.0874785i
$803$	2.89678	−	5.01737i	0.102225	−	0.177059i
$804$	5.48535			0.193453
$805$	9.79356	−	1.85360i	0.345178	−	0.0653307i
$806$	−6.86373			−0.241765
$807$	23.8136	−	41.2463i	0.838277	−	1.45194i
$808$	0.951800	+	1.64857i	0.0334842	+	0.0579964i
$809$	−5.83026	−	10.0983i	−0.204981	−	0.355038i	0.745146	−	0.666902i	$-0.232380\pi$
$809$	−5.83026	−	10.0983i	−0.204981	−	0.355038i	−0.950127	+	0.311864i	$0.899047\pi$
$810$	−5.25374	+	9.09975i	−0.184598	+	0.319733i
$811$	−22.7909			−0.800296			−0.400148	−	0.916450i	$-0.631041\pi$
$811$	−22.7909			−0.800296			−0.400148	+	0.916450i	$0.631041\pi$
$812$	12.6956	−	2.40285i	0.445527	−	0.0843236i
$813$	66.6389			2.33713
$814$	−4.39316	+	7.60917i	−0.153980	+	0.266701i
$815$	2.02150	+	3.50134i	0.0708100	+	0.122647i
$816$	0.657766	+	1.13928i	0.0230264	+	0.0398829i
$817$	−38.4848	+	66.6576i	−1.34641	+	2.33206i
$818$	−9.89510			−0.345974
$819$	−26.7425	−	31.0719i	−0.934458	−	1.08574i
$820$	−1.13627			−0.0396802
$821$	−7.09981	+	12.2972i	−0.247785	+	0.429176i	−0.962911	−	0.269819i	$-0.913036\pi$
$821$	−7.09981	+	12.2972i	−0.247785	+	0.429176i	0.715126	+	0.698996i	$0.246369\pi$
$822$	20.9504	+	36.2872i	0.730730	+	1.26566i
$823$	−9.60610	−	16.6382i	−0.334847	−	0.579973i	0.648608	−	0.761123i	$-0.275351\pi$
$823$	−9.60610	−	16.6382i	−0.334847	−	0.579973i	−0.983456	+	0.181150i	$0.942018\pi$
$824$	−7.99276	+	13.8439i	−0.278441	+	0.482274i
$825$	−2.31553			−0.0806165
$826$	10.5330	−	30.1070i	0.366492	−	1.04756i
$827$	30.4282			1.05809			0.529046	−	0.848593i	$-0.322550\pi$
$827$	30.4282			1.05809			0.529046	+	0.848593i	$0.322550\pi$
$828$	4.44864	−	7.70527i	0.154601	−	0.267777i
$829$	6.79672	+	11.7723i	0.236060	+	0.408868i	0.959580	−	0.281435i	$-0.0908105\pi$
$829$	6.79672	+	11.7723i	0.236060	+	0.408868i	−0.723520	+	0.690303i	$0.757477\pi$
$830$	1.92983	+	3.34256i	0.0669852	+	0.116022i
$831$	34.1518	−	59.1527i	1.18471	−	2.05198i
$832$	6.56089			0.227458
$833$	0.592301	−	3.93258i	0.0205220	−	0.136256i
$834$	−37.9103			−1.31273
$835$	4.83499	−	8.37445i	0.167322	−	0.289810i
$836$	3.27048	+	5.66463i	0.113112	+	0.195915i
$837$	−0.773124	−	1.33909i	−0.0267231	−	0.0462857i
$838$	16.9905	−	29.4285i	0.586929	−	1.01659i
$839$	1.46857			0.0507008			0.0253504	−	0.999679i	$-0.491930\pi$
$839$	1.46857			0.0507008			0.0253504	+	0.999679i	$0.491930\pi$
$840$	2.02308	−	5.78265i	0.0698029	−	0.199520i
$841$	−5.14980			−0.177579
$842$	14.3722	−	24.8933i	0.495298	−	0.857881i
$843$	15.6238	+	27.0613i	0.538113	+	0.932039i
$844$	5.36059	+	9.28481i	0.184519	+	0.319596i
$845$	15.0226	−	26.0200i	0.516795	−	0.895114i
$846$	−17.7004			−0.608552
$847$	−1.72590	−	2.00531i	−0.0593026	−	0.0689033i
$848$	12.6039			0.432819
$849$	−1.94660	+	3.37161i	−0.0668071	+	0.115713i
$850$	0.284067	+	0.492018i	0.00974342	+	0.0168761i
$851$	−16.5505	−	28.6663i	−0.567343	−	0.982667i
$852$	−12.0971	+	20.9528i	−0.414439	+	0.717830i
$853$	−25.7447			−0.881481			−0.440741	−	0.897635i	$-0.645284\pi$
$853$	−25.7447			−0.881481			−0.440741	+	0.897635i	$0.645284\pi$
$854$	8.49906	−	1.60859i	0.290832	−	0.0550449i
$855$	−15.4477			−0.528301
$856$	−2.43187	+	4.21212i	−0.0831195	+	0.143967i
$857$	−7.35963	−	12.7473i	−0.251400	−	0.435438i	0.712511	−	0.701661i	$-0.247558\pi$
$857$	−7.35963	−	12.7473i	−0.251400	−	0.435438i	−0.963912	+	0.266223i	$0.914224\pi$
$858$	7.59598	+	13.1566i	0.259322	+	0.449160i
$859$	−14.2877	+	24.7470i	−0.487490	+	0.844357i	−0.999897	−	0.0143860i	$-0.995421\pi$
$859$	−14.2877	+	24.7470i	−0.487490	+	0.844357i	0.512407	+	0.858743i	$0.328754\pi$
$860$	−11.7673			−0.401263
$861$	6.83972	−	1.29453i	0.233097	−	0.0441175i
$862$	−5.20644			−0.177332
$863$	7.59664	−	13.1578i	0.258593	−	0.447896i	−0.707272	−	0.706941i	$-0.750075\pi$
$863$	7.59664	−	13.1578i	0.258593	−	0.447896i	0.965865	+	0.259045i	$0.0834079\pi$
$864$	0.739012	+	1.28001i	0.0251417	+	0.0435467i
$865$	−9.00162	−	15.5913i	−0.306064	−	0.530119i
$866$	−1.99276	+	3.45156i	−0.0677166	+	0.117289i
$867$	−38.6167			−1.31149
$868$	1.80557	+	2.09787i	0.0612849	+	0.0712064i
$869$	−0.110044			−0.00373297
$870$	5.65414	−	9.79327i	0.191693	−	0.332023i
$871$	−7.77116	−	13.4600i	−0.263316	−	0.456076i
$872$	4.14214	+	7.17439i	0.140270	+	0.242956i
$873$	−1.84799	+	3.20081i	−0.0625450	+	0.108331i
$874$	−24.6420			−0.833527
$875$	0.873699	−	2.49733i	0.0295364	−	0.0844251i
$876$	13.4152			0.453257
$877$	8.49234	−	14.7092i	0.286766	−	0.496693i	−0.686270	−	0.727347i	$-0.740753\pi$
$877$	8.49234	−	14.7092i	0.286766	−	0.496693i	0.973036	+	0.230654i	$0.0740865\pi$
$878$	−2.80966	−	4.86648i	−0.0948216	−	0.164236i
$879$	22.7235	+	39.3582i	0.766443	+	1.32752i
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	−41.9508			−1.41336			−0.706679	−	0.707534i	$-0.749807\pi$
$881$	−41.9508			−1.41336			−0.706679	+	0.707534i	$0.749807\pi$
$882$	−2.46215	+	16.3475i	−0.0829049	+	0.550448i
$883$	23.6425			0.795634			0.397817	−	0.917465i	$-0.369768\pi$
$883$	23.6425			0.795634			0.397817	+	0.917465i	$0.369768\pi$
$884$	1.86373	−	3.22808i	0.0626841	−	0.108572i
$885$	−13.9577	−	24.1754i	−0.469182	−	0.812647i
$886$	1.04395	+	1.80818i	0.0350722	+	0.0607468i
$887$	9.10976	−	15.7786i	0.305876	−	0.529792i	−0.671580	−	0.740932i	$-0.734384\pi$
$887$	9.10976	−	15.7786i	0.305876	−	0.529792i	0.977456	+	0.211140i	$0.0677175\pi$
$888$	−20.3450			−0.682733
$889$	2.21454	−	6.32989i	0.0742732	−	0.212298i
$890$	8.96874			0.300633
$891$	−5.25374	+	9.09975i	−0.176007	+	0.304853i
$892$	3.07017	+	5.31770i	0.102797	+	0.178050i
$893$	24.5116	+	42.4553i	0.820248	+	1.42071i
$894$	−20.8984	+	36.1972i	−0.698948	+	1.21061i
$895$	−23.4500			−0.783847
$896$	−1.72590	−	2.00531i	−0.0576583	−	0.0669927i
$897$	−57.2332			−1.91096
$898$	−9.43144	+	16.3357i	−0.314731	+	0.545131i
$899$	2.55454	+	4.42460i	0.0851988	+	0.147569i
$900$	−1.18085	−	2.04528i	−0.0393615	−	0.0681762i
$901$	3.58035	−	6.20134i	0.119279	−	0.206597i
$902$	−1.13627			−0.0378336
$903$	70.8330	−	13.4063i	2.35717	−	0.446135i
$904$	0.342710			0.0113984
$905$	1.27158	−	2.20244i	0.0422688	−	0.0732117i
$906$	−25.8509	−	44.7750i	−0.858837	−	1.48755i
$907$	−9.54081	−	16.5252i	−0.316797	−	0.548709i	0.663021	−	0.748601i	$-0.269274\pi$
$907$	−9.54081	−	16.5252i	−0.316797	−	0.548709i	−0.979818	+	0.199892i	$0.935941\pi$
$908$	−1.43911	+	2.49261i	−0.0477585	+	0.0827202i
$909$	−4.49572			−0.149114
$910$	−17.0557	+	3.22808i	−0.565391	+	0.107010i
$911$	41.0299			1.35938			0.679690	−	0.733499i	$-0.262114\pi$
$911$	41.0299			1.35938			0.679690	+	0.733499i	$0.262114\pi$
$912$	−7.57290	+	13.1166i	−0.250764	+	0.434336i
$913$	1.92983	+	3.34256i	0.0638679	+	0.110622i
$914$	−12.5158	−	21.6781i	−0.413987	−	0.717047i
$915$	3.78517	−	6.55611i	0.125134	−	0.216738i
$916$	20.4383			0.675299
$917$	9.37486	+	10.8926i	0.309585	+	0.359705i
$918$	0.839716			0.0277148
$919$	−22.7098	+	39.3346i	−0.749129	+	1.29753i	0.199112	+	0.979977i	$0.436194\pi$
$919$	−22.7098	+	39.3346i	−0.749129	+	1.29753i	−0.948241	+	0.317552i	$0.897139\pi$
$920$	−1.88367	−	3.26261i	−0.0621026	−	0.107565i
$921$	6.05348	+	10.4849i	0.199469	+	0.345490i
$922$	3.15887	−	5.47132i	0.104032	−	0.180188i
$923$	68.5524			2.25643
$924$	2.02308	−	5.78265i	0.0665544	−	0.190235i
$925$	−8.78631			−0.288892
$926$	2.19920	−	3.80912i	0.0722702	−	0.125176i
$927$	−18.8764	−	32.6949i	−0.619983	−	1.07384i
$928$	−2.44183	−	4.22938i	−0.0801571	−	0.138836i
$929$	1.80669	−	3.12927i	0.0592755	−	0.102668i	−0.834865	−	0.550455i	$-0.814454\pi$
$929$	1.80669	−	3.12927i	0.0592755	−	0.102668i	0.894140	+	0.447787i	$0.147788\pi$
$930$	2.42241			0.0794341
$931$	42.6198	−	16.7324i	1.39681	−	0.548383i
$932$	−10.5559			−0.345769
$933$	−4.03623	+	6.99096i	−0.132140	+	0.228874i
$934$	4.13331	+	7.15911i	0.135246	+	0.234253i
$935$	0.284067	+	0.492018i	0.00928998	+	0.0160907i
$936$	−7.74740	+	13.4189i	−0.253232	+	0.438610i
$937$	−12.4953			−0.408203			−0.204102	−	0.978950i	$-0.565427\pi$
$937$	−12.4953			−0.408203			−0.204102	+	0.978950i	$0.565427\pi$
$938$	−2.06974	+	5.91601i	−0.0675793	+	0.193165i
$939$	29.1775			0.952171
$940$	−3.74740	+	6.49068i	−0.122227	+	0.211703i
$941$	7.10753	+	12.3106i	0.231699	+	0.401314i	0.958308	−	0.285737i	$-0.0922383\pi$
$941$	7.10753	+	12.3106i	0.231699	+	0.401314i	−0.726609	+	0.687051i	$0.758905\pi$
$942$	7.71862	+	13.3690i	0.251486	+	0.435587i
$943$	2.14035	−	3.70719i	0.0696994	−	0.120723i
$944$	−12.0557			−0.392379
$945$	−2.55092	−	2.96390i	−0.0829815	−	0.0964156i
$946$	−11.7673			−0.382589
$947$	−2.70759	+	4.68968i	−0.0879847	+	0.152394i	−0.906659	−	0.421864i	$-0.861376\pi$
$947$	−2.70759	+	4.68968i	−0.0879847	+	0.152394i	0.818674	+	0.574258i	$0.194709\pi$
$948$	−0.127405	−	0.220671i	−0.00413791	−	0.00716707i
$949$	−19.0054	−	32.9184i	−0.616943	−	1.06858i
$950$	−3.27048	+	5.66463i	−0.106108	+	0.183785i
$951$	−2.40777			−0.0780774
$952$	−1.47692	+	0.279532i	−0.0478673	+	0.00905970i
$953$	−31.8449			−1.03156			−0.515778	−	0.856722i	$-0.672497\pi$
$953$	−31.8449			−1.03156			−0.515778	+	0.856722i	$0.672497\pi$
$954$	−14.8832	+	25.7785i	−0.481863	+	0.834611i
$955$	−10.9525	−	18.9702i	−0.354413	−	0.613862i
$956$	−12.6421	−	21.8968i	−0.408876	−	0.708194i
$957$	5.65414	−	9.79327i	0.182773	−	0.316571i
$958$	7.37659			0.238327
$959$	−47.0412	+	8.90335i	−1.51904	+	0.287504i
$960$	−2.31553			−0.0747335
$961$	14.9528	−	25.8990i	0.482348	−	0.835451i
$962$	28.8230	+	49.9229i	0.929291	+	1.60958i
$963$	−5.74332	−	9.94772i	−0.185076	−	0.320561i
$964$	−2.92983	+	5.07461i	−0.0943633	+	0.163442i
$965$	6.83655			0.220076
$966$	15.0557	+	17.4931i	0.484409	+	0.562831i
$967$	41.1974			1.32482			0.662410	−	0.749142i	$-0.269534\pi$
$967$	41.1974			1.32482			0.662410	+	0.749142i	$0.269534\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$	4.30242	+	7.45201i	0.138214	+	0.239393i
$970$	0.782486	+	1.35531i	0.0251241	+	0.0435162i
$971$	−11.8069	+	20.4502i	−0.378902	+	0.656277i	−0.990903	−	0.134580i	$-0.957032\pi$
$971$	−11.8069	+	20.4502i	−0.378902	+	0.656277i	0.612001	+	0.790857i	$0.290365\pi$
$972$	−19.8964			−0.638176
$973$	14.3044	−	40.8867i	0.458577	−	1.31077i
$974$	28.8746			0.925203
$975$	−7.59598	+	13.1566i	−0.243266	+	0.421349i
$976$	−1.63469	−	2.83136i	−0.0523251	−	0.0906297i
$977$	−7.54096	−	13.0613i	−0.241257	−	0.417869i	0.719816	−	0.694165i	$-0.244226\pi$
$977$	−7.54096	−	13.0613i	−0.241257	−	0.417869i	−0.961072	+	0.276296i	$0.910893\pi$
$978$	−4.68085	+	8.10746i	−0.149677	+	0.259248i
$979$	8.96874			0.286642
$980$	5.47330	+	4.36383i	0.174838	+	0.139397i
$981$	−19.5649			−0.624659
$982$	19.4740	−	33.7299i	0.621439	−	1.07636i
$983$	−24.6238	−	42.6497i	−0.785378	−	1.36031i	−0.928773	−	0.370649i	$-0.879135\pi$
$983$	−24.6238	−	42.6497i	−0.785378	−	1.36031i	0.143395	−	0.989666i	$-0.454198\pi$
$984$	−1.31553	−	2.27857i	−0.0419376	−	0.0726381i
$985$	4.48689	−	7.77152i	0.142964	−	0.247621i
$986$	−2.77458			−0.0883605
$987$	15.1626	−	43.3398i	0.482630	−	1.37952i
$988$	42.9145			1.36529
$989$	22.1657	−	38.3922i	0.704829	−	1.22080i
$990$	−1.18085	−	2.04528i	−0.0375297	−	0.0650034i
$991$	−3.08108	−	5.33659i	−0.0978737	−	0.169522i	0.812931	−	0.582361i	$-0.197871\pi$
$991$	−3.08108	−	5.33659i	−0.0978737	−	0.169522i	−0.910804	+	0.412838i	$0.864537\pi$
$992$	0.523079	−	0.906000i	0.0166078	−	0.0287655i
$993$	47.6973			1.51363
$994$	−18.0333	−	20.9528i	−0.571982	−	0.664581i
$995$	20.7696			0.658441
$996$	−4.46857	+	7.73980i	−0.141592	+	0.245245i
$997$	−0.933907	−	1.61757i	−0.0295771	−	0.0512291i	0.850858	−	0.525396i	$-0.176083\pi$
$997$	−0.933907	−	1.61757i	−0.0295771	−	0.0512291i	−0.880435	+	0.474167i	$0.842749\pi$
$998$	13.7791	+	23.8660i	0.436169	+	0.755467i
$999$	−6.49319	+	11.2465i	−0.205436	+	0.355825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.l.331.1	yes	8
7.2	even	3		5390.2.a.ce.1.4		4
7.4	even	3	inner	770.2.i.l.221.1	✓	8
7.5	odd	6		5390.2.a.cf.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.l.221.1	✓	8	7.4	even	3	inner
770.2.i.l.331.1	yes	8	1.1	even	1	trivial
5390.2.a.ce.1.4		4	7.2	even	3
5390.2.a.cf.1.1		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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.15777 - 2.00531i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.31553 q^{6} +(-0.873699 + 2.49733i) q^{7} +1.00000 q^{8} +(-1.18085 + 2.04528i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.15777 - 2.00531i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.31553 q^{6} +(-0.873699 + 2.49733i) q^{7} +1.00000 q^{8} +(-1.18085 + 2.04528i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.15777 + 2.00531i) q^{12} +6.56089 q^{13} +(-1.72590 - 2.00531i) q^{14} -2.31553 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.284067 + 0.492018i) q^{17} +(-1.18085 - 2.04528i) q^{18} +(-3.27048 + 5.66463i) q^{19} -1.00000 q^{20} +(6.01946 - 1.13928i) q^{21} -1.00000 q^{22} +(1.88367 - 3.26261i) q^{23} +(-1.15777 - 2.00531i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.28045 + 5.68190i) q^{26} -1.47802 q^{27} +(2.59960 - 0.492018i) q^{28} +4.88367 q^{29} +(1.15777 - 2.00531i) q^{30} +(0.523079 + 0.906000i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.15777 - 2.00531i) q^{33} -0.568134 q^{34} +(1.72590 + 2.00531i) q^{35} +2.36169 q^{36} +(4.39316 - 7.60917i) q^{37} +(-3.27048 - 5.66463i) q^{38} +(-7.59598 - 13.1566i) q^{39} +(0.500000 - 0.866025i) q^{40} +1.13627 q^{41} +(-2.02308 + 5.78265i) q^{42} +11.7673 q^{43} +(0.500000 - 0.866025i) q^{44} +(1.18085 + 2.04528i) q^{45} +(1.88367 + 3.26261i) q^{46} +(3.74740 - 6.49068i) q^{47} +2.31553 q^{48} +(-5.47330 - 4.36383i) q^{49} +1.00000 q^{50} +(0.657766 - 1.13928i) q^{51} +(-3.28045 - 5.68190i) q^{52} +(-6.30194 - 10.9153i) q^{53} +(0.739012 - 1.28001i) q^{54} +1.00000 q^{55} +(-0.873699 + 2.49733i) q^{56} +15.1458 q^{57} +(-2.44183 + 4.22938i) q^{58} +(6.02784 + 10.4405i) q^{59} +(1.15777 + 2.00531i) q^{60} +(-1.63469 + 2.83136i) q^{61} -1.04616 q^{62} +(-4.07604 - 4.73592i) q^{63} +1.00000 q^{64} +(3.28045 - 5.68190i) q^{65} +(1.15777 + 2.00531i) q^{66} +(-1.18447 - 2.05156i) q^{67} +(0.284067 - 0.492018i) q^{68} -8.72338 q^{69} +(-2.59960 + 0.492018i) q^{70} +10.4486 q^{71} +(-1.18085 + 2.04528i) q^{72} +(-2.89678 - 5.01737i) q^{73} +(4.39316 + 7.60917i) q^{74} +(-1.15777 + 2.00531i) q^{75} +6.54096 q^{76} +(-2.59960 + 0.492018i) q^{77} +15.1920 q^{78} +(-0.0550218 + 0.0953005i) q^{79} +(0.500000 + 0.866025i) q^{80} +(5.25374 + 9.09975i) q^{81} +(-0.568134 + 0.984037i) q^{82} +3.85965 q^{83} +(-3.99638 - 4.64336i) q^{84} +0.568134 q^{85} +(-5.88367 + 10.1908i) q^{86} +(-5.65414 - 9.79327i) q^{87} +(0.500000 + 0.866025i) q^{88} +(4.48437 - 7.76716i) q^{89} -2.36169 q^{90} +(-5.73225 + 16.3847i) q^{91} -3.76733 q^{92} +(1.21121 - 2.09787i) q^{93} +(3.74740 + 6.49068i) q^{94} +(3.27048 + 5.66463i) q^{95} +(-1.15777 + 2.00531i) q^{96} +1.56497 q^{97} +(6.51584 - 2.55810i) q^{98} -2.36169 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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