LMFDB - Embedded newform 322.2.e.b.93.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
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			93.2
Root			$2.11692 + 0.978886i$ of defining polynomial
Character	$\chi$	$=$	322.93
Dual form			322.2.e.b.277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.313577 + 0.543132i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.475705 - 0.823946i) q^{5} -0.627155 q^{6} +(2.62597 + 0.322894i) q^{7} +1.00000 q^{8} +(1.30334 - 2.25745i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.313577 + 0.543132i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.475705 - 0.823946i) q^{5} -0.627155 q^{6} +(2.62597 + 0.322894i) q^{7} +1.00000 q^{8} +(1.30334 - 2.25745i) q^{9} +(0.475705 + 0.823946i) q^{10} +(-1.61692 - 2.80058i) q^{11} +(0.313577 - 0.543132i) q^{12} +0.439551 q^{13} +(-1.59262 + 2.11271i) q^{14} +0.596681 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.88528 + 4.99745i) q^{17} +(1.30334 + 2.25745i) q^{18} +(1.89714 - 3.28594i) q^{19} -0.951411 q^{20} +(0.648072 + 1.52750i) q^{21} +3.23383 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.313577 + 0.543132i) q^{24} +(2.04741 + 3.54622i) q^{25} +(-0.219776 + 0.380663i) q^{26} +3.51625 q^{27} +(-1.03335 - 2.43561i) q^{28} -2.06671 q^{29} +(-0.298341 + 0.516741i) q^{30} +(0.804519 + 1.39347i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.01406 - 1.75640i) q^{33} -5.77056 q^{34} +(1.51524 - 2.01006i) q^{35} -2.60668 q^{36} +(-2.65027 + 4.59040i) q^{37} +(1.89714 + 3.28594i) q^{38} +(0.137833 + 0.238734i) q^{39} +(0.475705 - 0.823946i) q^{40} -7.18524 q^{41} +(-1.64689 - 0.202504i) q^{42} -2.60904 q^{43} +(-1.61692 + 2.80058i) q^{44} +(-1.24001 - 2.14776i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(1.23163 - 2.13325i) q^{47} -0.627155 q^{48} +(6.79148 + 1.69582i) q^{49} -4.09482 q^{50} +(-1.80952 + 3.13418i) q^{51} +(-0.219776 - 0.380663i) q^{52} +(1.01068 + 1.75055i) q^{53} +(-1.75813 + 3.04516i) q^{54} -3.07670 q^{55} +(2.62597 + 0.322894i) q^{56} +2.37960 q^{57} +(1.03335 - 1.78982i) q^{58} +(-4.86886 - 8.43312i) q^{59} +(-0.298341 - 0.516741i) q^{60} +(7.44337 - 12.8923i) q^{61} -1.60904 q^{62} +(4.15145 - 5.50716i) q^{63} +1.00000 q^{64} +(0.209097 - 0.362166i) q^{65} +(1.01406 + 1.75640i) q^{66} +(-0.998820 - 1.73001i) q^{67} +(2.88528 - 4.99745i) q^{68} -0.627155 q^{69} +(0.983143 + 2.31726i) q^{70} -13.6891 q^{71} +(1.30334 - 2.25745i) q^{72} +(3.63503 + 6.29606i) q^{73} +(-2.65027 - 4.59040i) q^{74} +(-1.28404 + 2.22403i) q^{75} -3.79428 q^{76} +(-3.34169 - 7.87634i) q^{77} -0.275667 q^{78} +(-4.20954 + 7.29113i) q^{79} +(0.475705 + 0.823946i) q^{80} +(-2.80740 - 4.86256i) q^{81} +(3.59262 - 6.22260i) q^{82} -12.5706 q^{83} +(0.998820 - 1.32500i) q^{84} +5.49017 q^{85} +(1.30452 - 2.25949i) q^{86} +(-0.648072 - 1.12249i) q^{87} +(-1.61692 - 2.80058i) q^{88} +(-3.08238 + 5.33884i) q^{89} +2.48002 q^{90} +(1.15425 + 0.141928i) q^{91} +1.00000 q^{92} +(-0.504558 + 0.873920i) q^{93} +(1.23163 + 2.13325i) q^{94} +(-1.80496 - 3.12628i) q^{95} +(0.313577 - 0.543132i) q^{96} -0.280060 q^{97} +(-4.86436 + 5.03368i) q^{98} -8.42956 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9	\( 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9} + 5 q^{10} + 2 q^{11} + 5 q^{12} - 14 q^{13} + q^{14} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{18} + 9 q^{19} - 10 q^{20} + 25 q^{21} - 4 q^{22} - 4 q^{23} + 5 q^{24} - 11 q^{25} + 7 q^{26} - 34 q^{27} - 2 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} - 4 q^{32} - 13 q^{33} + 6 q^{34} + 16 q^{35} + 14 q^{36} + 9 q^{38} + q^{39} + 5 q^{40} - 30 q^{41} - 8 q^{42} - 36 q^{43} + 2 q^{44} + 11 q^{45} - 4 q^{46} + 21 q^{47} - 10 q^{48} + 17 q^{49} + 22 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} + 17 q^{54} + 20 q^{55} + q^{56} - 18 q^{57} + 2 q^{58} + 16 q^{59} - q^{60} + q^{61} - 28 q^{62} + 37 q^{63} + 8 q^{64} - 2 q^{65} - 13 q^{66} + 17 q^{67} - 3 q^{68} - 10 q^{69} + 4 q^{70} - 2 q^{71} - 7 q^{72} + 4 q^{73} + 22 q^{75} - 18 q^{76} + 13 q^{77} - 2 q^{78} - 5 q^{79} + 5 q^{80} - 16 q^{81} + 15 q^{82} - 8 q^{83} - 17 q^{84} - 108 q^{85} + 18 q^{86} - 25 q^{87} + 2 q^{88} + 9 q^{89} - 22 q^{90} + 38 q^{91} + 8 q^{92} - 13 q^{93} + 21 q^{94} + 3 q^{95} + 5 q^{96} + 80 q^{97} + 2 q^{98} - 82 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9 + 5 * q^10 + 2 * q^11 + 5 * q^12 - 14 * q^13 + q^14 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^18 + 9 * q^19 - 10 * q^20 + 25 * q^21 - 4 * q^22 - 4 * q^23 + 5 * q^24 - 11 * q^25 + 7 * q^26 - 34 * q^27 - 2 * q^28 - 4 * q^29 - q^30 + 14 * q^31 - 4 * q^32 - 13 * q^33 + 6 * q^34 + 16 * q^35 + 14 * q^36 + 9 * q^38 + q^39 + 5 * q^40 - 30 * q^41 - 8 * q^42 - 36 * q^43 + 2 * q^44 + 11 * q^45 - 4 * q^46 + 21 * q^47 - 10 * q^48 + 17 * q^49 + 22 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 + 17 * q^54 + 20 * q^55 + q^56 - 18 * q^57 + 2 * q^58 + 16 * q^59 - q^60 + q^61 - 28 * q^62 + 37 * q^63 + 8 * q^64 - 2 * q^65 - 13 * q^66 + 17 * q^67 - 3 * q^68 - 10 * q^69 + 4 * q^70 - 2 * q^71 - 7 * q^72 + 4 * q^73 + 22 * q^75 - 18 * q^76 + 13 * q^77 - 2 * q^78 - 5 * q^79 + 5 * q^80 - 16 * q^81 + 15 * q^82 - 8 * q^83 - 17 * q^84 - 108 * q^85 + 18 * q^86 - 25 * q^87 + 2 * q^88 + 9 * q^89 - 22 * q^90 + 38 * q^91 + 8 * q^92 - 13 * q^93 + 21 * q^94 + 3 * q^95 + 5 * q^96 + 80 * q^97 + 2 * q^98 - 82 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.313577	+	0.543132i	0.181044	+	0.313577i	0.942236	−	0.334949i	$-0.108719\pi$
$3$	0.313577	+	0.543132i	0.181044	+	0.313577i	−0.761192	+	0.648526i	$0.775386\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.475705	−	0.823946i	0.212742	−	0.368480i	−0.739830	−	0.672794i	$-0.765094\pi$
$5$	0.475705	−	0.823946i	0.212742	−	0.368480i	0.952572	+	0.304314i	$0.0984273\pi$
$6$	−0.627155			−0.256035
$7$	2.62597	+	0.322894i	0.992525	+	0.122042i
$7$	2.62597	+	0.322894i	0.992525	+	0.122042i
$8$	1.00000			0.353553
$9$	1.30334	−	2.25745i	0.434446	−	0.752483i
$10$	0.475705	+	0.823946i	0.150431	+	0.260555i
$11$	−1.61692	−	2.80058i	−0.487518	−	0.844407i	0.512379	−	0.858760i	$-0.328764\pi$
$11$	−1.61692	−	2.80058i	−0.487518	−	0.844407i	−0.999897	+	0.0143529i	$0.995431\pi$
$12$	0.313577	−	0.543132i	0.0905220	−	0.156789i
$13$	0.439551			0.121910			0.0609548	−	0.998141i	$-0.480585\pi$
$13$	0.439551			0.121910			0.0609548	+	0.998141i	$0.480585\pi$
$14$	−1.59262	+	2.11271i	−0.425646	+	0.564646i
$15$	0.596681			0.154062
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.88528	+	4.99745i	0.699783	+	1.21206i	0.968541	+	0.248853i	$0.0800535\pi$
$17$	2.88528	+	4.99745i	0.699783	+	1.21206i	−0.268758	+	0.963208i	$0.586613\pi$
$18$	1.30334	+	2.25745i	0.307200	+	0.532086i
$19$	1.89714	−	3.28594i	0.435234	−	0.753847i	−0.562081	−	0.827082i	$-0.689999\pi$
$19$	1.89714	−	3.28594i	0.435234	−	0.753847i	0.997315	+	0.0732352i	$0.0233324\pi$
$20$	−0.951411			−0.212742
$21$	0.648072	+	1.52750i	0.141421	+	0.333328i
$22$	3.23383			0.689455
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i
$24$	0.313577	+	0.543132i	0.0640087	+	0.110866i
$25$	2.04741	+	3.54622i	0.409482	+	0.709243i
$26$	−0.219776	+	0.380663i	−0.0431016	+	0.0746541i
$27$	3.51625			0.676703
$28$	−1.03335	−	2.43561i	−0.195285	−	0.460286i
$29$	−2.06671			−0.383778			−0.191889	−	0.981417i	$-0.561461\pi$
$29$	−2.06671			−0.383778			−0.191889	+	0.981417i	$0.561461\pi$
$30$	−0.298341	+	0.516741i	−0.0544693	+	0.0943436i
$31$	0.804519	+	1.39347i	0.144496	+	0.250274i	0.929185	−	0.369616i	$-0.120511\pi$
$31$	0.804519	+	1.39347i	0.144496	+	0.250274i	−0.784689	+	0.619890i	$0.787177\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.01406	−	1.75640i	0.176525	−	0.305749i
$34$	−5.77056			−0.989643
$35$	1.51524	−	2.01006i	0.256122	−	0.339762i
$36$	−2.60668			−0.434446
$37$	−2.65027	+	4.59040i	−0.435702	+	0.754657i	−0.997353	−	0.0727170i	$-0.976833\pi$
$37$	−2.65027	+	4.59040i	−0.435702	+	0.754657i	0.561651	+	0.827374i	$0.310166\pi$
$38$	1.89714	+	3.28594i	0.307757	+	0.533050i
$39$	0.137833	+	0.238734i	0.0220710	+	0.0382281i
$40$	0.475705	−	0.823946i	0.0752156	−	0.130277i
$41$	−7.18524			−1.12215			−0.561073	−	0.827766i	$-0.689611\pi$
$41$	−7.18524			−1.12215			−0.561073	+	0.827766i	$0.689611\pi$
$42$	−1.64689	−	0.202504i	−0.254121	−	0.0312471i
$43$	−2.60904			−0.397875			−0.198937	−	0.980012i	$-0.563749\pi$
$43$	−2.60904			−0.397875			−0.198937	+	0.980012i	$0.563749\pi$
$44$	−1.61692	+	2.80058i	−0.243759	+	0.422203i
$45$	−1.24001	−	2.14776i	−0.184850	−	0.320169i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	1.23163	−	2.13325i	0.179652	−	0.311167i	−0.762109	−	0.647449i	$-0.775836\pi$
$47$	1.23163	−	2.13325i	0.179652	−	0.311167i	0.941762	+	0.336282i	$0.109169\pi$
$48$	−0.627155			−0.0905220
$49$	6.79148	+	1.69582i	0.970211	+	0.242260i
$50$	−4.09482			−0.579095
$51$	−1.80952	+	3.13418i	−0.253383	+	0.438872i
$52$	−0.219776	−	0.380663i	−0.0304774	−	0.0527884i
$53$	1.01068	+	1.75055i	0.138827	+	0.240456i	0.927053	−	0.374930i	$-0.122333\pi$
$53$	1.01068	+	1.75055i	0.138827	+	0.240456i	−0.788226	+	0.615386i	$0.789000\pi$
$54$	−1.75813	+	3.04516i	−0.239251	+	0.414394i
$55$	−3.07670			−0.414862
$56$	2.62597	+	0.322894i	0.350911	+	0.0431485i
$57$	2.37960			0.315186
$58$	1.03335	−	1.78982i	0.135686	−	0.235015i
$59$	−4.86886	−	8.43312i	−0.633872	−	1.09790i	−0.986753	−	0.162230i	$-0.948131\pi$
$59$	−4.86886	−	8.43312i	−0.633872	−	1.09790i	0.352881	−	0.935668i	$-0.385202\pi$
$60$	−0.298341	−	0.516741i	−0.0385156	−	0.0667110i
$61$	7.44337	−	12.8923i	0.953026	−	1.65069i	0.214203	−	0.976789i	$-0.431285\pi$
$61$	7.44337	−	12.8923i	0.953026	−	1.65069i	0.738823	−	0.673900i	$-0.235382\pi$
$62$	−1.60904			−0.204348
$63$	4.15145	−	5.50716i	0.523033	−	0.693837i
$64$	1.00000			0.125000
$65$	0.209097	−	0.362166i	0.0259353	−	0.0449212i
$66$	1.01406	+	1.75640i	0.124822	+	0.216197i
$67$	−0.998820	−	1.73001i	−0.122025	−	0.211354i	0.798541	−	0.601940i	$-0.205606\pi$
$67$	−0.998820	−	1.73001i	−0.122025	−	0.211354i	−0.920566	+	0.390587i	$0.872272\pi$
$68$	2.88528	−	4.99745i	0.349892	−	0.606030i
$69$	−0.627155			−0.0755005
$70$	0.983143	+	2.31726i	0.117508	+	0.276966i
$71$	−13.6891			−1.62460			−0.812301	−	0.583239i	$-0.801785\pi$
$71$	−13.6891			−1.62460			−0.812301	+	0.583239i	$0.801785\pi$
$72$	1.30334	−	2.25745i	0.153600	−	0.266043i
$73$	3.63503	+	6.29606i	0.425448	+	0.736898i	0.996462	−	0.0840423i	$-0.0267831\pi$
$73$	3.63503	+	6.29606i	0.425448	+	0.736898i	−0.571014	+	0.820940i	$0.693450\pi$
$74$	−2.65027	−	4.59040i	−0.308087	−	0.533623i
$75$	−1.28404	+	2.22403i	−0.148268	+	0.256808i
$76$	−3.79428			−0.435234
$77$	−3.34169	−	7.87634i	−0.380821	−	0.897593i
$78$	−0.275667			−0.0312131
$79$	−4.20954	+	7.29113i	−0.473610	+	0.820316i	−0.999544	−	0.0302091i	$-0.990383\pi$
$79$	−4.20954	+	7.29113i	−0.473610	+	0.820316i	0.525934	+	0.850526i	$0.323716\pi$
$80$	0.475705	+	0.823946i	0.0531855	+	0.0921199i
$81$	−2.80740	−	4.86256i	−0.311933	−	0.540284i
$82$	3.59262	−	6.22260i	0.396739	−	0.687171i
$83$	−12.5706			−1.37980			−0.689901	−	0.723903i	$-0.742346\pi$
$83$	−12.5706			−1.37980			−0.689901	+	0.723903i	$0.742346\pi$
$84$	0.998820	−	1.32500i	0.108980	−	0.144569i
$85$	5.49017			0.595493
$86$	1.30452	−	2.25949i	0.140670	−	0.243647i
$87$	−0.648072	−	1.12249i	−0.0694806	−	0.120344i
$88$	−1.61692	−	2.80058i	−0.172364	−	0.298543i
$89$	−3.08238	+	5.33884i	−0.326732	+	0.565916i	−0.981861	−	0.189600i	$-0.939281\pi$
$89$	−3.08238	+	5.33884i	−0.326732	+	0.565916i	0.655129	+	0.755517i	$0.272614\pi$
$90$	2.48002			0.261417
$91$	1.15425	+	0.141928i	0.120998	+	0.0148781i
$92$	1.00000			0.104257
$93$	−0.504558	+	0.873920i	−0.0523202	+	0.0906213i
$94$	1.23163	+	2.13325i	0.127033	+	0.220028i
$95$	−1.80496	−	3.12628i	−0.185185	−	0.320750i
$96$	0.313577	−	0.543132i	0.0320043	−	0.0554332i
$97$	−0.280060			−0.0284358			−0.0142179	−	0.999899i	$-0.504526\pi$
$97$	−0.280060			−0.0284358			−0.0142179	+	0.999899i	$0.504526\pi$
$98$	−4.86436	+	5.03368i	−0.491375	+	0.508479i
$99$	−8.42956			−0.847202
$100$	2.04741	−	3.54622i	0.204741	−	0.354622i
$101$	1.04115	+	1.80333i	0.103598	+	0.179438i	0.913165	−	0.407591i	$-0.133631\pi$
$101$	1.04115	+	1.80333i	0.103598	+	0.179438i	−0.809566	+	0.587029i	$0.800298\pi$
$102$	−1.80952	−	3.13418i	−0.179169	−	0.310330i
$103$	0.510239	−	0.883759i	0.0502753	−	0.0870794i	−0.839793	−	0.542907i	$-0.817323\pi$
$103$	0.510239	−	0.883759i	0.0502753	−	0.0870794i	0.890068	+	0.455828i	$0.150657\pi$
$104$	0.439551			0.0431016
$105$	1.56687	+	0.192665i	0.152911	+	0.0188021i
$106$	−2.02136			−0.196332
$107$	2.26718	−	3.92688i	0.219177	−	0.379626i	−0.735380	−	0.677655i	$-0.762996\pi$
$107$	2.26718	−	3.92688i	0.219177	−	0.379626i	0.954557	+	0.298030i	$0.0963294\pi$
$108$	−1.75813	−	3.04516i	−0.169176	−	0.293021i
$109$	5.37910	+	9.31688i	0.515225	+	0.892395i	0.999844	+	0.0176700i	$0.00562482\pi$
$109$	5.37910	+	9.31688i	0.515225	+	0.892395i	−0.484619	+	0.874725i	$0.661042\pi$
$110$	1.53835	−	2.66450i	0.146676	−	0.254050i
$111$	−3.32426			−0.315524
$112$	−1.59262	+	2.11271i	−0.150489	+	0.199633i
$113$	−10.6520			−1.00206			−0.501029	−	0.865430i	$-0.667045\pi$
$113$	−10.6520			−1.00206			−0.501029	+	0.865430i	$0.667045\pi$
$114$	−1.18980	+	2.06079i	−0.111435	+	0.193011i
$115$	0.475705	+	0.823946i	0.0443597	+	0.0768333i
$116$	1.03335	+	1.78982i	0.0959444	+	0.166181i
$117$	0.572884	−	0.992265i	0.0529632	−	0.0917349i
$118$	9.73773			0.896431
$119$	5.96303	+	14.0548i	0.546630	+	1.28840i
$120$	0.596681			0.0544693
$121$	0.271166	−	0.469674i	0.0246515	−	0.0426976i
$122$	7.44337	+	12.8923i	0.673891	+	1.16721i
$123$	−2.25313	−	3.90253i	−0.203158	−	0.351880i
$124$	0.804519	−	1.39347i	0.0722479	−	0.125137i
$125$	8.65291			0.773939
$126$	2.69362	+	6.34884i	0.239967	+	0.565600i
$127$	−19.3535			−1.71735			−0.858674	−	0.512523i	$-0.828711\pi$
$127$	−19.3535			−1.71735			−0.858674	+	0.512523i	$0.828711\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−0.818135	−	1.41705i	−0.0720328	−	0.124764i
$130$	0.209097	+	0.362166i	0.0183390	+	0.0317641i
$131$	2.98932	−	5.17766i	0.261178	−	0.452374i	−0.705377	−	0.708832i	$-0.749222\pi$
$131$	2.98932	−	5.17766i	0.261178	−	0.452374i	0.966555	+	0.256458i	$0.0825556\pi$
$132$	−2.02811			−0.176525
$133$	6.04285	−	8.01623i	0.523982	−	0.695095i
$134$	1.99764			0.172570
$135$	1.67270	−	2.89720i	0.143963	−	0.249351i
$136$	2.88528	+	4.99745i	0.247411	+	0.428528i
$137$	9.02531	+	15.6323i	0.771084	+	1.33556i	0.936969	+	0.349412i	$0.113619\pi$
$137$	9.02531	+	15.6323i	0.771084	+	1.33556i	−0.165885	+	0.986145i	$0.553048\pi$
$138$	0.313577	−	0.543132i	0.0266935	−	0.0462344i
$139$	14.0258			1.18965			0.594824	−	0.803856i	$-0.297222\pi$
$139$	14.0258			1.18965			0.594824	+	0.803856i	$0.297222\pi$
$140$	−2.49838	−	0.307204i	−0.211152	−	0.0259635i
$141$	1.54485			0.130100
$142$	6.84457	−	11.8551i	0.574383	−	0.994861i
$143$	−0.710717	−	1.23100i	−0.0594332	−	0.102941i
$144$	1.30334	+	2.25745i	0.108612	+	0.188121i
$145$	−0.983143	+	1.70285i	−0.0816456	+	0.141414i
$146$	−7.27006			−0.601675
$147$	1.20860	+	4.22044i	0.0996836	+	0.348096i
$148$	5.30054			0.435702
$149$	−8.90721	+	15.4277i	−0.729707	+	1.26389i	0.227299	+	0.973825i	$0.427010\pi$
$149$	−8.90721	+	15.4277i	−0.729707	+	1.26389i	−0.957007	+	0.290065i	$0.906323\pi$
$150$	−1.28404	−	2.22403i	−0.104842	−	0.181591i
$151$	−4.63665	−	8.03092i	−0.377325	−	0.653547i	0.613347	−	0.789814i	$-0.289823\pi$
$151$	−4.63665	−	8.03092i	−0.377325	−	0.653547i	−0.990672	+	0.136267i	$0.956490\pi$
$152$	1.89714	−	3.28594i	0.153878	−	0.266525i
$153$	15.0420			1.21607
$154$	8.49196	+	1.04418i	0.684301	+	0.0841427i
$155$	1.53086			0.122961
$156$	0.137833	−	0.238734i	0.0110355	−	0.0191140i
$157$	2.83169	+	4.90464i	0.225994	+	0.391433i	0.956617	−	0.291348i	$-0.0941038\pi$
$157$	2.83169	+	4.90464i	0.225994	+	0.391433i	−0.730623	+	0.682781i	$0.760770\pi$
$158$	−4.20954	−	7.29113i	−0.334893	−	0.580051i
$159$	−0.633852	+	1.09786i	−0.0502677	+	0.0870662i
$160$	−0.951411			−0.0752156
$161$	−1.59262	+	2.11271i	−0.125516	+	0.166505i
$162$	5.61480			0.441140
$163$	−6.64571	+	11.5107i	−0.520532	+	0.901588i	0.479183	+	0.877715i	$0.340933\pi$
$163$	−6.64571	+	11.5107i	−0.520532	+	0.901588i	−0.999715	+	0.0238732i	$0.992400\pi$
$164$	3.59262	+	6.22260i	0.280537	+	0.485904i
$165$	−0.964784	−	1.67105i	−0.0751083	−	0.130091i
$166$	6.28530	−	10.8865i	0.487834	−	0.844953i
$167$	4.23059			0.327373			0.163686	−	0.986512i	$-0.447661\pi$
$167$	4.23059			0.327373			0.163686	+	0.986512i	$0.447661\pi$
$168$	0.648072	+	1.52750i	0.0499998	+	0.117849i
$169$	−12.8068			−0.985138
$170$	−2.74509	+	4.75463i	−0.210539	+	0.364663i
$171$	−4.94523	−	8.56539i	−0.378171	−	0.655012i
$172$	1.30452	+	2.25949i	0.0994686	+	0.172285i
$173$	−6.38866	+	11.0655i	−0.485721	+	0.841293i	−0.999865	−	0.0164106i	$-0.994776\pi$
$173$	−6.38866	+	11.0655i	−0.485721	+	0.841293i	0.514145	+	0.857703i	$0.328109\pi$
$174$	1.29614			0.0982604
$175$	4.23139	+	9.97337i	0.319863	+	0.753916i
$176$	3.23383			0.243759
$177$	3.05353	−	5.28887i	0.229517	−	0.397536i
$178$	−3.08238	−	5.33884i	−0.231034	−	0.400163i
$179$	5.87004	+	10.1672i	0.438748	+	0.759933i	0.997593	−	0.0693385i	$-0.0220888\pi$
$179$	5.87004	+	10.1672i	0.438748	+	0.759933i	−0.558845	+	0.829272i	$0.688756\pi$
$180$	−1.24001	+	2.14776i	−0.0924249	+	0.160085i
$181$	19.6257			1.45876			0.729382	−	0.684106i	$-0.239808\pi$
$181$	19.6257			1.45876			0.729382	+	0.684106i	$0.239808\pi$
$182$	−0.700039	+	0.928646i	−0.0518903	+	0.0688358i
$183$	9.33628			0.690158
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	2.52149	+	4.36736i	0.185384	+	0.321094i
$186$	−0.504558	−	0.873920i	−0.0369960	−	0.0640789i
$187$	9.33051	−	16.1609i	0.682315	−	1.18180i
$188$	−2.46327			−0.179652
$189$	9.23359	+	1.13538i	0.671645	+	0.0825864i
$190$	3.60992			0.261891
$191$	−10.1027	+	17.4984i	−0.731005	+	1.26614i	0.225449	+	0.974255i	$0.427615\pi$
$191$	−10.1027	+	17.4984i	−0.731005	+	1.26614i	−0.956454	+	0.291883i	$0.905718\pi$
$192$	0.313577	+	0.543132i	0.0226305	+	0.0391972i
$193$	−10.3055	−	17.8497i	−0.741809	−	1.28485i	−0.951671	−	0.307119i	$-0.900635\pi$
$193$	−10.3055	−	17.8497i	−0.741809	−	1.28485i	0.209862	−	0.977731i	$-0.432698\pi$
$194$	0.140030	−	0.242539i	0.0100536	−	0.0174133i
$195$	0.262272			0.0187817
$196$	−1.92712	−	6.72950i	−0.137651	−	0.480679i
$197$	10.4258			0.742810			0.371405	−	0.928471i	$-0.378876\pi$
$197$	10.4258			0.742810			0.371405	+	0.928471i	$0.378876\pi$
$198$	4.21478	−	7.30021i	0.299531	−	0.518803i
$199$	7.74915	+	13.4219i	0.549322	+	0.951454i	0.998321	+	0.0579220i	$0.0184475\pi$
$199$	7.74915	+	13.4219i	0.549322	+	0.951454i	−0.448999	+	0.893532i	$0.648219\pi$
$200$	2.04741	+	3.54622i	0.144774	+	0.250755i
$201$	0.626414	−	1.08498i	0.0441838	−	0.0765287i
$202$	−2.08230			−0.146510
$203$	−5.42712	−	0.667326i	−0.380909	−	0.0468371i
$204$	3.61903			0.253383
$205$	−3.41806	+	5.92025i	−0.238728	+	0.413488i
$206$	0.510239	+	0.883759i	0.0355500	+	0.0615744i
$207$	1.30334	+	2.25745i	0.0905883	+	0.156904i
$208$	−0.219776	+	0.380663i	−0.0152387	+	0.0263942i
$209$	−12.2701			−0.848738
$210$	−0.950287	+	1.26062i	−0.0655761	+	0.0869908i
$211$	−14.1490			−0.974058			−0.487029	−	0.873386i	$-0.661919\pi$
$211$	−14.1490			−0.974058			−0.487029	+	0.873386i	$0.661919\pi$
$212$	1.01068	−	1.75055i	0.0694137	−	0.120228i
$213$	−4.29260	−	7.43501i	−0.294124	−	0.509438i
$214$	2.26718	+	3.92688i	0.154982	+	0.268436i
$215$	−1.24113	+	2.14971i	−0.0846446	+	0.146609i
$216$	3.51625			0.239251
$217$	1.66270	+	3.91898i	0.112872	+	0.266038i
$218$	−10.7582			−0.728638
$219$	−2.27973	+	3.94860i	−0.154050	+	0.266822i
$220$	1.53835	+	2.66450i	0.103716	+	0.179641i
$221$	1.26823	+	2.19664i	0.0853103	+	0.147762i
$222$	1.66213	−	2.87889i	0.111555	−	0.193218i
$223$	16.1888			1.08408			0.542040	−	0.840353i	$-0.317652\pi$
$223$	16.1888			1.08408			0.542040	+	0.840353i	$0.317652\pi$
$224$	−1.03335	−	2.43561i	−0.0690438	−	0.162736i
$225$	10.6739			0.711591
$226$	5.32601	−	9.22492i	0.354281	−	0.613633i
$227$	−11.2999	−	19.5719i	−0.749998	−	1.29903i	−0.947823	−	0.318797i	$-0.896721\pi$
$227$	−11.2999	−	19.5719i	−0.749998	−	1.29903i	0.197825	−	0.980237i	$-0.436612\pi$
$228$	−1.18980	−	2.06079i	−0.0787964	−	0.136479i
$229$	−14.8275	+	25.6819i	−0.979827	+	1.69711i	−0.316839	+	0.948479i	$0.602622\pi$
$229$	−14.8275	+	25.6819i	−0.979827	+	1.69711i	−0.662988	+	0.748630i	$0.730712\pi$
$230$	−0.951411			−0.0627342
$231$	3.23001	−	4.28482i	0.212519	−	0.281920i
$232$	−2.06671			−0.135686
$233$	10.7812	−	18.6737i	0.706303	−	1.22335i	−0.259917	−	0.965631i	$-0.583695\pi$
$233$	10.7812	−	18.6737i	0.706303	−	1.22335i	0.966219	−	0.257721i	$-0.0829715\pi$
$234$	0.572884	+	0.992265i	0.0374506	+	0.0648664i
$235$	−1.17179	−	2.02960i	−0.0764392	−	0.132397i
$236$	−4.86886	+	8.43312i	−0.316936	+	0.548949i
$237$	−5.28006			−0.342977
$238$	−15.1533	−	1.86328i	−0.982246	−	0.120778i
$239$	2.61579			0.169202			0.0846008	−	0.996415i	$-0.473039\pi$
$239$	2.61579			0.169202			0.0846008	+	0.996415i	$0.473039\pi$
$240$	−0.298341	+	0.516741i	−0.0192578	+	0.0333555i
$241$	−6.74083	−	11.6755i	−0.434215	−	0.752082i	0.563016	−	0.826446i	$-0.309641\pi$
$241$	−6.74083	−	11.6755i	−0.434215	−	0.752082i	−0.997231	+	0.0743634i	$0.976308\pi$
$242$	0.271166	+	0.469674i	0.0174312	+	0.0301918i
$243$	7.03505	−	12.1851i	0.451299	−	0.781672i
$244$	−14.8867			−0.953026
$245$	4.62801	−	4.78910i	0.295673	−	0.305964i
$246$	4.50626			0.287308
$247$	0.833890	−	1.44434i	0.0530592	−	0.0919012i
$248$	0.804519	+	1.39347i	0.0510870	+	0.0884853i
$249$	−3.94185	−	6.82749i	−0.249805	−	0.432675i
$250$	−4.32645	+	7.49364i	−0.273629	+	0.473939i
$251$	−14.6719			−0.926082			−0.463041	−	0.886337i	$-0.653242\pi$
$251$	−14.6719			−0.926082			−0.463041	+	0.886337i	$0.653242\pi$
$252$	−6.84507	−	0.841680i	−0.431199	−	0.0530208i
$253$	3.23383			0.203309
$254$	9.67676	−	16.7606i	0.607174	−	1.05166i
$255$	1.72159	+	2.98189i	0.107810	+	0.186733i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.81621	−	6.60988i	0.238049	−	0.412313i	−0.722105	−	0.691783i	$-0.756825\pi$
$257$	3.81621	−	6.60988i	0.238049	−	0.412313i	0.960154	+	0.279470i	$0.0901588\pi$
$258$	1.63627			0.101870
$259$	−8.44175	+	11.1985i	−0.524545	+	0.695842i
$260$	−0.418194			−0.0259353
$261$	−2.69362	+	4.66548i	−0.166731	+	0.288786i
$262$	2.98932	+	5.17766i	0.184681	+	0.319877i
$263$	−1.91026	−	3.30867i	−0.117792	−	0.204021i	0.801101	−	0.598530i	$-0.204248\pi$
$263$	−1.91026	−	3.30867i	−0.117792	−	0.204021i	−0.918892	+	0.394509i	$0.870915\pi$
$264$	1.01406	−	1.75640i	0.0624108	−	0.108099i
$265$	1.92314			0.118138
$266$	3.92083	+	9.24138i	0.240402	+	0.566625i
$267$	−3.86626			−0.236611
$268$	−0.998820	+	1.73001i	−0.0610126	+	0.105677i
$269$	−4.59018	−	7.95043i	−0.279868	−	0.484746i	0.691483	−	0.722392i	$-0.256957\pi$
$269$	−4.59018	−	7.95043i	−0.279868	−	0.484746i	−0.971352	+	0.237646i	$0.923624\pi$
$270$	1.67270	+	2.89720i	0.101797	+	0.176318i
$271$	11.4587	−	19.8470i	0.696065	−	1.20562i	−0.273755	−	0.961800i	$-0.588266\pi$
$271$	11.4587	−	19.8470i	0.696065	−	1.20562i	0.969820	−	0.243821i	$-0.0784010\pi$
$272$	−5.77056			−0.349892
$273$	0.284861	+	0.671415i	0.0172406	+	0.0406359i
$274$	−18.0506			−1.09048
$275$	6.62098	−	11.4679i	0.399260	−	0.691538i
$276$	0.313577	+	0.543132i	0.0188751	+	0.0326927i
$277$	−4.95155	−	8.57633i	−0.297510	−	0.515302i	0.678056	−	0.735010i	$-0.262823\pi$
$277$	−4.95155	−	8.57633i	−0.297510	−	0.515302i	−0.975566	+	0.219709i	$0.929489\pi$
$278$	−7.01288	+	12.1467i	−0.420604	+	0.728508i
$279$	4.19424			0.251103
$280$	1.51524	−	2.01006i	0.0905527	−	0.120124i
$281$	−4.04387			−0.241237			−0.120618	−	0.992699i	$-0.538488\pi$
$281$	−4.04387			−0.241237			−0.120618	+	0.992699i	$0.538488\pi$
$282$	−0.772425	+	1.33788i	−0.0459973	+	0.0796696i
$283$	−3.77668	−	6.54141i	−0.224500	−	0.388846i	0.731669	−	0.681660i	$-0.238742\pi$
$283$	−3.77668	−	6.54141i	−0.224500	−	0.388846i	−0.956169	+	0.292814i	$0.905408\pi$
$284$	6.84457	+	11.8551i	0.406150	+	0.703473i
$285$	1.13199	−	1.96066i	0.0670532	−	0.116140i
$286$	1.42143			0.0840512
$287$	−18.8683	−	2.32007i	−1.11376	−	0.136949i
$288$	−2.60668			−0.153600
$289$	−8.14969	+	14.1157i	−0.479394	+	0.830334i
$290$	−0.983143	−	1.70285i	−0.0577321	−	0.0999950i
$291$	−0.0878205	−	0.152110i	−0.00514813	−	0.00891682i
$292$	3.63503	−	6.29606i	0.212724	−	0.368449i
$293$	3.36049			0.196322			0.0981609	−	0.995171i	$-0.468704\pi$
$293$	3.36049			0.196322			0.0981609	+	0.995171i	$0.468704\pi$
$294$	−4.25931	−	1.06354i	−0.248408	−	0.0620270i
$295$	−9.26458			−0.539405
$296$	−2.65027	+	4.59040i	−0.154044	+	0.266812i
$297$	−5.68549	−	9.84755i	−0.329905	−	0.571413i
$298$	−8.90721	−	15.4277i	−0.515981	−	0.893705i
$299$	−0.219776	+	0.380663i	−0.0127100	+	0.0220143i
$300$	2.56808			0.148268
$301$	−6.85127	−	0.842442i	−0.394900	−	0.0485575i
$302$	9.27331			0.533619
$303$	−0.652963	+	1.13097i	−0.0375117	+	0.0649723i
$304$	1.89714	+	3.28594i	0.108808	+	0.188462i
$305$	−7.08170	−	12.2659i	−0.405497	−	0.702341i
$306$	−7.52100	+	13.0267i	−0.429947	+	0.744690i
$307$	−8.51186			−0.485797			−0.242899	−	0.970052i	$-0.578098\pi$
$307$	−8.51186			−0.485797			−0.242899	+	0.970052i	$0.578098\pi$
$308$	−5.15027	+	6.83216i	−0.293464	+	0.389298i
$309$	0.639997			0.0364082
$310$	−0.765428	+	1.32576i	−0.0434734	+	0.0752981i
$311$	11.9599	+	20.7151i	0.678182	+	1.17465i	0.975528	+	0.219875i	$0.0705651\pi$
$311$	11.9599	+	20.7151i	0.678182	+	1.17465i	−0.297346	+	0.954770i	$0.596102\pi$
$312$	0.137833	+	0.238734i	0.00780327	+	0.0135157i
$313$	−10.5610	+	18.2921i	−0.596941	+	1.03393i	0.396329	+	0.918109i	$0.370284\pi$
$313$	−10.5610	+	18.2921i	−0.596941	+	1.03393i	−0.993270	+	0.115824i	$0.963049\pi$
$314$	−5.66339			−0.319603
$315$	−2.56274	−	6.04035i	−0.144394	−	0.340335i
$316$	8.41907			0.473610
$317$	11.4681	−	19.8633i	0.644113	−	1.11564i	−0.340393	−	0.940283i	$-0.610560\pi$
$317$	11.4681	−	19.8633i	0.644113	−	1.11564i	0.984506	−	0.175353i	$-0.0561066\pi$
$318$	−0.633852	−	1.09786i	−0.0355446	−	0.0615651i
$319$	3.34169	+	5.78798i	0.187099	+	0.324064i
$320$	0.475705	−	0.823946i	0.0265927	−	0.0460600i
$321$	2.84375			0.158723
$322$	−1.03335	−	2.43561i	−0.0575865	−	0.135731i
$323$	21.8951			1.21828
$324$	−2.80740	+	4.86256i	−0.155967	+	0.270142i
$325$	0.899941	+	1.55874i	0.0499198	+	0.0864636i
$326$	−6.64571	−	11.5107i	−0.368072	−	0.637519i
$327$	−3.37353	+	5.84312i	−0.186557	+	0.323125i
$328$	−7.18524			−0.396739
$329$	3.92306	−	5.20418i	0.216285	−	0.286916i
$330$	1.92957			0.106219
$331$	17.5965	−	30.4781i	0.967192	−	1.67523i	0.263586	−	0.964636i	$-0.415095\pi$
$331$	17.5965	−	30.4781i	0.967192	−	1.67523i	0.703607	−	0.710590i	$-0.251572\pi$
$332$	6.28530	+	10.8865i	0.344951	+	0.597472i
$333$	6.90840	+	11.9657i	0.378578	+	0.655716i
$334$	−2.11530	+	3.66380i	−0.115744	+	0.200474i
$335$	−1.90057			−0.103839
$336$	−1.64689	−	0.202504i	−0.0898453	−	0.0110475i
$337$	23.5388			1.28224			0.641119	−	0.767441i	$-0.278470\pi$
$337$	23.5388			1.28224			0.641119	+	0.767441i	$0.278470\pi$
$338$	6.40340	−	11.0910i	0.348299	−	0.603271i
$339$	−3.34023	−	5.78545i	−0.181417	−	0.314223i
$340$	−2.74509	−	4.75463i	−0.148873	−	0.257856i
$341$	2.60168	−	4.50624i	0.140889	−	0.244027i
$342$	9.89046			0.534815
$343$	17.2867	+	6.64611i	0.933393	+	0.358856i
$344$	−2.60904			−0.140670
$345$	−0.298341	+	0.516741i	−0.0160621	+	0.0278204i
$346$	−6.38866	−	11.0655i	−0.343456	−	0.594884i
$347$	−7.77726	−	13.4706i	−0.417505	−	0.723140i	0.578183	−	0.815907i	$-0.303762\pi$
$347$	−7.77726	−	13.4706i	−0.417505	−	0.723140i	−0.995688	+	0.0927672i	$0.970429\pi$
$348$	−0.648072	+	1.12249i	−0.0347403	+	0.0601720i
$349$	12.7806			0.684128			0.342064	−	0.939677i	$-0.388874\pi$
$349$	12.7806			0.684128			0.342064	+	0.939677i	$0.388874\pi$
$350$	−10.7529	−	1.32219i	−0.574766	−	0.0706741i
$351$	1.54557			0.0824966
$352$	−1.61692	+	2.80058i	−0.0861819	+	0.149271i
$353$	−1.60550	−	2.78080i	−0.0854520	−	0.148007i	0.820132	−	0.572175i	$-0.193900\pi$
$353$	−1.60550	−	2.78080i	−0.0854520	−	0.148007i	−0.905584	+	0.424168i	$0.860567\pi$
$354$	3.05353	+	5.28887i	0.162293	+	0.281100i
$355$	−6.51200	+	11.2791i	−0.345621	+	0.598633i
$356$	6.16476			0.326732
$357$	−5.76375	+	7.64598i	−0.305050	+	0.404668i
$358$	−11.7401			−0.620483
$359$	−13.8937	+	24.0647i	−0.733283	+	1.27008i	0.222189	+	0.975004i	$0.428680\pi$
$359$	−13.8937	+	24.0647i	−0.733283	+	1.27008i	−0.955472	+	0.295080i	$0.904654\pi$
$360$	−1.24001	−	2.14776i	−0.0653543	−	0.113197i
$361$	2.30172	+	3.98669i	0.121143	+	0.209826i
$362$	−9.81284	+	16.9963i	−0.515751	+	0.893307i
$363$	0.340126			0.0178520
$364$	−0.454212	−	1.07057i	−0.0238072	−	0.0561133i
$365$	6.91682			0.362043
$366$	−4.66814	+	8.08546i	−0.244008	+	0.422634i
$367$	−6.96429	−	12.0625i	−0.363533	−	0.629657i	0.625007	−	0.780619i	$-0.285096\pi$
$367$	−6.96429	−	12.0625i	−0.363533	−	0.629657i	−0.988540	+	0.150962i	$0.951763\pi$
$368$	−0.500000	−	0.866025i	−0.0260643	−	0.0451447i
$369$	−9.36480	+	16.2203i	−0.487512	+	0.844396i
$370$	−5.04299			−0.262172
$371$	2.08878	+	4.92323i	0.108444	+	0.255602i
$372$	1.00912			0.0523202
$373$	−1.14071	+	1.97577i	−0.0590639	+	0.102302i	−0.894045	−	0.447976i	$-0.852145\pi$
$373$	−1.14071	+	1.97577i	−0.0590639	+	0.102302i	0.834982	+	0.550278i	$0.185478\pi$
$374$	9.33051	+	16.1609i	0.482469	+	0.835661i
$375$	2.71335	+	4.69967i	0.140117	+	0.242690i
$376$	1.23163	−	2.13325i	0.0635167	−	0.110014i
$377$	−0.908423			−0.0467862
$378$	−5.60006	+	7.42883i	−0.288036	+	0.382098i
$379$	−16.7773			−0.861793			−0.430896	−	0.902401i	$-0.641803\pi$
$379$	−16.7773			−0.861793			−0.430896	+	0.902401i	$0.641803\pi$
$380$	−1.80496	+	3.12628i	−0.0925925	+	0.160375i
$381$	−6.06882	−	10.5115i	−0.310915	−	0.538521i
$382$	−10.1027	−	17.4984i	−0.516899	−	0.895295i
$383$	4.18231	−	7.24396i	0.213706	−	0.370149i	−0.739166	−	0.673524i	$-0.764780\pi$
$383$	4.18231	−	7.24396i	0.213706	−	0.370149i	0.952871	+	0.303374i	$0.0981133\pi$
$384$	−0.627155			−0.0320043
$385$	−8.07934	−	0.993447i	−0.411761	−	0.0506308i
$386$	20.6111			1.04908
$387$	−3.40046	+	5.88977i	−0.172855	+	0.299394i
$388$	0.140030	+	0.242539i	0.00710895	+	0.0123131i
$389$	4.87447	+	8.44282i	0.247145	+	0.428068i	0.962733	−	0.270455i	$-0.0871742\pi$
$389$	4.87447	+	8.44282i	0.247145	+	0.428068i	−0.715587	+	0.698523i	$0.753841\pi$
$390$	−0.131136	+	0.227134i	−0.00664033	+	0.0115014i
$391$	−5.77056			−0.291830
$392$	6.79148	+	1.69582i	0.343022	+	0.0856519i
$393$	3.74953			0.189139
$394$	−5.21291	+	9.02903i	−0.262623	+	0.454876i
$395$	4.00500	+	6.93686i	0.201513	+	0.349031i
$396$	4.21478	+	7.30021i	0.211801	+	0.366849i
$397$	−16.0682	+	27.8309i	−0.806438	+	1.39679i	0.108878	+	0.994055i	$0.465274\pi$
$397$	−16.0682	+	27.8309i	−0.806438	+	1.39679i	−0.915316	+	0.402736i	$0.868059\pi$
$398$	−15.4983			−0.776859
$399$	6.24877	+	0.768358i	0.312830	+	0.0384660i
$400$	−4.09482			−0.204741
$401$	18.6542	−	32.3100i	0.931545	−	1.61348i	0.150862	−	0.988555i	$-0.451795\pi$
$401$	18.6542	−	32.3100i	0.931545	−	1.61348i	0.780683	−	0.624928i	$-0.214872\pi$
$402$	0.626414	+	1.08498i	0.0312427	+	0.0541139i
$403$	0.353627	+	0.612501i	0.0176154	+	0.0305108i
$404$	1.04115	−	1.80333i	0.0517992	−	0.0897189i
$405$	−5.34198			−0.265445
$406$	3.29148	−	4.36636i	0.163353	−	0.216699i
$407$	17.1410			0.849650
$408$	−1.80952	+	3.13418i	−0.0895844	+	0.155165i
$409$	−12.3231	−	21.3442i	−0.609337	−	1.05540i	−0.991350	−	0.131245i	$-0.958102\pi$
$409$	−12.3231	−	21.3442i	−0.609337	−	1.05540i	0.382013	−	0.924157i	$-0.375231\pi$
$410$	−3.41806	−	5.92025i	−0.168806	−	0.292380i
$411$	−5.66026	+	9.80387i	−0.279200	+	0.483589i
$412$	−1.02048			−0.0502753
$413$	−10.0625	−	23.7173i	−0.495144	−	1.16705i
$414$	−2.60668			−0.128111
$415$	−5.97990	+	10.3575i	−0.293542	+	0.508429i
$416$	−0.219776	−	0.380663i	−0.0107754	−	0.0186635i
$417$	4.39816	+	7.61783i	0.215379	+	0.373047i
$418$	6.13503	−	10.6262i	0.300074	−	0.519744i
$419$	22.0087			1.07519			0.537597	−	0.843202i	$-0.319332\pi$
$419$	22.0087			1.07519			0.537597	+	0.843202i	$0.319332\pi$
$420$	−0.616582	−	1.45328i	−0.0300861	−	0.0709129i
$421$	−26.1419			−1.27408			−0.637040	−	0.770831i	$-0.719841\pi$
$421$	−26.1419			−1.27408			−0.637040	+	0.770831i	$0.719841\pi$
$422$	7.07450	−	12.2534i	0.344382	−	0.596486i
$423$	−3.21047	−	5.56071i	−0.156099	−	0.270371i
$424$	1.01068	+	1.75055i	0.0490829	+	0.0850141i
$425$	−11.8147	+	20.4637i	−0.573097	+	0.992633i
$426$	8.58520			0.415955
$427$	23.7089	−	31.4514i	1.14736	−	1.52204i
$428$	−4.53437			−0.219177
$429$	0.445730	−	0.772026i	0.0215200	−	0.0372738i
$430$	−1.24113	−	2.14971i	−0.0598528	−	0.103668i
$431$	2.46895	+	4.27635i	0.118925	+	0.205984i	0.919342	−	0.393459i	$-0.128722\pi$
$431$	2.46895	+	4.27635i	0.118925	+	0.205984i	−0.800417	+	0.599444i	$0.795388\pi$
$432$	−1.75813	+	3.04516i	−0.0845879	+	0.146511i
$433$	13.5694			0.652106			0.326053	−	0.945351i	$-0.394281\pi$
$433$	13.5694			0.652106			0.326053	+	0.945351i	$0.394281\pi$
$434$	−4.22529	−	0.519548i	−0.202821	−	0.0249391i
$435$	−1.23316			−0.0591257
$436$	5.37910	−	9.31688i	0.257612	−	0.446198i
$437$	1.89714	+	3.28594i	0.0907525	+	0.157188i
$438$	−2.27973	−	3.94860i	−0.108930	−	0.188672i
$439$	−4.98460	+	8.63358i	−0.237902	+	0.412058i	−0.960112	−	0.279615i	$-0.909793\pi$
$439$	−4.98460	+	8.63358i	−0.237902	+	0.412058i	0.722210	+	0.691674i	$0.243126\pi$
$440$	−3.07670			−0.146676
$441$	12.6798	−	13.1212i	0.603801	−	0.624818i
$442$	−2.53646			−0.120647
$443$	13.3339	−	23.0950i	0.633512	−	1.09728i	−0.353316	−	0.935504i	$-0.614946\pi$
$443$	13.3339	−	23.0950i	0.633512	−	1.09728i	0.986828	−	0.161771i	$-0.0517207\pi$
$444$	1.66213	+	2.87889i	0.0788811	+	0.136626i
$445$	2.93261	+	5.07943i	0.139019	+	0.240788i
$446$	−8.09438	+	14.0199i	−0.383280	+	0.663860i
$447$	−11.1724			−0.528436
$448$	2.62597	+	0.322894i	0.124066	+	0.0152553i
$449$	22.0820			1.04211			0.521056	−	0.853522i	$-0.325538\pi$
$449$	22.0820			1.04211			0.521056	+	0.853522i	$0.325538\pi$
$450$	−5.33693	+	9.24384i	−0.251585	+	0.435759i
$451$	11.6179	+	20.1228i	0.547067	+	0.947548i
$452$	5.32601	+	9.22492i	0.250515	+	0.433904i
$453$	2.90790	−	5.03663i	0.136625	−	0.236641i
$454$	22.5997			1.06066
$455$	0.666024	−	0.883524i	0.0312237	−	0.0414202i
$456$	2.37960			0.111435
$457$	−15.7587	+	27.2949i	−0.737161	+	1.27680i	0.216608	+	0.976259i	$0.430501\pi$
$457$	−15.7587	+	27.2949i	−0.737161	+	1.27680i	−0.953769	+	0.300542i	$0.902833\pi$
$458$	−14.8275	−	25.6819i	−0.692842	−	1.20004i
$459$	10.1454	+	17.5723i	0.473546	+	0.820205i
$460$	0.475705	−	0.823946i	0.0221799	−	0.0384167i
$461$	−5.58653			−0.260191			−0.130095	−	0.991501i	$-0.541528\pi$
$461$	−5.58653			−0.260191			−0.130095	+	0.991501i	$0.541528\pi$
$462$	2.09576	+	4.93968i	0.0975034	+	0.229815i
$463$	9.96931			0.463313			0.231657	−	0.972798i	$-0.425585\pi$
$463$	9.96931			0.463313			0.231657	+	0.972798i	$0.425585\pi$
$464$	1.03335	−	1.78982i	0.0479722	−	0.0830903i
$465$	0.480042	+	0.831456i	0.0222614	+	0.0385579i
$466$	10.7812	+	18.6737i	0.499431	+	0.865040i
$467$	8.67338	−	15.0227i	0.401356	−	0.695170i	−0.592534	−	0.805546i	$-0.701872\pi$
$467$	8.67338	−	15.0227i	0.401356	−	0.695170i	0.993890	+	0.110376i	$0.0352056\pi$
$468$	−1.14577			−0.0529632
$469$	−2.06427	−	4.86546i	−0.0953190	−	0.224666i
$470$	2.34358			0.108101
$471$	−1.77591	+	3.07597i	−0.0818296	+	0.141733i
$472$	−4.86886	−	8.43312i	−0.224108	−	0.388166i
$473$	4.21860	+	7.30682i	0.193971	+	0.335968i
$474$	2.64003	−	4.57267i	0.121261	−	0.210030i
$475$	15.5369			0.712881
$476$	9.19032	−	12.1915i	0.421238	−	0.558798i
$477$	5.26903			0.241252
$478$	−1.30790	+	2.26534i	−0.0598218	+	0.103614i
$479$	14.6605	+	25.3927i	0.669856	+	1.16022i	0.977944	+	0.208866i	$0.0669774\pi$
$479$	14.6605	+	25.3927i	0.669856	+	1.16022i	−0.308089	+	0.951358i	$0.599689\pi$
$480$	−0.298341	−	0.516741i	−0.0136173	−	0.0235859i
$481$	−1.16493	+	2.01772i	−0.0531162	+	0.0919999i
$482$	13.4817			0.614073
$483$	−1.64689	−	0.202504i	−0.0749362	−	0.00921426i
$484$	−0.542332			−0.0246515
$485$	−0.133226	+	0.230754i	−0.00604949	+	0.0104780i
$486$	7.03505	+	12.1851i	0.319116	+	0.552726i
$487$	7.96997	+	13.8044i	0.361154	+	0.625537i	0.988151	−	0.153485i	$-0.0490496\pi$
$487$	7.96997	+	13.8044i	0.361154	+	0.625537i	−0.626997	+	0.779021i	$0.715716\pi$
$488$	7.44337	−	12.8923i	0.336945	−	0.583607i
$489$	−8.33578			−0.376957
$490$	1.83348	+	6.40252i	0.0828281	+	0.289236i
$491$	33.8088			1.52577			0.762886	−	0.646534i	$-0.223782\pi$
$491$	33.8088			1.52577			0.762886	+	0.646534i	$0.223782\pi$
$492$	−2.25313	+	3.90253i	−0.101579	+	0.175940i
$493$	−5.96303	−	10.3283i	−0.268561	−	0.465162i
$494$	0.833890	+	1.44434i	0.0375185	+	0.0649840i
$495$	−4.00998	+	6.94550i	−0.180235	+	0.312177i
$496$	−1.60904			−0.0722479
$497$	−35.9473	−	4.42014i	−1.61246	−	0.198270i
$498$	7.88371			0.353277
$499$	5.97159	−	10.3431i	0.267325	−	0.463020i	−0.700845	−	0.713313i	$-0.747194\pi$
$499$	5.97159	−	10.3431i	0.267325	−	0.463020i	0.968170	+	0.250293i	$0.0805269\pi$
$500$	−4.32645	−	7.49364i	−0.193485	−	0.335126i
$501$	1.32662	+	2.29777i	0.0592689	+	0.102657i
$502$	7.33595	−	12.7062i	0.327420	−	0.567107i
$503$	16.8766			0.752490			0.376245	−	0.926520i	$-0.377215\pi$
$503$	16.8766			0.752490			0.376245	+	0.926520i	$0.377215\pi$
$504$	4.15145	−	5.50716i	0.184920	−	0.245308i
$505$	1.98113			0.0881589
$506$	−1.61692	+	2.80058i	−0.0718807	+	0.124501i
$507$	−4.01592	−	6.95578i	−0.178353	−	0.308917i
$508$	9.67676	+	16.7606i	0.429337	+	0.743633i
$509$	20.5134	−	35.5302i	0.909240	−	1.57485i	0.0941182	−	0.995561i	$-0.469997\pi$
$509$	20.5134	−	35.5302i	0.909240	−	1.57485i	0.815122	−	0.579289i	$-0.196670\pi$
$510$	−3.44319			−0.152467
$511$	7.51254	+	17.7070i	0.332335	+	0.783312i
$512$	1.00000			0.0441942
$513$	6.67082	−	11.5542i	0.294524	−	0.510131i
$514$	3.81621	+	6.60988i	0.168326	+	0.291549i
$515$	−0.485446	−	0.840818i	−0.0213913	−	0.0370509i
$516$	−0.818135	+	1.41705i	−0.0360164	+	0.0623822i
$517$	−7.96580			−0.350335
$518$	−5.47733	−	12.9100i	−0.240660	−	0.567234i
$519$	−8.01335			−0.351747
$520$	0.209097	−	0.362166i	0.00916950	−	0.0158820i
$521$	−4.89942	−	8.48604i	−0.214647	−	0.371780i	0.738516	−	0.674236i	$-0.235527\pi$
$521$	−4.89942	−	8.48604i	−0.214647	−	0.371780i	−0.953163	+	0.302456i	$0.902194\pi$
$522$	−2.69362	−	4.66548i	−0.117896	−	0.204203i
$523$	0.286481	−	0.496200i	0.0125270	−	0.0216973i	−0.859694	−	0.510809i	$-0.829346\pi$
$523$	0.286481	−	0.496200i	0.0125270	−	0.0216973i	0.872221	+	0.489112i	$0.162679\pi$
$524$	−5.97864			−0.261178
$525$	−4.08998	+	5.42562i	−0.178502	+	0.236794i
$526$	3.82052			0.166582
$527$	−4.64253	+	8.04109i	−0.202232	+	0.350276i
$528$	1.01406	+	1.75640i	0.0441311	+	0.0764374i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−0.961570	+	1.66549i	−0.0417680	+	0.0723442i
$531$	−25.3831			−1.10153
$532$	−9.96368	−	1.22515i	−0.431980	−	0.0531170i
$533$	−3.15828			−0.136800
$534$	1.93313	−	3.34828i	0.0836547	−	0.144894i
$535$	−2.15702	−	3.73607i	−0.0932563	−	0.161525i
$536$	−0.998820	−	1.73001i	−0.0431424	−	0.0747249i
$537$	−3.68142	+	6.37641i	−0.158865	+	0.275163i
$538$	9.18036			0.395794
$539$	−6.23197	−	21.7621i	−0.268430	−	0.937359i
$540$	−3.34540			−0.143963
$541$	−15.0455	+	26.0595i	−0.646856	+	1.12039i	0.337013	+	0.941500i	$0.390583\pi$
$541$	−15.0455	+	26.0595i	−0.646856	+	1.12039i	−0.983869	+	0.178888i	$0.942750\pi$
$542$	11.4587	+	19.8470i	0.492193	+	0.852503i
$543$	6.15416	+	10.6593i	0.264100	+	0.457435i
$544$	2.88528	−	4.99745i	0.123705	−	0.214264i
$545$	10.2355			0.438439
$546$	−0.723893	−	0.0890110i	−0.0309798	−	0.00380932i
$547$	18.5121			0.791522			0.395761	−	0.918354i	$-0.370481\pi$
$547$	18.5121			0.791522			0.395761	+	0.918354i	$0.370481\pi$
$548$	9.02531	−	15.6323i	0.385542	−	0.667779i
$549$	−19.4025	−	33.6060i	−0.828077	−	1.43427i
$550$	6.62098	+	11.4679i	0.282319	+	0.488991i
$551$	−3.92083	+	6.79108i	−0.167033	+	0.289310i
$552$	−0.627155			−0.0266935
$553$	−13.4084	+	17.7871i	−0.570183	+	0.756384i
$554$	9.90309			0.420742
$555$	−1.58137	+	2.73901i	−0.0671253	+	0.116264i
$556$	−7.01288	−	12.1467i	−0.297412	−	0.515133i
$557$	7.12759	+	12.3454i	0.302006	+	0.523090i	0.976590	−	0.215108i	$-0.0690104\pi$
$557$	7.12759	+	12.3454i	0.302006	+	0.523090i	−0.674584	+	0.738198i	$0.735677\pi$
$558$	−2.09712	+	3.63232i	−0.0887782	+	0.153768i
$559$	−1.14681			−0.0485047
$560$	0.983143	+	2.31726i	0.0415454	+	0.0979222i
$561$	11.7033			0.494116
$562$	2.02193	−	3.50209i	0.0852901	−	0.147727i
$563$	4.58008	+	7.93293i	0.193027	+	0.334333i	0.946252	−	0.323430i	$-0.104836\pi$
$563$	4.58008	+	7.93293i	0.193027	+	0.334333i	−0.753225	+	0.657763i	$0.771503\pi$
$564$	−0.772425	−	1.33788i	−0.0325250	−	0.0563349i
$565$	−5.06722	+	8.77669i	−0.213180	+	0.369238i
$566$	7.55337			0.317492
$567$	−5.80207	−	13.6754i	−0.243664	−	0.574315i
$568$	−13.6891			−0.574383
$569$	1.03445	−	1.79173i	0.0433666	−	0.0751131i	−0.843527	−	0.537086i	$-0.819525\pi$
$569$	1.03445	−	1.79173i	0.0433666	−	0.0751131i	0.886894	+	0.461973i	$0.152858\pi$
$570$	1.13199	+	1.96066i	0.0474138	+	0.0821231i
$571$	4.29392	+	7.43729i	0.179695	+	0.311241i	0.941776	−	0.336241i	$-0.109156\pi$
$571$	4.29392	+	7.43729i	0.179695	+	0.311241i	−0.762081	+	0.647482i	$0.775822\pi$
$572$	−0.710717	+	1.23100i	−0.0297166	+	0.0514706i
$573$	−12.6719			−0.529376
$574$	11.4434	−	15.1804i	0.477637	−	0.633616i
$575$	−4.09482			−0.170766
$576$	1.30334	−	2.25745i	0.0543058	−	0.0940604i
$577$	−5.79884	−	10.0439i	−0.241409	−	0.418132i	0.719707	−	0.694278i	$-0.244276\pi$
$577$	−5.79884	−	10.0439i	−0.241409	−	0.418132i	−0.961116	+	0.276146i	$0.910943\pi$
$578$	−8.14969	−	14.1157i	−0.338983	−	0.587135i
$579$	6.46316	−	11.1945i	0.268600	−	0.465229i
$580$	1.96629			0.0816456
$581$	−33.0101	−	4.05897i	−1.36949	−	0.168394i
$582$	0.175641			0.00728056
$583$	3.26837	−	5.66097i	0.135362	−	0.234454i
$584$	3.63503	+	6.29606i	0.150419	+	0.260533i
$585$	−0.545048	−	0.944051i	−0.0225350	−	0.0390317i
$586$	−1.68024	+	2.91027i	−0.0694103	+	0.120222i
$587$	7.07807			0.292143			0.146072	−	0.989274i	$-0.453337\pi$
$587$	7.07807			0.292143			0.146072	+	0.989274i	$0.453337\pi$
$588$	3.05071	−	3.15690i	0.125809	−	0.130188i
$589$	6.10514			0.251558
$590$	4.63229	−	8.02336i	0.190708	−	0.330316i
$591$	3.26930	+	5.66260i	0.134481	+	0.232928i
$592$	−2.65027	−	4.59040i	−0.108925	−	0.188664i
$593$	−18.1246	+	31.3926i	−0.744286	+	1.28914i	0.206241	+	0.978501i	$0.433877\pi$
$593$	−18.1246	+	31.3926i	−0.744286	+	1.28914i	−0.950528	+	0.310640i	$0.899457\pi$
$594$	11.3710			0.466557
$595$	14.4171	+	1.77274i	0.591042	+	0.0726753i
$596$	17.8144			0.729707
$597$	−4.85991	+	8.41762i	−0.198903	+	0.344510i
$598$	−0.219776	−	0.380663i	−0.00898729	−	0.0155665i
$599$	8.89428	+	15.4053i	0.363411	+	0.629445i	0.988520	−	0.151092i	$-0.0482789\pi$
$599$	8.89428	+	15.4053i	0.363411	+	0.629445i	−0.625109	+	0.780537i	$0.714946\pi$
$600$	−1.28404	+	2.22403i	−0.0524208	+	0.0907955i
$601$	−36.6458			−1.49481			−0.747407	−	0.664366i	$-0.768702\pi$
$601$	−36.6458			−1.49481			−0.747407	+	0.664366i	$0.768702\pi$
$602$	4.15521	−	5.51215i	0.169354	−	0.224658i
$603$	−5.20720			−0.212054
$604$	−4.63665	+	8.03092i	−0.188663	+	0.326773i
$605$	−0.257990	−	0.446852i	−0.0104888	−	0.0181671i
$606$	−0.652963	−	1.13097i	−0.0265248	−	0.0459423i
$607$	−3.92643	+	6.80078i	−0.159369	+	0.276035i	−0.934641	−	0.355592i	$-0.884279\pi$
$607$	−3.92643	+	6.80078i	−0.159369	+	0.276035i	0.775272	+	0.631627i	$0.217613\pi$
$608$	−3.79428			−0.153878
$609$	−1.33937	−	3.15690i	−0.0542742	−	0.127924i
$610$	14.1634			0.573459
$611$	0.541367	−	0.937675i	0.0219014	−	0.0379343i
$612$	−7.52100	−	13.0267i	−0.304018	−	0.526575i
$613$	0.433294	+	0.750488i	0.0175006	+	0.0303119i	0.874643	−	0.484767i	$-0.161096\pi$
$613$	0.433294	+	0.750488i	0.0175006	+	0.0303119i	−0.857142	+	0.515079i	$0.827762\pi$
$614$	4.25593	−	7.37149i	0.171755	−	0.297489i
$615$	−4.28730			−0.172881
$616$	−3.34169	−	7.87634i	−0.134641	−	0.317347i
$617$	33.0629			1.33106			0.665530	−	0.746371i	$-0.268205\pi$
$617$	33.0629			1.33106			0.665530	+	0.746371i	$0.268205\pi$
$618$	−0.319998	+	0.554254i	−0.0128722	+	0.0222953i
$619$	4.29436	+	7.43805i	0.172605	+	0.298960i	0.939330	−	0.343015i	$-0.111448\pi$
$619$	4.29436	+	7.43805i	0.172605	+	0.298960i	−0.766725	+	0.641976i	$0.778115\pi$
$620$	−0.765428	−	1.32576i	−0.0307403	−	0.0532438i
$621$	−1.75813	+	3.04516i	−0.0705512	+	0.122198i
$622$	−23.9197			−0.959094
$623$	−9.81814	+	13.0244i	−0.393355	+	0.521811i
$624$	−0.275667			−0.0110355
$625$	−6.12081	+	10.6016i	−0.244832	+	0.424062i
$626$	−10.5610	−	18.2921i	−0.422101	−	0.731101i
$627$	−3.84761	−	6.66426i	−0.153659	−	0.266145i
$628$	2.83169	−	4.90464i	0.112997	−	0.195716i
$629$	−30.5871			−1.21959
$630$	6.51247	+	0.800783i	0.259463	+	0.0319040i
$631$	17.2833			0.688037			0.344019	−	0.938963i	$-0.388212\pi$
$631$	17.2833			0.688037			0.344019	+	0.938963i	$0.388212\pi$
$632$	−4.20954	+	7.29113i	−0.167446	+	0.290026i
$633$	−4.43681	−	7.68478i	−0.176347	−	0.305442i
$634$	11.4681	+	19.8633i	0.455457	+	0.788874i
$635$	−9.20657	+	15.9463i	−0.365352	+	0.632808i
$636$	1.26770			0.0502677
$637$	2.98520	+	0.745400i	0.118278	+	0.0295338i
$638$	−6.68338			−0.264598
$639$	−17.8416	+	30.9025i	−0.705802	+	1.22249i
$640$	0.475705	+	0.823946i	0.0188039	+	0.0325693i
$641$	−4.37617	−	7.57974i	−0.172848	−	0.299382i	0.766566	−	0.642165i	$-0.221964\pi$
$641$	−4.37617	−	7.57974i	−0.172848	−	0.299382i	−0.939414	+	0.342783i	$0.888630\pi$
$642$	−1.42188	+	2.46276i	−0.0561169	+	0.0971974i
$643$	5.01488			0.197767			0.0988837	−	0.995099i	$-0.468473\pi$
$643$	5.01488			0.197767			0.0988837	+	0.995099i	$0.468473\pi$
$644$	2.62597	+	0.322894i	0.103478	+	0.0127238i
$645$	−1.55676			−0.0612975
$646$	−10.9476	+	18.9617i	−0.430726	+	0.746040i
$647$	16.2327	+	28.1158i	0.638171	+	1.10535i	0.985834	+	0.167725i	$0.0536422\pi$
$647$	16.2327	+	28.1158i	0.638171	+	1.10535i	−0.347662	+	0.937620i	$0.613024\pi$
$648$	−2.80740	−	4.86256i	−0.110285	−	0.191019i
$649$	−15.7451	+	27.2713i	−0.618049	+	1.07049i
$650$	−1.79988			−0.0705972
$651$	−1.60714	+	2.13197i	−0.0629887	+	0.0835586i
$652$	13.2914			0.520532
$653$	16.9265	−	29.3176i	0.662386	−	1.14729i	−0.317601	−	0.948224i	$-0.602877\pi$
$653$	16.9265	−	29.3176i	0.662386	−	1.14729i	0.979987	−	0.199061i	$-0.0637893\pi$
$654$	−3.37353	−	5.84312i	−0.131915	−	0.228484i
$655$	−2.84407	−	4.92608i	−0.111127	−	0.192478i
$656$	3.59262	−	6.22260i	0.140268	−	0.242952i
$657$	18.9507			0.739338
$658$	2.54543	+	5.99956i	0.0992311	+	0.233887i
$659$	−36.7919			−1.43321			−0.716604	−	0.697481i	$-0.754304\pi$
$659$	−36.7919			−1.43321			−0.716604	+	0.697481i	$0.754304\pi$
$660$	−0.964784	+	1.67105i	−0.0375542	+	0.0650457i
$661$	−22.2958	−	38.6175i	−0.867207	−	1.50205i	−0.864839	−	0.502049i	$-0.832580\pi$
$661$	−22.2958	−	38.6175i	−0.867207	−	1.50205i	−0.00236749	−	0.999997i	$-0.500754\pi$
$662$	17.5965	+	30.4781i	0.683908	+	1.18456i
$663$	−0.795376	+	1.37763i	−0.0308898	+	0.0535027i
$664$	−12.5706			−0.487834
$665$	−3.73032	−	8.79234i	−0.144656	−	0.340952i
$666$	−13.8168			−0.535390
$667$	1.03335	−	1.78982i	0.0400116	−	0.0693021i
$668$	−2.11530	−	3.66380i	−0.0818432	−	0.141757i
$669$	5.07643	+	8.79263i	0.196266	+	0.339943i
$670$	0.950287	−	1.64595i	0.0367128	−	0.0635884i
$671$	−48.1412			−1.85847
$672$	0.998820	−	1.32500i	0.0385303	−	0.0511129i
$673$	−6.43104			−0.247898			−0.123949	−	0.992289i	$-0.539556\pi$
$673$	−6.43104			−0.247898			−0.123949	+	0.992289i	$0.539556\pi$
$674$	−11.7694	+	20.3852i	−0.453340	+	0.785207i
$675$	7.19921	+	12.4694i	0.277098	+	0.479947i
$676$	6.40340	+	11.0910i	0.246285	+	0.426577i
$677$	−4.52328	+	7.83455i	−0.173844	+	0.301106i	−0.939761	−	0.341834i	$-0.888952\pi$
$677$	−4.52328	+	7.83455i	−0.173844	+	0.301106i	0.765917	+	0.642940i	$0.222285\pi$
$678$	6.68047			0.256562
$679$	−0.735431	−	0.0904297i	−0.0282232	−	0.00347037i
$680$	5.49017			0.210539
$681$	7.08675	−	12.2746i	0.271565	−	0.470364i
$682$	2.60168	+	4.50624i	0.0996234	+	0.172553i
$683$	−10.4909	−	18.1707i	−0.401423	−	0.695284i	0.592475	−	0.805589i	$-0.298151\pi$
$683$	−10.4909	−	18.1707i	−0.401423	−	0.695284i	−0.993898	+	0.110304i	$0.964817\pi$
$684$	−4.94523	+	8.56539i	−0.189086	+	0.327506i
$685$	17.1736			0.656168
$686$	−14.3990	+	11.6476i	−0.549758	+	0.444709i
$687$	−18.5982			−0.709567
$688$	1.30452	−	2.25949i	0.0497343	−	0.0861424i
$689$	0.444245	+	0.769455i	0.0169244	+	0.0293139i
$690$	−0.298341	−	0.516741i	−0.0113576	−	0.0196720i
$691$	14.4778	−	25.0763i	0.550761	−	0.953947i	−0.447459	−	0.894305i	$-0.647671\pi$
$691$	14.4778	−	25.0763i	0.550761	−	0.953947i	0.998220	−	0.0596419i	$-0.0189959\pi$
$692$	12.7773			0.485721
$693$	−22.1358	−	2.72185i	−0.840869	−	0.103395i
$694$	15.5545			0.590441
$695$	6.67212	−	11.5565i	0.253088	−	0.438361i
$696$	−0.648072	−	1.12249i	−0.0245651	−	0.0425480i
$697$	−20.7314	−	35.9079i	−0.785259	−	1.36011i
$698$	−6.39028	+	11.0683i	−0.241876	+	0.418941i
$699$	13.5230			0.511487
$700$	6.52149	−	8.65118i	0.246489	−	0.326984i
$701$	12.4447			0.470029			0.235014	−	0.971992i	$-0.424486\pi$
$701$	12.4447			0.470029			0.235014	+	0.971992i	$0.424486\pi$
$702$	−0.772787	+	1.33851i	−0.0291670	+	0.0505187i
$703$	10.0559	+	17.4173i	0.379264	+	0.656905i
$704$	−1.61692	−	2.80058i	−0.0609398	−	0.105551i
$705$	0.734894	−	1.27287i	0.0276777	−	0.0479392i
$706$	3.21099			0.120847
$707$	2.15175	+	5.07167i	0.0809251	+	0.190740i
$708$	−6.10706			−0.229517
$709$	5.07332	−	8.78726i	0.190533	−	0.330012i	−0.754894	−	0.655847i	$-0.772312\pi$
$709$	5.07332	−	8.78726i	0.190533	−	0.330012i	0.945427	+	0.325834i	$0.105645\pi$
$710$	−6.51200	−	11.2791i	−0.244391	−	0.423297i
$711$	10.9729	+	19.0056i	0.411516	+	0.712767i
$712$	−3.08238	+	5.33884i	−0.115517	+	0.200082i
$713$	−1.60904			−0.0602590
$714$	−3.73974	−	8.81454i	−0.139956	−	0.329876i
$715$	−1.35237			−0.0505757
$716$	5.87004	−	10.1672i	0.219374	−	0.379967i
$717$	0.820253	+	1.42072i	0.0306329	+	0.0530578i
$718$	−13.8937	−	24.0647i	−0.518510	−	0.898085i
$719$	19.3055	−	33.4380i	0.719972	−	1.24703i	−0.241039	−	0.970516i	$-0.577488\pi$
$719$	19.3055	−	33.4380i	0.719972	−	1.24703i	0.961010	−	0.276512i	$-0.0891786\pi$
$720$	2.48002			0.0924249
$721$	1.62523	−	2.15598i	0.0605269	−	0.0802927i
$722$	−4.60344			−0.171322
$723$	4.22754	−	7.32232i	0.157224	−	0.272320i
$724$	−9.81284	−	16.9963i	−0.364691	−	0.631664i
$725$	−4.23139	−	7.32899i	−0.157150	−	0.272192i
$726$	−0.170063	+	0.294558i	−0.00631163	+	0.0109321i
$727$	−8.68311			−0.322039			−0.161019	−	0.986951i	$-0.551478\pi$
$727$	−8.68311			−0.322039			−0.161019	+	0.986951i	$0.551478\pi$
$728$	1.15425	+	0.141928i	0.0427794	+	0.00526021i
$729$	−8.02026			−0.297047
$730$	−3.45841	+	5.99014i	−0.128001	+	0.221705i
$731$	−7.52781	−	13.0385i	−0.278426	−	0.482248i
$732$	−4.66814	−	8.08546i	−0.172540	−	0.298847i
$733$	13.2032	−	22.8686i	0.487671	−	0.844671i	−0.512228	−	0.858849i	$-0.671180\pi$
$733$	13.2032	−	22.8686i	0.487671	−	0.844671i	0.999899	+	0.0141781i	$0.00451319\pi$
$734$	13.9286			0.514113
$735$	4.05235	+	1.01186i	0.149473	+	0.0373232i
$736$	1.00000			0.0368605
$737$	−3.23001	+	5.59455i	−0.118979	+	0.206078i
$738$	−9.36480	−	16.2203i	−0.344723	−	0.597078i
$739$	−19.7071	−	34.1336i	−0.724936	−	1.25563i	−0.959000	−	0.283405i	$-0.908536\pi$
$739$	−19.7071	−	34.1336i	−0.724936	−	1.25563i	0.234064	−	0.972221i	$-0.424797\pi$
$740$	2.52149	−	4.36736i	0.0926920	−	0.160547i
$741$	1.04596			0.0384242
$742$	−5.30803	−	0.652684i	−0.194864	−	0.0239608i
$743$	−49.9431			−1.83224			−0.916118	−	0.400909i	$-0.868694\pi$
$743$	−49.9431			−1.83224			−0.916118	+	0.400909i	$0.868694\pi$
$744$	−0.504558	+	0.873920i	−0.0184980	+	0.0320395i
$745$	8.47442	+	14.6781i	0.310479	+	0.537765i
$746$	−1.14071	−	1.97577i	−0.0417645	−	0.0723382i
$747$	−16.3838	+	28.3775i	−0.599450	+	1.03828i
$748$	−18.6610			−0.682315
$749$	7.22153	−	9.57982i	0.263869	−	0.350039i
$750$	−5.42671			−0.198155
$751$	11.8504	−	20.5255i	0.432427	−	0.748985i	−0.564655	−	0.825327i	$-0.690991\pi$
$751$	11.8504	−	20.5255i	0.432427	−	0.748985i	0.997082	+	0.0763420i	$0.0243241\pi$
$752$	1.23163	+	2.13325i	0.0449131	+	0.0777918i
$753$	−4.60077	−	7.96878i	−0.167662	−	0.290398i
$754$	0.454212	−	0.786718i	0.0165414	−	0.0286506i
$755$	−8.82272			−0.321092
$756$	−3.63353	−	8.56421i	−0.132150	−	0.311477i
$757$	−31.2133			−1.13447			−0.567233	−	0.823557i	$-0.691986\pi$
$757$	−31.2133			−1.13447			−0.567233	+	0.823557i	$0.691986\pi$
$758$	8.38866	−	14.5296i	0.304690	−	0.527738i
$759$	1.01406	+	1.75640i	0.0368079	+	0.0637532i
$760$	−1.80496	−	3.12628i	−0.0654728	−	0.113402i
$761$	17.6575	−	30.5838i	0.640085	−	1.10866i	−0.345328	−	0.938482i	$-0.612232\pi$
$761$	17.6575	−	30.5838i	0.640085	−	1.10866i	0.985413	−	0.170178i	$-0.0544344\pi$
$762$	12.1376			0.439701
$763$	11.1170	+	26.2028i	0.402463	+	0.948604i
$764$	20.2054			0.731005
$765$	7.15556	−	12.3938i	0.258710	−	0.448098i
$766$	4.18231	+	7.24396i	0.151113	+	0.261735i
$767$	−2.14012	−	3.70679i	−0.0772751	−	0.133844i
$768$	0.313577	−	0.543132i	0.0113152	−	0.0195986i
$769$	31.8302			1.14783			0.573913	−	0.818916i	$-0.305425\pi$
$769$	31.8302			1.14783			0.573913	+	0.818916i	$0.305425\pi$
$770$	4.90002	−	6.50019i	0.176584	−	0.234251i
$771$	4.78671			0.172389
$772$	−10.3055	+	17.8497i	−0.370904	+	0.642425i
$773$	20.2940	+	35.1503i	0.729926	+	1.26427i	0.956914	+	0.290371i	$0.0937787\pi$
$773$	20.2940	+	35.1503i	0.729926	+	1.26427i	−0.226988	+	0.973897i	$0.572888\pi$
$774$	−3.40046	−	5.88977i	−0.122227	−	0.211703i
$775$	−3.29436	+	5.70600i	−0.118337	+	0.204965i
$776$	−0.280060			−0.0100536
$777$	−8.72941	−	1.07338i	−0.313166	−	0.0385073i
$778$	−9.74893			−0.349516
$779$	−13.6314	+	23.6103i	−0.488396	+	0.845927i
$780$	−0.131136	−	0.227134i	−0.00469542	−	0.00813271i
$781$	22.1342	+	38.3375i	0.792023	+	1.37182i
$782$	2.88528	−	4.99745i	0.103177	−	0.178709i
$783$	−7.26706			−0.259704
$784$	−4.86436	+	5.03368i	−0.173727	+	0.179774i
$785$	5.38821			0.192313
$786$	−1.87477	+	3.24719i	−0.0668707	+	0.115823i
$787$	−12.7785	−	22.1330i	−0.455505	−	0.788958i	0.543212	−	0.839596i	$-0.317208\pi$
$787$	−12.7785	−	22.1330i	−0.455505	−	0.788958i	−0.998717	+	0.0506377i	$0.983875\pi$
$788$	−5.21291	−	9.02903i	−0.185702	−	0.321646i
$789$	1.19803	−	2.07504i	0.0426509	−	0.0738735i
$790$	−8.01000			−0.284983
$791$	−27.9719	−	3.43947i	−0.994568	−	0.122294i
$792$	−8.42956			−0.299531
$793$	3.27174	−	5.66682i	0.116183	−	0.201235i
$794$	−16.0682	−	27.8309i	−0.570238	−	0.987681i
$795$	0.603053	+	1.04452i	0.0213881	+	0.0370453i
$796$	7.74915	−	13.4219i	0.274661	−	0.475727i
$797$	−39.3262			−1.39301			−0.696503	−	0.717554i	$-0.745262\pi$
$797$	−39.3262			−1.39301			−0.696503	+	0.717554i	$0.745262\pi$
$798$	−3.78980	+	5.02741i	−0.134158	+	0.177968i
$799$	14.2145			0.502871
$800$	2.04741	−	3.54622i	0.0723868	−	0.125378i
$801$	8.03478	+	13.9166i	0.283895	+	0.491720i
$802$	18.6542	+	32.3100i	0.658701	+	1.14090i
$803$	11.7551	−	20.3604i	0.414828	−	0.718503i
$804$	−1.25283			−0.0441838
$805$	0.983143	+	2.31726i	0.0346512	+	0.0816728i
$806$	−0.707255			−0.0249120
$807$	2.87875	−	4.98615i	0.101337	−	0.175521i
$808$	1.04115	+	1.80333i	0.0366276	+	0.0634409i
$809$	5.60945	+	9.71585i	0.197218	+	0.341591i	0.947625	−	0.319384i	$-0.103476\pi$
$809$	5.60945	+	9.71585i	0.197218	+	0.341591i	−0.750408	+	0.660975i	$0.770143\pi$
$810$	2.67099	−	4.62629i	0.0938490	−	0.162551i
$811$	−29.2759			−1.02802			−0.514009	−	0.857785i	$-0.671840\pi$
$811$	−29.2759			−1.02802			−0.514009	+	0.857785i	$0.671840\pi$
$812$	2.13564	+	5.03368i	0.0749461	+	0.176648i
$813$	14.3727			0.504074
$814$	−8.57052	+	14.8446i	−0.300397	+	0.520302i
$815$	6.32280	+	10.9514i	0.221478	+	0.383611i
$816$	−1.80952	−	3.13418i	−0.0633458	−	0.109718i
$817$	−4.94971	+	8.57315i	−0.173168	+	0.299937i
$818$	24.6462			0.861732
$819$	1.82477	−	2.42068i	0.0637628	−	0.0845854i
$820$	6.83612			0.238728
$821$	17.1355	−	29.6796i	0.598033	−	1.03582i	−0.395078	−	0.918648i	$-0.629282\pi$
$821$	17.1355	−	29.6796i	0.598033	−	1.03582i	0.993111	−	0.117176i	$-0.0373842\pi$
$822$	−5.66026	−	9.80387i	−0.197424	−	0.341949i
$823$	−15.0975	−	26.1497i	−0.526266	−	0.911520i	−0.999532	−	0.0306000i	$-0.990258\pi$
$823$	−15.0975	−	26.1497i	−0.526266	−	0.911520i	0.473266	−	0.880920i	$-0.343075\pi$
$824$	0.510239	−	0.883759i	0.0177750	−	0.0307872i
$825$	8.30475			0.289134
$826$	25.5710	+	3.14425i	0.889730	+	0.109402i
$827$	−24.7904			−0.862046			−0.431023	−	0.902341i	$-0.641847\pi$
$827$	−24.7904			−0.862046			−0.431023	+	0.902341i	$0.641847\pi$
$828$	1.30334	−	2.25745i	0.0452941	−	0.0784518i
$829$	−5.97422	−	10.3477i	−0.207493	−	0.359389i	0.743431	−	0.668813i	$-0.233197\pi$
$829$	−5.97422	−	10.3477i	−0.207493	−	0.359389i	−0.950924	+	0.309424i	$0.899864\pi$
$830$	−5.97990	−	10.3575i	−0.207565	−	0.359514i
$831$	3.10538	−	5.37868i	0.107725	−	0.186584i
$832$	0.439551			0.0152387
$833$	11.1205	+	38.8330i	0.385304	+	1.34548i
$834$	−8.79631			−0.304591
$835$	2.01251	−	3.48578i	0.0696459	−	0.120630i
$836$	6.13503	+	10.6262i	0.212185	+	0.367514i
$837$	2.82889	+	4.89979i	0.0977808	+	0.169361i
$838$	−11.0043	+	19.0601i	−0.380138	+	0.658419i
$839$	56.0222			1.93410			0.967050	−	0.254586i	$-0.0819391\pi$
$839$	56.0222			1.93410			0.967050	+	0.254586i	$0.0819391\pi$
$840$	1.56687	+	0.192665i	0.0540621	+	0.00664756i
$841$	−24.7287			−0.852715
$842$	13.0710	−	22.6396i	0.450455	−	0.780211i
$843$	−1.26806	−	2.19635i	−0.0436745	−	0.0756464i
$844$	7.07450	+	12.2534i	0.243514	+	0.421779i
$845$	−6.09226	+	10.5521i	−0.209580	+	0.363003i
$846$	6.42095			0.220757
$847$	0.863730	−	1.14579i	0.0296781	−	0.0393699i
$848$	−2.02136			−0.0694137
$849$	2.36856	−	4.10247i	0.0812889	−	0.140797i
$850$	−11.8147	−	20.4637i	−0.405241	−	0.701898i
$851$	−2.65027	−	4.59040i	−0.0908500	−	0.157357i
$852$	−4.29260	+	7.43501i	−0.147062	+	0.254719i
$853$	−10.6759			−0.365536			−0.182768	−	0.983156i	$-0.558506\pi$
$853$	−10.6759			−0.365536			−0.182768	+	0.983156i	$0.558506\pi$
$854$	15.3833	+	36.2582i	0.526404	+	1.24073i
$855$	−9.40989			−0.321812
$856$	2.26718	−	3.92688i	0.0774908	−	0.134218i
$857$	25.1349	+	43.5349i	0.858591	+	1.48712i	0.873273	+	0.487231i	$0.161993\pi$
$857$	25.1349	+	43.5349i	0.858591	+	1.48712i	−0.0146826	+	0.999892i	$0.504674\pi$
$858$	0.445730	+	0.772026i	0.0152170	+	0.0263565i
$859$	20.6206	−	35.7159i	0.703565	−	1.21861i	−0.263642	−	0.964621i	$-0.584924\pi$
$859$	20.6206	−	35.7159i	0.703565	−	1.21861i	0.967207	−	0.253989i	$-0.0817428\pi$
$860$	2.48227			0.0846446
$861$	−4.65655	−	10.9755i	−0.158695	−	0.374043i
$862$	−4.93790			−0.168186
$863$	7.69192	−	13.3228i	0.261836	−	0.453513i	−0.704894	−	0.709313i	$-0.749005\pi$
$863$	7.69192	−	13.3228i	0.261836	−	0.453513i	0.966730	+	0.255800i	$0.0823387\pi$
$864$	−1.75813	−	3.04516i	−0.0598127	−	0.103599i
$865$	6.07824	+	10.5278i	0.206666	+	0.357956i
$866$	−6.78472	+	11.7515i	−0.230554	+	0.399332i
$867$	−10.2222			−0.347165
$868$	2.56259	−	3.39944i	0.0869799	−	0.115384i
$869$	27.2259			0.923574
$870$	0.616582	−	1.06795i	0.0209041	−	0.0362070i
$871$	−0.439032	−	0.760426i	−0.0148760	−	0.0257661i
$872$	5.37910	+	9.31688i	0.182159	+	0.315509i
$873$	−0.365013	+	0.632222i	−0.0123538	+	0.0213975i
$874$	−3.79428			−0.128343
$875$	22.7223	+	2.79397i	0.768154	+	0.0944534i
$876$	4.55945			0.154050
$877$	−3.83277	+	6.63855i	−0.129423	+	0.224168i	−0.923453	−	0.383711i	$-0.874646\pi$
$877$	−3.83277	+	6.63855i	−0.129423	+	0.224168i	0.794030	+	0.607879i	$0.207979\pi$
$878$	−4.98460	−	8.63358i	−0.168222	−	0.291369i
$879$	1.05377	+	1.82519i	0.0355429	+	0.0615621i
$880$	1.53835	−	2.66450i	0.0518578	−	0.0898203i
$881$	22.6933			0.764557			0.382279	−	0.924047i	$-0.375139\pi$
$881$	22.6933			0.764557			0.382279	+	0.924047i	$0.375139\pi$
$882$	5.02337	+	17.5416i	0.169146	+	0.590658i
$883$	31.5430			1.06151			0.530754	−	0.847526i	$-0.321909\pi$
$883$	31.5430			1.06151			0.530754	+	0.847526i	$0.321909\pi$
$884$	1.26823	−	2.19664i	0.0426552	−	0.0738809i
$885$	−2.90516	−	5.03189i	−0.0976559	−	0.169145i
$886$	13.3339	+	23.0950i	0.447961	+	0.775891i
$887$	22.3890	−	38.7790i	0.751750	−	1.30207i	−0.195223	−	0.980759i	$-0.562543\pi$
$887$	22.3890	−	38.7790i	0.751750	−	1.30207i	0.946974	−	0.321311i	$-0.104124\pi$
$888$	−3.32426			−0.111555
$889$	−50.8218	−	6.24913i	−1.70451	−	0.209589i
$890$	−5.86522			−0.196603
$891$	−9.07866	+	15.7247i	−0.304146	+	0.526797i
$892$	−8.09438	−	14.0199i	−0.271020	−	0.469420i
$893$	−4.67317	−	8.09416i	−0.156382	−	0.270861i
$894$	5.58620	−	9.67558i	0.186830	−	0.323600i
$895$	11.1696			0.373360
$896$	−1.59262	+	2.11271i	−0.0532057	+	0.0705808i
$897$	−0.275667			−0.00920424
$898$	−11.0410	+	19.1236i	−0.368443	+	0.638161i
$899$	−1.66270	−	2.87989i	−0.0554543	−	0.0960497i
$900$	−5.33693	−	9.24384i	−0.177898	−	0.308128i
$901$	−5.83218	+	10.1016i	−0.194298	+	0.336534i
$902$	−23.2359			−0.773670
$903$	−1.69084	−	3.98531i	−0.0562678	−	0.132623i
$904$	−10.6520			−0.354281
$905$	9.33604	−	16.1705i	0.310340	−	0.537525i
$906$	2.90790	+	5.03663i	0.0966084	+	0.167331i
$907$	19.1918	+	33.2411i	0.637252	+	1.10375i	0.986033	+	0.166549i	$0.0532625\pi$
$907$	19.1918	+	33.2411i	0.637252	+	1.10375i	−0.348781	+	0.937204i	$0.613404\pi$
$908$	−11.2999	+	19.5719i	−0.374999	+	0.649517i
$909$	5.42789			0.180032
$910$	0.432142	+	1.01856i	0.0143254	+	0.0337648i
$911$	43.6978			1.44777			0.723886	−	0.689920i	$-0.242354\pi$
$911$	43.6978			1.44777			0.723886	+	0.689920i	$0.242354\pi$
$912$	−1.18980	+	2.06079i	−0.0393982	+	0.0682397i
$913$	20.3256	+	35.2050i	0.672679	+	1.16511i
$914$	−15.7587	−	27.2949i	−0.521252	−	0.902834i
$915$	4.44132	−	7.69259i	0.146826	−	0.254309i
$916$	29.6549			0.979827
$917$	9.52171	−	12.6312i	0.314435	−	0.417118i
$918$	−20.2908			−0.669695
$919$	−14.8371	+	25.6986i	−0.489431	+	0.847719i	−0.999926	−	0.0121615i	$-0.996129\pi$
$919$	−14.8371	+	25.6986i	−0.489431	+	0.847719i	0.510495	+	0.859881i	$0.329462\pi$
$920$	0.475705	+	0.823946i	0.0156835	+	0.0271647i
$921$	−2.66913	−	4.62306i	−0.0879507	−	0.152335i
$922$	2.79326	−	4.83808i	0.0919913	−	0.159334i
$923$	−6.01708			−0.198055
$924$	−5.32577	−	0.654865i	−0.175205	−	0.0215435i
$925$	−21.7047			−0.713647
$926$	−4.98466	+	8.63368i	−0.163806	+	0.283720i
$927$	−1.33003	−	2.30368i	−0.0436838	−	0.0756626i
$928$	1.03335	+	1.78982i	0.0339215	+	0.0587537i
$929$	−6.88860	+	11.9314i	−0.226008	+	0.391457i	−0.956621	−	0.291334i	$-0.905901\pi$
$929$	−6.88860	+	11.9314i	−0.226008	+	0.391457i	0.730614	+	0.682791i	$0.239234\pi$
$930$	−0.960083			−0.0314824
$931$	18.4568	−	19.0992i	0.604896	−	0.625951i
$932$	−21.5625			−0.706303
$933$	−7.50068	+	12.9916i	−0.245561	+	0.425325i
$934$	8.67338	+	15.0227i	0.283802	+	0.491559i
$935$	−8.87715	−	15.3757i	−0.290314	−	0.502838i
$936$	0.572884	−	0.992265i	0.0187253	−	0.0324332i
$937$	−1.72725			−0.0564267			−0.0282133	−	0.999602i	$-0.508982\pi$
$937$	−1.72725			−0.0564267			−0.0282133	+	0.999602i	$0.508982\pi$
$938$	5.24575	+	0.645025i	0.171280	+	0.0210608i
$939$	−13.2467			−0.432290
$940$	−1.17179	+	2.02960i	−0.0382196	+	0.0661983i
$941$	10.5339	+	18.2453i	0.343396	+	0.594780i	0.985061	−	0.172205i	$-0.0550893\pi$
$941$	10.5339	+	18.2453i	0.343396	+	0.594780i	−0.641665	+	0.766985i	$0.721756\pi$
$942$	−1.77591	−	3.07597i	−0.0578623	−	0.100220i
$943$	3.59262	−	6.22260i	0.116992	−	0.202636i
$944$	9.73773			0.316936
$945$	5.32795	−	7.06787i	0.173318	−	0.229918i
$946$	−8.43719			−0.274317
$947$	−9.11381	+	15.7856i	−0.296159	+	0.512963i	−0.975254	−	0.221088i	$-0.929039\pi$
$947$	−9.11381	+	15.7856i	−0.296159	+	0.512963i	0.679095	+	0.734051i	$0.262373\pi$
$948$	2.64003	+	4.57267i	0.0857442	+	0.148513i
$949$	1.59778	+	2.76744i	0.0518662	+	0.0898350i
$950$	−7.76844	+	13.4553i	−0.252042	+	0.436549i
$951$	14.3845			0.466451
$952$	5.96303	+	14.0548i	0.193263	+	0.455519i
$953$	28.0461			0.908501			0.454250	−	0.890874i	$-0.349907\pi$
$953$	28.0461			0.908501			0.454250	+	0.890874i	$0.349907\pi$
$954$	−2.63451	+	4.56311i	−0.0852955	+	0.147736i
$955$	9.61181	+	16.6481i	0.311031	+	0.538721i
$956$	−1.30790	−	2.26534i	−0.0423004	−	0.0732664i
$957$	−2.09576	+	3.62996i	−0.0677462	+	0.117340i
$958$	−29.3210			−0.947319
$959$	18.6527	+	43.9642i	0.602326	+	1.41968i
$960$	0.596681			0.0192578
$961$	14.2055	−	24.6046i	0.458242	−	0.793698i
$962$	−1.16493	−	2.01772i	−0.0375588	−	0.0650538i
$963$	−5.90982	−	10.2361i	−0.190441	−	0.329854i
$964$	−6.74083	+	11.6755i	−0.217107	+	0.376041i
$965$	−19.6096			−0.631255
$966$	0.998820	−	1.32500i	0.0321365	−	0.0426311i
$967$	−28.8423			−0.927505			−0.463752	−	0.885965i	$-0.653497\pi$
$967$	−28.8423			−0.927505			−0.463752	+	0.885965i	$0.653497\pi$
$968$	0.271166	−	0.469674i	0.00871561	−	0.0150959i
$969$	6.86581	+	11.8919i	0.220562	+	0.382024i
$970$	−0.133226	−	0.230754i	−0.00427763	−	0.00740908i
$971$	−5.91279	+	10.2413i	−0.189750	+	0.328657i	−0.945167	−	0.326587i	$-0.894101\pi$
$971$	−5.91279	+	10.2413i	−0.189750	+	0.328657i	0.755417	+	0.655245i	$0.227435\pi$
$972$	−14.0701			−0.451299
$973$	36.8313	+	4.52883i	1.18076	+	0.145188i
$974$	−15.9399			−0.510748
$975$	−0.564402	+	0.977573i	−0.0180753	+	0.0313074i
$976$	7.44337	+	12.8923i	0.238256	+	0.412672i
$977$	−8.78918	−	15.2233i	−0.281191	−	0.487036i	0.690488	−	0.723344i	$-0.257396\pi$
$977$	−8.78918	−	15.2233i	−0.281191	−	0.487036i	−0.971678	+	0.236308i	$0.924063\pi$
$978$	4.16789	−	7.21899i	0.133274	−	0.230838i
$979$	19.9358			0.637151
$980$	−6.46149	−	1.61342i	−0.206405	−	0.0515389i
$981$	28.0432			0.895349
$982$	−16.9044	+	29.2793i	−0.539442	+	0.934340i
$983$	19.2484	+	33.3392i	0.613929	+	1.06336i	0.990571	+	0.136997i	$0.0437452\pi$
$983$	19.2484	+	33.3392i	0.613929	+	1.06336i	−0.376643	+	0.926359i	$0.622922\pi$
$984$	−2.25313	−	3.90253i	−0.0718271	−	0.124408i
$985$	4.95962	−	8.59032i	0.158027	−	0.273710i
$986$	11.9261			0.379803
$987$	4.05674	+	0.498823i	0.129127	+	0.0158777i
$988$	−1.66778			−0.0530592
$989$	1.30452	−	2.25949i	0.0414813	−	0.0718477i
$990$	−4.00998	−	6.94550i	−0.127446	−	0.220742i
$991$	7.62963	+	13.2149i	0.242363	+	0.419785i	0.961387	−	0.275200i	$-0.0887441\pi$
$991$	7.62963	+	13.2149i	0.242363	+	0.419785i	−0.719024	+	0.694985i	$0.755411\pi$
$992$	0.804519	−	1.39347i	0.0255435	−	0.0442427i
$993$	22.0715			0.700417
$994$	21.8016	−	28.9212i	0.691505	−	0.917326i
$995$	14.7452			0.467456
$996$	−3.94185	+	6.82749i	−0.124902	+	0.216337i
$997$	13.8739	+	24.0303i	0.439391	+	0.761048i	0.997643	−	0.0686237i	$-0.0218608\pi$
$997$	13.8739	+	24.0303i	0.439391	+	0.761048i	−0.558251	+	0.829672i	$0.688527\pi$
$998$	5.97159	+	10.3431i	0.189027	+	0.327405i
$999$	−9.31902	+	16.1410i	−0.294841	+	0.510679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.e.b.93.2	✓	8
7.2	even	3		2254.2.a.w.1.3		4
7.4	even	3	inner	322.2.e.b.277.2	yes	8
7.5	odd	6		2254.2.a.ba.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.b.93.2	✓	8	1.1	even	1	trivial
322.2.e.b.277.2	yes	8	7.4	even	3	inner
2254.2.a.w.1.3		4	7.2	even	3
2254.2.a.ba.1.2		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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.313577 + 0.543132i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.475705 - 0.823946i) q^{5} -0.627155 q^{6} +(2.62597 + 0.322894i) q^{7} +1.00000 q^{8} +(1.30334 - 2.25745i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.313577 + 0.543132i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.475705 - 0.823946i) q^{5} -0.627155 q^{6} +(2.62597 + 0.322894i) q^{7} +1.00000 q^{8} +(1.30334 - 2.25745i) q^{9} +(0.475705 + 0.823946i) q^{10} +(-1.61692 - 2.80058i) q^{11} +(0.313577 - 0.543132i) q^{12} +0.439551 q^{13} +(-1.59262 + 2.11271i) q^{14} +0.596681 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.88528 + 4.99745i) q^{17} +(1.30334 + 2.25745i) q^{18} +(1.89714 - 3.28594i) q^{19} -0.951411 q^{20} +(0.648072 + 1.52750i) q^{21} +3.23383 q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.313577 + 0.543132i) q^{24} +(2.04741 + 3.54622i) q^{25} +(-0.219776 + 0.380663i) q^{26} +3.51625 q^{27} +(-1.03335 - 2.43561i) q^{28} -2.06671 q^{29} +(-0.298341 + 0.516741i) q^{30} +(0.804519 + 1.39347i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.01406 - 1.75640i) q^{33} -5.77056 q^{34} +(1.51524 - 2.01006i) q^{35} -2.60668 q^{36} +(-2.65027 + 4.59040i) q^{37} +(1.89714 + 3.28594i) q^{38} +(0.137833 + 0.238734i) q^{39} +(0.475705 - 0.823946i) q^{40} -7.18524 q^{41} +(-1.64689 - 0.202504i) q^{42} -2.60904 q^{43} +(-1.61692 + 2.80058i) q^{44} +(-1.24001 - 2.14776i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(1.23163 - 2.13325i) q^{47} -0.627155 q^{48} +(6.79148 + 1.69582i) q^{49} -4.09482 q^{50} +(-1.80952 + 3.13418i) q^{51} +(-0.219776 - 0.380663i) q^{52} +(1.01068 + 1.75055i) q^{53} +(-1.75813 + 3.04516i) q^{54} -3.07670 q^{55} +(2.62597 + 0.322894i) q^{56} +2.37960 q^{57} +(1.03335 - 1.78982i) q^{58} +(-4.86886 - 8.43312i) q^{59} +(-0.298341 - 0.516741i) q^{60} +(7.44337 - 12.8923i) q^{61} -1.60904 q^{62} +(4.15145 - 5.50716i) q^{63} +1.00000 q^{64} +(0.209097 - 0.362166i) q^{65} +(1.01406 + 1.75640i) q^{66} +(-0.998820 - 1.73001i) q^{67} +(2.88528 - 4.99745i) q^{68} -0.627155 q^{69} +(0.983143 + 2.31726i) q^{70} -13.6891 q^{71} +(1.30334 - 2.25745i) q^{72} +(3.63503 + 6.29606i) q^{73} +(-2.65027 - 4.59040i) q^{74} +(-1.28404 + 2.22403i) q^{75} -3.79428 q^{76} +(-3.34169 - 7.87634i) q^{77} -0.275667 q^{78} +(-4.20954 + 7.29113i) q^{79} +(0.475705 + 0.823946i) q^{80} +(-2.80740 - 4.86256i) q^{81} +(3.59262 - 6.22260i) q^{82} -12.5706 q^{83} +(0.998820 - 1.32500i) q^{84} +5.49017 q^{85} +(1.30452 - 2.25949i) q^{86} +(-0.648072 - 1.12249i) q^{87} +(-1.61692 - 2.80058i) q^{88} +(-3.08238 + 5.33884i) q^{89} +2.48002 q^{90} +(1.15425 + 0.141928i) q^{91} +1.00000 q^{92} +(-0.504558 + 0.873920i) q^{93} +(1.23163 + 2.13325i) q^{94} +(-1.80496 - 3.12628i) q^{95} +(0.313577 - 0.543132i) q^{96} -0.280060 q^{97} +(-4.86436 + 5.03368i) q^{98} -8.42956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9	\( 8 q - 4 q^{2} + 5 q^{3} - 4 q^{4} + 5 q^{5} - 10 q^{6} + q^{7} + 8 q^{8} - 7 q^{9} + 5 q^{10} + 2 q^{11} + 5 q^{12} - 14 q^{13} + q^{14} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{18} + 9 q^{19} - 10 q^{20} + 25 q^{21} - 4 q^{22} - 4 q^{23} + 5 q^{24} - 11 q^{25} + 7 q^{26} - 34 q^{27} - 2 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} - 4 q^{32} - 13 q^{33} + 6 q^{34} + 16 q^{35} + 14 q^{36} + 9 q^{38} + q^{39} + 5 q^{40} - 30 q^{41} - 8 q^{42} - 36 q^{43} + 2 q^{44} + 11 q^{45} - 4 q^{46} + 21 q^{47} - 10 q^{48} + 17 q^{49} + 22 q^{50} - 6 q^{51} + 7 q^{52} + 3 q^{53} + 17 q^{54} + 20 q^{55} + q^{56} - 18 q^{57} + 2 q^{58} + 16 q^{59} - q^{60} + q^{61} - 28 q^{62} + 37 q^{63} + 8 q^{64} - 2 q^{65} - 13 q^{66} + 17 q^{67} - 3 q^{68} - 10 q^{69} + 4 q^{70} - 2 q^{71} - 7 q^{72} + 4 q^{73} + 22 q^{75} - 18 q^{76} + 13 q^{77} - 2 q^{78} - 5 q^{79} + 5 q^{80} - 16 q^{81} + 15 q^{82} - 8 q^{83} - 17 q^{84} - 108 q^{85} + 18 q^{86} - 25 q^{87} + 2 q^{88} + 9 q^{89} - 22 q^{90} + 38 q^{91} + 8 q^{92} - 13 q^{93} + 21 q^{94} + 3 q^{95} + 5 q^{96} + 80 q^{97} + 2 q^{98} - 82 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 5 * q^3 - 4 * q^4 + 5 * q^5 - 10 * q^6 + q^7 + 8 * q^8 - 7 * q^9 + 5 * q^10 + 2 * q^11 + 5 * q^12 - 14 * q^13 + q^14 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^18 + 9 * q^19 - 10 * q^20 + 25 * q^21 - 4 * q^22 - 4 * q^23 + 5 * q^24 - 11 * q^25 + 7 * q^26 - 34 * q^27 - 2 * q^28 - 4 * q^29 - q^30 + 14 * q^31 - 4 * q^32 - 13 * q^33 + 6 * q^34 + 16 * q^35 + 14 * q^36 + 9 * q^38 + q^39 + 5 * q^40 - 30 * q^41 - 8 * q^42 - 36 * q^43 + 2 * q^44 + 11 * q^45 - 4 * q^46 + 21 * q^47 - 10 * q^48 + 17 * q^49 + 22 * q^50 - 6 * q^51 + 7 * q^52 + 3 * q^53 + 17 * q^54 + 20 * q^55 + q^56 - 18 * q^57 + 2 * q^58 + 16 * q^59 - q^60 + q^61 - 28 * q^62 + 37 * q^63 + 8 * q^64 - 2 * q^65 - 13 * q^66 + 17 * q^67 - 3 * q^68 - 10 * q^69 + 4 * q^70 - 2 * q^71 - 7 * q^72 + 4 * q^73 + 22 * q^75 - 18 * q^76 + 13 * q^77 - 2 * q^78 - 5 * q^79 + 5 * q^80 - 16 * q^81 + 15 * q^82 - 8 * q^83 - 17 * q^84 - 108 * q^85 + 18 * q^86 - 25 * q^87 + 2 * q^88 + 9 * q^89 - 22 * q^90 + 38 * q^91 + 8 * q^92 - 13 * q^93 + 21 * q^94 + 3 * q^95 + 5 * q^96 + 80 * q^97 + 2 * q^98 - 82 * q^99

Introduction

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