LMFDB - Embedded newform 670.2.e.j.171.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(171,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("670.171");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 17 x^{10} - 18 x^{9} + 172 x^{8} - 170 x^{7} + 887 x^{6} - 312 x^{5} + 2516 x^{4} + \cdots + 289 $ x^12 - 2x^11 + 17x^10 - 18x^9 + 172x^8 - 170x^7 + 887x^6 - 312x^5 + 2516x^4 - 1220x^3 + 3001x^2 + 816*x + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			171.5
Root			$-0.943122 + 1.63354i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.j.431.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +1.88624 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.943122 + 1.63354i) q^{6} +(-1.99648 + 3.45801i) q^{7} -1.00000 q^{8} +0.557917 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +1.88624 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.943122 + 1.63354i) q^{6} +(-1.99648 + 3.45801i) q^{7} -1.00000 q^{8} +0.557917 q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.721042 - 1.24888i) q^{11} +(-0.943122 + 1.63354i) q^{12} +(2.48010 + 4.29566i) q^{13} -3.99297 q^{14} -1.88624 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.20575 + 5.55253i) q^{17} +(0.278958 + 0.483170i) q^{18} +(-2.48367 - 4.30185i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-3.76586 + 6.52266i) q^{21} +1.44208 q^{22} +(0.970862 + 1.68158i) q^{23} -1.88624 q^{24} +1.00000 q^{25} +(-2.48010 + 4.29566i) q^{26} -4.60636 q^{27} +(-1.99648 - 3.45801i) q^{28} +(-3.00784 + 5.20973i) q^{29} +(-0.943122 - 1.63354i) q^{30} +(1.41896 - 2.45770i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.36006 - 2.35569i) q^{33} +(-3.20575 + 5.55253i) q^{34} +(1.99648 - 3.45801i) q^{35} +(-0.278958 + 0.483170i) q^{36} +(-2.17698 - 3.77063i) q^{37} +(2.48367 - 4.30185i) q^{38} +(4.67807 + 8.10266i) q^{39} +1.00000 q^{40} +(4.73034 - 8.19318i) q^{41} -7.53171 q^{42} +8.98302 q^{43} +(0.721042 + 1.24888i) q^{44} -0.557917 q^{45} +(-0.970862 + 1.68158i) q^{46} +(-4.39548 + 7.61320i) q^{47} +(-0.943122 - 1.63354i) q^{48} +(-4.47190 - 7.74556i) q^{49} +(0.500000 + 0.866025i) q^{50} +(6.04683 + 10.4734i) q^{51} -4.96020 q^{52} +5.31415 q^{53} +(-2.30318 - 3.98923i) q^{54} +(-0.721042 + 1.24888i) q^{55} +(1.99648 - 3.45801i) q^{56} +(-4.68481 - 8.11434i) q^{57} -6.01568 q^{58} +13.4600 q^{59} +(0.943122 - 1.63354i) q^{60} +(0.371414 + 0.643309i) q^{61} +2.83791 q^{62} +(-1.11387 + 1.92928i) q^{63} +1.00000 q^{64} +(-2.48010 - 4.29566i) q^{65} +2.72012 q^{66} +(7.39939 - 3.49987i) q^{67} -6.41151 q^{68} +(1.83128 + 3.17187i) q^{69} +3.99297 q^{70} +(-0.291770 + 0.505360i) q^{71} -0.557917 q^{72} +(-3.56673 - 6.17777i) q^{73} +(2.17698 - 3.77063i) q^{74} +1.88624 q^{75} +4.96735 q^{76} +(2.87910 + 4.98674i) q^{77} +(-4.67807 + 8.10266i) q^{78} +(6.04130 - 10.4638i) q^{79} +(0.500000 + 0.866025i) q^{80} -10.3625 q^{81} +9.46067 q^{82} +(-2.39086 - 4.14109i) q^{83} +(-3.76586 - 6.52266i) q^{84} +(-3.20575 - 5.55253i) q^{85} +(4.49151 + 7.77953i) q^{86} +(-5.67352 + 9.82682i) q^{87} +(-0.721042 + 1.24888i) q^{88} -6.43713 q^{89} +(-0.278958 - 0.483170i) q^{90} -19.8059 q^{91} -1.94172 q^{92} +(2.67650 - 4.63583i) q^{93} -8.79096 q^{94} +(2.48367 + 4.30185i) q^{95} +(0.943122 - 1.63354i) q^{96} +(4.93815 + 8.55313i) q^{97} +(4.47190 - 7.74556i) q^{98} +(0.402281 - 0.696772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9} - 6 q^{10} + 2 q^{12} + 6 q^{14} + 4 q^{15} - 6 q^{16} + 13 q^{17} + 12 q^{18} - 9 q^{19} + 6 q^{20} + 11 q^{21} - 3 q^{23} + 4 q^{24} + 12 q^{25} - 16 q^{27} + 3 q^{28} - 5 q^{29} + 2 q^{30} + 14 q^{31} + 6 q^{32} + 10 q^{33} - 13 q^{34} - 3 q^{35} - 12 q^{36} + 2 q^{37} + 9 q^{38} + 14 q^{39} + 12 q^{40} + 15 q^{41} + 22 q^{42} + 4 q^{43} - 24 q^{45} + 3 q^{46} - 11 q^{47} + 2 q^{48} - 43 q^{49} + 6 q^{50} + 15 q^{51} - 52 q^{53} - 8 q^{54} - 3 q^{56} + 3 q^{57} - 10 q^{58} + 54 q^{59} - 2 q^{60} - 6 q^{61} + 28 q^{62} - 4 q^{63} + 12 q^{64} + 20 q^{66} - 5 q^{67} - 26 q^{68} + 13 q^{69} - 6 q^{70} - 6 q^{71} - 24 q^{72} - 15 q^{73} - 2 q^{74} - 4 q^{75} + 18 q^{76} - 10 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} + 12 q^{81} + 30 q^{82} - 15 q^{83} + 11 q^{84} - 13 q^{85} + 2 q^{86} + 5 q^{87} - 14 q^{89} - 12 q^{90} + 4 q^{91} + 6 q^{92} + 28 q^{93} - 22 q^{94} + 9 q^{95} - 2 q^{96} + 21 q^{97} + 43 q^{98} - 72 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9 - 6 * q^10 + 2 * q^12 + 6 * q^14 + 4 * q^15 - 6 * q^16 + 13 * q^17 + 12 * q^18 - 9 * q^19 + 6 * q^20 + 11 * q^21 - 3 * q^23 + 4 * q^24 + 12 * q^25 - 16 * q^27 + 3 * q^28 - 5 * q^29 + 2 * q^30 + 14 * q^31 + 6 * q^32 + 10 * q^33 - 13 * q^34 - 3 * q^35 - 12 * q^36 + 2 * q^37 + 9 * q^38 + 14 * q^39 + 12 * q^40 + 15 * q^41 + 22 * q^42 + 4 * q^43 - 24 * q^45 + 3 * q^46 - 11 * q^47 + 2 * q^48 - 43 * q^49 + 6 * q^50 + 15 * q^51 - 52 * q^53 - 8 * q^54 - 3 * q^56 + 3 * q^57 - 10 * q^58 + 54 * q^59 - 2 * q^60 - 6 * q^61 + 28 * q^62 - 4 * q^63 + 12 * q^64 + 20 * q^66 - 5 * q^67 - 26 * q^68 + 13 * q^69 - 6 * q^70 - 6 * q^71 - 24 * q^72 - 15 * q^73 - 2 * q^74 - 4 * q^75 + 18 * q^76 - 10 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 + 12 * q^81 + 30 * q^82 - 15 * q^83 + 11 * q^84 - 13 * q^85 + 2 * q^86 + 5 * q^87 - 14 * q^89 - 12 * q^90 + 4 * q^91 + 6 * q^92 + 28 * q^93 - 22 * q^94 + 9 * q^95 - 2 * q^96 + 21 * q^97 + 43 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	1.88624			1.08902			0.544512	−	0.838753i	$-0.316715\pi$
$3$	1.88624			1.08902			0.544512	+	0.838753i	$0.316715\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.943122	+	1.63354i	0.385028	+	0.666888i
$7$	−1.99648	+	3.45801i	−0.754600	+	1.30701i	0.190973	+	0.981595i	$0.438836\pi$
$7$	−1.99648	+	3.45801i	−0.754600	+	1.30701i	−0.945573	+	0.325411i	$0.894498\pi$
$8$	−1.00000			−0.353553
$9$	0.557917			0.185972
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	0.721042	−	1.24888i	0.217402	−	0.376552i	−0.736611	−	0.676317i	$-0.763575\pi$
$11$	0.721042	−	1.24888i	0.217402	−	0.376552i	0.954013	+	0.299765i	$0.0969083\pi$
$12$	−0.943122	+	1.63354i	−0.272256	+	0.471561i
$13$	2.48010	+	4.29566i	0.687856	+	1.19140i	0.972530	+	0.232777i	$0.0747812\pi$
$13$	2.48010	+	4.29566i	0.687856	+	1.19140i	−0.284674	+	0.958624i	$0.591885\pi$
$14$	−3.99297			−1.06717
$15$	−1.88624			−0.487026
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.20575	+	5.55253i	0.777509	+	1.34669i	0.933373	+	0.358907i	$0.116851\pi$
$17$	3.20575	+	5.55253i	0.777509	+	1.34669i	−0.155864	+	0.987779i	$0.549816\pi$
$18$	0.278958	+	0.483170i	0.0657511	+	0.113884i
$19$	−2.48367	−	4.30185i	−0.569794	−	0.986912i	−0.996586	−	0.0825619i	$-0.973690\pi$
$19$	−2.48367	−	4.30185i	−0.569794	−	0.986912i	0.426792	−	0.904350i	$-0.359644\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−3.76586	+	6.52266i	−0.821777	+	1.42336i
$22$	1.44208			0.307453
$23$	0.970862	+	1.68158i	0.202439	+	0.350634i	0.949314	−	0.314330i	$-0.101780\pi$
$23$	0.970862	+	1.68158i	0.202439	+	0.350634i	−0.746875	+	0.664964i	$0.768447\pi$
$24$	−1.88624			−0.385028
$25$	1.00000			0.200000
$26$	−2.48010	+	4.29566i	−0.486387	+	0.842448i
$27$	−4.60636			−0.886495
$28$	−1.99648	−	3.45801i	−0.377300	−	0.653503i
$29$	−3.00784	+	5.20973i	−0.558542	+	0.967422i	0.439077	+	0.898449i	$0.355306\pi$
$29$	−3.00784	+	5.20973i	−0.558542	+	0.967422i	−0.997619	+	0.0689730i	$0.978028\pi$
$30$	−0.943122	−	1.63354i	−0.172190	−	0.298241i
$31$	1.41896	−	2.45770i	0.254852	−	0.441417i	−0.710003	−	0.704198i	$-0.751307\pi$
$31$	1.41896	−	2.45770i	0.254852	−	0.441417i	0.964855	+	0.262782i	$0.0846399\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.36006	−	2.35569i	0.236756	−	0.410074i
$34$	−3.20575	+	5.55253i	−0.549782	+	0.952251i
$35$	1.99648	−	3.45801i	0.337467	−	0.584511i
$36$	−0.278958	+	0.483170i	−0.0464931	+	0.0805284i
$37$	−2.17698	−	3.77063i	−0.357892	−	0.619888i	0.629716	−	0.776825i	$-0.283171\pi$
$37$	−2.17698	−	3.77063i	−0.357892	−	0.619888i	−0.987609	+	0.156937i	$0.949838\pi$
$38$	2.48367	−	4.30185i	0.402905	−	0.697852i
$39$	4.67807	+	8.10266i	0.749091	+	1.29746i
$40$	1.00000			0.158114
$41$	4.73034	−	8.19318i	0.738755	−	1.27956i	−0.214302	−	0.976768i	$-0.568748\pi$
$41$	4.73034	−	8.19318i	0.738755	−	1.27956i	0.953056	−	0.302793i	$-0.0979191\pi$
$42$	−7.53171			−1.16217
$43$	8.98302			1.36990			0.684949	−	0.728591i	$-0.259824\pi$
$43$	8.98302			1.36990			0.684949	+	0.728591i	$0.259824\pi$
$44$	0.721042	+	1.24888i	0.108701	+	0.188276i
$45$	−0.557917			−0.0831694
$46$	−0.970862	+	1.68158i	−0.143146	+	0.247936i
$47$	−4.39548	+	7.61320i	−0.641147	+	1.11050i	0.344030	+	0.938959i	$0.388208\pi$
$47$	−4.39548	+	7.61320i	−0.641147	+	1.11050i	−0.985177	+	0.171540i	$0.945126\pi$
$48$	−0.943122	−	1.63354i	−0.136128	−	0.235781i
$49$	−4.47190	−	7.74556i	−0.638843	−	1.10651i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	6.04683	+	10.4734i	0.846726	+	1.46657i
$52$	−4.96020			−0.687856
$53$	5.31415			0.729954			0.364977	−	0.931016i	$-0.381077\pi$
$53$	5.31415			0.729954			0.364977	+	0.931016i	$0.381077\pi$
$54$	−2.30318	−	3.98923i	−0.313423	−	0.542865i
$55$	−0.721042	+	1.24888i	−0.0972252	+	0.168399i
$56$	1.99648	−	3.45801i	0.266791	−	0.462096i
$57$	−4.68481	−	8.11434i	−0.620519	−	1.07477i
$58$	−6.01568			−0.789897
$59$	13.4600			1.75234			0.876168	−	0.482005i	$-0.160091\pi$
$59$	13.4600			1.75234			0.876168	+	0.482005i	$0.160091\pi$
$60$	0.943122	−	1.63354i	0.121757	−	0.210889i
$61$	0.371414	+	0.643309i	0.0475547	+	0.0823672i	0.888823	−	0.458251i	$-0.151524\pi$
$61$	0.371414	+	0.643309i	0.0475547	+	0.0823672i	−0.841268	+	0.540618i	$0.818190\pi$
$62$	2.83791			0.360415
$63$	−1.11387	+	1.92928i	−0.140335	+	0.243067i
$64$	1.00000			0.125000
$65$	−2.48010	−	4.29566i	−0.307618	−	0.532811i
$66$	2.72012			0.334824
$67$	7.39939	−	3.49987i	0.903979	−	0.427577i
$67$	7.39939	−	3.49987i	0.903979	−	0.427577i
$68$	−6.41151			−0.777509
$69$	1.83128	+	3.17187i	0.220460	+	0.381849i
$70$	3.99297			0.477251
$71$	−0.291770	+	0.505360i	−0.0346267	+	0.0599752i	−0.882819	−	0.469713i	$-0.844358\pi$
$71$	−0.291770	+	0.505360i	−0.0346267	+	0.0599752i	0.848193	+	0.529688i	$0.177691\pi$
$72$	−0.557917			−0.0657511
$73$	−3.56673	−	6.17777i	−0.417455	−	0.723053i	0.578228	−	0.815875i	$-0.303744\pi$
$73$	−3.56673	−	6.17777i	−0.417455	−	0.723053i	−0.995683	+	0.0928225i	$0.970411\pi$
$74$	2.17698	−	3.77063i	0.253068	−	0.438327i
$75$	1.88624			0.217805
$76$	4.96735			0.569794
$77$	2.87910	+	4.98674i	0.328103	+	0.568292i
$78$	−4.67807	+	8.10266i	−0.529687	+	0.917445i
$79$	6.04130	−	10.4638i	0.679699	−	1.17727i	−0.295372	−	0.955382i	$-0.595444\pi$
$79$	6.04130	−	10.4638i	0.679699	−	1.17727i	0.975071	−	0.221892i	$-0.0712231\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−10.3625			−1.15139
$82$	9.46067			1.04476
$83$	−2.39086	−	4.14109i	−0.262431	−	0.454543i	0.704457	−	0.709747i	$-0.251191\pi$
$83$	−2.39086	−	4.14109i	−0.262431	−	0.454543i	−0.966887	+	0.255204i	$0.917857\pi$
$84$	−3.76586	−	6.52266i	−0.410889	−	0.711680i
$85$	−3.20575	−	5.55253i	−0.347713	−	0.602256i
$86$	4.49151	+	7.77953i	0.484332	+	0.838888i
$87$	−5.67352	+	9.82682i	−0.608265	+	1.05355i
$88$	−0.721042	+	1.24888i	−0.0768633	+	0.133131i
$89$	−6.43713			−0.682334			−0.341167	−	0.940003i	$-0.610822\pi$
$89$	−6.43713			−0.682334			−0.341167	+	0.940003i	$0.610822\pi$
$90$	−0.278958	−	0.483170i	−0.0294048	−	0.0509306i
$91$	−19.8059			−2.07622
$92$	−1.94172			−0.202439
$93$	2.67650	−	4.63583i	0.277540	−	0.480713i
$94$	−8.79096			−0.906719
$95$	2.48367	+	4.30185i	0.254819	+	0.441360i
$96$	0.943122	−	1.63354i	0.0962570	−	0.166722i
$97$	4.93815	+	8.55313i	0.501393	+	0.868438i	0.999999	+	0.00160934i	$0.000512269\pi$
$97$	4.93815	+	8.55313i	0.501393	+	0.868438i	−0.498606	+	0.866829i	$0.666154\pi$
$98$	4.47190	−	7.74556i	0.451730	−	0.782420i
$99$	0.402281	−	0.696772i	0.0404308	−	0.0700282i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	8.87817	−	15.3774i	0.883411	−	1.53011i	0.0358876	−	0.999356i	$-0.488574\pi$
$101$	8.87817	−	15.3774i	0.883411	−	1.53011i	0.847524	−	0.530757i	$-0.178092\pi$
$102$	−6.04683	+	10.4734i	−0.598726	+	1.03702i
$103$	1.47658	−	2.55752i	0.145492	−	0.252000i	−0.784064	−	0.620680i	$-0.786857\pi$
$103$	1.47658	−	2.55752i	0.145492	−	0.252000i	0.929556	+	0.368680i	$0.120190\pi$
$104$	−2.48010	−	4.29566i	−0.243194	−	0.421224i
$105$	3.76586	−	6.52266i	0.367510	−	0.636546i
$106$	2.65707	+	4.60219i	0.258078	+	0.447004i
$107$	−9.65677			−0.933555			−0.466778	−	0.884375i	$-0.654585\pi$
$107$	−9.65677			−0.933555			−0.466778	+	0.884375i	$0.654585\pi$
$108$	2.30318	−	3.98923i	0.221624	−	0.383864i
$109$	−1.66256			−0.159245			−0.0796224	−	0.996825i	$-0.525371\pi$
$109$	−1.66256			−0.159245			−0.0796224	+	0.996825i	$0.525371\pi$
$110$	−1.44208			−0.137497
$111$	−4.10631	−	7.11233i	−0.389753	−	0.675073i
$112$	3.99297			0.377300
$113$	−9.03876	+	15.6556i	−0.850295	+	1.47275i	0.0306465	+	0.999530i	$0.490243\pi$
$113$	−9.03876	+	15.6556i	−0.850295	+	1.47275i	−0.880942	+	0.473224i	$0.843090\pi$
$114$	4.68481	−	8.11434i	0.438773	−	0.759977i
$115$	−0.970862	−	1.68158i	−0.0905333	−	0.156808i
$116$	−3.00784	−	5.20973i	−0.279271	−	0.483711i
$117$	1.38369	+	2.39662i	0.127922	+	0.221568i
$118$	6.72998	+	11.6567i	0.619545	+	1.07308i
$119$	−25.6009			−2.34684
$120$	1.88624			0.172190
$121$	4.46020	+	7.72529i	0.405473	+	0.702299i
$122$	−0.371414	+	0.643309i	−0.0336263	+	0.0582424i
$123$	8.92257	−	15.4543i	0.804521	−	1.39347i
$124$	1.41896	+	2.45770i	0.127426	+	0.220708i
$125$	−1.00000			−0.0894427
$126$	−2.22775			−0.198463
$127$	3.74127	−	6.48008i	0.331984	−	0.575014i	−0.650917	−	0.759149i	$-0.725615\pi$
$127$	3.74127	−	6.48008i	0.331984	−	0.575014i	0.982901	+	0.184136i	$0.0589486\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	16.9442			1.49185
$130$	2.48010	−	4.29566i	0.217519	−	0.376754i
$131$	−18.1566			−1.58635			−0.793173	−	0.608997i	$-0.791572\pi$
$131$	−18.1566			−1.58635			−0.793173	+	0.608997i	$0.791572\pi$
$132$	1.36006	+	2.35569i	0.118378	+	0.205037i
$133$	19.8345			1.71987
$134$	6.73067	+	4.65812i	0.581441	+	0.402400i
$135$	4.60636			0.396453
$136$	−3.20575	−	5.55253i	−0.274891	−	0.476125i
$137$	−2.13211			−0.182159			−0.0910794	−	0.995844i	$-0.529032\pi$
$137$	−2.13211			−0.182159			−0.0910794	+	0.995844i	$0.529032\pi$
$138$	−1.83128	+	3.17187i	−0.155889	+	0.270008i
$139$	22.2195			1.88463			0.942317	−	0.334722i	$-0.108643\pi$
$139$	22.2195			1.88463			0.942317	+	0.334722i	$0.108643\pi$
$140$	1.99648	+	3.45801i	0.168734	+	0.292255i
$141$	−8.29095	+	14.3603i	−0.698224	+	1.20936i
$142$	−0.583540			−0.0489696
$143$	7.15302			0.598165
$144$	−0.278958	−	0.483170i	−0.0232465	−	0.0402642i
$145$	3.00784	−	5.20973i	0.249787	−	0.432644i
$146$	3.56673	−	6.17777i	0.295185	−	0.511276i
$147$	−8.43510	−	14.6100i	−0.695715	−	1.20501i
$148$	4.35395			0.357892
$149$	1.86546			0.152824			0.0764121	−	0.997076i	$-0.475654\pi$
$149$	1.86546			0.152824			0.0764121	+	0.997076i	$0.475654\pi$
$150$	0.943122	+	1.63354i	0.0770056	+	0.133378i
$151$	10.6614	+	18.4661i	0.867612	+	1.50275i	0.864430	+	0.502753i	$0.167680\pi$
$151$	10.6614	+	18.4661i	0.867612	+	1.50275i	0.00318237	+	0.999995i	$0.498987\pi$
$152$	2.48367	+	4.30185i	0.201452	+	0.348926i
$153$	1.78854	+	3.09785i	0.144595	+	0.250446i
$154$	−2.87910	+	4.98674i	−0.232004	+	0.401843i
$155$	−1.41896	+	2.45770i	−0.113973	+	0.197408i
$156$	−9.35614			−0.749091
$157$	−0.763090	−	1.32171i	−0.0609012	−	0.105484i	0.833967	−	0.551814i	$-0.186064\pi$
$157$	−0.763090	−	1.32171i	−0.0609012	−	0.105484i	−0.894868	+	0.446330i	$0.852731\pi$
$158$	12.0826			0.961240
$159$	10.0238			0.794938
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−7.75324			−0.611041
$162$	−5.18124	−	8.97417i	−0.407077	−	0.705077i
$163$	7.90799	−	13.6970i	0.619402	−	1.07284i	−0.370193	−	0.928955i	$-0.620709\pi$
$163$	7.90799	−	13.6970i	0.619402	−	1.07284i	0.989595	−	0.143881i	$-0.0459581\pi$
$164$	4.73034	+	8.19318i	0.369377	+	0.639780i
$165$	−1.36006	+	2.35569i	−0.105881	+	0.183390i
$166$	2.39086	−	4.14109i	0.185566	−	0.321411i
$167$	2.37421	−	4.11226i	0.183722	−	0.318216i	−0.759423	−	0.650597i	$-0.774519\pi$
$167$	2.37421	−	4.11226i	0.183722	−	0.318216i	0.943145	+	0.332381i	$0.107852\pi$
$168$	3.76586	−	6.52266i	0.290542	−	0.503234i
$169$	−5.80178	+	10.0490i	−0.446291	+	0.772999i
$170$	3.20575	−	5.55253i	0.245870	−	0.425859i
$171$	−1.38568	−	2.40007i	−0.105966	−	0.183538i
$172$	−4.49151	+	7.77953i	−0.342475	+	0.593183i
$173$	−3.32667	−	5.76196i	−0.252922	−	0.438074i	0.711407	−	0.702780i	$-0.248058\pi$
$173$	−3.32667	−	5.76196i	−0.252922	−	0.438074i	−0.964329	+	0.264707i	$0.914725\pi$
$174$	−11.3470			−0.860217
$175$	−1.99648	+	3.45801i	−0.150920	+	0.261401i
$176$	−1.44208			−0.108701
$177$	25.3888			1.90834
$178$	−3.21857	−	5.57472i	−0.241242	−	0.417843i
$179$	−5.23728			−0.391453			−0.195726	−	0.980659i	$-0.562706\pi$
$179$	−5.23728			−0.391453			−0.195726	+	0.980659i	$0.562706\pi$
$180$	0.278958	−	0.483170i	0.0207923	−	0.0360134i
$181$	−11.0908	+	19.2098i	−0.824372	+	1.42785i	0.0780268	+	0.996951i	$0.475138\pi$
$181$	−11.0908	+	19.2098i	−0.824372	+	1.42785i	−0.902399	+	0.430902i	$0.858195\pi$
$182$	−9.90296	−	17.1524i	−0.734056	−	1.27142i
$183$	0.700578	+	1.21344i	0.0517882	+	0.0896999i
$184$	−0.970862	−	1.68158i	−0.0715729	−	0.123968i
$185$	2.17698	+	3.77063i	0.160054	+	0.277222i
$186$	5.35300			0.392501
$187$	9.24593			0.676129
$188$	−4.39548	−	7.61320i	−0.320573	−	0.555250i
$189$	9.19654	−	15.9289i	0.668950	−	1.15865i
$190$	−2.48367	+	4.30185i	−0.180185	+	0.312089i
$191$	8.58744	+	14.8739i	0.621366	+	1.07624i	0.989232	+	0.146358i	$0.0467551\pi$
$191$	8.58744	+	14.8739i	0.621366	+	1.07624i	−0.367866	+	0.929879i	$0.619912\pi$
$192$	1.88624			0.136128
$193$	−16.8970			−1.21627			−0.608135	−	0.793833i	$-0.708082\pi$
$193$	−16.8970			−1.21627			−0.608135	+	0.793833i	$0.708082\pi$
$194$	−4.93815	+	8.55313i	−0.354538	+	0.614079i
$195$	−4.67807	−	8.10266i	−0.335004	−	0.580243i
$196$	8.94380			0.638843
$197$	−1.51604	+	2.62585i	−0.108013	+	0.187084i	−0.914965	−	0.403533i	$-0.867782\pi$
$197$	−1.51604	+	2.62585i	−0.108013	+	0.187084i	0.806952	+	0.590617i	$0.201116\pi$
$198$	0.804563			0.0571778
$199$	−1.71746	−	2.97472i	−0.121747	−	0.210872i	0.798710	−	0.601717i	$-0.205516\pi$
$199$	−1.71746	−	2.97472i	−0.121747	−	0.210872i	−0.920457	+	0.390844i	$0.872183\pi$
$200$	−1.00000			−0.0707107
$201$	13.9570	−	6.60161i	0.984454	−	0.465641i
$202$	17.7563			1.24933
$203$	−12.0102	−	20.8023i	−0.842951	−	1.46003i
$204$	−12.0937			−0.846726
$205$	−4.73034	+	8.19318i	−0.330381	+	0.572237i
$206$	2.95317			0.205757
$207$	0.541660	+	0.938183i	0.0376480	+	0.0652082i
$208$	2.48010	−	4.29566i	0.171964	−	0.297850i
$209$	−7.16333			−0.495498
$210$	7.53171			0.519738
$211$	−10.7834	−	18.6773i	−0.742357	−	1.28580i	−0.951420	−	0.307897i	$-0.900375\pi$
$211$	−10.7834	−	18.6773i	−0.742357	−	1.28580i	0.209063	−	0.977902i	$-0.432959\pi$
$212$	−2.65707	+	4.60219i	−0.182489	+	0.316080i
$213$	−0.550349	+	0.953233i	−0.0377093	+	0.0653145i
$214$	−4.82839	−	8.36301i	−0.330062	−	0.571684i
$215$	−8.98302			−0.612637
$216$	4.60636			0.313423
$217$	5.66585	+	9.81354i	0.384623	+	0.666186i
$218$	−0.831282	−	1.43982i	−0.0563015	−	0.0975171i
$219$	−6.72773	−	11.6528i	−0.454618	−	0.787422i
$220$	−0.721042	−	1.24888i	−0.0486126	−	0.0841995i
$221$	−15.9012	+	27.5416i	−1.06963	+	1.85265i
$222$	4.10631	−	7.11233i	0.275597	−	0.477348i
$223$	18.8808			1.26435			0.632177	−	0.774824i	$-0.282162\pi$
$223$	18.8808			1.26435			0.632177	+	0.774824i	$0.282162\pi$
$224$	1.99648	+	3.45801i	0.133396	+	0.231048i
$225$	0.557917			0.0371945
$226$	−18.0775			−1.20250
$227$	4.05232	−	7.01883i	0.268962	−	0.465856i	−0.699632	−	0.714503i	$-0.746653\pi$
$227$	4.05232	−	7.01883i	0.268962	−	0.465856i	0.968594	+	0.248647i	$0.0799860\pi$
$228$	9.36963			0.620519
$229$	0.460070	+	0.796864i	0.0304023	+	0.0526583i	0.880826	−	0.473440i	$-0.156988\pi$
$229$	0.460070	+	0.796864i	0.0304023	+	0.0526583i	−0.850424	+	0.526098i	$0.823655\pi$
$230$	0.970862	−	1.68158i	0.0640167	−	0.110880i
$231$	5.43068	+	9.40621i	0.357312	+	0.618883i
$232$	3.00784	−	5.20973i	0.197474	−	0.342035i
$233$	5.97121	−	10.3424i	0.391187	−	0.677556i	−0.601419	−	0.798934i	$-0.705398\pi$
$233$	5.97121	−	10.3424i	0.391187	−	0.677556i	0.992606	+	0.121378i	$0.0387312\pi$
$234$	−1.38369	+	2.39662i	−0.0904546	+	0.156672i
$235$	4.39548	−	7.61320i	0.286730	−	0.496630i
$236$	−6.72998	+	11.6567i	−0.438084	+	0.758784i
$237$	11.3954	−	19.7374i	0.740209	−	1.28208i
$238$	−12.8005	−	22.1711i	−0.829732	−	1.43714i
$239$	−8.26498	+	14.3154i	−0.534617	+	0.925984i	0.464565	+	0.885539i	$0.346211\pi$
$239$	−8.26498	+	14.3154i	−0.534617	+	0.925984i	−0.999182	+	0.0404448i	$0.987122\pi$
$240$	0.943122	+	1.63354i	0.0608783	+	0.105444i
$241$	16.8372			1.08458			0.542290	−	0.840191i	$-0.317557\pi$
$241$	16.8372			1.08458			0.542290	+	0.840191i	$0.317557\pi$
$242$	−4.46020	+	7.72529i	−0.286712	+	0.496600i
$243$	−5.72707			−0.367392
$244$	−0.742829			−0.0475547
$245$	4.47190	+	7.74556i	0.285699	+	0.494846i
$246$	17.8451			1.13776
$247$	12.3195	−	21.3380i	0.783872	−	1.35771i
$248$	−1.41896	+	2.45770i	−0.0901038	+	0.156064i
$249$	−4.50974	−	7.81110i	−0.285793	−	0.495008i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−3.95778	−	6.85508i	−0.249813	−	0.432689i	0.713661	−	0.700491i	$-0.247036\pi$
$251$	−3.95778	−	6.85508i	−0.249813	−	0.432689i	−0.963474	+	0.267803i	$0.913702\pi$
$252$	−1.11387	−	1.92928i	−0.0701674	−	0.121533i
$253$	2.80013			0.176042
$254$	7.48255			0.469497
$255$	−6.04683	−	10.4734i	−0.378667	−	0.655871i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.65470	+	8.06217i	−0.290352	+	0.502904i	−0.973893	−	0.227008i	$-0.927106\pi$
$257$	−4.65470	+	8.06217i	−0.290352	+	0.502904i	0.683541	+	0.729912i	$0.260439\pi$
$258$	8.47209	+	14.6741i	0.527449	+	0.913569i
$259$	17.3852			1.08026
$260$	4.96020			0.307618
$261$	−1.67812	+	2.90660i	−0.103873	+	0.179914i
$262$	−9.07828	−	15.7240i	−0.560858	−	0.971434i
$263$	13.6710			0.842989			0.421494	−	0.906831i	$-0.361506\pi$
$263$	13.6710			0.842989			0.421494	+	0.906831i	$0.361506\pi$
$264$	−1.36006	+	2.35569i	−0.0837059	+	0.144983i
$265$	−5.31415			−0.326446
$266$	9.91723	+	17.1771i	0.608064	+	1.05320i
$267$	−12.1420			−0.743078
$268$	−0.668718	+	8.15799i	−0.0408485	+	0.498329i
$269$	4.48604			0.273519			0.136759	−	0.990604i	$-0.456331\pi$
$269$	4.48604			0.273519			0.136759	+	0.990604i	$0.456331\pi$
$270$	2.30318	+	3.98923i	0.140167	+	0.242777i
$271$	−3.32395			−0.201916			−0.100958	−	0.994891i	$-0.532191\pi$
$271$	−3.32395			−0.201916			−0.100958	+	0.994891i	$0.532191\pi$
$272$	3.20575	−	5.55253i	0.194377	−	0.336671i
$273$	−37.3588			−2.26106
$274$	−1.06606	−	1.84647i	−0.0644029	−	0.111549i
$275$	0.721042	−	1.24888i	0.0434804	−	0.0753103i
$276$	−3.66256			−0.220460
$277$	−0.0173137			−0.00104028			−0.000520139	−	1.00000i	$-0.500166\pi$
$277$	−0.0173137			−0.00104028			−0.000520139		1.00000i	$0.500166\pi$
$278$	11.1098	+	19.2427i	0.666319	+	1.15410i
$279$	0.791660	−	1.37120i	0.0473954	−	0.0820913i
$280$	−1.99648	+	3.45801i	−0.119313	+	0.206656i
$281$	−10.0822	−	17.4630i	−0.601456	−	1.04175i	−0.992601	−	0.121423i	$-0.961254\pi$
$281$	−10.0822	−	17.4630i	−0.601456	−	1.04175i	0.391145	−	0.920329i	$-0.372079\pi$
$282$	−16.5819			−0.987438
$283$	2.62334			0.155941			0.0779706	−	0.996956i	$-0.475156\pi$
$283$	2.62334			0.155941			0.0779706	+	0.996956i	$0.475156\pi$
$284$	−0.291770	−	0.505360i	−0.0173134	−	0.0299876i
$285$	4.68481	+	8.11434i	0.277504	+	0.480652i
$286$	3.57651	+	6.19470i	0.211483	+	0.366300i
$287$	18.8881	+	32.7151i	1.11493	+	1.93111i
$288$	0.278958	−	0.483170i	0.0164378	−	0.0284711i
$289$	−12.0537	+	20.8776i	−0.709042	+	1.22810i
$290$	6.01568			0.353253
$291$	9.31455	+	16.1333i	0.546029	+	0.945750i
$292$	7.13347			0.417455
$293$	−9.36395			−0.547048			−0.273524	−	0.961865i	$-0.588189\pi$
$293$	−9.36395			−0.547048			−0.273524	+	0.961865i	$0.588189\pi$
$294$	8.43510	−	14.6100i	0.491945	−	0.852073i
$295$	−13.4600			−0.783669
$296$	2.17698	+	3.77063i	0.126534	+	0.219163i
$297$	−3.32138	+	5.75280i	−0.192726	+	0.333811i
$298$	0.932729	+	1.61553i	0.0540315	+	0.0935853i
$299$	−4.81567	+	8.34098i	−0.278497	+	0.482371i
$300$	−0.943122	+	1.63354i	−0.0544512	+	0.0943122i
$301$	−17.9345	+	31.0634i	−1.03373	+	1.79047i
$302$	−10.6614	+	18.4661i	−0.613494	+	1.06260i
$303$	16.7464	−	29.0056i	0.962056	−	1.66633i
$304$	−2.48367	+	4.30185i	−0.142448	+	0.246728i
$305$	−0.371414	−	0.643309i	−0.0212671	−	0.0368357i
$306$	−1.78854	+	3.09785i	−0.102244	+	0.177092i
$307$	−2.23067	−	3.86363i	−0.127311	−	0.220509i	0.795323	−	0.606186i	$-0.207301\pi$
$307$	−2.23067	−	3.86363i	−0.127311	−	0.220509i	−0.922634	+	0.385677i	$0.873968\pi$
$308$	−5.75819			−0.328103
$309$	2.78520	−	4.82410i	0.158444	−	0.274434i
$310$	−2.83791			−0.161183
$311$	−32.8498			−1.86274			−0.931370	−	0.364073i	$-0.881386\pi$
$311$	−32.8498			−1.86274			−0.931370	+	0.364073i	$0.881386\pi$
$312$	−4.67807	−	8.10266i	−0.264844	−	0.458723i
$313$	−28.1336			−1.59020			−0.795102	−	0.606476i	$-0.792582\pi$
$313$	−28.1336			−1.59020			−0.795102	+	0.606476i	$0.792582\pi$
$314$	0.763090	−	1.32171i	0.0430636	−	0.0745884i
$315$	1.11387	−	1.92928i	0.0627596	−	0.108703i
$316$	6.04130	+	10.4638i	0.339850	+	0.588637i
$317$	13.6526	+	23.6470i	0.766807	+	1.32815i	0.939286	+	0.343135i	$0.111489\pi$
$317$	13.6526	+	23.6470i	0.766807	+	1.32815i	−0.172479	+	0.985013i	$0.555178\pi$
$318$	5.01189	+	8.68085i	0.281053	+	0.486798i
$319$	4.33755	+	7.51286i	0.242856	+	0.420640i
$320$	−1.00000			−0.0559017
$321$	−18.2150			−1.01666
$322$	−3.87662	−	6.71450i	−0.216036	−	0.374185i
$323$	15.9241	−	27.5813i	0.886040	−	1.53467i
$324$	5.18124	−	8.97417i	0.287847	−	0.498565i
$325$	2.48010	+	4.29566i	0.137571	+	0.238280i
$326$	15.8160			0.875966
$327$	−3.13600			−0.173421
$328$	−4.73034	+	8.19318i	−0.261189	+	0.452393i
$329$	−17.5510	−	30.3993i	−0.967619	−	1.67597i
$330$	−2.72012			−0.149738
$331$	4.36908	−	7.56747i	0.240146	−	0.415946i	−0.720609	−	0.693341i	$-0.756138\pi$
$331$	4.36908	−	7.56747i	0.240146	−	0.415946i	0.960756	+	0.277395i	$0.0894712\pi$
$332$	4.78171			0.262431
$333$	−1.21457	−	2.10370i	−0.0665581	−	0.115282i
$334$	4.74842			0.259822
$335$	−7.39939	+	3.49987i	−0.404272	+	0.191218i
$336$	7.53171			0.410889
$337$	2.38943	+	4.13861i	0.130160	+	0.225445i	0.923738	−	0.383024i	$-0.125117\pi$
$337$	2.38943	+	4.13861i	0.130160	+	0.225445i	−0.793578	+	0.608469i	$0.791784\pi$
$338$	−11.6036			−0.631151
$339$	−17.0493	+	29.5303i	−0.925992	+	1.60386i
$340$	6.41151			0.347713
$341$	−2.04625	−	3.54421i	−0.110811	−	0.191930i
$342$	1.38568	−	2.40007i	0.0749292	−	0.129781i
$343$	7.76154			0.419084
$344$	−8.98302			−0.484332
$345$	−1.83128	−	3.17187i	−0.0985929	−	0.170768i
$346$	3.32667	−	5.76196i	0.178843	−	0.309765i
$347$	−6.90043	+	11.9519i	−0.370434	+	0.641611i	−0.989632	−	0.143624i	$-0.954124\pi$
$347$	−6.90043	+	11.9519i	−0.370434	+	0.641611i	0.619198	+	0.785235i	$0.287458\pi$
$348$	−5.67352	−	9.82682i	−0.304132	−	0.526773i
$349$	1.56664			0.0838605			0.0419302	−	0.999121i	$-0.486649\pi$
$349$	1.56664			0.0838605			0.0419302	+	0.999121i	$0.486649\pi$
$350$	−3.99297			−0.213433
$351$	−11.4242	−	19.7874i	−0.609781	−	1.05617i
$352$	−0.721042	−	1.24888i	−0.0384316	−	0.0665656i
$353$	11.8424	+	20.5117i	0.630309	+	1.09173i	0.987488	+	0.157692i	$0.0504053\pi$
$353$	11.8424	+	20.5117i	0.630309	+	1.09173i	−0.357179	+	0.934036i	$0.616261\pi$
$354$	12.6944	+	21.9873i	0.674699	+	1.16861i
$355$	0.291770	−	0.505360i	0.0154855	−	0.0268217i
$356$	3.21857	−	5.57472i	0.170584	−	0.295459i
$357$	−48.2896			−2.55576
$358$	−2.61864	−	4.53562i	−0.138399	−	0.239715i
$359$	−21.6979			−1.14517			−0.572585	−	0.819845i	$-0.694059\pi$
$359$	−21.6979			−1.14517			−0.572585	+	0.819845i	$0.694059\pi$
$360$	0.557917			0.0294048
$361$	−2.83726	+	4.91428i	−0.149330	+	0.258647i
$362$	−22.1816			−1.16584
$363$	8.41302	+	14.5718i	0.441569	+	0.764820i
$364$	9.90296	−	17.1524i	0.519056	−	0.899032i
$365$	3.56673	+	6.17777i	0.186691	+	0.323359i
$366$	−0.700578	+	1.21344i	−0.0366198	+	0.0634274i
$367$	3.54354	−	6.13759i	0.184971	−	0.320380i	−0.758596	−	0.651562i	$-0.774114\pi$
$367$	3.54354	−	6.13759i	0.184971	−	0.320380i	0.943567	+	0.331182i	$0.107447\pi$
$368$	0.970862	−	1.68158i	0.0506097	−	0.0876585i
$369$	2.63914	−	4.57112i	0.137388	−	0.237963i
$370$	−2.17698	+	3.77063i	−0.113176	+	0.196026i
$371$	−10.6096	+	18.3764i	−0.550824	+	0.954055i
$372$	2.67650	+	4.63583i	0.138770	+	0.240357i
$373$	−5.47473	+	9.48250i	−0.283471	+	0.490985i	−0.972237	−	0.233998i	$-0.924819\pi$
$373$	−5.47473	+	9.48250i	−0.283471	+	0.490985i	0.688767	+	0.724983i	$0.258152\pi$
$374$	4.62296	+	8.00721i	0.239048	+	0.414043i
$375$	−1.88624			−0.0974052
$376$	4.39548	−	7.61320i	0.226680	−	0.392621i
$377$	−29.8390			−1.53678
$378$	18.3931			0.946038
$379$	8.18791	+	14.1819i	0.420585	+	0.728474i	0.995997	−	0.0893896i	$-0.0284916\pi$
$379$	8.18791	+	14.1819i	0.420585	+	0.728474i	−0.575412	+	0.817864i	$0.695158\pi$
$380$	−4.96735			−0.254819
$381$	7.05695	−	12.2230i	0.361539	−	0.626203i
$382$	−8.58744	+	14.8739i	−0.439372	+	0.761014i
$383$	−11.1863	−	19.3752i	−0.571592	−	0.990026i	−0.996403	−	0.0847439i	$-0.972993\pi$
$383$	−11.1863	−	19.3752i	−0.571592	−	0.990026i	0.424811	−	0.905282i	$-0.360341\pi$
$384$	0.943122	+	1.63354i	0.0481285	+	0.0833610i
$385$	−2.87910	−	4.98674i	−0.146732	−	0.254148i
$386$	−8.44848	−	14.6332i	−0.430017	−	0.744810i
$387$	5.01178			0.254763
$388$	−9.87630			−0.501393
$389$	10.6573	+	18.4589i	0.540345	+	0.935904i	0.998884	+	0.0472303i	$0.0150395\pi$
$389$	10.6573	+	18.4589i	0.540345	+	0.935904i	−0.458539	+	0.888674i	$0.651627\pi$
$390$	4.67807	−	8.10266i	0.236883	−	0.410294i
$391$	−6.22469	+	10.7815i	−0.314796	+	0.545242i
$392$	4.47190	+	7.74556i	0.225865	+	0.391210i
$393$	−34.2477			−1.72757
$394$	−3.03207			−0.152754
$395$	−6.04130	+	10.4638i	−0.303971	+	0.526493i
$396$	0.402281	+	0.696772i	0.0202154	+	0.0350141i
$397$	2.85249			0.143162			0.0715812	−	0.997435i	$-0.477195\pi$
$397$	2.85249			0.143162			0.0715812	+	0.997435i	$0.477195\pi$
$398$	1.71746	−	2.97472i	0.0860883	−	0.149109i
$399$	37.4126			1.87297
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−19.7022			−0.983882			−0.491941	−	0.870628i	$-0.663712\pi$
$401$	−19.7022			−0.983882			−0.491941	+	0.870628i	$0.663712\pi$
$402$	12.6957	+	8.78636i	0.633203	+	0.438224i
$403$	14.0766			0.701206
$404$	8.87817	+	15.3774i	0.441706	+	0.765057i
$405$	10.3625			0.514916
$406$	12.0102	−	20.8023i	0.596057	−	1.03240i
$407$	−6.27876			−0.311226
$408$	−6.04683	−	10.4734i	−0.299363	−	0.518512i
$409$	−11.6951	+	20.2565i	−0.578285	+	1.00162i	0.417391	+	0.908727i	$0.362944\pi$
$409$	−11.6951	+	20.2565i	−0.578285	+	1.00162i	−0.995676	+	0.0928921i	$0.970389\pi$
$410$	−9.46067			−0.467229
$411$	−4.02169			−0.198375
$412$	1.47658	+	2.55752i	0.0727461	+	0.126000i
$413$	−26.8726	+	46.5447i	−1.32231	+	2.29031i
$414$	−0.541660	+	0.938183i	−0.0266211	+	0.0461092i
$415$	2.39086	+	4.14109i	0.117363	+	0.203278i
$416$	4.96020			0.243194
$417$	41.9114			2.05241
$418$	−3.58166	−	6.20362i	−0.175185	−	0.303429i
$419$	15.9335	+	27.5976i	0.778402	+	1.34823i	0.932863	+	0.360232i	$0.117303\pi$
$419$	15.9335	+	27.5976i	0.778402	+	1.34823i	−0.154461	+	0.987999i	$0.549364\pi$
$420$	3.76586	+	6.52266i	0.183755	+	0.318273i
$421$	−17.7001	−	30.6576i	−0.862652	−	1.49416i	−0.869359	−	0.494180i	$-0.835468\pi$
$421$	−17.7001	−	30.6576i	−0.862652	−	1.49416i	0.00670687	−	0.999978i	$-0.497865\pi$
$422$	10.7834	−	18.6773i	0.524925	−	0.909197i
$423$	−2.45231	+	4.24753i	−0.119236	+	0.206522i
$424$	−5.31415			−0.258078
$425$	3.20575	+	5.55253i	0.155502	+	0.269337i
$426$	−1.10070			−0.0533290
$427$	−2.96609			−0.143539
$428$	4.82839	−	8.36301i	0.233389	−	0.404241i
$429$	13.4923			0.651416
$430$	−4.49151	−	7.77953i	−0.216600	−	0.375162i
$431$	17.9641	−	31.1147i	0.865300	−	1.49874i	−0.00144835	−	0.999999i	$-0.500461\pi$
$431$	17.9641	−	31.1147i	0.865300	−	1.49874i	0.866749	−	0.498745i	$-0.166206\pi$
$432$	2.30318	+	3.98923i	0.110812	+	0.191932i
$433$	−1.58956	+	2.75320i	−0.0763894	+	0.132310i	−0.901690	−	0.432384i	$-0.857673\pi$
$433$	−1.58956	+	2.75320i	−0.0763894	+	0.132310i	0.825300	+	0.564694i	$0.191006\pi$
$434$	−5.66585	+	9.81354i	−0.271969	+	0.471065i
$435$	5.67352	−	9.82682i	0.272024	−	0.471160i
$436$	0.831282	−	1.43982i	0.0398112	−	0.0689550i
$437$	4.82261	−	8.35300i	0.230696	−	0.399578i
$438$	6.72773	−	11.6528i	0.321463	−	0.556791i
$439$	5.47369	+	9.48070i	0.261245	+	0.452489i	0.966573	−	0.256392i	$-0.0825337\pi$
$439$	5.47369	+	9.48070i	0.261245	+	0.452489i	−0.705328	+	0.708881i	$0.749200\pi$
$440$	0.721042	−	1.24888i	0.0343743	−	0.0595380i
$441$	−2.49495	−	4.32138i	−0.118807	−	0.205780i
$442$	−31.8023			−1.51268
$443$	5.16269	−	8.94203i	0.245287	−	0.424849i	−0.716926	−	0.697150i	$-0.754451\pi$
$443$	5.16269	−	8.94203i	0.245287	−	0.424849i	0.962212	+	0.272301i	$0.0877846\pi$
$444$	8.21261			0.389753
$445$	6.43713			0.305149
$446$	9.44041	+	16.3513i	0.447017	+	0.774255i
$447$	3.51871			0.166429
$448$	−1.99648	+	3.45801i	−0.0943250	+	0.163376i
$449$	10.7833	−	18.6772i	0.508895	−	0.881431i	−0.491052	−	0.871130i	$-0.663388\pi$
$449$	10.7833	−	18.6772i	0.508895	−	0.881431i	0.999947	−	0.0103012i	$-0.00327903\pi$
$450$	0.278958	+	0.483170i	0.0131502	+	0.0227769i
$451$	−6.82154	−	11.8153i	−0.321214	−	0.556359i
$452$	−9.03876	−	15.6556i	−0.425148	−	0.736377i
$453$	20.1100	+	34.8315i	0.944850	+	1.63653i
$454$	8.10465			0.380370
$455$	19.8059			0.928516
$456$	4.68481	+	8.11434i	0.219386	+	0.379989i
$457$	17.2956	−	29.9568i	0.809053	−	1.40132i	−0.104467	−	0.994528i	$-0.533314\pi$
$457$	17.2956	−	29.9568i	0.809053	−	1.40132i	0.913520	−	0.406793i	$-0.133353\pi$
$458$	−0.460070	+	0.796864i	−0.0214976	+	0.0372350i
$459$	−14.7669	−	25.5770i	−0.689258	−	1.19383i
$460$	1.94172			0.0905333
$461$	−8.19835			−0.381835			−0.190918	−	0.981606i	$-0.561146\pi$
$461$	−8.19835			−0.381835			−0.190918	+	0.981606i	$0.561146\pi$
$462$	−5.43068	+	9.40621i	−0.252658	+	0.437617i
$463$	−20.4313	−	35.3881i	−0.949525	−	1.64463i	−0.746428	−	0.665467i	$-0.768233\pi$
$463$	−20.4313	−	35.3881i	−0.949525	−	1.64463i	−0.203097	−	0.979159i	$-0.565101\pi$
$464$	6.01568			0.279271
$465$	−2.67650	+	4.63583i	−0.124120	+	0.214982i
$466$	11.9424			0.553222
$467$	−7.29549	−	12.6362i	−0.337595	−	0.584732i	0.646385	−	0.763012i	$-0.276280\pi$
$467$	−7.29549	−	12.6362i	−0.337595	−	0.584732i	−0.983980	+	0.178280i	$0.942947\pi$
$468$	−2.76738			−0.127922
$469$	−2.67017	+	32.5746i	−0.123297	+	1.50416i
$470$	8.79096			0.405497
$471$	−1.43937	−	2.49307i	−0.0663228	−	0.114875i
$472$	−13.4600			−0.619545
$473$	6.47713	−	11.2187i	0.297819	−	0.515837i
$474$	22.7907			1.04681
$475$	−2.48367	−	4.30185i	−0.113959	−	0.197382i
$476$	12.8005	−	22.1711i	0.586709	−	1.01621i
$477$	2.96485			0.135751
$478$	−16.5300			−0.756063
$479$	−9.53238	−	16.5106i	−0.435546	−	0.754387i	0.561794	−	0.827277i	$-0.310111\pi$
$479$	−9.53238	−	16.5106i	−0.435546	−	0.754387i	−0.997340	+	0.0728897i	$0.976778\pi$
$480$	−0.943122	+	1.63354i	−0.0430474	+	0.0745603i
$481$	10.7982	−	18.7031i	0.492357	−	0.852787i
$482$	8.41861	+	14.5815i	0.383457	+	0.664167i
$483$	−14.6245			−0.665438
$484$	−8.92040			−0.405473
$485$	−4.93815	−	8.55313i	−0.224230	−	0.388377i
$486$	−2.86354	−	4.95979i	−0.129893	−	0.224981i
$487$	8.82737	+	15.2894i	0.400006	+	0.692831i	0.993726	−	0.111841i	$-0.0356746\pi$
$487$	8.82737	+	15.2894i	0.400006	+	0.692831i	−0.593720	+	0.804672i	$0.702341\pi$
$488$	−0.371414	−	0.643309i	−0.0168131	−	0.0291212i
$489$	14.9164	−	25.8360i	0.674543	−	1.16834i
$490$	−4.47190	+	7.74556i	−0.202020	+	0.349909i
$491$	37.5840			1.69614			0.848071	−	0.529883i	$-0.177764\pi$
$491$	37.5840			1.69614			0.848071	+	0.529883i	$0.177764\pi$
$492$	8.92257	+	15.4543i	0.402261	+	0.696736i
$493$	−38.5696			−1.73709
$494$	24.6390			1.10856
$495$	−0.402281	+	0.696772i	−0.0180812	+	0.0313176i
$496$	−2.83791			−0.127426
$497$	−1.16503	−	2.01789i	−0.0522587	−	0.0905147i
$498$	4.50974	−	7.81110i	0.202086	−	0.350024i
$499$	−2.39346	−	4.14560i	−0.107146	−	0.185582i	0.807467	−	0.589913i	$-0.200838\pi$
$499$	−2.39346	−	4.14560i	−0.107146	−	0.185582i	−0.914613	+	0.404330i	$0.867505\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	4.47834	−	7.75672i	0.200078	−	0.346545i
$502$	3.95778	−	6.85508i	0.176644	−	0.305957i
$503$	−6.87679	+	11.9109i	−0.306621	+	0.531083i	−0.977621	−	0.210374i	$-0.932532\pi$
$503$	−6.87679	+	11.9109i	−0.306621	+	0.531083i	0.671000	+	0.741457i	$0.265865\pi$
$504$	1.11387	−	1.92928i	0.0496158	−	0.0859371i
$505$	−8.87817	+	15.3774i	−0.395074	+	0.684287i
$506$	1.40006	+	2.42498i	0.0622404	+	0.107804i
$507$	−10.9436	+	18.9548i	−0.486021	+	0.841814i
$508$	3.74127	+	6.48008i	0.165992	+	0.287507i
$509$	9.15174			0.405644			0.202822	−	0.979216i	$-0.434989\pi$
$509$	9.15174			0.405644			0.202822	+	0.979216i	$0.434989\pi$
$510$	6.04683	−	10.4734i	0.267758	−	0.463771i
$511$	28.4837			1.26005
$512$	−1.00000			−0.0441942
$513$	11.4407	+	19.8159i	0.505119	+	0.874892i
$514$	−9.30939			−0.410620
$515$	−1.47658	+	2.55752i	−0.0650660	+	0.112698i
$516$	−8.47209	+	14.6741i	−0.372963	+	0.645991i
$517$	6.33865	+	10.9789i	0.278773	+	0.482850i
$518$	8.69259	+	15.0560i	0.381931	+	0.661523i
$519$	−6.27491	−	10.8685i	−0.275438	−	0.477073i
$520$	2.48010	+	4.29566i	0.108760	+	0.188377i
$521$	−26.5549			−1.16339			−0.581695	−	0.813407i	$-0.697610\pi$
$521$	−26.5549			−1.16339			−0.581695	+	0.813407i	$0.697610\pi$
$522$	−3.35625			−0.146899
$523$	−2.27652	−	3.94305i	−0.0995452	−	0.172417i	0.811951	−	0.583725i	$-0.198405\pi$
$523$	−2.27652	−	3.94305i	−0.0995452	−	0.172417i	−0.911497	+	0.411308i	$0.865072\pi$
$524$	9.07828	−	15.7240i	0.396586	−	0.686908i
$525$	−3.76586	+	6.52266i	−0.164355	+	0.284672i
$526$	6.83549	+	11.8394i	0.298041	+	0.516223i
$527$	18.1953			0.792600
$528$	−2.72012			−0.118378
$529$	9.61486	−	16.6534i	0.418037	−	0.724062i
$530$	−2.65707	−	4.60219i	−0.115416	−	0.199906i
$531$	7.50954			0.325886
$532$	−9.91723	+	17.1771i	−0.429966	+	0.744724i
$533$	46.9268			2.03263
$534$	−6.07100	−	10.5153i	−0.262718	−	0.455041i
$535$	9.65677			0.417499
$536$	−7.39939	+	3.49987i	−0.319605	+	0.151171i
$537$	−9.87879			−0.426301
$538$	2.24302	+	3.88503i	0.0967035	+	0.167495i
$539$	−12.8977			−0.555543
$540$	−2.30318	+	3.98923i	−0.0991132	+	0.171669i
$541$	9.55075			0.410619			0.205309	−	0.978697i	$-0.434180\pi$
$541$	9.55075			0.410619			0.205309	+	0.978697i	$0.434180\pi$
$542$	−1.66198	−	2.87863i	−0.0713880	−	0.123648i
$543$	−20.9199	+	36.2344i	−0.897760	+	1.55497i
$544$	6.41151			0.274891
$545$	1.66256			0.0712164
$546$	−18.6794	−	32.3537i	−0.799404	−	1.38461i
$547$	20.9598	−	36.3035i	0.896178	−	1.55223i	0.0638381	−	0.997960i	$-0.479666\pi$
$547$	20.9598	−	36.3035i	0.896178	−	1.55223i	0.832340	−	0.554266i	$-0.187001\pi$
$548$	1.06606	−	1.84647i	0.0455397	−	0.0788771i
$549$	0.207218	+	0.358913i	0.00884387	+	0.0153180i
$550$	1.44208			0.0614906
$551$	29.8819			1.27301
$552$	−1.83128	−	3.17187i	−0.0779445	−	0.135004i
$553$	24.1227	+	41.7818i	1.02580	+	1.77674i
$554$	−0.00865684	−	0.0149941i	−0.000367794	−	0.000637037i
$555$	4.10631	+	7.11233i	0.174303	+	0.301902i
$556$	−11.1098	+	19.2427i	−0.471158	+	0.816070i
$557$	−4.82646	+	8.35967i	−0.204504	+	0.354211i	−0.949974	−	0.312328i	$-0.898891\pi$
$557$	−4.82646	+	8.35967i	−0.204504	+	0.354211i	0.745471	+	0.666538i	$0.232225\pi$
$558$	1.58332			0.0670273
$559$	22.2788	+	38.5880i	0.942292	+	1.63210i
$560$	−3.99297			−0.168734
$561$	17.4401			0.736320
$562$	10.0822	−	17.4630i	0.425294	−	0.736630i
$563$	−18.1287			−0.764035			−0.382018	−	0.924155i	$-0.624771\pi$
$563$	−18.1287			−0.764035			−0.382018	+	0.924155i	$0.624771\pi$
$564$	−8.29095	−	14.3603i	−0.349112	−	0.604680i
$565$	9.03876	−	15.6556i	0.380264	−	0.658636i
$566$	1.31167	+	2.27188i	0.0551336	+	0.0954942i
$567$	20.6885	−	35.8336i	0.868837	−	1.50487i
$568$	0.291770	−	0.505360i	0.0122424	−	0.0212045i
$569$	−16.9296	+	29.3229i	−0.709725	+	1.22928i	0.255234	+	0.966879i	$0.417847\pi$
$569$	−16.9296	+	29.3229i	−0.709725	+	1.22928i	−0.964959	+	0.262400i	$0.915486\pi$
$570$	−4.68481	+	8.11434i	−0.196225	+	0.339872i
$571$	7.78142	−	13.4778i	0.325642	−	0.564029i	−0.656000	−	0.754761i	$-0.727753\pi$
$571$	7.78142	−	13.4778i	0.325642	−	0.564029i	0.981642	+	0.190732i	$0.0610861\pi$
$572$	−3.57651	+	6.19470i	−0.149541	+	0.259013i
$573$	16.1980	+	28.0558i	0.676682	+	1.17205i
$574$	−18.8881	+	32.7151i	−0.788374	+	1.36550i
$575$	0.970862	+	1.68158i	0.0404877	+	0.0701268i
$576$	0.557917			0.0232465
$577$	7.37303	−	12.7705i	0.306943	−	0.531642i	−0.670749	−	0.741685i	$-0.734027\pi$
$577$	7.37303	−	12.7705i	0.306943	−	0.531642i	0.977692	+	0.210043i	$0.0673604\pi$
$578$	−24.1074			−1.00274
$579$	−31.8718			−1.32455
$580$	3.00784	+	5.20973i	0.124894	+	0.216322i
$581$	19.0932			0.792121
$582$	−9.31455	+	16.1333i	−0.386101	+	0.668746i
$583$	3.83172	−	6.63674i	0.158694	−	0.274866i
$584$	3.56673	+	6.17777i	0.147593	+	0.255638i
$585$	−1.38369	−	2.39662i	−0.0572085	−	0.0990881i
$586$	−4.68198	−	8.10942i	−0.193411	−	0.334997i
$587$	2.89324	+	5.01123i	0.119417	+	0.206836i	0.919537	−	0.393004i	$-0.128564\pi$
$587$	2.89324	+	5.01123i	0.119417	+	0.206836i	−0.800120	+	0.599840i	$0.795231\pi$
$588$	16.8702			0.695715
$589$	−14.0969			−0.580852
$590$	−6.72998	−	11.6567i	−0.277069	−	0.479897i
$591$	−2.85962	+	4.95300i	−0.117629	+	0.203739i
$592$	−2.17698	+	3.77063i	−0.0894731	+	0.154972i
$593$	21.4936	+	37.2281i	0.882638	+	1.52877i	0.848397	+	0.529361i	$0.177568\pi$
$593$	21.4936	+	37.2281i	0.882638	+	1.52877i	0.0342417	+	0.999414i	$0.489098\pi$
$594$	−6.64276			−0.272556
$595$	25.6009			1.04954
$596$	−0.932729	+	1.61553i	−0.0382061	+	0.0661748i
$597$	−3.23954	−	5.61105i	−0.132586	−	0.229645i
$598$	−9.63133			−0.393854
$599$	14.9238	−	25.8488i	0.609771	−	1.05615i	−0.381507	−	0.924366i	$-0.624595\pi$
$599$	14.9238	−	25.8488i	0.609771	−	1.05615i	0.991278	−	0.131789i	$-0.0420720\pi$
$600$	−1.88624			−0.0770056
$601$	−16.8694	−	29.2187i	−0.688118	−	1.19186i	−0.972446	−	0.233128i	$-0.925104\pi$
$601$	−16.8694	−	29.2187i	−0.688118	−	1.19186i	0.284328	−	0.958727i	$-0.408229\pi$
$602$	−35.8689			−1.46191
$603$	4.12824	−	1.95264i	0.168115	−	0.0795175i
$604$	−21.3228			−0.867612
$605$	−4.46020	−	7.72529i	−0.181333	−	0.314078i
$606$	33.4928			1.36055
$607$	10.2164	−	17.6954i	0.414672	−	0.718232i	−0.580722	−	0.814102i	$-0.697230\pi$
$607$	10.2164	−	17.6954i	0.414672	−	0.718232i	0.995394	+	0.0958693i	$0.0305631\pi$
$608$	−4.96735			−0.201452
$609$	−22.6542	−	39.2382i	−0.917994	−	1.59001i
$610$	0.371414	−	0.643309i	0.0150381	−	0.0260468i
$611$	−43.6049			−1.76407
$612$	−3.57709			−0.144595
$613$	−18.4883	−	32.0227i	−0.746736	−	1.29339i	−0.949379	−	0.314133i	$-0.898286\pi$
$613$	−18.4883	−	32.0227i	−0.746736	−	1.29339i	0.202643	−	0.979253i	$-0.435047\pi$
$614$	2.23067	−	3.86363i	0.0900224	−	0.155923i
$615$	−8.92257	+	15.4543i	−0.359793	+	0.623179i
$616$	−2.87910	−	4.98674i	−0.116002	−	0.200922i
$617$	−26.1261			−1.05180			−0.525898	−	0.850548i	$-0.676271\pi$
$617$	−26.1261			−1.05180			−0.525898	+	0.850548i	$0.676271\pi$
$618$	5.57039			0.224074
$619$	−3.54544	−	6.14088i	−0.142503	−	0.246823i	0.785935	−	0.618308i	$-0.212182\pi$
$619$	−3.54544	−	6.14088i	−0.142503	−	0.246823i	−0.928439	+	0.371486i	$0.878848\pi$
$620$	−1.41896	−	2.45770i	−0.0569867	−	0.0987038i
$621$	−4.47214	−	7.74598i	−0.179461	−	0.310835i
$622$	−16.4249	−	28.4488i	−0.658578	−	1.14069i
$623$	12.8516	−	22.2597i	0.514890	−	0.891815i
$624$	4.67807	−	8.10266i	0.187273	−	0.324366i
$625$	1.00000			0.0400000
$626$	−14.0668	−	24.3644i	−0.562222	−	0.973797i
$627$	−13.5118			−0.539609
$628$	1.52618			0.0609012
$629$	13.9577	−	24.1754i	0.556530	−	0.963938i
$630$	2.22775			0.0887555
$631$	−15.6220	−	27.0582i	−0.621904	−	1.07717i	−0.989131	−	0.147038i	$-0.953026\pi$
$631$	−15.6220	−	27.0582i	−0.621904	−	1.07717i	0.367227	−	0.930131i	$-0.380307\pi$
$632$	−6.04130	+	10.4638i	−0.240310	+	0.416229i
$633$	−20.3400	−	35.2300i	−0.808444	−	1.40027i
$634$	−13.6526	+	23.6470i	−0.542214	+	0.939143i
$635$	−3.74127	+	6.48008i	−0.148468	+	0.257154i
$636$	−5.01189	+	8.68085i	−0.198734	+	0.344218i
$637$	22.1815	−	38.4195i	0.878864	−	1.52224i
$638$	−4.33755	+	7.51286i	−0.171725	+	0.297437i
$639$	−0.162783	+	0.281949i	−0.00643961	+	0.0111537i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	13.8140	−	23.9266i	0.545621	−	0.945043i	−0.452947	−	0.891538i	$-0.649627\pi$
$641$	13.8140	−	23.9266i	0.545621	−	0.945043i	0.998568	−	0.0535056i	$-0.0170395\pi$
$642$	−9.10751	−	15.7747i	−0.359445	−	0.622577i
$643$	11.3120			0.446100			0.223050	−	0.974807i	$-0.428399\pi$
$643$	11.3120			0.446100			0.223050	+	0.974807i	$0.428399\pi$
$644$	3.87662	−	6.71450i	0.152760	−	0.264588i
$645$	−16.9442			−0.667176
$646$	31.8482			1.25305
$647$	4.47218	+	7.74604i	0.175819	+	0.304528i	0.940445	−	0.339947i	$-0.110409\pi$
$647$	4.47218	+	7.74604i	0.175819	+	0.304528i	−0.764625	+	0.644475i	$0.777076\pi$
$648$	10.3625			0.407077
$649$	9.70519	−	16.8099i	0.380962	−	0.659845i
$650$	−2.48010	+	4.29566i	−0.0972775	+	0.168490i
$651$	10.6872	+	18.5107i	0.418863	+	0.725493i
$652$	7.90799	+	13.6970i	0.309701	+	0.536418i
$653$	19.4502	+	33.6888i	0.761146	+	1.31834i	0.942260	+	0.334882i	$0.108696\pi$
$653$	19.4502	+	33.6888i	0.761146	+	1.31834i	−0.181114	+	0.983462i	$0.557970\pi$
$654$	−1.56800	−	2.71586i	−0.0613137	−	0.106198i
$655$	18.1566			0.709435
$656$	−9.46067			−0.369377
$657$	−1.98994	−	3.44668i	−0.0776350	−	0.134468i
$658$	17.5510	−	30.3993i	0.684210	−	1.18509i
$659$	−13.4606	+	23.3144i	−0.524350	+	0.908201i	0.475248	+	0.879852i	$0.342358\pi$
$659$	−13.4606	+	23.3144i	−0.524350	+	0.908201i	−0.999598	+	0.0283490i	$0.990975\pi$
$660$	−1.36006	−	2.35569i	−0.0529403	−	0.0916952i
$661$	46.5163			1.80927			0.904637	−	0.426183i	$-0.140142\pi$
$661$	46.5163			1.80927			0.904637	+	0.426183i	$0.140142\pi$
$662$	8.73816			0.339618
$663$	−29.9935	+	51.9503i	−1.16485	+	2.01758i
$664$	2.39086	+	4.14109i	0.0927832	+	0.160705i
$665$	−19.8345			−0.769147
$666$	1.21457	−	2.10370i	0.0470637	−	0.0815167i
$667$	−11.6808			−0.452282
$668$	2.37421	+	4.11226i	0.0918610	+	0.159108i
$669$	35.6139			1.37691
$670$	−6.73067	−	4.65812i	−0.260028	−	0.179959i
$671$	1.07122			0.0413540
$672$	3.76586	+	6.52266i	0.145271	+	0.251617i
$673$	−5.19728			−0.200341			−0.100170	−	0.994970i	$-0.531939\pi$
$673$	−5.19728			−0.200341			−0.100170	+	0.994970i	$0.531939\pi$
$674$	−2.38943	+	4.13861i	−0.0920374	+	0.159413i
$675$	−4.60636			−0.177299
$676$	−5.80178	−	10.0490i	−0.223146	−	0.386499i
$677$	−10.9866	+	19.0294i	−0.422250	+	0.731358i	−0.996159	−	0.0875609i	$-0.972093\pi$
$677$	−10.9866	+	19.0294i	−0.422250	+	0.731358i	0.573910	+	0.818919i	$0.305426\pi$
$678$	−34.0986			−1.30955
$679$	−39.4358			−1.51341
$680$	3.20575	+	5.55253i	0.122935	+	0.212930i
$681$	7.64367	−	13.2392i	0.292906	−	0.507328i
$682$	2.04625	−	3.54421i	0.0783551	−	0.135715i
$683$	−13.2547	−	22.9578i	−0.507176	−	0.878455i	−0.999966	−	0.00830620i	$-0.997356\pi$
$683$	−13.2547	−	22.9578i	−0.507176	−	0.878455i	0.492789	−	0.870149i	$-0.335977\pi$
$684$	2.77137			0.105966
$685$	2.13211			0.0814639
$686$	3.88077	+	6.72169i	0.148168	+	0.256635i
$687$	0.867804	+	1.50308i	0.0331088	+	0.0573461i
$688$	−4.49151	−	7.77953i	−0.171237	−	0.296592i
$689$	13.1796	+	22.8278i	0.502103	+	0.869668i
$690$	1.83128	−	3.17187i	0.0697157	−	0.120751i
$691$	11.3876	−	19.7239i	0.433204	−	0.750331i	−0.563943	−	0.825814i	$-0.690716\pi$
$691$	11.3876	−	19.7239i	0.433204	−	0.750331i	0.997147	+	0.0754822i	$0.0240496\pi$
$692$	6.65334			0.252922
$693$	1.60630	+	2.78219i	0.0610182	+	0.105687i
$694$	−13.8009			−0.523873
$695$	−22.2195			−0.842834
$696$	5.67352	−	9.82682i	0.215054	−	0.372485i
$697$	60.6572			2.29755
$698$	0.783321	+	1.35675i	0.0296492	+	0.0513538i
$699$	11.2632	−	19.5084i	0.426012	−	0.737874i
$700$	−1.99648	−	3.45801i	−0.0754600	−	0.130701i
$701$	18.6341	−	32.2753i	0.703801	−	1.21902i	−0.263321	−	0.964708i	$-0.584818\pi$
$701$	18.6341	−	32.2753i	0.703801	−	1.21902i	0.967122	−	0.254311i	$-0.0818488\pi$
$702$	11.4242	−	19.7874i	0.431180	−	0.746826i
$703$	−10.8138	+	18.7300i	−0.407850	+	0.706416i
$704$	0.721042	−	1.24888i	0.0271753	−	0.0470690i
$705$	8.29095	−	14.3603i	0.312255	−	0.540842i
$706$	−11.8424	+	20.5117i	−0.445696	+	0.771968i
$707$	35.4503	+	61.4017i	1.33324	+	2.30925i
$708$	−12.6944	+	21.9873i	−0.477084	+	0.826334i
$709$	−7.64170	−	13.2358i	−0.286990	−	0.497081i	0.686100	−	0.727507i	$-0.259321\pi$
$709$	−7.64170	−	13.2358i	−0.286990	−	0.497081i	−0.973090	+	0.230426i	$0.925988\pi$
$710$	0.583540			0.0218999
$711$	3.37054	−	5.83795i	0.126405	−	0.218940i
$712$	6.43713			0.241242
$713$	5.51044			0.206368
$714$	−24.1448	−	41.8201i	−0.903597	−	1.56508i
$715$	−7.15302			−0.267508
$716$	2.61864	−	4.53562i	0.0978632	−	0.169504i
$717$	−15.5898	+	27.0023i	−0.582211	+	1.00842i
$718$	−10.8489	−	18.7909i	−0.404879	−	0.701271i
$719$	2.56675	+	4.44574i	0.0957235	+	0.165798i	0.909910	−	0.414805i	$-0.136150\pi$
$719$	2.56675	+	4.44574i	0.0957235	+	0.165798i	−0.814187	+	0.580603i	$0.802817\pi$
$720$	0.278958	+	0.483170i	0.0103962	+	0.0180067i
$721$	5.89595	+	10.2121i	0.219577	+	0.380318i
$722$	−5.67453			−0.211184
$723$	31.7591			1.18113
$724$	−11.0908	−	19.2098i	−0.412186	−	0.713927i
$725$	−3.00784	+	5.20973i	−0.111708	+	0.193484i
$726$	−8.41302	+	14.5718i	−0.312237	+	0.540810i
$727$	−11.1550	−	19.3210i	−0.413716	−	0.716577i	0.581577	−	0.813492i	$-0.302436\pi$
$727$	−11.1550	−	19.3210i	−0.413716	−	0.716577i	−0.995293	+	0.0969144i	$0.969103\pi$
$728$	19.8059			0.734056
$729$	20.2848			0.751288
$730$	−3.56673	+	6.17777i	−0.132011	+	0.228649i
$731$	28.7974	+	49.8785i	1.06511	+	1.84482i
$732$	−1.40116			−0.0517882
$733$	−6.48188	+	11.2269i	−0.239414	+	0.414677i	−0.960546	−	0.278121i	$-0.910289\pi$
$733$	−6.48188	+	11.2269i	−0.239414	+	0.414677i	0.721133	+	0.692797i	$0.243622\pi$
$734$	7.08708			0.261589
$735$	8.43510	+	14.6100i	0.311133	+	0.538899i
$736$	1.94172			0.0715729
$737$	0.964347	−	11.7645i	0.0355222	−	0.433351i
$738$	5.27827			0.194296
$739$	15.6869	+	27.1704i	0.577050	+	0.999481i	0.995816	+	0.0913861i	$0.0291297\pi$
$739$	15.6869	+	27.1704i	0.577050	+	0.999481i	−0.418765	+	0.908095i	$0.637537\pi$
$740$	−4.35395			−0.160054
$741$	23.2376	−	40.2487i	0.853655	−	1.47857i
$742$	−21.2192			−0.778982
$743$	−0.859296	−	1.48834i	−0.0315245	−	0.0546020i	0.849833	−	0.527053i	$-0.176703\pi$
$743$	−0.859296	−	1.48834i	−0.0315245	−	0.0546020i	−0.881357	+	0.472450i	$0.843370\pi$
$744$	−2.67650	+	4.63583i	−0.0981252	+	0.169958i
$745$	−1.86546			−0.0683451
$746$	−10.9495			−0.400888
$747$	−1.33390	−	2.31038i	−0.0488048	−	0.0845325i
$748$	−4.62296	+	8.00721i	−0.169032	+	0.292772i
$749$	19.2796	−	33.3932i	0.704461	−	1.22016i
$750$	−0.943122	−	1.63354i	−0.0344379	−	0.0596483i
$751$	−11.8129			−0.431059			−0.215530	−	0.976497i	$-0.569148\pi$
$751$	−11.8129			−0.431059			−0.215530	+	0.976497i	$0.569148\pi$
$752$	8.79096			0.320573
$753$	−7.46534	−	12.9303i	−0.272052	−	0.471208i
$754$	−14.9195	−	25.8413i	−0.543335	−	0.941084i
$755$	−10.6614	−	18.4661i	−0.388008	−	0.672050i
$756$	9.19654	+	15.9289i	0.334475	+	0.579327i
$757$	−19.9109	+	34.4867i	−0.723674	+	1.25344i	0.235844	+	0.971791i	$0.424215\pi$
$757$	−19.9109	+	34.4867i	−0.723674	+	1.25344i	−0.959517	+	0.281649i	$0.909119\pi$
$758$	−8.18791	+	14.1819i	−0.297398	+	0.515109i
$759$	5.28172			0.191714
$760$	−2.48367	−	4.30185i	−0.0900923	−	0.156044i
$761$	−1.14186			−0.0413922			−0.0206961	−	0.999786i	$-0.506588\pi$
$761$	−1.14186			−0.0413922			−0.0206961	+	0.999786i	$0.506588\pi$
$762$	14.1139			0.511293
$763$	3.31928	−	5.74917i	0.120166	−	0.208134i
$764$	−17.1749			−0.621366
$765$	−1.78854	−	3.09785i	−0.0646650	−	0.112003i
$766$	11.1863	−	19.3752i	0.404176	−	0.700054i
$767$	33.3820	+	57.8194i	1.20535	+	2.08774i
$768$	−0.943122	+	1.63354i	−0.0340320	+	0.0589451i
$769$	−0.920426	+	1.59422i	−0.0331914	+	0.0574892i	−0.882144	−	0.470980i	$-0.843900\pi$
$769$	−0.920426	+	1.59422i	−0.0331914	+	0.0574892i	0.848953	+	0.528469i	$0.177234\pi$
$770$	2.87910	−	4.98674i	0.103755	−	0.179710i
$771$	−8.77989	+	15.2072i	−0.316200	+	0.547675i
$772$	8.44848	−	14.6332i	0.304068	−	0.526661i
$773$	−2.40806	+	4.17089i	−0.0866120	+	0.150016i	−0.906077	−	0.423113i	$-0.860937\pi$
$773$	−2.40806	+	4.17089i	−0.0866120	+	0.150016i	0.819465	+	0.573129i	$0.194271\pi$
$774$	2.50589	+	4.34033i	0.0900724	+	0.156010i
$775$	1.41896	−	2.45770i	0.0509704	−	0.0882834i
$776$	−4.93815	−	8.55313i	−0.177269	−	0.307039i
$777$	32.7927			1.17643
$778$	−10.6573	+	18.4589i	−0.382081	+	0.661784i
$779$	−46.9944			−1.68375
$780$	9.35614			0.335004
$781$	0.420757	+	0.728772i	0.0150559	+	0.0260775i
$782$	−12.4494			−0.445189
$783$	13.8552	−	23.9979i	0.495145	−	0.857615i
$784$	−4.47190	+	7.74556i	−0.159711	+	0.276627i
$785$	0.763090	+	1.32171i	0.0272358	+	0.0471739i
$786$	−17.1238	−	29.6594i	−0.610787	−	1.05791i
$787$	−9.02515	−	15.6320i	−0.321712	−	0.557221i	0.659130	−	0.752029i	$-0.270925\pi$
$787$	−9.02515	−	15.6320i	−0.321712	−	0.557221i	−0.980841	+	0.194808i	$0.937592\pi$
$788$	−1.51604	−	2.62585i	−0.0540066	−	0.0935422i
$789$	25.7868			0.918034
$790$	−12.0826			−0.429880
$791$	−36.0915	−	62.5123i	−1.28327	−	2.22268i
$792$	−0.402281	+	0.696772i	−0.0142944	+	0.0247587i
$793$	−1.84229	+	3.19094i	−0.0654216	+	0.113314i
$794$	1.42625	+	2.47033i	0.0506156	+	0.0876688i
$795$	−10.0238			−0.355507
$796$	3.43491			0.121747
$797$	15.7065	−	27.2044i	0.556352	−	0.963630i	−0.441445	−	0.897288i	$-0.645534\pi$
$797$	15.7065	−	27.2044i	0.556352	−	0.963630i	0.997797	−	0.0663415i	$-0.0211327\pi$
$798$	18.7063	+	32.4003i	0.662196	+	1.14696i
$799$	−56.3633			−1.99399
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−3.59138			−0.126895
$802$	−9.85111	−	17.0626i	−0.347855	−	0.602502i
$803$	−10.2871			−0.363022
$804$	−1.26137	+	15.3880i	−0.0444849	+	0.542692i
$805$	7.75324			0.273266
$806$	7.03831	+	12.1907i	0.247914	+	0.429399i
$807$	8.46177			0.297868
$808$	−8.87817	+	15.3774i	−0.312333	+	0.540977i
$809$	7.57114			0.266187			0.133094	−	0.991103i	$-0.457509\pi$
$809$	7.57114			0.266187			0.133094	+	0.991103i	$0.457509\pi$
$810$	5.18124	+	8.97417i	0.182050	+	0.315320i
$811$	18.1401	−	31.4196i	0.636986	−	1.10329i	−0.349105	−	0.937084i	$-0.613514\pi$
$811$	18.1401	−	31.4196i	0.636986	−	1.10329i	0.986091	−	0.166208i	$-0.0531524\pi$
$812$	24.0204			0.842951
$813$	−6.26979			−0.219891
$814$	−3.13938	−	5.43756i	−0.110035	−	0.190587i
$815$	−7.90799	+	13.6970i	−0.277005	+	0.479786i
$816$	6.04683	−	10.4734i	0.211682	−	0.366643i
$817$	−22.3109	−	38.6436i	−0.780559	−	1.35197i
$818$	−23.3902			−0.817818
$819$	−11.0501			−0.386120
$820$	−4.73034	−	8.19318i	−0.165191	−	0.286118i
$821$	14.1555	+	24.5180i	0.494029	+	0.855683i	0.999976	−	0.00688095i	$-0.00219029\pi$
$821$	14.1555	+	24.5180i	0.494029	+	0.855683i	−0.505947	+	0.862564i	$0.668857\pi$
$822$	−2.01084	−	3.48288i	−0.0701362	−	0.121480i
$823$	19.2383	+	33.3216i	0.670603	+	1.16152i	0.977733	+	0.209852i	$0.0672981\pi$
$823$	19.2383	+	33.3216i	0.670603	+	1.16152i	−0.307130	+	0.951668i	$0.599369\pi$
$824$	−1.47658	+	2.55752i	−0.0514392	+	0.0890954i
$825$	1.36006	−	2.35569i	0.0473512	−	0.0820147i
$826$	−53.7452			−1.87003
$827$	3.11863	+	5.40162i	0.108445	+	0.187833i	0.915141	−	0.403135i	$-0.132079\pi$
$827$	3.11863	+	5.40162i	0.108445	+	0.187833i	−0.806695	+	0.590968i	$0.798746\pi$
$828$	−1.08332			−0.0376480
$829$	−17.0231			−0.591238			−0.295619	−	0.955306i	$-0.595526\pi$
$829$	−17.0231			−0.591238			−0.295619	+	0.955306i	$0.595526\pi$
$830$	−2.39086	+	4.14109i	−0.0829879	+	0.143739i
$831$	−0.0326578			−0.00113289
$832$	2.48010	+	4.29566i	0.0859820	+	0.148925i
$833$	28.6716	−	49.6607i	0.993413	−	1.72064i
$834$	20.9557	+	36.2963i	0.725637	+	1.25684i
$835$	−2.37421	+	4.11226i	−0.0821630	+	0.142311i
$836$	3.58166	−	6.20362i	0.123874	−	0.214557i
$837$	−6.53623	+	11.3211i	−0.225925	+	0.391314i
$838$	−15.9335	+	27.5976i	−0.550413	+	0.953344i
$839$	25.7220	−	44.5519i	0.888023	−	1.53810i	0.0458146	−	0.998950i	$-0.485412\pi$
$839$	25.7220	−	44.5519i	0.888023	−	1.53810i	0.842209	−	0.539152i	$-0.181255\pi$
$840$	−3.76586	+	6.52266i	−0.129934	+	0.225053i
$841$	−3.59419	−	6.22531i	−0.123937	−	0.214666i
$842$	17.7001	−	30.6576i	0.609987	−	1.05653i
$843$	−19.0176	−	32.9394i	−0.655000	−	1.13449i
$844$	21.5667			0.742357
$845$	5.80178	−	10.0490i	0.199587	−	0.345696i
$846$	−4.90463			−0.168625
$847$	−35.6189			−1.22388
$848$	−2.65707	−	4.60219i	−0.0912443	−	0.158040i
$849$	4.94826			0.169824
$850$	−3.20575	+	5.55253i	−0.109956	+	0.190450i
$851$	4.22708	−	7.32152i	0.144903	−	0.250979i
$852$	−0.550349	−	0.953233i	−0.0188547	−	0.0326572i
$853$	−5.63324	−	9.75705i	−0.192878	−	0.334075i	0.753325	−	0.657649i	$-0.228449\pi$
$853$	−5.63324	−	9.75705i	−0.192878	−	0.334075i	−0.946203	+	0.323574i	$0.895116\pi$
$854$	−1.48305	−	2.56871i	−0.0507488	−	0.0878995i
$855$	1.38568	+	2.40007i	0.0473894	+	0.0820808i
$856$	9.65677			0.330062
$857$	−12.1317			−0.414410			−0.207205	−	0.978298i	$-0.566437\pi$
$857$	−12.1317			−0.414410			−0.207205	+	0.978298i	$0.566437\pi$
$858$	6.74617	+	11.6847i	0.230310	+	0.398909i
$859$	−28.6101	+	49.5541i	−0.976164	+	1.69076i	−0.300123	+	0.953901i	$0.597028\pi$
$859$	−28.6101	+	49.5541i	−0.976164	+	1.69076i	−0.676041	+	0.736864i	$0.736306\pi$
$860$	4.49151	−	7.77953i	0.153159	−	0.265280i
$861$	35.6276	+	61.7087i	1.21418	+	2.10303i
$862$	35.9282			1.22372
$863$	6.23264			0.212162			0.106081	−	0.994358i	$-0.466170\pi$
$863$	6.23264			0.212162			0.106081	+	0.994358i	$0.466170\pi$
$864$	−2.30318	+	3.98923i	−0.0783559	+	0.135716i
$865$	3.32667	+	5.76196i	0.113110	+	0.195913i
$866$	−3.17912			−0.108031
$867$	−22.7362	+	39.3803i	−0.772163	+	1.33743i
$868$	−11.3317			−0.384623
$869$	−8.71206	−	15.0897i	−0.295536	−	0.511884i
$870$	11.3470			0.384701
$871$	33.3854	+	23.1052i	1.13122	+	0.782890i
$872$	1.66256			0.0563015
$873$	2.75508	+	4.77193i	0.0932452	+	0.161505i
$874$	9.64521			0.326254
$875$	1.99648	−	3.45801i	0.0674935	−	0.116902i
$876$	13.4555			0.454618
$877$	−4.63781	−	8.03292i	−0.156608	−	0.271253i	0.777036	−	0.629457i	$-0.216723\pi$
$877$	−4.63781	−	8.03292i	−0.156608	−	0.271253i	−0.933643	+	0.358204i	$0.883389\pi$
$878$	−5.47369	+	9.48070i	−0.184728	+	0.319958i
$879$	−17.6627			−0.595748
$880$	1.44208			0.0486126
$881$	10.1357	+	17.5555i	0.341479	+	0.591459i	0.984708	−	0.174215i	$-0.0557389\pi$
$881$	10.1357	+	17.5555i	0.341479	+	0.591459i	−0.643229	+	0.765674i	$0.722406\pi$
$882$	2.49495	−	4.32138i	0.0840093	−	0.145508i
$883$	24.6405	−	42.6786i	0.829219	−	1.43625i	−0.0694322	−	0.997587i	$-0.522119\pi$
$883$	24.6405	−	42.6786i	0.829219	−	1.43625i	0.898651	−	0.438663i	$-0.144548\pi$
$884$	−15.9012	−	27.5416i	−0.534814	−	0.926326i
$885$	−25.3888			−0.853434
$886$	10.3254			0.346888
$887$	22.9049	+	39.6724i	0.769070	+	1.33207i	0.938068	+	0.346452i	$0.112614\pi$
$887$	22.9049	+	39.6724i	0.769070	+	1.33207i	−0.168998	+	0.985616i	$0.554053\pi$
$888$	4.10631	+	7.11233i	0.137799	+	0.238674i
$889$	14.9388	+	25.8747i	0.501031	+	0.867811i
$890$	3.21857	+	5.57472i	0.107887	+	0.186865i
$891$	−7.47178	+	12.9415i	−0.250314	+	0.433557i
$892$	−9.44041	+	16.3513i	−0.316088	+	0.547481i
$893$	43.6678			1.46129
$894$	1.75935	+	3.04729i	0.0588416	+	0.101917i
$895$	5.23728			0.175063
$896$	−3.99297			−0.133396
$897$	−9.08352	+	15.7331i	−0.303290	+	0.525314i
$898$	21.5666			0.719686
$899$	8.53598	+	14.7848i	0.284691	+	0.493099i
$900$	−0.278958	+	0.483170i	−0.00929862	+	0.0161057i
$901$	17.0359	+	29.5070i	0.567546	+	0.983019i
$902$	6.82154	−	11.8153i	0.227132	−	0.393405i
$903$	−33.8288	+	58.5932i	−1.12575	+	1.94986i
$904$	9.03876	−	15.6556i	0.300625	−	0.520697i
$905$	11.0908	−	19.2098i	0.368670	−	0.638556i
$906$	−20.1100	+	34.8315i	−0.668110	+	1.15720i
$907$	2.68889	−	4.65729i	0.0892831	−	0.154643i	−0.817925	−	0.575325i	$-0.804876\pi$
$907$	2.68889	−	4.65729i	0.0892831	−	0.154643i	0.907208	+	0.420682i	$0.138209\pi$
$908$	4.05232	+	7.01883i	0.134481	+	0.232928i
$909$	4.95328	−	8.57934i	0.164290	−	0.284559i
$910$	9.90296	+	17.1524i	0.328280	+	0.568597i
$911$	−31.5685			−1.04591			−0.522955	−	0.852360i	$-0.675170\pi$
$911$	−31.5685			−1.04591			−0.522955	+	0.852360i	$0.675170\pi$
$912$	−4.68481	+	8.11434i	−0.155130	+	0.268692i
$913$	−6.89563			−0.228212
$914$	34.5912			1.14417
$915$	−0.700578	−	1.21344i	−0.0231604	−	0.0401150i
$916$	−0.920140			−0.0304023
$917$	36.2493	−	62.7856i	1.19706	−	2.07336i
$918$	14.7669	−	25.5770i	0.487379	−	0.844166i
$919$	−19.8984	−	34.4650i	−0.656387	−	1.13690i	−0.981544	−	0.191236i	$-0.938750\pi$
$919$	−19.8984	−	34.4650i	−0.656387	−	1.13690i	0.325157	−	0.945660i	$-0.394583\pi$
$920$	0.970862	+	1.68158i	0.0320084	+	0.0554401i
$921$	−4.20758	−	7.28775i	−0.138645	−	0.240139i
$922$	−4.09918	−	7.09998i	−0.134999	−	0.233825i
$923$	−2.89447			−0.0952728
$924$	−10.8614			−0.357312
$925$	−2.17698	−	3.77063i	−0.0715785	−	0.123978i
$926$	20.4313	−	35.3881i	0.671415	−	1.16293i
$927$	0.823811	−	1.42688i	0.0270575	−	0.0468650i
$928$	3.00784	+	5.20973i	0.0987371	+	0.171018i
$929$	−28.8815			−0.947572			−0.473786	−	0.880640i	$-0.657113\pi$
$929$	−28.8815			−0.947572			−0.473786	+	0.880640i	$0.657113\pi$
$930$	−5.35300			−0.175532
$931$	−22.2135	+	38.4749i	−0.728017	+	1.26096i
$932$	5.97121	+	10.3424i	0.195594	+	0.338778i
$933$	−61.9627			−2.02857
$934$	7.29549	−	12.6362i	0.238716	−	0.413468i
$935$	−9.24593			−0.302374
$936$	−1.38369	−	2.39662i	−0.0452273	−	0.0783360i
$937$	−40.6927			−1.32937			−0.664687	−	0.747122i	$-0.731435\pi$
$937$	−40.6927			−1.32937			−0.664687	+	0.747122i	$0.731435\pi$
$938$	−29.5455	+	13.9749i	−0.964695	+	0.456296i
$939$	−53.0668			−1.73177
$940$	4.39548	+	7.61320i	0.143365	+	0.248315i
$941$	−48.9517			−1.59578			−0.797889	−	0.602804i	$-0.794050\pi$
$941$	−48.9517			−1.59578			−0.797889	+	0.602804i	$0.794050\pi$
$942$	1.43937	−	2.49307i	0.0468973	−	0.0812285i
$943$	18.3700			0.598210
$944$	−6.72998	−	11.6567i	−0.219042	−	0.379392i
$945$	−9.19654	+	15.9289i	−0.299163	+	0.518166i
$946$	12.9543			0.421179
$947$	−2.41548			−0.0784924			−0.0392462	−	0.999230i	$-0.512496\pi$
$947$	−2.41548			−0.0784924			−0.0392462	+	0.999230i	$0.512496\pi$
$948$	11.3954	+	19.7374i	0.370104	+	0.641039i
$949$	17.6917	−	30.6429i	0.574297	−	0.994712i
$950$	2.48367	−	4.30185i	0.0805810	−	0.139570i
$951$	25.7522	+	44.6040i	0.835071	+	1.44638i
$952$	25.6009			0.829732
$953$	−31.6682			−1.02583			−0.512917	−	0.858438i	$-0.671435\pi$
$953$	−31.6682			−1.02583			−0.512917	+	0.858438i	$0.671435\pi$
$954$	1.48243	+	2.56764i	0.0479953	+	0.0831304i
$955$	−8.58744	−	14.8739i	−0.277883	−	0.481308i
$956$	−8.26498	−	14.3154i	−0.267309	−	0.462992i
$957$	8.18168	+	14.1711i	0.264476	+	0.458086i
$958$	9.53238	−	16.5106i	0.307977	−	0.533432i
$959$	4.25673	−	7.37288i	0.137457	−	0.238083i
$960$	−1.88624			−0.0608783
$961$	11.4731	+	19.8720i	0.370101	+	0.641033i
$962$	21.5965			0.696298
$963$	−5.38768			−0.173615
$964$	−8.41861	+	14.5815i	−0.271145	+	0.469637i
$965$	16.8970			0.543933
$966$	−7.31225	−	12.6652i	−0.235268	−	0.407496i
$967$	26.3552	−	45.6485i	0.847525	−	1.46796i	−0.0358857	−	0.999356i	$-0.511425\pi$
$967$	26.3552	−	45.6485i	0.847525	−	1.46796i	0.883410	−	0.468600i	$-0.155241\pi$
$968$	−4.46020	−	7.72529i	−0.143356	−	0.248300i
$969$	30.0367	−	52.0251i	0.964918	−	1.67129i
$970$	4.93815	−	8.55313i	0.158554	−	0.274624i
$971$	−2.54746	+	4.41233i	−0.0817519	+	0.141598i	−0.904003	−	0.427527i	$-0.859385\pi$
$971$	−2.54746	+	4.41233i	−0.0817519	+	0.141598i	0.822251	+	0.569126i	$0.192718\pi$
$972$	2.86354	−	4.95979i	0.0918480	−	0.159085i
$973$	−44.3609	+	76.8353i	−1.42214	+	2.46323i
$974$	−8.82737	+	15.2894i	−0.282847	+	0.489905i
$975$	4.67807	+	8.10266i	0.149818	+	0.259493i
$976$	0.371414	−	0.643309i	0.0118887	−	0.0205918i
$977$	−5.57195	−	9.65089i	−0.178262	−	0.308759i	0.763023	−	0.646371i	$-0.223714\pi$
$977$	−5.57195	−	9.65089i	−0.178262	−	0.308759i	−0.941285	+	0.337612i	$0.890381\pi$
$978$	29.8328			0.953948
$979$	−4.64144	+	8.03921i	−0.148341	+	0.256934i
$980$	−8.94380			−0.285699
$981$	−0.927572			−0.0296151
$982$	18.7920	+	32.5487i	0.599677	+	1.03867i
$983$	−40.2661			−1.28429			−0.642144	−	0.766584i	$-0.721955\pi$
$983$	−40.2661			−1.28429			−0.642144	+	0.766584i	$0.721955\pi$
$984$	−8.92257	+	15.4543i	−0.284441	+	0.492667i
$985$	1.51604	−	2.62585i	0.0483050	−	0.0836666i
$986$	−19.2848	−	33.4022i	−0.614152	−	1.06374i
$987$	−33.1055	−	57.3404i	−1.05376	−	1.82517i
$988$	12.3195	+	21.3380i	0.391936	+	0.678853i
$989$	8.72127	+	15.1057i	0.277320	+	0.480333i
$990$	−0.804563			−0.0255707
$991$	27.3569			0.869019			0.434510	−	0.900667i	$-0.356922\pi$
$991$	27.3569			0.869019			0.434510	+	0.900667i	$0.356922\pi$
$992$	−1.41896	−	2.45770i	−0.0450519	−	0.0780322i
$993$	8.24115	−	14.2741i	0.261525	−	0.452975i
$994$	1.16503	−	2.01789i	0.0369525	−	0.0640035i
$995$	1.71746	+	2.97472i	0.0544470	+	0.0943050i
$996$	9.01948			0.285793
$997$	−4.62886			−0.146597			−0.0732987	−	0.997310i	$-0.523353\pi$
$997$	−4.62886			−0.146597			−0.0732987	+	0.997310i	$0.523353\pi$
$998$	2.39346	−	4.14560i	0.0757637	−	0.131227i
$999$	10.0279	+	17.3689i	0.317270	+	0.549528i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.j.171.5	✓	12
67.29	even	3	inner	670.2.e.j.431.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.j.171.5	✓	12	1.1	even	1	trivial
670.2.e.j.431.5	yes	12	67.29	even	3	inner

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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +1.88624 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.943122 + 1.63354i) q^{6} +(-1.99648 + 3.45801i) q^{7} -1.00000 q^{8} +0.557917 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +1.88624 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.943122 + 1.63354i) q^{6} +(-1.99648 + 3.45801i) q^{7} -1.00000 q^{8} +0.557917 q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.721042 - 1.24888i) q^{11} +(-0.943122 + 1.63354i) q^{12} +(2.48010 + 4.29566i) q^{13} -3.99297 q^{14} -1.88624 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.20575 + 5.55253i) q^{17} +(0.278958 + 0.483170i) q^{18} +(-2.48367 - 4.30185i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-3.76586 + 6.52266i) q^{21} +1.44208 q^{22} +(0.970862 + 1.68158i) q^{23} -1.88624 q^{24} +1.00000 q^{25} +(-2.48010 + 4.29566i) q^{26} -4.60636 q^{27} +(-1.99648 - 3.45801i) q^{28} +(-3.00784 + 5.20973i) q^{29} +(-0.943122 - 1.63354i) q^{30} +(1.41896 - 2.45770i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.36006 - 2.35569i) q^{33} +(-3.20575 + 5.55253i) q^{34} +(1.99648 - 3.45801i) q^{35} +(-0.278958 + 0.483170i) q^{36} +(-2.17698 - 3.77063i) q^{37} +(2.48367 - 4.30185i) q^{38} +(4.67807 + 8.10266i) q^{39} +1.00000 q^{40} +(4.73034 - 8.19318i) q^{41} -7.53171 q^{42} +8.98302 q^{43} +(0.721042 + 1.24888i) q^{44} -0.557917 q^{45} +(-0.970862 + 1.68158i) q^{46} +(-4.39548 + 7.61320i) q^{47} +(-0.943122 - 1.63354i) q^{48} +(-4.47190 - 7.74556i) q^{49} +(0.500000 + 0.866025i) q^{50} +(6.04683 + 10.4734i) q^{51} -4.96020 q^{52} +5.31415 q^{53} +(-2.30318 - 3.98923i) q^{54} +(-0.721042 + 1.24888i) q^{55} +(1.99648 - 3.45801i) q^{56} +(-4.68481 - 8.11434i) q^{57} -6.01568 q^{58} +13.4600 q^{59} +(0.943122 - 1.63354i) q^{60} +(0.371414 + 0.643309i) q^{61} +2.83791 q^{62} +(-1.11387 + 1.92928i) q^{63} +1.00000 q^{64} +(-2.48010 - 4.29566i) q^{65} +2.72012 q^{66} +(7.39939 - 3.49987i) q^{67} -6.41151 q^{68} +(1.83128 + 3.17187i) q^{69} +3.99297 q^{70} +(-0.291770 + 0.505360i) q^{71} -0.557917 q^{72} +(-3.56673 - 6.17777i) q^{73} +(2.17698 - 3.77063i) q^{74} +1.88624 q^{75} +4.96735 q^{76} +(2.87910 + 4.98674i) q^{77} +(-4.67807 + 8.10266i) q^{78} +(6.04130 - 10.4638i) q^{79} +(0.500000 + 0.866025i) q^{80} -10.3625 q^{81} +9.46067 q^{82} +(-2.39086 - 4.14109i) q^{83} +(-3.76586 - 6.52266i) q^{84} +(-3.20575 - 5.55253i) q^{85} +(4.49151 + 7.77953i) q^{86} +(-5.67352 + 9.82682i) q^{87} +(-0.721042 + 1.24888i) q^{88} -6.43713 q^{89} +(-0.278958 - 0.483170i) q^{90} -19.8059 q^{91} -1.94172 q^{92} +(2.67650 - 4.63583i) q^{93} -8.79096 q^{94} +(2.48367 + 4.30185i) q^{95} +(0.943122 - 1.63354i) q^{96} +(4.93815 + 8.55313i) q^{97} +(4.47190 - 7.74556i) q^{98} +(0.402281 - 0.696772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9} - 6 q^{10} + 2 q^{12} + 6 q^{14} + 4 q^{15} - 6 q^{16} + 13 q^{17} + 12 q^{18} - 9 q^{19} + 6 q^{20} + 11 q^{21} - 3 q^{23} + 4 q^{24} + 12 q^{25} - 16 q^{27} + 3 q^{28} - 5 q^{29} + 2 q^{30} + 14 q^{31} + 6 q^{32} + 10 q^{33} - 13 q^{34} - 3 q^{35} - 12 q^{36} + 2 q^{37} + 9 q^{38} + 14 q^{39} + 12 q^{40} + 15 q^{41} + 22 q^{42} + 4 q^{43} - 24 q^{45} + 3 q^{46} - 11 q^{47} + 2 q^{48} - 43 q^{49} + 6 q^{50} + 15 q^{51} - 52 q^{53} - 8 q^{54} - 3 q^{56} + 3 q^{57} - 10 q^{58} + 54 q^{59} - 2 q^{60} - 6 q^{61} + 28 q^{62} - 4 q^{63} + 12 q^{64} + 20 q^{66} - 5 q^{67} - 26 q^{68} + 13 q^{69} - 6 q^{70} - 6 q^{71} - 24 q^{72} - 15 q^{73} - 2 q^{74} - 4 q^{75} + 18 q^{76} - 10 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} + 12 q^{81} + 30 q^{82} - 15 q^{83} + 11 q^{84} - 13 q^{85} + 2 q^{86} + 5 q^{87} - 14 q^{89} - 12 q^{90} + 4 q^{91} + 6 q^{92} + 28 q^{93} - 22 q^{94} + 9 q^{95} - 2 q^{96} + 21 q^{97} + 43 q^{98} - 72 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9 - 6 * q^10 + 2 * q^12 + 6 * q^14 + 4 * q^15 - 6 * q^16 + 13 * q^17 + 12 * q^18 - 9 * q^19 + 6 * q^20 + 11 * q^21 - 3 * q^23 + 4 * q^24 + 12 * q^25 - 16 * q^27 + 3 * q^28 - 5 * q^29 + 2 * q^30 + 14 * q^31 + 6 * q^32 + 10 * q^33 - 13 * q^34 - 3 * q^35 - 12 * q^36 + 2 * q^37 + 9 * q^38 + 14 * q^39 + 12 * q^40 + 15 * q^41 + 22 * q^42 + 4 * q^43 - 24 * q^45 + 3 * q^46 - 11 * q^47 + 2 * q^48 - 43 * q^49 + 6 * q^50 + 15 * q^51 - 52 * q^53 - 8 * q^54 - 3 * q^56 + 3 * q^57 - 10 * q^58 + 54 * q^59 - 2 * q^60 - 6 * q^61 + 28 * q^62 - 4 * q^63 + 12 * q^64 + 20 * q^66 - 5 * q^67 - 26 * q^68 + 13 * q^69 - 6 * q^70 - 6 * q^71 - 24 * q^72 - 15 * q^73 - 2 * q^74 - 4 * q^75 + 18 * q^76 - 10 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 + 12 * q^81 + 30 * q^82 - 15 * q^83 + 11 * q^84 - 13 * q^85 + 2 * q^86 + 5 * q^87 - 14 * q^89 - 12 * q^90 + 4 * q^91 + 6 * q^92 + 28 * q^93 - 22 * q^94 + 9 * q^95 - 2 * q^96 + 21 * q^97 + 43 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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