LMFDB - Embedded newform 670.2.e.j.171.1

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			171.1
Root			$1.56111 - 2.70392i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.j.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} -3.12222 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.56111 - 2.70392i) q^{6} +(-2.17160 + 3.76132i) q^{7} -1.00000 q^{8} +6.74824 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} -3.12222 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.56111 - 2.70392i) q^{6} +(-2.17160 + 3.76132i) q^{7} -1.00000 q^{8} +6.74824 q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.37412 + 4.11210i) q^{11} +(1.56111 - 2.70392i) q^{12} +(-2.63644 - 4.56645i) q^{13} -4.34320 q^{14} +3.12222 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.77110 + 4.79969i) q^{17} +(3.37412 + 5.84415i) q^{18} +(-1.45809 - 2.52549i) q^{19} +(0.500000 - 0.866025i) q^{20} +(6.78021 - 11.7437i) q^{21} -4.74824 q^{22} +(-1.25542 - 2.17445i) q^{23} +3.12222 q^{24} +1.00000 q^{25} +(2.63644 - 4.56645i) q^{26} -11.7028 q^{27} +(-2.17160 - 3.76132i) q^{28} +(1.83076 - 3.17096i) q^{29} +(1.56111 + 2.70392i) q^{30} +(2.72774 - 4.72458i) q^{31} +(0.500000 - 0.866025i) q^{32} +(7.41252 - 12.8389i) q^{33} +(-2.77110 + 4.79969i) q^{34} +(2.17160 - 3.76132i) q^{35} +(-3.37412 + 5.84415i) q^{36} +(2.22172 + 3.84813i) q^{37} +(1.45809 - 2.52549i) q^{38} +(8.23155 + 14.2575i) q^{39} +1.00000 q^{40} +(3.01099 - 5.21519i) q^{41} +13.5604 q^{42} -2.74533 q^{43} +(-2.37412 - 4.11210i) q^{44} -6.74824 q^{45} +(1.25542 - 2.17445i) q^{46} +(3.50324 - 6.06779i) q^{47} +(1.56111 + 2.70392i) q^{48} +(-5.93171 - 10.2740i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-8.65198 - 14.9857i) q^{51} +5.27289 q^{52} -13.7163 q^{53} +(-5.85141 - 10.1349i) q^{54} +(2.37412 - 4.11210i) q^{55} +(2.17160 - 3.76132i) q^{56} +(4.55247 + 7.88512i) q^{57} +3.66151 q^{58} +13.4968 q^{59} +(-1.56111 + 2.70392i) q^{60} +(1.41016 + 2.44246i) q^{61} +5.45548 q^{62} +(-14.6545 + 25.3823i) q^{63} +1.00000 q^{64} +(2.63644 + 4.56645i) q^{65} +14.8250 q^{66} +(-7.69113 + 2.80115i) q^{67} -5.54220 q^{68} +(3.91970 + 6.78912i) q^{69} +4.34320 q^{70} +(-4.58763 + 7.94601i) q^{71} -6.74824 q^{72} +(6.01554 + 10.4192i) q^{73} +(-2.22172 + 3.84813i) q^{74} -3.12222 q^{75} +2.91618 q^{76} +(-10.3113 - 17.8597i) q^{77} +(-8.23155 + 14.2575i) q^{78} +(-1.23449 + 2.13820i) q^{79} +(0.500000 + 0.866025i) q^{80} +16.2940 q^{81} +6.02199 q^{82} +(-5.15945 - 8.93643i) q^{83} +(6.78021 + 11.7437i) q^{84} +(-2.77110 - 4.79969i) q^{85} +(-1.37267 - 2.37753i) q^{86} +(-5.71602 + 9.90044i) q^{87} +(2.37412 - 4.11210i) q^{88} -7.96923 q^{89} +(-3.37412 - 5.84415i) q^{90} +22.9012 q^{91} +2.51084 q^{92} +(-8.51659 + 14.7512i) q^{93} +7.00648 q^{94} +(1.45809 + 2.52549i) q^{95} +(-1.56111 + 2.70392i) q^{96} +(-3.60538 - 6.24470i) q^{97} +(5.93171 - 10.2740i) q^{98} +(-16.0211 + 27.7494i) 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
$3$	−3.12222			−1.80261			−0.901306	−	0.433182i	$-0.857391\pi$
$3$	−3.12222			−1.80261			−0.901306	+	0.433182i	$0.857391\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.56111	−	2.70392i	−0.637320	−	1.10387i
$7$	−2.17160	+	3.76132i	−0.820788	+	1.42165i	0.0843076	+	0.996440i	$0.473132\pi$
$7$	−2.17160	+	3.76132i	−0.820788	+	1.42165i	−0.905096	+	0.425207i	$0.860201\pi$
$8$	−1.00000			−0.353553
$9$	6.74824			2.24941
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−2.37412	+	4.11210i	−0.715824	+	1.23984i	0.246817	+	0.969062i	$0.420615\pi$
$11$	−2.37412	+	4.11210i	−0.715824	+	1.23984i	−0.962641	+	0.270781i	$0.912718\pi$
$12$	1.56111	−	2.70392i	0.450653	−	0.780554i
$13$	−2.63644	−	4.56645i	−0.731218	−	1.26651i	−0.956363	−	0.292181i	$-0.905619\pi$
$13$	−2.63644	−	4.56645i	−0.731218	−	1.26651i	0.225145	−	0.974325i	$-0.427714\pi$
$14$	−4.34320			−1.16077
$15$	3.12222			0.806153
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.77110	+	4.79969i	0.672091	+	1.16410i	0.977310	+	0.211813i	$0.0679369\pi$
$17$	2.77110	+	4.79969i	0.672091	+	1.16410i	−0.305219	+	0.952282i	$0.598730\pi$
$18$	3.37412	+	5.84415i	0.795288	+	1.37748i
$19$	−1.45809	−	2.52549i	−0.334509	−	0.579386i	0.648882	−	0.760889i	$-0.275237\pi$
$19$	−1.45809	−	2.52549i	−0.334509	−	0.579386i	−0.983390	+	0.181503i	$0.941904\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	6.78021	−	11.7437i	1.47956	−	2.56268i
$22$	−4.74824			−1.01233
$23$	−1.25542	−	2.17445i	−0.261774	−	0.453405i	0.704940	−	0.709267i	$-0.250974\pi$
$23$	−1.25542	−	2.17445i	−0.261774	−	0.453405i	−0.966713	+	0.255862i	$0.917641\pi$
$24$	3.12222			0.637320
$25$	1.00000			0.200000
$26$	2.63644	−	4.56645i	0.517049	−	0.895555i
$27$	−11.7028			−2.25221
$28$	−2.17160	−	3.76132i	−0.410394	−	0.710824i
$29$	1.83076	−	3.17096i	0.339963	−	0.588833i	−0.644462	−	0.764636i	$-0.722919\pi$
$29$	1.83076	−	3.17096i	0.339963	−	0.588833i	0.984425	+	0.175803i	$0.0562521\pi$
$30$	1.56111	+	2.70392i	0.285018	+	0.493666i
$31$	2.72774	−	4.72458i	0.489916	−	0.848560i	−0.510016	−	0.860165i	$-0.670361\pi$
$31$	2.72774	−	4.72458i	0.489916	−	0.848560i	0.999933	+	0.0116047i	$0.00369399\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	7.41252	−	12.8389i	1.29035	−	2.23496i
$34$	−2.77110	+	4.79969i	−0.475240	+	0.823140i
$35$	2.17160	−	3.76132i	0.367068	−	0.635780i
$36$	−3.37412	+	5.84415i	−0.562353	+	0.974024i
$37$	2.22172	+	3.84813i	0.365248	+	0.632628i	0.988816	−	0.149141i	$-0.0476509\pi$
$37$	2.22172	+	3.84813i	0.365248	+	0.632628i	−0.623568	+	0.781769i	$0.714318\pi$
$38$	1.45809	−	2.52549i	0.236533	−	0.409688i
$39$	8.23155	+	14.2575i	1.31810	+	2.28302i
$40$	1.00000			0.158114
$41$	3.01099	−	5.21519i	0.470238	−	0.814477i	−0.529183	−	0.848508i	$-0.677501\pi$
$41$	3.01099	−	5.21519i	0.470238	−	0.814477i	0.999421	+	0.0340315i	$0.0108346\pi$
$42$	13.5604			2.09242
$43$	−2.74533			−0.418660			−0.209330	−	0.977845i	$-0.567128\pi$
$43$	−2.74533			−0.418660			−0.209330	+	0.977845i	$0.567128\pi$
$44$	−2.37412	−	4.11210i	−0.357912	−	0.619922i
$45$	−6.74824			−1.00597
$46$	1.25542	−	2.17445i	0.185102	−	0.320606i
$47$	3.50324	−	6.06779i	0.511000	−	0.885078i	−0.488919	−	0.872329i	$-0.662609\pi$
$47$	3.50324	−	6.06779i	0.511000	−	0.885078i	0.999919	−	0.0127486i	$-0.00405811\pi$
$48$	1.56111	+	2.70392i	0.225327	+	0.390277i
$49$	−5.93171	−	10.2740i	−0.847387	−	1.46772i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−8.65198	−	14.9857i	−1.21152	−	2.09841i
$52$	5.27289			0.731218
$53$	−13.7163			−1.88408			−0.942041	−	0.335498i	$-0.891095\pi$
$53$	−13.7163			−1.88408			−0.942041	+	0.335498i	$0.891095\pi$
$54$	−5.85141	−	10.1349i	−0.796276	−	1.37919i
$55$	2.37412	−	4.11210i	0.320126	−	0.554475i
$56$	2.17160	−	3.76132i	0.290192	−	0.502628i
$57$	4.55247	+	7.88512i	0.602990	+	1.04441i
$58$	3.66151			0.480780
$59$	13.4968			1.75713			0.878566	−	0.477622i	$-0.158501\pi$
$59$	13.4968			1.75713			0.878566	+	0.477622i	$0.158501\pi$
$60$	−1.56111	+	2.70392i	−0.201538	+	0.349074i
$61$	1.41016	+	2.44246i	0.180552	+	0.312726i	0.942069	−	0.335420i	$-0.108878\pi$
$61$	1.41016	+	2.44246i	0.180552	+	0.312726i	−0.761517	+	0.648145i	$0.775545\pi$
$62$	5.45548			0.692846
$63$	−14.6545	+	25.3823i	−1.84629	+	3.19787i
$64$	1.00000			0.125000
$65$	2.63644	+	4.56645i	0.327011	+	0.566399i
$66$	14.8250			1.82484
$67$	−7.69113	+	2.80115i	−0.939622	+	0.342215i
$67$	−7.69113	+	2.80115i	−0.939622	+	0.342215i
$68$	−5.54220			−0.672091
$69$	3.91970	+	6.78912i	0.471876	+	0.817314i
$70$	4.34320			0.519112
$71$	−4.58763	+	7.94601i	−0.544452	+	0.943018i	0.454190	+	0.890905i	$0.349929\pi$
$71$	−4.58763	+	7.94601i	−0.544452	+	0.943018i	−0.998641	+	0.0521129i	$0.983404\pi$
$72$	−6.74824			−0.795288
$73$	6.01554	+	10.4192i	0.704065	+	1.21948i	0.967028	+	0.254671i	$0.0819670\pi$
$73$	6.01554	+	10.4192i	0.704065	+	1.21948i	−0.262963	+	0.964806i	$0.584700\pi$
$74$	−2.22172	+	3.84813i	−0.258269	+	0.447336i
$75$	−3.12222			−0.360523
$76$	2.91618			0.334509
$77$	−10.3113	−	17.8597i	−1.17508	−	2.03530i
$78$	−8.23155	+	14.2575i	−0.932040	+	1.61434i
$79$	−1.23449	+	2.13820i	−0.138891	+	0.240566i	−0.927077	−	0.374871i	$-0.877687\pi$
$79$	−1.23449	+	2.13820i	−0.138891	+	0.240566i	0.788186	+	0.615437i	$0.211020\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	16.2940			1.81045
$82$	6.02199			0.665017
$83$	−5.15945	−	8.93643i	−0.566323	−	0.980900i	−0.996925	−	0.0783583i	$-0.975032\pi$
$83$	−5.15945	−	8.93643i	−0.566323	−	0.980900i	0.430602	−	0.902542i	$-0.358301\pi$
$84$	6.78021	+	11.7437i	0.739782	+	1.28134i
$85$	−2.77110	−	4.79969i	−0.300568	−	0.520599i
$86$	−1.37267	−	2.37753i	−0.148019	−	0.256376i
$87$	−5.71602	+	9.90044i	−0.612822	+	1.06144i
$88$	2.37412	−	4.11210i	0.253082	−	0.438351i
$89$	−7.96923			−0.844736			−0.422368	−	0.906424i	$-0.638801\pi$
$89$	−7.96923			−0.844736			−0.422368	+	0.906424i	$0.638801\pi$
$90$	−3.37412	−	5.84415i	−0.355663	−	0.616027i
$91$	22.9012			2.40070
$92$	2.51084			0.261774
$93$	−8.51659	+	14.7512i	−0.883129	+	1.52963i
$94$	7.00648			0.722663
$95$	1.45809	+	2.52549i	0.149597	+	0.259109i
$96$	−1.56111	+	2.70392i	−0.159330	+	0.275968i
$97$	−3.60538	−	6.24470i	−0.366071	−	0.634053i	0.622877	−	0.782320i	$-0.285964\pi$
$97$	−3.60538	−	6.24470i	−0.366071	−	0.634053i	−0.988947	+	0.148267i	$0.952630\pi$
$98$	5.93171	−	10.2740i	0.599193	−	1.03783i
$99$	−16.0211	+	27.7494i	−1.61018	+	2.78892i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	0.533856	−	0.924666i	0.0531206	−	0.0920077i	−0.838242	−	0.545298i	$-0.816417\pi$
$101$	0.533856	−	0.924666i	0.0531206	−	0.0920077i	0.891363	+	0.453290i	$0.149750\pi$
$102$	8.65198	−	14.9857i	0.856674	−	1.48380i
$103$	−3.46484	+	6.00128i	−0.341401	+	0.591324i	−0.984693	−	0.174297i	$-0.944235\pi$
$103$	−3.46484	+	6.00128i	−0.341401	+	0.591324i	0.643292	+	0.765621i	$0.277568\pi$
$104$	2.63644	+	4.56645i	0.258525	+	0.447778i
$105$	−6.78021	+	11.7437i	−0.661681	+	1.14607i
$106$	−6.85816	−	11.8787i	−0.666123	−	1.15376i
$107$	4.20864			0.406865			0.203432	−	0.979089i	$-0.434790\pi$
$107$	4.20864			0.406865			0.203432	+	0.979089i	$0.434790\pi$
$108$	5.85141	−	10.1349i	0.563052	−	0.975235i
$109$	−5.83940			−0.559313			−0.279656	−	0.960100i	$-0.590221\pi$
$109$	−5.83940			−0.559313			−0.279656	+	0.960100i	$0.590221\pi$
$110$	4.74824			0.452727
$111$	−6.93668	−	12.0147i	−0.658401	−	1.14038i
$112$	4.34320			0.410394
$113$	8.99591	−	15.5814i	0.846264	−	1.46577i	−0.0382556	−	0.999268i	$-0.512180\pi$
$113$	8.99591	−	15.5814i	0.846264	−	1.46577i	0.884519	−	0.466504i	$-0.154487\pi$
$114$	−4.55247	+	7.88512i	−0.426378	+	0.738509i
$115$	1.25542	+	2.17445i	0.117069	+	0.202769i
$116$	1.83076	+	3.17096i	0.169982	+	0.294417i
$117$	−17.7914	−	30.8155i	−1.64481	−	2.84890i
$118$	6.74839	+	11.6886i	0.621240	+	1.07602i
$119$	−24.0709			−2.20658
$120$	−3.12222			−0.285018
$121$	−5.77289	−	9.99894i	−0.524808	−	0.908994i
$122$	−1.41016	+	2.44246i	−0.127670	+	0.221130i
$123$	−9.40098	+	16.2830i	−0.847658	+	1.46819i
$124$	2.72774	+	4.72458i	0.244958	+	0.424280i
$125$	−1.00000			−0.0894427
$126$	−29.3090			−2.61105
$127$	−5.52011	+	9.56110i	−0.489830	+	0.848411i	−0.999932	−	0.0117036i	$-0.996275\pi$
$127$	−5.52011	+	9.56110i	−0.489830	+	0.848411i	0.510101	+	0.860114i	$0.329608\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	8.57153			0.754681
$130$	−2.63644	+	4.56645i	−0.231231	+	0.400505i
$131$	1.61965			0.141510			0.0707548	−	0.997494i	$-0.477459\pi$
$131$	1.61965			0.141510			0.0707548	+	0.997494i	$0.477459\pi$
$132$	7.41252	+	12.8389i	0.645177	+	1.11748i
$133$	12.6656			1.09824
$134$	−6.27144	−	5.26014i	−0.541770	−	0.454407i
$135$	11.7028			1.00722
$136$	−2.77110	−	4.79969i	−0.237620	−	0.411570i
$137$	7.17210			0.612754			0.306377	−	0.951910i	$-0.400883\pi$
$137$	7.17210			0.612754			0.306377	+	0.951910i	$0.400883\pi$
$138$	−3.91970	+	6.78912i	−0.333667	+	0.577928i
$139$	−13.9848			−1.18617			−0.593086	−	0.805139i	$-0.702091\pi$
$139$	−13.9848			−1.18617			−0.593086	+	0.805139i	$0.702091\pi$
$140$	2.17160	+	3.76132i	0.183534	+	0.317890i
$141$	−10.9379	+	18.9450i	−0.921135	+	1.59545i
$142$	−9.17526			−0.769971
$143$	25.0369			2.09369
$144$	−3.37412	−	5.84415i	−0.281177	−	0.487012i
$145$	−1.83076	+	3.17096i	−0.152036	+	0.263334i
$146$	−6.01554	+	10.4192i	−0.497849	+	0.862300i
$147$	18.5201	+	32.0777i	1.52751	+	2.64573i
$148$	−4.44343			−0.365248
$149$	−21.7990			−1.78584			−0.892921	−	0.450214i	$-0.851348\pi$
$149$	−21.7990			−1.78584			−0.892921	+	0.450214i	$0.851348\pi$
$150$	−1.56111	−	2.70392i	−0.127464	−	0.220774i
$151$	−3.51732	−	6.09217i	−0.286235	−	0.495774i	0.686673	−	0.726967i	$-0.259070\pi$
$151$	−3.51732	−	6.09217i	−0.286235	−	0.495774i	−0.972908	+	0.231193i	$0.925737\pi$
$152$	1.45809	+	2.52549i	0.118267	+	0.204844i
$153$	18.7001	+	32.3894i	1.51181	+	2.61853i
$154$	10.3113	−	17.8597i	0.830907	−	1.43917i
$155$	−2.72774	+	4.72458i	−0.219097	+	0.379488i
$156$	−16.4631			−1.31810
$157$	−6.21936	−	10.7723i	−0.496359	−	0.859719i	0.503632	−	0.863918i	$-0.331997\pi$
$157$	−6.21936	−	10.7723i	−0.496359	−	0.859719i	−0.999991	+	0.00419888i	$0.998663\pi$
$158$	−2.46898			−0.196422
$159$	42.8253			3.39627
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	10.9051			0.859443
$162$	8.14701	+	14.1110i	0.640089	+	1.10867i
$163$	7.21380	−	12.4947i	0.565029	−	0.978658i	−0.432018	−	0.901865i	$-0.642198\pi$
$163$	7.21380	−	12.4947i	0.565029	−	0.978658i	0.997047	−	0.0767936i	$-0.0244683\pi$
$164$	3.01099	+	5.21519i	0.235119	+	0.407238i
$165$	−7.41252	+	12.8389i	−0.577064	+	0.999504i
$166$	5.15945	−	8.93643i	0.400451	−	0.693601i
$167$	7.30963	−	12.6606i	0.565636	−	0.979710i	−0.431354	−	0.902183i	$-0.641964\pi$
$167$	7.30963	−	12.6606i	0.565636	−	0.979710i	0.996990	−	0.0775276i	$-0.0247026\pi$
$168$	−6.78021	+	11.7437i	−0.523105	+	0.906044i
$169$	−7.40167	+	12.8201i	−0.569359	+	0.986160i
$170$	2.77110	−	4.79969i	0.212534	−	0.368119i
$171$	−9.83954	−	17.0426i	−0.752448	−	1.30328i
$172$	1.37267	−	2.37753i	0.104665	−	0.181285i
$173$	2.36197	+	4.09104i	0.179577	+	0.311036i	0.941736	−	0.336354i	$-0.109194\pi$
$173$	2.36197	+	4.09104i	0.179577	+	0.311036i	−0.762159	+	0.647390i	$0.775860\pi$
$174$	−11.4320			−0.866661
$175$	−2.17160	+	3.76132i	−0.164158	+	0.284329i
$176$	4.74824			0.357912
$177$	−42.1399			−3.16743
$178$	−3.98461	−	6.90155i	−0.298659	−	0.517293i
$179$	20.9974			1.56942			0.784709	−	0.619864i	$-0.212812\pi$
$179$	20.9974			1.56942			0.784709	+	0.619864i	$0.212812\pi$
$180$	3.37412	−	5.84415i	0.251492	−	0.435597i
$181$	−8.40722	+	14.5617i	−0.624904	+	1.08236i	0.363656	+	0.931533i	$0.381528\pi$
$181$	−8.40722	+	14.5617i	−0.624904	+	1.08236i	−0.988560	+	0.150831i	$0.951805\pi$
$182$	11.4506	+	19.8330i	0.848776	+	1.47012i
$183$	−4.40282	−	7.62591i	−0.325466	−	0.563723i
$184$	1.25542	+	2.17445i	0.0925509	+	0.160303i
$185$	−2.22172	−	3.84813i	−0.163344	−	0.282920i
$186$	−17.0332			−1.24893
$187$	−26.3157			−1.92439
$188$	3.50324	+	6.06779i	0.255500	+	0.442539i
$189$	25.4139	−	44.0181i	1.84859	−	3.20185i
$190$	−1.45809	+	2.52549i	−0.105781	+	0.183218i
$191$	−0.366645	−	0.635047i	−0.0265295	−	0.0459504i	0.852456	−	0.522799i	$-0.175112\pi$
$191$	−0.366645	−	0.635047i	−0.0265295	−	0.0459504i	−0.878985	+	0.476849i	$0.841779\pi$
$192$	−3.12222			−0.225327
$193$	−9.93373			−0.715046			−0.357523	−	0.933904i	$-0.616379\pi$
$193$	−9.93373			−0.715046			−0.357523	+	0.933904i	$0.616379\pi$
$194$	3.60538	−	6.24470i	0.258851	−	0.448343i
$195$	−8.23155	−	14.2575i	−0.589474	−	1.02100i
$196$	11.8634			0.847387
$197$	9.89891	−	17.1454i	0.705268	−	1.22156i	−0.261327	−	0.965250i	$-0.584160\pi$
$197$	9.89891	−	17.1454i	0.705268	−	1.22156i	0.966595	−	0.256310i	$-0.0825067\pi$
$198$	−32.0423			−2.27714
$199$	−12.9757	−	22.4746i	−0.919823	−	1.59318i	−0.799683	−	0.600423i	$-0.794999\pi$
$199$	−12.9757	−	22.4746i	−0.919823	−	1.59318i	−0.120140	−	0.992757i	$-0.538334\pi$
$200$	−1.00000			−0.0707107
$201$	24.0134	−	8.74580i	1.69377	−	0.616881i
$202$	1.06771			0.0751239
$203$	7.95135	+	13.7721i	0.558075	+	0.966615i
$204$	17.3040			1.21152
$205$	−3.01099	+	5.21519i	−0.210297	+	0.364245i
$206$	−6.92968			−0.482814
$207$	−8.47189	−	14.6737i	−0.588837	−	1.01990i
$208$	−2.63644	+	4.56645i	−0.182804	+	0.316627i
$209$	13.8467			0.957798
$210$	−13.5604			−0.935758
$211$	4.96325	+	8.59660i	0.341684	+	0.591815i	0.984746	−	0.174000i	$-0.0556693\pi$
$211$	4.96325	+	8.59660i	0.341684	+	0.591815i	−0.643061	+	0.765815i	$0.722336\pi$
$212$	6.85816	−	11.8787i	0.471020	−	0.815831i
$213$	14.3236	−	24.8092i	0.981436	−	1.69990i
$214$	2.10432	+	3.64479i	0.143848	+	0.249153i
$215$	2.74533			0.187230
$216$	11.7028			0.796276
$217$	11.8471	+	20.5198i	0.804235	+	1.39298i
$218$	−2.91970	−	5.05707i	−0.197747	−	0.342508i
$219$	−18.7818	−	32.5310i	−1.26916	−	2.19824i
$220$	2.37412	+	4.11210i	0.160063	+	0.277237i
$221$	14.6117	−	25.3082i	0.982890	−	1.70241i
$222$	6.93668	−	12.0147i	0.465560	−	0.806373i
$223$	5.24588			0.351290			0.175645	−	0.984454i	$-0.443799\pi$
$223$	5.24588			0.351290			0.175645	+	0.984454i	$0.443799\pi$
$224$	2.17160	+	3.76132i	0.145096	+	0.251314i
$225$	6.74824			0.449883
$226$	17.9918			1.19680
$227$	3.04558	−	5.27510i	0.202142	−	0.350121i	−0.747076	−	0.664738i	$-0.768543\pi$
$227$	3.04558	−	5.27510i	0.202142	−	0.350121i	0.949218	+	0.314618i	$0.101876\pi$
$228$	−9.10495			−0.602990
$229$	0.139192	+	0.241088i	0.00919807	+	0.0159315i	0.870588	−	0.492013i	$-0.163739\pi$
$229$	0.139192	+	0.241088i	0.00919807	+	0.0159315i	−0.861390	+	0.507945i	$0.830405\pi$
$230$	−1.25542	+	2.17445i	−0.0827801	+	0.143379i
$231$	32.1941	+	55.7618i	2.11821	+	3.66885i
$232$	−1.83076	+	3.17096i	−0.120195	+	0.208184i
$233$	−4.13013	+	7.15359i	−0.270574	+	0.468648i	−0.969009	−	0.247026i	$-0.920547\pi$
$233$	−4.13013	+	7.15359i	−0.270574	+	0.468648i	0.698435	+	0.715673i	$0.253880\pi$
$234$	17.7914	−	30.8155i	1.16306	−	2.01447i
$235$	−3.50324	+	6.06779i	−0.228526	+	0.395819i
$236$	−6.74839	+	11.6886i	−0.439283	+	0.760860i
$237$	3.85435	−	6.67593i	0.250367	−	0.433648i
$238$	−12.0355	−	20.8460i	−0.780143	−	1.35125i
$239$	8.19611	−	14.1961i	0.530162	−	0.918268i	−0.469219	−	0.883082i	$-0.655464\pi$
$239$	8.19611	−	14.1961i	0.530162	−	0.918268i	0.999381	−	0.0351856i	$-0.0112022\pi$
$240$	−1.56111	−	2.70392i	−0.100769	−	0.174537i
$241$	−13.9584			−0.899142			−0.449571	−	0.893245i	$-0.648423\pi$
$241$	−13.9584			−0.899142			−0.449571	+	0.893245i	$0.648423\pi$
$242$	5.77289	−	9.99894i	0.371095	−	0.642756i
$243$	−15.7650			−1.01133
$244$	−2.82032			−0.180552
$245$	5.93171	+	10.2740i	0.378963	+	0.656383i
$246$	−18.8020			−1.19877
$247$	−7.68835	+	13.3166i	−0.489198	+	0.847315i
$248$	−2.72774	+	4.72458i	−0.173212	+	0.300011i
$249$	16.1089	+	27.9015i	1.02086	+	1.76818i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−1.85198	−	3.20772i	−0.116896	−	0.202470i	0.801640	−	0.597807i	$-0.203961\pi$
$251$	−1.85198	−	3.20772i	−0.116896	−	0.202470i	−0.918536	+	0.395337i	$0.870628\pi$
$252$	−14.6545	−	25.3823i	−0.923146	−	1.59894i
$253$	11.9221			0.749535
$254$	−11.0402			−0.692724
$255$	8.65198	+	14.9857i	0.541808	+	0.938439i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.12512	+	7.14492i	−0.257318	+	0.445688i	−0.965523	−	0.260319i	$-0.916172\pi$
$257$	−4.12512	+	7.14492i	−0.257318	+	0.445688i	0.708205	+	0.706007i	$0.249505\pi$
$258$	4.28576	+	7.42316i	0.266820	+	0.462146i
$259$	−19.2987			−1.19916
$260$	−5.27289			−0.327011
$261$	12.3544	−	21.3984i	0.764717	−	1.32453i
$262$	0.809826	+	1.40266i	0.0500312	+	0.0866566i
$263$	−8.54346			−0.526812			−0.263406	−	0.964685i	$-0.584846\pi$
$263$	−8.54346			−0.526812			−0.263406	+	0.964685i	$0.584846\pi$
$264$	−7.41252	+	12.8389i	−0.456209	+	0.790177i
$265$	13.7163			0.842587
$266$	6.33278	+	10.9687i	0.388288	+	0.672534i
$267$	24.8817			1.52273
$268$	1.41970	−	8.06129i	0.0867219	−	0.492422i
$269$	23.2732			1.41899			0.709495	−	0.704710i	$-0.248923\pi$
$269$	23.2732			1.41899			0.709495	+	0.704710i	$0.248923\pi$
$270$	5.85141	+	10.1349i	0.356105	+	0.616793i
$271$	−24.7286			−1.50216			−0.751079	−	0.660212i	$-0.770466\pi$
$271$	−24.7286			−1.50216			−0.751079	+	0.660212i	$0.770466\pi$
$272$	2.77110	−	4.79969i	0.168023	−	0.291024i
$273$	−71.5026			−4.32753
$274$	3.58605	+	6.21122i	0.216641	+	0.375234i
$275$	−2.37412	+	4.11210i	−0.143165	+	0.247969i
$276$	−7.83940			−0.471876
$277$	6.36200			0.382255			0.191128	−	0.981565i	$-0.438786\pi$
$277$	6.36200			0.382255			0.191128	+	0.981565i	$0.438786\pi$
$278$	−6.99238	−	12.1112i	−0.419375	−	0.726379i
$279$	18.4074	−	31.8826i	1.10202	−	1.90876i
$280$	−2.17160	+	3.76132i	−0.129778	+	0.224782i
$281$	2.73159	+	4.73125i	0.162953	+	0.282242i	0.935926	−	0.352196i	$-0.114565\pi$
$281$	2.73159	+	4.73125i	0.162953	+	0.282242i	−0.772974	+	0.634438i	$0.781232\pi$
$282$	−21.8757			−1.30268
$283$	0.740126			0.0439959			0.0219980	−	0.999758i	$-0.492997\pi$
$283$	0.740126			0.0439959			0.0219980	+	0.999758i	$0.492997\pi$
$284$	−4.58763	−	7.94601i	−0.272226	−	0.471509i
$285$	−4.55247	−	7.88512i	−0.269665	−	0.467074i
$286$	12.5185	+	21.6826i	0.740232	+	1.28212i
$287$	13.0774	+	22.6507i	0.771932	+	1.33703i
$288$	3.37412	−	5.84415i	0.198822	−	0.344370i
$289$	−6.85800	+	11.8784i	−0.403412	+	0.698730i
$290$	−3.66151			−0.215012
$291$	11.2568	+	19.4973i	0.659884	+	1.14295i
$292$	−12.0311			−0.704065
$293$	−2.08731			−0.121942			−0.0609710	−	0.998140i	$-0.519420\pi$
$293$	−2.08731			−0.121942			−0.0609710	+	0.998140i	$0.519420\pi$
$294$	−18.5201	+	32.0777i	−1.08011	+	1.87081i
$295$	−13.4968			−0.785813
$296$	−2.22172	−	3.84813i	−0.129135	−	0.223668i
$297$	27.7839	−	48.1231i	1.61218	−	2.79239i
$298$	−10.8995	−	18.8785i	−0.631390	−	1.09360i
$299$	−6.61970	+	11.4657i	−0.382827	+	0.663076i
$300$	1.56111	−	2.70392i	0.0901306	−	0.156111i
$301$	5.96177	−	10.3261i	0.343631	−	0.595186i
$302$	3.51732	−	6.09217i	0.202399	−	0.350565i
$303$	−1.66681	+	2.88701i	−0.0957560	+	0.165854i
$304$	−1.45809	+	2.52549i	−0.0836272	+	0.144847i
$305$	−1.41016	−	2.44246i	−0.0807454	−	0.139855i
$306$	−18.7001	+	32.3894i	−1.06901	+	1.85158i
$307$	−13.8102	−	23.9200i	−0.788191	−	1.36519i	−0.927074	−	0.374879i	$-0.877684\pi$
$307$	−13.8102	−	23.9200i	−0.788191	−	1.36519i	0.138883	−	0.990309i	$-0.455649\pi$
$308$	20.6226			1.17508
$309$	10.8180	−	18.7373i	0.615414	−	1.06593i
$310$	−5.45548			−0.309850
$311$	−28.8950			−1.63848			−0.819242	−	0.573448i	$-0.805605\pi$
$311$	−28.8950			−1.63848			−0.819242	+	0.573448i	$0.805605\pi$
$312$	−8.23155	−	14.2575i	−0.466020	−	0.807170i
$313$	−5.22658			−0.295424			−0.147712	−	0.989030i	$-0.547191\pi$
$313$	−5.22658			−0.295424			−0.147712	+	0.989030i	$0.547191\pi$
$314$	6.21936	−	10.7723i	0.350979	−	0.607913i
$315$	14.6545	−	25.3823i	0.825687	−	1.43013i
$316$	−1.23449	−	2.13820i	−0.0694455	−	0.120283i
$317$	−0.386451	−	0.669353i	−0.0217053	−	0.0375946i	0.854969	−	0.518680i	$-0.173576\pi$
$317$	−0.386451	−	0.669353i	−0.0217053	−	0.0375946i	−0.876674	+	0.481085i	$0.840243\pi$
$318$	21.4127	+	37.0878i	1.20076	+	2.07978i
$319$	8.69287	+	15.0565i	0.486707	+	0.843002i
$320$	−1.00000			−0.0559017
$321$	−13.1403			−0.733419
$322$	5.45255	+	9.44410i	0.303859	+	0.526299i
$323$	8.08103	−	13.9968i	0.449641	−	0.778800i
$324$	−8.14701	+	14.1110i	−0.452612	+	0.783946i
$325$	−2.63644	−	4.56645i	−0.146244	−	0.253301i
$326$	14.4276			0.799071
$327$	18.2319			1.00822
$328$	−3.01099	+	5.21519i	−0.166254	+	0.287961i
$329$	15.2153	+	26.3536i	0.838846	+	1.45292i
$330$	−14.8250			−0.816091
$331$	−6.72161	+	11.6422i	−0.369453	+	0.639911i	−0.989480	−	0.144669i	$-0.953788\pi$
$331$	−6.72161	+	11.6422i	−0.369453	+	0.639911i	0.620027	+	0.784580i	$0.287122\pi$
$332$	10.3189			0.566323
$333$	14.9927	+	25.9681i	0.821593	+	1.42304i
$334$	14.6193			0.799930
$335$	7.69113	−	2.80115i	0.420212	−	0.153043i
$336$	−13.5604			−0.739782
$337$	8.48861	+	14.7027i	0.462404	+	0.800907i	0.999080	−	0.0428810i	$-0.0136536\pi$
$337$	8.48861	+	14.7027i	0.462404	+	0.800907i	−0.536676	+	0.843788i	$0.680320\pi$
$338$	−14.8033			−0.805196
$339$	−28.0872	+	48.6484i	−1.52549	+	2.64222i
$340$	5.54220			0.300568
$341$	12.9520	+	22.4334i	0.701388	+	1.21484i
$342$	9.83954	−	17.0426i	0.532061	−	0.921557i
$343$	21.1228			1.14052
$344$	2.74533			0.148019
$345$	−3.91970	−	6.78912i	−0.211030	−	0.365514i
$346$	−2.36197	+	4.09104i	−0.126980	+	0.219936i
$347$	4.50400	−	7.80116i	0.241788	−	0.418788i	−0.719436	−	0.694559i	$-0.755600\pi$
$347$	4.50400	−	7.80116i	0.241788	−	0.418788i	0.961224	+	0.275770i	$0.0889329\pi$
$348$	−5.71602	−	9.90044i	−0.306411	−	0.530719i
$349$	0.146756			0.00785569			0.00392784	−	0.999992i	$-0.498750\pi$
$349$	0.146756			0.00785569			0.00392784	+	0.999992i	$0.498750\pi$
$350$	−4.34320			−0.232154
$351$	30.8538	+	53.4404i	1.64686	+	2.85244i
$352$	2.37412	+	4.11210i	0.126541	+	0.219175i
$353$	−1.92804	−	3.33946i	−0.102619	−	0.177742i	0.810144	−	0.586231i	$-0.199389\pi$
$353$	−1.92804	−	3.33946i	−0.102619	−	0.177742i	−0.912763	+	0.408490i	$0.866056\pi$
$354$	−21.0699	−	36.4942i	−1.11985	−	1.93964i
$355$	4.58763	−	7.94601i	0.243486	−	0.421730i
$356$	3.98461	−	6.90155i	0.211184	−	0.365782i
$357$	75.1546			3.97760
$358$	10.4987	+	18.1843i	0.554873	+	0.961069i
$359$	−11.0158			−0.581391			−0.290696	−	0.956816i	$-0.593887\pi$
$359$	−11.0158			−0.581391			−0.290696	+	0.956816i	$0.593887\pi$
$360$	6.74824			0.355663
$361$	5.24795	−	9.08971i	0.276208	−	0.478406i
$362$	−16.8144			−0.883747
$363$	18.0242	+	31.2188i	0.946026	+	1.63856i
$364$	−11.4506	+	19.8330i	−0.600175	+	1.03953i
$365$	−6.01554	−	10.4192i	−0.314868	−	0.545367i
$366$	4.40282	−	7.62591i	0.230139	−	0.398612i
$367$	−8.94300	+	15.4897i	−0.466821	+	0.808558i	−0.999282	−	0.0378970i	$-0.987934\pi$
$367$	−8.94300	+	15.4897i	−0.466821	+	0.808558i	0.532461	+	0.846455i	$0.321267\pi$
$368$	−1.25542	+	2.17445i	−0.0654434	+	0.113351i
$369$	20.3189	−	35.1934i	1.05776	−	1.83209i
$370$	2.22172	−	3.84813i	0.115502	−	0.200055i
$371$	29.7864	−	51.5915i	1.54643	−	2.67850i
$372$	−8.51659	−	14.7512i	−0.441565	−	0.764813i
$373$	4.80173	−	8.31684i	0.248624	−	0.430630i	−0.714520	−	0.699615i	$-0.753355\pi$
$373$	4.80173	−	8.31684i	0.248624	−	0.430630i	0.963144	+	0.268985i	$0.0866882\pi$
$374$	−13.1579	−	22.7901i	−0.680376	−	1.17845i
$375$	3.12222			0.161231
$376$	−3.50324	+	6.06779i	−0.180666	+	0.312922i
$377$	−19.3068			−0.994348
$378$	50.8277			2.61430
$379$	−3.75282	−	6.50007i	−0.192769	−	0.333886i	0.753398	−	0.657565i	$-0.228414\pi$
$379$	−3.75282	−	6.50007i	−0.192769	−	0.333886i	−0.946167	+	0.323679i	$0.895080\pi$
$380$	−2.91618			−0.149597
$381$	17.2350	−	29.8518i	0.882974	−	1.52936i
$382$	0.366645	−	0.635047i	0.0187592	−	0.0324919i
$383$	−8.16340	−	14.1394i	−0.417130	−	0.722491i	0.578519	−	0.815669i	$-0.303631\pi$
$383$	−8.16340	−	14.1394i	−0.417130	−	0.722491i	−0.995649	+	0.0931781i	$0.970297\pi$
$384$	−1.56111	−	2.70392i	−0.0796650	−	0.137984i
$385$	10.3113	+	17.8597i	0.525512	+	0.910213i
$386$	−4.96687	−	8.60287i	−0.252807	−	0.437874i
$387$	−18.5262			−0.941738
$388$	7.21075			0.366071
$389$	5.84991	+	10.1323i	0.296602	+	0.513730i	0.975356	−	0.220636i	$-0.0708132\pi$
$389$	5.84991	+	10.1323i	0.296602	+	0.513730i	−0.678754	+	0.734366i	$0.737480\pi$
$390$	8.23155	−	14.2575i	0.416821	−	0.721955i
$391$	6.95780	−	12.0513i	0.351871	−	0.609459i
$392$	5.93171	+	10.2740i	0.299597	+	0.518916i
$393$	−5.05691			−0.255087
$394$	19.7978			0.997400
$395$	1.23449	−	2.13820i	0.0621140	−	0.107585i
$396$	−16.0211	−	27.7494i	−0.805092	−	1.39446i
$397$	−14.1712			−0.711233			−0.355617	−	0.934632i	$-0.615729\pi$
$397$	−14.1712			−0.711233			−0.355617	+	0.934632i	$0.615729\pi$
$398$	12.9757	−	22.4746i	0.650413	−	1.12655i
$399$	−39.5446			−1.97971
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−13.3054			−0.664440			−0.332220	−	0.943202i	$-0.607798\pi$
$401$	−13.3054			−0.664440			−0.332220	+	0.943202i	$0.607798\pi$
$402$	19.5808	+	16.4233i	0.976601	+	0.819120i
$403$	−28.7661			−1.43294
$404$	0.533856	+	0.924666i	0.0265603	+	0.0460038i
$405$	−16.2940			−0.809656
$406$	−7.95135	+	13.7721i	−0.394619	+	0.683500i
$407$	−21.0985			−1.04581
$408$	8.65198	+	14.9857i	0.428337	+	0.741901i
$409$	−3.25364	+	5.63546i	−0.160882	+	0.278656i	−0.935185	−	0.354159i	$-0.884767\pi$
$409$	−3.25364	+	5.63546i	−0.160882	+	0.278656i	0.774303	+	0.632815i	$0.218100\pi$
$410$	−6.02199			−0.297405
$411$	−22.3928			−1.10456
$412$	−3.46484	−	6.00128i	−0.170701	−	0.295662i
$413$	−29.3096	+	50.7658i	−1.44223	+	2.49802i
$414$	8.47189	−	14.6737i	0.416371	−	0.721175i
$415$	5.15945	+	8.93643i	0.253267	+	0.438672i
$416$	−5.27289			−0.258525
$417$	43.6635			2.13821
$418$	6.92336	+	11.9916i	0.338633	+	0.586529i
$419$	−7.38277	−	12.7873i	−0.360672	−	0.624702i	0.627400	−	0.778697i	$-0.284119\pi$
$419$	−7.38277	−	12.7873i	−0.360672	−	0.624702i	−0.988072	+	0.153995i	$0.950786\pi$
$420$	−6.78021	−	11.7437i	−0.330840	−	0.573033i
$421$	−3.93113	−	6.80892i	−0.191592	−	0.331846i	0.754186	−	0.656661i	$-0.228032\pi$
$421$	−3.93113	−	6.80892i	−0.191592	−	0.331846i	−0.945778	+	0.324814i	$0.894698\pi$
$422$	−4.96325	+	8.59660i	−0.241607	+	0.418476i
$423$	23.6407	−	40.9469i	1.14945	−	1.99091i
$424$	13.7163			0.666123
$425$	2.77110	+	4.79969i	0.134418	+	0.232819i
$426$	28.6472			1.38796
$427$	−12.2492			−0.592781
$428$	−2.10432	+	3.64479i	−0.101716	+	0.176178i
$429$	−78.1707			−3.77412
$430$	1.37267	+	2.37753i	0.0661959	+	0.114655i
$431$	−9.81480	+	16.9997i	−0.472762	+	0.818848i	−0.999514	−	0.0311711i	$-0.990076\pi$
$431$	−9.81480	+	16.9997i	−0.472762	+	0.818848i	0.526752	+	0.850019i	$0.323410\pi$
$432$	5.85141	+	10.1349i	0.281526	+	0.487617i
$433$	9.48798	−	16.4337i	0.455963	−	0.789752i	−0.542780	−	0.839875i	$-0.682628\pi$
$433$	9.48798	−	16.4337i	0.455963	−	0.789752i	0.998743	+	0.0501235i	$0.0159615\pi$
$434$	−11.8471	+	20.5198i	−0.568680	+	0.984983i
$435$	5.71602	−	9.90044i	0.274062	−	0.474690i
$436$	2.91970	−	5.05707i	0.139828	−	0.242190i
$437$	−3.66104	+	6.34110i	−0.175131	+	0.303336i
$438$	18.7818	−	32.5310i	0.897429	−	1.55439i
$439$	−8.48886	−	14.7031i	−0.405151	−	0.701743i	0.589188	−	0.807996i	$-0.299448\pi$
$439$	−8.48886	−	14.7031i	−0.405151	−	0.701743i	−0.994339	+	0.106254i	$0.966114\pi$
$440$	−2.37412	+	4.11210i	−0.113182	+	0.196036i
$441$	−40.0286	−	69.3316i	−1.90612	−	3.30150i
$442$	29.2234			1.39002
$443$	6.25222	−	10.8292i	0.297052	−	0.514509i	−0.678408	−	0.734685i	$-0.737330\pi$
$443$	6.25222	−	10.8292i	0.297052	−	0.514509i	0.975460	+	0.220176i	$0.0706632\pi$
$444$	13.8734			0.658401
$445$	7.96923			0.377778
$446$	2.62294	+	4.54306i	0.124200	+	0.215120i
$447$	68.0611			3.21918
$448$	−2.17160	+	3.76132i	−0.102599	+	0.177706i
$449$	−15.3667	+	26.6159i	−0.725199	+	1.25608i	0.233693	+	0.972311i	$0.424919\pi$
$449$	−15.3667	+	26.6159i	−0.725199	+	1.25608i	−0.958892	+	0.283772i	$0.908414\pi$
$450$	3.37412	+	5.84415i	0.159058	+	0.275496i
$451$	14.2969	+	24.7630i	0.673216	+	1.16604i
$452$	8.99591	+	15.5814i	0.423132	+	0.732886i
$453$	10.9818	+	19.0211i	0.515971	+	0.893688i
$454$	6.09116			0.285872
$455$	−22.9012			−1.07363
$456$	−4.55247	−	7.88512i	−0.213189	−	0.369254i
$457$	−9.76545	+	16.9142i	−0.456808	+	0.791215i	−0.998790	−	0.0491750i	$-0.984341\pi$
$457$	−9.76545	+	16.9142i	−0.456808	+	0.791215i	0.541982	+	0.840390i	$0.317674\pi$
$458$	−0.139192	+	0.241088i	−0.00650402	+	0.0112653i
$459$	−32.4297	−	56.1699i	−1.51369	−	2.62178i
$460$	−2.51084			−0.117069
$461$	−4.31067			−0.200768			−0.100384	−	0.994949i	$-0.532007\pi$
$461$	−4.31067			−0.200768			−0.100384	+	0.994949i	$0.532007\pi$
$462$	−32.1941	+	55.7618i	−1.49780	+	2.59427i
$463$	−14.2752	−	24.7254i	−0.663425	−	1.14909i	−0.979710	−	0.200421i	$-0.935769\pi$
$463$	−14.2752	−	24.7254i	−0.663425	−	1.14909i	0.316285	−	0.948664i	$-0.397564\pi$
$464$	−3.66151			−0.169982
$465$	8.51659	−	14.7512i	0.394948	−	0.684069i
$466$	−8.26026			−0.382649
$467$	−19.5318	−	33.8301i	−0.903825	−	1.56547i	−0.822487	−	0.568784i	$-0.807414\pi$
$467$	−19.5318	−	33.8301i	−0.903825	−	1.56547i	−0.0813378	−	0.996687i	$-0.525919\pi$
$468$	35.5827			1.64481
$469$	6.16604	−	35.0118i	0.284721	−	1.61670i
$470$	−7.00648			−0.323185
$471$	19.4182	+	33.6333i	0.894744	+	1.54974i
$472$	−13.4968			−0.621240
$473$	6.51775	−	11.2891i	0.299687	−	0.519072i
$474$	7.70870			0.354072
$475$	−1.45809	−	2.52549i	−0.0669018	−	0.115877i
$476$	12.0355	−	20.8460i	0.551644	−	0.955476i
$477$	−92.5610			−4.23808
$478$	16.3922			0.749762
$479$	−2.55072	−	4.41798i	−0.116545	−	0.201863i	0.801851	−	0.597524i	$-0.203849\pi$
$479$	−2.55072	−	4.41798i	−0.116545	−	0.201863i	−0.918396	+	0.395661i	$0.870515\pi$
$480$	1.56111	−	2.70392i	0.0712545	−	0.123416i
$481$	11.7149	−	20.2907i	0.534152	−	0.925178i
$482$	−6.97922	−	12.0884i	−0.317895	−	0.550610i
$483$	−34.0481			−1.54924
$484$	11.5458			0.524808
$485$	3.60538	+	6.24470i	0.163712	+	0.283557i
$486$	−7.88250	−	13.6529i	−0.357558	−	0.619308i
$487$	11.9703	+	20.7331i	0.542425	+	0.939508i	0.998764	+	0.0497021i	$0.0158272\pi$
$487$	11.9703	+	20.7331i	0.542425	+	0.939508i	−0.456339	+	0.889806i	$0.650839\pi$
$488$	−1.41016	−	2.44246i	−0.0638348	−	0.110565i
$489$	−22.5231	+	39.0111i	−1.01853	+	1.76414i
$490$	−5.93171	+	10.2740i	−0.267967	+	0.464133i
$491$	−12.5631			−0.566966			−0.283483	−	0.958977i	$-0.591490\pi$
$491$	−12.5631			−0.566966			−0.283483	+	0.958977i	$0.591490\pi$
$492$	−9.40098	−	16.2830i	−0.423829	−	0.734093i
$493$	20.2929			0.913944
$494$	−15.3767			−0.691830
$495$	16.0211	−	27.7494i	0.720096	−	1.24724i
$496$	−5.45548			−0.244958
$497$	−19.9250	−	34.5111i	−0.893759	−	1.54804i
$498$	−16.1089	+	27.9015i	−0.721858	+	1.25029i
$499$	8.61136	+	14.9153i	0.385498	+	0.667701i	0.991838	−	0.127504i	$-0.0406965\pi$
$499$	8.61136	+	14.9153i	0.385498	+	0.667701i	−0.606340	+	0.795205i	$0.707363\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−22.8222	+	39.5293i	−1.01962	+	1.76604i
$502$	1.85198	−	3.20772i	0.0826579	−	0.143168i
$503$	11.5062	−	19.9294i	0.513037	−	0.888606i	−0.486849	−	0.873486i	$-0.661854\pi$
$503$	11.5062	−	19.9294i	0.513037	−	0.888606i	0.999886	−	0.0151197i	$-0.00481295\pi$
$504$	14.6545	−	25.3823i	0.652763	−	1.13062i
$505$	−0.533856	+	0.924666i	−0.0237563	+	0.0411471i
$506$	5.96104	+	10.3248i	0.265001	+	0.458995i
$507$	23.1096	−	40.0271i	1.02633	−	1.77766i
$508$	−5.52011	−	9.56110i	−0.244915	−	0.424205i
$509$	−27.2348			−1.20716			−0.603580	−	0.797302i	$-0.706260\pi$
$509$	−27.2348			−1.20716			−0.603580	+	0.797302i	$0.706260\pi$
$510$	−8.65198	+	14.9857i	−0.383116	+	0.663577i
$511$	−52.2534			−2.31155
$512$	−1.00000			−0.0441942
$513$	17.0638	+	29.5553i	0.753383	+	1.30490i
$514$	−8.25024			−0.363903
$515$	3.46484	−	6.00128i	0.152679	−	0.264448i
$516$	−4.28576	+	7.42316i	−0.188670	+	0.326787i
$517$	16.6342	+	28.8113i	0.731572	+	1.26712i
$518$	−9.64937	−	16.7132i	−0.423969	−	0.734336i
$519$	−7.37457	−	12.7731i	−0.323708	−	0.560678i
$520$	−2.63644	−	4.56645i	−0.115616	−	0.200252i
$521$	21.1984			0.928720			0.464360	−	0.885647i	$-0.346284\pi$
$521$	21.1984			0.928720			0.464360	+	0.885647i	$0.346284\pi$
$522$	24.7088			1.08147
$523$	10.6168	+	18.3888i	0.464238	+	0.804085i	0.999167	−	0.0408129i	$-0.0129947\pi$
$523$	10.6168	+	18.3888i	0.464238	+	0.804085i	−0.534928	+	0.844897i	$0.679661\pi$
$524$	−0.809826	+	1.40266i	−0.0353774	+	0.0612755i
$525$	6.78021	−	11.7437i	0.295913	−	0.512536i
$526$	−4.27173	−	7.39885i	−0.186256	−	0.322605i
$527$	30.2354			1.31707
$528$	−14.8250			−0.645177
$529$	8.34783	−	14.4589i	0.362949	−	0.628647i
$530$	6.85816	+	11.8787i	0.297899	+	0.515977i
$531$	91.0795			3.95251
$532$	−6.33278	+	10.9687i	−0.274561	+	0.475553i
$533$	−31.7533			−1.37539
$534$	12.4408	+	21.5481i	0.538367	+	0.932479i
$535$	−4.20864			−0.181955
$536$	7.69113	−	2.80115i	0.332206	−	0.120991i
$537$	−65.5584			−2.82905
$538$	11.6366	+	20.1552i	0.501689	+	0.868951i
$539$	56.3303			2.42632
$540$	−5.85141	+	10.1349i	−0.251805	+	0.436138i
$541$	−4.71545			−0.202733			−0.101367	−	0.994849i	$-0.532321\pi$
$541$	−4.71545			−0.202733			−0.101367	+	0.994849i	$0.532321\pi$
$542$	−12.3643	−	21.4156i	−0.531093	−	0.919880i
$543$	26.2492	−	45.4649i	1.12646	−	1.95108i
$544$	5.54220			0.237620
$545$	5.83940			0.250132
$546$	−35.7513	−	61.9231i	−1.53001	−	2.65006i
$547$	−12.1172	+	20.9875i	−0.518092	+	0.897362i	0.481687	+	0.876343i	$0.340024\pi$
$547$	−12.1172	+	20.9875i	−0.518092	+	0.897362i	−0.999779	+	0.0210186i	$0.993309\pi$
$548$	−3.58605	+	6.21122i	−0.153188	+	0.265330i
$549$	9.51608	+	16.4823i	0.406136	+	0.703449i
$550$	−4.74824			−0.202466
$551$	−10.6776			−0.454883
$552$	−3.91970	−	6.78912i	−0.166833	−	0.288964i
$553$	−5.36164	−	9.28664i	−0.228000	−	0.394908i
$554$	3.18100	+	5.50965i	0.135148	+	0.234083i
$555$	6.93668	+	12.0147i	0.294446	+	0.509995i
$556$	6.99238	−	12.1112i	0.296543	−	0.513628i
$557$	−6.73701	+	11.6688i	−0.285456	+	0.494424i	−0.972720	−	0.231984i	$-0.925478\pi$
$557$	−6.73701	+	11.6688i	−0.285456	+	0.494424i	0.687264	+	0.726408i	$0.258812\pi$
$558$	36.8149			1.55850
$559$	7.23792	+	12.5364i	0.306131	+	0.530235i
$560$	−4.34320			−0.183534
$561$	82.1633			3.46894
$562$	−2.73159	+	4.73125i	−0.115225	+	0.199576i
$563$	40.6612			1.71367			0.856833	−	0.515593i	$-0.172429\pi$
$563$	40.6612			1.71367			0.856833	+	0.515593i	$0.172429\pi$
$564$	−10.9379	−	18.9450i	−0.460568	−	0.797726i
$565$	−8.99591	+	15.5814i	−0.378461	+	0.655513i
$566$	0.370063	+	0.640968i	0.0155549	+	0.0269419i
$567$	−35.3841	+	61.2871i	−1.48599	+	2.57382i
$568$	4.58763	−	7.94601i	0.192493	−	0.333407i
$569$	−0.805128	+	1.39452i	−0.0337527	+	0.0584614i	−0.882408	−	0.470484i	$-0.844079\pi$
$569$	−0.805128	+	1.39452i	−0.0337527	+	0.0584614i	0.848656	+	0.528946i	$0.177413\pi$
$570$	4.55247	−	7.88512i	0.190682	−	0.330271i
$571$	0.878075	−	1.52087i	0.0367463	−	0.0636465i	−0.847067	−	0.531486i	$-0.821634\pi$
$571$	0.878075	−	1.52087i	0.0367463	−	0.0636465i	0.883814	+	0.467839i	$0.154967\pi$
$572$	−12.5185	+	21.6826i	−0.523423	+	0.906596i
$573$	1.14474	+	1.98276i	0.0478224	+	0.0828308i
$574$	−13.0774	+	22.6507i	−0.545838	+	0.945420i
$575$	−1.25542	−	2.17445i	−0.0523547	−	0.0906810i
$576$	6.74824			0.281177
$577$	12.3973	−	21.4727i	0.516105	−	0.893920i	−0.483720	−	0.875223i	$-0.660715\pi$
$577$	12.3973	−	21.4727i	0.516105	−	0.893920i	0.999825	−	0.0186973i	$-0.00595187\pi$
$578$	−13.7160			−0.570511
$579$	31.0153			1.28895
$580$	−1.83076	−	3.17096i	−0.0760181	−	0.131667i
$581$	44.8171			1.85933
$582$	−11.2568	+	19.4973i	−0.466608	+	0.808189i
$583$	32.5642	−	56.4028i	1.34867	−	2.33597i
$584$	−6.01554	−	10.4192i	−0.248925	−	0.431150i
$585$	17.7914	+	30.8155i	0.735582	+	1.27407i
$586$	−1.04365	−	1.80766i	−0.0431130	−	0.0746739i
$587$	−3.32383	−	5.75705i	−0.137189	−	0.237619i	0.789242	−	0.614082i	$-0.210474\pi$
$587$	−3.32383	−	5.75705i	−0.137189	−	0.237619i	−0.926432	+	0.376463i	$0.877140\pi$
$588$	−37.0402			−1.52751
$589$	−15.9092			−0.655525
$590$	−6.74839	−	11.6886i	−0.277827	−	0.481210i
$591$	−30.9065	+	53.5317i	−1.27133	+	2.20200i
$592$	2.22172	−	3.84813i	0.0913120	−	0.158157i
$593$	2.68607	+	4.65240i	0.110304	+	0.191051i	0.915893	−	0.401423i	$-0.131484\pi$
$593$	2.68607	+	4.65240i	0.110304	+	0.191051i	−0.805589	+	0.592475i	$0.798151\pi$
$594$	55.5678			2.27997
$595$	24.0709			0.986811
$596$	10.8995	−	18.8785i	0.446460	−	0.773292i
$597$	40.5129	+	70.1705i	1.65808	+	2.87189i
$598$	−13.2394			−0.541399
$599$	−8.03049	+	13.9092i	−0.328117	+	0.568315i	−0.982138	−	0.188161i	$-0.939747\pi$
$599$	−8.03049	+	13.9092i	−0.328117	+	0.568315i	0.654021	+	0.756476i	$0.273081\pi$
$600$	3.12222			0.127464
$601$	−3.98210	−	6.89720i	−0.162433	−	0.281343i	0.773307	−	0.634031i	$-0.218601\pi$
$601$	−3.98210	−	6.89720i	−0.162433	−	0.281343i	−0.935741	+	0.352688i	$0.885268\pi$
$602$	11.9235			0.485967
$603$	−51.9016	+	18.9028i	−2.11360	+	0.769783i
$604$	7.03463			0.286235
$605$	5.77289	+	9.99894i	0.234701	+	0.406515i
$606$	−3.33363			−0.135419
$607$	3.56092	−	6.16769i	0.144533	−	0.250339i	−0.784666	−	0.619919i	$-0.787165\pi$
$607$	3.56092	−	6.16769i	0.144533	−	0.250339i	0.929199	+	0.369581i	$0.120499\pi$
$608$	−2.91618			−0.118267
$609$	−24.8258	−	42.9996i	−1.00599	−	1.74243i
$610$	1.41016	−	2.44246i	0.0570956	−	0.0988925i
$611$	−36.9444			−1.49461
$612$	−37.4001			−1.51181
$613$	8.83751	+	15.3070i	0.356944	+	0.618244i	0.987449	−	0.157941i	$-0.0504855\pi$
$613$	8.83751	+	15.3070i	0.356944	+	0.618244i	−0.630505	+	0.776185i	$0.717152\pi$
$614$	13.8102	−	23.9200i	0.557335	−	0.965333i
$615$	9.40098	−	16.2830i	0.379084	−	0.656593i
$616$	10.3113	+	17.8597i	0.415454	+	0.719587i
$617$	−36.3837			−1.46475			−0.732377	−	0.680899i	$-0.761589\pi$
$617$	−36.3837			−1.46475			−0.732377	+	0.680899i	$0.761589\pi$
$618$	21.6360			0.870327
$619$	2.74770	+	4.75916i	0.110439	+	0.191287i	0.915948	−	0.401298i	$-0.131441\pi$
$619$	2.74770	+	4.75916i	0.110439	+	0.191287i	−0.805508	+	0.592585i	$0.798108\pi$
$620$	−2.72774	−	4.72458i	−0.109549	−	0.189744i
$621$	14.6920	+	25.4472i	0.589568	+	1.02116i
$622$	−14.4475	−	25.0238i	−0.579292	−	1.00336i
$623$	17.3060	−	29.9748i	0.693350	−	1.20092i
$624$	8.23155	−	14.2575i	0.329526	−	0.570755i
$625$	1.00000			0.0400000
$626$	−2.61329	−	4.52635i	−0.104448	−	0.180909i
$627$	−43.2325			−1.72654
$628$	12.4387			0.496359
$629$	−12.3132	+	21.3271i	−0.490959	+	0.850367i
$630$	29.3090			1.16770
$631$	−13.0413	−	22.5882i	−0.519166	−	0.899222i	−0.999752	−	0.0222743i	$-0.992909\pi$
$631$	−13.0413	−	22.5882i	−0.519166	−	0.899222i	0.480586	−	0.876948i	$-0.340424\pi$
$632$	1.23449	−	2.13820i	0.0491054	−	0.0850531i
$633$	−15.4963	−	26.8405i	−0.615925	−	1.06681i
$634$	0.386451	−	0.669353i	0.0153479	−	0.0265834i
$635$	5.52011	−	9.56110i	0.219059	−	0.379421i
$636$	−21.4127	+	37.0878i	−0.849067	+	1.47063i
$637$	−31.2772	+	54.1738i	−1.23925	+	2.14644i
$638$	−8.69287	+	15.0565i	−0.344154	+	0.596092i
$639$	−30.9584	+	53.6216i	−1.22470	+	2.12124i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−19.8859	+	34.4434i	−0.785446	+	1.36043i	0.143286	+	0.989681i	$0.454233\pi$
$641$	−19.8859	+	34.4434i	−0.785446	+	1.36043i	−0.928732	+	0.370751i	$0.879100\pi$
$642$	−6.57015	−	11.3798i	−0.259303	−	0.449126i
$643$	−44.3309			−1.74824			−0.874120	−	0.485711i	$-0.838561\pi$
$643$	−44.3309			−1.74824			−0.874120	+	0.485711i	$0.838561\pi$
$644$	−5.45255	+	9.44410i	−0.214861	+	0.372150i
$645$	−8.57153			−0.337504
$646$	16.1621			0.635888
$647$	24.4509	+	42.3503i	0.961266	+	1.66496i	0.719329	+	0.694669i	$0.244449\pi$
$647$	24.4509	+	42.3503i	0.961266	+	1.66496i	0.241937	+	0.970292i	$0.422217\pi$
$648$	−16.2940			−0.640089
$649$	−32.0430	+	55.5000i	−1.25780	+	2.17857i
$650$	2.63644	−	4.56645i	0.103410	−	0.179111i
$651$	−36.9893	−	64.0673i	−1.44972	−	2.51100i
$652$	7.21380	+	12.4947i	0.282514	+	0.489329i
$653$	10.0419	+	17.3931i	0.392970	+	0.680643i	0.992840	−	0.119454i	$-0.0381144\pi$
$653$	10.0419	+	17.3931i	0.392970	+	0.680643i	−0.599870	+	0.800097i	$0.704781\pi$
$654$	9.11593	+	15.7893i	0.356461	+	0.617409i
$655$	−1.61965			−0.0632851
$656$	−6.02199			−0.235119
$657$	40.5943	+	70.3113i	1.58373	+	2.74311i
$658$	−15.2153	+	26.3536i	−0.593153	+	1.02737i
$659$	14.1432	−	24.4967i	0.550941	−	0.954257i	−0.447266	−	0.894401i	$-0.647602\pi$
$659$	14.1432	−	24.4967i	0.550941	−	0.954257i	0.998207	−	0.0598563i	$-0.0190643\pi$
$660$	−7.41252	−	12.8389i	−0.288532	−	0.499752i
$661$	−29.8626			−1.16152			−0.580759	−	0.814075i	$-0.697244\pi$
$661$	−29.8626			−1.16152			−0.580759	+	0.814075i	$0.697244\pi$
$662$	−13.4432			−0.522485
$663$	−45.6209	+	79.0177i	−1.77177	+	3.06879i
$664$	5.15945	+	8.93643i	0.200225	+	0.346801i
$665$	−12.6656			−0.491149
$666$	−14.9927	+	25.9681i	−0.580954	+	1.00624i
$667$	−9.19349			−0.355973
$668$	7.30963	+	12.6606i	0.282818	+	0.489855i
$669$	−16.3788			−0.633240
$670$	6.27144	+	5.26014i	0.242287	+	0.203217i
$671$	−13.3915			−0.516974
$672$	−6.78021	−	11.7437i	−0.261552	−	0.453022i
$673$	20.8114			0.802219			0.401109	−	0.916030i	$-0.368625\pi$
$673$	20.8114			0.802219			0.401109	+	0.916030i	$0.368625\pi$
$674$	−8.48861	+	14.7027i	−0.326969	+	0.566327i
$675$	−11.7028			−0.450442
$676$	−7.40167	−	12.8201i	−0.284680	−	0.493080i
$677$	25.4492	−	44.0792i	0.978091	−	1.69410i	0.308757	−	0.951141i	$-0.400087\pi$
$677$	25.4492	−	44.0792i	0.978091	−	1.69410i	0.669333	−	0.742962i	$-0.266580\pi$
$678$	−56.1743			−2.15736
$679$	31.3178			1.20187
$680$	2.77110	+	4.79969i	0.106267	+	0.184060i
$681$	−9.50896	+	16.4700i	−0.364384	+	0.631132i
$682$	−12.9520	+	22.4334i	−0.495956	+	0.859021i
$683$	12.9510	+	22.4317i	0.495555	+	0.858326i	0.999987	−	0.00512504i	$-0.00163136\pi$
$683$	12.9510	+	22.4317i	0.495555	+	0.858326i	−0.504432	+	0.863452i	$0.668298\pi$
$684$	19.6791			0.752448
$685$	−7.17210			−0.274032
$686$	10.5614	+	18.2929i	0.403236	+	0.698426i
$687$	−0.434588	−	0.752728i	−0.0165806	−	0.0287184i
$688$	1.37267	+	2.37753i	0.0523324	+	0.0906425i
$689$	36.1623	+	62.6350i	1.37767	+	2.38620i
$690$	3.91970	−	6.78912i	0.149220	−	0.258457i
$691$	−21.1166	+	36.5750i	−0.803312	+	1.39138i	0.114113	+	0.993468i	$0.463597\pi$
$691$	−21.1166	+	36.5750i	−0.803312	+	1.39138i	−0.917425	+	0.397909i	$0.869736\pi$
$692$	−4.72393			−0.179577
$693$	−69.5830	−	120.521i	−2.64324	−	4.57823i
$694$	9.00801			0.341939
$695$	13.9848			0.530472
$696$	5.71602	−	9.90044i	0.216665	−	0.375275i
$697$	33.3751			1.26417
$698$	0.0733782	+	0.127095i	0.00277740	+	0.00481061i
$699$	12.8952	−	22.3351i	0.487740	−	0.844790i
$700$	−2.17160	−	3.76132i	−0.0820788	−	0.142165i
$701$	15.1886	−	26.3074i	0.573665	−	0.993616i	−0.422521	−	0.906353i	$-0.638855\pi$
$701$	15.1886	−	26.3074i	0.573665	−	0.993616i	0.996185	−	0.0872629i	$-0.0278120\pi$
$702$	−30.8538	+	53.4404i	−1.16450	+	2.01698i
$703$	6.47892	−	11.2218i	0.244357	−	0.423239i
$704$	−2.37412	+	4.11210i	−0.0894780	+	0.154980i
$705$	10.9379	−	18.9450i	0.411944	−	0.713508i
$706$	1.92804	−	3.33946i	0.0725627	−	0.125682i
$707$	2.31864	+	4.01601i	0.0872016	+	0.151038i
$708$	21.0699	−	36.4942i	0.791857	−	1.37154i
$709$	−1.20354	−	2.08460i	−0.0452000	−	0.0782887i	0.842540	−	0.538633i	$-0.181059\pi$
$709$	−1.20354	−	2.08460i	−0.0452000	−	0.0782887i	−0.887740	+	0.460345i	$0.847726\pi$
$710$	9.17526			0.344341
$711$	−8.33064	+	14.4291i	−0.312423	+	0.541133i
$712$	7.96923			0.298659
$713$	−13.6979			−0.512989
$714$	37.5773	+	65.0858i	1.40630	+	2.43578i
$715$	−25.0369			−0.936328
$716$	−10.4987	+	18.1843i	−0.392355	+	0.679578i
$717$	−25.5900	+	44.3232i	−0.955677	+	1.65528i
$718$	−5.50790	−	9.53996i	−0.205553	−	0.356028i
$719$	−15.1059	−	26.1641i	−0.563354	−	0.975758i	−0.997201	−	0.0747711i	$-0.976177\pi$
$719$	−15.1059	−	26.1641i	−0.563354	−	0.975758i	0.433847	−	0.900987i	$-0.357156\pi$
$720$	3.37412	+	5.84415i	0.125746	+	0.217798i
$721$	−15.0485	−	26.0648i	−0.560436	−	0.970704i
$722$	10.4959			0.390617
$723$	43.5813			1.62080
$724$	−8.40722	−	14.5617i	−0.312452	−	0.541182i
$725$	1.83076	−	3.17096i	0.0679926	−	0.117767i
$726$	−18.0242	+	31.2188i	−0.668941	+	1.15864i
$727$	19.9601	+	34.5719i	0.740278	+	1.28220i	0.952369	+	0.304949i	$0.0986395\pi$
$727$	19.9601	+	34.5719i	0.740278	+	1.28220i	−0.212090	+	0.977250i	$0.568027\pi$
$728$	−22.9012			−0.848776
$729$	0.339713			0.0125820
$730$	6.01554	−	10.4192i	0.222645	−	0.385632i
$731$	−7.60760	−	13.1767i	−0.281377	−	0.487360i
$732$	8.80564			0.325466
$733$	−25.0954	+	43.4664i	−0.926918	+	1.60547i	−0.138472	+	0.990366i	$0.544219\pi$
$733$	−25.0954	+	43.4664i	−0.926918	+	1.60547i	−0.788447	+	0.615103i	$0.789114\pi$
$734$	−17.8860			−0.660185
$735$	−18.5201	−	32.0777i	−0.683124	−	1.18320i
$736$	−2.51084			−0.0925509
$737$	6.74107	−	38.2770i	0.248311	−	1.40995i
$738$	40.6378			1.49590
$739$	16.4925	+	28.5658i	0.606686	+	1.05081i	0.991783	+	0.127934i	$0.0408347\pi$
$739$	16.4925	+	28.5658i	0.606686	+	1.05081i	−0.385097	+	0.922876i	$0.625832\pi$
$740$	4.44343			0.163344
$741$	24.0047	−	41.5773i	0.881834	−	1.52738i
$742$	59.5728			2.18699
$743$	20.0690	+	34.7605i	0.736260	+	1.27524i	0.954168	+	0.299270i	$0.0967432\pi$
$743$	20.0690	+	34.7605i	0.736260	+	1.27524i	−0.217909	+	0.975969i	$0.569923\pi$
$744$	8.51659	−	14.7512i	0.312233	−	0.540804i
$745$	21.7990			0.798653
$746$	9.60346			0.351608
$747$	−34.8172	−	60.3051i	−1.27389	−	2.20645i
$748$	13.1579	−	22.7901i	0.481099	−	0.833287i
$749$	−9.13949	+	15.8301i	−0.333950	+	0.578418i
$750$	1.56111	+	2.70392i	0.0570036	+	0.0987332i
$751$	38.0599			1.38882			0.694412	−	0.719577i	$-0.255664\pi$
$751$	38.0599			1.38882			0.694412	+	0.719577i	$0.255664\pi$
$752$	−7.00648			−0.255500
$753$	5.78228	+	10.0152i	0.210718	+	0.364975i
$754$	−9.65338	−	16.7201i	−0.351555	−	0.608912i
$755$	3.51732	+	6.09217i	0.128008	+	0.221717i
$756$	25.4139	+	44.0181i	0.924293	+	1.60092i
$757$	23.1303	−	40.0628i	0.840684	−	1.45611i	−0.0486326	−	0.998817i	$-0.515486\pi$
$757$	23.1303	−	40.0628i	0.840684	−	1.45611i	0.889317	−	0.457291i	$-0.151180\pi$
$758$	3.75282	−	6.50007i	0.136308	−	0.236093i
$759$	−37.2233			−1.35112
$760$	−1.45809	−	2.52549i	−0.0528905	−	0.0916090i
$761$	28.2332			1.02345			0.511727	−	0.859148i	$-0.329006\pi$
$761$	28.2332			1.02345			0.511727	+	0.859148i	$0.329006\pi$
$762$	34.4699			1.24871
$763$	12.6808	−	21.9639i	0.459078	−	0.795146i
$764$	0.733290			0.0265295
$765$	−18.7001	−	32.3894i	−0.676102	−	1.17104i
$766$	8.16340	−	14.1394i	0.294956	−	0.510878i
$767$	−35.5835	−	61.6324i	−1.28485	−	2.22542i
$768$	1.56111	−	2.70392i	0.0563317	−	0.0975693i
$769$	−24.9349	+	43.1886i	−0.899177	+	1.55742i	−0.0706280	+	0.997503i	$0.522500\pi$
$769$	−24.9349	+	43.1886i	−0.899177	+	1.55742i	−0.828549	+	0.559917i	$0.810833\pi$
$770$	−10.3113	+	17.8597i	−0.371593	+	0.643618i
$771$	12.8795	−	22.3080i	0.463845	−	0.803403i
$772$	4.96687	−	8.60287i	0.178761	−	0.309624i
$773$	2.11040	−	3.65532i	0.0759058	−	0.131473i	−0.825574	−	0.564294i	$-0.809149\pi$
$773$	2.11040	−	3.65532i	0.0759058	−	0.131473i	0.901480	+	0.432821i	$0.142482\pi$
$774$	−9.26309	−	16.0441i	−0.332955	−	0.576695i
$775$	2.72774	−	4.72458i	0.0979833	−	0.169712i
$776$	3.60538	+	6.24470i	0.129426	+	0.224172i
$777$	60.2548			2.16163
$778$	−5.84991	+	10.1323i	−0.209729	+	0.363262i
$779$	−17.5612			−0.629195
$780$	16.4631			0.589474
$781$	−21.7832	−	37.7296i	−0.779463	−	1.35007i
$782$	13.9156			0.497621
$783$	−21.4250	+	37.1092i	−0.765668	+	1.32618i
$784$	−5.93171	+	10.2740i	−0.211847	+	0.366929i
$785$	6.21936	+	10.7723i	0.221979	+	0.384478i
$786$	−2.52845	−	4.37941i	−0.0901869	−	0.156208i
$787$	19.9495	+	34.5536i	0.711123	+	1.23170i	0.964436	+	0.264317i	$0.0851466\pi$
$787$	19.9495	+	34.5536i	0.711123	+	1.23170i	−0.253312	+	0.967385i	$0.581520\pi$
$788$	9.89891	+	17.1454i	0.352634	+	0.610780i
$789$	26.6745			0.949638
$790$	2.46898			0.0878424
$791$	39.0711	+	67.6730i	1.38921	+	2.40618i
$792$	16.0211	−	27.7494i	0.569286	−	0.986032i
$793$	7.43560	−	12.8788i	0.264046	−	0.457341i
$794$	−7.08561	−	12.2726i	−0.251459	−	0.435540i
$795$	−42.8253			−1.51886
$796$	25.9514			0.919823
$797$	20.6862	−	35.8295i	0.732742	−	1.26915i	−0.222965	−	0.974826i	$-0.571574\pi$
$797$	20.6862	−	35.8295i	0.732742	−	1.26915i	0.955707	−	0.294319i	$-0.0950930\pi$
$798$	−19.7723	−	34.2467i	−0.699933	−	1.21232i
$799$	38.8313			1.37375
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−53.7782			−1.90016
$802$	−6.65270	−	11.5228i	−0.234915	−	0.406884i
$803$	−57.1264			−2.01595
$804$	−4.43261	+	25.1691i	−0.156326	+	0.887646i
$805$	−10.9051			−0.384354
$806$	−14.3831	−	24.9122i	−0.506622	−	0.877495i
$807$	−72.6639			−2.55789
$808$	−0.533856	+	0.924666i	−0.0187810	+	0.0325296i
$809$	−41.1590			−1.44707			−0.723536	−	0.690286i	$-0.757485\pi$
$809$	−41.1590			−1.44707			−0.723536	+	0.690286i	$0.757485\pi$
$810$	−8.14701	−	14.1110i	−0.286257	−	0.495811i
$811$	−18.1401	+	31.4196i	−0.636986	+	1.10329i	0.349105	+	0.937084i	$0.386486\pi$
$811$	−18.1401	+	31.4196i	−0.636986	+	1.10329i	−0.986091	+	0.166208i	$0.946848\pi$
$812$	−15.9027			−0.558075
$813$	77.2082			2.70781
$814$	−10.5492	−	18.2718i	−0.369751	−	0.640427i
$815$	−7.21380	+	12.4947i	−0.252689	+	0.437669i
$816$	−8.65198	+	14.9857i	−0.302880	+	0.524603i
$817$	4.00294	+	6.93330i	0.140045	+	0.242566i
$818$	−6.50727			−0.227521
$819$	154.543			5.40017
$820$	−3.01099	−	5.21519i	−0.105148	−	0.182122i
$821$	8.27915	+	14.3399i	0.288944	+	0.500467i	0.973558	−	0.228440i	$-0.0733624\pi$
$821$	8.27915	+	14.3399i	0.288944	+	0.500467i	−0.684614	+	0.728906i	$0.740029\pi$
$822$	−11.1964	−	19.3928i	−0.390520	−	0.676401i
$823$	−20.5386	−	35.5739i	−0.715931	−	1.24003i	−0.962599	−	0.270929i	$-0.912669\pi$
$823$	−20.5386	−	35.5739i	−0.715931	−	1.24003i	0.246668	−	0.969100i	$-0.420664\pi$
$824$	3.46484	−	6.00128i	0.120703	−	0.209065i
$825$	7.41252	−	12.8389i	0.258071	−	0.446992i
$826$	−58.6193			−2.03962
$827$	8.44566	+	14.6283i	0.293684	+	0.508676i	0.974678	−	0.223613i	$-0.0717853\pi$
$827$	8.44566	+	14.6283i	0.293684	+	0.508676i	−0.680994	+	0.732289i	$0.738452\pi$
$828$	16.9438			0.588837
$829$	−5.85362			−0.203305			−0.101652	−	0.994820i	$-0.532413\pi$
$829$	−5.85362			−0.203305			−0.101652	+	0.994820i	$0.532413\pi$
$830$	−5.15945	+	8.93643i	−0.179087	+	0.310188i
$831$	−19.8635			−0.689058
$832$	−2.63644	−	4.56645i	−0.0914022	−	0.158313i
$833$	32.8747	−	56.9407i	1.13904	−	1.97288i
$834$	21.8317	+	37.8137i	0.755971	+	1.30938i
$835$	−7.30963	+	12.6606i	−0.252960	+	0.438140i
$836$	−6.92336	+	11.9916i	−0.239449	+	0.414739i
$837$	−31.9222	+	55.2909i	−1.10339	+	1.91113i
$838$	7.38277	−	12.7873i	0.255033	−	0.441731i
$839$	22.8464	−	39.5711i	0.788745	−	1.36615i	−0.137991	−	0.990434i	$-0.544064\pi$
$839$	22.8464	−	39.5711i	0.788745	−	1.36615i	0.926736	−	0.375713i	$-0.122602\pi$
$840$	6.78021	−	11.7437i	0.233940	−	0.405195i
$841$	7.79666	+	13.5042i	0.268850	+	0.465662i
$842$	3.93113	−	6.80892i	0.135476	−	0.234651i
$843$	−8.52860	−	14.7720i	−0.293741	−	0.508774i
$844$	−9.92650			−0.341684
$845$	7.40167	−	12.8201i	0.254625	−	0.441024i
$846$	47.2814			1.62557
$847$	50.1457			1.72303
$848$	6.85816	+	11.8787i	0.235510	+	0.407916i
$849$	−2.31084			−0.0793077
$850$	−2.77110	+	4.79969i	−0.0950480	+	0.164628i
$851$	5.57838	−	9.66204i	0.191224	−	0.331211i
$852$	14.3236	+	24.8092i	0.490718	+	0.849948i
$853$	−2.87591	−	4.98122i	−0.0984692	−	0.170554i	0.812582	−	0.582847i	$-0.198061\pi$
$853$	−2.87591	−	4.98122i	−0.0984692	−	0.170554i	−0.911051	+	0.412293i	$0.864728\pi$
$854$	−6.12460	−	10.6081i	−0.209580	−	0.363002i
$855$	9.83954	+	17.0426i	0.336505	+	0.582844i
$856$	−4.20864			−0.143848
$857$	−30.1827			−1.03102			−0.515510	−	0.856883i	$-0.672398\pi$
$857$	−30.1827			−1.03102			−0.515510	+	0.856883i	$0.672398\pi$
$858$	−39.0854	−	67.6978i	−1.33435	−	2.31117i
$859$	−18.4691	+	31.9894i	−0.630156	+	1.09146i	0.357363	+	0.933965i	$0.383676\pi$
$859$	−18.4691	+	31.9894i	−0.630156	+	1.09146i	−0.987519	+	0.157497i	$0.949658\pi$
$860$	−1.37267	+	2.37753i	−0.0468076	+	0.0810731i
$861$	−40.8304	−	70.7203i	−1.39149	−	2.41014i
$862$	−19.6296			−0.668587
$863$	7.69401			0.261907			0.130953	−	0.991389i	$-0.458196\pi$
$863$	7.69401			0.261907			0.130953	+	0.991389i	$0.458196\pi$
$864$	−5.85141	+	10.1349i	−0.199069	+	0.344798i
$865$	−2.36197	−	4.09104i	−0.0803092	−	0.139100i
$866$	18.9760			0.644829
$867$	21.4122	−	37.0870i	0.727196	−	1.25954i
$868$	−23.6942			−0.804235
$869$	−5.86166	−	10.1527i	−0.198843	−	0.344406i
$870$	11.4320			0.387583
$871$	33.0686	+	27.7361i	1.12049	+	0.939803i
$872$	5.83940			0.197747
$873$	−24.3299	−	42.1407i	−0.823444	−	1.42625i
$874$	−7.32207			−0.247673
$875$	2.17160	−	3.76132i	0.0734135	−	0.127156i
$876$	37.5636			1.26916
$877$	−8.79916	−	15.2406i	−0.297127	−	0.514638i	0.678351	−	0.734738i	$-0.262695\pi$
$877$	−8.79916	−	15.2406i	−0.297127	−	0.514638i	−0.975477	+	0.220100i	$0.929362\pi$
$878$	8.48886	−	14.7031i	0.286485	−	0.496207i
$879$	6.51703			0.219814
$880$	−4.74824			−0.160063
$881$	12.9539	+	22.4368i	0.436427	+	0.755914i	0.997411	−	0.0719126i	$-0.0229103\pi$
$881$	12.9539	+	22.4368i	0.436427	+	0.755914i	−0.560984	+	0.827827i	$0.689577\pi$
$882$	40.0286	−	69.3316i	1.34783	−	2.33451i
$883$	−4.42877	+	7.67085i	−0.149040	+	0.258145i	−0.930873	−	0.365343i	$-0.880952\pi$
$883$	−4.42877	+	7.67085i	−0.149040	+	0.258145i	0.781833	+	0.623488i	$0.214285\pi$
$884$	14.6117	+	25.3082i	0.491445	+	0.851207i
$885$	42.1399			1.41652
$886$	12.5044			0.420095
$887$	−16.8370	−	29.1625i	−0.565330	−	0.979181i	−0.997019	−	0.0771580i	$-0.975415\pi$
$887$	−16.8370	−	29.1625i	−0.565330	−	0.979181i	0.431689	−	0.902023i	$-0.357918\pi$
$888$	6.93668	+	12.0147i	0.232780	+	0.403186i
$889$	−23.9749	−	41.5258i	−0.804094	−	1.39273i
$890$	3.98461	+	6.90155i	0.133565	+	0.231341i
$891$	−38.6839	+	67.0026i	−1.29596	+	2.24467i
$892$	−2.62294	+	4.54306i	−0.0878225	+	0.152113i
$893$	−20.4322			−0.683736
$894$	34.0306	+	58.9427i	1.13815	+	1.97134i
$895$	−20.9974			−0.701865
$896$	−4.34320			−0.145096
$897$	20.6681	−	35.7983i	0.690089	−	1.19527i
$898$	−30.7334			−1.02559
$899$	−9.98765	−	17.2991i	−0.333107	−	0.576958i
$900$	−3.37412	+	5.84415i	−0.112471	+	0.194805i
$901$	−38.0093	−	65.8341i	−1.26627	−	2.19325i
$902$	−14.2969	+	24.7630i	−0.476035	+	0.824517i
$903$	−18.6139	+	32.2403i	−0.619433	+	1.07289i
$904$	−8.99591	+	15.5814i	−0.299199	+	0.518229i
$905$	8.40722	−	14.5617i	0.279465	−	0.484048i
$906$	−10.9818	+	19.0211i	−0.364847	+	0.631933i
$907$	−20.1858	+	34.9629i	−0.670260	+	1.16092i	0.307571	+	0.951525i	$0.400484\pi$
$907$	−20.1858	+	34.9629i	−0.670260	+	1.16092i	−0.977830	+	0.209398i	$0.932849\pi$
$908$	3.04558	+	5.27510i	0.101071	+	0.175060i
$909$	3.60259	−	6.23986i	0.119490	−	0.206963i
$910$	−11.4506	−	19.8330i	−0.379584	−	0.657459i
$911$	11.3336			0.375499			0.187750	−	0.982217i	$-0.439881\pi$
$911$	11.3336			0.375499			0.187750	+	0.982217i	$0.439881\pi$
$912$	4.55247	−	7.88512i	0.150747	−	0.261102i
$913$	48.9966			1.62155
$914$	−19.5309			−0.646024
$915$	4.40282	+	7.62591i	0.145553	+	0.252105i
$916$	−0.278384			−0.00919807
$917$	−3.51724	+	6.09204i	−0.116149	+	0.201177i
$918$	32.4297	−	56.1699i	1.07034	−	1.85388i
$919$	−11.4663	−	19.8602i	−0.378238	−	0.655127i	0.612568	−	0.790418i	$-0.290137\pi$
$919$	−11.4663	−	19.8602i	−0.378238	−	0.655127i	−0.990806	+	0.135291i	$0.956803\pi$
$920$	−1.25542	−	2.17445i	−0.0413900	−	0.0716896i
$921$	43.1185	+	74.6835i	1.42080	+	2.46090i
$922$	−2.15533	−	3.73315i	−0.0709822	−	0.122945i
$923$	48.3801			1.59245
$924$	−64.3881			−2.11821
$925$	2.22172	+	3.84813i	0.0730496	+	0.126526i
$926$	14.2752	−	24.7254i	0.469112	−	0.812526i
$927$	−23.3816	+	40.4981i	−0.767952	+	1.33013i
$928$	−1.83076	−	3.17096i	−0.0600975	−	0.104092i
$929$	19.4758			0.638981			0.319490	−	0.947590i	$-0.396488\pi$
$929$	19.4758			0.638981			0.319490	+	0.947590i	$0.396488\pi$
$930$	17.0332			0.558540
$931$	−17.2979	+	29.9609i	−0.566917	+	0.981929i
$932$	−4.13013	−	7.15359i	−0.135287	−	0.234324i
$933$	90.2164			2.95355
$934$	19.5318	−	33.8301i	0.639101	−	1.10695i
$935$	26.3157			0.860615
$936$	17.7914	+	30.8155i	0.581529	+	1.00724i
$937$	10.5971			0.346192			0.173096	−	0.984905i	$-0.444623\pi$
$937$	10.5971			0.346192			0.173096	+	0.984905i	$0.444623\pi$
$938$	33.4042	−	12.1660i	1.09068	−	0.397233i
$939$	16.3185			0.532534
$940$	−3.50324	−	6.06779i	−0.114263	−	0.197909i
$941$	−25.1941			−0.821304			−0.410652	−	0.911792i	$-0.634699\pi$
$941$	−25.1941			−0.821304			−0.410652	+	0.911792i	$0.634699\pi$
$942$	−19.4182	+	33.6333i	−0.632679	+	1.09583i
$943$	−15.1203			−0.492384
$944$	−6.74839	−	11.6886i	−0.219641	−	0.380430i
$945$	−25.4139	+	44.0181i	−0.826713	+	1.43191i
$946$	13.0355			0.423821
$947$	−41.5551			−1.35036			−0.675180	−	0.737653i	$-0.735934\pi$
$947$	−41.5551			−1.35036			−0.675180	+	0.737653i	$0.735934\pi$
$948$	3.85435	+	6.67593i	0.125183	+	0.216824i
$949$	31.7192	−	54.9393i	1.02965	−	1.78341i
$950$	1.45809	−	2.52549i	0.0473067	−	0.0819376i
$951$	1.20658	+	2.08987i	0.0391262	+	0.0677686i
$952$	24.0709			0.780143
$953$	−27.6214			−0.894744			−0.447372	−	0.894348i	$-0.647640\pi$
$953$	−27.6214			−0.894744			−0.447372	+	0.894348i	$0.647640\pi$
$954$	−46.2805	−	80.1602i	−1.49839	−	2.59528i
$955$	0.366645	+	0.635047i	0.0118643	+	0.0205497i
$956$	8.19611	+	14.1961i	0.265081	+	0.459134i
$957$	−27.1410	−	47.0097i	−0.877345	−	1.51961i
$958$	2.55072	−	4.41798i	0.0824101	−	0.142738i
$959$	−15.5749	+	26.9766i	−0.502941	+	0.871120i
$960$	3.12222			0.100769
$961$	0.618883	+	1.07194i	0.0199640	+	0.0345786i
$962$	23.4297			0.755405
$963$	28.4009			0.915207
$964$	6.97922	−	12.0884i	0.224785	−	0.389340i
$965$	9.93373			0.319778
$966$	−17.0241	−	29.4865i	−0.547740	−	0.948713i
$967$	12.1900	−	21.1138i	0.392005	−	0.678973i	−0.600709	−	0.799468i	$-0.705115\pi$
$967$	12.1900	−	21.1138i	0.392005	−	0.678973i	0.992714	+	0.120495i	$0.0384483\pi$
$968$	5.77289	+	9.99894i	0.185548	+	0.321378i
$969$	−25.2307	+	43.7009i	−0.810528	+	1.40388i
$970$	−3.60538	+	6.24470i	−0.115762	+	0.200505i
$971$	−10.8585	+	18.8074i	−0.348465	+	0.603560i	−0.985977	−	0.166881i	$-0.946630\pi$
$971$	−10.8585	+	18.8074i	−0.348465	+	0.603560i	0.637512	+	0.770441i	$0.279964\pi$
$972$	7.88250	−	13.6529i	0.252831	−	0.437917i
$973$	30.3693	−	52.6012i	0.973596	−	1.68632i
$974$	−11.9703	+	20.7331i	−0.383553	+	0.664333i
$975$	8.23155	+	14.2575i	0.263621	+	0.456604i
$976$	1.41016	−	2.44246i	0.0451380	−	0.0781814i
$977$	−3.37852	−	5.85176i	−0.108088	−	0.187214i	0.806907	−	0.590678i	$-0.201140\pi$
$977$	−3.37852	−	5.85176i	−0.108088	−	0.187214i	−0.914996	+	0.403463i	$0.867806\pi$
$978$	−45.0461			−1.44042
$979$	18.9199	−	32.7702i	0.604682	−	1.04734i
$980$	−11.8634			−0.378963
$981$	−39.4057			−1.25813
$982$	−6.28156	−	10.8800i	−0.200453	−	0.347194i
$983$	15.3942			0.491000			0.245500	−	0.969397i	$-0.421048\pi$
$983$	15.3942			0.491000			0.245500	+	0.969397i	$0.421048\pi$
$984$	9.40098	−	16.2830i	0.299692	−	0.519082i
$985$	−9.89891	+	17.1454i	−0.315405	+	0.546298i
$986$	10.1464	+	17.5741i	0.323128	+	0.559674i
$987$	−47.5054	−	82.2818i	−1.51211	−	2.61906i
$988$	−7.68835	−	13.3166i	−0.244599	−	0.423658i
$989$	3.44655	+	5.96960i	0.109594	+	0.189822i
$990$	32.0423			1.01837
$991$	1.34045			0.0425807			0.0212903	−	0.999773i	$-0.493223\pi$
$991$	1.34045			0.0425807			0.0212903	+	0.999773i	$0.493223\pi$
$992$	−2.72774	−	4.72458i	−0.0866058	−	0.150006i
$993$	20.9863	−	36.3494i	0.665981	−	1.15351i
$994$	19.9250	−	34.5111i	0.631983	−	1.09463i
$995$	12.9757	+	22.4746i	0.411357	+	0.712492i
$996$	−32.2178			−1.02086
$997$	−49.0457			−1.55329			−0.776647	−	0.629936i	$-0.783081\pi$
$997$	−49.0457			−1.55329			−0.776647	+	0.629936i	$0.783081\pi$
$998$	−8.61136	+	14.9153i	−0.272588	+	0.472136i
$999$	−26.0003	−	45.0339i	−0.822614	−	1.42481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.j.171.1	✓	12
67.29	even	3	inner	670.2.e.j.431.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.j.171.1	✓	12	1.1	even	1	trivial
670.2.e.j.431.1	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} -3.12222 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.56111 - 2.70392i) q^{6} +(-2.17160 + 3.76132i) q^{7} -1.00000 q^{8} +6.74824 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} -3.12222 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.56111 - 2.70392i) q^{6} +(-2.17160 + 3.76132i) q^{7} -1.00000 q^{8} +6.74824 q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.37412 + 4.11210i) q^{11} +(1.56111 - 2.70392i) q^{12} +(-2.63644 - 4.56645i) q^{13} -4.34320 q^{14} +3.12222 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.77110 + 4.79969i) q^{17} +(3.37412 + 5.84415i) q^{18} +(-1.45809 - 2.52549i) q^{19} +(0.500000 - 0.866025i) q^{20} +(6.78021 - 11.7437i) q^{21} -4.74824 q^{22} +(-1.25542 - 2.17445i) q^{23} +3.12222 q^{24} +1.00000 q^{25} +(2.63644 - 4.56645i) q^{26} -11.7028 q^{27} +(-2.17160 - 3.76132i) q^{28} +(1.83076 - 3.17096i) q^{29} +(1.56111 + 2.70392i) q^{30} +(2.72774 - 4.72458i) q^{31} +(0.500000 - 0.866025i) q^{32} +(7.41252 - 12.8389i) q^{33} +(-2.77110 + 4.79969i) q^{34} +(2.17160 - 3.76132i) q^{35} +(-3.37412 + 5.84415i) q^{36} +(2.22172 + 3.84813i) q^{37} +(1.45809 - 2.52549i) q^{38} +(8.23155 + 14.2575i) q^{39} +1.00000 q^{40} +(3.01099 - 5.21519i) q^{41} +13.5604 q^{42} -2.74533 q^{43} +(-2.37412 - 4.11210i) q^{44} -6.74824 q^{45} +(1.25542 - 2.17445i) q^{46} +(3.50324 - 6.06779i) q^{47} +(1.56111 + 2.70392i) q^{48} +(-5.93171 - 10.2740i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-8.65198 - 14.9857i) q^{51} +5.27289 q^{52} -13.7163 q^{53} +(-5.85141 - 10.1349i) q^{54} +(2.37412 - 4.11210i) q^{55} +(2.17160 - 3.76132i) q^{56} +(4.55247 + 7.88512i) q^{57} +3.66151 q^{58} +13.4968 q^{59} +(-1.56111 + 2.70392i) q^{60} +(1.41016 + 2.44246i) q^{61} +5.45548 q^{62} +(-14.6545 + 25.3823i) q^{63} +1.00000 q^{64} +(2.63644 + 4.56645i) q^{65} +14.8250 q^{66} +(-7.69113 + 2.80115i) q^{67} -5.54220 q^{68} +(3.91970 + 6.78912i) q^{69} +4.34320 q^{70} +(-4.58763 + 7.94601i) q^{71} -6.74824 q^{72} +(6.01554 + 10.4192i) q^{73} +(-2.22172 + 3.84813i) q^{74} -3.12222 q^{75} +2.91618 q^{76} +(-10.3113 - 17.8597i) q^{77} +(-8.23155 + 14.2575i) q^{78} +(-1.23449 + 2.13820i) q^{79} +(0.500000 + 0.866025i) q^{80} +16.2940 q^{81} +6.02199 q^{82} +(-5.15945 - 8.93643i) q^{83} +(6.78021 + 11.7437i) q^{84} +(-2.77110 - 4.79969i) q^{85} +(-1.37267 - 2.37753i) q^{86} +(-5.71602 + 9.90044i) q^{87} +(2.37412 - 4.11210i) q^{88} -7.96923 q^{89} +(-3.37412 - 5.84415i) q^{90} +22.9012 q^{91} +2.51084 q^{92} +(-8.51659 + 14.7512i) q^{93} +7.00648 q^{94} +(1.45809 + 2.52549i) q^{95} +(-1.56111 + 2.70392i) q^{96} +(-3.60538 - 6.24470i) q^{97} +(5.93171 - 10.2740i) q^{98} +(-16.0211 + 27.7494i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more