LMFDB - Embedded newform 670.2.e.i.431.3

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 31x^{6} - 2x^{5} + 597x^{4} - 4x^{3} + 5860x^{2} + 5264x + 35344 $ x^8 - 2x^7 + 31x^6 - 2x^5 + 597x^4 - 4x^3 + 5860x^2 + 5264*x + 35344
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			431.3
Root			$-1.81630 - 3.14593i$ of defining polynomial
Character	$\chi$	$=$	670.431
Dual form			670.2.e.i.171.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +2.41421 q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.20711 + 2.09077i) q^{6} +(0.707107 + 1.22474i) q^{7} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +2.41421 q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.20711 + 2.09077i) q^{6} +(0.707107 + 1.22474i) q^{7} +1.00000 q^{8} +2.82843 q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-1.20711 - 2.09077i) q^{12} +(-2.56864 + 4.44901i) q^{13} -1.41421 q^{14} +2.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.52341 + 4.37067i) q^{17} +(-1.41421 + 2.44949i) q^{18} +(2.81630 - 4.87798i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.70711 + 2.95680i) q^{21} -2.00000 q^{22} +(4.33971 - 7.51660i) q^{23} +2.41421 q^{24} +1.00000 q^{25} +(-2.56864 - 4.44901i) q^{26} -0.414214 q^{27} +(0.707107 - 1.22474i) q^{28} +(2.15443 + 3.73158i) q^{29} +(-1.20711 + 2.09077i) q^{30} +(3.37366 + 5.84335i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.41421 + 4.18154i) q^{33} +(-2.52341 - 4.37067i) q^{34} +(0.707107 + 1.22474i) q^{35} +(-1.41421 - 2.44949i) q^{36} +(3.73052 - 6.46144i) q^{37} +(2.81630 + 4.87798i) q^{38} +(-6.20125 + 10.7409i) q^{39} +1.00000 q^{40} +(-0.487876 - 0.845025i) q^{41} -3.41421 q^{42} -2.33310 q^{43} +(1.00000 - 1.73205i) q^{44} +2.82843 q^{45} +(4.33971 + 7.51660i) q^{46} +(-4.68996 - 8.12325i) q^{47} +(-1.20711 + 2.09077i) q^{48} +(2.50000 - 4.33013i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-6.09205 + 10.5517i) q^{51} +5.13728 q^{52} -2.50467 q^{53} +(0.207107 - 0.358719i) q^{54} +(1.00000 + 1.73205i) q^{55} +(0.707107 + 1.22474i) q^{56} +(6.79916 - 11.7765i) q^{57} -4.30885 q^{58} +3.63261 q^{59} +(-1.20711 - 2.09077i) q^{60} +(6.10417 - 10.5727i) q^{61} -6.74732 q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(-2.56864 + 4.44901i) q^{65} -4.82843 q^{66} +(-7.78787 - 2.51973i) q^{67} +5.04682 q^{68} +(10.4770 - 18.1467i) q^{69} -1.41421 q^{70} +(3.02341 + 5.23670i) q^{71} +2.82843 q^{72} +(-6.35184 + 11.0017i) q^{73} +(3.73052 + 6.46144i) q^{74} +2.41421 q^{75} -5.63261 q^{76} +(-1.41421 + 2.44949i) q^{77} +(-6.20125 - 10.7409i) q^{78} +(-7.46103 - 12.9229i) q^{79} +(-0.500000 + 0.866025i) q^{80} -9.48528 q^{81} +0.975751 q^{82} +(-5.78787 + 10.0249i) q^{83} +(1.70711 - 2.95680i) q^{84} +(-2.52341 + 4.37067i) q^{85} +(1.16655 - 2.02053i) q^{86} +(5.20125 + 9.00882i) q^{87} +(1.00000 + 1.73205i) q^{88} -14.2652 q^{89} +(-1.41421 + 2.44949i) q^{90} -7.26521 q^{91} -8.67942 q^{92} +(8.14473 + 14.1071i) q^{93} +9.37992 q^{94} +(2.81630 - 4.87798i) q^{95} +(-1.20711 - 2.09077i) q^{96} +(1.58076 - 2.73796i) q^{97} +(2.50000 + 4.33013i) q^{98} +(2.82843 + 4.89898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8	$ 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8} - 4 q^{10} + 8 q^{11} - 4 q^{12} + 8 q^{15} - 4 q^{16} + 2 q^{17} + 6 q^{19} - 4 q^{20} + 8 q^{21} - 16 q^{22} - 4 q^{23} + 8 q^{24} + 8 q^{25} + 8 q^{27} + 8 q^{29} - 4 q^{30} + 6 q^{31} - 4 q^{32} + 8 q^{33} + 2 q^{34} + 2 q^{37} + 6 q^{38} + 4 q^{39} + 8 q^{40} - 10 q^{41} - 16 q^{42} + 12 q^{43} + 8 q^{44} - 4 q^{46} - 4 q^{48} + 20 q^{49} - 4 q^{50} - 6 q^{51} - 12 q^{53} - 4 q^{54} + 8 q^{55} + 6 q^{57} - 16 q^{58} - 4 q^{59} - 4 q^{60} - 12 q^{62} + 16 q^{63} + 8 q^{64} - 16 q^{66} - 30 q^{67} - 4 q^{68} + 4 q^{69} + 2 q^{71} - 6 q^{73} + 2 q^{74} + 8 q^{75} - 12 q^{76} + 4 q^{78} - 4 q^{79} - 4 q^{80} - 8 q^{81} + 20 q^{82} - 14 q^{83} + 8 q^{84} + 2 q^{85} - 6 q^{86} - 12 q^{87} + 8 q^{88} - 48 q^{89} + 8 q^{91} + 8 q^{92} + 26 q^{93} + 6 q^{95} - 4 q^{96} - 14 q^{97} + 20 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8 - 4 * q^10 + 8 * q^11 - 4 * q^12 + 8 * q^15 - 4 * q^16 + 2 * q^17 + 6 * q^19 - 4 * q^20 + 8 * q^21 - 16 * q^22 - 4 * q^23 + 8 * q^24 + 8 * q^25 + 8 * q^27 + 8 * q^29 - 4 * q^30 + 6 * q^31 - 4 * q^32 + 8 * q^33 + 2 * q^34 + 2 * q^37 + 6 * q^38 + 4 * q^39 + 8 * q^40 - 10 * q^41 - 16 * q^42 + 12 * q^43 + 8 * q^44 - 4 * q^46 - 4 * q^48 + 20 * q^49 - 4 * q^50 - 6 * q^51 - 12 * q^53 - 4 * q^54 + 8 * q^55 + 6 * q^57 - 16 * q^58 - 4 * q^59 - 4 * q^60 - 12 * q^62 + 16 * q^63 + 8 * q^64 - 16 * q^66 - 30 * q^67 - 4 * q^68 + 4 * q^69 + 2 * q^71 - 6 * q^73 + 2 * q^74 + 8 * q^75 - 12 * q^76 + 4 * q^78 - 4 * q^79 - 4 * q^80 - 8 * q^81 + 20 * q^82 - 14 * q^83 + 8 * q^84 + 2 * q^85 - 6 * q^86 - 12 * q^87 + 8 * q^88 - 48 * q^89 + 8 * q^91 + 8 * q^92 + 26 * q^93 + 6 * q^95 - 4 * q^96 - 14 * q^97 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	2.41421			1.39385			0.696923	−	0.717146i	$-0.254552\pi$
$3$	2.41421			1.39385			0.696923	+	0.717146i	$0.254552\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.20711	+	2.09077i	−0.492799	+	0.853553i
$7$	0.707107	+	1.22474i	0.267261	+	0.462910i	0.968154	−	0.250357i	$-0.0805480\pi$
$7$	0.707107	+	1.22474i	0.267261	+	0.462910i	−0.700892	+	0.713267i	$0.747215\pi$
$8$	1.00000			0.353553
$9$	2.82843			0.942809
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	−1.20711	−	2.09077i	−0.348462	−	0.603553i
$13$	−2.56864	+	4.44901i	−0.712413	+	1.23393i	0.251537	+	0.967848i	$0.419064\pi$
$13$	−2.56864	+	4.44901i	−0.712413	+	1.23393i	−0.963949	+	0.266087i	$0.914269\pi$
$14$	−1.41421			−0.377964
$15$	2.41421			0.623347
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.52341	+	4.37067i	−0.612017	+	1.06004i	0.378883	+	0.925444i	$0.376308\pi$
$17$	−2.52341	+	4.37067i	−0.612017	+	1.06004i	−0.990900	+	0.134600i	$0.957025\pi$
$18$	−1.41421	+	2.44949i	−0.333333	+	0.577350i
$19$	2.81630	−	4.87798i	0.646104	−	1.11909i	−0.337941	−	0.941167i	$-0.609730\pi$
$19$	2.81630	−	4.87798i	0.646104	−	1.11909i	0.984045	−	0.177918i	$-0.0569362\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	1.70711	+	2.95680i	0.372521	+	0.645226i
$22$	−2.00000			−0.426401
$23$	4.33971	−	7.51660i	0.904893	−	1.56732i	0.0838311	−	0.996480i	$-0.473284\pi$
$23$	4.33971	−	7.51660i	0.904893	−	1.56732i	0.821061	−	0.570840i	$-0.193382\pi$
$24$	2.41421			0.492799
$25$	1.00000			0.200000
$26$	−2.56864	−	4.44901i	−0.503752	−	0.872524i
$27$	−0.414214			−0.0797154
$28$	0.707107	−	1.22474i	0.133631	−	0.231455i
$29$	2.15443	+	3.73158i	0.400067	+	0.692936i	0.993734	−	0.111775i	$-0.0356535\pi$
$29$	2.15443	+	3.73158i	0.400067	+	0.692936i	−0.593667	+	0.804711i	$0.702320\pi$
$30$	−1.20711	+	2.09077i	−0.220387	+	0.381721i
$31$	3.37366	+	5.84335i	0.605927	+	1.04950i	0.991904	+	0.126988i	$0.0405309\pi$
$31$	3.37366	+	5.84335i	0.605927	+	1.04950i	−0.385977	+	0.922508i	$0.626136\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.41421	+	4.18154i	0.420261	+	0.727913i
$34$	−2.52341	−	4.37067i	−0.432761	−	0.749564i
$35$	0.707107	+	1.22474i	0.119523	+	0.207020i
$36$	−1.41421	−	2.44949i	−0.235702	−	0.408248i
$37$	3.73052	−	6.46144i	0.613293	−	1.06225i	−0.377388	−	0.926055i	$-0.623178\pi$
$37$	3.73052	−	6.46144i	0.613293	−	1.06225i	0.990681	−	0.136200i	$-0.0434889\pi$
$38$	2.81630	+	4.87798i	0.456865	+	0.791313i
$39$	−6.20125	+	10.7409i	−0.992994	+	1.71992i
$40$	1.00000			0.158114
$41$	−0.487876	−	0.845025i	−0.0761934	−	0.131971i	0.825411	−	0.564532i	$-0.190943\pi$
$41$	−0.487876	−	0.845025i	−0.0761934	−	0.131971i	−0.901605	+	0.432561i	$0.857610\pi$
$42$	−3.41421			−0.526825
$43$	−2.33310			−0.355795			−0.177897	−	0.984049i	$-0.556929\pi$
$43$	−2.33310			−0.355795			−0.177897	+	0.984049i	$0.556929\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$	2.82843			0.421637
$46$	4.33971	+	7.51660i	0.639856	+	1.10826i
$47$	−4.68996	−	8.12325i	−0.684101	−	1.18490i	−0.973718	−	0.227755i	$-0.926861\pi$
$47$	−4.68996	−	8.12325i	−0.684101	−	1.18490i	0.289617	−	0.957142i	$-0.406472\pi$
$48$	−1.20711	+	2.09077i	−0.174231	+	0.301777i
$49$	2.50000	−	4.33013i	0.357143	−	0.618590i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−6.09205	+	10.5517i	−0.853058	+	1.47754i
$52$	5.13728			0.712413
$53$	−2.50467			−0.344043			−0.172022	−	0.985093i	$-0.555030\pi$
$53$	−2.50467			−0.344043			−0.172022	+	0.985093i	$0.555030\pi$
$54$	0.207107	−	0.358719i	0.0281837	−	0.0488155i
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	0.707107	+	1.22474i	0.0944911	+	0.163663i
$57$	6.79916	−	11.7765i	0.900570	−	1.55983i
$58$	−4.30885			−0.565780
$59$	3.63261			0.472925			0.236462	−	0.971641i	$-0.424012\pi$
$59$	3.63261			0.472925			0.236462	+	0.971641i	$0.424012\pi$
$60$	−1.20711	−	2.09077i	−0.155837	−	0.269917i
$61$	6.10417	−	10.5727i	0.781559	−	1.35370i	−0.149474	−	0.988766i	$-0.547758\pi$
$61$	6.10417	−	10.5727i	0.781559	−	1.35370i	0.931033	−	0.364935i	$-0.118909\pi$
$62$	−6.74732			−0.856910
$63$	2.00000	+	3.46410i	0.251976	+	0.436436i
$64$	1.00000			0.125000
$65$	−2.56864	+	4.44901i	−0.318601	+	0.551832i
$66$	−4.82843			−0.594338
$67$	−7.78787	−	2.51973i	−0.951440	−	0.307835i
$67$	−7.78787	−	2.51973i	−0.951440	−	0.307835i
$68$	5.04682			0.612017
$69$	10.4770	−	18.1467i	1.26128	−	2.18460i
$70$	−1.41421			−0.169031
$71$	3.02341	+	5.23670i	0.358813	+	0.621482i	0.987763	−	0.155964i	$-0.0498483\pi$
$71$	3.02341	+	5.23670i	0.358813	+	0.621482i	−0.628950	+	0.777446i	$0.716515\pi$
$72$	2.82843			0.333333
$73$	−6.35184	+	11.0017i	−0.743426	+	1.28765i	0.207500	+	0.978235i	$0.433467\pi$
$73$	−6.35184	+	11.0017i	−0.743426	+	1.28765i	−0.950926	+	0.309417i	$0.899866\pi$
$74$	3.73052	+	6.46144i	0.433664	+	0.751128i
$75$	2.41421			0.278769
$76$	−5.63261			−0.646104
$77$	−1.41421	+	2.44949i	−0.161165	+	0.279145i
$78$	−6.20125	−	10.7409i	−0.702153	−	1.21616i
$79$	−7.46103	−	12.9229i	−0.839432	−	1.45394i	−0.890370	−	0.455237i	$-0.849555\pi$
$79$	−7.46103	−	12.9229i	−0.839432	−	1.45394i	0.0509387	−	0.998702i	$-0.483779\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−9.48528			−1.05392
$82$	0.975751			0.107754
$83$	−5.78787	+	10.0249i	−0.635301	+	1.10037i	0.351150	+	0.936319i	$0.385791\pi$
$83$	−5.78787	+	10.0249i	−0.635301	+	1.10037i	−0.986451	+	0.164055i	$0.947543\pi$
$84$	1.70711	−	2.95680i	0.186261	−	0.322613i
$85$	−2.52341	+	4.37067i	−0.273702	+	0.474066i
$86$	1.16655	−	2.02053i	0.125792	−	0.217879i
$87$	5.20125	+	9.00882i	0.557632	+	0.965847i
$88$	1.00000	+	1.73205i	0.106600	+	0.184637i
$89$	−14.2652			−1.51211			−0.756055	−	0.654508i	$-0.772876\pi$
$89$	−14.2652			−1.51211			−0.756055	+	0.654508i	$0.772876\pi$
$90$	−1.41421	+	2.44949i	−0.149071	+	0.258199i
$91$	−7.26521			−0.761601
$92$	−8.67942			−0.904893
$93$	8.14473	+	14.1071i	0.844569	+	1.46284i
$94$	9.37992			0.967465
$95$	2.81630	−	4.87798i	0.288947	−	0.500470i
$96$	−1.20711	−	2.09077i	−0.123200	−	0.213388i
$97$	1.58076	−	2.73796i	0.160502	−	0.277998i	−0.774547	−	0.632517i	$-0.782022\pi$
$97$	1.58076	−	2.73796i	0.160502	−	0.277998i	0.935049	+	0.354519i	$0.115355\pi$
$98$	2.50000	+	4.33013i	0.252538	+	0.437409i
$99$	2.82843	+	4.89898i	0.284268	+	0.492366i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	2.09707	+	3.63223i	0.208666	+	0.361421i	0.951295	−	0.308283i	$-0.0997544\pi$
$101$	2.09707	+	3.63223i	0.208666	+	0.361421i	−0.742628	+	0.669704i	$0.766421\pi$
$102$	−6.09205	−	10.5517i	−0.603203	−	1.04478i
$103$	5.90835	+	10.2336i	0.582167	+	1.00834i	0.995222	+	0.0976371i	$0.0311284\pi$
$103$	5.90835	+	10.2336i	0.582167	+	1.00834i	−0.413055	+	0.910706i	$0.635538\pi$
$104$	−2.56864	+	4.44901i	−0.251876	+	0.436262i
$105$	1.70711	+	2.95680i	0.166597	+	0.288554i
$106$	1.25234	−	2.16911i	0.121638	−	0.210683i
$107$	−2.26203			−0.218679			−0.109340	−	0.994004i	$-0.534874\pi$
$107$	−2.26203			−0.218679			−0.109340	+	0.994004i	$0.534874\pi$
$108$	0.207107	+	0.358719i	0.0199289	+	0.0345178i
$109$	−6.40486			−0.613475			−0.306737	−	0.951794i	$-0.599237\pi$
$109$	−6.40486			−0.613475			−0.306737	+	0.951794i	$0.599237\pi$
$110$	−2.00000			−0.190693
$111$	9.00626	−	15.5993i	0.854837	−	1.48062i
$112$	−1.41421			−0.133631
$113$	−0.970729	−	1.68135i	−0.0913185	−	0.158168i	0.816748	−	0.576995i	$-0.195775\pi$
$113$	−0.970729	−	1.68135i	−0.0913185	−	0.158168i	−0.908066	+	0.418827i	$0.862441\pi$
$114$	6.79916	+	11.7765i	0.636799	+	1.10297i
$115$	4.33971	−	7.51660i	0.404680	−	0.700927i
$116$	2.15443	−	3.73158i	0.200033	−	0.346468i
$117$	−7.26521	+	12.5837i	−0.671669	+	1.16336i
$118$	−1.81630	+	3.14593i	−0.167204	+	0.289606i
$119$	−7.13728			−0.654273
$120$	2.41421			0.220387
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	6.10417	+	10.5727i	0.552646	+	0.957211i
$123$	−1.17784	−	2.04007i	−0.106202	−	0.183947i
$124$	3.37366	−	5.84335i	0.302963	−	0.524748i
$125$	1.00000			0.0894427
$126$	−4.00000			−0.356348
$127$	−4.21839	−	7.30647i	−0.374322	−	0.648344i	0.615904	−	0.787822i	$-0.288791\pi$
$127$	−4.21839	−	7.30647i	−0.374322	−	0.648344i	−0.990225	+	0.139477i	$0.955458\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.63261			−0.495923
$130$	−2.56864	−	4.44901i	−0.225285	−	0.390204i
$131$	9.03677			0.789547			0.394773	−	0.918779i	$-0.370823\pi$
$131$	9.03677			0.789547			0.394773	+	0.918779i	$0.370823\pi$
$132$	2.41421	−	4.18154i	0.210130	−	0.363956i
$133$	7.96571			0.690714
$134$	6.07609	−	5.48463i	0.524894	−	0.473800i
$135$	−0.414214			−0.0356498
$136$	−2.52341	+	4.37067i	−0.216381	+	0.374782i
$137$	−0.429114			−0.0366617			−0.0183308	−	0.999832i	$-0.505835\pi$
$137$	−0.429114			−0.0366617			−0.0183308	+	0.999832i	$0.505835\pi$
$138$	10.4770	+	18.1467i	0.891861	+	1.54475i
$139$	9.42188			0.799154			0.399577	−	0.916700i	$-0.369157\pi$
$139$	9.42188			0.799154			0.399577	+	0.916700i	$0.369157\pi$
$140$	0.707107	−	1.22474i	0.0597614	−	0.103510i
$141$	−11.3226	−	19.6113i	−0.953532	−	1.65157i
$142$	−6.04682			−0.507438
$143$	−10.2746			−0.859202
$144$	−1.41421	+	2.44949i	−0.117851	+	0.204124i
$145$	2.15443	+	3.73158i	0.178915	+	0.309891i
$146$	−6.35184	−	11.0017i	−0.525682	−	0.910507i
$147$	6.03553	−	10.4539i	0.497802	−	0.862219i
$148$	−7.46103			−0.613293
$149$	−20.3020			−1.66320			−0.831602	−	0.555372i	$-0.812576\pi$
$149$	−20.3020			−1.66320			−0.831602	+	0.555372i	$0.812576\pi$
$150$	−1.20711	+	2.09077i	−0.0985599	+	0.170711i
$151$	9.94230	−	17.2206i	0.809093	−	1.40139i	−0.104400	−	0.994535i	$-0.533292\pi$
$151$	9.94230	−	17.2206i	0.809093	−	1.40139i	0.913493	−	0.406854i	$-0.133374\pi$
$152$	2.81630	−	4.87798i	0.228432	−	0.395656i
$153$	−7.13728	+	12.3621i	−0.577015	+	0.999419i
$154$	−1.41421	−	2.44949i	−0.113961	−	0.197386i
$155$	3.37366	+	5.84335i	0.270979	+	0.469349i
$156$	12.4025			0.992994
$157$	6.17868	−	10.7018i	0.493112	−	0.854095i	−0.506857	−	0.862030i	$-0.669193\pi$
$157$	6.17868	−	10.7018i	0.493112	−	0.854095i	0.999969	+	0.00793544i	$0.00252596\pi$
$158$	14.9221			1.18714
$159$	−6.04682			−0.479544
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	12.2746			0.967371
$162$	4.74264	−	8.21449i	0.372617	−	0.645392i
$163$	−6.66814	−	11.5496i	−0.522289	−	0.904631i	−0.999664	−	0.0259312i	$-0.991745\pi$
$163$	−6.66814	−	11.5496i	−0.522289	−	0.904631i	0.477375	−	0.878700i	$-0.341588\pi$
$164$	−0.487876	+	0.845025i	−0.0380967	+	0.0659854i
$165$	2.41421	+	4.18154i	0.187946	+	0.325532i
$166$	−5.78787	−	10.0249i	−0.449226	−	0.778082i
$167$	6.49414	+	11.2482i	0.502532	+	0.870410i	0.999996	+	0.00292562i	$0.000931256\pi$
$167$	6.49414	+	11.2482i	0.502532	+	0.870410i	−0.497464	+	0.867485i	$0.665735\pi$
$168$	1.70711	+	2.95680i	0.131706	+	0.228122i
$169$	−6.69582	−	11.5975i	−0.515063	−	0.892116i
$170$	−2.52341	−	4.37067i	−0.193537	−	0.335215i
$171$	7.96571	−	13.7970i	0.609153	−	1.05508i
$172$	1.16655	+	2.02053i	0.0889487	+	0.154064i
$173$	4.47073	−	7.74353i	0.339903	−	0.588730i	−0.644511	−	0.764595i	$-0.722939\pi$
$173$	4.47073	−	7.74353i	0.339903	−	0.588730i	0.984414	+	0.175865i	$0.0562723\pi$
$174$	−10.4025			−0.788611
$175$	0.707107	+	1.22474i	0.0534522	+	0.0925820i
$176$	−2.00000			−0.150756
$177$	8.76989			0.659185
$178$	7.13261	−	12.3540i	0.534611	−	0.925974i
$179$	1.15050			0.0859925			0.0429962	−	0.999075i	$-0.486310\pi$
$179$	1.15050			0.0859925			0.0429962	+	0.999075i	$0.486310\pi$
$180$	−1.41421	−	2.44949i	−0.105409	−	0.182574i
$181$	−7.03086	−	12.1778i	−0.522600	−	0.905169i	−0.999654	−	0.0262955i	$-0.991629\pi$
$181$	−7.03086	−	12.1778i	−0.522600	−	0.905169i	0.477055	−	0.878874i	$-0.341704\pi$
$182$	3.63261	−	6.29186i	0.269267	−	0.466383i
$183$	14.7368	−	25.5249i	1.08937	−	1.88685i
$184$	4.33971	−	7.51660i	0.319928	−	0.554131i
$185$	3.73052	−	6.46144i	0.274273	−	0.475055i
$186$	−16.2895			−1.19440
$187$	−10.0936			−0.738120
$188$	−4.68996	+	8.12325i	−0.342051	+	0.592449i
$189$	−0.292893	−	0.507306i	−0.0213048	−	0.0369011i
$190$	2.81630	+	4.87798i	0.204316	+	0.353886i
$191$	−7.98912	+	13.8376i	−0.578072	+	1.00125i	0.417628	+	0.908618i	$0.362861\pi$
$191$	−7.98912	+	13.8376i	−0.578072	+	1.00125i	−0.995700	+	0.0926324i	$0.970472\pi$
$192$	2.41421			0.174231
$193$	−12.5030			−0.899985			−0.449993	−	0.893032i	$-0.648573\pi$
$193$	−12.5030			−0.899985			−0.449993	+	0.893032i	$0.648573\pi$
$194$	1.58076	+	2.73796i	0.113492	+	0.196574i
$195$	−6.20125	+	10.7409i	−0.444080	+	0.769170i
$196$	−5.00000			−0.357143
$197$	8.48528	+	14.6969i	0.604551	+	1.04711i	0.992122	+	0.125274i	$0.0399809\pi$
$197$	8.48528	+	14.6969i	0.604551	+	1.04711i	−0.387571	+	0.921840i	$0.626686\pi$
$198$	−5.65685			−0.402015
$199$	5.46187	−	9.46024i	0.387182	−	0.670619i	−0.604887	−	0.796311i	$-0.706782\pi$
$199$	5.46187	−	9.46024i	0.387182	−	0.670619i	0.992069	+	0.125692i	$0.0401152\pi$
$200$	1.00000			0.0707107
$201$	−18.8016	−	6.08318i	−1.32616	−	0.429074i
$202$	−4.19414			−0.295099
$203$	−3.04682	+	5.27725i	−0.213845	+	0.370390i
$204$	12.1841			0.853058
$205$	−0.487876	−	0.845025i	−0.0340747	−	0.0590191i
$206$	−11.8167			−0.823309
$207$	12.2746	−	21.2602i	0.853141	−	1.47768i
$208$	−2.56864	−	4.44901i	−0.178103	−	0.308484i
$209$	11.2652			0.779231
$210$	−3.41421			−0.235603
$211$	−6.48201	+	11.2272i	−0.446240	+	0.772911i	−0.998138	−	0.0610012i	$-0.980571\pi$
$211$	−6.48201	+	11.2272i	−0.446240	+	0.772911i	0.551897	+	0.833912i	$0.313904\pi$
$212$	1.25234	+	2.16911i	0.0860109	+	0.148975i
$213$	7.29916	+	12.6425i	0.500130	+	0.866250i
$214$	1.13102	−	1.95898i	0.0773147	−	0.133913i
$215$	−2.33310			−0.159116
$216$	−0.414214			−0.0281837
$217$	−4.77107	+	8.26374i	−0.323881	+	0.560979i
$218$	3.20243	−	5.54678i	0.216896	−	0.375675i
$219$	−15.3347	+	26.5605i	−1.03622	+	1.79479i
$220$	1.00000	−	1.73205i	0.0674200	−	0.116775i
$221$	−12.9635	−	22.4534i	−0.872017	−	1.51038i
$222$	9.00626	+	15.5993i	0.604461	+	1.04696i
$223$	19.6677			1.31705			0.658523	−	0.752560i	$-0.271181\pi$
$223$	19.6677			1.31705			0.658523	+	0.752560i	$0.271181\pi$
$224$	0.707107	−	1.22474i	0.0472456	−	0.0818317i
$225$	2.82843			0.188562
$226$	1.94146			0.129144
$227$	9.79289	+	16.9618i	0.649977	+	1.12579i	0.983128	+	0.182920i	$0.0585549\pi$
$227$	9.79289	+	16.9618i	0.649977	+	1.12579i	−0.333151	+	0.942874i	$0.608112\pi$
$228$	−13.5983			−0.900570
$229$	12.0231	−	20.8246i	0.794506	−	1.37613i	−0.128646	−	0.991691i	$-0.541063\pi$
$229$	12.0231	−	20.8246i	0.794506	−	1.37613i	0.923152	−	0.384435i	$-0.125604\pi$
$230$	4.33971	+	7.51660i	0.286152	+	0.495630i
$231$	−3.41421	+	5.91359i	−0.224639	+	0.389086i
$232$	2.15443	+	3.73158i	0.141445	+	0.244990i
$233$	5.89080	+	10.2032i	0.385919	+	0.668432i	0.991896	−	0.127050i	$-0.0405509\pi$
$233$	5.89080	+	10.2032i	0.385919	+	0.668432i	−0.605977	+	0.795482i	$0.707218\pi$
$234$	−7.26521	−	12.5837i	−0.474942	−	0.822623i
$235$	−4.68996	−	8.12325i	−0.305939	−	0.529902i
$236$	−1.81630	−	3.14593i	−0.118231	−	0.204783i
$237$	−18.0125	−	31.1986i	−1.17004	−	2.02657i
$238$	3.56864	−	6.18107i	0.231321	−	0.400659i
$239$	−8.18410	−	14.1753i	−0.529385	−	0.916922i	−0.999413	−	0.0342704i	$-0.989089\pi$
$239$	−8.18410	−	14.1753i	−0.529385	−	0.916922i	0.470027	−	0.882652i	$-0.344244\pi$
$240$	−1.20711	+	2.09077i	−0.0779184	+	0.134959i
$241$	14.3831			0.926497			0.463248	−	0.886228i	$-0.346684\pi$
$241$	14.3831			0.926497			0.463248	+	0.886228i	$0.346684\pi$
$242$	3.50000	+	6.06218i	0.224989	+	0.389692i
$243$	−21.6569			−1.38929
$244$	−12.2083			−0.781559
$245$	2.50000	−	4.33013i	0.159719	−	0.276642i
$246$	2.35567			0.150192
$247$	14.4681	+	25.0595i	0.920585	+	1.59450i
$248$	3.37366	+	5.84335i	0.214227	+	0.371053i
$249$	−13.9732	+	24.2022i	−0.885513	+	1.53375i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−4.89791	+	8.48342i	−0.309153	+	0.535469i	−0.978177	−	0.207772i	$-0.933379\pi$
$251$	−4.89791	+	8.48342i	−0.309153	+	0.535469i	0.669024	+	0.743241i	$0.266712\pi$
$252$	2.00000	−	3.46410i	0.125988	−	0.218218i
$253$	17.3588			1.09134
$254$	8.43678			0.529371
$255$	−6.09205	+	10.5517i	−0.381499	+	0.660776i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.05617	−	10.4896i	−0.377773	−	0.654323i	0.612965	−	0.790110i	$-0.289977\pi$
$257$	−6.05617	−	10.4896i	−0.377773	−	0.654323i	−0.990738	+	0.135788i	$0.956643\pi$
$258$	2.81630	−	4.87798i	0.175335	−	0.303690i
$259$	10.5515			0.655638
$260$	5.13728			0.318601
$261$	6.09364	+	10.5545i	0.377187	+	0.653307i
$262$	−4.51839	+	7.82608i	−0.279147	+	0.483497i
$263$	−23.7162			−1.46240			−0.731202	−	0.682161i	$-0.761040\pi$
$263$	−23.7162			−1.46240			−0.731202	+	0.682161i	$0.761040\pi$
$264$	2.41421	+	4.18154i	0.148585	+	0.257356i
$265$	−2.50467			−0.153861
$266$	−3.98285	+	6.89850i	−0.244204	+	0.422974i
$267$	−34.4393			−2.10765
$268$	1.71178	+	8.00436i	0.104564	+	0.488944i
$269$	−3.87207			−0.236084			−0.118042	−	0.993009i	$-0.537662\pi$
$269$	−3.87207			−0.236084			−0.118042	+	0.993009i	$0.537662\pi$
$270$	0.207107	−	0.358719i	0.0126041	−	0.0218310i
$271$	3.77226			0.229148			0.114574	−	0.993415i	$-0.463450\pi$
$271$	3.77226			0.229148			0.114574	+	0.993415i	$0.463450\pi$
$272$	−2.52341	−	4.37067i	−0.153004	−	0.265011i
$273$	−17.5398			−1.06156
$274$	0.214557	−	0.371623i	0.0129619	−	0.0224506i
$275$	1.00000	+	1.73205i	0.0603023	+	0.104447i
$276$	−20.9540			−1.26128
$277$	−20.7747			−1.24823			−0.624117	−	0.781331i	$-0.714541\pi$
$277$	−20.7747			−1.24823			−0.624117	+	0.781331i	$0.714541\pi$
$278$	−4.71094	+	8.15959i	−0.282544	+	0.489380i
$279$	9.54214	+	16.5275i	0.571273	+	0.989474i
$280$	0.707107	+	1.22474i	0.0422577	+	0.0731925i
$281$	8.15685	−	14.1281i	0.486597	−	0.842811i	−0.513284	−	0.858219i	$-0.671571\pi$
$281$	8.15685	−	14.1281i	0.486597	−	0.842811i	0.999881	+	0.0154078i	$0.00490464\pi$
$282$	22.6451			1.34850
$283$	3.84782			0.228729			0.114365	−	0.993439i	$-0.463517\pi$
$283$	3.84782			0.228729			0.114365	+	0.993439i	$0.463517\pi$
$284$	3.02341	−	5.23670i	0.179406	−	0.310741i
$285$	6.79916	−	11.7765i	0.402747	−	0.697579i
$286$	5.13728	−	8.89803i	0.303774	−	0.526152i
$287$	0.689960	−	1.19505i	0.0407271	−	0.0705413i
$288$	−1.41421	−	2.44949i	−0.0833333	−	0.144338i
$289$	−4.23519	−	7.33557i	−0.249129	−	0.431504i
$290$	−4.30885			−0.253025
$291$	3.81630	−	6.61003i	0.223716	−	0.387487i
$292$	12.7037			0.743426
$293$	24.9027			1.45483			0.727415	−	0.686198i	$-0.240722\pi$
$293$	24.9027			1.45483			0.727415	+	0.686198i	$0.240722\pi$
$294$	6.03553	+	10.4539i	0.351999	+	0.609681i
$295$	3.63261			0.211498
$296$	3.73052	−	6.46144i	0.216832	−	0.375564i
$297$	−0.414214	−	0.717439i	−0.0240351	−	0.0416300i
$298$	10.1510	−	17.5820i	0.588031	−	1.01850i
$299$	22.2943	+	38.6149i	1.28931	+	2.23316i
$300$	−1.20711	−	2.09077i	−0.0696923	−	0.120711i
$301$	−1.64975	−	2.85745i	−0.0950901	−	0.164701i
$302$	9.94230	+	17.2206i	0.572115	+	0.990932i
$303$	5.06278	+	8.76899i	0.290849	+	0.503765i
$304$	2.81630	+	4.87798i	0.161526	+	0.279771i
$305$	6.10417	−	10.5727i	0.349524	−	0.605393i
$306$	−7.13728	−	12.3621i	−0.408011	−	0.706696i
$307$	−1.32182	+	2.28945i	−0.0754401	+	0.130666i	−0.901278	−	0.433242i	$-0.857369\pi$
$307$	−1.32182	+	2.28945i	−0.0754401	+	0.130666i	0.825837	+	0.563908i	$0.190703\pi$
$308$	2.82843			0.161165
$309$	14.2640	+	24.7060i	0.811452	+	1.40548i
$310$	−6.74732			−0.383222
$311$	8.27624			0.469302			0.234651	−	0.972080i	$-0.424605\pi$
$311$	8.27624			0.469302			0.234651	+	0.972080i	$0.424605\pi$
$312$	−6.20125	+	10.7409i	−0.351076	+	0.608082i
$313$	−22.7311			−1.28484			−0.642419	−	0.766354i	$-0.722069\pi$
$313$	−22.7311			−1.28484			−0.642419	+	0.766354i	$0.722069\pi$
$314$	6.17868	+	10.7018i	0.348683	+	0.603936i
$315$	2.00000	+	3.46410i	0.112687	+	0.195180i
$316$	−7.46103	+	12.9229i	−0.419716	+	0.726969i
$317$	−4.62516	+	8.01100i	−0.259775	+	0.449943i	−0.966181	−	0.257863i	$-0.916982\pi$
$317$	−4.62516	+	8.01100i	−0.259775	+	0.449943i	0.706407	+	0.707806i	$0.250315\pi$
$318$	3.02341	−	5.23670i	0.169544	−	0.293659i
$319$	−4.30885	+	7.46315i	−0.241249	+	0.417856i
$320$	1.00000			0.0559017
$321$	−5.46103			−0.304805
$322$	−6.13728	+	10.6301i	−0.342017	+	0.592391i
$323$	14.2134	+	24.6183i	0.790853	+	1.36980i
$324$	4.74264	+	8.21449i	0.263480	+	0.456361i
$325$	−2.56864	+	4.44901i	−0.142483	+	0.246787i
$326$	13.3363			0.738628
$327$	−15.4627			−0.855090
$328$	−0.487876	−	0.845025i	−0.0269384	−	0.0466587i
$329$	6.63261	−	11.4880i	0.365667	−	0.633354i
$330$	−4.82843			−0.265796
$331$	6.50745	+	11.2712i	0.357682	+	0.619523i	0.987573	−	0.157160i	$-0.0502339\pi$
$331$	6.50745	+	11.2712i	0.357682	+	0.619523i	−0.629891	+	0.776683i	$0.716901\pi$
$332$	11.5757			0.635301
$333$	10.5515	−	18.2757i	0.578218	−	1.00150i
$334$	−12.9883			−0.710687
$335$	−7.78787	−	2.51973i	−0.425497	−	0.137668i
$336$	−3.41421			−0.186261
$337$	−7.82724	+	13.5572i	−0.426377	+	0.738507i	−0.996548	−	0.0830195i	$-0.973544\pi$
$337$	−7.82724	+	13.5572i	−0.426377	+	0.738507i	0.570171	+	0.821526i	$0.306877\pi$
$338$	13.3916			0.728409
$339$	−2.34355	−	4.05914i	−0.127284	−	0.220462i
$340$	5.04682			0.273702
$341$	−6.74732	+	11.6867i	−0.365388	+	0.632870i
$342$	7.96571	+	13.7970i	0.430736	+	0.746057i
$343$	16.9706			0.916324
$344$	−2.33310			−0.125792
$345$	10.4770	−	18.1467i	0.564062	−	0.976985i
$346$	4.47073	+	7.74353i	0.240348	+	0.416295i
$347$	2.15720	+	3.73638i	0.115805	+	0.200580i	0.918101	−	0.396346i	$-0.129722\pi$
$347$	2.15720	+	3.73638i	0.115805	+	0.200580i	−0.802296	+	0.596926i	$0.796389\pi$
$348$	5.20125	−	9.00882i	0.278816	−	0.482923i
$349$	−33.9721			−1.81848			−0.909241	−	0.416269i	$-0.863337\pi$
$349$	−33.9721			−1.81848			−0.909241	+	0.416269i	$0.863337\pi$
$350$	−1.41421			−0.0755929
$351$	1.06397	−	1.84284i	0.0567903	−	0.0983636i
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	−9.54264	+	16.5283i	−0.507903	+	0.879714i	0.492055	+	0.870564i	$0.336246\pi$
$353$	−9.54264	+	16.5283i	−0.507903	+	0.879714i	−0.999958	+	0.00915009i	$0.997087\pi$
$354$	−4.38494	+	7.59494i	−0.233057	+	0.403667i
$355$	3.02341	+	5.23670i	0.160466	+	0.277935i
$356$	7.13261	+	12.3540i	0.378027	+	0.654763i
$357$	−17.2309			−0.911957
$358$	−0.575251	+	0.996363i	−0.0304029	+	0.0526594i
$359$	15.2139			0.802959			0.401479	−	0.915868i	$-0.368496\pi$
$359$	15.2139			0.802959			0.401479	+	0.915868i	$0.368496\pi$
$360$	2.82843			0.149071
$361$	−6.36312	−	11.0212i	−0.334901	−	0.580066i
$362$	14.0617			0.739068
$363$	8.44975	−	14.6354i	0.443497	−	0.768159i
$364$	3.63261	+	6.29186i	0.190400	+	0.329783i
$365$	−6.35184	+	11.0017i	−0.332470	+	0.575855i
$366$	14.7368	+	25.5249i	0.770304	+	1.33421i
$367$	12.3640	+	21.4150i	0.645394	+	1.11785i	0.984210	+	0.177002i	$0.0566399\pi$
$367$	12.3640	+	21.4150i	0.645394	+	1.11785i	−0.338817	+	0.940852i	$0.610027\pi$
$368$	4.33971	+	7.51660i	0.226223	+	0.391830i
$369$	−1.37992	−	2.39009i	−0.0718358	−	0.124423i
$370$	3.73052	+	6.46144i	0.193940	+	0.335914i
$371$	−1.77107	−	3.06759i	−0.0919495	−	0.159261i
$372$	8.14473	−	14.1071i	0.422285	−	0.731418i
$373$	6.31630	+	10.9402i	0.327046	+	0.566460i	0.981924	−	0.189274i	$-0.0606135\pi$
$373$	6.31630	+	10.9402i	0.327046	+	0.566460i	−0.654878	+	0.755734i	$0.727280\pi$
$374$	5.04682	−	8.74135i	0.260965	−	0.452004i
$375$	2.41421			0.124669
$376$	−4.68996	−	8.12325i	−0.241866	−	0.418925i
$377$	−22.1358			−1.14005
$378$	0.585786			0.0301296
$379$	−14.6226	+	25.3270i	−0.751111	+	1.30096i	0.196174	+	0.980569i	$0.437148\pi$
$379$	−14.6226	+	25.3270i	−0.751111	+	1.30096i	−0.947285	+	0.320393i	$0.896185\pi$
$380$	−5.63261			−0.288947
$381$	−10.1841	−	17.6394i	−0.521747	−	0.903693i
$382$	−7.98912	−	13.8376i	−0.408759	−	0.707991i
$383$	−11.9883	+	20.7643i	−0.612572	+	1.06101i	0.378233	+	0.925710i	$0.376532\pi$
$383$	−11.9883	+	20.7643i	−0.612572	+	1.06101i	−0.990805	+	0.135296i	$0.956801\pi$
$384$	−1.20711	+	2.09077i	−0.0615999	+	0.106694i
$385$	−1.41421	+	2.44949i	−0.0720750	+	0.124838i
$386$	6.25150	−	10.8279i	0.318193	−	0.551126i
$387$	−6.59901			−0.335446
$388$	−3.16153			−0.160502
$389$	−1.50586	+	2.60823i	−0.0763502	+	0.132242i	−0.901673	−	0.432419i	$-0.857660\pi$
$389$	−1.50586	+	2.60823i	−0.0763502	+	0.132242i	0.825322	+	0.564662i	$0.190993\pi$
$390$	−6.20125	−	10.7409i	−0.314012	−	0.543885i
$391$	21.9017	+	37.9349i	1.10762	+	1.91845i
$392$	2.50000	−	4.33013i	0.126269	−	0.218704i
$393$	21.8167			1.10051
$394$	−16.9706			−0.854965
$395$	−7.46103	−	12.9229i	−0.375405	−	0.650221i
$396$	2.82843	−	4.89898i	0.142134	−	0.246183i
$397$	19.0351			0.955344			0.477672	−	0.878538i	$-0.341481\pi$
$397$	19.0351			0.955344			0.477672	+	0.878538i	$0.341481\pi$
$398$	5.46187	+	9.46024i	0.273779	+	0.474199i
$399$	19.2309			0.962750
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	31.9314			1.59458			0.797289	−	0.603597i	$-0.206267\pi$
$401$	31.9314			1.59458			0.797289	+	0.603597i	$0.206267\pi$
$402$	14.6690	−	13.2411i	0.731622	−	0.660404i
$403$	−34.6628			−1.72668
$404$	2.09707	−	3.63223i	0.104333	−	0.180710i
$405$	−9.48528			−0.471327
$406$	−3.04682	−	5.27725i	−0.151211	−	0.261905i
$407$	14.9221			0.739659
$408$	−6.09205	+	10.5517i	−0.301601	+	0.522389i
$409$	−0.465306	−	0.805933i	−0.0230079	−	0.0398508i	0.854292	−	0.519793i	$-0.173991\pi$
$409$	−0.465306	−	0.805933i	−0.0230079	−	0.0398508i	−0.877300	+	0.479942i	$0.840658\pi$
$410$	0.975751			0.0481889
$411$	−1.03597			−0.0511007
$412$	5.90835	−	10.2336i	0.291084	−	0.504172i
$413$	2.56864	+	4.44901i	0.126395	+	0.218922i
$414$	12.2746	+	21.2602i	0.603262	+	1.04488i
$415$	−5.78787	+	10.0249i	−0.284115	+	0.492102i
$416$	5.13728			0.251876
$417$	22.7464			1.11390
$418$	−5.63261	+	9.75596i	−0.275500	+	0.477180i
$419$	−8.04404	+	13.9327i	−0.392977	+	0.680657i	−0.992841	−	0.119446i	$-0.961888\pi$
$419$	−8.04404	+	13.9327i	−0.392977	+	0.680657i	0.599863	+	0.800102i	$0.295222\pi$
$420$	1.70711	−	2.95680i	0.0832983	−	0.144277i
$421$	1.75736	−	3.04384i	0.0856485	−	0.148347i	−0.820019	−	0.572336i	$-0.806037\pi$
$421$	1.75736	−	3.04384i	0.0856485	−	0.148347i	0.905667	+	0.423989i	$0.139370\pi$
$422$	−6.48201	−	11.2272i	−0.315540	−	0.546530i
$423$	−13.2652	−	22.9760i	−0.644977	−	1.11713i
$424$	−2.50467			−0.121638
$425$	−2.52341	+	4.37067i	−0.122403	+	0.212009i
$426$	−14.5983			−0.707291
$427$	17.2652			0.835522
$428$	1.13102	+	1.95898i	0.0546698	+	0.0946908i
$429$	−24.8050			−1.19760
$430$	1.16655	−	2.02053i	0.0562561	−	0.0974384i
$431$	7.02341	+	12.1649i	0.338306	+	0.585963i	0.984114	−	0.177537i	$-0.0568129\pi$
$431$	7.02341	+	12.1649i	0.338306	+	0.585963i	−0.645808	+	0.763499i	$0.723480\pi$
$432$	0.207107	−	0.358719i	0.00996443	−	0.0172589i
$433$	−3.15601	−	5.46638i	−0.151668	−	0.262697i	0.780173	−	0.625564i	$-0.215131\pi$
$433$	−3.15601	−	5.46638i	−0.151668	−	0.262697i	−0.931841	+	0.362867i	$0.881798\pi$
$434$	−4.77107	−	8.26374i	−0.229019	−	0.396672i
$435$	5.20125	+	9.00882i	0.249381	+	0.431940i
$436$	3.20243	+	5.54678i	0.153369	+	0.265642i
$437$	−24.4439	−	42.3381i	−1.16931	−	2.02530i
$438$	−15.3347	−	26.5605i	−0.732720	−	1.26911i
$439$	−6.85184	+	11.8677i	−0.327020	+	0.566416i	−0.981919	−	0.189301i	$-0.939378\pi$
$439$	−6.85184	+	11.8677i	−0.327020	+	0.566416i	0.654899	+	0.755717i	$0.272711\pi$
$440$	1.00000	+	1.73205i	0.0476731	+	0.0825723i
$441$	7.07107	−	12.2474i	0.336718	−	0.583212i
$442$	25.9269			1.23322
$443$	0.253926	+	0.439812i	0.0120644	+	0.0208961i	0.871995	−	0.489516i	$-0.162826\pi$
$443$	0.253926	+	0.439812i	0.0120644	+	0.0208961i	−0.859930	+	0.510412i	$0.829493\pi$
$444$	−18.0125			−0.854837
$445$	−14.2652			−0.676236
$446$	−9.83385	+	17.0327i	−0.465646	+	0.806523i
$447$	−49.0133			−2.31825
$448$	0.707107	+	1.22474i	0.0334077	+	0.0578638i
$449$	13.0619	+	22.6239i	0.616431	+	1.06769i	0.990132	+	0.140140i	$0.0447554\pi$
$449$	13.0619	+	22.6239i	0.616431	+	1.06769i	−0.373701	+	0.927549i	$0.621911\pi$
$450$	−1.41421	+	2.44949i	−0.0666667	+	0.115470i
$451$	0.975751	−	1.69005i	0.0459463	−	0.0795814i
$452$	−0.970729	+	1.68135i	−0.0456593	+	0.0790841i
$453$	24.0028	−	41.5741i	1.12775	−	1.95332i
$454$	−19.5858			−0.919207
$455$	−7.26521			−0.340598
$456$	6.79916	−	11.7765i	0.318400	−	0.551484i
$457$	−2.27072	−	3.93301i	−0.106220	−	0.183978i	0.808016	−	0.589161i	$-0.200541\pi$
$457$	−2.27072	−	3.93301i	−0.106220	−	0.183978i	−0.914236	+	0.405182i	$0.867208\pi$
$458$	12.0231	+	20.8246i	0.561801	+	0.973067i
$459$	1.04523	−	1.81039i	0.0487872	−	0.0845019i
$460$	−8.67942			−0.404680
$461$	−20.8118			−0.969304			−0.484652	−	0.874707i	$-0.661054\pi$
$461$	−20.8118			−0.969304			−0.484652	+	0.874707i	$0.661054\pi$
$462$	−3.41421	−	5.91359i	−0.158844	−	0.275125i
$463$	20.4770	−	35.4672i	0.951647	−	1.64830i	0.209784	−	0.977748i	$-0.432724\pi$
$463$	20.4770	−	35.4672i	0.951647	−	1.64830i	0.741862	−	0.670552i	$-0.233943\pi$
$464$	−4.30885			−0.200033
$465$	8.14473	+	14.1071i	0.377703	+	0.654200i
$466$	−11.7816			−0.545772
$467$	−15.9869	+	27.6901i	−0.739784	+	1.28134i	0.212808	+	0.977094i	$0.431739\pi$
$467$	−15.9869	+	27.6901i	−0.739784	+	1.28134i	−0.952592	+	0.304250i	$0.901594\pi$
$468$	14.5304			0.671669
$469$	−2.42082	−	11.3199i	−0.111783	−	0.522703i
$470$	9.37992			0.432663
$471$	14.9166	−	25.8364i	0.687323	−	1.19048i
$472$	3.63261			0.167204
$473$	−2.33310	−	4.04105i	−0.107276	−	0.185808i
$474$	36.0251			1.65469
$475$	2.81630	−	4.87798i	0.129221	−	0.223817i
$476$	3.56864	+	6.18107i	0.163568	+	0.283309i
$477$	−7.08429			−0.324367
$478$	16.3682			0.748664
$479$	13.5250	−	23.4260i	0.617973	−	1.07036i	−0.371882	−	0.928280i	$-0.621287\pi$
$479$	13.5250	−	23.4260i	0.617973	−	1.07036i	0.989855	−	0.142081i	$-0.0453792\pi$
$480$	−1.20711	−	2.09077i	−0.0550966	−	0.0954302i
$481$	19.1647	+	33.1942i	0.873835	+	1.51353i
$482$	−7.19155	+	12.4561i	−0.327566	+	0.567361i
$483$	29.6334			1.34837
$484$	−7.00000			−0.318182
$485$	1.58076	−	2.73796i	0.0717788	−	0.124325i
$486$	10.8284	−	18.7554i	0.491187	−	0.850762i
$487$	−0.878680	+	1.52192i	−0.0398168	+	0.0689647i	−0.885247	−	0.465121i	$-0.846011\pi$
$487$	−0.878680	+	1.52192i	−0.0398168	+	0.0689647i	0.845430	+	0.534086i	$0.179344\pi$
$488$	6.10417	−	10.5727i	0.276323	−	0.478605i
$489$	−16.0983	−	27.8831i	−0.727991	−	1.26092i
$490$	2.50000	+	4.33013i	0.112938	+	0.195615i
$491$	−19.5429			−0.881961			−0.440980	−	0.897517i	$-0.645369\pi$
$491$	−19.5429			−0.881961			−0.440980	+	0.897517i	$0.645369\pi$
$492$	−1.17784	+	2.04007i	−0.0531009	+	0.0919735i
$493$	−21.7460			−0.979391
$494$	−28.9363			−1.30190
$495$	2.82843	+	4.89898i	0.127128	+	0.220193i
$496$	−6.74732			−0.302963
$497$	−4.27575	+	7.40581i	−0.191793	+	0.332196i
$498$	−13.9732	−	24.2022i	−0.626152	−	1.08453i
$499$	13.1283	−	22.7389i	0.587705	−	1.01793i	−0.406827	−	0.913505i	$-0.633365\pi$
$499$	13.1283	−	22.7389i	0.587705	−	1.01793i	0.994532	−	0.104430i	$-0.0333017\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	15.6782	+	27.1555i	0.700452	+	1.21322i
$502$	−4.89791	−	8.48342i	−0.218604	−	0.378634i
$503$	−10.7919	−	18.6921i	−0.481186	−	0.833439i	0.518580	−	0.855029i	$-0.326461\pi$
$503$	−10.7919	−	18.6921i	−0.481186	−	0.833439i	−0.999767	+	0.0215894i	$0.993127\pi$
$504$	2.00000	+	3.46410i	0.0890871	+	0.154303i
$505$	2.09707	+	3.63223i	0.0933185	+	0.161632i
$506$	−8.67942	+	15.0332i	−0.385847	+	0.668307i
$507$	−16.1651	−	27.9989i	−0.717919	−	1.24347i
$508$	−4.21839	+	7.30647i	−0.187161	+	0.324172i
$509$	2.60448			0.115442			0.0577209	−	0.998333i	$-0.481617\pi$
$509$	2.60448			0.115442			0.0577209	+	0.998333i	$0.481617\pi$
$510$	−6.09205	−	10.5517i	−0.269760	−	0.467239i
$511$	−17.9657			−0.794756
$512$	1.00000			0.0441942
$513$	−1.16655	+	2.02053i	−0.0515045	+	0.0892084i
$514$	12.1123			0.534252
$515$	5.90835	+	10.2336i	0.260353	+	0.450945i
$516$	2.81630	+	4.87798i	0.123981	+	0.214741i
$517$	9.37992	−	16.2465i	0.412528	−	0.714520i
$518$	−5.27575	+	9.13786i	−0.231803	+	0.401495i
$519$	10.7933	−	18.6945i	0.473773	−	0.820599i
$520$	−2.56864	+	4.44901i	−0.112642	+	0.195102i
$521$	−13.0787			−0.572990			−0.286495	−	0.958082i	$-0.592490\pi$
$521$	−13.0787			−0.572990			−0.286495	+	0.958082i	$0.592490\pi$
$522$	−12.1873			−0.533423
$523$	−0.979366	+	1.69631i	−0.0428247	+	0.0741745i	−0.886643	−	0.462454i	$-0.846969\pi$
$523$	−0.979366	+	1.69631i	−0.0428247	+	0.0741745i	0.843819	+	0.536629i	$0.180302\pi$
$524$	−4.51839	−	7.82608i	−0.197387	−	0.341884i
$525$	1.70711	+	2.95680i	0.0745042	+	0.129045i
$526$	11.8581	−	20.5388i	0.517038	−	0.895536i
$527$	−34.0525			−1.48335
$528$	−4.82843			−0.210130
$529$	−26.1662	−	45.3212i	−1.13766	−	1.97049i
$530$	1.25234	−	2.16911i	0.0543981	−	0.0942202i
$531$	10.2746			0.445878
$532$	−3.98285	−	6.89850i	−0.172679	−	0.299088i
$533$	5.01271			0.217124
$534$	17.2196	−	29.8253i	0.745166	−	1.29067i
$535$	−2.26203			−0.0977962
$536$	−7.78787	−	2.51973i	−0.336385	−	0.108836i
$537$	2.77756			0.119860
$538$	1.93603	−	3.35331i	0.0834684	−	0.144571i
$539$	10.0000			0.430730
$540$	0.207107	+	0.358719i	0.00891246	+	0.0154368i
$541$	35.9269			1.54462			0.772309	−	0.635246i	$-0.219101\pi$
$541$	35.9269			1.54462			0.772309	+	0.635246i	$0.219101\pi$
$542$	−1.88613	+	3.26687i	−0.0810162	+	0.140324i
$543$	−16.9740	−	29.3998i	−0.728424	−	1.26167i
$544$	5.04682			0.216381
$545$	−6.40486			−0.274354
$546$	8.76989	−	15.1899i	0.375316	−	0.650067i
$547$	8.54523	+	14.8008i	0.365368	+	0.632835i	0.988835	−	0.149014i	$-0.0476099\pi$
$547$	8.54523	+	14.8008i	0.365368	+	0.632835i	−0.623467	+	0.781849i	$0.714277\pi$
$548$	0.214557	+	0.371623i	0.00916541	+	0.0158750i
$549$	17.2652	−	29.9042i	0.736861	−	1.27628i
$550$	−2.00000			−0.0852803
$551$	24.2701			1.03394
$552$	10.4770	−	18.1467i	0.445930	−	0.772374i
$553$	10.5515	−	18.2757i	0.448695	−	0.777163i
$554$	10.3874	−	17.9915i	0.441317	−	0.764384i
$555$	9.00626	−	15.5993i	0.382295	−	0.662154i
$556$	−4.71094	−	8.15959i	−0.199788	−	0.346044i
$557$	4.45358	+	7.71383i	0.188704	+	0.326846i	0.944819	−	0.327594i	$-0.106238\pi$
$557$	4.45358	+	7.71383i	0.188704	+	0.326846i	−0.756114	+	0.654440i	$0.772905\pi$
$558$	−19.0843			−0.807902
$559$	5.99290	−	10.3800i	0.253473	−	0.439027i
$560$	−1.41421			−0.0597614
$561$	−24.3682			−1.02883
$562$	8.15685	+	14.1281i	0.344076	+	0.595957i
$563$	20.7138			0.872984			0.436492	−	0.899708i	$-0.356221\pi$
$563$	20.7138			0.872984			0.436492	+	0.899708i	$0.356221\pi$
$564$	−11.3226	+	19.6113i	−0.476766	+	0.825783i
$565$	−0.970729	−	1.68135i	−0.0408389	−	0.0707350i
$566$	−1.92391	+	3.33231i	−0.0808680	+	0.140067i
$567$	−6.70711	−	11.6170i	−0.281672	−	0.487870i
$568$	3.02341	+	5.23670i	0.126859	+	0.219727i
$569$	−13.1888	−	22.8436i	−0.552902	−	0.957655i	−0.998063	−	0.0622042i	$-0.980187\pi$
$569$	−13.1888	−	22.8436i	−0.552902	−	0.957655i	0.445161	−	0.895450i	$-0.353146\pi$
$570$	6.79916	+	11.7765i	0.284785	+	0.493263i
$571$	−5.31163	−	9.20001i	−0.222285	−	0.385008i	0.733217	−	0.679995i	$-0.238018\pi$
$571$	−5.31163	−	9.20001i	−0.222285	−	0.385008i	−0.955501	+	0.294987i	$0.904685\pi$
$572$	5.13728	+	8.89803i	0.214800	+	0.372045i
$573$	−19.2874	+	33.4068i	−0.805744	+	1.39559i
$574$	0.689960	+	1.19505i	0.0287984	+	0.0498803i
$575$	4.33971	−	7.51660i	0.180979	−	0.313464i
$576$	2.82843			0.117851
$577$	−9.59280	−	16.6152i	−0.399353	−	0.691700i	0.594293	−	0.804249i	$-0.297432\pi$
$577$	−9.59280	−	16.6152i	−0.399353	−	0.691700i	−0.993646	+	0.112548i	$0.964099\pi$
$578$	8.47038			0.352321
$579$	−30.1849			−1.25444
$580$	2.15443	−	3.73158i	0.0894577	−	0.154945i
$581$	−16.3706			−0.679166
$582$	3.81630	+	6.61003i	0.158191	+	0.273995i
$583$	−2.50467	−	4.33822i	−0.103733	−	0.179671i
$584$	−6.35184	+	11.0017i	−0.262841	+	0.455254i
$585$	−7.26521	+	12.5837i	−0.300379	+	0.520273i
$586$	−12.4513	+	21.5663i	−0.514360	+	0.890898i
$587$	22.2758	−	38.5828i	0.919421	−	1.59248i	0.119124	−	0.992879i	$-0.461991\pi$
$587$	22.2758	−	38.5828i	0.919421	−	1.59248i	0.800297	−	0.599604i	$-0.204675\pi$
$588$	−12.0711			−0.497802
$589$	38.0050			1.56597
$590$	−1.81630	+	3.14593i	−0.0747760	+	0.129516i
$591$	20.4853	+	35.4815i	0.842652	+	1.45952i
$592$	3.73052	+	6.46144i	0.153323	+	0.265564i
$593$	−0.615057	+	1.06531i	−0.0252574	+	0.0437471i	−0.878378	−	0.477967i	$-0.841374\pi$
$593$	−0.615057	+	1.06531i	−0.0252574	+	0.0437471i	0.853120	+	0.521714i	$0.174707\pi$
$594$	0.828427			0.0339908
$595$	−7.13728			−0.292600
$596$	10.1510	+	17.5820i	0.415801	+	0.720188i
$597$	13.1861	−	22.8390i	0.539672	−	0.934740i
$598$	−44.5886			−1.82336
$599$	16.4930	+	28.5666i	0.673884	+	1.16720i	0.976794	+	0.214182i	$0.0687085\pi$
$599$	16.4930	+	28.5666i	0.673884	+	1.16720i	−0.302910	+	0.953019i	$0.597958\pi$
$600$	2.41421			0.0985599
$601$	−6.12683	+	10.6120i	−0.249919	+	0.432872i	−0.963503	−	0.267697i	$-0.913737\pi$
$601$	−6.12683	+	10.6120i	−0.249919	+	0.432872i	0.713584	+	0.700569i	$0.247071\pi$
$602$	3.29950			0.134478
$603$	−22.0274	−	7.12689i	−0.897026	−	0.290229i
$604$	−19.8846			−0.809093
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$	−10.1256			−0.411323
$607$	14.9017	+	25.8106i	0.604843	+	1.04762i	0.992076	+	0.125637i	$0.0400975\pi$
$607$	14.9017	+	25.8106i	0.604843	+	1.04762i	−0.387233	+	0.921982i	$0.626569\pi$
$608$	−5.63261			−0.228432
$609$	−7.35567	+	12.7404i	−0.298067	+	0.516267i
$610$	6.10417	+	10.5727i	0.247151	+	0.428078i
$611$	48.1873			1.94945
$612$	14.2746			0.577015
$613$	6.36312	−	11.0212i	0.257004	−	0.445144i	−0.708434	−	0.705777i	$-0.750598\pi$
$613$	6.36312	−	11.0212i	0.257004	−	0.445144i	0.965438	+	0.260633i	$0.0839313\pi$
$614$	−1.32182	−	2.28945i	−0.0533442	−	0.0923948i
$615$	−1.17784	−	2.04007i	−0.0474949	−	0.0822636i
$616$	−1.41421	+	2.44949i	−0.0569803	+	0.0986928i
$617$	−5.95249			−0.239638			−0.119819	−	0.992796i	$-0.538231\pi$
$617$	−5.95249			−0.239638			−0.119819	+	0.992796i	$0.538231\pi$
$618$	−28.5280			−1.14757
$619$	−16.5950	+	28.7435i	−0.667011	+	1.15530i	0.311725	+	0.950172i	$0.399093\pi$
$619$	−16.5950	+	28.7435i	−0.667011	+	1.15530i	−0.978736	+	0.205125i	$0.934240\pi$
$620$	3.37366	−	5.84335i	0.135489	−	0.234674i
$621$	−1.79757	+	3.11348i	−0.0721339	+	0.124940i
$622$	−4.13812	+	7.16743i	−0.165923	+	0.287388i
$623$	−10.0870	−	17.4712i	−0.404128	−	0.699971i
$624$	−6.20125	−	10.7409i	−0.248248	−	0.429979i
$625$	1.00000			0.0400000
$626$	11.3655	−	19.6857i	0.454259	−	0.786799i
$627$	27.1966			1.08613
$628$	−12.3574			−0.493112
$629$	18.8272	+	32.6097i	0.750691	+	1.30024i
$630$	−4.00000			−0.159364
$631$	−19.0125	+	32.9307i	−0.756877	+	1.31095i	0.187559	+	0.982253i	$0.439942\pi$
$631$	−19.0125	+	32.9307i	−0.756877	+	1.31095i	−0.944436	+	0.328696i	$0.893391\pi$
$632$	−7.46103	−	12.9229i	−0.296784	−	0.514045i
$633$	−15.6490	+	27.1048i	−0.621991	+	1.07732i
$634$	−4.62516	−	8.01100i	−0.183688	−	0.318158i
$635$	−4.21839	−	7.30647i	−0.167402	−	0.289948i
$636$	3.02341	+	5.23670i	0.119886	+	0.207649i
$637$	12.8432	+	22.2451i	0.508866	+	0.881382i
$638$	−4.30885	−	7.46315i	−0.170589	−	0.295469i
$639$	8.55149	+	14.8116i	0.338292	+	0.585939i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	12.4389	+	21.5447i	0.491306	+	0.850966i	0.999950	−	0.0100105i	$-0.00318650\pi$
$641$	12.4389	+	21.5447i	0.491306	+	0.850966i	−0.508644	+	0.860977i	$0.669853\pi$
$642$	2.73052	−	4.72939i	0.107765	−	0.186654i
$643$	−41.9603			−1.65475			−0.827377	−	0.561647i	$-0.810168\pi$
$643$	−41.9603			−1.65475			−0.827377	+	0.561647i	$0.810168\pi$
$644$	−6.13728	−	10.6301i	−0.241843	−	0.418884i
$645$	−5.63261			−0.221784
$646$	−28.4267			−1.11844
$647$	−4.03747	+	6.99310i	−0.158729	+	0.274927i	−0.934411	−	0.356197i	$-0.884073\pi$
$647$	−4.03747	+	6.99310i	−0.158729	+	0.274927i	0.775681	+	0.631125i	$0.217406\pi$
$648$	−9.48528			−0.372617
$649$	3.63261	+	6.29186i	0.142592	+	0.246977i
$650$	−2.56864	−	4.44901i	−0.100750	−	0.174505i
$651$	−11.5184	+	19.9504i	−0.451441	+	0.781919i
$652$	−6.66814	+	11.5496i	−0.261144	+	0.452316i
$653$	−4.84298	+	8.38829i	−0.189520	+	0.328259i	−0.945090	−	0.326809i	$-0.894027\pi$
$653$	−4.84298	+	8.38829i	−0.189520	+	0.328259i	0.755570	+	0.655068i	$0.227360\pi$
$654$	7.73136	−	13.3911i	0.302320	−	0.523633i
$655$	9.03677			0.353096
$656$	0.975751			0.0380967
$657$	−17.9657	+	31.1175i	−0.700909	+	1.21401i
$658$	6.63261	+	11.4880i	0.258566	+	0.447849i
$659$	−4.18687	−	7.25188i	−0.163097	−	0.282493i	0.772881	−	0.634552i	$-0.218815\pi$
$659$	−4.18687	−	7.25188i	−0.163097	−	0.282493i	−0.935978	+	0.352058i	$0.885482\pi$
$660$	2.41421	−	4.18154i	0.0939731	−	0.162766i
$661$	37.4142			1.45524			0.727622	−	0.685978i	$-0.240625\pi$
$661$	37.4142			1.45524			0.727622	+	0.685978i	$0.240625\pi$
$662$	−13.0149			−0.505838
$663$	−31.2966	−	54.2072i	−1.21546	−	2.10523i
$664$	−5.78787	+	10.0249i	−0.224613	+	0.389041i
$665$	7.96571			0.308897
$666$	10.5515	+	18.2757i	0.408862	+	0.708170i
$667$	37.3984			1.44807
$668$	6.49414	−	11.2482i	0.251266	−	0.435205i
$669$	47.4820			1.83576
$670$	6.07609	−	5.48463i	0.234740	−	0.211890i
$671$	24.4167			0.942596
$672$	1.70711	−	2.95680i	0.0658531	−	0.114061i
$673$	14.0198			0.540422			0.270211	−	0.962801i	$-0.412907\pi$
$673$	14.0198			0.540422			0.270211	+	0.962801i	$0.412907\pi$
$674$	−7.82724	−	13.5572i	−0.301494	−	0.522203i
$675$	−0.414214			−0.0159431
$676$	−6.69582	+	11.5975i	−0.257532	+	0.446058i
$677$	−21.1088	−	36.5614i	−0.811275	−	1.40517i	−0.911972	−	0.410253i	$-0.865440\pi$
$677$	−21.1088	−	36.5614i	−0.811275	−	1.40517i	0.100696	−	0.994917i	$-0.467893\pi$
$678$	4.68709			0.180007
$679$	4.47108			0.171584
$680$	−2.52341	+	4.37067i	−0.0967683	+	0.167608i
$681$	23.6421	+	40.9494i	0.905969	+	1.56918i
$682$	−6.74732	−	11.6867i	−0.258368	−	0.447507i
$683$	−2.44040	+	4.22689i	−0.0933793	+	0.161738i	−0.908931	−	0.416946i	$-0.863100\pi$
$683$	−2.44040	+	4.22689i	−0.0933793	+	0.161738i	0.815552	+	0.578684i	$0.196434\pi$
$684$	−15.9314			−0.609153
$685$	−0.429114			−0.0163956
$686$	−8.48528	+	14.6969i	−0.323970	+	0.561132i
$687$	29.0262	−	50.2749i	1.10742	−	1.91811i
$688$	1.16655	−	2.02053i	0.0444743	−	0.0770318i
$689$	6.43361	−	11.1433i	0.245101	−	0.424527i
$690$	10.4770	+	18.1467i	0.398852	+	0.690832i
$691$	11.3900	+	19.7280i	0.433295	+	0.750488i	0.997155	−	0.0753820i	$-0.0240176\pi$
$691$	11.3900	+	19.7280i	0.433295	+	0.750488i	−0.563860	+	0.825870i	$0.690684\pi$
$692$	−8.94146			−0.339903
$693$	−4.00000	+	6.92820i	−0.151947	+	0.263181i
$694$	−4.31440			−0.163773
$695$	9.42188			0.357392
$696$	5.20125	+	9.00882i	0.197153	+	0.341478i
$697$	4.92444			0.186526
$698$	16.9860	−	29.4207i	0.642931	−	1.11359i
$699$	14.2217	+	24.6326i	0.537913	+	0.931692i
$700$	0.707107	−	1.22474i	0.0267261	−	0.0462910i
$701$	−5.51720	−	9.55607i	−0.208382	−	0.360928i	0.742823	−	0.669488i	$-0.233486\pi$
$701$	−5.51720	−	9.55607i	−0.208382	−	0.360928i	−0.951205	+	0.308560i	$0.900153\pi$
$702$	1.06397	+	1.84284i	0.0401568	+	0.0695536i
$703$	−21.0125	−	36.3948i	−0.792502	−	1.37265i
$704$	1.00000	+	1.73205i	0.0376889	+	0.0652791i
$705$	−11.3226	−	19.6113i	−0.426432	−	0.738603i
$706$	−9.54264	−	16.5283i	−0.359142	−	0.622052i
$707$	−2.96571	+	5.13676i	−0.111537	+	0.193188i
$708$	−4.38494	−	7.59494i	−0.164796	−	0.285435i
$709$	20.0610	−	34.7467i	0.753408	−	1.30494i	−0.192755	−	0.981247i	$-0.561742\pi$
$709$	20.0610	−	34.7467i	0.753408	−	1.30494i	0.946162	−	0.323693i	$-0.104925\pi$
$710$	−6.04682			−0.226933
$711$	−21.1030	−	36.5514i	−0.791424	−	1.37079i
$712$	−14.2652			−0.534611
$713$	58.5628			2.19319
$714$	8.61546	−	14.9224i	0.322425	−	0.558457i
$715$	−10.2746			−0.384247
$716$	−0.575251	−	0.996363i	−0.0214981	−	0.0372358i
$717$	−19.7582	−	34.2221i	−0.737882	−	1.27805i
$718$	−7.60695	+	13.1756i	−0.283889	+	0.491710i
$719$	−15.0999	+	26.1538i	−0.563131	+	0.975372i	0.434090	+	0.900870i	$0.357070\pi$
$719$	−15.0999	+	26.1538i	−0.563131	+	0.975372i	−0.997221	+	0.0745023i	$0.976263\pi$
$720$	−1.41421	+	2.44949i	−0.0527046	+	0.0912871i
$721$	−8.35567	+	14.4724i	−0.311181	+	0.538982i
$722$	12.7262			0.473622
$723$	34.7239			1.29139
$724$	−7.03086	+	12.1778i	−0.261300	+	0.452585i
$725$	2.15443	+	3.73158i	0.0800134	+	0.138587i
$726$	8.44975	+	14.6354i	0.313600	+	0.543170i
$727$	−18.9782	+	32.8713i	−0.703864	+	1.21913i	0.263236	+	0.964731i	$0.415210\pi$
$727$	−18.9782	+	32.8713i	−0.703864	+	1.21913i	−0.967100	+	0.254396i	$0.918123\pi$
$728$	−7.26521			−0.269267
$729$	−23.8284			−0.882534
$730$	−6.35184	−	11.0017i	−0.235092	−	0.407191i
$731$	5.88737	−	10.1972i	0.217752	−	0.377158i
$732$	−29.4736			−1.08937
$733$	9.73987	+	16.8699i	0.359750	+	0.623105i	0.987919	−	0.154972i	$-0.0495286\pi$
$733$	9.73987	+	16.8699i	0.359750	+	0.623105i	−0.628169	+	0.778077i	$0.716195\pi$
$734$	−24.7279			−0.912724
$735$	6.03553	−	10.4539i	0.222624	−	0.385596i
$736$	−8.67942			−0.319928
$737$	−3.42356	−	16.0087i	−0.126109	−	0.589689i
$738$	2.75984			0.101591
$739$	−8.08151	+	13.9976i	−0.297283	+	0.514910i	−0.975513	−	0.219940i	$-0.929414\pi$
$739$	−8.08151	+	13.9976i	−0.297283	+	0.514910i	0.678230	+	0.734850i	$0.262747\pi$
$740$	−7.46103			−0.274273
$741$	34.9292	+	60.4991i	1.28316	+	2.22249i
$742$	3.54214			0.130036
$743$	−5.13503	+	8.89414i	−0.188386	+	0.326294i	−0.944712	−	0.327900i	$-0.893659\pi$
$743$	−5.13503	+	8.89414i	−0.188386	+	0.326294i	0.756326	+	0.654195i	$0.226992\pi$
$744$	8.14473	+	14.1071i	0.298600	+	0.517191i
$745$	−20.3020			−0.743807
$746$	−12.6326			−0.462513
$747$	−16.3706	+	28.3547i	−0.598968	+	1.03744i
$748$	5.04682	+	8.74135i	0.184530	+	0.319615i
$749$	−1.59950	−	2.77041i	−0.0584444	−	0.101229i
$750$	−1.20711	+	2.09077i	−0.0440773	+	0.0763441i
$751$	−17.8503			−0.651367			−0.325683	−	0.945479i	$-0.605594\pi$
$751$	−17.8503			−0.651367			−0.325683	+	0.945479i	$0.605594\pi$
$752$	9.37992			0.342051
$753$	−11.8246	+	20.4808i	−0.430912	+	0.746362i
$754$	11.0679	−	19.1701i	0.403069	−	0.698136i
$755$	9.94230	−	17.2206i	0.361837	−	0.626721i
$756$	−0.292893	+	0.507306i	−0.0106524	+	0.0184505i
$757$	18.2820	+	31.6654i	0.664471	+	1.15090i	0.979428	+	0.201792i	$0.0646764\pi$
$757$	18.2820	+	31.6654i	0.664471	+	1.15090i	−0.314958	+	0.949106i	$0.601990\pi$
$758$	−14.6226	−	25.3270i	−0.531115	−	0.919919i
$759$	41.9080			1.52116
$760$	2.81630	−	4.87798i	0.102158	−	0.176943i
$761$	3.93660			0.142702			0.0713509	−	0.997451i	$-0.477269\pi$
$761$	3.93660			0.142702			0.0713509	+	0.997451i	$0.477269\pi$
$762$	20.3682			0.737862
$763$	−4.52892	−	7.84433i	−0.163958	−	0.283984i
$764$	15.9782			0.578072
$765$	−7.13728	+	12.3621i	−0.258049	+	0.446954i
$766$	−11.9883	−	20.7643i	−0.433154	−	0.750245i
$767$	−9.33086	+	16.1615i	−0.336918	+	0.583558i
$768$	−1.20711	−	2.09077i	−0.0435577	−	0.0754442i
$769$	−17.5276	−	30.3588i	−0.632063	−	1.09477i	−0.987129	−	0.159924i	$-0.948875\pi$
$769$	−17.5276	−	30.3588i	−0.632063	−	1.09477i	0.355066	−	0.934841i	$-0.384458\pi$
$770$	−1.41421	−	2.44949i	−0.0509647	−	0.0882735i
$771$	−14.6209	−	25.3241i	−0.526558	−	0.912026i
$772$	6.25150	+	10.8279i	0.224996	+	0.389705i
$773$	−7.89204	−	13.6694i	−0.283857	−	0.491655i	0.688474	−	0.725261i	$-0.258281\pi$
$773$	−7.89204	−	13.6694i	−0.283857	−	0.491655i	−0.972331	+	0.233606i	$0.924947\pi$
$774$	3.29950	−	5.71491i	0.118598	−	0.205418i
$775$	3.37366	+	5.84335i	0.121185	+	0.209899i
$776$	1.58076	−	2.73796i	0.0567461	−	0.0982872i
$777$	25.4736			0.913859
$778$	−1.50586	−	2.60823i	−0.0539878	−	0.0935095i
$779$	−5.49602			−0.196915
$780$	12.4025			0.444080
$781$	−6.04682	+	10.4734i	−0.216372	+	0.374768i
$782$	−43.8035			−1.56641
$783$	−0.892393	−	1.54567i	−0.0318915	−	0.0552377i
$784$	2.50000	+	4.33013i	0.0892857	+	0.154647i
$785$	6.17868	−	10.7018i	0.220526	−	0.381963i
$786$	−10.9084	+	18.8938i	−0.389088	+	0.673920i
$787$	5.48906	−	9.50734i	0.195664	−	0.338900i	−0.751454	−	0.659785i	$-0.770647\pi$
$787$	5.48906	−	9.50734i	0.195664	−	0.338900i	0.947118	+	0.320886i	$0.103980\pi$
$788$	8.48528	−	14.6969i	0.302276	−	0.523557i
$789$	−57.2560			−2.03837
$790$	14.9221			0.530903
$791$	1.37282	−	2.37779i	0.0488118	−	0.0845445i
$792$	2.82843	+	4.89898i	0.100504	+	0.174078i
$793$	31.3588	+	54.3151i	1.11359	+	1.92879i
$794$	−9.51755	+	16.4849i	−0.337765	+	0.585026i
$795$	−6.04682			−0.214459
$796$	−10.9237			−0.387182
$797$	−3.87727	−	6.71563i	−0.137340	−	0.237880i	0.789149	−	0.614202i	$-0.210522\pi$
$797$	−3.87727	−	6.71563i	−0.137340	−	0.237880i	−0.926489	+	0.376322i	$0.877189\pi$
$798$	−9.61546	+	16.6545i	−0.340384	+	0.589562i
$799$	47.3388			1.67472
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−40.3481			−1.42563
$802$	−15.9657	+	27.6534i	−0.563769	+	0.976476i
$803$	−25.4073			−0.896606
$804$	4.13261	+	19.3242i	0.145746	+	0.681513i
$805$	12.2746			0.432621
$806$	17.3314	−	30.0189i	0.610473	−	1.05737i
$807$	−9.34800			−0.329065
$808$	2.09707	+	3.63223i	0.0737747	+	0.127782i
$809$	−43.0795			−1.51460			−0.757298	−	0.653069i	$-0.773481\pi$
$809$	−43.0795			−1.51460			−0.757298	+	0.653069i	$0.773481\pi$
$810$	4.74264	−	8.21449i	0.166639	−	0.288628i
$811$	18.9677	+	32.8530i	0.666046	+	1.15363i	0.979001	+	0.203857i	$0.0653479\pi$
$811$	18.9677	+	32.8530i	0.666046	+	1.15363i	−0.312955	+	0.949768i	$0.601319\pi$
$812$	6.09364			0.213845
$813$	9.10704			0.319398
$814$	−7.46103	+	12.9229i	−0.261509	+	0.452947i
$815$	−6.66814	−	11.5496i	−0.233575	−	0.404563i
$816$	−6.09205	−	10.5517i	−0.213264	−	0.369385i
$817$	−6.57072	+	11.3808i	−0.229880	+	0.398165i
$818$	0.930611			0.0325381
$819$	−20.5491			−0.718044
$820$	−0.487876	+	0.845025i	−0.0170374	+	0.0295096i
$821$	−8.24145	+	14.2746i	−0.287629	+	0.498188i	−0.973243	−	0.229777i	$-0.926200\pi$
$821$	−8.24145	+	14.2746i	−0.287629	+	0.498188i	0.685615	+	0.727965i	$0.259534\pi$
$822$	0.517986	−	0.897178i	0.0180668	−	0.0312927i
$823$	3.91889	−	6.78771i	0.136604	−	0.236605i	−0.789605	−	0.613615i	$-0.789715\pi$
$823$	3.91889	−	6.78771i	0.136604	−	0.236605i	0.926209	+	0.377010i	$0.123048\pi$
$824$	5.90835	+	10.2336i	0.205827	+	0.356503i
$825$	2.41421	+	4.18154i	0.0840521	+	0.145583i
$826$	−5.13728			−0.178749
$827$	−0.375065	+	0.649631i	−0.0130423	+	0.0225899i	−0.872473	−	0.488663i	$-0.837485\pi$
$827$	−0.375065	+	0.649631i	−0.0130423	+	0.0225899i	0.859431	+	0.511252i	$0.170818\pi$
$828$	−24.5491			−0.853141
$829$	−12.4877			−0.433714			−0.216857	−	0.976203i	$-0.569581\pi$
$829$	−12.4877			−0.433714			−0.216857	+	0.976203i	$0.569581\pi$
$830$	−5.78787	−	10.0249i	−0.200900	−	0.347969i
$831$	−50.1547			−1.73985
$832$	−2.56864	+	4.44901i	−0.0890516	+	0.154242i
$833$	12.6170	+	21.8534i	0.437155	+	0.757174i
$834$	−11.3732	+	19.6990i	−0.393822	+	0.682120i
$835$	6.49414	+	11.2482i	0.224739	+	0.389259i
$836$	−5.63261	−	9.75596i	−0.194808	−	0.337417i
$837$	−1.39741	−	2.42039i	−0.0483017	−	0.0836610i
$838$	−8.04404	−	13.9327i	−0.277877	−	0.481297i
$839$	−28.7099	−	49.7271i	−0.991177	−	1.71677i	−0.610375	−	0.792112i	$-0.708981\pi$
$839$	−28.7099	−	49.7271i	−0.991177	−	1.71677i	−0.380802	−	0.924657i	$-0.624352\pi$
$840$	1.70711	+	2.95680i	0.0589008	+	0.102019i
$841$	5.21689	−	9.03593i	0.179893	−	0.311584i
$842$	1.75736	+	3.04384i	0.0605626	+	0.104898i
$843$	19.6924	−	34.1082i	0.678242	−	1.17475i
$844$	12.9640			0.446240
$845$	−6.69582	−	11.5975i	−0.230343	−	0.398966i
$846$	26.5304			0.912135
$847$	9.89949			0.340151
$848$	1.25234	−	2.16911i	0.0430054	−	0.0744876i
$849$	9.28946			0.318813
$850$	−2.52341	−	4.37067i	−0.0865522	−	0.149913i
$851$	−32.3787	−	56.0816i	−1.10993	−	1.92245i
$852$	7.29916	−	12.6425i	0.250065	−	0.433125i
$853$	27.2869	−	47.2622i	0.934284	−	1.61823i	0.158380	−	0.987378i	$-0.449373\pi$
$853$	27.2869	−	47.2622i	0.934284	−	1.61823i	0.775905	−	0.630850i	$-0.217294\pi$
$854$	−8.63261	+	14.9521i	−0.295402	+	0.511651i
$855$	7.96571	−	13.7970i	0.272421	−	0.471848i
$856$	−2.26203			−0.0773147
$857$	−0.780913			−0.0266755			−0.0133377	−	0.999911i	$-0.504246\pi$
$857$	−0.780913			−0.0266755			−0.0133377	+	0.999911i	$0.504246\pi$
$858$	12.4025	−	21.4817i	0.423414	−	0.733375i
$859$	−4.30158	−	7.45056i	−0.146768	−	0.254210i	0.783263	−	0.621690i	$-0.213554\pi$
$859$	−4.30158	−	7.45056i	−0.146768	−	0.254210i	−0.930031	+	0.367481i	$0.880220\pi$
$860$	1.16655	+	2.02053i	0.0397791	+	0.0688993i
$861$	1.66571	−	2.88510i	0.0567673	−	0.0983238i
$862$	−14.0468			−0.478437
$863$	13.8903			0.472830			0.236415	−	0.971652i	$-0.424028\pi$
$863$	13.8903			0.472830			0.236415	+	0.971652i	$0.424028\pi$
$864$	0.207107	+	0.358719i	0.00704592	+	0.0122039i
$865$	4.47073	−	7.74353i	0.152009	−	0.263288i
$866$	6.31203			0.214491
$867$	−10.2247	−	17.7096i	−0.347247	−	0.601450i
$868$	9.54214			0.323881
$869$	14.9221	−	25.8458i	0.506196	−	0.876758i
$870$	−10.4025			−0.352677
$871$	31.2146	−	28.1761i	1.05767	−	0.954709i
$872$	−6.40486			−0.216896
$873$	4.47108	−	7.74413i	0.151323	−	0.262099i
$874$	48.8878			1.65365
$875$	0.707107	+	1.22474i	0.0239046	+	0.0414039i
$876$	30.6694			1.03622
$877$	3.53504	−	6.12287i	0.119370	−	0.206755i	−0.800148	−	0.599802i	$-0.795246\pi$
$877$	3.53504	−	6.12287i	0.119370	−	0.206755i	0.919518	+	0.393048i	$0.128579\pi$
$878$	−6.85184	−	11.8677i	−0.231238	−	0.400516i
$879$	60.1204			2.02781
$880$	−2.00000			−0.0674200
$881$	1.51212	−	2.61908i	0.0509448	−	0.0882389i	−0.839428	−	0.543470i	$-0.817110\pi$
$881$	1.51212	−	2.61908i	0.0509448	−	0.0882389i	0.890373	+	0.455231i	$0.150443\pi$
$882$	7.07107	+	12.2474i	0.238095	+	0.412393i
$883$	7.25199	+	12.5608i	0.244049	+	0.422705i	0.961864	−	0.273529i	$-0.0881909\pi$
$883$	7.25199	+	12.5608i	0.244049	+	0.422705i	−0.717815	+	0.696234i	$0.754858\pi$
$884$	−12.9635	+	22.4534i	−0.436008	+	0.755189i
$885$	8.76989			0.294796
$886$	−0.507851			−0.0170616
$887$	12.2049	−	21.1395i	0.409801	−	0.709796i	−0.585066	−	0.810985i	$-0.698932\pi$
$887$	12.2049	−	21.1395i	0.409801	−	0.709796i	0.994867	+	0.101190i	$0.0322648\pi$
$888$	9.00626	−	15.5993i	0.302230	−	0.523478i
$889$	5.96571	−	10.3329i	0.200083	−	0.346555i
$890$	7.13261	−	12.3540i	0.239085	−	0.414108i
$891$	−9.48528	−	16.4290i	−0.317769	−	0.550392i
$892$	−9.83385	−	17.0327i	−0.329262	−	0.570298i
$893$	−52.8334			−1.76800
$894$	24.5067	−	42.4468i	0.819625	−	1.41963i
$895$	1.15050			0.0384570
$896$	−1.41421			−0.0472456
$897$	53.8232	+	93.2246i	1.79711	+	3.11268i
$898$	−26.1239			−0.871765
$899$	−14.5366	+	25.1781i	−0.484823	+	0.839737i
$900$	−1.41421	−	2.44949i	−0.0471405	−	0.0816497i
$901$	6.32032	−	10.9471i	0.210560	−	0.364701i
$902$	0.975751	+	1.69005i	0.0324890	+	0.0562725i
$903$	−3.98285	−	6.89850i	−0.132541	−	0.229568i
$904$	−0.970729	−	1.68135i	−0.0322860	−	0.0559209i
$905$	−7.03086	−	12.1778i	−0.233714	−	0.404804i
$906$	24.0028	+	41.5741i	0.797441	+	1.38121i
$907$	−8.59205	−	14.8819i	−0.285294	−	0.494144i	0.687386	−	0.726292i	$-0.258758\pi$
$907$	−8.59205	−	14.8819i	−0.285294	−	0.494144i	−0.972681	+	0.232148i	$0.925425\pi$
$908$	9.79289	−	16.9618i	0.324989	−	0.562897i
$909$	5.93141	+	10.2735i	0.196733	+	0.340751i
$910$	3.63261	−	6.29186i	0.120420	−	0.208573i
$911$	−12.4243			−0.411634			−0.205817	−	0.978590i	$-0.565985\pi$
$911$	−12.4243			−0.411634			−0.205817	+	0.978590i	$0.565985\pi$
$912$	6.79916	+	11.7765i	0.225143	+	0.389958i
$913$	−23.1515			−0.766202
$914$	4.54145			0.150218
$915$	14.7368	−	25.5249i	0.487183	−	0.843826i
$916$	−24.0461			−0.794506
$917$	6.38996	+	11.0677i	0.211015	+	0.365489i
$918$	1.04523	+	1.81039i	0.0344977	+	0.0597518i
$919$	−24.1749	+	41.8721i	−0.797456	+	1.38123i	0.123812	+	0.992306i	$0.460488\pi$
$919$	−24.1749	+	41.8721i	−0.797456	+	1.38123i	−0.921268	+	0.388929i	$0.872845\pi$
$920$	4.33971	−	7.51660i	0.143076	−	0.247815i
$921$	−3.19115	+	5.52723i	−0.105152	+	0.182128i
$922$	10.4059	−	18.0236i	0.342701	−	0.593575i
$923$	−31.0642			−1.02249
$924$	6.82843			0.224639
$925$	3.73052	−	6.46144i	0.122659	−	0.212451i
$926$	20.4770	+	35.4672i	0.672916	+	1.16552i
$927$	16.7113	+	28.9449i	0.548873	+	0.950675i
$928$	2.15443	−	3.73158i	0.0707225	−	0.122495i
$929$	54.5547			1.78988			0.894940	−	0.446186i	$-0.147218\pi$
$929$	54.5547			1.78988			0.894940	+	0.446186i	$0.147218\pi$
$930$	−16.2895			−0.534152
$931$	−14.0815	−	24.3899i	−0.461503	−	0.799347i
$932$	5.89080	−	10.2032i	0.192960	−	0.334216i
$933$	19.9806			0.654136
$934$	−15.9869	−	27.6901i	−0.523106	−	0.906047i
$935$	−10.0936			−0.330097
$936$	−7.26521	+	12.5837i	−0.237471	+	0.411312i
$937$	−47.1742			−1.54111			−0.770556	−	0.637372i	$-0.780022\pi$
$937$	−47.1742			−1.54111			−0.770556	+	0.637372i	$0.780022\pi$
$938$	11.0137	+	3.56344i	0.359610	+	0.116351i
$939$	−54.8777			−1.79087
$940$	−4.68996	+	8.12325i	−0.152970	+	0.264951i
$941$	52.2466			1.70319			0.851596	−	0.524199i	$-0.175635\pi$
$941$	52.2466			1.70319			0.851596	+	0.524199i	$0.175635\pi$
$942$	14.9166	+	25.8364i	0.486010	+	0.841795i
$943$	−8.46896			−0.275787
$944$	−1.81630	+	3.14593i	−0.0591156	+	0.102391i
$945$	−0.292893	−	0.507306i	−0.00952782	−	0.0165027i
$946$	4.66620			0.151711
$947$	44.0053			1.42998			0.714990	−	0.699135i	$-0.246431\pi$
$947$	44.0053			1.42998			0.714990	+	0.699135i	$0.246431\pi$
$948$	−18.0125	+	31.1986i	−0.585020	+	1.01328i
$949$	−32.6312	−	56.5188i	−1.05925	−	1.83468i
$950$	2.81630	+	4.87798i	0.0913729	+	0.158263i
$951$	−11.1661	+	19.3403i	−0.362086	+	0.627151i
$952$	−7.13728			−0.231321
$953$	−28.0150			−0.907495			−0.453748	−	0.891130i	$-0.649913\pi$
$953$	−28.0150			−0.907495			−0.453748	+	0.891130i	$0.649913\pi$
$954$	3.54214	−	6.13517i	0.114681	−	0.198634i
$955$	−7.98912	+	13.8376i	−0.258522	+	0.447773i
$956$	−8.18410	+	14.1753i	−0.264693	+	0.458461i
$957$	−10.4025	+	18.0176i	−0.336265	+	0.582428i
$958$	13.5250	+	23.4260i	0.436973	+	0.756859i
$959$	−0.303429	−	0.525555i	−0.00979824	−	0.0169710i
$960$	2.41421			0.0779184
$961$	−7.26313	+	12.5801i	−0.234295	+	0.405810i
$962$	−38.3294			−1.23579
$963$	−6.39800			−0.206173
$964$	−7.19155	−	12.4561i	−0.231624	−	0.401185i
$965$	−12.5030			−0.402486
$966$	−14.8167	+	25.6633i	−0.476720	+	0.825703i
$967$	21.1191	+	36.5793i	0.679144	+	1.17631i	0.975239	+	0.221153i	$0.0709820\pi$
$967$	21.1191	+	36.5793i	0.679144	+	1.17631i	−0.296096	+	0.955158i	$0.595685\pi$
$968$	3.50000	−	6.06218i	0.112494	−	0.194846i
$969$	34.3141	+	59.4338i	1.10233	+	1.90929i
$970$	1.58076	+	2.73796i	0.0507553	+	0.0879107i
$971$	−17.2205	−	29.8267i	−0.552631	−	0.957185i	−0.998084	−	0.0618798i	$-0.980290\pi$
$971$	−17.2205	−	29.8267i	−0.552631	−	0.957185i	0.445452	−	0.895306i	$-0.353043\pi$
$972$	10.8284	+	18.7554i	0.347322	+	0.601579i
$973$	6.66228	+	11.5394i	0.213583	+	0.369936i
$974$	−0.878680	−	1.52192i	−0.0281547	−	0.0487654i
$975$	−6.20125	+	10.7409i	−0.198599	+	0.343983i
$976$	6.10417	+	10.5727i	0.195390	+	0.338425i
$977$	−29.9115	+	51.8083i	−0.956955	+	1.65749i	−0.227124	+	0.973866i	$0.572932\pi$
$977$	−29.9115	+	51.8083i	−0.956955	+	1.65749i	−0.729830	+	0.683628i	$0.760401\pi$
$978$	32.1966			1.02953
$979$	−14.2652	−	24.7081i	−0.455918	−	0.789673i
$980$	−5.00000			−0.159719
$981$	−18.1157			−0.578390
$982$	9.77147	−	16.9247i	0.311820	−	0.540089i
$983$	−18.0960			−0.577173			−0.288587	−	0.957454i	$-0.593185\pi$
$983$	−18.0960			−0.577173			−0.288587	+	0.957454i	$0.593185\pi$
$984$	−1.17784	−	2.04007i	−0.0375480	−	0.0650351i
$985$	8.48528	+	14.6969i	0.270364	+	0.468283i
$986$	10.8730	−	18.8326i	0.346267	−	0.599752i
$987$	16.0125	−	27.7345i	0.509684	−	0.882799i
$988$	14.4681	−	25.0595i	0.460293	−	0.797250i
$989$	−10.1250	+	17.5370i	−0.321956	+	0.557644i
$990$	−5.65685			−0.179787
$991$	12.9438			0.411174			0.205587	−	0.978639i	$-0.434090\pi$
$991$	12.9438			0.411174			0.205587	+	0.978639i	$0.434090\pi$
$992$	3.37366	−	5.84335i	0.107114	−	0.185526i
$993$	15.7104	+	27.2112i	0.498554	+	0.863520i
$994$	−4.27575	−	7.40581i	−0.135618	−	0.234898i
$995$	5.46187	−	9.46024i	0.173153	−	0.299910i
$996$	27.9463			0.885513
$997$	61.8233			1.95797			0.978983	−	0.203944i	$-0.0653761\pi$
$997$	61.8233			1.95797			0.978983	+	0.203944i	$0.0653761\pi$
$998$	13.1283	+	22.7389i	0.415570	+	0.719789i
$999$	−1.54523	+	2.67642i	−0.0488889	+	0.0846781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.i.431.3	yes	8
67.37	even	3	inner	670.2.e.i.171.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.i.171.3	✓	8	67.37	even	3	inner
670.2.e.i.431.3	yes	8	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +2.41421 q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.20711 + 2.09077i) q^{6} +(0.707107 + 1.22474i) q^{7} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +2.41421 q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-1.20711 + 2.09077i) q^{6} +(0.707107 + 1.22474i) q^{7} +1.00000 q^{8} +2.82843 q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-1.20711 - 2.09077i) q^{12} +(-2.56864 + 4.44901i) q^{13} -1.41421 q^{14} +2.41421 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.52341 + 4.37067i) q^{17} +(-1.41421 + 2.44949i) q^{18} +(2.81630 - 4.87798i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.70711 + 2.95680i) q^{21} -2.00000 q^{22} +(4.33971 - 7.51660i) q^{23} +2.41421 q^{24} +1.00000 q^{25} +(-2.56864 - 4.44901i) q^{26} -0.414214 q^{27} +(0.707107 - 1.22474i) q^{28} +(2.15443 + 3.73158i) q^{29} +(-1.20711 + 2.09077i) q^{30} +(3.37366 + 5.84335i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.41421 + 4.18154i) q^{33} +(-2.52341 - 4.37067i) q^{34} +(0.707107 + 1.22474i) q^{35} +(-1.41421 - 2.44949i) q^{36} +(3.73052 - 6.46144i) q^{37} +(2.81630 + 4.87798i) q^{38} +(-6.20125 + 10.7409i) q^{39} +1.00000 q^{40} +(-0.487876 - 0.845025i) q^{41} -3.41421 q^{42} -2.33310 q^{43} +(1.00000 - 1.73205i) q^{44} +2.82843 q^{45} +(4.33971 + 7.51660i) q^{46} +(-4.68996 - 8.12325i) q^{47} +(-1.20711 + 2.09077i) q^{48} +(2.50000 - 4.33013i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-6.09205 + 10.5517i) q^{51} +5.13728 q^{52} -2.50467 q^{53} +(0.207107 - 0.358719i) q^{54} +(1.00000 + 1.73205i) q^{55} +(0.707107 + 1.22474i) q^{56} +(6.79916 - 11.7765i) q^{57} -4.30885 q^{58} +3.63261 q^{59} +(-1.20711 - 2.09077i) q^{60} +(6.10417 - 10.5727i) q^{61} -6.74732 q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(-2.56864 + 4.44901i) q^{65} -4.82843 q^{66} +(-7.78787 - 2.51973i) q^{67} +5.04682 q^{68} +(10.4770 - 18.1467i) q^{69} -1.41421 q^{70} +(3.02341 + 5.23670i) q^{71} +2.82843 q^{72} +(-6.35184 + 11.0017i) q^{73} +(3.73052 + 6.46144i) q^{74} +2.41421 q^{75} -5.63261 q^{76} +(-1.41421 + 2.44949i) q^{77} +(-6.20125 - 10.7409i) q^{78} +(-7.46103 - 12.9229i) q^{79} +(-0.500000 + 0.866025i) q^{80} -9.48528 q^{81} +0.975751 q^{82} +(-5.78787 + 10.0249i) q^{83} +(1.70711 - 2.95680i) q^{84} +(-2.52341 + 4.37067i) q^{85} +(1.16655 - 2.02053i) q^{86} +(5.20125 + 9.00882i) q^{87} +(1.00000 + 1.73205i) q^{88} -14.2652 q^{89} +(-1.41421 + 2.44949i) q^{90} -7.26521 q^{91} -8.67942 q^{92} +(8.14473 + 14.1071i) q^{93} +9.37992 q^{94} +(2.81630 - 4.87798i) q^{95} +(-1.20711 - 2.09077i) q^{96} +(1.58076 - 2.73796i) q^{97} +(2.50000 + 4.33013i) q^{98} +(2.82843 + 4.89898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8} - 4 q^{10} + 8 q^{11} - 4 q^{12} + 8 q^{15} - 4 q^{16} + 2 q^{17} + 6 q^{19} - 4 q^{20} + 8 q^{21} - 16 q^{22} - 4 q^{23} + 8 q^{24} + 8 q^{25} + 8 q^{27} + 8 q^{29} - 4 q^{30} + 6 q^{31} - 4 q^{32} + 8 q^{33} + 2 q^{34} + 2 q^{37} + 6 q^{38} + 4 q^{39} + 8 q^{40} - 10 q^{41} - 16 q^{42} + 12 q^{43} + 8 q^{44} - 4 q^{46} - 4 q^{48} + 20 q^{49} - 4 q^{50} - 6 q^{51} - 12 q^{53} - 4 q^{54} + 8 q^{55} + 6 q^{57} - 16 q^{58} - 4 q^{59} - 4 q^{60} - 12 q^{62} + 16 q^{63} + 8 q^{64} - 16 q^{66} - 30 q^{67} - 4 q^{68} + 4 q^{69} + 2 q^{71} - 6 q^{73} + 2 q^{74} + 8 q^{75} - 12 q^{76} + 4 q^{78} - 4 q^{79} - 4 q^{80} - 8 q^{81} + 20 q^{82} - 14 q^{83} + 8 q^{84} + 2 q^{85} - 6 q^{86} - 12 q^{87} + 8 q^{88} - 48 q^{89} + 8 q^{91} + 8 q^{92} + 26 q^{93} + 6 q^{95} - 4 q^{96} - 14 q^{97} + 20 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8 - 4 * q^10 + 8 * q^11 - 4 * q^12 + 8 * q^15 - 4 * q^16 + 2 * q^17 + 6 * q^19 - 4 * q^20 + 8 * q^21 - 16 * q^22 - 4 * q^23 + 8 * q^24 + 8 * q^25 + 8 * q^27 + 8 * q^29 - 4 * q^30 + 6 * q^31 - 4 * q^32 + 8 * q^33 + 2 * q^34 + 2 * q^37 + 6 * q^38 + 4 * q^39 + 8 * q^40 - 10 * q^41 - 16 * q^42 + 12 * q^43 + 8 * q^44 - 4 * q^46 - 4 * q^48 + 20 * q^49 - 4 * q^50 - 6 * q^51 - 12 * q^53 - 4 * q^54 + 8 * q^55 + 6 * q^57 - 16 * q^58 - 4 * q^59 - 4 * q^60 - 12 * q^62 + 16 * q^63 + 8 * q^64 - 16 * q^66 - 30 * q^67 - 4 * q^68 + 4 * q^69 + 2 * q^71 - 6 * q^73 + 2 * q^74 + 8 * q^75 - 12 * q^76 + 4 * q^78 - 4 * q^79 - 4 * q^80 - 8 * q^81 + 20 * q^82 - 14 * q^83 + 8 * q^84 + 2 * q^85 - 6 * q^86 - 12 * q^87 + 8 * q^88 - 48 * q^89 + 8 * q^91 + 8 * q^92 + 26 * q^93 + 6 * q^95 - 4 * q^96 - 14 * q^97 + 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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