LMFDB - Embedded newform 670.2.e.i.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:	$8$
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			171.1
Root			$1.93979 - 3.35982i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.i.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -0.414214 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.207107 + 0.358719i) q^{6} +(-0.707107 + 1.22474i) q^{7} +1.00000 q^{8} -2.82843 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -0.414214 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.207107 + 0.358719i) 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} +(0.207107 - 0.358719i) q^{12} +(-2.74328 - 4.75150i) q^{13} +1.41421 q^{14} -0.414214 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.64690 + 4.58456i) q^{17} +(1.41421 + 2.44949i) q^{18} +(-0.939791 - 1.62777i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.292893 - 0.507306i) q^{21} -2.00000 q^{22} +(-4.58669 - 7.94438i) q^{23} -0.414214 q^{24} +1.00000 q^{25} +(-2.74328 + 4.75150i) q^{26} +2.41421 q^{27} +(-0.707107 - 1.22474i) q^{28} +(5.15749 - 8.93304i) q^{29} +(0.207107 + 0.358719i) q^{30} +(3.06175 - 5.30311i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.414214 + 0.717439i) q^{33} +(2.64690 - 4.58456i) q^{34} +(-0.707107 + 1.22474i) q^{35} +(1.41421 - 2.44949i) q^{36} +(-2.85400 - 4.94328i) q^{37} +(-0.939791 + 1.62777i) q^{38} +(1.13630 + 1.96813i) q^{39} +1.00000 q^{40} +(-2.38864 + 4.13724i) q^{41} -0.585786 q^{42} -4.53771 q^{43} +(1.00000 + 1.73205i) q^{44} -2.82843 q^{45} +(-4.58669 + 7.94438i) q^{46} +(-0.621958 + 1.07726i) q^{47} +(0.207107 + 0.358719i) q^{48} +(2.50000 + 4.33013i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.09638 - 1.89899i) q^{51} +5.48656 q^{52} -10.3661 q^{53} +(-1.20711 - 2.09077i) q^{54} +(1.00000 - 1.73205i) q^{55} +(-0.707107 + 1.22474i) q^{56} +(0.389274 + 0.674243i) q^{57} -10.3150 q^{58} -3.87958 q^{59} +(0.207107 - 0.358719i) q^{60} +(-0.792255 - 1.37223i) q^{61} -6.12350 q^{62} +(2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(-2.74328 - 4.75150i) q^{65} +0.828427 q^{66} +(-4.64754 - 6.73798i) q^{67} -5.29380 q^{68} +(1.89987 + 3.29067i) q^{69} +1.41421 q^{70} +(-2.14690 + 3.71854i) q^{71} -2.82843 q^{72} +(4.47532 + 7.75149i) q^{73} +(-2.85400 + 4.94328i) q^{74} -0.414214 q^{75} +1.87958 q^{76} +(1.41421 + 2.44949i) q^{77} +(1.13630 - 1.96813i) q^{78} +(5.70801 - 9.88656i) q^{79} +(-0.500000 - 0.866025i) q^{80} +7.48528 q^{81} +4.77727 q^{82} +(-2.64754 - 4.58567i) q^{83} +(0.292893 + 0.507306i) q^{84} +(2.64690 + 4.58456i) q^{85} +(2.26886 + 3.92977i) q^{86} +(-2.13630 + 3.70019i) q^{87} +(1.00000 - 1.73205i) q^{88} +0.759164 q^{89} +(1.41421 + 2.44949i) q^{90} +7.75916 q^{91} +9.17338 q^{92} +(-1.26822 + 2.19662i) q^{93} +1.24392 q^{94} +(-0.939791 - 1.62777i) q^{95} +(0.207107 - 0.358719i) q^{96} +(-0.145358 - 0.251767i) 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 $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.414214			−0.239146			−0.119573	−	0.992825i	$-0.538153\pi$
$3$	−0.414214			−0.239146			−0.119573	+	0.992825i	$0.538153\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.207107	+	0.358719i	0.0845510	+	0.146447i
$7$	−0.707107	+	1.22474i	−0.267261	+	0.462910i	−0.968154	−	0.250357i	$-0.919452\pi$
$7$	−0.707107	+	1.22474i	−0.267261	+	0.462910i	0.700892	+	0.713267i	$0.252785\pi$
$8$	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	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	0.207107	−	0.358719i	0.0597866	−	0.103553i
$13$	−2.74328	−	4.75150i	−0.760849	−	1.31783i	−0.942414	−	0.334449i	$-0.891450\pi$
$13$	−2.74328	−	4.75150i	−0.760849	−	1.31783i	0.181565	−	0.983379i	$-0.441884\pi$
$14$	1.41421			0.377964
$15$	−0.414214			−0.106949
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.64690	+	4.58456i	0.641967	+	1.11192i	0.984993	+	0.172594i	$0.0552147\pi$
$17$	2.64690	+	4.58456i	0.641967	+	1.11192i	−0.343026	+	0.939326i	$0.611452\pi$
$18$	1.41421	+	2.44949i	0.333333	+	0.577350i
$19$	−0.939791	−	1.62777i	−0.215603	−	0.373435i	0.737856	−	0.674958i	$-0.235838\pi$
$19$	−0.939791	−	1.62777i	−0.215603	−	0.373435i	−0.953459	+	0.301523i	$0.902505\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.292893	−	0.507306i	0.0639145	−	0.110703i
$22$	−2.00000			−0.426401
$23$	−4.58669	−	7.94438i	−0.956391	−	1.65652i	−0.731153	−	0.682213i	$-0.761018\pi$
$23$	−4.58669	−	7.94438i	−0.956391	−	1.65652i	−0.225238	−	0.974304i	$-0.572316\pi$
$24$	−0.414214			−0.0845510
$25$	1.00000			0.200000
$26$	−2.74328	+	4.75150i	−0.538001	+	0.931845i
$27$	2.41421			0.464616
$28$	−0.707107	−	1.22474i	−0.133631	−	0.231455i
$29$	5.15749	−	8.93304i	0.957722	−	1.65882i	0.229710	−	0.973259i	$-0.426222\pi$
$29$	5.15749	−	8.93304i	0.957722	−	1.65882i	0.728012	−	0.685565i	$-0.240445\pi$
$30$	0.207107	+	0.358719i	0.0378124	+	0.0654929i
$31$	3.06175	−	5.30311i	0.549906	−	0.952466i	−0.448374	−	0.893846i	$-0.647997\pi$
$31$	3.06175	−	5.30311i	0.549906	−	0.952466i	0.998280	−	0.0586197i	$-0.0186699\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.414214	+	0.717439i	−0.0721053	+	0.124890i
$34$	2.64690	−	4.58456i	0.453939	−	0.786246i
$35$	−0.707107	+	1.22474i	−0.119523	+	0.207020i
$36$	1.41421	−	2.44949i	0.235702	−	0.408248i
$37$	−2.85400	−	4.94328i	−0.469195	−	0.812670i	0.530184	−	0.847882i	$-0.322123\pi$
$37$	−2.85400	−	4.94328i	−0.469195	−	0.812670i	−0.999380	+	0.0352120i	$0.988789\pi$
$38$	−0.939791	+	1.62777i	−0.152454	+	0.264058i
$39$	1.13630	+	1.96813i	0.181954	+	0.315154i
$40$	1.00000			0.158114
$41$	−2.38864	+	4.13724i	−0.373042	+	0.646128i	−0.990032	−	0.140843i	$-0.955019\pi$
$41$	−2.38864	+	4.13724i	−0.373042	+	0.646128i	0.616990	+	0.786971i	$0.288352\pi$
$42$	−0.585786			−0.0903888
$43$	−4.53771			−0.691995			−0.345997	−	0.938236i	$-0.612459\pi$
$43$	−4.53771			−0.691995			−0.345997	+	0.938236i	$0.612459\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$	−2.82843			−0.421637
$46$	−4.58669	+	7.94438i	−0.676270	+	1.17133i
$47$	−0.621958	+	1.07726i	−0.0907219	+	0.157135i	−0.907815	−	0.419371i	$-0.862251\pi$
$47$	−0.621958	+	1.07726i	−0.0907219	+	0.157135i	0.817093	+	0.576506i	$0.195584\pi$
$48$	0.207107	+	0.358719i	0.0298933	+	0.0517767i
$49$	2.50000	+	4.33013i	0.357143	+	0.618590i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−1.09638	−	1.89899i	−0.153524	−	0.265911i
$52$	5.48656			0.760849
$53$	−10.3661			−1.42390			−0.711949	−	0.702231i	$-0.752187\pi$
$53$	−10.3661			−1.42390			−0.711949	+	0.702231i	$0.752187\pi$
$54$	−1.20711	−	2.09077i	−0.164266	−	0.284518i
$55$	1.00000	−	1.73205i	0.134840	−	0.233550i
$56$	−0.707107	+	1.22474i	−0.0944911	+	0.163663i
$57$	0.389274	+	0.674243i	0.0515606	+	0.0893056i
$58$	−10.3150			−1.35442
$59$	−3.87958			−0.505079			−0.252539	−	0.967587i	$-0.581266\pi$
$59$	−3.87958			−0.505079			−0.252539	+	0.967587i	$0.581266\pi$
$60$	0.207107	−	0.358719i	0.0267374	−	0.0463105i
$61$	−0.792255	−	1.37223i	−0.101438	−	0.175696i	0.810839	−	0.585269i	$-0.199011\pi$
$61$	−0.792255	−	1.37223i	−0.101438	−	0.175696i	−0.912277	+	0.409573i	$0.865678\pi$
$62$	−6.12350			−0.777685
$63$	2.00000	−	3.46410i	0.251976	−	0.436436i
$64$	1.00000			0.125000
$65$	−2.74328	−	4.75150i	−0.340262	−	0.589351i
$66$	0.828427			0.101972
$67$	−4.64754	−	6.73798i	−0.567787	−	0.823176i
$67$	−4.64754	−	6.73798i	−0.567787	−	0.823176i
$68$	−5.29380			−0.641967
$69$	1.89987	+	3.29067i	0.228717	+	0.396150i
$70$	1.41421			0.169031
$71$	−2.14690	+	3.71854i	−0.254790	+	0.441309i	−0.964838	−	0.262844i	$-0.915340\pi$
$71$	−2.14690	+	3.71854i	−0.254790	+	0.441309i	0.710049	+	0.704153i	$0.248673\pi$
$72$	−2.82843			−0.333333
$73$	4.47532	+	7.75149i	0.523797	+	0.907243i	0.999616	+	0.0277001i	$0.00881835\pi$
$73$	4.47532	+	7.75149i	0.523797	+	0.907243i	−0.475819	+	0.879543i	$0.657848\pi$
$74$	−2.85400	+	4.94328i	−0.331771	+	0.574645i
$75$	−0.414214			−0.0478293
$76$	1.87958			0.215603
$77$	1.41421	+	2.44949i	0.161165	+	0.279145i
$78$	1.13630	−	1.96813i	0.128661	−	0.222847i
$79$	5.70801	−	9.88656i	0.642201	−	1.11233i	−0.342739	−	0.939431i	$-0.611355\pi$
$79$	5.70801	−	9.88656i	0.642201	−	1.11233i	0.984940	−	0.172894i	$-0.0553120\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	7.48528			0.831698
$82$	4.77727			0.527561
$83$	−2.64754	−	4.58567i	−0.290605	−	0.503342i	0.683348	−	0.730093i	$-0.260523\pi$
$83$	−2.64754	−	4.58567i	−0.290605	−	0.503342i	−0.973953	+	0.226750i	$0.927190\pi$
$84$	0.292893	+	0.507306i	0.0319573	+	0.0553516i
$85$	2.64690	+	4.58456i	0.287096	+	0.497265i
$86$	2.26886	+	3.92977i	0.244657	+	0.423758i
$87$	−2.13630	+	3.70019i	−0.229036	+	0.396702i
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	0.759164			0.0804712			0.0402356	−	0.999190i	$-0.487189\pi$
$89$	0.759164			0.0804712			0.0402356	+	0.999190i	$0.487189\pi$
$90$	1.41421	+	2.44949i	0.149071	+	0.258199i
$91$	7.75916			0.813381
$92$	9.17338			0.956391
$93$	−1.26822	+	2.19662i	−0.131508	+	0.227779i
$94$	1.24392			0.128300
$95$	−0.939791	−	1.62777i	−0.0964205	−	0.167005i
$96$	0.207107	−	0.358719i	0.0211377	−	0.0366117i
$97$	−0.145358	−	0.251767i	−0.0147588	−	0.0255631i	0.858552	−	0.512727i	$-0.171365\pi$
$97$	−0.145358	−	0.251767i	−0.0147588	−	0.0255631i	−0.873310	+	0.487164i	$0.838031\pi$
$98$	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
$101$	1.65595	−	2.86819i	0.164773	−	0.285396i	−0.771801	−	0.635864i	$-0.780644\pi$
$101$	1.65595	−	2.86819i	0.164773	−	0.285396i	0.936575	+	0.350468i	$0.113977\pi$
$102$	−1.09638	+	1.89899i	−0.108558	+	0.188028i
$103$	−2.84341	+	4.92493i	−0.280170	+	0.485268i	−0.971426	−	0.237341i	$-0.923724\pi$
$103$	−2.84341	+	4.92493i	−0.280170	+	0.485268i	0.691257	+	0.722609i	$0.257057\pi$
$104$	−2.74328	−	4.75150i	−0.269001	−	0.465923i
$105$	0.292893	−	0.507306i	0.0285835	−	0.0495080i
$106$	5.18307	+	8.97734i	0.503424	+	0.871956i
$107$	−18.6088			−1.79898			−0.899489	−	0.436943i	$-0.856061\pi$
$107$	−18.6088			−1.79898			−0.899489	+	0.436943i	$0.856061\pi$
$108$	−1.20711	+	2.09077i	−0.116154	+	0.201184i
$109$	12.1465			1.16342			0.581711	−	0.813395i	$-0.302383\pi$
$109$	12.1465			1.16342			0.581711	+	0.813395i	$0.302383\pi$
$110$	−2.00000			−0.190693
$111$	1.18217	+	2.04757i	0.112206	+	0.194347i
$112$	1.41421			0.133631
$113$	−0.217701	+	0.377070i	−0.0204796	+	0.0354717i	−0.876084	−	0.482159i	$-0.839853\pi$
$113$	−0.217701	+	0.377070i	−0.0204796	+	0.0354717i	0.855604	+	0.517631i	$0.173186\pi$
$114$	0.389274	−	0.674243i	0.0364589	−	0.0631486i
$115$	−4.58669	−	7.94438i	−0.427711	−	0.740817i
$116$	5.15749	+	8.93304i	0.478861	+	0.829412i
$117$	7.75916	+	13.4393i	0.717335	+	1.24246i
$118$	1.93979	+	3.35982i	0.178572	+	0.309296i
$119$	−7.48656			−0.686292
$120$	−0.414214			−0.0378124
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−0.792255	+	1.37223i	−0.0717274	+	0.124236i
$123$	0.989406	−	1.71370i	0.0892117	−	0.154519i
$124$	3.06175	+	5.30311i	0.274953	+	0.476233i
$125$	1.00000			0.0894427
$126$	−4.00000			−0.356348
$127$	0.465368	−	0.806041i	0.0412947	−	0.0715246i	−0.844639	−	0.535336i	$-0.820185\pi$
$127$	0.465368	−	0.806041i	0.0412947	−	0.0715246i	0.885934	+	0.463811i	$0.153518\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.87958			0.165488
$130$	−2.74328	+	4.75150i	−0.240601	+	0.416734i
$131$	−10.4129			−0.909783			−0.454891	−	0.890547i	$-0.650322\pi$
$131$	−10.4129			−0.909783			−0.454891	+	0.890547i	$0.650322\pi$
$132$	−0.414214	−	0.717439i	−0.0360527	−	0.0624450i
$133$	2.65813			0.230489
$134$	−3.51150	+	7.39388i	−0.303347	+	0.638734i
$135$	2.41421			0.207782
$136$	2.64690	+	4.58456i	0.226970	+	0.393123i
$137$	21.9238			1.87307			0.936537	−	0.350569i	$-0.114012\pi$
$137$	21.9238			1.87307			0.936537	+	0.350569i	$0.114012\pi$
$138$	1.89987	−	3.29067i	0.161728	−	0.280120i
$139$	19.5788			1.66065			0.830327	−	0.557277i	$-0.188154\pi$
$139$	19.5788			1.66065			0.830327	+	0.557277i	$0.188154\pi$
$140$	−0.707107	−	1.22474i	−0.0597614	−	0.103510i
$141$	0.257624	−	0.446217i	0.0216958	−	0.0375783i
$142$	4.29380			0.360327
$143$	−10.9731			−0.917618
$144$	1.41421	+	2.44949i	0.117851	+	0.204124i
$145$	5.15749	−	8.93304i	0.428306	−	0.741848i
$146$	4.47532	−	7.75149i	0.370381	−	0.641518i
$147$	−1.03553	−	1.79360i	−0.0854094	−	0.147933i
$148$	5.70801			0.469195
$149$	14.1721			1.16102			0.580512	−	0.814252i	$-0.302852\pi$
$149$	14.1721			1.16102			0.580512	+	0.814252i	$0.302852\pi$
$150$	0.207107	+	0.358719i	0.0169102	+	0.0292893i
$151$	9.80503	+	16.9828i	0.797922	+	1.38204i	0.920967	+	0.389640i	$0.127401\pi$
$151$	9.80503	+	16.9828i	0.797922	+	1.38204i	−0.123045	+	0.992401i	$0.539266\pi$
$152$	−0.939791	−	1.62777i	−0.0762271	−	0.132029i
$153$	−7.48656	−	12.9671i	−0.605252	−	1.04833i
$154$	1.41421	−	2.44949i	0.113961	−	0.197386i
$155$	3.06175	−	5.30311i	0.245926	−	0.425956i
$156$	−2.27261			−0.181954
$157$	5.38022	+	9.31881i	0.429388	+	0.743722i	0.996819	−	0.0796988i	$-0.0253959\pi$
$157$	5.38022	+	9.31881i	0.429388	+	0.743722i	−0.567431	+	0.823421i	$0.692063\pi$
$158$	−11.4160			−0.908210
$159$	4.29380			0.340520
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	12.9731			1.02242
$162$	−3.74264	−	6.48244i	−0.294050	−	0.509309i
$163$	7.91512	−	13.7094i	0.619960	−	1.07380i	−0.369533	−	0.929218i	$-0.620482\pi$
$163$	7.91512	−	13.7094i	0.619960	−	1.07380i	0.989493	−	0.144584i	$-0.0461844\pi$
$164$	−2.38864	−	4.13724i	−0.186521	−	0.323064i
$165$	−0.414214	+	0.717439i	−0.0322465	+	0.0558525i
$166$	−2.64754	+	4.58567i	−0.205489	+	0.355917i
$167$	0.570804	−	0.988661i	0.0441701	−	0.0765049i	−0.843095	−	0.537764i	$-0.819269\pi$
$167$	0.570804	−	0.988661i	0.0441701	−	0.0765049i	0.887265	+	0.461260i	$0.152602\pi$
$168$	0.292893	−	0.507306i	0.0225972	−	0.0391395i
$169$	−8.55115	+	14.8110i	−0.657781	+	1.13931i
$170$	2.64690	−	4.58456i	0.203008	−	0.351620i
$171$	2.65813	+	4.60402i	0.203272	+	0.352078i
$172$	2.26886	−	3.92977i	0.172999	−	0.299642i
$173$	3.71770	+	6.43925i	0.282652	+	0.489567i	0.972037	−	0.234828i	$-0.0754526\pi$
$173$	3.71770	+	6.43925i	0.282652	+	0.489567i	−0.689385	+	0.724395i	$0.742119\pi$
$174$	4.27261			0.323905
$175$	−0.707107	+	1.22474i	−0.0534522	+	0.0925820i
$176$	−2.00000			−0.150756
$177$	1.60698			0.120788
$178$	−0.379582	−	0.657455i	−0.0284509	−	0.0492783i
$179$	−20.7622			−1.55184			−0.775921	−	0.630830i	$-0.782715\pi$
$179$	−20.7622			−1.55184			−0.775921	+	0.630830i	$0.782715\pi$
$180$	1.41421	−	2.44949i	0.105409	−	0.182574i
$181$	7.90167	−	13.6861i	0.587327	−	1.01728i	−0.407254	−	0.913315i	$-0.633514\pi$
$181$	7.90167	−	13.6861i	0.587327	−	1.01728i	0.994581	−	0.103965i	$-0.0331530\pi$
$182$	−3.87958	−	6.71963i	−0.287574	−	0.498092i
$183$	0.328163	+	0.568395i	0.0242585	+	0.0420170i
$184$	−4.58669	−	7.94438i	−0.338135	−	0.585667i
$185$	−2.85400	−	4.94328i	−0.209831	−	0.363437i
$186$	2.53644			0.185981
$187$	10.5876			0.774241
$188$	−0.621958	−	1.07726i	−0.0453610	−	0.0785675i
$189$	−1.70711	+	2.95680i	−0.124174	+	0.215075i
$190$	−0.939791	+	1.62777i	−0.0681796	+	0.118091i
$191$	2.48877	+	4.31067i	0.180081	+	0.311909i	0.941908	−	0.335871i	$-0.109031\pi$
$191$	2.48877	+	4.31067i	0.180081	+	0.311909i	−0.761827	+	0.647781i	$0.775697\pi$
$192$	−0.414214			−0.0298933
$193$	−17.6269			−1.26881			−0.634406	−	0.773000i	$-0.718755\pi$
$193$	−17.6269			−1.26881			−0.634406	+	0.773000i	$0.718755\pi$
$194$	−0.145358	+	0.251767i	−0.0104361	+	0.0180758i
$195$	1.13630	+	1.96813i	0.0813724	+	0.140941i
$196$	−5.00000			−0.357143
$197$	−8.48528	+	14.6969i	−0.604551	+	1.04711i	0.387571	+	0.921840i	$0.373314\pi$
$197$	−8.48528	+	14.6969i	−0.604551	+	1.04711i	−0.992122	+	0.125274i	$0.960019\pi$
$198$	5.65685			0.402015
$199$	−6.33838	−	10.9784i	−0.449316	−	0.778238i	0.549026	−	0.835806i	$-0.314999\pi$
$199$	−6.33838	−	10.9784i	−0.449316	−	0.778238i	−0.998342	+	0.0575673i	$0.981666\pi$
$200$	1.00000			0.0707107
$201$	1.92507	+	2.79096i	0.135784	+	0.196859i
$202$	−3.31190			−0.233025
$203$	7.29380	+	12.6332i	0.511924	+	0.886679i
$204$	2.19276			0.153524
$205$	−2.38864	+	4.13724i	−0.166830	+	0.288957i
$206$	5.68682			0.396220
$207$	12.9731	+	22.4701i	0.901694	+	1.56178i
$208$	−2.74328	+	4.75150i	−0.190212	+	0.329457i
$209$	−3.75916			−0.260027
$210$	−0.585786			−0.0404231
$211$	−2.45944	−	4.25987i	−0.169315	−	0.293262i	0.768864	−	0.639412i	$-0.220822\pi$
$211$	−2.45944	−	4.25987i	−0.169315	−	0.293262i	−0.938179	+	0.346150i	$0.887489\pi$
$212$	5.18307	−	8.97734i	0.355975	−	0.616566i
$213$	0.889274	−	1.54027i	0.0609321	−	0.105537i
$214$	9.30439	+	16.1157i	0.636035	+	1.10164i
$215$	−4.53771			−0.309469
$216$	2.41421			0.164266
$217$	4.32997	+	7.49972i	0.293937	+	0.509114i
$218$	−6.07325	−	10.5192i	−0.411332	−	0.712448i
$219$	−1.85374	−	3.21077i	−0.125264	−	0.216964i
$220$	1.00000	+	1.73205i	0.0674200	+	0.116775i
$221$	14.5224	−	25.1535i	0.976879	−	1.69200i
$222$	1.18217	−	2.04757i	0.0793419	−	0.137424i
$223$	−10.0318			−0.671777			−0.335889	−	0.941902i	$-0.609037\pi$
$223$	−10.0318			−0.671777			−0.335889	+	0.941902i	$0.609037\pi$
$224$	−0.707107	−	1.22474i	−0.0472456	−	0.0818317i
$225$	−2.82843			−0.188562
$226$	0.435403			0.0289625
$227$	11.2071	−	19.4113i	0.743842	−	1.28837i	−0.206892	−	0.978364i	$-0.566335\pi$
$227$	11.2071	−	19.4113i	0.743842	−	1.28837i	0.950734	−	0.310008i	$-0.100332\pi$
$228$	−0.778548			−0.0515606
$229$	10.1597	+	17.5971i	0.671370	+	1.16285i	0.977516	+	0.210862i	$0.0676271\pi$
$229$	10.1597	+	17.5971i	0.671370	+	1.16285i	−0.306146	+	0.951985i	$0.599040\pi$
$230$	−4.58669	+	7.94438i	−0.302437	+	0.523837i
$231$	−0.585786	−	1.01461i	−0.0385419	−	0.0667566i
$232$	5.15749	−	8.93304i	0.338606	−	0.586483i
$233$	8.23268	−	14.2594i	0.539341	−	0.934166i	−0.459599	−	0.888127i	$-0.652007\pi$
$233$	8.23268	−	14.2594i	0.539341	−	0.934166i	0.998940	−	0.0460394i	$-0.0146600\pi$
$234$	7.75916	−	13.4393i	0.507232	−	0.878552i
$235$	−0.621958	+	1.07726i	−0.0405721	+	0.0702729i
$236$	1.93979	−	3.35982i	0.126270	−	0.218705i
$237$	−2.36433	+	4.09515i	−0.153580	+	0.266008i
$238$	3.74328	+	6.48355i	0.242641	+	0.420266i
$239$	1.80724	−	3.13023i	0.116901	−	0.202478i	−0.801637	−	0.597811i	$-0.796037\pi$
$239$	1.80724	−	3.13023i	0.116901	−	0.202478i	0.918538	+	0.395333i	$0.129371\pi$
$240$	0.207107	+	0.358719i	0.0133687	+	0.0231552i
$241$	−25.1240			−1.61838			−0.809190	−	0.587546i	$-0.800094\pi$
$241$	−25.1240			−1.61838			−0.809190	+	0.587546i	$0.800094\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	−10.3431			−0.663513
$244$	1.58451			0.101438
$245$	2.50000	+	4.33013i	0.159719	+	0.276642i
$246$	−1.97881			−0.126164
$247$	−5.15622	+	8.93083i	−0.328082	+	0.568255i
$248$	3.06175	−	5.30311i	0.194421	−	0.336748i
$249$	1.09665	+	1.89945i	0.0694971	+	0.120372i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−0.784477	−	1.35875i	−0.0495157	−	0.0857638i	0.840205	−	0.542269i	$-0.182434\pi$
$251$	−0.784477	−	1.35875i	−0.0495157	−	0.0857638i	−0.889721	+	0.456505i	$0.849101\pi$
$252$	2.00000	+	3.46410i	0.125988	+	0.218218i
$253$	−18.3468			−1.15345
$254$	−0.930736			−0.0583996
$255$	−1.09638	−	1.89899i	−0.0686580	−	0.118919i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−11.4385	+	19.8120i	−0.713513	+	1.23584i	0.250017	+	0.968241i	$0.419564\pi$
$257$	−11.4385	+	19.8120i	−0.713513	+	1.23584i	−0.963530	+	0.267599i	$0.913770\pi$
$258$	−0.939791	−	1.62777i	−0.0585088	−	0.101340i
$259$	8.07234			0.501591
$260$	5.48656			0.340262
$261$	−14.5876	+	25.2664i	−0.902949	+	1.56395i
$262$	5.20647	+	9.01787i	0.321657	+	0.557126i
$263$	13.5863			0.837768			0.418884	−	0.908040i	$-0.362421\pi$
$263$	13.5863			0.837768			0.418884	+	0.908040i	$0.362421\pi$
$264$	−0.414214	+	0.717439i	−0.0254931	+	0.0441553i
$265$	−10.3661			−0.636787
$266$	−1.32907	−	2.30201i	−0.0814902	−	0.141145i
$267$	−0.314456			−0.0192444
$268$	8.15903	−	0.655892i	0.498392	−	0.0400650i
$269$	−19.2457			−1.17343			−0.586716	−	0.809793i	$-0.699580\pi$
$269$	−19.2457			−1.17343			−0.586716	+	0.809793i	$0.699580\pi$
$270$	−1.20711	−	2.09077i	−0.0734622	−	0.127240i
$271$	−7.26691			−0.441433			−0.220717	−	0.975338i	$-0.570840\pi$
$271$	−7.26691			−0.441433			−0.220717	+	0.975338i	$0.570840\pi$
$272$	2.64690	−	4.58456i	0.160492	−	0.277980i
$273$	−3.21395			−0.194517
$274$	−10.9619	−	18.9865i	−0.662232	−	1.14702i
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$	−3.79974			−0.228717
$277$	15.0217			0.902568			0.451284	−	0.892381i	$-0.350966\pi$
$277$	15.0217			0.902568			0.451284	+	0.892381i	$0.350966\pi$
$278$	−9.78941	−	16.9558i	−0.587130	−	1.01694i
$279$	−8.65993	+	14.9994i	−0.518457	+	0.897993i
$280$	−0.707107	+	1.22474i	−0.0422577	+	0.0731925i
$281$	−3.15685	−	5.46783i	−0.188322	−	0.326184i	0.756369	−	0.654145i	$-0.226972\pi$
$281$	−3.15685	−	5.46783i	−0.188322	−	0.326184i	−0.944691	+	0.327962i	$0.893638\pi$
$282$	−0.515247			−0.0306825
$283$	23.0230			1.36857			0.684287	−	0.729212i	$-0.260113\pi$
$283$	23.0230			1.36857			0.684287	+	0.729212i	$0.260113\pi$
$284$	−2.14690	−	3.71854i	−0.127395	−	0.220655i
$285$	0.389274	+	0.674243i	0.0230586	+	0.0399387i
$286$	5.48656	+	9.50300i	0.324427	+	0.561924i
$287$	−3.37804	−	5.85094i	−0.199400	−	0.345370i
$288$	1.41421	−	2.44949i	0.0833333	−	0.144338i
$289$	−5.51213	+	9.54730i	−0.324243	+	0.561606i
$290$	−10.3150			−0.605717
$291$	0.0602091	+	0.104285i	0.00352952	+	0.00611331i
$292$	−8.95065			−0.523797
$293$	−26.2674			−1.53456			−0.767280	−	0.641312i	$-0.778390\pi$
$293$	−26.2674			−1.53456			−0.767280	+	0.641312i	$0.778390\pi$
$294$	−1.03553	+	1.79360i	−0.0603936	+	0.104605i
$295$	−3.87958			−0.225878
$296$	−2.85400	−	4.94328i	−0.165886	−	0.287322i
$297$	2.41421	−	4.18154i	0.140087	−	0.242638i
$298$	−7.08605	−	12.2734i	−0.410484	−	0.710979i
$299$	−25.1651	+	43.5873i	−1.45534	+	2.52072i
$300$	0.207107	−	0.358719i	0.0119573	−	0.0207107i
$301$	3.20865	−	5.55754i	0.184943	−	0.320331i
$302$	9.80503	−	16.9828i	0.564216	−	0.977251i
$303$	−0.685918	+	1.18804i	−0.0394050	+	0.0682514i
$304$	−0.939791	+	1.62777i	−0.0539007	+	0.0933588i
$305$	−0.792255	−	1.37223i	−0.0453644	−	0.0785735i
$306$	−7.48656	+	12.9671i	−0.427978	+	0.741280i
$307$	−6.79597	−	11.7710i	−0.387867	−	0.671805i	0.604296	−	0.796760i	$-0.293455\pi$
$307$	−6.79597	−	11.7710i	−0.387867	−	0.671805i	−0.992162	+	0.124955i	$0.960121\pi$
$308$	−2.82843			−0.161165
$309$	1.17778	−	2.03997i	0.0670015	−	0.116050i
$310$	−6.12350			−0.347791
$311$	11.7124			0.664147			0.332074	−	0.943253i	$-0.392252\pi$
$311$	11.7124			0.664147			0.332074	+	0.943253i	$0.392252\pi$
$312$	1.13630	+	1.96813i	0.0643305	+	0.111424i
$313$	34.0959			1.92721			0.963606	−	0.267326i	$-0.0861401\pi$
$313$	34.0959			1.92721			0.963606	+	0.267326i	$0.0861401\pi$
$314$	5.38022	−	9.31881i	0.303623	−	0.525891i
$315$	2.00000	−	3.46410i	0.112687	−	0.195180i
$316$	5.70801	+	9.88656i	0.321101	+	0.556163i
$317$	−6.87519	−	11.9082i	−0.386149	−	0.668830i	0.605779	−	0.795633i	$-0.292862\pi$
$317$	−6.87519	−	11.9082i	−0.386149	−	0.668830i	−0.991928	+	0.126803i	$0.959528\pi$
$318$	−2.14690	−	3.71854i	−0.120392	−	0.208525i
$319$	−10.3150	−	17.8661i	−0.577528	−	1.00031i
$320$	1.00000			0.0559017
$321$	7.70801			0.430219
$322$	−6.48656	−	11.2350i	−0.361482	−	0.626105i
$323$	4.97506	−	8.61706i	0.276820	−	0.479466i
$324$	−3.74264	+	6.48244i	−0.207924	+	0.360136i
$325$	−2.74328	−	4.75150i	−0.152170	−	0.263566i
$326$	−15.8302			−0.876755
$327$	−5.03124			−0.278228
$328$	−2.38864	+	4.13724i	−0.131890	+	0.228441i
$329$	−0.879582	−	1.52348i	−0.0484929	−	0.0839922i
$330$	0.828427			0.0456034
$331$	−3.25478	+	5.63744i	−0.178899	+	0.309862i	−0.941504	−	0.337003i	$-0.890587\pi$
$331$	−3.25478	+	5.63744i	−0.178899	+	0.309862i	0.762605	+	0.646865i	$0.223920\pi$
$332$	5.29507			0.290605
$333$	8.07234	+	13.9817i	0.442362	+	0.766193i
$334$	−1.14161			−0.0624660
$335$	−4.64754	−	6.73798i	−0.253922	−	0.368135i
$336$	−0.585786			−0.0319573
$337$	−4.10852	−	7.11616i	−0.223805	−	0.387642i	0.732155	−	0.681138i	$-0.238515\pi$
$337$	−4.10852	−	7.11616i	−0.223805	−	0.387642i	−0.955960	+	0.293496i	$0.905181\pi$
$338$	17.1023			0.930243
$339$	0.0901748	−	0.156187i	0.00489762	−	0.00848293i
$340$	−5.29380			−0.287096
$341$	−6.12350	−	10.6062i	−0.331606	−	0.574358i
$342$	2.65813	−	4.60402i	0.143735	−	0.248957i
$343$	−16.9706			−0.916324
$344$	−4.53771			−0.244657
$345$	1.89987	+	3.29067i	0.102285	+	0.177164i
$346$	3.71770	−	6.43925i	0.199865	−	0.346176i
$347$	−12.4634	+	21.5873i	−0.669072	+	1.15887i	0.309093	+	0.951032i	$0.399975\pi$
$347$	−12.4634	+	21.5873i	−0.669072	+	1.15887i	−0.978164	+	0.207834i	$0.933359\pi$
$348$	−2.13630	−	3.70019i	−0.114518	−	0.198351i
$349$	34.0778			1.82414			0.912070	−	0.410034i	$-0.134483\pi$
$349$	34.0778			1.82414			0.912070	+	0.410034i	$0.134483\pi$
$350$	1.41421			0.0755929
$351$	−6.62286	−	11.4711i	−0.353502	−	0.612284i
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	3.98374	+	6.90004i	0.212033	+	0.367252i	0.952351	−	0.305005i	$-0.0986582\pi$
$353$	3.98374	+	6.90004i	0.212033	+	0.367252i	−0.740318	+	0.672257i	$0.765325\pi$
$354$	−0.803488	−	1.39168i	−0.0427049	−	0.0739670i
$355$	−2.14690	+	3.71854i	−0.113945	+	0.197359i
$356$	−0.379582	+	0.657455i	−0.0201178	+	0.0348450i
$357$	3.10103			0.164124
$358$	10.3811	+	17.9806i	0.548659	+	0.950306i
$359$	−33.8263			−1.78529			−0.892643	−	0.450764i	$-0.851151\pi$
$359$	−33.8263			−1.78529			−0.892643	+	0.450764i	$0.851151\pi$
$360$	−2.82843			−0.149071
$361$	7.73359	−	13.3950i	0.407031	−	0.704998i
$362$	−15.8033			−0.830605
$363$	−1.44975	−	2.51104i	−0.0760920	−	0.131795i
$364$	−3.87958	+	6.71963i	−0.203345	+	0.352204i
$365$	4.47532	+	7.75149i	0.234249	+	0.405732i
$366$	0.328163	−	0.568395i	0.0171533	−	0.0297105i
$367$	−0.363961	+	0.630399i	−0.0189986	+	0.0329066i	−0.875368	−	0.483456i	$-0.839381\pi$
$367$	−0.363961	+	0.630399i	−0.0189986	+	0.0329066i	0.856370	+	0.516363i	$0.172714\pi$
$368$	−4.58669	+	7.94438i	−0.239098	+	0.414129i
$369$	6.75608	−	11.7019i	0.351708	−	0.609176i
$370$	−2.85400	+	4.94328i	−0.148373	+	0.256989i
$371$	7.32997	−	12.6959i	0.380553	−	0.659137i
$372$	−1.26822	−	2.19662i	−0.0657540	−	0.113889i
$373$	2.56021	−	4.43441i	0.132563	−	0.229605i	−0.792101	−	0.610390i	$-0.791013\pi$
$373$	2.56021	−	4.43441i	0.132563	−	0.229605i	0.924664	+	0.380785i	$0.124346\pi$
$374$	−5.29380	−	9.16912i	−0.273736	−	0.474124i
$375$	−0.414214			−0.0213899
$376$	−0.621958	+	1.07726i	−0.0320750	+	0.0555556i
$377$	−56.5938			−2.91473
$378$	3.41421			0.175608
$379$	1.99872	+	3.46189i	0.102668	+	0.177825i	0.912783	−	0.408445i	$-0.133929\pi$
$379$	1.99872	+	3.46189i	0.102668	+	0.177825i	−0.810115	+	0.586271i	$0.800596\pi$
$380$	1.87958			0.0964205
$381$	−0.192762	+	0.333873i	−0.00987549	+	0.0171048i
$382$	2.48877	−	4.31067i	0.127336	−	0.220553i
$383$	−0.141607	−	0.245271i	−0.00723579	−	0.0125328i	0.862385	−	0.506253i	$-0.168970\pi$
$383$	−0.141607	−	0.245271i	−0.00723579	−	0.0125328i	−0.869621	+	0.493721i	$0.835637\pi$
$384$	0.207107	+	0.358719i	0.0105689	+	0.0183058i
$385$	1.41421	+	2.44949i	0.0720750	+	0.124838i
$386$	8.81344	+	15.2653i	0.448593	+	0.776985i
$387$	12.8346			0.652419
$388$	0.290715			0.0147588
$389$	−7.42920	−	12.8677i	−0.376675	−	0.652421i	0.613901	−	0.789383i	$-0.289599\pi$
$389$	−7.42920	−	12.8677i	−0.376675	−	0.652421i	−0.990576	+	0.136962i	$0.956266\pi$
$390$	1.13630	−	1.96813i	0.0575389	−	0.0996604i
$391$	24.2810	−	42.0559i	1.22794	−	2.12686i
$392$	2.50000	+	4.33013i	0.126269	+	0.218704i
$393$	4.31318			0.217571
$394$	16.9706			0.854965
$395$	5.70801	−	9.88656i	0.287201	−	0.497447i
$396$	−2.82843	−	4.89898i	−0.142134	−	0.246183i
$397$	−3.15219			−0.158204			−0.0791019	−	0.996867i	$-0.525205\pi$
$397$	−3.15219			−0.158204			−0.0791019	+	0.996867i	$0.525205\pi$
$398$	−6.33838	+	10.9784i	−0.317714	+	0.550298i
$399$	−1.10103			−0.0551206
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	21.3163			1.06448			0.532242	−	0.846593i	$-0.321350\pi$
$401$	21.3163			1.06448			0.532242	+	0.846593i	$0.321350\pi$
$402$	1.45451	−	3.06264i	0.0725443	−	0.152751i
$403$	−33.5969			−1.67358
$404$	1.65595	+	2.86819i	0.0823867	+	0.142698i
$405$	7.48528			0.371947
$406$	7.29380	−	12.6332i	0.361985	−	0.626976i
$407$	−11.4160			−0.565871
$408$	−1.09638	−	1.89899i	−0.0542789	−	0.0940139i
$409$	−8.90516	+	15.4242i	−0.440332	+	0.762677i	−0.997714	−	0.0675791i	$-0.978473\pi$
$409$	−8.90516	+	15.4242i	−0.440332	+	0.762677i	0.557382	+	0.830256i	$0.311806\pi$
$410$	4.77727			0.235933
$411$	−9.08112			−0.447939
$412$	−2.84341	−	4.92493i	−0.140085	−	0.242634i
$413$	2.74328	−	4.75150i	0.134988	−	0.233806i
$414$	12.9731	−	22.4701i	0.637594	−	1.10434i
$415$	−2.64754	−	4.58567i	−0.129962	−	0.225101i
$416$	5.48656			0.269001
$417$	−8.10981			−0.397139
$418$	1.87958	+	3.25553i	0.0919333	+	0.159233i
$419$	−15.3271	−	26.5473i	−0.748779	−	1.29692i	−0.948408	−	0.317051i	$-0.897307\pi$
$419$	−15.3271	−	26.5473i	−0.748779	−	1.29692i	0.199630	−	0.979871i	$-0.436026\pi$
$420$	0.292893	+	0.507306i	0.0142917	+	0.0247540i
$421$	10.2426	+	17.7408i	0.499196	+	0.864632i	1.00000		0.000928405i	$-0.000295520\pi$
$421$	10.2426	+	17.7408i	0.499196	+	0.864632i	−0.500804	+	0.865561i	$0.666962\pi$
$422$	−2.45944	+	4.25987i	−0.119724	+	0.207367i
$423$	1.75916	−	3.04696i	0.0855335	−	0.148148i
$424$	−10.3661			−0.503424
$425$	2.64690	+	4.58456i	0.128393	+	0.222384i
$426$	−1.77855			−0.0861709
$427$	2.24084			0.108442
$428$	9.30439	−	16.1157i	0.449745	−	0.778981i
$429$	4.54521			0.219445
$430$	2.26886	+	3.92977i	0.109414	+	0.189511i
$431$	1.85310	−	3.20967i	0.0892608	−	0.154604i	−0.817938	−	0.575306i	$-0.804883\pi$
$431$	1.85310	−	3.20967i	0.0892608	−	0.154604i	0.907199	+	0.420702i	$0.138216\pi$
$432$	−1.20711	−	2.09077i	−0.0580770	−	0.100592i
$433$	9.52648	−	16.5003i	0.457813	−	0.792956i	−0.541032	−	0.841002i	$-0.681966\pi$
$433$	9.52648	−	16.5003i	0.457813	−	0.792956i	0.998845	+	0.0480461i	$0.0152995\pi$
$434$	4.32997	−	7.49972i	0.207845	−	0.359998i
$435$	−2.13630	+	3.70019i	−0.102428	+	0.177410i
$436$	−6.07325	+	10.5192i	−0.290856	+	0.503777i
$437$	−8.62106	+	14.9321i	−0.412401	+	0.714300i
$438$	−1.85374	+	3.21077i	−0.0885751	+	0.153417i
$439$	3.97532	+	6.88546i	0.189732	+	0.328625i	0.945161	−	0.326605i	$-0.105905\pi$
$439$	3.97532	+	6.88546i	0.189732	+	0.328625i	−0.755429	+	0.655231i	$0.772571\pi$
$440$	1.00000	−	1.73205i	0.0476731	−	0.0825723i
$441$	−7.07107	−	12.2474i	−0.336718	−	0.583212i
$442$	−29.0447			−1.38152
$443$	−11.5009	+	19.9201i	−0.546424	+	0.946435i	0.452091	+	0.891972i	$0.350678\pi$
$443$	−11.5009	+	19.9201i	−0.546424	+	0.946435i	−0.998516	+	0.0544631i	$0.982655\pi$
$444$	−2.36433			−0.112206
$445$	0.759164			0.0359878
$446$	5.01588	+	8.68777i	0.237509	+	0.411378i
$447$	−5.87028			−0.277655
$448$	−0.707107	+	1.22474i	−0.0334077	+	0.0578638i
$449$	5.94446	−	10.2961i	0.280536	−	0.485903i	−0.690981	−	0.722873i	$-0.742821\pi$
$449$	5.94446	−	10.2961i	0.280536	−	0.485903i	0.971517	+	0.236970i	$0.0761544\pi$
$450$	1.41421	+	2.44949i	0.0666667	+	0.115470i
$451$	4.77727	+	8.27448i	0.224953	+	0.389630i
$452$	−0.217701	−	0.377070i	−0.0102398	−	0.0177359i
$453$	−4.06138	−	7.03451i	−0.190820	−	0.330510i
$454$	−22.4142			−1.05195
$455$	7.75916			0.363755
$456$	0.389274	+	0.674243i	0.0182294	+	0.0315743i
$457$	3.52340	−	6.10271i	0.164818	−	0.285473i	−0.771773	−	0.635898i	$-0.780630\pi$
$457$	3.52340	−	6.10271i	0.164818	−	0.285473i	0.936591	+	0.350426i	$0.113963\pi$
$458$	10.1597	−	17.5971i	0.474730	−	0.822257i
$459$	6.39018	+	11.0681i	0.298268	+	0.516615i
$460$	9.17338			0.427711
$461$	−31.9419			−1.48768			−0.743841	−	0.668357i	$-0.766998\pi$
$461$	−31.9419			−1.48768			−0.743841	+	0.668357i	$0.766998\pi$
$462$	−0.585786	+	1.01461i	−0.0272533	+	0.0472040i
$463$	11.8999	+	20.6112i	0.553034	+	0.957883i	0.998054	+	0.0623619i	$0.0198633\pi$
$463$	11.8999	+	20.6112i	0.553034	+	0.957883i	−0.445020	+	0.895521i	$0.646803\pi$
$464$	−10.3150			−0.478861
$465$	−1.26822	+	2.19662i	−0.0588122	+	0.101866i
$466$	−16.4654			−0.762743
$467$	16.6693	+	28.8720i	0.771361	+	1.33604i	0.936817	+	0.349819i	$0.113757\pi$
$467$	16.6693	+	28.8720i	0.771361	+	1.33604i	−0.165456	+	0.986217i	$0.552910\pi$
$468$	−15.5183			−0.717335
$469$	11.5386	−	0.927572i	0.532804	−	0.0428313i
$470$	1.24392			0.0573776
$471$	−2.22856	−	3.85998i	−0.102687	−	0.177858i
$472$	−3.87958			−0.178572
$473$	−4.53771	+	7.85955i	−0.208644	+	0.361382i
$474$	4.72867			0.217195
$475$	−0.939791	−	1.62777i	−0.0431206	−	0.0746870i
$476$	3.74328	−	6.48355i	0.171573	−	0.297173i
$477$	29.3199			1.34246
$478$	−3.61448			−0.165322
$479$	−7.33087	−	12.6974i	−0.334956	−	0.580161i	0.648520	−	0.761197i	$-0.275388\pi$
$479$	−7.33087	−	12.6974i	−0.334956	−	0.580161i	−0.983476	+	0.181037i	$0.942055\pi$
$480$	0.207107	−	0.358719i	0.00945309	−	0.0163732i
$481$	−15.6587	+	27.1216i	−0.713973	+	1.23664i
$482$	12.5620	+	21.7580i	0.572184	+	0.991052i
$483$	−5.37364			−0.244509
$484$	−7.00000			−0.318182
$485$	−0.145358	−	0.251767i	−0.00660035	−	0.0114321i
$486$	5.17157	+	8.95743i	0.234587	+	0.406317i
$487$	−5.12132	−	8.87039i	−0.232069	−	0.401956i	0.726348	−	0.687327i	$-0.241216\pi$
$487$	−5.12132	−	8.87039i	−0.232069	−	0.401956i	−0.958417	+	0.285372i	$0.907883\pi$
$488$	−0.792255	−	1.37223i	−0.0358637	−	0.0621178i
$489$	−3.27855	+	5.67861i	−0.148261	+	0.256796i
$490$	2.50000	−	4.33013i	0.112938	−	0.195615i
$491$	26.1540			1.18031			0.590157	−	0.807289i	$-0.299066\pi$
$491$	26.1540			1.18031			0.590157	+	0.807289i	$0.299066\pi$
$492$	0.989406	+	1.71370i	0.0446058	+	0.0772596i
$493$	54.6054			2.45930
$494$	10.3124			0.463978
$495$	−2.82843	+	4.89898i	−0.127128	+	0.220193i
$496$	−6.12350			−0.274953
$497$	−3.03617	−	5.25880i	−0.136191	−	0.235890i
$498$	1.09665	−	1.89945i	0.0491418	−	0.0851162i
$499$	−15.9927	−	27.7003i	−0.715934	−	1.24003i	−0.962598	−	0.270933i	$-0.912668\pi$
$499$	−15.9927	−	27.7003i	−0.715934	−	1.24003i	0.246664	−	0.969101i	$-0.420665\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−0.236435	+	0.409517i	−0.0105631	+	0.0182959i
$502$	−0.784477	+	1.35875i	−0.0350129	+	0.0606441i
$503$	22.3508	−	38.7127i	0.996572	−	1.72611i	0.426641	−	0.904421i	$-0.359697\pi$
$503$	22.3508	−	38.7127i	0.996572	−	1.72611i	0.569931	−	0.821693i	$-0.306970\pi$
$504$	2.00000	−	3.46410i	0.0890871	−	0.154303i
$505$	1.65595	−	2.86819i	0.0736889	−	0.127633i
$506$	9.17338	+	15.8888i	0.407806	+	0.706341i
$507$	3.54200	−	6.13493i	0.157306	−	0.272462i
$508$	0.465368	+	0.806041i	0.0206474	+	0.0357623i
$509$	36.8788			1.63462			0.817311	−	0.576196i	$-0.195464\pi$
$509$	36.8788			1.63462			0.817311	+	0.576196i	$0.195464\pi$
$510$	−1.09638	+	1.89899i	−0.0485486	+	0.0840886i
$511$	−12.6581			−0.559963
$512$	1.00000			0.0441942
$513$	−2.26886	−	3.92977i	−0.100172	−	0.173504i
$514$	22.8770			1.00906
$515$	−2.84341	+	4.92493i	−0.125296	+	0.217018i
$516$	−0.939791	+	1.62777i	−0.0413720	+	0.0716584i
$517$	1.24392	+	2.15453i	0.0547074	+	0.0947560i
$518$	−4.03617	−	6.99085i	−0.177339	−	0.307161i
$519$	−1.53992	−	2.66722i	−0.0675951	−	0.117078i
$520$	−2.74328	−	4.75150i	−0.120301	−	0.208367i
$521$	−11.9220			−0.522311			−0.261155	−	0.965297i	$-0.584103\pi$
$521$	−11.9220			−0.522311			−0.261155	+	0.965297i	$0.584103\pi$
$522$	29.1752			1.27696
$523$	11.4740	+	19.8736i	0.501724	+	0.869011i	0.999998	+	0.00199151i	$0.000633917\pi$
$523$	11.4740	+	19.8736i	0.501724	+	0.869011i	−0.498274	+	0.867019i	$0.666033\pi$
$524$	5.20647	−	9.01787i	0.227446	−	0.393947i
$525$	0.292893	−	0.507306i	0.0127829	−	0.0221406i
$526$	−6.79316	−	11.7661i	−0.296196	−	0.513026i
$527$	32.4165			1.41209
$528$	0.828427			0.0360527
$529$	−30.5754	+	52.9582i	−1.32937	+	2.30253i
$530$	5.18307	+	8.97734i	0.225138	+	0.389951i
$531$	10.9731			0.476193
$532$	−1.32907	+	2.30201i	−0.0576223	+	0.0998047i
$533$	26.2108			1.13531
$534$	0.157228	+	0.272327i	0.00680392	+	0.0117847i
$535$	−18.6088			−0.804528
$536$	−4.64754	−	6.73798i	−0.200743	−	0.291037i
$537$	8.60000			0.371118
$538$	9.62286	+	16.6673i	0.414871	+	0.718578i
$539$	10.0000			0.430730
$540$	−1.20711	+	2.09077i	−0.0519456	+	0.0899724i
$541$	−19.0447			−0.818796			−0.409398	−	0.912356i	$-0.634261\pi$
$541$	−19.0447			−0.818796			−0.409398	+	0.912356i	$0.634261\pi$
$542$	3.63345	+	6.29333i	0.156070	+	0.270322i
$543$	−3.27298	+	5.66897i	−0.140457	+	0.243279i
$544$	−5.29380			−0.226970
$545$	12.1465			0.520299
$546$	1.60698	+	2.78336i	0.0687722	+	0.119117i
$547$	13.8902	−	24.0585i	0.593901	−	1.02867i	−0.399800	−	0.916602i	$-0.630920\pi$
$547$	13.8902	−	24.0585i	0.593901	−	1.02867i	0.993701	−	0.112064i	$-0.0357463\pi$
$548$	−10.9619	+	18.9865i	−0.468268	+	0.811065i
$549$	2.24084	+	3.88124i	0.0956366	+	0.165647i
$550$	−2.00000			−0.0852803
$551$	−19.3879			−0.825950
$552$	1.89987	+	3.29067i	0.0808638	+	0.140060i
$553$	8.07234	+	13.9817i	0.343271	+	0.594563i
$554$	−7.51086	−	13.0092i	−0.319106	−	0.552707i
$555$	1.18217	+	2.04757i	0.0501802	+	0.0869147i
$556$	−9.78941	+	16.9558i	−0.415163	+	0.719084i
$557$	1.04677	−	1.81305i	0.0443529	−	0.0768215i	−0.842997	−	0.537919i	$-0.819211\pi$
$557$	1.04677	−	1.81305i	0.0443529	−	0.0768215i	0.887350	+	0.461097i	$0.152544\pi$
$558$	17.3199			0.733208
$559$	12.4482	+	21.5609i	0.526503	+	0.911930i
$560$	1.41421			0.0597614
$561$	−4.38552			−0.185157
$562$	−3.15685	+	5.46783i	−0.133164	+	0.230647i
$563$	−12.7124			−0.535765			−0.267883	−	0.963452i	$-0.586324\pi$
$563$	−12.7124			−0.535765			−0.267883	+	0.963452i	$0.586324\pi$
$564$	0.257624	+	0.446217i	0.0108479	+	0.0187891i
$565$	−0.217701	+	0.377070i	−0.00915876	+	0.0158634i
$566$	−11.5115	−	19.9385i	−0.483864	−	0.838078i
$567$	−5.29289	+	9.16756i	−0.222281	+	0.385001i
$568$	−2.14690	+	3.71854i	−0.0900818	+	0.156026i
$569$	−11.0589	+	19.1546i	−0.463613	+	0.803002i	−0.999138	−	0.0415180i	$-0.986781\pi$
$569$	−11.0589	+	19.1546i	−0.463613	+	0.803002i	0.535525	+	0.844520i	$0.320114\pi$
$570$	0.389274	−	0.674243i	0.0163049	−	0.0282409i
$571$	6.30593	−	10.9222i	0.263895	−	0.457079i	−0.703379	−	0.710815i	$-0.748326\pi$
$571$	6.30593	−	10.9222i	0.263895	−	0.457079i	0.967274	+	0.253736i	$0.0816594\pi$
$572$	5.48656	−	9.50300i	0.229404	−	0.397340i
$573$	−1.03088	−	1.78554i	−0.0430657	−	0.0745920i
$574$	−3.37804	+	5.85094i	−0.140997	+	0.244214i
$575$	−4.58669	−	7.94438i	−0.191278	−	0.331303i
$576$	−2.82843			−0.117851
$577$	12.4572	−	21.5765i	0.518601	−	0.898243i	−0.481166	−	0.876630i	$-0.659786\pi$
$577$	12.4572	−	21.5765i	0.518601	−	0.898243i	0.999766	−	0.0216131i	$-0.00688019\pi$
$578$	11.0243			0.458549
$579$	7.30130			0.303432
$580$	5.15749	+	8.93304i	0.214153	+	0.370924i
$581$	7.48836			0.310670
$582$	0.0602091	−	0.104285i	0.00249575	−	0.00432276i
$583$	−10.3661	+	17.9547i	−0.429322	+	0.743607i
$584$	4.47532	+	7.75149i	0.185190	+	0.320759i
$585$	7.75916	+	13.4393i	0.320802	+	0.555645i
$586$	13.1337	+	22.7483i	0.542549	+	0.939722i
$587$	10.5957	+	18.3523i	0.437332	+	0.757481i	0.997483	−	0.0709097i	$-0.0225902\pi$
$587$	10.5957	+	18.3523i	0.437332	+	0.757481i	−0.560151	+	0.828391i	$0.689257\pi$
$588$	2.07107			0.0854094
$589$	−11.5096			−0.474245
$590$	1.93979	+	3.35982i	0.0798599	+	0.138321i
$591$	3.51472	−	6.08767i	0.144576	−	0.250413i
$592$	−2.85400	+	4.94328i	−0.117299	+	0.203168i
$593$	−4.19651	−	7.26857i	−0.172330	−	0.298484i	0.766904	−	0.641762i	$-0.221796\pi$
$593$	−4.19651	−	7.26857i	−0.172330	−	0.298484i	−0.939234	+	0.343277i	$0.888463\pi$
$594$	−4.82843			−0.198113
$595$	−7.48656			−0.306919
$596$	−7.08605	+	12.2734i	−0.290256	+	0.502738i
$597$	2.62544	+	4.54740i	0.107452	+	0.186113i
$598$	50.3303			2.05816
$599$	12.5077	−	21.6641i	0.511053	−	0.885169i	−0.488865	−	0.872359i	$-0.662589\pi$
$599$	12.5077	−	21.6641i	0.511053	−	0.885169i	0.999918	−	0.0128099i	$-0.00407762\pi$
$600$	−0.414214			−0.0169102
$601$	−11.1144	−	19.2508i	−0.453368	−	0.785256i	0.545225	−	0.838290i	$-0.316444\pi$
$601$	−11.1144	−	19.2508i	−0.453368	−	0.785256i	−0.998593	+	0.0530339i	$0.983111\pi$
$602$	−6.41729			−0.261549
$603$	13.1452	+	19.0579i	0.535315	+	0.776097i
$604$	−19.6101			−0.797922
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$	1.37184			0.0557270
$607$	17.2810	−	29.9316i	0.701414	−	1.21488i	−0.266556	−	0.963819i	$-0.585886\pi$
$607$	17.2810	−	29.9316i	0.701414	−	1.21488i	0.967970	−	0.251065i	$-0.0807808\pi$
$608$	1.87958			0.0762271
$609$	−3.02119	−	5.23285i	−0.122425	−	0.212046i
$610$	−0.792255	+	1.37223i	−0.0320775	+	0.0555598i
$611$	6.82482			0.276103
$612$	14.9731			0.605252
$613$	−7.73359	−	13.3950i	−0.312357	−	0.541018i	0.666515	−	0.745491i	$-0.267785\pi$
$613$	−7.73359	−	13.3950i	−0.312357	−	0.541018i	−0.978872	+	0.204474i	$0.934452\pi$
$614$	−6.79597	+	11.7710i	−0.274263	+	0.475038i
$615$	0.989406	−	1.71370i	0.0398967	−	0.0691031i
$616$	1.41421	+	2.44949i	0.0569803	+	0.0986928i
$617$	−22.9069			−0.922198			−0.461099	−	0.887349i	$-0.652545\pi$
$617$	−22.9069			−0.922198			−0.461099	+	0.887349i	$0.652545\pi$
$618$	−2.35556			−0.0947544
$619$	−16.7233	−	28.9656i	−0.672165	−	1.16422i	−0.977289	−	0.211911i	$-0.932031\pi$
$619$	−16.7233	−	28.9656i	−0.672165	−	1.16422i	0.305124	−	0.952313i	$-0.401302\pi$
$620$	3.06175	+	5.30311i	0.122963	+	0.212978i
$621$	−11.0732	−	19.1794i	−0.444354	−	0.769644i
$622$	−5.85618	−	10.1432i	−0.234812	−	0.406705i
$623$	−0.536810	+	0.929782i	−0.0215068	+	0.0372509i
$624$	1.13630	−	1.96813i	0.0454885	−	0.0787885i
$625$	1.00000			0.0400000
$626$	−17.0479	−	29.5279i	−0.681372	−	1.18017i
$627$	1.55710			0.0621844
$628$	−10.7604			−0.429388
$629$	15.1085	−	26.1687i	0.602416	−	1.04342i
$630$	−4.00000			−0.159364
$631$	−3.36433	−	5.82720i	−0.133932	−	0.231977i	0.791257	−	0.611484i	$-0.209427\pi$
$631$	−3.36433	−	5.82720i	−0.133932	−	0.231977i	−0.925189	+	0.379507i	$0.876094\pi$
$632$	5.70801	−	9.88656i	0.227052	−	0.393266i
$633$	1.01873	+	1.76450i	0.0404910	+	0.0701325i
$634$	−6.87519	+	11.9082i	−0.273049	+	0.472934i
$635$	0.465368	−	0.806041i	0.0184676	−	0.0319868i
$636$	−2.14690	+	3.71854i	−0.0851300	+	0.147450i
$637$	13.7164	−	23.7575i	0.543463	−	0.941306i
$638$	−10.3150	+	17.8661i	−0.408374	+	0.707325i
$639$	6.07234	−	10.5176i	0.240218	−	0.416070i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−7.93852	+	13.7499i	−0.313552	+	0.543089i	−0.979129	−	0.203241i	$-0.934853\pi$
$641$	−7.93852	+	13.7499i	−0.313552	+	0.543089i	0.665576	+	0.746330i	$0.268186\pi$
$642$	−3.85400	−	6.67533i	−0.152105	−	0.263454i
$643$	37.9361			1.49606			0.748028	−	0.663667i	$-0.231001\pi$
$643$	37.9361			1.49606			0.748028	+	0.663667i	$0.231001\pi$
$644$	−6.48656	+	11.2350i	−0.255606	+	0.442723i
$645$	1.87958			0.0740085
$646$	−9.95012			−0.391482
$647$	22.0261	+	38.1503i	0.865934	+	1.49984i	0.866116	+	0.499842i	$0.166609\pi$
$647$	22.0261	+	38.1503i	0.865934	+	1.49984i	−0.000182203		1.00000i	$0.500058\pi$
$648$	7.48528			0.294050
$649$	−3.87958	+	6.71963i	−0.152287	+	0.263769i
$650$	−2.74328	+	4.75150i	−0.107600	+	0.186369i
$651$	−1.79353	−	3.10649i	−0.0702940	−	0.121753i
$652$	7.91512	+	13.7094i	0.309980	+	0.536901i
$653$	17.0314	+	29.4993i	0.666491	+	1.15440i	0.978879	+	0.204441i	$0.0655377\pi$
$653$	17.0314	+	29.4993i	0.666491	+	1.15440i	−0.312388	+	0.949954i	$0.601129\pi$
$654$	2.51562	+	4.35718i	0.0983686	+	0.170379i
$655$	−10.4129			−0.406867
$656$	4.77727			0.186521
$657$	−12.6581	−	21.9245i	−0.493841	−	0.855357i
$658$	−0.879582	+	1.52348i	−0.0342897	+	0.0593914i
$659$	23.4282	−	40.5787i	0.912631	−	1.58072i	0.102298	−	0.994754i	$-0.467380\pi$
$659$	23.4282	−	40.5787i	0.912631	−	1.58072i	0.810333	−	0.585970i	$-0.199286\pi$
$660$	−0.414214	−	0.717439i	−0.0161232	−	0.0279263i
$661$	34.5858			1.34523			0.672616	−	0.739992i	$-0.265171\pi$
$661$	34.5858			1.34523			0.672616	+	0.739992i	$0.265171\pi$
$662$	6.50955			0.253001
$663$	−6.01536	+	10.4189i	−0.233617	+	0.404637i
$664$	−2.64754	−	4.58567i	−0.102744	−	0.177958i
$665$	2.65813			0.103078
$666$	8.07234	−	13.9817i	0.312797	−	0.541780i
$667$	−94.6232			−3.66383
$668$	0.570804	+	0.988661i	0.0220851	+	0.0382524i
$669$	4.15530			0.160653
$670$	−3.51150	+	7.39388i	−0.135661	+	0.285650i
$671$	−3.16902			−0.122339
$672$	0.292893	+	0.507306i	0.0112986	+	0.0195698i
$673$	−34.1382			−1.31593			−0.657966	−	0.753047i	$-0.728583\pi$
$673$	−34.1382			−1.31593			−0.657966	+	0.753047i	$0.728583\pi$
$674$	−4.10852	+	7.11616i	−0.158254	+	0.274104i
$675$	2.41421			0.0929231
$676$	−8.55115	−	14.8110i	−0.328891	−	0.569655i
$677$	−3.65066	+	6.32313i	−0.140306	+	0.243018i	−0.927612	−	0.373545i	$-0.878142\pi$
$677$	−3.65066	+	6.32313i	−0.140306	+	0.243018i	0.787306	+	0.616563i	$0.211475\pi$
$678$	−0.180350			−0.00692629
$679$	0.411134			0.0157779
$680$	2.64690	+	4.58456i	0.101504	+	0.175810i
$681$	−4.64214	+	8.04041i	−0.177887	+	0.308109i
$682$	−6.12350	+	10.6062i	−0.234481	+	0.406133i
$683$	23.1820	+	40.1524i	0.887036	+	1.53639i	0.843363	+	0.537345i	$0.180573\pi$
$683$	23.1820	+	40.1524i	0.887036	+	1.53639i	0.0436729	+	0.999046i	$0.486094\pi$
$684$	−5.31626			−0.203272
$685$	21.9238			0.837664
$686$	8.48528	+	14.6969i	0.323970	+	0.561132i
$687$	−4.20827	−	7.28894i	−0.160556	−	0.278091i
$688$	2.26886	+	3.92977i	0.0864993	+	0.149821i
$689$	28.4372	+	49.2547i	1.08337	+	1.87645i
$690$	1.89987	−	3.29067i	0.0723268	−	0.125274i
$691$	12.3631	−	21.4134i	0.470313	−	0.814606i	−0.529111	−	0.848553i	$-0.677474\pi$
$691$	12.3631	−	21.4134i	0.470313	−	0.814606i	0.999424	+	0.0339469i	$0.0108077\pi$
$692$	−7.43540			−0.282652
$693$	−4.00000	−	6.92820i	−0.151947	−	0.263181i
$694$	24.9268			0.946210
$695$	19.5788			0.742667
$696$	−2.13630	+	3.70019i	−0.0809764	+	0.140255i
$697$	−25.2899			−0.957923
$698$	−17.0389	−	29.5122i	−0.644931	−	1.11705i
$699$	−3.41009	+	5.90645i	−0.128981	+	0.223402i
$700$	−0.707107	−	1.22474i	−0.0267261	−	0.0462910i
$701$	2.26953	−	3.93094i	0.0857188	−	0.148469i	−0.819978	−	0.572394i	$-0.806015\pi$
$701$	2.26953	−	3.93094i	0.0857188	−	0.148469i	0.905697	+	0.423925i	$0.139348\pi$
$702$	−6.62286	+	11.4711i	−0.249964	+	0.432950i
$703$	−5.36433	+	9.29130i	−0.202320	+	0.350428i
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$	0.257624	−	0.446217i	0.00970266	−	0.0168055i
$706$	3.98374	−	6.90004i	0.149930	−	0.259687i
$707$	2.34187	+	4.05624i	0.0880751	+	0.152551i
$708$	−0.803488	+	1.39168i	−0.0301969	+	0.0523026i
$709$	−3.19021	−	5.52561i	−0.119811	−	0.207519i	0.799882	−	0.600158i	$-0.204895\pi$
$709$	−3.19021	−	5.52561i	−0.119811	−	0.207519i	−0.919693	+	0.392639i	$0.871562\pi$
$710$	4.29380			0.161143
$711$	−16.1447	+	27.9634i	−0.605473	+	1.04871i
$712$	0.759164			0.0284509
$713$	−56.1732			−2.10370
$714$	−1.55052	−	2.68557i	−0.0580266	−	0.100505i
$715$	−10.9731			−0.410371
$716$	10.3811	−	17.9806i	0.387961	−	0.671968i
$717$	−0.748583	+	1.29658i	−0.0279563	+	0.0484218i
$718$	16.9132	+	29.2945i	0.631194	+	1.09326i
$719$	13.4054	+	23.2189i	0.499938	+	0.865918i	1.00000		7.16718e-5i	$-2.28138e-5\pi$
$719$	13.4054	+	23.2189i	0.499938	+	0.865918i	−0.500062	+	0.865990i	$0.666689\pi$
$720$	1.41421	+	2.44949i	0.0527046	+	0.0912871i
$721$	−4.02119	−	6.96490i	−0.149757	−	0.259387i
$722$	−15.4672			−0.575629
$723$	10.4067			0.387030
$724$	7.90167	+	13.6861i	0.293663	+	0.508640i
$725$	5.15749	−	8.93304i	0.191544	−	0.331765i
$726$	−1.44975	+	2.51104i	−0.0538052	+	0.0931933i
$727$	1.97754	+	3.42519i	0.0733427	+	0.127033i	0.900364	−	0.435137i	$-0.143300\pi$
$727$	1.97754	+	3.42519i	0.0733427	+	0.127033i	−0.827022	+	0.562170i	$0.809967\pi$
$728$	7.75916			0.287574
$729$	−18.1716			−0.673021
$730$	4.47532	−	7.75149i	0.165639	−	0.286896i
$731$	−12.0109	−	20.8034i	−0.444238	−	0.769442i
$732$	−0.656326			−0.0242585
$733$	18.8783	−	32.6981i	0.697285	−	1.20773i	−0.272119	−	0.962263i	$-0.587725\pi$
$733$	18.8783	−	32.6981i	0.697285	−	1.20773i	0.969404	−	0.245469i	$-0.0789421\pi$
$734$	0.727922			0.0268681
$735$	−1.03553	−	1.79360i	−0.0381962	−	0.0661578i
$736$	9.17338			0.338135
$737$	−16.3181	+	1.31178i	−0.601084	+	0.0483202i
$738$	−13.5122			−0.497390
$739$	10.6990	+	18.5311i	0.393567	+	0.681679i	0.992917	−	0.118809i	$-0.0379075\pi$
$739$	10.6990	+	18.5311i	0.393567	+	0.681679i	−0.599350	+	0.800487i	$0.704574\pi$
$740$	5.70801			0.209831
$741$	2.13577	−	3.69927i	0.0784596	−	0.135896i
$742$	−14.6599			−0.538183
$743$	16.6939	+	28.9147i	0.612441	+	1.06078i	0.990828	+	0.135131i	$0.0431456\pi$
$743$	16.6939	+	28.9147i	0.612441	+	1.06078i	−0.378387	+	0.925648i	$0.623521\pi$
$744$	−1.26822	+	2.19662i	−0.0464951	+	0.0805319i
$745$	14.1721			0.519226
$746$	−5.12042			−0.187472
$747$	7.48836	+	12.9702i	0.273985	+	0.474556i
$748$	−5.29380	+	9.16912i	−0.193560	+	0.335256i
$749$	13.1584	−	22.7910i	0.480797	−	0.832765i
$750$	0.207107	+	0.358719i	0.00756247	+	0.0130986i
$751$	−12.2682			−0.447672			−0.223836	−	0.974627i	$-0.571858\pi$
$751$	−12.2682			−0.447672			−0.223836	+	0.974627i	$0.571858\pi$
$752$	1.24392			0.0453610
$753$	0.324941	+	0.562814i	0.0118415	+	0.0205101i
$754$	28.2969	+	49.0116i	1.03051	+	1.78490i
$755$	9.80503	+	16.9828i	0.356841	+	0.618068i
$756$	−1.70711	−	2.95680i	−0.0620869	−	0.107538i
$757$	9.21834	−	15.9666i	0.335046	−	0.580317i	−0.648447	−	0.761259i	$-0.724581\pi$
$757$	9.21834	−	15.9666i	0.335046	−	0.580317i	0.983494	+	0.180942i	$0.0579147\pi$
$758$	1.99872	−	3.46189i	0.0725969	−	0.125742i
$759$	7.59947			0.275843
$760$	−0.939791	−	1.62777i	−0.0340898	−	0.0590453i
$761$	31.0641			1.12607			0.563036	−	0.826432i	$-0.309633\pi$
$761$	31.0641			1.12607			0.563036	+	0.826432i	$0.309633\pi$
$762$	0.385524			0.0139660
$763$	−8.58887	+	14.8764i	−0.310938	+	0.538560i
$764$	−4.97754			−0.180081
$765$	−7.48656	−	12.9671i	−0.270677	−	0.468826i
$766$	−0.141607	+	0.245271i	−0.00511648	+	0.00886200i
$767$	10.6428	+	18.4338i	0.384288	+	0.665607i
$768$	0.207107	−	0.358719i	0.00747332	−	0.0129442i
$769$	−5.10259	+	8.83794i	−0.184004	+	0.318704i	−0.943240	−	0.332111i	$-0.892239\pi$
$769$	−5.10259	+	8.83794i	−0.184004	+	0.318704i	0.759236	+	0.650815i	$0.225573\pi$
$770$	1.41421	−	2.44949i	0.0509647	−	0.0882735i
$771$	4.73797	−	8.20641i	0.170634	−	0.295547i
$772$	8.81344	−	15.2653i	0.317203	−	0.549411i
$773$	2.14472	−	3.71476i	0.0771402	−	0.133611i	−0.824875	−	0.565316i	$-0.808754\pi$
$773$	2.14472	−	3.71476i	0.0771402	−	0.133611i	0.902015	+	0.431705i	$0.142088\pi$
$774$	−6.41729	−	11.1151i	−0.230665	−	0.399523i
$775$	3.06175	−	5.30311i	0.109981	−	0.190493i
$776$	−0.145358	−	0.251767i	−0.00521804	−	0.00903790i
$777$	−3.34367			−0.119954
$778$	−7.42920	+	12.8677i	−0.266350	+	0.461331i
$779$	8.97927			0.321716
$780$	−2.27261			−0.0813724
$781$	4.29380	+	7.43707i	0.153644	+	0.266119i
$782$	−48.5620			−1.73657
$783$	12.4513	−	21.5663i	0.444973	−	0.770715i
$784$	2.50000	−	4.33013i	0.0892857	−	0.154647i
$785$	5.38022	+	9.31881i	0.192028	+	0.332603i
$786$	−2.15659	−	3.73532i	−0.0769230	−	0.133235i
$787$	5.45169	+	9.44261i	0.194332	+	0.336593i	0.946681	−	0.322172i	$-0.104413\pi$
$787$	5.45169	+	9.44261i	0.194332	+	0.336593i	−0.752349	+	0.658764i	$0.771079\pi$
$788$	−8.48528	−	14.6969i	−0.302276	−	0.523557i
$789$	−5.62764			−0.200349
$790$	−11.4160			−0.406164
$791$	−0.307876	−	0.533257i	−0.0109468	−	0.0189604i
$792$	−2.82843	+	4.89898i	−0.100504	+	0.174078i
$793$	−4.34675	+	7.52880i	−0.154358	+	0.267355i
$794$	1.57609	+	2.72988i	0.0559335	+	0.0968796i
$795$	4.29380			0.152285
$796$	12.6768			0.449316
$797$	12.6895	−	21.9789i	0.449487	−	0.778534i	−0.548866	−	0.835910i	$-0.684940\pi$
$797$	12.6895	−	21.9789i	0.449487	−	0.778534i	0.998353	+	0.0573768i	$0.0182736\pi$
$798$	0.550517	+	0.953523i	0.0194881	+	0.0337543i
$799$	−6.58504			−0.232962
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−2.14724			−0.0758689
$802$	−10.6581	−	18.4604i	−0.376352	−	0.651860i
$803$	17.9013			0.631723
$804$	−3.37958	+	0.271680i	−0.119189	+	0.00958140i
$805$	12.9731			0.457242
$806$	16.7985	+	29.0958i	0.591701	+	1.02486i
$807$	7.97184			0.280622
$808$	1.65595	−	2.86819i	0.0582562	−	0.100903i
$809$	−14.4279			−0.507258			−0.253629	−	0.967302i	$-0.581624\pi$
$809$	−14.4279			−0.507258			−0.253629	+	0.967302i	$0.581624\pi$
$810$	−3.74264	−	6.48244i	−0.131503	−	0.227770i
$811$	−15.7729	+	27.3194i	−0.553860	+	0.959314i	0.444131	+	0.895962i	$0.353513\pi$
$811$	−15.7729	+	27.3194i	−0.553860	+	0.959314i	−0.997991	+	0.0633524i	$0.979821\pi$
$812$	−14.5876			−0.511924
$813$	3.01005			0.105567
$814$	5.70801	+	9.88656i	0.200066	+	0.346524i
$815$	7.91512	−	13.7094i	0.277254	−	0.480219i
$816$	−1.09638	+	1.89899i	−0.0383810	+	0.0664779i
$817$	4.26450	+	7.38633i	0.149196	+	0.258415i
$818$	17.8103			0.622723
$819$	−21.9462			−0.766863
$820$	−2.38864	−	4.13724i	−0.0834148	−	0.144479i
$821$	−1.69430	−	2.93462i	−0.0591315	−	0.102419i	0.834944	−	0.550335i	$-0.185500\pi$
$821$	−1.69430	−	2.93462i	−0.0591315	−	0.102419i	−0.894076	+	0.447916i	$0.852166\pi$
$822$	4.54056	+	7.86448i	0.158370	+	0.274305i
$823$	8.95193	+	15.5052i	0.312045	+	0.540477i	0.978805	−	0.204795i	$-0.0656529\pi$
$823$	8.95193	+	15.5052i	0.312045	+	0.540477i	−0.666760	+	0.745272i	$0.732320\pi$
$824$	−2.84341	+	4.92493i	−0.0990549	+	0.171568i
$825$	−0.414214	+	0.717439i	−0.0144211	+	0.0249780i
$826$	−5.48656			−0.190902
$827$	−20.8726	−	36.1524i	−0.725812	−	1.25714i	−0.958639	−	0.284625i	$-0.908131\pi$
$827$	−20.8726	−	36.1524i	−0.725812	−	1.25714i	0.232827	−	0.972518i	$-0.425202\pi$
$828$	−25.9462			−0.901694
$829$	8.35917			0.290326			0.145163	−	0.989408i	$-0.453629\pi$
$829$	8.35917			0.290326			0.145163	+	0.989408i	$0.453629\pi$
$830$	−2.64754	+	4.58567i	−0.0918973	+	0.159171i
$831$	−6.22220			−0.215846
$832$	−2.74328	−	4.75150i	−0.0951061	−	0.164729i
$833$	−13.2345	+	22.9228i	−0.458548	+	0.794228i
$834$	4.05491	+	7.02330i	0.140410	+	0.243197i
$835$	0.570804	−	0.988661i	0.0197535	−	0.0342140i
$836$	1.87958	−	3.25553i	0.0650067	−	0.112595i
$837$	7.39172	−	12.8028i	0.255495	−	0.442530i
$838$	−15.3271	+	26.5473i	−0.529467	+	0.917063i
$839$	0.768482	−	1.33105i	0.0265310	−	0.0459530i	−0.852455	−	0.522800i	$-0.824887\pi$
$839$	0.768482	−	1.33105i	0.0265310	−	0.0459530i	0.878986	+	0.476848i	$0.158221\pi$
$840$	0.292893	−	0.507306i	0.0101058	−	0.0175037i
$841$	−38.6995	−	67.0294i	−1.33446	−	2.31136i
$842$	10.2426	−	17.7408i	0.352985	−	0.611387i
$843$	1.30761	+	2.26485i	0.0450365	+	0.0780056i
$844$	4.91888			0.169315
$845$	−8.55115	+	14.8110i	−0.294169	+	0.509515i
$846$	−3.51833			−0.120963
$847$	−9.89949			−0.340151
$848$	5.18307	+	8.97734i	0.177987	+	0.308283i
$849$	−9.53644			−0.327290
$850$	2.64690	−	4.58456i	0.0907878	−	0.157249i
$851$	−26.1809	+	45.3466i	−0.897468	+	1.55446i
$852$	0.889274	+	1.54027i	0.0304660	+	0.0527687i
$853$	−10.4104	−	18.0313i	−0.356444	−	0.617379i	0.630920	−	0.775848i	$-0.282678\pi$
$853$	−10.4104	−	18.0313i	−0.356444	−	0.617379i	−0.987364	+	0.158469i	$0.949344\pi$
$854$	−1.12042	−	1.94062i	−0.0383399	−	0.0664067i
$855$	2.65813	+	4.60402i	0.0909061	+	0.157454i
$856$	−18.6088			−0.636035
$857$	−12.0785			−0.412594			−0.206297	−	0.978489i	$-0.566141\pi$
$857$	−12.0785			−0.412594			−0.206297	+	0.978489i	$0.566141\pi$
$858$	−2.27261	−	3.93627i	−0.0775855	−	0.134382i
$859$	16.4251	−	28.4491i	0.560416	−	0.970669i	−0.437044	−	0.899440i	$-0.643975\pi$
$859$	16.4251	−	28.4491i	0.560416	−	0.970669i	0.997460	−	0.0712291i	$-0.0226922\pi$
$860$	2.26886	−	3.92977i	0.0773673	−	0.134004i
$861$	1.39923	+	2.42354i	0.0476857	+	0.0825940i
$862$	−3.70620			−0.126234
$863$	−42.5127			−1.44715			−0.723574	−	0.690246i	$-0.757502\pi$
$863$	−42.5127			−1.44715			−0.723574	+	0.690246i	$0.757502\pi$
$864$	−1.20711	+	2.09077i	−0.0410666	+	0.0711294i
$865$	3.71770	+	6.43925i	0.126406	+	0.218941i
$866$	−19.0530			−0.647446
$867$	2.28320	−	3.95462i	0.0775416	−	0.134306i
$868$	−8.65993			−0.293937
$869$	−11.4160	−	19.7731i	−0.387262	−	0.670757i
$870$	4.27261			0.144855
$871$	−19.2660	+	40.5669i	−0.652804	+	1.37456i
$872$	12.1465			0.411332
$873$	0.411134	+	0.712104i	0.0139148	+	0.0241011i
$874$	17.2421			0.583223
$875$	−0.707107	+	1.22474i	−0.0239046	+	0.0414039i
$876$	3.70748			0.125264
$877$	−8.21173	−	14.2231i	−0.277290	−	0.480281i	0.693420	−	0.720534i	$-0.256103\pi$
$877$	−8.21173	−	14.2231i	−0.277290	−	0.480281i	−0.970710	+	0.240253i	$0.922770\pi$
$878$	3.97532	−	6.88546i	0.134161	−	0.232373i
$879$	10.8803			0.366984
$880$	−2.00000			−0.0674200
$881$	−0.388636	−	0.673138i	−0.0130935	−	0.0226786i	0.859404	−	0.511296i	$-0.170835\pi$
$881$	−0.388636	−	0.673138i	−0.0130935	−	0.0226786i	−0.872498	+	0.488618i	$0.837501\pi$
$882$	−7.07107	+	12.2474i	−0.238095	+	0.412393i
$883$	14.4896	−	25.0968i	0.487615	−	0.844574i	−0.512283	−	0.858816i	$-0.671200\pi$
$883$	14.4896	−	25.0968i	0.487615	−	0.844574i	0.999899	+	0.0142423i	$0.00453361\pi$
$884$	14.5224	+	25.1535i	0.488440	+	0.846002i
$885$	1.60698			0.0540179
$886$	23.0018			0.772761
$887$	−21.8281	−	37.8073i	−0.732914	−	1.26944i	−0.955632	−	0.294562i	$-0.904826\pi$
$887$	−21.8281	−	37.8073i	−0.732914	−	1.26944i	0.222718	−	0.974883i	$-0.428507\pi$
$888$	1.18217	+	2.04757i	0.0396709	+	0.0687121i
$889$	0.658130	+	1.13991i	0.0220730	+	0.0382315i
$890$	−0.379582	−	0.657455i	−0.0127236	−	0.0220379i
$891$	7.48528	−	12.9649i	0.250766	−	0.434340i
$892$	5.01588	−	8.68777i	0.167944	−	0.290888i
$893$	2.33804			0.0782396
$894$	2.93514	+	5.08381i	0.0981657	+	0.170028i
$895$	−20.7622			−0.694005
$896$	1.41421			0.0472456
$897$	10.4237	−	18.0544i	0.348038	−	0.602820i
$898$	−11.8889			−0.396738
$899$	−31.5819	−	54.7014i	−1.05332	−	1.82440i
$900$	1.41421	−	2.44949i	0.0471405	−	0.0816497i
$901$	−27.4381	−	47.5242i	−0.914096	−	1.58326i
$902$	4.77727	−	8.27448i	0.159066	−	0.275510i
$903$	−1.32907	+	2.30201i	−0.0442285	+	0.0766060i
$904$	−0.217701	+	0.377070i	−0.00724064	+	0.0125411i
$905$	7.90167	−	13.6861i	0.262660	−	0.454941i
$906$	−4.06138	+	7.03451i	−0.134930	+	0.233706i
$907$	−3.59638	+	6.22911i	−0.119416	+	0.206834i	−0.919536	−	0.393005i	$-0.871436\pi$
$907$	−3.59638	+	6.22911i	−0.119416	+	0.206834i	0.800120	+	0.599839i	$0.204769\pi$
$908$	11.2071	+	19.4113i	0.371921	+	0.644186i
$909$	−4.68374	+	8.11248i	−0.155350	+	0.269074i
$910$	−3.87958	−	6.71963i	−0.128607	−	0.222754i
$911$	−18.7049			−0.619722			−0.309861	−	0.950782i	$-0.600283\pi$
$911$	−18.7049			−0.619722			−0.309861	+	0.950782i	$0.600283\pi$
$912$	0.389274	−	0.674243i	0.0128902	−	0.0223264i
$913$	−10.5901			−0.350483
$914$	−7.04680			−0.233087
$915$	0.328163	+	0.568395i	0.0108487	+	0.0187906i
$916$	−20.3193			−0.671370
$917$	7.36306	−	12.7532i	0.243150	−	0.421148i
$918$	6.39018	−	11.0681i	0.210907	−	0.365302i
$919$	−6.44324	−	11.1600i	−0.212543	−	0.368135i	0.739967	−	0.672644i	$-0.234841\pi$
$919$	−6.44324	−	11.1600i	−0.212543	−	0.368135i	−0.952510	+	0.304508i	$0.901508\pi$
$920$	−4.58669	−	7.94438i	−0.151219	−	0.261918i
$921$	2.81498	+	4.87570i	0.0927569	+	0.160660i
$922$	15.9709	+	27.6625i	0.525975	+	0.911015i
$923$	23.5582			0.775426
$924$	1.17157			0.0385419
$925$	−2.85400	−	4.94328i	−0.0938391	−	0.162534i
$926$	11.8999	−	20.6112i	0.391054	−	0.677325i
$927$	8.04238	−	13.9298i	0.264146	−	0.457515i
$928$	5.15749	+	8.93304i	0.169303	+	0.293241i
$929$	20.7044			0.679289			0.339645	−	0.940554i	$-0.389693\pi$
$929$	20.7044			0.679289			0.339645	+	0.940554i	$0.389693\pi$
$930$	2.53644			0.0831730
$931$	4.69895	−	8.13883i	0.154002	−	0.266739i
$932$	8.23268	+	14.2594i	0.269671	+	0.467083i
$933$	−4.85142			−0.158828
$934$	16.6693	−	28.8720i	0.545435	−	0.944720i
$935$	10.5876			0.346251
$936$	7.75916	+	13.4393i	0.253616	+	0.439276i
$937$	−7.19270			−0.234975			−0.117488	−	0.993074i	$-0.537484\pi$
$937$	−7.19270			−0.234975			−0.117488	+	0.993074i	$0.537484\pi$
$938$	−6.57261	−	9.52895i	−0.214603	−	0.311131i
$939$	−14.1230			−0.460886
$940$	−0.621958	−	1.07726i	−0.0202860	−	0.0351365i
$941$	−15.1046			−0.492397			−0.246199	−	0.969219i	$-0.579182\pi$
$941$	−15.1046			−0.492397			−0.246199	+	0.969219i	$0.579182\pi$
$942$	−2.22856	+	3.85998i	−0.0726104	+	0.125765i
$943$	43.8237			1.42710
$944$	1.93979	+	3.35982i	0.0631348	+	0.109353i
$945$	−1.70711	+	2.95680i	−0.0555322	+	0.0961846i
$946$	9.07542			0.295067
$947$	60.8669			1.97791			0.988954	−	0.148220i	$-0.0473543\pi$
$947$	60.8669			1.97791			0.988954	+	0.148220i	$0.0473543\pi$
$948$	−2.36433	−	4.09515i	−0.0767900	−	0.133004i
$949$	24.5541	−	42.5290i	0.797061	−	1.38055i
$950$	−0.939791	+	1.62777i	−0.0304908	+	0.0528117i
$951$	2.84780	+	4.93253i	0.0923462	+	0.159948i
$952$	−7.48656			−0.242641
$953$	12.3905			0.401367			0.200683	−	0.979656i	$-0.435684\pi$
$953$	12.3905			0.401367			0.200683	+	0.979656i	$0.435684\pi$
$954$	−14.6599	−	25.3918i	−0.474633	−	0.822088i
$955$	2.48877	+	4.31067i	0.0805346	+	0.139490i
$956$	1.80724	+	3.13023i	0.0584503	+	0.101239i
$957$	4.27261	+	7.40037i	0.138114	+	0.239220i
$958$	−7.33087	+	12.6974i	−0.236850	+	0.410236i
$959$	−15.5024	+	26.8510i	−0.500600	+	0.867065i
$960$	−0.414214			−0.0133687
$961$	−3.24862	−	5.62677i	−0.104794	−	0.181509i
$962$	31.3173			1.00971
$963$	52.6336			1.69609
$964$	12.5620	−	21.7580i	0.404595	−	0.700779i
$965$	−17.6269			−0.567430
$966$	2.68682	+	4.65371i	0.0864470	+	0.149731i
$967$	−5.30181	+	9.18300i	−0.170495	+	0.295305i	−0.938593	−	0.345027i	$-0.887870\pi$
$967$	−5.30181	+	9.18300i	−0.170495	+	0.295305i	0.768098	+	0.640332i	$0.221203\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$	−2.06074	+	3.56930i	−0.0662004	+	0.114663i
$970$	−0.145358	+	0.251767i	−0.00466715	+	0.00808375i
$971$	−1.52685	+	2.64459i	−0.0489990	+	0.0848688i	−0.889485	−	0.456965i	$-0.848936\pi$
$971$	−1.52685	+	2.64459i	−0.0489990	+	0.0848688i	0.840486	+	0.541834i	$0.182270\pi$
$972$	5.17157	−	8.95743i	0.165878	−	0.287310i
$973$	−13.8443	+	23.9791i	−0.443828	+	0.768733i
$974$	−5.12132	+	8.87039i	−0.164098	+	0.284226i
$975$	1.13630	+	1.96813i	0.0363908	+	0.0630308i
$976$	−0.792255	+	1.37223i	−0.0253595	+	0.0439239i
$977$	10.2114	+	17.6866i	0.326690	+	0.565844i	0.981853	−	0.189644i	$-0.0607333\pi$
$977$	10.2114	+	17.6866i	0.326690	+	0.565844i	−0.655163	+	0.755488i	$0.727400\pi$
$978$	6.55710			0.209673
$979$	0.759164	−	1.31491i	0.0242630	−	0.0420247i
$980$	−5.00000			−0.159719
$981$	−34.3555			−1.09689
$982$	−13.0770	−	22.6500i	−0.417304	−	0.722791i
$983$	6.46148			0.206089			0.103045	−	0.994677i	$-0.467142\pi$
$983$	6.46148			0.206089			0.103045	+	0.994677i	$0.467142\pi$
$984$	0.989406	−	1.71370i	0.0315411	−	0.0546308i
$985$	−8.48528	+	14.6969i	−0.270364	+	0.468283i
$986$	−27.3027	−	47.2897i	−0.869495	−	1.50601i
$987$	0.364335	+	0.631046i	0.0115969	+	0.0200864i
$988$	−5.15622	−	8.93083i	−0.164041	−	0.284128i
$989$	20.8131	+	36.0493i	0.661817	+	1.14630i
$990$	5.65685			0.179787
$991$	7.56152			0.240200			0.120100	−	0.992762i	$-0.461679\pi$
$991$	7.56152			0.240200			0.120100	+	0.992762i	$0.461679\pi$
$992$	3.06175	+	5.30311i	0.0972106	+	0.168374i
$993$	1.34817	−	2.33510i	0.0427829	−	0.0741022i
$994$	−3.03617	+	5.25880i	−0.0963015	+	0.166799i
$995$	−6.33838	−	10.9784i	−0.200940	−	0.348039i
$996$	−2.19329			−0.0694971
$997$	−2.45719			−0.0778198			−0.0389099	−	0.999243i	$-0.512389\pi$
$997$	−2.45719			−0.0778198			−0.0389099	+	0.999243i	$0.512389\pi$
$998$	−15.9927	+	27.7003i	−0.506242	+	0.876836i
$999$	−6.89018	−	11.9341i	−0.217996	−	0.377579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.i.171.1	✓	8
67.29	even	3	inner	670.2.e.i.431.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.i.171.1	✓	8	1.1	even	1	trivial
670.2.e.i.431.1	yes	8	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -0.414214 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.207107 + 0.358719i) q^{6} +(-0.707107 + 1.22474i) q^{7} +1.00000 q^{8} -2.82843 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -0.414214 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.207107 + 0.358719i) 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} +(0.207107 - 0.358719i) q^{12} +(-2.74328 - 4.75150i) q^{13} +1.41421 q^{14} -0.414214 q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.64690 + 4.58456i) q^{17} +(1.41421 + 2.44949i) q^{18} +(-0.939791 - 1.62777i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.292893 - 0.507306i) q^{21} -2.00000 q^{22} +(-4.58669 - 7.94438i) q^{23} -0.414214 q^{24} +1.00000 q^{25} +(-2.74328 + 4.75150i) q^{26} +2.41421 q^{27} +(-0.707107 - 1.22474i) q^{28} +(5.15749 - 8.93304i) q^{29} +(0.207107 + 0.358719i) q^{30} +(3.06175 - 5.30311i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.414214 + 0.717439i) q^{33} +(2.64690 - 4.58456i) q^{34} +(-0.707107 + 1.22474i) q^{35} +(1.41421 - 2.44949i) q^{36} +(-2.85400 - 4.94328i) q^{37} +(-0.939791 + 1.62777i) q^{38} +(1.13630 + 1.96813i) q^{39} +1.00000 q^{40} +(-2.38864 + 4.13724i) q^{41} -0.585786 q^{42} -4.53771 q^{43} +(1.00000 + 1.73205i) q^{44} -2.82843 q^{45} +(-4.58669 + 7.94438i) q^{46} +(-0.621958 + 1.07726i) q^{47} +(0.207107 + 0.358719i) q^{48} +(2.50000 + 4.33013i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.09638 - 1.89899i) q^{51} +5.48656 q^{52} -10.3661 q^{53} +(-1.20711 - 2.09077i) q^{54} +(1.00000 - 1.73205i) q^{55} +(-0.707107 + 1.22474i) q^{56} +(0.389274 + 0.674243i) q^{57} -10.3150 q^{58} -3.87958 q^{59} +(0.207107 - 0.358719i) q^{60} +(-0.792255 - 1.37223i) q^{61} -6.12350 q^{62} +(2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(-2.74328 - 4.75150i) q^{65} +0.828427 q^{66} +(-4.64754 - 6.73798i) q^{67} -5.29380 q^{68} +(1.89987 + 3.29067i) q^{69} +1.41421 q^{70} +(-2.14690 + 3.71854i) q^{71} -2.82843 q^{72} +(4.47532 + 7.75149i) q^{73} +(-2.85400 + 4.94328i) q^{74} -0.414214 q^{75} +1.87958 q^{76} +(1.41421 + 2.44949i) q^{77} +(1.13630 - 1.96813i) q^{78} +(5.70801 - 9.88656i) q^{79} +(-0.500000 - 0.866025i) q^{80} +7.48528 q^{81} +4.77727 q^{82} +(-2.64754 - 4.58567i) q^{83} +(0.292893 + 0.507306i) q^{84} +(2.64690 + 4.58456i) q^{85} +(2.26886 + 3.92977i) q^{86} +(-2.13630 + 3.70019i) q^{87} +(1.00000 - 1.73205i) q^{88} +0.759164 q^{89} +(1.41421 + 2.44949i) q^{90} +7.75916 q^{91} +9.17338 q^{92} +(-1.26822 + 2.19662i) q^{93} +1.24392 q^{94} +(-0.939791 - 1.62777i) q^{95} +(0.207107 - 0.358719i) q^{96} +(-0.145358 - 0.251767i) 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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