LMFDB - Embedded newform 670.2.e.d.431.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			431.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	670.431
Dual form			670.2.e.d.171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} -2.00000 q^{9} +(-0.500000 + 0.866025i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} -2.00000 q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{18} +(2.00000 - 3.46410i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{21} -6.00000 q^{22} +(3.00000 - 5.19615i) q^{23} -1.00000 q^{24} +1.00000 q^{25} +(1.00000 + 1.73205i) q^{26} -5.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(3.00000 + 5.19615i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(-2.50000 - 4.33013i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +(3.00000 + 5.19615i) q^{34} +(1.00000 + 1.73205i) q^{35} +(1.00000 + 1.73205i) q^{36} +(3.50000 - 6.06218i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(-1.00000 + 1.73205i) q^{39} +1.00000 q^{40} +(-1.50000 - 2.59808i) q^{41} -2.00000 q^{42} +8.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} +2.00000 q^{45} +(-3.00000 - 5.19615i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-3.00000 + 5.19615i) q^{51} +2.00000 q^{52} -3.00000 q^{53} +(-2.50000 + 4.33013i) q^{54} +(3.00000 + 5.19615i) q^{55} +(1.00000 + 1.73205i) q^{56} +(2.00000 - 3.46410i) q^{57} +6.00000 q^{58} -6.00000 q^{59} +(0.500000 + 0.866025i) q^{60} +(-4.00000 + 6.92820i) q^{61} -5.00000 q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} -6.00000 q^{66} +(2.50000 + 7.79423i) q^{67} +6.00000 q^{68} +(3.00000 - 5.19615i) q^{69} +2.00000 q^{70} +(7.50000 + 12.9904i) q^{71} +2.00000 q^{72} +(2.00000 - 3.46410i) q^{73} +(-3.50000 - 6.06218i) q^{74} +1.00000 q^{75} -4.00000 q^{76} +(-6.00000 + 10.3923i) q^{77} +(1.00000 + 1.73205i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +1.00000 q^{81} -3.00000 q^{82} +(7.50000 - 12.9904i) q^{83} +(-1.00000 + 1.73205i) q^{84} +(3.00000 - 5.19615i) q^{85} +(4.00000 - 6.92820i) q^{86} +(3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{88} +9.00000 q^{89} +(1.00000 - 1.73205i) q^{90} +4.00000 q^{91} -6.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} -6.00000 q^{94} +(-2.00000 + 3.46410i) q^{95} +(0.500000 + 0.866025i) q^{96} +(5.00000 - 8.66025i) q^{97} +(-1.50000 - 2.59808i) q^{98} +(6.00000 + 10.3923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 2 q^{3} - q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) $ 2 * q + q^2 + 2 * q^3 - q^4 - 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 4 * q^9	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 4 q^{9} - q^{10} - 6 q^{11} - q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} - q^{16} - 6 q^{17} - 2 q^{18} + 4 q^{19} + q^{20} - 2 q^{21} - 12 q^{22} + 6 q^{23} - 2 q^{24} + 2 q^{25} + 2 q^{26} - 10 q^{27} - 2 q^{28} + 6 q^{29} - q^{30} - 5 q^{31} + q^{32} - 6 q^{33} + 6 q^{34} + 2 q^{35} + 2 q^{36} + 7 q^{37} - 4 q^{38} - 2 q^{39} + 2 q^{40} - 3 q^{41} - 4 q^{42} + 16 q^{43} - 6 q^{44} + 4 q^{45} - 6 q^{46} - 6 q^{47} - q^{48} + 3 q^{49} + q^{50} - 6 q^{51} + 4 q^{52} - 6 q^{53} - 5 q^{54} + 6 q^{55} + 2 q^{56} + 4 q^{57} + 12 q^{58} - 12 q^{59} + q^{60} - 8 q^{61} - 10 q^{62} + 4 q^{63} + 2 q^{64} + 2 q^{65} - 12 q^{66} + 5 q^{67} + 12 q^{68} + 6 q^{69} + 4 q^{70} + 15 q^{71} + 4 q^{72} + 4 q^{73} - 7 q^{74} + 2 q^{75} - 8 q^{76} - 12 q^{77} + 2 q^{78} - 8 q^{79} + q^{80} + 2 q^{81} - 6 q^{82} + 15 q^{83} - 2 q^{84} + 6 q^{85} + 8 q^{86} + 6 q^{87} + 6 q^{88} + 18 q^{89} + 2 q^{90} + 8 q^{91} - 12 q^{92} - 5 q^{93} - 12 q^{94} - 4 q^{95} + q^{96} + 10 q^{97} - 3 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 4 * q^9 - q^10 - 6 * q^11 - q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 - q^16 - 6 * q^17 - 2 * q^18 + 4 * q^19 + q^20 - 2 * q^21 - 12 * q^22 + 6 * q^23 - 2 * q^24 + 2 * q^25 + 2 * q^26 - 10 * q^27 - 2 * q^28 + 6 * q^29 - q^30 - 5 * q^31 + q^32 - 6 * q^33 + 6 * q^34 + 2 * q^35 + 2 * q^36 + 7 * q^37 - 4 * q^38 - 2 * q^39 + 2 * q^40 - 3 * q^41 - 4 * q^42 + 16 * q^43 - 6 * q^44 + 4 * q^45 - 6 * q^46 - 6 * q^47 - q^48 + 3 * q^49 + q^50 - 6 * q^51 + 4 * q^52 - 6 * q^53 - 5 * q^54 + 6 * q^55 + 2 * q^56 + 4 * q^57 + 12 * q^58 - 12 * q^59 + q^60 - 8 * q^61 - 10 * q^62 + 4 * q^63 + 2 * q^64 + 2 * q^65 - 12 * q^66 + 5 * q^67 + 12 * q^68 + 6 * q^69 + 4 * q^70 + 15 * q^71 + 4 * q^72 + 4 * q^73 - 7 * q^74 + 2 * q^75 - 8 * q^76 - 12 * q^77 + 2 * q^78 - 8 * q^79 + q^80 + 2 * q^81 - 6 * q^82 + 15 * q^83 - 2 * q^84 + 6 * q^85 + 8 * q^86 + 6 * q^87 + 6 * q^88 + 18 * q^89 + 2 * q^90 + 8 * q^91 - 12 * q^92 - 5 * q^93 - 12 * q^94 - 4 * q^95 + q^96 + 10 * q^97 - 3 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.00000			0.577350			0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000			0.577350			0.288675	+	0.957427i	$0.406785\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	−1.00000			−0.353553
$9$	−2.00000			−0.666667
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−2.00000			−0.534522
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$	−1.00000	+	1.73205i	−0.235702	+	0.408248i
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−1.00000	−	1.73205i	−0.218218	−	0.377964i
$22$	−6.00000			−1.27920
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	−1.00000			−0.204124
$25$	1.00000			0.200000
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	−5.00000			−0.962250
$28$	−1.00000	+	1.73205i	−0.188982	+	0.327327i
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−3.00000	−	5.19615i	−0.522233	−	0.904534i
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	−2.00000	−	3.46410i	−0.324443	−	0.561951i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$	1.00000			0.158114
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$	−2.00000			−0.308607
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	−3.00000	+	5.19615i	−0.452267	+	0.783349i
$45$	2.00000			0.298142
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	2.00000			0.277350
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$	3.00000	+	5.19615i	0.404520	+	0.700649i
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$	2.00000	−	3.46410i	0.264906	−	0.458831i
$58$	6.00000			0.787839
$59$	−6.00000			−0.781133			−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000			−0.781133			−0.390567	+	0.920575i	$0.627721\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−5.00000			−0.635001
$63$	2.00000	+	3.46410i	0.251976	+	0.436436i
$64$	1.00000			0.125000
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$	−6.00000			−0.738549
$67$	2.50000	+	7.79423i	0.305424	+	0.952217i
$67$	2.50000	+	7.79423i	0.305424	+	0.952217i
$68$	6.00000			0.727607
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	2.00000			0.239046
$71$	7.50000	+	12.9904i	0.890086	+	1.54167i	0.839771	+	0.542941i	$0.182689\pi$
$71$	7.50000	+	12.9904i	0.890086	+	1.54167i	0.0503155	+	0.998733i	$0.483977\pi$
$72$	2.00000			0.235702
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	−0.724923	−	0.688830i	$-0.758125\pi$
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	0.959006	+	0.283387i	$0.0914581\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$	1.00000			0.115470
$76$	−4.00000			−0.458831
$77$	−6.00000	+	10.3923i	−0.683763	+	1.18431i
$78$	1.00000	+	1.73205i	0.113228	+	0.196116i
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	1.00000			0.111111
$82$	−3.00000			−0.331295
$83$	7.50000	−	12.9904i	0.823232	−	1.42588i	−0.0800311	−	0.996792i	$-0.525502\pi$
$83$	7.50000	−	12.9904i	0.823232	−	1.42588i	0.903263	−	0.429087i	$-0.141165\pi$
$84$	−1.00000	+	1.73205i	−0.109109	+	0.188982i
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	9.00000			0.953998			0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000			0.953998			0.476999	+	0.878904i	$0.341725\pi$
$90$	1.00000	−	1.73205i	0.105409	−	0.182574i
$91$	4.00000			0.419314
$92$	−6.00000			−0.625543
$93$	−2.50000	−	4.33013i	−0.259238	−	0.449013i
$94$	−6.00000			−0.618853
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	−0.492287	−	0.870433i	$-0.663839\pi$
$97$	5.00000	−	8.66025i	0.507673	−	0.879316i	0.999961	−	0.00888289i	$-0.00282755\pi$
$98$	−1.50000	−	2.59808i	−0.151523	−	0.262445i
$99$	6.00000	+	10.3923i	0.603023	+	1.04447i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$	3.00000	+	5.19615i	0.297044	+	0.514496i
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$	1.00000	+	1.73205i	0.0975900	+	0.169031i
$106$	−1.50000	+	2.59808i	−0.145693	+	0.252347i
$107$	−9.00000			−0.870063			−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000			−0.870063			−0.435031	+	0.900415i	$0.643263\pi$
$108$	2.50000	+	4.33013i	0.240563	+	0.416667i
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$	6.00000			0.572078
$111$	3.50000	−	6.06218i	0.332205	−	0.575396i
$112$	2.00000			0.188982
$113$	9.00000	+	15.5885i	0.846649	+	1.46644i	0.884182	+	0.467143i	$0.154717\pi$
$113$	9.00000	+	15.5885i	0.846649	+	1.46644i	−0.0375328	+	0.999295i	$0.511950\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	2.00000	−	3.46410i	0.184900	−	0.320256i
$118$	−3.00000	+	5.19615i	−0.276172	+	0.478345i
$119$	12.0000			1.10004
$120$	1.00000			0.0912871
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	4.00000	+	6.92820i	0.362143	+	0.627250i
$123$	−1.50000	−	2.59808i	−0.135250	−	0.234261i
$124$	−2.50000	+	4.33013i	−0.224507	+	0.388857i
$125$	−1.00000			−0.0894427
$126$	4.00000			0.356348
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	0.632166	−	0.774833i	$-0.282166\pi$
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	−0.987108	+	0.160055i	$0.948833\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	8.00000			0.704361
$130$	−1.00000	−	1.73205i	−0.0877058	−	0.151911i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	−3.00000	+	5.19615i	−0.261116	+	0.452267i
$133$	−8.00000			−0.693688
$134$	8.00000	+	1.73205i	0.691095	+	0.149626i
$135$	5.00000			0.430331
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$	−3.00000	−	5.19615i	−0.255377	−	0.442326i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$	−3.00000	−	5.19615i	−0.252646	−	0.437595i
$142$	15.0000			1.25877
$143$	12.0000			1.00349
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	−3.00000	−	5.19615i	−0.249136	−	0.431517i
$146$	−2.00000	−	3.46410i	−0.165521	−	0.286691i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$	−7.00000			−0.575396
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	9.50000	−	16.4545i	0.773099	−	1.33905i	0.935857	−	0.352381i	$-0.114628\pi$
$152$	−2.00000	+	3.46410i	−0.162221	+	0.280976i
$153$	6.00000	−	10.3923i	0.485071	−	0.840168i
$154$	6.00000	+	10.3923i	0.483494	+	0.837436i
$155$	2.50000	+	4.33013i	0.200805	+	0.347804i
$156$	2.00000			0.160128
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.0242497	−	0.999706i	$-0.492280\pi$
$157$	11.0000	−	19.0526i	0.877896	−	1.52056i	0.853646	−	0.520854i	$-0.174386\pi$
$158$	−8.00000			−0.636446
$159$	−3.00000			−0.237915
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−12.0000			−0.945732
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	0.950615	+	0.310372i	$0.100454\pi$
$163$	9.50000	+	16.4545i	0.744097	+	1.28881i	−0.206518	+	0.978443i	$0.566213\pi$
$164$	−1.50000	+	2.59808i	−0.117130	+	0.202876i
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$	−7.50000	−	12.9904i	−0.582113	−	1.00825i
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$	1.00000	+	1.73205i	0.0771517	+	0.133631i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−3.00000	−	5.19615i	−0.230089	−	0.398527i
$171$	−4.00000	+	6.92820i	−0.305888	+	0.529813i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	−0.803354	−	0.595502i	$-0.796953\pi$
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	0.917397	+	0.397974i	$0.130287\pi$
$174$	6.00000			0.454859
$175$	−1.00000	−	1.73205i	−0.0755929	−	0.130931i
$176$	6.00000			0.452267
$177$	−6.00000			−0.450988
$178$	4.50000	−	7.79423i	0.337289	−	0.584202i
$179$	−6.00000			−0.448461			−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000			−0.448461			−0.224231	+	0.974536i	$0.571987\pi$
$180$	−1.00000	−	1.73205i	−0.0745356	−	0.129099i
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	0.826465	−	0.562988i	$-0.190348\pi$
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	−0.900794	+	0.434246i	$0.857015\pi$
$182$	2.00000	−	3.46410i	0.148250	−	0.256776i
$183$	−4.00000	+	6.92820i	−0.295689	+	0.512148i
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	−3.50000	+	6.06218i	−0.257325	+	0.445700i
$186$	−5.00000			−0.366618
$187$	36.0000			2.63258
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$	5.00000	+	8.66025i	0.363696	+	0.629941i
$190$	2.00000	+	3.46410i	0.145095	+	0.251312i
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	−0.915177	−	0.403051i	$-0.867950\pi$
$191$	−1.50000	+	2.59808i	−0.108536	+	0.187990i	0.806641	+	0.591041i	$0.201283\pi$
$192$	1.00000			0.0721688
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$	−5.00000	−	8.66025i	−0.358979	−	0.621770i
$195$	1.00000	−	1.73205i	0.0716115	−	0.124035i
$196$	−3.00000			−0.214286
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	0.739141	−	0.673550i	$-0.235232\pi$
$197$	−3.00000	−	5.19615i	−0.213741	−	0.370211i	−0.952882	+	0.303340i	$0.901898\pi$
$198$	12.0000			0.852803
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$	−1.00000			−0.0707107
$201$	2.50000	+	7.79423i	0.176336	+	0.549762i
$202$	−12.0000			−0.844317
$203$	6.00000	−	10.3923i	0.421117	−	0.729397i
$204$	6.00000			0.420084
$205$	1.50000	+	2.59808i	0.104765	+	0.181458i
$206$	4.00000			0.278693
$207$	−6.00000	+	10.3923i	−0.417029	+	0.722315i
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−24.0000			−1.66011
$210$	2.00000			0.138013
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$	7.50000	+	12.9904i	0.513892	+	0.890086i
$214$	−4.50000	+	7.79423i	−0.307614	+	0.532803i
$215$	−8.00000			−0.545595
$216$	5.00000			0.340207
$217$	−5.00000	+	8.66025i	−0.339422	+	0.587896i
$218$	−2.00000	+	3.46410i	−0.135457	+	0.234619i
$219$	2.00000	−	3.46410i	0.135147	−	0.234082i
$220$	3.00000	−	5.19615i	0.202260	−	0.350325i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	−3.50000	−	6.06218i	−0.234905	−	0.406867i
$223$	20.0000			1.33930			0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000			1.33930			0.669650	+	0.742677i	$0.266444\pi$
$224$	1.00000	−	1.73205i	0.0668153	−	0.115728i
$225$	−2.00000			−0.133333
$226$	18.0000			1.19734
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$	−4.00000			−0.264906
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$	3.00000	+	5.19615i	0.197814	+	0.342624i
$231$	−6.00000	+	10.3923i	−0.394771	+	0.683763i
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	6.00000	+	10.3923i	0.393073	+	0.680823i	0.992853	−	0.119342i	$-0.0380786\pi$
$233$	6.00000	+	10.3923i	0.393073	+	0.680823i	−0.599780	+	0.800165i	$0.704745\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$	6.00000	−	10.3923i	0.388922	−	0.673633i
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−13.0000			−0.837404			−0.418702	−	0.908124i	$-0.637515\pi$
$241$	−13.0000			−0.837404			−0.418702	+	0.908124i	$0.637515\pi$
$242$	12.5000	+	21.6506i	0.803530	+	1.39176i
$243$	16.0000			1.02640
$244$	8.00000			0.512148
$245$	−1.50000	+	2.59808i	−0.0958315	+	0.165985i
$246$	−3.00000			−0.191273
$247$	4.00000	+	6.92820i	0.254514	+	0.440831i
$248$	2.50000	+	4.33013i	0.158750	+	0.274963i
$249$	7.50000	−	12.9904i	0.475293	−	0.823232i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$	2.00000	−	3.46410i	0.125988	−	0.218218i
$253$	−36.0000			−2.26330
$254$	−8.00000			−0.501965
$255$	3.00000	−	5.19615i	0.187867	−	0.325396i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.0000	−	20.7846i	−0.748539	−	1.29651i	−0.948523	−	0.316709i	$-0.897422\pi$
$257$	−12.0000	−	20.7846i	−0.748539	−	1.29651i	0.199983	−	0.979799i	$-0.435911\pi$
$258$	4.00000	−	6.92820i	0.249029	−	0.431331i
$259$	−14.0000			−0.869918
$260$	−2.00000			−0.124035
$261$	−6.00000	−	10.3923i	−0.371391	−	0.643268i
$262$	−6.00000	+	10.3923i	−0.370681	+	0.642039i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$	3.00000			0.184289
$266$	−4.00000	+	6.92820i	−0.245256	+	0.424795i
$267$	9.00000			0.550791
$268$	5.50000	−	6.06218i	0.335966	−	0.370306i
$269$	−18.0000			−1.09748			−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000			−1.09748			−0.548740	+	0.835993i	$0.684892\pi$
$270$	2.50000	−	4.33013i	0.152145	−	0.263523i
$271$	−13.0000			−0.789694			−0.394847	−	0.918747i	$-0.629202\pi$
$271$	−13.0000			−0.789694			−0.394847	+	0.918747i	$0.629202\pi$
$272$	−3.00000	−	5.19615i	−0.181902	−	0.315063i
$273$	4.00000			0.242091
$274$	−3.00000	+	5.19615i	−0.181237	+	0.313911i
$275$	−3.00000	−	5.19615i	−0.180907	−	0.313340i
$276$	−6.00000			−0.361158
$277$	17.0000			1.02143			0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000			1.02143			0.510716	+	0.859750i	$0.329381\pi$
$278$	−5.00000	+	8.66025i	−0.299880	+	0.519408i
$279$	5.00000	+	8.66025i	0.299342	+	0.518476i
$280$	−1.00000	−	1.73205i	−0.0597614	−	0.103510i
$281$	−16.5000	+	28.5788i	−0.984307	+	1.70487i	−0.339333	+	0.940666i	$0.610201\pi$
$281$	−16.5000	+	28.5788i	−0.984307	+	1.70487i	−0.644974	+	0.764204i	$0.723132\pi$
$282$	−6.00000			−0.357295
$283$	32.0000			1.90220			0.951101	−	0.308879i	$-0.0999539\pi$
$283$	32.0000			1.90220			0.951101	+	0.308879i	$0.0999539\pi$
$284$	7.50000	−	12.9904i	0.445043	−	0.770837i
$285$	−2.00000	+	3.46410i	−0.118470	+	0.205196i
$286$	6.00000	−	10.3923i	0.354787	−	0.614510i
$287$	−3.00000	+	5.19615i	−0.177084	+	0.306719i
$288$	−1.00000	−	1.73205i	−0.0589256	−	0.102062i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−6.00000			−0.352332
$291$	5.00000	−	8.66025i	0.293105	−	0.507673i
$292$	−4.00000			−0.234082
$293$	−21.0000			−1.22683			−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000			−1.22683			−0.613417	+	0.789760i	$0.710205\pi$
$294$	−1.50000	−	2.59808i	−0.0874818	−	0.151523i
$295$	6.00000			0.349334
$296$	−3.50000	+	6.06218i	−0.203433	+	0.352357i
$297$	15.0000	+	25.9808i	0.870388	+	1.50756i
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	−8.00000	−	13.8564i	−0.461112	−	0.798670i
$302$	−9.50000	−	16.4545i	−0.546664	−	0.946849i
$303$	−6.00000	−	10.3923i	−0.344691	−	0.597022i
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	4.00000	−	6.92820i	0.229039	−	0.396708i
$306$	−6.00000	−	10.3923i	−0.342997	−	0.594089i
$307$	3.50000	−	6.06218i	0.199756	−	0.345987i	−0.748694	−	0.662916i	$-0.769319\pi$
$307$	3.50000	−	6.06218i	0.199756	−	0.345987i	0.948449	+	0.316929i	$0.102652\pi$
$308$	12.0000			0.683763
$309$	2.00000	+	3.46410i	0.113776	+	0.197066i
$310$	5.00000			0.283981
$311$	−21.0000			−1.19080			−0.595400	−	0.803429i	$-0.703007\pi$
$311$	−21.0000			−1.19080			−0.595400	+	0.803429i	$0.703007\pi$
$312$	1.00000	−	1.73205i	0.0566139	−	0.0980581i
$313$	−22.0000			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$314$	−11.0000	−	19.0526i	−0.620766	−	1.07520i
$315$	−2.00000	−	3.46410i	−0.112687	−	0.195180i
$316$	−4.00000	+	6.92820i	−0.225018	+	0.389742i
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	−0.820822	−	0.571184i	$-0.806484\pi$
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	0.905071	+	0.425261i	$0.139818\pi$
$318$	−1.50000	+	2.59808i	−0.0841158	+	0.145693i
$319$	18.0000	−	31.1769i	1.00781	−	1.74557i
$320$	−1.00000			−0.0559017
$321$	−9.00000			−0.502331
$322$	−6.00000	+	10.3923i	−0.334367	+	0.579141i
$323$	12.0000	+	20.7846i	0.667698	+	1.15649i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$	19.0000			1.05231
$327$	−4.00000			−0.221201
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$	6.00000			0.330289
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$	−15.0000			−0.823232
$333$	−7.00000	+	12.1244i	−0.383598	+	0.664411i
$334$	−12.0000			−0.656611
$335$	−2.50000	−	7.79423i	−0.136590	−	0.425844i
$336$	2.00000			0.109109
$337$	−10.0000	+	17.3205i	−0.544735	+	0.943508i	0.453889	+	0.891058i	$0.350036\pi$
$337$	−10.0000	+	17.3205i	−0.544735	+	0.943508i	−0.998624	+	0.0524499i	$0.983297\pi$
$338$	9.00000			0.489535
$339$	9.00000	+	15.5885i	0.488813	+	0.846649i
$340$	−6.00000			−0.325396
$341$	−15.0000	+	25.9808i	−0.812296	+	1.40694i
$342$	4.00000	+	6.92820i	0.216295	+	0.374634i
$343$	−20.0000			−1.07990
$344$	−8.00000			−0.431331
$345$	−3.00000	+	5.19615i	−0.161515	+	0.279751i
$346$	−1.50000	−	2.59808i	−0.0806405	−	0.139673i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$	3.00000	−	5.19615i	0.160817	−	0.278543i
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$	−2.00000			−0.106904
$351$	5.00000	−	8.66025i	0.266880	−	0.462250i
$352$	3.00000	−	5.19615i	0.159901	−	0.276956i
$353$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$353$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$354$	−3.00000	+	5.19615i	−0.159448	+	0.276172i
$355$	−7.50000	−	12.9904i	−0.398059	−	0.689458i
$356$	−4.50000	−	7.79423i	−0.238500	−	0.413093i
$357$	12.0000			0.635107
$358$	−3.00000	+	5.19615i	−0.158555	+	0.274625i
$359$	−27.0000			−1.42501			−0.712503	−	0.701669i	$-0.752438\pi$
$359$	−27.0000			−1.42501			−0.712503	+	0.701669i	$0.752438\pi$
$360$	−2.00000			−0.105409
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	−2.00000			−0.105118
$363$	−12.5000	+	21.6506i	−0.656080	+	1.13636i
$364$	−2.00000	−	3.46410i	−0.104828	−	0.181568i
$365$	−2.00000	+	3.46410i	−0.104685	+	0.181319i
$366$	4.00000	+	6.92820i	0.209083	+	0.362143i
$367$	−7.00000	−	12.1244i	−0.365397	−	0.632886i	0.623443	−	0.781869i	$-0.285733\pi$
$367$	−7.00000	−	12.1244i	−0.365397	−	0.632886i	−0.988840	+	0.148983i	$0.952400\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	3.00000	+	5.19615i	0.156174	+	0.270501i
$370$	3.50000	+	6.06218i	0.181956	+	0.315158i
$371$	3.00000	+	5.19615i	0.155752	+	0.269771i
$372$	−2.50000	+	4.33013i	−0.129619	+	0.224507i
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	−0.993484	−	0.113975i	$-0.963641\pi$
$373$	−11.5000	−	19.9186i	−0.595447	−	1.03135i	0.398036	−	0.917370i	$-0.369692\pi$
$374$	18.0000	−	31.1769i	0.930758	−	1.61212i
$375$	−1.00000			−0.0516398
$376$	3.00000	+	5.19615i	0.154713	+	0.267971i
$377$	−12.0000			−0.618031
$378$	10.0000			0.514344
$379$	−19.0000	+	32.9090i	−0.975964	+	1.69042i	−0.299249	+	0.954175i	$0.596736\pi$
$379$	−19.0000	+	32.9090i	−0.975964	+	1.69042i	−0.676715	+	0.736245i	$0.736597\pi$
$380$	4.00000			0.205196
$381$	−4.00000	−	6.92820i	−0.204926	−	0.354943i
$382$	1.50000	+	2.59808i	0.0767467	+	0.132929i
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	−0.932436	−	0.361335i	$-0.882321\pi$
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	0.779143	+	0.626846i	$0.215654\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	6.00000	−	10.3923i	0.305788	−	0.529641i
$386$	7.00000	−	12.1244i	0.356291	−	0.617113i
$387$	−16.0000			−0.813326
$388$	−10.0000			−0.507673
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	−0.542445	−	0.840091i	$-0.682501\pi$
$389$	9.00000	−	15.5885i	0.456318	−	0.790366i	0.998763	+	0.0497253i	$0.0158346\pi$
$390$	−1.00000	−	1.73205i	−0.0506370	−	0.0877058i
$391$	18.0000	+	31.1769i	0.910299	+	1.57668i
$392$	−1.50000	+	2.59808i	−0.0757614	+	0.131223i
$393$	−12.0000			−0.605320
$394$	−6.00000			−0.302276
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$	6.00000	−	10.3923i	0.301511	−	0.522233i
$397$	5.00000			0.250943			0.125471	−	0.992097i	$-0.459956\pi$
$397$	5.00000			0.250943			0.125471	+	0.992097i	$0.459956\pi$
$398$	−3.50000	−	6.06218i	−0.175439	−	0.303870i
$399$	−8.00000			−0.400501
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	18.0000			0.898877			0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000			0.898877			0.449439	+	0.893311i	$0.351624\pi$
$402$	8.00000	+	1.73205i	0.399004	+	0.0863868i
$403$	10.0000			0.498135
$404$	−6.00000	+	10.3923i	−0.298511	+	0.517036i
$405$	−1.00000			−0.0496904
$406$	−6.00000	−	10.3923i	−0.297775	−	0.515761i
$407$	−42.0000			−2.08186
$408$	3.00000	−	5.19615i	0.148522	−	0.257248i
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	−0.766426	+	0.642333i	$0.777967\pi$
$410$	3.00000			0.148159
$411$	−6.00000			−0.295958
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$	6.00000	+	10.3923i	0.295241	+	0.511372i
$414$	6.00000	+	10.3923i	0.294884	+	0.510754i
$415$	−7.50000	+	12.9904i	−0.368161	+	0.637673i
$416$	−2.00000			−0.0980581
$417$	−10.0000			−0.489702
$418$	−12.0000	+	20.7846i	−0.586939	+	1.01661i
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	−0.408481	−	0.912767i	$-0.633942\pi$
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	0.994720	−	0.102628i	$-0.0327251\pi$
$420$	1.00000	−	1.73205i	0.0487950	−	0.0845154i
$421$	14.0000	−	24.2487i	0.682318	−	1.18181i	−0.291953	−	0.956433i	$-0.594305\pi$
$421$	14.0000	−	24.2487i	0.682318	−	1.18181i	0.974272	−	0.225377i	$-0.0723615\pi$
$422$	−2.00000	−	3.46410i	−0.0973585	−	0.168630i
$423$	6.00000	+	10.3923i	0.291730	+	0.505291i
$424$	3.00000			0.145693
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$	15.0000			0.726752
$427$	16.0000			0.774294
$428$	4.50000	+	7.79423i	0.217516	+	0.376748i
$429$	12.0000			0.579365
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$	16.5000	+	28.5788i	0.794777	+	1.37659i	0.922981	+	0.384846i	$0.125746\pi$
$431$	16.5000	+	28.5788i	0.794777	+	1.37659i	−0.128204	+	0.991748i	$0.540921\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	0.991693	−	0.128624i	$-0.0410559\pi$
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	−0.607238	+	0.794520i	$0.707723\pi$
$434$	5.00000	+	8.66025i	0.240008	+	0.415705i
$435$	−3.00000	−	5.19615i	−0.143839	−	0.249136i
$436$	2.00000	+	3.46410i	0.0957826	+	0.165900i
$437$	−12.0000	−	20.7846i	−0.574038	−	0.994263i
$438$	−2.00000	−	3.46410i	−0.0955637	−	0.165521i
$439$	9.50000	−	16.4545i	0.453410	−	0.785330i	−0.545185	−	0.838316i	$-0.683541\pi$
$439$	9.50000	−	16.4545i	0.453410	−	0.785330i	0.998595	+	0.0529862i	$0.0168739\pi$
$440$	−3.00000	−	5.19615i	−0.143019	−	0.247717i
$441$	−3.00000	+	5.19615i	−0.142857	+	0.247436i
$442$	−12.0000			−0.570782
$443$	−13.5000	−	23.3827i	−0.641404	−	1.11094i	−0.985119	−	0.171871i	$-0.945019\pi$
$443$	−13.5000	−	23.3827i	−0.641404	−	1.11094i	0.343715	−	0.939074i	$-0.388315\pi$
$444$	−7.00000			−0.332205
$445$	−9.00000			−0.426641
$446$	10.0000	−	17.3205i	0.473514	−	0.820150i
$447$	6.00000			0.283790
$448$	−1.00000	−	1.73205i	−0.0472456	−	0.0818317i
$449$	−10.5000	−	18.1865i	−0.495526	−	0.858276i	0.504461	−	0.863434i	$-0.331691\pi$
$449$	−10.5000	−	18.1865i	−0.495526	−	0.858276i	−0.999987	+	0.00515887i	$0.998358\pi$
$450$	−1.00000	+	1.73205i	−0.0471405	+	0.0816497i
$451$	−9.00000	+	15.5885i	−0.423793	+	0.734032i
$452$	9.00000	−	15.5885i	0.423324	−	0.733219i
$453$	9.50000	−	16.4545i	0.446349	−	0.773099i
$454$	3.00000			0.140797
$455$	−4.00000			−0.187523
$456$	−2.00000	+	3.46410i	−0.0936586	+	0.162221i
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	0.999857	+	0.0168929i	$0.00537742\pi$
$457$	11.0000	+	19.0526i	0.514558	+	0.891241i	−0.485299	+	0.874348i	$0.661289\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$	15.0000	−	25.9808i	0.700140	−	1.21268i
$460$	6.00000			0.279751
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$	6.00000	+	10.3923i	0.279145	+	0.483494i
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	−0.815802	−	0.578331i	$-0.803704\pi$
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	0.908750	+	0.417340i	$0.137038\pi$
$464$	−6.00000			−0.278543
$465$	2.50000	+	4.33013i	0.115935	+	0.200805i
$466$	12.0000			0.555889
$467$	16.5000	−	28.5788i	0.763529	−	1.32247i	−0.177492	−	0.984122i	$-0.556798\pi$
$467$	16.5000	−	28.5788i	0.763529	−	1.32247i	0.941021	−	0.338349i	$-0.109868\pi$
$468$	−4.00000			−0.184900
$469$	11.0000	−	12.1244i	0.507933	−	0.559851i
$470$	6.00000			0.276759
$471$	11.0000	−	19.0526i	0.506853	−	0.877896i
$472$	6.00000			0.276172
$473$	−24.0000	−	41.5692i	−1.10352	−	1.91135i
$474$	−8.00000			−0.367452
$475$	2.00000	−	3.46410i	0.0917663	−	0.158944i
$476$	−6.00000	−	10.3923i	−0.275010	−	0.476331i
$477$	6.00000			0.274721
$478$		0			0
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	−0.969920	−	0.243426i	$-0.921729\pi$
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	0.695773	+	0.718262i	$0.255062\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	7.00000	+	12.1244i	0.319173	+	0.552823i
$482$	−6.50000	+	11.2583i	−0.296067	+	0.512803i
$483$	−12.0000			−0.546019
$484$	25.0000			1.13636
$485$	−5.00000	+	8.66025i	−0.227038	+	0.393242i
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	4.00000	−	6.92820i	0.181071	−	0.313625i
$489$	9.50000	+	16.4545i	0.429605	+	0.744097i
$490$	1.50000	+	2.59808i	0.0677631	+	0.117369i
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$	−1.50000	+	2.59808i	−0.0676252	+	0.117130i
$493$	−36.0000			−1.62136
$494$	8.00000			0.359937
$495$	−6.00000	−	10.3923i	−0.269680	−	0.467099i
$496$	5.00000			0.224507
$497$	15.0000	−	25.9808i	0.672842	−	1.16540i
$498$	−7.50000	−	12.9904i	−0.336083	−	0.582113i
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.0619186	−	0.998081i	$-0.480278\pi$
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.833404	−	0.552664i	$-0.186389\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	6.00000	+	10.3923i	0.267793	+	0.463831i
$503$	15.0000	+	25.9808i	0.668817	+	1.15842i	0.978235	+	0.207499i	$0.0665323\pi$
$503$	15.0000	+	25.9808i	0.668817	+	1.15842i	−0.309418	+	0.950926i	$0.600134\pi$
$504$	−2.00000	−	3.46410i	−0.0890871	−	0.154303i
$505$	6.00000	+	10.3923i	0.266996	+	0.462451i
$506$	−18.0000	+	31.1769i	−0.800198	+	1.38598i
$507$	4.50000	+	7.79423i	0.199852	+	0.346154i
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	−18.0000			−0.797836			−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000			−0.797836			−0.398918	+	0.916987i	$0.630614\pi$
$510$	−3.00000	−	5.19615i	−0.132842	−	0.230089i
$511$	−8.00000			−0.353899
$512$	−1.00000			−0.0441942
$513$	−10.0000	+	17.3205i	−0.441511	+	0.764719i
$514$	−24.0000			−1.05859
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	−18.0000	+	31.1769i	−0.791639	+	1.37116i
$518$	−7.00000	+	12.1244i	−0.307562	+	0.532714i
$519$	1.50000	−	2.59808i	0.0658427	−	0.114043i
$520$	−1.00000	+	1.73205i	−0.0438529	+	0.0759555i
$521$	42.0000			1.84005			0.920027	−	0.391856i	$-0.128167\pi$
$521$	42.0000			1.84005			0.920027	+	0.391856i	$0.128167\pi$
$522$	−12.0000			−0.525226
$523$	−2.50000	+	4.33013i	−0.109317	+	0.189343i	−0.915494	−	0.402332i	$-0.868200\pi$
$523$	−2.50000	+	4.33013i	−0.109317	+	0.189343i	0.806177	+	0.591675i	$0.201533\pi$
$524$	6.00000	+	10.3923i	0.262111	+	0.453990i
$525$	−1.00000	−	1.73205i	−0.0436436	−	0.0755929i
$526$		0			0
$527$	30.0000			1.30682
$528$	6.00000			0.261116
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	1.50000	−	2.59808i	0.0651558	−	0.112853i
$531$	12.0000			0.520756
$532$	4.00000	+	6.92820i	0.173422	+	0.300376i
$533$	6.00000			0.259889
$534$	4.50000	−	7.79423i	0.194734	−	0.337289i
$535$	9.00000			0.389104
$536$	−2.50000	−	7.79423i	−0.107984	−	0.336659i
$537$	−6.00000			−0.258919
$538$	−9.00000	+	15.5885i	−0.388018	+	0.672066i
$539$	−18.0000			−0.775315
$540$	−2.50000	−	4.33013i	−0.107583	−	0.186339i
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$	−6.50000	+	11.2583i	−0.279199	+	0.483587i
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$	−6.00000			−0.257248
$545$	4.00000			0.171341
$546$	2.00000	−	3.46410i	0.0855921	−	0.148250i
$547$	12.5000	+	21.6506i	0.534461	+	0.925714i	0.999189	+	0.0402607i	$0.0128188\pi$
$547$	12.5000	+	21.6506i	0.534461	+	0.925714i	−0.464728	+	0.885454i	$0.653848\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$	8.00000	−	13.8564i	0.341432	−	0.591377i
$550$	−6.00000			−0.255841
$551$	24.0000			1.02243
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	−8.00000	+	13.8564i	−0.340195	+	0.589234i
$554$	8.50000	−	14.7224i	0.361130	−	0.625496i
$555$	−3.50000	+	6.06218i	−0.148567	+	0.257325i
$556$	5.00000	+	8.66025i	0.212047	+	0.367277i
$557$	−19.5000	−	33.7750i	−0.826242	−	1.43109i	−0.900967	−	0.433888i	$-0.857141\pi$
$557$	−19.5000	−	33.7750i	−0.826242	−	1.43109i	0.0747252	−	0.997204i	$-0.476192\pi$
$558$	10.0000			0.423334
$559$	−8.00000	+	13.8564i	−0.338364	+	0.586064i
$560$	−2.00000			−0.0845154
$561$	36.0000			1.51992
$562$	16.5000	+	28.5788i	0.696010	+	1.20553i
$563$	−3.00000			−0.126435			−0.0632175	−	0.998000i	$-0.520136\pi$
$563$	−3.00000			−0.126435			−0.0632175	+	0.998000i	$0.520136\pi$
$564$	−3.00000	+	5.19615i	−0.126323	+	0.218797i
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$	16.0000	−	27.7128i	0.672530	−	1.16486i
$567$	−1.00000	−	1.73205i	−0.0419961	−	0.0727393i
$568$	−7.50000	−	12.9904i	−0.314693	−	0.545064i
$569$	13.5000	+	23.3827i	0.565949	+	0.980253i	0.996961	+	0.0779066i	$0.0248236\pi$
$569$	13.5000	+	23.3827i	0.565949	+	0.980253i	−0.431011	+	0.902347i	$0.641843\pi$
$570$	2.00000	+	3.46410i	0.0837708	+	0.145095i
$571$	20.0000	+	34.6410i	0.836974	+	1.44968i	0.892413	+	0.451219i	$0.149011\pi$
$571$	20.0000	+	34.6410i	0.836974	+	1.44968i	−0.0554391	+	0.998462i	$0.517656\pi$
$572$	−6.00000	−	10.3923i	−0.250873	−	0.434524i
$573$	−1.50000	+	2.59808i	−0.0626634	+	0.108536i
$574$	3.00000	+	5.19615i	0.125218	+	0.216883i
$575$	3.00000	−	5.19615i	0.125109	−	0.216695i
$576$	−2.00000			−0.0833333
$577$	8.00000	+	13.8564i	0.333044	+	0.576850i	0.983107	−	0.183031i	$-0.0585908\pi$
$577$	8.00000	+	13.8564i	0.333044	+	0.576850i	−0.650063	+	0.759880i	$0.725257\pi$
$578$	−19.0000			−0.790296
$579$	14.0000			0.581820
$580$	−3.00000	+	5.19615i	−0.124568	+	0.215758i
$581$	−30.0000			−1.24461
$582$	−5.00000	−	8.66025i	−0.207257	−	0.358979i
$583$	9.00000	+	15.5885i	0.372742	+	0.645608i
$584$	−2.00000	+	3.46410i	−0.0827606	+	0.143346i
$585$	−2.00000	+	3.46410i	−0.0826898	+	0.143223i
$586$	−10.5000	+	18.1865i	−0.433751	+	0.751279i
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	−0.293640	−	0.955916i	$-0.594867\pi$
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	0.974668	−	0.223659i	$-0.0718001\pi$
$588$	−3.00000			−0.123718
$589$	−20.0000			−0.824086
$590$	3.00000	−	5.19615i	0.123508	−	0.213922i
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$593$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$594$	30.0000			1.23091
$595$	−12.0000			−0.491952
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$	3.50000	−	6.06218i	0.143245	−	0.248108i
$598$	12.0000			0.490716
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$	−1.00000			−0.0408248
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	−0.745845	−	0.666120i	$-0.767954\pi$
$601$	5.00000	−	8.66025i	0.203954	−	0.353259i	0.949799	+	0.312861i	$0.101287\pi$
$602$	−16.0000			−0.652111
$603$	−5.00000	−	15.5885i	−0.203616	−	0.634811i
$604$	−19.0000			−0.773099
$605$	12.5000	−	21.6506i	0.508197	−	0.880223i
$606$	−12.0000			−0.487467
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	4.00000			0.162221
$609$	6.00000	−	10.3923i	0.243132	−	0.421117i
$610$	−4.00000	−	6.92820i	−0.161955	−	0.280515i
$611$	12.0000			0.485468
$612$	−12.0000			−0.485071
$613$	21.5000	−	37.2391i	0.868377	−	1.50407i	0.00472215	−	0.999989i	$-0.498497\pi$
$613$	21.5000	−	37.2391i	0.868377	−	1.50407i	0.863655	−	0.504084i	$-0.168170\pi$
$614$	−3.50000	−	6.06218i	−0.141249	−	0.244650i
$615$	1.50000	+	2.59808i	0.0604858	+	0.104765i
$616$	6.00000	−	10.3923i	0.241747	−	0.418718i
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	4.00000			0.160904
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$	2.50000	−	4.33013i	0.100402	−	0.173902i
$621$	−15.0000	+	25.9808i	−0.601929	+	1.04257i
$622$	−10.5000	+	18.1865i	−0.421012	+	0.729214i
$623$	−9.00000	−	15.5885i	−0.360577	−	0.624538i
$624$	−1.00000	−	1.73205i	−0.0400320	−	0.0693375i
$625$	1.00000			0.0400000
$626$	−11.0000	+	19.0526i	−0.439648	+	0.761493i
$627$	−24.0000			−0.958468
$628$	−22.0000			−0.877896
$629$	21.0000	+	36.3731i	0.837325	+	1.45029i
$630$	−4.00000			−0.159364
$631$	−4.00000	+	6.92820i	−0.159237	+	0.275807i	−0.934594	−	0.355716i	$-0.884237\pi$
$631$	−4.00000	+	6.92820i	−0.159237	+	0.275807i	0.775356	+	0.631524i	$0.217570\pi$
$632$	4.00000	+	6.92820i	0.159111	+	0.275589i
$633$	2.00000	−	3.46410i	0.0794929	−	0.137686i
$634$	−1.50000	−	2.59808i	−0.0595726	−	0.103183i
$635$	4.00000	+	6.92820i	0.158735	+	0.274937i
$636$	1.50000	+	2.59808i	0.0594789	+	0.103020i
$637$	3.00000	+	5.19615i	0.118864	+	0.205879i
$638$	−18.0000	−	31.1769i	−0.712627	−	1.23431i
$639$	−15.0000	−	25.9808i	−0.593391	−	1.02778i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$	−4.50000	+	7.79423i	−0.177601	+	0.307614i
$643$	41.0000			1.61688			0.808441	−	0.588577i	$-0.200312\pi$
$643$	41.0000			1.61688			0.808441	+	0.588577i	$0.200312\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$	−8.00000			−0.315000
$646$	24.0000			0.944267
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	−1.00000			−0.0392837
$649$	18.0000	+	31.1769i	0.706562	+	1.22380i
$650$	1.00000	+	1.73205i	0.0392232	+	0.0679366i
$651$	−5.00000	+	8.66025i	−0.195965	+	0.339422i
$652$	9.50000	−	16.4545i	0.372049	−	0.644407i
$653$	22.5000	−	38.9711i	0.880493	−	1.52506i	0.0296993	−	0.999559i	$-0.490545\pi$
$653$	22.5000	−	38.9711i	0.880493	−	1.52506i	0.850794	−	0.525500i	$-0.176122\pi$
$654$	−2.00000	+	3.46410i	−0.0782062	+	0.135457i
$655$	12.0000			0.468879
$656$	3.00000			0.117130
$657$	−4.00000	+	6.92820i	−0.156055	+	0.270295i
$658$	6.00000	+	10.3923i	0.233904	+	0.405134i
$659$	9.00000	+	15.5885i	0.350590	+	0.607240i	0.986353	−	0.164644i	$-0.0526477\pi$
$659$	9.00000	+	15.5885i	0.350590	+	0.607240i	−0.635763	+	0.771885i	$0.719314\pi$
$660$	3.00000	−	5.19615i	0.116775	−	0.202260i
$661$	−40.0000			−1.55582			−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000			−1.55582			−0.777910	+	0.628376i	$0.783720\pi$
$662$	−8.00000			−0.310929
$663$	−6.00000	−	10.3923i	−0.233021	−	0.403604i
$664$	−7.50000	+	12.9904i	−0.291056	+	0.504125i
$665$	8.00000			0.310227
$666$	7.00000	+	12.1244i	0.271244	+	0.469809i
$667$	36.0000			1.39393
$668$	−6.00000	+	10.3923i	−0.232147	+	0.402090i
$669$	20.0000			0.773245
$670$	−8.00000	−	1.73205i	−0.309067	−	0.0669150i
$671$	48.0000			1.85302
$672$	1.00000	−	1.73205i	0.0385758	−	0.0668153i
$673$	20.0000			0.770943			0.385472	−	0.922720i	$-0.374039\pi$
$673$	20.0000			0.770943			0.385472	+	0.922720i	$0.374039\pi$
$674$	10.0000	+	17.3205i	0.385186	+	0.667161i
$675$	−5.00000			−0.192450
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	4.50000	+	7.79423i	0.172949	+	0.299557i	0.939450	−	0.342687i	$-0.111337\pi$
$677$	4.50000	+	7.79423i	0.172949	+	0.299557i	−0.766501	+	0.642244i	$0.778004\pi$
$678$	18.0000			0.691286
$679$	−20.0000			−0.767530
$680$	−3.00000	+	5.19615i	−0.115045	+	0.199263i
$681$	1.50000	+	2.59808i	0.0574801	+	0.0995585i
$682$	15.0000	+	25.9808i	0.574380	+	0.994855i
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	−0.939184	−	0.343413i	$-0.888417\pi$
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	0.766997	+	0.641651i	$0.221750\pi$
$684$	8.00000			0.305888
$685$	6.00000			0.229248
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	5.00000	−	8.66025i	0.190762	−	0.330409i
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	3.00000	−	5.19615i	0.114291	−	0.197958i
$690$	3.00000	+	5.19615i	0.114208	+	0.197814i
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	0.0555386	−	0.998457i	$-0.482312\pi$
$692$	−3.00000			−0.114043
$693$	12.0000	−	20.7846i	0.455842	−	0.789542i
$694$	12.0000			0.455514
$695$	10.0000			0.379322
$696$	−3.00000	−	5.19615i	−0.113715	−	0.196960i
$697$	18.0000			0.681799
$698$	−5.00000	+	8.66025i	−0.189253	+	0.327795i
$699$	6.00000	+	10.3923i	0.226941	+	0.393073i
$700$	−1.00000	+	1.73205i	−0.0377964	+	0.0654654i
$701$	15.0000	+	25.9808i	0.566542	+	0.981280i	0.996904	+	0.0786236i	$0.0250525\pi$
$701$	15.0000	+	25.9808i	0.566542	+	0.981280i	−0.430362	+	0.902656i	$0.641614\pi$
$702$	−5.00000	−	8.66025i	−0.188713	−	0.326860i
$703$	−14.0000	−	24.2487i	−0.528020	−	0.914557i
$704$	−3.00000	−	5.19615i	−0.113067	−	0.195837i
$705$	3.00000	+	5.19615i	0.112987	+	0.195698i
$706$		0			0
$707$	−12.0000	+	20.7846i	−0.451306	+	0.781686i
$708$	3.00000	+	5.19615i	0.112747	+	0.195283i
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$	−15.0000			−0.562940
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$	−9.00000			−0.337289
$713$	−30.0000			−1.12351
$714$	6.00000	−	10.3923i	0.224544	−	0.388922i
$715$	−12.0000			−0.448775
$716$	3.00000	+	5.19615i	0.112115	+	0.194189i
$717$		0			0
$718$	−13.5000	+	23.3827i	−0.503816	+	0.872634i
$719$	−19.5000	+	33.7750i	−0.727227	+	1.25959i	0.230823	+	0.972996i	$0.425858\pi$
$719$	−19.5000	+	33.7750i	−0.727227	+	1.25959i	−0.958051	+	0.286599i	$0.907475\pi$
$720$	−1.00000	+	1.73205i	−0.0372678	+	0.0645497i
$721$	4.00000	−	6.92820i	0.148968	−	0.258020i
$722$	3.00000			0.111648
$723$	−13.0000			−0.483475
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	3.00000	+	5.19615i	0.111417	+	0.192980i
$726$	12.5000	+	21.6506i	0.463919	+	0.803530i
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	−0.480519	−	0.876984i	$-0.659552\pi$
$727$	14.0000	−	24.2487i	0.519231	−	0.899335i	0.999750	−	0.0223506i	$-0.00711500\pi$
$728$	−4.00000			−0.148250
$729$	13.0000			0.481481
$730$	2.00000	+	3.46410i	0.0740233	+	0.128212i
$731$	−24.0000	+	41.5692i	−0.887672	+	1.53749i
$732$	8.00000			0.295689
$733$	−2.50000	−	4.33013i	−0.0923396	−	0.159937i	0.816156	−	0.577832i	$-0.196101\pi$
$733$	−2.50000	−	4.33013i	−0.0923396	−	0.159937i	−0.908495	+	0.417895i	$0.862768\pi$
$734$	−14.0000			−0.516749
$735$	−1.50000	+	2.59808i	−0.0553283	+	0.0958315i
$736$	6.00000			0.221163
$737$	33.0000	−	36.3731i	1.21557	−	1.33982i
$738$	6.00000			0.220863
$739$	−4.00000	+	6.92820i	−0.147142	+	0.254858i	−0.930170	−	0.367129i	$-0.880341\pi$
$739$	−4.00000	+	6.92820i	−0.147142	+	0.254858i	0.783028	+	0.621987i	$0.213674\pi$
$740$	7.00000			0.257325
$741$	4.00000	+	6.92820i	0.146944	+	0.254514i
$742$	6.00000			0.220267
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	−0.915794	−	0.401648i	$-0.868437\pi$
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	0.805735	+	0.592277i	$0.201771\pi$
$744$	2.50000	+	4.33013i	0.0916544	+	0.158750i
$745$	−6.00000			−0.219823
$746$	−23.0000			−0.842090
$747$	−15.0000	+	25.9808i	−0.548821	+	0.950586i
$748$	−18.0000	−	31.1769i	−0.658145	−	1.13994i
$749$	9.00000	+	15.5885i	0.328853	+	0.569590i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	41.0000			1.49611			0.748056	−	0.663636i	$-0.230988\pi$
$751$	41.0000			1.49611			0.748056	+	0.663636i	$0.230988\pi$
$752$	6.00000			0.218797
$753$	−6.00000	+	10.3923i	−0.218652	+	0.378717i
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$	−9.50000	+	16.4545i	−0.345740	+	0.598840i
$756$	5.00000	−	8.66025i	0.181848	−	0.314970i
$757$	−14.5000	−	25.1147i	−0.527011	−	0.912811i	−0.999505	−	0.0314762i	$-0.989979\pi$
$757$	−14.5000	−	25.1147i	−0.527011	−	0.912811i	0.472493	−	0.881334i	$-0.343354\pi$
$758$	19.0000	+	32.9090i	0.690111	+	1.19531i
$759$	−36.0000			−1.30672
$760$	2.00000	−	3.46410i	0.0725476	−	0.125656i
$761$	33.0000			1.19625			0.598125	−	0.801403i	$-0.295913\pi$
$761$	33.0000			1.19625			0.598125	+	0.801403i	$0.295913\pi$
$762$	−8.00000			−0.289809
$763$	4.00000	+	6.92820i	0.144810	+	0.250818i
$764$	3.00000			0.108536
$765$	−6.00000	+	10.3923i	−0.216930	+	0.375735i
$766$	3.00000	+	5.19615i	0.108394	+	0.187745i
$767$	6.00000	−	10.3923i	0.216647	−	0.375244i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$	−6.00000	−	10.3923i	−0.216225	−	0.374513i
$771$	−12.0000	−	20.7846i	−0.432169	−	0.748539i
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	0.613062	−	0.790034i	$-0.289937\pi$
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	−0.990721	+	0.135910i	$0.956604\pi$
$774$	−8.00000	+	13.8564i	−0.287554	+	0.498058i
$775$	−2.50000	−	4.33013i	−0.0898027	−	0.155543i
$776$	−5.00000	+	8.66025i	−0.179490	+	0.310885i
$777$	−14.0000			−0.502247
$778$	−9.00000	−	15.5885i	−0.322666	−	0.558873i
$779$	−12.0000			−0.429945
$780$	−2.00000			−0.0716115
$781$	45.0000	−	77.9423i	1.61023	−	2.78899i
$782$	36.0000			1.28736
$783$	−15.0000	−	25.9808i	−0.536056	−	0.928477i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$	−11.0000	+	19.0526i	−0.392607	+	0.680015i
$786$	−6.00000	+	10.3923i	−0.214013	+	0.370681i
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	−0.976812	−	0.214097i	$-0.931319\pi$
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	0.673820	+	0.738896i	$0.264652\pi$
$788$	−3.00000	+	5.19615i	−0.106871	+	0.185105i
$789$		0			0
$790$	8.00000			0.284627
$791$	18.0000	−	31.1769i	0.640006	−	1.10852i
$792$	−6.00000	−	10.3923i	−0.213201	−	0.369274i
$793$	−8.00000	−	13.8564i	−0.284088	−	0.492055i
$794$	2.50000	−	4.33013i	0.0887217	−	0.153670i
$795$	3.00000			0.106399
$796$	−7.00000			−0.248108
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	0.999687	−	0.0249984i	$-0.00795805\pi$
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	−0.521493	+	0.853256i	$0.674625\pi$
$798$	−4.00000	+	6.92820i	−0.141598	+	0.245256i
$799$	36.0000			1.27359
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−18.0000			−0.635999
$802$	9.00000	−	15.5885i	0.317801	−	0.550448i
$803$	−24.0000			−0.846942
$804$	5.50000	−	6.06218i	0.193970	−	0.213797i
$805$	12.0000			0.422944
$806$	5.00000	−	8.66025i	0.176117	−	0.305044i
$807$	−18.0000			−0.633630
$808$	6.00000	+	10.3923i	0.211079	+	0.365600i
$809$	30.0000			1.05474			0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000			1.05474			0.527372	+	0.849635i	$0.323177\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−19.0000	−	32.9090i	−0.667180	−	1.15559i	−0.978689	−	0.205347i	$-0.934168\pi$
$811$	−19.0000	−	32.9090i	−0.667180	−	1.15559i	0.311509	−	0.950243i	$-0.399166\pi$
$812$	−12.0000			−0.421117
$813$	−13.0000			−0.455930
$814$	−21.0000	+	36.3731i	−0.736050	+	1.27488i
$815$	−9.50000	−	16.4545i	−0.332770	−	0.576375i
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	16.0000	−	27.7128i	0.559769	−	0.969549i
$818$	7.00000			0.244749
$819$	−8.00000			−0.279543
$820$	1.50000	−	2.59808i	0.0523823	−	0.0907288i
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	−0.222731	−	0.974880i	$-0.571497\pi$
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	0.955636	−	0.294549i	$-0.0951694\pi$
$822$	−3.00000	+	5.19615i	−0.104637	+	0.181237i
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	−0.961851	−	0.273573i	$-0.911795\pi$
$823$	−7.00000	+	12.1244i	−0.244005	+	0.422628i	0.717847	+	0.696201i	$0.245128\pi$
$824$	−2.00000	−	3.46410i	−0.0696733	−	0.120678i
$825$	−3.00000	−	5.19615i	−0.104447	−	0.180907i
$826$	12.0000			0.417533
$827$	6.00000	−	10.3923i	0.208640	−	0.361376i	−0.742646	−	0.669684i	$-0.766429\pi$
$827$	6.00000	−	10.3923i	0.208640	−	0.361376i	0.951286	+	0.308308i	$0.0997628\pi$
$828$	12.0000			0.417029
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$	7.50000	+	12.9904i	0.260329	+	0.450903i
$831$	17.0000			0.589723
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	9.00000	+	15.5885i	0.311832	+	0.540108i
$834$	−5.00000	+	8.66025i	−0.173136	+	0.299880i
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$	12.0000	+	20.7846i	0.415029	+	0.718851i
$837$	12.5000	+	21.6506i	0.432063	+	0.748355i
$838$	−12.0000	−	20.7846i	−0.414533	−	0.717992i
$839$	−13.5000	−	23.3827i	−0.466072	−	0.807260i	0.533177	−	0.846003i	$-0.320998\pi$
$839$	−13.5000	−	23.3827i	−0.466072	−	0.807260i	−0.999249	+	0.0387435i	$0.987664\pi$
$840$	−1.00000	−	1.73205i	−0.0345033	−	0.0597614i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−14.0000	−	24.2487i	−0.482472	−	0.835666i
$843$	−16.5000	+	28.5788i	−0.568290	+	0.984307i
$844$	−4.00000			−0.137686
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$	12.0000			0.412568
$847$	50.0000			1.71802
$848$	1.50000	−	2.59808i	0.0515102	−	0.0892183i
$849$	32.0000			1.09824
$850$	3.00000	+	5.19615i	0.102899	+	0.178227i
$851$	−21.0000	−	36.3731i	−0.719871	−	1.24685i
$852$	7.50000	−	12.9904i	0.256946	−	0.445043i
$853$	−2.50000	+	4.33013i	−0.0855984	+	0.148261i	−0.905646	−	0.424034i	$-0.860614\pi$
$853$	−2.50000	+	4.33013i	−0.0855984	+	0.148261i	0.820048	+	0.572295i	$0.193947\pi$
$854$	8.00000	−	13.8564i	0.273754	−	0.474156i
$855$	4.00000	−	6.92820i	0.136797	−	0.236940i
$856$	9.00000			0.307614
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$	6.00000	−	10.3923i	0.204837	−	0.354787i
$859$	−13.0000	−	22.5167i	−0.443554	−	0.768259i	0.554396	−	0.832253i	$-0.312949\pi$
$859$	−13.0000	−	22.5167i	−0.443554	−	0.768259i	−0.997950	+	0.0639945i	$0.979616\pi$
$860$	4.00000	+	6.92820i	0.136399	+	0.236250i
$861$	−3.00000	+	5.19615i	−0.102240	+	0.177084i
$862$	33.0000			1.12398
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$	−1.50000	+	2.59808i	−0.0510015	+	0.0883372i
$866$	16.0000			0.543702
$867$	−9.50000	−	16.4545i	−0.322637	−	0.558824i
$868$	10.0000			0.339422
$869$	−24.0000	+	41.5692i	−0.814144	+	1.41014i
$870$	−6.00000			−0.203419
$871$	−16.0000	−	3.46410i	−0.542139	−	0.117377i
$872$	4.00000			0.135457
$873$	−10.0000	+	17.3205i	−0.338449	+	0.586210i
$874$	−24.0000			−0.811812
$875$	1.00000	+	1.73205i	0.0338062	+	0.0585540i
$876$	−4.00000			−0.135147
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	0.0421327	+	0.999112i	$0.486585\pi$
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	−0.886323	+	0.463068i	$0.846749\pi$
$878$	−9.50000	−	16.4545i	−0.320609	−	0.555312i
$879$	−21.0000			−0.708312
$880$	−6.00000			−0.202260
$881$	−22.5000	+	38.9711i	−0.758044	+	1.31297i	0.185802	+	0.982587i	$0.440512\pi$
$881$	−22.5000	+	38.9711i	−0.758044	+	1.31297i	−0.943847	+	0.330384i	$0.892822\pi$
$882$	3.00000	+	5.19615i	0.101015	+	0.174964i
$883$	20.0000	+	34.6410i	0.673054	+	1.16576i	0.977034	+	0.213085i	$0.0683510\pi$
$883$	20.0000	+	34.6410i	0.673054	+	1.16576i	−0.303980	+	0.952678i	$0.598316\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$	6.00000			0.201688
$886$	−27.0000			−0.907083
$887$	−15.0000	+	25.9808i	−0.503651	+	0.872349i	0.496340	+	0.868128i	$0.334677\pi$
$887$	−15.0000	+	25.9808i	−0.503651	+	0.872349i	−0.999991	+	0.00422062i	$0.998657\pi$
$888$	−3.50000	+	6.06218i	−0.117452	+	0.203433i
$889$	−8.00000	+	13.8564i	−0.268311	+	0.464729i
$890$	−4.50000	+	7.79423i	−0.150840	+	0.261263i
$891$	−3.00000	−	5.19615i	−0.100504	−	0.174078i
$892$	−10.0000	−	17.3205i	−0.334825	−	0.579934i
$893$	−24.0000			−0.803129
$894$	3.00000	−	5.19615i	0.100335	−	0.173785i
$895$	6.00000			0.200558
$896$	−2.00000			−0.0668153
$897$	6.00000	+	10.3923i	0.200334	+	0.346989i
$898$	−21.0000			−0.700779
$899$	15.0000	−	25.9808i	0.500278	−	0.866507i
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$	9.00000	+	15.5885i	0.299667	+	0.519039i
$903$	−8.00000	−	13.8564i	−0.266223	−	0.461112i
$904$	−9.00000	−	15.5885i	−0.299336	−	0.518464i
$905$	1.00000	+	1.73205i	0.0332411	+	0.0575753i
$906$	−9.50000	−	16.4545i	−0.315616	−	0.546664i
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	0.990510	+	0.137441i	$0.0438878\pi$
$907$	18.5000	+	32.0429i	0.614282	+	1.06397i	−0.376228	+	0.926527i	$0.622779\pi$
$908$	1.50000	−	2.59808i	0.0497792	−	0.0862202i
$909$	12.0000	+	20.7846i	0.398015	+	0.689382i
$910$	−2.00000	+	3.46410i	−0.0662994	+	0.114834i
$911$	27.0000			0.894550			0.447275	−	0.894397i	$-0.352395\pi$
$911$	27.0000			0.894550			0.447275	+	0.894397i	$0.352395\pi$
$912$	2.00000	+	3.46410i	0.0662266	+	0.114708i
$913$	−90.0000			−2.97857
$914$	22.0000			0.727695
$915$	4.00000	−	6.92820i	0.132236	−	0.229039i
$916$	−10.0000			−0.330409
$917$	12.0000	+	20.7846i	0.396275	+	0.686368i
$918$	−15.0000	−	25.9808i	−0.495074	−	0.857493i
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	−0.999691	−	0.0248659i	$-0.992084\pi$
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	0.521380	+	0.853325i	$0.325417\pi$
$920$	3.00000	−	5.19615i	0.0989071	−	0.171312i
$921$	3.50000	−	6.06218i	0.115329	−	0.199756i
$922$	6.00000	−	10.3923i	0.197599	−	0.342252i
$923$	−30.0000			−0.987462
$924$	12.0000			0.394771
$925$	3.50000	−	6.06218i	0.115079	−	0.199323i
$926$	−2.00000	−	3.46410i	−0.0657241	−	0.113837i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	42.0000			1.37798			0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000			1.37798			0.688988	+	0.724773i	$0.258055\pi$
$930$	5.00000			0.163956
$931$	−6.00000	−	10.3923i	−0.196642	−	0.340594i
$932$	6.00000	−	10.3923i	0.196537	−	0.340411i
$933$	−21.0000			−0.687509
$934$	−16.5000	−	28.5788i	−0.539896	−	0.935128i
$935$	−36.0000			−1.17733
$936$	−2.00000	+	3.46410i	−0.0653720	+	0.113228i
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$	−5.00000	−	15.5885i	−0.163256	−	0.508981i
$939$	−22.0000			−0.717943
$940$	3.00000	−	5.19615i	0.0978492	−	0.169480i
$941$	30.0000			0.977972			0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000			0.977972			0.488986	+	0.872292i	$0.337367\pi$
$942$	−11.0000	−	19.0526i	−0.358399	−	0.620766i
$943$	−18.0000			−0.586161
$944$	3.00000	−	5.19615i	0.0976417	−	0.169120i
$945$	−5.00000	−	8.66025i	−0.162650	−	0.281718i
$946$	−48.0000			−1.56061
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$	−4.00000	+	6.92820i	−0.129914	+	0.225018i
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$	−2.00000	−	3.46410i	−0.0648886	−	0.112390i
$951$	1.50000	−	2.59808i	0.0486408	−	0.0842484i
$952$	−12.0000			−0.388922
$953$	30.0000			0.971795			0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000			0.971795			0.485898	+	0.874016i	$0.338493\pi$
$954$	3.00000	−	5.19615i	0.0971286	−	0.168232i
$955$	1.50000	−	2.59808i	0.0485389	−	0.0840718i
$956$		0			0
$957$	18.0000	−	31.1769i	0.581857	−	1.00781i
$958$	6.00000	+	10.3923i	0.193851	+	0.335760i
$959$	6.00000	+	10.3923i	0.193750	+	0.335585i
$960$	−1.00000			−0.0322749
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	14.0000			0.451378
$963$	18.0000			0.580042
$964$	6.50000	+	11.2583i	0.209351	+	0.362606i
$965$	−14.0000			−0.450676
$966$	−6.00000	+	10.3923i	−0.193047	+	0.334367i
$967$	−7.00000	−	12.1244i	−0.225105	−	0.389893i	0.731246	−	0.682114i	$-0.238939\pi$
$967$	−7.00000	−	12.1244i	−0.225105	−	0.389893i	−0.956351	+	0.292221i	$0.905606\pi$
$968$	12.5000	−	21.6506i	0.401765	−	0.695878i
$969$	12.0000	+	20.7846i	0.385496	+	0.667698i
$970$	5.00000	+	8.66025i	0.160540	+	0.278064i
$971$	−27.0000	−	46.7654i	−0.866471	−	1.50077i	−0.865579	−	0.500773i	$-0.833049\pi$
$971$	−27.0000	−	46.7654i	−0.866471	−	1.50077i	−0.000892350	−	1.00000i	$-0.500284\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$	10.0000	+	17.3205i	0.320585	+	0.555270i
$974$	−8.00000	−	13.8564i	−0.256337	−	0.443988i
$975$	−1.00000	+	1.73205i	−0.0320256	+	0.0554700i
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	−0.973317	−	0.229465i	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$	19.0000			0.607553
$979$	−27.0000	−	46.7654i	−0.862924	−	1.49463i
$980$	3.00000			0.0958315
$981$	8.00000			0.255420
$982$	−18.0000	+	31.1769i	−0.574403	+	0.994895i
$983$	36.0000			1.14822			0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000			1.14822			0.574111	+	0.818778i	$0.305348\pi$
$984$	1.50000	+	2.59808i	0.0478183	+	0.0828236i
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$	−18.0000	+	31.1769i	−0.573237	+	0.992875i
$987$	−6.00000	+	10.3923i	−0.190982	+	0.330791i
$988$	4.00000	−	6.92820i	0.127257	−	0.220416i
$989$	24.0000	−	41.5692i	0.763156	−	1.32182i
$990$	−12.0000			−0.381385
$991$	5.00000			0.158830			0.0794151	−	0.996842i	$-0.474695\pi$
$991$	5.00000			0.158830			0.0794151	+	0.996842i	$0.474695\pi$
$992$	2.50000	−	4.33013i	0.0793751	−	0.137482i
$993$	−4.00000	−	6.92820i	−0.126936	−	0.219860i
$994$	−15.0000	−	25.9808i	−0.475771	−	0.824060i
$995$	−3.50000	+	6.06218i	−0.110957	+	0.192184i
$996$	−15.0000			−0.475293
$997$	−1.00000			−0.0316703			−0.0158352	−	0.999875i	$-0.505041\pi$
$997$	−1.00000			−0.0316703			−0.0158352	+	0.999875i	$0.505041\pi$
$998$	−20.0000	−	34.6410i	−0.633089	−	1.09654i
$999$	−17.5000	+	30.3109i	−0.553675	+	0.958994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.d.431.1	yes	2
67.37	even	3	inner	670.2.e.d.171.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.d.171.1	✓	2	67.37	even	3	inner
670.2.e.d.431.1	yes	2	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 - 1.73205i) q^{7} -1.00000 q^{8} -2.00000 q^{9} +(-0.500000 + 0.866025i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} -2.00000 q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(-1.00000 + 1.73205i) q^{18} +(2.00000 - 3.46410i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{21} -6.00000 q^{22} +(3.00000 - 5.19615i) q^{23} -1.00000 q^{24} +1.00000 q^{25} +(1.00000 + 1.73205i) q^{26} -5.00000 q^{27} +(-1.00000 + 1.73205i) q^{28} +(3.00000 + 5.19615i) q^{29} +(-0.500000 + 0.866025i) q^{30} +(-2.50000 - 4.33013i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +(3.00000 + 5.19615i) q^{34} +(1.00000 + 1.73205i) q^{35} +(1.00000 + 1.73205i) q^{36} +(3.50000 - 6.06218i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(-1.00000 + 1.73205i) q^{39} +1.00000 q^{40} +(-1.50000 - 2.59808i) q^{41} -2.00000 q^{42} +8.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} +2.00000 q^{45} +(-3.00000 - 5.19615i) q^{46} +(-3.00000 - 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-3.00000 + 5.19615i) q^{51} +2.00000 q^{52} -3.00000 q^{53} +(-2.50000 + 4.33013i) q^{54} +(3.00000 + 5.19615i) q^{55} +(1.00000 + 1.73205i) q^{56} +(2.00000 - 3.46410i) q^{57} +6.00000 q^{58} -6.00000 q^{59} +(0.500000 + 0.866025i) q^{60} +(-4.00000 + 6.92820i) q^{61} -5.00000 q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} +(1.00000 - 1.73205i) q^{65} -6.00000 q^{66} +(2.50000 + 7.79423i) q^{67} +6.00000 q^{68} +(3.00000 - 5.19615i) q^{69} +2.00000 q^{70} +(7.50000 + 12.9904i) q^{71} +2.00000 q^{72} +(2.00000 - 3.46410i) q^{73} +(-3.50000 - 6.06218i) q^{74} +1.00000 q^{75} -4.00000 q^{76} +(-6.00000 + 10.3923i) q^{77} +(1.00000 + 1.73205i) q^{78} +(-4.00000 - 6.92820i) q^{79} +(0.500000 - 0.866025i) q^{80} +1.00000 q^{81} -3.00000 q^{82} +(7.50000 - 12.9904i) q^{83} +(-1.00000 + 1.73205i) q^{84} +(3.00000 - 5.19615i) q^{85} +(4.00000 - 6.92820i) q^{86} +(3.00000 + 5.19615i) q^{87} +(3.00000 + 5.19615i) q^{88} +9.00000 q^{89} +(1.00000 - 1.73205i) q^{90} +4.00000 q^{91} -6.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} -6.00000 q^{94} +(-2.00000 + 3.46410i) q^{95} +(0.500000 + 0.866025i) q^{96} +(5.00000 - 8.66025i) q^{97} +(-1.50000 - 2.59808i) q^{98} +(6.00000 + 10.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 4 * q^9	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 4 q^{9} - q^{10} - 6 q^{11} - q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} - q^{16} - 6 q^{17} - 2 q^{18} + 4 q^{19} + q^{20} - 2 q^{21} - 12 q^{22} + 6 q^{23} - 2 q^{24} + 2 q^{25} + 2 q^{26} - 10 q^{27} - 2 q^{28} + 6 q^{29} - q^{30} - 5 q^{31} + q^{32} - 6 q^{33} + 6 q^{34} + 2 q^{35} + 2 q^{36} + 7 q^{37} - 4 q^{38} - 2 q^{39} + 2 q^{40} - 3 q^{41} - 4 q^{42} + 16 q^{43} - 6 q^{44} + 4 q^{45} - 6 q^{46} - 6 q^{47} - q^{48} + 3 q^{49} + q^{50} - 6 q^{51} + 4 q^{52} - 6 q^{53} - 5 q^{54} + 6 q^{55} + 2 q^{56} + 4 q^{57} + 12 q^{58} - 12 q^{59} + q^{60} - 8 q^{61} - 10 q^{62} + 4 q^{63} + 2 q^{64} + 2 q^{65} - 12 q^{66} + 5 q^{67} + 12 q^{68} + 6 q^{69} + 4 q^{70} + 15 q^{71} + 4 q^{72} + 4 q^{73} - 7 q^{74} + 2 q^{75} - 8 q^{76} - 12 q^{77} + 2 q^{78} - 8 q^{79} + q^{80} + 2 q^{81} - 6 q^{82} + 15 q^{83} - 2 q^{84} + 6 q^{85} + 8 q^{86} + 6 q^{87} + 6 q^{88} + 18 q^{89} + 2 q^{90} + 8 q^{91} - 12 q^{92} - 5 q^{93} - 12 q^{94} - 4 q^{95} + q^{96} + 10 q^{97} - 3 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 4 * q^9 - q^10 - 6 * q^11 - q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 - q^16 - 6 * q^17 - 2 * q^18 + 4 * q^19 + q^20 - 2 * q^21 - 12 * q^22 + 6 * q^23 - 2 * q^24 + 2 * q^25 + 2 * q^26 - 10 * q^27 - 2 * q^28 + 6 * q^29 - q^30 - 5 * q^31 + q^32 - 6 * q^33 + 6 * q^34 + 2 * q^35 + 2 * q^36 + 7 * q^37 - 4 * q^38 - 2 * q^39 + 2 * q^40 - 3 * q^41 - 4 * q^42 + 16 * q^43 - 6 * q^44 + 4 * q^45 - 6 * q^46 - 6 * q^47 - q^48 + 3 * q^49 + q^50 - 6 * q^51 + 4 * q^52 - 6 * q^53 - 5 * q^54 + 6 * q^55 + 2 * q^56 + 4 * q^57 + 12 * q^58 - 12 * q^59 + q^60 - 8 * q^61 - 10 * q^62 + 4 * q^63 + 2 * q^64 + 2 * q^65 - 12 * q^66 + 5 * q^67 + 12 * q^68 + 6 * q^69 + 4 * q^70 + 15 * q^71 + 4 * q^72 + 4 * q^73 - 7 * q^74 + 2 * q^75 - 8 * q^76 - 12 * q^77 + 2 * q^78 - 8 * q^79 + q^80 + 2 * q^81 - 6 * q^82 + 15 * q^83 - 2 * q^84 + 6 * q^85 + 8 * q^86 + 6 * q^87 + 6 * q^88 + 18 * q^89 + 2 * q^90 + 8 * q^91 - 12 * q^92 - 5 * q^93 - 12 * q^94 - 4 * q^95 + q^96 + 10 * q^97 - 3 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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