LMFDB - Embedded newform 574.2.e.a.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(165,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("574.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.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:	$4.58341307602$
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			165.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	574.165
Dual form			574.2.e.a.247.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +2.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +2.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-1.00000 - 1.73205i) q^{12} +1.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} -4.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +(3.00000 + 5.19615i) q^{19} -2.00000 q^{20} +(-4.00000 + 3.46410i) q^{21} -4.00000 q^{22} +(1.00000 + 1.73205i) q^{23} +(-1.00000 + 1.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} -4.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -5.00000 q^{29} +(2.00000 + 3.46410i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.00000 + 6.92820i) q^{33} +(1.00000 + 5.19615i) q^{35} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(1.00000 + 1.73205i) q^{40} +1.00000 q^{41} +(5.00000 + 1.73205i) q^{42} -1.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(1.00000 - 1.73205i) q^{45} +(1.00000 - 1.73205i) q^{46} +(4.00000 + 6.92820i) q^{47} +2.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -1.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(5.00000 - 8.66025i) q^{53} +(2.00000 + 3.46410i) q^{54} +8.00000 q^{55} +(2.50000 + 0.866025i) q^{56} -12.0000 q^{57} +(2.50000 + 4.33013i) q^{58} +(-0.500000 + 0.866025i) q^{59} +(2.00000 - 3.46410i) q^{60} +(-7.00000 - 12.1244i) q^{61} +4.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(4.00000 - 6.92820i) q^{66} +(-5.00000 + 8.66025i) q^{67} -4.00000 q^{69} +(4.00000 - 3.46410i) q^{70} -15.0000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-3.50000 + 6.06218i) q^{73} +(1.00000 - 1.73205i) q^{74} +(1.00000 + 1.73205i) q^{75} -6.00000 q^{76} +(8.00000 - 6.92820i) q^{77} +2.00000 q^{78} +(1.00000 - 1.73205i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-0.500000 - 0.866025i) q^{82} +9.00000 q^{83} +(-1.00000 - 5.19615i) q^{84} +(0.500000 + 0.866025i) q^{86} +(5.00000 - 8.66025i) q^{87} +(2.00000 - 3.46410i) q^{88} -2.00000 q^{90} +(2.50000 + 0.866025i) q^{91} -2.00000 q^{92} +(-4.00000 - 6.92820i) q^{93} +(4.00000 - 6.92820i) q^{94} +(-6.00000 + 10.3923i) q^{95} +(-1.00000 - 1.73205i) q^{96} -4.00000 q^{97} +(1.00000 - 6.92820i) q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} + 2 q^{5} + 4 q^{6} + 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 + 2 * q^5 + 4 * q^6 + 5 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} - 2 q^{3} - q^{4} + 2 q^{5} + 4 q^{6} + 5 q^{7} + 2 q^{8} - q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} + 2 q^{13} - q^{14} - 8 q^{15} - q^{16} - q^{18} + 6 q^{19} - 4 q^{20} - 8 q^{21} - 8 q^{22} + 2 q^{23} - 2 q^{24} + q^{25} - q^{26} - 8 q^{27} - 4 q^{28} - 10 q^{29} + 4 q^{30} - 4 q^{31} - q^{32} + 8 q^{33} + 2 q^{35} + 2 q^{36} + 2 q^{37} + 6 q^{38} - 2 q^{39} + 2 q^{40} + 2 q^{41} + 10 q^{42} - 2 q^{43} + 4 q^{44} + 2 q^{45} + 2 q^{46} + 8 q^{47} + 4 q^{48} + 11 q^{49} - 2 q^{50} - q^{52} + 10 q^{53} + 4 q^{54} + 16 q^{55} + 5 q^{56} - 24 q^{57} + 5 q^{58} - q^{59} + 4 q^{60} - 14 q^{61} + 8 q^{62} - q^{63} + 2 q^{64} + 2 q^{65} + 8 q^{66} - 10 q^{67} - 8 q^{69} + 8 q^{70} - 30 q^{71} - q^{72} - 7 q^{73} + 2 q^{74} + 2 q^{75} - 12 q^{76} + 16 q^{77} + 4 q^{78} + 2 q^{80} + 11 q^{81} - q^{82} + 18 q^{83} - 2 q^{84} + q^{86} + 10 q^{87} + 4 q^{88} - 4 q^{90} + 5 q^{91} - 4 q^{92} - 8 q^{93} + 8 q^{94} - 12 q^{95} - 2 q^{96} - 8 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 + 2 * q^5 + 4 * q^6 + 5 * q^7 + 2 * q^8 - q^9 + 2 * q^10 + 4 * q^11 - 2 * q^12 + 2 * q^13 - q^14 - 8 * q^15 - q^16 - q^18 + 6 * q^19 - 4 * q^20 - 8 * q^21 - 8 * q^22 + 2 * q^23 - 2 * q^24 + q^25 - q^26 - 8 * q^27 - 4 * q^28 - 10 * q^29 + 4 * q^30 - 4 * q^31 - q^32 + 8 * q^33 + 2 * q^35 + 2 * q^36 + 2 * q^37 + 6 * q^38 - 2 * q^39 + 2 * q^40 + 2 * q^41 + 10 * q^42 - 2 * q^43 + 4 * q^44 + 2 * q^45 + 2 * q^46 + 8 * q^47 + 4 * q^48 + 11 * q^49 - 2 * q^50 - q^52 + 10 * q^53 + 4 * q^54 + 16 * q^55 + 5 * q^56 - 24 * q^57 + 5 * q^58 - q^59 + 4 * q^60 - 14 * q^61 + 8 * q^62 - q^63 + 2 * q^64 + 2 * q^65 + 8 * q^66 - 10 * q^67 - 8 * q^69 + 8 * q^70 - 30 * q^71 - q^72 - 7 * q^73 + 2 * q^74 + 2 * q^75 - 12 * q^76 + 16 * q^77 + 4 * q^78 + 2 * q^80 + 11 * q^81 - q^82 + 18 * q^83 - 2 * q^84 + q^86 + 10 * q^87 + 4 * q^88 - 4 * q^90 + 5 * q^91 - 4 * q^92 - 8 * q^93 + 8 * q^94 - 12 * q^95 - 2 * q^96 - 8 * q^97 + 2 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$	2.00000			0.816497
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000	−	1.73205i	0.316228	−	0.547723i
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$	−4.00000			−1.03280
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	−2.00000			−0.447214
$21$	−4.00000	+	3.46410i	−0.872872	+	0.755929i
$22$	−4.00000			−0.852803
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	0.951247	−	0.308431i	$-0.0998038\pi$
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	−0.742732	+	0.669588i	$0.766471\pi$
$24$	−1.00000	+	1.73205i	−0.204124	+	0.353553i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$	−4.00000			−0.769800
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$	2.00000	+	3.46410i	0.365148	+	0.632456i
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	4.00000	+	6.92820i	0.696311	+	1.20605i
$34$		0			0
$35$	1.00000	+	5.19615i	0.169031	+	0.878310i
$36$	1.00000			0.166667
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	3.00000	−	5.19615i	0.486664	−	0.842927i
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$	1.00000	+	1.73205i	0.158114	+	0.273861i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	5.00000	+	1.73205i	0.771517	+	0.267261i
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	2.00000	+	3.46410i	0.301511	+	0.522233i
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$	1.00000	−	1.73205i	0.147442	−	0.255377i
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$	2.00000			0.288675
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	−0.286064	−	0.958211i	$-0.592347\pi$
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	0.972867	−	0.231367i	$-0.0743197\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$	8.00000			1.07872
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$	−12.0000			−1.58944
$58$	2.50000	+	4.33013i	0.328266	+	0.568574i
$59$	−0.500000	+	0.866025i	−0.0650945	+	0.112747i	−0.896736	−	0.442566i	$-0.854068\pi$
$59$	−0.500000	+	0.866025i	−0.0650945	+	0.112747i	0.831641	+	0.555313i	$0.187402\pi$
$60$	2.00000	−	3.46410i	0.258199	−	0.447214i
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.0640184	−	0.997949i	$-0.520392\pi$
$62$	4.00000			0.508001
$63$	−0.500000	−	2.59808i	−0.0629941	−	0.327327i
$64$	1.00000			0.125000
$65$	1.00000	+	1.73205i	0.124035	+	0.214834i
$66$	4.00000	−	6.92820i	0.492366	−	0.852803i
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	0.380251	+	0.924883i	$0.375838\pi$
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	−0.991098	+	0.133135i	$0.957496\pi$
$68$		0			0
$69$	−4.00000			−0.481543
$70$	4.00000	−	3.46410i	0.478091	−	0.414039i
$71$	−15.0000			−1.78017			−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000			−1.78017			−0.890086	+	0.455792i	$0.849356\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−3.50000	+	6.06218i	−0.409644	+	0.709524i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−3.50000	+	6.06218i	−0.409644	+	0.709524i	0.585206	+	0.810885i	$0.301014\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	1.00000	+	1.73205i	0.115470	+	0.200000i
$76$	−6.00000			−0.688247
$77$	8.00000	−	6.92820i	0.911685	−	0.789542i
$78$	2.00000			0.226455
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	1.00000	−	1.73205i	0.111803	−	0.193649i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−0.500000	−	0.866025i	−0.0552158	−	0.0956365i
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$	−1.00000	−	5.19615i	−0.109109	−	0.566947i
$85$		0			0
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	5.00000	−	8.66025i	0.536056	−	0.928477i
$88$	2.00000	−	3.46410i	0.213201	−	0.369274i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$	−2.00000			−0.210819
$91$	2.50000	+	0.866025i	0.262071	+	0.0907841i
$92$	−2.00000			−0.208514
$93$	−4.00000	−	6.92820i	−0.414781	−	0.718421i
$94$	4.00000	−	6.92820i	0.412568	−	0.714590i
$95$	−6.00000	+	10.3923i	−0.615587	+	1.06623i
$96$	−1.00000	−	1.73205i	−0.102062	−	0.176777i
$97$	−4.00000			−0.406138			−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000			−0.406138			−0.203069	+	0.979164i	$0.565092\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$	−4.00000			−0.402015
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	−0.502477	−	0.864590i	$-0.667578\pi$
$101$	5.00000	−	8.66025i	0.497519	−	0.861727i	0.999996	+	0.00286291i	$0.000911295\pi$
$102$		0			0
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	0.999964	−	0.00844953i	$-0.00268960\pi$
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	−0.507300	+	0.861770i	$0.669356\pi$
$104$	1.00000			0.0980581
$105$	−10.0000	−	3.46410i	−0.975900	−	0.338062i
$106$	−10.0000			−0.971286
$107$	−6.50000	−	11.2583i	−0.628379	−	1.08838i	−0.987877	−	0.155238i	$-0.950386\pi$
$107$	−6.50000	−	11.2583i	−0.628379	−	1.08838i	0.359498	−	0.933146i	$-0.382948\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	−0.648292	−	0.761392i	$-0.724516\pi$
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	0.983531	+	0.180741i	$0.0578495\pi$
$110$	−4.00000	−	6.92820i	−0.381385	−	0.660578i
$111$	−4.00000			−0.379663
$112$	−0.500000	−	2.59808i	−0.0472456	−	0.245495i
$113$	−3.00000			−0.282216			−0.141108	−	0.989994i	$-0.545067\pi$
$113$	−3.00000			−0.282216			−0.141108	+	0.989994i	$0.545067\pi$
$114$	6.00000	+	10.3923i	0.561951	+	0.973329i
$115$	−2.00000	+	3.46410i	−0.186501	+	0.323029i
$116$	2.50000	−	4.33013i	0.232119	−	0.402042i
$117$	−0.500000	−	0.866025i	−0.0462250	−	0.0800641i
$118$	1.00000			0.0920575
$119$		0			0
$120$	−4.00000			−0.365148
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−7.00000	+	12.1244i	−0.633750	+	1.09769i
$123$	−1.00000	+	1.73205i	−0.0901670	+	0.156174i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	12.0000			1.07331
$126$	−2.00000	+	1.73205i	−0.178174	+	0.154303i
$127$	4.00000			0.354943			0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000			0.354943			0.177471	+	0.984126i	$0.443208\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.00000	−	1.73205i	0.0880451	−	0.152499i
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	−8.00000			−0.696311
$133$	3.00000	+	15.5885i	0.260133	+	1.35169i
$134$	10.0000			0.863868
$135$	−4.00000	−	6.92820i	−0.344265	−	0.596285i
$136$		0			0
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$	2.00000	+	3.46410i	0.170251	+	0.294884i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$	−5.00000	−	1.73205i	−0.422577	−	0.146385i
$141$	−16.0000			−1.34744
$142$	7.50000	+	12.9904i	0.629386	+	1.09013i
$143$	2.00000	−	3.46410i	0.167248	−	0.289683i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−5.00000	−	8.66025i	−0.415227	−	0.719195i
$146$	7.00000			0.579324
$147$	−13.0000	+	5.19615i	−1.07222	+	0.428571i
$148$	−2.00000			−0.164399
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$	1.00000	−	1.73205i	0.0816497	−	0.141421i
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	3.00000	+	5.19615i	0.243332	+	0.421464i
$153$		0			0
$154$	−10.0000	−	3.46410i	−0.805823	−	0.279145i
$155$	−8.00000			−0.642575
$156$	−1.00000	−	1.73205i	−0.0800641	−	0.138675i
$157$	7.50000	−	12.9904i	0.598565	−	1.03675i	−0.394468	−	0.918910i	$-0.629071\pi$
$157$	7.50000	−	12.9904i	0.598565	−	1.03675i	0.993033	−	0.117836i	$-0.0375956\pi$
$158$		0			0
$159$	10.0000	+	17.3205i	0.793052	+	1.37361i
$160$	−2.00000			−0.158114
$161$	1.00000	+	5.19615i	0.0788110	+	0.409514i
$162$	−11.0000			−0.864242
$163$	11.5000	+	19.9186i	0.900750	+	1.56014i	0.826523	+	0.562902i	$0.190315\pi$
$163$	11.5000	+	19.9186i	0.900750	+	1.56014i	0.0742262	+	0.997241i	$0.476351\pi$
$164$	−0.500000	+	0.866025i	−0.0390434	+	0.0676252i
$165$	−8.00000	+	13.8564i	−0.622799	+	1.07872i
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	5.00000			0.386912			0.193456	−	0.981109i	$-0.438030\pi$
$167$	5.00000			0.386912			0.193456	+	0.981109i	$0.438030\pi$
$168$	−4.00000	+	3.46410i	−0.308607	+	0.267261i
$169$	−12.0000			−0.923077
$170$		0			0
$171$	3.00000	−	5.19615i	0.229416	−	0.397360i
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	−12.0000	−	20.7846i	−0.912343	−	1.58022i	−0.810745	−	0.585399i	$-0.800938\pi$
$173$	−12.0000	−	20.7846i	−0.912343	−	1.58022i	−0.101598	−	0.994826i	$-0.532395\pi$
$174$	−10.0000			−0.758098
$175$	2.00000	−	1.73205i	0.151186	−	0.130931i
$176$	−4.00000			−0.301511
$177$	−1.00000	−	1.73205i	−0.0751646	−	0.130189i
$178$		0			0
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	−0.616417	−	0.787420i	$-0.711416\pi$
$179$	5.00000	−	8.66025i	0.373718	−	0.647298i	0.990134	+	0.140122i	$0.0447496\pi$
$180$	1.00000	+	1.73205i	0.0745356	+	0.129099i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−0.500000	−	2.59808i	−0.0370625	−	0.192582i
$183$	28.0000			2.06982
$184$	1.00000	+	1.73205i	0.0737210	+	0.127688i
$185$	−2.00000	+	3.46410i	−0.147043	+	0.254686i
$186$	−4.00000	+	6.92820i	−0.293294	+	0.508001i
$187$		0			0
$188$	−8.00000			−0.583460
$189$	−10.0000	−	3.46410i	−0.727393	−	0.251976i
$190$	12.0000			0.870572
$191$	−2.50000	−	4.33013i	−0.180894	−	0.313317i	0.761291	−	0.648410i	$-0.224566\pi$
$191$	−2.50000	−	4.33013i	−0.180894	−	0.313317i	−0.942185	+	0.335093i	$0.891232\pi$
$192$	−1.00000	+	1.73205i	−0.0721688	+	0.125000i
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	2.00000	+	3.46410i	0.143592	+	0.248708i
$195$	−4.00000			−0.286446
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	2.00000	+	3.46410i	0.142134	+	0.246183i
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	−0.807950	−	0.589252i	$-0.799423\pi$
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	0.914282	+	0.405079i	$0.132756\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−10.0000	−	17.3205i	−0.705346	−	1.22169i
$202$	−10.0000			−0.703598
$203$	−12.5000	−	4.33013i	−0.877328	−	0.303915i
$204$		0			0
$205$	1.00000	+	1.73205i	0.0698430	+	0.120972i
$206$	5.00000	−	8.66025i	0.348367	−	0.603388i
$207$	1.00000	−	1.73205i	0.0695048	−	0.120386i
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	24.0000			1.66011
$210$	2.00000	+	10.3923i	0.138013	+	0.717137i
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$	5.00000	+	8.66025i	0.343401	+	0.594789i
$213$	15.0000	−	25.9808i	1.02778	−	1.78017i
$214$	−6.50000	+	11.2583i	−0.444331	+	0.769604i
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$	−4.00000			−0.272166
$217$	−8.00000	+	6.92820i	−0.543075	+	0.470317i
$218$	−7.00000			−0.474100
$219$	−7.00000	−	12.1244i	−0.473016	−	0.819288i
$220$	−4.00000	+	6.92820i	−0.269680	+	0.467099i
$221$		0			0
$222$	2.00000	+	3.46410i	0.134231	+	0.232495i
$223$	26.0000			1.74109			0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000			1.74109			0.870544	+	0.492090i	$0.163767\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$	−1.00000			−0.0666667
$226$	1.50000	+	2.59808i	0.0997785	+	0.172821i
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$	6.00000	−	10.3923i	0.397360	−	0.688247i
$229$	10.5000	+	18.1865i	0.693860	+	1.20180i	0.970564	+	0.240845i	$0.0774245\pi$
$229$	10.5000	+	18.1865i	0.693860	+	1.20180i	−0.276704	+	0.960955i	$0.589242\pi$
$230$	4.00000			0.263752
$231$	4.00000	+	20.7846i	0.263181	+	1.36753i
$232$	−5.00000			−0.328266
$233$	8.00000	+	13.8564i	0.524097	+	0.907763i	0.999606	+	0.0280525i	$0.00893057\pi$
$233$	8.00000	+	13.8564i	0.524097	+	0.907763i	−0.475509	+	0.879711i	$0.657736\pi$
$234$	−0.500000	+	0.866025i	−0.0326860	+	0.0566139i
$235$	−8.00000	+	13.8564i	−0.521862	+	0.903892i
$236$	−0.500000	−	0.866025i	−0.0325472	−	0.0563735i
$237$		0			0
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$	2.00000	+	3.46410i	0.129099	+	0.223607i
$241$	2.50000	−	4.33013i	0.161039	−	0.278928i	−0.774202	−	0.632938i	$-0.781849\pi$
$241$	2.50000	−	4.33013i	0.161039	−	0.278928i	0.935242	+	0.354010i	$0.115182\pi$
$242$	−2.50000	+	4.33013i	−0.160706	+	0.278351i
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	14.0000			0.896258
$245$	−2.00000	+	13.8564i	−0.127775	+	0.885253i
$246$	2.00000			0.127515
$247$	3.00000	+	5.19615i	0.190885	+	0.330623i
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$	−9.00000	+	15.5885i	−0.570352	+	0.987878i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−9.00000			−0.568075			−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000			−0.568075			−0.284037	+	0.958813i	$0.591674\pi$
$252$	2.50000	+	0.866025i	0.157485	+	0.0545545i
$253$	8.00000			0.502956
$254$	−2.00000	−	3.46410i	−0.125491	−	0.217357i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	0.895528	−	0.445005i	$-0.146798\pi$
$257$	1.00000	+	1.73205i	0.0623783	+	0.108042i	−0.833150	+	0.553047i	$0.813465\pi$
$258$	−2.00000			−0.124515
$259$	1.00000	+	5.19615i	0.0621370	+	0.322873i
$260$	−2.00000			−0.124035
$261$	2.50000	+	4.33013i	0.154746	+	0.268028i
$262$	−6.00000	+	10.3923i	−0.370681	+	0.642039i
$263$	15.5000	−	26.8468i	0.955771	−	1.65544i	0.223177	−	0.974778i	$-0.428357\pi$
$263$	15.5000	−	26.8468i	0.955771	−	1.65544i	0.732594	−	0.680666i	$-0.238309\pi$
$264$	4.00000	+	6.92820i	0.246183	+	0.426401i
$265$	20.0000			1.22859
$266$	12.0000	−	10.3923i	0.735767	−	0.637193i
$267$		0			0
$268$	−5.00000	−	8.66025i	−0.305424	−	0.529009i
$269$	−8.00000	+	13.8564i	−0.487769	+	0.844840i	−0.999901	−	0.0140665i	$-0.995522\pi$
$269$	−8.00000	+	13.8564i	−0.487769	+	0.844840i	0.512132	+	0.858906i	$0.328856\pi$
$270$	−4.00000	+	6.92820i	−0.243432	+	0.421637i
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	−0.991658	−	0.128897i	$-0.958856\pi$
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	0.384201	−	0.923249i	$-0.374477\pi$
$272$		0			0
$273$	−4.00000	+	3.46410i	−0.242091	+	0.209657i
$274$	−18.0000			−1.08742
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$	2.00000	−	3.46410i	0.120386	−	0.208514i
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	−2.00000	−	3.46410i	−0.119952	−	0.207763i
$279$	4.00000			0.239474
$280$	1.00000	+	5.19615i	0.0597614	+	0.310530i
$281$	14.0000			0.835170			0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000			0.835170			0.417585	+	0.908638i	$0.362877\pi$
$282$	8.00000	+	13.8564i	0.476393	+	0.825137i
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	−0.850782	−	0.525519i	$-0.823871\pi$
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	0.880504	+	0.474039i	$0.157204\pi$
$284$	7.50000	−	12.9904i	0.445043	−	0.770837i
$285$	−12.0000	−	20.7846i	−0.710819	−	1.23117i
$286$	−4.00000			−0.236525
$287$	2.50000	+	0.866025i	0.147570	+	0.0511199i
$288$	1.00000			0.0589256
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−5.00000	+	8.66025i	−0.293610	+	0.508548i
$291$	4.00000	−	6.92820i	0.234484	−	0.406138i
$292$	−3.50000	−	6.06218i	−0.204822	−	0.354762i
$293$	3.00000			0.175262			0.0876309	−	0.996153i	$-0.472070\pi$
$293$	3.00000			0.175262			0.0876309	+	0.996153i	$0.472070\pi$
$294$	11.0000	+	8.66025i	0.641533	+	0.505076i
$295$	−2.00000			−0.116445
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$	−8.00000	+	13.8564i	−0.464207	+	0.804030i
$298$	−0.500000	+	0.866025i	−0.0289642	+	0.0501675i
$299$	1.00000	+	1.73205i	0.0578315	+	0.100167i
$300$	−2.00000			−0.115470
$301$	−2.50000	−	0.866025i	−0.144098	−	0.0499169i
$302$	19.0000			1.09333
$303$	10.0000	+	17.3205i	0.574485	+	0.995037i
$304$	3.00000	−	5.19615i	0.172062	−	0.298020i
$305$	14.0000	−	24.2487i	0.801638	−	1.38848i
$306$		0			0
$307$	9.00000			0.513657			0.256829	−	0.966457i	$-0.417322\pi$
$307$	9.00000			0.513657			0.256829	+	0.966457i	$0.417322\pi$
$308$	2.00000	+	10.3923i	0.113961	+	0.592157i
$309$	−20.0000			−1.13776
$310$	4.00000	+	6.92820i	0.227185	+	0.393496i
$311$	−6.50000	+	11.2583i	−0.368581	+	0.638401i	−0.989344	−	0.145597i	$-0.953490\pi$
$311$	−6.50000	+	11.2583i	−0.368581	+	0.638401i	0.620763	+	0.783998i	$0.286823\pi$
$312$	−1.00000	+	1.73205i	−0.0566139	+	0.0980581i
$313$	−8.00000	−	13.8564i	−0.452187	−	0.783210i	0.546335	−	0.837567i	$-0.316023\pi$
$313$	−8.00000	−	13.8564i	−0.452187	−	0.783210i	−0.998522	+	0.0543564i	$0.982689\pi$
$314$	−15.0000			−0.846499
$315$	4.00000	−	3.46410i	0.225374	−	0.195180i
$316$		0			0
$317$	1.00000	+	1.73205i	0.0561656	+	0.0972817i	0.892741	−	0.450570i	$-0.148779\pi$
$317$	1.00000	+	1.73205i	0.0561656	+	0.0972817i	−0.836576	+	0.547852i	$0.815446\pi$
$318$	10.0000	−	17.3205i	0.560772	−	0.971286i
$319$	−10.0000	+	17.3205i	−0.559893	+	0.969762i
$320$	1.00000	+	1.73205i	0.0559017	+	0.0968246i
$321$	26.0000			1.45118
$322$	4.00000	−	3.46410i	0.222911	−	0.193047i
$323$		0			0
$324$	5.50000	+	9.52628i	0.305556	+	0.529238i
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$	11.5000	−	19.9186i	0.636926	−	1.10319i
$327$	7.00000	+	12.1244i	0.387101	+	0.670478i
$328$	1.00000			0.0552158
$329$	4.00000	+	20.7846i	0.220527	+	1.14589i
$330$	16.0000			0.880771
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	0.652680	−	0.757634i	$-0.273645\pi$
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	−0.982470	+	0.186421i	$0.940311\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$	1.00000	−	1.73205i	0.0547997	−	0.0949158i
$334$	−2.50000	−	4.33013i	−0.136794	−	0.236934i
$335$	−20.0000			−1.09272
$336$	5.00000	+	1.73205i	0.272772	+	0.0944911i
$337$	31.0000			1.68868			0.844339	−	0.535810i	$-0.179994\pi$
$337$	31.0000			1.68868			0.844339	+	0.535810i	$0.179994\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$		0			0
$341$	8.00000	+	13.8564i	0.433224	+	0.750366i
$342$	−6.00000			−0.324443
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−1.00000			−0.0539164
$345$	−4.00000	−	6.92820i	−0.215353	−	0.373002i
$346$	−12.0000	+	20.7846i	−0.645124	+	1.11739i
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	−0.340293	−	0.940319i	$-0.610526\pi$
$347$	12.0000	−	20.7846i	0.644194	−	1.11578i	0.984487	−	0.175457i	$-0.0561403\pi$
$348$	5.00000	+	8.66025i	0.268028	+	0.464238i
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$	−2.50000	−	0.866025i	−0.133631	−	0.0462910i
$351$	−4.00000			−0.213504
$352$	2.00000	+	3.46410i	0.106600	+	0.184637i
$353$	−10.5000	+	18.1865i	−0.558859	+	0.967972i	0.438733	+	0.898617i	$0.355427\pi$
$353$	−10.5000	+	18.1865i	−0.558859	+	0.967972i	−0.997592	+	0.0693543i	$0.977906\pi$
$354$	−1.00000	+	1.73205i	−0.0531494	+	0.0920575i
$355$	−15.0000	−	25.9808i	−0.796117	−	1.37892i
$356$		0			0
$357$		0			0
$358$	−10.0000			−0.528516
$359$	−7.00000	−	12.1244i	−0.369446	−	0.639899i	0.620033	−	0.784576i	$-0.287119\pi$
$359$	−7.00000	−	12.1244i	−0.369446	−	0.639899i	−0.989479	+	0.144677i	$0.953786\pi$
$360$	1.00000	−	1.73205i	0.0527046	−	0.0912871i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−1.00000	−	1.73205i	−0.0525588	−	0.0910346i
$363$	10.0000			0.524864
$364$	−2.00000	+	1.73205i	−0.104828	+	0.0907841i
$365$	−14.0000			−0.732793
$366$	−14.0000	−	24.2487i	−0.731792	−	1.26750i
$367$	9.00000	−	15.5885i	0.469796	−	0.813711i	−0.529607	−	0.848243i	$-0.677661\pi$
$367$	9.00000	−	15.5885i	0.469796	−	0.813711i	0.999404	+	0.0345320i	$0.0109941\pi$
$368$	1.00000	−	1.73205i	0.0521286	−	0.0902894i
$369$	−0.500000	−	0.866025i	−0.0260290	−	0.0450835i
$370$	4.00000			0.207950
$371$	20.0000	−	17.3205i	1.03835	−	0.899236i
$372$	8.00000			0.414781
$373$	−8.00000	−	13.8564i	−0.414224	−	0.717458i	0.581122	−	0.813816i	$-0.302614\pi$
$373$	−8.00000	−	13.8564i	−0.414224	−	0.717458i	−0.995347	+	0.0963587i	$0.969280\pi$
$374$		0			0
$375$	−12.0000	+	20.7846i	−0.619677	+	1.07331i
$376$	4.00000	+	6.92820i	0.206284	+	0.357295i
$377$	−5.00000			−0.257513
$378$	2.00000	+	10.3923i	0.102869	+	0.534522i
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$	−6.00000	−	10.3923i	−0.307794	−	0.533114i
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$	−2.50000	+	4.33013i	−0.127911	+	0.221549i
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$	2.00000			0.102062
$385$	20.0000	+	6.92820i	1.01929	+	0.353094i
$386$	−10.0000			−0.508987
$387$	0.500000	+	0.866025i	0.0254164	+	0.0440225i
$388$	2.00000	−	3.46410i	0.101535	−	0.175863i
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$	2.00000	+	3.46410i	0.101274	+	0.175412i
$391$		0			0
$392$	5.50000	+	4.33013i	0.277792	+	0.218704i
$393$	24.0000			1.21064
$394$	1.00000	+	1.73205i	0.0503793	+	0.0872595i
$395$		0			0
$396$	2.00000	−	3.46410i	0.100504	−	0.174078i
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	−0.982526	−	0.186124i	$-0.940407\pi$
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	0.330075	−	0.943955i	$-0.392926\pi$
$398$	−3.00000			−0.150376
$399$	−30.0000	−	10.3923i	−1.50188	−	0.520266i
$400$	−1.00000			−0.0500000
$401$	−12.5000	−	21.6506i	−0.624220	−	1.08118i	−0.988691	−	0.149966i	$-0.952083\pi$
$401$	−12.5000	−	21.6506i	−0.624220	−	1.08118i	0.364471	−	0.931215i	$-0.381250\pi$
$402$	−10.0000	+	17.3205i	−0.498755	+	0.863868i
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	5.00000	+	8.66025i	0.248759	+	0.430864i
$405$	22.0000			1.09319
$406$	2.50000	+	12.9904i	0.124073	+	0.644702i
$407$	8.00000			0.396545
$408$		0			0
$409$	−17.5000	+	30.3109i	−0.865319	+	1.49878i	0.00141047	+	0.999999i	$0.499551\pi$
$409$	−17.5000	+	30.3109i	−0.865319	+	1.49878i	−0.866730	+	0.498778i	$0.833782\pi$
$410$	1.00000	−	1.73205i	0.0493865	−	0.0855399i
$411$	18.0000	+	31.1769i	0.887875	+	1.53784i
$412$	−10.0000			−0.492665
$413$	−2.00000	+	1.73205i	−0.0984136	+	0.0852286i
$414$	−2.00000			−0.0982946
$415$	9.00000	+	15.5885i	0.441793	+	0.765207i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$	−4.00000	+	6.92820i	−0.195881	+	0.339276i
$418$	−12.0000	−	20.7846i	−0.586939	−	1.01661i
$419$	−33.0000			−1.61216			−0.806078	−	0.591810i	$-0.798414\pi$
$419$	−33.0000			−1.61216			−0.806078	+	0.591810i	$0.798414\pi$
$420$	8.00000	−	6.92820i	0.390360	−	0.338062i
$421$	−30.0000			−1.46211			−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000			−1.46211			−0.731055	+	0.682318i	$0.760972\pi$
$422$		0			0
$423$	4.00000	−	6.92820i	0.194487	−	0.336861i
$424$	5.00000	−	8.66025i	0.242821	−	0.420579i
$425$		0			0
$426$	−30.0000			−1.45350
$427$	−7.00000	−	36.3731i	−0.338754	−	1.76022i
$428$	13.0000			0.628379
$429$	4.00000	+	6.92820i	0.193122	+	0.334497i
$430$	−1.00000	+	1.73205i	−0.0482243	+	0.0835269i
$431$	−13.0000	+	22.5167i	−0.626188	+	1.08459i	0.362122	+	0.932131i	$0.382052\pi$
$431$	−13.0000	+	22.5167i	−0.626188	+	1.08459i	−0.988310	+	0.152459i	$0.951281\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	10.0000	+	3.46410i	0.480015	+	0.166282i
$435$	20.0000			0.958927
$436$	3.50000	+	6.06218i	0.167620	+	0.290326i
$437$	−6.00000	+	10.3923i	−0.287019	+	0.497131i
$438$	−7.00000	+	12.1244i	−0.334473	+	0.579324i
$439$	3.50000	+	6.06218i	0.167046	+	0.289332i	0.937380	−	0.348309i	$-0.113244\pi$
$439$	3.50000	+	6.06218i	0.167046	+	0.289332i	−0.770334	+	0.637641i	$0.779911\pi$
$440$	8.00000			0.381385
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		0			0
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	0.987346	−	0.158583i	$-0.0506926\pi$
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	−0.631010	+	0.775775i	$0.717359\pi$
$444$	2.00000	−	3.46410i	0.0949158	−	0.164399i
$445$		0			0
$446$	−13.0000	−	22.5167i	−0.615568	−	1.06619i
$447$	2.00000			0.0945968
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	11.0000			0.519122			0.259561	−	0.965727i	$-0.416422\pi$
$449$	11.0000			0.519122			0.259561	+	0.965727i	$0.416422\pi$
$450$	0.500000	+	0.866025i	0.0235702	+	0.0408248i
$451$	2.00000	−	3.46410i	0.0941763	−	0.163118i
$452$	1.50000	−	2.59808i	0.0705541	−	0.122203i
$453$	−19.0000	−	32.9090i	−0.892698	−	1.54620i
$454$	−18.0000			−0.844782
$455$	1.00000	+	5.19615i	0.0468807	+	0.243599i
$456$	−12.0000			−0.561951
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	−0.991551	−	0.129718i	$-0.958593\pi$
$457$	−13.0000	−	22.5167i	−0.608114	−	1.05328i	0.383437	−	0.923567i	$-0.374740\pi$
$458$	10.5000	−	18.1865i	0.490633	−	0.849801i
$459$		0			0
$460$	−2.00000	−	3.46410i	−0.0932505	−	0.161515i
$461$	−20.0000			−0.931493			−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000			−0.931493			−0.465746	+	0.884918i	$0.654214\pi$
$462$	16.0000	−	13.8564i	0.744387	−	0.644658i
$463$	−7.00000			−0.325318			−0.162659	−	0.986682i	$-0.552007\pi$
$463$	−7.00000			−0.325318			−0.162659	+	0.986682i	$0.552007\pi$
$464$	2.50000	+	4.33013i	0.116060	+	0.201021i
$465$	8.00000	−	13.8564i	0.370991	−	0.642575i
$466$	8.00000	−	13.8564i	0.370593	−	0.641886i
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$	1.00000			0.0462250
$469$	−20.0000	+	17.3205i	−0.923514	+	0.799787i
$470$	16.0000			0.738025
$471$	15.0000	+	25.9808i	0.691164	+	1.19713i
$472$	−0.500000	+	0.866025i	−0.0230144	+	0.0398621i
$473$	−2.00000	+	3.46410i	−0.0919601	+	0.159280i
$474$		0			0
$475$	6.00000			0.275299
$476$		0			0
$477$	−10.0000			−0.457869
$478$	−8.00000	−	13.8564i	−0.365911	−	0.633777i
$479$	3.50000	−	6.06218i	0.159919	−	0.276988i	−0.774920	−	0.632059i	$-0.782210\pi$
$479$	3.50000	−	6.06218i	0.159919	−	0.276988i	0.934839	+	0.355071i	$0.115543\pi$
$480$	2.00000	−	3.46410i	0.0912871	−	0.158114i
$481$	1.00000	+	1.73205i	0.0455961	+	0.0789747i
$482$	−5.00000			−0.227744
$483$	−10.0000	−	3.46410i	−0.455016	−	0.157622i
$484$	5.00000			0.227273
$485$	−4.00000	−	6.92820i	−0.181631	−	0.314594i
$486$	5.00000	−	8.66025i	0.226805	−	0.392837i
$487$	−11.0000	+	19.0526i	−0.498458	+	0.863354i	−0.999998	−	0.00178012i	$-0.999433\pi$
$487$	−11.0000	+	19.0526i	−0.498458	+	0.863354i	0.501541	+	0.865134i	$0.332767\pi$
$488$	−7.00000	−	12.1244i	−0.316875	−	0.548844i
$489$	−46.0000			−2.08019
$490$	13.0000	−	5.19615i	0.587280	−	0.234738i
$491$	−13.0000			−0.586682			−0.293341	−	0.956008i	$-0.594767\pi$
$491$	−13.0000			−0.586682			−0.293341	+	0.956008i	$0.594767\pi$
$492$	−1.00000	−	1.73205i	−0.0450835	−	0.0780869i
$493$		0			0
$494$	3.00000	−	5.19615i	0.134976	−	0.233786i
$495$	−4.00000	−	6.92820i	−0.179787	−	0.311400i
$496$	4.00000			0.179605
$497$	−37.5000	−	12.9904i	−1.68210	−	0.582698i
$498$	18.0000			0.806599
$499$	−18.0000	−	31.1769i	−0.805791	−	1.39567i	−0.915756	−	0.401735i	$-0.868407\pi$
$499$	−18.0000	−	31.1769i	−0.805791	−	1.39567i	0.109965	−	0.993935i	$-0.464926\pi$
$500$	−6.00000	+	10.3923i	−0.268328	+	0.464758i
$501$	−5.00000	+	8.66025i	−0.223384	+	0.386912i
$502$	4.50000	+	7.79423i	0.200845	+	0.347873i
$503$	−16.0000			−0.713405			−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000			−0.713405			−0.356702	+	0.934218i	$0.616099\pi$
$504$	−0.500000	−	2.59808i	−0.0222718	−	0.115728i
$505$	20.0000			0.889988
$506$	−4.00000	−	6.92820i	−0.177822	−	0.307996i
$507$	12.0000	−	20.7846i	0.532939	−	0.923077i
$508$	−2.00000	+	3.46410i	−0.0887357	+	0.153695i
$509$	−9.50000	−	16.4545i	−0.421080	−	0.729332i	0.574965	−	0.818178i	$-0.305016\pi$
$509$	−9.50000	−	16.4545i	−0.421080	−	0.729332i	−0.996045	+	0.0888457i	$0.971682\pi$
$510$		0			0
$511$	−14.0000	+	12.1244i	−0.619324	+	0.536350i
$512$	1.00000			0.0441942
$513$	−12.0000	−	20.7846i	−0.529813	−	0.917663i
$514$	1.00000	−	1.73205i	0.0441081	−	0.0763975i
$515$	−10.0000	+	17.3205i	−0.440653	+	0.763233i
$516$	1.00000	+	1.73205i	0.0440225	+	0.0762493i
$517$	32.0000			1.40736
$518$	4.00000	−	3.46410i	0.175750	−	0.152204i
$519$	48.0000			2.10697
$520$	1.00000	+	1.73205i	0.0438529	+	0.0759555i
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.120656	−	0.992694i	$-0.461500\pi$
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.799370	−	0.600839i	$-0.205167\pi$
$522$	2.50000	−	4.33013i	0.109422	−	0.189525i
$523$	18.0000	+	31.1769i	0.787085	+	1.36327i	0.927746	+	0.373213i	$0.121744\pi$
$523$	18.0000	+	31.1769i	0.787085	+	1.36327i	−0.140660	+	0.990058i	$0.544923\pi$
$524$	12.0000			0.524222
$525$	1.00000	+	5.19615i	0.0436436	+	0.226779i
$526$	−31.0000			−1.35166
$527$		0			0
$528$	4.00000	−	6.92820i	0.174078	−	0.301511i
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$	−10.0000	−	17.3205i	−0.434372	−	0.752355i
$531$	1.00000			0.0433963
$532$	−15.0000	−	5.19615i	−0.650332	−	0.225282i
$533$	1.00000			0.0433148
$534$		0			0
$535$	13.0000	−	22.5167i	0.562039	−	0.973480i
$536$	−5.00000	+	8.66025i	−0.215967	+	0.374066i
$537$	10.0000	+	17.3205i	0.431532	+	0.747435i
$538$	16.0000			0.689809
$539$	26.0000	−	10.3923i	1.11990	−	0.447628i
$540$	8.00000			0.344265
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	−10.0000	+	17.3205i	−0.429537	+	0.743980i
$543$	−2.00000	+	3.46410i	−0.0858282	+	0.148659i
$544$		0			0
$545$	14.0000			0.599694
$546$	5.00000	+	1.73205i	0.213980	+	0.0741249i
$547$	−4.00000			−0.171028			−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000			−0.171028			−0.0855138	+	0.996337i	$0.527253\pi$
$548$	9.00000	+	15.5885i	0.384461	+	0.665906i
$549$	−7.00000	+	12.1244i	−0.298753	+	0.517455i
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$	−15.0000	−	25.9808i	−0.639021	−	1.10682i
$552$	−4.00000			−0.170251
$553$		0			0
$554$	8.00000			0.339887
$555$	−4.00000	−	6.92820i	−0.169791	−	0.294086i
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	−13.5000	+	23.3827i	−0.572013	+	0.990756i	0.424346	+	0.905500i	$0.360504\pi$
$557$	−13.5000	+	23.3827i	−0.572013	+	0.990756i	−0.996359	+	0.0852559i	$0.972829\pi$
$558$	−2.00000	−	3.46410i	−0.0846668	−	0.146647i
$559$	−1.00000			−0.0422955
$560$	4.00000	−	3.46410i	0.169031	−	0.146385i
$561$		0			0
$562$	−7.00000	−	12.1244i	−0.295277	−	0.511435i
$563$	−8.00000	+	13.8564i	−0.337160	+	0.583978i	−0.983897	−	0.178735i	$-0.942800\pi$
$563$	−8.00000	+	13.8564i	−0.337160	+	0.583978i	0.646737	+	0.762713i	$0.276133\pi$
$564$	8.00000	−	13.8564i	0.336861	−	0.583460i
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$	−1.00000			−0.0420331
$567$	22.0000	−	19.0526i	0.923913	−	0.800132i
$568$	−15.0000			−0.629386
$569$	1.50000	+	2.59808i	0.0628833	+	0.108917i	0.895753	−	0.444552i	$-0.146637\pi$
$569$	1.50000	+	2.59808i	0.0628833	+	0.108917i	−0.832870	+	0.553469i	$0.813304\pi$
$570$	−12.0000	+	20.7846i	−0.502625	+	0.870572i
$571$	21.0000	−	36.3731i	0.878823	−	1.52217i	0.0261885	−	0.999657i	$-0.491663\pi$
$571$	21.0000	−	36.3731i	0.878823	−	1.52217i	0.852634	−	0.522508i	$-0.175004\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$	10.0000			0.417756
$574$	−0.500000	−	2.59808i	−0.0208696	−	0.108442i
$575$	2.00000			0.0834058
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−3.00000	+	5.19615i	−0.124892	+	0.216319i	−0.921691	−	0.387926i	$-0.873192\pi$
$577$	−3.00000	+	5.19615i	−0.124892	+	0.216319i	0.796799	+	0.604245i	$0.206525\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$	10.0000	+	17.3205i	0.415586	+	0.719816i
$580$	10.0000			0.415227
$581$	22.5000	+	7.79423i	0.933457	+	0.323359i
$582$	−8.00000			−0.331611
$583$	−20.0000	−	34.6410i	−0.828315	−	1.43468i
$584$	−3.50000	+	6.06218i	−0.144831	+	0.250855i
$585$	1.00000	−	1.73205i	0.0413449	−	0.0716115i
$586$	−1.50000	−	2.59808i	−0.0619644	−	0.107326i
$587$	18.0000			0.742940			0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000			0.742940			0.371470	+	0.928445i	$0.378854\pi$
$588$	2.00000	−	13.8564i	0.0824786	−	0.571429i
$589$	−24.0000			−0.988903
$590$	1.00000	+	1.73205i	0.0411693	+	0.0713074i
$591$	2.00000	−	3.46410i	0.0822690	−	0.142494i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	19.0000	+	32.9090i	0.780236	+	1.35141i	0.931804	+	0.362962i	$0.118235\pi$
$593$	19.0000	+	32.9090i	0.780236	+	1.35141i	−0.151567	+	0.988447i	$0.548432\pi$
$594$	16.0000			0.656488
$595$		0			0
$596$	1.00000			0.0409616
$597$	3.00000	+	5.19615i	0.122782	+	0.212664i
$598$	1.00000	−	1.73205i	0.0408930	−	0.0708288i
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$	1.00000	+	1.73205i	0.0408248	+	0.0707107i
$601$	2.00000			0.0815817			0.0407909	−	0.999168i	$-0.487012\pi$
$601$	2.00000			0.0815817			0.0407909	+	0.999168i	$0.487012\pi$
$602$	0.500000	+	2.59808i	0.0203785	+	0.105890i
$603$	10.0000			0.407231
$604$	−9.50000	−	16.4545i	−0.386550	−	0.669523i
$605$	5.00000	−	8.66025i	0.203279	−	0.352089i
$606$	10.0000	−	17.3205i	0.406222	−	0.703598i
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	−0.983262	−	0.182199i	$-0.941678\pi$
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	0.333842	−	0.942629i	$-0.391655\pi$
$608$	−6.00000			−0.243332
$609$	20.0000	−	17.3205i	0.810441	−	0.701862i
$610$	−28.0000			−1.13369
$611$	4.00000	+	6.92820i	0.161823	+	0.280285i
$612$		0			0
$613$	3.00000	−	5.19615i	0.121169	−	0.209871i	−0.799060	−	0.601251i	$-0.794669\pi$
$613$	3.00000	−	5.19615i	0.121169	−	0.209871i	0.920229	+	0.391381i	$0.128002\pi$
$614$	−4.50000	−	7.79423i	−0.181605	−	0.314549i
$615$	−4.00000			−0.161296
$616$	8.00000	−	6.92820i	0.322329	−	0.279145i
$617$	−3.00000			−0.120775			−0.0603877	−	0.998175i	$-0.519234\pi$
$617$	−3.00000			−0.120775			−0.0603877	+	0.998175i	$0.519234\pi$
$618$	10.0000	+	17.3205i	0.402259	+	0.696733i
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	−0.412341	−	0.911030i	$-0.635289\pi$
$619$	14.5000	−	25.1147i	0.582804	−	1.00945i	0.995145	−	0.0984169i	$-0.0313779\pi$
$620$	4.00000	−	6.92820i	0.160644	−	0.278243i
$621$	−4.00000	−	6.92820i	−0.160514	−	0.278019i
$622$	13.0000			0.521253
$623$		0			0
$624$	2.00000			0.0800641
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−8.00000	+	13.8564i	−0.319744	+	0.553813i
$627$	−24.0000	+	41.5692i	−0.958468	+	1.66011i
$628$	7.50000	+	12.9904i	0.299283	+	0.518373i
$629$		0			0
$630$	−5.00000	−	1.73205i	−0.199205	−	0.0690066i
$631$	30.0000			1.19428			0.597141	−	0.802137i	$-0.296303\pi$
$631$	30.0000			1.19428			0.597141	+	0.802137i	$0.296303\pi$
$632$		0			0
$633$		0			0
$634$	1.00000	−	1.73205i	0.0397151	−	0.0687885i
$635$	4.00000	+	6.92820i	0.158735	+	0.274937i
$636$	−20.0000			−0.793052
$637$	5.50000	+	4.33013i	0.217918	+	0.171566i
$638$	20.0000			0.791808
$639$	7.50000	+	12.9904i	0.296695	+	0.513892i
$640$	1.00000	−	1.73205i	0.0395285	−	0.0684653i
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	−0.800678	−	0.599095i	$-0.795527\pi$
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	0.919171	+	0.393860i	$0.128860\pi$
$642$	−13.0000	−	22.5167i	−0.513069	−	0.888662i
$643$	24.0000			0.946468			0.473234	−	0.880937i	$-0.343087\pi$
$643$	24.0000			0.946468			0.473234	+	0.880937i	$0.343087\pi$
$644$	−5.00000	−	1.73205i	−0.197028	−	0.0682524i
$645$	4.00000			0.157500
$646$		0			0
$647$	−17.0000	+	29.4449i	−0.668339	+	1.15760i	0.310029	+	0.950727i	$0.399661\pi$
$647$	−17.0000	+	29.4449i	−0.668339	+	1.15760i	−0.978368	+	0.206870i	$0.933672\pi$
$648$	5.50000	−	9.52628i	0.216060	−	0.374228i
$649$	2.00000	+	3.46410i	0.0785069	+	0.135978i
$650$	−1.00000			−0.0392232
$651$	−4.00000	−	20.7846i	−0.156772	−	0.814613i
$652$	−23.0000			−0.900750
$653$	−7.50000	−	12.9904i	−0.293498	−	0.508353i	0.681137	−	0.732156i	$-0.261486\pi$
$653$	−7.50000	−	12.9904i	−0.293498	−	0.508353i	−0.974634	+	0.223803i	$0.928153\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$	12.0000	−	20.7846i	0.468879	−	0.812122i
$656$	−0.500000	−	0.866025i	−0.0195217	−	0.0338126i
$657$	7.00000			0.273096
$658$	16.0000	−	13.8564i	0.623745	−	0.540179i
$659$	22.0000			0.856998			0.428499	−	0.903542i	$-0.359042\pi$
$659$	22.0000			0.856998			0.428499	+	0.903542i	$0.359042\pi$
$660$	−8.00000	−	13.8564i	−0.311400	−	0.539360i
$661$	9.00000	−	15.5885i	0.350059	−	0.606321i	−0.636200	−	0.771524i	$-0.719495\pi$
$661$	9.00000	−	15.5885i	0.350059	−	0.606321i	0.986260	+	0.165203i	$0.0528281\pi$
$662$	−6.00000	+	10.3923i	−0.233197	+	0.403908i
$663$		0			0
$664$	9.00000			0.349268
$665$	−24.0000	+	20.7846i	−0.930680	+	0.805993i
$666$	−2.00000			−0.0774984
$667$	−5.00000	−	8.66025i	−0.193601	−	0.335326i
$668$	−2.50000	+	4.33013i	−0.0967279	+	0.167538i
$669$	−26.0000	+	45.0333i	−1.00522	+	1.74109i
$670$	10.0000	+	17.3205i	0.386334	+	0.669150i
$671$	−56.0000			−2.16186
$672$	−1.00000	−	5.19615i	−0.0385758	−	0.200446i
$673$	40.0000			1.54189			0.770943	−	0.636904i	$-0.219785\pi$
$673$	40.0000			1.54189			0.770943	+	0.636904i	$0.219785\pi$
$674$	−15.5000	−	26.8468i	−0.597038	−	1.03410i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	0.727386	−	0.686229i	$-0.240735\pi$
$677$	−6.00000	−	10.3923i	−0.230599	−	0.399409i	−0.957984	+	0.286820i	$0.907402\pi$
$678$	−6.00000			−0.230429
$679$	−10.0000	−	3.46410i	−0.383765	−	0.132940i
$680$		0			0
$681$	18.0000	+	31.1769i	0.689761	+	1.19470i
$682$	8.00000	−	13.8564i	0.306336	−	0.530589i
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	−0.825222	−	0.564809i	$-0.808950\pi$
$683$	2.00000	−	3.46410i	0.0765279	−	0.132550i	0.901750	+	0.432259i	$0.142283\pi$
$684$	3.00000	+	5.19615i	0.114708	+	0.198680i
$685$	36.0000			1.37549
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$	−42.0000			−1.60240
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	5.00000	−	8.66025i	0.190485	−	0.329929i
$690$	−4.00000	+	6.92820i	−0.152277	+	0.263752i
$691$	15.0000	+	25.9808i	0.570627	+	0.988355i	0.996502	+	0.0835727i	$0.0266331\pi$
$691$	15.0000	+	25.9808i	0.570627	+	0.988355i	−0.425875	+	0.904782i	$0.640034\pi$
$692$	24.0000			0.912343
$693$	−10.0000	−	3.46410i	−0.379869	−	0.131590i
$694$	−24.0000			−0.911028
$695$	4.00000	+	6.92820i	0.151729	+	0.262802i
$696$	5.00000	−	8.66025i	0.189525	−	0.328266i
$697$		0			0
$698$	13.0000	+	22.5167i	0.492057	+	0.852268i
$699$	−32.0000			−1.21035
$700$	0.500000	+	2.59808i	0.0188982	+	0.0981981i
$701$	−44.0000			−1.66186			−0.830929	−	0.556379i	$-0.812190\pi$
$701$	−44.0000			−1.66186			−0.830929	+	0.556379i	$0.812190\pi$
$702$	2.00000	+	3.46410i	0.0754851	+	0.130744i
$703$	−6.00000	+	10.3923i	−0.226294	+	0.391953i
$704$	2.00000	−	3.46410i	0.0753778	−	0.130558i
$705$	−16.0000	−	27.7128i	−0.602595	−	1.04372i
$706$	21.0000			0.790345
$707$	20.0000	−	17.3205i	0.752177	−	0.651405i
$708$	2.00000			0.0751646
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	−0.981331	−	0.192328i	$-0.938396\pi$
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	0.324104	−	0.946021i	$-0.394937\pi$
$710$	−15.0000	+	25.9808i	−0.562940	+	0.975041i
$711$		0			0
$712$		0			0
$713$	−8.00000			−0.299602
$714$		0			0
$715$	8.00000			0.299183
$716$	5.00000	+	8.66025i	0.186859	+	0.323649i
$717$	−16.0000	+	27.7128i	−0.597531	+	1.03495i
$718$	−7.00000	+	12.1244i	−0.261238	+	0.452477i
$719$	15.5000	+	26.8468i	0.578052	+	1.00122i	0.995703	+	0.0926083i	$0.0295204\pi$
$719$	15.5000	+	26.8468i	0.578052	+	1.00122i	−0.417650	+	0.908608i	$0.637146\pi$
$720$	−2.00000			−0.0745356
$721$	5.00000	+	25.9808i	0.186210	+	0.967574i
$722$	17.0000			0.632674
$723$	5.00000	+	8.66025i	0.185952	+	0.322078i
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	−2.50000	+	4.33013i	−0.0928477	+	0.160817i
$726$	−5.00000	−	8.66025i	−0.185567	−	0.321412i
$727$	−43.0000			−1.59478			−0.797391	−	0.603463i	$-0.793787\pi$
$727$	−43.0000			−1.59478			−0.797391	+	0.603463i	$0.793787\pi$
$728$	2.50000	+	0.866025i	0.0926562	+	0.0320970i
$729$	13.0000			0.481481
$730$	7.00000	+	12.1244i	0.259082	+	0.448743i
$731$		0			0
$732$	−14.0000	+	24.2487i	−0.517455	+	0.896258i
$733$	21.0000	+	36.3731i	0.775653	+	1.34347i	0.934427	+	0.356155i	$0.115912\pi$
$733$	21.0000	+	36.3731i	0.775653	+	1.34347i	−0.158774	+	0.987315i	$0.550754\pi$
$734$	−18.0000			−0.664392
$735$	−22.0000	−	17.3205i	−0.811482	−	0.638877i
$736$	−2.00000			−0.0737210
$737$	20.0000	+	34.6410i	0.736709	+	1.27602i
$738$	−0.500000	+	0.866025i	−0.0184053	+	0.0318788i
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	−0.694468	−	0.719524i	$-0.744360\pi$
$739$	7.50000	−	12.9904i	0.275892	−	0.477859i	0.970360	+	0.241665i	$0.0776935\pi$
$740$	−2.00000	−	3.46410i	−0.0735215	−	0.127343i
$741$	−12.0000			−0.440831
$742$	−25.0000	−	8.66025i	−0.917779	−	0.317928i
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$	−4.00000	−	6.92820i	−0.146647	−	0.254000i
$745$	1.00000	−	1.73205i	0.0366372	−	0.0634574i
$746$	−8.00000	+	13.8564i	−0.292901	+	0.507319i
$747$	−4.50000	−	7.79423i	−0.164646	−	0.285176i
$748$		0			0
$749$	−6.50000	−	33.7750i	−0.237505	−	1.23411i
$750$	24.0000			0.876356
$751$	−2.50000	−	4.33013i	−0.0912263	−	0.158009i	0.816801	−	0.576919i	$-0.195745\pi$
$751$	−2.50000	−	4.33013i	−0.0912263	−	0.158009i	−0.908027	+	0.418911i	$0.862412\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$	9.00000	−	15.5885i	0.327978	−	0.568075i
$754$	2.50000	+	4.33013i	0.0910446	+	0.157694i
$755$	−38.0000			−1.38296
$756$	8.00000	−	6.92820i	0.290957	−	0.251976i
$757$	31.0000			1.12671			0.563357	−	0.826214i	$-0.309510\pi$
$757$	31.0000			1.12671			0.563357	+	0.826214i	$0.309510\pi$
$758$	14.5000	+	25.1147i	0.526664	+	0.912208i
$759$	−8.00000	+	13.8564i	−0.290382	+	0.502956i
$760$	−6.00000	+	10.3923i	−0.217643	+	0.376969i
$761$	25.0000	+	43.3013i	0.906249	+	1.56967i	0.819231	+	0.573463i	$0.194400\pi$
$761$	25.0000	+	43.3013i	0.906249	+	1.56967i	0.0870179	+	0.996207i	$0.472266\pi$
$762$	8.00000			0.289809
$763$	14.0000	−	12.1244i	0.506834	−	0.438931i
$764$	5.00000			0.180894
$765$		0			0
$766$	7.50000	−	12.9904i	0.270986	−	0.469362i
$767$	−0.500000	+	0.866025i	−0.0180540	+	0.0312704i
$768$	−1.00000	−	1.73205i	−0.0360844	−	0.0625000i
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$	−4.00000	−	20.7846i	−0.144150	−	0.749025i
$771$	−4.00000			−0.144056
$772$	5.00000	+	8.66025i	0.179954	+	0.311689i
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	−0.712241	−	0.701935i	$-0.752320\pi$
$773$	7.00000	−	12.1244i	0.251773	−	0.436083i	0.964014	+	0.265852i	$0.0856532\pi$
$774$	0.500000	−	0.866025i	0.0179721	−	0.0311286i
$775$	2.00000	+	3.46410i	0.0718421	+	0.124434i
$776$	−4.00000			−0.143592
$777$	−10.0000	−	3.46410i	−0.358748	−	0.124274i
$778$		0			0
$779$	3.00000	+	5.19615i	0.107486	+	0.186171i
$780$	2.00000	−	3.46410i	0.0716115	−	0.124035i
$781$	−30.0000	+	51.9615i	−1.07348	+	1.85933i
$782$		0			0
$783$	20.0000			0.714742
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	30.0000			1.07075
$786$	−12.0000	−	20.7846i	−0.428026	−	0.741362i
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	0.250832	+	0.968031i	$0.419296\pi$
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	−0.963755	+	0.266788i	$0.914038\pi$
$788$	1.00000	−	1.73205i	0.0356235	−	0.0617018i
$789$	31.0000	+	53.6936i	1.10363	+	1.91154i
$790$		0			0
$791$	−7.50000	−	2.59808i	−0.266669	−	0.0923770i
$792$	−4.00000			−0.142134
$793$	−7.00000	−	12.1244i	−0.248577	−	0.430548i
$794$	−13.0000	+	22.5167i	−0.461353	+	0.799086i
$795$	−20.0000	+	34.6410i	−0.709327	+	1.22859i
$796$	1.50000	+	2.59808i	0.0531661	+	0.0920864i
$797$	−14.0000			−0.495905			−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−14.0000			−0.495905			−0.247953	+	0.968772i	$0.579758\pi$
$798$	6.00000	+	31.1769i	0.212398	+	1.10365i
$799$		0			0
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	−12.5000	+	21.6506i	−0.441390	+	0.764511i
$803$	14.0000	+	24.2487i	0.494049	+	0.855718i
$804$	20.0000			0.705346
$805$	−8.00000	+	6.92820i	−0.281963	+	0.244187i
$806$	4.00000			0.140894
$807$	−16.0000	−	27.7128i	−0.563227	−	0.975537i
$808$	5.00000	−	8.66025i	0.175899	−	0.304667i
$809$	25.0000	−	43.3013i	0.878953	−	1.52239i	0.0264621	−	0.999650i	$-0.491576\pi$
$809$	25.0000	−	43.3013i	0.878953	−	1.52239i	0.852491	−	0.522742i	$-0.175091\pi$
$810$	−11.0000	−	19.0526i	−0.386501	−	0.669439i
$811$	33.0000			1.15879			0.579393	−	0.815048i	$-0.303290\pi$
$811$	33.0000			1.15879			0.579393	+	0.815048i	$0.303290\pi$
$812$	10.0000	−	8.66025i	0.350931	−	0.303915i
$813$	40.0000			1.40286
$814$	−4.00000	−	6.92820i	−0.140200	−	0.242833i
$815$	−23.0000	+	39.8372i	−0.805655	+	1.39544i
$816$		0			0
$817$	−3.00000	−	5.19615i	−0.104957	−	0.181790i
$818$	35.0000			1.22375
$819$	−0.500000	−	2.59808i	−0.0174714	−	0.0907841i
$820$	−2.00000			−0.0698430
$821$	26.0000	+	45.0333i	0.907406	+	1.57167i	0.817654	+	0.575710i	$0.195274\pi$
$821$	26.0000	+	45.0333i	0.907406	+	1.57167i	0.0897520	+	0.995964i	$0.471393\pi$
$822$	18.0000	−	31.1769i	0.627822	−	1.08742i
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	−0.439961	−	0.898017i	$-0.645008\pi$
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	0.997686	−	0.0679910i	$-0.0216589\pi$
$824$	5.00000	+	8.66025i	0.174183	+	0.301694i
$825$	8.00000			0.278524
$826$	2.50000	+	0.866025i	0.0869861	+	0.0301329i
$827$	−54.0000			−1.87776			−0.938882	−	0.344239i	$-0.888137\pi$
$827$	−54.0000			−1.87776			−0.938882	+	0.344239i	$0.888137\pi$
$828$	1.00000	+	1.73205i	0.0347524	+	0.0601929i
$829$	15.0000	−	25.9808i	0.520972	−	0.902349i	−0.478731	−	0.877962i	$-0.658903\pi$
$829$	15.0000	−	25.9808i	0.520972	−	0.902349i	0.999703	−	0.0243876i	$-0.00776357\pi$
$830$	9.00000	−	15.5885i	0.312395	−	0.541083i
$831$	−8.00000	−	13.8564i	−0.277517	−	0.480673i
$832$	1.00000			0.0346688
$833$		0			0
$834$	8.00000			0.277017
$835$	5.00000	+	8.66025i	0.173032	+	0.299700i
$836$	−12.0000	+	20.7846i	−0.415029	+	0.718851i
$837$	8.00000	−	13.8564i	0.276520	−	0.478947i
$838$	16.5000	+	28.5788i	0.569983	+	0.987240i
$839$	−29.0000			−1.00119			−0.500596	−	0.865681i	$-0.666886\pi$
$839$	−29.0000			−1.00119			−0.500596	+	0.865681i	$0.666886\pi$
$840$	−10.0000	−	3.46410i	−0.345033	−	0.119523i
$841$	−4.00000			−0.137931
$842$	15.0000	+	25.9808i	0.516934	+	0.895356i
$843$	−14.0000	+	24.2487i	−0.482186	+	0.835170i
$844$		0			0
$845$	−12.0000	−	20.7846i	−0.412813	−	0.715012i
$846$	−8.00000			−0.275046
$847$	−2.50000	−	12.9904i	−0.0859010	−	0.446355i
$848$	−10.0000			−0.343401
$849$	1.00000	+	1.73205i	0.0343199	+	0.0594438i
$850$		0			0
$851$	−2.00000	+	3.46410i	−0.0685591	+	0.118748i
$852$	15.0000	+	25.9808i	0.513892	+	0.890086i
$853$	−38.0000			−1.30110			−0.650548	−	0.759465i	$-0.725461\pi$
$853$	−38.0000			−1.30110			−0.650548	+	0.759465i	$0.725461\pi$
$854$	−28.0000	+	24.2487i	−0.958140	+	0.829774i
$855$	12.0000			0.410391
$856$	−6.50000	−	11.2583i	−0.222165	−	0.384802i
$857$	26.5000	−	45.8993i	0.905223	−	1.56789i	0.0846048	−	0.996415i	$-0.473037\pi$
$857$	26.5000	−	45.8993i	0.905223	−	1.56789i	0.820618	−	0.571477i	$-0.193629\pi$
$858$	4.00000	−	6.92820i	0.136558	−	0.236525i
$859$	6.50000	+	11.2583i	0.221777	+	0.384129i	0.955348	−	0.295484i	$-0.0954809\pi$
$859$	6.50000	+	11.2583i	0.221777	+	0.384129i	−0.733571	+	0.679613i	$0.762148\pi$
$860$	2.00000			0.0681994
$861$	−4.00000	+	3.46410i	−0.136320	+	0.118056i
$862$	26.0000			0.885564
$863$	−18.0000	−	31.1769i	−0.612727	−	1.06127i	−0.990779	−	0.135490i	$-0.956739\pi$
$863$	−18.0000	−	31.1769i	−0.612727	−	1.06127i	0.378052	−	0.925785i	$-0.376594\pi$
$864$	2.00000	−	3.46410i	0.0680414	−	0.117851i
$865$	24.0000	−	41.5692i	0.816024	−	1.41340i
$866$	−1.00000	−	1.73205i	−0.0339814	−	0.0588575i
$867$	−34.0000			−1.15470
$868$	−2.00000	−	10.3923i	−0.0678844	−	0.352738i
$869$		0			0
$870$	−10.0000	−	17.3205i	−0.339032	−	0.587220i
$871$	−5.00000	+	8.66025i	−0.169419	+	0.293442i
$872$	3.50000	−	6.06218i	0.118525	−	0.205291i
$873$	2.00000	+	3.46410i	0.0676897	+	0.117242i
$874$	12.0000			0.405906
$875$	30.0000	+	10.3923i	1.01419	+	0.351324i
$876$	14.0000			0.473016
$877$	26.0000	+	45.0333i	0.877958	+	1.52067i	0.853578	+	0.520964i	$0.174428\pi$
$877$	26.0000	+	45.0333i	0.877958	+	1.52067i	0.0243792	+	0.999703i	$0.492239\pi$
$878$	3.50000	−	6.06218i	0.118119	−	0.204589i
$879$	−3.00000	+	5.19615i	−0.101187	+	0.175262i
$880$	−4.00000	−	6.92820i	−0.134840	−	0.233550i
$881$	−7.00000			−0.235836			−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000			−0.235836			−0.117918	+	0.993023i	$0.537622\pi$
$882$	−6.50000	+	2.59808i	−0.218866	+	0.0874818i
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	2.00000	−	3.46410i	0.0672293	−	0.116445i
$886$	7.50000	−	12.9904i	0.251967	−	0.436420i
$887$	−6.50000	−	11.2583i	−0.218249	−	0.378018i	0.736024	−	0.676955i	$-0.236701\pi$
$887$	−6.50000	−	11.2583i	−0.218249	−	0.378018i	−0.954273	+	0.298938i	$0.903368\pi$
$888$	−4.00000			−0.134231
$889$	10.0000	+	3.46410i	0.335389	+	0.116182i
$890$		0			0
$891$	−22.0000	−	38.1051i	−0.737028	−	1.27657i
$892$	−13.0000	+	22.5167i	−0.435272	+	0.753914i
$893$	−24.0000	+	41.5692i	−0.803129	+	1.39106i
$894$	−1.00000	−	1.73205i	−0.0334450	−	0.0579284i
$895$	20.0000			0.668526
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$	−4.00000			−0.133556
$898$	−5.50000	−	9.52628i	−0.183537	−	0.317896i
$899$	10.0000	−	17.3205i	0.333519	−	0.577671i
$900$	0.500000	−	0.866025i	0.0166667	−	0.0288675i
$901$		0			0
$902$	−4.00000			−0.133185
$903$	4.00000	−	3.46410i	0.133112	−	0.115278i
$904$	−3.00000			−0.0997785
$905$	2.00000	+	3.46410i	0.0664822	+	0.115151i
$906$	−19.0000	+	32.9090i	−0.631233	+	1.09333i
$907$	−11.5000	+	19.9186i	−0.381851	+	0.661386i	−0.991327	−	0.131419i	$-0.958047\pi$
$907$	−11.5000	+	19.9186i	−0.381851	+	0.661386i	0.609476	+	0.792805i	$0.291380\pi$
$908$	9.00000	+	15.5885i	0.298675	+	0.517321i
$909$	−10.0000			−0.331679
$910$	4.00000	−	3.46410i	0.132599	−	0.114834i
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$	6.00000	+	10.3923i	0.198680	+	0.344124i
$913$	18.0000	−	31.1769i	0.595713	−	1.03181i
$914$	−13.0000	+	22.5167i	−0.430002	+	0.744785i
$915$	28.0000	+	48.4974i	0.925651	+	1.60328i
$916$	−21.0000			−0.693860
$917$	−6.00000	−	31.1769i	−0.198137	−	1.02955i
$918$		0			0
$919$	−11.5000	−	19.9186i	−0.379350	−	0.657053i	0.611618	−	0.791153i	$-0.290519\pi$
$919$	−11.5000	−	19.9186i	−0.379350	−	0.657053i	−0.990968	+	0.134100i	$0.957186\pi$
$920$	−2.00000	+	3.46410i	−0.0659380	+	0.114208i
$921$	−9.00000	+	15.5885i	−0.296560	+	0.513657i
$922$	10.0000	+	17.3205i	0.329332	+	0.570421i
$923$	−15.0000			−0.493731
$924$	−20.0000	−	6.92820i	−0.657952	−	0.227921i
$925$	2.00000			0.0657596
$926$	3.50000	+	6.06218i	0.115017	+	0.199216i
$927$	5.00000	−	8.66025i	0.164222	−	0.284440i
$928$	2.50000	−	4.33013i	0.0820665	−	0.142143i
$929$	19.0000	+	32.9090i	0.623370	+	1.07971i	0.988854	+	0.148890i	$0.0475702\pi$
$929$	19.0000	+	32.9090i	0.623370	+	1.07971i	−0.365484	+	0.930818i	$0.619096\pi$
$930$	−16.0000			−0.524661
$931$	−6.00000	+	41.5692i	−0.196642	+	1.36238i
$932$	−16.0000			−0.524097
$933$	−13.0000	−	22.5167i	−0.425601	−	0.737162i
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$		0			0
$936$	−0.500000	−	0.866025i	−0.0163430	−	0.0283069i
$937$	30.0000			0.980057			0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000			0.980057			0.490029	+	0.871706i	$0.336986\pi$
$938$	25.0000	+	8.66025i	0.816279	+	0.282767i
$939$	32.0000			1.04428
$940$	−8.00000	−	13.8564i	−0.260931	−	0.451946i
$941$	−18.0000	+	31.1769i	−0.586783	+	1.01634i	0.407867	+	0.913041i	$0.366273\pi$
$941$	−18.0000	+	31.1769i	−0.586783	+	1.01634i	−0.994651	+	0.103297i	$0.967061\pi$
$942$	15.0000	−	25.9808i	0.488726	−	0.846499i
$943$	1.00000	+	1.73205i	0.0325645	+	0.0564033i
$944$	1.00000			0.0325472
$945$	−4.00000	−	20.7846i	−0.130120	−	0.676123i
$946$	4.00000			0.130051
$947$	−22.5000	−	38.9711i	−0.731152	−	1.26639i	−0.956391	−	0.292089i	$-0.905650\pi$
$947$	−22.5000	−	38.9711i	−0.731152	−	1.26639i	0.225240	−	0.974303i	$-0.427684\pi$
$948$		0			0
$949$	−3.50000	+	6.06218i	−0.113615	+	0.196787i
$950$	−3.00000	−	5.19615i	−0.0973329	−	0.168585i
$951$	−4.00000			−0.129709
$952$		0			0
$953$	−9.00000			−0.291539			−0.145769	−	0.989319i	$-0.546566\pi$
$953$	−9.00000			−0.291539			−0.145769	+	0.989319i	$0.546566\pi$
$954$	5.00000	+	8.66025i	0.161881	+	0.280386i
$955$	5.00000	−	8.66025i	0.161796	−	0.280239i
$956$	−8.00000	+	13.8564i	−0.258738	+	0.448148i
$957$	−20.0000	−	34.6410i	−0.646508	−	1.11979i
$958$	−7.00000			−0.226160
$959$	36.0000	−	31.1769i	1.16250	−	1.00676i
$960$	−4.00000			−0.129099
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	1.00000	−	1.73205i	0.0322413	−	0.0558436i
$963$	−6.50000	+	11.2583i	−0.209460	+	0.362795i
$964$	2.50000	+	4.33013i	0.0805196	+	0.139464i
$965$	20.0000			0.643823
$966$	2.00000	+	10.3923i	0.0643489	+	0.334367i
$967$	31.0000			0.996893			0.498446	−	0.866921i	$-0.333904\pi$
$967$	31.0000			0.996893			0.498446	+	0.866921i	$0.333904\pi$
$968$	−2.50000	−	4.33013i	−0.0803530	−	0.139176i
$969$		0			0
$970$	−4.00000	+	6.92820i	−0.128432	+	0.222451i
$971$	−1.00000	−	1.73205i	−0.0320915	−	0.0555842i	0.849534	−	0.527535i	$-0.176883\pi$
$971$	−1.00000	−	1.73205i	−0.0320915	−	0.0555842i	−0.881625	+	0.471950i	$0.843550\pi$
$972$	−10.0000			−0.320750
$973$	10.0000	+	3.46410i	0.320585	+	0.111054i
$974$	22.0000			0.704925
$975$	1.00000	+	1.73205i	0.0320256	+	0.0554700i
$976$	−7.00000	+	12.1244i	−0.224065	+	0.388091i
$977$	1.00000	−	1.73205i	0.0319928	−	0.0554132i	−0.849586	−	0.527451i	$-0.823148\pi$
$977$	1.00000	−	1.73205i	0.0319928	−	0.0554132i	0.881579	+	0.472037i	$0.156481\pi$
$978$	23.0000	+	39.8372i	0.735459	+	1.27385i
$979$		0			0
$980$	−11.0000	−	8.66025i	−0.351382	−	0.276642i
$981$	−7.00000			−0.223493
$982$	6.50000	+	11.2583i	0.207423	+	0.359268i
$983$	−22.0000	+	38.1051i	−0.701691	+	1.21536i	0.266181	+	0.963923i	$0.414238\pi$
$983$	−22.0000	+	38.1051i	−0.701691	+	1.21536i	−0.967872	+	0.251442i	$0.919095\pi$
$984$	−1.00000	+	1.73205i	−0.0318788	+	0.0552158i
$985$	−2.00000	−	3.46410i	−0.0637253	−	0.110375i
$986$		0			0
$987$	−40.0000	−	13.8564i	−1.27321	−	0.441054i
$988$	−6.00000			−0.190885
$989$	−1.00000	−	1.73205i	−0.0317982	−	0.0550760i
$990$	−4.00000	+	6.92820i	−0.127128	+	0.220193i
$991$	9.50000	−	16.4545i	0.301777	−	0.522694i	−0.674761	−	0.738036i	$-0.735753\pi$
$991$	9.50000	−	16.4545i	0.301777	−	0.522694i	0.976539	+	0.215342i	$0.0690867\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	24.0000			0.761617
$994$	7.50000	+	38.9711i	0.237886	+	1.23609i
$995$	6.00000			0.190213
$996$	−9.00000	−	15.5885i	−0.285176	−	0.493939i
$997$	17.5000	−	30.3109i	0.554231	−	0.959955i	−0.443732	−	0.896159i	$-0.646346\pi$
$997$	17.5000	−	30.3109i	0.554231	−	0.959955i	0.997963	−	0.0637961i	$-0.0203207\pi$
$998$	−18.0000	+	31.1769i	−0.569780	+	0.986888i
$999$	−4.00000	−	6.92820i	−0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.e.a.165.1	✓	2
7.2	even	3	inner	574.2.e.a.247.1	yes	2
7.3	odd	6		4018.2.a.l.1.1		1
7.4	even	3		4018.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.a.165.1	✓	2	1.1	even	1	trivial
574.2.e.a.247.1	yes	2	7.2	even	3	inner
4018.2.a.l.1.1		1	7.3	odd	6
4018.2.a.r.1.1		1	7.4	even	3

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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +2.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +2.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{10} +(2.00000 - 3.46410i) q^{11} +(-1.00000 - 1.73205i) q^{12} +1.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} -4.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +(3.00000 + 5.19615i) q^{19} -2.00000 q^{20} +(-4.00000 + 3.46410i) q^{21} -4.00000 q^{22} +(1.00000 + 1.73205i) q^{23} +(-1.00000 + 1.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} -4.00000 q^{27} +(-2.00000 + 1.73205i) q^{28} -5.00000 q^{29} +(2.00000 + 3.46410i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.00000 + 6.92820i) q^{33} +(1.00000 + 5.19615i) q^{35} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(1.00000 + 1.73205i) q^{40} +1.00000 q^{41} +(5.00000 + 1.73205i) q^{42} -1.00000 q^{43} +(2.00000 + 3.46410i) q^{44} +(1.00000 - 1.73205i) q^{45} +(1.00000 - 1.73205i) q^{46} +(4.00000 + 6.92820i) q^{47} +2.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -1.00000 q^{50} +(-0.500000 + 0.866025i) q^{52} +(5.00000 - 8.66025i) q^{53} +(2.00000 + 3.46410i) q^{54} +8.00000 q^{55} +(2.50000 + 0.866025i) q^{56} -12.0000 q^{57} +(2.50000 + 4.33013i) q^{58} +(-0.500000 + 0.866025i) q^{59} +(2.00000 - 3.46410i) q^{60} +(-7.00000 - 12.1244i) q^{61} +4.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(4.00000 - 6.92820i) q^{66} +(-5.00000 + 8.66025i) q^{67} -4.00000 q^{69} +(4.00000 - 3.46410i) q^{70} -15.0000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-3.50000 + 6.06218i) q^{73} +(1.00000 - 1.73205i) q^{74} +(1.00000 + 1.73205i) q^{75} -6.00000 q^{76} +(8.00000 - 6.92820i) q^{77} +2.00000 q^{78} +(1.00000 - 1.73205i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-0.500000 - 0.866025i) q^{82} +9.00000 q^{83} +(-1.00000 - 5.19615i) q^{84} +(0.500000 + 0.866025i) q^{86} +(5.00000 - 8.66025i) q^{87} +(2.00000 - 3.46410i) q^{88} -2.00000 q^{90} +(2.50000 + 0.866025i) q^{91} -2.00000 q^{92} +(-4.00000 - 6.92820i) q^{93} +(4.00000 - 6.92820i) q^{94} +(-6.00000 + 10.3923i) q^{95} +(-1.00000 - 1.73205i) q^{96} -4.00000 q^{97} +(1.00000 - 6.92820i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} + 2 q^{5} + 4 q^{6} + 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 + 2 * q^5 + 4 * q^6 + 5 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} + 2 q^{5} + 4 q^{6} + 5 q^{7} + 2 q^{8} - q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} + 2 q^{13} - q^{14} - 8 q^{15} - q^{16} - q^{18} + 6 q^{19} - 4 q^{20} - 8 q^{21} - 8 q^{22} + 2 q^{23} - 2 q^{24} + q^{25} - q^{26} - 8 q^{27} - 4 q^{28} - 10 q^{29} + 4 q^{30} - 4 q^{31} - q^{32} + 8 q^{33} + 2 q^{35} + 2 q^{36} + 2 q^{37} + 6 q^{38} - 2 q^{39} + 2 q^{40} + 2 q^{41} + 10 q^{42} - 2 q^{43} + 4 q^{44} + 2 q^{45} + 2 q^{46} + 8 q^{47} + 4 q^{48} + 11 q^{49} - 2 q^{50} - q^{52} + 10 q^{53} + 4 q^{54} + 16 q^{55} + 5 q^{56} - 24 q^{57} + 5 q^{58} - q^{59} + 4 q^{60} - 14 q^{61} + 8 q^{62} - q^{63} + 2 q^{64} + 2 q^{65} + 8 q^{66} - 10 q^{67} - 8 q^{69} + 8 q^{70} - 30 q^{71} - q^{72} - 7 q^{73} + 2 q^{74} + 2 q^{75} - 12 q^{76} + 16 q^{77} + 4 q^{78} + 2 q^{80} + 11 q^{81} - q^{82} + 18 q^{83} - 2 q^{84} + q^{86} + 10 q^{87} + 4 q^{88} - 4 q^{90} + 5 q^{91} - 4 q^{92} - 8 q^{93} + 8 q^{94} - 12 q^{95} - 2 q^{96} - 8 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 + 2 * q^5 + 4 * q^6 + 5 * q^7 + 2 * q^8 - q^9 + 2 * q^10 + 4 * q^11 - 2 * q^12 + 2 * q^13 - q^14 - 8 * q^15 - q^16 - q^18 + 6 * q^19 - 4 * q^20 - 8 * q^21 - 8 * q^22 + 2 * q^23 - 2 * q^24 + q^25 - q^26 - 8 * q^27 - 4 * q^28 - 10 * q^29 + 4 * q^30 - 4 * q^31 - q^32 + 8 * q^33 + 2 * q^35 + 2 * q^36 + 2 * q^37 + 6 * q^38 - 2 * q^39 + 2 * q^40 + 2 * q^41 + 10 * q^42 - 2 * q^43 + 4 * q^44 + 2 * q^45 + 2 * q^46 + 8 * q^47 + 4 * q^48 + 11 * q^49 - 2 * q^50 - q^52 + 10 * q^53 + 4 * q^54 + 16 * q^55 + 5 * q^56 - 24 * q^57 + 5 * q^58 - q^59 + 4 * q^60 - 14 * q^61 + 8 * q^62 - q^63 + 2 * q^64 + 2 * q^65 + 8 * q^66 - 10 * q^67 - 8 * q^69 + 8 * q^70 - 30 * q^71 - q^72 - 7 * q^73 + 2 * q^74 + 2 * q^75 - 12 * q^76 + 16 * q^77 + 4 * q^78 + 2 * q^80 + 11 * q^81 - q^82 + 18 * q^83 - 2 * q^84 + q^86 + 10 * q^87 + 4 * q^88 - 4 * q^90 + 5 * q^91 - 4 * q^92 - 8 * q^93 + 8 * q^94 - 12 * q^95 - 2 * q^96 - 8 * q^97 + 2 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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