LMFDB - Embedded newform 430.2.e.b.221.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(221,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("430.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.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:	$3.43356728692$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	430.221
Dual form			430.2.e.b.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{10} +4.00000 q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.00000 + 1.73205i) q^{13} +(2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{15} +1.00000 q^{16} +(2.00000 + 3.46410i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-3.00000 + 5.19615i) q^{19} +(-0.500000 + 0.866025i) q^{20} +4.00000 q^{21} -4.00000 q^{22} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} -5.00000 q^{27} +(-2.00000 - 3.46410i) q^{28} +(0.500000 + 0.866025i) q^{29} +(0.500000 + 0.866025i) q^{30} +(-5.00000 + 8.66025i) q^{31} -1.00000 q^{32} +(-2.00000 + 3.46410i) q^{33} +(-2.00000 - 3.46410i) q^{34} +4.00000 q^{35} +(1.00000 + 1.73205i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} -2.00000 q^{39} +(0.500000 - 0.866025i) q^{40} +5.00000 q^{41} -4.00000 q^{42} +(6.50000 - 0.866025i) q^{43} +4.00000 q^{44} -2.00000 q^{45} +1.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(0.500000 + 0.866025i) q^{50} -4.00000 q^{51} +(1.00000 + 1.73205i) q^{52} +(-5.00000 + 8.66025i) q^{53} +5.00000 q^{54} +(-2.00000 + 3.46410i) q^{55} +(2.00000 + 3.46410i) q^{56} +(-3.00000 - 5.19615i) q^{57} +(-0.500000 - 0.866025i) q^{58} +14.0000 q^{59} +(-0.500000 - 0.866025i) q^{60} +(3.00000 + 5.19615i) q^{61} +(5.00000 - 8.66025i) q^{62} +(4.00000 - 6.92820i) q^{63} +1.00000 q^{64} -2.00000 q^{65} +(2.00000 - 3.46410i) q^{66} +(1.50000 - 2.59808i) q^{67} +(2.00000 + 3.46410i) q^{68} -4.00000 q^{70} +(-5.00000 - 8.66025i) q^{71} +(-1.00000 - 1.73205i) q^{72} +(7.00000 + 12.1244i) q^{73} +(1.00000 - 1.73205i) q^{74} +1.00000 q^{75} +(-3.00000 + 5.19615i) q^{76} +(-8.00000 - 13.8564i) q^{77} +2.00000 q^{78} +(-8.00000 - 13.8564i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} -5.00000 q^{82} +(7.50000 - 12.9904i) q^{83} +4.00000 q^{84} -4.00000 q^{85} +(-6.50000 + 0.866025i) q^{86} -1.00000 q^{87} -4.00000 q^{88} +(1.50000 - 2.59808i) q^{89} +2.00000 q^{90} +(4.00000 - 6.92820i) q^{91} +(-5.00000 - 8.66025i) q^{93} -1.00000 q^{94} +(-3.00000 - 5.19615i) q^{95} +(0.500000 - 0.866025i) q^{96} -12.0000 q^{97} +(4.50000 - 7.79423i) q^{98} +(4.00000 + 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} - q^{5} + q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 - q^5 + q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} - q^{5} + q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} - q^{12} + 2 q^{13} + 4 q^{14} - q^{15} + 2 q^{16} + 4 q^{17} - 2 q^{18} - 6 q^{19} - q^{20} + 8 q^{21} - 8 q^{22} + q^{24} - q^{25} - 2 q^{26} - 10 q^{27} - 4 q^{28} + q^{29} + q^{30} - 10 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} + 8 q^{35} + 2 q^{36} - 2 q^{37} + 6 q^{38} - 4 q^{39} + q^{40} + 10 q^{41} - 8 q^{42} + 13 q^{43} + 8 q^{44} - 4 q^{45} + 2 q^{47} - q^{48} - 9 q^{49} + q^{50} - 8 q^{51} + 2 q^{52} - 10 q^{53} + 10 q^{54} - 4 q^{55} + 4 q^{56} - 6 q^{57} - q^{58} + 28 q^{59} - q^{60} + 6 q^{61} + 10 q^{62} + 8 q^{63} + 2 q^{64} - 4 q^{65} + 4 q^{66} + 3 q^{67} + 4 q^{68} - 8 q^{70} - 10 q^{71} - 2 q^{72} + 14 q^{73} + 2 q^{74} + 2 q^{75} - 6 q^{76} - 16 q^{77} + 4 q^{78} - 16 q^{79} - q^{80} - q^{81} - 10 q^{82} + 15 q^{83} + 8 q^{84} - 8 q^{85} - 13 q^{86} - 2 q^{87} - 8 q^{88} + 3 q^{89} + 4 q^{90} + 8 q^{91} - 10 q^{93} - 2 q^{94} - 6 q^{95} + q^{96} - 24 q^{97} + 9 q^{98} + 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 - q^5 + q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9 + q^10 + 8 * q^11 - q^12 + 2 * q^13 + 4 * q^14 - q^15 + 2 * q^16 + 4 * q^17 - 2 * q^18 - 6 * q^19 - q^20 + 8 * q^21 - 8 * q^22 + q^24 - q^25 - 2 * q^26 - 10 * q^27 - 4 * q^28 + q^29 + q^30 - 10 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 + 8 * q^35 + 2 * q^36 - 2 * q^37 + 6 * q^38 - 4 * q^39 + q^40 + 10 * q^41 - 8 * q^42 + 13 * q^43 + 8 * q^44 - 4 * q^45 + 2 * q^47 - q^48 - 9 * q^49 + q^50 - 8 * q^51 + 2 * q^52 - 10 * q^53 + 10 * q^54 - 4 * q^55 + 4 * q^56 - 6 * q^57 - q^58 + 28 * q^59 - q^60 + 6 * q^61 + 10 * q^62 + 8 * q^63 + 2 * q^64 - 4 * q^65 + 4 * q^66 + 3 * q^67 + 4 * q^68 - 8 * q^70 - 10 * q^71 - 2 * q^72 + 14 * q^73 + 2 * q^74 + 2 * q^75 - 6 * q^76 - 16 * q^77 + 4 * q^78 - 16 * q^79 - q^80 - q^81 - 10 * q^82 + 15 * q^83 + 8 * q^84 - 8 * q^85 - 13 * q^86 - 2 * q^87 - 8 * q^88 + 3 * q^89 + 4 * q^90 + 8 * q^91 - 10 * q^93 - 2 * q^94 - 6 * q^95 + q^96 - 24 * q^97 + 9 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	0.188982	−	0.981981i	$-0.439481\pi$
$8$	−1.00000			−0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	4.00000			1.20605			0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000			1.20605			0.603023	+	0.797724i	$0.293963\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	2.00000	+	3.46410i	0.534522	+	0.925820i
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$	1.00000			0.250000
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$	−1.00000	−	1.73205i	−0.235702	−	0.408248i
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	4.00000			0.872872
$22$	−4.00000			−0.852803
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$	−5.00000			−0.962250
$28$	−2.00000	−	3.46410i	−0.377964	−	0.654654i
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.0680129	+	0.997684i	$0.521666\pi$
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.830014	+	0.557743i	$0.811667\pi$
$32$	−1.00000			−0.176777
$33$	−2.00000	+	3.46410i	−0.348155	+	0.603023i
$34$	−2.00000	−	3.46410i	−0.342997	−	0.594089i
$35$	4.00000			0.676123
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	3.00000	−	5.19615i	0.486664	−	0.842927i
$39$	−2.00000			−0.320256
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	5.00000			0.780869			0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000			0.780869			0.390434	+	0.920631i	$0.372325\pi$
$42$	−4.00000			−0.617213
$43$	6.50000	−	0.866025i	0.991241	−	0.132068i
$43$	6.50000	−	0.866025i	0.991241	−	0.132068i
$44$	4.00000			0.603023
$45$	−2.00000			−0.298142
$46$		0			0
$47$	1.00000			0.145865			0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000			0.145865			0.0729325	+	0.997337i	$0.476764\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−4.00000			−0.560112
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	−5.00000	+	8.66025i	−0.686803	+	1.18958i	0.286064	+	0.958211i	$0.407653\pi$
$53$	−5.00000	+	8.66025i	−0.686803	+	1.18958i	−0.972867	+	0.231367i	$0.925680\pi$
$54$	5.00000			0.680414
$55$	−2.00000	+	3.46410i	−0.269680	+	0.467099i
$56$	2.00000	+	3.46410i	0.267261	+	0.462910i
$57$	−3.00000	−	5.19615i	−0.397360	−	0.688247i
$58$	−0.500000	−	0.866025i	−0.0656532	−	0.113715i
$59$	14.0000			1.82264			0.911322	−	0.411693i	$-0.135063\pi$
$59$	14.0000			1.82264			0.911322	+	0.411693i	$0.135063\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	5.00000	−	8.66025i	0.635001	−	1.09985i
$63$	4.00000	−	6.92820i	0.503953	−	0.872872i
$64$	1.00000			0.125000
$65$	−2.00000			−0.248069
$66$	2.00000	−	3.46410i	0.246183	−	0.426401i
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$		0			0
$70$	−4.00000			−0.478091
$71$	−5.00000	−	8.66025i	−0.593391	−	1.02778i	−0.993772	−	0.111434i	$-0.964456\pi$
$71$	−5.00000	−	8.66025i	−0.593391	−	1.02778i	0.400381	−	0.916349i	$-0.368878\pi$
$72$	−1.00000	−	1.73205i	−0.117851	−	0.204124i
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	0.906208	+	0.422833i	$0.138964\pi$
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	−0.0869195	+	0.996215i	$0.527702\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	1.00000			0.115470
$76$	−3.00000	+	5.19615i	−0.344124	+	0.596040i
$77$	−8.00000	−	13.8564i	−0.911685	−	1.57908i
$78$	2.00000			0.226455
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.827401	−	0.561611i	$-0.810182\pi$
$79$	−8.00000	−	13.8564i	−0.900070	−	1.55897i	−0.0726692	−	0.997356i	$-0.523152\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.00000			−0.552158
$83$	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	$-0.141165\pi$
$84$	4.00000			0.436436
$85$	−4.00000			−0.433861
$86$	−6.50000	+	0.866025i	−0.700913	+	0.0933859i
$87$	−1.00000			−0.107211
$88$	−4.00000			−0.426401
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	−0.775509	−	0.631337i	$-0.782506\pi$
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	0.934508	+	0.355942i	$0.115840\pi$
$90$	2.00000			0.210819
$91$	4.00000	−	6.92820i	0.419314	−	0.726273i
$92$		0			0
$93$	−5.00000	−	8.66025i	−0.518476	−	0.898027i
$94$	−1.00000			−0.103142
$95$	−3.00000	−	5.19615i	−0.307794	−	0.533114i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−12.0000			−1.21842			−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000			−1.21842			−0.609208	+	0.793011i	$0.708512\pi$
$98$	4.50000	−	7.79423i	0.454569	−	0.787336i
$99$	4.00000	+	6.92820i	0.402015	+	0.696311i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−0.500000	−	0.866025i	−0.0497519	−	0.0861727i	0.840077	−	0.542467i	$-0.182510\pi$
$101$	−0.500000	−	0.866025i	−0.0497519	−	0.0861727i	−0.889829	+	0.456294i	$0.849176\pi$
$102$	4.00000			0.396059
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$	−2.00000	+	3.46410i	−0.195180	+	0.338062i
$106$	5.00000	−	8.66025i	0.485643	−	0.841158i
$107$	−1.00000			−0.0966736			−0.0483368	−	0.998831i	$-0.515392\pi$
$107$	−1.00000			−0.0966736			−0.0483368	+	0.998831i	$0.515392\pi$
$108$	−5.00000			−0.481125
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	−0.472708	−	0.881219i	$-0.656723\pi$
$109$	5.50000	−	9.52628i	0.526804	−	0.912452i	0.999512	−	0.0312328i	$-0.00994332\pi$
$110$	2.00000	−	3.46410i	0.190693	−	0.330289i
$111$	−1.00000	−	1.73205i	−0.0949158	−	0.164399i
$112$	−2.00000	−	3.46410i	−0.188982	−	0.327327i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$		0			0
$116$	0.500000	+	0.866025i	0.0464238	+	0.0804084i
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$	−14.0000			−1.28880
$119$	8.00000	−	13.8564i	0.733359	−	1.27021i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	5.00000			0.454545
$122$	−3.00000	−	5.19615i	−0.271607	−	0.470438i
$123$	−2.50000	+	4.33013i	−0.225417	+	0.390434i
$124$	−5.00000	+	8.66025i	−0.449013	+	0.777714i
$125$	1.00000			0.0894427
$126$	−4.00000	+	6.92820i	−0.356348	+	0.617213i
$127$	−17.0000			−1.50851			−0.754253	−	0.656584i	$-0.772001\pi$
$127$	−17.0000			−1.50851			−0.754253	+	0.656584i	$0.772001\pi$
$128$	−1.00000			−0.0883883
$129$	−2.50000	+	6.06218i	−0.220113	+	0.533745i
$130$	2.00000			0.175412
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$	−2.00000	+	3.46410i	−0.174078	+	0.301511i
$133$	24.0000			2.08106
$134$	−1.50000	+	2.59808i	−0.129580	+	0.224440i
$135$	2.50000	−	4.33013i	0.215166	−	0.372678i
$136$	−2.00000	−	3.46410i	−0.171499	−	0.297044i
$137$	2.00000			0.170872			0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000			0.170872			0.0854358	+	0.996344i	$0.472772\pi$
$138$		0			0
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	−0.905314	−	0.424743i	$-0.860365\pi$
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	0.820495	+	0.571654i	$0.193698\pi$
$140$	4.00000			0.338062
$141$	−0.500000	+	0.866025i	−0.0421076	+	0.0729325i
$142$	5.00000	+	8.66025i	0.419591	+	0.726752i
$143$	4.00000	+	6.92820i	0.334497	+	0.579365i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$	−1.00000			−0.0830455
$146$	−7.00000	−	12.1244i	−0.579324	−	1.00342i
$147$	−4.50000	−	7.79423i	−0.371154	−	0.642857i
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	−0.885779	−	0.464107i	$-0.846375\pi$
$149$	−0.500000	+	0.866025i	−0.0409616	+	0.0709476i	0.844818	+	0.535054i	$0.179709\pi$
$150$	−1.00000			−0.0816497
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$	3.00000	−	5.19615i	0.243332	−	0.421464i
$153$	−4.00000	+	6.92820i	−0.323381	+	0.560112i
$154$	8.00000	+	13.8564i	0.644658	+	1.11658i
$155$	−5.00000	−	8.66025i	−0.401610	−	0.695608i
$156$	−2.00000			−0.160128
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$	8.00000	+	13.8564i	0.636446	+	1.10236i
$159$	−5.00000	−	8.66025i	−0.396526	−	0.686803i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$		0			0
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	5.50000	+	9.52628i	0.430793	+	0.746156i	0.996942	−	0.0781474i	$-0.0249005\pi$
$163$	5.50000	+	9.52628i	0.430793	+	0.746156i	−0.566149	+	0.824303i	$0.691567\pi$
$164$	5.00000			0.390434
$165$	−2.00000	−	3.46410i	−0.155700	−	0.269680i
$166$	−7.50000	+	12.9904i	−0.582113	+	1.00825i
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	−0.985933	−	0.167139i	$-0.946547\pi$
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	0.637713	+	0.770274i	$0.279881\pi$
$168$	−4.00000			−0.308607
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	4.00000			0.306786
$171$	−12.0000			−0.917663
$172$	6.50000	−	0.866025i	0.495620	−	0.0660338i
$173$		0			0			−	1.00000i	$-0.5\pi$
$173$		0			0				1.00000i	$0.5\pi$
$174$	1.00000			0.0758098
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	4.00000			0.301511
$177$	−7.00000	+	12.1244i	−0.526152	+	0.911322i
$178$	−1.50000	+	2.59808i	−0.112430	+	0.194734i
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	0.549825	−	0.835280i	$-0.314694\pi$
$179$	−6.00000	−	10.3923i	−0.448461	−	0.776757i	−0.998286	+	0.0585225i	$0.981361\pi$
$180$	−2.00000			−0.149071
$181$	−11.0000	−	19.0526i	−0.817624	−	1.41617i	−0.907429	−	0.420206i	$-0.861958\pi$
$181$	−11.0000	−	19.0526i	−0.817624	−	1.41617i	0.0898051	−	0.995959i	$-0.471376\pi$
$182$	−4.00000	+	6.92820i	−0.296500	+	0.513553i
$183$	−6.00000			−0.443533
$184$		0			0
$185$	−1.00000	−	1.73205i	−0.0735215	−	0.127343i
$186$	5.00000	+	8.66025i	0.366618	+	0.635001i
$187$	8.00000	+	13.8564i	0.585018	+	1.01328i
$188$	1.00000			0.0729325
$189$	10.0000	+	17.3205i	0.727393	+	1.25988i
$190$	3.00000	+	5.19615i	0.217643	+	0.376969i
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	−0.929267	−	0.369410i	$-0.879560\pi$
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	0.784552	+	0.620063i	$0.212893\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−16.0000			−1.15171			−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000			−1.15171			−0.575853	+	0.817554i	$0.695330\pi$
$194$	12.0000			0.861550
$195$	1.00000	−	1.73205i	0.0716115	−	0.124035i
$196$	−4.50000	+	7.79423i	−0.321429	+	0.556731i
$197$	7.00000	+	12.1244i	0.498729	+	0.863825i	0.999999	−	0.00146660i	$-0.000466833\pi$
$197$	7.00000	+	12.1244i	0.498729	+	0.863825i	−0.501270	+	0.865291i	$0.667133\pi$
$198$	−4.00000	−	6.92820i	−0.284268	−	0.492366i
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	1.50000	+	2.59808i	0.105802	+	0.183254i
$202$	0.500000	+	0.866025i	0.0351799	+	0.0609333i
$203$	2.00000	−	3.46410i	0.140372	−	0.243132i
$204$	−4.00000			−0.280056
$205$	−2.50000	+	4.33013i	−0.174608	+	0.302429i
$206$	−2.50000	−	4.33013i	−0.174183	−	0.301694i
$207$		0			0
$208$	1.00000	+	1.73205i	0.0693375	+	0.120096i
$209$	−12.0000	+	20.7846i	−0.830057	+	1.43770i
$210$	2.00000	−	3.46410i	0.138013	−	0.239046i
$211$	−22.0000			−1.51454			−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000			−1.51454			−0.757271	+	0.653101i	$0.773468\pi$
$212$	−5.00000	+	8.66025i	−0.343401	+	0.594789i
$213$	10.0000			0.685189
$214$	1.00000			0.0683586
$215$	−2.50000	+	6.06218i	−0.170499	+	0.413437i
$216$	5.00000			0.340207
$217$	40.0000			2.71538
$218$	−5.50000	+	9.52628i	−0.372507	+	0.645201i
$219$	−14.0000			−0.946032
$220$	−2.00000	+	3.46410i	−0.134840	+	0.233550i
$221$	−4.00000	+	6.92820i	−0.269069	+	0.466041i
$222$	1.00000	+	1.73205i	0.0671156	+	0.116248i
$223$	19.0000			1.27233			0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000			1.27233			0.636167	+	0.771551i	$0.280519\pi$
$224$	2.00000	+	3.46410i	0.133631	+	0.231455i
$225$	1.00000	−	1.73205i	0.0666667	−	0.115470i
$226$		0			0
$227$	6.50000	−	11.2583i	0.431420	−	0.747242i	−0.565576	−	0.824696i	$-0.691346\pi$
$227$	6.50000	−	11.2583i	0.431420	−	0.747242i	0.996996	+	0.0774548i	$0.0246793\pi$
$228$	−3.00000	−	5.19615i	−0.198680	−	0.344124i
$229$	−3.50000	−	6.06218i	−0.231287	−	0.400600i	0.726900	−	0.686743i	$-0.240960\pi$
$229$	−3.50000	−	6.06218i	−0.231287	−	0.400600i	−0.958187	+	0.286143i	$0.907627\pi$
$230$		0			0
$231$	16.0000			1.05272
$232$	−0.500000	−	0.866025i	−0.0328266	−	0.0568574i
$233$	7.00000	+	12.1244i	0.458585	+	0.794293i	0.998886	−	0.0471787i	$-0.0150230\pi$
$233$	7.00000	+	12.1244i	0.458585	+	0.794293i	−0.540301	+	0.841472i	$0.681690\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$	−0.500000	+	0.866025i	−0.0326164	+	0.0564933i
$236$	14.0000			0.911322
$237$	16.0000			1.03931
$238$	−8.00000	+	13.8564i	−0.518563	+	0.898177i
$239$	8.00000	−	13.8564i	0.517477	−	0.896296i	−0.482317	−	0.875997i	$-0.660205\pi$
$239$	8.00000	−	13.8564i	0.517477	−	0.896296i	0.999794	−	0.0202996i	$-0.00646202\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	1.50000	+	2.59808i	0.0966235	+	0.167357i	0.910285	−	0.413982i	$-0.135862\pi$
$241$	1.50000	+	2.59808i	0.0966235	+	0.167357i	−0.813662	+	0.581339i	$0.802529\pi$
$242$	−5.00000			−0.321412
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	3.00000	+	5.19615i	0.192055	+	0.332650i
$245$	−4.50000	−	7.79423i	−0.287494	−	0.497955i
$246$	2.50000	−	4.33013i	0.159394	−	0.276079i
$247$	−12.0000			−0.763542
$248$	5.00000	−	8.66025i	0.317500	−	0.549927i
$249$	7.50000	+	12.9904i	0.475293	+	0.823232i
$250$	−1.00000			−0.0632456
$251$	8.00000	+	13.8564i	0.504956	+	0.874609i	0.999984	+	0.00573163i	$0.00182444\pi$
$251$	8.00000	+	13.8564i	0.504956	+	0.874609i	−0.495028	+	0.868877i	$0.664842\pi$
$252$	4.00000	−	6.92820i	0.251976	−	0.436436i
$253$		0			0
$254$	17.0000			1.06667
$255$	2.00000	−	3.46410i	0.125245	−	0.216930i
$256$	1.00000			0.0625000
$257$	22.0000			1.37232			0.686161	−	0.727450i	$-0.259294\pi$
$257$	22.0000			1.37232			0.686161	+	0.727450i	$0.259294\pi$
$258$	2.50000	−	6.06218i	0.155643	−	0.377415i
$259$	8.00000			0.497096
$260$	−2.00000			−0.124035
$261$	−1.00000	+	1.73205i	−0.0618984	+	0.107211i
$262$	−12.0000			−0.741362
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	−0.970758	−	0.240059i	$-0.922833\pi$
$263$	−4.50000	+	7.79423i	−0.277482	+	0.480613i	0.693276	+	0.720672i	$0.256167\pi$
$264$	2.00000	−	3.46410i	0.123091	−	0.213201i
$265$	−5.00000	−	8.66025i	−0.307148	−	0.531995i
$266$	−24.0000			−1.47153
$267$	1.50000	+	2.59808i	0.0917985	+	0.159000i
$268$	1.50000	−	2.59808i	0.0916271	−	0.158703i
$269$	−15.0000			−0.914566			−0.457283	−	0.889321i	$-0.651177\pi$
$269$	−15.0000			−0.914566			−0.457283	+	0.889321i	$0.651177\pi$
$270$	−2.50000	+	4.33013i	−0.152145	+	0.263523i
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	0.957328	+	0.289003i	$0.0933238\pi$
$271$	12.0000	+	20.7846i	0.728948	+	1.26258i	−0.228380	+	0.973572i	$0.573343\pi$
$272$	2.00000	+	3.46410i	0.121268	+	0.210042i
$273$	4.00000	+	6.92820i	0.242091	+	0.419314i
$274$	−2.00000			−0.120824
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$		0			0
$277$	−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	$0.243925\pi$
$278$	1.00000	−	1.73205i	0.0599760	−	0.103882i
$279$	−20.0000			−1.19737
$280$	−4.00000			−0.239046
$281$	−9.00000	+	15.5885i	−0.536895	+	0.929929i	0.462174	+	0.886789i	$0.347070\pi$
$281$	−9.00000	+	15.5885i	−0.536895	+	0.929929i	−0.999069	+	0.0431402i	$0.986264\pi$
$282$	0.500000	−	0.866025i	0.0297746	−	0.0515711i
$283$	−14.0000	−	24.2487i	−0.832214	−	1.44144i	−0.896279	−	0.443491i	$-0.853740\pi$
$283$	−14.0000	−	24.2487i	−0.832214	−	1.44144i	0.0640654	−	0.997946i	$-0.479593\pi$
$284$	−5.00000	−	8.66025i	−0.296695	−	0.513892i
$285$	6.00000			0.355409
$286$	−4.00000	−	6.92820i	−0.236525	−	0.409673i
$287$	−10.0000	−	17.3205i	−0.590281	−	1.02240i
$288$	−1.00000	−	1.73205i	−0.0589256	−	0.102062i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	1.00000			0.0587220
$291$	6.00000	−	10.3923i	0.351726	−	0.609208i
$292$	7.00000	+	12.1244i	0.409644	+	0.709524i
$293$	18.0000			1.05157			0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000			1.05157			0.525786	+	0.850617i	$0.323771\pi$
$294$	4.50000	+	7.79423i	0.262445	+	0.454569i
$295$	−7.00000	+	12.1244i	−0.407556	+	0.705907i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	−20.0000			−1.16052
$298$	0.500000	−	0.866025i	0.0289642	−	0.0501675i
$299$		0			0
$300$	1.00000			0.0577350
$301$	−16.0000	−	20.7846i	−0.922225	−	1.19800i
$302$	−16.0000			−0.920697
$303$	1.00000			0.0574485
$304$	−3.00000	+	5.19615i	−0.172062	+	0.298020i
$305$	−6.00000			−0.343559
$306$	4.00000	−	6.92820i	0.228665	−	0.396059i
$307$	7.50000	−	12.9904i	0.428048	−	0.741400i	−0.568652	−	0.822578i	$-0.692535\pi$
$307$	7.50000	−	12.9904i	0.428048	−	0.741400i	0.996700	+	0.0811780i	$0.0258682\pi$
$308$	−8.00000	−	13.8564i	−0.455842	−	0.789542i
$309$	−5.00000			−0.284440
$310$	5.00000	+	8.66025i	0.283981	+	0.491869i
$311$	−14.0000	+	24.2487i	−0.793867	+	1.37502i	0.129689	+	0.991555i	$0.458602\pi$
$311$	−14.0000	+	24.2487i	−0.793867	+	1.37502i	−0.923556	+	0.383464i	$0.874731\pi$
$312$	2.00000			0.113228
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	−0.730554	−	0.682855i	$-0.760738\pi$
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	0.956647	+	0.291250i	$0.0940712\pi$
$314$	7.00000	+	12.1244i	0.395033	+	0.684217i
$315$	4.00000	+	6.92820i	0.225374	+	0.390360i
$316$	−8.00000	−	13.8564i	−0.450035	−	0.779484i
$317$	32.0000			1.79730			0.898650	−	0.438667i	$-0.144549\pi$
$317$	32.0000			1.79730			0.898650	+	0.438667i	$0.144549\pi$
$318$	5.00000	+	8.66025i	0.280386	+	0.485643i
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	0.500000	−	0.866025i	0.0279073	−	0.0483368i
$322$		0			0
$323$	−24.0000			−1.33540
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	1.00000	−	1.73205i	0.0554700	−	0.0960769i
$326$	−5.50000	−	9.52628i	−0.304617	−	0.527612i
$327$	5.50000	+	9.52628i	0.304151	+	0.526804i
$328$	−5.00000			−0.276079
$329$	−2.00000	−	3.46410i	−0.110264	−	0.190982i
$330$	2.00000	+	3.46410i	0.110096	+	0.190693i
$331$	−16.0000	−	27.7128i	−0.879440	−	1.52323i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	−16.0000	−	27.7128i	−0.879440	−	1.52323i	−0.0274825	−	0.999622i	$-0.508749\pi$
$332$	7.50000	−	12.9904i	0.411616	−	0.712940i
$333$	−4.00000			−0.219199
$334$	4.50000	−	7.79423i	0.246229	−	0.426481i
$335$	1.50000	+	2.59808i	0.0819538	+	0.141948i
$336$	4.00000			0.218218
$337$	3.00000	+	5.19615i	0.163420	+	0.283052i	0.936093	−	0.351752i	$-0.114414\pi$
$337$	3.00000	+	5.19615i	0.163420	+	0.283052i	−0.772673	+	0.634804i	$0.781081\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$		0			0
$340$	−4.00000			−0.216930
$341$	−20.0000	+	34.6410i	−1.08306	+	1.87592i
$342$	12.0000			0.648886
$343$	8.00000			0.431959
$344$	−6.50000	+	0.866025i	−0.350457	+	0.0466930i
$345$		0			0
$346$		0			0
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	−0.719590	−	0.694399i	$-0.755670\pi$
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	0.961162	+	0.275983i	$0.0890035\pi$
$348$	−1.00000			−0.0536056
$349$	10.5000	−	18.1865i	0.562052	−	0.973503i	−0.435265	−	0.900302i	$-0.643345\pi$
$349$	10.5000	−	18.1865i	0.562052	−	0.973503i	0.997317	−	0.0732005i	$-0.0233213\pi$
$350$	2.00000	−	3.46410i	0.106904	−	0.185164i
$351$	−5.00000	−	8.66025i	−0.266880	−	0.462250i
$352$	−4.00000			−0.213201
$353$	−13.0000	−	22.5167i	−0.691920	−	1.19844i	−0.971208	−	0.238233i	$-0.923432\pi$
$353$	−13.0000	−	22.5167i	−0.691920	−	1.19844i	0.279288	−	0.960207i	$-0.409902\pi$
$354$	7.00000	−	12.1244i	0.372046	−	0.644402i
$355$	10.0000			0.530745
$356$	1.50000	−	2.59808i	0.0794998	−	0.137698i
$357$	8.00000	+	13.8564i	0.423405	+	0.733359i
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$	2.00000			0.105409
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	11.0000	+	19.0526i	0.578147	+	1.00138i
$363$	−2.50000	+	4.33013i	−0.131216	+	0.227273i
$364$	4.00000	−	6.92820i	0.209657	−	0.363137i
$365$	−14.0000			−0.732793
$366$	6.00000			0.313625
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$		0			0
$369$	5.00000	+	8.66025i	0.260290	+	0.450835i
$370$	1.00000	+	1.73205i	0.0519875	+	0.0900450i
$371$	40.0000			2.07670
$372$	−5.00000	−	8.66025i	−0.259238	−	0.449013i
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$	−8.00000	−	13.8564i	−0.413670	−	0.716498i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	−1.00000			−0.0515711
$377$	−1.00000	+	1.73205i	−0.0515026	+	0.0892052i
$378$	−10.0000	−	17.3205i	−0.514344	−	0.890871i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−3.00000	−	5.19615i	−0.153897	−	0.266557i
$381$	8.50000	−	14.7224i	0.435468	−	0.754253i
$382$	2.00000	−	3.46410i	0.102329	−	0.177239i
$383$	9.00000			0.459879			0.229939	−	0.973205i	$-0.426147\pi$
$383$	9.00000			0.459879			0.229939	+	0.973205i	$0.426147\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	16.0000			0.815436
$386$	16.0000			0.814379
$387$	8.00000	+	10.3923i	0.406663	+	0.528271i
$388$	−12.0000			−0.609208
$389$	26.0000			1.31825			0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000			1.31825			0.659126	+	0.752032i	$0.270926\pi$
$390$	−1.00000	+	1.73205i	−0.0506370	+	0.0877058i
$391$		0			0
$392$	4.50000	−	7.79423i	0.227284	−	0.393668i
$393$	−6.00000	+	10.3923i	−0.302660	+	0.524222i
$394$	−7.00000	−	12.1244i	−0.352655	−	0.610816i
$395$	16.0000			0.805047
$396$	4.00000	+	6.92820i	0.201008	+	0.348155i
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	−0.446051	−	0.895008i	$-0.647170\pi$
$397$	11.0000	−	19.0526i	0.552074	−	0.956221i	0.998125	−	0.0612128i	$-0.0194968\pi$
$398$	8.00000			0.401004
$399$	−12.0000	+	20.7846i	−0.600751	+	1.04053i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	0.781345	−	0.624099i	$-0.214534\pi$
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	−0.931158	+	0.364615i	$0.881200\pi$
$402$	−1.50000	−	2.59808i	−0.0748132	−	0.129580i
$403$	−20.0000			−0.996271
$404$	−0.500000	−	0.866025i	−0.0248759	−	0.0430864i
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	−2.00000	+	3.46410i	−0.0992583	+	0.171920i
$407$	−4.00000	+	6.92820i	−0.198273	+	0.343418i
$408$	4.00000			0.198030
$409$	−5.00000			−0.247234			−0.123617	−	0.992330i	$-0.539449\pi$
$409$	−5.00000			−0.247234			−0.123617	+	0.992330i	$0.539449\pi$
$410$	2.50000	−	4.33013i	0.123466	−	0.213850i
$411$	−1.00000	+	1.73205i	−0.0493264	+	0.0854358i
$412$	2.50000	+	4.33013i	0.123166	+	0.213330i
$413$	−28.0000	−	48.4974i	−1.37779	−	2.38640i
$414$		0			0
$415$	7.50000	+	12.9904i	0.368161	+	0.637673i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	−1.00000	−	1.73205i	−0.0489702	−	0.0848189i
$418$	12.0000	−	20.7846i	0.586939	−	1.01661i
$419$	−20.0000			−0.977064			−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000			−0.977064			−0.488532	+	0.872546i	$0.662467\pi$
$420$	−2.00000	+	3.46410i	−0.0975900	+	0.169031i
$421$	−11.5000	−	19.9186i	−0.560476	−	0.970772i	−0.997455	−	0.0713008i	$-0.977285\pi$
$421$	−11.5000	−	19.9186i	−0.560476	−	0.970772i	0.436979	−	0.899472i	$-0.356048\pi$
$422$	22.0000			1.07094
$423$	1.00000	+	1.73205i	0.0486217	+	0.0842152i
$424$	5.00000	−	8.66025i	0.242821	−	0.420579i
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$	−10.0000			−0.484502
$427$	12.0000	−	20.7846i	0.580721	−	1.00584i
$428$	−1.00000			−0.0483368
$429$	−8.00000			−0.386244
$430$	2.50000	−	6.06218i	0.120561	−	0.292344i
$431$	36.0000			1.73406			0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000			1.73406			0.867029	+	0.498257i	$0.166026\pi$
$432$	−5.00000			−0.240563
$433$	−7.00000	+	12.1244i	−0.336399	+	0.582659i	−0.983752	−	0.179530i	$-0.942542\pi$
$433$	−7.00000	+	12.1244i	−0.336399	+	0.582659i	0.647354	+	0.762190i	$0.275876\pi$
$434$	−40.0000			−1.92006
$435$	0.500000	−	0.866025i	0.0239732	−	0.0415227i
$436$	5.50000	−	9.52628i	0.263402	−	0.456226i
$437$		0			0
$438$	14.0000			0.668946
$439$	13.0000	+	22.5167i	0.620456	+	1.07466i	0.989401	+	0.145210i	$0.0463858\pi$
$439$	13.0000	+	22.5167i	0.620456	+	1.07466i	−0.368945	+	0.929451i	$0.620281\pi$
$440$	2.00000	−	3.46410i	0.0953463	−	0.165145i
$441$	−18.0000			−0.857143
$442$	4.00000	−	6.92820i	0.190261	−	0.329541i
$443$	−0.500000	−	0.866025i	−0.0237557	−	0.0411461i	0.853903	−	0.520432i	$-0.174229\pi$
$443$	−0.500000	−	0.866025i	−0.0237557	−	0.0411461i	−0.877659	+	0.479286i	$0.840896\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$	1.50000	+	2.59808i	0.0711068	+	0.123161i
$446$	−19.0000			−0.899676
$447$	−0.500000	−	0.866025i	−0.0236492	−	0.0409616i
$448$	−2.00000	−	3.46410i	−0.0944911	−	0.163663i
$449$	2.50000	−	4.33013i	0.117982	−	0.204351i	−0.800986	−	0.598684i	$-0.795691\pi$
$449$	2.50000	−	4.33013i	0.117982	−	0.204351i	0.918968	+	0.394332i	$0.129024\pi$
$450$	−1.00000	+	1.73205i	−0.0471405	+	0.0816497i
$451$	20.0000			0.941763
$452$		0			0
$453$	−8.00000	+	13.8564i	−0.375873	+	0.651031i
$454$	−6.50000	+	11.2583i	−0.305060	+	0.528380i
$455$	4.00000	+	6.92820i	0.187523	+	0.324799i
$456$	3.00000	+	5.19615i	0.140488	+	0.243332i
$457$	30.0000			1.40334			0.701670	−	0.712502i	$-0.252438\pi$
$457$	30.0000			1.40334			0.701670	+	0.712502i	$0.252438\pi$
$458$	3.50000	+	6.06218i	0.163544	+	0.283267i
$459$	−10.0000	−	17.3205i	−0.466760	−	0.808452i
$460$		0			0
$461$	7.50000	−	12.9904i	0.349310	−	0.605022i	−0.636817	−	0.771015i	$-0.719749\pi$
$461$	7.50000	−	12.9904i	0.349310	−	0.605022i	0.986127	+	0.165992i	$0.0530827\pi$
$462$	−16.0000			−0.744387
$463$	10.5000	−	18.1865i	0.487976	−	0.845200i	−0.511928	−	0.859028i	$-0.671069\pi$
$463$	10.5000	−	18.1865i	0.487976	−	0.845200i	0.999904	+	0.0138285i	$0.00440188\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$	10.0000			0.463739
$466$	−7.00000	−	12.1244i	−0.324269	−	0.561650i
$467$	−16.0000	+	27.7128i	−0.740392	+	1.28240i	0.211925	+	0.977286i	$0.432027\pi$
$467$	−16.0000	+	27.7128i	−0.740392	+	1.28240i	−0.952317	+	0.305110i	$0.901307\pi$
$468$	−2.00000	+	3.46410i	−0.0924500	+	0.160128i
$469$	−12.0000			−0.554109
$470$	0.500000	−	0.866025i	0.0230633	−	0.0399468i
$471$	14.0000			0.645086
$472$	−14.0000			−0.644402
$473$	26.0000	−	3.46410i	1.19548	−	0.159280i
$474$	−16.0000			−0.734904
$475$	6.00000			0.275299
$476$	8.00000	−	13.8564i	0.366679	−	0.635107i
$477$	−20.0000			−0.915737
$478$	−8.00000	+	13.8564i	−0.365911	+	0.633777i
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	−0.926388	−	0.376571i	$-0.877103\pi$
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	−4.00000			−0.182384
$482$	−1.50000	−	2.59808i	−0.0683231	−	0.118339i
$483$		0			0
$484$	5.00000			0.227273
$485$	6.00000	−	10.3923i	0.272446	−	0.471890i
$486$	8.00000	+	13.8564i	0.362887	+	0.628539i
$487$	13.5000	+	23.3827i	0.611743	+	1.05957i	0.990947	+	0.134257i	$0.0428648\pi$
$487$	13.5000	+	23.3827i	0.611743	+	1.05957i	−0.379203	+	0.925313i	$0.623802\pi$
$488$	−3.00000	−	5.19615i	−0.135804	−	0.235219i
$489$	−11.0000			−0.497437
$490$	4.50000	+	7.79423i	0.203289	+	0.352107i
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	0.911230	+	0.411897i	$0.135134\pi$
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	−0.0989017	+	0.995097i	$0.531533\pi$
$492$	−2.50000	+	4.33013i	−0.112709	+	0.195217i
$493$	−2.00000	+	3.46410i	−0.0900755	+	0.156015i
$494$	12.0000			0.539906
$495$	−8.00000			−0.359573
$496$	−5.00000	+	8.66025i	−0.224507	+	0.388857i
$497$	−20.0000	+	34.6410i	−0.897123	+	1.55386i
$498$	−7.50000	−	12.9904i	−0.336083	−	0.582113i
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	1.00000			0.0447214
$501$	−4.50000	−	7.79423i	−0.201045	−	0.348220i
$502$	−8.00000	−	13.8564i	−0.357057	−	0.618442i
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	0.748091	−	0.663596i	$-0.230970\pi$
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	−0.948736	+	0.316068i	$0.897637\pi$
$504$	−4.00000	+	6.92820i	−0.178174	+	0.308607i
$505$	1.00000			0.0444994
$506$		0			0
$507$	4.50000	+	7.79423i	0.199852	+	0.346154i
$508$	−17.0000			−0.754253
$509$	−17.5000	−	30.3109i	−0.775674	−	1.34351i	−0.934415	−	0.356186i	$-0.884077\pi$
$509$	−17.5000	−	30.3109i	−0.775674	−	1.34351i	0.158741	−	0.987320i	$-0.449256\pi$
$510$	−2.00000	+	3.46410i	−0.0885615	+	0.153393i
$511$	28.0000	−	48.4974i	1.23865	−	2.14540i
$512$	−1.00000			−0.0441942
$513$	15.0000	−	25.9808i	0.662266	−	1.14708i
$514$	−22.0000			−0.970378
$515$	−5.00000			−0.220326
$516$	−2.50000	+	6.06218i	−0.110056	+	0.266872i
$517$	4.00000			0.175920
$518$	−8.00000			−0.351500
$519$		0			0
$520$	2.00000			0.0877058
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	−0.977633	−	0.210318i	$-0.932550\pi$
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	0.670957	+	0.741496i	$0.265883\pi$
$522$	1.00000	−	1.73205i	0.0437688	−	0.0758098i
$523$	17.5000	+	30.3109i	0.765222	+	1.32540i	0.940129	+	0.340818i	$0.110704\pi$
$523$	17.5000	+	30.3109i	0.765222	+	1.32540i	−0.174908	+	0.984585i	$0.555963\pi$
$524$	12.0000			0.524222
$525$	−2.00000	−	3.46410i	−0.0872872	−	0.151186i
$526$	4.50000	−	7.79423i	0.196209	−	0.339845i
$527$	−40.0000			−1.74243
$528$	−2.00000	+	3.46410i	−0.0870388	+	0.150756i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	5.00000	+	8.66025i	0.217186	+	0.376177i
$531$	14.0000	+	24.2487i	0.607548	+	1.05230i
$532$	24.0000			1.04053
$533$	5.00000	+	8.66025i	0.216574	+	0.375117i
$534$	−1.50000	−	2.59808i	−0.0649113	−	0.112430i
$535$	0.500000	−	0.866025i	0.0216169	−	0.0374415i
$536$	−1.50000	+	2.59808i	−0.0647901	+	0.112220i
$537$	12.0000			0.517838
$538$	15.0000			0.646696
$539$	−18.0000	+	31.1769i	−0.775315	+	1.34288i
$540$	2.50000	−	4.33013i	0.107583	−	0.186339i
$541$	19.5000	+	33.7750i	0.838370	+	1.45210i	0.891256	+	0.453500i	$0.149825\pi$
$541$	19.5000	+	33.7750i	0.838370	+	1.45210i	−0.0528859	+	0.998601i	$0.516842\pi$
$542$	−12.0000	−	20.7846i	−0.515444	−	0.892775i
$543$	22.0000			0.944110
$544$	−2.00000	−	3.46410i	−0.0857493	−	0.148522i
$545$	5.50000	+	9.52628i	0.235594	+	0.408061i
$546$	−4.00000	−	6.92820i	−0.171184	−	0.296500i
$547$	−2.50000	+	4.33013i	−0.106892	+	0.185143i	−0.914510	−	0.404564i	$-0.867423\pi$
$547$	−2.50000	+	4.33013i	−0.106892	+	0.185143i	0.807617	+	0.589707i	$0.200757\pi$
$548$	2.00000			0.0854358
$549$	−6.00000	+	10.3923i	−0.256074	+	0.443533i
$550$	2.00000	+	3.46410i	0.0852803	+	0.147710i
$551$	−6.00000			−0.255609
$552$		0			0
$553$	−32.0000	+	55.4256i	−1.36078	+	2.35694i
$554$	4.00000	−	6.92820i	0.169944	−	0.294351i
$555$	2.00000			0.0848953
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	−2.00000			−0.0847427			−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000			−0.0847427			−0.0423714	+	0.999102i	$0.513491\pi$
$558$	20.0000			0.846668
$559$	8.00000	+	10.3923i	0.338364	+	0.439548i
$560$	4.00000			0.169031
$561$	−16.0000			−0.675521
$562$	9.00000	−	15.5885i	0.379642	−	0.657559i
$563$	−9.00000			−0.379305			−0.189652	−	0.981851i	$-0.560736\pi$
$563$	−9.00000			−0.379305			−0.189652	+	0.981851i	$0.560736\pi$
$564$	−0.500000	+	0.866025i	−0.0210538	+	0.0364662i
$565$		0			0
$566$	14.0000	+	24.2487i	0.588464	+	1.01925i
$567$	4.00000			0.167984
$568$	5.00000	+	8.66025i	0.209795	+	0.363376i
$569$	0.500000	−	0.866025i	0.0209611	−	0.0363057i	−0.855355	−	0.518043i	$-0.826661\pi$
$569$	0.500000	−	0.866025i	0.0209611	−	0.0363057i	0.876316	+	0.481737i	$0.159994\pi$
$570$	−6.00000			−0.251312
$571$	−8.00000	+	13.8564i	−0.334790	+	0.579873i	−0.983444	−	0.181210i	$-0.941999\pi$
$571$	−8.00000	+	13.8564i	−0.334790	+	0.579873i	0.648655	+	0.761083i	$0.275332\pi$
$572$	4.00000	+	6.92820i	0.167248	+	0.289683i
$573$	−2.00000	−	3.46410i	−0.0835512	−	0.144715i
$574$	10.0000	+	17.3205i	0.417392	+	0.722944i
$575$		0			0
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	−1.00000	−	1.73205i	−0.0416305	−	0.0721062i	0.844459	−	0.535620i	$-0.179922\pi$
$577$	−1.00000	−	1.73205i	−0.0416305	−	0.0721062i	−0.886090	+	0.463513i	$0.846589\pi$
$578$	−0.500000	+	0.866025i	−0.0207973	+	0.0360219i
$579$	8.00000	−	13.8564i	0.332469	−	0.575853i
$580$	−1.00000			−0.0415227
$581$	−60.0000			−2.48922
$582$	−6.00000	+	10.3923i	−0.248708	+	0.430775i
$583$	−20.0000	+	34.6410i	−0.828315	+	1.43468i
$584$	−7.00000	−	12.1244i	−0.289662	−	0.501709i
$585$	−2.00000	−	3.46410i	−0.0826898	−	0.143223i
$586$	−18.0000			−0.743573
$587$	−4.50000	−	7.79423i	−0.185735	−	0.321702i	0.758089	−	0.652151i	$-0.226133\pi$
$587$	−4.50000	−	7.79423i	−0.185735	−	0.321702i	−0.943824	+	0.330449i	$0.892800\pi$
$588$	−4.50000	−	7.79423i	−0.185577	−	0.321429i
$589$	−30.0000	−	51.9615i	−1.23613	−	2.14104i
$590$	7.00000	−	12.1244i	0.288185	−	0.499152i
$591$	−14.0000			−0.575883
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	0.999965	−	0.00831589i	$-0.00264706\pi$
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	−0.507184	+	0.861838i	$0.669314\pi$
$594$	20.0000			0.820610
$595$	8.00000	+	13.8564i	0.327968	+	0.568057i
$596$	−0.500000	+	0.866025i	−0.0204808	+	0.0354738i
$597$	4.00000	−	6.92820i	0.163709	−	0.283552i
$598$		0			0
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	−0.377869	−	0.925859i	$-0.623343\pi$
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	0.990752	−	0.135686i	$-0.0433238\pi$
$600$	−1.00000			−0.0408248
$601$	17.0000			0.693444			0.346722	−	0.937968i	$-0.387295\pi$
$601$	17.0000			0.693444			0.346722	+	0.937968i	$0.387295\pi$
$602$	16.0000	+	20.7846i	0.652111	+	0.847117i
$603$	6.00000			0.244339
$604$	16.0000			0.651031
$605$	−2.50000	+	4.33013i	−0.101639	+	0.176045i
$606$	−1.00000			−0.0406222
$607$	14.5000	−	25.1147i	0.588537	−	1.01938i	−0.405887	−	0.913923i	$-0.633038\pi$
$607$	14.5000	−	25.1147i	0.588537	−	1.01938i	0.994424	−	0.105453i	$-0.0336291\pi$
$608$	3.00000	−	5.19615i	0.121666	−	0.210732i
$609$	2.00000	+	3.46410i	0.0810441	+	0.140372i
$610$	6.00000			0.242933
$611$	1.00000	+	1.73205i	0.0404557	+	0.0700713i
$612$	−4.00000	+	6.92820i	−0.161690	+	0.280056i
$613$	32.0000			1.29247			0.646234	−	0.763139i	$-0.276343\pi$
$613$	32.0000			1.29247			0.646234	+	0.763139i	$0.276343\pi$
$614$	−7.50000	+	12.9904i	−0.302675	+	0.524249i
$615$	−2.50000	−	4.33013i	−0.100810	−	0.174608i
$616$	8.00000	+	13.8564i	0.322329	+	0.558291i
$617$	−19.0000	−	32.9090i	−0.764911	−	1.32487i	−0.940294	−	0.340365i	$-0.889449\pi$
$617$	−19.0000	−	32.9090i	−0.764911	−	1.32487i	0.175382	−	0.984500i	$-0.443884\pi$
$618$	5.00000			0.201129
$619$	−8.00000	−	13.8564i	−0.321547	−	0.556936i	0.659260	−	0.751915i	$-0.270870\pi$
$619$	−8.00000	−	13.8564i	−0.321547	−	0.556936i	−0.980807	+	0.194979i	$0.937536\pi$
$620$	−5.00000	−	8.66025i	−0.200805	−	0.347804i
$621$		0			0
$622$	14.0000	−	24.2487i	0.561349	−	0.972285i
$623$	−12.0000			−0.480770
$624$	−2.00000			−0.0800641
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−4.00000	+	6.92820i	−0.159872	+	0.276907i
$627$	−12.0000	−	20.7846i	−0.479234	−	0.830057i
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	−8.00000			−0.318981
$630$	−4.00000	−	6.92820i	−0.159364	−	0.276026i
$631$	−17.0000	−	29.4449i	−0.676759	−	1.17218i	−0.975951	−	0.217989i	$-0.930050\pi$
$631$	−17.0000	−	29.4449i	−0.676759	−	1.17218i	0.299192	−	0.954193i	$-0.403283\pi$
$632$	8.00000	+	13.8564i	0.318223	+	0.551178i
$633$	11.0000	−	19.0526i	0.437211	−	0.757271i
$634$	−32.0000			−1.27088
$635$	8.50000	−	14.7224i	0.337312	−	0.584242i
$636$	−5.00000	−	8.66025i	−0.198263	−	0.343401i
$637$	−18.0000			−0.713186
$638$	−2.00000	−	3.46410i	−0.0791808	−	0.137145i
$639$	10.0000	−	17.3205i	0.395594	−	0.685189i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−23.0000			−0.908445			−0.454223	−	0.890888i	$-0.650083\pi$
$641$	−23.0000			−0.908445			−0.454223	+	0.890888i	$0.650083\pi$
$642$	−0.500000	+	0.866025i	−0.0197334	+	0.0341793i
$643$	−39.0000			−1.53801			−0.769005	−	0.639243i	$-0.779248\pi$
$643$	−39.0000			−1.53801			−0.769005	+	0.639243i	$0.779248\pi$
$644$		0			0
$645$	−4.00000	−	5.19615i	−0.157500	−	0.204598i
$646$	24.0000			0.944267
$647$	21.0000			0.825595			0.412798	−	0.910823i	$-0.364552\pi$
$647$	21.0000			0.825595			0.412798	+	0.910823i	$0.364552\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	56.0000			2.19819
$650$	−1.00000	+	1.73205i	−0.0392232	+	0.0679366i
$651$	−20.0000	+	34.6410i	−0.783862	+	1.35769i
$652$	5.50000	+	9.52628i	0.215397	+	0.373078i
$653$	6.00000			0.234798			0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$	−5.50000	−	9.52628i	−0.215067	−	0.372507i
$655$	−6.00000	+	10.3923i	−0.234439	+	0.406061i
$656$	5.00000			0.195217
$657$	−14.0000	+	24.2487i	−0.546192	+	0.946032i
$658$	2.00000	+	3.46410i	0.0779681	+	0.135045i
$659$	−7.00000	−	12.1244i	−0.272681	−	0.472298i	0.696866	−	0.717201i	$-0.254577\pi$
$659$	−7.00000	−	12.1244i	−0.272681	−	0.472298i	−0.969548	+	0.244903i	$0.921244\pi$
$660$	−2.00000	−	3.46410i	−0.0778499	−	0.134840i
$661$	18.0000			0.700119			0.350059	−	0.936727i	$-0.386161\pi$
$661$	18.0000			0.700119			0.350059	+	0.936727i	$0.386161\pi$
$662$	16.0000	+	27.7128i	0.621858	+	1.07709i
$663$	−4.00000	−	6.92820i	−0.155347	−	0.269069i
$664$	−7.50000	+	12.9904i	−0.291056	+	0.504125i
$665$	−12.0000	+	20.7846i	−0.465340	+	0.805993i
$666$	4.00000			0.154997
$667$		0			0
$668$	−4.50000	+	7.79423i	−0.174110	+	0.301568i
$669$	−9.50000	+	16.4545i	−0.367291	+	0.636167i
$670$	−1.50000	−	2.59808i	−0.0579501	−	0.100372i
$671$	12.0000	+	20.7846i	0.463255	+	0.802381i
$672$	−4.00000			−0.154303
$673$	−18.0000	−	31.1769i	−0.693849	−	1.20178i	−0.970567	−	0.240831i	$-0.922580\pi$
$673$	−18.0000	−	31.1769i	−0.693849	−	1.20178i	0.276718	−	0.960951i	$-0.410753\pi$
$674$	−3.00000	−	5.19615i	−0.115556	−	0.200148i
$675$	2.50000	+	4.33013i	0.0962250	+	0.166667i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	44.0000			1.69106			0.845529	−	0.533930i	$-0.179285\pi$
$677$	44.0000			1.69106			0.845529	+	0.533930i	$0.179285\pi$
$678$		0			0
$679$	24.0000	+	41.5692i	0.921035	+	1.59528i
$680$	4.00000			0.153393
$681$	6.50000	+	11.2583i	0.249081	+	0.431420i
$682$	20.0000	−	34.6410i	0.765840	−	1.32647i
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$	−12.0000			−0.458831
$685$	−1.00000	+	1.73205i	−0.0382080	+	0.0661783i
$686$	−8.00000			−0.305441
$687$	7.00000			0.267067
$688$	6.50000	−	0.866025i	0.247810	−	0.0330169i
$689$	−20.0000			−0.761939
$690$		0			0
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	0.466691	+	0.884420i	$0.345446\pi$
$691$	−14.0000	+	24.2487i	−0.532585	+	0.922464i	−0.999276	+	0.0380440i	$0.987887\pi$
$692$		0			0
$693$	16.0000	−	27.7128i	0.607790	−	1.05272i
$694$	−4.50000	+	7.79423i	−0.170818	+	0.295865i
$695$	−1.00000	−	1.73205i	−0.0379322	−	0.0657004i
$696$	1.00000			0.0379049
$697$	10.0000	+	17.3205i	0.378777	+	0.656061i
$698$	−10.5000	+	18.1865i	−0.397431	+	0.688370i
$699$	−14.0000			−0.529529
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	16.5000	+	28.5788i	0.623196	+	1.07941i	0.988887	+	0.148671i	$0.0474996\pi$
$701$	16.5000	+	28.5788i	0.623196	+	1.07941i	−0.365690	+	0.930737i	$0.619167\pi$
$702$	5.00000	+	8.66025i	0.188713	+	0.326860i
$703$	−6.00000	−	10.3923i	−0.226294	−	0.391953i
$704$	4.00000			0.150756
$705$	−0.500000	−	0.866025i	−0.0188311	−	0.0326164i
$706$	13.0000	+	22.5167i	0.489261	+	0.847426i
$707$	−2.00000	+	3.46410i	−0.0752177	+	0.130281i
$708$	−7.00000	+	12.1244i	−0.263076	+	0.455661i
$709$	35.0000			1.31445			0.657226	−	0.753693i	$-0.271730\pi$
$709$	35.0000			1.31445			0.657226	+	0.753693i	$0.271730\pi$
$710$	−10.0000			−0.375293
$711$	16.0000	−	27.7128i	0.600047	−	1.03931i
$712$	−1.50000	+	2.59808i	−0.0562149	+	0.0973670i
$713$		0			0
$714$	−8.00000	−	13.8564i	−0.299392	−	0.518563i
$715$	−8.00000			−0.299183
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	8.00000	+	13.8564i	0.298765	+	0.517477i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	−0.438141	−	0.898906i	$-0.644363\pi$
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	0.997546	−	0.0700124i	$-0.0223039\pi$
$720$	−2.00000			−0.0745356
$721$	10.0000	−	17.3205i	0.372419	−	0.645049i
$722$	8.50000	+	14.7224i	0.316337	+	0.547912i
$723$	−3.00000			−0.111571
$724$	−11.0000	−	19.0526i	−0.408812	−	0.708083i
$725$	0.500000	−	0.866025i	0.0185695	−	0.0321634i
$726$	2.50000	−	4.33013i	0.0927837	−	0.160706i
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$	−4.00000	+	6.92820i	−0.148250	+	0.256776i
$729$	13.0000			0.481481
$730$	14.0000			0.518163
$731$	16.0000	+	20.7846i	0.591781	+	0.768747i
$732$	−6.00000			−0.221766
$733$	32.0000			1.18195			0.590973	−	0.806691i	$-0.298744\pi$
$733$	32.0000			1.18195			0.590973	+	0.806691i	$0.298744\pi$
$734$	8.00000	−	13.8564i	0.295285	−	0.511449i
$735$	9.00000			0.331970
$736$		0			0
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$	−5.00000	−	8.66025i	−0.184053	−	0.318788i
$739$	−10.0000			−0.367856			−0.183928	−	0.982940i	$-0.558881\pi$
$739$	−10.0000			−0.367856			−0.183928	+	0.982940i	$0.558881\pi$
$740$	−1.00000	−	1.73205i	−0.0367607	−	0.0636715i
$741$	6.00000	−	10.3923i	0.220416	−	0.381771i
$742$	−40.0000			−1.46845
$743$	−14.0000	+	24.2487i	−0.513610	+	0.889599i	0.486265	+	0.873811i	$0.338359\pi$
$743$	−14.0000	+	24.2487i	−0.513610	+	0.889599i	−0.999875	+	0.0157876i	$0.994974\pi$
$744$	5.00000	+	8.66025i	0.183309	+	0.317500i
$745$	−0.500000	−	0.866025i	−0.0183186	−	0.0317287i
$746$	−2.00000	−	3.46410i	−0.0732252	−	0.126830i
$747$	30.0000			1.09764
$748$	8.00000	+	13.8564i	0.292509	+	0.506640i
$749$	2.00000	+	3.46410i	0.0730784	+	0.126576i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	1.00000			0.0364662
$753$	−16.0000			−0.583072
$754$	1.00000	−	1.73205i	0.0364179	−	0.0630776i
$755$	−8.00000	+	13.8564i	−0.291150	+	0.504286i
$756$	10.0000	+	17.3205i	0.363696	+	0.629941i
$757$	−8.00000	−	13.8564i	−0.290765	−	0.503620i	0.683226	−	0.730207i	$-0.260576\pi$
$757$	−8.00000	−	13.8564i	−0.290765	−	0.503620i	−0.973991	+	0.226587i	$0.927243\pi$
$758$	20.0000			0.726433
$759$		0			0
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	−19.5000	−	33.7750i	−0.706874	−	1.22434i	−0.966011	−	0.258502i	$-0.916771\pi$
$761$	−19.5000	−	33.7750i	−0.706874	−	1.22434i	0.259136	−	0.965841i	$-0.416562\pi$
$762$	−8.50000	+	14.7224i	−0.307923	+	0.533337i
$763$	−44.0000			−1.59291
$764$	−2.00000	+	3.46410i	−0.0723575	+	0.125327i
$765$	−4.00000	−	6.92820i	−0.144620	−	0.250490i
$766$	−9.00000			−0.325183
$767$	14.0000	+	24.2487i	0.505511	+	0.875570i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	15.0000	−	25.9808i	0.540914	−	0.936890i	−0.457938	−	0.888984i	$-0.651412\pi$
$769$	15.0000	−	25.9808i	0.540914	−	0.936890i	0.998852	−	0.0479061i	$-0.0152548\pi$
$770$	−16.0000			−0.576600
$771$	−11.0000	+	19.0526i	−0.396155	+	0.686161i
$772$	−16.0000			−0.575853
$773$	−26.0000			−0.935155			−0.467578	−	0.883952i	$-0.654873\pi$
$773$	−26.0000			−0.935155			−0.467578	+	0.883952i	$0.654873\pi$
$774$	−8.00000	−	10.3923i	−0.287554	−	0.373544i
$775$	10.0000			0.359211
$776$	12.0000			0.430775
$777$	−4.00000	+	6.92820i	−0.143499	+	0.248548i
$778$	−26.0000			−0.932145
$779$	−15.0000	+	25.9808i	−0.537431	+	0.930857i
$780$	1.00000	−	1.73205i	0.0358057	−	0.0620174i
$781$	−20.0000	−	34.6410i	−0.715656	−	1.23955i
$782$		0			0
$783$	−2.50000	−	4.33013i	−0.0893427	−	0.154746i
$784$	−4.50000	+	7.79423i	−0.160714	+	0.278365i
$785$	14.0000			0.499681
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$	−3.50000	−	6.06218i	−0.124762	−	0.216093i	0.796878	−	0.604140i	$-0.206483\pi$
$787$	−3.50000	−	6.06218i	−0.124762	−	0.216093i	−0.921640	+	0.388047i	$0.873150\pi$
$788$	7.00000	+	12.1244i	0.249365	+	0.431912i
$789$	−4.50000	−	7.79423i	−0.160204	−	0.277482i
$790$	−16.0000			−0.569254
$791$		0			0
$792$	−4.00000	−	6.92820i	−0.142134	−	0.246183i
$793$	−6.00000	+	10.3923i	−0.213066	+	0.369042i
$794$	−11.0000	+	19.0526i	−0.390375	+	0.676150i
$795$	10.0000			0.354663
$796$	−8.00000			−0.283552
$797$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$797$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$798$	12.0000	−	20.7846i	0.424795	−	0.735767i
$799$	2.00000	+	3.46410i	0.0707549	+	0.122551i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	6.00000			0.212000
$802$	3.00000	+	5.19615i	0.105934	+	0.183483i
$803$	28.0000	+	48.4974i	0.988099	+	1.71144i
$804$	1.50000	+	2.59808i	0.0529009	+	0.0916271i
$805$		0			0
$806$	20.0000			0.704470
$807$	7.50000	−	12.9904i	0.264013	−	0.457283i
$808$	0.500000	+	0.866025i	0.0175899	+	0.0304667i
$809$	5.00000			0.175791			0.0878953	−	0.996130i	$-0.471986\pi$
$809$	5.00000			0.175791			0.0878953	+	0.996130i	$0.471986\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	19.0000	−	32.9090i	0.667180	−	1.15559i	−0.311509	−	0.950243i	$-0.600834\pi$
$811$	19.0000	−	32.9090i	0.667180	−	1.15559i	0.978689	−	0.205347i	$-0.0658323\pi$
$812$	2.00000	−	3.46410i	0.0701862	−	0.121566i
$813$	−24.0000			−0.841717
$814$	4.00000	−	6.92820i	0.140200	−	0.242833i
$815$	−11.0000			−0.385313
$816$	−4.00000			−0.140028
$817$	−15.0000	+	36.3731i	−0.524784	+	1.27253i
$818$	5.00000			0.174821
$819$	16.0000			0.559085
$820$	−2.50000	+	4.33013i	−0.0873038	+	0.151215i
$821$	−22.0000			−0.767805			−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000			−0.767805			−0.383903	+	0.923374i	$0.625420\pi$
$822$	1.00000	−	1.73205i	0.0348790	−	0.0604122i
$823$	0.500000	−	0.866025i	0.0174289	−	0.0301877i	−0.857179	−	0.515018i	$-0.827785\pi$
$823$	0.500000	−	0.866025i	0.0174289	−	0.0301877i	0.874608	+	0.484830i	$0.161119\pi$
$824$	−2.50000	−	4.33013i	−0.0870916	−	0.150847i
$825$	4.00000			0.139262
$826$	28.0000	+	48.4974i	0.974245	+	1.68744i
$827$	10.0000	−	17.3205i	0.347734	−	0.602293i	−0.638112	−	0.769943i	$-0.720285\pi$
$827$	10.0000	−	17.3205i	0.347734	−	0.602293i	0.985847	+	0.167650i	$0.0536179\pi$
$828$		0			0
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	−0.997225	−	0.0744432i	$-0.976282\pi$
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	0.563082	+	0.826401i	$0.309615\pi$
$830$	−7.50000	−	12.9904i	−0.260329	−	0.450903i
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$	1.00000	+	1.73205i	0.0346688	+	0.0600481i
$833$	−36.0000			−1.24733
$834$	1.00000	+	1.73205i	0.0346272	+	0.0599760i
$835$	−4.50000	−	7.79423i	−0.155729	−	0.269730i
$836$	−12.0000	+	20.7846i	−0.415029	+	0.718851i
$837$	25.0000	−	43.3013i	0.864126	−	1.49671i
$838$	20.0000			0.690889
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$	2.00000	−	3.46410i	0.0690066	−	0.119523i
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	11.5000	+	19.9186i	0.396316	+	0.686440i
$843$	−9.00000	−	15.5885i	−0.309976	−	0.536895i
$844$	−22.0000			−0.757271
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$	−1.00000	−	1.73205i	−0.0343807	−	0.0595491i
$847$	−10.0000	−	17.3205i	−0.343604	−	0.595140i
$848$	−5.00000	+	8.66025i	−0.171701	+	0.297394i
$849$	28.0000			0.960958
$850$	−2.00000	+	3.46410i	−0.0685994	+	0.118818i
$851$		0			0
$852$	10.0000			0.342594
$853$	8.00000	+	13.8564i	0.273915	+	0.474434i	0.969861	−	0.243660i	$-0.0783480\pi$
$853$	8.00000	+	13.8564i	0.273915	+	0.474434i	−0.695946	+	0.718094i	$0.745015\pi$
$854$	−12.0000	+	20.7846i	−0.410632	+	0.711235i
$855$	6.00000	−	10.3923i	0.205196	−	0.355409i
$856$	1.00000			0.0341793
$857$	−14.0000	+	24.2487i	−0.478231	+	0.828320i	−0.999689	−	0.0249570i	$-0.992055\pi$
$857$	−14.0000	+	24.2487i	−0.478231	+	0.828320i	0.521458	+	0.853277i	$0.325388\pi$
$858$	8.00000			0.273115
$859$	40.0000			1.36478			0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000			1.36478			0.682391	+	0.730987i	$0.260940\pi$
$860$	−2.50000	+	6.06218i	−0.0852493	+	0.206719i
$861$	20.0000			0.681598
$862$	−36.0000			−1.22616
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$	5.00000			0.170103
$865$		0			0
$866$	7.00000	−	12.1244i	0.237870	−	0.412002i
$867$	0.500000	+	0.866025i	0.0169809	+	0.0294118i
$868$	40.0000			1.35769
$869$	−32.0000	−	55.4256i	−1.08553	−	1.88019i
$870$	−0.500000	+	0.866025i	−0.0169516	+	0.0293610i
$871$	6.00000			0.203302
$872$	−5.50000	+	9.52628i	−0.186254	+	0.322601i
$873$	−12.0000	−	20.7846i	−0.406138	−	0.703452i
$874$		0			0
$875$	−2.00000	−	3.46410i	−0.0676123	−	0.117108i
$876$	−14.0000			−0.473016
$877$	−16.0000	−	27.7128i	−0.540282	−	0.935795i	−0.998888	−	0.0471555i	$-0.984984\pi$
$877$	−16.0000	−	27.7128i	−0.540282	−	0.935795i	0.458606	−	0.888640i	$-0.348349\pi$
$878$	−13.0000	−	22.5167i	−0.438729	−	0.759900i
$879$	−9.00000	+	15.5885i	−0.303562	+	0.525786i
$880$	−2.00000	+	3.46410i	−0.0674200	+	0.116775i
$881$	−15.0000			−0.505363			−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000			−0.505363			−0.252681	+	0.967550i	$0.581312\pi$
$882$	18.0000			0.606092
$883$	20.5000	−	35.5070i	0.689880	−	1.19491i	−0.281996	−	0.959415i	$-0.590997\pi$
$883$	20.5000	−	35.5070i	0.689880	−	1.19491i	0.971876	−	0.235492i	$-0.0756700\pi$
$884$	−4.00000	+	6.92820i	−0.134535	+	0.233021i
$885$	−7.00000	−	12.1244i	−0.235302	−	0.407556i
$886$	0.500000	+	0.866025i	0.0167978	+	0.0290947i
$887$	−44.0000			−1.47738			−0.738688	−	0.674048i	$-0.764554\pi$
$887$	−44.0000			−1.47738			−0.738688	+	0.674048i	$0.764554\pi$
$888$	1.00000	+	1.73205i	0.0335578	+	0.0581238i
$889$	34.0000	+	58.8897i	1.14032	+	1.97510i
$890$	−1.50000	−	2.59808i	−0.0502801	−	0.0870877i
$891$	−2.00000	+	3.46410i	−0.0670025	+	0.116052i
$892$	19.0000			0.636167
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$	0.500000	+	0.866025i	0.0167225	+	0.0289642i
$895$	12.0000			0.401116
$896$	2.00000	+	3.46410i	0.0668153	+	0.115728i
$897$		0			0
$898$	−2.50000	+	4.33013i	−0.0834261	+	0.144498i
$899$	−10.0000			−0.333519
$900$	1.00000	−	1.73205i	0.0333333	−	0.0577350i
$901$	−40.0000			−1.33259
$902$	−20.0000			−0.665927
$903$	26.0000	−	3.46410i	0.865226	−	0.115278i
$904$		0			0
$905$	22.0000			0.731305
$906$	8.00000	−	13.8564i	0.265782	−	0.460348i
$907$	−12.0000			−0.398453			−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000			−0.398453			−0.199227	+	0.979953i	$0.563843\pi$
$908$	6.50000	−	11.2583i	0.215710	−	0.373621i
$909$	1.00000	−	1.73205i	0.0331679	−	0.0574485i
$910$	−4.00000	−	6.92820i	−0.132599	−	0.229668i
$911$	−22.0000			−0.728893			−0.364446	−	0.931224i	$-0.618742\pi$
$911$	−22.0000			−0.728893			−0.364446	+	0.931224i	$0.618742\pi$
$912$	−3.00000	−	5.19615i	−0.0993399	−	0.172062i
$913$	30.0000	−	51.9615i	0.992855	−	1.71968i
$914$	−30.0000			−0.992312
$915$	3.00000	−	5.19615i	0.0991769	−	0.171780i
$916$	−3.50000	−	6.06218i	−0.115643	−	0.200300i
$917$	−24.0000	−	41.5692i	−0.792550	−	1.37274i
$918$	10.0000	+	17.3205i	0.330049	+	0.571662i
$919$	2.00000			0.0659739			0.0329870	−	0.999456i	$-0.489498\pi$
$919$	2.00000			0.0659739			0.0329870	+	0.999456i	$0.489498\pi$
$920$		0			0
$921$	7.50000	+	12.9904i	0.247133	+	0.428048i
$922$	−7.50000	+	12.9904i	−0.246999	+	0.427815i
$923$	10.0000	−	17.3205i	0.329154	−	0.570111i
$924$	16.0000			0.526361
$925$	2.00000			0.0657596
$926$	−10.5000	+	18.1865i	−0.345051	+	0.597647i
$927$	−5.00000	+	8.66025i	−0.164222	+	0.284440i
$928$	−0.500000	−	0.866025i	−0.0164133	−	0.0284287i
$929$	25.0000	+	43.3013i	0.820223	+	1.42067i	0.905516	+	0.424313i	$0.139484\pi$
$929$	25.0000	+	43.3013i	0.820223	+	1.42067i	−0.0852924	+	0.996356i	$0.527182\pi$
$930$	−10.0000			−0.327913
$931$	−27.0000	−	46.7654i	−0.884889	−	1.53267i
$932$	7.00000	+	12.1244i	0.229293	+	0.397146i
$933$	−14.0000	−	24.2487i	−0.458339	−	0.793867i
$934$	16.0000	−	27.7128i	0.523536	−	0.906791i
$935$	−16.0000			−0.523256
$936$	2.00000	−	3.46410i	0.0653720	−	0.113228i
$937$	12.0000	+	20.7846i	0.392023	+	0.679004i	0.992716	−	0.120476i	$-0.0384421\pi$
$937$	12.0000	+	20.7846i	0.392023	+	0.679004i	−0.600693	+	0.799480i	$0.705109\pi$
$938$	12.0000			0.391814
$939$	4.00000	+	6.92820i	0.130535	+	0.226093i
$940$	−0.500000	+	0.866025i	−0.0163082	+	0.0282466i
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	−0.288988	−	0.957333i	$-0.593319\pi$
$941$	21.0000	−	36.3731i	0.684580	−	1.18573i	0.973568	−	0.228395i	$-0.0733479\pi$
$942$	−14.0000			−0.456145
$943$		0			0
$944$	14.0000			0.455661
$945$	−20.0000			−0.650600
$946$	−26.0000	+	3.46410i	−0.845333	+	0.112628i
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$	16.0000			0.519656
$949$	−14.0000	+	24.2487i	−0.454459	+	0.787146i
$950$	−6.00000			−0.194666
$951$	−16.0000	+	27.7128i	−0.518836	+	0.898650i
$952$	−8.00000	+	13.8564i	−0.259281	+	0.449089i
$953$	−22.0000	−	38.1051i	−0.712650	−	1.23435i	−0.963859	−	0.266413i	$-0.914162\pi$
$953$	−22.0000	−	38.1051i	−0.712650	−	1.23435i	0.251209	−	0.967933i	$-0.419172\pi$
$954$	20.0000			0.647524
$955$	−2.00000	−	3.46410i	−0.0647185	−	0.112096i
$956$	8.00000	−	13.8564i	0.258738	−	0.448148i
$957$	−4.00000			−0.129302
$958$	3.00000	−	5.19615i	0.0969256	−	0.167880i
$959$	−4.00000	−	6.92820i	−0.129167	−	0.223723i
$960$	−0.500000	−	0.866025i	−0.0161374	−	0.0279508i
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	4.00000			0.128965
$963$	−1.00000	−	1.73205i	−0.0322245	−	0.0558146i
$964$	1.50000	+	2.59808i	0.0483117	+	0.0836784i
$965$	8.00000	−	13.8564i	0.257529	−	0.446054i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	−5.00000			−0.160706
$969$	12.0000	−	20.7846i	0.385496	−	0.667698i
$970$	−6.00000	+	10.3923i	−0.192648	+	0.333677i
$971$	20.0000	+	34.6410i	0.641831	+	1.11168i	0.985024	+	0.172418i	$0.0551581\pi$
$971$	20.0000	+	34.6410i	0.641831	+	1.11168i	−0.343193	+	0.939265i	$0.611509\pi$
$972$	−8.00000	−	13.8564i	−0.256600	−	0.444444i
$973$	8.00000			0.256468
$974$	−13.5000	−	23.3827i	−0.432568	−	0.749230i
$975$	1.00000	+	1.73205i	0.0320256	+	0.0554700i
$976$	3.00000	+	5.19615i	0.0960277	+	0.166325i
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	0.973317	+	0.229465i	$0.0736978\pi$
$978$	11.0000			0.351741
$979$	6.00000	−	10.3923i	0.191761	−	0.332140i
$980$	−4.50000	−	7.79423i	−0.143747	−	0.248978i
$981$	22.0000			0.702406
$982$	−18.0000	−	31.1769i	−0.574403	−	0.994895i
$983$	−27.5000	+	47.6314i	−0.877114	+	1.51921i	−0.0226199	+	0.999744i	$0.507201\pi$
$983$	−27.5000	+	47.6314i	−0.877114	+	1.51921i	−0.854494	+	0.519461i	$0.826133\pi$
$984$	2.50000	−	4.33013i	0.0796971	−	0.138039i
$985$	−14.0000			−0.446077
$986$	2.00000	−	3.46410i	0.0636930	−	0.110319i
$987$	4.00000			0.127321
$988$	−12.0000			−0.381771
$989$		0			0
$990$	8.00000			0.254257
$991$	22.0000			0.698853			0.349427	−	0.936964i	$-0.386376\pi$
$991$	22.0000			0.698853			0.349427	+	0.936964i	$0.386376\pi$
$992$	5.00000	−	8.66025i	0.158750	−	0.274963i
$993$	32.0000			1.01549
$994$	20.0000	−	34.6410i	0.634361	−	1.09875i
$995$	4.00000	−	6.92820i	0.126809	−	0.219639i
$996$	7.50000	+	12.9904i	0.237647	+	0.411616i
$997$	−4.00000			−0.126681			−0.0633406	−	0.997992i	$-0.520175\pi$
$997$	−4.00000			−0.126681			−0.0633406	+	0.997992i	$0.520175\pi$
$998$	−2.00000	−	3.46410i	−0.0633089	−	0.109654i
$999$	5.00000	−	8.66025i	0.158193	−	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.e.b.221.1	✓	2
43.36	even	3	inner	430.2.e.b.251.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.e.b.221.1	✓	2	1.1	even	1	trivial
430.2.e.b.251.1	yes	2	43.36	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.500000 - 0.866025i) q^{10} +4.00000 q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.00000 + 1.73205i) q^{13} +(2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{15} +1.00000 q^{16} +(2.00000 + 3.46410i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-3.00000 + 5.19615i) q^{19} +(-0.500000 + 0.866025i) q^{20} +4.00000 q^{21} -4.00000 q^{22} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} -5.00000 q^{27} +(-2.00000 - 3.46410i) q^{28} +(0.500000 + 0.866025i) q^{29} +(0.500000 + 0.866025i) q^{30} +(-5.00000 + 8.66025i) q^{31} -1.00000 q^{32} +(-2.00000 + 3.46410i) q^{33} +(-2.00000 - 3.46410i) q^{34} +4.00000 q^{35} +(1.00000 + 1.73205i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(3.00000 - 5.19615i) q^{38} -2.00000 q^{39} +(0.500000 - 0.866025i) q^{40} +5.00000 q^{41} -4.00000 q^{42} +(6.50000 - 0.866025i) q^{43} +4.00000 q^{44} -2.00000 q^{45} +1.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(0.500000 + 0.866025i) q^{50} -4.00000 q^{51} +(1.00000 + 1.73205i) q^{52} +(-5.00000 + 8.66025i) q^{53} +5.00000 q^{54} +(-2.00000 + 3.46410i) q^{55} +(2.00000 + 3.46410i) q^{56} +(-3.00000 - 5.19615i) q^{57} +(-0.500000 - 0.866025i) q^{58} +14.0000 q^{59} +(-0.500000 - 0.866025i) q^{60} +(3.00000 + 5.19615i) q^{61} +(5.00000 - 8.66025i) q^{62} +(4.00000 - 6.92820i) q^{63} +1.00000 q^{64} -2.00000 q^{65} +(2.00000 - 3.46410i) q^{66} +(1.50000 - 2.59808i) q^{67} +(2.00000 + 3.46410i) q^{68} -4.00000 q^{70} +(-5.00000 - 8.66025i) q^{71} +(-1.00000 - 1.73205i) q^{72} +(7.00000 + 12.1244i) q^{73} +(1.00000 - 1.73205i) q^{74} +1.00000 q^{75} +(-3.00000 + 5.19615i) q^{76} +(-8.00000 - 13.8564i) q^{77} +2.00000 q^{78} +(-8.00000 - 13.8564i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} -5.00000 q^{82} +(7.50000 - 12.9904i) q^{83} +4.00000 q^{84} -4.00000 q^{85} +(-6.50000 + 0.866025i) q^{86} -1.00000 q^{87} -4.00000 q^{88} +(1.50000 - 2.59808i) q^{89} +2.00000 q^{90} +(4.00000 - 6.92820i) q^{91} +(-5.00000 - 8.66025i) q^{93} -1.00000 q^{94} +(-3.00000 - 5.19615i) q^{95} +(0.500000 - 0.866025i) q^{96} -12.0000 q^{97} +(4.50000 - 7.79423i) q^{98} +(4.00000 + 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} - q^{5} + q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 - q^5 + q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} - q^{5} + q^{6} - 4 q^{7} - 2 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} - q^{12} + 2 q^{13} + 4 q^{14} - q^{15} + 2 q^{16} + 4 q^{17} - 2 q^{18} - 6 q^{19} - q^{20} + 8 q^{21} - 8 q^{22} + q^{24} - q^{25} - 2 q^{26} - 10 q^{27} - 4 q^{28} + q^{29} + q^{30} - 10 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} + 8 q^{35} + 2 q^{36} - 2 q^{37} + 6 q^{38} - 4 q^{39} + q^{40} + 10 q^{41} - 8 q^{42} + 13 q^{43} + 8 q^{44} - 4 q^{45} + 2 q^{47} - q^{48} - 9 q^{49} + q^{50} - 8 q^{51} + 2 q^{52} - 10 q^{53} + 10 q^{54} - 4 q^{55} + 4 q^{56} - 6 q^{57} - q^{58} + 28 q^{59} - q^{60} + 6 q^{61} + 10 q^{62} + 8 q^{63} + 2 q^{64} - 4 q^{65} + 4 q^{66} + 3 q^{67} + 4 q^{68} - 8 q^{70} - 10 q^{71} - 2 q^{72} + 14 q^{73} + 2 q^{74} + 2 q^{75} - 6 q^{76} - 16 q^{77} + 4 q^{78} - 16 q^{79} - q^{80} - q^{81} - 10 q^{82} + 15 q^{83} + 8 q^{84} - 8 q^{85} - 13 q^{86} - 2 q^{87} - 8 q^{88} + 3 q^{89} + 4 q^{90} + 8 q^{91} - 10 q^{93} - 2 q^{94} - 6 q^{95} + q^{96} - 24 q^{97} + 9 q^{98} + 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 - q^5 + q^6 - 4 * q^7 - 2 * q^8 + 2 * q^9 + q^10 + 8 * q^11 - q^12 + 2 * q^13 + 4 * q^14 - q^15 + 2 * q^16 + 4 * q^17 - 2 * q^18 - 6 * q^19 - q^20 + 8 * q^21 - 8 * q^22 + q^24 - q^25 - 2 * q^26 - 10 * q^27 - 4 * q^28 + q^29 + q^30 - 10 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 + 8 * q^35 + 2 * q^36 - 2 * q^37 + 6 * q^38 - 4 * q^39 + q^40 + 10 * q^41 - 8 * q^42 + 13 * q^43 + 8 * q^44 - 4 * q^45 + 2 * q^47 - q^48 - 9 * q^49 + q^50 - 8 * q^51 + 2 * q^52 - 10 * q^53 + 10 * q^54 - 4 * q^55 + 4 * q^56 - 6 * q^57 - q^58 + 28 * q^59 - q^60 + 6 * q^61 + 10 * q^62 + 8 * q^63 + 2 * q^64 - 4 * q^65 + 4 * q^66 + 3 * q^67 + 4 * q^68 - 8 * q^70 - 10 * q^71 - 2 * q^72 + 14 * q^73 + 2 * q^74 + 2 * q^75 - 6 * q^76 - 16 * q^77 + 4 * q^78 - 16 * q^79 - q^80 - q^81 - 10 * q^82 + 15 * q^83 + 8 * q^84 - 8 * q^85 - 13 * q^86 - 2 * q^87 - 8 * q^88 + 3 * q^89 + 4 * q^90 + 8 * q^91 - 10 * q^93 - 2 * q^94 - 6 * q^95 + q^96 - 24 * q^97 + 9 * q^98 + 8 * q^99

Introduction

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