LMFDB - Embedded newform 670.2.e.a.171.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(171,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("670.171");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.34997693543$
Analytic rank:	$1$
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			171.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.a.431.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -3.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 2.59808i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +6.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -3.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 2.59808i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +6.00000 q^{9} +(0.500000 + 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{12} +(-3.00000 - 5.19615i) q^{13} -2.00000 q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-3.00000 - 5.19615i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-3.00000 + 5.19615i) q^{21} +(2.00000 + 3.46410i) q^{23} -3.00000 q^{24} +1.00000 q^{25} +(-3.00000 + 5.19615i) q^{26} -9.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(3.00000 - 5.19615i) q^{29} +(-1.50000 - 2.59808i) q^{30} +(-4.00000 + 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(-1.00000 + 1.73205i) q^{35} +(-3.00000 + 5.19615i) q^{36} +(1.00000 + 1.73205i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(9.00000 + 15.5885i) q^{39} -1.00000 q^{40} +(-5.00000 + 8.66025i) q^{41} +6.00000 q^{42} -1.00000 q^{43} -6.00000 q^{45} +(2.00000 - 3.46410i) q^{46} +(-4.00000 + 6.92820i) q^{47} +(1.50000 + 2.59808i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(4.50000 + 7.79423i) q^{51} +6.00000 q^{52} -2.00000 q^{53} +(4.50000 + 7.79423i) q^{54} +(1.00000 - 1.73205i) q^{56} +(1.50000 + 2.59808i) q^{57} -6.00000 q^{58} -9.00000 q^{59} +(-1.50000 + 2.59808i) q^{60} +(-4.00000 - 6.92820i) q^{61} +8.00000 q^{62} +(6.00000 - 10.3923i) q^{63} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-8.00000 + 1.73205i) q^{67} +3.00000 q^{68} +(-6.00000 - 10.3923i) q^{69} +2.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +6.00000 q^{72} +(-6.50000 - 11.2583i) q^{73} +(1.00000 - 1.73205i) q^{74} -3.00000 q^{75} +1.00000 q^{76} +(9.00000 - 15.5885i) q^{78} +(4.00000 - 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +9.00000 q^{81} +10.0000 q^{82} +(6.00000 + 10.3923i) q^{83} +(-3.00000 - 5.19615i) q^{84} +(1.50000 + 2.59808i) q^{85} +(0.500000 + 0.866025i) q^{86} +(-9.00000 + 15.5885i) q^{87} +15.0000 q^{89} +(3.00000 + 5.19615i) q^{90} -12.0000 q^{91} -4.00000 q^{92} +(12.0000 - 20.7846i) q^{93} +8.00000 q^{94} +(0.500000 + 0.866025i) q^{95} +(1.50000 - 2.59808i) q^{96} +(-7.50000 - 12.9904i) q^{97} +(1.50000 - 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 6 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + 2 q^{7} + 2 q^{8} + 12 q^{9}+O(q^{10}) $ 2 * q - q^2 - 6 * q^3 - q^4 - 2 * q^5 + 3 * q^6 + 2 * q^7 + 2 * q^8 + 12 * q^9	$ 2 q - q^{2} - 6 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + 2 q^{7} + 2 q^{8} + 12 q^{9} + q^{10} + 3 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - q^{16} - 3 q^{17} - 6 q^{18} - q^{19} + q^{20} - 6 q^{21} + 4 q^{23} - 6 q^{24} + 2 q^{25} - 6 q^{26} - 18 q^{27} + 2 q^{28} + 6 q^{29} - 3 q^{30} - 8 q^{31} - q^{32} - 3 q^{34} - 2 q^{35} - 6 q^{36} + 2 q^{37} - q^{38} + 18 q^{39} - 2 q^{40} - 10 q^{41} + 12 q^{42} - 2 q^{43} - 12 q^{45} + 4 q^{46} - 8 q^{47} + 3 q^{48} + 3 q^{49} - q^{50} + 9 q^{51} + 12 q^{52} - 4 q^{53} + 9 q^{54} + 2 q^{56} + 3 q^{57} - 12 q^{58} - 18 q^{59} - 3 q^{60} - 8 q^{61} + 16 q^{62} + 12 q^{63} + 2 q^{64} + 6 q^{65} - 16 q^{67} + 6 q^{68} - 12 q^{69} + 4 q^{70} - 6 q^{71} + 12 q^{72} - 13 q^{73} + 2 q^{74} - 6 q^{75} + 2 q^{76} + 18 q^{78} + 8 q^{79} + q^{80} + 18 q^{81} + 20 q^{82} + 12 q^{83} - 6 q^{84} + 3 q^{85} + q^{86} - 18 q^{87} + 30 q^{89} + 6 q^{90} - 24 q^{91} - 8 q^{92} + 24 q^{93} + 16 q^{94} + q^{95} + 3 q^{96} - 15 q^{97} + 3 q^{98}+O(q^{100}) $ 2 * q - q^2 - 6 * q^3 - q^4 - 2 * q^5 + 3 * q^6 + 2 * q^7 + 2 * q^8 + 12 * q^9 + q^10 + 3 * q^12 - 6 * q^13 - 4 * q^14 + 6 * q^15 - q^16 - 3 * q^17 - 6 * q^18 - q^19 + q^20 - 6 * q^21 + 4 * q^23 - 6 * q^24 + 2 * q^25 - 6 * q^26 - 18 * q^27 + 2 * q^28 + 6 * q^29 - 3 * q^30 - 8 * q^31 - q^32 - 3 * q^34 - 2 * q^35 - 6 * q^36 + 2 * q^37 - q^38 + 18 * q^39 - 2 * q^40 - 10 * q^41 + 12 * q^42 - 2 * q^43 - 12 * q^45 + 4 * q^46 - 8 * q^47 + 3 * q^48 + 3 * q^49 - q^50 + 9 * q^51 + 12 * q^52 - 4 * q^53 + 9 * q^54 + 2 * q^56 + 3 * q^57 - 12 * q^58 - 18 * q^59 - 3 * q^60 - 8 * q^61 + 16 * q^62 + 12 * q^63 + 2 * q^64 + 6 * q^65 - 16 * q^67 + 6 * q^68 - 12 * q^69 + 4 * q^70 - 6 * q^71 + 12 * q^72 - 13 * q^73 + 2 * q^74 - 6 * q^75 + 2 * q^76 + 18 * q^78 + 8 * q^79 + q^80 + 18 * q^81 + 20 * q^82 + 12 * q^83 - 6 * q^84 + 3 * q^85 + q^86 - 18 * q^87 + 30 * q^89 + 6 * q^90 - 24 * q^91 - 8 * q^92 + 24 * q^93 + 16 * q^94 + q^95 + 3 * q^96 - 15 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−3.00000			−1.73205			−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−3.00000			−1.73205			−0.866025	+	0.500000i	$0.833333\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.50000	+	2.59808i	0.612372	+	1.06066i
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$	1.00000			0.353553
$9$	6.00000			2.00000
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$	−2.00000			−0.534522
$15$	3.00000			0.774597
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	−3.00000	−	5.19615i	−0.707107	−	1.22474i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−3.00000	+	5.19615i	−0.654654	+	1.13389i
$22$		0			0
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	−3.00000			−0.612372
$25$	1.00000			0.200000
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$	−9.00000			−1.73205
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$	−1.50000	−	2.59808i	−0.273861	−	0.474342i
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	0.243204	+	0.969975i	$0.421802\pi$
$31$	−4.00000	+	6.92820i	−0.718421	+	1.24434i	−0.961625	+	0.274367i	$0.911532\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$	−3.00000	+	5.19615i	−0.500000	+	0.866025i
$37$	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	$0.780765\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$	9.00000	+	15.5885i	1.44115	+	2.49615i
$40$	−1.00000			−0.158114
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	0.150567	+	0.988600i	$0.451890\pi$
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	−0.931436	+	0.363905i	$0.881443\pi$
$42$	6.00000			0.925820
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$		0			0
$45$	−6.00000			−0.894427
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	0.411606	+	0.911362i	$0.364968\pi$
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	−0.995066	+	0.0992202i	$0.968365\pi$
$48$	1.50000	+	2.59808i	0.216506	+	0.375000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	4.50000	+	7.79423i	0.630126	+	1.09141i
$52$	6.00000			0.832050
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$	4.50000	+	7.79423i	0.612372	+	1.06066i
$55$		0			0
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$	1.50000	+	2.59808i	0.198680	+	0.344124i
$58$	−6.00000			−0.787839
$59$	−9.00000			−1.17170			−0.585850	−	0.810419i	$-0.699239\pi$
$59$	−9.00000			−1.17170			−0.585850	+	0.810419i	$0.699239\pi$
$60$	−1.50000	+	2.59808i	−0.193649	+	0.335410i
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	8.00000			1.01600
$63$	6.00000	−	10.3923i	0.755929	−	1.30931i
$64$	1.00000			0.125000
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$		0			0
$67$	−8.00000	+	1.73205i	−0.977356	+	0.211604i
$67$	−8.00000	+	1.73205i	−0.977356	+	0.211604i
$68$	3.00000			0.363803
$69$	−6.00000	−	10.3923i	−0.722315	−	1.25109i
$70$	2.00000			0.239046
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	6.00000			0.707107
$73$	−6.50000	−	11.2583i	−0.760767	−	1.31769i	−0.942455	−	0.334332i	$-0.891489\pi$
$73$	−6.50000	−	11.2583i	−0.760767	−	1.31769i	0.181688	−	0.983356i	$-0.441844\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$	−3.00000			−0.346410
$76$	1.00000			0.114708
$77$		0			0
$78$	9.00000	−	15.5885i	1.01905	−	1.76505i
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	9.00000			1.00000
$82$	10.0000			1.10432
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$	−3.00000	−	5.19615i	−0.327327	−	0.566947i
$85$	1.50000	+	2.59808i	0.162698	+	0.281801i
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	−9.00000	+	15.5885i	−0.964901	+	1.67126i
$88$		0			0
$89$	15.0000			1.59000			0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$	3.00000	+	5.19615i	0.316228	+	0.547723i
$91$	−12.0000			−1.25794
$92$	−4.00000			−0.417029
$93$	12.0000	−	20.7846i	1.24434	−	2.15526i
$94$	8.00000			0.825137
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	1.50000	−	2.59808i	0.153093	−	0.265165i
$97$	−7.50000	−	12.9904i	−0.761510	−	1.31897i	−0.942072	−	0.335410i	$-0.891125\pi$
$97$	−7.50000	−	12.9904i	−0.761510	−	1.31897i	0.180563	−	0.983563i	$-0.442208\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$	4.50000	−	7.79423i	0.445566	−	0.771744i
$103$	−6.00000	+	10.3923i	−0.591198	+	1.02398i	0.402874	+	0.915255i	$0.368011\pi$
$103$	−6.00000	+	10.3923i	−0.591198	+	1.02398i	−0.994071	+	0.108729i	$0.965322\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$	3.00000	−	5.19615i	0.292770	−	0.507093i
$106$	1.00000	+	1.73205i	0.0971286	+	0.168232i
$107$	4.00000			0.386695			0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000			0.386695			0.193347	+	0.981130i	$0.438066\pi$
$108$	4.50000	−	7.79423i	0.433013	−	0.750000i
$109$	−6.00000			−0.574696			−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000			−0.574696			−0.287348	+	0.957826i	$0.592774\pi$
$110$		0			0
$111$	−3.00000	−	5.19615i	−0.284747	−	0.493197i
$112$	−2.00000			−0.188982
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	−0.996262	−	0.0863794i	$-0.972470\pi$
$113$	−4.50000	+	7.79423i	−0.423324	+	0.733219i	0.572938	+	0.819599i	$0.305804\pi$
$114$	1.50000	−	2.59808i	0.140488	−	0.243332i
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	−18.0000	−	31.1769i	−1.66410	−	2.88231i
$118$	4.50000	+	7.79423i	0.414259	+	0.717517i
$119$	−6.00000			−0.550019
$120$	3.00000			0.273861
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−4.00000	+	6.92820i	−0.362143	+	0.627250i
$123$	15.0000	−	25.9808i	1.35250	−	2.34261i
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$	−1.00000			−0.0894427
$126$	−12.0000			−1.06904
$127$	−7.00000	+	12.1244i	−0.621150	+	1.07586i	0.368122	+	0.929777i	$0.380001\pi$
$127$	−7.00000	+	12.1244i	−0.621150	+	1.07586i	−0.989272	+	0.146085i	$0.953333\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	3.00000			0.264135
$130$	3.00000	−	5.19615i	0.263117	−	0.455733i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	−2.00000			−0.173422
$134$	5.50000	+	6.06218i	0.475128	+	0.523692i
$135$	9.00000			0.774597
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	11.0000			0.939793			0.469897	−	0.882721i	$-0.344291\pi$
$137$	11.0000			0.939793			0.469897	+	0.882721i	$0.344291\pi$
$138$	−6.00000	+	10.3923i	−0.510754	+	0.884652i
$139$	1.00000			0.0848189			0.0424094	−	0.999100i	$-0.486497\pi$
$139$	1.00000			0.0848189			0.0424094	+	0.999100i	$0.486497\pi$
$140$	−1.00000	−	1.73205i	−0.0845154	−	0.146385i
$141$	12.0000	−	20.7846i	1.01058	−	1.75038i
$142$	6.00000			0.503509
$143$		0			0
$144$	−3.00000	−	5.19615i	−0.250000	−	0.433013i
$145$	−3.00000	+	5.19615i	−0.249136	+	0.431517i
$146$	−6.50000	+	11.2583i	−0.537944	+	0.931746i
$147$	−4.50000	−	7.79423i	−0.371154	−	0.642857i
$148$	−2.00000			−0.164399
$149$	−4.00000			−0.327693			−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000			−0.327693			−0.163846	+	0.986486i	$0.552390\pi$
$150$	1.50000	+	2.59808i	0.122474	+	0.212132i
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	−0.500000	−	0.866025i	−0.0405554	−	0.0702439i
$153$	−9.00000	−	15.5885i	−0.727607	−	1.26025i
$154$		0			0
$155$	4.00000	−	6.92820i	0.321288	−	0.556487i
$156$	−18.0000			−1.44115
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	0.594565	−	0.804048i	$-0.297324\pi$
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	−0.993608	+	0.112884i	$0.963991\pi$
$158$	−8.00000			−0.636446
$159$	6.00000			0.475831
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	8.00000			0.630488
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	10.5000	−	18.1865i	0.822423	−	1.42448i	−0.0814491	−	0.996678i	$-0.525955\pi$
$163$	10.5000	−	18.1865i	0.822423	−	1.42448i	0.903873	−	0.427802i	$-0.140712\pi$
$164$	−5.00000	−	8.66025i	−0.390434	−	0.676252i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$	−3.00000	+	5.19615i	−0.231455	+	0.400892i
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	1.50000	−	2.59808i	0.115045	−	0.199263i
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	0.999293	+	0.0375896i	$0.0119679\pi$
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	−0.467093	+	0.884208i	$0.654699\pi$
$174$	18.0000			1.36458
$175$	1.00000	−	1.73205i	0.0755929	−	0.130931i
$176$		0			0
$177$	27.0000			2.02944
$178$	−7.50000	−	12.9904i	−0.562149	−	0.973670i
$179$	−20.0000			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$180$	3.00000	−	5.19615i	0.223607	−	0.387298i
$181$	2.00000	−	3.46410i	0.148659	−	0.257485i	−0.782073	−	0.623187i	$-0.785838\pi$
$181$	2.00000	−	3.46410i	0.148659	−	0.257485i	0.930732	+	0.365702i	$0.119171\pi$
$182$	6.00000	+	10.3923i	0.444750	+	0.770329i
$183$	12.0000	+	20.7846i	0.887066	+	1.53644i
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	−1.00000	−	1.73205i	−0.0735215	−	0.127343i
$186$	−24.0000			−1.75977
$187$		0			0
$188$	−4.00000	−	6.92820i	−0.291730	−	0.505291i
$189$	−9.00000	+	15.5885i	−0.654654	+	1.13389i
$190$	0.500000	−	0.866025i	0.0362738	−	0.0628281i
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$	−3.00000			−0.216506
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$	−7.50000	+	12.9904i	−0.538469	+	0.932655i
$195$	−9.00000	−	15.5885i	−0.644503	−	1.11631i
$196$	−3.00000			−0.214286
$197$	−4.00000	+	6.92820i	−0.284988	+	0.493614i	−0.972606	−	0.232458i	$-0.925323\pi$
$197$	−4.00000	+	6.92820i	−0.284988	+	0.493614i	0.687618	+	0.726073i	$0.258656\pi$
$198$		0			0
$199$	−1.00000	−	1.73205i	−0.0708881	−	0.122782i	0.828403	−	0.560133i	$-0.189250\pi$
$199$	−1.00000	−	1.73205i	−0.0708881	−	0.122782i	−0.899291	+	0.437351i	$0.855917\pi$
$200$	1.00000			0.0707107
$201$	24.0000	−	5.19615i	1.69283	−	0.366508i
$202$	10.0000			0.703598
$203$	−6.00000	−	10.3923i	−0.421117	−	0.729397i
$204$	−9.00000			−0.630126
$205$	5.00000	−	8.66025i	0.349215	−	0.604858i
$206$	12.0000			0.836080
$207$	12.0000	+	20.7846i	0.834058	+	1.44463i
$208$	−3.00000	+	5.19615i	−0.208013	+	0.360288i
$209$		0			0
$210$	−6.00000			−0.414039
$211$	0.500000	+	0.866025i	0.0344214	+	0.0596196i	0.882723	−	0.469894i	$-0.155708\pi$
$211$	0.500000	+	0.866025i	0.0344214	+	0.0596196i	−0.848301	+	0.529514i	$0.822374\pi$
$212$	1.00000	−	1.73205i	0.0686803	−	0.118958i
$213$	9.00000	−	15.5885i	0.616670	−	1.06810i
$214$	−2.00000	−	3.46410i	−0.136717	−	0.236801i
$215$	1.00000			0.0681994
$216$	−9.00000			−0.612372
$217$	8.00000	+	13.8564i	0.543075	+	0.940634i
$218$	3.00000	+	5.19615i	0.203186	+	0.351928i
$219$	19.5000	+	33.7750i	1.31769	+	2.28230i
$220$		0			0
$221$	−9.00000	+	15.5885i	−0.605406	+	1.04859i
$222$	−3.00000	+	5.19615i	−0.201347	+	0.348743i
$223$	−18.0000			−1.20537			−0.602685	−	0.797980i	$-0.705902\pi$
$223$	−18.0000			−1.20537			−0.602685	+	0.797980i	$0.705902\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$	6.00000			0.400000
$226$	9.00000			0.598671
$227$	−6.50000	+	11.2583i	−0.431420	+	0.747242i	−0.996996	−	0.0774548i	$-0.975321\pi$
$227$	−6.50000	+	11.2583i	−0.431420	+	0.747242i	0.565576	+	0.824696i	$0.308654\pi$
$228$	−3.00000			−0.198680
$229$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$229$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$230$	−2.00000	+	3.46410i	−0.131876	+	0.228416i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	−12.5000	+	21.6506i	−0.818902	+	1.41838i	0.0875895	+	0.996157i	$0.472084\pi$
$233$	−12.5000	+	21.6506i	−0.818902	+	1.41838i	−0.906492	+	0.422224i	$0.861250\pi$
$234$	−18.0000	+	31.1769i	−1.17670	+	2.03810i
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$	−12.0000	+	20.7846i	−0.779484	+	1.35011i
$238$	3.00000	+	5.19615i	0.194461	+	0.336817i
$239$	15.0000	−	25.9808i	0.970269	−	1.68056i	0.275533	−	0.961292i	$-0.411146\pi$
$239$	15.0000	−	25.9808i	0.970269	−	1.68056i	0.694737	−	0.719264i	$-0.255521\pi$
$240$	−1.50000	−	2.59808i	−0.0968246	−	0.167705i
$241$	10.0000			0.644157			0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000			0.644157			0.322078	+	0.946713i	$0.395619\pi$
$242$	5.50000	−	9.52628i	0.353553	−	0.612372i
$243$		0			0
$244$	8.00000			0.512148
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$	−30.0000			−1.91273
$247$	−3.00000	+	5.19615i	−0.190885	+	0.330623i
$248$	−4.00000	+	6.92820i	−0.254000	+	0.439941i
$249$	−18.0000	−	31.1769i	−1.14070	−	1.97576i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	6.50000	+	11.2583i	0.410276	+	0.710620i	0.994920	−	0.100671i	$-0.0320989\pi$
$251$	6.50000	+	11.2583i	0.410276	+	0.710620i	−0.584643	+	0.811290i	$0.698766\pi$
$252$	6.00000	+	10.3923i	0.377964	+	0.654654i
$253$		0			0
$254$	14.0000			0.878438
$255$	−4.50000	−	7.79423i	−0.281801	−	0.488094i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.0000	−	19.0526i	0.686161	−	1.18847i	−0.286909	−	0.957958i	$-0.592628\pi$
$257$	11.0000	−	19.0526i	0.686161	−	1.18847i	0.973070	−	0.230508i	$-0.0740389\pi$
$258$	−1.50000	−	2.59808i	−0.0933859	−	0.161749i
$259$	4.00000			0.248548
$260$	−6.00000			−0.372104
$261$	18.0000	−	31.1769i	1.11417	−	1.92980i
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$		0			0
$265$	2.00000			0.122859
$266$	1.00000	+	1.73205i	0.0613139	+	0.106199i
$267$	−45.0000			−2.75396
$268$	2.50000	−	7.79423i	0.152712	−	0.476108i
$269$	4.00000			0.243884			0.121942	−	0.992537i	$-0.461088\pi$
$269$	4.00000			0.243884			0.121942	+	0.992537i	$0.461088\pi$
$270$	−4.50000	−	7.79423i	−0.273861	−	0.474342i
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	36.0000			2.17882
$274$	−5.50000	−	9.52628i	−0.332267	−	0.575504i
$275$		0			0
$276$	12.0000			0.722315
$277$	−4.00000			−0.240337			−0.120168	−	0.992754i	$-0.538343\pi$
$277$	−4.00000			−0.240337			−0.120168	+	0.992754i	$0.538343\pi$
$278$	−0.500000	−	0.866025i	−0.0299880	−	0.0519408i
$279$	−24.0000	+	41.5692i	−1.43684	+	2.48868i
$280$	−1.00000	+	1.73205i	−0.0597614	+	0.103510i
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	−0.916060	−	0.401042i	$-0.868648\pi$
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	0.110717	−	0.993852i	$-0.464685\pi$
$282$	−24.0000			−1.42918
$283$	−29.0000			−1.72387			−0.861936	−	0.507018i	$-0.830748\pi$
$283$	−29.0000			−1.72387			−0.861936	+	0.507018i	$0.830748\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	−1.50000	−	2.59808i	−0.0888523	−	0.153897i
$286$		0			0
$287$	10.0000	+	17.3205i	0.590281	+	1.02240i
$288$	−3.00000	+	5.19615i	−0.176777	+	0.306186i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	6.00000			0.352332
$291$	22.5000	+	38.9711i	1.31897	+	2.28453i
$292$	13.0000			0.760767
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$	−4.50000	+	7.79423i	−0.262445	+	0.454569i
$295$	9.00000			0.524000
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$		0			0
$298$	2.00000	+	3.46410i	0.115857	+	0.200670i
$299$	12.0000	−	20.7846i	0.693978	−	1.20201i
$300$	1.50000	−	2.59808i	0.0866025	−	0.150000i
$301$	−1.00000	+	1.73205i	−0.0576390	+	0.0998337i
$302$	−4.00000	+	6.92820i	−0.230174	+	0.398673i
$303$	15.0000	−	25.9808i	0.861727	−	1.49256i
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$	4.00000	+	6.92820i	0.229039	+	0.396708i
$306$	−9.00000	+	15.5885i	−0.514496	+	0.891133i
$307$	12.5000	+	21.6506i	0.713413	+	1.23567i	0.963569	+	0.267461i	$0.0861848\pi$
$307$	12.5000	+	21.6506i	0.713413	+	1.23567i	−0.250156	+	0.968206i	$0.580482\pi$
$308$		0			0
$309$	18.0000	−	31.1769i	1.02398	−	1.77359i
$310$	−8.00000			−0.454369
$311$	28.0000			1.58773			0.793867	−	0.608091i	$-0.208065\pi$
$311$	28.0000			1.58773			0.793867	+	0.608091i	$0.208065\pi$
$312$	9.00000	+	15.5885i	0.509525	+	0.882523i
$313$	−1.00000			−0.0565233			−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000			−0.0565233			−0.0282617	+	0.999601i	$0.508997\pi$
$314$	−5.00000	+	8.66025i	−0.282166	+	0.488726i
$315$	−6.00000	+	10.3923i	−0.338062	+	0.585540i
$316$	4.00000	+	6.92820i	0.225018	+	0.389742i
$317$	7.00000	+	12.1244i	0.393159	+	0.680972i	0.992864	−	0.119249i	$-0.0380488\pi$
$317$	7.00000	+	12.1244i	0.393159	+	0.680972i	−0.599705	+	0.800221i	$0.704715\pi$
$318$	−3.00000	−	5.19615i	−0.168232	−	0.291386i
$319$		0			0
$320$	−1.00000			−0.0559017
$321$	−12.0000			−0.669775
$322$	−4.00000	−	6.92820i	−0.222911	−	0.386094i
$323$	−1.50000	+	2.59808i	−0.0834622	+	0.144561i
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−3.00000	−	5.19615i	−0.166410	−	0.288231i
$326$	−21.0000			−1.16308
$327$	18.0000			0.995402
$328$	−5.00000	+	8.66025i	−0.276079	+	0.478183i
$329$	8.00000	+	13.8564i	0.441054	+	0.763928i
$330$		0			0
$331$	−2.50000	+	4.33013i	−0.137412	+	0.238005i	−0.926516	−	0.376254i	$-0.877212\pi$
$331$	−2.50000	+	4.33013i	−0.137412	+	0.238005i	0.789104	+	0.614260i	$0.210545\pi$
$332$	−12.0000			−0.658586
$333$	6.00000	+	10.3923i	0.328798	+	0.569495i
$334$	12.0000			0.656611
$335$	8.00000	−	1.73205i	0.437087	−	0.0946320i
$336$	6.00000			0.327327
$337$	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	$0.781081\pi$
$338$	23.0000			1.25104
$339$	13.5000	−	23.3827i	0.733219	−	1.26997i
$340$	−3.00000			−0.162698
$341$		0			0
$342$	−3.00000	+	5.19615i	−0.162221	+	0.280976i
$343$	20.0000			1.07990
$344$	−1.00000			−0.0539164
$345$	6.00000	+	10.3923i	0.323029	+	0.559503i
$346$	7.00000	−	12.1244i	0.376322	−	0.651809i
$347$	−12.5000	+	21.6506i	−0.671035	+	1.16227i	0.306576	+	0.951846i	$0.400817\pi$
$347$	−12.5000	+	21.6506i	−0.671035	+	1.16227i	−0.977611	+	0.210421i	$0.932517\pi$
$348$	−9.00000	−	15.5885i	−0.482451	−	0.835629i
$349$	−20.0000			−1.07058			−0.535288	−	0.844670i	$-0.679797\pi$
$349$	−20.0000			−1.07058			−0.535288	+	0.844670i	$0.679797\pi$
$350$	−2.00000			−0.106904
$351$	27.0000	+	46.7654i	1.44115	+	2.49615i
$352$		0			0
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	0.617388	−	0.786659i	$-0.288191\pi$
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	−0.989960	+	0.141344i	$0.954858\pi$
$354$	−13.5000	−	23.3827i	−0.717517	−	1.24278i
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$	−7.50000	+	12.9904i	−0.397499	+	0.688489i
$357$	18.0000			0.952661
$358$	10.0000	+	17.3205i	0.528516	+	0.915417i
$359$	−6.00000			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$360$	−6.00000			−0.316228
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	−4.00000			−0.210235
$363$	−16.5000	−	28.5788i	−0.866025	−	1.50000i
$364$	6.00000	−	10.3923i	0.314485	−	0.544705i
$365$	6.50000	+	11.2583i	0.340226	+	0.589288i
$366$	12.0000	−	20.7846i	0.627250	−	1.08643i
$367$	13.0000	−	22.5167i	0.678594	−	1.17536i	−0.296810	−	0.954937i	$-0.595923\pi$
$367$	13.0000	−	22.5167i	0.678594	−	1.17536i	0.975404	−	0.220423i	$-0.0707439\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$	−30.0000	+	51.9615i	−1.56174	+	2.70501i
$370$	−1.00000	+	1.73205i	−0.0519875	+	0.0900450i
$371$	−2.00000	+	3.46410i	−0.103835	+	0.179847i
$372$	12.0000	+	20.7846i	0.622171	+	1.07763i
$373$	−15.0000	+	25.9808i	−0.776671	+	1.34523i	0.157180	+	0.987570i	$0.449760\pi$
$373$	−15.0000	+	25.9808i	−0.776671	+	1.34523i	−0.933851	+	0.357663i	$0.883574\pi$
$374$		0			0
$375$	3.00000			0.154919
$376$	−4.00000	+	6.92820i	−0.206284	+	0.357295i
$377$	−36.0000			−1.85409
$378$	18.0000			0.925820
$379$	−14.0000	−	24.2487i	−0.719132	−	1.24557i	−0.961344	−	0.275349i	$-0.911206\pi$
$379$	−14.0000	−	24.2487i	−0.719132	−	1.24557i	0.242213	−	0.970223i	$-0.422127\pi$
$380$	−1.00000			−0.0512989
$381$	21.0000	−	36.3731i	1.07586	−	1.86345i
$382$	−4.00000	+	6.92820i	−0.204658	+	0.354478i
$383$	−5.00000	−	8.66025i	−0.255488	−	0.442518i	0.709540	−	0.704665i	$-0.248903\pi$
$383$	−5.00000	−	8.66025i	−0.255488	−	0.442518i	−0.965028	+	0.262147i	$0.915569\pi$
$384$	1.50000	+	2.59808i	0.0765466	+	0.132583i
$385$		0			0
$386$	−3.00000	−	5.19615i	−0.152696	−	0.264477i
$387$	−6.00000			−0.304997
$388$	15.0000			0.761510
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	0.977086	−	0.212847i	$-0.0682735\pi$
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	−0.672874	+	0.739758i	$0.734940\pi$
$390$	−9.00000	+	15.5885i	−0.455733	+	0.789352i
$391$	6.00000	−	10.3923i	0.303433	−	0.525561i
$392$	1.50000	+	2.59808i	0.0757614	+	0.131223i
$393$	−36.0000			−1.81596
$394$	8.00000			0.403034
$395$	−4.00000	+	6.92820i	−0.201262	+	0.348596i
$396$		0			0
$397$	−12.0000			−0.602263			−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−12.0000			−0.602263			−0.301131	+	0.953583i	$0.597364\pi$
$398$	−1.00000	+	1.73205i	−0.0501255	+	0.0868199i
$399$	6.00000			0.300376
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−38.0000			−1.89763			−0.948815	−	0.315833i	$-0.897716\pi$
$401$	−38.0000			−1.89763			−0.948815	+	0.315833i	$0.897716\pi$
$402$	−16.5000	−	18.1865i	−0.822945	−	0.907062i
$403$	48.0000			2.39105
$404$	−5.00000	−	8.66025i	−0.248759	−	0.430864i
$405$	−9.00000			−0.447214
$406$	−6.00000	+	10.3923i	−0.297775	+	0.515761i
$407$		0			0
$408$	4.50000	+	7.79423i	0.222783	+	0.385872i
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	−0.715523	−	0.698589i	$-0.753812\pi$
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	0.962757	+	0.270367i	$0.0871450\pi$
$410$	−10.0000			−0.493865
$411$	−33.0000			−1.62777
$412$	−6.00000	−	10.3923i	−0.295599	−	0.511992i
$413$	−9.00000	+	15.5885i	−0.442861	+	0.767058i
$414$	12.0000	−	20.7846i	0.589768	−	1.02151i
$415$	−6.00000	−	10.3923i	−0.294528	−	0.510138i
$416$	6.00000			0.294174
$417$	−3.00000			−0.146911
$418$		0			0
$419$	−2.50000	−	4.33013i	−0.122133	−	0.211541i	0.798476	−	0.602027i	$-0.205640\pi$
$419$	−2.50000	−	4.33013i	−0.122133	−	0.211541i	−0.920609	+	0.390487i	$0.872307\pi$
$420$	3.00000	+	5.19615i	0.146385	+	0.253546i
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	0.946883	−	0.321577i	$-0.104213\pi$
$421$	4.00000	+	6.92820i	0.194948	+	0.337660i	−0.751935	+	0.659237i	$0.770879\pi$
$422$	0.500000	−	0.866025i	0.0243396	−	0.0421575i
$423$	−24.0000	+	41.5692i	−1.16692	+	2.02116i
$424$	−2.00000			−0.0971286
$425$	−1.50000	−	2.59808i	−0.0727607	−	0.126025i
$426$	−18.0000			−0.872103
$427$	−16.0000			−0.774294
$428$	−2.00000	+	3.46410i	−0.0966736	+	0.167444i
$429$		0			0
$430$	−0.500000	−	0.866025i	−0.0241121	−	0.0417635i
$431$	−11.0000	+	19.0526i	−0.529851	+	0.917729i	0.469542	+	0.882910i	$0.344419\pi$
$431$	−11.0000	+	19.0526i	−0.529851	+	0.917729i	−0.999394	+	0.0348195i	$0.988914\pi$
$432$	4.50000	+	7.79423i	0.216506	+	0.375000i
$433$	−17.5000	+	30.3109i	−0.840996	+	1.45665i	0.0480569	+	0.998845i	$0.484697\pi$
$433$	−17.5000	+	30.3109i	−0.840996	+	1.45665i	−0.889053	+	0.457804i	$0.848636\pi$
$434$	8.00000	−	13.8564i	0.384012	−	0.665129i
$435$	9.00000	−	15.5885i	0.431517	−	0.747409i
$436$	3.00000	−	5.19615i	0.143674	−	0.248851i
$437$	2.00000	−	3.46410i	0.0956730	−	0.165710i
$438$	19.5000	−	33.7750i	0.931746	−	1.61383i
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$		0			0
$441$	9.00000	+	15.5885i	0.428571	+	0.742307i
$442$	18.0000			0.856173
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	−0.705278	−	0.708931i	$-0.749178\pi$
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	0.966591	+	0.256323i	$0.0825112\pi$
$444$	6.00000			0.284747
$445$	−15.0000			−0.711068
$446$	9.00000	+	15.5885i	0.426162	+	0.738135i
$447$	12.0000			0.567581
$448$	1.00000	−	1.73205i	0.0472456	−	0.0818317i
$449$	19.0000	−	32.9090i	0.896665	−	1.55307i	0.0649356	−	0.997889i	$-0.479316\pi$
$449$	19.0000	−	32.9090i	0.896665	−	1.55307i	0.831730	−	0.555181i	$-0.187351\pi$
$450$	−3.00000	−	5.19615i	−0.141421	−	0.244949i
$451$		0			0
$452$	−4.50000	−	7.79423i	−0.211662	−	0.366610i
$453$	12.0000	+	20.7846i	0.563809	+	0.976546i
$454$	13.0000			0.610120
$455$	12.0000			0.562569
$456$	1.50000	+	2.59808i	0.0702439	+	0.121666i
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	−0.595818	−	0.803120i	$-0.703172\pi$
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	0.993431	+	0.114433i	$0.0365053\pi$
$458$		0			0
$459$	13.5000	+	23.3827i	0.630126	+	1.09141i
$460$	4.00000			0.186501
$461$	−22.0000			−1.02464			−0.512321	−	0.858794i	$-0.671214\pi$
$461$	−22.0000			−1.02464			−0.512321	+	0.858794i	$0.671214\pi$
$462$		0			0
$463$	15.0000	+	25.9808i	0.697109	+	1.20743i	0.969465	+	0.245232i	$0.0788640\pi$
$463$	15.0000	+	25.9808i	0.697109	+	1.20743i	−0.272355	+	0.962197i	$0.587803\pi$
$464$	−6.00000			−0.278543
$465$	−12.0000	+	20.7846i	−0.556487	+	0.963863i
$466$	25.0000			1.15810
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	−0.895696	−	0.444667i	$-0.853322\pi$
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	0.0627555	−	0.998029i	$-0.480011\pi$
$468$	36.0000			1.66410
$469$	−5.00000	+	15.5885i	−0.230879	+	0.719808i
$470$	−8.00000			−0.369012
$471$	15.0000	+	25.9808i	0.691164	+	1.19713i
$472$	−9.00000			−0.414259
$473$		0			0
$474$	24.0000			1.10236
$475$	−0.500000	−	0.866025i	−0.0229416	−	0.0397360i
$476$	3.00000	−	5.19615i	0.137505	−	0.238165i
$477$	−12.0000			−0.549442
$478$	−30.0000			−1.37217
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	0.695773	−	0.718262i	$-0.255062\pi$
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	−0.969920	+	0.243426i	$0.921729\pi$
$480$	−1.50000	+	2.59808i	−0.0684653	+	0.118585i
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$	−5.00000	−	8.66025i	−0.227744	−	0.394464i
$483$	−24.0000			−1.09204
$484$	−11.0000			−0.500000
$485$	7.50000	+	12.9904i	0.340557	+	0.589863i
$486$		0			0
$487$	−14.0000	−	24.2487i	−0.634401	−	1.09881i	−0.986642	−	0.162905i	$-0.947914\pi$
$487$	−14.0000	−	24.2487i	−0.634401	−	1.09881i	0.352241	−	0.935909i	$-0.385420\pi$
$488$	−4.00000	−	6.92820i	−0.181071	−	0.313625i
$489$	−31.5000	+	54.5596i	−1.42448	+	2.46727i
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	−1.00000			−0.0451294			−0.0225647	−	0.999745i	$-0.507183\pi$
$491$	−1.00000			−0.0451294			−0.0225647	+	0.999745i	$0.507183\pi$
$492$	15.0000	+	25.9808i	0.676252	+	1.17130i
$493$	−18.0000			−0.810679
$494$	6.00000			0.269953
$495$		0			0
$496$	8.00000			0.359211
$497$	6.00000	+	10.3923i	0.269137	+	0.466159i
$498$	−18.0000	+	31.1769i	−0.806599	+	1.39707i
$499$	2.50000	+	4.33013i	0.111915	+	0.193843i	0.916542	−	0.399937i	$-0.130968\pi$
$499$	2.50000	+	4.33013i	0.111915	+	0.193843i	−0.804627	+	0.593780i	$0.797635\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	18.0000	−	31.1769i	0.804181	−	1.39288i
$502$	6.50000	−	11.2583i	0.290109	−	0.502484i
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	−0.925124	−	0.379664i	$-0.876040\pi$
$503$	−3.00000	+	5.19615i	−0.133763	+	0.231685i	0.791361	+	0.611349i	$0.209373\pi$
$504$	6.00000	−	10.3923i	0.267261	−	0.462910i
$505$	5.00000	−	8.66025i	0.222497	−	0.385376i
$506$		0			0
$507$	34.5000	−	59.7558i	1.53220	−	2.65385i
$508$	−7.00000	−	12.1244i	−0.310575	−	0.537931i
$509$	−34.0000			−1.50702			−0.753512	−	0.657434i	$-0.771642\pi$
$509$	−34.0000			−1.50702			−0.753512	+	0.657434i	$0.771642\pi$
$510$	−4.50000	+	7.79423i	−0.199263	+	0.345134i
$511$	−26.0000			−1.15017
$512$	1.00000			0.0441942
$513$	4.50000	+	7.79423i	0.198680	+	0.344124i
$514$	−22.0000			−0.970378
$515$	6.00000	−	10.3923i	0.264392	−	0.457940i
$516$	−1.50000	+	2.59808i	−0.0660338	+	0.114374i
$517$		0			0
$518$	−2.00000	−	3.46410i	−0.0878750	−	0.152204i
$519$	−21.0000	−	36.3731i	−0.921798	−	1.59660i
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$	1.00000			0.0438108			0.0219054	−	0.999760i	$-0.493027\pi$
$521$	1.00000			0.0438108			0.0219054	+	0.999760i	$0.493027\pi$
$522$	−36.0000			−1.57568
$523$	11.5000	+	19.9186i	0.502860	+	0.870979i	0.999995	+	0.00330547i	$0.00105217\pi$
$523$	11.5000	+	19.9186i	0.502860	+	0.870979i	−0.497135	+	0.867673i	$0.665615\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$	−3.00000	+	5.19615i	−0.130931	+	0.226779i
$526$	6.00000	+	10.3923i	0.261612	+	0.453126i
$527$	24.0000			1.04546
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−1.00000	−	1.73205i	−0.0434372	−	0.0752355i
$531$	−54.0000			−2.34340
$532$	1.00000	−	1.73205i	0.0433555	−	0.0750939i
$533$	60.0000			2.59889
$534$	22.5000	+	38.9711i	0.973670	+	1.68645i
$535$	−4.00000			−0.172935
$536$	−8.00000	+	1.73205i	−0.345547	+	0.0748132i
$537$	60.0000			2.58919
$538$	−2.00000	−	3.46410i	−0.0862261	−	0.149348i
$539$		0			0
$540$	−4.50000	+	7.79423i	−0.193649	+	0.335410i
$541$	−8.00000			−0.343947			−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000			−0.343947			−0.171973	+	0.985102i	$0.555014\pi$
$542$	−1.00000	−	1.73205i	−0.0429537	−	0.0743980i
$543$	−6.00000	+	10.3923i	−0.257485	+	0.445976i
$544$	3.00000			0.128624
$545$	6.00000			0.257012
$546$	−18.0000	−	31.1769i	−0.770329	−	1.33425i
$547$	10.0000	−	17.3205i	0.427569	−	0.740571i	−0.569087	−	0.822277i	$-0.692703\pi$
$547$	10.0000	−	17.3205i	0.427569	−	0.740571i	0.996657	+	0.0817056i	$0.0260367\pi$
$548$	−5.50000	+	9.52628i	−0.234948	+	0.406942i
$549$	−24.0000	−	41.5692i	−1.02430	−	1.77413i
$550$		0			0
$551$	−6.00000			−0.255609
$552$	−6.00000	−	10.3923i	−0.255377	−	0.442326i
$553$	−8.00000	−	13.8564i	−0.340195	−	0.589234i
$554$	2.00000	+	3.46410i	0.0849719	+	0.147176i
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$	−0.500000	+	0.866025i	−0.0212047	+	0.0367277i
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	0.491496	+	0.870880i	$0.336450\pi$
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	−0.999952	+	0.00979220i	$0.996883\pi$
$558$	48.0000			2.03200
$559$	3.00000	+	5.19615i	0.126886	+	0.219774i
$560$	2.00000			0.0845154
$561$		0			0
$562$	−13.5000	+	23.3827i	−0.569463	+	0.986339i
$563$	−1.00000			−0.0421450			−0.0210725	−	0.999778i	$-0.506708\pi$
$563$	−1.00000			−0.0421450			−0.0210725	+	0.999778i	$0.506708\pi$
$564$	12.0000	+	20.7846i	0.505291	+	0.875190i
$565$	4.50000	−	7.79423i	0.189316	−	0.327906i
$566$	14.5000	+	25.1147i	0.609480	+	1.05565i
$567$	9.00000	−	15.5885i	0.377964	−	0.654654i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	−20.5000	+	35.5070i	−0.859405	+	1.48853i	0.0130929	+	0.999914i	$0.495832\pi$
$569$	−20.5000	+	35.5070i	−0.859405	+	1.48853i	−0.872498	+	0.488618i	$0.837501\pi$
$570$	−1.50000	+	2.59808i	−0.0628281	+	0.108821i
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	−0.913584	−	0.406651i	$-0.866697\pi$
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	0.808962	+	0.587861i	$0.200030\pi$
$572$		0			0
$573$	12.0000	+	20.7846i	0.501307	+	0.868290i
$574$	10.0000	−	17.3205i	0.417392	−	0.722944i
$575$	2.00000	+	3.46410i	0.0834058	+	0.144463i
$576$	6.00000			0.250000
$577$	19.5000	−	33.7750i	0.811796	−	1.40607i	−0.0998105	−	0.995006i	$-0.531824\pi$
$577$	19.5000	−	33.7750i	0.811796	−	1.40607i	0.911606	−	0.411065i	$-0.134843\pi$
$578$	−8.00000			−0.332756
$579$	−18.0000			−0.748054
$580$	−3.00000	−	5.19615i	−0.124568	−	0.215758i
$581$	24.0000			0.995688
$582$	22.5000	−	38.9711i	0.932655	−	1.61541i
$583$		0			0
$584$	−6.50000	−	11.2583i	−0.268972	−	0.465873i
$585$	18.0000	+	31.1769i	0.744208	+	1.28901i
$586$	−3.00000	−	5.19615i	−0.123929	−	0.214651i
$587$	−17.5000	−	30.3109i	−0.722302	−	1.25106i	−0.960075	−	0.279743i	$-0.909751\pi$
$587$	−17.5000	−	30.3109i	−0.722302	−	1.25106i	0.237773	−	0.971321i	$-0.423583\pi$
$588$	9.00000			0.371154
$589$	8.00000			0.329634
$590$	−4.50000	−	7.79423i	−0.185262	−	0.320883i
$591$	12.0000	−	20.7846i	0.493614	−	0.854965i
$592$	1.00000	−	1.73205i	0.0410997	−	0.0711868i
$593$	3.50000	+	6.06218i	0.143728	+	0.248944i	0.928898	−	0.370337i	$-0.120758\pi$
$593$	3.50000	+	6.06218i	0.143728	+	0.248944i	−0.785170	+	0.619281i	$0.787424\pi$
$594$		0			0
$595$	6.00000			0.245976
$596$	2.00000	−	3.46410i	0.0819232	−	0.141895i
$597$	3.00000	+	5.19615i	0.122782	+	0.212664i
$598$	−24.0000			−0.981433
$599$	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	$-0.0433238\pi$
$600$	−3.00000			−0.122474
$601$	−5.50000	−	9.52628i	−0.224350	−	0.388585i	0.731774	−	0.681547i	$-0.238692\pi$
$601$	−5.50000	−	9.52628i	−0.224350	−	0.388585i	−0.956124	+	0.292962i	$0.905359\pi$
$602$	2.00000			0.0815139
$603$	−48.0000	+	10.3923i	−1.95471	+	0.423207i
$604$	8.00000			0.325515
$605$	−5.50000	−	9.52628i	−0.223607	−	0.387298i
$606$	−30.0000			−1.21867
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	−0.428497	−	0.903543i	$-0.640957\pi$
$607$	14.0000	−	24.2487i	0.568242	−	0.984225i	0.996740	−	0.0806818i	$-0.0257098\pi$
$608$	1.00000			0.0405554
$609$	18.0000	+	31.1769i	0.729397	+	1.26335i
$610$	4.00000	−	6.92820i	0.161955	−	0.280515i
$611$	48.0000			1.94187
$612$	18.0000			0.727607
$613$	17.0000	+	29.4449i	0.686624	+	1.18927i	0.972924	+	0.231127i	$0.0742412\pi$
$613$	17.0000	+	29.4449i	0.686624	+	1.18927i	−0.286300	+	0.958140i	$0.592425\pi$
$614$	12.5000	−	21.6506i	0.504459	−	0.873749i
$615$	−15.0000	+	25.9808i	−0.604858	+	1.04765i
$616$		0			0
$617$	−42.0000			−1.69086			−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000			−1.69086			−0.845428	+	0.534089i	$0.820655\pi$
$618$	−36.0000			−1.44813
$619$	15.5000	+	26.8468i	0.622998	+	1.07906i	0.988924	+	0.148420i	$0.0474187\pi$
$619$	15.5000	+	26.8468i	0.622998	+	1.07906i	−0.365927	+	0.930644i	$0.619248\pi$
$620$	4.00000	+	6.92820i	0.160644	+	0.278243i
$621$	−18.0000	−	31.1769i	−0.722315	−	1.25109i
$622$	−14.0000	−	24.2487i	−0.561349	−	0.972285i
$623$	15.0000	−	25.9808i	0.600962	−	1.04090i
$624$	9.00000	−	15.5885i	0.360288	−	0.624038i
$625$	1.00000			0.0400000
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$		0			0
$628$	10.0000			0.399043
$629$	3.00000	−	5.19615i	0.119618	−	0.207184i
$630$	12.0000			0.478091
$631$	13.0000	+	22.5167i	0.517522	+	0.896374i	0.999793	+	0.0203520i	$0.00647871\pi$
$631$	13.0000	+	22.5167i	0.517522	+	0.896374i	−0.482271	+	0.876022i	$0.660188\pi$
$632$	4.00000	−	6.92820i	0.159111	−	0.275589i
$633$	−1.50000	−	2.59808i	−0.0596196	−	0.103264i
$634$	7.00000	−	12.1244i	0.278006	−	0.481520i
$635$	7.00000	−	12.1244i	0.277787	−	0.481140i
$636$	−3.00000	+	5.19615i	−0.118958	+	0.206041i
$637$	9.00000	−	15.5885i	0.356593	−	0.617637i
$638$		0			0
$639$	−18.0000	+	31.1769i	−0.712069	+	1.23334i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−8.50000	+	14.7224i	−0.335730	+	0.581501i	−0.983625	−	0.180229i	$-0.942316\pi$
$641$	−8.50000	+	14.7224i	−0.335730	+	0.581501i	0.647895	+	0.761730i	$0.275650\pi$
$642$	6.00000	+	10.3923i	0.236801	+	0.410152i
$643$	−3.00000			−0.118308			−0.0591542	−	0.998249i	$-0.518840\pi$
$643$	−3.00000			−0.118308			−0.0591542	+	0.998249i	$0.518840\pi$
$644$	−4.00000	+	6.92820i	−0.157622	+	0.273009i
$645$	−3.00000			−0.118125
$646$	3.00000			0.118033
$647$	−7.00000	−	12.1244i	−0.275198	−	0.476658i	0.694987	−	0.719023i	$-0.255410\pi$
$647$	−7.00000	−	12.1244i	−0.275198	−	0.476658i	−0.970185	+	0.242365i	$0.922077\pi$
$648$	9.00000			0.353553
$649$		0			0
$650$	−3.00000	+	5.19615i	−0.117670	+	0.203810i
$651$	−24.0000	−	41.5692i	−0.940634	−	1.62923i
$652$	10.5000	+	18.1865i	0.411212	+	0.712240i
$653$	−19.0000	−	32.9090i	−0.743527	−	1.28783i	−0.950880	−	0.309561i	$-0.899818\pi$
$653$	−19.0000	−	32.9090i	−0.743527	−	1.28783i	0.207352	−	0.978266i	$-0.433515\pi$
$654$	−9.00000	−	15.5885i	−0.351928	−	0.609557i
$655$	−12.0000			−0.468879
$656$	10.0000			0.390434
$657$	−39.0000	−	67.5500i	−1.52153	−	2.63538i
$658$	8.00000	−	13.8564i	0.311872	−	0.540179i
$659$	8.50000	−	14.7224i	0.331113	−	0.573505i	−0.651617	−	0.758548i	$-0.725909\pi$
$659$	8.50000	−	14.7224i	0.331113	−	0.573505i	0.982730	+	0.185043i	$0.0592425\pi$
$660$		0			0
$661$	−8.00000			−0.311164			−0.155582	−	0.987823i	$-0.549725\pi$
$661$	−8.00000			−0.311164			−0.155582	+	0.987823i	$0.549725\pi$
$662$	5.00000			0.194331
$663$	27.0000	−	46.7654i	1.04859	−	1.81622i
$664$	6.00000	+	10.3923i	0.232845	+	0.403300i
$665$	2.00000			0.0775567
$666$	6.00000	−	10.3923i	0.232495	−	0.402694i
$667$	24.0000			0.929284
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$	54.0000			2.08776
$670$	−5.50000	−	6.06218i	−0.212484	−	0.234202i
$671$		0			0
$672$	−3.00000	−	5.19615i	−0.115728	−	0.200446i
$673$	31.0000			1.19496			0.597481	−	0.801883i	$-0.296168\pi$
$673$	31.0000			1.19496			0.597481	+	0.801883i	$0.296168\pi$
$674$	3.00000	−	5.19615i	0.115556	−	0.200148i
$675$	−9.00000			−0.346410
$676$	−11.5000	−	19.9186i	−0.442308	−	0.766099i
$677$	17.0000	−	29.4449i	0.653363	−	1.13166i	−0.328938	−	0.944351i	$-0.606691\pi$
$677$	17.0000	−	29.4449i	0.653363	−	1.13166i	0.982301	−	0.187307i	$-0.0599758\pi$
$678$	−27.0000			−1.03693
$679$	−30.0000			−1.15129
$680$	1.50000	+	2.59808i	0.0575224	+	0.0996317i
$681$	19.5000	−	33.7750i	0.747242	−	1.29426i
$682$		0			0
$683$	6.50000	+	11.2583i	0.248716	+	0.430788i	0.963170	−	0.268894i	$-0.0866582\pi$
$683$	6.50000	+	11.2583i	0.248716	+	0.430788i	−0.714454	+	0.699682i	$0.753325\pi$
$684$	6.00000			0.229416
$685$	−11.0000			−0.420288
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$		0			0
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$	6.00000	−	10.3923i	0.228416	−	0.395628i
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	−0.729039	−	0.684472i	$-0.760033\pi$
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	0.957290	+	0.289130i	$0.0933661\pi$
$692$	−14.0000			−0.532200
$693$		0			0
$694$	25.0000			0.948987
$695$	−1.00000			−0.0379322
$696$	−9.00000	+	15.5885i	−0.341144	+	0.590879i
$697$	30.0000			1.13633
$698$	10.0000	+	17.3205i	0.378506	+	0.655591i
$699$	37.5000	−	64.9519i	1.41838	−	2.45671i
$700$	1.00000	+	1.73205i	0.0377964	+	0.0654654i
$701$	1.00000	−	1.73205i	0.0377695	−	0.0654187i	−0.846523	−	0.532353i	$-0.821308\pi$
$701$	1.00000	−	1.73205i	0.0377695	−	0.0654187i	0.884292	+	0.466934i	$0.154641\pi$
$702$	27.0000	−	46.7654i	1.01905	−	1.76505i
$703$	1.00000	−	1.73205i	0.0377157	−	0.0653255i
$704$		0			0
$705$	−12.0000	+	20.7846i	−0.451946	+	0.782794i
$706$	−7.00000	+	12.1244i	−0.263448	+	0.456306i
$707$	10.0000	+	17.3205i	0.376089	+	0.651405i
$708$	−13.5000	+	23.3827i	−0.507361	+	0.878775i
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	−0.900978	−	0.433865i	$-0.857149\pi$
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	0.0747503	−	0.997202i	$-0.476184\pi$
$710$	−6.00000			−0.225176
$711$	24.0000	−	41.5692i	0.900070	−	1.55897i
$712$	15.0000			0.562149
$713$	−32.0000			−1.19841
$714$	−9.00000	−	15.5885i	−0.336817	−	0.583383i
$715$		0			0
$716$	10.0000	−	17.3205i	0.373718	−	0.647298i
$717$	−45.0000	+	77.9423i	−1.68056	+	2.91081i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	−25.0000	−	43.3013i	−0.932343	−	1.61486i	−0.779305	−	0.626644i	$-0.784428\pi$
$719$	−25.0000	−	43.3013i	−0.932343	−	1.61486i	−0.153037	−	0.988220i	$-0.548906\pi$
$720$	3.00000	+	5.19615i	0.111803	+	0.193649i
$721$	12.0000	+	20.7846i	0.446903	+	0.774059i
$722$	−18.0000			−0.669891
$723$	−30.0000			−1.11571
$724$	2.00000	+	3.46410i	0.0743294	+	0.128742i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$	−16.5000	+	28.5788i	−0.612372	+	1.06066i
$727$	17.0000	+	29.4449i	0.630495	+	1.09205i	0.987451	+	0.157928i	$0.0504814\pi$
$727$	17.0000	+	29.4449i	0.630495	+	1.09205i	−0.356956	+	0.934121i	$0.616185\pi$
$728$	−12.0000			−0.444750
$729$	−27.0000			−1.00000
$730$	6.50000	−	11.2583i	0.240576	−	0.416689i
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$	−24.0000			−0.887066
$733$	6.00000	−	10.3923i	0.221615	−	0.383849i	−0.733683	−	0.679491i	$-0.762200\pi$
$733$	6.00000	−	10.3923i	0.221615	−	0.383849i	0.955299	+	0.295643i	$0.0955338\pi$
$734$	−26.0000			−0.959678
$735$	4.50000	+	7.79423i	0.165985	+	0.287494i
$736$	−4.00000			−0.147442
$737$		0			0
$738$	60.0000			2.20863
$739$	17.5000	+	30.3109i	0.643748	+	1.11500i	0.984589	+	0.174883i	$0.0559548\pi$
$739$	17.5000	+	30.3109i	0.643748	+	1.11500i	−0.340841	+	0.940121i	$0.610712\pi$
$740$	2.00000			0.0735215
$741$	9.00000	−	15.5885i	0.330623	−	0.572656i
$742$	4.00000			0.146845
$743$	−27.0000	−	46.7654i	−0.990534	−	1.71566i	−0.614145	−	0.789193i	$-0.710499\pi$
$743$	−27.0000	−	46.7654i	−0.990534	−	1.71566i	−0.376389	−	0.926462i	$-0.622834\pi$
$744$	12.0000	−	20.7846i	0.439941	−	0.762001i
$745$	4.00000			0.146549
$746$	30.0000			1.09838
$747$	36.0000	+	62.3538i	1.31717	+	2.28141i
$748$		0			0
$749$	4.00000	−	6.92820i	0.146157	−	0.253151i
$750$	−1.50000	−	2.59808i	−0.0547723	−	0.0948683i
$751$	−30.0000			−1.09472			−0.547358	−	0.836899i	$-0.684366\pi$
$751$	−30.0000			−1.09472			−0.547358	+	0.836899i	$0.684366\pi$
$752$	8.00000			0.291730
$753$	−19.5000	−	33.7750i	−0.710620	−	1.23083i
$754$	18.0000	+	31.1769i	0.655521	+	1.13540i
$755$	4.00000	+	6.92820i	0.145575	+	0.252143i
$756$	−9.00000	−	15.5885i	−0.327327	−	0.566947i
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	−0.993701	−	0.112062i	$-0.964254\pi$
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	0.593899	+	0.804539i	$0.297588\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$		0			0
$760$	0.500000	+	0.866025i	0.0181369	+	0.0314140i
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$	−42.0000			−1.52150
$763$	−6.00000	+	10.3923i	−0.217215	+	0.376227i
$764$	8.00000			0.289430
$765$	9.00000	+	15.5885i	0.325396	+	0.563602i
$766$	−5.00000	+	8.66025i	−0.180657	+	0.312908i
$767$	27.0000	+	46.7654i	0.974913	+	1.68860i
$768$	1.50000	−	2.59808i	0.0541266	−	0.0937500i
$769$	3.50000	−	6.06218i	0.126213	−	0.218608i	−0.795993	−	0.605305i	$-0.793051\pi$
$769$	3.50000	−	6.06218i	0.126213	−	0.218608i	0.922207	+	0.386698i	$0.126384\pi$
$770$		0			0
$771$	−33.0000	+	57.1577i	−1.18847	+	2.05848i
$772$	−3.00000	+	5.19615i	−0.107972	+	0.187014i
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	0.0729331	+	0.997337i	$0.476764\pi$
$773$	−23.0000	+	39.8372i	−0.827253	+	1.43284i	−0.900186	+	0.435507i	$0.856569\pi$
$774$	3.00000	+	5.19615i	0.107833	+	0.186772i
$775$	−4.00000	+	6.92820i	−0.143684	+	0.248868i
$776$	−7.50000	−	12.9904i	−0.269234	−	0.466328i
$777$	−12.0000			−0.430498
$778$	6.00000	−	10.3923i	0.215110	−	0.372582i
$779$	10.0000			0.358287
$780$	18.0000			0.644503
$781$		0			0
$782$	−12.0000			−0.429119
$783$	−27.0000	+	46.7654i	−0.964901	+	1.67126i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$	5.00000	+	8.66025i	0.178458	+	0.309098i
$786$	18.0000	+	31.1769i	0.642039	+	1.11204i
$787$	−26.0000	−	45.0333i	−0.926800	−	1.60526i	−0.788641	−	0.614855i	$-0.789215\pi$
$787$	−26.0000	−	45.0333i	−0.926800	−	1.60526i	−0.138159	−	0.990410i	$-0.544119\pi$
$788$	−4.00000	−	6.92820i	−0.142494	−	0.246807i
$789$	36.0000			1.28163
$790$	8.00000			0.284627
$791$	9.00000	+	15.5885i	0.320003	+	0.554262i
$792$		0			0
$793$	−24.0000	+	41.5692i	−0.852265	+	1.47617i
$794$	6.00000	+	10.3923i	0.212932	+	0.368809i
$795$	−6.00000			−0.212798
$796$	2.00000			0.0708881
$797$	−4.00000	+	6.92820i	−0.141687	+	0.245410i	−0.928132	−	0.372251i	$-0.878586\pi$
$797$	−4.00000	+	6.92820i	−0.141687	+	0.245410i	0.786445	+	0.617661i	$0.211919\pi$
$798$	−3.00000	−	5.19615i	−0.106199	−	0.183942i
$799$	24.0000			0.849059
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	90.0000			3.17999
$802$	19.0000	+	32.9090i	0.670913	+	1.16206i
$803$		0			0
$804$	−7.50000	+	23.3827i	−0.264505	+	0.824644i
$805$	−8.00000			−0.281963
$806$	−24.0000	−	41.5692i	−0.845364	−	1.46421i
$807$	−12.0000			−0.422420
$808$	−5.00000	+	8.66025i	−0.175899	+	0.304667i
$809$	26.0000			0.914111			0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000			0.914111			0.457056	+	0.889438i	$0.348904\pi$
$810$	4.50000	+	7.79423i	0.158114	+	0.273861i
$811$	−28.0000	+	48.4974i	−0.983213	+	1.70297i	−0.333590	+	0.942718i	$0.608260\pi$
$811$	−28.0000	+	48.4974i	−0.983213	+	1.70297i	−0.649623	+	0.760257i	$0.725073\pi$
$812$	12.0000			0.421117
$813$	−6.00000			−0.210429
$814$		0			0
$815$	−10.5000	+	18.1865i	−0.367799	+	0.637046i
$816$	4.50000	−	7.79423i	0.157532	−	0.272853i
$817$	0.500000	+	0.866025i	0.0174928	+	0.0302984i
$818$	−10.0000			−0.349642
$819$	−72.0000			−2.51588
$820$	5.00000	+	8.66025i	0.174608	+	0.302429i
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	0.991616	−	0.129217i	$-0.0412465\pi$
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	−0.607714	+	0.794156i	$0.707913\pi$
$822$	16.5000	+	28.5788i	0.575504	+	0.996801i
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	−6.00000	+	10.3923i	−0.209020	+	0.362033i
$825$		0			0
$826$	18.0000			0.626300
$827$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$827$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$828$	−24.0000			−0.834058
$829$	−46.0000			−1.59765			−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000			−1.59765			−0.798823	+	0.601566i	$0.794544\pi$
$830$	−6.00000	+	10.3923i	−0.208263	+	0.360722i
$831$	12.0000			0.416275
$832$	−3.00000	−	5.19615i	−0.104006	−	0.180144i
$833$	4.50000	−	7.79423i	0.155916	−	0.270054i
$834$	1.50000	+	2.59808i	0.0519408	+	0.0899640i
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$		0			0
$837$	36.0000	−	62.3538i	1.24434	−	2.15526i
$838$	−2.50000	+	4.33013i	−0.0863611	+	0.149582i
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	−0.481927	−	0.876211i	$-0.660063\pi$
$839$	15.0000	−	25.9808i	0.517858	−	0.896956i	0.999785	−	0.0207443i	$-0.00660359\pi$
$840$	3.00000	−	5.19615i	0.103510	−	0.179284i
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	4.00000	−	6.92820i	0.137849	−	0.238762i
$843$	40.5000	+	70.1481i	1.39489	+	2.41603i
$844$	−1.00000			−0.0344214
$845$	11.5000	−	19.9186i	0.395612	−	0.685220i
$846$	48.0000			1.65027
$847$	22.0000			0.755929
$848$	1.00000	+	1.73205i	0.0343401	+	0.0594789i
$849$	87.0000			2.98583
$850$	−1.50000	+	2.59808i	−0.0514496	+	0.0891133i
$851$	−4.00000	+	6.92820i	−0.137118	+	0.237496i
$852$	9.00000	+	15.5885i	0.308335	+	0.534052i
$853$	−13.0000	−	22.5167i	−0.445112	−	0.770956i	0.552948	−	0.833215i	$-0.313503\pi$
$853$	−13.0000	−	22.5167i	−0.445112	−	0.770956i	−0.998060	+	0.0622597i	$0.980169\pi$
$854$	8.00000	+	13.8564i	0.273754	+	0.474156i
$855$	3.00000	+	5.19615i	0.102598	+	0.177705i
$856$	4.00000			0.136717
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$		0			0
$859$	−11.5000	+	19.9186i	−0.392375	+	0.679613i	−0.992762	−	0.120096i	$-0.961680\pi$
$859$	−11.5000	+	19.9186i	−0.392375	+	0.679613i	0.600387	+	0.799709i	$0.295013\pi$
$860$	−0.500000	+	0.866025i	−0.0170499	+	0.0295312i
$861$	−30.0000	−	51.9615i	−1.02240	−	1.77084i
$862$	22.0000			0.749323
$863$	20.0000			0.680808			0.340404	−	0.940279i	$-0.389436\pi$
$863$	20.0000			0.680808			0.340404	+	0.940279i	$0.389436\pi$
$864$	4.50000	−	7.79423i	0.153093	−	0.265165i
$865$	−7.00000	−	12.1244i	−0.238007	−	0.412240i
$866$	35.0000			1.18935
$867$	−12.0000	+	20.7846i	−0.407541	+	0.705882i
$868$	−16.0000			−0.543075
$869$		0			0
$870$	−18.0000			−0.610257
$871$	33.0000	+	36.3731i	1.11816	+	1.23245i
$872$	−6.00000			−0.203186
$873$	−45.0000	−	77.9423i	−1.52302	−	2.63795i
$874$	−4.00000			−0.135302
$875$	−1.00000	+	1.73205i	−0.0338062	+	0.0585540i
$876$	−39.0000			−1.31769
$877$	−10.0000	−	17.3205i	−0.337676	−	0.584872i	0.646319	−	0.763067i	$-0.276307\pi$
$877$	−10.0000	−	17.3205i	−0.337676	−	0.584872i	−0.983995	+	0.178195i	$0.942974\pi$
$878$	−14.0000	+	24.2487i	−0.472477	+	0.818354i
$879$	−18.0000			−0.607125
$880$		0			0
$881$	25.0000	+	43.3013i	0.842271	+	1.45886i	0.887970	+	0.459902i	$0.152115\pi$
$881$	25.0000	+	43.3013i	0.842271	+	1.45886i	−0.0456985	+	0.998955i	$0.514551\pi$
$882$	9.00000	−	15.5885i	0.303046	−	0.524891i
$883$	−10.0000	+	17.3205i	−0.336527	+	0.582882i	−0.983777	−	0.179396i	$-0.942586\pi$
$883$	−10.0000	+	17.3205i	−0.336527	+	0.582882i	0.647250	+	0.762278i	$0.275919\pi$
$884$	−9.00000	−	15.5885i	−0.302703	−	0.524297i
$885$	−27.0000			−0.907595
$886$	−11.0000			−0.369552
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$	−3.00000	−	5.19615i	−0.100673	−	0.174371i
$889$	14.0000	+	24.2487i	0.469545	+	0.813276i
$890$	7.50000	+	12.9904i	0.251401	+	0.435439i
$891$		0			0
$892$	9.00000	−	15.5885i	0.301342	−	0.521940i
$893$	8.00000			0.267710
$894$	−6.00000	−	10.3923i	−0.200670	−	0.347571i
$895$	20.0000			0.668526
$896$	−2.00000			−0.0668153
$897$	−36.0000	+	62.3538i	−1.20201	+	2.08193i
$898$	−38.0000			−1.26808
$899$	24.0000	+	41.5692i	0.800445	+	1.38641i
$900$	−3.00000	+	5.19615i	−0.100000	+	0.173205i
$901$	3.00000	+	5.19615i	0.0999445	+	0.173109i
$902$		0			0
$903$	3.00000	−	5.19615i	0.0998337	−	0.172917i
$904$	−4.50000	+	7.79423i	−0.149668	+	0.259232i
$905$	−2.00000	+	3.46410i	−0.0664822	+	0.115151i
$906$	12.0000	−	20.7846i	0.398673	−	0.690522i
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	−6.50000	−	11.2583i	−0.215710	−	0.373621i
$909$	−30.0000	+	51.9615i	−0.995037	+	1.72345i
$910$	−6.00000	−	10.3923i	−0.198898	−	0.344502i
$911$	−38.0000			−1.25900			−0.629498	−	0.777002i	$-0.716739\pi$
$911$	−38.0000			−1.25900			−0.629498	+	0.777002i	$0.716739\pi$
$912$	1.50000	−	2.59808i	0.0496700	−	0.0860309i
$913$		0			0
$914$	−17.0000			−0.562310
$915$	−12.0000	−	20.7846i	−0.396708	−	0.687118i
$916$		0			0
$917$	12.0000	−	20.7846i	0.396275	−	0.686368i
$918$	13.5000	−	23.3827i	0.445566	−	0.771744i
$919$	5.00000	+	8.66025i	0.164935	+	0.285675i	0.936632	−	0.350315i	$-0.113925\pi$
$919$	5.00000	+	8.66025i	0.164935	+	0.285675i	−0.771697	+	0.635990i	$0.780592\pi$
$920$	−2.00000	−	3.46410i	−0.0659380	−	0.114208i
$921$	−37.5000	−	64.9519i	−1.23567	−	2.14024i
$922$	11.0000	+	19.0526i	0.362266	+	0.627463i
$923$	36.0000			1.18495
$924$		0			0
$925$	1.00000	+	1.73205i	0.0328798	+	0.0569495i
$926$	15.0000	−	25.9808i	0.492931	−	0.853781i
$927$	−36.0000	+	62.3538i	−1.18240	+	2.04797i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	29.0000			0.951459			0.475730	−	0.879592i	$-0.342184\pi$
$929$	29.0000			0.951459			0.475730	+	0.879592i	$0.342184\pi$
$930$	24.0000			0.786991
$931$	1.50000	−	2.59808i	0.0491605	−	0.0851485i
$932$	−12.5000	−	21.6506i	−0.409451	−	0.709190i
$933$	−84.0000			−2.75004
$934$	−18.0000	+	31.1769i	−0.588978	+	1.02014i
$935$		0			0
$936$	−18.0000	−	31.1769i	−0.588348	−	1.01905i
$937$	−30.0000			−0.980057			−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000			−0.980057			−0.490029	+	0.871706i	$0.663014\pi$
$938$	16.0000	−	3.46410i	0.522419	−	0.113107i
$939$	3.00000			0.0979013
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	24.0000			0.782378			0.391189	−	0.920310i	$-0.372064\pi$
$941$	24.0000			0.782378			0.391189	+	0.920310i	$0.372064\pi$
$942$	15.0000	−	25.9808i	0.488726	−	0.846499i
$943$	−40.0000			−1.30258
$944$	4.50000	+	7.79423i	0.146463	+	0.253681i
$945$	9.00000	−	15.5885i	0.292770	−	0.507093i
$946$		0			0
$947$	−15.0000			−0.487435			−0.243717	−	0.969846i	$-0.578367\pi$
$947$	−15.0000			−0.487435			−0.243717	+	0.969846i	$0.578367\pi$
$948$	−12.0000	−	20.7846i	−0.389742	−	0.675053i
$949$	−39.0000	+	67.5500i	−1.26599	+	2.19277i
$950$	−0.500000	+	0.866025i	−0.0162221	+	0.0280976i
$951$	−21.0000	−	36.3731i	−0.680972	−	1.17948i
$952$	−6.00000			−0.194461
$953$	51.0000			1.65205			0.826026	−	0.563632i	$-0.190596\pi$
$953$	51.0000			1.65205			0.826026	+	0.563632i	$0.190596\pi$
$954$	6.00000	+	10.3923i	0.194257	+	0.336463i
$955$	4.00000	+	6.92820i	0.129437	+	0.224191i
$956$	15.0000	+	25.9808i	0.485135	+	0.840278i
$957$		0			0
$958$	−6.00000	+	10.3923i	−0.193851	+	0.335760i
$959$	11.0000	−	19.0526i	0.355209	−	0.615239i
$960$	3.00000			0.0968246
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−12.0000			−0.386896
$963$	24.0000			0.773389
$964$	−5.00000	+	8.66025i	−0.161039	+	0.278928i
$965$	−6.00000			−0.193147
$966$	12.0000	+	20.7846i	0.386094	+	0.668734i
$967$	−13.0000	+	22.5167i	−0.418052	+	0.724087i	−0.995743	−	0.0921681i	$-0.970620\pi$
$967$	−13.0000	+	22.5167i	−0.418052	+	0.724087i	0.577692	+	0.816255i	$0.303954\pi$
$968$	5.50000	+	9.52628i	0.176777	+	0.306186i
$969$	4.50000	−	7.79423i	0.144561	−	0.250387i
$970$	7.50000	−	12.9904i	0.240810	−	0.417096i
$971$	10.5000	−	18.1865i	0.336961	−	0.583634i	−0.646899	−	0.762576i	$-0.723934\pi$
$971$	10.5000	−	18.1865i	0.336961	−	0.583634i	0.983860	+	0.178942i	$0.0572676\pi$
$972$		0			0
$973$	1.00000	−	1.73205i	0.0320585	−	0.0555270i
$974$	−14.0000	+	24.2487i	−0.448589	+	0.776979i
$975$	9.00000	+	15.5885i	0.288231	+	0.499230i
$976$	−4.00000	+	6.92820i	−0.128037	+	0.221766i
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	0.814038	−	0.580812i	$-0.197265\pi$
$977$	−3.00000	−	5.19615i	−0.0959785	−	0.166240i	−0.910017	+	0.414572i	$0.863931\pi$
$978$	63.0000			2.01452
$979$		0			0
$980$	3.00000			0.0958315
$981$	−36.0000			−1.14939
$982$	0.500000	+	0.866025i	0.0159556	+	0.0276360i
$983$	−52.0000			−1.65854			−0.829271	−	0.558846i	$-0.811244\pi$
$983$	−52.0000			−1.65854			−0.829271	+	0.558846i	$0.811244\pi$
$984$	15.0000	−	25.9808i	0.478183	−	0.828236i
$985$	4.00000	−	6.92820i	0.127451	−	0.220751i
$986$	9.00000	+	15.5885i	0.286618	+	0.496438i
$987$	−24.0000	−	41.5692i	−0.763928	−	1.32316i
$988$	−3.00000	−	5.19615i	−0.0954427	−	0.165312i
$989$	−2.00000	−	3.46410i	−0.0635963	−	0.110152i
$990$		0			0
$991$	−58.0000			−1.84243			−0.921215	−	0.389053i	$-0.872802\pi$
$991$	−58.0000			−1.84243			−0.921215	+	0.389053i	$0.872802\pi$
$992$	−4.00000	−	6.92820i	−0.127000	−	0.219971i
$993$	7.50000	−	12.9904i	0.238005	−	0.412237i
$994$	6.00000	−	10.3923i	0.190308	−	0.329624i
$995$	1.00000	+	1.73205i	0.0317021	+	0.0549097i
$996$	36.0000			1.14070
$997$	36.0000			1.14013			0.570066	−	0.821599i	$-0.306918\pi$
$997$	36.0000			1.14013			0.570066	+	0.821599i	$0.306918\pi$
$998$	2.50000	−	4.33013i	0.0791361	−	0.137068i
$999$	−9.00000	−	15.5885i	−0.284747	−	0.493197i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.a.171.1	✓	2	1.1	even	1	trivial
670.2.e.a.431.1	yes	2	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -3.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 2.59808i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +6.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -3.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(1.50000 + 2.59808i) q^{6} +(1.00000 - 1.73205i) q^{7} +1.00000 q^{8} +6.00000 q^{9} +(0.500000 + 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{12} +(-3.00000 - 5.19615i) q^{13} -2.00000 q^{14} +3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-3.00000 - 5.19615i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-3.00000 + 5.19615i) q^{21} +(2.00000 + 3.46410i) q^{23} -3.00000 q^{24} +1.00000 q^{25} +(-3.00000 + 5.19615i) q^{26} -9.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(3.00000 - 5.19615i) q^{29} +(-1.50000 - 2.59808i) q^{30} +(-4.00000 + 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(-1.00000 + 1.73205i) q^{35} +(-3.00000 + 5.19615i) q^{36} +(1.00000 + 1.73205i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(9.00000 + 15.5885i) q^{39} -1.00000 q^{40} +(-5.00000 + 8.66025i) q^{41} +6.00000 q^{42} -1.00000 q^{43} -6.00000 q^{45} +(2.00000 - 3.46410i) q^{46} +(-4.00000 + 6.92820i) q^{47} +(1.50000 + 2.59808i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(4.50000 + 7.79423i) q^{51} +6.00000 q^{52} -2.00000 q^{53} +(4.50000 + 7.79423i) q^{54} +(1.00000 - 1.73205i) q^{56} +(1.50000 + 2.59808i) q^{57} -6.00000 q^{58} -9.00000 q^{59} +(-1.50000 + 2.59808i) q^{60} +(-4.00000 - 6.92820i) q^{61} +8.00000 q^{62} +(6.00000 - 10.3923i) q^{63} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} +(-8.00000 + 1.73205i) q^{67} +3.00000 q^{68} +(-6.00000 - 10.3923i) q^{69} +2.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +6.00000 q^{72} +(-6.50000 - 11.2583i) q^{73} +(1.00000 - 1.73205i) q^{74} -3.00000 q^{75} +1.00000 q^{76} +(9.00000 - 15.5885i) q^{78} +(4.00000 - 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +9.00000 q^{81} +10.0000 q^{82} +(6.00000 + 10.3923i) q^{83} +(-3.00000 - 5.19615i) q^{84} +(1.50000 + 2.59808i) q^{85} +(0.500000 + 0.866025i) q^{86} +(-9.00000 + 15.5885i) q^{87} +15.0000 q^{89} +(3.00000 + 5.19615i) q^{90} -12.0000 q^{91} -4.00000 q^{92} +(12.0000 - 20.7846i) q^{93} +8.00000 q^{94} +(0.500000 + 0.866025i) q^{95} +(1.50000 - 2.59808i) q^{96} +(-7.50000 - 12.9904i) q^{97} +(1.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 6 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + 2 q^{7} + 2 q^{8} + 12 q^{9}+O(q^{10}) \) 2 * q - q^2 - 6 * q^3 - q^4 - 2 * q^5 + 3 * q^6 + 2 * q^7 + 2 * q^8 + 12 * q^9	\( 2 q - q^{2} - 6 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} + 2 q^{7} + 2 q^{8} + 12 q^{9} + q^{10} + 3 q^{12} - 6 q^{13} - 4 q^{14} + 6 q^{15} - q^{16} - 3 q^{17} - 6 q^{18} - q^{19} + q^{20} - 6 q^{21} + 4 q^{23} - 6 q^{24} + 2 q^{25} - 6 q^{26} - 18 q^{27} + 2 q^{28} + 6 q^{29} - 3 q^{30} - 8 q^{31} - q^{32} - 3 q^{34} - 2 q^{35} - 6 q^{36} + 2 q^{37} - q^{38} + 18 q^{39} - 2 q^{40} - 10 q^{41} + 12 q^{42} - 2 q^{43} - 12 q^{45} + 4 q^{46} - 8 q^{47} + 3 q^{48} + 3 q^{49} - q^{50} + 9 q^{51} + 12 q^{52} - 4 q^{53} + 9 q^{54} + 2 q^{56} + 3 q^{57} - 12 q^{58} - 18 q^{59} - 3 q^{60} - 8 q^{61} + 16 q^{62} + 12 q^{63} + 2 q^{64} + 6 q^{65} - 16 q^{67} + 6 q^{68} - 12 q^{69} + 4 q^{70} - 6 q^{71} + 12 q^{72} - 13 q^{73} + 2 q^{74} - 6 q^{75} + 2 q^{76} + 18 q^{78} + 8 q^{79} + q^{80} + 18 q^{81} + 20 q^{82} + 12 q^{83} - 6 q^{84} + 3 q^{85} + q^{86} - 18 q^{87} + 30 q^{89} + 6 q^{90} - 24 q^{91} - 8 q^{92} + 24 q^{93} + 16 q^{94} + q^{95} + 3 q^{96} - 15 q^{97} + 3 q^{98}+O(q^{100}) \) 2 * q - q^2 - 6 * q^3 - q^4 - 2 * q^5 + 3 * q^6 + 2 * q^7 + 2 * q^8 + 12 * q^9 + q^10 + 3 * q^12 - 6 * q^13 - 4 * q^14 + 6 * q^15 - q^16 - 3 * q^17 - 6 * q^18 - q^19 + q^20 - 6 * q^21 + 4 * q^23 - 6 * q^24 + 2 * q^25 - 6 * q^26 - 18 * q^27 + 2 * q^28 + 6 * q^29 - 3 * q^30 - 8 * q^31 - q^32 - 3 * q^34 - 2 * q^35 - 6 * q^36 + 2 * q^37 - q^38 + 18 * q^39 - 2 * q^40 - 10 * q^41 + 12 * q^42 - 2 * q^43 - 12 * q^45 + 4 * q^46 - 8 * q^47 + 3 * q^48 + 3 * q^49 - q^50 + 9 * q^51 + 12 * q^52 - 4 * q^53 + 9 * q^54 + 2 * q^56 + 3 * q^57 - 12 * q^58 - 18 * q^59 - 3 * q^60 - 8 * q^61 + 16 * q^62 + 12 * q^63 + 2 * q^64 + 6 * q^65 - 16 * q^67 + 6 * q^68 - 12 * q^69 + 4 * q^70 - 6 * q^71 + 12 * q^72 - 13 * q^73 + 2 * q^74 - 6 * q^75 + 2 * q^76 + 18 * q^78 + 8 * q^79 + q^80 + 18 * q^81 + 20 * q^82 + 12 * q^83 - 6 * q^84 + 3 * q^85 + q^86 - 18 * q^87 + 30 * q^89 + 6 * q^90 - 24 * q^91 - 8 * q^92 + 24 * q^93 + 16 * q^94 + q^95 + 3 * q^96 - 15 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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