LMFDB - Embedded newform 1110.2.i.e.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.i (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1110.121
Dual form			1110.2.i.e.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -2.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(2.50000 + 4.33013i) q^{13} +3.00000 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.50000 + 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.50000 + 2.59808i) q^{21} +(-1.00000 + 1.73205i) q^{22} -8.00000 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{26} -1.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +1.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +8.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(1.00000 + 1.73205i) q^{34} +(1.50000 - 2.59808i) q^{35} +1.00000 q^{36} +(-0.500000 - 6.06218i) q^{37} +5.00000 q^{38} +(-2.50000 + 4.33013i) q^{39} +(0.500000 + 0.866025i) q^{40} +(4.00000 + 6.92820i) q^{41} +(1.50000 + 2.59808i) q^{42} +(1.00000 + 1.73205i) q^{44} +1.00000 q^{45} +(-4.00000 + 6.92820i) q^{46} +6.00000 q^{47} -1.00000 q^{48} +(-1.00000 + 1.73205i) q^{49} +(0.500000 + 0.866025i) q^{50} -2.00000 q^{51} +(2.50000 - 4.33013i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-1.50000 - 2.59808i) q^{56} +(-2.50000 + 4.33013i) q^{57} +(0.500000 - 0.866025i) q^{58} +(4.00000 - 6.92820i) q^{59} -1.00000 q^{60} +(5.00000 + 8.66025i) q^{61} +(4.00000 - 6.92820i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(2.50000 - 4.33013i) q^{65} -2.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +2.00000 q^{68} +(-4.00000 - 6.92820i) q^{69} +(-1.50000 - 2.59808i) q^{70} +(0.500000 + 0.866025i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-5.50000 - 2.59808i) q^{74} -1.00000 q^{75} +(2.50000 - 4.33013i) q^{76} +(-3.00000 - 5.19615i) q^{77} +(2.50000 + 4.33013i) q^{78} +(-2.00000 - 3.46410i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +8.00000 q^{82} +(0.500000 - 0.866025i) q^{83} +3.00000 q^{84} +2.00000 q^{85} +(0.500000 + 0.866025i) q^{87} +2.00000 q^{88} +(4.00000 - 6.92820i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-7.50000 + 12.9904i) q^{91} +(4.00000 + 6.92820i) q^{92} +(4.00000 + 6.92820i) q^{93} +(3.00000 - 5.19615i) q^{94} +(2.50000 - 4.33013i) q^{95} +(-0.500000 + 0.866025i) q^{96} -8.00000 q^{97} +(1.00000 + 1.73205i) q^{98} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 4 q^{11} + q^{12} + 5 q^{13} + 6 q^{14} + q^{15} - q^{16} - 2 q^{17} + q^{18} + 5 q^{19} - q^{20} - 3 q^{21} - 2 q^{22} - 16 q^{23} - q^{24} - q^{25} + 10 q^{26} - 2 q^{27} + 3 q^{28} + 2 q^{29} - q^{30} + 16 q^{31} + q^{32} - 2 q^{33} + 2 q^{34} + 3 q^{35} + 2 q^{36} - q^{37} + 10 q^{38} - 5 q^{39} + q^{40} + 8 q^{41} + 3 q^{42} + 2 q^{44} + 2 q^{45} - 8 q^{46} + 12 q^{47} - 2 q^{48} - 2 q^{49} + q^{50} - 4 q^{51} + 5 q^{52} - 12 q^{53} - q^{54} + 2 q^{55} - 3 q^{56} - 5 q^{57} + q^{58} + 8 q^{59} - 2 q^{60} + 10 q^{61} + 8 q^{62} - 6 q^{63} + 2 q^{64} + 5 q^{65} - 4 q^{66} - 2 q^{67} + 4 q^{68} - 8 q^{69} - 3 q^{70} + q^{71} + q^{72} - 11 q^{74} - 2 q^{75} + 5 q^{76} - 6 q^{77} + 5 q^{78} - 4 q^{79} + 2 q^{80} - q^{81} + 16 q^{82} + q^{83} + 6 q^{84} + 4 q^{85} + q^{87} + 4 q^{88} + 8 q^{89} + q^{90} - 15 q^{91} + 8 q^{92} + 8 q^{93} + 6 q^{94} + 5 q^{95} - q^{96} - 16 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 - q^9 - 2 * q^10 - 4 * q^11 + q^12 + 5 * q^13 + 6 * q^14 + q^15 - q^16 - 2 * q^17 + q^18 + 5 * q^19 - q^20 - 3 * q^21 - 2 * q^22 - 16 * q^23 - q^24 - q^25 + 10 * q^26 - 2 * q^27 + 3 * q^28 + 2 * q^29 - q^30 + 16 * q^31 + q^32 - 2 * q^33 + 2 * q^34 + 3 * q^35 + 2 * q^36 - q^37 + 10 * q^38 - 5 * q^39 + q^40 + 8 * q^41 + 3 * q^42 + 2 * q^44 + 2 * q^45 - 8 * q^46 + 12 * q^47 - 2 * q^48 - 2 * q^49 + q^50 - 4 * q^51 + 5 * q^52 - 12 * q^53 - q^54 + 2 * q^55 - 3 * q^56 - 5 * q^57 + q^58 + 8 * q^59 - 2 * q^60 + 10 * q^61 + 8 * q^62 - 6 * q^63 + 2 * q^64 + 5 * q^65 - 4 * q^66 - 2 * q^67 + 4 * q^68 - 8 * q^69 - 3 * q^70 + q^71 + q^72 - 11 * q^74 - 2 * q^75 + 5 * q^76 - 6 * q^77 + 5 * q^78 - 4 * q^79 + 2 * q^80 - q^81 + 16 * q^82 + q^83 + 6 * q^84 + 4 * q^85 + q^87 + 4 * q^88 + 8 * q^89 + q^90 - 15 * q^91 + 8 * q^92 + 8 * q^93 + 6 * q^94 + 5 * q^95 - q^96 - 16 * q^97 + 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	1.00000			0.408248
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	0.996866	+	0.0791130i	$0.0252088\pi$
$7$	1.50000	+	2.59808i	0.566947	+	0.981981i	−0.429919	+	0.902867i	$0.641458\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000			−0.316228
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$	3.00000			0.801784
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−1.50000	+	2.59808i	−0.327327	+	0.566947i
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	−8.00000			−1.66812			−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	5.00000			0.980581
$27$	−1.00000			−0.192450
$28$	1.50000	−	2.59808i	0.283473	−	0.490990i
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$	1.00000			0.166667
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$38$	5.00000			0.811107
$39$	−2.50000	+	4.33013i	−0.400320	+	0.693375i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	4.00000	+	6.92820i	0.624695	+	1.08200i	0.988600	+	0.150567i	$0.0481100\pi$
$41$	4.00000	+	6.92820i	0.624695	+	1.08200i	−0.363905	+	0.931436i	$0.618557\pi$
$42$	1.50000	+	2.59808i	0.231455	+	0.400892i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$	1.00000			0.149071
$46$	−4.00000	+	6.92820i	−0.589768	+	1.02151i
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$	−1.00000			−0.144338
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−2.00000			−0.280056
$52$	2.50000	−	4.33013i	0.346688	−	0.600481i
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$	−2.50000	+	4.33013i	−0.331133	+	0.573539i
$58$	0.500000	−	0.866025i	0.0656532	−	0.113715i
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$	−1.00000			−0.129099
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	4.00000	−	6.92820i	0.508001	−	0.879883i
$63$	−3.00000			−0.377964
$64$	1.00000			0.125000
$65$	2.50000	−	4.33013i	0.310087	−	0.537086i
$66$	−2.00000			−0.246183
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	2.00000			0.242536
$69$	−4.00000	−	6.92820i	−0.481543	−	0.834058i
$70$	−1.50000	−	2.59808i	−0.179284	−	0.310530i
$71$	0.500000	+	0.866025i	0.0593391	+	0.102778i	0.894169	−	0.447730i	$-0.147767\pi$
$71$	0.500000	+	0.866025i	0.0593391	+	0.102778i	−0.834830	+	0.550508i	$0.814434\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−5.50000	−	2.59808i	−0.639362	−	0.302020i
$75$	−1.00000			−0.115470
$76$	2.50000	−	4.33013i	0.286770	−	0.496700i
$77$	−3.00000	−	5.19615i	−0.341882	−	0.592157i
$78$	2.50000	+	4.33013i	0.283069	+	0.490290i
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$	1.00000			0.111803
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	8.00000			0.883452
$83$	0.500000	−	0.866025i	0.0548821	−	0.0950586i	−0.837279	−	0.546776i	$-0.815855\pi$
$83$	0.500000	−	0.866025i	0.0548821	−	0.0950586i	0.892161	+	0.451717i	$0.149188\pi$
$84$	3.00000			0.327327
$85$	2.00000			0.216930
$86$		0			0
$87$	0.500000	+	0.866025i	0.0536056	+	0.0928477i
$88$	2.00000			0.213201
$89$	4.00000	−	6.92820i	0.423999	−	0.734388i	−0.572327	−	0.820025i	$-0.693959\pi$
$89$	4.00000	−	6.92820i	0.423999	−	0.734388i	0.996326	+	0.0856373i	$0.0272926\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	−7.50000	+	12.9904i	−0.786214	+	1.36176i
$92$	4.00000	+	6.92820i	0.417029	+	0.722315i
$93$	4.00000	+	6.92820i	0.414781	+	0.718421i
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$	2.50000	−	4.33013i	0.256495	−	0.444262i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$	1.00000	+	1.73205i	0.101015	+	0.174964i
$99$	1.00000	−	1.73205i	0.100504	−	0.174078i
$100$	1.00000			0.100000
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$	−1.00000	+	1.73205i	−0.0990148	+	0.171499i
$103$	5.00000			0.492665			0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000			0.492665			0.246332	+	0.969185i	$0.420775\pi$
$104$	−2.50000	−	4.33013i	−0.245145	−	0.424604i
$105$	3.00000			0.292770
$106$	6.00000	+	10.3923i	0.582772	+	1.00939i
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	2.00000			0.190693
$111$	5.00000	−	3.46410i	0.474579	−	0.328798i
$112$	−3.00000			−0.283473
$113$	−9.50000	+	16.4545i	−0.893685	+	1.54791i	−0.0582609	+	0.998301i	$0.518556\pi$
$113$	−9.50000	+	16.4545i	−0.893685	+	1.54791i	−0.835424	+	0.549606i	$0.814778\pi$
$114$	2.50000	+	4.33013i	0.234146	+	0.405554i
$115$	4.00000	+	6.92820i	0.373002	+	0.646058i
$116$	−0.500000	−	0.866025i	−0.0464238	−	0.0804084i
$117$	−5.00000			−0.462250
$118$	−4.00000	−	6.92820i	−0.368230	−	0.637793i
$119$	−6.00000			−0.550019
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	−7.00000			−0.636364
$122$	10.0000			0.905357
$123$	−4.00000	+	6.92820i	−0.360668	+	0.624695i
$124$	−4.00000	−	6.92820i	−0.359211	−	0.622171i
$125$	1.00000			0.0894427
$126$	−1.50000	+	2.59808i	−0.133631	+	0.231455i
$127$	2.50000	−	4.33013i	0.221839	−	0.384237i	−0.733527	−	0.679660i	$-0.762127\pi$
$127$	2.50000	−	4.33013i	0.221839	−	0.384237i	0.955366	+	0.295423i	$0.0954607\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.50000	−	4.33013i	−0.219265	−	0.379777i
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$	−1.00000	+	1.73205i	−0.0870388	+	0.150756i
$133$	−7.50000	+	12.9904i	−0.650332	+	1.12641i
$134$	−2.00000			−0.172774
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	5.00000			0.427179			0.213589	−	0.976924i	$-0.431485\pi$
$137$	5.00000			0.427179			0.213589	+	0.976924i	$0.431485\pi$
$138$	−8.00000			−0.681005
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	−0.491033	−	0.871141i	$-0.663381\pi$
$139$	6.00000	−	10.3923i	0.508913	−	0.881464i	0.999947	−	0.0103230i	$-0.00328598\pi$
$140$	−3.00000			−0.253546
$141$	3.00000	+	5.19615i	0.252646	+	0.437595i
$142$	1.00000			0.0839181
$143$	−5.00000	−	8.66025i	−0.418121	−	0.724207i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.500000	−	0.866025i	−0.0415227	−	0.0719195i
$146$		0			0
$147$	−2.00000			−0.164957
$148$	−5.00000	+	3.46410i	−0.410997	+	0.284747i
$149$	−15.0000			−1.22885			−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000			−1.22885			−0.614424	+	0.788976i	$0.710612\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	−0.994540	+	0.104357i	$0.966722\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$	−1.00000	−	1.73205i	−0.0808452	−	0.140028i
$154$	−6.00000			−0.483494
$155$	−4.00000	−	6.92820i	−0.321288	−	0.556487i
$156$	5.00000			0.400320
$157$	−6.50000	+	11.2583i	−0.518756	+	0.898513i	0.481006	+	0.876717i	$0.340272\pi$
$157$	−6.50000	+	11.2583i	−0.518756	+	0.898513i	−0.999762	+	0.0217953i	$0.993062\pi$
$158$	−4.00000			−0.318223
$159$	−12.0000			−0.951662
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−12.0000	−	20.7846i	−0.945732	−	1.63806i
$162$	−1.00000			−0.0785674
$163$	9.00000	−	15.5885i	0.704934	−	1.22098i	−0.261781	−	0.965127i	$-0.584310\pi$
$163$	9.00000	−	15.5885i	0.704934	−	1.22098i	0.966715	−	0.255855i	$-0.0823569\pi$
$164$	4.00000	−	6.92820i	0.312348	−	0.541002i
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$	−0.500000	−	0.866025i	−0.0388075	−	0.0672166i
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	0.824737	−	0.565516i	$-0.191323\pi$
$167$	−1.00000	−	1.73205i	−0.0773823	−	0.134030i	−0.902120	+	0.431486i	$0.857990\pi$
$168$	1.50000	−	2.59808i	0.115728	−	0.200446i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	1.00000	−	1.73205i	0.0766965	−	0.132842i
$171$	−5.00000			−0.382360
$172$		0			0
$173$	10.0000	−	17.3205i	0.760286	−	1.31685i	−0.182417	−	0.983221i	$-0.558392\pi$
$173$	10.0000	−	17.3205i	0.760286	−	1.31685i	0.942703	−	0.333633i	$-0.108275\pi$
$174$	1.00000			0.0758098
$175$	−3.00000			−0.226779
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$	8.00000			0.601317
$178$	−4.00000	−	6.92820i	−0.299813	−	0.519291i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	11.0000	+	19.0526i	0.817624	+	1.41617i	0.907429	+	0.420206i	$0.138042\pi$
$181$	11.0000	+	19.0526i	0.817624	+	1.41617i	−0.0898051	+	0.995959i	$0.528624\pi$
$182$	7.50000	+	12.9904i	0.555937	+	0.962911i
$183$	−5.00000	+	8.66025i	−0.369611	+	0.640184i
$184$	8.00000			0.589768
$185$	−5.00000	+	3.46410i	−0.367607	+	0.254686i
$186$	8.00000			0.586588
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$	−3.00000	−	5.19615i	−0.218797	−	0.378968i
$189$	−1.50000	−	2.59808i	−0.109109	−	0.188982i
$190$	−2.50000	−	4.33013i	−0.181369	−	0.314140i
$191$	−4.00000			−0.289430			−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000			−0.289430			−0.144715	+	0.989473i	$0.546227\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−4.00000			−0.287926			−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000			−0.287926			−0.143963	+	0.989583i	$0.545985\pi$
$194$	−4.00000	+	6.92820i	−0.287183	+	0.497416i
$195$	5.00000			0.358057
$196$	2.00000			0.142857
$197$	10.0000	−	17.3205i	0.712470	−	1.23404i	−0.251457	−	0.967869i	$-0.580910\pi$
$197$	10.0000	−	17.3205i	0.712470	−	1.23404i	0.963927	−	0.266167i	$-0.0857571\pi$
$198$	−1.00000	−	1.73205i	−0.0710669	−	0.123091i
$199$	−2.00000			−0.141776			−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000			−0.141776			−0.0708881	+	0.997484i	$0.522583\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	−3.00000	+	5.19615i	−0.211079	+	0.365600i
$203$	1.50000	+	2.59808i	0.105279	+	0.182349i
$204$	1.00000	+	1.73205i	0.0700140	+	0.121268i
$205$	4.00000	−	6.92820i	0.279372	−	0.483887i
$206$	2.50000	−	4.33013i	0.174183	−	0.301694i
$207$	4.00000	−	6.92820i	0.278019	−	0.481543i
$208$	−5.00000			−0.346688
$209$	−5.00000	−	8.66025i	−0.345857	−	0.599042i
$210$	1.50000	−	2.59808i	0.103510	−	0.179284i
$211$	−25.0000			−1.72107			−0.860535	−	0.509390i	$-0.829871\pi$
$211$	−25.0000			−1.72107			−0.860535	+	0.509390i	$0.829871\pi$
$212$	12.0000			0.824163
$213$	−0.500000	+	0.866025i	−0.0342594	+	0.0593391i
$214$	4.00000			0.273434
$215$		0			0
$216$	1.00000			0.0680414
$217$	12.0000	+	20.7846i	0.814613	+	1.41095i
$218$	−5.00000	−	8.66025i	−0.338643	−	0.586546i
$219$		0			0
$220$	1.00000	−	1.73205i	0.0674200	−	0.116775i
$221$	−10.0000			−0.672673
$222$	−0.500000	−	6.06218i	−0.0335578	−	0.406867i
$223$	−12.0000			−0.803579			−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000			−0.803579			−0.401790	+	0.915732i	$0.631612\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	9.50000	+	16.4545i	0.631931	+	1.09454i
$227$	3.50000	+	6.06218i	0.232303	+	0.402361i	0.958485	−	0.285141i	$-0.0920405\pi$
$227$	3.50000	+	6.06218i	0.232303	+	0.402361i	−0.726182	+	0.687502i	$0.758707\pi$
$228$	5.00000			0.331133
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	−0.980401	−	0.197013i	$-0.936876\pi$
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	0.319582	−	0.947559i	$-0.396457\pi$
$230$	8.00000			0.527504
$231$	3.00000	−	5.19615i	0.197386	−	0.341882i
$232$	−1.00000			−0.0656532
$233$	13.0000			0.851658			0.425829	−	0.904804i	$-0.359982\pi$
$233$	13.0000			0.851658			0.425829	+	0.904804i	$0.359982\pi$
$234$	−2.50000	+	4.33013i	−0.163430	+	0.283069i
$235$	−3.00000	−	5.19615i	−0.195698	−	0.338960i
$236$	−8.00000			−0.520756
$237$	2.00000	−	3.46410i	0.129914	−	0.225018i
$238$	−3.00000	+	5.19615i	−0.194461	+	0.336817i
$239$	6.50000	−	11.2583i	0.420450	−	0.728241i	−0.575533	−	0.817778i	$-0.695206\pi$
$239$	6.50000	−	11.2583i	0.420450	−	0.728241i	0.995983	+	0.0895374i	$0.0285389\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	0.998443	−	0.0557856i	$-0.0177663\pi$
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	−0.547533	+	0.836784i	$0.684433\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	5.00000	−	8.66025i	0.320092	−	0.554416i
$245$	2.00000			0.127775
$246$	4.00000	+	6.92820i	0.255031	+	0.441726i
$247$	−12.5000	+	21.6506i	−0.795356	+	1.37760i
$248$	−8.00000			−0.508001
$249$	1.00000			0.0633724
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$	1.50000	+	2.59808i	0.0944911	+	0.163663i
$253$	16.0000			1.00591
$254$	−2.50000	−	4.33013i	−0.156864	−	0.271696i
$255$	1.00000	+	1.73205i	0.0626224	+	0.108465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.50000	−	11.2583i	0.405459	−	0.702275i	−0.588916	−	0.808194i	$-0.700445\pi$
$257$	6.50000	−	11.2583i	0.405459	−	0.702275i	0.994375	+	0.105919i	$0.0337784\pi$
$258$		0			0
$259$	15.0000	−	10.3923i	0.932055	−	0.645746i
$260$	−5.00000			−0.310087
$261$	−0.500000	+	0.866025i	−0.0309492	+	0.0536056i
$262$	−9.00000	−	15.5885i	−0.556022	−	0.963058i
$263$	2.00000	+	3.46410i	0.123325	+	0.213606i	0.921077	−	0.389380i	$-0.127311\pi$
$263$	2.00000	+	3.46410i	0.123325	+	0.213606i	−0.797752	+	0.602986i	$0.793977\pi$
$264$	1.00000	+	1.73205i	0.0615457	+	0.106600i
$265$	12.0000			0.737154
$266$	7.50000	+	12.9904i	0.459855	+	0.796491i
$267$	8.00000			0.489592
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	7.00000			0.426798			0.213399	−	0.976965i	$-0.431547\pi$
$269$	7.00000			0.426798			0.213399	+	0.976965i	$0.431547\pi$
$270$	1.00000			0.0608581
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	−1.00000	−	1.73205i	−0.0606339	−	0.105021i
$273$	−15.0000			−0.907841
$274$	2.50000	−	4.33013i	0.151031	−	0.261593i
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$	−4.00000	+	6.92820i	−0.240772	+	0.417029i
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	0.850613	−	0.525792i	$-0.176231\pi$
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	−0.880656	+	0.473757i	$0.842897\pi$
$278$	−6.00000	−	10.3923i	−0.359856	−	0.623289i
$279$	−4.00000	+	6.92820i	−0.239474	+	0.414781i
$280$	−1.50000	+	2.59808i	−0.0896421	+	0.155265i
$281$	13.0000	−	22.5167i	0.775515	−	1.34323i	−0.158990	−	0.987280i	$-0.550824\pi$
$281$	13.0000	−	22.5167i	0.775515	−	1.34323i	0.934505	−	0.355951i	$-0.115843\pi$
$282$	6.00000			0.357295
$283$	9.00000	+	15.5885i	0.534994	+	0.926638i	0.999164	+	0.0408910i	$0.0130196\pi$
$283$	9.00000	+	15.5885i	0.534994	+	0.926638i	−0.464169	+	0.885747i	$0.653647\pi$
$284$	0.500000	−	0.866025i	0.0296695	−	0.0513892i
$285$	5.00000			0.296174
$286$	−10.0000			−0.591312
$287$	−12.0000	+	20.7846i	−0.708338	+	1.22688i
$288$	−1.00000			−0.0589256
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−1.00000			−0.0587220
$291$	−4.00000	−	6.92820i	−0.234484	−	0.406138i
$292$		0			0
$293$	12.0000	+	20.7846i	0.701047	+	1.21425i	0.968099	+	0.250568i	$0.0806172\pi$
$293$	12.0000	+	20.7846i	0.701047	+	1.21425i	−0.267052	+	0.963682i	$0.586049\pi$
$294$	−1.00000	+	1.73205i	−0.0583212	+	0.101015i
$295$	−8.00000			−0.465778
$296$	0.500000	+	6.06218i	0.0290619	+	0.352357i
$297$	2.00000			0.116052
$298$	−7.50000	+	12.9904i	−0.434463	+	0.752513i
$299$	−20.0000	−	34.6410i	−1.15663	−	2.00334i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$		0			0
$302$	−10.0000			−0.575435
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$	−5.00000			−0.286770
$305$	5.00000	−	8.66025i	0.286299	−	0.495885i
$306$	−2.00000			−0.114332
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$	−3.00000	+	5.19615i	−0.170941	+	0.296078i
$309$	2.50000	+	4.33013i	0.142220	+	0.246332i
$310$	−8.00000			−0.454369
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	2.50000	−	4.33013i	0.141535	−	0.245145i
$313$	−16.0000	+	27.7128i	−0.904373	+	1.56642i	−0.0826174	+	0.996581i	$0.526328\pi$
$313$	−16.0000	+	27.7128i	−0.904373	+	1.56642i	−0.821756	+	0.569839i	$0.807005\pi$
$314$	6.50000	+	11.2583i	0.366816	+	0.635344i
$315$	1.50000	+	2.59808i	0.0845154	+	0.146385i
$316$	−2.00000	+	3.46410i	−0.112509	+	0.194871i
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	−0.302777	−	0.953062i	$-0.597914\pi$
$317$	12.0000	−	20.7846i	0.673987	−	1.16738i	0.976764	−	0.214318i	$-0.0687530\pi$
$318$	−6.00000	+	10.3923i	−0.336463	+	0.582772i
$319$	−2.00000			−0.111979
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−2.00000	+	3.46410i	−0.111629	+	0.193347i
$322$	−24.0000			−1.33747
$323$	−10.0000			−0.556415
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−5.00000			−0.277350
$326$	−9.00000	−	15.5885i	−0.498464	−	0.863365i
$327$	10.0000			0.553001
$328$	−4.00000	−	6.92820i	−0.220863	−	0.382546i
$329$	9.00000	+	15.5885i	0.496186	+	0.859419i
$330$	1.00000	+	1.73205i	0.0550482	+	0.0953463i
$331$	−7.50000	+	12.9904i	−0.412237	+	0.714016i	−0.995134	−	0.0985303i	$-0.968586\pi$
$331$	−7.50000	+	12.9904i	−0.412237	+	0.714016i	0.582897	+	0.812546i	$0.301919\pi$
$332$	−1.00000			−0.0548821
$333$	5.50000	+	2.59808i	0.301398	+	0.142374i
$334$	−2.00000			−0.109435
$335$	−1.00000	+	1.73205i	−0.0546358	+	0.0946320i
$336$	−1.50000	−	2.59808i	−0.0818317	−	0.141737i
$337$	−13.0000	−	22.5167i	−0.708155	−	1.22656i	−0.965541	−	0.260252i	$-0.916194\pi$
$337$	−13.0000	−	22.5167i	−0.708155	−	1.22656i	0.257386	−	0.966309i	$-0.417139\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	−19.0000			−1.03194
$340$	−1.00000	−	1.73205i	−0.0542326	−	0.0939336i
$341$	−16.0000			−0.866449
$342$	−2.50000	+	4.33013i	−0.135185	+	0.234146i
$343$	15.0000			0.809924
$344$		0			0
$345$	−4.00000	+	6.92820i	−0.215353	+	0.373002i
$346$	−10.0000	−	17.3205i	−0.537603	−	0.931156i
$347$	−33.0000			−1.77153			−0.885766	−	0.464131i	$-0.846367\pi$
$347$	−33.0000			−1.77153			−0.885766	+	0.464131i	$0.846367\pi$
$348$	0.500000	−	0.866025i	0.0268028	−	0.0464238i
$349$	2.00000	−	3.46410i	0.107058	−	0.185429i	−0.807519	−	0.589841i	$-0.799190\pi$
$349$	2.00000	−	3.46410i	0.107058	−	0.185429i	0.914577	+	0.404412i	$0.132524\pi$
$350$	−1.50000	+	2.59808i	−0.0801784	+	0.138873i
$351$	−2.50000	−	4.33013i	−0.133440	−	0.231125i
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	−14.5000	+	25.1147i	−0.771757	+	1.33672i	0.164842	+	0.986320i	$0.447289\pi$
$353$	−14.5000	+	25.1147i	−0.771757	+	1.33672i	−0.936599	+	0.350403i	$0.886045\pi$
$354$	4.00000	−	6.92820i	0.212598	−	0.368230i
$355$	0.500000	−	0.866025i	0.0265372	−	0.0459639i
$356$	−8.00000			−0.423999
$357$	−3.00000	−	5.19615i	−0.158777	−	0.275010i
$358$		0			0
$359$	7.00000			0.369446			0.184723	−	0.982791i	$-0.440861\pi$
$359$	7.00000			0.369446			0.184723	+	0.982791i	$0.440861\pi$
$360$	−1.00000			−0.0527046
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	22.0000			1.15629
$363$	−3.50000	−	6.06218i	−0.183702	−	0.318182i
$364$	15.0000			0.786214
$365$		0			0
$366$	5.00000	+	8.66025i	0.261354	+	0.452679i
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	−0.992776	−	0.119982i	$-0.961716\pi$
$367$	−11.5000	−	19.9186i	−0.600295	−	1.03974i	0.392481	−	0.919760i	$-0.371617\pi$
$368$	4.00000	−	6.92820i	0.208514	−	0.361158i
$369$	−8.00000			−0.416463
$370$	0.500000	+	6.06218i	0.0259938	+	0.315158i
$371$	−36.0000			−1.86903
$372$	4.00000	−	6.92820i	0.207390	−	0.359211i
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	0.647225	−	0.762299i	$-0.275929\pi$
$373$	−6.50000	−	11.2583i	−0.336557	−	0.582934i	−0.983783	+	0.179364i	$0.942596\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	−6.00000			−0.309426
$377$	2.50000	+	4.33013i	0.128757	+	0.223013i
$378$	−3.00000			−0.154303
$379$	14.5000	−	25.1147i	0.744815	−	1.29006i	−0.205466	−	0.978664i	$-0.565871\pi$
$379$	14.5000	−	25.1147i	0.744815	−	1.29006i	0.950281	−	0.311393i	$-0.100796\pi$
$380$	−5.00000			−0.256495
$381$	5.00000			0.256158
$382$	−2.00000	+	3.46410i	−0.102329	+	0.177239i
$383$	13.0000	+	22.5167i	0.664269	+	1.15055i	0.979483	+	0.201527i	$0.0645904\pi$
$383$	13.0000	+	22.5167i	0.664269	+	1.15055i	−0.315214	+	0.949021i	$0.602076\pi$
$384$	1.00000			0.0510310
$385$	−3.00000	+	5.19615i	−0.152894	+	0.264820i
$386$	−2.00000	+	3.46410i	−0.101797	+	0.176318i
$387$		0			0
$388$	4.00000	+	6.92820i	0.203069	+	0.351726i
$389$	9.50000	+	16.4545i	0.481669	+	0.834275i	0.999779	−	0.0210389i	$-0.00669738\pi$
$389$	9.50000	+	16.4545i	0.481669	+	0.834275i	−0.518110	+	0.855314i	$0.673364\pi$
$390$	2.50000	−	4.33013i	0.126592	−	0.219265i
$391$	8.00000	−	13.8564i	0.404577	−	0.700749i
$392$	1.00000	−	1.73205i	0.0505076	−	0.0874818i
$393$	18.0000			0.907980
$394$	−10.0000	−	17.3205i	−0.503793	−	0.872595i
$395$	−2.00000	+	3.46410i	−0.100631	+	0.174298i
$396$	−2.00000			−0.100504
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	−1.00000	+	1.73205i	−0.0501255	+	0.0868199i
$399$	−15.0000			−0.750939
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	22.0000			1.09863			0.549314	−	0.835616i	$-0.314889\pi$
$401$	22.0000			1.09863			0.549314	+	0.835616i	$0.314889\pi$
$402$	−1.00000	−	1.73205i	−0.0498755	−	0.0863868i
$403$	20.0000	+	34.6410i	0.996271	+	1.72559i
$404$	3.00000	+	5.19615i	0.149256	+	0.258518i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	3.00000			0.148888
$407$	1.00000	+	12.1244i	0.0495682	+	0.600982i
$408$	2.00000			0.0990148
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	−0.999402	−	0.0345902i	$-0.988987\pi$
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	0.529657	+	0.848212i	$0.322321\pi$
$410$	−4.00000	−	6.92820i	−0.197546	−	0.342160i
$411$	2.50000	+	4.33013i	0.123316	+	0.213589i
$412$	−2.50000	−	4.33013i	−0.123166	−	0.213330i
$413$	24.0000			1.18096
$414$	−4.00000	−	6.92820i	−0.196589	−	0.340503i
$415$	−1.00000			−0.0490881
$416$	−2.50000	+	4.33013i	−0.122573	+	0.212302i
$417$	12.0000			0.587643
$418$	−10.0000			−0.489116
$419$	11.0000	−	19.0526i	0.537385	−	0.930778i	−0.461659	−	0.887058i	$-0.652745\pi$
$419$	11.0000	−	19.0526i	0.537385	−	0.930778i	0.999044	−	0.0437207i	$-0.0139212\pi$
$420$	−1.50000	−	2.59808i	−0.0731925	−	0.126773i
$421$	16.0000			0.779792			0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000			0.779792			0.389896	+	0.920859i	$0.372511\pi$
$422$	−12.5000	+	21.6506i	−0.608490	+	1.05394i
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$	0.500000	+	0.866025i	0.0242251	+	0.0419591i
$427$	−15.0000	+	25.9808i	−0.725901	+	1.25730i
$428$	2.00000	−	3.46410i	0.0966736	−	0.167444i
$429$	5.00000	−	8.66025i	0.241402	−	0.418121i
$430$		0			0
$431$	1.50000	+	2.59808i	0.0722525	+	0.125145i	0.899888	−	0.436121i	$-0.143648\pi$
$431$	1.50000	+	2.59808i	0.0722525	+	0.125145i	−0.827636	+	0.561266i	$0.810315\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	38.0000			1.82616			0.913082	−	0.407777i	$-0.133696\pi$
$433$	38.0000			1.82616			0.913082	+	0.407777i	$0.133696\pi$
$434$	24.0000			1.15204
$435$	0.500000	−	0.866025i	0.0239732	−	0.0415227i
$436$	−10.0000			−0.478913
$437$	−20.0000	−	34.6410i	−0.956730	−	1.65710i
$438$		0			0
$439$	3.00000	+	5.19615i	0.143182	+	0.247999i	0.928693	−	0.370849i	$-0.120933\pi$
$439$	3.00000	+	5.19615i	0.143182	+	0.247999i	−0.785511	+	0.618848i	$0.787600\pi$
$440$	−1.00000	−	1.73205i	−0.0476731	−	0.0825723i
$441$	−1.00000	−	1.73205i	−0.0476190	−	0.0824786i
$442$	−5.00000	+	8.66025i	−0.237826	+	0.411926i
$443$	21.0000			0.997740			0.498870	−	0.866677i	$-0.333748\pi$
$443$	21.0000			0.997740			0.498870	+	0.866677i	$0.333748\pi$
$444$	−5.50000	−	2.59808i	−0.261018	−	0.123299i
$445$	−8.00000			−0.379236
$446$	−6.00000	+	10.3923i	−0.284108	+	0.492090i
$447$	−7.50000	−	12.9904i	−0.354738	−	0.614424i
$448$	1.50000	+	2.59808i	0.0708683	+	0.122748i
$449$	18.0000	+	31.1769i	0.849473	+	1.47133i	0.881680	+	0.471848i	$0.156413\pi$
$449$	18.0000	+	31.1769i	0.849473	+	1.47133i	−0.0322072	+	0.999481i	$0.510254\pi$
$450$	−1.00000			−0.0471405
$451$	−8.00000	−	13.8564i	−0.376705	−	0.652473i
$452$	19.0000			0.893685
$453$	5.00000	−	8.66025i	0.234920	−	0.406894i
$454$	7.00000			0.328526
$455$	15.0000			0.703211
$456$	2.50000	−	4.33013i	0.117073	−	0.202777i
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	−20.0000			−0.934539
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$	4.00000	−	6.92820i	0.186501	−	0.323029i
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	−0.828978	−	0.559281i	$-0.811077\pi$
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	0.898840	+	0.438276i	$0.144411\pi$
$462$	−3.00000	−	5.19615i	−0.139573	−	0.241747i
$463$	7.50000	+	12.9904i	0.348555	+	0.603714i	0.985993	−	0.166787i	$-0.0533393\pi$
$463$	7.50000	+	12.9904i	0.348555	+	0.603714i	−0.637438	+	0.770501i	$0.720006\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$	4.00000	−	6.92820i	0.185496	−	0.321288i
$466$	6.50000	−	11.2583i	0.301107	−	0.521532i
$467$	39.0000			1.80470			0.902352	−	0.430999i	$-0.141839\pi$
$467$	39.0000			1.80470			0.902352	+	0.430999i	$0.141839\pi$
$468$	2.50000	+	4.33013i	0.115563	+	0.200160i
$469$	3.00000	−	5.19615i	0.138527	−	0.239936i
$470$	−6.00000			−0.276759
$471$	−13.0000			−0.599008
$472$	−4.00000	+	6.92820i	−0.184115	+	0.318896i
$473$		0			0
$474$	−2.00000	−	3.46410i	−0.0918630	−	0.159111i
$475$	−5.00000			−0.229416
$476$	3.00000	+	5.19615i	0.137505	+	0.238165i
$477$	−6.00000	−	10.3923i	−0.274721	−	0.475831i
$478$	−6.50000	−	11.2583i	−0.297303	−	0.514944i
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	−0.695773	−	0.718262i	$-0.744938\pi$
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	0.969920	+	0.243426i	$0.0782712\pi$
$480$	1.00000			0.0456435
$481$	25.0000	−	17.3205i	1.13990	−	0.789747i
$482$	14.0000			0.637683
$483$	12.0000	−	20.7846i	0.546019	−	0.945732i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	4.00000	+	6.92820i	0.181631	+	0.314594i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−33.0000			−1.49537			−0.747686	−	0.664052i	$-0.768835\pi$
$487$	−33.0000			−1.49537			−0.747686	+	0.664052i	$0.768835\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$	18.0000			0.813988
$490$	1.00000	−	1.73205i	0.0451754	−	0.0782461i
$491$	−14.0000			−0.631811			−0.315906	−	0.948791i	$-0.602308\pi$
$491$	−14.0000			−0.631811			−0.315906	+	0.948791i	$0.602308\pi$
$492$	8.00000			0.360668
$493$	−1.00000	+	1.73205i	−0.0450377	+	0.0780076i
$494$	12.5000	+	21.6506i	0.562402	+	0.974108i
$495$	−2.00000			−0.0898933
$496$	−4.00000	+	6.92820i	−0.179605	+	0.311086i
$497$	−1.50000	+	2.59808i	−0.0672842	+	0.116540i
$498$	0.500000	−	0.866025i	0.0224055	−	0.0388075i
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	−0.997532	−	0.0702185i	$-0.977630\pi$
$499$	−12.5000	−	21.6506i	−0.559577	−	0.969216i	0.437955	−	0.898997i	$-0.355703\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	1.00000	−	1.73205i	0.0446767	−	0.0773823i
$502$	−9.00000	+	15.5885i	−0.401690	+	0.695747i
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	0.464107	+	0.885779i	$0.346375\pi$
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	−0.999161	+	0.0409609i	$0.986958\pi$
$504$	3.00000			0.133631
$505$	3.00000	+	5.19615i	0.133498	+	0.231226i
$506$	8.00000	−	13.8564i	0.355643	−	0.615992i
$507$	−12.0000			−0.532939
$508$	−5.00000			−0.221839
$509$	11.5000	−	19.9186i	0.509729	−	0.882876i	−0.490208	−	0.871606i	$-0.663079\pi$
$509$	11.5000	−	19.9186i	0.509729	−	0.882876i	0.999936	−	0.0112702i	$-0.00358750\pi$
$510$	2.00000			0.0885615
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−2.50000	−	4.33013i	−0.110378	−	0.191180i
$514$	−6.50000	−	11.2583i	−0.286703	−	0.496584i
$515$	−2.50000	−	4.33013i	−0.110163	−	0.190808i
$516$		0			0
$517$	−12.0000			−0.527759
$518$	−1.50000	−	18.1865i	−0.0659062	−	0.799070i
$519$	20.0000			0.877903
$520$	−2.50000	+	4.33013i	−0.109632	+	0.189889i
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.799370	+	0.600839i	$0.205167\pi$
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.120656	+	0.992694i	$0.461500\pi$
$522$	0.500000	+	0.866025i	0.0218844	+	0.0379049i
$523$	1.00000	+	1.73205i	0.0437269	+	0.0757373i	0.887061	−	0.461653i	$-0.152744\pi$
$523$	1.00000	+	1.73205i	0.0437269	+	0.0757373i	−0.843334	+	0.537390i	$0.819410\pi$
$524$	−18.0000			−0.786334
$525$	−1.50000	−	2.59808i	−0.0654654	−	0.113389i
$526$	4.00000			0.174408
$527$	−8.00000	+	13.8564i	−0.348485	+	0.603595i
$528$	2.00000			0.0870388
$529$	41.0000			1.78261
$530$	6.00000	−	10.3923i	0.260623	−	0.451413i
$531$	4.00000	+	6.92820i	0.173585	+	0.300658i
$532$	15.0000			0.650332
$533$	−20.0000	+	34.6410i	−0.866296	+	1.50047i
$534$	4.00000	−	6.92820i	0.173097	−	0.299813i
$535$	2.00000	−	3.46410i	0.0864675	−	0.149766i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$		0			0
$538$	3.50000	−	6.06218i	0.150896	−	0.261359i
$539$	2.00000	−	3.46410i	0.0861461	−	0.149209i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	−6.00000			−0.257960			−0.128980	−	0.991647i	$-0.541170\pi$
$541$	−6.00000			−0.257960			−0.128980	+	0.991647i	$0.541170\pi$
$542$	−8.00000	−	13.8564i	−0.343629	−	0.595184i
$543$	−11.0000	+	19.0526i	−0.472055	+	0.817624i
$544$	−2.00000			−0.0857493
$545$	−10.0000			−0.428353
$546$	−7.50000	+	12.9904i	−0.320970	+	0.555937i
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$	−2.50000	−	4.33013i	−0.106795	−	0.184974i
$549$	−10.0000			−0.426790
$550$	−1.00000	−	1.73205i	−0.0426401	−	0.0738549i
$551$	2.50000	+	4.33013i	0.106504	+	0.184470i
$552$	4.00000	+	6.92820i	0.170251	+	0.294884i
$553$	6.00000	−	10.3923i	0.255146	−	0.441926i
$554$	−1.00000			−0.0424859
$555$	−5.50000	−	2.59808i	−0.233462	−	0.110282i
$556$	−12.0000			−0.508913
$557$	−3.00000	+	5.19615i	−0.127114	+	0.220168i	−0.922557	−	0.385860i	$-0.873905\pi$
$557$	−3.00000	+	5.19615i	−0.127114	+	0.220168i	0.795443	+	0.606028i	$0.207238\pi$
$558$	4.00000	+	6.92820i	0.169334	+	0.293294i
$559$		0			0
$560$	1.50000	+	2.59808i	0.0633866	+	0.109789i
$561$	4.00000			0.168880
$562$	−13.0000	−	22.5167i	−0.548372	−	0.949808i
$563$	21.0000			0.885044			0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000			0.885044			0.442522	+	0.896758i	$0.354084\pi$
$564$	3.00000	−	5.19615i	0.126323	−	0.218797i
$565$	19.0000			0.799336
$566$	18.0000			0.756596
$567$	1.50000	−	2.59808i	0.0629941	−	0.109109i
$568$	−0.500000	−	0.866025i	−0.0209795	−	0.0363376i
$569$	−4.00000			−0.167689			−0.0838444	−	0.996479i	$-0.526720\pi$
$569$	−4.00000			−0.167689			−0.0838444	+	0.996479i	$0.526720\pi$
$570$	2.50000	−	4.33013i	0.104713	−	0.181369i
$571$	13.5000	−	23.3827i	0.564957	−	0.978535i	−0.432096	−	0.901828i	$-0.642226\pi$
$571$	13.5000	−	23.3827i	0.564957	−	0.978535i	0.997054	−	0.0767074i	$-0.0244407\pi$
$572$	−5.00000	+	8.66025i	−0.209061	+	0.362103i
$573$	−2.00000	−	3.46410i	−0.0835512	−	0.144715i
$574$	12.0000	+	20.7846i	0.500870	+	0.867533i
$575$	4.00000	−	6.92820i	0.166812	−	0.288926i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−11.0000	+	19.0526i	−0.457936	+	0.793168i	−0.998852	−	0.0479084i	$-0.984744\pi$
$577$	−11.0000	+	19.0526i	−0.457936	+	0.793168i	0.540916	+	0.841077i	$0.318078\pi$
$578$	13.0000			0.540729
$579$	−2.00000	−	3.46410i	−0.0831172	−	0.143963i
$580$	−0.500000	+	0.866025i	−0.0207614	+	0.0359597i
$581$	3.00000			0.124461
$582$	−8.00000			−0.331611
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$		0			0
$585$	2.50000	+	4.33013i	0.103362	+	0.179029i
$586$	24.0000			0.991431
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	0.974668	+	0.223659i	$0.0718001\pi$
$587$	16.5000	+	28.5788i	0.681028	+	1.17957i	−0.293640	+	0.955916i	$0.594867\pi$
$588$	1.00000	+	1.73205i	0.0412393	+	0.0714286i
$589$	20.0000	+	34.6410i	0.824086	+	1.42736i
$590$	−4.00000	+	6.92820i	−0.164677	+	0.285230i
$591$	20.0000			0.822690
$592$	5.50000	+	2.59808i	0.226049	+	0.106780i
$593$	34.0000			1.39621			0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000			1.39621			0.698106	+	0.715994i	$0.254026\pi$
$594$	1.00000	−	1.73205i	0.0410305	−	0.0710669i
$595$	3.00000	+	5.19615i	0.122988	+	0.213021i
$596$	7.50000	+	12.9904i	0.307212	+	0.532107i
$597$	−1.00000	−	1.73205i	−0.0409273	−	0.0708881i
$598$	−40.0000			−1.63572
$599$	−16.5000	−	28.5788i	−0.674172	−	1.16770i	−0.976710	−	0.214563i	$-0.931167\pi$
$599$	−16.5000	−	28.5788i	−0.674172	−	1.16770i	0.302539	−	0.953137i	$-0.402166\pi$
$600$	1.00000			0.0408248
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	0.469095	+	0.883148i	$0.344580\pi$
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	2.00000			0.0814463
$604$	−5.00000	+	8.66025i	−0.203447	+	0.352381i
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$	−6.00000			−0.243733
$607$	11.5000	−	19.9186i	0.466771	−	0.808470i	−0.532509	−	0.846424i	$-0.678751\pi$
$607$	11.5000	−	19.9186i	0.466771	−	0.808470i	0.999279	+	0.0379540i	$0.0120840\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$	−1.50000	+	2.59808i	−0.0607831	+	0.105279i
$610$	−5.00000	−	8.66025i	−0.202444	−	0.350643i
$611$	15.0000	+	25.9808i	0.606835	+	1.05107i
$612$	−1.00000	+	1.73205i	−0.0404226	+	0.0700140i
$613$	20.5000	−	35.5070i	0.827987	−	1.43412i	−0.0716275	−	0.997431i	$-0.522819\pi$
$613$	20.5000	−	35.5070i	0.827987	−	1.43412i	0.899615	−	0.436684i	$-0.143847\pi$
$614$	−9.00000	+	15.5885i	−0.363210	+	0.629099i
$615$	8.00000			0.322591
$616$	3.00000	+	5.19615i	0.120873	+	0.209359i
$617$	−4.50000	+	7.79423i	−0.181163	+	0.313784i	−0.942277	−	0.334835i	$-0.891320\pi$
$617$	−4.50000	+	7.79423i	−0.181163	+	0.313784i	0.761114	+	0.648618i	$0.224653\pi$
$618$	5.00000			0.201129
$619$	44.0000			1.76851			0.884255	−	0.467005i	$-0.154667\pi$
$619$	44.0000			1.76851			0.884255	+	0.467005i	$0.154667\pi$
$620$	−4.00000	+	6.92820i	−0.160644	+	0.278243i
$621$	8.00000			0.321029
$622$		0			0
$623$	24.0000			0.961540
$624$	−2.50000	−	4.33013i	−0.100080	−	0.173344i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	16.0000	+	27.7128i	0.639489	+	1.10763i
$627$	5.00000	−	8.66025i	0.199681	−	0.345857i
$628$	13.0000			0.518756
$629$	11.0000	+	5.19615i	0.438599	+	0.207184i
$630$	3.00000			0.119523
$631$	20.0000	−	34.6410i	0.796187	−	1.37904i	−0.125895	−	0.992044i	$-0.540180\pi$
$631$	20.0000	−	34.6410i	0.796187	−	1.37904i	0.922082	−	0.386994i	$-0.126486\pi$
$632$	2.00000	+	3.46410i	0.0795557	+	0.137795i
$633$	−12.5000	−	21.6506i	−0.496830	−	0.860535i
$634$	−12.0000	−	20.7846i	−0.476581	−	0.825462i
$635$	−5.00000			−0.198419
$636$	6.00000	+	10.3923i	0.237915	+	0.412082i
$637$	−10.0000			−0.396214
$638$	−1.00000	+	1.73205i	−0.0395904	+	0.0685725i
$639$	−1.00000			−0.0395594
$640$	−1.00000			−0.0395285
$641$	5.00000	−	8.66025i	0.197488	−	0.342059i	−0.750225	−	0.661182i	$-0.770055\pi$
$641$	5.00000	−	8.66025i	0.197488	−	0.342059i	0.947713	+	0.319123i	$0.103388\pi$
$642$	2.00000	+	3.46410i	0.0789337	+	0.136717i
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$	−12.0000	+	20.7846i	−0.472866	+	0.819028i
$645$		0			0
$646$	−5.00000	+	8.66025i	−0.196722	+	0.340733i
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	0.885013	−	0.465566i	$-0.154149\pi$
$647$	1.00000	+	1.73205i	0.0393141	+	0.0680939i	−0.845699	+	0.533660i	$0.820816\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−8.00000	+	13.8564i	−0.314027	+	0.543912i
$650$	−2.50000	+	4.33013i	−0.0980581	+	0.169842i
$651$	−12.0000	+	20.7846i	−0.470317	+	0.814613i
$652$	−18.0000			−0.704934
$653$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$653$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$654$	5.00000	−	8.66025i	0.195515	−	0.338643i
$655$	−18.0000			−0.703318
$656$	−8.00000			−0.312348
$657$		0			0
$658$	18.0000			0.701713
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	0.531855	−	0.846836i	$-0.321495\pi$
$659$	−12.0000	−	20.7846i	−0.467454	−	0.809653i	−0.999309	+	0.0371821i	$0.988162\pi$
$660$	2.00000			0.0778499
$661$	−14.0000	−	24.2487i	−0.544537	−	0.943166i	−0.998636	−	0.0522143i	$-0.983372\pi$
$661$	−14.0000	−	24.2487i	−0.544537	−	0.943166i	0.454099	−	0.890951i	$-0.349961\pi$
$662$	7.50000	+	12.9904i	0.291496	+	0.504885i
$663$	−5.00000	−	8.66025i	−0.194184	−	0.336336i
$664$	−0.500000	+	0.866025i	−0.0194038	+	0.0336083i
$665$	15.0000			0.581675
$666$	5.00000	−	3.46410i	0.193746	−	0.134231i
$667$	−8.00000			−0.309761
$668$	−1.00000	+	1.73205i	−0.0386912	+	0.0670151i
$669$	−6.00000	−	10.3923i	−0.231973	−	0.401790i
$670$	1.00000	+	1.73205i	0.0386334	+	0.0669150i
$671$	−10.0000	−	17.3205i	−0.386046	−	0.668651i
$672$	−3.00000			−0.115728
$673$	10.0000	+	17.3205i	0.385472	+	0.667657i	0.991835	−	0.127532i	$-0.0407054\pi$
$673$	10.0000	+	17.3205i	0.385472	+	0.667657i	−0.606363	+	0.795188i	$0.707372\pi$
$674$	−26.0000			−1.00148
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	12.0000			0.461538
$677$	30.0000			1.15299			0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000			1.15299			0.576497	+	0.817099i	$0.304419\pi$
$678$	−9.50000	+	16.4545i	−0.364845	+	0.631931i
$679$	−12.0000	−	20.7846i	−0.460518	−	0.797640i
$680$	−2.00000			−0.0766965
$681$	−3.50000	+	6.06218i	−0.134120	+	0.232303i
$682$	−8.00000	+	13.8564i	−0.306336	+	0.530589i
$683$	−14.0000	+	24.2487i	−0.535695	+	0.927851i	0.463434	+	0.886131i	$0.346617\pi$
$683$	−14.0000	+	24.2487i	−0.535695	+	0.927851i	−0.999129	+	0.0417198i	$0.986716\pi$
$684$	2.50000	+	4.33013i	0.0955899	+	0.165567i
$685$	−2.50000	−	4.33013i	−0.0955201	−	0.165446i
$686$	7.50000	−	12.9904i	0.286351	−	0.495975i
$687$	10.0000	−	17.3205i	0.381524	−	0.660819i
$688$		0			0
$689$	−60.0000			−2.28582
$690$	4.00000	+	6.92820i	0.152277	+	0.263752i
$691$	14.5000	−	25.1147i	0.551606	−	0.955410i	−0.446553	−	0.894757i	$-0.647349\pi$
$691$	14.5000	−	25.1147i	0.551606	−	0.955410i	0.998159	−	0.0606524i	$-0.0193181\pi$
$692$	−20.0000			−0.760286
$693$	6.00000			0.227921
$694$	−16.5000	+	28.5788i	−0.626331	+	1.08484i
$695$	−12.0000			−0.455186
$696$	−0.500000	−	0.866025i	−0.0189525	−	0.0328266i
$697$	−16.0000			−0.606043
$698$	−2.00000	−	3.46410i	−0.0757011	−	0.131118i
$699$	6.50000	+	11.2583i	0.245853	+	0.425829i
$700$	1.50000	+	2.59808i	0.0566947	+	0.0981981i
$701$	−1.00000	+	1.73205i	−0.0377695	+	0.0654187i	−0.884292	−	0.466934i	$-0.845359\pi$
$701$	−1.00000	+	1.73205i	−0.0377695	+	0.0654187i	0.846523	+	0.532353i	$0.178692\pi$
$702$	−5.00000			−0.188713
$703$	25.0000	−	17.3205i	0.942893	−	0.653255i
$704$	−2.00000			−0.0753778
$705$	3.00000	−	5.19615i	0.112987	−	0.195698i
$706$	14.5000	+	25.1147i	0.545715	+	0.945206i
$707$	−9.00000	−	15.5885i	−0.338480	−	0.586264i
$708$	−4.00000	−	6.92820i	−0.150329	−	0.260378i
$709$	42.0000			1.57734			0.788672	−	0.614815i	$-0.210769\pi$
$709$	42.0000			1.57734			0.788672	+	0.614815i	$0.210769\pi$
$710$	−0.500000	−	0.866025i	−0.0187647	−	0.0325014i
$711$	4.00000			0.150012
$712$	−4.00000	+	6.92820i	−0.149906	+	0.259645i
$713$	−64.0000			−2.39682
$714$	−6.00000			−0.224544
$715$	−5.00000	+	8.66025i	−0.186989	+	0.323875i
$716$		0			0
$717$	13.0000			0.485494
$718$	3.50000	−	6.06218i	0.130619	−	0.226238i
$719$	−9.50000	+	16.4545i	−0.354290	+	0.613649i	−0.986996	−	0.160743i	$-0.948611\pi$
$719$	−9.50000	+	16.4545i	−0.354290	+	0.613649i	0.632706	+	0.774392i	$0.281944\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$	7.50000	+	12.9904i	0.279315	+	0.483787i
$722$	3.00000	+	5.19615i	0.111648	+	0.193381i
$723$	−7.00000	+	12.1244i	−0.260333	+	0.450910i
$724$	11.0000	−	19.0526i	0.408812	−	0.708083i
$725$	−0.500000	+	0.866025i	−0.0185695	+	0.0321634i
$726$	−7.00000			−0.259794
$727$	1.50000	+	2.59808i	0.0556319	+	0.0963573i	0.892500	−	0.451047i	$-0.148949\pi$
$727$	1.50000	+	2.59808i	0.0556319	+	0.0963573i	−0.836868	+	0.547404i	$0.815616\pi$
$728$	7.50000	−	12.9904i	0.277968	−	0.481456i
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$	10.0000			0.369611
$733$	−25.0000	−	43.3013i	−0.923396	−	1.59937i	−0.794121	−	0.607760i	$-0.792068\pi$
$733$	−25.0000	−	43.3013i	−0.923396	−	1.59937i	−0.129275	−	0.991609i	$-0.541265\pi$
$734$	−23.0000			−0.848945
$735$	1.00000	+	1.73205i	0.0368856	+	0.0638877i
$736$	−4.00000	−	6.92820i	−0.147442	−	0.255377i
$737$	2.00000	+	3.46410i	0.0736709	+	0.127602i
$738$	−4.00000	+	6.92820i	−0.147242	+	0.255031i
$739$	33.0000			1.21392			0.606962	−	0.794731i	$-0.292388\pi$
$739$	33.0000			1.21392			0.606962	+	0.794731i	$0.292388\pi$
$740$	5.50000	+	2.59808i	0.202184	+	0.0955072i
$741$	−25.0000			−0.918398
$742$	−18.0000	+	31.1769i	−0.660801	+	1.14454i
$743$	−4.00000	−	6.92820i	−0.146746	−	0.254171i	0.783277	−	0.621673i	$-0.213547\pi$
$743$	−4.00000	−	6.92820i	−0.146746	−	0.254171i	−0.930023	+	0.367502i	$0.880213\pi$
$744$	−4.00000	−	6.92820i	−0.146647	−	0.254000i
$745$	7.50000	+	12.9904i	0.274779	+	0.475931i
$746$	−13.0000			−0.475964
$747$	0.500000	+	0.866025i	0.0182940	+	0.0316862i
$748$	−4.00000			−0.146254
$749$	−6.00000	+	10.3923i	−0.219235	+	0.379727i
$750$	1.00000			0.0365148
$751$	−10.0000			−0.364905			−0.182453	−	0.983215i	$-0.558404\pi$
$751$	−10.0000			−0.364905			−0.182453	+	0.983215i	$0.558404\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$	−9.00000	−	15.5885i	−0.327978	−	0.568075i
$754$	5.00000			0.182089
$755$	−5.00000	+	8.66025i	−0.181969	+	0.315179i
$756$	−1.50000	+	2.59808i	−0.0545545	+	0.0944911i
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	−0.959634	−	0.281251i	$-0.909251\pi$
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	0.723388	+	0.690442i	$0.242584\pi$
$758$	−14.5000	−	25.1147i	−0.526664	−	0.912208i
$759$	8.00000	+	13.8564i	0.290382	+	0.502956i
$760$	−2.50000	+	4.33013i	−0.0906845	+	0.157070i
$761$	−14.0000	+	24.2487i	−0.507500	+	0.879015i	0.492463	+	0.870334i	$0.336097\pi$
$761$	−14.0000	+	24.2487i	−0.507500	+	0.879015i	−0.999962	+	0.00868155i	$0.997237\pi$
$762$	2.50000	−	4.33013i	0.0905654	−	0.156864i
$763$	30.0000			1.08607
$764$	2.00000	+	3.46410i	0.0723575	+	0.125327i
$765$	−1.00000	+	1.73205i	−0.0361551	+	0.0626224i
$766$	26.0000			0.939418
$767$	40.0000			1.44432
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	23.0000			0.829401			0.414701	−	0.909958i	$-0.363886\pi$
$769$	23.0000			0.829401			0.414701	+	0.909958i	$0.363886\pi$
$770$	3.00000	+	5.19615i	0.108112	+	0.187256i
$771$	13.0000			0.468184
$772$	2.00000	+	3.46410i	0.0719816	+	0.124676i
$773$	−24.0000	−	41.5692i	−0.863220	−	1.49514i	−0.868804	−	0.495156i	$-0.835111\pi$
$773$	−24.0000	−	41.5692i	−0.863220	−	1.49514i	0.00558380	−	0.999984i	$-0.498223\pi$
$774$		0			0
$775$	−4.00000	+	6.92820i	−0.143684	+	0.248868i
$776$	8.00000			0.287183
$777$	16.5000	+	7.79423i	0.591934	+	0.279616i
$778$	19.0000			0.681183
$779$	−20.0000	+	34.6410i	−0.716574	+	1.24114i
$780$	−2.50000	−	4.33013i	−0.0895144	−	0.155043i
$781$	−1.00000	−	1.73205i	−0.0357828	−	0.0619777i
$782$	−8.00000	−	13.8564i	−0.286079	−	0.495504i
$783$	−1.00000			−0.0357371
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$	13.0000			0.463990
$786$	9.00000	−	15.5885i	0.321019	−	0.556022i
$787$	−4.00000			−0.142585			−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000			−0.142585			−0.0712923	+	0.997455i	$0.522712\pi$
$788$	−20.0000			−0.712470
$789$	−2.00000	+	3.46410i	−0.0712019	+	0.123325i
$790$	2.00000	+	3.46410i	0.0711568	+	0.123247i
$791$	−57.0000			−2.02669
$792$	−1.00000	+	1.73205i	−0.0355335	+	0.0615457i
$793$	−25.0000	+	43.3013i	−0.887776	+	1.53767i
$794$	1.00000	−	1.73205i	0.0354887	−	0.0614682i
$795$	6.00000	+	10.3923i	0.212798	+	0.368577i
$796$	1.00000	+	1.73205i	0.0354441	+	0.0613909i
$797$	14.0000	−	24.2487i	0.495905	−	0.858933i	−0.504083	−	0.863655i	$-0.668170\pi$
$797$	14.0000	−	24.2487i	0.495905	−	0.858933i	0.999989	+	0.00472155i	$0.00150292\pi$
$798$	−7.50000	+	12.9904i	−0.265497	+	0.459855i
$799$	−6.00000	+	10.3923i	−0.212265	+	0.367653i
$800$	−1.00000			−0.0353553
$801$	4.00000	+	6.92820i	0.141333	+	0.244796i
$802$	11.0000	−	19.0526i	0.388424	−	0.672769i
$803$		0			0
$804$	−2.00000			−0.0705346
$805$	−12.0000	+	20.7846i	−0.422944	+	0.732561i
$806$	40.0000			1.40894
$807$	3.50000	+	6.06218i	0.123206	+	0.213399i
$808$	6.00000			0.211079
$809$	2.00000	+	3.46410i	0.0703163	+	0.121791i	0.899040	−	0.437867i	$-0.144266\pi$
$809$	2.00000	+	3.46410i	0.0703163	+	0.121791i	−0.828724	+	0.559658i	$0.810932\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	20.0000	+	34.6410i	0.702295	+	1.21641i	0.967659	+	0.252262i	$0.0811746\pi$
$811$	20.0000	+	34.6410i	0.702295	+	1.21641i	−0.265364	+	0.964148i	$0.585492\pi$
$812$	1.50000	−	2.59808i	0.0526397	−	0.0911746i
$813$	16.0000			0.561144
$814$	11.0000	+	5.19615i	0.385550	+	0.182125i
$815$	−18.0000			−0.630512
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$		0			0
$818$	9.50000	+	16.4545i	0.332160	+	0.575317i
$819$	−7.50000	−	12.9904i	−0.262071	−	0.453921i
$820$	−8.00000			−0.279372
$821$	−22.5000	−	38.9711i	−0.785255	−	1.36010i	−0.928846	−	0.370465i	$-0.879198\pi$
$821$	−22.5000	−	38.9711i	−0.785255	−	1.36010i	0.143591	−	0.989637i	$-0.454135\pi$
$822$	5.00000			0.174395
$823$	20.5000	−	35.5070i	0.714585	−	1.23770i	−0.248534	−	0.968623i	$-0.579949\pi$
$823$	20.5000	−	35.5070i	0.714585	−	1.23770i	0.963119	−	0.269075i	$-0.0867178\pi$
$824$	−5.00000			−0.174183
$825$	2.00000			0.0696311
$826$	12.0000	−	20.7846i	0.417533	−	0.723189i
$827$	16.5000	+	28.5788i	0.573761	+	0.993784i	0.996175	+	0.0873805i	$0.0278496\pi$
$827$	16.5000	+	28.5788i	0.573761	+	0.993784i	−0.422414	+	0.906403i	$0.638817\pi$
$828$	−8.00000			−0.278019
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	−0.985771	−	0.168091i	$-0.946240\pi$
$829$	−10.0000	+	17.3205i	−0.347314	+	0.601566i	0.638457	+	0.769657i	$0.279573\pi$
$830$	−0.500000	+	0.866025i	−0.0173553	+	0.0300602i
$831$	0.500000	−	0.866025i	0.0173448	−	0.0300421i
$832$	2.50000	+	4.33013i	0.0866719	+	0.150120i
$833$	−2.00000	−	3.46410i	−0.0692959	−	0.120024i
$834$	6.00000	−	10.3923i	0.207763	−	0.359856i
$835$	−1.00000	+	1.73205i	−0.0346064	+	0.0599401i
$836$	−5.00000	+	8.66025i	−0.172929	+	0.299521i
$837$	−8.00000			−0.276520
$838$	−11.0000	−	19.0526i	−0.379989	−	0.658160i
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	−0.950813	−	0.309764i	$-0.899750\pi$
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	0.743670	+	0.668546i	$0.233083\pi$
$840$	−3.00000			−0.103510
$841$	−28.0000			−0.965517
$842$	8.00000	−	13.8564i	0.275698	−	0.477523i
$843$	26.0000			0.895488
$844$	12.5000	+	21.6506i	0.430268	+	0.745246i
$845$	12.0000			0.412813
$846$	3.00000	+	5.19615i	0.103142	+	0.178647i
$847$	−10.5000	−	18.1865i	−0.360784	−	0.624897i
$848$	−6.00000	−	10.3923i	−0.206041	−	0.356873i
$849$	−9.00000	+	15.5885i	−0.308879	+	0.534994i
$850$	−2.00000			−0.0685994
$851$	4.00000	+	48.4974i	0.137118	+	1.66247i
$852$	1.00000			0.0342594
$853$	3.00000	−	5.19615i	0.102718	−	0.177913i	−0.810086	−	0.586312i	$-0.800579\pi$
$853$	3.00000	−	5.19615i	0.102718	−	0.177913i	0.912804	+	0.408399i	$0.133913\pi$
$854$	15.0000	+	25.9808i	0.513289	+	0.889043i
$855$	2.50000	+	4.33013i	0.0854982	+	0.148087i
$856$	−2.00000	−	3.46410i	−0.0683586	−	0.118401i
$857$	−33.0000			−1.12726			−0.563629	−	0.826028i	$-0.690595\pi$
$857$	−33.0000			−1.12726			−0.563629	+	0.826028i	$0.690595\pi$
$858$	−5.00000	−	8.66025i	−0.170697	−	0.295656i
$859$	−39.0000			−1.33066			−0.665331	−	0.746548i	$-0.731710\pi$
$859$	−39.0000			−1.33066			−0.665331	+	0.746548i	$0.731710\pi$
$860$		0			0
$861$	−24.0000			−0.817918
$862$	3.00000			0.102180
$863$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$863$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−20.0000			−0.680020
$866$	19.0000	−	32.9090i	0.645646	−	1.11829i
$867$	−6.50000	+	11.2583i	−0.220752	+	0.382353i
$868$	12.0000	−	20.7846i	0.407307	−	0.705476i
$869$	4.00000	+	6.92820i	0.135691	+	0.235023i
$870$	−0.500000	−	0.866025i	−0.0169516	−	0.0293610i
$871$	5.00000	−	8.66025i	0.169419	−	0.293442i
$872$	−5.00000	+	8.66025i	−0.169321	+	0.293273i
$873$	4.00000	−	6.92820i	0.135379	−	0.234484i
$874$	−40.0000			−1.35302
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$		0			0
$877$	−27.0000			−0.911725			−0.455863	−	0.890050i	$-0.650669\pi$
$877$	−27.0000			−0.911725			−0.455863	+	0.890050i	$0.650669\pi$
$878$	6.00000			0.202490
$879$	−12.0000	+	20.7846i	−0.404750	+	0.701047i
$880$	−2.00000			−0.0674200
$881$	−21.0000	−	36.3731i	−0.707508	−	1.22544i	−0.965779	−	0.259367i	$-0.916486\pi$
$881$	−21.0000	−	36.3731i	−0.707508	−	1.22544i	0.258271	−	0.966073i	$-0.416847\pi$
$882$	−2.00000			−0.0673435
$883$	11.0000	+	19.0526i	0.370179	+	0.641170i	0.989593	−	0.143895i	$-0.0459629\pi$
$883$	11.0000	+	19.0526i	0.370179	+	0.641170i	−0.619413	+	0.785065i	$0.712630\pi$
$884$	5.00000	+	8.66025i	0.168168	+	0.291276i
$885$	−4.00000	−	6.92820i	−0.134459	−	0.232889i
$886$	10.5000	−	18.1865i	0.352754	−	0.610989i
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$	−5.00000	+	3.46410i	−0.167789	+	0.116248i
$889$	15.0000			0.503084
$890$	−4.00000	+	6.92820i	−0.134080	+	0.232234i
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$	6.00000	+	10.3923i	0.200895	+	0.347960i
$893$	15.0000	+	25.9808i	0.501956	+	0.869413i
$894$	−15.0000			−0.501675
$895$		0			0
$896$	3.00000			0.100223
$897$	20.0000	−	34.6410i	0.667781	−	1.15663i
$898$	36.0000			1.20134
$899$	8.00000			0.266815
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−12.0000	−	20.7846i	−0.399778	−	0.692436i
$902$	−16.0000			−0.532742
$903$		0			0
$904$	9.50000	−	16.4545i	0.315965	−	0.547268i
$905$	11.0000	−	19.0526i	0.365652	−	0.633328i
$906$	−5.00000	−	8.66025i	−0.166114	−	0.287718i
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	0.749051	−	0.662512i	$-0.230510\pi$
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	−0.948278	+	0.317441i	$0.897176\pi$
$908$	3.50000	−	6.06218i	0.116152	−	0.201180i
$909$	3.00000	−	5.19615i	0.0995037	−	0.172345i
$910$	7.50000	−	12.9904i	0.248623	−	0.430627i
$911$	−13.0000			−0.430709			−0.215355	−	0.976536i	$-0.569091\pi$
$911$	−13.0000			−0.430709			−0.215355	+	0.976536i	$0.569091\pi$
$912$	−2.50000	−	4.33013i	−0.0827833	−	0.143385i
$913$	−1.00000	+	1.73205i	−0.0330952	+	0.0573225i
$914$	18.0000			0.595387
$915$	10.0000			0.330590
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$	54.0000			1.78324
$918$	−1.00000	−	1.73205i	−0.0330049	−	0.0571662i
$919$	12.0000			0.395843			0.197922	−	0.980218i	$-0.436581\pi$
$919$	12.0000			0.395843			0.197922	+	0.980218i	$0.436581\pi$
$920$	−4.00000	−	6.92820i	−0.131876	−	0.228416i
$921$	−9.00000	−	15.5885i	−0.296560	−	0.513657i
$922$	−1.50000	−	2.59808i	−0.0493999	−	0.0855631i
$923$	−2.50000	+	4.33013i	−0.0822885	+	0.142528i
$924$	−6.00000			−0.197386
$925$	5.50000	+	2.59808i	0.180839	+	0.0854242i
$926$	15.0000			0.492931
$927$	−2.50000	+	4.33013i	−0.0821108	+	0.142220i
$928$	0.500000	+	0.866025i	0.0164133	+	0.0284287i
$929$	−5.00000	−	8.66025i	−0.164045	−	0.284134i	0.772271	−	0.635293i	$-0.219121\pi$
$929$	−5.00000	−	8.66025i	−0.164045	−	0.284134i	−0.936316	+	0.351160i	$0.885787\pi$
$930$	−4.00000	−	6.92820i	−0.131165	−	0.227185i
$931$	−10.0000			−0.327737
$932$	−6.50000	−	11.2583i	−0.212915	−	0.368779i
$933$		0			0
$934$	19.5000	−	33.7750i	0.638059	−	1.10515i
$935$	−4.00000			−0.130814
$936$	5.00000			0.163430
$937$	−16.0000	+	27.7128i	−0.522697	+	0.905338i	0.476954	+	0.878928i	$0.341741\pi$
$937$	−16.0000	+	27.7128i	−0.522697	+	0.905338i	−0.999651	+	0.0264099i	$0.991593\pi$
$938$	−3.00000	−	5.19615i	−0.0979535	−	0.169660i
$939$	−32.0000			−1.04428
$940$	−3.00000	+	5.19615i	−0.0978492	+	0.169480i
$941$	−22.5000	+	38.9711i	−0.733479	+	1.27042i	0.221908	+	0.975068i	$0.428771\pi$
$941$	−22.5000	+	38.9711i	−0.733479	+	1.27042i	−0.955387	+	0.295355i	$0.904562\pi$
$942$	−6.50000	+	11.2583i	−0.211781	+	0.366816i
$943$	−32.0000	−	55.4256i	−1.04206	−	1.80491i
$944$	4.00000	+	6.92820i	0.130189	+	0.225494i
$945$	−1.50000	+	2.59808i	−0.0487950	+	0.0845154i
$946$		0			0
$947$	2.50000	−	4.33013i	0.0812391	−	0.140710i	−0.822543	−	0.568702i	$-0.807446\pi$
$947$	2.50000	−	4.33013i	0.0812391	−	0.140710i	0.903782	+	0.427992i	$0.140779\pi$
$948$	−4.00000			−0.129914
$949$		0			0
$950$	−2.50000	+	4.33013i	−0.0811107	+	0.140488i
$951$	24.0000			0.778253
$952$	6.00000			0.194461
$953$	−14.5000	+	25.1147i	−0.469701	+	0.813546i	−0.999400	−	0.0346397i	$-0.988972\pi$
$953$	−14.5000	+	25.1147i	−0.469701	+	0.813546i	0.529699	+	0.848186i	$0.322305\pi$
$954$	−12.0000			−0.388514
$955$	2.00000	+	3.46410i	0.0647185	+	0.112096i
$956$	−13.0000			−0.420450
$957$	−1.00000	−	1.73205i	−0.0323254	−	0.0559893i
$958$	−6.00000	−	10.3923i	−0.193851	−	0.335760i
$959$	7.50000	+	12.9904i	0.242188	+	0.419481i
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	33.0000			1.06452
$962$	−2.50000	−	30.3109i	−0.0806032	−	0.977262i
$963$	−4.00000			−0.128898
$964$	7.00000	−	12.1244i	0.225455	−	0.390499i
$965$	2.00000	+	3.46410i	0.0643823	+	0.111513i
$966$	−12.0000	−	20.7846i	−0.386094	−	0.668734i
$967$	−11.5000	−	19.9186i	−0.369815	−	0.640538i	0.619721	−	0.784822i	$-0.287246\pi$
$967$	−11.5000	−	19.9186i	−0.369815	−	0.640538i	−0.989536	+	0.144283i	$0.953912\pi$
$968$	7.00000			0.224989
$969$	−5.00000	−	8.66025i	−0.160623	−	0.278207i
$970$	8.00000			0.256865
$971$	−28.0000	+	48.4974i	−0.898563	+	1.55636i	−0.0692304	+	0.997601i	$0.522054\pi$
$971$	−28.0000	+	48.4974i	−0.898563	+	1.55636i	−0.829332	+	0.558756i	$0.811279\pi$
$972$	−1.00000			−0.0320750
$973$	36.0000			1.15411
$974$	−16.5000	+	28.5788i	−0.528694	+	0.915725i
$975$	−2.50000	−	4.33013i	−0.0800641	−	0.138675i
$976$	−10.0000			−0.320092
$977$	−29.5000	+	51.0955i	−0.943789	+	1.63469i	−0.185630	+	0.982620i	$0.559433\pi$
$977$	−29.5000	+	51.0955i	−0.943789	+	1.63469i	−0.758159	+	0.652070i	$0.773901\pi$
$978$	9.00000	−	15.5885i	0.287788	−	0.498464i
$979$	−8.00000	+	13.8564i	−0.255681	+	0.442853i
$980$	−1.00000	−	1.73205i	−0.0319438	−	0.0553283i
$981$	5.00000	+	8.66025i	0.159638	+	0.276501i
$982$	−7.00000	+	12.1244i	−0.223379	+	0.386904i
$983$	3.00000	−	5.19615i	0.0956851	−	0.165732i	−0.814209	−	0.580572i	$-0.802829\pi$
$983$	3.00000	−	5.19615i	0.0956851	−	0.165732i	0.909894	+	0.414840i	$0.136162\pi$
$984$	4.00000	−	6.92820i	0.127515	−	0.220863i
$985$	−20.0000			−0.637253
$986$	1.00000	+	1.73205i	0.0318465	+	0.0551597i
$987$	−9.00000	+	15.5885i	−0.286473	+	0.496186i
$988$	25.0000			0.795356
$989$		0			0
$990$	−1.00000	+	1.73205i	−0.0317821	+	0.0550482i
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$	−15.0000			−0.476011
$994$	1.50000	+	2.59808i	0.0475771	+	0.0824060i
$995$	1.00000	+	1.73205i	0.0317021	+	0.0549097i
$996$	−0.500000	−	0.866025i	−0.0158431	−	0.0274411i
$997$	13.5000	−	23.3827i	0.427549	−	0.740537i	−0.569105	−	0.822265i	$-0.692710\pi$
$997$	13.5000	−	23.3827i	0.427549	−	0.740537i	0.996655	+	0.0817275i	$0.0260437\pi$
$998$	−25.0000			−0.791361
$999$	0.500000	+	6.06218i	0.0158193	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.e.121.1	✓	2
37.26	even	3	inner	1110.2.i.e.211.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.e.121.1	✓	2	1.1	even	1	trivial
1110.2.i.e.211.1	yes	2	37.26	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -2.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(2.50000 + 4.33013i) q^{13} +3.00000 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.50000 + 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-1.50000 + 2.59808i) q^{21} +(-1.00000 + 1.73205i) q^{22} -8.00000 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{26} -1.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +1.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +8.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(1.00000 + 1.73205i) q^{34} +(1.50000 - 2.59808i) q^{35} +1.00000 q^{36} +(-0.500000 - 6.06218i) q^{37} +5.00000 q^{38} +(-2.50000 + 4.33013i) q^{39} +(0.500000 + 0.866025i) q^{40} +(4.00000 + 6.92820i) q^{41} +(1.50000 + 2.59808i) q^{42} +(1.00000 + 1.73205i) q^{44} +1.00000 q^{45} +(-4.00000 + 6.92820i) q^{46} +6.00000 q^{47} -1.00000 q^{48} +(-1.00000 + 1.73205i) q^{49} +(0.500000 + 0.866025i) q^{50} -2.00000 q^{51} +(2.50000 - 4.33013i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-1.50000 - 2.59808i) q^{56} +(-2.50000 + 4.33013i) q^{57} +(0.500000 - 0.866025i) q^{58} +(4.00000 - 6.92820i) q^{59} -1.00000 q^{60} +(5.00000 + 8.66025i) q^{61} +(4.00000 - 6.92820i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(2.50000 - 4.33013i) q^{65} -2.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +2.00000 q^{68} +(-4.00000 - 6.92820i) q^{69} +(-1.50000 - 2.59808i) q^{70} +(0.500000 + 0.866025i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-5.50000 - 2.59808i) q^{74} -1.00000 q^{75} +(2.50000 - 4.33013i) q^{76} +(-3.00000 - 5.19615i) q^{77} +(2.50000 + 4.33013i) q^{78} +(-2.00000 - 3.46410i) q^{79} +1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +8.00000 q^{82} +(0.500000 - 0.866025i) q^{83} +3.00000 q^{84} +2.00000 q^{85} +(0.500000 + 0.866025i) q^{87} +2.00000 q^{88} +(4.00000 - 6.92820i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-7.50000 + 12.9904i) q^{91} +(4.00000 + 6.92820i) q^{92} +(4.00000 + 6.92820i) q^{93} +(3.00000 - 5.19615i) q^{94} +(2.50000 - 4.33013i) q^{95} +(-0.500000 + 0.866025i) q^{96} -8.00000 q^{97} +(1.00000 + 1.73205i) q^{98} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} + 3 q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 4 q^{11} + q^{12} + 5 q^{13} + 6 q^{14} + q^{15} - q^{16} - 2 q^{17} + q^{18} + 5 q^{19} - q^{20} - 3 q^{21} - 2 q^{22} - 16 q^{23} - q^{24} - q^{25} + 10 q^{26} - 2 q^{27} + 3 q^{28} + 2 q^{29} - q^{30} + 16 q^{31} + q^{32} - 2 q^{33} + 2 q^{34} + 3 q^{35} + 2 q^{36} - q^{37} + 10 q^{38} - 5 q^{39} + q^{40} + 8 q^{41} + 3 q^{42} + 2 q^{44} + 2 q^{45} - 8 q^{46} + 12 q^{47} - 2 q^{48} - 2 q^{49} + q^{50} - 4 q^{51} + 5 q^{52} - 12 q^{53} - q^{54} + 2 q^{55} - 3 q^{56} - 5 q^{57} + q^{58} + 8 q^{59} - 2 q^{60} + 10 q^{61} + 8 q^{62} - 6 q^{63} + 2 q^{64} + 5 q^{65} - 4 q^{66} - 2 q^{67} + 4 q^{68} - 8 q^{69} - 3 q^{70} + q^{71} + q^{72} - 11 q^{74} - 2 q^{75} + 5 q^{76} - 6 q^{77} + 5 q^{78} - 4 q^{79} + 2 q^{80} - q^{81} + 16 q^{82} + q^{83} + 6 q^{84} + 4 q^{85} + q^{87} + 4 q^{88} + 8 q^{89} + q^{90} - 15 q^{91} + 8 q^{92} + 8 q^{93} + 6 q^{94} + 5 q^{95} - q^{96} - 16 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 - q^5 + 2 * q^6 + 3 * q^7 - 2 * q^8 - q^9 - 2 * q^10 - 4 * q^11 + q^12 + 5 * q^13 + 6 * q^14 + q^15 - q^16 - 2 * q^17 + q^18 + 5 * q^19 - q^20 - 3 * q^21 - 2 * q^22 - 16 * q^23 - q^24 - q^25 + 10 * q^26 - 2 * q^27 + 3 * q^28 + 2 * q^29 - q^30 + 16 * q^31 + q^32 - 2 * q^33 + 2 * q^34 + 3 * q^35 + 2 * q^36 - q^37 + 10 * q^38 - 5 * q^39 + q^40 + 8 * q^41 + 3 * q^42 + 2 * q^44 + 2 * q^45 - 8 * q^46 + 12 * q^47 - 2 * q^48 - 2 * q^49 + q^50 - 4 * q^51 + 5 * q^52 - 12 * q^53 - q^54 + 2 * q^55 - 3 * q^56 - 5 * q^57 + q^58 + 8 * q^59 - 2 * q^60 + 10 * q^61 + 8 * q^62 - 6 * q^63 + 2 * q^64 + 5 * q^65 - 4 * q^66 - 2 * q^67 + 4 * q^68 - 8 * q^69 - 3 * q^70 + q^71 + q^72 - 11 * q^74 - 2 * q^75 + 5 * q^76 - 6 * q^77 + 5 * q^78 - 4 * q^79 + 2 * q^80 - q^81 + 16 * q^82 + q^83 + 6 * q^84 + 4 * q^85 + q^87 + 4 * q^88 + 8 * q^89 + q^90 - 15 * q^91 + 8 * q^92 + 8 * q^93 + 6 * q^94 + 5 * q^95 - q^96 - 16 * q^97 + 2 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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