LMFDB - Embedded newform 1110.2.i.h.211.1

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			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1110.211
Dual form			1110.2.i.h.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.50000 - 4.33013i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(2.50000 - 4.33013i) 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} +5.00000 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} +(-2.50000 - 4.33013i) q^{21} +(1.00000 + 1.73205i) q^{22} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -5.00000 q^{26} -1.00000 q^{27} +(2.50000 + 4.33013i) q^{28} -9.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} +(1.00000 - 1.73205i) q^{34} +(-2.50000 - 4.33013i) 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} +(2.50000 - 4.33013i) q^{42} +4.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} -1.00000 q^{45} +2.00000 q^{47} -1.00000 q^{48} +(-9.00000 - 15.5885i) q^{49} +(0.500000 - 0.866025i) q^{50} -2.00000 q^{51} +(-2.50000 - 4.33013i) q^{52} +(4.00000 + 6.92820i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 - 1.73205i) q^{55} +(-2.50000 + 4.33013i) q^{56} +(-2.50000 - 4.33013i) q^{57} +(-4.50000 - 7.79423i) q^{58} +(2.00000 + 3.46410i) q^{59} +1.00000 q^{60} +(-7.00000 + 12.1244i) q^{61} +(2.00000 + 3.46410i) q^{62} -5.00000 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} +(2.50000 - 4.33013i) q^{70} +(-4.50000 + 7.79423i) q^{71} +(0.500000 + 0.866025i) q^{72} +16.0000 q^{73} +(5.50000 - 2.59808i) q^{74} -1.00000 q^{75} +(2.50000 + 4.33013i) q^{76} +(5.00000 - 8.66025i) q^{77} +(-2.50000 + 4.33013i) q^{78} +(6.00000 - 10.3923i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +8.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +5.00000 q^{84} -2.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-4.50000 + 7.79423i) q^{87} -2.00000 q^{88} +(-0.500000 - 0.866025i) q^{90} +(12.5000 + 21.6506i) q^{91} +(2.00000 - 3.46410i) q^{93} +(1.00000 + 1.73205i) q^{94} +(-2.50000 - 4.33013i) q^{95} +(-0.500000 - 0.866025i) q^{96} -4.00000 q^{97} +(9.00000 - 15.5885i) 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} + 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} + 5 q^{7} - 2 q^{8} - q^{9} + 2 q^{10} + 4 q^{11} + q^{12} - 5 q^{13} + 10 q^{14} - q^{15} - q^{16} - 2 q^{17} + q^{18} + 5 q^{19} + q^{20} - 5 q^{21} + 2 q^{22} - q^{24} - q^{25} - 10 q^{26} - 2 q^{27} + 5 q^{28} - 18 q^{29} + q^{30} + 8 q^{31} + q^{32} + 2 q^{33} + 2 q^{34} - 5 q^{35} + 2 q^{36} + q^{37} + 10 q^{38} + 5 q^{39} - q^{40} + 8 q^{41} + 5 q^{42} + 8 q^{43} - 2 q^{44} - 2 q^{45} + 4 q^{47} - 2 q^{48} - 18 q^{49} + q^{50} - 4 q^{51} - 5 q^{52} + 8 q^{53} - q^{54} + 2 q^{55} - 5 q^{56} - 5 q^{57} - 9 q^{58} + 4 q^{59} + 2 q^{60} - 14 q^{61} + 4 q^{62} - 10 q^{63} + 2 q^{64} + 5 q^{65} + 4 q^{66} + 2 q^{67} + 4 q^{68} + 5 q^{70} - 9 q^{71} + q^{72} + 32 q^{73} + 11 q^{74} - 2 q^{75} + 5 q^{76} + 10 q^{77} - 5 q^{78} + 12 q^{79} - 2 q^{80} - q^{81} + 16 q^{82} + 9 q^{83} + 10 q^{84} - 4 q^{85} + 4 q^{86} - 9 q^{87} - 4 q^{88} - q^{90} + 25 q^{91} + 4 q^{93} + 2 q^{94} - 5 q^{95} - q^{96} - 8 q^{97} + 18 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9 + 2 * q^10 + 4 * q^11 + q^12 - 5 * q^13 + 10 * q^14 - q^15 - q^16 - 2 * q^17 + q^18 + 5 * q^19 + q^20 - 5 * q^21 + 2 * q^22 - q^24 - q^25 - 10 * q^26 - 2 * q^27 + 5 * q^28 - 18 * q^29 + q^30 + 8 * q^31 + q^32 + 2 * q^33 + 2 * q^34 - 5 * q^35 + 2 * q^36 + q^37 + 10 * q^38 + 5 * q^39 - q^40 + 8 * q^41 + 5 * q^42 + 8 * q^43 - 2 * q^44 - 2 * q^45 + 4 * q^47 - 2 * q^48 - 18 * q^49 + q^50 - 4 * q^51 - 5 * q^52 + 8 * q^53 - q^54 + 2 * q^55 - 5 * q^56 - 5 * q^57 - 9 * q^58 + 4 * q^59 + 2 * q^60 - 14 * q^61 + 4 * q^62 - 10 * q^63 + 2 * q^64 + 5 * q^65 + 4 * q^66 + 2 * q^67 + 4 * q^68 + 5 * q^70 - 9 * q^71 + q^72 + 32 * q^73 + 11 * q^74 - 2 * q^75 + 5 * q^76 + 10 * q^77 - 5 * q^78 + 12 * q^79 - 2 * q^80 - q^81 + 16 * q^82 + 9 * q^83 + 10 * q^84 - 4 * q^85 + 4 * q^86 - 9 * q^87 - 4 * q^88 - q^90 + 25 * q^91 + 4 * q^93 + 2 * q^94 - 5 * q^95 - q^96 - 8 * q^97 + 18 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	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
$7$	2.50000	−	4.33013i	0.944911	−	1.63663i	0.188982	−	0.981981i	$-0.439481\pi$
$7$	2.50000	−	4.33013i	0.944911	−	1.63663i	0.755929	−	0.654654i	$-0.227186\pi$
$8$	−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	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	5.00000			1.33631
$15$	−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	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	−0.422659	−	0.906289i	$-0.638903\pi$
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	0.996199	−	0.0871106i	$-0.0277634\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−2.50000	−	4.33013i	−0.545545	−	0.944911i
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	−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
$28$	2.50000	+	4.33013i	0.472456	+	0.818317i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	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
$35$	−2.50000	−	4.33013i	−0.422577	−	0.731925i
$36$	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	−0.363905	−	0.931436i	$-0.618557\pi$
$41$	4.00000	−	6.92820i	0.624695	−	1.08200i	0.988600	−	0.150567i	$-0.0481100\pi$
$42$	2.50000	−	4.33013i	0.385758	−	0.668153i
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	−1.00000			−0.149071
$46$		0			0
$47$	2.00000			0.291730			0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000			0.291730			0.145865	+	0.989305i	$0.453403\pi$
$48$	−1.00000			−0.144338
$49$	−9.00000	−	15.5885i	−1.28571	−	2.22692i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−2.00000			−0.280056
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	4.00000	+	6.92820i	0.549442	+	0.951662i	0.998313	+	0.0580651i	$0.0184931\pi$
$53$	4.00000	+	6.92820i	0.549442	+	0.951662i	−0.448871	+	0.893597i	$0.648174\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	1.00000	−	1.73205i	0.134840	−	0.233550i
$56$	−2.50000	+	4.33013i	−0.334077	+	0.578638i
$57$	−2.50000	−	4.33013i	−0.331133	−	0.573539i
$58$	−4.50000	−	7.79423i	−0.590879	−	1.02343i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$	1.00000			0.129099
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.0640184	+	0.997949i	$0.520392\pi$
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	−5.00000			−0.629941
$64$	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	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	2.00000			0.242536
$69$		0			0
$70$	2.50000	−	4.33013i	0.298807	−	0.517549i
$71$	−4.50000	+	7.79423i	−0.534052	+	0.925005i	0.465157	+	0.885228i	$0.345998\pi$
$71$	−4.50000	+	7.79423i	−0.534052	+	0.925005i	−0.999209	+	0.0397765i	$0.987335\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	16.0000			1.87266			0.936329	−	0.351123i	$-0.114200\pi$
$73$	16.0000			1.87266			0.936329	+	0.351123i	$0.114200\pi$
$74$	5.50000	−	2.59808i	0.639362	−	0.302020i
$75$	−1.00000			−0.115470
$76$	2.50000	+	4.33013i	0.286770	+	0.496700i
$77$	5.00000	−	8.66025i	0.569803	−	0.986928i
$78$	−2.50000	+	4.33013i	−0.283069	+	0.490290i
$79$	6.00000	−	10.3923i	0.675053	−	1.16923i	−0.301401	−	0.953498i	$-0.597454\pi$
$79$	6.00000	−	10.3923i	0.675053	−	1.16923i	0.976453	−	0.215728i	$-0.0692125\pi$
$80$	−1.00000			−0.111803
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	8.00000			0.883452
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$	5.00000			0.545545
$85$	−2.00000			−0.216930
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	−2.00000			−0.213201
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	12.5000	+	21.6506i	1.31036	+	2.26960i
$92$		0			0
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$	1.00000	+	1.73205i	0.103142	+	0.178647i
$95$	−2.50000	−	4.33013i	−0.256495	−	0.444262i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−4.00000			−0.406138			−0.203069	−	0.979164i	$-0.565092\pi$
$97$	−4.00000			−0.406138			−0.203069	+	0.979164i	$0.565092\pi$
$98$	9.00000	−	15.5885i	0.909137	−	1.57467i
$99$	−1.00000	−	1.73205i	−0.100504	−	0.174078i
$100$	1.00000			0.100000
$101$	−2.00000			−0.199007			−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000			−0.199007			−0.0995037	+	0.995037i	$0.531726\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	3.00000			0.295599			0.147799	−	0.989017i	$-0.452781\pi$
$103$	3.00000			0.295599			0.147799	+	0.989017i	$0.452781\pi$
$104$	2.50000	−	4.33013i	0.245145	−	0.424604i
$105$	−5.00000			−0.487950
$106$	−4.00000	+	6.92820i	−0.388514	+	0.672927i
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	0.977769	+	0.209687i	$0.0672444\pi$
$109$	7.00000	+	12.1244i	0.670478	+	1.16130i	−0.307290	+	0.951616i	$0.599422\pi$
$110$	2.00000			0.190693
$111$	−5.00000	−	3.46410i	−0.474579	−	0.328798i
$112$	−5.00000			−0.472456
$113$	6.50000	+	11.2583i	0.611469	+	1.05909i	0.990993	+	0.133913i	$0.0427543\pi$
$113$	6.50000	+	11.2583i	0.611469	+	1.05909i	−0.379525	+	0.925182i	$0.623912\pi$
$114$	2.50000	−	4.33013i	0.234146	−	0.405554i
$115$		0			0
$116$	4.50000	−	7.79423i	0.417815	−	0.723676i
$117$	5.00000			0.462250
$118$	−2.00000	+	3.46410i	−0.184115	+	0.318896i
$119$	−10.0000			−0.916698
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−7.00000			−0.636364
$122$	−14.0000			−1.26750
$123$	−4.00000	−	6.92820i	−0.360668	−	0.624695i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	−1.00000			−0.0894427
$126$	−2.50000	−	4.33013i	−0.222718	−	0.385758i
$127$	−2.50000	−	4.33013i	−0.221839	−	0.384237i	0.733527	−	0.679660i	$-0.237873\pi$
$127$	−2.50000	−	4.33013i	−0.221839	−	0.384237i	−0.955366	+	0.295423i	$0.904539\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$	−2.50000	+	4.33013i	−0.219265	+	0.379777i
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$	1.00000	+	1.73205i	0.0870388	+	0.150756i
$133$	−12.5000	−	21.6506i	−1.08389	−	1.87735i
$134$	2.00000			0.172774
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	−3.00000			−0.256307			−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000			−0.256307			−0.128154	+	0.991754i	$0.540905\pi$
$138$		0			0
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	−0.999947	−	0.0103230i	$-0.996714\pi$
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	0.491033	−	0.871141i	$-0.336619\pi$
$140$	5.00000			0.422577
$141$	1.00000	−	1.73205i	0.0842152	−	0.145865i
$142$	−9.00000			−0.755263
$143$	−5.00000	+	8.66025i	−0.418121	+	0.724207i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$	8.00000	+	13.8564i	0.662085	+	1.14676i
$147$	−18.0000			−1.48461
$148$	5.00000	+	3.46410i	0.410997	+	0.284747i
$149$	15.0000			1.22885			0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000			1.22885			0.614424	+	0.788976i	$0.289388\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	3.00000	−	5.19615i	0.244137	−	0.422857i	−0.717752	−	0.696299i	$-0.754829\pi$
$151$	3.00000	−	5.19615i	0.244137	−	0.422857i	0.961888	+	0.273442i	$0.0881622\pi$
$152$	−2.50000	+	4.33013i	−0.202777	+	0.351220i
$153$	−1.00000	+	1.73205i	−0.0808452	+	0.140028i
$154$	10.0000			0.805823
$155$	2.00000	−	3.46410i	0.160644	−	0.278243i
$156$	−5.00000			−0.400320
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$	12.0000			0.954669
$159$	8.00000			0.634441
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	0.902528	−	0.430632i	$-0.141709\pi$
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	−0.824202	+	0.566296i	$0.808376\pi$
$164$	4.00000	+	6.92820i	0.312348	+	0.541002i
$165$	−1.00000	−	1.73205i	−0.0778499	−	0.134840i
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	0.273252	+	0.961943i	$0.411901\pi$
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	−0.969693	+	0.244328i	$0.921432\pi$
$168$	2.50000	+	4.33013i	0.192879	+	0.334077i
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$	−1.00000	−	1.73205i	−0.0766965	−	0.132842i
$171$	−5.00000			−0.382360
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	−9.00000			−0.682288
$175$	−5.00000			−0.377964
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$	4.00000			0.300658
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	7.00000	−	12.1244i	0.520306	−	0.901196i	−0.479415	−	0.877588i	$-0.659151\pi$
$181$	7.00000	−	12.1244i	0.520306	−	0.901196i	0.999721	−	0.0236082i	$-0.00751541\pi$
$182$	−12.5000	+	21.6506i	−0.926562	+	1.60485i
$183$	7.00000	+	12.1244i	0.517455	+	0.896258i
$184$		0			0
$185$	−5.00000	−	3.46410i	−0.367607	−	0.254686i
$186$	4.00000			0.293294
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$	−1.00000	+	1.73205i	−0.0729325	+	0.126323i
$189$	−2.50000	+	4.33013i	−0.181848	+	0.314970i
$190$	2.50000	−	4.33013i	0.181369	−	0.314140i
$191$	4.00000			0.289430			0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000			0.289430			0.144715	+	0.989473i	$0.453773\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−16.0000			−1.15171			−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000			−1.15171			−0.575853	+	0.817554i	$0.695330\pi$
$194$	−2.00000	−	3.46410i	−0.143592	−	0.248708i
$195$	5.00000			0.358057
$196$	18.0000			1.28571
$197$	12.0000	+	20.7846i	0.854965	+	1.48084i	0.876678	+	0.481078i	$0.159755\pi$
$197$	12.0000	+	20.7846i	0.854965	+	1.48084i	−0.0217133	+	0.999764i	$0.506912\pi$
$198$	1.00000	−	1.73205i	0.0710669	−	0.123091i
$199$	14.0000			0.992434			0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000			0.992434			0.496217	+	0.868199i	$0.334722\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−1.00000	−	1.73205i	−0.0705346	−	0.122169i
$202$	−1.00000	−	1.73205i	−0.0703598	−	0.121867i
$203$	−22.5000	+	38.9711i	−1.57919	+	2.73524i
$204$	1.00000	−	1.73205i	0.0700140	−	0.121268i
$205$	−4.00000	−	6.92820i	−0.279372	−	0.483887i
$206$	1.50000	+	2.59808i	0.104510	+	0.181017i
$207$		0			0
$208$	5.00000			0.346688
$209$	5.00000	−	8.66025i	0.345857	−	0.599042i
$210$	−2.50000	−	4.33013i	−0.172516	−	0.298807i
$211$	−17.0000			−1.17033			−0.585164	−	0.810915i	$-0.698970\pi$
$211$	−17.0000			−1.17033			−0.585164	+	0.810915i	$0.698970\pi$
$212$	−8.00000			−0.549442
$213$	4.50000	+	7.79423i	0.308335	+	0.534052i
$214$	−12.0000			−0.820303
$215$	2.00000	−	3.46410i	0.136399	−	0.236250i
$216$	1.00000			0.0680414
$217$	10.0000	−	17.3205i	0.678844	−	1.17579i
$218$	−7.00000	+	12.1244i	−0.474100	+	0.821165i
$219$	8.00000	−	13.8564i	0.540590	−	0.936329i
$220$	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	$-0.368388\pi$
$223$	12.0000			0.803579			0.401790	+	0.915732i	$0.368388\pi$
$224$	−2.50000	−	4.33013i	−0.167038	−	0.289319i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	−6.50000	+	11.2583i	−0.432374	+	0.748893i
$227$	−12.5000	+	21.6506i	−0.829654	+	1.43700i	0.0686556	+	0.997640i	$0.478129\pi$
$227$	−12.5000	+	21.6506i	−0.829654	+	1.43700i	−0.898310	+	0.439363i	$0.855204\pi$
$228$	5.00000			0.331133
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	−0.792347	−	0.610071i	$-0.791141\pi$
$229$	2.00000	−	3.46410i	0.132164	−	0.228914i	0.924510	+	0.381157i	$0.124474\pi$
$230$		0			0
$231$	−5.00000	−	8.66025i	−0.328976	−	0.569803i
$232$	9.00000			0.590879
$233$	−3.00000			−0.196537			−0.0982683	−	0.995160i	$-0.531330\pi$
$233$	−3.00000			−0.196537			−0.0982683	+	0.995160i	$0.531330\pi$
$234$	2.50000	+	4.33013i	0.163430	+	0.283069i
$235$	1.00000	−	1.73205i	0.0652328	−	0.112987i
$236$	−4.00000			−0.260378
$237$	−6.00000	−	10.3923i	−0.389742	−	0.675053i
$238$	−5.00000	−	8.66025i	−0.324102	−	0.561361i
$239$	13.5000	+	23.3827i	0.873242	+	1.51250i	0.858623	+	0.512607i	$0.171320\pi$
$239$	13.5000	+	23.3827i	0.873242	+	1.51250i	0.0146191	+	0.999893i	$0.495346\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−7.00000	−	12.1244i	−0.448129	−	0.776182i
$245$	−18.0000			−1.14998
$246$	4.00000	−	6.92820i	0.255031	−	0.441726i
$247$	12.5000	+	21.6506i	0.795356	+	1.37760i
$248$	−4.00000			−0.254000
$249$	9.00000			0.570352
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	14.0000			0.883672			0.441836	−	0.897096i	$-0.354327\pi$
$251$	14.0000			0.883672			0.441836	+	0.897096i	$0.354327\pi$
$252$	2.50000	−	4.33013i	0.157485	−	0.272772i
$253$		0			0
$254$	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	0.994375	−	0.105919i	$-0.0337784\pi$
$257$	6.50000	+	11.2583i	0.405459	+	0.702275i	−0.588916	+	0.808194i	$0.700445\pi$
$258$	4.00000			0.249029
$259$	−25.0000	−	17.3205i	−1.55342	−	1.07624i
$260$	−5.00000			−0.310087
$261$	4.50000	+	7.79423i	0.278543	+	0.482451i
$262$	9.00000	−	15.5885i	0.556022	−	0.963058i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$	−1.00000	+	1.73205i	−0.0615457	+	0.106600i
$265$	8.00000			0.491436
$266$	12.5000	−	21.6506i	0.766424	−	1.32749i
$267$		0			0
$268$	1.00000	+	1.73205i	0.0610847	+	0.105802i
$269$	−15.0000			−0.914566			−0.457283	−	0.889321i	$-0.651177\pi$
$269$	−15.0000			−0.914566			−0.457283	+	0.889321i	$0.651177\pi$
$270$	−1.00000			−0.0608581
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	−0.991658	−	0.128897i	$-0.958856\pi$
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	0.384201	−	0.923249i	$-0.374477\pi$
$272$	−1.00000	+	1.73205i	−0.0606339	+	0.105021i
$273$	25.0000			1.51307
$274$	−1.50000	−	2.59808i	−0.0906183	−	0.156956i
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$		0			0
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$	6.00000	−	10.3923i	0.359856	−	0.623289i
$279$	−2.00000	−	3.46410i	−0.119737	−	0.207390i
$280$	2.50000	+	4.33013i	0.149404	+	0.258775i
$281$	9.00000	+	15.5885i	0.536895	+	0.929929i	0.999069	+	0.0431402i	$0.0137362\pi$
$281$	9.00000	+	15.5885i	0.536895	+	0.929929i	−0.462174	+	0.886789i	$0.652930\pi$
$282$	2.00000			0.119098
$283$	−3.00000	+	5.19615i	−0.178331	+	0.308879i	−0.941309	−	0.337546i	$-0.890403\pi$
$283$	−3.00000	+	5.19615i	−0.178331	+	0.308879i	0.762978	+	0.646425i	$0.223737\pi$
$284$	−4.50000	−	7.79423i	−0.267026	−	0.462502i
$285$	−5.00000			−0.296174
$286$	−10.0000			−0.591312
$287$	−20.0000	−	34.6410i	−1.18056	−	2.04479i
$288$	−1.00000			−0.0589256
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	−9.00000			−0.528498
$291$	−2.00000	+	3.46410i	−0.117242	+	0.203069i
$292$	−8.00000	+	13.8564i	−0.468165	+	0.810885i
$293$	−12.0000	+	20.7846i	−0.701047	+	1.21425i	0.267052	+	0.963682i	$0.413951\pi$
$293$	−12.0000	+	20.7846i	−0.701047	+	1.21425i	−0.968099	+	0.250568i	$0.919383\pi$
$294$	−9.00000	−	15.5885i	−0.524891	−	0.909137i
$295$	4.00000			0.232889
$296$	−0.500000	+	6.06218i	−0.0290619	+	0.352357i
$297$	−2.00000			−0.116052
$298$	7.50000	+	12.9904i	0.434463	+	0.752513i
$299$		0			0
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	10.0000	−	17.3205i	0.576390	−	0.998337i
$302$	6.00000			0.345261
$303$	−1.00000	+	1.73205i	−0.0574485	+	0.0995037i
$304$	−5.00000			−0.286770
$305$	7.00000	+	12.1244i	0.400819	+	0.694239i
$306$	−2.00000			−0.114332
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	5.00000	+	8.66025i	0.284901	+	0.493464i
$309$	1.50000	−	2.59808i	0.0853320	−	0.147799i
$310$	4.00000			0.227185
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	0.974841	+	0.222900i	$0.0715523\pi$
$311$	12.0000	+	20.7846i	0.680458	+	1.17859i	−0.294384	+	0.955687i	$0.595114\pi$
$312$	−2.50000	−	4.33013i	−0.141535	−	0.245145i
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$	−6.50000	+	11.2583i	−0.366816	+	0.635344i
$315$	−2.50000	+	4.33013i	−0.140859	+	0.243975i
$316$	6.00000	+	10.3923i	0.337526	+	0.584613i
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.829222	−	0.558920i	$-0.811216\pi$
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.0694277	−	0.997587i	$-0.522117\pi$
$318$	4.00000	+	6.92820i	0.224309	+	0.388514i
$319$	−18.0000			−1.00781
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	6.00000	+	10.3923i	0.334887	+	0.580042i
$322$		0			0
$323$	−10.0000			−0.556415
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	5.00000			0.277350
$326$	−1.00000	+	1.73205i	−0.0553849	+	0.0959294i
$327$	14.0000			0.774202
$328$	−4.00000	+	6.92820i	−0.220863	+	0.382546i
$329$	5.00000	−	8.66025i	0.275659	−	0.477455i
$330$	1.00000	−	1.73205i	0.0550482	−	0.0953463i
$331$	−3.50000	−	6.06218i	−0.192377	−	0.333207i	0.753660	−	0.657264i	$-0.228286\pi$
$331$	−3.50000	−	6.06218i	−0.192377	−	0.333207i	−0.946038	+	0.324057i	$0.894953\pi$
$332$	−9.00000			−0.493939
$333$	−5.50000	+	2.59808i	−0.301398	+	0.142374i
$334$	−18.0000			−0.984916
$335$	−1.00000	−	1.73205i	−0.0546358	−	0.0946320i
$336$	−2.50000	+	4.33013i	−0.136386	+	0.236228i
$337$	7.00000	−	12.1244i	0.381314	−	0.660456i	−0.609936	−	0.792451i	$-0.708805\pi$
$337$	7.00000	−	12.1244i	0.381314	−	0.660456i	0.991250	+	0.131995i	$0.0421382\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$	13.0000			0.706063
$340$	1.00000	−	1.73205i	0.0542326	−	0.0939336i
$341$	8.00000			0.433224
$342$	−2.50000	−	4.33013i	−0.135185	−	0.234146i
$343$	−55.0000			−2.96972
$344$	−4.00000			−0.215666
$345$		0			0
$346$		0			0
$347$	−17.0000			−0.912608			−0.456304	−	0.889824i	$-0.650827\pi$
$347$	−17.0000			−0.912608			−0.456304	+	0.889824i	$0.650827\pi$
$348$	−4.50000	−	7.79423i	−0.241225	−	0.417815i
$349$	10.0000	+	17.3205i	0.535288	+	0.927146i	0.999149	+	0.0412379i	$0.0131301\pi$
$349$	10.0000	+	17.3205i	0.535288	+	0.927146i	−0.463862	+	0.885908i	$0.653537\pi$
$350$	−2.50000	−	4.33013i	−0.133631	−	0.231455i
$351$	2.50000	−	4.33013i	0.133440	−	0.231125i
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	−2.50000	−	4.33013i	−0.133062	−	0.230469i	0.791794	−	0.610789i	$-0.209147\pi$
$353$	−2.50000	−	4.33013i	−0.133062	−	0.230469i	−0.924855	+	0.380319i	$0.875814\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$	4.50000	+	7.79423i	0.238835	+	0.413675i
$356$		0			0
$357$	−5.00000	+	8.66025i	−0.264628	+	0.458349i
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$	17.0000			0.897226			0.448613	−	0.893726i	$-0.351918\pi$
$359$	17.0000			0.897226			0.448613	+	0.893726i	$0.351918\pi$
$360$	1.00000			0.0527046
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	14.0000			0.735824
$363$	−3.50000	+	6.06218i	−0.183702	+	0.318182i
$364$	−25.0000			−1.31036
$365$	8.00000	−	13.8564i	0.418739	−	0.725277i
$366$	−7.00000	+	12.1244i	−0.365896	+	0.633750i
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$		0			0
$369$	−8.00000			−0.416463
$370$	0.500000	−	6.06218i	0.0259938	−	0.315158i
$371$	40.0000			2.07670
$372$	2.00000	+	3.46410i	0.103695	+	0.179605i
$373$	−1.50000	+	2.59808i	−0.0776671	+	0.134523i	−0.902243	−	0.431228i	$-0.858080\pi$
$373$	−1.50000	+	2.59808i	−0.0776671	+	0.134523i	0.824576	+	0.565751i	$0.191414\pi$
$374$	2.00000	−	3.46410i	0.103418	−	0.179124i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	−2.00000			−0.103142
$377$	22.5000	−	38.9711i	1.15881	−	2.00712i
$378$	−5.00000			−0.257172
$379$	6.50000	+	11.2583i	0.333883	+	0.578302i	0.983270	−	0.182157i	$-0.0583078\pi$
$379$	6.50000	+	11.2583i	0.333883	+	0.578302i	−0.649387	+	0.760458i	$0.724974\pi$
$380$	5.00000			0.256495
$381$	−5.00000			−0.256158
$382$	2.00000	+	3.46410i	0.102329	+	0.177239i
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	−0.932436	−	0.361335i	$-0.882321\pi$
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	0.779143	+	0.626846i	$0.215654\pi$
$384$	1.00000			0.0510310
$385$	−5.00000	−	8.66025i	−0.254824	−	0.441367i
$386$	−8.00000	−	13.8564i	−0.407189	−	0.705273i
$387$	−2.00000	−	3.46410i	−0.101666	−	0.176090i
$388$	2.00000	−	3.46410i	0.101535	−	0.175863i
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	−0.466915	−	0.884302i	$-0.654634\pi$
$389$	10.5000	−	18.1865i	0.532371	−	0.922094i	0.999286	−	0.0377914i	$-0.0120322\pi$
$390$	2.50000	+	4.33013i	0.126592	+	0.219265i
$391$		0			0
$392$	9.00000	+	15.5885i	0.454569	+	0.787336i
$393$	−18.0000			−0.907980
$394$	−12.0000	+	20.7846i	−0.604551	+	1.04711i
$395$	−6.00000	−	10.3923i	−0.301893	−	0.522894i
$396$	2.00000			0.100504
$397$	−2.00000			−0.100377			−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000			−0.100377			−0.0501886	+	0.998740i	$0.515982\pi$
$398$	7.00000	+	12.1244i	0.350878	+	0.607739i
$399$	−25.0000			−1.25157
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−30.0000			−1.49813			−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000			−1.49813			−0.749064	+	0.662497i	$0.769497\pi$
$402$	1.00000	−	1.73205i	0.0498755	−	0.0863868i
$403$	−10.0000	+	17.3205i	−0.498135	+	0.862796i
$404$	1.00000	−	1.73205i	0.0497519	−	0.0861727i
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	−45.0000			−2.23331
$407$	1.00000	−	12.1244i	0.0495682	−	0.600982i
$408$	2.00000			0.0990148
$409$	−1.50000	−	2.59808i	−0.0741702	−	0.128467i	0.826555	−	0.562856i	$-0.190297\pi$
$409$	−1.50000	−	2.59808i	−0.0741702	−	0.128467i	−0.900725	+	0.434389i	$0.856964\pi$
$410$	4.00000	−	6.92820i	0.197546	−	0.342160i
$411$	−1.50000	+	2.59808i	−0.0739895	+	0.128154i
$412$	−1.50000	+	2.59808i	−0.0738997	+	0.127998i
$413$	20.0000			0.984136
$414$		0			0
$415$	9.00000			0.441793
$416$	2.50000	+	4.33013i	0.122573	+	0.212302i
$417$	−12.0000			−0.587643
$418$	10.0000			0.489116
$419$	−17.0000	−	29.4449i	−0.830504	−	1.43848i	−0.897639	−	0.440732i	$-0.854719\pi$
$419$	−17.0000	−	29.4449i	−0.830504	−	1.43848i	0.0671345	−	0.997744i	$-0.478614\pi$
$420$	2.50000	−	4.33013i	0.121988	−	0.211289i
$421$	−8.00000			−0.389896			−0.194948	−	0.980814i	$-0.562454\pi$
$421$	−8.00000			−0.389896			−0.194948	+	0.980814i	$0.562454\pi$
$422$	−8.50000	−	14.7224i	−0.413774	−	0.716677i
$423$	−1.00000	−	1.73205i	−0.0486217	−	0.0842152i
$424$	−4.00000	−	6.92820i	−0.194257	−	0.336463i
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$	−4.50000	+	7.79423i	−0.218026	+	0.377632i
$427$	35.0000	+	60.6218i	1.69377	+	2.93369i
$428$	−6.00000	−	10.3923i	−0.290021	−	0.502331i
$429$	5.00000	+	8.66025i	0.241402	+	0.418121i
$430$	4.00000			0.192897
$431$	6.50000	−	11.2583i	0.313094	−	0.542295i	−0.665937	−	0.746008i	$-0.731968\pi$
$431$	6.50000	−	11.2583i	0.313094	−	0.542295i	0.979030	+	0.203714i	$0.0653012\pi$
$432$	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	$0.133696\pi$
$434$	20.0000			0.960031
$435$	4.50000	+	7.79423i	0.215758	+	0.373705i
$436$	−14.0000			−0.670478
$437$		0			0
$438$	16.0000			0.764510
$439$	−11.0000	+	19.0526i	−0.525001	+	0.909329i	0.474575	+	0.880215i	$0.342602\pi$
$439$	−11.0000	+	19.0526i	−0.525001	+	0.909329i	−0.999576	+	0.0291138i	$0.990731\pi$
$440$	−1.00000	+	1.73205i	−0.0476731	+	0.0825723i
$441$	−9.00000	+	15.5885i	−0.428571	+	0.742307i
$442$	5.00000	+	8.66025i	0.237826	+	0.411926i
$443$	−3.00000			−0.142534			−0.0712672	−	0.997457i	$-0.522704\pi$
$443$	−3.00000			−0.142534			−0.0712672	+	0.997457i	$0.522704\pi$
$444$	5.50000	−	2.59808i	0.261018	−	0.123299i
$445$		0			0
$446$	6.00000	+	10.3923i	0.284108	+	0.492090i
$447$	7.50000	−	12.9904i	0.354738	−	0.614424i
$448$	2.50000	−	4.33013i	0.118114	−	0.204579i
$449$	−10.0000	+	17.3205i	−0.471929	+	0.817405i	−0.999484	−	0.0321156i	$-0.989776\pi$
$449$	−10.0000	+	17.3205i	−0.471929	+	0.817405i	0.527555	+	0.849521i	$0.323109\pi$
$450$	−1.00000			−0.0471405
$451$	8.00000	−	13.8564i	0.376705	−	0.652473i
$452$	−13.0000			−0.611469
$453$	−3.00000	−	5.19615i	−0.140952	−	0.244137i
$454$	−25.0000			−1.17331
$455$	25.0000			1.17202
$456$	2.50000	+	4.33013i	0.117073	+	0.202777i
$457$	19.0000	−	32.9090i	0.888783	−	1.53942i	0.0474665	−	0.998873i	$-0.484885\pi$
$457$	19.0000	−	32.9090i	0.888783	−	1.53942i	0.841316	−	0.540544i	$-0.181781\pi$
$458$	4.00000			0.186908
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$		0			0
$461$	−17.5000	−	30.3109i	−0.815056	−	1.41172i	−0.909288	−	0.416169i	$-0.863373\pi$
$461$	−17.5000	−	30.3109i	−0.815056	−	1.41172i	0.0942312	−	0.995550i	$-0.469961\pi$
$462$	5.00000	−	8.66025i	0.232621	−	0.402911i
$463$	−11.5000	+	19.9186i	−0.534450	+	0.925695i	0.464739	+	0.885448i	$0.346148\pi$
$463$	−11.5000	+	19.9186i	−0.534450	+	0.925695i	−0.999190	+	0.0402476i	$0.987185\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$	−2.00000	−	3.46410i	−0.0927478	−	0.160644i
$466$	−1.50000	−	2.59808i	−0.0694862	−	0.120354i
$467$	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
$469$	−5.00000	−	8.66025i	−0.230879	−	0.399893i
$470$	2.00000			0.0922531
$471$	13.0000			0.599008
$472$	−2.00000	−	3.46410i	−0.0920575	−	0.159448i
$473$	8.00000			0.367840
$474$	6.00000	−	10.3923i	0.275589	−	0.477334i
$475$	−5.00000			−0.229416
$476$	5.00000	−	8.66025i	0.229175	−	0.396942i
$477$	4.00000	−	6.92820i	0.183147	−	0.317221i
$478$	−13.5000	+	23.3827i	−0.617476	+	1.06950i
$479$	−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	$0.921729\pi$
$480$	−1.00000			−0.0456435
$481$	25.0000	+	17.3205i	1.13990	+	0.789747i
$482$	−18.0000			−0.819878
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	−2.00000	+	3.46410i	−0.0908153	+	0.157297i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	33.0000			1.49537			0.747686	−	0.664052i	$-0.231165\pi$
$487$	33.0000			1.49537			0.747686	+	0.664052i	$0.231165\pi$
$488$	7.00000	−	12.1244i	0.316875	−	0.548844i
$489$	2.00000			0.0904431
$490$	−9.00000	−	15.5885i	−0.406579	−	0.704215i
$491$	6.00000			0.270776			0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000			0.270776			0.135388	+	0.990793i	$0.456772\pi$
$492$	8.00000			0.360668
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	−12.5000	+	21.6506i	−0.562402	+	0.974108i
$495$	−2.00000			−0.0898933
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	22.5000	+	38.9711i	1.00926	+	1.74809i
$498$	4.50000	+	7.79423i	0.201650	+	0.349268i
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	−0.276683	−	0.960961i	$-0.589235\pi$
$499$	15.5000	−	26.8468i	0.693875	−	1.20183i	0.970558	−	0.240866i	$-0.0774314\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	9.00000	+	15.5885i	0.402090	+	0.696441i
$502$	7.00000	+	12.1244i	0.312425	+	0.541136i
$503$	−6.00000	−	10.3923i	−0.267527	−	0.463370i	0.700696	−	0.713460i	$-0.252873\pi$
$503$	−6.00000	−	10.3923i	−0.267527	−	0.463370i	−0.968223	+	0.250090i	$0.919540\pi$
$504$	5.00000			0.222718
$505$	−1.00000	+	1.73205i	−0.0444994	+	0.0770752i
$506$		0			0
$507$	−12.0000			−0.532939
$508$	5.00000			0.221839
$509$	4.50000	+	7.79423i	0.199459	+	0.345473i	0.948353	−	0.317217i	$-0.102748\pi$
$509$	4.50000	+	7.79423i	0.199459	+	0.345473i	−0.748894	+	0.662690i	$0.769415\pi$
$510$	−2.00000			−0.0885615
$511$	40.0000	−	69.2820i	1.76950	−	3.06486i
$512$	−1.00000			−0.0441942
$513$	−2.50000	+	4.33013i	−0.110378	+	0.191180i
$514$	−6.50000	+	11.2583i	−0.286703	+	0.496584i
$515$	1.50000	−	2.59808i	0.0660979	−	0.114485i
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$	4.00000			0.175920
$518$	2.50000	−	30.3109i	0.109844	−	1.33178i
$519$		0			0
$520$	−2.50000	−	4.33013i	−0.109632	−	0.189889i
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	0.924229	+	0.381839i	$0.124709\pi$
$522$	−4.50000	+	7.79423i	−0.196960	+	0.341144i
$523$	−21.0000	+	36.3731i	−0.918266	+	1.59048i	−0.116218	+	0.993224i	$0.537077\pi$
$523$	−21.0000	+	36.3731i	−0.918266	+	1.59048i	−0.802048	+	0.597259i	$0.796256\pi$
$524$	18.0000			0.786334
$525$	−2.50000	+	4.33013i	−0.109109	+	0.188982i
$526$		0			0
$527$	−4.00000	−	6.92820i	−0.174243	−	0.301797i
$528$	−2.00000			−0.0870388
$529$	−23.0000			−1.00000
$530$	4.00000	+	6.92820i	0.173749	+	0.300942i
$531$	2.00000	−	3.46410i	0.0867926	−	0.150329i
$532$	25.0000			1.08389
$533$	20.0000	+	34.6410i	0.866296	+	1.50047i
$534$		0			0
$535$	6.00000	+	10.3923i	0.259403	+	0.449299i
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$	−6.00000	+	10.3923i	−0.258919	+	0.448461i
$538$	−7.50000	−	12.9904i	−0.323348	−	0.560055i
$539$	−18.0000	−	31.1769i	−0.775315	−	1.34288i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	38.0000			1.63375			0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000			1.63375			0.816874	+	0.576816i	$0.195705\pi$
$542$	10.0000	−	17.3205i	0.429537	−	0.743980i
$543$	−7.00000	−	12.1244i	−0.300399	−	0.520306i
$544$	−2.00000			−0.0857493
$545$	14.0000			0.599694
$546$	12.5000	+	21.6506i	0.534951	+	0.926562i
$547$	40.0000			1.71028			0.855138	−	0.518400i	$-0.173472\pi$
$547$	40.0000			1.71028			0.855138	+	0.518400i	$0.173472\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$	14.0000			0.597505
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$	−22.5000	+	38.9711i	−0.958532	+	1.66023i
$552$		0			0
$553$	−30.0000	−	51.9615i	−1.27573	−	2.20963i
$554$	1.00000			0.0424859
$555$	−5.50000	+	2.59808i	−0.233462	+	0.110282i
$556$	12.0000			0.508913
$557$	−7.00000	−	12.1244i	−0.296600	−	0.513725i	0.678756	−	0.734364i	$-0.262519\pi$
$557$	−7.00000	−	12.1244i	−0.296600	−	0.513725i	−0.975356	+	0.220638i	$0.929186\pi$
$558$	2.00000	−	3.46410i	0.0846668	−	0.146647i
$559$	−10.0000	+	17.3205i	−0.422955	+	0.732579i
$560$	−2.50000	+	4.33013i	−0.105644	+	0.182981i
$561$	−4.00000			−0.168880
$562$	−9.00000	+	15.5885i	−0.379642	+	0.657559i
$563$	−11.0000			−0.463595			−0.231797	−	0.972764i	$-0.574461\pi$
$563$	−11.0000			−0.463595			−0.231797	+	0.972764i	$0.574461\pi$
$564$	1.00000	+	1.73205i	0.0421076	+	0.0729325i
$565$	13.0000			0.546914
$566$	−6.00000			−0.252199
$567$	2.50000	+	4.33013i	0.104990	+	0.181848i
$568$	4.50000	−	7.79423i	0.188816	−	0.327039i
$569$	12.0000			0.503066			0.251533	−	0.967849i	$-0.419065\pi$
$569$	12.0000			0.503066			0.251533	+	0.967849i	$0.419065\pi$
$570$	−2.50000	−	4.33013i	−0.104713	−	0.181369i
$571$	9.50000	+	16.4545i	0.397563	+	0.688599i	0.993425	−	0.114488i	$-0.0365228\pi$
$571$	9.50000	+	16.4545i	0.397563	+	0.688599i	−0.595862	+	0.803087i	$0.703189\pi$
$572$	−5.00000	−	8.66025i	−0.209061	−	0.362103i
$573$	2.00000	−	3.46410i	0.0835512	−	0.144715i
$574$	20.0000	−	34.6410i	0.834784	−	1.44589i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−13.0000	−	22.5167i	−0.541197	−	0.937381i	−0.998836	−	0.0482425i	$-0.984638\pi$
$577$	−13.0000	−	22.5167i	−0.541197	−	0.937381i	0.457639	−	0.889138i	$-0.348695\pi$
$578$	13.0000			0.540729
$579$	−8.00000	+	13.8564i	−0.332469	+	0.575853i
$580$	−4.50000	−	7.79423i	−0.186852	−	0.323638i
$581$	45.0000			1.86691
$582$	−4.00000			−0.165805
$583$	8.00000	+	13.8564i	0.331326	+	0.573874i
$584$	−16.0000			−0.662085
$585$	2.50000	−	4.33013i	0.103362	−	0.179029i
$586$	−24.0000			−0.991431
$587$	−3.50000	+	6.06218i	−0.144460	+	0.250213i	−0.929172	−	0.369649i	$-0.879478\pi$
$587$	−3.50000	+	6.06218i	−0.144460	+	0.250213i	0.784711	+	0.619862i	$0.212811\pi$
$588$	9.00000	−	15.5885i	0.371154	−	0.642857i
$589$	10.0000	−	17.3205i	0.412043	−	0.713679i
$590$	2.00000	+	3.46410i	0.0823387	+	0.142615i
$591$	24.0000			0.987228
$592$	−5.50000	+	2.59808i	−0.226049	+	0.106780i
$593$	18.0000			0.739171			0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000			0.739171			0.369586	+	0.929197i	$0.379500\pi$
$594$	−1.00000	−	1.73205i	−0.0410305	−	0.0710669i
$595$	−5.00000	+	8.66025i	−0.204980	+	0.355036i
$596$	−7.50000	+	12.9904i	−0.307212	+	0.532107i
$597$	7.00000	−	12.1244i	0.286491	−	0.496217i
$598$		0			0
$599$	8.50000	−	14.7224i	0.347301	−	0.601542i	−0.638468	−	0.769648i	$-0.720432\pi$
$599$	8.50000	−	14.7224i	0.347301	−	0.601542i	0.985769	+	0.168106i	$0.0537650\pi$
$600$	1.00000			0.0408248
$601$	−17.0000	−	29.4449i	−0.693444	−	1.20108i	−0.970702	−	0.240285i	$-0.922759\pi$
$601$	−17.0000	−	29.4449i	−0.693444	−	1.20108i	0.277258	−	0.960796i	$-0.410574\pi$
$602$	20.0000			0.815139
$603$	−2.00000			−0.0814463
$604$	3.00000	+	5.19615i	0.122068	+	0.211428i
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$	−2.00000			−0.0812444
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	0.875994	−	0.482322i	$-0.160206\pi$
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	−0.855700	+	0.517472i	$0.826873\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$	22.5000	+	38.9711i	0.911746	+	1.57919i
$610$	−7.00000	+	12.1244i	−0.283422	+	0.490901i
$611$	−5.00000	+	8.66025i	−0.202278	+	0.350356i
$612$	−1.00000	−	1.73205i	−0.0404226	−	0.0700140i
$613$	7.50000	+	12.9904i	0.302922	+	0.524677i	0.976797	−	0.214169i	$-0.0687045\pi$
$613$	7.50000	+	12.9904i	0.302922	+	0.524677i	−0.673874	+	0.738846i	$0.735371\pi$
$614$	−1.00000	−	1.73205i	−0.0403567	−	0.0698999i
$615$	−8.00000			−0.322591
$616$	−5.00000	+	8.66025i	−0.201456	+	0.348932i
$617$	−12.5000	−	21.6506i	−0.503231	−	0.871622i	−0.999993	−	0.00373492i	$-0.998811\pi$
$617$	−12.5000	−	21.6506i	−0.503231	−	0.871622i	0.496762	−	0.867887i	$-0.334522\pi$
$618$	3.00000			0.120678
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$	2.00000	+	3.46410i	0.0803219	+	0.139122i
$621$		0			0
$622$	−12.0000	+	20.7846i	−0.481156	+	0.833387i
$623$		0			0
$624$	2.50000	−	4.33013i	0.100080	−	0.173344i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−5.00000	−	8.66025i	−0.199681	−	0.345857i
$628$	−13.0000			−0.518756
$629$	−11.0000	+	5.19615i	−0.438599	+	0.207184i
$630$	−5.00000			−0.199205
$631$	−16.0000	−	27.7128i	−0.636950	−	1.10323i	−0.986098	−	0.166162i	$-0.946862\pi$
$631$	−16.0000	−	27.7128i	−0.636950	−	1.10323i	0.349148	−	0.937067i	$-0.386471\pi$
$632$	−6.00000	+	10.3923i	−0.238667	+	0.413384i
$633$	−8.50000	+	14.7224i	−0.337845	+	0.585164i
$634$	16.0000	−	27.7128i	0.635441	−	1.10062i
$635$	−5.00000			−0.198419
$636$	−4.00000	+	6.92820i	−0.158610	+	0.274721i
$637$	90.0000			3.56593
$638$	−9.00000	−	15.5885i	−0.356313	−	0.617153i
$639$	9.00000			0.356034
$640$	1.00000			0.0395285
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	−0.898470	−	0.439034i	$-0.855321\pi$
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	0.0690201	−	0.997615i	$-0.478013\pi$
$642$	−6.00000	+	10.3923i	−0.236801	+	0.410152i
$643$	26.0000			1.02534			0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000			1.02534			0.512670	+	0.858586i	$0.328656\pi$
$644$		0			0
$645$	−2.00000	−	3.46410i	−0.0787499	−	0.136399i
$646$	−5.00000	−	8.66025i	−0.196722	−	0.340733i
$647$	−13.0000	+	22.5167i	−0.511083	+	0.885221i	0.488835	+	0.872376i	$0.337422\pi$
$647$	−13.0000	+	22.5167i	−0.511083	+	0.885221i	−0.999918	+	0.0128449i	$0.995911\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	4.00000	+	6.92820i	0.157014	+	0.271956i
$650$	2.50000	+	4.33013i	0.0980581	+	0.169842i
$651$	−10.0000	−	17.3205i	−0.391931	−	0.678844i
$652$	−2.00000			−0.0783260
$653$	−14.0000	+	24.2487i	−0.547862	+	0.948925i	0.450558	+	0.892747i	$0.351225\pi$
$653$	−14.0000	+	24.2487i	−0.547862	+	0.948925i	−0.998421	+	0.0561784i	$0.982108\pi$
$654$	7.00000	+	12.1244i	0.273722	+	0.474100i
$655$	−18.0000			−0.703318
$656$	−8.00000			−0.312348
$657$	−8.00000	−	13.8564i	−0.312110	−	0.540590i
$658$	10.0000			0.389841
$659$	24.0000	−	41.5692i	0.934907	−	1.61931i	0.160108	−	0.987099i	$-0.448816\pi$
$659$	24.0000	−	41.5692i	0.934907	−	1.61931i	0.774799	−	0.632207i	$-0.217851\pi$
$660$	2.00000			0.0778499
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	0.366723	+	0.930330i	$0.380480\pi$
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	−0.989051	+	0.147573i	$0.952854\pi$
$662$	3.50000	−	6.06218i	0.136031	−	0.235613i
$663$	5.00000	−	8.66025i	0.194184	−	0.336336i
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$	−25.0000			−0.969458
$666$	−5.00000	−	3.46410i	−0.193746	−	0.134231i
$667$		0			0
$668$	−9.00000	−	15.5885i	−0.348220	−	0.603136i
$669$	6.00000	−	10.3923i	0.231973	−	0.401790i
$670$	1.00000	−	1.73205i	0.0386334	−	0.0669150i
$671$	−14.0000	+	24.2487i	−0.540464	+	0.936111i
$672$	−5.00000			−0.192879
$673$	4.00000	−	6.92820i	0.154189	−	0.267063i	−0.778575	−	0.627552i	$-0.784057\pi$
$673$	4.00000	−	6.92820i	0.154189	−	0.267063i	0.932763	+	0.360489i	$0.117390\pi$
$674$	14.0000			0.539260
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	12.0000			0.461538
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$	6.50000	+	11.2583i	0.249631	+	0.432374i
$679$	−10.0000	+	17.3205i	−0.383765	+	0.664700i
$680$	2.00000			0.0766965
$681$	12.5000	+	21.6506i	0.479001	+	0.829654i
$682$	4.00000	+	6.92820i	0.153168	+	0.265295i
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	−0.972242	−	0.233977i	$-0.924826\pi$
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	0.283491	−	0.958975i	$-0.408507\pi$
$684$	2.50000	−	4.33013i	0.0955899	−	0.165567i
$685$	−1.50000	+	2.59808i	−0.0573121	+	0.0992674i
$686$	−27.5000	−	47.6314i	−1.04995	−	1.81858i
$687$	−2.00000	−	3.46410i	−0.0763048	−	0.132164i
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	−40.0000			−1.52388
$690$		0			0
$691$	22.5000	+	38.9711i	0.855940	+	1.48253i	0.875770	+	0.482729i	$0.160354\pi$
$691$	22.5000	+	38.9711i	0.855940	+	1.48253i	−0.0198296	+	0.999803i	$0.506312\pi$
$692$		0			0
$693$	−10.0000			−0.379869
$694$	−8.50000	−	14.7224i	−0.322656	−	0.558856i
$695$	−12.0000			−0.455186
$696$	4.50000	−	7.79423i	0.170572	−	0.295439i
$697$	−16.0000			−0.606043
$698$	−10.0000	+	17.3205i	−0.378506	+	0.655591i
$699$	−1.50000	+	2.59808i	−0.0567352	+	0.0982683i
$700$	2.50000	−	4.33013i	0.0944911	−	0.163663i
$701$	−15.0000	−	25.9808i	−0.566542	−	0.981280i	−0.996904	−	0.0786236i	$-0.974947\pi$
$701$	−15.0000	−	25.9808i	−0.566542	−	0.981280i	0.430362	−	0.902656i	$-0.358386\pi$
$702$	5.00000			0.188713
$703$	−25.0000	−	17.3205i	−0.942893	−	0.653255i
$704$	2.00000			0.0753778
$705$	−1.00000	−	1.73205i	−0.0376622	−	0.0652328i
$706$	2.50000	−	4.33013i	0.0940887	−	0.162966i
$707$	−5.00000	+	8.66025i	−0.188044	+	0.325702i
$708$	−2.00000	+	3.46410i	−0.0751646	+	0.130189i
$709$	38.0000			1.42712			0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000			1.42712			0.713560	+	0.700594i	$0.247082\pi$
$710$	−4.50000	+	7.79423i	−0.168882	+	0.292512i
$711$	−12.0000			−0.450035
$712$		0			0
$713$		0			0
$714$	−10.0000			−0.374241
$715$	5.00000	+	8.66025i	0.186989	+	0.323875i
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$	27.0000			1.00833
$718$	8.50000	+	14.7224i	0.317217	+	0.549436i
$719$	21.5000	+	37.2391i	0.801815	+	1.38878i	0.918421	+	0.395606i	$0.129465\pi$
$719$	21.5000	+	37.2391i	0.801815	+	1.38878i	−0.116606	+	0.993178i	$0.537201\pi$
$720$	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
$723$	9.00000	+	15.5885i	0.334714	+	0.579741i
$724$	7.00000	+	12.1244i	0.260153	+	0.450598i
$725$	4.50000	+	7.79423i	0.167126	+	0.289470i
$726$	−7.00000			−0.259794
$727$	−17.5000	+	30.3109i	−0.649039	+	1.12417i	0.334314	+	0.942462i	$0.391496\pi$
$727$	−17.5000	+	30.3109i	−0.649039	+	1.12417i	−0.983353	+	0.181707i	$0.941838\pi$
$728$	−12.5000	−	21.6506i	−0.463281	−	0.802426i
$729$	1.00000			0.0370370
$730$	16.0000			0.592187
$731$	−4.00000	−	6.92820i	−0.147945	−	0.256249i
$732$	−14.0000			−0.517455
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	0.443940	+	0.896056i	$0.353580\pi$
$733$	−15.0000	+	25.9808i	−0.554038	+	0.959621i	−0.997978	+	0.0635649i	$0.979753\pi$
$734$	−17.0000			−0.627481
$735$	−9.00000	+	15.5885i	−0.331970	+	0.574989i
$736$		0			0
$737$	2.00000	−	3.46410i	0.0736709	−	0.127602i
$738$	−4.00000	−	6.92820i	−0.147242	−	0.255031i
$739$	17.0000			0.625355			0.312678	−	0.949859i	$-0.398774\pi$
$739$	17.0000			0.625355			0.312678	+	0.949859i	$0.398774\pi$
$740$	5.50000	−	2.59808i	0.202184	−	0.0955072i
$741$	25.0000			0.918398
$742$	20.0000	+	34.6410i	0.734223	+	1.27171i
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	−0.320166	−	0.947361i	$-0.603739\pi$
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	0.980522	−	0.196409i	$-0.0629279\pi$
$744$	−2.00000	+	3.46410i	−0.0733236	+	0.127000i
$745$	7.50000	−	12.9904i	0.274779	−	0.475931i
$746$	−3.00000			−0.109838
$747$	4.50000	−	7.79423i	0.164646	−	0.285176i
$748$	4.00000			0.146254
$749$	30.0000	+	51.9615i	1.09618	+	1.89863i
$750$	−1.00000			−0.0365148
$751$	−46.0000			−1.67856			−0.839282	−	0.543696i	$-0.817024\pi$
$751$	−46.0000			−1.67856			−0.839282	+	0.543696i	$0.817024\pi$
$752$	−1.00000	−	1.73205i	−0.0364662	−	0.0631614i
$753$	7.00000	−	12.1244i	0.255094	−	0.441836i
$754$	45.0000			1.63880
$755$	−3.00000	−	5.19615i	−0.109181	−	0.189107i
$756$	−2.50000	−	4.33013i	−0.0909241	−	0.157485i
$757$	6.50000	+	11.2583i	0.236247	+	0.409191i	0.959634	−	0.281251i	$-0.0907494\pi$
$757$	6.50000	+	11.2583i	0.236247	+	0.409191i	−0.723388	+	0.690442i	$0.757416\pi$
$758$	−6.50000	+	11.2583i	−0.236091	+	0.408921i
$759$		0			0
$760$	2.50000	+	4.33013i	0.0906845	+	0.157070i
$761$	−4.00000	−	6.92820i	−0.145000	−	0.251147i	0.784373	−	0.620289i	$-0.212985\pi$
$761$	−4.00000	−	6.92820i	−0.145000	−	0.251147i	−0.929373	+	0.369142i	$0.879652\pi$
$762$	−2.50000	−	4.33013i	−0.0905654	−	0.156864i
$763$	70.0000			2.53417
$764$	−2.00000	+	3.46410i	−0.0723575	+	0.125327i
$765$	1.00000	+	1.73205i	0.0361551	+	0.0626224i
$766$	−6.00000			−0.216789
$767$	−20.0000			−0.722158
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−41.0000			−1.47850			−0.739249	−	0.673432i	$-0.764819\pi$
$769$	−41.0000			−1.47850			−0.739249	+	0.673432i	$0.764819\pi$
$770$	5.00000	−	8.66025i	0.180187	−	0.312094i
$771$	13.0000			0.468184
$772$	8.00000	−	13.8564i	0.287926	−	0.498703i
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	−0.00558380	−	0.999984i	$-0.501777\pi$
$773$	24.0000	−	41.5692i	0.863220	−	1.49514i	0.868804	−	0.495156i	$-0.164889\pi$
$774$	2.00000	−	3.46410i	0.0718885	−	0.124515i
$775$	−2.00000	−	3.46410i	−0.0718421	−	0.124434i
$776$	4.00000			0.143592
$777$	−27.5000	+	12.9904i	−0.986557	+	0.466027i
$778$	21.0000			0.752886
$779$	−20.0000	−	34.6410i	−0.716574	−	1.24114i
$780$	−2.50000	+	4.33013i	−0.0895144	+	0.155043i
$781$	−9.00000	+	15.5885i	−0.322045	+	0.557799i
$782$		0			0
$783$	9.00000			0.321634
$784$	−9.00000	+	15.5885i	−0.321429	+	0.556731i
$785$	13.0000			0.463990
$786$	−9.00000	−	15.5885i	−0.321019	−	0.556022i
$787$		0			0			−	1.00000i	$-0.5\pi$
$787$		0			0				1.00000i	$0.5\pi$
$788$	−24.0000			−0.854965
$789$		0			0
$790$	6.00000	−	10.3923i	0.213470	−	0.369742i
$791$	65.0000			2.31113
$792$	1.00000	+	1.73205i	0.0355335	+	0.0615457i
$793$	−35.0000	−	60.6218i	−1.24289	−	2.15274i
$794$	−1.00000	−	1.73205i	−0.0354887	−	0.0614682i
$795$	4.00000	−	6.92820i	0.141865	−	0.245718i
$796$	−7.00000	+	12.1244i	−0.248108	+	0.429736i
$797$	12.0000	+	20.7846i	0.425062	+	0.736229i	0.996426	−	0.0844678i	$-0.0269190\pi$
$797$	12.0000	+	20.7846i	0.425062	+	0.736229i	−0.571364	+	0.820696i	$0.693586\pi$
$798$	−12.5000	−	21.6506i	−0.442495	−	0.766424i
$799$	−2.00000	−	3.46410i	−0.0707549	−	0.122551i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$	−15.0000	−	25.9808i	−0.529668	−	0.917413i
$803$	32.0000			1.12926
$804$	2.00000			0.0705346
$805$		0			0
$806$	−20.0000			−0.704470
$807$	−7.50000	+	12.9904i	−0.264013	+	0.457283i
$808$	2.00000			0.0703598
$809$	24.0000	−	41.5692i	0.843795	−	1.46150i	−0.0428684	−	0.999081i	$-0.513650\pi$
$809$	24.0000	−	41.5692i	0.843795	−	1.46150i	0.886664	−	0.462415i	$-0.153017\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−20.0000	+	34.6410i	−0.702295	+	1.21641i	0.265364	+	0.964148i	$0.414508\pi$
$811$	−20.0000	+	34.6410i	−0.702295	+	1.21641i	−0.967659	+	0.252262i	$0.918825\pi$
$812$	−22.5000	−	38.9711i	−0.789595	−	1.36762i
$813$	−20.0000			−0.701431
$814$	11.0000	−	5.19615i	0.385550	−	0.182125i
$815$	2.00000			0.0700569
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$	10.0000	−	17.3205i	0.349856	−	0.605968i
$818$	1.50000	−	2.59808i	0.0524463	−	0.0908396i
$819$	12.5000	−	21.6506i	0.436785	−	0.756534i
$820$	8.00000			0.279372
$821$	2.50000	−	4.33013i	0.0872506	−	0.151122i	−0.819097	−	0.573654i	$-0.805525\pi$
$821$	2.50000	−	4.33013i	0.0872506	−	0.151122i	0.906348	+	0.422532i	$0.138859\pi$
$822$	−3.00000			−0.104637
$823$	−20.5000	−	35.5070i	−0.714585	−	1.23770i	−0.963119	−	0.269075i	$-0.913282\pi$
$823$	−20.5000	−	35.5070i	−0.714585	−	1.23770i	0.248534	−	0.968623i	$-0.420051\pi$
$824$	−3.00000			−0.104510
$825$	−2.00000			−0.0696311
$826$	10.0000	+	17.3205i	0.347945	+	0.602658i
$827$	−7.50000	+	12.9904i	−0.260801	+	0.451720i	−0.966455	−	0.256836i	$-0.917320\pi$
$827$	−7.50000	+	12.9904i	−0.260801	+	0.451720i	0.705654	+	0.708556i	$0.250653\pi$
$828$		0			0
$829$	−20.0000	−	34.6410i	−0.694629	−	1.20313i	−0.970306	−	0.241882i	$-0.922235\pi$
$829$	−20.0000	−	34.6410i	−0.694629	−	1.20313i	0.275677	−	0.961250i	$-0.411098\pi$
$830$	4.50000	+	7.79423i	0.156197	+	0.270542i
$831$	−0.500000	−	0.866025i	−0.0173448	−	0.0300421i
$832$	−2.50000	+	4.33013i	−0.0866719	+	0.150120i
$833$	−18.0000	+	31.1769i	−0.623663	+	1.08022i
$834$	−6.00000	−	10.3923i	−0.207763	−	0.359856i
$835$	9.00000	+	15.5885i	0.311458	+	0.539461i
$836$	5.00000	+	8.66025i	0.172929	+	0.299521i
$837$	−4.00000			−0.138260
$838$	17.0000	−	29.4449i	0.587255	−	1.01716i
$839$	−2.00000	−	3.46410i	−0.0690477	−	0.119594i	0.829435	−	0.558604i	$-0.188663\pi$
$839$	−2.00000	−	3.46410i	−0.0690477	−	0.119594i	−0.898482	+	0.439010i	$0.855329\pi$
$840$	5.00000			0.172516
$841$	52.0000			1.79310
$842$	−4.00000	−	6.92820i	−0.137849	−	0.238762i
$843$	18.0000			0.619953
$844$	8.50000	−	14.7224i	0.292582	−	0.506767i
$845$	−12.0000			−0.412813
$846$	1.00000	−	1.73205i	0.0343807	−	0.0595491i
$847$	−17.5000	+	30.3109i	−0.601307	+	1.04149i
$848$	4.00000	−	6.92820i	0.137361	−	0.237915i
$849$	3.00000	+	5.19615i	0.102960	+	0.178331i
$850$	−2.00000			−0.0685994
$851$		0			0
$852$	−9.00000			−0.308335
$853$	13.0000	+	22.5167i	0.445112	+	0.770956i	0.998060	−	0.0622597i	$-0.0198307\pi$
$853$	13.0000	+	22.5167i	0.445112	+	0.770956i	−0.552948	+	0.833215i	$0.686497\pi$
$854$	−35.0000	+	60.6218i	−1.19768	+	2.07443i
$855$	−2.50000	+	4.33013i	−0.0854982	+	0.148087i
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	−41.0000			−1.40053			−0.700267	−	0.713881i	$-0.746936\pi$
$857$	−41.0000			−1.40053			−0.700267	+	0.713881i	$0.746936\pi$
$858$	−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	$0.731710\pi$
$860$	2.00000	+	3.46410i	0.0681994	+	0.118125i
$861$	−40.0000			−1.36320
$862$	13.0000			0.442782
$863$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$863$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	19.0000	+	32.9090i	0.645646	+	1.11829i
$867$	−6.50000	−	11.2583i	−0.220752	−	0.382353i
$868$	10.0000	+	17.3205i	0.339422	+	0.587896i
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$	−4.50000	+	7.79423i	−0.152564	+	0.264249i
$871$	5.00000	+	8.66025i	0.169419	+	0.293442i
$872$	−7.00000	−	12.1244i	−0.237050	−	0.410582i
$873$	2.00000	+	3.46410i	0.0676897	+	0.117242i
$874$		0			0
$875$	−2.50000	+	4.33013i	−0.0845154	+	0.146385i
$876$	8.00000	+	13.8564i	0.270295	+	0.468165i
$877$	−13.0000			−0.438979			−0.219489	−	0.975615i	$-0.570439\pi$
$877$	−13.0000			−0.438979			−0.219489	+	0.975615i	$0.570439\pi$
$878$	−22.0000			−0.742464
$879$	12.0000	+	20.7846i	0.404750	+	0.701047i
$880$	−2.00000			−0.0674200
$881$	9.00000	−	15.5885i	0.303218	−	0.525188i	−0.673645	−	0.739055i	$-0.735272\pi$
$881$	9.00000	−	15.5885i	0.303218	−	0.525188i	0.976863	+	0.213866i	$0.0686057\pi$
$882$	−18.0000			−0.606092
$883$	1.00000	−	1.73205i	0.0336527	−	0.0582882i	−0.848709	−	0.528861i	$-0.822619\pi$
$883$	1.00000	−	1.73205i	0.0336527	−	0.0582882i	0.882361	+	0.470573i	$0.155953\pi$
$884$	−5.00000	+	8.66025i	−0.168168	+	0.291276i
$885$	2.00000	−	3.46410i	0.0672293	−	0.116445i
$886$	−1.50000	−	2.59808i	−0.0503935	−	0.0872841i
$887$	−20.0000			−0.671534			−0.335767	−	0.941945i	$-0.608996\pi$
$887$	−20.0000			−0.671534			−0.335767	+	0.941945i	$0.608996\pi$
$888$	5.00000	+	3.46410i	0.167789	+	0.116248i
$889$	−25.0000			−0.838473
$890$		0			0
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	−6.00000	+	10.3923i	−0.200895	+	0.347960i
$893$	5.00000	−	8.66025i	0.167319	−	0.289804i
$894$	15.0000			0.501675
$895$	−6.00000	+	10.3923i	−0.200558	+	0.347376i
$896$	5.00000			0.167038
$897$		0			0
$898$	−20.0000			−0.667409
$899$	−36.0000			−1.20067
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	8.00000	−	13.8564i	0.266519	−	0.461624i
$902$	16.0000			0.532742
$903$	−10.0000	−	17.3205i	−0.332779	−	0.576390i
$904$	−6.50000	−	11.2583i	−0.216187	−	0.374446i
$905$	−7.00000	−	12.1244i	−0.232688	−	0.403027i
$906$	3.00000	−	5.19615i	0.0996683	−	0.172631i
$907$	16.0000	−	27.7128i	0.531271	−	0.920189i	−0.468063	−	0.883695i	$-0.655048\pi$
$907$	16.0000	−	27.7128i	0.531271	−	0.920189i	0.999334	−	0.0364935i	$-0.0116188\pi$
$908$	−12.5000	−	21.6506i	−0.414827	−	0.718502i
$909$	1.00000	+	1.73205i	0.0331679	+	0.0574485i
$910$	12.5000	+	21.6506i	0.414371	+	0.717712i
$911$	−27.0000			−0.894550			−0.447275	−	0.894397i	$-0.647605\pi$
$911$	−27.0000			−0.894550			−0.447275	+	0.894397i	$0.647605\pi$
$912$	−2.50000	+	4.33013i	−0.0827833	+	0.143385i
$913$	9.00000	+	15.5885i	0.297857	+	0.515903i
$914$	38.0000			1.25693
$915$	14.0000			0.462826
$916$	2.00000	+	3.46410i	0.0660819	+	0.114457i
$917$	−90.0000			−2.97206
$918$	−1.00000	+	1.73205i	−0.0330049	+	0.0571662i
$919$	−32.0000			−1.05558			−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000			−1.05558			−0.527791	+	0.849374i	$0.676980\pi$
$920$		0			0
$921$	−1.00000	+	1.73205i	−0.0329511	+	0.0570730i
$922$	17.5000	−	30.3109i	0.576332	−	0.998236i
$923$	−22.5000	−	38.9711i	−0.740597	−	1.28275i
$924$	10.0000			0.328976
$925$	−5.50000	+	2.59808i	−0.180839	+	0.0854242i
$926$	−23.0000			−0.755827
$927$	−1.50000	−	2.59808i	−0.0492665	−	0.0853320i
$928$	−4.50000	+	7.79423i	−0.147720	+	0.255858i
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$	2.00000	−	3.46410i	0.0655826	−	0.113592i
$931$	−90.0000			−2.94963
$932$	1.50000	−	2.59808i	0.0491341	−	0.0851028i
$933$	24.0000			0.785725
$934$	19.5000	+	33.7750i	0.638059	+	1.10515i
$935$	−4.00000			−0.130814
$936$	−5.00000			−0.163430
$937$	−4.00000	−	6.92820i	−0.130674	−	0.226335i	0.793262	−	0.608880i	$-0.208381\pi$
$937$	−4.00000	−	6.92820i	−0.130674	−	0.226335i	−0.923937	+	0.382545i	$0.875048\pi$
$938$	5.00000	−	8.66025i	0.163256	−	0.282767i
$939$		0			0
$940$	1.00000	+	1.73205i	0.0326164	+	0.0564933i
$941$	−17.5000	−	30.3109i	−0.570484	−	0.988107i	−0.996516	−	0.0833989i	$-0.973422\pi$
$941$	−17.5000	−	30.3109i	−0.570484	−	0.988107i	0.426033	−	0.904708i	$-0.359911\pi$
$942$	6.50000	+	11.2583i	0.211781	+	0.366816i
$943$		0			0
$944$	2.00000	−	3.46410i	0.0650945	−	0.112747i
$945$	2.50000	+	4.33013i	0.0813250	+	0.140859i
$946$	4.00000	+	6.92820i	0.130051	+	0.225255i
$947$	−21.5000	−	37.2391i	−0.698656	−	1.21011i	−0.968933	−	0.247325i	$-0.920448\pi$
$947$	−21.5000	−	37.2391i	−0.698656	−	1.21011i	0.270276	−	0.962783i	$-0.412885\pi$
$948$	12.0000			0.389742
$949$	−40.0000	+	69.2820i	−1.29845	+	2.24899i
$950$	−2.50000	−	4.33013i	−0.0811107	−	0.140488i
$951$	−32.0000			−1.03767
$952$	10.0000			0.324102
$953$	1.50000	+	2.59808i	0.0485898	+	0.0841599i	0.889297	−	0.457329i	$-0.151194\pi$
$953$	1.50000	+	2.59808i	0.0485898	+	0.0841599i	−0.840708	+	0.541489i	$0.817861\pi$
$954$	8.00000			0.259010
$955$	2.00000	−	3.46410i	0.0647185	−	0.112096i
$956$	−27.0000			−0.873242
$957$	−9.00000	+	15.5885i	−0.290929	+	0.503903i
$958$	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
$961$	−15.0000			−0.483871
$962$	−2.50000	+	30.3109i	−0.0806032	+	0.977262i
$963$	12.0000			0.386695
$964$	−9.00000	−	15.5885i	−0.289870	−	0.502070i
$965$	−8.00000	+	13.8564i	−0.257529	+	0.446054i
$966$		0			0
$967$	−0.500000	+	0.866025i	−0.0160789	+	0.0278495i	−0.873953	−	0.486011i	$-0.838452\pi$
$967$	−0.500000	+	0.866025i	−0.0160789	+	0.0278495i	0.857874	+	0.513860i	$0.171785\pi$
$968$	7.00000			0.224989
$969$	−5.00000	+	8.66025i	−0.160623	+	0.278207i
$970$	−4.00000			−0.128432
$971$	16.0000	+	27.7128i	0.513464	+	0.889346i	0.999878	+	0.0156178i	$0.00497150\pi$
$971$	16.0000	+	27.7128i	0.513464	+	0.889346i	−0.486414	+	0.873729i	$0.661695\pi$
$972$	−1.00000			−0.0320750
$973$	−60.0000			−1.92351
$974$	16.5000	+	28.5788i	0.528694	+	0.915725i
$975$	2.50000	−	4.33013i	0.0800641	−	0.138675i
$976$	14.0000			0.448129
$977$	6.50000	+	11.2583i	0.207953	+	0.360186i	0.951070	−	0.308976i	$-0.0999864\pi$
$977$	6.50000	+	11.2583i	0.207953	+	0.360186i	−0.743116	+	0.669162i	$0.766653\pi$
$978$	1.00000	+	1.73205i	0.0319765	+	0.0553849i
$979$		0			0
$980$	9.00000	−	15.5885i	0.287494	−	0.497955i
$981$	7.00000	−	12.1244i	0.223493	−	0.387101i
$982$	3.00000	+	5.19615i	0.0957338	+	0.165816i
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	0.814209	−	0.580572i	$-0.197171\pi$
$983$	−3.00000	−	5.19615i	−0.0956851	−	0.165732i	−0.909894	+	0.414840i	$0.863838\pi$
$984$	4.00000	+	6.92820i	0.127515	+	0.220863i
$985$	24.0000			0.764704
$986$	−9.00000	+	15.5885i	−0.286618	+	0.496438i
$987$	−5.00000	−	8.66025i	−0.159152	−	0.275659i
$988$	−25.0000			−0.795356
$989$		0			0
$990$	−1.00000	−	1.73205i	−0.0317821	−	0.0550482i
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	−7.00000			−0.222138
$994$	−22.5000	+	38.9711i	−0.713657	+	1.23609i
$995$	7.00000	−	12.1244i	0.221915	−	0.384368i
$996$	−4.50000	+	7.79423i	−0.142588	+	0.246970i
$997$	−1.50000	−	2.59808i	−0.0475055	−	0.0822819i	0.841295	−	0.540576i	$-0.181794\pi$
$997$	−1.50000	−	2.59808i	−0.0475055	−	0.0822819i	−0.888800	+	0.458295i	$0.848460\pi$
$998$	31.0000			0.981288
$999$	−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.h.211.1	yes	2
37.10	even	3	inner	1110.2.i.h.121.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.h.121.1	✓	2	37.10	even	3	inner
1110.2.i.h.211.1	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(2.50000 - 4.33013i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(2.50000 - 4.33013i) 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} +5.00000 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} +(-2.50000 - 4.33013i) q^{21} +(1.00000 + 1.73205i) q^{22} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -5.00000 q^{26} -1.00000 q^{27} +(2.50000 + 4.33013i) q^{28} -9.00000 q^{29} +(0.500000 - 0.866025i) q^{30} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} +(1.00000 - 1.73205i) q^{34} +(-2.50000 - 4.33013i) 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} +(2.50000 - 4.33013i) q^{42} +4.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} -1.00000 q^{45} +2.00000 q^{47} -1.00000 q^{48} +(-9.00000 - 15.5885i) q^{49} +(0.500000 - 0.866025i) q^{50} -2.00000 q^{51} +(-2.50000 - 4.33013i) q^{52} +(4.00000 + 6.92820i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 - 1.73205i) q^{55} +(-2.50000 + 4.33013i) q^{56} +(-2.50000 - 4.33013i) q^{57} +(-4.50000 - 7.79423i) q^{58} +(2.00000 + 3.46410i) q^{59} +1.00000 q^{60} +(-7.00000 + 12.1244i) q^{61} +(2.00000 + 3.46410i) q^{62} -5.00000 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} +(2.50000 - 4.33013i) q^{70} +(-4.50000 + 7.79423i) q^{71} +(0.500000 + 0.866025i) q^{72} +16.0000 q^{73} +(5.50000 - 2.59808i) q^{74} -1.00000 q^{75} +(2.50000 + 4.33013i) q^{76} +(5.00000 - 8.66025i) q^{77} +(-2.50000 + 4.33013i) q^{78} +(6.00000 - 10.3923i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +8.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +5.00000 q^{84} -2.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(-4.50000 + 7.79423i) q^{87} -2.00000 q^{88} +(-0.500000 - 0.866025i) q^{90} +(12.5000 + 21.6506i) q^{91} +(2.00000 - 3.46410i) q^{93} +(1.00000 + 1.73205i) q^{94} +(-2.50000 - 4.33013i) q^{95} +(-0.500000 - 0.866025i) q^{96} -4.00000 q^{97} +(9.00000 - 15.5885i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} + 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} + 2 q^{6} + 5 q^{7} - 2 q^{8} - q^{9} + 2 q^{10} + 4 q^{11} + q^{12} - 5 q^{13} + 10 q^{14} - q^{15} - q^{16} - 2 q^{17} + q^{18} + 5 q^{19} + q^{20} - 5 q^{21} + 2 q^{22} - q^{24} - q^{25} - 10 q^{26} - 2 q^{27} + 5 q^{28} - 18 q^{29} + q^{30} + 8 q^{31} + q^{32} + 2 q^{33} + 2 q^{34} - 5 q^{35} + 2 q^{36} + q^{37} + 10 q^{38} + 5 q^{39} - q^{40} + 8 q^{41} + 5 q^{42} + 8 q^{43} - 2 q^{44} - 2 q^{45} + 4 q^{47} - 2 q^{48} - 18 q^{49} + q^{50} - 4 q^{51} - 5 q^{52} + 8 q^{53} - q^{54} + 2 q^{55} - 5 q^{56} - 5 q^{57} - 9 q^{58} + 4 q^{59} + 2 q^{60} - 14 q^{61} + 4 q^{62} - 10 q^{63} + 2 q^{64} + 5 q^{65} + 4 q^{66} + 2 q^{67} + 4 q^{68} + 5 q^{70} - 9 q^{71} + q^{72} + 32 q^{73} + 11 q^{74} - 2 q^{75} + 5 q^{76} + 10 q^{77} - 5 q^{78} + 12 q^{79} - 2 q^{80} - q^{81} + 16 q^{82} + 9 q^{83} + 10 q^{84} - 4 q^{85} + 4 q^{86} - 9 q^{87} - 4 q^{88} - q^{90} + 25 q^{91} + 4 q^{93} + 2 q^{94} - 5 q^{95} - q^{96} - 8 q^{97} + 18 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 - q^9 + 2 * q^10 + 4 * q^11 + q^12 - 5 * q^13 + 10 * q^14 - q^15 - q^16 - 2 * q^17 + q^18 + 5 * q^19 + q^20 - 5 * q^21 + 2 * q^22 - q^24 - q^25 - 10 * q^26 - 2 * q^27 + 5 * q^28 - 18 * q^29 + q^30 + 8 * q^31 + q^32 + 2 * q^33 + 2 * q^34 - 5 * q^35 + 2 * q^36 + q^37 + 10 * q^38 + 5 * q^39 - q^40 + 8 * q^41 + 5 * q^42 + 8 * q^43 - 2 * q^44 - 2 * q^45 + 4 * q^47 - 2 * q^48 - 18 * q^49 + q^50 - 4 * q^51 - 5 * q^52 + 8 * q^53 - q^54 + 2 * q^55 - 5 * q^56 - 5 * q^57 - 9 * q^58 + 4 * q^59 + 2 * q^60 - 14 * q^61 + 4 * q^62 - 10 * q^63 + 2 * q^64 + 5 * q^65 + 4 * q^66 + 2 * q^67 + 4 * q^68 + 5 * q^70 - 9 * q^71 + q^72 + 32 * q^73 + 11 * q^74 - 2 * q^75 + 5 * q^76 + 10 * q^77 - 5 * q^78 + 12 * q^79 - 2 * q^80 - q^81 + 16 * q^82 + 9 * q^83 + 10 * q^84 - 4 * q^85 + 4 * q^86 - 9 * q^87 - 4 * q^88 - q^90 + 25 * q^91 + 4 * q^93 + 2 * q^94 - 5 * q^95 - q^96 - 8 * q^97 + 18 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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