LMFDB - Embedded newform 1110.2.i.d.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.d.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(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} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +6.00000 q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{13} +1.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(3.50000 - 6.06218i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.500000 + 0.866025i) q^{21} +(3.00000 + 5.19615i) q^{22} -6.00000 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +9.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +(3.00000 - 5.19615i) q^{34} +(-0.500000 - 0.866025i) q^{35} +1.00000 q^{36} +(5.50000 + 2.59808i) q^{37} +7.00000 q^{38} +(0.500000 + 0.866025i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(-0.500000 + 0.866025i) q^{42} +2.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} -1.00000 q^{45} +(-3.00000 - 5.19615i) q^{46} +12.0000 q^{47} +1.00000 q^{48} +(3.00000 + 5.19615i) q^{49} +(0.500000 - 0.866025i) q^{50} +6.00000 q^{51} +(0.500000 + 0.866025i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +(3.00000 - 5.19615i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(3.50000 + 6.06218i) q^{57} +(4.50000 + 7.79423i) q^{58} +(3.00000 + 5.19615i) q^{59} -1.00000 q^{60} +(-4.00000 + 6.92820i) q^{61} +(-2.00000 - 3.46410i) q^{62} -1.00000 q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} -6.00000 q^{66} +(5.00000 - 8.66025i) q^{67} +6.00000 q^{68} +(3.00000 - 5.19615i) q^{69} +(0.500000 - 0.866025i) q^{70} +(1.50000 - 2.59808i) q^{71} +(0.500000 + 0.866025i) q^{72} -10.0000 q^{73} +(0.500000 + 6.06218i) q^{74} +1.00000 q^{75} +(3.50000 + 6.06218i) q^{76} +(3.00000 - 5.19615i) q^{77} +(-0.500000 + 0.866025i) q^{78} +(-7.00000 + 12.1244i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -6.00000 q^{82} +(1.50000 + 2.59808i) q^{83} -1.00000 q^{84} -6.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(-4.50000 + 7.79423i) q^{87} -6.00000 q^{88} +(-0.500000 - 0.866025i) q^{90} +(-0.500000 - 0.866025i) q^{91} +(3.00000 - 5.19615i) q^{92} +(2.00000 - 3.46410i) q^{93} +(6.00000 + 10.3923i) q^{94} +(-3.50000 - 6.06218i) q^{95} +(0.500000 + 0.866025i) q^{96} -10.0000 q^{97} +(-3.00000 + 5.19615i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 + q^5 - 2 * q^6 + q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9} + 2 q^{10} + 12 q^{11} - q^{12} + q^{13} + 2 q^{14} + q^{15} - q^{16} - 6 q^{17} + q^{18} + 7 q^{19} + q^{20} + q^{21} + 6 q^{22} - 12 q^{23} + q^{24} - q^{25} + 2 q^{26} + 2 q^{27} + q^{28} + 18 q^{29} - q^{30} - 8 q^{31} + q^{32} - 6 q^{33} + 6 q^{34} - q^{35} + 2 q^{36} + 11 q^{37} + 14 q^{38} + q^{39} - q^{40} - 6 q^{41} - q^{42} + 4 q^{43} - 6 q^{44} - 2 q^{45} - 6 q^{46} + 24 q^{47} + 2 q^{48} + 6 q^{49} + q^{50} + 12 q^{51} + q^{52} - 6 q^{53} + q^{54} + 6 q^{55} - q^{56} + 7 q^{57} + 9 q^{58} + 6 q^{59} - 2 q^{60} - 8 q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} - q^{65} - 12 q^{66} + 10 q^{67} + 12 q^{68} + 6 q^{69} + q^{70} + 3 q^{71} + q^{72} - 20 q^{73} + q^{74} + 2 q^{75} + 7 q^{76} + 6 q^{77} - q^{78} - 14 q^{79} - 2 q^{80} - q^{81} - 12 q^{82} + 3 q^{83} - 2 q^{84} - 12 q^{85} + 2 q^{86} - 9 q^{87} - 12 q^{88} - q^{90} - q^{91} + 6 q^{92} + 4 q^{93} + 12 q^{94} - 7 q^{95} + q^{96} - 20 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + q^5 - 2 * q^6 + q^7 - 2 * q^8 - q^9 + 2 * q^10 + 12 * q^11 - q^12 + q^13 + 2 * q^14 + q^15 - q^16 - 6 * q^17 + q^18 + 7 * q^19 + q^20 + q^21 + 6 * q^22 - 12 * q^23 + q^24 - q^25 + 2 * q^26 + 2 * q^27 + q^28 + 18 * q^29 - q^30 - 8 * q^31 + q^32 - 6 * q^33 + 6 * q^34 - q^35 + 2 * q^36 + 11 * q^37 + 14 * q^38 + q^39 - q^40 - 6 * q^41 - q^42 + 4 * q^43 - 6 * q^44 - 2 * q^45 - 6 * q^46 + 24 * q^47 + 2 * q^48 + 6 * q^49 + q^50 + 12 * q^51 + q^52 - 6 * q^53 + q^54 + 6 * q^55 - q^56 + 7 * q^57 + 9 * q^58 + 6 * q^59 - 2 * q^60 - 8 * q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 - q^65 - 12 * q^66 + 10 * q^67 + 12 * q^68 + 6 * q^69 + q^70 + 3 * q^71 + q^72 - 20 * q^73 + q^74 + 2 * q^75 + 7 * q^76 + 6 * q^77 - q^78 - 14 * q^79 - 2 * q^80 - q^81 - 12 * q^82 + 3 * q^83 - 2 * q^84 - 12 * q^85 + 2 * q^86 - 9 * q^87 - 12 * q^88 - q^90 - q^91 + 6 * q^92 + 4 * q^93 + 12 * q^94 - 7 * q^95 + q^96 - 20 * q^97 - 6 * q^98 - 6 * 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
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000			0.316228
$11$	6.00000			1.80907			0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000			1.80907			0.904534	+	0.426401i	$0.140219\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$	1.00000			0.267261
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	0.500000	+	0.866025i	0.109109	+	0.188982i
$22$	3.00000	+	5.19615i	0.639602	+	1.10782i
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000			0.196116
$27$	1.00000			0.192450
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$	3.00000	−	5.19615i	0.514496	−	0.891133i
$35$	−0.500000	−	0.866025i	−0.0845154	−	0.146385i
$36$	1.00000			0.166667
$37$	5.50000	+	2.59808i	0.904194	+	0.427121i
$37$	5.50000	+	2.59808i	0.904194	+	0.427121i
$38$	7.00000			1.13555
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−3.00000	+	5.19615i	−0.452267	+	0.783349i
$45$	−1.00000			−0.149071
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	12.0000			1.75038			0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000			1.75038			0.875190	+	0.483779i	$0.160736\pi$
$48$	1.00000			0.144338
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	6.00000			0.840168
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	3.00000	−	5.19615i	0.404520	−	0.700649i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	3.50000	+	6.06218i	0.463586	+	0.802955i
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$	−1.00000			−0.129099
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	−1.00000			−0.125988
$64$	1.00000			0.125000
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	−6.00000			−0.738549
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	−0.380251	−	0.924883i	$-0.624162\pi$
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	0.991098	−	0.133135i	$-0.0425044\pi$
$68$	6.00000			0.727607
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	0.500000	−	0.866025i	0.0597614	−	0.103510i
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	−0.763184	−	0.646181i	$-0.776365\pi$
$71$	1.50000	−	2.59808i	0.178017	−	0.308335i	0.941201	+	0.337846i	$0.109698\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$	0.500000	+	6.06218i	0.0581238	+	0.704714i
$75$	1.00000			0.115470
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$	3.00000	−	5.19615i	0.341882	−	0.592157i
$78$	−0.500000	+	0.866025i	−0.0566139	+	0.0980581i
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	0.139895	+	0.990166i	$0.455323\pi$
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	−0.927457	+	0.373930i	$0.878010\pi$
$80$	−1.00000			−0.111803
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−6.00000			−0.662589
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	0.936530	−	0.350588i	$-0.114018\pi$
$83$	1.50000	+	2.59808i	0.164646	+	0.285176i	−0.771883	+	0.635764i	$0.780685\pi$
$84$	−1.00000			−0.109109
$85$	−6.00000			−0.650791
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	−6.00000			−0.639602
$89$		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
$91$	−0.500000	−	0.866025i	−0.0524142	−	0.0907841i
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$	−3.50000	−	6.06218i	−0.359092	−	0.621966i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	−3.00000	−	5.19615i	−0.301511	−	0.522233i
$100$	1.00000			0.100000
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$	3.00000	+	5.19615i	0.297044	+	0.514496i
$103$	−13.0000			−1.28093			−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−13.0000			−1.28093			−0.640464	+	0.767988i	$0.721258\pi$
$104$	−0.500000	+	0.866025i	−0.0490290	+	0.0849208i
$105$	1.00000			0.0975900
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$	6.00000			0.572078
$111$	−5.00000	+	3.46410i	−0.474579	+	0.328798i
$112$	−1.00000			−0.0944911
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	0.996262	−	0.0863794i	$-0.0275297\pi$
$113$	4.50000	+	7.79423i	0.423324	+	0.733219i	−0.572938	+	0.819599i	$0.694196\pi$
$114$	−3.50000	+	6.06218i	−0.327805	+	0.567775i
$115$	−3.00000	+	5.19615i	−0.279751	+	0.484544i
$116$	−4.50000	+	7.79423i	−0.417815	+	0.723676i
$117$	−1.00000			−0.0924500
$118$	−3.00000	+	5.19615i	−0.276172	+	0.478345i
$119$	−6.00000			−0.550019
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	25.0000			2.27273
$122$	−8.00000			−0.724286
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−1.00000			−0.0894427
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	−8.50000	−	14.7224i	−0.754253	−	1.30640i	−0.945745	−	0.324910i	$-0.894666\pi$
$127$	−8.50000	−	14.7224i	−0.754253	−	1.30640i	0.191492	−	0.981494i	$-0.438667\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.00000	+	1.73205i	−0.0880451	+	0.152499i
$130$	0.500000	−	0.866025i	0.0438529	−	0.0759555i
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	−3.00000	−	5.19615i	−0.261116	−	0.452267i
$133$	−3.50000	−	6.06218i	−0.303488	−	0.525657i
$134$	10.0000			0.863868
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	21.0000			1.79415			0.897076	−	0.441877i	$-0.145687\pi$
$137$	21.0000			1.79415			0.897076	+	0.441877i	$0.145687\pi$
$138$	6.00000			0.510754
$139$	−10.0000	−	17.3205i	−0.848189	−	1.46911i	−0.882823	−	0.469706i	$-0.844360\pi$
$139$	−10.0000	−	17.3205i	−0.848189	−	1.46911i	0.0346338	−	0.999400i	$-0.488974\pi$
$140$	1.00000			0.0845154
$141$	−6.00000	+	10.3923i	−0.505291	+	0.875190i
$142$	3.00000			0.251754
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	4.50000	−	7.79423i	0.373705	−	0.647275i
$146$	−5.00000	−	8.66025i	−0.413803	−	0.716728i
$147$	−6.00000			−0.494872
$148$	−5.00000	+	3.46410i	−0.410997	+	0.284747i
$149$	21.0000			1.72039			0.860194	−	0.509968i	$-0.170343\pi$
$149$	21.0000			1.72039			0.860194	+	0.509968i	$0.170343\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$	−3.50000	+	6.06218i	−0.283887	+	0.491708i
$153$	−3.00000	+	5.19615i	−0.242536	+	0.420084i
$154$	6.00000			0.483494
$155$	−2.00000	+	3.46410i	−0.160644	+	0.278243i
$156$	−1.00000			−0.0800641
$157$	−2.50000	−	4.33013i	−0.199522	−	0.345582i	0.748852	−	0.662738i	$-0.230606\pi$
$157$	−2.50000	−	4.33013i	−0.199522	−	0.345582i	−0.948373	+	0.317156i	$0.897272\pi$
$158$	−14.0000			−1.11378
$159$	6.00000			0.475831
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−3.00000	+	5.19615i	−0.236433	+	0.409514i
$162$	−1.00000			−0.0785674
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$	−1.50000	+	2.59808i	−0.116423	+	0.201650i
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	−0.958440	−	0.285295i	$-0.907908\pi$
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	0.726293	+	0.687386i	$0.241242\pi$
$168$	−0.500000	−	0.866025i	−0.0385758	−	0.0668153i
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	−3.00000	−	5.19615i	−0.230089	−	0.398527i
$171$	−7.00000			−0.535303
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	−9.00000			−0.682288
$175$	−1.00000			−0.0755929
$176$	−3.00000	−	5.19615i	−0.226134	−	0.391675i
$177$	−6.00000			−0.450988
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	−0.900794	−	0.434246i	$-0.857015\pi$
$181$	−1.00000	+	1.73205i	−0.0743294	+	0.128742i	0.826465	+	0.562988i	$0.190348\pi$
$182$	0.500000	−	0.866025i	0.0370625	−	0.0641941i
$183$	−4.00000	−	6.92820i	−0.295689	−	0.512148i
$184$	6.00000			0.442326
$185$	5.00000	−	3.46410i	0.367607	−	0.254686i
$186$	4.00000			0.293294
$187$	−18.0000	−	31.1769i	−1.31629	−	2.27988i
$188$	−6.00000	+	10.3923i	−0.437595	+	0.757937i
$189$	0.500000	−	0.866025i	0.0363696	−	0.0629941i
$190$	3.50000	−	6.06218i	0.253917	−	0.439797i
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−10.0000			−0.719816			−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000			−0.719816			−0.359908	+	0.932988i	$0.617192\pi$
$194$	−5.00000	−	8.66025i	−0.358979	−	0.621770i
$195$	1.00000			0.0716115
$196$	−6.00000			−0.428571
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	0.952882	−	0.303340i	$-0.0981018\pi$
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	−0.739141	+	0.673550i	$0.764768\pi$
$198$	3.00000	−	5.19615i	0.213201	−	0.369274i
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	5.00000	+	8.66025i	0.352673	+	0.610847i
$202$	3.00000	+	5.19615i	0.211079	+	0.365600i
$203$	4.50000	−	7.79423i	0.315838	−	0.547048i
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$	−6.50000	−	11.2583i	−0.452876	−	0.784405i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	−1.00000			−0.0693375
$209$	21.0000	−	36.3731i	1.45260	−	2.51598i
$210$	0.500000	+	0.866025i	0.0345033	+	0.0597614i
$211$	−19.0000			−1.30801			−0.654007	−	0.756489i	$-0.726913\pi$
$211$	−19.0000			−1.30801			−0.654007	+	0.756489i	$0.726913\pi$
$212$	6.00000			0.412082
$213$	1.50000	+	2.59808i	0.102778	+	0.178017i
$214$		0			0
$215$	1.00000	−	1.73205i	0.0681994	−	0.118125i
$216$	−1.00000			−0.0680414
$217$	−2.00000	+	3.46410i	−0.135769	+	0.235159i
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$	3.00000	+	5.19615i	0.202260	+	0.350325i
$221$	−6.00000			−0.403604
$222$	−5.50000	−	2.59808i	−0.369136	−	0.174371i
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	−4.50000	+	7.79423i	−0.299336	+	0.518464i
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	−0.999997	−	0.00254715i	$-0.999189\pi$
$227$	−7.50000	+	12.9904i	−0.497792	+	0.862202i	0.502204	+	0.864749i	$0.332523\pi$
$228$	−7.00000			−0.463586
$229$	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	$0.124474\pi$
$230$	−6.00000			−0.395628
$231$	3.00000	+	5.19615i	0.197386	+	0.341882i
$232$	−9.00000			−0.590879
$233$	9.00000			0.589610			0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000			0.589610			0.294805	+	0.955557i	$0.404745\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	6.00000	−	10.3923i	0.391397	−	0.677919i
$236$	−6.00000			−0.390567
$237$	−7.00000	−	12.1244i	−0.454699	−	0.787562i
$238$	−3.00000	−	5.19615i	−0.194461	−	0.336817i
$239$	−4.50000	−	7.79423i	−0.291081	−	0.504167i	0.682985	−	0.730433i	$-0.260682\pi$
$239$	−4.50000	−	7.79423i	−0.291081	−	0.504167i	−0.974066	+	0.226266i	$0.927348\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$	12.5000	+	21.6506i	0.803530	+	1.39176i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−4.00000	−	6.92820i	−0.256074	−	0.443533i
$245$	6.00000			0.383326
$246$	3.00000	−	5.19615i	0.191273	−	0.331295i
$247$	−3.50000	−	6.06218i	−0.222700	−	0.385727i
$248$	4.00000			0.254000
$249$	−3.00000			−0.190117
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$	0.500000	−	0.866025i	0.0314970	−	0.0545545i
$253$	−36.0000			−2.26330
$254$	8.50000	−	14.7224i	0.533337	−	0.923768i
$255$	3.00000	−	5.19615i	0.187867	−	0.325396i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.5000	−	23.3827i	−0.842107	−	1.45857i	−0.888110	−	0.459631i	$-0.847982\pi$
$257$	−13.5000	−	23.3827i	−0.842107	−	1.45857i	0.0460033	−	0.998941i	$-0.485352\pi$
$258$	−2.00000			−0.124515
$259$	5.00000	−	3.46410i	0.310685	−	0.215249i
$260$	1.00000			0.0620174
$261$	−4.50000	−	7.79423i	−0.278543	−	0.482451i
$262$	6.00000	−	10.3923i	0.370681	−	0.642039i
$263$	9.00000	−	15.5885i	0.554964	−	0.961225i	−0.442943	−	0.896550i	$-0.646065\pi$
$263$	9.00000	−	15.5885i	0.554964	−	0.961225i	0.997906	−	0.0646755i	$-0.0206012\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$	−6.00000			−0.368577
$266$	3.50000	−	6.06218i	0.214599	−	0.371696i
$267$		0			0
$268$	5.00000	+	8.66025i	0.305424	+	0.529009i
$269$	15.0000			0.914566			0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000			0.914566			0.457283	+	0.889321i	$0.348823\pi$
$270$	1.00000			0.0608581
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	0.880812	+	0.473466i	$0.156997\pi$
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	−3.00000	+	5.19615i	−0.181902	+	0.315063i
$273$	1.00000			0.0605228
$274$	10.5000	+	18.1865i	0.634328	+	1.09869i
$275$	−3.00000	−	5.19615i	−0.180907	−	0.313340i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	0.489207	+	0.872167i	$0.337286\pi$
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	−0.999923	+	0.0124177i	$0.996047\pi$
$278$	10.0000	−	17.3205i	0.599760	−	1.03882i
$279$	2.00000	+	3.46410i	0.119737	+	0.207390i
$280$	0.500000	+	0.866025i	0.0298807	+	0.0517549i
$281$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$281$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$282$	−12.0000			−0.714590
$283$	−13.0000	+	22.5167i	−0.772770	+	1.33848i	0.163270	+	0.986581i	$0.447796\pi$
$283$	−13.0000	+	22.5167i	−0.772770	+	1.33848i	−0.936039	+	0.351895i	$0.885537\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$	7.00000			0.414644
$286$	6.00000			0.354787
$287$	3.00000	+	5.19615i	0.177084	+	0.306719i
$288$	−1.00000			−0.0589256
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	9.00000			0.528498
$291$	5.00000	−	8.66025i	0.293105	−	0.507673i
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	−15.0000	+	25.9808i	−0.876309	+	1.51781i	−0.0209480	+	0.999781i	$0.506668\pi$
$293$	−15.0000	+	25.9808i	−0.876309	+	1.51781i	−0.855361	+	0.518032i	$0.826665\pi$
$294$	−3.00000	−	5.19615i	−0.174964	−	0.303046i
$295$	6.00000			0.349334
$296$	−5.50000	−	2.59808i	−0.319681	−	0.151010i
$297$	6.00000			0.348155
$298$	10.5000	+	18.1865i	0.608249	+	1.05352i
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$	10.0000			0.575435
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$	−7.00000			−0.401478
$305$	4.00000	+	6.92820i	0.229039	+	0.396708i
$306$	−6.00000			−0.342997
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$	3.00000	+	5.19615i	0.170941	+	0.296078i
$309$	6.50000	−	11.2583i	0.369772	−	0.640464i
$310$	−4.00000			−0.227185
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$	−0.500000	−	0.866025i	−0.0283069	−	0.0490290i
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	0.998522	−	0.0543564i	$-0.0173107\pi$
$313$	8.00000	+	13.8564i	0.452187	+	0.783210i	−0.546335	+	0.837567i	$0.683977\pi$
$314$	2.50000	−	4.33013i	0.141083	−	0.244363i
$315$	−0.500000	+	0.866025i	−0.0281718	+	0.0487950i
$316$	−7.00000	−	12.1244i	−0.393781	−	0.682048i
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$	3.00000	+	5.19615i	0.168232	+	0.291386i
$319$	54.0000			3.02342
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$		0			0
$322$	−6.00000			−0.334367
$323$	−42.0000			−2.33694
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.00000			−0.0554700
$326$	−8.00000	+	13.8564i	−0.443079	+	0.767435i
$327$	2.00000			0.110600
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$	−3.00000	+	5.19615i	−0.165145	+	0.286039i
$331$	−2.50000	−	4.33013i	−0.137412	−	0.238005i	0.789104	−	0.614260i	$-0.210545\pi$
$331$	−2.50000	−	4.33013i	−0.137412	−	0.238005i	−0.926516	+	0.376254i	$0.877212\pi$
$332$	−3.00000			−0.164646
$333$	−0.500000	−	6.06218i	−0.0273998	−	0.332205i
$334$	−6.00000			−0.328305
$335$	−5.00000	−	8.66025i	−0.273179	−	0.473160i
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	5.00000	−	8.66025i	0.272367	−	0.471754i	−0.697100	−	0.716974i	$-0.745527\pi$
$337$	5.00000	−	8.66025i	0.272367	−	0.471754i	0.969468	+	0.245220i	$0.0788601\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	−9.00000			−0.488813
$340$	3.00000	−	5.19615i	0.162698	−	0.281801i
$341$	−24.0000			−1.29967
$342$	−3.50000	−	6.06218i	−0.189258	−	0.327805i
$343$	13.0000			0.701934
$344$	−2.00000			−0.107833
$345$	−3.00000	−	5.19615i	−0.161515	−	0.279751i
$346$		0			0
$347$	−3.00000			−0.161048			−0.0805242	−	0.996753i	$-0.525659\pi$
$347$	−3.00000			−0.161048			−0.0805242	+	0.996753i	$0.525659\pi$
$348$	−4.50000	−	7.79423i	−0.241225	−	0.417815i
$349$	14.0000	+	24.2487i	0.749403	+	1.29800i	0.948109	+	0.317945i	$0.102993\pi$
$349$	14.0000	+	24.2487i	0.749403	+	1.29800i	−0.198706	+	0.980059i	$0.563674\pi$
$350$	−0.500000	−	0.866025i	−0.0267261	−	0.0462910i
$351$	0.500000	−	0.866025i	0.0266880	−	0.0462250i
$352$	3.00000	−	5.19615i	0.159901	−	0.276956i
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	−0.997592	−	0.0693543i	$-0.977906\pi$
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	0.438733	−	0.898617i	$-0.355427\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$	−1.50000	−	2.59808i	−0.0796117	−	0.137892i
$356$		0			0
$357$	3.00000	−	5.19615i	0.158777	−	0.275010i
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−27.0000			−1.42501			−0.712503	−	0.701669i	$-0.752438\pi$
$359$	−27.0000			−1.42501			−0.712503	+	0.701669i	$0.752438\pi$
$360$	1.00000			0.0527046
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	−2.00000			−0.105118
$363$	−12.5000	+	21.6506i	−0.656080	+	1.13636i
$364$	1.00000			0.0524142
$365$	−5.00000	+	8.66025i	−0.261712	+	0.453298i
$366$	4.00000	−	6.92820i	0.209083	−	0.362143i
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	−0.504093	−	0.863649i	$-0.668173\pi$
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	0.999989	+	0.00473247i	$0.00150640\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	6.00000			0.312348
$370$	5.50000	+	2.59808i	0.285931	+	0.135068i
$371$	−6.00000			−0.311504
$372$	2.00000	+	3.46410i	0.103695	+	0.179605i
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	−0.997697	−	0.0678218i	$-0.978395\pi$
$373$	−8.50000	+	14.7224i	−0.440113	+	0.762299i	0.557584	+	0.830120i	$0.311728\pi$
$374$	18.0000	−	31.1769i	0.930758	−	1.61212i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−12.0000			−0.618853
$377$	4.50000	−	7.79423i	0.231762	−	0.401423i
$378$	1.00000			0.0514344
$379$	−14.5000	−	25.1147i	−0.744815	−	1.29006i	−0.950281	−	0.311393i	$-0.899204\pi$
$379$	−14.5000	−	25.1147i	−0.744815	−	1.29006i	0.205466	−	0.978664i	$-0.434129\pi$
$380$	7.00000			0.359092
$381$	17.0000			0.870936
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$	9.00000	−	15.5885i	0.459879	−	0.796533i	−0.539076	−	0.842257i	$-0.681226\pi$
$383$	9.00000	−	15.5885i	0.459879	−	0.796533i	0.998954	+	0.0457244i	$0.0145596\pi$
$384$	−1.00000			−0.0510310
$385$	−3.00000	−	5.19615i	−0.152894	−	0.264820i
$386$	−5.00000	−	8.66025i	−0.254493	−	0.440795i
$387$	−1.00000	−	1.73205i	−0.0508329	−	0.0880451i
$388$	5.00000	−	8.66025i	0.253837	−	0.439658i
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	0.0561516	+	0.998422i	$0.482117\pi$
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	−0.892735	+	0.450582i	$0.851216\pi$
$390$	0.500000	+	0.866025i	0.0253185	+	0.0438529i
$391$	18.0000	+	31.1769i	0.910299	+	1.57668i
$392$	−3.00000	−	5.19615i	−0.151523	−	0.262445i
$393$	12.0000			0.605320
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	7.00000	+	12.1244i	0.352208	+	0.610043i
$396$	6.00000			0.301511
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	−8.00000	−	13.8564i	−0.401004	−	0.694559i
$399$	7.00000			0.350438
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	18.0000			0.898877			0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000			0.898877			0.449439	+	0.893311i	$0.351624\pi$
$402$	−5.00000	+	8.66025i	−0.249377	+	0.431934i
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	−3.00000	+	5.19615i	−0.149256	+	0.258518i
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	9.00000			0.446663
$407$	33.0000	+	15.5885i	1.63575	+	0.772691i
$408$	−6.00000			−0.297044
$409$	0.500000	+	0.866025i	0.0247234	+	0.0428222i	0.878122	−	0.478436i	$-0.158796\pi$
$409$	0.500000	+	0.866025i	0.0247234	+	0.0428222i	−0.853399	+	0.521258i	$0.825463\pi$
$410$	−3.00000	+	5.19615i	−0.148159	+	0.256620i
$411$	−10.5000	+	18.1865i	−0.517927	+	0.897076i
$412$	6.50000	−	11.2583i	0.320232	−	0.554658i
$413$	6.00000			0.295241
$414$	−3.00000	+	5.19615i	−0.147442	+	0.255377i
$415$	3.00000			0.147264
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	20.0000			0.979404
$418$	42.0000			2.05429
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.852047	−	0.523465i	$-0.824639\pi$
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.0273103	−	0.999627i	$-0.508694\pi$
$420$	−0.500000	+	0.866025i	−0.0243975	+	0.0422577i
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$	−9.50000	−	16.4545i	−0.462453	−	0.800992i
$423$	−6.00000	−	10.3923i	−0.291730	−	0.505291i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$	−1.50000	+	2.59808i	−0.0726752	+	0.125877i
$427$	4.00000	+	6.92820i	0.193574	+	0.335279i
$428$		0			0
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$	2.00000			0.0964486
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	−0.899888	−	0.436121i	$-0.856352\pi$
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	0.827636	+	0.561266i	$0.189685\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	20.0000			0.961139			0.480569	−	0.876957i	$-0.340430\pi$
$433$	20.0000			0.961139			0.480569	+	0.876957i	$0.340430\pi$
$434$	−4.00000			−0.192006
$435$	4.50000	+	7.79423i	0.215758	+	0.373705i
$436$	2.00000			0.0957826
$437$	−21.0000	+	36.3731i	−1.00457	+	1.73996i
$438$	10.0000			0.477818
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	−0.999661	−	0.0260459i	$-0.991708\pi$
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	0.522387	+	0.852709i	$0.325042\pi$
$440$	−3.00000	+	5.19615i	−0.143019	+	0.247717i
$441$	3.00000	−	5.19615i	0.142857	−	0.247436i
$442$	−3.00000	−	5.19615i	−0.142695	−	0.247156i
$443$	−9.00000			−0.427603			−0.213801	−	0.976877i	$-0.568585\pi$
$443$	−9.00000			−0.427603			−0.213801	+	0.976877i	$0.568585\pi$
$444$	−0.500000	−	6.06218i	−0.0237289	−	0.287698i
$445$		0			0
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$	−10.5000	+	18.1865i	−0.496633	+	0.860194i
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$449$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$450$	−1.00000			−0.0471405
$451$	−18.0000	+	31.1769i	−0.847587	+	1.46806i
$452$	−9.00000			−0.423324
$453$	5.00000	+	8.66025i	0.234920	+	0.406894i
$454$	−15.0000			−0.703985
$455$	−1.00000			−0.0468807
$456$	−3.50000	−	6.06218i	−0.163903	−	0.283887i
$457$	−13.0000	+	22.5167i	−0.608114	+	1.05328i	0.383437	+	0.923567i	$0.374740\pi$
$457$	−13.0000	+	22.5167i	−0.608114	+	1.05328i	−0.991551	+	0.129718i	$0.958593\pi$
$458$	4.00000			0.186908
$459$	−3.00000	−	5.19615i	−0.140028	−	0.242536i
$460$	−3.00000	−	5.19615i	−0.139876	−	0.242272i
$461$	7.50000	+	12.9904i	0.349310	+	0.605022i	0.986127	−	0.165992i	$-0.0530827\pi$
$461$	7.50000	+	12.9904i	0.349310	+	0.605022i	−0.636817	+	0.771015i	$0.719749\pi$
$462$	−3.00000	+	5.19615i	−0.139573	+	0.241747i
$463$	−5.50000	+	9.52628i	−0.255607	+	0.442724i	−0.965060	−	0.262029i	$-0.915609\pi$
$463$	−5.50000	+	9.52628i	−0.255607	+	0.442724i	0.709453	+	0.704752i	$0.248942\pi$
$464$	−4.50000	−	7.79423i	−0.208907	−	0.361838i
$465$	−2.00000	−	3.46410i	−0.0927478	−	0.160644i
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	−27.0000			−1.24941			−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000			−1.24941			−0.624705	+	0.780860i	$0.714781\pi$
$468$	0.500000	−	0.866025i	0.0231125	−	0.0400320i
$469$	−5.00000	−	8.66025i	−0.230879	−	0.399893i
$470$	12.0000			0.553519
$471$	5.00000			0.230388
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	12.0000			0.551761
$474$	7.00000	−	12.1244i	0.321521	−	0.556890i
$475$	−7.00000			−0.321182
$476$	3.00000	−	5.19615i	0.137505	−	0.238165i
$477$	−3.00000	+	5.19615i	−0.137361	+	0.237915i
$478$	4.50000	−	7.79423i	0.205825	−	0.356500i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	1.00000			0.0456435
$481$	5.00000	−	3.46410i	0.227980	−	0.157949i
$482$	−2.00000			−0.0910975
$483$	−3.00000	−	5.19615i	−0.136505	−	0.236433i
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	−5.00000	+	8.66025i	−0.227038	+	0.393242i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−7.00000			−0.317200			−0.158600	−	0.987343i	$-0.550698\pi$
$487$	−7.00000			−0.317200			−0.158600	+	0.987343i	$0.550698\pi$
$488$	4.00000	−	6.92820i	0.181071	−	0.313625i
$489$	−16.0000			−0.723545
$490$	3.00000	+	5.19615i	0.135526	+	0.234738i
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$	6.00000			0.270501
$493$	−27.0000	−	46.7654i	−1.21602	−	2.10621i
$494$	3.50000	−	6.06218i	0.157472	−	0.272750i
$495$	−6.00000			−0.269680
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	−1.50000	−	2.59808i	−0.0672842	−	0.116540i
$498$	−1.50000	−	2.59808i	−0.0672166	−	0.116423i
$499$	6.50000	−	11.2583i	0.290980	−	0.503992i	−0.683062	−	0.730361i	$-0.739352\pi$
$499$	6.50000	−	11.2583i	0.290980	−	0.503992i	0.974042	+	0.226369i	$0.0726854\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−3.00000	−	5.19615i	−0.134030	−	0.232147i
$502$	9.00000	+	15.5885i	0.401690	+	0.695747i
$503$	3.00000	+	5.19615i	0.133763	+	0.231685i	0.925124	−	0.379664i	$-0.123960\pi$
$503$	3.00000	+	5.19615i	0.133763	+	0.231685i	−0.791361	+	0.611349i	$0.790627\pi$
$504$	1.00000			0.0445435
$505$	3.00000	−	5.19615i	0.133498	−	0.231226i
$506$	−18.0000	−	31.1769i	−0.800198	−	1.38598i
$507$	−12.0000			−0.532939
$508$	17.0000			0.754253
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$	6.00000			0.265684
$511$	−5.00000	+	8.66025i	−0.221187	+	0.383107i
$512$	−1.00000			−0.0441942
$513$	3.50000	−	6.06218i	0.154529	−	0.267652i
$514$	13.5000	−	23.3827i	0.595459	−	1.03137i
$515$	−6.50000	+	11.2583i	−0.286424	+	0.496101i
$516$	−1.00000	−	1.73205i	−0.0440225	−	0.0762493i
$517$	72.0000			3.16656
$518$	5.50000	+	2.59808i	0.241656	+	0.114153i
$519$		0			0
$520$	0.500000	+	0.866025i	0.0219265	+	0.0379777i
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	−0.967002	−	0.254769i	$-0.918001\pi$
$521$	−6.00000	+	10.3923i	−0.262865	+	0.455295i	0.704137	+	0.710064i	$0.251334\pi$
$522$	4.50000	−	7.79423i	0.196960	−	0.341144i
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	−0.636401	−	0.771358i	$-0.719578\pi$
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	0.986216	+	0.165460i	$0.0529109\pi$
$524$	12.0000			0.524222
$525$	0.500000	−	0.866025i	0.0218218	−	0.0377964i
$526$	18.0000			0.784837
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$	6.00000			0.261116
$529$	13.0000			0.565217
$530$	−3.00000	−	5.19615i	−0.130312	−	0.225706i
$531$	3.00000	−	5.19615i	0.130189	−	0.225494i
$532$	7.00000			0.303488
$533$	3.00000	+	5.19615i	0.129944	+	0.225070i
$534$		0			0
$535$		0			0
$536$	−5.00000	+	8.66025i	−0.215967	+	0.374066i
$537$	−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
$541$	−16.0000			−0.687894			−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000			−0.687894			−0.343947	+	0.938989i	$0.611764\pi$
$542$	−14.0000	+	24.2487i	−0.601351	+	1.04157i
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$	−6.00000			−0.257248
$545$	−2.00000			−0.0856706
$546$	0.500000	+	0.866025i	0.0213980	+	0.0370625i
$547$	−4.00000			−0.171028			−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000			−0.171028			−0.0855138	+	0.996337i	$0.527253\pi$
$548$	−10.5000	+	18.1865i	−0.448538	+	0.776890i
$549$	8.00000			0.341432
$550$	3.00000	−	5.19615i	0.127920	−	0.221565i
$551$	31.5000	−	54.5596i	1.34195	−	2.32432i
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	7.00000	+	12.1244i	0.297670	+	0.515580i
$554$	−17.0000			−0.722261
$555$	0.500000	+	6.06218i	0.0212238	+	0.257325i
$556$	20.0000			0.848189
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	0.986394	+	0.164399i	$0.0525683\pi$
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	−0.350824	+	0.936442i	$0.614098\pi$
$558$	−2.00000	+	3.46410i	−0.0846668	+	0.146647i
$559$	1.00000	−	1.73205i	0.0422955	−	0.0732579i
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$	36.0000			1.51992
$562$		0			0
$563$	39.0000			1.64365			0.821827	−	0.569737i	$-0.192955\pi$
$563$	39.0000			1.64365			0.821827	+	0.569737i	$0.192955\pi$
$564$	−6.00000	−	10.3923i	−0.252646	−	0.437595i
$565$	9.00000			0.378633
$566$	−26.0000			−1.09286
$567$	0.500000	+	0.866025i	0.0209980	+	0.0363696i
$568$	−1.50000	+	2.59808i	−0.0629386	+	0.109013i
$569$	−42.0000			−1.76073			−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000			−1.76073			−0.880366	+	0.474295i	$0.842703\pi$
$570$	3.50000	+	6.06218i	0.146599	+	0.253917i
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	0.518509	−	0.855072i	$-0.326487\pi$
$571$	−11.5000	−	19.9186i	−0.481260	−	0.833567i	−0.999769	+	0.0215055i	$0.993154\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$	12.0000	−	20.7846i	0.501307	−	0.868290i
$574$	−3.00000	+	5.19615i	−0.125218	+	0.216883i
$575$	3.00000	+	5.19615i	0.125109	+	0.216695i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−10.0000	−	17.3205i	−0.416305	−	0.721062i	0.579259	−	0.815144i	$-0.303342\pi$
$577$	−10.0000	−	17.3205i	−0.416305	−	0.721062i	−0.995565	+	0.0940813i	$0.970009\pi$
$578$	−19.0000			−0.790296
$579$	5.00000	−	8.66025i	0.207793	−	0.359908i
$580$	4.50000	+	7.79423i	0.186852	+	0.323638i
$581$	3.00000			0.124461
$582$	10.0000			0.414513
$583$	−18.0000	−	31.1769i	−0.745484	−	1.29122i
$584$	10.0000			0.413803
$585$	−0.500000	+	0.866025i	−0.0206725	+	0.0358057i
$586$	−30.0000			−1.23929
$587$	−10.5000	+	18.1865i	−0.433381	+	0.750639i	−0.997162	−	0.0752860i	$-0.976013\pi$
$587$	−10.5000	+	18.1865i	−0.433381	+	0.750639i	0.563781	+	0.825925i	$0.309346\pi$
$588$	3.00000	−	5.19615i	0.123718	−	0.214286i
$589$	−14.0000	+	24.2487i	−0.576860	+	0.999151i
$590$	3.00000	+	5.19615i	0.123508	+	0.213922i
$591$	−6.00000			−0.246807
$592$	−0.500000	−	6.06218i	−0.0205499	−	0.249154i
$593$	−30.0000			−1.23195			−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000			−1.23195			−0.615976	+	0.787765i	$0.711238\pi$
$594$	3.00000	+	5.19615i	0.123091	+	0.213201i
$595$	−3.00000	+	5.19615i	−0.122988	+	0.213021i
$596$	−10.5000	+	18.1865i	−0.430097	+	0.744949i
$597$	8.00000	−	13.8564i	0.327418	−	0.567105i
$598$	−6.00000			−0.245358
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	−0.759328	−	0.650708i	$-0.774472\pi$
$599$	4.50000	−	7.79423i	0.183865	−	0.318464i	0.943193	+	0.332244i	$0.107806\pi$
$600$	−1.00000			−0.0408248
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$	2.00000			0.0815139
$603$	−10.0000			−0.407231
$604$	5.00000	+	8.66025i	0.203447	+	0.352381i
$605$	12.5000	−	21.6506i	0.508197	−	0.880223i
$606$	−6.00000			−0.243733
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	0.967256	−	0.253804i	$-0.0816819\pi$
$607$	6.50000	+	11.2583i	0.263827	+	0.456962i	−0.703429	+	0.710766i	$0.748349\pi$
$608$	−3.50000	−	6.06218i	−0.141944	−	0.245854i
$609$	4.50000	+	7.79423i	0.182349	+	0.315838i
$610$	−4.00000	+	6.92820i	−0.161955	+	0.280515i
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	0.999984	+	0.00563283i	$0.00179300\pi$
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	−0.495114	+	0.868828i	$0.664874\pi$
$614$	−2.00000	−	3.46410i	−0.0807134	−	0.139800i
$615$	−6.00000			−0.241943
$616$	−3.00000	+	5.19615i	−0.120873	+	0.209359i
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	0.998700	+	0.0509678i	$0.0162306\pi$
$617$	13.5000	+	23.3827i	0.543490	+	0.941351i	−0.455211	+	0.890384i	$0.650436\pi$
$618$	13.0000			0.522937
$619$	20.0000			0.803868			0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000			0.803868			0.401934	+	0.915669i	$0.368338\pi$
$620$	−2.00000	−	3.46410i	−0.0803219	−	0.139122i
$621$	−6.00000			−0.240772
$622$	−6.00000	+	10.3923i	−0.240578	+	0.416693i
$623$		0			0
$624$	0.500000	−	0.866025i	0.0200160	−	0.0346688i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−8.00000	+	13.8564i	−0.319744	+	0.553813i
$627$	21.0000	+	36.3731i	0.838659	+	1.45260i
$628$	5.00000			0.199522
$629$	−3.00000	−	36.3731i	−0.119618	−	1.45029i
$630$	−1.00000			−0.0398410
$631$	17.0000	+	29.4449i	0.676759	+	1.17218i	0.975951	+	0.217989i	$0.0699496\pi$
$631$	17.0000	+	29.4449i	0.676759	+	1.17218i	−0.299192	+	0.954193i	$0.596717\pi$
$632$	7.00000	−	12.1244i	0.278445	−	0.482281i
$633$	9.50000	−	16.4545i	0.377591	−	0.654007i
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$	−17.0000			−0.674624
$636$	−3.00000	+	5.19615i	−0.118958	+	0.206041i
$637$	6.00000			0.237729
$638$	27.0000	+	46.7654i	1.06894	+	1.85146i
$639$	−3.00000			−0.118678
$640$	1.00000			0.0395285
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	0.525584	−	0.850741i	$-0.323847\pi$
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	−0.999556	+	0.0297987i	$0.990513\pi$
$642$		0			0
$643$	−16.0000			−0.630978			−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000			−0.630978			−0.315489	+	0.948929i	$0.602169\pi$
$644$	−3.00000	−	5.19615i	−0.118217	−	0.204757i
$645$	1.00000	+	1.73205i	0.0393750	+	0.0681994i
$646$	−21.0000	−	36.3731i	−0.826234	−	1.43108i
$647$	−15.0000	+	25.9808i	−0.589711	+	1.02141i	0.404559	+	0.914512i	$0.367425\pi$
$647$	−15.0000	+	25.9808i	−0.589711	+	1.02141i	−0.994270	+	0.106897i	$0.965908\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	18.0000	+	31.1769i	0.706562	+	1.22380i
$650$	−0.500000	−	0.866025i	−0.0196116	−	0.0339683i
$651$	−2.00000	−	3.46410i	−0.0783862	−	0.135769i
$652$	−16.0000			−0.626608
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	−0.634437	−	0.772975i	$-0.718768\pi$
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	0.986634	+	0.162951i	$0.0521013\pi$
$654$	1.00000	+	1.73205i	0.0391031	+	0.0677285i
$655$	−12.0000			−0.468879
$656$	6.00000			0.234261
$657$	5.00000	+	8.66025i	0.195069	+	0.337869i
$658$	12.0000			0.467809
$659$	3.00000	−	5.19615i	0.116863	−	0.202413i	−0.801660	−	0.597781i	$-0.796049\pi$
$659$	3.00000	−	5.19615i	0.116863	−	0.202413i	0.918523	+	0.395367i	$0.129383\pi$
$660$	−6.00000			−0.233550
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$	2.50000	−	4.33013i	0.0971653	−	0.168295i
$663$	3.00000	−	5.19615i	0.116510	−	0.201802i
$664$	−1.50000	−	2.59808i	−0.0582113	−	0.100825i
$665$	−7.00000			−0.271448
$666$	5.00000	−	3.46410i	0.193746	−	0.134231i
$667$	−54.0000			−2.09089
$668$	−3.00000	−	5.19615i	−0.116073	−	0.201045i
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$	5.00000	−	8.66025i	0.193167	−	0.334575i
$671$	−24.0000	+	41.5692i	−0.926510	+	1.60476i
$672$	1.00000			0.0385758
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	0.498886	+	0.866668i	$0.333743\pi$
$673$	−13.0000	+	22.5167i	−0.501113	+	0.867953i	−0.999999	+	0.00128586i	$0.999591\pi$
$674$	10.0000			0.385186
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−12.0000			−0.461538
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$	−4.50000	−	7.79423i	−0.172821	−	0.299336i
$679$	−5.00000	+	8.66025i	−0.191882	+	0.332350i
$680$	6.00000			0.230089
$681$	−7.50000	−	12.9904i	−0.287401	−	0.497792i
$682$	−12.0000	−	20.7846i	−0.459504	−	0.795884i
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	0.998917	−	0.0465244i	$-0.0148145\pi$
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	−0.539750	+	0.841825i	$0.681481\pi$
$684$	3.50000	−	6.06218i	0.133826	−	0.231793i
$685$	10.5000	−	18.1865i	0.401184	−	0.694872i
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$	2.00000	+	3.46410i	0.0763048	+	0.132164i
$688$	−1.00000	−	1.73205i	−0.0381246	−	0.0660338i
$689$	−6.00000			−0.228582
$690$	3.00000	−	5.19615i	0.114208	−	0.197814i
$691$	15.5000	+	26.8468i	0.589648	+	1.02130i	0.994278	+	0.106820i	$0.0340668\pi$
$691$	15.5000	+	26.8468i	0.589648	+	1.02130i	−0.404631	+	0.914480i	$0.632600\pi$
$692$		0			0
$693$	−6.00000			−0.227921
$694$	−1.50000	−	2.59808i	−0.0569392	−	0.0986216i
$695$	−20.0000			−0.758643
$696$	4.50000	−	7.79423i	0.170572	−	0.295439i
$697$	36.0000			1.36360
$698$	−14.0000	+	24.2487i	−0.529908	+	0.917827i
$699$	−4.50000	+	7.79423i	−0.170206	+	0.294805i
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	9.00000	+	15.5885i	0.339925	+	0.588768i	0.984418	−	0.175842i	$-0.0562649\pi$
$701$	9.00000	+	15.5885i	0.339925	+	0.588768i	−0.644493	+	0.764610i	$0.722932\pi$
$702$	1.00000			0.0377426
$703$	35.0000	−	24.2487i	1.32005	−	0.914557i
$704$	6.00000			0.226134
$705$	6.00000	+	10.3923i	0.225973	+	0.391397i
$706$	10.5000	−	18.1865i	0.395173	−	0.684459i
$707$	3.00000	−	5.19615i	0.112827	−	0.195421i
$708$	3.00000	−	5.19615i	0.112747	−	0.195283i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$	1.50000	−	2.59808i	0.0562940	−	0.0975041i
$711$	14.0000			0.525041
$712$		0			0
$713$	24.0000			0.898807
$714$	6.00000			0.224544
$715$	−3.00000	−	5.19615i	−0.112194	−	0.194325i
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	9.00000			0.336111
$718$	−13.5000	−	23.3827i	−0.503816	−	0.872634i
$719$	7.50000	+	12.9904i	0.279703	+	0.484459i	0.971311	−	0.237814i	$-0.0764307\pi$
$719$	7.50000	+	12.9904i	0.279703	+	0.484459i	−0.691608	+	0.722273i	$0.743097\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$	−6.50000	+	11.2583i	−0.242073	+	0.419282i
$722$	15.0000	−	25.9808i	0.558242	−	0.966904i
$723$	−1.00000	−	1.73205i	−0.0371904	−	0.0644157i
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	−4.50000	−	7.79423i	−0.167126	−	0.289470i
$726$	−25.0000			−0.927837
$727$	12.5000	−	21.6506i	0.463599	−	0.802978i	−0.535538	−	0.844511i	$-0.679891\pi$
$727$	12.5000	−	21.6506i	0.463599	−	0.802978i	0.999137	+	0.0415337i	$0.0132244\pi$
$728$	0.500000	+	0.866025i	0.0185312	+	0.0320970i
$729$	1.00000			0.0370370
$730$	−10.0000			−0.370117
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$	8.00000			0.295689
$733$	−19.0000	+	32.9090i	−0.701781	+	1.21552i	0.266060	+	0.963957i	$0.414278\pi$
$733$	−19.0000	+	32.9090i	−0.701781	+	1.21552i	−0.967841	+	0.251564i	$0.919055\pi$
$734$	19.0000			0.701303
$735$	−3.00000	+	5.19615i	−0.110657	+	0.191663i
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$	30.0000	−	51.9615i	1.10506	−	1.91403i
$738$	3.00000	+	5.19615i	0.110432	+	0.191273i
$739$	47.0000			1.72892			0.864461	−	0.502699i	$-0.167660\pi$
$739$	47.0000			1.72892			0.864461	+	0.502699i	$0.167660\pi$
$740$	0.500000	+	6.06218i	0.0183804	+	0.222850i
$741$	7.00000			0.257151
$742$	−3.00000	−	5.19615i	−0.110133	−	0.190757i
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	0.320166	+	0.947361i	$0.396261\pi$
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	−0.980522	+	0.196409i	$0.937072\pi$
$744$	−2.00000	+	3.46410i	−0.0733236	+	0.127000i
$745$	10.5000	−	18.1865i	0.384690	−	0.666303i
$746$	−17.0000			−0.622414
$747$	1.50000	−	2.59808i	0.0548821	−	0.0950586i
$748$	36.0000			1.31629
$749$		0			0
$750$	1.00000			0.0365148
$751$	−16.0000			−0.583848			−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000			−0.583848			−0.291924	+	0.956441i	$0.594295\pi$
$752$	−6.00000	−	10.3923i	−0.218797	−	0.378968i
$753$	−9.00000	+	15.5885i	−0.327978	+	0.568075i
$754$	9.00000			0.327761
$755$	−5.00000	−	8.66025i	−0.181969	−	0.315179i
$756$	0.500000	+	0.866025i	0.0181848	+	0.0314970i
$757$	−2.50000	−	4.33013i	−0.0908640	−	0.157381i	0.817011	−	0.576622i	$-0.195630\pi$
$757$	−2.50000	−	4.33013i	−0.0908640	−	0.157381i	−0.907875	+	0.419241i	$0.862296\pi$
$758$	14.5000	−	25.1147i	0.526664	−	0.912208i
$759$	18.0000	−	31.1769i	0.653359	−	1.13165i
$760$	3.50000	+	6.06218i	0.126958	+	0.219898i
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	0.942207	+	0.335032i	$0.108747\pi$
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	−0.180957	+	0.983491i	$0.557920\pi$
$762$	8.50000	+	14.7224i	0.307923	+	0.533337i
$763$	−2.00000			−0.0724049
$764$	12.0000	−	20.7846i	0.434145	−	0.751961i
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$	18.0000			0.650366
$767$	6.00000			0.216647
$768$	−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
$771$	27.0000			0.972381
$772$	5.00000	−	8.66025i	0.179954	−	0.311689i
$773$	−12.0000	+	20.7846i	−0.431610	+	0.747570i	−0.997012	−	0.0772449i	$-0.975388\pi$
$773$	−12.0000	+	20.7846i	−0.431610	+	0.747570i	0.565402	+	0.824815i	$0.308721\pi$
$774$	1.00000	−	1.73205i	0.0359443	−	0.0622573i
$775$	2.00000	+	3.46410i	0.0718421	+	0.124434i
$776$	10.0000			0.358979
$777$	0.500000	+	6.06218i	0.0179374	+	0.217479i
$778$	−33.0000			−1.18311
$779$	21.0000	+	36.3731i	0.752403	+	1.30320i
$780$	−0.500000	+	0.866025i	−0.0179029	+	0.0310087i
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$	−18.0000	+	31.1769i	−0.643679	+	1.11488i
$783$	9.00000			0.321634
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	−5.00000			−0.178458
$786$	6.00000	+	10.3923i	0.214013	+	0.370681i
$787$	−22.0000			−0.784215			−0.392108	−	0.919919i	$-0.628254\pi$
$787$	−22.0000			−0.784215			−0.392108	+	0.919919i	$0.628254\pi$
$788$	−6.00000			−0.213741
$789$	9.00000	+	15.5885i	0.320408	+	0.554964i
$790$	−7.00000	+	12.1244i	−0.249049	+	0.431365i
$791$	9.00000			0.320003
$792$	3.00000	+	5.19615i	0.106600	+	0.184637i
$793$	4.00000	+	6.92820i	0.142044	+	0.246028i
$794$	1.00000	+	1.73205i	0.0354887	+	0.0614682i
$795$	3.00000	−	5.19615i	0.106399	−	0.184289i
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	0.661441	−	0.749997i	$-0.269945\pi$
$797$	−9.00000	−	15.5885i	−0.318796	−	0.552171i	−0.980237	+	0.197826i	$0.936612\pi$
$798$	3.50000	+	6.06218i	0.123899	+	0.214599i
$799$	−36.0000	−	62.3538i	−1.27359	−	2.20592i
$800$	−1.00000			−0.0353553
$801$		0			0
$802$	9.00000	+	15.5885i	0.317801	+	0.550448i
$803$	−60.0000			−2.11735
$804$	−10.0000			−0.352673
$805$	3.00000	+	5.19615i	0.105736	+	0.183140i
$806$	−4.00000			−0.140894
$807$	−7.50000	+	12.9904i	−0.264013	+	0.457283i
$808$	−6.00000			−0.211079
$809$	−6.00000	+	10.3923i	−0.210949	+	0.365374i	−0.952012	−	0.306062i	$-0.900989\pi$
$809$	−6.00000	+	10.3923i	−0.210949	+	0.365374i	0.741063	+	0.671436i	$0.234322\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	26.0000	−	45.0333i	0.912983	−	1.58133i	0.103156	−	0.994665i	$-0.467106\pi$
$811$	26.0000	−	45.0333i	0.912983	−	1.58133i	0.809827	−	0.586669i	$-0.199561\pi$
$812$	4.50000	+	7.79423i	0.157919	+	0.273524i
$813$	−28.0000			−0.982003
$814$	3.00000	+	36.3731i	0.105150	+	1.27488i
$815$	16.0000			0.560456
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	7.00000	−	12.1244i	0.244899	−	0.424178i
$818$	−0.500000	+	0.866025i	−0.0174821	+	0.0302799i
$819$	−0.500000	+	0.866025i	−0.0174714	+	0.0302614i
$820$	−6.00000			−0.209529
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	0.143591	+	0.989637i	$0.454135\pi$
$821$	−22.5000	+	38.9711i	−0.785255	+	1.36010i	−0.928846	+	0.370465i	$0.879198\pi$
$822$	−21.0000			−0.732459
$823$	9.50000	+	16.4545i	0.331149	+	0.573567i	0.982737	−	0.185006i	$-0.0592303\pi$
$823$	9.50000	+	16.4545i	0.331149	+	0.573567i	−0.651588	+	0.758573i	$0.725897\pi$
$824$	13.0000			0.452876
$825$	6.00000			0.208893
$826$	3.00000	+	5.19615i	0.104383	+	0.180797i
$827$	−4.50000	+	7.79423i	−0.156480	+	0.271032i	−0.933597	−	0.358325i	$-0.883348\pi$
$827$	−4.50000	+	7.79423i	−0.156480	+	0.271032i	0.777117	+	0.629356i	$0.216681\pi$
$828$	−6.00000			−0.208514
$829$	−22.0000	−	38.1051i	−0.764092	−	1.32345i	−0.940726	−	0.339169i	$-0.889854\pi$
$829$	−22.0000	−	38.1051i	−0.764092	−	1.32345i	0.176634	−	0.984277i	$-0.443479\pi$
$830$	1.50000	+	2.59808i	0.0520658	+	0.0901805i
$831$	−8.50000	−	14.7224i	−0.294862	−	0.510716i
$832$	0.500000	−	0.866025i	0.0173344	−	0.0300240i
$833$	18.0000	−	31.1769i	0.623663	−	1.08022i
$834$	10.0000	+	17.3205i	0.346272	+	0.599760i
$835$	3.00000	+	5.19615i	0.103819	+	0.179820i
$836$	21.0000	+	36.3731i	0.726300	+	1.25799i
$837$	−4.00000			−0.138260
$838$	18.0000	−	31.1769i	0.621800	−	1.07699i
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$	−1.00000			−0.0345033
$841$	52.0000			1.79310
$842$	4.00000	+	6.92820i	0.137849	+	0.238762i
$843$		0			0
$844$	9.50000	−	16.4545i	0.327003	−	0.566387i
$845$	12.0000			0.412813
$846$	6.00000	−	10.3923i	0.206284	−	0.357295i
$847$	12.5000	−	21.6506i	0.429505	−	0.743925i
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$	−13.0000	−	22.5167i	−0.446159	−	0.772770i
$850$	−6.00000			−0.205798
$851$	−33.0000	−	15.5885i	−1.13123	−	0.534365i
$852$	−3.00000			−0.102778
$853$	−13.0000	−	22.5167i	−0.445112	−	0.770956i	0.552948	−	0.833215i	$-0.313503\pi$
$853$	−13.0000	−	22.5167i	−0.445112	−	0.770956i	−0.998060	+	0.0622597i	$0.980169\pi$
$854$	−4.00000	+	6.92820i	−0.136877	+	0.237078i
$855$	−3.50000	+	6.06218i	−0.119697	+	0.207322i
$856$		0			0
$857$	27.0000			0.922302			0.461151	−	0.887322i	$-0.347437\pi$
$857$	27.0000			0.922302			0.461151	+	0.887322i	$0.347437\pi$
$858$	−3.00000	+	5.19615i	−0.102418	+	0.177394i
$859$	47.0000			1.60362			0.801810	−	0.597580i	$-0.203871\pi$
$859$	47.0000			1.60362			0.801810	+	0.597580i	$0.203871\pi$
$860$	1.00000	+	1.73205i	0.0340997	+	0.0590624i
$861$	−6.00000			−0.204479
$862$	−3.00000			−0.102180
$863$	−6.00000	−	10.3923i	−0.204242	−	0.353758i	0.745649	−	0.666339i	$-0.232140\pi$
$863$	−6.00000	−	10.3923i	−0.204242	−	0.353758i	−0.949891	+	0.312581i	$0.898806\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	10.0000	+	17.3205i	0.339814	+	0.588575i
$867$	−9.50000	−	16.4545i	−0.322637	−	0.558824i
$868$	−2.00000	−	3.46410i	−0.0678844	−	0.117579i
$869$	−42.0000	+	72.7461i	−1.42475	+	2.46774i
$870$	−4.50000	+	7.79423i	−0.152564	+	0.264249i
$871$	−5.00000	−	8.66025i	−0.169419	−	0.293442i
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$	5.00000	+	8.66025i	0.169224	+	0.293105i
$874$	−42.0000			−1.42067
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	5.00000	+	8.66025i	0.168934	+	0.292603i
$877$	−31.0000			−1.04680			−0.523398	−	0.852088i	$-0.675336\pi$
$877$	−31.0000			−1.04680			−0.523398	+	0.852088i	$0.675336\pi$
$878$	−20.0000			−0.674967
$879$	−15.0000	−	25.9808i	−0.505937	−	0.876309i
$880$	−6.00000			−0.202260
$881$	21.0000	−	36.3731i	0.707508	−	1.22544i	−0.258271	−	0.966073i	$-0.583153\pi$
$881$	21.0000	−	36.3731i	0.707508	−	1.22544i	0.965779	−	0.259367i	$-0.0835140\pi$
$882$	6.00000			0.202031
$883$	8.00000	−	13.8564i	0.269221	−	0.466305i	−0.699440	−	0.714692i	$-0.746567\pi$
$883$	8.00000	−	13.8564i	0.269221	−	0.466305i	0.968661	+	0.248387i	$0.0799003\pi$
$884$	3.00000	−	5.19615i	0.100901	−	0.174766i
$885$	−3.00000	+	5.19615i	−0.100844	+	0.174667i
$886$	−4.50000	−	7.79423i	−0.151180	−	0.261852i
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$	5.00000	−	3.46410i	0.167789	−	0.116248i
$889$	−17.0000			−0.570162
$890$		0			0
$891$	−3.00000	+	5.19615i	−0.100504	+	0.174078i
$892$	8.00000	−	13.8564i	0.267860	−	0.463947i
$893$	42.0000	−	72.7461i	1.40548	−	2.43436i
$894$	−21.0000			−0.702345
$895$	6.00000	−	10.3923i	0.200558	−	0.347376i
$896$	1.00000			0.0334077
$897$	−3.00000	−	5.19615i	−0.100167	−	0.173494i
$898$		0			0
$899$	−36.0000			−1.20067
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$	−36.0000			−1.19867
$903$	1.00000	+	1.73205i	0.0332779	+	0.0576390i
$904$	−4.50000	−	7.79423i	−0.149668	−	0.259232i
$905$	1.00000	+	1.73205i	0.0332411	+	0.0575753i
$906$	−5.00000	+	8.66025i	−0.166114	+	0.287718i
$907$	20.0000	−	34.6410i	0.664089	−	1.15024i	−0.315442	−	0.948945i	$-0.602153\pi$
$907$	20.0000	−	34.6410i	0.664089	−	1.15024i	0.979531	−	0.201291i	$-0.0645138\pi$
$908$	−7.50000	−	12.9904i	−0.248896	−	0.431101i
$909$	−3.00000	−	5.19615i	−0.0995037	−	0.172345i
$910$	−0.500000	−	0.866025i	−0.0165748	−	0.0287085i
$911$	−27.0000			−0.894550			−0.447275	−	0.894397i	$-0.647605\pi$
$911$	−27.0000			−0.894550			−0.447275	+	0.894397i	$0.647605\pi$
$912$	3.50000	−	6.06218i	0.115897	−	0.200739i
$913$	9.00000	+	15.5885i	0.297857	+	0.515903i
$914$	−26.0000			−0.860004
$915$	−8.00000			−0.264472
$916$	2.00000	+	3.46410i	0.0660819	+	0.114457i
$917$	−12.0000			−0.396275
$918$	3.00000	−	5.19615i	0.0990148	−	0.171499i
$919$	−4.00000			−0.131948			−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000			−0.131948			−0.0659739	+	0.997821i	$0.521015\pi$
$920$	3.00000	−	5.19615i	0.0989071	−	0.171312i
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$	−7.50000	+	12.9904i	−0.246999	+	0.427815i
$923$	−1.50000	−	2.59808i	−0.0493731	−	0.0855167i
$924$	−6.00000			−0.197386
$925$	−0.500000	−	6.06218i	−0.0164399	−	0.199323i
$926$	−11.0000			−0.361482
$927$	6.50000	+	11.2583i	0.213488	+	0.369772i
$928$	4.50000	−	7.79423i	0.147720	−	0.255858i
$929$	−21.0000	+	36.3731i	−0.688988	+	1.19336i	0.283178	+	0.959067i	$0.408611\pi$
$929$	−21.0000	+	36.3731i	−0.688988	+	1.19336i	−0.972166	+	0.234294i	$0.924722\pi$
$930$	2.00000	−	3.46410i	0.0655826	−	0.113592i
$931$	42.0000			1.37649
$932$	−4.50000	+	7.79423i	−0.147402	+	0.255308i
$933$	−12.0000			−0.392862
$934$	−13.5000	−	23.3827i	−0.441733	−	0.765105i
$935$	−36.0000			−1.17733
$936$	1.00000			0.0326860
$937$	−16.0000	−	27.7128i	−0.522697	−	0.905338i	−0.999651	−	0.0264099i	$-0.991593\pi$
$937$	−16.0000	−	27.7128i	−0.522697	−	0.905338i	0.476954	−	0.878928i	$-0.341741\pi$
$938$	5.00000	−	8.66025i	0.163256	−	0.282767i
$939$	−16.0000			−0.522140
$940$	6.00000	+	10.3923i	0.195698	+	0.338960i
$941$	−22.5000	−	38.9711i	−0.733479	−	1.27042i	−0.955387	−	0.295355i	$-0.904562\pi$
$941$	−22.5000	−	38.9711i	−0.733479	−	1.27042i	0.221908	−	0.975068i	$-0.428771\pi$
$942$	2.50000	+	4.33013i	0.0814544	+	0.141083i
$943$	18.0000	−	31.1769i	0.586161	−	1.01526i
$944$	3.00000	−	5.19615i	0.0976417	−	0.169120i
$945$	−0.500000	−	0.866025i	−0.0162650	−	0.0281718i
$946$	6.00000	+	10.3923i	0.195077	+	0.337883i
$947$	19.5000	+	33.7750i	0.633665	+	1.09754i	0.986796	+	0.161966i	$0.0517835\pi$
$947$	19.5000	+	33.7750i	0.633665	+	1.09754i	−0.353131	+	0.935574i	$0.614883\pi$
$948$	14.0000			0.454699
$949$	−5.00000	+	8.66025i	−0.162307	+	0.281124i
$950$	−3.50000	−	6.06218i	−0.113555	−	0.196683i
$951$	−18.0000			−0.583690
$952$	6.00000			0.194461
$953$	−16.5000	−	28.5788i	−0.534487	−	0.925759i	−0.999188	−	0.0402915i	$-0.987171\pi$
$953$	−16.5000	−	28.5788i	−0.534487	−	0.925759i	0.464701	−	0.885468i	$-0.346162\pi$
$954$	−6.00000			−0.194257
$955$	−12.0000	+	20.7846i	−0.388311	+	0.672574i
$956$	9.00000			0.291081
$957$	−27.0000	+	46.7654i	−0.872786	+	1.51171i
$958$		0			0
$959$	10.5000	−	18.1865i	0.339063	−	0.587274i
$960$	0.500000	+	0.866025i	0.0161374	+	0.0279508i
$961$	−15.0000			−0.483871
$962$	5.50000	+	2.59808i	0.177327	+	0.0837653i
$963$		0			0
$964$	−1.00000	−	1.73205i	−0.0322078	−	0.0557856i
$965$	−5.00000	+	8.66025i	−0.160956	+	0.278783i
$966$	3.00000	−	5.19615i	0.0965234	−	0.167183i
$967$	−14.5000	+	25.1147i	−0.466289	+	0.807635i	−0.999259	−	0.0384986i	$-0.987742\pi$
$967$	−14.5000	+	25.1147i	−0.466289	+	0.807635i	0.532970	+	0.846134i	$0.321076\pi$
$968$	−25.0000			−0.803530
$969$	21.0000	−	36.3731i	0.674617	−	1.16847i
$970$	−10.0000			−0.321081
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	−0.937455	−	0.348107i	$-0.886825\pi$
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	0.167258	−	0.985913i	$-0.446509\pi$
$972$	1.00000			0.0320750
$973$	−20.0000			−0.641171
$974$	−3.50000	−	6.06218i	−0.112147	−	0.194245i
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$	8.00000			0.256074
$977$	10.5000	+	18.1865i	0.335925	+	0.581839i	0.983662	−	0.180025i	$-0.0576179\pi$
$977$	10.5000	+	18.1865i	0.335925	+	0.581839i	−0.647737	+	0.761864i	$0.724285\pi$
$978$	−8.00000	−	13.8564i	−0.255812	−	0.443079i
$979$		0			0
$980$	−3.00000	+	5.19615i	−0.0958315	+	0.165985i
$981$	−1.00000	+	1.73205i	−0.0319275	+	0.0553001i
$982$	15.0000	+	25.9808i	0.478669	+	0.829079i
$983$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$	3.00000	+	5.19615i	0.0956365	+	0.165647i
$985$	6.00000			0.191176
$986$	27.0000	−	46.7654i	0.859855	−	1.48931i
$987$	6.00000	+	10.3923i	0.190982	+	0.330791i
$988$	7.00000			0.222700
$989$	−12.0000			−0.381578
$990$	−3.00000	−	5.19615i	−0.0953463	−	0.165145i
$991$	38.0000			1.20711			0.603555	−	0.797321i	$-0.293750\pi$
$991$	38.0000			1.20711			0.603555	+	0.797321i	$0.293750\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	5.00000			0.158670
$994$	1.50000	−	2.59808i	0.0475771	−	0.0824060i
$995$	−8.00000	+	13.8564i	−0.253617	+	0.439278i
$996$	1.50000	−	2.59808i	0.0475293	−	0.0823232i
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	0.699457	−	0.714675i	$-0.253425\pi$
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	−0.968655	+	0.248410i	$0.920092\pi$
$998$	13.0000			0.411508
$999$	5.50000	+	2.59808i	0.174012	+	0.0821995i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.d.121.1	✓	2	37.10	even	3	inner
1110.2.i.d.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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(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} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} +6.00000 q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{13} +1.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(3.50000 - 6.06218i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.500000 + 0.866025i) q^{21} +(3.00000 + 5.19615i) q^{22} -6.00000 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +9.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +(3.00000 - 5.19615i) q^{34} +(-0.500000 - 0.866025i) q^{35} +1.00000 q^{36} +(5.50000 + 2.59808i) q^{37} +7.00000 q^{38} +(0.500000 + 0.866025i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(-0.500000 + 0.866025i) q^{42} +2.00000 q^{43} +(-3.00000 + 5.19615i) q^{44} -1.00000 q^{45} +(-3.00000 - 5.19615i) q^{46} +12.0000 q^{47} +1.00000 q^{48} +(3.00000 + 5.19615i) q^{49} +(0.500000 - 0.866025i) q^{50} +6.00000 q^{51} +(0.500000 + 0.866025i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(0.500000 + 0.866025i) q^{54} +(3.00000 - 5.19615i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(3.50000 + 6.06218i) q^{57} +(4.50000 + 7.79423i) q^{58} +(3.00000 + 5.19615i) q^{59} -1.00000 q^{60} +(-4.00000 + 6.92820i) q^{61} +(-2.00000 - 3.46410i) q^{62} -1.00000 q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} -6.00000 q^{66} +(5.00000 - 8.66025i) q^{67} +6.00000 q^{68} +(3.00000 - 5.19615i) q^{69} +(0.500000 - 0.866025i) q^{70} +(1.50000 - 2.59808i) q^{71} +(0.500000 + 0.866025i) q^{72} -10.0000 q^{73} +(0.500000 + 6.06218i) q^{74} +1.00000 q^{75} +(3.50000 + 6.06218i) q^{76} +(3.00000 - 5.19615i) q^{77} +(-0.500000 + 0.866025i) q^{78} +(-7.00000 + 12.1244i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -6.00000 q^{82} +(1.50000 + 2.59808i) q^{83} -1.00000 q^{84} -6.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(-4.50000 + 7.79423i) q^{87} -6.00000 q^{88} +(-0.500000 - 0.866025i) q^{90} +(-0.500000 - 0.866025i) q^{91} +(3.00000 - 5.19615i) q^{92} +(2.00000 - 3.46410i) q^{93} +(6.00000 + 10.3923i) q^{94} +(-3.50000 - 6.06218i) q^{95} +(0.500000 + 0.866025i) q^{96} -10.0000 q^{97} +(-3.00000 + 5.19615i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 + q^5 - 2 * q^6 + q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} + q^{5} - 2 q^{6} + q^{7} - 2 q^{8} - q^{9} + 2 q^{10} + 12 q^{11} - q^{12} + q^{13} + 2 q^{14} + q^{15} - q^{16} - 6 q^{17} + q^{18} + 7 q^{19} + q^{20} + q^{21} + 6 q^{22} - 12 q^{23} + q^{24} - q^{25} + 2 q^{26} + 2 q^{27} + q^{28} + 18 q^{29} - q^{30} - 8 q^{31} + q^{32} - 6 q^{33} + 6 q^{34} - q^{35} + 2 q^{36} + 11 q^{37} + 14 q^{38} + q^{39} - q^{40} - 6 q^{41} - q^{42} + 4 q^{43} - 6 q^{44} - 2 q^{45} - 6 q^{46} + 24 q^{47} + 2 q^{48} + 6 q^{49} + q^{50} + 12 q^{51} + q^{52} - 6 q^{53} + q^{54} + 6 q^{55} - q^{56} + 7 q^{57} + 9 q^{58} + 6 q^{59} - 2 q^{60} - 8 q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} - q^{65} - 12 q^{66} + 10 q^{67} + 12 q^{68} + 6 q^{69} + q^{70} + 3 q^{71} + q^{72} - 20 q^{73} + q^{74} + 2 q^{75} + 7 q^{76} + 6 q^{77} - q^{78} - 14 q^{79} - 2 q^{80} - q^{81} - 12 q^{82} + 3 q^{83} - 2 q^{84} - 12 q^{85} + 2 q^{86} - 9 q^{87} - 12 q^{88} - q^{90} - q^{91} + 6 q^{92} + 4 q^{93} + 12 q^{94} - 7 q^{95} + q^{96} - 20 q^{97} - 6 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + q^5 - 2 * q^6 + q^7 - 2 * q^8 - q^9 + 2 * q^10 + 12 * q^11 - q^12 + q^13 + 2 * q^14 + q^15 - q^16 - 6 * q^17 + q^18 + 7 * q^19 + q^20 + q^21 + 6 * q^22 - 12 * q^23 + q^24 - q^25 + 2 * q^26 + 2 * q^27 + q^28 + 18 * q^29 - q^30 - 8 * q^31 + q^32 - 6 * q^33 + 6 * q^34 - q^35 + 2 * q^36 + 11 * q^37 + 14 * q^38 + q^39 - q^40 - 6 * q^41 - q^42 + 4 * q^43 - 6 * q^44 - 2 * q^45 - 6 * q^46 + 24 * q^47 + 2 * q^48 + 6 * q^49 + q^50 + 12 * q^51 + q^52 - 6 * q^53 + q^54 + 6 * q^55 - q^56 + 7 * q^57 + 9 * q^58 + 6 * q^59 - 2 * q^60 - 8 * q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 - q^65 - 12 * q^66 + 10 * q^67 + 12 * q^68 + 6 * q^69 + q^70 + 3 * q^71 + q^72 - 20 * q^73 + q^74 + 2 * q^75 + 7 * q^76 + 6 * q^77 - q^78 - 14 * q^79 - 2 * q^80 - q^81 - 12 * q^82 + 3 * q^83 - 2 * q^84 - 12 * q^85 + 2 * q^86 - 9 * q^87 - 12 * q^88 - q^90 - q^91 + 6 * q^92 + 4 * q^93 + 12 * q^94 - 7 * q^95 + q^96 - 20 * q^97 - 6 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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