LMFDB - Embedded newform 390.2.i.f.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(61,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, 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("390.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.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:	$3.11416567883$
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			61.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	390.61
Dual form			390.2.i.f.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.50000 - 4.33013i) q^{11} -1.00000 q^{12} +(-1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} -1.00000 q^{18} +(1.00000 + 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{20} +2.00000 q^{21} +(-2.50000 - 4.33013i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(-3.50000 - 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 - 1.73205i) q^{28} +(-2.50000 + 4.33013i) q^{29} +(-0.500000 - 0.866025i) q^{30} -11.0000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.50000 - 4.33013i) q^{33} +2.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.50000 + 2.59808i) q^{37} +2.00000 q^{38} +(-3.50000 - 0.866025i) q^{39} -1.00000 q^{40} +(1.00000 - 1.73205i) q^{41} +(1.00000 - 1.73205i) q^{42} +(5.50000 + 9.52628i) q^{43} -5.00000 q^{44} +(-0.500000 - 0.866025i) q^{45} +(-0.500000 - 0.866025i) q^{46} +9.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} +2.00000 q^{51} +(-2.50000 + 2.59808i) q^{52} +6.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.50000 - 4.33013i) q^{55} +(-1.00000 - 1.73205i) q^{56} +2.00000 q^{57} +(2.50000 + 4.33013i) q^{58} +(7.50000 + 12.9904i) q^{59} -1.00000 q^{60} +(-5.00000 - 8.66025i) q^{61} +(-5.50000 + 9.52628i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 - 3.46410i) q^{65} -5.00000 q^{66} +(-8.00000 + 13.8564i) q^{67} +(1.00000 - 1.73205i) q^{68} +(-0.500000 - 0.866025i) q^{69} +2.00000 q^{70} +(0.500000 + 0.866025i) q^{72} -6.00000 q^{73} +(1.50000 + 2.59808i) q^{74} +(0.500000 - 0.866025i) q^{75} +(1.00000 - 1.73205i) q^{76} +10.0000 q^{77} +(-2.50000 + 2.59808i) q^{78} -11.0000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} +6.00000 q^{83} +(-1.00000 - 1.73205i) q^{84} +(1.00000 + 1.73205i) q^{85} +11.0000 q^{86} +(2.50000 + 4.33013i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(-1.00000 + 1.73205i) q^{89} -1.00000 q^{90} +(5.00000 - 5.19615i) q^{91} -1.00000 q^{92} +(-5.50000 + 9.52628i) q^{93} +(4.50000 - 7.79423i) q^{94} +(1.00000 + 1.73205i) q^{95} +1.00000 q^{96} +(1.00000 + 1.73205i) q^{97} +(-1.50000 - 2.59808i) q^{98} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9} + q^{10} + 5 q^{11} - 2 q^{12} - 2 q^{13} + 4 q^{14} + q^{15} - q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} - q^{20} + 4 q^{21} - 5 q^{22} + q^{23} - q^{24} + 2 q^{25} - 7 q^{26} - 2 q^{27} + 2 q^{28} - 5 q^{29} - q^{30} - 22 q^{31} + q^{32} - 5 q^{33} + 4 q^{34} + 2 q^{35} - q^{36} - 3 q^{37} + 4 q^{38} - 7 q^{39} - 2 q^{40} + 2 q^{41} + 2 q^{42} + 11 q^{43} - 10 q^{44} - q^{45} - q^{46} + 18 q^{47} + q^{48} + 3 q^{49} + q^{50} + 4 q^{51} - 5 q^{52} + 12 q^{53} - q^{54} + 5 q^{55} - 2 q^{56} + 4 q^{57} + 5 q^{58} + 15 q^{59} - 2 q^{60} - 10 q^{61} - 11 q^{62} + 2 q^{63} + 2 q^{64} - 2 q^{65} - 10 q^{66} - 16 q^{67} + 2 q^{68} - q^{69} + 4 q^{70} + q^{72} - 12 q^{73} + 3 q^{74} + q^{75} + 2 q^{76} + 20 q^{77} - 5 q^{78} - 22 q^{79} - q^{80} - q^{81} - 2 q^{82} + 12 q^{83} - 2 q^{84} + 2 q^{85} + 22 q^{86} + 5 q^{87} - 5 q^{88} - 2 q^{89} - 2 q^{90} + 10 q^{91} - 2 q^{92} - 11 q^{93} + 9 q^{94} + 2 q^{95} + 2 q^{96} + 2 q^{97} - 3 q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 - 2 * q^8 - q^9 + q^10 + 5 * q^11 - 2 * q^12 - 2 * q^13 + 4 * q^14 + q^15 - q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 - q^20 + 4 * q^21 - 5 * q^22 + q^23 - q^24 + 2 * q^25 - 7 * q^26 - 2 * q^27 + 2 * q^28 - 5 * q^29 - q^30 - 22 * q^31 + q^32 - 5 * q^33 + 4 * q^34 + 2 * q^35 - q^36 - 3 * q^37 + 4 * q^38 - 7 * q^39 - 2 * q^40 + 2 * q^41 + 2 * q^42 + 11 * q^43 - 10 * q^44 - q^45 - q^46 + 18 * q^47 + q^48 + 3 * q^49 + q^50 + 4 * q^51 - 5 * q^52 + 12 * q^53 - q^54 + 5 * q^55 - 2 * q^56 + 4 * q^57 + 5 * q^58 + 15 * q^59 - 2 * q^60 - 10 * q^61 - 11 * q^62 + 2 * q^63 + 2 * q^64 - 2 * q^65 - 10 * q^66 - 16 * q^67 + 2 * q^68 - q^69 + 4 * q^70 + q^72 - 12 * q^73 + 3 * q^74 + q^75 + 2 * q^76 + 20 * q^77 - 5 * q^78 - 22 * q^79 - q^80 - q^81 - 2 * q^82 + 12 * q^83 - 2 * q^84 + 2 * q^85 + 22 * q^86 + 5 * q^87 - 5 * q^88 - 2 * q^89 - 2 * q^90 + 10 * q^91 - 2 * q^92 - 11 * q^93 + 9 * q^94 + 2 * q^95 + 2 * q^96 + 2 * q^97 - 3 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	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
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	2.50000	−	4.33013i	0.753778	−	1.30558i	0.945979	−	0.324227i	$-0.105104\pi$
$12$	−1.00000			−0.288675
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$	2.00000			0.534522
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	−1.00000			−0.235702
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	2.00000			0.436436
$22$	−2.50000	−	4.33013i	−0.533002	−	0.923186i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	1.00000			0.200000
$26$	−3.50000	−	0.866025i	−0.686406	−	0.169842i
$27$	−1.00000			−0.192450
$28$	1.00000	−	1.73205i	0.188982	−	0.327327i
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	−0.999167	−	0.0408130i	$-0.987005\pi$
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	0.534928	+	0.844897i	$0.320339\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−11.0000			−1.97566			−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−11.0000			−1.97566			−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.50000	−	4.33013i	−0.435194	−	0.753778i
$34$	2.00000			0.342997
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$	2.00000			0.324443
$39$	−3.50000	−	0.866025i	−0.560449	−	0.138675i
$40$	−1.00000			−0.158114
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	−0.777312	−	0.629115i	$-0.783417\pi$
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$42$	1.00000	−	1.73205i	0.154303	−	0.267261i
$43$	5.50000	+	9.52628i	0.838742	+	1.45274i	0.890947	+	0.454108i	$0.150042\pi$
$43$	5.50000	+	9.52628i	0.838742	+	1.45274i	−0.0522047	+	0.998636i	$0.516625\pi$
$44$	−5.00000			−0.753778
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	9.00000			1.31278			0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000			1.31278			0.656392	+	0.754420i	$0.272082\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	2.00000			0.280056
$52$	−2.50000	+	2.59808i	−0.346688	+	0.360288i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	2.50000	−	4.33013i	0.337100	−	0.583874i
$56$	−1.00000	−	1.73205i	−0.133631	−	0.231455i
$57$	2.00000			0.264906
$58$	2.50000	+	4.33013i	0.328266	+	0.568574i
$59$	7.50000	+	12.9904i	0.976417	+	1.69120i	0.675178	+	0.737655i	$0.264067\pi$
$59$	7.50000	+	12.9904i	0.976417	+	1.69120i	0.301239	+	0.953549i	$0.402600\pi$
$60$	−1.00000			−0.129099
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	−5.50000	+	9.52628i	−0.698501	+	1.20984i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	1.00000			0.125000
$65$	−1.00000	−	3.46410i	−0.124035	−	0.429669i
$66$	−5.00000			−0.615457
$67$	−8.00000	+	13.8564i	−0.977356	+	1.69283i	−0.305424	+	0.952217i	$0.598798\pi$
$67$	−8.00000	+	13.8564i	−0.977356	+	1.69283i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	−0.500000	−	0.866025i	−0.0601929	−	0.104257i
$70$	2.00000			0.239046
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	1.50000	+	2.59808i	0.174371	+	0.302020i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	1.00000	−	1.73205i	0.114708	−	0.198680i
$77$	10.0000			1.13961
$78$	−2.50000	+	2.59808i	−0.283069	+	0.294174i
$79$	−11.0000			−1.23760			−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000			−1.23760			−0.618798	+	0.785550i	$0.712380\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−1.00000	−	1.73205i	−0.109109	−	0.188982i
$85$	1.00000	+	1.73205i	0.108465	+	0.187867i
$86$	11.0000			1.18616
$87$	2.50000	+	4.33013i	0.268028	+	0.464238i
$88$	−2.50000	+	4.33013i	−0.266501	+	0.461593i
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	−0.914146	−	0.405385i	$-0.867138\pi$
$89$	−1.00000	+	1.73205i	−0.106000	+	0.183597i	0.808146	+	0.588982i	$0.200471\pi$
$90$	−1.00000			−0.105409
$91$	5.00000	−	5.19615i	0.524142	−	0.544705i
$92$	−1.00000			−0.104257
$93$	−5.50000	+	9.52628i	−0.570323	+	0.987829i
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$	1.00000			0.102062
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	−1.50000	−	2.59808i	−0.151523	−	0.262445i
$99$	−5.00000			−0.502519
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$	1.00000	−	1.73205i	0.0990148	−	0.171499i
$103$	10.0000			0.985329			0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000			0.985329			0.492665	+	0.870219i	$0.336023\pi$
$104$	1.00000	+	3.46410i	0.0980581	+	0.339683i
$105$	2.00000			0.195180
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	−5.00000	+	8.66025i	−0.483368	+	0.837218i	−0.999818	−	0.0190994i	$-0.993920\pi$
$107$	−5.00000	+	8.66025i	−0.483368	+	0.837218i	0.516449	+	0.856318i	$0.327253\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−2.50000	−	4.33013i	−0.238366	−	0.412861i
$111$	1.50000	+	2.59808i	0.142374	+	0.246598i
$112$	−2.00000			−0.188982
$113$	−5.50000	−	9.52628i	−0.517396	−	0.896157i	−0.999796	−	0.0202056i	$-0.993568\pi$
$113$	−5.50000	−	9.52628i	−0.517396	−	0.896157i	0.482399	−	0.875951i	$-0.339765\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$	0.500000	−	0.866025i	0.0466252	−	0.0807573i
$116$	5.00000			0.464238
$117$	−2.50000	+	2.59808i	−0.231125	+	0.240192i
$118$	15.0000			1.38086
$119$	−2.00000	+	3.46410i	−0.183340	+	0.317554i
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	−7.00000	−	12.1244i	−0.636364	−	1.10221i
$122$	−10.0000			−0.905357
$123$	−1.00000	−	1.73205i	−0.0901670	−	0.156174i
$124$	5.50000	+	9.52628i	0.493915	+	0.855485i
$125$	1.00000			0.0894427
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	−0.906977	−	0.421180i	$-0.861616\pi$
$127$	−1.00000	+	1.73205i	−0.0887357	+	0.153695i	0.818241	+	0.574875i	$0.194949\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	11.0000			0.968496
$130$	−3.50000	−	0.866025i	−0.306970	−	0.0759555i
$131$	−1.00000			−0.0873704			−0.0436852	−	0.999045i	$-0.513910\pi$
$131$	−1.00000			−0.0873704			−0.0436852	+	0.999045i	$0.513910\pi$
$132$	−2.50000	+	4.33013i	−0.217597	+	0.376889i
$133$	−2.00000	+	3.46410i	−0.173422	+	0.300376i
$134$	8.00000	+	13.8564i	0.691095	+	1.19701i
$135$	−1.00000			−0.0860663
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	5.50000	+	9.52628i	0.469897	+	0.813885i	0.999408	−	0.0344182i	$-0.0109578\pi$
$137$	5.50000	+	9.52628i	0.469897	+	0.813885i	−0.529511	+	0.848303i	$0.677624\pi$
$138$	−1.00000			−0.0851257
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	0.820495	−	0.571654i	$-0.193698\pi$
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	−0.905314	+	0.424743i	$0.860365\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$	4.50000	−	7.79423i	0.378968	−	0.656392i
$142$		0			0
$143$	−17.5000	−	4.33013i	−1.46342	−	0.362103i
$144$	1.00000			0.0833333
$145$	−2.50000	+	4.33013i	−0.207614	+	0.359597i
$146$	−3.00000	+	5.19615i	−0.248282	+	0.430037i
$147$	−1.50000	−	2.59808i	−0.123718	−	0.214286i
$148$	3.00000			0.246598
$149$	−8.50000	−	14.7224i	−0.696347	−	1.20611i	−0.969724	−	0.244202i	$-0.921474\pi$
$149$	−8.50000	−	14.7224i	−0.696347	−	1.20611i	0.273377	−	0.961907i	$-0.411859\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$	1.00000	−	1.73205i	0.0808452	−	0.140028i
$154$	5.00000	−	8.66025i	0.402911	−	0.697863i
$155$	−11.0000			−0.883541
$156$	1.00000	+	3.46410i	0.0800641	+	0.277350i
$157$	−7.00000			−0.558661			−0.279330	−	0.960195i	$-0.590112\pi$
$157$	−7.00000			−0.558661			−0.279330	+	0.960195i	$0.590112\pi$
$158$	−5.50000	+	9.52628i	−0.437557	+	0.757870i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	2.00000			0.157622
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	7.50000	+	12.9904i	0.587445	+	1.01749i	0.994566	+	0.104111i	$0.0331996\pi$
$163$	7.50000	+	12.9904i	0.587445	+	1.01749i	−0.407120	+	0.913375i	$0.633467\pi$
$164$	−2.00000			−0.156174
$165$	−2.50000	−	4.33013i	−0.194625	−	0.337100i
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$	−2.00000			−0.154303
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	2.00000			0.153393
$171$	1.00000	−	1.73205i	0.0764719	−	0.132453i
$172$	5.50000	−	9.52628i	0.419371	−	0.726372i
$173$	−10.0000	−	17.3205i	−0.760286	−	1.31685i	−0.942703	−	0.333633i	$-0.891725\pi$
$173$	−10.0000	−	17.3205i	−0.760286	−	1.31685i	0.182417	−	0.983221i	$-0.441608\pi$
$174$	5.00000			0.379049
$175$	1.00000	+	1.73205i	0.0755929	+	0.130931i
$176$	2.50000	+	4.33013i	0.188445	+	0.326396i
$177$	15.0000			1.12747
$178$	1.00000	+	1.73205i	0.0749532	+	0.129823i
$179$	6.50000	−	11.2583i	0.485833	−	0.841487i	−0.514035	−	0.857769i	$-0.671850\pi$
$179$	6.50000	−	11.2583i	0.485833	−	0.841487i	0.999867	+	0.0162823i	$0.00518305\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	−2.00000	−	6.92820i	−0.148250	−	0.513553i
$183$	−10.0000			−0.739221
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−1.50000	+	2.59808i	−0.110282	+	0.191014i
$186$	5.50000	+	9.52628i	0.403280	+	0.698501i
$187$	10.0000			0.731272
$188$	−4.50000	−	7.79423i	−0.328196	−	0.568453i
$189$	−1.00000	−	1.73205i	−0.0727393	−	0.125988i
$190$	2.00000			0.145095
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	12.0000	−	20.7846i	0.863779	−	1.49611i	−0.00447566	−	0.999990i	$-0.501425\pi$
$193$	12.0000	−	20.7846i	0.863779	−	1.49611i	0.868255	−	0.496119i	$-0.165242\pi$
$194$	2.00000			0.143592
$195$	−3.50000	−	0.866025i	−0.250640	−	0.0620174i
$196$	−3.00000			−0.214286
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	−0.687618	−	0.726073i	$-0.741344\pi$
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	0.972606	+	0.232458i	$0.0746770\pi$
$198$	−2.50000	+	4.33013i	−0.177667	+	0.307729i
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	−0.880616	−	0.473831i	$-0.842871\pi$
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	0.0299585	−	0.999551i	$-0.490462\pi$
$200$	−1.00000			−0.0707107
$201$	8.00000	+	13.8564i	0.564276	+	0.977356i
$202$	1.00000	+	1.73205i	0.0703598	+	0.121867i
$203$	−10.0000			−0.701862
$204$	−1.00000	−	1.73205i	−0.0700140	−	0.121268i
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$	5.00000	−	8.66025i	0.348367	−	0.603388i
$207$	−1.00000			−0.0695048
$208$	3.50000	+	0.866025i	0.242681	+	0.0600481i
$209$	10.0000			0.691714
$210$	1.00000	−	1.73205i	0.0690066	−	0.119523i
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$	5.00000	+	8.66025i	0.341793	+	0.592003i
$215$	5.50000	+	9.52628i	0.375097	+	0.649687i
$216$	1.00000			0.0680414
$217$	−11.0000	−	19.0526i	−0.746729	−	1.29337i
$218$	−1.00000	+	1.73205i	−0.0677285	+	0.117309i
$219$	−3.00000	+	5.19615i	−0.202721	+	0.351123i
$220$	−5.00000			−0.337100
$221$	5.00000	−	5.19615i	0.336336	−	0.349531i
$222$	3.00000			0.201347
$223$	−13.0000	+	22.5167i	−0.870544	+	1.50783i	−0.00910984	+	0.999959i	$0.502900\pi$
$223$	−13.0000	+	22.5167i	−0.870544	+	1.50783i	−0.861435	+	0.507869i	$0.830434\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−11.0000			−0.731709
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	10.0000			0.660819			0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000			0.660819			0.330409	+	0.943838i	$0.392813\pi$
$230$	−0.500000	−	0.866025i	−0.0329690	−	0.0571040i
$231$	5.00000	−	8.66025i	0.328976	−	0.569803i
$232$	2.50000	−	4.33013i	0.164133	−	0.284287i
$233$	1.00000			0.0655122			0.0327561	−	0.999463i	$-0.489572\pi$
$233$	1.00000			0.0655122			0.0327561	+	0.999463i	$0.489572\pi$
$234$	1.00000	+	3.46410i	0.0653720	+	0.226455i
$235$	9.00000			0.587095
$236$	7.50000	−	12.9904i	0.488208	−	0.845602i
$237$	−5.50000	+	9.52628i	−0.357263	+	0.618798i
$238$	2.00000	+	3.46410i	0.129641	+	0.224544i
$239$	−20.0000			−1.29369			−0.646846	−	0.762620i	$-0.723912\pi$
$239$	−20.0000			−1.29369			−0.646846	+	0.762620i	$0.723912\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	0.956456	−	0.291877i	$-0.0942799\pi$
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	−0.731001	+	0.682376i	$0.760947\pi$
$242$	−14.0000			−0.899954
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−5.00000	+	8.66025i	−0.320092	+	0.554416i
$245$	1.50000	−	2.59808i	0.0958315	−	0.165985i
$246$	−2.00000			−0.127515
$247$	5.00000	−	5.19615i	0.318142	−	0.330623i
$248$	11.0000			0.698501
$249$	3.00000	−	5.19615i	0.190117	−	0.329293i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−12.5000	−	21.6506i	−0.788993	−	1.36658i	−0.926584	−	0.376087i	$-0.877269\pi$
$251$	−12.5000	−	21.6506i	−0.788993	−	1.36658i	0.137591	−	0.990489i	$-0.456064\pi$
$252$	−2.00000			−0.125988
$253$	−2.50000	−	4.33013i	−0.157174	−	0.272233i
$254$	1.00000	+	1.73205i	0.0627456	+	0.108679i
$255$	2.00000			0.125245
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.50000	−	14.7224i	0.530215	−	0.918360i	−0.469163	−	0.883112i	$-0.655444\pi$
$257$	8.50000	−	14.7224i	0.530215	−	0.918360i	0.999379	−	0.0352486i	$-0.0112223\pi$
$258$	5.50000	−	9.52628i	0.342415	−	0.593080i
$259$	−6.00000			−0.372822
$260$	−2.50000	+	2.59808i	−0.155043	+	0.161126i
$261$	5.00000			0.309492
$262$	−0.500000	+	0.866025i	−0.0308901	+	0.0535032i
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	0.336270	+	0.941766i	$0.390834\pi$
$263$	−10.5000	+	18.1865i	−0.647458	+	1.12143i	−0.983728	+	0.179664i	$0.942499\pi$
$264$	2.50000	+	4.33013i	0.153864	+	0.266501i
$265$	6.00000			0.368577
$266$	2.00000	+	3.46410i	0.122628	+	0.212398i
$267$	1.00000	+	1.73205i	0.0611990	+	0.106000i
$268$	16.0000			0.977356
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	0.569789	−	0.821791i	$-0.307025\pi$
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	−0.996586	+	0.0825561i	$0.973692\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	6.50000	−	11.2583i	0.394847	−	0.683895i	−0.598235	−	0.801321i	$-0.704131\pi$
$271$	6.50000	−	11.2583i	0.394847	−	0.683895i	0.993082	+	0.117426i	$0.0374643\pi$
$272$	−2.00000			−0.121268
$273$	−2.00000	−	6.92820i	−0.121046	−	0.419314i
$274$	11.0000			0.664534
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	5.50000	+	9.52628i	0.330463	+	0.572379i	0.982603	−	0.185720i	$-0.0594618\pi$
$277$	5.50000	+	9.52628i	0.330463	+	0.572379i	−0.652140	+	0.758099i	$0.726128\pi$
$278$	−2.00000			−0.119952
$279$	5.50000	+	9.52628i	0.329276	+	0.570323i
$280$	−1.00000	−	1.73205i	−0.0597614	−	0.103510i
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$	−4.50000	−	7.79423i	−0.267971	−	0.464140i
$283$	−9.50000	+	16.4545i	−0.564716	+	0.978117i	0.432360	+	0.901701i	$0.357681\pi$
$283$	−9.50000	+	16.4545i	−0.564716	+	0.978117i	−0.997076	+	0.0764162i	$0.975652\pi$
$284$		0			0
$285$	2.00000			0.118470
$286$	−12.5000	+	12.9904i	−0.739140	+	0.768137i
$287$	4.00000			0.236113
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	2.50000	+	4.33013i	0.146805	+	0.254274i
$291$	2.00000			0.117242
$292$	3.00000	+	5.19615i	0.175562	+	0.304082i
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	0.764990	−	0.644042i	$-0.222744\pi$
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	−0.940252	+	0.340480i	$0.889411\pi$
$294$	−3.00000			−0.174964
$295$	7.50000	+	12.9904i	0.436667	+	0.756329i
$296$	1.50000	−	2.59808i	0.0871857	−	0.151010i
$297$	−2.50000	+	4.33013i	−0.145065	+	0.251259i
$298$	−17.0000			−0.984784
$299$	−3.50000	−	0.866025i	−0.202410	−	0.0500835i
$300$	−1.00000			−0.0577350
$301$	−11.0000	+	19.0526i	−0.634029	+	1.09817i
$302$	4.00000	−	6.92820i	0.230174	−	0.398673i
$303$	1.00000	+	1.73205i	0.0574485	+	0.0995037i
$304$	−2.00000			−0.114708
$305$	−5.00000	−	8.66025i	−0.286299	−	0.495885i
$306$	−1.00000	−	1.73205i	−0.0571662	−	0.0990148i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	−5.00000	−	8.66025i	−0.284901	−	0.493464i
$309$	5.00000	−	8.66025i	0.284440	−	0.492665i
$310$	−5.50000	+	9.52628i	−0.312379	+	0.541056i
$311$	20.0000			1.13410			0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000			1.13410			0.567048	+	0.823685i	$0.308085\pi$
$312$	3.50000	+	0.866025i	0.198148	+	0.0490290i
$313$	20.0000			1.13047			0.565233	−	0.824931i	$-0.308786\pi$
$313$	20.0000			1.13047			0.565233	+	0.824931i	$0.308786\pi$
$314$	−3.50000	+	6.06218i	−0.197516	+	0.342108i
$315$	1.00000	−	1.73205i	0.0563436	−	0.0975900i
$316$	5.50000	+	9.52628i	0.309399	+	0.535895i
$317$	16.0000			0.898650			0.449325	−	0.893368i	$-0.351665\pi$
$317$	16.0000			0.898650			0.449325	+	0.893368i	$0.351665\pi$
$318$	−3.00000	−	5.19615i	−0.168232	−	0.291386i
$319$	12.5000	+	21.6506i	0.699866	+	1.21220i
$320$	1.00000			0.0559017
$321$	5.00000	+	8.66025i	0.279073	+	0.483368i
$322$	1.00000	−	1.73205i	0.0557278	−	0.0965234i
$323$	−2.00000	+	3.46410i	−0.111283	+	0.192748i
$324$	1.00000			0.0555556
$325$	−1.00000	−	3.46410i	−0.0554700	−	0.192154i
$326$	15.0000			0.830773
$327$	−1.00000	+	1.73205i	−0.0553001	+	0.0957826i
$328$	−1.00000	+	1.73205i	−0.0552158	+	0.0956365i
$329$	9.00000	+	15.5885i	0.496186	+	0.859419i
$330$	−5.00000			−0.275241
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	3.00000			0.164399
$334$	1.50000	+	2.59808i	0.0820763	+	0.142160i
$335$	−8.00000	+	13.8564i	−0.437087	+	0.757056i
$336$	−1.00000	+	1.73205i	−0.0545545	+	0.0944911i
$337$	−2.00000			−0.108947			−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000			−0.108947			−0.0544735	+	0.998515i	$0.517348\pi$
$338$	0.500000	+	12.9904i	0.0271964	+	0.706584i
$339$	−11.0000			−0.597438
$340$	1.00000	−	1.73205i	0.0542326	−	0.0939336i
$341$	−27.5000	+	47.6314i	−1.48921	+	2.57938i
$342$	−1.00000	−	1.73205i	−0.0540738	−	0.0936586i
$343$	20.0000			1.07990
$344$	−5.50000	−	9.52628i	−0.296540	−	0.513623i
$345$	−0.500000	−	0.866025i	−0.0269191	−	0.0466252i
$346$	−20.0000			−1.07521
$347$	−17.0000	−	29.4449i	−0.912608	−	1.58068i	−0.810366	−	0.585923i	$-0.800732\pi$
$347$	−17.0000	−	29.4449i	−0.912608	−	1.58068i	−0.102241	−	0.994760i	$-0.532601\pi$
$348$	2.50000	−	4.33013i	0.134014	−	0.232119i
$349$	−10.0000	+	17.3205i	−0.535288	+	0.927146i	0.463862	+	0.885908i	$0.346463\pi$
$349$	−10.0000	+	17.3205i	−0.535288	+	0.927146i	−0.999149	+	0.0412379i	$0.986870\pi$
$350$	2.00000			0.106904
$351$	1.00000	+	3.46410i	0.0533761	+	0.184900i
$352$	5.00000			0.266501
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$	7.50000	−	12.9904i	0.398621	−	0.690431i
$355$		0			0
$356$	2.00000			0.106000
$357$	2.00000	+	3.46410i	0.105851	+	0.183340i
$358$	−6.50000	−	11.2583i	−0.343536	−	0.595021i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−8.00000	+	13.8564i	−0.420471	+	0.728277i
$363$	−14.0000			−0.734809
$364$	−7.00000	−	1.73205i	−0.366900	−	0.0907841i
$365$	−6.00000			−0.314054
$366$	−5.00000	+	8.66025i	−0.261354	+	0.452679i
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	−0.578101	−	0.815966i	$-0.696206\pi$
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	0.995697	+	0.0926670i	$0.0295392\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	−2.00000			−0.104116
$370$	1.50000	+	2.59808i	0.0779813	+	0.135068i
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$	11.0000			0.570323
$373$	9.50000	+	16.4545i	0.491891	+	0.851981i	0.999956	−	0.00933789i	$-0.00297238\pi$
$373$	9.50000	+	16.4545i	0.491891	+	0.851981i	−0.508065	+	0.861319i	$0.669639\pi$
$374$	5.00000	−	8.66025i	0.258544	−	0.447811i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−9.00000			−0.464140
$377$	17.5000	+	4.33013i	0.901296	+	0.223013i
$378$	−2.00000			−0.102869
$379$	1.00000	−	1.73205i	0.0513665	−	0.0889695i	−0.839199	−	0.543825i	$-0.816976\pi$
$379$	1.00000	−	1.73205i	0.0513665	−	0.0889695i	0.890565	+	0.454855i	$0.150309\pi$
$380$	1.00000	−	1.73205i	0.0512989	−	0.0888523i
$381$	1.00000	+	1.73205i	0.0512316	+	0.0887357i
$382$	−4.00000			−0.204658
$383$	−15.5000	−	26.8468i	−0.792013	−	1.37181i	−0.924719	−	0.380651i	$-0.875700\pi$
$383$	−15.5000	−	26.8468i	−0.792013	−	1.37181i	0.132706	−	0.991155i	$-0.457633\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	10.0000			0.509647
$386$	−12.0000	−	20.7846i	−0.610784	−	1.05791i
$387$	5.50000	−	9.52628i	0.279581	−	0.484248i
$388$	1.00000	−	1.73205i	0.0507673	−	0.0879316i
$389$	5.00000			0.253510			0.126755	−	0.991934i	$-0.459544\pi$
$389$	5.00000			0.253510			0.126755	+	0.991934i	$0.459544\pi$
$390$	−2.50000	+	2.59808i	−0.126592	+	0.131559i
$391$	2.00000			0.101144
$392$	−1.50000	+	2.59808i	−0.0757614	+	0.131223i
$393$	−0.500000	+	0.866025i	−0.0252217	+	0.0436852i
$394$	−4.00000	−	6.92820i	−0.201517	−	0.349038i
$395$	−11.0000			−0.553470
$396$	2.50000	+	4.33013i	0.125630	+	0.217597i
$397$	−1.50000	−	2.59808i	−0.0752828	−	0.130394i	0.825926	−	0.563778i	$-0.190653\pi$
$397$	−1.50000	−	2.59808i	−0.0752828	−	0.130394i	−0.901209	+	0.433384i	$0.857319\pi$
$398$	−24.0000			−1.20301
$399$	2.00000	+	3.46410i	0.100125	+	0.173422i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−18.0000	+	31.1769i	−0.898877	+	1.55690i	−0.0699455	+	0.997551i	$0.522283\pi$
$401$	−18.0000	+	31.1769i	−0.898877	+	1.55690i	−0.828932	+	0.559350i	$0.811051\pi$
$402$	16.0000			0.798007
$403$	11.0000	+	38.1051i	0.547949	+	1.89815i
$404$	2.00000			0.0995037
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	−5.00000	+	8.66025i	−0.248146	+	0.429801i
$407$	7.50000	+	12.9904i	0.371761	+	0.643909i
$408$	−2.00000			−0.0990148
$409$	−15.0000	−	25.9808i	−0.741702	−	1.28467i	−0.951720	−	0.306968i	$-0.900685\pi$
$409$	−15.0000	−	25.9808i	−0.741702	−	1.28467i	0.210017	−	0.977698i	$-0.432648\pi$
$410$	−1.00000	−	1.73205i	−0.0493865	−	0.0855399i
$411$	11.0000			0.542590
$412$	−5.00000	−	8.66025i	−0.246332	−	0.426660i
$413$	−15.0000	+	25.9808i	−0.738102	+	1.27843i
$414$	−0.500000	+	0.866025i	−0.0245737	+	0.0425628i
$415$	6.00000			0.294528
$416$	2.50000	−	2.59808i	0.122573	−	0.127381i
$417$	−2.00000			−0.0979404
$418$	5.00000	−	8.66025i	0.244558	−	0.423587i
$419$	2.00000	−	3.46410i	0.0977064	−	0.169232i	−0.813029	−	0.582224i	$-0.802183\pi$
$419$	2.00000	−	3.46410i	0.0977064	−	0.169232i	0.910735	+	0.412991i	$0.135516\pi$
$420$	−1.00000	−	1.73205i	−0.0487950	−	0.0845154i
$421$	−16.0000			−0.779792			−0.389896	−	0.920859i	$-0.627489\pi$
$421$	−16.0000			−0.779792			−0.389896	+	0.920859i	$0.627489\pi$
$422$	−2.00000	−	3.46410i	−0.0973585	−	0.168630i
$423$	−4.50000	−	7.79423i	−0.218797	−	0.378968i
$424$	−6.00000			−0.291386
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$	10.0000	−	17.3205i	0.483934	−	0.838198i
$428$	10.0000			0.483368
$429$	−12.5000	+	12.9904i	−0.603506	+	0.627182i
$430$	11.0000			0.530467
$431$	−20.0000	+	34.6410i	−0.963366	+	1.66860i	−0.249424	+	0.968394i	$0.580241\pi$
$431$	−20.0000	+	34.6410i	−0.963366	+	1.66860i	−0.713942	+	0.700205i	$0.753092\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−14.0000	−	24.2487i	−0.672797	−	1.16532i	−0.977108	−	0.212746i	$-0.931759\pi$
$433$	−14.0000	−	24.2487i	−0.672797	−	1.16532i	0.304311	−	0.952573i	$-0.401574\pi$
$434$	−22.0000			−1.05603
$435$	2.50000	+	4.33013i	0.119866	+	0.207614i
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	2.00000			0.0956730
$438$	3.00000	+	5.19615i	0.143346	+	0.248282i
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	−0.814344	−	0.580383i	$-0.802903\pi$
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	0.909798	+	0.415051i	$0.136236\pi$
$440$	−2.50000	+	4.33013i	−0.119183	+	0.206431i
$441$	−3.00000			−0.142857
$442$	−2.00000	−	6.92820i	−0.0951303	−	0.329541i
$443$	20.0000			0.950229			0.475114	−	0.879924i	$-0.342407\pi$
$443$	20.0000			0.950229			0.475114	+	0.879924i	$0.342407\pi$
$444$	1.50000	−	2.59808i	0.0711868	−	0.123299i
$445$	−1.00000	+	1.73205i	−0.0474045	+	0.0821071i
$446$	13.0000	+	22.5167i	0.615568	+	1.06619i
$447$	−17.0000			−0.804072
$448$	1.00000	+	1.73205i	0.0472456	+	0.0818317i
$449$	−6.00000	−	10.3923i	−0.283158	−	0.490443i	0.689003	−	0.724758i	$-0.258049\pi$
$449$	−6.00000	−	10.3923i	−0.283158	−	0.490443i	−0.972161	+	0.234315i	$0.924715\pi$
$450$	−1.00000			−0.0471405
$451$	−5.00000	−	8.66025i	−0.235441	−	0.407795i
$452$	−5.50000	+	9.52628i	−0.258698	+	0.448078i
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$		0			0
$455$	5.00000	−	5.19615i	0.234404	−	0.243599i
$456$	−2.00000			−0.0936586
$457$	−19.0000	+	32.9090i	−0.888783	+	1.53942i	−0.0474665	+	0.998873i	$0.515115\pi$
$457$	−19.0000	+	32.9090i	−0.888783	+	1.53942i	−0.841316	+	0.540544i	$0.818219\pi$
$458$	5.00000	−	8.66025i	0.233635	−	0.404667i
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$	−1.00000			−0.0466252
$461$	19.5000	+	33.7750i	0.908206	+	1.57306i	0.816556	+	0.577267i	$0.195881\pi$
$461$	19.5000	+	33.7750i	0.908206	+	1.57306i	0.0916500	+	0.995791i	$0.470786\pi$
$462$	−5.00000	−	8.66025i	−0.232621	−	0.402911i
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$	−2.50000	−	4.33013i	−0.116060	−	0.201021i
$465$	−5.50000	+	9.52628i	−0.255056	+	0.441771i
$466$	0.500000	−	0.866025i	0.0231621	−	0.0401179i
$467$	6.00000			0.277647			0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000			0.277647			0.138823	+	0.990317i	$0.455668\pi$
$468$	3.50000	+	0.866025i	0.161788	+	0.0400320i
$469$	−32.0000			−1.47762
$470$	4.50000	−	7.79423i	0.207570	−	0.359521i
$471$	−3.50000	+	6.06218i	−0.161271	+	0.279330i
$472$	−7.50000	−	12.9904i	−0.345215	−	0.597931i
$473$	55.0000			2.52890
$474$	5.50000	+	9.52628i	0.252623	+	0.437557i
$475$	1.00000	+	1.73205i	0.0458831	+	0.0794719i
$476$	4.00000			0.183340
$477$	−3.00000	−	5.19615i	−0.137361	−	0.237915i
$478$	−10.0000	+	17.3205i	−0.457389	+	0.792222i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$	1.00000			0.0456435
$481$	10.5000	+	2.59808i	0.478759	+	0.118462i
$482$	7.00000			0.318841
$483$	1.00000	−	1.73205i	0.0455016	−	0.0788110i
$484$	−7.00000	+	12.1244i	−0.318182	+	0.551107i
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$	1.00000			0.0453609
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$	5.00000	+	8.66025i	0.226339	+	0.392031i
$489$	15.0000			0.678323
$490$	−1.50000	−	2.59808i	−0.0677631	−	0.117369i
$491$	8.00000	−	13.8564i	0.361035	−	0.625331i	−0.627096	−	0.778942i	$-0.715757\pi$
$491$	8.00000	−	13.8564i	0.361035	−	0.625331i	0.988131	+	0.153611i	$0.0490902\pi$
$492$	−1.00000	+	1.73205i	−0.0450835	+	0.0780869i
$493$	−10.0000			−0.450377
$494$	−2.00000	−	6.92820i	−0.0899843	−	0.311715i
$495$	−5.00000			−0.224733
$496$	5.50000	−	9.52628i	0.246957	−	0.427743i
$497$		0			0
$498$	−3.00000	−	5.19615i	−0.134433	−	0.232845i
$499$	28.0000			1.25345			0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000			1.25345			0.626726	+	0.779240i	$0.284395\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	1.50000	+	2.59808i	0.0670151	+	0.116073i
$502$	−25.0000			−1.11580
$503$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$503$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$504$	−1.00000	+	1.73205i	−0.0445435	+	0.0771517i
$505$	−1.00000	+	1.73205i	−0.0444994	+	0.0770752i
$506$	−5.00000			−0.222277
$507$	0.500000	+	12.9904i	0.0222058	+	0.576923i
$508$	2.00000			0.0887357
$509$	−14.5000	+	25.1147i	−0.642701	+	1.11319i	0.342126	+	0.939654i	$0.388853\pi$
$509$	−14.5000	+	25.1147i	−0.642701	+	1.11319i	−0.984827	+	0.173537i	$0.944480\pi$
$510$	1.00000	−	1.73205i	0.0442807	−	0.0766965i
$511$	−6.00000	−	10.3923i	−0.265424	−	0.459728i
$512$	−1.00000			−0.0441942
$513$	−1.00000	−	1.73205i	−0.0441511	−	0.0764719i
$514$	−8.50000	−	14.7224i	−0.374919	−	0.649379i
$515$	10.0000			0.440653
$516$	−5.50000	−	9.52628i	−0.242124	−	0.419371i
$517$	22.5000	−	38.9711i	0.989549	−	1.71395i
$518$	−3.00000	+	5.19615i	−0.131812	+	0.228306i
$519$	−20.0000			−0.877903
$520$	1.00000	+	3.46410i	0.0438529	+	0.151911i
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	2.50000	−	4.33013i	0.109422	−	0.189525i
$523$	15.5000	−	26.8468i	0.677768	−	1.17393i	−0.297884	−	0.954602i	$-0.596281\pi$
$523$	15.5000	−	26.8468i	0.677768	−	1.17393i	0.975652	−	0.219326i	$-0.0703858\pi$
$524$	0.500000	+	0.866025i	0.0218426	+	0.0378325i
$525$	2.00000			0.0872872
$526$	10.5000	+	18.1865i	0.457822	+	0.792971i
$527$	−11.0000	−	19.0526i	−0.479168	−	0.829943i
$528$	5.00000			0.217597
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	3.00000	−	5.19615i	0.130312	−	0.225706i
$531$	7.50000	−	12.9904i	0.325472	−	0.563735i
$532$	4.00000			0.173422
$533$	−7.00000	−	1.73205i	−0.303204	−	0.0750234i
$534$	2.00000			0.0865485
$535$	−5.00000	+	8.66025i	−0.216169	+	0.374415i
$536$	8.00000	−	13.8564i	0.345547	−	0.598506i
$537$	−6.50000	−	11.2583i	−0.280496	−	0.485833i
$538$	−14.0000			−0.603583
$539$	−7.50000	−	12.9904i	−0.323048	−	0.559535i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$		0			0			−	1.00000i	$-0.5\pi$
$541$		0			0				1.00000i	$0.5\pi$
$542$	−6.50000	−	11.2583i	−0.279199	−	0.483587i
$543$	−8.00000	+	13.8564i	−0.343313	+	0.594635i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	−2.00000			−0.0856706
$546$	−7.00000	−	1.73205i	−0.299572	−	0.0741249i
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	5.50000	−	9.52628i	0.234948	−	0.406942i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$	−2.50000	−	4.33013i	−0.106600	−	0.184637i
$551$	−10.0000			−0.426014
$552$	0.500000	+	0.866025i	0.0212814	+	0.0368605i
$553$	−11.0000	−	19.0526i	−0.467768	−	0.810197i
$554$	11.0000			0.467345
$555$	1.50000	+	2.59808i	0.0636715	+	0.110282i
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	−13.0000	+	22.5167i	−0.550828	+	0.954062i	0.447387	+	0.894340i	$0.352355\pi$
$557$	−13.0000	+	22.5167i	−0.550828	+	0.954062i	−0.998215	+	0.0597213i	$0.980979\pi$
$558$	11.0000			0.465667
$559$	27.5000	−	28.5788i	1.16313	−	1.20876i
$560$	−2.00000			−0.0845154
$561$	5.00000	−	8.66025i	0.211100	−	0.365636i
$562$	−5.00000	+	8.66025i	−0.210912	+	0.365311i
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	0.711445	−	0.702742i	$-0.248041\pi$
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	−0.964315	+	0.264758i	$0.914708\pi$
$564$	−9.00000			−0.378968
$565$	−5.50000	−	9.52628i	−0.231387	−	0.400774i
$566$	9.50000	+	16.4545i	0.399315	+	0.691633i
$567$	−2.00000			−0.0839921
$568$		0			0
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	−0.537874	−	0.843025i	$-0.680772\pi$
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	0.999018	+	0.0443003i	$0.0141058\pi$
$570$	1.00000	−	1.73205i	0.0418854	−	0.0725476i
$571$	−16.0000			−0.669579			−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000			−0.669579			−0.334790	+	0.942293i	$0.608665\pi$
$572$	5.00000	+	17.3205i	0.209061	+	0.724207i
$573$	−4.00000			−0.167102
$574$	2.00000	−	3.46410i	0.0834784	−	0.144589i
$575$	0.500000	−	0.866025i	0.0208514	−	0.0361158i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−22.0000			−0.915872			−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000			−0.915872			−0.457936	+	0.888985i	$0.651411\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$	−12.0000	−	20.7846i	−0.498703	−	0.863779i
$580$	5.00000			0.207614
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$	1.00000	−	1.73205i	0.0414513	−	0.0717958i
$583$	15.0000	−	25.9808i	0.621237	−	1.07601i
$584$	6.00000			0.248282
$585$	−2.50000	+	2.59808i	−0.103362	+	0.107417i
$586$	−6.00000			−0.247858
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	−0.618322	−	0.785925i	$-0.712187\pi$
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	0.989792	+	0.142520i	$0.0455206\pi$
$588$	−1.50000	+	2.59808i	−0.0618590	+	0.107143i
$589$	−11.0000	−	19.0526i	−0.453247	−	0.785047i
$590$	15.0000			0.617540
$591$	−4.00000	−	6.92820i	−0.164538	−	0.284988i
$592$	−1.50000	−	2.59808i	−0.0616496	−	0.106780i
$593$	31.0000			1.27302			0.636509	−	0.771270i	$-0.280378\pi$
$593$	31.0000			1.27302			0.636509	+	0.771270i	$0.280378\pi$
$594$	2.50000	+	4.33013i	0.102576	+	0.177667i
$595$	−2.00000	+	3.46410i	−0.0819920	+	0.142014i
$596$	−8.50000	+	14.7224i	−0.348174	+	0.603054i
$597$	−24.0000			−0.982255
$598$	−2.50000	+	2.59808i	−0.102233	+	0.106243i
$599$	42.0000			1.71607			0.858037	−	0.513588i	$-0.171684\pi$
$599$	42.0000			1.71607			0.858037	+	0.513588i	$0.171684\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	1.50000	−	2.59808i	0.0611863	−	0.105978i	−0.833810	−	0.552052i	$-0.813845\pi$
$601$	1.50000	−	2.59808i	0.0611863	−	0.105978i	0.894996	+	0.446074i	$0.147178\pi$
$602$	11.0000	+	19.0526i	0.448327	+	0.776524i
$603$	16.0000			0.651570
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$	2.00000			0.0812444
$607$	−9.00000	−	15.5885i	−0.365299	−	0.632716i	0.623525	−	0.781803i	$-0.285700\pi$
$607$	−9.00000	−	15.5885i	−0.365299	−	0.632716i	−0.988824	+	0.149087i	$0.952366\pi$
$608$	−1.00000	+	1.73205i	−0.0405554	+	0.0702439i
$609$	−5.00000	+	8.66025i	−0.202610	+	0.350931i
$610$	−10.0000			−0.404888
$611$	−9.00000	−	31.1769i	−0.364101	−	1.26128i
$612$	−2.00000			−0.0808452
$613$	14.5000	−	25.1147i	0.585649	−	1.01437i	−0.409145	−	0.912470i	$-0.634173\pi$
$613$	14.5000	−	25.1147i	0.585649	−	1.01437i	0.994794	−	0.101905i	$-0.0324938\pi$
$614$		0			0
$615$	−1.00000	−	1.73205i	−0.0403239	−	0.0698430i
$616$	−10.0000			−0.402911
$617$	−20.5000	−	35.5070i	−0.825299	−	1.42946i	−0.901691	−	0.432382i	$-0.857673\pi$
$617$	−20.5000	−	35.5070i	−0.825299	−	1.42946i	0.0763917	−	0.997078i	$-0.475660\pi$
$618$	−5.00000	−	8.66025i	−0.201129	−	0.348367i
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$	5.50000	+	9.52628i	0.220885	+	0.382585i
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$	10.0000	−	17.3205i	0.400963	−	0.694489i
$623$	−4.00000			−0.160257
$624$	2.50000	−	2.59808i	0.100080	−	0.104006i
$625$	1.00000			0.0400000
$626$	10.0000	−	17.3205i	0.399680	−	0.692267i
$627$	5.00000	−	8.66025i	0.199681	−	0.345857i
$628$	3.50000	+	6.06218i	0.139665	+	0.241907i
$629$	−6.00000			−0.239236
$630$	−1.00000	−	1.73205i	−0.0398410	−	0.0690066i
$631$	−20.0000	−	34.6410i	−0.796187	−	1.37904i	−0.922082	−	0.386994i	$-0.873514\pi$
$631$	−20.0000	−	34.6410i	−0.796187	−	1.37904i	0.125895	−	0.992044i	$-0.459820\pi$
$632$	11.0000			0.437557
$633$	−2.00000	−	3.46410i	−0.0794929	−	0.137686i
$634$	8.00000	−	13.8564i	0.317721	−	0.550308i
$635$	−1.00000	+	1.73205i	−0.0396838	+	0.0687343i
$636$	−6.00000			−0.237915
$637$	−10.5000	−	2.59808i	−0.416025	−	0.102940i
$638$	25.0000			0.989759
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$	10.0000			0.394669
$643$	−4.00000	−	6.92820i	−0.157745	−	0.273222i	0.776310	−	0.630351i	$-0.217089\pi$
$643$	−4.00000	−	6.92820i	−0.157745	−	0.273222i	−0.934055	+	0.357129i	$0.883756\pi$
$644$	−1.00000	−	1.73205i	−0.0394055	−	0.0682524i
$645$	11.0000			0.433125
$646$	2.00000	+	3.46410i	0.0786889	+	0.136293i
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	75.0000			2.94401
$650$	−3.50000	−	0.866025i	−0.137281	−	0.0339683i
$651$	−22.0000			−0.862248
$652$	7.50000	−	12.9904i	0.293723	−	0.508743i
$653$	−17.0000	+	29.4449i	−0.665261	+	1.15227i	0.313953	+	0.949439i	$0.398347\pi$
$653$	−17.0000	+	29.4449i	−0.665261	+	1.15227i	−0.979214	+	0.202828i	$0.934987\pi$
$654$	1.00000	+	1.73205i	0.0391031	+	0.0677285i
$655$	−1.00000			−0.0390732
$656$	1.00000	+	1.73205i	0.0390434	+	0.0676252i
$657$	3.00000	+	5.19615i	0.117041	+	0.202721i
$658$	18.0000			0.701713
$659$	19.5000	+	33.7750i	0.759612	+	1.31569i	0.943049	+	0.332655i	$0.107945\pi$
$659$	19.5000	+	33.7750i	0.759612	+	1.31569i	−0.183436	+	0.983032i	$0.558722\pi$
$660$	−2.50000	+	4.33013i	−0.0973124	+	0.168550i
$661$	−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	$0.952854\pi$
$662$	28.0000			1.08825
$663$	−2.00000	−	6.92820i	−0.0776736	−	0.269069i
$664$	−6.00000			−0.232845
$665$	−2.00000	+	3.46410i	−0.0775567	+	0.134332i
$666$	1.50000	−	2.59808i	0.0581238	−	0.100673i
$667$	2.50000	+	4.33013i	0.0968004	+	0.167663i
$668$	3.00000			0.116073
$669$	13.0000	+	22.5167i	0.502609	+	0.870544i
$670$	8.00000	+	13.8564i	0.309067	+	0.535320i
$671$	−50.0000			−1.93023
$672$	1.00000	+	1.73205i	0.0385758	+	0.0668153i
$673$	−4.00000	+	6.92820i	−0.154189	+	0.267063i	−0.932763	−	0.360489i	$-0.882610\pi$
$673$	−4.00000	+	6.92820i	−0.154189	+	0.267063i	0.778575	+	0.627552i	$0.215943\pi$
$674$	−1.00000	+	1.73205i	−0.0385186	+	0.0667161i
$675$	−1.00000			−0.0384900
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$	−4.00000			−0.153732			−0.0768662	−	0.997041i	$-0.524491\pi$
$677$	−4.00000			−0.153732			−0.0768662	+	0.997041i	$0.524491\pi$
$678$	−5.50000	+	9.52628i	−0.211226	+	0.365855i
$679$	−2.00000	+	3.46410i	−0.0767530	+	0.132940i
$680$	−1.00000	−	1.73205i	−0.0383482	−	0.0664211i
$681$		0			0
$682$	27.5000	+	47.6314i	1.05303	+	1.82390i
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$	−2.00000			−0.0764719
$685$	5.50000	+	9.52628i	0.210144	+	0.363980i
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$	5.00000	−	8.66025i	0.190762	−	0.330409i
$688$	−11.0000			−0.419371
$689$	−6.00000	−	20.7846i	−0.228582	−	0.791831i
$690$	−1.00000			−0.0380693
$691$	15.0000	−	25.9808i	0.570627	−	0.988355i	−0.425875	−	0.904782i	$-0.640034\pi$
$691$	15.0000	−	25.9808i	0.570627	−	0.988355i	0.996502	−	0.0835727i	$-0.0266331\pi$
$692$	−10.0000	+	17.3205i	−0.380143	+	0.658427i
$693$	−5.00000	−	8.66025i	−0.189934	−	0.328976i
$694$	−34.0000			−1.29062
$695$	−1.00000	−	1.73205i	−0.0379322	−	0.0657004i
$696$	−2.50000	−	4.33013i	−0.0947623	−	0.164133i
$697$	4.00000			0.151511
$698$	10.0000	+	17.3205i	0.378506	+	0.655591i
$699$	0.500000	−	0.866025i	0.0189117	−	0.0327561i
$700$	1.00000	−	1.73205i	0.0377964	−	0.0654654i
$701$	13.0000			0.491003			0.245502	−	0.969396i	$-0.421047\pi$
$701$	13.0000			0.491003			0.245502	+	0.969396i	$0.421047\pi$
$702$	3.50000	+	0.866025i	0.132099	+	0.0326860i
$703$	−6.00000			−0.226294
$704$	2.50000	−	4.33013i	0.0942223	−	0.163198i
$705$	4.50000	−	7.79423i	0.169480	−	0.293548i
$706$	−9.00000	−	15.5885i	−0.338719	−	0.586679i
$707$	−4.00000			−0.150435
$708$	−7.50000	−	12.9904i	−0.281867	−	0.488208i
$709$	4.00000	+	6.92820i	0.150223	+	0.260194i	0.931309	−	0.364229i	$-0.118667\pi$
$709$	4.00000	+	6.92820i	0.150223	+	0.260194i	−0.781086	+	0.624423i	$0.785334\pi$
$710$		0			0
$711$	5.50000	+	9.52628i	0.206266	+	0.357263i
$712$	1.00000	−	1.73205i	0.0374766	−	0.0649113i
$713$	−5.50000	+	9.52628i	−0.205977	+	0.356762i
$714$	4.00000			0.149696
$715$	−17.5000	−	4.33013i	−0.654463	−	0.161938i
$716$	−13.0000			−0.485833
$717$	−10.0000	+	17.3205i	−0.373457	+	0.646846i
$718$	6.00000	−	10.3923i	0.223918	−	0.387837i
$719$	−12.0000	−	20.7846i	−0.447524	−	0.775135i	0.550700	−	0.834703i	$-0.314361\pi$
$719$	−12.0000	−	20.7846i	−0.447524	−	0.775135i	−0.998224	+	0.0595683i	$0.981028\pi$
$720$	1.00000			0.0372678
$721$	10.0000	+	17.3205i	0.372419	+	0.645049i
$722$	−7.50000	−	12.9904i	−0.279121	−	0.483452i
$723$	7.00000			0.260333
$724$	8.00000	+	13.8564i	0.297318	+	0.514969i
$725$	−2.50000	+	4.33013i	−0.0928477	+	0.160817i
$726$	−7.00000	+	12.1244i	−0.259794	+	0.449977i
$727$	−40.0000			−1.48352			−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000			−1.48352			−0.741759	+	0.670667i	$0.766008\pi$
$728$	−5.00000	+	5.19615i	−0.185312	+	0.192582i
$729$	1.00000			0.0370370
$730$	−3.00000	+	5.19615i	−0.111035	+	0.192318i
$731$	−11.0000	+	19.0526i	−0.406850	+	0.704684i
$732$	5.00000	+	8.66025i	0.184805	+	0.320092i
$733$	6.00000			0.221615			0.110808	−	0.993842i	$-0.464656\pi$
$733$	6.00000			0.221615			0.110808	+	0.993842i	$0.464656\pi$
$734$	−8.00000	−	13.8564i	−0.295285	−	0.511449i
$735$	−1.50000	−	2.59808i	−0.0553283	−	0.0958315i
$736$	1.00000			0.0368605
$737$	40.0000	+	69.2820i	1.47342	+	2.55204i
$738$	−1.00000	+	1.73205i	−0.0368105	+	0.0637577i
$739$	−22.0000	+	38.1051i	−0.809283	+	1.40172i	0.104078	+	0.994569i	$0.466811\pi$
$739$	−22.0000	+	38.1051i	−0.809283	+	1.40172i	−0.913361	+	0.407150i	$0.866523\pi$
$740$	3.00000			0.110282
$741$	−2.00000	−	6.92820i	−0.0734718	−	0.254514i
$742$	12.0000			0.440534
$743$	−25.5000	+	44.1673i	−0.935504	+	1.62034i	−0.161772	+	0.986828i	$0.551721\pi$
$743$	−25.5000	+	44.1673i	−0.935504	+	1.62034i	−0.773732	+	0.633513i	$0.781612\pi$
$744$	5.50000	−	9.52628i	0.201640	−	0.349250i
$745$	−8.50000	−	14.7224i	−0.311416	−	0.539388i
$746$	19.0000			0.695639
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$	−5.00000	−	8.66025i	−0.182818	−	0.316650i
$749$	−20.0000			−0.730784
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	11.5000	−	19.9186i	0.419641	−	0.726839i	−0.576262	−	0.817265i	$-0.695489\pi$
$751$	11.5000	−	19.9186i	0.419641	−	0.726839i	0.995903	+	0.0904254i	$0.0288227\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	−25.0000			−0.911051
$754$	12.5000	−	12.9904i	0.455223	−	0.473082i
$755$	8.00000			0.291150
$756$	−1.00000	+	1.73205i	−0.0363696	+	0.0629941i
$757$	−5.00000	+	8.66025i	−0.181728	+	0.314762i	−0.942469	−	0.334293i	$-0.891502\pi$
$757$	−5.00000	+	8.66025i	−0.181728	+	0.314762i	0.760741	+	0.649056i	$0.224836\pi$
$758$	−1.00000	−	1.73205i	−0.0363216	−	0.0629109i
$759$	−5.00000			−0.181489
$760$	−1.00000	−	1.73205i	−0.0362738	−	0.0628281i
$761$	−10.0000	−	17.3205i	−0.362500	−	0.627868i	0.625872	−	0.779926i	$-0.284743\pi$
$761$	−10.0000	−	17.3205i	−0.362500	−	0.627868i	−0.988372	+	0.152058i	$0.951410\pi$
$762$	2.00000			0.0724524
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$	−2.00000	+	3.46410i	−0.0723575	+	0.125327i
$765$	1.00000	−	1.73205i	0.0361551	−	0.0626224i
$766$	−31.0000			−1.12008
$767$	37.5000	−	38.9711i	1.35405	−	1.40717i
$768$	−1.00000			−0.0360844
$769$	−21.5000	+	37.2391i	−0.775310	+	1.34288i	0.159310	+	0.987229i	$0.449073\pi$
$769$	−21.5000	+	37.2391i	−0.775310	+	1.34288i	−0.934620	+	0.355647i	$0.884260\pi$
$770$	5.00000	−	8.66025i	0.180187	−	0.312094i
$771$	−8.50000	−	14.7224i	−0.306120	−	0.530215i
$772$	−24.0000			−0.863779
$773$	−16.0000	−	27.7128i	−0.575480	−	0.996761i	−0.995989	−	0.0894724i	$-0.971482\pi$
$773$	−16.0000	−	27.7128i	−0.575480	−	0.996761i	0.420509	−	0.907288i	$-0.361851\pi$
$774$	−5.50000	−	9.52628i	−0.197693	−	0.342415i
$775$	−11.0000			−0.395132
$776$	−1.00000	−	1.73205i	−0.0358979	−	0.0621770i
$777$	−3.00000	+	5.19615i	−0.107624	+	0.186411i
$778$	2.50000	−	4.33013i	0.0896293	−	0.155243i
$779$	4.00000			0.143315
$780$	1.00000	+	3.46410i	0.0358057	+	0.124035i
$781$		0			0
$782$	1.00000	−	1.73205i	0.0357599	−	0.0619380i
$783$	2.50000	−	4.33013i	0.0893427	−	0.154746i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$	−7.00000			−0.249841
$786$	0.500000	+	0.866025i	0.0178344	+	0.0308901i
$787$	15.5000	+	26.8468i	0.552515	+	0.956985i	0.998092	+	0.0617409i	$0.0196653\pi$
$787$	15.5000	+	26.8468i	0.552515	+	0.956985i	−0.445577	+	0.895244i	$0.647001\pi$
$788$	−8.00000			−0.284988
$789$	10.5000	+	18.1865i	0.373810	+	0.647458i
$790$	−5.50000	+	9.52628i	−0.195681	+	0.338930i
$791$	11.0000	−	19.0526i	0.391115	−	0.677431i
$792$	5.00000			0.177667
$793$	−25.0000	+	25.9808i	−0.887776	+	0.922604i
$794$	−3.00000			−0.106466
$795$	3.00000	−	5.19615i	0.106399	−	0.184289i
$796$	−12.0000	+	20.7846i	−0.425329	+	0.736691i
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	0.739975	−	0.672634i	$-0.234837\pi$
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	−0.952506	+	0.304520i	$0.901504\pi$
$798$	4.00000			0.141598
$799$	9.00000	+	15.5885i	0.318397	+	0.551480i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	2.00000			0.0706665
$802$	18.0000	+	31.1769i	0.635602	+	1.10090i
$803$	−15.0000	+	25.9808i	−0.529339	+	0.916841i
$804$	8.00000	−	13.8564i	0.282138	−	0.488678i
$805$	2.00000			0.0704907
$806$	38.5000	+	9.52628i	1.35610	+	0.335549i
$807$	−14.0000			−0.492823
$808$	1.00000	−	1.73205i	0.0351799	−	0.0609333i
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	5.00000	+	8.66025i	0.175466	+	0.303915i
$813$	−6.50000	−	11.2583i	−0.227965	−	0.394847i
$814$	15.0000			0.525750
$815$	7.50000	+	12.9904i	0.262714	+	0.455033i
$816$	−1.00000	+	1.73205i	−0.0350070	+	0.0606339i
$817$	−11.0000	+	19.0526i	−0.384841	+	0.666565i
$818$	−30.0000			−1.04893
$819$	−7.00000	−	1.73205i	−0.244600	−	0.0605228i
$820$	−2.00000			−0.0698430
$821$	25.5000	−	44.1673i	0.889956	−	1.54145i	0.0500305	−	0.998748i	$-0.484068\pi$
$821$	25.5000	−	44.1673i	0.889956	−	1.54145i	0.839926	−	0.542702i	$-0.182599\pi$
$822$	5.50000	−	9.52628i	0.191835	−	0.332267i
$823$	1.00000	+	1.73205i	0.0348578	+	0.0603755i	0.882928	−	0.469508i	$-0.155569\pi$
$823$	1.00000	+	1.73205i	0.0348578	+	0.0603755i	−0.848070	+	0.529884i	$0.822235\pi$
$824$	−10.0000			−0.348367
$825$	−2.50000	−	4.33013i	−0.0870388	−	0.150756i
$826$	15.0000	+	25.9808i	0.521917	+	0.903986i
$827$	−50.0000			−1.73867			−0.869335	−	0.494223i	$-0.835453\pi$
$827$	−50.0000			−1.73867			−0.869335	+	0.494223i	$0.835453\pi$
$828$	0.500000	+	0.866025i	0.0173762	+	0.0300965i
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	−0.961601	−	0.274450i	$-0.911504\pi$
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	0.718481	+	0.695546i	$0.244838\pi$
$830$	3.00000	−	5.19615i	0.104132	−	0.180361i
$831$	11.0000			0.381586
$832$	−1.00000	−	3.46410i	−0.0346688	−	0.120096i
$833$	6.00000			0.207888
$834$	−1.00000	+	1.73205i	−0.0346272	+	0.0599760i
$835$	−1.50000	+	2.59808i	−0.0519096	+	0.0899101i
$836$	−5.00000	−	8.66025i	−0.172929	−	0.299521i
$837$	11.0000			0.380216
$838$	−2.00000	−	3.46410i	−0.0690889	−	0.119665i
$839$	27.0000	+	46.7654i	0.932144	+	1.61452i	0.779650	+	0.626215i	$0.215397\pi$
$839$	27.0000	+	46.7654i	0.932144	+	1.61452i	0.152493	+	0.988304i	$0.451270\pi$
$840$	−2.00000			−0.0690066
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$	−8.00000	+	13.8564i	−0.275698	+	0.477523i
$843$	−5.00000	+	8.66025i	−0.172209	+	0.298275i
$844$	−4.00000			−0.137686
$845$	−11.0000	+	6.92820i	−0.378412	+	0.238337i
$846$	−9.00000			−0.309426
$847$	14.0000	−	24.2487i	0.481046	−	0.833196i
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$	9.50000	+	16.4545i	0.326039	+	0.564716i
$850$	2.00000			0.0685994
$851$	1.50000	+	2.59808i	0.0514193	+	0.0890609i
$852$		0			0
$853$	−49.0000			−1.67773			−0.838864	−	0.544341i	$-0.816780\pi$
$853$	−49.0000			−1.67773			−0.838864	+	0.544341i	$0.816780\pi$
$854$	−10.0000	−	17.3205i	−0.342193	−	0.592696i
$855$	1.00000	−	1.73205i	0.0341993	−	0.0592349i
$856$	5.00000	−	8.66025i	0.170896	−	0.296001i
$857$	−25.0000			−0.853984			−0.426992	−	0.904255i	$-0.640427\pi$
$857$	−25.0000			−0.853984			−0.426992	+	0.904255i	$0.640427\pi$
$858$	5.00000	+	17.3205i	0.170697	+	0.591312i
$859$	−50.0000			−1.70598			−0.852989	−	0.521929i	$-0.825213\pi$
$859$	−50.0000			−1.70598			−0.852989	+	0.521929i	$0.825213\pi$
$860$	5.50000	−	9.52628i	0.187548	−	0.324843i
$861$	2.00000	−	3.46410i	0.0681598	−	0.118056i
$862$	20.0000	+	34.6410i	0.681203	+	1.17988i
$863$	39.0000			1.32758			0.663788	−	0.747921i	$-0.268948\pi$
$863$	39.0000			1.32758			0.663788	+	0.747921i	$0.268948\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−10.0000	−	17.3205i	−0.340010	−	0.588915i
$866$	−28.0000			−0.951479
$867$	−6.50000	−	11.2583i	−0.220752	−	0.382353i
$868$	−11.0000	+	19.0526i	−0.373364	+	0.646686i
$869$	−27.5000	+	47.6314i	−0.932874	+	1.61578i
$870$	5.00000			0.169516
$871$	56.0000	+	13.8564i	1.89749	+	0.469506i
$872$	2.00000			0.0677285
$873$	1.00000	−	1.73205i	0.0338449	−	0.0586210i
$874$	1.00000	−	1.73205i	0.0338255	−	0.0585875i
$875$	1.00000	+	1.73205i	0.0338062	+	0.0585540i
$876$	6.00000			0.202721
$877$	9.50000	+	16.4545i	0.320792	+	0.555628i	0.980652	−	0.195761i	$-0.0627176\pi$
$877$	9.50000	+	16.4545i	0.320792	+	0.555628i	−0.659860	+	0.751389i	$0.729384\pi$
$878$	−2.00000	−	3.46410i	−0.0674967	−	0.116908i
$879$	−6.00000			−0.202375
$880$	2.50000	+	4.33013i	0.0842750	+	0.145969i
$881$	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	$0.0686057\pi$
$882$	−1.50000	+	2.59808i	−0.0505076	+	0.0874818i
$883$	−1.00000			−0.0336527			−0.0168263	−	0.999858i	$-0.505356\pi$
$883$	−1.00000			−0.0336527			−0.0168263	+	0.999858i	$0.505356\pi$
$884$	−7.00000	−	1.73205i	−0.235435	−	0.0582552i
$885$	15.0000			0.504219
$886$	10.0000	−	17.3205i	0.335957	−	0.581894i
$887$	−1.50000	+	2.59808i	−0.0503651	+	0.0872349i	−0.890109	−	0.455748i	$-0.849372\pi$
$887$	−1.50000	+	2.59808i	−0.0503651	+	0.0872349i	0.839744	+	0.542983i	$0.182705\pi$
$888$	−1.50000	−	2.59808i	−0.0503367	−	0.0871857i
$889$	−4.00000			−0.134156
$890$	1.00000	+	1.73205i	0.0335201	+	0.0580585i
$891$	2.50000	+	4.33013i	0.0837532	+	0.145065i
$892$	26.0000			0.870544
$893$	9.00000	+	15.5885i	0.301174	+	0.521648i
$894$	−8.50000	+	14.7224i	−0.284283	+	0.492392i
$895$	6.50000	−	11.2583i	0.217271	−	0.376324i
$896$	2.00000			0.0668153
$897$	−2.50000	+	2.59808i	−0.0834726	+	0.0867472i
$898$	−12.0000			−0.400445
$899$	27.5000	−	47.6314i	0.917176	−	1.58860i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	6.00000	+	10.3923i	0.199889	+	0.346218i
$902$	−10.0000			−0.332964
$903$	11.0000	+	19.0526i	0.366057	+	0.634029i
$904$	5.50000	+	9.52628i	0.182927	+	0.316839i
$905$	−16.0000			−0.531858
$906$	−4.00000	−	6.92820i	−0.132891	−	0.230174i
$907$	−9.50000	+	16.4545i	−0.315442	+	0.546362i	−0.979531	−	0.201291i	$-0.935486\pi$
$907$	−9.50000	+	16.4545i	−0.315442	+	0.546362i	0.664089	+	0.747653i	$0.268820\pi$
$908$		0			0
$909$	2.00000			0.0663358
$910$	−2.00000	−	6.92820i	−0.0662994	−	0.229668i
$911$	−18.0000			−0.596367			−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000			−0.596367			−0.298183	+	0.954509i	$0.596381\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	15.0000	−	25.9808i	0.496428	−	0.859838i
$914$	19.0000	+	32.9090i	0.628464	+	1.08853i
$915$	−10.0000			−0.330590
$916$	−5.00000	−	8.66025i	−0.165205	−	0.286143i
$917$	−1.00000	−	1.73205i	−0.0330229	−	0.0571974i
$918$	−2.00000			−0.0660098
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$	−0.500000	+	0.866025i	−0.0164845	+	0.0285520i
$921$		0			0
$922$	39.0000			1.28440
$923$		0			0
$924$	−10.0000			−0.328976
$925$	−1.50000	+	2.59808i	−0.0493197	+	0.0854242i
$926$	7.00000	−	12.1244i	0.230034	−	0.398431i
$927$	−5.00000	−	8.66025i	−0.164222	−	0.284440i
$928$	−5.00000			−0.164133
$929$	8.00000	+	13.8564i	0.262471	+	0.454614i	0.966898	−	0.255163i	$-0.0821291\pi$
$929$	8.00000	+	13.8564i	0.262471	+	0.454614i	−0.704427	+	0.709777i	$0.748796\pi$
$930$	5.50000	+	9.52628i	0.180352	+	0.312379i
$931$	6.00000			0.196642
$932$	−0.500000	−	0.866025i	−0.0163780	−	0.0283676i
$933$	10.0000	−	17.3205i	0.327385	−	0.567048i
$934$	3.00000	−	5.19615i	0.0981630	−	0.170023i
$935$	10.0000			0.327035
$936$	2.50000	−	2.59808i	0.0817151	−	0.0849208i
$937$	−50.0000			−1.63343			−0.816714	−	0.577042i	$-0.804207\pi$
$937$	−50.0000			−1.63343			−0.816714	+	0.577042i	$0.804207\pi$
$938$	−16.0000	+	27.7128i	−0.522419	+	0.904855i
$939$	10.0000	−	17.3205i	0.326338	−	0.565233i
$940$	−4.50000	−	7.79423i	−0.146774	−	0.254220i
$941$	−50.0000			−1.62995			−0.814977	−	0.579494i	$-0.803250\pi$
$941$	−50.0000			−1.62995			−0.814977	+	0.579494i	$0.803250\pi$
$942$	3.50000	+	6.06218i	0.114036	+	0.197516i
$943$	−1.00000	−	1.73205i	−0.0325645	−	0.0564033i
$944$	−15.0000			−0.488208
$945$	−1.00000	−	1.73205i	−0.0325300	−	0.0563436i
$946$	27.5000	−	47.6314i	0.894102	−	1.54863i
$947$	−4.00000	+	6.92820i	−0.129983	+	0.225136i	−0.923670	−	0.383190i	$-0.874825\pi$
$947$	−4.00000	+	6.92820i	−0.129983	+	0.225136i	0.793687	+	0.608326i	$0.208159\pi$
$948$	11.0000			0.357263
$949$	6.00000	+	20.7846i	0.194768	+	0.674697i
$950$	2.00000			0.0648886
$951$	8.00000	−	13.8564i	0.259418	−	0.449325i
$952$	2.00000	−	3.46410i	0.0648204	−	0.112272i
$953$	25.5000	+	44.1673i	0.826026	+	1.43072i	0.901133	+	0.433544i	$0.142737\pi$
$953$	25.5000	+	44.1673i	0.826026	+	1.43072i	−0.0751066	+	0.997176i	$0.523930\pi$
$954$	−6.00000			−0.194257
$955$	−2.00000	−	3.46410i	−0.0647185	−	0.112096i
$956$	10.0000	+	17.3205i	0.323423	+	0.560185i
$957$	25.0000			0.808135
$958$	−12.0000	−	20.7846i	−0.387702	−	0.671520i
$959$	−11.0000	+	19.0526i	−0.355209	+	0.615239i
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	90.0000			2.90323
$962$	7.50000	−	7.79423i	0.241810	−	0.251296i
$963$	10.0000			0.322245
$964$	3.50000	−	6.06218i	0.112727	−	0.195250i
$965$	12.0000	−	20.7846i	0.386294	−	0.669080i
$966$	−1.00000	−	1.73205i	−0.0321745	−	0.0557278i
$967$	20.0000			0.643157			0.321578	−	0.946883i	$-0.395787\pi$
$967$	20.0000			0.643157			0.321578	+	0.946883i	$0.395787\pi$
$968$	7.00000	+	12.1244i	0.224989	+	0.389692i
$969$	2.00000	+	3.46410i	0.0642493	+	0.111283i
$970$	2.00000			0.0642161
$971$	−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	$-0.446509\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	2.00000	−	3.46410i	0.0641171	−	0.111054i
$974$	−2.00000			−0.0640841
$975$	−3.50000	−	0.866025i	−0.112090	−	0.0277350i
$976$	10.0000			0.320092
$977$	10.5000	−	18.1865i	0.335925	−	0.581839i	−0.647737	−	0.761864i	$-0.724285\pi$
$977$	10.5000	−	18.1865i	0.335925	−	0.581839i	0.983662	+	0.180025i	$0.0576179\pi$
$978$	7.50000	−	12.9904i	0.239824	−	0.415387i
$979$	5.00000	+	8.66025i	0.159801	+	0.276783i
$980$	−3.00000			−0.0958315
$981$	1.00000	+	1.73205i	0.0319275	+	0.0553001i
$982$	−8.00000	−	13.8564i	−0.255290	−	0.442176i
$983$	−3.00000			−0.0956851			−0.0478426	−	0.998855i	$-0.515235\pi$
$983$	−3.00000			−0.0956851			−0.0478426	+	0.998855i	$0.515235\pi$
$984$	1.00000	+	1.73205i	0.0318788	+	0.0552158i
$985$	4.00000	−	6.92820i	0.127451	−	0.220751i
$986$	−5.00000	+	8.66025i	−0.159232	+	0.275799i
$987$	18.0000			0.572946
$988$	−7.00000	−	1.73205i	−0.222700	−	0.0551039i
$989$	11.0000			0.349780
$990$	−2.50000	+	4.33013i	−0.0794552	+	0.137620i
$991$	8.50000	−	14.7224i	0.270011	−	0.467673i	−0.698853	−	0.715265i	$-0.746306\pi$
$991$	8.50000	−	14.7224i	0.270011	−	0.467673i	0.968864	+	0.247592i	$0.0796392\pi$
$992$	−5.50000	−	9.52628i	−0.174625	−	0.302460i
$993$	28.0000			0.888553
$994$		0			0
$995$	−12.0000	−	20.7846i	−0.380426	−	0.658916i
$996$	−6.00000			−0.190117
$997$	1.00000	+	1.73205i	0.0316703	+	0.0548546i	0.881426	−	0.472322i	$-0.156584\pi$
$997$	1.00000	+	1.73205i	0.0316703	+	0.0548546i	−0.849756	+	0.527176i	$0.823251\pi$
$998$	14.0000	−	24.2487i	0.443162	−	0.767580i
$999$	1.50000	−	2.59808i	0.0474579	−	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.i.f.61.1	✓	2
3.2	odd	2		1170.2.i.a.451.1		2
5.2	odd	4		1950.2.z.e.1699.2		4
5.3	odd	4		1950.2.z.e.1699.1		4
5.4	even	2		1950.2.i.d.451.1		2
13.3	even	3	inner	390.2.i.f.211.1	yes	2
13.4	even	6		5070.2.a.p.1.1		1
13.6	odd	12		5070.2.b.h.1351.2		2
13.7	odd	12		5070.2.b.h.1351.1		2
13.9	even	3		5070.2.a.d.1.1		1
39.29	odd	6		1170.2.i.a.991.1		2
65.3	odd	12		1950.2.z.e.1849.2		4
65.29	even	6		1950.2.i.d.601.1		2
65.42	odd	12		1950.2.z.e.1849.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.f.61.1	✓	2	1.1	even	1	trivial
390.2.i.f.211.1	yes	2	13.3	even	3	inner
1170.2.i.a.451.1		2	3.2	odd	2
1170.2.i.a.991.1		2	39.29	odd	6
1950.2.i.d.451.1		2	5.4	even	2
1950.2.i.d.601.1		2	65.29	even	6
1950.2.z.e.1699.1		4	5.3	odd	4
1950.2.z.e.1699.2		4	5.2	odd	4
1950.2.z.e.1849.1		4	65.42	odd	12
1950.2.z.e.1849.2		4	65.3	odd	12
5070.2.a.d.1.1		1	13.9	even	3
5070.2.a.p.1.1		1	13.4	even	6
5070.2.b.h.1351.1		2	13.7	odd	12
5070.2.b.h.1351.2		2	13.6	odd	12

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.50000 - 4.33013i) q^{11} -1.00000 q^{12} +(-1.00000 - 3.46410i) q^{13} +2.00000 q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} -1.00000 q^{18} +(1.00000 + 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{20} +2.00000 q^{21} +(-2.50000 - 4.33013i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(-3.50000 - 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 - 1.73205i) q^{28} +(-2.50000 + 4.33013i) q^{29} +(-0.500000 - 0.866025i) q^{30} -11.0000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.50000 - 4.33013i) q^{33} +2.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.50000 + 2.59808i) q^{37} +2.00000 q^{38} +(-3.50000 - 0.866025i) q^{39} -1.00000 q^{40} +(1.00000 - 1.73205i) q^{41} +(1.00000 - 1.73205i) q^{42} +(5.50000 + 9.52628i) q^{43} -5.00000 q^{44} +(-0.500000 - 0.866025i) q^{45} +(-0.500000 - 0.866025i) q^{46} +9.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +(0.500000 - 0.866025i) q^{50} +2.00000 q^{51} +(-2.50000 + 2.59808i) q^{52} +6.00000 q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.50000 - 4.33013i) q^{55} +(-1.00000 - 1.73205i) q^{56} +2.00000 q^{57} +(2.50000 + 4.33013i) q^{58} +(7.50000 + 12.9904i) q^{59} -1.00000 q^{60} +(-5.00000 - 8.66025i) q^{61} +(-5.50000 + 9.52628i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 - 3.46410i) q^{65} -5.00000 q^{66} +(-8.00000 + 13.8564i) q^{67} +(1.00000 - 1.73205i) q^{68} +(-0.500000 - 0.866025i) q^{69} +2.00000 q^{70} +(0.500000 + 0.866025i) q^{72} -6.00000 q^{73} +(1.50000 + 2.59808i) q^{74} +(0.500000 - 0.866025i) q^{75} +(1.00000 - 1.73205i) q^{76} +10.0000 q^{77} +(-2.50000 + 2.59808i) q^{78} -11.0000 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} +6.00000 q^{83} +(-1.00000 - 1.73205i) q^{84} +(1.00000 + 1.73205i) q^{85} +11.0000 q^{86} +(2.50000 + 4.33013i) q^{87} +(-2.50000 + 4.33013i) q^{88} +(-1.00000 + 1.73205i) q^{89} -1.00000 q^{90} +(5.00000 - 5.19615i) q^{91} -1.00000 q^{92} +(-5.50000 + 9.52628i) q^{93} +(4.50000 - 7.79423i) q^{94} +(1.00000 + 1.73205i) q^{95} +1.00000 q^{96} +(1.00000 + 1.73205i) q^{97} +(-1.50000 - 2.59808i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9} + q^{10} + 5 q^{11} - 2 q^{12} - 2 q^{13} + 4 q^{14} + q^{15} - q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} - q^{20} + 4 q^{21} - 5 q^{22} + q^{23} - q^{24} + 2 q^{25} - 7 q^{26} - 2 q^{27} + 2 q^{28} - 5 q^{29} - q^{30} - 22 q^{31} + q^{32} - 5 q^{33} + 4 q^{34} + 2 q^{35} - q^{36} - 3 q^{37} + 4 q^{38} - 7 q^{39} - 2 q^{40} + 2 q^{41} + 2 q^{42} + 11 q^{43} - 10 q^{44} - q^{45} - q^{46} + 18 q^{47} + q^{48} + 3 q^{49} + q^{50} + 4 q^{51} - 5 q^{52} + 12 q^{53} - q^{54} + 5 q^{55} - 2 q^{56} + 4 q^{57} + 5 q^{58} + 15 q^{59} - 2 q^{60} - 10 q^{61} - 11 q^{62} + 2 q^{63} + 2 q^{64} - 2 q^{65} - 10 q^{66} - 16 q^{67} + 2 q^{68} - q^{69} + 4 q^{70} + q^{72} - 12 q^{73} + 3 q^{74} + q^{75} + 2 q^{76} + 20 q^{77} - 5 q^{78} - 22 q^{79} - q^{80} - q^{81} - 2 q^{82} + 12 q^{83} - 2 q^{84} + 2 q^{85} + 22 q^{86} + 5 q^{87} - 5 q^{88} - 2 q^{89} - 2 q^{90} + 10 q^{91} - 2 q^{92} - 11 q^{93} + 9 q^{94} + 2 q^{95} + 2 q^{96} + 2 q^{97} - 3 q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 - 2 * q^8 - q^9 + q^10 + 5 * q^11 - 2 * q^12 - 2 * q^13 + 4 * q^14 + q^15 - q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 - q^20 + 4 * q^21 - 5 * q^22 + q^23 - q^24 + 2 * q^25 - 7 * q^26 - 2 * q^27 + 2 * q^28 - 5 * q^29 - q^30 - 22 * q^31 + q^32 - 5 * q^33 + 4 * q^34 + 2 * q^35 - q^36 - 3 * q^37 + 4 * q^38 - 7 * q^39 - 2 * q^40 + 2 * q^41 + 2 * q^42 + 11 * q^43 - 10 * q^44 - q^45 - q^46 + 18 * q^47 + q^48 + 3 * q^49 + q^50 + 4 * q^51 - 5 * q^52 + 12 * q^53 - q^54 + 5 * q^55 - 2 * q^56 + 4 * q^57 + 5 * q^58 + 15 * q^59 - 2 * q^60 - 10 * q^61 - 11 * q^62 + 2 * q^63 + 2 * q^64 - 2 * q^65 - 10 * q^66 - 16 * q^67 + 2 * q^68 - q^69 + 4 * q^70 + q^72 - 12 * q^73 + 3 * q^74 + q^75 + 2 * q^76 + 20 * q^77 - 5 * q^78 - 22 * q^79 - q^80 - q^81 - 2 * q^82 + 12 * q^83 - 2 * q^84 + 2 * q^85 + 22 * q^86 + 5 * q^87 - 5 * q^88 - 2 * q^89 - 2 * q^90 + 10 * q^91 - 2 * q^92 - 11 * q^93 + 9 * q^94 + 2 * q^95 + 2 * q^96 + 2 * q^97 - 3 * q^98 - 10 * q^99

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