LMFDB - Embedded newform 770.2.i.c.221.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(221,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("770.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.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:	$6.14848095564$
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			221.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	770.221
Dual form			770.2.i.c.331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(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 + 2.59808i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(2.50000 - 0.866025i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(1.00000 - 1.73205i) q^{18} +(2.00000 + 3.46410i) q^{19} +1.00000 q^{20} +(2.00000 + 1.73205i) q^{21} -1.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} +5.00000 q^{27} +(-2.00000 - 1.73205i) q^{28} +3.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +2.00000 q^{34} +(2.50000 - 0.866025i) q^{35} -2.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(0.500000 - 0.866025i) q^{39} +(-0.500000 - 0.866025i) q^{40} +8.00000 q^{41} +(0.500000 - 2.59808i) q^{42} -8.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.00000 - 1.73205i) q^{45} +(2.00000 - 3.46410i) q^{46} +(-1.00000 - 1.73205i) q^{47} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +1.00000 q^{50} +(1.00000 + 1.73205i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(5.00000 - 8.66025i) q^{53} +(-2.50000 - 4.33013i) q^{54} -1.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} +4.00000 q^{57} +(-1.50000 - 2.59808i) q^{58} +(4.50000 - 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-0.500000 - 0.866025i) q^{61} -4.00000 q^{62} +(-5.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-2.50000 + 4.33013i) q^{67} +(-1.00000 - 1.73205i) q^{68} +4.00000 q^{69} +(-2.00000 - 1.73205i) q^{70} +2.00000 q^{71} +(1.00000 + 1.73205i) q^{72} +(-4.00000 + 6.92820i) q^{73} +(4.00000 - 6.92820i) q^{74} +(0.500000 + 0.866025i) q^{75} -4.00000 q^{76} +(2.00000 + 1.73205i) q^{77} -1.00000 q^{78} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.00000 - 6.92820i) q^{82} -10.0000 q^{83} +(-2.50000 + 0.866025i) q^{84} +2.00000 q^{85} +(4.00000 + 6.92820i) q^{86} +(1.50000 - 2.59808i) q^{87} +(0.500000 - 0.866025i) q^{88} +(1.00000 + 1.73205i) q^{89} -2.00000 q^{90} +(-0.500000 + 2.59808i) q^{91} -4.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(-1.00000 + 1.73205i) q^{94} +(2.00000 - 3.46410i) q^{95} +(0.500000 + 0.866025i) q^{96} +7.00000 q^{97} +(1.00000 + 6.92820i) q^{98} +2.00000 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} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - q^{10} + q^{11} + q^{12} + 2 q^{13} + 5 q^{14} - 2 q^{15} - q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + q^{24} - q^{25} - q^{26} + 10 q^{27} - 4 q^{28} + 6 q^{29} + q^{30} + 4 q^{31} - q^{32} - q^{33} + 4 q^{34} + 5 q^{35} - 4 q^{36} + 8 q^{37} + 4 q^{38} + q^{39} - q^{40} + 16 q^{41} + q^{42} - 16 q^{43} + q^{44} + 2 q^{45} + 4 q^{46} - 2 q^{47} - 2 q^{48} - 13 q^{49} + 2 q^{50} + 2 q^{51} - q^{52} + 10 q^{53} - 5 q^{54} - 2 q^{55} - q^{56} + 8 q^{57} - 3 q^{58} + 9 q^{59} + q^{60} - q^{61} - 8 q^{62} - 10 q^{63} + 2 q^{64} - q^{65} - q^{66} - 5 q^{67} - 2 q^{68} + 8 q^{69} - 4 q^{70} + 4 q^{71} + 2 q^{72} - 8 q^{73} + 8 q^{74} + q^{75} - 8 q^{76} + 4 q^{77} - 2 q^{78} + 11 q^{79} - q^{80} - q^{81} - 8 q^{82} - 20 q^{83} - 5 q^{84} + 4 q^{85} + 8 q^{86} + 3 q^{87} + q^{88} + 2 q^{89} - 4 q^{90} - q^{91} - 8 q^{92} - 4 q^{93} - 2 q^{94} + 4 q^{95} + q^{96} + 14 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - q^10 + q^11 + q^12 + 2 * q^13 + 5 * q^14 - 2 * q^15 - q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + q^24 - q^25 - q^26 + 10 * q^27 - 4 * q^28 + 6 * q^29 + q^30 + 4 * q^31 - q^32 - q^33 + 4 * q^34 + 5 * q^35 - 4 * q^36 + 8 * q^37 + 4 * q^38 + q^39 - q^40 + 16 * q^41 + q^42 - 16 * q^43 + q^44 + 2 * q^45 + 4 * q^46 - 2 * q^47 - 2 * q^48 - 13 * q^49 + 2 * q^50 + 2 * q^51 - q^52 + 10 * q^53 - 5 * q^54 - 2 * q^55 - q^56 + 8 * q^57 - 3 * q^58 + 9 * q^59 + q^60 - q^61 - 8 * q^62 - 10 * q^63 + 2 * q^64 - q^65 - q^66 - 5 * q^67 - 2 * q^68 + 8 * q^69 - 4 * q^70 + 4 * q^71 + 2 * q^72 - 8 * q^73 + 8 * q^74 + q^75 - 8 * q^76 + 4 * q^77 - 2 * q^78 + 11 * q^79 - q^80 - q^81 - 8 * q^82 - 20 * q^83 - 5 * q^84 + 4 * q^85 + 8 * q^86 + 3 * q^87 + q^88 + 2 * q^89 - 4 * q^90 - q^91 - 8 * q^92 - 4 * q^93 - 2 * q^94 + 4 * q^95 + q^96 + 14 * q^97 + 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	−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	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	1.00000			0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$	−1.00000			−0.258199
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	1.00000	−	1.73205i	0.235702	−	0.408248i
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	1.00000			0.223607
$21$	2.00000	+	1.73205i	0.436436	+	0.377964i
$22$	−1.00000			−0.213201
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.500000	−	0.866025i	−0.0980581	−	0.169842i
$27$	5.00000			0.962250
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	2.00000			0.342997
$35$	2.50000	−	0.866025i	0.422577	−	0.146385i
$36$	−2.00000			−0.333333
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	8.00000			1.24939			0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000			1.24939			0.624695	+	0.780869i	$0.285223\pi$
$42$	0.500000	−	2.59808i	0.0771517	−	0.400892i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	−1.00000	−	1.73205i	−0.145865	−	0.252646i	0.783830	−	0.620975i	$-0.213263\pi$
$47$	−1.00000	−	1.73205i	−0.145865	−	0.252646i	−0.929695	+	0.368329i	$0.879930\pi$
$48$	−1.00000			−0.144338
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	1.00000			0.141421
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	−0.286064	−	0.958211i	$-0.592347\pi$
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	0.972867	−	0.231367i	$-0.0743197\pi$
$54$	−2.50000	−	4.33013i	−0.340207	−	0.589256i
$55$	−1.00000			−0.134840
$56$	−0.500000	+	2.59808i	−0.0668153	+	0.347183i
$57$	4.00000			0.529813
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	−0.408919	−	0.912571i	$-0.634094\pi$
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	0.994769	−	0.102151i	$-0.0325726\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	−4.00000			−0.508001
$63$	−5.00000	+	1.73205i	−0.629941	+	0.218218i
$64$	1.00000			0.125000
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	−0.500000	+	0.866025i	−0.0615457	+	0.106600i
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$	4.00000			0.481543
$70$	−2.00000	−	1.73205i	−0.239046	−	0.207020i
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	1.00000	+	1.73205i	0.117851	+	0.204124i
$73$	−4.00000	+	6.92820i	−0.468165	+	0.810885i	−0.999338	−	0.0363782i	$-0.988418\pi$
$73$	−4.00000	+	6.92820i	−0.468165	+	0.810885i	0.531174	+	0.847263i	$0.321751\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−4.00000			−0.458831
$77$	2.00000	+	1.73205i	0.227921	+	0.197386i
$78$	−1.00000			−0.113228
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.00000	−	6.92820i	−0.441726	−	0.765092i
$83$	−10.0000			−1.09764			−0.548821	−	0.835940i	$-0.684923\pi$
$83$	−10.0000			−1.09764			−0.548821	+	0.835940i	$0.684923\pi$
$84$	−2.50000	+	0.866025i	−0.272772	+	0.0944911i
$85$	2.00000			0.216930
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	0.914146	−	0.405385i	$-0.132862\pi$
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	−0.808146	+	0.588982i	$0.799529\pi$
$90$	−2.00000			−0.210819
$91$	−0.500000	+	2.59808i	−0.0524142	+	0.272352i
$92$	−4.00000			−0.417029
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$	−1.00000	+	1.73205i	−0.103142	+	0.178647i
$95$	2.00000	−	3.46410i	0.205196	−	0.355409i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	1.00000	+	6.92820i	0.101015	+	0.699854i
$99$	2.00000			0.201008
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$	1.00000	−	1.73205i	0.0990148	−	0.171499i
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	−0.971925	−	0.235291i	$-0.924396\pi$
$103$	−7.00000	−	12.1244i	−0.689730	−	1.19465i	0.282194	−	0.959357i	$-0.408938\pi$
$104$	1.00000			0.0980581
$105$	0.500000	−	2.59808i	0.0487950	−	0.253546i
$106$	−10.0000			−0.971286
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.861931	+	0.507026i	$0.169255\pi$
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.00813215	+	0.999967i	$0.497411\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	0.500000	+	0.866025i	0.0476731	+	0.0825723i
$111$	8.00000			0.759326
$112$	2.50000	−	0.866025i	0.236228	−	0.0818317i
$113$	−11.0000			−1.03479			−0.517396	−	0.855746i	$-0.673099\pi$
$113$	−11.0000			−1.03479			−0.517396	+	0.855746i	$0.673099\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$	1.00000	+	1.73205i	0.0924500	+	0.160128i
$118$	−9.00000			−0.828517
$119$	−4.00000	−	3.46410i	−0.366679	−	0.317554i
$120$	−1.00000			−0.0912871
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.500000	+	0.866025i	−0.0452679	+	0.0784063i
$123$	4.00000	−	6.92820i	0.360668	−	0.624695i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	1.00000			0.0894427
$126$	4.00000	+	3.46410i	0.356348	+	0.308607i
$127$	−15.0000			−1.33103			−0.665517	−	0.746382i	$-0.731789\pi$
$127$	−15.0000			−1.33103			−0.665517	+	0.746382i	$0.731789\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$	−0.500000	+	0.866025i	−0.0438529	+	0.0759555i
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$	1.00000			0.0870388
$133$	−10.0000	+	3.46410i	−0.867110	+	0.300376i
$134$	5.00000			0.431934
$135$	−2.50000	−	4.33013i	−0.215166	−	0.372678i
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	2.50000	−	4.33013i	0.213589	−	0.369948i	−0.739246	−	0.673436i	$-0.764818\pi$
$137$	2.50000	−	4.33013i	0.213589	−	0.369948i	0.952835	+	0.303488i	$0.0981512\pi$
$138$	−2.00000	−	3.46410i	−0.170251	−	0.294884i
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$	−0.500000	+	2.59808i	−0.0422577	+	0.219578i
$141$	−2.00000			−0.168430
$142$	−1.00000	−	1.73205i	−0.0839181	−	0.145350i
$143$	0.500000	−	0.866025i	0.0418121	−	0.0724207i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$	−1.50000	−	2.59808i	−0.124568	−	0.215758i
$146$	8.00000			0.662085
$147$	−5.50000	+	4.33013i	−0.453632	+	0.357143i
$148$	−8.00000			−0.657596
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−4.50000	+	7.79423i	−0.366205	+	0.634285i	−0.988969	−	0.148124i	$-0.952676\pi$
$151$	−4.50000	+	7.79423i	−0.366205	+	0.634285i	0.622764	+	0.782410i	$0.286010\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$	−4.00000			−0.323381
$154$	0.500000	−	2.59808i	0.0402911	−	0.209359i
$155$	−4.00000			−0.321288
$156$	0.500000	+	0.866025i	0.0400320	+	0.0693375i
$157$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$157$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$158$	5.50000	−	9.52628i	0.437557	−	0.757870i
$159$	−5.00000	−	8.66025i	−0.396526	−	0.686803i
$160$	1.00000			0.0790569
$161$	−10.0000	+	3.46410i	−0.788110	+	0.273009i
$162$	1.00000			0.0785674
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	0.566149	−	0.824303i	$-0.308433\pi$
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	−0.996942	+	0.0781474i	$0.975100\pi$
$164$	−4.00000	+	6.92820i	−0.312348	+	0.541002i
$165$	−0.500000	+	0.866025i	−0.0389249	+	0.0674200i
$166$	5.00000	+	8.66025i	0.388075	+	0.672166i
$167$	−9.00000			−0.696441			−0.348220	−	0.937413i	$-0.613214\pi$
$167$	−9.00000			−0.696441			−0.348220	+	0.937413i	$0.613214\pi$
$168$	2.00000	+	1.73205i	0.154303	+	0.133631i
$169$	−12.0000			−0.923077
$170$	−1.00000	−	1.73205i	−0.0766965	−	0.132842i
$171$	−4.00000	+	6.92820i	−0.305888	+	0.529813i
$172$	4.00000	−	6.92820i	0.304997	−	0.528271i
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	0.996544	+	0.0830722i	$0.0264732\pi$
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	−0.426329	+	0.904568i	$0.640193\pi$
$174$	−3.00000			−0.227429
$175$	−2.00000	−	1.73205i	−0.151186	−	0.130931i
$176$	−1.00000			−0.0753778
$177$	−4.50000	−	7.79423i	−0.338241	−	0.585850i
$178$	1.00000	−	1.73205i	0.0749532	−	0.129823i
$179$	−11.5000	+	19.9186i	−0.859550	+	1.48878i	0.0128080	+	0.999918i	$0.495923\pi$
$179$	−11.5000	+	19.9186i	−0.859550	+	1.48878i	−0.872358	+	0.488867i	$0.837410\pi$
$180$	1.00000	+	1.73205i	0.0745356	+	0.129099i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$	2.50000	−	0.866025i	0.185312	−	0.0641941i
$183$	−1.00000			−0.0739221
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	4.00000	−	6.92820i	0.294086	−	0.509372i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$	1.00000	+	1.73205i	0.0731272	+	0.126660i
$188$	2.00000			0.145865
$189$	−2.50000	+	12.9904i	−0.181848	+	0.944911i
$190$	−4.00000			−0.290191
$191$	−1.00000	−	1.73205i	−0.0723575	−	0.125327i	0.827577	−	0.561353i	$-0.189719\pi$
$191$	−1.00000	−	1.73205i	−0.0723575	−	0.125327i	−0.899934	+	0.436026i	$0.856386\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	−3.50000	−	6.06218i	−0.251285	−	0.435239i
$195$	−1.00000			−0.0716115
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	7.00000			0.498729			0.249365	−	0.968410i	$-0.419778\pi$
$197$	7.00000			0.498729			0.249365	+	0.968410i	$0.419778\pi$
$198$	−1.00000	−	1.73205i	−0.0710669	−	0.123091i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	2.50000	+	4.33013i	0.176336	+	0.305424i
$202$	−9.00000			−0.633238
$203$	−1.50000	+	7.79423i	−0.105279	+	0.547048i
$204$	−2.00000			−0.140028
$205$	−4.00000	−	6.92820i	−0.279372	−	0.483887i
$206$	−7.00000	+	12.1244i	−0.487713	+	0.844744i
$207$	−4.00000	+	6.92820i	−0.278019	+	0.481543i
$208$	−0.500000	−	0.866025i	−0.0346688	−	0.0600481i
$209$	4.00000			0.276686
$210$	−2.50000	+	0.866025i	−0.172516	+	0.0597614i
$211$	−24.0000			−1.65223			−0.826114	−	0.563503i	$-0.809453\pi$
$211$	−24.0000			−1.65223			−0.826114	+	0.563503i	$0.809453\pi$
$212$	5.00000	+	8.66025i	0.343401	+	0.594789i
$213$	1.00000	−	1.73205i	0.0685189	−	0.118678i
$214$	9.00000	−	15.5885i	0.615227	−	1.06561i
$215$	4.00000	+	6.92820i	0.272798	+	0.472500i
$216$	5.00000			0.340207
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$	−10.0000			−0.677285
$219$	4.00000	+	6.92820i	0.270295	+	0.468165i
$220$	0.500000	−	0.866025i	0.0337100	−	0.0583874i
$221$	−1.00000	+	1.73205i	−0.0672673	+	0.116510i
$222$	−4.00000	−	6.92820i	−0.268462	−	0.464991i
$223$	−24.0000			−1.60716			−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000			−1.60716			−0.803579	+	0.595198i	$0.797074\pi$
$224$	−2.00000	−	1.73205i	−0.133631	−	0.115728i
$225$	−2.00000			−0.133333
$226$	5.50000	+	9.52628i	0.365855	+	0.633679i
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	−0.999184	−	0.0403978i	$-0.987137\pi$
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	0.534577	+	0.845120i	$0.320471\pi$
$228$	−2.00000	+	3.46410i	−0.132453	+	0.229416i
$229$	−6.00000	−	10.3923i	−0.396491	−	0.686743i	0.596799	−	0.802391i	$-0.296439\pi$
$229$	−6.00000	−	10.3923i	−0.396491	−	0.686743i	−0.993290	+	0.115648i	$0.963106\pi$
$230$	−4.00000			−0.263752
$231$	2.50000	−	0.866025i	0.164488	−	0.0569803i
$232$	3.00000			0.196960
$233$	−14.0000	−	24.2487i	−0.917170	−	1.58859i	−0.803692	−	0.595045i	$-0.797134\pi$
$233$	−14.0000	−	24.2487i	−0.917170	−	1.58859i	−0.113478	−	0.993540i	$-0.536199\pi$
$234$	1.00000	−	1.73205i	0.0653720	−	0.113228i
$235$	−1.00000	+	1.73205i	−0.0652328	+	0.112987i
$236$	4.50000	+	7.79423i	0.292925	+	0.507361i
$237$	11.0000			0.714527
$238$	−1.00000	+	5.19615i	−0.0648204	+	0.336817i
$239$	−9.00000			−0.582162			−0.291081	−	0.956698i	$-0.594015\pi$
$239$	−9.00000			−0.582162			−0.291081	+	0.956698i	$0.594015\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	−0.794393	−	0.607404i	$-0.792211\pi$
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	0.923224	+	0.384262i	$0.125544\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	1.00000			0.0640184
$245$	1.00000	+	6.92820i	0.0638877	+	0.442627i
$246$	−8.00000			−0.510061
$247$	2.00000	+	3.46410i	0.127257	+	0.220416i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$	−5.00000	+	8.66025i	−0.316862	+	0.548821i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	1.00000	−	5.19615i	0.0629941	−	0.327327i
$253$	4.00000			0.251478
$254$	7.50000	+	12.9904i	0.470592	+	0.815089i
$255$	1.00000	−	1.73205i	0.0626224	−	0.108465i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.50000	−	16.4545i	−0.592594	−	1.02640i	−0.993882	−	0.110450i	$-0.964771\pi$
$257$	−9.50000	−	16.4545i	−0.592594	−	1.02640i	0.401288	−	0.915952i	$-0.368563\pi$
$258$	8.00000			0.498058
$259$	−20.0000	+	6.92820i	−1.24274	+	0.430498i
$260$	1.00000			0.0620174
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$	6.00000	−	10.3923i	0.370681	−	0.642039i
$263$	8.50000	−	14.7224i	0.524132	−	0.907824i	−0.475473	−	0.879730i	$-0.657723\pi$
$263$	8.50000	−	14.7224i	0.524132	−	0.907824i	0.999605	−	0.0280936i	$-0.00894366\pi$
$264$	−0.500000	−	0.866025i	−0.0307729	−	0.0533002i
$265$	−10.0000			−0.614295
$266$	8.00000	+	6.92820i	0.490511	+	0.424795i
$267$	2.00000			0.122398
$268$	−2.50000	−	4.33013i	−0.152712	−	0.264505i
$269$	16.0000	−	27.7128i	0.975537	−	1.68968i	0.297386	−	0.954757i	$-0.403885\pi$
$269$	16.0000	−	27.7128i	0.975537	−	1.68968i	0.678151	−	0.734923i	$-0.262782\pi$
$270$	−2.50000	+	4.33013i	−0.152145	+	0.263523i
$271$	−0.500000	−	0.866025i	−0.0303728	−	0.0526073i	0.850439	−	0.526073i	$-0.176336\pi$
$271$	−0.500000	−	0.866025i	−0.0303728	−	0.0526073i	−0.880812	+	0.473466i	$0.843003\pi$
$272$	2.00000			0.121268
$273$	2.00000	+	1.73205i	0.121046	+	0.104828i
$274$	−5.00000			−0.302061
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	−2.00000	+	3.46410i	−0.120386	+	0.208514i
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	−0.489207	−	0.872167i	$-0.662714\pi$
$277$	8.50000	−	14.7224i	0.510716	−	0.884585i	0.999923	−	0.0124177i	$-0.00395278\pi$
$278$	−6.00000	−	10.3923i	−0.359856	−	0.623289i
$279$	8.00000			0.478947
$280$	2.50000	−	0.866025i	0.149404	−	0.0517549i
$281$	8.00000			0.477240			0.238620	−	0.971113i	$-0.423305\pi$
$281$	8.00000			0.477240			0.238620	+	0.971113i	$0.423305\pi$
$282$	1.00000	+	1.73205i	0.0595491	+	0.103142i
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	−0.399188	−	0.916869i	$-0.630708\pi$
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	0.993626	−	0.112728i	$-0.0359589\pi$
$284$	−1.00000	+	1.73205i	−0.0593391	+	0.102778i
$285$	−2.00000	−	3.46410i	−0.118470	−	0.205196i
$286$	−1.00000			−0.0591312
$287$	−4.00000	+	20.7846i	−0.236113	+	1.22688i
$288$	−2.00000			−0.117851
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	−1.50000	+	2.59808i	−0.0880830	+	0.152564i
$291$	3.50000	−	6.06218i	0.205174	−	0.355371i
$292$	−4.00000	−	6.92820i	−0.234082	−	0.405442i
$293$	22.0000			1.28525			0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000			1.28525			0.642627	+	0.766179i	$0.277845\pi$
$294$	6.50000	+	2.59808i	0.379088	+	0.151523i
$295$	−9.00000			−0.524000
$296$	4.00000	+	6.92820i	0.232495	+	0.402694i
$297$	2.50000	−	4.33013i	0.145065	−	0.251259i
$298$	5.00000	−	8.66025i	0.289642	−	0.501675i
$299$	2.00000	+	3.46410i	0.115663	+	0.200334i
$300$	−1.00000			−0.0577350
$301$	4.00000	−	20.7846i	0.230556	−	1.19800i
$302$	9.00000			0.517892
$303$	−4.50000	−	7.79423i	−0.258518	−	0.447767i
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−0.500000	+	0.866025i	−0.0286299	+	0.0495885i
$306$	2.00000	+	3.46410i	0.114332	+	0.198030i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	−2.50000	+	0.866025i	−0.142451	+	0.0493464i
$309$	−14.0000			−0.796432
$310$	2.00000	+	3.46410i	0.113592	+	0.196748i
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	−0.0301210	−	0.999546i	$-0.509589\pi$
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	0.880693	−	0.473688i	$-0.157077\pi$
$312$	0.500000	−	0.866025i	0.0283069	−	0.0490290i
$313$	−4.50000	−	7.79423i	−0.254355	−	0.440556i	0.710365	−	0.703833i	$-0.248530\pi$
$313$	−4.50000	−	7.79423i	−0.254355	−	0.440556i	−0.964720	+	0.263278i	$0.915197\pi$
$314$		0			0
$315$	4.00000	+	3.46410i	0.225374	+	0.195180i
$316$	−11.0000			−0.618798
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$	−5.00000	+	8.66025i	−0.280386	+	0.485643i
$319$	1.50000	−	2.59808i	0.0839839	−	0.145464i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	18.0000			1.00466
$322$	8.00000	+	6.92820i	0.445823	+	0.386094i
$323$	−8.00000			−0.445132
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−0.500000	+	0.866025i	−0.0277350	+	0.0480384i
$326$	−5.50000	+	9.52628i	−0.304617	+	0.527612i
$327$	−5.00000	−	8.66025i	−0.276501	−	0.478913i
$328$	8.00000			0.441726
$329$	5.00000	−	1.73205i	0.275659	−	0.0954911i
$330$	1.00000			0.0550482
$331$	−12.5000	−	21.6506i	−0.687062	−	1.19003i	−0.972784	−	0.231714i	$-0.925567\pi$
$331$	−12.5000	−	21.6506i	−0.687062	−	1.19003i	0.285722	−	0.958313i	$-0.407767\pi$
$332$	5.00000	−	8.66025i	0.274411	−	0.475293i
$333$	−8.00000	+	13.8564i	−0.438397	+	0.759326i
$334$	4.50000	+	7.79423i	0.246229	+	0.426481i
$335$	5.00000			0.273179
$336$	0.500000	−	2.59808i	0.0272772	−	0.141737i
$337$	8.00000			0.435788			0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000			0.435788			0.217894	+	0.975972i	$0.430081\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	−5.50000	+	9.52628i	−0.298719	+	0.517396i
$340$	−1.00000	+	1.73205i	−0.0542326	+	0.0939336i
$341$	−2.00000	−	3.46410i	−0.108306	−	0.187592i
$342$	8.00000			0.432590
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−8.00000			−0.431331
$345$	−2.00000	−	3.46410i	−0.107676	−	0.186501i
$346$	7.50000	−	12.9904i	0.403202	−	0.698367i
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	0.110885	+	0.993833i	$0.464631\pi$
$347$	−15.0000	+	25.9808i	−0.805242	+	1.39472i	−0.916127	+	0.400887i	$0.868702\pi$
$348$	1.50000	+	2.59808i	0.0804084	+	0.139272i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	−0.500000	+	2.59808i	−0.0267261	+	0.138873i
$351$	5.00000			0.266880
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	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	$0.00765819\pi$
$354$	−4.50000	+	7.79423i	−0.239172	+	0.414259i
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$	−2.00000			−0.106000
$357$	−5.00000	+	1.73205i	−0.264628	+	0.0916698i
$358$	23.0000			1.21559
$359$	−8.50000	−	14.7224i	−0.448613	−	0.777020i	0.549683	−	0.835373i	$-0.314748\pi$
$359$	−8.50000	−	14.7224i	−0.448613	−	0.777020i	−0.998296	+	0.0583530i	$0.981415\pi$
$360$	1.00000	−	1.73205i	0.0527046	−	0.0912871i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−5.00000	−	8.66025i	−0.262794	−	0.455173i
$363$	−1.00000			−0.0524864
$364$	−2.00000	−	1.73205i	−0.104828	−	0.0907841i
$365$	8.00000			0.418739
$366$	0.500000	+	0.866025i	0.0261354	+	0.0452679i
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	−0.361874	−	0.932227i	$-0.617863\pi$
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	0.988269	−	0.152721i	$-0.0488036\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$	8.00000	+	13.8564i	0.416463	+	0.721336i
$370$	−8.00000			−0.415900
$371$	20.0000	+	17.3205i	1.03835	+	0.899236i
$372$	4.00000			0.207390
$373$	10.5000	+	18.1865i	0.543669	+	0.941663i	0.998689	+	0.0511818i	$0.0162988\pi$
$373$	10.5000	+	18.1865i	0.543669	+	0.941663i	−0.455020	+	0.890481i	$0.650368\pi$
$374$	1.00000	−	1.73205i	0.0517088	−	0.0895622i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	−1.00000	−	1.73205i	−0.0515711	−	0.0893237i
$377$	3.00000			0.154508
$378$	12.5000	−	4.33013i	0.642931	−	0.222718i
$379$	−11.0000			−0.565032			−0.282516	−	0.959263i	$-0.591169\pi$
$379$	−11.0000			−0.565032			−0.282516	+	0.959263i	$0.591169\pi$
$380$	2.00000	+	3.46410i	0.102598	+	0.177705i
$381$	−7.50000	+	12.9904i	−0.384237	+	0.665517i
$382$	−1.00000	+	1.73205i	−0.0511645	+	0.0886194i
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	0.779143	−	0.626846i	$-0.215654\pi$
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	−0.932436	+	0.361335i	$0.882321\pi$
$384$	−1.00000			−0.0510310
$385$	0.500000	−	2.59808i	0.0254824	−	0.132410i
$386$	4.00000			0.203595
$387$	−8.00000	−	13.8564i	−0.406663	−	0.704361i
$388$	−3.50000	+	6.06218i	−0.177686	+	0.307760i
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	−0.321716	−	0.946836i	$-0.604260\pi$
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	0.980842	−	0.194804i	$-0.0624070\pi$
$390$	0.500000	+	0.866025i	0.0253185	+	0.0438529i
$391$	−8.00000			−0.404577
$392$	−6.50000	−	2.59808i	−0.328300	−	0.131223i
$393$	12.0000			0.605320
$394$	−3.50000	−	6.06218i	−0.176327	−	0.305408i
$395$	5.50000	−	9.52628i	0.276735	−	0.479319i
$396$	−1.00000	+	1.73205i	−0.0502519	+	0.0870388i
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	0.998492	−	0.0549046i	$-0.0174855\pi$
$397$	9.00000	+	15.5885i	0.451697	+	0.782362i	−0.546795	+	0.837267i	$0.684152\pi$
$398$		0			0
$399$	−2.00000	+	10.3923i	−0.100125	+	0.520266i
$400$	1.00000			0.0500000
$401$	4.50000	+	7.79423i	0.224719	+	0.389225i	0.956235	−	0.292599i	$-0.0945202\pi$
$401$	4.50000	+	7.79423i	0.224719	+	0.389225i	−0.731516	+	0.681824i	$0.761187\pi$
$402$	2.50000	−	4.33013i	0.124689	−	0.215967i
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$	4.50000	+	7.79423i	0.223883	+	0.387777i
$405$	1.00000			0.0496904
$406$	7.50000	−	2.59808i	0.372219	−	0.128940i
$407$	8.00000			0.396545
$408$	1.00000	+	1.73205i	0.0495074	+	0.0857493i
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	−0.889689	−	0.456566i	$-0.849079\pi$
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	0.840243	+	0.542211i	$0.182412\pi$
$410$	−4.00000	+	6.92820i	−0.197546	+	0.342160i
$411$	−2.50000	−	4.33013i	−0.123316	−	0.213589i
$412$	14.0000			0.689730
$413$	18.0000	+	15.5885i	0.885722	+	0.767058i
$414$	8.00000			0.393179
$415$	5.00000	+	8.66025i	0.245440	+	0.425115i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$	6.00000	−	10.3923i	0.293821	−	0.508913i
$418$	−2.00000	−	3.46410i	−0.0978232	−	0.169435i
$419$	8.00000			0.390826			0.195413	−	0.980721i	$-0.437395\pi$
$419$	8.00000			0.390826			0.195413	+	0.980721i	$0.437395\pi$
$420$	2.00000	+	1.73205i	0.0975900	+	0.0845154i
$421$	4.00000			0.194948			0.0974740	−	0.995238i	$-0.468924\pi$
$421$	4.00000			0.194948			0.0974740	+	0.995238i	$0.468924\pi$
$422$	12.0000	+	20.7846i	0.584151	+	1.01178i
$423$	2.00000	−	3.46410i	0.0972433	−	0.168430i
$424$	5.00000	−	8.66025i	0.242821	−	0.420579i
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$	−2.00000			−0.0969003
$427$	2.50000	−	0.866025i	0.120983	−	0.0419099i
$428$	−18.0000			−0.870063
$429$	−0.500000	−	0.866025i	−0.0241402	−	0.0418121i
$430$	4.00000	−	6.92820i	0.192897	−	0.334108i
$431$	−6.50000	+	11.2583i	−0.313094	+	0.542295i	−0.979030	−	0.203714i	$-0.934699\pi$
$431$	−6.50000	+	11.2583i	−0.313094	+	0.542295i	0.665937	+	0.746008i	$0.268032\pi$
$432$	−2.50000	−	4.33013i	−0.120281	−	0.208333i
$433$	22.0000			1.05725			0.528626	−	0.848855i	$-0.322707\pi$
$433$	22.0000			1.05725			0.528626	+	0.848855i	$0.322707\pi$
$434$	2.00000	−	10.3923i	0.0960031	−	0.498847i
$435$	−3.00000			−0.143839
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	−8.00000	+	13.8564i	−0.382692	+	0.662842i
$438$	4.00000	−	6.92820i	0.191127	−	0.331042i
$439$	−3.50000	−	6.06218i	−0.167046	−	0.289332i	0.770334	−	0.637641i	$-0.220089\pi$
$439$	−3.50000	−	6.06218i	−0.167046	−	0.289332i	−0.937380	+	0.348309i	$0.886756\pi$
$440$	−1.00000			−0.0476731
$441$	−2.00000	−	13.8564i	−0.0952381	−	0.659829i
$442$	2.00000			0.0951303
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$	−4.00000	+	6.92820i	−0.189832	+	0.328798i
$445$	1.00000	−	1.73205i	0.0474045	−	0.0821071i
$446$	12.0000	+	20.7846i	0.568216	+	0.984180i
$447$	10.0000			0.472984
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	1.00000	+	1.73205i	0.0471405	+	0.0816497i
$451$	4.00000	−	6.92820i	0.188353	−	0.326236i
$452$	5.50000	−	9.52628i	0.258698	−	0.448078i
$453$	4.50000	+	7.79423i	0.211428	+	0.366205i
$454$	14.0000			0.657053
$455$	2.50000	−	0.866025i	0.117202	−	0.0405999i
$456$	4.00000			0.187317
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	0.888466	−	0.458942i	$-0.151771\pi$
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	−0.841688	+	0.539964i	$0.818438\pi$
$458$	−6.00000	+	10.3923i	−0.280362	+	0.485601i
$459$	−5.00000	+	8.66025i	−0.233380	+	0.404226i
$460$	2.00000	+	3.46410i	0.0932505	+	0.161515i
$461$	35.0000			1.63011			0.815056	−	0.579382i	$-0.196706\pi$
$461$	35.0000			1.63011			0.815056	+	0.579382i	$0.196706\pi$
$462$	−2.00000	−	1.73205i	−0.0930484	−	0.0805823i
$463$	−2.00000			−0.0929479			−0.0464739	−	0.998920i	$-0.514798\pi$
$463$	−2.00000			−0.0929479			−0.0464739	+	0.998920i	$0.514798\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	−14.0000	+	24.2487i	−0.648537	+	1.12330i
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	−0.895696	−	0.444667i	$-0.853322\pi$
$467$	−18.0000	−	31.1769i	−0.832941	−	1.44270i	0.0627555	−	0.998029i	$-0.480011\pi$
$468$	−2.00000			−0.0924500
$469$	−10.0000	−	8.66025i	−0.461757	−	0.399893i
$470$	2.00000			0.0922531
$471$		0			0
$472$	4.50000	−	7.79423i	0.207129	−	0.358758i
$473$	−4.00000	+	6.92820i	−0.183920	+	0.318559i
$474$	−5.50000	−	9.52628i	−0.252623	−	0.437557i
$475$	−4.00000			−0.183533
$476$	5.00000	−	1.73205i	0.229175	−	0.0793884i
$477$	20.0000			0.915737
$478$	4.50000	+	7.79423i	0.205825	+	0.356500i
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	−0.519973	−	0.854183i	$-0.674058\pi$
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	0.999730	+	0.0232187i	$0.00739140\pi$
$480$	0.500000	−	0.866025i	0.0228218	−	0.0395285i
$481$	4.00000	+	6.92820i	0.182384	+	0.315899i
$482$	−4.00000			−0.182195
$483$	−2.00000	+	10.3923i	−0.0910032	+	0.472866i
$484$	1.00000			0.0454545
$485$	−3.50000	−	6.06218i	−0.158927	−	0.275269i
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	−12.0000	+	20.7846i	−0.543772	+	0.941841i	0.454911	+	0.890537i	$0.349671\pi$
$487$	−12.0000	+	20.7846i	−0.543772	+	0.941841i	−0.998683	+	0.0513038i	$0.983662\pi$
$488$	−0.500000	−	0.866025i	−0.0226339	−	0.0392031i
$489$	−11.0000			−0.497437
$490$	5.50000	−	4.33013i	0.248465	−	0.195615i
$491$	−34.0000			−1.53440			−0.767199	−	0.641409i	$-0.778350\pi$
$491$	−34.0000			−1.53440			−0.767199	+	0.641409i	$0.778350\pi$
$492$	4.00000	+	6.92820i	0.180334	+	0.312348i
$493$	−3.00000	+	5.19615i	−0.135113	+	0.234023i
$494$	2.00000	−	3.46410i	0.0899843	−	0.155857i
$495$	−1.00000	−	1.73205i	−0.0449467	−	0.0778499i
$496$	−4.00000			−0.179605
$497$	−1.00000	+	5.19615i	−0.0448561	+	0.233079i
$498$	10.0000			0.448111
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	0.998233	−	0.0594153i	$-0.0189236\pi$
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	−0.550572	+	0.834788i	$0.685590\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−4.50000	+	7.79423i	−0.201045	+	0.348220i
$502$		0			0
$503$	−9.00000			−0.401290			−0.200645	−	0.979664i	$-0.564304\pi$
$503$	−9.00000			−0.401290			−0.200645	+	0.979664i	$0.564304\pi$
$504$	−5.00000	+	1.73205i	−0.222718	+	0.0771517i
$505$	−9.00000			−0.400495
$506$	−2.00000	−	3.46410i	−0.0889108	−	0.153998i
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$	7.50000	−	12.9904i	0.332759	−	0.576355i
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	0.594675	−	0.803966i	$-0.297281\pi$
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	−0.993593	+	0.113020i	$0.963948\pi$
$510$	−2.00000			−0.0885615
$511$	−16.0000	−	13.8564i	−0.707798	−	0.612971i
$512$	1.00000			0.0441942
$513$	10.0000	+	17.3205i	0.441511	+	0.764719i
$514$	−9.50000	+	16.4545i	−0.419027	+	0.725776i
$515$	−7.00000	+	12.1244i	−0.308457	+	0.534263i
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	−2.00000			−0.0879599
$518$	16.0000	+	13.8564i	0.703000	+	0.608816i
$519$	15.0000			0.658427
$520$	−0.500000	−	0.866025i	−0.0219265	−	0.0379777i
$521$	19.0000	−	32.9090i	0.832405	−	1.44177i	−0.0637207	−	0.997968i	$-0.520297\pi$
$521$	19.0000	−	32.9090i	0.832405	−	1.44177i	0.896126	−	0.443800i	$-0.146370\pi$
$522$	3.00000	−	5.19615i	0.131306	−	0.227429i
$523$	3.00000	+	5.19615i	0.131181	+	0.227212i	0.924132	−	0.382073i	$-0.124790\pi$
$523$	3.00000	+	5.19615i	0.131181	+	0.227212i	−0.792951	+	0.609285i	$0.791456\pi$
$524$	−12.0000			−0.524222
$525$	−2.50000	+	0.866025i	−0.109109	+	0.0377964i
$526$	−17.0000			−0.741235
$527$	4.00000	+	6.92820i	0.174243	+	0.301797i
$528$	−0.500000	+	0.866025i	−0.0217597	+	0.0376889i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	5.00000	+	8.66025i	0.217186	+	0.376177i
$531$	18.0000			0.781133
$532$	2.00000	−	10.3923i	0.0867110	−	0.450564i
$533$	8.00000			0.346518
$534$	−1.00000	−	1.73205i	−0.0432742	−	0.0749532i
$535$	9.00000	−	15.5885i	0.389104	−	0.673948i
$536$	−2.50000	+	4.33013i	−0.107984	+	0.187033i
$537$	11.5000	+	19.9186i	0.496262	+	0.859550i
$538$	−32.0000			−1.37962
$539$	−5.50000	+	4.33013i	−0.236902	+	0.186512i
$540$	5.00000			0.215166
$541$	−18.5000	−	32.0429i	−0.795377	−	1.37763i	−0.922599	−	0.385759i	$-0.873939\pi$
$541$	−18.5000	−	32.0429i	−0.795377	−	1.37763i	0.127222	−	0.991874i	$-0.459394\pi$
$542$	−0.500000	+	0.866025i	−0.0214768	+	0.0371990i
$543$	5.00000	−	8.66025i	0.214571	−	0.371647i
$544$	−1.00000	−	1.73205i	−0.0428746	−	0.0742611i
$545$	−10.0000			−0.428353
$546$	0.500000	−	2.59808i	0.0213980	−	0.111187i
$547$	−14.0000			−0.598597			−0.299298	−	0.954160i	$-0.596753\pi$
$547$	−14.0000			−0.598597			−0.299298	+	0.954160i	$0.596753\pi$
$548$	2.50000	+	4.33013i	0.106795	+	0.184974i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$	0.500000	−	0.866025i	0.0213201	−	0.0369274i
$551$	6.00000	+	10.3923i	0.255609	+	0.442727i
$552$	4.00000			0.170251
$553$	−27.5000	+	9.52628i	−1.16942	+	0.405099i
$554$	−17.0000			−0.722261
$555$	−4.00000	−	6.92820i	−0.169791	−	0.294086i
$556$	−6.00000	+	10.3923i	−0.254457	+	0.440732i
$557$	−17.0000	+	29.4449i	−0.720313	+	1.24762i	0.240561	+	0.970634i	$0.422669\pi$
$557$	−17.0000	+	29.4449i	−0.720313	+	1.24762i	−0.960874	+	0.276985i	$0.910665\pi$
$558$	−4.00000	−	6.92820i	−0.169334	−	0.293294i
$559$	−8.00000			−0.338364
$560$	−2.00000	−	1.73205i	−0.0845154	−	0.0731925i
$561$	2.00000			0.0844401
$562$	−4.00000	−	6.92820i	−0.168730	−	0.292249i
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$	1.00000	−	1.73205i	0.0421076	−	0.0729325i
$565$	5.50000	+	9.52628i	0.231387	+	0.400774i
$566$	−20.0000			−0.840663
$567$	−2.00000	−	1.73205i	−0.0839921	−	0.0727393i
$568$	2.00000			0.0839181
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	0.821054	−	0.570851i	$-0.193387\pi$
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	−0.904898	+	0.425628i	$0.860053\pi$
$570$	−2.00000	+	3.46410i	−0.0837708	+	0.145095i
$571$	3.00000	−	5.19615i	0.125546	−	0.217452i	−0.796400	−	0.604770i	$-0.793265\pi$
$571$	3.00000	−	5.19615i	0.125546	−	0.217452i	0.921946	+	0.387318i	$0.126598\pi$
$572$	0.500000	+	0.866025i	0.0209061	+	0.0362103i
$573$	−2.00000			−0.0835512
$574$	20.0000	−	6.92820i	0.834784	−	0.289178i
$575$	−4.00000			−0.166812
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	−22.5000	+	38.9711i	−0.936687	+	1.62239i	−0.165090	+	0.986278i	$0.552791\pi$
$577$	−22.5000	+	38.9711i	−0.936687	+	1.62239i	−0.771597	+	0.636111i	$0.780542\pi$
$578$	6.50000	−	11.2583i	0.270364	−	0.468285i
$579$	2.00000	+	3.46410i	0.0831172	+	0.143963i
$580$	3.00000			0.124568
$581$	5.00000	−	25.9808i	0.207435	−	1.07786i
$582$	−7.00000			−0.290159
$583$	−5.00000	−	8.66025i	−0.207079	−	0.358671i
$584$	−4.00000	+	6.92820i	−0.165521	+	0.286691i
$585$	1.00000	−	1.73205i	0.0413449	−	0.0716115i
$586$	−11.0000	−	19.0526i	−0.454406	−	0.787054i
$587$	15.0000			0.619116			0.309558	−	0.950881i	$-0.399819\pi$
$587$	15.0000			0.619116			0.309558	+	0.950881i	$0.399819\pi$
$588$	−1.00000	−	6.92820i	−0.0412393	−	0.285714i
$589$	16.0000			0.659269
$590$	4.50000	+	7.79423i	0.185262	+	0.320883i
$591$	3.50000	−	6.06218i	0.143971	−	0.249365i
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	7.00000	+	12.1244i	0.287456	+	0.497888i	0.973202	−	0.229953i	$-0.0738573\pi$
$593$	7.00000	+	12.1244i	0.287456	+	0.497888i	−0.685746	+	0.727841i	$0.740524\pi$
$594$	−5.00000			−0.205152
$595$	−1.00000	+	5.19615i	−0.0409960	+	0.213021i
$596$	−10.0000			−0.409616
$597$		0			0
$598$	2.00000	−	3.46410i	0.0817861	−	0.141658i
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	−0.219061	−	0.975711i	$-0.570299\pi$
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	0.954521	−	0.298143i	$-0.0963673\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	−20.0000	+	6.92820i	−0.815139	+	0.282372i
$603$	−10.0000			−0.407231
$604$	−4.50000	−	7.79423i	−0.183102	−	0.317143i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	−4.50000	+	7.79423i	−0.182800	+	0.316619i
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	−0.983262	−	0.182199i	$-0.941678\pi$
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	0.333842	−	0.942629i	$-0.391655\pi$
$608$	−4.00000			−0.162221
$609$	6.00000	+	5.19615i	0.243132	+	0.210559i
$610$	1.00000			0.0404888
$611$	−1.00000	−	1.73205i	−0.0404557	−	0.0700713i
$612$	2.00000	−	3.46410i	0.0808452	−	0.140028i
$613$	3.00000	−	5.19615i	0.121169	−	0.209871i	−0.799060	−	0.601251i	$-0.794669\pi$
$613$	3.00000	−	5.19615i	0.121169	−	0.209871i	0.920229	+	0.391381i	$0.128002\pi$
$614$	1.00000	+	1.73205i	0.0403567	+	0.0698999i
$615$	−8.00000			−0.322591
$616$	2.00000	+	1.73205i	0.0805823	+	0.0697863i
$617$	−7.00000			−0.281809			−0.140905	−	0.990023i	$-0.545001\pi$
$617$	−7.00000			−0.281809			−0.140905	+	0.990023i	$0.545001\pi$
$618$	7.00000	+	12.1244i	0.281581	+	0.487713i
$619$	−2.00000	+	3.46410i	−0.0803868	+	0.139234i	−0.903416	−	0.428765i	$-0.858949\pi$
$619$	−2.00000	+	3.46410i	−0.0803868	+	0.139234i	0.823029	+	0.567999i	$0.192282\pi$
$620$	2.00000	−	3.46410i	0.0803219	−	0.139122i
$621$	10.0000	+	17.3205i	0.401286	+	0.695048i
$622$	−30.0000			−1.20289
$623$	−5.00000	+	1.73205i	−0.200321	+	0.0693932i
$624$	−1.00000			−0.0400320
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.50000	+	7.79423i	−0.179856	+	0.311520i
$627$	2.00000	−	3.46410i	0.0798723	−	0.138343i
$628$		0			0
$629$	−16.0000			−0.637962
$630$	1.00000	−	5.19615i	0.0398410	−	0.207020i
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	5.50000	+	9.52628i	0.218778	+	0.378935i
$633$	−12.0000	+	20.7846i	−0.476957	+	0.826114i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$	7.50000	+	12.9904i	0.297628	+	0.515508i
$636$	10.0000			0.396526
$637$	−6.50000	−	2.59808i	−0.257539	−	0.102940i
$638$	−3.00000			−0.118771
$639$	2.00000	+	3.46410i	0.0791188	+	0.137038i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−10.5000	+	18.1865i	−0.414725	+	0.718325i	−0.995400	−	0.0958109i	$-0.969456\pi$
$641$	−10.5000	+	18.1865i	−0.414725	+	0.718325i	0.580674	+	0.814136i	$0.302789\pi$
$642$	−9.00000	−	15.5885i	−0.355202	−	0.615227i
$643$	−21.0000			−0.828159			−0.414080	−	0.910241i	$-0.635896\pi$
$643$	−21.0000			−0.828159			−0.414080	+	0.910241i	$0.635896\pi$
$644$	2.00000	−	10.3923i	0.0788110	−	0.409514i
$645$	8.00000			0.315000
$646$	4.00000	+	6.92820i	0.157378	+	0.272587i
$647$	−21.0000	+	36.3731i	−0.825595	+	1.42997i	0.0758684	+	0.997118i	$0.475827\pi$
$647$	−21.0000	+	36.3731i	−0.825595	+	1.42997i	−0.901464	+	0.432855i	$0.857506\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−4.50000	−	7.79423i	−0.176640	−	0.305950i
$650$	1.00000			0.0392232
$651$	10.0000	−	3.46410i	0.391931	−	0.135769i
$652$	11.0000			0.430793
$653$	2.00000	+	3.46410i	0.0782660	+	0.135561i	0.902502	−	0.430686i	$-0.141728\pi$
$653$	2.00000	+	3.46410i	0.0782660	+	0.135561i	−0.824236	+	0.566247i	$0.808395\pi$
$654$	−5.00000	+	8.66025i	−0.195515	+	0.338643i
$655$	6.00000	−	10.3923i	0.234439	−	0.406061i
$656$	−4.00000	−	6.92820i	−0.156174	−	0.270501i
$657$	−16.0000			−0.624219
$658$	−4.00000	−	3.46410i	−0.155936	−	0.135045i
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$	−0.500000	−	0.866025i	−0.0194625	−	0.0337100i
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	−12.5000	+	21.6506i	−0.485826	+	0.841476i
$663$	1.00000	+	1.73205i	0.0388368	+	0.0672673i
$664$	−10.0000			−0.388075
$665$	8.00000	+	6.92820i	0.310227	+	0.268664i
$666$	16.0000			0.619987
$667$	6.00000	+	10.3923i	0.232321	+	0.402392i
$668$	4.50000	−	7.79423i	0.174110	−	0.301568i
$669$	−12.0000	+	20.7846i	−0.463947	+	0.803579i
$670$	−2.50000	−	4.33013i	−0.0965834	−	0.167287i
$671$	−1.00000			−0.0386046
$672$	−2.50000	+	0.866025i	−0.0964396	+	0.0334077i
$673$	46.0000			1.77317			0.886585	−	0.462566i	$-0.153071\pi$
$673$	46.0000			1.77317			0.886585	+	0.462566i	$0.153071\pi$
$674$	−4.00000	−	6.92820i	−0.154074	−	0.266864i
$675$	−2.50000	+	4.33013i	−0.0962250	+	0.166667i
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	−23.0000	−	39.8372i	−0.883962	−	1.53107i	−0.846899	−	0.531754i	$-0.821533\pi$
$677$	−23.0000	−	39.8372i	−0.883962	−	1.53107i	−0.0370628	−	0.999313i	$-0.511800\pi$
$678$	11.0000			0.422452
$679$	−3.50000	+	18.1865i	−0.134318	+	0.697935i
$680$	2.00000			0.0766965
$681$	7.00000	+	12.1244i	0.268241	+	0.464606i
$682$	−2.00000	+	3.46410i	−0.0765840	+	0.132647i
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	−0.939184	−	0.343413i	$-0.888417\pi$
$683$	−4.50000	+	7.79423i	−0.172188	+	0.298238i	0.766997	+	0.641651i	$0.221750\pi$
$684$	−4.00000	−	6.92820i	−0.152944	−	0.264906i
$685$	−5.00000			−0.191040
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$	−12.0000			−0.457829
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	5.00000	−	8.66025i	0.190485	−	0.329929i
$690$	−2.00000	+	3.46410i	−0.0761387	+	0.131876i
$691$	−6.50000	−	11.2583i	−0.247272	−	0.428287i	0.715496	−	0.698617i	$-0.246201\pi$
$691$	−6.50000	−	11.2583i	−0.247272	−	0.428287i	−0.962768	+	0.270330i	$0.912867\pi$
$692$	−15.0000			−0.570214
$693$	−1.00000	+	5.19615i	−0.0379869	+	0.197386i
$694$	30.0000			1.13878
$695$	−6.00000	−	10.3923i	−0.227593	−	0.394203i
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$	−8.00000	+	13.8564i	−0.303022	+	0.524849i
$698$	7.00000	+	12.1244i	0.264954	+	0.458914i
$699$	−28.0000			−1.05906
$700$	2.50000	−	0.866025i	0.0944911	−	0.0327327i
$701$	−43.0000			−1.62409			−0.812044	−	0.583597i	$-0.801645\pi$
$701$	−43.0000			−1.62409			−0.812044	+	0.583597i	$0.801645\pi$
$702$	−2.50000	−	4.33013i	−0.0943564	−	0.163430i
$703$	−16.0000	+	27.7128i	−0.603451	+	1.04521i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	1.00000	+	1.73205i	0.0376622	+	0.0652328i
$706$	−18.0000			−0.677439
$707$	18.0000	+	15.5885i	0.676960	+	0.586264i
$708$	9.00000			0.338241
$709$	−6.00000	−	10.3923i	−0.225335	−	0.390291i	0.731085	−	0.682286i	$-0.239014\pi$
$709$	−6.00000	−	10.3923i	−0.225335	−	0.390291i	−0.956420	+	0.291995i	$0.905681\pi$
$710$	−1.00000	+	1.73205i	−0.0375293	+	0.0650027i
$711$	−11.0000	+	19.0526i	−0.412532	+	0.714527i
$712$	1.00000	+	1.73205i	0.0374766	+	0.0649113i
$713$	16.0000			0.599205
$714$	4.00000	+	3.46410i	0.149696	+	0.129641i
$715$	−1.00000			−0.0373979
$716$	−11.5000	−	19.9186i	−0.429775	−	0.744392i
$717$	−4.50000	+	7.79423i	−0.168056	+	0.291081i
$718$	−8.50000	+	14.7224i	−0.317217	+	0.549436i
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	0.997546	+	0.0700124i	$0.0223039\pi$
$719$	15.0000	+	25.9808i	0.559406	+	0.968919i	−0.438141	+	0.898906i	$0.644363\pi$
$720$	−2.00000			−0.0745356
$721$	35.0000	−	12.1244i	1.30347	−	0.451535i
$722$	−3.00000			−0.111648
$723$	−2.00000	−	3.46410i	−0.0743808	−	0.128831i
$724$	−5.00000	+	8.66025i	−0.185824	+	0.321856i
$725$	−1.50000	+	2.59808i	−0.0557086	+	0.0964901i
$726$	0.500000	+	0.866025i	0.0185567	+	0.0321412i
$727$	42.0000			1.55769			0.778847	−	0.627214i	$-0.215805\pi$
$727$	42.0000			1.55769			0.778847	+	0.627214i	$0.215805\pi$
$728$	−0.500000	+	2.59808i	−0.0185312	+	0.0962911i
$729$	13.0000			0.481481
$730$	−4.00000	−	6.92820i	−0.148047	−	0.256424i
$731$	8.00000	−	13.8564i	0.295891	−	0.512498i
$732$	0.500000	−	0.866025i	0.0184805	−	0.0320092i
$733$	17.5000	+	30.3109i	0.646377	+	1.11956i	0.983982	+	0.178270i	$0.0570501\pi$
$733$	17.5000	+	30.3109i	0.646377	+	1.11956i	−0.337604	+	0.941288i	$0.609617\pi$
$734$	−24.0000			−0.885856
$735$	6.50000	+	2.59808i	0.239756	+	0.0958315i
$736$	−4.00000			−0.147442
$737$	2.50000	+	4.33013i	0.0920887	+	0.159502i
$738$	8.00000	−	13.8564i	0.294484	−	0.510061i
$739$	−17.0000	+	29.4449i	−0.625355	+	1.08315i	0.363117	+	0.931744i	$0.381713\pi$
$739$	−17.0000	+	29.4449i	−0.625355	+	1.08315i	−0.988472	+	0.151403i	$0.951621\pi$
$740$	4.00000	+	6.92820i	0.147043	+	0.254686i
$741$	4.00000			0.146944
$742$	5.00000	−	25.9808i	0.183556	−	0.953784i
$743$	4.00000			0.146746			0.0733729	−	0.997305i	$-0.476624\pi$
$743$	4.00000			0.146746			0.0733729	+	0.997305i	$0.476624\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$	5.00000	−	8.66025i	0.183186	−	0.317287i
$746$	10.5000	−	18.1865i	0.384432	−	0.665856i
$747$	−10.0000	−	17.3205i	−0.365881	−	0.633724i
$748$	−2.00000			−0.0731272
$749$	−45.0000	+	15.5885i	−1.64426	+	0.569590i
$750$	−1.00000			−0.0365148
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	−1.00000	+	1.73205i	−0.0364662	+	0.0631614i
$753$		0			0
$754$	−1.50000	−	2.59808i	−0.0546268	−	0.0946164i
$755$	9.00000			0.327544
$756$	−10.0000	−	8.66025i	−0.363696	−	0.314970i
$757$	50.0000			1.81728			0.908640	−	0.417579i	$-0.137121\pi$
$757$	50.0000			1.81728			0.908640	+	0.417579i	$0.137121\pi$
$758$	5.50000	+	9.52628i	0.199769	+	0.346010i
$759$	2.00000	−	3.46410i	0.0725954	−	0.125739i
$760$	2.00000	−	3.46410i	0.0725476	−	0.125656i
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$	15.0000			0.543393
$763$	20.0000	+	17.3205i	0.724049	+	0.627044i
$764$	2.00000			0.0723575
$765$	2.00000	+	3.46410i	0.0723102	+	0.125245i
$766$	−3.00000	+	5.19615i	−0.108394	+	0.187745i
$767$	4.50000	−	7.79423i	0.162486	−	0.281433i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	10.0000			0.360609			0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000			0.360609			0.180305	+	0.983611i	$0.442292\pi$
$770$	−2.50000	+	0.866025i	−0.0900937	+	0.0312094i
$771$	−19.0000			−0.684268
$772$	−2.00000	−	3.46410i	−0.0719816	−	0.124676i
$773$	−16.0000	+	27.7128i	−0.575480	+	0.996761i	0.420509	+	0.907288i	$0.361851\pi$
$773$	−16.0000	+	27.7128i	−0.575480	+	0.996761i	−0.995989	+	0.0894724i	$0.971482\pi$
$774$	−8.00000	+	13.8564i	−0.287554	+	0.498058i
$775$	2.00000	+	3.46410i	0.0718421	+	0.124434i
$776$	7.00000			0.251285
$777$	−4.00000	+	20.7846i	−0.143499	+	0.745644i
$778$	−26.0000			−0.932145
$779$	16.0000	+	27.7128i	0.573259	+	0.992915i
$780$	0.500000	−	0.866025i	0.0179029	−	0.0310087i
$781$	1.00000	−	1.73205i	0.0357828	−	0.0619777i
$782$	4.00000	+	6.92820i	0.143040	+	0.247752i
$783$	15.0000			0.536056
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$		0			0
$786$	−6.00000	−	10.3923i	−0.214013	−	0.370681i
$787$	−6.00000	+	10.3923i	−0.213877	+	0.370446i	−0.952925	−	0.303207i	$-0.901942\pi$
$787$	−6.00000	+	10.3923i	−0.213877	+	0.370446i	0.739048	+	0.673653i	$0.235276\pi$
$788$	−3.50000	+	6.06218i	−0.124682	+	0.215956i
$789$	−8.50000	−	14.7224i	−0.302608	−	0.524132i
$790$	−11.0000			−0.391362
$791$	5.50000	−	28.5788i	0.195557	−	1.01615i
$792$	2.00000			0.0710669
$793$	−0.500000	−	0.866025i	−0.0177555	−	0.0307535i
$794$	9.00000	−	15.5885i	0.319398	−	0.553214i
$795$	−5.00000	+	8.66025i	−0.177332	+	0.307148i
$796$		0			0
$797$	−14.0000			−0.495905			−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−14.0000			−0.495905			−0.247953	+	0.968772i	$0.579758\pi$
$798$	10.0000	−	3.46410i	0.353996	−	0.122628i
$799$	4.00000			0.141510
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−2.00000	+	3.46410i	−0.0706665	+	0.122398i
$802$	4.50000	−	7.79423i	0.158901	−	0.275224i
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$	−5.00000			−0.176336
$805$	8.00000	+	6.92820i	0.281963	+	0.244187i
$806$	−4.00000			−0.140894
$807$	−16.0000	−	27.7128i	−0.563227	−	0.975537i
$808$	4.50000	−	7.79423i	0.158309	−	0.274200i
$809$	−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
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$	−6.00000	−	5.19615i	−0.210559	−	0.182349i
$813$	−1.00000			−0.0350715
$814$	−4.00000	−	6.92820i	−0.140200	−	0.242833i
$815$	−5.50000	+	9.52628i	−0.192657	+	0.333691i
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$	−16.0000	−	27.7128i	−0.559769	−	0.969549i
$818$	2.00000			0.0699284
$819$	−5.00000	+	1.73205i	−0.174714	+	0.0605228i
$820$	8.00000			0.279372
$821$	−25.5000	−	44.1673i	−0.889956	−	1.54145i	−0.839926	−	0.542702i	$-0.817401\pi$
$821$	−25.5000	−	44.1673i	−0.889956	−	1.54145i	−0.0500305	−	0.998748i	$-0.515932\pi$
$822$	−2.50000	+	4.33013i	−0.0871975	+	0.151031i
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	−0.717847	−	0.696201i	$-0.754872\pi$
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	0.961851	+	0.273573i	$0.0882054\pi$
$824$	−7.00000	−	12.1244i	−0.243857	−	0.422372i
$825$	1.00000			0.0348155
$826$	4.50000	−	23.3827i	0.156575	−	0.813588i
$827$	16.0000			0.556375			0.278187	−	0.960527i	$-0.410266\pi$
$827$	16.0000			0.556375			0.278187	+	0.960527i	$0.410266\pi$
$828$	−4.00000	−	6.92820i	−0.139010	−	0.240772i
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	0.403739	+	0.914874i	$0.367710\pi$
$829$	−17.0000	+	29.4449i	−0.590434	+	1.02266i	−0.994174	+	0.107788i	$0.965623\pi$
$830$	5.00000	−	8.66025i	0.173553	−	0.300602i
$831$	−8.50000	−	14.7224i	−0.294862	−	0.510716i
$832$	1.00000			0.0346688
$833$	11.0000	−	8.66025i	0.381127	−	0.300060i
$834$	−12.0000			−0.415526
$835$	4.50000	+	7.79423i	0.155729	+	0.269730i
$836$	−2.00000	+	3.46410i	−0.0691714	+	0.119808i
$837$	10.0000	−	17.3205i	0.345651	−	0.598684i
$838$	−4.00000	−	6.92820i	−0.138178	−	0.239331i
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$	0.500000	−	2.59808i	0.0172516	−	0.0896421i
$841$	−20.0000			−0.689655
$842$	−2.00000	−	3.46410i	−0.0689246	−	0.119381i
$843$	4.00000	−	6.92820i	0.137767	−	0.238620i
$844$	12.0000	−	20.7846i	0.413057	−	0.715436i
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$	−4.00000			−0.137523
$847$	2.50000	−	0.866025i	0.0859010	−	0.0297570i
$848$	−10.0000			−0.343401
$849$	−10.0000	−	17.3205i	−0.343199	−	0.594438i
$850$	−1.00000	+	1.73205i	−0.0342997	+	0.0594089i
$851$	−16.0000	+	27.7128i	−0.548473	+	0.949983i
$852$	1.00000	+	1.73205i	0.0342594	+	0.0593391i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$	−2.00000	−	1.73205i	−0.0684386	−	0.0592696i
$855$	8.00000			0.273594
$856$	9.00000	+	15.5885i	0.307614	+	0.532803i
$857$	−6.00000	+	10.3923i	−0.204956	+	0.354994i	−0.950119	−	0.311888i	$-0.899038\pi$
$857$	−6.00000	+	10.3923i	−0.204956	+	0.354994i	0.745163	+	0.666883i	$0.232372\pi$
$858$	−0.500000	+	0.866025i	−0.0170697	+	0.0295656i
$859$	27.5000	+	47.6314i	0.938288	+	1.62516i	0.768663	+	0.639654i	$0.220922\pi$
$859$	27.5000	+	47.6314i	0.938288	+	1.62516i	0.169625	+	0.985509i	$0.445745\pi$
$860$	−8.00000			−0.272798
$861$	16.0000	+	13.8564i	0.545279	+	0.472225i
$862$	13.0000			0.442782
$863$	4.00000	+	6.92820i	0.136162	+	0.235839i	0.926041	−	0.377424i	$-0.123190\pi$
$863$	4.00000	+	6.92820i	0.136162	+	0.235839i	−0.789879	+	0.613263i	$0.789857\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$	7.50000	−	12.9904i	0.255008	−	0.441686i
$866$	−11.0000	−	19.0526i	−0.373795	−	0.647432i
$867$	13.0000			0.441503
$868$	−10.0000	+	3.46410i	−0.339422	+	0.117579i
$869$	11.0000			0.373149
$870$	1.50000	+	2.59808i	0.0508548	+	0.0880830i
$871$	−2.50000	+	4.33013i	−0.0847093	+	0.146721i
$872$	5.00000	−	8.66025i	0.169321	−	0.293273i
$873$	7.00000	+	12.1244i	0.236914	+	0.410347i
$874$	16.0000			0.541208
$875$	−0.500000	+	2.59808i	−0.0169031	+	0.0878310i
$876$	−8.00000			−0.270295
$877$	−17.5000	−	30.3109i	−0.590933	−	1.02353i	−0.994107	−	0.108403i	$-0.965426\pi$
$877$	−17.5000	−	30.3109i	−0.590933	−	1.02353i	0.403174	−	0.915123i	$-0.367907\pi$
$878$	−3.50000	+	6.06218i	−0.118119	+	0.204589i
$879$	11.0000	−	19.0526i	0.371021	−	0.642627i
$880$	0.500000	+	0.866025i	0.0168550	+	0.0291937i
$881$	−35.0000			−1.17918			−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000			−1.17918			−0.589590	+	0.807703i	$0.700711\pi$
$882$	−11.0000	+	8.66025i	−0.370389	+	0.291606i
$883$	7.00000			0.235569			0.117784	−	0.993039i	$-0.462421\pi$
$883$	7.00000			0.235569			0.117784	+	0.993039i	$0.462421\pi$
$884$	−1.00000	−	1.73205i	−0.0336336	−	0.0582552i
$885$	−4.50000	+	7.79423i	−0.151266	+	0.262000i
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	0.545302	−	0.838240i	$-0.316415\pi$
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	−0.998588	+	0.0531258i	$0.983082\pi$
$888$	8.00000			0.268462
$889$	7.50000	−	38.9711i	0.251542	−	1.30705i
$890$	−2.00000			−0.0670402
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	12.0000	−	20.7846i	0.401790	−	0.695920i
$893$	4.00000	−	6.92820i	0.133855	−	0.231843i
$894$	−5.00000	−	8.66025i	−0.167225	−	0.289642i
$895$	23.0000			0.768805
$896$	2.50000	−	0.866025i	0.0835191	−	0.0289319i
$897$	4.00000			0.133556
$898$	3.00000	+	5.19615i	0.100111	+	0.173398i
$899$	6.00000	−	10.3923i	0.200111	−	0.346603i
$900$	1.00000	−	1.73205i	0.0333333	−	0.0577350i
$901$	10.0000	+	17.3205i	0.333148	+	0.577030i
$902$	−8.00000			−0.266371
$903$	−16.0000	−	13.8564i	−0.532447	−	0.461112i
$904$	−11.0000			−0.365855
$905$	−5.00000	−	8.66025i	−0.166206	−	0.287877i
$906$	4.50000	−	7.79423i	0.149502	−	0.258946i
$907$	10.0000	−	17.3205i	0.332045	−	0.575118i	−0.650868	−	0.759191i	$-0.725595\pi$
$907$	10.0000	−	17.3205i	0.332045	−	0.575118i	0.982913	+	0.184073i	$0.0589282\pi$
$908$	−7.00000	−	12.1244i	−0.232303	−	0.402361i
$909$	18.0000			0.597022
$910$	−2.00000	−	1.73205i	−0.0662994	−	0.0574169i
$911$	−10.0000			−0.331315			−0.165657	−	0.986183i	$-0.552975\pi$
$911$	−10.0000			−0.331315			−0.165657	+	0.986183i	$0.552975\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$	−5.00000	+	8.66025i	−0.165476	+	0.286613i
$914$	1.00000	−	1.73205i	0.0330771	−	0.0572911i
$915$	0.500000	+	0.866025i	0.0165295	+	0.0286299i
$916$	12.0000			0.396491
$917$	−30.0000	+	10.3923i	−0.990687	+	0.343184i
$918$	10.0000			0.330049
$919$	18.0000	+	31.1769i	0.593765	+	1.02843i	0.993720	+	0.111897i	$0.0356925\pi$
$919$	18.0000	+	31.1769i	0.593765	+	1.02843i	−0.399955	+	0.916535i	$0.630974\pi$
$920$	2.00000	−	3.46410i	0.0659380	−	0.114208i
$921$	−1.00000	+	1.73205i	−0.0329511	+	0.0570730i
$922$	−17.5000	−	30.3109i	−0.576332	−	0.998236i
$923$	2.00000			0.0658308
$924$	−0.500000	+	2.59808i	−0.0164488	+	0.0854704i
$925$	−8.00000			−0.263038
$926$	1.00000	+	1.73205i	0.0328620	+	0.0569187i
$927$	14.0000	−	24.2487i	0.459820	−	0.796432i
$928$	−1.50000	+	2.59808i	−0.0492399	+	0.0852860i
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	−0.985482	−	0.169779i	$-0.945695\pi$
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	0.345708	−	0.938342i	$-0.387639\pi$
$930$	4.00000			0.131165
$931$	−4.00000	−	27.7128i	−0.131095	−	0.908251i
$932$	28.0000			0.917170
$933$	−15.0000	−	25.9808i	−0.491078	−	0.850572i
$934$	−18.0000	+	31.1769i	−0.588978	+	1.02014i
$935$	1.00000	−	1.73205i	0.0327035	−	0.0566441i
$936$	1.00000	+	1.73205i	0.0326860	+	0.0566139i
$937$	−10.0000			−0.326686			−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000			−0.326686			−0.163343	+	0.986569i	$0.552228\pi$
$938$	−2.50000	+	12.9904i	−0.0816279	+	0.424151i
$939$	−9.00000			−0.293704
$940$	−1.00000	−	1.73205i	−0.0326164	−	0.0564933i
$941$	−6.50000	+	11.2583i	−0.211894	+	0.367011i	−0.952307	−	0.305141i	$-0.901296\pi$
$941$	−6.50000	+	11.2583i	−0.211894	+	0.367011i	0.740413	+	0.672152i	$0.234630\pi$
$942$		0			0
$943$	16.0000	+	27.7128i	0.521032	+	0.902453i
$944$	−9.00000			−0.292925
$945$	12.5000	−	4.33013i	0.406625	−	0.140859i
$946$	8.00000			0.260102
$947$	−2.00000	−	3.46410i	−0.0649913	−	0.112568i	0.831699	−	0.555227i	$-0.187369\pi$
$947$	−2.00000	−	3.46410i	−0.0649913	−	0.112568i	−0.896690	+	0.442659i	$0.854035\pi$
$948$	−5.50000	+	9.52628i	−0.178632	+	0.309399i
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$	2.00000	+	3.46410i	0.0648886	+	0.112390i
$951$	−12.0000			−0.389127
$952$	−4.00000	−	3.46410i	−0.129641	−	0.112272i
$953$	42.0000			1.36051			0.680257	−	0.732974i	$-0.261868\pi$
$953$	42.0000			1.36051			0.680257	+	0.732974i	$0.261868\pi$
$954$	−10.0000	−	17.3205i	−0.323762	−	0.560772i
$955$	−1.00000	+	1.73205i	−0.0323592	+	0.0560478i
$956$	4.50000	−	7.79423i	0.145540	−	0.252083i
$957$	−1.50000	−	2.59808i	−0.0484881	−	0.0839839i
$958$	−21.0000			−0.678479
$959$	10.0000	+	8.66025i	0.322917	+	0.279654i
$960$	−1.00000			−0.0322749
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	4.00000	−	6.92820i	0.128965	−	0.223374i
$963$	−18.0000	+	31.1769i	−0.580042	+	1.00466i
$964$	2.00000	+	3.46410i	0.0644157	+	0.111571i
$965$	4.00000			0.128765
$966$	10.0000	−	3.46410i	0.321745	−	0.111456i
$967$	8.00000			0.257263			0.128631	−	0.991692i	$-0.458942\pi$
$967$	8.00000			0.257263			0.128631	+	0.991692i	$0.458942\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	−4.00000	+	6.92820i	−0.128499	+	0.222566i
$970$	−3.50000	+	6.06218i	−0.112378	+	0.194645i
$971$	13.5000	+	23.3827i	0.433236	+	0.750386i	0.997150	−	0.0754473i	$-0.0240385\pi$
$971$	13.5000	+	23.3827i	0.433236	+	0.750386i	−0.563914	+	0.825833i	$0.690705\pi$
$972$	−16.0000			−0.513200
$973$	−6.00000	+	31.1769i	−0.192351	+	0.999486i
$974$	24.0000			0.769010
$975$	0.500000	+	0.866025i	0.0160128	+	0.0277350i
$976$	−0.500000	+	0.866025i	−0.0160046	+	0.0277208i
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	−0.881579	−	0.472037i	$-0.843519\pi$
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	0.849586	+	0.527451i	$0.176852\pi$
$978$	5.50000	+	9.52628i	0.175871	+	0.304617i
$979$	2.00000			0.0639203
$980$	−6.50000	−	2.59808i	−0.207635	−	0.0829925i
$981$	20.0000			0.638551
$982$	17.0000	+	29.4449i	0.542492	+	0.939623i
$983$	21.0000	−	36.3731i	0.669796	−	1.16012i	−0.308165	−	0.951333i	$-0.599715\pi$
$983$	21.0000	−	36.3731i	0.669796	−	1.16012i	0.977961	−	0.208788i	$-0.0669518\pi$
$984$	4.00000	−	6.92820i	0.127515	−	0.220863i
$985$	−3.50000	−	6.06218i	−0.111519	−	0.193157i
$986$	6.00000			0.191079
$987$	1.00000	−	5.19615i	0.0318304	−	0.165395i
$988$	−4.00000			−0.127257
$989$	−16.0000	−	27.7128i	−0.508770	−	0.881216i
$990$	−1.00000	+	1.73205i	−0.0317821	+	0.0550482i
$991$	17.0000	−	29.4449i	0.540023	−	0.935347i	−0.458879	−	0.888499i	$-0.651749\pi$
$991$	17.0000	−	29.4449i	0.540023	−	0.935347i	0.998902	−	0.0468483i	$-0.0149177\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	−25.0000			−0.793351
$994$	5.00000	−	1.73205i	0.158590	−	0.0549373i
$995$		0			0
$996$	−5.00000	−	8.66025i	−0.158431	−	0.274411i
$997$	−25.0000	+	43.3013i	−0.791758	+	1.37136i	0.133120	+	0.991100i	$0.457501\pi$
$997$	−25.0000	+	43.3013i	−0.791758	+	1.37136i	−0.924878	+	0.380265i	$0.875833\pi$
$998$	10.0000	−	17.3205i	0.316544	−	0.548271i
$999$	20.0000	+	34.6410i	0.632772	+	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.c.221.1	✓	2
7.2	even	3	inner	770.2.i.c.331.1	yes	2
7.3	odd	6		5390.2.a.bc.1.1		1
7.4	even	3		5390.2.a.y.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.c.221.1	✓	2	1.1	even	1	trivial
770.2.i.c.331.1	yes	2	7.2	even	3	inner
5390.2.a.y.1.1		1	7.4	even	3
5390.2.a.bc.1.1		1	7.3	odd	6

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(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 + 2.59808i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(2.50000 - 0.866025i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(1.00000 - 1.73205i) q^{18} +(2.00000 + 3.46410i) q^{19} +1.00000 q^{20} +(2.00000 + 1.73205i) q^{21} -1.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.500000 - 0.866025i) q^{26} +5.00000 q^{27} +(-2.00000 - 1.73205i) q^{28} +3.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +2.00000 q^{34} +(2.50000 - 0.866025i) q^{35} -2.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(0.500000 - 0.866025i) q^{39} +(-0.500000 - 0.866025i) q^{40} +8.00000 q^{41} +(0.500000 - 2.59808i) q^{42} -8.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.00000 - 1.73205i) q^{45} +(2.00000 - 3.46410i) q^{46} +(-1.00000 - 1.73205i) q^{47} -1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +1.00000 q^{50} +(1.00000 + 1.73205i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(5.00000 - 8.66025i) q^{53} +(-2.50000 - 4.33013i) q^{54} -1.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} +4.00000 q^{57} +(-1.50000 - 2.59808i) q^{58} +(4.50000 - 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-0.500000 - 0.866025i) q^{61} -4.00000 q^{62} +(-5.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-0.500000 + 0.866025i) q^{66} +(-2.50000 + 4.33013i) q^{67} +(-1.00000 - 1.73205i) q^{68} +4.00000 q^{69} +(-2.00000 - 1.73205i) q^{70} +2.00000 q^{71} +(1.00000 + 1.73205i) q^{72} +(-4.00000 + 6.92820i) q^{73} +(4.00000 - 6.92820i) q^{74} +(0.500000 + 0.866025i) q^{75} -4.00000 q^{76} +(2.00000 + 1.73205i) q^{77} -1.00000 q^{78} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.00000 - 6.92820i) q^{82} -10.0000 q^{83} +(-2.50000 + 0.866025i) q^{84} +2.00000 q^{85} +(4.00000 + 6.92820i) q^{86} +(1.50000 - 2.59808i) q^{87} +(0.500000 - 0.866025i) q^{88} +(1.00000 + 1.73205i) q^{89} -2.00000 q^{90} +(-0.500000 + 2.59808i) q^{91} -4.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(-1.00000 + 1.73205i) q^{94} +(2.00000 - 3.46410i) q^{95} +(0.500000 + 0.866025i) q^{96} +7.00000 q^{97} +(1.00000 + 6.92820i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - q^{10} + q^{11} + q^{12} + 2 q^{13} + 5 q^{14} - 2 q^{15} - q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 4 q^{21} - 2 q^{22} + 4 q^{23} + q^{24} - q^{25} - q^{26} + 10 q^{27} - 4 q^{28} + 6 q^{29} + q^{30} + 4 q^{31} - q^{32} - q^{33} + 4 q^{34} + 5 q^{35} - 4 q^{36} + 8 q^{37} + 4 q^{38} + q^{39} - q^{40} + 16 q^{41} + q^{42} - 16 q^{43} + q^{44} + 2 q^{45} + 4 q^{46} - 2 q^{47} - 2 q^{48} - 13 q^{49} + 2 q^{50} + 2 q^{51} - q^{52} + 10 q^{53} - 5 q^{54} - 2 q^{55} - q^{56} + 8 q^{57} - 3 q^{58} + 9 q^{59} + q^{60} - q^{61} - 8 q^{62} - 10 q^{63} + 2 q^{64} - q^{65} - q^{66} - 5 q^{67} - 2 q^{68} + 8 q^{69} - 4 q^{70} + 4 q^{71} + 2 q^{72} - 8 q^{73} + 8 q^{74} + q^{75} - 8 q^{76} + 4 q^{77} - 2 q^{78} + 11 q^{79} - q^{80} - q^{81} - 8 q^{82} - 20 q^{83} - 5 q^{84} + 4 q^{85} + 8 q^{86} + 3 q^{87} + q^{88} + 2 q^{89} - 4 q^{90} - q^{91} - 8 q^{92} - 4 q^{93} - 2 q^{94} + 4 q^{95} + q^{96} + 14 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 - 2 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - q^10 + q^11 + q^12 + 2 * q^13 + 5 * q^14 - 2 * q^15 - q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 4 * q^21 - 2 * q^22 + 4 * q^23 + q^24 - q^25 - q^26 + 10 * q^27 - 4 * q^28 + 6 * q^29 + q^30 + 4 * q^31 - q^32 - q^33 + 4 * q^34 + 5 * q^35 - 4 * q^36 + 8 * q^37 + 4 * q^38 + q^39 - q^40 + 16 * q^41 + q^42 - 16 * q^43 + q^44 + 2 * q^45 + 4 * q^46 - 2 * q^47 - 2 * q^48 - 13 * q^49 + 2 * q^50 + 2 * q^51 - q^52 + 10 * q^53 - 5 * q^54 - 2 * q^55 - q^56 + 8 * q^57 - 3 * q^58 + 9 * q^59 + q^60 - q^61 - 8 * q^62 - 10 * q^63 + 2 * q^64 - q^65 - q^66 - 5 * q^67 - 2 * q^68 + 8 * q^69 - 4 * q^70 + 4 * q^71 + 2 * q^72 - 8 * q^73 + 8 * q^74 + q^75 - 8 * q^76 + 4 * q^77 - 2 * q^78 + 11 * q^79 - q^80 - q^81 - 8 * q^82 - 20 * q^83 - 5 * q^84 + 4 * q^85 + 8 * q^86 + 3 * q^87 + q^88 + 2 * q^89 - 4 * q^90 - q^91 - 8 * q^92 - 4 * q^93 - 2 * q^94 + 4 * q^95 + q^96 + 14 * q^97 + 2 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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Database

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