LMFDB - Embedded newform 154.2.e.a.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [154,2,Mod(23,154)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(154, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("154.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 154 = 2 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	154.e (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:	$1.22969619113$
Analytic rank:	$1$
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			23.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	154.23
Dual form			154.2.e.a.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +3.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +3.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.50000 + 2.59808i) q^{12} -7.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-3.00000 - 5.19615i) q^{18} +2.00000 q^{20} +(6.00000 + 5.19615i) q^{21} -1.00000 q^{22} +(4.00000 - 6.92820i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(0.500000 + 0.866025i) q^{25} +(3.50000 - 6.06218i) q^{26} +9.00000 q^{27} +(2.00000 + 1.73205i) q^{28} -5.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +2.00000 q^{34} +(1.00000 - 5.19615i) q^{35} +6.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(10.5000 + 18.1865i) q^{39} +(-1.00000 + 1.73205i) q^{40} +4.00000 q^{41} +(-7.50000 + 2.59808i) q^{42} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-6.00000 - 10.3923i) q^{45} +(4.00000 + 6.92820i) q^{46} +(-1.00000 + 1.73205i) q^{47} +3.00000 q^{48} +(5.50000 - 4.33013i) q^{49} -1.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(3.50000 + 6.06218i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-4.50000 + 7.79423i) q^{54} -2.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +(2.50000 - 4.33013i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(-0.500000 + 0.866025i) q^{61} +4.00000 q^{62} +(3.00000 - 15.5885i) q^{63} +1.00000 q^{64} +(7.00000 - 12.1244i) q^{65} +(1.50000 + 2.59808i) q^{66} +(-4.50000 - 7.79423i) q^{67} +(-1.00000 + 1.73205i) q^{68} -24.0000 q^{69} +(4.00000 + 3.46410i) q^{70} -2.00000 q^{71} +(-3.00000 + 5.19615i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(1.50000 - 2.59808i) q^{75} +(-2.00000 - 1.73205i) q^{77} -21.0000 q^{78} +(-4.50000 + 7.79423i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-2.00000 + 3.46410i) q^{82} +6.00000 q^{83} +(1.50000 - 7.79423i) q^{84} +4.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(7.50000 + 12.9904i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-3.00000 + 5.19615i) q^{89} +12.0000 q^{90} +(17.5000 - 6.06218i) q^{91} -8.00000 q^{92} +(-6.00000 + 10.3923i) q^{93} +(-1.00000 - 1.73205i) q^{94} +(-1.50000 + 2.59808i) q^{96} +7.00000 q^{97} +(1.00000 + 6.92820i) q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} + 6 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - q^2 - 3 * q^3 - q^4 - 2 * q^5 + 6 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9	\( 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} + 6 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 2 q^{10} + q^{11} - 3 q^{12} - 14 q^{13} + q^{14} + 12 q^{15} - q^{16} - 2 q^{17} - 6 q^{18} + 4 q^{20} + 12 q^{21} - 2 q^{22} + 8 q^{23} - 3 q^{24} + q^{25} + 7 q^{26} + 18 q^{27} + 4 q^{28} - 10 q^{29} - 6 q^{30} - 4 q^{31} - q^{32} + 3 q^{33} + 4 q^{34} + 2 q^{35} + 12 q^{36} - 4 q^{37} + 21 q^{39} - 2 q^{40} + 8 q^{41} - 15 q^{42} - 16 q^{43} + q^{44} - 12 q^{45} + 8 q^{46} - 2 q^{47} + 6 q^{48} + 11 q^{49} - 2 q^{50} - 6 q^{51} + 7 q^{52} + 6 q^{53} - 9 q^{54} - 4 q^{55} - 5 q^{56} + 5 q^{58} - 3 q^{59} - 6 q^{60} - q^{61} + 8 q^{62} + 6 q^{63} + 2 q^{64} + 14 q^{65} + 3 q^{66} - 9 q^{67} - 2 q^{68} - 48 q^{69} + 8 q^{70} - 4 q^{71} - 6 q^{72} - 4 q^{73} - 4 q^{74} + 3 q^{75} - 4 q^{77} - 42 q^{78} - 9 q^{79} - 2 q^{80} - 9 q^{81} - 4 q^{82} + 12 q^{83} + 3 q^{84} + 8 q^{85} + 8 q^{86} + 15 q^{87} + q^{88} - 6 q^{89} + 24 q^{90} + 35 q^{91} - 16 q^{92} - 12 q^{93} - 2 q^{94} - 3 q^{96} + 14 q^{97} + 2 q^{98} - 12 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 - q^4 - 2 * q^5 + 6 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 - 2 * q^10 + q^11 - 3 * q^12 - 14 * q^13 + q^14 + 12 * q^15 - q^16 - 2 * q^17 - 6 * q^18 + 4 * q^20 + 12 * q^21 - 2 * q^22 + 8 * q^23 - 3 * q^24 + q^25 + 7 * q^26 + 18 * q^27 + 4 * q^28 - 10 * q^29 - 6 * q^30 - 4 * q^31 - q^32 + 3 * q^33 + 4 * q^34 + 2 * q^35 + 12 * q^36 - 4 * q^37 + 21 * q^39 - 2 * q^40 + 8 * q^41 - 15 * q^42 - 16 * q^43 + q^44 - 12 * q^45 + 8 * q^46 - 2 * q^47 + 6 * q^48 + 11 * q^49 - 2 * q^50 - 6 * q^51 + 7 * q^52 + 6 * q^53 - 9 * q^54 - 4 * q^55 - 5 * q^56 + 5 * q^58 - 3 * q^59 - 6 * q^60 - q^61 + 8 * q^62 + 6 * q^63 + 2 * q^64 + 14 * q^65 + 3 * q^66 - 9 * q^67 - 2 * q^68 - 48 * q^69 + 8 * q^70 - 4 * q^71 - 6 * q^72 - 4 * q^73 - 4 * q^74 + 3 * q^75 - 4 * q^77 - 42 * q^78 - 9 * q^79 - 2 * q^80 - 9 * q^81 - 4 * q^82 + 12 * q^83 + 3 * q^84 + 8 * q^85 + 8 * q^86 + 15 * q^87 + q^88 - 6 * q^89 + 24 * q^90 + 35 * q^91 - 16 * q^92 - 12 * q^93 - 2 * q^94 - 3 * q^96 + 14 * q^97 + 2 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/154\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.50000	−	2.59808i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−1.50000	−	2.59808i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$	3.00000			1.22474
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	1.00000			0.353553
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	−1.00000	−	1.73205i	−0.316228	−	0.547723i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−1.50000	+	2.59808i	−0.433013	+	0.750000i
$13$	−7.00000			−1.94145			−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−7.00000			−1.94145			−0.970725	+	0.240192i	$0.922790\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$	6.00000			1.54919
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	−3.00000	−	5.19615i	−0.707107	−	1.22474i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	2.00000			0.447214
$21$	6.00000	+	5.19615i	1.30931	+	1.13389i
$22$	−1.00000			−0.213201
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	−0.0607377	−	0.998154i	$-0.519345\pi$
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	0.894795	−	0.446476i	$-0.147321\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	3.50000	−	6.06218i	0.686406	−	1.18889i
$27$	9.00000			1.73205
$28$	2.00000	+	1.73205i	0.377964	+	0.327327i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$	−3.00000	+	5.19615i	−0.547723	+	0.948683i
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$	2.00000			0.342997
$35$	1.00000	−	5.19615i	0.169031	−	0.878310i
$36$	6.00000			1.00000
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$		0			0
$39$	10.5000	+	18.1865i	1.68135	+	2.91218i
$40$	−1.00000	+	1.73205i	−0.158114	+	0.273861i
$41$	4.00000			0.624695			0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000			0.624695			0.312348	+	0.949968i	$0.398885\pi$
$42$	−7.50000	+	2.59808i	−1.15728	+	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
$45$	−6.00000	−	10.3923i	−0.894427	−	1.54919i
$46$	4.00000	+	6.92820i	0.589768	+	1.02151i
$47$	−1.00000	+	1.73205i	−0.145865	+	0.252646i	−0.929695	−	0.368329i	$-0.879930\pi$
$47$	−1.00000	+	1.73205i	−0.145865	+	0.252646i	0.783830	+	0.620975i	$0.213263\pi$
$48$	3.00000			0.433013
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−1.00000			−0.141421
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	3.50000	+	6.06218i	0.485363	+	0.840673i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	−4.50000	+	7.79423i	−0.612372	+	1.06066i
$55$	−2.00000			−0.269680
$56$	−2.50000	+	0.866025i	−0.334077	+	0.115728i
$57$		0			0
$58$	2.50000	−	4.33013i	0.328266	−	0.568574i
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$	−3.00000	−	5.19615i	−0.387298	−	0.670820i
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$	4.00000			0.508001
$63$	3.00000	−	15.5885i	0.377964	−	1.96396i
$64$	1.00000			0.125000
$65$	7.00000	−	12.1244i	0.868243	−	1.50384i
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	−4.50000	−	7.79423i	−0.549762	−	0.952217i	−0.998290	−	0.0584478i	$-0.981385\pi$
$67$	−4.50000	−	7.79423i	−0.549762	−	0.952217i	0.448528	−	0.893769i	$-0.351948\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$	−24.0000			−2.88926
$70$	4.00000	+	3.46410i	0.478091	+	0.414039i
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$	−3.00000	+	5.19615i	−0.353553	+	0.612372i
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	0.724923	−	0.688830i	$-0.241875\pi$
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	−0.959006	+	0.283387i	$0.908542\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$	1.50000	−	2.59808i	0.173205	−	0.300000i
$76$		0			0
$77$	−2.00000	−	1.73205i	−0.227921	−	0.197386i
$78$	−21.0000			−2.37778
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	0.493684	+	0.869641i	$0.335650\pi$
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	−0.999974	+	0.00727784i	$0.997683\pi$
$80$	−1.00000	−	1.73205i	−0.111803	−	0.193649i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−2.00000	+	3.46410i	−0.220863	+	0.382546i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	1.50000	−	7.79423i	0.163663	−	0.850420i
$85$	4.00000			0.433861
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	7.50000	+	12.9904i	0.804084	+	1.39272i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	12.0000			1.26491
$91$	17.5000	−	6.06218i	1.83450	−	0.635489i
$92$	−8.00000			−0.834058
$93$	−6.00000	+	10.3923i	−0.622171	+	1.07763i
$94$	−1.00000	−	1.73205i	−0.103142	−	0.178647i
$95$		0			0
$96$	−1.50000	+	2.59808i	−0.153093	+	0.265165i
$97$	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
$99$	−6.00000			−0.603023
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	−9.00000	+	15.5885i	−0.886796	+	1.53598i	−0.0431555	+	0.999068i	$0.513741\pi$
$103$	−9.00000	+	15.5885i	−0.886796	+	1.53598i	−0.843641	+	0.536908i	$0.819592\pi$
$104$	−7.00000			−0.686406
$105$	−15.0000	+	5.19615i	−1.46385	+	0.507093i
$106$	−6.00000			−0.582772
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	−0.910306	−	0.413936i	$-0.864154\pi$
$107$	−1.00000	+	1.73205i	−0.0966736	+	0.167444i	0.813632	+	0.581380i	$0.197487\pi$
$108$	−4.50000	−	7.79423i	−0.433013	−	0.750000i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$	12.0000			1.13899
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	5.00000			0.470360			0.235180	−	0.971952i	$-0.424432\pi$
$113$	5.00000			0.470360			0.235180	+	0.971952i	$0.424432\pi$
$114$		0			0
$115$	8.00000	+	13.8564i	0.746004	+	1.29212i
$116$	2.50000	+	4.33013i	0.232119	+	0.402042i
$117$	21.0000	−	36.3731i	1.94145	−	3.36269i
$118$	3.00000			0.276172
$119$	4.00000	+	3.46410i	0.366679	+	0.317554i
$120$	6.00000			0.547723
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−0.500000	−	0.866025i	−0.0452679	−	0.0784063i
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	−12.0000			−1.07331
$126$	12.0000	+	10.3923i	1.06904	+	0.925820i
$127$	−19.0000			−1.68598			−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000			−1.68598			−0.842989	+	0.537931i	$0.819206\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	12.0000	+	20.7846i	1.05654	+	1.82998i
$130$	7.00000	+	12.1244i	0.613941	+	1.06338i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	−3.00000			−0.261116
$133$		0			0
$134$	9.00000			0.777482
$135$	−9.00000	+	15.5885i	−0.774597	+	1.34164i
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$	12.0000	−	20.7846i	1.02151	−	1.76930i
$139$	−4.00000			−0.339276			−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000			−0.339276			−0.169638	+	0.985506i	$0.554260\pi$
$140$	−5.00000	+	1.73205i	−0.422577	+	0.146385i
$141$	6.00000			0.505291
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$	−3.50000	−	6.06218i	−0.292685	−	0.506945i
$144$	−3.00000	−	5.19615i	−0.250000	−	0.433013i
$145$	5.00000	−	8.66025i	0.415227	−	0.719195i
$146$	4.00000			0.331042
$147$	−19.5000	−	7.79423i	−1.60833	−	0.642857i
$148$	4.00000			0.328798
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	1.50000	+	2.59808i	0.122474	+	0.212132i
$151$	1.50000	+	2.59808i	0.122068	+	0.211428i	0.920583	−	0.390547i	$-0.127714\pi$
$151$	1.50000	+	2.59808i	0.122068	+	0.211428i	−0.798515	+	0.601975i	$0.794381\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$	2.50000	−	0.866025i	0.201456	−	0.0697863i
$155$	8.00000			0.642575
$156$	10.5000	−	18.1865i	0.840673	−	1.45609i
$157$	−8.00000	−	13.8564i	−0.638470	−	1.10586i	−0.985769	−	0.168107i	$-0.946235\pi$
$157$	−8.00000	−	13.8564i	−0.638470	−	1.10586i	0.347299	−	0.937754i	$-0.387099\pi$
$158$	−4.50000	−	7.79423i	−0.358001	−	0.620076i
$159$	9.00000	−	15.5885i	0.713746	−	1.23625i
$160$	2.00000			0.158114
$161$	−4.00000	+	20.7846i	−0.315244	+	1.63806i
$162$	9.00000			0.707107
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	0.979076	−	0.203497i	$-0.0652307\pi$
$164$	−2.00000	−	3.46410i	−0.156174	−	0.270501i
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	19.0000			1.47026			0.735132	−	0.677924i	$-0.237120\pi$
$167$	19.0000			1.47026			0.735132	+	0.677924i	$0.237120\pi$
$168$	6.00000	+	5.19615i	0.462910	+	0.400892i
$169$	36.0000			2.76923
$170$	−2.00000	+	3.46410i	−0.153393	+	0.265684i
$171$		0			0
$172$	4.00000	+	6.92820i	0.304997	+	0.528271i
$173$	−12.5000	+	21.6506i	−0.950357	+	1.64607i	−0.205706	+	0.978614i	$0.565949\pi$
$173$	−12.5000	+	21.6506i	−0.950357	+	1.64607i	−0.744652	+	0.667453i	$0.767384\pi$
$174$	−15.0000			−1.13715
$175$	−2.00000	−	1.73205i	−0.151186	−	0.130931i
$176$	−1.00000			−0.0753778
$177$	−4.50000	+	7.79423i	−0.338241	+	0.585850i
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−9.50000	−	16.4545i	−0.710063	−	1.22987i	−0.964833	−	0.262864i	$-0.915333\pi$
$179$	−9.50000	−	16.4545i	−0.710063	−	1.22987i	0.254770	−	0.967002i	$-0.418000\pi$
$180$	−6.00000	+	10.3923i	−0.447214	+	0.774597i
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$	−3.50000	+	18.1865i	−0.259437	+	1.34808i
$183$	3.00000			0.221766
$184$	4.00000	−	6.92820i	0.294884	−	0.510754i
$185$	−4.00000	−	6.92820i	−0.294086	−	0.509372i
$186$	−6.00000	−	10.3923i	−0.439941	−	0.762001i
$187$	1.00000	−	1.73205i	0.0731272	−	0.126660i
$188$	2.00000			0.145865
$189$	−22.5000	+	7.79423i	−1.63663	+	0.566947i
$190$		0			0
$191$	−1.00000	+	1.73205i	−0.0723575	+	0.125327i	−0.899934	−	0.436026i	$-0.856386\pi$
$191$	−1.00000	+	1.73205i	−0.0723575	+	0.125327i	0.827577	+	0.561353i	$0.189719\pi$
$192$	−1.50000	−	2.59808i	−0.108253	−	0.187500i
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	0.685388	−	0.728178i	$-0.259632\pi$
$193$	−4.00000	−	6.92820i	−0.287926	−	0.498703i	−0.973315	+	0.229475i	$0.926299\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$	−42.0000			−3.00768
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	15.0000			1.06871			0.534353	−	0.845262i	$-0.320555\pi$
$197$	15.0000			1.06871			0.534353	+	0.845262i	$0.320555\pi$
$198$	3.00000	−	5.19615i	0.213201	−	0.369274i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−13.5000	+	23.3827i	−0.952217	+	1.64929i
$202$	−9.00000			−0.633238
$203$	12.5000	−	4.33013i	0.877328	−	0.303915i
$204$	6.00000			0.420084
$205$	−4.00000	+	6.92820i	−0.279372	+	0.483887i
$206$	−9.00000	−	15.5885i	−0.627060	−	1.08610i
$207$	24.0000	+	41.5692i	1.66812	+	2.88926i
$208$	3.50000	−	6.06218i	0.242681	−	0.420336i
$209$		0			0
$210$	3.00000	−	15.5885i	0.207020	−	1.07571i
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$	−1.00000	−	1.73205i	−0.0683586	−	0.118401i
$215$	8.00000	−	13.8564i	0.545595	−	0.944999i
$216$	9.00000			0.612372
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$	−2.00000			−0.135457
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$	1.00000	+	1.73205i	0.0674200	+	0.116775i
$221$	7.00000	+	12.1244i	0.470871	+	0.815572i
$222$	−6.00000	+	10.3923i	−0.402694	+	0.697486i
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$	−6.00000			−0.400000
$226$	−2.50000	+	4.33013i	−0.166298	+	0.288036i
$227$	1.00000	+	1.73205i	0.0663723	+	0.114960i	0.897302	−	0.441417i	$-0.145524\pi$
$227$	1.00000	+	1.73205i	0.0663723	+	0.114960i	−0.830930	+	0.556378i	$0.812191\pi$
$228$		0			0
$229$	14.0000	−	24.2487i	0.925146	−	1.60240i	0.133820	−	0.991006i	$-0.457276\pi$
$229$	14.0000	−	24.2487i	0.925146	−	1.60240i	0.791326	−	0.611394i	$-0.209391\pi$
$230$	−16.0000			−1.05501
$231$	−1.50000	+	7.79423i	−0.0986928	+	0.512823i
$232$	−5.00000			−0.328266
$233$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$233$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$234$	21.0000	+	36.3731i	1.37281	+	2.37778i
$235$	−2.00000	−	3.46410i	−0.130466	−	0.225973i
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	27.0000			1.75384
$238$	−5.00000	+	1.73205i	−0.324102	+	0.112272i
$239$	−5.00000			−0.323423			−0.161712	−	0.986838i	$-0.551701\pi$
$239$	−5.00000			−0.323423			−0.161712	+	0.986838i	$0.551701\pi$
$240$	−3.00000	+	5.19615i	−0.193649	+	0.335410i
$241$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$241$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$		0			0
$244$	1.00000			0.0640184
$245$	2.00000	+	13.8564i	0.127775	+	0.885253i
$246$	12.0000			0.765092
$247$		0			0
$248$	−2.00000	−	3.46410i	−0.127000	−	0.219971i
$249$	−9.00000	−	15.5885i	−0.570352	−	0.987878i
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$	−15.0000	+	5.19615i	−0.944911	+	0.327327i
$253$	8.00000			0.502956
$254$	9.50000	−	16.4545i	0.596083	−	1.03245i
$255$	−6.00000	−	10.3923i	−0.375735	−	0.650791i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$	−24.0000			−1.49417
$259$	2.00000	−	10.3923i	0.124274	−	0.645746i
$260$	−14.0000			−0.868243
$261$	15.0000	−	25.9808i	0.928477	−	1.60817i
$262$		0			0
$263$	−13.5000	−	23.3827i	−0.832446	−	1.44184i	−0.896093	−	0.443866i	$-0.853607\pi$
$263$	−13.5000	−	23.3827i	−0.832446	−	1.44184i	0.0636476	−	0.997972i	$-0.479727\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$	−12.0000			−0.737154
$266$		0			0
$267$	18.0000			1.10158
$268$	−4.50000	+	7.79423i	−0.274881	+	0.476108i
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	0.956176	+	0.292791i	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$	−9.00000	−	15.5885i	−0.547723	−	0.948683i
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	−0.649211	−	0.760609i	$-0.724901\pi$
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	0.983312	+	0.181928i	$0.0582339\pi$
$272$	2.00000			0.121268
$273$	−42.0000	−	36.3731i	−2.54196	−	2.20140i
$274$	3.00000			0.181237
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	12.0000	+	20.7846i	0.722315	+	1.25109i
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	0.968959	−	0.247222i	$-0.0795177\pi$
$277$	4.50000	+	7.79423i	0.270379	+	0.468310i	−0.698580	+	0.715532i	$0.746184\pi$
$278$	2.00000	−	3.46410i	0.119952	−	0.207763i
$279$	24.0000			1.43684
$280$	1.00000	−	5.19615i	0.0597614	−	0.310530i
$281$	−28.0000			−1.67034			−0.835170	−	0.549992i	$-0.814631\pi$
$281$	−28.0000			−1.67034			−0.835170	+	0.549992i	$0.814631\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$	1.00000	+	1.73205i	0.0593391	+	0.102778i
$285$		0			0
$286$	7.00000			0.413919
$287$	−10.0000	+	3.46410i	−0.590281	+	0.204479i
$288$	6.00000			0.353553
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	5.00000	+	8.66025i	0.293610	+	0.508548i
$291$	−10.5000	−	18.1865i	−0.615521	−	1.06611i
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	−18.0000			−1.05157			−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000			−1.05157			−0.525786	+	0.850617i	$0.676229\pi$
$294$	16.5000	−	12.9904i	0.962300	−	0.757614i
$295$	6.00000			0.349334
$296$	−2.00000	+	3.46410i	−0.116248	+	0.201347i
$297$	4.50000	+	7.79423i	0.261116	+	0.452267i
$298$	5.00000	+	8.66025i	0.289642	+	0.501675i
$299$	−28.0000	+	48.4974i	−1.61928	+	2.80468i
$300$	−3.00000			−0.173205
$301$	20.0000	−	6.92820i	1.15278	−	0.399335i
$302$	−3.00000			−0.172631
$303$	13.5000	−	23.3827i	0.775555	−	1.34330i
$304$		0			0
$305$	−1.00000	−	1.73205i	−0.0572598	−	0.0991769i
$306$	−6.00000	+	10.3923i	−0.342997	+	0.594089i
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	−0.500000	+	2.59808i	−0.0284901	+	0.148039i
$309$	54.0000			3.07195
$310$	−4.00000	+	6.92820i	−0.227185	+	0.393496i
$311$	5.00000	+	8.66025i	0.283524	+	0.491078i	0.972250	−	0.233944i	$-0.0751631\pi$
$311$	5.00000	+	8.66025i	0.283524	+	0.491078i	−0.688726	+	0.725022i	$0.741830\pi$
$312$	10.5000	+	18.1865i	0.594445	+	1.02961i
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$	16.0000			0.902932
$315$	24.0000	+	20.7846i	1.35225	+	1.17108i
$316$	9.00000			0.506290
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	−0.646872	−	0.762598i	$-0.723923\pi$
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	0.983866	+	0.178908i	$0.0572566\pi$
$318$	9.00000	+	15.5885i	0.504695	+	0.874157i
$319$	−2.50000	−	4.33013i	−0.139973	−	0.242441i
$320$	−1.00000	+	1.73205i	−0.0559017	+	0.0968246i
$321$	6.00000			0.334887
$322$	−16.0000	−	13.8564i	−0.891645	−	0.772187i
$323$		0			0
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−3.50000	−	6.06218i	−0.194145	−	0.336269i
$326$	8.50000	+	14.7224i	0.470771	+	0.815400i
$327$	3.00000	−	5.19615i	0.165900	−	0.287348i
$328$	4.00000			0.220863
$329$	1.00000	−	5.19615i	0.0551318	−	0.286473i
$330$	−6.00000			−0.330289
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	−0.987504	−	0.157593i	$-0.949627\pi$
$331$	−6.50000	+	11.2583i	−0.357272	+	0.618814i	0.630232	+	0.776407i	$0.282960\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	−12.0000	−	20.7846i	−0.657596	−	1.13899i
$334$	−9.50000	+	16.4545i	−0.519817	+	0.900349i
$335$	18.0000			0.983445
$336$	−7.50000	+	2.59808i	−0.409159	+	0.141737i
$337$	−12.0000			−0.653682			−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000			−0.653682			−0.326841	+	0.945079i	$0.605984\pi$
$338$	−18.0000	+	31.1769i	−0.979071	+	1.69580i
$339$	−7.50000	−	12.9904i	−0.407344	−	0.705541i
$340$	−2.00000	−	3.46410i	−0.108465	−	0.187867i
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−8.00000			−0.431331
$345$	24.0000	−	41.5692i	1.29212	−	2.23801i
$346$	−12.5000	−	21.6506i	−0.672004	−	1.16395i
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	0.994164	+	0.107883i	$0.0344071\pi$
$347$	11.0000	+	19.0526i	0.590511	+	1.02279i	−0.403653	+	0.914912i	$0.632260\pi$
$348$	7.50000	−	12.9904i	0.402042	−	0.696358i
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$	2.50000	−	0.866025i	0.133631	−	0.0462910i
$351$	−63.0000			−3.36269
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$	−4.50000	−	7.79423i	−0.239172	−	0.414259i
$355$	2.00000	−	3.46410i	0.106149	−	0.183855i
$356$	6.00000			0.317999
$357$	3.00000	−	15.5885i	0.158777	−	0.825029i
$358$	19.0000			1.00418
$359$	9.50000	−	16.4545i	0.501391	−	0.868434i	−0.498608	−	0.866828i	$-0.666155\pi$
$359$	9.50000	−	16.4545i	0.501391	−	0.868434i	0.999999	−	0.00160673i	$-0.000511438\pi$
$360$	−6.00000	−	10.3923i	−0.316228	−	0.547723i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	11.0000	−	19.0526i	0.578147	−	1.00138i
$363$	3.00000			0.157459
$364$	−14.0000	−	12.1244i	−0.733799	−	0.635489i
$365$	8.00000			0.418739
$366$	−1.50000	+	2.59808i	−0.0784063	+	0.135804i
$367$	−2.00000	−	3.46410i	−0.104399	−	0.180825i	0.809093	−	0.587680i	$-0.199959\pi$
$367$	−2.00000	−	3.46410i	−0.104399	−	0.180825i	−0.913493	+	0.406855i	$0.866625\pi$
$368$	4.00000	+	6.92820i	0.208514	+	0.361158i
$369$	−12.0000	+	20.7846i	−0.624695	+	1.08200i
$370$	8.00000			0.415900
$371$	−12.0000	−	10.3923i	−0.623009	−	0.539542i
$372$	12.0000			0.622171
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	−0.972556	−	0.232671i	$-0.925254\pi$
$373$	−5.50000	+	9.52628i	−0.284779	+	0.493252i	0.687776	+	0.725923i	$0.258587\pi$
$374$	1.00000	+	1.73205i	0.0517088	+	0.0895622i
$375$	18.0000	+	31.1769i	0.929516	+	1.60997i
$376$	−1.00000	+	1.73205i	−0.0515711	+	0.0893237i
$377$	35.0000			1.80259
$378$	4.50000	−	23.3827i	0.231455	−	1.20268i
$379$	1.00000			0.0513665			0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000			0.0513665			0.0256833	+	0.999670i	$0.491824\pi$
$380$		0			0
$381$	28.5000	+	49.3634i	1.46010	+	2.52897i
$382$	−1.00000	−	1.73205i	−0.0511645	−	0.0886194i
$383$	−13.0000	+	22.5167i	−0.664269	+	1.15055i	0.315214	+	0.949021i	$0.397924\pi$
$383$	−13.0000	+	22.5167i	−0.664269	+	1.15055i	−0.979483	+	0.201527i	$0.935410\pi$
$384$	3.00000			0.153093
$385$	5.00000	−	1.73205i	0.254824	−	0.0882735i
$386$	8.00000			0.407189
$387$	24.0000	−	41.5692i	1.21999	−	2.11308i
$388$	−3.50000	−	6.06218i	−0.177686	−	0.307760i
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$	21.0000	−	36.3731i	1.06338	−	1.84182i
$391$	−16.0000			−0.809155
$392$	5.50000	−	4.33013i	0.277792	−	0.218704i
$393$		0			0
$394$	−7.50000	+	12.9904i	−0.377845	+	0.654446i
$395$	−9.00000	−	15.5885i	−0.452839	−	0.784340i
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	−3.00000	+	5.19615i	−0.150566	+	0.260787i	−0.931436	−	0.363906i	$-0.881443\pi$
$397$	−3.00000	+	5.19615i	−0.150566	+	0.260787i	0.780870	+	0.624694i	$0.214776\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	−0.731516	−	0.681824i	$-0.761187\pi$
$401$	4.50000	−	7.79423i	0.224719	−	0.389225i	0.956235	+	0.292599i	$0.0945202\pi$
$402$	−13.5000	−	23.3827i	−0.673319	−	1.16622i
$403$	14.0000	+	24.2487i	0.697390	+	1.20791i
$404$	4.50000	−	7.79423i	0.223883	−	0.387777i
$405$	18.0000			0.894427
$406$	−2.50000	+	12.9904i	−0.124073	+	0.644702i
$407$	−4.00000			−0.198273
$408$	−3.00000	+	5.19615i	−0.148522	+	0.257248i
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	−0.998674	−	0.0514740i	$-0.983608\pi$
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	0.454759	−	0.890614i	$-0.349725\pi$
$410$	−4.00000	−	6.92820i	−0.197546	−	0.342160i
$411$	−4.50000	+	7.79423i	−0.221969	+	0.384461i
$412$	18.0000			0.886796
$413$	6.00000	+	5.19615i	0.295241	+	0.255686i
$414$	−48.0000			−2.35907
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	3.50000	+	6.06218i	0.171602	+	0.297223i
$417$	6.00000	+	10.3923i	0.293821	+	0.508913i
$418$		0			0
$419$	16.0000			0.781651			0.390826	−	0.920465i	$-0.372190\pi$
$419$	16.0000			0.781651			0.390826	+	0.920465i	$0.372190\pi$
$420$	12.0000	+	10.3923i	0.585540	+	0.507093i
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$	10.0000	−	17.3205i	0.486792	−	0.843149i
$423$	−6.00000	−	10.3923i	−0.291730	−	0.505291i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$	−6.00000			−0.290701
$427$	0.500000	−	2.59808i	0.0241967	−	0.125730i
$428$	2.00000			0.0966736
$429$	−10.5000	+	18.1865i	−0.506945	+	0.878054i
$430$	8.00000	+	13.8564i	0.385794	+	0.668215i
$431$	−12.5000	−	21.6506i	−0.602104	−	1.04287i	−0.992502	−	0.122228i	$-0.960996\pi$
$431$	−12.5000	−	21.6506i	−0.602104	−	1.04287i	0.390398	−	0.920646i	$-0.372337\pi$
$432$	−4.50000	+	7.79423i	−0.216506	+	0.375000i
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$	−10.0000	+	3.46410i	−0.480015	+	0.166282i
$435$	−30.0000			−1.43839
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$		0			0
$438$	−6.00000	−	10.3923i	−0.286691	−	0.496564i
$439$	2.50000	−	4.33013i	0.119318	−	0.206666i	−0.800179	−	0.599761i	$-0.795262\pi$
$439$	2.50000	−	4.33013i	0.119318	−	0.206666i	0.919498	+	0.393095i	$0.128596\pi$
$440$	−2.00000			−0.0953463
$441$	6.00000	+	41.5692i	0.285714	+	1.97949i
$442$	−14.0000			−0.665912
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	0.0212481	+	0.999774i	$0.493236\pi$
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	−0.876454	+	0.481486i	$0.840097\pi$
$444$	−6.00000	−	10.3923i	−0.284747	−	0.493197i
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	−2.00000	+	3.46410i	−0.0947027	+	0.164030i
$447$	−30.0000			−1.41895
$448$	−2.50000	+	0.866025i	−0.118114	+	0.0409159i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	3.00000	−	5.19615i	0.141421	−	0.244949i
$451$	2.00000	+	3.46410i	0.0941763	+	0.163118i
$452$	−2.50000	−	4.33013i	−0.117590	−	0.203672i
$453$	4.50000	−	7.79423i	0.211428	−	0.366205i
$454$	−2.00000			−0.0938647
$455$	−7.00000	+	36.3731i	−0.328165	+	1.70520i
$456$		0			0
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	−0.982004	−	0.188858i	$-0.939521\pi$
$457$	−7.00000	+	12.1244i	−0.327446	+	0.567153i	0.654558	+	0.756012i	$0.272855\pi$
$458$	14.0000	+	24.2487i	0.654177	+	1.13307i
$459$	−9.00000	−	15.5885i	−0.420084	−	0.727607i
$460$	8.00000	−	13.8564i	0.373002	−	0.646058i
$461$	27.0000			1.25752			0.628758	−	0.777601i	$-0.283564\pi$
$461$	27.0000			1.25752			0.628758	+	0.777601i	$0.283564\pi$
$462$	−6.00000	−	5.19615i	−0.279145	−	0.241747i
$463$	−2.00000			−0.0929479			−0.0464739	−	0.998920i	$-0.514798\pi$
$463$	−2.00000			−0.0929479			−0.0464739	+	0.998920i	$0.514798\pi$
$464$	2.50000	−	4.33013i	0.116060	−	0.201021i
$465$	−12.0000	−	20.7846i	−0.556487	−	0.963863i
$466$		0			0
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$	−42.0000			−1.94145
$469$	18.0000	+	15.5885i	0.831163	+	0.719808i
$470$	4.00000			0.184506
$471$	−24.0000	+	41.5692i	−1.10586	+	1.91541i
$472$	−1.50000	−	2.59808i	−0.0690431	−	0.119586i
$473$	−4.00000	−	6.92820i	−0.183920	−	0.318559i
$474$	−13.5000	+	23.3827i	−0.620076	+	1.07400i
$475$		0			0
$476$	1.00000	−	5.19615i	0.0458349	−	0.238165i
$477$	−36.0000			−1.64833
$478$	2.50000	−	4.33013i	0.114347	−	0.198055i
$479$	0.500000	+	0.866025i	0.0228456	+	0.0395697i	0.877222	−	0.480085i	$-0.159394\pi$
$479$	0.500000	+	0.866025i	0.0228456	+	0.0395697i	−0.854377	+	0.519654i	$0.826061\pi$
$480$	−3.00000	−	5.19615i	−0.136931	−	0.237171i
$481$	14.0000	−	24.2487i	0.638345	−	1.10565i
$482$		0			0
$483$	60.0000	−	20.7846i	2.73009	−	0.945732i
$484$	1.00000			0.0454545
$485$	−7.00000	+	12.1244i	−0.317854	+	0.550539i
$486$		0			0
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.819181	+	0.573535i	$0.194428\pi$
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.0871056	+	0.996199i	$0.472238\pi$
$488$	−0.500000	+	0.866025i	−0.0226339	+	0.0392031i
$489$	−51.0000			−2.30630
$490$	−13.0000	−	5.19615i	−0.587280	−	0.234738i
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$	5.00000	+	8.66025i	0.225189	+	0.390038i
$494$		0			0
$495$	6.00000	−	10.3923i	0.269680	−	0.467099i
$496$	4.00000			0.179605
$497$	5.00000	−	1.73205i	0.224281	−	0.0776931i
$498$	18.0000			0.806599
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	−0.998233	−	0.0594153i	$-0.981076\pi$
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	0.550572	+	0.834788i	$0.314410\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$	−28.5000	−	49.3634i	−1.27329	−	2.20540i
$502$	12.0000	−	20.7846i	0.535586	−	0.927663i
$503$	3.00000			0.133763			0.0668817	−	0.997761i	$-0.478695\pi$
$503$	3.00000			0.133763			0.0668817	+	0.997761i	$0.478695\pi$
$504$	3.00000	−	15.5885i	0.133631	−	0.694365i
$505$	−18.0000			−0.800989
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$	−54.0000	−	93.5307i	−2.39822	−	4.15385i
$508$	9.50000	+	16.4545i	0.421494	+	0.730050i
$509$	11.0000	−	19.0526i	0.487566	−	0.844490i	−0.512331	−	0.858788i	$-0.671218\pi$
$509$	11.0000	−	19.0526i	0.487566	−	0.844490i	0.999898	+	0.0142980i	$0.00455136\pi$
$510$	12.0000			0.531369
$511$	8.00000	+	6.92820i	0.353899	+	0.306486i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−1.50000	−	2.59808i	−0.0661622	−	0.114596i
$515$	−18.0000	−	31.1769i	−0.793175	−	1.37382i
$516$	12.0000	−	20.7846i	0.528271	−	0.914991i
$517$	−2.00000			−0.0879599
$518$	8.00000	+	6.92820i	0.351500	+	0.304408i
$519$	75.0000			3.29213
$520$	7.00000	−	12.1244i	0.306970	−	0.531688i
$521$	−5.00000	−	8.66025i	−0.219054	−	0.379413i	0.735465	−	0.677563i	$-0.236964\pi$
$521$	−5.00000	−	8.66025i	−0.219054	−	0.379413i	−0.954519	+	0.298150i	$0.903630\pi$
$522$	15.0000	+	25.9808i	0.656532	+	1.13715i
$523$	5.00000	−	8.66025i	0.218635	−	0.378686i	−0.735756	−	0.677247i	$-0.763173\pi$
$523$	5.00000	−	8.66025i	0.218635	−	0.378686i	0.954391	+	0.298560i	$0.0965063\pi$
$524$		0			0
$525$	−1.50000	+	7.79423i	−0.0654654	+	0.340168i
$526$	27.0000			1.17726
$527$	−4.00000	+	6.92820i	−0.174243	+	0.301797i
$528$	1.50000	+	2.59808i	0.0652791	+	0.113067i
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	6.00000	−	10.3923i	0.260623	−	0.451413i
$531$	18.0000			0.781133
$532$		0			0
$533$	−28.0000			−1.21281
$534$	−9.00000	+	15.5885i	−0.389468	+	0.674579i
$535$	−2.00000	−	3.46410i	−0.0864675	−	0.149766i
$536$	−4.50000	−	7.79423i	−0.194370	−	0.336659i
$537$	−28.5000	+	49.3634i	−1.22987	+	2.13019i
$538$	−24.0000			−1.03471
$539$	6.50000	+	2.59808i	0.279975	+	0.111907i
$540$	18.0000			0.774597
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	−0.914750	−	0.404020i	$-0.867613\pi$
$541$	−2.50000	+	4.33013i	−0.107483	+	0.186167i	0.807267	+	0.590187i	$0.200946\pi$
$542$	5.50000	+	9.52628i	0.236245	+	0.409189i
$543$	33.0000	+	57.1577i	1.41617	+	2.45287i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	−4.00000			−0.171341
$546$	52.5000	−	18.1865i	2.24679	−	0.778312i
$547$	30.0000			1.28271			0.641354	−	0.767245i	$-0.278373\pi$
$547$	30.0000			1.28271			0.641354	+	0.767245i	$0.278373\pi$
$548$	−1.50000	+	2.59808i	−0.0640768	+	0.110984i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$		0			0
$552$	−24.0000			−1.02151
$553$	4.50000	−	23.3827i	0.191359	−	0.994333i
$554$	−9.00000			−0.382373
$555$	−12.0000	+	20.7846i	−0.509372	+	0.882258i
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	−13.0000	−	22.5167i	−0.550828	−	0.954062i	−0.998215	−	0.0597213i	$-0.980979\pi$
$557$	−13.0000	−	22.5167i	−0.550828	−	0.954062i	0.447387	−	0.894340i	$-0.352355\pi$
$558$	−12.0000	+	20.7846i	−0.508001	+	0.879883i
$559$	56.0000			2.36855
$560$	4.00000	+	3.46410i	0.169031	+	0.146385i
$561$	−6.00000			−0.253320
$562$	14.0000	−	24.2487i	0.590554	−	1.02287i
$563$	−10.0000	−	17.3205i	−0.421450	−	0.729972i	0.574632	−	0.818412i	$-0.305145\pi$
$563$	−10.0000	−	17.3205i	−0.421450	−	0.729972i	−0.996082	+	0.0884397i	$0.971812\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$	−5.00000	+	8.66025i	−0.210352	+	0.364340i
$566$		0			0
$567$	18.0000	+	15.5885i	0.755929	+	0.654654i
$568$	−2.00000			−0.0839181
$569$	6.00000	−	10.3923i	0.251533	−	0.435668i	−0.712415	−	0.701758i	$-0.752399\pi$
$569$	6.00000	−	10.3923i	0.251533	−	0.435668i	0.963948	+	0.266090i	$0.0857319\pi$
$570$		0			0
$571$	−11.0000	−	19.0526i	−0.460336	−	0.797325i	0.538642	−	0.842535i	$-0.318938\pi$
$571$	−11.0000	−	19.0526i	−0.460336	−	0.797325i	−0.998978	+	0.0452101i	$0.985604\pi$
$572$	−3.50000	+	6.06218i	−0.146342	+	0.253472i
$573$	6.00000			0.250654
$574$	2.00000	−	10.3923i	0.0834784	−	0.433766i
$575$	8.00000			0.333623
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	21.5000	+	37.2391i	0.895057	+	1.55028i	0.833734	+	0.552166i	$0.186198\pi$
$577$	21.5000	+	37.2391i	0.895057	+	1.55028i	0.0613223	+	0.998118i	$0.480468\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	−12.0000	+	20.7846i	−0.498703	+	0.863779i
$580$	−10.0000			−0.415227
$581$	−15.0000	+	5.19615i	−0.622305	+	0.215573i
$582$	21.0000			0.870478
$583$	−3.00000	+	5.19615i	−0.124247	+	0.215203i
$584$	−2.00000	−	3.46410i	−0.0827606	−	0.143346i
$585$	42.0000	+	72.7461i	1.73649	+	3.00768i
$586$	9.00000	−	15.5885i	0.371787	−	0.643953i
$587$	27.0000			1.11441			0.557205	−	0.830375i	$-0.311874\pi$
$587$	27.0000			1.11441			0.557205	+	0.830375i	$0.311874\pi$
$588$	3.00000	+	20.7846i	0.123718	+	0.857143i
$589$		0			0
$590$	−3.00000	+	5.19615i	−0.123508	+	0.213922i
$591$	−22.5000	−	38.9711i	−0.925526	−	1.60306i
$592$	−2.00000	−	3.46410i	−0.0821995	−	0.142374i
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	−0.921026	−	0.389501i	$-0.872647\pi$
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	0.797831	+	0.602881i	$0.205981\pi$
$594$	−9.00000			−0.369274
$595$	−10.0000	+	3.46410i	−0.409960	+	0.142014i
$596$	−10.0000			−0.409616
$597$	−6.00000	+	10.3923i	−0.245564	+	0.425329i
$598$	−28.0000	−	48.4974i	−1.14501	−	1.98321i
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	−0.954521	−	0.298143i	$-0.903633\pi$
$599$	−18.0000	−	31.1769i	−0.735460	−	1.27385i	0.219061	−	0.975711i	$-0.429701\pi$
$600$	1.50000	−	2.59808i	0.0612372	−	0.106066i
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	−4.00000	+	20.7846i	−0.163028	+	0.847117i
$603$	54.0000			2.19905
$604$	1.50000	−	2.59808i	0.0610341	−	0.105714i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$	13.5000	+	23.3827i	0.548400	+	0.949857i
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	−0.935713	−	0.352763i	$-0.885242\pi$
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	0.773358	+	0.633970i	$0.218576\pi$
$608$		0			0
$609$	−30.0000	−	25.9808i	−1.21566	−	1.05279i
$610$	2.00000			0.0809776
$611$	7.00000	−	12.1244i	0.283190	−	0.490499i
$612$	−6.00000	−	10.3923i	−0.242536	−	0.420084i
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	0.938967	+	0.344008i	$0.111785\pi$
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	−0.171564	+	0.985173i	$0.554882\pi$
$614$	−1.00000	+	1.73205i	−0.0403567	+	0.0698999i
$615$	24.0000			0.967773
$616$	−2.00000	−	1.73205i	−0.0805823	−	0.0697863i
$617$	−15.0000			−0.603877			−0.301939	−	0.953327i	$-0.597634\pi$
$617$	−15.0000			−0.603877			−0.301939	+	0.953327i	$0.597634\pi$
$618$	−27.0000	+	46.7654i	−1.08610	+	1.88118i
$619$	14.0000	+	24.2487i	0.562708	+	0.974638i	0.997259	+	0.0739910i	$0.0235736\pi$
$619$	14.0000	+	24.2487i	0.562708	+	0.974638i	−0.434551	+	0.900647i	$0.643093\pi$
$620$	−4.00000	−	6.92820i	−0.160644	−	0.278243i
$621$	36.0000	−	62.3538i	1.44463	−	2.50217i
$622$	−10.0000			−0.400963
$623$	3.00000	−	15.5885i	0.120192	−	0.624538i
$624$	−21.0000			−0.840673
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	−0.500000	−	0.866025i	−0.0199840	−	0.0346133i
$627$		0			0
$628$	−8.00000	+	13.8564i	−0.319235	+	0.552931i
$629$	8.00000			0.318981
$630$	−30.0000	+	10.3923i	−1.19523	+	0.414039i
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$	−4.50000	+	7.79423i	−0.179000	+	0.310038i
$633$	30.0000	+	51.9615i	1.19239	+	2.06529i
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$	19.0000	−	32.9090i	0.753992	−	1.30595i
$636$	−18.0000			−0.713746
$637$	−38.5000	+	30.3109i	−1.52543	+	1.20096i
$638$	5.00000			0.197952
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$	−1.00000	−	1.73205i	−0.0395285	−	0.0684653i
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	0.999247	+	0.0387913i	$0.0123508\pi$
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	−0.466029	+	0.884769i	$0.654316\pi$
$642$	−3.00000	+	5.19615i	−0.118401	+	0.205076i
$643$	31.0000			1.22252			0.611260	−	0.791430i	$-0.290663\pi$
$643$	31.0000			1.22252			0.611260	+	0.791430i	$0.290663\pi$
$644$	20.0000	−	6.92820i	0.788110	−	0.273009i
$645$	−48.0000			−1.89000
$646$		0			0
$647$	−15.0000	−	25.9808i	−0.589711	−	1.02141i	−0.994270	−	0.106897i	$-0.965908\pi$
$647$	−15.0000	−	25.9808i	−0.589711	−	1.02141i	0.404559	−	0.914512i	$-0.367425\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	1.50000	−	2.59808i	0.0588802	−	0.101983i
$650$	7.00000			0.274563
$651$	6.00000	−	31.1769i	0.235159	−	1.22192i
$652$	−17.0000			−0.665771
$653$	−20.0000	+	34.6410i	−0.782660	+	1.35561i	0.147726	+	0.989028i	$0.452805\pi$
$653$	−20.0000	+	34.6410i	−0.782660	+	1.35561i	−0.930387	+	0.366579i	$0.880529\pi$
$654$	3.00000	+	5.19615i	0.117309	+	0.203186i
$655$		0			0
$656$	−2.00000	+	3.46410i	−0.0780869	+	0.135250i
$657$	24.0000			0.936329
$658$	4.00000	+	3.46410i	0.155936	+	0.135045i
$659$	28.0000			1.09073			0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000			1.09073			0.545363	+	0.838200i	$0.316392\pi$
$660$	3.00000	−	5.19615i	0.116775	−	0.202260i
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	−6.50000	−	11.2583i	−0.252630	−	0.437567i
$663$	21.0000	−	36.3731i	0.815572	−	1.41261i
$664$	6.00000			0.232845
$665$		0			0
$666$	24.0000			0.929981
$667$	−20.0000	+	34.6410i	−0.774403	+	1.34131i
$668$	−9.50000	−	16.4545i	−0.367566	−	0.636643i
$669$	−6.00000	−	10.3923i	−0.231973	−	0.401790i
$670$	−9.00000	+	15.5885i	−0.347700	+	0.602235i
$671$	−1.00000			−0.0386046
$672$	1.50000	−	7.79423i	0.0578638	−	0.300669i
$673$	34.0000			1.31060			0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000			1.31060			0.655302	+	0.755367i	$0.272541\pi$
$674$	6.00000	−	10.3923i	0.231111	−	0.400297i
$675$	4.50000	+	7.79423i	0.173205	+	0.300000i
$676$	−18.0000	−	31.1769i	−0.692308	−	1.19911i
$677$	−7.00000	+	12.1244i	−0.269032	+	0.465977i	−0.968612	−	0.248577i	$-0.920037\pi$
$677$	−7.00000	+	12.1244i	−0.269032	+	0.465977i	0.699580	+	0.714554i	$0.253370\pi$
$678$	15.0000			0.576072
$679$	−17.5000	+	6.06218i	−0.671588	+	0.232645i
$680$	4.00000			0.153393
$681$	3.00000	−	5.19615i	0.114960	−	0.199117i
$682$	2.00000	+	3.46410i	0.0765840	+	0.132647i
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	0.592168	−	0.805814i	$-0.298272\pi$
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	−0.993940	+	0.109926i	$0.964939\pi$
$684$		0			0
$685$	6.00000			0.229248
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$	−84.0000			−3.20480
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	−21.0000	−	36.3731i	−0.800036	−	1.38570i
$690$	24.0000	+	41.5692i	0.913664	+	1.58251i
$691$	−16.5000	+	28.5788i	−0.627690	+	1.08719i	0.360325	+	0.932827i	$0.382666\pi$
$691$	−16.5000	+	28.5788i	−0.627690	+	1.08719i	−0.988014	+	0.154363i	$0.950667\pi$
$692$	25.0000			0.950357
$693$	15.0000	−	5.19615i	0.569803	−	0.197386i
$694$	−22.0000			−0.835109
$695$	4.00000	−	6.92820i	0.151729	−	0.262802i
$696$	7.50000	+	12.9904i	0.284287	+	0.492399i
$697$	−4.00000	−	6.92820i	−0.151511	−	0.262424i
$698$	−1.00000	+	1.73205i	−0.0378506	+	0.0655591i
$699$		0			0
$700$	−0.500000	+	2.59808i	−0.0188982	+	0.0981981i
$701$	−27.0000			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$702$	31.5000	−	54.5596i	1.18889	−	2.05922i
$703$		0			0
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−6.00000	+	10.3923i	−0.225973	+	0.391397i
$706$	−18.0000			−0.677439
$707$	−18.0000	−	15.5885i	−0.676960	−	0.586264i
$708$	9.00000			0.338241
$709$	24.0000	−	41.5692i	0.901339	−	1.56116i	0.0755813	−	0.997140i	$-0.475919\pi$
$709$	24.0000	−	41.5692i	0.901339	−	1.56116i	0.825758	−	0.564025i	$-0.190748\pi$
$710$	2.00000	+	3.46410i	0.0750587	+	0.130005i
$711$	−27.0000	−	46.7654i	−1.01258	−	1.75384i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$	−32.0000			−1.19841
$714$	12.0000	+	10.3923i	0.449089	+	0.388922i
$715$	14.0000			0.523570
$716$	−9.50000	+	16.4545i	−0.355032	+	0.614933i
$717$	7.50000	+	12.9904i	0.280093	+	0.485135i
$718$	9.50000	+	16.4545i	0.354537	+	0.614076i
$719$	19.0000	−	32.9090i	0.708580	−	1.22730i	−0.256803	−	0.966464i	$-0.582669\pi$
$719$	19.0000	−	32.9090i	0.708580	−	1.22730i	0.965384	−	0.260834i	$-0.0839974\pi$
$720$	12.0000			0.447214
$721$	9.00000	−	46.7654i	0.335178	−	1.74163i
$722$	−19.0000			−0.707107
$723$		0			0
$724$	11.0000	+	19.0526i	0.408812	+	0.708083i
$725$	−2.50000	−	4.33013i	−0.0928477	−	0.160817i
$726$	−1.50000	+	2.59808i	−0.0556702	+	0.0964237i
$727$	−22.0000			−0.815935			−0.407967	−	0.912996i	$-0.633762\pi$
$727$	−22.0000			−0.815935			−0.407967	+	0.912996i	$0.633762\pi$
$728$	17.5000	−	6.06218i	0.648593	−	0.224679i
$729$	−27.0000			−1.00000
$730$	−4.00000	+	6.92820i	−0.148047	+	0.256424i
$731$	8.00000	+	13.8564i	0.295891	+	0.512498i
$732$	−1.50000	−	2.59808i	−0.0554416	−	0.0960277i
$733$	9.50000	−	16.4545i	0.350891	−	0.607760i	−0.635515	−	0.772088i	$-0.719212\pi$
$733$	9.50000	−	16.4545i	0.350891	−	0.607760i	0.986406	+	0.164328i	$0.0525456\pi$
$734$	4.00000			0.147643
$735$	33.0000	−	25.9808i	1.21722	−	0.958315i
$736$	−8.00000			−0.294884
$737$	4.50000	−	7.79423i	0.165760	−	0.287104i
$738$	−12.0000	−	20.7846i	−0.441726	−	0.765092i
$739$	−21.0000	−	36.3731i	−0.772497	−	1.33800i	−0.936190	−	0.351494i	$-0.885674\pi$
$739$	−21.0000	−	36.3731i	−0.772497	−	1.33800i	0.163693	−	0.986511i	$-0.447659\pi$
$740$	−4.00000	+	6.92820i	−0.147043	+	0.254686i
$741$		0			0
$742$	15.0000	−	5.19615i	0.550667	−	0.190757i
$743$	12.0000			0.440237			0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000			0.440237			0.220119	+	0.975473i	$0.429356\pi$
$744$	−6.00000	+	10.3923i	−0.219971	+	0.381000i
$745$	10.0000	+	17.3205i	0.366372	+	0.634574i
$746$	−5.50000	−	9.52628i	−0.201369	−	0.348782i
$747$	−18.0000	+	31.1769i	−0.658586	+	1.14070i
$748$	−2.00000			−0.0731272
$749$	1.00000	−	5.19615i	0.0365392	−	0.189863i
$750$	−36.0000			−1.31453
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	0.489053	+	0.872254i	$0.337342\pi$
$751$	−14.0000	+	24.2487i	−0.510867	+	0.884848i	−0.999921	+	0.0125942i	$0.995991\pi$
$752$	−1.00000	−	1.73205i	−0.0364662	−	0.0631614i
$753$	36.0000	+	62.3538i	1.31191	+	2.27230i
$754$	−17.5000	+	30.3109i	−0.637312	+	1.10386i
$755$	−6.00000			−0.218362
$756$	18.0000	+	15.5885i	0.654654	+	0.566947i
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−0.500000	+	0.866025i	−0.0181608	+	0.0314555i
$759$	−12.0000	−	20.7846i	−0.435572	−	0.754434i
$760$		0			0
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$	−57.0000			−2.06489
$763$	−4.00000	−	3.46410i	−0.144810	−	0.125409i
$764$	2.00000			0.0723575
$765$	−12.0000	+	20.7846i	−0.433861	+	0.751469i
$766$	−13.0000	−	22.5167i	−0.469709	−	0.813560i
$767$	10.5000	+	18.1865i	0.379133	+	0.656678i
$768$	−1.50000	+	2.59808i	−0.0541266	+	0.0937500i
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$	−1.00000	+	5.19615i	−0.0360375	+	0.187256i
$771$	9.00000			0.324127
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	0.565402	−	0.824815i	$-0.308721\pi$
$773$	−12.0000	−	20.7846i	−0.431610	−	0.747570i	−0.997012	+	0.0772449i	$0.975388\pi$
$774$	24.0000	+	41.5692i	0.862662	+	1.49417i
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$	7.00000			0.251285
$777$	−30.0000	+	10.3923i	−1.07624	+	0.372822i
$778$	18.0000			0.645331
$779$		0			0
$780$	21.0000	+	36.3731i	0.751921	+	1.30236i
$781$	−1.00000	−	1.73205i	−0.0357828	−	0.0619777i
$782$	8.00000	−	13.8564i	0.286079	−	0.495504i
$783$	−45.0000			−1.60817
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	32.0000			1.14213
$786$		0			0
$787$	20.0000	+	34.6410i	0.712923	+	1.23482i	0.963755	+	0.266788i	$0.0859624\pi$
$787$	20.0000	+	34.6410i	0.712923	+	1.23482i	−0.250832	+	0.968031i	$0.580704\pi$
$788$	−7.50000	−	12.9904i	−0.267176	−	0.462763i
$789$	−40.5000	+	70.1481i	−1.44184	+	2.49734i
$790$	18.0000			0.640411
$791$	−12.5000	+	4.33013i	−0.444449	+	0.153962i
$792$	−6.00000			−0.213201
$793$	3.50000	−	6.06218i	0.124289	−	0.215274i
$794$	−3.00000	−	5.19615i	−0.106466	−	0.184405i
$795$	18.0000	+	31.1769i	0.638394	+	1.10573i
$796$	−2.00000	+	3.46410i	−0.0708881	+	0.122782i
$797$	50.0000			1.77109			0.885545	−	0.464553i	$-0.153785\pi$
$797$	50.0000			1.77109			0.885545	+	0.464553i	$0.153785\pi$
$798$		0			0
$799$	4.00000			0.141510
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−18.0000	−	31.1769i	−0.635999	−	1.10158i
$802$	4.50000	+	7.79423i	0.158901	+	0.275224i
$803$	2.00000	−	3.46410i	0.0705785	−	0.122245i
$804$	27.0000			0.952217
$805$	−32.0000	−	27.7128i	−1.12785	−	0.976748i
$806$	−28.0000			−0.986258
$807$	36.0000	−	62.3538i	1.26726	−	2.19496i
$808$	4.50000	+	7.79423i	0.158309	+	0.274200i
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	0.741063	−	0.671436i	$-0.234322\pi$
$809$	−6.00000	−	10.3923i	−0.210949	−	0.365374i	−0.952012	+	0.306062i	$0.900989\pi$
$810$	−9.00000	+	15.5885i	−0.316228	+	0.547723i
$811$	8.00000			0.280918			0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000			0.280918			0.140459	+	0.990086i	$0.455142\pi$
$812$	−10.0000	−	8.66025i	−0.350931	−	0.303915i
$813$	−33.0000			−1.15736
$814$	2.00000	−	3.46410i	0.0701000	−	0.121417i
$815$	17.0000	+	29.4449i	0.595484	+	1.03141i
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$		0			0
$818$	22.0000			0.769212
$819$	−21.0000	+	109.119i	−0.733799	+	3.81293i
$820$	8.00000			0.279372
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	−0.143591	−	0.989637i	$-0.545865\pi$
$821$	22.5000	−	38.9711i	0.785255	−	1.36010i	0.928846	−	0.370465i	$-0.120802\pi$
$822$	−4.50000	−	7.79423i	−0.156956	−	0.271855i
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	0.545428	−	0.838157i	$-0.316367\pi$
$823$	−13.0000	−	22.5167i	−0.453152	−	0.784881i	−0.998580	+	0.0532760i	$0.983034\pi$
$824$	−9.00000	+	15.5885i	−0.313530	+	0.543050i
$825$	3.00000			0.104447
$826$	−7.50000	+	2.59808i	−0.260958	+	0.0903986i
$827$	−4.00000			−0.139094			−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000			−0.139094			−0.0695468	+	0.997579i	$0.522155\pi$
$828$	24.0000	−	41.5692i	0.834058	−	1.44463i
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$	−6.00000	−	10.3923i	−0.208263	−	0.360722i
$831$	13.5000	−	23.3827i	0.468310	−	0.811136i
$832$	−7.00000			−0.242681
$833$	−13.0000	−	5.19615i	−0.450423	−	0.180036i
$834$	−12.0000			−0.415526
$835$	−19.0000	+	32.9090i	−0.657522	+	1.13886i
$836$		0			0
$837$	−18.0000	−	31.1769i	−0.622171	−	1.07763i
$838$	−8.00000	+	13.8564i	−0.276355	+	0.478662i
$839$	−18.0000			−0.621429			−0.310715	−	0.950503i	$-0.600568\pi$
$839$	−18.0000			−0.621429			−0.310715	+	0.950503i	$0.600568\pi$
$840$	−15.0000	+	5.19615i	−0.517549	+	0.179284i
$841$	−4.00000			−0.137931
$842$	10.0000	−	17.3205i	0.344623	−	0.596904i
$843$	42.0000	+	72.7461i	1.44656	+	2.50551i
$844$	10.0000	+	17.3205i	0.344214	+	0.596196i
$845$	−36.0000	+	62.3538i	−1.23844	+	2.14504i
$846$	12.0000			0.412568
$847$	0.500000	−	2.59808i	0.0171802	−	0.0892710i
$848$	−6.00000			−0.206041
$849$		0			0
$850$	1.00000	+	1.73205i	0.0342997	+	0.0594089i
$851$	16.0000	+	27.7128i	0.548473	+	0.949983i
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$	2.00000	+	1.73205i	0.0684386	+	0.0592696i
$855$		0			0
$856$	−1.00000	+	1.73205i	−0.0341793	+	0.0592003i
$857$	−22.0000	−	38.1051i	−0.751506	−	1.30165i	−0.947093	−	0.320960i	$-0.895995\pi$
$857$	−22.0000	−	38.1051i	−0.751506	−	1.30165i	0.195587	−	0.980686i	$-0.437339\pi$
$858$	−10.5000	−	18.1865i	−0.358464	−	0.620878i
$859$	−6.50000	+	11.2583i	−0.221777	+	0.384129i	−0.955348	−	0.295484i	$-0.904519\pi$
$859$	−6.50000	+	11.2583i	−0.221777	+	0.384129i	0.733571	+	0.679613i	$0.237852\pi$
$860$	−16.0000			−0.545595
$861$	24.0000	+	20.7846i	0.817918	+	0.708338i
$862$	25.0000			0.851503
$863$	−2.00000	+	3.46410i	−0.0680808	+	0.117919i	−0.898056	−	0.439880i	$-0.855021\pi$
$863$	−2.00000	+	3.46410i	−0.0680808	+	0.117919i	0.829976	+	0.557800i	$0.188354\pi$
$864$	−4.50000	−	7.79423i	−0.153093	−	0.265165i
$865$	−25.0000	−	43.3013i	−0.850026	−	1.47229i
$866$	17.0000	−	29.4449i	0.577684	−	1.00058i
$867$	−39.0000			−1.32451
$868$	2.00000	−	10.3923i	0.0678844	−	0.352738i
$869$	−9.00000			−0.305304
$870$	15.0000	−	25.9808i	0.508548	−	0.880830i
$871$	31.5000	+	54.5596i	1.06734	+	1.84868i
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$	−21.0000	+	36.3731i	−0.710742	+	1.23104i
$874$		0			0
$875$	30.0000	−	10.3923i	1.01419	−	0.351324i
$876$	12.0000			0.405442
$877$	14.5000	−	25.1147i	0.489630	−	0.848064i	−0.510299	−	0.859997i	$-0.670465\pi$
$877$	14.5000	−	25.1147i	0.489630	−	0.848064i	0.999929	+	0.0119329i	$0.00379845\pi$
$878$	2.50000	+	4.33013i	0.0843709	+	0.146135i
$879$	27.0000	+	46.7654i	0.910687	+	1.57736i
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	21.0000			0.707508			0.353754	−	0.935339i	$-0.384905\pi$
$881$	21.0000			0.707508			0.353754	+	0.935339i	$0.384905\pi$
$882$	−39.0000	−	15.5885i	−1.31320	−	0.524891i
$883$	−29.0000			−0.975928			−0.487964	−	0.872864i	$-0.662260\pi$
$883$	−29.0000			−0.975928			−0.487964	+	0.872864i	$0.662260\pi$
$884$	7.00000	−	12.1244i	0.235435	−	0.407786i
$885$	−9.00000	−	15.5885i	−0.302532	−	0.524000i
$886$	−18.0000	−	31.1769i	−0.604722	−	1.04741i
$887$	20.5000	−	35.5070i	0.688323	−	1.19221i	−0.284058	−	0.958807i	$-0.591681\pi$
$887$	20.5000	−	35.5070i	0.688323	−	1.19221i	0.972380	−	0.233403i	$-0.0749860\pi$
$888$	12.0000			0.402694
$889$	47.5000	−	16.4545i	1.59310	−	0.551866i
$890$	12.0000			0.402241
$891$	4.50000	−	7.79423i	0.150756	−	0.261116i
$892$	−2.00000	−	3.46410i	−0.0669650	−	0.115987i
$893$		0			0
$894$	15.0000	−	25.9808i	0.501675	−	0.868927i
$895$	38.0000			1.27020
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$	168.000			5.60936
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	10.0000	+	17.3205i	0.333519	+	0.577671i
$900$	3.00000	+	5.19615i	0.100000	+	0.173205i
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$	−4.00000			−0.133185
$903$	−48.0000	−	41.5692i	−1.59734	−	1.38334i
$904$	5.00000			0.166298
$905$	22.0000	−	38.1051i	0.731305	−	1.26666i
$906$	4.50000	+	7.79423i	0.149502	+	0.258946i
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	1.00000	−	1.73205i	0.0331862	−	0.0574801i
$909$	−54.0000			−1.79107
$910$	−28.0000	−	24.2487i	−0.928191	−	0.803837i
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$		0			0
$913$	3.00000	+	5.19615i	0.0992855	+	0.171968i
$914$	−7.00000	−	12.1244i	−0.231539	−	0.401038i
$915$	−3.00000	+	5.19615i	−0.0991769	+	0.171780i
$916$	−28.0000			−0.925146
$917$		0			0
$918$	18.0000			0.594089
$919$	−18.0000	+	31.1769i	−0.593765	+	1.02843i	0.399955	+	0.916535i	$0.369026\pi$
$919$	−18.0000	+	31.1769i	−0.593765	+	1.02843i	−0.993720	+	0.111897i	$0.964307\pi$
$920$	8.00000	+	13.8564i	0.263752	+	0.456832i
$921$	−3.00000	−	5.19615i	−0.0988534	−	0.171219i
$922$	−13.5000	+	23.3827i	−0.444599	+	0.770068i
$923$	14.0000			0.460816
$924$	7.50000	−	2.59808i	0.246732	−	0.0854704i
$925$	−4.00000			−0.131519
$926$	1.00000	−	1.73205i	0.0328620	−	0.0569187i
$927$	−54.0000	−	93.5307i	−1.77359	−	3.07195i
$928$	2.50000	+	4.33013i	0.0820665	+	0.142143i
$929$	−7.50000	+	12.9904i	−0.246067	+	0.426201i	−0.962431	−	0.271526i	$-0.912472\pi$
$929$	−7.50000	+	12.9904i	−0.246067	+	0.426201i	0.716364	+	0.697727i	$0.245805\pi$
$930$	24.0000			0.786991
$931$		0			0
$932$		0			0
$933$	15.0000	−	25.9808i	0.491078	−	0.850572i
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	2.00000	+	3.46410i	0.0654070	+	0.113288i
$936$	21.0000	−	36.3731i	0.686406	−	1.18889i
$937$	−30.0000			−0.980057			−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000			−0.980057			−0.490029	+	0.871706i	$0.663014\pi$
$938$	−22.5000	+	7.79423i	−0.734651	+	0.254491i
$939$	3.00000			0.0979013
$940$	−2.00000	+	3.46410i	−0.0652328	+	0.112987i
$941$	5.50000	+	9.52628i	0.179295	+	0.310548i	0.941639	−	0.336624i	$-0.109285\pi$
$941$	5.50000	+	9.52628i	0.179295	+	0.310548i	−0.762344	+	0.647172i	$0.775952\pi$
$942$	−24.0000	−	41.5692i	−0.781962	−	1.35440i
$943$	16.0000	−	27.7128i	0.521032	−	0.902453i
$944$	3.00000			0.0976417
$945$	9.00000	−	46.7654i	0.292770	−	1.52128i
$946$	8.00000			0.260102
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	−0.831699	−	0.555227i	$-0.812631\pi$
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	0.896690	+	0.442659i	$0.145965\pi$
$948$	−13.5000	−	23.3827i	−0.438460	−	0.759434i
$949$	14.0000	+	24.2487i	0.454459	+	0.787146i
$950$		0			0
$951$	−36.0000			−1.16738
$952$	4.00000	+	3.46410i	0.129641	+	0.112272i
$953$	14.0000			0.453504			0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000			0.453504			0.226752	+	0.973952i	$0.427189\pi$
$954$	18.0000	−	31.1769i	0.582772	−	1.00939i
$955$	−2.00000	−	3.46410i	−0.0647185	−	0.112096i
$956$	2.50000	+	4.33013i	0.0808558	+	0.140046i
$957$	−7.50000	+	12.9904i	−0.242441	+	0.419919i
$958$	−1.00000			−0.0323085
$959$	6.00000	+	5.19615i	0.193750	+	0.167793i
$960$	6.00000			0.193649
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	14.0000	+	24.2487i	0.451378	+	0.781810i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$		0			0
$965$	16.0000			0.515058
$966$	−12.0000	+	62.3538i	−0.386094	+	2.00620i
$967$	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
$969$		0			0
$970$	−7.00000	−	12.1244i	−0.224756	−	0.389290i
$971$	−20.5000	+	35.5070i	−0.657876	+	1.13948i	0.323288	+	0.946301i	$0.395212\pi$
$971$	−20.5000	+	35.5070i	−0.657876	+	1.13948i	−0.981164	+	0.193175i	$0.938122\pi$
$972$		0			0
$973$	10.0000	−	3.46410i	0.320585	−	0.111054i
$974$	−40.0000			−1.28168
$975$	−10.5000	+	18.1865i	−0.336269	+	0.582435i
$976$	−0.500000	−	0.866025i	−0.0160046	−	0.0277208i
$977$	23.0000	+	39.8372i	0.735835	+	1.27450i	0.954356	+	0.298672i	$0.0965435\pi$
$977$	23.0000	+	39.8372i	0.735835	+	1.27450i	−0.218521	+	0.975832i	$0.570123\pi$
$978$	25.5000	−	44.1673i	0.815400	−	1.41231i
$979$	−6.00000			−0.191761
$980$	11.0000	−	8.66025i	0.351382	−	0.276642i
$981$	−12.0000			−0.383131
$982$	−15.0000	+	25.9808i	−0.478669	+	0.829079i
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	0.973106	−	0.230360i	$-0.0739903\pi$
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	−0.686050	+	0.727554i	$0.740657\pi$
$984$	−6.00000	−	10.3923i	−0.191273	−	0.331295i
$985$	−15.0000	+	25.9808i	−0.477940	+	0.827816i
$986$	−10.0000			−0.318465
$987$	−15.0000	+	5.19615i	−0.477455	+	0.165395i
$988$		0			0
$989$	−32.0000	+	55.4256i	−1.01754	+	1.76243i
$990$	6.00000	+	10.3923i	0.190693	+	0.330289i
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	0.775617	−	0.631204i	$-0.217439\pi$
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	−0.934447	+	0.356102i	$0.884106\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$	39.0000			1.23763
$994$	−1.00000	+	5.19615i	−0.0317181	+	0.164812i
$995$	8.00000			0.253617
$996$	−9.00000	+	15.5885i	−0.285176	+	0.493939i
$997$	3.00000	+	5.19615i	0.0950110	+	0.164564i	0.909613	−	0.415456i	$-0.136378\pi$
$997$	3.00000	+	5.19615i	0.0950110	+	0.164564i	−0.814602	+	0.580020i	$0.803045\pi$
$998$	−10.0000	−	17.3205i	−0.316544	−	0.548271i
$999$	−18.0000	+	31.1769i	−0.569495	+	0.986394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	154.2.e.a.23.1	✓	2
3.2	odd	2		1386.2.k.o.793.1		2
4.3	odd	2		1232.2.q.e.177.1		2
7.2	even	3		1078.2.a.m.1.1		1
7.3	odd	6		1078.2.e.f.67.1		2
7.4	even	3	inner	154.2.e.a.67.1	yes	2
7.5	odd	6		1078.2.a.g.1.1		1
7.6	odd	2		1078.2.e.f.177.1		2
21.2	odd	6		9702.2.a.i.1.1		1
21.5	even	6		9702.2.a.y.1.1		1
21.11	odd	6		1386.2.k.o.991.1		2
28.11	odd	6		1232.2.q.e.529.1		2
28.19	even	6		8624.2.a.be.1.1		1
28.23	odd	6		8624.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.a.23.1	✓	2	1.1	even	1	trivial
154.2.e.a.67.1	yes	2	7.4	even	3	inner
1078.2.a.g.1.1		1	7.5	odd	6
1078.2.a.m.1.1		1	7.2	even	3
1078.2.e.f.67.1		2	7.3	odd	6
1078.2.e.f.177.1		2	7.6	odd	2
1232.2.q.e.177.1		2	4.3	odd	2
1232.2.q.e.529.1		2	28.11	odd	6
1386.2.k.o.793.1		2	3.2	odd	2
1386.2.k.o.991.1		2	21.11	odd	6
8624.2.a.b.1.1		1	28.23	odd	6
8624.2.a.be.1.1		1	28.19	even	6
9702.2.a.i.1.1		1	21.2	odd	6
9702.2.a.y.1.1		1	21.5	even	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:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +3.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +3.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-3.00000 + 5.19615i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.50000 + 2.59808i) q^{12} -7.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-3.00000 - 5.19615i) q^{18} +2.00000 q^{20} +(6.00000 + 5.19615i) q^{21} -1.00000 q^{22} +(4.00000 - 6.92820i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(0.500000 + 0.866025i) q^{25} +(3.50000 - 6.06218i) q^{26} +9.00000 q^{27} +(2.00000 + 1.73205i) q^{28} -5.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} +2.00000 q^{34} +(1.00000 - 5.19615i) q^{35} +6.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(10.5000 + 18.1865i) q^{39} +(-1.00000 + 1.73205i) q^{40} +4.00000 q^{41} +(-7.50000 + 2.59808i) q^{42} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-6.00000 - 10.3923i) q^{45} +(4.00000 + 6.92820i) q^{46} +(-1.00000 + 1.73205i) q^{47} +3.00000 q^{48} +(5.50000 - 4.33013i) q^{49} -1.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(3.50000 + 6.06218i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-4.50000 + 7.79423i) q^{54} -2.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +(2.50000 - 4.33013i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(-0.500000 + 0.866025i) q^{61} +4.00000 q^{62} +(3.00000 - 15.5885i) q^{63} +1.00000 q^{64} +(7.00000 - 12.1244i) q^{65} +(1.50000 + 2.59808i) q^{66} +(-4.50000 - 7.79423i) q^{67} +(-1.00000 + 1.73205i) q^{68} -24.0000 q^{69} +(4.00000 + 3.46410i) q^{70} -2.00000 q^{71} +(-3.00000 + 5.19615i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(1.50000 - 2.59808i) q^{75} +(-2.00000 - 1.73205i) q^{77} -21.0000 q^{78} +(-4.50000 + 7.79423i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-2.00000 + 3.46410i) q^{82} +6.00000 q^{83} +(1.50000 - 7.79423i) q^{84} +4.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(7.50000 + 12.9904i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-3.00000 + 5.19615i) q^{89} +12.0000 q^{90} +(17.5000 - 6.06218i) q^{91} -8.00000 q^{92} +(-6.00000 + 10.3923i) q^{93} +(-1.00000 - 1.73205i) q^{94} +(-1.50000 + 2.59808i) q^{96} +7.00000 q^{97} +(1.00000 + 6.92820i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} + 6 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - q^2 - 3 * q^3 - q^4 - 2 * q^5 + 6 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9	\( 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} + 6 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 2 q^{10} + q^{11} - 3 q^{12} - 14 q^{13} + q^{14} + 12 q^{15} - q^{16} - 2 q^{17} - 6 q^{18} + 4 q^{20} + 12 q^{21} - 2 q^{22} + 8 q^{23} - 3 q^{24} + q^{25} + 7 q^{26} + 18 q^{27} + 4 q^{28} - 10 q^{29} - 6 q^{30} - 4 q^{31} - q^{32} + 3 q^{33} + 4 q^{34} + 2 q^{35} + 12 q^{36} - 4 q^{37} + 21 q^{39} - 2 q^{40} + 8 q^{41} - 15 q^{42} - 16 q^{43} + q^{44} - 12 q^{45} + 8 q^{46} - 2 q^{47} + 6 q^{48} + 11 q^{49} - 2 q^{50} - 6 q^{51} + 7 q^{52} + 6 q^{53} - 9 q^{54} - 4 q^{55} - 5 q^{56} + 5 q^{58} - 3 q^{59} - 6 q^{60} - q^{61} + 8 q^{62} + 6 q^{63} + 2 q^{64} + 14 q^{65} + 3 q^{66} - 9 q^{67} - 2 q^{68} - 48 q^{69} + 8 q^{70} - 4 q^{71} - 6 q^{72} - 4 q^{73} - 4 q^{74} + 3 q^{75} - 4 q^{77} - 42 q^{78} - 9 q^{79} - 2 q^{80} - 9 q^{81} - 4 q^{82} + 12 q^{83} + 3 q^{84} + 8 q^{85} + 8 q^{86} + 15 q^{87} + q^{88} - 6 q^{89} + 24 q^{90} + 35 q^{91} - 16 q^{92} - 12 q^{93} - 2 q^{94} - 3 q^{96} + 14 q^{97} + 2 q^{98} - 12 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 - q^4 - 2 * q^5 + 6 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 - 2 * q^10 + q^11 - 3 * q^12 - 14 * q^13 + q^14 + 12 * q^15 - q^16 - 2 * q^17 - 6 * q^18 + 4 * q^20 + 12 * q^21 - 2 * q^22 + 8 * q^23 - 3 * q^24 + q^25 + 7 * q^26 + 18 * q^27 + 4 * q^28 - 10 * q^29 - 6 * q^30 - 4 * q^31 - q^32 + 3 * q^33 + 4 * q^34 + 2 * q^35 + 12 * q^36 - 4 * q^37 + 21 * q^39 - 2 * q^40 + 8 * q^41 - 15 * q^42 - 16 * q^43 + q^44 - 12 * q^45 + 8 * q^46 - 2 * q^47 + 6 * q^48 + 11 * q^49 - 2 * q^50 - 6 * q^51 + 7 * q^52 + 6 * q^53 - 9 * q^54 - 4 * q^55 - 5 * q^56 + 5 * q^58 - 3 * q^59 - 6 * q^60 - q^61 + 8 * q^62 + 6 * q^63 + 2 * q^64 + 14 * q^65 + 3 * q^66 - 9 * q^67 - 2 * q^68 - 48 * q^69 + 8 * q^70 - 4 * q^71 - 6 * q^72 - 4 * q^73 - 4 * q^74 + 3 * q^75 - 4 * q^77 - 42 * q^78 - 9 * q^79 - 2 * q^80 - 9 * q^81 - 4 * q^82 + 12 * q^83 + 3 * q^84 + 8 * q^85 + 8 * q^86 + 15 * q^87 + q^88 - 6 * q^89 + 24 * q^90 + 35 * q^91 - 16 * q^92 - 12 * q^93 - 2 * q^94 - 3 * q^96 + 14 * q^97 + 2 * q^98 - 12 * q^99

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