LMFDB - Embedded newform 190.2.e.b.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(11,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("190.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.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:	$1.51715763840$
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			11.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	190.11
Dual form			190.2.e.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +2.00000 q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(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} +(-0.500000 - 0.866025i) q^{6} +2.00000 q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-0.500000 - 0.866025i) q^{10} -3.00000 q^{11} -1.00000 q^{12} +(-3.00000 - 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +2.00000 q^{18} +(3.50000 + 2.59808i) q^{19} -1.00000 q^{20} +(1.00000 - 1.73205i) q^{21} +(-1.50000 + 2.59808i) q^{22} +(4.00000 + 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -6.00000 q^{26} +5.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(1.00000 + 1.73205i) q^{29} -1.00000 q^{30} -8.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +(1.00000 + 1.73205i) q^{34} +(1.00000 - 1.73205i) q^{35} +(1.00000 - 1.73205i) q^{36} +8.00000 q^{37} +(4.00000 - 1.73205i) q^{38} -6.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(1.50000 + 2.59808i) q^{44} +2.00000 q^{45} +8.00000 q^{46} +(3.00000 + 5.19615i) q^{47} +(0.500000 + 0.866025i) q^{48} -3.00000 q^{49} -1.00000 q^{50} +(1.00000 + 1.73205i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(2.50000 - 4.33013i) q^{54} +(-1.50000 + 2.59808i) q^{55} -2.00000 q^{56} +(4.00000 - 1.73205i) q^{57} +2.00000 q^{58} +(-2.50000 + 4.33013i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-7.00000 - 12.1244i) q^{61} +(-4.00000 + 6.92820i) q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} -6.00000 q^{65} +(1.50000 + 2.59808i) q^{66} +(2.50000 + 4.33013i) q^{67} +2.00000 q^{68} +8.00000 q^{69} +(-1.00000 - 1.73205i) q^{70} +(3.00000 - 5.19615i) q^{71} +(-1.00000 - 1.73205i) q^{72} +(4.50000 - 7.79423i) q^{73} +(4.00000 - 6.92820i) q^{74} -1.00000 q^{75} +(0.500000 - 4.33013i) q^{76} -6.00000 q^{77} +(-3.00000 + 5.19615i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.50000 + 4.33013i) q^{82} -11.0000 q^{83} -2.00000 q^{84} +(1.00000 + 1.73205i) q^{85} +2.00000 q^{87} +3.00000 q^{88} +(-7.00000 - 12.1244i) q^{89} +(1.00000 - 1.73205i) q^{90} +(-6.00000 - 10.3923i) q^{91} +(4.00000 - 6.92820i) q^{92} +(-4.00000 + 6.92820i) q^{93} +6.00000 q^{94} +(4.00000 - 1.73205i) q^{95} +1.00000 q^{96} +(7.50000 - 12.9904i) q^{97} +(-1.50000 + 2.59808i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 - q^4 + q^5 - q^6 + 4 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + 4 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} - 6 q^{11} - 2 q^{12} - 6 q^{13} + 2 q^{14} - q^{15} - q^{16} - 2 q^{17} + 4 q^{18} + 7 q^{19} - 2 q^{20} + 2 q^{21} - 3 q^{22} + 8 q^{23} - q^{24} - q^{25} - 12 q^{26} + 10 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} - 16 q^{31} + q^{32} - 3 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 16 q^{37} + 8 q^{38} - 12 q^{39} - q^{40} - 5 q^{41} - 2 q^{42} + 3 q^{44} + 4 q^{45} + 16 q^{46} + 6 q^{47} + q^{48} - 6 q^{49} - 2 q^{50} + 2 q^{51} - 6 q^{52} - 6 q^{53} + 5 q^{54} - 3 q^{55} - 4 q^{56} + 8 q^{57} + 4 q^{58} - 5 q^{59} - q^{60} - 14 q^{61} - 8 q^{62} + 4 q^{63} + 2 q^{64} - 12 q^{65} + 3 q^{66} + 5 q^{67} + 4 q^{68} + 16 q^{69} - 2 q^{70} + 6 q^{71} - 2 q^{72} + 9 q^{73} + 8 q^{74} - 2 q^{75} + q^{76} - 12 q^{77} - 6 q^{78} - 8 q^{79} + q^{80} - q^{81} + 5 q^{82} - 22 q^{83} - 4 q^{84} + 2 q^{85} + 4 q^{87} + 6 q^{88} - 14 q^{89} + 2 q^{90} - 12 q^{91} + 8 q^{92} - 8 q^{93} + 12 q^{94} + 8 q^{95} + 2 q^{96} + 15 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + q^5 - q^6 + 4 * q^7 - 2 * q^8 + 2 * q^9 - q^10 - 6 * q^11 - 2 * q^12 - 6 * q^13 + 2 * q^14 - q^15 - q^16 - 2 * q^17 + 4 * q^18 + 7 * q^19 - 2 * q^20 + 2 * q^21 - 3 * q^22 + 8 * q^23 - q^24 - q^25 - 12 * q^26 + 10 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 - 16 * q^31 + q^32 - 3 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 16 * q^37 + 8 * q^38 - 12 * q^39 - q^40 - 5 * q^41 - 2 * q^42 + 3 * q^44 + 4 * q^45 + 16 * q^46 + 6 * q^47 + q^48 - 6 * q^49 - 2 * q^50 + 2 * q^51 - 6 * q^52 - 6 * q^53 + 5 * q^54 - 3 * q^55 - 4 * q^56 + 8 * q^57 + 4 * q^58 - 5 * q^59 - q^60 - 14 * q^61 - 8 * q^62 + 4 * q^63 + 2 * q^64 - 12 * q^65 + 3 * q^66 + 5 * q^67 + 4 * q^68 + 16 * q^69 - 2 * q^70 + 6 * q^71 - 2 * q^72 + 9 * q^73 + 8 * q^74 - 2 * q^75 + q^76 - 12 * q^77 - 6 * q^78 - 8 * q^79 + q^80 - q^81 + 5 * q^82 - 22 * q^83 - 4 * q^84 + 2 * q^85 + 4 * q^87 + 6 * q^88 - 14 * q^89 + 2 * q^90 - 12 * q^91 + 8 * q^92 - 8 * q^93 + 12 * q^94 + 8 * q^95 + 2 * q^96 + 15 * q^97 - 3 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−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
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$	−1.00000			−0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	−1.00000			−0.288675
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$	1.00000	−	1.73205i	0.267261	−	0.462910i
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	2.00000			0.471405
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$20$	−1.00000			−0.223607
$21$	1.00000	−	1.73205i	0.218218	−	0.377964i
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	0.894795	+	0.446476i	$0.147321\pi$
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−6.00000			−1.17670
$27$	5.00000			0.962250
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	0.943811	−	0.330487i	$-0.107213\pi$
$29$	1.00000	+	1.73205i	0.185695	+	0.321634i	−0.758115	+	0.652121i	$0.773880\pi$
$30$	−1.00000			−0.182574
$31$	−8.00000			−1.43684			−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000			−1.43684			−0.718421	+	0.695608i	$0.755135\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	4.00000	−	1.73205i	0.648886	−	0.280976i
$39$	−6.00000			−0.960769
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$	−1.00000	−	1.73205i	−0.154303	−	0.267261i
$43$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$43$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$	2.00000			0.298142
$46$	8.00000			1.17954
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−3.00000			−0.428571
$50$	−1.00000			−0.141421
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$	−3.00000	+	5.19615i	−0.416025	+	0.720577i
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	0.583036	−	0.812447i	$-0.301865\pi$
$53$	−3.00000	−	5.19615i	−0.412082	−	0.713746i	−0.995117	+	0.0987002i	$0.968532\pi$
$54$	2.50000	−	4.33013i	0.340207	−	0.589256i
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$	−2.00000			−0.267261
$57$	4.00000	−	1.73205i	0.529813	−	0.229416i
$58$	2.00000			0.262613
$59$	−2.50000	+	4.33013i	−0.325472	+	0.563735i	−0.981608	−	0.190909i	$-0.938857\pi$
$59$	−2.50000	+	4.33013i	−0.325472	+	0.563735i	0.656136	+	0.754643i	$0.272190\pi$
$60$	−0.500000	+	0.866025i	−0.0645497	+	0.111803i
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.0640184	−	0.997949i	$-0.520392\pi$
$62$	−4.00000	+	6.92820i	−0.508001	+	0.879883i
$63$	2.00000	+	3.46410i	0.251976	+	0.436436i
$64$	1.00000			0.125000
$65$	−6.00000			−0.744208
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	0.977356	−	0.211604i	$-0.0678686\pi$
$67$	2.50000	+	4.33013i	0.305424	+	0.529009i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	2.00000			0.242536
$69$	8.00000			0.963087
$70$	−1.00000	−	1.73205i	−0.119523	−	0.207020i
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$	−1.00000	−	1.73205i	−0.117851	−	0.204124i
$73$	4.50000	−	7.79423i	0.526685	−	0.912245i	−0.472831	−	0.881153i	$-0.656768\pi$
$73$	4.50000	−	7.79423i	0.526685	−	0.912245i	0.999517	−	0.0310925i	$-0.00989865\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$	−1.00000			−0.115470
$76$	0.500000	−	4.33013i	0.0573539	−	0.496700i
$77$	−6.00000			−0.683763
$78$	−3.00000	+	5.19615i	−0.339683	+	0.588348i
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.50000	+	4.33013i	0.276079	+	0.478183i
$83$	−11.0000			−1.20741			−0.603703	−	0.797209i	$-0.706309\pi$
$83$	−11.0000			−1.20741			−0.603703	+	0.797209i	$0.706309\pi$
$84$	−2.00000			−0.218218
$85$	1.00000	+	1.73205i	0.108465	+	0.187867i
$86$		0			0
$87$	2.00000			0.214423
$88$	3.00000			0.319801
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$	1.00000	−	1.73205i	0.105409	−	0.182574i
$91$	−6.00000	−	10.3923i	−0.628971	−	1.08941i
$92$	4.00000	−	6.92820i	0.417029	−	0.722315i
$93$	−4.00000	+	6.92820i	−0.414781	+	0.718421i
$94$	6.00000			0.618853
$95$	4.00000	−	1.73205i	0.410391	−	0.177705i
$96$	1.00000			0.102062
$97$	7.50000	−	12.9904i	0.761510	−	1.31897i	−0.180563	−	0.983563i	$-0.557792\pi$
$97$	7.50000	−	12.9904i	0.761510	−	1.31897i	0.942072	−	0.335410i	$-0.108875\pi$
$98$	−1.50000	+	2.59808i	−0.151523	+	0.262445i
$99$	−3.00000	−	5.19615i	−0.301511	−	0.522233i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$	2.00000			0.198030
$103$	6.00000			0.591198			0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000			0.591198			0.295599	+	0.955312i	$0.404481\pi$
$104$	3.00000	+	5.19615i	0.294174	+	0.509525i
$105$	−1.00000	−	1.73205i	−0.0975900	−	0.169031i
$106$	−6.00000			−0.582772
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$	−2.50000	−	4.33013i	−0.240563	−	0.416667i
$109$	4.00000	−	6.92820i	0.383131	−	0.663602i	−0.608377	−	0.793648i	$-0.708179\pi$
$109$	4.00000	−	6.92820i	0.383131	−	0.663602i	0.991508	+	0.130046i	$0.0415126\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$	4.00000	−	6.92820i	0.379663	−	0.657596i
$112$	−1.00000	+	1.73205i	−0.0944911	+	0.163663i
$113$	−13.0000			−1.22294			−0.611469	−	0.791269i	$-0.709421\pi$
$113$	−13.0000			−1.22294			−0.611469	+	0.791269i	$0.709421\pi$
$114$	0.500000	−	4.33013i	0.0468293	−	0.405554i
$115$	8.00000			0.746004
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$	6.00000	−	10.3923i	0.554700	−	0.960769i
$118$	2.50000	+	4.33013i	0.230144	+	0.398621i
$119$	−2.00000	+	3.46410i	−0.183340	+	0.317554i
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−2.00000			−0.181818
$122$	−14.0000			−1.26750
$123$	2.50000	+	4.33013i	0.225417	+	0.390434i
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$	−1.00000			−0.0894427
$126$	4.00000			0.356348
$127$	−3.00000	−	5.19615i	−0.266207	−	0.461084i	0.701672	−	0.712500i	$-0.252437\pi$
$127$	−3.00000	−	5.19615i	−0.266207	−	0.461084i	−0.967879	+	0.251416i	$0.919104\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−3.00000	+	5.19615i	−0.263117	+	0.455733i
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	−0.977438	−	0.211221i	$-0.932256\pi$
$131$	−3.50000	+	6.06218i	−0.305796	+	0.529655i	0.671642	+	0.740876i	$0.265589\pi$
$132$	3.00000			0.261116
$133$	7.00000	+	5.19615i	0.606977	+	0.450564i
$134$	5.00000			0.431934
$135$	2.50000	−	4.33013i	0.215166	−	0.372678i
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$	4.00000	−	6.92820i	0.340503	−	0.589768i
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	0.609618	−	0.792695i	$-0.291323\pi$
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	−0.991303	+	0.131597i	$0.957989\pi$
$140$	−2.00000			−0.169031
$141$	6.00000			0.505291
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	9.00000	+	15.5885i	0.752618	+	1.30357i
$144$	−2.00000			−0.166667
$145$	2.00000			0.166091
$146$	−4.50000	−	7.79423i	−0.372423	−	0.645055i
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$	−4.00000	−	6.92820i	−0.328798	−	0.569495i
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	−0.936245	−	0.351348i	$-0.885723\pi$
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	0.772399	+	0.635138i	$0.219057\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	−3.50000	−	2.59808i	−0.283887	−	0.210732i
$153$	−4.00000			−0.323381
$154$	−3.00000	+	5.19615i	−0.241747	+	0.418718i
$155$	−4.00000	+	6.92820i	−0.321288	+	0.556487i
$156$	3.00000	+	5.19615i	0.240192	+	0.416025i
$157$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$157$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$	−6.00000			−0.475831
$160$	1.00000			0.0790569
$161$	8.00000	+	13.8564i	0.630488	+	1.09204i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	3.00000			0.234978			0.117489	−	0.993074i	$-0.462515\pi$
$163$	3.00000			0.234978			0.117489	+	0.993074i	$0.462515\pi$
$164$	5.00000			0.390434
$165$	1.50000	+	2.59808i	0.116775	+	0.202260i
$166$	−5.50000	+	9.52628i	−0.426883	+	0.739383i
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	0.668730	−	0.743505i	$-0.266838\pi$
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	−0.978259	+	0.207385i	$0.933505\pi$
$168$	−1.00000	+	1.73205i	−0.0771517	+	0.133631i
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	2.00000			0.153393
$171$	−1.00000	+	8.66025i	−0.0764719	+	0.662266i
$172$		0			0
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	−0.289412	−	0.957205i	$-0.593460\pi$
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	0.973670	−	0.227964i	$-0.0732068\pi$
$174$	1.00000	−	1.73205i	0.0758098	−	0.131306i
$175$	−1.00000	−	1.73205i	−0.0755929	−	0.130931i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	2.50000	+	4.33013i	0.187912	+	0.325472i
$178$	−14.0000			−1.04934
$179$	3.00000			0.224231			0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000			0.224231			0.112115	+	0.993695i	$0.464237\pi$
$180$	−1.00000	−	1.73205i	−0.0745356	−	0.129099i
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	0.993598	+	0.112972i	$0.0360369\pi$
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	−0.398963	+	0.916967i	$0.630630\pi$
$182$	−12.0000			−0.889499
$183$	−14.0000			−1.03491
$184$	−4.00000	−	6.92820i	−0.294884	−	0.510754i
$185$	4.00000	−	6.92820i	0.294086	−	0.509372i
$186$	4.00000	+	6.92820i	0.293294	+	0.508001i
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$	3.00000	−	5.19615i	0.218797	−	0.378968i
$189$	10.0000			0.727393
$190$	0.500000	−	4.33013i	0.0362738	−	0.314140i
$191$	−4.00000			−0.289430			−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000			−0.289430			−0.144715	+	0.989473i	$0.546227\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	−0.987945	−	0.154805i	$-0.950525\pi$
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	0.628037	+	0.778183i	$0.283859\pi$
$194$	−7.50000	−	12.9904i	−0.538469	−	0.932655i
$195$	−3.00000	+	5.19615i	−0.214834	+	0.372104i
$196$	1.50000	+	2.59808i	0.107143	+	0.185577i
$197$	8.00000			0.569976			0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000			0.569976			0.284988	+	0.958531i	$0.408010\pi$
$198$	−6.00000			−0.426401
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	0.932075	+	0.362267i	$0.117997\pi$
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	−0.152305	+	0.988334i	$0.548670\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	5.00000			0.352673
$202$	10.0000			0.703598
$203$	2.00000	+	3.46410i	0.140372	+	0.243132i
$204$	1.00000	−	1.73205i	0.0700140	−	0.121268i
$205$	2.50000	+	4.33013i	0.174608	+	0.302429i
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$	−8.00000	+	13.8564i	−0.556038	+	0.963087i
$208$	6.00000			0.416025
$209$	−10.5000	−	7.79423i	−0.726300	−	0.539138i
$210$	−2.00000			−0.138013
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$		0			0
$216$	−5.00000			−0.340207
$217$	−16.0000			−1.08615
$218$	−4.00000	−	6.92820i	−0.270914	−	0.469237i
$219$	−4.50000	−	7.79423i	−0.304082	−	0.526685i
$220$	3.00000			0.202260
$221$	12.0000			0.807207
$222$	−4.00000	−	6.92820i	−0.268462	−	0.464991i
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	−0.463409	−	0.886145i	$-0.653374\pi$
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	0.999128	−	0.0417488i	$-0.0132929\pi$
$224$	1.00000	+	1.73205i	0.0668153	+	0.115728i
$225$	1.00000	−	1.73205i	0.0666667	−	0.115470i
$226$	−6.50000	+	11.2583i	−0.432374	+	0.748893i
$227$	−7.00000			−0.464606			−0.232303	−	0.972643i	$-0.574626\pi$
$227$	−7.00000			−0.464606			−0.232303	+	0.972643i	$0.574626\pi$
$228$	−3.50000	−	2.59808i	−0.231793	−	0.172062i
$229$	−24.0000			−1.58596			−0.792982	−	0.609245i	$-0.791473\pi$
$229$	−24.0000			−1.58596			−0.792982	+	0.609245i	$0.791473\pi$
$230$	4.00000	−	6.92820i	0.263752	−	0.456832i
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$	−1.00000	−	1.73205i	−0.0656532	−	0.113715i
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	−0.988013	−	0.154371i	$-0.950665\pi$
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	0.627696	+	0.778459i	$0.283998\pi$
$234$	−6.00000	−	10.3923i	−0.392232	−	0.679366i
$235$	6.00000			0.391397
$236$	5.00000			0.325472
$237$	4.00000	+	6.92820i	0.259828	+	0.450035i
$238$	2.00000	+	3.46410i	0.129641	+	0.224544i
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	1.00000			0.0645497
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	0.990912	+	0.134515i	$0.0429475\pi$
$241$	9.50000	+	16.4545i	0.611949	+	1.05993i	−0.378963	+	0.925412i	$0.623719\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	−7.00000	+	12.1244i	−0.448129	+	0.776182i
$245$	−1.50000	+	2.59808i	−0.0958315	+	0.165985i
$246$	5.00000			0.318788
$247$	3.00000	−	25.9808i	0.190885	−	1.65312i
$248$	8.00000			0.508001
$249$	−5.50000	+	9.52628i	−0.348548	+	0.603703i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	8.50000	+	14.7224i	0.536515	+	0.929272i	0.999088	+	0.0426905i	$0.0135929\pi$
$251$	8.50000	+	14.7224i	0.536515	+	0.929272i	−0.462573	+	0.886581i	$0.653074\pi$
$252$	2.00000	−	3.46410i	0.125988	−	0.218218i
$253$	−12.0000	−	20.7846i	−0.754434	−	1.30672i
$254$	−6.00000			−0.376473
$255$	2.00000			0.125245
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$		0			0
$259$	16.0000			0.994192
$260$	3.00000	+	5.19615i	0.186052	+	0.322252i
$261$	−2.00000	+	3.46410i	−0.123797	+	0.214423i
$262$	3.50000	+	6.06218i	0.216231	+	0.374523i
$263$	13.0000	−	22.5167i	0.801614	−	1.38844i	−0.116939	−	0.993139i	$-0.537308\pi$
$263$	13.0000	−	22.5167i	0.801614	−	1.38844i	0.918553	−	0.395298i	$-0.129359\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$	−6.00000			−0.368577
$266$	8.00000	−	3.46410i	0.490511	−	0.212398i
$267$	−14.0000			−0.856786
$268$	2.50000	−	4.33013i	0.152712	−	0.264505i
$269$	14.0000	−	24.2487i	0.853595	−	1.47847i	−0.0243472	−	0.999704i	$-0.507751\pi$
$269$	14.0000	−	24.2487i	0.853595	−	1.47847i	0.877942	−	0.478766i	$-0.158916\pi$
$270$	−2.50000	−	4.33013i	−0.152145	−	0.263523i
$271$	11.0000	−	19.0526i	0.668202	−	1.15736i	−0.310204	−	0.950670i	$-0.600397\pi$
$271$	11.0000	−	19.0526i	0.668202	−	1.15736i	0.978406	−	0.206691i	$-0.0662693\pi$
$272$	−1.00000	−	1.73205i	−0.0606339	−	0.105021i
$273$	−12.0000			−0.726273
$274$	3.00000			0.181237
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	−14.0000			−0.841178			−0.420589	−	0.907251i	$-0.638177\pi$
$277$	−14.0000			−0.841178			−0.420589	+	0.907251i	$0.638177\pi$
$278$	−9.00000			−0.539784
$279$	−8.00000	−	13.8564i	−0.478947	−	0.829561i
$280$	−1.00000	+	1.73205i	−0.0597614	+	0.103510i
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	0.742542	−	0.669800i	$-0.233620\pi$
$281$	−3.50000	−	6.06218i	−0.208792	−	0.361639i	−0.951334	+	0.308160i	$0.900287\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$	14.5000	−	25.1147i	0.861936	−	1.49292i	−0.00812260	−	0.999967i	$-0.502586\pi$
$283$	14.5000	−	25.1147i	0.861936	−	1.49292i	0.870058	−	0.492949i	$-0.164081\pi$
$284$	−6.00000			−0.356034
$285$	0.500000	−	4.33013i	0.0296174	−	0.256495i
$286$	18.0000			1.06436
$287$	−5.00000	+	8.66025i	−0.295141	+	0.511199i
$288$	−1.00000	+	1.73205i	−0.0589256	+	0.102062i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	1.00000	−	1.73205i	0.0587220	−	0.101710i
$291$	−7.50000	−	12.9904i	−0.439658	−	0.761510i
$292$	−9.00000			−0.526685
$293$	22.0000			1.28525			0.642627	−	0.766179i	$-0.277845\pi$
$293$	22.0000			1.28525			0.642627	+	0.766179i	$0.277845\pi$
$294$	1.50000	+	2.59808i	0.0874818	+	0.151523i
$295$	2.50000	+	4.33013i	0.145556	+	0.252110i
$296$	−8.00000			−0.464991
$297$	−15.0000			−0.870388
$298$	2.00000	+	3.46410i	0.115857	+	0.200670i
$299$	24.0000	−	41.5692i	1.38796	−	2.40401i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$		0			0
$302$	6.00000	−	10.3923i	0.345261	−	0.598010i
$303$	10.0000			0.574485
$304$	−4.00000	+	1.73205i	−0.229416	+	0.0993399i
$305$	−14.0000			−0.801638
$306$	−2.00000	+	3.46410i	−0.114332	+	0.198030i
$307$	2.50000	−	4.33013i	0.142683	−	0.247133i	−0.785823	−	0.618451i	$-0.787761\pi$
$307$	2.50000	−	4.33013i	0.142683	−	0.247133i	0.928506	+	0.371318i	$0.121094\pi$
$308$	3.00000	+	5.19615i	0.170941	+	0.296078i
$309$	3.00000	−	5.19615i	0.170664	−	0.295599i
$310$	4.00000	+	6.92820i	0.227185	+	0.393496i
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$	6.00000			0.339683
$313$	−6.50000	−	11.2583i	−0.367402	−	0.636358i	0.621757	−	0.783210i	$-0.286419\pi$
$313$	−6.50000	−	11.2583i	−0.367402	−	0.636358i	−0.989158	+	0.146852i	$0.953086\pi$
$314$		0			0
$315$	4.00000			0.225374
$316$	8.00000			0.450035
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	0.887788	+	0.460252i	$0.152241\pi$
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	−0.0453045	+	0.998973i	$0.514426\pi$
$318$	−3.00000	+	5.19615i	−0.168232	+	0.291386i
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$	16.0000			0.891645
$323$	−8.00000	+	3.46410i	−0.445132	+	0.192748i
$324$	1.00000			0.0555556
$325$	−3.00000	+	5.19615i	−0.166410	+	0.288231i
$326$	1.50000	−	2.59808i	0.0830773	−	0.143894i
$327$	−4.00000	−	6.92820i	−0.221201	−	0.383131i
$328$	2.50000	−	4.33013i	0.138039	−	0.239091i
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$	3.00000			0.165145
$331$	−17.0000			−0.934405			−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000			−0.934405			−0.467202	+	0.884150i	$0.654738\pi$
$332$	5.50000	+	9.52628i	0.301852	+	0.522823i
$333$	8.00000	+	13.8564i	0.438397	+	0.759326i
$334$	−8.00000			−0.437741
$335$	5.00000			0.273179
$336$	1.00000	+	1.73205i	0.0545545	+	0.0944911i
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	0.482295	+	0.876009i	$0.339803\pi$
$337$	−9.50000	+	16.4545i	−0.517498	+	0.896333i	−0.999793	+	0.0203242i	$0.993530\pi$
$338$	11.5000	+	19.9186i	0.625518	+	1.08343i
$339$	−6.50000	+	11.2583i	−0.353032	+	0.611469i
$340$	1.00000	−	1.73205i	0.0542326	−	0.0939336i
$341$	24.0000			1.29967
$342$	7.00000	+	5.19615i	0.378517	+	0.280976i
$343$	−20.0000			−1.07990
$344$		0			0
$345$	4.00000	−	6.92820i	0.215353	−	0.373002i
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	13.5000	−	23.3827i	0.724718	−	1.25525i	−0.234372	−	0.972147i	$-0.575303\pi$
$347$	13.5000	−	23.3827i	0.724718	−	1.25525i	0.959090	−	0.283101i	$-0.0913633\pi$
$348$	−1.00000	−	1.73205i	−0.0536056	−	0.0928477i
$349$	16.0000			0.856460			0.428230	−	0.903670i	$-0.359137\pi$
$349$	16.0000			0.856460			0.428230	+	0.903670i	$0.359137\pi$
$350$	−2.00000			−0.106904
$351$	−15.0000	−	25.9808i	−0.800641	−	1.38675i
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	−21.0000			−1.11772			−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000			−1.11772			−0.558859	+	0.829263i	$0.688761\pi$
$354$	5.00000			0.265747
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	−7.00000	+	12.1244i	−0.370999	+	0.642590i
$357$	2.00000	+	3.46410i	0.105851	+	0.183340i
$358$	1.50000	−	2.59808i	0.0792775	−	0.137313i
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$	−2.00000			−0.105409
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$	16.0000			0.840941
$363$	−1.00000	+	1.73205i	−0.0524864	+	0.0909091i
$364$	−6.00000	+	10.3923i	−0.314485	+	0.544705i
$365$	−4.50000	−	7.79423i	−0.235541	−	0.407969i
$366$	−7.00000	+	12.1244i	−0.365896	+	0.633750i
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941834\pi$
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	−0.225750	+	0.974185i	$0.572483\pi$
$368$	−8.00000			−0.417029
$369$	−10.0000			−0.520579
$370$	−4.00000	−	6.92820i	−0.207950	−	0.360180i
$371$	−6.00000	−	10.3923i	−0.311504	−	0.539542i
$372$	8.00000			0.414781
$373$	−24.0000			−1.24267			−0.621336	−	0.783544i	$-0.713410\pi$
$373$	−24.0000			−1.24267			−0.621336	+	0.783544i	$0.713410\pi$
$374$	−3.00000	−	5.19615i	−0.155126	−	0.268687i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	6.00000	−	10.3923i	0.309016	−	0.535231i
$378$	5.00000	−	8.66025i	0.257172	−	0.445435i
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	−3.50000	−	2.59808i	−0.179546	−	0.133278i
$381$	−6.00000			−0.307389
$382$	−2.00000	+	3.46410i	−0.102329	+	0.177239i
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	−0.932436	−	0.361335i	$-0.882321\pi$
$383$	−3.00000	+	5.19615i	−0.153293	+	0.265511i	0.779143	+	0.626846i	$0.215654\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−3.00000	+	5.19615i	−0.152894	+	0.264820i
$386$	5.00000	+	8.66025i	0.254493	+	0.440795i
$387$		0			0
$388$	−15.0000			−0.761510
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$	3.00000	+	5.19615i	0.151911	+	0.263117i
$391$	−16.0000			−0.809155
$392$	3.00000			0.151523
$393$	3.50000	+	6.06218i	0.176552	+	0.305796i
$394$	4.00000	−	6.92820i	0.201517	−	0.349038i
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	−8.00000	+	13.8564i	−0.401508	+	0.695433i	−0.993908	−	0.110211i	$-0.964847\pi$
$397$	−8.00000	+	13.8564i	−0.401508	+	0.695433i	0.592400	+	0.805644i	$0.298181\pi$
$398$	22.0000			1.10276
$399$	8.00000	−	3.46410i	0.400501	−	0.173422i
$400$	1.00000			0.0500000
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$	2.50000	−	4.33013i	0.124689	−	0.215967i
$403$	24.0000	+	41.5692i	1.19553	+	2.07071i
$404$	5.00000	−	8.66025i	0.248759	−	0.430864i
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	4.00000			0.198517
$407$	−24.0000			−1.18964
$408$	−1.00000	−	1.73205i	−0.0495074	−	0.0857493i
$409$	9.50000	+	16.4545i	0.469745	+	0.813622i	0.999402	−	0.0345902i	$-0.0110126\pi$
$409$	9.50000	+	16.4545i	0.469745	+	0.813622i	−0.529657	+	0.848212i	$0.677679\pi$
$410$	5.00000			0.246932
$411$	3.00000			0.147979
$412$	−3.00000	−	5.19615i	−0.147799	−	0.255996i
$413$	−5.00000	+	8.66025i	−0.246034	+	0.426143i
$414$	8.00000	+	13.8564i	0.393179	+	0.681005i
$415$	−5.50000	+	9.52628i	−0.269984	+	0.467627i
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$	−9.00000			−0.440732
$418$	−12.0000	+	5.19615i	−0.586939	+	0.254152i
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$	−1.00000	+	1.73205i	−0.0487950	+	0.0845154i
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	−0.751935	−	0.659237i	$-0.770879\pi$
$421$	4.00000	−	6.92820i	0.194948	−	0.337660i	0.946883	+	0.321577i	$0.104213\pi$
$422$	−2.00000	−	3.46410i	−0.0973585	−	0.168630i
$423$	−6.00000	+	10.3923i	−0.291730	+	0.505291i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$	2.00000			0.0970143
$426$	−6.00000			−0.290701
$427$	−14.0000	−	24.2487i	−0.677507	−	1.17348i
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$	18.0000			0.869048
$430$		0			0
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	0.929188	−	0.369607i	$-0.120508\pi$
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	−0.784683	+	0.619897i	$0.787174\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	−15.0000	−	25.9808i	−0.720854	−	1.24856i	−0.960658	−	0.277734i	$-0.910416\pi$
$433$	−15.0000	−	25.9808i	−0.720854	−	1.24856i	0.239804	−	0.970821i	$-0.422917\pi$
$434$	−8.00000	+	13.8564i	−0.384012	+	0.665129i
$435$	1.00000	−	1.73205i	0.0479463	−	0.0830455i
$436$	−8.00000			−0.383131
$437$	−4.00000	+	34.6410i	−0.191346	+	1.65710i
$438$	−9.00000			−0.430037
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	−0.754642	−	0.656136i	$-0.772190\pi$
$439$	4.00000	−	6.92820i	0.190910	−	0.330665i	0.945552	+	0.325471i	$0.105523\pi$
$440$	1.50000	−	2.59808i	0.0715097	−	0.123858i
$441$	−3.00000	−	5.19615i	−0.142857	−	0.247436i
$442$	6.00000	−	10.3923i	0.285391	−	0.494312i
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	0.952901	−	0.303281i	$-0.0980821\pi$
$443$	4.50000	+	7.79423i	0.213801	+	0.370315i	−0.739100	+	0.673596i	$0.764749\pi$
$444$	−8.00000			−0.379663
$445$	−14.0000			−0.663664
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$	2.00000	+	3.46410i	0.0945968	+	0.163846i
$448$	2.00000			0.0944911
$449$	29.0000			1.36859			0.684297	−	0.729203i	$-0.260109\pi$
$449$	29.0000			1.36859			0.684297	+	0.729203i	$0.260109\pi$
$450$	−1.00000	−	1.73205i	−0.0471405	−	0.0816497i
$451$	7.50000	−	12.9904i	0.353161	−	0.611693i
$452$	6.50000	+	11.2583i	0.305734	+	0.529547i
$453$	6.00000	−	10.3923i	0.281905	−	0.488273i
$454$	−3.50000	+	6.06218i	−0.164263	+	0.284512i
$455$	−12.0000			−0.562569
$456$	−4.00000	+	1.73205i	−0.187317	+	0.0811107i
$457$	13.0000			0.608114			0.304057	−	0.952654i	$-0.401659\pi$
$457$	13.0000			0.608114			0.304057	+	0.952654i	$0.401659\pi$
$458$	−12.0000	+	20.7846i	−0.560723	+	0.971201i
$459$	−5.00000	+	8.66025i	−0.233380	+	0.404226i
$460$	−4.00000	−	6.92820i	−0.186501	−	0.323029i
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	−0.487577	−	0.873080i	$-0.662119\pi$
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	0.999898	−	0.0142861i	$-0.00454755\pi$
$462$	3.00000	+	5.19615i	0.139573	+	0.241747i
$463$	34.0000			1.58011			0.790057	−	0.613033i	$-0.210051\pi$
$463$	34.0000			1.58011			0.790057	+	0.613033i	$0.210051\pi$
$464$	−2.00000			−0.0928477
$465$	4.00000	+	6.92820i	0.185496	+	0.321288i
$466$	5.50000	+	9.52628i	0.254783	+	0.441296i
$467$	7.00000			0.323921			0.161961	−	0.986797i	$-0.448218\pi$
$467$	7.00000			0.323921			0.161961	+	0.986797i	$0.448218\pi$
$468$	−12.0000			−0.554700
$469$	5.00000	+	8.66025i	0.230879	+	0.399893i
$470$	3.00000	−	5.19615i	0.138380	−	0.239681i
$471$		0			0
$472$	2.50000	−	4.33013i	0.115072	−	0.199310i
$473$		0			0
$474$	8.00000			0.367452
$475$	0.500000	−	4.33013i	0.0229416	−	0.198680i
$476$	4.00000			0.183340
$477$	6.00000	−	10.3923i	0.274721	−	0.475831i
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	0.695773	−	0.718262i	$-0.255062\pi$
$479$	−6.00000	−	10.3923i	−0.274147	−	0.474837i	−0.969920	+	0.243426i	$0.921729\pi$
$480$	0.500000	−	0.866025i	0.0228218	−	0.0395285i
$481$	−24.0000	−	41.5692i	−1.09431	−	1.89539i
$482$	19.0000			0.865426
$483$	16.0000			0.728025
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−7.50000	−	12.9904i	−0.340557	−	0.589863i
$486$	16.0000			0.725775
$487$	4.00000			0.181257			0.0906287	−	0.995885i	$-0.471112\pi$
$487$	4.00000			0.181257			0.0906287	+	0.995885i	$0.471112\pi$
$488$	7.00000	+	12.1244i	0.316875	+	0.548844i
$489$	1.50000	−	2.59808i	0.0678323	−	0.117489i
$490$	1.50000	+	2.59808i	0.0677631	+	0.117369i
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	−0.998467	−	0.0553560i	$-0.982371\pi$
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	0.547173	+	0.837020i	$0.315704\pi$
$492$	2.50000	−	4.33013i	0.112709	−	0.195217i
$493$	−4.00000			−0.180151
$494$	−21.0000	−	15.5885i	−0.944835	−	0.701358i
$495$	−6.00000			−0.269680
$496$	4.00000	−	6.92820i	0.179605	−	0.311086i
$497$	6.00000	−	10.3923i	0.269137	−	0.466159i
$498$	5.50000	+	9.52628i	0.246461	+	0.426883i
$499$	−16.5000	+	28.5788i	−0.738641	+	1.27936i	0.214466	+	0.976732i	$0.431199\pi$
$499$	−16.5000	+	28.5788i	−0.738641	+	1.27936i	−0.953107	+	0.302633i	$0.902134\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−8.00000			−0.357414
$502$	17.0000			0.758747
$503$	−2.00000	−	3.46410i	−0.0891756	−	0.154457i	0.817987	−	0.575236i	$-0.195090\pi$
$503$	−2.00000	−	3.46410i	−0.0891756	−	0.154457i	−0.907163	+	0.420780i	$0.861757\pi$
$504$	−2.00000	−	3.46410i	−0.0890871	−	0.154303i
$505$	10.0000			0.444994
$506$	−24.0000			−1.06693
$507$	11.5000	+	19.9186i	0.510733	+	0.884615i
$508$	−3.00000	+	5.19615i	−0.133103	+	0.230542i
$509$	−6.00000	−	10.3923i	−0.265945	−	0.460631i	0.701866	−	0.712309i	$-0.252351\pi$
$509$	−6.00000	−	10.3923i	−0.265945	−	0.460631i	−0.967811	+	0.251679i	$0.919017\pi$
$510$	1.00000	−	1.73205i	0.0442807	−	0.0766965i
$511$	9.00000	−	15.5885i	0.398137	−	0.689593i
$512$	−1.00000			−0.0441942
$513$	17.5000	+	12.9904i	0.772644	+	0.573539i
$514$	−3.00000			−0.132324
$515$	3.00000	−	5.19615i	0.132196	−	0.228970i
$516$		0			0
$517$	−9.00000	−	15.5885i	−0.395820	−	0.685580i
$518$	8.00000	−	13.8564i	0.351500	−	0.608816i
$519$	−9.00000	−	15.5885i	−0.395056	−	0.684257i
$520$	6.00000			0.263117
$521$	21.0000			0.920027			0.460013	−	0.887912i	$-0.347845\pi$
$521$	21.0000			0.920027			0.460013	+	0.887912i	$0.347845\pi$
$522$	2.00000	+	3.46410i	0.0875376	+	0.151620i
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	0.765222	−	0.643767i	$-0.222629\pi$
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	−0.940129	+	0.340818i	$0.889296\pi$
$524$	7.00000			0.305796
$525$	−2.00000			−0.0872872
$526$	−13.0000	−	22.5167i	−0.566827	−	0.981773i
$527$	8.00000	−	13.8564i	0.348485	−	0.603595i
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	−10.0000			−0.433963
$532$	1.00000	−	8.66025i	0.0433555	−	0.375470i
$533$	30.0000			1.29944
$534$	−7.00000	+	12.1244i	−0.302920	+	0.524672i
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$	−2.50000	−	4.33013i	−0.107984	−	0.187033i
$537$	1.50000	−	2.59808i	0.0647298	−	0.112115i
$538$	−14.0000	−	24.2487i	−0.603583	−	1.04544i
$539$	9.00000			0.387657
$540$	−5.00000			−0.215166
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	−11.0000	−	19.0526i	−0.472490	−	0.818377i
$543$	16.0000			0.686626
$544$	−2.00000			−0.0857493
$545$	−4.00000	−	6.92820i	−0.171341	−	0.296772i
$546$	−6.00000	+	10.3923i	−0.256776	+	0.444750i
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	0.938779	−	0.344519i	$-0.111958\pi$
$547$	4.00000	+	6.92820i	0.171028	+	0.296229i	−0.767752	+	0.640747i	$0.778625\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$	14.0000	−	24.2487i	0.597505	−	1.03491i
$550$	3.00000			0.127920
$551$	−1.00000	+	8.66025i	−0.0426014	+	0.368939i
$552$	−8.00000			−0.340503
$553$	−8.00000	+	13.8564i	−0.340195	+	0.589234i
$554$	−7.00000	+	12.1244i	−0.297402	+	0.515115i
$555$	−4.00000	−	6.92820i	−0.169791	−	0.294086i
$556$	−4.50000	+	7.79423i	−0.190843	+	0.330549i
$557$	20.0000	+	34.6410i	0.847427	+	1.46779i	0.883497	+	0.468438i	$0.155183\pi$
$557$	20.0000	+	34.6410i	0.847427	+	1.46779i	−0.0360693	+	0.999349i	$0.511484\pi$
$558$	−16.0000			−0.677334
$559$		0			0
$560$	1.00000	+	1.73205i	0.0422577	+	0.0731925i
$561$	−3.00000	−	5.19615i	−0.126660	−	0.219382i
$562$	−7.00000			−0.295277
$563$	−23.0000			−0.969334			−0.484667	−	0.874699i	$-0.661059\pi$
$563$	−23.0000			−0.969334			−0.484667	+	0.874699i	$0.661059\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$	−6.50000	+	11.2583i	−0.273457	+	0.473642i
$566$	−14.5000	−	25.1147i	−0.609480	−	1.05565i
$567$	−1.00000	+	1.73205i	−0.0419961	+	0.0727393i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	34.0000			1.42535			0.712677	−	0.701492i	$-0.247483\pi$
$569$	34.0000			1.42535			0.712677	+	0.701492i	$0.247483\pi$
$570$	−3.50000	−	2.59808i	−0.146599	−	0.108821i
$571$	−29.0000			−1.21361			−0.606806	−	0.794850i	$-0.707550\pi$
$571$	−29.0000			−1.21361			−0.606806	+	0.794850i	$0.707550\pi$
$572$	9.00000	−	15.5885i	0.376309	−	0.651786i
$573$	−2.00000	+	3.46410i	−0.0835512	+	0.144715i
$574$	5.00000	+	8.66025i	0.208696	+	0.361472i
$575$	4.00000	−	6.92820i	0.166812	−	0.288926i
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	7.00000			0.291414			0.145707	−	0.989328i	$-0.453454\pi$
$577$	7.00000			0.291414			0.145707	+	0.989328i	$0.453454\pi$
$578$	13.0000			0.540729
$579$	5.00000	+	8.66025i	0.207793	+	0.359908i
$580$	−1.00000	−	1.73205i	−0.0415227	−	0.0719195i
$581$	−22.0000			−0.912714
$582$	−15.0000			−0.621770
$583$	9.00000	+	15.5885i	0.372742	+	0.645608i
$584$	−4.50000	+	7.79423i	−0.186211	+	0.322527i
$585$	−6.00000	−	10.3923i	−0.248069	−	0.429669i
$586$	11.0000	−	19.0526i	0.454406	−	0.787054i
$587$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$587$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$588$	3.00000			0.123718
$589$	−28.0000	−	20.7846i	−1.15372	−	0.856415i
$590$	5.00000			0.205847
$591$	4.00000	−	6.92820i	0.164538	−	0.284988i
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	6.50000	+	11.2583i	0.266923	+	0.462324i	0.968066	−	0.250697i	$-0.0806597\pi$
$593$	6.50000	+	11.2583i	0.266923	+	0.462324i	−0.701143	+	0.713021i	$0.747326\pi$
$594$	−7.50000	+	12.9904i	−0.307729	+	0.533002i
$595$	2.00000	+	3.46410i	0.0819920	+	0.142014i
$596$	4.00000			0.163846
$597$	22.0000			0.900400
$598$	−24.0000	−	41.5692i	−0.981433	−	1.69989i
$599$	−24.0000	−	41.5692i	−0.980613	−	1.69847i	−0.660006	−	0.751260i	$-0.729446\pi$
$599$	−24.0000	−	41.5692i	−0.980613	−	1.69847i	−0.320607	−	0.947212i	$-0.603887\pi$
$600$	1.00000			0.0408248
$601$	−37.0000			−1.50926			−0.754631	−	0.656150i	$-0.772184\pi$
$601$	−37.0000			−1.50926			−0.754631	+	0.656150i	$0.772184\pi$
$602$		0			0
$603$	−5.00000	+	8.66025i	−0.203616	+	0.352673i
$604$	−6.00000	−	10.3923i	−0.244137	−	0.422857i
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$	5.00000	−	8.66025i	0.203111	−	0.351799i
$607$	−14.0000			−0.568242			−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000			−0.568242			−0.284121	+	0.958788i	$0.591702\pi$
$608$	−0.500000	+	4.33013i	−0.0202777	+	0.175610i
$609$	4.00000			0.162088
$610$	−7.00000	+	12.1244i	−0.283422	+	0.490901i
$611$	18.0000	−	31.1769i	0.728202	−	1.26128i
$612$	2.00000	+	3.46410i	0.0808452	+	0.140028i
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	−0.286300	−	0.958140i	$-0.592425\pi$
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	0.972924	−	0.231127i	$-0.0742412\pi$
$614$	−2.50000	−	4.33013i	−0.100892	−	0.174750i
$615$	5.00000			0.201619
$616$	6.00000			0.241747
$617$	−9.50000	−	16.4545i	−0.382456	−	0.662433i	0.608957	−	0.793203i	$-0.291588\pi$
$617$	−9.50000	−	16.4545i	−0.382456	−	0.662433i	−0.991413	+	0.130771i	$0.958255\pi$
$618$	−3.00000	−	5.19615i	−0.120678	−	0.209020i
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$	8.00000			0.321288
$621$	20.0000	+	34.6410i	0.802572	+	1.39010i
$622$	−12.0000	+	20.7846i	−0.481156	+	0.833387i
$623$	−14.0000	−	24.2487i	−0.560898	−	0.971504i
$624$	3.00000	−	5.19615i	0.120096	−	0.208013i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−13.0000			−0.519584
$627$	−12.0000	+	5.19615i	−0.479234	+	0.207514i
$628$		0			0
$629$	−8.00000	+	13.8564i	−0.318981	+	0.552491i
$630$	2.00000	−	3.46410i	0.0796819	−	0.138013i
$631$	15.0000	+	25.9808i	0.597141	+	1.03428i	0.993241	+	0.116071i	$0.0370299\pi$
$631$	15.0000	+	25.9808i	0.597141	+	1.03428i	−0.396100	+	0.918207i	$0.629637\pi$
$632$	4.00000	−	6.92820i	0.159111	−	0.275589i
$633$	−2.00000	−	3.46410i	−0.0794929	−	0.137686i
$634$	30.0000			1.19145
$635$	−6.00000			−0.238103
$636$	3.00000	+	5.19615i	0.118958	+	0.206041i
$637$	9.00000	+	15.5885i	0.356593	+	0.617637i
$638$	−6.00000			−0.237542
$639$	12.0000			0.474713
$640$	−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	$0.302789\pi$
$642$	6.00000	+	10.3923i	0.236801	+	0.410152i
$643$	2.50000	−	4.33013i	0.0985904	−	0.170764i	−0.812511	−	0.582946i	$-0.801900\pi$
$643$	2.50000	−	4.33013i	0.0985904	−	0.170764i	0.911101	+	0.412182i	$0.135233\pi$
$644$	8.00000	−	13.8564i	0.315244	−	0.546019i
$645$		0			0
$646$	−1.00000	+	8.66025i	−0.0393445	+	0.340733i
$647$	6.00000			0.235884			0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000			0.235884			0.117942	+	0.993020i	$0.462370\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	7.50000	−	12.9904i	0.294401	−	0.509917i
$650$	3.00000	+	5.19615i	0.117670	+	0.203810i
$651$	−8.00000	+	13.8564i	−0.313545	+	0.543075i
$652$	−1.50000	−	2.59808i	−0.0587445	−	0.101749i
$653$	−36.0000			−1.40879			−0.704394	−	0.709809i	$-0.748781\pi$
$653$	−36.0000			−1.40879			−0.704394	+	0.709809i	$0.748781\pi$
$654$	−8.00000			−0.312825
$655$	3.50000	+	6.06218i	0.136756	+	0.236869i
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$	18.0000			0.702247
$658$	12.0000			0.467809
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	0.958902	−	0.283738i	$-0.0915745\pi$
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	−0.725175	+	0.688565i	$0.758241\pi$
$660$	1.50000	−	2.59808i	0.0583874	−	0.101130i
$661$	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	$0.692604\pi$
$662$	−8.50000	+	14.7224i	−0.330362	+	0.572204i
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$	11.0000			0.426883
$665$	8.00000	−	3.46410i	0.310227	−	0.134332i
$666$	16.0000			0.619987
$667$	−8.00000	+	13.8564i	−0.309761	+	0.536522i
$668$	−4.00000	+	6.92820i	−0.154765	+	0.268060i
$669$	−8.00000	−	13.8564i	−0.309298	−	0.535720i
$670$	2.50000	−	4.33013i	0.0965834	−	0.167287i
$671$	21.0000	+	36.3731i	0.810696	+	1.40417i
$672$	2.00000			0.0771517
$673$	26.0000			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$674$	9.50000	+	16.4545i	0.365926	+	0.633803i
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$	23.0000			0.884615
$677$	−2.00000			−0.0768662			−0.0384331	−	0.999261i	$-0.512237\pi$
$677$	−2.00000			−0.0768662			−0.0384331	+	0.999261i	$0.512237\pi$
$678$	6.50000	+	11.2583i	0.249631	+	0.432374i
$679$	15.0000	−	25.9808i	0.575647	−	0.997050i
$680$	−1.00000	−	1.73205i	−0.0383482	−	0.0664211i
$681$	−3.50000	+	6.06218i	−0.134120	+	0.232303i
$682$	12.0000	−	20.7846i	0.459504	−	0.795884i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	8.00000	−	3.46410i	0.305888	−	0.132453i
$685$	3.00000			0.114624
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	−12.0000	+	20.7846i	−0.457829	+	0.792982i
$688$		0			0
$689$	−18.0000	+	31.1769i	−0.685745	+	1.18775i
$690$	−4.00000	−	6.92820i	−0.152277	−	0.263752i
$691$	28.0000			1.06517			0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000			1.06517			0.532585	+	0.846376i	$0.321221\pi$
$692$	−18.0000			−0.684257
$693$	−6.00000	−	10.3923i	−0.227921	−	0.394771i
$694$	−13.5000	−	23.3827i	−0.512453	−	0.887595i
$695$	−9.00000			−0.341389
$696$	−2.00000			−0.0758098
$697$	−5.00000	−	8.66025i	−0.189389	−	0.328031i
$698$	8.00000	−	13.8564i	0.302804	−	0.524473i
$699$	5.50000	+	9.52628i	0.208029	+	0.360317i
$700$	−1.00000	+	1.73205i	−0.0377964	+	0.0654654i
$701$	21.0000	−	36.3731i	0.793159	−	1.37379i	−0.130843	−	0.991403i	$-0.541768\pi$
$701$	21.0000	−	36.3731i	0.793159	−	1.37379i	0.924002	−	0.382389i	$-0.124898\pi$
$702$	−30.0000			−1.13228
$703$	28.0000	+	20.7846i	1.05604	+	0.783906i
$704$	−3.00000			−0.113067
$705$	3.00000	−	5.19615i	0.112987	−	0.195698i
$706$	−10.5000	+	18.1865i	−0.395173	+	0.684459i
$707$	10.0000	+	17.3205i	0.376089	+	0.651405i
$708$	2.50000	−	4.33013i	0.0939558	−	0.162736i
$709$	−10.0000	−	17.3205i	−0.375558	−	0.650485i	0.614852	−	0.788642i	$-0.289216\pi$
$709$	−10.0000	−	17.3205i	−0.375558	−	0.650485i	−0.990410	+	0.138157i	$0.955882\pi$
$710$	−6.00000			−0.225176
$711$	−16.0000			−0.600047
$712$	7.00000	+	12.1244i	0.262336	+	0.454379i
$713$	−32.0000	−	55.4256i	−1.19841	−	2.07571i
$714$	4.00000			0.149696
$715$	18.0000			0.673162
$716$	−1.50000	−	2.59808i	−0.0560576	−	0.0970947i
$717$	6.00000	−	10.3923i	0.224074	−	0.388108i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	−25.0000	+	43.3013i	−0.932343	+	1.61486i	−0.153037	+	0.988220i	$0.548906\pi$
$719$	−25.0000	+	43.3013i	−0.932343	+	1.61486i	−0.779305	+	0.626644i	$0.784428\pi$
$720$	−1.00000	+	1.73205i	−0.0372678	+	0.0645497i
$721$	12.0000			0.446903
$722$	18.5000	+	4.33013i	0.688499	+	0.161151i
$723$	19.0000			0.706618
$724$	8.00000	−	13.8564i	0.297318	−	0.514969i
$725$	1.00000	−	1.73205i	0.0371391	−	0.0643268i
$726$	1.00000	+	1.73205i	0.0371135	+	0.0642824i
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$	6.00000	+	10.3923i	0.222375	+	0.385164i
$729$	13.0000			0.481481
$730$	−9.00000			−0.333105
$731$		0			0
$732$	7.00000	+	12.1244i	0.258727	+	0.448129i
$733$		0			0			−	1.00000i	$-0.5\pi$
$733$		0			0				1.00000i	$0.5\pi$
$734$	28.0000			1.03350
$735$	1.50000	+	2.59808i	0.0553283	+	0.0958315i
$736$	−4.00000	+	6.92820i	−0.147442	+	0.255377i
$737$	−7.50000	−	12.9904i	−0.276266	−	0.478507i
$738$	−5.00000	+	8.66025i	−0.184053	+	0.318788i
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	−0.908337	−	0.418238i	$-0.862648\pi$
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	0.816373	+	0.577524i	$0.195981\pi$
$740$	−8.00000			−0.294086
$741$	−21.0000	−	15.5885i	−0.771454	−	0.572656i
$742$	−12.0000			−0.440534
$743$	−2.00000	+	3.46410i	−0.0733729	+	0.127086i	−0.900378	−	0.435110i	$-0.856710\pi$
$743$	−2.00000	+	3.46410i	−0.0733729	+	0.127086i	0.827005	+	0.562195i	$0.190043\pi$
$744$	4.00000	−	6.92820i	0.146647	−	0.254000i
$745$	2.00000	+	3.46410i	0.0732743	+	0.126915i
$746$	−12.0000	+	20.7846i	−0.439351	+	0.760979i
$747$	−11.0000	−	19.0526i	−0.402469	−	0.697097i
$748$	−6.00000			−0.219382
$749$	−24.0000			−0.876941
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	0.970744	+	0.240118i	$0.0771860\pi$
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	−0.277424	+	0.960748i	$0.589481\pi$
$752$	−6.00000			−0.218797
$753$	17.0000			0.619514
$754$	−6.00000	−	10.3923i	−0.218507	−	0.378465i
$755$	6.00000	−	10.3923i	0.218362	−	0.378215i
$756$	−5.00000	−	8.66025i	−0.181848	−	0.314970i
$757$	−17.0000	+	29.4449i	−0.617876	+	1.07019i	0.371997	+	0.928234i	$0.378673\pi$
$757$	−17.0000	+	29.4449i	−0.617876	+	1.07019i	−0.989873	+	0.141958i	$0.954660\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$	−24.0000			−0.871145
$760$	−4.00000	+	1.73205i	−0.145095	+	0.0628281i
$761$	−3.00000			−0.108750			−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000			−0.108750			−0.0543750	+	0.998521i	$0.517317\pi$
$762$	−3.00000	+	5.19615i	−0.108679	+	0.188237i
$763$	8.00000	−	13.8564i	0.289619	−	0.501636i
$764$	2.00000	+	3.46410i	0.0723575	+	0.125327i
$765$	−2.00000	+	3.46410i	−0.0723102	+	0.125245i
$766$	3.00000	+	5.19615i	0.108394	+	0.187745i
$767$	30.0000			1.08324
$768$	−1.00000			−0.0360844
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.825518	+	0.564376i	$0.190883\pi$
$769$	25.0000	+	43.3013i	0.901523	+	1.56148i	0.0760054	+	0.997107i	$0.475783\pi$
$770$	3.00000	+	5.19615i	0.108112	+	0.187256i
$771$	−3.00000			−0.108042
$772$	10.0000			0.359908
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	−0.998930	−	0.0462427i	$-0.985275\pi$
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	0.459418	−	0.888220i	$-0.348058\pi$
$774$		0			0
$775$	4.00000	+	6.92820i	0.143684	+	0.248868i
$776$	−7.50000	+	12.9904i	−0.269234	+	0.466328i
$777$	8.00000	−	13.8564i	0.286998	−	0.497096i
$778$		0			0
$779$	−20.0000	+	8.66025i	−0.716574	+	0.310286i
$780$	6.00000			0.214834
$781$	−9.00000	+	15.5885i	−0.322045	+	0.557799i
$782$	−8.00000	+	13.8564i	−0.286079	+	0.495504i
$783$	5.00000	+	8.66025i	0.178685	+	0.309492i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$		0			0
$786$	7.00000			0.249682
$787$	−1.00000			−0.0356462			−0.0178231	−	0.999841i	$-0.505674\pi$
$787$	−1.00000			−0.0356462			−0.0178231	+	0.999841i	$0.505674\pi$
$788$	−4.00000	−	6.92820i	−0.142494	−	0.246807i
$789$	−13.0000	−	22.5167i	−0.462812	−	0.801614i
$790$	8.00000			0.284627
$791$	−26.0000			−0.924454
$792$	3.00000	+	5.19615i	0.106600	+	0.184637i
$793$	−42.0000	+	72.7461i	−1.49146	+	2.58329i
$794$	8.00000	+	13.8564i	0.283909	+	0.491745i
$795$	−3.00000	+	5.19615i	−0.106399	+	0.184289i
$796$	11.0000	−	19.0526i	0.389885	−	0.675300i
$797$	−28.0000			−0.991811			−0.495905	−	0.868377i	$-0.665164\pi$
$797$	−28.0000			−0.991811			−0.495905	+	0.868377i	$0.665164\pi$
$798$	1.00000	−	8.66025i	0.0353996	−	0.306570i
$799$	−12.0000			−0.424529
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	14.0000	−	24.2487i	0.494666	−	0.856786i
$802$	−1.50000	−	2.59808i	−0.0529668	−	0.0917413i
$803$	−13.5000	+	23.3827i	−0.476405	+	0.825157i
$804$	−2.50000	−	4.33013i	−0.0881682	−	0.152712i
$805$	16.0000			0.563926
$806$	48.0000			1.69073
$807$	−14.0000	−	24.2487i	−0.492823	−	0.853595i
$808$	−5.00000	−	8.66025i	−0.175899	−	0.304667i
$809$	−51.0000			−1.79306			−0.896532	−	0.442978i	$-0.853922\pi$
$809$	−51.0000			−1.79306			−0.896532	+	0.442978i	$0.853922\pi$
$810$	1.00000			0.0351364
$811$	−10.0000	−	17.3205i	−0.351147	−	0.608205i	0.635303	−	0.772263i	$-0.280875\pi$
$811$	−10.0000	−	17.3205i	−0.351147	−	0.608205i	−0.986451	+	0.164057i	$0.947542\pi$
$812$	2.00000	−	3.46410i	0.0701862	−	0.121566i
$813$	−11.0000	−	19.0526i	−0.385787	−	0.668202i
$814$	−12.0000	+	20.7846i	−0.420600	+	0.728500i
$815$	1.50000	−	2.59808i	0.0525427	−	0.0910066i
$816$	−2.00000			−0.0700140
$817$		0			0
$818$	19.0000			0.664319
$819$	12.0000	−	20.7846i	0.419314	−	0.726273i
$820$	2.50000	−	4.33013i	0.0873038	−	0.151215i
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	0.961935	−	0.273278i	$-0.0881079\pi$
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	−0.717633	+	0.696421i	$0.754775\pi$
$822$	1.50000	−	2.59808i	0.0523185	−	0.0906183i
$823$	−1.00000	−	1.73205i	−0.0348578	−	0.0603755i	0.848070	−	0.529884i	$-0.177765\pi$
$823$	−1.00000	−	1.73205i	−0.0348578	−	0.0603755i	−0.882928	+	0.469508i	$0.844431\pi$
$824$	−6.00000			−0.209020
$825$	3.00000			0.104447
$826$	5.00000	+	8.66025i	0.173972	+	0.301329i
$827$	−13.5000	−	23.3827i	−0.469441	−	0.813096i	0.529949	−	0.848030i	$-0.322211\pi$
$827$	−13.5000	−	23.3827i	−0.469441	−	0.813096i	−0.999390	+	0.0349341i	$0.988878\pi$
$828$	16.0000			0.556038
$829$	48.0000			1.66711			0.833554	−	0.552437i	$-0.186302\pi$
$829$	48.0000			1.66711			0.833554	+	0.552437i	$0.186302\pi$
$830$	5.50000	+	9.52628i	0.190908	+	0.330662i
$831$	−7.00000	+	12.1244i	−0.242827	+	0.420589i
$832$	−3.00000	−	5.19615i	−0.104006	−	0.180144i
$833$	3.00000	−	5.19615i	0.103944	−	0.180036i
$834$	−4.50000	+	7.79423i	−0.155822	+	0.269892i
$835$	−8.00000			−0.276851
$836$	−1.50000	+	12.9904i	−0.0518786	+	0.449282i
$837$	−40.0000			−1.38260
$838$	14.0000	−	24.2487i	0.483622	−	0.837658i
$839$	−21.0000	+	36.3731i	−0.725001	+	1.25574i	0.233973	+	0.972243i	$0.424827\pi$
$839$	−21.0000	+	36.3731i	−0.725001	+	1.25574i	−0.958974	+	0.283495i	$0.908506\pi$
$840$	1.00000	+	1.73205i	0.0345033	+	0.0597614i
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	−4.00000	−	6.92820i	−0.137849	−	0.238762i
$843$	−7.00000			−0.241093
$844$	−4.00000			−0.137686
$845$	11.5000	+	19.9186i	0.395612	+	0.685220i
$846$	6.00000	+	10.3923i	0.206284	+	0.357295i
$847$	−4.00000			−0.137442
$848$	6.00000			0.206041
$849$	−14.5000	−	25.1147i	−0.497639	−	0.861936i
$850$	1.00000	−	1.73205i	0.0342997	−	0.0594089i
$851$	32.0000	+	55.4256i	1.09695	+	1.89997i
$852$	−3.00000	+	5.19615i	−0.102778	+	0.178017i
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	−0.767642	−	0.640879i	$-0.778570\pi$
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	0.938839	+	0.344358i	$0.111903\pi$
$854$	−28.0000			−0.958140
$855$	7.00000	+	5.19615i	0.239395	+	0.177705i
$856$	12.0000			0.410152
$857$	7.50000	−	12.9904i	0.256195	−	0.443743i	−0.709024	−	0.705184i	$-0.750864\pi$
$857$	7.50000	−	12.9904i	0.256195	−	0.443743i	0.965219	+	0.261441i	$0.0841977\pi$
$858$	9.00000	−	15.5885i	0.307255	−	0.532181i
$859$	−11.5000	−	19.9186i	−0.392375	−	0.679613i	0.600387	−	0.799709i	$-0.295013\pi$
$859$	−11.5000	−	19.9186i	−0.392375	−	0.679613i	−0.992762	+	0.120096i	$0.961680\pi$
$860$		0			0
$861$	5.00000	+	8.66025i	0.170400	+	0.295141i
$862$	6.00000			0.204361
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$	−9.00000	−	15.5885i	−0.306009	−	0.530023i
$866$	−30.0000			−1.01944
$867$	13.0000			0.441503
$868$	8.00000	+	13.8564i	0.271538	+	0.470317i
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$	−1.00000	−	1.73205i	−0.0339032	−	0.0587220i
$871$	15.0000	−	25.9808i	0.508256	−	0.880325i
$872$	−4.00000	+	6.92820i	−0.135457	+	0.234619i
$873$	30.0000			1.01535
$874$	28.0000	+	20.7846i	0.947114	+	0.703050i
$875$	−2.00000			−0.0676123
$876$	−4.50000	+	7.79423i	−0.152041	+	0.263343i
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	−0.343495	−	0.939155i	$-0.611611\pi$
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	0.985079	−	0.172102i	$-0.0550559\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$	11.0000	−	19.0526i	0.371021	−	0.642627i
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	35.0000			1.17918			0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000			1.17918			0.589590	+	0.807703i	$0.299289\pi$
$882$	−6.00000			−0.202031
$883$	−11.5000	−	19.9186i	−0.387006	−	0.670314i	0.605039	−	0.796196i	$-0.293157\pi$
$883$	−11.5000	−	19.9186i	−0.387006	−	0.670314i	−0.992045	+	0.125882i	$0.959824\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$	5.00000			0.168073
$886$	9.00000			0.302361
$887$	−2.00000	−	3.46410i	−0.0671534	−	0.116313i	0.830494	−	0.557028i	$-0.188058\pi$
$887$	−2.00000	−	3.46410i	−0.0671534	−	0.116313i	−0.897647	+	0.440715i	$0.854725\pi$
$888$	−4.00000	+	6.92820i	−0.134231	+	0.232495i
$889$	−6.00000	−	10.3923i	−0.201234	−	0.348547i
$890$	−7.00000	+	12.1244i	−0.234641	+	0.406409i
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	−16.0000			−0.535720
$893$	−3.00000	+	25.9808i	−0.100391	+	0.869413i
$894$	4.00000			0.133780
$895$	1.50000	−	2.59808i	0.0501395	−	0.0868441i
$896$	1.00000	−	1.73205i	0.0334077	−	0.0578638i
$897$	−24.0000	−	41.5692i	−0.801337	−	1.38796i
$898$	14.5000	−	25.1147i	0.483871	−	0.838090i
$899$	−8.00000	−	13.8564i	−0.266815	−	0.462137i
$900$	−2.00000			−0.0666667
$901$	12.0000			0.399778
$902$	−7.50000	−	12.9904i	−0.249723	−	0.432532i
$903$		0			0
$904$	13.0000			0.432374
$905$	16.0000			0.531858
$906$	−6.00000	−	10.3923i	−0.199337	−	0.345261i
$907$	−23.5000	+	40.7032i	−0.780305	+	1.35153i	0.151460	+	0.988463i	$0.451603\pi$
$907$	−23.5000	+	40.7032i	−0.780305	+	1.35153i	−0.931764	+	0.363064i	$0.881731\pi$
$908$	3.50000	+	6.06218i	0.116152	+	0.201180i
$909$	−10.0000	+	17.3205i	−0.331679	+	0.574485i
$910$	−6.00000	+	10.3923i	−0.198898	+	0.344502i
$911$	−32.0000			−1.06021			−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000			−1.06021			−0.530104	+	0.847933i	$0.677847\pi$
$912$	−0.500000	+	4.33013i	−0.0165567	+	0.143385i
$913$	33.0000			1.09214
$914$	6.50000	−	11.2583i	0.215001	−	0.372392i
$915$	−7.00000	+	12.1244i	−0.231413	+	0.400819i
$916$	12.0000	+	20.7846i	0.396491	+	0.686743i
$917$	−7.00000	+	12.1244i	−0.231160	+	0.400381i
$918$	5.00000	+	8.66025i	0.165025	+	0.285831i
$919$	14.0000			0.461817			0.230909	−	0.972975i	$-0.425830\pi$
$919$	14.0000			0.461817			0.230909	+	0.972975i	$0.425830\pi$
$920$	−8.00000			−0.263752
$921$	−2.50000	−	4.33013i	−0.0823778	−	0.142683i
$922$	−11.0000	−	19.0526i	−0.362266	−	0.627463i
$923$	−36.0000			−1.18495
$924$	6.00000			0.197386
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	17.0000	−	29.4449i	0.558655	−	0.967618i
$927$	6.00000	+	10.3923i	0.197066	+	0.341328i
$928$	−1.00000	+	1.73205i	−0.0328266	+	0.0568574i
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	−0.554984	−	0.831861i	$-0.687276\pi$
$929$	13.5000	−	23.3827i	0.442921	−	0.767161i	0.997905	+	0.0646999i	$0.0206090\pi$
$930$	8.00000			0.262330
$931$	−10.5000	−	7.79423i	−0.344124	−	0.255446i
$932$	11.0000			0.360317
$933$	−12.0000	+	20.7846i	−0.392862	+	0.680458i
$934$	3.50000	−	6.06218i	0.114523	−	0.198361i
$935$	−3.00000	−	5.19615i	−0.0981105	−	0.169932i
$936$	−6.00000	+	10.3923i	−0.196116	+	0.339683i
$937$	−17.5000	−	30.3109i	−0.571700	−	0.990214i	−0.996392	−	0.0848755i	$-0.972951\pi$
$937$	−17.5000	−	30.3109i	−0.571700	−	0.990214i	0.424691	−	0.905338i	$-0.360383\pi$
$938$	10.0000			0.326512
$939$	−13.0000			−0.424239
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	−0.989599	−	0.143856i	$-0.954050\pi$
$941$	−19.0000	−	32.9090i	−0.619382	−	1.07280i	0.370216	−	0.928946i	$-0.379284\pi$
$942$		0			0
$943$	−40.0000			−1.30258
$944$	−2.50000	−	4.33013i	−0.0813681	−	0.140934i
$945$	5.00000	−	8.66025i	0.162650	−	0.281718i
$946$		0			0
$947$	26.0000	−	45.0333i	0.844886	−	1.46339i	−0.0408333	−	0.999166i	$-0.513001\pi$
$947$	26.0000	−	45.0333i	0.844886	−	1.46339i	0.885720	−	0.464220i	$-0.153665\pi$
$948$	4.00000	−	6.92820i	0.129914	−	0.225018i
$949$	−54.0000			−1.75291
$950$	−3.50000	−	2.59808i	−0.113555	−	0.0842927i
$951$	30.0000			0.972817
$952$	2.00000	−	3.46410i	0.0648204	−	0.112272i
$953$	3.50000	−	6.06218i	0.113376	−	0.196373i	−0.803753	−	0.594963i	$-0.797167\pi$
$953$	3.50000	−	6.06218i	0.113376	−	0.196373i	0.917129	+	0.398589i	$0.130500\pi$
$954$	−6.00000	−	10.3923i	−0.194257	−	0.336463i
$955$	−2.00000	+	3.46410i	−0.0647185	+	0.112096i
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$	−6.00000			−0.193952
$958$	−12.0000			−0.387702
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$	−0.500000	−	0.866025i	−0.0161374	−	0.0279508i
$961$	33.0000			1.06452
$962$	−48.0000			−1.54758
$963$	−12.0000	−	20.7846i	−0.386695	−	0.669775i
$964$	9.50000	−	16.4545i	0.305974	−	0.529963i
$965$	5.00000	+	8.66025i	0.160956	+	0.278783i
$966$	8.00000	−	13.8564i	0.257396	−	0.445823i
$967$	27.0000	−	46.7654i	0.868261	−	1.50387i	0.00448958	−	0.999990i	$-0.498571\pi$
$967$	27.0000	−	46.7654i	0.868261	−	1.50387i	0.863772	−	0.503883i	$-0.168096\pi$
$968$	2.00000			0.0642824
$969$	−1.00000	+	8.66025i	−0.0321246	+	0.278207i
$970$	−15.0000			−0.481621
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$	8.00000	−	13.8564i	0.256600	−	0.444444i
$973$	−9.00000	−	15.5885i	−0.288527	−	0.499743i
$974$	2.00000	−	3.46410i	0.0640841	−	0.110997i
$975$	3.00000	+	5.19615i	0.0960769	+	0.166410i
$976$	14.0000			0.448129
$977$	33.0000			1.05576			0.527882	−	0.849318i	$-0.322986\pi$
$977$	33.0000			1.05576			0.527882	+	0.849318i	$0.322986\pi$
$978$	−1.50000	−	2.59808i	−0.0479647	−	0.0830773i
$979$	21.0000	+	36.3731i	0.671163	+	1.16249i
$980$	3.00000			0.0958315
$981$	16.0000			0.510841
$982$	10.0000	+	17.3205i	0.319113	+	0.552720i
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$	−2.50000	−	4.33013i	−0.0796971	−	0.138039i
$985$	4.00000	−	6.92820i	0.127451	−	0.220751i
$986$	−2.00000	+	3.46410i	−0.0636930	+	0.110319i
$987$	12.0000			0.381964
$988$	−24.0000	+	10.3923i	−0.763542	+	0.330623i
$989$		0			0
$990$	−3.00000	+	5.19615i	−0.0953463	+	0.165145i
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$	−4.00000	−	6.92820i	−0.127000	−	0.219971i
$993$	−8.50000	+	14.7224i	−0.269739	+	0.467202i
$994$	−6.00000	−	10.3923i	−0.190308	−	0.329624i
$995$	22.0000			0.697447
$996$	11.0000			0.348548
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	0.849756	−	0.527176i	$-0.176749\pi$
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	−0.881426	+	0.472322i	$0.843416\pi$
$998$	16.5000	+	28.5788i	0.522298	+	0.904647i
$999$	40.0000			1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.e.b.11.1	✓	2
3.2	odd	2		1710.2.l.b.1531.1		2
4.3	odd	2		1520.2.q.e.961.1		2
5.2	odd	4		950.2.j.a.49.2		4
5.3	odd	4		950.2.j.a.49.1		4
5.4	even	2		950.2.e.a.201.1		2
19.7	even	3	inner	190.2.e.b.121.1	yes	2
19.8	odd	6		3610.2.a.i.1.1		1
19.11	even	3		3610.2.a.a.1.1		1
57.26	odd	6		1710.2.l.b.1261.1		2
76.7	odd	6		1520.2.q.e.881.1		2
95.7	odd	12		950.2.j.a.349.1		4
95.64	even	6		950.2.e.a.501.1		2
95.83	odd	12		950.2.j.a.349.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.e.b.11.1	✓	2	1.1	even	1	trivial
190.2.e.b.121.1	yes	2	19.7	even	3	inner
950.2.e.a.201.1		2	5.4	even	2
950.2.e.a.501.1		2	95.64	even	6
950.2.j.a.49.1		4	5.3	odd	4
950.2.j.a.49.2		4	5.2	odd	4
950.2.j.a.349.1		4	95.7	odd	12
950.2.j.a.349.2		4	95.83	odd	12
1520.2.q.e.881.1		2	76.7	odd	6
1520.2.q.e.961.1		2	4.3	odd	2
1710.2.l.b.1261.1		2	57.26	odd	6
1710.2.l.b.1531.1		2	3.2	odd	2
3610.2.a.a.1.1		1	19.11	even	3
3610.2.a.i.1.1		1	19.8	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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +2.00000 q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(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} +(-0.500000 - 0.866025i) q^{6} +2.00000 q^{7} -1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-0.500000 - 0.866025i) q^{10} -3.00000 q^{11} -1.00000 q^{12} +(-3.00000 - 5.19615i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +2.00000 q^{18} +(3.50000 + 2.59808i) q^{19} -1.00000 q^{20} +(1.00000 - 1.73205i) q^{21} +(-1.50000 + 2.59808i) q^{22} +(4.00000 + 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} -6.00000 q^{26} +5.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(1.00000 + 1.73205i) q^{29} -1.00000 q^{30} -8.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +(1.00000 + 1.73205i) q^{34} +(1.00000 - 1.73205i) q^{35} +(1.00000 - 1.73205i) q^{36} +8.00000 q^{37} +(4.00000 - 1.73205i) q^{38} -6.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(-1.00000 - 1.73205i) q^{42} +(1.50000 + 2.59808i) q^{44} +2.00000 q^{45} +8.00000 q^{46} +(3.00000 + 5.19615i) q^{47} +(0.500000 + 0.866025i) q^{48} -3.00000 q^{49} -1.00000 q^{50} +(1.00000 + 1.73205i) q^{51} +(-3.00000 + 5.19615i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(2.50000 - 4.33013i) q^{54} +(-1.50000 + 2.59808i) q^{55} -2.00000 q^{56} +(4.00000 - 1.73205i) q^{57} +2.00000 q^{58} +(-2.50000 + 4.33013i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-7.00000 - 12.1244i) q^{61} +(-4.00000 + 6.92820i) q^{62} +(2.00000 + 3.46410i) q^{63} +1.00000 q^{64} -6.00000 q^{65} +(1.50000 + 2.59808i) q^{66} +(2.50000 + 4.33013i) q^{67} +2.00000 q^{68} +8.00000 q^{69} +(-1.00000 - 1.73205i) q^{70} +(3.00000 - 5.19615i) q^{71} +(-1.00000 - 1.73205i) q^{72} +(4.50000 - 7.79423i) q^{73} +(4.00000 - 6.92820i) q^{74} -1.00000 q^{75} +(0.500000 - 4.33013i) q^{76} -6.00000 q^{77} +(-3.00000 + 5.19615i) q^{78} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.50000 + 4.33013i) q^{82} -11.0000 q^{83} -2.00000 q^{84} +(1.00000 + 1.73205i) q^{85} +2.00000 q^{87} +3.00000 q^{88} +(-7.00000 - 12.1244i) q^{89} +(1.00000 - 1.73205i) q^{90} +(-6.00000 - 10.3923i) q^{91} +(4.00000 - 6.92820i) q^{92} +(-4.00000 + 6.92820i) q^{93} +6.00000 q^{94} +(4.00000 - 1.73205i) q^{95} +1.00000 q^{96} +(7.50000 - 12.9904i) q^{97} +(-1.50000 + 2.59808i) q^{98} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 - q^4 + q^5 - q^6 + 4 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q + q^{2} + q^{3} - q^{4} + q^{5} - q^{6} + 4 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} - 6 q^{11} - 2 q^{12} - 6 q^{13} + 2 q^{14} - q^{15} - q^{16} - 2 q^{17} + 4 q^{18} + 7 q^{19} - 2 q^{20} + 2 q^{21} - 3 q^{22} + 8 q^{23} - q^{24} - q^{25} - 12 q^{26} + 10 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} - 16 q^{31} + q^{32} - 3 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 16 q^{37} + 8 q^{38} - 12 q^{39} - q^{40} - 5 q^{41} - 2 q^{42} + 3 q^{44} + 4 q^{45} + 16 q^{46} + 6 q^{47} + q^{48} - 6 q^{49} - 2 q^{50} + 2 q^{51} - 6 q^{52} - 6 q^{53} + 5 q^{54} - 3 q^{55} - 4 q^{56} + 8 q^{57} + 4 q^{58} - 5 q^{59} - q^{60} - 14 q^{61} - 8 q^{62} + 4 q^{63} + 2 q^{64} - 12 q^{65} + 3 q^{66} + 5 q^{67} + 4 q^{68} + 16 q^{69} - 2 q^{70} + 6 q^{71} - 2 q^{72} + 9 q^{73} + 8 q^{74} - 2 q^{75} + q^{76} - 12 q^{77} - 6 q^{78} - 8 q^{79} + q^{80} - q^{81} + 5 q^{82} - 22 q^{83} - 4 q^{84} + 2 q^{85} + 4 q^{87} + 6 q^{88} - 14 q^{89} + 2 q^{90} - 12 q^{91} + 8 q^{92} - 8 q^{93} + 12 q^{94} + 8 q^{95} + 2 q^{96} + 15 q^{97} - 3 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 - q^4 + q^5 - q^6 + 4 * q^7 - 2 * q^8 + 2 * q^9 - q^10 - 6 * q^11 - 2 * q^12 - 6 * q^13 + 2 * q^14 - q^15 - q^16 - 2 * q^17 + 4 * q^18 + 7 * q^19 - 2 * q^20 + 2 * q^21 - 3 * q^22 + 8 * q^23 - q^24 - q^25 - 12 * q^26 + 10 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 - 16 * q^31 + q^32 - 3 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 16 * q^37 + 8 * q^38 - 12 * q^39 - q^40 - 5 * q^41 - 2 * q^42 + 3 * q^44 + 4 * q^45 + 16 * q^46 + 6 * q^47 + q^48 - 6 * q^49 - 2 * q^50 + 2 * q^51 - 6 * q^52 - 6 * q^53 + 5 * q^54 - 3 * q^55 - 4 * q^56 + 8 * q^57 + 4 * q^58 - 5 * q^59 - q^60 - 14 * q^61 - 8 * q^62 + 4 * q^63 + 2 * q^64 - 12 * q^65 + 3 * q^66 + 5 * q^67 + 4 * q^68 + 16 * q^69 - 2 * q^70 + 6 * q^71 - 2 * q^72 + 9 * q^73 + 8 * q^74 - 2 * q^75 + q^76 - 12 * q^77 - 6 * q^78 - 8 * q^79 + q^80 - q^81 + 5 * q^82 - 22 * q^83 - 4 * q^84 + 2 * q^85 + 4 * q^87 + 6 * q^88 - 14 * q^89 + 2 * q^90 - 12 * q^91 + 8 * q^92 - 8 * q^93 + 12 * q^94 + 8 * q^95 + 2 * q^96 + 15 * q^97 - 3 * q^98 - 6 * q^99

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