LMFDB - Embedded newform 74.2.c.b.63.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,2,Mod(47,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("74.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.c (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:	$0.590892974957$
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			63.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	74.63
Dual form			74.2.c.b.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +2.00000 q^{6} +(2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +2.00000 q^{6} +(2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -3.00000 q^{10} -6.00000 q^{11} +(1.00000 + 1.73205i) q^{12} +(-1.00000 + 1.73205i) q^{13} +4.00000 q^{14} +(3.00000 + 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(-4.00000 - 6.92820i) q^{21} +(-3.00000 - 5.19615i) q^{22} +6.00000 q^{23} +(-1.00000 + 1.73205i) q^{24} +(-2.00000 - 3.46410i) q^{25} -2.00000 q^{26} +4.00000 q^{27} +(2.00000 + 3.46410i) q^{28} +3.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.00000 + 10.3923i) q^{33} +(1.50000 - 2.59808i) q^{34} +(6.00000 + 10.3923i) q^{35} +1.00000 q^{36} +(5.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(2.00000 + 3.46410i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(4.00000 - 6.92820i) q^{42} -4.00000 q^{43} +(3.00000 - 5.19615i) q^{44} +3.00000 q^{45} +(3.00000 + 5.19615i) q^{46} -6.00000 q^{47} -2.00000 q^{48} +(-4.50000 - 7.79423i) q^{49} +(2.00000 - 3.46410i) q^{50} -6.00000 q^{51} +(-1.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.00000 + 3.46410i) q^{54} +(9.00000 - 15.5885i) q^{55} +(-2.00000 + 3.46410i) q^{56} +(2.00000 + 3.46410i) q^{57} +(1.50000 + 2.59808i) q^{58} -6.00000 q^{60} +(0.500000 - 0.866025i) q^{61} +(1.00000 + 1.73205i) q^{62} -4.00000 q^{63} +1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} -12.0000 q^{66} +(-1.00000 + 1.73205i) q^{67} +3.00000 q^{68} +(6.00000 - 10.3923i) q^{69} +(-6.00000 + 10.3923i) q^{70} +(6.00000 - 10.3923i) q^{71} +(0.500000 + 0.866025i) q^{72} -10.0000 q^{73} +(5.00000 + 3.46410i) q^{74} -8.00000 q^{75} +(-1.00000 - 1.73205i) q^{76} +(-12.0000 + 20.7846i) q^{77} +(-2.00000 + 3.46410i) q^{78} +(-7.00000 + 12.1244i) q^{79} +3.00000 q^{80} +(5.50000 - 9.52628i) q^{81} -3.00000 q^{82} +(-3.00000 - 5.19615i) q^{83} +8.00000 q^{84} +9.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(3.00000 - 5.19615i) q^{87} +6.00000 q^{88} +(-1.50000 - 2.59808i) q^{89} +(1.50000 + 2.59808i) q^{90} +(4.00000 + 6.92820i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(2.00000 - 3.46410i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(-3.00000 - 5.19615i) q^{95} +(-1.00000 - 1.73205i) q^{96} -13.0000 q^{97} +(4.50000 - 7.79423i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 + 2 * q^3 - q^4 - 3 * q^5 + 4 * q^6 + 4 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} - 6 q^{10} - 12 q^{11} + 2 q^{12} - 2 q^{13} + 8 q^{14} + 6 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - 3 q^{20} - 8 q^{21} - 6 q^{22} + 12 q^{23} - 2 q^{24} - 4 q^{25} - 4 q^{26} + 8 q^{27} + 4 q^{28} + 6 q^{29} - 6 q^{30} + 4 q^{31} + q^{32} - 12 q^{33} + 3 q^{34} + 12 q^{35} + 2 q^{36} + 11 q^{37} - 4 q^{38} + 4 q^{39} + 3 q^{40} - 3 q^{41} + 8 q^{42} - 8 q^{43} + 6 q^{44} + 6 q^{45} + 6 q^{46} - 12 q^{47} - 4 q^{48} - 9 q^{49} + 4 q^{50} - 12 q^{51} - 2 q^{52} + 6 q^{53} + 4 q^{54} + 18 q^{55} - 4 q^{56} + 4 q^{57} + 3 q^{58} - 12 q^{60} + q^{61} + 2 q^{62} - 8 q^{63} + 2 q^{64} - 6 q^{65} - 24 q^{66} - 2 q^{67} + 6 q^{68} + 12 q^{69} - 12 q^{70} + 12 q^{71} + q^{72} - 20 q^{73} + 10 q^{74} - 16 q^{75} - 2 q^{76} - 24 q^{77} - 4 q^{78} - 14 q^{79} + 6 q^{80} + 11 q^{81} - 6 q^{82} - 6 q^{83} + 16 q^{84} + 18 q^{85} - 4 q^{86} + 6 q^{87} + 12 q^{88} - 3 q^{89} + 3 q^{90} + 8 q^{91} - 6 q^{92} + 4 q^{93} - 6 q^{94} - 6 q^{95} - 2 q^{96} - 26 q^{97} + 9 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 3 * q^5 + 4 * q^6 + 4 * q^7 - 2 * q^8 - q^9 - 6 * q^10 - 12 * q^11 + 2 * q^12 - 2 * q^13 + 8 * q^14 + 6 * q^15 - q^16 - 3 * q^17 + q^18 - 2 * q^19 - 3 * q^20 - 8 * q^21 - 6 * q^22 + 12 * q^23 - 2 * q^24 - 4 * q^25 - 4 * q^26 + 8 * q^27 + 4 * q^28 + 6 * q^29 - 6 * q^30 + 4 * q^31 + q^32 - 12 * q^33 + 3 * q^34 + 12 * q^35 + 2 * q^36 + 11 * q^37 - 4 * q^38 + 4 * q^39 + 3 * q^40 - 3 * q^41 + 8 * q^42 - 8 * q^43 + 6 * q^44 + 6 * q^45 + 6 * q^46 - 12 * q^47 - 4 * q^48 - 9 * q^49 + 4 * q^50 - 12 * q^51 - 2 * q^52 + 6 * q^53 + 4 * q^54 + 18 * q^55 - 4 * q^56 + 4 * q^57 + 3 * q^58 - 12 * q^60 + q^61 + 2 * q^62 - 8 * q^63 + 2 * q^64 - 6 * q^65 - 24 * q^66 - 2 * q^67 + 6 * q^68 + 12 * q^69 - 12 * q^70 + 12 * q^71 + q^72 - 20 * q^73 + 10 * q^74 - 16 * q^75 - 2 * q^76 - 24 * q^77 - 4 * q^78 - 14 * q^79 + 6 * q^80 + 11 * q^81 - 6 * q^82 - 6 * q^83 + 16 * q^84 + 18 * q^85 - 4 * q^86 + 6 * q^87 + 12 * q^88 - 3 * q^89 + 3 * q^90 + 8 * q^91 - 6 * q^92 + 4 * q^93 - 6 * q^94 - 6 * q^95 - 2 * q^96 - 26 * q^97 + 9 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	−0.418432	−	0.908248i	$-0.637420\pi$
$3$	1.00000	−	1.73205i	0.577350	−	1.00000i	0.995782	−	0.0917517i	$-0.0292466\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$	2.00000			0.816497
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	2.00000	−	3.46410i	0.755929	−	1.30931i	0.944911	−	0.327327i	$-0.106148\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−3.00000			−0.948683
$11$	−6.00000			−1.80907			−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000			−1.80907			−0.904534	+	0.426401i	$0.859781\pi$
$12$	1.00000	+	1.73205i	0.288675	+	0.500000i
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	4.00000			1.06904
$15$	3.00000	+	5.19615i	0.774597	+	1.34164i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$	−4.00000	−	6.92820i	−0.872872	−	1.51186i
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$	−1.00000	+	1.73205i	−0.204124	+	0.353553i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−2.00000			−0.392232
$27$	4.00000			0.769800
$28$	2.00000	+	3.46410i	0.377964	+	0.654654i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	−3.00000	+	5.19615i	−0.547723	+	0.948683i
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−6.00000	+	10.3923i	−1.04447	+	1.80907i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$	6.00000	+	10.3923i	1.01419	+	1.75662i
$36$	1.00000			0.166667
$37$	5.50000	−	2.59808i	0.904194	−	0.427121i
$37$	5.50000	−	2.59808i	0.904194	−	0.427121i
$38$	−2.00000			−0.324443
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$	4.00000	−	6.92820i	0.617213	−	1.06904i
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	3.00000	−	5.19615i	0.452267	−	0.783349i
$45$	3.00000			0.447214
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	−2.00000			−0.288675
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$	−6.00000			−0.840168
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	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	$0.698135\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$	9.00000	−	15.5885i	1.21356	−	2.10195i
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$	2.00000	+	3.46410i	0.264906	+	0.458831i
$58$	1.50000	+	2.59808i	0.196960	+	0.341144i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	−6.00000			−0.774597
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	1.00000	+	1.73205i	0.127000	+	0.219971i
$63$	−4.00000			−0.503953
$64$	1.00000			0.125000
$65$	−3.00000	−	5.19615i	−0.372104	−	0.644503i
$66$	−12.0000			−1.47710
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	3.00000			0.363803
$69$	6.00000	−	10.3923i	0.722315	−	1.25109i
$70$	−6.00000	+	10.3923i	−0.717137	+	1.24212i
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	−0.252010	−	0.967725i	$-0.581092\pi$
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	0.964079	−	0.265615i	$-0.0855750\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$	5.00000	+	3.46410i	0.581238	+	0.402694i
$75$	−8.00000			−0.923760
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−12.0000	+	20.7846i	−1.36753	+	2.36863i
$78$	−2.00000	+	3.46410i	−0.226455	+	0.392232i
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	0.139895	+	0.990166i	$0.455323\pi$
$79$	−7.00000	+	12.1244i	−0.787562	+	1.36410i	−0.927457	+	0.373930i	$0.878010\pi$
$80$	3.00000			0.335410
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	−3.00000			−0.331295
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	0.653079	−	0.757290i	$-0.273477\pi$
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	−0.982372	+	0.186938i	$0.940144\pi$
$84$	8.00000			0.872872
$85$	9.00000			0.976187
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$	6.00000			0.639602
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	0.775509	−	0.631337i	$-0.217494\pi$
$89$	−1.50000	−	2.59808i	−0.159000	−	0.275396i	−0.934508	+	0.355942i	$0.884160\pi$
$90$	1.50000	+	2.59808i	0.158114	+	0.273861i
$91$	4.00000	+	6.92820i	0.419314	+	0.726273i
$92$	−3.00000	+	5.19615i	−0.312772	+	0.541736i
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	−3.00000	−	5.19615i	−0.307794	−	0.533114i
$96$	−1.00000	−	1.73205i	−0.102062	−	0.176777i
$97$	−13.0000			−1.31995			−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000			−1.31995			−0.659975	+	0.751288i	$0.729433\pi$
$98$	4.50000	−	7.79423i	0.454569	−	0.787336i
$99$	3.00000	+	5.19615i	0.301511	+	0.522233i
$100$	4.00000			0.400000
$101$	3.00000			0.298511			0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000			0.298511			0.149256	+	0.988799i	$0.452312\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$	24.0000			2.34216
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	−2.00000	+	3.46410i	−0.192450	+	0.333333i
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	0.888977	−	0.457951i	$-0.151417\pi$
$109$	0.500000	+	0.866025i	0.0478913	+	0.0829502i	−0.841086	+	0.540901i	$0.818083\pi$
$110$	18.0000			1.71623
$111$	1.00000	−	12.1244i	0.0949158	−	1.15079i
$112$	−4.00000			−0.377964
$113$	9.00000	+	15.5885i	0.846649	+	1.46644i	0.884182	+	0.467143i	$0.154717\pi$
$113$	9.00000	+	15.5885i	0.846649	+	1.46644i	−0.0375328	+	0.999295i	$0.511950\pi$
$114$	−2.00000	+	3.46410i	−0.187317	+	0.324443i
$115$	−9.00000	+	15.5885i	−0.839254	+	1.45363i
$116$	−1.50000	+	2.59808i	−0.139272	+	0.241225i
$117$	2.00000			0.184900
$118$		0			0
$119$	−12.0000			−1.10004
$120$	−3.00000	−	5.19615i	−0.273861	−	0.474342i
$121$	25.0000			2.27273
$122$	1.00000			0.0905357
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	−3.00000			−0.268328
$126$	−2.00000	−	3.46410i	−0.178174	−	0.308607i
$127$	5.00000	+	8.66025i	0.443678	+	0.768473i	0.997959	−	0.0638564i	$-0.0203400\pi$
$127$	5.00000	+	8.66025i	0.443678	+	0.768473i	−0.554281	+	0.832330i	$0.687007\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$	3.00000	−	5.19615i	0.263117	−	0.455733i
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$	−6.00000	−	10.3923i	−0.522233	−	0.904534i
$133$	4.00000	+	6.92820i	0.346844	+	0.600751i
$134$	−2.00000			−0.172774
$135$	−6.00000	+	10.3923i	−0.516398	+	0.894427i
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	3.00000			0.256307			0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000			0.256307			0.128154	+	0.991754i	$0.459095\pi$
$138$	12.0000			1.02151
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	0.820495	−	0.571654i	$-0.193698\pi$
$139$	−1.00000	−	1.73205i	−0.0848189	−	0.146911i	−0.905314	+	0.424743i	$0.860365\pi$
$140$	−12.0000			−1.01419
$141$	−6.00000	+	10.3923i	−0.505291	+	0.875190i
$142$	12.0000			1.00702
$143$	6.00000	−	10.3923i	0.501745	−	0.869048i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$	−5.00000	−	8.66025i	−0.413803	−	0.716728i
$147$	−18.0000			−1.48461
$148$	−0.500000	+	6.06218i	−0.0410997	+	0.498308i
$149$	−21.0000			−1.72039			−0.860194	−	0.509968i	$-0.829657\pi$
$149$	−21.0000			−1.72039			−0.860194	+	0.509968i	$0.829657\pi$
$150$	−4.00000	−	6.92820i	−0.326599	−	0.565685i
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.0615699	−	0.998103i	$-0.480389\pi$
$151$	11.0000	−	19.0526i	0.895167	−	1.55048i	0.833597	−	0.552372i	$-0.186277\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	−1.50000	+	2.59808i	−0.121268	+	0.210042i
$154$	−24.0000			−1.93398
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$	−4.00000			−0.320256
$157$	−5.50000	−	9.52628i	−0.438948	−	0.760280i	0.558661	−	0.829396i	$-0.311315\pi$
$157$	−5.50000	−	9.52628i	−0.438948	−	0.760280i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	−14.0000			−1.11378
$159$	12.0000			0.951662
$160$	1.50000	+	2.59808i	0.118585	+	0.205396i
$161$	12.0000	−	20.7846i	0.945732	−	1.63806i
$162$	11.0000			0.864242
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$	−18.0000	−	31.1769i	−1.40130	−	2.42712i
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$	4.00000	+	6.92820i	0.308607	+	0.534522i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	4.50000	+	7.79423i	0.345134	+	0.597790i
$171$	2.00000			0.152944
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	0.920722	+	0.390218i	$0.127601\pi$
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	−0.122422	+	0.992478i	$0.539066\pi$
$174$	6.00000			0.454859
$175$	−16.0000			−1.20949
$176$	3.00000	+	5.19615i	0.226134	+	0.391675i
$177$		0			0
$178$	1.50000	−	2.59808i	0.112430	−	0.194734i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	−1.50000	+	2.59808i	−0.111803	+	0.193649i
$181$	0.500000	−	0.866025i	0.0371647	−	0.0643712i	−0.846845	−	0.531840i	$-0.821501\pi$
$181$	0.500000	−	0.866025i	0.0371647	−	0.0643712i	0.884009	+	0.467469i	$0.154834\pi$
$182$	−4.00000	+	6.92820i	−0.296500	+	0.513553i
$183$	−1.00000	−	1.73205i	−0.0739221	−	0.128037i
$184$	−6.00000			−0.442326
$185$	−1.50000	+	18.1865i	−0.110282	+	1.33710i
$186$	4.00000			0.293294
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$	3.00000	−	5.19615i	0.218797	−	0.378968i
$189$	8.00000	−	13.8564i	0.581914	−	1.00791i
$190$	3.00000	−	5.19615i	0.217643	−	0.376969i
$191$	−6.00000			−0.434145			−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000			−0.434145			−0.217072	+	0.976156i	$0.569651\pi$
$192$	1.00000	−	1.73205i	0.0721688	−	0.125000i
$193$	11.0000			0.791797			0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000			0.791797			0.395899	+	0.918294i	$0.370433\pi$
$194$	−6.50000	−	11.2583i	−0.466673	−	0.808301i
$195$	−12.0000			−0.859338
$196$	9.00000			0.642857
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	0.807630	−	0.589689i	$-0.200750\pi$
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	−0.914501	+	0.404584i	$0.867416\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$	1.50000	+	2.59808i	0.105540	+	0.182800i
$203$	6.00000	−	10.3923i	0.421117	−	0.729397i
$204$	3.00000	−	5.19615i	0.210042	−	0.363803i
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	−2.00000	−	3.46410i	−0.139347	−	0.241355i
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$	2.00000			0.138675
$209$	6.00000	−	10.3923i	0.415029	−	0.718851i
$210$	12.0000	+	20.7846i	0.828079	+	1.43427i
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$	−6.00000			−0.412082
$213$	−12.0000	−	20.7846i	−0.822226	−	1.42414i
$214$	12.0000			0.820303
$215$	6.00000	−	10.3923i	0.409197	−	0.708749i
$216$	−4.00000			−0.272166
$217$	4.00000	−	6.92820i	0.271538	−	0.470317i
$218$	−0.500000	+	0.866025i	−0.0338643	+	0.0586546i
$219$	−10.0000	+	17.3205i	−0.675737	+	1.17041i
$220$	9.00000	+	15.5885i	0.606780	+	1.05097i
$221$	6.00000			0.403604
$222$	11.0000	−	5.19615i	0.738272	−	0.348743i
$223$	14.0000			0.937509			0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000			0.937509			0.468755	+	0.883328i	$0.344703\pi$
$224$	−2.00000	−	3.46410i	−0.133631	−	0.231455i
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$	−4.00000			−0.264906
$229$	−5.50000	+	9.52628i	−0.363450	+	0.629514i	−0.988526	−	0.151050i	$-0.951735\pi$
$229$	−5.50000	+	9.52628i	−0.363450	+	0.629514i	0.625076	+	0.780564i	$0.285068\pi$
$230$	−18.0000			−1.18688
$231$	24.0000	+	41.5692i	1.57908	+	2.73505i
$232$	−3.00000			−0.196960
$233$	−9.00000			−0.589610			−0.294805	−	0.955557i	$-0.595255\pi$
$233$	−9.00000			−0.589610			−0.294805	+	0.955557i	$0.595255\pi$
$234$	1.00000	+	1.73205i	0.0653720	+	0.113228i
$235$	9.00000	−	15.5885i	0.587095	−	1.01688i
$236$		0			0
$237$	14.0000	+	24.2487i	0.909398	+	1.57512i
$238$	−6.00000	−	10.3923i	−0.388922	−	0.673633i
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$	3.00000	−	5.19615i	0.193649	−	0.335410i
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	12.5000	+	21.6506i	0.803530	+	1.39176i
$243$	−5.00000	−	8.66025i	−0.320750	−	0.555556i
$244$	0.500000	+	0.866025i	0.0320092	+	0.0554416i
$245$	27.0000			1.72497
$246$	−3.00000	+	5.19615i	−0.191273	+	0.331295i
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$	−2.00000			−0.127000
$249$	−12.0000			−0.760469
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	2.00000	−	3.46410i	0.125988	−	0.218218i
$253$	−36.0000			−2.26330
$254$	−5.00000	+	8.66025i	−0.313728	+	0.543393i
$255$	9.00000	−	15.5885i	0.563602	−	0.976187i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−13.5000	−	23.3827i	−0.842107	−	1.45857i	−0.888110	−	0.459631i	$-0.847982\pi$
$257$	−13.5000	−	23.3827i	−0.842107	−	1.45857i	0.0460033	−	0.998941i	$-0.485352\pi$
$258$	−8.00000			−0.498058
$259$	2.00000	−	24.2487i	0.124274	−	1.50674i
$260$	6.00000			0.372104
$261$	−1.50000	−	2.59808i	−0.0928477	−	0.160817i
$262$	9.00000	−	15.5885i	0.556022	−	0.963058i
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$	6.00000	−	10.3923i	0.369274	−	0.639602i
$265$	−18.0000			−1.10573
$266$	−4.00000	+	6.92820i	−0.245256	+	0.424795i
$267$	−6.00000			−0.367194
$268$	−1.00000	−	1.73205i	−0.0610847	−	0.105802i
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$	−12.0000			−0.730297
$271$	5.00000	+	8.66025i	0.303728	+	0.526073i	0.976977	−	0.213343i	$-0.0684351\pi$
$271$	5.00000	+	8.66025i	0.303728	+	0.526073i	−0.673249	+	0.739416i	$0.735102\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$	16.0000			0.968364
$274$	1.50000	+	2.59808i	0.0906183	+	0.156956i
$275$	12.0000	+	20.7846i	0.723627	+	1.25336i
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$	1.00000	−	1.73205i	0.0599760	−	0.103882i
$279$	−1.00000	−	1.73205i	−0.0598684	−	0.103695i
$280$	−6.00000	−	10.3923i	−0.358569	−	0.621059i
$281$	−7.50000	−	12.9904i	−0.447412	−	0.774941i	0.550804	−	0.834634i	$-0.314321\pi$
$281$	−7.50000	−	12.9904i	−0.447412	−	0.774941i	−0.998217	+	0.0596933i	$0.980988\pi$
$282$	−12.0000			−0.714590
$283$	8.00000	−	13.8564i	0.475551	−	0.823678i	−0.524057	−	0.851683i	$-0.675582\pi$
$283$	8.00000	−	13.8564i	0.475551	−	0.823678i	0.999608	+	0.0280052i	$0.00891551\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$	−12.0000			−0.710819
$286$	12.0000			0.709575
$287$	6.00000	+	10.3923i	0.354169	+	0.613438i
$288$	−1.00000			−0.0589256
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−9.00000			−0.528498
$291$	−13.0000	+	22.5167i	−0.762073	+	1.31995i
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	−1.50000	+	2.59808i	−0.0876309	+	0.151781i	−0.906509	−	0.422186i	$-0.861263\pi$
$293$	−1.50000	+	2.59808i	−0.0876309	+	0.151781i	0.818878	+	0.573967i	$0.194596\pi$
$294$	−9.00000	−	15.5885i	−0.524891	−	0.909137i
$295$		0			0
$296$	−5.50000	+	2.59808i	−0.319681	+	0.151010i
$297$	−24.0000			−1.39262
$298$	−10.5000	−	18.1865i	−0.608249	−	1.05352i
$299$	−6.00000	+	10.3923i	−0.346989	+	0.601003i
$300$	4.00000	−	6.92820i	0.230940	−	0.400000i
$301$	−8.00000	+	13.8564i	−0.461112	+	0.798670i
$302$	22.0000			1.26596
$303$	3.00000	−	5.19615i	0.172345	−	0.298511i
$304$	2.00000			0.114708
$305$	1.50000	+	2.59808i	0.0858898	+	0.148765i
$306$	−3.00000			−0.171499
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−12.0000	−	20.7846i	−0.683763	−	1.18431i
$309$	−4.00000	+	6.92820i	−0.227552	+	0.394132i
$310$	−6.00000			−0.340777
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$	−2.00000	−	3.46410i	−0.113228	−	0.196116i
$313$	6.50000	+	11.2583i	0.367402	+	0.636358i	0.989158	−	0.146852i	$-0.0469141\pi$
$313$	6.50000	+	11.2583i	0.367402	+	0.636358i	−0.621757	+	0.783210i	$0.713581\pi$
$314$	5.50000	−	9.52628i	0.310383	−	0.537599i
$315$	6.00000	−	10.3923i	0.338062	−	0.585540i
$316$	−7.00000	−	12.1244i	−0.393781	−	0.682048i
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	0.994266	+	0.106932i	$0.0341026\pi$
$317$	10.5000	+	18.1865i	0.589739	+	1.02146i	−0.404528	+	0.914526i	$0.632564\pi$
$318$	6.00000	+	10.3923i	0.336463	+	0.582772i
$319$	−18.0000			−1.00781
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$	−12.0000	−	20.7846i	−0.669775	−	1.16008i
$322$	24.0000			1.33747
$323$	6.00000			0.333849
$324$	5.50000	+	9.52628i	0.305556	+	0.529238i
$325$	8.00000			0.443760
$326$	−8.00000	+	13.8564i	−0.443079	+	0.767435i
$327$	2.00000			0.110600
$328$	1.50000	−	2.59808i	0.0828236	−	0.143455i
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$	18.0000	−	31.1769i	0.990867	−	1.71623i
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	6.00000			0.329293
$333$	−5.00000	−	3.46410i	−0.273998	−	0.189832i
$334$	−12.0000			−0.656611
$335$	−3.00000	−	5.19615i	−0.163908	−	0.283896i
$336$	−4.00000	+	6.92820i	−0.218218	+	0.377964i
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	−0.293783	−	0.955872i	$-0.594914\pi$
$337$	12.5000	−	21.6506i	0.680918	−	1.17939i	0.974701	−	0.223513i	$-0.0717525\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	36.0000			1.95525
$340$	−4.50000	+	7.79423i	−0.244047	+	0.422701i
$341$	−12.0000			−0.649836
$342$	1.00000	+	1.73205i	0.0540738	+	0.0936586i
$343$	−8.00000			−0.431959
$344$	4.00000			0.215666
$345$	18.0000	+	31.1769i	0.969087	+	1.67851i
$346$	−10.5000	+	18.1865i	−0.564483	+	0.977714i
$347$	6.00000			0.322097			0.161048	−	0.986947i	$-0.448512\pi$
$347$	6.00000			0.322097			0.161048	+	0.986947i	$0.448512\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	0.500000	+	0.866025i	0.0267644	+	0.0463573i	0.879097	−	0.476642i	$-0.158146\pi$
$349$	0.500000	+	0.866025i	0.0267644	+	0.0463573i	−0.852333	+	0.523000i	$0.824813\pi$
$350$	−8.00000	−	13.8564i	−0.427618	−	0.740656i
$351$	−4.00000	+	6.92820i	−0.213504	+	0.369800i
$352$	−3.00000	+	5.19615i	−0.159901	+	0.276956i
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	0.997592	+	0.0693543i	$0.0220939\pi$
$353$	10.5000	+	18.1865i	0.558859	+	0.967972i	−0.438733	+	0.898617i	$0.644573\pi$
$354$		0			0
$355$	18.0000	+	31.1769i	0.955341	+	1.65470i
$356$	3.00000			0.159000
$357$	−12.0000	+	20.7846i	−0.635107	+	1.10004i
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	−3.00000			−0.158114
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	1.00000			0.0525588
$363$	25.0000	−	43.3013i	1.31216	−	2.27273i
$364$	−8.00000			−0.419314
$365$	15.0000	−	25.9808i	0.785136	−	1.35990i
$366$	1.00000	−	1.73205i	0.0522708	−	0.0905357i
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	0.913493	+	0.406855i	$0.133375\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$	3.00000			0.156174
$370$	−16.5000	+	7.79423i	−0.857794	+	0.405203i
$371$	24.0000			1.24602
$372$	2.00000	+	3.46410i	0.103695	+	0.179605i
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$	−9.00000	+	15.5885i	−0.465379	+	0.806060i
$375$	−3.00000	+	5.19615i	−0.154919	+	0.268328i
$376$	6.00000			0.309426
$377$	−3.00000	+	5.19615i	−0.154508	+	0.267615i
$378$	16.0000			0.822951
$379$	8.00000	+	13.8564i	0.410932	+	0.711756i	0.994992	−	0.0999550i	$-0.0318699\pi$
$379$	8.00000	+	13.8564i	0.410932	+	0.711756i	−0.584060	+	0.811711i	$0.698537\pi$
$380$	6.00000			0.307794
$381$	20.0000			1.02463
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$	−6.00000	+	10.3923i	−0.306586	+	0.531022i	−0.977613	−	0.210411i	$-0.932520\pi$
$383$	−6.00000	+	10.3923i	−0.306586	+	0.531022i	0.671027	+	0.741433i	$0.265853\pi$
$384$	2.00000			0.102062
$385$	−36.0000	−	62.3538i	−1.83473	−	3.17785i
$386$	5.50000	+	9.52628i	0.279943	+	0.484875i
$387$	2.00000	+	3.46410i	0.101666	+	0.176090i
$388$	6.50000	−	11.2583i	0.329988	−	0.571555i
$389$	4.50000	−	7.79423i	0.228159	−	0.395183i	−0.729103	−	0.684403i	$-0.760063\pi$
$389$	4.50000	−	7.79423i	0.228159	−	0.395183i	0.957263	+	0.289220i	$0.0933960\pi$
$390$	−6.00000	−	10.3923i	−0.303822	−	0.526235i
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$	4.50000	+	7.79423i	0.227284	+	0.393668i
$393$	−36.0000			−1.81596
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$	−21.0000	−	36.3731i	−1.05662	−	1.83013i
$396$	−6.00000			−0.301511
$397$	35.0000			1.75660			0.878300	−	0.478110i	$-0.158678\pi$
$397$	35.0000			1.75660			0.878300	+	0.478110i	$0.158678\pi$
$398$	4.00000	+	6.92820i	0.200502	+	0.347279i
$399$	16.0000			0.801002
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$	−2.00000	+	3.46410i	−0.0997509	+	0.172774i
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	−1.50000	+	2.59808i	−0.0746278	+	0.129259i
$405$	16.5000	+	28.5788i	0.819892	+	1.42009i
$406$	12.0000			0.595550
$407$	−33.0000	+	15.5885i	−1.63575	+	0.772691i
$408$	6.00000			0.297044
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	0.697406	−	0.716677i	$-0.254338\pi$
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	−0.969363	+	0.245633i	$0.921004\pi$
$410$	4.50000	−	7.79423i	0.222239	−	0.384930i
$411$	3.00000	−	5.19615i	0.147979	−	0.256307i
$412$	2.00000	−	3.46410i	0.0985329	−	0.170664i
$413$		0			0
$414$	3.00000	−	5.19615i	0.147442	−	0.255377i
$415$	18.0000			0.883585
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$	−4.00000			−0.195881
$418$	12.0000			0.586939
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$	−12.0000	+	20.7846i	−0.585540	+	1.01419i
$421$	−37.0000			−1.80327			−0.901635	−	0.432498i	$-0.857632\pi$
$421$	−37.0000			−1.80327			−0.901635	+	0.432498i	$0.857632\pi$
$422$	−8.00000	−	13.8564i	−0.389434	−	0.674519i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	−3.00000	−	5.19615i	−0.145693	−	0.252347i
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$	12.0000	−	20.7846i	0.581402	−	1.00702i
$427$	−2.00000	−	3.46410i	−0.0967868	−	0.167640i
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$	−12.0000	−	20.7846i	−0.579365	−	1.00349i
$430$	12.0000			0.578691
$431$	−3.00000	+	5.19615i	−0.144505	+	0.250290i	−0.929188	−	0.369607i	$-0.879492\pi$
$431$	−3.00000	+	5.19615i	−0.144505	+	0.250290i	0.784683	+	0.619897i	$0.212826\pi$
$432$	−2.00000	−	3.46410i	−0.0962250	−	0.166667i
$433$	−25.0000			−1.20142			−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000			−1.20142			−0.600712	+	0.799466i	$0.705116\pi$
$434$	8.00000			0.384012
$435$	9.00000	+	15.5885i	0.431517	+	0.747409i
$436$	−1.00000			−0.0478913
$437$	−6.00000	+	10.3923i	−0.287019	+	0.497131i
$438$	−20.0000			−0.955637
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	0.177325	+	0.984152i	$0.443256\pi$
$439$	−16.0000	+	27.7128i	−0.763638	+	1.32266i	−0.940963	+	0.338508i	$0.890078\pi$
$440$	−9.00000	+	15.5885i	−0.429058	+	0.743151i
$441$	−4.50000	+	7.79423i	−0.214286	+	0.371154i
$442$	3.00000	+	5.19615i	0.142695	+	0.247156i
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$	10.0000	+	6.92820i	0.474579	+	0.328798i
$445$	9.00000			0.426641
$446$	7.00000	+	12.1244i	0.331460	+	0.574105i
$447$	−21.0000	+	36.3731i	−0.993266	+	1.72039i
$448$	2.00000	−	3.46410i	0.0944911	−	0.163663i
$449$	−3.00000	+	5.19615i	−0.141579	+	0.245222i	−0.928091	−	0.372353i	$-0.878551\pi$
$449$	−3.00000	+	5.19615i	−0.141579	+	0.245222i	0.786513	+	0.617574i	$0.211885\pi$
$450$	−4.00000			−0.188562
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	−18.0000			−0.846649
$453$	−22.0000	−	38.1051i	−1.03365	−	1.79033i
$454$	18.0000			0.844782
$455$	−24.0000			−1.12514
$456$	−2.00000	−	3.46410i	−0.0936586	−	0.162221i
$457$	18.5000	−	32.0429i	0.865393	−	1.49891i	−0.00126243	−	0.999999i	$-0.500402\pi$
$457$	18.5000	−	32.0429i	0.865393	−	1.49891i	0.866656	−	0.498906i	$-0.166265\pi$
$458$	−11.0000			−0.513996
$459$	−6.00000	−	10.3923i	−0.280056	−	0.485071i
$460$	−9.00000	−	15.5885i	−0.419627	−	0.726816i
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	0.968945	+	0.247276i	$0.0795353\pi$
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	−0.270326	+	0.962769i	$0.587131\pi$
$462$	−24.0000	+	41.5692i	−1.11658	+	1.93398i
$463$	8.00000	−	13.8564i	0.371792	−	0.643962i	−0.618050	−	0.786139i	$-0.712077\pi$
$463$	8.00000	−	13.8564i	0.371792	−	0.643962i	0.989841	+	0.142177i	$0.0454103\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$	6.00000	+	10.3923i	0.278243	+	0.481932i
$466$	−4.50000	−	7.79423i	−0.208458	−	0.361061i
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$	−1.00000	+	1.73205i	−0.0462250	+	0.0800641i
$469$	4.00000	+	6.92820i	0.184703	+	0.319915i
$470$	18.0000			0.830278
$471$	−22.0000			−1.01371
$472$		0			0
$473$	24.0000			1.10352
$474$	−14.0000	+	24.2487i	−0.643041	+	1.11378i
$475$	8.00000			0.367065
$476$	6.00000	−	10.3923i	0.275010	−	0.476331i
$477$	3.00000	−	5.19615i	0.137361	−	0.237915i
$478$		0			0
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$	6.00000			0.273861
$481$	−1.00000	+	12.1244i	−0.0455961	+	0.552823i
$482$	−14.0000			−0.637683
$483$	−24.0000	−	41.5692i	−1.09204	−	1.89146i
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	19.5000	−	33.7750i	0.885449	−	1.53364i
$486$	5.00000	−	8.66025i	0.226805	−	0.392837i
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	−0.500000	+	0.866025i	−0.0226339	+	0.0392031i
$489$	32.0000			1.44709
$490$	13.5000	+	23.3827i	0.609868	+	1.05632i
$491$	6.00000			0.270776			0.135388	−	0.990793i	$-0.456772\pi$
$491$	6.00000			0.270776			0.135388	+	0.990793i	$0.456772\pi$
$492$	−6.00000			−0.270501
$493$	−4.50000	−	7.79423i	−0.202670	−	0.351034i
$494$	2.00000	−	3.46410i	0.0899843	−	0.155857i
$495$	−18.0000			−0.809040
$496$	−1.00000	−	1.73205i	−0.0449013	−	0.0777714i
$497$	−24.0000	−	41.5692i	−1.07655	−	1.86463i
$498$	−6.00000	−	10.3923i	−0.268866	−	0.465690i
$499$	−7.00000	+	12.1244i	−0.313363	+	0.542761i	−0.979088	−	0.203436i	$-0.934789\pi$
$499$	−7.00000	+	12.1244i	−0.313363	+	0.542761i	0.665725	+	0.746197i	$0.268122\pi$
$500$	1.50000	−	2.59808i	0.0670820	−	0.116190i
$501$	12.0000	+	20.7846i	0.536120	+	0.928588i
$502$		0			0
$503$	−15.0000	−	25.9808i	−0.668817	−	1.15842i	−0.978235	−	0.207499i	$-0.933468\pi$
$503$	−15.0000	−	25.9808i	−0.668817	−	1.15842i	0.309418	−	0.950926i	$-0.399866\pi$
$504$	4.00000			0.178174
$505$	−4.50000	+	7.79423i	−0.200247	+	0.346839i
$506$	−18.0000	−	31.1769i	−0.800198	−	1.38598i
$507$	18.0000			0.799408
$508$	−10.0000			−0.443678
$509$	−13.5000	−	23.3827i	−0.598377	−	1.03642i	−0.993061	−	0.117602i	$-0.962479\pi$
$509$	−13.5000	−	23.3827i	−0.598377	−	1.03642i	0.394684	−	0.918817i	$-0.370854\pi$
$510$	18.0000			0.797053
$511$	−20.0000	+	34.6410i	−0.884748	+	1.53243i
$512$	−1.00000			−0.0441942
$513$	−4.00000	+	6.92820i	−0.176604	+	0.305888i
$514$	13.5000	−	23.3827i	0.595459	−	1.03137i
$515$	6.00000	−	10.3923i	0.264392	−	0.457940i
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	36.0000			1.58328
$518$	22.0000	−	10.3923i	0.966625	−	0.456612i
$519$	42.0000			1.84360
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	−0.924229	−	0.381839i	$-0.875291\pi$
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	0.792797	+	0.609486i	$0.208624\pi$
$522$	1.50000	−	2.59808i	0.0656532	−	0.113715i
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	0.428269	+	0.903651i	$0.359124\pi$
$523$	−13.0000	+	22.5167i	−0.568450	+	0.984585i	−0.996719	+	0.0809336i	$0.974210\pi$
$524$	18.0000			0.786334
$525$	−16.0000	+	27.7128i	−0.698297	+	1.20949i
$526$		0			0
$527$	−3.00000	−	5.19615i	−0.130682	−	0.226348i
$528$	12.0000			0.522233
$529$	13.0000			0.565217
$530$	−9.00000	−	15.5885i	−0.390935	−	0.677119i
$531$		0			0
$532$	−8.00000			−0.346844
$533$	−3.00000	−	5.19615i	−0.129944	−	0.225070i
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$	18.0000	+	31.1769i	0.778208	+	1.34790i
$536$	1.00000	−	1.73205i	0.0431934	−	0.0748132i
$537$		0			0
$538$	9.00000	+	15.5885i	0.388018	+	0.672066i
$539$	27.0000	+	46.7654i	1.16297	+	2.01433i
$540$	−6.00000	−	10.3923i	−0.258199	−	0.447214i
$541$	35.0000			1.50477			0.752384	−	0.658725i	$-0.228904\pi$
$541$	35.0000			1.50477			0.752384	+	0.658725i	$0.228904\pi$
$542$	−5.00000	+	8.66025i	−0.214768	+	0.371990i
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$	−3.00000			−0.128624
$545$	−3.00000			−0.128506
$546$	8.00000	+	13.8564i	0.342368	+	0.592999i
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$	−1.50000	+	2.59808i	−0.0640768	+	0.110984i
$549$	−1.00000			−0.0426790
$550$	−12.0000	+	20.7846i	−0.511682	+	0.886259i
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$	−6.00000	+	10.3923i	−0.255377	+	0.442326i
$553$	28.0000	+	48.4974i	1.19068	+	2.06232i
$554$	1.00000			0.0424859
$555$	30.0000	+	20.7846i	1.27343	+	0.882258i
$556$	2.00000			0.0848189
$557$	16.5000	+	28.5788i	0.699127	+	1.21092i	0.968769	+	0.247964i	$0.0797613\pi$
$557$	16.5000	+	28.5788i	0.699127	+	1.21092i	−0.269642	+	0.962961i	$0.586905\pi$
$558$	1.00000	−	1.73205i	0.0423334	−	0.0733236i
$559$	4.00000	−	6.92820i	0.169182	−	0.293032i
$560$	6.00000	−	10.3923i	0.253546	−	0.439155i
$561$	36.0000			1.51992
$562$	7.50000	−	12.9904i	0.316368	−	0.547966i
$563$	6.00000			0.252870			0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000			0.252870			0.126435	+	0.991975i	$0.459647\pi$
$564$	−6.00000	−	10.3923i	−0.252646	−	0.437595i
$565$	−54.0000			−2.27180
$566$	16.0000			0.672530
$567$	−22.0000	−	38.1051i	−0.923913	−	1.60026i
$568$	−6.00000	+	10.3923i	−0.251754	+	0.436051i
$569$	3.00000			0.125767			0.0628833	−	0.998021i	$-0.479970\pi$
$569$	3.00000			0.125767			0.0628833	+	0.998021i	$0.479970\pi$
$570$	−6.00000	−	10.3923i	−0.251312	−	0.435286i
$571$	−19.0000	−	32.9090i	−0.795125	−	1.37720i	−0.922760	−	0.385376i	$-0.874072\pi$
$571$	−19.0000	−	32.9090i	−0.795125	−	1.37720i	0.127634	−	0.991821i	$-0.459262\pi$
$572$	6.00000	+	10.3923i	0.250873	+	0.434524i
$573$	−6.00000	+	10.3923i	−0.250654	+	0.434145i
$574$	−6.00000	+	10.3923i	−0.250435	+	0.433766i
$575$	−12.0000	−	20.7846i	−0.500435	−	0.866778i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	17.0000	+	29.4449i	0.707719	+	1.22581i	0.965701	+	0.259656i	$0.0836092\pi$
$577$	17.0000	+	29.4449i	0.707719	+	1.22581i	−0.257982	+	0.966150i	$0.583058\pi$
$578$	8.00000			0.332756
$579$	11.0000	−	19.0526i	0.457144	−	0.791797i
$580$	−4.50000	−	7.79423i	−0.186852	−	0.323638i
$581$	−24.0000			−0.995688
$582$	−26.0000			−1.07773
$583$	−18.0000	−	31.1769i	−0.745484	−	1.29122i
$584$	10.0000			0.413803
$585$	−3.00000	+	5.19615i	−0.124035	+	0.214834i
$586$	−3.00000			−0.123929
$587$	−9.00000	+	15.5885i	−0.371470	+	0.643404i	−0.989792	−	0.142520i	$-0.954479\pi$
$587$	−9.00000	+	15.5885i	−0.371470	+	0.643404i	0.618322	+	0.785925i	$0.287813\pi$
$588$	9.00000	−	15.5885i	0.371154	−	0.642857i
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$		0			0
$591$	−6.00000			−0.246807
$592$	−5.00000	−	3.46410i	−0.205499	−	0.142374i
$593$	27.0000			1.10876			0.554379	−	0.832265i	$-0.312956\pi$
$593$	27.0000			1.10876			0.554379	+	0.832265i	$0.312956\pi$
$594$	−12.0000	−	20.7846i	−0.492366	−	0.852803i
$595$	18.0000	−	31.1769i	0.737928	−	1.27813i
$596$	10.5000	−	18.1865i	0.430097	−	0.744949i
$597$	8.00000	−	13.8564i	0.327418	−	0.567105i
$598$	−12.0000			−0.490716
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	−0.798206	−	0.602384i	$-0.794218\pi$
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	0.920783	+	0.390075i	$0.127551\pi$
$600$	8.00000			0.326599
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	0.967600	−	0.252486i	$-0.0812483\pi$
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	−0.702460	+	0.711723i	$0.747915\pi$
$602$	−16.0000			−0.652111
$603$	2.00000			0.0814463
$604$	11.0000	+	19.0526i	0.447584	+	0.775238i
$605$	−37.5000	+	64.9519i	−1.52459	+	2.64067i
$606$	6.00000			0.243733
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	0.998154	−	0.0607380i	$-0.0193454\pi$
$607$	11.0000	+	19.0526i	0.446476	+	0.773320i	−0.551678	+	0.834058i	$0.686012\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$	−12.0000	−	20.7846i	−0.486265	−	0.842235i
$610$	−1.50000	+	2.59808i	−0.0607332	+	0.105193i
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$	−1.50000	−	2.59808i	−0.0606339	−	0.105021i
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	0.999984	+	0.00563283i	$0.00179300\pi$
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	−0.495114	+	0.868828i	$0.664874\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$	−18.0000			−0.725830
$616$	12.0000	−	20.7846i	0.483494	−	0.837436i
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	0.988343	−	0.152242i	$-0.0486493\pi$
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	−0.626017	+	0.779809i	$0.715316\pi$
$618$	−8.00000			−0.321807
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$	−3.00000	−	5.19615i	−0.120483	−	0.208683i
$621$	24.0000			0.963087
$622$		0			0
$623$	−12.0000			−0.480770
$624$	2.00000	−	3.46410i	0.0800641	−	0.138675i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−6.50000	+	11.2583i	−0.259792	+	0.449973i
$627$	−12.0000	−	20.7846i	−0.479234	−	0.830057i
$628$	11.0000			0.438948
$629$	−15.0000	−	10.3923i	−0.598089	−	0.414368i
$630$	12.0000			0.478091
$631$	5.00000	+	8.66025i	0.199047	+	0.344759i	0.948220	−	0.317615i	$-0.102882\pi$
$631$	5.00000	+	8.66025i	0.199047	+	0.344759i	−0.749173	+	0.662375i	$0.769549\pi$
$632$	7.00000	−	12.1244i	0.278445	−	0.482281i
$633$	−16.0000	+	27.7128i	−0.635943	+	1.10149i
$634$	−10.5000	+	18.1865i	−0.417008	+	0.722280i
$635$	−30.0000			−1.19051
$636$	−6.00000	+	10.3923i	−0.237915	+	0.412082i
$637$	18.0000			0.713186
$638$	−9.00000	−	15.5885i	−0.356313	−	0.617153i
$639$	−12.0000			−0.474713
$640$	−3.00000			−0.118585
$641$	10.5000	+	18.1865i	0.414725	+	0.718325i	0.995400	−	0.0958109i	$-0.0305444\pi$
$641$	10.5000	+	18.1865i	0.414725	+	0.718325i	−0.580674	+	0.814136i	$0.697211\pi$
$642$	12.0000	−	20.7846i	0.473602	−	0.820303i
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$	12.0000	+	20.7846i	0.472866	+	0.819028i
$645$	−12.0000	−	20.7846i	−0.472500	−	0.818393i
$646$	3.00000	+	5.19615i	0.118033	+	0.204440i
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	−0.999478	−	0.0322975i	$-0.989718\pi$
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	0.527710	+	0.849425i	$0.323051\pi$
$648$	−5.50000	+	9.52628i	−0.216060	+	0.374228i
$649$		0			0
$650$	4.00000	+	6.92820i	0.156893	+	0.271746i
$651$	−8.00000	−	13.8564i	−0.313545	−	0.543075i
$652$	−16.0000			−0.626608
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	−0.893882	−	0.448303i	$-0.852029\pi$
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	0.835182	+	0.549973i	$0.185362\pi$
$654$	1.00000	+	1.73205i	0.0391031	+	0.0677285i
$655$	54.0000			2.10995
$656$	3.00000			0.117130
$657$	5.00000	+	8.66025i	0.195069	+	0.337869i
$658$	−24.0000			−0.935617
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$	36.0000			1.40130
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	−0.513680	−	0.857982i	$-0.671718\pi$
$661$	12.5000	−	21.6506i	0.486194	−	0.842112i	0.999874	+	0.0158695i	$0.00505163\pi$
$662$	−2.00000	+	3.46410i	−0.0777322	+	0.134636i
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$	3.00000	+	5.19615i	0.116423	+	0.201650i
$665$	−24.0000			−0.930680
$666$	0.500000	−	6.06218i	0.0193746	−	0.234905i
$667$	18.0000			0.696963
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$	14.0000	−	24.2487i	0.541271	−	0.937509i
$670$	3.00000	−	5.19615i	0.115900	−	0.200745i
$671$	−3.00000	+	5.19615i	−0.115814	+	0.200595i
$672$	−8.00000			−0.308607
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	−0.753420	−	0.657539i	$-0.771597\pi$
$673$	5.00000	−	8.66025i	0.192736	−	0.333828i	0.946156	+	0.323711i	$0.104931\pi$
$674$	25.0000			0.962964
$675$	−8.00000	−	13.8564i	−0.307920	−	0.533333i
$676$	−9.00000			−0.346154
$677$	3.00000			0.115299			0.0576497	−	0.998337i	$-0.481639\pi$
$677$	3.00000			0.115299			0.0576497	+	0.998337i	$0.481639\pi$
$678$	18.0000	+	31.1769i	0.691286	+	1.19734i
$679$	−26.0000	+	45.0333i	−0.997788	+	1.72822i
$680$	−9.00000			−0.345134
$681$	−18.0000	−	31.1769i	−0.689761	−	1.19470i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$	−1.00000	+	1.73205i	−0.0382360	+	0.0662266i
$685$	−4.50000	+	7.79423i	−0.171936	+	0.297802i
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$	11.0000	+	19.0526i	0.419676	+	0.726900i
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−12.0000			−0.457164
$690$	−18.0000	+	31.1769i	−0.685248	+	1.18688i
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.743170	−	0.669102i	$-0.766679\pi$
$691$	−25.0000	−	43.3013i	−0.951045	−	1.64726i	−0.207875	−	0.978155i	$-0.566655\pi$
$692$	−21.0000			−0.798300
$693$	24.0000			0.911685
$694$	3.00000	+	5.19615i	0.113878	+	0.197243i
$695$	6.00000			0.227593
$696$	−3.00000	+	5.19615i	−0.113715	+	0.196960i
$697$	9.00000			0.340899
$698$	−0.500000	+	0.866025i	−0.0189253	+	0.0327795i
$699$	−9.00000	+	15.5885i	−0.340411	+	0.589610i
$700$	8.00000	−	13.8564i	0.302372	−	0.523723i
$701$	−15.0000	−	25.9808i	−0.566542	−	0.981280i	−0.996904	−	0.0786236i	$-0.974947\pi$
$701$	−15.0000	−	25.9808i	−0.566542	−	0.981280i	0.430362	−	0.902656i	$-0.358386\pi$
$702$	−8.00000			−0.301941
$703$	−1.00000	+	12.1244i	−0.0377157	+	0.457279i
$704$	−6.00000			−0.226134
$705$	−18.0000	−	31.1769i	−0.677919	−	1.17419i
$706$	−10.5000	+	18.1865i	−0.395173	+	0.684459i
$707$	6.00000	−	10.3923i	0.225653	−	0.390843i
$708$		0			0
$709$	−22.0000			−0.826227			−0.413114	−	0.910679i	$-0.635559\pi$
$709$	−22.0000			−0.826227			−0.413114	+	0.910679i	$0.635559\pi$
$710$	−18.0000	+	31.1769i	−0.675528	+	1.17005i
$711$	14.0000			0.525041
$712$	1.50000	+	2.59808i	0.0562149	+	0.0973670i
$713$	12.0000			0.449404
$714$	−24.0000			−0.898177
$715$	18.0000	+	31.1769i	0.673162	+	1.16595i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	21.0000	+	36.3731i	0.783168	+	1.35649i	0.930087	+	0.367338i	$0.119731\pi$
$719$	21.0000	+	36.3731i	0.783168	+	1.35649i	−0.146920	+	0.989148i	$0.546936\pi$
$720$	−1.50000	−	2.59808i	−0.0559017	−	0.0968246i
$721$	−8.00000	+	13.8564i	−0.297936	+	0.516040i
$722$	−7.50000	+	12.9904i	−0.279121	+	0.483452i
$723$	14.0000	+	24.2487i	0.520666	+	0.901819i
$724$	0.500000	+	0.866025i	0.0185824	+	0.0321856i
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$	50.0000			1.85567
$727$	2.00000	−	3.46410i	0.0741759	−	0.128476i	−0.826552	−	0.562861i	$-0.809701\pi$
$727$	2.00000	−	3.46410i	0.0741759	−	0.128476i	0.900728	+	0.434384i	$0.143034\pi$
$728$	−4.00000	−	6.92820i	−0.148250	−	0.256776i
$729$	13.0000			0.481481
$730$	30.0000			1.11035
$731$	6.00000	+	10.3923i	0.221918	+	0.384373i
$732$	2.00000			0.0739221
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	−0.883902	−	0.467671i	$-0.845093\pi$
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	0.846967	+	0.531646i	$0.178426\pi$
$734$	4.00000			0.147643
$735$	27.0000	−	46.7654i	0.995910	−	1.72497i
$736$	3.00000	−	5.19615i	0.110581	−	0.191533i
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$	1.50000	+	2.59808i	0.0552158	+	0.0956365i
$739$	38.0000			1.39785			0.698926	−	0.715194i	$-0.253662\pi$
$739$	38.0000			1.39785			0.698926	+	0.715194i	$0.253662\pi$
$740$	−15.0000	−	10.3923i	−0.551411	−	0.382029i
$741$	−8.00000			−0.293887
$742$	12.0000	+	20.7846i	0.440534	+	0.763027i
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$	−2.00000	+	3.46410i	−0.0733236	+	0.127000i
$745$	31.5000	−	54.5596i	1.15407	−	1.99891i
$746$	25.0000			0.915315
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$	−18.0000			−0.658145
$749$	−24.0000	−	41.5692i	−0.876941	−	1.51891i
$750$	−6.00000			−0.219089
$751$	−16.0000			−0.583848			−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000			−0.583848			−0.291924	+	0.956441i	$0.594295\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$		0			0
$754$	−6.00000			−0.218507
$755$	33.0000	+	57.1577i	1.20099	+	2.08018i
$756$	8.00000	+	13.8564i	0.290957	+	0.503953i
$757$	−17.5000	−	30.3109i	−0.636048	−	1.10167i	−0.986292	−	0.165009i	$-0.947235\pi$
$757$	−17.5000	−	30.3109i	−0.636048	−	1.10167i	0.350244	−	0.936659i	$-0.386099\pi$
$758$	−8.00000	+	13.8564i	−0.290573	+	0.503287i
$759$	−36.0000	+	62.3538i	−1.30672	+	2.26330i
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	0.510551	−	0.859848i	$-0.329442\pi$
$761$	−13.5000	−	23.3827i	−0.489375	−	0.847622i	−0.999925	+	0.0122260i	$0.996108\pi$
$762$	10.0000	+	17.3205i	0.362262	+	0.627456i
$763$	4.00000			0.144810
$764$	3.00000	−	5.19615i	0.108536	−	0.187990i
$765$	−4.50000	−	7.79423i	−0.162698	−	0.281801i
$766$	−12.0000			−0.433578
$767$		0			0
$768$	1.00000	+	1.73205i	0.0360844	+	0.0625000i
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$	36.0000	−	62.3538i	1.29735	−	2.24708i
$771$	−54.0000			−1.94476
$772$	−5.50000	+	9.52628i	−0.197949	+	0.342858i
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	−0.613062	−	0.790034i	$-0.710063\pi$
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	0.990721	+	0.135910i	$0.0433959\pi$
$774$	−2.00000	+	3.46410i	−0.0718885	+	0.124515i
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$	13.0000			0.466673
$777$	−40.0000	−	27.7128i	−1.43499	−	0.994192i
$778$	9.00000			0.322666
$779$	−3.00000	−	5.19615i	−0.107486	−	0.186171i
$780$	6.00000	−	10.3923i	0.214834	−	0.372104i
$781$	−36.0000	+	62.3538i	−1.28818	+	2.23120i
$782$	9.00000	−	15.5885i	0.321839	−	0.557442i
$783$	12.0000			0.428845
$784$	−4.50000	+	7.79423i	−0.160714	+	0.278365i
$785$	33.0000			1.17782
$786$	−18.0000	−	31.1769i	−0.642039	−	1.11204i
$787$	20.0000			0.712923			0.356462	−	0.934310i	$-0.383983\pi$
$787$	20.0000			0.712923			0.356462	+	0.934310i	$0.383983\pi$
$788$	3.00000			0.106871
$789$		0			0
$790$	21.0000	−	36.3731i	0.747146	−	1.29410i
$791$	72.0000			2.56003
$792$	−3.00000	−	5.19615i	−0.106600	−	0.184637i
$793$	1.00000	+	1.73205i	0.0355110	+	0.0615069i
$794$	17.5000	+	30.3109i	0.621052	+	1.07569i
$795$	−18.0000	+	31.1769i	−0.638394	+	1.10573i
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	0.980237	−	0.197826i	$-0.0633881\pi$
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	−0.661441	+	0.749997i	$0.730055\pi$
$798$	8.00000	+	13.8564i	0.283197	+	0.490511i
$799$	9.00000	+	15.5885i	0.318397	+	0.551480i
$800$	−4.00000			−0.141421
$801$	−1.50000	+	2.59808i	−0.0529999	+	0.0917985i
$802$	3.00000	+	5.19615i	0.105934	+	0.183483i
$803$	60.0000			2.11735
$804$	−4.00000			−0.141069
$805$	36.0000	+	62.3538i	1.26883	+	2.19768i
$806$	−4.00000			−0.140894
$807$	18.0000	−	31.1769i	0.633630	−	1.09748i
$808$	−3.00000			−0.105540
$809$	−21.0000	+	36.3731i	−0.738321	+	1.27881i	0.214930	+	0.976629i	$0.431048\pi$
$809$	−21.0000	+	36.3731i	−0.738321	+	1.27881i	−0.953251	+	0.302180i	$0.902286\pi$
$810$	−16.5000	+	28.5788i	−0.579751	+	1.00416i
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	−0.690693	−	0.723148i	$-0.742694\pi$
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	0.971611	+	0.236584i	$0.0760278\pi$
$812$	6.00000	+	10.3923i	0.210559	+	0.364698i
$813$	20.0000			0.701431
$814$	−30.0000	−	20.7846i	−1.05150	−	0.728500i
$815$	−48.0000			−1.68137
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	4.00000	−	6.92820i	0.139942	−	0.242387i
$818$	5.50000	−	9.52628i	0.192303	−	0.333079i
$819$	4.00000	−	6.92820i	0.139771	−	0.242091i
$820$	9.00000			0.314294
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	−0.979246	−	0.202674i	$-0.935037\pi$
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	0.665144	+	0.746715i	$0.268370\pi$
$822$	6.00000			0.209274
$823$	17.0000	+	29.4449i	0.592583	+	1.02638i	0.993883	+	0.110437i	$0.0352250\pi$
$823$	17.0000	+	29.4449i	0.592583	+	1.02638i	−0.401300	+	0.915947i	$0.631442\pi$
$824$	4.00000			0.139347
$825$	48.0000			1.67115
$826$		0			0
$827$	−12.0000	+	20.7846i	−0.417281	+	0.722752i	−0.995665	−	0.0930129i	$-0.970350\pi$
$827$	−12.0000	+	20.7846i	−0.417281	+	0.722752i	0.578384	+	0.815765i	$0.303684\pi$
$828$	6.00000			0.208514
$829$	−13.0000	−	22.5167i	−0.451509	−	0.782036i	0.546971	−	0.837151i	$-0.315781\pi$
$829$	−13.0000	−	22.5167i	−0.451509	−	0.782036i	−0.998480	+	0.0551154i	$0.982447\pi$
$830$	9.00000	+	15.5885i	0.312395	+	0.541083i
$831$	−1.00000	−	1.73205i	−0.0346896	−	0.0600842i
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	−13.5000	+	23.3827i	−0.467747	+	0.810162i
$834$	−2.00000	−	3.46410i	−0.0692543	−	0.119952i
$835$	−18.0000	−	31.1769i	−0.622916	−	1.07892i
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$	8.00000			0.276520
$838$		0			0
$839$	−3.00000	−	5.19615i	−0.103572	−	0.179391i	0.809582	−	0.587007i	$-0.199694\pi$
$839$	−3.00000	−	5.19615i	−0.103572	−	0.179391i	−0.913154	+	0.407615i	$0.866360\pi$
$840$	−24.0000			−0.828079
$841$	−20.0000			−0.689655
$842$	−18.5000	−	32.0429i	−0.637552	−	1.10427i
$843$	−30.0000			−1.03325
$844$	8.00000	−	13.8564i	0.275371	−	0.476957i
$845$	−27.0000			−0.928828
$846$	−3.00000	+	5.19615i	−0.103142	+	0.178647i
$847$	50.0000	−	86.6025i	1.71802	−	2.97570i
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$	−16.0000	−	27.7128i	−0.549119	−	0.951101i
$850$	−12.0000			−0.411597
$851$	33.0000	−	15.5885i	1.13123	−	0.534365i
$852$	24.0000			0.822226
$853$	18.5000	+	32.0429i	0.633428	+	1.09713i	0.986846	+	0.161664i	$0.0516860\pi$
$853$	18.5000	+	32.0429i	0.633428	+	1.09713i	−0.353418	+	0.935466i	$0.614981\pi$
$854$	2.00000	−	3.46410i	0.0684386	−	0.118539i
$855$	−3.00000	+	5.19615i	−0.102598	+	0.177705i
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	3.00000			0.102478			0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000			0.102478			0.0512390	+	0.998686i	$0.483683\pi$
$858$	12.0000	−	20.7846i	0.409673	−	0.709575i
$859$	−52.0000			−1.77422			−0.887109	−	0.461561i	$-0.847290\pi$
$859$	−52.0000			−1.77422			−0.887109	+	0.461561i	$0.847290\pi$
$860$	6.00000	+	10.3923i	0.204598	+	0.354375i
$861$	24.0000			0.817918
$862$	−6.00000			−0.204361
$863$	−24.0000	−	41.5692i	−0.816970	−	1.41503i	−0.907905	−	0.419176i	$-0.862319\pi$
$863$	−24.0000	−	41.5692i	−0.816970	−	1.41503i	0.0909355	−	0.995857i	$-0.471014\pi$
$864$	2.00000	−	3.46410i	0.0680414	−	0.117851i
$865$	−63.0000			−2.14206
$866$	−12.5000	−	21.6506i	−0.424767	−	0.735719i
$867$	−8.00000	−	13.8564i	−0.271694	−	0.470588i
$868$	4.00000	+	6.92820i	0.135769	+	0.235159i
$869$	42.0000	−	72.7461i	1.42475	−	2.46774i
$870$	−9.00000	+	15.5885i	−0.305129	+	0.528498i
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$	−0.500000	−	0.866025i	−0.0169321	−	0.0293273i
$873$	6.50000	+	11.2583i	0.219992	+	0.381037i
$874$	−12.0000			−0.405906
$875$	−6.00000	+	10.3923i	−0.202837	+	0.351324i
$876$	−10.0000	−	17.3205i	−0.337869	−	0.585206i
$877$	−25.0000			−0.844190			−0.422095	−	0.906552i	$-0.638705\pi$
$877$	−25.0000			−0.844190			−0.422095	+	0.906552i	$0.638705\pi$
$878$	−32.0000			−1.07995
$879$	3.00000	+	5.19615i	0.101187	+	0.175262i
$880$	−18.0000			−0.606780
$881$	−25.5000	+	44.1673i	−0.859117	+	1.48803i	0.0136556	+	0.999907i	$0.495653\pi$
$881$	−25.5000	+	44.1673i	−0.859117	+	1.48803i	−0.872772	+	0.488127i	$0.837680\pi$
$882$	−9.00000			−0.303046
$883$	−1.00000	+	1.73205i	−0.0336527	+	0.0582882i	−0.882361	−	0.470573i	$-0.844047\pi$
$883$	−1.00000	+	1.73205i	−0.0336527	+	0.0582882i	0.848709	+	0.528861i	$0.177381\pi$
$884$	−3.00000	+	5.19615i	−0.100901	+	0.174766i
$885$		0			0
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	6.00000			0.201460			0.100730	−	0.994914i	$-0.467882\pi$
$887$	6.00000			0.201460			0.100730	+	0.994914i	$0.467882\pi$
$888$	−1.00000	+	12.1244i	−0.0335578	+	0.406867i
$889$	40.0000			1.34156
$890$	4.50000	+	7.79423i	0.150840	+	0.261263i
$891$	−33.0000	+	57.1577i	−1.10554	+	1.91485i
$892$	−7.00000	+	12.1244i	−0.234377	+	0.405953i
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$	−42.0000			−1.40469
$895$		0			0
$896$	4.00000			0.133631
$897$	12.0000	+	20.7846i	0.400668	+	0.693978i
$898$	−6.00000			−0.200223
$899$	6.00000			0.200111
$900$	−2.00000	−	3.46410i	−0.0666667	−	0.115470i
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$	18.0000			0.599334
$903$	16.0000	+	27.7128i	0.532447	+	0.922225i
$904$	−9.00000	−	15.5885i	−0.299336	−	0.518464i
$905$	1.50000	+	2.59808i	0.0498617	+	0.0863630i
$906$	22.0000	−	38.1051i	0.730901	−	1.26596i
$907$	29.0000	−	50.2295i	0.962929	−	1.66784i	0.247851	−	0.968798i	$-0.420276\pi$
$907$	29.0000	−	50.2295i	0.962929	−	1.66784i	0.715079	−	0.699044i	$-0.246391\pi$
$908$	9.00000	+	15.5885i	0.298675	+	0.517321i
$909$	−1.50000	−	2.59808i	−0.0497519	−	0.0861727i
$910$	−12.0000	−	20.7846i	−0.397796	−	0.689003i
$911$	−42.0000			−1.39152			−0.695761	−	0.718273i	$-0.744933\pi$
$911$	−42.0000			−1.39152			−0.695761	+	0.718273i	$0.744933\pi$
$912$	2.00000	−	3.46410i	0.0662266	−	0.114708i
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$	37.0000			1.22385
$915$	6.00000			0.198354
$916$	−5.50000	−	9.52628i	−0.181725	−	0.314757i
$917$	−72.0000			−2.37765
$918$	6.00000	−	10.3923i	0.198030	−	0.342997i
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$	9.00000	−	15.5885i	0.296721	−	0.513936i
$921$	−28.0000	+	48.4974i	−0.922631	+	1.59804i
$922$	−15.0000	+	25.9808i	−0.493999	+	0.855631i
$923$	12.0000	+	20.7846i	0.394985	+	0.684134i
$924$	−48.0000			−1.57908
$925$	−20.0000	−	13.8564i	−0.657596	−	0.455596i
$926$	16.0000			0.525793
$927$	2.00000	+	3.46410i	0.0656886	+	0.113776i
$928$	1.50000	−	2.59808i	0.0492399	−	0.0852860i
$929$	4.50000	−	7.79423i	0.147640	−	0.255720i	−0.782715	−	0.622381i	$-0.786166\pi$
$929$	4.50000	−	7.79423i	0.147640	−	0.255720i	0.930355	+	0.366660i	$0.119499\pi$
$930$	−6.00000	+	10.3923i	−0.196748	+	0.340777i
$931$	18.0000			0.589926
$932$	4.50000	−	7.79423i	0.147402	−	0.255308i
$933$		0			0
$934$	18.0000	+	31.1769i	0.588978	+	1.02014i
$935$	−54.0000			−1.76599
$936$	−2.00000			−0.0653720
$937$	0.500000	+	0.866025i	0.0163343	+	0.0282918i	0.874077	−	0.485787i	$-0.161467\pi$
$937$	0.500000	+	0.866025i	0.0163343	+	0.0282918i	−0.857743	+	0.514079i	$0.828134\pi$
$938$	−4.00000	+	6.92820i	−0.130605	+	0.226214i
$939$	26.0000			0.848478
$940$	9.00000	+	15.5885i	0.293548	+	0.508439i
$941$	−13.5000	−	23.3827i	−0.440087	−	0.762254i	0.557608	−	0.830104i	$-0.311719\pi$
$941$	−13.5000	−	23.3827i	−0.440087	−	0.762254i	−0.997695	+	0.0678506i	$0.978386\pi$
$942$	−11.0000	−	19.0526i	−0.358399	−	0.620766i
$943$	−9.00000	+	15.5885i	−0.293080	+	0.507630i
$944$		0			0
$945$	24.0000	+	41.5692i	0.780720	+	1.35225i
$946$	12.0000	+	20.7846i	0.390154	+	0.675766i
$947$	24.0000	+	41.5692i	0.779895	+	1.35082i	0.932002	+	0.362454i	$0.118061\pi$
$947$	24.0000	+	41.5692i	0.779895	+	1.35082i	−0.152106	+	0.988364i	$0.548606\pi$
$948$	−28.0000			−0.909398
$949$	10.0000	−	17.3205i	0.324614	−	0.562247i
$950$	4.00000	+	6.92820i	0.129777	+	0.224781i
$951$	42.0000			1.36194
$952$	12.0000			0.388922
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	0.910516	−	0.413473i	$-0.135685\pi$
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	−0.813337	+	0.581793i	$0.802351\pi$
$954$	6.00000			0.194257
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$		0			0
$957$	−18.0000	+	31.1769i	−0.581857	+	1.00781i
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	6.00000	−	10.3923i	0.193750	−	0.335585i
$960$	3.00000	+	5.19615i	0.0968246	+	0.167705i
$961$	−27.0000			−0.870968
$962$	−11.0000	+	5.19615i	−0.354654	+	0.167531i
$963$	−12.0000			−0.386695
$964$	−7.00000	−	12.1244i	−0.225455	−	0.390499i
$965$	−16.5000	+	28.5788i	−0.531154	+	0.919985i
$966$	24.0000	−	41.5692i	0.772187	−	1.33747i
$967$	26.0000	−	45.0333i	0.836104	−	1.44817i	−0.0570251	−	0.998373i	$-0.518161\pi$
$967$	26.0000	−	45.0333i	0.836104	−	1.44817i	0.893129	−	0.449801i	$-0.148505\pi$
$968$	−25.0000			−0.803530
$969$	6.00000	−	10.3923i	0.192748	−	0.333849i
$970$	39.0000			1.25221
$971$	−15.0000	−	25.9808i	−0.481373	−	0.833762i	0.518399	−	0.855139i	$-0.326528\pi$
$971$	−15.0000	−	25.9808i	−0.481373	−	0.833762i	−0.999771	+	0.0213768i	$0.993195\pi$
$972$	10.0000			0.320750
$973$	−8.00000			−0.256468
$974$	1.00000	+	1.73205i	0.0320421	+	0.0554985i
$975$	8.00000	−	13.8564i	0.256205	−	0.443760i
$976$	−1.00000			−0.0320092
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	−0.685381	+	0.728184i	$0.740364\pi$
$978$	16.0000	+	27.7128i	0.511624	+	0.886158i
$979$	9.00000	+	15.5885i	0.287641	+	0.498209i
$980$	−13.5000	+	23.3827i	−0.431242	+	0.746933i
$981$	0.500000	−	0.866025i	0.0159638	−	0.0276501i
$982$	3.00000	+	5.19615i	0.0957338	+	0.165816i
$983$	15.0000	+	25.9808i	0.478426	+	0.828658i	0.999694	−	0.0247352i	$-0.00787426\pi$
$983$	15.0000	+	25.9808i	0.478426	+	0.828658i	−0.521268	+	0.853393i	$0.674541\pi$
$984$	−3.00000	−	5.19615i	−0.0956365	−	0.165647i
$985$	9.00000			0.286764
$986$	4.50000	−	7.79423i	0.143309	−	0.248219i
$987$	24.0000	+	41.5692i	0.763928	+	1.32316i
$988$	4.00000			0.127257
$989$	−24.0000			−0.763156
$990$	−9.00000	−	15.5885i	−0.286039	−	0.495434i
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	8.00000			0.253872
$994$	24.0000	−	41.5692i	0.761234	−	1.31850i
$995$	−12.0000	+	20.7846i	−0.380426	+	0.658916i
$996$	6.00000	−	10.3923i	0.190117	−	0.329293i
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$	−14.0000			−0.443162
$999$	22.0000	−	10.3923i	0.696049	−	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.2.c.b.63.1	yes	2
3.2	odd	2		666.2.f.d.433.1		2
4.3	odd	2		592.2.i.a.433.1		2
37.10	even	3	inner	74.2.c.b.47.1	✓	2
37.11	even	6		2738.2.a.c.1.1		1
37.26	even	3		2738.2.a.a.1.1		1
111.47	odd	6		666.2.f.d.343.1		2
148.47	odd	6		592.2.i.a.417.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.c.b.47.1	✓	2	37.10	even	3	inner
74.2.c.b.63.1	yes	2	1.1	even	1	trivial
592.2.i.a.417.1		2	148.47	odd	6
592.2.i.a.433.1		2	4.3	odd	2
666.2.f.d.343.1		2	111.47	odd	6
666.2.f.d.433.1		2	3.2	odd	2
2738.2.a.a.1.1		1	37.26	even	3
2738.2.a.c.1.1		1	37.11	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +2.00000 q^{6} +(2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +2.00000 q^{6} +(2.00000 - 3.46410i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -3.00000 q^{10} -6.00000 q^{11} +(1.00000 + 1.73205i) q^{12} +(-1.00000 + 1.73205i) q^{13} +4.00000 q^{14} +(3.00000 + 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(-4.00000 - 6.92820i) q^{21} +(-3.00000 - 5.19615i) q^{22} +6.00000 q^{23} +(-1.00000 + 1.73205i) q^{24} +(-2.00000 - 3.46410i) q^{25} -2.00000 q^{26} +4.00000 q^{27} +(2.00000 + 3.46410i) q^{28} +3.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-6.00000 + 10.3923i) q^{33} +(1.50000 - 2.59808i) q^{34} +(6.00000 + 10.3923i) q^{35} +1.00000 q^{36} +(5.50000 - 2.59808i) q^{37} -2.00000 q^{38} +(2.00000 + 3.46410i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-1.50000 + 2.59808i) q^{41} +(4.00000 - 6.92820i) q^{42} -4.00000 q^{43} +(3.00000 - 5.19615i) q^{44} +3.00000 q^{45} +(3.00000 + 5.19615i) q^{46} -6.00000 q^{47} -2.00000 q^{48} +(-4.50000 - 7.79423i) q^{49} +(2.00000 - 3.46410i) q^{50} -6.00000 q^{51} +(-1.00000 - 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.00000 + 3.46410i) q^{54} +(9.00000 - 15.5885i) q^{55} +(-2.00000 + 3.46410i) q^{56} +(2.00000 + 3.46410i) q^{57} +(1.50000 + 2.59808i) q^{58} -6.00000 q^{60} +(0.500000 - 0.866025i) q^{61} +(1.00000 + 1.73205i) q^{62} -4.00000 q^{63} +1.00000 q^{64} +(-3.00000 - 5.19615i) q^{65} -12.0000 q^{66} +(-1.00000 + 1.73205i) q^{67} +3.00000 q^{68} +(6.00000 - 10.3923i) q^{69} +(-6.00000 + 10.3923i) q^{70} +(6.00000 - 10.3923i) q^{71} +(0.500000 + 0.866025i) q^{72} -10.0000 q^{73} +(5.00000 + 3.46410i) q^{74} -8.00000 q^{75} +(-1.00000 - 1.73205i) q^{76} +(-12.0000 + 20.7846i) q^{77} +(-2.00000 + 3.46410i) q^{78} +(-7.00000 + 12.1244i) q^{79} +3.00000 q^{80} +(5.50000 - 9.52628i) q^{81} -3.00000 q^{82} +(-3.00000 - 5.19615i) q^{83} +8.00000 q^{84} +9.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(3.00000 - 5.19615i) q^{87} +6.00000 q^{88} +(-1.50000 - 2.59808i) q^{89} +(1.50000 + 2.59808i) q^{90} +(4.00000 + 6.92820i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(2.00000 - 3.46410i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(-3.00000 - 5.19615i) q^{95} +(-1.00000 - 1.73205i) q^{96} -13.0000 q^{97} +(4.50000 - 7.79423i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 3 * q^5 + 4 * q^6 + 4 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} + 2 q^{3} - q^{4} - 3 q^{5} + 4 q^{6} + 4 q^{7} - 2 q^{8} - q^{9} - 6 q^{10} - 12 q^{11} + 2 q^{12} - 2 q^{13} + 8 q^{14} + 6 q^{15} - q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - 3 q^{20} - 8 q^{21} - 6 q^{22} + 12 q^{23} - 2 q^{24} - 4 q^{25} - 4 q^{26} + 8 q^{27} + 4 q^{28} + 6 q^{29} - 6 q^{30} + 4 q^{31} + q^{32} - 12 q^{33} + 3 q^{34} + 12 q^{35} + 2 q^{36} + 11 q^{37} - 4 q^{38} + 4 q^{39} + 3 q^{40} - 3 q^{41} + 8 q^{42} - 8 q^{43} + 6 q^{44} + 6 q^{45} + 6 q^{46} - 12 q^{47} - 4 q^{48} - 9 q^{49} + 4 q^{50} - 12 q^{51} - 2 q^{52} + 6 q^{53} + 4 q^{54} + 18 q^{55} - 4 q^{56} + 4 q^{57} + 3 q^{58} - 12 q^{60} + q^{61} + 2 q^{62} - 8 q^{63} + 2 q^{64} - 6 q^{65} - 24 q^{66} - 2 q^{67} + 6 q^{68} + 12 q^{69} - 12 q^{70} + 12 q^{71} + q^{72} - 20 q^{73} + 10 q^{74} - 16 q^{75} - 2 q^{76} - 24 q^{77} - 4 q^{78} - 14 q^{79} + 6 q^{80} + 11 q^{81} - 6 q^{82} - 6 q^{83} + 16 q^{84} + 18 q^{85} - 4 q^{86} + 6 q^{87} + 12 q^{88} - 3 q^{89} + 3 q^{90} + 8 q^{91} - 6 q^{92} + 4 q^{93} - 6 q^{94} - 6 q^{95} - 2 q^{96} - 26 q^{97} + 9 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 - q^4 - 3 * q^5 + 4 * q^6 + 4 * q^7 - 2 * q^8 - q^9 - 6 * q^10 - 12 * q^11 + 2 * q^12 - 2 * q^13 + 8 * q^14 + 6 * q^15 - q^16 - 3 * q^17 + q^18 - 2 * q^19 - 3 * q^20 - 8 * q^21 - 6 * q^22 + 12 * q^23 - 2 * q^24 - 4 * q^25 - 4 * q^26 + 8 * q^27 + 4 * q^28 + 6 * q^29 - 6 * q^30 + 4 * q^31 + q^32 - 12 * q^33 + 3 * q^34 + 12 * q^35 + 2 * q^36 + 11 * q^37 - 4 * q^38 + 4 * q^39 + 3 * q^40 - 3 * q^41 + 8 * q^42 - 8 * q^43 + 6 * q^44 + 6 * q^45 + 6 * q^46 - 12 * q^47 - 4 * q^48 - 9 * q^49 + 4 * q^50 - 12 * q^51 - 2 * q^52 + 6 * q^53 + 4 * q^54 + 18 * q^55 - 4 * q^56 + 4 * q^57 + 3 * q^58 - 12 * q^60 + q^61 + 2 * q^62 - 8 * q^63 + 2 * q^64 - 6 * q^65 - 24 * q^66 - 2 * q^67 + 6 * q^68 + 12 * q^69 - 12 * q^70 + 12 * q^71 + q^72 - 20 * q^73 + 10 * q^74 - 16 * q^75 - 2 * q^76 - 24 * q^77 - 4 * q^78 - 14 * q^79 + 6 * q^80 + 11 * q^81 - 6 * q^82 - 6 * q^83 + 16 * q^84 + 18 * q^85 - 4 * q^86 + 6 * q^87 + 12 * q^88 - 3 * q^89 + 3 * q^90 + 8 * q^91 - 6 * q^92 + 4 * q^93 - 6 * q^94 - 6 * q^95 - 2 * q^96 - 26 * q^97 + 9 * q^98 + 6 * q^99

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