LMFDB - Embedded newform 930.2.o.c.161.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	930.161
Dual form			930.2.o.c.491.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.59808 + 4.50000i) q^{11} +(-0.866025 - 1.50000i) q^{12} +(-3.00000 - 1.73205i) q^{13} +(0.866025 - 0.500000i) q^{14} -1.73205i q^{15} +1.00000 q^{16} +(-1.73205 - 3.00000i) q^{17} +(2.59808 + 1.50000i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-0.866025 + 1.50000i) q^{21} +(4.50000 + 2.59808i) q^{22} -6.92820 q^{23} +(-1.50000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.73205 + 3.00000i) q^{26} -5.19615 q^{27} +(-0.500000 - 0.866025i) q^{28} +1.73205 q^{29} -1.73205 q^{30} +(-5.50000 + 0.866025i) q^{31} -1.00000i q^{32} -9.00000 q^{33} +(-3.00000 + 1.73205i) q^{34} -1.00000i q^{35} +(1.50000 - 2.59808i) q^{36} +(6.00000 - 3.46410i) q^{37} +(-3.46410 + 2.00000i) q^{38} -6.00000i q^{39} +(0.500000 - 0.866025i) q^{40} +(5.19615 + 3.00000i) q^{41} +(1.50000 + 0.866025i) q^{42} +(3.00000 - 1.73205i) q^{43} +(2.59808 - 4.50000i) q^{44} +(2.59808 - 1.50000i) q^{45} +6.92820i q^{46} +12.0000i q^{47} +(0.866025 + 1.50000i) q^{48} +(3.00000 - 5.19615i) q^{49} +(0.866025 - 0.500000i) q^{50} +(3.00000 - 5.19615i) q^{51} +(3.00000 + 1.73205i) q^{52} +(-6.06218 + 10.5000i) q^{53} +5.19615i q^{54} +(4.50000 - 2.59808i) q^{55} +(-0.866025 + 0.500000i) q^{56} +(3.46410 - 6.00000i) q^{57} -1.73205i q^{58} +(-12.9904 + 7.50000i) q^{59} +1.73205i q^{60} +3.46410i q^{61} +(0.866025 + 5.50000i) q^{62} -3.00000 q^{63} -1.00000 q^{64} +(1.73205 + 3.00000i) q^{65} +9.00000i q^{66} +(1.00000 - 1.73205i) q^{67} +(1.73205 + 3.00000i) q^{68} +(-6.00000 - 10.3923i) q^{69} -1.00000 q^{70} +(-10.3923 - 6.00000i) q^{71} +(-2.59808 - 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +(-3.46410 - 6.00000i) q^{74} +(-0.866025 + 1.50000i) q^{75} +(2.00000 + 3.46410i) q^{76} -5.19615 q^{77} -6.00000 q^{78} +(-9.00000 + 5.19615i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(3.00000 - 5.19615i) q^{82} +(2.59808 - 4.50000i) q^{83} +(0.866025 - 1.50000i) q^{84} +3.46410i q^{85} +(-1.73205 - 3.00000i) q^{86} +(1.50000 + 2.59808i) q^{87} +(-4.50000 - 2.59808i) q^{88} +10.3923 q^{89} +(-1.50000 - 2.59808i) q^{90} -3.46410i q^{91} +6.92820 q^{92} +(-6.06218 - 7.50000i) q^{93} +12.0000 q^{94} +4.00000i q^{95} +(1.50000 - 0.866025i) q^{96} -1.00000 q^{97} +(-5.19615 - 3.00000i) q^{98} +(-7.79423 - 13.5000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 6 q^{6} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 6 * q^6 + 2 * q^7 - 6 * q^9	$ 4 q - 4 q^{4} + 6 q^{6} + 2 q^{7} - 6 q^{9} - 2 q^{10} - 12 q^{13} + 4 q^{16} - 8 q^{19} + 18 q^{22} - 6 q^{24} + 2 q^{25} - 2 q^{28} - 22 q^{31} - 36 q^{33} - 12 q^{34} + 6 q^{36} + 24 q^{37} + 2 q^{40} + 6 q^{42} + 12 q^{43} + 12 q^{49} + 12 q^{51} + 12 q^{52} + 18 q^{55} - 12 q^{63} - 4 q^{64} + 4 q^{67} - 24 q^{69} - 4 q^{70} + 24 q^{73} + 8 q^{76} - 24 q^{78} - 36 q^{79} - 18 q^{81} + 12 q^{82} + 6 q^{87} - 18 q^{88} - 6 q^{90} + 48 q^{94} + 6 q^{96} - 4 q^{97}+O(q^{100}) $ 4 * q - 4 * q^4 + 6 * q^6 + 2 * q^7 - 6 * q^9 - 2 * q^10 - 12 * q^13 + 4 * q^16 - 8 * q^19 + 18 * q^22 - 6 * q^24 + 2 * q^25 - 2 * q^28 - 22 * q^31 - 36 * q^33 - 12 * q^34 + 6 * q^36 + 24 * q^37 + 2 * q^40 + 6 * q^42 + 12 * q^43 + 12 * q^49 + 12 * q^51 + 12 * q^52 + 18 * q^55 - 12 * q^63 - 4 * q^64 + 4 * q^67 - 24 * q^69 - 4 * q^70 + 24 * q^73 + 8 * q^76 - 24 * q^78 - 36 * q^79 - 18 * q^81 + 12 * q^82 + 6 * q^87 - 18 * q^88 - 6 * q^90 + 48 * q^94 + 6 * q^96 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i
$4$	−1.00000			−0.500000
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	1.50000	−	0.866025i	0.612372	−	0.353553i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$			1.00000i			0.353553i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.59808	+	4.50000i	−0.783349	+	1.35680i	0.146631	+	0.989191i	$0.453157\pi$
$11$	−2.59808	+	4.50000i	−0.783349	+	1.35680i	−0.929980	+	0.367610i	$0.880176\pi$
$12$	−0.866025	−	1.50000i	−0.250000	−	0.433013i
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	0.0225039	−	0.999747i	$-0.492836\pi$
$13$	−3.00000	−	1.73205i	−0.832050	−	0.480384i	−0.854554	+	0.519362i	$0.826170\pi$
$14$	0.866025	−	0.500000i	0.231455	−	0.133631i
$15$		−	1.73205i		−	0.447214i
$16$	1.00000			0.250000
$17$	−1.73205	−	3.00000i	−0.420084	−	0.727607i	0.575863	−	0.817546i	$-0.304666\pi$
$17$	−1.73205	−	3.00000i	−0.420084	−	0.727607i	−0.995947	+	0.0899392i	$0.971333\pi$
$18$	2.59808	+	1.50000i	0.612372	+	0.353553i
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−0.866025	+	1.50000i	−0.188982	+	0.327327i
$22$	4.50000	+	2.59808i	0.959403	+	0.553912i
$23$	−6.92820			−1.44463			−0.722315	−	0.691564i	$-0.756922\pi$
$23$	−6.92820			−1.44463			−0.722315	+	0.691564i	$0.756922\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−1.73205	+	3.00000i	−0.339683	+	0.588348i
$27$	−5.19615			−1.00000
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	1.73205			0.321634			0.160817	−	0.986984i	$-0.448587\pi$
$29$	1.73205			0.321634			0.160817	+	0.986984i	$0.448587\pi$
$30$	−1.73205			−0.316228
$31$	−5.50000	+	0.866025i	−0.987829	+	0.155543i
$31$	−5.50000	+	0.866025i	−0.987829	+	0.155543i
$32$		−	1.00000i		−	0.176777i
$33$	−9.00000			−1.56670
$34$	−3.00000	+	1.73205i	−0.514496	+	0.297044i
$35$		−	1.00000i		−	0.169031i
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	6.00000	−	3.46410i	0.986394	−	0.569495i	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	6.00000	−	3.46410i	0.986394	−	0.569495i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−3.46410	+	2.00000i	−0.561951	+	0.324443i
$39$		−	6.00000i		−	0.960769i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	5.19615	+	3.00000i	0.811503	+	0.468521i	0.847477	−	0.530831i	$-0.178120\pi$
$41$	5.19615	+	3.00000i	0.811503	+	0.468521i	−0.0359748	+	0.999353i	$0.511454\pi$
$42$	1.50000	+	0.866025i	0.231455	+	0.133631i
$43$	3.00000	−	1.73205i	0.457496	−	0.264135i	−0.253495	−	0.967337i	$-0.581580\pi$
$43$	3.00000	−	1.73205i	0.457496	−	0.264135i	0.710991	+	0.703201i	$0.248247\pi$
$44$	2.59808	−	4.50000i	0.391675	−	0.678401i
$45$	2.59808	−	1.50000i	0.387298	−	0.223607i
$46$			6.92820i			1.02151i
$47$			12.0000i			1.75038i	0.483779	+	0.875190i	$0.339264\pi$
$47$			12.0000i			1.75038i	−0.483779	+	0.875190i	$0.660736\pi$
$48$	0.866025	+	1.50000i	0.125000	+	0.216506i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	3.00000	+	1.73205i	0.416025	+	0.240192i
$53$	−6.06218	+	10.5000i	−0.832704	+	1.44229i	0.0631819	+	0.998002i	$0.479875\pi$
$53$	−6.06218	+	10.5000i	−0.832704	+	1.44229i	−0.895886	+	0.444284i	$0.853458\pi$
$54$			5.19615i			0.707107i
$55$	4.50000	−	2.59808i	0.606780	−	0.350325i
$56$	−0.866025	+	0.500000i	−0.115728	+	0.0668153i
$57$	3.46410	−	6.00000i	0.458831	−	0.794719i
$58$		−	1.73205i		−	0.227429i
$59$	−12.9904	+	7.50000i	−1.69120	+	0.976417i	−0.737655	+	0.675178i	$0.764067\pi$
$59$	−12.9904	+	7.50000i	−1.69120	+	0.976417i	−0.953549	+	0.301239i	$0.902600\pi$
$60$			1.73205i			0.223607i
$61$			3.46410i			0.443533i	0.975100	+	0.221766i	$0.0711822\pi$
$61$			3.46410i			0.443533i	−0.975100	+	0.221766i	$0.928818\pi$
$62$	0.866025	+	5.50000i	0.109985	+	0.698501i
$63$	−3.00000			−0.377964
$64$	−1.00000			−0.125000
$65$	1.73205	+	3.00000i	0.214834	+	0.372104i
$66$			9.00000i			1.10782i
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	1.73205	+	3.00000i	0.210042	+	0.363803i
$69$	−6.00000	−	10.3923i	−0.722315	−	1.25109i
$70$	−1.00000			−0.119523
$71$	−10.3923	−	6.00000i	−1.23334	−	0.712069i	−0.265615	−	0.964079i	$-0.585575\pi$
$71$	−10.3923	−	6.00000i	−1.23334	−	0.712069i	−0.967725	+	0.252010i	$0.918908\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	0.808184	−	0.588930i	$-0.200451\pi$
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	−0.105937	+	0.994373i	$0.533784\pi$
$74$	−3.46410	−	6.00000i	−0.402694	−	0.697486i
$75$	−0.866025	+	1.50000i	−0.100000	+	0.173205i
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	−5.19615			−0.592157
$78$	−6.00000			−0.679366
$79$	−9.00000	+	5.19615i	−1.01258	+	0.584613i	−0.911946	−	0.410311i	$-0.865420\pi$
$79$	−9.00000	+	5.19615i	−1.01258	+	0.584613i	−0.100633	+	0.994924i	$0.532087\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	3.00000	−	5.19615i	0.331295	−	0.573819i
$83$	2.59808	−	4.50000i	0.285176	−	0.493939i	−0.687476	−	0.726207i	$-0.741281\pi$
$83$	2.59808	−	4.50000i	0.285176	−	0.493939i	0.972652	+	0.232268i	$0.0746146\pi$
$84$	0.866025	−	1.50000i	0.0944911	−	0.163663i
$85$			3.46410i			0.375735i
$86$	−1.73205	−	3.00000i	−0.186772	−	0.323498i
$87$	1.50000	+	2.59808i	0.160817	+	0.278543i
$88$	−4.50000	−	2.59808i	−0.479702	−	0.276956i
$89$	10.3923			1.10158			0.550791	−	0.834643i	$-0.314326\pi$
$89$	10.3923			1.10158			0.550791	+	0.834643i	$0.314326\pi$
$90$	−1.50000	−	2.59808i	−0.158114	−	0.273861i
$91$		−	3.46410i		−	0.363137i
$92$	6.92820			0.722315
$93$	−6.06218	−	7.50000i	−0.628619	−	0.777714i
$94$	12.0000			1.23771
$95$			4.00000i			0.410391i
$96$	1.50000	−	0.866025i	0.153093	−	0.0883883i
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	−5.19615	−	3.00000i	−0.524891	−	0.303046i
$99$	−7.79423	−	13.5000i	−0.783349	−	1.35680i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$			15.0000i			1.49256i	0.665635	+	0.746278i	$0.268161\pi$
$101$			15.0000i			1.49256i	−0.665635	+	0.746278i	$0.731839\pi$
$102$	−5.19615	−	3.00000i	−0.514496	−	0.297044i
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−3.50000	+	6.06218i	−0.344865	+	0.597324i	0.640464	+	0.767988i	$0.278742\pi$
$104$	1.73205	−	3.00000i	0.169842	−	0.294174i
$105$	1.50000	−	0.866025i	0.146385	−	0.0845154i
$106$	10.5000	+	6.06218i	1.01985	+	0.588811i
$107$	2.59808	−	1.50000i	0.251166	−	0.145010i	−0.369132	−	0.929377i	$-0.620345\pi$
$107$	2.59808	−	1.50000i	0.251166	−	0.145010i	0.620298	+	0.784366i	$0.287012\pi$
$108$	5.19615			0.500000
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$	−2.59808	−	4.50000i	−0.247717	−	0.429058i
$111$	10.3923	+	6.00000i	0.986394	+	0.569495i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$113$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$114$	−6.00000	−	3.46410i	−0.561951	−	0.324443i
$115$	6.00000	+	3.46410i	0.559503	+	0.323029i
$116$	−1.73205			−0.160817
$117$	9.00000	−	5.19615i	0.832050	−	0.480384i
$118$	7.50000	+	12.9904i	0.690431	+	1.19586i
$119$	1.73205	−	3.00000i	0.158777	−	0.275010i
$120$	1.73205			0.158114
$121$	−8.00000	−	13.8564i	−0.727273	−	1.25967i
$122$	3.46410			0.313625
$123$			10.3923i			0.937043i
$124$	5.50000	−	0.866025i	0.493915	−	0.0777714i
$125$		−	1.00000i		−	0.0894427i
$126$			3.00000i			0.267261i
$127$	10.5000	−	6.06218i	0.931724	−	0.537931i	0.0443678	−	0.999015i	$-0.485873\pi$
$127$	10.5000	−	6.06218i	0.931724	−	0.537931i	0.887357	+	0.461084i	$0.152539\pi$
$128$			1.00000i			0.0883883i
$129$	5.19615	+	3.00000i	0.457496	+	0.264135i
$130$	3.00000	−	1.73205i	0.263117	−	0.151911i
$131$	10.3923	−	6.00000i	0.907980	−	0.524222i	0.0281993	−	0.999602i	$-0.491023\pi$
$131$	10.3923	−	6.00000i	0.907980	−	0.524222i	0.879781	+	0.475380i	$0.157689\pi$
$132$	9.00000			0.783349
$133$	2.00000	−	3.46410i	0.173422	−	0.300376i
$134$	−1.73205	−	1.00000i	−0.149626	−	0.0863868i
$135$	4.50000	+	2.59808i	0.387298	+	0.223607i
$136$	3.00000	−	1.73205i	0.257248	−	0.148522i
$137$	6.92820	−	12.0000i	0.591916	−	1.02523i	−0.402058	−	0.915614i	$-0.631705\pi$
$137$	6.92820	−	12.0000i	0.591916	−	1.02523i	0.993974	−	0.109615i	$-0.0349618\pi$
$138$	−10.3923	+	6.00000i	−0.884652	+	0.510754i
$139$			20.7846i			1.76293i	0.472252	+	0.881464i	$0.343441\pi$
$139$			20.7846i			1.76293i	−0.472252	+	0.881464i	$0.656559\pi$
$140$			1.00000i			0.0845154i
$141$	−18.0000	+	10.3923i	−1.51587	+	0.875190i
$142$	−6.00000	+	10.3923i	−0.503509	+	0.872103i
$143$	15.5885	−	9.00000i	1.30357	−	0.752618i
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	−1.50000	−	0.866025i	−0.124568	−	0.0719195i
$146$	3.46410	−	6.00000i	0.286691	−	0.496564i
$147$	10.3923			0.857143
$148$	−6.00000	+	3.46410i	−0.493197	+	0.284747i
$149$	12.9904	−	7.50000i	1.06421	−	0.614424i	0.137619	−	0.990485i	$-0.456055\pi$
$149$	12.9904	−	7.50000i	1.06421	−	0.614424i	0.926595	+	0.376061i	$0.122722\pi$
$150$	1.50000	+	0.866025i	0.122474	+	0.0707107i
$151$			8.66025i			0.704761i	0.935857	+	0.352381i	$0.114628\pi$
$151$			8.66025i			0.704761i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	3.46410	−	2.00000i	0.280976	−	0.162221i
$153$	10.3923			0.840168
$154$			5.19615i			0.418718i
$155$	5.19615	+	2.00000i	0.417365	+	0.160644i
$156$			6.00000i			0.480384i
$157$	10.0000			0.798087			0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000			0.798087			0.399043	+	0.916932i	$0.369342\pi$
$158$	5.19615	+	9.00000i	0.413384	+	0.716002i
$159$	−21.0000			−1.66541
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−3.46410	−	6.00000i	−0.273009	−	0.472866i
$162$	−7.79423	+	4.50000i	−0.612372	+	0.353553i
$163$	8.00000			0.626608			0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000			0.626608			0.313304	+	0.949653i	$0.398564\pi$
$164$	−5.19615	−	3.00000i	−0.405751	−	0.234261i
$165$	7.79423	+	4.50000i	0.606780	+	0.350325i
$166$	−4.50000	−	2.59808i	−0.349268	−	0.201650i
$167$	−5.19615	−	9.00000i	−0.402090	−	0.696441i	0.591888	−	0.806020i	$-0.298383\pi$
$167$	−5.19615	−	9.00000i	−0.402090	−	0.696441i	−0.993978	+	0.109580i	$0.965050\pi$
$168$	−1.50000	−	0.866025i	−0.115728	−	0.0668153i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	3.46410			0.265684
$171$	12.0000			0.917663
$172$	−3.00000	+	1.73205i	−0.228748	+	0.132068i
$173$	−2.59808	−	1.50000i	−0.197528	−	0.114043i	0.397974	−	0.917397i	$-0.369713\pi$
$173$	−2.59808	−	1.50000i	−0.197528	−	0.114043i	−0.595502	+	0.803354i	$0.703047\pi$
$174$	2.59808	−	1.50000i	0.196960	−	0.113715i
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	−2.59808	+	4.50000i	−0.195837	+	0.339200i
$177$	−22.5000	−	12.9904i	−1.69120	−	0.976417i
$178$		−	10.3923i		−	0.778936i
$179$	7.79423	+	13.5000i	0.582568	+	1.00904i	0.995174	+	0.0981277i	$0.0312854\pi$
$179$	7.79423	+	13.5000i	0.582568	+	1.00904i	−0.412606	+	0.910910i	$0.635381\pi$
$180$	−2.59808	+	1.50000i	−0.193649	+	0.111803i
$181$	3.00000	+	1.73205i	0.222988	+	0.128742i	0.607333	−	0.794447i	$-0.292239\pi$
$181$	3.00000	+	1.73205i	0.222988	+	0.128742i	−0.384345	+	0.923190i	$0.625573\pi$
$182$	−3.46410			−0.256776
$183$	−5.19615	+	3.00000i	−0.384111	+	0.221766i
$184$		−	6.92820i		−	0.510754i
$185$	−6.92820			−0.509372
$186$	−7.50000	+	6.06218i	−0.549927	+	0.444500i
$187$	18.0000			1.31629
$188$		−	12.0000i		−	0.875190i
$189$	−2.59808	−	4.50000i	−0.188982	−	0.327327i
$190$	4.00000			0.290191
$191$	−10.3923	−	6.00000i	−0.751961	−	0.434145i	0.0744412	−	0.997225i	$-0.476283\pi$
$191$	−10.3923	−	6.00000i	−0.751961	−	0.434145i	−0.826402	+	0.563081i	$0.809616\pi$
$192$	−0.866025	−	1.50000i	−0.0625000	−	0.108253i
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	0.993215	−	0.116289i	$-0.0370998\pi$
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	−0.597317	+	0.802005i	$0.703766\pi$
$194$			1.00000i			0.0717958i
$195$	−3.00000	+	5.19615i	−0.214834	+	0.372104i
$196$	−3.00000	+	5.19615i	−0.214286	+	0.371154i
$197$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$197$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$198$	−13.5000	+	7.79423i	−0.959403	+	0.553912i
$199$	−10.5000	−	6.06218i	−0.744325	−	0.429736i	0.0793146	−	0.996850i	$-0.474727\pi$
$199$	−10.5000	−	6.06218i	−0.744325	−	0.429736i	−0.823640	+	0.567113i	$0.808060\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	3.46410			0.244339
$202$	15.0000			1.05540
$203$	0.866025	+	1.50000i	0.0607831	+	0.105279i
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$	6.06218	+	3.50000i	0.422372	+	0.243857i
$207$	10.3923	−	18.0000i	0.722315	−	1.25109i
$208$	−3.00000	−	1.73205i	−0.208013	−	0.120096i
$209$	20.7846			1.43770
$210$	−0.866025	−	1.50000i	−0.0597614	−	0.103510i
$211$	5.00000	+	8.66025i	0.344214	+	0.596196i	0.985211	−	0.171347i	$-0.0548120\pi$
$211$	5.00000	+	8.66025i	0.344214	+	0.596196i	−0.640996	+	0.767544i	$0.721479\pi$
$212$	6.06218	−	10.5000i	0.416352	−	0.721143i
$213$		−	20.7846i		−	1.42414i
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$	−3.46410			−0.236250
$216$		−	5.19615i		−	0.353553i
$217$	−3.50000	−	4.33013i	−0.237595	−	0.293948i
$218$			4.00000i			0.270914i
$219$			12.0000i			0.810885i
$220$	−4.50000	+	2.59808i	−0.303390	+	0.175162i
$221$			12.0000i			0.807207i
$222$	6.00000	−	10.3923i	0.402694	−	0.697486i
$223$	13.5000	−	7.79423i	0.904027	−	0.521940i	0.0255224	−	0.999674i	$-0.491875\pi$
$223$	13.5000	−	7.79423i	0.904027	−	0.521940i	0.878504	+	0.477734i	$0.158542\pi$
$224$	0.866025	−	0.500000i	0.0578638	−	0.0334077i
$225$	−3.00000			−0.200000
$226$		0			0
$227$	−12.9904	−	7.50000i	−0.862202	−	0.497792i	0.00254715	−	0.999997i	$-0.499189\pi$
$227$	−12.9904	−	7.50000i	−0.862202	−	0.497792i	−0.864749	+	0.502204i	$0.832523\pi$
$228$	−3.46410	+	6.00000i	−0.229416	+	0.397360i
$229$	−24.0000	+	13.8564i	−1.58596	+	0.915657i	−0.592002	+	0.805936i	$0.701662\pi$
$229$	−24.0000	+	13.8564i	−1.58596	+	0.915657i	−0.993962	+	0.109721i	$0.965004\pi$
$230$	3.46410	−	6.00000i	0.228416	−	0.395628i
$231$	−4.50000	−	7.79423i	−0.296078	−	0.512823i
$232$			1.73205i			0.113715i
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$	−5.19615	−	9.00000i	−0.339683	−	0.588348i
$235$	6.00000	−	10.3923i	0.391397	−	0.677919i
$236$	12.9904	−	7.50000i	0.845602	−	0.488208i
$237$	−15.5885	−	9.00000i	−1.01258	−	0.584613i
$238$	−3.00000	−	1.73205i	−0.194461	−	0.112272i
$239$	−13.8564	+	24.0000i	−0.896296	+	1.55243i	−0.0641045	+	0.997943i	$0.520419\pi$
$239$	−13.8564	+	24.0000i	−0.896296	+	1.55243i	−0.832192	+	0.554488i	$0.812914\pi$
$240$		−	1.73205i		−	0.111803i
$241$	−13.5000	+	7.79423i	−0.869611	+	0.502070i	−0.867219	−	0.497927i	$-0.834095\pi$
$241$	−13.5000	+	7.79423i	−0.869611	+	0.502070i	−0.00239235	+	0.999997i	$0.500762\pi$
$242$	−13.8564	+	8.00000i	−0.890724	+	0.514259i
$243$	7.79423	−	13.5000i	0.500000	−	0.866025i
$244$		−	3.46410i		−	0.221766i
$245$	−5.19615	+	3.00000i	−0.331970	+	0.191663i
$246$	10.3923			0.662589
$247$			13.8564i			0.881662i
$248$	−0.866025	−	5.50000i	−0.0549927	−	0.349250i
$249$	9.00000			0.570352
$250$	−1.00000			−0.0632456
$251$	−5.19615	−	9.00000i	−0.327978	−	0.568075i	0.654132	−	0.756380i	$-0.273034\pi$
$251$	−5.19615	−	9.00000i	−0.327978	−	0.568075i	−0.982111	+	0.188305i	$0.939701\pi$
$252$	3.00000			0.188982
$253$	18.0000	−	31.1769i	1.13165	−	1.96008i
$254$	−6.06218	−	10.5000i	−0.380375	−	0.658829i
$255$	−5.19615	+	3.00000i	−0.325396	+	0.187867i
$256$	1.00000			0.0625000
$257$	20.7846	+	12.0000i	1.29651	+	0.748539i	0.979799	−	0.199983i	$-0.0640888\pi$
$257$	20.7846	+	12.0000i	1.29651	+	0.748539i	0.316709	+	0.948523i	$0.397422\pi$
$258$	3.00000	−	5.19615i	0.186772	−	0.323498i
$259$	6.00000	+	3.46410i	0.372822	+	0.215249i
$260$	−1.73205	−	3.00000i	−0.107417	−	0.186052i
$261$	−2.59808	+	4.50000i	−0.160817	+	0.278543i
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$	3.46410			0.213606			0.106803	−	0.994280i	$-0.465939\pi$
$263$	3.46410			0.213606			0.106803	+	0.994280i	$0.465939\pi$
$264$		−	9.00000i		−	0.553912i
$265$	10.5000	−	6.06218i	0.645010	−	0.372397i
$266$	−3.46410	−	2.00000i	−0.212398	−	0.122628i
$267$	9.00000	+	15.5885i	0.550791	+	0.953998i
$268$	−1.00000	+	1.73205i	−0.0610847	+	0.105802i
$269$	−13.8564	+	24.0000i	−0.844840	+	1.46331i	0.0409201	+	0.999162i	$0.486971\pi$
$269$	−13.8564	+	24.0000i	−0.844840	+	1.46331i	−0.885760	+	0.464143i	$0.846362\pi$
$270$	2.59808	−	4.50000i	0.158114	−	0.273861i
$271$		−	12.1244i		−	0.736502i	−0.929726	−	0.368251i	$-0.879957\pi$
$271$		−	12.1244i		−	0.736502i	0.929726	−	0.368251i	$-0.120043\pi$
$272$	−1.73205	−	3.00000i	−0.105021	−	0.181902i
$273$	5.19615	−	3.00000i	0.314485	−	0.181568i
$274$	−12.0000	−	6.92820i	−0.724947	−	0.418548i
$275$	−5.19615			−0.313340
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$	20.7846			1.24658
$279$	6.00000	−	15.5885i	0.359211	−	0.933257i
$280$	1.00000			0.0597614
$281$		−	12.0000i		−	0.715860i	−0.933748	−	0.357930i	$-0.883483\pi$
$281$		−	12.0000i		−	0.715860i	0.933748	−	0.357930i	$-0.116517\pi$
$282$	10.3923	+	18.0000i	0.618853	+	1.07188i
$283$	−22.0000			−1.30776			−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−22.0000			−1.30776			−0.653882	+	0.756596i	$0.726861\pi$
$284$	10.3923	+	6.00000i	0.616670	+	0.356034i
$285$	−6.00000	+	3.46410i	−0.355409	+	0.205196i
$286$	−9.00000	−	15.5885i	−0.532181	−	0.921765i
$287$			6.00000i			0.354169i
$288$	2.59808	+	1.50000i	0.153093	+	0.0883883i
$289$	2.50000	−	4.33013i	0.147059	−	0.254713i
$290$	−0.866025	+	1.50000i	−0.0508548	+	0.0880830i
$291$	−0.866025	−	1.50000i	−0.0507673	−	0.0879316i
$292$	−6.00000	−	3.46410i	−0.351123	−	0.202721i
$293$	7.79423	−	4.50000i	0.455344	−	0.262893i	−0.254741	−	0.967009i	$-0.581990\pi$
$293$	7.79423	−	4.50000i	0.455344	−	0.262893i	0.710084	+	0.704117i	$0.248657\pi$
$294$		−	10.3923i		−	0.606092i
$295$	15.0000			0.873334
$296$	3.46410	+	6.00000i	0.201347	+	0.348743i
$297$	13.5000	−	23.3827i	0.783349	−	1.35680i
$298$	−7.50000	−	12.9904i	−0.434463	−	0.752513i
$299$	20.7846	+	12.0000i	1.20201	+	0.693978i
$300$	0.866025	−	1.50000i	0.0500000	−	0.0866025i
$301$	3.00000	+	1.73205i	0.172917	+	0.0998337i
$302$	8.66025			0.498342
$303$	−22.5000	+	12.9904i	−1.29259	+	0.746278i
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$	1.73205	−	3.00000i	0.0991769	−	0.171780i
$306$		−	10.3923i		−	0.594089i
$307$	7.00000	+	12.1244i	0.399511	+	0.691974i	0.993666	−	0.112377i	$-0.0358466\pi$
$307$	7.00000	+	12.1244i	0.399511	+	0.691974i	−0.594154	+	0.804351i	$0.702513\pi$
$308$	5.19615			0.296078
$309$	−12.1244			−0.689730
$310$	2.00000	−	5.19615i	0.113592	−	0.295122i
$311$		−	30.0000i		−	1.70114i	−0.525859	−	0.850572i	$-0.676256\pi$
$311$		−	30.0000i		−	1.70114i	0.525859	−	0.850572i	$-0.323744\pi$
$312$	6.00000			0.339683
$313$	−22.5000	+	12.9904i	−1.27178	+	0.734260i	−0.975322	−	0.220788i	$-0.929137\pi$
$313$	−22.5000	+	12.9904i	−1.27178	+	0.734260i	−0.296453	+	0.955047i	$0.595804\pi$
$314$		−	10.0000i		−	0.564333i
$315$	2.59808	+	1.50000i	0.146385	+	0.0845154i
$316$	9.00000	−	5.19615i	0.506290	−	0.292306i
$317$	2.59808	−	1.50000i	0.145922	−	0.0842484i	−0.425261	−	0.905071i	$-0.639818\pi$
$317$	2.59808	−	1.50000i	0.145922	−	0.0842484i	0.571184	+	0.820822i	$0.306484\pi$
$318$			21.0000i			1.17762i
$319$	−4.50000	+	7.79423i	−0.251952	+	0.436393i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	4.50000	+	2.59808i	0.251166	+	0.145010i
$322$	−6.00000	+	3.46410i	−0.334367	+	0.193047i
$323$	−6.92820	+	12.0000i	−0.385496	+	0.667698i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$		−	3.46410i		−	0.192154i
$326$		−	8.00000i		−	0.443079i
$327$	−3.46410	−	6.00000i	−0.191565	−	0.331801i
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	−10.3923	+	6.00000i	−0.572946	+	0.330791i
$330$	4.50000	−	7.79423i	0.247717	−	0.429058i
$331$	−15.0000	−	8.66025i	−0.824475	−	0.476011i	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	−15.0000	−	8.66025i	−0.824475	−	0.476011i	−0.851957	+	0.523612i	$0.824584\pi$
$332$	−2.59808	+	4.50000i	−0.142588	+	0.246970i
$333$			20.7846i			1.13899i
$334$	−9.00000	+	5.19615i	−0.492458	+	0.284321i
$335$	−1.73205	+	1.00000i	−0.0946320	+	0.0546358i
$336$	−0.866025	+	1.50000i	−0.0472456	+	0.0818317i
$337$		−	12.1244i		−	0.660456i	−0.943901	−	0.330228i	$-0.892874\pi$
$337$		−	12.1244i		−	0.660456i	0.943901	−	0.330228i	$-0.107126\pi$
$338$	−0.866025	+	0.500000i	−0.0471056	+	0.0271964i
$339$		0			0
$340$		−	3.46410i		−	0.187867i
$341$	10.3923	−	27.0000i	0.562775	−	1.46213i
$342$		−	12.0000i		−	0.648886i
$343$	13.0000			0.701934
$344$	1.73205	+	3.00000i	0.0933859	+	0.161749i
$345$			12.0000i			0.646058i
$346$	−1.50000	+	2.59808i	−0.0806405	+	0.139673i
$347$	9.52628	+	16.5000i	0.511397	+	0.885766i	0.999913	+	0.0132111i	$0.00420533\pi$
$347$	9.52628	+	16.5000i	0.511397	+	0.885766i	−0.488515	+	0.872555i	$0.662461\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	−8.00000			−0.428230			−0.214115	−	0.976808i	$-0.568687\pi$
$349$	−8.00000			−0.428230			−0.214115	+	0.976808i	$0.568687\pi$
$350$	0.866025	+	0.500000i	0.0462910	+	0.0267261i
$351$	15.5885	+	9.00000i	0.832050	+	0.480384i
$352$	4.50000	+	2.59808i	0.239851	+	0.138478i
$353$	−17.3205	−	30.0000i	−0.921878	−	1.59674i	−0.796507	−	0.604629i	$-0.793321\pi$
$353$	−17.3205	−	30.0000i	−0.921878	−	1.59674i	−0.125370	−	0.992110i	$-0.540012\pi$
$354$	−12.9904	+	22.5000i	−0.690431	+	1.19586i
$355$	6.00000	+	10.3923i	0.318447	+	0.551566i
$356$	−10.3923			−0.550791
$357$	6.00000			0.317554
$358$	13.5000	−	7.79423i	0.713497	−	0.411938i
$359$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$359$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$360$	1.50000	+	2.59808i	0.0790569	+	0.136931i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	1.73205	−	3.00000i	0.0910346	−	0.157676i
$363$	13.8564	−	24.0000i	0.727273	−	1.25967i
$364$			3.46410i			0.181568i
$365$	−3.46410	−	6.00000i	−0.181319	−	0.314054i
$366$	3.00000	+	5.19615i	0.156813	+	0.271607i
$367$	9.00000	+	5.19615i	0.469796	+	0.271237i	0.716154	−	0.697942i	$-0.245901\pi$
$367$	9.00000	+	5.19615i	0.469796	+	0.271237i	−0.246358	+	0.969179i	$0.579234\pi$
$368$	−6.92820			−0.361158
$369$	−15.5885	+	9.00000i	−0.811503	+	0.468521i
$370$			6.92820i			0.360180i
$371$	−12.1244			−0.629465
$372$	6.06218	+	7.50000i	0.314309	+	0.388857i
$373$	−28.0000			−1.44979			−0.724893	−	0.688862i	$-0.758111\pi$
$373$	−28.0000			−1.44979			−0.724893	+	0.688862i	$0.758111\pi$
$374$		−	18.0000i		−	0.930758i
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$	−12.0000			−0.618853
$377$	−5.19615	−	3.00000i	−0.267615	−	0.154508i
$378$	−4.50000	+	2.59808i	−0.231455	+	0.133631i
$379$	−7.00000	−	12.1244i	−0.359566	−	0.622786i	0.628322	−	0.777953i	$-0.283742\pi$
$379$	−7.00000	−	12.1244i	−0.359566	−	0.622786i	−0.987888	+	0.155167i	$0.950409\pi$
$380$		−	4.00000i		−	0.205196i
$381$	18.1865	+	10.5000i	0.931724	+	0.537931i
$382$	−6.00000	+	10.3923i	−0.306987	+	0.531717i
$383$	−5.19615	+	9.00000i	−0.265511	+	0.459879i	−0.967697	−	0.252115i	$-0.918874\pi$
$383$	−5.19615	+	9.00000i	−0.265511	+	0.459879i	0.702186	+	0.711993i	$0.252207\pi$
$384$	−1.50000	+	0.866025i	−0.0765466	+	0.0441942i
$385$	4.50000	+	2.59808i	0.229341	+	0.132410i
$386$	9.52628	−	5.50000i	0.484875	−	0.279943i
$387$			10.3923i			0.528271i
$388$	1.00000			0.0507673
$389$	−13.8564	−	24.0000i	−0.702548	−	1.21685i	−0.967569	−	0.252606i	$-0.918712\pi$
$389$	−13.8564	−	24.0000i	−0.702548	−	1.21685i	0.265022	−	0.964242i	$-0.414621\pi$
$390$	5.19615	+	3.00000i	0.263117	+	0.151911i
$391$	12.0000	+	20.7846i	0.606866	+	1.05112i
$392$	5.19615	+	3.00000i	0.262445	+	0.151523i
$393$	18.0000	+	10.3923i	0.907980	+	0.524222i
$394$		0			0
$395$	10.3923			0.522894
$396$	7.79423	+	13.5000i	0.391675	+	0.678401i
$397$	14.0000	+	24.2487i	0.702640	+	1.21701i	0.967537	+	0.252731i	$0.0813288\pi$
$397$	14.0000	+	24.2487i	0.702640	+	1.21701i	−0.264897	+	0.964277i	$0.585338\pi$
$398$	−6.06218	+	10.5000i	−0.303870	+	0.526317i
$399$	6.92820			0.346844
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−6.92820			−0.345978			−0.172989	−	0.984924i	$-0.555343\pi$
$401$	−6.92820			−0.345978			−0.172989	+	0.984924i	$0.555343\pi$
$402$		−	3.46410i		−	0.172774i
$403$	18.0000	+	6.92820i	0.896644	+	0.345118i
$404$		−	15.0000i		−	0.746278i
$405$			9.00000i			0.447214i
$406$	1.50000	−	0.866025i	0.0744438	−	0.0429801i
$407$			36.0000i			1.78445i
$408$	5.19615	+	3.00000i	0.257248	+	0.148522i
$409$	−10.5000	+	6.06218i	−0.519192	+	0.299755i	−0.736604	−	0.676324i	$-0.763572\pi$
$409$	−10.5000	+	6.06218i	−0.519192	+	0.299755i	0.217412	+	0.976080i	$0.430238\pi$
$410$	−5.19615	+	3.00000i	−0.256620	+	0.148159i
$411$	24.0000			1.18383
$412$	3.50000	−	6.06218i	0.172433	−	0.298662i
$413$	−12.9904	−	7.50000i	−0.639215	−	0.369051i
$414$	−18.0000	−	10.3923i	−0.884652	−	0.510754i
$415$	−4.50000	+	2.59808i	−0.220896	+	0.127535i
$416$	−1.73205	+	3.00000i	−0.0849208	+	0.147087i
$417$	−31.1769	+	18.0000i	−1.52674	+	0.881464i
$418$		−	20.7846i		−	1.01661i
$419$			33.0000i			1.61216i	0.591810	+	0.806078i	$0.298414\pi$
$419$			33.0000i			1.61216i	−0.591810	+	0.806078i	$0.701586\pi$
$420$	−1.50000	+	0.866025i	−0.0731925	+	0.0422577i
$421$	10.0000	−	17.3205i	0.487370	−	0.844150i	−0.512524	−	0.858673i	$-0.671290\pi$
$421$	10.0000	−	17.3205i	0.487370	−	0.844150i	0.999895	+	0.0145228i	$0.00462290\pi$
$422$	8.66025	−	5.00000i	0.421575	−	0.243396i
$423$	−31.1769	−	18.0000i	−1.51587	−	0.875190i
$424$	−10.5000	−	6.06218i	−0.509925	−	0.294405i
$425$	1.73205	−	3.00000i	0.0840168	−	0.145521i
$426$	−20.7846			−1.00702
$427$	−3.00000	+	1.73205i	−0.145180	+	0.0838198i
$428$	−2.59808	+	1.50000i	−0.125583	+	0.0725052i
$429$	27.0000	+	15.5885i	1.30357	+	0.752618i
$430$			3.46410i			0.167054i
$431$	−25.9808	+	15.0000i	−1.25145	+	0.722525i	−0.971397	−	0.237460i	$-0.923685\pi$
$431$	−25.9808	+	15.0000i	−1.25145	+	0.722525i	−0.280052	+	0.959985i	$0.590352\pi$
$432$	−5.19615			−0.250000
$433$			27.7128i			1.33179i	0.746044	+	0.665896i	$0.231951\pi$
$433$			27.7128i			1.33179i	−0.746044	+	0.665896i	$0.768049\pi$
$434$	−4.33013	+	3.50000i	−0.207853	+	0.168005i
$435$		−	3.00000i		−	0.143839i
$436$	4.00000			0.191565
$437$	13.8564	+	24.0000i	0.662842	+	1.14808i
$438$	12.0000			0.573382
$439$	8.50000	−	14.7224i	0.405683	−	0.702663i	−0.588718	−	0.808339i	$-0.700367\pi$
$439$	8.50000	−	14.7224i	0.405683	−	0.702663i	0.994401	+	0.105675i	$0.0337004\pi$
$440$	2.59808	+	4.50000i	0.123858	+	0.214529i
$441$	9.00000	+	15.5885i	0.428571	+	0.742307i
$442$	12.0000			0.570782
$443$	−10.3923	−	6.00000i	−0.493753	−	0.285069i	0.232377	−	0.972626i	$-0.425350\pi$
$443$	−10.3923	−	6.00000i	−0.493753	−	0.285069i	−0.726130	+	0.687557i	$0.758683\pi$
$444$	−10.3923	−	6.00000i	−0.493197	−	0.284747i
$445$	−9.00000	−	5.19615i	−0.426641	−	0.246321i
$446$	−7.79423	−	13.5000i	−0.369067	−	0.639244i
$447$	22.5000	+	12.9904i	1.06421	+	0.614424i
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	6.92820			0.326962			0.163481	−	0.986546i	$-0.447728\pi$
$449$	6.92820			0.326962			0.163481	+	0.986546i	$0.447728\pi$
$450$			3.00000i			0.141421i
$451$	−27.0000	+	15.5885i	−1.27138	+	0.734032i
$452$		0			0
$453$	−12.9904	+	7.50000i	−0.610341	+	0.352381i
$454$	−7.50000	+	12.9904i	−0.351992	+	0.609669i
$455$	−1.73205	+	3.00000i	−0.0811998	+	0.140642i
$456$	6.00000	+	3.46410i	0.280976	+	0.162221i
$457$		−	6.92820i		−	0.324088i	−0.986784	−	0.162044i	$-0.948191\pi$
$457$		−	6.92820i		−	0.324088i	0.986784	−	0.162044i	$-0.0518086\pi$
$458$	13.8564	+	24.0000i	0.647467	+	1.12145i
$459$	9.00000	+	15.5885i	0.420084	+	0.727607i
$460$	−6.00000	−	3.46410i	−0.279751	−	0.161515i
$461$	−39.8372			−1.85540			−0.927701	−	0.373324i	$-0.878218\pi$
$461$	−39.8372			−1.85540			−0.927701	+	0.373324i	$0.878218\pi$
$462$	−7.79423	+	4.50000i	−0.362620	+	0.209359i
$463$			12.1244i			0.563467i	0.959493	+	0.281733i	$0.0909093\pi$
$463$			12.1244i			0.563467i	−0.959493	+	0.281733i	$0.909091\pi$
$464$	1.73205			0.0804084
$465$	1.50000	+	9.52628i	0.0695608	+	0.441771i
$466$	−18.0000			−0.833834
$467$			27.0000i			1.24941i	0.780860	+	0.624705i	$0.214781\pi$
$467$			27.0000i			1.24941i	−0.780860	+	0.624705i	$0.785219\pi$
$468$	−9.00000	+	5.19615i	−0.416025	+	0.240192i
$469$	2.00000			0.0923514
$470$	−10.3923	−	6.00000i	−0.479361	−	0.276759i
$471$	8.66025	+	15.0000i	0.399043	+	0.691164i
$472$	−7.50000	−	12.9904i	−0.345215	−	0.597931i
$473$			18.0000i			0.827641i
$474$	−9.00000	+	15.5885i	−0.413384	+	0.716002i
$475$	2.00000	−	3.46410i	0.0917663	−	0.158944i
$476$	−1.73205	+	3.00000i	−0.0793884	+	0.137505i
$477$	−18.1865	−	31.5000i	−0.832704	−	1.44229i
$478$	24.0000	+	13.8564i	1.09773	+	0.633777i
$479$	−10.3923	+	6.00000i	−0.474837	+	0.274147i	−0.718262	−	0.695773i	$-0.755062\pi$
$479$	−10.3923	+	6.00000i	−0.474837	+	0.274147i	0.243426	+	0.969920i	$0.421729\pi$
$480$	−1.73205			−0.0790569
$481$	−24.0000			−1.09431
$482$	7.79423	+	13.5000i	0.355017	+	0.614908i
$483$	6.00000	−	10.3923i	0.273009	−	0.472866i
$484$	8.00000	+	13.8564i	0.363636	+	0.629837i
$485$	0.866025	+	0.500000i	0.0393242	+	0.0227038i
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	31.5000	+	18.1865i	1.42740	+	0.824110i	0.996915	−	0.0784867i	$-0.0250088\pi$
$487$	31.5000	+	18.1865i	1.42740	+	0.824110i	0.430486	+	0.902597i	$0.358342\pi$
$488$	−3.46410			−0.156813
$489$	6.92820	+	12.0000i	0.313304	+	0.542659i
$490$	3.00000	+	5.19615i	0.135526	+	0.234738i
$491$	18.1865	−	31.5000i	0.820747	−	1.42158i	−0.0843802	−	0.996434i	$-0.526891\pi$
$491$	18.1865	−	31.5000i	0.820747	−	1.42158i	0.905127	−	0.425141i	$-0.139776\pi$
$492$		−	10.3923i		−	0.468521i
$493$	−3.00000	−	5.19615i	−0.135113	−	0.234023i
$494$	13.8564			0.623429
$495$			15.5885i			0.700649i
$496$	−5.50000	+	0.866025i	−0.246957	+	0.0388857i
$497$		−	12.0000i		−	0.538274i
$498$		−	9.00000i		−	0.403300i
$499$	−21.0000	+	12.1244i	−0.940089	+	0.542761i	−0.889988	−	0.455983i	$-0.849288\pi$
$499$	−21.0000	+	12.1244i	−0.940089	+	0.542761i	−0.0501009	+	0.998744i	$0.515954\pi$
$500$			1.00000i			0.0447214i
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$	−9.00000	+	5.19615i	−0.401690	+	0.231916i
$503$	31.1769	−	18.0000i	1.39011	−	0.802580i	0.396783	−	0.917912i	$-0.370127\pi$
$503$	31.1769	−	18.0000i	1.39011	−	0.802580i	0.993327	+	0.115332i	$0.0367932\pi$
$504$		−	3.00000i		−	0.133631i
$505$	7.50000	−	12.9904i	0.333746	−	0.578064i
$506$	−31.1769	−	18.0000i	−1.38598	−	0.800198i
$507$	0.866025	−	1.50000i	0.0384615	−	0.0666173i
$508$	−10.5000	+	6.06218i	−0.465862	+	0.268966i
$509$	−12.9904	+	22.5000i	−0.575789	+	0.997295i	0.420167	+	0.907447i	$0.361972\pi$
$509$	−12.9904	+	22.5000i	−0.575789	+	0.997295i	−0.995955	+	0.0898481i	$0.971362\pi$
$510$	3.00000	+	5.19615i	0.132842	+	0.230089i
$511$			6.92820i			0.306486i
$512$		−	1.00000i		−	0.0441942i
$513$	10.3923	+	18.0000i	0.458831	+	0.794719i
$514$	12.0000	−	20.7846i	0.529297	−	0.916770i
$515$	6.06218	−	3.50000i	0.267131	−	0.154228i
$516$	−5.19615	−	3.00000i	−0.228748	−	0.132068i
$517$	−54.0000	−	31.1769i	−2.37492	−	1.37116i
$518$	3.46410	−	6.00000i	0.152204	−	0.263625i
$519$		−	5.19615i		−	0.228086i
$520$	−3.00000	+	1.73205i	−0.131559	+	0.0759555i
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$	4.50000	+	2.59808i	0.196960	+	0.113715i
$523$			17.3205i			0.757373i	0.925525	+	0.378686i	$0.123624\pi$
$523$			17.3205i			0.757373i	−0.925525	+	0.378686i	$0.876376\pi$
$524$	−10.3923	+	6.00000i	−0.453990	+	0.262111i
$525$	−1.73205			−0.0755929
$526$		−	3.46410i		−	0.151042i
$527$	12.1244	+	15.0000i	0.528145	+	0.653410i
$528$	−9.00000			−0.391675
$529$	25.0000			1.08696
$530$	−6.06218	−	10.5000i	−0.263324	−	0.456091i
$531$		−	45.0000i		−	1.95283i
$532$	−2.00000	+	3.46410i	−0.0867110	+	0.150188i
$533$	−10.3923	−	18.0000i	−0.450141	−	0.779667i
$534$	15.5885	−	9.00000i	0.674579	−	0.389468i
$535$	−3.00000			−0.129701
$536$	1.73205	+	1.00000i	0.0748132	+	0.0431934i
$537$	−13.5000	+	23.3827i	−0.582568	+	1.00904i
$538$	24.0000	+	13.8564i	1.03471	+	0.597392i
$539$	15.5885	+	27.0000i	0.671442	+	1.16297i
$540$	−4.50000	−	2.59808i	−0.193649	−	0.111803i
$541$	4.00000	+	6.92820i	0.171973	+	0.297867i	0.939110	−	0.343617i	$-0.111652\pi$
$541$	4.00000	+	6.92820i	0.171973	+	0.297867i	−0.767136	+	0.641484i	$0.778319\pi$
$542$	−12.1244			−0.520786
$543$			6.00000i			0.257485i
$544$	−3.00000	+	1.73205i	−0.128624	+	0.0742611i
$545$	3.46410	+	2.00000i	0.148386	+	0.0856706i
$546$	−3.00000	−	5.19615i	−0.128388	−	0.222375i
$547$	13.0000	−	22.5167i	0.555840	−	0.962743i	−0.441998	−	0.897016i	$-0.645730\pi$
$547$	13.0000	−	22.5167i	0.555840	−	0.962743i	0.997838	−	0.0657267i	$-0.0209366\pi$
$548$	−6.92820	+	12.0000i	−0.295958	+	0.512615i
$549$	−9.00000	−	5.19615i	−0.384111	−	0.221766i
$550$			5.19615i			0.221565i
$551$	−3.46410	−	6.00000i	−0.147576	−	0.255609i
$552$	10.3923	−	6.00000i	0.442326	−	0.255377i
$553$	−9.00000	−	5.19615i	−0.382719	−	0.220963i
$554$		0			0
$555$	−6.00000	−	10.3923i	−0.254686	−	0.441129i
$556$		−	20.7846i		−	0.881464i
$557$	−5.19615			−0.220168			−0.110084	−	0.993922i	$-0.535112\pi$
$557$	−5.19615			−0.220168			−0.110084	+	0.993922i	$0.535112\pi$
$558$	−15.5885	−	6.00000i	−0.659912	−	0.254000i
$559$	−12.0000			−0.507546
$560$		−	1.00000i		−	0.0422577i
$561$	15.5885	+	27.0000i	0.658145	+	1.13994i
$562$	−12.0000			−0.506189
$563$	28.5788	+	16.5000i	1.20445	+	0.695392i	0.961542	−	0.274656i	$-0.0885641\pi$
$563$	28.5788	+	16.5000i	1.20445	+	0.695392i	0.242912	+	0.970048i	$0.421897\pi$
$564$	18.0000	−	10.3923i	0.757937	−	0.437595i
$565$		0			0
$566$			22.0000i			0.924729i
$567$	4.50000	−	7.79423i	0.188982	−	0.327327i
$568$	6.00000	−	10.3923i	0.251754	−	0.436051i
$569$	−20.7846	+	36.0000i	−0.871336	+	1.50920i	−0.0107211	+	0.999943i	$0.503413\pi$
$569$	−20.7846	+	36.0000i	−0.871336	+	1.50920i	−0.860615	+	0.509256i	$0.829921\pi$
$570$	3.46410	+	6.00000i	0.145095	+	0.251312i
$571$	36.0000	+	20.7846i	1.50655	+	0.869809i	0.999971	+	0.00761713i	$0.00242463\pi$
$571$	36.0000	+	20.7846i	1.50655	+	0.869809i	0.506582	+	0.862192i	$0.330909\pi$
$572$	−15.5885	+	9.00000i	−0.651786	+	0.376309i
$573$		−	20.7846i		−	0.868290i
$574$	6.00000			0.250435
$575$	−3.46410	−	6.00000i	−0.144463	−	0.250217i
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	0.886090	−	0.463513i	$-0.153411\pi$
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	−0.844459	+	0.535620i	$0.820078\pi$
$578$	−4.33013	−	2.50000i	−0.180110	−	0.103986i
$579$	−9.52628	+	16.5000i	−0.395899	+	0.685717i
$580$	1.50000	+	0.866025i	0.0622841	+	0.0359597i
$581$	5.19615			0.215573
$582$	−1.50000	+	0.866025i	−0.0621770	+	0.0358979i
$583$	−31.5000	−	54.5596i	−1.30460	−	2.25963i
$584$	−3.46410	+	6.00000i	−0.143346	+	0.248282i
$585$	−10.3923			−0.429669
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	−25.9808			−1.07234			−0.536170	−	0.844110i	$-0.680130\pi$
$587$	−25.9808			−1.07234			−0.536170	+	0.844110i	$0.680130\pi$
$588$	−10.3923			−0.428571
$589$	14.0000	+	17.3205i	0.576860	+	0.713679i
$590$		−	15.0000i		−	0.617540i
$591$		0			0
$592$	6.00000	−	3.46410i	0.246598	−	0.142374i
$593$			6.00000i			0.246390i	0.992382	+	0.123195i	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$	−23.3827	−	13.5000i	−0.959403	−	0.553912i
$595$	−3.00000	+	1.73205i	−0.122988	+	0.0710072i
$596$	−12.9904	+	7.50000i	−0.532107	+	0.307212i
$597$		−	21.0000i		−	0.859473i
$598$	12.0000	−	20.7846i	0.490716	−	0.849946i
$599$	−5.19615	−	3.00000i	−0.212309	−	0.122577i	0.390075	−	0.920783i	$-0.372449\pi$
$599$	−5.19615	−	3.00000i	−0.212309	−	0.122577i	−0.602384	+	0.798206i	$0.705782\pi$
$600$	−1.50000	−	0.866025i	−0.0612372	−	0.0353553i
$601$	−12.0000	+	6.92820i	−0.489490	+	0.282607i	−0.724363	−	0.689419i	$-0.757866\pi$
$601$	−12.0000	+	6.92820i	−0.489490	+	0.282607i	0.234873	+	0.972026i	$0.424533\pi$
$602$	1.73205	−	3.00000i	0.0705931	−	0.122271i
$603$	3.00000	+	5.19615i	0.122169	+	0.211604i
$604$		−	8.66025i		−	0.352381i
$605$			16.0000i			0.650493i
$606$	12.9904	+	22.5000i	0.527698	+	0.914000i
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	−0.333842	−	0.942629i	$-0.608345\pi$
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	0.983262	−	0.182199i	$-0.0583216\pi$
$608$	−3.46410	+	2.00000i	−0.140488	+	0.0811107i
$609$	−1.50000	+	2.59808i	−0.0607831	+	0.105279i
$610$	−3.00000	−	1.73205i	−0.121466	−	0.0701287i
$611$	20.7846	−	36.0000i	0.840855	−	1.45640i
$612$	−10.3923			−0.420084
$613$	3.00000	−	1.73205i	0.121169	−	0.0699569i	−0.438191	−	0.898882i	$-0.644380\pi$
$613$	3.00000	−	1.73205i	0.121169	−	0.0699569i	0.559359	+	0.828925i	$0.311047\pi$
$614$	12.1244	−	7.00000i	0.489299	−	0.282497i
$615$	5.19615	−	9.00000i	0.209529	−	0.362915i
$616$		−	5.19615i		−	0.209359i
$617$	36.3731	−	21.0000i	1.46432	−	0.845428i	0.465118	−	0.885249i	$-0.346012\pi$
$617$	36.3731	−	21.0000i	1.46432	−	0.845428i	0.999207	+	0.0398207i	$0.0126787\pi$
$618$			12.1244i			0.487713i
$619$			20.7846i			0.835404i	0.908584	+	0.417702i	$0.137164\pi$
$619$			20.7846i			0.835404i	−0.908584	+	0.417702i	$0.862836\pi$
$620$	−5.19615	−	2.00000i	−0.208683	−	0.0803219i
$621$	36.0000			1.44463
$622$	−30.0000			−1.20289
$623$	5.19615	+	9.00000i	0.208179	+	0.360577i
$624$		−	6.00000i		−	0.240192i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	12.9904	+	22.5000i	0.519200	+	0.899281i
$627$	18.0000	+	31.1769i	0.718851	+	1.24509i
$628$	−10.0000			−0.399043
$629$	−20.7846	−	12.0000i	−0.828737	−	0.478471i
$630$	1.50000	−	2.59808i	0.0597614	−	0.103510i
$631$	10.5000	+	6.06218i	0.417998	+	0.241331i	0.694221	−	0.719762i	$-0.255749\pi$
$631$	10.5000	+	6.06218i	0.417998	+	0.241331i	−0.276222	+	0.961094i	$0.589083\pi$
$632$	−5.19615	−	9.00000i	−0.206692	−	0.358001i
$633$	−8.66025	+	15.0000i	−0.344214	+	0.596196i
$634$	−1.50000	−	2.59808i	−0.0595726	−	0.103183i
$635$	−12.1244			−0.481140
$636$	21.0000			0.832704
$637$	−18.0000	+	10.3923i	−0.713186	+	0.411758i
$638$	7.79423	+	4.50000i	0.308576	+	0.178157i
$639$	31.1769	−	18.0000i	1.23334	−	0.712069i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−1.73205	+	3.00000i	−0.0684119	+	0.118493i	−0.898202	−	0.439582i	$-0.855127\pi$
$641$	−1.73205	+	3.00000i	−0.0684119	+	0.118493i	0.829790	+	0.558075i	$0.188460\pi$
$642$	2.59808	−	4.50000i	0.102538	−	0.177601i
$643$			3.46410i			0.136611i	0.997664	+	0.0683054i	$0.0217592\pi$
$643$			3.46410i			0.136611i	−0.997664	+	0.0683054i	$0.978241\pi$
$644$	3.46410	+	6.00000i	0.136505	+	0.236433i
$645$	−3.00000	−	5.19615i	−0.118125	−	0.204598i
$646$	12.0000	+	6.92820i	0.472134	+	0.272587i
$647$	17.3205			0.680939			0.340470	−	0.940255i	$-0.389414\pi$
$647$	17.3205			0.680939			0.340470	+	0.940255i	$0.389414\pi$
$648$	7.79423	−	4.50000i	0.306186	−	0.176777i
$649$		−	77.9423i		−	3.05950i
$650$	−3.46410			−0.135873
$651$	3.46410	−	9.00000i	0.135769	−	0.352738i
$652$	−8.00000			−0.313304
$653$			9.00000i			0.352197i	0.984373	+	0.176099i	$0.0563478\pi$
$653$			9.00000i			0.352197i	−0.984373	+	0.176099i	$0.943652\pi$
$654$	−6.00000	+	3.46410i	−0.234619	+	0.135457i
$655$	−12.0000			−0.468879
$656$	5.19615	+	3.00000i	0.202876	+	0.117130i
$657$	−18.0000	+	10.3923i	−0.702247	+	0.405442i
$658$	6.00000	+	10.3923i	0.233904	+	0.405134i
$659$		−	21.0000i		−	0.818044i	−0.912525	−	0.409022i	$-0.865870\pi$
$659$		−	21.0000i		−	0.818044i	0.912525	−	0.409022i	$-0.134130\pi$
$660$	−7.79423	−	4.50000i	−0.303390	−	0.175162i
$661$	2.00000	−	3.46410i	0.0777910	−	0.134738i	−0.824506	−	0.565854i	$-0.808547\pi$
$661$	2.00000	−	3.46410i	0.0777910	−	0.134738i	0.902297	+	0.431116i	$0.141880\pi$
$662$	−8.66025	+	15.0000i	−0.336590	+	0.582992i
$663$	−18.0000	+	10.3923i	−0.699062	+	0.403604i
$664$	4.50000	+	2.59808i	0.174634	+	0.100825i
$665$	−3.46410	+	2.00000i	−0.134332	+	0.0775567i
$666$	20.7846			0.805387
$667$	−12.0000			−0.464642
$668$	5.19615	+	9.00000i	0.201045	+	0.348220i
$669$	23.3827	+	13.5000i	0.904027	+	0.521940i
$670$	1.00000	+	1.73205i	0.0386334	+	0.0669150i
$671$	−15.5885	−	9.00000i	−0.601786	−	0.347441i
$672$	1.50000	+	0.866025i	0.0578638	+	0.0334077i
$673$	4.50000	+	2.59808i	0.173462	+	0.100148i	0.584217	−	0.811597i	$-0.301402\pi$
$673$	4.50000	+	2.59808i	0.173462	+	0.100148i	−0.410755	+	0.911746i	$0.634735\pi$
$674$	−12.1244			−0.467013
$675$	−2.59808	−	4.50000i	−0.100000	−	0.173205i
$676$	0.500000	+	0.866025i	0.0192308	+	0.0333087i
$677$	−16.4545	+	28.5000i	−0.632397	+	1.09534i	0.354663	+	0.934994i	$0.384596\pi$
$677$	−16.4545	+	28.5000i	−0.632397	+	1.09534i	−0.987060	+	0.160350i	$0.948738\pi$
$678$		0			0
$679$	−0.500000	−	0.866025i	−0.0191882	−	0.0332350i
$680$	−3.46410			−0.132842
$681$		−	25.9808i		−	0.995585i
$682$	−27.0000	−	10.3923i	−1.03388	−	0.397942i
$683$			9.00000i			0.344375i	0.985064	+	0.172188i	$0.0550836\pi$
$683$			9.00000i			0.344375i	−0.985064	+	0.172188i	$0.944916\pi$
$684$	−12.0000			−0.458831
$685$	−12.0000	+	6.92820i	−0.458496	+	0.264713i
$686$		−	13.0000i		−	0.496342i
$687$	−41.5692	−	24.0000i	−1.58596	−	0.915657i
$688$	3.00000	−	1.73205i	0.114374	−	0.0660338i
$689$	36.3731	−	21.0000i	1.38570	−	0.800036i
$690$	12.0000			0.456832
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$	2.59808	+	1.50000i	0.0987640	+	0.0570214i
$693$	7.79423	−	13.5000i	0.296078	−	0.512823i
$694$	16.5000	−	9.52628i	0.626331	−	0.361613i
$695$	10.3923	−	18.0000i	0.394203	−	0.682779i
$696$	−2.59808	+	1.50000i	−0.0984798	+	0.0568574i
$697$		−	20.7846i		−	0.787273i
$698$			8.00000i			0.302804i
$699$	27.0000	−	15.5885i	1.02123	−	0.589610i
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	12.9904	−	7.50000i	0.490640	−	0.283271i	−0.234200	−	0.972188i	$-0.575247\pi$
$701$	12.9904	−	7.50000i	0.490640	−	0.283271i	0.724840	+	0.688917i	$0.241914\pi$
$702$	9.00000	−	15.5885i	0.339683	−	0.588348i
$703$	−24.0000	−	13.8564i	−0.905177	−	0.522604i
$704$	2.59808	−	4.50000i	0.0979187	−	0.169600i
$705$	20.7846			0.782794
$706$	−30.0000	+	17.3205i	−1.12906	+	0.651866i
$707$	−12.9904	+	7.50000i	−0.488554	+	0.282067i
$708$	22.5000	+	12.9904i	0.845602	+	0.488208i
$709$			24.2487i			0.910679i	0.890318	+	0.455340i	$0.150482\pi$
$709$			24.2487i			0.910679i	−0.890318	+	0.455340i	$0.849518\pi$
$710$	10.3923	−	6.00000i	0.390016	−	0.225176i
$711$		−	31.1769i		−	1.16923i
$712$			10.3923i			0.389468i
$713$	38.1051	−	6.00000i	1.42705	−	0.224702i
$714$		−	6.00000i		−	0.224544i
$715$	−18.0000			−0.673162
$716$	−7.79423	−	13.5000i	−0.291284	−	0.504519i
$717$	−48.0000			−1.79259
$718$		0			0
$719$	−3.46410	−	6.00000i	−0.129189	−	0.223762i	0.794173	−	0.607691i	$-0.207904\pi$
$719$	−3.46410	−	6.00000i	−0.129189	−	0.223762i	−0.923363	+	0.383929i	$0.874571\pi$
$720$	2.59808	−	1.50000i	0.0968246	−	0.0559017i
$721$	−7.00000			−0.260694
$722$	−2.59808	−	1.50000i	−0.0966904	−	0.0558242i
$723$	−23.3827	−	13.5000i	−0.869611	−	0.502070i
$724$	−3.00000	−	1.73205i	−0.111494	−	0.0643712i
$725$	0.866025	+	1.50000i	0.0321634	+	0.0557086i
$726$	−24.0000	−	13.8564i	−0.890724	−	0.514259i
$727$	−17.5000	−	30.3109i	−0.649039	−	1.12417i	−0.983353	−	0.181707i	$-0.941838\pi$
$727$	−17.5000	−	30.3109i	−0.649039	−	1.12417i	0.334314	−	0.942462i	$-0.391496\pi$
$728$	3.46410			0.128388
$729$	27.0000			1.00000
$730$	−6.00000	+	3.46410i	−0.222070	+	0.128212i
$731$	−10.3923	−	6.00000i	−0.384373	−	0.221918i
$732$	5.19615	−	3.00000i	0.192055	−	0.110883i
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	−0.707303	−	0.706910i	$-0.750088\pi$
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	0.965854	+	0.259087i	$0.0834217\pi$
$734$	5.19615	−	9.00000i	0.191793	−	0.332196i
$735$	−9.00000	−	5.19615i	−0.331970	−	0.191663i
$736$			6.92820i			0.255377i
$737$	5.19615	+	9.00000i	0.191403	+	0.331519i
$738$	9.00000	+	15.5885i	0.331295	+	0.573819i
$739$	−3.00000	−	1.73205i	−0.110357	−	0.0637145i	0.443806	−	0.896123i	$-0.353628\pi$
$739$	−3.00000	−	1.73205i	−0.110357	−	0.0637145i	−0.554162	+	0.832409i	$0.686961\pi$
$740$	6.92820			0.254686
$741$	−20.7846	+	12.0000i	−0.763542	+	0.440831i
$742$			12.1244i			0.445099i
$743$	−20.7846			−0.762513			−0.381257	−	0.924469i	$-0.624509\pi$
$743$	−20.7846			−0.762513			−0.381257	+	0.924469i	$0.624509\pi$
$744$	7.50000	−	6.06218i	0.274963	−	0.222250i
$745$	−15.0000			−0.549557
$746$			28.0000i			1.02515i
$747$	7.79423	+	13.5000i	0.285176	+	0.493939i
$748$	−18.0000			−0.658145
$749$	2.59808	+	1.50000i	0.0949316	+	0.0548088i
$750$	−0.866025	−	1.50000i	−0.0316228	−	0.0547723i
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	−0.996993	−	0.0774878i	$-0.975310\pi$
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	0.431390	−	0.902165i	$-0.358023\pi$
$752$			12.0000i			0.437595i
$753$	9.00000	−	15.5885i	0.327978	−	0.568075i
$754$	−3.00000	+	5.19615i	−0.109254	+	0.189233i
$755$	4.33013	−	7.50000i	0.157589	−	0.272953i
$756$	2.59808	+	4.50000i	0.0944911	+	0.163663i
$757$	−3.00000	−	1.73205i	−0.109037	−	0.0629525i	0.444490	−	0.895784i	$-0.353385\pi$
$757$	−3.00000	−	1.73205i	−0.109037	−	0.0629525i	−0.553527	+	0.832831i	$0.686718\pi$
$758$	−12.1244	+	7.00000i	−0.440376	+	0.254251i
$759$	62.3538			2.26330
$760$	−4.00000			−0.145095
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$	10.5000	−	18.1865i	0.380375	−	0.658829i
$763$	−2.00000	−	3.46410i	−0.0724049	−	0.125409i
$764$	10.3923	+	6.00000i	0.375980	+	0.217072i
$765$	−9.00000	−	5.19615i	−0.325396	−	0.187867i
$766$	9.00000	+	5.19615i	0.325183	+	0.187745i
$767$	51.9615			1.87622
$768$	0.866025	+	1.50000i	0.0312500	+	0.0541266i
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	0.995397	−	0.0958377i	$-0.0305530\pi$
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	−0.580696	+	0.814120i	$0.697220\pi$
$770$	2.59808	−	4.50000i	0.0936282	−	0.162169i
$771$			41.5692i			1.49708i
$772$	−5.50000	−	9.52628i	−0.197949	−	0.342858i
$773$	−27.7128			−0.996761			−0.498380	−	0.866959i	$-0.666072\pi$
$773$	−27.7128			−0.996761			−0.498380	+	0.866959i	$0.666072\pi$
$774$	10.3923			0.373544
$775$	−3.50000	−	4.33013i	−0.125724	−	0.155543i
$776$		−	1.00000i		−	0.0358979i
$777$			12.0000i			0.430498i
$778$	−24.0000	+	13.8564i	−0.860442	+	0.496776i
$779$		−	24.0000i		−	0.859889i
$780$	3.00000	−	5.19615i	0.107417	−	0.186052i
$781$	54.0000	−	31.1769i	1.93227	−	1.11560i
$782$	20.7846	−	12.0000i	0.743256	−	0.429119i
$783$	−9.00000			−0.321634
$784$	3.00000	−	5.19615i	0.107143	−	0.185577i
$785$	−8.66025	−	5.00000i	−0.309098	−	0.178458i
$786$	10.3923	−	18.0000i	0.370681	−	0.642039i
$787$	−9.00000	+	5.19615i	−0.320815	+	0.185223i	−0.651756	−	0.758429i	$-0.725967\pi$
$787$	−9.00000	+	5.19615i	−0.320815	+	0.185223i	0.330941	+	0.943652i	$0.392634\pi$
$788$		0			0
$789$	3.00000	+	5.19615i	0.106803	+	0.184988i
$790$		−	10.3923i		−	0.369742i
$791$		0			0
$792$	13.5000	−	7.79423i	0.479702	−	0.276956i
$793$	6.00000	−	10.3923i	0.213066	−	0.369042i
$794$	24.2487	−	14.0000i	0.860555	−	0.496841i
$795$	18.1865	+	10.5000i	0.645010	+	0.372397i
$796$	10.5000	+	6.06218i	0.372163	+	0.214868i
$797$	19.9186	−	34.5000i	0.705552	−	1.22205i	−0.260939	−	0.965355i	$-0.584032\pi$
$797$	19.9186	−	34.5000i	0.705552	−	1.22205i	0.966492	−	0.256697i	$-0.0826344\pi$
$798$		−	6.92820i		−	0.245256i
$799$	36.0000	−	20.7846i	1.27359	−	0.735307i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−15.5885	+	27.0000i	−0.550791	+	0.953998i
$802$			6.92820i			0.244643i
$803$	−31.1769	+	18.0000i	−1.10021	+	0.635206i
$804$	−3.46410			−0.122169
$805$			6.92820i			0.244187i
$806$	6.92820	−	18.0000i	0.244036	−	0.634023i
$807$	−48.0000			−1.68968
$808$	−15.0000			−0.527698
$809$	−13.8564	−	24.0000i	−0.487165	−	0.843795i	0.512726	−	0.858552i	$-0.328636\pi$
$809$	−13.8564	−	24.0000i	−0.487165	−	0.843795i	−0.999891	+	0.0147574i	$0.995302\pi$
$810$	9.00000			0.316228
$811$	−20.0000	+	34.6410i	−0.702295	+	1.21641i	0.265364	+	0.964148i	$0.414508\pi$
$811$	−20.0000	+	34.6410i	−0.702295	+	1.21641i	−0.967659	+	0.252262i	$0.918825\pi$
$812$	−0.866025	−	1.50000i	−0.0303915	−	0.0526397i
$813$	18.1865	−	10.5000i	0.637830	−	0.368251i
$814$	36.0000			1.26180
$815$	−6.92820	−	4.00000i	−0.242684	−	0.140114i
$816$	3.00000	−	5.19615i	0.105021	−	0.181902i
$817$	−12.0000	−	6.92820i	−0.419827	−	0.242387i
$818$	6.06218	+	10.5000i	0.211959	+	0.367124i
$819$	9.00000	+	5.19615i	0.314485	+	0.181568i
$820$	3.00000	+	5.19615i	0.104765	+	0.181458i
$821$	12.1244			0.423143			0.211571	−	0.977363i	$-0.432142\pi$
$821$	12.1244			0.423143			0.211571	+	0.977363i	$0.432142\pi$
$822$		−	24.0000i		−	0.837096i
$823$	1.50000	−	0.866025i	0.0522867	−	0.0301877i	−0.473629	−	0.880725i	$-0.657056\pi$
$823$	1.50000	−	0.866025i	0.0522867	−	0.0301877i	0.525915	+	0.850537i	$0.323723\pi$
$824$	−6.06218	−	3.50000i	−0.211186	−	0.121928i
$825$	−4.50000	−	7.79423i	−0.156670	−	0.271360i
$826$	−7.50000	+	12.9904i	−0.260958	+	0.451993i
$827$	−19.0526	+	33.0000i	−0.662522	+	1.14752i	0.317428	+	0.948282i	$0.397181\pi$
$827$	−19.0526	+	33.0000i	−0.662522	+	1.14752i	−0.979951	+	0.199240i	$0.936153\pi$
$828$	−10.3923	+	18.0000i	−0.361158	+	0.625543i
$829$		−	3.46410i		−	0.120313i	−0.998189	−	0.0601566i	$-0.980840\pi$
$829$		−	3.46410i		−	0.120313i	0.998189	−	0.0601566i	$-0.0191600\pi$
$830$	2.59808	+	4.50000i	0.0901805	+	0.156197i
$831$		0			0
$832$	3.00000	+	1.73205i	0.104006	+	0.0600481i
$833$	−20.7846			−0.720144
$834$	18.0000	+	31.1769i	0.623289	+	1.07957i
$835$			10.3923i			0.359641i
$836$	−20.7846			−0.718851
$837$	28.5788	−	4.50000i	0.987829	−	0.155543i
$838$	33.0000			1.13997
$839$			12.0000i			0.414286i	0.978311	+	0.207143i	$0.0664165\pi$
$839$			12.0000i			0.414286i	−0.978311	+	0.207143i	$0.933583\pi$
$840$	0.866025	+	1.50000i	0.0298807	+	0.0517549i
$841$	−26.0000			−0.896552
$842$	−17.3205	−	10.0000i	−0.596904	−	0.344623i
$843$	18.0000	−	10.3923i	0.619953	−	0.357930i
$844$	−5.00000	−	8.66025i	−0.172107	−	0.298098i
$845$			1.00000i			0.0344010i
$846$	−18.0000	+	31.1769i	−0.618853	+	1.07188i
$847$	8.00000	−	13.8564i	0.274883	−	0.476112i
$848$	−6.06218	+	10.5000i	−0.208176	+	0.360571i
$849$	−19.0526	−	33.0000i	−0.653882	−	1.13256i
$850$	−3.00000	−	1.73205i	−0.102899	−	0.0594089i
$851$	−41.5692	+	24.0000i	−1.42497	+	0.822709i
$852$			20.7846i			0.712069i
$853$	−2.00000			−0.0684787			−0.0342393	−	0.999414i	$-0.510901\pi$
$853$	−2.00000			−0.0684787			−0.0342393	+	0.999414i	$0.510901\pi$
$854$	1.73205	+	3.00000i	0.0592696	+	0.102658i
$855$	−10.3923	−	6.00000i	−0.355409	−	0.205196i
$856$	1.50000	+	2.59808i	0.0512689	+	0.0888004i
$857$	−25.9808	−	15.0000i	−0.887486	−	0.512390i	−0.0143666	−	0.999897i	$-0.504573\pi$
$857$	−25.9808	−	15.0000i	−0.887486	−	0.512390i	−0.873119	+	0.487507i	$0.837907\pi$
$858$	15.5885	−	27.0000i	0.532181	−	0.921765i
$859$	−3.00000	−	1.73205i	−0.102359	−	0.0590968i	0.447947	−	0.894060i	$-0.352155\pi$
$859$	−3.00000	−	1.73205i	−0.102359	−	0.0590968i	−0.550305	+	0.834963i	$0.685489\pi$
$860$	3.46410			0.118125
$861$	−9.00000	+	5.19615i	−0.306719	+	0.177084i
$862$	15.0000	+	25.9808i	0.510902	+	0.884908i
$863$	−6.92820	+	12.0000i	−0.235839	+	0.408485i	−0.959516	−	0.281654i	$-0.909117\pi$
$863$	−6.92820	+	12.0000i	−0.235839	+	0.408485i	0.723677	+	0.690138i	$0.242450\pi$
$864$			5.19615i			0.176777i
$865$	1.50000	+	2.59808i	0.0510015	+	0.0883372i
$866$	27.7128			0.941720
$867$	8.66025			0.294118
$868$	3.50000	+	4.33013i	0.118798	+	0.146974i
$869$		−	54.0000i		−	1.83182i
$870$	−3.00000			−0.101710
$871$	−6.00000	+	3.46410i	−0.203302	+	0.117377i
$872$		−	4.00000i		−	0.135457i
$873$	1.50000	−	2.59808i	0.0507673	−	0.0879316i
$874$	24.0000	−	13.8564i	0.811812	−	0.468700i
$875$	0.866025	−	0.500000i	0.0292770	−	0.0169031i
$876$		−	12.0000i		−	0.405442i
$877$	−17.0000	+	29.4449i	−0.574049	+	0.994282i	0.422095	+	0.906552i	$0.361295\pi$
$877$	−17.0000	+	29.4449i	−0.574049	+	0.994282i	−0.996144	+	0.0877308i	$0.972038\pi$
$878$	−14.7224	−	8.50000i	−0.496858	−	0.286861i
$879$	13.5000	+	7.79423i	0.455344	+	0.262893i
$880$	4.50000	−	2.59808i	0.151695	−	0.0875811i
$881$	−3.46410	+	6.00000i	−0.116709	+	0.202145i	−0.918461	−	0.395511i	$-0.870568\pi$
$881$	−3.46410	+	6.00000i	−0.116709	+	0.202145i	0.801753	+	0.597656i	$0.203901\pi$
$882$	15.5885	−	9.00000i	0.524891	−	0.303046i
$883$			20.7846i			0.699458i	0.936851	+	0.349729i	$0.113726\pi$
$883$			20.7846i			0.699458i	−0.936851	+	0.349729i	$0.886274\pi$
$884$		−	12.0000i		−	0.403604i
$885$	12.9904	+	22.5000i	0.436667	+	0.756329i
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	20.7846	−	12.0000i	0.697879	−	0.402921i	−0.108678	−	0.994077i	$-0.534662\pi$
$887$	20.7846	−	12.0000i	0.697879	−	0.402921i	0.806557	+	0.591156i	$0.201328\pi$
$888$	−6.00000	+	10.3923i	−0.201347	+	0.348743i
$889$	10.5000	+	6.06218i	0.352159	+	0.203319i
$890$	−5.19615	+	9.00000i	−0.174175	+	0.301681i
$891$	46.7654			1.56670
$892$	−13.5000	+	7.79423i	−0.452013	+	0.260970i
$893$	41.5692	−	24.0000i	1.39106	−	0.803129i
$894$	12.9904	−	22.5000i	0.434463	−	0.752513i
$895$		−	15.5885i		−	0.521065i
$896$	−0.866025	+	0.500000i	−0.0289319	+	0.0167038i
$897$			41.5692i			1.38796i
$898$		−	6.92820i		−	0.231197i
$899$	−9.52628	+	1.50000i	−0.317719	+	0.0500278i
$900$	3.00000			0.100000
$901$	42.0000			1.39922
$902$	15.5885	+	27.0000i	0.519039	+	0.899002i
$903$			6.00000i			0.199667i
$904$		0			0
$905$	−1.73205	−	3.00000i	−0.0575753	−	0.0997234i
$906$	7.50000	+	12.9904i	0.249171	+	0.431577i
$907$	16.0000			0.531271			0.265636	−	0.964073i	$-0.414418\pi$
$907$	16.0000			0.531271			0.265636	+	0.964073i	$0.414418\pi$
$908$	12.9904	+	7.50000i	0.431101	+	0.248896i
$909$	−38.9711	−	22.5000i	−1.29259	−	0.746278i
$910$	3.00000	+	1.73205i	0.0994490	+	0.0574169i
$911$	8.66025	+	15.0000i	0.286927	+	0.496972i	0.973075	−	0.230490i	$-0.0740329\pi$
$911$	8.66025	+	15.0000i	0.286927	+	0.496972i	−0.686148	+	0.727462i	$0.740700\pi$
$912$	3.46410	−	6.00000i	0.114708	−	0.198680i
$913$	13.5000	+	23.3827i	0.446785	+	0.773854i
$914$	−6.92820			−0.229165
$915$	6.00000			0.198354
$916$	24.0000	−	13.8564i	0.792982	−	0.457829i
$917$	10.3923	+	6.00000i	0.343184	+	0.198137i
$918$	15.5885	−	9.00000i	0.514496	−	0.297044i
$919$	8.50000	−	14.7224i	0.280389	−	0.485648i	−0.691091	−	0.722767i	$-0.742870\pi$
$919$	8.50000	−	14.7224i	0.280389	−	0.485648i	0.971481	+	0.237119i	$0.0762032\pi$
$920$	−3.46410	+	6.00000i	−0.114208	+	0.197814i
$921$	−12.1244	+	21.0000i	−0.399511	+	0.691974i
$922$			39.8372i			1.31197i
$923$	20.7846	+	36.0000i	0.684134	+	1.18495i
$924$	4.50000	+	7.79423i	0.148039	+	0.256411i
$925$	6.00000	+	3.46410i	0.197279	+	0.113899i
$926$	12.1244			0.398431
$927$	−10.5000	−	18.1865i	−0.344865	−	0.597324i
$928$		−	1.73205i		−	0.0568574i
$929$	45.0333			1.47750			0.738748	−	0.673982i	$-0.235418\pi$
$929$	45.0333			1.47750			0.738748	+	0.673982i	$0.235418\pi$
$930$	9.52628	−	1.50000i	0.312379	−	0.0491869i
$931$	−24.0000			−0.786568
$932$			18.0000i			0.589610i
$933$	45.0000	−	25.9808i	1.47323	−	0.850572i
$934$	27.0000			0.883467
$935$	−15.5885	−	9.00000i	−0.509797	−	0.294331i
$936$	5.19615	+	9.00000i	0.169842	+	0.294174i
$937$	−5.00000	−	8.66025i	−0.163343	−	0.282918i	0.772723	−	0.634744i	$-0.218894\pi$
$937$	−5.00000	−	8.66025i	−0.163343	−	0.282918i	−0.936066	+	0.351826i	$0.885561\pi$
$938$		−	2.00000i		−	0.0653023i
$939$	−38.9711	−	22.5000i	−1.27178	−	0.734260i
$940$	−6.00000	+	10.3923i	−0.195698	+	0.338960i
$941$	−6.06218	+	10.5000i	−0.197621	+	0.342290i	−0.947757	−	0.318994i	$-0.896655\pi$
$941$	−6.06218	+	10.5000i	−0.197621	+	0.342290i	0.750135	+	0.661284i	$0.229988\pi$
$942$	15.0000	−	8.66025i	0.488726	−	0.282166i
$943$	−36.0000	−	20.7846i	−1.17232	−	0.676840i
$944$	−12.9904	+	7.50000i	−0.422801	+	0.244104i
$945$			5.19615i			0.169031i
$946$	18.0000			0.585230
$947$	−12.1244	−	21.0000i	−0.393989	−	0.682408i	0.598983	−	0.800762i	$-0.295572\pi$
$947$	−12.1244	−	21.0000i	−0.393989	−	0.682408i	−0.992972	+	0.118354i	$0.962238\pi$
$948$	15.5885	+	9.00000i	0.506290	+	0.292306i
$949$	−12.0000	−	20.7846i	−0.389536	−	0.674697i
$950$	−3.46410	−	2.00000i	−0.112390	−	0.0648886i
$951$	4.50000	+	2.59808i	0.145922	+	0.0842484i
$952$	3.00000	+	1.73205i	0.0972306	+	0.0561361i
$953$	−10.3923			−0.336640			−0.168320	−	0.985732i	$-0.553834\pi$
$953$	−10.3923			−0.336640			−0.168320	+	0.985732i	$0.553834\pi$
$954$	−31.5000	+	18.1865i	−1.01985	+	0.588811i
$955$	6.00000	+	10.3923i	0.194155	+	0.336287i
$956$	13.8564	−	24.0000i	0.448148	−	0.776215i
$957$	−15.5885			−0.503903
$958$	6.00000	+	10.3923i	0.193851	+	0.335760i
$959$	13.8564			0.447447
$960$			1.73205i			0.0559017i
$961$	29.5000	−	9.52628i	0.951613	−	0.307299i
$962$			24.0000i			0.773791i
$963$			9.00000i			0.290021i
$964$	13.5000	−	7.79423i	0.434806	−	0.251035i
$965$		−	11.0000i		−	0.354103i
$966$	−10.3923	−	6.00000i	−0.334367	−	0.193047i
$967$	−27.0000	+	15.5885i	−0.868261	+	0.501291i	−0.866770	−	0.498708i	$-0.833808\pi$
$967$	−27.0000	+	15.5885i	−0.868261	+	0.501291i	−0.00149135	+	0.999999i	$0.500475\pi$
$968$	13.8564	−	8.00000i	0.445362	−	0.257130i
$969$	−24.0000			−0.770991
$970$	0.500000	−	0.866025i	0.0160540	−	0.0278064i
$971$	−23.3827	−	13.5000i	−0.750386	−	0.433236i	0.0754473	−	0.997150i	$-0.475962\pi$
$971$	−23.3827	−	13.5000i	−0.750386	−	0.433236i	−0.825833	+	0.563914i	$0.809295\pi$
$972$	−7.79423	+	13.5000i	−0.250000	+	0.433013i
$973$	−18.0000	+	10.3923i	−0.577054	+	0.333162i
$974$	18.1865	−	31.5000i	0.582734	−	1.00933i
$975$	5.19615	−	3.00000i	0.166410	−	0.0960769i
$976$			3.46410i			0.110883i
$977$			12.0000i			0.383914i	0.981403	+	0.191957i	$0.0614834\pi$
$977$			12.0000i			0.383914i	−0.981403	+	0.191957i	$0.938517\pi$
$978$	12.0000	−	6.92820i	0.383718	−	0.221540i
$979$	−27.0000	+	46.7654i	−0.862924	+	1.49463i
$980$	5.19615	−	3.00000i	0.165985	−	0.0958315i
$981$	6.00000	−	10.3923i	0.191565	−	0.331801i
$982$	−31.5000	−	18.1865i	−1.00521	−	0.580356i
$983$	8.66025	−	15.0000i	0.276219	−	0.478426i	−0.694223	−	0.719760i	$-0.744252\pi$
$983$	8.66025	−	15.0000i	0.276219	−	0.478426i	0.970442	+	0.241334i	$0.0775851\pi$
$984$	−10.3923			−0.331295
$985$		0			0
$986$	−5.19615	+	3.00000i	−0.165479	+	0.0955395i
$987$	−18.0000	−	10.3923i	−0.572946	−	0.330791i
$988$		−	13.8564i		−	0.440831i
$989$	−20.7846	+	12.0000i	−0.660912	+	0.381578i
$990$	15.5885			0.495434
$991$		−	24.2487i		−	0.770286i	−0.922857	−	0.385143i	$-0.874152\pi$
$991$		−	24.2487i		−	0.770286i	0.922857	−	0.385143i	$-0.125848\pi$
$992$	0.866025	+	5.50000i	0.0274963	+	0.174625i
$993$		−	30.0000i		−	0.952021i
$994$	−12.0000			−0.380617
$995$	6.06218	+	10.5000i	0.192184	+	0.332872i
$996$	−9.00000			−0.285176
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	−0.881426	−	0.472322i	$-0.843416\pi$
$997$	−1.00000	+	1.73205i	−0.0316703	+	0.0548546i	0.849756	+	0.527176i	$0.176749\pi$
$998$	12.1244	+	21.0000i	0.383790	+	0.664743i
$999$	−31.1769	+	18.0000i	−0.986394	+	0.569495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.c.161.1	✓	4
3.2	odd	2	inner	930.2.o.c.161.2	yes	4
31.26	odd	6	inner	930.2.o.c.491.1	yes	4
93.26	even	6	inner	930.2.o.c.491.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.c.161.1	✓	4	1.1	even	1	trivial
930.2.o.c.161.2	yes	4	3.2	odd	2	inner
930.2.o.c.491.1	yes	4	31.26	odd	6	inner
930.2.o.c.491.2	yes	4	93.26	even	6	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.866025 + 1.50000i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.50000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.59808 + 4.50000i) q^{11} +(-0.866025 - 1.50000i) q^{12} +(-3.00000 - 1.73205i) q^{13} +(0.866025 - 0.500000i) q^{14} -1.73205i q^{15} +1.00000 q^{16} +(-1.73205 - 3.00000i) q^{17} +(2.59808 + 1.50000i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-0.866025 + 1.50000i) q^{21} +(4.50000 + 2.59808i) q^{22} -6.92820 q^{23} +(-1.50000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-1.73205 + 3.00000i) q^{26} -5.19615 q^{27} +(-0.500000 - 0.866025i) q^{28} +1.73205 q^{29} -1.73205 q^{30} +(-5.50000 + 0.866025i) q^{31} -1.00000i q^{32} -9.00000 q^{33} +(-3.00000 + 1.73205i) q^{34} -1.00000i q^{35} +(1.50000 - 2.59808i) q^{36} +(6.00000 - 3.46410i) q^{37} +(-3.46410 + 2.00000i) q^{38} -6.00000i q^{39} +(0.500000 - 0.866025i) q^{40} +(5.19615 + 3.00000i) q^{41} +(1.50000 + 0.866025i) q^{42} +(3.00000 - 1.73205i) q^{43} +(2.59808 - 4.50000i) q^{44} +(2.59808 - 1.50000i) q^{45} +6.92820i q^{46} +12.0000i q^{47} +(0.866025 + 1.50000i) q^{48} +(3.00000 - 5.19615i) q^{49} +(0.866025 - 0.500000i) q^{50} +(3.00000 - 5.19615i) q^{51} +(3.00000 + 1.73205i) q^{52} +(-6.06218 + 10.5000i) q^{53} +5.19615i q^{54} +(4.50000 - 2.59808i) q^{55} +(-0.866025 + 0.500000i) q^{56} +(3.46410 - 6.00000i) q^{57} -1.73205i q^{58} +(-12.9904 + 7.50000i) q^{59} +1.73205i q^{60} +3.46410i q^{61} +(0.866025 + 5.50000i) q^{62} -3.00000 q^{63} -1.00000 q^{64} +(1.73205 + 3.00000i) q^{65} +9.00000i q^{66} +(1.00000 - 1.73205i) q^{67} +(1.73205 + 3.00000i) q^{68} +(-6.00000 - 10.3923i) q^{69} -1.00000 q^{70} +(-10.3923 - 6.00000i) q^{71} +(-2.59808 - 1.50000i) q^{72} +(6.00000 + 3.46410i) q^{73} +(-3.46410 - 6.00000i) q^{74} +(-0.866025 + 1.50000i) q^{75} +(2.00000 + 3.46410i) q^{76} -5.19615 q^{77} -6.00000 q^{78} +(-9.00000 + 5.19615i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(3.00000 - 5.19615i) q^{82} +(2.59808 - 4.50000i) q^{83} +(0.866025 - 1.50000i) q^{84} +3.46410i q^{85} +(-1.73205 - 3.00000i) q^{86} +(1.50000 + 2.59808i) q^{87} +(-4.50000 - 2.59808i) q^{88} +10.3923 q^{89} +(-1.50000 - 2.59808i) q^{90} -3.46410i q^{91} +6.92820 q^{92} +(-6.06218 - 7.50000i) q^{93} +12.0000 q^{94} +4.00000i q^{95} +(1.50000 - 0.866025i) q^{96} -1.00000 q^{97} +(-5.19615 - 3.00000i) q^{98} +(-7.79423 - 13.5000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 6 q^{6} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 6 * q^6 + 2 * q^7 - 6 * q^9	\( 4 q - 4 q^{4} + 6 q^{6} + 2 q^{7} - 6 q^{9} - 2 q^{10} - 12 q^{13} + 4 q^{16} - 8 q^{19} + 18 q^{22} - 6 q^{24} + 2 q^{25} - 2 q^{28} - 22 q^{31} - 36 q^{33} - 12 q^{34} + 6 q^{36} + 24 q^{37} + 2 q^{40} + 6 q^{42} + 12 q^{43} + 12 q^{49} + 12 q^{51} + 12 q^{52} + 18 q^{55} - 12 q^{63} - 4 q^{64} + 4 q^{67} - 24 q^{69} - 4 q^{70} + 24 q^{73} + 8 q^{76} - 24 q^{78} - 36 q^{79} - 18 q^{81} + 12 q^{82} + 6 q^{87} - 18 q^{88} - 6 q^{90} + 48 q^{94} + 6 q^{96} - 4 q^{97}+O(q^{100}) \) 4 * q - 4 * q^4 + 6 * q^6 + 2 * q^7 - 6 * q^9 - 2 * q^10 - 12 * q^13 + 4 * q^16 - 8 * q^19 + 18 * q^22 - 6 * q^24 + 2 * q^25 - 2 * q^28 - 22 * q^31 - 36 * q^33 - 12 * q^34 + 6 * q^36 + 24 * q^37 + 2 * q^40 + 6 * q^42 + 12 * q^43 + 12 * q^49 + 12 * q^51 + 12 * q^52 + 18 * q^55 - 12 * q^63 - 4 * q^64 + 4 * q^67 - 24 * q^69 - 4 * q^70 + 24 * q^73 + 8 * q^76 - 24 * q^78 - 36 * q^79 - 18 * q^81 + 12 * q^82 + 6 * q^87 - 18 * q^88 - 6 * q^90 + 48 * q^94 + 6 * q^96 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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